Collapsing high-dimensional normal distributions

README.md

My friend Colin has been trying to give me a better intuition for higher dimensions. His first fun fact was that the volume of an n-dimensional hypersphere peaks somewhere around n=6 or so, I forget, and then approaches 0 as n approaches infinity. Damn! Meanwhile, of course the volume of a hypercube just diverges to infinity, as you'd expect. So if you inscribe a hypersphere in a hypercube, as dimension increases, more and more of the volume is in "the corners" — ultimately, almost all of it.

That's not what I'm trying to show here, it's just cool. This is somewhat different.

Colin also pointed out that, in a high-dimensional multivariate random normal distribution (with identity covariance matrix), all the mass ends up coming to be found in a sort of donut at some distance from the middle. There's very little mass in the middle. Of course the origin is still the mean/median/mode. The problem is that the middle is just so dang small, and there's SO MUCH SPACE as you go a little further out. So if you're just looking at the distribution of distances from the middle, most are a ways out — more so the more dimensions you're in.

This is a lot like the old joke that the average family has 2.2 kids, but no single family has 2.2 kids, God willing. Now consider lots of other attributes (dimensions) too: their ages, genders, heights, locations, professions, pets, hobbies, politics, faiths, vices, material possessions, favorite books, dreams, crimes, secrets, loves, etc. Of course people are mostly normal. But almost no person is normal.

Unlike the incredible shrinking hypersphere, this is evident even in low human-scale dimensions, like 2, and 3.

INSTRUCTIONS:

1. Mouse around to admire the lil parallax that shows you that the third blob of points is 3D.

2. Drag "3D" to "2D" to flatten the third dimension, while keeping every point the same distance from the origin, i.e. the same radius. Imagine every point is on a fixed arm that can rotate around the origin, but can't extend or shrink. (That'd be a good thing to visualize if I had more time!)

3. Drag "2D" to "1D" to flatten the second dimension, again keeping every point the same distance from the origin. Like sweeping up every point on its little invisible fixed arm and collecting them so they're all facing the same way. (This also sweeps up the 1D points with a negative radius around to the positive side.)

When you let go on 1D, the points will "relax" a bit to show you their distribution of distances from the origin.

Notice that on the left (1D), the mode (fattest part of the distribution) is right at the origin. But in the middle (2D), it's a bit removed. And on the right (3D) it's farther still.

Hopefully you can kinda imagine how, every time you add a dimension, it contributes some non-negative component to the radius. Like, when you add a third dimension perpendicular to the screen, you can't initially see the point's displacement along that axis — but it is probably displaced somewhat, and when you rotate that onto the visible plane, it'll appear to get a little further away from the origin. Like you add a perpendicular leg to a line and take the hypotenuse and that's gotta be longer than the original line.

Where does it end??

colin's python & chart etc

also: THAT GUY'S TALK!!

• Here's a helpful little library https://github.com/tulip/multivariate-normal-js that I didn't actually need because I didn't need covariance.
• I had a version that I wanted to generalize to arbitrarily many dimensions but got kinda hung up on the hyperdimensional spherical coordinates. Vestiges preserved in index2.html. You know it's good when there's an index2!

d3.v4.js

// https://d3js.org Version 4.0.0. Copyright 2016 Mike Bostock.
(function (global, factory) {
  typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
  typeof define === 'function' && define.amd ? define(['exports'], factory) :
  (factory((global.d3 = global.d3 || {})));
}(this, function (exports) { 'use strict';

  var version = "4.0.0";

  function ascending(a, b) {
    return a < b ? -1 : a > b ? 1 : a >= b ? 0 : NaN;
  }

  function bisector(compare) {
    if (compare.length === 1) compare = ascendingComparator(compare);
    return {
      left: function(a, x, lo, hi) {
        if (lo == null) lo = 0;
        if (hi == null) hi = a.length;
        while (lo < hi) {
          var mid = lo + hi >>> 1;
          if (compare(a[mid], x) < 0) lo = mid + 1;
          else hi = mid;
        }
        return lo;
      },
      right: function(a, x, lo, hi) {
        if (lo == null) lo = 0;
        if (hi == null) hi = a.length;
        while (lo < hi) {
          var mid = lo + hi >>> 1;
          if (compare(a[mid], x) > 0) hi = mid;
          else lo = mid + 1;
        }
        return lo;
      }
    };
  }

  function ascendingComparator(f) {
    return function(d, x) {
      return ascending(f(d), x);
    };
  }

  var ascendingBisect = bisector(ascending);
  var bisectRight = ascendingBisect.right;
  var bisectLeft = ascendingBisect.left;

  function descending(a, b) {
    return b < a ? -1 : b > a ? 1 : b >= a ? 0 : NaN;
  }

  function number(x) {
    return x === null ? NaN : +x;
  }

  function variance(array, f) {
    var n = array.length,
        m = 0,
        a,
        d,
        s = 0,
        i = -1,
        j = 0;

    if (f == null) {
      while (++i < n) {
        if (!isNaN(a = number(array[i]))) {
          d = a - m;
          m += d / ++j;
          s += d * (a - m);
        }
      }
    }

    else {
      while (++i < n) {
        if (!isNaN(a = number(f(array[i], i, array)))) {
          d = a - m;
          m += d / ++j;
          s += d * (a - m);
        }
      }
    }

    if (j > 1) return s / (j - 1);
  }

  function deviation(array, f) {
    var v = variance(array, f);
    return v ? Math.sqrt(v) : v;
  }

  function extent(array, f) {
    var i = -1,
        n = array.length,
        a,
        b,
        c;

    if (f == null) {
      while (++i < n) if ((b = array[i]) != null && b >= b) { a = c = b; break; }
      while (++i < n) if ((b = array[i]) != null) {
        if (a > b) a = b;
        if (c < b) c = b;
      }
    }

    else {
      while (++i < n) if ((b = f(array[i], i, array)) != null && b >= b) { a = c = b; break; }
      while (++i < n) if ((b = f(array[i], i, array)) != null) {
        if (a > b) a = b;
        if (c < b) c = b;
      }
    }

    return [a, c];
  }

  var array = Array.prototype;

  var slice = array.slice;
  var map = array.map;

  function constant(x) {
    return function() {
      return x;
    };
  }

  function identity(x) {
    return x;
  }

  function range(start, stop, step) {
    start = +start, stop = +stop, step = (n = arguments.length) < 2 ? (stop = start, start = 0, 1) : n < 3 ? 1 : +step;

    var i = -1,
        n = Math.max(0, Math.ceil((stop - start) / step)) | 0,
        range = new Array(n);

    while (++i < n) {
      range[i] = start + i * step;
    }

    return range;
  }

  var e10 = Math.sqrt(50);
  var e5 = Math.sqrt(10);
  var e2 = Math.sqrt(2);
  function ticks(start, stop, count) {
    var step = tickStep(start, stop, count);
    return range(
      Math.ceil(start / step) * step,
      Math.floor(stop / step) * step + step / 2, // inclusive
      step
    );
  }

  function tickStep(start, stop, count) {
    var step0 = Math.abs(stop - start) / Math.max(0, count),
        step1 = Math.pow(10, Math.floor(Math.log(step0) / Math.LN10)),
        error = step0 / step1;
    if (error >= e10) step1 *= 10;
    else if (error >= e5) step1 *= 5;
    else if (error >= e2) step1 *= 2;
    return stop < start ? -step1 : step1;
  }

  function sturges(values) {
    return Math.ceil(Math.log(values.length) / Math.LN2) + 1;
  }

  function histogram() {
    var value = identity,
        domain = extent,
        threshold = sturges;

    function histogram(data) {
      var i,
          n = data.length,
          x,
          values = new Array(n);

      for (i = 0; i < n; ++i) {
        values[i] = value(data[i], i, data);
      }

      var xz = domain(values),
          x0 = xz[0],
          x1 = xz[1],
          tz = threshold(values, x0, x1);

      // Convert number of thresholds into uniform thresholds.
      if (!Array.isArray(tz)) tz = ticks(x0, x1, tz);

      // Remove any thresholds outside the domain.
      var m = tz.length;
      while (tz[0] <= x0) tz.shift(), --m;
      while (tz[m - 1] >= x1) tz.pop(), --m;

      var bins = new Array(m + 1),
          bin;

      // Initialize bins.
      for (i = 0; i <= m; ++i) {
        bin = bins[i] = [];
        bin.x0 = i > 0 ? tz[i - 1] : x0;
        bin.x1 = i < m ? tz[i] : x1;
      }

      // Assign data to bins by value, ignoring any outside the domain.
      for (i = 0; i < n; ++i) {
        x = values[i];
        if (x0 <= x && x <= x1) {
          bins[bisectRight(tz, x, 0, m)].push(data[i]);
        }
      }

      return bins;
    }

    histogram.value = function(_) {
      return arguments.length ? (value = typeof _ === "function" ? _ : constant(_), histogram) : value;
    };

    histogram.domain = function(_) {
      return arguments.length ? (domain = typeof _ === "function" ? _ : constant([_[0], _[1]]), histogram) : domain;
    };

    histogram.thresholds = function(_) {
      return arguments.length ? (threshold = typeof _ === "function" ? _ : Array.isArray(_) ? constant(slice.call(_)) : constant(_), histogram) : threshold;
    };

    return histogram;
  }

  function threshold(array, p, f) {
    if (f == null) f = number;
    if (!(n = array.length)) return;
    if ((p = +p) <= 0 || n < 2) return +f(array[0], 0, array);
    if (p >= 1) return +f(array[n - 1], n - 1, array);
    var n,
        h = (n - 1) * p,
        i = Math.floor(h),
        a = +f(array[i], i, array),
        b = +f(array[i + 1], i + 1, array);
    return a + (b - a) * (h - i);
  }

  function freedmanDiaconis(values, min, max) {
    values = map.call(values, number).sort(ascending);
    return Math.ceil((max - min) / (2 * (threshold(values, 0.75) - threshold(values, 0.25)) * Math.pow(values.length, -1 / 3)));
  }

  function scott(values, min, max) {
    return Math.ceil((max - min) / (3.5 * deviation(values) * Math.pow(values.length, -1 / 3)));
  }

  function max(array, f) {
    var i = -1,
        n = array.length,
        a,
        b;

    if (f == null) {
      while (++i < n) if ((b = array[i]) != null && b >= b) { a = b; break; }
      while (++i < n) if ((b = array[i]) != null && b > a) a = b;
    }

    else {
      while (++i < n) if ((b = f(array[i], i, array)) != null && b >= b) { a = b; break; }
      while (++i < n) if ((b = f(array[i], i, array)) != null && b > a) a = b;
    }

    return a;
  }

  function mean(array, f) {
    var s = 0,
        n = array.length,
        a,
        i = -1,
        j = n;

    if (f == null) {
      while (++i < n) if (!isNaN(a = number(array[i]))) s += a; else --j;
    }

    else {
      while (++i < n) if (!isNaN(a = number(f(array[i], i, array)))) s += a; else --j;
    }

    if (j) return s / j;
  }

  function median(array, f) {
    var numbers = [],
        n = array.length,
        a,
        i = -1;

    if (f == null) {
      while (++i < n) if (!isNaN(a = number(array[i]))) numbers.push(a);
    }

    else {
      while (++i < n) if (!isNaN(a = number(f(array[i], i, array)))) numbers.push(a);
    }

    return threshold(numbers.sort(ascending), 0.5);
  }

  function merge(arrays) {
    var n = arrays.length,
        m,
        i = -1,
        j = 0,
        merged,
        array;

    while (++i < n) j += arrays[i].length;
    merged = new Array(j);

    while (--n >= 0) {
      array = arrays[n];
      m = array.length;
      while (--m >= 0) {
        merged[--j] = array[m];
      }
    }

    return merged;
  }

  function min(array, f) {
    var i = -1,
        n = array.length,
        a,
        b;

    if (f == null) {
      while (++i < n) if ((b = array[i]) != null && b >= b) { a = b; break; }
      while (++i < n) if ((b = array[i]) != null && a > b) a = b;
    }

    else {
      while (++i < n) if ((b = f(array[i], i, array)) != null && b >= b) { a = b; break; }
      while (++i < n) if ((b = f(array[i], i, array)) != null && a > b) a = b;
    }

    return a;
  }

  function pairs(array) {
    var i = 0, n = array.length - 1, p = array[0], pairs = new Array(n < 0 ? 0 : n);
    while (i < n) pairs[i] = [p, p = array[++i]];
    return pairs;
  }

  function permute(array, indexes) {
    var i = indexes.length, permutes = new Array(i);
    while (i--) permutes[i] = array[indexes[i]];
    return permutes;
  }

  function scan(array, compare) {
    if (!(n = array.length)) return;
    var i = 0,
        n,
        j = 0,
        xi,
        xj = array[j];

    if (!compare) compare = ascending;

    while (++i < n) if (compare(xi = array[i], xj) < 0 || compare(xj, xj) !== 0) xj = xi, j = i;

    if (compare(xj, xj) === 0) return j;
  }

  function shuffle(array, i0, i1) {
    var m = (i1 == null ? array.length : i1) - (i0 = i0 == null ? 0 : +i0),
        t,
        i;

    while (m) {
      i = Math.random() * m-- | 0;
      t = array[m + i0];
      array[m + i0] = array[i + i0];
      array[i + i0] = t;
    }

    return array;
  }

  function sum(array, f) {
    var s = 0,
        n = array.length,
        a,
        i = -1;

    if (f == null) {
      while (++i < n) if (a = +array[i]) s += a; // Note: zero and null are equivalent.
    }

    else {
      while (++i < n) if (a = +f(array[i], i, array)) s += a;
    }

    return s;
  }

  function transpose(matrix) {
    if (!(n = matrix.length)) return [];
    for (var i = -1, m = min(matrix, length), transpose = new Array(m); ++i < m;) {
      for (var j = -1, n, row = transpose[i] = new Array(n); ++j < n;) {
        row[j] = matrix[j][i];
      }
    }
    return transpose;
  }

  function length(d) {
    return d.length;
  }

  function zip() {
    return transpose(arguments);
  }

  var prefix = "$";

  function Map() {}

  Map.prototype = map$1.prototype = {
    constructor: Map,
    has: function(key) {
      return (prefix + key) in this;
    },
    get: function(key) {
      return this[prefix + key];
    },
    set: function(key, value) {
      this[prefix + key] = value;
      return this;
    },
    remove: function(key) {
      var property = prefix + key;
      return property in this && delete this[property];
    },
    clear: function() {
      for (var property in this) if (property[0] === prefix) delete this[property];
    },
    keys: function() {
      var keys = [];
      for (var property in this) if (property[0] === prefix) keys.push(property.slice(1));
      return keys;
    },
    values: function() {
      var values = [];
      for (var property in this) if (property[0] === prefix) values.push(this[property]);
      return values;
    },
    entries: function() {
      var entries = [];
      for (var property in this) if (property[0] === prefix) entries.push({key: property.slice(1), value: this[property]});
      return entries;
    },
    size: function() {
      var size = 0;
      for (var property in this) if (property[0] === prefix) ++size;
      return size;
    },
    empty: function() {
      for (var property in this) if (property[0] === prefix) return false;
      return true;
    },
    each: function(f) {
      for (var property in this) if (property[0] === prefix) f(this[property], property.slice(1), this);
    }
  };

  function map$1(object, f) {
    var map = new Map;

    // Copy constructor.
    if (object instanceof Map) object.each(function(value, key) { map.set(key, value); });

    // Index array by numeric index or specified key function.
    else if (Array.isArray(object)) {
      var i = -1,
          n = object.length,
          o;

      if (f == null) while (++i < n) map.set(i, object[i]);
      else while (++i < n) map.set(f(o = object[i], i, object), o);
    }

    // Convert object to map.
    else if (object) for (var key in object) map.set(key, object[key]);

    return map;
  }

  function nest() {
    var keys = [],
        sortKeys = [],
        sortValues,
        rollup,
        nest;

    function apply(array, depth, createResult, setResult) {
      if (depth >= keys.length) return rollup != null
          ? rollup(array) : (sortValues != null
          ? array.sort(sortValues)
          : array);

      var i = -1,
          n = array.length,
          key = keys[depth++],
          keyValue,
          value,
          valuesByKey = map$1(),
          values,
          result = createResult();

      while (++i < n) {
        if (values = valuesByKey.get(keyValue = key(value = array[i]) + "")) {
          values.push(value);
        } else {
          valuesByKey.set(keyValue, [value]);
        }
      }

      valuesByKey.each(function(values, key) {
        setResult(result, key, apply(values, depth, createResult, setResult));
      });

      return result;
    }

    function entries(map, depth) {
      if (++depth > keys.length) return map;
      var array, sortKey = sortKeys[depth - 1];
      if (rollup != null && depth >= keys.length) array = map.entries();
      else array = [], map.each(function(v, k) { array.push({key: k, values: entries(v, depth)}); });
      return sortKey != null ? array.sort(function(a, b) { return sortKey(a.key, b.key); }) : array;
    }

    return nest = {
      object: function(array) { return apply(array, 0, createObject, setObject); },
      map: function(array) { return apply(array, 0, createMap, setMap); },
      entries: function(array) { return entries(apply(array, 0, createMap, setMap), 0); },
      key: function(d) { keys.push(d); return nest; },
      sortKeys: function(order) { sortKeys[keys.length - 1] = order; return nest; },
      sortValues: function(order) { sortValues = order; return nest; },
      rollup: function(f) { rollup = f; return nest; }
    };
  }

  function createObject() {
    return {};
  }

  function setObject(object, key, value) {
    object[key] = value;
  }

  function createMap() {
    return map$1();
  }

  function setMap(map, key, value) {
    map.set(key, value);
  }

  function Set() {}

  var proto = map$1.prototype;

  Set.prototype = set.prototype = {
    constructor: Set,
    has: proto.has,
    add: function(value) {
      value += "";
      this[prefix + value] = value;
      return this;
    },
    remove: proto.remove,
    clear: proto.clear,
    values: proto.keys,
    size: proto.size,
    empty: proto.empty,
    each: proto.each
  };

  function set(object, f) {
    var set = new Set;

    // Copy constructor.
    if (object instanceof Set) object.each(function(value) { set.add(value); });

    // Otherwise, assume it’s an array.
    else if (object) {
      var i = -1, n = object.length;
      if (f == null) while (++i < n) set.add(object[i]);
      else while (++i < n) set.add(f(object[i], i, object));
    }

    return set;
  }

  function keys(map) {
    var keys = [];
    for (var key in map) keys.push(key);
    return keys;
  }

  function values(map) {
    var values = [];
    for (var key in map) values.push(map[key]);
    return values;
  }

  function entries(map) {
    var entries = [];
    for (var key in map) entries.push({key: key, value: map[key]});
    return entries;
  }

  function uniform(min, max) {
    min = min == null ? 0 : +min;
    max = max == null ? 1 : +max;
    if (arguments.length === 1) max = min, min = 0;
    else max -= min;
    return function() {
      return Math.random() * max + min;
    };
  }

  function normal(mu, sigma) {
    var x, r;
    mu = mu == null ? 0 : +mu;
    sigma = sigma == null ? 1 : +sigma;
    return function() {
      var y;

      // If available, use the second previously-generated uniform random.
      if (x != null) y = x, x = null;

      // Otherwise, generate a new x and y.
      else do {
        x = Math.random() * 2 - 1;
        y = Math.random() * 2 - 1;
        r = x * x + y * y;
      } while (!r || r > 1);

      return mu + sigma * y * Math.sqrt(-2 * Math.log(r) / r);
    };
  }

  function logNormal() {
    var randomNormal = normal.apply(this, arguments);
    return function() {
      return Math.exp(randomNormal());
    };
  }

  function irwinHall(n) {
    return function() {
      for (var sum = 0, i = 0; i < n; ++i) sum += Math.random();
      return sum;
    };
  }

  function bates(n) {
    var randomIrwinHall = irwinHall(n);
    return function() {
      return randomIrwinHall() / n;
    };
  }

  function exponential(lambda) {
    return function() {
      return -Math.log(1 - Math.random()) / lambda;
    };
  }

  function linear(t) {
    return +t;
  }

  function quadIn(t) {
    return t * t;
  }

  function quadOut(t) {
    return t * (2 - t);
  }

  function quadInOut(t) {
    return ((t *= 2) <= 1 ? t * t : --t * (2 - t) + 1) / 2;
  }

  function cubicIn(t) {
    return t * t * t;
  }

  function cubicOut(t) {
    return --t * t * t + 1;
  }

  function easeCubicInOut(t) {
    return ((t *= 2) <= 1 ? t * t * t : (t -= 2) * t * t + 2) / 2;
  }

  var exponent = 3;

  var polyIn = (function custom(e) {
    e = +e;

    function polyIn(t) {
      return Math.pow(t, e);
    }

    polyIn.exponent = custom;

    return polyIn;
  })(exponent);

  var polyOut = (function custom(e) {
    e = +e;

    function polyOut(t) {
      return 1 - Math.pow(1 - t, e);
    }

    polyOut.exponent = custom;

    return polyOut;
  })(exponent);

  var polyInOut = (function custom(e) {
    e = +e;

    function polyInOut(t) {
      return ((t *= 2) <= 1 ? Math.pow(t, e) : 2 - Math.pow(2 - t, e)) / 2;
    }

    polyInOut.exponent = custom;

    return polyInOut;
  })(exponent);

  var pi = Math.PI;
  var halfPi = pi / 2;
  function sinIn(t) {
    return 1 - Math.cos(t * halfPi);
  }

  function sinOut(t) {
    return Math.sin(t * halfPi);
  }

  function sinInOut(t) {
    return (1 - Math.cos(pi * t)) / 2;
  }

  function expIn(t) {
    return Math.pow(2, 10 * t - 10);
  }

  function expOut(t) {
    return 1 - Math.pow(2, -10 * t);
  }

  function expInOut(t) {
    return ((t *= 2) <= 1 ? Math.pow(2, 10 * t - 10) : 2 - Math.pow(2, 10 - 10 * t)) / 2;
  }

  function circleIn(t) {
    return 1 - Math.sqrt(1 - t * t);
  }

  function circleOut(t) {
    return Math.sqrt(1 - --t * t);
  }

  function circleInOut(t) {
    return ((t *= 2) <= 1 ? 1 - Math.sqrt(1 - t * t) : Math.sqrt(1 - (t -= 2) * t) + 1) / 2;
  }

  var b1 = 4 / 11;
  var b2 = 6 / 11;
  var b3 = 8 / 11;
  var b4 = 3 / 4;
  var b5 = 9 / 11;
  var b6 = 10 / 11;
  var b7 = 15 / 16;
  var b8 = 21 / 22;
  var b9 = 63 / 64;
  var b0 = 1 / b1 / b1;
  function bounceIn(t) {
    return 1 - bounceOut(1 - t);
  }

  function bounceOut(t) {
    return (t = +t) < b1 ? b0 * t * t : t < b3 ? b0 * (t -= b2) * t + b4 : t < b6 ? b0 * (t -= b5) * t + b7 : b0 * (t -= b8) * t + b9;
  }

  function bounceInOut(t) {
    return ((t *= 2) <= 1 ? 1 - bounceOut(1 - t) : bounceOut(t - 1) + 1) / 2;
  }

  var overshoot = 1.70158;

  var backIn = (function custom(s) {
    s = +s;

    function backIn(t) {
      return t * t * ((s + 1) * t - s);
    }

    backIn.overshoot = custom;

    return backIn;
  })(overshoot);

  var backOut = (function custom(s) {
    s = +s;

    function backOut(t) {
      return --t * t * ((s + 1) * t + s) + 1;
    }

    backOut.overshoot = custom;

    return backOut;
  })(overshoot);

  var backInOut = (function custom(s) {
    s = +s;

    function backInOut(t) {
      return ((t *= 2) < 1 ? t * t * ((s + 1) * t - s) : (t -= 2) * t * ((s + 1) * t + s) + 2) / 2;
    }

    backInOut.overshoot = custom;

    return backInOut;
  })(overshoot);

  var tau = 2 * Math.PI;
  var amplitude = 1;
  var period = 0.3;
  var elasticIn = (function custom(a, p) {
    var s = Math.asin(1 / (a = Math.max(1, a))) * (p /= tau);

    function elasticIn(t) {
      return a * Math.pow(2, 10 * --t) * Math.sin((s - t) / p);
    }

    elasticIn.amplitude = function(a) { return custom(a, p * tau); };
    elasticIn.period = function(p) { return custom(a, p); };

    return elasticIn;
  })(amplitude, period);

  var elasticOut = (function custom(a, p) {
    var s = Math.asin(1 / (a = Math.max(1, a))) * (p /= tau);

    function elasticOut(t) {
      return 1 - a * Math.pow(2, -10 * (t = +t)) * Math.sin((t + s) / p);
    }

    elasticOut.amplitude = function(a) { return custom(a, p * tau); };
    elasticOut.period = function(p) { return custom(a, p); };

    return elasticOut;
  })(amplitude, period);

  var elasticInOut = (function custom(a, p) {
    var s = Math.asin(1 / (a = Math.max(1, a))) * (p /= tau);

    function elasticInOut(t) {
      return ((t = t * 2 - 1) < 0
          ? a * Math.pow(2, 10 * t) * Math.sin((s - t) / p)
          : 2 - a * Math.pow(2, -10 * t) * Math.sin((s + t) / p)) / 2;
    }

    elasticInOut.amplitude = function(a) { return custom(a, p * tau); };
    elasticInOut.period = function(p) { return custom(a, p); };

    return elasticInOut;
  })(amplitude, period);

  function area(polygon) {
    var i = -1,
        n = polygon.length,
        a,
        b = polygon[n - 1],
        area = 0;

    while (++i < n) {
      a = b;
      b = polygon[i];
      area += a[1] * b[0] - a[0] * b[1];
    }

    return area / 2;
  }

  function centroid(polygon) {
    var i = -1,
        n = polygon.length,
        x = 0,
        y = 0,
        a,
        b = polygon[n - 1],
        c,
        k = 0;

    while (++i < n) {
      a = b;
      b = polygon[i];
      k += c = a[0] * b[1] - b[0] * a[1];
      x += (a[0] + b[0]) * c;
      y += (a[1] + b[1]) * c;
    }

    return k *= 3, [x / k, y / k];
  }

  // Returns the 2D cross product of AB and AC vectors, i.e., the z-component of
  // the 3D cross product in a quadrant I Cartesian coordinate system (+x is
  // right, +y is up). Returns a positive value if ABC is counter-clockwise,
  // negative if clockwise, and zero if the points are collinear.
  function cross(a, b, c) {
    return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]);
  }

  function lexicographicOrder(a, b) {
    return a[0] - b[0] || a[1] - b[1];
  }

  // Computes the upper convex hull per the monotone chain algorithm.
  // Assumes points.length >= 3, is sorted by x, unique in y.
  // Returns an array of indices into points in left-to-right order.
  function computeUpperHullIndexes(points) {
    var n = points.length,
        indexes = [0, 1],
        size = 2;

    for (var i = 2; i < n; ++i) {
      while (size > 1 && cross(points[indexes[size - 2]], points[indexes[size - 1]], points[i]) <= 0) --size;
      indexes[size++] = i;
    }

    return indexes.slice(0, size); // remove popped points
  }

  function hull(points) {
    if ((n = points.length) < 3) return null;

    var i,
        n,
        sortedPoints = new Array(n),
        flippedPoints = new Array(n);

    for (i = 0; i < n; ++i) sortedPoints[i] = [+points[i][0], +points[i][1], i];
    sortedPoints.sort(lexicographicOrder);
    for (i = 0; i < n; ++i) flippedPoints[i] = [sortedPoints[i][0], -sortedPoints[i][1]];

    var upperIndexes = computeUpperHullIndexes(sortedPoints),
        lowerIndexes = computeUpperHullIndexes(flippedPoints);

    // Construct the hull polygon, removing possible duplicate endpoints.
    var skipLeft = lowerIndexes[0] === upperIndexes[0],
        skipRight = lowerIndexes[lowerIndexes.length - 1] === upperIndexes[upperIndexes.length - 1],
        hull = [];

    // Add upper hull in right-to-l order.
    // Then add lower hull in left-to-right order.
    for (i = upperIndexes.length - 1; i >= 0; --i) hull.push(points[sortedPoints[upperIndexes[i]][2]]);
    for (i = +skipLeft; i < lowerIndexes.length - skipRight; ++i) hull.push(points[sortedPoints[lowerIndexes[i]][2]]);

    return hull;
  }

  function contains(polygon, point) {
    var n = polygon.length,
        p = polygon[n - 1],
        x = point[0], y = point[1],
        x0 = p[0], y0 = p[1],
        x1, y1,
        inside = false;

    for (var i = 0; i < n; ++i) {
      p = polygon[i], x1 = p[0], y1 = p[1];
      if (((y1 > y) !== (y0 > y)) && (x < (x0 - x1) * (y - y1) / (y0 - y1) + x1)) inside = !inside;
      x0 = x1, y0 = y1;
    }

    return inside;
  }

  function length$1(polygon) {
    var i = -1,
        n = polygon.length,
        b = polygon[n - 1],
        xa,
        ya,
        xb = b[0],
        yb = b[1],
        perimeter = 0;

    while (++i < n) {
      xa = xb;
      ya = yb;
      b = polygon[i];
      xb = b[0];
      yb = b[1];
      xa -= xb;
      ya -= yb;
      perimeter += Math.sqrt(xa * xa + ya * ya);
    }

    return perimeter;
  }

var   pi$1 = Math.PI;
var   tau$1 = 2 * pi$1;
  var epsilon = 1e-6;
  var tauEpsilon = tau$1 - epsilon;
  function Path() {
    this._x0 = this._y0 = // start of current subpath
    this._x1 = this._y1 = null; // end of current subpath
    this._ = [];
  }

  function path() {
    return new Path;
  }

  Path.prototype = path.prototype = {
    constructor: Path,
    moveTo: function(x, y) {
      this._.push("M", this._x0 = this._x1 = +x, ",", this._y0 = this._y1 = +y);
    },
    closePath: function() {
      if (this._x1 !== null) {
        this._x1 = this._x0, this._y1 = this._y0;
        this._.push("Z");
      }
    },
    lineTo: function(x, y) {
      this._.push("L", this._x1 = +x, ",", this._y1 = +y);
    },
    quadraticCurveTo: function(x1, y1, x, y) {
      this._.push("Q", +x1, ",", +y1, ",", this._x1 = +x, ",", this._y1 = +y);
    },
    bezierCurveTo: function(x1, y1, x2, y2, x, y) {
      this._.push("C", +x1, ",", +y1, ",", +x2, ",", +y2, ",", this._x1 = +x, ",", this._y1 = +y);
    },
    arcTo: function(x1, y1, x2, y2, r) {
      x1 = +x1, y1 = +y1, x2 = +x2, y2 = +y2, r = +r;
      var x0 = this._x1,
          y0 = this._y1,
          x21 = x2 - x1,
          y21 = y2 - y1,
          x01 = x0 - x1,
          y01 = y0 - y1,
          l01_2 = x01 * x01 + y01 * y01;

      // Is the radius negative? Error.
      if (r < 0) throw new Error("negative radius: " + r);

      // Is this path empty? Move to (x1,y1).
      if (this._x1 === null) {
        this._.push(
          "M", this._x1 = x1, ",", this._y1 = y1
        );
      }

      // Or, is (x1,y1) coincident with (x0,y0)? Do nothing.
      else if (!(l01_2 > epsilon));

      // Or, are (x0,y0), (x1,y1) and (x2,y2) collinear?
      // Equivalently, is (x1,y1) coincident with (x2,y2)?
      // Or, is the radius zero? Line to (x1,y1).
      else if (!(Math.abs(y01 * x21 - y21 * x01) > epsilon) || !r) {
        this._.push(
          "L", this._x1 = x1, ",", this._y1 = y1
        );
      }

      // Otherwise, draw an arc!
      else {
        var x20 = x2 - x0,
            y20 = y2 - y0,
            l21_2 = x21 * x21 + y21 * y21,
            l20_2 = x20 * x20 + y20 * y20,
            l21 = Math.sqrt(l21_2),
            l01 = Math.sqrt(l01_2),
            l = r * Math.tan((pi$1 - Math.acos((l21_2 + l01_2 - l20_2) / (2 * l21 * l01))) / 2),
            t01 = l / l01,
            t21 = l / l21;

        // If the start tangent is not coincident with (x0,y0), line to.
        if (Math.abs(t01 - 1) > epsilon) {
          this._.push(
            "L", x1 + t01 * x01, ",", y1 + t01 * y01
          );
        }

        this._.push(
          "A", r, ",", r, ",0,0,", +(y01 * x20 > x01 * y20), ",", this._x1 = x1 + t21 * x21, ",", this._y1 = y1 + t21 * y21
        );
      }
    },
    arc: function(x, y, r, a0, a1, ccw) {
      x = +x, y = +y, r = +r;
      var dx = r * Math.cos(a0),
          dy = r * Math.sin(a0),
          x0 = x + dx,
          y0 = y + dy,
          cw = 1 ^ ccw,
          da = ccw ? a0 - a1 : a1 - a0;

      // Is the radius negative? Error.
      if (r < 0) throw new Error("negative radius: " + r);

      // Is this path empty? Move to (x0,y0).
      if (this._x1 === null) {
        this._.push(
          "M", x0, ",", y0
        );
      }

      // Or, is (x0,y0) not coincident with the previous point? Line to (x0,y0).
      else if (Math.abs(this._x1 - x0) > epsilon || Math.abs(this._y1 - y0) > epsilon) {
        this._.push(
          "L", x0, ",", y0
        );
      }

      // Is this arc empty? We’re done.
      if (!r) return;

      // Is this a complete circle? Draw two arcs to complete the circle.
      if (da > tauEpsilon) {
        this._.push(
          "A", r, ",", r, ",0,1,", cw, ",", x - dx, ",", y - dy,
          "A", r, ",", r, ",0,1,", cw, ",", this._x1 = x0, ",", this._y1 = y0
        );
      }

      // Otherwise, draw an arc!
      else {
        if (da < 0) da = da % tau$1 + tau$1;
        this._.push(
          "A", r, ",", r, ",0,", +(da >= pi$1), ",", cw, ",", this._x1 = x + r * Math.cos(a1), ",", this._y1 = y + r * Math.sin(a1)
        );
      }
    },
    rect: function(x, y, w, h) {
      this._.push("M", this._x0 = this._x1 = +x, ",", this._y0 = this._y1 = +y, "h", +w, "v", +h, "h", -w, "Z");
    },
    toString: function() {
      return this._.join("");
    }
  };

  function tree_add(d) {
    var x = +this._x.call(null, d),
        y = +this._y.call(null, d);
    return add(this.cover(x, y), x, y, d);
  }

  function add(tree, x, y, d) {
    if (isNaN(x) || isNaN(y)) return tree; // ignore invalid points

    var parent,
        node = tree._root,
        leaf = {data: d},
        x0 = tree._x0,
        y0 = tree._y0,
        x1 = tree._x1,
        y1 = tree._y1,
        xm,
        ym,
        xp,
        yp,
        right,
        bottom,
        i,
        j;

    // If the tree is empty, initialize the root as a leaf.
    if (!node) return tree._root = leaf, tree;

    // Find the existing leaf for the new point, or add it.
    while (node.length) {
      if (right = x >= (xm = (x0 + x1) / 2)) x0 = xm; else x1 = xm;
      if (bottom = y >= (ym = (y0 + y1) / 2)) y0 = ym; else y1 = ym;
      if (parent = node, !(node = node[i = bottom << 1 | right])) return parent[i] = leaf, tree;
    }

    // Is the new point is exactly coincident with the existing point?
    xp = +tree._x.call(null, node.data);
    yp = +tree._y.call(null, node.data);
    if (x === xp && y === yp) return leaf.next = node, parent ? parent[i] = leaf : tree._root = leaf, tree;

    // Otherwise, split the leaf node until the old and new point are separated.
    do {
      parent = parent ? parent[i] = new Array(4) : tree._root = new Array(4);
      if (right = x >= (xm = (x0 + x1) / 2)) x0 = xm; else x1 = xm;
      if (bottom = y >= (ym = (y0 + y1) / 2)) y0 = ym; else y1 = ym;
    } while ((i = bottom << 1 | right) === (j = (yp >= ym) << 1 | (xp >= xm)));
    return parent[j] = node, parent[i] = leaf, tree;
  }

  function addAll(data) {
    var d, i, n = data.length,
        x,
        y,
        xz = new Array(n),
        yz = new Array(n),
        x0 = Infinity,
        y0 = Infinity,
        x1 = -Infinity,
        y1 = -Infinity;

    // Compute the points and their extent.
    for (i = 0; i < n; ++i) {
      if (isNaN(x = +this._x.call(null, d = data[i])) || isNaN(y = +this._y.call(null, d))) continue;
      xz[i] = x;
      yz[i] = y;
      if (x < x0) x0 = x;
      if (x > x1) x1 = x;
      if (y < y0) y0 = y;
      if (y > y1) y1 = y;
    }

    // If there were no (valid) points, inherit the existing extent.
    if (x1 < x0) x0 = this._x0, x1 = this._x1;
    if (y1 < y0) y0 = this._y0, y1 = this._y1;

    // Expand the tree to cover the new points.
    this.cover(x0, y0).cover(x1, y1);

    // Add the new points.
    for (i = 0; i < n; ++i) {
      add(this, xz[i], yz[i], data[i]);
    }

    return this;
  }

  function tree_cover(x, y) {
    if (isNaN(x = +x) || isNaN(y = +y)) return this; // ignore invalid points

    var x0 = this._x0,
        y0 = this._y0,
        x1 = this._x1,
        y1 = this._y1;

    // If the quadtree has no extent, initialize them.
    // Integer extent are necessary so that if we later double the extent,
    // the existing quadrant boundaries don’t change due to floating point error!
    if (isNaN(x0)) {
      x1 = (x0 = Math.floor(x)) + 1;
      y1 = (y0 = Math.floor(y)) + 1;
    }

    // Otherwise, double repeatedly to cover.
    else if (x0 > x || x > x1 || y0 > y || y > y1) {
      var z = x1 - x0,
          node = this._root,
          parent,
          i;

      switch (i = (y < (y0 + y1) / 2) << 1 | (x < (x0 + x1) / 2)) {
        case 0: {
          do parent = new Array(4), parent[i] = node, node = parent;
          while (z *= 2, x1 = x0 + z, y1 = y0 + z, x > x1 || y > y1);
          break;
        }
        case 1: {
          do parent = new Array(4), parent[i] = node, node = parent;
          while (z *= 2, x0 = x1 - z, y1 = y0 + z, x0 > x || y > y1);
          break;
        }
        case 2: {
          do parent = new Array(4), parent[i] = node, node = parent;
          while (z *= 2, x1 = x0 + z, y0 = y1 - z, x > x1 || y0 > y);
          break;
        }
        case 3: {
          do parent = new Array(4), parent[i] = node, node = parent;
          while (z *= 2, x0 = x1 - z, y0 = y1 - z, x0 > x || y0 > y);
          break;
        }
      }

      if (this._root && this._root.length) this._root = node;
    }

    // If the quadtree covers the point already, just return.
    else return this;

    this._x0 = x0;
    this._y0 = y0;
    this._x1 = x1;
    this._y1 = y1;
    return this;
  }

  function tree_data() {
    var data = [];
    this.visit(function(node) {
      if (!node.length) do data.push(node.data); while (node = node.next)
    });
    return data;
  }

  function tree_extent(_) {
    return arguments.length
        ? this.cover(+_[0][0], +_[0][1]).cover(+_[1][0], +_[1][1])
        : isNaN(this._x0) ? undefined : [[this._x0, this._y0], [this._x1, this._y1]];
  }

  function Quad(node, x0, y0, x1, y1) {
    this.node = node;
    this.x0 = x0;
    this.y0 = y0;
    this.x1 = x1;
    this.y1 = y1;
  }

  function tree_find(x, y, radius) {
    var data,
        x0 = this._x0,
        y0 = this._y0,
        x1,
        y1,
        x2,
        y2,
        x3 = this._x1,
        y3 = this._y1,
        quads = [],
        node = this._root,
        q,
        i;

    if (node) quads.push(new Quad(node, x0, y0, x3, y3));
    if (radius == null) radius = Infinity;
    else {
      x0 = x - radius, y0 = y - radius;
      x3 = x + radius, y3 = y + radius;
      radius *= radius;
    }

    while (q = quads.pop()) {

      // Stop searching if this quadrant can’t contain a closer node.
      if (!(node = q.node)
          || (x1 = q.x0) > x3
          || (y1 = q.y0) > y3
          || (x2 = q.x1) < x0
          || (y2 = q.y1) < y0) continue;

      // Bisect the current quadrant.
      if (node.length) {
        var xm = (x1 + x2) / 2,
            ym = (y1 + y2) / 2;

        quads.push(
          new Quad(node[3], xm, ym, x2, y2),
          new Quad(node[2], x1, ym, xm, y2),
          new Quad(node[1], xm, y1, x2, ym),
          new Quad(node[0], x1, y1, xm, ym)
        );

        // Visit the closest quadrant first.
        if (i = (y >= ym) << 1 | (x >= xm)) {
          q = quads[quads.length - 1];
          quads[quads.length - 1] = quads[quads.length - 1 - i];
          quads[quads.length - 1 - i] = q;
        }
      }

      // Visit this point. (Visiting coincident points isn’t necessary!)
      else {
        var dx = x - +this._x.call(null, node.data),
            dy = y - +this._y.call(null, node.data),
            d2 = dx * dx + dy * dy;
        if (d2 < radius) {
          var d = Math.sqrt(radius = d2);
          x0 = x - d, y0 = y - d;
          x3 = x + d, y3 = y + d;
          data = node.data;
        }
      }
    }

    return data;
  }

  function tree_remove(d) {
    if (isNaN(x = +this._x.call(null, d)) || isNaN(y = +this._y.call(null, d))) return this; // ignore invalid points

    var parent,
        node = this._root,
        retainer,
        previous,
        next,
        x0 = this._x0,
        y0 = this._y0,
        x1 = this._x1,
        y1 = this._y1,
        x,
        y,
        xm,
        ym,
        right,
        bottom,
        i,
        j;

    // If the tree is empty, initialize the root as a leaf.
    if (!node) return this;

    // Find the leaf node for the point.
    // While descending, also retain the deepest parent with a non-removed sibling.
    if (node.length) while (true) {
      if (right = x >= (xm = (x0 + x1) / 2)) x0 = xm; else x1 = xm;
      if (bottom = y >= (ym = (y0 + y1) / 2)) y0 = ym; else y1 = ym;
      if (!(parent = node, node = node[i = bottom << 1 | right])) return this;
      if (!node.length) break;
      if (parent[(i + 1) & 3] || parent[(i + 2) & 3] || parent[(i + 3) & 3]) retainer = parent, j = i;
    }

    // Find the point to remove.
    while (node.data !== d) if (!(previous = node, node = node.next)) return this;
    if (next = node.next) delete node.next;

    // If there are multiple coincident points, remove just the point.
    if (previous) return (next ? previous.next = next : delete previous.next), this;

    // If this is the root point, remove it.
    if (!parent) return this._root = next, this;

    // Remove this leaf.
    next ? parent[i] = next : delete parent[i];

    // If the parent now contains exactly one leaf, collapse superfluous parents.
    if ((node = parent[0] || parent[1] || parent[2] || parent[3])
        && node === (parent[3] || parent[2] || parent[1] || parent[0])
        && !node.length) {
      if (retainer) retainer[j] = node;
      else this._root = node;
    }

    return this;
  }

  function removeAll(data) {
    for (var i = 0, n = data.length; i < n; ++i) this.remove(data[i]);
    return this;
  }

  function tree_root() {
    return this._root;
  }

  function tree_size() {
    var size = 0;
    this.visit(function(node) {
      if (!node.length) do ++size; while (node = node.next)
    });
    return size;
  }

  function tree_visit(callback) {
    var quads = [], q, node = this._root, child, x0, y0, x1, y1;
    if (node) quads.push(new Quad(node, this._x0, this._y0, this._x1, this._y1));
    while (q = quads.pop()) {
      if (!callback(node = q.node, x0 = q.x0, y0 = q.y0, x1 = q.x1, y1 = q.y1) && node.length) {
        var xm = (x0 + x1) / 2, ym = (y0 + y1) / 2;
        if (child = node[3]) quads.push(new Quad(child, xm, ym, x1, y1));
        if (child = node[2]) quads.push(new Quad(child, x0, ym, xm, y1));
        if (child = node[1]) quads.push(new Quad(child, xm, y0, x1, ym));
        if (child = node[0]) quads.push(new Quad(child, x0, y0, xm, ym));
      }
    }
    return this;
  }

  function tree_visitAfter(callback) {
    var quads = [], next = [], q;
    if (this._root) quads.push(new Quad(this._root, this._x0, this._y0, this._x1, this._y1));
    while (q = quads.pop()) {
      var node = q.node;
      if (node.length) {
        var child, x0 = q.x0, y0 = q.y0, x1 = q.x1, y1 = q.y1, xm = (x0 + x1) / 2, ym = (y0 + y1) / 2;
        if (child = node[0]) quads.push(new Quad(child, x0, y0, xm, ym));
        if (child = node[1]) quads.push(new Quad(child, xm, y0, x1, ym));
        if (child = node[2]) quads.push(new Quad(child, x0, ym, xm, y1));
        if (child = node[3]) quads.push(new Quad(child, xm, ym, x1, y1));
      }
      next.push(q);
    }
    while (q = next.pop()) {
      callback(q.node, q.x0, q.y0, q.x1, q.y1);
    }
    return this;
  }

  function defaultX(d) {
    return d[0];
  }

  function tree_x(_) {
    return arguments.length ? (this._x = _, this) : this._x;
  }

  function defaultY(d) {
    return d[1];
  }

  function tree_y(_) {
    return arguments.length ? (this._y = _, this) : this._y;
  }

  function quadtree(nodes, x, y) {
    var tree = new Quadtree(x == null ? defaultX : x, y == null ? defaultY : y, NaN, NaN, NaN, NaN);
    return nodes == null ? tree : tree.addAll(nodes);
  }

  function Quadtree(x, y, x0, y0, x1, y1) {
    this._x = x;
    this._y = y;
    this._x0 = x0;
    this._y0 = y0;
    this._x1 = x1;
    this._y1 = y1;
    this._root = undefined;
  }

  function leaf_copy(leaf) {
    var copy = {data: leaf.data}, next = copy;
    while (leaf = leaf.next) next = next.next = {data: leaf.data};
    return copy;
  }

  var treeProto = quadtree.prototype = Quadtree.prototype;

  treeProto.copy = function() {
    var copy = new Quadtree(this._x, this._y, this._x0, this._y0, this._x1, this._y1),
        node = this._root,
        nodes,
        child;

    if (!node) return copy;

    if (!node.length) return copy._root = leaf_copy(node), copy;

    nodes = [{source: node, target: copy._root = new Array(4)}];
    while (node = nodes.pop()) {
      for (var i = 0; i < 4; ++i) {
        if (child = node.source[i]) {
          if (child.length) nodes.push({source: child, target: node.target[i] = new Array(4)});
          else node.target[i] = leaf_copy(child);
        }
      }
    }

    return copy;
  };

  treeProto.add = tree_add;
  treeProto.addAll = addAll;
  treeProto.cover = tree_cover;
  treeProto.data = tree_data;
  treeProto.extent = tree_extent;
  treeProto.find = tree_find;
  treeProto.remove = tree_remove;
  treeProto.removeAll = removeAll;
  treeProto.root = tree_root;
  treeProto.size = tree_size;
  treeProto.visit = tree_visit;
  treeProto.visitAfter = tree_visitAfter;
  treeProto.x = tree_x;
  treeProto.y = tree_y;

  var slice$1 = [].slice;

  var noabort = {};

  function Queue(size) {
    if (!(size >= 1)) throw new Error;
    this._size = size;
    this._call =
    this._error = null;
    this._tasks = [];
    this._data = [];
    this._waiting =
    this._active =
    this._ended =
    this._start = 0; // inside a synchronous task callback?
  }

  Queue.prototype = queue.prototype = {
    constructor: Queue,
    defer: function(callback) {
      if (typeof callback !== "function" || this._call) throw new Error;
      if (this._error != null) return this;
      var t = slice$1.call(arguments, 1);
      t.push(callback);
      ++this._waiting, this._tasks.push(t);
      poke(this);
      return this;
    },
    abort: function() {
      if (this._error == null) abort(this, new Error("abort"));
      return this;
    },
    await: function(callback) {
      if (typeof callback !== "function" || this._call) throw new Error;
      this._call = function(error, results) { callback.apply(null, [error].concat(results)); };
      maybeNotify(this);
      return this;
    },
    awaitAll: function(callback) {
      if (typeof callback !== "function" || this._call) throw new Error;
      this._call = callback;
      maybeNotify(this);
      return this;
    }
  };

  function poke(q) {
    if (!q._start) try { start(q); } // let the current task complete
    catch (e) { if (q._tasks[q._ended + q._active - 1]) abort(q, e); } // task errored synchronously
  }

  function start(q) {
    while (q._start = q._waiting && q._active < q._size) {
      var i = q._ended + q._active,
          t = q._tasks[i],
          j = t.length - 1,
          c = t[j];
      t[j] = end(q, i);
      --q._waiting, ++q._active;
      t = c.apply(null, t);
      if (!q._tasks[i]) continue; // task finished synchronously
      q._tasks[i] = t || noabort;
    }
  }

  function end(q, i) {
    return function(e, r) {
      if (!q._tasks[i]) return; // ignore multiple callbacks
      --q._active, ++q._ended;
      q._tasks[i] = null;
      if (q._error != null) return; // ignore secondary errors
      if (e != null) {
        abort(q, e);
      } else {
        q._data[i] = r;
        if (q._waiting) poke(q);
        else maybeNotify(q);
      }
    };
  }

  function abort(q, e) {
    var i = q._tasks.length, t;
    q._error = e; // ignore active callbacks
    q._data = undefined; // allow gc
    q._waiting = NaN; // prevent starting

    while (--i >= 0) {
      if (t = q._tasks[i]) {
        q._tasks[i] = null;
        if (t.abort) try { t.abort(); }
        catch (e) { /* ignore */ }
      }
    }

    q._active = NaN; // allow notification
    maybeNotify(q);
  }

  function maybeNotify(q) {
    if (!q._active && q._call) q._call(q._error, q._data);
  }

  function queue(concurrency) {
    return new Queue(arguments.length ? +concurrency : Infinity);
  }

  function constant$1(x) {
    return function constant() {
      return x;
    };
  }

  var epsilon$1 = 1e-12;
  var pi$2 = Math.PI;
  var halfPi$1 = pi$2 / 2;
  var tau$2 = 2 * pi$2;

  function arcInnerRadius(d) {
    return d.innerRadius;
  }

  function arcOuterRadius(d) {
    return d.outerRadius;
  }

  function arcStartAngle(d) {
    return d.startAngle;
  }

  function arcEndAngle(d) {
    return d.endAngle;
  }

  function arcPadAngle(d) {
    return d && d.padAngle; // Note: optional!
  }

  function asin(x) {
    return x >= 1 ? halfPi$1 : x <= -1 ? -halfPi$1 : Math.asin(x);
  }

  function intersect(x0, y0, x1, y1, x2, y2, x3, y3) {
    var x10 = x1 - x0, y10 = y1 - y0,
        x32 = x3 - x2, y32 = y3 - y2,
        t = (x32 * (y0 - y2) - y32 * (x0 - x2)) / (y32 * x10 - x32 * y10);
    return [x0 + t * x10, y0 + t * y10];
  }

  // Compute perpendicular offset line of length rc.
  // http://mathworld.wolfram.com/Circle-LineIntersection.html
  function cornerTangents(x0, y0, x1, y1, r1, rc, cw) {
    var x01 = x0 - x1,
        y01 = y0 - y1,
        lo = (cw ? rc : -rc) / Math.sqrt(x01 * x01 + y01 * y01),
        ox = lo * y01,
        oy = -lo * x01,
        x11 = x0 + ox,
        y11 = y0 + oy,
        x10 = x1 + ox,
        y10 = y1 + oy,
        x00 = (x11 + x10) / 2,
        y00 = (y11 + y10) / 2,
        dx = x10 - x11,
        dy = y10 - y11,
        d2 = dx * dx + dy * dy,
        r = r1 - rc,
        D = x11 * y10 - x10 * y11,
        d = (dy < 0 ? -1 : 1) * Math.sqrt(Math.max(0, r * r * d2 - D * D)),
        cx0 = (D * dy - dx * d) / d2,
        cy0 = (-D * dx - dy * d) / d2,
        cx1 = (D * dy + dx * d) / d2,
        cy1 = (-D * dx + dy * d) / d2,
        dx0 = cx0 - x00,
        dy0 = cy0 - y00,
        dx1 = cx1 - x00,
        dy1 = cy1 - y00;

    // Pick the closer of the two intersection points.
    // TODO Is there a faster way to determine which intersection to use?
    if (dx0 * dx0 + dy0 * dy0 > dx1 * dx1 + dy1 * dy1) cx0 = cx1, cy0 = cy1;

    return {
      cx: cx0,
      cy: cy0,
      x01: -ox,
      y01: -oy,
      x11: cx0 * (r1 / r - 1),
      y11: cy0 * (r1 / r - 1)
    };
  }

  function arc() {
    var innerRadius = arcInnerRadius,
        outerRadius = arcOuterRadius,
        cornerRadius = constant$1(0),
        padRadius = null,
        startAngle = arcStartAngle,
        endAngle = arcEndAngle,
        padAngle = arcPadAngle,
        context = null;

    function arc() {
      var buffer,
          r,
          r0 = +innerRadius.apply(this, arguments),
          r1 = +outerRadius.apply(this, arguments),
          a0 = startAngle.apply(this, arguments) - halfPi$1,
          a1 = endAngle.apply(this, arguments) - halfPi$1,
          da = Math.abs(a1 - a0),
          cw = a1 > a0;

      if (!context) context = buffer = path();

      // Ensure that the outer radius is always larger than the inner radius.
      if (r1 < r0) r = r1, r1 = r0, r0 = r;

      // Is it a point?
      if (!(r1 > epsilon$1)) context.moveTo(0, 0);

      // Or is it a circle or annulus?
      else if (da > tau$2 - epsilon$1) {
        context.moveTo(r1 * Math.cos(a0), r1 * Math.sin(a0));
        context.arc(0, 0, r1, a0, a1, !cw);
        if (r0 > epsilon$1) {
          context.moveTo(r0 * Math.cos(a1), r0 * Math.sin(a1));
          context.arc(0, 0, r0, a1, a0, cw);
        }
      }

      // Or is it a circular or annular sector?
      else {
        var a01 = a0,
            a11 = a1,
            a00 = a0,
            a10 = a1,
            da0 = da,
            da1 = da,
            ap = padAngle.apply(this, arguments) / 2,
            rp = (ap > epsilon$1) && (padRadius ? +padRadius.apply(this, arguments) : Math.sqrt(r0 * r0 + r1 * r1)),
            rc = Math.min(Math.abs(r1 - r0) / 2, +cornerRadius.apply(this, arguments)),
            rc0 = rc,
            rc1 = rc,
            t0,
            t1;

        // Apply padding? Note that since r1 ≥ r0, da1 ≥ da0.
        if (rp > epsilon$1) {
          var p0 = asin(rp / r0 * Math.sin(ap)),
              p1 = asin(rp / r1 * Math.sin(ap));
          if ((da0 -= p0 * 2) > epsilon$1) p0 *= (cw ? 1 : -1), a00 += p0, a10 -= p0;
          else da0 = 0, a00 = a10 = (a0 + a1) / 2;
          if ((da1 -= p1 * 2) > epsilon$1) p1 *= (cw ? 1 : -1), a01 += p1, a11 -= p1;
          else da1 = 0, a01 = a11 = (a0 + a1) / 2;
        }

        var x01 = r1 * Math.cos(a01),
            y01 = r1 * Math.sin(a01),
            x10 = r0 * Math.cos(a10),
            y10 = r0 * Math.sin(a10);

        // Apply rounded corners?
        if (rc > epsilon$1) {
          var x11 = r1 * Math.cos(a11),
              y11 = r1 * Math.sin(a11),
              x00 = r0 * Math.cos(a00),
              y00 = r0 * Math.sin(a00);

          // Restrict the corner radius according to the sector angle.
          if (da < pi$2) {
            var oc = da0 > epsilon$1 ? intersect(x01, y01, x00, y00, x11, y11, x10, y10) : [x10, y10],
                ax = x01 - oc[0],
                ay = y01 - oc[1],
                bx = x11 - oc[0],
                by = y11 - oc[1],
                kc = 1 / Math.sin(Math.acos((ax * bx + ay * by) / (Math.sqrt(ax * ax + ay * ay) * Math.sqrt(bx * bx + by * by))) / 2),
                lc = Math.sqrt(oc[0] * oc[0] + oc[1] * oc[1]);
            rc0 = Math.min(rc, (r0 - lc) / (kc - 1));
            rc1 = Math.min(rc, (r1 - lc) / (kc + 1));
          }
        }

        // Is the sector collapsed to a line?
        if (!(da1 > epsilon$1)) context.moveTo(x01, y01);

        // Does the sector’s outer ring have rounded corners?
        else if (rc1 > epsilon$1) {
          t0 = cornerTangents(x00, y00, x01, y01, r1, rc1, cw);
          t1 = cornerTangents(x11, y11, x10, y10, r1, rc1, cw);

          context.moveTo(t0.cx + t0.x01, t0.cy + t0.y01);

          // Have the corners merged?
          if (rc1 < rc) context.arc(t0.cx, t0.cy, rc1, Math.atan2(t0.y01, t0.x01), Math.atan2(t1.y01, t1.x01), !cw);

          // Otherwise, draw the two corners and the ring.
          else {
            context.arc(t0.cx, t0.cy, rc1, Math.atan2(t0.y01, t0.x01), Math.atan2(t0.y11, t0.x11), !cw);
            context.arc(0, 0, r1, Math.atan2(t0.cy + t0.y11, t0.cx + t0.x11), Math.atan2(t1.cy + t1.y11, t1.cx + t1.x11), !cw);
            context.arc(t1.cx, t1.cy, rc1, Math.atan2(t1.y11, t1.x11), Math.atan2(t1.y01, t1.x01), !cw);
          }
        }

        // Or is the outer ring just a circular arc?
        else context.moveTo(x01, y01), context.arc(0, 0, r1, a01, a11, !cw);

        // Is there no inner ring, and it’s a circular sector?
        // Or perhaps it’s an annular sector collapsed due to padding?
        if (!(r0 > epsilon$1) || !(da0 > epsilon$1)) context.lineTo(x10, y10);

        // Does the sector’s inner ring (or point) have rounded corners?
        else if (rc0 > epsilon$1) {
          t0 = cornerTangents(x10, y10, x11, y11, r0, -rc0, cw);
          t1 = cornerTangents(x01, y01, x00, y00, r0, -rc0, cw);

          context.lineTo(t0.cx + t0.x01, t0.cy + t0.y01);

          // Have the corners merged?
          if (rc0 < rc) context.arc(t0.cx, t0.cy, rc0, Math.atan2(t0.y01, t0.x01), Math.atan2(t1.y01, t1.x01), !cw);

          // Otherwise, draw the two corners and the ring.
          else {
            context.arc(t0.cx, t0.cy, rc0, Math.atan2(t0.y01, t0.x01), Math.atan2(t0.y11, t0.x11), !cw);
            context.arc(0, 0, r0, Math.atan2(t0.cy + t0.y11, t0.cx + t0.x11), Math.atan2(t1.cy + t1.y11, t1.cx + t1.x11), cw);
            context.arc(t1.cx, t1.cy, rc0, Math.atan2(t1.y11, t1.x11), Math.atan2(t1.y01, t1.x01), !cw);
          }
        }

        // Or is the inner ring just a circular arc?
        else context.arc(0, 0, r0, a10, a00, cw);
      }

      context.closePath();

      if (buffer) return context = null, buffer + "" || null;
    }

    arc.centroid = function() {
      var r = (+innerRadius.apply(this, arguments) + +outerRadius.apply(this, arguments)) / 2,
          a = (+startAngle.apply(this, arguments) + +endAngle.apply(this, arguments)) / 2 - pi$2 / 2;
      return [Math.cos(a) * r, Math.sin(a) * r];
    };

    arc.innerRadius = function(_) {
      return arguments.length ? (innerRadius = typeof _ === "function" ? _ : constant$1(+_), arc) : innerRadius;
    };

    arc.outerRadius = function(_) {
      return arguments.length ? (outerRadius = typeof _ === "function" ? _ : constant$1(+_), arc) : outerRadius;
    };

    arc.cornerRadius = function(_) {
      return arguments.length ? (cornerRadius = typeof _ === "function" ? _ : constant$1(+_), arc) : cornerRadius;
    };

    arc.padRadius = function(_) {
      return arguments.length ? (padRadius = _ == null ? null : typeof _ === "function" ? _ : constant$1(+_), arc) : padRadius;
    };

    arc.startAngle = function(_) {
      return arguments.length ? (startAngle = typeof _ === "function" ? _ : constant$1(+_), arc) : startAngle;
    };

    arc.endAngle = function(_) {
      return arguments.length ? (endAngle = typeof _ === "function" ? _ : constant$1(+_), arc) : endAngle;
    };

    arc.padAngle = function(_) {
      return arguments.length ? (padAngle = typeof _ === "function" ? _ : constant$1(+_), arc) : padAngle;
    };

    arc.context = function(_) {
      return arguments.length ? ((context = _ == null ? null : _), arc) : context;
    };

    return arc;
  }

  function Linear(context) {
    this._context = context;
  }

  Linear.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._point = 0;
    },
    lineEnd: function() {
      if (this._line || (this._line !== 0 && this._point === 1)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; this._line ? this._context.lineTo(x, y) : this._context.moveTo(x, y); break;
        case 1: this._point = 2; // proceed
        default: this._context.lineTo(x, y); break;
      }
    }
  };

  function curveLinear(context) {
    return new Linear(context);
  }

  function x(p) {
    return p[0];
  }

  function y(p) {
    return p[1];
  }

  function line() {
    var x$$ = x,
        y$$ = y,
        defined = constant$1(true),
        context = null,
        curve = curveLinear,
        output = null;

    function line(data) {
      var i,
          n = data.length,
          d,
          defined0 = false,
          buffer;

      if (context == null) output = curve(buffer = path());

      for (i = 0; i <= n; ++i) {
        if (!(i < n && defined(d = data[i], i, data)) === defined0) {
          if (defined0 = !defined0) output.lineStart();
          else output.lineEnd();
        }
        if (defined0) output.point(+x$$(d, i, data), +y$$(d, i, data));
      }

      if (buffer) return output = null, buffer + "" || null;
    }

    line.x = function(_) {
      return arguments.length ? (x$$ = typeof _ === "function" ? _ : constant$1(+_), line) : x$$;
    };

    line.y = function(_) {
      return arguments.length ? (y$$ = typeof _ === "function" ? _ : constant$1(+_), line) : y$$;
    };

    line.defined = function(_) {
      return arguments.length ? (defined = typeof _ === "function" ? _ : constant$1(!!_), line) : defined;
    };

    line.curve = function(_) {
      return arguments.length ? (curve = _, context != null && (output = curve(context)), line) : curve;
    };

    line.context = function(_) {
      return arguments.length ? (_ == null ? context = output = null : output = curve(context = _), line) : context;
    };

    return line;
  }

  function area$1() {
    var x0 = x,
        x1 = null,
        y0 = constant$1(0),
        y1 = y,
        defined = constant$1(true),
        context = null,
        curve = curveLinear,
        output = null;

    function area(data) {
      var i,
          j,
          k,
          n = data.length,
          d,
          defined0 = false,
          buffer,
          x0z = new Array(n),
          y0z = new Array(n);

      if (context == null) output = curve(buffer = path());

      for (i = 0; i <= n; ++i) {
        if (!(i < n && defined(d = data[i], i, data)) === defined0) {
          if (defined0 = !defined0) {
            j = i;
            output.areaStart();
            output.lineStart();
          } else {
            output.lineEnd();
            output.lineStart();
            for (k = i - 1; k >= j; --k) {
              output.point(x0z[k], y0z[k]);
            }
            output.lineEnd();
            output.areaEnd();
          }
        }
        if (defined0) {
          x0z[i] = +x0(d, i, data), y0z[i] = +y0(d, i, data);
          output.point(x1 ? +x1(d, i, data) : x0z[i], y1 ? +y1(d, i, data) : y0z[i]);
        }
      }

      if (buffer) return output = null, buffer + "" || null;
    }

    function arealine() {
      return line().defined(defined).curve(curve).context(context);
    }

    area.x = function(_) {
      return arguments.length ? (x0 = typeof _ === "function" ? _ : constant$1(+_), x1 = null, area) : x0;
    };

    area.x0 = function(_) {
      return arguments.length ? (x0 = typeof _ === "function" ? _ : constant$1(+_), area) : x0;
    };

    area.x1 = function(_) {
      return arguments.length ? (x1 = _ == null ? null : typeof _ === "function" ? _ : constant$1(+_), area) : x1;
    };

    area.y = function(_) {
      return arguments.length ? (y0 = typeof _ === "function" ? _ : constant$1(+_), y1 = null, area) : y0;
    };

    area.y0 = function(_) {
      return arguments.length ? (y0 = typeof _ === "function" ? _ : constant$1(+_), area) : y0;
    };

    area.y1 = function(_) {
      return arguments.length ? (y1 = _ == null ? null : typeof _ === "function" ? _ : constant$1(+_), area) : y1;
    };

    area.lineX0 =
    area.lineY0 = function() {
      return arealine().x(x0).y(y0);
    };

    area.lineY1 = function() {
      return arealine().x(x0).y(y1);
    };

    area.lineX1 = function() {
      return arealine().x(x1).y(y0);
    };

    area.defined = function(_) {
      return arguments.length ? (defined = typeof _ === "function" ? _ : constant$1(!!_), area) : defined;
    };

    area.curve = function(_) {
      return arguments.length ? (curve = _, context != null && (output = curve(context)), area) : curve;
    };

    area.context = function(_) {
      return arguments.length ? (_ == null ? context = output = null : output = curve(context = _), area) : context;
    };

    return area;
  }

  function descending$1(a, b) {
    return b < a ? -1 : b > a ? 1 : b >= a ? 0 : NaN;
  }

  function identity$1(d) {
    return d;
  }

  function pie() {
    var value = identity$1,
        sortValues = descending$1,
        sort = null,
        startAngle = constant$1(0),
        endAngle = constant$1(tau$2),
        padAngle = constant$1(0);

    function pie(data) {
      var i,
          n = data.length,
          j,
          k,
          sum = 0,
          index = new Array(n),
          arcs = new Array(n),
          a0 = +startAngle.apply(this, arguments),
          da = Math.min(tau$2, Math.max(-tau$2, endAngle.apply(this, arguments) - a0)),
          a1,
          p = Math.min(Math.abs(da) / n, padAngle.apply(this, arguments)),
          pa = p * (da < 0 ? -1 : 1),
          v;

      for (i = 0; i < n; ++i) {
        if ((v = arcs[index[i] = i] = +value(data[i], i, data)) > 0) {
          sum += v;
        }
      }

      // Optionally sort the arcs by previously-computed values or by data.
      if (sortValues != null) index.sort(function(i, j) { return sortValues(arcs[i], arcs[j]); });
      else if (sort != null) index.sort(function(i, j) { return sort(data[i], data[j]); });

      // Compute the arcs! They are stored in the original data's order.
      for (i = 0, k = sum ? (da - n * pa) / sum : 0; i < n; ++i, a0 = a1) {
        j = index[i], v = arcs[j], a1 = a0 + (v > 0 ? v * k : 0) + pa, arcs[j] = {
          data: data[j],
          index: i,
          value: v,
          startAngle: a0,
          endAngle: a1,
          padAngle: p
        };
      }

      return arcs;
    }

    pie.value = function(_) {
      return arguments.length ? (value = typeof _ === "function" ? _ : constant$1(+_), pie) : value;
    };

    pie.sortValues = function(_) {
      return arguments.length ? (sortValues = _, sort = null, pie) : sortValues;
    };

    pie.sort = function(_) {
      return arguments.length ? (sort = _, sortValues = null, pie) : sort;
    };

    pie.startAngle = function(_) {
      return arguments.length ? (startAngle = typeof _ === "function" ? _ : constant$1(+_), pie) : startAngle;
    };

    pie.endAngle = function(_) {
      return arguments.length ? (endAngle = typeof _ === "function" ? _ : constant$1(+_), pie) : endAngle;
    };

    pie.padAngle = function(_) {
      return arguments.length ? (padAngle = typeof _ === "function" ? _ : constant$1(+_), pie) : padAngle;
    };

    return pie;
  }

  var curveRadialLinear = curveRadial(curveLinear);

  function Radial(curve) {
    this._curve = curve;
  }

  Radial.prototype = {
    areaStart: function() {
      this._curve.areaStart();
    },
    areaEnd: function() {
      this._curve.areaEnd();
    },
    lineStart: function() {
      this._curve.lineStart();
    },
    lineEnd: function() {
      this._curve.lineEnd();
    },
    point: function(a, r) {
      this._curve.point(r * Math.sin(a), r * -Math.cos(a));
    }
  };

  function curveRadial(curve) {

    function radial(context) {
      return new Radial(curve(context));
    }

    radial._curve = curve;

    return radial;
  }

  function radialLine(l) {
    var c = l.curve;

    l.angle = l.x, delete l.x;
    l.radius = l.y, delete l.y;

    l.curve = function(_) {
      return arguments.length ? c(curveRadial(_)) : c()._curve;
    };

    return l;
  }

  function radialLine$1() {
    return radialLine(line().curve(curveRadialLinear));
  }

  function radialArea() {
    var a = area$1().curve(curveRadialLinear),
        c = a.curve,
        x0 = a.lineX0,
        x1 = a.lineX1,
        y0 = a.lineY0,
        y1 = a.lineY1;

    a.angle = a.x, delete a.x;
    a.startAngle = a.x0, delete a.x0;
    a.endAngle = a.x1, delete a.x1;
    a.radius = a.y, delete a.y;
    a.innerRadius = a.y0, delete a.y0;
    a.outerRadius = a.y1, delete a.y1;
    a.lineStartAngle = function() { return radialLine(x0()); }, delete a.lineX0;
    a.lineEndAngle = function() { return radialLine(x1()); }, delete a.lineX1;
    a.lineInnerRadius = function() { return radialLine(y0()); }, delete a.lineY0;
    a.lineOuterRadius = function() { return radialLine(y1()); }, delete a.lineY1;

    a.curve = function(_) {
      return arguments.length ? c(curveRadial(_)) : c()._curve;
    };

    return a;
  }

  var circle = {
    draw: function(context, size) {
      var r = Math.sqrt(size / pi$2);
      context.moveTo(r, 0);
      context.arc(0, 0, r, 0, tau$2);
    }
  };

  var cross$1 = {
    draw: function(context, size) {
      var r = Math.sqrt(size / 5) / 2;
      context.moveTo(-3 * r, -r);
      context.lineTo(-r, -r);
      context.lineTo(-r, -3 * r);
      context.lineTo(r, -3 * r);
      context.lineTo(r, -r);
      context.lineTo(3 * r, -r);
      context.lineTo(3 * r, r);
      context.lineTo(r, r);
      context.lineTo(r, 3 * r);
      context.lineTo(-r, 3 * r);
      context.lineTo(-r, r);
      context.lineTo(-3 * r, r);
      context.closePath();
    }
  };

  var tan30 = Math.sqrt(1 / 3);
  var tan30_2 = tan30 * 2;
  var diamond = {
    draw: function(context, size) {
      var y = Math.sqrt(size / tan30_2),
          x = y * tan30;
      context.moveTo(0, -y);
      context.lineTo(x, 0);
      context.lineTo(0, y);
      context.lineTo(-x, 0);
      context.closePath();
    }
  };

  var ka = 0.89081309152928522810;
  var kr = Math.sin(pi$2 / 10) / Math.sin(7 * pi$2 / 10);
  var kx = Math.sin(tau$2 / 10) * kr;
  var ky = -Math.cos(tau$2 / 10) * kr;
  var star = {
    draw: function(context, size) {
      var r = Math.sqrt(size * ka),
          x = kx * r,
          y = ky * r;
      context.moveTo(0, -r);
      context.lineTo(x, y);
      for (var i = 1; i < 5; ++i) {
        var a = tau$2 * i / 5,
            c = Math.cos(a),
            s = Math.sin(a);
        context.lineTo(s * r, -c * r);
        context.lineTo(c * x - s * y, s * x + c * y);
      }
      context.closePath();
    }
  };

  var square = {
    draw: function(context, size) {
      var w = Math.sqrt(size),
          x = -w / 2;
      context.rect(x, x, w, w);
    }
  };

  var sqrt3 = Math.sqrt(3);

  var triangle = {
    draw: function(context, size) {
      var y = -Math.sqrt(size / (sqrt3 * 3));
      context.moveTo(0, y * 2);
      context.lineTo(-sqrt3 * y, -y);
      context.lineTo(sqrt3 * y, -y);
      context.closePath();
    }
  };

  var c = -0.5;
  var s = Math.sqrt(3) / 2;
  var k = 1 / Math.sqrt(12);
  var a = (k / 2 + 1) * 3;
  var wye = {
    draw: function(context, size) {
      var r = Math.sqrt(size / a),
          x0 = r / 2,
          y0 = r * k,
          x1 = x0,
          y1 = r * k + r,
          x2 = -x1,
          y2 = y1;
      context.moveTo(x0, y0);
      context.lineTo(x1, y1);
      context.lineTo(x2, y2);
      context.lineTo(c * x0 - s * y0, s * x0 + c * y0);
      context.lineTo(c * x1 - s * y1, s * x1 + c * y1);
      context.lineTo(c * x2 - s * y2, s * x2 + c * y2);
      context.lineTo(c * x0 + s * y0, c * y0 - s * x0);
      context.lineTo(c * x1 + s * y1, c * y1 - s * x1);
      context.lineTo(c * x2 + s * y2, c * y2 - s * x2);
      context.closePath();
    }
  };

  var symbols = [
    circle,
    cross$1,
    diamond,
    square,
    star,
    triangle,
    wye
  ];

  function symbol() {
    var type = constant$1(circle),
        size = constant$1(64),
        context = null;

    function symbol() {
      var buffer;
      if (!context) context = buffer = path();
      type.apply(this, arguments).draw(context, +size.apply(this, arguments));
      if (buffer) return context = null, buffer + "" || null;
    }

    symbol.type = function(_) {
      return arguments.length ? (type = typeof _ === "function" ? _ : constant$1(_), symbol) : type;
    };

    symbol.size = function(_) {
      return arguments.length ? (size = typeof _ === "function" ? _ : constant$1(+_), symbol) : size;
    };

    symbol.context = function(_) {
      return arguments.length ? (context = _ == null ? null : _, symbol) : context;
    };

    return symbol;
  }

  function noop() {}

  function point(that, x, y) {
    that._context.bezierCurveTo(
      (2 * that._x0 + that._x1) / 3,
      (2 * that._y0 + that._y1) / 3,
      (that._x0 + 2 * that._x1) / 3,
      (that._y0 + 2 * that._y1) / 3,
      (that._x0 + 4 * that._x1 + x) / 6,
      (that._y0 + 4 * that._y1 + y) / 6
    );
  }

  function Basis(context) {
    this._context = context;
  }

  Basis.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x0 = this._x1 =
      this._y0 = this._y1 = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      switch (this._point) {
        case 3: point(this, this._x1, this._y1); // proceed
        case 2: this._context.lineTo(this._x1, this._y1); break;
      }
      if (this._line || (this._line !== 0 && this._point === 1)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; this._line ? this._context.lineTo(x, y) : this._context.moveTo(x, y); break;
        case 1: this._point = 2; break;
        case 2: this._point = 3; this._context.lineTo((5 * this._x0 + this._x1) / 6, (5 * this._y0 + this._y1) / 6); // proceed
        default: point(this, x, y); break;
      }
      this._x0 = this._x1, this._x1 = x;
      this._y0 = this._y1, this._y1 = y;
    }
  };

  function basis(context) {
    return new Basis(context);
  }

  function BasisClosed(context) {
    this._context = context;
  }

  BasisClosed.prototype = {
    areaStart: noop,
    areaEnd: noop,
    lineStart: function() {
      this._x0 = this._x1 = this._x2 = this._x3 = this._x4 =
      this._y0 = this._y1 = this._y2 = this._y3 = this._y4 = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      switch (this._point) {
        case 1: {
          this._context.moveTo(this._x2, this._y2);
          this._context.closePath();
          break;
        }
        case 2: {
          this._context.moveTo((this._x2 + 2 * this._x3) / 3, (this._y2 + 2 * this._y3) / 3);
          this._context.lineTo((this._x3 + 2 * this._x2) / 3, (this._y3 + 2 * this._y2) / 3);
          this._context.closePath();
          break;
        }
        case 3: {
          this.point(this._x2, this._y2);
          this.point(this._x3, this._y3);
          this.point(this._x4, this._y4);
          break;
        }
      }
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; this._x2 = x, this._y2 = y; break;
        case 1: this._point = 2; this._x3 = x, this._y3 = y; break;
        case 2: this._point = 3; this._x4 = x, this._y4 = y; this._context.moveTo((this._x0 + 4 * this._x1 + x) / 6, (this._y0 + 4 * this._y1 + y) / 6); break;
        default: point(this, x, y); break;
      }
      this._x0 = this._x1, this._x1 = x;
      this._y0 = this._y1, this._y1 = y;
    }
  };

  function basisClosed(context) {
    return new BasisClosed(context);
  }

  function BasisOpen(context) {
    this._context = context;
  }

  BasisOpen.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x0 = this._x1 =
      this._y0 = this._y1 = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      if (this._line || (this._line !== 0 && this._point === 3)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; break;
        case 1: this._point = 2; break;
        case 2: this._point = 3; var x0 = (this._x0 + 4 * this._x1 + x) / 6, y0 = (this._y0 + 4 * this._y1 + y) / 6; this._line ? this._context.lineTo(x0, y0) : this._context.moveTo(x0, y0); break;
        case 3: this._point = 4; // proceed
        default: point(this, x, y); break;
      }
      this._x0 = this._x1, this._x1 = x;
      this._y0 = this._y1, this._y1 = y;
    }
  };

  function basisOpen(context) {
    return new BasisOpen(context);
  }

  function Bundle(context, beta) {
    this._basis = new Basis(context);
    this._beta = beta;
  }

  Bundle.prototype = {
    lineStart: function() {
      this._x = [];
      this._y = [];
      this._basis.lineStart();
    },
    lineEnd: function() {
      var x = this._x,
          y = this._y,
          j = x.length - 1;

      if (j > 0) {
        var x0 = x[0],
            y0 = y[0],
            dx = x[j] - x0,
            dy = y[j] - y0,
            i = -1,
            t;

        while (++i <= j) {
          t = i / j;
          this._basis.point(
            this._beta * x[i] + (1 - this._beta) * (x0 + t * dx),
            this._beta * y[i] + (1 - this._beta) * (y0 + t * dy)
          );
        }
      }

      this._x = this._y = null;
      this._basis.lineEnd();
    },
    point: function(x, y) {
      this._x.push(+x);
      this._y.push(+y);
    }
  };

  var bundle = (function custom(beta) {

    function bundle(context) {
      return beta === 1 ? new Basis(context) : new Bundle(context, beta);
    }

    bundle.beta = function(beta) {
      return custom(+beta);
    };

    return bundle;
  })(0.85);

  function point$1(that, x, y) {
    that._context.bezierCurveTo(
      that._x1 + that._k * (that._x2 - that._x0),
      that._y1 + that._k * (that._y2 - that._y0),
      that._x2 + that._k * (that._x1 - x),
      that._y2 + that._k * (that._y1 - y),
      that._x2,
      that._y2
    );
  }

  function Cardinal(context, tension) {
    this._context = context;
    this._k = (1 - tension) / 6;
  }

  Cardinal.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x0 = this._x1 = this._x2 =
      this._y0 = this._y1 = this._y2 = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      switch (this._point) {
        case 2: this._context.lineTo(this._x2, this._y2); break;
        case 3: point$1(this, this._x1, this._y1); break;
      }
      if (this._line || (this._line !== 0 && this._point === 1)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; this._line ? this._context.lineTo(x, y) : this._context.moveTo(x, y); break;
        case 1: this._point = 2; this._x1 = x, this._y1 = y; break;
        case 2: this._point = 3; // proceed
        default: point$1(this, x, y); break;
      }
      this._x0 = this._x1, this._x1 = this._x2, this._x2 = x;
      this._y0 = this._y1, this._y1 = this._y2, this._y2 = y;
    }
  };

  var cardinal = (function custom(tension) {

    function cardinal(context) {
      return new Cardinal(context, tension);
    }

    cardinal.tension = function(tension) {
      return custom(+tension);
    };

    return cardinal;
  })(0);

  function CardinalClosed(context, tension) {
    this._context = context;
    this._k = (1 - tension) / 6;
  }

  CardinalClosed.prototype = {
    areaStart: noop,
    areaEnd: noop,
    lineStart: function() {
      this._x0 = this._x1 = this._x2 = this._x3 = this._x4 = this._x5 =
      this._y0 = this._y1 = this._y2 = this._y3 = this._y4 = this._y5 = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      switch (this._point) {
        case 1: {
          this._context.moveTo(this._x3, this._y3);
          this._context.closePath();
          break;
        }
        case 2: {
          this._context.lineTo(this._x3, this._y3);
          this._context.closePath();
          break;
        }
        case 3: {
          this.point(this._x3, this._y3);
          this.point(this._x4, this._y4);
          this.point(this._x5, this._y5);
          break;
        }
      }
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; this._x3 = x, this._y3 = y; break;
        case 1: this._point = 2; this._context.moveTo(this._x4 = x, this._y4 = y); break;
        case 2: this._point = 3; this._x5 = x, this._y5 = y; break;
        default: point$1(this, x, y); break;
      }
      this._x0 = this._x1, this._x1 = this._x2, this._x2 = x;
      this._y0 = this._y1, this._y1 = this._y2, this._y2 = y;
    }
  };

  var cardinalClosed = (function custom(tension) {

    function cardinal(context) {
      return new CardinalClosed(context, tension);
    }

    cardinal.tension = function(tension) {
      return custom(+tension);
    };

    return cardinal;
  })(0);

  function CardinalOpen(context, tension) {
    this._context = context;
    this._k = (1 - tension) / 6;
  }

  CardinalOpen.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x0 = this._x1 = this._x2 =
      this._y0 = this._y1 = this._y2 = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      if (this._line || (this._line !== 0 && this._point === 3)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; break;
        case 1: this._point = 2; break;
        case 2: this._point = 3; this._line ? this._context.lineTo(this._x2, this._y2) : this._context.moveTo(this._x2, this._y2); break;
        case 3: this._point = 4; // proceed
        default: point$1(this, x, y); break;
      }
      this._x0 = this._x1, this._x1 = this._x2, this._x2 = x;
      this._y0 = this._y1, this._y1 = this._y2, this._y2 = y;
    }
  };

  var cardinalOpen = (function custom(tension) {

    function cardinal(context) {
      return new CardinalOpen(context, tension);
    }

    cardinal.tension = function(tension) {
      return custom(+tension);
    };

    return cardinal;
  })(0);

  function point$2(that, x, y) {
    var x1 = that._x1,
        y1 = that._y1,
        x2 = that._x2,
        y2 = that._y2;

    if (that._l01_a > epsilon$1) {
      var a = 2 * that._l01_2a + 3 * that._l01_a * that._l12_a + that._l12_2a,
          n = 3 * that._l01_a * (that._l01_a + that._l12_a);
      x1 = (x1 * a - that._x0 * that._l12_2a + that._x2 * that._l01_2a) / n;
      y1 = (y1 * a - that._y0 * that._l12_2a + that._y2 * that._l01_2a) / n;
    }

    if (that._l23_a > epsilon$1) {
      var b = 2 * that._l23_2a + 3 * that._l23_a * that._l12_a + that._l12_2a,
          m = 3 * that._l23_a * (that._l23_a + that._l12_a);
      x2 = (x2 * b + that._x1 * that._l23_2a - x * that._l12_2a) / m;
      y2 = (y2 * b + that._y1 * that._l23_2a - y * that._l12_2a) / m;
    }

    that._context.bezierCurveTo(x1, y1, x2, y2, that._x2, that._y2);
  }

  function CatmullRom(context, alpha) {
    this._context = context;
    this._alpha = alpha;
  }

  CatmullRom.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x0 = this._x1 = this._x2 =
      this._y0 = this._y1 = this._y2 = NaN;
      this._l01_a = this._l12_a = this._l23_a =
      this._l01_2a = this._l12_2a = this._l23_2a =
      this._point = 0;
    },
    lineEnd: function() {
      switch (this._point) {
        case 2: this._context.lineTo(this._x2, this._y2); break;
        case 3: this.point(this, this._x2, this._y2); break;
      }
      if (this._line || (this._line !== 0 && this._point === 1)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;

      if (this._point) {
        var x23 = this._x2 - x,
            y23 = this._y2 - y;
        this._l23_a = Math.sqrt(this._l23_2a = Math.pow(x23 * x23 + y23 * y23, this._alpha));
      }

      switch (this._point) {
        case 0: this._point = 1; this._line ? this._context.lineTo(x, y) : this._context.moveTo(x, y); break;
        case 1: this._point = 2; break;
        case 2: this._point = 3; // proceed
        default: point$2(this, x, y); break;
      }

      this._l01_a = this._l12_a, this._l12_a = this._l23_a;
      this._l01_2a = this._l12_2a, this._l12_2a = this._l23_2a;
      this._x0 = this._x1, this._x1 = this._x2, this._x2 = x;
      this._y0 = this._y1, this._y1 = this._y2, this._y2 = y;
    }
  };

  var catmullRom = (function custom(alpha) {

    function catmullRom(context) {
      return alpha ? new CatmullRom(context, alpha) : new Cardinal(context, 0);
    }

    catmullRom.alpha = function(alpha) {
      return custom(+alpha);
    };

    return catmullRom;
  })(0.5);

  function CatmullRomClosed(context, alpha) {
    this._context = context;
    this._alpha = alpha;
  }

  CatmullRomClosed.prototype = {
    areaStart: noop,
    areaEnd: noop,
    lineStart: function() {
      this._x0 = this._x1 = this._x2 = this._x3 = this._x4 = this._x5 =
      this._y0 = this._y1 = this._y2 = this._y3 = this._y4 = this._y5 = NaN;
      this._l01_a = this._l12_a = this._l23_a =
      this._l01_2a = this._l12_2a = this._l23_2a =
      this._point = 0;
    },
    lineEnd: function() {
      switch (this._point) {
        case 1: {
          this._context.moveTo(this._x3, this._y3);
          this._context.closePath();
          break;
        }
        case 2: {
          this._context.lineTo(this._x3, this._y3);
          this._context.closePath();
          break;
        }
        case 3: {
          this.point(this._x3, this._y3);
          this.point(this._x4, this._y4);
          this.point(this._x5, this._y5);
          break;
        }
      }
    },
    point: function(x, y) {
      x = +x, y = +y;

      if (this._point) {
        var x23 = this._x2 - x,
            y23 = this._y2 - y;
        this._l23_a = Math.sqrt(this._l23_2a = Math.pow(x23 * x23 + y23 * y23, this._alpha));
      }

      switch (this._point) {
        case 0: this._point = 1; this._x3 = x, this._y3 = y; break;
        case 1: this._point = 2; this._context.moveTo(this._x4 = x, this._y4 = y); break;
        case 2: this._point = 3; this._x5 = x, this._y5 = y; break;
        default: point$2(this, x, y); break;
      }

      this._l01_a = this._l12_a, this._l12_a = this._l23_a;
      this._l01_2a = this._l12_2a, this._l12_2a = this._l23_2a;
      this._x0 = this._x1, this._x1 = this._x2, this._x2 = x;
      this._y0 = this._y1, this._y1 = this._y2, this._y2 = y;
    }
  };

  var catmullRomClosed = (function custom(alpha) {

    function catmullRom(context) {
      return alpha ? new CatmullRomClosed(context, alpha) : new CardinalClosed(context, 0);
    }

    catmullRom.alpha = function(alpha) {
      return custom(+alpha);
    };

    return catmullRom;
  })(0.5);

  function CatmullRomOpen(context, alpha) {
    this._context = context;
    this._alpha = alpha;
  }

  CatmullRomOpen.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x0 = this._x1 = this._x2 =
      this._y0 = this._y1 = this._y2 = NaN;
      this._l01_a = this._l12_a = this._l23_a =
      this._l01_2a = this._l12_2a = this._l23_2a =
      this._point = 0;
    },
    lineEnd: function() {
      if (this._line || (this._line !== 0 && this._point === 3)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;

      if (this._point) {
        var x23 = this._x2 - x,
            y23 = this._y2 - y;
        this._l23_a = Math.sqrt(this._l23_2a = Math.pow(x23 * x23 + y23 * y23, this._alpha));
      }

      switch (this._point) {
        case 0: this._point = 1; break;
        case 1: this._point = 2; break;
        case 2: this._point = 3; this._line ? this._context.lineTo(this._x2, this._y2) : this._context.moveTo(this._x2, this._y2); break;
        case 3: this._point = 4; // proceed
        default: point$2(this, x, y); break;
      }

      this._l01_a = this._l12_a, this._l12_a = this._l23_a;
      this._l01_2a = this._l12_2a, this._l12_2a = this._l23_2a;
      this._x0 = this._x1, this._x1 = this._x2, this._x2 = x;
      this._y0 = this._y1, this._y1 = this._y2, this._y2 = y;
    }
  };

  var catmullRomOpen = (function custom(alpha) {

    function catmullRom(context) {
      return alpha ? new CatmullRomOpen(context, alpha) : new CardinalOpen(context, 0);
    }

    catmullRom.alpha = function(alpha) {
      return custom(+alpha);
    };

    return catmullRom;
  })(0.5);

  function LinearClosed(context) {
    this._context = context;
  }

  LinearClosed.prototype = {
    areaStart: noop,
    areaEnd: noop,
    lineStart: function() {
      this._point = 0;
    },
    lineEnd: function() {
      if (this._point) this._context.closePath();
    },
    point: function(x, y) {
      x = +x, y = +y;
      if (this._point) this._context.lineTo(x, y);
      else this._point = 1, this._context.moveTo(x, y);
    }
  };

  function linearClosed(context) {
    return new LinearClosed(context);
  }

  function sign(x) {
    return x < 0 ? -1 : 1;
  }

  // Calculate the slopes of the tangents (Hermite-type interpolation) based on
  // the following paper: Steffen, M. 1990. A Simple Method for Monotonic
  // Interpolation in One Dimension. Astronomy and Astrophysics, Vol. 239, NO.
  // NOV(II), P. 443, 1990.
  function slope3(that, x2, y2) {
    var h0 = that._x1 - that._x0,
        h1 = x2 - that._x1,
        s0 = (that._y1 - that._y0) / (h0 || h1 < 0 && -0),
        s1 = (y2 - that._y1) / (h1 || h0 < 0 && -0),
        p = (s0 * h1 + s1 * h0) / (h0 + h1);
    return (sign(s0) + sign(s1)) * Math.min(Math.abs(s0), Math.abs(s1), 0.5 * Math.abs(p)) || 0;
  }

  // Calculate a one-sided slope.
  function slope2(that, t) {
    var h = that._x1 - that._x0;
    return h ? (3 * (that._y1 - that._y0) / h - t) / 2 : t;
  }

  // According to https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Representations
  // "you can express cubic Hermite interpolation in terms of cubic Bézier curves
  // with respect to the four values p0, p0 + m0 / 3, p1 - m1 / 3, p1".
  function point$3(that, t0, t1) {
    var x0 = that._x0,
        y0 = that._y0,
        x1 = that._x1,
        y1 = that._y1,
        dx = (x1 - x0) / 3;
    that._context.bezierCurveTo(x0 + dx, y0 + dx * t0, x1 - dx, y1 - dx * t1, x1, y1);
  }

  function MonotoneX(context) {
    this._context = context;
  }

  MonotoneX.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x0 = this._x1 =
      this._y0 = this._y1 =
      this._t0 = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      switch (this._point) {
        case 2: this._context.lineTo(this._x1, this._y1); break;
        case 3: point$3(this, this._t0, slope2(this, this._t0)); break;
      }
      if (this._line || (this._line !== 0 && this._point === 1)) this._context.closePath();
      this._line = 1 - this._line;
    },
    point: function(x, y) {
      var t1 = NaN;

      x = +x, y = +y;
      if (x === this._x1 && y === this._y1) return; // Ignore coincident points.
      switch (this._point) {
        case 0: this._point = 1; this._line ? this._context.lineTo(x, y) : this._context.moveTo(x, y); break;
        case 1: this._point = 2; break;
        case 2: this._point = 3; point$3(this, slope2(this, t1 = slope3(this, x, y)), t1); break;
        default: point$3(this, this._t0, t1 = slope3(this, x, y)); break;
      }

      this._x0 = this._x1, this._x1 = x;
      this._y0 = this._y1, this._y1 = y;
      this._t0 = t1;
    }
  }

  function MonotoneY(context) {
    this._context = new ReflectContext(context);
  }

  (MonotoneY.prototype = Object.create(MonotoneX.prototype)).point = function(x, y) {
    MonotoneX.prototype.point.call(this, y, x);
  };

  function ReflectContext(context) {
    this._context = context;
  }

  ReflectContext.prototype = {
    moveTo: function(x, y) { this._context.moveTo(y, x); },
    closePath: function() { this._context.closePath(); },
    lineTo: function(x, y) { this._context.lineTo(y, x); },
    bezierCurveTo: function(x1, y1, x2, y2, x, y) { this._context.bezierCurveTo(y1, x1, y2, x2, y, x); }
  };

  function monotoneX(context) {
    return new MonotoneX(context);
  }

  function monotoneY(context) {
    return new MonotoneY(context);
  }

  function Natural(context) {
    this._context = context;
  }

  Natural.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x = [];
      this._y = [];
    },
    lineEnd: function() {
      var x = this._x,
          y = this._y,
          n = x.length;

      if (n) {
        this._line ? this._context.lineTo(x[0], y[0]) : this._context.moveTo(x[0], y[0]);
        if (n === 2) {
          this._context.lineTo(x[1], y[1]);
        } else {
          var px = controlPoints(x),
              py = controlPoints(y);
          for (var i0 = 0, i1 = 1; i1 < n; ++i0, ++i1) {
            this._context.bezierCurveTo(px[0][i0], py[0][i0], px[1][i0], py[1][i0], x[i1], y[i1]);
          }
        }
      }

      if (this._line || (this._line !== 0 && n === 1)) this._context.closePath();
      this._line = 1 - this._line;
      this._x = this._y = null;
    },
    point: function(x, y) {
      this._x.push(+x);
      this._y.push(+y);
    }
  };

  // See https://www.particleincell.com/2012/bezier-splines/ for derivation.
  function controlPoints(x) {
    var i,
        n = x.length - 1,
        m,
        a = new Array(n),
        b = new Array(n),
        r = new Array(n);
    a[0] = 0, b[0] = 2, r[0] = x[0] + 2 * x[1];
    for (i = 1; i < n - 1; ++i) a[i] = 1, b[i] = 4, r[i] = 4 * x[i] + 2 * x[i + 1];
    a[n - 1] = 2, b[n - 1] = 7, r[n - 1] = 8 * x[n - 1] + x[n];
    for (i = 1; i < n; ++i) m = a[i] / b[i - 1], b[i] -= m, r[i] -= m * r[i - 1];
    a[n - 1] = r[n - 1] / b[n - 1];
    for (i = n - 2; i >= 0; --i) a[i] = (r[i] - a[i + 1]) / b[i];
    b[n - 1] = (x[n] + a[n - 1]) / 2;
    for (i = 0; i < n - 1; ++i) b[i] = 2 * x[i + 1] - a[i + 1];
    return [a, b];
  }

  function natural(context) {
    return new Natural(context);
  }

  function Step(context, t) {
    this._context = context;
    this._t = t;
  }

  Step.prototype = {
    areaStart: function() {
      this._line = 0;
    },
    areaEnd: function() {
      this._line = NaN;
    },
    lineStart: function() {
      this._x = this._y = NaN;
      this._point = 0;
    },
    lineEnd: function() {
      if (0 < this._t && this._t < 1 && this._point === 2) this._context.lineTo(this._x, this._y);
      if (this._line || (this._line !== 0 && this._point === 1)) this._context.closePath();
      if (this._line >= 0) this._t = 1 - this._t, this._line = 1 - this._line;
    },
    point: function(x, y) {
      x = +x, y = +y;
      switch (this._point) {
        case 0: this._point = 1; this._line ? this._context.lineTo(x, y) : this._context.moveTo(x, y); break;
        case 1: this._point = 2; // proceed
        default: {
          if (this._t <= 0) {
            this._context.lineTo(this._x, y);
            this._context.lineTo(x, y);
          } else {
            var x1 = this._x * (1 - this._t) + x * this._t;
            this._context.lineTo(x1, this._y);
            this._context.lineTo(x1, y);
          }
          break;
        }
      }
      this._x = x, this._y = y;
    }
  };

  function step(context) {
    return new Step(context, 0.5);
  }

  function stepBefore(context) {
    return new Step(context, 0);
  }

  function stepAfter(context) {
    return new Step(context, 1);
  }

  var slice$2 = Array.prototype.slice;

  function none(series, order) {
    if (!((n = series.length) > 1)) return;
    for (var i = 1, s0, s1 = series[order[0]], n, m = s1.length; i < n; ++i) {
      s0 = s1, s1 = series[order[i]];
      for (var j = 0; j < m; ++j) {
        s1[j][1] += s1[j][0] = isNaN(s0[j][1]) ? s0[j][0] : s0[j][1];
      }
    }
  }

  function none$1(series) {
    var n = series.length, o = new Array(n);
    while (--n >= 0) o[n] = n;
    return o;
  }

  function stackValue(d, key) {
    return d[key];
  }

  function stack() {
    var keys = constant$1([]),
        order = none$1,
        offset = none,
        value = stackValue;

    function stack(data) {
      var kz = keys.apply(this, arguments),
          i,
          m = data.length,
          n = kz.length,
          sz = new Array(n),
          oz;

      for (i = 0; i < n; ++i) {
        for (var ki = kz[i], si = sz[i] = new Array(m), j = 0, sij; j < m; ++j) {
          si[j] = sij = [0, +value(data[j], ki, j, data)];
          sij.data = data[j];
        }
        si.key = ki;
      }

      for (i = 0, oz = order(sz); i < n; ++i) {
        sz[oz[i]].index = i;
      }

      offset(sz, oz);
      return sz;
    }

    stack.keys = function(_) {
      return arguments.length ? (keys = typeof _ === "function" ? _ : constant$1(slice$2.call(_)), stack) : keys;
    };

    stack.value = function(_) {
      return arguments.length ? (value = typeof _ === "function" ? _ : constant$1(+_), stack) : value;
    };

    stack.order = function(_) {
      return arguments.length ? (order = _ == null ? none$1 : typeof _ === "function" ? _ : constant$1(slice$2.call(_)), stack) : order;
    };

    stack.offset = function(_) {
      return arguments.length ? (offset = _ == null ? none : _, stack) : offset;
    };

    return stack;
  }

  function expand(series, order) {
    if (!((n = series.length) > 0)) return;
    for (var i, n, j = 0, m = series[0].length, y; j < m; ++j) {
      for (y = i = 0; i < n; ++i) y += series[i][j][1] || 0;
      if (y) for (i = 0; i < n; ++i) series[i][j][1] /= y;
    }
    none(series, order);
  }

  function silhouette(series, order) {
    if (!((n = series.length) > 0)) return;
    for (var j = 0, s0 = series[order[0]], n, m = s0.length; j < m; ++j) {
      for (var i = 0, y = 0; i < n; ++i) y += series[i][j][1] || 0;
      s0[j][1] += s0[j][0] = -y / 2;
    }
    none(series, order);
  }

  function wiggle(series, order) {
    if (!((n = series.length) > 0) || !((m = (s0 = series[order[0]]).length) > 0)) return;
    for (var y = 0, j = 1, s0, m, n; j < m; ++j) {
      for (var i = 0, s1 = 0, s2 = 0; i < n; ++i) {
        var si = series[order[i]],
            sij0 = si[j][1] || 0,
            sij1 = si[j - 1][1] || 0,
            s3 = (sij0 - sij1) / 2;
        for (var k = 0; k < i; ++k) {
          var sk = series[order[k]],
              skj0 = sk[j][1] || 0,
              skj1 = sk[j - 1][1] || 0;
          s3 += skj0 - skj1;
        }
        s1 += sij0, s2 += s3 * sij0;
      }
      s0[j - 1][1] += s0[j - 1][0] = y;
      if (s1) y -= s2 / s1;
    }
    s0[j - 1][1] += s0[j - 1][0] = y;
    none(series, order);
  }

  function ascending$1(series) {
    var sums = series.map(sum$1);
    return none$1(series).sort(function(a, b) { return sums[a] - sums[b]; });
  }

  function sum$1(series) {
    var s = 0, i = -1, n = series.length, v;
    while (++i < n) if (v = +series[i][1]) s += v;
    return s;
  }

  function descending$2(series) {
    return ascending$1(series).reverse();
  }

  function insideOut(series) {
    var n = series.length,
        i,
        j,
        sums = series.map(sum$1),
        order = none$1(series).sort(function(a, b) { return sums[b] - sums[a]; }),
        top = 0,
        bottom = 0,
        tops = [],
        bottoms = [];

    for (i = 0; i < n; ++i) {
      j = order[i];
      if (top < bottom) {
        top += sums[j];
        tops.push(j);
      } else {
        bottom += sums[j];
        bottoms.push(j);
      }
    }

    return bottoms.reverse().concat(tops);
  }

  function reverse(series) {
    return none$1(series).reverse();
  }

  function define(constructor, factory, prototype) {
    constructor.prototype = factory.prototype = prototype;
    prototype.constructor = constructor;
  }

  function extend(parent, definition) {
    var prototype = Object.create(parent.prototype);
    for (var key in definition) prototype[key] = definition[key];
    return prototype;
  }

  function Color() {}

  var darker = 0.7;
  var brighter = 1 / darker;

  var reHex3 = /^#([0-9a-f]{3})$/;
  var reHex6 = /^#([0-9a-f]{6})$/;
  var reRgbInteger = /^rgb\(\s*([-+]?\d+)\s*,\s*([-+]?\d+)\s*,\s*([-+]?\d+)\s*\)$/;
  var reRgbPercent = /^rgb\(\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*\)$/;
  var reRgbaInteger = /^rgba\(\s*([-+]?\d+)\s*,\s*([-+]?\d+)\s*,\s*([-+]?\d+)\s*,\s*([-+]?\d+(?:\.\d+)?)\s*\)$/;
  var reRgbaPercent = /^rgba\(\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)\s*\)$/;
  var reHslPercent = /^hsl\(\s*([-+]?\d+(?:\.\d+)?)\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*\)$/;
  var reHslaPercent = /^hsla\(\s*([-+]?\d+(?:\.\d+)?)\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)%\s*,\s*([-+]?\d+(?:\.\d+)?)\s*\)$/;
  var named = {
    aliceblue: 0xf0f8ff,
    antiquewhite: 0xfaebd7,
    aqua: 0x00ffff,
    aquamarine: 0x7fffd4,
    azure: 0xf0ffff,
    beige: 0xf5f5dc,
    bisque: 0xffe4c4,
    black: 0x000000,
    blanchedalmond: 0xffebcd,
    blue: 0x0000ff,
    blueviolet: 0x8a2be2,
    brown: 0xa52a2a,
    burlywood: 0xdeb887,
    cadetblue: 0x5f9ea0,
    chartreuse: 0x7fff00,
    chocolate: 0xd2691e,
    coral: 0xff7f50,
    cornflowerblue: 0x6495ed,
    cornsilk: 0xfff8dc,
    crimson: 0xdc143c,
    cyan: 0x00ffff,
    darkblue: 0x00008b,
    darkcyan: 0x008b8b,
    darkgoldenrod: 0xb8860b,
    darkgray: 0xa9a9a9,
    darkgreen: 0x006400,
    darkgrey: 0xa9a9a9,
    darkkhaki: 0xbdb76b,
    darkmagenta: 0x8b008b,
    darkolivegreen: 0x556b2f,
    darkorange: 0xff8c00,
    darkorchid: 0x9932cc,
    darkred: 0x8b0000,
    darksalmon: 0xe9967a,
    darkseagreen: 0x8fbc8f,
    darkslateblue: 0x483d8b,
    darkslategray: 0x2f4f4f,
    darkslategrey: 0x2f4f4f,
    darkturquoise: 0x00ced1,
    darkviolet: 0x9400d3,
    deeppink: 0xff1493,
    deepskyblue: 0x00bfff,
    dimgray: 0x696969,
    dimgrey: 0x696969,
    dodgerblue: 0x1e90ff,
    firebrick: 0xb22222,
    floralwhite: 0xfffaf0,
    forestgreen: 0x228b22,
    fuchsia: 0xff00ff,
    gainsboro: 0xdcdcdc,
    ghostwhite: 0xf8f8ff,
    gold: 0xffd700,
    goldenrod: 0xdaa520,
    gray: 0x808080,
    green: 0x008000,
    greenyellow: 0xadff2f,
    grey: 0x808080,
    honeydew: 0xf0fff0,
    hotpink: 0xff69b4,
    indianred: 0xcd5c5c,
    indigo: 0x4b0082,
    ivory: 0xfffff0,
    khaki: 0xf0e68c,
    lavender: 0xe6e6fa,
    lavenderblush: 0xfff0f5,
    lawngreen: 0x7cfc00,
    lemonchiffon: 0xfffacd,
    lightblue: 0xadd8e6,
    lightcoral: 0xf08080,
    lightcyan: 0xe0ffff,
    lightgoldenrodyellow: 0xfafad2,
    lightgray: 0xd3d3d3,
    lightgreen: 0x90ee90,
    lightgrey: 0xd3d3d3,
    lightpink: 0xffb6c1,
    lightsalmon: 0xffa07a,
    lightseagreen: 0x20b2aa,
    lightskyblue: 0x87cefa,
    lightslategray: 0x778899,
    lightslategrey: 0x778899,
    lightsteelblue: 0xb0c4de,
    lightyellow: 0xffffe0,
    lime: 0x00ff00,
    limegreen: 0x32cd32,
    linen: 0xfaf0e6,
    magenta: 0xff00ff,
    maroon: 0x800000,
    mediumaquamarine: 0x66cdaa,
    mediumblue: 0x0000cd,
    mediumorchid: 0xba55d3,
    mediumpurple: 0x9370db,
    mediumseagreen: 0x3cb371,
    mediumslateblue: 0x7b68ee,
    mediumspringgreen: 0x00fa9a,
    mediumturquoise: 0x48d1cc,
    mediumvioletred: 0xc71585,
    midnightblue: 0x191970,
    mintcream: 0xf5fffa,
    mistyrose: 0xffe4e1,
    moccasin: 0xffe4b5,
    navajowhite: 0xffdead,
    navy: 0x000080,
    oldlace: 0xfdf5e6,
    olive: 0x808000,
    olivedrab: 0x6b8e23,
    orange: 0xffa500,
    orangered: 0xff4500,
    orchid: 0xda70d6,
    palegoldenrod: 0xeee8aa,
    palegreen: 0x98fb98,
    paleturquoise: 0xafeeee,
    palevioletred: 0xdb7093,
    papayawhip: 0xffefd5,
    peachpuff: 0xffdab9,
    peru: 0xcd853f,
    pink: 0xffc0cb,
    plum: 0xdda0dd,
    powderblue: 0xb0e0e6,
    purple: 0x800080,
    rebeccapurple: 0x663399,
    red: 0xff0000,
    rosybrown: 0xbc8f8f,
    royalblue: 0x4169e1,
    saddlebrown: 0x8b4513,
    salmon: 0xfa8072,
    sandybrown: 0xf4a460,
    seagreen: 0x2e8b57,
    seashell: 0xfff5ee,
    sienna: 0xa0522d,
    silver: 0xc0c0c0,
    skyblue: 0x87ceeb,
    slateblue: 0x6a5acd,
    slategray: 0x708090,
    slategrey: 0x708090,
    snow: 0xfffafa,
    springgreen: 0x00ff7f,
    steelblue: 0x4682b4,
    tan: 0xd2b48c,
    teal: 0x008080,
    thistle: 0xd8bfd8,
    tomato: 0xff6347,
    turquoise: 0x40e0d0,
    violet: 0xee82ee,
    wheat: 0xf5deb3,
    white: 0xffffff,
    whitesmoke: 0xf5f5f5,
    yellow: 0xffff00,
    yellowgreen: 0x9acd32
  };

  define(Color, color, {
    displayable: function() {
      return this.rgb().displayable();
    },
    toString: function() {
      return this.rgb() + "";
    }
  });

  function color(format) {
    var m;
    format = (format + "").trim().toLowerCase();
    return (m = reHex3.exec(format)) ? (m = parseInt(m[1], 16), new Rgb((m >> 8 & 0xf) | (m >> 4 & 0x0f0), (m >> 4 & 0xf) | (m & 0xf0), ((m & 0xf) << 4) | (m & 0xf), 1)) // #f00
        : (m = reHex6.exec(format)) ? rgbn(parseInt(m[1], 16)) // #ff0000
        : (m = reRgbInteger.exec(format)) ? new Rgb(m[1], m[2], m[3], 1) // rgb(255, 0, 0)
        : (m = reRgbPercent.exec(format)) ? new Rgb(m[1] * 255 / 100, m[2] * 255 / 100, m[3] * 255 / 100, 1) // rgb(100%, 0%, 0%)
        : (m = reRgbaInteger.exec(format)) ? rgba(m[1], m[2], m[3], m[4]) // rgba(255, 0, 0, 1)
        : (m = reRgbaPercent.exec(format)) ? rgba(m[1] * 255 / 100, m[2] * 255 / 100, m[3] * 255 / 100, m[4]) // rgb(100%, 0%, 0%, 1)
        : (m = reHslPercent.exec(format)) ? hsla(m[1], m[2] / 100, m[3] / 100, 1) // hsl(120, 50%, 50%)
        : (m = reHslaPercent.exec(format)) ? hsla(m[1], m[2] / 100, m[3] / 100, m[4]) // hsla(120, 50%, 50%, 1)
        : named.hasOwnProperty(format) ? rgbn(named[format])
        : format === "transparent" ? new Rgb(NaN, NaN, NaN, 0)
        : null;
  }

  function rgbn(n) {
    return new Rgb(n >> 16 & 0xff, n >> 8 & 0xff, n & 0xff, 1);
  }

  function rgba(r, g, b, a) {
    if (a <= 0) r = g = b = NaN;
    return new Rgb(r, g, b, a);
  }

  function rgbConvert(o) {
    if (!(o instanceof Color)) o = color(o);
    if (!o) return new Rgb;
    o = o.rgb();
    return new Rgb(o.r, o.g, o.b, o.opacity);
  }

  function colorRgb(r, g, b, opacity) {
    return arguments.length === 1 ? rgbConvert(r) : new Rgb(r, g, b, opacity == null ? 1 : opacity);
  }

  function Rgb(r, g, b, opacity) {
    this.r = +r;
    this.g = +g;
    this.b = +b;
    this.opacity = +opacity;
  }

  define(Rgb, colorRgb, extend(Color, {
    brighter: function(k) {
      k = k == null ? brighter : Math.pow(brighter, k);
      return new Rgb(this.r * k, this.g * k, this.b * k, this.opacity);
    },
    darker: function(k) {
      k = k == null ? darker : Math.pow(darker, k);
      return new Rgb(this.r * k, this.g * k, this.b * k, this.opacity);
    },
    rgb: function() {
      return this;
    },
    displayable: function() {
      return (0 <= this.r && this.r <= 255)
          && (0 <= this.g && this.g <= 255)
          && (0 <= this.b && this.b <= 255)
          && (0 <= this.opacity && this.opacity <= 1);
    },
    toString: function() {
      var a = this.opacity; a = isNaN(a) ? 1 : Math.max(0, Math.min(1, a));
      return (a === 1 ? "rgb(" : "rgba(")
          + Math.max(0, Math.min(255, Math.round(this.r) || 0)) + ", "
          + Math.max(0, Math.min(255, Math.round(this.g) || 0)) + ", "
          + Math.max(0, Math.min(255, Math.round(this.b) || 0))
          + (a === 1 ? ")" : ", " + a + ")");
    }
  }));

  function hsla(h, s, l, a) {
    if (a <= 0) h = s = l = NaN;
    else if (l <= 0 || l >= 1) h = s = NaN;
    else if (s <= 0) h = NaN;
    return new Hsl(h, s, l, a);
  }

  function hslConvert(o) {
    if (o instanceof Hsl) return new Hsl(o.h, o.s, o.l, o.opacity);
    if (!(o instanceof Color)) o = color(o);
    if (!o) return new Hsl;
    if (o instanceof Hsl) return o;
    o = o.rgb();
    var r = o.r / 255,
        g = o.g / 255,
        b = o.b / 255,
        min = Math.min(r, g, b),
        max = Math.max(r, g, b),
        h = NaN,
        s = max - min,
        l = (max + min) / 2;
    if (s) {
      if (r === max) h = (g - b) / s + (g < b) * 6;
      else if (g === max) h = (b - r) / s + 2;
      else h = (r - g) / s + 4;
      s /= l < 0.5 ? max + min : 2 - max - min;
      h *= 60;
    } else {
      s = l > 0 && l < 1 ? 0 : h;
    }
    return new Hsl(h, s, l, o.opacity);
  }

  function colorHsl(h, s, l, opacity) {
    return arguments.length === 1 ? hslConvert(h) : new Hsl(h, s, l, opacity == null ? 1 : opacity);
  }

  function Hsl(h, s, l, opacity) {
    this.h = +h;
    this.s = +s;
    this.l = +l;
    this.opacity = +opacity;
  }

  define(Hsl, colorHsl, extend(Color, {
    brighter: function(k) {
      k = k == null ? brighter : Math.pow(brighter, k);
      return new Hsl(this.h, this.s, this.l * k, this.opacity);
    },
    darker: function(k) {
      k = k == null ? darker : Math.pow(darker, k);
      return new Hsl(this.h, this.s, this.l * k, this.opacity);
    },
    rgb: function() {
      var h = this.h % 360 + (this.h < 0) * 360,
          s = isNaN(h) || isNaN(this.s) ? 0 : this.s,
          l = this.l,
          m2 = l + (l < 0.5 ? l : 1 - l) * s,
          m1 = 2 * l - m2;
      return new Rgb(
        hsl2rgb(h >= 240 ? h - 240 : h + 120, m1, m2),
        hsl2rgb(h, m1, m2),
        hsl2rgb(h < 120 ? h + 240 : h - 120, m1, m2),
        this.opacity
      );
    },
    displayable: function() {
      return (0 <= this.s && this.s <= 1 || isNaN(this.s))
          && (0 <= this.l && this.l <= 1)
          && (0 <= this.opacity && this.opacity <= 1);
    }
  }));

  /* From FvD 13.37, CSS Color Module Level 3 */
  function hsl2rgb(h, m1, m2) {
    return (h < 60 ? m1 + (m2 - m1) * h / 60
        : h < 180 ? m2
        : h < 240 ? m1 + (m2 - m1) * (240 - h) / 60
        : m1) * 255;
  }

  var deg2rad = Math.PI / 180;
  var rad2deg = 180 / Math.PI;

  var Kn = 18;
  var Xn = 0.950470;
  var Yn = 1;
  var Zn = 1.088830;
  var t0 = 4 / 29;
  var t1 = 6 / 29;
  var t2 = 3 * t1 * t1;
  var t3 = t1 * t1 * t1;
  function labConvert(o) {
    if (o instanceof Lab) return new Lab(o.l, o.a, o.b, o.opacity);
    if (o instanceof Hcl) {
      var h = o.h * deg2rad;
      return new Lab(o.l, Math.cos(h) * o.c, Math.sin(h) * o.c, o.opacity);
    }
    if (!(o instanceof Rgb)) o = rgbConvert(o);
    var b = rgb2xyz(o.r),
        a = rgb2xyz(o.g),
        l = rgb2xyz(o.b),
        x = xyz2lab((0.4124564 * b + 0.3575761 * a + 0.1804375 * l) / Xn),
        y = xyz2lab((0.2126729 * b + 0.7151522 * a + 0.0721750 * l) / Yn),
        z = xyz2lab((0.0193339 * b + 0.1191920 * a + 0.9503041 * l) / Zn);
    return new Lab(116 * y - 16, 500 * (x - y), 200 * (y - z), o.opacity);
  }

  function lab(l, a, b, opacity) {
    return arguments.length === 1 ? labConvert(l) : new Lab(l, a, b, opacity == null ? 1 : opacity);
  }

  function Lab(l, a, b, opacity) {
    this.l = +l;
    this.a = +a;
    this.b = +b;
    this.opacity = +opacity;
  }

  define(Lab, lab, extend(Color, {
    brighter: function(k) {
      return new Lab(this.l + Kn * (k == null ? 1 : k), this.a, this.b, this.opacity);
    },
    darker: function(k) {
      return new Lab(this.l - Kn * (k == null ? 1 : k), this.a, this.b, this.opacity);
    },
    rgb: function() {
      var y = (this.l + 16) / 116,
          x = isNaN(this.a) ? y : y + this.a / 500,
          z = isNaN(this.b) ? y : y - this.b / 200;
      y = Yn * lab2xyz(y);
      x = Xn * lab2xyz(x);
      z = Zn * lab2xyz(z);
      return new Rgb(
        xyz2rgb( 3.2404542 * x - 1.5371385 * y - 0.4985314 * z), // D65 -> sRGB
        xyz2rgb(-0.9692660 * x + 1.8760108 * y + 0.0415560 * z),
        xyz2rgb( 0.0556434 * x - 0.2040259 * y + 1.0572252 * z),
        this.opacity
      );
    }
  }));

  function xyz2lab(t) {
    return t > t3 ? Math.pow(t, 1 / 3) : t / t2 + t0;
  }

  function lab2xyz(t) {
    return t > t1 ? t * t * t : t2 * (t - t0);
  }

  function xyz2rgb(x) {
    return 255 * (x <= 0.0031308 ? 12.92 * x : 1.055 * Math.pow(x, 1 / 2.4) - 0.055);
  }

  function rgb2xyz(x) {
    return (x /= 255) <= 0.04045 ? x / 12.92 : Math.pow((x + 0.055) / 1.055, 2.4);
  }

  function hclConvert(o) {
    if (o instanceof Hcl) return new Hcl(o.h, o.c, o.l, o.opacity);
    if (!(o instanceof Lab)) o = labConvert(o);
    var h = Math.atan2(o.b, o.a) * rad2deg;
    return new Hcl(h < 0 ? h + 360 : h, Math.sqrt(o.a * o.a + o.b * o.b), o.l, o.opacity);
  }

  function colorHcl(h, c, l, opacity) {
    return arguments.length === 1 ? hclConvert(h) : new Hcl(h, c, l, opacity == null ? 1 : opacity);
  }

  function Hcl(h, c, l, opacity) {
    this.h = +h;
    this.c = +c;
    this.l = +l;
    this.opacity = +opacity;
  }

  define(Hcl, colorHcl, extend(Color, {
    brighter: function(k) {
      return new Hcl(this.h, this.c, this.l + Kn * (k == null ? 1 : k), this.opacity);
    },
    darker: function(k) {
      return new Hcl(this.h, this.c, this.l - Kn * (k == null ? 1 : k), this.opacity);
    },
    rgb: function() {
      return labConvert(this).rgb();
    }
  }));

  var A = -0.14861;
  var B = +1.78277;
  var C = -0.29227;
  var D = -0.90649;
  var E = +1.97294;
  var ED = E * D;
  var EB = E * B;
  var BC_DA = B * C - D * A;
  function cubehelixConvert(o) {
    if (o instanceof Cubehelix) return new Cubehelix(o.h, o.s, o.l, o.opacity);
    if (!(o instanceof Rgb)) o = rgbConvert(o);
    var r = o.r / 255,
        g = o.g / 255,
        b = o.b / 255,
        l = (BC_DA * b + ED * r - EB * g) / (BC_DA + ED - EB),
        bl = b - l,
        k = (E * (g - l) - C * bl) / D,
        s = Math.sqrt(k * k + bl * bl) / (E * l * (1 - l)), // NaN if l=0 or l=1
        h = s ? Math.atan2(k, bl) * rad2deg - 120 : NaN;
    return new Cubehelix(h < 0 ? h + 360 : h, s, l, o.opacity);
  }

  function cubehelix(h, s, l, opacity) {
    return arguments.length === 1 ? cubehelixConvert(h) : new Cubehelix(h, s, l, opacity == null ? 1 : opacity);
  }

  function Cubehelix(h, s, l, opacity) {
    this.h = +h;
    this.s = +s;
    this.l = +l;
    this.opacity = +opacity;
  }

  define(Cubehelix, cubehelix, extend(Color, {
    brighter: function(k) {
      k = k == null ? brighter : Math.pow(brighter, k);
      return new Cubehelix(this.h, this.s, this.l * k, this.opacity);
    },
    darker: function(k) {
      k = k == null ? darker : Math.pow(darker, k);
      return new Cubehelix(this.h, this.s, this.l * k, this.opacity);
    },
    rgb: function() {
      var h = isNaN(this.h) ? 0 : (this.h + 120) * deg2rad,
          l = +this.l,
          a = isNaN(this.s) ? 0 : this.s * l * (1 - l),
          cosh = Math.cos(h),
          sinh = Math.sin(h);
      return new Rgb(
        255 * (l + a * (A * cosh + B * sinh)),
        255 * (l + a * (C * cosh + D * sinh)),
        255 * (l + a * (E * cosh)),
        this.opacity
      );
    }
  }));

  function basis$1(t1, v0, v1, v2, v3) {
    var t2 = t1 * t1, t3 = t2 * t1;
    return ((1 - 3 * t1 + 3 * t2 - t3) * v0
        + (4 - 6 * t2 + 3 * t3) * v1
        + (1 + 3 * t1 + 3 * t2 - 3 * t3) * v2
        + t3 * v3) / 6;
  }

  function basis$2(values) {
    var n = values.length - 1;
    return function(t) {
      var i = t <= 0 ? (t = 0) : t >= 1 ? (t = 1, n - 1) : Math.floor(t * n),
          v1 = values[i],
          v2 = values[i + 1],
          v0 = i > 0 ? values[i - 1] : 2 * v1 - v2,
          v3 = i < n - 1 ? values[i + 2] : 2 * v2 - v1;
      return basis$1((t - i / n) * n, v0, v1, v2, v3);
    };
  }

  function basisClosed$1(values) {
    var n = values.length;
    return function(t) {
      var i = Math.floor(((t %= 1) < 0 ? ++t : t) * n),
          v0 = values[(i + n - 1) % n],
          v1 = values[i % n],
          v2 = values[(i + 1) % n],
          v3 = values[(i + 2) % n];
      return basis$1((t - i / n) * n, v0, v1, v2, v3);
    };
  }

  function constant$2(x) {
    return function() {
      return x;
    };
  }

  function linear$1(a, d) {
    return function(t) {
      return a + t * d;
    };
  }

  function exponential$1(a, b, y) {
    return a = Math.pow(a, y), b = Math.pow(b, y) - a, y = 1 / y, function(t) {
      return Math.pow(a + t * b, y);
    };
  }

  function hue(a, b) {
    var d = b - a;
    return d ? linear$1(a, d > 180 || d < -180 ? d - 360 * Math.round(d / 360) : d) : constant$2(isNaN(a) ? b : a);
  }

  function gamma(y) {
    return (y = +y) === 1 ? nogamma : function(a, b) {
      return b - a ? exponential$1(a, b, y) : constant$2(isNaN(a) ? b : a);
    };
  }

  function nogamma(a, b) {
    var d = b - a;
    return d ? linear$1(a, d) : constant$2(isNaN(a) ? b : a);
  }

  var interpolateRgb = (function rgbGamma(y) {
    var color = gamma(y);

    function rgb(start, end) {
      var r = color((start = colorRgb(start)).r, (end = colorRgb(end)).r),
          g = color(start.g, end.g),
          b = color(start.b, end.b),
          opacity = color(start.opacity, end.opacity);
      return function(t) {
        start.r = r(t);
        start.g = g(t);
        start.b = b(t);
        start.opacity = opacity(t);
        return start + "";
      };
    }

    rgb.gamma = rgbGamma;

    return rgb;
  })(1);

  function rgbSpline(spline) {
    return function(colors) {
      var n = colors.length,
          r = new Array(n),
          g = new Array(n),
          b = new Array(n),
          i, color;
      for (i = 0; i < n; ++i) {
        color = colorRgb(colors[i]);
        r[i] = color.r || 0;
        g[i] = color.g || 0;
        b[i] = color.b || 0;
      }
      r = spline(r);
      g = spline(g);
      b = spline(b);
      color.opacity = 1;
      return function(t) {
        color.r = r(t);
        color.g = g(t);
        color.b = b(t);
        return color + "";
      };
    };
  }

  var rgbBasis = rgbSpline(basis$2);
  var rgbBasisClosed = rgbSpline(basisClosed$1);

  function array$1(a, b) {
    var nb = b ? b.length : 0,
        na = a ? Math.min(nb, a.length) : 0,
        x = new Array(nb),
        c = new Array(nb),
        i;

    for (i = 0; i < na; ++i) x[i] = interpolate(a[i], b[i]);
    for (; i < nb; ++i) c[i] = b[i];

    return function(t) {
      for (i = 0; i < na; ++i) c[i] = x[i](t);
      return c;
    };
  }

  function interpolateNumber(a, b) {
    return a = +a, b -= a, function(t) {
      return a + b * t;
    };
  }

  function object(a, b) {
    var i = {},
        c = {},
        k;

    if (a === null || typeof a !== "object") a = {};
    if (b === null || typeof b !== "object") b = {};

    for (k in b) {
      if (k in a) {
        i[k] = interpolate(a[k], b[k]);
      } else {
        c[k] = b[k];
      }
    }

    return function(t) {
      for (k in i) c[k] = i[k](t);
      return c;
    };
  }

  var reA = /[-+]?(?:\d+\.?\d*|\.?\d+)(?:[eE][-+]?\d+)?/g;
  var reB = new RegExp(reA.source, "g");
  function zero(b) {
    return function() {
      return b;
    };
  }

  function one(b) {
    return function(t) {
      return b(t) + "";
    };
  }

  function interpolateString(a, b) {
    var bi = reA.lastIndex = reB.lastIndex = 0, // scan index for next number in b
        am, // current match in a
        bm, // current match in b
        bs, // string preceding current number in b, if any
        i = -1, // index in s
        s = [], // string constants and placeholders
        q = []; // number interpolators

    // Coerce inputs to strings.
    a = a + "", b = b + "";

    // Interpolate pairs of numbers in a & b.
    while ((am = reA.exec(a))
        && (bm = reB.exec(b))) {
      if ((bs = bm.index) > bi) { // a string precedes the next number in b
        bs = b.slice(bi, bs);
        if (s[i]) s[i] += bs; // coalesce with previous string
        else s[++i] = bs;
      }
      if ((am = am[0]) === (bm = bm[0])) { // numbers in a & b match
        if (s[i]) s[i] += bm; // coalesce with previous string
        else s[++i] = bm;
      } else { // interpolate non-matching numbers
        s[++i] = null;
        q.push({i: i, x: interpolateNumber(am, bm)});
      }
      bi = reB.lastIndex;
    }

    // Add remains of b.
    if (bi < b.length) {
      bs = b.slice(bi);
      if (s[i]) s[i] += bs; // coalesce with previous string
      else s[++i] = bs;
    }

    // Special optimization for only a single match.
    // Otherwise, interpolate each of the numbers and rejoin the string.
    return s.length < 2 ? (q[0]
        ? one(q[0].x)
        : zero(b))
        : (b = q.length, function(t) {
            for (var i = 0, o; i < b; ++i) s[(o = q[i]).i] = o.x(t);
            return s.join("");
          });
  }

  function interpolate(a, b) {
    var t = typeof b, c;
    return b == null || t === "boolean" ? constant$2(b)
        : (t === "number" ? interpolateNumber
        : t === "string" ? ((c = color(b)) ? (b = c, interpolateRgb) : interpolateString)
        : b instanceof color ? interpolateRgb
        : Array.isArray(b) ? array$1
        : object)(a, b);
  }

  function interpolateRound(a, b) {
    return a = +a, b -= a, function(t) {
      return Math.round(a + b * t);
    };
  }

  var degrees = 180 / Math.PI;

  var identity$2 = {
    translateX: 0,
    translateY: 0,
    rotate: 0,
    skewX: 0,
    scaleX: 1,
    scaleY: 1
  };

  function decompose(a, b, c, d, e, f) {
    var scaleX, scaleY, skewX;
    if (scaleX = Math.sqrt(a * a + b * b)) a /= scaleX, b /= scaleX;
    if (skewX = a * c + b * d) c -= a * skewX, d -= b * skewX;
    if (scaleY = Math.sqrt(c * c + d * d)) c /= scaleY, d /= scaleY, skewX /= scaleY;
    if (a * d < b * c) a = -a, b = -b, skewX = -skewX, scaleX = -scaleX;
    return {
      translateX: e,
      translateY: f,
      rotate: Math.atan2(b, a) * degrees,
      skewX: Math.atan(skewX) * degrees,
      scaleX: scaleX,
      scaleY: scaleY
    };
  }

  var cssNode;
  var cssRoot;
  var cssView;
  var svgNode;
  function parseCss(value) {
    if (value === "none") return identity$2;
    if (!cssNode) cssNode = document.createElement("DIV"), cssRoot = document.documentElement, cssView = document.defaultView;
    cssNode.style.transform = value;
    value = cssView.getComputedStyle(cssRoot.appendChild(cssNode), null).getPropertyValue("transform");
    cssRoot.removeChild(cssNode);
    var m = value.slice(7, -1).split(",");
    return decompose(+m[0], +m[1], +m[2], +m[3], +m[4], +m[5]);
  }

  function parseSvg(value) {
    if (!svgNode) svgNode = document.createElementNS("http://www.w3.org/2000/svg", "g");
    svgNode.setAttribute("transform", value == null ? "" : value);
    var m = svgNode.transform.baseVal.consolidate().matrix;
    return decompose(m.a, m.b, m.c, m.d, m.e, m.f);
  }

  function interpolateTransform(parse, pxComma, pxParen, degParen) {

    function pop(s) {
      return s.length ? s.pop() + " " : "";
    }

    function translate(xa, ya, xb, yb, s, q) {
      if (xa !== xb || ya !== yb) {
        var i = s.push("translate(", null, pxComma, null, pxParen);
        q.push({i: i - 4, x: interpolateNumber(xa, xb)}, {i: i - 2, x: interpolateNumber(ya, yb)});
      } else if (xb || yb) {
        s.push("translate(" + xb + pxComma + yb + pxParen);
      }
    }

    function rotate(a, b, s, q) {
      if (a !== b) {
        if (a - b > 180) b += 360; else if (b - a > 180) a += 360; // shortest path
        q.push({i: s.push(pop(s) + "rotate(", null, degParen) - 2, x: interpolateNumber(a, b)});
      } else if (b) {
        s.push(pop(s) + "rotate(" + b + degParen);
      }
    }

    function skewX(a, b, s, q) {
      if (a !== b) {
        q.push({i: s.push(pop(s) + "skewX(", null, degParen) - 2, x: interpolateNumber(a, b)});
      } else if (b) {
        s.push(pop(s) + "skewX(" + b + degParen);
      }
    }

    function scale(xa, ya, xb, yb, s, q) {
      if (xa !== xb || ya !== yb) {
        var i = s.push(pop(s) + "scale(", null, ",", null, ")");
        q.push({i: i - 4, x: interpolateNumber(xa, xb)}, {i: i - 2, x: interpolateNumber(ya, yb)});
      } else if (xb !== 1 || yb !== 1) {
        s.push(pop(s) + "scale(" + xb + "," + yb + ")");
      }
    }

    return function(a, b) {
      var s = [], // string constants and placeholders
          q = []; // number interpolators
      a = parse(a), b = parse(b);
      translate(a.translateX, a.translateY, b.translateX, b.translateY, s, q);
      rotate(a.rotate, b.rotate, s, q);
      skewX(a.skewX, b.skewX, s, q);
      scale(a.scaleX, a.scaleY, b.scaleX, b.scaleY, s, q);
      a = b = null; // gc
      return function(t) {
        var i = -1, n = q.length, o;
        while (++i < n) s[(o = q[i]).i] = o.x(t);
        return s.join("");
      };
    };
  }

  var interpolateTransform$1 = interpolateTransform(parseCss, "px, ", "px)", "deg)");
  var interpolateTransform$2 = interpolateTransform(parseSvg, ", ", ")", ")");

  var rho = Math.SQRT2;
  var rho2 = 2;
  var rho4 = 4;
  var epsilon2 = 1e-12;
  function cosh(x) {
    return ((x = Math.exp(x)) + 1 / x) / 2;
  }

  function sinh(x) {
    return ((x = Math.exp(x)) - 1 / x) / 2;
  }

  function tanh(x) {
    return ((x = Math.exp(2 * x)) - 1) / (x + 1);
  }

  // p0 = [ux0, uy0, w0]
  // p1 = [ux1, uy1, w1]
  function interpolateZoom(p0, p1) {
    var ux0 = p0[0], uy0 = p0[1], w0 = p0[2],
        ux1 = p1[0], uy1 = p1[1], w1 = p1[2],
        dx = ux1 - ux0,
        dy = uy1 - uy0,
        d2 = dx * dx + dy * dy,
        i,
        S;

    // Special case for u0 ≅ u1.
    if (d2 < epsilon2) {
      S = Math.log(w1 / w0) / rho;
      i = function(t) {
        return [
          ux0 + t * dx,
          uy0 + t * dy,
          w0 * Math.exp(rho * t * S)
        ];
      }
    }

    // General case.
    else {
      var d1 = Math.sqrt(d2),
          b0 = (w1 * w1 - w0 * w0 + rho4 * d2) / (2 * w0 * rho2 * d1),
          b1 = (w1 * w1 - w0 * w0 - rho4 * d2) / (2 * w1 * rho2 * d1),
          r0 = Math.log(Math.sqrt(b0 * b0 + 1) - b0),
          r1 = Math.log(Math.sqrt(b1 * b1 + 1) - b1);
      S = (r1 - r0) / rho;
      i = function(t) {
        var s = t * S,
            coshr0 = cosh(r0),
            u = w0 / (rho2 * d1) * (coshr0 * tanh(rho * s + r0) - sinh(r0));
        return [
          ux0 + u * dx,
          uy0 + u * dy,
          w0 * coshr0 / cosh(rho * s + r0)
        ];
      }
    }

    i.duration = S * 1000;

    return i;
  }

  function hsl(hue) {
    return function(start, end) {
      var h = hue((start = colorHsl(start)).h, (end = colorHsl(end)).h),
          s = nogamma(start.s, end.s),
          l = nogamma(start.l, end.l),
          opacity = nogamma(start.opacity, end.opacity);
      return function(t) {
        start.h = h(t);
        start.s = s(t);
        start.l = l(t);
        start.opacity = opacity(t);
        return start + "";
      };
    }
  }

  var hsl$1 = hsl(hue);
  var hslLong = hsl(nogamma);

  function lab$1(start, end) {
    var l = nogamma((start = lab(start)).l, (end = lab(end)).l),
        a = nogamma(start.a, end.a),
        b = nogamma(start.b, end.b),
        opacity = nogamma(start.opacity, end.opacity);
    return function(t) {
      start.l = l(t);
      start.a = a(t);
      start.b = b(t);
      start.opacity = opacity(t);
      return start + "";
    };
  }

  function hcl(hue) {
    return function(start, end) {
      var h = hue((start = colorHcl(start)).h, (end = colorHcl(end)).h),
          c = nogamma(start.c, end.c),
          l = nogamma(start.l, end.l),
          opacity = nogamma(start.opacity, end.opacity);
      return function(t) {
        start.h = h(t);
        start.c = c(t);
        start.l = l(t);
        start.opacity = opacity(t);
        return start + "";
      };
    }
  }

  var hcl$1 = hcl(hue);
  var hclLong = hcl(nogamma);

  function cubehelix$1(hue) {
    return (function cubehelixGamma(y) {
      y = +y;

      function cubehelix$$(start, end) {
        var h = hue((start = cubehelix(start)).h, (end = cubehelix(end)).h),
            s = nogamma(start.s, end.s),
            l = nogamma(start.l, end.l),
            opacity = nogamma(start.opacity, end.opacity);
        return function(t) {
          start.h = h(t);
          start.s = s(t);
          start.l = l(Math.pow(t, y));
          start.opacity = opacity(t);
          return start + "";
        };
      }

      cubehelix$$.gamma = cubehelixGamma;

      return cubehelix$$;
    })(1);
  }

  var cubehelix$2 = cubehelix$1(hue);
  var interpolateCubehelixLong = cubehelix$1(nogamma);

  function quantize(interpolate, n) {
    var samples = new Array(n);
    for (var i = 0; i < n; ++i) samples[i] = interpolate(i / (n - 1));
    return samples;
  }

  var noop$1 = {value: function() {}};

  function dispatch() {
    for (var i = 0, n = arguments.length, _ = {}, t; i < n; ++i) {
      if (!(t = arguments[i] + "") || (t in _)) throw new Error("illegal type: " + t);
      _[t] = [];
    }
    return new Dispatch(_);
  }

  function Dispatch(_) {
    this._ = _;
  }

  function parseTypenames(typenames, types) {
    return typenames.trim().split(/^|\s+/).map(function(t) {
      var name = "", i = t.indexOf(".");
      if (i >= 0) name = t.slice(i + 1), t = t.slice(0, i);
      if (t && !types.hasOwnProperty(t)) throw new Error("unknown type: " + t);
      return {type: t, name: name};
    });
  }

  Dispatch.prototype = dispatch.prototype = {
    constructor: Dispatch,
    on: function(typename, callback) {
      var _ = this._,
          T = parseTypenames(typename + "", _),
          t,
          i = -1,
          n = T.length;

      // If no callback was specified, return the callback of the given type and name.
      if (arguments.length < 2) {
        while (++i < n) if ((t = (typename = T[i]).type) && (t = get(_[t], typename.name))) return t;
        return;
      }

      // If a type was specified, set the callback for the given type and name.
      // Otherwise, if a null callback was specified, remove callbacks of the given name.
      if (callback != null && typeof callback !== "function") throw new Error("invalid callback: " + callback);
      while (++i < n) {
        if (t = (typename = T[i]).type) _[t] = set$1(_[t], typename.name, callback);
        else if (callback == null) for (t in _) _[t] = set$1(_[t], typename.name, null);
      }

      return this;
    },
    copy: function() {
      var copy = {}, _ = this._;
      for (var t in _) copy[t] = _[t].slice();
      return new Dispatch(copy);
    },
    call: function(type, that) {
      if ((n = arguments.length - 2) > 0) for (var args = new Array(n), i = 0, n, t; i < n; ++i) args[i] = arguments[i + 2];
      if (!this._.hasOwnProperty(type)) throw new Error("unknown type: " + type);
      for (t = this._[type], i = 0, n = t.length; i < n; ++i) t[i].value.apply(that, args);
    },
    apply: function(type, that, args) {
      if (!this._.hasOwnProperty(type)) throw new Error("unknown type: " + type);
      for (var t = this._[type], i = 0, n = t.length; i < n; ++i) t[i].value.apply(that, args);
    }
  };

  function get(type, name) {
    for (var i = 0, n = type.length, c; i < n; ++i) {
      if ((c = type[i]).name === name) {
        return c.value;
      }
    }
  }

  function set$1(type, name, callback) {
    for (var i = 0, n = type.length; i < n; ++i) {
      if (type[i].name === name) {
        type[i] = noop$1, type = type.slice(0, i).concat(type.slice(i + 1));
        break;
      }
    }
    if (callback != null) type.push({name: name, value: callback});
    return type;
  }

  function objectConverter(columns) {
    return new Function("d", "return {" + columns.map(function(name, i) {
      return JSON.stringify(name) + ": d[" + i + "]";
    }).join(",") + "}");
  }

  function customConverter(columns, f) {
    var object = objectConverter(columns);
    return function(row, i) {
      return f(object(row), i, columns);
    };
  }

  // Compute unique columns in order of discovery.
  function inferColumns(rows) {
    var columnSet = Object.create(null),
        columns = [];

    rows.forEach(function(row) {
      for (var column in row) {
        if (!(column in columnSet)) {
          columns.push(columnSet[column] = column);
        }
      }
    });

    return columns;
  }

  function dsv(delimiter) {
    var reFormat = new RegExp("[\"" + delimiter + "\n]"),
        delimiterCode = delimiter.charCodeAt(0);

    function parse(text, f) {
      var convert, columns, rows = parseRows(text, function(row, i) {
        if (convert) return convert(row, i - 1);
        columns = row, convert = f ? customConverter(row, f) : objectConverter(row);
      });
      rows.columns = columns;
      return rows;
    }

    function parseRows(text, f) {
      var EOL = {}, // sentinel value for end-of-line
          EOF = {}, // sentinel value for end-of-file
          rows = [], // output rows
          N = text.length,
          I = 0, // current character index
          n = 0, // the current line number
          t, // the current token
          eol; // is the current token followed by EOL?

      function token() {
        if (I >= N) return EOF; // special case: end of file
        if (eol) return eol = false, EOL; // special case: end of line

        // special case: quotes
        var j = I, c;
        if (text.charCodeAt(j) === 34) {
          var i = j;
          while (i++ < N) {
            if (text.charCodeAt(i) === 34) {
              if (text.charCodeAt(i + 1) !== 34) break;
              ++i;
            }
          }
          I = i + 2;
          c = text.charCodeAt(i + 1);
          if (c === 13) {
            eol = true;
            if (text.charCodeAt(i + 2) === 10) ++I;
          } else if (c === 10) {
            eol = true;
          }
          return text.slice(j + 1, i).replace(/""/g, "\"");
        }

        // common case: find next delimiter or newline
        while (I < N) {
          var k = 1;
          c = text.charCodeAt(I++);
          if (c === 10) eol = true; // \n
          else if (c === 13) { eol = true; if (text.charCodeAt(I) === 10) ++I, ++k; } // \r|\r\n
          else if (c !== delimiterCode) continue;
          return text.slice(j, I - k);
        }

        // special case: last token before EOF
        return text.slice(j);
      }

      while ((t = token()) !== EOF) {
        var a = [];
        while (t !== EOL && t !== EOF) {
          a.push(t);
          t = token();
        }
        if (f && (a = f(a, n++)) == null) continue;
        rows.push(a);
      }

      return rows;
    }

    function format(rows, columns) {
      if (columns == null) columns = inferColumns(rows);
      return [columns.map(formatValue).join(delimiter)].concat(rows.map(function(row) {
        return columns.map(function(column) {
          return formatValue(row[column]);
        }).join(delimiter);
      })).join("\n");
    }

    function formatRows(rows) {
      return rows.map(formatRow).join("\n");
    }

    function formatRow(row) {
      return row.map(formatValue).join(delimiter);
    }

    function formatValue(text) {
      return text == null ? ""
          : reFormat.test(text += "") ? "\"" + text.replace(/\"/g, "\"\"") + "\""
          : text;
    }

    return {
      parse: parse,
      parseRows: parseRows,
      format: format,
      formatRows: formatRows
    };
  }

  var csv = dsv(",");

  var csvParse = csv.parse;
  var csvParseRows = csv.parseRows;
  var csvFormat = csv.format;
  var csvFormatRows = csv.formatRows;

  var tsv = dsv("\t");

  var tsvParse = tsv.parse;
  var tsvParseRows = tsv.parseRows;
  var tsvFormat = tsv.format;
  var tsvFormatRows = tsv.formatRows;

  function request(url, callback) {
    var request,
        event = dispatch("beforesend", "progress", "load", "error"),
        mimeType,
        headers = map$1(),
        xhr = new XMLHttpRequest,
        user = null,
        password = null,
        response,
        responseType,
        timeout = 0;

    // If IE does not support CORS, use XDomainRequest.
    if (typeof XDomainRequest !== "undefined"
        && !("withCredentials" in xhr)
        && /^(http(s)?:)?\/\//.test(url)) xhr = new XDomainRequest;

    "onload" in xhr
        ? xhr.onload = xhr.onerror = xhr.ontimeout = respond
        : xhr.onreadystatechange = function(o) { xhr.readyState > 3 && respond(o); };

    function respond(o) {
      var status = xhr.status, result;
      if (!status && hasResponse(xhr)
          || status >= 200 && status < 300
          || status === 304) {
        if (response) {
          try {
            result = response.call(request, xhr);
          } catch (e) {
            event.call("error", request, e);
            return;
          }
        } else {
          result = xhr;
        }
        event.call("load", request, result);
      } else {
        event.call("error", request, o);
      }
    }

    xhr.onprogress = function(e) {
      event.call("progress", request, e);
    };

    request = {
      header: function(name, value) {
        name = (name + "").toLowerCase();
        if (arguments.length < 2) return headers.get(name);
        if (value == null) headers.remove(name);
        else headers.set(name, value + "");
        return request;
      },

      // If mimeType is non-null and no Accept header is set, a default is used.
      mimeType: function(value) {
        if (!arguments.length) return mimeType;
        mimeType = value == null ? null : value + "";
        return request;
      },

      // Specifies what type the response value should take;
      // for instance, arraybuffer, blob, document, or text.
      responseType: function(value) {
        if (!arguments.length) return responseType;
        responseType = value;
        return request;
      },

      timeout: function(value) {
        if (!arguments.length) return timeout;
        timeout = +value;
        return request;
      },

      user: function(value) {
        return arguments.length < 1 ? user : (user = value == null ? null : value + "", request);
      },

      password: function(value) {
        return arguments.length < 1 ? password : (password = value == null ? null : value + "", request);
      },

      // Specify how to convert the response content to a specific type;
      // changes the callback value on "load" events.
      response: function(value) {
        response = value;
        return request;
      },

      // Alias for send("GET", …).
      get: function(data, callback) {
        return request.send("GET", data, callback);
      },

      // Alias for send("POST", …).
      post: function(data, callback) {
        return request.send("POST", data, callback);
      },

      // If callback is non-null, it will be used for error and load events.
      send: function(method, data, callback) {
        if (!callback && typeof data === "function") callback = data, data = null;
        if (callback && callback.length === 1) callback = fixCallback(callback);
        xhr.open(method, url, true, user, password);
        if (mimeType != null && !headers.has("accept")) headers.set("accept", mimeType + ",*/*");
        if (xhr.setRequestHeader) headers.each(function(value, name) { xhr.setRequestHeader(name, value); });
        if (mimeType != null && xhr.overrideMimeType) xhr.overrideMimeType(mimeType);
        if (responseType != null) xhr.responseType = responseType;
        if (timeout > 0) xhr.timeout = timeout;
        if (callback) request.on("error", callback).on("load", function(xhr) { callback(null, xhr); });
        event.call("beforesend", request, xhr);
        xhr.send(data == null ? null : data);
        return request;
      },

      abort: function() {
        xhr.abort();
        return request;
      },

      on: function() {
        var value = event.on.apply(event, arguments);
        return value === event ? request : value;
      }
    };

    return callback
        ? request.get(callback)
        : request;
  }

  function fixCallback(callback) {
    return function(error, xhr) {
      callback(error == null ? xhr : null);
    };
  }

  function hasResponse(xhr) {
    var type = xhr.responseType;
    return type && type !== "text"
        ? xhr.response // null on error
        : xhr.responseText; // "" on error
  }

  function type(defaultMimeType, response) {
    return function(url, callback) {
      var r = request(url).mimeType(defaultMimeType).response(response);
      return callback ? r.get(callback) : r;
    };
  }

  var html = type("text/html", function(xhr) {
    return document.createRange().createContextualFragment(xhr.responseText);
  });

  var json = type("application/json", function(xhr) {
    return JSON.parse(xhr.responseText);
  });

  var text = type("text/plain", function(xhr) {
    return xhr.responseText;
  });

  var xml = type("application/xml", function(xhr) {
    var xml = xhr.responseXML;
    if (!xml) throw new Error("parse error");
    return xml;
  });

  function dsv$1(defaultMimeType, parse) {
    return function(url, row, callback) {
      if (arguments.length < 3) callback = row, row = null;
      var r = request(url).mimeType(defaultMimeType);
      r.row = function(_) { return arguments.length ? r.response(responseOf(parse, row = _)) : row; };
      r.row(row);
      return callback ? r.get(callback) : r;
    };
  }

  function responseOf(parse, row) {
    return function(request) {
      return parse(request.responseText, row);
    };
  }

  var csv$1 = dsv$1("text/csv", csvParse);

  var tsv$1 = dsv$1("text/tab-separated-values", tsvParse);

  var frame = 0;
  var timeout = 0;
  var interval = 0;
  var pokeDelay = 1000;
  var taskHead;
  var taskTail;
  var clockLast = 0;
  var clockNow = 0;
  var clockSkew = 0;
  var clock = typeof performance === "object" ? performance : Date;
  var setFrame = typeof requestAnimationFrame === "function"
          ? (clock === Date ? function(f) { requestAnimationFrame(function() { f(clock.now()); }); } : requestAnimationFrame)
          : function(f) { setTimeout(f, 17); };
  function now() {
    return clockNow || (setFrame(clearNow), clockNow = clock.now() + clockSkew);
  }

  function clearNow() {
    clockNow = 0;
  }

  function Timer() {
    this._call =
    this._time =
    this._next = null;
  }

  Timer.prototype = timer.prototype = {
    constructor: Timer,
    restart: function(callback, delay, time) {
      if (typeof callback !== "function") throw new TypeError("callback is not a function");
      time = (time == null ? now() : +time) + (delay == null ? 0 : +delay);
      if (!this._next && taskTail !== this) {
        if (taskTail) taskTail._next = this;
        else taskHead = this;
        taskTail = this;
      }
      this._call = callback;
      this._time = time;
      sleep();
    },
    stop: function() {
      if (this._call) {
        this._call = null;
        this._time = Infinity;
        sleep();
      }
    }
  };

  function timer(callback, delay, time) {
    var t = new Timer;
    t.restart(callback, delay, time);
    return t;
  }

  function timerFlush() {
    now(); // Get the current time, if not already set.
    ++frame; // Pretend we’ve set an alarm, if we haven’t already.
    var t = taskHead, e;
    while (t) {
      if ((e = clockNow - t._time) >= 0) t._call.call(null, e);
      t = t._next;
    }
    --frame;
  }

  function wake(time) {
    clockNow = (clockLast = time || clock.now()) + clockSkew;
    frame = timeout = 0;
    try {
      timerFlush();
    } finally {
      frame = 0;
      nap();
      clockNow = 0;
    }
  }

  function poke$1() {
    var now = clock.now(), delay = now - clockLast;
    if (delay > pokeDelay) clockSkew -= delay, clockLast = now;
  }

  function nap() {
    var t0, t1 = taskHead, t2, time = Infinity;
    while (t1) {
      if (t1._call) {
        if (time > t1._time) time = t1._time;
        t0 = t1, t1 = t1._next;
      } else {
        t2 = t1._next, t1._next = null;
        t1 = t0 ? t0._next = t2 : taskHead = t2;
      }
    }
    taskTail = t0;
    sleep(time);
  }

  function sleep(time) {
    if (frame) return; // Soonest alarm already set, or will be.
    if (timeout) timeout = clearTimeout(timeout);
    var delay = time - clockNow;
    if (delay > 24) {
      if (time < Infinity) timeout = setTimeout(wake, delay);
      if (interval) interval = clearInterval(interval);
    } else {
      if (!interval) interval = setInterval(poke$1, pokeDelay);
      frame = 1, setFrame(wake);
    }
  }

  function timeout$1(callback, delay, time) {
    var t = new Timer;
    delay = delay == null ? 0 : +delay;
    t.restart(function(elapsed) {
      t.stop();
      callback(elapsed + delay);
    }, delay, time);
    return t;
  }

  function interval$1(callback, delay, time) {
    var t = new Timer, total = delay;
    if (delay == null) return t.restart(callback, delay, time), t;
    delay = +delay, time = time == null ? now() : +time;
    t.restart(function tick(elapsed) {
      elapsed += total;
      t.restart(tick, total += delay, time);
      callback(elapsed);
    }, delay, time);
    return t;
  }

var   t0$1 = new Date;
var   t1$1 = new Date;
  function newInterval(floori, offseti, count, field) {

    function interval(date) {
      return floori(date = new Date(+date)), date;
    }

    interval.floor = interval;

    interval.ceil = function(date) {
      return floori(date = new Date(date - 1)), offseti(date, 1), floori(date), date;
    };

    interval.round = function(date) {
      var d0 = interval(date),
          d1 = interval.ceil(date);
      return date - d0 < d1 - date ? d0 : d1;
    };

    interval.offset = function(date, step) {
      return offseti(date = new Date(+date), step == null ? 1 : Math.floor(step)), date;
    };

    interval.range = function(start, stop, step) {
      var range = [];
      start = interval.ceil(start);
      step = step == null ? 1 : Math.floor(step);
      if (!(start < stop) || !(step > 0)) return range; // also handles Invalid Date
      do range.push(new Date(+start)); while (offseti(start, step), floori(start), start < stop)
      return range;
    };

    interval.filter = function(test) {
      return newInterval(function(date) {
        while (floori(date), !test(date)) date.setTime(date - 1);
      }, function(date, step) {
        while (--step >= 0) while (offseti(date, 1), !test(date));
      });
    };

    if (count) {
      interval.count = function(start, end) {
        t0$1.setTime(+start), t1$1.setTime(+end);
        floori(t0$1), floori(t1$1);
        return Math.floor(count(t0$1, t1$1));
      };

      interval.every = function(step) {
        step = Math.floor(step);
        return !isFinite(step) || !(step > 0) ? null
            : !(step > 1) ? interval
            : interval.filter(field
                ? function(d) { return field(d) % step === 0; }
                : function(d) { return interval.count(0, d) % step === 0; });
      };
    }

    return interval;
  }

  var millisecond = newInterval(function() {
    // noop
  }, function(date, step) {
    date.setTime(+date + step);
  }, function(start, end) {
    return end - start;
  });

  // An optimized implementation for this simple case.
  millisecond.every = function(k) {
    k = Math.floor(k);
    if (!isFinite(k) || !(k > 0)) return null;
    if (!(k > 1)) return millisecond;
    return newInterval(function(date) {
      date.setTime(Math.floor(date / k) * k);
    }, function(date, step) {
      date.setTime(+date + step * k);
    }, function(start, end) {
      return (end - start) / k;
    });
  };

  var milliseconds = millisecond.range;

  var durationSecond = 1e3;
  var durationMinute = 6e4;
  var durationHour = 36e5;
  var durationDay = 864e5;
  var durationWeek = 6048e5;

  var second = newInterval(function(date) {
    date.setTime(Math.floor(date / durationSecond) * durationSecond);
  }, function(date, step) {
    date.setTime(+date + step * durationSecond);
  }, function(start, end) {
    return (end - start) / durationSecond;
  }, function(date) {
    return date.getUTCSeconds();
  });

  var seconds = second.range;

  var minute = newInterval(function(date) {
    date.setTime(Math.floor(date / durationMinute) * durationMinute);
  }, function(date, step) {
    date.setTime(+date + step * durationMinute);
  }, function(start, end) {
    return (end - start) / durationMinute;
  }, function(date) {
    return date.getMinutes();
  });

  var minutes = minute.range;

  var hour = newInterval(function(date) {
    var offset = date.getTimezoneOffset() * durationMinute % durationHour;
    if (offset < 0) offset += durationHour;
    date.setTime(Math.floor((+date - offset) / durationHour) * durationHour + offset);
  }, function(date, step) {
    date.setTime(+date + step * durationHour);
  }, function(start, end) {
    return (end - start) / durationHour;
  }, function(date) {
    return date.getHours();
  });

  var hours = hour.range;

  var day = newInterval(function(date) {
    date.setHours(0, 0, 0, 0);
  }, function(date, step) {
    date.setDate(date.getDate() + step);
  }, function(start, end) {
    return (end - start - (end.getTimezoneOffset() - start.getTimezoneOffset()) * durationMinute) / durationDay;
  }, function(date) {
    return date.getDate() - 1;
  });

  var days = day.range;

  function weekday(i) {
    return newInterval(function(date) {
      date.setDate(date.getDate() - (date.getDay() + 7 - i) % 7);
      date.setHours(0, 0, 0, 0);
    }, function(date, step) {
      date.setDate(date.getDate() + step * 7);
    }, function(start, end) {
      return (end - start - (end.getTimezoneOffset() - start.getTimezoneOffset()) * durationMinute) / durationWeek;
    });
  }

  var timeWeek = weekday(0);
  var timeMonday = weekday(1);
  var tuesday = weekday(2);
  var wednesday = weekday(3);
  var thursday = weekday(4);
  var friday = weekday(5);
  var saturday = weekday(6);

  var sundays = timeWeek.range;
  var mondays = timeMonday.range;
  var tuesdays = tuesday.range;
  var wednesdays = wednesday.range;
  var thursdays = thursday.range;
  var fridays = friday.range;
  var saturdays = saturday.range;

  var month = newInterval(function(date) {
    date.setDate(1);
    date.setHours(0, 0, 0, 0);
  }, function(date, step) {
    date.setMonth(date.getMonth() + step);
  }, function(start, end) {
    return end.getMonth() - start.getMonth() + (end.getFullYear() - start.getFullYear()) * 12;
  }, function(date) {
    return date.getMonth();
  });

  var months = month.range;

  var year = newInterval(function(date) {
    date.setMonth(0, 1);
    date.setHours(0, 0, 0, 0);
  }, function(date, step) {
    date.setFullYear(date.getFullYear() + step);
  }, function(start, end) {
    return end.getFullYear() - start.getFullYear();
  }, function(date) {
    return date.getFullYear();
  });

  // An optimized implementation for this simple case.
  year.every = function(k) {
    return !isFinite(k = Math.floor(k)) || !(k > 0) ? null : newInterval(function(date) {
      date.setFullYear(Math.floor(date.getFullYear() / k) * k);
      date.setMonth(0, 1);
      date.setHours(0, 0, 0, 0);
    }, function(date, step) {
      date.setFullYear(date.getFullYear() + step * k);
    });
  };

  var years = year.range;

  var utcMinute = newInterval(function(date) {
    date.setUTCSeconds(0, 0);
  }, function(date, step) {
    date.setTime(+date + step * durationMinute);
  }, function(start, end) {
    return (end - start) / durationMinute;
  }, function(date) {
    return date.getUTCMinutes();
  });

  var utcMinutes = utcMinute.range;

  var utcHour = newInterval(function(date) {
    date.setUTCMinutes(0, 0, 0);
  }, function(date, step) {
    date.setTime(+date + step * durationHour);
  }, function(start, end) {
    return (end - start) / durationHour;
  }, function(date) {
    return date.getUTCHours();
  });

  var utcHours = utcHour.range;

  var utcDay = newInterval(function(date) {
    date.setUTCHours(0, 0, 0, 0);
  }, function(date, step) {
    date.setUTCDate(date.getUTCDate() + step);
  }, function(start, end) {
    return (end - start) / durationDay;
  }, function(date) {
    return date.getUTCDate() - 1;
  });

  var utcDays = utcDay.range;

  function utcWeekday(i) {
    return newInterval(function(date) {
      date.setUTCDate(date.getUTCDate() - (date.getUTCDay() + 7 - i) % 7);
      date.setUTCHours(0, 0, 0, 0);
    }, function(date, step) {
      date.setUTCDate(date.getUTCDate() + step * 7);
    }, function(start, end) {
      return (end - start) / durationWeek;
    });
  }

  var utcWeek = utcWeekday(0);
  var utcMonday = utcWeekday(1);
  var utcTuesday = utcWeekday(2);
  var utcWednesday = utcWeekday(3);
  var utcThursday = utcWeekday(4);
  var utcFriday = utcWeekday(5);
  var utcSaturday = utcWeekday(6);

  var utcSundays = utcWeek.range;
  var utcMondays = utcMonday.range;
  var utcTuesdays = utcTuesday.range;
  var utcWednesdays = utcWednesday.range;
  var utcThursdays = utcThursday.range;
  var utcFridays = utcFriday.range;
  var utcSaturdays = utcSaturday.range;

  var utcMonth = newInterval(function(date) {
    date.setUTCDate(1);
    date.setUTCHours(0, 0, 0, 0);
  }, function(date, step) {
    date.setUTCMonth(date.getUTCMonth() + step);
  }, function(start, end) {
    return end.getUTCMonth() - start.getUTCMonth() + (end.getUTCFullYear() - start.getUTCFullYear()) * 12;
  }, function(date) {
    return date.getUTCMonth();
  });

  var utcMonths = utcMonth.range;

  var utcYear = newInterval(function(date) {
    date.setUTCMonth(0, 1);
    date.setUTCHours(0, 0, 0, 0);
  }, function(date, step) {
    date.setUTCFullYear(date.getUTCFullYear() + step);
  }, function(start, end) {
    return end.getUTCFullYear() - start.getUTCFullYear();
  }, function(date) {
    return date.getUTCFullYear();
  });

  // An optimized implementation for this simple case.
  utcYear.every = function(k) {
    return !isFinite(k = Math.floor(k)) || !(k > 0) ? null : newInterval(function(date) {
      date.setUTCFullYear(Math.floor(date.getUTCFullYear() / k) * k);
      date.setUTCMonth(0, 1);
      date.setUTCHours(0, 0, 0, 0);
    }, function(date, step) {
      date.setUTCFullYear(date.getUTCFullYear() + step * k);
    });
  };

  var utcYears = utcYear.range;

  // Computes the decimal coefficient and exponent of the specified number x with
  // significant digits p, where x is positive and p is in [1, 21] or undefined.
  // For example, formatDecimal(1.23) returns ["123", 0].
  function formatDecimal(x, p) {
    if ((i = (x = p ? x.toExponential(p - 1) : x.toExponential()).indexOf("e")) < 0) return null; // NaN, ±Infinity
    var i, coefficient = x.slice(0, i);

    // The string returned by toExponential either has the form \d\.\d+e[-+]\d+
    // (e.g., 1.2e+3) or the form \de[-+]\d+ (e.g., 1e+3).
    return [
      coefficient.length > 1 ? coefficient[0] + coefficient.slice(2) : coefficient,
      +x.slice(i + 1)
    ];
  }

  function exponent$1(x) {
    return x = formatDecimal(Math.abs(x)), x ? x[1] : NaN;
  }

  function formatGroup(grouping, thousands) {
    return function(value, width) {
      var i = value.length,
          t = [],
          j = 0,
          g = grouping[0],
          length = 0;

      while (i > 0 && g > 0) {
        if (length + g + 1 > width) g = Math.max(1, width - length);
        t.push(value.substring(i -= g, i + g));
        if ((length += g + 1) > width) break;
        g = grouping[j = (j + 1) % grouping.length];
      }

      return t.reverse().join(thousands);
    };
  }

  function formatDefault(x, p) {
    x = x.toPrecision(p);

    out: for (var n = x.length, i = 1, i0 = -1, i1; i < n; ++i) {
      switch (x[i]) {
        case ".": i0 = i1 = i; break;
        case "0": if (i0 === 0) i0 = i; i1 = i; break;
        case "e": break out;
        default: if (i0 > 0) i0 = 0; break;
      }
    }

    return i0 > 0 ? x.slice(0, i0) + x.slice(i1 + 1) : x;
  }

  var prefixExponent;

  function formatPrefixAuto(x, p) {
    var d = formatDecimal(x, p);
    if (!d) return x + "";
    var coefficient = d[0],
        exponent = d[1],
        i = exponent - (prefixExponent = Math.max(-8, Math.min(8, Math.floor(exponent / 3))) * 3) + 1,
        n = coefficient.length;
    return i === n ? coefficient
        : i > n ? coefficient + new Array(i - n + 1).join("0")
        : i > 0 ? coefficient.slice(0, i) + "." + coefficient.slice(i)
        : "0." + new Array(1 - i).join("0") + formatDecimal(x, Math.max(0, p + i - 1))[0]; // less than 1y!
  }

  function formatRounded(x, p) {
    var d = formatDecimal(x, p);
    if (!d) return x + "";
    var coefficient = d[0],
        exponent = d[1];
    return exponent < 0 ? "0." + new Array(-exponent).join("0") + coefficient
        : coefficient.length > exponent + 1 ? coefficient.slice(0, exponent + 1) + "." + coefficient.slice(exponent + 1)
        : coefficient + new Array(exponent - coefficient.length + 2).join("0");
  }

  var formatTypes = {
    "": formatDefault,
    "%": function(x, p) { return (x * 100).toFixed(p); },
    "b": function(x) { return Math.round(x).toString(2); },
    "c": function(x) { return x + ""; },
    "d": function(x) { return Math.round(x).toString(10); },
    "e": function(x, p) { return x.toExponential(p); },
    "f": function(x, p) { return x.toFixed(p); },
    "g": function(x, p) { return x.toPrecision(p); },
    "o": function(x) { return Math.round(x).toString(8); },
    "p": function(x, p) { return formatRounded(x * 100, p); },
    "r": formatRounded,
    "s": formatPrefixAuto,
    "X": function(x) { return Math.round(x).toString(16).toUpperCase(); },
    "x": function(x) { return Math.round(x).toString(16); }
  };

  // [[fill]align][sign][symbol][0][width][,][.precision][type]
  var re = /^(?:(.)?([<>=^]))?([+\-\( ])?([$#])?(0)?(\d+)?(,)?(\.\d+)?([a-z%])?$/i;

  function formatSpecifier(specifier) {
    return new FormatSpecifier(specifier);
  }

  function FormatSpecifier(specifier) {
    if (!(match = re.exec(specifier))) throw new Error("invalid format: " + specifier);

    var match,
        fill = match[1] || " ",
        align = match[2] || ">",
        sign = match[3] || "-",
        symbol = match[4] || "",
        zero = !!match[5],
        width = match[6] && +match[6],
        comma = !!match[7],
        precision = match[8] && +match[8].slice(1),
        type = match[9] || "";

    // The "n" type is an alias for ",g".
    if (type === "n") comma = true, type = "g";

    // Map invalid types to the default format.
    else if (!formatTypes[type]) type = "";

    // If zero fill is specified, padding goes after sign and before digits.
    if (zero || (fill === "0" && align === "=")) zero = true, fill = "0", align = "=";

    this.fill = fill;
    this.align = align;
    this.sign = sign;
    this.symbol = symbol;
    this.zero = zero;
    this.width = width;
    this.comma = comma;
    this.precision = precision;
    this.type = type;
  }

  FormatSpecifier.prototype.toString = function() {
    return this.fill
        + this.align
        + this.sign
        + this.symbol
        + (this.zero ? "0" : "")
        + (this.width == null ? "" : Math.max(1, this.width | 0))
        + (this.comma ? "," : "")
        + (this.precision == null ? "" : "." + Math.max(0, this.precision | 0))
        + this.type;
  };

  var prefixes = ["y","z","a","f","p","n","\xB5","m","","k","M","G","T","P","E","Z","Y"];

  function identity$3(x) {
    return x;
  }

  function formatLocale(locale) {
    var group = locale.grouping && locale.thousands ? formatGroup(locale.grouping, locale.thousands) : identity$3,
        currency = locale.currency,
        decimal = locale.decimal;

    function newFormat(specifier) {
      specifier = formatSpecifier(specifier);

      var fill = specifier.fill,
          align = specifier.align,
          sign = specifier.sign,
          symbol = specifier.symbol,
          zero = specifier.zero,
          width = specifier.width,
          comma = specifier.comma,
          precision = specifier.precision,
          type = specifier.type;

      // Compute the prefix and suffix.
      // For SI-prefix, the suffix is lazily computed.
      var prefix = symbol === "$" ? currency[0] : symbol === "#" && /[boxX]/.test(type) ? "0" + type.toLowerCase() : "",
          suffix = symbol === "$" ? currency[1] : /[%p]/.test(type) ? "%" : "";

      // What format function should we use?
      // Is this an integer type?
      // Can this type generate exponential notation?
      var formatType = formatTypes[type],
          maybeSuffix = !type || /[defgprs%]/.test(type);

      // Set the default precision if not specified,
      // or clamp the specified precision to the supported range.
      // For significant precision, it must be in [1, 21].
      // For fixed precision, it must be in [0, 20].
      precision = precision == null ? (type ? 6 : 12)
          : /[gprs]/.test(type) ? Math.max(1, Math.min(21, precision))
          : Math.max(0, Math.min(20, precision));

      function format(value) {
        var valuePrefix = prefix,
            valueSuffix = suffix,
            i, n, c;

        if (type === "c") {
          valueSuffix = formatType(value) + valueSuffix;
          value = "";
        } else {
          value = +value;

          // Convert negative to positive, and compute the prefix.
          // Note that -0 is not less than 0, but 1 / -0 is!
          var valueNegative = (value < 0 || 1 / value < 0) && (value *= -1, true);

          // Perform the initial formatting.
          value = formatType(value, precision);

          // If the original value was negative, it may be rounded to zero during
          // formatting; treat this as (positive) zero.
          if (valueNegative) {
            i = -1, n = value.length;
            valueNegative = false;
            while (++i < n) {
              if (c = value.charCodeAt(i), (48 < c && c < 58)
                  || (type === "x" && 96 < c && c < 103)
                  || (type === "X" && 64 < c && c < 71)) {
                valueNegative = true;
                break;
              }
            }
          }

          // Compute the prefix and suffix.
          valuePrefix = (valueNegative ? (sign === "(" ? sign : "-") : sign === "-" || sign === "(" ? "" : sign) + valuePrefix;
          valueSuffix = valueSuffix + (type === "s" ? prefixes[8 + prefixExponent / 3] : "") + (valueNegative && sign === "(" ? ")" : "");

          // Break the formatted value into the integer “value” part that can be
          // grouped, and fractional or exponential “suffix” part that is not.
          if (maybeSuffix) {
            i = -1, n = value.length;
            while (++i < n) {
              if (c = value.charCodeAt(i), 48 > c || c > 57) {
                valueSuffix = (c === 46 ? decimal + value.slice(i + 1) : value.slice(i)) + valueSuffix;
                value = value.slice(0, i);
                break;
              }
            }
          }
        }

        // If the fill character is not "0", grouping is applied before padding.
        if (comma && !zero) value = group(value, Infinity);

        // Compute the padding.
        var length = valuePrefix.length + value.length + valueSuffix.length,
            padding = length < width ? new Array(width - length + 1).join(fill) : "";

        // If the fill character is "0", grouping is applied after padding.
        if (comma && zero) value = group(padding + value, padding.length ? width - valueSuffix.length : Infinity), padding = "";

        // Reconstruct the final output based on the desired alignment.
        switch (align) {
          case "<": return valuePrefix + value + valueSuffix + padding;
          case "=": return valuePrefix + padding + value + valueSuffix;
          case "^": return padding.slice(0, length = padding.length >> 1) + valuePrefix + value + valueSuffix + padding.slice(length);
        }
        return padding + valuePrefix + value + valueSuffix;
      }

      format.toString = function() {
        return specifier + "";
      };

      return format;
    }

    function formatPrefix(specifier, value) {
      var f = newFormat((specifier = formatSpecifier(specifier), specifier.type = "f", specifier)),
          e = Math.max(-8, Math.min(8, Math.floor(exponent$1(value) / 3))) * 3,
          k = Math.pow(10, -e),
          prefix = prefixes[8 + e / 3];
      return function(value) {
        return f(k * value) + prefix;
      };
    }

    return {
      format: newFormat,
      formatPrefix: formatPrefix
    };
  }

  var locale;
  exports.format;
  exports.formatPrefix;

  defaultLocale({
    decimal: ".",
    thousands: ",",
    grouping: [3],
    currency: ["$", ""]
  });

  function defaultLocale(definition) {
    locale = formatLocale(definition);
    exports.format = locale.format;
    exports.formatPrefix = locale.formatPrefix;
    return locale;
  }

  function precisionFixed(step) {
    return Math.max(0, -exponent$1(Math.abs(step)));
  }

  function precisionPrefix(step, value) {
    return Math.max(0, Math.max(-8, Math.min(8, Math.floor(exponent$1(value) / 3))) * 3 - exponent$1(Math.abs(step)));
  }

  function precisionRound(step, max) {
    step = Math.abs(step), max = Math.abs(max) - step;
    return Math.max(0, exponent$1(max) - exponent$1(step)) + 1;
  }

  function localDate(d) {
    if (0 <= d.y && d.y < 100) {
      var date = new Date(-1, d.m, d.d, d.H, d.M, d.S, d.L);
      date.setFullYear(d.y);
      return date;
    }
    return new Date(d.y, d.m, d.d, d.H, d.M, d.S, d.L);
  }

  function utcDate(d) {
    if (0 <= d.y && d.y < 100) {
      var date = new Date(Date.UTC(-1, d.m, d.d, d.H, d.M, d.S, d.L));
      date.setUTCFullYear(d.y);
      return date;
    }
    return new Date(Date.UTC(d.y, d.m, d.d, d.H, d.M, d.S, d.L));
  }

  function newYear(y) {
    return {y: y, m: 0, d: 1, H: 0, M: 0, S: 0, L: 0};
  }

  function formatLocale$1(locale) {
    var locale_dateTime = locale.dateTime,
        locale_date = locale.date,
        locale_time = locale.time,
        locale_periods = locale.periods,
        locale_weekdays = locale.days,
        locale_shortWeekdays = locale.shortDays,
        locale_months = locale.months,
        locale_shortMonths = locale.shortMonths;

    var periodRe = formatRe(locale_periods),
        periodLookup = formatLookup(locale_periods),
        weekdayRe = formatRe(locale_weekdays),
        weekdayLookup = formatLookup(locale_weekdays),
        shortWeekdayRe = formatRe(locale_shortWeekdays),
        shortWeekdayLookup = formatLookup(locale_shortWeekdays),
        monthRe = formatRe(locale_months),
        monthLookup = formatLookup(locale_months),
        shortMonthRe = formatRe(locale_shortMonths),
        shortMonthLookup = formatLookup(locale_shortMonths);

    var formats = {
      "a": formatShortWeekday,
      "A": formatWeekday,
      "b": formatShortMonth,
      "B": formatMonth,
      "c": null,
      "d": formatDayOfMonth,
      "e": formatDayOfMonth,
      "H": formatHour24,
      "I": formatHour12,
      "j": formatDayOfYear,
      "L": formatMilliseconds,
      "m": formatMonthNumber,
      "M": formatMinutes,
      "p": formatPeriod,
      "S": formatSeconds,
      "U": formatWeekNumberSunday,
      "w": formatWeekdayNumber,
      "W": formatWeekNumberMonday,
      "x": null,
      "X": null,
      "y": formatYear,
      "Y": formatFullYear,
      "Z": formatZone,
      "%": formatLiteralPercent
    };

    var utcFormats = {
      "a": formatUTCShortWeekday,
      "A": formatUTCWeekday,
      "b": formatUTCShortMonth,
      "B": formatUTCMonth,
      "c": null,
      "d": formatUTCDayOfMonth,
      "e": formatUTCDayOfMonth,
      "H": formatUTCHour24,
      "I": formatUTCHour12,
      "j": formatUTCDayOfYear,
      "L": formatUTCMilliseconds,
      "m": formatUTCMonthNumber,
      "M": formatUTCMinutes,
      "p": formatUTCPeriod,
      "S": formatUTCSeconds,
      "U": formatUTCWeekNumberSunday,
      "w": formatUTCWeekdayNumber,
      "W": formatUTCWeekNumberMonday,
      "x": null,
      "X": null,
      "y": formatUTCYear,
      "Y": formatUTCFullYear,
      "Z": formatUTCZone,
      "%": formatLiteralPercent
    };

    var parses = {
      "a": parseShortWeekday,
      "A": parseWeekday,
      "b": parseShortMonth,
      "B": parseMonth,
      "c": parseLocaleDateTime,
      "d": parseDayOfMonth,
      "e": parseDayOfMonth,
      "H": parseHour24,
      "I": parseHour24,
      "j": parseDayOfYear,
      "L": parseMilliseconds,
      "m": parseMonthNumber,
      "M": parseMinutes,
      "p": parsePeriod,
      "S": parseSeconds,
      "U": parseWeekNumberSunday,
      "w": parseWeekdayNumber,
      "W": parseWeekNumberMonday,
      "x": parseLocaleDate,
      "X": parseLocaleTime,
      "y": parseYear,
      "Y": parseFullYear,
      "Z": parseZone,
      "%": parseLiteralPercent
    };

    // These recursive directive definitions must be deferred.
    formats.x = newFormat(locale_date, formats);
    formats.X = newFormat(locale_time, formats);
    formats.c = newFormat(locale_dateTime, formats);
    utcFormats.x = newFormat(locale_date, utcFormats);
    utcFormats.X = newFormat(locale_time, utcFormats);
    utcFormats.c = newFormat(locale_dateTime, utcFormats);

    function newFormat(specifier, formats) {
      return function(date) {
        var string = [],
            i = -1,
            j = 0,
            n = specifier.length,
            c,
            pad,
            format;

        if (!(date instanceof Date)) date = new Date(+date);

        while (++i < n) {
          if (specifier.charCodeAt(i) === 37) {
            string.push(specifier.slice(j, i));
            if ((pad = pads[c = specifier.charAt(++i)]) != null) c = specifier.charAt(++i);
            else pad = c === "e" ? " " : "0";
            if (format = formats[c]) c = format(date, pad);
            string.push(c);
            j = i + 1;
          }
        }

        string.push(specifier.slice(j, i));
        return string.join("");
      };
    }

    function newParse(specifier, newDate) {
      return function(string) {
        var d = newYear(1900),
            i = parseSpecifier(d, specifier, string += "", 0);
        if (i != string.length) return null;

        // The am-pm flag is 0 for AM, and 1 for PM.
        if ("p" in d) d.H = d.H % 12 + d.p * 12;

        // Convert day-of-week and week-of-year to day-of-year.
        if ("W" in d || "U" in d) {
          if (!("w" in d)) d.w = "W" in d ? 1 : 0;
          var day = "Z" in d ? utcDate(newYear(d.y)).getUTCDay() : newDate(newYear(d.y)).getDay();
          d.m = 0;
          d.d = "W" in d ? (d.w + 6) % 7 + d.W * 7 - (day + 5) % 7 : d.w + d.U * 7 - (day + 6) % 7;
        }

        // If a time zone is specified, all fields are interpreted as UTC and then
        // offset according to the specified time zone.
        if ("Z" in d) {
          d.H += d.Z / 100 | 0;
          d.M += d.Z % 100;
          return utcDate(d);
        }

        // Otherwise, all fields are in local time.
        return newDate(d);
      };
    }

    function parseSpecifier(d, specifier, string, j) {
      var i = 0,
          n = specifier.length,
          m = string.length,
          c,
          parse;

      while (i < n) {
        if (j >= m) return -1;
        c = specifier.charCodeAt(i++);
        if (c === 37) {
          c = specifier.charAt(i++);
          parse = parses[c in pads ? specifier.charAt(i++) : c];
          if (!parse || ((j = parse(d, string, j)) < 0)) return -1;
        } else if (c != string.charCodeAt(j++)) {
          return -1;
        }
      }

      return j;
    }

    function parsePeriod(d, string, i) {
      var n = periodRe.exec(string.slice(i));
      return n ? (d.p = periodLookup[n[0].toLowerCase()], i + n[0].length) : -1;
    }

    function parseShortWeekday(d, string, i) {
      var n = shortWeekdayRe.exec(string.slice(i));
      return n ? (d.w = shortWeekdayLookup[n[0].toLowerCase()], i + n[0].length) : -1;
    }

    function parseWeekday(d, string, i) {
      var n = weekdayRe.exec(string.slice(i));
      return n ? (d.w = weekdayLookup[n[0].toLowerCase()], i + n[0].length) : -1;
    }

    function parseShortMonth(d, string, i) {
      var n = shortMonthRe.exec(string.slice(i));
      return n ? (d.m = shortMonthLookup[n[0].toLowerCase()], i + n[0].length) : -1;
    }

    function parseMonth(d, string, i) {
      var n = monthRe.exec(string.slice(i));
      return n ? (d.m = monthLookup[n[0].toLowerCase()], i + n[0].length) : -1;
    }

    function parseLocaleDateTime(d, string, i) {
      return parseSpecifier(d, locale_dateTime, string, i);
    }

    function parseLocaleDate(d, string, i) {
      return parseSpecifier(d, locale_date, string, i);
    }

    function parseLocaleTime(d, string, i) {
      return parseSpecifier(d, locale_time, string, i);
    }

    function formatShortWeekday(d) {
      return locale_shortWeekdays[d.getDay()];
    }

    function formatWeekday(d) {
      return locale_weekdays[d.getDay()];
    }

    function formatShortMonth(d) {
      return locale_shortMonths[d.getMonth()];
    }

    function formatMonth(d) {
      return locale_months[d.getMonth()];
    }

    function formatPeriod(d) {
      return locale_periods[+(d.getHours() >= 12)];
    }

    function formatUTCShortWeekday(d) {
      return locale_shortWeekdays[d.getUTCDay()];
    }

    function formatUTCWeekday(d) {
      return locale_weekdays[d.getUTCDay()];
    }

    function formatUTCShortMonth(d) {
      return locale_shortMonths[d.getUTCMonth()];
    }

    function formatUTCMonth(d) {
      return locale_months[d.getUTCMonth()];
    }

    function formatUTCPeriod(d) {
      return locale_periods[+(d.getUTCHours() >= 12)];
    }

    return {
      format: function(specifier) {
        var f = newFormat(specifier += "", formats);
        f.toString = function() { return specifier; };
        return f;
      },
      parse: function(specifier) {
        var p = newParse(specifier += "", localDate);
        p.toString = function() { return specifier; };
        return p;
      },
      utcFormat: function(specifier) {
        var f = newFormat(specifier += "", utcFormats);
        f.toString = function() { return specifier; };
        return f;
      },
      utcParse: function(specifier) {
        var p = newParse(specifier, utcDate);
        p.toString = function() { return specifier; };
        return p;
      }
    };
  }

  var pads = {"-": "", "_": " ", "0": "0"};
  var numberRe = /^\s*\d+/;
  var percentRe = /^%/;
  var requoteRe = /[\\\^\$\*\+\?\|\[\]\(\)\.\{\}]/g;
  function pad(value, fill, width) {
    var sign = value < 0 ? "-" : "",
        string = (sign ? -value : value) + "",
        length = string.length;
    return sign + (length < width ? new Array(width - length + 1).join(fill) + string : string);
  }

  function requote(s) {
    return s.replace(requoteRe, "\\$&");
  }

  function formatRe(names) {
    return new RegExp("^(?:" + names.map(requote).join("|") + ")", "i");
  }

  function formatLookup(names) {
    var map = {}, i = -1, n = names.length;
    while (++i < n) map[names[i].toLowerCase()] = i;
    return map;
  }

  function parseWeekdayNumber(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 1));
    return n ? (d.w = +n[0], i + n[0].length) : -1;
  }

  function parseWeekNumberSunday(d, string, i) {
    var n = numberRe.exec(string.slice(i));
    return n ? (d.U = +n[0], i + n[0].length) : -1;
  }

  function parseWeekNumberMonday(d, string, i) {
    var n = numberRe.exec(string.slice(i));
    return n ? (d.W = +n[0], i + n[0].length) : -1;
  }

  function parseFullYear(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 4));
    return n ? (d.y = +n[0], i + n[0].length) : -1;
  }

  function parseYear(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 2));
    return n ? (d.y = +n[0] + (+n[0] > 68 ? 1900 : 2000), i + n[0].length) : -1;
  }

  function parseZone(d, string, i) {
    var n = /^(Z)|([+-]\d\d)(?:\:?(\d\d))?/.exec(string.slice(i, i + 6));
    return n ? (d.Z = n[1] ? 0 : -(n[2] + (n[3] || "00")), i + n[0].length) : -1;
  }

  function parseMonthNumber(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 2));
    return n ? (d.m = n[0] - 1, i + n[0].length) : -1;
  }

  function parseDayOfMonth(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 2));
    return n ? (d.d = +n[0], i + n[0].length) : -1;
  }

  function parseDayOfYear(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 3));
    return n ? (d.m = 0, d.d = +n[0], i + n[0].length) : -1;
  }

  function parseHour24(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 2));
    return n ? (d.H = +n[0], i + n[0].length) : -1;
  }

  function parseMinutes(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 2));
    return n ? (d.M = +n[0], i + n[0].length) : -1;
  }

  function parseSeconds(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 2));
    return n ? (d.S = +n[0], i + n[0].length) : -1;
  }

  function parseMilliseconds(d, string, i) {
    var n = numberRe.exec(string.slice(i, i + 3));
    return n ? (d.L = +n[0], i + n[0].length) : -1;
  }

  function parseLiteralPercent(d, string, i) {
    var n = percentRe.exec(string.slice(i, i + 1));
    return n ? i + n[0].length : -1;
  }

  function formatDayOfMonth(d, p) {
    return pad(d.getDate(), p, 2);
  }

  function formatHour24(d, p) {
    return pad(d.getHours(), p, 2);
  }

  function formatHour12(d, p) {
    return pad(d.getHours() % 12 || 12, p, 2);
  }

  function formatDayOfYear(d, p) {
    return pad(1 + day.count(year(d), d), p, 3);
  }

  function formatMilliseconds(d, p) {
    return pad(d.getMilliseconds(), p, 3);
  }

  function formatMonthNumber(d, p) {
    return pad(d.getMonth() + 1, p, 2);
  }

  function formatMinutes(d, p) {
    return pad(d.getMinutes(), p, 2);
  }

  function formatSeconds(d, p) {
    return pad(d.getSeconds(), p, 2);
  }

  function formatWeekNumberSunday(d, p) {
    return pad(timeWeek.count(year(d), d), p, 2);
  }

  function formatWeekdayNumber(d) {
    return d.getDay();
  }

  function formatWeekNumberMonday(d, p) {
    return pad(timeMonday.count(year(d), d), p, 2);
  }

  function formatYear(d, p) {
    return pad(d.getFullYear() % 100, p, 2);
  }

  function formatFullYear(d, p) {
    return pad(d.getFullYear() % 10000, p, 4);
  }

  function formatZone(d) {
    var z = d.getTimezoneOffset();
    return (z > 0 ? "-" : (z *= -1, "+"))
        + pad(z / 60 | 0, "0", 2)
        + pad(z % 60, "0", 2);
  }

  function formatUTCDayOfMonth(d, p) {
    return pad(d.getUTCDate(), p, 2);
  }

  function formatUTCHour24(d, p) {
    return pad(d.getUTCHours(), p, 2);
  }

  function formatUTCHour12(d, p) {
    return pad(d.getUTCHours() % 12 || 12, p, 2);
  }

  function formatUTCDayOfYear(d, p) {
    return pad(1 + utcDay.count(utcYear(d), d), p, 3);
  }

  function formatUTCMilliseconds(d, p) {
    return pad(d.getUTCMilliseconds(), p, 3);
  }

  function formatUTCMonthNumber(d, p) {
    return pad(d.getUTCMonth() + 1, p, 2);
  }

  function formatUTCMinutes(d, p) {
    return pad(d.getUTCMinutes(), p, 2);
  }

  function formatUTCSeconds(d, p) {
    return pad(d.getUTCSeconds(), p, 2);
  }

  function formatUTCWeekNumberSunday(d, p) {
    return pad(utcWeek.count(utcYear(d), d), p, 2);
  }

  function formatUTCWeekdayNumber(d) {
    return d.getUTCDay();
  }

  function formatUTCWeekNumberMonday(d, p) {
    return pad(utcMonday.count(utcYear(d), d), p, 2);
  }

  function formatUTCYear(d, p) {
    return pad(d.getUTCFullYear() % 100, p, 2);
  }

  function formatUTCFullYear(d, p) {
    return pad(d.getUTCFullYear() % 10000, p, 4);
  }

  function formatUTCZone() {
    return "+0000";
  }

  function formatLiteralPercent() {
    return "%";
  }

  var locale$1;
  exports.timeFormat;
  exports.timeParse;
  exports.utcFormat;
  exports.utcParse;

  defaultLocale$1({
    dateTime: "%x, %X",
    date: "%-m/%-d/%Y",
    time: "%-I:%M:%S %p",
    periods: ["AM", "PM"],
    days: ["Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"],
    shortDays: ["Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"],
    months: ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"],
    shortMonths: ["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
  });

  function defaultLocale$1(definition) {
    locale$1 = formatLocale$1(definition);
    exports.timeFormat = locale$1.format;
    exports.timeParse = locale$1.parse;
    exports.utcFormat = locale$1.utcFormat;
    exports.utcParse = locale$1.utcParse;
    return locale$1;
  }

  var isoSpecifier = "%Y-%m-%dT%H:%M:%S.%LZ";

  function formatIsoNative(date) {
    return date.toISOString();
  }

  var formatIso = Date.prototype.toISOString
      ? formatIsoNative
      : exports.utcFormat(isoSpecifier);

  function parseIsoNative(string) {
    var date = new Date(string);
    return isNaN(date) ? null : date;
  }

  var parseIso = +new Date("2000-01-01T00:00:00.000Z")
      ? parseIsoNative
      : exports.utcParse(isoSpecifier);

  var array$2 = Array.prototype;

  var map$2 = array$2.map;
  var slice$3 = array$2.slice;

  var implicit = {name: "implicit"};

  function ordinal(range) {
    var index = map$1(),
        domain = [],
        unknown = implicit;

    range = range == null ? [] : slice$3.call(range);

    function scale(d) {
      var key = d + "", i = index.get(key);
      if (!i) {
        if (unknown !== implicit) return unknown;
        index.set(key, i = domain.push(d));
      }
      return range[(i - 1) % range.length];
    }

    scale.domain = function(_) {
      if (!arguments.length) return domain.slice();
      domain = [], index = map$1();
      var i = -1, n = _.length, d, key;
      while (++i < n) if (!index.has(key = (d = _[i]) + "")) index.set(key, domain.push(d));
      return scale;
    };

    scale.range = function(_) {
      return arguments.length ? (range = slice$3.call(_), scale) : range.slice();
    };

    scale.unknown = function(_) {
      return arguments.length ? (unknown = _, scale) : unknown;
    };

    scale.copy = function() {
      return ordinal()
          .domain(domain)
          .range(range)
          .unknown(unknown);
    };

    return scale;
  }

  function band() {
    var scale = ordinal().unknown(undefined),
        domain = scale.domain,
        ordinalRange = scale.range,
        range$$ = [0, 1],
        step,
        bandwidth,
        round = false,
        paddingInner = 0,
        paddingOuter = 0,
        align = 0.5;

    delete scale.unknown;

    function rescale() {
      var n = domain().length,
          reverse = range$$[1] < range$$[0],
          start = range$$[reverse - 0],
          stop = range$$[1 - reverse];
      step = (stop - start) / Math.max(1, n - paddingInner + paddingOuter * 2);
      if (round) step = Math.floor(step);
      start += (stop - start - step * (n - paddingInner)) * align;
      bandwidth = step * (1 - paddingInner);
      if (round) start = Math.round(start), bandwidth = Math.round(bandwidth);
      var values = range(n).map(function(i) { return start + step * i; });
      return ordinalRange(reverse ? values.reverse() : values);
    }

    scale.domain = function(_) {
      return arguments.length ? (domain(_), rescale()) : domain();
    };

    scale.range = function(_) {
      return arguments.length ? (range$$ = [+_[0], +_[1]], rescale()) : range$$.slice();
    };

    scale.rangeRound = function(_) {
      return range$$ = [+_[0], +_[1]], round = true, rescale();
    };

    scale.bandwidth = function() {
      return bandwidth;
    };

    scale.step = function() {
      return step;
    };

    scale.round = function(_) {
      return arguments.length ? (round = !!_, rescale()) : round;
    };

    scale.padding = function(_) {
      return arguments.length ? (paddingInner = paddingOuter = Math.max(0, Math.min(1, _)), rescale()) : paddingInner;
    };

    scale.paddingInner = function(_) {
      return arguments.length ? (paddingInner = Math.max(0, Math.min(1, _)), rescale()) : paddingInner;
    };

    scale.paddingOuter = function(_) {
      return arguments.length ? (paddingOuter = Math.max(0, Math.min(1, _)), rescale()) : paddingOuter;
    };

    scale.align = function(_) {
      return arguments.length ? (align = Math.max(0, Math.min(1, _)), rescale()) : align;
    };

    scale.copy = function() {
      return band()
          .domain(domain())
          .range(range$$)
          .round(round)
          .paddingInner(paddingInner)
          .paddingOuter(paddingOuter)
          .align(align);
    };

    return rescale();
  }

  function pointish(scale) {
    var copy = scale.copy;

    scale.padding = scale.paddingOuter;
    delete scale.paddingInner;
    delete scale.paddingOuter;

    scale.copy = function() {
      return pointish(copy());
    };

    return scale;
  }

  function point$4() {
    return pointish(band().paddingInner(1));
  }

  function constant$3(x) {
    return function() {
      return x;
    };
  }

  function number$1(x) {
    return +x;
  }

  var unit = [0, 1];

  function deinterpolate(a, b) {
    return (b -= (a = +a))
        ? function(x) { return (x - a) / b; }
        : constant$3(b);
  }

  function deinterpolateClamp(deinterpolate) {
    return function(a, b) {
      var d = deinterpolate(a = +a, b = +b);
      return function(x) { return x <= a ? 0 : x >= b ? 1 : d(x); };
    };
  }

  function reinterpolateClamp(reinterpolate) {
    return function(a, b) {
      var r = reinterpolate(a = +a, b = +b);
      return function(t) { return t <= 0 ? a : t >= 1 ? b : r(t); };
    };
  }

  function bimap(domain, range, deinterpolate, reinterpolate) {
    var d0 = domain[0], d1 = domain[1], r0 = range[0], r1 = range[1];
    if (d1 < d0) d0 = deinterpolate(d1, d0), r0 = reinterpolate(r1, r0);
    else d0 = deinterpolate(d0, d1), r0 = reinterpolate(r0, r1);
    return function(x) { return r0(d0(x)); };
  }

  function polymap(domain, range, deinterpolate, reinterpolate) {
    var j = Math.min(domain.length, range.length) - 1,
        d = new Array(j),
        r = new Array(j),
        i = -1;

    // Reverse descending domains.
    if (domain[j] < domain[0]) {
      domain = domain.slice().reverse();
      range = range.slice().reverse();
    }

    while (++i < j) {
      d[i] = deinterpolate(domain[i], domain[i + 1]);
      r[i] = reinterpolate(range[i], range[i + 1]);
    }

    return function(x) {
      var i = bisectRight(domain, x, 1, j) - 1;
      return r[i](d[i](x));
    };
  }

  function copy(source, target) {
    return target
        .domain(source.domain())
        .range(source.range())
        .interpolate(source.interpolate())
        .clamp(source.clamp());
  }

  // deinterpolate(a, b)(x) takes a domain value x in [a,b] and returns the corresponding parameter t in [0,1].
  // reinterpolate(a, b)(t) takes a parameter t in [0,1] and returns the corresponding domain value x in [a,b].
  function continuous(deinterpolate$$, reinterpolate) {
    var domain = unit,
        range = unit,
        interpolate$$ = interpolate,
        clamp = false,
        piecewise,
        output,
        input;

    function rescale() {
      piecewise = Math.min(domain.length, range.length) > 2 ? polymap : bimap;
      output = input = null;
      return scale;
    }

    function scale(x) {
      return (output || (output = piecewise(domain, range, clamp ? deinterpolateClamp(deinterpolate$$) : deinterpolate$$, interpolate$$)))(+x);
    }

    scale.invert = function(y) {
      return (input || (input = piecewise(range, domain, deinterpolate, clamp ? reinterpolateClamp(reinterpolate) : reinterpolate)))(+y);
    };

    scale.domain = function(_) {
      return arguments.length ? (domain = map$2.call(_, number$1), rescale()) : domain.slice();
    };

    scale.range = function(_) {
      return arguments.length ? (range = slice$3.call(_), rescale()) : range.slice();
    };

    scale.rangeRound = function(_) {
      return range = slice$3.call(_), interpolate$$ = interpolateRound, rescale();
    };

    scale.clamp = function(_) {
      return arguments.length ? (clamp = !!_, rescale()) : clamp;
    };

    scale.interpolate = function(_) {
      return arguments.length ? (interpolate$$ = _, rescale()) : interpolate$$;
    };

    return rescale();
  }

  function tickFormat(domain, count, specifier) {
    var start = domain[0],
        stop = domain[domain.length - 1],
        step = tickStep(start, stop, count == null ? 10 : count),
        precision;
    specifier = formatSpecifier(specifier == null ? ",f" : specifier);
    switch (specifier.type) {
      case "s": {
        var value = Math.max(Math.abs(start), Math.abs(stop));
        if (specifier.precision == null && !isNaN(precision = precisionPrefix(step, value))) specifier.precision = precision;
        return exports.formatPrefix(specifier, value);
      }
      case "":
      case "e":
      case "g":
      case "p":
      case "r": {
        if (specifier.precision == null && !isNaN(precision = precisionRound(step, Math.max(Math.abs(start), Math.abs(stop))))) specifier.precision = precision - (specifier.type === "e");
        break;
      }
      case "f":
      case "%": {
        if (specifier.precision == null && !isNaN(precision = precisionFixed(step))) specifier.precision = precision - (specifier.type === "%") * 2;
        break;
      }
    }
    return exports.format(specifier);
  }

  function linearish(scale) {
    var domain = scale.domain;

    scale.ticks = function(count) {
      var d = domain();
      return ticks(d[0], d[d.length - 1], count == null ? 10 : count);
    };

    scale.tickFormat = function(count, specifier) {
      return tickFormat(domain(), count, specifier);
    };

    scale.nice = function(count) {
      var d = domain(),
          i = d.length - 1,
          n = count == null ? 10 : count,
          start = d[0],
          stop = d[i],
          step = tickStep(start, stop, n);

      if (step) {
        step = tickStep(Math.floor(start / step) * step, Math.ceil(stop / step) * step, n);
        d[0] = Math.floor(start / step) * step;
        d[i] = Math.ceil(stop / step) * step;
        domain(d);
      }

      return scale;
    };

    return scale;
  }

  function linear$2() {
    var scale = continuous(deinterpolate, interpolateNumber);

    scale.copy = function() {
      return copy(scale, linear$2());
    };

    return linearish(scale);
  }

  function identity$4() {
    var domain = [0, 1];

    function scale(x) {
      return +x;
    }

    scale.invert = scale;

    scale.domain = scale.range = function(_) {
      return arguments.length ? (domain = map$2.call(_, number$1), scale) : domain.slice();
    };

    scale.copy = function() {
      return identity$4().domain(domain);
    };

    return linearish(scale);
  }

  function nice(domain, interval) {
    domain = domain.slice();

    var i0 = 0,
        i1 = domain.length - 1,
        x0 = domain[i0],
        x1 = domain[i1],
        t;

    if (x1 < x0) {
      t = i0, i0 = i1, i1 = t;
      t = x0, x0 = x1, x1 = t;
    }

    domain[i0] = interval.floor(x0);
    domain[i1] = interval.ceil(x1);
    return domain;
  }

  function deinterpolate$1(a, b) {
    return (b = Math.log(b / a))
        ? function(x) { return Math.log(x / a) / b; }
        : constant$3(b);
  }

  function reinterpolate(a, b) {
    return a < 0
        ? function(t) { return -Math.pow(-b, t) * Math.pow(-a, 1 - t); }
        : function(t) { return Math.pow(b, t) * Math.pow(a, 1 - t); };
  }

  function pow10(x) {
    return isFinite(x) ? +("1e" + x) : x < 0 ? 0 : x;
  }

  function powp(base) {
    return base === 10 ? pow10
        : base === Math.E ? Math.exp
        : function(x) { return Math.pow(base, x); };
  }

  function logp(base) {
    return base === Math.E ? Math.log
        : base === 10 && Math.log10
        || base === 2 && Math.log2
        || (base = Math.log(base), function(x) { return Math.log(x) / base; });
  }

  function reflect(f) {
    return function(x) {
      return -f(-x);
    };
  }

  function log() {
    var scale = continuous(deinterpolate$1, reinterpolate).domain([1, 10]),
        domain = scale.domain,
        base = 10,
        logs = logp(10),
        pows = powp(10);

    function rescale() {
      logs = logp(base), pows = powp(base);
      if (domain()[0] < 0) logs = reflect(logs), pows = reflect(pows);
      return scale;
    }

    scale.base = function(_) {
      return arguments.length ? (base = +_, rescale()) : base;
    };

    scale.domain = function(_) {
      return arguments.length ? (domain(_), rescale()) : domain();
    };

    scale.ticks = function(count) {
      var d = domain(),
          u = d[0],
          v = d[d.length - 1],
          r;

      if (r = v < u) i = u, u = v, v = i;

      var i = logs(u),
          j = logs(v),
          p,
          k,
          t,
          n = count == null ? 10 : +count,
          z = [];

      if (!(base % 1) && j - i < n) {
        i = Math.round(i) - 1, j = Math.round(j) + 1;
        if (u > 0) for (; i < j; ++i) {
          for (k = 1, p = pows(i); k < base; ++k) {
            t = p * k;
            if (t < u) continue;
            if (t > v) break;
            z.push(t);
          }
        } else for (; i < j; ++i) {
          for (k = base - 1, p = pows(i); k >= 1; --k) {
            t = p * k;
            if (t < u) continue;
            if (t > v) break;
            z.push(t);
          }
        }
      } else {
        z = ticks(i, j, Math.min(j - i, n)).map(pows);
      }

      return r ? z.reverse() : z;
    };

    scale.tickFormat = function(count, specifier) {
      if (specifier == null) specifier = base === 10 ? ".0e" : ",";
      if (typeof specifier !== "function") specifier = exports.format(specifier);
      if (count === Infinity) return specifier;
      if (count == null) count = 10;
      var k = Math.max(1, base * count / scale.ticks().length); // TODO fast estimate?
      return function(d) {
        var i = d / pows(Math.round(logs(d)));
        if (i * base < base - 0.5) i *= base;
        return i <= k ? specifier(d) : "";
      };
    };

    scale.nice = function() {
      return domain(nice(domain(), {
        floor: function(x) { return pows(Math.floor(logs(x))); },
        ceil: function(x) { return pows(Math.ceil(logs(x))); }
      }));
    };

    scale.copy = function() {
      return copy(scale, log().base(base));
    };

    return scale;
  }

  function raise(x, exponent) {
    return x < 0 ? -Math.pow(-x, exponent) : Math.pow(x, exponent);
  }

  function pow() {
    var exponent = 1,
        scale = continuous(deinterpolate, reinterpolate),
        domain = scale.domain;

    function deinterpolate(a, b) {
      return (b = raise(b, exponent) - (a = raise(a, exponent)))
          ? function(x) { return (raise(x, exponent) - a) / b; }
          : constant$3(b);
    }

    function reinterpolate(a, b) {
      b = raise(b, exponent) - (a = raise(a, exponent));
      return function(t) { return raise(a + b * t, 1 / exponent); };
    }

    scale.exponent = function(_) {
      return arguments.length ? (exponent = +_, domain(domain())) : exponent;
    };

    scale.copy = function() {
      return copy(scale, pow().exponent(exponent));
    };

    return linearish(scale);
  }

  function sqrt() {
    return pow().exponent(0.5);
  }

  function quantile() {
    var domain = [],
        range = [],
        thresholds = [];

    function rescale() {
      var i = 0, n = Math.max(1, range.length);
      thresholds = new Array(n - 1);
      while (++i < n) thresholds[i - 1] = threshold(domain, i / n);
      return scale;
    }

    function scale(x) {
      if (!isNaN(x = +x)) return range[bisectRight(thresholds, x)];
    }

    scale.invertExtent = function(y) {
      var i = range.indexOf(y);
      return i < 0 ? [NaN, NaN] : [
        i > 0 ? thresholds[i - 1] : domain[0],
        i < thresholds.length ? thresholds[i] : domain[domain.length - 1]
      ];
    };

    scale.domain = function(_) {
      if (!arguments.length) return domain.slice();
      domain = [];
      for (var i = 0, n = _.length, d; i < n; ++i) if (d = _[i], d != null && !isNaN(d = +d)) domain.push(d);
      domain.sort(ascending);
      return rescale();
    };

    scale.range = function(_) {
      return arguments.length ? (range = slice$3.call(_), rescale()) : range.slice();
    };

    scale.quantiles = function() {
      return thresholds.slice();
    };

    scale.copy = function() {
      return quantile()
          .domain(domain)
          .range(range);
    };

    return scale;
  }

  function quantize$1() {
    var x0 = 0,
        x1 = 1,
        n = 1,
        domain = [0.5],
        range = [0, 1];

    function scale(x) {
      if (x <= x) return range[bisectRight(domain, x, 0, n)];
    }

    function rescale() {
      var i = -1;
      domain = new Array(n);
      while (++i < n) domain[i] = ((i + 1) * x1 - (i - n) * x0) / (n + 1);
      return scale;
    }

    scale.domain = function(_) {
      return arguments.length ? (x0 = +_[0], x1 = +_[1], rescale()) : [x0, x1];
    };

    scale.range = function(_) {
      return arguments.length ? (n = (range = slice$3.call(_)).length - 1, rescale()) : range.slice();
    };

    scale.invertExtent = function(y) {
      var i = range.indexOf(y);
      return i < 0 ? [NaN, NaN]
          : i < 1 ? [x0, domain[0]]
          : i >= n ? [domain[n - 1], x1]
          : [domain[i - 1], domain[i]];
    };

    scale.copy = function() {
      return quantize$1()
          .domain([x0, x1])
          .range(range);
    };

    return linearish(scale);
  }

  function threshold$1() {
    var domain = [0.5],
        range = [0, 1],
        n = 1;

    function scale(x) {
      if (x <= x) return range[bisectRight(domain, x, 0, n)];
    }

    scale.domain = function(_) {
      return arguments.length ? (domain = slice$3.call(_), n = Math.min(domain.length, range.length - 1), scale) : domain.slice();
    };

    scale.range = function(_) {
      return arguments.length ? (range = slice$3.call(_), n = Math.min(domain.length, range.length - 1), scale) : range.slice();
    };

    scale.invertExtent = function(y) {
      var i = range.indexOf(y);
      return [domain[i - 1], domain[i]];
    };

    scale.copy = function() {
      return threshold$1()
          .domain(domain)
          .range(range);
    };

    return scale;
  }

var   durationSecond$1 = 1000;
var   durationMinute$1 = durationSecond$1 * 60;
var   durationHour$1 = durationMinute$1 * 60;
var   durationDay$1 = durationHour$1 * 24;
var   durationWeek$1 = durationDay$1 * 7;
  var durationMonth = durationDay$1 * 30;
  var durationYear = durationDay$1 * 365;
  function date(t) {
    return new Date(t);
  }

  function number$2(t) {
    return t instanceof Date ? +t : +new Date(+t);
  }

  function calendar(year, month, week, day, hour, minute, second, millisecond, format) {
    var scale = continuous(deinterpolate, interpolateNumber),
        invert = scale.invert,
        domain = scale.domain;

    var formatMillisecond = format(".%L"),
        formatSecond = format(":%S"),
        formatMinute = format("%I:%M"),
        formatHour = format("%I %p"),
        formatDay = format("%a %d"),
        formatWeek = format("%b %d"),
        formatMonth = format("%B"),
        formatYear = format("%Y");

    var tickIntervals = [
      [second,  1,      durationSecond$1],
      [second,  5,  5 * durationSecond$1],
      [second, 15, 15 * durationSecond$1],
      [second, 30, 30 * durationSecond$1],
      [minute,  1,      durationMinute$1],
      [minute,  5,  5 * durationMinute$1],
      [minute, 15, 15 * durationMinute$1],
      [minute, 30, 30 * durationMinute$1],
      [  hour,  1,      durationHour$1  ],
      [  hour,  3,  3 * durationHour$1  ],
      [  hour,  6,  6 * durationHour$1  ],
      [  hour, 12, 12 * durationHour$1  ],
      [   day,  1,      durationDay$1   ],
      [   day,  2,  2 * durationDay$1   ],
      [  week,  1,      durationWeek$1  ],
      [ month,  1,      durationMonth ],
      [ month,  3,  3 * durationMonth ],
      [  year,  1,      durationYear  ]
    ];

    function tickFormat(date) {
      return (second(date) < date ? formatMillisecond
          : minute(date) < date ? formatSecond
          : hour(date) < date ? formatMinute
          : day(date) < date ? formatHour
          : month(date) < date ? (week(date) < date ? formatDay : formatWeek)
          : year(date) < date ? formatMonth
          : formatYear)(date);
    }

    function tickInterval(interval, start, stop, step) {
      if (interval == null) interval = 10;

      // If a desired tick count is specified, pick a reasonable tick interval
      // based on the extent of the domain and a rough estimate of tick size.
      // Otherwise, assume interval is already a time interval and use it.
      if (typeof interval === "number") {
        var target = Math.abs(stop - start) / interval,
            i = bisector(function(i) { return i[2]; }).right(tickIntervals, target);
        if (i === tickIntervals.length) {
          step = tickStep(start / durationYear, stop / durationYear, interval);
          interval = year;
        } else if (i) {
          i = tickIntervals[target / tickIntervals[i - 1][2] < tickIntervals[i][2] / target ? i - 1 : i];
          step = i[1];
          interval = i[0];
        } else {
          step = tickStep(start, stop, interval);
          interval = millisecond;
        }
      }

      return step == null ? interval : interval.every(step);
    }

    scale.invert = function(y) {
      return new Date(invert(y));
    };

    scale.domain = function(_) {
      return arguments.length ? domain(map$2.call(_, number$2)) : domain().map(date);
    };

    scale.ticks = function(interval, step) {
      var d = domain(),
          t0 = d[0],
          t1 = d[d.length - 1],
          r = t1 < t0,
          t;
      if (r) t = t0, t0 = t1, t1 = t;
      t = tickInterval(interval, t0, t1, step);
      t = t ? t.range(t0, t1 + 1) : []; // inclusive stop
      return r ? t.reverse() : t;
    };

    scale.tickFormat = function(count, specifier) {
      return specifier == null ? tickFormat : format(specifier);
    };

    scale.nice = function(interval, step) {
      var d = domain();
      return (interval = tickInterval(interval, d[0], d[d.length - 1], step))
          ? domain(nice(d, interval))
          : scale;
    };

    scale.copy = function() {
      return copy(scale, calendar(year, month, week, day, hour, minute, second, millisecond, format));
    };

    return scale;
  }

  function time() {
    return calendar(year, month, timeWeek, day, hour, minute, second, millisecond, exports.timeFormat).domain([new Date(2000, 0, 1), new Date(2000, 0, 2)]);
  }

  function utcTime() {
    return calendar(utcYear, utcMonth, utcWeek, utcDay, utcHour, utcMinute, second, millisecond, exports.utcFormat).domain([Date.UTC(2000, 0, 1), Date.UTC(2000, 0, 2)]);
  }

  function colors(s) {
    return s.match(/.{6}/g).map(function(x) {
      return "#" + x;
    });
  }

  var category10 = colors("1f77b4ff7f0e2ca02cd627289467bd8c564be377c27f7f7fbcbd2217becf");

  var category20b = colors("393b795254a36b6ecf9c9ede6379398ca252b5cf6bcedb9c8c6d31bd9e39e7ba52e7cb94843c39ad494ad6616be7969c7b4173a55194ce6dbdde9ed6");

  var category20c = colors("3182bd6baed69ecae1c6dbefe6550dfd8d3cfdae6bfdd0a231a35474c476a1d99bc7e9c0756bb19e9ac8bcbddcdadaeb636363969696bdbdbdd9d9d9");

  var category20 = colors("1f77b4aec7e8ff7f0effbb782ca02c98df8ad62728ff98969467bdc5b0d58c564bc49c94e377c2f7b6d27f7f7fc7c7c7bcbd22dbdb8d17becf9edae5");

  var cubehelix$3 = interpolateCubehelixLong(cubehelix(300, 0.5, 0.0), cubehelix(-240, 0.5, 1.0));

  var warm = interpolateCubehelixLong(cubehelix(-100, 0.75, 0.35), cubehelix(80, 1.50, 0.8));

  var cool = interpolateCubehelixLong(cubehelix(260, 0.75, 0.35), cubehelix(80, 1.50, 0.8));

  var rainbow = cubehelix();

  function rainbow$1(t) {
    if (t < 0 || t > 1) t -= Math.floor(t);
    var ts = Math.abs(t - 0.5);
    rainbow.h = 360 * t - 100;
    rainbow.s = 1.5 - 1.5 * ts;
    rainbow.l = 0.8 - 0.9 * ts;
    return rainbow + "";
  }

  function ramp(range) {
    var n = range.length;
    return function(t) {
      return range[Math.max(0, Math.min(n - 1, Math.floor(t * n)))];
    };
  }

  var viridis = ramp(colors("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"));

  var magma = ramp(colors("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"));

  var inferno = ramp(colors("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"));

  var plasma = ramp(colors("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"));

  function sequential(interpolator) {
    var x0 = 0,
        x1 = 1,
        clamp = false;

    function scale(x) {
      var t = (x - x0) / (x1 - x0);
      return interpolator(clamp ? Math.max(0, Math.min(1, t)) : t);
    }

    scale.domain = function(_) {
      return arguments.length ? (x0 = +_[0], x1 = +_[1], scale) : [x0, x1];
    };

    scale.clamp = function(_) {
      return arguments.length ? (clamp = !!_, scale) : clamp;
    };

    scale.interpolator = function(_) {
      return arguments.length ? (interpolator = _, scale) : interpolator;
    };

    scale.copy = function() {
      return sequential(interpolator).domain([x0, x1]).clamp(clamp);
    };

    return linearish(scale);
  }

  var xhtml = "http://www.w3.org/1999/xhtml";

  var namespaces = {
    svg: "http://www.w3.org/2000/svg",
    xhtml: xhtml,
    xlink: "http://www.w3.org/1999/xlink",
    xml: "http://www.w3.org/XML/1998/namespace",
    xmlns: "http://www.w3.org/2000/xmlns/"
  };

  function namespace(name) {
    var prefix = name += "", i = prefix.indexOf(":");
    if (i >= 0 && (prefix = name.slice(0, i)) !== "xmlns") name = name.slice(i + 1);
    return namespaces.hasOwnProperty(prefix) ? {space: namespaces[prefix], local: name} : name;
  }

  function creatorInherit(name) {
    return function() {
      var document = this.ownerDocument,
          uri = this.namespaceURI;
      return uri === xhtml && document.documentElement.namespaceURI === xhtml
          ? document.createElement(name)
          : document.createElementNS(uri, name);
    };
  }

  function creatorFixed(fullname) {
    return function() {
      return this.ownerDocument.createElementNS(fullname.space, fullname.local);
    };
  }

  function creator(name) {
    var fullname = namespace(name);
    return (fullname.local
        ? creatorFixed
        : creatorInherit)(fullname);
  }

  var nextId = 0;

  function local() {
    return new Local;
  }

  function Local() {
    this._ = "@" + (++nextId).toString(36);
  }

  Local.prototype = local.prototype = {
    constructor: Local,
    get: function(node) {
      var id = this._;
      while (!(id in node)) if (!(node = node.parentNode)) return;
      return node[id];
    },
    set: function(node, value) {
      return node[this._] = value;
    },
    remove: function(node) {
      return this._ in node && delete node[this._];
    },
    toString: function() {
      return this._;
    }
  };

  var matcher = function(selector) {
    return function() {
      return this.matches(selector);
    };
  };

  if (typeof document !== "undefined") {
    var element = document.documentElement;
    if (!element.matches) {
      var vendorMatches = element.webkitMatchesSelector
          || element.msMatchesSelector
          || element.mozMatchesSelector
          || element.oMatchesSelector;
      matcher = function(selector) {
        return function() {
          return vendorMatches.call(this, selector);
        };
      };
    }
  }

  var matcher$1 = matcher;

  var filterEvents = {};

  exports.event = null;

  if (typeof document !== "undefined") {
    var element$1 = document.documentElement;
    if (!("onmouseenter" in element$1)) {
      filterEvents = {mouseenter: "mouseover", mouseleave: "mouseout"};
    }
  }

  function filterContextListener(listener, index, group) {
    listener = contextListener(listener, index, group);
    return function(event) {
      var related = event.relatedTarget;
      if (!related || (related !== this && !(related.compareDocumentPosition(this) & 8))) {
        listener.call(this, event);
      }
    };
  }

  function contextListener(listener, index, group) {
    return function(event1) {
      var event0 = exports.event; // Events can be reentrant (e.g., focus).
      exports.event = event1;
      try {
        listener.call(this, this.__data__, index, group);
      } finally {
        exports.event = event0;
      }
    };
  }

  function parseTypenames$1(typenames) {
    return typenames.trim().split(/^|\s+/).map(function(t) {
      var name = "", i = t.indexOf(".");
      if (i >= 0) name = t.slice(i + 1), t = t.slice(0, i);
      return {type: t, name: name};
    });
  }

  function onRemove(typename) {
    return function() {
      var on = this.__on;
      if (!on) return;
      for (var j = 0, i = -1, m = on.length, o; j < m; ++j) {
        if (o = on[j], (!typename.type || o.type === typename.type) && o.name === typename.name) {
          this.removeEventListener(o.type, o.listener, o.capture);
        } else {
          on[++i] = o;
        }
      }
      if (++i) on.length = i;
      else delete this.__on;
    };
  }

  function onAdd(typename, value, capture) {
    var wrap = filterEvents.hasOwnProperty(typename.type) ? filterContextListener : contextListener;
    return function(d, i, group) {
      var on = this.__on, o, listener = wrap(value, i, group);
      if (on) for (var j = 0, m = on.length; j < m; ++j) {
        if ((o = on[j]).type === typename.type && o.name === typename.name) {
          this.removeEventListener(o.type, o.listener, o.capture);
          this.addEventListener(o.type, o.listener = listener, o.capture = capture);
          o.value = value;
          return;
        }
      }
      this.addEventListener(typename.type, listener, capture);
      o = {type: typename.type, name: typename.name, value: value, listener: listener, capture: capture};
      if (!on) this.__on = [o];
      else on.push(o);
    };
  }

  function selection_on(typename, value, capture) {
    var typenames = parseTypenames$1(typename + ""), i, n = typenames.length, t;

    if (arguments.length < 2) {
      var on = this.node().__on;
      if (on) for (var j = 0, m = on.length, o; j < m; ++j) {
        for (i = 0, o = on[j]; i < n; ++i) {
          if ((t = typenames[i]).type === o.type && t.name === o.name) {
            return o.value;
          }
        }
      }
      return;
    }

    on = value ? onAdd : onRemove;
    if (capture == null) capture = false;
    for (i = 0; i < n; ++i) this.each(on(typenames[i], value, capture));
    return this;
  }

  function customEvent(event1, listener, that, args) {
    var event0 = exports.event;
    event1.sourceEvent = exports.event;
    exports.event = event1;
    try {
      return listener.apply(that, args);
    } finally {
      exports.event = event0;
    }
  }

  function sourceEvent() {
    var current = exports.event, source;
    while (source = current.sourceEvent) current = source;
    return current;
  }

  function point$5(node, event) {
    var svg = node.ownerSVGElement || node;

    if (svg.createSVGPoint) {
      var point = svg.createSVGPoint();
      point.x = event.clientX, point.y = event.clientY;
      point = point.matrixTransform(node.getScreenCTM().inverse());
      return [point.x, point.y];
    }

    var rect = node.getBoundingClientRect();
    return [event.clientX - rect.left - node.clientLeft, event.clientY - rect.top - node.clientTop];
  }

  function mouse(node) {
    var event = sourceEvent();
    if (event.changedTouches) event = event.changedTouches[0];
    return point$5(node, event);
  }

  function none$2() {}

  function selector(selector) {
    return selector == null ? none$2 : function() {
      return this.querySelector(selector);
    };
  }

  function selection_select(select) {
    if (typeof select !== "function") select = selector(select);

    for (var groups = this._groups, m = groups.length, subgroups = new Array(m), j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, subgroup = subgroups[j] = new Array(n), node, subnode, i = 0; i < n; ++i) {
        if ((node = group[i]) && (subnode = select.call(node, node.__data__, i, group))) {
          if ("__data__" in node) subnode.__data__ = node.__data__;
          subgroup[i] = subnode;
        }
      }
    }

    return new Selection(subgroups, this._parents);
  }

  function empty() {
    return [];
  }

  function selectorAll(selector) {
    return selector == null ? empty : function() {
      return this.querySelectorAll(selector);
    };
  }

  function selection_selectAll(select) {
    if (typeof select !== "function") select = selectorAll(select);

    for (var groups = this._groups, m = groups.length, subgroups = [], parents = [], j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, node, i = 0; i < n; ++i) {
        if (node = group[i]) {
          subgroups.push(select.call(node, node.__data__, i, group));
          parents.push(node);
        }
      }
    }

    return new Selection(subgroups, parents);
  }

  function selection_filter(match) {
    if (typeof match !== "function") match = matcher$1(match);

    for (var groups = this._groups, m = groups.length, subgroups = new Array(m), j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, subgroup = subgroups[j] = [], node, i = 0; i < n; ++i) {
        if ((node = group[i]) && match.call(node, node.__data__, i, group)) {
          subgroup.push(node);
        }
      }
    }

    return new Selection(subgroups, this._parents);
  }

  function sparse(update) {
    return new Array(update.length);
  }

  function selection_enter() {
    return new Selection(this._enter || this._groups.map(sparse), this._parents);
  }

  function EnterNode(parent, datum) {
    this.ownerDocument = parent.ownerDocument;
    this.namespaceURI = parent.namespaceURI;
    this._next = null;
    this._parent = parent;
    this.__data__ = datum;
  }

  EnterNode.prototype = {
    constructor: EnterNode,
    appendChild: function(child) { return this._parent.insertBefore(child, this._next); },
    insertBefore: function(child, next) { return this._parent.insertBefore(child, next); },
    querySelector: function(selector) { return this._parent.querySelector(selector); },
    querySelectorAll: function(selector) { return this._parent.querySelectorAll(selector); }
  };

  function constant$4(x) {
    return function() {
      return x;
    };
  }

  var keyPrefix = "$"; // Protect against keys like “__proto__”.

  function bindIndex(parent, group, enter, update, exit, data) {
    var i = 0,
        node,
        groupLength = group.length,
        dataLength = data.length;

    // Put any non-null nodes that fit into update.
    // Put any null nodes into enter.
    // Put any remaining data into enter.
    for (; i < dataLength; ++i) {
      if (node = group[i]) {
        node.__data__ = data[i];
        update[i] = node;
      } else {
        enter[i] = new EnterNode(parent, data[i]);
      }
    }

    // Put any non-null nodes that don’t fit into exit.
    for (; i < groupLength; ++i) {
      if (node = group[i]) {
        exit[i] = node;
      }
    }
  }

  function bindKey(parent, group, enter, update, exit, data, key) {
    var i,
        node,
        nodeByKeyValue = {},
        groupLength = group.length,
        dataLength = data.length,
        keyValues = new Array(groupLength),
        keyValue;

    // Compute the key for each node.
    // If multiple nodes have the same key, the duplicates are added to exit.
    for (i = 0; i < groupLength; ++i) {
      if (node = group[i]) {
        keyValues[i] = keyValue = keyPrefix + key.call(node, node.__data__, i, group);
        if (keyValue in nodeByKeyValue) {
          exit[i] = node;
        } else {
          nodeByKeyValue[keyValue] = node;
        }
      }
    }

    // Compute the key for each datum.
    // If there a node associated with this key, join and add it to update.
    // If there is not (or the key is a duplicate), add it to enter.
    for (i = 0; i < dataLength; ++i) {
      keyValue = keyPrefix + key.call(parent, data[i], i, data);
      if (node = nodeByKeyValue[keyValue]) {
        update[i] = node;
        node.__data__ = data[i];
        nodeByKeyValue[keyValue] = null;
      } else {
        enter[i] = new EnterNode(parent, data[i]);
      }
    }

    // Add any remaining nodes that were not bound to data to exit.
    for (i = 0; i < groupLength; ++i) {
      if ((node = group[i]) && (nodeByKeyValue[keyValues[i]] === node)) {
        exit[i] = node;
      }
    }
  }

  function selection_data(value, key) {
    if (!value) {
      data = new Array(this.size()), j = -1;
      this.each(function(d) { data[++j] = d; });
      return data;
    }

    var bind = key ? bindKey : bindIndex,
        parents = this._parents,
        groups = this._groups;

    if (typeof value !== "function") value = constant$4(value);

    for (var m = groups.length, update = new Array(m), enter = new Array(m), exit = new Array(m), j = 0; j < m; ++j) {
      var parent = parents[j],
          group = groups[j],
          groupLength = group.length,
          data = value.call(parent, parent && parent.__data__, j, parents),
          dataLength = data.length,
          enterGroup = enter[j] = new Array(dataLength),
          updateGroup = update[j] = new Array(dataLength),
          exitGroup = exit[j] = new Array(groupLength);

      bind(parent, group, enterGroup, updateGroup, exitGroup, data, key);

      // Now connect the enter nodes to their following update node, such that
      // appendChild can insert the materialized enter node before this node,
      // rather than at the end of the parent node.
      for (var i0 = 0, i1 = 0, previous, next; i0 < dataLength; ++i0) {
        if (previous = enterGroup[i0]) {
          if (i0 >= i1) i1 = i0 + 1;
          while (!(next = updateGroup[i1]) && ++i1 < dataLength);
          previous._next = next || null;
        }
      }
    }

    update = new Selection(update, parents);
    update._enter = enter;
    update._exit = exit;
    return update;
  }

  function selection_exit() {
    return new Selection(this._exit || this._groups.map(sparse), this._parents);
  }

  function selection_merge(selection) {

    for (var groups0 = this._groups, groups1 = selection._groups, m0 = groups0.length, m1 = groups1.length, m = Math.min(m0, m1), merges = new Array(m0), j = 0; j < m; ++j) {
      for (var group0 = groups0[j], group1 = groups1[j], n = group0.length, merge = merges[j] = new Array(n), node, i = 0; i < n; ++i) {
        if (node = group0[i] || group1[i]) {
          merge[i] = node;
        }
      }
    }

    for (; j < m0; ++j) {
      merges[j] = groups0[j];
    }

    return new Selection(merges, this._parents);
  }

  function selection_order() {

    for (var groups = this._groups, j = -1, m = groups.length; ++j < m;) {
      for (var group = groups[j], i = group.length - 1, next = group[i], node; --i >= 0;) {
        if (node = group[i]) {
          if (next && next !== node.nextSibling) next.parentNode.insertBefore(node, next);
          next = node;
        }
      }
    }

    return this;
  }

  function selection_sort(compare) {
    if (!compare) compare = ascending$2;

    function compareNode(a, b) {
      return a && b ? compare(a.__data__, b.__data__) : !a - !b;
    }

    for (var groups = this._groups, m = groups.length, sortgroups = new Array(m), j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, sortgroup = sortgroups[j] = new Array(n), node, i = 0; i < n; ++i) {
        if (node = group[i]) {
          sortgroup[i] = node;
        }
      }
      sortgroup.sort(compareNode);
    }

    return new Selection(sortgroups, this._parents).order();
  }

  function ascending$2(a, b) {
    return a < b ? -1 : a > b ? 1 : a >= b ? 0 : NaN;
  }

  function selection_call() {
    var callback = arguments[0];
    arguments[0] = this;
    callback.apply(null, arguments);
    return this;
  }

  function selection_nodes() {
    var nodes = new Array(this.size()), i = -1;
    this.each(function() { nodes[++i] = this; });
    return nodes;
  }

  function selection_node() {

    for (var groups = this._groups, j = 0, m = groups.length; j < m; ++j) {
      for (var group = groups[j], i = 0, n = group.length; i < n; ++i) {
        var node = group[i];
        if (node) return node;
      }
    }

    return null;
  }

  function selection_size() {
    var size = 0;
    this.each(function() { ++size; });
    return size;
  }

  function selection_empty() {
    return !this.node();
  }

  function selection_each(callback) {

    for (var groups = this._groups, j = 0, m = groups.length; j < m; ++j) {
      for (var group = groups[j], i = 0, n = group.length, node; i < n; ++i) {
        if (node = group[i]) callback.call(node, node.__data__, i, group);
      }
    }

    return this;
  }

  function attrRemove(name) {
    return function() {
      this.removeAttribute(name);
    };
  }

  function attrRemoveNS(fullname) {
    return function() {
      this.removeAttributeNS(fullname.space, fullname.local);
    };
  }

  function attrConstant(name, value) {
    return function() {
      this.setAttribute(name, value);
    };
  }

  function attrConstantNS(fullname, value) {
    return function() {
      this.setAttributeNS(fullname.space, fullname.local, value);
    };
  }

  function attrFunction(name, value) {
    return function() {
      var v = value.apply(this, arguments);
      if (v == null) this.removeAttribute(name);
      else this.setAttribute(name, v);
    };
  }

  function attrFunctionNS(fullname, value) {
    return function() {
      var v = value.apply(this, arguments);
      if (v == null) this.removeAttributeNS(fullname.space, fullname.local);
      else this.setAttributeNS(fullname.space, fullname.local, v);
    };
  }

  function selection_attr(name, value) {
    var fullname = namespace(name);

    if (arguments.length < 2) {
      var node = this.node();
      return fullname.local
          ? node.getAttributeNS(fullname.space, fullname.local)
          : node.getAttribute(fullname);
    }

    return this.each((value == null
        ? (fullname.local ? attrRemoveNS : attrRemove) : (typeof value === "function"
        ? (fullname.local ? attrFunctionNS : attrFunction)
        : (fullname.local ? attrConstantNS : attrConstant)))(fullname, value));
  }

  function window(node) {
    return (node.ownerDocument && node.ownerDocument.defaultView) // node is a Node
        || (node.document && node) // node is a Window
        || node.defaultView; // node is a Document
  }

  function styleRemove(name) {
    return function() {
      this.style.removeProperty(name);
    };
  }

  function styleConstant(name, value, priority) {
    return function() {
      this.style.setProperty(name, value, priority);
    };
  }

  function styleFunction(name, value, priority) {
    return function() {
      var v = value.apply(this, arguments);
      if (v == null) this.style.removeProperty(name);
      else this.style.setProperty(name, v, priority);
    };
  }

  function selection_style(name, value, priority) {
    var node;
    return arguments.length > 1
        ? this.each((value == null
              ? styleRemove : typeof value === "function"
              ? styleFunction
              : styleConstant)(name, value, priority == null ? "" : priority))
        : window(node = this.node())
            .getComputedStyle(node, null)
            .getPropertyValue(name);
  }

  function propertyRemove(name) {
    return function() {
      delete this[name];
    };
  }

  function propertyConstant(name, value) {
    return function() {
      this[name] = value;
    };
  }

  function propertyFunction(name, value) {
    return function() {
      var v = value.apply(this, arguments);
      if (v == null) delete this[name];
      else this[name] = v;
    };
  }

  function selection_property(name, value) {
    return arguments.length > 1
        ? this.each((value == null
            ? propertyRemove : typeof value === "function"
            ? propertyFunction
            : propertyConstant)(name, value))
        : this.node()[name];
  }

  function classArray(string) {
    return string.trim().split(/^|\s+/);
  }

  function classList(node) {
    return node.classList || new ClassList(node);
  }

  function ClassList(node) {
    this._node = node;
    this._names = classArray(node.getAttribute("class") || "");
  }

  ClassList.prototype = {
    add: function(name) {
      var i = this._names.indexOf(name);
      if (i < 0) {
        this._names.push(name);
        this._node.setAttribute("class", this._names.join(" "));
      }
    },
    remove: function(name) {
      var i = this._names.indexOf(name);
      if (i >= 0) {
        this._names.splice(i, 1);
        this._node.setAttribute("class", this._names.join(" "));
      }
    },
    contains: function(name) {
      return this._names.indexOf(name) >= 0;
    }
  };

  function classedAdd(node, names) {
    var list = classList(node), i = -1, n = names.length;
    while (++i < n) list.add(names[i]);
  }

  function classedRemove(node, names) {
    var list = classList(node), i = -1, n = names.length;
    while (++i < n) list.remove(names[i]);
  }

  function classedTrue(names) {
    return function() {
      classedAdd(this, names);
    };
  }

  function classedFalse(names) {
    return function() {
      classedRemove(this, names);
    };
  }

  function classedFunction(names, value) {
    return function() {
      (value.apply(this, arguments) ? classedAdd : classedRemove)(this, names);
    };
  }

  function selection_classed(name, value) {
    var names = classArray(name + "");

    if (arguments.length < 2) {
      var list = classList(this.node()), i = -1, n = names.length;
      while (++i < n) if (!list.contains(names[i])) return false;
      return true;
    }

    return this.each((typeof value === "function"
        ? classedFunction : value
        ? classedTrue
        : classedFalse)(names, value));
  }

  function textRemove() {
    this.textContent = "";
  }

  function textConstant(value) {
    return function() {
      this.textContent = value;
    };
  }

  function textFunction(value) {
    return function() {
      var v = value.apply(this, arguments);
      this.textContent = v == null ? "" : v;
    };
  }

  function selection_text(value) {
    return arguments.length
        ? this.each(value == null
            ? textRemove : (typeof value === "function"
            ? textFunction
            : textConstant)(value))
        : this.node().textContent;
  }

  function htmlRemove() {
    this.innerHTML = "";
  }

  function htmlConstant(value) {
    return function() {
      this.innerHTML = value;
    };
  }

  function htmlFunction(value) {
    return function() {
      var v = value.apply(this, arguments);
      this.innerHTML = v == null ? "" : v;
    };
  }

  function selection_html(value) {
    return arguments.length
        ? this.each(value == null
            ? htmlRemove : (typeof value === "function"
            ? htmlFunction
            : htmlConstant)(value))
        : this.node().innerHTML;
  }

  function raise$1() {
    if (this.nextSibling) this.parentNode.appendChild(this);
  }

  function selection_raise() {
    return this.each(raise$1);
  }

  function lower() {
    if (this.previousSibling) this.parentNode.insertBefore(this, this.parentNode.firstChild);
  }

  function selection_lower() {
    return this.each(lower);
  }

  function selection_append(name) {
    var create = typeof name === "function" ? name : creator(name);
    return this.select(function() {
      return this.appendChild(create.apply(this, arguments));
    });
  }

  function constantNull() {
    return null;
  }

  function selection_insert(name, before) {
    var create = typeof name === "function" ? name : creator(name),
        select = before == null ? constantNull : typeof before === "function" ? before : selector(before);
    return this.select(function() {
      return this.insertBefore(create.apply(this, arguments), select.apply(this, arguments) || null);
    });
  }

  function remove() {
    var parent = this.parentNode;
    if (parent) parent.removeChild(this);
  }

  function selection_remove() {
    return this.each(remove);
  }

  function selection_datum(value) {
    return arguments.length
        ? this.property("__data__", value)
        : this.node().__data__;
  }

  function dispatchEvent(node, type, params) {
    var window$$ = window(node),
        event = window$$.CustomEvent;

    if (event) {
      event = new event(type, params);
    } else {
      event = window$$.document.createEvent("Event");
      if (params) event.initEvent(type, params.bubbles, params.cancelable), event.detail = params.detail;
      else event.initEvent(type, false, false);
    }

    node.dispatchEvent(event);
  }

  function dispatchConstant(type, params) {
    return function() {
      return dispatchEvent(this, type, params);
    };
  }

  function dispatchFunction(type, params) {
    return function() {
      return dispatchEvent(this, type, params.apply(this, arguments));
    };
  }

  function selection_dispatch(type, params) {
    return this.each((typeof params === "function"
        ? dispatchFunction
        : dispatchConstant)(type, params));
  }

  var root = [null];

  function Selection(groups, parents) {
    this._groups = groups;
    this._parents = parents;
  }

  function selection() {
    return new Selection([[document.documentElement]], root);
  }

  Selection.prototype = selection.prototype = {
    constructor: Selection,
    select: selection_select,
    selectAll: selection_selectAll,
    filter: selection_filter,
    data: selection_data,
    enter: selection_enter,
    exit: selection_exit,
    merge: selection_merge,
    order: selection_order,
    sort: selection_sort,
    call: selection_call,
    nodes: selection_nodes,
    node: selection_node,
    size: selection_size,
    empty: selection_empty,
    each: selection_each,
    attr: selection_attr,
    style: selection_style,
    property: selection_property,
    classed: selection_classed,
    text: selection_text,
    html: selection_html,
    raise: selection_raise,
    lower: selection_lower,
    append: selection_append,
    insert: selection_insert,
    remove: selection_remove,
    datum: selection_datum,
    on: selection_on,
    dispatch: selection_dispatch
  };

  function select(selector) {
    return typeof selector === "string"
        ? new Selection([[document.querySelector(selector)]], [document.documentElement])
        : new Selection([[selector]], root);
  }

  function selectAll(selector) {
    return typeof selector === "string"
        ? new Selection([document.querySelectorAll(selector)], [document.documentElement])
        : new Selection([selector == null ? [] : selector], root);
  }

  function touch(node, touches, identifier) {
    if (arguments.length < 3) identifier = touches, touches = sourceEvent().changedTouches;

    for (var i = 0, n = touches ? touches.length : 0, touch; i < n; ++i) {
      if ((touch = touches[i]).identifier === identifier) {
        return point$5(node, touch);
      }
    }

    return null;
  }

  function touches(node, touches) {
    if (touches == null) touches = sourceEvent().touches;

    for (var i = 0, n = touches ? touches.length : 0, points = new Array(n); i < n; ++i) {
      points[i] = point$5(node, touches[i]);
    }

    return points;
  }

  var emptyOn = dispatch("start", "end", "interrupt");
  var emptyTween = [];

  var CREATED = 0;
  var SCHEDULED = 1;
  var STARTING = 2;
  var STARTED = 3;
  var ENDING = 4;
  var ENDED = 5;

  function schedule(node, name, id, index, group, timing) {
    var schedules = node.__transition;
    if (!schedules) node.__transition = {};
    else if (id in schedules) return;
    create(node, id, {
      name: name,
      index: index, // For context during callback.
      group: group, // For context during callback.
      on: emptyOn,
      tween: emptyTween,
      time: timing.time,
      delay: timing.delay,
      duration: timing.duration,
      ease: timing.ease,
      timer: null,
      state: CREATED
    });
  }

  function init(node, id) {
    var schedule = node.__transition;
    if (!schedule || !(schedule = schedule[id]) || schedule.state > CREATED) throw new Error("too late");
    return schedule;
  }

  function set$2(node, id) {
    var schedule = node.__transition;
    if (!schedule || !(schedule = schedule[id]) || schedule.state > STARTING) throw new Error("too late");
    return schedule;
  }

  function get$1(node, id) {
    var schedule = node.__transition;
    if (!schedule || !(schedule = schedule[id])) throw new Error("too late");
    return schedule;
  }

  function create(node, id, self) {
    var schedules = node.__transition,
        tween;

    // Initialize the self timer when the transition is created.
    // Note the actual delay is not known until the first callback!
    schedules[id] = self;
    self.timer = timer(schedule, 0, self.time);

    // If the delay is greater than this first sleep, sleep some more;
    // otherwise, start immediately.
    function schedule(elapsed) {
      self.state = SCHEDULED;
      if (self.delay <= elapsed) start(elapsed - self.delay);
      else self.timer.restart(start, self.delay, self.time);
    }

    function start(elapsed) {
      var i, j, n, o;

      for (i in schedules) {
        o = schedules[i];
        if (o.name !== self.name) continue;

        // Interrupt the active transition, if any.
        // Dispatch the interrupt event.
        if (o.state === STARTED) {
          o.state = ENDED;
          o.timer.stop();
          o.on.call("interrupt", node, node.__data__, o.index, o.group);
          delete schedules[i];
        }

        // Cancel any pre-empted transitions. No interrupt event is dispatched
        // because the cancelled transitions never started. Note that this also
        // removes this transition from the pending list!
        else if (+i < id) {
          o.state = ENDED;
          o.timer.stop();
          delete schedules[i];
        }
      }

      // Defer the first tick to end of the current frame; see mbostock/d3#1576.
      // Note the transition may be canceled after start and before the first tick!
      // Note this must be scheduled before the start event; see d3/d3-transition#16!
      // Assuming this is successful, subsequent callbacks go straight to tick.
      timeout$1(function() {
        if (self.state === STARTED) {
          self.timer.restart(tick, self.delay, self.time);
          tick(elapsed);
        }
      });

      // Dispatch the start event.
      // Note this must be done before the tween are initialized.
      self.state = STARTING;
      self.on.call("start", node, node.__data__, self.index, self.group);
      if (self.state !== STARTING) return; // interrupted
      self.state = STARTED;

      // Initialize the tween, deleting null tween.
      tween = new Array(n = self.tween.length);
      for (i = 0, j = -1; i < n; ++i) {
        if (o = self.tween[i].value.call(node, node.__data__, self.index, self.group)) {
          tween[++j] = o;
        }
      }
      tween.length = j + 1;
    }

    function tick(elapsed) {
      var t = elapsed < self.duration ? self.ease.call(null, elapsed / self.duration) : (self.state = ENDING, 1),
          i = -1,
          n = tween.length;

      while (++i < n) {
        tween[i].call(null, t);
      }

      // Dispatch the end event.
      if (self.state === ENDING) {
        self.state = ENDED;
        self.timer.stop();
        self.on.call("end", node, node.__data__, self.index, self.group);
        for (i in schedules) if (+i !== id) return void delete schedules[id];
        delete node.__transition;
      }
    }
  }

  function interrupt(node, name) {
    var schedules = node.__transition,
        schedule,
        active,
        empty = true,
        i;

    if (!schedules) return;

    name = name == null ? null : name + "";

    for (i in schedules) {
      if ((schedule = schedules[i]).name !== name) { empty = false; continue; }
      active = schedule.state === STARTED;
      schedule.state = ENDED;
      schedule.timer.stop();
      if (active) schedule.on.call("interrupt", node, node.__data__, schedule.index, schedule.group);
      delete schedules[i];
    }

    if (empty) delete node.__transition;
  }

  function selection_interrupt(name) {
    return this.each(function() {
      interrupt(this, name);
    });
  }

  function tweenRemove(id, name) {
    var tween0, tween1;
    return function() {
      var schedule = set$2(this, id),
          tween = schedule.tween;

      // If this node shared tween with the previous node,
      // just assign the updated shared tween and we’re done!
      // Otherwise, copy-on-write.
      if (tween !== tween0) {
        tween1 = tween0 = tween;
        for (var i = 0, n = tween1.length; i < n; ++i) {
          if (tween1[i].name === name) {
            tween1 = tween1.slice();
            tween1.splice(i, 1);
            break;
          }
        }
      }

      schedule.tween = tween1;
    };
  }

  function tweenFunction(id, name, value) {
    var tween0, tween1;
    if (typeof value !== "function") throw new Error;
    return function() {
      var schedule = set$2(this, id),
          tween = schedule.tween;

      // If this node shared tween with the previous node,
      // just assign the updated shared tween and we’re done!
      // Otherwise, copy-on-write.
      if (tween !== tween0) {
        tween1 = (tween0 = tween).slice();
        for (var t = {name: name, value: value}, i = 0, n = tween1.length; i < n; ++i) {
          if (tween1[i].name === name) {
            tween1[i] = t;
            break;
          }
        }
        if (i === n) tween1.push(t);
      }

      schedule.tween = tween1;
    };
  }

  function transition_tween(name, value) {
    var id = this._id;

    name += "";

    if (arguments.length < 2) {
      var tween = get$1(this.node(), id).tween;
      for (var i = 0, n = tween.length, t; i < n; ++i) {
        if ((t = tween[i]).name === name) {
          return t.value;
        }
      }
      return null;
    }

    return this.each((value == null ? tweenRemove : tweenFunction)(id, name, value));
  }

  function tweenValue(transition, name, value) {
    var id = transition._id;

    transition.each(function() {
      var schedule = set$2(this, id);
      (schedule.value || (schedule.value = {}))[name] = value.apply(this, arguments);
    });

    return function(node) {
      return get$1(node, id).value[name];
    };
  }

  function interpolate$1(a, b) {
    var c;
    return (typeof b === "number" ? interpolateNumber
        : b instanceof color ? interpolateRgb
        : (c = color(b)) ? (b = c, interpolateRgb)
        : interpolateString)(a, b);
  }

  function attrRemove$1(name) {
    return function() {
      this.removeAttribute(name);
    };
  }

  function attrRemoveNS$1(fullname) {
    return function() {
      this.removeAttributeNS(fullname.space, fullname.local);
    };
  }

  function attrConstant$1(name, interpolate, value1) {
    var value00,
        interpolate0;
    return function() {
      var value0 = this.getAttribute(name);
      return value0 === value1 ? null
          : value0 === value00 ? interpolate0
          : interpolate0 = interpolate(value00 = value0, value1);
    };
  }

  function attrConstantNS$1(fullname, interpolate, value1) {
    var value00,
        interpolate0;
    return function() {
      var value0 = this.getAttributeNS(fullname.space, fullname.local);
      return value0 === value1 ? null
          : value0 === value00 ? interpolate0
          : interpolate0 = interpolate(value00 = value0, value1);
    };
  }

  function attrFunction$1(name, interpolate, value) {
    var value00,
        value10,
        interpolate0;
    return function() {
      var value0, value1 = value(this);
      if (value1 == null) return void this.removeAttribute(name);
      value0 = this.getAttribute(name);
      return value0 === value1 ? null
          : value0 === value00 && value1 === value10 ? interpolate0
          : interpolate0 = interpolate(value00 = value0, value10 = value1);
    };
  }

  function attrFunctionNS$1(fullname, interpolate, value) {
    var value00,
        value10,
        interpolate0;
    return function() {
      var value0, value1 = value(this);
      if (value1 == null) return void this.removeAttributeNS(fullname.space, fullname.local);
      value0 = this.getAttributeNS(fullname.space, fullname.local);
      return value0 === value1 ? null
          : value0 === value00 && value1 === value10 ? interpolate0
          : interpolate0 = interpolate(value00 = value0, value10 = value1);
    };
  }

  function transition_attr(name, value) {
    var fullname = namespace(name), i = fullname === "transform" ? interpolateTransform$2 : interpolate$1;
    return this.attrTween(name, typeof value === "function"
        ? (fullname.local ? attrFunctionNS$1 : attrFunction$1)(fullname, i, tweenValue(this, "attr." + name, value))
        : value == null ? (fullname.local ? attrRemoveNS$1 : attrRemove$1)(fullname)
        : (fullname.local ? attrConstantNS$1 : attrConstant$1)(fullname, i, value));
  }

  function attrTweenNS(fullname, value) {
    function tween() {
      var node = this, i = value.apply(node, arguments);
      return i && function(t) {
        node.setAttributeNS(fullname.space, fullname.local, i(t));
      };
    }
    tween._value = value;
    return tween;
  }

  function attrTween(name, value) {
    function tween() {
      var node = this, i = value.apply(node, arguments);
      return i && function(t) {
        node.setAttribute(name, i(t));
      };
    }
    tween._value = value;
    return tween;
  }

  function transition_attrTween(name, value) {
    var key = "attr." + name;
    if (arguments.length < 2) return (key = this.tween(key)) && key._value;
    if (value == null) return this.tween(key, null);
    if (typeof value !== "function") throw new Error;
    var fullname = namespace(name);
    return this.tween(key, (fullname.local ? attrTweenNS : attrTween)(fullname, value));
  }

  function delayFunction(id, value) {
    return function() {
      init(this, id).delay = +value.apply(this, arguments);
    };
  }

  function delayConstant(id, value) {
    return value = +value, function() {
      init(this, id).delay = value;
    };
  }

  function transition_delay(value) {
    var id = this._id;

    return arguments.length
        ? this.each((typeof value === "function"
            ? delayFunction
            : delayConstant)(id, value))
        : get$1(this.node(), id).delay;
  }

  function durationFunction(id, value) {
    return function() {
      set$2(this, id).duration = +value.apply(this, arguments);
    };
  }

  function durationConstant(id, value) {
    return value = +value, function() {
      set$2(this, id).duration = value;
    };
  }

  function transition_duration(value) {
    var id = this._id;

    return arguments.length
        ? this.each((typeof value === "function"
            ? durationFunction
            : durationConstant)(id, value))
        : get$1(this.node(), id).duration;
  }

  function easeConstant(id, value) {
    if (typeof value !== "function") throw new Error;
    return function() {
      set$2(this, id).ease = value;
    };
  }

  function transition_ease(value) {
    var id = this._id;

    return arguments.length
        ? this.each(easeConstant(id, value))
        : get$1(this.node(), id).ease;
  }

  function transition_filter(match) {
    if (typeof match !== "function") match = matcher$1(match);

    for (var groups = this._groups, m = groups.length, subgroups = new Array(m), j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, subgroup = subgroups[j] = [], node, i = 0; i < n; ++i) {
        if ((node = group[i]) && match.call(node, node.__data__, i, group)) {
          subgroup.push(node);
        }
      }
    }

    return new Transition(subgroups, this._parents, this._name, this._id);
  }

  function transition_merge(transition) {
    if (transition._id !== this._id) throw new Error;

    for (var groups0 = this._groups, groups1 = transition._groups, m0 = groups0.length, m1 = groups1.length, m = Math.min(m0, m1), merges = new Array(m0), j = 0; j < m; ++j) {
      for (var group0 = groups0[j], group1 = groups1[j], n = group0.length, merge = merges[j] = new Array(n), node, i = 0; i < n; ++i) {
        if (node = group0[i] || group1[i]) {
          merge[i] = node;
        }
      }
    }

    for (; j < m0; ++j) {
      merges[j] = groups0[j];
    }

    return new Transition(merges, this._parents, this._name, this._id);
  }

  function start$1(name) {
    return (name + "").trim().split(/^|\s+/).every(function(t) {
      var i = t.indexOf(".");
      if (i >= 0) t = t.slice(0, i);
      return !t || t === "start";
    });
  }

  function onFunction(id, name, listener) {
    var on0, on1, sit = start$1(name) ? init : set$2;
    return function() {
      var schedule = sit(this, id),
          on = schedule.on;

      // If this node shared a dispatch with the previous node,
      // just assign the updated shared dispatch and we’re done!
      // Otherwise, copy-on-write.
      if (on !== on0) (on1 = (on0 = on).copy()).on(name, listener);

      schedule.on = on1;
    };
  }

  function transition_on(name, listener) {
    var id = this._id;

    return arguments.length < 2
        ? get$1(this.node(), id).on.on(name)
        : this.each(onFunction(id, name, listener));
  }

  function removeFunction(id) {
    return function() {
      var parent = this.parentNode;
      for (var i in this.__transition) if (+i !== id) return;
      if (parent) parent.removeChild(this);
    };
  }

  function transition_remove() {
    return this.on("end.remove", removeFunction(this._id));
  }

  function transition_select(select) {
    var name = this._name,
        id = this._id;

    if (typeof select !== "function") select = selector(select);

    for (var groups = this._groups, m = groups.length, subgroups = new Array(m), j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, subgroup = subgroups[j] = new Array(n), node, subnode, i = 0; i < n; ++i) {
        if ((node = group[i]) && (subnode = select.call(node, node.__data__, i, group))) {
          if ("__data__" in node) subnode.__data__ = node.__data__;
          subgroup[i] = subnode;
          schedule(subgroup[i], name, id, i, subgroup, get$1(node, id));
        }
      }
    }

    return new Transition(subgroups, this._parents, name, id);
  }

  function transition_selectAll(select) {
    var name = this._name,
        id = this._id;

    if (typeof select !== "function") select = selectorAll(select);

    for (var groups = this._groups, m = groups.length, subgroups = [], parents = [], j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, node, i = 0; i < n; ++i) {
        if (node = group[i]) {
          for (var children = select.call(node, node.__data__, i, group), child, inherit = get$1(node, id), k = 0, l = children.length; k < l; ++k) {
            if (child = children[k]) {
              schedule(child, name, id, k, children, inherit);
            }
          }
          subgroups.push(children);
          parents.push(node);
        }
      }
    }

    return new Transition(subgroups, parents, name, id);
  }

  var Selection$1 = selection.prototype.constructor;

  function transition_selection() {
    return new Selection$1(this._groups, this._parents);
  }

  function styleRemove$1(name, interpolate) {
    var value00,
        value10,
        interpolate0;
    return function() {
      var style = window(this).getComputedStyle(this, null),
          value0 = style.getPropertyValue(name),
          value1 = (this.style.removeProperty(name), style.getPropertyValue(name));
      return value0 === value1 ? null
          : value0 === value00 && value1 === value10 ? interpolate0
          : interpolate0 = interpolate(value00 = value0, value10 = value1);
    };
  }

  function styleRemoveEnd(name) {
    return function() {
      this.style.removeProperty(name);
    };
  }

  function styleConstant$1(name, interpolate, value1) {
    var value00,
        interpolate0;
    return function() {
      var value0 = window(this).getComputedStyle(this, null).getPropertyValue(name);
      return value0 === value1 ? null
          : value0 === value00 ? interpolate0
          : interpolate0 = interpolate(value00 = value0, value1);
    };
  }

  function styleFunction$1(name, interpolate, value) {
    var value00,
        value10,
        interpolate0;
    return function() {
      var style = window(this).getComputedStyle(this, null),
          value0 = style.getPropertyValue(name),
          value1 = value(this);
      if (value1 == null) value1 = (this.style.removeProperty(name), style.getPropertyValue(name));
      return value0 === value1 ? null
          : value0 === value00 && value1 === value10 ? interpolate0
          : interpolate0 = interpolate(value00 = value0, value10 = value1);
    };
  }

  function transition_style(name, value, priority) {
    var i = (name += "") === "transform" ? interpolateTransform$1 : interpolate$1;
    return value == null ? this
            .styleTween(name, styleRemove$1(name, i))
            .on("end.style." + name, styleRemoveEnd(name))
        : this.styleTween(name, typeof value === "function"
            ? styleFunction$1(name, i, tweenValue(this, "style." + name, value))
            : styleConstant$1(name, i, value), priority);
  }

  function styleTween(name, value, priority) {
    function tween() {
      var node = this, i = value.apply(node, arguments);
      return i && function(t) {
        node.style.setProperty(name, i(t), priority);
      };
    }
    tween._value = value;
    return tween;
  }

  function transition_styleTween(name, value, priority) {
    var key = "style." + (name += "");
    if (arguments.length < 2) return (key = this.tween(key)) && key._value;
    if (value == null) return this.tween(key, null);
    if (typeof value !== "function") throw new Error;
    return this.tween(key, styleTween(name, value, priority == null ? "" : priority));
  }

  function textConstant$1(value) {
    return function() {
      this.textContent = value;
    };
  }

  function textFunction$1(value) {
    return function() {
      var value1 = value(this);
      this.textContent = value1 == null ? "" : value1;
    };
  }

  function transition_text(value) {
    return this.tween("text", typeof value === "function"
        ? textFunction$1(tweenValue(this, "text", value))
        : textConstant$1(value == null ? "" : value + ""));
  }

  function transition_transition() {
    var name = this._name,
        id0 = this._id,
        id1 = newId();

    for (var groups = this._groups, m = groups.length, j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, node, i = 0; i < n; ++i) {
        if (node = group[i]) {
          var inherit = get$1(node, id0);
          schedule(node, name, id1, i, group, {
            time: inherit.time + inherit.delay + inherit.duration,
            delay: 0,
            duration: inherit.duration,
            ease: inherit.ease
          });
        }
      }
    }

    return new Transition(groups, this._parents, name, id1);
  }

  var id = 0;

  function Transition(groups, parents, name, id) {
    this._groups = groups;
    this._parents = parents;
    this._name = name;
    this._id = id;
  }

  function transition(name) {
    return selection().transition(name);
  }

  function newId() {
    return ++id;
  }

  var selection_prototype = selection.prototype;

  Transition.prototype = transition.prototype = {
    constructor: Transition,
    select: transition_select,
    selectAll: transition_selectAll,
    filter: transition_filter,
    merge: transition_merge,
    selection: transition_selection,
    transition: transition_transition,
    call: selection_prototype.call,
    nodes: selection_prototype.nodes,
    node: selection_prototype.node,
    size: selection_prototype.size,
    empty: selection_prototype.empty,
    each: selection_prototype.each,
    on: transition_on,
    attr: transition_attr,
    attrTween: transition_attrTween,
    style: transition_style,
    styleTween: transition_styleTween,
    text: transition_text,
    remove: transition_remove,
    tween: transition_tween,
    delay: transition_delay,
    duration: transition_duration,
    ease: transition_ease
  };

  var defaultTiming = {
    time: null, // Set on use.
    delay: 0,
    duration: 250,
    ease: easeCubicInOut
  };

  function inherit(node, id) {
    var timing;
    while (!(timing = node.__transition) || !(timing = timing[id])) {
      if (!(node = node.parentNode)) {
        return defaultTiming.time = now(), defaultTiming;
      }
    }
    return timing;
  }

  function selection_transition(name) {
    var id,
        timing;

    if (name instanceof Transition) {
      id = name._id, name = name._name;
    } else {
      id = newId(), (timing = defaultTiming).time = now(), name = name == null ? null : name + "";
    }

    for (var groups = this._groups, m = groups.length, j = 0; j < m; ++j) {
      for (var group = groups[j], n = group.length, node, i = 0; i < n; ++i) {
        if (node = group[i]) {
          schedule(node, name, id, i, group, timing || inherit(node, id));
        }
      }
    }

    return new Transition(groups, this._parents, name, id);
  }

  selection.prototype.interrupt = selection_interrupt;
  selection.prototype.transition = selection_transition;

  var root$1 = [null];

  function active(node, name) {
    var schedules = node.__transition,
        schedule,
        i;

    if (schedules) {
      name = name == null ? null : name + "";
      for (i in schedules) {
        if ((schedule = schedules[i]).state > SCHEDULED && schedule.name === name) {
          return new Transition([[node]], root$1, name, +i);
        }
      }
    }

    return null;
  }

  var slice$4 = Array.prototype.slice;

  function identity$5(x) {
    return x;
  }

  var top = 1;
  var right = 2;
  var bottom = 3;
  var left = 4;
var   epsilon$2 = 1e-6;
  function translateX(scale0, scale1, d) {
    var x = scale0(d);
    return "translate(" + (isFinite(x) ? x : scale1(d)) + ",0)";
  }

  function translateY(scale0, scale1, d) {
    var y = scale0(d);
    return "translate(0," + (isFinite(y) ? y : scale1(d)) + ")";
  }

  function center(scale) {
    var width = scale.bandwidth() / 2;
    return function(d) {
      return scale(d) + width;
    };
  }

  function entering() {
    return !this.__axis;
  }

  function axis(orient, scale) {
    var tickArguments = [],
        tickValues = null,
        tickFormat = null,
        tickSizeInner = 6,
        tickSizeOuter = 6,
        tickPadding = 3;

    function axis(context) {
      var values = tickValues == null ? (scale.ticks ? scale.ticks.apply(scale, tickArguments) : scale.domain()) : tickValues,
          format = tickFormat == null ? (scale.tickFormat ? scale.tickFormat.apply(scale, tickArguments) : identity$5) : tickFormat,
          spacing = Math.max(tickSizeInner, 0) + tickPadding,
          transform = orient === top || orient === bottom ? translateX : translateY,
          range = scale.range(),
          range0 = range[0] + 0.5,
          range1 = range[range.length - 1] + 0.5,
          position = (scale.bandwidth ? center : identity$5)(scale.copy()),
          selection = context.selection ? context.selection() : context,
          path = selection.selectAll(".domain").data([null]),
          tick = selection.selectAll(".tick").data(values, scale).order(),
          tickExit = tick.exit(),
          tickEnter = tick.enter().append("g").attr("class", "tick"),
          line = tick.select("line"),
          text = tick.select("text"),
          k = orient === top || orient === left ? -1 : 1,
          x, y = orient === left || orient === right ? (x = "x", "y") : (x = "y", "x");

      path = path.merge(path.enter().insert("path", ".tick")
          .attr("class", "domain")
          .attr("stroke", "#000"));

      tick = tick.merge(tickEnter);

      line = line.merge(tickEnter.append("line")
          .attr("stroke", "#000")
          .attr(x + "2", k * tickSizeInner)
          .attr(y + "1", 0.5)
          .attr(y + "2", 0.5));

      text = text.merge(tickEnter.append("text")
          .attr("fill", "#000")
          .attr(x, k * spacing)
          .attr(y, 0.5)
          .attr("dy", orient === top ? "0em" : orient === bottom ? ".71em" : ".32em"));

      if (context !== selection) {
        path = path.transition(context);
        tick = tick.transition(context);
        line = line.transition(context);
        text = text.transition(context);

        tickExit = tickExit.transition(context)
            .attr("opacity", epsilon$2)
            .attr("transform", function(d) { return transform(position, this.parentNode.__axis || position, d); });

        tickEnter
            .attr("opacity", epsilon$2)
            .attr("transform", function(d) { return transform(this.parentNode.__axis || position, position, d); });
      }

      tickExit.remove();

      path
          .attr("d", orient === left || orient == right
              ? "M" + k * tickSizeOuter + "," + range0 + "H0.5V" + range1 + "H" + k * tickSizeOuter
              : "M" + range0 + "," + k * tickSizeOuter + "V0.5H" + range1 + "V" + k * tickSizeOuter);

      tick
          .attr("opacity", 1)
          .attr("transform", function(d) { return transform(position, position, d); });

      line
          .attr(x + "2", k * tickSizeInner);

      text
          .attr(x, k * spacing)
          .text(format);

      selection.filter(entering)
          .attr("fill", "none")
          .attr("font-size", 10)
          .attr("font-family", "sans-serif")
          .attr("text-anchor", orient === right ? "start" : orient === left ? "end" : "middle");

      selection
          .each(function() { this.__axis = position; });
    }

    axis.scale = function(_) {
      return arguments.length ? (scale = _, axis) : scale;
    };

    axis.ticks = function() {
      return tickArguments = slice$4.call(arguments), axis;
    };

    axis.tickArguments = function(_) {
      return arguments.length ? (tickArguments = _ == null ? [] : slice$4.call(_), axis) : tickArguments.slice();
    };

    axis.tickValues = function(_) {
      return arguments.length ? (tickValues = _ == null ? null : slice$4.call(_), axis) : tickValues && tickValues.slice();
    };

    axis.tickFormat = function(_) {
      return arguments.length ? (tickFormat = _, axis) : tickFormat;
    };

    axis.tickSize = function(_) {
      return arguments.length ? (tickSizeInner = tickSizeOuter = +_, axis) : tickSizeInner;
    };

    axis.tickSizeInner = function(_) {
      return arguments.length ? (tickSizeInner = +_, axis) : tickSizeInner;
    };

    axis.tickSizeOuter = function(_) {
      return arguments.length ? (tickSizeOuter = +_, axis) : tickSizeOuter;
    };

    axis.tickPadding = function(_) {
      return arguments.length ? (tickPadding = +_, axis) : tickPadding;
    };

    return axis;
  }

  function axisTop(scale) {
    return axis(top, scale);
  }

  function axisRight(scale) {
    return axis(right, scale);
  }

  function axisBottom(scale) {
    return axis(bottom, scale);
  }

  function axisLeft(scale) {
    return axis(left, scale);
  }

  function defaultSeparation(a, b) {
    return a.parent === b.parent ? 1 : 2;
  }

  function meanX(children) {
    return children.reduce(meanXReduce, 0) / children.length;
  }

  function meanXReduce(x, c) {
    return x + c.x;
  }

  function maxY(children) {
    return 1 + children.reduce(maxYReduce, 0);
  }

  function maxYReduce(y, c) {
    return Math.max(y, c.y);
  }

  function leafLeft(node) {
    var children;
    while (children = node.children) node = children[0];
    return node;
  }

  function leafRight(node) {
    var children;
    while (children = node.children) node = children[children.length - 1];
    return node;
  }

  function cluster() {
    var separation = defaultSeparation,
        dx = 1,
        dy = 1,
        nodeSize = false;

    function cluster(root) {
      var previousNode,
          x = 0;

      // First walk, computing the initial x & y values.
      root.eachAfter(function(node) {
        var children = node.children;
        if (children) {
          node.x = meanX(children);
          node.y = maxY(children);
        } else {
          node.x = previousNode ? x += separation(node, previousNode) : 0;
          node.y = 0;
          previousNode = node;
        }
      });

      var left = leafLeft(root),
          right = leafRight(root),
          x0 = left.x - separation(left, right) / 2,
          x1 = right.x + separation(right, left) / 2;

      // Second walk, normalizing x & y to the desired size.
      return root.eachAfter(nodeSize ? function(node) {
        node.x = (node.x - root.x) * dx;
        node.y = (root.y - node.y) * dy;
      } : function(node) {
        node.x = (node.x - x0) / (x1 - x0) * dx;
        node.y = (1 - (root.y ? node.y / root.y : 1)) * dy;
      });
    }

    cluster.separation = function(x) {
      return arguments.length ? (separation = x, cluster) : separation;
    };

    cluster.size = function(x) {
      return arguments.length ? (nodeSize = false, dx = +x[0], dy = +x[1], cluster) : (nodeSize ? null : [dx, dy]);
    };

    cluster.nodeSize = function(x) {
      return arguments.length ? (nodeSize = true, dx = +x[0], dy = +x[1], cluster) : (nodeSize ? [dx, dy] : null);
    };

    return cluster;
  }

  function node_each(callback) {
    var node = this, current, next = [node], children, i, n;
    do {
      current = next.reverse(), next = [];
      while (node = current.pop()) {
        callback(node), children = node.children;
        if (children) for (i = 0, n = children.length; i < n; ++i) {
          next.push(children[i]);
        }
      }
    } while (next.length);
    return this;
  }

  function node_eachBefore(callback) {
    var node = this, nodes = [node], children, i;
    while (node = nodes.pop()) {
      callback(node), children = node.children;
      if (children) for (i = children.length - 1; i >= 0; --i) {
        nodes.push(children[i]);
      }
    }
    return this;
  }

  function node_eachAfter(callback) {
    var node = this, nodes = [node], next = [], children, i, n;
    while (node = nodes.pop()) {
      next.push(node), children = node.children;
      if (children) for (i = 0, n = children.length; i < n; ++i) {
        nodes.push(children[i]);
      }
    }
    while (node = next.pop()) {
      callback(node);
    }
    return this;
  }

  function node_sum(value) {
    return this.eachAfter(function(node) {
      var sum = +value(node.data) || 0,
          children = node.children,
          i = children && children.length;
      while (--i >= 0) sum += children[i].value;
      node.value = sum;
    });
  }

  function node_sort(compare) {
    return this.eachBefore(function(node) {
      if (node.children) {
        node.children.sort(compare);
      }
    });
  }

  function node_path(end) {
    var start = this,
        ancestor = leastCommonAncestor(start, end),
        nodes = [start];
    while (start !== ancestor) {
      start = start.parent;
      nodes.push(start);
    }
    var k = nodes.length;
    while (end !== ancestor) {
      nodes.splice(k, 0, end);
      end = end.parent;
    }
    return nodes;
  }

  function leastCommonAncestor(a, b) {
    if (a === b) return a;
    var aNodes = a.ancestors(),
        bNodes = b.ancestors(),
        c = null;
    a = aNodes.pop();
    b = bNodes.pop();
    while (a === b) {
      c = a;
      a = aNodes.pop();
      b = bNodes.pop();
    }
    return c;
  }

  function node_ancestors() {
    var node = this, nodes = [node];
    while (node = node.parent) {
      nodes.push(node);
    }
    return nodes;
  }

  function node_descendants() {
    var nodes = [];
    this.each(function(node) {
      nodes.push(node);
    });
    return nodes;
  }

  function node_leaves() {
    var leaves = [];
    this.eachBefore(function(node) {
      if (!node.children) {
        leaves.push(node);
      }
    });
    return leaves;
  }

  function node_links() {
    var root = this, links = [];
    root.each(function(node) {
      if (node !== root) { // Don’t include the root’s parent, if any.
        links.push({source: node.parent, target: node});
      }
    });
    return links;
  }

  function hierarchy(data, children) {
    var root = new Node(data),
        valued = +data.value && (root.value = data.value),
        node,
        nodes = [root],
        child,
        childs,
        i,
        n;

    if (children == null) children = defaultChildren;

    while (node = nodes.pop()) {
      if (valued) node.value = +node.data.value;
      if ((childs = children(node.data)) && (n = childs.length)) {
        node.children = new Array(n);
        for (i = n - 1; i >= 0; --i) {
          nodes.push(child = node.children[i] = new Node(childs[i]));
          child.parent = node;
          child.depth = node.depth + 1;
        }
      }
    }

    return root.eachBefore(computeHeight);
  }

  function node_copy() {
    return hierarchy(this).eachBefore(copyData);
  }

  function defaultChildren(d) {
    return d.children;
  }

  function copyData(node) {
    node.data = node.data.data;
  }

  function computeHeight(node) {
    var height = 0;
    do node.height = height;
    while ((node = node.parent) && (node.height < ++height));
  }

  function Node(data) {
    this.data = data;
    this.depth =
    this.height = 0;
    this.parent = null;
  }

  Node.prototype = hierarchy.prototype = {
    constructor: Node,
    each: node_each,
    eachAfter: node_eachAfter,
    eachBefore: node_eachBefore,
    sum: node_sum,
    sort: node_sort,
    path: node_path,
    ancestors: node_ancestors,
    descendants: node_descendants,
    leaves: node_leaves,
    links: node_links,
    copy: node_copy
  };

  function Node$2(value) {
    this._ = value;
    this.next = null;
  }

  function shuffle$1(array) {
    var i,
        n = (array = array.slice()).length,
        head = null,
        node = head;

    while (n) {
      var next = new Node$2(array[n - 1]);
      if (node) node = node.next = next;
      else node = head = next;
      array[i] = array[--n];
    }

    return {
      head: head,
      tail: node
    };
  }

  function enclose(circles) {
    return encloseN(shuffle$1(circles), []);
  }

  function encloses(a, b) {
    var dx = b.x - a.x,
        dy = b.y - a.y,
        dr = a.r - b.r;
    return dr * dr + 1e-6 > dx * dx + dy * dy;
  }

  // Returns the smallest circle that contains circles L and intersects circles B.
  function encloseN(L, B) {
    var circle,
        l0 = null,
        l1 = L.head,
        l2,
        p1;

    switch (B.length) {
      case 1: circle = enclose1(B[0]); break;
      case 2: circle = enclose2(B[0], B[1]); break;
      case 3: circle = enclose3(B[0], B[1], B[2]); break;
    }

    while (l1) {
      p1 = l1._, l2 = l1.next;
      if (!circle || !encloses(circle, p1)) {

        // Temporarily truncate L before l1.
        if (l0) L.tail = l0, l0.next = null;
        else L.head = L.tail = null;

        B.push(p1);
        circle = encloseN(L, B); // Note: reorders L!
        B.pop();

        // Move l1 to the front of L and reconnect the truncated list L.
        if (L.head) l1.next = L.head, L.head = l1;
        else l1.next = null, L.head = L.tail = l1;
        l0 = L.tail, l0.next = l2;

      } else {
        l0 = l1;
      }
      l1 = l2;
    }

    L.tail = l0;
    return circle;
  }

  function enclose1(a) {
    return {
      x: a.x,
      y: a.y,
      r: a.r
    };
  }

  function enclose2(a, b) {
    var x1 = a.x, y1 = a.y, r1 = a.r,
        x2 = b.x, y2 = b.y, r2 = b.r,
        x21 = x2 - x1, y21 = y2 - y1, r21 = r2 - r1,
        l = Math.sqrt(x21 * x21 + y21 * y21);
    return {
      x: (x1 + x2 + x21 / l * r21) / 2,
      y: (y1 + y2 + y21 / l * r21) / 2,
      r: (l + r1 + r2) / 2
    };
  }

  function enclose3(a, b, c) {
    var x1 = a.x, y1 = a.y, r1 = a.r,
        x2 = b.x, y2 = b.y, r2 = b.r,
        x3 = c.x, y3 = c.y, r3 = c.r,
        a2 = 2 * (x1 - x2),
        b2 = 2 * (y1 - y2),
        c2 = 2 * (r2 - r1),
        d2 = x1 * x1 + y1 * y1 - r1 * r1 - x2 * x2 - y2 * y2 + r2 * r2,
        a3 = 2 * (x1 - x3),
        b3 = 2 * (y1 - y3),
        c3 = 2 * (r3 - r1),
        d3 = x1 * x1 + y1 * y1 - r1 * r1 - x3 * x3 - y3 * y3 + r3 * r3,
        ab = a3 * b2 - a2 * b3,
        xa = (b2 * d3 - b3 * d2) / ab - x1,
        xb = (b3 * c2 - b2 * c3) / ab,
        ya = (a3 * d2 - a2 * d3) / ab - y1,
        yb = (a2 * c3 - a3 * c2) / ab,
        A = xb * xb + yb * yb - 1,
        B = 2 * (xa * xb + ya * yb + r1),
        C = xa * xa + ya * ya - r1 * r1,
        r = (-B - Math.sqrt(B * B - 4 * A * C)) / (2 * A);
    return {
      x: xa + xb * r + x1,
      y: ya + yb * r + y1,
      r: r
    };
  }

  function place(a, b, c) {
    var ax = a.x,
        ay = a.y,
        da = b.r + c.r,
        db = a.r + c.r,
        dx = b.x - ax,
        dy = b.y - ay,
        dc = dx * dx + dy * dy;
    if (dc) {
      var x = 0.5 + ((db *= db) - (da *= da)) / (2 * dc),
          y = Math.sqrt(Math.max(0, 2 * da * (db + dc) - (db -= dc) * db - da * da)) / (2 * dc);
      c.x = ax + x * dx + y * dy;
      c.y = ay + x * dy - y * dx;
    } else {
      c.x = ax + db;
      c.y = ay;
    }
  }

  function intersects(a, b) {
    var dx = b.x - a.x,
        dy = b.y - a.y,
        dr = a.r + b.r;
    return dr * dr > dx * dx + dy * dy;
  }

  function distance2(circle, x, y) {
    var dx = circle.x - x,
        dy = circle.y - y;
    return dx * dx + dy * dy;
  }

  function Node$1(circle) {
    this._ = circle;
    this.next = null;
    this.previous = null;
  }

  function packEnclose(circles) {
    if (!(n = circles.length)) return 0;

    var a, b, c, n;

    // Place the first circle.
    a = circles[0], a.x = 0, a.y = 0;
    if (!(n > 1)) return a.r;

    // Place the second circle.
    b = circles[1], a.x = -b.r, b.x = a.r, b.y = 0;
    if (!(n > 2)) return a.r + b.r;

    // Place the third circle.
    place(b, a, c = circles[2]);

    // Initialize the weighted centroid.
    var aa = a.r * a.r,
        ba = b.r * b.r,
        ca = c.r * c.r,
        oa = aa + ba + ca,
        ox = aa * a.x + ba * b.x + ca * c.x,
        oy = aa * a.y + ba * b.y + ca * c.y,
        cx, cy, i, j, k, sj, sk;

    // Initialize the front-chain using the first three circles a, b and c.
    a = new Node$1(a), b = new Node$1(b), c = new Node$1(c);
    a.next = c.previous = b;
    b.next = a.previous = c;
    c.next = b.previous = a;

    // Attempt to place each remaining circle…
    pack: for (i = 3; i < n; ++i) {
      place(a._, b._, c = circles[i]), c = new Node$1(c);

      // If there are only three elements in the front-chain…
      if ((k = a.previous) === (j = b.next)) {
        // If the new circle intersects the third circle,
        // rotate the front chain to try the next position.
        if (intersects(j._, c._)) {
          a = b, b = j, --i;
          continue pack;
        }
      }

      // Find the closest intersecting circle on the front-chain, if any.
      else {
        sj = j._.r, sk = k._.r;
        do {
          if (sj <= sk) {
            if (intersects(j._, c._)) {
              b = j, a.next = b, b.previous = a, --i;
              continue pack;
            }
            j = j.next, sj += j._.r;
          } else {
            if (intersects(k._, c._)) {
              a = k, a.next = b, b.previous = a, --i;
              continue pack;
            }
            k = k.previous, sk += k._.r;
          }
        } while (j !== k.next);
      }

      // Success! Insert the new circle c between a and b.
      c.previous = a, c.next = b, a.next = b.previous = b = c;

      // Update the weighted centroid.
      oa += ca = c._.r * c._.r;
      ox += ca * c._.x;
      oy += ca * c._.y;

      // Compute the new closest circle a to centroid.
      aa = distance2(a._, cx = ox / oa, cy = oy / oa);
      while ((c = c.next) !== b) {
        if ((ca = distance2(c._, cx, cy)) < aa) {
          a = c, aa = ca;
        }
      }
      b = a.next;
    }

    // Compute the enclosing circle of the front chain.
    a = [b._], c = b; while ((c = c.next) !== b) a.push(c._); c = enclose(a);

    // Translate the circles to put the enclosing circle around the origin.
    for (i = 0; i < n; ++i) a = circles[i], a.x -= c.x, a.y -= c.y;

    return c.r;
  }

  function siblings(circles) {
    packEnclose(circles);
    return circles;
  }

  function optional(f) {
    return f == null ? null : required(f);
  }

  function required(f) {
    if (typeof f !== "function") throw new Error;
    return f;
  }

  function constantZero() {
    return 0;
  }

  function constant$5(x) {
    return function() {
      return x;
    };
  }

  function defaultRadius(d) {
    return Math.sqrt(d.value);
  }

  function index() {
    var radius = null,
        dx = 1,
        dy = 1,
        padding = constantZero;

    function pack(root) {
      root.x = dx / 2, root.y = dy / 2;
      if (radius) {
        root.eachBefore(radiusLeaf(radius))
            .eachAfter(packChildren(padding, 0.5))
            .eachBefore(translateChild(1));
      } else {
        root.eachBefore(radiusLeaf(defaultRadius))
            .eachAfter(packChildren(constantZero, 1))
            .eachAfter(packChildren(padding, root.r / Math.min(dx, dy)))
            .eachBefore(translateChild(Math.min(dx, dy) / (2 * root.r)));
      }
      return root;
    }

    pack.radius = function(x) {
      return arguments.length ? (radius = optional(x), pack) : radius;
    };

    pack.size = function(x) {
      return arguments.length ? (dx = +x[0], dy = +x[1], pack) : [dx, dy];
    };

    pack.padding = function(x) {
      return arguments.length ? (padding = typeof x === "function" ? x : constant$5(+x), pack) : padding;
    };

    return pack;
  }

  function radiusLeaf(radius) {
    return function(node) {
      if (!node.children) {
        node.r = Math.max(0, +radius(node) || 0);
      }
    };
  }

  function packChildren(padding, k) {
    return function(node) {
      if (children = node.children) {
        var children,
            i,
            n = children.length,
            r = padding(node) * k || 0,
            e;

        if (r) for (i = 0; i < n; ++i) children[i].r += r;
        e = packEnclose(children);
        if (r) for (i = 0; i < n; ++i) children[i].r -= r;
        node.r = e + r;
      }
    };
  }

  function translateChild(k) {
    return function(node) {
      var parent = node.parent;
      node.r *= k;
      if (parent) {
        node.x = parent.x + k * node.x;
        node.y = parent.y + k * node.y;
      }
    };
  }

  function roundNode(node) {
    node.x0 = Math.round(node.x0);
    node.y0 = Math.round(node.y0);
    node.x1 = Math.round(node.x1);
    node.y1 = Math.round(node.y1);
  }

  function treemapDice(parent, x0, y0, x1, y1) {
    var nodes = parent.children,
        node,
        i = -1,
        n = nodes.length,
        k = parent.value && (x1 - x0) / parent.value;

    while (++i < n) {
      node = nodes[i], node.y0 = y0, node.y1 = y1;
      node.x0 = x0, node.x1 = x0 += node.value * k;
    }
  }

  function partition() {
    var dx = 1,
        dy = 1,
        padding = 0,
        round = false;

    function partition(root) {
      var n = root.height + 1;
      root.x0 =
      root.y0 = padding;
      root.x1 = dx;
      root.y1 = dy / n;
      root.eachBefore(positionNode(dy, n));
      if (round) root.eachBefore(roundNode);
      return root;
    }

    function positionNode(dy, n) {
      return function(node) {
        if (node.children) {
          treemapDice(node, node.x0, dy * (node.depth + 1) / n, node.x1, dy * (node.depth + 2) / n);
        }
        var x0 = node.x0,
            y0 = node.y0,
            x1 = node.x1 - padding,
            y1 = node.y1 - padding;
        if (x1 < x0) x0 = x1 = (x0 + x1) / 2;
        if (y1 < y0) y0 = y1 = (y0 + y1) / 2;
        node.x0 = x0;
        node.y0 = y0;
        node.x1 = x1;
        node.y1 = y1;
      };
    }

    partition.round = function(x) {
      return arguments.length ? (round = !!x, partition) : round;
    };

    partition.size = function(x) {
      return arguments.length ? (dx = +x[0], dy = +x[1], partition) : [dx, dy];
    };

    partition.padding = function(x) {
      return arguments.length ? (padding = +x, partition) : padding;
    };

    return partition;
  }

var   keyPrefix$1 = "$";
  var preroot = {depth: -1};
  var ambiguous = {};
  function defaultId(d) {
    return d.id;
  }

  function defaultParentId(d) {
    return d.parentId;
  }

  function stratify() {
    var id = defaultId,
        parentId = defaultParentId;

    function stratify(data) {
      var d,
          i,
          n = data.length,
          root,
          parent,
          node,
          nodes = new Array(n),
          nodeId,
          nodeKey,
          nodeByKey = {};

      for (i = 0; i < n; ++i) {
        d = data[i], node = nodes[i] = new Node(d);
        if ((nodeId = id(d, i, data)) != null && (nodeId += "")) {
          nodeKey = keyPrefix$1 + (node.id = nodeId);
          nodeByKey[nodeKey] = nodeKey in nodeByKey ? ambiguous : node;
        }
      }

      for (i = 0; i < n; ++i) {
        node = nodes[i], nodeId = parentId(data[i], i, data);
        if (nodeId == null || !(nodeId += "")) {
          if (root) throw new Error("multiple roots");
          root = node;
        } else {
          parent = nodeByKey[keyPrefix$1 + nodeId];
          if (!parent) throw new Error("missing: " + nodeId);
          if (parent === ambiguous) throw new Error("ambiguous: " + nodeId);
          if (parent.children) parent.children.push(node);
          else parent.children = [node];
          node.parent = parent;
        }
      }

      if (!root) throw new Error("no root");
      root.parent = preroot;
      root.eachBefore(function(node) { node.depth = node.parent.depth + 1; --n; }).eachBefore(computeHeight);
      root.parent = null;
      if (n > 0) throw new Error("cycle");

      return root;
    }

    stratify.id = function(x) {
      return arguments.length ? (id = required(x), stratify) : id;
    };

    stratify.parentId = function(x) {
      return arguments.length ? (parentId = required(x), stratify) : parentId;
    };

    return stratify;
  }

  function defaultSeparation$1(a, b) {
    return a.parent === b.parent ? 1 : 2;
  }

  // function radialSeparation(a, b) {
  //   return (a.parent === b.parent ? 1 : 2) / a.depth;
  // }

  // This function is used to traverse the left contour of a subtree (or
  // subforest). It returns the successor of v on this contour. This successor is
  // either given by the leftmost child of v or by the thread of v. The function
  // returns null if and only if v is on the highest level of its subtree.
  function nextLeft(v) {
    var children = v.children;
    return children ? children[0] : v.t;
  }

  // This function works analogously to nextLeft.
  function nextRight(v) {
    var children = v.children;
    return children ? children[children.length - 1] : v.t;
  }

  // Shifts the current subtree rooted at w+. This is done by increasing
  // prelim(w+) and mod(w+) by shift.
  function moveSubtree(wm, wp, shift) {
    var change = shift / (wp.i - wm.i);
    wp.c -= change;
    wp.s += shift;
    wm.c += change;
    wp.z += shift;
    wp.m += shift;
  }

  // All other shifts, applied to the smaller subtrees between w- and w+, are
  // performed by this function. To prepare the shifts, we have to adjust
  // change(w+), shift(w+), and change(w-).
  function executeShifts(v) {
    var shift = 0,
        change = 0,
        children = v.children,
        i = children.length,
        w;
    while (--i >= 0) {
      w = children[i];
      w.z += shift;
      w.m += shift;
      shift += w.s + (change += w.c);
    }
  }

  // If vi-’s ancestor is a sibling of v, returns vi-’s ancestor. Otherwise,
  // returns the specified (default) ancestor.
  function nextAncestor(vim, v, ancestor) {
    return vim.a.parent === v.parent ? vim.a : ancestor;
  }

  function TreeNode(node, i) {
    this._ = node;
    this.parent = null;
    this.children = null;
    this.A = null; // default ancestor
    this.a = this; // ancestor
    this.z = 0; // prelim
    this.m = 0; // mod
    this.c = 0; // change
    this.s = 0; // shift
    this.t = null; // thread
    this.i = i; // number
  }

  TreeNode.prototype = Object.create(Node.prototype);

  function treeRoot(root) {
    var tree = new TreeNode(root, 0),
        node,
        nodes = [tree],
        child,
        children,
        i,
        n;

    while (node = nodes.pop()) {
      if (children = node._.children) {
        node.children = new Array(n = children.length);
        for (i = n - 1; i >= 0; --i) {
          nodes.push(child = node.children[i] = new TreeNode(children[i], i));
          child.parent = node;
        }
      }
    }

    (tree.parent = new TreeNode(null, 0)).children = [tree];
    return tree;
  }

  // Node-link tree diagram using the Reingold-Tilford "tidy" algorithm
  function tree() {
    var separation = defaultSeparation$1,
        dx = 1,
        dy = 1,
        nodeSize = null;

    function tree(root) {
      var t = treeRoot(root);

      // Compute the layout using Buchheim et al.’s algorithm.
      t.eachAfter(firstWalk), t.parent.m = -t.z;
      t.eachBefore(secondWalk);

      // If a fixed node size is specified, scale x and y.
      if (nodeSize) root.eachBefore(sizeNode);

      // If a fixed tree size is specified, scale x and y based on the extent.
      // Compute the left-most, right-most, and depth-most nodes for extents.
      else {
        var left = root,
            right = root,
            bottom = root;
        root.eachBefore(function(node) {
          if (node.x < left.x) left = node;
          if (node.x > right.x) right = node;
          if (node.depth > bottom.depth) bottom = node;
        });
        var s = left === right ? 1 : separation(left, right) / 2,
            tx = s - left.x,
            kx = dx / (right.x + s + tx),
            ky = dy / (bottom.depth || 1);
        root.eachBefore(function(node) {
          node.x = (node.x + tx) * kx;
          node.y = node.depth * ky;
        });
      }

      return root;
    }

    // Computes a preliminary x-coordinate for v. Before that, FIRST WALK is
    // applied recursively to the children of v, as well as the function
    // APPORTION. After spacing out the children by calling EXECUTE SHIFTS, the
    // node v is placed to the midpoint of its outermost children.
    function firstWalk(v) {
      var children = v.children,
          siblings = v.parent.children,
          w = v.i ? siblings[v.i - 1] : null;
      if (children) {
        executeShifts(v);
        var midpoint = (children[0].z + children[children.length - 1].z) / 2;
        if (w) {
          v.z = w.z + separation(v._, w._);
          v.m = v.z - midpoint;
        } else {
          v.z = midpoint;
        }
      } else if (w) {
        v.z = w.z + separation(v._, w._);
      }
      v.parent.A = apportion(v, w, v.parent.A || siblings[0]);
    }

    // Computes all real x-coordinates by summing up the modifiers recursively.
    function secondWalk(v) {
      v._.x = v.z + v.parent.m;
      v.m += v.parent.m;
    }

    // The core of the algorithm. Here, a new subtree is combined with the
    // previous subtrees. Threads are used to traverse the inside and outside
    // contours of the left and right subtree up to the highest common level. The
    // vertices used for the traversals are vi+, vi-, vo-, and vo+, where the
    // superscript o means outside and i means inside, the subscript - means left
    // subtree and + means right subtree. For summing up the modifiers along the
    // contour, we use respective variables si+, si-, so-, and so+. Whenever two
    // nodes of the inside contours conflict, we compute the left one of the
    // greatest uncommon ancestors using the function ANCESTOR and call MOVE
    // SUBTREE to shift the subtree and prepare the shifts of smaller subtrees.
    // Finally, we add a new thread (if necessary).
    function apportion(v, w, ancestor) {
      if (w) {
        var vip = v,
            vop = v,
            vim = w,
            vom = vip.parent.children[0],
            sip = vip.m,
            sop = vop.m,
            sim = vim.m,
            som = vom.m,
            shift;
        while (vim = nextRight(vim), vip = nextLeft(vip), vim && vip) {
          vom = nextLeft(vom);
          vop = nextRight(vop);
          vop.a = v;
          shift = vim.z + sim - vip.z - sip + separation(vim._, vip._);
          if (shift > 0) {
            moveSubtree(nextAncestor(vim, v, ancestor), v, shift);
            sip += shift;
            sop += shift;
          }
          sim += vim.m;
          sip += vip.m;
          som += vom.m;
          sop += vop.m;
        }
        if (vim && !nextRight(vop)) {
          vop.t = vim;
          vop.m += sim - sop;
        }
        if (vip && !nextLeft(vom)) {
          vom.t = vip;
          vom.m += sip - som;
          ancestor = v;
        }
      }
      return ancestor;
    }

    function sizeNode(node) {
      node.x *= dx;
      node.y = node.depth * dy;
    }

    tree.separation = function(x) {
      return arguments.length ? (separation = x, tree) : separation;
    };

    tree.size = function(x) {
      return arguments.length ? (nodeSize = false, dx = +x[0], dy = +x[1], tree) : (nodeSize ? null : [dx, dy]);
    };

    tree.nodeSize = function(x) {
      return arguments.length ? (nodeSize = true, dx = +x[0], dy = +x[1], tree) : (nodeSize ? [dx, dy] : null);
    };

    return tree;
  }

  function treemapSlice(parent, x0, y0, x1, y1) {
    var nodes = parent.children,
        node,
        i = -1,
        n = nodes.length,
        k = parent.value && (y1 - y0) / parent.value;

    while (++i < n) {
      node = nodes[i], node.x0 = x0, node.x1 = x1;
      node.y0 = y0, node.y1 = y0 += node.value * k;
    }
  }

  var phi = (1 + Math.sqrt(5)) / 2;

  function squarifyRatio(ratio, parent, x0, y0, x1, y1) {
    var rows = [],
        nodes = parent.children,
        row,
        nodeValue,
        i0 = 0,
        i1,
        n = nodes.length,
        dx, dy,
        value = parent.value,
        sumValue,
        minValue,
        maxValue,
        newRatio,
        minRatio,
        alpha,
        beta;

    while (i0 < n) {
      dx = x1 - x0, dy = y1 - y0;
      minValue = maxValue = sumValue = nodes[i0].value;
      alpha = Math.max(dy / dx, dx / dy) / (value * ratio);
      beta = sumValue * sumValue * alpha;
      minRatio = Math.max(maxValue / beta, beta / minValue);

      // Keep adding nodes while the aspect ratio maintains or improves.
      for (i1 = i0 + 1; i1 < n; ++i1) {
        sumValue += nodeValue = nodes[i1].value;
        if (nodeValue < minValue) minValue = nodeValue;
        if (nodeValue > maxValue) maxValue = nodeValue;
        beta = sumValue * sumValue * alpha;
        newRatio = Math.max(maxValue / beta, beta / minValue);
        if (newRatio > minRatio) { sumValue -= nodeValue; break; }
        minRatio = newRatio;
      }

      // Position and record the row orientation.
      rows.push(row = {value: sumValue, dice: dx < dy, children: nodes.slice(i0, i1)});
      if (row.dice) treemapDice(row, x0, y0, x1, value ? y0 += dy * sumValue / value : y1);
      else treemapSlice(row, x0, y0, value ? x0 += dx * sumValue / value : x1, y1);
      value -= sumValue, i0 = i1;
    }

    return rows;
  }

  var squarify = (function custom(ratio) {

    function squarify(parent, x0, y0, x1, y1) {
      squarifyRatio(ratio, parent, x0, y0, x1, y1);
    }

    squarify.ratio = function(x) {
      return custom((x = +x) > 1 ? x : 1);
    };

    return squarify;
  })(phi);

  function index$1() {
    var tile = squarify,
        round = false,
        dx = 1,
        dy = 1,
        paddingStack = [0],
        paddingInner = constantZero,
        paddingTop = constantZero,
        paddingRight = constantZero,
        paddingBottom = constantZero,
        paddingLeft = constantZero;

    function treemap(root) {
      root.x0 =
      root.y0 = 0;
      root.x1 = dx;
      root.y1 = dy;
      root.eachBefore(positionNode);
      paddingStack = [0];
      if (round) root.eachBefore(roundNode);
      return root;
    }

    function positionNode(node) {
      var p = paddingStack[node.depth],
          x0 = node.x0 + p,
          y0 = node.y0 + p,
          x1 = node.x1 - p,
          y1 = node.y1 - p;
      if (x1 < x0) x0 = x1 = (x0 + x1) / 2;
      if (y1 < y0) y0 = y1 = (y0 + y1) / 2;
      node.x0 = x0;
      node.y0 = y0;
      node.x1 = x1;
      node.y1 = y1;
      if (node.children) {
        p = paddingStack[node.depth + 1] = paddingInner(node) / 2;
        x0 += paddingLeft(node) - p;
        y0 += paddingTop(node) - p;
        x1 -= paddingRight(node) - p;
        y1 -= paddingBottom(node) - p;
        if (x1 < x0) x0 = x1 = (x0 + x1) / 2;
        if (y1 < y0) y0 = y1 = (y0 + y1) / 2;
        tile(node, x0, y0, x1, y1);
      }
    }

    treemap.round = function(x) {
      return arguments.length ? (round = !!x, treemap) : round;
    };

    treemap.size = function(x) {
      return arguments.length ? (dx = +x[0], dy = +x[1], treemap) : [dx, dy];
    };

    treemap.tile = function(x) {
      return arguments.length ? (tile = required(x), treemap) : tile;
    };

    treemap.padding = function(x) {
      return arguments.length ? treemap.paddingInner(x).paddingOuter(x) : treemap.paddingInner();
    };

    treemap.paddingInner = function(x) {
      return arguments.length ? (paddingInner = typeof x === "function" ? x : constant$5(+x), treemap) : paddingInner;
    };

    treemap.paddingOuter = function(x) {
      return arguments.length ? treemap.paddingTop(x).paddingRight(x).paddingBottom(x).paddingLeft(x) : treemap.paddingTop();
    };

    treemap.paddingTop = function(x) {
      return arguments.length ? (paddingTop = typeof x === "function" ? x : constant$5(+x), treemap) : paddingTop;
    };

    treemap.paddingRight = function(x) {
      return arguments.length ? (paddingRight = typeof x === "function" ? x : constant$5(+x), treemap) : paddingRight;
    };

    treemap.paddingBottom = function(x) {
      return arguments.length ? (paddingBottom = typeof x === "function" ? x : constant$5(+x), treemap) : paddingBottom;
    };

    treemap.paddingLeft = function(x) {
      return arguments.length ? (paddingLeft = typeof x === "function" ? x : constant$5(+x), treemap) : paddingLeft;
    };

    return treemap;
  }

  function binary(parent, x0, y0, x1, y1) {
    var nodes = parent.children,
        i, n = nodes.length,
        sum, sums = new Array(n + 1);

    for (sums[0] = sum = i = 0; i < n; ++i) {
      sums[i + 1] = sum += nodes[i].value;
    }

    partition(0, n, parent.value, x0, y0, x1, y1);

    function partition(i, j, value, x0, y0, x1, y1) {
      if (i >= j - 1) {
        var node = nodes[i];
        node.x0 = x0, node.y0 = y0;
        node.x1 = x1, node.y1 = y1;
        return;
      }

      var valueOffset = sums[i],
          valueTarget = (value / 2) + valueOffset,
          k = i + 1,
          hi = j - 1;

      while (k < hi) {
        var mid = k + hi >>> 1;
        if (sums[mid] < valueTarget) k = mid + 1;
        else hi = mid;
      }

      var valueLeft = sums[k] - valueOffset,
          valueRight = value - valueLeft;

      if ((y1 - y0) > (x1 - x0)) {
        var yk = (y0 * valueRight + y1 * valueLeft) / value;
        partition(i, k, valueLeft, x0, y0, x1, yk);
        partition(k, j, valueRight, x0, yk, x1, y1);
      } else {
        var xk = (x0 * valueRight + x1 * valueLeft) / value;
        partition(i, k, valueLeft, x0, y0, xk, y1);
        partition(k, j, valueRight, xk, y0, x1, y1);
      }
    }
  }

  function sliceDice(parent, x0, y0, x1, y1) {
    (parent.depth & 1 ? treemapSlice : treemapDice)(parent, x0, y0, x1, y1);
  }

  var resquarify = (function custom(ratio) {

    function resquarify(parent, x0, y0, x1, y1) {
      if ((rows = parent._squarify) && (rows.ratio === ratio)) {
        var rows,
            row,
            nodes,
            i,
            j = -1,
            n,
            m = rows.length,
            value = parent.value;

        while (++j < m) {
          row = rows[j], nodes = row.children;
          for (i = row.value = 0, n = nodes.length; i < n; ++i) row.value += nodes[i].value;
          if (row.dice) treemapDice(row, x0, y0, x1, y0 += (y1 - y0) * row.value / value);
          else treemapSlice(row, x0, y0, x0 += (x1 - x0) * row.value / value, y1);
          value -= row.value;
        }
      } else {
        parent._squarify = rows = squarifyRatio(ratio, parent, x0, y0, x1, y1);
        rows.ratio = ratio;
      }
    }

    resquarify.ratio = function(x) {
      return custom((x = +x) > 1 ? x : 1);
    };

    return resquarify;
  })(phi);

  function center$1(x, y) {
    var nodes;

    if (x == null) x = 0;
    if (y == null) y = 0;

    function force() {
      var i,
          n = nodes.length,
          node,
          sx = 0,
          sy = 0;

      for (i = 0; i < n; ++i) {
        node = nodes[i], sx += node.x, sy += node.y;
      }

      for (sx = sx / n - x, sy = sy / n - y, i = 0; i < n; ++i) {
        node = nodes[i], node.x -= sx, node.y -= sy;
      }
    }

    force.initialize = function(_) {
      nodes = _;
    };

    force.x = function(_) {
      return arguments.length ? (x = +_, force) : x;
    };

    force.y = function(_) {
      return arguments.length ? (y = +_, force) : y;
    };

    return force;
  }

  function constant$6(x) {
    return function() {
      return x;
    };
  }

  function jiggle() {
    return (Math.random() - 0.5) * 1e-6;
  }

  function x$1(d) {
    return d.x + d.vx;
  }

  function y$1(d) {
    return d.y + d.vy;
  }

  function collide(radius) {
    var nodes,
        radii,
        strength = 1,
        iterations = 1;

    if (typeof radius !== "function") radius = constant$6(radius == null ? 1 : +radius);

    function force() {
      var i, n = nodes.length,
          tree,
          node,
          xi,
          yi,
          ri,
          ri2;

      for (var k = 0; k < iterations; ++k) {
        tree = quadtree(nodes, x$1, y$1).visitAfter(prepare);
        for (i = 0; i < n; ++i) {
          node = nodes[i];
          ri = radii[i], ri2 = ri * ri;
          xi = node.x + node.vx;
          yi = node.y + node.vy;
          tree.visit(apply);
        }
      }

      function apply(quad, x0, y0, x1, y1) {
        var data = quad.data, rj = quad.r, r = ri + rj;
        if (data) {
          if (data.index > i) {
            var x = xi - data.x - data.vx,
                y = yi - data.y - data.vy,
                l = x * x + y * y;
            if (l < r * r) {
              if (x === 0) x = jiggle(), l += x * x;
              if (y === 0) y = jiggle(), l += y * y;
              l = (r - (l = Math.sqrt(l))) / l * strength;
              node.vx += (x *= l) * (r = (rj *= rj) / (ri2 + rj));
              node.vy += (y *= l) * r;
              data.vx -= x * (r = 1 - r);
              data.vy -= y * r;
            }
          }
          return;
        }
        return x0 > xi + r || x1 < xi - r || y0 > yi + r || y1 < yi - r;
      }
    }

    function prepare(quad) {
      if (quad.data) return quad.r = radii[quad.data.index];
      for (var i = quad.r = 0; i < 4; ++i) {
        if (quad[i] && quad[i].r > quad.r) {
          quad.r = quad[i].r;
        }
      }
    }

    force.initialize = function(_) {
      var i, n = (nodes = _).length; radii = new Array(n);
      for (i = 0; i < n; ++i) radii[i] = +radius(nodes[i], i, nodes);
    };

    force.iterations = function(_) {
      return arguments.length ? (iterations = +_, force) : iterations;
    };

    force.strength = function(_) {
      return arguments.length ? (strength = +_, force) : strength;
    };

    force.radius = function(_) {
      return arguments.length ? (radius = typeof _ === "function" ? _ : constant$6(+_), force) : radius;
    };

    return force;
  }

  function index$2(d, i) {
    return i;
  }

  function link(links) {
    var id = index$2,
        strength = defaultStrength,
        strengths,
        distance = constant$6(30),
        distances,
        nodes,
        count,
        bias,
        iterations = 1;

    if (links == null) links = [];

    function defaultStrength(link) {
      return 1 / Math.min(count[link.source.index], count[link.target.index]);
    }

    function force(alpha) {
      for (var k = 0, n = links.length; k < iterations; ++k) {
        for (var i = 0, link, source, target, x, y, l, b; i < n; ++i) {
          link = links[i], source = link.source, target = link.target;
          x = target.x + target.vx - source.x - source.vx || jiggle();
          y = target.y + target.vy - source.y - source.vy || jiggle();
          l = Math.sqrt(x * x + y * y);
          l = (l - distances[i]) / l * alpha * strengths[i];
          x *= l, y *= l;
          target.vx -= x * (b = bias[i]);
          target.vy -= y * b;
          source.vx += x * (b = 1 - b);
          source.vy += y * b;
        }
      }
    }

    function initialize() {
      if (!nodes) return;

      var i,
          n = nodes.length,
          m = links.length,
          nodeById = map$1(nodes, id),
          link;

      for (i = 0, count = new Array(n); i < n; ++i) {
        count[i] = 0;
      }

      for (i = 0; i < m; ++i) {
        link = links[i], link.index = i;
        if (typeof link.source !== "object") link.source = nodeById.get(link.source);
        if (typeof link.target !== "object") link.target = nodeById.get(link.target);
        ++count[link.source.index], ++count[link.target.index];
      }

      for (i = 0, bias = new Array(m); i < m; ++i) {
        link = links[i], bias[i] = count[link.source.index] / (count[link.source.index] + count[link.target.index]);
      }

      strengths = new Array(m), initializeStrength();
      distances = new Array(m), initializeDistance();
    }

    function initializeStrength() {
      if (!nodes) return;

      for (var i = 0, n = links.length; i < n; ++i) {
        strengths[i] = +strength(links[i], i, links);
      }
    }

    function initializeDistance() {
      if (!nodes) return;

      for (var i = 0, n = links.length; i < n; ++i) {
        distances[i] = +distance(links[i], i, links);
      }
    }

    force.initialize = function(_) {
      nodes = _;
      initialize();
    };

    force.links = function(_) {
      return arguments.length ? (links = _, initialize(), force) : links;
    };

    force.id = function(_) {
      return arguments.length ? (id = _, force) : id;
    };

    force.iterations = function(_) {
      return arguments.length ? (iterations = +_, force) : iterations;
    };

    force.strength = function(_) {
      return arguments.length ? (strength = typeof _ === "function" ? _ : constant$6(+_), initializeStrength(), force) : strength;
    };

    force.distance = function(_) {
      return arguments.length ? (distance = typeof _ === "function" ? _ : constant$6(+_), initializeDistance(), force) : distance;
    };

    return force;
  }

  function x$2(d) {
    return d.x;
  }

  function y$2(d) {
    return d.y;
  }

  var initialRadius = 10;
  var initialAngle = Math.PI * (3 - Math.sqrt(5));
  function simulation(nodes) {
    var simulation,
        alpha = 1,
        alphaMin = 0.001,
        alphaDecay = 1 - Math.pow(alphaMin, 1 / 300),
        alphaTarget = 0,
        velocityDecay = 0.6,
        forces = map$1(),
        stepper = timer(step),
        event = dispatch("tick", "end");

    if (nodes == null) nodes = [];

    function step() {
      tick();
      event.call("tick", simulation);
      if (alpha < alphaMin) {
        stepper.stop();
        event.call("end", simulation);
      }
    }

    function tick() {
      var i, n = nodes.length, node;

      alpha += (alphaTarget - alpha) * alphaDecay;

      forces.each(function(force) {
        force(alpha);
      });

      for (i = 0; i < n; ++i) {
        node = nodes[i];
        if (node.fx == null) node.x += node.vx *= velocityDecay;
        else node.x = node.fx, node.vx = 0;
        if (node.fy == null) node.y += node.vy *= velocityDecay;
        else node.y = node.fy, node.vy = 0;
      }
    }

    function initializeNodes() {
      for (var i = 0, n = nodes.length, node; i < n; ++i) {
        node = nodes[i], node.index = i;
        if (isNaN(node.x) || isNaN(node.y)) {
          var radius = initialRadius * Math.sqrt(i), angle = i * initialAngle;
          node.x = radius * Math.cos(angle);
          node.y = radius * Math.sin(angle);
        }
        if (isNaN(node.vx) || isNaN(node.vy)) {
          node.vx = node.vy = 0;
        }
      }
    }

    function initializeForce(force) {
      if (force.initialize) force.initialize(nodes);
      return force;
    }

    initializeNodes();

    return simulation = {
      tick: tick,

      restart: function() {
        return stepper.restart(step), simulation;
      },

      stop: function() {
        return stepper.stop(), simulation;
      },

      nodes: function(_) {
        return arguments.length ? (nodes = _, initializeNodes(), forces.each(initializeForce), simulation) : nodes;
      },

      alpha: function(_) {
        return arguments.length ? (alpha = +_, simulation) : alpha;
      },

      alphaMin: function(_) {
        return arguments.length ? (alphaMin = +_, simulation) : alphaMin;
      },

      alphaDecay: function(_) {
        return arguments.length ? (alphaDecay = +_, simulation) : +alphaDecay;
      },

      alphaTarget: function(_) {
        return arguments.length ? (alphaTarget = +_, simulation) : alphaTarget;
      },

      velocityDecay: function(_) {
        return arguments.length ? (velocityDecay = 1 - _, simulation) : 1 - velocityDecay;
      },

      force: function(name, _) {
        return arguments.length > 1 ? ((_ == null ? forces.remove(name) : forces.set(name, initializeForce(_))), simulation) : forces.get(name);
      },

      find: function(x, y, radius) {
        var i = 0,
            n = nodes.length,
            dx,
            dy,
            d2,
            node,
            closest;

        if (radius == null) radius = Infinity;
        else radius *= radius;

        for (i = 0; i < n; ++i) {
          node = nodes[i];
          dx = x - node.x;
          dy = y - node.y;
          d2 = dx * dx + dy * dy;
          if (d2 < radius) closest = node, radius = d2;
        }

        return closest;
      },

      on: function(name, _) {
        return arguments.length > 1 ? (event.on(name, _), simulation) : event.on(name);
      }
    };
  }

  function manyBody() {
    var nodes,
        node,
        alpha,
        strength = constant$6(-30),
        strengths,
        distanceMin2 = 1,
        distanceMax2 = Infinity,
        theta2 = 0.81;

    function force(_) {
      var i, n = nodes.length, tree = quadtree(nodes, x$2, y$2).visitAfter(accumulate);
      for (alpha = _, i = 0; i < n; ++i) node = nodes[i], tree.visit(apply);
    }

    function initialize() {
      if (!nodes) return;
      var i, n = nodes.length;
      strengths = new Array(n);
      for (i = 0; i < n; ++i) strengths[i] = +strength(nodes[i], i, nodes);
    }

    function accumulate(quad) {
      var strength = 0, q, c, x, y, i;

      // For internal nodes, accumulate forces from child quadrants.
      if (quad.length) {
        for (x = y = i = 0; i < 4; ++i) {
          if ((q = quad[i]) && (c = q.value)) {
            strength += c, x += c * q.x, y += c * q.y;
          }
        }
        quad.x = x / strength;
        quad.y = y / strength;
      }

      // For leaf nodes, accumulate forces from coincident quadrants.
      else {
        q = quad;
        q.x = q.data.x;
        q.y = q.data.y;
        do strength += strengths[q.data.index];
        while (q = q.next);
      }

      quad.value = strength;
    }

    function apply(quad, x1, _, x2) {
      if (!quad.value) return true;

      var x = quad.x - node.x,
          y = quad.y - node.y,
          w = x2 - x1,
          l = x * x + y * y;

      // Apply the Barnes-Hut approximation if possible.
      // Limit forces for very close nodes; randomize direction if coincident.
      if (w * w / theta2 < l) {
        if (l < distanceMax2) {
          if (x === 0) x = jiggle(), l += x * x;
          if (y === 0) y = jiggle(), l += y * y;
          if (l < distanceMin2) l = Math.sqrt(distanceMin2 * l);
          node.vx += x * quad.value * alpha / l;
          node.vy += y * quad.value * alpha / l;
        }
        return true;
      }

      // Otherwise, process points directly.
      else if (quad.length || l >= distanceMax2) return;

      // Limit forces for very close nodes; randomize direction if coincident.
      if (quad.data !== node || quad.next) {
        if (x === 0) x = jiggle(), l += x * x;
        if (y === 0) y = jiggle(), l += y * y;
        if (l < distanceMin2) l = Math.sqrt(distanceMin2 * l);
      }

      do if (quad.data !== node) {
        w = strengths[quad.data.index] * alpha / l;
        node.vx += x * w;
        node.vy += y * w;
      } while (quad = quad.next);
    }

    force.initialize = function(_) {
      nodes = _;
      initialize();
    };

    force.strength = function(_) {
      return arguments.length ? (strength = typeof _ === "function" ? _ : constant$6(+_), initialize(), force) : strength;
    };

    force.distanceMin = function(_) {
      return arguments.length ? (distanceMin2 = _ * _, force) : Math.sqrt(distanceMin2);
    };

    force.distanceMax = function(_) {
      return arguments.length ? (distanceMax2 = _ * _, force) : Math.sqrt(distanceMax2);
    };

    force.theta = function(_) {
      return arguments.length ? (theta2 = _ * _, force) : Math.sqrt(theta2);
    };

    return force;
  }

  function x$3(x) {
    var strength = constant$6(0.1),
        nodes,
        strengths,
        xz;

    if (typeof x !== "function") x = constant$6(x == null ? 0 : +x);

    function force(alpha) {
      for (var i = 0, n = nodes.length, node; i < n; ++i) {
        node = nodes[i], node.vx += (xz[i] - node.x) * strengths[i] * alpha;
      }
    }

    function initialize() {
      if (!nodes) return;
      var i, n = nodes.length;
      strengths = new Array(n);
      xz = new Array(n);
      for (i = 0; i < n; ++i) {
        strengths[i] = isNaN(xz[i] = +x(nodes[i], i, nodes)) ? 0 : +strength(nodes[i], i, nodes);
      }
    }

    force.initialize = function(_) {
      nodes = _;
      initialize();
    };

    force.strength = function(_) {
      return arguments.length ? (strength = typeof _ === "function" ? _ : constant$6(+_), initialize(), force) : strength;
    };

    force.x = function(_) {
      return arguments.length ? (x = typeof _ === "function" ? _ : constant$6(+_), initialize(), force) : x;
    };

    return force;
  }

  function y$3(y) {
    var strength = constant$6(0.1),
        nodes,
        strengths,
        yz;

    if (typeof y !== "function") y = constant$6(y == null ? 0 : +y);

    function force(alpha) {
      for (var i = 0, n = nodes.length, node; i < n; ++i) {
        node = nodes[i], node.vy += (yz[i] - node.y) * strengths[i] * alpha;
      }
    }

    function initialize() {
      if (!nodes) return;
      var i, n = nodes.length;
      strengths = new Array(n);
      yz = new Array(n);
      for (i = 0; i < n; ++i) {
        strengths[i] = isNaN(yz[i] = +y(nodes[i], i, nodes)) ? 0 : +strength(nodes[i], i, nodes);
      }
    }

    force.initialize = function(_) {
      nodes = _;
      initialize();
    };

    force.strength = function(_) {
      return arguments.length ? (strength = typeof _ === "function" ? _ : constant$6(+_), initialize(), force) : strength;
    };

    force.y = function(_) {
      return arguments.length ? (y = typeof _ === "function" ? _ : constant$6(+_), initialize(), force) : y;
    };

    return force;
  }

  function nopropagation() {
    exports.event.stopImmediatePropagation();
  }

  function noevent() {
    exports.event.preventDefault();
    exports.event.stopImmediatePropagation();
  }

  function dragDisable(view) {
    var root = view.document.documentElement,
        selection = select(view).on("dragstart.drag", noevent, true);
    if ("onselectstart" in root) {
      selection.on("selectstart.drag", noevent, true);
    } else {
      root.__noselect = root.style.MozUserSelect;
      root.style.MozUserSelect = "none";
    }
  }

  function dragEnable(view, noclick) {
    var root = view.document.documentElement,
        selection = select(view).on("dragstart.drag", null);
    if (noclick) {
      selection.on("click.drag", noevent, true);
      setTimeout(function() { selection.on("click.drag", null); }, 0);
    }
    if ("onselectstart" in root) {
      selection.on("selectstart.drag", null);
    } else {
      root.style.MozUserSelect = root.__noselect;
      delete root.__noselect;
    }
  }

  function constant$7(x) {
    return function() {
      return x;
    };
  }

  function DragEvent(target, type, subject, id, active, x, y, dx, dy, dispatch) {
    this.target = target;
    this.type = type;
    this.subject = subject;
    this.identifier = id;
    this.active = active;
    this.x = x;
    this.y = y;
    this.dx = dx;
    this.dy = dy;
    this._ = dispatch;
  }

  DragEvent.prototype.on = function() {
    var value = this._.on.apply(this._, arguments);
    return value === this._ ? this : value;
  };

  // Ignore right-click, since that should open the context menu.
  function defaultFilter() {
    return !exports.event.button;
  }

  function defaultContainer() {
    return this.parentNode;
  }

  function defaultSubject(d) {
    return d == null ? {x: exports.event.x, y: exports.event.y} : d;
  }

  function drag() {
    var filter = defaultFilter,
        container = defaultContainer,
        subject = defaultSubject,
        gestures = {},
        listeners = dispatch("start", "drag", "end"),
        active = 0,
        mousemoving,
        touchending;

    function drag(selection) {
      selection
          .on("mousedown.drag", mousedowned)
          .on("touchstart.drag", touchstarted)
          .on("touchmove.drag", touchmoved)
          .on("touchend.drag touchcancel.drag", touchended)
          .style("-webkit-tap-highlight-color", "rgba(0,0,0,0)");
    }

    function mousedowned() {
      if (touchending || !filter.apply(this, arguments)) return;
      var gesture = beforestart("mouse", container.apply(this, arguments), mouse, this, arguments);
      if (!gesture) return;
      select(exports.event.view).on("mousemove.drag", mousemoved, true).on("mouseup.drag", mouseupped, true);
      dragDisable(exports.event.view);
      nopropagation();
      mousemoving = false;
      gesture("start");
    }

    function mousemoved() {
      noevent();
      mousemoving = true;
      gestures.mouse("drag");
    }

    function mouseupped() {
      select(exports.event.view).on("mousemove.drag mouseup.drag", null);
      dragEnable(exports.event.view, mousemoving);
      noevent();
      gestures.mouse("end");
    }

    function touchstarted() {
      if (!filter.apply(this, arguments)) return;
      var touches = exports.event.changedTouches,
          c = container.apply(this, arguments),
          n = touches.length, i, gesture;

      for (i = 0; i < n; ++i) {
        if (gesture = beforestart(touches[i].identifier, c, touch, this, arguments)) {
          nopropagation();
          gesture("start");
        }
      }
    }

    function touchmoved() {
      var touches = exports.event.changedTouches,
          n = touches.length, i, gesture;

      for (i = 0; i < n; ++i) {
        if (gesture = gestures[touches[i].identifier]) {
          noevent();
          gesture("drag");
        }
      }
    }

    function touchended() {
      var touches = exports.event.changedTouches,
          n = touches.length, i, gesture;

      if (touchending) clearTimeout(touchending);
      touchending = setTimeout(function() { touchending = null; }, 500); // Ghost clicks are delayed!
      for (i = 0; i < n; ++i) {
        if (gesture = gestures[touches[i].identifier]) {
          nopropagation();
          gesture("end");
        }
      }
    }

    function beforestart(id, container, point, that, args) {
      var p = point(container, id), s, dx, dy,
          sublisteners = listeners.copy();

      if (!customEvent(new DragEvent(drag, "beforestart", s, id, active, p[0], p[1], 0, 0, sublisteners), function() {
        if ((exports.event.subject = s = subject.apply(that, args)) == null) return false;
        dx = s.x - p[0] || 0;
        dy = s.y - p[1] || 0;
        return true;
      })) return;

      return function gesture(type) {
        var p0 = p, n;
        switch (type) {
          case "start": gestures[id] = gesture, n = active++; break;
          case "end": delete gestures[id], --active; // nobreak
          case "drag": p = point(container, id), n = active; break;
        }
        customEvent(new DragEvent(drag, type, s, id, n, p[0] + dx, p[1] + dy, p[0] - p0[0], p[1] - p0[1], sublisteners), sublisteners.apply, sublisteners, [type, that, args]);
      };
    }

    drag.filter = function(_) {
      return arguments.length ? (filter = typeof _ === "function" ? _ : constant$7(!!_), drag) : filter;
    };

    drag.container = function(_) {
      return arguments.length ? (container = typeof _ === "function" ? _ : constant$7(_), drag) : container;
    };

    drag.subject = function(_) {
      return arguments.length ? (subject = typeof _ === "function" ? _ : constant$7(_), drag) : subject;
    };

    drag.on = function() {
      var value = listeners.on.apply(listeners, arguments);
      return value === listeners ? drag : value;
    };

    return drag;
  }

  function constant$8(x) {
    return function() {
      return x;
    };
  }

  function x$4(d) {
    return d[0];
  }

  function y$4(d) {
    return d[1];
  }

  function RedBlackTree() {
    this._ = null; // root node
  }

  function RedBlackNode(node) {
    node.U = // parent node
    node.C = // color - true for red, false for black
    node.L = // left node
    node.R = // right node
    node.P = // previous node
    node.N = null; // next node
  }

  RedBlackTree.prototype = {
    constructor: RedBlackTree,

    insert: function(after, node) {
      var parent, grandpa, uncle;

      if (after) {
        node.P = after;
        node.N = after.N;
        if (after.N) after.N.P = node;
        after.N = node;
        if (after.R) {
          after = after.R;
          while (after.L) after = after.L;
          after.L = node;
        } else {
          after.R = node;
        }
        parent = after;
      } else if (this._) {
        after = RedBlackFirst(this._);
        node.P = null;
        node.N = after;
        after.P = after.L = node;
        parent = after;
      } else {
        node.P = node.N = null;
        this._ = node;
        parent = null;
      }
      node.L = node.R = null;
      node.U = parent;
      node.C = true;

      after = node;
      while (parent && parent.C) {
        grandpa = parent.U;
        if (parent === grandpa.L) {
          uncle = grandpa.R;
          if (uncle && uncle.C) {
            parent.C = uncle.C = false;
            grandpa.C = true;
            after = grandpa;
          } else {
            if (after === parent.R) {
              RedBlackRotateLeft(this, parent);
              after = parent;
              parent = after.U;
            }
            parent.C = false;
            grandpa.C = true;
            RedBlackRotateRight(this, grandpa);
          }
        } else {
          uncle = grandpa.L;
          if (uncle && uncle.C) {
            parent.C = uncle.C = false;
            grandpa.C = true;
            after = grandpa;
          } else {
            if (after === parent.L) {
              RedBlackRotateRight(this, parent);
              after = parent;
              parent = after.U;
            }
            parent.C = false;
            grandpa.C = true;
            RedBlackRotateLeft(this, grandpa);
          }
        }
        parent = after.U;
      }
      this._.C = false;
    },

    remove: function(node) {
      if (node.N) node.N.P = node.P;
      if (node.P) node.P.N = node.N;
      node.N = node.P = null;

      var parent = node.U,
          sibling,
          left = node.L,
          right = node.R,
          next,
          red;

      if (!left) next = right;
      else if (!right) next = left;
      else next = RedBlackFirst(right);

      if (parent) {
        if (parent.L === node) parent.L = next;
        else parent.R = next;
      } else {
        this._ = next;
      }

      if (left && right) {
        red = next.C;
        next.C = node.C;
        next.L = left;
        left.U = next;
        if (next !== right) {
          parent = next.U;
          next.U = node.U;
          node = next.R;
          parent.L = node;
          next.R = right;
          right.U = next;
        } else {
          next.U = parent;
          parent = next;
          node = next.R;
        }
      } else {
        red = node.C;
        node = next;
      }

      if (node) node.U = parent;
      if (red) return;
      if (node && node.C) { node.C = false; return; }

      do {
        if (node === this._) break;
        if (node === parent.L) {
          sibling = parent.R;
          if (sibling.C) {
            sibling.C = false;
            parent.C = true;
            RedBlackRotateLeft(this, parent);
            sibling = parent.R;
          }
          if ((sibling.L && sibling.L.C)
              || (sibling.R && sibling.R.C)) {
            if (!sibling.R || !sibling.R.C) {
              sibling.L.C = false;
              sibling.C = true;
              RedBlackRotateRight(this, sibling);
              sibling = parent.R;
            }
            sibling.C = parent.C;
            parent.C = sibling.R.C = false;
            RedBlackRotateLeft(this, parent);
            node = this._;
            break;
          }
        } else {
          sibling = parent.L;
          if (sibling.C) {
            sibling.C = false;
            parent.C = true;
            RedBlackRotateRight(this, parent);
            sibling = parent.L;
          }
          if ((sibling.L && sibling.L.C)
            || (sibling.R && sibling.R.C)) {
            if (!sibling.L || !sibling.L.C) {
              sibling.R.C = false;
              sibling.C = true;
              RedBlackRotateLeft(this, sibling);
              sibling = parent.L;
            }
            sibling.C = parent.C;
            parent.C = sibling.L.C = false;
            RedBlackRotateRight(this, parent);
            node = this._;
            break;
          }
        }
        sibling.C = true;
        node = parent;
        parent = parent.U;
      } while (!node.C);

      if (node) node.C = false;
    }
  };

  function RedBlackRotateLeft(tree, node) {
    var p = node,
        q = node.R,
        parent = p.U;

    if (parent) {
      if (parent.L === p) parent.L = q;
      else parent.R = q;
    } else {
      tree._ = q;
    }

    q.U = parent;
    p.U = q;
    p.R = q.L;
    if (p.R) p.R.U = p;
    q.L = p;
  }

  function RedBlackRotateRight(tree, node) {
    var p = node,
        q = node.L,
        parent = p.U;

    if (parent) {
      if (parent.L === p) parent.L = q;
      else parent.R = q;
    } else {
      tree._ = q;
    }

    q.U = parent;
    p.U = q;
    p.L = q.R;
    if (p.L) p.L.U = p;
    q.R = p;
  }

  function RedBlackFirst(node) {
    while (node.L) node = node.L;
    return node;
  }

  function createEdge(left, right, v0, v1) {
    var edge = [null, null],
        index = edges.push(edge) - 1;
    edge.left = left;
    edge.right = right;
    if (v0) setEdgeEnd(edge, left, right, v0);
    if (v1) setEdgeEnd(edge, right, left, v1);
    cells[left.index].halfedges.push(index);
    cells[right.index].halfedges.push(index);
    return edge;
  }

  function createBorderEdge(left, v0, v1) {
    var edge = [v0, v1];
    edge.left = left;
    return edge;
  }

  function setEdgeEnd(edge, left, right, vertex) {
    if (!edge[0] && !edge[1]) {
      edge[0] = vertex;
      edge.left = left;
      edge.right = right;
    } else if (edge.left === right) {
      edge[1] = vertex;
    } else {
      edge[0] = vertex;
    }
  }

  // Liang–Barsky line clipping.
  function clipEdge(edge, x0, y0, x1, y1) {
    var a = edge[0],
        b = edge[1],
        ax = a[0],
        ay = a[1],
        bx = b[0],
        by = b[1],
        t0 = 0,
        t1 = 1,
        dx = bx - ax,
        dy = by - ay,
        r;

    r = x0 - ax;
    if (!dx && r > 0) return;
    r /= dx;
    if (dx < 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    } else if (dx > 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    }

    r = x1 - ax;
    if (!dx && r < 0) return;
    r /= dx;
    if (dx < 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    } else if (dx > 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    }

    r = y0 - ay;
    if (!dy && r > 0) return;
    r /= dy;
    if (dy < 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    } else if (dy > 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    }

    r = y1 - ay;
    if (!dy && r < 0) return;
    r /= dy;
    if (dy < 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    } else if (dy > 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    }

    if (!(t0 > 0) && !(t1 < 1)) return true; // TODO Better check?

    if (t0 > 0) edge[0] = [ax + t0 * dx, ay + t0 * dy];
    if (t1 < 1) edge[1] = [ax + t1 * dx, ay + t1 * dy];
    return true;
  }

  function connectEdge(edge, x0, y0, x1, y1) {
    var v1 = edge[1];
    if (v1) return true;

    var v0 = edge[0],
        left = edge.left,
        right = edge.right,
        lx = left[0],
        ly = left[1],
        rx = right[0],
        ry = right[1],
        fx = (lx + rx) / 2,
        fy = (ly + ry) / 2,
        fm,
        fb;

    if (ry === ly) {
      if (fx < x0 || fx >= x1) return;
      if (lx > rx) {
        if (!v0) v0 = [fx, y0];
        else if (v0[1] >= y1) return;
        v1 = [fx, y1];
      } else {
        if (!v0) v0 = [fx, y1];
        else if (v0[1] < y0) return;
        v1 = [fx, y0];
      }
    } else {
      fm = (lx - rx) / (ry - ly);
      fb = fy - fm * fx;
      if (fm < -1 || fm > 1) {
        if (lx > rx) {
          if (!v0) v0 = [(y0 - fb) / fm, y0];
          else if (v0[1] >= y1) return;
          v1 = [(y1 - fb) / fm, y1];
        } else {
          if (!v0) v0 = [(y1 - fb) / fm, y1];
          else if (v0[1] < y0) return;
          v1 = [(y0 - fb) / fm, y0];
        }
      } else {
        if (ly < ry) {
          if (!v0) v0 = [x0, fm * x0 + fb];
          else if (v0[0] >= x1) return;
          v1 = [x1, fm * x1 + fb];
        } else {
          if (!v0) v0 = [x1, fm * x1 + fb];
          else if (v0[0] < x0) return;
          v1 = [x0, fm * x0 + fb];
        }
      }
    }

    edge[0] = v0;
    edge[1] = v1;
    return true;
  }

  function clipEdges(x0, y0, x1, y1) {
    var i = edges.length,
        edge;

    while (i--) {
      if (!connectEdge(edge = edges[i], x0, y0, x1, y1)
          || !clipEdge(edge, x0, y0, x1, y1)
          || !(Math.abs(edge[0][0] - edge[1][0]) > epsilon$3
              || Math.abs(edge[0][1] - edge[1][1]) > epsilon$3)) {
        delete edges[i];
      }
    }
  }

  function createCell(site) {
    return cells[site.index] = {
      site: site,
      halfedges: []
    };
  }

  function cellHalfedgeAngle(cell, edge) {
    var site = cell.site,
        va = edge.left,
        vb = edge.right;
    if (site === vb) vb = va, va = site;
    if (vb) return Math.atan2(vb[1] - va[1], vb[0] - va[0]);
    if (site === va) va = edge[1], vb = edge[0];
    else va = edge[0], vb = edge[1];
    return Math.atan2(va[0] - vb[0], vb[1] - va[1]);
  }

  function cellHalfedgeStart(cell, edge) {
    return edge[+(edge.left !== cell.site)];
  }

  function cellHalfedgeEnd(cell, edge) {
    return edge[+(edge.left === cell.site)];
  }

  function sortCellHalfedges() {
    for (var i = 0, n = cells.length, cell, halfedges, j, m; i < n; ++i) {
      if ((cell = cells[i]) && (m = (halfedges = cell.halfedges).length)) {
        var index = new Array(m),
            array = new Array(m);
        for (j = 0; j < m; ++j) index[j] = j, array[j] = cellHalfedgeAngle(cell, edges[halfedges[j]]);
        index.sort(function(i, j) { return array[j] - array[i]; });
        for (j = 0; j < m; ++j) array[j] = halfedges[index[j]];
        for (j = 0; j < m; ++j) halfedges[j] = array[j];
      }
    }
  }

  function clipCells(x0, y0, x1, y1) {
    var nCells = cells.length,
        iCell,
        cell,
        site,
        iHalfedge,
        halfedges,
        nHalfedges,
        start,
        startX,
        startY,
        end,
        endX,
        endY,
        cover = true;

    for (iCell = 0; iCell < nCells; ++iCell) {
      if (cell = cells[iCell]) {
        site = cell.site;
        halfedges = cell.halfedges;
        iHalfedge = halfedges.length;

        // Remove any dangling clipped edges.
        while (iHalfedge--) {
          if (!edges[halfedges[iHalfedge]]) {
            halfedges.splice(iHalfedge, 1);
          }
        }

        // Insert any border edges as necessary.
        iHalfedge = 0, nHalfedges = halfedges.length;
        while (iHalfedge < nHalfedges) {
          end = cellHalfedgeEnd(cell, edges[halfedges[iHalfedge]]), endX = end[0], endY = end[1];
          start = cellHalfedgeStart(cell, edges[halfedges[++iHalfedge % nHalfedges]]), startX = start[0], startY = start[1];
          if (Math.abs(endX - startX) > epsilon$3 || Math.abs(endY - startY) > epsilon$3) {
            halfedges.splice(iHalfedge, 0, edges.push(createBorderEdge(site, end,
                Math.abs(endX - x0) < epsilon$3 && y1 - endY > epsilon$3 ? [x0, Math.abs(startX - x0) < epsilon$3 ? startY : y1]
                : Math.abs(endY - y1) < epsilon$3 && x1 - endX > epsilon$3 ? [Math.abs(startY - y1) < epsilon$3 ? startX : x1, y1]
                : Math.abs(endX - x1) < epsilon$3 && endY - y0 > epsilon$3 ? [x1, Math.abs(startX - x1) < epsilon$3 ? startY : y0]
                : Math.abs(endY - y0) < epsilon$3 && endX - x0 > epsilon$3 ? [Math.abs(startY - y0) < epsilon$3 ? startX : x0, y0]
                : null)) - 1);
            ++nHalfedges;
          }
        }

        if (nHalfedges) cover = false;
      }
    }

    // If there weren’t any edges, have the closest site cover the extent.
    // It doesn’t matter which corner of the extent we measure!
    if (cover) {
      var dx, dy, d2, dc = Infinity;

      for (iCell = 0, cover = null; iCell < nCells; ++iCell) {
        if (cell = cells[iCell]) {
          site = cell.site;
          dx = site[0] - x0;
          dy = site[1] - y0;
          d2 = dx * dx + dy * dy;
          if (d2 < dc) dc = d2, cover = cell;
        }
      }

      if (cover) {
        var v00 = [x0, y0], v01 = [x0, y1], v11 = [x1, y1], v10 = [x1, y0];
        cover.halfedges.push(
          edges.push(createBorderEdge(site = cover.site, v00, v01)) - 1,
          edges.push(createBorderEdge(site, v01, v11)) - 1,
          edges.push(createBorderEdge(site, v11, v10)) - 1,
          edges.push(createBorderEdge(site, v10, v00)) - 1
        );
      }
    }

    // Lastly delete any cells with no edges; these were entirely clipped.
    for (iCell = 0; iCell < nCells; ++iCell) {
      if (cell = cells[iCell]) {
        if (!cell.halfedges.length) {
          delete cells[iCell];
        }
      }
    }
  }

  var circlePool = [];

  var firstCircle;

  function Circle() {
    RedBlackNode(this);
    this.x =
    this.y =
    this.arc =
    this.site =
    this.cy = null;
  }

  function attachCircle(arc) {
    var lArc = arc.P,
        rArc = arc.N;

    if (!lArc || !rArc) return;

    var lSite = lArc.site,
        cSite = arc.site,
        rSite = rArc.site;

    if (lSite === rSite) return;

    var bx = cSite[0],
        by = cSite[1],
        ax = lSite[0] - bx,
        ay = lSite[1] - by,
        cx = rSite[0] - bx,
        cy = rSite[1] - by;

    var d = 2 * (ax * cy - ay * cx);
    if (d >= -epsilon2$1) return;

    var ha = ax * ax + ay * ay,
        hc = cx * cx + cy * cy,
        x = (cy * ha - ay * hc) / d,
        y = (ax * hc - cx * ha) / d;

    var circle = circlePool.pop() || new Circle;
    circle.arc = arc;
    circle.site = cSite;
    circle.x = x + bx;
    circle.y = (circle.cy = y + by) + Math.sqrt(x * x + y * y); // y bottom

    arc.circle = circle;

    var before = null,
        node = circles._;

    while (node) {
      if (circle.y < node.y || (circle.y === node.y && circle.x <= node.x)) {
        if (node.L) node = node.L;
        else { before = node.P; break; }
      } else {
        if (node.R) node = node.R;
        else { before = node; break; }
      }
    }

    circles.insert(before, circle);
    if (!before) firstCircle = circle;
  }

  function detachCircle(arc) {
    var circle = arc.circle;
    if (circle) {
      if (!circle.P) firstCircle = circle.N;
      circles.remove(circle);
      circlePool.push(circle);
      RedBlackNode(circle);
      arc.circle = null;
    }
  }

  var beachPool = [];

  function Beach() {
    RedBlackNode(this);
    this.edge =
    this.site =
    this.circle = null;
  }

  function createBeach(site) {
    var beach = beachPool.pop() || new Beach;
    beach.site = site;
    return beach;
  }

  function detachBeach(beach) {
    detachCircle(beach);
    beaches.remove(beach);
    beachPool.push(beach);
    RedBlackNode(beach);
  }

  function removeBeach(beach) {
    var circle = beach.circle,
        x = circle.x,
        y = circle.cy,
        vertex = [x, y],
        previous = beach.P,
        next = beach.N,
        disappearing = [beach];

    detachBeach(beach);

    var lArc = previous;
    while (lArc.circle
        && Math.abs(x - lArc.circle.x) < epsilon$3
        && Math.abs(y - lArc.circle.cy) < epsilon$3) {
      previous = lArc.P;
      disappearing.unshift(lArc);
      detachBeach(lArc);
      lArc = previous;
    }

    disappearing.unshift(lArc);
    detachCircle(lArc);

    var rArc = next;
    while (rArc.circle
        && Math.abs(x - rArc.circle.x) < epsilon$3
        && Math.abs(y - rArc.circle.cy) < epsilon$3) {
      next = rArc.N;
      disappearing.push(rArc);
      detachBeach(rArc);
      rArc = next;
    }

    disappearing.push(rArc);
    detachCircle(rArc);

    var nArcs = disappearing.length,
        iArc;
    for (iArc = 1; iArc < nArcs; ++iArc) {
      rArc = disappearing[iArc];
      lArc = disappearing[iArc - 1];
      setEdgeEnd(rArc.edge, lArc.site, rArc.site, vertex);
    }

    lArc = disappearing[0];
    rArc = disappearing[nArcs - 1];
    rArc.edge = createEdge(lArc.site, rArc.site, null, vertex);

    attachCircle(lArc);
    attachCircle(rArc);
  }

  function addBeach(site) {
    var x = site[0],
        directrix = site[1],
        lArc,
        rArc,
        dxl,
        dxr,
        node = beaches._;

    while (node) {
      dxl = leftBreakPoint(node, directrix) - x;
      if (dxl > epsilon$3) node = node.L; else {
        dxr = x - rightBreakPoint(node, directrix);
        if (dxr > epsilon$3) {
          if (!node.R) {
            lArc = node;
            break;
          }
          node = node.R;
        } else {
          if (dxl > -epsilon$3) {
            lArc = node.P;
            rArc = node;
          } else if (dxr > -epsilon$3) {
            lArc = node;
            rArc = node.N;
          } else {
            lArc = rArc = node;
          }
          break;
        }
      }
    }

    createCell(site);
    var newArc = createBeach(site);
    beaches.insert(lArc, newArc);

    if (!lArc && !rArc) return;

    if (lArc === rArc) {
      detachCircle(lArc);
      rArc = createBeach(lArc.site);
      beaches.insert(newArc, rArc);
      newArc.edge = rArc.edge = createEdge(lArc.site, newArc.site);
      attachCircle(lArc);
      attachCircle(rArc);
      return;
    }

    if (!rArc) { // && lArc
      newArc.edge = createEdge(lArc.site, newArc.site);
      return;
    }

    // else lArc !== rArc
    detachCircle(lArc);
    detachCircle(rArc);

    var lSite = lArc.site,
        ax = lSite[0],
        ay = lSite[1],
        bx = site[0] - ax,
        by = site[1] - ay,
        rSite = rArc.site,
        cx = rSite[0] - ax,
        cy = rSite[1] - ay,
        d = 2 * (bx * cy - by * cx),
        hb = bx * bx + by * by,
        hc = cx * cx + cy * cy,
        vertex = [(cy * hb - by * hc) / d + ax, (bx * hc - cx * hb) / d + ay];

    setEdgeEnd(rArc.edge, lSite, rSite, vertex);
    newArc.edge = createEdge(lSite, site, null, vertex);
    rArc.edge = createEdge(site, rSite, null, vertex);
    attachCircle(lArc);
    attachCircle(rArc);
  }

  function leftBreakPoint(arc, directrix) {
    var site = arc.site,
        rfocx = site[0],
        rfocy = site[1],
        pby2 = rfocy - directrix;

    if (!pby2) return rfocx;

    var lArc = arc.P;
    if (!lArc) return -Infinity;

    site = lArc.site;
    var lfocx = site[0],
        lfocy = site[1],
        plby2 = lfocy - directrix;

    if (!plby2) return lfocx;

    var hl = lfocx - rfocx,
        aby2 = 1 / pby2 - 1 / plby2,
        b = hl / plby2;

    if (aby2) return (-b + Math.sqrt(b * b - 2 * aby2 * (hl * hl / (-2 * plby2) - lfocy + plby2 / 2 + rfocy - pby2 / 2))) / aby2 + rfocx;

    return (rfocx + lfocx) / 2;
  }

  function rightBreakPoint(arc, directrix) {
    var rArc = arc.N;
    if (rArc) return leftBreakPoint(rArc, directrix);
    var site = arc.site;
    return site[1] === directrix ? site[0] : Infinity;
  }

  var epsilon$3 = 1e-6;
  var epsilon2$1 = 1e-12;
  var beaches;
  var cells;
  var circles;
  var edges;

  function triangleArea(a, b, c) {
    return (a[0] - c[0]) * (b[1] - a[1]) - (a[0] - b[0]) * (c[1] - a[1]);
  }

  function lexicographic(a, b) {
    return b[1] - a[1]
        || b[0] - a[0];
  }

  function Diagram(sites, extent) {
    var site = sites.sort(lexicographic).pop(),
        x,
        y,
        circle;

    edges = [];
    cells = new Array(sites.length);
    beaches = new RedBlackTree;
    circles = new RedBlackTree;

    while (true) {
      circle = firstCircle;
      if (site && (!circle || site[1] < circle.y || (site[1] === circle.y && site[0] < circle.x))) {
        if (site[0] !== x || site[1] !== y) {
          addBeach(site);
          x = site[0], y = site[1];
        }
        site = sites.pop();
      } else if (circle) {
        removeBeach(circle.arc);
      } else {
        break;
      }
    }

    sortCellHalfedges();

    if (extent) {
      var x0 = +extent[0][0],
          y0 = +extent[0][1],
          x1 = +extent[1][0],
          y1 = +extent[1][1];
      clipEdges(x0, y0, x1, y1);
      clipCells(x0, y0, x1, y1);
    }

    this.edges = edges;
    this.cells = cells;

    beaches =
    circles =
    edges =
    cells = null;
  }

  Diagram.prototype = {
    constructor: Diagram,

    polygons: function() {
      var edges = this.edges;

      return this.cells.map(function(cell) {
        var polygon = cell.halfedges.map(function(i) { return cellHalfedgeStart(cell, edges[i]); });
        polygon.data = cell.site.data;
        return polygon;
      });
    },

    triangles: function() {
      var triangles = [],
          edges = this.edges;

      this.cells.forEach(function(cell, i) {
        var site = cell.site,
            halfedges = cell.halfedges,
            j = -1,
            m = halfedges.length,
            s0,
            e1 = edges[halfedges[m - 1]],
            s1 = e1.left === site ? e1.right : e1.left;

        while (++j < m) {
          s0 = s1;
          e1 = edges[halfedges[j]];
          s1 = e1.left === site ? e1.right : e1.left;
          if (i < s0.index && i < s1.index && triangleArea(site, s0, s1) < 0) {
            triangles.push([site.data, s0.data, s1.data]);
          }
        }
      });

      return triangles;
    },

    links: function() {
      return this.edges.filter(function(edge) {
        return edge.right;
      }).map(function(edge) {
        return {
          source: edge.left.data,
          target: edge.right.data
        };
      });
    }
  }

  function voronoi() {
    var x = x$4,
        y = y$4,
        extent = null;

    function voronoi(data) {
      return new Diagram(data.map(function(d, i) {
        var s = [Math.round(x(d, i, data) / epsilon$3) * epsilon$3, Math.round(y(d, i, data) / epsilon$3) * epsilon$3];
        s.index = i;
        s.data = d;
        return s;
      }), extent);
    }

    voronoi.polygons = function(data) {
      return voronoi(data).polygons();
    };

    voronoi.links = function(data) {
      return voronoi(data).links();
    };

    voronoi.triangles = function(data) {
      return voronoi(data).triangles();
    };

    voronoi.x = function(_) {
      return arguments.length ? (x = typeof _ === "function" ? _ : constant$8(+_), voronoi) : x;
    };

    voronoi.y = function(_) {
      return arguments.length ? (y = typeof _ === "function" ? _ : constant$8(+_), voronoi) : y;
    };

    voronoi.extent = function(_) {
      return arguments.length ? (extent = _ == null ? null : [[+_[0][0], +_[0][1]], [+_[1][0], +_[1][1]]], voronoi) : extent && [[extent[0][0], extent[0][1]], [extent[1][0], extent[1][1]]];
    };

    voronoi.size = function(_) {
      return arguments.length ? (extent = _ == null ? null : [[0, 0], [+_[0], +_[1]]], voronoi) : extent && [extent[1][0], extent[1][1]];
    };

    return voronoi;
  }

  function constant$9(x) {
    return function() {
      return x;
    };
  }

  function ZoomEvent(target, type, transform) {
    this.target = target;
    this.type = type;
    this.transform = transform;
  }

  function Transform(k, x, y) {
    this.k = k;
    this.x = x;
    this.y = y;
  }

  Transform.prototype = {
    constructor: Transform,
    scale: function(k) {
      return k === 1 ? this : new Transform(this.k * k, this.x, this.y);
    },
    translate: function(x, y) {
      return x === 0 & y === 0 ? this : new Transform(this.k, this.x + this.k * x, this.y + this.k * y);
    },
    apply: function(point) {
      return [point[0] * this.k + this.x, point[1] * this.k + this.y];
    },
    applyX: function(x) {
      return x * this.k + this.x;
    },
    applyY: function(y) {
      return y * this.k + this.y;
    },
    invert: function(location) {
      return [(location[0] - this.x) / this.k, (location[1] - this.y) / this.k];
    },
    invertX: function(x) {
      return (x - this.x) / this.k;
    },
    invertY: function(y) {
      return (y - this.y) / this.k;
    },
    rescaleX: function(x) {
      return x.copy().domain(x.range().map(this.invertX, this).map(x.invert, x));
    },
    rescaleY: function(y) {
      return y.copy().domain(y.range().map(this.invertY, this).map(y.invert, y));
    },
    toString: function() {
      return "translate(" + this.x + "," + this.y + ") scale(" + this.k + ")";
    }
  };

  var identity$6 = new Transform(1, 0, 0);

  transform.prototype = Transform.prototype;

  function transform(node) {
    return node.__zoom || identity$6;
  }

  function nopropagation$1() {
    exports.event.stopImmediatePropagation();
  }

  function noevent$1() {
    exports.event.preventDefault();
    exports.event.stopImmediatePropagation();
  }

  // Ignore right-click, since that should open the context menu.
  function defaultFilter$1() {
    return !exports.event.button;
  }

  function defaultExtent() {
    var e = this, w, h;
    if (e instanceof SVGElement) {
      e = e.ownerSVGElement || e;
      w = e.width.baseVal.value;
      h = e.height.baseVal.value;
    } else {
      w = e.clientWidth;
      h = e.clientHeight;
    }
    return [[0, 0], [w, h]];
  }

  function defaultTransform() {
    return this.__zoom || identity$6;
  }

  function zoom() {
    var filter = defaultFilter$1,
        extent = defaultExtent,
        k0 = 0,
        k1 = Infinity,
        x0 = -k1,
        x1 = k1,
        y0 = x0,
        y1 = x1,
        duration = 250,
        gestures = [],
        listeners = dispatch("start", "zoom", "end"),
        mousemoving,
        mousePoint,
        mouseLocation,
        touchstarting,
        touchending,
        touchDelay = 500,
        wheelTimer,
        wheelDelay = 150;

    function zoom(selection) {
      selection
          .on("wheel.zoom", wheeled)
          .on("mousedown.zoom", mousedowned)
          .on("dblclick.zoom", dblclicked)
          .on("touchstart.zoom", touchstarted)
          .on("touchmove.zoom", touchmoved)
          .on("touchend.zoom touchcancel.zoom", touchended)
          .style("-webkit-tap-highlight-color", "rgba(0,0,0,0)")
          .property("__zoom", defaultTransform);
    }

    zoom.transform = function(collection, transform) {
      var selection = collection.selection ? collection.selection() : collection;
      selection.property("__zoom", defaultTransform);
      if (collection !== selection) {
        schedule(collection, transform);
      } else {
        selection.interrupt().each(function() {
          gesture(this, arguments)
              .start()
              .zoom(null, typeof transform === "function" ? transform.apply(this, arguments) : transform)
              .end();
        });
      }
    };

    zoom.scaleBy = function(selection, k) {
      zoom.scaleTo(selection, function() {
        var k0 = this.__zoom.k,
            k1 = typeof k === "function" ? k.apply(this, arguments) : k;
        return k0 * k1;
      });
    };

    zoom.scaleTo = function(selection, k) {
      zoom.transform(selection, function() {
        var e = extent.apply(this, arguments),
            t0 = this.__zoom,
            p0 = centroid(e),
            p1 = t0.invert(p0),
            k1 = typeof k === "function" ? k.apply(this, arguments) : k;
        return constrain(translate(scale(t0, k1), p0, p1), e);
      });
    };

    zoom.translateBy = function(selection, x, y) {
      zoom.transform(selection, function() {
        return constrain(this.__zoom.translate(
          typeof x === "function" ? x.apply(this, arguments) : x,
          typeof y === "function" ? y.apply(this, arguments) : y
        ), extent.apply(this, arguments));
      });
    };

    function scale(transform, k) {
      k = Math.max(k0, Math.min(k1, k));
      return k === transform.k ? transform : new Transform(k, transform.x, transform.y);
    }

    function translate(transform, p0, p1) {
      var x = p0[0] - p1[0] * transform.k, y = p0[1] - p1[1] * transform.k;
      return x === transform.x && y === transform.y ? transform : new Transform(transform.k, x, y);
    }

    function constrain(transform, extent) {
      var dx = Math.min(0, transform.invertX(extent[0][0]) - x0) || Math.max(0, transform.invertX(extent[1][0]) - x1),
          dy = Math.min(0, transform.invertY(extent[0][1]) - y0) || Math.max(0, transform.invertY(extent[1][1]) - y1);
      return dx || dy ? transform.translate(dx, dy) : transform;
    }

    function centroid(extent) {
      return [(+extent[0][0] + +extent[1][0]) / 2, (+extent[0][1] + +extent[1][1]) / 2];
    }

    function schedule(transition, transform, center) {
      transition
          .on("start.zoom", function() { gesture(this, arguments).start(); })
          .on("interrupt.zoom end.zoom", function() { gesture(this, arguments).end(); })
          .tween("zoom", function() {
            var that = this,
                args = arguments,
                g = gesture(that, args),
                e = extent.apply(that, args),
                p = center || centroid(e),
                w = Math.max(e[1][0] - e[0][0], e[1][1] - e[0][1]),
                a = that.__zoom,
                b = typeof transform === "function" ? transform.apply(that, args) : transform,
                i = interpolateZoom(a.invert(p).concat(w / a.k), b.invert(p).concat(w / b.k));
            return function(t) {
              if (t === 1) t = b; // Avoid rounding error on end.
              else { var l = i(t), k = w / l[2]; t = new Transform(k, p[0] - l[0] * k, p[1] - l[1] * k); }
              g.zoom(null, t);
            };
          });
    }

    function gesture(that, args) {
      for (var i = 0, n = gestures.length, g; i < n; ++i) {
        if ((g = gestures[i]).that === that) {
          return g;
        }
      }
      return new Gesture(that, args);
    }

    function Gesture(that, args) {
      this.that = that;
      this.args = args;
      this.index = -1;
      this.active = 0;
    }

    Gesture.prototype = {
      start: function() {
        if (++this.active === 1) {
          this.index = gestures.push(this) - 1;
          this.emit("start");
        }
        return this;
      },
      zoom: function(key, transform) {
        if (mousePoint && key !== "mouse") mouseLocation = transform.invert(mousePoint);
        if (this.touch0 && key !== "touch") this.touch0[1] = transform.invert(this.touch0[0]);
        if (this.touch1 && key !== "touch") this.touch1[1] = transform.invert(this.touch1[0]);
        this.that.__zoom = transform;
        this.emit("zoom");
        return this;
      },
      end: function() {
        if (--this.active === 0) {
          gestures.splice(this.index, 1);
          mousePoint = mouseLocation = null;
          this.index = -1;
          this.emit("end");
        }
        return this;
      },
      emit: function(type) {
        customEvent(new ZoomEvent(zoom, type, this.that.__zoom), listeners.apply, listeners, [type, this.that, this.args]);
      }
    };

    function wheeled() {
      if (!filter.apply(this, arguments)) return;
      var g = gesture(this, arguments),
          t = this.__zoom,
          k = Math.max(k0, Math.min(k1, t.k * Math.pow(2, -exports.event.deltaY * (exports.event.deltaMode ? 120 : 1) / 500)));

      // If the mouse is in the same location as before, reuse it.
      // If there were recent wheel events, reset the wheel idle timeout.
      if (wheelTimer) {
        var point = mouse(this);
        if (mousePoint[0] !== point[0] || mousePoint[1] !== point[1]) {
          mouseLocation = t.invert(mousePoint = point);
        }
        clearTimeout(wheelTimer);
      }

      // If this wheel event won’t trigger a transform change, ignore it.
      else if (t.k === k) return;

      // Otherwise, capture the mouse point and location at the start.
      else {
        g.extent = extent.apply(this, arguments);
        mouseLocation = t.invert(mousePoint = mouse(this));
        interrupt(this);
        g.start();
      }

      noevent$1();
      wheelTimer = setTimeout(wheelidled, wheelDelay);
      g.zoom("mouse", constrain(translate(scale(t, k), mousePoint, mouseLocation), g.extent));

      function wheelidled() {
        wheelTimer = null;
        g.end();
      }
    }

    function mousedowned() {
      if (touchending || !filter.apply(this, arguments)) return;
      var g = gesture(this, arguments),
          v = select(exports.event.view).on("mousemove.zoom", mousemoved, true).on("mouseup.zoom", mouseupped, true);

      dragDisable(exports.event.view);
      nopropagation$1();
      mousemoving = false;
      g.extent = extent.apply(this, arguments);
      mouseLocation = this.__zoom.invert(mousePoint = mouse(this));
      interrupt(this);
      g.start();

      function mousemoved() {
        noevent$1();
        mousemoving = true;
        g.zoom("mouse", constrain(translate(g.that.__zoom, mousePoint = mouse(g.that), mouseLocation), g.extent));
      }

      function mouseupped() {
        v.on("mousemove.zoom mouseup.zoom", null);
        dragEnable(exports.event.view, mousemoving);
        noevent$1();
        g.end();
      }
    }

    function dblclicked() {
      if (!filter.apply(this, arguments)) return;
      var t0 = this.__zoom,
          p0 = mouse(this),
          p1 = t0.invert(p0),
          k1 = t0.k * (exports.event.shiftKey ? 0.5 : 2),
          t1 = constrain(translate(scale(t0, k1), p0, p1), extent.apply(this, arguments));

      noevent$1();
      if (duration > 0) select(this).transition().duration(duration).call(schedule, t1, p0);
      else select(this).call(zoom.transform, t1);
    }

    function touchstarted() {
      if (!filter.apply(this, arguments)) return;
      var g = gesture(this, arguments),
          touches = exports.event.changedTouches,
          n = touches.length, i, t, p;

      nopropagation$1();
      for (i = 0; i < n; ++i) {
        t = touches[i], p = touch(this, touches, t.identifier);
        p = [p, this.__zoom.invert(p), t.identifier];
        if (!g.touch0) g.touch0 = p;
        else if (!g.touch1) g.touch1 = p;
      }
      if (touchstarting) {
        touchstarting = clearTimeout(touchstarting);
        if (!g.touch1) return g.end(), dblclicked.apply(this, arguments);
      }
      if (exports.event.touches.length === n) {
        touchstarting = setTimeout(function() { touchstarting = null; }, touchDelay);
        interrupt(this);
        g.extent = extent.apply(this, arguments);
        g.start();
      }
    }

    function touchmoved() {
      var g = gesture(this, arguments),
          touches = exports.event.changedTouches,
          n = touches.length, i, t, p, l;

      noevent$1();
      if (touchstarting) touchstarting = clearTimeout(touchstarting);
      for (i = 0; i < n; ++i) {
        t = touches[i], p = touch(this, touches, t.identifier);
        if (g.touch0 && g.touch0[2] === t.identifier) g.touch0[0] = p;
        else if (g.touch1 && g.touch1[2] === t.identifier) g.touch1[0] = p;
      }
      t = g.that.__zoom;
      if (g.touch1) {
        var p0 = g.touch0[0], l0 = g.touch0[1],
            p1 = g.touch1[0], l1 = g.touch1[1],
            dp = (dp = p1[0] - p0[0]) * dp + (dp = p1[1] - p0[1]) * dp,
            dl = (dl = l1[0] - l0[0]) * dl + (dl = l1[1] - l0[1]) * dl;
        t = scale(t, Math.sqrt(dp / dl));
        p = [(p0[0] + p1[0]) / 2, (p0[1] + p1[1]) / 2];
        l = [(l0[0] + l1[0]) / 2, (l0[1] + l1[1]) / 2];
      }
      else if (g.touch0) p = g.touch0[0], l = g.touch0[1];
      else return;
      g.zoom("touch", constrain(translate(t, p, l), g.extent));
    }

    function touchended() {
      var g = gesture(this, arguments),
          touches = exports.event.changedTouches,
          n = touches.length, i, t;

      nopropagation$1();
      if (touchending) clearTimeout(touchending);
      touchending = setTimeout(function() { touchending = null; }, touchDelay);
      for (i = 0; i < n; ++i) {
        t = touches[i];
        if (g.touch0 && g.touch0[2] === t.identifier) delete g.touch0;
        else if (g.touch1 && g.touch1[2] === t.identifier) delete g.touch1;
      }
      if (g.touch1 && !g.touch0) g.touch0 = g.touch1, delete g.touch1;
      if (!g.touch0) g.end();
    }

    zoom.filter = function(_) {
      return arguments.length ? (filter = typeof _ === "function" ? _ : constant$9(!!_), zoom) : filter;
    };

    zoom.extent = function(_) {
      return arguments.length ? (extent = typeof _ === "function" ? _ : constant$9([[+_[0][0], +_[0][1]], [+_[1][0], +_[1][1]]]), zoom) : extent;
    };

    zoom.scaleExtent = function(_) {
      return arguments.length ? (k0 = +_[0], k1 = +_[1], zoom) : [k0, k1];
    };

    zoom.translateExtent = function(_) {
      return arguments.length ? (x0 = +_[0][0], x1 = +_[1][0], y0 = +_[0][1], y1 = +_[1][1], zoom) : [[x0, y0], [x1, y1]];
    };

    zoom.duration = function(_) {
      return arguments.length ? (duration = +_, zoom) : duration;
    };

    zoom.on = function() {
      var value = listeners.on.apply(listeners, arguments);
      return value === listeners ? zoom : value;
    };

    return zoom;
  }

  function constant$10(x) {
    return function() {
      return x;
    };
  }

  function BrushEvent(target, type, selection) {
    this.target = target;
    this.type = type;
    this.selection = selection;
  }

  function nopropagation$2() {
    exports.event.stopImmediatePropagation();
  }

  function noevent$2() {
    exports.event.preventDefault();
    exports.event.stopImmediatePropagation();
  }

  var MODE_DRAG = {name: "drag"};
  var MODE_SPACE = {name: "space"};
  var MODE_HANDLE = {name: "handle"};
  var MODE_CENTER = {name: "center"};
  var X = {
    name: "x",
    handles: ["e", "w"].map(type$1),
    input: function(x, e) { return x && [[x[0], e[0][1]], [x[1], e[1][1]]]; },
    output: function(xy) { return xy && [xy[0][0], xy[1][0]]; }
  };

  var Y = {
    name: "y",
    handles: ["n", "s"].map(type$1),
    input: function(y, e) { return y && [[e[0][0], y[0]], [e[1][0], y[1]]]; },
    output: function(xy) { return xy && [xy[0][1], xy[1][1]]; }
  };

  var XY = {
    name: "xy",
    handles: ["n", "e", "s", "w", "nw", "ne", "se", "sw"].map(type$1),
    input: function(xy) { return xy; },
    output: function(xy) { return xy; }
  };

  var cursors = {
    overlay: "crosshair",
    selection: "move",
    n: "ns-resize",
    e: "ew-resize",
    s: "ns-resize",
    w: "ew-resize",
    nw: "nwse-resize",
    ne: "nesw-resize",
    se: "nwse-resize",
    sw: "nesw-resize"
  };

  var flipX = {
    e: "w",
    w: "e",
    nw: "ne",
    ne: "nw",
    se: "sw",
    sw: "se"
  };

  var flipY = {
    n: "s",
    s: "n",
    nw: "sw",
    ne: "se",
    se: "ne",
    sw: "nw"
  };

  var signsX = {
    overlay: +1,
    selection: +1,
    n: null,
    e: +1,
    s: null,
    w: -1,
    nw: -1,
    ne: +1,
    se: +1,
    sw: -1
  };

  var signsY = {
    overlay: +1,
    selection: +1,
    n: -1,
    e: null,
    s: +1,
    w: null,
    nw: -1,
    ne: -1,
    se: +1,
    sw: +1
  };

  function type$1(t) {
    return {type: t};
  }

  // Ignore right-click, since that should open the context menu.
  function defaultFilter$2() {
    return !exports.event.button;
  }

  function defaultExtent$1() {
    var svg = this.ownerSVGElement || this;
    return [[0, 0], [svg.width.baseVal.value, svg.height.baseVal.value]];
  }

  // Like d3.local, but with the name “__brush” rather than auto-generated.
  function local$1(node) {
    while (!node.__brush) if (!(node = node.parentNode)) return;
    return node.__brush;
  }

  function empty$1(extent) {
    return extent[0][0] === extent[1][0]
        || extent[0][1] === extent[1][1];
  }

  function brushSelection(node) {
    var state = node.__brush;
    return state ? state.dim.output(state.selection) : null;
  }

  function brushX() {
    return brush$1(X);
  }

  function brushY() {
    return brush$1(Y);
  }

  function brush() {
    return brush$1(XY);
  }

  function brush$1(dim) {
    var extent = defaultExtent$1,
        filter = defaultFilter$2,
        listeners = dispatch(brush, "start", "brush", "end"),
        handleSize = 6,
        touchending;

    function brush(group) {
      var overlay = group
          .property("__brush", initialize)
        .selectAll(".overlay")
        .data([type$1("overlay")]);

      overlay.enter().append("rect")
          .attr("class", "overlay")
          .attr("pointer-events", "all")
          .attr("cursor", cursors.overlay)
        .merge(overlay)
          .each(function() {
            var extent = local$1(this).extent;
            select(this)
                .attr("x", extent[0][0])
                .attr("y", extent[0][1])
                .attr("width", extent[1][0] - extent[0][0])
                .attr("height", extent[1][1] - extent[0][1]);
          });

      group.selectAll(".selection")
        .data([type$1("selection")])
        .enter().append("rect")
          .attr("class", "selection")
          .attr("cursor", cursors.selection)
          .attr("fill", "#777")
          .attr("fill-opacity", 0.3)
          .attr("stroke", "#fff")
          .attr("shape-rendering", "crispEdges");

      var handle = group.selectAll(".handle")
        .data(dim.handles, function(d) { return d.type; });

      handle.exit().remove();

      handle.enter().append("rect")
          .attr("class", function(d) { return "handle handle--" + d.type; })
          .attr("cursor", function(d) { return cursors[d.type]; });

      group
          .each(redraw)
          .attr("fill", "none")
          .attr("pointer-events", "all")
          .style("-webkit-tap-highlight-color", "rgba(0,0,0,0)")
          .on("mousedown.brush touchstart.brush", started);
    }

    brush.move = function(group, selection) {
      if (group.selection) {
        group
            .on("start.brush", function() { emitter(this, arguments).beforestart().start(); })
            .on("interrupt.brush end.brush", function() { emitter(this, arguments).end(); })
            .tween("brush", function() {
              var that = this,
                  state = that.__brush,
                  emit = emitter(that, arguments),
                  selection0 = state.selection,
                  selection1 = dim.input(typeof selection === "function" ? selection.apply(this, arguments) : selection, state.extent),
                  i = interpolate(selection0, selection1);

              function tween(t) {
                state.selection = t === 1 && empty$1(selection1) ? null : i(t);
                redraw.call(that);
                emit.brush();
              }

              return selection0 && selection1 ? tween : tween(1);
            });
      } else {
        group
            .each(function() {
              var that = this,
                  args = arguments,
                  state = that.__brush,
                  selection1 = dim.input(typeof selection === "function" ? selection.apply(that, args) : selection, state.extent),
                  emit = emitter(that, args).beforestart();

              interrupt(that);
              state.selection = selection1 == null || empty$1(selection1) ? null : selection1;
              redraw.call(that);
              emit.start().brush().end();
            });
      }
    };

    function redraw() {
      var group = select(this),
          selection = local$1(this).selection;

      if (selection) {
        group.selectAll(".selection")
            .style("display", null)
            .attr("x", selection[0][0])
            .attr("y", selection[0][1])
            .attr("width", selection[1][0] - selection[0][0])
            .attr("height", selection[1][1] - selection[0][1]);

        group.selectAll(".handle")
            .style("display", null)
            .attr("x", function(d) { return d.type[d.type.length - 1] === "e" ? selection[1][0] - handleSize / 2 : selection[0][0] - handleSize / 2; })
            .attr("y", function(d) { return d.type[0] === "s" ? selection[1][1] - handleSize / 2 : selection[0][1] - handleSize / 2; })
            .attr("width", function(d) { return d.type === "n" || d.type === "s" ? selection[1][0] - selection[0][0] + handleSize : handleSize; })
            .attr("height", function(d) { return d.type === "e" || d.type === "w" ? selection[1][1] - selection[0][1] + handleSize : handleSize; });
      }

      else {
        group.selectAll(".selection,.handle")
            .style("display", "none")
            .attr("x", null)
            .attr("y", null)
            .attr("width", null)
            .attr("height", null);
      }
    }

    function emitter(that, args) {
      return that.__brush.emitter || new Emitter(that, args);
    }

    function Emitter(that, args) {
      this.that = that;
      this.args = args;
      this.state = that.__brush;
      this.active = 0;
    }

    Emitter.prototype = {
      beforestart: function() {
        if (++this.active === 1) this.state.emitter = this, this.starting = true;
        return this;
      },
      start: function() {
        if (this.starting) this.starting = false, this.emit("start");
        return this;
      },
      brush: function() {
        this.emit("brush");
        return this;
      },
      end: function() {
        if (--this.active === 0) delete this.state.emitter, this.emit("end");
        return this;
      },
      emit: function(type) {
        customEvent(new BrushEvent(brush, type, dim.output(this.state.selection)), listeners.apply, listeners, [type, this.that, this.args]);
      }
    };

    function started() {
      if (exports.event.touches) { if (exports.event.changedTouches.length < exports.event.touches.length) return noevent$2(); }
      else if (touchending) return;
      if (!filter.apply(this, arguments)) return;

      var that = this,
          type = exports.event.target.__data__.type,
          mode = (exports.event.metaKey ? type = "overlay" : type) === "selection" ? MODE_DRAG : (exports.event.altKey ? MODE_CENTER : MODE_HANDLE),
          signX = dim === Y ? null : signsX[type],
          signY = dim === X ? null : signsY[type],
          state = local$1(that),
          extent = state.extent,
          selection = state.selection,
          W = extent[0][0], w0, w1,
          N = extent[0][1], n0, n1,
          E = extent[1][0], e0, e1,
          S = extent[1][1], s0, s1,
          dx,
          dy,
          moving,
          shifting = signX && signY && exports.event.shiftKey,
          lockX,
          lockY,
          point0 = mouse(that),
          point = point0,
          emit = emitter(that, arguments).beforestart();

      if (type === "overlay") {
        state.selection = selection = [
          [w0 = dim === Y ? W : point0[0], n0 = dim === X ? N : point0[1]],
          [e0 = dim === Y ? E : w0, s0 = dim === X ? S : n0]
        ];
      } else {
        w0 = selection[0][0];
        n0 = selection[0][1];
        e0 = selection[1][0];
        s0 = selection[1][1];
      }

      w1 = w0;
      n1 = n0;
      e1 = e0;
      s1 = s0;

      var group = select(that)
          .attr("pointer-events", "none");

      var overlay = group.selectAll(".overlay")
          .attr("cursor", cursors[type]);

      if (exports.event.touches) {
        group
            .on("touchmove.brush", moved, true)
            .on("touchend.brush touchcancel.brush", ended, true);
      } else {
        var view = select(exports.event.view)
            .on("keydown.brush", keydowned, true)
            .on("keyup.brush", keyupped, true)
            .on("mousemove.brush", moved, true)
            .on("mouseup.brush", ended, true);

        dragDisable(exports.event.view);
      }

      nopropagation$2();
      interrupt(that);
      redraw.call(that);
      emit.start();

      function moved() {
        var point1 = mouse(that);
        if (shifting && !lockX && !lockY) {
          if (Math.abs(point1[0] - point[0]) > Math.abs(point1[1] - point[1])) lockY = true;
          else lockX = true;
        }
        point = point1;
        moving = true;
        noevent$2();
        move();
      }

      function move() {
        var t;

        dx = point[0] - point0[0];
        dy = point[1] - point0[1];

        switch (mode) {
          case MODE_SPACE:
          case MODE_DRAG: {
            if (signX) dx = Math.max(W - w0, Math.min(E - e0, dx)), w1 = w0 + dx, e1 = e0 + dx;
            if (signY) dy = Math.max(N - n0, Math.min(S - s0, dy)), n1 = n0 + dy, s1 = s0 + dy;
            break;
          }
          case MODE_HANDLE: {
            if (signX < 0) dx = Math.max(W - w0, Math.min(E - w0, dx)), w1 = w0 + dx, e1 = e0;
            else if (signX > 0) dx = Math.max(W - e0, Math.min(E - e0, dx)), w1 = w0, e1 = e0 + dx;
            if (signY < 0) dy = Math.max(N - n0, Math.min(S - n0, dy)), n1 = n0 + dy, s1 = s0;
            else if (signY > 0) dy = Math.max(N - s0, Math.min(S - s0, dy)), n1 = n0, s1 = s0 + dy;
            break;
          }
          case MODE_CENTER: {
            if (signX) w1 = Math.max(W, Math.min(E, w0 - dx * signX)), e1 = Math.max(W, Math.min(E, e0 + dx * signX));
            if (signY) n1 = Math.max(N, Math.min(S, n0 - dy * signY)), s1 = Math.max(N, Math.min(S, s0 + dy * signY));
            break;
          }
        }

        if (e1 < w1) {
          signX *= -1;
          t = w0, w0 = e0, e0 = t;
          t = w1, w1 = e1, e1 = t;
          if (type in flipX) overlay.attr("cursor", cursors[type = flipX[type]]);
        }

        if (s1 < n1) {
          signY *= -1;
          t = n0, n0 = s0, s0 = t;
          t = n1, n1 = s1, s1 = t;
          if (type in flipY) overlay.attr("cursor", cursors[type = flipY[type]]);
        }

        selection = state.selection; // May be set by brush.move!

        if (lockX) w1 = selection[0][0], e1 = selection[1][0];
        if (lockY) n1 = selection[0][1], s1 = selection[1][1];

        if (selection[0][0] !== w1
            || selection[0][1] !== n1
            || selection[1][0] !== e1
            || selection[1][1] !== s1) {
          state.selection = [[w1, n1], [e1, s1]];
          redraw.call(that);
          emit.brush();
        }
      }

      function ended() {
        nopropagation$2();
        if (exports.event.touches) {
          if (exports.event.touches.length) return;
          if (touchending) clearTimeout(touchending);
          touchending = setTimeout(function() { touchending = null; }, 500); // Ghost clicks are delayed!
          group.on("touchmove.brush touchend.brush touchcancel.brush", null);
        } else {
          dragEnable(exports.event.view, moving);
          view.on("keydown.brush keyup.brush mousemove.brush mouseup.brush", null);
        }
        group.attr("pointer-events", "all");
        overlay.attr("cursor", cursors.overlay);
        if (empty$1(selection)) state.selection = null, redraw.call(that);
        emit.end();
      }

      function keydowned() {
        switch (exports.event.keyCode) {
          case 16: { // SHIFT
            shifting = signX && signY;
            break;
          }
          case 18: { // ALT
            if (mode === MODE_HANDLE) {
              if (signX) e0 = e1 - dx * signX, w0 = w1 + dx * signX;
              if (signY) s0 = s1 - dy * signY, n0 = n1 + dy * signY;
              mode = MODE_CENTER;
              move();
            }
            break;
          }
          case 32: { // SPACE; takes priority over ALT
            if (mode === MODE_HANDLE || mode === MODE_CENTER) {
              if (signX < 0) e0 = e1 - dx; else if (signX > 0) w0 = w1 - dx;
              if (signY < 0) s0 = s1 - dy; else if (signY > 0) n0 = n1 - dy;
              mode = MODE_SPACE;
              overlay.attr("cursor", cursors.selection);
              move();
            }
            break;
          }
          default: return;
        }
        noevent$2();
      }

      function keyupped() {
        switch (exports.event.keyCode) {
          case 16: { // SHIFT
            if (shifting) {
              lockX = lockY = shifting = false;
              move();
            }
            break;
          }
          case 18: { // ALT
            if (mode === MODE_CENTER) {
              if (signX < 0) e0 = e1; else if (signX > 0) w0 = w1;
              if (signY < 0) s0 = s1; else if (signY > 0) n0 = n1;
              mode = MODE_HANDLE;
              move();
            }
            break;
          }
          case 32: { // SPACE
            if (mode === MODE_SPACE) {
              if (exports.event.altKey) {
                if (signX) e0 = e1 - dx * signX, w0 = w1 + dx * signX;
                if (signY) s0 = s1 - dy * signY, n0 = n1 + dy * signY;
                mode = MODE_CENTER;
              } else {
                if (signX < 0) e0 = e1; else if (signX > 0) w0 = w1;
                if (signY < 0) s0 = s1; else if (signY > 0) n0 = n1;
                mode = MODE_HANDLE;
              }
              overlay.attr("cursor", cursors[type]);
              move();
            }
            break;
          }
          default: return;
        }
        noevent$2();
      }
    }

    function initialize() {
      var state = this.__brush || {selection: null};
      state.extent = extent.apply(this, arguments);
      state.dim = dim;
      return state;
    }

    brush.extent = function(_) {
      return arguments.length ? (extent = typeof _ === "function" ? _ : constant$10([[+_[0][0], +_[0][1]], [+_[1][0], +_[1][1]]]), brush) : extent;
    };

    brush.filter = function(_) {
      return arguments.length ? (filter = typeof _ === "function" ? _ : constant$10(!!_), brush) : filter;
    };

    brush.handleSize = function(_) {
      return arguments.length ? (handleSize = +_, brush) : handleSize;
    };

    brush.on = function() {
      var value = listeners.on.apply(listeners, arguments);
      return value === listeners ? brush : value;
    };

    return brush;
  }

  // Adds floating point numbers with twice the normal precision.
  // Reference: J. R. Shewchuk, Adaptive Precision Floating-Point Arithmetic and
  // Fast Robust Geometric Predicates, Discrete & Computational Geometry 18(3)
  // 305–363 (1997).
  // Code adapted from GeographicLib by Charles F. F. Karney,
  // http://geographiclib.sourceforge.net/

  function adder() {
    return new Adder;
  }

  function Adder() {
    this.reset();
  }

  Adder.prototype = {
    constructor: Adder,
    reset: function() {
      this.s = // rounded value
      this.t = 0; // exact error
    },
    add: function(y) {
      add$1(temp, y, this.t);
      add$1(this, temp.s, this.s);
      if (this.s) this.t += temp.t;
      else this.s = temp.t;
    },
    valueOf: function() {
      return this.s;
    }
  };

  var temp = new Adder;

  function add$1(adder, a, b) {
    var x = adder.s = a + b,
        bv = x - a,
        av = x - bv;
    adder.t = (a - av) + (b - bv);
  }

  var epsilon$4 = 1e-6;
  var epsilon2$2 = 1e-12;
  var pi$3 = Math.PI;
  var halfPi$2 = pi$3 / 2;
  var quarterPi = pi$3 / 4;
  var tau$3 = pi$3 * 2;

  var degrees$1 = 180 / pi$3;
  var radians = pi$3 / 180;

  var abs = Math.abs;
  var atan = Math.atan;
  var atan2 = Math.atan2;
  var cos = Math.cos;
  var ceil = Math.ceil;
  var exp = Math.exp;
  var log$1 = Math.log;
  var pow$1 = Math.pow;
  var sin = Math.sin;
  var sign$1 = Math.sign || function(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; };
  var sqrt$1 = Math.sqrt;
  var tan = Math.tan;

  function acos(x) {
    return x > 1 ? 0 : x < -1 ? pi$3 : Math.acos(x);
  }

  function asin$1(x) {
    return x > 1 ? halfPi$2 : x < -1 ? -halfPi$2 : Math.asin(x);
  }

  function haversin(x) {
    return (x = sin(x / 2)) * x;
  }

  function noop$2() {}

  function streamGeometry(geometry, stream) {
    if (geometry && streamGeometryType.hasOwnProperty(geometry.type)) {
      streamGeometryType[geometry.type](geometry, stream);
    }
  }

  var streamObjectType = {
    Feature: function(feature, stream) {
      streamGeometry(feature.geometry, stream);
    },
    FeatureCollection: function(object, stream) {
      var features = object.features, i = -1, n = features.length;
      while (++i < n) streamGeometry(features[i].geometry, stream);
    }
  };

  var streamGeometryType = {
    Sphere: function(object, stream) {
      stream.sphere();
    },
    Point: function(object, stream) {
      object = object.coordinates;
      stream.point(object[0], object[1], object[2]);
    },
    MultiPoint: function(object, stream) {
      var coordinates = object.coordinates, i = -1, n = coordinates.length;
      while (++i < n) object = coordinates[i], stream.point(object[0], object[1], object[2]);
    },
    LineString: function(object, stream) {
      streamLine(object.coordinates, stream, 0);
    },
    MultiLineString: function(object, stream) {
      var coordinates = object.coordinates, i = -1, n = coordinates.length;
      while (++i < n) streamLine(coordinates[i], stream, 0);
    },
    Polygon: function(object, stream) {
      streamPolygon(object.coordinates, stream);
    },
    MultiPolygon: function(object, stream) {
      var coordinates = object.coordinates, i = -1, n = coordinates.length;
      while (++i < n) streamPolygon(coordinates[i], stream);
    },
    GeometryCollection: function(object, stream) {
      var geometries = object.geometries, i = -1, n = geometries.length;
      while (++i < n) streamGeometry(geometries[i], stream);
    }
  };

  function streamLine(coordinates, stream, closed) {
    var i = -1, n = coordinates.length - closed, coordinate;
    stream.lineStart();
    while (++i < n) coordinate = coordinates[i], stream.point(coordinate[0], coordinate[1], coordinate[2]);
    stream.lineEnd();
  }

  function streamPolygon(coordinates, stream) {
    var i = -1, n = coordinates.length;
    stream.polygonStart();
    while (++i < n) streamLine(coordinates[i], stream, 1);
    stream.polygonEnd();
  }

  function stream(object, stream) {
    if (object && streamObjectType.hasOwnProperty(object.type)) {
      streamObjectType[object.type](object, stream);
    } else {
      streamGeometry(object, stream);
    }
  }

  var areaRingSum;

  var areaSum;
  var lambda00;
  var phi00;
  var lambda0;
  var cosPhi0;
  var sinPhi0;
  var areaStream = {
    point: noop$2,
    lineStart: noop$2,
    lineEnd: noop$2,
    polygonStart: function() {
      areaRingSum.reset();
      areaStream.lineStart = areaRingStart;
      areaStream.lineEnd = areaRingEnd;
    },
    polygonEnd: function() {
      var areaRing = +areaRingSum;
      areaSum.add(areaRing < 0 ? tau$3 + areaRing : areaRing);
      this.lineStart = this.lineEnd = this.point = noop$2;
    },
    sphere: function() {
      areaSum.add(tau$3);
    }
  };

  function areaRingStart() {
    areaStream.point = areaPointFirst;
  }

  function areaRingEnd() {
    areaPoint(lambda00, phi00);
  }

  function areaPointFirst(lambda, phi) {
    areaStream.point = areaPoint;
    lambda00 = lambda, phi00 = phi;
    lambda *= radians, phi *= radians;
    lambda0 = lambda, cosPhi0 = cos(phi = phi / 2 + quarterPi), sinPhi0 = sin(phi);
  }

  function areaPoint(lambda, phi) {
    lambda *= radians, phi *= radians;
    phi = phi / 2 + quarterPi; // half the angular distance from south pole

    // Spherical excess E for a spherical triangle with vertices: south pole,
    // previous point, current point.  Uses a formula derived from Cagnoli’s
    // theorem.  See Todhunter, Spherical Trig. (1871), Sec. 103, Eq. (2).
    var dLambda = lambda - lambda0,
        sdLambda = dLambda >= 0 ? 1 : -1,
        adLambda = sdLambda * dLambda,
        cosPhi = cos(phi),
        sinPhi = sin(phi),
        k = sinPhi0 * sinPhi,
        u = cosPhi0 * cosPhi + k * cos(adLambda),
        v = k * sdLambda * sin(adLambda);
    areaRingSum.add(atan2(v, u));

    // Advance the previous points.
    lambda0 = lambda, cosPhi0 = cosPhi, sinPhi0 = sinPhi;
  }

  function area$2(object) {
    if (areaSum) areaSum.reset();
    else areaSum = adder(), areaRingSum = adder();
    stream(object, areaStream);
    return areaSum * 2;
  }

  function spherical(cartesian) {
    return [atan2(cartesian[1], cartesian[0]), asin$1(cartesian[2])];
  }

  function cartesian(spherical) {
    var lambda = spherical[0], phi = spherical[1], cosPhi = cos(phi);
    return [cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi)];
  }

  function cartesianDot(a, b) {
    return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
  }

  function cartesianCross(a, b) {
    return [a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]];
  }

  // TODO return a
  function cartesianAddInPlace(a, b) {
    a[0] += b[0], a[1] += b[1], a[2] += b[2];
  }

  function cartesianScale(vector, k) {
    return [vector[0] * k, vector[1] * k, vector[2] * k];
  }

  // TODO return d
  function cartesianNormalizeInPlace(d) {
    var l = sqrt$1(d[0] * d[0] + d[1] * d[1] + d[2] * d[2]);
    d[0] /= l, d[1] /= l, d[2] /= l;
  }

var   lambda0$1;
  var phi0;
  var lambda1;
  var phi1;
  var lambda2;
var   lambda00$1;
var   phi00$1;
  var p0;
  var deltaSum;
  var ranges;
var   range$1;
  var boundsStream = {
    point: boundsPoint,
    lineStart: boundsLineStart,
    lineEnd: boundsLineEnd,
    polygonStart: function() {
      boundsStream.point = boundsRingPoint;
      boundsStream.lineStart = boundsRingStart;
      boundsStream.lineEnd = boundsRingEnd;
      deltaSum.reset();
      areaStream.polygonStart();
    },
    polygonEnd: function() {
      areaStream.polygonEnd();
      boundsStream.point = boundsPoint;
      boundsStream.lineStart = boundsLineStart;
      boundsStream.lineEnd = boundsLineEnd;
      if (areaRingSum < 0) lambda0$1 = -(lambda1 = 180), phi0 = -(phi1 = 90);
      else if (deltaSum > epsilon$4) phi1 = 90;
      else if (deltaSum < -epsilon$4) phi0 = -90;
      range$1[0] = lambda0$1, range$1[1] = lambda1;
    }
  };

  function boundsPoint(lambda, phi) {
    ranges.push(range$1 = [lambda0$1 = lambda, lambda1 = lambda]);
    if (phi < phi0) phi0 = phi;
    if (phi > phi1) phi1 = phi;
  }

  function linePoint(lambda, phi) {
    var p = cartesian([lambda * radians, phi * radians]);
    if (p0) {
      var normal = cartesianCross(p0, p),
          equatorial = [normal[1], -normal[0], 0],
          inflection = cartesianCross(equatorial, normal);
      cartesianNormalizeInPlace(inflection);
      inflection = spherical(inflection);
      var delta = lambda - lambda2,
          sign = delta > 0 ? 1 : -1,
          lambdai = inflection[0] * degrees$1 * sign,
          phii,
          antimeridian = abs(delta) > 180;
      if (antimeridian ^ (sign * lambda2 < lambdai && lambdai < sign * lambda)) {
        phii = inflection[1] * degrees$1;
        if (phii > phi1) phi1 = phii;
      } else if (lambdai = (lambdai + 360) % 360 - 180, antimeridian ^ (sign * lambda2 < lambdai && lambdai < sign * lambda)) {
        phii = -inflection[1] * degrees$1;
        if (phii < phi0) phi0 = phii;
      } else {
        if (phi < phi0) phi0 = phi;
        if (phi > phi1) phi1 = phi;
      }
      if (antimeridian) {
        if (lambda < lambda2) {
          if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda;
        } else {
          if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda;
        }
      } else {
        if (lambda1 >= lambda0$1) {
          if (lambda < lambda0$1) lambda0$1 = lambda;
          if (lambda > lambda1) lambda1 = lambda;
        } else {
          if (lambda > lambda2) {
            if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda;
          } else {
            if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda;
          }
        }
      }
    } else {
      boundsPoint(lambda, phi);
    }
    p0 = p, lambda2 = lambda;
  }

  function boundsLineStart() {
    boundsStream.point = linePoint;
  }

  function boundsLineEnd() {
    range$1[0] = lambda0$1, range$1[1] = lambda1;
    boundsStream.point = boundsPoint;
    p0 = null;
  }

  function boundsRingPoint(lambda, phi) {
    if (p0) {
      var delta = lambda - lambda2;
      deltaSum.add(abs(delta) > 180 ? delta + (delta > 0 ? 360 : -360) : delta);
    } else {
      lambda00$1 = lambda, phi00$1 = phi;
    }
    areaStream.point(lambda, phi);
    linePoint(lambda, phi);
  }

  function boundsRingStart() {
    areaStream.lineStart();
  }

  function boundsRingEnd() {
    boundsRingPoint(lambda00$1, phi00$1);
    areaStream.lineEnd();
    if (abs(deltaSum) > epsilon$4) lambda0$1 = -(lambda1 = 180);
    range$1[0] = lambda0$1, range$1[1] = lambda1;
    p0 = null;
  }

  // Finds the left-right distance between two longitudes.
  // This is almost the same as (lambda1 - lambda0 + 360°) % 360°, except that we want
  // the distance between ±180° to be 360°.
  function angle(lambda0, lambda1) {
    return (lambda1 -= lambda0) < 0 ? lambda1 + 360 : lambda1;
  }

  function rangeCompare(a, b) {
    return a[0] - b[0];
  }

  function rangeContains(range, x) {
    return range[0] <= range[1] ? range[0] <= x && x <= range[1] : x < range[0] || range[1] < x;
  }

  function bounds(feature) {
    var i, n, a, b, merged, deltaMax, delta;

    if (deltaSum) deltaSum.reset();
    else deltaSum = adder();
    phi1 = lambda1 = -(lambda0$1 = phi0 = Infinity);
    ranges = [];
    stream(feature, boundsStream);

    // First, sort ranges by their minimum longitudes.
    if (n = ranges.length) {
      ranges.sort(rangeCompare);

      // Then, merge any ranges that overlap.
      for (i = 1, a = ranges[0], merged = [a]; i < n; ++i) {
        b = ranges[i];
        if (rangeContains(a, b[0]) || rangeContains(a, b[1])) {
          if (angle(a[0], b[1]) > angle(a[0], a[1])) a[1] = b[1];
          if (angle(b[0], a[1]) > angle(a[0], a[1])) a[0] = b[0];
        } else {
          merged.push(a = b);
        }
      }

      // Finally, find the largest gap between the merged ranges.
      // The final bounding box will be the inverse of this gap.
      for (deltaMax = -Infinity, n = merged.length - 1, i = 0, a = merged[n]; i <= n; a = b, ++i) {
        b = merged[i];
        if ((delta = angle(a[1], b[0])) > deltaMax) deltaMax = delta, lambda0$1 = b[0], lambda1 = a[1];
      }
    }

    ranges = range$1 = null;

    return lambda0$1 === Infinity || phi0 === Infinity
        ? [[NaN, NaN], [NaN, NaN]]
        : [[lambda0$1, phi0], [lambda1, phi1]];
  }

  var W0;
  var W1;
  var X0;
  var Y0;
  var Z0;
  var X1;
  var Y1;
  var Z1;
  var X2;
  var Y2;
  var Z2;
var   lambda00$2;
var   phi00$2;
  var x0;
  var y0;
  var z0;
  // previous point

  var centroidStream = {
    sphere: noop$2,
    point: centroidPoint,
    lineStart: centroidLineStart,
    lineEnd: centroidLineEnd,
    polygonStart: function() {
      centroidStream.lineStart = centroidRingStart;
      centroidStream.lineEnd = centroidRingEnd;
    },
    polygonEnd: function() {
      centroidStream.lineStart = centroidLineStart;
      centroidStream.lineEnd = centroidLineEnd;
    }
  };

  // Arithmetic mean of Cartesian vectors.
  function centroidPoint(lambda, phi) {
    lambda *= radians, phi *= radians;
    var cosPhi = cos(phi);
    centroidPointCartesian(cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi));
  }

  function centroidPointCartesian(x, y, z) {
    ++W0;
    X0 += (x - X0) / W0;
    Y0 += (y - Y0) / W0;
    Z0 += (z - Z0) / W0;
  }

  function centroidLineStart() {
    centroidStream.point = centroidLinePointFirst;
  }

  function centroidLinePointFirst(lambda, phi) {
    lambda *= radians, phi *= radians;
    var cosPhi = cos(phi);
    x0 = cosPhi * cos(lambda);
    y0 = cosPhi * sin(lambda);
    z0 = sin(phi);
    centroidStream.point = centroidLinePoint;
    centroidPointCartesian(x0, y0, z0);
  }

  function centroidLinePoint(lambda, phi) {
    lambda *= radians, phi *= radians;
    var cosPhi = cos(phi),
        x = cosPhi * cos(lambda),
        y = cosPhi * sin(lambda),
        z = sin(phi),
        w = atan2(sqrt$1((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w), x0 * x + y0 * y + z0 * z);
    W1 += w;
    X1 += w * (x0 + (x0 = x));
    Y1 += w * (y0 + (y0 = y));
    Z1 += w * (z0 + (z0 = z));
    centroidPointCartesian(x0, y0, z0);
  }

  function centroidLineEnd() {
    centroidStream.point = centroidPoint;
  }

  // See J. E. Brock, The Inertia Tensor for a Spherical Triangle,
  // J. Applied Mechanics 42, 239 (1975).
  function centroidRingStart() {
    centroidStream.point = centroidRingPointFirst;
  }

  function centroidRingEnd() {
    centroidRingPoint(lambda00$2, phi00$2);
    centroidStream.point = centroidPoint;
  }

  function centroidRingPointFirst(lambda, phi) {
    lambda00$2 = lambda, phi00$2 = phi;
    lambda *= radians, phi *= radians;
    centroidStream.point = centroidRingPoint;
    var cosPhi = cos(phi);
    x0 = cosPhi * cos(lambda);
    y0 = cosPhi * sin(lambda);
    z0 = sin(phi);
    centroidPointCartesian(x0, y0, z0);
  }

  function centroidRingPoint(lambda, phi) {
    lambda *= radians, phi *= radians;
    var cosPhi = cos(phi),
        x = cosPhi * cos(lambda),
        y = cosPhi * sin(lambda),
        z = sin(phi),
        cx = y0 * z - z0 * y,
        cy = z0 * x - x0 * z,
        cz = x0 * y - y0 * x,
        m = sqrt$1(cx * cx + cy * cy + cz * cz),
        u = x0 * x + y0 * y + z0 * z,
        v = m && -acos(u) / m, // area weight
        w = atan2(m, u); // line weight
    X2 += v * cx;
    Y2 += v * cy;
    Z2 += v * cz;
    W1 += w;
    X1 += w * (x0 + (x0 = x));
    Y1 += w * (y0 + (y0 = y));
    Z1 += w * (z0 + (z0 = z));
    centroidPointCartesian(x0, y0, z0);
  }

  function centroid$1(object) {
    W0 = W1 =
    X0 = Y0 = Z0 =
    X1 = Y1 = Z1 =
    X2 = Y2 = Z2 = 0;
    stream(object, centroidStream);

    var x = X2,
        y = Y2,
        z = Z2,
        m = x * x + y * y + z * z;

    // If the area-weighted ccentroid is undefined, fall back to length-weighted ccentroid.
    if (m < epsilon2$2) {
      x = X1, y = Y1, z = Z1;
      // If the feature has zero length, fall back to arithmetic mean of point vectors.
      if (W1 < epsilon$4) x = X0, y = Y0, z = Z0;
      m = x * x + y * y + z * z;
      // If the feature still has an undefined ccentroid, then return.
      if (m < epsilon2$2) return [NaN, NaN];
    }

    return [atan2(y, x) * degrees$1, asin$1(z / sqrt$1(m)) * degrees$1];
  }

  function constant$11(x) {
    return function() {
      return x;
    };
  }

  function compose(a, b) {

    function compose(x, y) {
      return x = a(x, y), b(x[0], x[1]);
    }

    if (a.invert && b.invert) compose.invert = function(x, y) {
      return x = b.invert(x, y), x && a.invert(x[0], x[1]);
    };

    return compose;
  }

  function rotationIdentity(lambda, phi) {
    return [lambda > pi$3 ? lambda - tau$3 : lambda < -pi$3 ? lambda + tau$3 : lambda, phi];
  }

  rotationIdentity.invert = rotationIdentity;

  function rotateRadians(deltaLambda, deltaPhi, deltaGamma) {
    return (deltaLambda %= tau$3) ? (deltaPhi || deltaGamma ? compose(rotationLambda(deltaLambda), rotationPhiGamma(deltaPhi, deltaGamma))
      : rotationLambda(deltaLambda))
      : (deltaPhi || deltaGamma ? rotationPhiGamma(deltaPhi, deltaGamma)
      : rotationIdentity);
  }

  function forwardRotationLambda(deltaLambda) {
    return function(lambda, phi) {
      return lambda += deltaLambda, [lambda > pi$3 ? lambda - tau$3 : lambda < -pi$3 ? lambda + tau$3 : lambda, phi];
    };
  }

  function rotationLambda(deltaLambda) {
    var rotation = forwardRotationLambda(deltaLambda);
    rotation.invert = forwardRotationLambda(-deltaLambda);
    return rotation;
  }

  function rotationPhiGamma(deltaPhi, deltaGamma) {
    var cosDeltaPhi = cos(deltaPhi),
        sinDeltaPhi = sin(deltaPhi),
        cosDeltaGamma = cos(deltaGamma),
        sinDeltaGamma = sin(deltaGamma);

    function rotation(lambda, phi) {
      var cosPhi = cos(phi),
          x = cos(lambda) * cosPhi,
          y = sin(lambda) * cosPhi,
          z = sin(phi),
          k = z * cosDeltaPhi + x * sinDeltaPhi;
      return [
        atan2(y * cosDeltaGamma - k * sinDeltaGamma, x * cosDeltaPhi - z * sinDeltaPhi),
        asin$1(k * cosDeltaGamma + y * sinDeltaGamma)
      ];
    }

    rotation.invert = function(lambda, phi) {
      var cosPhi = cos(phi),
          x = cos(lambda) * cosPhi,
          y = sin(lambda) * cosPhi,
          z = sin(phi),
          k = z * cosDeltaGamma - y * sinDeltaGamma;
      return [
        atan2(y * cosDeltaGamma + z * sinDeltaGamma, x * cosDeltaPhi + k * sinDeltaPhi),
        asin$1(k * cosDeltaPhi - x * sinDeltaPhi)
      ];
    };

    return rotation;
  }

  function rotation(rotate) {
    rotate = rotateRadians(rotate[0] * radians, rotate[1] * radians, rotate.length > 2 ? rotate[2] * radians : 0);

    function forward(coordinates) {
      coordinates = rotate(coordinates[0] * radians, coordinates[1] * radians);
      return coordinates[0] *= degrees$1, coordinates[1] *= degrees$1, coordinates;
    }

    forward.invert = function(coordinates) {
      coordinates = rotate.invert(coordinates[0] * radians, coordinates[1] * radians);
      return coordinates[0] *= degrees$1, coordinates[1] *= degrees$1, coordinates;
    };

    return forward;
  }

  // Generates a circle centered at [0°, 0°], with a given radius and precision.
  function circleStream(stream, radius, delta, direction, t0, t1) {
    if (!delta) return;
    var cosRadius = cos(radius),
        sinRadius = sin(radius),
        step = direction * delta;
    if (t0 == null) {
      t0 = radius + direction * tau$3;
      t1 = radius - step / 2;
    } else {
      t0 = circleRadius(cosRadius, t0);
      t1 = circleRadius(cosRadius, t1);
      if (direction > 0 ? t0 < t1 : t0 > t1) t0 += direction * tau$3;
    }
    for (var point, t = t0; direction > 0 ? t > t1 : t < t1; t -= step) {
      point = spherical([cosRadius, -sinRadius * cos(t), -sinRadius * sin(t)]);
      stream.point(point[0], point[1]);
    }
  }

  // Returns the signed angle of a cartesian point relative to [cosRadius, 0, 0].
  function circleRadius(cosRadius, point) {
    point = cartesian(point), point[0] -= cosRadius;
    cartesianNormalizeInPlace(point);
    var radius = acos(-point[1]);
    return ((-point[2] < 0 ? -radius : radius) + tau$3 - epsilon$4) % tau$3;
  }

  function circle$1() {
    var center = constant$11([0, 0]),
        radius = constant$11(90),
        precision = constant$11(6),
        ring,
        rotate,
        stream = {point: point};

    function point(x, y) {
      ring.push(x = rotate(x, y));
      x[0] *= degrees$1, x[1] *= degrees$1;
    }

    function circle() {
      var c = center.apply(this, arguments),
          r = radius.apply(this, arguments) * radians,
          p = precision.apply(this, arguments) * radians;
      ring = [];
      rotate = rotateRadians(-c[0] * radians, -c[1] * radians, 0).invert;
      circleStream(stream, r, p, 1);
      c = {type: "Polygon", coordinates: [ring]};
      ring = rotate = null;
      return c;
    }

    circle.center = function(_) {
      return arguments.length ? (center = typeof _ === "function" ? _ : constant$11([+_[0], +_[1]]), circle) : center;
    };

    circle.radius = function(_) {
      return arguments.length ? (radius = typeof _ === "function" ? _ : constant$11(+_), circle) : radius;
    };

    circle.precision = function(_) {
      return arguments.length ? (precision = typeof _ === "function" ? _ : constant$11(+_), circle) : precision;
    };

    return circle;
  }

  function clipBuffer() {
    var lines = [],
        line;
    return {
      point: function(x, y) {
        line.push([x, y]);
      },
      lineStart: function() {
        lines.push(line = []);
      },
      lineEnd: noop$2,
      rejoin: function() {
        if (lines.length > 1) lines.push(lines.pop().concat(lines.shift()));
      },
      result: function() {
        var result = lines;
        lines = [];
        line = null;
        return result;
      }
    };
  }

  function clipLine(a, b, x0, y0, x1, y1) {
    var ax = a[0],
        ay = a[1],
        bx = b[0],
        by = b[1],
        t0 = 0,
        t1 = 1,
        dx = bx - ax,
        dy = by - ay,
        r;

    r = x0 - ax;
    if (!dx && r > 0) return;
    r /= dx;
    if (dx < 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    } else if (dx > 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    }

    r = x1 - ax;
    if (!dx && r < 0) return;
    r /= dx;
    if (dx < 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    } else if (dx > 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    }

    r = y0 - ay;
    if (!dy && r > 0) return;
    r /= dy;
    if (dy < 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    } else if (dy > 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    }

    r = y1 - ay;
    if (!dy && r < 0) return;
    r /= dy;
    if (dy < 0) {
      if (r > t1) return;
      if (r > t0) t0 = r;
    } else if (dy > 0) {
      if (r < t0) return;
      if (r < t1) t1 = r;
    }

    if (t0 > 0) a[0] = ax + t0 * dx, a[1] = ay + t0 * dy;
    if (t1 < 1) b[0] = ax + t1 * dx, b[1] = ay + t1 * dy;
    return true;
  }

  function pointEqual(a, b) {
    return abs(a[0] - b[0]) < epsilon$4 && abs(a[1] - b[1]) < epsilon$4;
  }

  function Intersection(point, points, other, entry) {
    this.x = point;
    this.z = points;
    this.o = other; // another intersection
    this.e = entry; // is an entry?
    this.v = false; // visited
    this.n = this.p = null; // next & previous
  }

  // A generalized polygon clipping algorithm: given a polygon that has been cut
  // into its visible line segments, and rejoins the segments by interpolating
  // along the clip edge.
  function clipPolygon(segments, compareIntersection, startInside, interpolate, stream) {
    var subject = [],
        clip = [],
        i,
        n;

    segments.forEach(function(segment) {
      if ((n = segment.length - 1) <= 0) return;
      var n, p0 = segment[0], p1 = segment[n], x;

      // If the first and last points of a segment are coincident, then treat as a
      // closed ring. TODO if all rings are closed, then the winding order of the
      // exterior ring should be checked.
      if (pointEqual(p0, p1)) {
        stream.lineStart();
        for (i = 0; i < n; ++i) stream.point((p0 = segment[i])[0], p0[1]);
        stream.lineEnd();
        return;
      }

      subject.push(x = new Intersection(p0, segment, null, true));
      clip.push(x.o = new Intersection(p0, null, x, false));
      subject.push(x = new Intersection(p1, segment, null, false));
      clip.push(x.o = new Intersection(p1, null, x, true));
    });

    if (!subject.length) return;

    clip.sort(compareIntersection);
    link$1(subject);
    link$1(clip);

    for (i = 0, n = clip.length; i < n; ++i) {
      clip[i].e = startInside = !startInside;
    }

    var start = subject[0],
        points,
        point;

    while (1) {
      // Find first unvisited intersection.
      var current = start,
          isSubject = true;
      while (current.v) if ((current = current.n) === start) return;
      points = current.z;
      stream.lineStart();
      do {
        current.v = current.o.v = true;
        if (current.e) {
          if (isSubject) {
            for (i = 0, n = points.length; i < n; ++i) stream.point((point = points[i])[0], point[1]);
          } else {
            interpolate(current.x, current.n.x, 1, stream);
          }
          current = current.n;
        } else {
          if (isSubject) {
            points = current.p.z;
            for (i = points.length - 1; i >= 0; --i) stream.point((point = points[i])[0], point[1]);
          } else {
            interpolate(current.x, current.p.x, -1, stream);
          }
          current = current.p;
        }
        current = current.o;
        points = current.z;
        isSubject = !isSubject;
      } while (!current.v);
      stream.lineEnd();
    }
  }

  function link$1(array) {
    if (!(n = array.length)) return;
    var n,
        i = 0,
        a = array[0],
        b;
    while (++i < n) {
      a.n = b = array[i];
      b.p = a;
      a = b;
    }
    a.n = b = array[0];
    b.p = a;
  }

  var clipMax = 1e9;
  var clipMin = -clipMax;
  // TODO Use d3-polygon’s polygonContains here for the ring check?
  // TODO Eliminate duplicate buffering in clipBuffer and polygon.push?

  function clipExtent(x0, y0, x1, y1) {

    function visible(x, y) {
      return x0 <= x && x <= x1 && y0 <= y && y <= y1;
    }

    function interpolate(from, to, direction, stream) {
      var a = 0, a1 = 0;
      if (from == null
          || (a = corner(from, direction)) !== (a1 = corner(to, direction))
          || comparePoint(from, to) < 0 ^ direction > 0) {
        do stream.point(a === 0 || a === 3 ? x0 : x1, a > 1 ? y1 : y0);
        while ((a = (a + direction + 4) % 4) !== a1);
      } else {
        stream.point(to[0], to[1]);
      }
    }

    function corner(p, direction) {
      return abs(p[0] - x0) < epsilon$4 ? direction > 0 ? 0 : 3
          : abs(p[0] - x1) < epsilon$4 ? direction > 0 ? 2 : 1
          : abs(p[1] - y0) < epsilon$4 ? direction > 0 ? 1 : 0
          : direction > 0 ? 3 : 2; // abs(p[1] - y1) < epsilon
    }

    function compareIntersection(a, b) {
      return comparePoint(a.x, b.x);
    }

    function comparePoint(a, b) {
      var ca = corner(a, 1),
          cb = corner(b, 1);
      return ca !== cb ? ca - cb
          : ca === 0 ? b[1] - a[1]
          : ca === 1 ? a[0] - b[0]
          : ca === 2 ? a[1] - b[1]
          : b[0] - a[0];
    }

    return function(stream) {
      var activeStream = stream,
          bufferStream = clipBuffer(),
          segments,
          polygon,
          ring,
          x__, y__, v__, // first point
          x_, y_, v_, // previous point
          first,
          clean;

      var clipStream = {
        point: point,
        lineStart: lineStart,
        lineEnd: lineEnd,
        polygonStart: polygonStart,
        polygonEnd: polygonEnd
      };

      function point(x, y) {
        if (visible(x, y)) activeStream.point(x, y);
      }

      function polygonInside() {
        var winding = 0;

        for (var i = 0, n = polygon.length; i < n; ++i) {
          for (var ring = polygon[i], j = 1, m = ring.length, point = ring[0], a0, a1, b0 = point[0], b1 = point[1]; j < m; ++j) {
            a0 = b0, a1 = b1, point = ring[j], b0 = point[0], b1 = point[1];
            if (a1 <= y1) { if (b1 > y1 && (b0 - a0) * (y1 - a1) > (b1 - a1) * (x0 - a0)) ++winding; }
            else { if (b1 <= y1 && (b0 - a0) * (y1 - a1) < (b1 - a1) * (x0 - a0)) --winding; }
          }
        }

        return winding;
      }

      // Buffer geometry within a polygon and then clip it en masse.
      function polygonStart() {
        activeStream = bufferStream, segments = [], polygon = [], clean = true;
      }

      function polygonEnd() {
        var startInside = polygonInside(),
            cleanInside = clean && startInside,
            visible = (segments = merge(segments)).length;
        if (cleanInside || visible) {
          stream.polygonStart();
          if (cleanInside) {
            stream.lineStart();
            interpolate(null, null, 1, stream);
            stream.lineEnd();
          }
          if (visible) {
            clipPolygon(segments, compareIntersection, startInside, interpolate, stream);
          }
          stream.polygonEnd();
        }
        activeStream = stream, segments = polygon = ring = null;
      }

      function lineStart() {
        clipStream.point = linePoint;
        if (polygon) polygon.push(ring = []);
        first = true;
        v_ = false;
        x_ = y_ = NaN;
      }

      // TODO rather than special-case polygons, simply handle them separately.
      // Ideally, coincident intersection points should be jittered to avoid
      // clipping issues.
      function lineEnd() {
        if (segments) {
          linePoint(x__, y__);
          if (v__ && v_) bufferStream.rejoin();
          segments.push(bufferStream.result());
        }
        clipStream.point = point;
        if (v_) activeStream.lineEnd();
      }

      function linePoint(x, y) {
        var v = visible(x, y);
        if (polygon) ring.push([x, y]);
        if (first) {
          x__ = x, y__ = y, v__ = v;
          first = false;
          if (v) {
            activeStream.lineStart();
            activeStream.point(x, y);
          }
        } else {
          if (v && v_) activeStream.point(x, y);
          else {
            var a = [x_ = Math.max(clipMin, Math.min(clipMax, x_)), y_ = Math.max(clipMin, Math.min(clipMax, y_))],
                b = [x = Math.max(clipMin, Math.min(clipMax, x)), y = Math.max(clipMin, Math.min(clipMax, y))];
            if (clipLine(a, b, x0, y0, x1, y1)) {
              if (!v_) {
                activeStream.lineStart();
                activeStream.point(a[0], a[1]);
              }
              activeStream.point(b[0], b[1]);
              if (!v) activeStream.lineEnd();
              clean = false;
            } else if (v) {
              activeStream.lineStart();
              activeStream.point(x, y);
              clean = false;
            }
          }
        }
        x_ = x, y_ = y, v_ = v;
      }

      return clipStream;
    };
  }

  function extent$1() {
    var x0 = 0,
        y0 = 0,
        x1 = 960,
        y1 = 500,
        cache,
        cacheStream,
        clip;

    return clip = {
      stream: function(stream) {
        return cache && cacheStream === stream ? cache : cache = clipExtent(x0, y0, x1, y1)(cacheStream = stream);
      },
      extent: function(_) {
        return arguments.length ? (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1], cache = cacheStream = null, clip) : [[x0, y0], [x1, y1]];
      }
    };
  }

  var lengthSum;
var   lambda0$2;
var   sinPhi0$1;
var   cosPhi0$1;
  var lengthStream = {
    sphere: noop$2,
    point: noop$2,
    lineStart: lengthLineStart,
    lineEnd: noop$2,
    polygonStart: noop$2,
    polygonEnd: noop$2
  };

  function lengthLineStart() {
    lengthStream.point = lengthPointFirst;
    lengthStream.lineEnd = lengthLineEnd;
  }

  function lengthLineEnd() {
    lengthStream.point = lengthStream.lineEnd = noop$2;
  }

  function lengthPointFirst(lambda, phi) {
    lambda *= radians, phi *= radians;
    lambda0$2 = lambda, sinPhi0$1 = sin(phi), cosPhi0$1 = cos(phi);
    lengthStream.point = lengthPoint;
  }

  function lengthPoint(lambda, phi) {
    lambda *= radians, phi *= radians;
    var sinPhi = sin(phi),
        cosPhi = cos(phi),
        delta = abs(lambda - lambda0$2),
        cosDelta = cos(delta),
        sinDelta = sin(delta),
        x = cosPhi * sinDelta,
        y = cosPhi0$1 * sinPhi - sinPhi0$1 * cosPhi * cosDelta,
        z = sinPhi0$1 * sinPhi + cosPhi0$1 * cosPhi * cosDelta;
    lengthSum.add(atan2(sqrt$1(x * x + y * y), z));
    lambda0$2 = lambda, sinPhi0$1 = sinPhi, cosPhi0$1 = cosPhi;
  }

  function length$2(object) {
    if (lengthSum) lengthSum.reset();
    else lengthSum = adder();
    stream(object, lengthStream);
    return +lengthSum;
  }

  var coordinates = [null, null];
var   object$1 = {type: "LineString", coordinates: coordinates};
  function distance(a, b) {
    coordinates[0] = a;
    coordinates[1] = b;
    return length$2(object$1);
  }

  function graticuleX(y0, y1, dy) {
    var y = range(y0, y1 - epsilon$4, dy).concat(y1);
    return function(x) { return y.map(function(y) { return [x, y]; }); };
  }

  function graticuleY(x0, x1, dx) {
    var x = range(x0, x1 - epsilon$4, dx).concat(x1);
    return function(y) { return x.map(function(x) { return [x, y]; }); };
  }

  function graticule() {
    var x1, x0, X1, X0,
        y1, y0, Y1, Y0,
        dx = 10, dy = dx, DX = 90, DY = 360,
        x, y, X, Y,
        precision = 2.5;

    function graticule() {
      return {type: "MultiLineString", coordinates: lines()};
    }

    function lines() {
      return range(ceil(X0 / DX) * DX, X1, DX).map(X)
          .concat(range(ceil(Y0 / DY) * DY, Y1, DY).map(Y))
          .concat(range(ceil(x0 / dx) * dx, x1, dx).filter(function(x) { return abs(x % DX) > epsilon$4; }).map(x))
          .concat(range(ceil(y0 / dy) * dy, y1, dy).filter(function(y) { return abs(y % DY) > epsilon$4; }).map(y));
    }

    graticule.lines = function() {
      return lines().map(function(coordinates) { return {type: "LineString", coordinates: coordinates}; });
    };

    graticule.outline = function() {
      return {
        type: "Polygon",
        coordinates: [
          X(X0).concat(
          Y(Y1).slice(1),
          X(X1).reverse().slice(1),
          Y(Y0).reverse().slice(1))
        ]
      };
    };

    graticule.extent = function(_) {
      if (!arguments.length) return graticule.extentMinor();
      return graticule.extentMajor(_).extentMinor(_);
    };

    graticule.extentMajor = function(_) {
      if (!arguments.length) return [[X0, Y0], [X1, Y1]];
      X0 = +_[0][0], X1 = +_[1][0];
      Y0 = +_[0][1], Y1 = +_[1][1];
      if (X0 > X1) _ = X0, X0 = X1, X1 = _;
      if (Y0 > Y1) _ = Y0, Y0 = Y1, Y1 = _;
      return graticule.precision(precision);
    };

    graticule.extentMinor = function(_) {
      if (!arguments.length) return [[x0, y0], [x1, y1]];
      x0 = +_[0][0], x1 = +_[1][0];
      y0 = +_[0][1], y1 = +_[1][1];
      if (x0 > x1) _ = x0, x0 = x1, x1 = _;
      if (y0 > y1) _ = y0, y0 = y1, y1 = _;
      return graticule.precision(precision);
    };

    graticule.step = function(_) {
      if (!arguments.length) return graticule.stepMinor();
      return graticule.stepMajor(_).stepMinor(_);
    };

    graticule.stepMajor = function(_) {
      if (!arguments.length) return [DX, DY];
      DX = +_[0], DY = +_[1];
      return graticule;
    };

    graticule.stepMinor = function(_) {
      if (!arguments.length) return [dx, dy];
      dx = +_[0], dy = +_[1];
      return graticule;
    };

    graticule.precision = function(_) {
      if (!arguments.length) return precision;
      precision = +_;
      x = graticuleX(y0, y1, 90);
      y = graticuleY(x0, x1, precision);
      X = graticuleX(Y0, Y1, 90);
      Y = graticuleY(X0, X1, precision);
      return graticule;
    };

    return graticule
        .extentMajor([[-180, -90 + epsilon$4], [180, 90 - epsilon$4]])
        .extentMinor([[-180, -80 - epsilon$4], [180, 80 + epsilon$4]]);
  }

  function interpolate$2(a, b) {
    var x0 = a[0] * radians,
        y0 = a[1] * radians,
        x1 = b[0] * radians,
        y1 = b[1] * radians,
        cy0 = cos(y0),
        sy0 = sin(y0),
        cy1 = cos(y1),
        sy1 = sin(y1),
        kx0 = cy0 * cos(x0),
        ky0 = cy0 * sin(x0),
        kx1 = cy1 * cos(x1),
        ky1 = cy1 * sin(x1),
        d = 2 * asin$1(sqrt$1(haversin(y1 - y0) + cy0 * cy1 * haversin(x1 - x0))),
        k = sin(d);

    var interpolate = d ? function(t) {
      var B = sin(t *= d) / k,
          A = sin(d - t) / k,
          x = A * kx0 + B * kx1,
          y = A * ky0 + B * ky1,
          z = A * sy0 + B * sy1;
      return [
        atan2(y, x) * degrees$1,
        atan2(z, sqrt$1(x * x + y * y)) * degrees$1
      ];
    } : function() {
      return [x0 * degrees$1, y0 * degrees$1];
    };

    interpolate.distance = d;

    return interpolate;
  }

  function identity$7(x) {
    return x;
  }

var   areaSum$1 = adder();
var   areaRingSum$1 = adder();
  var x00;
  var y00;
var   x0$1;
var   y0$1;
  var areaStream$1 = {
    point: noop$2,
    lineStart: noop$2,
    lineEnd: noop$2,
    polygonStart: function() {
      areaStream$1.lineStart = areaRingStart$1;
      areaStream$1.lineEnd = areaRingEnd$1;
    },
    polygonEnd: function() {
      areaStream$1.lineStart = areaStream$1.lineEnd = areaStream$1.point = noop$2;
      areaSum$1.add(abs(areaRingSum$1));
      areaRingSum$1.reset();
    },
    result: function() {
      var area = areaSum$1 / 2;
      areaSum$1.reset();
      return area;
    }
  };

  function areaRingStart$1() {
    areaStream$1.point = areaPointFirst$1;
  }

  function areaPointFirst$1(x, y) {
    areaStream$1.point = areaPoint$1;
    x00 = x0$1 = x, y00 = y0$1 = y;
  }

  function areaPoint$1(x, y) {
    areaRingSum$1.add(y0$1 * x - x0$1 * y);
    x0$1 = x, y0$1 = y;
  }

  function areaRingEnd$1() {
    areaPoint$1(x00, y00);
  }

var   x0$2 = Infinity;
var   y0$2 = x0$2;
  var x1 = -x0$2;
  var y1 = x1;
  var boundsStream$1 = {
    point: boundsPoint$1,
    lineStart: noop$2,
    lineEnd: noop$2,
    polygonStart: noop$2,
    polygonEnd: noop$2,
    result: function() {
      var bounds = [[x0$2, y0$2], [x1, y1]];
      x1 = y1 = -(y0$2 = x0$2 = Infinity);
      return bounds;
    }
  };

  function boundsPoint$1(x, y) {
    if (x < x0$2) x0$2 = x;
    if (x > x1) x1 = x;
    if (y < y0$2) y0$2 = y;
    if (y > y1) y1 = y;
  }

var   X0$1 = 0;
var   Y0$1 = 0;
var   Z0$1 = 0;
var   X1$1 = 0;
var   Y1$1 = 0;
var   Z1$1 = 0;
var   X2$1 = 0;
var   Y2$1 = 0;
var   Z2$1 = 0;
var   x00$1;
var   y00$1;
var   x0$3;
var   y0$3;
  var centroidStream$1 = {
    point: centroidPoint$1,
    lineStart: centroidLineStart$1,
    lineEnd: centroidLineEnd$1,
    polygonStart: function() {
      centroidStream$1.lineStart = centroidRingStart$1;
      centroidStream$1.lineEnd = centroidRingEnd$1;
    },
    polygonEnd: function() {
      centroidStream$1.point = centroidPoint$1;
      centroidStream$1.lineStart = centroidLineStart$1;
      centroidStream$1.lineEnd = centroidLineEnd$1;
    },
    result: function() {
      var centroid = Z2$1 ? [X2$1 / Z2$1, Y2$1 / Z2$1]
          : Z1$1 ? [X1$1 / Z1$1, Y1$1 / Z1$1]
          : Z0$1 ? [X0$1 / Z0$1, Y0$1 / Z0$1]
          : [NaN, NaN];
      X0$1 = Y0$1 = Z0$1 =
      X1$1 = Y1$1 = Z1$1 =
      X2$1 = Y2$1 = Z2$1 = 0;
      return centroid;
    }
  };

  function centroidPoint$1(x, y) {
    X0$1 += x;
    Y0$1 += y;
    ++Z0$1;
  }

  function centroidLineStart$1() {
    centroidStream$1.point = centroidPointFirstLine;
  }

  function centroidPointFirstLine(x, y) {
    centroidStream$1.point = centroidPointLine;
    centroidPoint$1(x0$3 = x, y0$3 = y);
  }

  function centroidPointLine(x, y) {
    var dx = x - x0$3, dy = y - y0$3, z = sqrt$1(dx * dx + dy * dy);
    X1$1 += z * (x0$3 + x) / 2;
    Y1$1 += z * (y0$3 + y) / 2;
    Z1$1 += z;
    centroidPoint$1(x0$3 = x, y0$3 = y);
  }

  function centroidLineEnd$1() {
    centroidStream$1.point = centroidPoint$1;
  }

  function centroidRingStart$1() {
    centroidStream$1.point = centroidPointFirstRing;
  }

  function centroidRingEnd$1() {
    centroidPointRing(x00$1, y00$1);
  }

  function centroidPointFirstRing(x, y) {
    centroidStream$1.point = centroidPointRing;
    centroidPoint$1(x00$1 = x0$3 = x, y00$1 = y0$3 = y);
  }

  function centroidPointRing(x, y) {
    var dx = x - x0$3,
        dy = y - y0$3,
        z = sqrt$1(dx * dx + dy * dy);

    X1$1 += z * (x0$3 + x) / 2;
    Y1$1 += z * (y0$3 + y) / 2;
    Z1$1 += z;

    z = y0$3 * x - x0$3 * y;
    X2$1 += z * (x0$3 + x);
    Y2$1 += z * (y0$3 + y);
    Z2$1 += z * 3;
    centroidPoint$1(x0$3 = x, y0$3 = y);
  }

  function PathContext(context) {
    var pointRadius = 4.5;

    var stream = {
      point: point,

      // While inside a line, override point to moveTo then lineTo.
      lineStart: function() { stream.point = pointLineStart; },
      lineEnd: lineEnd,

      // While inside a polygon, override lineEnd to closePath.
      polygonStart: function() { stream.lineEnd = lineEndPolygon; },
      polygonEnd: function() { stream.lineEnd = lineEnd; stream.point = point; },

      pointRadius: function(_) {
        pointRadius = _;
        return stream;
      },

      result: noop$2
    };

    function point(x, y) {
      context.moveTo(x + pointRadius, y);
      context.arc(x, y, pointRadius, 0, tau$3);
    }

    function pointLineStart(x, y) {
      context.moveTo(x, y);
      stream.point = pointLine;
    }

    function pointLine(x, y) {
      context.lineTo(x, y);
    }

    function lineEnd() {
      stream.point = point;
    }

    function lineEndPolygon() {
      context.closePath();
    }

    return stream;
  }

  function PathString() {
    var pointCircle = circle$2(4.5),
        string = [];

    var stream = {
      point: point,
      lineStart: lineStart,
      lineEnd: lineEnd,
      polygonStart: function() {
        stream.lineEnd = lineEndPolygon;
      },
      polygonEnd: function() {
        stream.lineEnd = lineEnd;
        stream.point = point;
      },
      pointRadius: function(_) {
        pointCircle = circle$2(_);
        return stream;
      },
      result: function() {
        if (string.length) {
          var result = string.join("");
          string = [];
          return result;
        }
      }
    };

    function point(x, y) {
      string.push("M", x, ",", y, pointCircle);
    }

    function pointLineStart(x, y) {
      string.push("M", x, ",", y);
      stream.point = pointLine;
    }

    function pointLine(x, y) {
      string.push("L", x, ",", y);
    }

    function lineStart() {
      stream.point = pointLineStart;
    }

    function lineEnd() {
      stream.point = point;
    }

    function lineEndPolygon() {
      string.push("Z");
    }

    return stream;
  }

  function circle$2(radius) {
    return "m0," + radius
        + "a" + radius + "," + radius + " 0 1,1 0," + -2 * radius
        + "a" + radius + "," + radius + " 0 1,1 0," + 2 * radius
        + "z";
  }

  function index$3() {
    var pointRadius = 4.5,
        projection,
        projectionStream,
        context,
        contextStream;

    function path(object) {
      if (object) {
        if (typeof pointRadius === "function") contextStream.pointRadius(+pointRadius.apply(this, arguments));
        stream(object, projectionStream(contextStream));
      }
      return contextStream.result();
    }

    path.area = function(object) {
      stream(object, projectionStream(areaStream$1));
      return areaStream$1.result();
    };

    path.bounds = function(object) {
      stream(object, projectionStream(boundsStream$1));
      return boundsStream$1.result();
    };

    path.centroid = function(object) {
      stream(object, projectionStream(centroidStream$1));
      return centroidStream$1.result();
    };

    path.projection = function(_) {
      return arguments.length ? (projectionStream = (projection = _) == null ? identity$7 : _.stream, path) : projection;
    };

    path.context = function(_) {
      if (!arguments.length) return context;
      contextStream = (context = _) == null ? new PathString : new PathContext(_);
      if (typeof pointRadius !== "function") contextStream.pointRadius(pointRadius);
      return path;
    };

    path.pointRadius = function(_) {
      if (!arguments.length) return pointRadius;
      pointRadius = typeof _ === "function" ? _ : (contextStream.pointRadius(+_), +_);
      return path;
    };

    return path.projection(null).context(null);
  }

  var sum$2 = adder();

  function polygonContains(polygon, point) {
    var lambda = point[0],
        phi = point[1],
        normal = [sin(lambda), -cos(lambda), 0],
        angle = 0,
        winding = 0;

    for (var i = 0, n = polygon.length; i < n; ++i) {
      if (!(m = (ring = polygon[i]).length)) continue;
      var ring,
          m,
          point0 = ring[m - 1],
          lambda0 = point0[0],
          phi0 = point0[1] / 2 + quarterPi,
          sinPhi0 = sin(phi0),
          cosPhi0 = cos(phi0);

      for (var j = 0; j < m; ++j, lambda0 = lambda1, sinPhi0 = sinPhi1, cosPhi0 = cosPhi1, point0 = point1) {
        var point1 = ring[j],
            lambda1 = point1[0],
            phi1 = point1[1] / 2 + quarterPi,
            sinPhi1 = sin(phi1),
            cosPhi1 = cos(phi1),
            delta = lambda1 - lambda0,
            sign = delta >= 0 ? 1 : -1,
            absDelta = sign * delta,
            antimeridian = absDelta > pi$3,
            k = sinPhi0 * sinPhi1;

        sum$2.add(atan2(k * sign * sin(absDelta), cosPhi0 * cosPhi1 + k * cos(absDelta)));
        angle += antimeridian ? delta + sign * tau$3 : delta;

        // Are the longitudes either side of the point’s meridian (lambda),
        // and are the latitudes smaller than the parallel (phi)?
        if (antimeridian ^ lambda0 >= lambda ^ lambda1 >= lambda) {
          var arc = cartesianCross(cartesian(point0), cartesian(point1));
          cartesianNormalizeInPlace(arc);
          var intersection = cartesianCross(normal, arc);
          cartesianNormalizeInPlace(intersection);
          var phiArc = (antimeridian ^ delta >= 0 ? -1 : 1) * asin$1(intersection[2]);
          if (phi > phiArc || phi === phiArc && (arc[0] || arc[1])) {
            winding += antimeridian ^ delta >= 0 ? 1 : -1;
          }
        }
      }
    }

    // First, determine whether the South pole is inside or outside:
    //
    // It is inside if:
    // * the polygon winds around it in a clockwise direction.
    // * the polygon does not (cumulatively) wind around it, but has a negative
    //   (counter-clockwise) area.
    //
    // Second, count the (signed) number of times a segment crosses a lambda
    // from the point to the South pole.  If it is zero, then the point is the
    // same side as the South pole.

    var contains = (angle < -epsilon$4 || angle < epsilon$4 && sum$2 < -epsilon$4) ^ (winding & 1);
    sum$2.reset();
    return contains;
  }

  function clip(pointVisible, clipLine, interpolate, start) {
    return function(rotate, sink) {
      var line = clipLine(sink),
          rotatedStart = rotate.invert(start[0], start[1]),
          ringBuffer = clipBuffer(),
          ringSink = clipLine(ringBuffer),
          polygonStarted = false,
          polygon,
          segments,
          ring;

      var clip = {
        point: point,
        lineStart: lineStart,
        lineEnd: lineEnd,
        polygonStart: function() {
          clip.point = pointRing;
          clip.lineStart = ringStart;
          clip.lineEnd = ringEnd;
          segments = [];
          polygon = [];
        },
        polygonEnd: function() {
          clip.point = point;
          clip.lineStart = lineStart;
          clip.lineEnd = lineEnd;
          segments = merge(segments);
          var startInside = polygonContains(polygon, rotatedStart);
          if (segments.length) {
            if (!polygonStarted) sink.polygonStart(), polygonStarted = true;
            clipPolygon(segments, compareIntersection, startInside, interpolate, sink);
          } else if (startInside) {
            if (!polygonStarted) sink.polygonStart(), polygonStarted = true;
            sink.lineStart();
            interpolate(null, null, 1, sink);
            sink.lineEnd();
          }
          if (polygonStarted) sink.polygonEnd(), polygonStarted = false;
          segments = polygon = null;
        },
        sphere: function() {
          sink.polygonStart();
          sink.lineStart();
          interpolate(null, null, 1, sink);
          sink.lineEnd();
          sink.polygonEnd();
        }
      };

      function point(lambda, phi) {
        var point = rotate(lambda, phi);
        if (pointVisible(lambda = point[0], phi = point[1])) sink.point(lambda, phi);
      }

      function pointLine(lambda, phi) {
        var point = rotate(lambda, phi);
        line.point(point[0], point[1]);
      }

      function lineStart() {
        clip.point = pointLine;
        line.lineStart();
      }

      function lineEnd() {
        clip.point = point;
        line.lineEnd();
      }

      function pointRing(lambda, phi) {
        ring.push([lambda, phi]);
        var point = rotate(lambda, phi);
        ringSink.point(point[0], point[1]);
      }

      function ringStart() {
        ringSink.lineStart();
        ring = [];
      }

      function ringEnd() {
        pointRing(ring[0][0], ring[0][1]);
        ringSink.lineEnd();

        var clean = ringSink.clean(),
            ringSegments = ringBuffer.result(),
            i, n = ringSegments.length, m,
            segment,
            point;

        ring.pop();
        polygon.push(ring);
        ring = null;

        if (!n) return;

        // No intersections.
        if (clean & 1) {
          segment = ringSegments[0];
          if ((m = segment.length - 1) > 0) {
            if (!polygonStarted) sink.polygonStart(), polygonStarted = true;
            sink.lineStart();
            for (i = 0; i < m; ++i) sink.point((point = segment[i])[0], point[1]);
            sink.lineEnd();
          }
          return;
        }

        // Rejoin connected segments.
        // TODO reuse ringBuffer.rejoin()?
        if (n > 1 && clean & 2) ringSegments.push(ringSegments.pop().concat(ringSegments.shift()));

        segments.push(ringSegments.filter(validSegment));
      }

      return clip;
    };
  }

  function validSegment(segment) {
    return segment.length > 1;
  }

  // Intersections are sorted along the clip edge. For both antimeridian cutting
  // and circle clipping, the same comparison is used.
  function compareIntersection(a, b) {
    return ((a = a.x)[0] < 0 ? a[1] - halfPi$2 - epsilon$4 : halfPi$2 - a[1])
         - ((b = b.x)[0] < 0 ? b[1] - halfPi$2 - epsilon$4 : halfPi$2 - b[1]);
  }

  var clipAntimeridian = clip(
    function() { return true; },
    clipAntimeridianLine,
    clipAntimeridianInterpolate,
    [-pi$3, -halfPi$2]
  );

  // Takes a line and cuts into visible segments. Return values: 0 - there were
  // intersections or the line was empty; 1 - no intersections; 2 - there were
  // intersections, and the first and last segments should be rejoined.
  function clipAntimeridianLine(stream) {
    var lambda0 = NaN,
        phi0 = NaN,
        sign0 = NaN,
        clean; // no intersections

    return {
      lineStart: function() {
        stream.lineStart();
        clean = 1;
      },
      point: function(lambda1, phi1) {
        var sign1 = lambda1 > 0 ? pi$3 : -pi$3,
            delta = abs(lambda1 - lambda0);
        if (abs(delta - pi$3) < epsilon$4) { // line crosses a pole
          stream.point(lambda0, phi0 = (phi0 + phi1) / 2 > 0 ? halfPi$2 : -halfPi$2);
          stream.point(sign0, phi0);
          stream.lineEnd();
          stream.lineStart();
          stream.point(sign1, phi0);
          stream.point(lambda1, phi0);
          clean = 0;
        } else if (sign0 !== sign1 && delta >= pi$3) { // line crosses antimeridian
          if (abs(lambda0 - sign0) < epsilon$4) lambda0 -= sign0 * epsilon$4; // handle degeneracies
          if (abs(lambda1 - sign1) < epsilon$4) lambda1 -= sign1 * epsilon$4;
          phi0 = clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1);
          stream.point(sign0, phi0);
          stream.lineEnd();
          stream.lineStart();
          stream.point(sign1, phi0);
          clean = 0;
        }
        stream.point(lambda0 = lambda1, phi0 = phi1);
        sign0 = sign1;
      },
      lineEnd: function() {
        stream.lineEnd();
        lambda0 = phi0 = NaN;
      },
      clean: function() {
        return 2 - clean; // if intersections, rejoin first and last segments
      }
    };
  }

  function clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1) {
    var cosPhi0,
        cosPhi1,
        sinLambda0Lambda1 = sin(lambda0 - lambda1);
    return abs(sinLambda0Lambda1) > epsilon$4
        ? atan((sin(phi0) * (cosPhi1 = cos(phi1)) * sin(lambda1)
            - sin(phi1) * (cosPhi0 = cos(phi0)) * sin(lambda0))
            / (cosPhi0 * cosPhi1 * sinLambda0Lambda1))
        : (phi0 + phi1) / 2;
  }

  function clipAntimeridianInterpolate(from, to, direction, stream) {
    var phi;
    if (from == null) {
      phi = direction * halfPi$2;
      stream.point(-pi$3, phi);
      stream.point(0, phi);
      stream.point(pi$3, phi);
      stream.point(pi$3, 0);
      stream.point(pi$3, -phi);
      stream.point(0, -phi);
      stream.point(-pi$3, -phi);
      stream.point(-pi$3, 0);
      stream.point(-pi$3, phi);
    } else if (abs(from[0] - to[0]) > epsilon$4) {
      var lambda = from[0] < to[0] ? pi$3 : -pi$3;
      phi = direction * lambda / 2;
      stream.point(-lambda, phi);
      stream.point(0, phi);
      stream.point(lambda, phi);
    } else {
      stream.point(to[0], to[1]);
    }
  }

  function clipCircle(radius, delta) {
    var cr = cos(radius),
        smallRadius = cr > 0,
        notHemisphere = abs(cr) > epsilon$4; // TODO optimise for this common case

    function interpolate(from, to, direction, stream) {
      circleStream(stream, radius, delta, direction, from, to);
    }

    function visible(lambda, phi) {
      return cos(lambda) * cos(phi) > cr;
    }

    // Takes a line and cuts into visible segments. Return values used for polygon
    // clipping: 0 - there were intersections or the line was empty; 1 - no
    // intersections 2 - there were intersections, and the first and last segments
    // should be rejoined.
    function clipLine(stream) {
      var point0, // previous point
          c0, // code for previous point
          v0, // visibility of previous point
          v00, // visibility of first point
          clean; // no intersections
      return {
        lineStart: function() {
          v00 = v0 = false;
          clean = 1;
        },
        point: function(lambda, phi) {
          var point1 = [lambda, phi],
              point2,
              v = visible(lambda, phi),
              c = smallRadius
                ? v ? 0 : code(lambda, phi)
                : v ? code(lambda + (lambda < 0 ? pi$3 : -pi$3), phi) : 0;
          if (!point0 && (v00 = v0 = v)) stream.lineStart();
          // Handle degeneracies.
          // TODO ignore if not clipping polygons.
          if (v !== v0) {
            point2 = intersect(point0, point1);
            if (pointEqual(point0, point2) || pointEqual(point1, point2)) {
              point1[0] += epsilon$4;
              point1[1] += epsilon$4;
              v = visible(point1[0], point1[1]);
            }
          }
          if (v !== v0) {
            clean = 0;
            if (v) {
              // outside going in
              stream.lineStart();
              point2 = intersect(point1, point0);
              stream.point(point2[0], point2[1]);
            } else {
              // inside going out
              point2 = intersect(point0, point1);
              stream.point(point2[0], point2[1]);
              stream.lineEnd();
            }
            point0 = point2;
          } else if (notHemisphere && point0 && smallRadius ^ v) {
            var t;
            // If the codes for two points are different, or are both zero,
            // and there this segment intersects with the small circle.
            if (!(c & c0) && (t = intersect(point1, point0, true))) {
              clean = 0;
              if (smallRadius) {
                stream.lineStart();
                stream.point(t[0][0], t[0][1]);
                stream.point(t[1][0], t[1][1]);
                stream.lineEnd();
              } else {
                stream.point(t[1][0], t[1][1]);
                stream.lineEnd();
                stream.lineStart();
                stream.point(t[0][0], t[0][1]);
              }
            }
          }
          if (v && (!point0 || !pointEqual(point0, point1))) {
            stream.point(point1[0], point1[1]);
          }
          point0 = point1, v0 = v, c0 = c;
        },
        lineEnd: function() {
          if (v0) stream.lineEnd();
          point0 = null;
        },
        // Rejoin first and last segments if there were intersections and the first
        // and last points were visible.
        clean: function() {
          return clean | ((v00 && v0) << 1);
        }
      };
    }

    // Intersects the great circle between a and b with the clip circle.
    function intersect(a, b, two) {
      var pa = cartesian(a),
          pb = cartesian(b);

      // We have two planes, n1.p = d1 and n2.p = d2.
      // Find intersection line p(t) = c1 n1 + c2 n2 + t (n1 ⨯ n2).
      var n1 = [1, 0, 0], // normal
          n2 = cartesianCross(pa, pb),
          n2n2 = cartesianDot(n2, n2),
          n1n2 = n2[0], // cartesianDot(n1, n2),
          determinant = n2n2 - n1n2 * n1n2;

      // Two polar points.
      if (!determinant) return !two && a;

      var c1 =  cr * n2n2 / determinant,
          c2 = -cr * n1n2 / determinant,
          n1xn2 = cartesianCross(n1, n2),
          A = cartesianScale(n1, c1),
          B = cartesianScale(n2, c2);
      cartesianAddInPlace(A, B);

      // Solve |p(t)|^2 = 1.
      var u = n1xn2,
          w = cartesianDot(A, u),
          uu = cartesianDot(u, u),
          t2 = w * w - uu * (cartesianDot(A, A) - 1);

      if (t2 < 0) return;

      var t = sqrt$1(t2),
          q = cartesianScale(u, (-w - t) / uu);
      cartesianAddInPlace(q, A);
      q = spherical(q);

      if (!two) return q;

      // Two intersection points.
      var lambda0 = a[0],
          lambda1 = b[0],
          phi0 = a[1],
          phi1 = b[1],
          z;

      if (lambda1 < lambda0) z = lambda0, lambda0 = lambda1, lambda1 = z;

      var delta = lambda1 - lambda0,
          polar = abs(delta - pi$3) < epsilon$4,
          meridian = polar || delta < epsilon$4;

      if (!polar && phi1 < phi0) z = phi0, phi0 = phi1, phi1 = z;

      // Check that the first point is between a and b.
      if (meridian
          ? polar
            ? phi0 + phi1 > 0 ^ q[1] < (abs(q[0] - lambda0) < epsilon$4 ? phi0 : phi1)
            : phi0 <= q[1] && q[1] <= phi1
          : delta > pi$3 ^ (lambda0 <= q[0] && q[0] <= lambda1)) {
        var q1 = cartesianScale(u, (-w + t) / uu);
        cartesianAddInPlace(q1, A);
        return [q, spherical(q1)];
      }
    }

    // Generates a 4-bit vector representing the location of a point relative to
    // the small circle's bounding box.
    function code(lambda, phi) {
      var r = smallRadius ? radius : pi$3 - radius,
          code = 0;
      if (lambda < -r) code |= 1; // left
      else if (lambda > r) code |= 2; // right
      if (phi < -r) code |= 4; // below
      else if (phi > r) code |= 8; // above
      return code;
    }

    return clip(visible, clipLine, interpolate, smallRadius ? [0, -radius] : [-pi$3, radius - pi$3]);
  }

  function transform$1(prototype) {
    return {
      stream: transform$2(prototype)
    };
  }

  function transform$2(prototype) {
    function T() {}
    var p = T.prototype = Object.create(Transform$1.prototype);
    for (var k in prototype) p[k] = prototype[k];
    return function(stream) {
      var t = new T;
      t.stream = stream;
      return t;
    };
  }

  function Transform$1() {}

  Transform$1.prototype = {
    point: function(x, y) { this.stream.point(x, y); },
    sphere: function() { this.stream.sphere(); },
    lineStart: function() { this.stream.lineStart(); },
    lineEnd: function() { this.stream.lineEnd(); },
    polygonStart: function() { this.stream.polygonStart(); },
    polygonEnd: function() { this.stream.polygonEnd(); }
  };

  var maxDepth = 16;
  var cosMinDistance = cos(30 * radians);
  // cos(minimum angular distance)

  function resample(project, delta2) {
    return +delta2 ? resample$1(project, delta2) : resampleNone(project);
  }

  function resampleNone(project) {
    return transform$2({
      point: function(x, y) {
        x = project(x, y);
        this.stream.point(x[0], x[1]);
      }
    });
  }

  function resample$1(project, delta2) {

    function resampleLineTo(x0, y0, lambda0, a0, b0, c0, x1, y1, lambda1, a1, b1, c1, depth, stream) {
      var dx = x1 - x0,
          dy = y1 - y0,
          d2 = dx * dx + dy * dy;
      if (d2 > 4 * delta2 && depth--) {
        var a = a0 + a1,
            b = b0 + b1,
            c = c0 + c1,
            m = sqrt$1(a * a + b * b + c * c),
            phi2 = asin$1(c /= m),
            lambda2 = abs(abs(c) - 1) < epsilon$4 || abs(lambda0 - lambda1) < epsilon$4 ? (lambda0 + lambda1) / 2 : atan2(b, a),
            p = project(lambda2, phi2),
            x2 = p[0],
            y2 = p[1],
            dx2 = x2 - x0,
            dy2 = y2 - y0,
            dz = dy * dx2 - dx * dy2;
        if (dz * dz / d2 > delta2 // perpendicular projected distance
            || abs((dx * dx2 + dy * dy2) / d2 - 0.5) > 0.3 // midpoint close to an end
            || a0 * a1 + b0 * b1 + c0 * c1 < cosMinDistance) { // angular distance
          resampleLineTo(x0, y0, lambda0, a0, b0, c0, x2, y2, lambda2, a /= m, b /= m, c, depth, stream);
          stream.point(x2, y2);
          resampleLineTo(x2, y2, lambda2, a, b, c, x1, y1, lambda1, a1, b1, c1, depth, stream);
        }
      }
    }
    return function(stream) {
      var lambda00, x00, y00, a00, b00, c00, // first point
          lambda0, x0, y0, a0, b0, c0; // previous point

      var resampleStream = {
        point: point,
        lineStart: lineStart,
        lineEnd: lineEnd,
        polygonStart: function() { stream.polygonStart(); resampleStream.lineStart = ringStart; },
        polygonEnd: function() { stream.polygonEnd(); resampleStream.lineStart = lineStart; }
      };

      function point(x, y) {
        x = project(x, y);
        stream.point(x[0], x[1]);
      }

      function lineStart() {
        x0 = NaN;
        resampleStream.point = linePoint;
        stream.lineStart();
      }

      function linePoint(lambda, phi) {
        var c = cartesian([lambda, phi]), p = project(lambda, phi);
        resampleLineTo(x0, y0, lambda0, a0, b0, c0, x0 = p[0], y0 = p[1], lambda0 = lambda, a0 = c[0], b0 = c[1], c0 = c[2], maxDepth, stream);
        stream.point(x0, y0);
      }

      function lineEnd() {
        resampleStream.point = point;
        stream.lineEnd();
      }

      function ringStart() {
        lineStart();
        resampleStream.point = ringPoint;
        resampleStream.lineEnd = ringEnd;
      }

      function ringPoint(lambda, phi) {
        linePoint(lambda00 = lambda, phi), x00 = x0, y00 = y0, a00 = a0, b00 = b0, c00 = c0;
        resampleStream.point = linePoint;
      }

      function ringEnd() {
        resampleLineTo(x0, y0, lambda0, a0, b0, c0, x00, y00, lambda00, a00, b00, c00, maxDepth, stream);
        resampleStream.lineEnd = lineEnd;
        lineEnd();
      }

      return resampleStream;
    };
  }

  var transformRadians = transform$2({
    point: function(x, y) {
      this.stream.point(x * radians, y * radians);
    }
  });

  function projection(project) {
    return projectionMutator(function() { return project; })();
  }

  function projectionMutator(projectAt) {
    var project,
        k = 150, // scale
        x = 480, y = 250, // translate
        dx, dy, lambda = 0, phi = 0, // center
        deltaLambda = 0, deltaPhi = 0, deltaGamma = 0, rotate, projectRotate, // rotate
        theta = null, preclip = clipAntimeridian, // clip angle
        x0 = null, y0, x1, y1, postclip = identity$7, // clip extent
        delta2 = 0.5, projectResample = resample(projectTransform, delta2), // precision
        cache,
        cacheStream;

    function projection(point) {
      point = projectRotate(point[0] * radians, point[1] * radians);
      return [point[0] * k + dx, dy - point[1] * k];
    }

    function invert(point) {
      point = projectRotate.invert((point[0] - dx) / k, (dy - point[1]) / k);
      return point && [point[0] * degrees$1, point[1] * degrees$1];
    }

    function projectTransform(x, y) {
      return x = project(x, y), [x[0] * k + dx, dy - x[1] * k];
    }

    projection.stream = function(stream) {
      return cache && cacheStream === stream ? cache : cache = transformRadians(preclip(rotate, projectResample(postclip(cacheStream = stream))));
    };

    projection.clipAngle = function(_) {
      return arguments.length ? (preclip = +_ ? clipCircle(theta = _ * radians, 6 * radians) : (theta = null, clipAntimeridian), reset()) : theta * degrees$1;
    };

    projection.clipExtent = function(_) {
      return arguments.length ? (postclip = _ == null ? (x0 = y0 = x1 = y1 = null, identity$7) : clipExtent(x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1]), reset()) : x0 == null ? null : [[x0, y0], [x1, y1]];
    };

    projection.scale = function(_) {
      return arguments.length ? (k = +_, recenter()) : k;
    };

    projection.translate = function(_) {
      return arguments.length ? (x = +_[0], y = +_[1], recenter()) : [x, y];
    };

    projection.center = function(_) {
      return arguments.length ? (lambda = _[0] % 360 * radians, phi = _[1] % 360 * radians, recenter()) : [lambda * degrees$1, phi * degrees$1];
    };

    projection.rotate = function(_) {
      return arguments.length ? (deltaLambda = _[0] % 360 * radians, deltaPhi = _[1] % 360 * radians, deltaGamma = _.length > 2 ? _[2] % 360 * radians : 0, recenter()) : [deltaLambda * degrees$1, deltaPhi * degrees$1, deltaGamma * degrees$1];
    };

    projection.precision = function(_) {
      return arguments.length ? (projectResample = resample(projectTransform, delta2 = _ * _), reset()) : sqrt$1(delta2);
    };

    function recenter() {
      projectRotate = compose(rotate = rotateRadians(deltaLambda, deltaPhi, deltaGamma), project);
      var center = project(lambda, phi);
      dx = x - center[0] * k;
      dy = y + center[1] * k;
      return reset();
    }

    function reset() {
      cache = cacheStream = null;
      return projection;
    }

    return function() {
      project = projectAt.apply(this, arguments);
      projection.invert = project.invert && invert;
      return recenter();
    };
  }

  function conicProjection(projectAt) {
    var phi0 = 0,
        phi1 = pi$3 / 3,
        m = projectionMutator(projectAt),
        p = m(phi0, phi1);

    p.parallels = function(_) {
      return arguments.length ? m(phi0 = _[0] * radians, phi1 = _[1] * radians) : [phi0 * degrees$1, phi1 * degrees$1];
    };

    return p;
  }

  function conicEqualArea(y0, y1) {
    var sy0 = sin(y0),
        n = (sy0 + sin(y1)) / 2,
        c = 1 + sy0 * (2 * n - sy0),
        r0 = sqrt$1(c) / n;

    function project(x, y) {
      var r = sqrt$1(c - 2 * n * sin(y)) / n;
      return [r * sin(x *= n), r0 - r * cos(x)];
    }

    project.invert = function(x, y) {
      var r0y = r0 - y;
      return [atan2(x, r0y) / n, asin$1((c - (x * x + r0y * r0y) * n * n) / (2 * n))];
    };

    return project;
  }

  function conicEqualArea$1() {
    return conicProjection(conicEqualArea)
        .scale(151)
        .translate([480, 347]);
  }

  function albers() {
    return conicEqualArea$1()
        .parallels([29.5, 45.5])
        .scale(1070)
        .translate([480, 250])
        .rotate([96, 0])
        .center([-0.6, 38.7]);
  }

  // The projections must have mutually exclusive clip regions on the sphere,
  // as this will avoid emitting interleaving lines and polygons.
  function multiplex(streams) {
    var n = streams.length;
    return {
      point: function(x, y) { var i = -1; while (++i < n) streams[i].point(x, y); },
      sphere: function() { var i = -1; while (++i < n) streams[i].sphere(); },
      lineStart: function() { var i = -1; while (++i < n) streams[i].lineStart(); },
      lineEnd: function() { var i = -1; while (++i < n) streams[i].lineEnd(); },
      polygonStart: function() { var i = -1; while (++i < n) streams[i].polygonStart(); },
      polygonEnd: function() { var i = -1; while (++i < n) streams[i].polygonEnd(); }
    };
  }

  // A composite projection for the United States, configured by default for
  // 960×500. Also works quite well at 960×600 with scale 1285. The set of
  // standard parallels for each region comes from USGS, which is published here:
  // http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html#albers
  function albersUsa() {
    var cache,
        cacheStream,
        lower48 = albers(), lower48Point,
        alaska = conicEqualArea$1().rotate([154, 0]).center([-2, 58.5]).parallels([55, 65]), alaskaPoint, // EPSG:3338
        hawaii = conicEqualArea$1().rotate([157, 0]).center([-3, 19.9]).parallels([8, 18]), hawaiiPoint, // ESRI:102007
        point, pointStream = {point: function(x, y) { point = [x, y]; }};

    function albersUsa(coordinates) {
      var x = coordinates[0], y = coordinates[1];
      return point = null,
          (lower48Point.point(x, y), point)
          || (alaskaPoint.point(x, y), point)
          || (hawaiiPoint.point(x, y), point);
    }

    albersUsa.invert = function(coordinates) {
      var k = lower48.scale(),
          t = lower48.translate(),
          x = (coordinates[0] - t[0]) / k,
          y = (coordinates[1] - t[1]) / k;
      return (y >= 0.120 && y < 0.234 && x >= -0.425 && x < -0.214 ? alaska
          : y >= 0.166 && y < 0.234 && x >= -0.214 && x < -0.115 ? hawaii
          : lower48).invert(coordinates);
    };

    albersUsa.stream = function(stream) {
      return cache && cacheStream === stream ? cache : cache = multiplex([lower48.stream(cacheStream = stream), alaska.stream(stream), hawaii.stream(stream)]);
    };

    albersUsa.precision = function(_) {
      if (!arguments.length) return lower48.precision();
      lower48.precision(_), alaska.precision(_), hawaii.precision(_);
      return albersUsa;
    };

    albersUsa.scale = function(_) {
      if (!arguments.length) return lower48.scale();
      lower48.scale(_), alaska.scale(_ * 0.35), hawaii.scale(_);
      return albersUsa.translate(lower48.translate());
    };

    albersUsa.translate = function(_) {
      if (!arguments.length) return lower48.translate();
      var k = lower48.scale(), x = +_[0], y = +_[1];

      lower48Point = lower48
          .translate(_)
          .clipExtent([[x - 0.455 * k, y - 0.238 * k], [x + 0.455 * k, y + 0.238 * k]])
          .stream(pointStream);

      alaskaPoint = alaska
          .translate([x - 0.307 * k, y + 0.201 * k])
          .clipExtent([[x - 0.425 * k + epsilon$4, y + 0.120 * k + epsilon$4], [x - 0.214 * k - epsilon$4, y + 0.234 * k - epsilon$4]])
          .stream(pointStream);

      hawaiiPoint = hawaii
          .translate([x - 0.205 * k, y + 0.212 * k])
          .clipExtent([[x - 0.214 * k + epsilon$4, y + 0.166 * k + epsilon$4], [x - 0.115 * k - epsilon$4, y + 0.234 * k - epsilon$4]])
          .stream(pointStream);

      return albersUsa;
    };

    return albersUsa.scale(1070);
  }

  function azimuthal(scale) {
    return function(x, y) {
      var cx = cos(x),
          cy = cos(y),
          k = scale(cx * cy);
      return [
        k * cy * sin(x),
        k * sin(y)
      ];
    }
  }

  function azimuthalInvert(angle) {
    return function(x, y) {
      var z = sqrt$1(x * x + y * y),
          c = angle(z),
          sc = sin(c),
          cc = cos(c);
      return [
        atan2(x * sc, z * cc),
        asin$1(z && y * sc / z)
      ];
    }
  }

  var azimuthalEqualArea = azimuthal(function(cxcy) {
    return sqrt$1(2 / (1 + cxcy));
  });

  azimuthalEqualArea.invert = azimuthalInvert(function(z) {
    return 2 * asin$1(z / 2);
  });

  function azimuthalEqualArea$1() {
    return projection(azimuthalEqualArea)
        .scale(120)
        .clipAngle(180 - 1e-3);
  }

  var azimuthalEquidistant = azimuthal(function(c) {
    return (c = acos(c)) && c / sin(c);
  });

  azimuthalEquidistant.invert = azimuthalInvert(function(z) {
    return z;
  });

  function azimuthalEquidistant$1() {
    return projection(azimuthalEquidistant)
        .scale(480 / tau$3)
        .clipAngle(180 - 1e-3);
  }

  function mercator(lambda, phi) {
    return [lambda, log$1(tan((halfPi$2 + phi) / 2))];
  }

  mercator.invert = function(x, y) {
    return [x, 2 * atan(exp(y)) - halfPi$2];
  };

  function mercator$1() {
    return mercatorProjection(mercator);
  }

  function mercatorProjection(project) {
    var m = projection(project),
        scale = m.scale,
        translate = m.translate,
        clipExtent = m.clipExtent,
        clipAuto;

    m.scale = function(_) {
      return arguments.length ? (scale(_), clipAuto && m.clipExtent(null), m) : scale();
    };

    m.translate = function(_) {
      return arguments.length ? (translate(_), clipAuto && m.clipExtent(null), m) : translate();
    };

    m.clipExtent = function(_) {
      if (!arguments.length) return clipAuto ? null : clipExtent();
      if (clipAuto = _ == null) {
        var k = pi$3 * scale(), t = translate();
        _ = [[t[0] - k, t[1] - k], [t[0] + k, t[1] + k]];
      }
      clipExtent(_);
      return m;
    };

    return m.clipExtent(null).scale(961 / tau$3);
  }

  function tany(y) {
    return tan((halfPi$2 + y) / 2);
  }

  function conicConformal(y0, y1) {
    var cy0 = cos(y0),
        n = y0 === y1 ? sin(y0) : log$1(cy0 / cos(y1)) / log$1(tany(y1) / tany(y0)),
        f = cy0 * pow$1(tany(y0), n) / n;

    if (!n) return mercator;

    function project(x, y) {
      if (f > 0) { if (y < -halfPi$2 + epsilon$4) y = -halfPi$2 + epsilon$4; }
      else { if (y > halfPi$2 - epsilon$4) y = halfPi$2 - epsilon$4; }
      var r = f / pow$1(tany(y), n);
      return [r * sin(n * x), f - r * cos(n * x)];
    }

    project.invert = function(x, y) {
      var fy = f - y, r = sign$1(n) * sqrt$1(x * x + fy * fy);
      return [atan2(x, fy) / n, 2 * atan(pow$1(f / r, 1 / n)) - halfPi$2];
    };

    return project;
  }

  function conicConformal$1() {
    return conicProjection(conicConformal);
  }

  function equirectangular(lambda, phi) {
    return [lambda, phi];
  }

  equirectangular.invert = equirectangular;

  function equirectangular$1() {
    return projection(equirectangular).scale(480 / pi$3);
  }

  function conicEquidistant(y0, y1) {
    var cy0 = cos(y0),
        n = y0 === y1 ? sin(y0) : (cy0 - cos(y1)) / (y1 - y0),
        g = cy0 / n + y0;

    if (abs(n) < epsilon$4) return equirectangular;

    function project(x, y) {
      var gy = g - y, nx = n * x;
      return [gy * sin(nx), g - gy * cos(nx)];
    }

    project.invert = function(x, y) {
      var gy = g - y;
      return [atan2(x, gy) / n, g - sign$1(n) * sqrt$1(x * x + gy * gy)];
    };

    return project;
  }

  function conicEquidistant$1() {
    return conicProjection(conicEquidistant)
        .scale(128)
        .translate([480, 280]);
  }

  function gnomonic(x, y) {
    var cy = cos(y), k = cos(x) * cy;
    return [cy * sin(x) / k, sin(y) / k];
  }

  gnomonic.invert = azimuthalInvert(atan);

  function gnomonic$1() {
    return projection(gnomonic)
        .scale(139)
        .clipAngle(60);
  }

  function orthographic(x, y) {
    return [cos(y) * sin(x), sin(y)];
  }

  orthographic.invert = azimuthalInvert(asin$1);

  function orthographic$1() {
    return projection(orthographic)
        .scale(240)
        .clipAngle(90 + epsilon$4);
  }

  function stereographic(x, y) {
    var cy = cos(y), k = 1 + cos(x) * cy;
    return [cy * sin(x) / k, sin(y) / k];
  }

  stereographic.invert = azimuthalInvert(function(z) {
    return 2 + atan(z);
  });

  function stereographic$1() {
    return projection(stereographic)
        .scale(240)
        .clipAngle(142);
  }

  function transverseMercator(lambda, phi) {
    return [log$1(tan((halfPi$2 + phi) / 2)), -lambda];
  }

  transverseMercator.invert = function(x, y) {
    return [-y, 2 * atan(exp(x)) - halfPi$2];
  };

  function transverseMercator$1() {
    var m = mercatorProjection(transverseMercator),
        center = m.center,
        rotate = m.rotate;

    m.center = function(_) {
      return arguments.length ? center([-_[1], _[0]]) : (_ = center(), [_[1], -_[0]]);
    };

    m.rotate = function(_) {
      return arguments.length ? rotate([_[0], _[1], _.length > 2 ? _[2] + 90 : 90]) : (_ = rotate(), [_[0], _[1], _[2] - 90]);
    };

    return rotate([0, 0, 90]);
  }

  exports.version = version;
  exports.bisect = bisectRight;
  exports.bisectRight = bisectRight;
  exports.bisectLeft = bisectLeft;
  exports.ascending = ascending;
  exports.bisector = bisector;
  exports.descending = descending;
  exports.deviation = deviation;
  exports.extent = extent;
  exports.histogram = histogram;
  exports.thresholdFreedmanDiaconis = freedmanDiaconis;
  exports.thresholdScott = scott;
  exports.thresholdSturges = sturges;
  exports.max = max;
  exports.mean = mean;
  exports.median = median;
  exports.merge = merge;
  exports.min = min;
  exports.pairs = pairs;
  exports.permute = permute;
  exports.quantile = threshold;
  exports.range = range;
  exports.scan = scan;
  exports.shuffle = shuffle;
  exports.sum = sum;
  exports.ticks = ticks;
  exports.tickStep = tickStep;
  exports.transpose = transpose;
  exports.variance = variance;
  exports.zip = zip;
  exports.entries = entries;
  exports.keys = keys;
  exports.values = values;
  exports.map = map$1;
  exports.set = set;
  exports.nest = nest;
  exports.randomUniform = uniform;
  exports.randomNormal = normal;
  exports.randomLogNormal = logNormal;
  exports.randomBates = bates;
  exports.randomIrwinHall = irwinHall;
  exports.randomExponential = exponential;
  exports.easeLinear = linear;
  exports.easeQuad = quadInOut;
  exports.easeQuadIn = quadIn;
  exports.easeQuadOut = quadOut;
  exports.easeQuadInOut = quadInOut;
  exports.easeCubic = easeCubicInOut;
  exports.easeCubicIn = cubicIn;
  exports.easeCubicOut = cubicOut;
  exports.easeCubicInOut = easeCubicInOut;
  exports.easePoly = polyInOut;
  exports.easePolyIn = polyIn;
  exports.easePolyOut = polyOut;
  exports.easePolyInOut = polyInOut;
  exports.easeSin = sinInOut;
  exports.easeSinIn = sinIn;
  exports.easeSinOut = sinOut;
  exports.easeSinInOut = sinInOut;
  exports.easeExp = expInOut;
  exports.easeExpIn = expIn;
  exports.easeExpOut = expOut;
  exports.easeExpInOut = expInOut;
  exports.easeCircle = circleInOut;
  exports.easeCircleIn = circleIn;
  exports.easeCircleOut = circleOut;
  exports.easeCircleInOut = circleInOut;
  exports.easeBounce = bounceOut;
  exports.easeBounceIn = bounceIn;
  exports.easeBounceOut = bounceOut;
  exports.easeBounceInOut = bounceInOut;
  exports.easeBack = backInOut;
  exports.easeBackIn = backIn;
  exports.easeBackOut = backOut;
  exports.easeBackInOut = backInOut;
  exports.easeElastic = elasticOut;
  exports.easeElasticIn = elasticIn;
  exports.easeElasticOut = elasticOut;
  exports.easeElasticInOut = elasticInOut;
  exports.polygonArea = area;
  exports.polygonCentroid = centroid;
  exports.polygonHull = hull;
  exports.polygonContains = contains;
  exports.polygonLength = length$1;
  exports.path = path;
  exports.quadtree = quadtree;
  exports.queue = queue;
  exports.arc = arc;
  exports.area = area$1;
  exports.line = line;
  exports.pie = pie;
  exports.radialArea = radialArea;
  exports.radialLine = radialLine$1;
  exports.symbol = symbol;
  exports.symbols = symbols;
  exports.symbolCircle = circle;
  exports.symbolCross = cross$1;
  exports.symbolDiamond = diamond;
  exports.symbolSquare = square;
  exports.symbolStar = star;
  exports.symbolTriangle = triangle;
  exports.symbolWye = wye;
  exports.curveBasisClosed = basisClosed;
  exports.curveBasisOpen = basisOpen;
  exports.curveBasis = basis;
  exports.curveBundle = bundle;
  exports.curveCardinalClosed = cardinalClosed;
  exports.curveCardinalOpen = cardinalOpen;
  exports.curveCardinal = cardinal;
  exports.curveCatmullRomClosed = catmullRomClosed;
  exports.curveCatmullRomOpen = catmullRomOpen;
  exports.curveCatmullRom = catmullRom;
  exports.curveLinearClosed = linearClosed;
  exports.curveLinear = curveLinear;
  exports.curveMonotoneX = monotoneX;
  exports.curveMonotoneY = monotoneY;
  exports.curveNatural = natural;
  exports.curveStep = step;
  exports.curveStepAfter = stepAfter;
  exports.curveStepBefore = stepBefore;
  exports.stack = stack;
  exports.stackOffsetExpand = expand;
  exports.stackOffsetNone = none;
  exports.stackOffsetSilhouette = silhouette;
  exports.stackOffsetWiggle = wiggle;
  exports.stackOrderAscending = ascending$1;
  exports.stackOrderDescending = descending$2;
  exports.stackOrderInsideOut = insideOut;
  exports.stackOrderNone = none$1;
  exports.stackOrderReverse = reverse;
  exports.color = color;
  exports.rgb = colorRgb;
  exports.hsl = colorHsl;
  exports.lab = lab;
  exports.hcl = colorHcl;
  exports.cubehelix = cubehelix;
  exports.interpolate = interpolate;
  exports.interpolateArray = array$1;
  exports.interpolateNumber = interpolateNumber;
  exports.interpolateObject = object;
  exports.interpolateRound = interpolateRound;
  exports.interpolateString = interpolateString;
  exports.interpolateTransformCss = interpolateTransform$1;
  exports.interpolateTransformSvg = interpolateTransform$2;
  exports.interpolateZoom = interpolateZoom;
  exports.interpolateRgb = interpolateRgb;
  exports.interpolateRgbBasis = rgbBasis;
  exports.interpolateRgbBasisClosed = rgbBasisClosed;
  exports.interpolateHsl = hsl$1;
  exports.interpolateHslLong = hslLong;
  exports.interpolateLab = lab$1;
  exports.interpolateHcl = hcl$1;
  exports.interpolateHclLong = hclLong;
  exports.interpolateCubehelix = cubehelix$2;
  exports.interpolateCubehelixLong = interpolateCubehelixLong;
  exports.interpolateBasis = basis$2;
  exports.interpolateBasisClosed = basisClosed$1;
  exports.quantize = quantize;
  exports.dispatch = dispatch;
  exports.dsvFormat = dsv;
  exports.csvParse = csvParse;
  exports.csvParseRows = csvParseRows;
  exports.csvFormat = csvFormat;
  exports.csvFormatRows = csvFormatRows;
  exports.tsvParse = tsvParse;
  exports.tsvParseRows = tsvParseRows;
  exports.tsvFormat = tsvFormat;
  exports.tsvFormatRows = tsvFormatRows;
  exports.request = request;
  exports.html = html;
  exports.json = json;
  exports.text = text;
  exports.xml = xml;
  exports.csv = csv$1;
  exports.tsv = tsv$1;
  exports.now = now;
  exports.timer = timer;
  exports.timerFlush = timerFlush;
  exports.timeout = timeout$1;
  exports.interval = interval$1;
  exports.timeInterval = newInterval;
  exports.timeMillisecond = millisecond;
  exports.timeMilliseconds = milliseconds;
  exports.timeSecond = second;
  exports.timeSeconds = seconds;
  exports.timeMinute = minute;
  exports.timeMinutes = minutes;
  exports.timeHour = hour;
  exports.timeHours = hours;
  exports.timeDay = day;
  exports.timeDays = days;
  exports.timeWeek = timeWeek;
  exports.timeWeeks = sundays;
  exports.timeSunday = timeWeek;
  exports.timeSundays = sundays;
  exports.timeMonday = timeMonday;
  exports.timeMondays = mondays;
  exports.timeTuesday = tuesday;
  exports.timeTuesdays = tuesdays;
  exports.timeWednesday = wednesday;
  exports.timeWednesdays = wednesdays;
  exports.timeThursday = thursday;
  exports.timeThursdays = thursdays;
  exports.timeFriday = friday;
  exports.timeFridays = fridays;
  exports.timeSaturday = saturday;
  exports.timeSaturdays = saturdays;
  exports.timeMonth = month;
  exports.timeMonths = months;
  exports.timeYear = year;
  exports.timeYears = years;
  exports.utcMillisecond = millisecond;
  exports.utcMilliseconds = milliseconds;
  exports.utcSecond = second;
  exports.utcSeconds = seconds;
  exports.utcMinute = utcMinute;
  exports.utcMinutes = utcMinutes;
  exports.utcHour = utcHour;
  exports.utcHours = utcHours;
  exports.utcDay = utcDay;
  exports.utcDays = utcDays;
  exports.utcWeek = utcWeek;
  exports.utcWeeks = utcSundays;
  exports.utcSunday = utcWeek;
  exports.utcSundays = utcSundays;
  exports.utcMonday = utcMonday;
  exports.utcMondays = utcMondays;
  exports.utcTuesday = utcTuesday;
  exports.utcTuesdays = utcTuesdays;
  exports.utcWednesday = utcWednesday;
  exports.utcWednesdays = utcWednesdays;
  exports.utcThursday = utcThursday;
  exports.utcThursdays = utcThursdays;
  exports.utcFriday = utcFriday;
  exports.utcFridays = utcFridays;
  exports.utcSaturday = utcSaturday;
  exports.utcSaturdays = utcSaturdays;
  exports.utcMonth = utcMonth;
  exports.utcMonths = utcMonths;
  exports.utcYear = utcYear;
  exports.utcYears = utcYears;
  exports.formatLocale = formatLocale;
  exports.formatDefaultLocale = defaultLocale;
  exports.formatSpecifier = formatSpecifier;
  exports.precisionFixed = precisionFixed;
  exports.precisionPrefix = precisionPrefix;
  exports.precisionRound = precisionRound;
  exports.isoFormat = formatIso;
  exports.isoParse = parseIso;
  exports.timeFormatLocale = formatLocale$1;
  exports.timeFormatDefaultLocale = defaultLocale$1;
  exports.scaleBand = band;
  exports.scalePoint = point$4;
  exports.scaleIdentity = identity$4;
  exports.scaleLinear = linear$2;
  exports.scaleLog = log;
  exports.scaleOrdinal = ordinal;
  exports.scaleImplicit = implicit;
  exports.scalePow = pow;
  exports.scaleSqrt = sqrt;
  exports.scaleQuantile = quantile;
  exports.scaleQuantize = quantize$1;
  exports.scaleThreshold = threshold$1;
  exports.scaleTime = time;
  exports.scaleUtc = utcTime;
  exports.schemeCategory10 = category10;
  exports.schemeCategory20b = category20b;
  exports.schemeCategory20c = category20c;
  exports.schemeCategory20 = category20;
  exports.scaleSequential = sequential;
  exports.interpolateCubehelixDefault = cubehelix$3;
  exports.interpolateRainbow = rainbow$1;
  exports.interpolateWarm = warm;
  exports.interpolateCool = cool;
  exports.interpolateViridis = viridis;
  exports.interpolateMagma = magma;
  exports.interpolateInferno = inferno;
  exports.interpolatePlasma = plasma;
  exports.creator = creator;
  exports.customEvent = customEvent;
  exports.local = local;
  exports.matcher = matcher$1;
  exports.mouse = mouse;
  exports.namespace = namespace;
  exports.namespaces = namespaces;
  exports.select = select;
  exports.selectAll = selectAll;
  exports.selection = selection;
  exports.selector = selector;
  exports.selectorAll = selectorAll;
  exports.touch = touch;
  exports.touches = touches;
  exports.window = window;
  exports.active = active;
  exports.interrupt = interrupt;
  exports.transition = transition;
  exports.axisTop = axisTop;
  exports.axisRight = axisRight;
  exports.axisBottom = axisBottom;
  exports.axisLeft = axisLeft;
  exports.cluster = cluster;
  exports.hierarchy = hierarchy;
  exports.pack = index;
  exports.packSiblings = siblings;
  exports.packEnclose = enclose;
  exports.partition = partition;
  exports.stratify = stratify;
  exports.tree = tree;
  exports.treemap = index$1;
  exports.treemapBinary = binary;
  exports.treemapDice = treemapDice;
  exports.treemapSlice = treemapSlice;
  exports.treemapSliceDice = sliceDice;
  exports.treemapSquarify = squarify;
  exports.treemapResquarify = resquarify;
  exports.forceCenter = center$1;
  exports.forceCollide = collide;
  exports.forceLink = link;
  exports.forceManyBody = manyBody;
  exports.forceSimulation = simulation;
  exports.forceX = x$3;
  exports.forceY = y$3;
  exports.drag = drag;
  exports.dragDisable = dragDisable;
  exports.dragEnable = dragEnable;
  exports.voronoi = voronoi;
  exports.zoom = zoom;
  exports.zoomIdentity = identity$6;
  exports.zoomTransform = transform;
  exports.brush = brush;
  exports.brushX = brushX;
  exports.brushY = brushY;
  exports.brushSelection = brushSelection;
  exports.geoArea = area$2;
  exports.geoBounds = bounds;
  exports.geoCentroid = centroid$1;
  exports.geoCircle = circle$1;
  exports.geoClipExtent = extent$1;
  exports.geoDistance = distance;
  exports.geoGraticule = graticule;
  exports.geoInterpolate = interpolate$2;
  exports.geoLength = length$2;
  exports.geoPath = index$3;
  exports.geoAlbers = albers;
  exports.geoAlbersUsa = albersUsa;
  exports.geoAzimuthalEqualArea = azimuthalEqualArea$1;
  exports.geoAzimuthalEquidistant = azimuthalEquidistant$1;
  exports.geoConicConformal = conicConformal$1;
  exports.geoConicEqualArea = conicEqualArea$1;
  exports.geoConicEquidistant = conicEquidistant$1;
  exports.geoEquirectangular = equirectangular$1;
  exports.geoGnomonic = gnomonic$1;
  exports.geoProjection = projection;
  exports.geoProjectionMutator = projectionMutator;
  exports.geoMercator = mercator$1;
  exports.geoOrthographic = orthographic$1;
  exports.geoStereographic = stereographic$1;
  exports.geoTransverseMercator = transverseMercator$1;
  exports.geoRotation = rotation;
  exports.geoStream = stream;
  exports.geoTransform = transform$1;

  Object.defineProperty(exports, '__esModule', { value: true });

}));

index.html

<!DOCTYPE html>
<meta charset="utf-8">

<style>
html, body {
  margin: 0;
  padding: 0;
  width: 100%;
  height: 100%;
}

svg {
  width: 100%;
  height: 100%;
}

line {
  stroke: #eee;
  stroke-width: 1;
}
</style>

<body>
  <svg></svg>
</body>

<script src="d3.v4.js"></script>
<script>

var svg = d3.select("svg"),
    width = 960,
    height = 500,
    n = 3,
    scale = d3.scaleLinear()
      .domain([0,4])
      .range([0, width/n/2]),
    mouse = [0,0]

var dimensions = d3.range(n)
  .map(d => {
    var data = d3.range(1000).map(() => {
      var cartesian = [
        d3.randomNormal()(),
        d > 0 ? d3.randomNormal()() : 0,
        d > 1 ? d3.randomNormal()() : 0
      ]
      return {
        cartesian,
        spherical: cartesianToSpherical(cartesian),
        coords: cartesian
      }
    })

    var simulation = d3.forceSimulation(data)
        .force("x", d3.forceX(function(d) { return scale(d.spherical.r); }).strength(1))
        .force("y", d3.forceY(0))
        .force("collide", d3.forceCollide(1))
        .stop();

    for (var i = 0; i < 120; ++i) simulation.tick();

    return data;
  })

var dim = svg.selectAll("g.dimension")
  .data(dimensions)
  .enter()
  .append("g")
  .attr("class", "dimension")

dim
  .append("line")
  .attr("y1", 0)
  .attr("y2", 0)
  .attr("x1", -width/n/2)
  .attr("x2", width/n/2)

dim
  .call(render)

d3.select("body").on("mousemove", function() {
  mouse = d3.mouse(this);
  svg.selectAll("circle")
    .attr("transform", d => d.coords[2] ?
      "translate(" + d.coords[2]*5*mouse[0]/width +
              ", " + d.coords[2]*5*mouse[1]/height + ")" : null
    )
})

function render(selection) {
  selection.each(function(data, index) {
    var sel = d3.select(this)
      .attr("transform",
        "translate(" + width * (0.16 + 0.33 * index) + ", " + height / 2 + ")")

    var circle = sel.selectAll("circle")
      .data(data)
      .enter()
    .append("circle")
      .attr("r", d => Math.max(.1, 1 + d.coords[2]/5))
      .attr("cy", d => -scale(d.coords[0]))
      .attr("cx", d => scale(d.coords[1]))
    .transition()
      .delay(3000)
      .duration(3000)
      .tween("cx.flatten2d", function(d) {
        var node = this, i = d3.interpolate(d.spherical.theta, Math.PI/2);
        return function(t) {
          d.coords = sphericalToCartesian({
            r: d.spherical.r,
            theta: i(t),
            phi: d.spherical.phi
          })
          node.setAttribute("r", Math.max(.1, 1 + d.coords[2]/5));
          node.setAttribute("cy", -scale(d.coords[0]));
          node.setAttribute("cx", scale(d.coords[1]));
          node.setAttribute("transform", d.coords[2] ?
            "translate(" + d.coords[2]*5*mouse[0]/width +
                    ", " + d.coords[2]*5*mouse[1]/height + ")" : null
          )
        };
      })
    .transition()
      .duration(3000)
      .tween("cx.flatten1d", function(d) {
        var node = this, i = d3.interpolate(d.spherical.phi, 0);
        return function(t) {
          d.coords = sphericalToCartesian({
            r: d.spherical.r,
            theta: Math.PI/2,
            phi: i(t)
          })
          node.setAttribute("cy", -scale(d.coords[0]));
          node.setAttribute("cx", scale(d.coords[1]));
        };
      })
    .transition()
      .delay(1000)
      .duration(3000)
      // .attr("cx", d => d.x)
      .attr("cx", d => d.y)
  })
}

// https://en.wikipedia.org/wiki/Spherical_coordinate_system
// https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates
function cartesianToSpherical(cartesian) {
  return {
    r: distance(cartesian),
    theta: Math.acos(cartesian[2] / distance(cartesian)),
    phi: Math.atan2(cartesian[1], cartesian[0]) //atan2 for weird quadrant stuff!
  }
}

function sphericalToCartesian(spherical) {
  return [
    spherical.r * Math.sin(spherical.theta) * Math.cos(spherical.phi),
    spherical.r * Math.sin(spherical.theta) * Math.sin(spherical.phi),
    spherical.r * Math.cos(spherical.theta)
  ]
}

function distance(arr) {
  return Math.sqrt(sum(
      arr.map(d => Math.pow(d,2))
  ))
}

function product(arr) {
  return arr.reduce((acc, cur) => acc * cur, 1)
}

function sum(arr) {
  return arr.reduce((acc, cur) => acc + cur, 0)
}

</script>

index2.html

<!DOCTYPE html>
<meta charset="utf-8">

<style>
html, body {
  margin: 0;
  padding: 0;
  width: 100%;
  height: 100%;
}

</style>

<body>
  <canvas width="960" height="500" id="canvas"></canvas>
</body>

<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="multivariate-normal.min.js"></script>
<script>

var canvas = document.getElementById("canvas"),
    width = canvas.width,
    height = canvas.height,
    n = 6,
    nn = n,
    scale = d3.scaleLinear().domain([0,4]).range([0, width/n])
    context = canvas.getContext("2d"),
    context.fillStyle = '#000000',
    context.globalAlpha = .1;

var dimensions = d3.range(n)
  .map(d => d+1)
  .map(d => ({
    dim: d,
    dist: getDistribution(d),
    origin: [
      width/n + (2*width/n) * ((d-1) % (n/2)),
      height/4 + height/2 * ~~((d-1) / (n/2))
    ]
  }))

dimensions.forEach(getSamples)

var timeScale = d3.scaleLinear()
  .domain([0, 10000])
  .range([n, 0])

// d3.timer(function(t) {
//   context.clearRect(0, 0, width, height);
//   dimensions.forEach(function(d) {
//     context.save();
//     context.translate(d.origin[0], d.origin[1]);
//     d.samples.forEach(function(dd) {
//       var from = Math.min(dd.length, Math.ceil(timeScale(t))) - 1
//       var to = Math.min(dd.length, Math.floor(timeScale(t))) - 1
//
//       console.log(dd[from].spherical, dd[to].spherical)
//       debugger
//
//       var coords = interpolateSpherical(dd[from].spherical, dd[to].spherical)(t)
//       context.beginPath();
//       context.arc(scale(coords[0]), coords[1] ? scale(coords[1]) : 0, 2, 0, 2 * Math.PI);
//       context.fill();
//     })
//     context.restore();
//   })
// })

function interpolateSpherical(from, to) {
  return function(t) {
    return getEuclideanFromSpherical({
      r: from.r,
      angular: d3.interpolate(from.angular, to.angular)(t)
    })
  }
}

dimensions.forEach(d => renderDistribution(d, nn))

var interval = d3.interval(function() {
  if(nn > 0) {
    nn--;
    context.clearRect(0, 0, width, height);
    dimensions.forEach(d => renderDistribution(d, nn))
  } else {
    interval.stop();
  }
}, 1000)

function renderDistribution(d, n) {
  context.save();
  context.translate(d.origin[0], d.origin[1]);
  d.samples.forEach(function(dd) {
    var coords = dd[Math.min(dd.length-1, nn)].euclidean;
    context.beginPath();
    context.arc(scale(coords[0]), coords[1] ? scale(coords[1]) : 0, 2, 0, 2 * Math.PI);
    context.fill();
  })
  context.restore();
}

function getSamples(d) {
  var samples = d3.range(1000).map(() => {
    var sample = d.dist.sample()
    return {
      euclidean: sample,
      spherical: getSphericalFromEuclidean(sample)
    }
  })
  d.samples = samples.map(dd =>
    d3.range(d.dim).map(dim => {
      var angles = dd.spherical.angular.map((a,i,arr) => {
        if(i >= d.dim - dim - 1) {
          return a;
        } else {
          return 0;
        }
      })
      var truncatedSpherical = {
        r: dd.spherical.r,
        angular: angles
      }
      // var truncatedSpherical = {
      //   r: dd.spherical.r,
      //   // angular: dd.spherical.angular.slice(d.dim - dim - 1)
      //   // angular: dd.spherical.angular.slice(0, dim)
      // }
      return {
        euclidean: getEuclideanFromSpherical(truncatedSpherical),
        spherical: truncatedSpherical
      }
    })
  )
}

function distance(arr) {
  return Math.sqrt(sum(
      arr.map(d => Math.pow(d,2))
  ))
}

function product(arr) {
  return arr.reduce((acc, cur) => acc * cur, 1)
}

function sum(arr) {
  return arr.reduce((acc, cur) => acc + cur, 0)
}

// https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates
function getEuclideanFromSpherical(vector) {
  return vector.angular.concat([null]).map(
    (d,i,arr) => vector.r *
      product(arr.slice(0,i).map(Math.sin)) *
      (d == null ? 1 : Math.cos(d))
  )
}

function getSphericalFromEuclidean(vector) {
  return {
    r: distance(vector),
    angular: vector.slice(0, vector.length-1).map(
      (d,i,arr) => Math.acos(
        d / distance(vector.slice(i)) || 0
      )
      * (i == arr.length-1 && d < 0 ? -1 : 1) +
      + (i == arr.length-1 && d < 0 ? 2*Math.PI : 0)
    )
  }
}

function getDistribution(n) {
  return MultivariateNormal.default(
    getZeroVector(n),
    getIdentityMatrix(n)
  )
}

function getIdentityMatrix(n) {
  return d3.range(n).map(i => d3.range(n).map(j => j == i ? 1.0 : 0.0))
}

function getZeroVector(n) {
  return d3.range(n).map(d => 0)
}

</script>

multivariate-normal.min.js

(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.MultivariateNormal=f()}})(function(){var define,module,exports;return function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s}({1:[function(require,module,exports){"use strict";Object.defineProperty(exports,"__esModule",{value:true});var _validation=require("./validation.js");var _gaussian=require("gaussian");var _gaussian2=_interopRequireDefault(_gaussian);var _numeric=require("numeric");var _numeric2=_interopRequireDefault(_numeric);function _interopRequireDefault(obj){return obj&&obj.__esModule?obj:{"default":obj}}var standardNormalDist=(0,_gaussian2.default)(0,1);var standardNormalVector=function standardNormalVector(length){var ary=[];for(var i=0;i<length;i++){ary.push(standardNormalDist.ppf(Math.random()))}return ary};var Distribution=function Distribution(n,mean,cov,_ref){var u=_ref.u;var s=_ref.s;var v=_ref.v;return{sample:function sample(){var sqrtS=s.map(Math.sqrt);var scaledV=v.map(function(row){return row.map(function(val,colIdx){return val*sqrtS[colIdx]})});var standardNormal=standardNormalVector(n);var variants=_numeric2.default.dot(standardNormal,_numeric2.default.transpose(scaledV));return variants.map(function(variant,idx){return variant+mean[idx]})},getMean:function getMean(){return mean},setMean:function setMean(unvalidatedMean){var newMean=(0,_validation.validateMean)(unvalidatedMean,n);return Distribution(n,newMean,cov,{u:u,s:s,v:v})},getCov:function getCov(){return cov},setCov:function setCov(unvalidatedCov){var _validateCovAndGetSVD=(0,_validation.validateCovAndGetSVD)(unvalidatedCov,n);var newCov=_validateCovAndGetSVD.cov;var newSVD=_validateCovAndGetSVD.svd;return Distribution(n,mean,newCov,newSVD)}}};exports.default=Distribution},{"./validation.js":3,gaussian:4,numeric:6}],2:[function(require,module,exports){"use strict";Object.defineProperty(exports,"__esModule",{value:true});var _lodash=require("lodash");var _lodash2=_interopRequireDefault(_lodash);var _validation=require("./validation.js");var _distribution=require("./distribution.js");var _distribution2=_interopRequireDefault(_distribution);function _interopRequireDefault(obj){return obj&&obj.__esModule?obj:{"default":obj}}var MultivariateNormal=function MultivariateNormal(unvalidatedMean,unvalidatedCov){if(!_lodash2.default.isArray(unvalidatedMean)){throw new Error("mean must be an array")}var n=unvalidatedMean.length;var mean=(0,_validation.validateMean)(unvalidatedMean,n);var _validateCovAndGetSVD=(0,_validation.validateCovAndGetSVD)(unvalidatedCov,n);var cov=_validateCovAndGetSVD.cov;var svd=_validateCovAndGetSVD.svd;return(0,_distribution2.default)(n,mean,cov,svd)};exports.default=MultivariateNormal},{"./distribution.js":1,"./validation.js":3,lodash:5}],3:[function(require,module,exports){"use strict";Object.defineProperty(exports,"__esModule",{value:true});exports.validateCovAndGetSVD=exports.validateMean=undefined;var _lodash=require("lodash");var _lodash2=_interopRequireDefault(_lodash);var _numeric=require("numeric");var _numeric2=_interopRequireDefault(_numeric);function _interopRequireDefault(obj){return obj&&obj.__esModule?obj:{"default":obj}}var deepFreeze=function deepFreeze(ary){if(_lodash2.default.isArray(ary)){ary.forEach(deepFreeze);Object.freeze(ary)}};var validateMean=function validateMean(mean,n){if(!_lodash2.default.isArray(mean)){throw new Error("Mean must be an array")}if(!_lodash2.default.every(mean,_lodash2.default.isNumber)){throw new Error("Mean must be an array of numbers")}if(mean.length!==n){throw new Error("Expected mean to have length "+n+", but had length "+mean.length)}Object.freeze(mean);return mean};var validateCovAndGetSVD=function validateCovAndGetSVD(cov,n){if(!_lodash2.default.isArray(cov)){throw new Error("Covariance must be an array")}if(cov.length!==n){throw new Error("Covariance matrix had "+cov.length+" rows, but it should be a "+n+"x"+n+" square matrix")}cov.forEach(function(row,idx){if(!_lodash2.default.isArray(row)){throw new Error("Row "+idx+" of covariance matrix was not an array")}if(row.length!==n){throw new Error("Row "+idx+" of covariance matrix had length "+row.length+", but it should have length "+n)}if(!_lodash2.default.every(row,_lodash2.default.isNumber)){throw new Error("Row "+idx+" of covariance matrix contained a non-numeric value")}});var eigenvalues=_numeric2.default.eig(cov).lambda.x;if(_lodash2.default.some(eigenvalues,function(v){return v<0})){throw new Error("Covariance isn't positive semidefinite")}if(!_numeric2.default.same(_numeric2.default.transpose(cov),cov)){throw new Error("Covariance isn't symmetric")}var _Numeric$svd=_numeric2.default.svd(cov);var u=_Numeric$svd.U;var s=_Numeric$svd.S;var v=_Numeric$svd.V;deepFreeze(cov);deepFreeze(u);deepFreeze(s);deepFreeze(v);return{cov:cov,svd:{u:u,s:s,v:v}}};exports.validateMean=validateMean;exports.validateCovAndGetSVD=validateCovAndGetSVD},{lodash:5,numeric:6}],4:[function(require,module,exports){(function(exports){var erfc=function(x){var z=Math.abs(x);var t=1/(1+z/2);var r=t*Math.exp(-z*z-1.26551223+t*(1.00002368+t*(.37409196+t*(.09678418+t*(-.18628806+t*(.27886807+t*(-1.13520398+t*(1.48851587+t*(-.82215223+t*.17087277)))))))));return x>=0?r:2-r};var ierfc=function(x){if(x>=2){return-100}if(x<=0){return 100}var xx=x<1?x:2-x;var t=Math.sqrt(-2*Math.log(xx/2));var r=-.70711*((2.30753+t*.27061)/(1+t*(.99229+t*.04481))-t);for(var j=0;j<2;j++){var err=erfc(r)-xx;r+=err/(1.1283791670955126*Math.exp(-(r*r))-r*err)}return x<1?r:-r};var Gaussian=function(mean,variance){if(variance<=0){throw new Error("Variance must be > 0 (but was "+variance+")")}this.mean=mean;this.variance=variance;this.standardDeviation=Math.sqrt(variance)};Gaussian.prototype.pdf=function(x){var m=this.standardDeviation*Math.sqrt(2*Math.PI);var e=Math.exp(-Math.pow(x-this.mean,2)/(2*this.variance));return e/m};Gaussian.prototype.cdf=function(x){return.5*erfc(-(x-this.mean)/(this.standardDeviation*Math.sqrt(2)))};Gaussian.prototype.ppf=function(x){return this.mean-this.standardDeviation*Math.sqrt(2)*ierfc(2*x)};Gaussian.prototype.mul=function(d){if(typeof d==="number"){return this.scale(d)}var precision=1/this.variance;var dprecision=1/d.variance;return fromPrecisionMean(precision+dprecision,precision*this.mean+dprecision*d.mean)};Gaussian.prototype.div=function(d){if(typeof d==="number"){return this.scale(1/d)}var precision=1/this.variance;var dprecision=1/d.variance;return fromPrecisionMean(precision-dprecision,precision*this.mean-dprecision*d.mean)};Gaussian.prototype.add=function(d){return gaussian(this.mean+d.mean,this.variance+d.variance)};Gaussian.prototype.sub=function(d){return gaussian(this.mean-d.mean,this.variance+d.variance)};Gaussian.prototype.scale=function(c){return gaussian(this.mean*c,this.variance*c*c)};var gaussian=function(mean,variance){return new Gaussian(mean,variance)};var fromPrecisionMean=function(precision,precisionmean){return gaussian(precisionmean/precision,1/precision)};exports(gaussian)})(typeof exports!=="undefined"?function(e){module.exports=e}:function(e){this["gaussian"]=e})},{}],5:[function(require,module,exports){(function(global){(function(){var undefined;var VERSION="4.11.2";var LARGE_ARRAY_SIZE=200;var FUNC_ERROR_TEXT="Expected a function";var HASH_UNDEFINED="__lodash_hash_undefined__";var PLACEHOLDER="__lodash_placeholder__";var BIND_FLAG=1,BIND_KEY_FLAG=2,CURRY_BOUND_FLAG=4,CURRY_FLAG=8,CURRY_RIGHT_FLAG=16,PARTIAL_FLAG=32,PARTIAL_RIGHT_FLAG=64,ARY_FLAG=128,REARG_FLAG=256,FLIP_FLAG=512;var UNORDERED_COMPARE_FLAG=1,PARTIAL_COMPARE_FLAG=2;var DEFAULT_TRUNC_LENGTH=30,DEFAULT_TRUNC_OMISSION="...";var HOT_COUNT=150,HOT_SPAN=16;var LAZY_FILTER_FLAG=1,LAZY_MAP_FLAG=2,LAZY_WHILE_FLAG=3;var INFINITY=1/0,MAX_SAFE_INTEGER=9007199254740991,MAX_INTEGER=1.7976931348623157e308,NAN=0/0;var MAX_ARRAY_LENGTH=4294967295,MAX_ARRAY_INDEX=MAX_ARRAY_LENGTH-1,HALF_MAX_ARRAY_LENGTH=MAX_ARRAY_LENGTH>>>1;var argsTag="[object Arguments]",arrayTag="[object Array]",boolTag="[object 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mid=nativeFloor((low+high)/2),computed=iteratee(array[mid]),othIsDefined=computed!==undefined,othIsNull=computed===null,othIsReflexive=computed===computed,othIsSymbol=isSymbol(computed);if(valIsNaN){var setLow=retHighest||othIsReflexive}else if(valIsUndefined){setLow=othIsReflexive&&(retHighest||othIsDefined)}else if(valIsNull){setLow=othIsReflexive&&othIsDefined&&(retHighest||!othIsNull)}else if(valIsSymbol){setLow=othIsReflexive&&othIsDefined&&!othIsNull&&(retHighest||!othIsSymbol)}else if(othIsNull||othIsSymbol){setLow=false}else{setLow=retHighest?computed<=value:computed<value}if(setLow){low=mid+1}else{high=mid}}return nativeMin(high,MAX_ARRAY_INDEX)}function baseSortedUniq(array,iteratee){var index=-1,length=array.length,resIndex=0,result=[];while(++index<length){var value=array[index],computed=iteratee?iteratee(value):value;if(!index||!eq(computed,seen)){var seen=computed;result[resIndex++]=value===0?0:value}}return result}function baseToNumber(value){if(typeof value=="number"){return value}if(isSymbol(value)){return NAN}return+value}function baseToString(value){if(typeof value=="string"){return value}if(isSymbol(value)){return symbolToString?symbolToString.call(value):""}var result=value+"";return result=="0"&&1/value==-INFINITY?"-0":result}function baseUniq(array,iteratee,comparator){var index=-1,includes=arrayIncludes,length=array.length,isCommon=true,result=[],seen=result;if(comparator){isCommon=false;includes=arrayIncludesWith}else if(length>=LARGE_ARRAY_SIZE){var set=iteratee?null:createSet(array);if(set){return setToArray(set)}isCommon=false;includes=cacheHas;seen=new SetCache}else{seen=iteratee?[]:result}outer:while(++index<length){var value=array[index],computed=iteratee?iteratee(value):value;value=comparator||value!==0?value:0;if(isCommon&&computed===computed){var seenIndex=seen.length;while(seenIndex--){if(seen[seenIndex]===computed){continue outer}}if(iteratee){seen.push(computed)}result.push(value)}else if(!includes(seen,computed,comparator)){if(seen!==result){seen.push(computed)}result.push(value)}}return result}function baseUnset(object,path){path=isKey(path,object)?[path]:castPath(path);object=parent(object,path);var key=toKey(last(path));return!(object!=null&&baseHas(object,key))||delete object[key]}function baseUpdate(object,path,updater,customizer){return baseSet(object,path,updater(baseGet(object,path)),customizer)}function baseWhile(array,predicate,isDrop,fromRight){var length=array.length,index=fromRight?length:-1;while((fromRight?index--:++index<length)&&predicate(array[index],index,array)){}return isDrop?baseSlice(array,fromRight?0:index,fromRight?index+1:length):baseSlice(array,fromRight?index+1:0,fromRight?length:index)}function baseWrapperValue(value,actions){var result=value;if(result instanceof LazyWrapper){result=result.value()}return arrayReduce(actions,function(result,action){return action.func.apply(action.thisArg,arrayPush([result],action.args))},result)}function baseXor(arrays,iteratee,comparator){var index=-1,length=arrays.length;while(++index<length){var result=result?arrayPush(baseDifference(result,arrays[index],iteratee,comparator),baseDifference(arrays[index],result,iteratee,comparator)):arrays[index]}return result&&result.length?baseUniq(result,iteratee,comparator):[]}function baseZipObject(props,values,assignFunc){var index=-1,length=props.length,valsLength=values.length,result={};while(++index<length){var value=index<valsLength?values[index]:undefined;assignFunc(result,props[index],value)}return result}function castArrayLikeObject(value){return isArrayLikeObject(value)?value:[]}function castFunction(value){return typeof value=="function"?value:identity}function castPath(value){return isArray(value)?value:stringToPath(value)}function castSlice(array,start,end){var length=array.length;end=end===undefined?length:end;return!start&&end>=length?array:baseSlice(array,start,end)}function cloneBuffer(buffer,isDeep){if(isDeep){return buffer.slice()}var result=new buffer.constructor(buffer.length);buffer.copy(result);return result}function cloneArrayBuffer(arrayBuffer){var result=new arrayBuffer.constructor(arrayBuffer.byteLength);new Uint8Array(result).set(new Uint8Array(arrayBuffer));return result}function cloneDataView(dataView,isDeep){var buffer=isDeep?cloneArrayBuffer(dataView.buffer):dataView.buffer;return new dataView.constructor(buffer,dataView.byteOffset,dataView.byteLength)}function cloneMap(map,isDeep,cloneFunc){var array=isDeep?cloneFunc(mapToArray(map),true):mapToArray(map);return arrayReduce(array,addMapEntry,new map.constructor)}function cloneRegExp(regexp){var result=new regexp.constructor(regexp.source,reFlags.exec(regexp));result.lastIndex=regexp.lastIndex;return result}function cloneSet(set,isDeep,cloneFunc){var array=isDeep?cloneFunc(setToArray(set),true):setToArray(set);return arrayReduce(array,addSetEntry,new set.constructor)}function cloneSymbol(symbol){return symbolValueOf?Object(symbolValueOf.call(symbol)):{}}function cloneTypedArray(typedArray,isDeep){var buffer=isDeep?cloneArrayBuffer(typedArray.buffer):typedArray.buffer;return new typedArray.constructor(buffer,typedArray.byteOffset,typedArray.length)}function compareAscending(value,other){if(value!==other){var valIsDefined=value!==undefined,valIsNull=value===null,valIsReflexive=value===value,valIsSymbol=isSymbol(value);var othIsDefined=other!==undefined,othIsNull=other===null,othIsReflexive=other===other,othIsSymbol=isSymbol(other);if(!othIsNull&&!othIsSymbol&&!valIsSymbol&&value>other||valIsSymbol&&othIsDefined&&othIsReflexive&&!othIsNull&&!othIsSymbol||valIsNull&&othIsDefined&&othIsReflexive||!valIsDefined&&othIsReflexive||!valIsReflexive){return 1}if(!valIsNull&&!valIsSymbol&&!othIsSymbol&&value<other||othIsSymbol&&valIsDefined&&valIsReflexive&&!valIsNull&&!valIsSymbol||othIsNull&&valIsDefined&&valIsReflexive||!othIsDefined&&valIsReflexive||!othIsReflexive){return-1}}return 0}function compareMultiple(object,other,orders){var index=-1,objCriteria=object.criteria,othCriteria=other.criteria,length=objCriteria.length,ordersLength=orders.length;while(++index<length){var result=compareAscending(objCriteria[index],othCriteria[index]);if(result){if(index>=ordersLength){return result}var order=orders[index];return result*(order=="desc"?-1:1)}}return object.index-other.index}function composeArgs(args,partials,holders,isCurried){var argsIndex=-1,argsLength=args.length,holdersLength=holders.length,leftIndex=-1,leftLength=partials.length,rangeLength=nativeMax(argsLength-holdersLength,0),result=Array(leftLength+rangeLength),isUncurried=!isCurried;while(++leftIndex<leftLength){result[leftIndex]=partials[leftIndex]}while(++argsIndex<holdersLength){if(isUncurried||argsIndex<argsLength){result[holders[argsIndex]]=args[argsIndex]}}while(rangeLength--){result[leftIndex++]=args[argsIndex++]}return result}function composeArgsRight(args,partials,holders,isCurried){var argsIndex=-1,argsLength=args.length,holdersIndex=-1,holdersLength=holders.length,rightIndex=-1,rightLength=partials.length,rangeLength=nativeMax(argsLength-holdersLength,0),result=Array(rangeLength+rightLength),isUncurried=!isCurried;while(++argsIndex<rangeLength){result[argsIndex]=args[argsIndex]}var offset=argsIndex;while(++rightIndex<rightLength){result[offset+rightIndex]=partials[rightIndex]}while(++holdersIndex<holdersLength){if(isUncurried||argsIndex<argsLength){result[offset+holders[holdersIndex]]=args[argsIndex++]}}return result}function copyArray(source,array){var index=-1,length=source.length;array||(array=Array(length));while(++index<length){array[index]=source[index]}return array}function copyObject(source,props,object,customizer){object||(object={});var index=-1,length=props.length;while(++index<length){var key=props[index];var newValue=customizer?customizer(object[key],source[key],key,object,source):source[key];assignValue(object,key,newValue)}return object}function copySymbols(source,object){return copyObject(source,getSymbols(source),object)}function createAggregator(setter,initializer){return function(collection,iteratee){var func=isArray(collection)?arrayAggregator:baseAggregator,accumulator=initializer?initializer():{};return func(collection,setter,getIteratee(iteratee),accumulator)}}function createAssigner(assigner){return rest(function(object,sources){var index=-1,length=sources.length,customizer=length>1?sources[length-1]:undefined,guard=length>2?sources[2]:undefined;customizer=typeof customizer=="function"?(length--,customizer):undefined;if(guard&&isIterateeCall(sources[0],sources[1],guard)){customizer=length<3?undefined:customizer;length=1}object=Object(object);while(++index<length){var source=sources[index];if(source){assigner(object,source,index,customizer)}}return object})}function createBaseEach(eachFunc,fromRight){return function(collection,iteratee){if(collection==null){return collection}if(!isArrayLike(collection)){return eachFunc(collection,iteratee)}var length=collection.length,index=fromRight?length:-1,iterable=Object(collection);while(fromRight?index--:++index<length){if(iteratee(iterable[index],index,iterable)===false){break}}return collection}}function createBaseFor(fromRight){return function(object,iteratee,keysFunc){var index=-1,iterable=Object(object),props=keysFunc(object),length=props.length;while(length--){var key=props[fromRight?length:++index];if(iteratee(iterable[key],key,iterable)===false){break}}return object}}function createBaseWrapper(func,bitmask,thisArg){var isBind=bitmask&BIND_FLAG,Ctor=createCtorWrapper(func);function wrapper(){var fn=this&&this!==root&&this instanceof wrapper?Ctor:func;return fn.apply(isBind?thisArg:this,arguments)}return wrapper}function createCaseFirst(methodName){return function(string){string=toString(string);var strSymbols=reHasComplexSymbol.test(string)?stringToArray(string):undefined;var chr=strSymbols?strSymbols[0]:string.charAt(0);var trailing=strSymbols?castSlice(strSymbols,1).join(""):string.slice(1);return chr[methodName]()+trailing}}function createCompounder(callback){return function(string){return arrayReduce(words(deburr(string).replace(reApos,"")),callback,"")}}function createCtorWrapper(Ctor){return function(){var args=arguments;switch(args.length){case 0:return new Ctor;case 1:return new Ctor(args[0]);case 2:return new Ctor(args[0],args[1]);case 3:return new Ctor(args[0],args[1],args[2]);case 4:return new Ctor(args[0],args[1],args[2],args[3]);case 5:return new Ctor(args[0],args[1],args[2],args[3],args[4]);case 6:return new Ctor(args[0],args[1],args[2],args[3],args[4],args[5]);case 7:return new Ctor(args[0],args[1],args[2],args[3],args[4],args[5],args[6])}var thisBinding=baseCreate(Ctor.prototype),result=Ctor.apply(thisBinding,args);return isObject(result)?result:thisBinding}}function createCurryWrapper(func,bitmask,arity){var Ctor=createCtorWrapper(func);function wrapper(){var length=arguments.length,args=Array(length),index=length,placeholder=getPlaceholder(wrapper);while(index--){args[index]=arguments[index]}var holders=length<3&&args[0]!==placeholder&&args[length-1]!==placeholder?[]:replaceHolders(args,placeholder);length-=holders.length;if(length<arity){return createRecurryWrapper(func,bitmask,createHybridWrapper,wrapper.placeholder,undefined,args,holders,undefined,undefined,arity-length)}var fn=this&&this!==root&&this instanceof wrapper?Ctor:func;return apply(fn,this,args)}return wrapper}function createFlow(fromRight){return rest(function(funcs){funcs=baseFlatten(funcs,1);var length=funcs.length,index=length,prereq=LodashWrapper.prototype.thru;if(fromRight){funcs.reverse()}while(index--){var func=funcs[index];if(typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT)}if(prereq&&!wrapper&&getFuncName(func)=="wrapper"){var wrapper=new LodashWrapper([],true)}}index=wrapper?index:length;while(++index<length){func=funcs[index];var funcName=getFuncName(func),data=funcName=="wrapper"?getData(func):undefined;if(data&&isLaziable(data[0])&&data[1]==(ARY_FLAG|CURRY_FLAG|PARTIAL_FLAG|REARG_FLAG)&&!data[4].length&&data[9]==1){wrapper=wrapper[getFuncName(data[0])].apply(wrapper,data[3])}else{wrapper=func.length==1&&isLaziable(func)?wrapper[funcName]():wrapper.thru(func)}}return function(){var args=arguments,value=args[0];if(wrapper&&args.length==1&&isArray(value)&&value.length>=LARGE_ARRAY_SIZE){return wrapper.plant(value).value()}var index=0,result=length?funcs[index].apply(this,args):value;while(++index<length){result=funcs[index].call(this,result)}return result}})}function createHybridWrapper(func,bitmask,thisArg,partials,holders,partialsRight,holdersRight,argPos,ary,arity){var isAry=bitmask&ARY_FLAG,isBind=bitmask&BIND_FLAG,isBindKey=bitmask&BIND_KEY_FLAG,isCurried=bitmask&(CURRY_FLAG|CURRY_RIGHT_FLAG),isFlip=bitmask&FLIP_FLAG,Ctor=isBindKey?undefined:createCtorWrapper(func);function wrapper(){var length=arguments.length,index=length,args=Array(length);while(index--){args[index]=arguments[index]}if(isCurried){var placeholder=getPlaceholder(wrapper),holdersCount=countHolders(args,placeholder)}if(partials){args=composeArgs(args,partials,holders,isCurried)}if(partialsRight){args=composeArgsRight(args,partialsRight,holdersRight,isCurried)}length-=holdersCount;if(isCurried&&length<arity){var newHolders=replaceHolders(args,placeholder);return createRecurryWrapper(func,bitmask,createHybridWrapper,wrapper.placeholder,thisArg,args,newHolders,argPos,ary,arity-length)}var thisBinding=isBind?thisArg:this,fn=isBindKey?thisBinding[func]:func;length=args.length;if(argPos){args=reorder(args,argPos)}else if(isFlip&&length>1){args.reverse()}if(isAry&&ary<length){args.length=ary}if(this&&this!==root&&this instanceof wrapper){fn=Ctor||createCtorWrapper(fn)}return fn.apply(thisBinding,args)}return wrapper}function createInverter(setter,toIteratee){return function(object,iteratee){return baseInverter(object,setter,toIteratee(iteratee),{})}}function createMathOperation(operator){return function(value,other){var result;if(value===undefined&&other===undefined){return 0}if(value!==undefined){result=value}if(other!==undefined){if(result===undefined){return other}if(typeof value=="string"||typeof other=="string"){value=baseToString(value);other=baseToString(other)}else{value=baseToNumber(value);other=baseToNumber(other)}result=operator(value,other)}return result}}function createOver(arrayFunc){return rest(function(iteratees){iteratees=iteratees.length==1&&isArray(iteratees[0])?arrayMap(iteratees[0],baseUnary(getIteratee())):arrayMap(baseFlatten(iteratees,1,isFlattenableIteratee),baseUnary(getIteratee()));return rest(function(args){var thisArg=this;return arrayFunc(iteratees,function(iteratee){return apply(iteratee,thisArg,args)})})})}function createPadding(length,chars){chars=chars===undefined?" ":baseToString(chars);var charsLength=chars.length;if(charsLength<2){return charsLength?baseRepeat(chars,length):chars}var result=baseRepeat(chars,nativeCeil(length/stringSize(chars)));return reHasComplexSymbol.test(chars)?castSlice(stringToArray(result),0,length).join(""):result.slice(0,length)}function createPartialWrapper(func,bitmask,thisArg,partials){var isBind=bitmask&BIND_FLAG,Ctor=createCtorWrapper(func);function wrapper(){var argsIndex=-1,argsLength=arguments.length,leftIndex=-1,leftLength=partials.length,args=Array(leftLength+argsLength),fn=this&&this!==root&&this instanceof wrapper?Ctor:func;while(++leftIndex<leftLength){args[leftIndex]=partials[leftIndex]}while(argsLength--){args[leftIndex++]=arguments[++argsIndex]}return apply(fn,isBind?thisArg:this,args)}return wrapper}function createRange(fromRight){return function(start,end,step){if(step&&typeof step!="number"&&isIterateeCall(start,end,step)){end=step=undefined}start=toNumber(start);start=start===start?start:0;if(end===undefined){end=start;start=0}else{end=toNumber(end)||0}step=step===undefined?start<end?1:-1:toNumber(step)||0;
return baseRange(start,end,step,fromRight)}}function createRelationalOperation(operator){return function(value,other){if(!(typeof value=="string"&&typeof other=="string")){value=toNumber(value);other=toNumber(other)}return operator(value,other)}}function createRecurryWrapper(func,bitmask,wrapFunc,placeholder,thisArg,partials,holders,argPos,ary,arity){var isCurry=bitmask&CURRY_FLAG,newHolders=isCurry?holders:undefined,newHoldersRight=isCurry?undefined:holders,newPartials=isCurry?partials:undefined,newPartialsRight=isCurry?undefined:partials;bitmask|=isCurry?PARTIAL_FLAG:PARTIAL_RIGHT_FLAG;bitmask&=~(isCurry?PARTIAL_RIGHT_FLAG:PARTIAL_FLAG);if(!(bitmask&CURRY_BOUND_FLAG)){bitmask&=~(BIND_FLAG|BIND_KEY_FLAG)}var newData=[func,bitmask,thisArg,newPartials,newHolders,newPartialsRight,newHoldersRight,argPos,ary,arity];var result=wrapFunc.apply(undefined,newData);if(isLaziable(func)){setData(result,newData)}result.placeholder=placeholder;return result}function createRound(methodName){var func=Math[methodName];return function(number,precision){number=toNumber(number);precision=toInteger(precision);if(precision){var pair=(toString(number)+"e").split("e"),value=func(pair[0]+"e"+(+pair[1]+precision));pair=(toString(value)+"e").split("e");return+(pair[0]+"e"+(+pair[1]-precision))}return func(number)}}var createSet=!(Set&&1/setToArray(new Set([,-0]))[1]==INFINITY)?noop:function(values){return new Set(values)};function createWrapper(func,bitmask,thisArg,partials,holders,argPos,ary,arity){var isBindKey=bitmask&BIND_KEY_FLAG;if(!isBindKey&&typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT)}var length=partials?partials.length:0;if(!length){bitmask&=~(PARTIAL_FLAG|PARTIAL_RIGHT_FLAG);partials=holders=undefined}ary=ary===undefined?ary:nativeMax(toInteger(ary),0);arity=arity===undefined?arity:toInteger(arity);length-=holders?holders.length:0;if(bitmask&PARTIAL_RIGHT_FLAG){var partialsRight=partials,holdersRight=holders;partials=holders=undefined}var data=isBindKey?undefined:getData(func);var newData=[func,bitmask,thisArg,partials,holders,partialsRight,holdersRight,argPos,ary,arity];if(data){mergeData(newData,data)}func=newData[0];bitmask=newData[1];thisArg=newData[2];partials=newData[3];holders=newData[4];arity=newData[9]=newData[9]==null?isBindKey?0:func.length:nativeMax(newData[9]-length,0);if(!arity&&bitmask&(CURRY_FLAG|CURRY_RIGHT_FLAG)){bitmask&=~(CURRY_FLAG|CURRY_RIGHT_FLAG)}if(!bitmask||bitmask==BIND_FLAG){var result=createBaseWrapper(func,bitmask,thisArg)}else if(bitmask==CURRY_FLAG||bitmask==CURRY_RIGHT_FLAG){result=createCurryWrapper(func,bitmask,arity)}else if((bitmask==PARTIAL_FLAG||bitmask==(BIND_FLAG|PARTIAL_FLAG))&&!holders.length){result=createPartialWrapper(func,bitmask,thisArg,partials)}else{result=createHybridWrapper.apply(undefined,newData)}var setter=data?baseSetData:setData;return setter(result,newData)}function equalArrays(array,other,equalFunc,customizer,bitmask,stack){var index=-1,isPartial=bitmask&PARTIAL_COMPARE_FLAG,isUnordered=bitmask&UNORDERED_COMPARE_FLAG,arrLength=array.length,othLength=other.length;if(arrLength!=othLength&&!(isPartial&&othLength>arrLength)){return false}var stacked=stack.get(array);if(stacked){return stacked==other}var result=true;stack.set(array,other);while(++index<arrLength){var arrValue=array[index],othValue=other[index];if(customizer){var compared=isPartial?customizer(othValue,arrValue,index,other,array,stack):customizer(arrValue,othValue,index,array,other,stack)}if(compared!==undefined){if(compared){continue}result=false;break}if(isUnordered){if(!arraySome(other,function(othValue){return arrValue===othValue||equalFunc(arrValue,othValue,customizer,bitmask,stack)})){result=false;break}}else if(!(arrValue===othValue||equalFunc(arrValue,othValue,customizer,bitmask,stack))){result=false;break}}stack["delete"](array);return result}function equalByTag(object,other,tag,equalFunc,customizer,bitmask,stack){switch(tag){case dataViewTag:if(object.byteLength!=other.byteLength||object.byteOffset!=other.byteOffset){return false}object=object.buffer;other=other.buffer;case arrayBufferTag:if(object.byteLength!=other.byteLength||!equalFunc(new Uint8Array(object),new Uint8Array(other))){return false}return true;case boolTag:case dateTag:return+object==+other;case errorTag:return object.name==other.name&&object.message==other.message;case numberTag:return object!=+object?other!=+other:object==+other;case regexpTag:case stringTag:return object==other+"";case mapTag:var convert=mapToArray;case setTag:var isPartial=bitmask&PARTIAL_COMPARE_FLAG;convert||(convert=setToArray);if(object.size!=other.size&&!isPartial){return false}var stacked=stack.get(object);if(stacked){return stacked==other}bitmask|=UNORDERED_COMPARE_FLAG;stack.set(object,other);return equalArrays(convert(object),convert(other),equalFunc,customizer,bitmask,stack);case symbolTag:if(symbolValueOf){return symbolValueOf.call(object)==symbolValueOf.call(other)}}return false}function equalObjects(object,other,equalFunc,customizer,bitmask,stack){var isPartial=bitmask&PARTIAL_COMPARE_FLAG,objProps=keys(object),objLength=objProps.length,othProps=keys(other),othLength=othProps.length;if(objLength!=othLength&&!isPartial){return false}var index=objLength;while(index--){var key=objProps[index];if(!(isPartial?key in other:baseHas(other,key))){return false}}var stacked=stack.get(object);if(stacked){return stacked==other}var result=true;stack.set(object,other);var skipCtor=isPartial;while(++index<objLength){key=objProps[index];var objValue=object[key],othValue=other[key];if(customizer){var compared=isPartial?customizer(othValue,objValue,key,other,object,stack):customizer(objValue,othValue,key,object,other,stack)}if(!(compared===undefined?objValue===othValue||equalFunc(objValue,othValue,customizer,bitmask,stack):compared)){result=false;break}skipCtor||(skipCtor=key=="constructor")}if(result&&!skipCtor){var objCtor=object.constructor,othCtor=other.constructor;if(objCtor!=othCtor&&("constructor"in object&&"constructor"in other)&&!(typeof objCtor=="function"&&objCtor instanceof objCtor&&typeof othCtor=="function"&&othCtor instanceof othCtor)){result=false}}stack["delete"](object);return result}function getAllKeys(object){return baseGetAllKeys(object,keys,getSymbols)}function getAllKeysIn(object){return baseGetAllKeys(object,keysIn,getSymbolsIn)}var getData=!metaMap?noop:function(func){return metaMap.get(func)};function getFuncName(func){var result=func.name+"",array=realNames[result],length=hasOwnProperty.call(realNames,result)?array.length:0;while(length--){var data=array[length],otherFunc=data.func;if(otherFunc==null||otherFunc==func){return data.name}}return result}function getIteratee(){var result=lodash.iteratee||iteratee;result=result===iteratee?baseIteratee:result;return arguments.length?result(arguments[0],arguments[1]):result}var getLength=baseProperty("length");function getMatchData(object){var result=toPairs(object),length=result.length;while(length--){result[length][2]=isStrictComparable(result[length][1])}return result}function getNative(object,key){var value=object[key];return isNative(value)?value:undefined}function getPlaceholder(func){var object=hasOwnProperty.call(lodash,"placeholder")?lodash:func;return object.placeholder}function getPrototype(value){return nativeGetPrototype(Object(value))}function getSymbols(object){return getOwnPropertySymbols(Object(object))}if(!getOwnPropertySymbols){getSymbols=function(){return[]}}var getSymbolsIn=!getOwnPropertySymbols?getSymbols:function(object){var result=[];while(object){arrayPush(result,getSymbols(object));object=getPrototype(object)}return result};function getTag(value){return objectToString.call(value)}if(DataView&&getTag(new DataView(new ArrayBuffer(1)))!=dataViewTag||Map&&getTag(new Map)!=mapTag||Promise&&getTag(Promise.resolve())!=promiseTag||Set&&getTag(new Set)!=setTag||WeakMap&&getTag(new WeakMap)!=weakMapTag){getTag=function(value){var result=objectToString.call(value),Ctor=result==objectTag?value.constructor:undefined,ctorString=Ctor?toSource(Ctor):undefined;if(ctorString){switch(ctorString){case dataViewCtorString:return dataViewTag;case mapCtorString:return mapTag;case promiseCtorString:return promiseTag;case setCtorString:return setTag;case weakMapCtorString:return weakMapTag}}return result}}function getView(start,end,transforms){var index=-1,length=transforms.length;while(++index<length){var data=transforms[index],size=data.size;switch(data.type){case"drop":start+=size;break;case"dropRight":end-=size;break;case"take":end=nativeMin(end,start+size);break;case"takeRight":start=nativeMax(start,end-size);break}}return{start:start,end:end}}function hasPath(object,path,hasFunc){path=isKey(path,object)?[path]:castPath(path);var result,index=-1,length=path.length;while(++index<length){var key=toKey(path[index]);if(!(result=object!=null&&hasFunc(object,key))){break}object=object[key]}if(result){return result}var length=object?object.length:0;return!!length&&isLength(length)&&isIndex(key,length)&&(isArray(object)||isString(object)||isArguments(object))}function initCloneArray(array){var length=array.length,result=array.constructor(length);if(length&&typeof array[0]=="string"&&hasOwnProperty.call(array,"index")){result.index=array.index;result.input=array.input}return result}function initCloneObject(object){return typeof object.constructor=="function"&&!isPrototype(object)?baseCreate(getPrototype(object)):{}}function initCloneByTag(object,tag,cloneFunc,isDeep){var Ctor=object.constructor;switch(tag){case arrayBufferTag:return cloneArrayBuffer(object);case boolTag:case dateTag:return new Ctor(+object);case dataViewTag:return cloneDataView(object,isDeep);case float32Tag:case float64Tag:case int8Tag:case int16Tag:case int32Tag:case uint8Tag:case uint8ClampedTag:case uint16Tag:case uint32Tag:return cloneTypedArray(object,isDeep);case mapTag:return cloneMap(object,isDeep,cloneFunc);case numberTag:case stringTag:return new Ctor(object);case regexpTag:return cloneRegExp(object);case setTag:return cloneSet(object,isDeep,cloneFunc);case symbolTag:return cloneSymbol(object)}}function indexKeys(object){var length=object?object.length:undefined;if(isLength(length)&&(isArray(object)||isString(object)||isArguments(object))){return baseTimes(length,String)}return null}function isFlattenable(value){return isArrayLikeObject(value)&&(isArray(value)||isArguments(value))}function isFlattenableIteratee(value){return isArray(value)&&!(value.length==2&&!isFunction(value[0]))}function isIndex(value,length){length=length==null?MAX_SAFE_INTEGER:length;return!!length&&(typeof value=="number"||reIsUint.test(value))&&(value>-1&&value%1==0&&value<length)}function isIterateeCall(value,index,object){if(!isObject(object)){return false}var type=typeof index;if(type=="number"?isArrayLike(object)&&isIndex(index,object.length):type=="string"&&index in object){return eq(object[index],value)}return false}function isKey(value,object){if(isArray(value)){return false}var type=typeof value;if(type=="number"||type=="symbol"||type=="boolean"||value==null||isSymbol(value)){return true}return reIsPlainProp.test(value)||!reIsDeepProp.test(value)||object!=null&&value in Object(object)}function isKeyable(value){var type=typeof value;return type=="string"||type=="number"||type=="symbol"||type=="boolean"?value!=="__proto__":value===null}function isLaziable(func){var funcName=getFuncName(func),other=lodash[funcName];if(typeof other!="function"||!(funcName in LazyWrapper.prototype)){return false}if(func===other){return true}var data=getData(other);return!!data&&func===data[0]}function isPrototype(value){var Ctor=value&&value.constructor,proto=typeof Ctor=="function"&&Ctor.prototype||objectProto;return value===proto}function isStrictComparable(value){return value===value&&!isObject(value)}function matchesStrictComparable(key,srcValue){return function(object){if(object==null){return false}return object[key]===srcValue&&(srcValue!==undefined||key in Object(object))}}function mergeData(data,source){var bitmask=data[1],srcBitmask=source[1],newBitmask=bitmask|srcBitmask,isCommon=newBitmask<(BIND_FLAG|BIND_KEY_FLAG|ARY_FLAG);var isCombo=srcBitmask==ARY_FLAG&&bitmask==CURRY_FLAG||srcBitmask==ARY_FLAG&&bitmask==REARG_FLAG&&data[7].length<=source[8]||srcBitmask==(ARY_FLAG|REARG_FLAG)&&source[7].length<=source[8]&&bitmask==CURRY_FLAG;if(!(isCommon||isCombo)){return data}if(srcBitmask&BIND_FLAG){data[2]=source[2];newBitmask|=bitmask&BIND_FLAG?0:CURRY_BOUND_FLAG}var value=source[3];if(value){var partials=data[3];data[3]=partials?composeArgs(partials,value,source[4]):value;data[4]=partials?replaceHolders(data[3],PLACEHOLDER):source[4]}value=source[5];if(value){partials=data[5];data[5]=partials?composeArgsRight(partials,value,source[6]):value;data[6]=partials?replaceHolders(data[5],PLACEHOLDER):source[6]}value=source[7];if(value){data[7]=value}if(srcBitmask&ARY_FLAG){data[8]=data[8]==null?source[8]:nativeMin(data[8],source[8])}if(data[9]==null){data[9]=source[9]}data[0]=source[0];data[1]=newBitmask;return data}function mergeDefaults(objValue,srcValue,key,object,source,stack){if(isObject(objValue)&&isObject(srcValue)){baseMerge(objValue,srcValue,undefined,mergeDefaults,stack.set(srcValue,objValue))}return objValue}function parent(object,path){return path.length==1?object:baseGet(object,baseSlice(path,0,-1))}function reorder(array,indexes){var arrLength=array.length,length=nativeMin(indexes.length,arrLength),oldArray=copyArray(array);while(length--){var index=indexes[length];array[length]=isIndex(index,arrLength)?oldArray[index]:undefined}return array}var setData=function(){var count=0,lastCalled=0;return function(key,value){var stamp=now(),remaining=HOT_SPAN-(stamp-lastCalled);lastCalled=stamp;if(remaining>0){if(++count>=HOT_COUNT){return key}}else{count=0}return baseSetData(key,value)}}();var stringToPath=memoize(function(string){var result=[];toString(string).replace(rePropName,function(match,number,quote,string){result.push(quote?string.replace(reEscapeChar,"$1"):number||match)});return result});function toKey(value){if(typeof value=="string"||isSymbol(value)){return value}var result=value+"";return result=="0"&&1/value==-INFINITY?"-0":result}function toSource(func){if(func!=null){try{return funcToString.call(func)}catch(e){}try{return func+""}catch(e){}}return""}function wrapperClone(wrapper){if(wrapper instanceof LazyWrapper){return wrapper.clone()}var result=new LodashWrapper(wrapper.__wrapped__,wrapper.__chain__);result.__actions__=copyArray(wrapper.__actions__);result.__index__=wrapper.__index__;result.__values__=wrapper.__values__;return result}function chunk(array,size,guard){if(guard?isIterateeCall(array,size,guard):size===undefined){size=1}else{size=nativeMax(toInteger(size),0)}var length=array?array.length:0;if(!length||size<1){return[]}var index=0,resIndex=0,result=Array(nativeCeil(length/size));while(index<length){result[resIndex++]=baseSlice(array,index,index+=size)}return result}function compact(array){var index=-1,length=array?array.length:0,resIndex=0,result=[];while(++index<length){var value=array[index];if(value){result[resIndex++]=value}}return result}function concat(){var length=arguments.length,array=castArray(arguments[0]);if(length<2){return length?copyArray(array):[]}var args=Array(length-1);while(length--){args[length-1]=arguments[length]}return arrayConcat(array,baseFlatten(args,1))}var difference=rest(function(array,values){return isArrayLikeObject(array)?baseDifference(array,baseFlatten(values,1,isArrayLikeObject,true)):[]});var differenceBy=rest(function(array,values){var iteratee=last(values);if(isArrayLikeObject(iteratee)){iteratee=undefined}return isArrayLikeObject(array)?baseDifference(array,baseFlatten(values,1,isArrayLikeObject,true),getIteratee(iteratee)):[]});var differenceWith=rest(function(array,values){var comparator=last(values);if(isArrayLikeObject(comparator)){comparator=undefined}return isArrayLikeObject(array)?baseDifference(array,baseFlatten(values,1,isArrayLikeObject,true),undefined,comparator):[]});function drop(array,n,guard){var length=array?array.length:0;if(!length){return[]}n=guard||n===undefined?1:toInteger(n);return baseSlice(array,n<0?0:n,length)}function dropRight(array,n,guard){var length=array?array.length:0;if(!length){return[]}n=guard||n===undefined?1:toInteger(n);n=length-n;return baseSlice(array,0,n<0?0:n)}function dropRightWhile(array,predicate){return array&&array.length?baseWhile(array,getIteratee(predicate,3),true,true):[]}function dropWhile(array,predicate){return array&&array.length?baseWhile(array,getIteratee(predicate,3),true):[]}function fill(array,value,start,end){var length=array?array.length:0;if(!length){return[]}if(start&&typeof start!="number"&&isIterateeCall(array,value,start)){start=0;end=length}return baseFill(array,value,start,end)}function findIndex(array,predicate){return array&&array.length?baseFindIndex(array,getIteratee(predicate,3)):-1}function findLastIndex(array,predicate){return array&&array.length?baseFindIndex(array,getIteratee(predicate,3),true):-1}function flatten(array){var length=array?array.length:0;return length?baseFlatten(array,1):[]}function flattenDeep(array){var length=array?array.length:0;return length?baseFlatten(array,INFINITY):[]}function flattenDepth(array,depth){var length=array?array.length:0;if(!length){return[]}depth=depth===undefined?1:toInteger(depth);return baseFlatten(array,depth)}function fromPairs(pairs){var index=-1,length=pairs?pairs.length:0,result={};while(++index<length){var pair=pairs[index];result[pair[0]]=pair[1]}return result}function head(array){return array&&array.length?array[0]:undefined}function indexOf(array,value,fromIndex){var length=array?array.length:0;if(!length){return-1}fromIndex=toInteger(fromIndex);if(fromIndex<0){fromIndex=nativeMax(length+fromIndex,0)}return baseIndexOf(array,value,fromIndex)}function initial(array){return dropRight(array,1)}var intersection=rest(function(arrays){var mapped=arrayMap(arrays,castArrayLikeObject);return mapped.length&&mapped[0]===arrays[0]?baseIntersection(mapped):[]});var intersectionBy=rest(function(arrays){var iteratee=last(arrays),mapped=arrayMap(arrays,castArrayLikeObject);if(iteratee===last(mapped)){iteratee=undefined}else{mapped.pop()}return mapped.length&&mapped[0]===arrays[0]?baseIntersection(mapped,getIteratee(iteratee)):[]});var intersectionWith=rest(function(arrays){var comparator=last(arrays),mapped=arrayMap(arrays,castArrayLikeObject);if(comparator===last(mapped)){comparator=undefined}else{mapped.pop()}return mapped.length&&mapped[0]===arrays[0]?baseIntersection(mapped,undefined,comparator):[]});function join(array,separator){return array?nativeJoin.call(array,separator):""}function last(array){var length=array?array.length:0;return length?array[length-1]:undefined}function lastIndexOf(array,value,fromIndex){var length=array?array.length:0;if(!length){return-1}var index=length;if(fromIndex!==undefined){index=toInteger(fromIndex);index=(index<0?nativeMax(length+index,0):nativeMin(index,length-1))+1}if(value!==value){return indexOfNaN(array,index,true)}while(index--){if(array[index]===value){return index}}return-1}function nth(array,n){return array&&array.length?baseNth(array,toInteger(n)):undefined}var pull=rest(pullAll);function pullAll(array,values){return array&&array.length&&values&&values.length?basePullAll(array,values):array}function pullAllBy(array,values,iteratee){return array&&array.length&&values&&values.length?basePullAll(array,values,getIteratee(iteratee)):array}function pullAllWith(array,values,comparator){return array&&array.length&&values&&values.length?basePullAll(array,values,undefined,comparator):array}var pullAt=rest(function(array,indexes){indexes=baseFlatten(indexes,1);var length=array?array.length:0,result=baseAt(array,indexes);basePullAt(array,arrayMap(indexes,function(index){return isIndex(index,length)?+index:index}).sort(compareAscending));return result});function remove(array,predicate){var result=[];if(!(array&&array.length)){return result}var index=-1,indexes=[],length=array.length;predicate=getIteratee(predicate,3);while(++index<length){var value=array[index];if(predicate(value,index,array)){result.push(value);indexes.push(index)}}basePullAt(array,indexes);return result}function reverse(array){return array?nativeReverse.call(array):array}function slice(array,start,end){var length=array?array.length:0;if(!length){return[]}if(end&&typeof end!="number"&&isIterateeCall(array,start,end)){start=0;end=length}else{start=start==null?0:toInteger(start);end=end===undefined?length:toInteger(end)}return baseSlice(array,start,end)}function sortedIndex(array,value){return baseSortedIndex(array,value)}function sortedIndexBy(array,value,iteratee){return baseSortedIndexBy(array,value,getIteratee(iteratee))}function sortedIndexOf(array,value){var length=array?array.length:0;if(length){var index=baseSortedIndex(array,value);if(index<length&&eq(array[index],value)){return index}}return-1}function sortedLastIndex(array,value){return baseSortedIndex(array,value,true)}function sortedLastIndexBy(array,value,iteratee){return baseSortedIndexBy(array,value,getIteratee(iteratee),true)}function sortedLastIndexOf(array,value){var length=array?array.length:0;if(length){var index=baseSortedIndex(array,value,true)-1;if(eq(array[index],value)){return index}}return-1}function sortedUniq(array){return array&&array.length?baseSortedUniq(array):[]}function sortedUniqBy(array,iteratee){return array&&array.length?baseSortedUniq(array,getIteratee(iteratee)):[]}function tail(array){return drop(array,1)}function take(array,n,guard){if(!(array&&array.length)){return[]}n=guard||n===undefined?1:toInteger(n);return baseSlice(array,0,n<0?0:n)}function takeRight(array,n,guard){var length=array?array.length:0;if(!length){return[]}n=guard||n===undefined?1:toInteger(n);n=length-n;return baseSlice(array,n<0?0:n,length)}function takeRightWhile(array,predicate){return array&&array.length?baseWhile(array,getIteratee(predicate,3),false,true):[]}function takeWhile(array,predicate){return array&&array.length?baseWhile(array,getIteratee(predicate,3)):[]}var union=rest(function(arrays){return baseUniq(baseFlatten(arrays,1,isArrayLikeObject,true))});var unionBy=rest(function(arrays){var iteratee=last(arrays);if(isArrayLikeObject(iteratee)){iteratee=undefined}return baseUniq(baseFlatten(arrays,1,isArrayLikeObject,true),getIteratee(iteratee))});var unionWith=rest(function(arrays){var comparator=last(arrays);if(isArrayLikeObject(comparator)){comparator=undefined}return baseUniq(baseFlatten(arrays,1,isArrayLikeObject,true),undefined,comparator)});function uniq(array){return array&&array.length?baseUniq(array):[]}function uniqBy(array,iteratee){return array&&array.length?baseUniq(array,getIteratee(iteratee)):[]}function uniqWith(array,comparator){return array&&array.length?baseUniq(array,undefined,comparator):[]}function unzip(array){if(!(array&&array.length)){return[]}var length=0;array=arrayFilter(array,function(group){if(isArrayLikeObject(group)){length=nativeMax(group.length,length);return true}});return baseTimes(length,function(index){return arrayMap(array,baseProperty(index))})}function unzipWith(array,iteratee){if(!(array&&array.length)){return[]}var result=unzip(array);if(iteratee==null){return result}return arrayMap(result,function(group){return apply(iteratee,undefined,group)})}var without=rest(function(array,values){return isArrayLikeObject(array)?baseDifference(array,values):[]});var xor=rest(function(arrays){return baseXor(arrayFilter(arrays,isArrayLikeObject))});var xorBy=rest(function(arrays){var iteratee=last(arrays);if(isArrayLikeObject(iteratee)){iteratee=undefined}return baseXor(arrayFilter(arrays,isArrayLikeObject),getIteratee(iteratee))});var xorWith=rest(function(arrays){var comparator=last(arrays);if(isArrayLikeObject(comparator)){comparator=undefined}return baseXor(arrayFilter(arrays,isArrayLikeObject),undefined,comparator)});var zip=rest(unzip);function zipObject(props,values){return baseZipObject(props||[],values||[],assignValue)}function zipObjectDeep(props,values){return baseZipObject(props||[],values||[],baseSet)}var zipWith=rest(function(arrays){var length=arrays.length,iteratee=length>1?arrays[length-1]:undefined;iteratee=typeof iteratee=="function"?(arrays.pop(),iteratee):undefined;return unzipWith(arrays,iteratee)});function chain(value){var result=lodash(value);result.__chain__=true;return result}function tap(value,interceptor){interceptor(value);return value}function thru(value,interceptor){return interceptor(value)}var wrapperAt=rest(function(paths){paths=baseFlatten(paths,1);var length=paths.length,start=length?paths[0]:0,value=this.__wrapped__,interceptor=function(object){return baseAt(object,paths)};if(length>1||this.__actions__.length||!(value instanceof LazyWrapper)||!isIndex(start)){return this.thru(interceptor)}value=value.slice(start,+start+(length?1:0));value.__actions__.push({func:thru,args:[interceptor],thisArg:undefined});return new LodashWrapper(value,this.__chain__).thru(function(array){if(length&&!array.length){array.push(undefined)}return array})});function wrapperChain(){return chain(this)}function wrapperCommit(){return new LodashWrapper(this.value(),this.__chain__)}function wrapperNext(){if(this.__values__===undefined){this.__values__=toArray(this.value())}var done=this.__index__>=this.__values__.length,value=done?undefined:this.__values__[this.__index__++];return{done:done,value:value}}function wrapperToIterator(){return this}function wrapperPlant(value){var result,parent=this;while(parent instanceof baseLodash){var clone=wrapperClone(parent);clone.__index__=0;clone.__values__=undefined;if(result){previous.__wrapped__=clone}else{result=clone}var previous=clone;parent=parent.__wrapped__}previous.__wrapped__=value;return result}function wrapperReverse(){var value=this.__wrapped__;if(value instanceof LazyWrapper){var wrapped=value;if(this.__actions__.length){wrapped=new LazyWrapper(this)}wrapped=wrapped.reverse();wrapped.__actions__.push({func:thru,args:[reverse],thisArg:undefined});return new LodashWrapper(wrapped,this.__chain__)}return this.thru(reverse)}function wrapperValue(){return baseWrapperValue(this.__wrapped__,this.__actions__)}var countBy=createAggregator(function(result,value,key){hasOwnProperty.call(result,key)?++result[key]:result[key]=1});function every(collection,predicate,guard){var func=isArray(collection)?arrayEvery:baseEvery;if(guard&&isIterateeCall(collection,predicate,guard)){predicate=undefined}return func(collection,getIteratee(predicate,3))}function filter(collection,predicate){var func=isArray(collection)?arrayFilter:baseFilter;return func(collection,getIteratee(predicate,3))}function find(collection,predicate){predicate=getIteratee(predicate,3);if(isArray(collection)){var index=baseFindIndex(collection,predicate);return index>-1?collection[index]:undefined}return baseFind(collection,predicate,baseEach)}function findLast(collection,predicate){predicate=getIteratee(predicate,3);if(isArray(collection)){var index=baseFindIndex(collection,predicate,true);return index>-1?collection[index]:undefined}return baseFind(collection,predicate,baseEachRight)}function flatMap(collection,iteratee){return baseFlatten(map(collection,iteratee),1)}function flatMapDeep(collection,iteratee){return baseFlatten(map(collection,iteratee),INFINITY)}function flatMapDepth(collection,iteratee,depth){depth=depth===undefined?1:toInteger(depth);return baseFlatten(map(collection,iteratee),depth)}function forEach(collection,iteratee){return typeof iteratee=="function"&&isArray(collection)?arrayEach(collection,iteratee):baseEach(collection,getIteratee(iteratee))}function forEachRight(collection,iteratee){return typeof iteratee=="function"&&isArray(collection)?arrayEachRight(collection,iteratee):baseEachRight(collection,getIteratee(iteratee))}var groupBy=createAggregator(function(result,value,key){if(hasOwnProperty.call(result,key)){result[key].push(value)}else{result[key]=[value]}});function includes(collection,value,fromIndex,guard){collection=isArrayLike(collection)?collection:values(collection);fromIndex=fromIndex&&!guard?toInteger(fromIndex):0;var length=collection.length;if(fromIndex<0){fromIndex=nativeMax(length+fromIndex,0)}return isString(collection)?fromIndex<=length&&collection.indexOf(value,fromIndex)>-1:!!length&&baseIndexOf(collection,value,fromIndex)>-1}var invokeMap=rest(function(collection,path,args){var index=-1,isFunc=typeof path=="function",isProp=isKey(path),result=isArrayLike(collection)?Array(collection.length):[];baseEach(collection,function(value){var func=isFunc?path:isProp&&value!=null?value[path]:undefined;result[++index]=func?apply(func,value,args):baseInvoke(value,path,args)});return result});var keyBy=createAggregator(function(result,value,key){result[key]=value});function map(collection,iteratee){var func=isArray(collection)?arrayMap:baseMap;return func(collection,getIteratee(iteratee,3))}function orderBy(collection,iteratees,orders,guard){if(collection==null){return[]}if(!isArray(iteratees)){iteratees=iteratees==null?[]:[iteratees]}orders=guard?undefined:orders;if(!isArray(orders)){orders=orders==null?[]:[orders]}return baseOrderBy(collection,iteratees,orders)}var partition=createAggregator(function(result,value,key){result[key?0:1].push(value)},function(){return[[],[]]});function reduce(collection,iteratee,accumulator){var func=isArray(collection)?arrayReduce:baseReduce,initAccum=arguments.length<3;return func(collection,getIteratee(iteratee,4),accumulator,initAccum,baseEach)}function reduceRight(collection,iteratee,accumulator){var func=isArray(collection)?arrayReduceRight:baseReduce,initAccum=arguments.length<3;return func(collection,getIteratee(iteratee,4),accumulator,initAccum,baseEachRight)}function reject(collection,predicate){var func=isArray(collection)?arrayFilter:baseFilter;predicate=getIteratee(predicate,3);return func(collection,function(value,index,collection){return!predicate(value,index,collection)})}function sample(collection){var array=isArrayLike(collection)?collection:values(collection),length=array.length;return length>0?array[baseRandom(0,length-1)]:undefined}function sampleSize(collection,n,guard){var index=-1,result=toArray(collection),length=result.length,lastIndex=length-1;if(guard?isIterateeCall(collection,n,guard):n===undefined){n=1}else{n=baseClamp(toInteger(n),0,length)}while(++index<n){var rand=baseRandom(index,lastIndex),value=result[rand];result[rand]=result[index];result[index]=value}result.length=n;return result}function shuffle(collection){return sampleSize(collection,MAX_ARRAY_LENGTH)}function size(collection){if(collection==null){return 0}if(isArrayLike(collection)){var result=collection.length;return result&&isString(collection)?stringSize(collection):result}if(isObjectLike(collection)){var tag=getTag(collection);if(tag==mapTag||tag==setTag){return collection.size}}return keys(collection).length}function some(collection,predicate,guard){var func=isArray(collection)?arraySome:baseSome;if(guard&&isIterateeCall(collection,predicate,guard)){predicate=undefined}return func(collection,getIteratee(predicate,3))}var sortBy=rest(function(collection,iteratees){if(collection==null){return[]}var length=iteratees.length;if(length>1&&isIterateeCall(collection,iteratees[0],iteratees[1])){iteratees=[]}else if(length>2&&isIterateeCall(iteratees[0],iteratees[1],iteratees[2])){iteratees=[iteratees[0]]}iteratees=iteratees.length==1&&isArray(iteratees[0])?iteratees[0]:baseFlatten(iteratees,1,isFlattenableIteratee);return baseOrderBy(collection,iteratees,[])});var now=Date.now;function after(n,func){if(typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT)}n=toInteger(n);return function(){if(--n<1){return func.apply(this,arguments)}}}function ary(func,n,guard){n=guard?undefined:n;n=func&&n==null?func.length:n;return createWrapper(func,ARY_FLAG,undefined,undefined,undefined,undefined,n)}function before(n,func){var result;if(typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT);
}n=toInteger(n);return function(){if(--n>0){result=func.apply(this,arguments)}if(n<=1){func=undefined}return result}}var bind=rest(function(func,thisArg,partials){var bitmask=BIND_FLAG;if(partials.length){var holders=replaceHolders(partials,getPlaceholder(bind));bitmask|=PARTIAL_FLAG}return createWrapper(func,bitmask,thisArg,partials,holders)});var bindKey=rest(function(object,key,partials){var bitmask=BIND_FLAG|BIND_KEY_FLAG;if(partials.length){var holders=replaceHolders(partials,getPlaceholder(bindKey));bitmask|=PARTIAL_FLAG}return createWrapper(key,bitmask,object,partials,holders)});function curry(func,arity,guard){arity=guard?undefined:arity;var result=createWrapper(func,CURRY_FLAG,undefined,undefined,undefined,undefined,undefined,arity);result.placeholder=curry.placeholder;return result}function curryRight(func,arity,guard){arity=guard?undefined:arity;var result=createWrapper(func,CURRY_RIGHT_FLAG,undefined,undefined,undefined,undefined,undefined,arity);result.placeholder=curryRight.placeholder;return result}function debounce(func,wait,options){var lastArgs,lastThis,maxWait,result,timerId,lastCallTime=0,lastInvokeTime=0,leading=false,maxing=false,trailing=true;if(typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT)}wait=toNumber(wait)||0;if(isObject(options)){leading=!!options.leading;maxing="maxWait"in options;maxWait=maxing?nativeMax(toNumber(options.maxWait)||0,wait):maxWait;trailing="trailing"in options?!!options.trailing:trailing}function invokeFunc(time){var args=lastArgs,thisArg=lastThis;lastArgs=lastThis=undefined;lastInvokeTime=time;result=func.apply(thisArg,args);return result}function leadingEdge(time){lastInvokeTime=time;timerId=setTimeout(timerExpired,wait);return leading?invokeFunc(time):result}function remainingWait(time){var timeSinceLastCall=time-lastCallTime,timeSinceLastInvoke=time-lastInvokeTime,result=wait-timeSinceLastCall;return maxing?nativeMin(result,maxWait-timeSinceLastInvoke):result}function shouldInvoke(time){var timeSinceLastCall=time-lastCallTime,timeSinceLastInvoke=time-lastInvokeTime;return!lastCallTime||timeSinceLastCall>=wait||timeSinceLastCall<0||maxing&&timeSinceLastInvoke>=maxWait}function timerExpired(){var time=now();if(shouldInvoke(time)){return trailingEdge(time)}timerId=setTimeout(timerExpired,remainingWait(time))}function trailingEdge(time){clearTimeout(timerId);timerId=undefined;if(trailing&&lastArgs){return invokeFunc(time)}lastArgs=lastThis=undefined;return result}function cancel(){if(timerId!==undefined){clearTimeout(timerId)}lastCallTime=lastInvokeTime=0;lastArgs=lastThis=timerId=undefined}function flush(){return timerId===undefined?result:trailingEdge(now())}function debounced(){var time=now(),isInvoking=shouldInvoke(time);lastArgs=arguments;lastThis=this;lastCallTime=time;if(isInvoking){if(timerId===undefined){return leadingEdge(lastCallTime)}if(maxing){clearTimeout(timerId);timerId=setTimeout(timerExpired,wait);return invokeFunc(lastCallTime)}}if(timerId===undefined){timerId=setTimeout(timerExpired,wait)}return result}debounced.cancel=cancel;debounced.flush=flush;return debounced}var defer=rest(function(func,args){return baseDelay(func,1,args)});var delay=rest(function(func,wait,args){return baseDelay(func,toNumber(wait)||0,args)});function flip(func){return createWrapper(func,FLIP_FLAG)}function memoize(func,resolver){if(typeof func!="function"||resolver&&typeof resolver!="function"){throw new TypeError(FUNC_ERROR_TEXT)}var memoized=function(){var args=arguments,key=resolver?resolver.apply(this,args):args[0],cache=memoized.cache;if(cache.has(key)){return cache.get(key)}var result=func.apply(this,args);memoized.cache=cache.set(key,result);return result};memoized.cache=new(memoize.Cache||MapCache);return memoized}memoize.Cache=MapCache;function negate(predicate){if(typeof predicate!="function"){throw new TypeError(FUNC_ERROR_TEXT)}return function(){return!predicate.apply(this,arguments)}}function once(func){return before(2,func)}var overArgs=rest(function(func,transforms){transforms=transforms.length==1&&isArray(transforms[0])?arrayMap(transforms[0],baseUnary(getIteratee())):arrayMap(baseFlatten(transforms,1,isFlattenableIteratee),baseUnary(getIteratee()));var funcsLength=transforms.length;return rest(function(args){var index=-1,length=nativeMin(args.length,funcsLength);while(++index<length){args[index]=transforms[index].call(this,args[index])}return apply(func,this,args)})});var partial=rest(function(func,partials){var holders=replaceHolders(partials,getPlaceholder(partial));return createWrapper(func,PARTIAL_FLAG,undefined,partials,holders)});var partialRight=rest(function(func,partials){var holders=replaceHolders(partials,getPlaceholder(partialRight));return createWrapper(func,PARTIAL_RIGHT_FLAG,undefined,partials,holders)});var rearg=rest(function(func,indexes){return createWrapper(func,REARG_FLAG,undefined,undefined,undefined,baseFlatten(indexes,1))});function rest(func,start){if(typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT)}start=nativeMax(start===undefined?func.length-1:toInteger(start),0);return function(){var args=arguments,index=-1,length=nativeMax(args.length-start,0),array=Array(length);while(++index<length){array[index]=args[start+index]}switch(start){case 0:return func.call(this,array);case 1:return func.call(this,args[0],array);case 2:return func.call(this,args[0],args[1],array)}var otherArgs=Array(start+1);index=-1;while(++index<start){otherArgs[index]=args[index]}otherArgs[start]=array;return apply(func,this,otherArgs)}}function spread(func,start){if(typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT)}start=start===undefined?0:nativeMax(toInteger(start),0);return rest(function(args){var array=args[start],otherArgs=castSlice(args,0,start);if(array){arrayPush(otherArgs,array)}return apply(func,this,otherArgs)})}function throttle(func,wait,options){var leading=true,trailing=true;if(typeof func!="function"){throw new TypeError(FUNC_ERROR_TEXT)}if(isObject(options)){leading="leading"in options?!!options.leading:leading;trailing="trailing"in options?!!options.trailing:trailing}return debounce(func,wait,{leading:leading,maxWait:wait,trailing:trailing})}function unary(func){return ary(func,1)}function wrap(value,wrapper){wrapper=wrapper==null?identity:wrapper;return partial(wrapper,value)}function castArray(){if(!arguments.length){return[]}var value=arguments[0];return isArray(value)?value:[value]}function clone(value){return baseClone(value,false,true)}function cloneWith(value,customizer){return baseClone(value,false,true,customizer)}function cloneDeep(value){return baseClone(value,true,true)}function cloneDeepWith(value,customizer){return baseClone(value,true,true,customizer)}function eq(value,other){return value===other||value!==value&&other!==other}var gt=createRelationalOperation(baseGt);var gte=createRelationalOperation(function(value,other){return value>=other});function isArguments(value){return isArrayLikeObject(value)&&hasOwnProperty.call(value,"callee")&&(!propertyIsEnumerable.call(value,"callee")||objectToString.call(value)==argsTag)}var isArray=Array.isArray;function isArrayBuffer(value){return isObjectLike(value)&&objectToString.call(value)==arrayBufferTag}function isArrayLike(value){return value!=null&&isLength(getLength(value))&&!isFunction(value)}function isArrayLikeObject(value){return isObjectLike(value)&&isArrayLike(value)}function isBoolean(value){return value===true||value===false||isObjectLike(value)&&objectToString.call(value)==boolTag}var isBuffer=!Buffer?constant(false):function(value){return value instanceof Buffer};function isDate(value){return isObjectLike(value)&&objectToString.call(value)==dateTag}function isElement(value){return!!value&&value.nodeType===1&&isObjectLike(value)&&!isPlainObject(value)}function isEmpty(value){if(isArrayLike(value)&&(isArray(value)||isString(value)||isFunction(value.splice)||isArguments(value)||isBuffer(value))){return!value.length}if(isObjectLike(value)){var tag=getTag(value);if(tag==mapTag||tag==setTag){return!value.size}}for(var key in value){if(hasOwnProperty.call(value,key)){return false}}return!(nonEnumShadows&&keys(value).length)}function isEqual(value,other){return baseIsEqual(value,other)}function isEqualWith(value,other,customizer){customizer=typeof customizer=="function"?customizer:undefined;var result=customizer?customizer(value,other):undefined;return result===undefined?baseIsEqual(value,other,customizer):!!result}function isError(value){if(!isObjectLike(value)){return false}return objectToString.call(value)==errorTag||typeof value.message=="string"&&typeof value.name=="string"}function isFinite(value){return typeof value=="number"&&nativeIsFinite(value)}function isFunction(value){var tag=isObject(value)?objectToString.call(value):"";return tag==funcTag||tag==genTag}function isInteger(value){return typeof value=="number"&&value==toInteger(value)}function isLength(value){return typeof value=="number"&&value>-1&&value%1==0&&value<=MAX_SAFE_INTEGER}function isObject(value){var type=typeof value;return!!value&&(type=="object"||type=="function")}function isObjectLike(value){return!!value&&typeof value=="object"}function isMap(value){return isObjectLike(value)&&getTag(value)==mapTag}function isMatch(object,source){return object===source||baseIsMatch(object,source,getMatchData(source))}function isMatchWith(object,source,customizer){customizer=typeof customizer=="function"?customizer:undefined;return baseIsMatch(object,source,getMatchData(source),customizer)}function isNaN(value){return isNumber(value)&&value!=+value}function isNative(value){if(!isObject(value)){return false}var pattern=isFunction(value)||isHostObject(value)?reIsNative:reIsHostCtor;return pattern.test(toSource(value))}function isNull(value){return value===null}function isNil(value){return value==null}function isNumber(value){return typeof value=="number"||isObjectLike(value)&&objectToString.call(value)==numberTag}function isPlainObject(value){if(!isObjectLike(value)||objectToString.call(value)!=objectTag||isHostObject(value)){return false}var proto=getPrototype(value);if(proto===null){return true}var Ctor=hasOwnProperty.call(proto,"constructor")&&proto.constructor;return typeof Ctor=="function"&&Ctor instanceof Ctor&&funcToString.call(Ctor)==objectCtorString}function isRegExp(value){return isObject(value)&&objectToString.call(value)==regexpTag}function isSafeInteger(value){return isInteger(value)&&value>=-MAX_SAFE_INTEGER&&value<=MAX_SAFE_INTEGER}function isSet(value){return 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'' : __t) +\n'"}index=offset+match.length;return match});source+="';\n";var variable=options.variable;if(!variable){source="with (obj) {\n"+source+"\n}\n"}source=(isEvaluating?source.replace(reEmptyStringLeading,""):source).replace(reEmptyStringMiddle,"$1").replace(reEmptyStringTrailing,"$1;");source="function("+(variable||"obj")+") {\n"+(variable?"":"obj || (obj = {});\n")+"var __t, __p = ''"+(isEscaping?", __e = _.escape":"")+(isEvaluating?", __j = Array.prototype.join;\n"+"function print() { __p += __j.call(arguments, '') }\n":";\n")+source+"return __p\n}";var result=attempt(function(){return Function(importsKeys,sourceURL+"return "+source).apply(undefined,importsValues)});result.source=source;if(isError(result)){throw result}return result}function toLower(value){return toString(value).toLowerCase()}function toUpper(value){return toString(value).toUpperCase()}function trim(string,chars,guard){string=toString(string);if(string&&(guard||chars===undefined)){return string.replace(reTrim,"")}if(!string||!(chars=baseToString(chars))){return string}var strSymbols=stringToArray(string),chrSymbols=stringToArray(chars),start=charsStartIndex(strSymbols,chrSymbols),end=charsEndIndex(strSymbols,chrSymbols)+1;return castSlice(strSymbols,start,end).join("")}function trimEnd(string,chars,guard){string=toString(string);if(string&&(guard||chars===undefined)){return string.replace(reTrimEnd,"")}if(!string||!(chars=baseToString(chars))){return string}var strSymbols=stringToArray(string),end=charsEndIndex(strSymbols,stringToArray(chars))+1;return castSlice(strSymbols,0,end).join("")}function trimStart(string,chars,guard){string=toString(string);if(string&&(guard||chars===undefined)){return string.replace(reTrimStart,"")}if(!string||!(chars=baseToString(chars))){return string}var strSymbols=stringToArray(string),start=charsStartIndex(strSymbols,stringToArray(chars));return castSlice(strSymbols,start).join("")}function truncate(string,options){var length=DEFAULT_TRUNC_LENGTH,omission=DEFAULT_TRUNC_OMISSION;if(isObject(options)){var separator="separator"in options?options.separator:separator;length="length"in options?toInteger(options.length):length;omission="omission"in options?baseToString(options.omission):omission}string=toString(string);var strLength=string.length;if(reHasComplexSymbol.test(string)){var strSymbols=stringToArray(string);strLength=strSymbols.length}if(length>=strLength){return string}var end=length-stringSize(omission);if(end<1){return omission}var result=strSymbols?castSlice(strSymbols,0,end).join(""):string.slice(0,end);if(separator===undefined){return result+omission}if(strSymbols){end+=result.length-end}if(isRegExp(separator)){if(string.slice(end).search(separator)){var match,substring=result;if(!separator.global){separator=RegExp(separator.source,toString(reFlags.exec(separator))+"g")}separator.lastIndex=0;while(match=separator.exec(substring)){var newEnd=match.index}result=result.slice(0,newEnd===undefined?end:newEnd)}}else if(string.indexOf(baseToString(separator),end)!=end){var index=result.lastIndexOf(separator);if(index>-1){result=result.slice(0,index)}}return result+omission}function unescape(string){string=toString(string);return string&&reHasEscapedHtml.test(string)?string.replace(reEscapedHtml,unescapeHtmlChar):string}var upperCase=createCompounder(function(result,word,index){return result+(index?" 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crc=-1,y=0,n=a.length,i;for(i=from;i<to;i++){y=(crc^a[i])&255;crc=crc>>>8^table[y]}return crc^-1}var h=img[0].length,w=img[0][0].length,s1,s2,next,k,length,a,b,i,j,adler32,crc32;var stream=[137,80,78,71,13,10,26,10,0,0,0,13,73,72,68,82,w>>24&255,w>>16&255,w>>8&255,w&255,h>>24&255,h>>16&255,h>>8&255,h&255,8,2,0,0,0,-1,-2,-3,-4,-5,-6,-7,-8,73,68,65,84,8,29];crc32=crc32Array(stream,12,29);stream[29]=crc32>>24&255;stream[30]=crc32>>16&255;stream[31]=crc32>>8&255;stream[32]=crc32&255;s1=1;s2=0;for(i=0;i<h;i++){if(i<h-1){stream.push(0)}else{stream.push(1)}a=3*w+1+(i===0)&255;b=3*w+1+(i===0)>>8&255;stream.push(a);stream.push(b);stream.push(~a&255);stream.push(~b&255);if(i===0)stream.push(0);for(j=0;j<w;j++){for(k=0;k<3;k++){a=img[k][i][j];if(a>255)a=255;else if(a<0)a=0;else a=Math.round(a);s1=(s1+a)%65521;s2=(s2+s1)%65521;stream.push(a)}}stream.push(0)}adler32=(s2<<16)+s1;stream.push(adler32>>24&255);stream.push(adler32>>16&255);stream.push(adler32>>8&255);stream.push(adler32&255);length=stream.length-41;stream[33]=length>>24&255;stream[34]=length>>16&255;stream[35]=length>>8&255;stream[36]=length&255;crc32=crc32Array(stream,37);stream.push(crc32>>24&255);stream.push(crc32>>16&255);stream.push(crc32>>8&255);stream.push(crc32&255);stream.push(0);stream.push(0);stream.push(0);stream.push(0);stream.push(73);stream.push(69);stream.push(78);stream.push(68);stream.push(174);stream.push(66);stream.push(96);stream.push(130);return"data:image/png;base64,"+base64(stream)};numeric._dim=function _dim(x){var ret=[];while(typeof x==="object"){ret.push(x.length);x=x[0]}return ret};numeric.dim=function dim(x){var y,z;if(typeof x==="object"){y=x[0];if(typeof y==="object"){z=y[0];if(typeof z==="object"){return numeric._dim(x)}return[x.length,y.length]}return[x.length]}return[]};numeric.mapreduce=function mapreduce(body,init){return Function("x","accum","_s","_k",'if(typeof accum === "undefined") accum = '+init+";\n"+'if(typeof x === "number") { var xi = x; '+body+"; return accum; }\n"+'if(typeof _s === "undefined") _s = numeric.dim(x);\n'+'if(typeof _k === "undefined") _k = 0;\n'+"var _n = _s[_k];\n"+"var i,xi;\n"+"if(_k < _s.length-1) {\n"+"    for(i=_n-1;i>=0;i--) {\n"+"        accum = arguments.callee(x[i],accum,_s,_k+1);\n"+"    }"+"    return accum;\n"+"}\n"+"for(i=_n-1;i>=1;i-=2) { \n"+"    xi = x[i];\n"+"    "+body+";\n"+"    xi = x[i-1];\n"+"    "+body+";\n"+"}\n"+"if(i === 0) {\n"+"    xi = x[i];\n"+"    "+body+"\n"+"}\n"+"return accum;")};numeric.mapreduce2=function mapreduce2(body,setup){return Function("x","var n = x.length;\n"+"var i,xi;\n"+setup+";\n"+"for(i=n-1;i!==-1;--i) { \n"+"    xi = x[i];\n"+"    "+body+";\n"+"}\n"+"return accum;")};numeric.same=function same(x,y){var i,n;if(!(x instanceof Array)||!(y instanceof Array)){return false}n=x.length;if(n!==y.length){return false}for(i=0;i<n;i++){if(x[i]===y[i]){continue}if(typeof x[i]==="object"){if(!same(x[i],y[i]))return false}else{return false}}return true};numeric.rep=function rep(s,v,k){if(typeof k==="undefined"){k=0}var n=s[k],ret=Array(n),i;if(k===s.length-1){for(i=n-2;i>=0;i-=2){ret[i+1]=v;ret[i]=v}if(i===-1){ret[0]=v}return ret}for(i=n-1;i>=0;i--){ret[i]=numeric.rep(s,v,k+1)}return ret};numeric.dotMMsmall=function dotMMsmall(x,y){var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0;p=x.length;q=y.length;r=y[0].length;ret=Array(p);for(i=p-1;i>=0;i--){foo=Array(r);bar=x[i];for(k=r-1;k>=0;k--){woo=bar[q-1]*y[q-1][k];for(j=q-2;j>=1;j-=2){i0=j-1;woo+=bar[j]*y[j][k]+bar[i0]*y[i0][k]}if(j===0){woo+=bar[0]*y[0][k]}foo[k]=woo}ret[i]=foo}return ret};numeric._getCol=function _getCol(A,j,x){var n=A.length,i;for(i=n-1;i>0;--i){x[i]=A[i][j];--i;x[i]=A[i][j]}if(i===0)x[0]=A[0][j]};numeric.dotMMbig=function dotMMbig(x,y){var gc=numeric._getCol,p=y.length,v=Array(p);var m=x.length,n=y[0].length,A=new Array(m),xj;var VV=numeric.dotVV;var i,j,k,z;--p;--m;for(i=m;i!==-1;--i)A[i]=Array(n);--n;for(i=n;i!==-1;--i){gc(y,i,v);for(j=m;j!==-1;--j){z=0;xj=x[j];A[j][i]=VV(xj,v)}}return A};numeric.dotMV=function dotMV(x,y){var p=x.length,q=y.length,i;var ret=Array(p),dotVV=numeric.dotVV;for(i=p-1;i>=0;i--){ret[i]=dotVV(x[i],y)}return ret};numeric.dotVM=function dotVM(x,y){var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0,s1,s2,s3,baz,accum;p=x.length;q=y[0].length;ret=Array(q);for(k=q-1;k>=0;k--){woo=x[p-1]*y[p-1][k];for(j=p-2;j>=1;j-=2){i0=j-1;woo+=x[j]*y[j][k]+x[i0]*y[i0][k]}if(j===0){woo+=x[0]*y[0][k]}ret[k]=woo}return ret};numeric.dotVV=function dotVV(x,y){var i,n=x.length,i1,ret=x[n-1]*y[n-1];for(i=n-2;i>=1;i-=2){i1=i-1;ret+=x[i]*y[i]+x[i1]*y[i1]}if(i===0){ret+=x[0]*y[0]}return ret};numeric.dot=function dot(x,y){var d=numeric.dim;switch(d(x).length*1e3+d(y).length){case 2002:if(y.length<10)return numeric.dotMMsmall(x,y);else return numeric.dotMMbig(x,y);case 2001:return numeric.dotMV(x,y);case 1002:return numeric.dotVM(x,y);case 1001:return numeric.dotVV(x,y);case 1e3:return numeric.mulVS(x,y);case 1:return numeric.mulSV(x,y);case 0:return x*y;default:throw new Error("numeric.dot only works on vectors and matrices")}};numeric.diag=function diag(d){var i,i1,j,n=d.length,A=Array(n),Ai;for(i=n-1;i>=0;i--){Ai=Array(n);i1=i+2;for(j=n-1;j>=i1;j-=2){Ai[j]=0;Ai[j-1]=0}if(j>i){Ai[j]=0}Ai[i]=d[i];for(j=i-1;j>=1;j-=2){Ai[j]=0;Ai[j-1]=0}if(j===0){Ai[0]=0}A[i]=Ai}return A};numeric.getDiag=function(A){var n=Math.min(A.length,A[0].length),i,ret=Array(n);for(i=n-1;i>=1;--i){ret[i]=A[i][i];--i;ret[i]=A[i][i]}if(i===0){ret[0]=A[0][0]}return ret};numeric.identity=function identity(n){return numeric.diag(numeric.rep([n],1))};numeric.pointwise=function pointwise(params,body,setup){if(typeof setup==="undefined"){setup=""}var fun=[];var k;var avec=/\[i\]$/,p,thevec="";var haveret=false;for(k=0;k<params.length;k++){if(avec.test(params[k])){p=params[k].substring(0,params[k].length-3);thevec=p}else{p=params[k]}if(p==="ret")haveret=true;fun.push(p)}fun[params.length]="_s";fun[params.length+1]="_k";fun[params.length+2]='if(typeof _s === "undefined") _s = numeric.dim('+thevec+");\n"+'if(typeof _k === "undefined") _k = 0;\n'+"var _n = _s[_k];\n"+"var i"+(haveret?"":", ret = Array(_n)")+";\n"+"if(_k < _s.length-1) {\n"+"    for(i=_n-1;i>=0;i--) ret[i] = arguments.callee("+params.join(",")+",_s,_k+1);\n"+"    return ret;\n"+"}\n"+setup+"\n"+"for(i=_n-1;i!==-1;--i) {\n"+"    "+body+"\n"+"}\n"+"return ret;";return Function.apply(null,fun)};numeric.pointwise2=function pointwise2(params,body,setup){if(typeof setup==="undefined"){setup=""}var fun=[];var k;var avec=/\[i\]$/,p,thevec="";var haveret=false;for(k=0;k<params.length;k++){if(avec.test(params[k])){p=params[k].substring(0,params[k].length-3);thevec=p}else{p=params[k]}if(p==="ret")haveret=true;fun.push(p)}fun[params.length]="var _n = "+thevec+".length;\n"+"var i"+(haveret?"":", ret = Array(_n)")+";\n"+setup+"\n"+"for(i=_n-1;i!==-1;--i) {\n"+body+"\n"+"}\n"+"return ret;";return Function.apply(null,fun)};numeric._biforeach=function _biforeach(x,y,s,k,f){if(k===s.length-1){f(x,y);return}var i,n=s[k];for(i=n-1;i>=0;i--){_biforeach(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f)}};numeric._biforeach2=function _biforeach2(x,y,s,k,f){if(k===s.length-1){return f(x,y)}var i,n=s[k],ret=Array(n);for(i=n-1;i>=0;--i){ret[i]=_biforeach2(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f)}return ret};numeric._foreach=function _foreach(x,s,k,f){if(k===s.length-1){f(x);return}var i,n=s[k];for(i=n-1;i>=0;i--){_foreach(x[i],s,k+1,f)}};numeric._foreach2=function _foreach2(x,s,k,f){if(k===s.length-1){return f(x)}var i,n=s[k],ret=Array(n);for(i=n-1;i>=0;i--){ret[i]=_foreach2(x[i],s,k+1,f)}return ret};numeric.ops2={add:"+",sub:"-",mul:"*",div:"/",mod:"%",and:"&&",or:"||",eq:"===",neq:"!==",lt:"<",gt:">",leq:"<=",geq:">=",band:"&",bor:"|",bxor:"^",lshift:"<<",rshift:">>",rrshift:">>>"};numeric.opseq={addeq:"+=",subeq:"-=",muleq:"*=",diveq:"/=",modeq:"%=",lshifteq:"<<=",rshifteq:">>=",rrshifteq:">>>=",bandeq:"&=",boreq:"|=",bxoreq:"^="};numeric.mathfuns=["abs","acos","asin","atan","ceil","cos","exp","floor","log","round","sin","sqrt","tan","isNaN","isFinite"];numeric.mathfuns2=["atan2","pow","max","min"];numeric.ops1={neg:"-",not:"!",bnot:"~",clone:""};numeric.mapreducers={any:["if(xi) return true;","var accum = false;"],all:["if(!xi) return false;","var accum = true;"],sum:["accum += xi;","var accum = 0;"],prod:["accum *= xi;","var accum = 1;"],norm2Squared:["accum += xi*xi;","var accum = 0;"],norminf:["accum = max(accum,abs(xi));","var accum = 0, max = Math.max, abs = Math.abs;"],norm1:["accum += abs(xi)","var accum = 0, abs = Math.abs;"],sup:["accum = max(accum,xi);","var accum = -Infinity, max = Math.max;"],inf:["accum = min(accum,xi);","var accum = Infinity, min = Math.min;"]};(function(){var i,o;for(i=0;i<numeric.mathfuns2.length;++i){o=numeric.mathfuns2[i];numeric.ops2[o]=o}for(i in numeric.ops2){if(numeric.ops2.hasOwnProperty(i)){o=numeric.ops2[i];var code,codeeq,setup="";if(numeric.myIndexOf.call(numeric.mathfuns2,i)!==-1){setup="var "+o+" = Math."+o+";\n";code=function(r,x,y){return r+" = "+o+"("+x+","+y+")"};codeeq=function(x,y){return x+" = "+o+"("+x+","+y+")"}}else{code=function(r,x,y){return r+" = "+x+" "+o+" "+y};if(numeric.opseq.hasOwnProperty(i+"eq")){codeeq=function(x,y){return x+" "+o+"= "+y}}else{codeeq=function(x,y){return x+" = "+x+" "+o+" "+y}}}numeric[i+"VV"]=numeric.pointwise2(["x[i]","y[i]"],code("ret[i]","x[i]","y[i]"),setup);numeric[i+"SV"]=numeric.pointwise2(["x","y[i]"],code("ret[i]","x","y[i]"),setup);numeric[i+"VS"]=numeric.pointwise2(["x[i]","y"],code("ret[i]","x[i]","y"),setup);numeric[i]=Function("var n = arguments.length, i, x = arguments[0], y;\n"+"var VV = numeric."+i+"VV, VS = numeric."+i+"VS, SV = numeric."+i+"SV;\n"+"var dim = numeric.dim;\n"+"for(i=1;i!==n;++i) { \n"+"  y = arguments[i];\n"+'  if(typeof x === "object") {\n'+'      if(typeof y === "object") x = numeric._biforeach2(x,y,dim(x),0,VV);\n'+"      else x = numeric._biforeach2(x,y,dim(x),0,VS);\n"+'  } else if(typeof y === "object") x = numeric._biforeach2(x,y,dim(y),0,SV);\n'+"  else "+codeeq("x","y")+"\n"+"}\nreturn x;\n");numeric[o]=numeric[i];numeric[i+"eqV"]=numeric.pointwise2(["ret[i]","x[i]"],codeeq("ret[i]","x[i]"),setup);numeric[i+"eqS"]=numeric.pointwise2(["ret[i]","x"],codeeq("ret[i]","x"),setup);numeric[i+"eq"]=Function("var n = arguments.length, i, x = arguments[0], y;\n"+"var V = numeric."+i+"eqV, S = numeric."+i+"eqS\n"+"var s = numeric.dim(x);\n"+"for(i=1;i!==n;++i) { \n"+"  y = arguments[i];\n"+'  if(typeof y === "object") numeric._biforeach(x,y,s,0,V);\n'+"  else numeric._biforeach(x,y,s,0,S);\n"+"}\nreturn x;\n")}}for(i=0;i<numeric.mathfuns2.length;++i){o=numeric.mathfuns2[i];delete numeric.ops2[o]}for(i=0;i<numeric.mathfuns.length;++i){o=numeric.mathfuns[i];numeric.ops1[o]=o}for(i in numeric.ops1){if(numeric.ops1.hasOwnProperty(i)){setup="";o=numeric.ops1[i];if(numeric.myIndexOf.call(numeric.mathfuns,i)!==-1){if(Math.hasOwnProperty(o))setup="var "+o+" = Math."+o+";\n"}numeric[i+"eqV"]=numeric.pointwise2(["ret[i]"],"ret[i] = "+o+"(ret[i]);",setup);numeric[i+"eq"]=Function("x",'if(typeof x !== "object") return '+o+"x\n"+"var i;\n"+"var V = numeric."+i+"eqV;\n"+"var s = numeric.dim(x);\n"+"numeric._foreach(x,s,0,V);\n"+"return x;\n");numeric[i+"V"]=numeric.pointwise2(["x[i]"],"ret[i] = "+o+"(x[i]);",setup);numeric[i]=Function("x",'if(typeof x !== "object") return '+o+"(x)\n"+"var i;\n"+"var V = numeric."+i+"V;\n"+"var s = numeric.dim(x);\n"+"return numeric._foreach2(x,s,0,V);\n")}}for(i=0;i<numeric.mathfuns.length;++i){o=numeric.mathfuns[i];
delete numeric.ops1[o]}for(i in numeric.mapreducers){if(numeric.mapreducers.hasOwnProperty(i)){o=numeric.mapreducers[i];numeric[i+"V"]=numeric.mapreduce2(o[0],o[1]);numeric[i]=Function("x","s","k",o[1]+'if(typeof x !== "object") {'+"    xi = x;\n"+o[0]+";\n"+"    return accum;\n"+"}"+'if(typeof s === "undefined") s = numeric.dim(x);\n'+'if(typeof k === "undefined") k = 0;\n'+"if(k === s.length-1) return numeric."+i+"V(x);\n"+"var xi;\n"+"var n = x.length, i;\n"+"for(i=n-1;i!==-1;--i) {\n"+"   xi = arguments.callee(x[i]);\n"+o[0]+";\n"+"}\n"+"return accum;\n")}}})();numeric.truncVV=numeric.pointwise(["x[i]","y[i]"],"ret[i] = round(x[i]/y[i])*y[i];","var round = Math.round;");numeric.truncVS=numeric.pointwise(["x[i]","y"],"ret[i] = round(x[i]/y)*y;","var round = Math.round;");numeric.truncSV=numeric.pointwise(["x","y[i]"],"ret[i] = round(x/y[i])*y[i];","var round = Math.round;");numeric.trunc=function trunc(x,y){if(typeof x==="object"){if(typeof y==="object")return numeric.truncVV(x,y);return numeric.truncVS(x,y)}if(typeof y==="object")return numeric.truncSV(x,y);return Math.round(x/y)*y};numeric.inv=function inv(x){var s=numeric.dim(x),abs=Math.abs,m=s[0],n=s[1];var A=numeric.clone(x),Ai,Aj;var I=numeric.identity(m),Ii,Ij;var i,j,k,x;for(j=0;j<n;++j){var i0=-1;var v0=-1;for(i=j;i!==m;++i){k=abs(A[i][j]);if(k>v0){i0=i;v0=k}}Aj=A[i0];A[i0]=A[j];A[j]=Aj;Ij=I[i0];I[i0]=I[j];I[j]=Ij;x=Aj[j];for(k=j;k!==n;++k)Aj[k]/=x;for(k=n-1;k!==-1;--k)Ij[k]/=x;for(i=m-1;i!==-1;--i){if(i!==j){Ai=A[i];Ii=I[i];x=Ai[j];for(k=j+1;k!==n;++k)Ai[k]-=Aj[k]*x;for(k=n-1;k>0;--k){Ii[k]-=Ij[k]*x;--k;Ii[k]-=Ij[k]*x}if(k===0)Ii[0]-=Ij[0]*x}}}return I};numeric.det=function det(x){var s=numeric.dim(x);if(s.length!==2||s[0]!==s[1]){throw new Error("numeric: det() only works on square matrices")}var n=s[0],ret=1,i,j,k,A=numeric.clone(x),Aj,Ai,alpha,temp,k1,k2,k3;for(j=0;j<n-1;j++){k=j;for(i=j+1;i<n;i++){if(Math.abs(A[i][j])>Math.abs(A[k][j])){k=i}}if(k!==j){temp=A[k];A[k]=A[j];A[j]=temp;ret*=-1}Aj=A[j];for(i=j+1;i<n;i++){Ai=A[i];alpha=Ai[j]/Aj[j];for(k=j+1;k<n-1;k+=2){k1=k+1;Ai[k]-=Aj[k]*alpha;Ai[k1]-=Aj[k1]*alpha}if(k!==n){Ai[k]-=Aj[k]*alpha}}if(Aj[j]===0){return 0}ret*=Aj[j]}return ret*A[j][j]};numeric.transpose=function transpose(x){var i,j,m=x.length,n=x[0].length,ret=Array(n),A0,A1,Bj;for(j=0;j<n;j++)ret[j]=Array(m);for(i=m-1;i>=1;i-=2){A1=x[i];A0=x[i-1];for(j=n-1;j>=1;--j){Bj=ret[j];Bj[i]=A1[j];Bj[i-1]=A0[j];--j;Bj=ret[j];Bj[i]=A1[j];Bj[i-1]=A0[j]}if(j===0){Bj=ret[0];Bj[i]=A1[0];Bj[i-1]=A0[0]}}if(i===0){A0=x[0];for(j=n-1;j>=1;--j){ret[j][0]=A0[j];--j;ret[j][0]=A0[j]}if(j===0){ret[0][0]=A0[0]}}return ret};numeric.negtranspose=function negtranspose(x){var i,j,m=x.length,n=x[0].length,ret=Array(n),A0,A1,Bj;for(j=0;j<n;j++)ret[j]=Array(m);for(i=m-1;i>=1;i-=2){A1=x[i];A0=x[i-1];for(j=n-1;j>=1;--j){Bj=ret[j];Bj[i]=-A1[j];Bj[i-1]=-A0[j];--j;Bj=ret[j];Bj[i]=-A1[j];Bj[i-1]=-A0[j]}if(j===0){Bj=ret[0];Bj[i]=-A1[0];Bj[i-1]=-A0[0]}}if(i===0){A0=x[0];for(j=n-1;j>=1;--j){ret[j][0]=-A0[j];--j;ret[j][0]=-A0[j]}if(j===0){ret[0][0]=-A0[0]}}return ret};numeric._random=function _random(s,k){var i,n=s[k],ret=Array(n),rnd;if(k===s.length-1){rnd=Math.random;for(i=n-1;i>=1;i-=2){ret[i]=rnd();ret[i-1]=rnd()}if(i===0){ret[0]=rnd()}return ret}for(i=n-1;i>=0;i--)ret[i]=_random(s,k+1);return ret};numeric.random=function random(s){return numeric._random(s,0)};numeric.norm2=function norm2(x){return Math.sqrt(numeric.norm2Squared(x))};numeric.linspace=function linspace(a,b,n){if(typeof n==="undefined")n=Math.max(Math.round(b-a)+1,1);if(n<2){return n===1?[a]:[]}var i,ret=Array(n);n--;for(i=n;i>=0;i--){ret[i]=(i*b+(n-i)*a)/n}return ret};numeric.getBlock=function getBlock(x,from,to){var s=numeric.dim(x);function foo(x,k){var i,a=from[k],n=to[k]-a,ret=Array(n);if(k===s.length-1){for(i=n;i>=0;i--){ret[i]=x[i+a]}return ret}for(i=n;i>=0;i--){ret[i]=foo(x[i+a],k+1)}return ret}return foo(x,0)};numeric.setBlock=function setBlock(x,from,to,B){var s=numeric.dim(x);function foo(x,y,k){var i,a=from[k],n=to[k]-a;if(k===s.length-1){for(i=n;i>=0;i--){x[i+a]=y[i]}}for(i=n;i>=0;i--){foo(x[i+a],y[i],k+1)}}foo(x,B,0);return x};numeric.getRange=function getRange(A,I,J){var m=I.length,n=J.length;var i,j;var B=Array(m),Bi,AI;for(i=m-1;i!==-1;--i){B[i]=Array(n);Bi=B[i];AI=A[I[i]];for(j=n-1;j!==-1;--j)Bi[j]=AI[J[j]]}return B};numeric.blockMatrix=function blockMatrix(X){var s=numeric.dim(X);if(s.length<4)return numeric.blockMatrix([X]);var m=s[0],n=s[1],M,N,i,j,Xij;M=0;N=0;for(i=0;i<m;++i)M+=X[i][0].length;for(j=0;j<n;++j)N+=X[0][j][0].length;var Z=Array(M);for(i=0;i<M;++i)Z[i]=Array(N);var I=0,J,ZI,k,l,Xijk;for(i=0;i<m;++i){J=N;for(j=n-1;j!==-1;--j){Xij=X[i][j];J-=Xij[0].length;for(k=Xij.length-1;k!==-1;--k){Xijk=Xij[k];ZI=Z[I+k];for(l=Xijk.length-1;l!==-1;--l)ZI[J+l]=Xijk[l]}}I+=X[i][0].length}return Z};numeric.tensor=function tensor(x,y){if(typeof x==="number"||typeof y==="number")return numeric.mul(x,y);var s1=numeric.dim(x),s2=numeric.dim(y);if(s1.length!==1||s2.length!==1){throw new Error("numeric: tensor product is only defined for vectors")}var m=s1[0],n=s2[0],A=Array(m),Ai,i,j,xi;for(i=m-1;i>=0;i--){Ai=Array(n);xi=x[i];for(j=n-1;j>=3;--j){Ai[j]=xi*y[j];--j;Ai[j]=xi*y[j];--j;Ai[j]=xi*y[j];--j;Ai[j]=xi*y[j]}while(j>=0){Ai[j]=xi*y[j];--j}A[i]=Ai}return A};numeric.T=function T(x,y){this.x=x;this.y=y};numeric.t=function t(x,y){return new numeric.T(x,y)};numeric.Tbinop=function Tbinop(rr,rc,cr,cc,setup){var io=numeric.indexOf;if(typeof setup!=="string"){var k;setup="";for(k in numeric){if(numeric.hasOwnProperty(k)&&(rr.indexOf(k)>=0||rc.indexOf(k)>=0||cr.indexOf(k)>=0||cc.indexOf(k)>=0)&&k.length>1){setup+="var "+k+" = numeric."+k+";\n"}}}return Function(["y"],"var x = this;\n"+"if(!(y instanceof numeric.T)) { y = new numeric.T(y); }\n"+setup+"\n"+"if(x.y) {"+"  if(y.y) {"+"    return new numeric.T("+cc+");\n"+"  }\n"+"  return new numeric.T("+cr+");\n"+"}\n"+"if(y.y) {\n"+"  return new numeric.T("+rc+");\n"+"}\n"+"return new numeric.T("+rr+");\n")};numeric.T.prototype.add=numeric.Tbinop("add(x.x,y.x)","add(x.x,y.x),y.y","add(x.x,y.x),x.y","add(x.x,y.x),add(x.y,y.y)");numeric.T.prototype.sub=numeric.Tbinop("sub(x.x,y.x)","sub(x.x,y.x),neg(y.y)","sub(x.x,y.x),x.y","sub(x.x,y.x),sub(x.y,y.y)");numeric.T.prototype.mul=numeric.Tbinop("mul(x.x,y.x)","mul(x.x,y.x),mul(x.x,y.y)","mul(x.x,y.x),mul(x.y,y.x)","sub(mul(x.x,y.x),mul(x.y,y.y)),add(mul(x.x,y.y),mul(x.y,y.x))");numeric.T.prototype.reciprocal=function reciprocal(){var mul=numeric.mul,div=numeric.div;if(this.y){var d=numeric.add(mul(this.x,this.x),mul(this.y,this.y));return new numeric.T(div(this.x,d),div(numeric.neg(this.y),d))}return new T(div(1,this.x))};numeric.T.prototype.div=function div(y){if(!(y instanceof numeric.T))y=new numeric.T(y);if(y.y){return this.mul(y.reciprocal())}var div=numeric.div;if(this.y){return new numeric.T(div(this.x,y.x),div(this.y,y.x))}return new numeric.T(div(this.x,y.x))};numeric.T.prototype.dot=numeric.Tbinop("dot(x.x,y.x)","dot(x.x,y.x),dot(x.x,y.y)","dot(x.x,y.x),dot(x.y,y.x)","sub(dot(x.x,y.x),dot(x.y,y.y)),add(dot(x.x,y.y),dot(x.y,y.x))");numeric.T.prototype.transpose=function transpose(){var t=numeric.transpose,x=this.x,y=this.y;if(y){return new numeric.T(t(x),t(y))}return new numeric.T(t(x))};numeric.T.prototype.transjugate=function transjugate(){var t=numeric.transpose,x=this.x,y=this.y;if(y){return new numeric.T(t(x),numeric.negtranspose(y))}return new numeric.T(t(x))};numeric.Tunop=function Tunop(r,c,s){if(typeof s!=="string"){s=""}return Function("var x = this;\n"+s+"\n"+"if(x.y) {"+"  "+c+";\n"+"}\n"+r+";\n")};numeric.T.prototype.exp=numeric.Tunop("return new numeric.T(ex)","return new numeric.T(mul(cos(x.y),ex),mul(sin(x.y),ex))","var ex = numeric.exp(x.x), cos = numeric.cos, sin = numeric.sin, mul = numeric.mul;");numeric.T.prototype.conj=numeric.Tunop("return new numeric.T(x.x);","return new numeric.T(x.x,numeric.neg(x.y));");numeric.T.prototype.neg=numeric.Tunop("return new numeric.T(neg(x.x));","return new numeric.T(neg(x.x),neg(x.y));","var neg = numeric.neg;");numeric.T.prototype.sin=numeric.Tunop("return new numeric.T(numeric.sin(x.x))","return x.exp().sub(x.neg().exp()).div(new numeric.T(0,2));");numeric.T.prototype.cos=numeric.Tunop("return new numeric.T(numeric.cos(x.x))","return x.exp().add(x.neg().exp()).div(2);");numeric.T.prototype.abs=numeric.Tunop("return new numeric.T(numeric.abs(x.x));","return new numeric.T(numeric.sqrt(numeric.add(mul(x.x,x.x),mul(x.y,x.y))));","var mul = numeric.mul;");numeric.T.prototype.log=numeric.Tunop("return new numeric.T(numeric.log(x.x));","var theta = new numeric.T(numeric.atan2(x.y,x.x)), r = x.abs();\n"+"return new numeric.T(numeric.log(r.x),theta.x);");numeric.T.prototype.norm2=numeric.Tunop("return numeric.norm2(x.x);","var f = numeric.norm2Squared;\n"+"return Math.sqrt(f(x.x)+f(x.y));");numeric.T.prototype.inv=function inv(){var A=this;if(typeof A.y==="undefined"){return new numeric.T(numeric.inv(A.x))}var n=A.x.length,i,j,k;var Rx=numeric.identity(n),Ry=numeric.rep([n,n],0);var Ax=numeric.clone(A.x),Ay=numeric.clone(A.y);var Aix,Aiy,Ajx,Ajy,Rix,Riy,Rjx,Rjy;var i,j,k,d,d1,ax,ay,bx,by,temp;for(i=0;i<n;i++){ax=Ax[i][i];ay=Ay[i][i];d=ax*ax+ay*ay;k=i;for(j=i+1;j<n;j++){ax=Ax[j][i];ay=Ay[j][i];d1=ax*ax+ay*ay;if(d1>d){k=j;d=d1}}if(k!==i){temp=Ax[i];Ax[i]=Ax[k];Ax[k]=temp;temp=Ay[i];Ay[i]=Ay[k];Ay[k]=temp;temp=Rx[i];Rx[i]=Rx[k];Rx[k]=temp;temp=Ry[i];Ry[i]=Ry[k];Ry[k]=temp}Aix=Ax[i];Aiy=Ay[i];Rix=Rx[i];Riy=Ry[i];ax=Aix[i];ay=Aiy[i];for(j=i+1;j<n;j++){bx=Aix[j];by=Aiy[j];Aix[j]=(bx*ax+by*ay)/d;Aiy[j]=(by*ax-bx*ay)/d}for(j=0;j<n;j++){bx=Rix[j];by=Riy[j];Rix[j]=(bx*ax+by*ay)/d;Riy[j]=(by*ax-bx*ay)/d}for(j=i+1;j<n;j++){Ajx=Ax[j];Ajy=Ay[j];Rjx=Rx[j];Rjy=Ry[j];ax=Ajx[i];ay=Ajy[i];for(k=i+1;k<n;k++){bx=Aix[k];by=Aiy[k];Ajx[k]-=bx*ax-by*ay;Ajy[k]-=by*ax+bx*ay}for(k=0;k<n;k++){bx=Rix[k];by=Riy[k];Rjx[k]-=bx*ax-by*ay;Rjy[k]-=by*ax+bx*ay}}}for(i=n-1;i>0;i--){Rix=Rx[i];Riy=Ry[i];for(j=i-1;j>=0;j--){Rjx=Rx[j];Rjy=Ry[j];ax=Ax[j][i];ay=Ay[j][i];for(k=n-1;k>=0;k--){bx=Rix[k];by=Riy[k];Rjx[k]-=ax*bx-ay*by;Rjy[k]-=ax*by+ay*bx}}}return new numeric.T(Rx,Ry)};numeric.T.prototype.get=function get(i){var x=this.x,y=this.y,k=0,ik,n=i.length;if(y){while(k<n){ik=i[k];x=x[ik];y=y[ik];k++}return new numeric.T(x,y)}while(k<n){ik=i[k];x=x[ik];k++}return new numeric.T(x)};numeric.T.prototype.set=function set(i,v){var x=this.x,y=this.y,k=0,ik,n=i.length,vx=v.x,vy=v.y;if(n===0){if(vy){this.y=vy}else if(y){this.y=undefined}this.x=x;return this}if(vy){if(y){}else{y=numeric.rep(numeric.dim(x),0);this.y=y}while(k<n-1){ik=i[k];x=x[ik];y=y[ik];k++}ik=i[k];x[ik]=vx;y[ik]=vy;return this}if(y){while(k<n-1){ik=i[k];x=x[ik];y=y[ik];k++}ik=i[k];x[ik]=vx;if(vx instanceof Array)y[ik]=numeric.rep(numeric.dim(vx),0);else y[ik]=0;return this}while(k<n-1){ik=i[k];x=x[ik];k++}ik=i[k];x[ik]=vx;return this};numeric.T.prototype.getRows=function getRows(i0,i1){var n=i1-i0+1,j;var rx=Array(n),ry,x=this.x,y=this.y;for(j=i0;j<=i1;j++){rx[j-i0]=x[j]}if(y){ry=Array(n);for(j=i0;j<=i1;j++){ry[j-i0]=y[j]}return new numeric.T(rx,ry)}return new numeric.T(rx)};numeric.T.prototype.setRows=function setRows(i0,i1,A){var j;var rx=this.x,ry=this.y,x=A.x,y=A.y;for(j=i0;j<=i1;j++){rx[j]=x[j-i0]}if(y){if(!ry){ry=numeric.rep(numeric.dim(rx),0);this.y=ry}for(j=i0;j<=i1;j++){ry[j]=y[j-i0]}}else if(ry){for(j=i0;j<=i1;j++){ry[j]=numeric.rep([x[j-i0].length],0)}}return this};numeric.T.prototype.getRow=function getRow(k){var x=this.x,y=this.y;if(y){return new numeric.T(x[k],y[k])}return new numeric.T(x[k])};numeric.T.prototype.setRow=function setRow(i,v){var rx=this.x,ry=this.y,x=v.x,y=v.y;rx[i]=x;if(y){if(!ry){ry=numeric.rep(numeric.dim(rx),0);this.y=ry}ry[i]=y}else if(ry){ry=numeric.rep([x.length],0)}return this};numeric.T.prototype.getBlock=function getBlock(from,to){var x=this.x,y=this.y,b=numeric.getBlock;if(y){return new numeric.T(b(x,from,to),b(y,from,to))}return new numeric.T(b(x,from,to))};numeric.T.prototype.setBlock=function setBlock(from,to,A){if(!(A instanceof numeric.T))A=new numeric.T(A);var x=this.x,y=this.y,b=numeric.setBlock,Ax=A.x,Ay=A.y;if(Ay){if(!y){this.y=numeric.rep(numeric.dim(this),0);y=this.y}b(x,from,to,Ax);b(y,from,to,Ay);return this}b(x,from,to,Ax);if(y)b(y,from,to,numeric.rep(numeric.dim(Ax),0))};numeric.T.rep=function rep(s,v){var T=numeric.T;if(!(v instanceof T))v=new T(v);var x=v.x,y=v.y,r=numeric.rep;if(y)return new T(r(s,x),r(s,y));return new T(r(s,x))};numeric.T.diag=function diag(d){if(!(d instanceof numeric.T))d=new numeric.T(d);var x=d.x,y=d.y,diag=numeric.diag;if(y)return new numeric.T(diag(x),diag(y));return new numeric.T(diag(x))};numeric.T.eig=function eig(){if(this.y){throw new Error("eig: not implemented for complex matrices.")}return numeric.eig(this.x)};numeric.T.identity=function identity(n){return new numeric.T(numeric.identity(n))};numeric.T.prototype.getDiag=function getDiag(){var n=numeric;var x=this.x,y=this.y;if(y){return new n.T(n.getDiag(x),n.getDiag(y))}return new n.T(n.getDiag(x))};numeric.house=function house(x){var v=numeric.clone(x);var s=x[0]>=0?1:-1;var alpha=s*numeric.norm2(x);v[0]+=alpha;var foo=numeric.norm2(v);if(foo===0){throw new Error("eig: internal error")}return numeric.div(v,foo)};numeric.toUpperHessenberg=function toUpperHessenberg(me){var s=numeric.dim(me);if(s.length!==2||s[0]!==s[1]){throw new Error("numeric: toUpperHessenberg() only works on square matrices")}var m=s[0],i,j,k,x,v,A=numeric.clone(me),B,C,Ai,Ci,Q=numeric.identity(m),Qi;for(j=0;j<m-2;j++){x=Array(m-j-1);for(i=j+1;i<m;i++){x[i-j-1]=A[i][j]}if(numeric.norm2(x)>0){v=numeric.house(x);B=numeric.getBlock(A,[j+1,j],[m-1,m-1]);C=numeric.tensor(v,numeric.dot(v,B));for(i=j+1;i<m;i++){Ai=A[i];Ci=C[i-j-1];for(k=j;k<m;k++)Ai[k]-=2*Ci[k-j]}B=numeric.getBlock(A,[0,j+1],[m-1,m-1]);C=numeric.tensor(numeric.dot(B,v),v);for(i=0;i<m;i++){Ai=A[i];Ci=C[i];for(k=j+1;k<m;k++)Ai[k]-=2*Ci[k-j-1]}B=Array(m-j-1);for(i=j+1;i<m;i++)B[i-j-1]=Q[i];C=numeric.tensor(v,numeric.dot(v,B));for(i=j+1;i<m;i++){Qi=Q[i];Ci=C[i-j-1];for(k=0;k<m;k++)Qi[k]-=2*Ci[k]}}}return{H:A,Q:Q}};numeric.epsilon=2.220446049250313e-16;numeric.QRFrancis=function(H,maxiter){if(typeof maxiter==="undefined"){maxiter=1e4}H=numeric.clone(H);var H0=numeric.clone(H);var s=numeric.dim(H),m=s[0],x,v,a,b,c,d,det,tr,Hloc,Q=numeric.identity(m),Qi,Hi,B,C,Ci,i,j,k,iter;if(m<3){return{Q:Q,B:[[0,m-1]]}}var epsilon=numeric.epsilon;for(iter=0;iter<maxiter;iter++){for(j=0;j<m-1;j++){if(Math.abs(H[j+1][j])<epsilon*(Math.abs(H[j][j])+Math.abs(H[j+1][j+1]))){var QH1=numeric.QRFrancis(numeric.getBlock(H,[0,0],[j,j]),maxiter);var QH2=numeric.QRFrancis(numeric.getBlock(H,[j+1,j+1],[m-1,m-1]),maxiter);B=Array(j+1);for(i=0;i<=j;i++){B[i]=Q[i]}C=numeric.dot(QH1.Q,B);for(i=0;i<=j;i++){Q[i]=C[i]}B=Array(m-j-1);for(i=j+1;i<m;i++){B[i-j-1]=Q[i]}C=numeric.dot(QH2.Q,B);for(i=j+1;i<m;i++){Q[i]=C[i-j-1]}return{Q:Q,B:QH1.B.concat(numeric.add(QH2.B,j+1))}}}a=H[m-2][m-2];b=H[m-2][m-1];c=H[m-1][m-2];d=H[m-1][m-1];tr=a+d;det=a*d-b*c;Hloc=numeric.getBlock(H,[0,0],[2,2]);if(tr*tr>=4*det){var s1,s2;s1=.5*(tr+Math.sqrt(tr*tr-4*det));s2=.5*(tr-Math.sqrt(tr*tr-4*det));Hloc=numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),numeric.mul(Hloc,s1+s2)),numeric.diag(numeric.rep([3],s1*s2)))}else{Hloc=numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),numeric.mul(Hloc,tr)),numeric.diag(numeric.rep([3],det)))}x=[Hloc[0][0],Hloc[1][0],Hloc[2][0]];v=numeric.house(x);B=[H[0],H[1],H[2]];C=numeric.tensor(v,numeric.dot(v,B));for(i=0;i<3;i++){Hi=H[i];Ci=C[i];for(k=0;k<m;k++)Hi[k]-=2*Ci[k]}B=numeric.getBlock(H,[0,0],[m-1,2]);C=numeric.tensor(numeric.dot(B,v),v);for(i=0;i<m;i++){Hi=H[i];Ci=C[i];for(k=0;k<3;k++)Hi[k]-=2*Ci[k]}B=[Q[0],Q[1],Q[2]];C=numeric.tensor(v,numeric.dot(v,B));for(i=0;i<3;i++){Qi=Q[i];Ci=C[i];for(k=0;k<m;k++)Qi[k]-=2*Ci[k]}var J;for(j=0;j<m-2;j++){for(k=j;k<=j+1;k++){if(Math.abs(H[k+1][k])<epsilon*(Math.abs(H[k][k])+Math.abs(H[k+1][k+1]))){var QH1=numeric.QRFrancis(numeric.getBlock(H,[0,0],[k,k]),maxiter);var QH2=numeric.QRFrancis(numeric.getBlock(H,[k+1,k+1],[m-1,m-1]),maxiter);B=Array(k+1);for(i=0;i<=k;i++){B[i]=Q[i]}C=numeric.dot(QH1.Q,B);for(i=0;i<=k;i++){Q[i]=C[i]}B=Array(m-k-1);for(i=k+1;i<m;i++){B[i-k-1]=Q[i]}C=numeric.dot(QH2.Q,B);for(i=k+1;i<m;i++){Q[i]=C[i-k-1]}return{Q:Q,B:QH1.B.concat(numeric.add(QH2.B,k+1))}}}J=Math.min(m-1,j+3);x=Array(J-j);for(i=j+1;i<=J;i++){x[i-j-1]=H[i][j]}v=numeric.house(x);B=numeric.getBlock(H,[j+1,j],[J,m-1]);C=numeric.tensor(v,numeric.dot(v,B));for(i=j+1;i<=J;i++){Hi=H[i];Ci=C[i-j-1];for(k=j;k<m;k++)Hi[k]-=2*Ci[k-j]}B=numeric.getBlock(H,[0,j+1],[m-1,J]);C=numeric.tensor(numeric.dot(B,v),v);for(i=0;i<m;i++){Hi=H[i];Ci=C[i];for(k=j+1;k<=J;k++)Hi[k]-=2*Ci[k-j-1]}B=Array(J-j);for(i=j+1;i<=J;i++)B[i-j-1]=Q[i];C=numeric.tensor(v,numeric.dot(v,B));for(i=j+1;i<=J;i++){Qi=Q[i];Ci=C[i-j-1];for(k=0;k<m;k++)Qi[k]-=2*Ci[k]}}}throw new Error("numeric: eigenvalue iteration does not converge -- increase maxiter?")};numeric.eig=function eig(A,maxiter){var QH=numeric.toUpperHessenberg(A);var QB=numeric.QRFrancis(QH.H,maxiter);var T=numeric.T;var n=A.length,i,k,flag=false,B=QB.B,H=numeric.dot(QB.Q,numeric.dot(QH.H,numeric.transpose(QB.Q)));var Q=new T(numeric.dot(QB.Q,QH.Q)),Q0;var m=B.length,j;var a,b,c,d,p1,p2,disc,x,y,p,q,n1,n2;var sqrt=Math.sqrt;for(k=0;k<m;k++){i=B[k][0];if(i===B[k][1]){}else{j=i+1;a=H[i][i];b=H[i][j];c=H[j][i];d=H[j][j];if(b===0&&c===0)continue;p1=-a-d;p2=a*d-b*c;disc=p1*p1-4*p2;if(disc>=0){if(p1<0)x=-.5*(p1-sqrt(disc));else x=-.5*(p1+sqrt(disc));n1=(a-x)*(a-x)+b*b;n2=c*c+(d-x)*(d-x);if(n1>n2){n1=sqrt(n1);p=(a-x)/n1;q=b/n1}else{n2=sqrt(n2);p=c/n2;q=(d-x)/n2}Q0=new T([[q,-p],[p,q]]);Q.setRows(i,j,Q0.dot(Q.getRows(i,j)))}else{x=-.5*p1;y=.5*sqrt(-disc);n1=(a-x)*(a-x)+b*b;n2=c*c+(d-x)*(d-x);if(n1>n2){n1=sqrt(n1+y*y);p=(a-x)/n1;q=b/n1;x=0;y/=n1}else{n2=sqrt(n2+y*y);p=c/n2;q=(d-x)/n2;x=y/n2;y=0}Q0=new T([[q,-p],[p,q]],[[x,y],[y,-x]]);Q.setRows(i,j,Q0.dot(Q.getRows(i,j)))}}}var R=Q.dot(A).dot(Q.transjugate()),n=A.length,E=numeric.T.identity(n);for(j=0;j<n;j++){if(j>0){for(k=j-1;k>=0;k--){var Rk=R.get([k,k]),Rj=R.get([j,j]);if(numeric.neq(Rk.x,Rj.x)||numeric.neq(Rk.y,Rj.y)){x=R.getRow(k).getBlock([k],[j-1]);y=E.getRow(j).getBlock([k],[j-1]);E.set([j,k],R.get([k,j]).neg().sub(x.dot(y)).div(Rk.sub(Rj)))}else{E.setRow(j,E.getRow(k));continue}}}}for(j=0;j<n;j++){x=E.getRow(j);E.setRow(j,x.div(x.norm2()))}E=E.transpose();E=Q.transjugate().dot(E);return{lambda:R.getDiag(),E:E}};numeric.ccsSparse=function ccsSparse(A){var m=A.length,n,foo,i,j,counts=[];for(i=m-1;i!==-1;--i){foo=A[i];for(j in foo){j=parseInt(j);while(j>=counts.length)counts[counts.length]=0;if(foo[j]!==0)counts[j]++}}var n=counts.length;var Ai=Array(n+1);Ai[0]=0;for(i=0;i<n;++i)Ai[i+1]=Ai[i]+counts[i];var Aj=Array(Ai[n]),Av=Array(Ai[n]);for(i=m-1;i!==-1;--i){foo=A[i];for(j in foo){if(foo[j]!==0){counts[j]--;Aj[Ai[j]+counts[j]]=i;Av[Ai[j]+counts[j]]=foo[j]}}}return[Ai,Aj,Av]};numeric.ccsFull=function ccsFull(A){var Ai=A[0],Aj=A[1],Av=A[2],s=numeric.ccsDim(A),m=s[0],n=s[1],i,j,j0,j1,k;var B=numeric.rep([m,n],0);for(i=0;i<n;i++){j0=Ai[i];j1=Ai[i+1];for(j=j0;j<j1;++j){B[Aj[j]][i]=Av[j]}}return B};numeric.ccsTSolve=function ccsTSolve(A,b,x,bj,xj){var Ai=A[0],Aj=A[1],Av=A[2],m=Ai.length-1,max=Math.max,n=0;if(typeof bj==="undefined")x=numeric.rep([m],0);if(typeof bj==="undefined")bj=numeric.linspace(0,x.length-1);if(typeof xj==="undefined")xj=[];function dfs(j){var k;if(x[j]!==0)return;x[j]=1;for(k=Ai[j];k<Ai[j+1];++k)dfs(Aj[k]);xj[n]=j;++n}var i,j,j0,j1,k,l,l0,l1,a;for(i=bj.length-1;i!==-1;--i){dfs(bj[i])}xj.length=n;for(i=xj.length-1;i!==-1;--i){x[xj[i]]=0}for(i=bj.length-1;i!==-1;--i){j=bj[i];x[j]=b[j]}for(i=xj.length-1;i!==-1;--i){j=xj[i];j0=Ai[j];j1=max(Ai[j+1],j0);for(k=j0;k!==j1;++k){if(Aj[k]===j){x[j]/=Av[k];break}}a=x[j];for(k=j0;k!==j1;++k){l=Aj[k];if(l!==j)x[l]-=a*Av[k]}}return x};numeric.ccsDFS=function ccsDFS(n){this.k=Array(n);this.k1=Array(n);this.j=Array(n)};numeric.ccsDFS.prototype.dfs=function dfs(J,Ai,Aj,x,xj,Pinv){var m=0,foo,n=xj.length;var k=this.k,k1=this.k1,j=this.j,km,k11;if(x[J]!==0)return;x[J]=1;j[0]=J;k[0]=km=Ai[J];k1[0]=k11=Ai[J+1];while(1){if(km>=k11){xj[n]=j[m];if(m===0)return;++n;--m;km=k[m];k11=k1[m]}else{foo=Pinv[Aj[km]];if(x[foo]===0){x[foo]=1;k[m]=km;++m;j[m]=foo;km=Ai[foo];k1[m]=k11=Ai[foo+1]}else++km}}};numeric.ccsLPSolve=function ccsLPSolve(A,B,x,xj,I,Pinv,dfs){var Ai=A[0],Aj=A[1],Av=A[2],m=Ai.length-1,n=0;var Bi=B[0],Bj=B[1],Bv=B[2];var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;i0=Bi[I];i1=Bi[I+1];xj.length=0;for(i=i0;i<i1;++i){dfs.dfs(Pinv[Bj[i]],Ai,Aj,x,xj,Pinv)}for(i=xj.length-1;i!==-1;--i){x[xj[i]]=0}for(i=i0;i!==i1;++i){j=Pinv[Bj[i]];x[j]=Bv[i]}for(i=xj.length-1;i!==-1;--i){j=xj[i];j0=Ai[j];j1=Ai[j+1];for(k=j0;k<j1;++k){if(Pinv[Aj[k]]===j){x[j]/=Av[k];break}}a=x[j];for(k=j0;k<j1;++k){l=Pinv[Aj[k]];if(l!==j)x[l]-=a*Av[k]}}return x};numeric.ccsLUP1=function ccsLUP1(A,threshold){var m=A[0].length-1;var L=[numeric.rep([m+1],0),[],[]],U=[numeric.rep([m+1],0),[],[]];var Li=L[0],Lj=L[1],Lv=L[2],Ui=U[0],Uj=U[1],Uv=U[2];var x=numeric.rep([m],0),xj=numeric.rep([m],0);var i,j,k,j0,j1,a,e,c,d,K;var sol=numeric.ccsLPSolve,max=Math.max,abs=Math.abs;var P=numeric.linspace(0,m-1),Pinv=numeric.linspace(0,m-1);var dfs=new numeric.ccsDFS(m);if(typeof threshold==="undefined"){threshold=1}for(i=0;i<m;++i){sol(L,A,x,xj,i,Pinv,dfs);a=-1;e=-1;for(j=xj.length-1;j!==-1;--j){k=xj[j];if(k<=i)continue;c=abs(x[k]);if(c>a){e=k;a=c}}if(abs(x[i])<threshold*a){j=P[i];a=P[e];P[i]=a;Pinv[a]=i;P[e]=j;Pinv[j]=e;a=x[i];x[i]=x[e];x[e]=a}a=Li[i];e=Ui[i];d=x[i];Lj[a]=P[i];Lv[a]=1;++a;for(j=xj.length-1;j!==-1;--j){k=xj[j];c=x[k];xj[j]=0;x[k]=0;if(k<=i){Uj[e]=k;Uv[e]=c;++e}else{Lj[a]=P[k];Lv[a]=c/d;++a}}Li[i+1]=a;Ui[i+1]=e}for(j=Lj.length-1;j!==-1;--j){Lj[j]=Pinv[Lj[j]]}return{L:L,U:U,P:P,Pinv:Pinv}};numeric.ccsDFS0=function ccsDFS0(n){this.k=Array(n);this.k1=Array(n);this.j=Array(n)};numeric.ccsDFS0.prototype.dfs=function dfs(J,Ai,Aj,x,xj,Pinv,P){var m=0,foo,n=xj.length;var k=this.k,k1=this.k1,j=this.j,km,k11;if(x[J]!==0)return;x[J]=1;j[0]=J;k[0]=km=Ai[Pinv[J]];k1[0]=k11=Ai[Pinv[J]+1];while(1){if(isNaN(km))throw new Error("Ow!");if(km>=k11){xj[n]=Pinv[j[m]];if(m===0)return;++n;--m;km=k[m];k11=k1[m]}else{foo=Aj[km];if(x[foo]===0){x[foo]=1;k[m]=km;++m;j[m]=foo;foo=Pinv[foo];km=Ai[foo];k1[m]=k11=Ai[foo+1]}else++km}}};numeric.ccsLPSolve0=function ccsLPSolve0(A,B,y,xj,I,Pinv,P,dfs){var Ai=A[0],Aj=A[1],Av=A[2],m=Ai.length-1,n=0;var Bi=B[0],Bj=B[1],Bv=B[2];var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;i0=Bi[I];i1=Bi[I+1];xj.length=0;for(i=i0;i<i1;++i){dfs.dfs(Bj[i],Ai,Aj,y,xj,Pinv,P)}for(i=xj.length-1;i!==-1;--i){j=xj[i];y[P[j]]=0}for(i=i0;i!==i1;++i){j=Bj[i];y[j]=Bv[i]}for(i=xj.length-1;i!==-1;--i){j=xj[i];l=P[j];j0=Ai[j];j1=Ai[j+1];for(k=j0;k<j1;++k){if(Aj[k]===l){y[l]/=Av[k];break}}a=y[l];for(k=j0;k<j1;++k)y[Aj[k]]-=a*Av[k];y[l]=a}};numeric.ccsLUP0=function ccsLUP0(A,threshold){var m=A[0].length-1;var L=[numeric.rep([m+1],0),[],[]],U=[numeric.rep([m+1],0),[],[]];var Li=L[0],Lj=L[1],Lv=L[2],Ui=U[0],Uj=U[1],Uv=U[2];var y=numeric.rep([m],0),xj=numeric.rep([m],0);var i,j,k,j0,j1,a,e,c,d,K;var sol=numeric.ccsLPSolve0,max=Math.max,abs=Math.abs;var P=numeric.linspace(0,m-1),Pinv=numeric.linspace(0,m-1);var dfs=new numeric.ccsDFS0(m);if(typeof threshold==="undefined"){threshold=1}for(i=0;i<m;++i){sol(L,A,y,xj,i,Pinv,P,dfs);a=-1;e=-1;for(j=xj.length-1;j!==-1;--j){k=xj[j];if(k<=i)continue;c=abs(y[P[k]]);if(c>a){e=k;a=c}}if(abs(y[P[i]])<threshold*a){j=P[i];a=P[e];P[i]=a;Pinv[a]=i;P[e]=j;Pinv[j]=e}a=Li[i];e=Ui[i];d=y[P[i]];Lj[a]=P[i];Lv[a]=1;++a;for(j=xj.length-1;j!==-1;--j){k=xj[j];c=y[P[k]];xj[j]=0;y[P[k]]=0;if(k<=i){Uj[e]=k;Uv[e]=c;++e}else{Lj[a]=P[k];Lv[a]=c/d;++a}}Li[i+1]=a;Ui[i+1]=e}for(j=Lj.length-1;j!==-1;--j){Lj[j]=Pinv[Lj[j]]}return{L:L,U:U,P:P,Pinv:Pinv}};numeric.ccsLUP=numeric.ccsLUP0;numeric.ccsDim=function ccsDim(A){return[numeric.sup(A[1])+1,A[0].length-1]};numeric.ccsGetBlock=function ccsGetBlock(A,i,j){var s=numeric.ccsDim(A),m=s[0],n=s[1];if(typeof i==="undefined"){i=numeric.linspace(0,m-1)}else if(typeof i==="number"){i=[i]}if(typeof j==="undefined"){j=numeric.linspace(0,n-1)}else if(typeof j==="number"){j=[j]}var p,p0,p1,P=i.length,q,Q=j.length,r,jq,ip;var Bi=numeric.rep([n],0),Bj=[],Bv=[],B=[Bi,Bj,Bv];var Ai=A[0],Aj=A[1],Av=A[2];var x=numeric.rep([m],0),count=0,flags=numeric.rep([m],0);for(q=0;q<Q;++q){jq=j[q];var q0=Ai[jq];var q1=Ai[jq+1];for(p=q0;p<q1;++p){r=Aj[p];flags[r]=1;x[r]=Av[p]}for(p=0;p<P;++p){ip=i[p];if(flags[ip]){Bj[count]=p;Bv[count]=x[i[p]];++count}}for(p=q0;p<q1;++p){r=Aj[p];flags[r]=0}Bi[q+1]=count}return B};numeric.ccsDot=function ccsDot(A,B){var Ai=A[0],Aj=A[1],Av=A[2];var Bi=B[0],Bj=B[1],Bv=B[2];var sA=numeric.ccsDim(A),sB=numeric.ccsDim(B);var m=sA[0],n=sA[1],o=sB[1];var x=numeric.rep([m],0),flags=numeric.rep([m],0),xj=Array(m);var Ci=numeric.rep([o],0),Cj=[],Cv=[],C=[Ci,Cj,Cv];var i,j,k,j0,j1,i0,i1,l,p,a,b;for(k=0;k!==o;++k){j0=Bi[k];j1=Bi[k+1];p=0;for(j=j0;j<j1;++j){a=Bj[j];b=Bv[j];i0=Ai[a];i1=Ai[a+1];for(i=i0;i<i1;++i){l=Aj[i];if(flags[l]===0){xj[p]=l;flags[l]=1;p=p+1}x[l]=x[l]+Av[i]*b}}j0=Ci[k];j1=j0+p;Ci[k+1]=j1;for(j=p-1;j!==-1;--j){b=j0+j;i=xj[j];Cj[b]=i;Cv[b]=x[i];flags[i]=0;x[i]=0}Ci[k+1]=Ci[k]+p}return C};numeric.ccsLUPSolve=function ccsLUPSolve(LUP,B){var L=LUP.L,U=LUP.U,P=LUP.P;var Bi=B[0];var flag=false;if(typeof Bi!=="object"){B=[[0,B.length],numeric.linspace(0,B.length-1),B];Bi=B[0];flag=true}var Bj=B[1],Bv=B[2];var n=L[0].length-1,m=Bi.length-1;var x=numeric.rep([n],0),xj=Array(n);var b=numeric.rep([n],0),bj=Array(n);var Xi=numeric.rep([m+1],0),Xj=[],Xv=[];var sol=numeric.ccsTSolve;var i,j,j0,j1,k,J,N=0;for(i=0;i<m;++i){k=0;j0=Bi[i];j1=Bi[i+1];for(j=j0;j<j1;++j){J=LUP.Pinv[Bj[j]];bj[k]=J;b[J]=Bv[j];++k}bj.length=k;sol(L,b,x,bj,xj);for(j=bj.length-1;j!==-1;--j)b[bj[j]]=0;sol(U,x,b,xj,bj);if(flag)return b;for(j=xj.length-1;j!==-1;--j)x[xj[j]]=0;for(j=bj.length-1;j!==-1;--j){J=bj[j];Xj[N]=J;Xv[N]=b[J];b[J]=0;++N}Xi[i+1]=N}return[Xi,Xj,Xv]};numeric.ccsbinop=function ccsbinop(body,setup){if(typeof setup==="undefined")setup="";return Function("X","Y","var Xi = X[0], Xj = X[1], Xv = X[2];\n"+"var Yi = Y[0], Yj = Y[1], Yv = Y[2];\n"+"var n = Xi.length-1,m = Math.max(numeric.sup(Xj),numeric.sup(Yj))+1;\n"+"var Zi = numeric.rep([n+1],0), Zj = [], Zv = [];\n"+"var x = numeric.rep([m],0),y = numeric.rep([m],0);\n"+"var xk,yk,zk;\n"+"var i,j,j0,j1,k,p=0;\n"+setup+"for(i=0;i<n;++i) {\n"+"  j0 = Xi[i]; j1 = Xi[i+1];\n"+"  for(j=j0;j!==j1;++j) {\n"+"    k = Xj[j];\n"+"    x[k] = 1;\n"+"    Zj[p] = k;\n"+"    ++p;\n"+"  }\n"+"  j0 = Yi[i]; j1 = Yi[i+1];\n"+"  for(j=j0;j!==j1;++j) {\n"+"    k = Yj[j];\n"+"    y[k] = Yv[j];\n"+"    if(x[k] === 0) {\n"+"      Zj[p] = k;\n"+"      ++p;\n"+"    }\n"+"  }\n"+"  Zi[i+1] = p;\n"+"  j0 = Xi[i]; j1 = Xi[i+1];\n"+"  for(j=j0;j!==j1;++j) x[Xj[j]] = Xv[j];\n"+"  j0 = Zi[i]; j1 = Zi[i+1];\n"+"  for(j=j0;j!==j1;++j) {\n"+"    k = Zj[j];\n"+"    xk = x[k];\n"+"    yk = y[k];\n"+body+"\n"+"    Zv[j] = zk;\n"+"  }\n"+"  j0 = Xi[i]; j1 = Xi[i+1];\n"+"  for(j=j0;j!==j1;++j) x[Xj[j]] = 0;\n"+"  j0 = Yi[i]; j1 = Yi[i+1];\n"+"  for(j=j0;j!==j1;++j) y[Yj[j]] = 0;\n"+"}\n"+"return [Zi,Zj,Zv];")};(function(){var k,A,B,C;for(k in numeric.ops2){if(isFinite(eval("1"+numeric.ops2[k]+"0")))A="[Y[0],Y[1],numeric."+k+"(X,Y[2])]";else A="NaN";if(isFinite(eval("0"+numeric.ops2[k]+"1")))B="[X[0],X[1],numeric."+k+"(X[2],Y)]";else B="NaN";if(isFinite(eval("1"+numeric.ops2[k]+"0"))&&isFinite(eval("0"+numeric.ops2[k]+"1")))C="numeric.ccs"+k+"MM(X,Y)";else C="NaN";numeric["ccs"+k+"MM"]=numeric.ccsbinop("zk = xk "+numeric.ops2[k]+"yk;");numeric["ccs"+k]=Function("X","Y",'if(typeof X === "number") return '+A+";\n"+'if(typeof Y === "number") return '+B+";\n"+"return "+C+";\n")}})();numeric.ccsScatter=function ccsScatter(A){var Ai=A[0],Aj=A[1],Av=A[2];var n=numeric.sup(Aj)+1,m=Ai.length;var Ri=numeric.rep([n],0),Rj=Array(m),Rv=Array(m);var counts=numeric.rep([n],0),i;for(i=0;i<m;++i)counts[Aj[i]]++;for(i=0;i<n;++i)Ri[i+1]=Ri[i]+counts[i];var ptr=Ri.slice(0),k,Aii;for(i=0;i<m;++i){Aii=Aj[i];k=ptr[Aii];Rj[k]=Ai[i];Rv[k]=Av[i];ptr[Aii]=ptr[Aii]+1}return[Ri,Rj,Rv]};numeric.ccsGather=function ccsGather(A){var Ai=A[0],Aj=A[1],Av=A[2];var n=Ai.length-1,m=Aj.length;var Ri=Array(m),Rj=Array(m),Rv=Array(m);var i,j,j0,j1,p;p=0;for(i=0;i<n;++i){j0=Ai[i];j1=Ai[i+1];for(j=j0;j!==j1;++j){Rj[p]=i;Ri[p]=Aj[j];Rv[p]=Av[j];++p}}return[Ri,Rj,Rv]};numeric.sdim=function dim(A,ret,k){if(typeof ret==="undefined"){ret=[]}if(typeof A!=="object")return ret;if(typeof k==="undefined"){k=0}if(!(k in ret)){ret[k]=0}if(A.length>ret[k])ret[k]=A.length;var i;for(i in A){if(A.hasOwnProperty(i))dim(A[i],ret,k+1)}return ret};numeric.sclone=function clone(A,k,n){if(typeof k==="undefined"){k=0}if(typeof n==="undefined"){n=numeric.sdim(A).length}var i,ret=Array(A.length);if(k===n-1){for(i in A){if(A.hasOwnProperty(i))ret[i]=A[i]}return ret}for(i in A){if(A.hasOwnProperty(i))ret[i]=clone(A[i],k+1,n)}return ret};numeric.sdiag=function diag(d){var n=d.length,i,ret=Array(n),i1,i2,i3;for(i=n-1;i>=1;i-=2){i1=i-1;ret[i]=[];ret[i][i]=d[i];ret[i1]=[];ret[i1][i1]=d[i1]}if(i===0){ret[0]=[];ret[0][0]=d[i]}return ret};numeric.sidentity=function identity(n){return numeric.sdiag(numeric.rep([n],1))};numeric.stranspose=function transpose(A){var ret=[],n=A.length,i,j,Ai;for(i in A){if(!A.hasOwnProperty(i))continue;Ai=A[i];for(j in Ai){if(!Ai.hasOwnProperty(j))continue;if(typeof ret[j]!=="object"){ret[j]=[]}ret[j][i]=Ai[j]}}return ret};numeric.sLUP=function LUP(A,tol){throw new Error("The function numeric.sLUP had a bug in it and has been removed. Please use the new numeric.ccsLUP function instead.")};numeric.sdotMM=function dotMM(A,B){var p=A.length,q=B.length,BT=numeric.stranspose(B),r=BT.length,Ai,BTk;var i,j,k,accum;var ret=Array(p),reti;for(i=p-1;i>=0;i--){reti=[];Ai=A[i];for(k=r-1;k>=0;k--){accum=0;BTk=BT[k];for(j in Ai){if(!Ai.hasOwnProperty(j))continue;if(j in BTk){accum+=Ai[j]*BTk[j]}}if(accum)reti[k]=accum}ret[i]=reti}return ret};numeric.sdotMV=function dotMV(A,x){var p=A.length,Ai,i,j;var ret=Array(p),accum;for(i=p-1;i>=0;i--){Ai=A[i];accum=0;for(j in Ai){if(!Ai.hasOwnProperty(j))continue;if(x[j])accum+=Ai[j]*x[j]}if(accum)ret[i]=accum}return ret};numeric.sdotVM=function dotMV(x,A){var i,j,Ai,alpha;var ret=[],accum;for(i in x){if(!x.hasOwnProperty(i))continue;Ai=A[i];alpha=x[i];for(j in Ai){if(!Ai.hasOwnProperty(j))continue;if(!ret[j]){ret[j]=0}ret[j]+=alpha*Ai[j]}}return ret};numeric.sdotVV=function dotVV(x,y){var i,ret=0;for(i in x){if(x[i]&&y[i])ret+=x[i]*y[i]}return ret};numeric.sdot=function dot(A,B){var m=numeric.sdim(A).length,n=numeric.sdim(B).length;var k=m*1e3+n;switch(k){case 0:return A*B;case 1001:return numeric.sdotVV(A,B);case 2001:return numeric.sdotMV(A,B);case 1002:return numeric.sdotVM(A,B);case 2002:return numeric.sdotMM(A,B);default:throw new Error("numeric.sdot not implemented for tensors of order "+m+" and "+n)}};numeric.sscatter=function scatter(V){var n=V[0].length,Vij,i,j,m=V.length,A=[],Aj;for(i=n-1;i>=0;--i){if(!V[m-1][i])continue;Aj=A;for(j=0;j<m-2;j++){Vij=V[j][i];if(!Aj[Vij])Aj[Vij]=[];Aj=Aj[Vij]}Aj[V[j][i]]=V[j+1][i]}return A};numeric.sgather=function gather(A,ret,k){if(typeof ret==="undefined")ret=[];if(typeof k==="undefined")k=[];var n,i,Ai;n=k.length;for(i in A){if(A.hasOwnProperty(i)){k[n]=parseInt(i);Ai=A[i];if(typeof Ai==="number"){if(Ai){if(ret.length===0){for(i=n+1;i>=0;--i)ret[i]=[]}for(i=n;i>=0;--i)ret[i].push(k[i]);ret[n+1].push(Ai)}}else gather(Ai,ret,k)}}if(k.length>n)k.pop();return ret};numeric.cLU=function LU(A){var I=A[0],J=A[1],V=A[2];var p=I.length,m=0,i,j,k,a,b,c;for(i=0;i<p;i++)if(I[i]>m)m=I[i];m++;var L=Array(m),U=Array(m),left=numeric.rep([m],Infinity),right=numeric.rep([m],-Infinity);var Ui,Uj,alpha;for(k=0;k<p;k++){i=I[k];j=J[k];if(j<left[i])left[i]=j;if(j>right[i])right[i]=j}for(i=0;i<m-1;i++){if(right[i]>right[i+1])right[i+1]=right[i]}for(i=m-1;i>=1;i--){if(left[i]<left[i-1])left[i-1]=left[i]}var countL=0,countU=0;for(i=0;i<m;i++){U[i]=numeric.rep([right[i]-left[i]+1],0);L[i]=numeric.rep([i-left[i]],0);countL+=i-left[i]+1;countU+=right[i]-i+1}for(k=0;k<p;k++){i=I[k];U[i][J[k]-left[i]]=V[k];
}for(i=0;i<m-1;i++){a=i-left[i];Ui=U[i];for(j=i+1;left[j]<=i&&j<m;j++){b=i-left[j];c=right[i]-i;Uj=U[j];alpha=Uj[b]/Ui[a];if(alpha){for(k=1;k<=c;k++){Uj[k+b]-=alpha*Ui[k+a]}L[j][i-left[j]]=alpha}}}var Ui=[],Uj=[],Uv=[],Li=[],Lj=[],Lv=[];var p,q,foo;p=0;q=0;for(i=0;i<m;i++){a=left[i];b=right[i];foo=U[i];for(j=i;j<=b;j++){if(foo[j-a]){Ui[p]=i;Uj[p]=j;Uv[p]=foo[j-a];p++}}foo=L[i];for(j=a;j<i;j++){if(foo[j-a]){Li[q]=i;Lj[q]=j;Lv[q]=foo[j-a];q++}}Li[q]=i;Lj[q]=i;Lv[q]=1;q++}return{U:[Ui,Uj,Uv],L:[Li,Lj,Lv]}};numeric.cLUsolve=function LUsolve(lu,b){var L=lu.L,U=lu.U,ret=numeric.clone(b);var Li=L[0],Lj=L[1],Lv=L[2];var Ui=U[0],Uj=U[1],Uv=U[2];var p=Ui.length,q=Li.length;var m=ret.length,i,j,k;k=0;for(i=0;i<m;i++){while(Lj[k]<i){ret[i]-=Lv[k]*ret[Lj[k]];k++}k++}k=p-1;for(i=m-1;i>=0;i--){while(Uj[k]>i){ret[i]-=Uv[k]*ret[Uj[k]];k--}ret[i]/=Uv[k];k--}return ret};numeric.cgrid=function grid(n,shape){if(typeof n==="number")n=[n,n];var ret=numeric.rep(n,-1);var i,j,count;if(typeof shape!=="function"){switch(shape){case"L":shape=function(i,j){return i>=n[0]/2||j<n[1]/2};break;default:shape=function(i,j){return true};break}}count=0;for(i=1;i<n[0]-1;i++)for(j=1;j<n[1]-1;j++)if(shape(i,j)){ret[i][j]=count;count++}return ret};numeric.cdelsq=function delsq(g){var dir=[[-1,0],[0,-1],[0,1],[1,0]];var s=numeric.dim(g),m=s[0],n=s[1],i,j,k,p,q;var Li=[],Lj=[],Lv=[];for(i=1;i<m-1;i++)for(j=1;j<n-1;j++){if(g[i][j]<0)continue;for(k=0;k<4;k++){p=i+dir[k][0];q=j+dir[k][1];if(g[p][q]<0)continue;Li.push(g[i][j]);Lj.push(g[p][q]);Lv.push(-1)}Li.push(g[i][j]);Lj.push(g[i][j]);Lv.push(4)}return[Li,Lj,Lv]};numeric.cdotMV=function dotMV(A,x){var ret,Ai=A[0],Aj=A[1],Av=A[2],k,p=Ai.length,N;N=0;for(k=0;k<p;k++){if(Ai[k]>N)N=Ai[k]}N++;ret=numeric.rep([N],0);for(k=0;k<p;k++){ret[Ai[k]]+=Av[k]*x[Aj[k]]}return ret};numeric.Spline=function Spline(x,yl,yr,kl,kr){this.x=x;this.yl=yl;this.yr=yr;this.kl=kl;this.kr=kr};numeric.Spline.prototype._at=function _at(x1,p){var x=this.x;var yl=this.yl;var yr=this.yr;var kl=this.kl;var kr=this.kr;var x1,a,b,t;var add=numeric.add,sub=numeric.sub,mul=numeric.mul;a=sub(mul(kl[p],x[p+1]-x[p]),sub(yr[p+1],yl[p]));b=add(mul(kr[p+1],x[p]-x[p+1]),sub(yr[p+1],yl[p]));t=(x1-x[p])/(x[p+1]-x[p]);var s=t*(1-t);return add(add(add(mul(1-t,yl[p]),mul(t,yr[p+1])),mul(a,s*(1-t))),mul(b,s*t))};numeric.Spline.prototype.at=function at(x0){if(typeof x0==="number"){var x=this.x;var n=x.length;var p,q,mid,floor=Math.floor,a,b,t;p=0;q=n-1;while(q-p>1){mid=floor((p+q)/2);if(x[mid]<=x0)p=mid;else q=mid}return this._at(x0,p)}var n=x0.length,i,ret=Array(n);for(i=n-1;i!==-1;--i)ret[i]=this.at(x0[i]);return ret};numeric.Spline.prototype.diff=function diff(){var x=this.x;var yl=this.yl;var yr=this.yr;var kl=this.kl;var kr=this.kr;var n=yl.length;var i,dx,dy;var zl=kl,zr=kr,pl=Array(n),pr=Array(n);var add=numeric.add,mul=numeric.mul,div=numeric.div,sub=numeric.sub;for(i=n-1;i!==-1;--i){dx=x[i+1]-x[i];dy=sub(yr[i+1],yl[i]);pl[i]=div(add(mul(dy,6),mul(kl[i],-4*dx),mul(kr[i+1],-2*dx)),dx*dx);pr[i+1]=div(add(mul(dy,-6),mul(kl[i],2*dx),mul(kr[i+1],4*dx)),dx*dx)}return new numeric.Spline(x,zl,zr,pl,pr)};numeric.Spline.prototype.roots=function roots(){function sqr(x){return x*x}function heval(y0,y1,k0,k1,x){var A=k0*2-(y1-y0);var B=-k1*2+(y1-y0);var t=(x+1)*.5;var s=t*(1-t);return(1-t)*y0+t*y1+A*s*(1-t)+B*s*t}var ret=[];var x=this.x,yl=this.yl,yr=this.yr,kl=this.kl,kr=this.kr;if(typeof yl[0]==="number"){yl=[yl];yr=[yr];kl=[kl];kr=[kr]}var m=yl.length,n=x.length-1,i,j,k,y,s,t;var ai,bi,ci,di,ret=Array(m),ri,k0,k1,y0,y1,A,B,D,dx,cx,stops,z0,z1,zm,t0,t1,tm;var sqrt=Math.sqrt;for(i=0;i!==m;++i){ai=yl[i];bi=yr[i];ci=kl[i];di=kr[i];ri=[];for(j=0;j!==n;j++){if(j>0&&bi[j]*ai[j]<0)ri.push(x[j]);dx=x[j+1]-x[j];cx=x[j];y0=ai[j];y1=bi[j+1];k0=ci[j]/dx;k1=di[j+1]/dx;D=sqr(k0-k1+3*(y0-y1))+12*k1*y0;A=k1+3*y0+2*k0-3*y1;B=3*(k1+k0+2*(y0-y1));if(D<=0){z0=A/B;if(z0>x[j]&&z0<x[j+1])stops=[x[j],z0,x[j+1]];else stops=[x[j],x[j+1]]}else{z0=(A-sqrt(D))/B;z1=(A+sqrt(D))/B;stops=[x[j]];if(z0>x[j]&&z0<x[j+1])stops.push(z0);if(z1>x[j]&&z1<x[j+1])stops.push(z1);stops.push(x[j+1])}t0=stops[0];z0=this._at(t0,j);for(k=0;k<stops.length-1;k++){t1=stops[k+1];z1=this._at(t1,j);if(z0===0){ri.push(t0);t0=t1;z0=z1;continue}if(z1===0||z0*z1>0){t0=t1;z0=z1;continue}var side=0;while(1){tm=(z0*t1-z1*t0)/(z0-z1);if(tm<=t0||tm>=t1){break}zm=this._at(tm,j);if(zm*z1>0){t1=tm;z1=zm;if(side===-1)z0*=.5;side=-1}else if(zm*z0>0){t0=tm;z0=zm;if(side===1)z1*=.5;side=1}else break}ri.push(tm);t0=stops[k+1];z0=this._at(t0,j)}if(z1===0)ri.push(t1)}ret[i]=ri}if(typeof this.yl[0]==="number")return ret[0];return ret};numeric.spline=function spline(x,y,k1,kn){var n=x.length,b=[],dx=[],dy=[];var i;var sub=numeric.sub,mul=numeric.mul,add=numeric.add;for(i=n-2;i>=0;i--){dx[i]=x[i+1]-x[i];dy[i]=sub(y[i+1],y[i])}if(typeof k1==="string"||typeof kn==="string"){k1=kn="periodic"}var T=[[],[],[]];switch(typeof k1){case"undefined":b[0]=mul(3/(dx[0]*dx[0]),dy[0]);T[0].push(0,0);T[1].push(0,1);T[2].push(2/dx[0],1/dx[0]);break;case"string":b[0]=add(mul(3/(dx[n-2]*dx[n-2]),dy[n-2]),mul(3/(dx[0]*dx[0]),dy[0]));T[0].push(0,0,0);T[1].push(n-2,0,1);T[2].push(1/dx[n-2],2/dx[n-2]+2/dx[0],1/dx[0]);break;default:b[0]=k1;T[0].push(0);T[1].push(0);T[2].push(1);break}for(i=1;i<n-1;i++){b[i]=add(mul(3/(dx[i-1]*dx[i-1]),dy[i-1]),mul(3/(dx[i]*dx[i]),dy[i]));T[0].push(i,i,i);T[1].push(i-1,i,i+1);T[2].push(1/dx[i-1],2/dx[i-1]+2/dx[i],1/dx[i])}switch(typeof kn){case"undefined":b[n-1]=mul(3/(dx[n-2]*dx[n-2]),dy[n-2]);T[0].push(n-1,n-1);T[1].push(n-2,n-1);T[2].push(1/dx[n-2],2/dx[n-2]);break;case"string":T[1][T[1].length-1]=0;break;default:b[n-1]=kn;T[0].push(n-1);T[1].push(n-1);T[2].push(1);break}if(typeof b[0]!=="number")b=numeric.transpose(b);else b=[b];var k=Array(b.length);if(typeof k1==="string"){for(i=k.length-1;i!==-1;--i){k[i]=numeric.ccsLUPSolve(numeric.ccsLUP(numeric.ccsScatter(T)),b[i]);k[i][n-1]=k[i][0]}}else{for(i=k.length-1;i!==-1;--i){k[i]=numeric.cLUsolve(numeric.cLU(T),b[i])}}if(typeof y[0]==="number")k=k[0];else k=numeric.transpose(k);return new numeric.Spline(x,y,y,k,k)};numeric.fftpow2=function fftpow2(x,y){var n=x.length;if(n===1)return;var cos=Math.cos,sin=Math.sin,i,j;var xe=Array(n/2),ye=Array(n/2),xo=Array(n/2),yo=Array(n/2);j=n/2;for(i=n-1;i!==-1;--i){--j;xo[j]=x[i];yo[j]=y[i];--i;xe[j]=x[i];ye[j]=y[i]}fftpow2(xe,ye);fftpow2(xo,yo);j=n/2;var t,k=-6.283185307179586/n,ci,si;for(i=n-1;i!==-1;--i){--j;if(j===-1)j=n/2-1;t=k*i;ci=cos(t);si=sin(t);x[i]=xe[j]+ci*xo[j]-si*yo[j];y[i]=ye[j]+ci*yo[j]+si*xo[j]}};numeric._ifftpow2=function _ifftpow2(x,y){var n=x.length;if(n===1)return;var cos=Math.cos,sin=Math.sin,i,j;var xe=Array(n/2),ye=Array(n/2),xo=Array(n/2),yo=Array(n/2);j=n/2;for(i=n-1;i!==-1;--i){--j;xo[j]=x[i];yo[j]=y[i];--i;xe[j]=x[i];ye[j]=y[i]}_ifftpow2(xe,ye);_ifftpow2(xo,yo);j=n/2;var t,k=6.283185307179586/n,ci,si;for(i=n-1;i!==-1;--i){--j;if(j===-1)j=n/2-1;t=k*i;ci=cos(t);si=sin(t);x[i]=xe[j]+ci*xo[j]-si*yo[j];y[i]=ye[j]+ci*yo[j]+si*xo[j]}};numeric.ifftpow2=function ifftpow2(x,y){numeric._ifftpow2(x,y);numeric.diveq(x,x.length);numeric.diveq(y,y.length)};numeric.convpow2=function convpow2(ax,ay,bx,by){numeric.fftpow2(ax,ay);numeric.fftpow2(bx,by);var i,n=ax.length,axi,bxi,ayi,byi;for(i=n-1;i!==-1;--i){axi=ax[i];ayi=ay[i];bxi=bx[i];byi=by[i];ax[i]=axi*bxi-ayi*byi;ay[i]=axi*byi+ayi*bxi}numeric.ifftpow2(ax,ay)};numeric.T.prototype.fft=function fft(){var x=this.x,y=this.y;var n=x.length,log=Math.log,log2=log(2),p=Math.ceil(log(2*n-1)/log2),m=Math.pow(2,p);var cx=numeric.rep([m],0),cy=numeric.rep([m],0),cos=Math.cos,sin=Math.sin;var k,c=-3.141592653589793/n,t;var a=numeric.rep([m],0),b=numeric.rep([m],0),nhalf=Math.floor(n/2);for(k=0;k<n;k++)a[k]=x[k];if(typeof y!=="undefined")for(k=0;k<n;k++)b[k]=y[k];cx[0]=1;for(k=1;k<=m/2;k++){t=c*k*k;cx[k]=cos(t);cy[k]=sin(t);cx[m-k]=cos(t);cy[m-k]=sin(t)}var X=new numeric.T(a,b),Y=new numeric.T(cx,cy);X=X.mul(Y);numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));X=X.mul(Y);X.x.length=n;X.y.length=n;return X};numeric.T.prototype.ifft=function ifft(){var x=this.x,y=this.y;var n=x.length,log=Math.log,log2=log(2),p=Math.ceil(log(2*n-1)/log2),m=Math.pow(2,p);var cx=numeric.rep([m],0),cy=numeric.rep([m],0),cos=Math.cos,sin=Math.sin;var k,c=3.141592653589793/n,t;var a=numeric.rep([m],0),b=numeric.rep([m],0),nhalf=Math.floor(n/2);for(k=0;k<n;k++)a[k]=x[k];if(typeof y!=="undefined")for(k=0;k<n;k++)b[k]=y[k];cx[0]=1;for(k=1;k<=m/2;k++){t=c*k*k;cx[k]=cos(t);cy[k]=sin(t);cx[m-k]=cos(t);cy[m-k]=sin(t)}var X=new numeric.T(a,b),Y=new numeric.T(cx,cy);X=X.mul(Y);numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));X=X.mul(Y);X.x.length=n;X.y.length=n;return X.div(n)};numeric.gradient=function gradient(f,x){var n=x.length;var f0=f(x);if(isNaN(f0))throw new Error("gradient: f(x) is a NaN!");var max=Math.max;var i,x0=numeric.clone(x),f1,f2,J=Array(n);var div=numeric.div,sub=numeric.sub,errest,roundoff,max=Math.max,eps=.001,abs=Math.abs,min=Math.min;var t0,t1,t2,it=0,d1,d2,N;for(i=0;i<n;i++){var h=max(1e-6*f0,1e-8);while(1){++it;if(it>20){throw new Error("Numerical gradient fails")}x0[i]=x[i]+h;f1=f(x0);x0[i]=x[i]-h;f2=f(x0);x0[i]=x[i];if(isNaN(f1)||isNaN(f2)){h/=16;continue}J[i]=(f1-f2)/(2*h);t0=x[i]-h;t1=x[i];t2=x[i]+h;d1=(f1-f0)/h;d2=(f0-f2)/h;N=max(abs(J[i]),abs(f0),abs(f1),abs(f2),abs(t0),abs(t1),abs(t2),1e-8);errest=min(max(abs(d1-J[i]),abs(d2-J[i]),abs(d1-d2))/N,h/N);if(errest>eps){h/=16}else break}}return J};numeric.uncmin=function uncmin(f,x0,tol,gradient,maxit,callback,options){var grad=numeric.gradient;if(typeof options==="undefined"){options={}}if(typeof tol==="undefined"){tol=1e-8}if(typeof gradient==="undefined"){gradient=function(x){return grad(f,x)}}if(typeof maxit==="undefined")maxit=1e3;x0=numeric.clone(x0);var n=x0.length;var f0=f(x0),f1,df0;if(isNaN(f0))throw new Error("uncmin: f(x0) is a NaN!");var max=Math.max,norm2=numeric.norm2;tol=max(tol,numeric.epsilon);var step,g0,g1,H1=options.Hinv||numeric.identity(n);var dot=numeric.dot,inv=numeric.inv,sub=numeric.sub,add=numeric.add,ten=numeric.tensor,div=numeric.div,mul=numeric.mul;var all=numeric.all,isfinite=numeric.isFinite,neg=numeric.neg;var it=0,i,s,x1,y,Hy,Hs,ys,i0,t,nstep,t1,t2;var msg="";g0=gradient(x0);while(it<maxit){if(typeof callback==="function"){if(callback(it,x0,f0,g0,H1)){msg="Callback returned true";break}}if(!all(isfinite(g0))){msg="Gradient has Infinity or NaN";break}step=neg(dot(H1,g0));if(!all(isfinite(step))){msg="Search direction has Infinity or NaN";break}nstep=norm2(step);if(nstep<tol){msg="Newton step smaller than tol";break}t=1;df0=dot(g0,step);x1=x0;while(it<maxit){if(t*nstep<tol){break}s=mul(step,t);x1=add(x0,s);f1=f(x1);if(f1-f0>=.1*t*df0||isNaN(f1)){t*=.5;++it;continue}break}if(t*nstep<tol){msg="Line search step size smaller than tol";break}if(it===maxit){msg="maxit reached during line search";break}g1=gradient(x1);y=sub(g1,g0);ys=dot(y,s);Hy=dot(H1,y);H1=sub(add(H1,mul((ys+dot(y,Hy))/(ys*ys),ten(s,s))),div(add(ten(Hy,s),ten(s,Hy)),ys));x0=x1;f0=f1;g0=g1;++it}return{solution:x0,f:f0,gradient:g0,invHessian:H1,iterations:it,message:msg}};numeric.Dopri=function Dopri(x,y,f,ymid,iterations,msg,events){this.x=x;this.y=y;this.f=f;this.ymid=ymid;this.iterations=iterations;this.events=events;this.message=msg};numeric.Dopri.prototype._at=function _at(xi,j){function sqr(x){return x*x}var sol=this;var xs=sol.x;var ys=sol.y;var k1=sol.f;var ymid=sol.ymid;var n=xs.length;var x0,x1,xh,y0,y1,yh,xi;var floor=Math.floor,h;var c=.5;var add=numeric.add,mul=numeric.mul,sub=numeric.sub,p,q,w;x0=xs[j];x1=xs[j+1];y0=ys[j];y1=ys[j+1];h=x1-x0;xh=x0+c*h;yh=ymid[j];p=sub(k1[j],mul(y0,1/(x0-xh)+2/(x0-x1)));q=sub(k1[j+1],mul(y1,1/(x1-xh)+2/(x1-x0)));w=[sqr(xi-x1)*(xi-xh)/sqr(x0-x1)/(x0-xh),sqr(xi-x0)*sqr(xi-x1)/sqr(x0-xh)/sqr(x1-xh),sqr(xi-x0)*(xi-xh)/sqr(x1-x0)/(x1-xh),(xi-x0)*sqr(xi-x1)*(xi-xh)/sqr(x0-x1)/(x0-xh),(xi-x1)*sqr(xi-x0)*(xi-xh)/sqr(x0-x1)/(x1-xh)];return add(add(add(add(mul(y0,w[0]),mul(yh,w[1])),mul(y1,w[2])),mul(p,w[3])),mul(q,w[4]))};numeric.Dopri.prototype.at=function at(x){var i,j,k,floor=Math.floor;if(typeof x!=="number"){var n=x.length,ret=Array(n);for(i=n-1;i!==-1;--i){ret[i]=this.at(x[i])}return ret}var x0=this.x;i=0;j=x0.length-1;while(j-i>1){k=floor(.5*(i+j));if(x0[k]<=x)i=k;else j=k}return this._at(x,i)};numeric.dopri=function dopri(x0,x1,y0,f,tol,maxit,event){if(typeof tol==="undefined"){tol=1e-6}if(typeof maxit==="undefined"){maxit=1e3}var xs=[x0],ys=[y0],k1=[f(x0,y0)],k2,k3,k4,k5,k6,k7,ymid=[];var A2=1/5;var A3=[3/40,9/40];var A4=[44/45,-56/15,32/9];var A5=[19372/6561,-25360/2187,64448/6561,-212/729];var A6=[9017/3168,-355/33,46732/5247,49/176,-5103/18656];var b=[35/384,0,500/1113,125/192,-2187/6784,11/84];var bm=[.5*6025192743/30085553152,0,.5*51252292925/65400821598,.5*-2691868925/45128329728,.5*187940372067/1594534317056,.5*-1776094331/19743644256,.5*11237099/235043384];var c=[1/5,3/10,4/5,8/9,1,1];var e=[-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40];var i=0,er,j;var h=(x1-x0)/10;var it=0;var add=numeric.add,mul=numeric.mul,y1,erinf;var max=Math.max,min=Math.min,abs=Math.abs,norminf=numeric.norminf,pow=Math.pow;var any=numeric.any,lt=numeric.lt,and=numeric.and,sub=numeric.sub;var e0,e1,ev;var ret=new numeric.Dopri(xs,ys,k1,ymid,-1,"");if(typeof event==="function")e0=event(x0,y0);while(x0<x1&&it<maxit){++it;if(x0+h>x1)h=x1-x0;k2=f(x0+c[0]*h,add(y0,mul(A2*h,k1[i])));k3=f(x0+c[1]*h,add(add(y0,mul(A3[0]*h,k1[i])),mul(A3[1]*h,k2)));k4=f(x0+c[2]*h,add(add(add(y0,mul(A4[0]*h,k1[i])),mul(A4[1]*h,k2)),mul(A4[2]*h,k3)));k5=f(x0+c[3]*h,add(add(add(add(y0,mul(A5[0]*h,k1[i])),mul(A5[1]*h,k2)),mul(A5[2]*h,k3)),mul(A5[3]*h,k4)));k6=f(x0+c[4]*h,add(add(add(add(add(y0,mul(A6[0]*h,k1[i])),mul(A6[1]*h,k2)),mul(A6[2]*h,k3)),mul(A6[3]*h,k4)),mul(A6[4]*h,k5)));y1=add(add(add(add(add(y0,mul(k1[i],h*b[0])),mul(k3,h*b[2])),mul(k4,h*b[3])),mul(k5,h*b[4])),mul(k6,h*b[5]));k7=f(x0+h,y1);er=add(add(add(add(add(mul(k1[i],h*e[0]),mul(k3,h*e[2])),mul(k4,h*e[3])),mul(k5,h*e[4])),mul(k6,h*e[5])),mul(k7,h*e[6]));if(typeof er==="number")erinf=abs(er);else erinf=norminf(er);if(erinf>tol){h=.2*h*pow(tol/erinf,.25);if(x0+h===x0){ret.msg="Step size became too small";break}continue}ymid[i]=add(add(add(add(add(add(y0,mul(k1[i],h*bm[0])),mul(k3,h*bm[2])),mul(k4,h*bm[3])),mul(k5,h*bm[4])),mul(k6,h*bm[5])),mul(k7,h*bm[6]));++i;xs[i]=x0+h;ys[i]=y1;k1[i]=k7;if(typeof event==="function"){var yi,xl=x0,xr=x0+.5*h,xi;e1=event(xr,ymid[i-1]);ev=and(lt(e0,0),lt(0,e1));if(!any(ev)){xl=xr;xr=x0+h;e0=e1;e1=event(xr,y1);ev=and(lt(e0,0),lt(0,e1))}if(any(ev)){var xc,yc,en,ei;var side=0,sl=1,sr=1;while(1){if(typeof e0==="number")xi=(sr*e1*xl-sl*e0*xr)/(sr*e1-sl*e0);else{xi=xr;for(j=e0.length-1;j!==-1;--j){if(e0[j]<0&&e1[j]>0)xi=min(xi,(sr*e1[j]*xl-sl*e0[j]*xr)/(sr*e1[j]-sl*e0[j]))}}if(xi<=xl||xi>=xr)break;yi=ret._at(xi,i-1);ei=event(xi,yi);en=and(lt(e0,0),lt(0,ei));if(any(en)){xr=xi;e1=ei;ev=en;sr=1;if(side===-1)sl*=.5;else sl=1;side=-1}else{xl=xi;e0=ei;sl=1;if(side===1)sr*=.5;else sr=1;side=1}}y1=ret._at(.5*(x0+xi),i-1);ret.f[i]=f(xi,yi);ret.x[i]=xi;ret.y[i]=yi;ret.ymid[i-1]=y1;ret.events=ev;ret.iterations=it;return ret}}x0+=h;y0=y1;e0=e1;h=min(.8*h*pow(tol/erinf,.25),4*h)}ret.iterations=it;return ret};numeric.LU=function(A,fast){fast=fast||false;var abs=Math.abs;var i,j,k,absAjk,Akk,Ak,Pk,Ai;var max;var n=A.length,n1=n-1;var P=new Array(n);if(!fast)A=numeric.clone(A);for(k=0;k<n;++k){Pk=k;Ak=A[k];max=abs(Ak[k]);for(j=k+1;j<n;++j){absAjk=abs(A[j][k]);if(max<absAjk){max=absAjk;Pk=j}}P[k]=Pk;if(Pk!=k){A[k]=A[Pk];A[Pk]=Ak;Ak=A[k]}Akk=Ak[k];for(i=k+1;i<n;++i){A[i][k]/=Akk}for(i=k+1;i<n;++i){Ai=A[i];for(j=k+1;j<n1;++j){Ai[j]-=Ai[k]*Ak[j];++j;Ai[j]-=Ai[k]*Ak[j]}if(j===n1)Ai[j]-=Ai[k]*Ak[j]}}return{LU:A,P:P}};numeric.LUsolve=function LUsolve(LUP,b){var i,j;var LU=LUP.LU;var n=LU.length;var x=numeric.clone(b);var P=LUP.P;var Pi,LUi,LUii,tmp;for(i=n-1;i!==-1;--i)x[i]=b[i];for(i=0;i<n;++i){Pi=P[i];if(P[i]!==i){tmp=x[i];x[i]=x[Pi];x[Pi]=tmp}LUi=LU[i];for(j=0;j<i;++j){x[i]-=x[j]*LUi[j]}}for(i=n-1;i>=0;--i){LUi=LU[i];for(j=i+1;j<n;++j){x[i]-=x[j]*LUi[j]}x[i]/=LUi[i]}return x};numeric.solve=function solve(A,b,fast){return numeric.LUsolve(numeric.LU(A,fast),b)};numeric.echelonize=function echelonize(A){var s=numeric.dim(A),m=s[0],n=s[1];var I=numeric.identity(m);var P=Array(m);var i,j,k,l,Ai,Ii,Z,a;var abs=Math.abs;var diveq=numeric.diveq;A=numeric.clone(A);for(i=0;i<m;++i){k=0;Ai=A[i];Ii=I[i];for(j=1;j<n;++j)if(abs(Ai[k])<abs(Ai[j]))k=j;P[i]=k;diveq(Ii,Ai[k]);diveq(Ai,Ai[k]);for(j=0;j<m;++j)if(j!==i){Z=A[j];a=Z[k];for(l=n-1;l!==-1;--l)Z[l]-=Ai[l]*a;Z=I[j];for(l=m-1;l!==-1;--l)Z[l]-=Ii[l]*a}}return{I:I,A:A,P:P}};numeric.__solveLP=function __solveLP(c,A,b,tol,maxit,x,flag){var sum=numeric.sum,log=numeric.log,mul=numeric.mul,sub=numeric.sub,dot=numeric.dot,div=numeric.div,add=numeric.add;var m=c.length,n=b.length,y;var unbounded=false,cb,i0=0;var alpha=1;var f0,df0,AT=numeric.transpose(A),svd=numeric.svd,transpose=numeric.transpose,leq=numeric.leq,sqrt=Math.sqrt,abs=Math.abs;var muleq=numeric.muleq;var norm=numeric.norminf,any=numeric.any,min=Math.min;var all=numeric.all,gt=numeric.gt;var p=Array(m),A0=Array(n),e=numeric.rep([n],1),H;var solve=numeric.solve,z=sub(b,dot(A,x)),count;var dotcc=dot(c,c);var g;for(count=i0;count<maxit;++count){var i,j,d;for(i=n-1;i!==-1;--i)A0[i]=div(A[i],z[i]);var A1=transpose(A0);for(i=m-1;i!==-1;--i)p[i]=sum(A1[i]);alpha=.25*abs(dotcc/dot(c,p));var a1=100*sqrt(dotcc/dot(p,p));if(!isFinite(alpha)||alpha>a1)alpha=a1;g=add(c,mul(alpha,p));H=dot(A1,A0);for(i=m-1;i!==-1;--i)H[i][i]+=1;d=solve(H,div(g,alpha),true);var t0=div(z,dot(A,d));var t=1;for(i=n-1;i!==-1;--i)if(t0[i]<0)t=min(t,-.999*t0[i]);y=sub(x,mul(d,t));z=sub(b,dot(A,y));if(!all(gt(z,0)))return{solution:x,message:"",iterations:count};x=y;if(alpha<tol)return{solution:y,message:"",iterations:count};if(flag){var s=dot(c,g),Ag=dot(A,g);unbounded=true;for(i=n-1;i!==-1;--i)if(s*Ag[i]<0){unbounded=false;break}}else{if(x[m-1]>=0)unbounded=false;else unbounded=true}if(unbounded)return{solution:y,message:"Unbounded",iterations:count}}return{solution:x,message:"maximum iteration count exceeded",iterations:count}};numeric._solveLP=function _solveLP(c,A,b,tol,maxit){var m=c.length,n=b.length,y;var sum=numeric.sum,log=numeric.log,mul=numeric.mul,sub=numeric.sub,dot=numeric.dot,div=numeric.div,add=numeric.add;var c0=numeric.rep([m],0).concat([1]);var J=numeric.rep([n,1],-1);var A0=numeric.blockMatrix([[A,J]]);var b0=b;var y=numeric.rep([m],0).concat(Math.max(0,numeric.sup(numeric.neg(b)))+1);var x0=numeric.__solveLP(c0,A0,b0,tol,maxit,y,false);var x=numeric.clone(x0.solution);x.length=m;var foo=numeric.inf(sub(b,dot(A,x)));if(foo<0){return{solution:NaN,message:"Infeasible",iterations:x0.iterations}}var ret=numeric.__solveLP(c,A,b,tol,maxit-x0.iterations,x,true);ret.iterations+=x0.iterations;return ret};numeric.solveLP=function solveLP(c,A,b,Aeq,beq,tol,maxit){if(typeof maxit==="undefined")maxit=1e3;if(typeof tol==="undefined")tol=numeric.epsilon;if(typeof Aeq==="undefined")return numeric._solveLP(c,A,b,tol,maxit);var m=Aeq.length,n=Aeq[0].length,o=A.length;var B=numeric.echelonize(Aeq);var flags=numeric.rep([n],0);var P=B.P;var Q=[];var i;for(i=P.length-1;i!==-1;--i)flags[P[i]]=1;for(i=n-1;i!==-1;--i)if(flags[i]===0)Q.push(i);var g=numeric.getRange;var I=numeric.linspace(0,m-1),J=numeric.linspace(0,o-1);var Aeq2=g(Aeq,I,Q),A1=g(A,J,P),A2=g(A,J,Q),dot=numeric.dot,sub=numeric.sub;var A3=dot(A1,B.I);var A4=sub(A2,dot(A3,Aeq2)),b4=sub(b,dot(A3,beq));var c1=Array(P.length),c2=Array(Q.length);for(i=P.length-1;i!==-1;--i)c1[i]=c[P[i]];for(i=Q.length-1;i!==-1;--i)c2[i]=c[Q[i]];var c4=sub(c2,dot(c1,dot(B.I,Aeq2)));var S=numeric._solveLP(c4,A4,b4,tol,maxit);var x2=S.solution;if(x2!==x2)return S;var x1=dot(B.I,sub(beq,dot(Aeq2,x2)));var x=Array(c.length);for(i=P.length-1;i!==-1;--i)x[P[i]]=x1[i];for(i=Q.length-1;i!==-1;--i)x[Q[i]]=x2[i];return{solution:x,message:S.message,iterations:S.iterations}};numeric.MPStoLP=function MPStoLP(MPS){if(MPS instanceof String){MPS.split("\n")}var state=0;var states=["Initial state","NAME","ROWS","COLUMNS","RHS","BOUNDS","ENDATA"];var n=MPS.length;var i,j,z,N=0,rows={},sign=[],rl=0,vars={},nv=0;var name;var c=[],A=[],b=[];function err(e){throw new Error("MPStoLP: "+e+"\nLine "+i+": "+MPS[i]+"\nCurrent state: "+states[state]+"\n")}for(i=0;i<n;++i){z=MPS[i];var w0=z.match(/\S*/g);var w=[];for(j=0;j<w0.length;++j)if(w0[j]!=="")w.push(w0[j]);if(w.length===0)continue;for(j=0;j<states.length;++j)if(z.substr(0,states[j].length)===states[j])break;if(j<states.length){state=j;if(j===1){name=w[1]}if(j===6)return{name:name,c:c,A:numeric.transpose(A),b:b,rows:rows,vars:vars};continue}switch(state){case 0:case 1:err("Unexpected line");case 2:switch(w[0]){case"N":if(N===0)N=w[1];else err("Two or more N rows");break;case"L":rows[w[1]]=rl;sign[rl]=1;b[rl]=0;++rl;break;case"G":rows[w[1]]=rl;sign[rl]=-1;b[rl]=0;++rl;break;case"E":rows[w[1]]=rl;sign[rl]=0;b[rl]=0;++rl;break;default:err("Parse error "+numeric.prettyPrint(w))}break;case 3:if(!vars.hasOwnProperty(w[0])){vars[w[0]]=nv;c[nv]=0;A[nv]=numeric.rep([rl],0);++nv}var p=vars[w[0]];for(j=1;j<w.length;j+=2){if(w[j]===N){c[p]=parseFloat(w[j+1]);continue}var q=rows[w[j]];A[p][q]=(sign[q]<0?-1:1)*parseFloat(w[j+1])}break;case 4:for(j=1;j<w.length;j+=2)b[rows[w[j]]]=(sign[rows[w[j]]]<0?-1:1)*parseFloat(w[j+1]);break;case 5:break;case 6:err("Internal error")}}err("Reached end of file without ENDATA")};numeric.seedrandom={pow:Math.pow,random:Math.random};(function(pool,math,width,chunks,significance,overflow,startdenom){math["seedrandom"]=function seedrandom(seed,use_entropy){var key=[];var arc4;seed=mixkey(flatten(use_entropy?[seed,pool]:arguments.length?seed:[(new Date).getTime(),pool,window],3),key);arc4=new ARC4(key);mixkey(arc4.S,pool);math["random"]=function random(){var n=arc4.g(chunks);var d=startdenom;var x=0;while(n<significance){n=(n+x)*width;d*=width;x=arc4.g(1)}while(n>=overflow){n/=2;d/=2;x>>>=1}return(n+x)/d};return seed};function ARC4(key){var t,u,me=this,keylen=key.length;var i=0,j=me.i=me.j=me.m=0;me.S=[];me.c=[];if(!keylen){key=[keylen++]}while(i<width){me.S[i]=i++}for(i=0;i<width;i++){t=me.S[i];j=lowbits(j+t+key[i%keylen]);u=me.S[j];me.S[i]=u;me.S[j]=t}me.g=function getnext(count){var s=me.S;var i=lowbits(me.i+1);var t=s[i];var j=lowbits(me.j+t);var u=s[j];s[i]=u;s[j]=t;var r=s[lowbits(t+u)];while(--count){i=lowbits(i+1);t=s[i];j=lowbits(j+t);u=s[j];s[i]=u;s[j]=t;r=r*width+s[lowbits(t+u)]}me.i=i;me.j=j;return r};me.g(width)}function flatten(obj,depth,result,prop,typ){result=[];typ=typeof obj;if(depth&&typ=="object"){for(prop in obj){if(prop.indexOf("S")<5){try{result.push(flatten(obj[prop],depth-1))}catch(e){}}}}return result.length?result:obj+(typ!="string"?"\x00":"")}function mixkey(seed,key,smear,j){seed+="";smear=0;for(j=0;j<seed.length;j++){key[lowbits(j)]=lowbits((smear^=key[lowbits(j)]*19)+seed.charCodeAt(j))}seed="";for(j in key){seed+=String.fromCharCode(key[j])}return seed}function lowbits(n){return n&width-1}startdenom=math.pow(width,chunks);significance=math.pow(2,significance);overflow=significance*2;mixkey(math.random(),pool)})([],numeric.seedrandom,256,6,52);(function(exports){function base0to1(A){if(typeof A!=="object"){return A}var ret=[],i,n=A.length;for(i=0;i<n;i++)ret[i+1]=base0to1(A[i]);return ret}function base1to0(A){if(typeof A!=="object"){return A}var ret=[],i,n=A.length;for(i=1;i<n;i++)ret[i-1]=base1to0(A[i]);return ret}function dpori(a,lda,n){var i,j,k,kp1,t;for(k=1;k<=n;k=k+1){a[k][k]=1/a[k][k];t=-a[k][k];for(i=1;i<k;i=i+1){a[i][k]=t*a[i][k]}kp1=k+1;if(n<kp1){break}for(j=kp1;j<=n;j=j+1){t=a[k][j];a[k][j]=0;for(i=1;i<=k;i=i+1){a[i][j]=a[i][j]+t*a[i][k]}}}}function dposl(a,lda,n,b){var i,k,kb,t;for(k=1;k<=n;k=k+1){t=0;for(i=1;i<k;i=i+1){t=t+a[i][k]*b[i]}b[k]=(b[k]-t)/a[k][k]}for(kb=1;kb<=n;kb=kb+1){k=n+1-kb;b[k]=b[k]/a[k][k];t=-b[k];for(i=1;i<k;i=i+1){b[i]=b[i]+t*a[i][k]}}}function dpofa(a,lda,n,info){var i,j,jm1,k,t,s;for(j=1;j<=n;j=j+1){info[1]=j;s=0;jm1=j-1;if(jm1<1){s=a[j][j]-s;if(s<=0){break}a[j][j]=Math.sqrt(s)}else{for(k=1;k<=jm1;k=k+1){t=a[k][j];for(i=1;i<k;i=i+1){t=t-a[i][j]*a[i][k]}t=t/a[k][k];a[k][j]=t;s=s+t*t}s=a[j][j]-s;if(s<=0){break}a[j][j]=Math.sqrt(s)}info[1]=0}}function qpgen2(dmat,dvec,fddmat,n,sol,crval,amat,bvec,fdamat,q,meq,iact,nact,iter,work,ierr){var i,j,l,l1,info,it1,iwzv,iwrv,iwrm,iwsv,iwuv,nvl,r,iwnbv,temp,sum,t1,tt,gc,gs,nu,t1inf,t2min,vsmall,tmpa,tmpb,go;r=Math.min(n,q);l=2*n+r*(r+5)/2+2*q+1;vsmall=1e-60;do{vsmall=vsmall+vsmall;tmpa=1+.1*vsmall;tmpb=1+.2*vsmall}while(tmpa<=1||tmpb<=1);for(i=1;i<=n;i=i+1){work[i]=dvec[i]}for(i=n+1;i<=l;i=i+1){work[i]=0}for(i=1;i<=q;i=i+1){iact[i]=0}info=[];if(ierr[1]===0){dpofa(dmat,fddmat,n,info);if(info[1]!==0){ierr[1]=2;return}dposl(dmat,fddmat,n,dvec);dpori(dmat,fddmat,n)}else{for(j=1;j<=n;j=j+1){sol[j]=0;for(i=1;i<=j;i=i+1){sol[j]=sol[j]+dmat[i][j]*dvec[i]}}for(j=1;j<=n;j=j+1){dvec[j]=0;for(i=j;i<=n;i=i+1){dvec[j]=dvec[j]+dmat[j][i]*sol[i]}}}crval[1]=0;for(j=1;j<=n;j=j+1){sol[j]=dvec[j];crval[1]=crval[1]+work[j]*sol[j];work[j]=0;for(i=j+1;i<=n;i=i+1){dmat[i][j]=0}}crval[1]=-crval[1]/2;ierr[1]=0;iwzv=n;iwrv=iwzv+n;iwuv=iwrv+r;iwrm=iwuv+r+1;iwsv=iwrm+r*(r+1)/2;iwnbv=iwsv+q;for(i=1;i<=q;i=i+1){sum=0;for(j=1;j<=n;j=j+1){sum=sum+amat[j][i]*amat[j][i]}work[iwnbv+i]=Math.sqrt(sum)}nact=0;iter[1]=0;iter[2]=0;function fn_goto_50(){iter[1]=iter[1]+1;l=iwsv;for(i=1;i<=q;i=i+1){l=l+1;sum=-bvec[i];for(j=1;j<=n;j=j+1){sum=sum+amat[j][i]*sol[j]}if(Math.abs(sum)<vsmall){sum=0}if(i>meq){work[l]=sum}else{work[l]=-Math.abs(sum);if(sum>0){for(j=1;j<=n;j=j+1){amat[j][i]=-amat[j][i]}bvec[i]=-bvec[i]}}}for(i=1;i<=nact;i=i+1){work[iwsv+iact[i]]=0}nvl=0;temp=0;for(i=1;i<=q;i=i+1){if(work[iwsv+i]<temp*work[iwnbv+i]){nvl=i;temp=work[iwsv+i]/work[iwnbv+i]}}if(nvl===0){return 999}return 0}function fn_goto_55(){for(i=1;i<=n;i=i+1){sum=0;for(j=1;j<=n;j=j+1){sum=sum+dmat[j][i]*amat[j][nvl]}work[i]=sum}l1=iwzv;for(i=1;i<=n;i=i+1){work[l1+i]=0}for(j=nact+1;j<=n;j=j+1){for(i=1;i<=n;i=i+1){work[l1+i]=work[l1+i]+dmat[i][j]*work[j]}}t1inf=true;for(i=nact;i>=1;i=i-1){sum=work[i];l=iwrm+i*(i+3)/2;l1=l-i;for(j=i+1;j<=nact;j=j+1){sum=sum-work[l]*work[iwrv+j];l=l+j}sum=sum/work[l1];work[iwrv+i]=sum;if(iact[i]<meq){break}if(sum<0){break}t1inf=false;it1=i}if(!t1inf){t1=work[iwuv+it1]/work[iwrv+it1];for(i=1;i<=nact;i=i+1){if(iact[i]<meq){break}if(work[iwrv+i]<0){break}temp=work[iwuv+i]/work[iwrv+i];if(temp<t1){t1=temp;it1=i}}}sum=0;for(i=iwzv+1;i<=iwzv+n;i=i+1){sum=sum+work[i]*work[i]}if(Math.abs(sum)<=vsmall){if(t1inf){ierr[1]=1;return 999}else{for(i=1;i<=nact;i=i+1){work[iwuv+i]=work[iwuv+i]-t1*work[iwrv+i]}work[iwuv+nact+1]=work[iwuv+nact+1]+t1;return 700}}else{sum=0;for(i=1;i<=n;i=i+1){sum=sum+work[iwzv+i]*amat[i][nvl]}tt=-work[iwsv+nvl]/sum;t2min=true;if(!t1inf){if(t1<tt){tt=t1;t2min=false}}for(i=1;i<=n;i=i+1){sol[i]=sol[i]+tt*work[iwzv+i];if(Math.abs(sol[i])<vsmall){sol[i]=0}}crval[1]=crval[1]+tt*sum*(tt/2+work[iwuv+nact+1]);for(i=1;i<=nact;i=i+1){work[iwuv+i]=work[iwuv+i]-tt*work[iwrv+i]}work[iwuv+nact+1]=work[iwuv+nact+1]+tt;if(t2min){nact=nact+1;iact[nact]=nvl;l=iwrm+(nact-1)*nact/2+1;for(i=1;i<=nact-1;i=i+1){work[l]=work[i];l=l+1}if(nact===n){work[l]=work[n]}else{for(i=n;i>=nact+1;i=i-1){if(work[i]===0){break}gc=Math.max(Math.abs(work[i-1]),Math.abs(work[i]));gs=Math.min(Math.abs(work[i-1]),Math.abs(work[i]));if(work[i-1]>=0){temp=Math.abs(gc*Math.sqrt(1+gs*gs/(gc*gc)))}else{temp=-Math.abs(gc*Math.sqrt(1+gs*gs/(gc*gc)))}gc=work[i-1]/temp;gs=work[i]/temp;if(gc===1){break}if(gc===0){work[i-1]=gs*temp;for(j=1;j<=n;j=j+1){temp=dmat[j][i-1];dmat[j][i-1]=dmat[j][i];dmat[j][i]=temp}}else{work[i-1]=temp;nu=gs/(1+gc);for(j=1;j<=n;j=j+1){temp=gc*dmat[j][i-1]+gs*dmat[j][i];dmat[j][i]=nu*(dmat[j][i-1]+temp)-dmat[j][i];dmat[j][i-1]=temp}}}work[l]=work[nact]}}else{sum=-bvec[nvl];for(j=1;j<=n;j=j+1){sum=sum+sol[j]*amat[j][nvl]}if(nvl>meq){work[iwsv+nvl]=sum}else{work[iwsv+nvl]=-Math.abs(sum);if(sum>0){for(j=1;j<=n;j=j+1){amat[j][nvl]=-amat[j][nvl]}bvec[nvl]=-bvec[nvl]}}return 700}}return 0}function fn_goto_797(){l=iwrm+it1*(it1+1)/2+1;l1=l+it1;if(work[l1]===0){return 798}gc=Math.max(Math.abs(work[l1-1]),Math.abs(work[l1]));gs=Math.min(Math.abs(work[l1-1]),Math.abs(work[l1]));if(work[l1-1]>=0){temp=Math.abs(gc*Math.sqrt(1+gs*gs/(gc*gc)))}else{temp=-Math.abs(gc*Math.sqrt(1+gs*gs/(gc*gc)))}gc=work[l1-1]/temp;gs=work[l1]/temp;if(gc===1){return 798}if(gc===0){for(i=it1+1;i<=nact;i=i+1){temp=work[l1-1];work[l1-1]=work[l1];work[l1]=temp;l1=l1+i}for(i=1;i<=n;i=i+1){temp=dmat[i][it1];dmat[i][it1]=dmat[i][it1+1];dmat[i][it1+1]=temp}}else{nu=gs/(1+gc);for(i=it1+1;i<=nact;i=i+1){temp=gc*work[l1-1]+gs*work[l1];work[l1]=nu*(work[l1-1]+temp)-work[l1];work[l1-1]=temp;l1=l1+i}for(i=1;i<=n;i=i+1){temp=gc*dmat[i][it1]+gs*dmat[i][it1+1];dmat[i][it1+1]=nu*(dmat[i][it1]+temp)-dmat[i][it1+1];dmat[i][it1]=temp}}return 0}function fn_goto_798(){l1=l-it1;for(i=1;i<=it1;i=i+1){work[l1]=work[l];l=l+1;l1=l1+1}work[iwuv+it1]=work[iwuv+it1+1];iact[it1]=iact[it1+1];it1=it1+1;if(it1<nact){return 797}return 0}function fn_goto_799(){work[iwuv+nact]=work[iwuv+nact+1];work[iwuv+nact+1]=0;iact[nact]=0;nact=nact-1;iter[2]=iter[2]+1;return 0}go=0;while(true){go=fn_goto_50();if(go===999){return}while(true){go=fn_goto_55();if(go===0){break}if(go===999){return}if(go===700){if(it1===nact){fn_goto_799()}else{while(true){fn_goto_797();go=fn_goto_798();if(go!==797){break}}fn_goto_799()}}}}}function solveQP(Dmat,dvec,Amat,bvec,meq,factorized){Dmat=base0to1(Dmat);dvec=base0to1(dvec);Amat=base0to1(Amat);var i,n,q,nact,r,crval=[],iact=[],sol=[],work=[],iter=[],message;meq=meq||0;factorized=factorized?base0to1(factorized):[undefined,0];bvec=bvec?base0to1(bvec):[];n=Dmat.length-1;q=Amat[1].length-1;if(!bvec){for(i=1;i<=q;i=i+1){bvec[i]=0}}for(i=1;i<=q;i=i+1){iact[i]=0}nact=0;r=Math.min(n,q);for(i=1;i<=n;i=i+1){sol[i]=0}crval[1]=0;for(i=1;i<=2*n+r*(r+5)/2+2*q+1;i=i+1){work[i]=0}for(i=1;i<=2;i=i+1){iter[i]=0}qpgen2(Dmat,dvec,n,n,sol,crval,Amat,bvec,n,q,meq,iact,nact,iter,work,factorized);message="";if(factorized[1]===1){message="constraints are inconsistent, no solution!"}if(factorized[1]===2){message="matrix D in quadratic function is not positive definite!"}return{solution:base1to0(sol),value:base1to0(crval),unconstrained_solution:base1to0(dvec),iterations:base1to0(iter),iact:base1to0(iact),message:message}}exports.solveQP=solveQP})(numeric);numeric.svd=function svd(A){var temp;var prec=numeric.epsilon;var tolerance=1e-64/prec;var itmax=50;var c=0;var i=0;var j=0;var k=0;var l=0;var u=numeric.clone(A);var m=u.length;var n=u[0].length;if(m<n)throw"Need more rows than columns";var e=new Array(n);var q=new Array(n);for(i=0;i<n;i++)e[i]=q[i]=0;var v=numeric.rep([n,n],0);function pythag(a,b){a=Math.abs(a);b=Math.abs(b);if(a>b)return a*Math.sqrt(1+b*b/a/a);else if(b==0)return a;return b*Math.sqrt(1+a*a/b/b)}var f=0;var g=0;var h=0;var x=0;var y=0;var z=0;var s=0;for(i=0;i<n;i++){e[i]=g;s=0;l=i+1;for(j=i;j<m;j++)s+=u[j][i]*u[j][i];if(s<=tolerance)g=0;else{f=u[i][i];g=Math.sqrt(s);if(f>=0)g=-g;h=f*g-s;u[i][i]=f-g;for(j=l;j<n;j++){s=0;for(k=i;k<m;k++)s+=u[k][i]*u[k][j];f=s/h;for(k=i;k<m;k++)u[k][j]+=f*u[k][i]}}q[i]=g;s=0;for(j=l;j<n;j++)s=s+u[i][j]*u[i][j];if(s<=tolerance)g=0;else{f=u[i][i+1];g=Math.sqrt(s);if(f>=0)g=-g;h=f*g-s;u[i][i+1]=f-g;for(j=l;j<n;j++)e[j]=u[i][j]/h;for(j=l;j<m;j++){s=0;for(k=l;k<n;k++)s+=u[j][k]*u[i][k];for(k=l;k<n;k++)u[j][k]+=s*e[k]}}y=Math.abs(q[i])+Math.abs(e[i]);if(y>x)x=y}for(i=n-1;i!=-1;i+=-1){if(g!=0){h=g*u[i][i+1];for(j=l;j<n;j++)v[j][i]=u[i][j]/h;for(j=l;j<n;j++){s=0;for(k=l;k<n;k++)s+=u[i][k]*v[k][j];for(k=l;k<n;k++)v[k][j]+=s*v[k][i]}}for(j=l;j<n;j++){v[i][j]=0;v[j][i]=0}v[i][i]=1;g=e[i];l=i}for(i=n-1;i!=-1;i+=-1){l=i+1;g=q[i];for(j=l;j<n;j++)u[i][j]=0;if(g!=0){h=u[i][i]*g;for(j=l;j<n;j++){s=0;for(k=l;k<m;k++)s+=u[k][i]*u[k][j];f=s/h;for(k=i;k<m;k++)u[k][j]+=f*u[k][i]}for(j=i;j<m;j++)u[j][i]=u[j][i]/g}else for(j=i;j<m;j++)u[j][i]=0;u[i][i]+=1}prec=prec*x;for(k=n-1;k!=-1;k+=-1){for(var iteration=0;iteration<itmax;iteration++){var test_convergence=false;for(l=k;l!=-1;l+=-1){
if(Math.abs(e[l])<=prec){test_convergence=true;break}if(Math.abs(q[l-1])<=prec)break}if(!test_convergence){c=0;s=1;var l1=l-1;for(i=l;i<k+1;i++){f=s*e[i];e[i]=c*e[i];if(Math.abs(f)<=prec)break;g=q[i];h=pythag(f,g);q[i]=h;c=g/h;s=-f/h;for(j=0;j<m;j++){y=u[j][l1];z=u[j][i];u[j][l1]=y*c+z*s;u[j][i]=-y*s+z*c}}}z=q[k];if(l==k){if(z<0){q[k]=-z;for(j=0;j<n;j++)v[j][k]=-v[j][k]}break}if(iteration>=itmax-1)throw"Error: no convergence.";x=q[l];y=q[k-1];g=e[k-1];h=e[k];f=((y-z)*(y+z)+(g-h)*(g+h))/(2*h*y);g=pythag(f,1);if(f<0)f=((x-z)*(x+z)+h*(y/(f-g)-h))/x;else f=((x-z)*(x+z)+h*(y/(f+g)-h))/x;c=1;s=1;for(i=l+1;i<k+1;i++){g=e[i];y=q[i];h=s*g;g=c*g;z=pythag(f,h);e[i-1]=z;c=f/z;s=h/z;f=x*c+g*s;g=-x*s+g*c;h=y*s;y=y*c;for(j=0;j<n;j++){x=v[j][i-1];z=v[j][i];v[j][i-1]=x*c+z*s;v[j][i]=-x*s+z*c}z=pythag(f,h);q[i-1]=z;c=f/z;s=h/z;f=c*g+s*y;x=-s*g+c*y;for(j=0;j<m;j++){y=u[j][i-1];z=u[j][i];u[j][i-1]=y*c+z*s;u[j][i]=-y*s+z*c}}e[l]=0;e[k]=f;q[k]=x}}for(i=0;i<q.length;i++)if(q[i]<prec)q[i]=0;for(i=0;i<n;i++){for(j=i-1;j>=0;j--){if(q[j]<q[i]){c=q[j];q[j]=q[i];q[i]=c;for(k=0;k<u.length;k++){temp=u[k][i];u[k][i]=u[k][j];u[k][j]=temp}for(k=0;k<v.length;k++){temp=v[k][i];v[k][i]=v[k][j];v[k][j]=temp}i=j}}}return{U:u,S:q,V:v}}}).call(this,typeof global!=="undefined"?global:typeof self!=="undefined"?self:typeof window!=="undefined"?window:{})},{}]},{},[2])(2)});