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stla/marchingCubes.js

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Marching cubes in Javascript
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marchingCubes.js
// -----------------------------------------------------------------------------
function minorMatrix(M, m, n, row, col) {
var out = new Array(m - 1);
for (var i = 0; i < m - 1; i++) {
out[i] = new Array(n - 1);
var ii = i < row ? i : i + 1;
for (var j = 0; j < n - 1; j++) {
var jj = j < col ? j : j + 1;
out[i][j] = M[ii][jj];
}
}
return out;
}
// -----------------------------------------------------------------------------
function scaleMatrix(k, M, m, n) {
var out = new Array(m);
for (var i = 0; i < m; i++) {
out[i] = new Array(n);
for (var j = 0; j < n; j++) {
out[i][j] = k * M[i][j];
}
}
return out;
}
// -----------------------------------------------------------------------------
function scaleMinorMatrix(k, M, m, n, row, col) {
var out = new Array(m - 1);
for (var i = 0; i < m - 1; i++) {
out[i] = new Array(n - 1);
var ii = i < row ? i : i + 1;
for (var j = 0; j < n - 1; j++) {
var jj = j < col ? j : j + 1;
out[i][j] = k*M[ii][jj];
}
}
return out;
}
// -----------------------------------------------------------------------------
function matricialSum(M1, M2, m, n) {
var out = new Array(m);
for (var i = 0; i < m; i++) {
out[i] = new Array(n);
for (var j = 0; j < n; j++) {
out[i][j] = M1[i][j] + M2[i][j];
}
}
return out;
}
// -----------------------------------------------------------------------------
function levelMatrix(M, m, n, level, strict) {
var out = new Array(m);
for (var i = 0; i < m; i++) {
out[i] = new Array(n);
for (var j = 0; j < n; j++) {
out[i][j] = (strict ? (M[i][j] > level) : (M[i][j] >= level)) ? 1 : 0;
}
}
return out;
}
// -----------------------------------------------------------------------------
function toMatrix(A, m, n, k) {
var out = new Array(m);
for (var i = 0; i < m; i++) {
out[i] = new Array(n);
for (var j = 0; j < n; j++) {
out[i][j] = A[i][j][k];
}
}
return out;
}
// ----------------------------------------------------------------------------
function maxArray(A, m, n, p) {
var max = null;
for (var k = 0; k < p; k++) {
for (var i = 0; i < m; i++) {
for (var j = 0; j < n; j++) {
max = Math.max(max, A[i][j][k]);
}
}
}
return max;
}
// -----------------------------------------------------------------------------
function whichIndicesAndItems(M, m, n) {
var out = { indices: [], items: [], length: null };
var k = 0; var ij = 0;
for (var j = 0; j < n; j++) {
for (var i = 0; i < m; i++) {
if (M[i][j] > 0 && M[i][j] < 255) {
out.indices.push(ij); out.items.push(M[i][j]);
k++;
}
ij++;
}
}
out.length = k;
return out;
}
// -----------------------------------------------------------------------------
function kro1(M, nx, ny, n) {
var out = new Array(nx * n + 1);
for (var i = 0; i < nx * n; i++) {
out[i] = new Array(ny);
for (var j = 0; j < ny; j++) {
out[i][j] = M[i % nx][j];
}
}
out[nx * n] = new Array(ny);
for (var j = 0; j < ny; j++) {
out[nx * n][j] = 0;
}
return out;
}
// -----------------------------------------------------------------------------
function kro2(M, nx, ny, n) {
var out = new Array(nx * n + 1);
var replicates = new Array(nx * n);
var count = 0;
for (var i = 0; i < nx; i++) {
for (var m = 0; m < n; m++) {
replicates[count] = i;
count++;
}
}
for (var i = 0; i < nx * n; i++) {
out[i] = new Array(ny);
for (var j = 0; j < ny; j++) {
out[i][j] = M[replicates[i]][j];
}
}
out[nx * n] = new Array(ny);
for (var j = 0; j < ny; j++) {
out[nx * n][j] = 0;
}
return out;
}
// -----------------------------------------------------------------------------
function replicate(x, counts, n) {
var total = 0;
for (var i = 0; i < n; i++) {
total += counts[i];
}
var out = new Array(total);
var count = 0;
for (var i = 0; i < n; i++) {
for (var j = 0; j < counts[i]; j++) {
out[count] = x[i];
count++;
}
}
return out;
}
// ----------------------------------------------------------------------------
function repeach(x, times, n) {
var out = new Array(n * times);
var count = 0;
for (var i = 0; i < n; i++) {
for (var j = 0; j < times; j++) {
out[count] = x[i];
count++;
}
}
return out;
}
// concatenate rows of a jagged array ------------------------------------------
function unlist(jagged, jaggedsizes, rows, nrows) {
var count = 0;
for (var i = 0; i < nrows; i++) {
count += jaggedsizes[rows[i]];
}
var out = new Array(count);
count = 0;
for (var i = 0; i < nrows; i++) {
for (var j = 0; j < jaggedsizes[rows[i]]; j++) {
out[count] = jagged[rows[i]][j];
count++;
}
}
return out;
}
// R: matrix(M, ncol=ncol, byrow=TRUE) ----------------------------------------
function vector2matrix(M, lengthM, ncol) {
var nrow = lengthM / ncol;
var out = new Array(nrow);
for (var i = 0; i < nrow; i++) {
out[i] = new Array(ncol);
for (var j = 0; j < ncol; j++) {
out[i][j] = M[i * ncol + j];
}
}
return out;
}
// ----------------------------------------------------------------------------
function matrix2vectorMinusFirstColumn(M, nrow, ncol) {
var out = new Array(nrow * (ncol - 1));
for (var i = 0; i < nrow; i++) {
for (var j = 1; j < ncol; j++) {
out[i * (ncol - 1) + j - 1] = M[i][j];
}
}
return out;
}
// -----------------------------------------------------------------------------
function cbind(M, v1, v2, nrow, ncol) {
var out = new Array(nrow);
for (var i = 0; i < nrow; i++) {
out[i] = new Array(ncol + 2);
for (var j = 0; j < ncol; j++) {
out[i][j] = M[i][j];
}
out[i][ncol] = v1[i]; out[i][ncol + 1] = v2[i];
}
return out;
}
// -----------------------------------------------------------------------------
function subsetMatrix(M, rows, cols, nrows, ncols) {
var out = new Array(nrows);
for (var i = 0; i < nrows; i++) {
out[i] = new Array(ncols);
for (var j = 0; j < ncols; j++) {
out[i][j] = M[rows[i]][cols[j]];
}
}
return out;
}
// -----------------------------------------------------------------------------
function whichEqual(v, x, lv) {
var out = [];
for (var i = 0; i < lv; i++) {
if (v[i] == x) {
out.push(i);
}
}
return out;
}
// -----------------------------------------------------------------------------
function jthColumn(M, lengthM, ncol, j) {
var nrow = lengthM / ncol;
var out = new Array(nrow);
for (var i = 0; i < nrow; i++) {
out[i] = M[i * ncol + j];
}
return out;
}
// -----------------------------------------------------------------------------
function jthColumn2(M, nrow, j) {
var out = new Array(nrow);
for (var i = 0; i < nrow; i++) {
out[i] = M[i][j];
}
return out;
}
// -----------------------------------------------------------------------------
function transpose(M, nrow, ncol) {
var out = new Array(ncol);
for (var i = 0; i < ncol; i++) {
out[i] = new Array(nrow);
for (var j = 0; j < nrow; j++) {
out[i][j] = M[j][i];
}
}
return out;
}
// -----------------------------------------------------------------------------
function vectorialSum(v1, v2, l) {
var out = new Array(l);
for (var i = 0; i < l; i++) {
out[i] = v1[i] + v2[i];
}
return out;
}
// -----------------------------------------------------------------------------
var CaseRotationFlip = [
[1, 24, 1],
[2, 19, 1],
[2, 17, 1],
[3, 17, 1],
[2, 24, 1],
[4, 24, 1],
[3, 24, 1],
[6, 10, 1],
[2, 15, 1],
[3, 19, 1],
[4, 17, 1],
[6, 9, 1],
[3, 9, 1],
[6, 8, 1],
[6, 1, 1],
[9, 23, -1],
[2, 20, 1],
[3, 18, 1],
[4, 7, 1],
[6, 16, 1],
[5, 24, 1],
[7, 5, 1],
[7, 24, 1],
[12, 9, 1],
[4, 20, 1],
[6, 22, 1],
[8, 24, 1],
[10, 24, -1],
[7, 9, 1],
[15, 24, -1],
[13, 20, -1],
[6, 20, -1],
[2, 21, 1],
[4, 6, 1],
[3, 16, 1],
[6, 4, 1],
[4, 16, 1],
[8, 23, 1],
[6, 14, 1],
[10, 23, -1],
[5, 21, 1],
[7, 10, 1],
[7, 16, 1],
[15, 9, 1],
[7, 2, 1],
[13, 8, 1],
[12, 23, -1],
[6, 6, -1],
[3, 6, 1],
[6, 17, 1],
[6, 18, 1],
[9, 18, 1],
[7, 4, 1],
[13, 17, 1],
[15, 18, 1],
[6, 13, -1],
[7, 6, 1],
[12, 16, 1],
[13, 18, 1],
[6, 2, -1],
[11, 24, 1],
[7, 3, -1],
[7, 12, -1],
[3, 12, -1],
[2, 23, 1],
[5, 23, 1],
[4, 23, 1],
[7, 1, 1],
[3, 14, 1],
[7, 14, 1],
[6, 21, 1],
[15, 23, -1],
[4, 15, 1],
[7, 19, 1],
[8, 19, 1],
[13, 23, -1],
[6, 11, 1],
[12, 17, -1],
[10, 19, -1],
[6, 23, -1],
[4, 12, 1],
[7, 18, 1],
[8, 22, 1],
[13, 16, 1],
[7, 13, 1],
[11, 23, 1],
[13, 21, 1],
[7, 15, -1],
[8, 21, 1],
[13, 22, 1],
[14, 24, -1],
[8, 15, -1],
[13, 11, 1],
[7, 7, -1],
[8, 12, -1],
[4, 22, -1],
[3, 23, 1],
[7, 23, 1],
[6, 24, 1],
[12, 18, 1],
[6, 7, 1],
[13, 19, -1],
[9, 24, 1],
[6, 19, -1],
[7, 21, 1],
[11, 18, 1],
[13, 24, 1],
[7, 20, -1],
[15, 16, -1],
[7, 22, -1],
[6, 15, -1],
[3, 22, -1],
[6, 3, 1],
[15, 17, 1],
[10, 22, -1],
[6, 12, -1],
[12, 24, 1],
[7, 11, -1],
[6, 5, -1],
[3, 15, -1],
[13, 10, -1],
[7, 8, -1],
[8, 20, -1],
[4, 9, -1],
[7, 17, -1],
[5, 22, -1],
[4, 18, -1],
[2, 22, -1],
[2, 22, 1],
[4, 18, 1],
[5, 22, 1],
[7, 17, 1],
[4, 9, 1],
[8, 20, 1],
[7, 8, 1],
[13, 10, 1],
[3, 15, 1],
[6, 5, 1],
[7, 11, 1],
[12, 24, -1],
[6, 12, 1],
[10, 22, 1],
[15, 17, -1],
[6, 3, -1],
[3, 22, 1],
[6, 15, 1],
[7, 22, 1],
[15, 16, 1],
[7, 20, 1],
[13, 24, -1],
[11, 18, -1],
[7, 21, -1],
[6, 19, 1],
[9, 24, -1],
[13, 19, 1],
[6, 7, -1],
[12, 18, -1],
[6, 24, -1],
[7, 23, -1],
[3, 23, -1],
[4, 22, 1],
[8, 12, 1],
[7, 7, 1],
[13, 11, -1],
[8, 15, 1],
[14, 24, 1],
[13, 22, -1],
[8, 21, -1],
[7, 15, 1],
[13, 21, -1],
[11, 23, -1],
[7, 13, -1],
[13, 16, -1],
[8, 22, -1],
[7, 18, -1],
[4, 12, -1],
[6, 23, 1],
[10, 19, 1],
[12, 17, 1],
[6, 11, -1],
[13, 23, 1],
[8, 19, -1],
[7, 19, -1],
[4, 15, -1],
[15, 23, 1],
[6, 21, -1],
[7, 14, -1],
[3, 14, -1],
[7, 1, -1],
[4, 23, -1],
[5, 23, -1],
[2, 23, -1],
[3, 12, 1],
[7, 12, 1],
[7, 3, 1],
[11, 24, -1],
[6, 2, 1],
[13, 18, -1],
[12, 16, -1],
[7, 6, -1],
[6, 13, 1],
[15, 18, -1],
[13, 17, -1],
[7, 4, -1],
[9, 18, -1],
[6, 18, -1],
[6, 17, -1],
[3, 6, -1],
[6, 6, 1],
[12, 23, 1],
[13, 8, -1],
[7, 2, -1],
[15, 9, -1],
[7, 16, -1],
[7, 10, -1],
[5, 21, -1],
[10, 23, 1],
[6, 14, -1],
[8, 23, -1],
[4, 16, -1],
[6, 4, -1],
[3, 16, -1],
[4, 6, -1],
[2, 21, -1],
[6, 20, 1],
[13, 20, 1],
[15, 24, 1],
[7, 9, -1],
[10, 24, 1],
[8, 24, -1],
[6, 22, -1],
[4, 20, -1],
[12, 9, -1],
[7, 24, -1],
[7, 5, -1],
[5, 24, -1],
[6, 16, -1],
[4, 7, -1],
[3, 18, -1],
[2, 20, -1],
[9, 23, 1],
[6, 1, -1],
[6, 8, -1],
[3, 9, -1],
[6, 9, -1],
[4, 17, -1],
[3, 19, -1],
[2, 15, -1],
[6, 10, -1],
[3, 24, -1],
[4, 24, -1],
[2, 24, -1],
[3, 17, -1],
[2, 17, -1],
[2, 19, -1],
[1, 24, -1]
];
// -----------------------------------------------------------------------------
var indexArray = [
[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0],
[0, 0, 1],
[1, 0, 1],
[1, 1, 1],
[0, 1, 1]
];
// -----------------------------------------------------------------------------
var EdgesLengths =
[3, 3, 6, 3, 18, 6, 9, 3, 6, 18, 9, 6, 9, 9, 6, 3, 6, 18, 9, 24, 48, 48,
12, 18, 9, 177, 12, 48, 12, 96, 9, 3, 18, 6, 9, 18, 177, 9, 12, 24, 48, 48,
12, 48, 96, 12, 9, 6, 9, 9, 6, 48, 96, 12, 9, 48, 12, 96, 9, 96, 48, 48, 6,
3, 24, 18, 48, 6, 48, 9, 12, 18, 48, 177, 96, 9, 12, 12, 9, 18, 48, 177,
96, 48, 96, 96, 48, 177, 96, 816, 177, 96, 48, 177, 18, 6, 48, 9, 12, 9,
96, 6, 9, 48, 96, 96, 48, 12, 48, 9, 6, 9, 12, 12, 9, 12, 48, 9, 6, 96, 48,
177, 18, 48, 24, 18, 3, 3, 18, 24, 48, 18, 177, 48, 96, 6, 9, 48, 12, 9,
12, 12, 9, 6, 9, 48, 12, 48, 96, 96, 48, 9, 6, 96, 9, 12, 9, 48, 6, 18,
177, 48, 96, 177, 816, 96, 177, 48, 96, 96, 48, 96, 177, 48, 18, 9, 12, 12,
9, 96, 177, 48, 18, 12, 9, 48, 6, 48, 18, 24, 3, 6, 48, 48, 96, 9, 96, 12,
48, 9, 12, 96, 48, 6, 9, 9, 6, 9, 12, 96, 48, 12, 48, 48, 24, 12, 9, 177,
18, 9, 6, 18, 3, 9, 96, 12, 48, 12, 177, 9, 18, 12, 48, 48, 24, 9, 18, 6,
3, 6, 9, 9, 6, 9, 18, 6, 3, 9, 6, 18, 3, 6, 3, 3];
// -----------------------------------------------------------------------------
var EdgePoints = [
[1, 1, 2],
[2, 2, 3],
[3, 3, 4],
[4, 4, 1],
[5, 5, 6],
[6, 6, 7],
[7, 7, 8],
[8, 8, 5],
[9, 1, 5],
[10, 2, 6],
[11, 3, 7],
[12, 4, 8],
[13, 9, 9]
];
// -----------------------------------------------------------------------------
var Edges = [
[4, 9, 1],
[1, 10, 2],
[9, 10, 4, 10, 2, 4],
[2, 11, 3],
[2, 11, 3, 4, 9, 1, 2, 11, 1, 11, 9, 1, 11, 4, 9, 11, 3, 4],
[10, 11, 1, 11, 3, 1],
[4, 9, 3, 3, 9, 11, 9, 10, 11],
[12, 4, 3],
[12, 9, 3, 9, 1, 3],
[1, 10, 2, 3, 12, 4, 1, 10, 4, 10, 12, 4, 10, 3, 12, 10, 2, 3],
[3, 12, 2, 2, 12, 10, 12, 9, 10],
[4, 2, 12, 2, 11, 12],
[2, 11, 1, 1, 11, 9, 11, 12, 9],
[1, 10, 4, 4, 10, 12, 10, 11, 12],
[11, 9, 10, 11, 12, 9],
[8, 5, 9],
[5, 1, 8, 1, 4, 8],
[10, 2, 1, 9, 8, 5, 10, 2, 5, 2, 8, 5, 2, 9, 8, 2, 1, 9],
[10, 2, 5, 5, 2, 8, 2, 4, 8],
[2, 11, 3, 9, 8, 5, 2, 9, 3, 9, 8, 3, 11, 3, 8, 2, 11, 5, 2, 5, 9, 11, 8, 5],
[4, 8, 1, 8, 5, 1, 2, 11, 3, 4, 8, 3, 8, 11, 3, 8, 5, 11, 2, 11, 5, 2, 5,
1, 4, 1, 2, 4, 2, 3, 3, 2, 11, 4, 8, 3, 8, 11, 3, 8, 5, 11, 2, 11, 5, 2, 5,
1],
[10, 11, 1, 11, 3, 1, 9, 8, 5, 10, 11, 5, 11, 8, 5, 11, 3, 8, 9, 8, 3, 9,
3, 1, 10, 1, 9, 10, 9, 5, 5, 9, 8, 10, 11, 5, 11, 8, 5, 11, 3, 8, 9, 8, 3,
9, 3, 1],
[3, 4, 8, 3, 8, 10, 3, 10, 11, 8, 5, 10],
[8, 5, 9, 4, 3, 12, 8, 5, 12, 5, 3, 12, 5, 4, 3, 5, 9, 4],
[8, 5, 12, 12, 5, 3, 5, 1, 3],
[2, 1, 10, 4, 3, 12, 9, 8, 5, 2, 1, 10, 4, 5, 9, 4, 3, 5, 8, 5, 3, 8, 3,
12, 4, 3, 12, 2, 1, 9, 2, 9, 8, 2, 5, 10, 2, 8, 5, 9, 8, 5, 2, 3, 12, 2,
12, 10, 10, 12, 4, 10, 4, 1, 2, 13, 10, 10, 13, 5, 8, 5, 13, 8, 13, 12, 12,
13, 3, 4, 3, 13, 4, 13, 9, 9, 13, 1, 2, 1, 13, 2, 13, 10, 2, 13, 3, 12, 13,
3, 8, 13, 12, 8, 5, 13, 9, 5, 13, 4, 13, 9, 4, 1, 13, 10, 13, 1, 8, 5, 13,
10, 13, 5, 2, 13, 10, 2, 3, 13, 12, 13, 3, 4, 13, 12, 4, 1, 13, 9, 13, 1,
9, 8, 13, 2, 3, 12, 2, 12, 5, 2, 5, 10, 8, 5, 12, 4,
1, 9, 2, 3, 1, 4, 1, 3, 4, 3, 12, 4, 12, 8, 4, 8, 9, 9, 8, 5, 9, 5, 1, 10,
1, 5, 2, 1, 10],
[2, 5, 10, 2, 3, 8, 2, 8, 5, 8, 3, 12],
[4, 2, 12, 2, 11, 12, 8, 5, 9, 4, 2, 9, 2, 5, 9, 2, 11, 5, 8, 5, 11, 8, 11,
12, 4, 12, 8, 4, 8, 9, 9, 8, 5, 4, 2, 9, 2, 5, 9, 2, 11, 5, 8, 5, 11, 8,
11, 12],
[2, 11, 12, 2, 12, 5, 2, 5, 1, 8, 12, 5],
[8, 5, 12, 5, 10, 12, 4, 1, 9, 12, 10, 11, 8, 4, 9, 8, 12, 4, 4, 11, 12, 4,
1, 11, 5, 10, 1, 5, 1, 9, 8, 5, 9, 1, 10, 11, 8, 5, 13, 5, 9, 13, 4, 13, 9,
1, 10, 13, 4, 1, 13, 11, 13, 10, 12, 13, 11, 8, 12, 13, 1, 9, 13, 8, 13, 9,
8, 5, 13, 5, 10, 13, 11, 13, 10, 12, 11, 13, 4, 13, 12, 4, 1, 13, 8, 5, 9,
4, 1, 10, 4, 10, 12, 12, 10, 11],
[8, 5, 12, 5, 10, 12, 12, 10, 11],
[6, 10, 5],
[5, 6, 10, 1, 4, 9, 5, 6, 9, 6, 4, 9, 6, 1, 4, 6, 10, 1],
[1, 5, 2, 5, 6, 2],
[5, 6, 9, 9, 6, 4, 6, 2, 4],
[10, 5, 6, 11, 3, 2, 10, 5, 2, 5, 3, 2, 5, 11, 3, 5, 6, 11],
[6, 10, 5, 2, 11, 3, 1, 4, 9, 6, 10, 5, 2, 9, 1, 2, 11, 9, 4, 9, 11, 4, 11,
3, 2, 11, 3, 6, 10, 1, 6, 1, 4, 6, 9, 5, 6, 4, 9, 1, 4, 9, 6, 11, 3, 6, 3,
5, 5, 3, 2, 5, 2, 10, 6, 13, 5, 5, 13, 9, 4, 9, 13, 4, 13, 3, 3, 13, 11, 2,
11, 13, 2, 13, 1, 1, 13, 10, 6, 10, 13, 6, 13, 5, 6, 13, 11, 3, 13, 11, 4,
13, 3, 4, 9, 13, 1, 9, 13, 2, 13, 1, 2, 10, 13, 5, 13, 10, 4, 9, 13, 5, 13,
9, 6, 13, 5, 6, 11, 13, 3, 13, 11, 2, 13, 3, 2, 10, 13, 1, 13, 10, 1, 4,
13, 6, 11, 3, 6, 3, 9, 6, 9, 5, 4, 9, 3, 2, 10, 1,
6, 11, 10, 2, 10, 11, 2, 11, 3, 2, 3, 4, 2, 4, 1, 1, 4, 9, 1, 9, 10, 5, 10,
9, 6, 10, 5],
[11, 3, 6, 6, 3, 5, 3, 1, 5],
[6, 9, 5, 6, 11, 4, 6, 4, 9, 4, 11, 3],
[6, 10, 5, 12, 4, 3, 6, 12, 5, 12, 4, 5, 10, 5, 4, 6, 10, 3, 6, 3, 12, 10,
4, 3],
[1, 3, 9, 3, 12, 9, 5, 6, 10, 1, 3, 10, 3, 6, 10, 3, 12, 6, 5, 6, 12, 5,
12, 9, 1, 9, 5, 1, 5, 10, 10, 5, 6, 1, 3, 10, 3, 6, 10, 3, 12, 6, 5, 6, 12,
5, 12, 9],
[1, 5, 2, 5, 6, 2, 3, 12, 4, 1, 5, 4, 5, 12, 4, 5, 6, 12, 3, 12, 6, 3, 6,
2, 1, 2, 3, 1, 3, 4, 4, 3, 12, 1, 5, 4, 5, 12, 4, 5, 6, 12, 3, 12, 6, 3, 6,
2],
[3, 6, 2, 3, 9, 6, 3, 12, 9, 5, 9, 6],
[11, 12, 2, 12, 4, 2, 10, 5, 6, 11, 12, 6, 12, 5, 6, 12, 4, 5, 10, 5, 4,
10, 4, 2, 11, 2, 10, 11, 10, 6, 6, 10, 5, 11, 12, 6, 12, 5, 6, 12, 4, 5,
10, 5, 4, 10, 4, 2],
[2, 11, 1, 1, 11, 9, 6, 10, 5, 11, 12, 9, 2, 10, 6, 2, 6, 11, 6, 11, 12, 6,
12, 5, 1, 5, 9, 1, 10, 5, 2, 10, 1, 5, 12, 9, 2, 13, 1, 1, 13, 10, 6, 10,
13, 5, 13, 9, 6, 13, 5, 12, 9, 13, 11, 12, 13, 2, 13, 11, 5, 13, 10, 2, 10,
13, 2, 13, 1, 1, 13, 9, 12, 9, 13, 11, 13, 12, 6, 11, 13, 6, 13, 5, 2, 10,
1, 6, 9, 5, 6, 11, 9, 11, 12, 9],
[6, 1, 5, 6, 12, 1, 6, 11, 12, 1, 12, 4],
[5, 6, 9, 6, 11, 9, 9, 11, 12],
[8, 6, 9, 6, 10, 9],
[1, 4, 10, 10, 4, 6, 4, 8, 6],
[9, 8, 1, 1, 8, 2, 8, 6, 2],
[4, 8, 6, 4, 6, 2],
[10, 9, 6, 9, 8, 6, 11, 3, 2, 10, 9, 2, 9, 3, 2, 9, 8, 3, 11, 3, 8, 11, 8,
6, 10, 6, 11, 10, 11, 2, 2, 11, 3, 10, 9, 2, 9, 3, 2, 9, 8, 3, 11, 3, 8,
11, 8, 6],
[1, 4, 10, 10, 4, 6, 3, 2, 11, 4, 8, 6, 1, 2, 3, 1, 3, 4, 3, 4, 8, 3, 8,
11, 10, 11, 6, 10, 2, 11, 1, 2, 10, 11, 8, 6, 1, 13, 10, 10, 13, 2, 3, 2,
13, 11, 13, 6, 3, 13, 11, 8, 6, 13, 4, 8, 13, 1, 13, 4, 11, 13, 2, 1, 2,
13, 1, 13, 10, 10, 13, 6, 8, 6, 13, 4, 13, 8, 3, 4, 13, 3, 13, 11, 1, 2,
10, 3, 6, 11, 3, 4, 6, 4, 8, 6],
[9, 3, 1, 9, 6, 3, 9, 8, 6, 11, 6, 3],
[11, 3, 6, 3, 4, 6, 6, 4, 8],
[8, 6, 9, 6, 10, 9, 4, 3, 12, 8, 6, 12, 6, 3, 12, 6, 10, 3, 4, 3, 10, 4,
10, 9, 8, 9, 4, 8, 4, 12, 12, 4, 3, 8, 6, 12, 6, 3, 12, 6, 10, 3, 4, 3, 10,
4, 10, 9],
[10, 1, 3, 10, 3, 8, 10, 8, 6, 3, 12, 8],
[9, 8, 1, 1, 8, 2, 12, 4, 3, 8, 6, 2, 9, 4, 12, 9, 12, 8, 12, 8, 6, 12, 6,
3, 1, 3, 2, 1, 4, 3, 9, 4, 1, 3, 6, 2, 9, 13, 1, 1, 13, 4, 12, 4, 13, 3,
13, 2, 12, 13, 3, 6, 2, 13, 8, 6, 13, 9, 13, 8, 3, 13, 4, 9, 4, 13, 9, 13,
1, 1, 13, 2, 6, 2, 13, 8, 13, 6, 12, 8, 13, 12, 13, 3, 9, 4, 1, 12, 2, 3,
12, 8, 2, 8, 6, 2],
[3, 12, 2, 12, 8, 2, 2, 8, 6],
[2, 11, 4, 10, 9, 6, 6, 9, 8, 11, 12, 4, 2, 11, 6, 2, 6, 10, 6, 11, 12, 6,
12, 8, 4, 12, 9, 9, 12, 8, 2, 10, 9, 2, 9, 4, 2, 10, 13, 2, 13, 4, 4, 13,
12, 11, 12, 13, 6, 11, 13, 6, 13, 8, 9, 8, 13, 10, 9, 13, 4, 13, 9, 2, 13,
4, 2, 11, 13, 11, 12, 13, 8, 13, 12, 6, 13, 8, 10, 13, 6, 10, 9, 13, 2, 10,
4, 10, 9, 4, 6, 11, 12, 6, 12, 8],
[6, 11, 8, 8, 11, 12, 2, 10, 1, 6, 10, 8, 8, 10, 1, 8, 1, 12, 2, 12, 1, 2,
11, 12, 6, 2, 11, 6, 10, 2, 10, 1, 2, 6, 10, 8, 8, 10, 1, 8, 1, 12, 2, 12,
1, 2, 11, 12],
[12, 8, 11, 11, 8, 6, 9, 4, 1, 12, 4, 11, 11, 4, 1, 11, 1, 6, 9, 6, 1, 9,
8, 6, 12, 9, 8, 12, 4, 9, 4, 1, 9, 12, 4, 11, 11, 4, 1, 11, 1, 6, 9, 6, 1,
9, 8, 6],
[12, 8, 11, 11, 8, 6],
[6, 7, 11],
[6, 7, 11, 1, 4, 9, 6, 1, 11, 1, 4, 11, 7, 11, 4, 6, 7, 9, 6, 9, 1, 7, 4, 9],
[6, 7, 11, 2, 1, 10, 6, 7, 10, 7, 1, 10, 7, 2, 1, 7, 11, 2],
[2, 4, 10, 4, 9, 10, 6, 7, 11, 2, 4, 11, 4, 7, 11, 4, 9, 7, 6, 7, 9, 6, 9,
10, 2, 10, 6, 2, 6, 11, 11, 6, 7, 2, 4, 11, 4, 7, 11, 4, 9, 7, 6, 7, 9, 6,
9, 10],
[2, 6, 3, 6, 7, 3],
[2, 6, 3, 6, 7, 3, 4, 9, 1, 2, 6, 1, 6, 9, 1, 6, 7, 9, 4, 9, 7, 4, 7, 3, 2,
3, 4, 2, 4, 1, 1, 4, 9, 2, 6, 1, 6, 9, 1, 6, 7, 9, 4, 9, 7, 4, 7, 3],
[6, 7, 10, 10, 7, 1, 7, 3, 1],
[6, 7, 3, 6, 3, 9, 6, 9, 10, 4, 3, 9],
[12, 4, 3, 11, 6, 7, 12, 4, 7, 4, 6, 7, 4, 11, 6, 4, 3, 11],
[12, 9, 3, 9, 1, 3, 11, 6, 7, 12, 9, 7, 9, 6, 7, 9, 1, 6, 11, 6, 1, 11, 1,
3, 12, 3, 11, 12, 11, 7, 7, 11, 6, 12, 9, 7, 9, 6, 7, 9, 1, 6, 11, 6, 1,
11, 1, 3],
[4, 3, 12, 2, 1, 10, 11, 6, 7, 4, 3, 12, 2, 7, 11, 2, 1, 7, 6, 7, 1, 6, 1,
10, 2, 1, 10, 4, 3, 11, 4, 11, 6, 4, 7, 12, 4, 6, 7, 11, 6, 7, 4, 1, 10, 4,
10, 12, 12, 10, 2, 12, 2, 3, 4, 13, 12, 12, 13, 7, 6, 7, 13, 6, 13, 10, 10,
13, 1, 2, 1, 13, 2, 13, 11, 11, 13, 3, 4, 3, 13, 4, 13, 12, 4, 13, 1, 10,
13, 1, 6, 13, 10, 6, 7, 13, 11, 7, 13, 2, 13, 11, 2, 3, 13, 12, 13, 3, 6,
7, 13, 12, 13, 7, 4, 13, 12, 4, 1, 13, 10, 13, 1, 2, 13, 10, 2, 3, 13, 11,
13, 3, 11, 6, 13, 4, 1, 10, 4, 10, 7, 4, 7, 12, 6,
7, 10, 2, 3, 11, 4, 1, 3, 2, 3, 1, 2, 1, 10, 2, 10, 6, 2, 6, 11, 11, 6, 7,
11, 7, 3, 12, 3, 7, 4, 3, 12],
[6, 7, 10, 7, 12, 10, 2, 3, 11, 10, 12, 9, 6, 2, 11, 6, 10, 2, 2, 9, 10, 2,
3, 9, 7, 12, 3, 7, 3, 11, 6, 7, 11, 3, 12, 9, 6, 7, 13, 7, 11, 13, 2, 13,
11, 3, 12, 13, 2, 3, 13, 9, 13, 12, 10, 13, 9, 6, 10, 13, 3, 11, 13, 6, 13,
11, 6, 7, 13, 7, 12, 13, 9, 13, 12, 10, 9, 13, 2, 13, 10, 2, 3, 13, 6, 7,
11, 2, 3, 12, 2, 12, 10, 10, 12, 9],
[12, 4, 7, 7, 4, 6, 4, 2, 6],
[1, 12, 9, 1, 6, 12, 1, 2, 6, 12, 6, 7],
[4, 7, 12, 4, 1, 6, 4, 6, 7, 6, 1, 10],
[6, 7, 10, 7, 12, 10, 10, 12, 9],
[7, 11, 6, 5, 9, 8, 7, 11, 8, 11, 9, 8, 11, 5, 9, 11, 6, 5],
[5, 1, 8, 1, 4, 8, 7, 11, 6, 5, 1, 6, 1, 11, 6, 1, 4, 11, 7, 11, 4, 7, 4,
8, 5, 8, 7, 5, 7, 6, 6, 7, 11, 5, 1, 6, 1, 11, 6, 1, 4, 11, 7, 11, 4, 7, 4,
8],
[8, 5, 9, 6, 7, 11, 10, 2, 1, 8, 5, 9, 6, 1, 10, 6, 7, 1, 2, 1, 7, 2, 7,
11, 6, 7, 11, 8, 5, 10, 8, 10, 2, 8, 1, 9, 8, 2, 1, 10, 2, 1, 8, 7, 11, 8,
11, 9, 9, 11, 6, 9, 6, 5, 8, 13, 9, 9, 13, 1, 2, 1, 13, 2, 13, 11, 11, 13,
7, 6, 7, 13, 6, 13, 10, 10, 13, 5, 8, 5, 13, 8, 13, 9, 8, 13, 7, 11, 13, 7,
2, 13, 11, 2, 1, 13, 10, 1, 13, 6, 13, 10, 6, 5, 13, 9, 13, 5, 2, 1, 13, 9,
13, 1, 8, 13, 9, 8, 7, 13, 11, 13, 7, 6, 13, 11, 6, 5, 13, 10, 13, 5, 10,
2, 13, 8, 7, 11, 8, 11, 1, 8, 1, 9, 2, 1, 11, 6, 5,
10, 8, 7, 5, 6, 5, 7, 6, 7, 11, 6, 11, 2, 6, 2, 10, 10, 2, 1, 10, 1, 5, 9,
5, 1, 8, 5, 9],
[10, 2, 5, 5, 2, 8, 11, 6, 7, 2, 4, 8, 10, 6, 11, 10, 11, 2, 11, 2, 4, 11,
4, 7, 5, 7, 8, 5, 6, 7, 10, 6, 5, 7, 4, 8, 10, 13, 5, 5, 13, 6, 11, 6, 13,
7, 13, 8, 11, 13, 7, 4, 8, 13, 2, 4, 13, 10, 13, 2, 7, 13, 6, 10, 6, 13,
10, 13, 5, 5, 13, 8, 4, 8, 13, 2, 13, 4, 11, 2, 13, 11, 13, 7, 10, 6, 5,
11, 8, 7, 11, 2, 8, 2, 4, 8],
[7, 3, 6, 3, 2, 6, 5, 9, 8, 7, 3, 8, 3, 9, 8, 3, 2, 9, 5, 9, 2, 5, 2, 6, 7,
6, 5, 7, 5, 8, 8, 5, 9, 7, 3, 8, 3, 9, 8, 3, 2, 9, 5, 9, 2, 5, 2, 6],
[6, 7, 2, 5, 1, 8, 8, 1, 4, 7, 3, 2, 6, 7, 8, 6, 8, 5, 8, 7, 3, 8, 3, 4, 2,
3, 1, 1, 3, 4, 6, 5, 1, 6, 1, 2, 6, 5, 13, 6, 13, 2, 2, 13, 3, 7, 3, 13, 8,
7, 13, 8, 13, 4, 1, 4, 13, 5, 1, 13, 2, 13, 1, 6, 13, 2, 6, 7, 13, 7, 3,
13, 4, 13, 3, 8, 13, 4, 5, 13, 8, 5, 1, 13, 6, 5, 2, 5, 1, 2, 8, 7, 3, 8,
3, 4],
[6, 7, 10, 10, 7, 1, 8, 5, 9, 7, 3, 1, 6, 5, 8, 6, 8, 7, 8, 7, 3, 8, 3, 9,
10, 9, 1, 10, 5, 9, 6, 5, 10, 9, 3, 1, 6, 13, 10, 10, 13, 5, 8, 5, 13, 9,
13, 1, 8, 13, 9, 3, 1, 13, 7, 3, 13, 6, 13, 7, 9, 13, 5, 6, 5, 13, 6, 13,
10, 10, 13, 1, 3, 1, 13, 7, 13, 3, 8, 7, 13, 8, 13, 9, 6, 5, 10, 8, 1, 9,
8, 7, 1, 7, 3, 1],
[8, 7, 4, 4, 7, 3, 6, 5, 10, 8, 5, 4, 4, 5, 10, 4, 10, 3, 6, 3, 10, 6, 7,
3, 8, 6, 7, 8, 5, 6, 5, 10, 6, 8, 5, 4, 4, 5, 10, 4, 10, 3, 6, 3, 10, 6, 7,
3],
[6, 7, 11, 8, 5, 9, 12, 4, 3, 6, 7, 11, 8, 3, 12, 8, 5, 3, 4, 3, 5, 4, 5,
9, 8, 5, 9, 6, 7, 12, 6, 12, 4, 6, 3, 11, 6, 4, 3, 12, 4, 3, 6, 5, 9, 6, 9,
11, 11, 9, 8, 11, 8, 7, 6, 13, 11, 11, 13, 3, 4, 3, 13, 4, 13, 9, 9, 13, 5,
8, 5, 13, 8, 13, 12, 12, 13, 7, 6, 7, 13, 6, 13, 11, 6, 13, 5, 9, 13, 5, 4,
13, 9, 4, 3, 13, 12, 3, 13, 8, 13, 12, 8, 7, 13, 11, 13, 7, 4, 3, 13, 11,
13, 3, 6, 13, 11, 6, 5, 13, 9, 13, 5, 8, 13, 9, 8, 7, 13, 12, 13, 7, 12, 4,
13, 6, 5, 9, 6, 9, 3, 6, 3, 11, 4, 3, 9, 8, 7, 12,
6, 5, 7, 8, 7, 5, 8, 5, 9, 8, 9, 4, 8, 4, 12, 12, 4, 3, 12, 3, 7, 11, 7, 3,
6, 7, 11],
[8, 5, 12, 12, 5, 3, 6, 7, 11, 5, 1, 3, 8, 7, 6, 8, 6, 5, 6, 5, 1, 6, 1,
11, 12, 11, 3, 12, 7, 11, 8, 7, 12, 11, 1, 3, 8, 13, 12, 12, 13, 7, 6, 7,
13, 11, 13, 3, 6, 13, 11, 1, 3, 13, 5, 1, 13, 8, 13, 5, 11, 13, 7, 8, 7,
13, 8, 13, 12, 12, 13, 3, 1, 3, 13, 5, 13, 1, 6, 5, 13, 6, 13, 11, 8, 7,
12, 6, 3, 11, 6, 5, 3, 5, 1, 3],
[8, 7, 12, 10, 5, 6, 2, 3, 11, 4, 1, 9, 10, 5, 6, 8, 7, 12, 3, 11, 4, 4, 9,
11, 11, 2, 9, 9, 1, 2, 2, 3, 11, 8, 7, 12, 1, 4, 10, 10, 6, 4, 4, 9, 6, 6,
5, 9, 4, 1, 9, 2, 3, 11, 5, 10, 8, 8, 12, 10, 10, 6, 12, 12, 7, 6, 4, 1, 9,
10, 5, 6, 7, 8, 11, 11, 2, 8, 8, 12, 2, 2, 3, 12, 4, 1, 9, 8, 7, 12, 10, 2,
5, 5, 3, 2, 5, 6, 3, 3, 11, 6, 10, 5, 6, 11, 3, 2, 4, 12, 1, 1, 7, 12, 1,
9, 7, 7, 8, 9, 8, 7, 12, 13, 5, 6, 13, 9, 5, 13, 4, 9, 13, 3, 4, 13, 11, 3,
13, 2, 11, 13, 1, 2, 13, 10, 1, 13, 6, 10, 10,
5, 6, 13, 1, 9, 13, 2, 1, 13, 11, 2, 13, 7, 11, 13, 8, 7, 13, 12, 8, 13, 3,
12, 13, 4, 3, 13, 9, 4, 8, 7, 12, 13, 4, 9, 13, 3, 4, 13, 11, 3, 13, 6, 11,
13, 5, 6, 13, 10, 5, 13, 2, 10, 13, 1, 2, 13, 9, 1, 10, 5, 6, 13, 2, 11,
13, 1, 2, 13, 9, 1, 13, 8, 9, 13, 7, 8, 13, 12, 7, 13, 4, 12, 13, 3, 4, 13,
11, 3, 2, 3, 11, 13, 7, 12, 13, 6, 7, 13, 10, 6, 13, 1, 10, 13, 4, 1, 13,
9, 4, 13, 5, 9, 13, 8, 5, 13, 12, 8, 8, 7, 12, 13, 9, 4, 13, 5, 9, 13, 6,
5, 13, 11, 6, 13, 3, 11, 13, 2, 3, 13, 10, 2, 13, 1,
10, 13, 4, 1, 2, 3, 11, 13, 10, 6, 13, 1, 10, 13, 4, 1, 13, 12, 4, 13, 7,
12, 13, 8, 7, 13, 9, 8, 13, 5, 9, 13, 6, 5, 4, 1, 9, 13, 3, 2, 13, 12, 3,
13, 8, 12, 13, 5, 8, 13, 10, 5, 13, 6, 10, 13, 7, 6, 13, 11, 7, 13, 2, 11,
4, 1, 9, 13, 8, 12, 13, 5, 8, 13, 10, 5, 13, 2, 10, 13, 3, 2, 13, 11, 3,
13, 6, 11, 13, 7, 6, 13, 12, 7, 2, 3, 11, 13, 6, 10, 13, 7, 6, 13, 12, 7,
13, 4, 12, 13, 1, 4, 13, 9, 1, 13, 8, 9, 13, 5, 8, 13, 10, 5, 4, 1, 9, 13,
12, 8, 13, 3, 12, 13, 2, 3, 13, 10, 2, 13, 5, 10, 13, 6,
5, 13, 11, 6, 13, 7, 11, 13, 8, 7, 10, 5, 6, 13, 11, 2, 13, 7, 11, 13, 8,
7, 13, 9, 8, 13, 1, 9, 13, 4, 1, 13, 12, 4, 13, 3, 12, 13, 2, 3, 13, 5, 6,
13, 9, 5, 13, 8, 9, 13, 7, 8, 13, 12, 7, 13, 4, 12, 13, 3, 4, 13, 11, 3,
13, 2, 11, 13, 1, 2, 13, 10, 1, 13, 6, 10, 13, 7, 11, 13, 8, 7, 13, 12, 8,
13, 3, 12, 13, 4, 3, 13, 9, 4, 13, 1, 9, 13, 2, 1, 13, 10, 2, 13, 5, 10,
13, 6, 5, 13, 11, 6, 13, 1, 10, 13, 4, 1, 13, 9, 4, 13, 5, 9, 13, 8, 5, 13,
12, 8, 13, 7, 12, 13, 6, 7, 13, 11, 6, 13, 3, 11, 13, 2,
3, 13, 10, 2, 13, 3, 2, 13, 12, 3, 13, 4, 12, 13, 1, 4, 13, 9, 1, 13, 8, 9,
13, 5, 8, 13, 10, 5, 13, 6, 10, 13, 7, 6, 13, 11, 7, 13, 2, 11, 8, 7, 12,
10, 1, 2, 6, 5, 11, 11, 9, 5, 11, 3, 9, 9, 4, 3, 6, 5, 10, 12, 3, 4, 11, 7,
2, 2, 8, 7, 2, 1, 8, 8, 9, 1, 2, 3, 11, 9, 5, 8, 10, 1, 6, 6, 4, 1, 6, 7,
4, 4, 12, 7, 4, 1, 9, 11, 7, 6, 2, 3, 10, 10, 12, 3, 10, 5, 12, 12, 8, 5,
2, 1, 10, 12, 3, 4, 12, 11, 3, 12, 7, 11, 11, 6, 7, 7, 5, 6, 7, 8, 5, 5, 9,
8, 8, 12, 9, 9, 4, 12, 12, 3, 4, 6, 7, 11, 6, 8, 7,
6, 5, 8, 8, 9, 5, 5, 1, 9, 5, 10, 1, 1, 2, 10, 10, 6, 2, 2, 11, 6, 9, 5, 8,
2, 1, 10, 2, 4, 1, 2, 3, 4, 4, 12, 3, 3, 7, 12, 3, 11, 7, 7, 6, 11, 11, 2,
6, 6, 10, 2, 6, 7, 11, 9, 5, 8, 9, 10, 5, 9, 1, 10, 10, 2, 1, 1, 3, 2, 1,
4, 3, 4, 12, 3, 4, 9, 12, 12, 8, 9],
[12, 8, 7, 11, 2, 3, 6, 5, 10, 12, 8, 7, 11, 6, 5, 11, 5, 3, 10, 3, 5, 10,
2, 3, 11, 2, 3, 12, 6, 7, 12, 10, 6, 12, 8, 5, 12, 5, 10, 6, 5, 10, 12, 2,
3, 12, 8, 2, 8, 11, 2, 8, 7, 11, 12, 8, 13, 8, 5, 13, 10, 13, 5, 10, 2, 13,
2, 3, 13, 11, 13, 3, 11, 6, 13, 6, 7, 13, 12, 13, 7, 12, 8, 13, 12, 3, 13,
2, 3, 13, 10, 2, 13, 10, 13, 5, 6, 13, 5, 11, 6, 13, 11, 13, 7, 8, 7, 13,
10, 13, 5, 8, 5, 13, 12, 8, 13, 12, 13, 3, 2, 3, 13, 11, 2, 13, 11, 13, 7,
6, 7, 13, 6, 13, 10, 12, 2, 3, 12, 5, 2, 12, 8, 5,
10, 2, 5, 11, 6, 7, 12, 7, 3, 11, 3, 7, 11, 2, 3, 11, 10, 2, 11, 6, 10, 6,
5, 10, 6, 7, 5, 8, 5, 7, 12, 8, 7],
[12, 4, 7, 7, 4, 6, 9, 8, 5, 4, 2, 6, 12, 8, 9, 12, 9, 4, 9, 4, 2, 9, 2, 5,
7, 5, 6, 7, 8, 5, 12, 8, 7, 5, 2, 6, 12, 13, 7, 7, 13, 8, 9, 8, 13, 5, 13,
6, 9, 13, 5, 2, 6, 13, 4, 2, 13, 12, 13, 4, 5, 13, 8, 12, 8, 13, 12, 13, 7,
7, 13, 6, 2, 6, 13, 4, 13, 2, 9, 4, 13, 9, 13, 5, 12, 8, 7, 9, 6, 5, 9, 4,
6, 4, 2, 6],
[6, 5, 2, 2, 5, 1, 8, 7, 12, 6, 7, 2, 2, 7, 12, 2, 12, 1, 8, 1, 12, 8, 5,
1, 6, 8, 5, 6, 7, 8, 7, 12, 8, 6, 7, 2, 2, 7, 12, 2, 12, 1, 8, 1, 12, 8, 5,
1],
[7, 12, 8, 5, 10, 6, 9, 4, 1, 7, 12, 8, 5, 9, 4, 5, 4, 6, 1, 6, 4, 1, 10,
6, 5, 10, 6, 7, 9, 8, 7, 1, 9, 7, 12, 4, 7, 4, 1, 9, 4, 1, 7, 10, 6, 7, 12,
10, 12, 5, 10, 12, 8, 5, 7, 12, 13, 12, 4, 13, 1, 13, 4, 1, 10, 13, 10, 6,
13, 5, 13, 6, 5, 9, 13, 9, 8, 13, 7, 13, 8, 7, 12, 13, 7, 6, 13, 10, 6, 13,
1, 10, 13, 1, 13, 4, 9, 13, 4, 5, 9, 13, 5, 13, 8, 12, 8, 13, 1, 13, 4, 12,
4, 13, 7, 12, 13, 7, 13, 6, 10, 6, 13, 5, 10, 13, 5, 13, 8, 9, 8, 13, 9,
13, 1, 7, 10, 6, 7, 4, 10, 7, 12, 4, 1, 10, 4, 5,
9, 8, 7, 8, 6, 5, 6, 8, 5, 10, 6, 5, 1, 10, 5, 9, 1, 9, 4, 1, 9, 8, 4, 12,
4, 8, 7, 12, 8],
[8, 7, 12, 6, 5, 10, 8, 5, 12, 12, 5, 10, 12, 10, 6, 12, 6, 7],
[5, 7, 10, 7, 11, 10],
[5, 7, 10, 7, 11, 10, 1, 4, 9, 5, 7, 9, 7, 4, 9, 7, 11, 4, 1, 4, 11, 1, 11,
10, 5, 10, 1, 5, 1, 9, 9, 1, 4, 5, 7, 9, 7, 4, 9, 7, 11, 4, 1, 4, 11, 1,
11, 10],
[2, 1, 11, 11, 1, 7, 1, 5, 7],
[9, 5, 7, 9, 7, 2, 9, 2, 4, 7, 11, 2],
[10, 5, 2, 2, 5, 3, 5, 7, 3],
[4, 9, 3, 9, 5, 3, 2, 10, 1, 3, 5, 7, 4, 2, 1, 4, 3, 2, 2, 7, 3, 2, 10, 7,
9, 5, 10, 9, 10, 1, 4, 9, 1, 10, 5, 7, 4, 9, 13, 9, 1, 13, 2, 13, 1, 10, 5,
13, 2, 10, 13, 7, 13, 5, 3, 13, 7, 4, 3, 13, 10, 1, 13, 4, 13, 1, 4, 9, 13,
9, 5, 13, 7, 13, 5, 3, 7, 13, 2, 13, 3, 2, 10, 13, 4, 9, 1, 2, 10, 5, 2, 5,
3, 3, 5, 7],
[3, 1, 5, 3, 5, 7],
[4, 9, 3, 9, 5, 3, 3, 5, 7],
[11, 10, 7, 10, 5, 7, 12, 4, 3, 11, 10, 3, 10, 4, 3, 10, 5, 4, 12, 4, 5,
12, 5, 7, 11, 7, 12, 11, 12, 3, 3, 12, 4, 11, 10, 3, 10, 4, 3, 10, 5, 4,
12, 4, 5, 12, 5, 7],
[9, 1, 12, 5, 7, 10, 10, 7, 11, 1, 3, 12, 9, 1, 10, 9, 10, 5, 10, 1, 3, 10,
3, 11, 12, 3, 7, 7, 3, 11, 9, 5, 7, 9, 7, 12, 9, 5, 13, 9, 13, 12, 12, 13,
3, 1, 3, 13, 10, 1, 13, 10, 13, 11, 7, 11, 13, 5, 7, 13, 12, 13, 7, 9, 13,
12, 9, 1, 13, 1, 3, 13, 11, 13, 3, 10, 13, 11, 5, 13, 10, 5, 7, 13, 9, 5,
12, 5, 7, 12, 10, 1, 3, 10, 3, 11],
[2, 1, 11, 11, 1, 7, 4, 3, 12, 1, 5, 7, 2, 3, 4, 2, 4, 1, 4, 1, 5, 4, 5,
12, 11, 12, 7, 11, 3, 12, 2, 3, 11, 12, 5, 7, 2, 13, 11, 11, 13, 3, 4, 3,
13, 12, 13, 7, 4, 13, 12, 5, 7, 13, 1, 5, 13, 2, 13, 1, 12, 13, 3, 2, 3,
13, 2, 13, 11, 11, 13, 7, 5, 7, 13, 1, 13, 5, 4, 1, 13, 4, 13, 12, 2, 3,
11, 4, 7, 12, 4, 1, 7, 1, 5, 7],
[7, 12, 5, 5, 12, 9, 3, 11, 2, 7, 11, 5, 5, 11, 2, 5, 2, 9, 3, 9, 2, 3, 12,
9, 7, 3, 12, 7, 11, 3, 11, 2, 3, 7, 11, 5, 5, 11, 2, 5, 2, 9, 3, 9, 2, 3,
12, 9],
[10, 5, 7, 10, 7, 4, 10, 4, 2, 12, 7, 4],
[9, 5, 12, 12, 5, 7, 10, 1, 2, 9, 1, 12, 12, 1, 2, 12, 2, 7, 10, 7, 2, 10,
5, 7, 9, 10, 5, 9, 1, 10, 1, 2, 10, 9, 1, 12, 12, 1, 2, 12, 2, 7, 10, 7, 2,
10, 5, 7],
[12, 4, 7, 4, 1, 7, 7, 1, 5],
[9, 5, 12, 12, 5, 7],
[7, 11, 8, 8, 11, 9, 11, 10, 9],
[1, 11, 10, 1, 8, 11, 1, 4, 8, 7, 8, 11],
[8, 1, 9, 8, 7, 2, 8, 2, 1, 2, 7, 11],
[7, 11, 8, 11, 2, 8, 8, 2, 4],
[2, 10, 9, 2, 9, 7, 2, 7, 3, 9, 8, 7],
[3, 4, 7, 7, 4, 8, 1, 2, 10, 3, 2, 7, 7, 2, 10, 7, 10, 8, 1, 8, 10, 1, 4,
8, 3, 1, 4, 3, 2, 1, 2, 10, 1, 3, 2, 7, 7, 2, 10, 7, 10, 8, 1, 8, 10, 1, 4,
8],
[9, 8, 1, 8, 7, 1, 1, 7, 3],
[8, 7, 4, 4, 7, 3],
[4, 3, 9, 3, 11, 9, 8, 7, 12, 9, 11, 10, 4, 8, 12, 4, 9, 8, 8, 10, 9, 8, 7,
10, 3, 11, 7, 3, 7, 12, 4, 3, 12, 7, 11, 10, 4, 3, 13, 3, 12, 13, 8, 13,
12, 7, 11, 13, 8, 7, 13, 10, 13, 11, 9, 13, 10, 4, 9, 13, 7, 12, 13, 4, 13,
12, 4, 3, 13, 3, 11, 13, 10, 13, 11, 9, 10, 13, 8, 13, 9, 8, 7, 13, 4, 3,
12, 8, 7, 11, 8, 11, 9, 9, 11, 10],
[3, 11, 1, 1, 11, 10, 7, 12, 8, 3, 12, 1, 1, 12, 8, 1, 8, 10, 7, 10, 8, 7,
11, 10, 3, 7, 11, 3, 12, 7, 12, 8, 7, 3, 12, 1, 1, 12, 8, 1, 8, 10, 7, 10,
8, 7, 11, 10],
[8, 7, 12, 4, 1, 9, 3, 11, 2, 8, 7, 12, 4, 3, 11, 4, 11, 9, 2, 9, 11, 2, 1,
9, 4, 1, 9, 8, 3, 12, 8, 2, 3, 8, 7, 11, 8, 11, 2, 3, 11, 2, 8, 1, 9, 8, 7,
1, 7, 4, 1, 7, 12, 4, 8, 7, 13, 7, 11, 13, 2, 13, 11, 2, 1, 13, 1, 9, 13,
4, 13, 9, 4, 3, 13, 3, 12, 13, 8, 13, 12, 8, 7, 13, 8, 9, 13, 1, 9, 13, 2,
1, 13, 2, 13, 11, 3, 13, 11, 4, 3, 13, 4, 13, 12, 7, 12, 13, 2, 13, 11, 7,
11, 13, 8, 7, 13, 8, 13, 9, 1, 9, 13, 4, 1, 13, 4, 13, 12, 3, 12, 13, 3,
13, 2, 8, 1, 9, 8, 11, 1, 8, 7, 11, 2, 1, 11, 4, 3,
12, 8, 12, 9, 4, 9, 12, 4, 1, 9, 4, 2, 1, 4, 3, 2, 3, 11, 2, 3, 12, 11, 7,
11, 12, 8, 7, 12],
[3, 11, 2, 7, 12, 8, 3, 12, 2, 2, 12, 8, 2, 8, 7, 2, 7, 11],
[9, 4, 10, 10, 4, 2, 12, 8, 7, 9, 8, 10, 10, 8, 7, 10, 7, 2, 12, 2, 7, 12,
4, 2, 9, 12, 4, 9, 8, 12, 8, 7, 12, 9, 8, 10, 10, 8, 7, 10, 7, 2, 12, 2, 7,
12, 4, 2],
[8, 7, 12, 10, 1, 2, 8, 7, 10, 10, 7, 2, 12, 2, 7, 8, 1, 12, 8, 10, 1, 12,
1, 2],
[9, 4, 1, 12, 8, 7, 9, 8, 1, 1, 8, 7, 1, 7, 12, 1, 12, 4],
[8, 7, 12],
[8, 12, 7],
[9, 1, 4, 12, 7, 8, 9, 1, 8, 1, 7, 8, 1, 12, 7, 1, 4, 12],
[8, 12, 7, 10, 2, 1, 8, 10, 7, 10, 2, 7, 12, 7, 2, 8, 12, 1, 8, 1, 10, 12,
2, 1],
[9, 10, 4, 10, 2, 4, 12, 7, 8, 9, 10, 8, 10, 7, 8, 10, 2, 7, 12, 7, 2, 12,
2, 4, 9, 4, 12, 9, 12, 8, 8, 12, 7, 9, 10, 8, 10, 7, 8, 10, 2, 7, 12, 7, 2,
12, 2, 4],
[3, 2, 11, 7, 8, 12, 3, 2, 12, 2, 8, 12, 2, 7, 8, 2, 11, 7],
[8, 12, 7, 4, 9, 1, 3, 2, 11, 8, 12, 7, 4, 11, 3, 4, 9, 11, 2, 11, 9, 2, 9,
1, 4, 9, 1, 8, 12, 3, 8, 3, 2, 8, 11, 7, 8, 2, 11, 3, 2, 11, 8, 9, 1, 8, 1,
7, 7, 1, 4, 7, 4, 12, 8, 13, 7, 7, 13, 11, 2, 11, 13, 2, 13, 1, 1, 13, 9,
4, 9, 13, 4, 13, 3, 3, 13, 12, 8, 12, 13, 8, 13, 7, 8, 13, 9, 1, 13, 9, 2,
13, 1, 2, 11, 13, 3, 11, 13, 4, 13, 3, 4, 12, 13, 7, 13, 12, 2, 11, 13, 7,
13, 11, 8, 13, 7, 8, 9, 13, 1, 13, 9, 4, 13, 1, 4, 12, 13, 3, 13, 12, 3, 2,
13, 8, 9, 1, 8, 1, 11, 8, 11, 7, 2, 11, 1, 4, 12,
3, 8, 9, 12, 4, 12, 9, 4, 9, 1, 4, 1, 2, 4, 2, 3, 3, 2, 11, 3, 11, 12, 7,
12, 11, 8, 12, 7],
[3, 1, 11, 1, 10, 11, 7, 8, 12, 3, 1, 12, 1, 8, 12, 1, 10, 8, 7, 8, 10, 7,
10, 11, 3, 11, 7, 3, 7, 12, 12, 7, 8, 3, 1, 12, 1, 8, 12, 1, 10, 8, 7, 8,
10, 7, 10, 11],
[4, 9, 3, 3, 9, 11, 8, 12, 7, 9, 10, 11, 4, 12, 8, 4, 8, 9, 8, 9, 10, 8,
10, 7, 3, 7, 11, 3, 12, 7, 4, 12, 3, 7, 10, 11, 4, 13, 3, 3, 13, 12, 8, 12,
13, 7, 13, 11, 8, 13, 7, 10, 11, 13, 9, 10, 13, 4, 13, 9, 7, 13, 12, 4, 12,
13, 4, 13, 3, 3, 13, 11, 10, 11, 13, 9, 13, 10, 8, 9, 13, 8, 13, 7, 4, 12,
3, 8, 11, 7, 8, 9, 11, 9, 10, 11],
[8, 4, 7, 4, 3, 7],
[9, 1, 8, 8, 1, 7, 1, 3, 7],
[3, 7, 4, 7, 8, 4, 1, 10, 2, 3, 7, 2, 7, 10, 2, 7, 8, 10, 1, 10, 8, 1, 8,
4, 3, 4, 1, 3, 1, 2, 2, 1, 10, 3, 7, 2, 7, 10, 2, 7, 8, 10, 1, 10, 8, 1, 8,
4],
[2, 9, 10, 2, 7, 9, 2, 3, 7, 9, 7, 8],
[7, 8, 11, 11, 8, 2, 8, 4, 2],
[8, 9, 1, 8, 2, 7, 8, 1, 2, 2, 11, 7],
[1, 10, 11, 1, 11, 8, 1, 8, 4, 7, 11, 8],
[7, 8, 11, 8, 9, 11, 11, 9, 10],
[9, 12, 5, 12, 7, 5],
[12, 7, 4, 4, 7, 1, 7, 5, 1],
[9, 12, 5, 12, 7, 5, 10, 2, 1, 9, 12, 1, 12, 2, 1, 12, 7, 2, 10, 2, 7, 10,
7, 5, 9, 5, 10, 9, 10, 1, 1, 10, 2, 9, 12, 1, 12, 2, 1, 12, 7, 2, 10, 2, 7,
10, 7, 5],
[10, 7, 5, 10, 4, 7, 10, 2, 4, 12, 4, 7],
[7, 5, 12, 5, 9, 12, 3, 2, 11, 7, 5, 11, 5, 2, 11, 5, 9, 2, 3, 2, 9, 3, 9,
12, 7, 12, 3, 7, 3, 11, 11, 3, 2, 7, 5, 11, 5, 2, 11, 5, 9, 2, 3, 2, 9, 3,
9, 12],
[2, 11, 1, 11, 7, 1, 4, 12, 3, 1, 7, 5, 2, 4, 3, 2, 1, 4, 4, 5, 1, 4, 12,
5, 11, 7, 12, 11, 12, 3, 2, 11, 3, 12, 7, 5, 2, 11, 13, 11, 3, 13, 4, 13,
3, 12, 7, 13, 4, 12, 13, 5, 13, 7, 1, 13, 5, 2, 1, 13, 12, 3, 13, 2, 13, 3,
2, 11, 13, 11, 7, 13, 5, 13, 7, 1, 5, 13, 4, 13, 1, 4, 12, 13, 2, 11, 3, 4,
12, 7, 4, 7, 1, 1, 7, 5],
[9, 12, 1, 5, 10, 7, 10, 11, 7, 1, 12, 3, 9, 10, 1, 9, 5, 10, 10, 3, 1, 10,
11, 3, 12, 7, 3, 7, 11, 3, 9, 7, 5, 9, 12, 7, 9, 13, 5, 9, 12, 13, 12, 3,
13, 1, 13, 3, 10, 13, 1, 10, 11, 13, 7, 13, 11, 5, 13, 7, 12, 7, 13, 9, 12,
13, 9, 13, 1, 1, 13, 3, 11, 3, 13, 10, 11, 13, 5, 10, 13, 5, 13, 7, 9, 12,
5, 5, 12, 7, 10, 3, 1, 10, 11, 3],
[11, 7, 10, 10, 7, 5, 12, 3, 4, 11, 3, 10, 10, 3, 4, 10, 4, 5, 12, 5, 4,
12, 7, 5, 11, 12, 7, 11, 3, 12, 3, 4, 12, 11, 3, 10, 10, 3, 4, 10, 4, 5,
12, 5, 4, 12, 7, 5],
[4, 3, 9, 9, 3, 5, 3, 7, 5],
[3, 5, 1, 3, 7, 5],
[4, 3, 9, 9, 3, 5, 2, 1, 10, 3, 7, 5, 4, 1, 2, 4, 2, 3, 2, 3, 7, 2, 7, 10,
9, 10, 5, 9, 1, 10, 4, 1, 9, 10, 7, 5, 4, 13, 9, 9, 13, 1, 2, 1, 13, 10,
13, 5, 2, 13, 10, 7, 5, 13, 3, 7, 13, 4, 13, 3, 10, 13, 1, 4, 1, 13, 4, 13,
9, 9, 13, 5, 7, 5, 13, 3, 13, 7, 2, 3, 13, 2, 13, 10, 4, 1, 9, 2, 5, 10, 2,
3, 5, 3, 7, 5],
[10, 2, 5, 2, 3, 5, 5, 3, 7],
[9, 7, 5, 9, 2, 7, 9, 4, 2, 7, 2, 11],
[2, 11, 1, 11, 7, 1, 1, 7, 5],
[5, 10, 7, 7, 10, 11, 1, 9, 4, 5, 9, 7, 7, 9, 4, 7, 4, 11, 1, 11, 4, 1, 10,
11, 5, 1, 10, 5, 9, 1, 9, 4, 1, 5, 9, 7, 7, 9, 4, 7, 4, 11, 1, 11, 4, 1,
10, 11],
[5, 10, 7, 7, 10, 11],
[8, 12, 7, 6, 10, 5, 8, 12, 5, 12, 10, 5, 12, 6, 10, 12, 7, 6],
[7, 8, 12, 5, 6, 10, 9, 1, 4, 7, 8, 12, 5, 4, 9, 5, 6, 4, 1, 4, 6, 1, 6,
10, 5, 6, 10, 7, 8, 9, 7, 9, 1, 7, 4, 12, 7, 1, 4, 9, 1, 4, 7, 6, 10, 7,
10, 12, 12, 10, 5, 12, 5, 8, 7, 13, 12, 12, 13, 4, 1, 4, 13, 1, 13, 10, 10,
13, 6, 5, 6, 13, 5, 13, 9, 9, 13, 8, 7, 8, 13, 7, 13, 12, 7, 13, 6, 10, 13,
6, 1, 13, 10, 1, 4, 13, 9, 4, 13, 5, 13, 9, 5, 8, 13, 12, 13, 8, 1, 4, 13,
12, 13, 4, 7, 13, 12, 7, 6, 13, 10, 13, 6, 5, 13, 10, 5, 8, 13, 9, 13, 8,
9, 1, 13, 7, 6, 10, 7, 10, 4, 7, 4, 12, 1, 4, 10, 5,
8, 9, 7, 6, 8, 5, 8, 6, 5, 6, 10, 5, 10, 1, 5, 1, 9, 9, 1, 4, 9, 4, 8, 12,
8, 4, 7, 8, 12],
[6, 2, 5, 2, 1, 5, 8, 12, 7, 6, 2, 7, 2, 12, 7, 2, 1, 12, 8, 12, 1, 8, 1,
5, 6, 5, 8, 6, 8, 7, 7, 8, 12, 6, 2, 7, 2, 12, 7, 2, 1, 12, 8, 12, 1, 8, 1,
5],
[12, 7, 4, 7, 6, 4, 9, 5, 8, 4, 6, 2, 12, 9, 8, 12, 4, 9, 9, 2, 4, 9, 5, 2,
7, 6, 5, 7, 5, 8, 12, 7, 8, 5, 6, 2, 12, 7, 13, 7, 8, 13, 9, 13, 8, 5, 6,
13, 9, 5, 13, 2, 13, 6, 4, 13, 2, 12, 4, 13, 5, 8, 13, 12, 13, 8, 12, 7,
13, 7, 6, 13, 2, 13, 6, 4, 2, 13, 9, 13, 4, 9, 5, 13, 12, 7, 8, 9, 5, 6, 9,
6, 4, 4, 6, 2],
[12, 7, 8, 11, 3, 2, 6, 10, 5, 12, 7, 8, 11, 5, 6, 11, 3, 5, 10, 5, 3, 10,
3, 2, 11, 3, 2, 12, 7, 6, 12, 6, 10, 12, 5, 8, 12, 10, 5, 6, 10, 5, 12, 3,
2, 12, 2, 8, 8, 2, 11, 8, 11, 7, 12, 13, 8, 8, 13, 5, 10, 5, 13, 10, 13, 2,
2, 13, 3, 11, 3, 13, 11, 13, 6, 6, 13, 7, 12, 7, 13, 12, 13, 8, 12, 13, 3,
2, 13, 3, 10, 13, 2, 10, 5, 13, 6, 5, 13, 11, 13, 6, 11, 7, 13, 8, 13, 7,
10, 5, 13, 8, 13, 5, 12, 13, 8, 12, 3, 13, 2, 13, 3, 11, 13, 2, 11, 7, 13,
6, 13, 7, 6, 10, 13, 12, 3, 2, 12, 2, 5, 12, 5, 8,
10, 5, 2, 11, 7, 6, 12, 3, 7, 11, 7, 3, 11, 3, 2, 11, 2, 10, 11, 10, 6, 6,
10, 5, 6, 5, 7, 8, 7, 5, 12, 7, 8],
[8, 12, 7, 10, 6, 5, 2, 11, 3, 4, 9, 1, 10, 6, 5, 8, 12, 7, 3, 4, 11, 4,
11, 9, 11, 9, 2, 9, 2, 1, 2, 11, 3, 8, 12, 7, 1, 10, 4, 10, 4, 6, 4, 6, 9,
6, 9, 5, 4, 9, 1, 2, 11, 3, 5, 8, 10, 8, 10, 12, 10, 12, 6, 12, 6, 7, 4, 9,
1, 10, 6, 5, 7, 11, 8, 11, 8, 2, 8, 2, 12, 2, 12, 3, 4, 9, 1, 8, 12, 7, 10,
5, 2, 5, 2, 3, 5, 3, 6, 3, 6, 11, 10, 6, 5, 11, 2, 3, 4, 1, 12, 1, 12, 7,
1, 7, 9, 7, 9, 8, 8, 12, 7, 13, 6, 5, 13, 5, 9, 13, 9, 4, 13, 4, 3, 13, 3,
11, 13, 11, 2, 13, 2, 1, 13, 1, 10, 13, 10, 6, 10,
6, 5, 13, 9, 1, 13, 1, 2, 13, 2, 11, 13, 11, 7, 13, 7, 8, 13, 8, 12, 13,
12, 3, 13, 3, 4, 13, 4, 9, 8, 12, 7, 13, 9, 4, 13, 4, 3, 13, 3, 11, 13, 11,
6, 13, 6, 5, 13, 5, 10, 13, 10, 2, 13, 2, 1, 13, 1, 9, 10, 6, 5, 13, 11, 2,
13, 2, 1, 13, 1, 9, 13, 9, 8, 13, 8, 7, 13, 7, 12, 13, 12, 4, 13, 4, 3, 13,
3, 11, 2, 11, 3, 13, 12, 7, 13, 7, 6, 13, 6, 10, 13, 10, 1, 13, 1, 4, 13,
4, 9, 13, 9, 5, 13, 5, 8, 13, 8, 12, 8, 12, 7, 13, 4, 9, 13, 9, 5, 13, 5,
6, 13, 6, 11, 13, 11, 3, 13, 3, 2, 13, 2, 10, 13, 10,
1, 13, 1, 4, 2, 11, 3, 13, 6, 10, 13, 10, 1, 13, 1, 4, 13, 4, 12, 13, 12,
7, 13, 7, 8, 13, 8, 9, 13, 9, 5, 13, 5, 6, 4, 9, 1, 13, 2, 3, 13, 3, 12,
13, 12, 8, 13, 8, 5, 13, 5, 10, 13, 10, 6, 13, 6, 7, 13, 7, 11, 13, 11, 2,
4, 9, 1, 13, 12, 8, 13, 8, 5, 13, 5, 10, 13, 10, 2, 13, 2, 3, 13, 3, 11,
13, 11, 6, 13, 6, 7, 13, 7, 12, 2, 11, 3, 13, 10, 6, 13, 6, 7, 13, 7, 12,
13, 12, 4, 13, 4, 1, 13, 1, 9, 13, 9, 8, 13, 8, 5, 13, 5, 10, 4, 9, 1, 13,
8, 12, 13, 12, 3, 13, 3, 2, 13, 2, 10, 13, 10, 5, 13, 5,
6, 13, 6, 11, 13, 11, 7, 13, 7, 8, 10, 6, 5, 13, 2, 11, 13, 11, 7, 13, 7,
8, 13, 8, 9, 13, 9, 1, 13, 1, 4, 13, 4, 12, 13, 12, 3, 13, 3, 2, 13, 6, 5,
13, 5, 9, 13, 9, 8, 13, 8, 7, 13, 7, 12, 13, 12, 4, 13, 4, 3, 13, 3, 11,
13, 11, 2, 13, 2, 1, 13, 1, 10, 13, 10, 6, 13, 11, 7, 13, 7, 8, 13, 8, 12,
13, 12, 3, 13, 3, 4, 13, 4, 9, 13, 9, 1, 13, 1, 2, 13, 2, 10, 13, 10, 5,
13, 5, 6, 13, 6, 11, 13, 10, 1, 13, 1, 4, 13, 4, 9, 13, 9, 5, 13, 5, 8, 13,
8, 12, 13, 12, 7, 13, 7, 6, 13, 6, 11, 13, 11, 3, 13, 3,
2, 13, 2, 10, 13, 2, 3, 13, 3, 12, 13, 12, 4, 13, 4, 1, 13, 1, 9, 13, 9, 8,
13, 8, 5, 13, 5, 10, 13, 10, 6, 13, 6, 7, 13, 7, 11, 13, 11, 2, 8, 12, 7,
10, 2, 1, 6, 11, 5, 11, 5, 9, 11, 9, 3, 9, 3, 4, 6, 10, 5, 12, 4, 3, 11, 2,
7, 2, 7, 8, 2, 8, 1, 8, 1, 9, 2, 11, 3, 9, 8, 5, 10, 6, 1, 6, 1, 4, 6, 4,
7, 4, 7, 12, 4, 9, 1, 11, 6, 7, 2, 10, 3, 10, 3, 12, 10, 12, 5, 12, 5, 8,
2, 10, 1, 12, 4, 3, 12, 3, 11, 12, 11, 7, 11, 7, 6, 7, 6, 5, 7, 5, 8, 5, 8,
9, 8, 9, 12, 9, 12, 4, 12, 4, 3, 6, 11, 7, 6, 7, 8,
6, 8, 5, 8, 5, 9, 5, 9, 1, 5, 1, 10, 1, 10, 2, 10, 2, 6, 2, 6, 11, 9, 8, 5,
2, 10, 1, 2, 1, 4, 2, 4, 3, 4, 3, 12, 3, 12, 7, 3, 7, 11, 7, 11, 6, 11, 6,
2, 6, 2, 10, 6, 11, 7, 9, 8, 5, 9, 5, 10, 9, 10, 1, 10, 1, 2, 1, 2, 3, 1,
3, 4, 4, 3, 12, 4, 12, 9, 12, 9, 8],
[8, 12, 5, 12, 3, 5, 6, 11, 7, 5, 3, 1, 8, 6, 7, 8, 5, 6, 6, 1, 5, 6, 11,
1, 12, 3, 11, 12, 11, 7, 8, 12, 7, 11, 3, 1, 8, 12, 13, 12, 7, 13, 6, 13,
7, 11, 3, 13, 6, 11, 13, 1, 13, 3, 5, 13, 1, 8, 5, 13, 11, 7, 13, 8, 13, 7,
8, 12, 13, 12, 3, 13, 1, 13, 3, 5, 1, 13, 6, 13, 5, 6, 11, 13, 8, 12, 7, 6,
11, 3, 6, 3, 5, 5, 3, 1],
[6, 11, 7, 8, 9, 5, 12, 3, 4, 6, 11, 7, 8, 12, 3, 8, 3, 5, 4, 5, 3, 4, 9,
5, 8, 9, 5, 6, 12, 7, 6, 4, 12, 6, 11, 3, 6, 3, 4, 12, 3, 4, 6, 9, 5, 6,
11, 9, 11, 8, 9, 11, 7, 8, 6, 11, 13, 11, 3, 13, 4, 13, 3, 4, 9, 13, 9, 5,
13, 8, 13, 5, 8, 12, 13, 12, 7, 13, 6, 13, 7, 6, 11, 13, 6, 5, 13, 9, 5,
13, 4, 9, 13, 4, 13, 3, 12, 13, 3, 8, 12, 13, 8, 13, 7, 11, 7, 13, 4, 13,
3, 11, 3, 13, 6, 11, 13, 6, 13, 5, 9, 5, 13, 8, 9, 13, 8, 13, 7, 12, 7, 13,
12, 13, 4, 6, 9, 5, 6, 3, 9, 6, 11, 3, 4, 9, 3, 8, 12,
7, 6, 7, 5, 8, 5, 7, 8, 9, 5, 8, 4, 9, 8, 12, 4, 12, 3, 4, 12, 7, 3, 11, 3,
7, 6, 11, 7],
[8, 4, 7, 4, 3, 7, 6, 10, 5, 8, 4, 5, 4, 10, 5, 4, 3, 10, 6, 10, 3, 6, 3,
7, 8, 7, 6, 8, 6, 5, 5, 6, 10, 8, 4, 5, 4, 10, 5, 4, 3, 10, 6, 10, 3, 6, 3,
7],
[6, 10, 7, 10, 1, 7, 8, 9, 5, 7, 1, 3, 6, 8, 5, 6, 7, 8, 8, 3, 7, 8, 9, 3,
10, 1, 9, 10, 9, 5, 6, 10, 5, 9, 1, 3, 6, 10, 13, 10, 5, 13, 8, 13, 5, 9,
1, 13, 8, 9, 13, 3, 13, 1, 7, 13, 3, 6, 7, 13, 9, 5, 13, 6, 13, 5, 6, 10,
13, 10, 1, 13, 3, 13, 1, 7, 3, 13, 8, 13, 7, 8, 9, 13, 6, 10, 5, 8, 9, 1,
8, 1, 7, 7, 1, 3],
[6, 2, 7, 5, 8, 1, 8, 4, 1, 7, 2, 3, 6, 8, 7, 6, 5, 8, 8, 3, 7, 8, 4, 3, 2,
1, 3, 1, 4, 3, 6, 1, 5, 6, 2, 1, 6, 13, 5, 6, 2, 13, 2, 3, 13, 7, 13, 3, 8,
13, 7, 8, 4, 13, 1, 13, 4, 5, 13, 1, 2, 1, 13, 6, 2, 13, 6, 13, 7, 7, 13,
3, 4, 3, 13, 8, 4, 13, 5, 8, 13, 5, 13, 1, 6, 2, 5, 5, 2, 1, 8, 3, 7, 8, 4,
3],
[7, 6, 3, 3, 6, 2, 5, 8, 9, 7, 8, 3, 3, 8, 9, 3, 9, 2, 5, 2, 9, 5, 6, 2, 7,
5, 6, 7, 8, 5, 8, 9, 5, 7, 8, 3, 3, 8, 9, 3, 9, 2, 5, 2, 9, 5, 6, 2],
[10, 5, 2, 5, 8, 2, 11, 7, 6, 2, 8, 4, 10, 11, 6, 10, 2, 11, 11, 4, 2, 11,
7, 4, 5, 8, 7, 5, 7, 6, 10, 5, 6, 7, 8, 4, 10, 5, 13, 5, 6, 13, 11, 13, 6,
7, 8, 13, 11, 7, 13, 4, 13, 8, 2, 13, 4, 10, 2, 13, 7, 6, 13, 10, 13, 6,
10, 5, 13, 5, 8, 13, 4, 13, 8, 2, 4, 13, 11, 13, 2, 11, 7, 13, 10, 5, 6,
11, 7, 8, 11, 8, 2, 2, 8, 4],
[8, 9, 5, 6, 11, 7, 10, 1, 2, 8, 9, 5, 6, 10, 1, 6, 1, 7, 2, 7, 1, 2, 11,
7, 6, 11, 7, 8, 10, 5, 8, 2, 10, 8, 9, 1, 8, 1, 2, 10, 1, 2, 8, 11, 7, 8,
9, 11, 9, 6, 11, 9, 5, 6, 8, 9, 13, 9, 1, 13, 2, 13, 1, 2, 11, 13, 11, 7,
13, 6, 13, 7, 6, 10, 13, 10, 5, 13, 8, 13, 5, 8, 9, 13, 8, 7, 13, 11, 7,
13, 2, 11, 13, 2, 13, 1, 10, 13, 1, 6, 10, 13, 6, 13, 5, 9, 5, 13, 2, 13,
1, 9, 1, 13, 8, 9, 13, 8, 13, 7, 11, 7, 13, 6, 11, 13, 6, 13, 5, 10, 5, 13,
10, 13, 2, 8, 11, 7, 8, 1, 11, 8, 9, 1, 2, 11, 1, 6, 10,
5, 8, 5, 7, 6, 7, 5, 6, 11, 7, 6, 2, 11, 6, 10, 2, 10, 1, 2, 10, 5, 1, 9,
1, 5, 8, 9, 5],
[5, 8, 1, 1, 8, 4, 7, 6, 11, 5, 6, 1, 1, 6, 11, 1, 11, 4, 7, 4, 11, 7, 8,
4, 5, 7, 8, 5, 6, 7, 6, 11, 7, 5, 6, 1, 1, 6, 11, 1, 11, 4, 7, 4, 11, 7, 8,
4],
[7, 6, 11, 5, 8, 9, 7, 8, 11, 11, 8, 9, 11, 9, 5, 11, 5, 6],
[6, 10, 7, 7, 10, 12, 10, 9, 12],
[4, 12, 7, 4, 6, 1, 4, 7, 6, 6, 10, 1],
[1, 9, 12, 1, 12, 6, 1, 6, 2, 12, 7, 6],
[12, 7, 4, 7, 6, 4, 4, 6, 2],
[6, 10, 7, 7, 10, 12, 2, 11, 3, 10, 9, 12, 6, 11, 2, 6, 2, 10, 2, 10, 9, 2,
9, 3, 7, 3, 12, 7, 11, 3, 6, 11, 7, 3, 9, 12, 6, 13, 7, 7, 13, 11, 2, 11,
13, 3, 13, 12, 2, 13, 3, 9, 12, 13, 10, 9, 13, 6, 13, 10, 3, 13, 11, 6, 11,
13, 6, 13, 7, 7, 13, 12, 9, 12, 13, 10, 13, 9, 2, 10, 13, 2, 13, 3, 6, 11,
7, 2, 12, 3, 2, 10, 12, 10, 9, 12],
[4, 12, 3, 2, 10, 1, 11, 7, 6, 4, 12, 3, 2, 11, 7, 2, 7, 1, 6, 1, 7, 6, 10,
1, 2, 10, 1, 4, 11, 3, 4, 6, 11, 4, 12, 7, 4, 7, 6, 11, 7, 6, 4, 10, 1, 4,
12, 10, 12, 2, 10, 12, 3, 2, 4, 12, 13, 12, 7, 13, 6, 13, 7, 6, 10, 13, 10,
1, 13, 2, 13, 1, 2, 11, 13, 11, 3, 13, 4, 13, 3, 4, 12, 13, 4, 1, 13, 10,
1, 13, 6, 10, 13, 6, 13, 7, 11, 13, 7, 2, 11, 13, 2, 13, 3, 12, 3, 13, 6,
13, 7, 12, 7, 13, 4, 12, 13, 4, 13, 1, 10, 1, 13, 2, 10, 13, 2, 13, 3, 11,
3, 13, 11, 13, 6, 4, 10, 1, 4, 7, 10, 4, 12, 7, 6,
10, 7, 2, 11, 3, 4, 3, 1, 2, 1, 3, 2, 10, 1, 2, 6, 10, 2, 11, 6, 11, 7, 6,
11, 3, 7, 12, 7, 3, 4, 12, 3],
[12, 3, 9, 9, 3, 1, 11, 7, 6, 12, 7, 9, 9, 7, 6, 9, 6, 1, 11, 1, 6, 11, 3,
1, 12, 11, 3, 12, 7, 11, 7, 6, 11, 12, 7, 9, 9, 7, 6, 9, 6, 1, 11, 1, 6,
11, 3, 1],
[12, 3, 4, 11, 7, 6, 12, 7, 4, 4, 7, 6, 4, 6, 11, 4, 11, 3],
[6, 3, 7, 6, 9, 3, 6, 10, 9, 4, 9, 3],
[6, 10, 7, 10, 1, 7, 7, 1, 3],
[2, 3, 6, 6, 3, 7, 4, 1, 9, 2, 1, 6, 6, 1, 9, 6, 9, 7, 4, 7, 9, 4, 3, 7, 2,
4, 3, 2, 1, 4, 1, 9, 4, 2, 1, 6, 6, 1, 9, 6, 9, 7, 4, 7, 9, 4, 3, 7],
[2, 3, 6, 6, 3, 7],
[2, 10, 4, 4, 10, 9, 6, 11, 7, 2, 11, 4, 4, 11, 7, 4, 7, 9, 6, 9, 7, 6, 10,
9, 2, 6, 10, 2, 11, 6, 11, 7, 6, 2, 11, 4, 4, 11, 7, 4, 7, 9, 6, 9, 7, 6,
10, 9],
[6, 11, 7, 2, 10, 1, 6, 10, 7, 7, 10, 1, 7, 1, 2, 7, 2, 11],
[6, 11, 7, 1, 9, 4, 6, 11, 1, 1, 11, 4, 7, 4, 11, 6, 9, 7, 6, 1, 9, 7, 9, 4],
[6, 11, 7],
[12, 11, 8, 11, 6, 8],
[12, 11, 8, 11, 6, 8, 9, 1, 4, 12, 11, 4, 11, 1, 4, 11, 6, 1, 9, 1, 6, 9,
6, 8, 12, 8, 9, 12, 9, 4, 4, 9, 1, 12, 11, 4, 11, 1, 4, 11, 6, 1, 9, 1, 6,
9, 6, 8],
[6, 8, 11, 8, 12, 11, 2, 1, 10, 6, 8, 10, 8, 1, 10, 8, 12, 1, 2, 1, 12, 2,
12, 11, 6, 11, 2, 6, 2, 10, 10, 2, 1, 6, 8, 10, 8, 1, 10, 8, 12, 1, 2, 1,
12, 2, 12, 11],
[2, 4, 11, 10, 6, 9, 6, 8, 9, 11, 4, 12, 2, 6, 11, 2, 10, 6, 6, 12, 11, 6,
8, 12, 4, 9, 12, 9, 8, 12, 2, 9, 10, 2, 4, 9, 2, 13, 10, 2, 4, 13, 4, 12,
13, 11, 13, 12, 6, 13, 11, 6, 8, 13, 9, 13, 8, 10, 13, 9, 4, 9, 13, 2, 4,
13, 2, 13, 11, 11, 13, 12, 8, 12, 13, 6, 8, 13, 10, 6, 13, 10, 13, 9, 2, 4,
10, 10, 4, 9, 6, 12, 11, 6, 8, 12],
[3, 2, 12, 12, 2, 8, 2, 6, 8],
[9, 1, 8, 1, 2, 8, 12, 3, 4, 8, 2, 6, 9, 12, 4, 9, 8, 12, 12, 6, 8, 12, 3,
6, 1, 2, 3, 1, 3, 4, 9, 1, 4, 3, 2, 6, 9, 1, 13, 1, 4, 13, 12, 13, 4, 3, 2,
13, 12, 3, 13, 6, 13, 2, 8, 13, 6, 9, 8, 13, 3, 4, 13, 9, 13, 4, 9, 1, 13,
1, 2, 13, 6, 13, 2, 8, 6, 13, 12, 13, 8, 12, 3, 13, 9, 1, 4, 12, 3, 2, 12,
2, 8, 8, 2, 6],
[10, 3, 1, 10, 8, 3, 10, 6, 8, 3, 8, 12],
[8, 9, 6, 6, 9, 10, 4, 12, 3, 8, 12, 6, 6, 12, 3, 6, 3, 10, 4, 10, 3, 4, 9,
10, 8, 4, 9, 8, 12, 4, 12, 3, 4, 8, 12, 6, 6, 12, 3, 6, 3, 10, 4, 10, 3, 4,
9, 10],
[11, 6, 3, 3, 6, 4, 6, 8, 4],
[9, 1, 3, 9, 3, 6, 9, 6, 8, 11, 3, 6],
[1, 10, 4, 10, 6, 4, 3, 11, 2, 4, 6, 8, 1, 3, 2, 1, 4, 3, 3, 8, 4, 3, 11,
8, 10, 6, 11, 10, 11, 2, 1, 10, 2, 11, 6, 8, 1, 10, 13, 10, 2, 13, 3, 13,
2, 11, 6, 13, 3, 11, 13, 8, 13, 6, 4, 13, 8, 1, 4, 13, 11, 2, 13, 1, 13, 2,
1, 10, 13, 10, 6, 13, 8, 13, 6, 4, 8, 13, 3, 13, 4, 3, 11, 13, 1, 10, 2, 3,
11, 6, 3, 6, 4, 4, 6, 8],
[10, 6, 9, 9, 6, 8, 11, 2, 3, 10, 2, 9, 9, 2, 3, 9, 3, 8, 11, 8, 3, 11, 6,
8, 10, 11, 6, 10, 2, 11, 2, 3, 11, 10, 2, 9, 9, 2, 3, 9, 3, 8, 11, 8, 3,
11, 6, 8],
[4, 6, 8, 4, 2, 6],
[9, 1, 8, 1, 2, 8, 8, 2, 6],
[1, 10, 4, 10, 6, 4, 4, 6, 8],
[8, 9, 6, 6, 9, 10],
[5, 9, 6, 6, 9, 11, 9, 12, 11],
[6, 5, 1, 6, 1, 12, 6, 12, 11, 1, 4, 12],
[2, 1, 11, 1, 9, 11, 6, 5, 10, 11, 9, 12, 2, 6, 10, 2, 11, 6, 6, 12, 11, 6,
5, 12, 1, 9, 5, 1, 5, 10, 2, 1, 10, 5, 9, 12, 2, 1, 13, 1, 10, 13, 6, 13,
10, 5, 9, 13, 6, 5, 13, 12, 13, 9, 11, 13, 12, 2, 11, 13, 5, 10, 13, 2, 13,
10, 2, 1, 13, 1, 9, 13, 12, 13, 9, 11, 12, 13, 6, 13, 11, 6, 5, 13, 2, 1,
10, 6, 5, 9, 6, 9, 11, 11, 9, 12],
[11, 2, 12, 12, 2, 4, 10, 6, 5, 11, 6, 12, 12, 6, 5, 12, 5, 4, 10, 4, 5,
10, 2, 4, 11, 10, 2, 11, 6, 10, 6, 5, 10, 11, 6, 12, 12, 6, 5, 12, 5, 4,
10, 4, 5, 10, 2, 4],
[3, 2, 6, 3, 6, 9, 3, 9, 12, 5, 6, 9],
[1, 2, 5, 5, 2, 6, 3, 4, 12, 1, 4, 5, 5, 4, 12, 5, 12, 6, 3, 6, 12, 3, 2,
6, 1, 3, 2, 1, 4, 3, 4, 12, 3, 1, 4, 5, 5, 4, 12, 5, 12, 6, 3, 6, 12, 3, 2,
6],
[1, 9, 3, 3, 9, 12, 5, 10, 6, 1, 10, 3, 3, 10, 6, 3, 6, 12, 5, 12, 6, 5, 9,
12, 1, 5, 9, 1, 10, 5, 10, 6, 5, 1, 10, 3, 3, 10, 6, 3, 6, 12, 5, 12, 6, 5,
9, 12],
[6, 5, 10, 12, 3, 4, 6, 5, 12, 12, 5, 4, 10, 4, 5, 6, 3, 10, 6, 12, 3, 10,
3, 4],
[6, 5, 9, 6, 4, 11, 6, 9, 4, 4, 3, 11],
[11, 6, 3, 6, 5, 3, 3, 5, 1],
[6, 5, 10, 2, 3, 11, 1, 9, 4, 6, 5, 10, 2, 1, 9, 2, 9, 11, 4, 11, 9, 4, 3,
11, 2, 3, 11, 6, 1, 10, 6, 4, 1, 6, 5, 9, 6, 9, 4, 1, 9, 4, 6, 3, 11, 6, 5,
3, 5, 2, 3, 5, 10, 2, 6, 5, 13, 5, 9, 13, 4, 13, 9, 4, 3, 13, 3, 11, 13, 2,
13, 11, 2, 1, 13, 1, 10, 13, 6, 13, 10, 6, 5, 13, 6, 11, 13, 3, 11, 13, 4,
3, 13, 4, 13, 9, 1, 13, 9, 2, 1, 13, 2, 13, 10, 5, 10, 13, 4, 13, 9, 5, 9,
13, 6, 5, 13, 6, 13, 11, 3, 11, 13, 2, 3, 13, 2, 13, 10, 1, 10, 13, 1, 13,
4, 6, 3, 11, 6, 9, 3, 6, 5, 9, 4, 3, 9, 2, 1, 10,
6, 10, 11, 2, 11, 10, 2, 3, 11, 2, 4, 3, 2, 1, 4, 1, 9, 4, 1, 10, 9, 5, 9,
10, 6, 5, 10],
[10, 6, 5, 11, 2, 3, 10, 2, 5, 5, 2, 3, 5, 3, 11, 5, 11, 6],
[5, 9, 6, 9, 4, 6, 6, 4, 2],
[1, 2, 5, 5, 2, 6],
[5, 10, 6, 1, 9, 4, 5, 9, 6, 6, 9, 4, 6, 4, 1, 6, 1, 10],
[6, 5, 10],
[8, 12, 5, 5, 12, 10, 12, 11, 10],
[8, 12, 5, 5, 12, 10, 4, 9, 1, 12, 11, 10, 8, 9, 4, 8, 4, 12, 4, 12, 11, 4,
11, 1, 5, 1, 10, 5, 9, 1, 8, 9, 5, 1, 11, 10, 8, 13, 5, 5, 13, 9, 4, 9, 13,
1, 13, 10, 4, 13, 1, 11, 10, 13, 12, 11, 13, 8, 13, 12, 1, 13, 9, 8, 9, 13,
8, 13, 5, 5, 13, 10, 11, 10, 13, 12, 13, 11, 4, 12, 13, 4, 13, 1, 8, 9, 5,
4, 10, 1, 4, 12, 10, 12, 11, 10],
[2, 12, 11, 2, 5, 12, 2, 1, 5, 8, 5, 12],
[4, 12, 2, 2, 12, 11, 8, 9, 5, 4, 9, 2, 2, 9, 5, 2, 5, 11, 8, 11, 5, 8, 12,
11, 4, 8, 12, 4, 9, 8, 9, 5, 8, 4, 9, 2, 2, 9, 5, 2, 5, 11, 8, 11, 5, 8,
12, 11],
[2, 10, 5, 2, 8, 3, 2, 5, 8, 8, 12, 3],
[2, 10, 1, 4, 12, 3, 9, 5, 8, 2, 10, 1, 4, 9, 5, 4, 5, 3, 8, 3, 5, 8, 12,
3, 4, 12, 3, 2, 9, 1, 2, 8, 9, 2, 10, 5, 2, 5, 8, 9, 5, 8, 2, 12, 3, 2, 10,
12, 10, 4, 12, 10, 1, 4, 2, 10, 13, 10, 5, 13, 8, 13, 5, 8, 12, 13, 12, 3,
13, 4, 13, 3, 4, 9, 13, 9, 1, 13, 2, 13, 1, 2, 10, 13, 2, 3, 13, 12, 3, 13,
8, 12, 13, 8, 13, 5, 9, 13, 5, 4, 9, 13, 4, 13, 1, 10, 1, 13, 8, 13, 5, 10,
5, 13, 2, 10, 13, 2, 13, 3, 12, 3, 13, 4, 12, 13, 4, 13, 1, 9, 1, 13, 9,
13, 8, 2, 12, 3, 2, 5, 12, 2, 10, 5, 8, 12, 5, 4,
9, 1, 2, 1, 3, 4, 3, 1, 4, 12, 3, 4, 8, 12, 4, 9, 8, 9, 5, 8, 9, 1, 5, 10,
5, 1, 2, 10, 1],
[8, 12, 5, 12, 3, 5, 5, 3, 1],
[8, 9, 5, 4, 12, 3, 8, 12, 5, 5, 12, 3, 5, 3, 4, 5, 4, 9],
[3, 8, 4, 3, 10, 8, 3, 11, 10, 8, 10, 5],
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1, 3, 10, 9, 1, 10, 5, 9, 5, 8, 9, 10, 5, 11, 11, 5, 8, 11, 8, 3, 9, 3, 8,
9, 1, 3],
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5, 4, 2, 1, 4, 3, 2, 3, 11, 2, 4, 3, 8, 8, 3, 11, 8, 11, 5, 2, 5, 11, 2, 1,
5],
[2, 3, 11, 9, 5, 8, 2, 3, 9, 9, 3, 8, 11, 8, 3, 2, 5, 11, 2, 9, 5, 11, 5, 8],
[10, 5, 2, 5, 8, 2, 2, 8, 4],
[10, 1, 2, 9, 5, 8, 10, 5, 2, 2, 5, 8, 2, 8, 9, 2, 9, 1],
[5, 8, 1, 1, 8, 4],
[8, 9, 5],
[11, 10, 9, 11, 9, 12],
[1, 4, 10, 4, 12, 10, 10, 12, 11],
[2, 1, 11, 1, 9, 11, 11, 9, 12],
[4, 12, 2, 2, 12, 11],
[3, 2, 12, 2, 10, 12, 12, 10, 9],
[1, 2, 10, 3, 4, 12, 1, 4, 10, 10, 4, 12, 10, 12, 3, 10, 3, 2],
[12, 3, 9, 9, 3, 1],
[12, 3, 4],
[4, 3, 9, 3, 11, 9, 9, 11, 10],
[10, 1, 11, 11, 1, 3],
[2, 3, 11, 4, 1, 9, 2, 1, 11, 11, 1, 9, 11, 9, 4, 11, 4, 3],
[2, 3, 11],
[9, 4, 10, 10, 4, 2],
[1, 2, 10],
[4, 1, 9]
];
// -----------------------------------------------------------------------------
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1, 2, 3, 3, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 4, 2, 3, 4, 7, 3, 4,
2, 3, 3, 2, 3, 4, 2, 1, 1, 1, 1, 1, 3, 4, 2, 1, 1, 1, 2, 1, 2,
1, 1, 1, 1, 2, 2, 3, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1,
3, 2, 1, 2, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 4, 1,
1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1];
// -----------------------------------------------------------------------------
var FacePoints = [
[1, 1, 6, 2, 5, 60],
[2, 2, 7, 3, 6, 252],
[3, 4, 7, 3, 8, 672],
[4, 1, 8, 4, 5, 160],
[5, 1, 3, 2, 4, 24],
[6, 5, 7, 6, 8, 1680]
];
// -----------------------------------------------------------------------------
var special_name = [3, 4, 6, 7, 10, 12, 13];
var special_nface = [1, 1, 2, 4, 3, 3, 7];
var special_nedge = [18, 24, 48, 177, 96, 96, 816];
var special_indSizes = [2, 2, 4, 16, 8, 8, 31];
// -----------------------------------------------------------------------------
var special_ind = [
[0, 1],
[0, 1],
[0, 2, 1, 3],
[0, 8, 4, 12, 2, 10, 1, 9, 6, 14, 5, 13, 3, 11, 15, 7],
[0, 4, 1, 5, 2, 6, 3, 7],
[0, 4, 2, 6, 1, 5, 3, 7],
[0, 1, 2, 4, 8, 16, 32, 3, 9, 17, 33, 6, 18, 34, 12, 20, 36, 24, 40, 35, 25,
22, 44, 19, 41, 38, 28, 83, 105, 102, 92]
];
// -----------------------------------------------------------------------------
var special_pos = [
[
[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
],
[
[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
],
[
[1, 2, 3, 4, 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,
28, 29, 30, 31, 32, 33],
[34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
[34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48]
],
[
[1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24],
[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24],
[25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
[25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
[40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54],
[40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54],
[55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 78, 79, 80, 81],
[55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 78, 79, 80, 81],
[82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,
100, 101, 102, 103, 104, 105, 106, 107, 108],
[82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,
100, 101, 102, 103, 104, 105, 106, 107, 108],
[109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,
124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135],
[109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,
124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135],
[136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150],
[151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165,
166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177]
],
[
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36],
[37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54,
55, 56, 57, 58, 59, 60],
[37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54,
55, 56, 57, 58, 59, 60],
[61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 81, 82, 83, 84],
[61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 81, 82, 83, 84],
[85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96],
[85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96]
],
[
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36],
[37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54,
55, 56, 57, 58, 59, 60],
[37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54,
55, 56, 57, 58, 59, 60],
[61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 81, 82, 83, 84],
[61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 81, 82, 83, 84],
[85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96],
[85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96]
],
[
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],
[31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
[49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66],
[67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84],
[85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102],
[103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117,
118, 119, 120],
[121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135,
136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150],
[151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165,
166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180],
[181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195,
196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210],
[211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225,
226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240],
[241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255,
256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270],
[271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285,
286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300],
[301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315,
316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330],
[331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345,
346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360],
[361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375,
376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390],
[391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405,
406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420],
[421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435,
436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450],
[451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465,
466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480],
[481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495,
496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510,
511, 512, 513, 514, 515, 516],
[517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531,
532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546,
547, 548, 549, 550, 551, 552],
[553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567,
568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582,
583, 584, 585, 586, 587, 588],
[589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603,
604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618,
619, 620, 621, 622, 623, 624],
[625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639,
640, 641, 642],
[643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657,
658, 659, 660],
[661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675,
676, 677, 678],
[679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693,
694, 695, 696],
[697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711,
712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726],
[727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741,
742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756],
[757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771,
772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786],
[787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801,
802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816]
]
];
// -----------------------------------------------------------------------------
var special_posSize = [
[6, 12],
[6, 18],
[9, 24, 15, 15],
[9, 9, 15, 15, 15, 15, 15, 15, 27, 27, 27, 27, 27, 27, 15, 27],
[12, 24, 24, 24, 24, 24, 12, 12],
[12, 24, 24, 24, 24, 24, 12, 12],
[12, 18, 18, 18, 18, 18, 18, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
36, 36, 36, 36, 18, 18, 18, 18, 30, 30, 30, 30]
];
// -----------------------------------------------------------------------------
function FacesNo7(faces, p1, values, l, j) {
var index = new Array(l);
for (var i = 0; i < l; i++) {
var f = Math.abs(faces[i]) - 1;
var e1 = FacePoints[f][1];
var e2 = FacePoints[f][2];
var e3 = FacePoints[f][3];
var e4 = FacePoints[f][4];
var p = p1[i] - 2;
var A = values[p + e1];
var B = values[p + e2];
var C = values[p + e3];
var D = values[p + e4];
var temp = faces[i] > 0 ? 1 : -1;
temp *= (A * B - C * D > 0 ? 1 : -1);
index[i] = temp == 1 ? 2 ** (j - 1) : 0;
}
return index;
}
// -----------------------------------------------------------------------------
function Faces7(faces, p1, values, l, j) {
var index = new Array(l);
for (var i = 0; i < l; i++) {
var p = p1[i] - 1;
var A0 = values[p];
var B0 = values[p + 3];
var C0 = values[p + 2];
var D0 = values[p + 1];
var A1 = values[p + 4];
var B1 = values[p + 7];
var C1 = values[p + 6];
var D1 = values[p + 5];
var a = (A1 - A0) * (C1 - C0) - (B1 - B0) * (D1 - D0);
var b = C0 * (A1 - A0) + A0 * (C1 - C0) - D0 * (B1 - B0) - B0 * (D1 - D0);
var c = A0 * C0 - B0 * D0;
var tmax = -b / (2 * a);
var maximum = a * tmax * tmax + b * tmax + c;
maximum = isNaN(maximum) ? -1 : maximum;
var cond1 = a < 0 ? 1 : 0;
var cond2 = tmax > 0 ? 1 : 0;
var cond3 = tmax < 1 ? 1 : 0;
var cond4 = maximum > 0 ? 1 : 0;
var totalcond = cond1 * cond2 * cond3 * cond4;
var temp = faces[i] > 0 ? 1 : -1;
temp *= (totalcond == 1 ? 1 : -1);
index[i] = temp == 1 ? 2 ** (j - 1) : 0;
}
return index;
}
// -----------------------------------------------------------------------------
function Voxel(f, xmin, xmax, ymin, ymax, zmin, zmax, nx, ny, nz) {
var out = new Array(nx);
for (var i = 0; i < nx; i++) {
out[i] = new Array(ny);
for (var j = 0; j < ny; j++) {
out[i][j] = new Array(nz);
for (var k = 0; k < nz; k++) {
out[i][j][k] =
f(xmin + (xmax - xmin) * i / (nx - 1),
ymin + (ymax - ymin) * j / (ny - 1),
zmin + (zmax - zmin) * k / (nz - 1));
}
}
}
return out;
}
// -----------------------------------------------------------------------------
function faceType(M, m, n, level, max) {
var L = levelMatrix(M, m, n, level, level < max);
var minorMat = minorMatrix(L, m, n, m - 1, n - 1);
var sminorMat2 = scaleMinorMatrix(2, L, m, n, 0, n - 1);
var sminorMat4 = scaleMinorMatrix(4, L, m, n, 0, 0);
var sminorMat8 = scaleMinorMatrix(8, L, m, n, m - 1, 0);
var sum1 = matricialSum(minorMat, sminorMat2, m - 1, n - 1);
var sum2 = matricialSum(sminorMat4, sminorMat8, m - 1, n - 1);
var out = matricialSum(sum1, sum2, m - 1, n - 1);
return out;
}
// -----------------------------------------------------------------------------
function levCells(A, nx, ny, nz, level, max) {
var cells = new Array(nz - 1);
var types = new Array(nz - 1);
var bottomTypes = faceType(toMatrix(A, nx, ny, 0), nx, ny, level, max);
var totallength = 0;
var lengths = new Array(nz - 1);
for (var k = 0; k < nz - 1; k++) {
var topTypes = faceType(toMatrix(A, nx, ny, k + 1), nx, ny, level, max);
var cellTypes =
matricialSum(bottomTypes,
scaleMatrix(16, topTypes, nx - 1, ny - 1), nx - 1, ny - 1);
var goodcells01 = whichIndicesAndItems(cellTypes, nx - 1, ny - 1);
cells[k] = new Array(goodcells01.length)
types[k] = new Array(goodcells01.length)
for (var l = 0; l < goodcells01.length; l++) {
cells[k][l] = goodcells01.indices[l] + (nx - 1) * (ny - 1) * k + 1;
types[k][l] = goodcells01.items[l];
}
bottomTypes = topTypes;
lengths[k] = goodcells01.length;
totallength += goodcells01.length;
}
var out = new Array(4);
out[0] = new Array(totallength); out[1] = new Array(totallength);
out[2] = new Array(totallength); out[3] = new Array(totallength);
var count = 0;
for (var k = 0; k < nz - 1; k++) {
for (var l = 0; l < lengths[k]; l++) {
var c = cells[k][l] - 1;
out[0][count] = c % (nx - 1) + 1;
out[1][count] = Math.floor(c / (nx - 1)) % (ny - 1) + 1;
out[2][count] = Math.floor(c / ((nx - 1) * (ny - 1))) + 1;
out[3][count] = types[k][l];
count++;
}
}
return { out: out, outnrow: totallength };
}
// -----------------------------------------------------------------------------
function GetBasic1(R, nR, vivjvk) {
var indexPtr = new Array(8);
for (var i = 0; i < 8; i++) {
indexPtr[i] = new Array(3);
for (var j = 0; j < 3; j++) {
indexPtr[i][j] = indexArray[i][j];
}
}
var cube1 = new Array(nR);
for (var i = 0; i < nR; i++) {
cube1[i] = new Array(3);
var vivjvkRi = vivjvk[R[i]];
for (var j = 0; j < 3; j++) {
cube1[i][j] = vivjvkRi[j];
}
}
var k1 = kro1(indexPtr, 8, 3, nR);
var k2 = kro2(cube1, nR, 3, 8);
var cubeco = matricialSum(k1, k2, 8 * nR + 1, 3);
return cubeco;
}
// -----------------------------------------------------------------------------
function GetBasic2(A, level, cubeco, nR) {
var values = new Array(8 * nR + 1);
for (var i = 0; i < 8 * nR; i++) {
values[i] = A[cubeco[i][0] - 1][cubeco[i][1] - 1][cubeco[i][2] - 1] - level;
}
values[8 * nR] = 0;
return values;
}
// -----------------------------------------------------------------------------
function get_tcase(types, nrow) {
var CRF =
[1, 2, 2, 3, 2, 4, 3, 6, 2, 3, 4, 6, 3, 6, 6, 9, 2, 3, 4, 6,
5, 7, 7, 12, 4, 6, 8, 10, 7, 15, 13, 6, 2, 4, 3, 6, 4, 8, 6,
10, 5, 7, 7, 15, 7, 13, 12, 6, 3, 6, 6, 9, 7, 13, 15, 6, 7, 12,
13, 6, 11, 7, 7, 3, 2, 5, 4, 7, 3, 7, 6, 15, 4, 7, 8, 13, 6,
12, 10, 6, 4, 7, 8, 13, 7, 11, 13, 7, 8, 13, 14, 8, 13, 7, 8,
4, 3, 7, 6, 12, 6, 13, 9, 6, 7, 11, 13, 7, 15, 7, 6, 3, 6, 15,
10, 6, 12, 7, 6, 3, 13, 7, 8, 4, 7, 5, 4, 2, 2, 4, 5, 7, 4, 8,
7, 13, 3, 6, 7, 12, 6, 10, 15, 6, 3, 6, 7, 15, 7, 13, 11, 7,
6, 9, 13, 6, 12, 6, 7, 3, 4, 8, 7, 13, 8, 14, 13, 8, 7, 13, 11,
7, 13, 8, 7, 4, 6, 10, 12, 6, 13, 8, 7, 4, 15, 6, 7, 3, 7, 4,
5, 2, 3, 7, 7, 11, 6, 13, 12, 7, 6, 15, 13, 7, 9, 6, 6, 3, 6,
12, 13, 7, 15, 7, 7, 5, 10, 6, 8, 4, 6, 3, 4, 2, 6, 13, 15, 7,
10, 8, 6, 4, 12, 7, 7, 5, 6, 4, 3, 2, 9, 6, 6, 3, 6, 4, 3, 2,
6, 3, 4, 2, 3, 2, 2, 1];
out = new Array(nrow);
for (var i = 0; i < nrow; i++) {
out[i] = CRF[types[i]] - 1;
}
return out;
}
// -----------------------------------------------------------------------------
function getR(tcase, nrow) {
out = [];
for (var i = 0; i < nrow; i++) {
var c = tcase[i];
if (c == 1 || c == 2 || c == 5 || c == 8 || c == 9 || c == 11 || c == 14) {
out.push(i);
}
}
return out;
}
// -----------------------------------------------------------------------------
function LambdaMu(x1, n) {
var lambdamu = new Array(2);
lambdamu[0] = new Array(n); lambdamu[1] = new Array(n);
for (var i = 0; i < n; i++) {
lambdamu[0][i] = Math.floor(x1[i] / 9);
lambdamu[1][i] = 1 - lambdamu[0][i];
}
return lambdamu;
}
function average(lambdamu, w1, w2, n) {
var lambda = lambdamu[0]; var mu = lambdamu[1];
var out = new Array(n);
for (var i = 0; i < n; i++) {
out[i] = mu[i] * w1[i] + lambda[i] * w2[i];
}
return out;
}
function average7(lambdamu, w, n) {
var lambda = lambdamu[0]; var mu = lambdamu[1];
var out = new Array(n);
for (var i = 0; i < n; i++) {
out[i] = mu[i] * w[i] + lambda[i];
}
return out;
}
function average8(lambdamu, w, n) {
var lambda = lambdamu[0]; var mu = lambdamu[1];
var out = new Array(n);
for (var i = 0; i < n; i++) {
out[i] = mu[i] * w[i] - lambda[i];
}
return out;
}
// -----------------------------------------------------------------------------
function GetPoints(cubeco, values, p1, x1, x2, n) {
var p1x1 = new Array(n); var p1x2 = new Array(n);
for (var i = 0; i < n; i++) {
p1x1[i] = p1[i] + x1[i]; p1x2[i] = p1[i] + x2[i];
}
var lambdamu = LambdaMu(x1, n);
var v1 = new Array(n); var v2 = new Array(n); var v3 = new Array(n);
var v4 = new Array(n); var v5 = new Array(n); var v6 = new Array(n);
var v7 = new Array(n); var v8 = new Array(n);
var w1 = new Array(n); var w2 = new Array(n); var w3 = new Array(n);
var w4 = new Array(n); var w5 = new Array(n); var w6 = new Array(n);
for (var i = 0; i < n; i++) {
v1[i] = cubeco[p1x1[i] - 2][0];
w1[i] = cubeco[p1[i] - 1][0];
v2[i] = cubeco[p1x2[i] - 2][0];
w2[i] = cubeco[p1[i]][0];
v3[i] = cubeco[p1x1[i] - 2][1];
w3[i] = cubeco[p1[i]][1];
v4[i] = cubeco[p1x2[i] - 2][1];
w4[i] = cubeco[p1[i] + 1][1];
v5[i] = cubeco[p1x1[i] - 2][2];
w5[i] = cubeco[p1[i]][2];
v6[i] = cubeco[p1x2[i] - 2][2];
w6[i] = cubeco[p1[i] + 4][2];
v7[i] = values[p1x1[i] - 2];
v8[i] = values[p1x2[i] - 2];
}
var out = new Array(8);
out[0] = average(lambdamu, v1, w1, n);
out[1] = average(lambdamu, v2, w2, n);
out[2] = average(lambdamu, v3, w3, n);
out[3] = average(lambdamu, v4, w4, n);
out[4] = average(lambdamu, v5, w5, n);
out[5] = average(lambdamu, v6, w6, n);
out[6] = average7(lambdamu, v7, n);
out[7] = average8(lambdamu, v8, n);
return (out);
}
// -----------------------------------------------------------------------------
function CalPoints(points, n) {
var x1 = points[0]; var x2 = points[1];
var y1 = points[2]; var y2 = points[3];
var z1 = points[4]; var z2 = points[5];
var v1 = points[6]; var v2 = points[7];
var x = new Array(n); var y = new Array(n); var z = new Array(n);
for (var i = 0; i < n; i++) {
var s = v1[i] / (v1[i] - v2[i]);
x[i] = x1[i] + s * (x2[i] - x1[i]);
y[i] = y1[i] + s * (y2[i] - y1[i]);
z[i] = z1[i] + s * (z2[i] - z1[i]);
}
var out = new Array(3);
out[0] = x; out[1] = y; out[2] = z;
return transpose(out, 3, n);
}
// -----------------------------------------------------------------------------
function computeContour3d(voxel, nx, ny, nz, max, level) {
var obj_ijkt = levCells(voxel, nx, ny, nz, level, max);
var ijkt = obj_ijkt.out;
var nrow = obj_ijkt.outnrow;
tcase = get_tcase(ijkt[3], nrow);
var R = getR(tcase, nrow);
var nR = R.length;
if (nR == 0) {
return [];
} else {
var vivjvk = new Array(nrow);
for (var i = 0; i < nrow; i++) {
vivjvk[i] = new Array(3);
for (var j = 0; j < 3; j++) {
vivjvk[i][j] = ijkt[j][i];
}
}
var cubeco = GetBasic1(R, nR, vivjvk);
var values = GetBasic2(voxel, level, cubeco, nR);
var p1 = new Array(nR);
for (var i = 0; i < nR; i++) {
p1[i] = i * 8 + 1;
}
var vt = ijkt[3];
var cases = new Array(nR);
for (var i = 0; i < nR; i++) {
cases[i] = vt[R[i]] - 1;
}
var edgeslengths = new Array(nR);
var totalLength = 0;
for (var i = 0; i < nR; i++) {
edgeslengths[i] = EdgesLengths[cases[i]];
totalLength += edgeslengths[i];
}
var p1rep = replicate(p1, edgeslengths, nR);
var edges = new Array(totalLength);
var edgeiter = 0;
for (var i = 0; i < nR; i++) {
for (var j = 0; j < edgeslengths[i]; j++) {
edges[edgeiter] = Edges[cases[i]][j];
edgeiter++;
}
}
var x1 = new Array(totalLength); var x2 = new Array(totalLength);
for (var i = 0; i < totalLength; i++) {
var EPi = EdgePoints[edges[i] - 1];
x1[i] = EPi[1]; x2[i] = EPi[2];
}
var points = GetPoints(cubeco, values, p1rep, x1, x2, totalLength);
var triangles = CalPoints(points, totalLength);
var special = 0;
for (var i = 0; i < nrow; i++) {
var tc = tcase[i];
if (tc == 3 || tc == 4 || tc == 6 || tc == 7 || tc == 10 || tc == 12 ||
tc == 13) {
special = tc;
break;
}
}
if (special) {
console.log("there are special cases")
}
for (var c = 0; c < 7; c++) {
var R3 = whichEqual(tcase, special_name[c], nrow);
var nR3 = R3.length;
if (nR3 > 0) {
var cubeco3 = GetBasic1(R3, nR3, vivjvk);
var values3 = GetBasic2(voxel, level, cubeco3, nR3);
var p13 = new Array(nR3);
for (var i = 0; i < nR3; i++) {
p13[i] = 8 * i + 1;
}
var cases3 = new Array(nR3);
for (var i = 0; i < nR3; i++) {
cases3[i] = vt[R3[i]] - 1;
}
var nedge = special_nedge[c];
var faces3 = unlist(Faces, FacesSizes, cases3, nR3);
var outlength3 = faces3.length;
var index3;
if (c == 0) {
index3 = FacesNo7(faces3, p13, values3, nR3, 1);
} else if (c == 1) {
index3 = Faces7(faces3, p13, values3, nR3, 1);
} else {
var nface = special_nface[c];
var facelast = jthColumn(faces3, outlength3, nface, nface - 1);
index3 = Faces7(facelast, p13, values3, nR3, nface);
for (var j = 0; j < nface - 1; j++) {
var facej = jthColumn(faces3, outlength3, nface, j);
var temp = FacesNo7(facej, p13, values3, nR3, j + 1);
index3 = vectorialSum(index3, temp, nR3);
}
}
var unlisted_edges3 = unlist(Edges, EdgesLengths, cases3, nR3);
outlength3 = unlisted_edges3.length;
var edges3 = vector2matrix(unlisted_edges3, outlength3, nedge);
var edgesp1index = cbind(edges3, p13, index3, nR3, nedge);
var ind3Size = special_indSizes[c];
var ind3 = new Array(ind3Size);
for (var i = 0; i < ind3Size; i++) {
ind3[i] = special_ind[c][i];
}
for (var j = 0; j < ind3Size; j++) {
var wrows = whichEqual(index3, ind3[j], nR3);
var lwrows = wrows.length;
if (lwrows > 0) {
var lwcols = special_posSize[c][j] + 1;
var wcols = new Array(lwcols);
wcols[0] = nedge;
for (var k = 1; k < lwcols; k++) {
wcols[k] = special_pos[c][j][k - 1] - 1;
}
var ed = subsetMatrix(edgesp1index, wrows, wcols, lwrows, lwcols);
var col0ed = new Array(lwrows);
for (var i = 0; i < lwrows; i++) {
col0ed[i] = ed[i][0];
}
var col0edrep = repeach(col0ed, lwcols - 1, lwrows);
var edge1 = matrix2vectorMinusFirstColumn(ed, lwrows, lwcols);
var totalLength3 = lwrows * (lwcols - 1);
var xx1 = new Array(totalLength3);
var xx2 = new Array(totalLength3);
for (var i = 0; i < totalLength3; i++) {
var EPi = EdgePoints[edge1[i] - 1];
xx1[i] = EPi[1]; xx2[i] = EPi[2];
}
var points3 = GetPoints(cubeco3, values3, col0edrep, xx1,
xx2, totalLength3);
var triangles3 = CalPoints(points3, totalLength3);
for (var i = 0; i < totalLength3; i++) {
triangles.push(triangles3[i]);
}
}
} /* end loop for(var j=0; j<ind3Size; j++) */
} /* end if(nR3>0) */
} /* end for(var i=0; i<7; i++) (loop over special_name) */
return triangles;
}
}
// ----------------------------------------------------------------------------
function marchingCubes(f, level, xmin, xmax, ymin, ymax, zmin, zmax,
nx, ny, nz, max, rescale, logBounds) {
// default values
if(typeof max === "undefined"){
max = null;
}
if(typeof rescale === "undefined"){
rescale = true;
}
if(typeof logBounds === "undefined"){
logBounds = true;
}
// voxel
console.log("Calculate voxel...");
var voxel = Voxel(f, xmin, xmax, ymin, ymax, zmin, zmax, nx, ny, nz);
if (max === null) {
max = maxArray(voxel, nx, ny, nz);
}
// marching cubes
console.log("Marching cubes...");
var triangles = computeContour3d(voxel, nx, ny, nz, max, level);
var nrows = triangles.length;
console.log("number of triangles: ", nrows / 3);
if (logBounds) {
var x = jthColumn2(triangles, nrows, 0);
var y = jthColumn2(triangles, nrows, 1);
var z = jthColumn2(triangles, nrows, 2);
var xm = x.reduce(function (p, v) {
return (p < v ? p : v);
});
var xM = x.reduce(function (p, v) {
return (p > v ? p : v);
});
var ym = y.reduce(function (p, v) {
return (p < v ? p : v);
});
var yM = y.reduce(function (p, v) {
return (p > v ? p : v);
});
var zm = z.reduce(function (p, v) {
return (p < v ? p : v);
});
var zM = z.reduce(function (p, v) {
return (p > v ? p : v);
});
var boundsx = [
xmin + (xmax - xmin) * xm / (nx - 1),
xmin + (xmax - xmin) * xM / (nx - 1)];
console.log("x-bounds: ", boundsx);
var boundsy = [
ymin + (ymax - ymin) * ym / (ny - 1),
ymin + (ymax - ymin) * yM / (ny - 1)];
console.log("y-bounds: ", boundsy);
var boundsz = [
zmin + (zmax - zmin) * zm / (nz - 1),
zmin + (zmax - zmin) * zM / (nz - 1)];
console.log("z-bounds: ", boundsz);
}
// rescaling
if (rescale) {
var rangex = xmax - xmin;
var rangey = ymax - ymin;
var rangez = zmax - zmin;
for (var i = 0; i < nrows; i++) {
var vertex = triangles[i];
vertex[0] = xmin + rangex * vertex[0] / (nx - 1);
vertex[1] = ymin + rangey * vertex[1] / (ny - 1);
vertex[2] = zmin + rangez * vertex[2] / (nz - 1);
triangles[i] = vertex;
}
}
//
return triangles;
}
// ----------------------------------------------------------------------------
Raw
threejs_cyclide.html
<html>
<head>
<title>Dupin cyclide</title>
<style>
canvas {
width: 100%;
height: 100%
}
</style>
</head>
<body>
<script src="http://threejs.org/build/three.min.js"></script>
<script src="marchingCubes.js"></script>
<script>
// marching cubes ---------------------------------------------------------
var f = function (x, y, z) {
var a = 0.94;
var c = 0.34;
var mu = 0.56;
var b = Math.sqrt(a * a - c * c);
return (x * x + y * y + z * z - mu * mu + b * b) ** 2
- 4 * (a * x - c * mu) ** 2
- 4 * b * b * y * y;
}
var tris = marchingCubes(f, 0, -2, 1.3, -1.6, 1.6, -1, 1, 100, 100, 50);
// three js rendering -----------------------------------------------------
var scene = new THREE.Scene();
var aspect = window.innerWidth / window.innerHeight;
var camera = new THREE.PerspectiveCamera(70, aspect, 1, 10000);
camera.position.z = 4;
scene.add(camera);
var renderer = new THREE.WebGLRenderer();
renderer.setSize(window.innerWidth, window.innerHeight);
document.body.appendChild(renderer.domElement);
var geom = new THREE.Geometry();
for (var i = 0; i < tris.length / 3; i++) {
var v1 = new THREE.Vector3(
tris[3 * i][0],
tris[3 * i][1],
tris[3 * i][2]);
var v2 = new THREE.Vector3(
tris[3 * i + 1][0],
tris[3 * i + 1][1],
tris[3 * i + 1][2]);
var v3 = new THREE.Vector3(
tris[3 * i + 2][0],
tris[3 * i + 2][1],
tris[3 * i + 2][2]);
geom.vertices.push(v1);
geom.vertices.push(v2);
geom.vertices.push(v3);
geom.faces.push(new THREE.Face3(3 * i, 3 * i + 2, 3 * i + 1));
}
geom.computeFaceNormals();
var mesh = new THREE.Mesh(geom, new THREE.MeshNormalMaterial());
scene.add(mesh);
renderer.render(scene, camera);
</script>
</body>
</html>
Raw
threejs_cyclide_bretzel.md

Imgur

var f = function (x, y, z) {
  return ((x * x + y * y / 4 - 1) * (x * x / 4 + y * y - 1)) ** 2 + z * z;
}

Imgur

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