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Chapter 1 A Brief Tutorial. A direct translation of Chapter 1 of D.J. Higham and N.J. Higham, MATLAB Guide (2005)
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction\n",
"\n",
"This [IPython](http://ipython.org/) notebook is a direct translation of Chapter 1 of\n",
"\n",
"* D. J. Higham and N.J. Higham. \n",
" [MATLAB Guide](http://gw2jh3xr2c.search.serialssolutions.com/?sid=sersol&SS_jc=TC0000667000&title=MATLAB%20Guide), Second edition, \n",
" Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, \n",
" 2005, ISBN 0-89871-578-4\n",
"\n",
"with MATLAB code converted to equivalent Python/Numpy (and IPython/Matplotlib/Scipy) code. There are a small number of additions in the text to address Python/Numpy/IPython differences and additions. You can find out more about IPython and the IPython Notebook [here](http://ipython.org/) and in reference [2]. All the errors here are, of course, mine. I hope you find it useful. \n",
"\n",
"Don MacMillen: don (sometimes) at macmillen dot net (see also [this blog entry](http://blogs.siam.org/from-matlab-guide-to-ipython-notebook))\n",
"\n",
"# Chapter 1 A Brief Tutorial\n",
"\n",
"The best way to learn Python/Numpy is by trying it yourself, and hence we begin with a whirlwind tour. Working through the examples below will give you a feel for the way that Python/Numpy operates and an appreciation of its power and flexibility. \n",
"\n",
"The tutorial is entirely independent of the rest of the book—all the Python/Numpy features introduced are discussed in greater detail in the subsequent chapters. Indeed, in order to keep this chapter brief, we have not explained all the functions used here. You can use the index in [1] to find out more about particular topics that interest you. \n",
"\n",
"We will be using the IPython interactive shell as well as the IPython notebook (which is what you are reading now) throughout this tutorial. You can install these by following the directions at [IPython install](http://ipython.org/install.html). This tutorial contains commands for you to type at the IPython command line. Alternatively, if you are viewing this notebook in a \"live\" mode served from a local IPython notebook server, you can directly modify any of the cells and rerun the cell. Just be aware that in some cases you may need to choose the \"Run All\" option from the cell drop down menu to satisfy intercell dependences.\n",
"\n",
"In the last part of this brief tutorial we give examples of script files and functions. These files are short, so you can type them in quickly or cut and paste them into an IPython shell (using the %cpaste magic), or you can just modify values in place in the IPython notebook and re-evaluate the cell. You should experiment as you proceed, keeping the following points in mind. \n",
"\n",
"* Upper and lower case characters are not equivalent (Python/Numpy are case sensitive). \n",
"* Typing the name of a variable will cause IPython to display its current value. \n",
"* Python/Numpy uses parentheses, ( ), square brackets, [ ], and curly braces, { }, and these are not interchangeable. \n",
"* In the IPython shell, the up arrow and down arrow keys can be used to scroll through your previous commands. Also, an old command can be recalled by typing the first few characters followed by up arrow. You can also use ctrl-p (type p while holding the control key down) to scroll back through the command history stack.\n",
"* You can type help(topic) to access online help on the command, function, or object topic. Note that hyperlinks, indicated by underlines, are provided that will take you to related help items and the Help browser. \n",
"* If you press the tab key after partially typing a function or variable name, IPython will attempt to complete it, offering you a selection of choices if there is more than one possible completion. \n",
"* You can quit IPython by typing exit or quit or ctrl-d twice.\n",
"\n",
"Having entered the IPython command, you should work through this tutorial by typing in the text that appears after the IPython prompt, 'In [n]:' where n is a number which indicates the command's location in the command stack, in the command window. After showing you what to type, we display the output that is produced. We begin with arrays. In native Python arrays are lists denoted with the square bracket syntax. However, we want Numpy arrays, so first you import the numpy module and shorten the prefix to \"np\" (this is a common usage convention)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
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"outputs": [
{
"data": {
"text/plain": [
"array([1, 2, 3])"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"a = np.array([1, 2, 3])\n",
"a"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you type in the three lines listed in the box 'In[1]:' above into the IPython shell, then you will see the result listed in 'Out[1]:'\n",
"\n",
"This example sets up a 3 element array, which is also called a vector. In some other languages, a distinction is made between a row vector and a column vector, but that is not the case in Numpy. If you define a new vector c"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([4, 5, 6])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = np.array([4, 5, 6])\n",
"c"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now you can multiply the arrays a and c:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 4, 10, 18])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a*c"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, you performed an element by element mulitpy of the two vectors, not the scalar or dot product that some other languages would have done. Notice that in this example, the product a\\*c was not explicitly assigned to any variable. When there is no explicit assignment, IPython automatically assigns the result of the expression to the variable named '\\_' (underscore) as you can see by the following:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 4, 10, 18])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you wanted to get the dot product of the two vectors, use the dot function from numpy, as in the following"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"32"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.dot(a, c)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Inputs to Python functions are specified after the function name and within parentheses, as you just saw above with the 'dot' function from the numpy module. You may also form the outer product of the two vectors by calling another function from numpy"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4, 8, 12],\n",
" [ 5, 10, 15],\n",
" [ 6, 12, 18]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = np.outer(c, a)\n",
"A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here the answer is a 3-by-3 array that has been assigned to A.\n",
"\n",
"The product a \\* a, since the '\\*' operation is element-wise, is equivalent to squaring a, which uses the '\\*\\*' operator"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 4, 9])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a * a"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 4, 9])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = a ** 2\n",
"b"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Arithmetic operations on matrices and vectors come in two distinct forms. Array sense operations are defined to act elementwise and, as mentioned before, are the default behavior of Numpy.\n",
"\n",
"Matrix sense operations are based on the normal rules of linear algebra and are obtained with either matrix objects, or calling the specific matrix function from numpy. For matrix objects, the usual symbols +, -, *."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"matrix([[32]])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"am = np.matrix(a)\n",
"cm = np.matrix(c)\n",
"am * cm.T"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that you had to take the transpose of c in order to make it into a column vector. For numpy matrix objects, there is a difference between row and column vectors. Also, matrix object can only have one or two dimensions. For instance, the numpy function 'ones' takes a tuple and returns a numpy array of that dimensionality. The following will give us a 3 by 3 by 3 array of ones."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[[ 1., 1., 1.],\n",
" [ 1., 1., 1.],\n",
" [ 1., 1., 1.]],\n",
"\n",
" [[ 1., 1., 1.],\n",
" [ 1., 1., 1.],\n",
" [ 1., 1., 1.]],\n",
"\n",
" [[ 1., 1., 1.],\n",
" [ 1., 1., 1.],\n",
" [ 1., 1., 1.]]])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g = np.ones( (3, 3, 3) )\n",
"g"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you try to turn this into a matrix object, you will get an error"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error has a problem???\n"
]
}
],
"source": [
"#h = np.matrix(g)\n",
"print(\"Error has a problem???\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here you see how errors are displayed in Python. You see the call stack from the top to the bottom and the error message that is finally displayed.\n",
"\n",
"Numpy has many mathematical functions that operate on arrays element wise when given an array argument. For example,"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 2.71828183, 7.3890561 , 20.08553692])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.exp(a)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1., 2., 3.])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(_)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , 1.41421356, 1.73205081])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.sqrt(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By default, Numpy displays floating point numbers to 8 decimal digits, but always stores numbers and computes to the equivalent of 16 decimal digits. The output format can be changed using the set_printoptions function"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 1. 1.4142 1.7321]\n"
]
}
],
"source": [
"np.set_printoptions(precision=4)\n",
"print (np.sqrt(a))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can find out much more about the function set_printoptions by using IPython's help command"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Help on function set_printoptions in module numpy.core.arrayprint:\n",
"\n",
"set_printoptions(precision=None, threshold=None, edgeitems=None, linewidth=None, suppress=None, nanstr=None, infstr=None, formatter=None)\n",
" Set printing options.\n",
" \n",
" These options determine the way floating point numbers, arrays and\n",
" other NumPy objects are displayed.\n",
" \n",
" Parameters\n",
" ----------\n",
" precision : int, optional\n",
" Number of digits of precision for floating point output (default 8).\n",
" threshold : int, optional\n",
" Total number of array elements which trigger summarization\n",
" rather than full repr (default 1000).\n",
" edgeitems : int, optional\n",
" Number of array items in summary at beginning and end of\n",
" each dimension (default 3).\n",
" linewidth : int, optional\n",
" The number of characters per line for the purpose of inserting\n",
" line breaks (default 75).\n",
" suppress : bool, optional\n",
" Whether or not suppress printing of small floating point values\n",
" using scientific notation (default False).\n",
" nanstr : str, optional\n",
" String representation of floating point not-a-number (default nan).\n",
" infstr : str, optional\n",
" String representation of floating point infinity (default inf).\n",
" formatter : dict of callables, optional\n",
" If not None, the keys should indicate the type(s) that the respective\n",
" formatting function applies to. Callables should return a string.\n",
" Types that are not specified (by their corresponding keys) are handled\n",
" by the default formatters. Individual types for which a formatter\n",
" can be set are::\n",
" \n",
" - 'bool'\n",
" - 'int'\n",
" - 'timedelta' : a `numpy.timedelta64`\n",
" - 'datetime' : a `numpy.datetime64`\n",
" - 'float'\n",
" - 'longfloat' : 128-bit floats\n",
" - 'complexfloat'\n",
" - 'longcomplexfloat' : composed of two 128-bit floats\n",
" - 'numpy_str' : types `numpy.string_` and `numpy.unicode_`\n",
" - 'str' : all other strings\n",
" \n",
" Other keys that can be used to set a group of types at once are::\n",
" \n",
" - 'all' : sets all types\n",
" - 'int_kind' : sets 'int'\n",
" - 'float_kind' : sets 'float' and 'longfloat'\n",
" - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'\n",
" - 'str_kind' : sets 'str' and 'numpystr'\n",
" \n",
" See Also\n",
" --------\n",
" get_printoptions, set_string_function, array2string\n",
" \n",
" Notes\n",
" -----\n",
" `formatter` is always reset with a call to `set_printoptions`.\n",
" \n",
" Examples\n",
" --------\n",
" Floating point precision can be set:\n",
" \n",
" >>> np.set_printoptions(precision=4)\n",
" >>> print(np.array([1.123456789]))\n",
" [ 1.1235]\n",
" \n",
" Long arrays can be summarised:\n",
" \n",
" >>> np.set_printoptions(threshold=5)\n",
" >>> print(np.arange(10))\n",
" [0 1 2 ..., 7 8 9]\n",
" \n",
" Small results can be suppressed:\n",
" \n",
" >>> eps = np.finfo(float).eps\n",
" >>> x = np.arange(4.)\n",
" >>> x**2 - (x + eps)**2\n",
" array([ -4.9304e-32, -4.4409e-16, 0.0000e+00, 0.0000e+00])\n",
" >>> np.set_printoptions(suppress=True)\n",
" >>> x**2 - (x + eps)**2\n",
" array([-0., -0., 0., 0.])\n",
" \n",
" A custom formatter can be used to display array elements as desired:\n",
" \n",
" >>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)})\n",
" >>> x = np.arange(3)\n",
" >>> x\n",
" array([int: 0, int: -1, int: -2])\n",
" >>> np.set_printoptions() # formatter gets reset\n",
" >>> x\n",
" array([0, 1, 2])\n",
" \n",
" To put back the default options, you can use:\n",
" \n",
" >>> np.set_printoptions(edgeitems=3,infstr='inf',\n",
" ... linewidth=75, nanstr='nan', precision=8,\n",
" ... suppress=False, threshold=1000, formatter=None)\n",
"\n"
]
}
],
"source": [
"help(np.set_printoptions)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You set precision back to 8 to get the default behavior"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , 1.41421356, 1.73205081])"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.set_printoptions(precision=8)\n",
"np.sqrt(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Large or small numbers are displayed in exponential notation, with a power of 10 scale factor preceded by e:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"5.960464477539063e-08"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"2 ** -24"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Various data analysis functions are also available. "
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"14"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b.sum()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"5.0"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c.mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here you see an example of the object oriented nature of Numpy. All Numpy arrays are of type \"ndarray\" and have many methods associated with them. You can list them all by using a 'dir' command in IPython, use the following"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['T',\n",
" '__abs__',\n",
" '__add__',\n",
" '__and__',\n",
" '__array__',\n",
" '__array_finalize__',\n",
" '__array_interface__',\n",
" '__array_prepare__',\n",
" '__array_priority__',\n",
" '__array_struct__',\n",
" '__array_wrap__',\n",
" '__bool__',\n",
" '__class__',\n",
" '__contains__',\n",
" '__copy__',\n",
" '__deepcopy__',\n",
" '__delattr__',\n",
" '__delitem__',\n",
" '__dir__',\n",
" '__divmod__',\n",
" '__doc__',\n",
" '__eq__',\n",
" '__float__',\n",
" '__floordiv__',\n",
" '__format__',\n",
" '__ge__',\n",
" '__getattribute__',\n",
" '__getitem__',\n",
" '__gt__',\n",
" '__hash__',\n",
" '__iadd__',\n",
" '__iand__',\n",
" '__ifloordiv__',\n",
" '__ilshift__',\n",
" '__imatmul__',\n",
" '__imod__',\n",
" '__imul__',\n",
" '__index__',\n",
" '__init__',\n",
" '__int__',\n",
" '__invert__',\n",
" '__ior__',\n",
" '__ipow__',\n",
" '__irshift__',\n",
" '__isub__',\n",
" '__iter__',\n",
" '__itruediv__',\n",
" '__ixor__',\n",
" '__le__',\n",
" '__len__',\n",
" '__lshift__',\n",
" '__lt__',\n",
" '__matmul__',\n",
" '__mod__',\n",
" '__mul__',\n",
" '__ne__',\n",
" '__neg__',\n",
" '__new__',\n",
" '__or__',\n",
" '__pos__',\n",
" '__pow__',\n",
" '__radd__',\n",
" '__rand__',\n",
" '__rdivmod__',\n",
" '__reduce__',\n",
" '__reduce_ex__',\n",
" '__repr__',\n",
" '__rfloordiv__',\n",
" '__rlshift__',\n",
" '__rmatmul__',\n",
" '__rmod__',\n",
" '__rmul__',\n",
" '__ror__',\n",
" '__rpow__',\n",
" '__rrshift__',\n",
" '__rshift__',\n",
" '__rsub__',\n",
" '__rtruediv__',\n",
" '__rxor__',\n",
" '__setattr__',\n",
" '__setitem__',\n",
" '__setstate__',\n",
" '__sizeof__',\n",
" '__str__',\n",
" '__sub__',\n",
" '__subclasshook__',\n",
" '__truediv__',\n",
" '__xor__',\n",
" 'all',\n",
" 'any',\n",
" 'argmax',\n",
" 'argmin',\n",
" 'argpartition',\n",
" 'argsort',\n",
" 'astype',\n",
" 'base',\n",
" 'byteswap',\n",
" 'choose',\n",
" 'clip',\n",
" 'compress',\n",
" 'conj',\n",
" 'conjugate',\n",
" 'copy',\n",
" 'ctypes',\n",
" 'cumprod',\n",
" 'cumsum',\n",
" 'data',\n",
" 'diagonal',\n",
" 'dot',\n",
" 'dtype',\n",
" 'dump',\n",
" 'dumps',\n",
" 'fill',\n",
" 'flags',\n",
" 'flat',\n",
" 'flatten',\n",
" 'getfield',\n",
" 'imag',\n",
" 'item',\n",
" 'itemset',\n",
" 'itemsize',\n",
" 'max',\n",
" 'mean',\n",
" 'min',\n",
" 'nbytes',\n",
" 'ndim',\n",
" 'newbyteorder',\n",
" 'nonzero',\n",
" 'partition',\n",
" 'prod',\n",
" 'ptp',\n",
" 'put',\n",
" 'ravel',\n",
" 'real',\n",
" 'repeat',\n",
" 'reshape',\n",
" 'resize',\n",
" 'round',\n",
" 'searchsorted',\n",
" 'setfield',\n",
" 'setflags',\n",
" 'shape',\n",
" 'size',\n",
" 'sort',\n",
" 'squeeze',\n",
" 'std',\n",
" 'strides',\n",
" 'sum',\n",
" 'swapaxes',\n",
" 'take',\n",
" 'tobytes',\n",
" 'tofile',\n",
" 'tolist',\n",
" 'tostring',\n",
" 'trace',\n",
" 'transpose',\n",
" 'var',\n",
" 'view']"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dir(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To find out more about any of these methods, use the help command"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Help on built-in function argmax:\n",
"\n",
"argmax(...) method of numpy.ndarray instance\n",
" a.argmax(axis=None, out=None)\n",
" \n",
" Return indices of the maximum values along the given axis.\n",
" \n",
" Refer to `numpy.argmax` for full documentation.\n",
" \n",
" See Also\n",
" --------\n",
" numpy.argmax : equivalent function\n",
"\n"
]
}
],
"source": [
"help(a.argmax)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"3.141592653589793"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.pi"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"3.141592653589793"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"_"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.57735026918962562"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y = np.tan(np.pi/6)\n",
"y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Variable np.pi is a permanent Variable with value $\\pi$. The variable \"\\_\" always contains the most recent unassigned expression, as described earlier, so after the assignment to y, \"\\_\" still holds the Value $\\pi$.\n",
"\n",
"You may set up a two dimensional array by concatenating columns using the np.c_[ ] array notation"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-3, 0, -1],\n",
" [ 2, 5, -7],\n",
" [-1, 4, 8]])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B = np.c_[[-3, 2, -1], [0, 5, 4], [-1, -7, 8]]\n",
"B"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At the heart of Numpy is a powerful range of linear algebra functions. For example, recalling that c is a 3-by-1 Vector, you may wish to solve the linear system $B * x = c$. This can be done with the solve function from the numpy.linalg module"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.29953917, 1.37788018, -0.10138249])"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy.linalg as nl\n",
"x = nl.solve(B, c)\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"7.2040771407550849e-17"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nl.norm(np.dot(B,x) - c) / (nl.norm(B) * nl.norm(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some times we see a 0 here, but we usually expect to see something nonzero because of rounding errors.\n",
"\n",
"The eigenvalues of B can be found using eig from the numpy.linalg module"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([-3.13605+0.j , 6.56803+5.10454j, 6.56803-5.10454j])"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.set_printoptions(precision=5) # make it the m*lab default\n",
"w, _ = nl.eig(B)\n",
"w"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice two things about this code snippet. First, nl.eig returns two values, w are the eigenvalues and v would be the eigenvectors. Since in this instance we did not want the eigenvectors we set it to the underscore '\\_', which is a common idiom in Python. Finally, the solution shows the j is the imaginary unit, $\\sqrt{-1}$. To get the eigenvectors you can do the calculation again"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.98290+0.j , -0.03854-0.03928j, -0.03854+0.03928j],\n",
" [-0.12656+0.j , -0.80053+0.j , -0.80053-0.j ],\n",
" [ 0.13372+0.j , 0.16831+0.57254j, 0.16831-0.57254j]])"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w, v = nl.eig(B)\n",
"v"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The columns of v are the eigenvectors of B.\n",
"\n",
"To get vectors of evenly spaced values, use the np.arange function"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 3, 4, 5])"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v = np.arange(6)\n",
"v"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the default starting value is zero. Also, as noted earlier, all Numpy arrays start at index zero and end at index n - 1 for an array of size n.\n",
"\n",
"Nonunit increments can be specified by a third number, often called the 'stride'."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([2, 5, 8])"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w = np.arange(2, 10, 3)\n",
"w"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , 0.75, 0.5 , 0.25])"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y = np.arange(1, 0, -0.25)\n",
"y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This last example illustrates a peculiarity of Python and numpy, that the ending value or index is actually one position short of what you might expect. In the previous example, to have the array actually increment down to zero, you have to specify an end value that is strictly *less* than 0 (but greater than -(0.25 + delta) ). Here we just use -0.001."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , 0.75, 0.5 , 0.25, 0. ])"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y = np.arange(1, -0.001, -0.25)\n",
"y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You may construct big matrices out of little ones by using the numpy functions hstack and vstack and the previously mentioned c\\_[ ] and r\\_[ ] notations"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4, 8, 12, 8],\n",
" [ 5, 10, 15, 9],\n",
" [ 6, 12, 18, 10]])"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C = np.c_[A, [8, 9, 10]]\n",
"C"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-3, 0, -1],\n",
" [ 2, 5, -7],\n",
" [-1, 4, 8],\n",
" [-3, 0, -1],\n",
" [ 2, 5, -7],\n",
" [-1, 4, 8],\n",
" [-3, 0, -1],\n",
" [ 2, 5, -7],\n",
" [-1, 4, 8]])"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"D = np.r_[B, B, B]\n",
"D"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-3, 0, -1],\n",
" [ 2, 5, -7],\n",
" [-1, 4, 8],\n",
" [-3, 0, -1],\n",
" [ 2, 5, -7],\n",
" [-1, 4, 8],\n",
" [ 1, 2, 3]])"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"E = np.vstack((B, B, a))\n",
"E"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice well that np.vstack takes a *single* argument that is a tuple of arrays. That way you can stack as many arrays as needed with a single call to vstack or just use the r\\_[ ] notation.\n",
"\n",
"The element in row i and column j of the matrix C (where i and j always start at 0) can be accessed as c[i, j]"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"15"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C[1, 2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"More generically, C[i1:i2, j1:j2] picks out the submatrix formed by the intersection of rows i1 to i2-1 and columns j1 to j2-1. This type of operation on arrays is generally called *slicing*."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 5, 10],\n",
" [ 6, 12]])"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C[1:3, 0:2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can build certain types of matrices automatically. For example, identities and matrices of zeros and ones can be constructed with eye, zeros, and ones:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 0., 0.],\n",
" [ 0., 1., 0.],\n",
" [ 0., 0., 1.]])"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"I3 = np.eye(3)\n",
"I3"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0., 0., 0., 0., 0.],\n",
" [ 0., 0., 0., 0., 0.],\n",
" [ 0., 0., 0., 0., 0.]])"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Y = np.zeros((3,5))\n",
"Y"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 1.],\n",
" [ 1., 1.]])"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z = np.ones((2,2))\n",
"Z"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that these functions take a single argument which is a tuple (except for np.eye, which has a different interface). The first argument of the tuple specifies the size of the first dimension of the array and so on. \n",
"\n",
"The methods rand and randm on an object returned from numpy.random.RandomState() do not take tuples. They are convenience functions that have a similar interface to another math envirionment. These two methods generate random entries from the uniform distribution over [0,1] and the normal (0,1) (ie zero mean with unit variance) distribution, respectively.\n",
"\n",
"Note that it is always good for you to intialize a new instance of RandomState when using random numbers. This ensures that the random stream is for you alone, and you can reset the seed to make the sequence repeatable. Here we set the starting seed to 20."
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.58813, 0.89771, 0.89153],\n",
" [ 0.81584, 0.03589, 0.69176],\n",
" [ 0.37868, 0.51851, 0.65795]])"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn = np.random.RandomState() # initialize a new RandomState object\n",
"rn.seed(20)\n",
"F = rn.rand(3, 3)\n",
"F"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0.62064, -0.83453, 0.91636, 0.70784, 0.41968]])"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"G = rn.randn(1, 5)\n",
"G"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At this point several variables have been created in the workspace. You can obtain a list with the %who command, where the % indicates an IPython 'magic' command."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A\t B\t C\t D\t E\t F\t G\t I3\t Y\t \n",
"Z\t a\t am\t b\t c\t cm\t g\t nl\t rn\t \n",
"v\t w\t x\t y\t \n"
]
}
],
"source": [
"%who"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The %whos magic will additionally give the types and some additional information"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Variable Type Data/Info\n",
"-----------------------------------\n",
"A ndarray 3x3: 9 elems, type `int64`, 72 bytes\n",
"B ndarray 3x3: 9 elems, type `int64`, 72 bytes\n",
"C ndarray 3x4: 12 elems, type `int64`, 96 bytes\n",
"D ndarray 9x3: 27 elems, type `int64`, 216 bytes\n",
"E ndarray 7x3: 21 elems, type `int64`, 168 bytes\n",
"F ndarray 3x3: 9 elems, type `float64`, 72 bytes\n",
"G ndarray 1x5: 5 elems, type `float64`, 40 bytes\n",
"I3 ndarray 3x3: 9 elems, type `float64`, 72 bytes\n",
"Y ndarray 3x5: 15 elems, type `float64`, 120 bytes\n",
"Z ndarray 2x2: 4 elems, type `float64`, 32 bytes\n",
"a ndarray 3: 3 elems, type `int64`, 24 bytes\n",
"am matrix [[1 2 3]]\n",
"b ndarray 3: 3 elems, type `int64`, 24 bytes\n",
"c ndarray 3: 3 elems, type `int64`, 24 bytes\n",
"cm matrix [[4 5 6]]\n",
"g ndarray 3x3x3: 27 elems, type `float64`, 216 bytes\n",
"nl module <module 'numpy.linalg' fr<...>umpy/linalg/__init__.py'>\n",
"rn RandomState <mtrand.RandomState object at 0x10e5f49d8>\n",
"v ndarray 6: 6 elems, type `int64`, 48 bytes\n",
"w ndarray 3: 3 elems, type `int64`, 24 bytes\n",
"x ndarray 3: 3 elems, type `float64`, 24 bytes\n",
"y ndarray 5: 5 elems, type `float64`, 40 bytes\n"
]
}
],
"source": [
"%whos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Like most languages Python has loop contructs. The following example uses a for loop to evaluate the continued fraction $\\cfrac{1}{1+\\cfrac{1}{1+\\cfrac{1}{1+\\cfrac{1}{1+\\cfrac{1}{1+\\cfrac{1}{1 + \\cfrac{1}{1 + \\cfrac{1}{1 + \\cfrac{1}{1 + \\cfrac{1}{1}}}}}}}}}}$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"which approximates the golden ratio, (1 + $\\sqrt{5}$)/2. The evaluation is done from the bottom up:"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1.6180555555555556"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g = 2.\n",
"for k in range(10):\n",
" g = 1 + 1 / g\n",
"g"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Many constants can be found in the scipy submodule constants. You can access them in the following way"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1.618033988749895"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import scipy.constants as sconst\n",
"sconst.golden"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Loops involving the while statement can be found later in this tutorial.\n",
"\n",
"The plot function from the matplotlib module pylab produce two dimensional pictures. You can assess these ploting and graphics functions by importing this module. It is a common practice to rename it to plt, as in the following example."
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x111f56c88>"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ckbQcZ6mrJblzdb+E/6/AvUSTydQuqGt5/PjBedC/kOJ+PCOQ6dQUdZbhvtwXASOS7I+Q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\nwGLn3E8Sf66y1l4OfIUudrCVYyTV5s65T7f9c6Ln428JNv/7z9CjzQ3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"text/plain": [
"<matplotlib.figure.Figure at 0x111f4f898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#import mpld3\n",
"#mpld3.enable_notebook()\n",
"import matplotlib.pylab as plt\n",
"t = np.arange(0, 1.005, 0.005)\n",
"z = np.exp(10 * t * (t - 1)) * np.sin(12 * np.pi * t)\n",
"plt.plot(t, z)\n",
"plt.title(\"Figure 1.2. Basic 2D picture produced by plt.plot\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, plt.plot(t, z) joins the points t[i], z[i] using the default solid linetype. Matplotlib opens a figure window in which the picture is displayed. In this IPython notebook, the matplotlib figures are included 'in line' since the notebook was invoked with the \"ipython notebook --pylab=inline\" (the --pylab=inline option will be deprecated in the 3.0 notebook in favor of the **%matplotlib inline** cell magic) command. When you are using IPython as a command line interpreter, after opening a plot figure window, you can close it in the normal way, ie by clicking on the x in the window title bar.\n",
"\n",
"You can produce a histogram with the function plt.hist"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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YNFJKDwIn1I9OZe4khwdJkjSF+FsVkiSpmMFBkiQVMzhIkqRiBgdJklTM4CBJ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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111f4f320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(np.random.randn(1000))\n",
"plt.title(\"Figure 1.3. Histogram produced by plt.hist.\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, hist is given 1000 points from the normal (0, 1) random number generator\n",
"\n",
"You are now ready for more challenging computations. A random Fibonacci sequency {$x_{n}$} is generated by choosing $x_{1}$ and $x_{2}$ and setting\n",
"\n",
"$$ x_{n + 1} = x_{n} \\pm x_{n -1}, \\; n \\ge 2 $$\n",
"\n",
"Here, the $\\pm$ indicates that + and - must have equal probability of being chosen. Viswanath [121] listed in [1] analyzed this recurrence and showed that, with probability 1, for large n the quantity $|x_{n}|$ increases like a multiple of $c^{n}$, where c = 1.13198824... (see also [25]). You can test Viswanath's result as follows:"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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9vIn9M1O4c0RHsvzWFLvsB+xnH6LOvBDVJAVbVATWQzVqjH39eez/3oZAAHXq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\n9wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b8bd828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%reset -f\n",
"import numpy as np\n",
"import pylab as plt\n",
"rd = np.random.RandomState()\n",
"rd.seed(100)\n",
"x = np.zeros(1000)\n",
"x[0:2] = 1, 2\n",
"for n in range(1, 999):\n",
" x[n + 1] = x[n] + np.sign(rd.rand(1) - 0.5) * x[n - 1]\n",
" \n",
"xx = np.arange(1, 1001)\n",
"plt.semilogy(xx, np.abs(x))\n",
"c = 1.13198824\n",
"plt.hold(True)\n",
"plt.semilogy(xx, c ** xx)\n",
"plt.title(\"Figure 1.4. Growth of a random Fibonacci sequence\")\n",
"plt.hold(False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, %reset -f removed all variables and imported modules from the workspace, which is why we needed to import numpy and pylab again. The for loop stores a random Fibonacci sequence in the array x; we preallocate x to the size needed and initial to zero using the np.zeros() function. The plt.semilogy function then plots n on the x-axis against $|X|$ on the y-axis, with logarithmic scaling for the y-axis. Typing np.hold(True) tells matplotlib to superimpose the next picture on top of the current one. The second semilogy plot produces a line of slope c. The overall picture, shown in Figure 1.4, is consistent with Viswanath’s theory.\n",
"\n",
"We can make the above code into a command by writing it out to a file. If you cut and paste it into a file called fib.py, you can then run it in IPython by typing \"run fib\" or \"run fib.py\" to reproduce the above graph.\n",
"\n",
"However, you can experiment directly in this IPython notebook by changing any of the values and then hitting the 'play' button above.\n",
"\n",
"Our next example involved the Collatz iteration, which, given a positive integer $x_{1}$, has the form $x_{k + 1} = f(x_{k})$, where\n",
"\n",
"$$f(x) = \\left\\{\n",
" \\begin{array}{lr}\n",
" 3x + 1 & : x \\: \\% \\: 2 == 0\\\\\n",
" x/2 & : x \\: \\% \\: 2 == 1\n",
" \\end{array}\n",
"\\right.\n",
"$$\n",
"\n",
"Here $x \\: \\% \\: y$ is the modulus function of x and y, sometimes also written as mod(x, y). It is the remainder of x when divided by y. In this case $x \\: \\% \\: 2 == 0$, if true, means that x is even and if $x \\: \\% \\: 2 == 1$ is true, then x is odd. Note that these are perfectly good Python functions"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x is odd\n"
]
}
],
"source": [
"x = 3\n",
"if x % 2 == 0:\n",
" print ('x is even')\n",
"else:\n",
" print ('x is odd')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But now returning to our quest, the equation above in words means:\n",
"if $x$ is odd, replace it by $3x + 1$, and if $x$ is even, halve it. It has been conjectured that this iteration will always lead to a value of 1 (and hence thereafter cycle between 4, 2, and 1) whatever starting value $x_{1}$ is chosen. There is ample computational evidence to support this conjecture, which is variously known as the Collatz problem, the $3x + 1$ problem, the Syracuse problem, Kakutani’s problem, Hasse’s algorithm, and Ulam’s problem. However, a rigorous proof has so far eluded mathematicians. For further details, see [63] listed in [1] or type “Collatz problem” into your favorite Web search engine. You can investigate the conjecture by creating the python script file collatz.py shown below. In this file a while loop and an if statement are used to implement the iteration. You can run this in the notebook simply by changing the value of n and hitting the play button. Or, you can save this to a file named collatz.py (remembering to uncommment out the line '#n = int(raw_input...\" and commenting out the line \"n = 27\". Then, from the IPython shell prompt, type \"run collatz\". The input command prompts you for a starting value. The appropriate response is to type an integer and then hit return."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11a0887f0>"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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kSBVSkCIiUs7C4Z5GBSlSfRSkiIiUs+G1e4LCWfVJkSqiIEVEpJwNZ1I0u0eq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"text/plain": [
"<matplotlib.figure.Figure at 0x119a7db00>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#COLLATZ Collatz iteration. \n",
"\n",
"#n = int(raw_input(’Enter an integer bigger than 2: ’))\n",
"init_n = n = 27\n",
"narray = np.zeros(1000) # only a maximum of 1000 iterations\n",
"narray[0] = n\n",
"count = 0\n",
"while n != 1:\n",
" if n % 2 == 1: # Remainder modulo 2. \n",
" n = 3 * n + 1\n",
" else:\n",
" n = n / 2\n",
" count += 1\n",
" narray[count] = n # Store the current iterate\n",
"\n",
"# Plot with * marker and solid line style.\n",
"# Only plot the non zero entries in narray\n",
"plt.plot(narray[narray != 0], '*-')\n",
"plt.title('Figure 1.5. Collatz iteration starting at %d' % init_n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A couple of things you should note about the code above. This first is that it will fail if the number of iterations goes beyond 1000. For most of the inputs I have tried, it 'converged' in under 200 iterations. But you should try to break it! The second thing to note is that we only want to plot the non zero values. All the zero values at the end of the array add no new information and we want to drop them. That is easily accomplished by using the narray[narray != 0] syntax which selects only the non-zero values out of narray.\n",
"\n",
"To investigate the Collatz problem further, the script collbar in the next listing plots a bar graph of the number of iterations required to reach the value 1, for starting Values 1,2,. . . ,29. The result is shown in Figure 1.6. For this picture, the function plt.grid adds grid lines that extend from the axis tick marks, while plt.title, plt.xlabel, and plt.ylabel add further information. "
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11a0889b0>"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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u5ufqcN8DEr8KTPcxWCRJ0oDoNmG5kWZo/sz8F3Ar0P7coPV6iEuSJOk+3d4l\ndCFl+P0h5wL/ExEXUpKgt1H6sUiSJPWs2xqWLwCrRcRqzfv3U4bj/wnwY2Bt4B29hydJktT9wHHf\noeWpx5l5cUQ8DtgeWAb8PDNv6kuEkiRp1ht3whIRawAfBs7NzFOHpmfmLbQkMZIkSf0y7iahzLwT\n2BfYsP/hSJIkrajbPiyLgKf2MxBJkqThdJuw/A/wyojYJyJ6eh6RJEnSaLpNNo4HlgPHAEdGxDXA\nnW1l6sx8eg+xSZIkAd0nLDdRBo+7tI+xSJIkddTtbc3b9zkOSZKkYXXbh0WSJGnSdN1hNiLWBvYD\ndgA2APbNzPMj4iGUpzl/NzMv60uUkiRpVuuqhiUiHkl5ntAhlCc3P437H4Z4E2Wclv37FKMkSZrl\nuq1h+STwYOAZwPXNq9W3gRf1EJckSdJ9uu3DshNwZGZeDNQd5v8V+Leuo5IkSWrRbcKyBrBkhPkP\n7nK9kiRJK+g2YbkY2G6E+btR+rhIkiT1rNs+LEcAX46I3wHfaKatFBGPBxYA2wB79CE+SZKk7mpY\nMvOrwAeBDwF/aiafQRn59pXA+zLz232JUJIkzXpdj8OSmR+OiBMoNSmPpyQ/fwG+mZl/7VN8kiRJ\n3SUsEbEJsCQzrwIO7zB/DWD9Zr4kSVJPuu10ezmw+wjz/6spI0mS1LNuE5ZqlPlzgOVdrluSJOkB\nxtwk1Dw7aN2WSQ9tmobarUvpePuPHmOTJEkCxteHZT7lziAoo9se0bw6qYCDeohLkiTpPuNJWH4A\n/IuSjHwCOAm4oK1MDdwOLMrM3/QlQkmSNOuNOWHJzF8AvwCIiLUoty//fqICkyRJGtLVbc2ZubDf\ngUiSJA1nTAlLRHyQ0tzz4cxc3rwfTZ2Zh/YUnSRJEmOvYTmYkrB8HLineT+aGjBhkSRJPRtTwpKZ\nK430XpIkaSKZeEiSpIHX9cMPp1pEPJzSRLUzsCbwZ2BeZl7QUuYQYB/KYHbnAW/OzMumIFxJktSD\naVnDEhFDCcjdwAuAJwPvAG5uKfMe4K3AvsBWlPFhzoyIVSc9YEmS1JPpWsPyXuCqzNynZdqVbWUO\nAA7NzFMBImJv4DpgNyAnJUpJktQX0zVheTFwRkQk8B/ANcDRmXksQEQ8BtgIOHtogcy8NSJ+BWyD\nCYskSdPKmJqEIuJtEfHEiQ5mHB4LvBm4FNgJ+BxwZES8ppm/EeW26uvalruumSdJkqaRsdawHA7c\nAPwJICIeEX9SAAAbJklEQVSWAXtl5okTFdgoVgLOz8wPNO9/GxFzKUnMV0dYrqIkMpIkaRoZa8Jy\nE7Bhy/tqAmIZj38Af2yb9kfgpc3v11Ji3JAH1rJsAFzYaYURsSewZ+u0uXPnrrNgwYJ+xCtJ0qy0\ncOHCwxcvXnxL2+STMvOk8axnrAnLj4GDI+IZwNBG946IZ42wTJ2ZB4wnmHE4D9i0bdqmNB1vM/Py\niLgW2BH4HUBErA1sDXy20wqbHde+8zYHFvUvbEmSZpcFCxbMBy4YteAoxpqw7AccQekvsgGlWWWn\n5jWcmnKnzkQ4HDgvIg6kdKDdmjLeyhtbyhwBHBQRlwFXUB4T8DfgOxMUkyRJmiBVXY+/S0dELAde\nM4V9WIiIXYCPAY8HLgc+lZlfaitzMPDflIHjfgq8ZZwDx20OLFqyZAlLly7tS9ySpNlnyV01+5xy\n6biWOXaPTVl/9anugdG9OXPmsP766wNswSTWsLSbB/y81433IjO/D3x/lDIHM7YHNUqSpAHWVcKS\nmV8e+j0ingI8qnl7ZWZe3I/AJEmShnQ9cFxEvAQ4DHh02/TLgbdn5nd7C02SJKno6llCTf+RbzZv\n3wfs3rzeR7md+JsR8cK+RChJkma9bmtYPgD8Ftg2M29vmf7diPgM8DNgAXBGj/FJkiR1/bTmpwFf\nbktWAGimHd+UkSRJ6lm3CctdwENGmP+QpowkSVLPuk1YzgEOiIht2mdExNbA24CzeglMkiRpSLd9\nWN4N/AL4WUScT3lqMpTh8bcCrgfe03t4kiRJXdawZObllD4qRwLrAa9oXusBnwaenplX9ClGSZI0\ny3U9DktmXg/Mb16SJEkTpts+LJIkSZPGhEWSJA08ExZJkjTwTFgkSdLAM2GRJEkDb9x3CUXEmsBP\ngS9k5uf6H5IkSdIDjbuGJTPvAB4D1P0PR5IkaUXdNgmdAbygn4FIkiQNp9uB4w4FvhERXwU+B1wO\n3NleKDNv6iE2SZIkoPuEZXHz8ynAniOUW7nL9UuSJN2n24TlEOzDIkmSJklXCUtmHtznOCRJkobV\nl3FYImKdiLD5R5IkTYiun9YcEVsCHwK2A1YFdgLOiYiHAV8EDs/MH/UjSEmSNLt1VcMSEc8GfgY8\nAfhq63oy8wZgHWDffgQoSZLUbZPQR4A/Uu4Sel+H+ecCW3cblCRJUqtuE5ZnAsdl5t10vlvoGmDj\nrqOSJElq0W3CsnSUZR8B3NbluiVJkh6g24Tll8DLOs2IiLWAecCPuw1KkiSpVbcJywJgy4g4Ddi5\nmfb0iNgHWASsTxm+X5IkqWddJSyZ+StgF+DxwFeayZ8CPk8Zjn+XzPxdXyKUJEmzXtfjsGTmOcCm\nEbEZJXFZCfgLsCgzHbZfkiT1TdcJy5DMvBC4sA+xSJIkddTLSLerAW+kNA09qpl8JfB94NjMvKv3\n8CRJkrof6faRwEXAkcDTgRuAG5vfjwQuaspIkiT1rNsals9SalUiM09unRERLwe+3JR5SW/hSZIk\ndX9b846Uhxue3D4jM78BfLopI0mS1LNuE5bbgOtHmH8tjnQrSZL6pNuE5TjgdRGxZvuMiHgQZaTb\nL/YSmCRJ0pAx9WGJiJe2TboQ2BW4JCK+DFzWTH8CsDdwE+DAcZIkqS/G2un2ZMpTmavmfevv7+9Q\n/pHASUD2FJ0kSRJjT1h2mNAoehQRBwIfBo7IzLc301YDDgNeAawGnAnsl5kj9b2RJEkDaEwJS2YO\n7JOXI+KZlAHsfts26wjKgxn3AG6l3GZ9CrDtpAYoSZJ61m2n24HQdPD9KrAP8M+W6WsDrwfmZ+aP\nm8cHzAOeExFbTUmwkiSpa70Mzf9cSlLwWGA97u/TMqTOzKf3ENtYfBY4NTPPiYgPtEzfkvLZzh6a\nkJmXRsRVwDbA+RMclyRJ6qOuEpaIeDvwSeAu4FLKXUGTKiJeCTyDkpy02xC4JzNvbZt+HbDRRMcm\nSZL6q9salncB5wEvzsxb+hjPmDTPKToC+M/MXDqORSvKHU6SJGka6TZhWRM4cSqSlcYWwPrAoogY\naopaGdguIt4KvBBYLSLWbqtl2YBSy7KCiNgT2LN12ty5c9dZsGBB34OXJGm2WLhw4eGLFy9uzxdO\nysyTxrOebhOWc4GndrlsP5wF/HvbtOOBPwIfA64BllKeZ/QtgIh4IrAJ8ItOK2x2XPvO2xxY1K+g\nJUmabRYsWDAfuKDX9XSbsOwP/CAi3gEcl5mT2oclM28HLm6dFhG3Azdm5h+b918EDouImynPNToS\nOC8z7XArSdI001XCkplXR8QxwP8DPhERdwHL2orVmblOrwGOQ3vflPmUmE6mDBx3BvCWSYxHkiT1\nSbd3CR1CGZL/GuA3wFT1ZblPZj6v7f3dlJqg/acmIkmS1C/dNgm9CTgN2C0zl/cxHkmSpBV0O9Lt\nqsBpJiuSJGkydJuwfA+fySNJkiZJt01CC4H/i4ijgS8CV7Fip1sm++4hSZI0M3WbsFza/HwGsO8I\n5Vbucv2SJEn36TZhOQSHuJckSZOk23FYDu5zHJIkScPqttOtJEnSpOl24LgPjqFYnZmHdrN+SZKk\nVt32YTl4hHk1UDU/TVgkSVLPuu3DskJTUkSsBDwKeCtljJadewtNkiSp6LaGZQXNqLeXA++IiK8B\nRwGv6tf6JUnS7DVRnW5/AuwyQeuWJEmzzEQlLFsCPmdIkiT1Rbd3Ce09zKx1ge2AlwLHdhuUJElS\nq277sBw/wrwbgI9RRsOVJEnqWbcJy2M6TKuBmzPzth7ikSRJWkG3tzVf2e9AJEmShuPQ/JIkaeCN\nuYYlIn43znXXmfn0cS4jSZK0gvE0Cd1E6acymo2ATcdYVpIkaVRjTlgyc/uR5kfERsB7gH2BZcAJ\nPUUmSZLU6Hlo/ojYEHgv8N/AHOCrwIcz8y+9rluSJAl6SFhaalRaE5UPZeZf+xSbJEkS0EXC0iQq\n7wXeSElUTqAkKpf3OTZJkiRgfHcJbcz9icoqwFcoTT8mKpIkaUKNp4blL8BqwEXAR4DLgfUiYr3h\nFsjMC3oLT5IkaXwJy+rNz82AHKVsRbmteeVugpIkSWo1noRl3oRFIUmSNILxjMPy5YkMRJIkaTg+\nS0iSJA08ExZJkjTwTFgkSdLAM2GRJEkDz4RFkiQNPBMWSZI08ExYJEnSwDNhkSRJA8+ERZIkDbzx\nDM0vSdK0dfuyijuWLh/XMmvOWYm1Vq4nKCKNx7RMWCLiQGB34EnAncDPgfdk5p9ayqwGHAa8gvKU\n6TOB/TLz+smPWJI01e5Yupx9Trl0XMscu8emrLVyNUERaTyma5PQtsBRwNbA84E5wA8iYo2WMkcA\nuwJ7ANsBDwdOmeQ4JUlSH0zLGpbM3KX1fUS8Drge2AL4WUSsDbweeGVm/rgpMw/4Y0RslZnnT3LI\nkiSpB9O1hqXdukAN3NS834KSjJ09VCAzLwWuAraZ9OgkSVJPpn3CEhEVpfnnZ5l5cTN5I+CezLy1\nrfh1zTxJkjSNTMsmoTZHA08BnjuGshWlJkaSJE0j0zphiYjPALsA22bm31tmXQusGhFrt9WybECp\nZem0rj2BPVunzZ07d50FCxb0OWpJM8V4b5NtvUXWW2w1WyxcuPDwxYsX39I2+aTMPGk865m2CUuT\nrLwE+I/MvKpt9iLgXmBH4FtN+ScCmwC/6LS+Zse177zNm3VJ0grGe5ts6y2y3mKr2WLBggXzgQt6\nXc+0TFgi4mhKbch/AbdHxIbNrFsy867MvDUivggcFhE3A7cBRwLneYeQJEnTz7RMWIA3Ufqi/Kht\n+jzgK83v84FlwMmUgePOAN4ySfFpmrKaXpIG07RMWDJz1LubMvNuYP/mJY2J1fSSNJimZcIiSdJs\nYgdvExZJkgaeHbxnwMBxkiRp5rOGRVLPrK6WNNFMWCT1zOpqSRPNJiFJkjTwrGHRwLGJQJLUzoRF\nA8cmAklSOxMWSdK42MlaU8GERZI0Lnay1lSw060kSRp41rBIA8KqckkangmLNCCsKpek4dkkJEmS\nBp4JiyRJGngmLJIkaeDZh0XSrGVHZ2n6MGGRNGvZ0VmaPmwSkiRJA8+ERZIkDTwTFkmSNPDswyJJ\nmjZ6efDidN62TFgkSdNILw9enM7blk1CkiRpGrCGRZoheqmudjwSSYPOhEWaIXqprnY8EkmDzoRF\nE8LOaZKkfjJh0YSwc5okqZ/sdCtJkgaeNSwDzI6QkoZjJ2vNNiYsA8yOkJKGYydrzTYmLFIf2dlY\nkiaGCYvUR3Y2lqSJYadbSZI08KxhUUd2ypMkDRITFnVkpzxJ0iCxSUiSJA08a1gkTWvemSXNDiYs\nkqY178ySZgcTFs04XnFL0sxjwqIZxytuSZp5ZnTCEhFvAd4JbAT8Ftg/M389tVFJkqTxmrF3CUXE\nK4BPAQuAzSgJy5kR8bApDWwS3b6sYsld9Zhfty+zlkGSNJhmcg3LfOCYzPwKQES8CdgVeD3wiakM\nbLLYNCJJmilmZA1LRMwBtgDOHpqWmTVwFrDNZMZiLYckSb2bqTUsDwNWBq5rm34dsOlkBmIthyRJ\nvZupCctwKmA896+uDrDKKt3vpjWW12y6wYPGXn7VOcyZU3W1bK/Lu2237bbdttt22+3Ld6vl3Ll6\nTytqVHU988afaJqE7gD2yMzvtkw/HlgnM3fvsMyewJ6t03beeedHzJs3b/MJDleSpBnruOOOu+D0\n00+/pm3ySZl50njWMyMTFoCI+CXwq8w8oHlfAVcBR2bmJ8e4moced9xxP5g3b97+wF0TFOqMtHDh\nwsMXLFgwf6rjmE7cZ91xv42f+6w77rdxW/244447at68eTsBN/a6spncJHQY8OWIWAScT7lraE3g\n+HGs48bTTz/9mnnz5v18AuKb0RYvXnwLcMFUxzGduM+6434bP/dZd9xv49ecQ3tOVmCG3iUEkJkJ\nvAM4BLgQeBrwgsxcMqWBSZKkcZvJNSxk5tHA0VMdhyRJ6s2MrWGRJEkzhwnL6MbVi1n3cb+Nn/us\nO+638XOfdcf9Nn5922cz9i4hSZI0c1jDIkmSBp4JiyRJGngmLJIkaeCZsEiSpIE3o8dh6VVEvAV4\nJ7AR8Ftg/8z89dRGNbgiYgGwoG3yJZn5lKmIZxBFxLbAu4AtgI2B3Vqfd9WUOQTYB1gXOA94c2Ze\nNtmxDpLR9ltEHAe8tm2xMzJzl8mLcrBExIHA7sCTgDuBnwPvycw/tZRZjTIq+CuA1YAzgf0y8/rJ\nj3jqjXGf/QjYrmWxGjgmM/ebxFAHSkS8CXgz8Ohm0mLgkMw8o5nfl+PMGpZhRMQrgE9RTsCbURKW\nMyPiYVMa2OD7A7AhJcnbCHju1IYzcNYCLgLeQocnh0fEe4C3AvsCWwG3U467VSczyAE04n5rnM4D\nj709hyk3W2wLHAVsDTwfmAP8ICLWaClzBLArsAflJPxw4JRJjnOQjGWf1cDnuf9Y2xh49yTHOWiu\nBt5DuaDYAjgH+E5EPLmZ35fjzBqW4c2nZM1fgfsyyF2B1wOfmMrABty9Pv5geM0Vx9BVR6dntx8A\nHJqZpzZl9gauA3YDcrLiHDRj2G8Ad3vs3a+9dikiXgdcTzmh/Cwi1qZ8n70yM3/clJkH/DEitsrM\n8yc55Ck32j5rmXWHx9r9MvO0tkkHRcSbgWdFxDX06TgzYekgIuZQDtCPDE3LzDoizgK2mbLApocn\nNAfoXcAvgAMz8+opjmlaiIjHUK7Yzh6alpm3RsSvKMfdrE1Yxmj7iLgOuJlyhXdQZt40xTENknUp\ntQND+2QLyjmg9Xi7NCKuohxvsy5h6aB9nw15dUTsBVwLnEq5yLhzsoMbRBGxEhCUhw3/gj4eZzYJ\ndfYwYGXKlW2r6ygnFHX2S+B1wAuANwGPAX4SEWtNZVDTyEaUL0ePu/E7HdgbeB6lev4/gO+PUBsz\nqzT74QjgZ5l5cTN5I+CezLy1rbjHG8PuM4CvAa8Btqdc1O4FnDDpAQ6YiHhqRNwG3E15ht/umXkJ\nfTzOrGEZn4rh289nvcw8s+XtHyLifOBKSrZ93NRENSN43I2ieTr7kMUR8XvgL5STyrlTEtRgORp4\nCmPrU+bxVgzts+e0TszMY1veLo6Ia4GzIuIxmXn5ZAY4YC4Bnk6pldoD+EpEbDdC+XEfZ9awdHYD\nsIzSqarVBqx49athZOYtwJ+Ax091LNPEtZR/Yo+7HjUnjhvw2CMiPgPsAmyfmX9vmXUtsGrTl6XV\nrD/e2vbZP0Yp/ivK/+2sPtYy897M/GtmXpCZ76fcqHIAfTzOTFg6yMylwCJgx6FpTfXgjpTb3DQG\nEfEg4HHAaP/w4r6T7LU88Lhbm3LHgsfdOETEI4GHMsuPvebE+xJgh8y8qm32IuBeHni8PRHYhNL3\nYFYaZZ91shmlpmBWH2sdrES5hblvx5kPPxxGRATwZcrtpedT7hp6GfAke4d3FhGfpHRAuxJ4BLAQ\neBrwlMy8cSpjGxRNf57HU67ILgDeTmmyuCkzr46Id1NuD3wdcAVwKDAXmJuZ90xFzINgpP3WvBZQ\nbpO8tin3ccqt0E9rLkBmnYg4mnJr939RajqH3JKZd7WU2RmYB9wGHAksz8xtJzncgTDaPouIxwKv\nAr4P3EhpAjkMuCoznzfZ8Q6KiPgwpR/Z1cCDgVdTxk3aKTPP6ddxZg3LMJo28XcAhwAXUk68LzBZ\nGdEjgRMpbZlfB5YAzzJZeYAtKcfTIspV2acoJ+CFAJn5Cco4EMdQqprXAHaezclKY6T9tozy//kd\n4FLgC8Cvge1ma7LSeBOwNvAj4O8tr2gpMx/4HnByS7k9JjPIATPaPruHMj7LmcAfgU8C36AkOLPZ\nhsBXKN/9Z1HuDNopM89p5vflOLOGRZIkDTxrWCRJ0sAzYZEkSQPPhEWSJA08ExZJkjTwTFgkSdLA\nM2GRJEkDz4RFkiQNPBMWSZI08ExYJEnSwDNhkTSlIuKKiPjSVMfRDxGxPCI+ONVxSDPRKlMdgKSJ\nFRH/Tnk44JaUZ37cCFwMfDczP9NS7kDg4sz8zgTEsA2wE3B4Zt7aNns55flAkjQsa1ikGSwink15\nEOC/A58H3kJ5OOAy4G1txd8HvGSCQnk28EFg3Q7zNgX+e4K2K2mGsIZFmtneD/wT2DIzb2udEREP\nm+iNR8SamXkHUA1XZpY/UVnSGPm0ZmkGi4g/An/PzB1HKTfULNOaWByfma+PiE2A9wLPAzYB7gDO\nAd6VmVe2rOO1wHHA9sArKY+PXwU4ktIk1br+GnhMZl4VEVcA52Tm69vW81zgZcBrgDWBHwBvzMwb\nW7ZZNet+I6X25pfAW4HTW9fZ4fPOAa4FvpWZ+7TNezBwPXBkZr6nKfsBYBfg8c1nugD4YGb+qMN+\nPDgzD2neHw/8R2Y+pq3cwc3yK7VNfw3wP8BTgDubz/yuzPxbp88hzSY2CUkz25XAFhExd5RyrwHu\nAX7S/P4a4Jhm3jOBZwEnAfsD/wvsCJwbEat3WNfRwJOAhcDHgFOaZQEOaNa9F7CkmTbcVdNRlKas\ng5t1vhj4TFuZj1Gams4H3gn8GTgTWGOkD9vU6nwL2D0i2muadwdWBb7evF8beD1wLvBuSoL0MOCM\niHjaSNuhfLZOn2+F6RHxfuDLwKXAfOBwyn7+cUSsPcp2pBnPJiFpZvt/wPeBiyLifOCnwNnAuZl5\n71ChzDwxIo4B/pqZJ7at43uZeUrrhIg4lVKbsQfwtbbyNwA7ZmbdUv4CSq3LdzLzqjHGviQzX9iy\njpWB/SPiwZl5W0RsQDmxfzMzX9ZS7oOUJGc0/0dJRHai7KMhr6Dshwub9zcBj27dXxHxBUpisT+l\ndqcnTS3WwcD7MvPjLdO/CVwE7EdJzqRZy4RFmsEy86ym4+17gRdQakreDSyJiH0y89QxrOPuod+b\n2oi1gb8CNwOb88CEpQa+0JqsdKmmdBJu9VNKc8mjgD9Qah9WptT4tDqKsSUs51CSq1fQJCwRsS7w\nfOATQ4Waz3JvM7+iND2tDPyG8vn7YQ9Kc9k3IuKhLdOvp9Qa7YAJi2Y5m4SkGS4zf9PUQKwHbAV8\nBHgQ5eT4pNGWj4jVI+KQiLgKuJtykr+ecuJep8MiV/Qp9Kvb3t/c/Fyv+fmo5udlrYUy8+aWssPK\nzGWU5qqXRMSqzeShfjfZWjYiXhsRvwXuotwWfj2wK50/fzceT/k+vozSVDb0up7SvLZBn7YjTVvW\nsEizRNOksQhYFBF/pnRsfTlw6CiLfgZ4LaVPxS+BWyg1IP9H54ueO/sU8rIO0ypGuOOoC/8H7Au8\nEPguEMAlmfn7oQJNR9jjgG9Sal6ub2J7H/DYUdY/XE3Tym3vV6KMR/PC5me7f42yHWnGM2GRZqff\nND83bpk23Ml1D8odQ+8emhARq9F5TJXh9Ot2xNb1DN2h9PiW34mIh3B/Lcxofgz8A3hFRJxHaXpp\nT+D2AP7S2k+m2c4hY1j/zXTeT49ue/8XSiJ2RWZetmJxSTYJSTNYRGw/zKxdm5+Xtky7nc4n12Ws\n+F3xNlasJRjJ7c3P8SQ5ozmbEtt+bdP3H+sKmv4pJ1PuQNqL8pmyrdgyVryjZ2tgmzFs4i/AOhHx\n1JZlNwZ2ayv3TUrNyoJOK2mSMGlWs4ZFmtmOiog1KbfwXkK5Xfc5lKaPv1KaOoYsAp4fEfOBvwOX\nZ+b5wPeAvSLiVsqQ/ttQOrze0GF7wzXXLGrmfSQivg4spTwaYLjmo+HWc9/0zLw+Ij4NvD0ivgOc\nATyd0qyyhLHX6vwfJclZCPw+My9tm/894KUR8W3gNEoz0L7AYkpfoJGcBHwc+HZEHAmsBbyJkije\n12E3M/8aEQdR9s9jgG8DtzXb2o1yi/lhY/w80oxkDYs0s72DcjfMzsCnmteWlH4p27Q91+ftlMTi\nUOBEyokVytgpXwFeRblNekPKnTT/YsWkoGOSkJm/AQ4CnkZJkk4E1m9ZZkzr6TD93U28WwKfpJzg\nd6J8t901zDraY/s5pYPvg7h/7JXW+ccDBzaxfxr4T+DVlH3VKe66ZdmbKQnH7ZTEZS/KHVvf67Cd\nj1Oan5ZRxpb5JPAiSiL23bF8Fmkmc6RbSTNKRKxD6Tvy/sz86FTHI6k/rGGRNG0NM9LufEotx48m\nNxpJE8k+LJKms1dExOsofUtuB7aljKh7Rmb+YioDk9RfJiySprPfUTrwvpsyAu91lPFiPjCVQUnq\nP/uwSJKkgWcfFkmSNPBMWCRJ0sAzYZEkSQPPhEWSJA08ExZJkjTwTFgkSdLAM2GRJEkDz4RFkiQN\nPBMWSZI08P4/5OSatmVdj6AAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119a62b38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#COLLBAR Collatz iteration bar graph.\n",
"N = 29 # Use starting values 1,2,...,N.\n",
"niter = np.zeros(N); # Preallocate array.\n",
"for i in range(N):\n",
" count = 0\n",
" n = i + 1\n",
" while n != 1:\n",
" if n % 2 == 1:\n",
" n = 3 * n + 1\n",
" else:\n",
" n = n / 2\n",
"\n",
" count += 1\n",
" niter[i] = count\n",
"\n",
"left = np.arange(29)\n",
"plt.bar(left, niter) # Bar graph.\n",
"plt.grid() # Add horizontal and vertical grid lines.\n",
"plt.title('Figure 1.6. Col1atz iteration counts')\n",
"plt.xlabel('Starting value') # Label X-axis.\n",
"plt.ylabel('Number of iterations') #Label y-axis."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Well-known and much studied Mandelbrot set can be approximated graphically in just a few lines of Python/Numpy. It is defined as the set of points c in the complex plane for which the sequence generated by the map $z \\mapsto z^{2} + c$, starting with $z = c$, remains bounded [91, Chap. 14] listed in [1]. The script mandel in the next listing produces the plot of the Mandelbrot set shown in Figure 1.7. The script contains calls to np.linspace of the form np.linspace (a, b ,n), which generate an equally spaced vector of n values between a and b. The meshgrid and complex functions are used to construct a matrix C that represents the rectangular region of interest in the complex plane. The plot itself is produced by plt.contourf, which plots a filled contour. The expression $abs(Z)<Z\\_max$ in the call to contourf detects points that have not exceeded the threshold Z_max and that are therefore assumed to lie in the Mandelbrot set; the double function is applied in order to convert the resulting logical array to numeric form. You can experiment with mandel by changing the region that is plotted, via the linspace calls, the number of iterations it_max, and the threshold Z_max. Also note that on some runs we may see a RuntimeWarning printed becase we have an overflow on z. This can be silenced with a context manager but we will wait to introduce detailed control of errors and warnings."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/phil/mini35/lib/python3.5/site-packages/ipykernel/__main__.py:13: RuntimeWarning: overflow encountered in square\n",
"/Users/phil/mini35/lib/python3.5/site-packages/ipykernel/__main__.py:13: RuntimeWarning: invalid value encountered in square\n",
"/Users/phil/mini35/lib/python3.5/site-packages/ipykernel/__main__.py:15: RuntimeWarning: invalid value encountered in less\n"
]
},
{
"data": {
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1wJeB077v/2E/2ykiIhApxtlaiXJwsUQ5Vhh0c2QE9Lsn4iHAp4GX4pZpbsnzvDjwHuBD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\ntnV0XT3PW8INZ3wRN1Hg5bjXizftOnMXJmU4o10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"text/plain": [
"<matplotlib.figure.Figure at 0x11a05bf28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#MANDEL Mandelbrot set.\n",
"\n",
"x = np.linspace(-2.1, 0.6, 301)\n",
"y = np.linspace(-1.1, 1.1, 301)\n",
"[X,Y] = np.meshgrid(x, y)\n",
"C = X + 1j * Y\n",
"\n",
"Z_max = 1e6\n",
"it_max = 50\n",
"Z = C\n",
"\n",
"for k in range(it_max):\n",
" Z = Z ** 2 + C\n",
"\n",
"plt.contourf(x, y, np.float64(np.abs(Z) < Z_max))\n",
"plt.title(\"Figure 1.7 Mandelbrot Set\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we solve the ordinary differential equation (ODE) system\n",
"\n",
"$$ d/dt \\; y_{1}(t) = 10 (y_{2}(t) - y_{1}(t)),$$\n",
"$$ $$\n",
"$$ d/dt \\; y_{2}(t) = 28 y_{1}(t) - y_{2}(t) - y_{1}(t) y_{3}(t),$$\n",
"$$ $$\n",
"$$ d/dt \\; y_{3}(t) = y_{1}(t) y_{2}(t) - 8 y_{3}(t) / 3. $$\n",
"\n",
"This is an example from the Lorenz equations family; see [H1] listed in [1]. We take initial conditions y(0) = [0, 1, 0] and solve over $0 \\le t \\le 50$. The next listing, titled Lorentz, is an example of a Python function. Given t and y, this function returns the right-hand side of the ODE as the vector **yprime**. This is the form required by Scipy’s ODE solving functions. The rest of the listing uses the scipy function odeint to solve the ODE numerically and then produces the (y1, y3) phase plane plot shown in Figure 1.8. You can try different values of the constants defining the derivatives to see what happens. For instance, change the 3 to an 8 in lorenzde and observe how the plot changes"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11c216240>"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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KxCJDb0E7XYr/+jOQmgKly+K/9yLeX54v2hxPu3ciTVsW+GmdMBIOtmyEKtVz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LbU4aFQLTtD++BraF9Og/btLNq3j/qSUHidZkDYc4Qv+pMciuuXKQWs34K7msUzIfdu8SJWpCQ9\nXtYtJiu/RSdGmH81CshXiNHnmbOyESlVwcFwSNYvhmxfC23IWNtnBoCbAdCHdgSiItmUtO7KzBMn\nZ6h2JCfLyrnQh3cBYmOgdX8L2rufEmUJDwMKFoVsWQl90miIIZNW5SpD+2khUNlufBfgD33sAETt\nY+qyypwF2ow1tveY+wvkdiCVEIaCRz+yx/pvoIqUhDZtFVTNRvzN/DgB8eOGQKISOEgCUC6u0Dr2\nhfbpVCBrDuhTJyJ+2iRGrL+CkudPETb3V+hjB0J2bYRq1BrapD+hde7/2hsRiYvjyG/CcGsjohq1\ngTb5r1QbEQkPhT5jCmTGZGsjYsmbn341HfuyETm+H/pn76TaiKg6TTnqNRuRDBmgjf+R58DiGck+\nT3t3IlTWHI6NiKsbZefH9llHEgCg/HpC+2o65MxRZimFPocaNBoqpxet4E8epBNqpRpWbx9VoRq0\n8T/B8vF30Oo2+4+RK5U1O7ShY0laP8i8J1XOF1CKSCNgleiacnkAHPmYlTUH/Tvsfr9mkKRVtpzA\nz0O17c77z5/k332qc0Rt8kvsy9mZDYe9VcOdG0RBo6PIgTHiN5IqmvNxRKPqNn/pDYMc2QOEhyVK\ni/+nVDoy8g8o5ewCVbsx5OB2SPteicKiVLuekLULGTlvjGKUZiH59cB2BsUBQOAVSHy8FU5X1epx\nZw4g7vJ5aEGPbeS+0hWIDFw6C5SqSClZ47Z8Xt3mVOmsmAutRSdK9c6fhDKD+/IW4Mno4ckT/84N\nm2U8AGga5O5NwDO7DSHJ6G4jhpnw4K1r1p2GxETTU6VafajSFdmIfPcJEBEO7e3xHJ08C4Yc3k3v\nkkf3bcQ0TeN4KG8BuDZsiejwcEhkOEMBw55zV+Jbi5HjW1dTDtzMD/LgLmT+75QW9hkOnDvJi3nR\nUtB6DyM3ZsUcKmEq1eDYy5gt6398Q1TpyUNHLsnXHxBKfvM9qPJVof/5PWTLKvIxls0GYmOgj+wF\nbcR4qIpVoU38hTvrM0fJsA95Cv2LkVBdBkDVb0Hex5Cx0A/vduABhP70GcmqvYbQa6Rtd0jtxtDH\nDGCD+Of3dJA9eYgoyfEDtpm7xQL15khIm67Qxw0BHt2jDLj/u9BqNU78+8yTn2Tdo3shy/6CPmEY\nvS4atU0TwzR5FgTZsgqyZzOinJw4imvS7h8T9ie3rhGxMFHAbDmZJ2NwF1J87vkT5IbYOXyqhq2R\n9a338DQ8gvLkxTMdflNJlpMzVK+hHN/tNxrTlp2hSldkw5Bc5faGNuB96F+PcrhZVatPu3JzxAOw\nMR88BnL9EvTP3gbi4hiMmcGZgZexcVC1GwPRUZDdG3hMjdvyvzTI+VFFSwEVqnDMWLc5fw8FipJQ\nX7eZVaIrkWHkhojg/9i7zuioqra7z0kjhCSQ0HvvvQtKEaRLd2jSBQHpvXfpRZAmiPQWRbpIB0F6\nEQEpUqTXFALpyTnfj33n3pmQBBX8hHe513K9L3dmbqbe85zn2QUOMRVImYqGhI5RE9lyky9itySI\nZ4MvSlWEjo0xDRFFmXd5XUno+ZWsCH3ioGWVAPBzTOENhARClHk36eDDkwctbxGH0dPrgNaa46li\nZd84Dpgd/3VG3hCISjVJynSUzNlvq8ZKVm9Z43z8nfeB58+4SNplsg5mXqJEOcBhXq1PHbJuc/cA\nCpWAPnOE9/v9AuWyiNeNsY9qLpw2d9ey4ce88fffAHd36EtnnR0C02UC7v5hGerYL7z2i4BxX33r\nuhVxf+UCeQ+G/b1aMouFSP/PgcIloX/4FmrIJ3wPfP3oHNq+Nxf9jzpAVK4NpPBGzPnTvACcOUpj\npTwF6Vlw5ijJf/mLkjOzYwOJXAYXRi+eCR0dSe192DO2t4OfQA6bQW7HmaPskDgQP/WmVSwGP+nH\nwsx+/NgBqE8bAqn8IUfMgChZHvrbJZQ6Vq/P1zdnHOK+HMe2/mfDOJe223hnzgG9aj7UvAm0bQYg\ny1eBnLDQ+e8f/wlqYEdKm8E2tFy4yfScUV9NgX4axNbwNaNLcsLhO5CWMmDxIQtcvWQW4ro2Nr8H\njhBCQJarDDl2Hv1xvlsGNb7Pi+ZQrwAd9ARq9VdQQzpzfFerCfzmfwv5hqQO65hoqA0ruNgbhYio\n2Rhy3LyXFiI6KhJqxTyO3ey/B29fyJ4jmRfkkYyS3XF9Xl6IFCoB+Uk/Op7+wTh7OXASEBxIfkgi\nEO17QVSs5lyIuLhANOtIuafD6EE07wzZdQjUmoUc/xUqCdGmB/TRA+y45C0CUfY98op+PQFRrznk\npMWQjVr/o4GDslJN4NZ1KgABwDeV+Rsxk8bthoxREVbMA7iB0/G5M36pzfcQAPlmDhBpMzjnAGXN\nlWgxoh/fJ6/N6B7ryAhGY6TJwKwuoxuZGOxdEeQt/MK4/pVx8Sxw7xakcf15E/FfMfKGQKTPDOQv\nan0hHW9zVKM4OC2KTNmArLmgjuyFNLojyrA4BwzpsINCRx/d73ze0u8CN66Qza41tGMhU7MRH3Nk\nP9uhIUHWTtAofPTRfUDuQpb9vL2wkBL6zh/ciQCm4ZNWxrjGXh+FhrBggDGzTelPs7RLvwLnT0O2\n6AykzQD11VQraG/aMsg6TUmg27mBqqJ1X9Np8eJZwNUdKFiCnZrYWJJAb14FUqdl9+TGFR7LmY+j\nsUO7gLhYFoM3r0Gvmk8FTM0m0Ds3QM0eA/lBA4iOfWgUFxJIUyMH6K+nQzRtZ/kbGFAD2kGfOQbZ\noQ8ddc8c44W7fW/e4dcTHO0EP4GsVAtyxEzA24cX20IlgCsXoMb2Ni2nRZr0kMNnmMUDACAqAmra\nUKj1yxj4JQRks46Qnxt8oSsXoBdO5c49f1EqeBZNMy/gQgjI+i0gpxs74thYqD4fQ+37AQlBJPfi\niGn4dMDdA2rKYCqJHO21/yL0k4dQK+dBDesMffwnpiJP/JrP6w0oQgBAX7sENao73YsBdhiGToNs\n2i5JF1UAVpHx04/W5qAou2KiSGlopRC+cRXUxIEJKzQcIBq3gciWxwqhy5Ybcuw8qCmD+XtMBHLs\nXEYMfL/cOli4FEc86xZbx3Lk5XdHxXFM9OCO+X3VC6eweKlQjZuXo/shqtaFnLAIsq4tSXvz1wZD\nUafvGMVgci+OOQEarAFW8OEjBz6lMfJwKkYyGDb09jFPyXi+G4YztLKPThq04jmN6AsnJE8BXLvk\nNKKJPLQHiAwH3Nwo6U8ioFLfvMZrE15/VwQA1O7N3MjkLfzyO/9L+K8YeYMgq9SmuuLOHy/e1oWW\nzWrZl07HRYX32Rmxz9AdJbWAczz07Rscn9hvK/EOkMKHevncBZyKFfEufxD6+2VGaJ67OfJxvPiK\n7Hm44MXGQBhjHty9yf9SpQZcXC0OhK+xY4ofzw1AX78CkacghBBQ+7bRRbbkOzQhO32YYXI1G0EH\nfA01vi8VKDny0mHT1hGiSh2IQiUhU6Yib+XBXaqQ3NypQnkaRFa9EBy73LzGi0rm7EBEOPk66TMB\nBQ3S5pkjtNz3S0Ny3rVLkMOm84Jy/jTJrQ7GRXrJLDortupiXvgAQH8zE3FjekKUqQQ5ciYlvcvn\nQDT8mOMjAGpQR6gTByHSZ4YcMpXdmgtngHQZgWSeXPC3r4dWiqmk9Vsg5efzrWAvAPrH9Xxf7hvv\nddqMkF9thDBIzyQYekN07MtRwege0Eb2BQAIH/qYiOadeb7VCxDXqT506IufFcBZuxw8hUTbX45B\njegKtX87tGN+0Uug79+G+mYm1LBPoU8dhqjfEnLS/+PC9ifA3Jevya0wNgKiXjPIUbMpTU3qsUpB\n/bjeKjKEZCRBqy7kRfmkpBz4i1EIWzE/cb8NAEjpD9l1CGX3hsxWtKQqRY3slujDRKVaVNSM/Ixd\nVPvxD6n2sitEeL4ukO17Q309A/rbbwzflibQ3y7mmLZSTbogH9lLpdv4+SzGvFIk9Kf/EYhkySnX\ntQfWeSa31G3BBifNKEYcCw/xQQN2dh2PGYt+fNmyHbJqXV5L7XyRcpVJRk3oeZWrxDFVcW5ItNaI\n3PE9O7N/XCV/LSlVlV3Om8wTolSFRO/3d6Af3AHOneSoM4nn8G/jv2LkTUKxcmw7JtAdgd0t7/I5\nZqsYsC82+vhPFolx+7fW4wqXstxSASpF7I91c6M50ZG9bCFePGupY+xsdIDcjMKlaRBmf6xdChwT\nxaCp65edkjMRHsbFP2tO4KqhNLDPKu07FscfRvhzwCclybBXztO4KCIcevMqjjYKl4KaNYbmQa0/\ngxwylYz/fdugAxbzf08cRMyvJ1mEeKVgERIeRvKY3do9IpykQaXoCXD3lsG+z8yOxHnDwdHNHXrF\nXMoOG7eFPrwXauZIyBqNOFK5donncszVuXIeetUCFo6Osdx3/oDq0giAgBw8GaJaPeYHpU5nOu/q\nhVMRN3MUICRkqy48x4M7VA/lL0ry6+wxZgfCLX8RyJkraaNtx92bUCO7Qf28h14LUkJ26s/3CmwD\n68UzIPuMBTJmhfpiFNSqBU7fJ1mtHuSMlWYAourXlkZrCViOCykhK9WEHD+fwY+r5kNNHAj9Ei8M\n/cfviJs/kZ2Gi79CfNSBxNTaTV9IsP43oS/9CjWiG2ftACW3I76gad5LHGp10BOoGSPIwVBxVF5l\nyQ45fCZklTrGjvwk1NiewKWXqGVKvgNh68huiFHIy5GzqDJbMCnRh8n+E4DYGBaidmTKxrA8ewQB\nQAdVw1RRje/NZOMOfaAf3KHJWdZcQK78LNhdXCCHTIVs1+vfiw7wS2PJnMPDLDt3+/grJbutcEjU\nFYVLAo/vO9m8i+LlnEeSV+KlnBcsbjqhIk16iDTprX/Hg75ygf5J9u/vH78j9voVCO+U9MIpXzXB\nxwGgg7CdlFuhWpK8kr8DvWcr4O0LUfbFDLQ3CW9cMWKz2brYbLazNpvtqfHfYZvNVsvhdg+bzTbX\nZrM9sdlsz2w223c2m+31OsP8SxCurhAVP4A+uo+sb8fbpLRULptXW8e9fYEiZaAP7oCoYYxWdmyw\nbndzc8qG0T/96Nw5qVTTkhZ6eTvbVxvJu/rofhIbb9+AvnWdtxl5J/rQLj7ut1+cDXpcXJlInKsA\n9LWLPObrxw6LvRhxdbNmupHh3OU8ukcL+TwFSeiKiaVE9ttvmP7bZxzg4go1pieN2YqWhWjSFqJq\nHaBIabjmLkCVS0QEixCdiH+MVixQtGIx9eAO/7+vH3k3UZEk9Z04BL1/G0nCvqloCvXwHhf4FD7A\nhdNUNtlbwwDUnPGmC6Uj1LBPoQ/tgvyoA2TPkcD1y9CHdptBiPjtDFTXxtCBjyFKVYQc8QW5KJfP\ns+i5dZ1jm0u/8jPwTA7ZqR85K44vbeksSh4NhYzImQ9y3nfk8gDMvynxDpNPD+92GgUBgPD2gcuC\nDaa7pf5uKVTnBtD2nWc8CG9fyHY9IQdN4uL3eT+o1Qugw63vmdYa+vJ5xM0cRdXSnT9YVE5cCFm9\nPoSDI+a/DR0ZAbVqAdT04aY6TDRoCTl8JkQSNt7m408f5ojj9wsmj0HUbMyul91Jdf0yqNlj2a1I\n7DsK0FU3fWaOSACgWFnIiYugxvZy4oc5wdWVo5tpQ81FDgB/I75+TkGaomZjyP6fQ637Gnr1AogK\n1SEq14JeMRd4eI+d1ZvXOIL4uBujEF7SEfrHYd9IANBPgyF8jU7Iowd0grYTWW9YxQhy5HUaQwMc\ne+pjxgYrW26S3e23la1EsznDEVnUaMjzGdc/J+QuSG+RypZ/iN73A2TaDNDPQoB8RZJ0BdbHDpjE\n2ddOXA17Tv5Vldqvvch53XjjihEAtwEMAlDK+G8vgE02m82wI8UXAOoCaAKgEoCMANb/C8/zH4Go\nVBOIinLqQpi31TVkZjs3OrXDZfUPORb5/YLZ+tcO/hgiXlCaI0FOpMvInffhvfQuObwbOsaZ0a03\nrCBPwielVcHb1TMR4UwCPn2Eu+fcxsfk6cmQvNwFKK0NCWSLME0Gay6eJr3FgeXfJasAACAASURB\nVImLo8rG3kpO6c9Zrn1GfHAXOz/Bj6GXzeZi/dkw6Id3mQGy7wfg1nXo58/ISI+fL/FnYO/mpPCh\n8ub4ASBnXsA7JbkkGbJQsrt3K9TiGZBtupNwe/FX+pw4zIT1usUk6Lbv5WQ9rVctQNzEASQhDp/B\nMdmSWRAtP+UFEYAa3JFyyTTpIQdNhqhSm6O4NOlZEM0YgbB1i83vgCxXGXL8Amfb/WMHuKs3jNOE\nmztcxs+HMGTgetV86C1rIQdNAbxSMHZgw0oqBwzI92pQWmxc3NXA9lCb1yTYJQEAkbsgF2xbB+jD\n+6CGd4U6vBf67AmoyYNYyIUGQ3QeADluHiWfb5jfgb5Cq3693+DM2Lsh9Zq/VDmkoyKhls+Bmj+J\n32chAB9fyD5jOc5wdWPHZPowy/Y/MaTNQAXT/u0mT0W06Q5Z7UOoIZ0SfZio0Qiy95gXRjeieWf+\nRn6zRnOy33iInHlp/X7nD4h2PaEDHzH+IH9RIHU6FvyFSvDzqlzrteek/C1ER5GUDpCPZhDl9bWL\nQI487DqFP7eSxMHvvyPx1E7yNuXP8UZNoo6Nmya7w3Spd6H3bUOC8ExOhaHds+R5KPTJQ3AvWpqB\ndAko1OzQWlud8Bx5revqa4I+tBNQcST4v+F444qRgICAbQEBAT8GBARcNf4bDuA5gPI2m80HQAcA\nfQICAg4EBAScAdAeQEWbzVY2qfO+LRD+aYAipeg4GO+iLzw8SM4EiaUm8hYGsuWG2rURsjdNshxZ\n9SKVPzzetTIO9J4tTsWMqFSLjpa5C1LRY8xFndz/Ah8yw+TYfnPBEqUq8rZknhyN3LoO2bgtjz1/\nxrZnpqz8t52EmSWnOcsV6TJaFwyflGyz2jsl7h50cs2YlVwWV1eIcpWhls1h27p0RagZw+m02qQt\nF2zfVIh78jBBTspfwtNgzqF9/SgbfBYClKpAaeuxAxAtu5DoOXEAkDodZN+xvCg+fhDPY+AG9JJZ\nkD1GmkUiAOZyfNoI8PCEHDSJo7LVX0FkzgbRtD0AQM2fxJwSFxcSRrsN5XsVEQZRqiLCv11Kjwe7\nAipdRsgxc/g+2BESBDW+D9TuzZYSqnwVyJnGzvjZU6hxveltUb8F9I71UBMHmLwTAJQWz1pjdl/0\nljVJd0lcXCCrN4AcO8cwYvsCas444N5tyB4jIEfOgizz3puxqDlAR0VBrV3EqABjBCDq2EgY/jPd\nkFvXSFI9spfdrKgIIF9RyJGzzCgFff4U1LjedPFNyvG5VAXINj3YmTHC8OSImcC920mqZeSAiYCU\nUNOGWQcz54Bo2t7ZcyR/UcipS5lBM38SA/Xqt4D+bgnJ3qUqcGPz4A4zmDr1dzJD/NcRFUFbgrg4\nflZ+qfn9vnaJ1zDAafQlKtXk9/XqRetY2UpWhxagy7IDRKasFiHY/vmdSHhEg/OnIKrVM/kY+vAe\nQCnoiHCmbMeP+XDE9csmIfa1d0Xi4qD3boUoU8lSNr7BeOOKEUfYbDZps9maA0gO4AjYKXEFYPYe\nAwICLgO4BeDNiiB8BcjKtdgOdJCcmbd1MJjtSx3cFoVgOuZvv1gjF8Dpx+ZZ9yPrJEGPgXOnrceX\nKAd4+0JfOQ/kKwJ9YLt1m5F3o9YsZIX//JnZHhbNmb+gD+5k1+ToPmfGeFws/UjSZbIY6wWKctzz\nPJRjgyeP2IlJ6Q8dEmR5kQgJBD4GUqelpXS23NzZREVAVqsP9fV0IF9RiOr1oTevYbvVxxcuGbM4\nZeH8bcTFsThycwOiooBTh1n0uXuwS1L6XSaiLp0NfXAXpZUZskCf/BkoXp7kXQNq2lCIujareLMf\n7/sxcPUiQ9Ta94I+fhD62H46XYIdLNXdBh0RDlGiPGXG7h7Qv55Asqp1gD9+J2nV4GgIN3c6rnZ2\ndtTU675mNo29cEnhQ0lvLY79uOjdgRw8BYiOghrfG+qnHU7FsCxXGXLWGnMXqga2h9qx4YWCWcfG\nQB3cCTXdWDTtvKDoSM7Vo6Ne5VP5R6Cv0UdD79nCA3alTKOPX9q50VpD7dvGwjTsGR2Hw55BNG4L\n2WsUSapxcZQEzxrDUYBD9yk+RNP2EPmLWRkxmXNATl4MNXMkTfQSgfx8AdTi6dA/Wk1i8V4NwD8N\niwz7sUatIVt/BjVnPPRPP/LvefsyeDNTdhbNpw5DFC8HOWYuzRHfIOjICBJV02akvDc6CiJHPuDh\nXeB5KDuxgBPRVFSqBX3miPOJsuWC/tlYRoyOpHn/ujZ2LAxejXivBsfRCX1uBYrRzKwcOSGMBvgR\nyF8EUSd/pgWBR+JqK7Mr4u7hvJF5HThzBAh6AlH9w9d73n8Ib2QxYrPZCttstmcAogDMA9AoICDg\nEoD0AKIDAgLiGyE8NG7730DhkoB/WqeiwA7hm8qaiV61PB5EqYqAXxronRu5QwIYuGbALW8hylkN\nKEcWvasbxLvVLSLr779BGw6DonwV3un8acA/DZA9D5TxIxZ2ohgAUagEZ59am9wEAJSylnwH+pdj\nDPvLX5T3uXyO0mStmPuSyp8jEjv3IiTQkgDfu81MCUPFok/8xOyMUhVJMi1ejkZDv/2CuDs3k5zB\n/2WEh7FLksKHLe7oKKBgCTqxhgRCfNSBzpSzxzBUrq4NOHuMi7bDbF1/PZ3Jvk3bmzwCgB0s9f0y\nyArVyEOJjIBaNhvyU6OgiImG6tkc+v5tiLQZyDsoXh6Re7cBeYsAyb2gJg2CcvBHkGXepTzTkYR8\n9jjHNvYOlRCQTdpCjqY6Sx8/APV5P8ieoyDKVYFeMRdq/kQngp9I7gWXacssqed3S9glCQ3hiGL3\nZqihn0Ivn8MMjmHT4bJwE+S89RD1mtPldlR3qzD9l6FjoqG+W+qslPmgAeTIL/4UL0KHh0F9NZnJ\nuD6pzPGBHDARsnYTCCmhQwKhZgx3KhISgkjhw8TcqxdpEQ9QXdRlEI3sHJQwTihSGnLsXJrXOTqL\ntvyUm4SzVrKs7P85RPrMHMuEP4do35smgof3khvy+L6RwTSQcvT/R5XMn8a9W4DWzE66domKsmy5\n6HcjJJAzH3RMDK9FdmTN6TyiqVgdEMJS0cRTmIgPGjh3UYqWSfBaDIBKmfdqWAXHxbMc7QgBe3RB\nYtBhz9hJAyDeqcrMndcItXszPUvslgtvON7IYgTAJQDFAJQDMB/AcpvNlrhIm8tWwoPstxBCurAa\nP3HQ2QLegOw/AQCgJg+2HuPiAvFBfS7U9qjyoCfOZNVqDhXyb2dMyS0AiPdqcuGNi2WXxCCyClc3\nkwmuD2yn4+L5UwzGA8x0Sv34IZnqv52BbG4lVurTRxlFH/YMuPQrGfhpM5LTki03FTEXz5Kxf++W\nqfzRQU84qomO5o7E3QO4dY1jnqP7uWBuXAEULkW31eM/AYVLwSV9Jqc8itcCpbij9fDkonDpVxZ/\nd/6A3rkBokUnwM2di1rGrJC9RvOC9DzUycpdH9wJvXkVbeAd/DP09vWIG9aFjx0+A8iZD2rRNIhm\nHS1p7sjPoA7vgfBIBvFJX3h16MWix82d78GyL6GWz2GCMUBp78hZznyh56FQkwZC7dli2cNnygY5\nb72p/lFDO1Mi3XUIfU7G9HLiHwGArPA+Rz2GtFj1a8MOzrffMNxszBy4dBsKYdjoCzc3yHrNIMd8\nSd+Y2WNoh/6q47RXgP7jd45VdnzPA/5pWUTYOr7UN8R6fG9yeVKlZrexYAkWMvbd+e+/0SDt3q2k\nxzK58sN3xAyor6aYTp+y7ziIrDmhhndJ9GGidTfIqnUo27XD25fy7dVfWcey5YacuoTqm/kTgQLF\nIGo2hl4+lyOPwqX4+0mdDnLkbMgy77709f9b0Hf+YNGRMQtVellzQrh7QJ89Tr6IZ3KG8hkQlWtx\nzOoQaieqf+gcHOjYgfb2hfDyhjIMJkUdG0c+gc5JvgBoCxAZ4VRwqP3b2bW5eQ3JqtZJcrxlL0QA\nmOKD1wV94wrtCN5gk7P4eCPt4AMCAmIB2GnLpw0+SC8AAQDcbTabT7zuSFqwO5IobDZbCwAtHI8V\nKlTId9SoUfDx8UmUlPdvQdX7CIFb1sDz7FEkr2dzvtHPD/b8Tt/YaLikZVNIfdgMQVvWwePwbrh0\n7o/nC6fBde1C+A4YDzc3N/hXr4fAVZbKwf3wHnh/0sc8Z0ixstDH9sOtWj1E7tqEVB17QXgkQ1z7\n7gg6ug/6u6XwX/YDAgO+geevx5C8QUvoBs3xZN3XwNXf4JIlB1xP/QzvXiPwxB7wFhEGr/BnCE+f\nGW7nT8K7UnU8K1EW0WeOwS9NGoQWKQX9+wWk6NgbwSvnwTvsGUK9UsDzWTCivH3hHhOFKCnh4emJ\niPDnSObigoiIcHi4uiAyJAjJyldB5M6NSFalNiL3/widMhWEV4oEi7hXRvhzegl4Joc+9TPcipSC\nDnuG2OVzkbx5R8Tduo6ohVOQrH4LJJu8EKFTh0NdOAOP6h8i8sAO8mGio6G+GIWUkxfh+VdTEWuX\nHz66B9WlEfyXb4cYORNhK+YhYt1iJKv+Idx6DMOzLz+HXjILrtcuwbvHMLg3bAnXHHkROn0EREgQ\n3Gs0QOS+7XC5dxM+/T83vxPoMRSRJcvh2YxR5svQaxfB/fZ1eHcdZGWGzF2LiJ2b8PyrqVALJsGt\ncEmknLYEz+ZOQMzMkfBs0BJezT8xJa3KRSC8QQtEfL/Cen+Ugl/XAYkblfn5QY+bg6ifduL50i+h\nR32G5B93RbLqHzo7+DrAzc0Nfn5+Cd72d6DjYhH+/UqEr/3aPJbsg/pI0bb7n8pP0VojYtu3CFsx\nDzKFL7SnF/SzEKTo2BvJajcheVJrRG7/Hs+Xzobw8iapOhF41mkKj4rVEDLIKuD95gUgYucmRGxc\nlejjUk1fiqijBxA+e6x5zDV/EXiUr4Iwh9iAZDUbwqtZR4R+OR4xZ0/Aq9WnUMGBiFg5D27FykJH\nhiP27DEkb9YRyRu3/seTmV/18wy9fR2xWXMgVZq0CLp6AckqVkNyD3cEXjgDr4+7ILmfH55dOAW7\nWD1lkzaIPvUzHNJq4F+0FEJGdocC4JojL2IdVDc+PYbBNToCQUYB7te4FULnTkBCpaQLAJey78E3\nD/fJcYGPEPTrcbhmz43Yx/fh06gVdCKvVcfFIWjfD9AAPN6tDp/8hf72e5IQQpfvQEzaDPCrUvMf\n/UztPJkxY8bMvHDhwtN4N68JCAhY8+KjEsYbWYwkAAnAA8ApALEAqgHYAAA2my0vgKwgpyRRGG9K\n/DemJIBToaGhiIlJfI7770BAlKqIsM1rEVG2ygtMftl1MNT8SQiaNBguw62LDyrVRMTOjZATebGN\nProfgQ8fwj9dOgSHhgI1GwEbuIBEbl+P6NofmRdhXeF9Eier1YcOe47AnVsgK1YDpBt5GOHPEfzL\nSYgS5RG2/XtEVPyARMRUqYHgJ4hL6Y+44wcRc/8+vTqMFvGzHRshSpRH5E87EN20A1CkDNSOjQg6\ncRg6V0Hob7/BUzcPwDM5Qn85Dp09D8LPnQbSZULEtctA8hSIfPwAUAoRxvgo8t5tIG0GRJ46DOTK\nj8hDu4H0mZjw+ro7I46IiWb3IYU3Yi7+SjvpQiUQvnohnVsbfoyIzasRceUCZLeh0AGLEbl7C/kl\nN66YO6yQQZ0g+4wBDuxwsuEObFObRNT6rSD80yNy5VxE3rwGOWAi1NQhiPppB6LOnkDq+d/iefos\nEMOmQy2YjMi92yCq1EXsmSMIGtABsusQCEOJhAIlmIEzYwRdbwFE/bwHUVcvQX421CIql34PMkc+\nqMGfIOb8aQR1bQo5cRHEiUOI2LQSEWeOQTZpy5HbwZ2AdIGo2QiibGV2CQAEtq1DtUxS8+8iZSDG\nzIH+bgmefzUVz/dshWz9GUTGrC/c1c/PD0F/MeU1MehH96EWz7B2xcm9IDv0QUyxsgiOiAQiIpN+\nfNhzkop/OQpkygYV9BjwTA45cBIicuRFRHAwM5ZWzoM+so9dvyScaUX7Xoh0cUXEsK48kCMvZK9R\nCJo0OGEJqQE5ZQmC509hirX9XJVqIi42FmFLLVNE0bobonMXROTgzpTLd+iDsIM7SVYvXxUxV84B\n0dGQvUcjqmAJRD2Nv5a8frzK56mVgjp1GKJidQSdPAIV9ARR+Yshcv8OIDYGEQWKI+LhQ6g91gj6\nqUdyqB8ceDTteiLw9k2oCySsOhYiAPA8Wx7oNST7ijLvIfjhfagzx/ACXF0Rd+cP6BadzdejNq8D\nXN0QGxQIFC8HnSZDoq9VnThkcvpiqn342r7jAGikd3gvRNN2CP6HP1M3NzekSZMGo0aN6gPg9Esf\nkATeuDGNzWb73GazvWuz2bIZ3JGJACoDWGl0QxYDmGGz2arYbLZSAJYA+DkgIOB4Uud9GyFqN6Es\n1nH+aYfdBO3mVafFV7xfjxHeP++20nAdZIT2Y3ZoxzTfomXJVTn1M3Nr9lrtfNMB9qvJnKk+fgCc\nZv0nuxvclHMnARVHL41WXa3zXjkPkS0XRzUXTtPR1S819NF9NCOKiwUu/ALkKQR94TREnkK8YGbM\nAty7RT+AR/ep2rEncoYEcUTx+AHDsITk+eNinZxJ/zE8fwYkS8a/ffU3iPJVoH89AX3yEES7XjQ6\nmzGCWR0NWtIsKW0GJx6JmjkKokAxM4/HPD6qO/Tpw5AVq0H2+xx4eA/qm5nM6QGAp0F40rIadEgQ\nREp/cgHKVYbevQmiYHEgYxZyURyTVzNlgxw339my/uFdjn8czez800Iu2GDKFNWQToCPL1/Tzas0\n8tq7lQnKk40E3aw5SYg1Mov0wqmIG9sLOipxsqpI4QPZrhdf07NQqLG9oTauNMdMrxNaa6ifdnDk\nYS9EipRmpkyxPyfC0zevseC6fI6f4b3bLB6GW/wSHfgIavJgK18qMhF5ubcvPVluXSeXCIBng5aQ\n3YdD9W6VeCGSKRvktGVQA9s7FyLNO5Fr4uApIgdMhEjpDzVhAODmDtm2OyX6924Z/jkH6eo6YiaE\nodB743HzKvOripQmB8Q3FZ2jTx4CcuWH8EvjTFyt3ZTXG8cIjdLvQe80iMDxMnTER+2BiAgzwVfU\n+chK842PXAVor57HsB6IiiQZ1YuheLJm40RfhlaK8RUAULQMhEPe1OuA3v8DO7gVP3it5/2n8cYV\nIwDSAVgO8kZ2gwqaGgEBAfZVsw+ArQC+A7AfwD3Qc+R/DiJzDlbYP3z7gs22EIJZCaAplXk8lT9l\na3s2QzRuw9s3rrQ4Ail8nCRkevu3dD0FaLpWqzH0iUO0ir913QqJMhYnhIfxB5e/KNSPdOZ0IkgV\nLkVVQrxZqb55lfLjfdto4FaOhmLwT8PjR/dRAnf1ImeukREsMJ49BSAocUydjsRWgNHgRuYNggNJ\nWn0aDB0d7RSO9Y/iuVX86KP7IYqUBsLDoNcvpW+IdIGaNAgiT2EWc/ZQuRKWQkGvmk8VQIc+ppET\nYEh7N66EyF2ANvReKaDmjGeCsd2PZEA76JvXyOtp25PJwId2AR6eTBddPgdq7SJKIEECquw21Pze\nmM9h0TTez2685OICl37jzQJUL53NxGBHLkVIIItBA0IIyLo2hvkBwO0bUN0/cjaeSgAiXxHIUbMg\n6jSF3vE9OSrxnTBfATo0hEqiFXNJnAZox95jBITPn5M7qp/3QE0eRFda/zTMc6rTlGoZb46k9G+/\nMFwxNNhy+00IWXNCDpgAFfCNqd4RnQciWfUPofq1SfRhompdFiv92zof7zwAeu0iK9I+pT/kpK+h\n796EmvM5UKAoRO2mUIsZRSDyFiZRvWI1yAET/j0X1b8B/etJdmhz5oM+/TOvURHhwIUzZqK4qYgC\nIGo0dM5YKlYWcJEWcTXepkVUqWMRVTNnB9JkSDy08Mp5ZznvgR85xhVgYZREDg1+PWHmfMnaTf/0\n6/8z0FFRVElVrP6nxo5vEt64YiQgIOCTgICAnAEBAZ4BAQHpAwICHAsRBAQERAUEBPQICAhIHRAQ\n4B0QEPBRQEBAAuyi/w3Iujbg0T1KRuNBGNW3/ulHc8EB+CNE0BOqT4yFK/qYw+7Xkcj6NJi7B/tt\nFatzx3DjMpArP9TWdSw4hIAwPET0hhWQtZpwp2J3A23Xiye4cQUIegx96md6YxjQh/eSTHbhDPSD\nu5TChT8Hzp0y83VE7gI0Pgt+Yo6F4OpKJ9Hnz+hSaB+nPQ+1ZMxREZZkNAnZ5D+C6Cg+T7803KGl\ny0hL/yWz+DlkzUlZZmQkZL/xVCzcu23Z6QPQP+2A3vE9ZN/xJLYaahu9LQBxc8YDqVJTIZWnENS8\nCRBV68LTsJFX4/tAHTvAYqBGI8jPhjMr6M5N5ors2wY1e6zJExJSkkzac5TTy9B7tvB5GnbZ+upv\nUIfiXYijoyCnLYNo0x36yD56kjiQoAHQqO2rDaYKS03oD7V0dpKZNcLNHbJ+SzrOpvCGmjqENvWv\nOG7TZ49DjepuKUqy5oIcOw92O/aXPj4mBmrlPMroM2Xjdy/oMWT3EUwSli7suuzeBPXFaMA7pVUg\nJ4RSFSA/HUhSq1GkyeEzIXxSIrhHi0QfJtr3Ztquo9mZT0qa/i2cah3LXRBy9JfQe7fRTfX9uhD5\nirCQzF0QSOHNOIXmnSA+7vbGGc4lBa0U9LH9EMXK8LoT9ASidEXoQ7sBASYI37lhvq/IkZeFyrmT\n5jlko9bOZpLBDuqjitUZ8GmMsGXjttAHd1idWEeUfAfwSmFFcURHkQidLhMQ9CTprojWUFuNrkje\nQibZ+XVBH9sPhD1nh/wtwxtXjPwHZ4jseYDCRnhbPEa+cHMDDEMdJxv3zNk5Ztm5wZSIhk61ZL4i\nUzbTyAcAE1/tu0Y3d1ofH91PFc31y1bBUZWGWvrEQSBXPiBLDqgfqUYQFYx47NAQ5ljs3Og8Enga\nzO5FCh/o/T9AZMrKxOGDOyHKGD9qw1pdnzkKUaoCGfJ5C1Na6+rKYiQkkIt1UrvP/28oRTVFmvQ0\ni3JxBfIWYiBe/qJ0tl06C/rSr5TvasVgOMei8O5NqCmDIQdMIA/F3nU4exxqYAfA3R3ys2EQFatD\nL50FkSyZ1bn4ejrUBhqZiWJlIIdMASLCOKqr35J+JBMGQD+4a/45UaQUuxhpHaLKr5yH6tsacT1b\nUKkV9BiiY1/Iud9a3Zj+bSFS+UMOnUrr9/F9oeKnQUsXyI59OYqA4ZfyaSPohBQJjo/LmBVy4ES6\nhR7ZCzWqO6ISiWtPCjo6CmrVfKg5402Lb1G7KeSQKRAZMr/k0cY5ggNpp/7zbv5W7t0EvLxZPBQr\nw/vExpIfsm4xkDmbaVCW4Gv7sAVkveaU4BqdOzlpMTsY04Ym+jg5aDKEVwrKce3IlA2yXS+ouZ9b\n5y9fFbLnSKgVc6B3bYRo1pGL67qv6V/xNAi4eRWy5wjIah++0YFpCeLKeZoKvluDoxP/tLzO7NsG\nUfo9CJ9U0PuskYps19N5xOLpBWTMykBLgI93gGjazipUhADyFk5cjv3bLxCVapmqK31wJ79nrq78\nPRnfj8QeC8MX6LV3RbRmjlKxshD2HLC3CP8VI28BZF0b27C/vEikkh/T9lmvXuBsUlWjEccsTyyR\nkd0aHADkBw2tk9y96bSDEJVr0eL47h8coWwzUkKTJbcyadYvY2fmtzO0PReCSaAAC49b14DfLzhJ\n1vTuLRDvfgD9827oyHCIavX4d58/BYqU5uJZ9j3Ow7PkBJ48hPBJycCr9FmA6Eiakb1OH5HXiccP\ngBS+/KyePOK4bMMKwDM5eSObVkHv3UZzsXQZoQ/tovGYw/hDjerODkq6TFZBEhJIx1YVxx1tw48R\nvu4b6HMnrRC8HwIQt2ASu1iZsnG0ky4T9NZ15B4JATWxP43tDIg06SFHzACKxrt4RoRBlKsMOWo2\nZPkqEO4ecBk+g6MngIGFe7dBDpsOUaI89OIZUMu+fIEjInIXhPxynel3ogZ/Qu+DJCCkC8P6xtCr\nJHTCQKhF08yOzcug796C+ryftRD5poLsO44us3+yE6Avnyc/JOgJOQEXz0KUeIfFjGG5r8OeQc0a\nTeOs9JmB2wnEyttfU+cBEHkKMq8GADJkgZy1hh3NJV8k+jg5bj70nRssquwoUAyycRuo2WOs89dr\nBtGiM+937iREpwHkkOzeAlG1LvTVi0B4GOSgKRCFS/2p9+BNgz64i9+j9BmhTx6EqFqXI+TARxDv\n14MOD7OSbwFy3xy9dz4dCFx0cFl1LIwz52C+liGHFh93pY16QtLzgiXoc2JIZnVMNIuWnPmA239A\n1GiYpLuwsnNFsuQACpX8629EUrj4C3D/9lsl53XEf8XIWwCRuyCQrwjUtoAXLeK9fbiTBpz09ShQ\nDMicA8rRBG3iAOv2wiWdyZQbHHglHskgqjdgiFvF6kwKNvgOoonBQ9m/neRT/7RmMJ+obRAxnzwE\n0mWC2rnRKlAA7hxT+gHRUdBH9rHN6esHvWsTQ6ZuXYdI4UO+yb2bHHfY+R8GJwT/sPTwlRESyEIu\n/Dn05fO0ot65kdb2LTpD790KvfZrBuXlLkDSaY2GTmQ6NbQzScE58znzSLo15aJS1wbvniOgjx6A\n2rzaNC7DqcNQo3vQXM7bl14VJcpDf7+cY5OsuaBmjjQJqzo2Fvr0USsryAH62AHozaudunGyal0W\nCeBuUPVoDtGqC0TbHszCmdjfTH22QyTzhMu4+czoAd1g4wZ1fCEIMj6Ef1rInqPg3WM49IUzTCM+\ndiBRCb7WGurAj0zBtfMnCpeCHDXbtGN/GcyRy4zh3Dn7p6GnTJO2EB37WjvhB3dJDL19gw698UZV\nJjy92OmKibFs3Eu+AzniC6gls8zMmYQgpy1j/MCqBdbBkhUgK9WE+nKc9T617ALx/oc8/+0bkN2G\ncSE9ewKiViPu9pN5Qg6ewm7kWwgdxogK8W4NFiVSQrxbHWrvNua55MjDL/VOZQAAIABJREFU7oQB\n+dkwkjgdghpRsLj1vtl9mOz37zaEHQsjvVqUehd6eyJdkWsXId6vZ/qH6J9387rk7sHRzTtJpPNe\nOW/yxkTtj157d0rt3sIiJ2/hl9/5DcR/xchbAlnXxm7D+RfVUwnm0QgBUbMhdw92J8W4WGijUyKE\ngDTUDwCYj+CQaimq1uXO/NE9yhiNil4kS26a/Ojvl3Okc/Ig9JOHTAi2R2VrzfMFP3GyOdZH9jFu\nfudGAALi/bqUQWbNAWTODrV3GxfwI/vpCnnuFJCnIOe/Li4AXuEHnNwLol1P7viHTYdo1dXZpfR1\nISTILJr0qcMs7I4fhL5wBqJDb+jTP0Mtmg7ZeSBEMRKUReVaTq1jNfgTyPa9OOpydGzt3RI6NATJ\nKtekedrVS1Ar5tJxFQDu3YLq1hQ6MoKfxyf9ID5oAL1xJUTm7JQYL5qGuKGdoYZ34c48bUYuVoaz\nqh16WwDUvAnOaq2MWSHnfAu4s2ujejSHyJUfcug0Lrqf94M++2KarKxQDXKqYUse9BiqRzPoBOIO\nHCGEQLIqtSDHzoUoUJzjqHkTXjBL02HPoRZMhl45zzQXEx91IEn1T2aq6JgY6GWzOXIpXp4E6rs3\nIbsPh6zVxCIqXjzLol4IcpYSK6r800IOmQJ95YLZ/RB1bJCdB0JN6GeamyUEOXst9PbvoLdYTgSi\nYnWIQsVpjGY/1qEPRPFyUFOHkMvy2VCadV27zKTrPVvYhRk4CcK+YXkLofdtA4SAKFeJm6ByVYCQ\nYHas3q9H0qaD5T3yF4E2xscAixPcvmEm4zp2i+GXGkidDmo5i2zRuA2zsJ4mwP3JlI3Powa7yjo2\nBnr7d0CB4lTUVa2bpGGevcOMtBkgSr3e9BL94A67YtXrv30jOAP/FSNvC/IXJaF027oXuyMOIWz6\n7i3reOn3mPmyYwN8x3L3bPeDAMDuSV7LbEdtXGV1R5J7QVSrB/3TDsqBL5yBvsHFw1Tp/LSDNuzJ\nvayo7eYGye7RPXY2tq6DaO3gEHnzKvNrnjwkq79yLcDFBXrfdo50zp2ktDc2GnB1B1QcC5ugxyQI\nxsX+7bdQtu0BWbE6F+XseSCr1IbLuPmQM1a8dgdEhATxuXt4QB/cCVGjAXDxLPSxA5BdhgBXzlEm\n3a4ng/K2rOWIymHWqwZ/QulsxWpc/IyiRPVrg7jAxxAFikH2GwfcvwO1YDLkxEUsErTiYv/sKQmr\nH3WAaNYRevdmXmgBjpQCH0GOmAmXHiNYUFR4H3LQZGeVwdnjUJMHQQc9Ng8JDw/IOd8yYBF0h9X3\nbnE0lLcQ1JxxUJtWvagAS+lvkFtZsKrP+0F9t+SlhoPCJyVk5wGQXQcD1y5Bjepudkn077+xG2KX\ndKZJDzl0OmSNhokaqcWHDg2hZPnYAb7Xl88BKg5y6DS6B9s/j0O7oGaNZvjjw7uJnzBrTsjBk5m4\nu4nGZaJNd4gPm1Exc+ePhB+X3Aty3nro1V85q0I+aABkycH8GAN2Hxk1ZTDzmroNgVr7NXD/DkTN\nRvw95i0M2WfMm2nr/iehIyOs8e6lX4GQQI6etq0D/FKTxOqYpdWmO0d0DjEGKFaW7xPA8EsHyG7D\nSOC3hyNWqgn943cJP5lH9yGqN2D3FoYtQnAg4OkJaGMDl9jruH7ZDOMTtZq89qBIvWcr3WMN/t3b\niP+KkbcEdukkrl1yHscYMEcxo7tbj3F15YXp6H5Ie45MeBi00ZYXQkA6yjzv3HDipYhqH3IRDA7k\n2MWxO2KwtfWm1RAfNIT+aSf04we88JU0qn53D7aJHz9wlrOePc4d+tZ1gEcyXmj2buU8O6U/9PGf\nmDtzlF0UPLpPcmjMK4asZU84b0R4+0J+1J5BcK8zGOzZU+7G/FJD79kCUbMRSaJ7t7AguXqR6pjm\nnRj4t309RNnKTgm/akgniDofsWjTiiMgAEGdG/H9zpEXcuBEIDQEatZoyNFz2KoFoPq2hg4OhA57\n9oIqQFSqxYTXLWuduB4idwF2WRxThu/eZMfDgXMkhIBs3c0i0S6aBv3tN5QON/yYXZUvx/NvO/5d\n6QLZsQ9kHzqH6h0bSG51XDwSgShZgeFtBY0uSecGXGSMTBZR5j3IEV9A5Mjz0nPZoe/cgJrQH3h0\nj/4bR/axmBg6zSzytdZ8n5Z9CRQpbUm0E0LhkpD9xkN/uwTayH+SXQbRGK5rE6cgS0e4ZMgMOX05\ns27sabEARIOWgH86yncNyD5jyOWaNgwQAvKzYVCrFgBPg9ip/CEAKFQCstuwP2Vt/yZD/7QDiAxn\nd2/LWqNTKOjnU9cGxCnob78x7y9Kv2uOjQEwbfr3C+YIxqnjkdKfJPx5vHaKFp3p6ZSQIipzDsDN\nDeIDgysSG8sxW97CwPkz7Ip4J+I8DEDZR3K+flb3+DVBhz2HPrwHokod0yH5bcR/xcjbhMKlOPe3\nt/scIBw6HNohd0FUrgWk8kf4mkUkTgJk9JuPKwwULG7+W21eY/mOpPCBqFybmTRVagNnj0MbRD3T\n4OrQLv64UvhAG/bVsoNhMf/4AZAmPdSGFZDtelpP9vI5Sg2Dn5CXUqsxEBtNb5QPGlDCV+Y9Su88\nvfi/vn6U93ok+/vvX9RLeArJveDy2VDIUbP//t+Ij9AQjpj800Hv2kRezdWLUDs3MP/l+mWoL8dB\nNPwYotqH0FvXcjzlYISkhnaGqNmYpLmIcHN3p4Z2pkw6UzYWJDExUNOGQXYeyO8KjHTd3q2gd3wP\nUe1DiI59AU8v6JtXKce+eBZq5ghT+gsYfI3BU5wUVwgNYUHyq/MIRpSqSDM18Lug+raGqNGQ0uEb\nV5gqnAC5UxQsznwbgJ2cPh9Dx4txTwjC28ck0jodb9UFolP/v+StoH85CjVpEP038hflBb1ybche\noyG8jIykuDgqZjavZqGYAIncfA7lq0B2GQz11VRTmSF7jQYKFIfq/lGij0OOvEg1ayUXRYdgO9Hw\nYyB5Cui1C81jsu84IH0WMwRTdh1CV9inwSxEtqwBipVlAfQWL0yAQQ7duZGGgr9fAB7dh6zfgqMo\n/7QQFao7d0U69X+hKyLKvAs11VArxRvZyb7jaFBnz3N6532OXRLCgzsQHzSEMBLB9bH9JMEKAUhB\nknhir+PWdfNzFTUbvfbPRR/aSXJ7lVovv/MbjP+KkbcIZnfk8jmnxF475EjK1hyJqsLNHaJ+C0Qd\n2edEhnRS1rzQHbHm2aJGQ/orhD3jbNXeHfF07I6sgqjfAvr4AZpwGd0OAJTgnj9Fprkjd+TQLu5i\nfvgW8PLhQrxrE8c+PqnYHSlbiYtfsbIsbLx9qab5m9D2HJiXQGTOTjlrviJ/+29ZJxMM6ooIpxfJ\nj99D1GvOImTvVs6z//gdat5EiCbt2ILeuBKifGXOqA2oIZ14MazVBHgaBGmMc9SIrixI0mZkQeLu\nDjWi6wvjLNl3PGTzTpDlq5BUGfSY3iad+gMP7kJNHeZkXS6Se0H2HMnCyA6toL4c52wkBUCkzwT5\nJePWEfaMRFu7osczOdSkAU4ur+bjUvjQudUYkamZI6HWLExybKOvX6ZPR/zjF88mnmwb/75aQ23/\njot/3sLsXJ04CNGsI2TLT80sDx0VxeTiQ7sg3qkKfTwBJ2T7a6lSG6JVF6gpQ5juDFDanCMvVK/E\nPUSQtzDk4MkInT7KWdHWoBULkTUOhUifMUCGzCxElILsNhRq2ZfkZdW1QW9aDRQtA9lpwFvlIZIY\n9L5twLMQ8l+2rrO6q6ePQNRrBsTFOXdFipa2gg8BFt7nHDh2joqsbLmBNOlNnxbRvhc7Ugl1RbLk\nYAfXkOLruDhet7LmJFekZmNzdJPg67B3RTyTOxlOvg7o6CjoXZshylX+0yZ+byr+K0beNhQvZxBK\nE+iOZMkBGBchfeGMdbx8Vbhkzg71/Qq28UGzLPP2nPmc5J1q4yqrO+KbCqJKbejdm9naP3XYiqG3\nd0cO74EoXhZInxlq/VLe1srovjwNAtJngtqwnIRRO+7cMBxVg8g9qdmEBmc7N7KwOXGQLfGnwRCp\n/NlhSOHzSqZmjimZL4Nw94BL/88hmrR9+Z2T/KMappNsXCwvgD9+x/fut19ond+NHBK9eAZEs0/4\nfq9fxoLOgWCrBnWA+KA+HTUf3TeLFTWiK4nJUZGAn0GCvXgWomI1swBUkwZCGz4YIksOjvXCnkMF\nLIbs2Bd49hRqyhBnboirG0mS8XZ9evUCqIDFTpwQkSw55Fcb+ZmBHRmEhpAYW7ICXV43rnzRK0cI\njsgGTea5924l38VRCQGjgNizlZ0M+3MsUhpy5kqOii6fhxrd/YXOzQsfR1wc9Iq5JF9XrkXFxcWz\nkJ8OgqzewLrf81ComSP4PpYzxjeJQNRuAtG4LdTn/UgyB2jgljErVO+WiT+ZgiUg+zMAMdoh8kHU\nb8nvyWpLSSN7juJoZuYoIDYGstcoqDVf0XujYWtKyPMWZiHypivO/gT0s1DorQEQlWrxevP4Absi\nm9eQAFq+KvTuTeb9Zffh9NhwGIOJMu9BzTEUNB6eTueXnw2DPmyZ+olS70L/kEhX5N5tFhz2DK8T\nP3F0HBcHJE/h7BcU/3Xcv23GA4jqDSCSeSZ6378DvX87C7Y6tpff+Q2Hy+jRo//t5/BvIgOAT8PD\nw6GSivh+gyCEoDvpj+shipaGsHNB7LeXfY/y0aP7IT5sTlWNlPDKmBlRm1ZBlHyHC71SEHkKmr4J\nIkNmyzjteShEpqxWcFn23DQX8k0FKAV9+RzZ/W7uQGQ4cP0y9KMHkDUaQm//DiJ3fgi7T4Z9xxr8\nhBbJqdNZuRpPHkIUKUV/kWr1ADcPGrU1aced7uP7EHkKQf9yjATeB3c5tnnJuCVRBD6CKPkOvUv+\n7PuduyBEtlzOzo1/FUoBbq7kbXj7Ug565QJEvWbQuzYD7h6QtZpwJh4aDNGyCwm+uzazGLrzh8n5\n0Ds3QvYYgWRSIPbMUe7OngZD79kCve8HIDaW5nSBj4HHD1louLgC1y5B7/vBfP3C24ey38N7oc8e\nh2zbgwF4h3ZDFC0DkYJjCiEERIHigLcPlU12XL/Mz6N4WZOMJ4SALFeZozSj0EK6TBD1W/Cz3bIG\n+u5Nnj9e8KPwS8Ou0I7vqfr6cT1EsbJIniETwoMCoRfPhN61EYBBsG74MWSrLuzCZczKxenmVb6H\nT4OAfEVe6A7oyAioBZOA04eZO/LrSSA4ELL3aIhCVj6LDnpCPkbwE4ji5ZMuRBq3oe34BHaYAFD+\n7J/25R2RvuM4AvrZypQR9ZpD5C4APW+CeUx2Hw7kK0rybNAjyL7joTaupI9P806Mg8icneqhN5wj\n4unpiYiIl/9+9ffLgDs3IDv0ZpFetAxE+szsGrb4FCKFD7SjxLlJO+j5k0wPIjlgIqW09rGaY6ew\nSGkaEU6kIaTsMhj68jng1Isu18iSA4iLg/ykL4SrG7SKYzfFw5OE1iZtIfMUTPS1hi+bw9+viytH\nZ6/x89GREdALJkOUrQRZodprO+9fgYuLC7y8vABgIYD7r3Ku/zojbyFE6YpA2oxQ2170KRBpM5oS\nUX3ykHncvVwlIHse8jfGkpWvZoyw1DNZc5lurgCgvlvqzB2p24wL1bsfcGEz7Ont3RH8cpR5Drny\n09FVKRI27UiXCWrDCogPHS7QIYFcnFUcRz3v1zO4JyshG7dmIZO3EC3XheDO3/PVdhbq++UvVW/E\nhyhWlrP6V0F0NIP+7t9mto+UVNk0aQN94Efoh3ch2nanNfzm1RBtetCNds1C2vA7FJ2qVwt4te5K\nUm+8UDU5ZCpk47Y0Q3Nzg5o2DKJqHZL9AKgxPaHv0xdDpEnPDom7O9TSWZCtPwM8kkFNGUxrbcfz\nVq3rZO8P8Pulvhz/gmeIrNmIXAkAeskX0AHfQNZuwsdfOEN1TuBjxIfw9nFW24zvg2fzJ0NN6G+F\nz6XwoYlZXZuTWkak9ONi3LobPU/G9qLZl/25hgazwLhyAeLDFiy8taaRmUOOiH78gKTY6CgWykl0\n00TLLhBV69JzxPAakWPmAH6poXo2T/RxyJ6HJNfNa5ydk9+vR6nuzJHWsXa9gEIloRZOoY9Iz1FU\nTpw9DtHiUxZfKf0gewyHeBU+1RsEff8OXZrrfMTMl4gwiEatodYuYu5L2UpOUl45dBr0+mVWwZE2\nA5AzL238ASCeqkp+0pcjIABI7kW3VQcZtRPuMlbB3tHQxw+y6IyNBVKnS3LsEvfgrqleE9XqmTyk\n1wW9dyvJvXWbvdbz/lv4rxh5CyGkC5Nefzn6wqIBwGp5L5xqFRRCQDZuw+yGO38A9oAsh92ArO/Q\nUg585FTMiKp1gdRpoc+fAoqVhV6/FDomGsLdw8ylUWN6QjZtxzTSEwcZiNfZ4K88vAvcu8WRTueB\n5nn1z3vYit3/I/D4Hm2ZTx6iiVC+IvTgqNEI+PUEZZaPH75ARPtLOHcSOHPkLz9MFChGX49XwfNn\ngE8q4PpljsaehdB7pHZTjg08kkE0bkvr/+M/0TUyUzbo1QsgW3RmV8jAkxbV2Cq2wyC8qoHtocOf\n07K93+eAiwsLkkq1TH8ENbKbGV8u/IzcG29fqMUzWJCkSg01bfgLxFNRovyLRdlvZ1jUxlPDiMIl\nzaJX796EuAn9gaKlIQdPBsLDoCb0M8d9To+zq22Mwidy9xbLVCxLDsjhMxI1MRNCQFaqBTnyC8An\nJdSUIZQY370FNXEgEBJEJ9zt6ykBHjyFxbsBff8OOR8urhB5CibdEWnTHaLC+1CTBpo28HK00RHp\nkUQhYvxdfXgP9Na15mGPd6tDvF/PeXzauA138KsXABdOQ3YdAn3pHIPQmndiIRMbQ25P8rdXvusI\nrTWLjlSpIQqX4ni4dlOO3+7fhmzxKTux9k5lttzspDnweWSv0dBb1lkndeh6iw84irOHi8pO/aG3\nrE44g6ZAMcplKxsxGFFR0BuW06DwaRBEg1ZJcnPCjYgGuLoxQfg1QoeHQe/YAPFeDQj/tyfsMCn8\nV4y8pRDlKtP9NIE5p0jlb7qrOlokiwLFgALF2B0xckPUV1OsgiVTVioGDOhlX5oOqMLNDbJJO+D8\nKbbtQwKt1FF7Lk1UJE2gipeD3rACOibGTNMEAKTPxEU3vwMxNCrCkA5ngFqziK8rXxGoVV9BNvuE\n44bYGCB1euiQQDq4SvnCbuevQK1awHP9RYjCpSwuzN9F0GNawZ84CFGyIjM3IsIhylaC+uYLiLyF\nKHVePsfIEhnJQuG7JXS8jQc5bz3ddAMfmnJc1asldGwMC41+n5N4Oms0RB2buZNTwz41+SHCJyVD\n+rx9ob6aAtmqK8nKM4a/UOyKAsWotHG3Entx4wr5JsHO76nIkBlyxkrrPp82AtJkJLE1bUaoaUOh\nThx84TVppaAT8OKQXQZBxMsUSQgibUbIARPJPdq6jnL3Z6Fm0Ydc+ehO6yDF1Hdu0DwsuRdE1pyU\neCZ2/o+7Uao7eZCVvjr6S36H+7ZO/Ikl84QcO5cjrGVfWscLlUCKDr2ghjuo3Kp9yKDDPZvZQWvd\nnYvuhuXkB1y5QFO2HiP+1HvytkAf3Q/8dgayVVeo75cDKf0g3qlGC4H3alKKu3iGeX/ZcyT9VQyI\nUhUBN3crmTceRKPW1jUzbUYgVRqONxPCpXMQtZtCeBjOu7s2Ak9DeO3JnN2JkP/C63h0j4U0ANGw\nVZIE178DvXsTEBPNTen/CP4rRt5SCFdXXlxPHnohORUAZA+2evWqBU6JvrJRG+D+bRoIJVSwONq3\nR0dB77JIYij5DpC7IPTBHRDv1YT+4Vvo0BDuSEfMBMDcEtmgFVOD92zmbWPn8vHGTF2vX2rumgFA\nHz8AUawcF+ZTP0O2/BQIfEg/kpqNGPz1fl3g2iWIHHlpv/wq0eehIXTsjPnrZFhZpQ5JxK+CJ48Y\n2nVkL9/H/T/ws8iaE2r+RKpt8hSk2iM0hF4rjx+Q6xMPetlsdlBSp2MhaHA9VO9WzKnxT0OH3qfB\nUHPGQTTrZJFaB3U03UyFtw8N1DyTQ82fyA6JX1qo6SOgjQXXDpErP+SgKRw32XH/NscvD5zNwIS3\nD+S870xJtur+Eb0x+o2jmmrhVKgdG8zRmY4Ih5o/CXrz6hdeqxrWxWn0khSEiwu7T3ZERVAiW6wM\nZPcRTiMNfeN3qKnDuBvPlM2pI/jCeVt2YYLu7NFmHo0cNRvIkAVqTC8rPdoOhy6enLYcuH3DKVcG\n2fNAdh6AwA4OJMji5SBsHYHzp6EDllAOmj031KLp/O4lTw598hBkhz4QRoDh/wJ0aAiD/cpWBuJi\ngHMnIW0daHAmBP1rjh2gsg5UHOlzJ83gOQAQbT6Dmj3W+Ifz8iZafwYEB5qKG/npAKiAr5EgsuUm\nUdZI19YhgZT9ps0AhAQx6yiJDZFav4z/x9v3tSfo6ueh7BhVqf0CZ/Btxt8uRmw2m5fNZkvUd9Zm\ns6Wx2Wxvrx3cWwBRoRpdThPIuBDePmZqrt5u3S5y5AFKVoDetJo+FzAKFsMqWaTPZMlyAXY4jC6C\nEALS1pG7Qb/UgBDmrFVkzWUmu+rTh+neumUtdOAjmkfZL5ru7iTshYU6+ZvoM0eYHxHwDReFDxpy\nRFO2Mo3Qzh6HKPMeia25C1Bd8yoz8muXqKr4G8RlexLy30ZcLL0QfFJC//YLyZfrl1K2DQG1eDpk\nu16UyY78jLs8ow0vqtSBaGTtvvWxA9DHD7KDAlgOk1GR5EgAEBmy8PZb16EWTYXo0IfdFDCF165c\nET6pWJC4ubEgadsDSOUPNX04tD3vxYAwXEadHC0DHzHpNl56rXBzh5y9ls67AFSfj4HQp1Tq1PkI\n+rsl0GsWQj+4Q1m6XVru6QXf4dMM+a8xYpo8CMqxQE4E+vQRqC/HAoVLMdDR/ly8fGAnwQKAvnGF\nWTQZMkNkzp5gwWc+tnlniMq1oL+ewc4EwC5RpmxQ8ye9mFGTK78pJ5UzVvDznNDfuj1VahqWOQbh\nZcxK0vHDe1CLpgJFSlE9NfdzIE06yIrVodcvJ4+hVAX8L0GvWwwIbojUygVUZqXwpbS6Ie0H9Dcz\nzfuL9+uSK2L/d7OOwB9XqdQDED9QU7z7AdRXHGGLCtXYkU3M2+bmVchmn5hjGL1hJQn50VGMp0gi\ncFBfuQCc5ihY2DqQ6P8aoXduoAChVuLeJm8j/nIxYrPZ2tpstpsAQgGE2my2JTabLaG84hoAEh+6\n/odXhnBzg6jZmAtSAmFnsiNjx/Wm1VbgHMBMmuBAkgINSa+jBbJo9LEpEQYAvX65dVuOPJQ67t4M\nUa0+9IEdpgW97MlsHL1lLXcDyVNAGT4JciBdDhESRCO0lfNpzmXHo/vMEQl/Dr1+KX0EvH0oPW35\nKcms2XKxRao1OSWvaKmsj+yFXj7nLxckwtWNWSx/F65uQNhz7ppDg6GjIoCM2aDWLIT4qD3w+29Q\ngzta98+WG/KLVSRn7v8B8PKGR0WLPa9XzKWMtudIjoHs/ihXzrPVDcq3ZZfBwPlT0CvnQfYYARhq\nKdWvrdklEin9mRosBNSCSZAd+wG+qViQxFtsRfrMLEgcxwRPg6GmDnWKJQBAW/pBkxnYB8qU8eAO\nZKPWfF37tkGN6GbyL2jrPhXuJcob8t8O9GQBoAMWI27mSLOAjg91eC+t9ouXh8ieh4ZvNRtDtOwC\nfXgPCbH3b0PfvEapbObsEFlzQR/ek+D5AEB81IGL39pFJplW9hoNkSs/F8T4WTPFy9EtGYAcvwBw\nT8bXbIe7B+WoB3dajq6ubvxchICaPxFI6Q/5ST+o5XOB588gP+5GX5H8RSzi+P8I9C/H2CG1fcLN\nVXQUZLNPoJbOImm1ci2olQ52+IMmQW9c6eQdIirVssi/8boicvSXVNYYhG/RpA03PgkhpT9QtAxE\nERYc+uY1EpkzZGGEQuO2iea/aKWgAhYDAFyy53Yae78O6NAQ6D1bSXb+C6rAtwF/qRix2WzVACwB\nEAZgJoDNAJoBOGez2V7vu/4f/hREpZqAr5+56Djd5mCyE7bc+iGLDJlJjPvhW/IDYBQsRotZ+KQy\n82cAQB/d50Q2FI3a0MQrOhJInRbKYLYLn1TmLlR9MxOyRSe6tv5ylETXNoZV/eMHwL3bL5JZTx6i\nudSBH4Hrlzkq+O0MdOBjI79lHXcD1y4Z4XlhgO+rGf3on3dDL50F/Rf9S0SOvEnujpJETDRVQX/8\nzsLhzFEqOh4/gP56uvU3mneicdPNq9AHd0BWqkUPkrWL4FmnibNL67g+3Gl3GUTFiNHd0tu/M703\nRJFSEG178jVvXw853Ji9x8bQh8TOHfJLQ6JqdDTUNzNIJk3hAzVzJLRhvW4+x9TpIPt/biVH4//Y\nO8/AqKquC69zEtITOiT03ntvUkSQpojo0HuTXgSRDoKAdAFFkCIdh46AgBTpCEjvvYQOgZBGSc75\nfqw7995Jgu+rgp/6sv+Imcn0zN1377WeBTJLxg9IoPsQQkC26cVGE0amzcUz7lk4AMPd+o2DCM7g\n/vtFSpu0V5w6AtXFkYBHorauhZ4ziWnTIRlItK3bGPKDlpBVakEOGAfExUEN7kyxaHB6iFwFLXdF\nIiVqfUjb+rrvzeuJdr0hChSD2vWTG2gLANdghqVUfjoGSBNCZomtZNuPuQa1raNkz2EQqdIyyv7B\nXciP+hLEdWgPZIuuJltItv34X8EScZV++ABq7mSgcCkI/wCuLxu0YeP9KIxTwuO/WvlDOfIRMWDT\nesghk6Ht7CX7VKRwKWqgphnY9xZdqU1J5AQOKVIDkeGQDXgyoLXmKid1CEnQhUtB5Mj74ueyf4e5\nNgpo0eW/zkf6b0v/uBzw8HB3Kv5L6ve+UgMB/AqgiNPp7O10OpsAKATgOoANDofjn09e+YeV8PLm\n2P7XPdCJZGa4guti1i9zs2CKdxoBMdFkfFQ2UniN5ErAcM/YDgbiyJYcAAAgAElEQVRq8QzrYJUy\nNbHtW9dxAnLiV2gjTdg1TsWF00DKtEDBEvzdJzGQdhtcilQUpeXIyykHQKLitUsMW5s7BciRj06b\npbPJIQkIZGNTvDxw9gTXNdFRCYBGv7f03m1Q4wYkEGD+p5KuUMA/UpERnCgYmGj7wVA42gAFS0Cv\nc0LkK8IGZPEMMjocbYB0GRExZSRkmx5uug3VozGQtwhE/RYcbRviNjVluJnWLMtWgajTkGeVx3+F\nnGQcDK9dhP7OwuCL1MGQPYYA924zFbjLQAACatKQhM6ZVGkplE2eSEOSCApe1m0C0awTH9voT9zu\nFwAFy7ZJntt9BaeH/HIRJ2RxsRTrGhoCtXEFrdDV6nK198MS8kjqWDookSErZBsbwfXyuReKHQHQ\nrfBeU6gdG0k4BSAad4AsVRH64hl3ISpAp5mx6hGtunNysnqhOSUBqHVAjnwUwBrl37wTRK4CULu3\nsElv0pF/D85Z5K88fkgNRase/6ozYq3ioGZP5FTI0QZq/ldAgWIQadIxz6leM05Ibass2fFTfj8Y\nJSrWAHx8E11XA4ZjZo1h3Q1KRlLrmiWJXhcR4RDV6louq0N7uZILycBk5HovFijrZ7b04ALF4FWo\nxH//QvwXpR89YDTHW+++dJvw36F+bzNSAMA8p9NpflM4nc4LAMoB2ARgkcPh6PKiX35dr6ZE6Uqk\nMzpnJSRcenmbtjK3ZiNlaojKtaA3rTQZFPqX7dBRhn7A05N2UlddveBmdRQ165Obcfk8m4fvv6XV\n1zOJqUVRI3ryNiIfk4cAMFkWYK6DlFCLpkOOnmXdz6WzEBmyAhHh0Cvmcm2RNDnU4hnUMFw4DaQJ\nBnx8DIhYEKDjgD8bm33nBtSIntB2sNd/KJE2nVvD9rvrwV33/8+WmwGB653krGgNNf8rNiBp0kHN\nnEDxZ4e+UI8fQq91EuduK/3tOIjq71Ffs+UH08qo+rUzA/HEOw2B4uXoSnhw13z99d6tUJtsIWMZ\nsnI1cv4k2S89hrHJmDIc2hU85rpumhCud+waksgIrncSy6YpXSWhwLBuE8jhX3NyMebTRFePACD8\nAiC/WmYmTqv+7RH31UjoZd/xs+zjC/3DYjYitd3Pj/Sdm1BTRpBeawOdJVpFyrApOH2UqzAA4u16\nkFVqQ4fdo63XXjnyWhkk5apClqsKfeqI+xl7AUMDYl/DFSwB33caQt+9Bb3oG4hyVemumjOJ0LjK\nNaGXzmEYW8E/OI37m5beuAo4exyydU9SZJ8+gWzQjuuZbLmpPbOHBPYazkmUzdYuGra1IjDi6TNE\n654U0xufa9ltCJvKxMCJ6TIB/gEmzVQ/f06idLbc/F4qUxnCFtGQ4LlsXkNxPUDn4UsuvX4pkMQL\nwkYK/jfV721GPAAkWNQ6nc4YAPUAzAPwpcPh+OwlPLbX9V+WkBLS0Rq4cj5RAZ4w+CH6wE6z2QAA\nUctoUjauhDDOFtUAK4RM5CtiJfAC0M6Z0DHRvMzHD+L95tzzFisH3LtjnpmIYmVNwaU+uJtn4ptX\nQ4dehkiVluIxgGuWI/ugjx8kddR1P9s3UJeybT1w9SJkqx4UnF69wInMT6shanxAwWBwBiBO/Tkx\nK8BJRdLkUJOHIW7aaDcs+m/Vy1LKiyq1SDXNVxgQEmrt95DNuwBHfoE+sItn87euQ69ZDJEmBIGd\nPoX+dTd0eJjbyFYf2AmcPgLRoiuQKi300f1APh50Vb+2dNhICdmqJ/H9X40APD0hB1IYqJfOodPK\n9bhyF4Rs+zE/Ozs2krVy4xozW+KttkTadJC9R5DD4KqoCK53bC4bHfGYotH4AsPg9NSh9B1NEe0X\nnyL2ygUkVsLTE7L3SEvEd2Qfd/1SciLyfvOEjUj4Q2oKfH15hmuLTEhQOfNBtvsYuHfL0iEULEEO\nzNMnUH3buF/fz58ZTgAdFC26QD8KcwOYIUUqyDY9oVcvsFw3SVNAtu4BADwAByVjeuz6pbTutupO\n7kZQsj8fTfA3K33xDPTqBRA13oe+d4tr2mZdoLesIRm3ZTfgzDHrJCh3QSaBb1pl3obsPZIgMleu\nUryJmihT2VrPlH+LonsbaM6tbl5jPpQLcLb1B54wJPGijda2uk7wXB4/ZDMFMIYhQ5Y/8Iq8uPSD\nu9A7NtFZ5ef/n3/hH1i/txk5D6B8Yhc4nU7ldDpbA5gArnMGJXa91/VqSuQqABQtA71irqn9MC/z\n9IR/Cw6s1DejrZ8HJqV1dts6iCxG7HpUBDHKRskPbaK76Ci3szxR/i2Cybb8APHWO9QnGDoBl51X\nr5hL1kja9FALppHM2tw2PAvOAL1kBoFmLu1AXCwtnFlycoSbLhMTSVcvhChaBgjJSLvv2/Wohs9f\n1M3W+ofr+mW6Ni6ehhrUCWrRdOg7iZ+dm69B+kx//P4Ck3LNkiELFfj5i0KvX2au3eDtTdrk0tlM\nKa3bGHrDCuhLZ+FdtgpdOEtmEspks3iqiUOIsO7UDwh/BBFk2Esjws0JlfD25tQjTtFhkCGL1ZCO\nH2iudQBAFC/PA+Tm1dBXLkB27s+wxnlfJaDZiuAM1JvY03MjwpkM/OAeCaejPyF8TwjAx9c8E1XT\nx0D9sp2alU9GA8lS4tHgLonC0QBqUNwAeI8eGI1IC8h4kCkdE02celwsZPOu7g6W+JUyDWTngcCz\np8ybAYBUaSHb96G4NP5EBIAoXdnUCsjhBuF4lG1q5eFBwfajMO79jZLtekMEBCFm/TLg/CnqI+7f\nhl7vpHX/1nVm5zTt+K8hrAJcOahpo4CsuZgLs2QmwXyCeSuiQVsK4CdaoEHZsZ/begb5iwJpQizS\narySo2eyOXdlMtVvAWWbDrtV6mAKZY1gSP34Eb/rsuQEzp2AqNv4N220erVFcBXvNnnh9f5o6XVO\nMnBesk3471S/txlZD+A9h8OR4kVXcDqdfQD0BZDrzzyw1/X7S9ZvyZySzWsSXOZb24DjnDnmHoZW\nvR7tm4tnQI6k80WN7W/pQ1KldUO4640rzAO0EIIi04cPGBqVJh3UvKnQKo4Bew3a8vb6t4ds2pHT\njR0bITw8IIcYXyC3QwEvb6i5k837B8AvkGQpgScxUN9NhqjbFEifBWrmBK5rIiOgb17nWf+ls+R0\nxES7w7j+QOlNqyCKlYN4613izgd1RNzkz6D2bnNLtTXrz+xuteIZclByYqcz52CuSngYV19LZvJs\nOC6OwXlv1yOLZMHX0HGx1AN5e9OZ1K63m3ZG9WkJkSYdROMOzCky3gv9w2KzYRQpUtGmbJyhyjJV\nLChav3ZuqxhZpTbEm3XI6pCSQti9W6E3uIs3AUCkz0xnjz1/Juw+1KdtoPq3B+7fBsBGQvYZCVmv\nKSmwAPTM8VB7tkAEJoX8eAQ8M2XnZMXWIJvPcfMa6olqfsDG2PWyXjnvtq7Uz59DfT0SuH8X8qNP\niXv/rYqOAqIes2ExdFayzygIH18yL+ILc2t9aGp+5KCJEP6BXAXYxL6iblMgc3aoYd2sn1V9ByJ3\nAeh7txG18BsGruXKD7VoOpA6hJ/BpXMgSr4B8UfF0n/D4vsxChASslUPqJnjyfR4sw7UvKkQJSpA\nvFGd75lRss9I6I3LLbcVANm+j7tV2laiWl2mHn9L15to3gV692Y3JolZSZMD9+9ANmpvumT06kV0\n7UWEA+kzQ1R5cROgb1wzWU2i1ocQdjH3Syh99ya1fTYs/b+xfm8zMgtsNNL+1pWcTudYAPUBvF7X\n/IUl0qaj2G39Mgre7Jd5eJh8DPuIWXh5U9dx6gj/UA32hzbSdwFA1HjfbfSuvrcRD9OmY+Db1rVc\nNVw+B73tR15mS7PU1y9DvFGdTIm7tyAyZLVsb+EPuZc/so/uEVcd2QdRsgJXOTs30ikSEw21ZjFk\n6+7M58iYldqVqAie3cTGJXRn/M7S29bRadSmF6c4kY+hZ0+E+rg54vq3R9zUEVCLvoFatQBq+pg/\ndieeSbgaSpseuHIOKFAc+pftfI02rYZ8twlw+wb04X0Q7zejBfTqRTZ1oVcQ8+MKCP8ANmanDkOf\nP+k+xn/2FGrHBoiyVThdWbPITE1Ww7pZZN2c+Uil/HE59LEDEE07mkA5NW6A2+RDONoAuQpATRsN\nkT0PY+tXzIU+lBCvL3Lkg/yoX+LPXSkLx54pO6+fKz+dJwD0nC85IfHzR9JB44FsuaG+HAZ91mpI\n1K6fCMiqUR/ImJW2XBe35tAeZtM8f06a65xJwIXTkJ36JTrVAEDUvocHNUp+/lADPrKsuf3GQqRI\nZawV3GFsomINaz1ZrxktwlfOu4sps+eBePs9umRclSaErjTw70kGJeP7cGAnJySN2pFwHB0F8Qr0\nB/9fpbWGXjiNOTud+pFTFHYPsm0vamQCgtg4bF5jvv6ibBU25PaJUq/hdK68gKQs3m8Ovdh4vVOk\ngsiRD3rVwsQf1PNnEBWqmQA5HXqFf2/JUjAtuMlHv+leUssMi7Cv3ythf+gfvgcCk0FUrvnSb/vv\nVL+rGXE6naFOp/Mrp9P5HzGITqdzpdPpNFGDDofDx+FwNHc4HL/ZyLyuP1eiTgPAw8NtbGheZkOz\n68MWF0EUKgkUKQ31/SzItjzT0JtWma4J4eUNacegHz/IjBrX77/9Plcnu7dAVHwbeuU82nGFsMSR\nS77lFCYoGdTsiZye2F0NKdOQL5Ilp5tlVR/eZ60qoiKpnTh2APrWDY6xN63iWVD4I8DXnysJT0/3\ns/I/WGrSEOilcyBrN4AcPZN2zsKluEY6dxJ68w9uZ2q/q+LiuGKQAngSw0TkB3eBVMG8/VOHIcpV\nIfitTGWCtZbPBTLngKhcE9GLv4V+9ICIegOaJkpWoO3RQE/r+V/zYNakI88Sf9luaoDUWCv0TlSv\nBxQqCTV7EvAwjERRgBokG2DMbGj9A6CmDIeoXg+ieHmoWROgr15M8BRF4ZIQrbon+vTlx8PNxGjz\n+tnzcD0DTkj00f0Q3j5cmWTPAzV5GPTZ49CH9kDP+wqiUg2IXPmZ6lq6MmT3oZBjDTfDjatQXRtA\nL5xGWmm7j93OtN3KL4BhbI07QFav554jkiIVkDUXdOTjhI1MukzQ4WH8d+pgfh6fP7dWOwB5Iq17\nsLHcucl6/i26QXh703Z9dD8CWnYDIJiZUrQMb3vTKjon/iXZIwAQs24pz/KbdoI+f5JTu+ZdoHdt\nBkKv8PN15wb/3o0S77dwQ8CL8m9RD7Xwm0TvQw6ZDJw9YWpNZM/hUPOnuif3uip3QUDDBAnSyjuL\n1vuHD6j/yJF4Ki8A6JOHAdNJ2BTCvp58CaVvXedJSu0P//aJzH+2/kocfFKQUZL/L7zP/7kS/oEQ\n7zSA3rkpAcYb4B4VANTXI90EiLJBWyA6gtHthqZDDepk/WLRsgyOMkrNGGu5Mzw9Kba8dpEjT19/\nqIXTTBy5C9CkPu/FL+ZL56A3rKCQ0rWaeXAX8PYln6SvpWvB40dElodkZHJprvwci6+cz6ydPAXp\nnKjbGLhyHp5Zc/LM28v7zztsACA6EmrqcKhP2xJ85OUDkb8Y7/uPNjxSsgnx8SXNNk8h6iIKFIfe\nt40up23rqZqPioDevpEY/7PHgZOH+Hom8TLDwMQHLXnmuHoR34cn1rpKDewA4edPEfCFU9QWAZxg\nHT/I35eS74u3D9TMcYCPD/NjAOils2m3Nkr4B0J2GQQ8CoOa8yVEqx58b6YON9HybmWLIrCXtqVC\n20vkzEfXDgA1dQSeHf+V+pYuA4EceaHGDeBkpkR5iLJvUgNVoDhEi64MZkyWktZfDw82dTs2coJz\n5Beu8eJXQCCTT6vUhqxYA/r2DWgbXAth96G+HgU1JKFJUFR823TPyE/HQAgBvWq++3U+aAmkDoEa\n2tX6WbmqbKJin3PKmLcwvMpUgt6+Hnj8EPKDVnSZGJEP/5ZSB3Yh6rspbGKDkkEvm2tOEvSWHziV\nSpPOrZmTY+eQQWL7bIkmH0EN7pzofYjq9ZiaPIlaE9GwHanNiWAP4OFp6UEM7ZHeu5WARc8kDEz8\njamUVnFQrqYpTQgtxi+59JrFQPIUEBVenA78b6m/OpvmJRwdXtd/KlG5FpA6rQkjc7ssZRozm0TP\nt4HQUqWFqOVgnkw2I1I98jH02eO8XAh3q29MNPQaa+wpsuXmimjjSq51jh+0eAuuL9QnMdC3Qqme\nX7MI+tpFiNTBVh5ORDhw5QKBXENs7ImzxyHSpmdjMncq3UG58kN9O446Gf8gOnCq18Pzw79wXB8T\nY/FLXladOAS93gn9/UyOkaMifv9tSMlmKSCIIk+t2ZTcDmWWyvXLZK88jeHqpVxVWhnzFWFezcoF\ngK8//N5vBr1rE/TtUOpz3m1EWNzzpxSExhkH+sgI6NNHIXIX4Apo1QLIbvyiVpM/M3Uhwj+QIK6L\nZ+hWypLTdA+o4T3cGTUhGdi8HNkHvWMDGwVtNKi25kNtXEk7eSJBbvrATobWJVIif1EztTd8aHfo\nS2c5nbNHpecpRER6xmyQ7ftA2BpD4RcA2X2odV9rv088gdfXn81S5hwQjtbQT59auTEpUkFO+Z5i\n3SP7LLeG6z7eb2FaTmXnATy4Xr3g5vQgObQmtQqudZe3L0R9vq56109cAzRox7+NDSvoNPPzZ/5T\nldr/GueEPnsCevYEphOXr2qh7ouWgZ47BaJMFYgqtU1cOwDI7kOgf9lhTh4AQA6fxqC7F0AKRf3m\nUHOM7440IRBGwniilSIV7cNVDM7S44dE0qdMw0yo+s3NJiXR57RrsxWU+H4Lt8/gyygdepkOozoN\nIZK8OB3431Kvg/L+hSU8XQm7h0wYmdvlrWgl1Hu2uBE1RfV6QKpgqEXTzCA7NW4AtOIBRoRkNLkV\ngLHKcSOzNiWY7PhBoHg5orMjH/PM2yBn6nlTuftMlwlq5gToZ0/dBLLw9SOE6uEDN+S1PriLXywH\nd0FvWA7ZoS/g48vY+3a9gajH0JfPwefN2sCxg6QuPn1iriz+FiUlGw8huRq4FUq1flwcJ0rRkUCy\nFNCnj9AZtXUdxFvv0gXz6y4ejK9dBM4cg2+NeryusQcXlWsDwemhls+j0DVpMsCwF6oJg+hi+qAl\np08/rzcJra4zSMDQj1R7D3rVAgLWatSnpgVg9oqtRJHSdDgt/46skvZ9gAunmGWkNdTqhQRApcvE\nvX7BEmYwo6v0xhVQPyeemCqKlrHcPaP6QB/dT/dFpuxMf57/FRARDtl5YILxtX5wF+rbceRD/Fb5\n+QPSA7JDXwjPJNBLZ5khbLL7UIoF0yXClShS2hLU5swHUaQ0MeAu54eQFGc2/gh4/swNjCbeawwR\nlJyArHVOiNKVINJnQszGVVyp1XbQ0q6Vm+bqn1z6xlU2jjnzI6BFF6ivRhJ1/0ErClkzZIFo3pmO\nEcNuLcpWAfwDLYgYANGwPfDsCfTaxIFlctS3wJH9Jppf9hgGtXAavwfiV9r0tA+36AZhxEroJTPZ\nNMbG0uXzG9MI/SSa4ECAGUQ2BMLLKrV6Edd/Zd986bf9d6zXzci/tYqW4fRg6Wy3s1UAzLRpT0iQ\nHb4kkiSBbNweOHcS+up5cy2jl31nXeedRnS5GKW+HWflmvj4QTbuCJw8zLP8uFjopQYqPji9hYr/\nrAczT+7d5rpFCAaJATwgB6eHmjWBWgnbWbU+YoTlrVoAXDjFZOLwMKgV8yiWvHSGeSVFywAnDzEf\nJPIxhWj/X+UCe3l503nz/DmQPAXgH0DhXIrUwPmTEPmKcoJR4g3ow/sgy1ej0yj2OZC3MPTWdZyO\nZMgKtWklYXa1G1A/cfsGV2V1GwOnDgNXznO8HHrFzBjSqxdyYtC4A3DsgAXPunDaLQlXvNeEa4XZ\nE2kP7mucqZ46bGaymNet15z26xljgfSZOC3YuIIC2bXfE9l/5yZEkTKQnfrz/YqnE9GLZiTaMAOA\nLFMF/s0NUuvUEcwr6ToI8LJZXOMJtfXTp7yul7c5XUm0MmQxhZMiZWro4wc5WQIgGrWHSJeJY/jP\nEtG8hN0HDM2UGTa5e7M1KRPkxohM2dyBZ6mD2TSCLB08fgTxTkPouDjErF8GUaYSkDwl9K5NEKUr\n/+ZZ+T+l9O1QslZSpoFs0wvhY/oD0ZGQHT7hZ0wIvk8nD7mh8UWDtvxcuSpDVoiylRl7ACRwzYn3\nmtKV52KKNOtEIvULPlu4e4vrmRBCC/XR/ZzkpglhzlOTj34T5a43rLBCED9s/cKsmj9a+sp54Mgv\nEO80eukTl79rvW5G/qXlChfDzWvQu39KcLk0VjXQmvt01+/lK0oK6NI5JoxJ/7TadOcIXz/IFrb9\n+YO7PPC4fr9wSUbD/7icgr49W6CPGtko7xso5agI6GP7Ieo3h968hgfhwKTm+gC3bxB6NX0M5CAr\npRNPY6hfyFeEgra4WIa/nT0GfXAnRMvueLpjI0TylDxbOXuCE5JHYX/9hMRlwUuajO6U5885/dAK\nCExmWYJ9/WglDcnIkW+23Hy8/gFAQBD0/h2QlWqSy3H7BsTb7wEnDiH25jWePQYmhf7JWA0ULUvr\n78oFXMVlz2Me/PX6pdT4FC3D12/5XPJAwCRc08qdxIvve+gV6ocCg7iqAKC++QI6wkLBC09PTkSe\nPqF+xDU1u3GVTeTlc0DhkhBtP4bw9ORtdR3sziABoL4d+0Laqm8tm2bi2VOGpd28xqYkY1ZOfQyr\nuenUuHsLsstAd82TvTyTEHBV80OIAsUJYfvKELfmK8ooBBh00Phn1b5+nE4BEM06QwQmhY6KsOjG\nvn7kQdRtzKj3H20BlHUaQHh6QsfGchVWujKx40f2QT24C/HmO8Cpo0DYfbfk7H9q6ds3oMYNBPwC\nILsNhvpuMmKvXYLsNpirlptXIbsMAKIirdcfgBw/j7RhG+tG9v4c6gubJfuZDW6WxAui1odW85Ip\nG0Th0m7kVrdKHQxkyQFRjUnQOjoKasE0Cudv34CoXMN01iT6vO7fMZtMUakGc6VecqnVi4DgDBCl\n/3eC7183I//iElly0mmxaiFUdFSCy02uyFefu4lZhaMN8PQJd9iGi0YNtfERChR35zqsd7q5KUSj\ndtRFXL0IFC4F9d2X0I/CIKQH5BhOSvSKeRB5CnH3P+dL6KgIBrm5HD+PwoDrl6DXLIb83GaJvHOD\no9TUwTwDzpCFaaw//wiEP4R/q24Uw2XOAaRNR3x8kTKckCRP9XJErf+p/Pz5GNOEULuSIhWbkKDk\nbEQACBegzXX268OzfeHrC3h5QV84zX36sYNAweJEnB/YyVweX388/XkDRBIvsj/2bIV+/IjrsLpN\ngAungHMn+e9b14GMdCfpuZOtJvXeHegbVwAjg8PNNZMlJ9c165dC37sNUaSMOSWz7/QBEFDWshtw\ndL97Ku2Du0DeIoR62fUcLr2Jq7QCYmKgpn4O/cRdYKq1RsTXX1Ao7DpLPbofomkniEIlKXT1CyCH\n5NED6F0/MWStaSeuCmOMz7xBAzYr9jnFoe805ErJ5rSQrbpRiPrgHvSKue6/l6sARNV3rce3YyN0\n2H0TJAcAePIEopYDwi/AXROTNj3BaDCcbA/vW6j+bevhmbcQJyn7trExzfrPxjTpOzehxg8A/Pwh\nPx7B1+L0UST9ZCT0wd3QB3ZQVJ0qLdRQ6+RGfvY1dTc2t54c8iX09h+Bm9cSuyvIL2Yx+M7Qt8nO\nA6EWfWO9//ZKw8A72bKbadfVK+fxul5egJfXbyYia625+gEAb5/fpLL+0dIXTgMnfoV4t5G5Qvpf\nqNfNyL+8RL2mwNMYxKxckPCy1MFA8XIAAL1gmvXzFKkg3mlEzYJLzBoRThub6zqONm70SzVnktnQ\niKDkEE07UueRMz/g4cGGQymI5CnJCwGghnWnZfjZU6hZE3m5sT4CAPj4QW9dC331ghkfD4Bq97Tp\n+HvTRpGlUaM+9NLZkH4BEHWbMDa+UEmeBZ07ARQrx9TNlGmsA9urKA9PnrX5+BEj7SH53xSpeRDM\nlI3OgCAjbTjQmNj4BQCeSaDv3AIyZiPzJU8hNhMx0dQlHNrDBqTUG3jy8wbaoyvVAKD5ZQxQmxGS\nEWrzav5+9jyAayd+YCf0k2iIDFkg3qgG/cMSnpkC5L/Y3CaiTgMGlC2eAa01JyAAyatHLFs4AE6f\nADaQIRmt28iYFcIzofBOFCnDbCPzNfMA7t4yPwOu0uuXctLVuicnKq6fb1xBp1ZQMsiew5hl06cV\n9UhvVIfImiueONadEguA79GNK2RVGDZ30fZjk7KppiREJMl3G5l6BdGiK/D4EVTf1uSBAPxsJU/B\nLJnoSDcrr6j1oXXw27IGyF0QImNW6EcPgHMn4Ptmbei4OOjjv0IUL/fSx/5/ZenboVDjBwI+fmxE\nNq6A/uVniNY9EHv5PPOwGrQjTsA27ZBdBlEEbEtBFm16AjExJmo9fsmO/ajLmc0JqmjVndiBRNg3\nAIB7d7j6SEdysj53kicyeQoxf+bD1hDxm1f7c9tvCWpFi66/ed0/Wmr1QoLWiicKO//X1h/+VnY4\nHKVf5gN5Xa+mRIrUENXeQ/Ta76EfJMxbkQZkTO/e7JZaK6q+A4RkgFr0DeRQjqDVpCHUZACWXdRV\nN65Cb7BBiUq+AVG2CvHcdRpQc2CQYUXx8lZeyswJkG17Mfl3/VKeuX9pMFIiH5M/MncqlfHVbbHZ\nv+7hZOXKBaiZ4+nxf6M6IqaNptD27XoEfZV8g43LmaOErN2/w0bglXn2NRsPLy/qJUpVBE4fpf7l\n/EmIrLko6HTpWIxJCWJjgaCkQGQ4RMZsFJDmLsjLLpwC8hfja/z4EUTpylAP7gJXLkAEBHEkvWcL\nD9BCUPR6dD+dGnUasrExbkvPZ9Mp6jYBYmOh9203YUp2S6vw8aXL4/hB7q4DgrgSA6C+GmlOMbTW\nTKV11a3rQN7CbA43LIe+dDbRV0nUbcoDAMAmzc8fOLrfTLRZqq4AACAASURBVNDVxw5Ar14IP0cr\niCw5Sel08R5uXYdeRMaESJHabG4BWmnVoI7WHaUJ4RoMAOJRTNWIXtAzx5uXiVIcieujB0yXhHm7\n1epCbV3Lf5eoAFmhGuTA8e5P6sFdw/ng5RZvj6BkloPtdihw8Qyk6zU/uBuQHvAqXZFTvOhIsmz+\noaUvn2MasY8vG5GfVnEl1bAd8PwZouZ/zXVVlVpQ33xhodrfaQgkTUZAnVGiTGWIfEUtYm48mKEo\nUYGTVxczJ1cBiCw53eFy9kodzBWOoV3Tz58RD58hK6cuufLz7/RFzy3ysbWOK1DMjdv0skqfPgqc\nOcZk61d50vQ3rD/zbPc6HI5zDodjkMPhyPZfXD8MQBUA/30s6ut6KSVq1If0C+Q4Mv5lSbwg2tLX\n7yZm9fSkG+DiGejLZ80vajtxVBSMt65ZvciNbSIadwCCkkLv2QpR9R3oFfOgjX07I+nBNOCw+6S4\nrlkEffIwG53+xDjjwV3Ax4eQrbfrMW3VdX8HdvJL/sgvTDtt2hHeZatAfTsOIk9hI+10NkTRsszA\nObafu/iIcPIlXoWOxMMDuHsT8PKGKF6OZ8fFyjK5NmlyXi4kIWcAhNGUCB9fTlNiooHkKYFHYbxO\nYFLom9ch8hjNxNkTQPbcEC7XEgBRvioPngYPRJSpDPgHcLSdvyjFmkaaqd6/HTr2OURQMoNnstZK\nKd2/A9oQ5QGgvqRgCajvZ1KkXKys6a7RqxaajYhe5+QqzCiRtwibncw5CESz2YLN63h40AXlEkNH\nhAPJU0GvWQK1fQObj0Il4Ve3MWFlfv6QXQZCfkGug/75R6g9W/lvW/CZ6t7YupN0max014xZ+Rrl\nLQw5fZUxUbJKNu7A9czzZ1BTh7s/WG9fhkEaZ9vCZXF/6p4BBYABj7HPLacFDF2BYc3Uv+ygrsRo\nOPThvUD+opD+gdDnT1BLZFBp/2mlTxziRCRtesi+o9mIbFwJ0bAdRIrU0POmwqd6XYh3GzNWwGC0\nIFd+iEo1qRtxTcaSeEG06Ao1xMYTiQctE20/5irN0JbIdh9TN5IY3CwkIxAWbz2z1snfDQwCHoVB\nNu38mxMpvXSOGXAoG3/08kWrcXHkzmTPQ/H9/1j9mWakKRicNwjAeYfDsdvhcHz0otwap9P53Ol0\nbnc6neGJXf66Xl0JH1/4NWoL/ct26MvnElwujXAoKMWUV9fv5S4AUaYyc1EatuMPj+wzGwoAEI7W\nllgTgJo9yXTvCB8/siuuXqBoMF1GqG/HQz99QueOy+47/ys2O/mLQs0cR3pr1lyW5Tf8IfAkGurr\nkWaGiav0gZ0Q5d/i/v6HJQjsNogCzWkjIUpWNJqguRD5iwE58kLv3QZR7k0e9D08qed4WeWZBPAL\n5IEvKgJ6/w6I8tVoPT1xCOLD1gwlLFEe+vJ5NkMuzHTK1Ewc9UzC9VdUBFcWwemBW9e5PkiZBrh6\nHkJ6wKtwKejjRl+fryjZFIYQWXh5Q5SuTOKqVuTOnDxsTgb0T8aEqvp7nI7s3GS+1vYgMupLWjGC\nffuP/H9jXaa3/AD97TjaU0tUAM4c5UGlXFU2J48fcer26IHbgdleIigZp2KuL/Xwh6QHL/ialts2\nvRA5ZzJw9yZkp/4Q/gHM0+lvANnmTIJaPhd6zxaIlt3drbCBSS3xqZScVkU9hmzWmXA0Q79hljHx\nSyzXSdRvwSh54zUTRjSCKRwOzmBeV00ZTjS9q6RkkCGMKdL+7RDFynJ68vQpcPEsRH5OCfXl8xRW\n/gPPiNW+bWzichWA7PkZ9FonCbIN20OkTc+TmCJlENC2F8MeXZMjXz/IroPpgrGh3eXYOSSsRibO\n8pHj5hJdYHBdZL+x0OuWJphomXXnBkQdh5mmq0MvM+sme25OLt9vbjprEit9+qj5vor3WySgB7+M\n0j+vpzi7UYd/9Jruj9Yf/tQ7nc5FTqezNoB0ALoDEAC+BnDT4XCscjgcHzgcjj+XWva6Xlr5VKlF\npPj3MxMlX5pi1qkjzFUMAIgPWtGiu3I+5CCOUNXwnlbD4RfANFJXXbsIvdkmhsyWm/qTTat4UAy7\nC+0kIl4EpzfPMtWgTsxZ8faF+mY09PPnkO824tktwC+la5egF02HnGA7uD1/Bn14L0SFatBrv8eT\nTas5ts+aG2ryMPIwajlIac2cg2j5nZsoyvTyYlPiOhNN4vXnMPKxz/mFGh1F4FXlWtBnjkIf3E2O\nwoFdQFQUXUa7f6JN+dI53me6TJwOBNqmNUIAQcmgXZbRkAzQt0L5UPMVAUIvQz9/BuHhAZG/mDkp\nAcCDbfhD4PQxJpF6e0OkCQEA5sloTVhaxbcJunMdyI/ud5uOiJCMEOXZYOiYaIiQDOZ12QhWhT5z\nDEiXCbLrYAby+fhAfT+TuUV1m1D3k0gTDAAid0FC8gCe0bqE1N4+0Ed+wZPNP0A06uAWyS6y5jQZ\nJHrDcjNt1dRuAHwtH9zl9UtVBI4dhKjTCCJ1MC27i9xR4mpwJ2bKuLQmLuto6mDa1A37swvgp6Mi\nrQNqIAF2svMAvic2mCDyFTGnYLhzg5bSotRp4eIpIC6W60YAuHYRInPORF+nv2tpFQe17DvoWRMh\nylSG7NiPdN3NqyEad4BIE0LGSP6ikG0/xtOdP7kJg+WYObT42nhFcvCX0L/uIRQukZI9PwNsEyzR\noA0DQl/ArEG6TNRg1DDeu7g4qO+mcF17+wb1O7+RhqufPbXSftNlcmMtvazSEeHQqxdR85T5nzkZ\n+7P1p1twp9N53+l0TnU6neUA5ATwOYA8AL4HcMfhcMxwOBwvf7n2un5XCQ8PyEYduHaxCevMy1MH\nm+AebfuiFkmTM3Rq5yYgItzck6rJlsCP65qq5v/rZd+ZB00AELU+AHLk4Vn0O404xXCNvKvUNkWP\nau4UNhKhl6GdxNbLwbZ48GQpuGb4eT0BR66KjIA+dQQoVg6Rsycxi6TrYCPP5DOInHkZQrbOycj6\nmvWJfc6YlY3I9ctAjrycSmjtln77X5dnEoYJhmTkqPnXPRTGhWSEbNsLevcW4PhByHa9+aX59ClJ\ntPt3cGIR/pAZNeky8YzeMwn1H77+JsZcpE1vrh08c+QhLM2VIFuwBFdeLlJolhyEg+3fAeHjC1Gq\nEicnLtGxa6VT9R3SdA/tgajFZGe93N1FIt5pRHeViy6ayoqX0ru3MH2322Dej58/xc2H9jB4r+q7\nQKbsUHOnuDW5brf/bmMgvpUy7B707Inwrvi22yrQ/B37ZOPimRcH4GXOAX3zGpDOAvbpPVvN1012\nHWQ5heyZMoZ1VNRpAGU0KOLt9yFcuT87jdVQYFLaQctVhShSmjk6bo+zkvVanTrCaVxuIvn15fPU\nyoRkZHDhozAg9T8nuktHR3IStGkVhKMNRJOOUDPHk4bcrDNEijRQX38OFCjGv+uThxAxZYT5+/LL\nxcygseVkyS6DgOhIQu2AhDyRyjWBnPmt9yp3QYii5aC+m4xEK08h4M4NyJbdTVeX3rKG9mxvb7Jr\nWnX/babID0usVVDzLq+E+6FXzgeEgHiv2Uu/7X9Kvex5YAyAaABPwElJHIC6ALY7HI4DDofjxYlD\nr+uVl4kEX/6dm1jVVdLQjuidm9zFrJVqcvXx3WTT6otTh6EvWHkPCdw1U4dbybDSg5CzmGjafYuW\ngZo3lVoRISD7GXyAE4egr16EaNSemoC929hETTask/duM0BszSLoi2cgB9oYJGH3gKsX4FWkNPR3\nk6EP7qQuJV8RqKmf8wy/SUfon3+kBqNxB5Janz4hr+PCaWo10mUCnsZQy2BHcb9obCqMjJmgpNz3\nByalSK5CNTpG4mI5on70gEmjl84yL6VRezYEVy9AVqpJ8JeHBzkjD+4CqQzYm1KW+ycgkFA4AJ6Z\nsgFCQBsHVZHLiHy6fN54WILE2pOHOAUpWQEIu2eB575jkydSBwMFS3B95MoJ2b3ZfO8Aw11VpTb0\n5tVQOzdBO60QMwCQPYZCuLgpAHU8+YpALZoOqDjI5p0pOt20MvGX0DPJC882faq9m+jIWu/d6v4D\nVzS8qyF0VdLkwLVLXM94ekI/ibGarXxFgIIliI5PBFlvTkVOGVTQtymg1kpZt5EtN5t0o2HS8SPq\nQ6+Yk0h9+hinOK615s3rPNMWAsogIb/s+PlXVfrGVaiRfYBL5yB7DCHifdIQNtydPoUISsbVS8ES\nDL87cYgTEqPkhPnQm1e76X1E4w5A2nRQ4wznnF+AO0/EL4A2/sXTKW4HIDt+CjVrvPl34Va+/sCZ\nY0aacjbzcetVC7m2u32DepbE3nvX87x2yRTmvyqmiL5yHnrXTxDvNYEI/It5SH+j+tPNiMPhCHQ4\nHK0cDsdmAFcBjARwBcAHAELANU4DAGnAoLzX9f9Yon5LIIkX1OKEinORxAvCcNfYmRFCCK5Qnj6B\n/n6m5a754lOLvuoX4O6uuXvLpK8CYGBes06W3TeJF9N74+IIUnPpRxZ8DZEhK7UHC76CvnKel7tY\nIzevUYz63WTg+VO3DBI8uIvYW9eBQiWh506B3vcz5Ed9IYqUZqCajy/PhM8ch961GbJDH+BRGPTJ\nQxB1GpKg+fA+UKgkw+bi4ujG8PFlQxAQaAG7PDzZeCRNQeFp2H06A86d4Kpj10/QG1cCsbEQzTpD\nNu8CtXoB9HonRP0WEAWKc/SbvyiQvyhH0nkKQfgHkr5oYMj1k2hLk+MSuIK6EAQm5dk0wC/XgCCS\nc12vef5inLiEXgFy5ef1XSmzoVdMzL+sUovToRtXLWHlbpvuAXST4EkM3QSFS9Ki7KrL592vKwSn\ncI8ekPmSKTvEW3Wh130PHZbQ0aWjI1+oK4mcPhb6mbtQ1JUhIkpXcl/ZAeRz2JOUjx0AipU1DyJ6\n00rrQPZhKzZtHh4Wkdb+PGp+YDnASlW0iKgGzwIAV0sZs0K4WC72VREAvXEl1PQxFPFevQCR3ULU\n69uhEEbj5MoI+kNTub+wtNZQ29ZBjegFeHpCDhgHpM0ANaYfcOMaG+6YGP69FSnFFW78RuSLWVzD\n2PgsokotiFIVLSeUkAkaDDl6JuMgjMmuHDgResvaxEPwADb3BYpbcLNnTxkT4OPLv/XCpZgF9KLn\nquKs9Yx/4KthiijFpj1dplcStPdPqj9j7a3rcDicAO4AmAUgEEAPACFOp/M9p9O5whCtxjmdzmUA\nRgAo+lIe9ev6wyX8Axh4d3ifuSqxl3RZ27SG+vlH6/dSpGYC5r6fgTuh5pmgGmeLoo+/rtm2zu0+\naPd9k7vRuo2B8yfN/bEITm/iu9WoPrQDZ8jKMfCDuxBpQkxiKG6HAslTQk0eTttkSwvZrW7f4G6+\naBnoeVMpbmzXm/C3WROgr11kKvDjR1CLZkA27QSkDuEKqXh5IGtuHsAyZaeq/e4tHsTTZwaex1Jk\nmiYdbYJxsdSIPHvCNUOB4kCxcjyDqvUhoUVpQqA3rICaMAh4HA7ZazhEoZK0KyZJAtm6J/TBXcC1\ni5A16kNHPgYun4PIa+gI7ty0xHJxcSbeHQCnN4boTwgBZM5O146rcuQDvLyhTx+BkB6EqB09QEw7\nAJw7yf/mK0oL9d5tkA46qvRCizsDwI2GiehIPi7DkaK+GW02NuZnITg9RMUaBKdFPOb76eMHvTyh\no0sv/AaIirQSnF2VLTfi7txMwJjQS2YCUkA0aAu9YZn777gE2AGBFjjs8SOKRyMeQ69fysdXpgpE\nBqOBiI7kSi1eiTyFLES8MVECbFOZYmV55m1kh+gn0Wa2DUCbMVHnh6H6t2eja9wnAOpaXHoSV2TD\n3xhyRVLt59CLpkO8UZ2Ot0dhUJ/3Ap7E0EFz/iT07IkQZd+EbNcHOPGrWyOSfMpi4PJ5989XznwQ\nH7ZxJ+Zqd12bHDoFCA+DNiiroslHPDn6YXHiDzZ9ZjZLrXuYKxi9bA5w5yYnJp5JIJv/B/fMlrXm\nxE007vBKmCJ67zbg8jmKVj3+vu/9X1F/ZjKyEkApABMB5HU6naWdTudXTqcz7AXXPwpg4Qsue11/\nZRUvT3/+ounQiZFZx7NB0AunWRoEgOuMImWgFkyDqGfsNi+dTQhDs4091bRR0IaQEABE4/a0+25b\nR3HjplVQv2znZUXLQLxlUCn7t+dZlZc302WjoyDyFmZYFsAv/cCkUJOGQGTPbf0coCjtViix9PO/\nht6xAaJlNxI3Vy2A3rqWDUnS5FDfjIIoWcEKKIuJIoHx5jVmvJStwnHxtUtsQHIXpL3vdijdMLkL\nAtnz8qBy9yZwghknev1S6PXLoC+egchbCLL7EJ41nj4CNbwHkMQL8pMvgOgoukeKl+PBb9dPtP4W\nL0+3xe0bVljbkxjuuV3l7c3myPXapkxrijYB0E6aKRtXYwBE3sLA3Zsm7lwZWSBCSr5Wh/ZwwmKU\nawWkQy8TApbUMMqdOwnZsR9Eow7WdX9N2Ni60pj12iUQvn7UHu3f7paFo37ZTl1Lk4/crdZJvIBL\nZ+FVsDgjA4xgOm2kQYsG7QiJs6fk2u+7QnVOhIIzMH9nnZPCapfwuvaH1mO3OTvspfobn6nkqawx\n/9MnZgKwCAji5Mtlwzx7wv0x5CkEUbQM5IDxZo4JLp+DdiX4RkUQ+w9Y7+uzRELd/p9Law19cBfU\nsK7AxdOQXQZylbrrJzbZ6TJB9h/Lk48V8yDeaQjRvAtw/KD7ROTz6Yi7HcqpiauSpYTsNYKfr4jE\njZay8wAgZWqoIQaptXApiMKlE9CAzUqfGbh5HbJtb3OapY/8wvc5Uza6s5p2gnCBBxN7zvfvmEJ7\n5C9qcmJeZunoKOjl30GUfAPC0BH9L9efaUaqOp3OLE6nc4DT6UycbGQrp9O53+l0tvoT9/e6XlIJ\nIRiY9iQmIfIaIEG1MQ806uPm5penEAKymRFctmAa5HAj2XfSEJMlQXdNH7fbU9+Os2BpPn6EZ90O\nZcNQpjL0vCnMnIFhFTaskmrKZ5DdBgOPHvDsOzYWsmodK8XyLs9y1ITBEEVKQXxo+3jdug4dehko\nVg560XQGxb3TiITGvdug5n9F0WWF6tCLZwD3b0N2H0Ib68YVEFXfoeZi7zYgLs5S2588DPgH0KGR\nIQvXG8cPcj2TLAWtvHUbQzTpCNGgDUSFtwDPJFBrFkP1bQO9dT1E9fchB07gdGZcfyBpCshmXaio\n37CCRNnApAz7i4uFyFeE933/tru2QQiY0fQAbcoPrRRmABCZc1iofhdEzVit2cfbotQbXF+cOQZh\nvMd6/VJivScOAVIFQxS1sQ/yFeF6w2gC9eLp1kHWdZuBSSFqfgi9/Ufou7f4vmXOAbXkW+ouHtyF\nXjgNolQlyNKVKGb09qXrKvY54BeA2GuXOCGbO5UZIotnEKpWuhLUYOtMOsHB4vEjruUGjCPXYvVC\naypSqhKE8RnTsbHWiihl4uJR0+0DkP7rqmdPOV535f+4HCH+gVzjGUwcEZLBnN7pzWugvh7JJj8u\nFvDgpEsavBX96EXncv8/pcPuQU0dQd1TttyQQyYDeQpDz50MvXgGROVakJ0HQC38BvpnClflu42h\n92xxb0RGzwLu3MDjz92/G+TwrymYt7+uthJ1mwCFSkBNGEz9lJCQLbqSPWM7UXKrm9ch3m1oHuD1\nwwdQcyezEbl1nUnJBnk60edsR74DkE06vhKrrV67hJq1D14fFoE/Z+3d9jIfyOv6a0ukSM2guu0b\nmG4Zr2SV2iYDw372KYKSQTbtSN7IpXPmQVqN7G1dJ1tuiA9tOSUXz7iNU0WmbBDNuzKHI11mIDgj\nv6AjHrPhcYXj3bhKbUen/kwSXjiNYsxW3blCAdiQSAk1YRBE6crwb2Yb9d6+wZWHwb7QcyfzwNdj\nKHD5PNSYfhBv1iY86dBeqO9nUllfogIPXndvEfvt4wO9dS0QGARR2wGkSE0XzMkjEAWKQdSsz+Yl\nMBn0mWMMFlw4jWuiFfMJckuZBqJZJ8gxsyHerA29eiHUF58AyVNB9v4c8PGFmmOISo2pk9q9mdk7\naY38mNCrpsYAAKFbSWxug4AgICqekC9jVuDODehnT9nghGQELlvnDubkK2M2IE0IbdKl6ADRB3ZC\nTWDQmShYnKuMAsV4fYOsKioYTpeIcGvtYytRtQ6j4NcvZXaOow1dP7/ugZo9CfD1h2jSgRyHnZsg\nPmxFe3C6TIwRePyQwuKwu1DdGzFpt1F7NrOuA7dfQII1kd6zhe4XHz++Z/bHZJuK4KgVEokwY6pU\nvJyVVgx+/l1RB/qYEfpYuhIDHguWsK7nWklKSfeOfaVmZJ/ITv3p/hnalVMaV4SCrx/fv9uWC+3/\ns/Szp1A/Loca3IUrxI794NGpPxDxGOrzXtD7d0K0IttFjekHnDgE2XkAxBvVodYuoabLKDl2DnDj\nCtQUd5icnLQI+sfllrsvnnMGBYpB1mlAoqphDZcjp1NAfcVdp2RW0hRA7gKWM0zF0TpsNH3w9nWb\n6CX63O3I9/ebvxqmyK3r0FvXQtR2/GNEy6+6/nl0ndf10kpUqkn767ypphDVXnKcsa5ZNsfdXVOs\nHCcaS2YQnAVwEnFoj3WdanWtzBIYZ9mnjli3XboSRLW60KvmE1/+9AnUjDEUtHp5W6TNTSuBqEhy\nOnb9BP3jMjYsfb+gcwLgauLpE6iJg+FTtY77hOThfZJX36wDve9nnq1lyQnZfyybmM8/JmCr/3jA\n05OOgBSpqU+JjIBeMA0iSy42JeEPaQ+OjuRBs1pdqu1/XE70efhDiPxFIT5oBdlzGOTAiZCDJjGm\nvmwVICoCavoYTkh2bISo04DPw9ePGOyThyDbfswk2CvngWMHTAS+fhQGhF4GctnGueFh1uoEYPOo\ntduB2XQKuLQlGbKwqalSiz83zuaFEGSVnDpiuT0AJsi+UZ3NRPV6tEynTGO6IIS3j3mwV7YIePP+\nvbwh3n4fet82hu7lyg8UKAY9Ywxw7gRkq+6AhyeFgrno9hKenpBNOgIR4ZDJU3FClMXQf+TIBxGS\nEWqwReYUxcsBh/YlvO/CJfmP2OcURLoqdYj5T7XaeMzZ85jYeFn2TXMtBAB4cBdq0lBmx7j0ImlC\ngPCHpotJa02tEsAANRcfx1VPogEfP65thk6hlRyAds7i6yIEkC23NV35fyqt4qD2bIEa2BF69QKI\nCm9BDvuKOTKbV0ON/Bjw8IAcOAEiWUr+/TyNgew3BihYnMLx1dbnQI6fB1y9xL872+RMTlzACAMD\n/4/ApO7OGU9PwtC2rTN1O/LTMdCH9vIkJrHKlI3urTa9zIA5vXElBcfZc9NV1bIbhP+LtR868rGF\nk0+f2RS/vszSWnPCZ0R1vC7W62bkf7iElJDNugD3bpsjbLfLA4LM8bL6pJXbGF40ak9A2dwpkJ+T\nS6KmjYY2FPBCCB5o7HbfaaOgHz+0bqN+SyBXASLbHW2AcycsQWuKVCZtVU0bRWBZnYbQK+dD7d/B\n2x/7nUUwDX8IhIchfHgviPJv8fZcFRkBvXsz9SjnT9E66OMH2W8sVzEzxkDv3AjZ9wtmqqxZDLVy\nPhNn6zSg1XnpbIhyb3LFJCT00jk8ky9cCrLjp9QwJE3GTJX5X0FNHAI1oifU4E5QI3pRiLvWSSLq\nh60hR89ibsz1y3QlHdoL0bY3RIFi0M+fk5uQIYuVaXJ4L7UkBkVVxUTzOae0NB7mAVfZ1iUu3Lqr\nmUyfGbhxFaIEb1e5AvYAroPu33Ej7EJI6JXz6Cap34L6kjeqQx/caa3mKr7N6547kWj+kahUk9OL\nHyk2lW8Y1/dMQp3MqoVA+EPIFl1MsaHImY9i5/CHXHu4bOSPH7lplJAiFR1GhuBRNP7IvEgN7Qat\n4kwSratcWgB956a78wbgfeUvarlo6jbhz88eh/qsu0lqhTdTlpHNcMfYSaFaMyH6BSWCknHKYD7O\nLohaOB0ia05OAKMiXvi7r6p0bCzUvp+hPusBPedLiGy5IT/7CrJhOzbRXw6lg6lyLcj+46CP/wo1\naSiQJQc1MWnTQ40fCL17s3mbctIi4PI5wslsoEU5YQE1HC5NRvJUCfQictJi4NQRszEQbSiS1Uvd\nbeVm5cjLZqNNLzNiQV8+x9ykomWZglu5pkm7feHr4Jxtunhki66vhCmCw3uB00chG7QzYwJe1+tm\n5H++RPpMhID9uAz6RsKIblm+Kp0JgPuqxS+A0fGnj0KfPGLmm6g+La3r+AeaDhkAwJMYt2RW4eFh\nilT1lh8g3mvmLmjNld/kmqihXcnuKF0Jes6XHJFLCTnV1kRFRiDu7i2osf0hSld0c9ng6RPozWsg\n3qgGhIfRmhh6hUmtjdpD/7weavxAiDJVID/9AoiJghrVG4iJhhw8ibTUFfOgFs+AKFIKsvdIiGJl\noXduYhO2aSVE0hSQ9VvwS/zz6ZADxkP2GQU5aCKbjylL4NFruBGedwRxXw7jfcQ+h/xkFGTJCqRD\nzhwP3LkJ2bon2RgqjgfHYmVMDkHs+VOA1hBZLasooiJ4Vm7/Ag0ymkHjy16EZODKwNUk2qZZLk2J\nGt7T+plWnFi07GY1CqUqAs+eWdk4KVKbE5vEqJnC25iO7NkK/egBlAsY5u3DlNYtPxjOo3Tuv/dB\nS+pi7AeqW9c5vXJdp8yb1kTOWEmZQtS4WAL4XHZbkzWznsLZX37mz3PmM8f+okR5IPyR9XpVqcVJ\nBmBF2PsFsLlLk86EoOHeLesxhj+0mkDzgUogvuOofFUGQL5VF9FrnZwoxMW6h+y94tLRUVCb10AN\n6AA9awLXhp+OIaQsZVqojSuhhnYBbodCdh8CUfMDWpWXzYGoUY+arufPoD5uQd0UAGTIAjltOfTJ\nQ1BTR7jdX8rZPwBnj0G7YgcS0TnJcXOB+7ehvhwKAHSmZcsFNWMMEq1UaZm4W/MDC60fE00bb3AG\nNpzJUv1HbYY+tNecfIm6jSFcbqyXWPrpUyjnbKBg1s9SOQAAIABJREFUCWty97oAvG5GXhf4x47U\naaHmT00cFW8wPvQPS6BtFk+RvyjD6JbNYd4LADx7BmVL7xU58kLUb2Hd2Kkj7hHhgUGMAb95jeKy\nMlXcBK2yci2uccAgP/FBSyBXAVoML5zmSP9rm70z9jkQGQE1pj9E3sLkirgqLpYNSe6CQKo0UOMG\ncCLyZh1OYaIioIZ3h756AXLwl6TF/rwOamw/Zm4Mm0rtxMoFHDsn8YL8eASFsAWKQR/dDzVtNNSg\nTlAje0PNnQq1YTnUOieUcxbU+IGI698eqldTCgKjIiBadIMcNAkiS07oqAh+eR/ZB9nhE4tdsX0D\ncPcW5Nv1zafy7Oh+Non2PI3I8IThf0bSqQvfb651EgsTs2kchA3xL5t0dNM/iNTBJJse3GVdx0U3\nXbskgX4DMKYnSZJAjSJ3QtRrxtd7RC8gOL3ponL7naBk8KtvYzvYpmwA6G4Ku2eedYs360Dv2gxR\npbZpE9Y/rTbzSkSVWrRdl6lMPY+LcxEQZLlsipaFPm2sE0MyQvgHQqTPbObhACAh9FaoFVUAWJOn\nkIz8DMZz5iAoGRAV6U6hzVkAuHcb4q26SPHV9+aESa9eCLVwGvTtGwlek5dRWsVBnzoM9e14qN4t\n+PebqwDkkC/h0X0IRPY80BdOUxuyfC5ExZpc1WhADesGXDrL0ML3W1B71acVG1wAokI14ty3roP+\ndpzb/crxc/H8whkrbDNdJvJ57NcZOgUQPPkAQE7I2+9DTf3cSl+OX0oB2XJbUyyAE5WIcE66HtyB\n7NgXwjXNSuw1efiAIXsAwXQ1P3zhdf9M6Y0rgPAwyAZtX8nt/5PrdTPyuiCSeHFdc/GMuZ91u9wv\ngBRFAKpfO7eGRdRvSYvsnEkcywLQy+cSwe26TvV6xJUbpVfMg7aJHUXm7BDNOvOsJEMWICQTmw1D\noCgcbQgiA6D6tIJs0xPInB1q8jDoqxf4+Kd8z9uOiabdNfY5WR4hGS3Cq+v+f9nOVN0S5aHnf029\nQqbsbEDKvQW9aDrU1BEQZatAfvY1kDUX9LfjoL4dD1GsHOTIGVxV7N4MNbwH1Don7Y19RkGOnUPr\nY7W6BFxJSbz7kxgm5RYrC9G6J+TomfDoP46TJwBq109QQ7qSOdB1sGkX1bdDoZfPg6hYg2N8EJT0\ndNdmiOLl3TDW+lYotQz2cq2xXM2HS2djcyJora2JjOtndv3HzYQTM1GyAnD8VyuR1/b+4lRCZ4Tw\n9aPYM+weULQMZC3ry142av/CcbiHPacj3sFIlKkCfWAH/yc4A91Asc8hqtSGSB1sOsLM65eqRG1M\n005m+ioAK33Xy5sTHkPbZI+Id7321nM8DJHWeq3N18HVMMVjRohkKbm+CbetKfMWpsbn+EF4pEgF\n2awzLecACcSDOiJuZG+ozaspeIznVvo9paMioA7shJo9Eap3S6iJQ6CvXYR4txHk6JmQbXpCZMgK\nfecm4qaNgvqiL50r/cdCvNeU69HJw4BM2SCHTIYoXApqx0Y3DL9o2J5/x0tnJ1inyPFzgYtn8Xik\n4abJljvB50r2/QJIHQz1uSGGT5oc8qO+FKDGX6e5Kmsu4PkzrlSN11zt+5m6kiw5gXMn6Gyz813i\nvzYqDmrWBPNvRLbu+UqYH/r+HegNy/ndkDbdf/6F/7F63Yy8LgDGSqRiDYaoxTtbAYwvZpeFcZmN\nrOrjS/KqgTmXvUcCANSQLiY5U0jJ6yS1fP1qbD83/ogsW4UJuyvnUfyqFJuNmGgrLdZl+e3bmtOU\n4Az8Ug29wscx1RDDRUeaCbBqzKeArz+bCnudPspGxsipUaM/AR7eh2zyEamuN69BDe4MfXA3ZPtP\n+Ly8vKEmD4P6dixEnkJsPDp8QgHq9zOhPm0D9eUw6NNHgZSpIaq+C9nhE3j0GAaPnsMg2/eB/KAV\nZNkq/J0Tv3Ji8kkr6LlTIHLl50rIcKzoRw+4l0+Rym26pH/dA3X/bkJ65LWLEPHj540DrXlW6Dpj\nfxJtXScygmTVI/tMYSUeP7Q4Ia50YPvnoWgZNn0GjVR4eJgQNH1wZ4LrA4ZGA4DImsudb2MXLtqv\nrzWil9ms5/GmOfrqBWui8WYd6J9/hCj1hqkZEGWruD9mQ7govH3cGg1cNLgneQsDnp7QB/j4RQ4L\n/Z1YI6B3brJ+7mpGvLwTXA+ANcG6ccV6PClSAXkLQ++wTgBEjnymAFuUqgQkTQ69fC7U4M5Qn7RC\n3DejodYsIon0wmno2zcIc4sIh370APrebegLp6D276AbZsZYTuN6NIGeMRb6+mWKUvuN5TqxRn2I\nZCmhH9yFWvgN1JDO5Ou07kktSGQE1NAuFFw3bA/ZbQjg6wc1Y6yVHwNA9hnJ0MVZEziNcpWfP+Tk\nJdCnj9GOCxAQeMmdBiF7fgZkzcXJoEHplQMnUjBuSxJ3q9wFqRPp1I+rQvAzphdOozbq4hnC2X6D\nsgoAeuMq63PcspsZKPmySy2dTSxALcd/vvL/YL0Cdc7r+qeWqN+Cq4ZF39CmF89bLwdPgurakNbV\nijUggtPz93Lmg6j+HvSahRCfjoGoVAN6+wao3i3hMZk6ExEYBNmhL5sDo9SXwyAHjDcPlOKDVtCh\nV4icb94FavYkqGmjuAbxTAI55EuoLg2A2FioMf0gPxkFNWEQ1MTBkH1GQQSnR6olW3G/4Zscld+9\nBQSnhxrbD7LrICaE9m1tqfpv3yAbodp7tPYO7wHhaAtR8W3IYV8xA2f5XOjdm9mkfDKKNM3VC3mW\nGJwe4s06kB36AioO+uQR4PgBaim2/ADz8BWYlHArIanBCH9kjrURmJTQowrVzLUMwAOtmvo5IAR3\n9UZOjn7+HHrNQngVLYO4bJZeRN8OpfMlR7zsjCiiz+HKjnG9pxomwVXNGAOcPQ7Ropt5gJHNOjMH\n6Icl0Ls2AXbLNEBHSso0dN8YrilR8g1axXdvgW7ayW21o4/sYzgZ2Ezh8SMeuAMCoX5aBY/E9uen\njyD27AnIbkMYVhd62f1yw2YLP3+IpMlJ6q1kWczjg9j0uRMQLm2LLVcJBopd5Cvirl/IYtMM2JOM\nK1SjNiY6ioJHR2tLIOvlzWlYjK3ZA8iHCUoGffEsRCHrucrKtaCmjcKzE4eAdFl4+2/VBS6dg/51\nN+RHnwBtewMXTkGfOkKNzc8/uiUrv7B8fIEMWXl/mXMwITmejVSHXoHeuIJ2Vl9/iLpNaceOiYae\nOZ6NWd7CkD2GQaRNBx16hasaW8lxc8nSmTwMOHPMuiBdJsiBE6D3bjM/V57ZcyP2YrxGpGM/IE8h\nrnUM3ogc8iX04b2m6DlB5SrAz2zL7hA5SBTWT6K5PvX24ecrOD1Ew3a/+RIxqdloeIuV/U08/J8p\nfeoIcGgvNWo+f2/k//9XvW5GXpdZws8fsnF7qGmjKWwsXt79ch8/yK6DoKYMhxrUEXL6StNCJ+o2\nhT57AmraaMhBk7juiYmCWrUA8r2mvE7OfEzPdeG9b12Hmj2J+ggpqf/o8AnU6E+gls4h3GjmODIL\nWvdkQzJpAVTXhtbv9vwMamx/qAmDID8ZBZEiBeS0FVBdHDyTvn0DyJgVamx/yDa9IKc6mTjsyheJ\niaJduExlrmMWfA19/CBki66QDdtBl6sKtegbOnCKlYV8twkx2BdPQ21eA734W+7VC5eGKF0RaN4V\n0tOTjohrlzhlCrvH5sOANiFZciBZSogsOSlgtDV9OjoKer2TgtUMWSG7DOCI///Y+8roqq5o67l3\nnBgJEtwDBHd31+JBS7EWKYUCxUuLQ4sVCkVKC4UWCcXdiru7W3ACISQhfvf+fsxzLQKlhTf6vpc1\nRgfNvcfPuWevvdYU8/frfwdCnsJ98ASE29wbfeYoB8JCidgCZi0Oc3sG5n1pGgGGvaDQWdf+1NCw\nbeeYAaXJ4IiEEBCFStjRtS0y8wAHFaN1o2NjoZb/DBQpDVm9PtSciaxKtewMpPfjjP1hMERWKwZD\naw21YTkc/QOgipSCuH2VInbmcPckYBeAqFKPoOesOa3sFhh6ETahpoxgOy8+3npdbM/JYGQAIBDY\n1ijRVtm2Um0LUJeqrglANhuVXHdPi/+N3fXyLwx98RTQopP1ixLlgdz5EfnrTOhhUyAcHdl66zEI\neuFUqJ8mQTRoCdG0A6QNE0RHhAPhL8niiYrkbXVwJO7H24eqsYlxK+Z1Y2OgTx2i/9D1i6y8tekG\nUbUeICXxHpuDAAcHiO4DLA7JatcG6JULredUpgpEj0HAkwdMAmyk8FG8HGSf4dC7NlpbNtlzJ0lE\nRJf+tG74fa4FgySHfc+JgplimzgyZgFuXoao28zS5tRKQf0yg8mkT3ogLBSy1zB6OKUQOiaaIFcA\n8PCE7PRmefh/GjohAWrFz5S9L1ftvW///5dIbdOkhl2IUpUo+b58AXRiAS2AsyyjFaB/t6oUCicn\ntiyio6B+nQE5kxURvTmIVunm5Rq0sscXnD5MJULz957ebJNEv4bavgai0+fQx/ZBm23cXdNQuwAA\nLpyEXv8H5MCx1AiZ9jVMz58aoNZVVrXS+3eA/IWp4vrXJshB4yn5bhP66F720Jt3oijVt305wGXP\nDTlkMkTXL4F7t6DGfAH96wzAywcOvYZBTvqZhmr3bzNJG/gxTHMmQB/dR5G08tUgm7aDDOwO2e5T\nyLbdIeu3pM6KXxYIIVjtuHIO6o+5bNn8tRmiaXtSjW0SEXVsH+3aW3SCY6581mNXJtKMS5RP8vLV\nD+9xkDInFmbzMSdnS89e1G8JXDoLnD3GwQWAfhFih+PQiWf6ABBQAnjygPRbgP43RmtEnz9pXXfL\nKiD8JWT7T4Ei1nsv6jZju8fbB3rvZvttXz0P3LqKNG268RptWmn/vQ39VZQsD5w7Ro0SYzDRryOB\na5yliwo1LC0+vXiWFaDq4WWv25LW10prDiiR4v5gXBeLi++ezdZB+lUoB0NbLx/zcZatAgTfsgOm\nCikhO/SE6cFdqxMwwGf4syEQLTrTbG9Ub6jDu62tT08viKw56cRdsgJEiQoQRcvQMiFLjiSJiI6K\nJGbkl+kErS6aCUgJ0WMQ5IQFFOI7dQjq617Qa37jczvuJ8gKNck++7avXSIiew7h7/3sUahJg+09\neeo1h/x8JKtqNokI7ttXtkTHXpCVa0OvXWJpVckBY8jOWTg9yfWzROQrKgC37mI9v00r2M7JmQ94\nfB+yW/+3tlv0ip9ZPQUguw/6YI65+q9NwJOH9J/5AMnO/y/xn6uMBAYGDgfQAkBBANEADgMYGhQU\ndN1mGRcA00E3YBcA2wH0CQoKepZ0i6nxriE79IT69nP6JnTum/T7IZOh+rZhz7xWE4hsuQAAIr0f\nZPcB1NTYtw1y2PesckwcBDnL8CeRErLHIGI0DFCa3rgCOmtOGtUBNMXr9w3ZLmeOQLTpCr1qEZRP\nOsjaTakCO3EB1IjPWIGREnLQeKgpIxA2sg/QfzSN9yYuYFvo1lXg0hnOaFf/Bjx7DNGhF0Ruf0qd\nm+PpIxrm1W1O4OjCadCH/2KLplIt6HJVoQ/sZIJ1fD8BpLWbQjYOhG7UBnh4l/oJV84TxGdKIJDR\nLyvt6D08OWvWmm2kiHDoZ4+ouhkXB3j7QtRrTrBqWl+7a66O7oVe9ANExVpJhJL0qcNkZfQcmvRm\nBt8GMmezJhZGeV/9Mc+6/s3LtIL/7CuIMlVgWjzLChb19OY6Tx8SEGgTIk9+tqLu3rAK3BUpDRzZ\nA314F9CxF3v4O9ZQDTVjFuizx+y34ehErMGOddAtP7EMomrHOiBbbjiXqoDI4Hv25+ToZFEuBQC1\nYiEAAVG+uvWczp+wYchUgGj1CdTgrtCnDgH3DeuBslUIZjZvZ9EsSwnd3IK0bM9WR8RgKImyVSHy\nFGAl0Yx7eXiPz9nDRMcMMAl396QvU3url5LI5Q+PLl8g8pcfoDL4QRqqxkJKYpqKl4Va9zsp7St+\nhihRgbPs3PmZcLu6WZMwpThYhz6HfnSfard3b/AeKcW2Td1mfI4yZKIc/skD0NvWkHVUuhJk848h\nMmVltWHPFsq1m8PZhQ7baX2g1ixJ0kYRXfuTrfTbLKvzc4Gi9k7HIChd1mgEtXU19Fay72TvYYCH\nF9SUEcmzvQAm1VJCfjrYKmx25iiZUUVKAZfPQtRvwWv0hmBliJooonZTC07rfYd+9RJ643KyuGza\nsKmRNP5zyQiAqgB+BHASPL5JAHYEBgYGBAUFGSgx/ACgIYBWAMIBzAGw2lg3Nf5lCJ90EC0/oaR5\nqYoWoS3L9y4ukAPHEa8xph/k3NUWfIAoVhaiURvotUshBo2jSunO9VD92kEuWM9ydRp3yL5fQ439\nEojlLVXzviPF1TAkE7n8iTGZPc4ySOuVC6HT+jIJyJAJcsI8qJG9qMtgMrGSMGsMTN8PgxwwFiJ7\nbsih30EvncPE6fBuDnyHdkM/fwrZcyjkhPk0AIuLM16AjlSFzFcIok036L82UeOkcSBnfDUbQRtl\ner17A/TkIUDu/GRwlCxPIbMm7WgJf+8mWUUP70G/COHg8DqSmAJHJ4LZcuYDKtSEKFiMImeJZk46\nNgZ67VJqcVSsBWEjDAaw1Kz/XEzdgpz24FWtNaXoS1W0fmZmJYTaiJPduspyvBnU6eJqNWzLU4Az\nzrAXABIxSnwzAJ7e0HeuW3EjhUowQYmLg372GGrFAt6/hm3I2Fn9mzXBuXwWKFYWomp96E1BNMCr\nVp/X7OIpiG4DIIRIqi+RkEgt+N5NzpRtaM36jIEXcXQECpciaLX7AOhfZlhmw/BKa0260vsBl05b\nAamJZ9UGrgRuaaxMmYQEsquM34IlHJ14z+PjIGzk+oWzC0Sdj5jMNmxlV/VybdgKr+/fhV6+ACoy\nAqJJoLUFmiUHHPqMYGJ3dA8TuqN7oW1xKo6OTDbi4+0H8oxZIHL5AxVrQRQrYwV6RkdB7VgHvXsD\n6bVFSkF27gthtLn0w2AyaqKtQGPRuguZcZHhlHY3JNPNIUdMBTJng5o42OJ2i6Jl6N1kE6J1F8i6\nzZjomEUOu/QHsufhJMUMBk4c+QJogDdyqhVD9TCY7Rn/Qqy85AuAaNE5+fWN0KEhtCIA6C3U8s3L\n/5vQa5YADo4QzTu+feH/4/GfS0aCgoIa2f4dGBjYBcAzAKUBHAwMDPQC0A1Au6CgoH3GMl0BXAkM\nDCwXFBSUAvQ6Nd4lRPUG0OeOQS2aSSqfBXNgfB9QnOyDK+egvhsGh5FWWqj4qAP0ratQC6YQP7Jn\nM5CQQGMtg24pMmYm/mSqjRLlrLGQ38ywuGmKoqVJFfztR4hmHSHKVoVaOB3S0xsifxGIjFmYTIzs\nSXnyhAT4jJuNF6O/JD6g3zfUOencFyp7bhrm7d8OlK4EXDkPNX4AZK9hkDOXQ6/8BXrvFuuLPPgm\n9N3rZPbEx0NvXE733486QlSsAVm7CXTNRsCFU1C7N0D/OgPa2ZnYkXJVgYLFeYy2bYB3CB0XC318\nP4WwIl9BtP+MCU/iZOXPRUDkK/q1JI4Hd4GXzy3+KTr0ucUzRA4YCzXjG17ndp+xHG8OFxcrqDNL\nduhzx6EjI5C4wCyEAHL5k9Vi/szDi6yrkCeUvL54GvLzERAuLlD7t1M86+vpUAunQ584yOTVJx1Q\nuAT04d1AtfrEy3j7snKhlB0oUlStZ/UyAVslevtaO8CoNpms6+QpaAVIl6/BWbiZUmqrnVK3GStV\nRstQ2DC/jJPlv0pZGTPmaxRQnOc0fiD3b2bHXLvASpHtZmo1YYK7bD6dj43tCiEoyuXmTuD09Yu0\nuLcRghN+Wail0awjdEwUcP8udNgLtoZMJuKRnJyY5PimZzXOxvZeK0UPoMN/USjOlEBl3XotLNVN\n/TqSbZNEFH85YT5ExszQF09DLZ5pR1EGDP8ZpaC+6mJN3PIVSpKIePQcjOgyVaGO7LFUXETb7hBF\nS0FNHpqy+V2J8sD5EwTSGtdEv46E+mkCzzUhAdCaFZM30HJJ451hoXbLHoPeiCv5NxF//SInQB17\nQ5gB5KmRYvxvwIykBbH/ZsRZaTCJ2m1ewHANDgZQMcnaqfGPwiLnrjXU4lnJUhtlP6PFcfcG1N6t\n1nUdHCA//QoQEurnqZBTifHQezZD2w4sBYrYt4FehUL9NMnOJ0dWqWtxXUWBIkC+AKjZEyxOtCJj\nZqvA1eHdiPx1Jn1lsueCmvEN9GVKh8uajSGHGNblpw5zJpzGA2ryEL4wOvQkvdAccXGAuxf09rVU\ne+3YGyJ3AejFMymZfe4EIARE8bJwGDgOcvJCiCbtoR/fh5ozEerLDjB9Nwxqw3La3r8IeatOhI6K\nhD57lIDZId2oUpmnAOTYnyBrNUmSiKi9W6D3bSMDKBkzL31oF6sQ+YtA375GtVeA1QwbpVRZu4n9\niiYFGLNyCwsnESDTHCJLdoKEbT8zuwxfPMXBuHh5Vng2LKfWR858ZN6cPQodz/aGqFSbOjc3LkMf\n2UMDQ0cnxNrIi8M3Awc423Pcvpb/8/CuVevj7g1LciICilmPSwhIW4r0aSvbRmTKam+ol7j6Yr72\nsTEWirqtw67ImQ9I1NpRcyYkdTJO407fnTNHrT43tsfXpC3koPFAyGOK5y2ZTf+jxNtxTQPhXwiy\nbFXIOs2IQ6rXHLJmY7alcuaDSOMBHRsLff4EabvDe0BNHwV9+xpEozaQE3+mpka2XNDxcVDb10B9\n2cEuEREdekHOXwf4pINauZCqqLaJSJHSFB0MC4Ua2t2aiGTNaZXwN2/rs8Fwq9cM6vh+4q4AiKbt\nIKrUhZo51h4Aa7tehRrEM7X/jJMgGEnFgin0rcqeG7h7E/KzwUnam4lDb11tUYoVrbt+sNaJNpkQ\n+fN0IEceiGr1Psg+/n+L/1xlxDYCAwMF2JI5GBQUZH6yMwGICwoKSvx2fGp8lxrvKYSXD2TX/lCz\nxhJUmWjQEo6OpMsO6cqWTsGiFmt24e0D+dlX9KvYvhpyxDSoiYOgpn0NOX0pHWQByKr1oB7dJysB\n4ID0x1zgky+ss8YmbWl4t2w+8SY71pE9M2gcRI68bNkYGJLYA6Rcyn6joeZ/B/XjOAoilarEl/d3\nv/ClaQAVRcWa0Et/Am5chujUB3L6Uqi5k4AblznjFJJ+KEtmA8XLQXT9kmJns8cB2XNzVlmmCl15\nG7YCGrai9sOVc9BXzrKVY24FuKUhndbTC0jjCUBzRhf9mq0DM10zvR/9darVT1EcKXrHOuhlC0gt\nNvQ9bENHRzHJqtmYLaWVCzlAhIUCEa8sWhrJRnys1UHVwEfYiYTZhl9W4EUIdHy81WcjbwBgNjdr\n/ylbLTvXA6/DLeVqUboS7QWM6oEoUR7azZ0YH2cXi2ZJxA/WBFFUqmUVOQMsFRgAgFJU123S1gpQ\nBdj+sr0uttiPO9et/++T3u4c1dI5kEXLWNsstrNnZWKSlkjGXJSvwaTZHAkJfN57DbVrIYnSlSAq\n14FeMgfaN0OSYxQFikKOn0cK7zbD1TZLDohCJSmklzUnlXTd0lixIgkJZNeEhZLmHXybFau7N5lY\npfeDKF6O2iV5C9qsF0/wtlme3RzFyjJRcfeAfniPrJNEOBjRoSdEjUbAmaP8zQBkaLm4JVlW9vsW\nomhpRO/aaFFmFXWaQdRvxd+SrR+SbZQoz/ZdjYaQNaxFc71mKXDlHET1+tSXadmZyspvCH3nOvS6\n3/lHgaKshn2g0NtWI+HuTbaOZcqVmtSwxn86GQHwE4BCAKq8bUGQ3PbPJQpTI9kQRctQjOzPRdAF\nCidRMhQ+6SB7DYOaRxl0OWeVpewp8heBaNkZ+s/FEHkDIJq2g964Amrgx/a04DZd+AK9SHEtfWgX\nNQIaUP5cCAF07A396iXU4lmQfUZArV0KNf0byIHjIHLkYUIy6Weo4Z8Cpw5DmUyQvYdDL/oBat73\nrHzUaAjhmwHyxxWkBwOchTdtxwrIvVuQvYZCDp5EUakFU6gfEfGKA9/ta9AXTlK2u3oD6CN/UeRp\n7RKC4CrWgvD05iw7U1agZiPOaENDgAf3iIV4FQpEhpPtIQTL6p5ZgMKlWFbPW/CNluU6Pg563e+I\n3LGObZsUZKX1ttXUirh+Ebh5BaJ2UyBTVug/jCSsQSsukwi4p7WmUJpZJM2cjKTwyxJ+WYhdeP6E\nUugAZ+TmBdw9ocPDoLevgajR2HpuWXJQp+T8CYgipSGcnIk3OXUIolJtCHdPi+miZV8BJcjM8fAk\npdXDy5KMiOoNoXesha7ZCPrGZeux50yEc0lJydPbx14bJDICevGPQI+BbKF4pbWeU+hzVkEe2W9L\nlKxoTUYKFmOr6NoFqAGdyDwpXdmaYHfqTezC7PGQnw4Gata335aTM/FWNRsDV85CHz9A3Y1dNoJi\njk6AFLw3CfGwdcWFX1bir0pXIubLL6s9hTwmCnrfdjsBQ/M25fApEDnysFqyYRlBqgn2gFI5+kcg\nUza+F3as44d5CxK3EZVI4n3odxD5AqB2rkekYY4nGgVCNGoN9ePYJOBWS+QvDFw+w2S1nbUNqY7t\n4/NUtir0od2cDNRvmfw2bM7XQuN1cYXs9qUd9up9hn54D3rjCrh91B5xNlTz1Hhz/GeTkcDAwNkA\nGgGoGhQU9MjmqycAnAMDA70SVUcygtWRlLbXHkB7288KFy7s/e2338LLy+tfSS3/bwgnJyf4+r65\nhJlS6B5f4uXNy8AvM+Dz/S8QLol6rHWb4NXpQ4g7fgAY2x++PwVZ123XHeH3biF+0Q/wmfIrXp05\nCtODu5DTR8FnohWlr4ZMQNiIXjA9uMv1Vv+GNJmywrWWzWxo6ESEjR0A04Lv4f3VeLz+fR5MM76B\n95iZcMzlD/j6Qixch2c9mgNnj0HO+Bppx87G66VzEf3HXDi/DIF7l74Qvr7Qq/YjYvYExO7bDr1x\nBVxrN0H8tYswjR8I9/Y94NakLXSlmohcOB0XErdMAAAgAElEQVSxB3dZBj3HPPlhOn4A+vBfcKvT\nFE4ftUPs4T2IXbsUes0SOJeqBNeaDeBcqpK1UpAuHeCfSIzsXe+B1oi/cAqRv86EevwAXt2/hHPD\nVslSBU1PHiLUcGEWTx7Cc9BYCLc0eDWebRqfmX8gas0SxALwrNMUrjbPhXr1Ei9MCfDMlhMuvr6I\ncnbCawBurq5wT+b5MeXKi1AAnqZ4OPv6QmuNVwe2waxM4hn+ErFH9iBWOsC302eQNv4yEeWqIu7k\nIfj4+EAIgVeODogD4FmxOlx8fRH+2yyYaxWOuf3hFh2JCK0hnV2hEGFX2fCqWAOvDu6Ey/5tiLl7\nAxqAY6588PHzszveVy+fIw6Aa92PELNzg+Vz36zZYXr8AOYGhHuXL/B68Y9wy1cA7q06IyF7Tst3\nHrHRiMtfGPHnT9r/pnx9EZo9N0z378A1W07ER72GyZjxq/nfwymgODx6DYGjoUmiR01D+A9jEPfT\nBMSEhcCnabvkZfEz1gOqs9RvevkcpscPoUJDoF69ZAIiBISzC6RvBjikSw+ZMQukrUaKTSQE30b0\n9rWI2bY2yXfe3/4Ap6KlIYRA3IXTiFwwBSpRwuVcoQa8+o2Ceh2BV2O+hDJ+ry7V6yN23/Yk2/SZ\n/hsccuRB1J+/IcpIRNw79oRbo9Z4NXEIVAqJiEO2XFAP78ExXyF4D51keefE376OsCWz4RRQHAnX\nL8IxT36kHTgm6TspUYT/OBexxm/Ys88wuOb7MEmCTkhA2OTZEJmzIW2nnkgQ/xuQEP88zO+fMWPG\nzLh06VJiJb7lQUFBy5OulcK2/ouDsJGINANQPSgo6Hai77wAhIAA1rXGZ/kBXAVQ4R0BrKUAnAoJ\nCUF8fPxbF/7fHL6+vggNTSr09HdDPwqGGj8QonIdyI69kn6vTFA9qbsgWn4C2dBq6qajIukEm8aD\nqql92ZsXTdpC2ppbPXtMEKANgl9+PtLi08JtvaZr69NH9K1Y/RuNsAaNh8iWG76+vnhx6wbUEMOh\n08kZctoS6GN7oZcvoJrkZ0OsaPwLJymCBgBeaSFKVIA+sJ1Yja5fcuZ/7QLUTOofAOCMNHtu4Okj\nIDaaOIgqdaDv3yUO4N5NtmQCSkAUKcWZv08iF9e/e91jY0gX3ruVPfjc+SE790W6YqWSvZ/6wR2o\nMYZbccFikF2/JFbHMC8U9VpAtukK06c0H5RTf7MDa+q7N6AmDIL8egZEzrxQG1dAb1gG0bIzZMPW\nSfcXEw31RVvqVZSvDn3mqFX2GyzF6z2bIJp1snsmeO1PQc0aAzl2DkTm7DCNG0BJ+xYfQzZqYzlG\nODpBNOsAfec6qcrPn0J07svWGcCqVfbcEBky25sw1mhIfIZNmCYMotx5pz7Qv1stAuTkhQRgjuAM\nXH6/CHr/duhNK6gQWrgUVF/66YjWXYi7WTwLctpSO30KtXcLtEGbll9NhJr2NSzqrObjKlcdohld\nirUyQa9fDr3tT7rdtu4KFCz2XvUodHgY9OnDZHYkoxcj+48GCpeknkvEK9LSj+xJulzv4XSqvnzW\nAn7m+VRLIjAHgFiu9H50Tt7B5Me9W39El6zEioiNP5VdpPEAnCjeJgdNsP5WQ0MIcnVy5jXVGnLE\nVEvLN6VQ+7dbFGBFzcaQiTyL3meoTSuhNy6HHDYF6UqX/1fv3P8N4eTkhAwZMgDEcp5+y+JvjP9c\n2hYYGPgTgI4AOgB4HRgY6Gf85woARjXkFwDTAwMDawQGBpYGsAjAoVQmzYcLkSUHRGB36L1bkmhF\nAICQDjTDAuhvYyNwJNJ4QPYaBjwKhl71K+RMw1Bv00rKhJuXy5iZHjQ2oeZMYKvBsi13yC/HABkz\nkw7cugvgmxFq2ihoY5YmfNJRdE0ICij1awdRvDxfuneuE7RqLu8XLWMVUQsPI2MmsDsQHgY1th/U\n7o2Af2HIH1dCmAe2hHjOyg1jNX3lHNSUEdCnDvJlN3wKtUDCXkAvnUNPkWE9aEC2OYgDw+1rZLfE\nxpI5Ex9Pj5EHd5ggbVoB06yxUAM/hl44DYCG7PcNt20wH2xDhzyBWvqTJRERDVtDtu4KNWc8BwJH\nR8DRkewTW/ZLItaIRZArg1FRMONd3D2QXAhXN16HiDAqra5cyLJ6WbLs9a71gJdPErwRANIxHRyg\nr15gC8ssF3/6iFV8zLjeomRF4NIZnocQdgmqqFwHOHPUTmYdAJCcOdrjB1zHw8sOB6Kmf2O/XEwU\nvXlKV6KJ2tMHFuE4ffs6ROFSgNZUVLW9HpXrAG7G4Ll/GzEyZnM+g/6sj++DGtkLphnfUhejWQek\nnbSAgO/po6AmDYY6sAM6BdDw20InxEPfucFn6KtPoAZ1ZoJkm4jkzg857HvS7YuUAuJi6S49smfS\nRKRgMf62S5SD2rDMmoh4elPGPXEi4urG31+6jFQ0NhIR0bkvXGs1ZmKfUiIC8FlzcYPsP9qaiLyO\noE+T1kxUIiPIlntLIqJvXrF66OQLgAjs9rbL949DP7gDvWklNXUSGyumxlvjv9im6QV2Qfcm+rwr\nAGPUwAAAJgB/gqJn2wB8/j90fP9nQ1RvAH3pNNRvsyBzzbLTSQAMwGv/0VAzR0ON7c8B3CwilTMv\nRPvP+GLIGwA59ieob/pAzZkIOWY2hGHHLgoUgfjkCztAnZoygo66BvJdpHGHHDAGavo3TEh6DyPS\nf9rXSBg3G/BIy2Xm/Ak1cRDw4C7UkK6Qo3+EHD6FSqkTB3Gml78IRdTmr4X+ZQbptCsXcjB194Re\n8TP0iQOQ7Yk50RWqE1+yaSW1N8JeUK+iaBliNBbPhHZxgyhbhZoj2XJB37wC3L1BX5Hta6FtKj8p\nRhoPIE9+iCZt2RNPji2jFHDzCvS+rdAnDlpm4KJ1FyD8Fc89Sw5en5+nEtfilRamRdRYsO3DW+Le\nTTtKqDaM3d5ITXR1A2JioLeuoj36wLHQB6xsHdGsQ7L0SeHqRgn+a+cJ4PX0hmjdBXrRTKipXwMA\npG96KN+M/D42xsCB5LN38I2NpoqrDUMIAISBYbELQ9cGHp72jJlnj6D/slGBjXptGDwOgPp+GHU1\nzM/7rSu857n8mUzbGPIJJ2fipP6YC318P3FLBYtRKXjod0DTdlB/Liae5PIZKIPtFVO/OWTzjkB8\nPNRfm6iN88dcIJc/RC5/IHseCB9f7tc1DSnGysQEI/Q59MsQ4OljmjQ+tWc32V2TRm0gajWxJKE6\nIQHq0C6CiRPRdQFAfjEKolhZVi2njKRAH8Dn/VGwvRcNQL2SvqMIKP55qkXiXXQfCFG8HF6NH5SE\nZWMX2XIx0Rg62SInoONiaaAXEQZkyQncusJEJbn7axM67AVl6gHKvfccaueX9D5DJyRALZoJ+GWB\naNr+7SukRpL4T7Zp/gcjtU3zjqEjwqHG9gMyZyfnPxkQmFo8k+qLbmkgZy63Ive1pjLjsX2kL0aG\nQ81hSV/O+N2OcaC2rrYaWAFs8YycZifxrF9HUmwq9Blkr+FQK36GCH8J0f9bi3utVspIMqi0Sdpv\nbqh53xHY2bY7RI1G1mO8fglqynDLPkTbHhzkHgVTbrz5xxCeXtBhoTQM3GHfexdlq9L59eYV4kyc\nXYCA4tTTyBdA4OPrSOAl9SEoua8BpSFcXcmSMHQikivV64R44M4NuN66jKi92+iZYhYRA8huiQwH\n4mMJEqzfgud6+xrk+HlAXAzUYLawbJNFc5gmD4HwSU/AJWBt54ycBpEr+dmeaWh3iLwFqZbboBVk\ns45QezZbvEVswcqJQ637HXr3RgpDVa4D0aQt1MBOVsCkgwNBug/vQV88DUS/hqjVFMjgB71oJkT5\n6jTrq/MR9IZlZLkYWhWJnymdEA/Vm60i+fUMqPEDLGaBiUN+PsKi4qnDQsnysaGeypHToG9ehv7z\nN8jvfrFvdSllVf51dob8ahLUr9S2kIMnQqT3g372iGwZW4dbc6RxJ4X56SMg5HGy3kDvEqJ6A4gq\ndWmWZ37O4+PZuty6Gnj2KOk6VeuxiuDsCr1nC/SKBdbv6nxELZjE6zTvRDXiyHB6ORmMGtl7GBBQ\ngrTgW1dTPtB8AcDjB/SYMiYn2mQiU+fKOaBoaeDUYYgu/SAr13njOev4eGoYGe7Acuhki6Hehwi1\naQX0xhWsXBq/k/f1zv0vx/ts0ziMHj36fRzT/9bIDKBnVFQU1L/8wf/Xw83NDdHRKSgbvkMIFxeI\n7LkpDuXiygE2cRQrx+8T4lliN3w+hBBA4dLQ1y6QKtyoDbEVNy4RHd+wtUWwSPgXItXSbO8eH0fm\nRZkq1mqLszNEmcqUgz64E7JLfzgE34Jp2xqI3PkhMmQiE6J0JbIOrl1gCTpjZsg2XcmY2Lgc+lEw\nRKESnNUaFF194xLwIgS4dJpUyCp16Ej71yaed/4ikEVKkaXi6madIT4KptiYXxaIEuUgcvkDIU+B\nfduI3di5AfrWFUvyILzSkn2TJSedcNP6kskSGU4WzuP7dGs9thdqx3ro5fOh929Dwv3bTHBKVQRu\nXLLO8qNfQ1SoCdl7GGSxshR527me9Obsuen58fQh8RSl7GV59OsIVoVqNYbImY+JnFkErHVXOzVR\nu/X2buUx+KSn6JSjI+moZvr0Rx1SxkDExVLsLD4Oskt/CJ90VAU1y6trDdmxD/Tqxbw2IU8gW3bm\nfYmOguzUB3rbaiYOt6/Z6aGIes0gXGySrehoK3amVhMet4cXE6E6zXgO5sidHyIvQcfC1Y3Vgd0b\nrd97ekPUaAS9ez3g7GonbieEgMgbQLE/kwn6xiXIXsPI0Nq7FSJvAYjseSAKl2KlIn9huKRNi4Sb\nxkAdH89E5HWEPUPm70aOPBAN20C26gzRsTdk8XIQadMRE/I6gkn0wmnAsX32njsA4JcVcuA4yGr1\ngdDnxFMd3GG9JgHF+EwlCjlgDGTlOtBPHpDRZk4Iv5oI5PJnInL7WpL1LFGkFHDnBic45omE1sT1\nnDwIUbEWcGwf24+GJ1BKobVmVekcu/aiQ0/IRKaf7zP0/TvQv8yAaNAS0qZK9r7euf/lcHBwgLu7\nOwAsAPD432zrv9imSY3/eIiA4hD1W1KmvEBRJJ4xCykhf/gD6suO0FtXQxcvb32xOzlB9h4ONWkI\n1I9jIYdNgb52Ebh5GWpwF85mzfTHVp8AUZFWxc3nT6Fmjubs0mgjCHdPynFPGwU1/zt4jZyCsKVz\noWaOgej2JaThkimbtIPKkJl+M0vnQF88RSBrgaJQv/0INW4A/87tD+HkDIfBk+hCPHUEcPYY9Nlj\nEF37sy2y4mfo3ZvYQilXjbPBus2gTxzkAHTvJnDnOgGXAJAjL0S95kwytIY2PGwQ+pz+NW+94BJI\nn5FaE43bQgQUg6eTI16N7m+/WK0mELWbWBUqL56ml0mNRtTxuHPD+oJOZBRoXh5KQRQ1sBdPrTNm\nkQI7A4BlZi3b9YBwcYE2mexUUhETzaQzuchpNfyz+MGYtUAyZ4eDkzPFzMJCidlwcwdy+zNpypWP\n6xQrC31gO9uIBosIAPTWNRBtu1v3FW+jlSIdCIQUgiDkj9pTw8Rc/UhULRAZMkGOng01miJ9esc6\nJlmVakPv2gBdq7Gd2qnInA3y85FsEzx5CLVwGmSf4VDL5kNN/ZrPToOWbBsUKgHPKrUQ36ordMQr\nPjv37wChIcRBmX1lbMPFjfT3LNlpI5A5O80A02VMUq3UWgO3rlB59fh+Vp2ckrYrZL9vmRQoBbV7\nI43kzOdTrT70pTPWZ9p2vXFz6WVz7QIrIgAgBOTYOYCDIyXek6m+WLZdujL02WNsCdm6Lm9YTgPI\nmo2gD+2iDUQyz23i0Pu2WZ4/UbEmtVA+ULA98wPvRZN2H2w//xciNRlJjX8UolkHAjd/ngY5akaS\ncr9w94QcPAlqynCoyUMgf1gGYYAghYcXjfAmDYaaOwly4FioPq2B1xHQ87+H6EXDNyEE0Kk3EPWa\nBmcA8R+zx3MGZdYz8fAyEpKReDVhMK3LPb2hf54KFR4GWcdoNZSvDp0pG8vzZ45C9W4JOWUx5KgZ\nUAumQH03FKL1JxC1P+LstkARyDmrCGA8fYROpwDEZ0NY4v51Bo31mrSFKFeVduaVa9ND5PBueuZE\nv6ZTqy0gM29Bgi0zZubg6ugE4cABRMfHA1pBuHmwXO+WhqDNVy+hb12FXrcUeo2CLYdOdOgJUb6G\nXcKgr12EmjcZKFSSrabYWGJIAIiOvZLFgOhj+4hRMJg/+o4xk00kymW3jq0WSHGCSvXh3fYLRYan\nnIyYhcaSU858fB/OLT9GzPWL9IMRAsiTnwPz/duAOdGs8xHbdYbVveXY9m2Frt/CRpUzUXXG2YXH\nFfKELZSvJlAQD0a1JxETR2TNQbGyQ7uAhHiyhBq35SC/bTVEy0/sly9RHqJjb87SH9yFmjkWsudg\n6HMnoDetIKakWQegpNXUTXh6068nMRj3H4R++gj6xH5WA589ZgIDQcsDmyRYfPw5W2QODsZveqq1\n7ZcjL0SufMlWQ1CoBNluzi5QB3dacV5Zc0IOmgC8eMrKSkRixqdNlKoEfeYIK3eFS1o+Vnu3Qm9a\nAVGjIY0gs+WmCd9btEH0jcu83gAZVp36fFCnXL1lFfDwHlk9ySR4qfH3I7VNk9qm+UchpANE/iLQ\nO9cBoc/t2A2WZdJlJMDu9jW+rJu2s1Y9PDwh8hSkKd2LEMghkyiu9Pg+kCYNRB6jkiIk5cTv3LDO\nWkNDoO/dpKqq2UHVxQWibFU4XDsP09bVkM06Ad6+xBHExxG3IQREWl+qkho+NHrnOm6naVuW8Tcu\nhw6+DVGwGM3VHBwhy1alE+lfm7j/U4cA77SQH/eFDnkMbFtNoJ4QdMhN68vqUYNWdCL2zUDw5UsD\nm/DyOdk4F08BZ44Cpw6xhH/yIHD6CKXCj++HPrSLA+qezdCH/2IryCjbOxUvCwyaABnYnS0pmxaK\nOrIHet53QL4AyN4jAEdHqOlfU6wrvR+VNRN73LwIgV4+n/fIqFaozUHA4/usrCTXjgOICwm+Tffi\noqVJRf5pEpAzL/EsAESFGknAzpb1d2+gPHfWnJBV6kI/Cua9McKjUy/qvLi6AY/u816lcYfeuxWy\nSVsav6X3o7T7uWPWQbZQCQIeY2OsRo9xsVZmR+U60BdOMiEJC4WoVIvU4CvnLCaCImfeJO69yJ3f\nKvJ16Qylyj08obetYdvM2z6pErn8WdU6ewyIieYMP6AEZMtPoO9cg962hg7QCfGId/P4Vx4mOiYK\nuHIeevdGqOUL2GK7e4M4GgcHtmRsk5BurAbK3PmBF89o+7B2qSVBFB914DNz5miSfYku/eEQ2B0Q\nEnrNErbRAIgyVchau3mF9N2oN4C1S5QHzp+E7DnY4tgNgGyzRTP5m7vNSowcOM6u8pTs+Yc+53Me\nF0tGz1cTknhqvc/Qwbehf53B1lGFGkm+T23TvOO2UpOR1GTkn4bw8CKLYeNyIHN2iKw5ki5UuCTt\nyZUJePYYolQl6/rpMgLpMzJhcHGF7NKPwLhLZyDyFYTIQLCqcHCgvsG1C1YJ7pAndIstVdkiFCWc\nXeBTtymirl6E3ryScur5CnH7z58CRcvSlt3FhYqNL0KAB3c4k3dyhmjeCSJHXg7+e7dQIjxrTiYx\n7p6QH7WnMuWJA5RAP7oXIncByMDu0C9CgF0bmLCEvaD8tqc3MSH+hSCr1oOo15wDY9YcfLEK8eZZ\no234F2JPuks/yDbd4NOgBWISzfT160hSKTcuh6hUi8qeTk5kMBl0bDl+PoGyiUJvDgIe3oXs2h/C\n0YmtFkOxUrb6JMkgC4CS9ysX8tpXb8Brs201cOk05KeDraXyCjV4rxOvrxSN+6JfAzHREA1akZHw\nzPpO8+g1GFGLZpFFEXwLslEb6IfBwKXTEO0+g3B0ZGLl6ETPIXOEPKF79M4NnPW7pWHyacaMlK8O\nfe8Gl335nI62GbNAZMpisZbXx/dDlKlsRx8Vrm6UXTfo0Xr/NsiajaAfP4Q+fZjqsYmEy0T2PBCF\nijP5iY0Brl8k/ql2U8gGLYGXLxC3exP0znWsAN67Cf3yBRATReyMEGRKxcdzoI0IAx7dg751DfrC\nCeg9W6DWLqWex7G9xGt4eLHqYyj+Wjxj/LLyHncfCJkjDxlgm1cyeTWYMqJcdYgipTjrt3V3NkJO\nmAcZUBw64hUTjmMEh4sm7SA69KQy8cKpSf19bKNoGeDyGTLabCpD+tpF6tQUKgE8fwaEhTIRSe+X\n8rZAZWI1a4yltSj7jkJKgOv3ETohHmrWOLJ0egxKFqCdmoy8W6S2aVLjX4WoVBu4eJo4jDz5kww6\nQgjIaUug+rWDPrYPKm9ByJqNLd/LCjWhnj2mZ0TGzNbWzoxvIcf+BJHZ8LpxcYX84hsyXcy+F1fO\nUTTri1FWUKuLK2SfEdBLZ3PW0rorRI9B0ItmQkeE00zLLQ0TnG5fQhUuSRzJut+hTx+GHDQecswc\n4kIWTiOtt2NvS+tClCgPOXcN9LY/odcvo6X70T1AyQqQI6ZRsnv/drZo8hbkYFaqMoRveh5j/sIQ\n+QvbXSMdE80BLiGBL3ClSO01BpS3lZl1Qjz0wV2kG8fFQHTpx/uiFfTC6VYm0bez7AS6LOuHhULv\n2QxRv4W13XblnHWB7HmSrhMbA7VktsUfRnj5UFxrG2Xf4WdlPSWWErfE9YvAi2f0k9m0ksyRRLod\nCXduABGvmCAJAeTOD5w9yuTXRnVTlK+exF9FVKtPwPDWVRAdepESa46oSAhvXw76zi7Qj+4zUczp\nbwz+rECpb/tCTllsZ8AmGrSCPrjLUmVQ878HCpek9Psv0+hFk2hwEvkKQY6ZzSrCgR1suy2ZTafn\nqvXhPWwywh8/BK6epw7M0T10H35buLiSDpsxMyXt4+NYdUuURIi6zciQMeiw+nUE1M71TELNkTk7\nRDlKrON5UjFrUa4aRJf+EE5O0DcukzFk/q77AHrzbFrJ5P9NUagEcPU8Ewab1owOvk2MTY48TKCe\nP6GY4dsovFpTR8XAs4gWH9tt90OE3rwKeBwMOXzqB6ML/1+L1MpIamXkX4UQAihUHPrQbuiLpzkL\nTmThLZycaEi3eyNw4RS1RGxnOvmLsNKxeRVElTrEKJw+wgGySl3OamGwZ0pUoLaDGavw4hn0jUsE\ntzk5wc3NDTGxscQvJCRQPTS9H0Gmu9ZDnzwIEVDCQvkU2XLRtG3vVg4Q21ZDFCkF2aAl3UwP7OBx\ne3pT60EIVlfyF4Fo2JoD1/VLwJMH7KvHxkD2GU5fjZAnZNHsWEv34Ihw4j+80tr1voWjE4S7Jysp\n3r5kPrh7kt2TQiLi5uaGqAfBrOIsmgmc2A9RrBxknxGQBYoAEa+gxg8CrlNuW46cZmEpJA4d9AsV\nbT8bbGn3qJULgaePIOo1hyxcKuk6qxcD1y+S/nnmKES9FqSpPgqG7D2U5XtzFaJsFQi/rEm3sX4Z\nEBcH2bYHK2J5CrBNZRMqMgKmR8EQWXMCSkHWaw61awOQ1hfSEFYDWD3TGxMpT6f3Y6Vr13q2YdJ4\ncD8J8YB/YZoBXjoNZMwMIQBRogK3c+Oy3WCsD++GqFofwjAPFGk8WKWwZd+EhgAmE6sLkRFAkVJJ\n7p1wdqFZXYly0K9eUg/EZALuXKeU+unDgJc3RJ4CfJ6Ll2e7L09Btg3zFIDInovmkDny0JTSxQW4\neYUA0RfP7GjKolw1yOYd2Y4pWgbC05vCeptXQs8ebz1+FzeINt0goPmsJ9NakV9NgKzXAhCCz7Ot\nz8vX0yD8i3BCsisZqrI5nJzhFFAM6uYVCpaZ3Z0B6OBbFJ7zSceW0uMHkF+OhsidP+Xtmdfdu8UK\nXC5ZAbJ9zw+LEwm+Bb3oBzKWyldPcbnUysg7bis1GUlNRv5tCCdnCP9C0Fv+5Eu5ePmkL2J3D4gC\nRQnsPPwXUe5mQKsQQNEy0FfPQe/ZDPlRe7ZILp/lQFKzEYRh3GahWZ46TJYGQFbK1fMQpSshjZc3\noqOjmTQEFKdw2YZlpIh+0o/YjF0bmIQYjrjCKy2VSe/fofjVkT2kv9ZrTlO8F88447txmYOA0YcW\nDg4cJBq2JjPj6nkmNPu2AqcPQ9RpCtmpD6Xjnz8FDu+mtsSuDdQhefqIbRoN4mTe4O6plYmYk5tX\noA/uROzq32BauRC4fQ2iaGnIHoMgazQktuLMEagJgyy0TTlubrKqrYC11SICu0H6s2KjX76wSKXL\nLv3stDoAkGq8bB4Bm47OtHevUAN62XyI5h0hA0oA0a8t2ApRoWYS92EdHQX92ywygIqWYeJy4zJF\nyQKKW5IB04O7QI68QGQERM48TEbXL4PwL2w3mAFgIvAo2Pr3o/uQn3wBvX8b8DqCz83hv4DIcAro\nZc0FHPkLyFcQCL5jrdjFxgAXTlq3Ex8HfeYojRAtzsQF2K4zkmJRvjoTi8hwCtw9vAtRsmKygEvh\n7QtZrhpExZrErISHWSm2zx5Ti+PiaR7DpTOsIF27QLGwuzfYIgq+xQqhbQUkYxaIKnUgW34C0bkv\nZJkqEJmyQUhJwb31fzCJsBEdEy07Q+TKR6l4Q8HYLkpXYiLrl5XVlLmTLI7MKFkBcshkQEi2SM6f\nSLq+OTJnBzJkgg6+RcGyAlYqtL53iwDkdBnYWgq+TZdf/7frgujrF6Hnf88/MmXleilQ0N9HsD0z\nFvBMC9l9wBt/s6nJyLtFquhZqujZewt1ZA9bI+0/g6yVjPw3YC+GNXO5PQMkMhxq0mBAOkAO/560\nYGN2LWcuswOw6ZAn9P0wQJIAgJz5kG7MLITF27cF1ImD0L9MBwoUgez8BdTy+cD5ExDNOlLnwdbN\n9Nxxqj0aYfZo0RdPQa1YSNxL1XpUFU0EjtNKAeeO23mzACBoNLA7Kz6Pgqmzcu0iGSFmzIiQlMF2\n9+S/Ts6GTksCMRUvQqzgQ29fuBQugVoSbgwAACAASURBVLgCxSBKVYRwdSN98+YV6jmY8QGFSkD2\nHJIi8E9HhtMLKF1GlsONgVMtm8c2Uy5/OIycZr9OxCtKzmfNAdl/NOndx/dRrC0ultfL0RH6xTOo\nYXQUlgPHMTG0vScHdkAv/Qly8kII3/QwffO5xVHXTCNF5mzAxdMQ1eiQLFp+DFG9EdTnrSE+/hyy\naj37bS6ZbcWp1G4KvXsjRNcvmSCu/wNywjyo3+cCF0+x8tCsI9Q3fUjPPbwbctoSuvO+egn1lcGM\nKVSSzrEAkDEL5MipVnXaO9ehvhvG+yIExKeDeX8NbRaA+Aoz1fpN4R0fg5fHDlDc7eE94MlDKz4q\ncXilpZZIhkx0482dn1W7RGwOHRtLNs3erRaMCwBWQpoEGpXD5UjsnWM59mHfWyj5+uYVqO+HW1V+\n230GUasxcP0i21Rvwj4VKc1k6+lDpP1mBiLSWdWE9b2brIhkyERV3KsXIPuOtIKO3xD6+VM+v68j\n6EE1asZbWzr/NtT6P6C3/gk5Yhpdkd8QqaJn7xapmJHUeG8hK9aECr4NvXIhdNacEAWKJl2mZmOo\n29egj+6F6t8ect5aq9CZhxdxIZOHQM2dDNn/W3qeHNoN1b+Dvbx8hkw03Zs2yqphcO8mwkb3g+43\n2g4bIctWgfbwhJr3HdT0UaT+5shDnMj92xTbMm+3eDliXCYPAUKeQI0fQCxFs06Qo2exJLxxBfSJ\n/dT8qNXEMggIKYGSFeDw8wbokCccqE8coD6KOUFxdqHpXLtPAb8sVGN9fB/66UPOkKMiWeZPiCco\n09GJ1Y70GYnHyZQNyJAJXunSITQ0lAPnoV12mhAAIPt/+8YXuk5I4CASG0NAo5GI6BfPmIgAkC0+\ntl9HKahffwBMCTQRlBIq+DYZF6HPIYdMtoI3bX1QHJK+ZvTh3UCh4hC+6flBxsyWZETfvUERMU8v\nap+4uwPxcRBZcwHPnwBaJz/Ax8cxiYuPo/eQUXGRI6YQHLrud6qfAhS6y5SVuByzKunV88RFePuQ\n6XH2GHD7KuSQycRHPHtEDMnI6WRM5c4P0e5TUkm1hv5lOoGhExfQvyXkCdTIXsRCDf3ujcwOB78s\nkFXqJr1OygTEJwBOjm+chVuWj4mCvnCKQFhbQC9AemzdZrw+6/9IMYEQ9ZpTadjJiQnN+t/tlGLl\n8ClkFe3aAP3nojcqxIpqDSjy9yoUcuB4OPkXAowBWt+9weuUMQvbM+eOU7L97yQiEeH0qjFX//qM\n+OCJiL53E3rLKojGgW9NRFLj3SO1TZPapnm/EVCc5lR/bSJWIDmxrJIVCACMiYI+e5xMDAvl1wsi\nTwHoLUHQD4Mhuw2AvneL7ZOtf1IoykzndXOnAuvF05YXqw4LJVOhdCU79U2RIROxIacPQ+9YB1mz\nEUTZqvSKOX0YolBJC61SuLhC1GpCnMiFU8Ctq9QTyV8EsnwNiCr1gKgI6G2rqc3hmoaCZLY4EHcP\nzr6btmMb4tVLtmVMJgJ+92ym1sT2NXyZZ8hMLEDR0hDlq7HEXrICRPGyBOPlzMvjefkc+so5JGxb\ng/jZ49kKuWidkIiuXxJAmZiSahNamaAX/whcOAn5xTeWF6vWmhoTzx7TSK1lZ/v1NiwHDu3iiz9H\nHm7H7HNTuTZk7abWhR/esxiuibrN7AZi/eQh9OrFZC9lzcnP/trESkC+QnTVrf0RsQs3LzMJe3iP\nnjsP7kKfOADRohOEq712iT57jGJeoc+Jgenanxig3PmBPPk5kGTKxnZEZDhEw9akjL96AXh4Q4SH\nQZSpbDyHntBH97Iy5ZMesv1nbL/FRJMOXrIChLcPRC5/VguuX+K/pw8DvoYSbcHiTLpeRxJnsXUV\nab7p/JJUMVL6fQohDcZQ8voaWpmA4DvQJw9CbVlF/NCpw5bEDgBExVqQTdoyuVuzhFTduNikG8uZ\nD3L493z2HBygb15mu+8acUcoUZ7+OmnTERC+Y90bFWJFU0NITilWx7LntpynvmMkIpmy8lk9dYiJ\nXNkqKW7Pcs6xMXTuNhtjdukHWebDKawChrz8rLF0Eu725vaMOVLbNO8WqW2a1DbNew9L+d/dA3LI\nd3asB8sy8fFQfegTImo1gWxvb9qmzx2HmjsJomxViK5fQk38ylJqlj+ttnuZ64hwqBmjABunYPim\nhxwwloOP7XZjoqmYePoIRNP2EKUrs2oR8QqiY68kgDT94hnbQWaNk5z5OBj7pod+GAy1biln0Oky\nUlekcp0UxY+01qyCnDtOurOtYNi/CFGuGkSdjyhY9lbmTQLN/E4c4MvfEA4DjHbWAvbfze0py3pn\nj0LNmWjxHwEog63GUgVWTl9qR4FVJw5AL5jC76YsstMZUWuXQu/dAjn1N0t/3+yBI5q2pwX7pJ+h\nD+ykDk26jKzgTF/KJG7Vr3wGEp2r+u1HtjgMVoUcMRXqz0UEyQ7/HmrcADtchBwymWq4yxdA1GkG\nvW8r5LSlVJFVCmrCQCD4NjUrxs8DEuKhRn9hwSqJHoMopKc1WTJGSxEAULQM8TZeaenCPGus/Y3w\n8ISoUJMS65mywSdffryMjU/x/mmt+bw8eUhn5ScPoB/cAa5eSJ5CW6AoQbt+WalXY6uIm0zYtWRi\nY1k1tAGjik+/ou/Ss8fEjZgZbSmEaPUJ9KYg4ji+GGXx7vH19cWLU0ehZnwLZMkOkTUX3Y07903S\ndkv2OphM/L0a+BTxUQfIph9e+VSt/R16+2pWxbIn4wadTKS2ad4tUisjqZWR9x7C2QWiYFEOuE8e\nAKUqJQW0OjhA1GrMysCd63SKtfmRi0xZAb9snI2/egn5+QjqP8REWX1sjEqEcHGBKFOVOiRmNkF0\nFKWkCxSFSJfBul1HJ4gyVQAHRwqchYVCfjaYuiEbl5NeWrCYZZAUadwhazeFyJGbLZdXoXxJOziw\npVOhBkSpCsDzZ9Db10Af2kkfnMw5kiQlQggyZvwLQTZsxapJ5bq0o8+cjW2GlHAC5siUFaJ8DXg2\na4+EFp0h2/ZgFcgn3dsTkfCXULMnUKOjx1eQ5axsFP30EbRhECgatLLz2NB3bkDNHgcULw/Z7lPL\nftTcSdTo6NALMlFLTl84aaEHixadLa04VlNmQpSuBFnCRl/CYMIIbx8mHh91gD6wnYDU6Nes1FSu\nDX32OBDyGLJu86Tnd+EU739cDAfo2FjImnzGRP4iEEVKQx/5y7pCxsx8bnas4z24fIYg0BwGa8o3\nAytfCQlA2EvIKnWJZ7l5mffp9BHg+VOIQiUgi5UhtfbSaVYLnj2CPrgDcHKCKFsVsnkniKKloZ89\nJs4pLo5eLacPQ+/fhuh1f7D9d3g3qeH7d0Af3Am9Yx3B06sXUyDt4E4mvzevsIJlfm85O1MQrn5L\nDs4ODtzOllUWj6DkQvQYxNaI8RvR1y5ATR5s9VoqVhZy8CRWKw9sh/5pYrLGgnbbbNaRbaDCJZmI\n2Ai5Od6/jejvhrGSmMsfeu8WiHafQv4NyXatNTVzThzgfqrUJQvoAzJnALaT9OKZEE3a2TG43hap\nlZF3i9TKSGpl5IOFPnkQav73EK27QNZvmfwyjx9AfdMHAAgKy20vVKQO7eaLoE4ziNZdoPq2sZbO\nJy+0a43omCg4zJ2M+Mtn7bYhPhuSbPlXnzsB9cs0IG06yM9HQt+5Dr1sHh2CewxM4vKpY2OgV/0K\nbWYTgC9zUbYqGQtPHkBv+ZPCU07OrFhUq48PIb70rvdTXzgJtWQOoEwcfGy0TnTUa6gxX7C9kS4j\n5Ng5Fql9/ewx8TMZMhHkav48MhxqAH1C5IL1SasUS+eQ6uyVFg7Tllj3dfE0/YVGTLXQNvXrSKgv\nO3ABIdhW6NofplF9rEJcNRpCduxNkGrwbTh8PT3JOapl86BvXKFYWHgYsS0Tf4aaM95Q5JzIBMqs\nKFqwGBwGjYdp8hDK8msFRL2GwwjSVrXWbCUYSZXsOwqieFkmVOsIZDSH2eVXX78EtXimncMv0vtB\n1GwMUaUO6cWxMcCVc9AXTkKfOfr3he9sI0sOKuXmygeRyx9I4w599TyVaG01YlII0W0An09zkvj8\nKdSqRWwzmZcxtEMQEQb12+w3s2XM69RrzuSuVhM6Ytu0M/Stq9CzxkBnzg6RKRvVaFt9Atmg1d86\nZbX+D+rRAECR0pSid/ywsEcdE80KmbOLoSny9/eXWhl5t0itjKRWRj5YiCw56OGxcQXBfhkzJ13G\n0wsitz/0sX2sZFSrZ4cFEDnyAJ7enGlpTQbH5iBWSE4dolS5GW/i6IS0dRoj6sp5+8Hg1CFqSuQN\nsBs0RaasECUrUHp953qIomUgm3eCvnKWJWZlAvIVslZgHB0p+V26MvSZI2StnD5CD40cuYG8AZCl\nKtKu3dkF+tRBzmzPHeds2TeDhaL8b+Pv3k8d8oT6D+t+B/IUILDVwGkARv99+ijgMQd9OWqGBd9B\nxtJIwDUN5MCxFvyP1poJSngYB5NkKJhq53pWALLksCu/63W/E4Da4mOrnf2u9daZOEC8SObsbMf4\npIeOjmLClzcA6sAODgzJ6DvoS2cIZnZ1Y8vh+VNACLrJblnFikf5GlZZ/9AQYoOcnIBdG9jqMlfT\n0mc03HcLssWhTNTRKVeVGjABxSHyBVDwDoA+cQD65mU+H40DWfm4d5P3Peo1cPkM93v/DgANUbAY\nZNmqkPVbQjRsBe8aDRCXL4C2BfkC+HspWIxu0kVKQZSvAVm7CX2QWn0CUbQMgc13rxP3tGklqcDJ\niJXZhuw1FOLTwZA58jCBjo0hdmnuZCvOpGQFyEHjIPMVIjts5hijvfWGiWuJChBZczLBaNsDslkH\nO5yLPn8CavZ4OObMC+XpDZw4wLZonWZvPF5zqL1boFf/xj9y5KVOiXPS9u/7DK01FYLv3oQcMOad\npeVTKyPvuK3UZCQ1GfmgUaAI9N2b1AspXSlZ7w3hl4VCR1fPMymo38JuBiJy+wMuLkxIXFxZxdiy\nCogMhz5xEKJGQ8vAlsbTEzGFS1Ey3JhVA+BsMeIVULiUPdDUw4v25CGP2SqIDIfsPpD72xwEfek0\nhH8hO60N4eUNWa8FRP7ClrK/PnGASVeeAkCOPJAFitJBN1d+MmV2b2RicvUcmSbevm92wn1LvO1+\n6gd3oFctZlk7MpxU2FZdLAJygFGRmDnairEYOM7iS2OhTjs4QH410dLzB0A/oqN7uU4ys1OtNfSq\nX8mAyV8EonQly/70ktkQ9ZpxoDNCfT/cbn3ZphsQHgq9dyucy1eH6e5NDvJ5ClAjJr1fsl5I+tY1\n4PZVMo7i4yEKlYA+uBMisDv0vVvQJw9BNGoNffsaB22tqTpapjIB15myAXEx0LevQVaqDQB8Xl1c\nqPcRHwd9/RIrCk5OBEXXa04Myd0bwPOn0Pu3QT+8B1mjIUSDVvzu4V3uy2TigH/mKFt6R/dAX78E\nPHsMx4Q4xDs4QKTLyPPLmBkinR+1eEwmVq1uXaUI36pFvAeGdPxbsUe5/MkY6zYAIksOCCEoxX9s\nH/R3Q6wA1XQZIXsPg2zUBoCAXjYf+s/FbAWplNVgRZuuPI4blyB7DqVhpE2oAztIrS9YDA4uLlDn\nT1KILRn2UHKhTx+G/vUH6zF+NQHC4597+Pzd0Ae2EzTftT/kG8wiU4rUZOTdIpXamxofNIR0gOwx\nEGriYKjZEyBHTEnCggAA2TgQpptXgIunoPoGQs5dbSezLOu3hIqNIRvA2ZVuup+3AZ48gBr0MeTU\nJVaKsJMzZO+h9OqwoSTqvVuhQ59TadSmQiHc0kB0HwhVpDT0H3Ohb15hmyagBNQv06HG9INo0Bqi\nUWs7QSVRsBjkgvXs7S+ZDQAc3AGIzn2pRlu8LByKl4WOeAV99hj0maPs/69cyIHQvxB9Z/IVIgj2\nH/a/tTIBD4OhL54izuHhPcAnPURgd4gq9ZKAiPWzR0wCXr3k9e3/rUULRN+7RRErF1fIQRMsUvgA\noK9dhF61iOdYuU7ylZ7Q51YRr2w2VZgT+wFlInDT/FlybeIMmWh1D8Apf2HE7t1qFbgLDwMKJqWM\nAyBmIzwMwtuHvkWd+lhE5mRgN6gx/Qmc7fs1nx1wwJGVahELsncLRPuedGM+f8LinCtqf0SRulOH\ngeBbUHMm8Ho5OVOEr0NP6JqNCZY9f4LVhHPHAd/0EHWbQ46YyhbKod12LBeEPKHy8OnDeD9QZvsQ\nzTpQOdY2kVRk/Kj1f1DLxLxsu8+Y1Ds4sKW3bL61yvIGjxnRYxCfB62YtNoopmqticvauIIKzKHP\nEX/9IgHgf9OVWF+/BDV3Mv9I405VVpvz+VChg29DL/8ZolqDN6qspsb7i9RkJDU+eIg0HpCfj4Ca\n+BXULz9A9h6WrDKl/GIU1KCPgcgIqIEfQ874w05aXjRtD8TGQq9YALi4QM5dDdW7FZfv1QLyJyub\nQUgHiMDuUBkyEwdijvMnoKaMsDBi7PZfvjp03oJMQL4fAdE4EPKbH6C3roHe+ict3zv1thPwEkJA\nnT8J+KanauytqwBA35ElsyHqt4So05QS71XrAVXrUX30wkng2kXoG5eA/dtZAPf0poiVXxbALyuQ\nLgOrJ27ugLmKEhcHxMchVgLqzi3Oxp/cB25dI9DT2Zky4i0+BgqXTOKbobW2S54Ae1EyffYY1MLp\nhprlN/aUXDOTwnzudWyovLb7uH3NukwWm2Tk8F9AkdL2g8ldw6yucElWH4xrqh/dB9L6WpMdczIS\nE83rkUyItD4cbJ1dOdD7pKMF/c51ELUaQ1StB71xJSthufy575tXoJ89ppz9ni0EMBcqCbVsPmSB\nYgRHCwHZpR/U08fAgzv0oJk5BrLPcIsAmsicDQ5fjCLYcecGCsGFPqfmDsAWXblqQLX6TNSePSbz\n5+mjNxvKvWOIqvWoButf2B5PpUzQJw+xumhjRCiqNYBo3pFS8aEhMK34OVmX3iSRxoNGhL/OoDv0\np4Pt/Ht0QgJNGw/torrx9UvA4/vw/noaIjPnfMOGraEf3iNwGmC77YtRSdhxHyJ0dBTU/O/owN2u\nxwffX2owUpOR1PgfCZE5O2T3gVBzJlCzIxk6npAScspiJhjRUVCjekOOn2fFbAgBtO7CUvqS2VRd\nnLcWalBn4HUEVJ9W0H/stNumrNkIOn1GqJ8mWV/6925CjfkCstewJMqgIr0f5FcTobeuIrvh8hnK\nPpevBvX7T1DTR0GUr86KgzFQy2btCVw9eYiz8+y5gft3ybzZvoaMoSw5qPZaojwrMeWqAQatVkeG\nswR/7xbw9BH0g7sswcdEp9ilDwfoc+ObEfDLwtZWvkJAbv8Ue+k6+DZU0C/WsnzadCx5+2WhS++6\n30lPLVGB5+xq1WmxOLSmcaewWLZcENlSoDgafjj4f+ydd3gU5RbGf9+kQeihg/TeexcUQUUUu1ER\nBWxYEFDRi1hQxAp2RbCiImoEUVRUUOmI9N57h5Dey37n/nGSTUI2DQIE3Pd57uNlMzs7s+WbM+e8\nBSCNkCyH98Oe7TgPjMqyqZ35lb6H19yK3bQmw4Ds8D6oVhNX2oVT0i+gSYlabHhCerJw8eJatERF\nqJfIojka4Hfd7cjyBciPU3HueEA9NAA78WV8nn/Pre5yhj6LfXcsMvNLzG33AWCKBeI8+gJ2/Ggd\n/23bgH1tFM7QZ9QJNQ2mdgPMfY8jwXcjy+Yr3+TYIQgPzSr9BS0+GzYDlws/Hx9S4mJ1hJearH+P\njfHsB5IZAcUwva7FtO2irqwnddYkJVlHiL98l4VHZTpdoqZ9VS9SA7w/fkB+/lZJvP4Bub6uueom\n5NgRZPrn+r3LpJaCNNLn5Ndhy1qV+C6br6ZnI1/Cv1kbt+lZbpDwUDU1SzPPc4b8Lxuh/ExARDRw\nMTpS+VNn0Frei6zwFiNenDWY1p0w1/XXtNsatTGZpJ3ubXz9cCZOxz50szpYvvokzlPjM0iqxsDt\nQ7RD8plajztvfqX+D0cOcOKOy3HenubOvQGUmDp6gno9pMsS4+O0sLhxoBqpZSa2+vhgrrkNSR/T\nPD8Mc82tOI++iPw7X8c/G1aqnXyPKzEX1cHc/wRy3R3aQVk2D4oFYtpfjESFa+bK4f2aAgzqQXHJ\nVdC4hRqslSwNrTpiWnV0H4OIaE5LfLx2POLj9ELt5w9+fpStWo1IcTx2mE6G7NupfJW00QekuWxe\ne4d6ahzah/3iPdi3U1OOr7g+q0V+fKyaTMXHYbr1Qn6bgfPgKE8vpdunk1ErVc0gwy75S+2+W53U\nnk9XfqRzttITgg/vx7TsiE3PXjmwW0dRqSnK4fAEdzGS1jk5ckCJpr2uRf78EdP7Wsz1dyLffoTp\neEla0bhHDdoO7MFcfSuybAF2/mzMzYM0ublRC3fEvSldFufxFzMInYf3Y8cOx9w+RLOWMn+HypTD\nXHkDXHkDEn4C2bQadm9DVi/NCKKLiYI05Ve+eyP1m2Cat8PUbwK1G3r08AEt3mTB70oOzsSHMx0v\nURJsWhq2bN+I/XqSEpiDKmSNV/AA56HR2OlTICZSu4ttsv6GJToC++6LcPSQjq9+/wFSUtSdN58O\nqRKb5q6a9ls1t93n5h2dacj82ciqJUr0zYeNvxeFB28x4sVZhekbrHfon7yF8+TLHpNkjZ8/znvf\nYR+5FfZsx747VkcG6QWJ48DAR8CVip08HjNwKM4L7yvhctsG7Ij+aqiVaRxgatTRguT9F9XIKg3y\nwxfI7q1qb34SodTUa4wz5l1k1jcaMvbvApw7H8K8OFF5H99+rITK6wdg2l+MqVwNM2gY0u92ddxc\nPEfJh03bYEqV1vFF6FHYsBKbHsQWVFEdaJu21jvbNCmkMUadXYsFAlnHSQA+QUGYXO4w5cQxtQWf\n92tWnkK9xjjB9ygZNDEB++NUvWBUrKIXjDTjK/d+4mL04nviOM4jz2AnvaYXtLqNPL/u0YNuLkJ6\n0Jm4XMiyeZhOl2YZG0lihmW87EgLb6tYGUlK0vepWg3spjS1YOhRiE6TwOakSCpTTq3njVE10/7d\nWoxceT0y/1dk1jeYO4Ygyxdgv3xPRzPpXJ+xw9VI7dZ71fitVSdo0xn7+Ts4Fau4gwZN2fI4/3sV\n+9EEVa8kJiCfv42sWIRzy2BVkJ0EE1TBPaJj4CN6fuGhEHYMOXEckhIo7utLQnSU5twUK64FVfFA\nLVQrVdM4gDyi6iU5STlXC/9wj7zcx9DxEsw1we6CQA7uwf74NaxbDgHF1XI/cyFiDFncVWvWxVzW\nD/vJBKhUHeeZN7NdrOXYYeVMJSdhbrtXR0L+ATj/ezVrSndu5xATnabuSsspuvLGrM6+ZxCydwcS\n8qnKktudWUdXL7LDq6bxqmnOKowxao++YaUSBtt2ydLFcG/n64fp3U9b28ePQOgxbUWn/91xoE0n\niIrURa94CZwBD+IfHorrwB71OkiLjXc/p3ggptMlGbP6dBw9pJbwjZpjSmclxxlfX0yzNphWHZHN\na7TdHR+Huflu3dfBvfDbdGT9cl1wK1bBBJZQW/dL+0LZIE1d3bJOJacde6hiJeKEjhwS4lVFtGiO\nmlvN/VFJjZFhOmpITQVfv2wXIrettssFsVFwYA+yfgWyaC72i3dVbbRhpabIAjRsjnPXUMz1A9QW\nfP5sZNKrsHU95qqbcO4dme2CIRFhWuBFhOKMeEF9Qw7sUa5EDrwNWTw3w5fj6mBMtZpqFvfPPJw7\nH85Kplzwuwbh3TxIDetCj6onR43ayILfca66GVYtxpYuB1Hhmgy9YhFOl14e7e6N4+jn6OMLPr6Y\npES15E/rJslv07U717YL8sdMTOky+h6nkW1l42qcW+9RHs7cn3AGDUN2bEIWztH9pBWrxtcP0+Fi\nLRq2b9TOw/Ejmg4cHqrfgVxkoMbXVyXtlaphajfA1G9CmfZdSKzdUGMJGjbH1G2EqVEXU7m6Kr5y\nsB+XpCRYt1zluR9PQFYuzhjHBJbEXHWzJjp366W8kONHkGkfId9MVjKwr7/6siQn53y89z+JSYhX\nCXvnS/XzP+l3IhtXadFavDjmsmtUhVOhivKRMnGzcluHtBB5JsPmvfd1mFsGn3FTM0jr/r35nB7z\nfU9kGTudKorKmnsm4TU9Kzx4Tc/OESQmCvvq/5SFP+q1bItbxnbR2MfUXMv06qcBc5n/LoLM/BL5\nbQbmmlspP2goYR+8khH29vz7mOpZ71bFupAfvlIuR2b4+GDuegSn62Wej8W6kAV/IDO/1AIh+G5t\n9+/aip0xRcmrjVviXNtf2+np/AcR2LNdC47lC3UeX7WG8lWKB0JkuLrLFjbKVdDY+4t7YypW0RC8\nBb8hi+ZCXKwWa/1uz+JQ6z7XvTuUrCrgPDoWjh1UO/iBj+QoyRQR7AvDVMnj44Pz5ldQvAT2xRFQ\nqiw+j76QZft0C3jnranYp+7TwqBRCyWafvIGzjvfwJihSJdLkd9nqiz31xCcES9oXo8H2M/eRo4c\nUNn1isU4r32qhNjUVLWuDyyhNvALfkemTcJ07un2CoG08dU1t2Fffhys6FjiPbVydx4bm70bcHAv\ndupEN3HZjcYtMZ17arZQJll4Tsjv71OsSwvPbRuR7Ru1s3EyGjbHuexqaNXJLbuWiDAtdpfMhcCS\nGhCYuWPmCaXK4Awejv1qIiTGq1Nq16yyXbFWR5M/fa2y+Wo19EagQ3fMwGHZxkg5nWe2QqRXP8yt\n956dQkREv+vbNmgMQiYO0OmgqK25ZwJe07PCg7czco5gAophWrZXX4a1yzGdenhsQ5uAAEyPK1Si\nu2e7OnQ2ap7xd2MwTVqDv7+OUmJjcN08GAywfaN2Xxo2y3LXb4yjZlI162rIXjqxVQTWLtOuReMW\n2Y7HGAdTp4HKFI8cgF+/V+5I4xY6qqlZNy13ZoYaZAWWUPt2x8GUq6B35b2vw9RuoO391Uu1nR4T\nhWnZURfwVh0wjVrqXXd0pFrE09CR/wAAIABJREFU5xf1GmNad8Rc2hen/wNqN1++oubKTJ+iEsyD\nezFdeuIMHqH25ieNptxqm0mvQaVqOCNeAFcK9r0X1fXypoE5XyD270Z+zeSQefHlsHktMmemdkUy\nLfIq+/xW39eO3dUQrHwlKF5CCbjHj2D63ISdMUXVL0cP6udz9JDyMypmN9ADkLBjsHwhzhXXIwv/\nUHl1iVL6GVSvpZ2tUqUxPfsi+3crZ6Nk6Qy1zq6tYBycmwdrDs7ubThDnlCvi3mztWuRSepsSpdV\nifNFdbTjlt6JOnEM1v6b4S1z7JB2wfwDoFixbMF3nn6fkpigwYCb1yHLF2Ln/qTS83m/qnX9sQxp\nLnUaYi6/DueuoTi9r1U/EcdBDuxBZnyh46hjB6FiVS2GM49k/Pyz+YiYex/HFCuGfPcp1GmAM/wF\nnEy/O0hTnXw8AebPViJraooaF17bH3P7/R7dSj2eZ0yUduDS8m5Mz6uVJ3IWChEA+WsW/PmzSv5P\nGlOeDoramnsm4PUZ8eKCgKlYBWfYGOyE0diJrygvxFNBUrY8zisfY5+6D5k1DZuWF5MZTp+bsIEl\nSJj6ISY8DDPwEahUFfn0Lewbz2BuuRvniqx5JqZ1J5xn38JOei1LfocsnotsXY8zeLhG2Xs4Hp8H\nRiHbNmJnTNEZd7M2ODcOxBnzrs7t5/yo+61YRVNru/bSAiwgANp0VudXlwt2bNKR1Y7NsGqxckyK\nB0LNepogW7kapnxldQn18dWLmeNQulRJolOszvqLBWqrPSwUCT8Bxw5hv/5Qi7foSL3YNG2NGfiI\njhsyqWQyQyLD9S5/3XKViN4+BBLisG+8pMqbu0fkeoGQBb9lvEdp3gz29xlQqz6cbBqVZrRGoxZ6\n7r6+mNoNkJhI5MhBzeqJilC31rJBSPVacGA3ecFcVAdJSYbSZcFxkM1r3d0M07C5Sn1/+FJJzXc/\nqgGMmS/qoOF8rhT1I3l7DPaL93AeeU7JzK+N0tHBZddkJVW37YLTuhNsWYedPxvWrVBlSlqir2zf\nlKGMchwoXQ7KlVf+i+MQGRCAKyUF4mK1oImNditJPMJxtIvUrK2aCWYqtsVa2LAKm+5sWyYIKlXV\n70LmgLuy5fV1Mhe8terj3DJYCc1REZj+Dyin6SSitBzerwq16AjMnQ9pCvehvThDntTsp3xCoiP1\n95NeiFx6lRYyZ6sQ2bUVmT5Ff6MeCPVenD14xzTeMc05h2zbgH17jAZ93fNYjgqRzDk2ZvDwbC1j\ngMAta4h5Z6zemQ95Eg7u1QsOQKuOqgA4eWFNSVY/iEyZM+kwl1+n1uU5SPxEBNb8g/3hKzh2SCWT\n192hY5G9O/TOeNUS5Yt06K53+XUbeVxsJSkJ9u7QILZD+9S59dhh5ZZkho8Pxj8ASUlRwuPJv+HA\nEprgW7uhEk3TVDs5QVJTtUP10zQdrwx4SHkVMdFqBx8breRWD3b+7n1ERWBH3aPFVLFAnPGfq9rk\n5ZEeL1Cu10bBzs1KKv7jB4iKxFSorJ2N2Bi1ZO96mT7/2bfVMC4tTM959AVMU89jGomPxY4YgLnr\nYTV/8/HBZ0TGeEgS47HPD4OyQTgjX4bjh9Xa3sOF33Tojrm0L/aDlzQFesiTaQqVWdC0DU7/IeoJ\n4+k4YqLVS2b9CuXDpHdMThVlykH1WuoG3LCFdkJOCmKU8BPIioU6hjt2SNVCJUvD4QMQlem3H1BM\nHY/TVT1pcJ4aj6xaol3Ieo21GPegKJFVS7Gfv6M+ONfcmmF6NvQZt4NvTsi8Dkl0pHZEDu8H0jxP\n7nggXwqxwoDExWDHjtDvwhOvFHrOTVFecwsLhTmm8RYj3mKkSEBWLdFQvV791MMjpyj1/buVgwDq\nE3KS5C8oKIiwBXOxk16BOo1whj4NiYnYJwbpBr6+Kv31cHG2/y5Q+/STL/5Va2hXIJfAO3G5kCVz\nkVnfQmyUXsiuvEHv1E8c0wTVZfN1BFSlunI5OvfMZryWbb8ieiE5cVyTiONjISGOQF8f4pNT1GvE\nx095CeUrQFBFHXXk485SXC69+Pw0DUKPKIfk5sGYkqWRsFDlSkRHqheJB5VIlvfu+8+13S2Cuawf\nJvhu7ISnISYK5/l3sxEw3XyRyT9inxiE6dYbIsKQ44dh3y7l4wRVVLfT8VNg91a3E2duxQiAa9xj\nKl2t3VDzbd78MguRWXZtxb4+SpUaN96lxfBbY7SwOxl1GuJcfSv2u48hLhbn3sdBrDqURoXr2O3y\n63IlrIoIRITB/l3qtxIdqTyhmEglKAO+Pj6kikDJMkqsLVVGTd+q1VSPmhx4J5IYj6z6R8MZt64H\nXz8tQnz91KAtc8ERVAFSUrIF85lbBmMqVFEPmqgIHTlefm22z0xcLmSmcq1M+4uhhToWU7UmztCn\nMWXLkxfS16FshUj3KzADHjp7hYi1WmTu2orz7NseeVOni6K+5hYGvMVI4cFbjBQh2HmzlVSYR5Kn\n7NyCfe1/AJhBw7NkYbgXux2b9WJauTrO8DHgF4Addqvbc8F57TOPhYAcOaAXPQ/kPtPvNkzf4Fzv\noCQpUTMt5s5SZUXTNjh9btQxhVhVziz9W4P2kpO1g9GiHaZFB6hVL9+L8el8nhIdgSz5G5n/q1q3\np3NB0uSrsme7LtS+fjiPPJeNAJxtf2Gh2Gce0DvuhDicFz+Ew/uwH7yMM2wMpkW7rNund7hKlMIZ\nPR779AM4w55Dli9CNq/RAuixF5HwUGTKuzgfzoD01wAd57Von+Px2OlTkH/+xnn6TeyoezEDHsDp\n0SfrNr9NR3740l3QyuqlGbbjmRFQHByDufEuZP1K2LBSC8nrB6R9zj+BWLXc73FllhDCgqAgn6eE\nHkU2rVa+05a1+j1q2AxKloGYSPW1yYzqtbRjlTmrCZRsfdt92JDPlIPSvB3Obfd57PbIiWPYz9+G\nHVswNwyAuBhVJLW/GDNoeI5+J57OM2zvLuyEZzLku916a3zCWSpEADV5mz4lz+/S6eB8WHNPF14C\na+HBS2AtQjB1GoBYZeZXqIRJN8A6ebugipjGLZGlf8Haf9WFsn4TIOM8TfmKmGZtlIS4bD6mRXv1\nkNi7XWWYf/6kJNagrHdEplQZTNde2rZPtypPx/aNyLrlmItqZXue+/m+vpi6jTE9r1bew+Y16sK6\nbjn4B2CatcXp2EPTYqtchImN1sCyeb8o5+LgXiRa82LIRdJZkM9TRNTZdcVi7IwpyDcfw46NypkZ\nPALniusxpcvqne9v09Xiu2oNnMdfzJeyQL7+UOWkYjHtu2M691Q+Qa16SmY8qUtjp06EIwdw7n0c\nOXZYOSr9h2iBlvaemxvvgj07MHu241x9KwQGuuPjTZvOuXdqfP2Qeb9qAF7kCXV+PVkBVL+JSrp/\nn6EmYk1aYWrUURlyZhQPhAqVYfFc5e+075bmrPoHpnErnAEPqafJkrk6klu7TI3q/P2hdJlsRNWc\nkNPnKdbCsUPIpjXIojnY7z5BZk3T4qFEaaheG6rXhEP7Yc82LYDTUamqFihHDmQdEwUUw3lxIkSG\nIVPe0RHL3SP0szqpAyMiyD9/I++P0/DB2+5T9dGaZZoeHHxPgcYbAUkJxI8bmVGIdLlMuUxnsRCR\nHZuRT9/Uztilfc/Y65wPa+7pwivtLTx4OyNFDCKikfdL/tRE2FwCtTKPbMyVN+DcPDjbeUroUez7\n4yAiTNnyzdtiZ3+PpNmQmzseIKcFSbaux05516MrpenSE3PzoBwlyZnPhy3rsHNmqnImoDimfTct\neBo0Vdmpy6V28BtXIpvXaXvd5dIRTI26erddobIG6VWoBGXLU65yFSLiE/WiB6oISkxU19aIMCT0\niPqVHNyrCpGYKOUJNG6pJNY2nbNceGTXVux3n8DenZirbtIuUB4mW5DJX6JSNQg7hjP2A2TDauS7\nj3GeezubZbyIYO/X2Hjnwx80w+fAHnzGvIPr3bHqjVI8EOedb9SOfdVSzEuTAXC9MEzVQINH5Ci/\nBpW/2scH6h13nQbYSa9pK75m1uJWkpKwE0ZD2HGcJ1/BVLkI2bjaHXYIqPlX8UD1xtmxCaKjtCBJ\nTNBjLVkac8lVmM6XwqG9yLIFyIYV2q0oHqj8oKo1MjKHSpTSxwNL6OeRkgIpyZQJLE7Ugf1IeKgW\nFOGhOtLZvztD6VOxCqZhMyheEhLikM1rdeyXGRWrKE8kLhaOH+ZkOC9NVtLmjC8gIRZz1S06TvTA\niZKYaC0cVy/FdOmpZOPvPlV59P1P5Gh8l+PnEhaKeW8srnSyaueemMHDciy4zwQkJkp5IhUrawhk\nIfiJ5ITzZc09HXjHNIUHbzFSBCEuF3bSq7B5Dc5j43KV28mxw+72venck/IjxxIREZF1m3QJ4sbV\nykXo1Q82rdaLKOgoZdhzHhcmSYxX+3cP5FaKB+rdZM+r87WoyYljyD/ztKNz4pheXDr3xLTuBDXq\nZPiSpCSrTHbvTti7XdUlYcdzJkEaR0dAJ6NskHZf6jXWzlHdxtmlvAf2ILO/V7OsGnVUEpzWZcrz\nfNIJgH7+EBGKufRqTO9rsWOGYtp3w7lraPbn7NyMfW2UBvG98AH2ycGYTpfi3DIY15vPqmFanYb4\njJ6A/fJ9fA7vQ0aNB8BOeQdZ8hfmjgdxLr0q12OzX3+IrFuB8/Jk7DMPYho2w7n70ezHExut6cWJ\nCcqNqVRVlSJjMh27vz8kJ2M6dIeSpZF//tZisXFLiI9VS/mUFGjWWiXaTVpCbLR6gezepo60J45m\nsWXPFYEl1Zm3cjUdsYgoX+jQXti1JbtBma8f1KqnSqujh7IXKKCdkIN7sbO+0a5E267qxJsDV0I2\nrtJCPDVVw+J2bUPmz4Z2XdU8LzC7UWFukAN7NAk6Utegc1KIWKvHsH+3Fqfl8ua4nA7OpzX3VOEt\nRgoP3mKkiEKSk5RUeOQAzv9ec2dpeNw2PBT7v3sA8GvZHtfQZ7MHhlkXMuNLZM5MJcv1HwIRYdjR\n97u3yYlHAiCb16jcMTz7Qk/1Wqqs8CAD9rgva2HHZmTpX+o1kpgAZctjWrbXTlDjlh4JtpKYAGGh\nEBVOSX8/YsLSXFytVe+KgOKa21KmvDqZ5pRbkpSIrF+pY6FtGzTq/to7MF0uzffFQUSUV7Jjk8pU\nE+JxXpyI/eQN2LcT54UPPDrrup57WD/TkS+5DdHSU4Ndrz4Ju7ZiuvbCGTwc14ev4OdyYYc+A4D9\n8yfku0/z5BRBWqfn1SdxHh2LHNqHzJiC8+KHHsdOEhmmHIaEODVUq1FHC62PxruzYwAt+gJLaFpx\naqoWqLHRUOUi7XLExqgbrsulHYqadTEX1dbk4lJltHvl46v/TYhHrAvj64ckJVLCgbi4OP17ZBhy\naL+SO48f9lzEBBSDhs21UImJgn07s28TVAHnqfGwZwd21jQ1FGvWBufa/jnb+SclIdM/18KjWRuc\nq27GfvsJHD2oJmSX9Cmw7Fa2rMNOfNnd4TFX3KAjnrM4mgGwP01Dfv0OZ/jzOZrmFSbOtzX3VOAt\nRgoP3mKkCEPiYrGvj9K71idfzZXxLjFR2Mfu1H9UrYEz5l2P3Qq75E/kq4kqXXxwFBQrjn3lSbfP\niLn3cZw0j4xsr5EQj3z/mSaxekKbzrrQpxFB83WOqSlamKxfiaxfrtb3Pj5wUR1MnYYq4azbSEPn\nMi3eBSI8WhccPoDs3qqkx02r9e66XmOc3tdCmy4FblfbWd+o1LZZG9i0Bmf4GCWcfjUR5+HRHj0b\nJDkJ+/AtgKpo5PcZyOzpOG9Pxfj64Xr+ETi0D3PjQJyrbsI1fjQBlaqQOnCYPn/LOvWkaNcVnwdy\nDuqDtGLp+UfUuO2+x7Gjh2CatMK5J3t3BNJkpu+8AKFHcO4bqWOZdL7E5+9kbOjrqwqYoAqYS66C\nMkEZ5nWuVA0DtKLhhhjPHatTRY06alomVo9h81qPCiDTrRfmjgdh8zotQvbvcjsDp+cFeXwPtqzD\nTv0QIk5gbh4EAcXVNr5ceZz7n8TUyCGlORfYfxcgn77plp+XGDiUxIuvKPB+Thf23wXIJ29grh+A\nc3XwWXnN83HNLSi8xUjhwVuMFHFI+Ans+KdARNvouQRuSXwcdvjt+o/AEjgTvszmxQBKYLMTX1Zu\nwtBnMNVqYhf+rkUKQKMWOCOez5EzIds3Yb/5SLkdHmA69lCbdQ/5KXlBjh5CtqyDPduQPdvdoXP4\n+ilvpGIVTMUqBFa7iHiL+pcUK64GX8nJkJKkDpsR4ZqxEnZMDaUSE9Qoq1Z9zQNq2zVX35DcYBfP\n1Zj1lh1g8xrtNPW4EvvyE5huvXDueNDz834NQX6ciunRB+fOh3C9PgpKlMLn4aeBTHLfh5/GtO6E\n6/lHKNayPSk3DtT3JjoS+/hd+py3v877OBf+jkz9UHkSm9Yg0ybhPDVBidIeIAnx2tnZsFKTba+5\nFeP4KHfikwkndUkMYMDfX7tZLdpj/PyQ7RuRXdu0q5F6GmtKUAWNDAiqqOOX5CQd+WQ2LTsJzogX\noG4jVWvN+1W9Rho0xbnuDkyjFjk+TyLDtchevlC3v+Y27J+z9H3o2gvTf0iuPjUe9ymixO0ZX7gf\nM/c8RoW+N571dUh2blbjww49MIOHnzVDtfN1zS0IvMVI4cFbjJwHkLBQNd9yubQgyUXhUa5EICf6\n93b/23k/xPPI48QxJbaGh2owVot2yPHD2KcfyHjuS5NzvGCLdSEL5yA/TnUHrWWBcZTkes2tp5V1\nIXGxaoR29KASUk8cg9CjmOgIJCFeRwInw3GUL1KhMqZ8JTdvhNoNCnxRORl28Vy1Fm/WVu+4K1XD\nuf8J7WAVC8QZPd4zGdJa7BB1wHXenKpeHSMHYQY8iNPjyqzE1nGTMJWr4XpiEIFXXEfS5Te495Ne\nsPh8PCvPY5WkJOxT96oN/x0PYl96DBwfPcacguesVQ7NrGnqMTJoWEbS7eH9aot/4ljWJ/n4aofC\n10/f4wZNMDXrKXk5JUXdcaMjM+z9RXDbsQYGQskyFC9VkoTICHB8dBx07BCyd0dG6F0OULn5Leq+\nO+9XzThKTtJi87JrsmQkZTtXl0sDE3+cCn7+mJsGQUqSFhDFiuPc8aDymQoIsS7ku0/V4h9UvfPg\nU5hmbc76OiShR9X0sFoNnBFjPd6cnCmcz2tufuEtRgoP3mLkPIGEn1CTpNRknMfHeXSGhDQfg+PH\nsE8MdhM+nbeneeQvSGI89pM3Yf1KjVe/5lZwubDjR7vtys1dQ3G659xWlrgYzcSZ/7vnlryPj5L1\nevfLpiw5HQQFBREWFpamoklQXoGfv5ItfXwL/e5PRFS6Ov1zaNVR79CNwXl8nHYTjh3GefoNLX48\nPX/tMuwHL0Olqvi8NBk7/zfkm8navSpVGklKxA7V9rkzaSY4Dvahmyk58GESOmcoZwpSjADYOTPV\nT2TsRIiJUjv36/rn2aqXnZuxU96DsGOYy6/H9LnJTf6V8FAdZ2xYma9joFQZJaUGFINixbTYSEnW\nDlZyknI+crN+Pwnm+gGYK26A1BRkzT/qNLt5LZQqg+l+pfI68jLT27VVIwMO7lV/lG69sdOnwPaN\n2um6eXA2snN+IMlJ2E/fhNX/uM/dGfYc6YaBZ3MdkvhYDeN0peI8NT5fgYWFifN9zc0PvMVI4cFb\njJxHcBMNkxK1Q+LBnMltemZdqvRIa2s7L07EVMlOghXrSrsT/hYaNMG5dySmXHnswj/UjRWgXAV1\nEc1FQSAH92C/+Vgj5XNCoxY4vftByw6nrSI4q4t6cpJKcP9dgOnQXQPmUpJwHh2rcuDtG/NUPblH\nMKPfwNRpgGvC0+Dj607ylbDj2FH3AlpoSFISdugtlBrxHPHN2mfbT36LEUlKUrVVnQb4PDQaO3Mq\n8scM5SDlIU2V5CTk1++RP39Uj5g+N2O6X+7+Hrhl2998lN1QrDDRtgtO32BMrXpIchJsWIldvhDW\nr9SOTINmyhPp0D3H2AL3OUWEIT9/gyyeq+qp24cgu7aoC2/ZIA00bNLqlA5T4mK027hziz5QobIS\ngjP9Ts/W91ZSU1U5s28XzlOve/ztn2lcCGtuXvAWI4UHbzFynkEiw7VDkhCPM3JctkUmS/aFCPLJ\nGzoLB5xHns3Rt0S2b8R+/IZ2XgaPwLTsoKOcp+5zb2PufhSnS8+cj01EJcOzvskIgvOECpVVDtyt\nF6ZEqfyeehactUV911aVeIYfx1zaVy3tA4rhPDQa+8OXsGWdvq9NW+e8j3TiKWmFRlQE9onBmDsf\ncned3JLfqjXwGfuBdsL+dzelnx5PXO2MoiFdceO8+RWmVJl8nUM6edEZ/jw0bqkcpPBQ7eTkw8Lc\nfQFf+rcG+nW5DNOtl/JvMnWgJC5GU5uX/AnbN+Xr2LLAcaB1J/WAad0ZU6x4mmHdIWTzWvUV2bpB\nvWRq1cd07K4mc3l0QUAlzPL7DOTvX7Ww6nc7plY97Lcfw/7dav9+7R35dlLNtv/jR3SElV6U1aij\nqpUyWX14zsb3VkSQqRPVq+jRsbnyZc4kLpQ1Nzd4i5HCg7cYOQ8h0RHaIYmL0Q5J2kwfPJ+nnT8b\n+XoSoDN259r+nvcbE42d8g6sX6F5IzfeBT6+Oob5NUQ3Kl4CZ9zEXM3ORESTe3+aliG5TPOqyAIf\nX2jRDtPxEkyrDhj//F8IzvTnKdERyC/fIfN/0wtfzXrI0j+hRl2cwcO1QDm4F+fBUZjm7XLeT2Yu\nyDNvYmrVx875UUcnE6a4W+dutUPva3FuvRc5uBf7wjDKvjKZmAoZvB371y/Itx9hBjyEc0kfj6/p\n8Rjeeg6OHcIZ8x4kJymPoHRZHfkVD8zffiLDNShv4e/K/yhfScnATVpBvca5d86sBevSEY0xYEyW\nQsbd0UtKgoN7kAO7lSu0ZZ3KyX189TWatlbTunySoyUxAflzFjJnJlir3+t23ZDfZiDLF8BFdXDu\neliVW6cI2bBSR3XpOTiNW2ogpYf39WysQ3bOj8j3n2EGDcPp1jvvJ5whXEhrbk7wFiOFB28xcp7C\nHT0eHalOimn5KTmdZ+Y8Gxo0zdF9UUSQv2Yh07+Ai2qr02SlqlnGCIDGnPe8OlduhojA+pXYn7/R\nosTHxzPhFFQV06YLpmN3aNg8z8LkTH2eEhWhRMg/Z4Hjg+nUQy3bt6zTEMN23ZQTkJykuTU5KFPS\nYf+Zp/byxQPxefdbJbI++xCmdn2c+0ZmbDfjC7VmT5NWy7aN2AmjKffeN0QXy+AuuA3JGjbH54mX\n839eYaHYFx7BtOiAufcxOLBbC9rqtXCGj1FFUn735XJpNMDqpciaZRAVoQVGtZpqU1+xqkqxywZB\nseJQLFD/a13K8UlJ1sI0KhwJPwERJ/CPjSZp705VT4nV70rVmpjGLbTr1KBZwY4xJVnDGX8NgYQ4\ndYnt1Q9Z/Ccy90c17Lt+gHbnTnFkKNYiv4Yo2TcNpvsVmNuH5EgUPeNF9Npl2ImvYPrciJOmwjpX\nuNDWXE/wFiOFB28xch5DYqK1IIkM0zvci2rnep6ZzdEgZ2IrgOzdoaZXMVFKYu3QXQuV36a7reQB\nnFc/zTPxU8c3a7DzflXSo0ga0dQvzY/iJPj5Q8NmmOZtMc3aqhrmpKKnMD9PSU3Vi+uSv5BVS8DH\nwXS8BHx8dORQJgjn9vtVdjzzK6hZV4u0XGTWkEYQfuQ2AJzn38dUr6nmcW+NUc5GJs8L17MPwtFD\nOC+8j6lWE1n9D/bDVyj/+S9EpmYQg9O5JJB/3kg67PKFyMcTMLfdh9OrH7J7m3ZMqtVUOXEuybs5\nnqMIhB5Bdm5RS/9jh9UrxoMLqkf4+0O5ivhVqkJq+cpqlFazrhY2efA/PB5PTBQy/zeV9sbGYLr2\nxFx9K7J1vWY+xccpIfeqGzHF8tcR8vg68bHYT9+C9Sv0AcfB9H8gz27VmVyHZN8uVXU1b4cz5Mm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Vtq2npiDFSsooVFQDFwWcSVAvt3Q+hR/XvNegR27kFik7YXXCicbN+Ife9FqFoD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\nRkRERKQyKBmBFo/2zTi1s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"text/plain": [
"<matplotlib.figure.Figure at 0x11a6cdeb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import scipy.integrate as si\n",
"\n",
"def lorenzde(y, t):\n",
" '''LORENZDE Lorenz equations.\n",
" YPRIME = LORENZDE(Y,T)\n",
" '''\n",
" yprime = np.array([10. * (y[1] - y[0]), 28. * y[0] - y[1] - y[0] * y[2], \n",
" y[0] * y[1] - 8. * y[2] / 3.])\n",
" return yprime\n",
"\n",
"#lrun ODE solving example: Lortez.\n",
"\n",
"t = np.arange(0, 50.01, .01) # time points on which to solve\n",
"yzero = np.array([0., 1., 0.])\n",
"print (len(yzero))\n",
"y = si.odeint(lorenzde, yzero, t)\n",
"\n",
"plt.plot(y[:, 0], y[:, 2])\n",
"plt.xlabel('y_0')\n",
"plt.ylabel('y_2')\n",
"plt.title('Figure 1.8 Lorenz equations')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we give an example of a recursive function, that is, a function that calls itself. The Sierpinski gasket [90, Sec. 2.2] listed in [1] is based on the following process. Given a triangle with vertices $P_{a}$, $P_{b}$, and $P_{c}$, We remove the triangle with vertices at the midpoints of the edges, $(P_{a} + P_{b})/2$, $(P_{b} + P_{c}) / 2$, and $(P_{c} + P_{a}) / 2$. This removes the “middle quarter” of the triangle, as illustrated in Figure 1.9. (The code in the function 'gasket' will be explained below)"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 1.0, 0.0, 0.90000000000000002)"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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fFCJGCgMhMoDFsqpmFbv9u11HyUsd4Q5mr59NR7TDdRQhnJPCQIgM4Av5uG7F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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11a6bc160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def gasket(pa, pb, pc, level):\n",
" '''\n",
" GASKET Recursively generated Sierpinski gasket. \n",
" GASKET(PA, PB, PC, LEVEL) generates an approximation to \n",
" the Sierpinski gasket, where the 2-vectors PA, PB, and PC Z define the triangle vertices. \n",
" LEVEL is the level of recursion.\n",
" '''\n",
" if level == 0:\n",
" # Fill the triangle with vertices Pa, Pb, Pc. \n",
" plt.fill([pa[0], pb[0], pc[0]], [pa[1], pb[1], pc[1]], 'g') \n",
" plt.hold(True)\n",
" else:\n",
" # Recursive calls for the three subtriangles. \n",
" gasket(pa, (pa + pb) / 2., (pa + pc) / 2., level - 1) \n",
" gasket(pb, (pb + pa) / 2., (pb + pc) / 2., level - 1) \n",
" gasket(pc, (pc + pa) / 2., (pc + pb) / 2., level - 1)\n",
" \n",
"pa = np.array([0, 0])\n",
"pb = np.array([1, 0])\n",
"pc = np.array([0.5, np.sqrt(3)/2.])\n",
"level = 1\n",
"gasket(pa, pb, pc, level)\n",
"plt.hold(False)\n",
"plt.title(\"Figure 1.9 Gasket level = 1\")\n",
"plt.axis('equal')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Effectively, we have replaced the original triangle with three “subtriangles”. We can now apply the middle quarter removal process to each of these subtriangles to generate nine subsubtriangles, and so on. The Sierpinski gasket is the set of all points that are never removed by repeated application of this process. The function gasket in the listing above implements the removal process. The input arguments $P\\_{a}$, $P\\_{b}$, and $P\\_{c}$ define the vertices of the triangle and level specifies how many times the process is to be applied. If level is nonzero then gasket calls itself three times with level reduced by 1, once for each of the three subtriangles. When level finally reaches zero, the recursion 'bottoms-out' and the appropriate triangle is drawn. The following code generates Figure 1.10."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 1.0, 0.0, 0.90000000000000002)"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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6XXbW6+oOu+OWJ+5z7mNj2UZ+/OkfoxqlOnQEHDy3/bkmZWfumskfhvyBT5/3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WpobKrfxB2r7+j7x0oC7GvZx+2rbu/z7dqf6C6hb4G0G5iZI4ri7cDtsWVXXXXV8JkzZzJs2LA+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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c331cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"level = 5\n",
"gasket(pa, pb, pc, level)\n",
"plt.hold(False)\n",
"plt.title(\"Figure 1.10 Gasket level = 5\")\n",
"plt.axis('equal')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(Figure 1.9 was generated in the same way with level = 1.) In the last line, the call to axis makes the units of the $x-$ and $y—$axes equal and turns off the axes and their labels. You should experiment with different initial Vertices $P_{a}$, $P_{b}$, and $P_{c}$, and diiferent levels of recursion, but keep in mind that setting level bigger than 8 may overstretch either your patience or your computer’s resources."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Sierpinski gasket can also be generated by playing Barnsley’s “chaos game” [90, Sec. 1.3] listed in [1]. We choose one of the vertices of a triangle as a starting point. Then we pick one of the three vertices at random, take the midpoint of the line joining this vertex with the starting point and plot this new point. Then we take the midpoint of the line joining this point and a randomly chosen vertex as the next point, which is plotted, and the process continues. The script barnsley in Listing 1.8 implements the game. Figure 1.11 shows the result of choosing 1000 iterations: "
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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L4vG45ThO2fqm8Xj8o8BHp2/btm1b00MPPUQsFiu+fS0Btm3T2nrl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"text/plain": [
"<matplotlib.figure.Figure at 0x11c5e8e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#BARNSLEY Barnsley’s game to compute Sierpinski gasket. \n",
"\n",
"rd = np.random.RandomState() # Initialize a new RandomState object\n",
"rd.seed(1) # and (re)set the seed\n",
"\n",
"V = np.c_[[0, 0], [1, 0], [0.5, np.sqrt(3)/2]] # Columns give triangle vertices. \n",
"point = V[:, 0] # Start at a Vertex. \n",
"\n",
"n = 1000 # Change this number to experiment\n",
"\n",
"for k in range(n):\n",
" node = int(np.ceil(3 * np.random.rand()) - 1) # node is 0, 1, or 2 with equal prob. \n",
" point = (V[:, node] + point)/2; \n",
" plt.plot(point[0], point[1], \".\", markersize=15) \n",
" plt.hold(True)\n",
"\n",
"plt.axis('equal') \n",
"plt.hold(False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Try experimenting with the number of points, $n$, the type and size of marker in the plot command, and the location of the starting point.\n",
"\n",
"We finish with the listing of sweep, which generates a volume—swept three—dimensional (3D) object; see Figure 1.12. Here, the command surf (X,Y,Z) creates a 3D surface where the height Z[i, j] is specified at the point (X[i, j] ,Y[i, j]) in the x-y plane. The script is not written in the most obvious fashion, which would use two nested for loops. Instead it is vectorized. To understand how it works you will need to be familiar with Chapter 5 and 21.4 of reference [1]. You can experiment with the script by changing the parameter N and the function that determines the variable radius: try replacing sqrt by other functions, such as log, sin, or abs."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11dc8b6a0>"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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SbyOVvuSqQaVS2dLwHK3u1Wq1V3PVZXyARCLxNlLpS+o9zqLyrWZ7tVpt89/7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\n7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0+fzpAhQ1wcjWtI0leXJH3hNlorBdTW1vL9998THx/f7NoA1h+7iqtb0I6MB2j8GrVn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\n/O7OPyGEk/w/TdICwm/UCXgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11dc1b9e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# SWEEP Generates a volume-swept 3D object.\n",
"import numpy as np\n",
"import matplotlib.pylab as pld\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"from matplotlib import cm\n",
"from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"\n",
"n = 10 # Number of increments - try increasing\n",
"\n",
"zz = np.linspace(-5, 5, n).reshape(n, 1)\n",
"radius = np.sqrt(1 + zz ** 2) # Try changing sqrt to cos, sin, log or abs\n",
"theta = 2 * np.pi * np.linspace(0, 1, n)\n",
"x = radius * np.cos(theta)\n",
"y = radius * np.sin(theta)\n",
"z = zz[:, n * [0]] # Tony's trick! Who is Tony? No idea.\n",
"\n",
"surf = ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap=cm.coolwarm,\n",
" linewidth=.2, antialiased=True)\n",
"\n",
"fig.colorbar(surf, shrink=0.5, aspect=5)\n",
"\n",
"plt.title('Figure 1.12 3D picture produced by sweep')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
">[1] D. J. Higham and N. J. Higham. \n",
">[MATLAB Guide](http://www.ec-securehost.com/SIAM/ot92.html), Second edition, \n",
">Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, \n",
">2005, ISBN 0-89871-578-4 \n",
"\n",
">[2] Fernando Pérez, Brian E. Granger, IPython: A System for Interactive Scientific \n",
">Computing, Computing in Science and Engineering, vol. 9, no. 3, pp. 21-29, May/June 2007, \n",
">doi:10.1109/MCSE.2007.53. URL: http://ipython.org"
]
}
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