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Battles Trefethen Ipython notebook
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gistfile1.txt
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chebfun in Python"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a demo following [the original paper of Battles & Trefethen][1].\n",
"\n",
"[1]: http://people.maths.ox.ac.uk/trefethen/publication/PDF/2004_107.pdf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initialisation"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_formats = {'svg', 'png'}\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In principle, it suffices to use the class `Chebfun`, but we'll import all the objects in `chebfun` for convenience."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"from pychebfun import Chebfun"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import pychebfun"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"x = Chebfun.identity()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is only for this IPython notebook"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"from IPython.core.display import HTML"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We define a convenience plotting function"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"def cplot(fun):\n",
" pychebfun.plot(fun, with_interpolation_points=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Chebfuns and barycentric interpolation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Creation of a chebfun"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A typical way of initialising a Chebfun is to use the function `chebfun`. It will work for any function."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"cube = pychebfun.chebfun(lambda x:x**3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A more pythonic way to achieve the same result would be using `Chebfun.from_function`, it will also work for any function."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"cube = Chebfun.from_function(lambda x:x**3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Another possibility is to use the variable `x` defined by `x = Chebfun.identity()`:\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"x = Chebfun.identity()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note however, that this will only work if the function of x has been registered in chebfun. Here it works because chebfun knows how to compute arbitray powers:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"cube = x**3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Other examples could include:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<Chebfun(13)>\n",
"<Chebfun(32)>\n",
"<Chebfun(20)>\n"
]
}
],
"source": [
"print(np.cos(x))\n",
"print(np.tan(x))\n",
"print(np.exp(np.sin(x)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Display"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The _size_ of `f` is the number of interpolation point."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"4"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube.size()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Displaying a Chebfun gives the interpolation values at the Chebyshev interpolation points:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Chebfun \n",
" domain length endpoint values\n",
" [ -1.0, 1.0] 4 -1.00 1.00\n",
" vscale = 1.00e+00\n"
]
}
],
"source": [
"print(repr(cube))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"8"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Chebfun.from_function(lambda x: x**7 - 3*x + 5).size()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"42"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f_sin5 = Chebfun.from_function(lambda x: np.sin(5*np.pi*x))\n",
"f_sin5.size()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Convergence"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For some functions, convergence is not achievable, and one must set a limit to the dichotomy algorithm."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"f_abs = Chebfun.from_function(abs, N=1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Evaluations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`Chebfun` objects behave as ordinary function, which can be evaluated at any point."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array(125.)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube(5)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array(-0.125)"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube(-.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is also possible (and more efficient) to evaluate a chebfun at several point at once.\n",
"For instance, we evaluate the Chebfun for $\\sin(5x)$ at several points at once:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3.17383112e-16, 7.07106781e-01, 1.00000000e+00, 7.07106781e-01,\n",
" -1.26628627e-15])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f_sin5(np.linspace(0, .2, 5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Operations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One can for instance add two chebfuns:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"42\n"
]
},
{
"data": {
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],
"source": [
"chebsum = cube+f_sin5\n",
"print(chebsum.size())\n",
"cplot(chebsum)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Or multiply them:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"43\n"
]
},
{
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"source": [
"chebmult = cube*f_sin5\n",
"print(chebmult.size())\n",
"cplot(chebmult)"
]
},
{
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"execution_count": 22,
"metadata": {
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"outputs": [
{
"name": "stdout",
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"text": [
"14\n",
"17\n"
]
}
],
"source": [
"f_sin = Chebfun.from_function(lambda x:np.sin(x))\n",
"print(f_sin.size())\n",
"print((f_sin*f_sin).size())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is also possible to add and multiply chebfuns with scalars:"
]
},
{
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"execution_count": 23,
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{
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],
"source": [
"plt.subplot(121)\n",
"cplot(3*f_sin)\n",
"plt.subplot(122)\n",
"cplot(3+f_sin)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
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},
"outputs": [
{
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f_cubic = Chebfun.from_function(lambda x: x**3 - x)\n",
"cplot(f_cubic)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
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lBmMMnzSlP3Zw0XmQBE7KcA/OzLEjtzPfhiQx0Wq4wG/RIYFDjAo+0KQ62wWA0nwnxuQ5EGHAoRaa8aYCF5IzUlw24UyLzXg/IYOQEgdi7TS5ND9lIQnEl6ko0Dg1mn0BdHT3wWqRRowLSYSLIRI4qcEYw/5TqXtwgOg2JM/cfB4AoMBlw1fOrVbs/JSGBA4xKvhAk84sTJIkTIt5cWigSo2P5XZOzavAmVYRPZ7PlonhSXd5ivNZOQ6H+nMqHGyKttMkTx5c9tSFJO//Hzf4qLBiCpzq6IG3pw82i4Szy1MXkgsnj4HNIqGzN4RGb6+CZ6gsJHCIjOntC+Noqx8AMCMNgQNAXkvnnglieD6OuZnTbedpseM/aSLDmwqywEmznT8TMx6HmrvI8KbAJ7H7flqa7Xx2WQHsVgm+3hAadGx41YKPr2eXF8BpS11IOm1WTC7Nj32GfscOEjhExhxq7kI4wlCS50BZgTOt9/KBbXtdm25TENWiJxhGHReSaXoWuAdn3ykvGjr0mQmhJtyzkG47T/TkwWqR0BkIoclHhnckuODm/TNVHDaLbHipjtbI8BCAqWl4bzjTDeBlJ4FDZMzBhEFqpPLf/alvixrsg42dui8mpTRHTnchwoDiXDvKClxpvZcX+fMHwrjwkbepnYchGIrgeFtUBJ5dlp7hddqsmDAmmmlCKcwj84mcnJBeOwNx7xplrI3M4VhfTCfOiROPd9JvO5PAITLmyOnozfOZFLNNOEYrJqU0vJ3THaQavT1Y80p8t2Zq5+E51uZHOMKQ77Sh3J2eRxKIiyIyvMPTF47IfXpqRXqeMgCYHLsPjtDeXyNyqIWPHekLST6u899Kj5DAITLmSEvUCzO5dOCmecNhtGJSSnOkJTOBQ+2cHnyzzMll+Wl7JIHkOBxiaI63dSMUYchzWFFVmJ5HEoC8RKVnw6sGkQiT2yidAGMOb+ejrX7dbthLAofImKOxm4ffCKlitGJSSnOY2lkVuMCZkmY7c86OzXip9MHwcKM7sTQvIyE5pSwv9jl+CugehgZvD7qDYditEsaXpH/Pjy3OgcNmQTAUwakz+vT6ksAhMiIYiuB4e9QTMDlNz4JcTCr2WIK+i0kpDY9XKM5zpPU+oxXtUprDGXrKONylT5lUw3P0NPf8ZtbO40qiAd1dgRCafYFsnpqh4MtTkzz5sFnTN/VWi4RJHi4m9ektI4FDZMTxhHiFdDOogGgxqVWLpwEAFkwsGXYXYTPz4vbjcir+nb//MO0g4SXnjcOTS88FAJTkOaidh0FeokpzyZXDPWadgRBaOsnwDgX3/E7yZCZwHDaL7JHQq+FVg9EEGHP0vhxIAofIiCOn48YgEzczAMyLbbp5qkOf7k+lafT24N6XRx8kvGBiCQCg3R9EZ29fVs/RKEQiDEdbR2cQHDYLziqOGl6e1k8MRB47yjITktH3Rn+jwxRoPCSJMWWZwsU+CRzCVBwZpZs5+t7ozXOqo4f2pBqEbAUJu112ePKjXja+PEAkc6qjB719ETisFozLIF6BMyHm0j9GAmdQGGPy2JGpBwfQv2dBDT6NZfONybNn/BnxjDV99mcSOERGHMnC7KAkz4HCHDsYoxnvYEz05KG/byzTIGEuJrmXgkjmWKwuU3VJTkbxCpyJsVo4dW3Unwej3R+EtyfqRZzoGYUHJ9afyYMzOBt31ss1sH7wx48zrn+ldyFJAofICB4XMppBSpIk3btAlaSyMEdeXgKi4ibTIOFJPOWTPDiDwgv8TRiTeX8GyIMzEnzcGFuUk9Zmpv3h4w7/3Yg4jd4erN60T37MRlH/irdzmz8Ib7f+lrdJ4BAZcSKWQTUadz4ATIy5qevbaaAaDIcteot+86JJeHfVFzIOEpY9OCRwBoX3v3FjRtufo+1MHsnBqePLUxkGcnP479To7UEwFBn1eRmJbNa/ynPaUBpLItHjGE0Ch0ibrkAIbf4ggNEbBC6QjpNLf1D4DPXS6eWjSu8eH/NM6HGQUgPe/zKpF5JIomchotPiaErC+9/4UY4bpflO5NitiDDg5Bnq04lkc2kbSBij2/U3RpPAIdKmPmZ0i3PtcLsyD2ADgHFjokabDO9A+sIROcNstJ4y/n5q58HhQnL8KJeoxhblwGaREAhF0Eibbg6A97/q4tH1Z0mS5D79+oEm2n4kgcrCHFw5q1J+PJqlbUDfYwcJHCJt6mNKftwojQEQv3lOtNMA1Z/Gjl6EIwxOmyWjWkOJVJdEBzdvT58u19KVhDGWtSUqW0IWFsXhDKQ+S0vbQLQQHQA8svlT2rC3H8WxzKlr5laNamkbSByjSeAQJkB2M2dhkBpXEhVJDbSWPgDuEh5XkgtL/z0X0iTXYZNTxU+QSz+J1q4guoNhSBJwVvHoqzxPoDicIeFGsnqUY0ejtwcHG33yY9pINhnukTx/imfUlcvjYQT6GzdUETjr1q3DhAkT4HK5UFNTgx07dgx57CWXXAJJkgb8XXXVVfIxN99884DXFy9erMalEIh39GzMwjz5DuTYrWCMCv71J5vtDMS9OHqciSkJ90hWFebAacs8s4fDf6+TOt2/RymyGbtX1+pH/wgn2kg2TrayAoH4b0VLVIOwceNGrFy5Evfddx92796NOXPmYNGiRWhpaRn0+E2bNqGxsVH+279/P6xWK7785S8nHbd48eKk4377298qfSlEjGy584HktXQ93kBKks12BvS9lq4k3ChmS0hyLxB5ypLhwrooC7F7Ez156F9AnTaSjRIMReTA69EGcwNxT31Dh/687IoLnMceewzLly/HsmXLMGPGDDzxxBPIzc3F+vXrBz2+pKQEFRUV8t+bb76J3NzcAQLH6XQmHVdcXKz0pRAxsrmODsTd1WR4k8lWZg+HBM7gHM9SZg+Hb9dAHpxksjluVBbm4I7Lp8qPrRJtJMs51dGDCANc9tHH7gFAaYETTpsFERYVOXpCUYETDAaxa9cu1NbWxr/QYkFtbS22bduW0mc8/fTTuP7665GXl+xq27p1K8rKyjB16lTcdtttaGtrG/IzAoEAfD5f0h+RGaFwBKdiA3e2DIJseClVPIn6dt7Oo3czAyQkh4L3u2x5yrgH5yS1cxLZir/h3Pr5SXI69MsrLqCNZGPEJ0aZ7xOYiJ697IoKnNbWVoTDYZSXlyc9X15ejqamphHfv2PHDuzfvx/f+MY3kp5fvHgxnn/+eWzZsgWPPPII/va3v+GKK65AODz4fkZr165FYWGh/FddXZ35RZmcRm8vQhEGh82C8gJXVj5zXAmliveHMSYb3mwZBD1nQyiJ7MEpya6QbPMH0R0MZeUzjUC2Pb8OmwVVRdGxI9Cnr6UTJcn20jYQn8we19nYIXQW1dNPP41Zs2ZhwYIFSc9ff/31+NKXvoRZs2bhmmuuwZ/+9Cfs3LkTW7duHfRzVq9eDa/XK/+dOHFChbM3JvE6FjmjzuzhxIPY9OX+VJI2fxD+WGYPDw4eLYnBr2EqQidT35bdJarCHDsKXDYAtEyVSLYFDpBgeHWY4aMUvM+NttZQItU6nRwpKnA8Hg+sViuam5uTnm9ubkZFRcWw7/X7/diwYQNuueWWEb9n0qRJ8Hg8OHz48KCvO51OuN3upD8iM7Kd2ZP4WSfau8EYGV4gbgwq3a6sZPYAQLnbBYfVglCEUTptjO5gPLMnW54yIG5cqMpuHCUEjl6XTpSEhxCMzULJA45eK84rKnAcDgfmz5+PLVu2yM9FIhFs2bIFCxcuHPa9v//97xEIBPC1r31txO85efIk2traUFlZOeKxxOhQYpDiQZldgRDOUBE6APFZ2FlZnIVZLZIcH0IGIQoPmixw2lCYM7rMnkTkTCrySgIAIhGGk+3ZqcqdiOxZICEpczLWp8cWZU/g6NVTpvgS1cqVK/Hkk0/iueeew8GDB3HbbbfB7/dj2bJlAIClS5di9erVA9739NNP45prrsGYMWOSnu/q6sKdd96J999/H8eOHcOWLVtw9dVXY8qUKVi0aJHSl2N6uEHIpuF12a0od+t3Qzcl4O2czVkYEDcIJ8nwAgBOdUS3U1CsncnwAgCaO3sRDEdgtUioLMxO7B4QF5J6y+5RklPy5Ch7fZqP93prZ5vSX7BkyRKcPn0aa9asQVNTE+bOnYvNmzfLgcf19fWwWJJ11qeffop3330Xb7zxxoDPs1qt+Oijj/Dcc8+ho6MDVVVVuPzyy/Hggw/C6Rx9ShwxPLyDV2VxdgBEZxvNvgAaOnowt7ooq5+tR+LtnD1jAMTjeUhIRuHGINv9mTw4yfB2rnC7YLNmb17Nf7eGDtr3CwB6+8Jo7QoAyK4Hh4tSX28Inb19KBhlHSO1UFzgAMCKFSuwYsWKQV8bLDB46tSpQ8Zi5OTk4PXXX8/m6RFpoJThrSrKwe76Dt3NEJRCKcMrGwSKwQGgoJDkMTgdJCSBeJXybHvKeH9u9PYgEmFZS3zQK7w/5zqsKMrNnggpcNnhdtng6w2h0durG4EjdBYVIRahcARNsR2Sszk7SPw82q4hyikF1tETP4+EZBR5KbAouxVwz4p5yiiLKgr3sGS7P5cXOGG1SOgLM5yOeS7MTOK4kY0aOIlU6XCMJoFDpEyTrxcRBjisFnnjxmxRRYY3iQaFBA6v9NroJZc+EA/IzLYHh8csdHT3obOXAud51l6229lmtaDCHf1MPRlepVDK8wvoc3JEAodIGT4LqyxyZd0VHHc1k+Ht7O2DrzdaIC77S1RRY9DY0YsI1cJJCJrPbjvnO20oji0RUBxOvJ2V2EqB92k9GV6lUGopENDnJJQEDpEycrwCDVKKwoVkUa4dec7shsmVu12wSEAwHEGr39wu/XCEoSkmqJWY8SbGh5idUwotUQH6NLxKodTSNqDPgG4SOETKnFIogwqI35CtXUH09g2+5YZZUFJI2q0WlLu5mNTPQKUELZ3RbUdsFgllWdp2JBHurWggr6Ri2ZdAQvwexTspkiLO4V6hg40+3Yh2EjhEysTjQrJvDApz7MixRyv2mn2Z6qSCxgCIp3w2mnzGK6cuF7pgVSD7hnslm3RiDJTCHwjB2xONQ8p2DE70M3nwq7nHDUBZD87BRi8A4JOmTlzw8FvYuLM+69+RbUjgECmj5CxMkiRapoqhVFwIR4/ZEEqgpDEAosIJiMY7mRk+2y9w2RRJL9Zj8KsSJC65ZjsGp9Hbg1/97aj8OMKAezbtF96TQwKHSBm+pKGUZ4HW0qMoVZuFM1aHa+lKoLTAqZKXqMzdn7lnRYklV4BqO3Gafcotuda1+tE/JyHMGI61il3niQQOkRKMMUUj9AEyvBwlUz2BhCUqkxsEpbbD4PB2bjL5kmujwoKdf25Hdx/8gZAi36EHeH9WYsl1oicP/T/SKkmY4Mlu/ahsQwKHSAlfbwhdscFD8ZkYeXAAKOhZoHYGoLyQTCx9MFRldjOg5NI2EK+ym/hdZoTHLioxPlcW5mDttbPkx5IEPHTtTEXS/rMJCRwiJfjAUZLnQI7Dqsh3kKtZ2WrRHArKjMINQjY3f0ykLLaBbCAUQbs/qMh36IFTCi9tJ362mePKuKewQqH+vOS8cVg0I7qH5Lcunowl541T5HuyCQkcIiWUjgtJ/GwzD1ItnQFEGGCzSFmvFs2Jp+QHEAiZNyWfC0mlZqFOm1X+Dc2cGai0RzLxs828vM37s1ICBwAml+UDgOzNFx0SOERK8AG6wq3GINVjWpc+H6TK3dmvFs0pyrXDZY/e+maND+ntC6OjO5q6zEv9K4FcOdqk7QzEY72U8pQBQDmPd/KZt50Txw6lqJS97PpoZxI4REo0y7MDZbwKQPzG7O2LyHUzzEazlw9SyrVzNCXf3MXReH922S1w52S3WnQiZg/oZozJxlDJJSouUpt1YniVQF6iUlDgyO2sEyFJAodICTVuHpfdKu/fY9aZmBpuZiAhw8es7ZzQn7O963IicjVjky6dnOnuQzAUAaCsZ4GPS2btz4DyMThAQjvrREiSwCFSQg33Z+LnN/vMuU8StbM6qNXO8VRxc3pw+Ex/TJ4DDpty5oYvUenFs5BtIhGGlk7lBU55zIPf2hVAKBxR7HuyBQkcIiWaVfIslJvc1dysgqcMSBQ4Jm1nOcBYYYGjs5iFbMOFZJnC/dnsHpw2fxB9YQZJAsoKlFve9uQ5YbVIiLDovoGiQwKHSAk+01d6xmv2gUqtJSq9raVnGx70W67SUqBZY3BaeH9WMKYMiMesdXT3mXKzXn4fe/KdsFuVM+sWiyQLKD2M0SRwiBHp7QvLQb+KL52Y3NWslpDkBkEPg5QSyB5J1ZaoehHpX+veBDR5o/1ZacFemGOHM7YEZsaxQ40YSU65juJwSOAQI8I7co7dKlcMVQpueM04SDHGVBuo+CDVYtYYHJXbuS/McKZbfJd+tpGXqLK8N1J/JEmSRZQZ48oaVYopA/Tl/SWBQ4xI4rKJkhkngLmXqHy9IfTE3OvqBRmb07Mge8oU9izYrRZ48h1J32kmWlRacgUSPAsmHDuaFa7KnUiFjrzsJHCIEWmWZwfKrqNHv8O8szDezm6XTbHtMDilBU5IEhCKMLSbzLMQiTA5q0mNAZB7L5o7xTcI2aZJxbHDzLVw1IrdA/QlJEngECPS5FXP/cm/o7UrgD4dpCFmEzXqWHDsVgvG5DmTvtcsrH+vDuGY0+raX/4DG3fWK/p93Li36MAgZBu1YsqA+H2jB8ObbdQdo/UTRkAChxgRPkipEcA2Js8Bm0UCY8DpTnN5cdSqzcLhVan1MFBli0ZvD3702kH5cYQB92zar2iWE/fgmC3eqS8cQZtfvbFDT56FbBPfV029GBw9TIxI4BAj0qyi4U1MQzST4QXUq4HDKedLJyYyvHWtfvTf5izMGI61div2nfKM12RLVC2dATAG2K0SinMdin+fmZeomtX04OgomJsEDjEiaq7vAuZNFdeqnc00453oyUP/MHmrJGGCJ1ex7ywzaVxZc0IGlVIbxyZi1tIHXYEQOmO7e6sxdnAh2RUICb+rOAkcYkTUXN8F9OUCzSZqxisAcQ+OmWJDKgtz8IVpZfJjqyThoWtnyntGKUE8Jd887QwkeCTVEuwJpQ9YfzedgeHjZL7ThnynsmU8ACDPaUNB7HtEn4Qq3xqErknc40SNTIjo9/CsE3POeNVaouIxOGab8Y7Jiy6XLDmvGrfXnq2ouAESgzLN2Z/VHjeC4Qja/UGMyVfne7VGrW10EilzO9F5OoRmby8ml+ar9r3pQh4cYljOdEf3OAGUL9bFMet+VGovUZl16YS383kTShQXN0C8P5/uCiBsoppDTSp7JB02iyxezdSnG1WO3QP0k7FGAocYFt6BPfnK7gaciJzdY6KgzL5wBK1d6hoEPVUkzSZqe8rG5DlgkYBwhMlZRWZAzeQEjhk3kdW2ncXuzyRwiGHR5OYpMF8MzumEjBM+C1Ua/pu2+4MIhMyzQWG83pA6Sxg2qwWefF4LR2yDkE3UFpKAfjwL2aRF5aVAQD+TI1UEzrp16zBhwgS4XC7U1NRgx44dQx777LPPQpKkpD+XK/kGYYxhzZo1qKysRE5ODmpra3Ho0CGlL8OUyJvlqSlwdJSGmC2aVM44AYDiXDscsZ2HzWJ4e4Jh+HqjmR9qivYyXuzPRF5Jtes6JX6XmSZHLbFYRV5eQw0qCvXRzooLnI0bN2LlypW47777sHv3bsyZMweLFi1CS0vLkO9xu91obGyU/44fP570+o9//GP87Gc/wxNPPIHt27cjLy8PixYtQm+v2I2tR2TDq8EgpYc0xGzB443KVJyFSZJkOsPLrzPHblUl44RjxppDLXIMDnkWlIQXRC1VKUYSiMdjiu4pU1zgPPbYY1i+fDmWLVuGGTNm4IknnkBubi7Wr18/5HskSUJFRYX8V15eLr/GGMNPf/pT3Hvvvbj66qsxe/ZsPP/882hoaMDLL7+s9OWYjhYN3MyJ6Y5mGahO8/gbFQcpIDEl3xyGlxuDMrdT8Y1jEykzmeFNnJyomd0jb4thogzMloQ+rRZ62XBTUYETDAaxa9cu1NbWxr/QYkFtbS22bds25Pu6urowfvx4VFdX4+qrr8aBAwfk1+rq6tDU1JT0mYWFhaipqRnyMwOBAHw+X9IfkRqnNbh5gITUWsFdoNkiPgtTuZ11MlBlC24MSlVOITZbqjhfuihw2ZDrUM9Txu8fs2zzwhiLjx0q9mnen1u7AogInBmoqMBpbW1FOBxO8sAAQHl5OZqamgZ9z9SpU7F+/Xq88sor+M1vfoNIJILzzz8fJ0+eBAD5fel85tq1a1FYWCj/VVdXj/bSTAP3LKhtELgLlH+/0eHufNUFToG5BI5mQtJkxf74UqCacSGA+QROVyCEnr5ogoCak1C+UW9fmMHb06fa96aLcFlUCxcuxNKlSzF37lxcfPHF2LRpE0pLS/GrX/0q489cvXo1vF6v/HfixIksnrGx0crwmm2g4kJObYPAB0XTtLMGAZmA+fajirezukuufNwQ3bOQLXg75zvV9ZQ5bBYU59oBiL0cqKjA8Xg8sFqtaG5uTnq+ubkZFRUVKX2G3W7HvHnzcPjwYQCQ35fOZzqdTrjd7qQ/YmQiESbXZlF7icp0AkcjzwL3zJnGUxYTGGq3c5nJgoy16s88HT8UYTjTHVT1u7WgRaN2BhK87AKP0YoKHIfDgfnz52PLli3yc5FIBFu2bMHChQtT+oxwOIx9+/ahsrISADBx4kRUVFQkfabP58P27dtT/kwiNTp6+hCKzYK4S1It+Axb5NlBNtHK8JpVSKrtWShLiFkIhSOqfrcWaCVw7FYLSmJ1pMwg2rUUOPLY0SWuV1LxJaqVK1fiySefxHPPPYeDBw/itttug9/vx7JlywAAS5cuxerVq+XjH3jgAbzxxhs4evQodu/eja997Ws4fvw4vvGNbwCIZljdfvvt+OEPf4hXX30V+/btw9KlS1FVVYVrrrlG6csxFXyQKs61q1bFmGMmwxv1lEVnm1q59M3QzoB2BmFMnhNWiwTGIP/WRkYrgQPEvZJmqO2kaTvrYOxQfNFuyZIlOH36NNasWYOmpibMnTsXmzdvloOE6+vrYbHEjeeZM2ewfPlyNDU1obi4GPPnz8c//vEPzJgxQz7mrrvugt/vx6233oqOjg5ceOGF2Lx584CCgMTooJtHHc50B+U9isbkq1PFmMPbub07iL5wBHarcGF5WUWrPm21SCjNd6LJ14uWzl5VU6e1QKuYMiDqLfu0udMUY4dWwdyAPsZoVaKSVqxYgRUrVgz62tatW5Me/8///A/+53/+Z9jPkyQJDzzwAB544IFsnSIxCPGbR/3BOO7+FPfmyRbcq1CS51BdYJTkOmC1SAhHGNr9QVWrzqpNdC8o7ilT3yCUu6MCxwxxOCJ4cMwwdojQziKHERh7ukaMChFunnZ/1LNgZLSoY8GxWCR4Yl4jkWdi2aDdH/WUSRLkOA014QGwrWR4FUUPnoVsoVVMGaCPDEwSOMSQaDlIFec6YIvtydRm8JgFrYopcsxiEPj1jclzwqbBUpxZ2rkvHEF7LINJC9FeaqIEBREmoSL3ZxI4xJDUt3cDAJwaGIOoZ8Ec+yRpVV2Xo4eBKhtolanGMYvAafcHwVg07qg4V31PWbydjT1uANpstMnRQxgBCRxiUDburMcbH0drDf387cPYuLNe9XMwi0HQchaW+L1GF5Jat7PHJEKSX58n3wGLRb39vjhmGTf6whG0x2LKtFwK7OjuQyAUVv37U4EEDjGARm8PVm/aJz9mAO7ZtB+N3h5Vz8MsA5W8HQZ5FhRFy9kukFxl18hoLSTLTNKfeT+yWSSUaOApK8yxwxHz7ota+oAEDjGAulY/+lc5DzOGY63dqp6HaZZOfBovnZgk60Rrw6sHl342kJcCtVpyjQXc+npD6O0T07OQDXidH0++UxNPmSRJwk+OSOAQA5joyUP/+8UqSZjgyVX1PMxiELT34Ihfcj0baFmbBTDfEpVW/dntssmFSY3c1lq3MwB4SOAQeqOyMAd3LZoqP7ZKwEPXzkRlYY6q5yH67CBbaJnqCZionTXaOJbDv7c7GIY/ENLkHNRAa8MrSZIpvJJaL7kCcS/d+0dbVQ9hSAUSOMSg1EwaAwDw5Dnw7qpLseS8caqfgxn2o+rtC6OzN2rstDa8hhc43FOm0dJJnsOKHLsVgLHjcOKeMu2KRpqhT2stJAHA19sHAHj63WO44OG3NElGGQ4SOMSg8JtnbEmu6p4bjpkGKYfNArdLlcLiA+Dt7De4Z4HHOpVpVK1ZkiR4CoxfVFEEw2uGyZGW2zQA0WSUnXXt8uMI0yYZZThI4BCDovVsF0gWOIyxEY7WJ4luZklSP1AQMIdnwR8IwR+MBpxqaXhLTVDNWASBY6bJkVbtXNfqR/9RWYtklOEggUMMitbVdYF4UGZPX1g2TkbjtMbF5wB9ZEOMFi4och1W5Du18ZQBJjO8gkyOjIpcIFSjpcCJnjz0n5JpkYwyHCRwiEHRurouAOQ5bchzRD0LRh2oRDAGgPENQosAXgXA+JlUonjKyuTMQOMWr9Tag1NZmIPbLpksP7ZKkibJKMNBAocYFK1vHo7RDa8InjLA+LVwhBOSBm/nXIcVeeQpUwzGWEL2pXZ9+oYF0eQTm0XC3+++RJNklOEggUMMiigCh8/EjLqNQNxTpl3GCWB8gxAPMBZE4HSKWfl1tGhd04lj9P7s7elDMBwBIEasUyjCkOe0a3YeQ0EChxgUEWYHgPEHKnGEpMHbWYCgeSBhicrgHhyt2znRU2bEBAXezm6XDa5YgoAWuOxWOftTxLGDBA4xgET3p9aG1/ACR+Pquhyjt3OLxkX+OPJ+VAZtZ1HGDU9+NB2/L8zQ0d2n6bkoAR83PBq3MyD2Zr0kcIgB+HpCsvvTI8pMzKAGQTTDa1jPggDF54DkWCcjexa0FuxOmxVFudElEyP2ab65pdbjMyD2GE0ChxjA6a6oEtfa/QkYO/g1EmFy+rIwAkfAQSobtMozXvV3XU6Et3MwFIGv13hFFUXx4ADG3qy3TZAlV0DsvexI4BADkIvPaVTxNZFSt3EHKW9PH0KxbdvH5ItheFu7Aoj030reALQJMuN12a0ocIobszBaRAkyTjwHEZdORgvvz1qPG0BC/J6Ak1ASOMQAuPtzTJ72N4+hZ2H+eKCg06atp2xMXrSd+8IM3h5jxSwwxhIMgjiG14jVjEXy4HAxy397I8H7Dr9vtUQOnPeJ159J4BAD4AGQIgSwlSUYg7DBPAs8VVhrrwIQ3QurOBazYLT9e3y98ZgyEUS7x8DLgdxbonXZAyB+X7UaUuCI48HhAd2tfvHamQQOMQDuWfAIYAyKY+cQYUBHt3g30GiQ21kAgQMYNw6HxysUOLWPKQOM65WMROKeMq1jnYC48Teip0yksYML9jYB25kEDjEAUeIVAMBujXsW2gScIYwGkdbRgbi7mw+eRoH3G1Ha2agZa77ehJgyAZZOSvPFNbyjJT5Ga9+nPXniLrmSwCEG0CpQvAIQPw+j1Q7hA68ohtdTYEyXPu83ovRno9bC4f3G7bLBYdPetMQ9OMbqz0BCDI4AfZp769q6gsKVPtC+FxLC0Sqa4RV4jXc0nJaDubUfpIB4fIqIM7HRwPuNCPE3QLw/G82DI6fiC2B0gcQYHGO1c3cwhO7YhqYieHBKYvdVKCJeggIJHGIA8fVd7W8ewPgeHBGCuYG4Z8FoLn1R29loMTjCLbnmi+tZGA28nR02C/I13NCU47TFt2sQzVtGAocYgEgxOEDCWrpBY0NECOYGEj04Yg1So0X2LAjSzjzDyGieBZECX4H4eQTDxiqqmNifJUnS+GyiiOotI4FDJJHo/hRhfRdIMLwG24G5TaB1dCCxbohYg9RoEakGDhCPWWjtChqqqKJIqctAtKgi93AYqU/z/uyyW9Ho7dH4bKKIWnOIBA6RBO+gTpsFeQ7tU2qBuGEymgdHNINg1KBM4ZZOYjFXYQFjFkaDSMXnOB4D9um/7G8EABxt9eOCh9/Cxp31Gp+RuCn5JHCIJBIDBcVxfxpvkOrtC6MrEHWbi+bSbzXYRpCtgi2dOGwWOWbBSKJdjnUSREgCCZMjwQxvpjR6e7Bp9yn5cYQB92zar7knJx7vJFY7qyJw1q1bhwkTJsDlcqGmpgY7duwY8tgnn3wSn//851FcXIzi4mLU1tYOOP7mm2+GJElJf4sXL1b6MkyBSPUVOGMEXd8dDTz+xm6VZGOnNXyQCoQi8MeWKY2AXJlboD4tl7c30LKraLF7QOLkyBhjR12rH/2nHmHGcKy1W5Pz4cj9WbBJqOICZ+PGjVi5ciXuu+8+7N69G3PmzMGiRYvQ0tIy6PFbt27FDTfcgLfffhvbtm1DdXU1Lr/8cpw6dSrpuMWLF6OxsVH+++1vf6v0pZgCPqMUJV4BSCzYJdbNMxraEtz5onjKch025MaWJY2SsZa4a7dISyfyjNdIHhy/WLFOQOLkyBhjx0RP3oDnrJKECZ5cDc4mjqieMsUFzmOPPYbly5dj2bJlmDFjBp544gnk5uZi/fr1gx7/wgsv4Fvf+hbmzp2LadOm4amnnkIkEsGWLVuSjnM6naioqJD/iouLlb4UUyDSRpscbgx6+sLwB4yRDSFarSGOx2DxTu0xo2uzSCjMsWt8NnFEDcocDfGCiuL0aVGzezKlsjAHU8riIscqSXjo2pmoLMzR8KyAUlmwi9WfFRU4wWAQu3btQm1tbfwLLRbU1tZi27ZtKX1Gd3c3+vr6UFJSkvT81q1bUVZWhqlTp+K2225DW1vbkJ8RCATg8/mS/ojBEalCJifPaUNObA8hoxiEVgHd+UDcOBll6YT355I8BywWMTxlgLgxC5nS2xdGp2AxZUB8icoo4wYAWKWo2V59xTS8u+oLWHLeOI3PSNwwAkUFTmtrK8LhMMrLy5OeLy8vR1NTU0qfcffdd6OqqipJJC1evBjPP/88tmzZgkceeQR/+9vfcMUVVyAcHjxuYO3atSgsLJT/qqurM78ogyNiDA6QYHgFu4EyRbTMHo7RPDgiCnYgvlxmlOrc7QLGlAHG8+AA8Xvz82eXau654YjqkRSnJw7Cww8/jA0bNmDr1q1wuVzy89dff738/1mzZmH27NmYPHkytm7dissuu2zA56xevRorV66UH/t8PhI5QyBasS7OmHwnTp7pMcyMt61LzHaWgzIN4sERVbDH29kY/blVwJgyIL7ULtrSSaaEI0wWkyL1aT5R6wqE0NsXhssuRokRRT04Ho8HVqsVzc3NSc83NzejoqJi2Pc++uijePjhh/HGG29g9uzZwx47adIkeDweHD58eNDXnU4n3G530h8xOKJ6FkRd482UuEEQq52NtqO4yIIdME5/FnXc8BhsY9OO7iB4bchigcaOAmd8g1WRvGWKChyHw4H58+cnBQjzgOGFCxcO+b4f//jHePDBB7F582ace+65I37PyZMn0dbWhsrKyqyct5kRsVgXkODSN8hAJW/TIJjhNVrMgohB84DxqkaLttEmxxMbNzpjngW9w/tzca4ddqs4ZewkSZK3QhEpY03xFlq5ciWefPJJPPfcczh48CBuu+02+P1+LFu2DACwdOlSrF69Wj7+kUcewfe//32sX78eEyZMQFNTE5qamtDV1QUA6Orqwp133on3338fx44dw5YtW3D11VdjypQpWLRokdKXY2iS3J8FghmEAqN5cMSc8Y6R61kYy/AKF4NjMCEZTxEXqz+7c2ywW6NLZkYYO0Tb3iURj4Cb9Soeg7NkyRKcPn0aa9asQVNTE+bOnYvNmzfLgcf19fWwWOI665e//CWCwSD+7d/+Lelz7rvvPvzgBz+A1WrFRx99hOeeew4dHR2oqqrC5ZdfjgcffBBOp3g/up5IdH+W5Io1UHEPjlEMr7gxOOINUqNB2KWTfp4FUWIWMiVeTFGs/ixJEsbkOdHk60VbVwBji8QIys0UHpQumkcSSNysV5yxQ5Ug4xUrVmDFihWDvrZ169akx8eOHRv2s3JycvD6669n6cyIRPgMpzjXDptA7k9AzNlBpkQiTNgZr9G2xeAxOKWCGV53jg02i4RQrC/o3fC2CRj4yvEUONDk6xXK8GaKqEISSMxYE2fsEMuKEZoSL9Ql4M0j4Ppupnh7+hCOucpEi3Xig5S3pw/BUETjsxk9PBtMNCEpSZKhauGIGrsHJMTvGWDsiAfNi9WfATFr4ZDAIWSEdn8aaOmED1JuVzzzQBQKc+ywxgrites8ZoExJuTWIxxRa4dkgqhLgYCxauHE21nE/ixeXJlYoyuhKXJcSIG4N8+Z7j6Ewvr2LIhaxRgALBYJJQKupWeCrzeEvjD3lIlneEWc8WaKqFlUgJiGN1NETU4A4r/9kdNdmu9uziGBQ8jIRdEENAZFuQ7wSvt69yyIug8Vx2OQGi1csBc4bUIG8XoMUoQuklR8TkSBQ0JSDfad8gIADjT4cMHDb2HjznqNz4gEDpGAqCm1AGC1SCgxyFp6m8AeHMA4VXZFnu0C8fPSezv7evsQisWUlQg4OTJSSr6oMTiN3h6sf69OfhxhwD2b9mvuySGBQ8iIbhDiGT76NghtuvHgGKWdRRWSxvCU8ftRxJgywFgeHDkGR7Bg7rpWPxhLfi7MGI61dmtzQjHE642EZoha1p5jFMMbD+YWs53HGCRjTeSgecA4MTgix5QBCZ4ynffn7mAI3cFoNWbRJkcTPXlyCAHHKkmY4MnV5oRikMAhZETdmJATd+nre6ASOZgbSNi/R++Gt1Psdub9ub6tW3NX/mgQf8k1el7t/oBcnkGP8HZ22izId4q1T3ZlYQ7WXjtLfmyRgIeunan5buckcAiZNoFrWQAJrma9e3AEDuYGEnZg1vmMV/ZICtrOu4+fAQAcb+8WJigzE+Kp+GK2M48LirBotXa9khhgLNKO7Zwl543DxJjH5qfXz8WS88ZpfEYkcIgYPcEw/IK6PzlGCRbUS2yI3j04ItcMafT2YN3bh+XHogRlZkLdaT8AwGUX05zYrRYU5doB6HuZSuRaQ5wKd9Rj0z8eRyvE7JGE6nBjJqL7k+PJM5rhFXOgMkoBOpGXTupa/ei/WiJCUGa6bNxZj2f+cQwA8PKeBmG9UEbYY03kFHFOfHlbjLGDBA4BIHEvGTHdn0DCjuKC3DyZ0NsXRmcgBEDcgUr2lPkDYKJMxTJA5HpDogZlpkOjtwerN+2THzOI64Xiy6563qy3TfCgeUC8DTdJ4BAAxE9dBhL3lBHj5skEPkjZrRLcLjE9ZbwP9IUZfD0hjc8mc+IzXvH6tKhBmemgJy9UfLNe/U6ORK5TxikVbFNkEjgEgMTN8sQzBpzEQUqvnoXEQG5RPWVOmxUFMfGl1xlvMBSBrzcqzkQNml9y3jjMHlsIAHjwmplCBGWmg568UB7BPAuZ0Cp4lisgXokJEjgEAPFrWQDxmycYjhsvvSF6/A2nVOcxC3zrAJtFQmGOXeOzGZrKIhcA6DJ9WU9eKCMEzrfpIQZHsHGDBA4BQOyME47LbkVBLABalBsoXfQQKAgkxuGIMRNLF97OJXkOWPq7GQQibnj12c5Xzx0r/3/z7RcJ64UaY4DAeT1MjkQrqkgChwAg7h4n/SnMiQqcfzZ3anwmmSH6dhgcvcc76SFeAUg0vPpsZy6AHVYLzi7L1/hshsYI27zI9YYEXXIFkj1lIoQRkMAhAIidccLZuLMeJzt6AQC3/Wa3sCmpw6EHNzMQz1gTZSaWLqJX5eZ4dF7bKTE5QdSYMiBxWwx9tnM4ccf2AnH7NLcfgVBErqumJSRwCABi1wwB9JWSOhx6SPUEjOPBEbU/c/TeznpYNgHiMWWieBbS5Ux3UM5YK8kVt61zHTbkOqwA4lulaAkJHAJAwtKJoO5PPaWkDodeDK9HsHTPdNGNkDRIrJOo4wZHNM9CunAhWZxrh80qttkWKaBb7JYiVCESYWgXPAZHTympw6GXGByPYOme6aKXGByRjEEm6KU/5zltyLFHPQt6FO16mRgBYol2EjhEkvuzWNAZL09JTVzmFzUldTj0EoMzRueGVy9LJ3xC0dkbQiCkR89CtH+UCt6fAfEyfNJBDzGSHO7NEyGujAQOISvt4lw77AK7P5ecNw4PXj0TADDnrEJhU1KHIpIQKCj6QMUNb7sAg1QmtOrE8Lpddthirsl2AWa86dKmk/4M6Fu066GMByceOK99O4trzQjV0Is7H4Ccitqpw0J/vt4+hGKuMvFjFqLn1xkIobdPj54FfRhei0VCCV8O7NSfwNFLDA4AlOo4Y42niIsu2AFaoiIEQzYGgi5PJaLnWRg/Z7fLBodN7FvP7bLBEfPmiTBQpQNjLF4zRAcGQY7D8euxT+tDSAKJSyc6bOdOHY3RAmUGij3KEqqgpwA27v709YYQDEU0Ppv00MN2GBxJkuIzMQEGqnTw9YTQF+aeMh0YBD17FnQ0dojkWUgXPQl23s5HT/s1L+NBAofQjTsfSI5ZaNPZjFdP7Qzo1/ByT0iB0wZXLHNGZETbvydVEmPK9CFwoueoxw1k9eQp23fSCwD4uNGHCx5+S9OCrCRwiIRtGsQfpCwWSbeGV0/tDIjlak4H3QnJPH16Frw98ZiyEh14ykQKfk0XvXjZG709ePq9OvlxhGlbkJUEDqGr2QGgX8PLK3vqpp11mlbbpqOgeSAhrkyAyq/pwAV7YY5d+JgyINFTpq/+DOhn65G6Vj/6F4rWsiCr+L2SUJw2HWVCAHpeOhG7WnR/SnW6dBKf7YptDDjyRpA68+DobmKk0xic7mAIPbFMRtFFu2gFWUngEAnBr/oYqPRa/bVNZ4ZXrwahVUc1QwD9xuDIXgWdCHbezme6gwiF9ZOgwNvZZbcgzyF2TBkvyMqxSNoWZFVF4Kxbtw4TJkyAy+VCTU0NduzYMezxv//97zFt2jS4XC7MmjULr732WtLrjDGsWbMGlZWVyMnJQW1tLQ4dOqTkJRgaPWVCAAlr6TozvKJvaNofvS4FyrFOOogLAXTskdRRdV0AKM51QJIAxoD2bv209ekED7vIO7Zzlpw3DhPGRD02/3v9XE0LsioucDZu3IiVK1fivvvuw+7duzFnzhwsWrQILS0tgx7/j3/8AzfccANuueUW7NmzB9dccw2uueYa7N+/Xz7mxz/+MX72s5/hiSeewPbt25GXl4dFixaht7dX6csZkUZvD/5xpFXz9LhU6QmG5c3n9DJQ6bUWjp4KKgJ6jsHRlweHn2ebX187XettYmS1SPJO3HoSk3qJv0mk3O0CAPyzuUtTW6i4wHnsscewfPlyLFu2DDNmzMATTzyB3NxcrF+/ftDj//d//xeLFy/GnXfeienTp+PBBx/EOeecg5///OcAot6bn/70p7j33ntx9dVXY/bs2Xj++efR0NCAl19+WenLGZaNO+txwcNv4atPbtc8PS5V+GzXYbMg32nT+GxSQ8460dEgBegvu0evSyd6yTjh8P7cF2bw9einQnerjrZp4MRFu376tN6EJBCNGwKAx986rKktVFTgBINB7Nq1C7W1tfEvtFhQW1uLbdu2Dfqebdu2JR0PAIsWLZKPr6urQ1NTU9IxhYWFqKmpGfIzA4EAfD5f0l+2afT2YNWmffKmlVqnx6WKHH+T59CF+xPQZwxOb18YnYHoTa+3mIV2fxCRiJ48C/oyvC67FQWxyYWeqhnHswL10Z8BfWZS6W0psNHbg32n4jZWS1uoqMBpbW1FOBxGeXl50vPl5eVoamoa9D1NTU3DHs//Tecz165di8LCQvmvuro6o+sZDtHS41JFnh0U0CClJLwgmt0qwZ2jD08Zr20SijD4evs0PpvU0VsWFaDPOBweA1eqq3bW3+RIb0Hzda3+Ac9pZQtNkUW1evVqeL1e+e/EiRNZ/46Jnjz0939omR6XKnrah4oTz+7RT8xCq84CBYHosqXbFfMs6MQgBEJh+GIbseolHR9IiMPRSTsD+qs3BOizqKK8Y7tOxuiJnjz0H+K0soWKChyPxwOr1Yrm5uak55ubm1FRUTHoeyoqKoY9nv+bzmc6nU643e6kv2xTWZiDb14ySX5slSRN0+NSpVVHe5xwShJjFnSyq7jelk043LOnl0Bj7imzWSQU5tg1PpvU4cZLL0ISiPdpPVQx5pTy/qyjoopcSJbqxMteWZiDh6+dBWtM5WhpCxUVOA6HA/Pnz8eWLVvk5yKRCLZs2YKFCxcO+p6FCxcmHQ8Ab775pnz8xIkTUVFRkXSMz+fD9u3bh/xMtVhybjQdzmWz4N1VX9A0PS5V5F1qdWR4k2IWdGIQ9JZBxfHk6Ws5MNHoWvpXHBMYvQnJpJgyHfVpPXpwWnVWiBWIpoq/u+oL+O3yz2lqCxUPBli5ciVuuukmnHvuuViwYAF++tOfwu/3Y9myZQCApUuXYuzYsVi7di0A4D/+4z9w8cUX47//+79x1VVXYcOGDfjggw/w61//GkB0l+Pbb78dP/zhD3H22Wdj4sSJ+P73v4+qqipcc801Sl/OsHCR0BuKoChHH4KBZ1GV6miQAqIGoTMQQltXEJNLtT6bkWnz6y/VE0heDtQD+hWS+mpn3p8d1vgyph7Q51Kg/iahQNSTo/UKhuI9c8mSJTh9+jTWrFmDpqYmzJ07F5s3b5aDhOvr62GxxB1J559/Pl588UXce++9uOeee3D22Wfj5ZdfxsyZM+Vj7rrrLvj9ftx6663o6OjAhRdeiM2bN8Plcil9OcOS77TBYZUQDDN83OjF/PElmp5PKuj15hmT50Bdq183A5UeUz2BhLRanbj09VaVmxPfj0ofnoW2hMwevcSUAfqr7RSOMLkood7GDhFQRXqvWLECK1asGPS1rVu3Dnjuy1/+Mr785S8P+XmSJOGBBx7AAw88kK1TzAq/++AEguFo0Ou/PbEND187S/hlKj26P4GEgUonruZWHQZzAwkp+TppZ70KSU9CsT89oNeJUWlCFhVjTHhxdqY7CMYASQKKc/UTUyYKpsiiUoNGbw9Wb9onP2Y6q4Ojt4FKbzsw6634HEdvLn29ZZxw9JYmrveJUSAUkSu4iwxv5+JcB2xWMtfpQi2WJepa/ehfC030OjiRCEO7XmNwaMarCh6dVY3WbQyOzirs6nVilOuwIcce3bBSD6Jdj9s0iAQJnCwh2jbxqdDR0yeLsmKdzXg9OpvxyhtA6szw6q0wml4NL/eE+HpDCITE9yzodSkQADwF+hGTevWUiQIJnCzBt4nnGkeCttvEpwIfpIpy7bDrzP05Rkfpy5EI068HR29CskufHsnCHDtssRlSuw7infSaFQjExw49BBrrVbCLgr6smuAsOW8cvnPpFABA7fRy4QOMT8uzA/3dPHraNM/X24dQzFWmt5kY9+B0BkLo7dODZ0GfBsFikeSCeXoQk3r2LOhJtOvZUyYCJHCyzKTSfABAd5/4FXbbdLbHSSJ6ilngszC3ywaHTV+3nNtlg90a9SyIXhyNMSYvBeqxT+tpOVCvQhJI9P7qp5316CkTAX2NtjpAT9kQenXnA/EZja83hGAoovHZDI+eZ2GSJOnGIPh6QugLc0+Z/gyCR0c1WvSaFQjoKwZHz4JdBEjgZJn4+q4ebh79zsLcLv3ELOh9HZ0bBNFFO99XrcBpgyuWKaMnPDpJyY9mX+q3T/Mx+pPmTuHLeJzWaf0sUSCBk2W4MWj3BxHunzcuGFyE6WmzPE5izILoYlKvGVQcvYh2XhNJj0YX0M8+SXqOKQOAfzZ3AgC2H23HBQ+/hY076zU+o6GRvb862WhTNEjgZJmS3OggFWFAR7fYA1W8rL0+bx69xCzo3vDqZOkkntlD/VlJ9BxT1ujtwcYPTsiPI4IXZG0jD86o0Ffv1AE2q0UuqS28QdDxOjqgn2yIVrm6rl7bWR9LJ4n7I+kR3QhJHY8bda1+MJ0UZPUHQuiJZS7qsa1FgASOAujFIOh1Y0KOXqoZcw+OXt3MspAUfOnktI6zAoF4sL9exg09Ckk9FWTlE7ccuxV5Tv3s2C4SJHAUQC8bQep5JgbE3bbCz3j50olO3cx6icHRfX/WiUdSzuzRoUeysjAHP/rXWfJjiyRuQdbTOvdIigAJHAXQw0aQPcGwvNmcXm8gvcQs6D1QUC9LJ/HUZX335zZ/dKdrUZE9vwX6bOcbFoyTwwievXmBsAVZ9S7YRYAEjgLIGxQKvHTCjYHTZkG+Tt2feonBaYkJ3YjgWXVDoZcl1za9B83Hxo2+MIOvR9xCoXKskw49OJyyAhcAQBLYAuo9hEAEBP559UvcIIhreBMLdUmSNMLRYqKHGJzfvH8c3TFP2Q1Pvi90SupQ8HZu9weFFmlyXSedLgW67FYUxCYbrQL3aSNU19XDciB5cEYPCRwF0MPSiZEGqdZOMQepRm8P1ryyX34sekrqUPB6Q6EIw6GWTo3PZmj0HswN6MTwGqC6rkcHY3QrxeCMGhI4CqCHmIX4zaPfQUr0mIW6Vj/6OzxETUkdjpf2nJT/f8X//l1IL1RvXxidgeiyjkfHSyd6mBy1GqA2iy7GaJ3XdRIBEjgKoIelE72784F+MQu94sUsTPTkof/qn6gpqUPR6O3B6k375MeieqF4f7ZbJbhz9BlTBiTGlYk7drTqPGge0EdcWbxAqH7bWWtI4CiAHoJfjTBIJcYsiDhQVRbm4Lp5Z8mPrZIkbErqUOjFC5UY+KrXmDIg0YMj5tgRCIXR2WsAT5kOtsWIV+bW7yRUa/Q71REYPkh1B8PoDoaQ6xCvmY3gZgairubOQAitXUFMKtX6bAYyqSwPAHDRZzx45LrZuhI3QLwwWqLIEdEL1abj4nOJiJ6ByTfZtFn07inTw1IgBRmPFvLgKECewwqnLTqLPNjo0/hsBofPeEt17MEBEuJwBB2oeAD09Eq37sQNEPVCrb12FrhPRIKYhdFOG8QYxGtoielZSBSS+vaUie1l7wtH0NHdB0D/k1AtIYGjAL/74AQCoeiU99+e2CZkUGarAWpZAHH3rahVo+WdxHXczkvOG4dlF0wAAFw9t0rIwmiG8eAIHr932jDjRtyDI2KCAveUWSSgOFfffVpLSOBkmf5BmUzUoEydVyPlCO/BkWOd9N3OE0vzAUDe/E80jFIzRHTPQnzcMEY7B0IRuaK7SPBxoyTPCUv/zbOIlCGBk2X0EJQZCkfQ3q3vHa45csyC4AaB2llZ9L5NA0f2SAoq2GUhqfNlk1yHDbkOKwAxt9ShKsbZgQROltHDbrVnuvvAGCBJ8SJuekX0uiFGCRQUvZ3jZQ903s6x8/f1hhAIiedZkNvZAIZX9pYJuBxoFI+k1pDAyTJ6CMqU3Z+5Dlh17v4UeVuMcITJa+l6n4mJvnRy2gBVjAGgMMcOW+yebBcwrswIBUI5XEyKmJJvFI+k1pDAUYAl543Ddy6dAgC4bHq5cEGZRgnIBBIqkgo4CzvTHZSXK4t17injQrIzEEKvgHE4RihcCQAWiyR7VUUUk0YpLwGInSoeH6P1LyS1hASOQkwuiwZldgfFq7ArZ/YY4OYRuagiP6fiXDvsVn3fam6XDXarmJ6FSJKnTP99mhu100IaXmN4ygCxx454DI7+21lL9D3qCkzc/SneIHXaQCXAeTt7e/oQDEU0Pptk2gzkzpckSdg+3dHTh3DMVab3mDJAbMMrZ1HpPNYJSFx2Fas/A7TRZrYggaMQIscsGKkEuMgxC6cNto4uap/mBqowxw6HTf9Dmqj7JDHGEnYS13+flpeoBBs3gLiXvdQAkyMtUXQ0aG9vx4033gi3242ioiLccsst6OrqGvb473znO5g6dSpycnIwbtw4fPe734XX6006TpKkAX8bNmxQ8lLSht887d1BeXYpCjwt0gjuz8SYBdE8C0ZbRxc1ZsFwQlLQfZJ8vSH0hY3jKYtXjRarPwPxStZGEJJaouhmIjfeeCMaGxvx5ptvoq+vD8uWLcOtt96KF198cdDjGxoa0NDQgEcffRQzZszA8ePH8c1vfhMNDQ34wx/+kHTsM888g8WLF8uPi4qKlLyUtCnOtUOSooX+znQHhRITRvLgANGBqqUzIJxB4ELAKLOweFqtWO1sNCEpquHl/bnAaYPLbtX4bEaPR1AhmegpE8lu6BHFBM7BgwexefNm7Ny5E+eeey4A4PHHH8eVV16JRx99FFVVVQPeM3PmTPzf//2f/Hjy5Mn40Y9+hK997WsIhUKw2eKnW1RUhIqKCqVOf9TYrBYU5zrQ7g+itSsgVEc1yjYNHLk4mmAGoc1AGSdAggdHuHY2mAdH0O1HjFLFmCNqFXRfj7E8ZVqi2BLVtm3bUFRUJIsbAKitrYXFYsH27dtT/hyv1wu3250kbgDg29/+NjweDxYsWID169cPu59IIBCAz+dL+lMDUYMFjTZQibp/j5FqhgDiLp0YLeOkVFDDKwfNG8To8vH5THcfQmFxEhR4yYsClzE8ZVqimAenqakJZWVlyV9ms6GkpARNTU0pfUZraysefPBB3HrrrUnPP/DAA7j00kuRm5uLN954A9/61rfQ1dWF7373u4N+ztq1a3H//fdndiGjIOoh6RIqZoExlrBhnjEGqjGC1g1pNdhSoKgxOHLgq0E8kqIGc7caqIoxABTlOmCRgAiLJiiUuV1anxIAY8VIak3aHpxVq1YNGuSb+PfJJ5+M+sR8Ph+uuuoqzJgxAz/4wQ+SXvv+97+PCy64APPmzcPdd9+Nu+66Cz/5yU+G/KzVq1fD6/XKfydOnBj1+aWC7GoWaKDqCoTkdGqj3EDxbQTEaWcgPlAZxoMjquE1yMaxnDEJHkmRdro2UtkDALAmJSiI06eNFiOpJWl7cO644w7cfPPNwx4zadIkVFRUoKWlJen5UCiE9vb2EWNnOjs7sXjxYhQUFOCll16C3W4f9viamho8+OCDCAQCcDoH3nxOp3PQ55VGxHRPfiO7bBZ09ASR4xBnC4lMiQtJcdo5MVDQKEHGonpwjBZTxj2SfWEGX08IhbnDj39qIW8fYBDPLxDt061dQaGWt43Wn7UkbYFTWlqK0tLSEY9buHAhOjo6sGvXLsyfPx8A8NZbbyESiaCmpmbI9/l8PixatAhOpxOvvvoqXK6R3YZ79+5FcXGxJiJmOESMwfndznoAQG8oggsefgtrr50l3FYS6VIqYAxOdzCM3r6op8woLn1+He3+ICIRBosg+5jJMWUGaWeX3YoCpw2dgRBa/QFhBI7RYvcAMSdHRvNIaoliQcbTp0/H4sWLsXz5cuzYsQPvvfceVqxYgeuvv17OoDp16hSmTZuGHTt2AIiKm8svvxx+vx9PP/00fD4fmpqa0NTUhHA4uv/NH//4Rzz11FPYv38/Dh8+jF/+8pd46KGH8J3vfEepS8kY0XZgbvT24Im/HZUfRxhwz6b9aPT2aHhWo0fEpRP+m7vsFuQ6jBEoyGeUoQiDr7dP47OJY5Qd2xMRsU/HswIN1M554m3WSx6c7KFoHZwXXngBK1aswGWXXQaLxYLrrrsOP/vZz+TX+/r68Omnn6K7uxsAsHv3bjnDasqUKUmfVVdXhwkTJsBut2PdunX43ve+B8YYpkyZgsceewzLly9X8lIygruaRUn3rGv1o/+KfpgxHGvtFmq383SJp3sGwRiDJGnvWUjM7BHhfLKBw2aB22WDrzeE1q4ginK1n2F2B0PoDkYnP0bxlAHRPn2srVuYyREQz+4xUjt7BIzfM9J+X1qjqMApKSkZsqgfAEyYMCEpiO6SSy4ZMahu8eLFSQX+RIZ3UFFicCZ68iABSSLHKkmY4MnV6pSyAheSwXAEvt4QCnO0d+kbLUWc48l3xgROAFNiG8pqCZ95O20W5DsVHc5UxSPgPknx7B7jCBwR96OSJ0cGinXSCv1v3CIwnoTNCUXIhqgszEHNpBL5sVWS8NC1M3XtvQHiMQuAOAMVN7ylBjIGgHhLJ4nLU0bxlAHiZQYGQmH4ekMAjLV04hEwBoc8ONnDOFMeAeHGoLcvgu5gGHkCzDB5WuTN50/Av188SffihjMm34HOQAht/iAmjRwDrzhGXUcXraii0QKMOR7B9lfj7Wy3SigSJOg5G8gxOIKEEQBxUWuUOmVaQh4cBclz2pATq0QpzIw3tonbuROKDSNuAPHKrsdrhhhrkBKttpNRlwIT48pE4HSnMT1l8TACMdq5ty+MrkDMU2awPq0FJHAUhhuE04IY3laDVX3l8NnOaUEGKqNtH8AZkydWZiCfeRtttiuap4wLnFKDLZvExw0xwgj4feWwRgP6idFBAkdhRPMstMoDlcEMgmAB3a0G9eCIFvzaatB4BZFjnYwEv55gKCJ7TrRETsXPdxjKU6YVJHAUhgeZirDGGwxFDBkoCMRjFkQxCPz3NkoVY45HsKUTo8YreATz/MoeHIP15xyHFXkOccIIjCoktYIEjsLEC0lpP1C1x4yuzSIJkUqdTcYI5tI3fGyIAIIdSPRIGqydY+NGZ28IgVBY47OJCy2jtTMg1tiR6MEhRg8JHIURKSiTG92SPIcwZfazhdzOndq3czAUQUd3tNKv0bJ74u2svTEAEgyvwYRkUa4ddmv0HhVp7DBafwYS4iQFGDtOkwcnq5DAURjeUUVwNRv55pErkoowC4udg80ioViAar/ZhNd26gyE0NsngGchJrTK3Mbq05IkyaLttABiMh5kPPLegHojniqufTuTBye7kMBRGO7SFWKQ8hnTGAAJBbtEaOeElFqjecrcOTbZs9Cu8TJVIBSGtyfqKSvNN57hFWrsMOhSIBBPuBAhBseoHkmtIIGjMHxAEMLwGvjm4QbO16u9Z8HIxkCSJHnGq7Xh5Us3DqsF7hzjpdSKJHBaDVpQERArTvJ0Zy8AY44dWkACR2FEGqSMbHjdOTY4bNHurHWNlhYDtzOQINo1bufE/mzElFpRxo6eYLz4nBH7tEhxkkYeo7WABI7C8I7aGQihJ0ieBaUQKWbBqCm1nLJY/2kRpJ2NVgOHI/fnrl5Nz4MLWZfdWBuacoSKk+QxZQaMddICEjgKU+C0wWUXw7Ng9JunVDDDa0QhCYjjWTC6kBSlnVsSYsqM7CnTOoygty++oalRxw61IYGjMJIkJRhebWdiRq5lAYhjEEjgqINZ2pkEu7KI1s4OG23TkC1I4KiAKEsnLT5jB7AJY3gNLiTLhBHs1J/VwOjVdXl/7gqE0B3UbruGxCQQI3rKtIAEjgrwgWr70XY0ens0OQd/IAR/LAbIqAZBtNiQMoO2syiG1/CehVhm4OlObTeCNHo75yeEEWjZp41a00lLSOCoAK/V8cw/juGCh9/Cxp31qp8Dn4Xl2ON7rxgNEQwvY8zwBkFuZ0FiyowegxMIRdCp4UaQRi4vAUTDCHhcopZjR4vB+7MWkMBRmEZvD7YfbZcfRxhwz6b9qntyEmcHRnV/lgqQDeEPhtETq8NjXJd+1Bi0+DT2LBh8KTDHYUVBLGtJS8PLg2+Nmq0GiBGHY/SJkRaQwFGYulY/+puAMGM41tqt6nkYfbYLiJENwds5z2FFngFTagExPAuJnjKjLgUCYnglje7BAeJ9SIQlKhI42YMEjsJM9OShv8PEKkmY4MlV9TyMPtsFgDK39jELZhikXHYrClzaehaie2FFABjXUwbEvSZkeJVFhExXo5fx0AISOApTWZiDb18yRX5slSQ8dO1MVBbmqHoeLT7jD1K8jHwwHJHjntSmxSSl1mWD4NPG8HJjUOC0IcegMWWA9h4cxpgcv0ceHGU51RENW7AabP86LSGBowJfrRkHALBagHfuugRLzhun+jmYYYnKabOiMMcOQLuBygyzXUD7eCdqZ3XoSvSUFRhvHyqO1jE4G3fW42CjDwCwatNHmiSiGBESOCrAXejhCJDr0CYuwwxLVID2M14zCEkgeTlQC4y+TQNHlP6c77RpNnapgZZZVI3eHqzetE9+zDRKRDEiJHBUwGGzoDg36lnQaoZglhoLWtfCibezsdfRuYDTKmbBNB4cjQWOkXcRT0RLD05dqx+RfiGDWiSiGBESOCqh9UAV9ywY3PBq3c4miFcAqJ3VQvN2NomQ5BOjtq4Awv3VhsJM9OShf9iNFokoRoQEjkrEi6OpP+ONRBICBQ0+UGkds2A2g0CGV1m078/R8crImWoAUJLngCRF65S1+dVt68rCHNxy4UT5sVaJKEbEuIuqgqHlflRnuoMIxWYlY8ziavbR0omSkGdBHfp7FtTOsOFLVEZvZ5vVgjF5TrR2BXC6M6B6qvZnqwoBADOr3HjypnNJ3GQJ8uCohJYGgc/+SvIcsFuN/ZPzGCMtZrzhCEOb3xwGQW5nEjiKoqVnATBP0DygbRwOb+cpZfkkbrKIsa2dQMjl7TW8eYxc8ZWTuEGh2pzpDiIcYZCkqGEyMtzgtfmD6AtHVP9+s8TgRD0L0b6k5eTI6NlqgLbLrmbJclUbEjgqoakHxySzXUDbduZF70pyje8pK851wBZbLmmLLWOoRTjC0NZlItGuYQpzc2ypt8LgWYGA1mOHOQqEqo2io3B7eztuvPFGuN1uFBUV4ZZbbkFXV9ew77nkkksgSVLS3ze/+c2kY+rr63HVVVchNzcXZWVluPPOOxEKabfbbioIIXAMPtsF4gbvTHcfgiF1PQtmmoVZLJIceKp2n273BxFhMIWnDNB27Gj2maO8BCCGB4e2acguigYZ33jjjWhsbMSbb76Jvr4+LFu2DLfeeitefPHFYd+3fPlyPPDAA/Lj3Nx4ulw4HMZVV12FiooK/OMf/0BjYyOWLl0Ku92Ohx56SLFrGS3xLCoNZgcm8uAU5thht0roC0czx6qK1FvPNpOnDIheZ5OvN1YLp1C17+XtPCbPAZvBPWWAdplUoXBEjvsxg+HVcj8qs40daqHY6HDw4EFs3rwZTz31FGpqanDhhRfi8ccfx4YNG9DQ0DDse3Nzc1FRUSH/ud1u+bU33ngDH3/8MX7zm99g7ty5uOKKK/Dggw9i3bp1CAbVdZWnAx+kOrr7EAiFVf1uM908WnoWzNTOgHYzXjkuxAQeSUA7D05rVxCMRfdGGmMCT5mW1YzNNnaohWICZ9u2bSgqKsK5554rP1dbWwuLxYLt27cP+94XXngBHo8HM2fOxOrVq9HdHa/ouG3bNsyaNQvl5eXyc4sWLYLP58OBAwcG/bxAIACfz5f0pzZFuVHPAhBPvVQLs908WmVDmLWdSUgqi1btzONvygqcsJhgA0itxo1gKIIz3dHNgc0QRqAmii1RNTU1oaysLPnLbDaUlJSgqalpyPd99atfxfjx41FVVYWPPvoId999Nz799FNs2rRJ/txEcQNAfjzU565duxb333//aC5n1EiShNJ8Jxq8vTjdGcBYNZdOTBQbAmjvWTDLIKWVQYgbXuMvmwDa7dwut7MJAowB7cYNXoTVbpVQFNvSh8gOaXtwVq1aNSAIuP/fJ598kvEJ3XrrrVi0aBFmzZqFG2+8Ec8//zxeeuklHDlyJOPPXL16Nbxer/x34sSJjD9rNGhVhE6O0DeZ4VV9xuuNtnM5GQRFkTN7Cs3Rn3kGU7PKsSHNsd+13CQTIz5udAfD6Aqol7SSmAQiScb3lKlJ2h6cO+64AzfffPOwx0yaNAkVFRVoaWlJej4UCqG9vR0VFRUpf19NTQ0A4PDhw5g8eTIqKiqwY8eOpGOam5sBYMjPdTqdcDq1v0mj6Z5eVWe8vX1h+HqjN2t5oTkMr1YbQXIDZBaBo1XgPBc4Zmnn8lgGU7OvF4wx1Yxgi8naOc9pQ57DCn8wjNOdAeQ71Sn0b6YkELVJ+xcsLS1FaWnpiMctXLgQHR0d2LVrF+bPnw8AeOuttxCJRGTRkgp79+4FAFRWVsqf+6Mf/QgtLS3yEtibb74Jt9uNGTNmpHk16sJnnM0qenCaYl6FXIcVBSrdsFpTyme8Krr0GWNyW5uhZgigXdZJU+x3NYvh5dfZ2xeBryeEQpWWMRJjcMxCaYET/rZutPh6MdGTp8p3NplsKVBNFAsynj59OhYvXozly5djx44deO+997BixQpcf/31qKqqAgCcOnUK06ZNkz0yR44cwYMPPohdu3bh2LFjePXVV7F06VJcdNFFmD17NgDg8ssvx4wZM/D1r38dH374IV5//XXce++9+Pa3vy2El2Y4ymMxA9wQqkFTwizMLO5PLjDUNLy+nhACsbo7ZqgZAsRjYJp9ATCm3g7MZvMsuOxWFOZERY2ay1Tcs2CWdgYSMqlU9Eo2m2xipCaKFpF44YUXMG3aNFx22WW48sorceGFF+LXv/61/HpfXx8+/fRTOUvK4XDgr3/9Ky6//HJMmzYNd9xxB6677jr88Y9/lN9jtVrxpz/9CVarFQsXLsTXvvY1LF26NKlujqjwJaJmFZeo4u58cxhdID5QaCEki3LtcNmtqn2vlnDDFwxF0BHLAlGacITJhtdMBkGLPm2mIn8cLQK6m+SYMvP0Z7VQdM2ipKRk2KJ+EyZMSJr5VVdX429/+9uInzt+/Hi89tprWTlHNZGDBVUdpMw3OyiPLQW2dgUQCkdUKQZnxnZ22KL7JLX5g2jy9aJYhVopbf7ortoWCfDkG782C6fM7cSnzZ2qLm+bzVMGxK9VzXY2W0yZmhi/DKhAcIXepGoMjvnczJ48J2wWCRGmnqvZrOvo5Sp7FvjM2pPvNEUVY06FyoY3GIqgzR+t12WmsYPHSao5RptxcqQW5hkhBIAPFN6ePvT2qVPN2IyzA4tFkgMj1TK88XV087jzAfVFe5PJUvE55SoHzp9OqM1SbKLaLGoL9sTvMkvZAzUhgaMibpcNLnu0yVUzvCZd35XjnVQyvGZLEeeobRD+2dIJAHLQrVkoV1lItsgZVOZJTgASYp1UaueeYLyMh9m8v2pAAkdFJElS3dXcZEIPDqB+xpoZlwIBdZdONu6sx082fwoAePdwKzburFf8O0VBzgxUS7CbMMAYACoLoxXmm7y9qmQG8vHZTGU81IQEjsqUqzhDYIzJMQtmyqICEpdO1HHp85R0s62jqxWz0OjtwepN+5Bocu7ZtB+N3h5Fv1cU+P2rmgeHeyRNsh0Ghwu6QCgCb4/ymYGJtbPM5ClTCxI4KlOh4tJJuz+IYDhWm8VkA1W5yjNes8eGKO0pq2v1I9JvQh1mDMdauwd/g8Hgwvl0ZzSLTGnMWF4CiNYc4jFHaohJM8ZIqgkJHJWJ17NQ3rPQLGecOOCwmeunVjMbIhSOyBvmlZssUFAtwT7Rk4f+G1pbJQkTPLmKfq8ojMl3whrLDGxVITMwvkRlPsPLxUajCsvbZo2RVAtzWT0BULPOgtl2XU5EzaXA1q4gIgywWiSMyTOZwIm185luZTMDKwtzsPbaWfJjiwQ8dO1MOWbC6FgtkrzHmppjhxk9C5VctKsgcOLlJcw1bqgFCRyVUVPgmLlCpppFFeVBqiA6yzYThTl2OGPeQaWrv14zb6z8/9e++3ksOW+cot8nGnIcjgp9mu9wbaZ9qDhqlj6gGjjKQgJHZdRcOjFrXAgQH6T8wTA6e5UNFpQ9ZSZsZ0mSVDMIXEA5bBZMrShQ9LtERJ4cqbDVi1mzLwGVJ6G0D5WikMBRmXjwq/IbFJo1swcAch02FLiiaZdKD1TxWZj5ZruAesuBiYGvZsw4KVfJK9kTDMt7i5nZ+6tODA6P3TNfO6sBCRyV4fEwwXAE7bFS6EoR9+CY0/CqFdBtdjezWsuBTWZvZ5UCunnqfZ7DCrfLfLVZZI+kwv05EmGmHzuUhgSOyjhsFnmTQKVnvE0mnx2o5VngAsqMS1SAejELZs7sAeLxMMr353jsnhk9ZWoJyTZ/EKEIgyTFdzEnsgsJHA3gXhylgzJbTD47UGst3eyzMLWEpNn7Mze8So8bDTGBU1Vkjgy1/qiVGcjHjTF5TthNtHGsmlCraoAaM95AKGzK3YAT4QHdagkc07azyktUZl1yVUtINnZEl6gqTer5TcwMVHLsiNfAMWd/VgMSOBqgRvXXxIwTM+0GnEiFCu0MJKbjm3OgUiszsEE2vCb1LMQEh7enD93BkGLf0yj3Z3O2syRJsrhTcuwwe0yZGpDA0QA1NihsMnnGCaDOEpWvtw+dsd2AzWp41coMbOgw99KJ22WXN2TkbaEE3INTZVIPDqCOt6zZxGU81IIEjgZUFkU7dIOCs4MGeZAypzEA4jNeJdM9G2OGpijXjjyT7gasRmZgOMJkYzPWpAIHiIs7fn8rAb9fKk3czmoEGjdSDRzFIYGjAWNVGKT4DI+MAXC6K4BgKKLIdzR4SUhGMwOjy1RKiUm+yaTNIpk644RPjpTcRV0WOCb24KhRC4ePHWOLzTt2KA0JHA3ghvdEezcaOpTZDVn24JhY4IzJc8Bps4Ax5dbS4+1sXmMAAGNj139KIdHOP7fc7TLddhiJ8Pv5lEJLVN3BELw90SJ/phY4KnhwzL7kqgYkcDTgvcOtAIBAKIILH3kbG3fWZ/07SOBEgwXHygZBGcNL7RxF6aUT/rlm9kgCynt/udEtcNpQ4DJncgIQj6dTSkgyxuQxyex9WklI4KhMo7cHa17ZLz+OMOCeTfuz7nI+RZ4FAGoYXpqFAcobXn5/VJq+P8fi9xRq5yY5/sbc7XxWbNno1Bll2rm1K4hgKAJJMud2GGpBAkdl6lr9iPRLNAkzhmOt2V2qohlvFKUNwiny4ABIXDohIakk3LOgVGwIjwsxa4o4h/ez1q6AIsX++HhUXuCiIn8KQi2rMhM9eegfQmCVJEzw5GbtOzp7++DjqcsmNwhKG17uWRhr8hkvD5RUyqXfQKnLAJC05KpESj7PCjR7Oxfn2pFjtwJQRkxS7J46kMBRmcrCHKy9dha4xpEAPHTtzKzWUOE3ZGGOHfkmTV3mKBmDE46wuEvf5DNeuZ0VcunL2WomF+zlbhckCQiGInKl8mzS5DN3MUWOJElx0a5AnybPrzqQwNGAJeeNw3cunQIAuHRaGZacNy6rn083TxwlY0NauwLoCzNYLZK8EaJZGau4S5+WqIBoSn4pT8lXwFvG29nMGVSc+OQo+5muVMZDHUjgaMT0SjcA4Ex39mdh8fgbGqTiQca9WXfpcyFZ4XbBZvJ19CIFXfq9fWG5gKCZ6w1xlFx2PXkmasypNgsU9eBQ9qU6mHtU1pBEw5tt6OaJwzMUevrCONPdl9XPpnX0OJIkKRbQzT8vz2GFO8fcS66Acl5JxhhOxox5dXH2YgL1StyDo8AYTUuuqkACRyN4x27u7EVfOLtVdsmdH8dlt8qVb7NtEBqpnZMYGzOK2fYsJPZns+6rlohSQrK1K4hAKAILpS4DUHqJiiZHakACRyPG5DngUKjKLsXgJKOUS59/ntkDMjlyNeMsu/Qb5Bo41M6AcqniJ2LLUxVuFxw2Mg3xzMDs9ufevjBau6JLrhSDoyzUizXCYpHkVEylXPpmT/XkjFV46YRinaIotXTCl02onaNwwX5SoXY+q4SWp4B4f27s6EW4f/GyUcCFaa7DisIc81aLVgNFBU57eztuvPFGuN1uFBUV4ZZbbkFXV9eQxx87dgySJA369/vf/14+brDXN2zYoOSlKIISnoXE1GXy4EThganZNrwnuOGlgEwAynnKTrZHPQvVZHgBANUlMYHTnt2lEx5gfBb1ZwDxfc9CEYaWzux5yxJjJGnJVVkUFTg33ngjDhw4gDfffBN/+tOf8M477+DWW28d8vjq6mo0NjYm/d1///3Iz8/HFVdckXTsM888k3TcNddco+SlKAIfSE5m0aXf6O1BKMJgt0ood9OMF1DG1cwYw4mYgRlXkpe1z9UzSnlw6uV2JoEDxIVemz+IrkAoa597oj3mwaEAYwCA1SLJu4pns0/LmWo0AVUcxVISDh48iM2bN2Pnzp0499xzAQCPP/44rrzySjz66KOoqqoa8B6r1YqKioqk51566SV85StfQX5+ftLzRUVFA47VG3zArs/iTIx/1lnFuabedTkRPmBns507uvtk40Iz3iiJmYGRCIMlS/2PBE4ybpcdxbl2nOnuw4n2brnkxGghD85Axhbn4FRHD06e6cH88dn5TOrP6qGYB2fbtm0oKiqSxQ0A1NbWwmKxYPv27Sl9xq5du7B3717ccsstA1779re/DY/HgwULFmD9+vXD1jgJBALw+XxJfyLAZ2L1bVkUOG108/Rn/JhoWxxv685aLRw+SFW4XXDF6r+YncpCF2wWCcFwBE2+7Lj0e/vCaOkMAKA+nQgfO05kUbRTivhAzlJg2fU4jdGqoZjAaWpqQllZWdJzNpsNJSUlaGpqSukznn76aUyfPh3nn39+0vMPPPAAfve73+HNN9/Eddddh29961t4/PHHh/yctWvXorCwUP6rrq5O/4IUYPyY6NKGEh4cunni8AG7szcEb092auHUy3EhNNvl2KwWefZ/PEuinXsVCpw2CshMoDrL3t9IhMnZb+TBiXOWAkJSXtoeQ2O00qQtcFatWjVkIDD/++STT0Z9Yj09PXjxxRcH9d58//vfxwUXXIB58+bh7rvvxl133YWf/OQnQ37W6tWr4fV65b8TJ06M+vyyARchTb7erJW3J4EzkByHVd5KIVuGt54CXwdlnCza/Vn5vMR2poDMOOOybHhPdwUQDEdgtUi0TUMCE2Ii5Fhr9gTOcRqjVSPtGJw77rgDN99887DHTJo0CRUVFWhpaUl6PhQKob29PaXYmT/84Q/o7u7G0qVLRzy2pqYGDz74IAKBAJzOgXsCOZ3OQZ/XmuJcOwqcNnQGQjh5phtTygpG/ZknyPAOyvgxuWjpDODNg80ocztHXbvmBA1SgzK+JL4cmA1oyXVwsh2/dyJhydXs244kwpe3s9XO3p4+dMQqqlOfVp60BU5paSlKS0tHPG7hwoXo6OjArl27MH/+fADAW2+9hUgkgpqamhHf//TTT+NLX/pSSt+1d+9eFBcXCylihkOSJFSX5OLjRh/q27MjcPiNOJ7cn0nwYtE/f+swfvH2Yay9dtaoNjklT9ngyPFOWTII9bHMHnLnJ5NtgSPH39CSaxI8jKDB24NAKAynbXTxdlxIevIdyHPStiNKo5hUnz59OhYvXozly5djx44deO+997BixQpcf/31cgbVqVOnMG3aNOzYsSPpvYcPH8Y777yDb3zjGwM+949//COeeuop7N+/H4cPH8Yvf/lLPPTQQ/jOd76j1KUoyrgsznh9vX3yfkvkwYnT6O3Bnvoz8uMIA+7ZtB+N3swDB0ngDE62A+d5dd1qigtJgseVnTzTg0gWitDFM6ioPycyJs+BPIcVjMXT6EcDBRiri6K+yBdeeAHTpk3DZZddhiuvvBIXXnghfv3rX8uv9/X14dNPP0V3d/JguH79epx11lm4/PLLB3ym3W7HunXrsHDhQsydOxe/+tWv8Nhjj+G+++5T8lIUI5suUG5UxuQ5kE+zA5m6Vj/6m4AwYxmvq/eFI3JdDBqokolnrGUnBoeWXAensihahC4QiuB0V2DUn3eMDO+gSJKU1bgymhipi6JWsKSkBC+++OKQr0+YMGHQtN2HHnoIDz300KDvWbx4MRYvXpy1c9SabM54yRgMzkRPHiQJSOxqVknCBE9m7dTQ0YMIA5w2i7yRJxGFD9y+3hC83X0ozM0884kxRgZhCOxWC6qKXDjR3oP69u5RF/U81ho13hM8VLSyPxPG5OJgoy8rgcZcJHHRRCgLRZNpTDbX0vef8gKAnDFERKkszMF/XTldfmyRgIeunZlxoHGi0aXMnmRyHTZZ9B0f5Yy3zR9EdzAMSaLtMAZjXBYnR8diHreJZHgHMC6bXnYS7KpCAkdjEpeoRrOWvnFnPdZtPQIAePPjZmzcWZ+V8zMKt1w4ETn2aHd/4RufowBjBclWJlViZs9ogzuNSLYmR529ffLu1pl6NY3MhJjoO5aFZVd+T1ASiDqQwNGYqqKcUa+lN3p7sHrTPvkxw+iDaI2GJElyRsRoaw7xGTMtBQ5Otma8dbFlEzIGg1Ndkp14J7704sl3oMBFxRT7Mz5LnjKK3VMfEjgaw9fSgfg6eLrUtfrR3/kzmiBao5KtANgjp6Pvn1RK7vzBGJclw3tUbuf8EY40J5M80XY5muG4wdl9IpphWDXK2lBGZXwsLunEmW6ER+FlP3UmHrtHYQTqQAJHAEY7UE305KH/voajCaI1KjyAsm6UBuFoaxeA+O9GJMOF5LFRznjj7UxCcjAmxwT2kZaujPdY27izHj945QAA4KNTXlraHoQKtwsOqwV9YTaqXcV5f44mPVDsnhqQwBGAybEZ6pGWrozeX1mYg+9eerb82DrKIFqjIrfz6cwFTl84IruqJ5eR4R0MWbCPop0T3z+ZPDiDMm5MLiwS4A/GNyRNB760nSiNaGl7IFaLJBdAHE1c2ZGWWH8uo/6sFiRwBIAbyiOnMxM4ADClPHrTnF2Wh3dXXTqqIFqjEhc4mbdzfXs3QhGGXIcVFaNMzTUqfABv7QrA253Z5qaRCJM9bbQUODhOm1VeDsykT9PSdupMlL3smY8d/Dciwa4eJHAEIBueBT7bnVNdTJ6bIeAu/UZvL7oCoYw+g3vZyM08NPlOmyz+Dp/uzOgzTnX0IBCKwG6VqLruMPD4pEy8ZbS0nTpTYqL9UHM2BA4JdrUggSMAXOCcONOdcYYPzQ5GpijXAU++AwBQl6GY5HFS1M7Dww0Cd8uny1E5gyoP1v5WmJDh8UnvHWpNe2mpsjAH92SxPpSROTvWn3cdP5PxEt4RWnJVHRI4AuDJd8DtsoGxzGst0OwgNfiMN1PPwtFYO9OyyfBwgXM4w+VAuZ0pwHhY2v3R+jV/OdCECx5+K+0g4RmVbgBAuduJ92hpe0j4cunHjb6M2rndH5R/Kxo71IMEjgBIkiTHLWQy42WMxQMyKYBtWEbrWaBZWGrwfng4w8D5I7KQpHYeikZvD17ae0p+nMkmsodiv8+ssUXkuRmCRm8PfrH1sPw4k3bm/XlsUQ5yHbRPoFqQwBEEbjAzMQiN3l50B8OwWSQqIDUCowk0ZozJvw/NwoaHexIzFTj/bIq+7zPlJHCGoq7Vj/7Z4ekGCf+zOerJpHYemmwEY/PYPZqAqgsJHEHgnoV/tqS/dPJpU/Q9Ez15sFvpJx0ObngPZWB4m3y98Pb0wWqR5N+LGBzePpnElTHG8EmTDwAwtaIg6+dmFLIRJMzvg8+UUzsPRTbbmUII1IWsoSBMiw3knzT60n7vwZgxmB5bTyeGZlpFtI3qWv1pG95PGqNCcnJpHu2NNAKl+U4U5tjBWPpenEZvL3y9IRKSI1BZmIO1186SH0tpBgkzxnAo5sGhdh4a3s5c40hIPxj7YGxcn15BY7SakMARBB7sl4nhPRgzvNMqaRY2EuVuJ4pz7QhHWNopn1xITqNBakQkSZL79MdpinbukZzkISE5EkvOG4cbFlQDAP7tnLPSChJu7QriTHcfLBIJnJFYct44rFo8DQBw7oTitNqZMRYXODQJVRUSOIJQWuDEmDwHIiw+wKfKJ3TzpIwkSZhRxQ2vN633fkJCMi3kdm5IT+DIQpL6c0rMH18CILocmA48/mZcSS5cdhKSI3H+FA+AqEcyna0xmn0BnOmOLm2fTbFOqkICRxAkSZIFysE0Zry9fWG5Zgi5P1ODtxP3fKUKjwuhdk6N0XpwplH8TUrIy9tNnWkZ3v2nogKfC1FieD5TkQ+bRcKZ7j40eHtTfh8fzyd58khIqgwJHIHgA9Vbn7SknIJ4qLkL4QhDca4d5W7aoTYV4h6c1A1vIBSWU8TJg5MavJ0PNvjSMryyp4wETkpMKcuH1SKho7sPzb7U96TaFxM4M8cWKnVqhsJps8pLeQdOpe79/Zg87JpBAkcgfL3RfXve+Lg55WJSiXEhtHVAaiR6ylI1vFxIFubYaQ+qFJlcmg+H1YLOQAgnz6Qm2Hv7wnIKPy1RpYbLbpULIqaz7Mo9OLNI4KTMZ6uibXUgjWVXEjjaQQJHEBq9Pfj9rpPy41SLSfFBim6e1JENb2/qhvejk9F2/mwVCclUcdgs8RlvigbhQIMXoQiDJ9+BqkISkqky66yo4d17IjWB4+vtw7HYztgzq0jgpMpnY17JdATOwQYucMgjqTYkcAQh06Jde+o7AADzxhUpc2IGxGGzyPVV9p7oSOk9e+rPAADOGVes1GkZEm4Q9p3qSOl43p/nVheRkEyDedVFAOL9dCT4xGhsUQ6K8xxKnZbh+KwcOJ+akOzoDsoxkrPPKlLqtIghIIEjCJkUk+oJhuUAtnPGk+FNh/mx9tp1PDWDsDtmOEhIpse8cem1856Y4JxHQjIteHt9eKIDkf5ldweBlqcyY0aVG5IENHh70eIbOdCYC/ZJnjyUkJBUHRI4gpBJMamPTnYgFGEodzvJnZ8m6QicfzZ1ygHGc2MzZSI1zpsQbee9JzrQF46MePzeBA8OkTpTKwrgslvg6w3JHoPh+DC2lMWXtojUKHDZ5TpYO461j3g8H19oAqoNJHAEYsl54/DIdbMBAONKckYsJrU7ZgzOGVdM7vw04QLn40YfuoOhIY/buLMei/73HfnxXw82K35uRmJyaT4Kc+zo7YuMWA/ndGcApzp6IEnAbDK8aWG3WmRvzEjLVIwx2TifS4Y3bRbERPsHx0aeHMkChzySmkACRzBqZ5QDAI6396CjOzjssbspLiRjqopyUFnoQjjC5Nlsfxq9PVi9aV9SbFS6uwibHYtFksXkByN4y3h/nlKajwKXXfFzMxp8mYpPfIbiWFs3TncG4LBaMIc8ZWlz3sRoYcUddcN7cELhiCw2aRNkbSCBIxgleQ5MjKV8DjdDiERYgvuzSI1TMxznyMtUgw9U2dhFmEhcDhzeIGw70gYAqJlUovg5GRHujXn/aNuwx+2MGeY51YVUeC4DFkyI9s+DTT65tMdg/O+WQ+gNRZdll67fnlLZDyK7kMARkIWTxwAA/n7o9JDHHGjwod0fRL7TRtH5GVITm4n9/VDroK9nYxdhAlgQa+f3j7YjPEwA7LuHo7/DhbGS+ER6fG7yGFgtEupa/Tg5zLYNvJ1rJo5R69QMRZnbhQljcsEYsGuISWijtwc/f+uw/DjVsh9EdiGBIyAXnV0KAHhnCMMbfS0qfhZOHgO7lX7GTLj4M9F23nX8DDoHmYlVFubgpoUT5MfWNHdrJqLMrS5CgcuGdn8QH53sGPSYJm8vDrd0QZKAhZNI4GSC22XHnFjs0nuHBx87whEmjx0XTy1V7dyMBp+Ebv20ZdDX61r96C/lyfurPmQZBeT8KfGZ2PG2wTMi+I110dlkDDJl/Jg8TPTkIRRheO/w4G79UMzjcOm0Ury76tK0dhEmotitFlm0P7/t+KCzWB68PeesIhTmUvxNpnw+1s5bDg5uePee6EBHdx/cLptcO4dIn0unRWMl/3qwZdBq6J78gdvmkPdXfUjgCIjbZZeXT/68r3HA603eXjlg87Lp5aqem9H4wtQyAMBrg7RzOMLwl/1NAIClCyeQ52YU5DqisR4v7Tk16DYkf9kfbf/FMytUPzcjwdtv6z9PoyswMDvw9QPR/vz5z5TCRp7fjLlwigdOmwWnOnoG3bR338nkxAWrJJH3VwOohwvKF+dUAQD++OFAw/vnfY1gLBpUWFVEN8xo+OKcSgDAmx83w9/PIGyva0NrVwCFOXZcQHEhGdPo7cH/7R56G5LWrgDePxoNfL2CBM6omFZRgImePARDEWzpV9IgHGF4Ze8pAMCXYuMLkRk5Dqu8xP3SnpMDXn/1wwYAwDcunIjfLv8c3l31BfL+aoBiAudHP/oRzj//fOTm5qKoqCil9zDGsGbNGlRWViInJwe1tbU4dOhQ0jHt7e248cYb4Xa7UVRUhFtuuQVdXV0KXIG2XDGzAnarhIONPnyYsJ0AYwwbdkRnv1+kQWrUzK0uwvgxuejpC+NPHzUkvfbC9mg7R38LmgtkykjZaBt21CMcYZhTXYTxY/I0OEPjIEmSPC688H6yl+zvh06j2RcV7JdQ/M2o+cq51QCATbtPIRiKF7E8eaZbDuT+as04LJw8hjw3GqHYqB0MBvHlL38Zt912W8rv+fGPf4yf/exneOKJJ7B9+3bk5eVh0aJF6O2Nl8S+8cYbceDAAbz55pv405/+hHfeeQe33nqrEpegKUW5Dnmg+tU7RwBEZ8K/3HoEh1q6kO+04V/PGavlKRoCSZLw1QXRmdWv3jkqZ/mcaO/G5oTlKSJzBstGs0jABE8uevvC+E3MEN98/ngNzs543FgzDjaLhB3H2pMmR7/YGh1HrjvnLDhtlB4+Wi6ZWoqyAifa/EH8IWGj5Kf+XodwhOGCKWMwqTRfwzMkFBM4999/P773ve9h1qxZKR3PGMNPf/pT3Hvvvbj66qsxe/ZsPP/882hoaMDLL78MADh48CA2b96Mp556CjU1Nbjwwgvx+OOPY8OGDWhoaBj+C3TIrRdNAgC8tq8JP/rzx7jg4bfw49c/BRDdE8lNxdCywo2fGw+3y4ajp/149h/HwBjDD149IA9SM6pop/bRwLchsSaInHPGFaOyMAfr3j6MJl8vKgtduHJWpXYnaSDK3S55CWpNrB//6aMG7Khrh8NqkccVYnTYrBbcdslkAMBP//pPtHUF8HGDDy/GPL+3XTxFy9MjIFAMTl1dHZqamlBbWys/V1hYiJqaGmzbtg0AsG3bNhQVFeHcc8+Vj6mtrYXFYsH27duH/OxAIACfz5f0pwemVbjxtc9FvQtP/r0uyc3/3uFWqqmQJfKdNty5eBoA4OG/HMSNT23Hlk9aYLdK+MEXP6vx2RmDJeeNw7urLsX3r5oOIFrV+OtPb8fP347WClnzLzPIq5BF7r5iGgqcNnx4ogNLfrUNd//hIwDA8osmooL2rcsaX60Zh4mePLR0BvCVX23DLc/tRDAcQe30clwwheoMaY0wAqepKbocUF6enBVUXl4uv9bU1ISysrKk1202G0pKSuRjBmPt2rUoLCyU/6qrq7N89spxz5XTMdkzMC4hwkA1FbLI12rG4Zq5VegLM/zjSBskCfjBlz6Ls8sLtD41w1BZmINbPj8J91wZFZN/P9QKxoClC8dT9lSWKXe78JMvz4HdKuGD42fgD4bx+bM9+F7tZ7Q+NUPhtFnx1E3nojjXjiOn/Wj09mKiJw+PXDeL9gcUAFs6B69atQqPPPLIsMccPHgQ06ZNG9VJZZvVq1dj5cqV8mOfz6cbkZPrsOHpm8/DFx7dmlQ4imoqZBdJkvDYV+Zi8cxKHGruxMVTS6lCtELcetFkzK0uxvtH2zDrrEJc8plSMgYKsHhmBV777ufxxsfNGFuUg6tmV1JquAJMLs3H67dfhFf2NsDlsOJf541FvjMt00ooRFq/wh133IGbb7552GMmTcpsfbeiIjqDa25uRmVlfC2+ubkZc+fOlY9paUkuYBUKhdDe3i6/fzCcTieczoGFl/TCBE8eHr5uFu7ZtB9hxqimgkJYLBIWz6wgb4IKLJhYIm/hQCjH2eUF5IVUgTK3C8sptkk40hI4paWlKC1VJr1w4sSJqKiowJYtW2RB4/P5sH37djkTa+HChejo6MCuXbswf/58AMBbb72FSCSCmpoaRc5LFJacNw4XfaYUx1q7McGTS+KGIAiCIIZBMX9lfX099u7di/r6eoTDYezduxd79+5Nqlkzbdo0vPTSSwCiSwS33347fvjDH+LVV1/Fvn37sHTpUlRVVeGaa64BAEyfPh2LFy/G8uXLsWPHDrz33ntYsWIFrr/+elRVGb8mTGVhDtVUIAiCIIgUUGyhcM2aNXjuuefkx/PmzQMAvP3227jkkksAAJ9++im83nhJ67vuugt+vx+33norOjo6cOGFF2Lz5s1wueJR/y+88AJWrFiByy67DBaLBddddx1+9rOfKXUZBEEQBEHoEIkNtlOYwfH5fCgsLITX64XbTTVOCIIgCEIPpGO/KaS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],
"source": [
"cplot(f_sin5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2D Chebfun"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the paper, they suggest to create two Chebfuns as follows:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(Chebfun \n",
" domain length endpoint values\n",
" [ -1.0, 1.0] 42 0.29 -0.29\n",
" vscale = 1.00e+00,\n",
" Chebfun \n",
" domain length endpoint values\n",
" [ -1.0, 1.0] 44 0.75 -0.75\n",
" vscale = 1.00e+00)"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.sin(16*x), np.sin(18*x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is certainly possible, but we can't create a 2D Chebfun from them, at the moment.\n",
"Instead we have to do it like this:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false,
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},
"outputs": [
{
"data": {
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88Od5dAYBXzcH3nugu/iYW+LR6A0Mbu/LkmmR1aI4aQVKhnz8N/YKGRcWjEJuIWFoy9Tl+N1kPjjWhCRwJMyF3iDw9/lc1kWn8c/FPFPYWiGXMbCdD8O7+HNXZ3+CbCg0rdLq2XM+l99PXWbP+dxqBcGuDgqGdGzJ7R1bMqi9b40dJdciCAKJueUcSMznYGI+hy4VVCtSFSMK4uvWlK3aGp2BQ5fy+fNMNn+dza5WayKXQe9WLRga7seQDi3pEuRRq6hFXpmag4n57EvIY39CdWFnJ5cxoJ0PI7oGMLJbAL5N0Dp8MaeMLScz+e3UZdILr4gaZ3sFt3dsyfCu/twZ7oeXi8NN91Oq0rLnXC7bzmTxz8W8ap+JqDbejI8M5Z7uAbWubakNgiBwJKmQpQeS2HVVV2C7lq5MjmrNQ72Da1z35WIlW05e5q+zOZxIKwbE1/7R/q157q4OeLve/LleS5lKy8s/n+bPOLEWa1S3AN59oLtpP9HJhUxfHo1So2dYZz9+mBJpEjJbT2fx9NrjdAv24I9nb6vPy/CvRxI4t0ASOBKNTUG5mg0x6aw5klbtbLhHiCcP9ApmdI8gWrrbTqG7Vm9g38U80xl+xVUCJNjLmWGd/birsz9Rbb1xtGtYTYlKq+dIUgG7z+WyIz67xkLkt8d0ZVyfkEY9YIIYqdmfkM/vp8XnWaa60qbdwsWeoeF+DO3kx20dfG950L8VgiAQf7mUHfHZ7IjP5mLOlaiQQi5jSAdfxvYKZniXgEat0ymq0PDryUx+isngXNaViJKrg4LhXQO4p3sgt3XwrXfBa4Vax+7zufwSm8G+hCupIjdHO8ZHhjB9YFiDojqCILDnfC5f70msFgkd1tmPmYPbMKCtT62Lso+nFfH17gT+vpAHiJG454d1ZPrAsFoJ1vPZpTz543GS8yuwV8h4Y3QXpvRvfd3jRycXMmXpUdQ6A3Pv7shzd3UA4LXNZ1h7NI2pA1rz9phutXwFJK5GEji3QBI4Eo1FYm453/9ziS0nL5tC9l4u9kyIDGV8ZCjt/dwsvMK6kZhbxoZj6Ww6nlmtpTnYy5nREYHc1yOIrkEeZjP/O5SYz+QlR2u8zdlewd1d/BnXJ4RB7X3rXfdRJTQ2HRcjGVf7oLR0d2REV3/u6RZIvzbeZi2cTcorZ0d8Dn/GZXE640phrKuDgpHdAnmoT3CdDt5XYzAIHLpUwIaYdHbEZZs+m/YKGXd08mNMzyDuCvdv9ILny8WVbDqewcbYDJO1gEwGd3f2Z+bgNkS18a718zEYBHbEZ/P1nkTOGoWZo52c8ZEhzBzUhrYt6//dOpiYzztbz5kEX89QLz4e14MO/tcXYVfx64lMXt10GpXWQJCnEwsf6U2vVi1uuP1PMem8/PNpZDL45cmB9AzxIur93eSVqVk5sx+3d2xZ7/X/m5EEzi2QBI5EQzmTUcK3exPZHp9tOmONCPFkyoAwRvcItKn2zwq1jq2ns9gQk16tTdjXzZH7IgK5LyKIXqFeTeJoXFObuwwI9HKq5u8T6OnEQ71DGNcnhLBa1lLkl6v5OTaDX2IzqtXU+Lg6MLpHIKMjgujdqnEM/erKpbxytpzIZPPJzGqpo7YtXZncrxUP9Q6hRS1SKcVKDT/FpPPjkTTSCq94F3UJ9GBiv1DujwhqcCSqNgiCwP6EfJYeSOafi3mm6yNCvXh+WAfu6Njyhp8nQRD4+0IuH++4aBIgrg4KpgwIY9bgNo0WCdUbBDYcS+f9becoU+twUMh54e6O3B8RSGqh0lT/ZTAIfPLXBb7dewmA2zr48uXEXrVKbb2w4SSbT2TSOdCDt8d0Zfyiw7g72hH7xt0NaiT4NyMJnFsgCRyJ+hKXWcLHOy5U+9G+u4s/T97Rjt43OZuzRtIKlKw6nMKGmHRTakYhlzG0kx8T+oYytFNLi7RubziWdl2r9sORoZzKKGHT8Qy2nLxcrbW+X5g3j/RvxchuAdelywwGgcNJBayNTuOv+GxTbY+DnZy7u/jzYK9ghnRsaTVF3oIgEJtaxC/HM/ntZKYpNehgJ+fe7oE82r81fVpf/zk7l1XKqsMpbD6RiUorRmvcnewY2zOYCX1D6Rbs2aTP42oSc8tYfjCFX45nmNYWEeLJ88M6cken6kLnSFIBH++4YBLa7o52zBgUxoxBbWol8OpDVkklr2+OY8/56m7fchm8dX9XDiTmsyNeLFR+6o52/N/wTrUWwQXlau789B9KKrV4OttTUqlldI9Avpncu9Gfx78FSeDcAkngSNSVlPwKPvnrAn+czgJEIXB/RBBP3tGOjjcJa1sbgiBw+FIByw+lsOtcjin61NrHhQl9QxnXOwS/W1jfNwVZJZU3bHNXafXsOpfDxpgM9ifkmaI9vm4OTOgbyuSo1rjYK/gpJp110WmkXOXC3DPUi4l9Q7mnRyAeTpbpYKot5Wodv528zJqjqdW6sXq18mLObW25u4s/+y7m8cO+JI5e1aocHuDO9IFhjOkZ3OSeOzcjr0zN4v1JrDqcYhI6PUO9+O+9nfFysee9bedNIsPJXs60gWE8MaSd2YTN1QiCwA//JPH+9ppH/jgo5HzwUHce7B1S530vPZDMgj/Omv5eOLk39/YIrPda/+1IAucWSAJHorYUVWj4fNdF1h4VjbxkMhgTEcTcuzvd0ADPGtEbBLadyeLbvZeqFZoO6diSGQPDuL1jS5tsWc0uUfFTTDprj6aRXXr9qAUQi13H9gpiUr9WdA2yXCSjvgiCwKmMEn48kspvV9V6XY1CLmNk1wCmDQyjb1gLqxiQeiPyy9Us3pfEqsOpVGqrj3iwk8uY2C+UZ+/scMsZU43NoUv5TF58ff2Xh5Mdy2f0pU9r73rtd/XhFN7YEm/6+92x3Xikf+t6r/Pfjs1OE5eQsBaq8vMf7ThvmgN1R6eWvDwinC5BtiOKNToDm09ksOifJJKNBm4uDgoe6h3CtIGta3S2tSUCPJ149s72dAv2YOaKmBq3ef3ezozrE2I1aai6IpOJvjQd/NzwdnXgh31J123zcGQo8+4Jt/qoFIi1Xf83vBMGQWDx/uRqt90Z7se8UZ1xdWz6Q1MbX1fkMq4bDjqmZ3C9xU1WSSXzf4uvdt2bW+K5s7OfRfyd/m1IERwpgiNxDafSi3lzSxynjJ0t4QHuvHlfFwa287XwymqPWqdnfXQ6i/65RJZxiKSXiz0zBrZh2sDWTVJoam50egNbz2Tx3d5LpgGSMpl4oLKTy0grVJpSIcFezswYFMbEfq1ws8DBsyGUqbSsOpzKkv1JJm8eDyc7vFwcUGr0pi4wDyc7Zg5uw4xBbSxmIFgb9l3M43+/x5OUJwpuB4UcZKIYB/G9entMV+7q7H+z3ZiFuRtOssk4huNqXhkZzpN3tKvz/m4UFVo3p3+9x0X825FSVLdAEjgSV5NVUklyfgWBHs78eDSVZQeTEQSxwPGFuzsydUBri81Jqis6vYFNxzP5cneCyY/Hz92Rx4a0ZVK/VhY5M25s1Do9v8RmsuifS6ZOIVcHBQ/3Da3muVJUoeHHI6msPJxCfrnY8u7uZMfMQW2YOagNni7WKwJANNNbeTCFJQeSTUXVbXxdefL2dozpFYSjnQK9QWDrmSy+3p1g6gxzd7RjxuA2zLmtDe5WFNFJL1TyztazpoJdXzcHXh4ZzrjeIchk8PeFXN74Nd70ub2newDz7+vaJKkqQRD4fFcCX+1OAOCOjr68PbYbP8dmmq57/Z7OzBnStk77zSqpZOD7e6oNcJXJ4NCrd0oRnHoiCZxbIAkciSo2HEtj3qYz14WlH+gVzLx7wvFzt3zBbW0wGAS2xWXx2V8XTbOEAjyceObO9oyPDGmwGZ81UKnRs+ZoKov3J5FTKkYtvF0dmDkojCkDwm4YtVBp9fx6IpMf9ieZogZujnZMG9iaWYPb1tnJ1twoNTqWH0zh+38uUWrsbmvb0pXn7uzA6B6BNYptg0Hgz7hsvtqdwIUcMZrl7erAs3e255Go1hZtSdbqDSw9kMwXuy6i0hpQyGVMGxDG83d3uC6lptTo+HJXAksOJKM3CLg72bFgTDfG9AwyW12RTm/g9c1xbIhJB+C5O9vzwt0dTY/35a4EPt91EYA3R3dh5uA2td53iVJL33d3otFf+YHpGuTB1uckF+P6IgmcWyAJHAmo2XMF4NOHI3ioHt0SluJoUgELtp4lLlMsHm7hYs/TQ9vzaP/WNuXHcyOq0m3f/J1oGnUQ4OHEY0PaMrFfaK3djatEwNd7EkwpLRcHBVP6t+axIW3xaYJRCTej6nl+vSfRlHbq4OfGs3d14N7ugbVqTTYYBLbHZ/PJXxdMYi7U25kXh3fivh5BTV5IHptaxOubz5he735tvHlnbLdbdh6evVzKvE2nTWnie3sE8u7Ybo2eWlVqdDy95jh/X8hDLoMFY7vxSNT1BcCf7bxoiuR8+0hv7uleuy6ohX8n8vGOC7Rr6cr0QW1449c43B3tODl/uMUGlNo6ksC5BZLAkQD4JTad/9t4+rrrbSU/nlag5P0/z5lm4rg52jHntrbMHBxmVamJ+qLVG/g5NoOvdydw2VhHFOzlzLN3tueB3sH1jkoZDAJ/nc3h6z0JpvZrVwcFs29ry2wLpHX0BoHNJzL5YtdFMorE9Ewrbxfm3t2R+yKC6nUg1OkNbIhJ54tdCSZR2D3Yk//d37VGH53Gpkyl5cPt51lzNA1BEEX3a/eIxd61jcTo9Aa+3XuJL3cnoDcI+Hs48sn4CG7r0DgOwMVKDTNWHONEWjFO9nK+ntSbu7vUXPcjCAJv/X6WFYdScLSTs+6x/rf0vVJp9Qz6YA8FFRq+mNCT+yKC6DZ/B5VaPbvmDrH5An9LIQmcWyAJHInNJzKYt+mMqQi1CoVMxoFXh1p1frxMpeXbvZdYuj8Zjd6AXAaT+rVi7t0dLR6FaAwMBoHfT1/m078ummpsqtJtD0eGNlq6pWrG0Wc7L5qEjrerA0/d0a7Jol/7E/J4d+s5U4TDz92R5+7qwIS+oY3S9aXU6Fi6P5nv9yVRrhbTXQ/2DubVkeFm8zs6kJDPK7+cNtXSjO8Twrx7Otc7FXgqvZgXfjpJUl4FMhk8e2cH/nNXhwZFQHJLVUxZGs2FnDI8ne1ZNr3vLYWf3iDw+OoYdp3LxcfVgd+fHXzToblV7eEhLZzZ++Id2CnkPPjtQY6nFfPlxJ6M6Rlc7/X/m5EEzi2QBM6/F5VWz5tb4vgpJgOAtr6upBRUYBAwueY2xeTq+iAIAtvOZPPW7/GmgZSD2/vy39GdCQ+w7c9xVaF3YbmG7/clcSZTTE34ujny1B3tmBzVymyCo6b6pSBPJ164uyMP9Q4hp0xFcn6Fybq/MUjIKeO9bedMQx89nOx48o72TB8YZhZzvvxyNR9tP2/63Ls52vHcXe2ZPrBNownGMpWW97adZ110GiCmxj56KKJRoqGVGj0Ltp5l7VFx37d18GXeqHCKK7V1fl/SC5U8uvQoqQVK/NwdWT0rik4BtYumVKh1PPz9YeIvl9K7lRcbHh9QoxDV6g0M/WQvGUWVvD2mK1MHhAHwxq9xrD6SyuO3t2XeqM61XrPEFSSBcwskgfPvJLtExeOrYziVUYJcBv+5qyPP3Nme3DLVDV1zrYW0AiVvbIkzjYho7ePCG/d24a7OflZt6lYbair0dnO044nb2zJzcJtGnyB+I3TGlNiXuxNMrfVBnk5klaoQBNG6//0HuzdIABeUq/l810XWRaejNwjYyWU82r81/7mrQ5M49p5ML2b+VRYI7f3c+ODB7kSG1c/npYr9CXm8+ssZU9Rm2oDWvDIqvNHfu80nMnhtU1w1g8C6vC8Xc8qYsvQoOaVqQr2dWTOrf50NO9MKlNz79X7KVDoeH9KWefdcL1TWRYufaV83B/a/fKdJtFa5Gt/bPZCFj0jjGuqDJHBugSRw/n2cSCvi8dWx5Jap8XKxZ+Hk3gxqb/2+NhqdgcX7k/hqdwJqnQEHhZwn72jHk3e0axYFxOeyShn15f5q18mAP54bbDHXYZVWz8pDKXy1O8E0C6qK+qYwdXoDq4+k8tnOi6a5X8O7+PPqqPAGTcWuDwaDwM/HM/jwz/OmifGP9m/FyyPrbhQoRm3OsS5a7EBq5e3CR+N60L+t+WrYDiTk8+jS6t4ytXlfTqUXM215NMVKLZ383Vk1q1+9W9C3x2XxxI/HAVg+oy9DO/mZblNp9Qz9ZC9ZJSreGN2FWVd1Xe2Iz+bx1bFEhHqx5elB9XrsfzuSk7GExFVsPpHBK7+cQaMz0NHfjSVT+9rEmIW4zBJe3HjKVJ8xsJ0PC8Z2o10THxDNgU5vYG10Gh/+ef3sHwEordQ1/aKMONkrePz2drT2cTEdxKrQCwLnLpfWSeAcvlTA/36LN7Vvdw3y4I3RXcwqAm6GXC7j4chQhnfx571t5/gpJoMfj6Sx82wOC8Z0Y3jXgFrtZ9/FPF795bSpAHz6wDBeHtnJ7BE3eQ0ZNb0gkJJfccP35dClfOasjKFCo6dnqBcrZvRtUEfWyG6BTBvQmpWHU3lt0xl2vDDEJA7XRaeRVaIi0NOJR6KqR5WCjTU7l4srr9unROMjCRyJZosgCCz6J4kPjQP0hnfx57MJPa3eyVajM/D1ngS+3XsJvUHA29WBN0Z3ZmzPYJtPR4HY1j7/t3iTcLsWhUxGmK/lBWhEqFeN1v0v/nya+fd14f6Im3uzZJVU8u7Wc6YBrV4u9rw0ohMT+7ayihZhLxcHPhoXwdiewczbfIbUAiWPrY5ldI9AFozpdsOUmVKjY8Ef50y1Nk0RtbmaG41UWH4whV6tWlwX2dx7IZfHVsei0RkY1N6HH6ZENorh5aujOrP3Yh6pBUre33ae9x/sjlKjY+HfiYBYDH3tWqpe0yrjRgnzIqWopBRVs8RgEHj7D7GtE+DxIW15ZWS41Q+UvDZqc2/3QN4e07VZdEfllqp4Z+s5fjt1GQBPZ3teHN4RhVzGG7/GoxcEqyv03nAsjdc2xaEXBOQyscuqyhW5f1tvFozpRodrPF10egMrDqXw2c6LKDV65DJ4JKo1/ze8o9WOyFBp9Xy5O4Ef9iWhNwj4uTvy4bge1VIvIH4+n1t/wuSx01RRm2u5+n2RycS0pkGAQe19+H5KpOkkZtfZHJ5acxyN3sCwzv58M7lXo6Z2jyQVMPGHIwCsnR3FyYxiPtp+gdY+Luyae/t1BcilKi09/vcXAOcXjGwWaeamRqrBuQWSwGneqHV65v50iq3GM+dr8+DWiN4gsOifS3y+8yI6Y9Tm7TFdGd0jyNJLazAGg8Ca6DQ++vM8ZWodMhlM7teKF4d3Mp3RZpVUWm2h99Vr83Z14Id/kvjm70TUOgN2chmzBrfhubs64Opox6n0YuZtOsNZ48T2Pq1b8PaYrjYzxfxUejFzfzrJJaOAmRzVitfv6YyzvYJlB5P5cPt5tHqBAA8nPpsQYdH5bFe/L5dyK3h8tZiCigj1YsX0vhxNLuCZtSfQGQTu6R7AlxN7mWXg6uubz7DmaBpBnk6UqXSUqXV8PiGCB3pdbxZqMAi0e30bggDHXh9GS3fbP3FpaiSBcwskgdN8UWn1PPljLH9fyMNeIePTh3tyf4R1i4Sskkpe2HCSI0mFAIzqFsCCsd3wbQZRm/PZpczbdIYTacUARIR48u4D3ekWbBsH/BuRXqjkrd/PsuucOFfJ09meFi72pBYqEQTx73mjwnk4MtTqo4bXotLq+Wj7BZYdFCd9uzgosJPLTGMjhnfx58OHejRJ11ddOJlezHRjEfHV3B8RxGcPR5htnlyxUsPtH+81pZ06+Lmx/fkhN0xDdnh9G1q9wOF50jyq+iAVGUv8K1Fp9Ty2OpZ9F/NwspezZGpfBnew7k6p7XHZvPLLaUoqtbg4KHjr/q51cnu1Vio1Yspjyf4kdAYBN0c7XhrRiUf7t7aK+pOGEurtwpJpkew+l8OslTGUVGpNB7jbO7bk04cjbFagOtkrePO+Lgzr7MfkJUdRXtVJ9s7YbjwS1coqP589Q73Y+PgA7v58n+m6ge18+HxCT7N+5rxcHHg4MoTF+0VB+NTQdjd9PPG1E/j3hRaaHkngSDQLKjV65qyK4UBiPi4OCpZN72uxLpXaoNLqefuPK8ZlPUI8+XJiL9r4ulp4ZQ3nWEohL208RUqB6EI8smsA/7u/KwGetjG4tLYUlKvZfCLzuuvPZJZwMDH/lkXI1oxKq+evsznXXb/7XA73dA+0ugGlVVRFCqvIKKokv1xt9onkl4tVpv9X1SfdiKpPhEFSOGbHciNmJSQaCZVWz+xVxziQmI+rg4IVM/pZtbhJL1QybtEh1h5NQyaDJ25vx89PDLR5cVOp0fPW7/E8/P1hUgqUBHg4sXhqJIum9GlW4kYQBLaczGTYZ//wx+ksFHIZT97Rjg2P9Sc8wJ3CCg3/WX+SWStjyClV3XqHVkZCThljFx40FejPGBTG/Pu64Ggn5+8LeYz6ch9Hkgosu8gaWHM0lZd/EWfL3RnuR7CXM2mFSiYtPkJumfneh5PpxWw9k2X6e8XBFEqUN+6S0hvbv5pDJNPakQSOhE2j0xv4z/oTHEwswNVBwapZ/ejXpmGurOZkz/kc7v1qP3GZpXi7OrBqZj9eHRXeaHb5luJoUgEjv9zH8oMpCAI8HBnCX3OH3HB4oa2SXaJi9soY/rP+JEVKLZ0DPdjy9CBeGRlOVFsffntmMC8O74iDQs6e87kM/3wfW05mYiuljhtj0rnvmwOczy7Dx9WB5dP7Mv++rswY1IYtzwyiXUtXckrVTF58hCX7k6zmea04mMzrm+MAUZAtnRbJ+sf6E+TpRFJeBY8sPkqh0dSwMREEgXe3ngXEGV+d/N0pU+tYfii5xu01OgM6o8BxsZcSKObGtn9VJf7VCILAa5vPsCM+BweFnMVTI+nT2jrFjd4g8PGO88xcEUOpSkfPUC/+eHZwo01GthQqrZ63fz/LhB+OkFqgJNDTiRUz+vLRuIg6u+JaM4Ig8OuJTIZ//g+7z+dir5Dxf3d35LdnBlUrmHawk/PMnR3Y+txgugd7UlKp5T/rT/LUmuMUlKst+Axujkqr59VfTvPSz6dRaQ3c1sGXP5+/jaHhV9rEwwM8+P3ZwTzYOxiDAO9sPcdz60+i1FjOlBFg8b4k/ve7KDIeH9KWN0d3QSaTEertwto5/fH3cCQht5xZK49ReY0zdUPZEZ/NsZQinOzlvDSiE8/d1QGAZQeSTcNNr+bqxzfHzDGJ6kgCR8Jmef9PcXigXAZfT+7FQCsdvVBSqWXGimMs/PsSIHqH/PT4gJtOIrYF4i+XcN/XB0zdNhP7hrLjhSHccY13iq1TUK7mqTXHeX7DSUpVOnqEeLL1udt49q4ON2w77uDvzqanBjL37o7YyWX8GZfN8M/3sSM+u4lXf2tSCyp46LtDrD+WjkwG/3d3R1bO6Ief+/VpRRcHOz4dH8HbY7piJ5fx+6nLPPjtIVILbl53Yi4W/p3Iu9vOAfDM0Pa8Oiq8Wt1TmK8ra2ZH4elsz4m0Yp5Zexyd3tAoj63RGfjA6MQ957a2BHo6M6pbAG1bulKq0rHpeMZ196kwikE7uczmo7a2gPQKS9gkKw+l8MO+JAA+eKgHI2ppL9/UJOdX8MC3B02dXV9O7Mn/7u9q0z9ueoPA9/9cYuzCgyTkluPr5sjyGX354KEezSpqA7DzbA4jvtjHn3HZ2MllzL27I788OZCO/reePm2vkPPcXR349elBdPJ3p6BCw+OrY5m36TRKjY6skkoOXconq8Rytv1/xWcz+usDxF8WU6arZ0bx7F0dbtraLpPJmDogjLVz+uPr5sj57DLu+/oA+xPymnDl8M2eBD7ecQGAF4Z15MURnWos6m7v587SaZE42snZfT6X//4a1yiptWUHk0kpUOLr5sjjt7cDxDEY04yTw1ccSsFwjd1yVZrM2lrsmyuSD47kg2Nz7L2Qy8wVxzAI8NKITjw9tL2ll1QjBxLyeXrtcUoqtQR6igW3tu7/kllcydwNJzmaLHr2DO/iz/sPdm8WTstXU67W8dZv8WyMFc/CO/q78dnDPev9/ql1ej7fmcD3+y4hCODr5kBBhabRppTXFZ3ewMd/XeD7f8SThN6tvFj4SO86+7Jkl6h4ck0sJ9KKUchlvHV/Vx7t39ocS67Gt3sT+Wi7KG5q+xuwIz6bJ3+MxSCIUapnjemk+pBTquLOT/ZSodHz8bgejI8MNd1WrtbR/73dlKt1rJrZjyEdr6Sh917IZfryY3QO9ODP/9xW78f/N1OX47ftnkZK/Cu5kF3GM2tPYBBgfJ8QnrqjnaWXVCOrDqcwbXk0JZVaerXyYss1tRq2yPa4LEZ+sY+jyYW4OCj48KHufD+lT7MTNyfSirjny/1sjM1AJhPrOn57ZnCD3j9HOwWvjgpnzewoWro5kl+uMfmgGAR4bVNck0VycstUPLLkqEnczBgUxvrHBtTLdC7A04n1j/Xnod4h6A0C//01jgV/nDV1CpmDH/ZdqrO4ARjRNYC3xnQD4NOdFxuULvzgz/NUaPT0auXFQ72rOxa7Odoxro943Y9HUqvdVjXmw9dNiuA0BZLAkbAZCsrVzFxxjHK1jqg23rz7QHer8xkxGATe+eMsb26JR28QeLBXMOvm9K+xnsFWUGn1vLkljid+PE6ZsUB623O3MaGvdRq+1Re9QeDr3QmMW3SYtEIlwV7OrJ/Tn3n3dG60mUED2/ny7gPdrn9sQSAlX9koj3EzjiQVcO9XBziaXIirg4KFk3sz/76GpUwd7RR8Mr4HL43oBMDSA8ni2IQaimwbypL9Sby3Tax7eWFYxzpHb6f0b820AWKEae6Gk1y4wcDXmxGTUsjmE5nIZPDW/V1rTOdN6idG4/6+kEvRVd1bVbYBLZvZSYG10iQCZ+HChYSFheHk5ERUVBTR0dE33PaOO+5AJpNdd7n33ntN20yfPv2620eOHNkUT0XCQugNAs+tP0FmcSVhPi4serSP1dWxqHV6nlt/giUHxKLbl0Z04tOHI2x6oF5SXjkPfnuIVYfFM9HHb2/LxicGEGbjnj3XklGkZOIPh/l050X0BoHRPQLZ9p/biDKDn1L3EE9qKnHJLzefV4sgCPyw7xKPLDlKXpmajv5u/PbsYO7tEdgo+5fJZDw9tD3fTO6Fo52cXedyGb/oMLmN6AO04mAy72wVC4qfu6sD/xlWvxTTf0d3YWA7Hyo0on9WUR3ax/UGgTe3xAMwITKUHiFeNW7XKcCdLoEeaPUCf1zlkZNRJIrYkBa23WBgK5j9CLFhwwbmzp3L/PnzOX78OBEREYwYMYLc3Nwat9+0aRNZWVmmS1xcHAqFgvHjx1fbbuTIkdW2W7dunbmfioQF+XznRQ4mFuDioGDx1EirK9IrUWqZujSaP05nYa+Q8cWEnjw9tL1NRzh+PZHJ6K8PcDZLLEBdMaMv80Z1NsvAQkuy7UwWo77cz7GUIlwdFHw6PoKvJ/XC09k8BdOBns68/2B3FNd8Nv6z/iTf7Ekgs0jZqMXHKq2e5zec5L1t59EbBB7oFcyvTw+iXUu3Rtn/1YzuEcT6x/rj6+bA2axSHlp0iJT8hndYrT6cYmoFf3poO16op7gBsfh74eTetPJ2Ib2wkufWn7iuGPhGrItO42xWKR5OdqaI1Y14sHcwQLVuqowi8T0N8Xap5+ol6oLZi4yjoqLo27cv33zzDQAGg4HQ0FCeffZZXn311Vve/4svvuDNN98kKysLV1fxrHH69OkUFxfz66+/1mtNUpGxbVE17wfgy4k9GdMz2MIrEskqqSQ5vwIXewUv/XyahNxy3B3tWDSlD4OstGW9Nqh1et76/coYiag23nw1qZfZ7e6bGpVWzztbz/LjEfF59gz14suJPWnt0zTRqapp2AEeTizcm8jPsdXbihuj+PhycSWPrY4hLrMUO7mMN+/rwpT+rc0uvFMLKpi6LJrUAiU+rg6smNGP7iH1q2FaezSN1zafAcQI4qsjwxtl/Reyyxiz8AAqraFWtTxFFRqGfrqXYqWW/93XhemD2tx0+9wyFf3f241BgAOvDCWkhQt3fPw3KQVK1s3pz4B21uu2bs1YTZGxRqMhNjaWYcOGXXlAuZxhw4Zx+PDhWu1j6dKlTJw40SRuqti7dy9+fn506tSJJ598koKCG1uHq9VqSktLq10kbIP0QiUvbDgJiP4x1iJuNhxLY9AHe5i8+Chjvz1EQm45/h6O/PTEAJsWN5nFlTy86LBpjMRzd3UwmqU1L3GTlFfOA98eMombJ+9ox8YnBjSZuAExkjOgnQ9tWrryyfgIXrsnvNrtDS0+jkkp5P5vDhCXWUoLF3tWz4pi6oCwJokqtvZx5ecnBtI1yIOCCg0TfzjMgYT8Ou/np2PpJnEze3CbRhM3IKaRFlQVHf91gaO3GD/xyV8XKFZqCQ9wr1WnmJ+7E5FG49FdZ3PQ6AymCE5rHymC0xSYVeDk5+ej1+vx969u1+7v70929q0r2KOjo4mLi2P27NnVrh85ciSrVq1i9+7dfPjhh/zzzz+MGjUKvb5ml8r3338fT09P0yU0NLTG7SSsC53ewAtGc7Verbx47Z7Oll4SIJ55z9t0hmuj2ose7UPnQNuNCB5IyOe+rw9wKqMET2d7lk3vy9y7Oza7mTlVqbdzWaXG6EJfXhkZbvHUW01dWvUtPl4fncakxUfIL9cQHuDOb88MbvKIQUt3R9Y/1t9U7zJjRTTb47JufUcjP8dm8MomcbbU9IFhvH5v50YXZ+MjQ03OzM+tP3FDt+njaUWsjRbF8P/u74pdLT8rVaNKdp7LIaWgAp1BwM3RjsBmNJvNmrHqZPrSpUvp3r07/fr1q3b9xIkTuf/+++nevTtjx47ljz/+4NixY+zdu7fG/cybN4+SkhLTJT09vQlWL9FQvtt7iZjUItwd7fhqYi+rKSpOzq+4TtwAqLSN45Da1BgMAgv/TmTqMnFeT7dgD/54djBDm5kjcdU4guc3nESp0dO/rTfb/nOb1Tgvt/F1va74WCGTEeZb+7N9rd7Am1vieHXTGbR6gVHdAvjlyYGEWqjmw93JnuUz+nJv90C0eoGn155gy8nrJ7Bfy+YTGbz08ykEAaYOaM38+7qYLfL0zthutPdzI6dUzUs/n77OBFCnN/D65jgEAR7qHVKnQb7DjALnaFIhsalFALT3c7Pp2jxbwqxHDF9fXxQKBTk5OdWuz8nJISDg5s6zFRUVrF+/nlmzZt3ycdq2bYuvry+JiYk13u7o6IiHh0e1i4R1cyKtiC92JwDw9tiuFvuBronC8uu7Lup6ILIWlBodT689zsc7LmAwDsn8+QnLHRDNRVqBsto4gueHdWDNbOtKvV1bfKyQyXjvwW619qcprNAwZelRU8fb3Ls78u0jvXF1tOxQR0c7BV9N6mXyynl+w0k2xtz4JPO3U5f5v59EcfNIVCveur+rWQWBi4Md30zuZRqQujGmei3UikMpnMsqxdPZ/ro04q1o4+tKez83dAaB5caRJh38Gr+4W6JmzPrJd3BwoE+fPuzevZuxY8cCYpHx7t27eeaZZ256340bN6JWq3n00Udv+TgZGRkUFBQQGNg4LY8SlkWp0fHChpPoDQL3RQQx1krqbgAOXyrgxZ9PVbuurgciayGjSMmcVbGcyyrFXiHj7THdTP4dzYldZ3OY+5OY6vR2deCrib0Y3ME666Qm9G3FkI4tSclXEubrUuvP1LmsUuasiiGjqBJXBwWfT+jJcCsaX6KQy/h4XA8c7OSsi07jpZ9Po9ULTI6q/nnbejqLFzacxCCIs80WjOnWJNGO8AAP/m94R97/8zxv/3GWAe18CPV24XJxJZ/tvAjAvFHh9TK1HNzel8Tcci7mlAPUasyHRONgdmk/d+5cpk2bRmRkJP369eOLL76goqKCGTNmADB16lSCg4N5//33q91v6dKljB07Fh+f6uHA8vJy3nrrLR566CECAgK4dOkSL7/8Mu3bt2fEiBHmfjoSTcAnOy6SYpxM/U4T/cDVhiNJBcxccQyV1sDtHVvy1v1dySpR1elAZC1EJxfy5I+xFFRo8HVzYNGjfYgMs85J7PVFpzfw2c6LfLtXHHJa33EETU2gp3Od1rg9LosXNpyiUquntY8Li6dGWuVBVC6X8d4D3XC0k7PiUAqvbT6DzmBgqnF2086zOfxn/Qn0BoFxfUJ474HuN52J1djMvq0tu87lcCyliJd+PsXa2f15+/ezKDV6+rRuwcOR9avdHNDOhxWHUkx/27qjuS1hdoEzYcIE8vLyePPNN8nOzqZnz55s377dVHiclpaGXF49U3bhwgUOHDjAX3/9dd3+FAoFp0+fZuXKlRQXFxMUFMTw4cNZsGABjo6SO6StczytiOWHxFDu+w92x9PFOoY3Hk0qYMbyY1Rq9Qzp2JLvp/TByV5hk4Z366LTeHNLHFq9QNcgD36YGkmwjU82v5aCcjXPrjvBoUtiZ8z0gWG8dk9nq6njagwEQeD7fUmmidaD2/vyzeReeLlYl0fU1chkMubf1wVHOznf70vizS3x2CvkBHs58/Sa4+iMPj0fPtSjScUNiFGmT8ZHMOrL/RxJKmT6imPsu5iHQi7j3Qe61Xs9/dtUP0nvFiyVSDQV0rBNqR7HalDr9Iz+6gAJueU82DuYzx7uaeklAWK0Y/ryaJQaPbd18GXx1EibdCfWGwTe3XqOZcZagHt7BPLJuAicHWzvudyMuMwSHl8dS2ZxpXFmVg/uiwiy9LIaFa3ewBu/xrH+mFjLMm1Aa94Y3aXW3T2WRhAE3tt2jsX7k6tdP6pbAF9P6mXR57H6cApvGN2KQZxFNq+BHZxhr241/T/lg3tvsqXErbAaHxwJibrw7d+XSMgtx8fVgTfu7WLp5QBwOqOYGUZxM7i97YobpUbH46tjTeLm/+7uyDeTejU7cbP5RAYPfXeIzOJK2vi6suXpQc1O3JRUapmx/Bjrj6Ujl8H8+7rw1phuNiNuQIzkvHZPZyJCvapd/+VEy4obgEeiqnvc1HckhITlsWx5vYSEkeT8Cr7dK3bBvTWmq1WMYkjIKWPasmgqjC3FtipucktVzFx5jLjMUhzs5Hz2cASjezSfg35WSSWJueX8cSqLDcbunDvD/fh8Qk+zjVuwFOmFSmauOEZCbjkuDgq+ntSLuzr73/qOVsj57DKS88qrXff3hVxGWLg4+lx2dSPYQ4kFpnZvCdtCEjgSVsHbv8ej1Qvc3rEl93a3fDdceqGSKUujKVJqiQjxZMm0vjYZ7TifXcrM5ce4XKLC29WBxVMj6dO6haWX1WhsOJZ2nenic3e25/lhHZu8hsPcnEgrYs6qGPLLNfh7OLJ0Wl+bLVhNzC3n0SVHTSaefu6O7IjP4dl1J1g1s1+dvGYaE53ewCu/nK523fzf4hnY3gcXh/odLvXXmGbpDUKzM8+0VmwnpinRbNl9Loe/L+Rhr5CZ1dCrtuSWqZiy9CjZpSo6+LmxYkY/3CzsJVIf9ifkMe67w1wuUdG2pSu/PjWoWYmbmhyl5TKYFNWq2YmbbWeymPiD6EzcJdCDLU8Ptllxk1ag5JElRygwmkqumNGPhZN7M7yLPxqdgTkrY4i/XGKRtS07mExcpjhM85+X7iDYy5nM4kq+/yep3vu8kF1W7e/E3PIbbCnR2EgCR8KiqHV63v5DnBI8c3Ab2pphwnFdKFVpmbbsGCkFSkJaOLN6VpRVpMvqyq8nMpmx/Bjlah3923qz+clBtGpm829+ic24zlHaIFCv0QbWiiAIfLs3kafWHEetM3BXuB8bnxhAgI1a/V8urmTykiPklKrp6O/GqplReDrbY6eQ89WkXkS18aZMrWPasmOkFTTt+5haUGHyvPnvvV1o7eNqGg/z/b5L9Z8JllpY7e/z2dIsxKZCEjgSFmX5wRRSC5T4uTvy7J2WLebT6g089eNxzmWV4uvmyJrZUTZ5IFm8L4nnN5xEZxC4PyJIPIhYSbt9YyAIAov+ucQnf1287jZbdZSuCa3ewKu/nOGj7RcAsdX9h6mRFncmri95ZWoeXXKUjKJKwnxc+HFWFN5XnTw42StYPC2SzoEe5JermbLsKHllNc+GamwEQeC1zWdQaQ0MbOfD+MgQAO7pHkDfsBaotAbT+1BXDiZWHzJ6SYrgNBmSwJGwGMVKDQv/FguLXx0VbtE0kCAIvPrLGQ4k5uPioGDFjL5NOlm6MTAYBN754yzvbjsHwMxBbfhiQs9m5f2i0ur5v42nTN4vUW28TfObbNVRuibKVGKn1IYYsVPqrfu78r/7u9ps7UaRcYxEUn4FwV7OrJnTH78axmR4ONmzckZfQr2dSS0QC6qVGp3Z17cxNoODiQU42sl574HupjS5TCbjjdFiR+fmE5mcTC+u0371BoHDRi+me3uItYWJeZLAaSqazy+fhM3x7d5LlKl0hAe4W3wcwxe7EvjleAYKuYyFj/S2ufoGjc7A3J9OsuSA2AY+b1Q4b4zu3KxqUQrK1Tyy5CibjmeikMtYMKYrGx4fwMFX72TdnP4ceHUoE/ra/qiJ3FIVE74/YhLbS6ZFMm1gmKWXVW9KVVqmLY/mfHYZfu6OrJ0TdVNjST8PJ1bPFKM7ZzJL+M/6k9cV6jYmuWUq3t0qnhTMvbvjdeadPUK8eLC3+Pv03rZz1w3jvBnxl0soVelwd7TjAeNvnFSD03RIAkfCIlwurjTZl78yKtyiB+KfYtL50jjY852x3WxuinalRs9jq2P49eRl7OQyPns4gsdvb2fxYu3GJDG3nAe+PURsahEeTnasnNGPKUaL/0BPZwa082kWkZtLeeU8+N0hzmaV4uvmwE+PD+DOcNttUVZqdMxcfozTGSV4uzqwZnZUrSKjYb6uLJ7aBwc7OTvP5vC+MSppDt76/SwllVq6Bnkwa3CbGrd5aUQnHOzkRCcXcuCalNPNOJgoRm+i2vrQKUAcn5GSr8RgRsEmcQVJ4EhYhM93XkSjMxDVxps7Ora02DqOJBXw2qYzADwztL3NDZssU2mZtiyavRfycLKXs3haJA/2DrH0shqVQ4n5PPjtQdIKlbTydmHz04OsdlhmQzieVsS47w6ZalQ2PTnI5iKJV6PS6nlsVSwxRlG6elY/OtRhRlaf1t58Mj4CgCUHkln4dyKHLuXXu9i3JnaezWHr6SwUchkfPtTjhiaDgZ7OPGo0APxkx4VaR3H2J+QBMKi9DwGeTshloNEbyCtvmtqifzuSwJFocpLzK/jleAYgRm8sFWlIL1Ty5I+x6IxTy/9veEeLrKO+FFZoeGTJUaJTCnF3tGP1rCibiz7dip9i0pm6LJpSlY4+rVuw+amBtLNwp5052H0uh8mLj5h8l355cqBNd71p9QaeWXuCA4n5uDooWDGzH12D6i7W7o8I4v/uFr+XH++4wOTFRxn0wR42HEtr8BqLlRpe2yye3My5re0txeSTd7TD2V7BqYwSdp7NueX+y1RajqWIHVRDO/lhr5ATYKw7yixuPJEmcWMkgSPR5Hy3NxGDAEM7taR3K8v4spSrdcxeGUORUkuPEE8+HtfDplI6OaUqJnx/2BT6X/dYf/o2o2ngBoPAxzvO8/LPp00CdM3sKHzcmt9A3fXRacxZFYNKa2Bop5ase6y/TT9Pg0Hg5Z9Ps+tcDo52cpZM69ug7/lDfarX5xkEeG1TXIMjOW//cZa8MjXtWrryfC3GMbR0d2TGoDAAPtt58ZZppoOJBWj1Am18XU11PcEtxDRqZpEkcJoCSeBINCnphUo2Hc8E4Nm7LNMWbjAIvLDhJBdyxKLHH6bY1giG9EIl4xcdJiG3nAAPJ356vL9NpzKupapgeuHflwB49s72fDmhp029R7VBEAS+3JXAq0azwvF9QvhhamS9HXOtAUEQ+N/v8Ww+kYmdXMZ3j/ZmQLuGuRKn1OCHoxeEBvkd7T6Xw6bjmchl8PH4iFp/th4f0g53RzvOZ5ex+3zuTbfde0G8/Y5OV1LwQcbiaimC0zRIAkeiSVn0zyV0BoHB7X0tFr35bOdFdp7NwcFOzg9TI23K6ya1oIKJPxwx1aNsfGIA7f1qX9dg7ZSqtExfHm0qmP54XA/+b3inZtUNBmL78Ou/xvH5LtHL55mh7floXA/sbWhgZk18+tdFVh1ORSaDTx+OaJQC6Ta+rtT09rfyrl9ReYlSa0pNzb6tbZ1+hzxd7Hl0gFiL8+3exBvW4hgMAn8bBc6d4VfSxlUpqqby9/m3Y9vfJgmbIrtExcYYsfbm2TvbW2QNO8/m8I3Re+fDh7rT85ppxtZMSr4objKLK2nb0pWNTwwg1Nt26zSuJaukkocXHebQpQJcHRQsm96X8ZGhll5Wo6PS6nnix1jWHk1DJoMFY7ry4ohONpUivZaskkpe23za9N16Z2w3xjSS9UOgpzPvP9gdxTWvzy/GSHBdWbD1LDmlatr6ujL37rrX3c0YFIaDnZwTacVEJxfWuM3pzBJyStW4Oijo1+ZK6rjK2LCoQlOvtUvUDduNhUrYHCsPp6DRG+gb1oIoCwzTS8mvYO5PJwHRBO+BXrbTbZSUV86kxaLFfXs/N9bOicLP3XYiT7fiQnYZ05dHk1WioqW7I8un2+4gyZtRrNQwa2UMsalFONjJ+WpiT0Z2s/xw2Yaw4Vgar/5yhqpYxshu/jxi7DhqLCb0bcWQji1JyVdyJrOY97ad57OdF+ka5FGnaep/X8jl59gMZDL4eHyPeqU9/dydGN8nhDVH0/jun0s1/pZtj8sG4I5wPxztrjxG1diXQqUkcJoCKYIj0SQoNTrWHhU7H2bf1rbJH79SI541l6l0RLZuwbx7wpt8DfUlMbecCT9cmd+zbk7/ZiVujiYVMG7RIbJKVLRr6cqmJwc2S3FTZeBX5eXz46womxc3WSWV1cQNwM743EZt5a6iyu/osSHtmGpME8396RQZRbWrxSlVaZn3i5iamjmoDX1a178o/7EhbZHLYO+FPM5lVZ8tJQgCf8WLAmdE14Bqt3m7SBGcpkQSOBJNwi/HMymp1NLK24VhdTjjagwEQeC/v8ZxPrsMXzcHvpnc22ZqHRJzy5n4wxHyytSEB7izbk5/WrrbbofNteyIz2bKsmjKVDr6hrXglycHNqu0WxXphUrGLTpsKmzf+MTAaqkLW+XXE5lcW4XS0ALg2vDfe7sQEepFSaWWp9eeQKMz3PI+7/5xjuxSFWE+Lrw4vFODHr+1jyujuovidKXRsLSKxNxykvIrcFDIGdqpuseXt5socAokgdMk2MavvIRNYzAILDeOEJgxKKzJ5+lsOJbOL8czkMvgq0m9bKaoODm/gsmLj5BfrqZLoAdr59h2+/C1rI9O48kfY9HoDAzv4s/qWVF4udje5PZbcTGnjIe+O2QqDP/lyYEmV1tb5lhKIV/ssszAUwc7Od9M6oWHkx2n0otNs8luxD8X89gQk45MBh+Ni8DZoeEdedON4zN+PZlJ8VUppz+N6amB7X1wd6o+5NbdOG+vQm3++VoSksCRaAL+ScgjKb8Cd0e7Ji8aTcgp43+/xwPw4ohODGxnGw646YVKJi8+Qq4xcrNmdvXJy7aMIAgs/DvR1B49ITKUbx/p3ezawAFOphfz8PeHyS1T08nfnZ+bSWF4XGYJM5cfQ60T6OTvZpGBp6HeLnz6cE8Alh1MZntcVo3blVRqeeXn04AoShorchbZugWdAz1QaQ1sOJYOiJ/tLSfF4ud7u1+ffqwSVkqNvlHWIHFzpCJjCbNTVXszLjKkSSeGq7R6nl13ApXWwG0dfHliSLsme+yGcLm4kkmLj5hqUn6cHWUqTrR1DAaBd7aeY9lBMaL31B3teMnGO4huxKHEfOasiqFCo6dXKy+WT+/bLCJUl/LKmbYsmjK1jn5h3qyc2Y/iSg0p+UrCfF2adCbY3V38eWxIW37Yl8RLG0/TNcjzOgH51m/xZJeqaOPryksjGpaauhqZTMb0ga155ZczrD6Syuzb2nIuq5RLeRU42MkZ2S3guvs4G0W8WmdAbxBsdjq8rSBFcCTMSk6pij1GQ6zJTTzn6b1t50x1N58+HGETXio5pSomLz5imke0dk5/fJtJWkqnN/B/G0+ZxM0bo7vw8kjLjeowJzvis5m+/BgVGj2D2/vyYzNJv2UWVzJlyVEKKjR0C/ZgyfRInB0UFh14+tKITvRu5UWZWscLG06i01+px9kel8WmE6Kh36cPRzS6ieKYnsF4udiTUVTJ3gu5pujNsM5+16WngGqPr9JKURxzIwkcCbOyMSYdvUGgb1iLOg3aayg74rNZdTgVgE8f7mkTXUcF5WoeWXKUlAIlIS2cWTunP/4e1r/u2qDW6Xl67XGTw+3nEyJuOLnZ1vklNoOn1hxHozcwsmsAS6dH4tqEkUtzkV+uZsqSo1w2RhZXzuiHRw0H8abGXiHny4m9cHO0Iya1iO/2ig7YeWVqXtscB8ATt7czi7Gok72Cccbhtuui0/nt1GWAG3oAOdlfOeRKaSrzIwkcCbORWaRkxcEUgCad0p1TquKVX8Sc+2ND2nK7BaeV15YylZbpy4+RmFtOoKcT6+b0N9m62zpVU6V3xOfgoJCz6NE+NuVBVBeWH0zm/zaeQm8QGN8nhG8m96rmg2KrlFRqmbo0mqT8CoK9nFk9y7rmgoV6u7BgbFcAvtidwIm0Il7bfIbCCg3hAe78pxazpupLVV3hrnM55JSq8XCyqzae4WpkMhl2xkiyoZYTySXqj+2fVkhYJRuOpfHqpjNUfYeb6mxFEMRBf8VKLd2CPRrcDtoUqLR6Zq+M4UymODhz9ayoZlGIClVDTY9xJKkQZ3sFi6dGMriDbRR61wVBEPhydwJf7EoAYNbgNrx+T2ebSIveikqNntkrj3E2qxRfNwd+nB1lleJ7bM9g/j6fx2+nLvPAt4cAsFfI+HxCT7OKzE4B7kSEeHIqowSAe7oH3vTxqjKyksAxP1IER6LRySqpZN5V4gZg/pZ4s5h/Xcu66HT+uZiHg52czx/uiYOddX/EtXoDz6w9ztHkQtwc7Vg5ox/t/dwsvaxGoUSpZcrSoxxJEp/bqln9mq24efuPsyZx8+Lwjvz33uYhbrR6A0+tieVYShHuTnasmhlFG+NkbGtDJpOxYGw3ri7pen5YRzoHepj9sa9OSd3fM+im21bVnEn6xvxIERyJRic5vwLDNV/eKvMvcxYhphUoeWfrWQBeHtGpSWt+6oPBIPDKz6fZdS4XBzs5S6ZF0j2keTj4FpSrmbI0mrNZpXi52LNqZj96hHhZelmNjsE4NHNdtNgp+PaYrkwdEGbZRTUSBoMYDf37Qh5O9nKWT+9LlyDzi4WG4O5oh71cjsZYaNw5sGl+A9ydrhxKXW9RyFylv6QIjvmx7tNbCZukja8r1567mtv8S28QeHHjKZQaPf3aeDNzkHUXsAqCwIKtZ9l0IhOFXMa3k3vT3wLzucxBTqmKCT8cMaU01j/Wv1mKG71B4KWfT7MuOg25DD4ZH9FsxI0giO38m6s+n4/0JjLM+p2XVx9JNYkbgNc3x1Gq0pr9cfdeyDP9f+uZmv14qqiKMEn6xvxIAkei0Qn0dCb8KqfWpjD/Wn4wmeiUQlwdFHw63vpbwn/Yl8RyYwH2J+N7MKxL046vMBfphUrGLzpsKpb+6fEBhAdY91l/fdDqDfxn/Ql+OZ6BQi7ji4m9GNen+RROf7v3kqmd/5PxPbgz3Po/n0l55bz/5zkAXh0VTpiPC1klKt7546xZH7dEqWXXuRzT31tPZyHcRL3ojeFtO4V1/0Y1BySBI9HoFFVoSMgtB8QfxwOvDmVCX/N1UaUVKPnkrwsA/Hd0F6sv0P31RCbvG63l/3tv52bTUZSUV86E7w+TVqgk1NuZnx4fQNuWzaOe6GrUOj1PrznOH6ezsFfIWDi5N/dH3LzuwpZYF53GxzvE79Mbo7vYxOdTqzfwwk+nUGkNDGrvw2O3teXj8RHIZPBTTAZ/G724zMGmExmodQba+rri6qAgs7iS42nFNW5rMAho9aLAcbCReXi2jPQKSzQ6u87loDMIhAe4M65PqFkjN4Ig8NrmM6i0Bga09WFi36YdBVFXDiTk89LPpwCx08YSk9XNwYXsMh7+/ojJI2Xj481zaKZKq+eJ1bH8dTYHBzs530/pU6Njra2yPS6L1zeLE7efHtrOZryKvt6TyKn0Yjyc7Ph4nBjB7Rt2JVU9b9MZs6SqBEEw1V/NGBTG3cZI7B+nL9e4/dXpM2tvgGgONMkrvHDhQsLCwnByciIqKoro6OgbbrtixQpkMlm1i5NTdbMzQRB48803CQwMxNnZmWHDhpGQkGDupyFRS3bEi+Hapvjh3xibwYHEfBzt5Lz/YHerdsWNv1zCEz/GotUL3NsjkNfv6WzpJTUKcZklTPjhMPnl4tysDY8PsJmBpnVBqdExe2WMqeh22bS+NpG6qS2HEvN5bt1JDAJM6hdqExYLALGpRXyzR/z9f/eB7tVa2F8c3okwHxeyS1V8aoxKNfZjX8wpx9lewZhewYzuIUbytp3JwnBtpwWSwGlqzP4Kb9iwgblz5zJ//nyOHz9OREQEI0aMIDf3xiFDDw8PsrKyTJfU1NRqt3/00Ud89dVXLFq0iKNHj+Lq6sqIESNQqVTmfjoSt0Cp0bE/QSy4G9HVvAInt0zFu1vFnPsLd3ckzErbVwEyipRMX36McrWO/m29+cxGRkfcivjLJTyy5CjFSi0RoV6sf6z5jJa4mnK1junLjnEgMR9XBwUrZzSvlvczGSXMWRVjcl9+Z6x1nyxUUW4cz2AQ4IFewdx3TarQ2UHBuw90B2DVkVROpBU16uOvNUZv7osIxMPJnts6+uLmaEdOqZozmSXXba/RXSVwpBSV2TH7K/zZZ58xZ84cZsyYQZcuXVi0aBEuLi4sW7bshveRyWQEBASYLv7+V86SBEHgiy++4L///S9jxoyhR48erFq1isuXL/Prr7+a++lI3IJ/LuSh1hlo5e1SrdDYHLz1+1lKKkVDv9lWHEovVWmZtSKGPONE6e+nRDYLd9tzWaU8uuQoJZVaeoZ68eOsfs1i3tK1lFSKfj7RKYW4O9qxalYUUc2k4w3E2qnpy6Op0OgZ0NaHLyb2tJkhkG//Hk9aoZJgL2feGtO1xm0Gtfflwd7BCIKYqtJeFUVpCCVKLVtPix1TVU7tjnYKhnQUhe/VhcdVVKh1ALg4KGxCQNo6ZhU4Go2G2NhYhg0bduUB5XKGDRvG4cOHb3i/8vJyWrduTWhoKGPGjCE+Pt50W3JyMtnZ2dX26enpSVRU1A33qVarKS0trXaRMA874rMBGN7F36xf4H0X89h6Ogu5DD54sAd2Vno2pNMbeGbtCS7klOHn7sjyGX3xdLb8/J6GciG7jEeWHKVIqSUixJNVs/rVOFzQ1imq0PDIkiOcSCvG09meNXOi6NO68WcaWYrsEhVTlkabhmf+MLUPTva2Ib63x2XxU0wGMhl89nDETedivX5PZ1q42HM+u4xlB5Ib5fE3G4uLwwPc6RnqZbr+LmPacte567MUZSpR4FztmyNhPsx6VMjPz0ev11eLwAD4+/uTnZ1d4306derEsmXL2LJlCz/++CMGg4GBAweSkZEBYLpfXfb5/vvv4+npabqEhlp3IaqtojcI/HNRTE/dbca2Z7VOz/9+E0XvtIFhdAu2TnM8QRCY/1s8+y7m4WyvYOm0vlZpcV9XEnLKmLz4CIUVGroHe7JqVpRVDF1sbPLL1UxafIS4zFJ8XB1YN6d5+fkUKzVMXXaUzOJK2vq6smKG7YjUnFIVr24Si6GfuL3dLSNqPm6OvGaseft810XSC5UNenxBEEzpqclRraqdzA0N90MuEyOcmcXV3dtLK8VCZ1t5nW0dqzvtHTBgAFOnTqVnz57cfvvtbNq0iZYtW/L999/Xe5/z5s2jpKTEdElPT2/EFUtUEZdZQpFSi7ujHb3NeJa7ZH8ySfkVtHR35IW7O5rtcRrK0gPJrDmahkwGX07s2SxcihNzy5m0+CgFFRq6Bnmwela/ZhGRupb8cjWTfjjC+Wwx8rb+sf5W7+JbF5QaHTNXHONiTjn+Ho6smtXPZmqnDEZTz2Kllq5BHrwwrHa/AeP6hNC/rTcqrcFUu1dfjqeJxcVO9vLrJod7uzqYJpfvuSZNVWqM4HhIEZwmwawCx9fXF4VCQU5O9Tc5JyeHgIDaFaDa29vTq1cvEhMTAUz3q8s+HR0d8fDwqHaRaHyqojcD2/tgb6aUUUaRkq+NHROv39PZaiMHf8Vn8+428Uf09Xs6M9zMBddNwaW8ciYtPkJ+uZrOgR78OCuqWdbcVImbhFzx4L/h8QFWP/ajLojzpY5z3Jh2Wz0ripAWttPSv+pwCvsTxM7JLyfWft6cTCbj7THdUMhlbI/P5kBCfr3XsPaoeJJ8X4+gGgX+nZ39ANh3zWOUqaQITlNiVoHj4OBAnz592L17t+k6g8HA7t27GTBgQK32odfrOXPmDIGBgQC0adOGgICAavssLS3l6NGjtd6nhHnYZxQ4Qzq2NNtjLPjjLCqtgag23oy5xVA7S3Euq5TnN5xEEOCRqFY24yVyM5LzK5j0wxHyysRW8DWzo2jh2vzFzfrHBljtcMn6UBX92FvV6j49ko42JN4u5pSZTDJfv7cz7f3qtvaO/u5MHdAagP/9Hl+vguMSpdbkczMpqmYD08HtxULjI5cK0F31GEVKDQBeLpLAaQrMnqKaO3cuixcvZuXKlZw7d44nn3ySiooKZsyYAcDUqVOZN2+eafu3336bv/76i6SkJI4fP86jjz5Kamoqs2fPBkQV/vzzz/POO+/w22+/cebMGaZOnUpQUBBjx44199ORuAGlKi0n0osBGNLBPALnYGI+O+JzUMirpgZbXxdCQbma2StjUGr0DGrvw1v3d7XKddaF1AJR3OQau8DWzI7CWxI3NkfV1PMtJy9jJ5fx3aN96NPa+udLVaHW6Xl+/UnUOgO3d2zJlP6t67Wf54d1xMfVgcTcclYeSqnz/ddGp5mKi3tdVVx8NV2DPPF0tqdMreP0Ve3i+eWiwLGVdKCtY/ZE4IQJE8jLy+PNN98kOzubnj17sn37dlORcFpaGnL5FZ1VVFTEnDlzyM7OpkWLFvTp04dDhw7RpUsX0zYvv/wyFRUVPPbYYxQXFzN48GC2b99+nSGgRNNxNKkQvUGgra+rWRxs9QaBBcaZMlP6t7bKs06NzsCTa46TWVxJax8XFk7ubbXdXbUlrUDJpB+OkF2qooOfG2vmROHTDH+cm7u4AfhmTyIrjAf0T8ZHMLSTn2UXVEc+2n6Bs1mleLs68PG4HvU+cfB0tuflkZ145ZczfLkrgft7BuHnXrtjR1phBT/suwSITuQ3WoNCLmNAWx+2x2dzKDHfVJOTX6YGJIHTVDTJr+8zzzxDamoqarWao0ePEhUVZbpt7969rFixwvT3559/bto2OzubrVu30qtXr2r7k8lkvP3222RnZ6NSqdi1axcdO1pvsem/gaNJBQD0b2cef5CfYtI5n12Gp7M9zw/rYJbHaChv/R5PdHIhbo52LJkaafP1KemFSiYtvjJ+Ye2c5mni928QN2uOpvLpzosAzL+vC2N7Bd/iHtbF3gu5LDW2d388rgd+Hg07mR3fJ5QeIZ6UqXV8bnxdbsWGY2nc/tFeipRiHY1ad/P01iCjEeSBxCt1OHnlVQLHtn8bbAXbPr2UsBqiUwoBiGrT+CHvMpWWT43DNJ+7q4NVCofVR1KrdUzZelFqTqmKyUuOmFqI183pT0v35iluJi9u3uJm25ks/vtrHADP3tmeGYNsqyYsr0zNixvF+W3TBrTmrs4Nt6CQy2W8OVrMCmw4ls7FnLKbbp9VUsm8TWe4evjC/C3xZJVU3vA+g4wne8dTi1Fp9cBVKapm+F2yRiSBI9FgytU64ox55r5hjS9wvtt7ifxyDW18XeuddzcnR5MKeMvoy/PyiPBG+QG2JEUVGh5dcpT0QjHVtnZO/wafMVsjVeKmqlW6OYqbg4n5PL9eLHifHNWKuVZsq1ATVUXR+eUawgPcmdeI89siw7wZ2TUAgwAfGAuXb0RyfgXXjpbSCwIp+Tf202nj64qvmwMavcH0+5hXJo4TatkMI6HWiCRwJBpMbGoRBgFCvZ0b3cgus7iSJcbQ9Gv3dLa6AXXZJSqeXnsCnUHg/oggnrjdtqeDl6t1TF8eTUJuOQEeTvw4K6pZDs78N4ib0xnFPGacL3VP9wAWjLHOwvybsexgMv9czMPRTs5Xk3o1usvyK6PCsZPL2HM+l0OXbtw2XtNnQyGTEeZ743pDmUxmqr2JTS1CpdWbIjjBzcDw0xawrqOFhE1yLFlMT5kjevPlrotodGJb+LDO1lUUKRYVx5qmaH/wkG0MKLwRKq2eOStjOJVRQgsXe36c3c8sBeOW5t8gbi7llTN9+TEqjN18n0+wnflSVcRllvDhdjGy8t/RXczSWNDG15VHjK3e7207V+MEcACdXuDqV08hk/Heg90I9Ly5UIkMEwVOTGoRl42uxi4OCqlNvImQ7BQlGsxJY3t4Y8/oScwt5+dYcUTHK6PCrU48LPjjLCfSivFwsuP7KX1wcbDdr5PWODPrcFIBbo52rJzZr84eI7ZAwb9A3OSUqpi6NJrCCg09QjxtcrirUqPjufUn0OoF7u7iz6M38JtpDJ67qwObjmcSl1nK76cvX+dMDLDiUAoC0C+sBS/c3YkwX5dbihvA1IZ/PLXINLYh2MvZ6n7LmitSBEeiQQiCwOmMYgAiGnlOz2c7L2AQxLlWVaFea+Hn2AxWH0kF4IuJPWntY7sHSYNB4OWfT7PrXA6OdnKWTItsVjOXqihWanh0aXSzFjcllVqmLYsms7iSNr6uLJ/eFzdH2xPeC/44S1JeBf4ejnz4UP1bwmuDj5sjjxtTy5/vvFjNmA/EJocNx0Tn4qeGtmdAO59aiRuAbsEeONjJKajQcDBR7DQNbiGlp5oKSeBINIiUAiWlKh0OdnI6BTTeGf/pjGK2nclGJoMXh3dqtP02BvGXS3h9szjo7z93deDOcNstKhYEgf/9Hs/mE5nYyWV8+0hv+t9icKEtUqrSMnVZNOeySvF1c2TdnP7NTtyotHrmrIrhfHYZLd0dWTWzn016Fm07k8W66HRkMvh8Qs8mMZWcMagN3q4OpBQo2XQ8s9ptG46lU67W0d7Pjdvr6NLuaKegS6A4GmhHvDgMWqq/aTokgSPRIKqiN10CPRp1/tTHO8S28Ad6BTeqcGoopSotT605jlpnYGinlvznLuv05Kktn+28yKrDqchk8OnDETbfAVYT5Wod05dFczqjBG9XB9bOiaJtSzdLL6tR0RsEnl9/kujkQtwd7Vg5wzbrpzKLK3n1l9MAPHl7Owa2822Sx3V1tOOpO9oB8OXuBNQ6sa1bqzeYzBFnDrqxsd/N6BYsCpzk/AoAm3xfbBVJ4Eg0iFPpYvtjzxtYlteHYymF7E/Ix14hq/Wk4KZAEARe/eU0qQVKgr2c+XxCT+Q2Vrh5NYv3JfH1HnGI7YIx3WqsPbB1KjV6Zq04xnFjrdTqWf2s0gW7IQiCwPzf4tgen42DQs4PUyNtcvK5Tm/ghfUnKVXpiAj14oUmbml/tH9r/NwdySyu5CdjSuq3k5fJKKrEx9WBB+ppjtgtyLPa322bWeTQmpEEjkSDiL8sCpxuwZ632LL2fLVbnBY+rk+oVZ3trDyUwrYz2dgrZHwzuZdVGg7Wlg3H0kzTzl8a0YlHrdBfqKGotHoeWx3DUaO79OpZUXQNarzPqbXw9Z5Efjwimkx+MbEnA8zkJm5uvtydQHSK+F59NbFno0aEa4OTvYJn72wPiK+pUqPj273iCcDs29ri7FC/Qu1rfxubW/TQmpEEjkS9EQSBC0YH0PBGSiPFphaxPyEfO7nMFDK2Bk6lF5sEwbxRnellZUXPdWHr6SzmbRJriB6/va1Vvc6NhUZn4Ok1x9mfkI+Lg4IVM/oS0YhRRmth7dE0PjOOGnjr/q7c0z3QwiuqHwcT8/nmb1FMvPdgd4sV7T/cN5RgL2dyy9RMX36MS3kVeDjZ8Wj/+ndxdfCvLmhaWdFJW3NHEjgS9SavTE2xUotcBu39GuespCp681DvEKuJ3pQotTy99jhavcDIrgHMGBRm6SXVm0OJ+Ty/4QQGASb1a8WrI62v/b6h6PQGnlt3gt3nc3G0k7N0Wl8izeDRZGl2xGfz319Fofrsne2ZOiDMsguqJ3llap7fILotT+wbyv0RQRZbi6OdgieNgj/a6O81fVAb3J3q71tzbYu+tZmVNmekV1qi3lRFb8J8XRvFYfRkejH/XMxDIZfx9ND2Dd5fYyAIAq/8cpqMokpCvZ35sAFTjC3NuaxSHl8di1YvcG/3QN4Za3vOtrdCbxCY+9MpUz3K4qmRNpuyuRnHUgp5bp0oVCf2DbW5EQxVGAwCc386SV6Zmo7+bsy/r6ull8S4PiHV/p4xMMwyC5FoMJLAkag3F7IbNz31tTF680CvYFr5WEf0Zm10GtvjxbqbhZN74+lsmw6kmcWVTF8eTZlaR1Qbbz6bEGFzzra3wmAQxehvpy6bWt6H1LGt1xa4kF3GrBXHUOsMDOvsb9NCddG+S+xPyMfJXs7Cyb3rXefSmDheE2Fxd7I9HyEJEUngSNSbKoHTGF0pF3PK2H0+F5kMq4neJOSUseCPs4A4RNNWze9KlFqmL4smp1Q8S/7BBp1tb4UgCLyxJY6fYzNQyGV8PakXw7o0v5b3zOJKpi2LplSlo0/rFnw9qRd2TVyM21jEphby6V9X6oc6WEl32+FLBdX+3nomy0IrkWgotvnNkLAKqnwdGqP+5od9SQCM7BpgFQZsKq2eZ9edQKU1MKRjS2YNbmPpJdULtU7PnNUxJOSK7r0rZvTDs5nNwREEgQV/nGPNUbGT6LOHIxhlo8W2N6OoQsO0ZdFkl6ro4OfG0mmRVhHxqA/FSg3PrTuJ3jik9uHIUEsvyURVsXMVC/9ORBBqnlFVG669b0P2JVE3JIEjUW9SCpQAhDWw4yG7RMWWk6J76GNDrGMa9/vbznE+uwxfNwc+HR9hk343BmM9SpX524oZ/Rp92rs18PnOiyw7KE6c//ChHs3Wz2fmymMk5pYT6OnEypn9bNamQBDE0SCZxZW09nHh3QesJ8UWm1rEoUsF2MllbH/+Ntwc7biYU84/F/Pqvc+sEtVN/5YwH5LAkagX5Wod+eVqgAbXyyw/mIxWLxDVxtsq2q93nc1h5WFxztQn4yNo6W57dvcgTkfeejoLe4WM76f0oXOg7Zm/3YrF+5L4ymhW+PaYrlYVCWgsdHoDz6w9zom0Yjyd7Vk107aF6qrDqfx1NgcHhVh305AOpcZmoTF682DvYMIDPJjYV/w8LdmfXO99VqXyq0gpqKj/AiXqhCRwJOpFqvFL6uPqgEcDfqBKVVrWHE0D4InbLe/Hklem5hWjVfyswW24o5OfhVdUP5YeSGbJAfFH+ZPxEQxs3zSW903JuujqZoW22iZ9MwRB4LXNZ0wt78umR1pNrUp9iMss4d2tRj+pe8Ib1SC0ocRllrDnfC5yGTx5h1gHOH1QGAq5jAOJ+Zy9XFrv/V5NRmFlg9cqUTskgSNRL1KN6anWDYze/GQcZNfR3407Olm240UQBOZtOk1BhYbwAHdeHmldQz5ry9bTWbyzVSyOfnVUeLNM2fx+6jKvbW7eZoUAn/x1gZ9iMpDL4JvJvenT2nb9fMpUWp5ddwKN3sDdXfyZbmXt11WGifdFBJnqAENauDCqWwAASw4k1Wu/p68ROOlFygasUqIuSAJHol5cETj1r7/RGwRWHk4B6j/IrjH5KSadXedycVDI+XxCT5vsNDqaVMALRtO0aQNa87iV1DQ1JnvO55ie4yNRzdOsEGDFwWQW/n0JgPce6M7dNtwVJp48nCE5v4IgTyc+tjI/qdjUIvacz0Uhl/H8NfPvZt8mfod+P3WZnNK618+cyRAFzl3hYjQ4vVASOE2FJHAk6kVWiRhmDfJyqvc+9pzPJb2wEk9ne4tHGVILKnjrdzHq8eKIjjZZr3Ixp4w5q2LQ6A2M6OrPm/d1taqDSGNwJKmAJ388js4gMKZnEAvGWE+BamPyx+nLvGW0KPi/uzsysV/9RwVYAz8eSeWP01nYyWV880hvqyuQ/mTHBQDG9Q65rouzZ6gXfcNaoNULrDbW5tWW3FIV2aUq5DIYYYwEpRdJKaqmQhI4EvWiqhMgwLP+xY4rD6UAMLFfqEXbXfUGgf/76RRKjZ5+bbyZNdj2oh65pSqmX+WP8uXEXs3OyO9UevFVBnd+fGKj3W234lBiPnM3nEIQYOqA1jxzp3X4QtWX0xnFLPhDrLt5dVQ4va2gkeBqDibmczipAAeFnOeGdahxmxmDRJuI9cfS0OgMtd73aWP0poOfO52MtVNSBKfpkASORL3INgqcQI/6RXAScso4kJiPXAZTLDzJ+vt9l4hJLcLN0Y5Px9uew69Kq2fO6lgul6ho6+vKkqmRjTI6w5q4mFPGtOXRVGj0DGjrwzeTezf5tOmmIC6zhMdWx6LRG7inewDzbTwKV1IpznHT6A0M7+JvdX5SgiDwsTF6MzmqFcE36E67u4s//h6O5Jdr2B6fXev9n84oBsSJ4oGe4m9lfrkavUHywmkKmt8vhESTcCWCUz+Bs8IYvbm7iz8hLSw3luFiThlf7BRHRMy/r4vVDPisLQaDwP9tPMWp9GK8XOxZNr0vLVytK/zfUNIKlDy65CjFSi09Q71YPK35CTgQn+f05ccoV+vo39abzx7uaXNi+2oEQeCljadILxTnuH08PsLqxNruc7mcTC/G2V7BU0NvXKhur5AzyZgm/LEOaaqY1CIAerf2wsfNEbkMDAIUGC02JMyLJHAk6oxGZzB54NTHj6NCrePXE6Kx3zQLtvbq9AZe2ngKjd7AneF+1w3ZswW+2J1g8rpZ9GgfwqzABboxyS5RMXnJEXLL1IQHuLNiRl/cHJvfbKD8cjVTlx0lv1xN50APfmgGUbilB5Kr+d1Y2xw3g0Hgk7/E6M30QWH4ud/8ZG1Sv1bYyWVEpxRyPvvWLeM6vYGT6cUARLb2RiGX4eMmemrllkkCpymQBI5EnakSN/YKGS3qYfv/+6nLVGj0tPF1teik58X7kzmVUYKHkx3vP9jd6s4ub8WWk5l8ZRxQ+u4D3enftnlNzS4oV/Po0qNkFImOt6tm2a57782oUOuYueIYKQVKQlo4s3JG3wZ5S1kDx9OK+ODP8wC8MbqzVc5x++NMFuezy3B3tKtVt6G/hxMjuoqFwrUpNj6XVYZSo8fDyY4OxnE2fu5VAkdyM24KJIEjUWcKKzQAtHBxqJcoWBctGvtN7BtqMVGRkFPG50bfizfv64p/PWuJLMXxtCJe+lk0JHx8SNtm5+BbrtYxY8WV0QQ/zoq65Rm2LaLVG3hqzXFOZ5Tg7erAqpn98LOxz+K1FFVoeGaN2Ok2ukcgj1q4xq4mdHoDXxi//3OGtK21cK56Lr+eyESp0d1025jUQgB6t25hKoY3CZxSKYLTFEgCR6LOVAkc73rUepy9XMqpjBLsFTIeslBKSKc38OLPp9HoDQzt1JKHetuWEV5GkZLHVsWg0YmGaS+PDLf0khoVtU7P46tjTAf91bOibK42qjZUecP8czEPZ3sFS6dF0rZlwwfXWhJx/tlJLpeoaOPrarWR0U3HM0nKr8Db1YGZdSh87t/WmzAfFyo0eraevvmU8ar6m8jWV7rGqsa+5EkpqiZBEjgSdaZIWX+Bs/6YGL25u4s/vm6WmfG09EAyp9KLcXey4/0Hrctw7FaUq3XMXhlDfrmGzoEefDHBtgtRr0VvEHhhw0kOJhbg6qBgxYy+jTKt3hr59K+L/BybgUIuY+EjvaxiDltDWbTvEn9fyMPRzvrmTFWh1un50pjaffL2dnWq6ZLJZIw3Rks3xmTccDtBEIhJESM4V7tPtzBGikoqtXVet0TdkQSORJ0xpajqKHBUWj2bjcXFkyxkXJZWoOTzXWJo+o17u9S7C8wS6A0Cz607wfnsMlq6O7J0WiSuzajgVhAE3twSx7Yz2cYBoZFWWbvRGKw+kso3xsGO747txp3htutSXMXRpAI+/Uv8br11f1e6BFmnWeaPR9LILK7E38ORKQPqnj57qHcIchlEpxSSlFde4zZJ+RXklKpxsJPTq5WX6XoPY6G1JHCahiYROAsXLiQsLAwnJyeioqKIjo6+4baLFy/mtttuo0WLFrRo0YJhw4Zdt/306dORyWTVLiNHjjT305AwUiVwfOoocP46m0OZSkewlzOD2jX98MeqwYUqrYGB7XwYH2lbXVPvbzvHHuPQxcVTI216onRNfLErgTVH05DJ4PMJPRncofkNCAXYEZ/N/C1xALwwzPZdikEsmn123Qn0BoEHewUzoa911oQVKzWmwvwXhnWsV6dagKcTt3cU5+ZtjK05inPoUgEAfVq1qPYYnpLAaVLMLnA2bNjA3LlzmT9/PsePHyciIoIRI0aQm5tb4/Z79+5l0qRJ/P333xw+fJjQ0FCGDx9OZmZmte1GjhxJVlaW6bJu3TpzPxUJI6XGL2ddOz02Hxd/DB7oFWwRB9pfjmdyIDEfRzs57z1gnbUBN2JddJppOvinD0fQM9TLsgtqZFYdTjGlDd4e043RPYIsvCLzEJNSyHPrTmAQYFK/UJ67y7ZdikGsaXtm7Qlyy9R08HNjwVjrHZ/xzZ5ESiq1dPJ3N6Wa6kNVUf8vsRno9Nc7Gx8xCpyB13SJVgmcYkngNAlmFzifffYZc+bMYcaMGXTp0oVFixbh4uLCsmXLatx+zZo1PPXUU/Ts2ZPw8HCWLFmCwWBg9+7d1bZzdHQkICDAdGnRwvbz17ZChUYPUKf0SF6Zmn0J+QA8YIGi3vxytWnC9n+GdbApv5hDl/J541fxjH/u3R2b3cH/91OXmf9bPCCeVVva2dpcJOaWMWtljGnURHOZo/XxjgtEJxfi6qBg0ZQ+Vps2TS2oMA33fe3ezg2qXbursz/erg7klqk5aBQzVRgMAoeTxOuutcHwMtpqlEoCp0kwq8DRaDTExsYybNiwKw8olzNs2DAOHz5cq30olUq0Wi3e3t7Vrt+7dy9+fn506tSJJ598koKCghvsAdRqNaWlpdUuEvWnqj3S1bH24d3fTl1GbxCICPWinQU6RRb8cZZipZbOgR7Muc12Zk2lFyp5as2V4ZLP2vhcomvZdzGPuT+dNM1dag4RjZrIKVUxbdkxSipFN+avJ/XGrhmMmtgel8X3+5IA+Hh8hEW+27Xlo+0X0OoFhnRsaUox1RcHOzn3dg8ERD+qq7mQU0ZhhQYXB8V1NWRVUe8y1c1bzCUaB7N+w/Lz89Hr9fj7Vy+g8/f3Jzu7dvM8XnnlFYKCgqqJpJEjR7Jq1Sp2797Nhx9+yD///MOoUaPQ6/U17uP999/H09PTdAkNtc78sK1QrjZGcBxqf6a2yZieskRL9r6LeWw5eRm5DD54sLvNzDBSanTMWRVDsVJLRKgXHz5kWx1ft+JkejFP/BiLVi/6pfzPxucu3YhSlZZpy6LJLK6kra8ry6b3tehw2cYiKa+cFzeKXkyzB7fhHuMB3xqJTS1k65ks5DJ47Z7GsVUY01OMpO6Iy0alvXLsOWCMVPcN88bBrvpvTVU9ztXbS5gP64wlGvnggw9Yv349e/fuxcnpSrfLxIkTTf/v3r07PXr0oF27duzdu5e77rrruv3MmzePuXPnmv4uLS2VRE4DUKrrFsFJyCkj/nIpdnJZk6dXVFo9bxoLOqcNDCPCRmpXBEHglV/OcD67DF83R75/tI/NW/dfTWJuOTOWR6PU6Lmtgy+fPdyzWU4GV+v0PL4q1vQ+rpzZr172CtaGUqPjyR+PU67W0S/Mm1dGWa8XkyAIvLNVnGb+cGQo4QGN093Vp3ULQlo4k1FUya5zOabftn8u5gHUGCVyNn6HKyWB0ySY9VTW19cXhUJBTk5OtetzcnIICAi46X0/+eQTPvjgA/766y969Ohx023btm2Lr68viYmJNd7u6OiIh4dHtYtE/amqwXGpZQTnD6Mh1pCOLZv8x/37f5JIKVDi5+7I3Ls7NuljN4TF+5P4/dRl7OQyvn2kt021s9+KrJJKpi49SpFSS0SIJ9892ue6M93mgMEg8OLG0xxOuuLp0xwMCwVB4PXNcVzIEUXbN5N7WXVUdOuZLE6kFePioGjU3wCZTMb9EaKo2XLyMiAKv+hk0f/m9k7XCxwne/F1Umn1CII0UdzcmPVT6eDgQJ8+faoVCFcVDA8YMOCG9/voo49YsGAB27dvJzIy8paPk5GRQUFBAYGB1hsibU6odaLAcazlQWnrGVHgjO7RtO9PakEFC/eKoveN0V2s0nSsJg4k5Jvm+My/rwv92njf4h62Q7FSw5Sl0VwuUdG2pSvLZ/RrlsMzAd7/85xJpC6a0oduwZ6WXlKj8OPRNDafyBQNCif3surREmqdng+3i9+lx4e0a/S1ju0lptz3XsilWKnh8KUCNHoDIS2caVtDI4OjMYJjEEBTQ/eVRONidtk9d+5cFi9ezMqVKzl37hxPPvkkFRUVzJgxA4CpU6cyb9480/Yffvghb7zxBsuWLSMsLIzs7Gyys7MpLxcNlcrLy3nppZc4cuQIKSkp7N69mzFjxtC+fXtGjBhh7qcjAej04plHbYokL+aUkZhbjoNCzrAuTWdmJprGxaPRGRjc3rfJxVV9SS9U8sy64xgEGN8nxCrn+NQXlVbPrJUxJOaWE+DhxOpZUc0iXVMTS/YnsXi/2Nb/8fge3NahYUWt1sLJ9GLe/l3seHtlZCeirHzA66pDqaQXiqZ+c4bUfiRDbeno7054gDtavcDOszmm9NQdnVrWWE/mfFWaWaWRBI65Mfup04QJE8jLy+PNN98kOzubnj17sn37dlPhcVpaGnL5lQPld999h0ajYdy4cdX2M3/+fP73v/+hUCg4ffo0K1eupLi4mKCgIIYPH86CBQtwdLSM9f+/jSrfB3vFrWsmrqSnfJt0QvKO+Gz+uZiHg0LO22Nso3i1UqPnsdWxYlFxiKdV+4nUlSoX5tjUIjyc7Fg1qx/BzcyosIrfTl021Xy8OiqcB3rZlqHkjSis0PCUsSh8ZNcAq+9GLKrQ8PUe0Vvp/4Z3qnVKva6M7BbA+ewytsdlk2h0Nr69o1+N2179m6nW6wHbiCrbKk0SG37mmWd45plnarxt79691f5OSUm56b6cnZ3ZsWNHI61Moj5oDcYIjvzmERxBENh6WsxN39uEEZRKjZ63fxc9bx6/va1NDDAUi4pPcy6rFF83BxZNaT5FxYIgMP+3OP46m4ODnZwl0/rS0d/d0ssyC4cu5fPiT6cAmD4wjMeHWLcIqC16g8B/1p8wDdH8eLz1d/R9uTuBUpWOzoEePNTbfCJzVLdAvtiVwO7zonmtg0J+ncFfFTKZDLlMTFEhleCYHeutDJOwWmobwUnILedSXgUOCjl3dW669NR3/1zicomKYC9nnh5qG74qS/Yn85uxXmPh5N4Eejaf6Ma3ey/x4xFxBMOXE3o2q5qiqzmXVcrjq2LR6A3c0z2AN0Z3sXoRUFu+3HWR/Qn5ONsrWPRoH6uvZ7uYU8bqI6kAvH5Pw0z9bkVHf7dq9TYD2vnc1OxQbvxMGCSBY3YkgSNRZ3TGb+atfjR2nhW75wa192my9FRGkZLv/7kEwOv3draJKMiBhHze/1NMabwxuovV1zXUhY0x6Xy84wIA/7uvK6Os2CulIWQWVzJ9eTRlah392njz2cPNZ8r7zrM5fLVHLNZ/78FudAqw7uibIAjM3xKP3iAwoqu/2WeayWQyRnS70hV89y1qDa8IHEnhmBtJ4EiYjSqBc3eXm1sCNCbvbTuHWmdgQFsfRnVrusetL+mFSp41FhWP6xPC1HpMN7ZW9l7I5dVNZwB44vZ2TBsYZtkFmYlipYZpy6LJKVXT0d+NxVMibUJY14akvHLmbjgJwLQBrW2inmjrmSwOJxXgaCfnv/d2aZLH7Bt2ZVTQ4PY3F1RVQT1J4JgfSeBI1JmqM9ObhVhzy1ScTC8G4K7ONRfcNTaHLuWz7Uw2chnMv9/60wOVGj2Pr46lSKmlR4gn7zSjouIzGSU8teY4eoPAA72CeXlEJ0svySyotHpmX9UZtmJGPzxdrDt9U1vK1ToeXx1LmVpH37AWvN5EYqEhKDU63jUWeD91R/sm8x3KKVWb/p+UX37TbasiOJK+MT+SwJGoM7UJse45JxbcRYR44t8EPhk6vYG3fhMLix/t37rR3ErNyRtb4jibVYqPqwOLmpFTcWpBBTNWiC7Fg9v78uFDPZqlS3FV4W1MahHuTnasnNmPoGbSGSYIAi//fIqE3HL83B1Z+EhvmzBjXPh3IlklKkJaOPP47U1X4L3r7BUz2z3GYuMbIUjVxU2G9X9iJayO2gicXeeq0lNNU1y8/lg6F3LK8HKxtwnH4p9i0vk5NgO5DL6e3KvZHBgLytVMWxZNfrmGLoEefPeobRwY64ogCPzvt3h2xOfgoJCzeGqk1dem1IXv9yWx7Uw29goZ3z3aBz936zXzqyI5v4LF+0TvoTdHd2myE4YylZb9ifmmv/8+n3dTl+IqH7Hm+L2wNqRXWKLOVJ2M62+Qo1Jp9ew3Dpxriu6pMpWWz3deBOD5uzrg5WLd5nHnskp541dxPtbcuzsysJ15iyCbCqVGx8yVMaQUKAn2cmbFjL5W321TX77de4nVR1KRyeDzCT3p34wKw/cn5PHR9ion7a70ad3iFvewPIIg8Nbv8Wj0Bm7v2LLJTqwAdp/LRaMzEOTphKOdnMziSi7m1JymEgTB1KRh1wyjmtaGJHAk6oypBucGRpzRyYWodQYCPZ0Ib4Kz2kX/XKKgQkNbX1cesXLn3zKVlqfXHEetE3+In7rDNtrYb4VOb+CZtSc4lV6Ml4s9K2f2s2oL/4bwc2yGqTPszdFdmtTjydyIRe8nTE7aj0S1svSSasXuc7nsvZCHvULG/Puatv6uahTNuD4hDDD639woTaXVXzkprI0TvETDkF5hiTpTNYNKo695Iu4+o135bR18zf5Dc7m4kiVGS/xXR4Vb9dA/QRCYt+kMSfkVBHo68fmE5jFBWxAE/vtrHHvO5+JoJ2fptEja+1m/uWJ92Hshl1d+OQ3A40PaMmNQ49v/WwqVVs8TP4pO2j1syElbpdXz1h/i+IjZtzWtsWeZSmsaz3BPj0DuDBcbKv6+ocC5clboYMW/Vc2F5jnlTsKsVOW2K28wS6UqPTWko/nn73yy4wJqnYF+bbybNCxdH348ksofp7Owk8v4ZnKvZjOHaeHfiaw/li7WE03qRZ/WzdPI73RGsakzbGzPIF4ZGW7pJTUagiDw2uYzxF8uxdvVge9sqOj9h31JpBdWEuDhxDNNbOxZlZ5q29KVTv7uuDrYAfEcTyuiXK27bpCsrloEx/rFo60jSUiJOuPsYBQ42usjONklKi7klCGTwSAz15acyShh04lMAP57b2erPts8nVHMgj+uzCdqLiLg1xOZfPKXWP/01v1dGd7V+r2H6kNqQQUzVxwzdYZ9NC6iWUTfqlh1OJVNxzORy+CbSb1sZk5YRpGShX+LJoSv39v5pg7C5qAqPXVv90BkMhmh3i608nZBZxCITi64bnuVTvzNlMukGpymQBI4EnWmaiJuTQJnX4IYru0R4kULM0coPtguCoYHegXTI8TLrI/VEEqUWp5acxyN3sDwLv7MGmz7aY2skkqWHkjixY0nAXhsSFumDAiz6JrMRX4z7ww7llLIgj9Ei4V5ozoz8BZGddbEO3+Ixp7923ozuolroUqUWv65IP7eXV2HNcj4+h1IuF7glKt1ALg62ln1CVlzQUpRSdSZKoGj0lwvcA5UpafMbI9+ICGfg4kFOCjkVt0WLggC/7fxFBlFlYR6O/Px+Aib/2HbcCyNeZvOmIweuwd78GozStdcjVKjY9aKY6QUKAlp0fw6w3JKVTy15jg6g8DoHoHMvs12xPeuszlsj89GIZfxv/u7Nvn3altcFhq9gfAA92q+W4Pb+7IuOo1Dl/Kvu0+FUeBcm7qSMA/N5zREoslwMqaolBpdtesFQeBIknjWYs7WZ0EQ+NDYxvpI/1ZN5lZaH5bsT2bXOdEr5dvJffB0tu2DY1ZJZTVxAxB/uZScMpXlFmUmtHoDT685zqmMkmbZGabS6nlsdSx5ZWo6+bvz4UPWPyG8igq1jje3iFYLs29rYxFjz1+N6fGxvYKrXT+gnQ8yGZzPLiP3mu9FhVo8KWzqVNq/FUngSNQZd+OXs0xVXeCkFCjJLVPjoJDTq5WX2R7/z7hszmSW4OqgsOpp4TEphXxgFGJv3teF7iGeFl5RwzmfVXrdiA6DACn5SsssyEwIgsDrm8/w94U8nOzlLJ3Wl3ZN2J1jbsTnF8ep9GI8ne35YWofmzrofvrXRS6XqAj1dub5u5o+gptZXMnR5EJkMrg/Iqjabd6uDnQJFAXX4UvV01QVV6WoJMyPJHAk6kxVFKKkUlvt+qPG6E3PUC+zdWDo9AY+MXqQzL6tLb5ujmZ5nIZSUK7mmbUn0BsE7o8Ishk/kZuhNwgsO5hy3fUKmYwwX+uNotWHz3de5KcYo9P0pN42YXZXF5YfTOGX4+Lz+2ZyL1r7uFp6SbXmTEYJKw6J1hDvjO1uanpoSn47eRmAqDbeNbqQDzT64RxNLqx2fYUx6u1qgTX/G5EEjkSd8TAKnOJrBY7xy9y/rfk6hH6OzSApvwJvVwerrRcQBIGXfj5NdqmKti1dee/B7jYT+r8ZC/44y/6EfBRymcnNWiGT8d6D3Qj0tI2um9qw5mgqX+0RO3MWjO1m9fYDdeVgYj7vbhML9F+7pzO3dTC/nUNjodMbeHXTaQyCGDm5vQmsKK5FEIQr6amewTVuExkm/gYeu0bglBp/M92dpAhOUyC9yhJ1pqYIztX1N1Fmsq1X6/R8uTsBgKeHtrfaYs+Vh1LYcz4XBzs5Cyf3bhYFhcsOJLPiUAoAX07sSZ/WLUjJVxLm69KsxM1f8dmmMRrP3dmeR6Ks2xm7rqQXKnl6rejl82CvYJvr6FtxKIX4y6V4ONnxxmjLTDePyyzlQk4ZDnZyRnWvuXMr0hjxS8gtp6hCY+ooLawQfzO9Xa0z8tzckCI4EnXGy+V6gZNRVElWiQp7hYzercwTzt9wLJ2sEhUBHk5Wm/I5l1XKe3+KdTevjQqnc6D1TzW/FdvjslmwVWwjfnVUOKN7BBHo6cyAdj7NStzEphaZxhQ8HBnCC1bcnVcfKtQ65qyKMTkV21pkMaNIyadGz6XX7ulMS3fLiISfYtIBGNk14IZNAz5ujrRrKab9YlKLTNcXKTUAeLta58lZc0MSOBJ1xhTBUV4ROMfTxC9x1yBPs+TEVVq9ydDr6TvbW6XLaqVGz3PrTqDRGbgz3I9pA8MsvaQGcyKtiOc3nEAQ4JGoVjw+pK2ll2QWEnPLmbXyGGqdgaGdWvLuA7Z18L8VYtr0FOezy/B1c+T7KbbjVAzi+t/cEk+lVk+/MG8ejgy1yDpUWj1bTorpqVutoV8bMU0Vk3IlTVVYIQqcFlY+ELi5IAkciTrjYwyvFlSoTdedSCsGxAJjc7AuOo2cUjVBnk48HBlilsdoKO9uO0tCbjkt3R35eJzttNzeiPRCJbNXxqDSigf9tyzgNdIU5JaqmLYsmmKllogQTxY+0tuqZ5rVh4V/J7LtTDb2ChnfT+ltc5G3rWey2HM+F3uFWPNlKRfpv87mUKrSEezlbCokvhGRRrfy6KsETnZJJQCSiXHT0Ly+xRJNQlVouKBCg844PO5EejGAWdrDVVo93+69BMAzd3bA0c76zjx3xGfz45E0AD57OAIfK+3uqi0llVpmrDhGQYWGrkEefDO5d7Ocflym0jJ9+TEyiysJ83Fh2fS+uDjYfs3U1ew6m8OnO8XUzttjutncmJCSSi1v/S6mSJ+8oz3t/dwttpaNxvTUQ31Cbimyqjrv4jNL0egMbDiWRnSKGOlesPUcG46lmXexEpLAkag7Pq4OKOQyBEEUOSqtnrOXSwDMUn/z45FU8srUBHs5M66P9UVvsktUpgnTjw1pa1NdKTVRZXCXmFtOgIcTy6b3bZa+HRqdgSd+jOVsVim+bg6snNnP5oXptSTmlvH8hpMIAkzp35pJ/ayzdu1mfLj9PHllatr6uvLUHe0sto6MIiUHEkV34vG1+B1q7eOCp7M9Gr2Bg4n5zNt0xnSbIMBrm+LIMkZ0JMyDJHAk6oxcLsPXTcwh55aqib9cglYv4OvmQEiLxg19q7R6Fv2TBMBzd7W3uhlAeoPACxtOUqzU0i3YgxeHd7L0khqEIAjM/y2eA4n5uDgoWDItEv9m5N5bhcEg8PLPpziYWICLg4Jl0/valBdMbSip1DJnVSzlah392njz5n2W6TpqCDEphaw9KkY63nuwu0XrhjYcS0cQRI+b2riny2QyehjNPfcn5F1nkKkXhGZnkGltWNfRQsJmqEpT5ZWrqtXfNHaNxoZj6eSXi9GbB3tbX/Tm+32XOJwkHiS/mtjL6gRYXVl6IJm1R9OQyeCrib3oFmz77ss18eH28/x68jJ2chnfPtLbqoe11ge9QeA/60+QnF9BsJcz39pgXZFKq+fln8XI6MORIfQ3k/1EbUgrrGDV4VSAOlkHVAmc3DLVdXU3zdEg09qwrU+8hNXg5y6e1eeUqom/XApA92CvRn0Mjc7A9/+ItTdP3N7W6n6gT6YX85mxbfV/93elrY1b+e86m2MygHv9ns4Ma2YGd1UsO5DM9/vEqOAHD/Xgjk5+Fl5R4/PBn+fYaxwz8f2UPlbr+H0zPv3rAkn5Ffh7OPL6PZaLPm04lsbtH+012WIUG1u9a0OVcE7MreDJ26+k15qjQaY1Yl1HDAmbIdBTFDhZxZWcNQqcrkGN6/ny64lMLpeoaOnuyHgLtYXeiHK1jv+sP4HOIHBvj8Ba5eStmfjLJTy3XmwHn9Svlc0ZwNWWraezTJ4+L43oZJU1XQ3lp5h0Fu8XRxl8Mj7CJqNwsamFLDkgPof3H+yOp4tlfGOqhstenV16c0t8rWtnIowC52JOmekEqIOfKwdeHcqEvrZXD2VrSAJHol4EG2ttLuVVkJhXDkDX4MYTOHqDwHfG6M2c29pYnWfHm1viSC1QEuzlzHs27pmSU6pi9soYlBo9g9v78vaY5tkOfiSpgBeMBbeP9m9l0YJVcxGTUsjrm8Vi1v/c1YHRPYJucQ/rQ6XV89LPpxEEeLB3MHeGWy6SmJxf0aDamQBPJ1q6O2IQYF9CHgAd/N2lyE0TIQkciXoR0kLMHe8+n4PeINDCxZ6ARixG3Xomi+T8Crxc7K3OLn/r6Sw2Hc9ELhPHFtzIzdQWUGp0zF4ZQ1aJinYtXZulBwzAhewy5qyKQaM3MLyLP2/d363ZibiMIiWPr45Fqxe4p3sA/7mrg6WXVC8+23mRpLwK/NwdmT+6q0XX0sbXlWs/JXWtnQkPENva95zLBZDETRPS/H7JJJqEYOMEXZVW9MHpGuTZaAcMQRD4zuh7M2NgG6tqUc4tU/HfX8Uz5KeHtjcN1bNFDAaBuRtOcSazBG9XB5ZN72vTYu1GZJVUMn15NGUqHX1at+CrSb1QNDOntQq1KFSrfIs+GR9hMTO8hhCbWsSS/WJ91HsPWC41VYWXs0O16HF9ameqxrWUqcVJ4q19pMLipsJ6jhwSNkXoNe3gXRqx/uZAYj7nskpxcVAwbaD1RG8EQWDeL2coUmrpGuTBs3fa5hlyFR/tuMD2+GwcFHJ+mNKn2bVJg9gqPX3ZMVOEasnUSKtLdzYUg9GqoGoMw+KpkTZpViimpk5hEODBXsFWUeS++UQmlVo9gV5OfDIugrYtXescgamK4FRRmxZzicahSSI4CxcuJCwsDCcnJ6KiooiOjr7p9hs3biQ8PBwnJye6d+/Otm3bqt0uCAJvvvkmgYGBODs7M2zYMBISEsz5FCSuwdfNsVpL9LVf4obwg7HD5eHIULysaGbLxpgMdp/PxUEh57OHe9p0S/hPMeksMtY4fTSuh01Hom6EWqfnsVUxXMgpw8/dkZUz+5mmOjcnPt15gb/O5uBgJ+eHqX0I8rLNFMjnV6em7rNsagrE48yKQ2Kh86xBbRjU3rde6aXwgOonf60kgdNkmP0XesOGDcydO5f58+dz/PhxIiIiGDFiBLm5uTVuf+jQISZNmsSsWbM4ceIEY8eOZezYscTFxZm2+eijj/jqq69YtGgRR48exdXVlREjRqBSqcz9dCSMyOWyal/U9n6N0yIdf7mE/Qn5KOQyq+rkSS9U8vYfYvfN3OEd6dSIgq6pOXypgNeMrqrP3dmesb2CLbyixsdgEJj70ymOJhfi5mjH8hl9TXVjzYktJzNZ+LcoVD94sLtZnMSbguNpRSy2otQUwKFLBVzMKcfFQdGgLs6qQcRVHL5U0NClSdQSswuczz77jDlz5jBjxgy6dOnCokWLcHFxYdmyZTVu/+WXXzJy5EheeuklOnfuzIIFC+jduzfffPMNIKrqL774gv/+97+MGTOGHj16sGrVKi5fvsyvv/5q7qcjcRUtrvoRatdIHjCLjdGbe7oHWk0o12AQJzGXq3VEtm7BnNtsd6J2Sn4FT/wYi84gMLpHIC/c3dHSSzIL7247x9bTWcbhkn3oGmR7rdK34mR6MS8ZjfCeuL2dVRph1gaVVs9LG8XU1ANWkpoCWH4wBYBxfULqXZuWVVLJm1viql03vw5t5hINw6wCR6PREBsby7Bhw648oFzOsGHDOHz4cI33OXz4cLXtAUaMGGHaPjk5mezs7GrbeHp6EhUVdcN9qtVqSktLq10kGs7V7ZOlKm2D95dZXMnvp7MAeMyKRMSKQykcSSrE2V7BJ+MjbLZAtVSlZfaqGEoqtUSEevHJ+Ihm10kEsGR/EkuNHiofj4tgUHtfC6+o8ckqqRS7wnQGhnX246URtjsi5ItdCVzKq6CluyPzrWScRFqBkt3ncwCYOiCs3vtpaJu5RMMwq8DJz89Hr9fj719dkfv7+5OdnV3jfbKzs2+6fdW/ddnn+++/j6enp+kSGmpdpnG2Sm7plZTgoA/2NHg67oqDyegNAgPa+tA9xDrOuBNzy/lw+3kAXru3M2G+tlmIqzcIPLfuhGmA5uIpfZpdsS3Ab6cu885W0Y351VHhzTL9VqnR89iqWPLK1HTyd+eLibbbFXYirYgf9okptvce6G41NXfLDiYjCDCkY8sGpd/b+LpKIxosiO1WSdaBefPmUVJSYrqkp6dbekk2T1ZJJelFV8KshgZOx61Q61h/THxfZt9mHbU3Or2B/9t4CrXOwG0dfHk0ynadR6+27l88NRK/ZjhA89ClfF786RQA0weG8fgQ64kCNhYGg8CLP4ut/S1c7FkyLRI3K7JRqAtKjY65P4mpqbE9g7jbSlJTRRUaNhh/ixoaSQ70dOb9B7tXu04a0dB0mFXg+Pr6olAoyMnJqXZ9Tk4OAQEBNd4nICDgpttX/VuXfTo6OuLh4VHtItEwkvMrrruuIaHXzScyKVPpaO3jwlArmQ303d5LnEovxt3Jjo/G9bDZdM7V1v2fju9pNdGxxuR8dimPr4pFozcwqlsAb4zuYrPv1834YtdFtp7Owk4uY9GjfaymTq0+vLP1HMn5FQR6OvHW/d0svRwTa46mUqnV0yXQg0HtGz7g89qRDNKIhqbDrALHwcGBPn36sHv3btN1BoOB3bt3M2DAgBrvM2DAgGrbA+zcudO0fZs2bQgICKi2TWlpKUePHr3hPiUanzY1pGrqG3oV2zFTAJg2IMwqDMriL5fw5W7ReuDtMV1t9ozr2DXW/ff2CLTwihqfzOJKpi2Lpkyto1+YN59P6GmzKZubsflEBl/tSQTg3Qe6EWXB6doNZdfZHNYeFVPan46PsIquKRALnlccEqeGPzbk/9k77/Cm6rcP30n3HnRRWii7zLLLkiEoKCogggjKBhe+bgW3OPDnFsXNEGQpggMZMkRktpQWaGkLpS3de4/s8/5xmtBCCx1pm8RzX1cubZJz8k1IzvmcZ3yeTkYRyQq1tsbfFSpNk/cpUT+aPbb5zDPPMHfuXAYNGsSQIUP49NNPKS8vZ/78+QDMmTOHdu3asXLlSgCefPJJRo8ezUcffcSkSZPYunUrp0+f5ttvvwVAJpPx1FNP8fbbb9O1a1c6duzIq6++ir+/P1OmTGnutyNRhZ+rPdZyGZqqCjqZrPGh16MJeSTklOFka8X0Qa3fCaLUaHlm21k0OoGJvfyY0s886zhSCyp4xAKs+29EcYWaeWvDyC5R0tXHme8s0MgPRKH64nZRqD48upNZRwFyS5W8+IvY/bX4lo4MN6Ei8J2R6eSVKfF3szfaxcC10e7UgkqztpkwJ5pd4Nx///3k5uby2muvkZWVRb9+/di7d6+hSDglJQW5/Gogafjw4WzevJlXXnmFl156ia5du/Lrr7/Su/fVEOYLL7xAeXk5S5YsoaioiJEjR7J3717s7S2vrsBUyS1VGsQNwPSBAY0+6K6vasecPigQF/vWv5L7/GAC8dmleDnb8s5U85xZVK7UsHiD+Vv33wiFWsviDae5lFOGr6sd6xcMMZlIgDG5kl/OwxvF9NuEXr68OCG4tZfUaARBYNkv58gvVxHs58JzJtT9pdMJBi+eBSM7Gm0mW3xWaY2/04sqJIHTQrRIddrSpUtZunRprY8dPnz4uvumT5/O9OnT69yfTCZjxYoVrFixwlhLlGggVwpq1tqkFjSuuDg8OZ+DcaLp45xhrT+WISaj2ODw+/aU3rRxtmvlFTUcnU7gqSrrfm8XO76fa57W/TdCqxN45qcowpILcLGzZv38IYb5aJZEcaWaBevDKShX0aedG5/c38+shermsBSDG/inM/thZ2060ba/LmSRmFuOi701M4cYL0IWk1Fc4++0QskDp6X4T3RRSRiflHxR4OgNsOKyShAE4UabXMe28BRmfH3S8Hd4coHxFtgINFodL/5yDo1O4I7efkzsbZ71Kh/tj2e/3rr/oYFmWz9UF4Ig8NauC+w+nyUa+c0ZaBhoaEmotToe2xTB5VyxENfchWpibhlv7xJb+F+Y2P26EQatiSAIfF5V3zRveJBRO9NiMkTfNf0+JYHTckgCR6JR6NvBx3T3Ri6Dwgo1OaXKBm2/fMd5qkuiprSZG4M1R5OITi/B1d6aNye3/iycxlDduv9/0/rQ30yt+2/Ed/8mGorSP5rRj+GdTaeGw1gIgsBrv8VwLCEfR1srvp87CF8zbu1Xa3U8vS2KSrWWEV3asGCEaVhB6Dl8MZeYjBIcbKyYb8S1CYLAhUxR4NzeSyzLSJcEToshCRyJRpFVZfLXwdPRYIR1Pq34RpvUwNQcPpPyyvl4/0UAXr2rJz4u5ncyqW7d/+iYzkzt3/oF28bmt6h03t0tGi++MqkH94T4t/KKmoc1R5PYEpaCTAarZvY3+1ETnx+8xNm0YlztrU2uHkwQBFZXRW9mh7bH04gDWTOKFRRVqLGWy7g1WLS/SCuUXIxbCkngSDSK5KrOAHtbK/oGuANwLq2o3tsbs828qeh0YuGj3tDvvoHmJwyySxQsMVj3+/L87aZTvGksjiXk8dzPopHfwpEdWWRC4zyMyf4L2byzW0zlvHxnD5OZzdRYIq4U8MXf+vb2PiaXMj2VVMDpK4XYWslZbGRzyJh08aKvq68LQW3EY15GsTQUuqWQBI5Eg9kWnsLRBHEi7gf74tFodQBENSCCU6ao6QVhJZO1msPn1vBUTiWJs6bendrH7LqmFGotD2+MIKdUSTdfZz6dad6FqLVxIaOEh6ta3if1bcvLd/Zo7SU1C9HpxTy5NRJBgAeGtGfhSNNK5TSUMqWGp7ddHaR5twlG3FZXia/pgwKMngaMrhI4vfxd8XERGxbyy5Rorw1fSzQL5luxJtEq6Gtn9AiCOP8HxAiOIAj1Egibw0STr1FdvXh0TBeCvBxbRdxkFleysupq+fkJ3c3OGVYQBF75NZqo1CLcHGz4bo75WvfXRVphBfPWhVGm1BDa0ZOPTCzFYSyyihUs+uE0FSotI7t4sWJyL7MT29ey4o8YUgoqaOfuYJJ1bRFXCvj3Uh5WchmPjO5s9P1HphYB0L+9O55Otshk4libgnIV3i7m16FpbkgRHIkGUVvtjE4AKzkUVajr1S6u1Gj5NTIdgPkjOjKsc5tWETeCIPDqr9GUKjX0b+/O3OFBLb6GprL+eDLbI9KQy2D1rAF0aGOew0DroqhCxdy1YYbo1LcWauRXodKwaEM4WSUKuvg4s3r2AKP5sLQWv5/N4KfTachk8PGMEFxNwOPqWj7ZL7qV3zcgwOgXNzqdQFRKEQD9Az2wtpLTxkkUNbkNaMiQaDzm/QuSaHHqmo7b1Uc0roqqRx3OwdgcCivU+LnaM6qbdzOssn7sOpfJgdgcbKxk/G9aX7Oz9z+ekGeYnP3SnT0Y2dWyuokUai2LfjhtaJP+YcEQgy2BJSFOeo8iOr0ETydb1s4dbPbvMzmvnJeqIr2Pj+likmMlwpMLOJqQh7VcxtJbuxh9/5dzyyhVanC0taKbr9iIoY/a5JRKdTgtgSRwJBpEWzcH/q+a5b++dia0oycAZ64U3nQfP50WJ/VOG9iu1URFQbmKN36PAWDp2K508zUvZ9HUggoe33wGrU7g3v7tzL5W41q0OoEnt0Zy+kohLvaikZ+pFacaA72nz4HYq75F7duYV5r0WpQaLU9siaRMqWFwkAdPjTfNESGfVHVNTh9k/OgNQGRV9KZvgBvWVdE4fR2OFMFpGSSBI9FghlSJGX93e44uG8v9g9szKEi872ZmfZnFlRy5mAvA9IGBzbvQG/DWrgvkl6vo7uvCo2OMn3tvTipU4hiGwgo1fQPcePde8yuMvhGCIPDG7zHsi8nG1krOd3MGWay1/dpjyQZPn09m9DP8jsyZ/+2J53x6Me6ONqx6oL/h5G5KnEzM5/jlfGysZDw+1vjRG4DIVPFir7oXVRtnsQU9v1zVLK8pURPT++ZJmDyF5WoAAtyvFgYPrjowx2aWUKpQ17ntjjPp6ARRJAXV0ireEhy5mMvOyHTkMvjffX2xtTafn4EgCDz381niskrxcrbjm4cGWlxNylf/XGbjySti7cb9IQw1wfSGMdgbncnbf14AYPkdwRYx6X3/hWzWHksC4MP7Qkwy6iYIgiF6M2NQIAEezRMxC0+uEjiB7ob73B1EgVNcWfcxUsJ4mM+RXcJkKKgQrz48nK7WCfi52RPo6YBOgDNVodlrEQSBn6vSUzMGtU70RqHW8tpv0QDMHR5Ev2oHH3Ng9d8JhhEFXz84wCRPIE1hx5k03t8bD8Crk3pyV1/Tays2BpEphTy5NQpBgAeHtmeJkf1XWoOMokqe337Vp8hU/XuOJuRxKqkAWyt5s0Vv8sqUJOSUAVcv/uDqaJuiCkngtASSwJFoMIVV4VUPx5qOn/of8uk60lRRqUUk51fgYGPFHb39mneRdfD1P5dJzq/A19WOZ27r1ipraCwHY7P5qOrKc8Xk3haRzqjOv5dyeaHKiXnJqE4ssLC6IhBTtDsj05i/LhylRsetwT68cbf5t4NrtDr+b0skRVVp0xcnmubEc51OMAjoB4d2wL+ZBrSGJYnHwGA/FzyqOSO7OYgWDiVSBKdFsCzDDIkWQZ+CurbTY0iQJzvOpBt+3Neibw2f0MsXp1bwaknOK+fLw+Kcplfv6omLCbat1kVCTmmNK/4HjDjt2BSITi/mkY0RaHQC94T4s8xET5BNYVt4Cst3nDfYLPi72fO5idaoNJRPDlwUC8LtrPn8gf4mm/bdE53F+fRinGyteHxs89XenUwUjVCvTa+6OYrHHClF1TKY5rdQwqQpU2oBrhMp+uLjyJQiKlXaGo+ptTp2ncsEYHL/di2wypoIgsBrv8egqhrHMKmP+dQ7FFeqWbwhgjKlhiEdPXntLtMzTGsKqQUVzF8fTrlKy/DObfhgel+LM/LTG2RW95DKKlFQcoN6NXPh6KU8w4XDyml9TNaLSa3V8eFfYvRm8ahOtHFuPqO9U4niRZ6+u1SPVIPTskgCR6LBlCvFMQuOtjWLWzt6OeHvZo9Kq+P0lZpRnKOX8sgvV9HGyZZburS8X8ue6CyOXMzF1lrOism9zSYloNMJPL0tiqS8cvzd7Ply9gCTvTpuDAXlopFfbqmSYD8Xvn5oIHbWllU0DZCYU7tBZmsNlzUWuaVKntoWZRgtYco1U9sj0kjKK8fTybZZ55gVlKuIzy4Frl706XGxFy8Kb9SIIWE8LOdIKdFi6AXOtSMBZDIZI6rEy9GEvBqP/RolpqfuDvFv8ZB8mVLDij/EbpVHR3euddCnqfLpwUscisvBzlrOt3MG4dWMV50tTaVKy6IfwkmsEm8/LBhikm63xuCvC1nX3ddaw2WNhV5855Up6e7rwut392ztJdWJQq3l0wNi/drjY7s06ziTE5fF9FQ3X+frokT6jsdKtfa67SSMjyRwJBpMuUoUOLXV0egFzrFqAqdCpeGvmGwAJvdr+Su8T/dfJKtEQYc2jmblebP/QjarDopW8u9O7UPvdm6tvCLjodHqeGJLJGdSinC1t+aHBUOMPujQVNgSlsIPJ64AoA8ctuZwWWPx1T+XOZqQh4ONFatn9zdpu4I1R5PILlHSzt2B2aHNW7+m9/m6pev1Lu0OVVHva1P4Es2DVGQs0WDKDTU41x/QhncRi+piMkooKFfh6WTLobgcKtVa2ns6tnhbdmxmCeuqjNTevKeXSR+Eq5OYW8Yz26IAmDusA9MGBrTugoyIvh5K7977/dzBdDUzJ+n68s/FXF75VbQleHJcV2YOCSQ5r6LVhssai+MJeXxUVc/y5uRedPEx3X+/vDIlX1XVCD03oVuzHgMEQeDfS3qBc30q3qHqtRVqXbOtQeIqUgRHosEoNaLAsa+lVsLHxZ7uvi4IAhy/LEZxdp8Xi4vv7NO2RWtfdDpx0rZWJ3BnHz/GdPdpsdduCmVKDQ9vjKC0yur+5UmmG/pvDKv/TmDzqRRkMvjs/n7X1SlYCtHpxTz2Y4Q4TmNAO54a35W2bg6tNlzWWGQWV/LElkh0Atw3MIDpJi6+Pz1wkTKlhr4BbkwOad4Gh8u5ZWQUK7C1lhPa8XqDSr3AUWl1aLSSyGluJIEj0WDUWrFa0qaOYlf90MfD8blUqDQcissBaPHOpZ8jUom4UoiTrRWv3mUeIkEQBF7YfpZLOWX4uNix2sKKin8+ncqHf4m1EG/c3Ys7zKibrSGk5Fcwb53YGTaiSxveu7ev2RS23wiVRsdjm86QX66iZ1tX3p5i2gX7CTmlbAkTzUVfurNHs3fn/XNRvKgbEuRpSEdVp/p9Co0kcJobyzlySrQY6qorD+s6Dha3BouRksPxORyIzUGh1hHo6UDvdq4ttsaCchUr98QB8PRt3czmivnrfxINTsVfPTgQHxfLqUs5HJ/DsqoJ04+M7szc4UGtu6BmoqBcxdx1YeSVKenR1pWvHxxoMSL17T8vEFlVN/X1g6Y/JmTl7ji0OoHbevq2yMgPfXpqVLfaO0Xtqn0PlFKhcbNjGb86iRZFL3Bs6uiGGhzkibOdNXllKv5XJTIm9fFv0Su9D/bFU1ShJtjPxWxOpP9eyuWDfeLn9frdvRjYweMmW5gP59OKeWyTOP18av92vDChe2svqVmoVGlZsD6cpLxy2rk7sH7+YLMylLwRv0ams6GqWPrTmf1Mfur58YQ8DsblYC2XsfyO5jeOrFBpDB1UtRUYAzWOgdfaBkgYH0ngSDQYjT5FVYfAsbWWGwrs0osqgZZNT8VkFLM1PAUQRxrUtU5TIrWgwlDXMGNQQLN3erQkKfkVzF8fRoVKy8guXvxvmuUZ+YG+M+wMUalFuDvaWFRnWGxmCct2iGM0/u/WLtwabJpzpvRotDpW7BKtIWaHtqeTt3Ozv+bRS3koNTrauTsQ7Fd30bVV1XdfJ0gKp7kx/SO/hMmh0qeorOo+SY0NvlrQ28695dJTgiCw4o8LCALc1betWRSwKtRaHvkxwjDHx5yMCG9GfpmyKl0j1mx89aBl1RTpEQSBV3+L5kCs6Fn0/ZxBdPFp/pNqS1BcqebRHyNQqHWM6ubNk+NNf4bblrAU4rJKcXOw4akWWu+BWNEK47aevjf8/eq1vSRwmh/LO9JItBg3OgWP6X41RBsS6NZiJ+y90VmcSirAzlrO8jt7tMhrNgVBEHhpx3liMkrwdLLlKzOoa6gvFSoNC344bZHpmmtZdTCBLWGpyGWw6oH+FjMIVacTeO7nsyTnV9DO3YHP7u9niECYKkUVKsNQ2mdv71Zj2GVzodUJHIwVmyluu8kUdXnVsVAr5aiaHUngSDQY/Q/0Rr/PNk4t77irUGt5Z3csAA+P6kS7ZpoUbEw2nLjCjsh0rOQyvpjV3yzWXB80Wh1PbI7kbLV0jY+FpGuuZVt4Cp9UueS+Obk3E3r5tfKKjMdX/1xm/4VsbK3kfPXggBYRC03l4/0XDfV3s1poKG1UahH55Spc7K1vGjXWC0QpgNP8SAJHosHoL+CEG/xCI1MKDf+fX6Zq7iUBoltpWmElfq72PGIGjsURVwp4q6pOYPkdwQzv3PIzupoDfbrmYNWIiTVzLSddcy2H4rJ5aado5Pf42M48NLRDK6/IeByrZua3YnIv+ga4t+6C6kFcVgk/nhQLoV+7u2eLjYXRp6fGdPe5ac2fJGxaDkngSDSY+kRw9lf94AFOXymksLx5RU52iYLVfycAsOyOYBxtTdukO69MyWObzqDRCUzq25aFIzu29pKMxrXpmoEdLCNdcy1RqUU8vinSYOT33O2W0xmWUVRZo+h9ZgtFQpqCIAi8+fsFdALc0duvxS4YBEFgb7Q4a2x8j5ubiWp0N69hlDAOksCRaDAy2c27AA5cuCpwtDqhhuBpDt7fG0+FSkv/9u6tMu+qIejTN9klSrr4OPP+NMswgQPLTtdUJzmvnAXrw6lUaxnVzZv/WdC/oVKj5bFNZygoV9G7nSsrJvdu7SXViz/OZXIiMR87azkvtWD9XWxmKUl55dhayxnX4+bdZZqqK0NTr2WyBCSBI9Fg9L/LuorkUgsquJxbjpVcxqKqyMS+6OunKRuLs6lF/HImDRD9Y0z9RPPR/oucSMzH0daKrx8cUOvQUnPk77gci03XVCe3VMmctWEUlKvo086NL2cPMAsrgvogCAIv74wmKrUINwcbvpptHkXvJQq1Id27dGwXAj1bzqPnz/MZAIzt7n3TKeVanWBIUdnILeM7Y8o06ydcUFDA7NmzcXV1xd3dnYULF1JWVnbD5z/xxBN0794dBwcH2rdvz//93/9RXFxc43kymey629atW5vzrUhUQ9/mq6pjlsrhqmm6A9t7MGNwIAD/XsqjRKE2+loEQeDNP2IAuLd/uxYf5tlQ/orJMgz++9+0viY9pLAhnE0tMhj5WVq6pjqlCjXz1oWRUlBBoKcDa+cNvulJzZxYeyyZ7RFpyGXwxaz+LSoUmsLHf10kt1RJRy8nlozu1GKvKwgCu8+LF2+T+t48cqyudsyUUlTNT7MKnNmzZxMTE8P+/fvZtWsXR44cYcmSJXU+PyMjg4yMDD788EOio6NZv349e/fuZeHChdc9d926dWRmZhpuU6ZMacZ3IlEde8NE3Nqtxv+JFwXO6O7edPVxpouPMyqtrlmiOL+fzeBMShEONla8MLH53UqbQnJeOc/+fBaA+SOCuDvEtFNp9SUpr5z5FpquqY5CrWXxhtPEZJTQxsmWDQtC8XZp+W7B5uLIxVze+VOMgrwyqWedbrymRnR6MRtOJANiMbRdLUOAm4sLmSUk5ZVjZy1nXHB96m+uRr0tJepnyjTbpUdsbCx79+4lPDycQYMGAfD5559z55138uGHH+Lvf/3BvXfv3vzyyy+Gvzt37sw777zDgw8+iEajwdr66nLd3d3x87PM/L6po5+Iq1RfH8FRaXSGKeKju3kjk8mY0s+fD/+6yO9nM5g+KNBo66hQaXivahTE42M74+dmum3IlSrRzK9UoWFgBw+W32H6Hj31IadUwZy1pywyXVMdrU7gya2RnEwswNnOmh8WDKGjl1NrL8toJOaWsXTzGXQCTB8YwPwRQa29pHqh0wm88ms0uipjz5YWZX+eywRgbHefeqWaq8+fssTfianRbJ/wiRMncHd3N4gbgPHjxyOXyzl16lS991NcXIyrq2sNcQPw+OOP4+XlxZAhQ1i7du0NW5aVSiUlJSU1bhKNRy9wKmuJ4JxOLqBCpcXL2Y6ebUX34ntC2gFi22lOqcJo61jzbxKZxQrauTuw6JaWC0s3FEEQD8JxWaW0cbJl9SzLcPMtVaiZvy6c1IJKOrRxtLh0jR7x3+88+2JEP5hv5wykdzu31l6W0ShRqFm04TQlCg0D2rvz9lTzcdLeGp5KVGoRznbWvHpXzxZ9bZ1O4Lcosf5mUt/6jaIpV4rHTAcbK6nIuAVotqNsVlYWPj41Q3bW1tZ4enqSlVW/VEVeXh5vvfXWdWmtFStW8NNPP7F//36mTZvGY489xueff17nflauXImbm5vhFhhovCjCfxE7G/FrU1uK6p9q03T184bat3Gkf3t3dALsOptplDXklyn55kgiAC9M7G7ShZBbw1P55YxY1/D5A/1NOtJUX5QaMSIVk1GCl7MtGxYMsah0TXU++utitbb3fhbjVwRVkaktkSTmltPWzZ6vHxrYoimeppBTomDlHtHY8+nburX43K/w5ALSiypxsbO+qXuxnjKlBsBiGgtMnQYLnGXLltVa5Fv9FhcX1+SFlZSUMGnSJHr27Mkbb7xR47FXX32VESNG0L9/f1588UVeeOEFPvjggzr3tXz5coqLiw231NTUJq/vv4w+glOhul7gXJ2mW/MkMKWfGMX5LSrdKGv44u8EypQaerdz5e56FPe1FufSinj9N7EI+rkJ3RnexfxPjqJ9/zmOJeTjZGvFunlD6NDGctI11Vl7NIkvqvyV3p7Sh4m9W25obEvw/r44/o7Pxd5GzndzBuHjYj7i+40/YihVaOjTzo25w1q+Y2/HGfFYdmeftvW+wKpQ6QWOeYhIc6fBMvLZZ59l3rx5N3xOp06d8PPzIycnp8b9Go2GgoKCm9bOlJaWMnHiRFxcXNi5cyc2NjeeXxMaGspbb72FUqnEzu76q0g7O7ta75doHPp5QqUKTY37iyvVRKeLHW/DOtU8kU/q25YVuy5wNq2Yy7lldG7CdN/UggqDW+myiT1MdjJ1UYWKR388g0qrY3wPXx4ZZfruyjdDEATe/jOWP85mYC2X8fVDA+kTYDnpmur8GplumEj93O3dmGVBE94Bdkam8c0/YhT0g/tCzCrttv9CNrvPZ2Ell/HetD4t5lisR6HWsvu8GI2eOqBdvbczRHBM3IjUUmjwp+zt7Y23980LuYYNG0ZRUREREREMHDgQgEOHDqHT6QgNDa1zu5KSEiZMmICdnR2///479vY3v6KIiorCw8NDEjEthJuDKHCKK2u2fYclFaAToJOX03VpGC9nO0Z38+ZQXA7bI9J4sQkdTx/9FY9aK3BLVy9GdjXNiIhOJ/DUtijSiypp7+nIRzNCTFaINYTv/k1k7bEkAD6cHmI2nTYN5e/4HJ6r6nibNzyIx8d2aeUVGZeo1CJe/OU8IPrGmFNHX6lCzau/in5Li27pSC//lhdm+y9kU6rU0M7dgSENGKyqj3pLEZyWodlkb48ePZg4cSKLFy8mLCyMY8eOsXTpUmbOnGnooEpPTyc4OJiwsDBAFDe333475eXlrFmzhpKSErKyssjKykKrFb8Yf/zxB99//z3R0dEkJCTw1Vdf8e677/LEE08011uRuIarAqfm+AV999Swzm1q3W7GoAAAfolIQ1OHh87NiE4v5teqwr6miKTm5qt/LnM4Phc7a3FIof4zM2d2nEnj3d1i+vnlO3swpX/9r1zNiYgrhTz6YwQancDkfv68dldPsym6rQ/ZJQqWbDiNSqPjtp6+PHNbt9ZeUoP4YF88WSUKOrRx5KlxrbP2HVXGolP7t2vQhYv+otDV3vyPB+ZAs8bJNm3axNKlSxk3bhxyuZxp06axatUqw+NqtZr4+HgqKioAOHPmjKHDqkuXmldMSUlJBAUFYWNjw+rVq3n66acRBIEuXbrw8ccfs3jx4uZ8KxLVcHMQvzbXRnD09Td1FWHeGuxLGydbckqV/HMxt1625tfy/j5x+N89If4mG1I/cTm/xpDC1rjCNDb/XMzlhe3nAFg0siOLR5lu11pTuJhdyoL14SjUOkZ38+aD+ywj8qZHodayZMNpckqVdPN15pP7+5nV+4u4UsDGqvT0u1P74GDb8pGQzOJK/qkyM21IegqgoGomn6cZTGW3BJpV4Hh6erJ58+Y6Hw8KCqrR3j1mzJgbtnsDTJw4kYkTJxptjRINx83x+hRVYbmKuKxSAIZ2qj1ka2stZ2r/dnx/NIlt4akNFjjHE/I4cjEXGyuZyTrl5pYq+b+t4pDCaQMCmGFE35/W4lxaUY2IRkvO+WlJ0osqmbMmjOJKNf0C3fnqQcto59cjCALLfjnH2bRi3B1t+H6OebX1K9Ranv/5HIIA9w0MYEQrFez/FJ6GToDQjp4NriUslAROi2I5v16JFsPdQfxxFpZfFTgRVwoB6OztRBvnumuh9KMbDsXlkFuqrPdrCoLAe3vF9Mjs0A60b2N6FvJ6M7jcUiVdfZx5a4rpz8W6Gcl55cxfF06FSsvILl4WF9HQk1+m5KE1p8gqUdDFx5l18wab/ET6hvLJgUv8GiUWh385a4BJ/oZuxMf7L5KYV46vqx2vTmpZzxs9Wp3AtvAUAB5oxIR1fQTHQxI4LYIkcCQajN7vJLfsqkA5XSVwBnW4ccFdN18X+gW6o9EJbI9Iq/dr7j6fxbm0YpxsrVh6q2kWfH528BLHL+fjYGPFVw8OMPsTpOhSHEZ+1VTprx8aaFERDT3FlWrmrA0jMbccfzd7NiwYYnEnoO0Raaw6eAmAd6b2Nju7gogrhXz3r9jxtfLePoYocktz5FIuGcUK3BxsmNi74U76BRVVERxHy/p+mSqWd7SSaHZ8qgROfpnSMFE84koBAAODPG66vb7ddnPYlTonkldHrdXxwT4xerNkVGe8bhAhai2OXMzl80PiCeTde3ub/RDNMqWG+evCSSmooL2nI+vmDTGrdEZ9qVBpWLg+3DBf6sdFofi7O7T2sozK8ct5LN8h1k89NqYz9w82r3Z3hVrL89vPIghw74B23Brc8No9Y7E1TIze3DugXaPMRaUITssiCRyJBtPG2Q65DHSCKHKUGi1n00T/m0Edbi5w7u7rj5uDDakFlfxzMeemz98ankpyfgVezrYsuqVjk9dvbLKKFTy9LQpBgAeGBDK1f0BrL6lJqDQ6HtkYUW2opGW6FCs1Wh7eGMHpK4W42FuzYeEQOjXBn8kUScgp5eGNEai1Anf1bWuytWs34pP9F0nMLcfHxY7X7+rVauvILlFwIFY8XjUmPaXfB4Cvq+X9nkwRSeBINBgrucxQZ5NTqiQ6vRiVRkcbJ9t6DSB0sLVi+kBRBGw8ceWGz1WotXxRFRn5v3FdTc7iXKPV8X9bIskvV9GjrSuv3916B2BjoNMJPL/9LEcT8nC0tWLd/MEEWdBQST0arY6ntkbx76U8HGysWD9/sEV0u1Unt1TJvHXhlCo0DOrgwYfTza9+KuJKgSE19e7U1ktNAWw6KUachwR50s234RFatVZHTlXdoSWMazEHJIEj0Sj0aaqcUgWRKUUA9G/vUe+i2tlDRWv1wxdzScmvqPN528JTyS5R4u9mz/2DTa8j6aP9FwlLFidMfzl7gEnPxKoP7+6O5beqQtSvHhxI3wD31l6S0dHpBJbtOM+e6CzD8MyBN6kdMzcqVVoWbThNWmElQW0c+XbOILP7bpYrNTy97Sy6qtTU+HrOe2oOlBotm6vSU3OHBzVqH7mlSgQBrOUyvJykCE5LIAkciUbhVzXYLrNYwbmq9FRIAyz7O3o5cUtXLwQBNp2qPYqjUGv58rA4B+ixsV1Mbgjgobhsvjp8GYD/Tetbr+iVKfPdkUS+Pyq6FL9/X19Gd7M8l2JBEFix6wLbI9KwkstY9UB/i3Nj1ukEnt4WxdnUItwdbVg3f4hZtiW//ecFUgoqaOfuwBv3tG5k9M9zmeSVqWjrZs/tvRontDKL9ekpe7OLpJkrksCRaBQBHmIhZmpBJeer5k/1DXRv0D7mDAsCYEtYCuVKzXWPbw1LMURvpg8yrbqW9KJKnvlJtPKfO6wDk/qa9xDGXyPTeWe3OJl5+R3B3DvAtD5vY/HJgUusP54MwPvT+jaqE8bUWbknlr0xYnTquzmDzFJ4H7iQzZawVGQycSRIazr/CoJg+M48OLQDNo2ce5VVJXD83aX0VEshCRyJRhHoKXpoXMgsISmvHIA+DXQWvjXYhw5tHClRaK5rGRejN2J0xNSiN2qtjqWbz1BUoaZvgBsvTTJv47sjF3MNc5cWjOjIEgt1Kf7+30RDq/SKyb2YNtDyRNzGk1f47l8xCvfB9L4MbsCcJFMhv0zJsh1XXbPrGv3SUkSmFnEurRhbazkzm5AmzyiqBMDPzbK69EwZSeBINIoAD1HgHKmyLA/wcGhwGNxKLmPhSLErau2xpBot41vDUsgpNc3ozYd/xROZUoSLvTWrZw0wKfHVUM6nFRtciu8O8eeVST3M3pywNraGpfD2n2KE6vkJ3Q3RQ0vi77gcXv9NHEL53O3dmNzP/GaFCYLA8h3nyStT0d3XhWdNoOtrTVXa9p4Q/xuamN6M5HzxQrCDp3kZLJozksCRaBSBnjWvQkIaWYx638AA3BxsuJJfwf4L2UDN6M3jt5pW9OZwfA7f/CN2dbw/ra8hkmWOJOeVM29dGOUqLSO6tOHD6X0tsjZg17kMlu8UJ2c/PKoTj43p3MorMj4xGcUs3XwGnSAOtTXX6edbwlL560I2NlYyPr4/pNULo6/kl7PnfCZAky0qrlQ1U3QwMwdpc0YSOBKN4toTe09/10btx9HWmtlVxn9rjorCYUv16M1A0+mcyi5R8GxV3c1DQztwRx/zrbvJLVUyd53oUtyzrStfPzjQpISksfg7LoentooeRbNC27PsjmCLi1Cl5Fcwd224Qai+M7WPWb7HS9mlrNgVA8Bzt3c3ibb97/9NQifAmO7eBPs17hinRx/BMceaKHNFEjgSjcLV3oY21VJSPdo23rl37vAgbKxkhCcXcuJyvqEz6fFbu5jMaACtTuCprVEGv5uXzbjupkypYcH6cK7kVxDo6cD6BYNxacUizubiWEIej1Sl3+4J8eetyb3N8sR/I3JLlTy09hR5ZUqC/Vz4cvbARhfBtiYKtZYntkSiUOu4pasXi29p/Tqw/DIlP51OBeDhUU2L+ik1WkMNToc2ksBpKczvlyBhMlQf1te9CVc3vq72TKmqF3jgu5PklCpp5+5gUtGbLw4lcCIxH0dbK76Y1b/VQ+eNRaXR8eiPEZxPL8bTyZYf5g/Bx8XyujrCkgpY9MNplBod43v48tGMEKwsLP1WqlAzb10YV/IrCPBwYMOCIbg5mKdQfW9PHHFZpbRxsuWjGaZhSPjDiSsoNTpCAtwY2qlpxdqpBZXoBHCytcLL2fxa9s0VSeBINBp5tath/yY6cz5yTV3E42NNJ3pzMjGfzw5eBOCtyb3pbKZ2/jqdwAvbzxrce9fNG2xxowkAzqQUMn9dGJVqLaO7ebN6dn+zjGrcCP2YCf04jY0LQ/FxNU+hejA229CG/eH0EJMQ3BUqDRtPJAPi/LumRv4ScsoA6OjtZHFRRFPGsn71Ei2KplrXU1N/tNeKhvtMpIW3oFzFk1sj0QkwbUCAWbcWv7c3jl8NLsUDCGmgb5E5EJ1ezNy1YuH0sE5t+OYhy6st0uoEntl2luOX83GytWL9/CFmW9eRXaLg+e1iS/iCER0ZG+zTyisS+fHkFQor1HRo42gUr6SL2aUAjRrxINF4JIEj0Wh09ZgEXl80Wl2Nv9MK6x7f0FIIgsBzP58lu0RJJ28nVkw23zlT3/+byLdHxCLu/03ry5jupnEiMSZxWSU8uOYUpQoNg4M8WDPP/MYT3AxBEHjj9xj+PJ9ZNWZiEH0a4CBuSmi0Op7YHElBVaH7i3e0fks4iGMu9L+Vx8d2MUpqM75K4AT7SQKnJZEEjkSjqZ4nV2q0TdrX7uisGn/rC41bkzVHkzgUl4OttZzVswaY3KDP+vJbVLrBA+bFicFmHYWqi4ScMh78/hRFFWpCAt1ZO28wjrbm+e91I1YdTGDjySvIZPDJ/f0Y0cWrtZfUaD6uNsdt9WzT8ZPadOoKeWUqAj0dmNrfOF5C8VlSBKc1kASORKOpVF0dr3Axq6zR+xEEgW/+EQXNmO7iXKCdkelcqWqrbA2iUot4b08cAK/e1ZMebZvWItpa/Hvpqkvx/BFBPDK69btTjE1yXjmzvjtJXpmKXv6ubJg/xCK7wn48eYVPDoi1YCvu6WXW40H+js8xeF29N62PyaTYFGot3+ijN2O6GKV2S6nRGtzeu0sRnBZFEjgSjUKnE0iuNgU8OqO40fs6lpBPTEYJDjZWfDKjH6O6eaPRCXxWZavf0pQo1Dyx5QwancAdvf14sMqnx9w4m1rEwxsjUGsFJvVty6uTelpcgWNaYQWzvz9FTqmS7r4ubFwYipuj5YmbPeczebXKpfj/xnXlITN2Ys4oquTpbVEAzBnWgbv6+rfugqqxJSyF3KouTmPNY0vIKUOrE3C1tzYMKZZoGSSBI9EoMoorUWmu1s1Epzde4HxdFb25f3AgHk62PHtbN0AcAKnvPmgpBEHglZ3RpBZUEuDhwHvT+pqlKLicW8a8dWFUVJm/fWwirbfGJLO4klnfnSK9qJJO3k78uCjULKdm34zjl/N4sppZ4dPju7b2khpN9Tlufdq5mZSfVKVKa0iNPza2s9G6OM+nicfGXv5uZnksMWckgSPRKPQhVz3RGSWN2k90ejFHE/JqzKUKCXTntp6+6AT4tCok31LsOJPO72czsJLL+Gxmf7P0FckqVjBnTRiFVSeRbx4aZDL1DcYip1TB7O9OkVJQQYc2jmxeNBRvl8bPCTJVotOLWbIhApVWxx29/czerHDl7jjOmOgct/XHk8kpVRLg4WDULs6zVQLHErsWTR1J4Eg0Cv1clc7eYu48NrME9TWdUPVBn+++q2/bGuMfnqmK4uw6l0lsZuPEU0NJzivntao0wFPjujKwg0eLvK4xKapQMWdtVVTDy4n18wfjbKbF0XVRUK7iwe9PkZhXTjt3BzYvHopfE32YTJGEnFLmrg2jTKlhaCdPPrm/n1mbFf4Wlc7aY+Lgyg+nh9QwCm1tiivVhkjy0+O7GVV4nUsrAiDETLvdzBlJ4Eg0ivQq2/ERXbxwsbdGpdEZOgXqS2pBBX+eywBgyaiaxa892rpyV1UR5Ud/xRthxTdGpdHx5NZIylVahnT05DEzHFZYqdKyYH04F7PL8HW144cFQ5o0/dgUKShXMeu7k1zMLsPP1Z7Ni0Np5+5w8w3NDLFw+hT55Sp6t3Pl2znm3fIel1XCsl/EgaePjenMhF5N95YxJt8euUxxpZpuvs5MMVLnFIhFy/rjYl8pgtPiSAJHolGkF4oCJ8DDgQHtxUjH6eSCBu3ju38T0Qkwqpt3rYP1nr6tG1ZyGQdicwhLati+G8rH+y9yNq0YNwcbPjXDK2W1VsdjmyI4k1KEq701GxaEmvWk89rQi5u4rFK8XezYtDjUIuf6pBdV1iycXhCKqxl3hRVXqnl4YwSVai23dPXi2dtNw+9GT06pgrVHkwFxyKcxf/sxGSVodAJezrZNdnuXaDiSwJFoFPoITjt3R0MqJyKlqN7bX8goZktYCgCPjKq9dbmztzP3DxbnUb2zOxZBMJ6xYHWOJeTxzRExPP2/aX3wN7OIgE4n8OL2c/wdn4udtZy18wZbXDvqteJmy+KhZjsy40ZklyiY9d1JQ4rxx0WheJhx4bROJ/DMtiiu5FfQzt2BVTP7m9zFw+cHE6hUa+nfXqz9MyaRKYUA9At0N+vaKXNFEjgSjUI/GbedhwODqgTOmSuF9dp2W3gKk1YdRa0VBUtKQd2uxU+N74qTrRVnU4vYdS6ziau+noJyFU9vEztUHhjSnom9zctbRBAE3t0dy47IdKzkMr6cPYBBQU0bDGhq1CZuuvhYnrjJL1My+/tThinvmxaHmn3h9KpDlzhYZZb5zUMDTU6sJeSUsbnqQuuFCcFGFyGnqiLPQzpa1m/SXJAEjkSD0Wh1ZJcoAPB3tyck0B0ruYz0okoyiytvuG1mcSXLd5yneizm5Z3RdW7n42LPw6PFQZzv74trsmNydQRB4IXt58gpVdLZ24lX7zKdltX68s2RRL4/KhZuvj+tL+N6GPcKtLX5r4ib4go1D64JIyGnjLZu9mxeNJS2buYVSbyWvdFZfHpA9LJ6e0pverczvSLbd3fHotUJjO/hy7DObYy6b51OIDxZL3CMu2+J+iEJHIkGU1CuQieAXAZtnOxwsrOmR1sxJXKzWpmkvHKuHWGlFQSS8+qO4iy6pSM+LnakFlSy8cSVJq9fz48nr3AgNhtbKzmfPzDA7Kz9fwpPNbgtv3xnD4sbwfBfETelCjVz1oURm1mCl7MdmxaZf/1UbGYJz/wUBcC84UHMGBTYuguqhX8v5XIoLgdruYyX7gw2+v4v5ZRRVKHG0daKXv7m6YRu7kgCR6LB5JYpAfB0sjPk04d1Eq9Qjifk33Db2izZrWQygrzqPqA72lrz7O1i2/iqg5fIr3r9phCfVWqYz7TsjmB6mtkBaP+FbJbtEKcwPzy6E4vrqGMyVwrKVcz+/pTFi5sKlYaF609zNrUID0cbNi0KpZOZ1xbllylZ9MNpKlRaRnbx4hUTMvPTo9HqeHuX+Pt/aFiHZvnMw5LEY+GA9h5GGfkg0XCkT12iweSVqQDwcr6aT9cP/TuakHfDYuDiSnWNv61kMt69t/dNw/H3DQykl78rJQoNHzaxbVyh1vLk1kiUGh1junszf0RQk/bX0oQlFbB08xl0Atw3MIBlE41/9dma6MWNPqJhqeJGodayZEMEYckFuNhbs3FhqNkXh6s0Oh7ddIb0oko6tHHki1n9sTbBk/tPp9OIzy7FzcGGJ8c1jzP0yUSp/qa1adZvXkFBAbNnz8bV1RV3d3cWLlxIWdmNrffHjBmDTCarcXvkkUdqPCclJYVJkybh6OiIj48Pzz//PBqNpo49Shib3FIxglK9AHJIR09srMQ6nCv5daeb9CmmMd292bJ4KEeXjeX+wTef9WQll/HmPb0A2BqeajDPagwf7IsnLqsUL2dbPpweYlbdDbGZJSz8IRylRse4YB/eu7ePWa3/ZlwrbrYusUxxo9LoeGzTGY4m5OFoa8X6+UNMskalIQiCwBt/xBCWJE4I/37OINwdTauoGEQzTP1F0lPjuzbLGjVaHUcT8gDMeuK7udOsAmf27NnExMSwf/9+du3axZEjR1iyZMlNt1u8eDGZmZmG2/vvv294TKvVMmnSJFQqFcePH+eHH35g/fr1vPbaa835ViSqkVeVIvKqZiLnaGtN/yo/HP0P+1qKK9XsOJMOwMOjOjOsc5sGFVIOCvJkSj9/BAFe/z0G3bXFPPXg6KU81lQV5X5wX0iN92DqpBZUMGdtGKUKDYODPPhi1gCTvDpuLP8VcaPR6nhqWySH4nKws5azZu5gs3TNvpa1x5LZfCoFmQxWPdCPrr6mGY368K94CspVdPN15sGhHZrlNc6mFVNcqcbNwUZyMG5Fmu3oGBsby969e/n+++8JDQ1l5MiRfP7552zdupWMjIwbbuvo6Iifn5/h5up6tT7ir7/+4sKFC/z444/069ePO+64g7feeovVq1ejUqma6+1IVEOfZnK/ZmrzSH2a6lLtAueXiDQq1Vq6+ToztFPjwrbL7+yBo60VkSlF7IxMb9C2RRUqnv05CoCHhnZgbLBPo9bQGuSVKXlozSlyS5UE+7nw/ZzBONiar7PttfxXxI1aq+P/tkay+3wWNlYyvnlooNG7d1qD/ReyefvPCwAsvyOYW4NNs5vvXFoRm06JbeErJvduttqYIxdzAfGYaEkXIeZGs33yJ06cwN3dnUGDBhnuGz9+PHK5nFOnTt1w202bNuHl5UXv3r1Zvnw5FRVXUx4nTpygT58++Ppe/QFNmDCBkpISYmJiat2fUqmkpKSkxk2i8ZRUCRyXa9xVR3XzBsQIzrXt3DqdwMaTYnrqoWFBjU6r+Lra88StYs585Z44iivUN9lCRBAEXtp5nuwSJZ28nXjpTtMrfKyLUoWaeevCSM6vIMDDgR8WDMHN0Xydba8lt1TJzG9PWLy4UWnESdp6cfPl7IGM6W4+IrsuotOL+b8tkQYvqcW3mGbBu04n8Oqv0QgCTO3fjqGdmk9YHrkkCpxR3aT0VGvSbAInKysLH5+aP15ra2s8PT3Jysqqc7tZs2bx448/8vfff7N8+XI2btzIgw8+WGO/1cUNYPi7rv2uXLkSNzc3wy0w0PRaFs2JUoVY7+RqX7Otum87N7xd7ChTajiVWLNd/N+EPJLyynGxs+beJs56WTAyiE7eTuSVKfnfvrh6bbPjTDq7z2dhLZfx2f39zSb6oS9EjU4voY2TLRsXhuLrajmW71nFCu7/9oRhfpalihulRstjmyLYF5ONrbWcbx8aZHTX3NYgs7iShT+EG8YwrJjcy2RrwraGp3I2rRgXO2uWN0NbuJ7CchVnU4uAqxd9Eq1DgwXOsmXLrisCvvYWF1e/k05tLFmyhAkTJtCnTx9mz57Nhg0b2LlzJ5cvX270PpcvX05xcbHhlpqa2uh9SYgRBeC6+ThyuYxbq65ID8Zm13hs44lkAKYNDMCpidOt7ayteHdqHwA2n0q56Qys1IIKXv9djO49fVs3+phJTlyrE3h6WxQnEvNxqipEra3N3lxJK6xgxjcnSMwVp4L/9PAwixQ3CrWWRzZGcCBWrLn5bs4gs0qP1kW5Umxxzy5R0tXHmdWzB5hsO3RemZL3qy6Gnrm9Gz4uzXeRcDAuB50AwX4uZm/WaO40+Nv47LPPEhsbe8Nbp06d8PPzIycnp8a2Go2GgoIC/PzqP0k2NDQUgISEBAD8/PzIzq558tT/Xdd+7ezscHV1rXGTaDz6CI6L/fVCZXzVVemB2BxDu3h2iYJDceJ3wVhFfUM7tWHGINHYbvmO86g0ulqfpxcJZUoNgzp48EiVK7KpIwgCr/4WzZ7oLGytxJOiuQiz+pCcV87935wkpaCC9p6ObHt4qEUOzlSotSzZGMHf8bnY24gFxaMt4KperdXx+OYzXMgswcvZlrXzBpv0QNA3/7hAUYWanm1deaiZCov17IsRMwmmNjH9v0iDL6W9vb3x9r75D3TYsGEUFRURERHBwIEDATh06BA6nc4gWupDVFQUAG3btjXs95133iEnJ8eQAtu/fz+urq707Nmzge9GojGUq8T6GsdaIjEju3hhZy0nvaiSuKxSerR1ZceZdHQCDOrgYdQr9Jfu7MHB2Bwu5ZTx7ZHLLL31ej+Lr/+5zOkrhTjbWfOJGU0J/2T/RUNHyqcz+zHcglpNE3LKmPXdSXJKxXqozYuG4meBk5YrVVoWbzjN0YQ8HGysWDNvEMM7m/+/oyAIvLTjPIerRNt3cwaZtPPywdhs/jibgZVcxvv39W3Wot8KlcZQYCwJnNan2f6le/TowcSJE1m8eDFhYWEcO3aMpUuXMnPmTPz9/QFIT08nODiYsLAwAC5fvsxbb71FREQEycnJ/P7778yZM4dRo0bRt29fAG6//XZ69uzJQw89xNmzZ9m3bx+vvPIKjz/+OHZ25tPya86oqgqIbWs5UDjYWnFLV/Egvud8JoIgsD1CTAneZ+RRAu6Otrx6lyhqVx1KIDG3psfSubQiPtl/EYA37+ll0gfh6vxwPJlVh8SI5VuTe3NnH/MaAHoj4rJKmPntCXJKlXT3dWHbkmEWKW4qVBoWrA+v5nMz2CLEDcDH+y/yc0QachmsnjXAYA9hipQq1LzyazQgjnxpbq+hIxdzUWp0BHo6GMbXSLQezZow3bRpE8HBwYwbN44777yTkSNH8u233xoeV6vVxMfHG7qkbG1tOXDgALfffjvBwcE8++yzTJs2jT/++MOwjZWVFbt27cLKyophw4bx4IMPMmfOHFasWNGcb0WiGiqtmA6yta796zOpr3hC3nUuk8jUIi7nlmNvIzfcb0wm9/Pnlq5eqDQ6nt9+Dm2VN06lSstT26LQ6AQm9WnLvQOaVtjcUvwamX61Xmh8t2bz6WgNotOLmfntSfLKVPTyd2XLkqFmPy27NsqUGuatDTfUTm1YMITQZuzYaUl+PHmFz6vE9ztT+5j8cNf398aTWaygQxtHnhrXrdlfb1+MWC4xoaefyRZb/5do1umCnp6ebN68uc7Hg4KCatj6BwYG8s8//9x0vx06dGD37t1GWaNEw9HXu9jVIXDG9/DF1lpOYl45K/4QvTHu6N32urZyYyCTyXhvWl8mfHKEiCuFrDuWxKJbOvHenlgSc8vxdbXjnam9zeJgczA2m2d/PgvA3GEd+L9xXVp5RcbjTEohc6tMCkMC3dkw37Ja3fWUKtTMXxfO6SuFuNhZ88PCIQww4QhHQ/grJovXfhOjIU+O68oDQ27uQN6ahCUVGKwpVk7t0+ydk5UqLfsviALnjj5SesoUMM2SdwmTRi9w6orguNjbGLqpoqraJac346Trdu4OvFw10O+DffFsPJHMD1UjIT64L8Qk7eKv5VRiPo9tOoNWJzClnz+v32267bYNJSypgIe+P2VwYP5xoWWKmxKFmjlrwzh9pRBXe2t+XBRqMeImLKmAJ7ZEohNg5uBAnhrfPPObjEWZUmMw9bx/UGCL1LD9HJFKmVKDn5u9xfy7mzuSwJFoMJqqNNCNCnbvCrmajmrn7tCsplogHnRv6eqFUqPj1d/EFM9DQzuYhQ9FdHoxi344bZgv9cH0EORmUgx9M44l5DF3bRjlKi3DO7fhhwVDmiWS19rklymZ9d1JIlOKcHOwYdOioYQEurf2soxCdHoxC9dfnX/29hTTj4i+82csqQWVtHN34JW7mt/Uc1t4Cq9VHXeyixX8dFqyIjEFJIEj0WDkVQe3GwwN59ZqPh8d2jg2+wlbn6qqTnOaeRmLxNwyMXWj1DCko6dJe4k0lL9ispi/XjSBG93Nm7XzBuNo26xZ8VYhvaiS6d+cIDq9BE8nWzYvDrWYlv7avp+mPnrg7/gctoSJ4xg+nB7S7II6s7iS5TvOG/4WgJd2RJNZXNmsrytxc0z7myphkly9eKtb4RRVG6GgbcRQzMYQnV5c4++kvPIWed3GklFUyUNrwsgvV9G7nSvfzx2EvY15OCzfjF8i0nh00xlUGh239/Tl2zkDLea9VSchp4z7vjpOYm45/m72/PzIMHr5W4a4McfvZ1GFihe3nwNg4ciOLTLnKymvnGsPcVpBIDmvovYNJFoMSeBINBh9BOdGuqX6IMzz6cWUKzXNuqa8MiUvVbuKAnhyaxSVKm0dW7Qu+VXDM9OLKunk7cQP84eYtFFaQ1h/LIlnfz6LVidw74B2fDl7AHbWpn1ibAzn04qZ8c0JMosVdPZ2Yvujw+nsbRlOzPllSh40s++nIAi8/Gs0OaVKuvg48/yE7i3yurW5i1vJZAR5mYcthSUjCRyJBqPPNunqyFEJglBD4FSotPx5PrPZ1iMIAi/vPE9+uYpgPxdOLh+Ht4sdCTllvLs7ttlet7GIwzPDuVx11b9xYShtnM2/XVoQBD47cIk3qjrn5g0P4sP7Qkw+pdEYTlzO54HvTlJQrqJPOzd+engY/u6WYctfXCkWSyea2ffz59Np/HkuE2u5jI9nhLRYtCm/TFXjbyuZjHfv7S2NaTABLO/II9Hs6IuLNdraBU5cVikJOWXYWssNoxF+bsaiu52R6eyLycbGSsZHM0Lwc7Pno+khAGw8eeW6uVitiUKtZdEPpzmfXoynky0bF4XSzgJOjDqdwIpdF/jkgGis+PT4brx+d0+LKZauzv4L2cxdF0aZUsPQTp5sXmweAqA+lFZ1gsVkVA13NZPvZ0JOqcE/6rkJ3ekb4N5ir701XKz3GRfsw5bFQzm6bCz3DzbtFvr/CpLAkWgwDlVXRgp17emfP85mADCmmzfzhgdhJZcRnlxIXFaJ0deSUVRpOLA9Oa6rof5hVDdvFo7sCMAL28+RXaIw+ms3FLVWx9LNZziVVICznTUbFgyxiJSGRiuaLK47lgzA63f35MnxXU2+06Yx/BKRxiM/RqDS6Bjfw5f18y2nK6xcqWH+unDOphbh7mjDpsWhZvH9VKi1PLElikq1lpFdvFhyS6cWe+0KlYZfI8Xjnb7mR4rcmA6SwJFoMA5VnTAVtdS3CILArnNiOuruEH/83Oy5vWoA5w/Hrxh1HYIg8OIv5yhVaOgX6H7dIM3nJ3SnR1tX8stVPLElEo229oGcLYFOJ/Di9nOGidLfzx3U7LbxLYFCreWxTWf45UwaVnIZH00PYf6Ijq29rGZh7dGrtUXTBgTw9YMDTL7otr5UqrQs/CH8qofPwlCC/cxjKPF7e+KIzRQjTh/PaFmLhT/OZlCm1BDUxrHZrTAkGo4kcCQajGOVI2htAudcWjEpBRU42FgxrofYKj53eBAgjiEortZd1VS2hKXy76U87KzlfDTj+loPexsrVs/qj5OtFWFJBXxcNZeqJcksruR4Qh4v/nKOHZHpWMllrJ41wCIOhmVKcd7SXxeysbWW89XsAUxrRkPH1kIQBD7+K54Vu8TaooUjO/JBMw9tbEnEieenOZlYFVlcGGo24ntfTBbrjycD8OGMEHxcW26umSAIhqjlA0PaW2Q61tyxjF+oRIuiT1FVqq/vjNodLUZvbu3hY/A8Ce3oSXdfFyrVWn6OME4tTlphBe/8KZ5wXpgYXGcovZO3s8Ef58vDl/k7Pscor18ftoWnMOK9Q8z6/hQ/R6QB8OH0vozvadrze+pDYbmK2d+f4vhlcd7S+vmDud0CpyfrdAKv/x5jGH763O3deGVSD4s5mSnUWh75MYJ/L10dCtrPTAwKk/LKee4ncbTJopEdGdvd5yZbGJcTl/OJyyrFwcaKmVLNjUkiCRyJBuNsJwqXUkVNgSMIAn9VDZubWO1kJ5PJDFGcDSeuNNkXRxAElu84T7lKy6AOHsyr2ndd3B3iz5xh4tDKp7dFkVHU/AZcevOv6m9VJsMiIjfZJQru//ZEtVqNoRYzKbs6CrWWpVvOsOHEFWQyeGtKb5beajm1RQq1lsUbTnM4Phd7GzFtOijIs7WXVS8qVBoe/TGCUqU4/uPFO1re1HPN0SQA7hsYYJGjRywBSeBINBgPJ3G2U2F5zXRTQk4ZSXnl2FrJGdO95oiEKf39cXOwIaWggr3RWU16/W3hV1NT79/X94YjI/S8PKkHfdq5UVSh5rFNZ1BqmtcfpzbzL0HA7M2/EnJKuffL41zMLsPX1Y6fHh5mNlf8DaGoQsWcNWHsPp+FjZWMz2b25yELmuxeqRK7+a5GboaYjUgVbSGiicsqxcvZji9mtbz7d2JuGQfjxGjw/BFBLfraEvVHEjgSDaZNlcApKFfWuH9fjChcRnRpc11niaOttSGK89U/CTWmyDeE9KJK3v5T9LZ5fkJ3OtWzy8PO2orVswbg5mBDVGoRr/4a3eg11IcrtQgZczf/irhSwH1fnyC9qJKOXk5sf2Q43XxdWntZRietsIL7vj5BWHIBLvbW/LBgCPeE+Lf2soxGhUqsnTqakFeVXhxiVpHFH0+lsLOqnu2LWf3xbcG6Gz366M24YJ96H4MkWh5J4Eg0GH0Ep+CaguF9VempCXXUYswbHoSDjRXR6SUcTchr8OvqU1NlSg0D2rs3uFunfRtHVj3QH7kMfjqdxuq/Ezh+Oc/oM2P+uZjLa79HA6CPLZm7+df+C9nM+u4URRVq+gW688ujwwn0NF+xVhcxGcVM/fI4CTll+LmKoxfMJbJRH8qVGuatC+dEYj7OdqJ4G9LRPNJSAOHJBaz4Q7SFeHFi91YRZlnFCn4+LdbULR7Vci3pEg3H8ibfSTQ7nk5idKZ6BCenRMH59GJkMhjXo/YiWk8nW2YOCWTdsWS+OnyZW7o2bNL3z6fTOHIxF1trOR9MD6lXaupaRnfz5sWJwazcE8eHf4ldVXIZrLy3j1HMuU4l5vPwxtOotQJ39vFj+R3BpBUqCPJyNFtxs/lUCq/8KtYT3Rrswxez+lvk0MwjF3N59McIylVauvu6sH7BYLP9N6uN4go189aHEZlShIudNT8sHMKA9h6tvax6k1ZYwSMbIwy/rcUt6HdTnW+OXEal1TE4yINQMxKH/0WkCI5Eg/FxEUPCWcVXzfMOx+cC0DfAHW+Xul1dF93SCWu5jOOX84m4Uljv18wsruStqjbdZ2/r1iQDsrtD2tb4WycYZ/rvubQiFv5wGoVax9ju3nx6f38CPZ3M1vxLEAQ+3n+Rl3aK4mbGoAC+fWigRYqbzadSmL8+nHKVlqGdPPnpkWFm+W9WF7mlSu7/9gSRKUW4Odjw46JQsxI3FSoNizdEkF+uomdbVz6cHtIqxd65pUrDpPInLKjg3FKRBI5Eg9Fbt2cUKQx1LPr267HdbxyVaefuwH1VXikf/RVfr9fTp6ZKlaKh36ImXrkl519fH9PU6b/xWaXMWXvVvv+rBwdia22+Py+NVsfyHedZdfASAE/c2oX/TbMc7xc9Op3Au7tjeWnnebQ6gan92/HDgiG4OVhOV0x6USUzvjlBXFYp3i5iYXiIGRWG63QCz/50ltjMErycbflu7qBWE9nfH01EodYREujOLV0tJ3VpqVjW0UqiRfBzEyM4lWothRVq1Fod/14Sa2rq40XxxLiu2FrJOX45n+P1qMX55Uw6h+PF1NSH0+vXNXUjOno5UdsuAjwaV6yYlFfOg2uu1qd8P3ewWTvcVqq0PLwxgq3hqchl8PaU3jx7e3eLu1qtVGl5dFME3x5JBOCp8V35eEaIRU0+T8wtY/pXx0nKK6eduwM/PzyM7n7mVRj+2cFL7IkWu9m+fnBgq83GyilVsPGE6Mb+5LguFvd7sEQkgSPRYOxtrAxpqIyiSiKuFFKm1NDGyZY+9XBAbefuwANDAgH4aP/FG3Yz5ZYqDampJ8d1pYtP0w/Obd0cWHlvH6yuOUCtOZrc4H2lF1Xy4PenyC1VEuznwg/zhxh8gsyRgnIVs74/ycE4caTEVw8O5EELao/Wk1OqYOa3J9gXk42tlZxP7+/HU+O7WdRJKzq9mBnfnCSjWEEnbyd+fmQYQV5Orb2sBrE9Io3PqqKI70zt06o+PZ8fTKBCpaVfoHuLmwpKNA7zPRJLtCrt3B3ILVWSWlDBhUxxiObIrl71dnh9fGwXtp1OJeJKIYfjcxkbXPsB480/YiiuVNOzrStLjNixcP/g9ozq5k1yXgWJeWW8vDOa9ceTCWrjyLx6dmfllCp48PtTpBdV0snLiY0LQ83a8Cu1oIK568JIzC3H1d6aNfMGM9hMjN8awoWMEhZvOE16USUejjZ889Ags+okqg/HE/JYsjGCMqWGnm1d2bBwCF5mNvH86KU8lv1yDoBHRndmxqDAVltLcl65ofZm2R3BFiWELRkpgiPRKDp5i1eCCTllhpbvEQ1op/VxtWfusCAAVu6JrXUQ5oEL2ew6l4lcBv+b1tfoZl5t3RwY1rkNs0M78OJE0Ql1xa4L7L+QfdNt9UZw+tD/j4tCb1hcbeqcTS1i6pfHScwtx9/Nnl8eHW6R4mZfTBb3fX3c4OWz47ERFidu/jibwdx1V+vBtj481OzETWxmCY/8GIFGJ3BPiD8vTOjequv58K94NDqBsd29zcoz6L+OJHAkGkUXH7GLKSq1iHNpxQAM79KwH/5jY7rg4WjDxewytoTXnFFVqlDz6m+il8ziWzrRJ6B5h/89MroTMwcHohNg6eYzhCcX1PncUoWauWvDiMsqxcfFjs2LQ/FvpboAY7A3OpP7vz1BXpmYZvvlseF0tSADP/3A0/f2xPLwxggqVFpGdvHi18dG0NHMUjY3Y+3RJJ7YEmlopV4/fwiu9uYVVcwsrmT+unDKlBpCO3rywfS+rTr762xqEbvOZSKTiXPvJMwHSeBINIouVW3aB+Ny0OoEgto4EuDRMOM3N0cbnr6tGwCf7L9IceVV48AP9sWTWaygvacjT43vZryF14FMJuOtKb25NdgHpUbHwvXhxGWVXPe8SpWWhT+c5mxaMR6OYrtthzbmeZIUBIFvj1zm0U1nUKh1jO7mzc8W1h5dfeDp1/+IxcTzhgexfv5gs04nXosgCLy3J84w8XzusA58/sAAsyt2L6pQMW9tOFklCrr4OPPtQ4NatehbpxN4o8pYcGq/dvRo69pqa5FoOJLAkWgU+giOnmGdGxe2nTWkPV19nCkoV/HFIbGY8HRyARtPit0KK+/tg4NtyxzgbKzkrJ41gIEdPChRaJi7Noy0wqut4yqNjkc3RRCWVICLnTUbFoSa7agCtVbHy79G8+7uOAQBHhragTVzB103YsOcqWvg6cOjO1lUu7tCreXJrVF8/c9lQBxh8sY9vZrcbdjS6F2W47PFyOi6ea0vQndEphOZUoSTrVWrDPSUaBqW8yuXaFHaezriUO3qsLH1GtZWcl6e1AOA9ceTickoZtmO8whVxnIjurSs14SDrRVr5w6mm68z2SVK5qwJI79MiUar48mtkYbJy2vnD272tFlzUaJQs2B9OJtPpSCTwat39WTF5F4WddIH2BedZZEDT6tTUK7ioTWn+P1sBtZyGe/f15fHx5pfC7NSI1oTRKWKRoQbF4a2+iiQEoWa9/bEAaK1RWvMvJJoGlIXlUSjsLaS09nHieh0MY0zqEPjCzXHdPdhXLAPB+NymLTqKABezna8fGdPo6y1obg52rBhQSjTvjpOYl45s78/RYCHAwdic7C1kvPdnEFmW4CbVljBgvXhXMwuw8HGilUP9Oe2nrWP1jBXBEFg06kU3v7zwnWPmfvA0+ok5paxYH04yfkVuNhb8/WDA1v8gsAYaLQ6ntwSxdEE/WTzwSbh1bPqwCXyypR08nJiQQPn3kmYBpZ1ySbRosi4epUY6Nm0uo03J/eq8feKyb1aNTzt52bPhoVDaONkS1xWKQdiRafmz2f1b/AMLVMhKrWIKauPczG7DJ8qR1tLEzdKjZblO87zyq/RaHTQp52bwdTR3AeeVudUYj73fnWc5PwKAjwc2PHocLMUNzqdwLId59kbk2W4eOhvAiMkotOLWXc8GYDX7u5p1q7k/2WkCI5Eo1FXa+1uakj8WndSUxhi18nLic4+zuQnXe2oGmmGJxEQO6We2haFQq0j2M+FtfMGm3XnV21klyh45McIIlOKxI6XCcE8MroTWSUKkvMqzHrgaXV+Pp3KyzujUWnFkQHfzxlklhYFOp04gmV7RBpymXjxYAoiTaPV8eIv59DqBCb1acsYydTPbJFkqUSjqV7EqFBrm7Sv7RFpNf5++8/YJu2vqQiCwIpdFwhLqtkuvvCHcCpVTXuvLYkgCHzzz9VOqbHdvdn+6HCLEzcnLuczadW/RKYU4Wpvzfr5Q3h0TGdkMpnB78jcxY1Gq+OtXRd4fvs5VFodd/T2Y+vioWYrbl7aeZ5tp8VxIJ/O7M+EXn6tvSwAvvs3iZiMEtwcbHjjnl4330DCZJEEjkSjKVFcbetuyGTwayksV/HublHQ3NnHD7kMdkamsy8mq8lrbAz6ltt1x5IBeH9aX359fATOdtacTCxg0YZwKlSaVllbQ1CotTz701lW7hE7peYO68B3cwaZ9SiJa9HpBL48nMDs70+SV6Yi2M+FP54Yyehu5plGrIviCjXz14ez5mgSII4tWT1rQIt1GBoTnU7g5V+jDbPOPrm/H/eE+Lf2sgCxrumTAxcBsfjeHMWjxFWaVeAUFBQwe/ZsXF1dcXd3Z+HChZSVldX5/OTkZGQyWa23n3/+2fC82h7funVrc74ViWsoqlCRWlBp+PvE5fxG7+u9PXEUVqjp7uvCZzP78/DozgC8tOM8eWXKJq+1oXy8/yLfVA1gfHtKb2YMDqRfoDvr5w/GydaKYwn5zFsbTmk1gWdqZBUruP+bE+yITMdKLuPNe3rx5uTeFtUpVVyhZsnGCN7fG49OgHsHtGPnYyPM1peoLhJyypjy5TH+vZSHg40VX84ewNO3dWtV87vGotMJvPJbNFvCUpDL4OMZ/Zjcr11rLwsQI2TP/XwWlUbHLV29mDbANNYl0Xia9Wg3e/ZsYmJi2L9/P7t27eLIkSMsWbKkzucHBgaSmZlZ4/bmm2/i7OzMHXfcUeO569atq/G8KVOmNOdbkbiGmIyaJngnEhsncMKTC9h2WnQxfmdqb2ys5Dw1vivBfi7kl6t4eef5Gw7jNDarDl7i80MJALx+d88agyYHBXmycVEoLvbWhCUX8NCasBrmhKZCxJVC7v7iqMGMcOOCIcwdHtTayzIq0enF3PXFvxyIFYdlvju1Dx9NDzHLiMaNOBibzdTVxwwjQbY/Oow7+7Rt7WU1itSCcuauCzPYE3w0I4Qp/U1HRKz++zJnUopwsbNm5b19zK7VXuJ6mk3gxMbGsnfvXr7//ntCQ0MZOXIkn3/+OVu3biUjI6PWbaysrPDz86tx27lzJzNmzMDZuaaxnLu7e43n2dtLHgUtSXxWKQA9q5w9z6YWNfhkr9bqeHnneQBmDg40TAq2s7bi4xn9sLGSsS8mm1/OpBtx5XXz9T+X+Xi/GJ5+6c5g5tfSGjqgvQebFw3F3dGGqNQiZn13ksJyVYusrz78dDqVB749aZhu/vvSkQxvYOFmZnElxy/nkVlcefMntzCCIPDjySvc+9VxUgsqCfBw4JdHhzMrtL1FnZC0OoGP/opn4Q+nKVVqGBzkwW9LR9DL3zy9l348eYVb3j/Mv5fEuXX3Dwpkav+AVl7VVc6kFLKqymj0rSm9G+zKLmGaNJvAOXHiBO7u7gwaNMhw3/jx45HL5Zw6dape+4iIiCAqKoqFCxde99jjjz+Ol5cXQ4YMYe3atTe8ylcqlZSUlNS4STSNSzliqvHWYB+6+Dij0Qkcjs9p0D7WHE3iYnYZnk62hmGXenr6uxpGNLz2WzQJOXWnNo3BmqNJBlOv5yd0Z8moznU+t0+AG1sWD6WNky0xGSXc/+2JVhcDGq2ON/+I4YWqAtSJvfz45dHhDTZL2xKWwvCVh5j13SlGvHeIbeEpzbTihlOiULN0SySv/BqNSqPj1mAfdj0x0mwNF+uisFzFvHVhhkjivOFBbFpkfgMz9STllvPKr9E17vv5dFqr/2b0lCk1PL0tCq1OYHI/f5OKKkk0jWYTOFlZWfj41Gyvs7a2xtPTk6ys+hWPrlmzhh49ejB8+PAa969YsYKffvqJ/fv3M23aNB577DE+//zzOvezcuVK3NzcDLfAwMCGvyGJGiTkiBGcrr7OBi8VvVdMfUgrrODTA/poSQ88nGyve84jozszvHMbKlRalm4+0+ROrbrYeCKZt6pm+PzfuK48PrbLTbfp0daVbQ8PxdfVjovZZdz31YlmF2F1UViuYs7aMENR9NPju/Hl7AE4NbCYOLO4kpd2nEd/qaAT4KUd0SZxIjqXVsRdq47y57lMrOUyXr6zB9/PGYS74/XfG3PmXFoRd31+1FBv8+n9/Xjjnl5m68NSolDzyI+nr7tfKwgm4SgtCAKv/hrNlfwK2rk7sGJy79ZekoQRafCvZtmyZXUWAutvcXFxTV5YZWUlmzdvrjV68+qrrzJixAj69+/Piy++yAsvvMAHH3xQ576WL19OcXGx4ZaamlrncyXqhz6C09XHhfE9RIFzOC4HlUZ3o80MvPNnLAq1jiEdPess5rOSy/h0Zj+8nEWzvTerht4Zk61hKbz6m7jfR0Z35unxXeu9bRcfF355dDidvJ1IL6pk+tfHiUxpfDdZY4jPKmXy6mMcv5yPk60V3zw0kCfHd21UAWpSXjnXxkG1gsCl7FLjLLYRCILA2qNJTPvqOCkF4kno50eGsXhUJ7Mssq0Lfertvq9PkF5USVAbR3Y+PtysowkZRZVM/+oE8dnXC39TcZT+8VQKO6sK8T+d2Q83B8uZxSbRCIHz7LPPEhsbe8Nbp06d8PPzIyen5hW9RqOhoKAAP7+b+x1s376diooK5syZc9PnhoaGkpaWhlJZe8eNnZ0drq6uNW4Sjae4Uk1RhVhvE+TlSP9Ad7yc7ShVajiWkHfT7Y8l5LEnOgu5DN68p9cNayd8XOz59P7+yGSwJSyVnZFpdT63oWyPSGN5VQ3QwpEdeXFi9wbXcQR4OLL9keGEBLpTWKFm1nenGpyqayx7o7OY+uUxUgoqCPR0YMdjI5rkJdLRy4naNMPK3XGkFrT81XZemZJFP5xmxa4LqLUCE3v5sfv/bjEJp1tjUqJQs3Tz1dTbbT19+f2JkQT7me9xKi6rhHu/PG4YnPl/47pgVfXbMhVH6ciUQlZUXTQtvyPYbMevSNRNgw0xvL298fa+ucfEsGHDKCoqIiIigoEDBwJw6NAhdDodoaGhN91+zZo13HPPPfV6raioKDw8PLCzM88ctbmhP9l5OdviaCt+he7q25b1x5PZEZnO2OC6nT/VWh2v/y4eVB4a2oEebW9+EB/Z1YsnxnZh1aEElv1yns7ezvQNcG/Se/gtKp0Xtp9FEGDOsA68MqlHo4tUPZ1s2bwolEc3neHIxVwW/XCat6b05oEh7Zu0xrrQaHV8sC/e0Mo+vHMbVs8aUGuaryG0dXNg5b19eGlHNFpBQC4TC75js0qZtOpfPpweQp8AN5Lyyuno5dSsJ6jD8Tk89/M58sqU2FrLefnOHswZ1sGiColBLM5/YkskKQUVWMtlvDgxmIUjO5p1dOp4Qh4Pb4ygVKmhi48z6+cPJsDDkQeGtDcZR+n8MiWPbTqDWitwR28/Fo6UZk1ZIs3m+NWjRw8mTpzI4sWL+frrr1Gr1SxdupSZM2fi7y+aOqWnpzNu3Dg2bNjAkCFDDNsmJCRw5MgRdu/efd1+//jjD7Kzsxk6dCj29vbs37+fd999l+eee6653orENaQVigKnXbVOg3sHtGP98WT+ismiVKHGxb72UO8Px5NJyBELi5+5rXu9X/PJ8d2IzijhUFwOSzZE8PvSEfg0crrvr5HpPPNTFDoBHhgSyBt33ziKVB+c7Kz5fs4gXvzlHDsj01m+4zzJeeW8ODHYqCernBIFS7dEGhyWF47syPI7go3mb3P/4PaM6uZtOBFpdQJLN0cSlVrEko0RhufJZbDy3j7cP9i4Ik6h1vLenjjWV80B6ubrzKoH+pt1NKM2BEFgzdEk/rc3DrVWIMDDgc8f6G/20alfI9N5fvtZ1FqBIUGefDtnoKFOqq2bQ6sLGwCVRsdjm86QWaygk5cT79/X1+KEs4RIs1aubdq0ieDgYMaNG8edd97JyJEj+fbbbw2Pq9Vq4uPjqaioGf5eu3YtAQEB3H777dft08bGhtWrVzNs2DD69evHN998w8cff8zrr7/enG9FohpphWLRaYDH1YNVn3ZudPZ2QqnRsSe69iLy3FIlnx0QWzFfmNC9QcM09Tnyzt5OZFXNHFJqGl50vONMmkHc3D8okHem9DGaALG1lvPxjBCeqqrj+eZIIo/8GGE01+OTifncueooYUkFONtZ8+XsAbx6V0+jm/dVH20Q4OHITw8P44HBNQvzm6MAOT6rlMlfHDOIm3nDg/h9qXmnamojt1TJgvXhvP1nrCGC8KeZp950OoH398bx1LYo1FqBO/v4sWHhEJMrAhcEcUTEqarf0NcPDazzYkzC/JEJLemiZiKUlJTg5uZGcXGxVI/TCFbujuWbI4ksGNGR1+7uabh/9d8JfLAvnv7t3dn52Ijrtnvu57Nsj0ijb4Abvz42otGFsJO/OEqJQsO9/dvx0YyQel99bY9I4/mqtNQDQ9rzzpTezZYK+C0qned/Flu2e7dz5fs5g/Fza1zESRAEvjmSyAf74tHqBLr7uvDVgwPo5O18842NxPHLecz67np7hy2LQxnWuWkDErU6ge//TeSjvy6i0urwcrblg/tCbpjqNFf2X8hm2S/nyC9XYWst59VJPXhwqHmn3vRt1vsvZANisf4LE7qbZJrty8MJvL83HrkM1s4bLA3SNEMacv42z95DiVYlr0w0tvNyqXl1NmNQILZWciJTijiXVlTjsTMphYaBmm/e06vRB7+OXk58MWsAVnIZOyLTeX9ffL22+yk81SBuZoc2r7gBmNyvHZsXh+LpZEt0egl3f3GU8OSCm294DcWV4jiC9/bEodUJ3Nu/HTsfH96i4gbqLkD+7OAlsksUjd7vlfxyZn57gpV74lBpRW+bPU+OsjhxU67UsHzHORZvOE1+edXMrKUjeWhYkFmLm9SCCu776jj7L4iO0h/PCGHZHcZNyxqLPeczeX+veLx4455ekrj5DyAJHIkGo58Pda3xmLeLHZP6ijby+jQDiOHrN/8QfWbuGxjQ5FD8qG7erLy3DwBfHb7MD9Veqza2hqXwwi/nEASxsPntZhY3egYFefLrYyPo7utCbqmSB749ycYTyfUePRGTUcw9Xxw1nDzendqHj2aEGAq7WxJ9AbK+E0YmE9OGJxMLuP2TI/wWld6gkRr6tug7PvuX8ORCnGyt+N+0PqyZO8jiBhxGphQyadW/bAlLRSaDJaM68dvSEXT3c2ntpTWJYwl5TF59jLisUryc7dj68FDuHWA67sTVOZ6Qx5NbowAx9TlnWFCrrkeiZbCcscISLUZRhRjB8awlvz5nWAd2Rqaz62wmy+4IxsfFnj/OZXA2tQgnWytemFj/wuIbMWNQIDklCj786yJv/BGDt4tdrTN6Np9K4aWqVvB5w4N4/e6eLXrF3L6NIzseG84Lv5zjz3OZvPpbDGfTinl7Sm/sbeqem7QtXPTnUWl0BHg48NXsga3u2HttAXKpQsMzP0URnV7Ck1uj2BeTxVuTe9PmJo676UWVLN9xniMXcwEY2smTD+4LabDrsqmjUGv57OAlvvnnMjoB2rrZ89H0kAaPzjA1dDqBr/65zEd/iUNOe/m78t2cQfi7t34BcW2cTS1i8YbTqLQ6JvTy5ZVJPVp7SRIthCRwJBpMuUos7nW0u/4E3b+9BwPau3MmpYjvjiTy7O3dDWHhR0Z3xsfFeDPDHh/bhewSJRtPXuHJrZE42FjVSG38ePKKwSJ+/oggXrurZcWNHic7a754oD8hAW68tyeO7RFpxGeVsnrWANq3qXlSL1NqeO3XaHZEivO3bg324eMZISZTrFm9E6atG+x8bASr/07gi0MJ7D6fRVhSAe9M7VOrH49OJ7ApLIX3dsdSrtJiZy3nxYnBzBseZJIpjaYQmVLI89vPGdyt7wnx563JvRtUWG+KFFeoeeanKA7GiV5P0wcG8NZNxHprkpBTyrx1YZSrtAzv3IbPZvY3elG+hOkiFRlLRcYNZsR7h0gvquTXx0fQL9D9usf/js9h/rpwHGyseGhYB749koifqz1/PzfG6NOetTqB/9sayZ/nMrG1lvP9nEGM6ubNhhPJvFblULxwZMcm+dwYk6OX8nhiyxkKK9S42Fnz3rS+hrReVGoRT26N5Ep+BXIZPHt7dx4d3dksTv7R6cU881MUF6tca+8O8ef1u3sa0pjJeeW8+Ms5TlW1tw/s4MH/pvWli0/L1hI1Nwq1lk8OXOS7I4noBDGN+/aU3kzs3XgDRlMhOr2YRzdFkFpQia21nLcm9zK6TYAxSc4rZ+a3J8kqURAS4MamxUNxbuD4EgnToyHnb0ngSAKnwfRf8ReFFWr+enoU3XyvryMQBIHJq49xLq3YcN9H00OYNrB58vNqrY4nNkeyNyYLO2s5o7t581dVR8eSUZ1YfkewSYgbPelFlfzflkgirohjHR4Y0h5vZ1u+PHwZjU6gnbsDn87sZ3bOqkqNlk/2X+LbI2JKxt3Rhpfu7EFxhZqP9sejUOtwsBHTlHOGBWFlBsKtIYQlFbB8xzku55YDMLV/O167q2eTDRhbG51OYO2xJN7fG49KqyPQU0yZ9m5nukNOE3PLeOC7k2SXKOni48xPDw/D08z/HSREJIFzEySB0zRC3vyL4ko1B54ZXecV+MHYbBb+IA7Za+NkS/jL45s1EiGad0XUGPj58OhOLJtoWuJGj1qr45P9F/ny8OUa90/q25Z3p/Yx65k459OKeeGXc8RmltS4f0SXNrx3b1+Lq7UpqlDx3p44toaLM+68Xex4d2ofwxBacyanVMFzP58z1Evd1tOXD+8LMelUW0KOKG5yS5V083Vm06KhFle4/l+mIedvKV4n0WCu6oW6tXGQl5Ph/22s5M2eZrG1ltO/vUcNgdMvwN0kxQ2In0lt4yYGdfDAxczD6EFejgzq4HGdwLmlq3ejvYBMEUEQ+C0qg7d2XSC/XCy8f2BIIMsm9jBpAVBf/o7L4fntZ8krU2FnLefVu3oyO7S9yf6mQDSLnP39KfLKlAT7ubBpUehNi94lLBfzPpJKtAryqgOc7gaxvw/2XvWnySpREJlS2GxOrYIg8OmBS3x28FKN+x/ffIb37u3LjGtceFubSpWWt/68wOZTKQD4udpjYy0jtaCSN/+4wIHYbD64L8Rku1LqQhAE9sVk8cbvF8iq8sYJCXCjTKnhcm457+2J45eINFZM7s2wzm1aebVNIymvnNd+i+bfS+Jw2a4+zrx7bx+zSyvWRplSw8rdsWyq+n4G+7nw+QP96VpLOtqUOJWYz6INpylVaOjZ1pUfF4VKaan/OJLAkWgwNlaiwFFpdLU+fj6tmL0xWchk0DfAnbOpRbz+eww7Hh1u9A4GQRB4d3cs3/2bBMDzE7rzyOjOvLzzPFvDU3nhl3MUVKh4eFQnk7jyvJBRwv9tjTR01zw8uhPP3tYdGysZP568wju7YzmWkM+ET4/w5j29mNq/nUms+2Yk55WzYtcFDlV113Ro48hbk3szqps3Op3A9jNp/G9PHJeq0geT+/nz8p098HG1J7O4skUGeBqDcqWGzw8lsOZoImqtgK21nP+7tQtLRnXG1tr8u3OOJ+Txwi/nDONY5g0PYtkdwSbbJaVnz/lMntwWhUqjY1AHD76fO8hkOg8lWg+pBkeqwWkw4z/+h4ScMrYsHlrrlfi8dWEcjs9lav92LL8jmPEf/0OJQsPyO4J5eHRno61DpxN49bdow5Xm63f3ZP4IcSqwIAi8tyfOMHH7gSHteXRMJ9IKK1vlRKrW6vjq8GU+P3QJtVbAx8WOj2f0Y2TXmp4oibllPPPTWaJSiwAY38OHFZN7m2w0p0KlYfXfCXx3JAmVVoeNlYyHR3Vm6a1drjspFleo+fCveH48dQVBAGc7a0Z382ZPdCY6ofkGeDYFvfgKauNIeHIh7+6OJbtENLoc1c2bFff0qpGONVfKlRre2xPHxpNXAHHO3PvT+pqFZ8/GE8m89nsMggC39/Rl1QP9TV6QSTQeqcj4JkgCp2lM/fIYkSlFfPPQwOv8Tk4nF3Df1yewlss4+OxoOrRx4qfTqbyw/Rx21nL2PHmLUcYMaLQ6Xth+jh2R6chk8L86UlFrjibx9p8XqP4tb+kT6YWMEp7ffpaYDLEm5faevrw3rW+d4XONVsfX/1zms4OiGHKyteLFO4J5MLSDybSMC4LArnOZvLs7lsxiMR11S1cvXr+7101bv8+nFfPqb9EGEVcdK5mMo8vGmkQkZ1t4Cst3nL8uFdve05FX7+rJ+B4+ZhFduxl/x+fw6q/RhqjN7ND2LL+zh8m3VKu1Ot7adYENJ0RRNiu0PW9N7m1x3XkSNZGKjCWaFfeqDp/CqsJKPYIg8EHVbKjpgwLp0Ea8sp0+MIA/zmbw76U8nvv5LNseHoZNE1JVSo2WJ7dEsTcmC2u5jI/v78c9If61PnfhyI642lvz/PZzhvv0k7BHdfNu1hOpWqvjy7/FqI1GJ+DuaMOb9/TinhD/G54Yra3kLL21K7f38mPZL+c4k1LEa7/F8GtkOu9N61tra35LEp1ezNt/XuBkouhpE+DhwKt39eT2nr71OuH3CXBjx6PDeW9PLN9WpRb1aAWB5LyKVhc4mcWVtYqbh0d15OnbultEhCCrWMGKXTHsPp8FQDt3B96/ry8jzCBqU1Cu4rFNEYbv4PMTuvPYmM4WITgljIckcCQajD5dkl5UWeP+Ywn5nEoqwNZKzhO3djHcL5PJWHlvH+747F/OpBTx4b54lt/ZOLv0CpWGR388wz8Xc7G1krN69oCbtuO287j+ZNncJ9ILGSU89/NZLmRejdq8PbV3g5ycu/m6sP2R4Ww6dYX/7Y3nTEoRk1b9y4IRHXliXNcWv8LOKlbwwb54dkSmIQhgZy3n0TGdeWR05waf8OVyGfNHduT7o0nXiYjNp67Q0cup1TquShVq3tsdV2sR/ZjuvmYvbrQ6gQ0nkvnor4uUKTVYyWXMHx7EU7d1M/moDYi/rSUbT5NWWImTrRWfzuxvES35EsbH9L/NEiaHXjCkF14VOIIg8PF+MXoze2j762pGAjwc+eC+vjzy4xm+OZLIkI6ejOvRsINSUYWKBevDOZNShIONFd/NGXRdDUtt6CdhX3vC+j0qnUFBHk2KJl1LY6M2dSGXy3hoWBDje/ry6q8xHIjN5psjieyITGf5HcEtUoRcrtTwzZFEvj1yGYVaLCy/J8SfFyZ2J8Cj8Z42+gGeL+2IRisIyBCNB/44l8lfF7KZOzyIR0d3bjGjPJVGx5awFD47eImCa6KTIKbPgrzM28PnVGI+K3ZdMKRL+wW6887U3vTyN13TPj2CILA5LIU3/7iASqOjQxtHvpszqNUjmhKmi1SDI9XgNJhd5zJYujmSfoHu/Pr4CABOJuYz89uT2FrLOfri2DojFW/8HsP648m4Odiw47HhdK5nPU5mcSVz1oRxKacMNwcb1s4bxMAO9W/J3Raect2JFETfmU9n9mvSiVpPTEYxz/98zhC1mdDLl7en9DGqydihuGxW/HGB5PwKQBx58OY9vZrFVVat1bE1PJVVBy+RW6o0vN4rk3oYteU/s7jSMMAzo6iS9/bEEZ4sujy72FmzZFQnFozsiFMzRRc0Wh07zqTz2cFLhqhkJ28nRnbxYtPJK2gFUdy8e29vkyqAbgipBRWs3BNrSEe52Fvz4sRgZg1pbzJ1XXWRWVxJTEYJm0+lGLr0xnT35tP7+0mdUv9BpCLjmyAJnKZxObeMcR/9g72NnOg3JmBtJWfu2jD+uZjLg0Pb8/aUPnVuq9LomPntCc6kFNHe05Gdjw2/qRFXQk4Zc9acIqNYgZ+rPRsWDmnUVVv1E+nZ1GKe//kspUoNLnbWvDm58S3Z5UoNnx64yNpjyWh1Ah6ONrw5uTd3923bLNEVpUbLmqNJfHEogQqVFpkMpvZrxzO3dzOKUNPpBH4/m8HH+y+SUiAKqfaejiy7I5g7evs1e8RIEAQOx+fy/r54g1mgl7Mtj47pwqwh7Y02z0yrE/j9bDqfHbhkEIw+LnY8Ma4rMwcHYmMlr/Gdae26oMZQqlCz+u/LrD0qdrnJZWJH4dO3dTPMCTNltoWnsGzHeUOTgFwGy+4IZtHITiYvzCSaB0ng3ARJ4DQNnU6gzxv7KFdp+evpUai1OiatOopcBoefG3vdhOxryStTMvXLY6QWVDKwgwebFoXWWdcQlVrE/HVhFFao6eTtxMaFobQzUsv0lfxynt4WxZmUIgDu7OPHO1P6NCglcuBCNq//HmO48r+zjx9v3tO7RazhM4srWbk7jt/PZgBgayVnzrAOPD62S6PSOoIgcCguhw/2xROXVQqIwmLp2C48ENoeO+uWrT3R6QT+OCcKrStVAsTL2ZbFt3TiwaEdGh3R0Wh1/Hk+k88PJRj8iNo42fLomM48OLSD2dfYgDj088eTV/jy8GVDum1kFy9euasHwX7mccxLzitn7IeHa/ily2VwbNmtZik2JYyDJHBugiRwms7Mb09wMrGAt6b0JiypgD/OZnBPiD+rHuhfr+0Tckq598vjlCg0jO7mzTcPDbzuxPLvpVwe3hhBhUpLSIAb6+YPMbozqb4l+9MDYs2Mt4sdb9zdizv73DhSkVZYwVu7LrAvRhzqGeDhwFuTezM22Meo66sPZ1OLeG9PHCcS8wEx/fDI6M7MGx5ULxGgFzarDl7ibNWAVP0+5o8IwtG2dUv11Fodv0SkXz7z+wAAIYVJREFUsfpwAqkFopD0cLRh0S2dmDOsAy729RuLoNRo2XEmna//uWwQTG4ONiwZ1anen5Wpo9bq2B6RxqqDlwzt+528nHjpzh6MM6O29jMphSzddIaMqvdQnbr8tyT+G0gC5yZIAqfprP47gQ/2xdPZ24nE3HIEYM+Tt9Cjbf0/z7CkAuauDaNSrWVsd2++fmigIUqwPSKN5TvOodYK3NLVi68fHNisJ6DzacU8/VOU4Yr+1mAf3ryn13WDIRVqLV//c5mvDl9GqdFhLZex6JZOPDmuq9FSJ41BEASOXMrjvT1xhrTOzUSAIAj8dSGbVQcvGYpOHWysmDs8iEdGdzK5+ga1Vsevkems/jvBkFJytbdm9tAOzBsehK9r7XVfFSoNm0+l8N2/iQaTPndHG+YP78j8kUG41lMgmTIarY4/zmXUSLf5u9nz5PiuTBsQYHQH8eaiuFLNJ/svsuFEcq1dbKbkkyTROkgC5yZIAqfpnEsr4p4vjtW473/TGm6ed/xyHgvWh6NQ6xjb3ZsvZg3gmyOJrKqaK3VPiD8fTg9pERt8hVrLl4cv89XhBNRaAQcbK54a35X5IzpiYyXjrwvZvLXrgsEQLbSjJ29O7mVSIX+dTuC3s+msOphAUl45IEYpFo7syLwR4slco9WxJzqLLw9fNoghR1srHhrWgcW3dDL52gyNVseuc5l8fugSl3PF92hjJWNyv3YsvqUT3f3E+qzM4ko2nLjC5lMpFFeqAfB1tWPxLZ14YEh7i4jYKNRafjmTxtf/XDZEt9o42fL42C7MCm1vNuk2QRDYcSadlXtiySsTU2pT+7ejb4Abb++KRSsIZl/oLWEcJIFzEySB03TSCysY8b+/a9zX2KurYwmiyFFeM9tq7rAOvH53rxYvJkzIKeOlnecJSyqo9fG2bva8dGcP7mqmImJjoBcBqw5dIrGaCLCSy9DqBNRa8WfvZCtGbBbd0snsBhPqdAIH43L47kgiYclX/63cHW3Q6QTKlBpDFKBDG0ceGd2Zewe0a/FaouagTKlhS1VUKqeqw83TyVYUsmaWbjufVsyKXTGGzrlO3k68eU8vbunqDWD2hd4SxkUSODdBEjhN5/jlPGZ9d+q6+xubH/87Lof568Nr3Neas4kEQeCLQwl8tP9ijftv6erFNw8NbPW6lPqi1QlsPJHMG39cuO6x8T18+XB6X5NLRTUGvU1Bbbw/rS/TBgZYhIV/Sn4FG04ks+10KqUKDSAK7iWjOjFzsPE6zFqC5LxyPvwrnl3nMgExPfp/47qycGRHixhcKtE8SKMaJJqdjrUMGGysEVpKfgVv/3n9CbilRipcS1GFiq//SWT98aTrHvv3Uh5PbY3i/8Z1bRbvGWNyLq2I9ceT2XU2s9bHD8Rm88iPETw4tAO39/Qzy5NKQk4ZW8JS+OVMWp3PefW3aMKSC5gd2p5+ge4mG3WrC0EQOHE5n3XHkzkQm21ome7k5cQjozszpX87s/q3yylR8PmhBLaEpaDRCchkMDnEnxcmBpvsUFkJ80QSOBKNolyprfG3DHj33t4NFiJHL+WxdMsZiirUeDrZUFCurvG4VhC4mF3aIgKnTKlh3dEkvj2SSKlSvDoeHOTBy5N64utqxwf74tkZmc5fF7L560I2t/X05UkTEzpKjZY957NYfzy5xjDLkAA3Fo/qxMRefsRllfLdv4nsOpfJycQCTiYW4OVsy/RBgTwwuP1N2/xbm3Klhr3RWWw7nVojjejvZs/MIe2ZOTgQZ3trfo/KYMOJK1zILGF7RBrbI9Lo4uPM9IEBTB3QrkFjM1qDgnIVO86k8dPpVC5mlxnuv6WrFwtGdGR0N2+z8oJJya/g6yOX2R6RhqoqHT2muzcvTAimp78USZcwPlKKSkpRNQp9F1UbJ1vyq3w2tj8yjEFB9XMXFgSBNUeTeHd3LDoBQgLdeWtyL6asPlbL9GYHPp7Rr977bihlSg0/nrzCd0cSDe8l2M+F527vfl1rbUJOKZ8fSuD3sxmGK+lbunqxYGRHRndtvRNOfFYp28JT2RmZRmGFKBJtrGTc1defucOD6Bfoft02GUWVbA1LYWt4qqGOQyYT/VLuGxjA7T39TCblodUJHEvIY2dkOnujs6hUiwJbLoNbg32ZHdqeUd28r0tDCYLAmZQifjx5hT3RmYZRE1ZyGWO6eXPfwADGBvsYinEziytJyiuno5dTq9R7aHUC/17K5afTqey/kG2olXKwsWLawHbMGx5EFx/zGk0Qm1nCN/9c5vezGYbf9qAOHjw3oTtDO0nt3hINQ6rBuQmSwGk6k784ytm0Ylbe24ezqUVsDU+lu68Lvy0dcdPODYVay/Id59kZmQ7AfQMDeHtKb+xtrGqMVJDLwMnWmlKlBpkM5g4L4pnbuxmtrbe4Us36Y8msPZZk6LIJauPI07d14+6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"source": [
"def vector_func(x):\n",
" return np.vstack([np.sin(16*x), np.sin(18*x)]).T\n",
"cheb_vec = Chebfun.from_function(vector_func)\n",
"cplot(cheb_vec)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Elementary functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, we explore the two ways to create a chebfun.\n",
"First, the general way, which works for any smooth functions:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"f_expsin = Chebfun.from_function(lambda x: np.exp(np.sin(x)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then, the “operator overloading” way.\n",
"We take advantage of the fact that `exp` and `sin` are defined on chebfuns.\n",
"Not all functions are, though.\n",
"This is very similar to ufuncs in numpy."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"g_expsin = np.exp(np.sin(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of course, both chebfuns are equivalent, as we demonstrate here."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"20\n",
"20\n"
]
}
],
"source": [
"print(f_expsin.size())\n",
"print(g_expsin.size())"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
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],
"source": [
"plt.subplot(121)\n",
"cplot(f_expsin)\n",
"plt.subplot(122)\n",
"cplot(g_expsin)"
]
},
{
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"metadata": {
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{
"data": {
"text/plain": [
"6.280369834735101e-16"
]
},
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"metadata": {},
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],
"source": [
"(f_expsin - g_expsin).norm()"
]
},
{
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"metadata": {},
"source": [
"## Approximation Theory"
]
},
{
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"metadata": {},
"source": [
"### Gibbs phenomenon"
]
},
{
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"source": [
"By limiting the accuracy of the chebfun, one observes the celebrated [Gibbs phenomenon](http://en.wikipedia.org/wiki/Gibbs_phenomenon)."
]
},
{
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"execution_count": 33,
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{
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tWWb3ylxNBut/XzrCpXpeIiMjUVRUZPRYUVERFAoFfH1Nd0l5e3tDoVAYfRFR5xIV5Gu4Bw/oPgz/b2qy1V3V+vNePQHoyZutH7QbFeSLYXEhhu/lkmS3emeMiu3weQ/llBu2HtB/hltbq6kaA308UNdo/v5R6ZeUeOCDNBSq6hEa4GU4V0dq09cjb75AfVnv77yAmZ8cxNki0zt3H79Yid+8vw8vrz+FJo1AYkRAh+q49vX13tyciSFLfsZd/9yD+9/fh6GvbcX0j37F7nOl8JLLMD4xzKzXa3F9EhAa4IUGtcDxi5U4XaALLoN7BOPR0bGQmzjnteeQScCUlCjcOzjaqIb7hnTD1ZchAVh6X4pTBu261JiXF154ARs3bkR6errhsYceegjl5eUcsEt0natuUCN58RYAwM/PjkXviECbnbtAWYc/fH4ERy9W4sXbkzB3bC+rzlde04hRS7ehQa3Fojv64raUKJvPYnp9Qwb+d6IA3YJ9semZm1ps8Nie4qp63PGPPSiuasAdA6Lw4u1JyC2rQ1yon01qLVDW4cTFSizddAY5ZbUI8vXE+78dilG9urZ53Nojl7BwbToa1Fr0i1Lgs9nD0aTRIqe01qraCpR1hnPszCzBovWn0Ni8YvHIniEY1TMUIf6eKK5qwO5zpYYp1n5ecsy/NRGzRsehqKq+w3XoX79bFx/8fLoYn/+ai+zmfbr0/LzkuHdwN8y5qSfiQv2Nam7v9a5uG6nwQVZxNc6X1MBDJqFvtALdgn1btDM12+ja5659rEBZhyO5FRACGBrXxab/rl1mwG51dTWysnSpfvDgwXjnnXcwYcIEhISEoEePHli4cCEuX76Mzz77DIBuqnRycjKefPJJPPbYY/jll1/w9NNPY8OGDWZPlWZ4IeqcMgurMOndXQjy9cTxxbfa/Pwr92Rjyf9O46beofjP7BFWnWvF9iy8tSUTyd0U+PGpMW3emuiomgY1bvv7buSV1+LuQdH4+7TBZh+r1mjx8Mf7sT+7HL3DA7DuyRsNty9srbS6AXM+O4SjeZWQyyQ8Pq4nnpyQAD8v49crUNbh/zaewY/HddOPJySG4e/TB1scysyVXVqDNzadwZbThSZvqXjIJNw1KBrPT0qyy6KAQgjklNUis7AKQgiEK3yQ0i0IXh4udUPEoSz5/LbrmJdDhw5hwoQJhu/1Y1NmzpyJ1atXo6CgAHl5eYbn4+PjsWHDBjz77LP4+9//ju7du+Pjjz/mGi9EhMuVukGB+v+DtLUxzfscHcguR32TpsOL4DWqtfiseaG2x25sfYE3a/l7e+BvDw7CAx+kYf2xfNzUOwy/Gdr+8vxCCLz4fTr2Z5cjwNsD//7tULsFF0C3oOB/54zEgu9OYN2xfKzYfh6f/5qHKQOikBQZiIYmLQ7nVmBrRhHUWgGZBDw1IQHPpPbp0IJ+5ooP9cf7jwzFpYpabDlVhFP5StQ1ahDo44EB3YNxa/8IhAfabyVjSZIQH+qPeBvs0XU9smt4GT9+fJvbpptaPXf8+PE4evSoHasiIneUX1kPAIi2U3jpExGAqCAfFCjrsftcaYcXlNuYXoAiVQPCAr1xh4VbAVhqaGwXPH1zb/xt61m8uDYdsV39cMNVY22uJYTA8p8y8fWhS5BJwLsPDkJCeIBdawQAH0853p02GJOTI7G0efG4L/fntWg3PD4EL0/ph5Tujts9u3sXP8weE++w1yPbcPvZRkR0fShS6cJLZJDtVte9miRJmNQ/Eqv35WDTyYIOhRchBFbtzQYAzBgZ65BbAE/dnIDTBUpsOVWEx1YfxMczhmFEz5bjSrRagdc2ZBjq+797U5DawYDWUZOTo3BLv0jsOluCfedLcbG8DnK5hKSIQExICkdyN8eFFnJvDC9E5BYKlc3hRWG/rvzbU6IMWwU0qrUWh4+DORU4cUkJLw8ZHhphm1VH2yOXSXj3wcGYsWo/DuZU4JFVB/Bsah88NibOsA7J2aIq/OX7dBzMqQAAvDSlL6YNd0x9puqdkBSOCUmmF3cjMgfDCxG5hcLmnpcIO4aXobFdEBbojZKqBuzNKrX4A/bDXbp9ge4b0g1dA+zTQ2SKr5cc/5k9Ak//9yh+Ol2ENzafwQe7zqNflAKVtU04XaACoJvNsuy+AbhroH1vZxHZ2/U7rJmI3EqRA8KLXCbhtuRIAMDao5ctOjaruApbM4ohScDvbuppj/La5OMpxwePDMXb9w9EhMIblbVN2He+DKcLVJAkYHL/SGx5ZiyDC3UK7HkhIrdQpNItjW+PaatXu39oDD5Ly8WWU4WorG1EsJ+XWcd9uOsCAOCWvhHoFWb/QbCmSJKE+4Z2x92DonH8UiXyymvh6+mBIT2CEW7H0EfkaOx5ISKXV9+kgbKuCYB9e14AILmbAn2jFGhUa7H+WL5Zx+RX1mHdUV3b349zfK/LtTzkMgyNDcG9g7tjcnIkgwt1OgwvROTy9IN1fT3lUPjYt8NYkiQ8MEy3Xsrnv+ZCa8aGL//Ydg6NGi1GxIdgaGzrU5WJyDYYXojI5RUapkn72G3Rt6tNHdIdgd4eOFdcja0ZRW22vVBSjW8OXwIAPD850e61ERHDCxG5Af1g3fBAx8zgCfL1xCOjYgHolvpvbbFNIQQW/3AKGq3AzUnh7HUhchCGFyJyeYY1Xuw8WPdqs8fEw8dThuOXlPjfiQKTbdYfy9ftAuwhw8t39HNYbUTXO4YXInJ5hplGDhx42jXAG0+MSwAAvPLjaRQ39/7oXSipxsvrTgIA/jSxN/eoIXIghhcicnmOWOPFlMfH90SfiACUVjdg9qeHUFKlC1GZhVX47cf7UdWgxg1xXTB3rPNnGBFdT7jOCxG5vKsH7DqSt4ccHz4yDPf8ay/SLysx/q3t6B0RiJOXlVBrBXqG+WPFw0PgKef/BxI5En/jiMjl6ce8OLrnBQDiQv3x3ROj0TdKgZpGDY5drIRaK5DaNxxf/34UwgO5hgqRo7HnhYhcmlYrUFylDy+O2y/oar3CArDhj2NwOK8CBcp69I0MRO+IQKfUQkQML0Tk4ipqG9Gk0U1VdmYvh0wm4YY4ToUmcgW8bURELk0/06irvxe8PPgni4gYXojIxZVU68JLmIMWqCMi18fwQkQuTT89meGFiPQYXojIpZXqe14CGF6ISIfhhYhcWmlzz0soe16IqBnDCxG5tBL2vBDRNRheiMil6W8bhQZ6ObkSInIVDC9E5NL0A3ZD2fNCRM0YXojIpZVWNwLgbCMiuoLhhYhcVpNGi4paXXhhzwsR6TG8EJHLKq9phBCAXCahix/HvBCRDsMLEbks/XiXEH8vyGWSk6shIlfB8EJELks/TZq3jIjoagwvROSySrk1ABGZwPBCRC5LP9MoNIDjXYjoCoYXInJZ3JSRiExheCEil8VNGYnIFIYXInJZ7HkhIlMYXojIZZVythERmcDwQkQui+GFiExheCEil6TWaFFR2wSAs42IyBjDCxG5pPLmPY0kCQjm1gBEdBWGFyJySeU1uvDSxY9bAxCRMYYXInJJ5c0L1IX4s9eFiIwxvBCRSyqrYXghItMYXojIJelvG3VleCGiazC8EJFLYs8LEbWG4YWIXFJ5jW6NF/a8ENG1GF6IyCWVs+eFiFrB8EJELqlMP9uIq+sS0TUYXojIJXHALhG1huGFiFwSbxsRUWsYXojI5Wi1AhW17HkhItMYXojI5VTWNUErdP/dheGFiK7B8EJELkc/TVrh4wFPOf9MEZEx/lUgIpejn2nUlTONiMgEhhcicjkcrEtEbWF4ISKXw60BiKgtDC9E5HK4xgsRtcUh4WXFihWIi4uDj48PRowYgQMHDrTadvXq1ZAkyejLx8fHEWUSkYvgbSMiaovdw8tXX32FefPmYfHixThy5AgGDhyISZMmobi4uNVjFAoFCgoKDF+5ubn2LpOIXAhvGxFRW+weXt555x3MmTMHs2bNQr9+/fD+++/Dz88Pq1atavUYSZIQGRlp+IqIiLB3mUTkQgw7SgcwvBBRS3YNL42NjTh8+DBSU1OvvKBMhtTUVKSlpbV6XHV1NWJjYxETE4O7774bp06darVtQ0MDVCqV0RcRuTfDpoz+nCpNRC3ZNbyUlpZCo9G06DmJiIhAYWGhyWMSExOxatUqrF+/Hp9//jm0Wi1Gjx6NS5cumWy/dOlSBAUFGb5iYmJsfh1E5FjcGoCI2uJys41GjRqFGTNmYNCgQRg3bhzWrl2LsLAwfPDBBybbL1y4EEql0vB18eJFB1dMRLYkhOCAXSJqk4c9Tx4aGgq5XI6ioiKjx4uKihAZGWnWOTw9PTF48GBkZWWZfN7b2xve3uxaJuosqhrUaNLoNjZieCEiU+za8+Ll5YWhQ4di27Zthse0Wi22bduGUaNGmXUOjUaD9PR0REVF2atMInIh5c3jXfy95PDxlDu5GiJyRXbteQGAefPmYebMmRg2bBiGDx+Od999FzU1NZg1axYAYMaMGejWrRuWLl0KAHj11VcxcuRIJCQkoLKyEm+99RZyc3Pxu9/9zt6lEpELMEyT5kwjImqF3cPLgw8+iJKSEixatAiFhYUYNGgQNm/ebBjEm5eXB5nsSgdQRUUF5syZg8LCQnTp0gVDhw7Fvn370K9fP3uXSkQuoEIfXvwYXojINEkIIZxdhC2pVCoEBQVBqVRCoVA4uxwistA3hy7iuW9PYFyfMHz62HBnl0NEDmLJ57fLzTYiouubsq4JABDs5+nkSojIVTG8EJFL0a/x0oW3jYioFQwvRORSKmrZ80JEbWN4ISKXUsmeFyJqB8MLEbmUihr2vBBR2xheiMilcMwLEbWH4YWIXEpl85gXhhciag3DCxG5FH3PC28bEVFrGF6IyGXUNWrQoNYCALpwU0YiagXDCxG5DH2vi6dcgr8XN2UkItMYXojIZejDS5CvFyRJcnI1ROSqGF6IyGUoDYN1Od6FiFrH8EJELqOCM42IyAwML0TkMjjTiIjMwfBCRC6DWwMQkTkYXojIZRg2ZfRnzwsRtY7hhYhcBrcGICJzMLwQkcuo5GwjIjIDwwsRuYwrA3bZ80JErWN4ISKXwU0ZicgcDC9E5DI4VZqIzMHwQkQuQaMVUNY1zzZieCGiNjC8EJFLqKpvghC6/w725W0jImodwwsRuQT9Gi8B3h7w8uCfJiJqHf9CEJFL4HgXIjIXwwsRuQRuDUBE5mJ4ISKXUFHDwbpEZB6GFyJyCdwagIjMxfBCRC6BWwMQkbkYXojIJeh7XoLY80JE7WB4ISKXwJ4XIjIXwwsRuQSOeSEiczG8EJFL0C9Sx9lGRNQehhcicglK9rwQkZkYXojIJVQYxrwwvBBR2xheiMjp6ps0qGvSAACC/XnbiIjaxvBCRE6nn2nkIZMQ6O3h5GqIyNUxvBCR0129KaMkSU6uhohcHcMLETndlfDC8S5E1D6GFyJyOv1to2BfjnchovYxvBCR07HnhYgswfBCRE7HrQGIyBIML0TkdBU1zQvU+bPnhYjax/BCRE7HrQGIyBIML0TkdMo6bg1AROZjeCEip6vgmBcisgDDCxE5HWcbEZElGF6IyOkquSkjEVmA4YWInEqrFais1Y954W0jImofwwsROVVVvRpaofvvIIYXIjIDwwsROZV+vIuflxzeHnInV0NE7oDhhYicqqKW06SJyDIML0TkVJVcoI6ILMTwQkROxZ4XIrKUQ8LLihUrEBcXBx8fH4wYMQIHDhxos/0333yDpKQk+Pj4ICUlBRs3bnREmUTkBNwagIgsZffw8tVXX2HevHlYvHgxjhw5goEDB2LSpEkoLi422X7fvn2YPn06Zs+ejaNHj+Kee+7BPffcg5MnT9q7VCJyAiV7XojIQnYPL++88w7mzJmDWbNmoV+/fnj//ffh5+eHVatWmWz/97//HZMnT8Zzzz2Hvn37YsmSJRgyZAj++c9/2rtUInICbg1ARJaya3hpbGzE4cOHkZqaeuUFZTKkpqYiLS3N5DFpaWlG7QFg0qRJrbYnIvfGrQGIyFIe9jx5aWkpNBoNIiIijB6PiIjAmTNnTB5TWFhosn1hYaHJ9g0NDWhoaDB8r1KprKyaiBzJsDWAP3teiMg8bj/baOnSpQgKCjJ8xcTEOLskIrKAoefFlz0vRGQeu4aX0NBQyOVyFBUVGT1eVFSEyMhIk8dERkZa1H7hwoVQKpWGr4sXL9qmeCJyCK7zQkSWsmt48fLywtChQ7Ft2zbDY1qtFtu2bcOoUaNMHjNq1Cij9gDw888/t9re29sbCoXC6IuI3AfXeSEiS9l1zAsAzJs3DzNnzsSwYcMwfPhwvPvuu6ipqcGsWbMAADNmzEC3bt2wdOlSAMCf/vQnjBs3Dm+//TamTJmCNWvW4NChQ/jwww/tXSoROViDWoPaRg0AhhciMp/dw8uDDz6IkpISLFq0CIWFhRg0aBA2b95sGJSbl5cHmexKB9Do0aPx5Zdf4qWXXsKLL76I3r17Y926dUhOTrZ3qUTkYPpbRjIJCPSx+58jIuokJCGEcHYRtqRSqRAUFASlUslbSEQu7kyhCpPf3Y0Qfy8cefkWZ5dDRE5kyee32882IiL3VVHDwbpEZDmGFyJyGmUdB+sSkeUYXojIabg1ABF1BMMLETmNfpp0EBeoIyILMLwQkdNUsueFiDqA4YWInKaipnnMiz97XojIfAwvROQ0FdwagIg6gOGFiJymklsDEFEHMLwQkdMYdpRmzwsRWYDhhYic5sqAXfa8EJH5GF6IyCmEEKisY3ghIssxvBCRU6jq1dBodVur8bYREVmC4YWInEI/WNfXUw4fT7mTqyEid8LwQkROwa0BiKijGF6IyCmuzDTieBcisgzDCxE5hWGNF3/2vBCRZRheiMgpKmr0q+uy54WILMPwQkROcWV1Xfa8EJFlGF6IyCkquEAdEXUQwwsROQUH7BJRRzG8EJFTVHKqNBF1EMMLETlFBXeUJqIOYnghIqfQ97xwawAishTDCxE5BXteiKijGF6IyOEa1BrUNmoAMLwQkeUYXojI4fS3jGQSEOjj4eRqiMjdMLwQkcNdPU1aJpOcXA0RuRuGFyJyuCtbA3CwLhFZjuGFiByukoN1icgKDC9E5HAVXKCOiKzA8EJEDsetAYjIGgwvRORw3FGaiKzB8EJEDldhWF2XPS9EZDmGFyJyOA7YJSJrMLwQkcNxwC4RWYPhhYgcjgN2icgaDC9E5HD67QG6+LPnhYgsx/BCRA6l1QqOeSEiqzC8EJFDVdWroRW6/+b2AETUEQwvRORQ+vEufl5yeHvInVwNEbkjhhcicqgK3jIiIisxvBCRQ1XWckdpIrIOwwsRORR7XojIWgwvRORQFex5ISIrMbwQkUNxmjQRWYvhhYgcqoI7ShORlRheiMihuKM0EVmL4YWIHMpw24hbAxBRBzG8EJFDVdSw54WIrMPwQkQOpR/zEsLwQkQdxPBCRA4jhEBZTXN48Wd4IaKOYXghIoepbdSgUa0FwPBCRB3H8EJEDlPe3Ovi7SGDnxc3ZSSijmF4ISKHKb/qlpEkSU6uhojcFcMLETlMOce7EJEN2DW8lJeX4+GHH4ZCoUBwcDBmz56N6urqNo8ZP348JEky+nr88cftWSYROQjDCxHZgoc9T/7www+joKAAP//8M5qamjBr1izMnTsXX375ZZvHzZkzB6+++qrhez8/P3uWSUQOwvBCRLZgt/CSkZGBzZs34+DBgxg2bBgA4L333sPtt9+O5cuXIzo6utVj/fz8EBkZaa/SiMhJymsZXojIena7bZSWlobg4GBDcAGA1NRUyGQy7N+/v81jv/jiC4SGhiI5ORkLFy5EbW1tq20bGhqgUqmMvojINZVXc4E6IrKe3XpeCgsLER4ebvxiHh4ICQlBYWFhq8c99NBDiI2NRXR0NE6cOIEXXngBmZmZWLt2rcn2S5cuxSuvvGLT2onIPgw9LwEML0TUcRaHlwULFuCNN95os01GRkaHC5o7d67hv1NSUhAVFYWJEyfi/Pnz6NWrV4v2CxcuxLx58wzfq1QqxMTEdPj1ich+DGNe2PNCRFawOLzMnz8fjz76aJttevbsicjISBQXFxs9rlarUV5ebtF4lhEjRgAAsrKyTIYXb29veHt7m30+InKeCg7YJSIbsDi8hIWFISwsrN12o0aNQmVlJQ4fPoyhQ4cCAH755RdotVpDIDHHsWPHAABRUVGWlkpELob7GhGRLdhtwG7fvn0xefJkzJkzBwcOHMDevXvx1FNPYdq0aYaZRpcvX0ZSUhIOHDgAADh//jyWLFmCw4cPIycnBz/88ANmzJiBsWPHYsCAAfYqlYgcoEmjhbKuCQDDCxFZx66L1H3xxRdISkrCxIkTcfvtt2PMmDH48MMPDc83NTUhMzPTMJvIy8sLW7duxa233oqkpCTMnz8f9913H3788Ud7lklEDlBZqwsukgQEc8wLEVnBrovUhYSEtLkgXVxcHIQQhu9jYmKwc+dOe5ZERE6iH6wb7OsJuYz7GhFRx3FvIyJyCK6uS0S2wvBCRA7B8EJEtsLwQkQOwa0BiMhWGF6IyCEMWwMwvBCRlRheiMghKtjzQkQ2wvBCRA6hX6CuC6dJE5GVGF6IyCH0WwN05aaMRGQlhhcicogrWwNwLzIisg7DCxE5RAV3lCYiG2F4ISK7E0JcWeeFt42IyEoML0Rkd9UNajRqtADY80JE1mN4ISK7K2te48XPSw5fL7mTqyEid8fwQkR2V1rdAAAIDeBgXSKyHsMLEdldaXPPSyjHuxCRDTC8EJHd6XteurLnhYhsgOGFiOyOt42IyJYYXojI7vThJYy3jYjIBhheiMju9LONeNuIiGyB4YWI7I63jYjIlhheiMjuONuIiGyJ4YWI7K60qrnnJZA9L0RkPYYXIrKr+iYNqhrUAIBQ7ihNRDbA8EJEdlXWvCGjl1wGha+Hk6shos6A4YWI7Ep/y6hrgBckSXJyNUTUGTC8EJFdcaYREdkawwsR2dWVNV4404iIbIPhhYjsqoQ9L0RkYwwvRGRXvG1ERLbG8EJEdsUF6ojI1hheiMiuytjzQkQ2xvBCRHbF20ZEZGsML0RkVyWGrQF424iIbIPhhYjspkGtQUVtEwAgUuHj5GqIqLNgeCEiuylW6XpdvDxkCPL1dHI1RNRZMLwQkd0UV9UDAMIDvbk1ABHZDMMLEdmNvuclgreMiMiGGF6IyG6KVLqelwgFZxoRke0wvBB1UkIIZ5eAouaZRuGB7HkhItvxcHYBRGRbPx7Px792nMfZoipEB/tg5qg4zLoxHnKZ48ecXOl5YXghIttheCHqJIQQeG1DBlbuyTY8drG8Dq9tyMCRvAq8N32IwwPMlTEvvG1ERLbD20ZEncS/dpzHyj3ZkCTgqQkJ2PnceCy5Jxlechk2phfizS1nHF6TvueFt42IyJYYXog6geMXK/HOz2cBAK/c1R9/npSI2K7+eGRkLN5+YCAA4MNdF3A4t8KhdRVXseeFiGyP4YXIzTWqtfjzN8eh0QrcMSAKM0bFGT1/58BoTB3SDUIAr2047bCBvPVNGijrdKvrhnPMCxHZEMMLkZv7/NdcnCuuRmiAF5bcnWyyzYLJSfD1lONoXiW2ZRQ7pC79eBcfTxkUPhxeR0S2w/BC5MZU9U1475dzAIBnb+mDLv6mNz8MV/hgxqhYADAa0GtPRVVXZhpxdV0isiWGFyI3tnpvDipqm9AzzB8PDotps+2M0XGQSUDahTJkFlbZvTbDNGkO1iUiG2N4IXJTDWoNPkvLBQD8aWJveMjb/nXuFuyLSf0jAQCr9+XYuzzDbaNwDtYlIhtjeCGykFbr/JVrAWDDiQKUVjcgQuGN21OizDrmkeZbR/87kY/6Jo09yzPcNuI0aSKyNY6iIzLDhZJq/GvHeezILEFpdQNCA7wwPjEcj4/rhYTwAIfXI4TAqr26sSszRsXBs51eF72R8V0RFeSDAmU9dmQWY3KyeaGnI7hAHRHZC3teiNoghMB7285h0ru78O3hSyit1n0gl1Y34tvDlzD53V34ePcFh+8jdCi3Aicvq+DtIcP04T3MPk4mk3DXwGgAwPpj+fYqDwBQoKwDAEQGseeFiGyLPS9ErWjSaDHv6+P48bjuQ35CYhh+P64Xeob540JJDT7cdQG/nCnGaxsyUFrdiBcmJzpsVs2q5hlD9w7uhpBWZhi15u5B3fDBrgvYdqYYVfVNCPTxtEeJyK/U3TaKDva1y/mJ6PrF8EIup6q+CRkFVSirbkBooDcGdg+Gl4djOwk1WoH5zcHFQybh9XuT8eANV3o4wgN9MCI+BB/vzsbrGzPw/s7zCPTxwJMTEuxe26WKWmw5VQgAmHVjvMXH940KRM9Qf1worcGus6WYMsD2t460WmHoeWF4ISJbY3ghl3G+pBp/+/ksfjpdhEa11vB4gLcHpg7phqcn9kZogGPGT7y5+Qx+aA4uH84YipuTIlq0kSQJc8b2hIdcwis/nsbynzLRNyrQZFtb+iwtF1oB3JjQFYmRgRYfL0kSJvYNx4Xd2diWUWSX8FJa3YAmjYBMAiICOeaFiGyLY17ISINag/RLSmzLKMLh3HJU1TfZ/TU1WoG/bz2HSX/bhf+dKECjWotuwb4Y3CMYoQHeqG5Q47O0XExYvgObTxbavZ4fj+fjg10XAABvPzCw3TAy68Z4PDSiB4QA5n99HCXN+/nYQ02DGmsO5AEAHutAr4vexL66a9qeWQyNHWZP5SuvLFDX3hRuIiJLseeFAACXK+uwYnsWfjyej6p6teFxL7kMNyeF448TE9A/Osjmr1vbqMYTnx/BzrMlAICbk8Ix75Y+6B+tgCRJ0GoF9p0vw7LNGTh5WYXHPz+M+bf0wVM3J9hlfMmZQhWe//YEAOD343ri7kHdzDrur3f2x9G8SmQUqPDSunS8/9uhdqlv7ZFLUNWrEdfVDxMSwzt8nmGxXRDk64mK2iYcyavADXEhNqwSyK/kLSMish+7/S/R66+/jtGjR8PPzw/BwcFmHSOEwKJFixAVFQVfX1+kpqbi3Llz9irRLWi0AhtOFOCJzw9jxP9txYC/bsGUf+zGOz+fNXxAWEMIgY93X8CE5Tvw5f48VNWr0cXPE/2jFYhU+KBRo8XmU4W44709+OsPp9Cgtt3aIMq6Jjyy8gB2ni2Br6ccb98/EKsevQHJ3YIMH/wymYQxvUPx/R9uxJybdD0Nb/98Fss2n7H5DJ/qBjX+8PkR1DVpMCYhFM/dmmj2sV4eMrx9/0B4yCRsOVWEH47bfiaPVivwSfPico+OjoNM1vFw5CGXYXxiGABga0aRLcozwvBCRPZkt56XxsZG3H///Rg1ahRWrlxp1jFvvvkm/vGPf+DTTz9FfHw8Xn75ZUyaNAmnT5+Gj4/zp1sWKOtwOLcCQggMa/4/1ezSGsSH+iMqyNeo3dG8Cuw9X4YjuZVQ1TUhPtQfdw6MwqheXXGpoq7FMaZea8vJQqzel4Ocslqj507lq3AqX4X3d57H7DHxeHBYDPKV7Z/z2vOfvKzCf9JysOtcKQBgeHwInkntjZHxXSGTSRBC4ExhFVZsz8L/ThRg9b4cHMwpx1/v6ocmjbDo9a597eMXK/HOz2dxtqgaCh8PrH5sOIb06NLqMZ5yGf4ypR8iFD54bUMGPth5AY1qLW7pF9HhOq6WX1mL579Nx4XSGkQF+eAf0wdbfLujX7QCf7y5N/629Sxe+fE0Arw90C9aYXVtet8fu4wLJTXw95LjN+1sBWCOiX0jsP5YPn48no9HR8fZrE4AOFdUDQBQ+LJzl4hsTxJ2XqBi9erVeOaZZ1BZWdlmOyEEoqOjMX/+fPz5z38GACiVSkRERGD16tWYNm2aWa+nUqkQFBQEpVIJhUJhbfkGXx3MwwvfpZt8TiYBS6em4MEbeuCLX3Px0rqTaO+HevUx1/pPWi4Wrb9yDh8PGWbfFI8JieEI9vPEiUtKrDlwEQdyys0+57XXsmBtOvTvvFyS8Ne7+uG3I2NbvdXxy5kizP/6OCpqr4yBMff1rn3thWvToR9m4e8lx9ePj7LoltRnaTlYtP6UVXVcW9OC79INP+/Hx/XEgtv6duhcDWoNblz2C0qrG21S29U16v/9SQCW3Wf9OT/Zm41Xfjxt0zoB+9RKRJ2fJZ/fLjOSLjs7G4WFhUhNTTU8FhQUhBEjRiAtLa3V4xoaGqBSqYy+bK1AWYcFa00HFwDQCmDB2nS8vuE0/nJNcJEk4MNHhuAP43u1OGbh2nTDdFK9H45fxsvrjc/RqNHityNjMSwuBAnhgZg6pDu++v1ILJua0uKcL5o459XyK2t1H9RXvYCAQGq/iDbHaNycFIHVs26w+PWuVqCsMwouAFDXpLF4nZJb+kXg6kp1dZw0uw5TNV398/5oV3aHzgUA5TWNKKtptElt19aoJ2Cbcy7532mb1qk/r61rJSK6lsuEl8JC3SySiAjjmR0RERGG50xZunQpgoKCDF8xMdZ3p18ru7QG7fVPCQF8tDvb5OOBPl4Y0zu0xXNaAby87iTWH7uMz3/NxbQP0/D0f4+ZbJdTanzrSJIk9Ojq16KtRgAHs8tbPA7oPlie+vJoi14hU+c3paax5XgXjQCymm8RtGfHmRJcO7HF3Ne+WnZpTYtr0Ahh8XkAILOwqkVNHT2XoTYbnk9/TlvWaK9z2vO8RERXs+iG9IIFC/DGG2+02SYjIwNJSUlWFWWJhQsXYt68eYbvVSqVzQNMfKg/ZBJa/FG+1oDuCqRfUhl9sMolCXGhupBh6hxbM4qxNaP4qva6Nq2dw5y65n99HPvOl2FSciS6BfuiSFWPn08X4etDF1HfpG1xntbOb+7rLf8pE32jFW2uwbItowivbTzd4nFzX9ucOtTaltfWFiEEPv81zyY1tVWbTEKHzwcAgT4tf02tqREwXafcyjpbP691tRIRXcuinpf58+cjIyOjza+ePXt2qJDIyEgAQFGR8cyHoqIiw3OmeHt7Q6FQGH3ZWlSQL5ZOTcG1d1X038olCW/cl4IfnroJy+5Lgby5oVyS8H9TkxEV5Gs4x5XngN+Nice0G2IwPD4E4/qE4ZnU3tj9ws2tnqO1uvRtZRKQEB6AJq3AmoMXMeuTg7j1b7vwyMoD+CwtF/VNWgyPC8EzE3ubdX5zXs/bQ4bjl5S467092HyyoMUMoNLqBixcm47Znx5CTYMG8V11H26WvnZbdejN//o4Lpab/3/47/2Sha0ZRZBJsLqmtmoL9PFAkG/Hl+DfctL4d8LaGq+u8+oJS0+n9rZ60G5UkC+eTe1t+F4uwepaiYiu5XIDdv/85z9j/vz5AHS9KOHh4S4xYBfQ3XY5klsBIYChcbqZMTmltYgL9Wsx28jU4+0915F2ptruv1CG745cwqHcCpRUNSA0wBsDuwdh6pDuuKl3KCRJsuj8bb1eTYMGcz87hAulNQCAmBBfjEkIRaCPJy6UVGPX2VI0anQ9Io+OjsOLt/dFWU1Dh1/bVB1d/b3w9JqjOFNYheggH3w2e0S7Oz1fPeh32dQUjEsMs0lNV9d2tqgKL3yXjkJlPf4wvheen2x5j2RNgxqjl/0CZV0Tlt6bjLjQAJvVqK9z7meHkH5ZhUV39MNjYzq+8J3etowizP70EGJD/LDm9yMZXIjILJZ8ftstvOTl5aG8vBw//PAD3nrrLezevRsAkJCQgIAA3QdLUlISli5dinvvvRcA8MYbb2DZsmVGU6VPnDhh0VRpe4YXMq26QY0Pd57Hyj3ZJsfFDOgehL/c3hcjena1Ww1FqnpM/+hXXCipQRc/T6x4eAhG9zIxzkgr8M/tWXjn57MAgCfG98ILHQgV5vrpVCHm/ucwPOUStjwzFj3D2g5V11qxPQtvbclEXFc/bJs/HnIr1nZpzQc7z2PppjOYmBSOlY/e0P4B7dDPYrotORL//u1QG1RIRNcDSz6/7bYIw6JFi/Dpp58avh88eDAAYPv27Rg/fjwAIDMzE0ql0tDm+eefR01NDebOnYvKykqMGTMGmzdvdok1Xqh1Ad4emHdrIh4f3ws7M0uQUViFqvomdAv2xaheXe2yMu+1IhQ++Pbx0Zi1+iCOX6zEwx/vx/ThPTD3pp6IC/WHEAJH8irw5uZM7G8e0Pz4uF54fpL5C9F1xC39IjAhMQzbM0uw+IdT+Oyx4WavvKusa8IHO88DAJ5J7WOX4AIANyboQt6vF8rQpNHC08rl/HOb1yUyNaCciMgW7H7byNHY83J9q21UY8n/MvDfA1cG4oYFeqNRrYWyTrdGjbeHDEvuScYDNljozRw5pTW49W+70KjR4r3pg3HnwGizjntj8xn8e8d59A4PwOZnxtotvGi1AkNf+xkVtU349vFRhgUYO+qx1Qfxy5livH5vMh4eEWujKomos3PLdV6IbMHPywNLp6ZgzdyRGNcnDDIJKKlqgLKuCT6eMvxmaHdsnTfOYcEFAOJC/fFE8zo/L607ada2DlnFVfh4t25zyOcnJ9ktuAC6LRhG9dLd0tt3vszq8+U1D5qODfG3+lxERKZw7W7qlEb27IqRPbtCVd+EvLJayGUS4kP94eMpd0o9T92cgB2ZxTh+SYl5Xx/DF78b2WogUWu0eHHtSTRpBCYmheOWfm3vam0Lo3uFYmN6IfZmleLpib3bP6AVWq24El5424iI7IQ9L9SpKXw8kdwtCH2jFE4LLoBub6Z3pw2Gn5ccv14oxys/nmp1Y8m3fz6LAznl8POS46939XdIfaObe16O5lWizsSga3MVVdWjUa2Fh0xCVBDHqhGRfTC8EDlIfKg/3vrNQEgS8FlaLpZuOgPtNSvtfbovB//eoRuk++ZvBiAmxDG9F7rNLXW7iB/KNb1Csznymgfrduvia/HGlkRE5uJtIyIHmjIgCqXV/bH4h1P4cNcFHM6twKOj4xDg7YFvDl/ExnTdVhhPjO+FOwaYN7DXFiRJN+5l7ZHL2He+DDf1DuvQeXKbbxn1cFDoIqLrE8MLkYPNHB0Hha8H/vL9SRzOrcDh3ArDczIJmHdLHzw5IcHhdd3YK9QQXjrqfLFun6teFq5nQ0RkCYYXIie4d3B3jIjvik/35SDtQhka1VqkdAvCzNFxSO5m/3VxTBmdoBv3kn6pEsq6pg5taXCuOby0t8IxEZE1GF6InCQ62BcLb+/r7DIMooJ80TPUHxdKa3Agu7xDs5zOFVcBAHozvBCRHXFEHREZ6Nd72ZtVavGxdY0aXKrQrWHDnhcisieGFyIy0G8VkNaBcS/nS6ohBBDi74WuAd62Lo2IyIDhhYgMRjZvnplZVIWSqgaLjs3ieBcichCGFyIyCPH3Qt8o3Z4iaRcs633Rj3dheCEie2N4ISIjN+r3ObJw3Mu5Il3PCwfrEpG9MbwQkRH9lGlL13s5XaACACRGBNq8JiKiqzG8EJGR4fFdIZdJyCuvxcXmFXPbU1nbaJhp1N9J69QQ0fWD4YWIjAR4e2BwTDAAYMfZErOOOZWv63XpEeLXocXtiIgswfBCRC1M7KtboG7r6SKz2qdfVgIAkrsp7FYTEZEewwsRtZDaNxyAbr2XmgZ1u+3TL+nCS/9o3jIiIvtjeCGiFhLCA9AjxA+NGi12n2v71pEQAgdzygEAQ2O7OKI8IrrOMbwQUQuSJCFVf+soo7jNtnnltSiuaoCnXMKg5rEyRET2xPBCRCbpbx1tP1MMjVa02u5gTgUAIKVbEHw85Q6pjYiubwwvRGTSDfEhCPbzRFlNY5sbNeoXs7shPsRRpRHRdY7hhYhM8pTLcNfAaADAd0cumWyj0QrDdOoJieEOq42Irm8ML0TUqvuGdAcAbDlViKr6phbPH7tYifKaRih8PDhYl4gchuGFiFo1oHsQEsIDUN+kxfpj+S2e33CiAAAwLjEcnnL+OSEix+BfGyJqlSRJeGh4DwDAx7svGA3cbVBr8P1R3e2kqYO7OaU+Iro+MbwQUZumDY9BsJ8ncspq8d3hK2Nf1h/NR0VtEyIVPhjbJ8yJFRLR9YbhhYja5OflgT+M7wUAWLopA/mVdaiqb8LynzIBAI+NiYNcJjmzRCK6zng4uwAicn2zbozH90fzkVGgwgMfpEHh44niqgb0CPHDzNFxzi6PiK4z7HkhonZ5ymVYOXMYunfxxaWKOpwuUEHh44F/PjQY3h5cmI6IHIs9L0RkluhgX2x4+iasO3oZ9U0a3DUoGlFBvs4ui4iuQwwvRGS2IF9P3iYiIqfjbSMiIiJyKwwvRERE5FYYXoiIiMitMLwQERGRW2F4ISIiIrfC8EJERERuheGFiIiI3ArDCxEREbkVhhciIiJyKwwvRERE5FYYXoiIiMitMLwQERGRW2F4ISIiIrfS6XaVFkIAAFQqlZMrISIiInPpP7f1n+Nt6XThpaqqCgAQExPj5EqIiIjIUlVVVQgKCmqzjSTMiThuRKvVIj8/H4GBgZAkyabnVqlUiImJwcWLF6FQKGx6blfQ2a8P6PzXyOtzf539Gnl97s9e1yiEQFVVFaKjoyGTtT2qpdP1vMhkMnTv3t2ur6FQKDrtP0qg818f0Pmvkdfn/jr7NfL63J89rrG9Hhc9DtglIiIit8LwQkRERG6F4cUC3t7eWLx4Mby9vZ1dil109usDOv818vrcX2e/Rl6f+3OFa+x0A3aJiIioc2PPCxEREbkVhhciIiJyKwwvRERE5FYYXoiIiMitMLxc5fXXX8fo0aPh5+eH4OBgs44RQmDRokWIioqCr68vUlNTce7cOaM25eXlePjhh6FQKBAcHIzZs2ejurraDlfQPktrycnJgSRJJr+++eYbQztTz69Zs8YRl2SkIz/r8ePHt6j98ccfN2qTl5eHKVOmwM/PD+Hh4XjuueegVqvteSkmWXp95eXl+OMf/4jExET4+vqiR48eePrpp6FUKo3aOfP9W7FiBeLi4uDj44MRI0bgwIEDbbb/5ptvkJSUBB8fH6SkpGDjxo1Gz5vzO+lIllzfRx99hJtuugldunRBly5dkJqa2qL9o48+2uK9mjx5sr0vo02WXOPq1atb1O/j42PUxp3fQ1N/TyRJwpQpUwxtXOk93LVrF+68805ER0dDkiSsW7eu3WN27NiBIUOGwNvbGwkJCVi9enWLNpb+XltMkMGiRYvEO++8I+bNmyeCgoLMOmbZsmUiKChIrFu3Thw/flzcddddIj4+XtTV1RnaTJ48WQwcOFD8+uuvYvfu3SIhIUFMnz7dTlfRNktrUavVoqCgwOjrlVdeEQEBAaKqqsrQDoD45JNPjNpd/TNwlI78rMeNGyfmzJljVLtSqTQ8r1arRXJyskhNTRVHjx4VGzduFKGhoWLhwoX2vpwWLL2+9PR0MXXqVPHDDz+IrKwssW3bNtG7d29x3333GbVz1vu3Zs0a4eXlJVatWiVOnTol5syZI4KDg0VRUZHJ9nv37hVyuVy8+eab4vTp0+Kll14Snp6eIj093dDGnN9JR7H0+h566CGxYsUKcfToUZGRkSEeffRRERQUJC5dumRoM3PmTDF58mSj96q8vNxRl9SCpdf4ySefCIVCYVR/YWGhURt3fg/LysqMru3kyZNCLpeLTz75xNDGld7DjRs3ir/85S9i7dq1AoD4/vvv22x/4cIF4efnJ+bNmydOnz4t3nvvPSGXy8XmzZsNbSz9mXUEw4sJn3zyiVnhRavVisjISPHWW28ZHqusrBTe3t7iv//9rxBCiNOnTwsA4uDBg4Y2mzZtEpIkicuXL9u89rbYqpZBgwaJxx57zOgxc/7R21tHr2/cuHHiT3/6U6vPb9y4UchkMqM/sP/+97+FQqEQDQ0NNqndHLZ6/77++mvh5eUlmpqaDI856/0bPny4ePLJJw3fazQaER0dLZYuXWqy/QMPPCCmTJli9NiIESPE73//eyGEeb+TjmTp9V1LrVaLwMBA8emnnxoemzlzprj77rttXWqHWXqN7f197Wzv4d/+9jcRGBgoqqurDY+52nuoZ87fgeeff17079/f6LEHH3xQTJo0yfC9tT8zc/C2kRWys7NRWFiI1NRUw2NBQUEYMWIE0tLSAABpaWkIDg7GsGHDDG1SU1Mhk8mwf/9+h9Zri1oOHz6MY8eOYfbs2S2ee/LJJxEaGorhw4dj1apVZm1rbkvWXN8XX3yB0NBQJCcnY+HChaitrTU6b0pKCiIiIgyPTZo0CSqVCqdOnbL9hbTCVv+WlEolFAoFPDyMtzZz9PvX2NiIw4cPG/3+yGQypKamGn5/rpWWlmbUHtC9F/r25vxOOkpHru9atbW1aGpqQkhIiNHjO3bsQHh4OBITE/HEE0+grKzMprWbq6PXWF1djdjYWMTExODuu+82+j3qbO/hypUrMW3aNPj7+xs97irvoaXa+x20xc/MHJ1uY0ZHKiwsBACjDzX99/rnCgsLER4ebvS8h4cHQkJCDG0cxRa1rFy5En379sXo0aONHn/11Vdx8803w8/PDz/99BP+8Ic/oLq6Gk8//bTN6m9PR6/voYceQmxsLKKjo3HixAm88MILyMzMxNq1aw3nNfUe659zFFu8f6WlpViyZAnmzp1r9Lgz3r/S0lJoNBqTP9szZ86YPKa19+Lq3zf9Y621cZSOXN+1XnjhBURHRxt9EEyePBlTp05FfHw8zp8/jxdffBG33XYb0tLSIJfLbXoN7enINSYmJmLVqlUYMGAAlEolli9fjtGjR+PUqVPo3r17p3oPDxw4gJMnT2LlypVGj7vSe2ip1n4HVSoV6urqUFFRYfW/e3N0+vCyYMECvPHGG222ycjIQFJSkoMqsj1zr9FadXV1+PLLL/Hyyy+3eO7qxwYPHoyamhq89dZbNvnws/f1Xf1BnpKSgqioKEycOBHnz59Hr169Onxecznq/VOpVJgyZQr69euHv/71r0bP2fP9o45ZtmwZ1qxZgx07dhgNaJ02bZrhv1NSUjBgwAD06tULO3bswMSJE51RqkVGjRqFUaNGGb4fPXo0+vbtiw8++ABLlixxYmW2t3LlSqSkpGD48OFGj7v7e+gKOn14mT9/Ph599NE22/Ts2bND546MjAQAFBUVISoqyvB4UVERBg0aZGhTXFxsdJxarUZ5ebnheGuZe43W1vLtt9+itrYWM2bMaLftiBEjsGTJEjQ0NFi9/4Wjrk9vxIgRAICsrCz06tULkZGRLUbKFxUVAYBN3kNHXF9VVRUmT56MwMBAfP/99/D09GyzvS3fv9aEhoZCLpcbfpZ6RUVFrV5PZGRkm+3N+Z10lI5cn97y5cuxbNkybN26FQMGDGizbc+ePREaGoqsrCyHf/BZc416np6eGDx4MLKysgB0nvewpqYGa9aswauvvtru6zjzPbRUa7+DCoUCvr6+kMvlVv+bMIvNRs90IpYO2F2+fLnhMaVSaXLA7qFDhwxttmzZ4tQBux2tZdy4cS1mqbTmtddeE126dOlwrR1hq5/1nj17BABx/PhxIcSVAbtXj5T/4IMPhEKhEPX19ba7gHZ09PqUSqUYOXKkGDdunKipqTHrtRz1/g0fPlw89dRThu81Go3o1q1bmwN277jjDqPHRo0a1WLAblu/k45k6fUJIcQbb7whFAqFSEtLM+s1Ll68KCRJEuvXr7e63o7oyDVeTa1Wi8TERPHss88KITrHeyiE7nPE29tblJaWtvsazn4P9WDmgN3k5GSjx6ZPn95iwK41/ybMqtVmZ+oEcnNzxdGjRw1TgY8ePSqOHj1qNCU4MTFRrF271vD9smXLRHBwsFi/fr04ceKEuPvuu01OlR48eLDYv3+/2LNnj+jdu7dTp0q3VculS5dEYmKi2L9/v9Fx586dE5IkiU2bNrU45w8//CA++ugjkZ6eLs6dOyf+9a9/CT8/P7Fo0SK7X8+1LL2+rKws8eqrr4pDhw6J7OxssX79etGzZ08xduxYwzH6qdK33nqrOHbsmNi8ebMICwtz2lRpS65PqVSKESNGiJSUFJGVlWU0NVO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],
"source": [
"f_sign = Chebfun.from_function(lambda x: np.sign(x), N=25)\n",
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pychebfun implements the method `compare` which plots a graph of the error."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
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"outputs_hidden": false
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{
"data": {
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]
},
"execution_count": 34,
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"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
" </g>\n",
" <g id=\"patch_11\">\n",
" <path d=\"M 30.103125 273.312 \n",
"L 387.223125 273.312 \n",
"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
" </g>\n",
" <g id=\"patch_12\">\n",
" <path d=\"M 30.103125 152.352 \n",
"L 387.223125 152.352 \n",
"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <defs>\n",
" <clipPath id=\"p6d317caea2\">\n",
" <rect x=\"30.103125\" y=\"7.2\" width=\"357.12\" height=\"120.96\"/>\n",
" </clipPath>\n",
" <clipPath id=\"p97793d7d5a\">\n",
" <rect x=\"30.103125\" y=\"152.352\" width=\"357.12\" height=\"120.96\"/>\n",
" </clipPath>\n",
" </defs>\n",
"</svg>\n"
],
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def absfive(x):\n",
" return np.abs(x)**5\n",
"#errors = array([(Chebfun(absfive, N) - exact).norm() for N in range(10, 20)])\n",
"#loglog(errors)\n",
"pychebfun.compare(Chebfun.from_function(absfive), absfive)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Interpolation of random data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A chebfun passing through random values at 50 Chebyshev points.\n",
"The method to initialise a Chebfun from data _at Chebyshev points_ is `from_data`:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"rng = np.random.default_rng(0)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"51"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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