Skip to content

Instantly share code, notes, and snippets.

@pjknowles
Created June 16, 2023 11:53
Show Gist options
  • Save pjknowles/3cb2f373fc96b3dd42b9c5e0e891fcf6 to your computer and use it in GitHub Desktop.
Save pjknowles/3cb2f373fc96b3dd42b9c5e0e891fcf6 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "1a33424a",
"metadata": {
"ExecuteTime": {
"end_time": "2023-06-15T22:23:22.694108Z",
"start_time": "2023-06-15T22:23:22.680788Z"
}
},
"outputs": [],
"source": [
"from sage.symbolic.integration.integral import definite_integral"
]
},
{
"cell_type": "markdown",
"id": "fd0330d7",
"metadata": {},
"source": [
"Make various densities with <1/r>=Z"
]
},
{
"cell_type": "code",
"execution_count": 265,
"outputs": [],
"source": [
"def normalised_gaussian(alpha):\n",
" return (2*alpha/pi)^(3/4)*exp(-alpha*r^2)\n",
"sto_scale=1/(.95909793)^2\n",
"sto_scale2=1/sqrt(2)\n",
"densities = {'exponential': pi ^ (-1) * (Z ^ 3 * exp(-2 * Z * r)),\n",
" # 'gaussian': pi ^ (-3 / 2) * ((Z ^ 2 * pi / 4)) ^ (3 / 2) * exp(-(Z ^ 2 * pi / 4) * r ^ 2),\n",
" 'STO-1G' : normalised_gaussian(Z^2*pi/8)^2,\n",
" # 'STO-2G' : (.678914*normalised_gaussian(Z*.151623*sto_scale)+.430129*normalised_gaussian(Z*.851819*sto_scale))^2,\n",
" 'STO-2G' : (.678914*normalised_gaussian(Z*.2331359749*sto_scale2)+.430129*normalised_gaussian(Z*1.309756366*sto_scale2))^2,\n",
" 'STO-3G' : (.1543289673*normalised_gaussian(Z*3.425240914*sto_scale2)+.5353281423*normalised_gaussian(Z*.6239137298*sto_scale2)+.4446345422*normalised_gaussian(Z*.168855404*sto_scale2))^2,\n",
" }"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:08.954749Z",
"start_time": "2023-06-16T11:53:08.948462Z"
}
}
},
{
"cell_type": "code",
"execution_count": 266,
"outputs": [
{
"data": {
"text/plain": "[[1,\n 1,\n 0.500000864255864*2^(1/4)*pi^(3/2)*(sqrt(2)*Z/pi)^(3/2)/Z^(3/2),\n 0.5000001143019573*pi^(3/2)*sqrt(sqrt(2)*Z)*(sqrt(2)*Z/pi)^(3/2)/Z^2],\n [3/2,\n 4/pi,\n 1.519385349211248*pi*(sqrt(2)*Z/pi)^(3/2)/Z,\n 1.516501445485956*pi*(sqrt(2)*Z/pi)^(3/2)/Z],\n [1,\n 1,\n 0.7452721612769007*sqrt(2)*pi*(sqrt(2)*Z/pi)^(3/2)/Z^2,\n 0.768666170728858*sqrt(2)*pi*(sqrt(2)*Z/pi)^(3/2)/Z^2]]"
},
"execution_count": 266,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[[definite_integral(4 * pi * r ^ 2 * r ^ power * d, r, 0, Infinity).simplify_full()*Z^power for d in densities.values()] for power in\n",
" [0, 1, -1]]"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:12.963424Z",
"start_time": "2023-06-16T11:53:12.633409Z"
}
}
},
{
"cell_type": "code",
"execution_count": 267,
"outputs": [
{
"data": {
"text/plain": "[[1.0, 1.0, 1.0000017285117282, 1.0000002286039147],\n [1.5, 1.2732395447351628, 1.4416687835206818, 1.4389323914805778],\n [1.0, 1.0, 1.0000632246093846, 1.031455096927522]]"
},
"execution_count": 267,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[[float((definite_integral(4 * pi * r ^ 2 * r ^ power * d, r, 0, Infinity).simplify_full()*Z^power).subs(Z=1)) for d in densities.values()] for power in\n",
" [0, 1, -1]]"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:13.557814Z",
"start_time": "2023-06-16T11:53:13.130772Z"
}
}
},
{
"cell_type": "code",
"execution_count": 268,
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": "Graphics object consisting of 4 graphics primitives"
},
"execution_count": 268,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot([d.subs(Z=1) for d in densities.values()],(r,0,5),legend_label=list(densities.keys()))\n"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:14.217434Z",
"start_time": "2023-06-16T11:53:14.019232Z"
}
}
},
{
"cell_type": "code",
"execution_count": 269,
"outputs": [
{
"data": {
"text/plain": "{'exponential': Z^5*e^(-2*Z*r)/pi,\n 'STO-1G': 1/128*pi^2*Z^7*r^2*e^(-1/4*pi*Z^2*r^2),\n 'STO-2G': (-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2,\n 'STO-3G': (-0.0197767255181375*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277020000000*sqrt(2)*Z*r^2) - 0.234470400256128*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956864900000*sqrt(2)*Z*r^2) - 1.33093521236387*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045700000*sqrt(2)*Z*r^2))^2}"
},
"execution_count": 269,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tau = { k: diff(sqrt(rho),r)^2 for k,rho in densities.items()}\n",
"tau"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:19.427781Z",
"start_time": "2023-06-16T11:53:19.422982Z"
}
}
},
{
"cell_type": "code",
"execution_count": 270,
"outputs": [
{
"data": {
"text/plain": "{'exponential': 3/10*6^(2/3)*pi^(2/3)*e^(-4/3*Z*r),\n 'STO-1G': 6/5*6^(2/3)*e^(-1/6*pi*Z^2*r^2)/(pi^(2/3)*Z^2*r^2),\n 'STO-2G': 3/10*6^(2/3)*pi^(4/3)*((0.227783223693540*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) + 0.526613044811009*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2,\n 'STO-3G': 3/10*6^(2/3)*pi^(4/3)*((0.117122254009339*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277020000000*sqrt(2)*Z*r^2) + 0.375805803041535*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956864900000*sqrt(2)*Z*r^2) + 0.388566890849614*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045700000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0197767255181375*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277020000000*sqrt(2)*Z*r^2) - 0.234470400256128*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956864900000*sqrt(2)*Z*r^2) - 1.33093521236387*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045700000*sqrt(2)*Z*r^2))^2}"
},
"execution_count": 270,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = { k: (3 / 10) * (6 * pi ^ 2) ^ (2 / 3) * densities[k] ^ (5 / 3) / tau[k] for k in densities.keys()}\n",
"t"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:20.785177Z",
"start_time": "2023-06-16T11:53:20.781360Z"
}
}
},
{
"cell_type": "code",
"execution_count": 271,
"outputs": [
{
"data": {
"text/plain": "{'exponential': (3*6^(2/3)*pi^(2/3)*e^(-4/3*Z*r) - 10)/(3*6^(2/3)*pi^(2/3)*e^(-4/3*Z*r) + 10),\n 'STO-1G': (6*6^(2/3)*e^(-1/6*pi*Z^2*r^2)/(pi^(2/3)*Z^2*r^2) - 5)/(6*6^(2/3)*e^(-1/6*pi*Z^2*r^2)/(pi^(2/3)*Z^2*r^2) + 5),\n 'STO-2G': (3*6^(2/3)*pi^(4/3)*((0.227783223693540*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) + 0.526613044811009*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2 - 10)/(3*6^(2/3)*pi^(4/3)*((0.227783223693540*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) + 0.526613044811009*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2 + 10),\n 'STO-3G': (3*6^(2/3)*pi^(4/3)*((0.117122254009339*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277020000000*sqrt(2)*Z*r^2) + 0.375805803041535*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956864900000*sqrt(2)*Z*r^2) + 0.388566890849614*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045700000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0197767255181375*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277020000000*sqrt(2)*Z*r^2) - 0.234470400256128*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956864900000*sqrt(2)*Z*r^2) - 1.33093521236387*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045700000*sqrt(2)*Z*r^2))^2 - 10)/(3*6^(2/3)*pi^(4/3)*((0.117122254009339*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277020000000*sqrt(2)*Z*r^2) + 0.375805803041535*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956864900000*sqrt(2)*Z*r^2) + 0.388566890849614*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045700000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0197767255181375*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277020000000*sqrt(2)*Z*r^2) - 0.234470400256128*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956864900000*sqrt(2)*Z*r^2) - 1.33093521236387*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045700000*sqrt(2)*Z*r^2))^2 + 10)}"
},
"execution_count": 271,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w = { k: (tt-1)/(tt+1) for k,tt in t.items()}\n",
"w"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:23.099630Z",
"start_time": "2023-06-16T11:53:23.092801Z"
}
}
},
{
"cell_type": "code",
"execution_count": 272,
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAnIAAAHUCAYAAAC+g8X7AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAACrA0lEQVR4nOzdd3hU1dr38e+eSe+9N1pCAiK9iBRBwHIUFJRyFBBRQJAqKiIINmwIKk2KggUFAQEVUVCKICq9pdHSE1JI72W/f/DCcyItZSZ7Eu7Pdc31PEz2Xus3O+PhZu291lJUVVURQgghhBD1jk7rAEIIIYQQomakkBNCCCGEqKekkBNCCCGEqKekkBNCCCGEqKekkBNCCCGEqKekkBNCCCGEqKekkBNCCCGEqKcaXCGnqio5OTnI8nhCCCGEaOgaXCGXm5uLo6Mjubm5WkcRQgghhDCqBlfICSGEEELcLqSQE0IIIYSop6SQE0IIIYSop6SQE0IIIYSop4xayO3du5eHHnoIHx8fFEVh8+bNtzxnz549tGvXDisrKxo3bsyyZcuMGVEIIYQQot4yM2bj+fn53HnnnTz11FMMHDjwlsdfuHCBBx54gGeeeYavvvqK/fv389xzz+Hu7l6l84UQQghxWUlJCWVlZVrHELdgZmaGhYVFjc9X1DpacE1RFL7//nsGDBhww2Neeukltm7dSkRExNX3xo4dy/Hjxzlw4ECV+snJycHR0ZHs7GwcHBxqG1sIIYSod0pKSjh9+jQVFRVaRxG3oNPpaNGiRY2LOaOOyFXXgQMH6Nu3b6X3+vXrx6pVqygtLcXc3Pyac4qLiykuLr7655ycHAAKyyt4/lgUxRFr6XUoC+vGUNHRHusAN7wsAvGxbIyPZWNs9PbG/VBCCCFEHSsrK6OiooKgoCCsra21jiNuoLCwkJiYGMrKyhpGIZeSkoKnp2el9zw9PSkrKyM9PR1vb+9rzpk3bx5z58695v2kohIOZhURYf8wm+4u5959CTz1bgSOFVGcaruDze3iONX9DBYu9vhYNKaRdQuaWt/JHXZdaWrTGjPFpC6NEEIIUW3W1tbY2NhoHUPcQnZ2NkVFRVhaWmJra1utc02uWlEUpdKfr9z5/ff7V8yYMYOpU6de/XNOTg7+/v40sbUivOedJBeV8k3SJT6ytWRYz0CejsnlqTVH6fTjRVQLhZy+es72T+NQpyPsvLSWErUYa50tLWy70Mrubu6wu5sw207Y6O2M96GFEEIIcdv68ccfyc/Px8HBgcGDB1ermDOpQs7Ly4uUlJRK76WmpmJmZoarq+t1z7G0tMTS0vKGbXpbmTO1sScTgtz54NxF3tAns/v9PqwL9MTr+wgy1hzBcXQZXRo9htvU+aQNVThZeoATeX/wXepHfJY8Bz16Wtp15W6nh+nq+DD+Vs0M+rmFEEIIcfuytbWltLSUnJwciouLq1XImdQ6cl26dGHHjh2V3vv1119p3779dZ+Pqw4LnY5XmnlzvHsYZjqFu6MS+OeJVoSdmEzzf8Zj29mfpEk/Q+t99N3ag3cabeHHO9P5IuwUkwI+wVbvwIrEVxl2OpgnTofxRfJbpBTH1iqTEEIIIcStBqVuxqiFXF5eHseOHePYsWPA5eVFjh07RlxcHHD5tujw4cOvHj927FhiY2OZOnUqERERfPbZZ6xatYoXXnjBYJmC7az4q2tz+rg78Mihc3ybeAnbDv40XjuUFuFTsesWRNyY74nsuJiCvxNoZN2CR9zH8W7TH/jxznTebrKZYJu2fJnyNo+dCuL5qJ78lP4Z+eU5BssohBBCCFEVRi3kDh06RJs2bWjTpg0AU6dOpU2bNsyePRuA5OTkq0UdQKNGjdi2bRu7d++mdevWvPHGG3z88ccGX0POzkzP+raNGebjwrCjF/gm8RIAViHuNF47lJADz6GqKlFdlhAzegNlWYUAWOtt6ebUn9mNvmJLqxRmBq1Br5jxbuxoHj7uydsxTxFVcMSgWYUQQgghbqTO1pGrK9VZR65CVXnqeAzfJmXya6dm9HD9v6VI1PIK0pf/Q8LLP6N3tKLRF49j37PJddtJLUngl4wv2ZK+jIslcbS07cJgz2l0d3oEnWJSd6+FEELcBgoKCoiIiCA0NFRmrZqwK7+nmJgYsrKyyM3NZfjw4bi4uFS5jdu6ytApCitaBdLNxY4Bh84RkVt49WeKXof7uM60ODkFy8YuRPdaScKL21BLy69px8PCjye9Z/Bty3O81eR7zBQLZp0fxJOnw/gp/XNKK0rq8mMJIYQQwkBWr16Nk5NTtc4JCgpi4cKFRsnzb7d1IQeXJ0FsbNcEPytzHjx4lsySytuZWAQ4EfzbM/i+ex8XF+wjutcKSpOv/zycmWJGd6cBfBKym2UhBwiwas47saMYcqoJm1IXS0EnhBBCmLDrFWCDBw8mOjpam0BVcNsXcgCO5np+6NCUzNJynjoew7/vNit6HV7TexCyZwzF5y8R0X4RBceSbtpmC7vOzGu6mS/CTtHavicfxU/kv6eb80vGV5Sr147qCSGEEML0WFtb4+HhoXWMG5JC7v8LsrFkzZ1BbLmYzUcXUq97jN1dgYQefh5zb3uiui0j+5dbV+iNrFswq9GXrA47QVObO3kz5klGhbfmz+yfrikYhRBCCFOjqirvvfcejRs3xtramjvvvJMNGzagqir33nsv991339W/z7KysggICGDmzJkA7N69G0VR+Omnn7jzzjuxsrKiU6dOnDx5slIfGzdupEWLFlhaWhIUFMT8+fMr/TwoKIi3336bUaNGYW9vT0BAAMuXL690TGJiIoMHD8bZ2RlXV1f69+9PTEzM1Z+PHDmSAQMG8MEHH+Dt7Y2rqyvjx4+ntLQUgJ49exIbG8uUKVNQFOXqRgT/vrV67tw5+vfvj6enJ3Z2dnTo0IGdO3ca5FrXhBRy/+NhLycmNfJgRmQiUXlF1z3G3Mue4N3PYt+zMWcfXE36qoNVaruRdQvebvI9y0IO4GTuzktn/8O0s/dxoTDckB9BCCGEMKhXX32Vzz//nKVLl3L69GmmTJnCE088wd69e1mzZg3//PMPH3/8MXB5GTFPT0/mzJlTqY3p06fzwQcfcPDgQTw8PHj44YevFlCHDx/m8ccfZ8iQIZw8eZI5c+Ywa9YsVq9eXamN+fPn0759e44ePcpzzz3HuHHjiIyMBC5PGrjnnnuws7Nj79697Nu3Dzs7O+677z5KSv7vsaZdu3Zx7tw5du3axZo1a1i9evXVfjZt2oSfnx+vv/46ycnJJCcnX/d65OXl8cADD7Bz506OHj1Kv379eOihhyqtwlGn1AYmOztbBdTs7OwanZ9fVq42/e2k2mVfhFpWUXHD4ypKy9SYsZvUQ7ykJs76Ra24ybHXnFtRof6RuUUdcrKp2uOQXl0UP03NL8utUV4hhBDi3/Lz89VDhw6p+fn5//NeuXr4cP5NX/n55ZXaycvLU62srNQ///yz0vtPP/20OnToUFVVVXX9+vWqpaWlOmPGDNXGxkaNioq6etyuXbtUQP3222+vvpeRkaFaW1ur69atU1VVVYcNG6b26dOnUvvTp09Xw8LCrv45MDBQfeKJJ67+uaKiQvXw8FCXLl2qqqqqrlq1Sg0JCan0d3FxcbFqbW2t/vLLL6qqquqIESPUwMBAtays7Ooxjz32mDp48OBK/SxYsKBSls8//1x1dHT89yWuJCwsTP3kk09u2s71XPk9bdiwQV25cqW6YMECNSMj45bn/S+T2qLLFNjodXzeOojuf0ax8Hwq05p4Xvc4xUxPwJIBWAY5k/jydsoyC/H/6CEU3a0HORVF4W6nh+no0I/1qQtYnfQ6v19az+SAT+jm1N/QH0kIIYQgMrKIdu0ibnrM4cOhtG37f8uVhIeHU1RURJ8+fSodV1JScnWN2Mcee4zvv/+eefPmsXTpUoKDg69pt0uXLlf/fxcXF0JCQoiIuJwlIiKC/v0r/93XtWtXFi5cSHl5OXq9HoBWrVpd/bmiKHh5eZGamvr/cx/m7Nmz2NvbV2qnqKiIc+fOXf1zixYtrrYH4O3tfc1t3lvJz89n7ty5/PjjjyQlJVFWVkZhYaFmI3JSyF3H3S52TGrkwatRiTzk6UiwndV1j1MUBa+XeqJ3tiZu7GbU0goClg64el/9Vix0ljzh9TK9nAezIG4Cr5wbwN2ODzMtYCluFj6G/EhCCCFuc82bW3H4cOgtj/lfFRUVAPz000/4+vpW+tmVLaUKCgo4fPgwer2eM2fOVDnPlb8rVVW95u9N9TrPkP97q05FUa7mq6iooF27dnz99dfXnOfu7l6lNqpq+vTp/PLLL3zwwQc0bdoUa2trBg0aVOkWbl2SQu4G3mruy5aLWUw6Hc+2jk1vWpy5P9sJxVxP7KgNKBb6yyNzVSzmAHwsG/Fe0x/Zk7WJBXETGB7ekikBi7jXeWi12hFCCCFuxMZGV2m0rSrCwsKwtLQkLi6OHj16XPeYadOmodPp+Pnnn3nggQd48MEH6dWrV6Vj/vrrLwICAgDIzMwkOjqa5s2bX+1j3759lY7/888/CQ4OrjR6djNt27Zl3bp1eHh43HIzgJuxsLCgvPzmK0v88ccfjBw5kkceeQS4/Mzc/06qqGsy2eEGbPQ6PgzzZ3taDj+lZt/yeLen2hOw7BHSPvmTxBd/rvaMVEVR6Ok8kC9anKKjQz9ev/BfZp1/jMzStJp+BCGEEKJW7O3teeGFF5gyZQpr1qzh3LlzHD16lMWLF7NmzRp++uknPvvsM77++mv69OnDyy+/zIgRI8jMzKzUzuuvv85vv/3GqVOnGDlyJG5ubgwYMAC4XAj+9ttvvPHGG0RHR7NmzRoWLVpUrX3W//vf/+Lm5kb//v35448/uHDhAnv27GHSpEkkJCRUuZ2goCD27t1LYmIi6enp1z2madOmbNq0iWPHjnH8+HGGDRtW7VE9Q5JC7ib6ezpyr5s9U04nUFx+61+S+5hO+H/8EBc/2EvKvN016tPRzJU5jb/h9cbrOZa7m+HhLdibtblGbQkhhBC19cYbbzB79mzmzZtHaGgo/fr144cffiAoKIinn36aOXPm0LZtWwBee+01fHx8GDt2bKU23nnnHSZNmkS7du1ITk5m69atWFhYAJdH09avX8+3335Ly5YtmT17Nq+//jojR46sckYbGxv27t1LQEAAjz76KKGhoYwaNYrCwsJqjdC9/vrrxMTE0KRJk0q3ZP/XggULcHZ25q677uKhhx6iX79+Vz+/Fm7rvVarIjy3kFZ7w3krxJeXmnpV6ZykuTtJnrOTwJUDcXu6Q437vlR6kfdjn2Vf9lYednuWif4fYam7/vN6QgghxBWmstfq7t27ueeee8jMzKz2Nle3A9lrtQ6E2VszIciDN88kk1JUWqVzvGf3xm1sJ2Kf3UTWDzVfJ87F3JO3m2zmxcAVbM/4gnGRXUgoOlvj9oQQQgjRsEghVwVzgr0x1ym8dfb6iwP+m6IoBCzqj9OAMC4M+YaCo4k17ltRFB5yG82nzf+isCKP0RHt2J25scbtCSGEEKLhaDCF3OLFiwkLC6NDh5rfyrwRJ3Mzpjfx5NPYdGILiqt0jqLX0ejLwViFeXL2oTWUJOXUKkNTmztZGXqYjo79mHV+EB/HT6a0QpupzkIIIURV9OzZE1VV5baqETWYQm78+PGEh4dz8GDVtsyqrueDPHA21/PGmaqNygHobCxounU4KArnHl5DeX7tCi9bvQNzG61jsv8nfJ+2hAnR3blYotGWIEIIIYTQXIMp5IzNzkzPjKZerE7I4MwN9mG9HnNvB5r+MIKiyDRin95Q7WVJ/k1RFAZ6TGBxyD4ulabwdHhbjubuqVWbQgghxI2kpqYyZswYAgICsLS0xMvLi379+jFv3ryrm8vf6HVlH9Py8nIWLFhAq1atsLKywsnJifvvv5/9+/dXKcOVGa+Wlpa0bt36useoqsqKFSvo0qULDg4O2NnZ0aJFCyZNmsTZsw33+XIp5KphbKA7XpbmzImu+qgcgE1rH4I+H0TmuhOkLtx36xOqIMy2I6tCj9DE5k6mRN/L1rTlBmlXCCGE+F8DBw7k+PHjrFmzhujoaLZu3UrPnj0JCwu7url8cnIyjz/+OPfdd1+l9wYPHoyqqgwZMoTXX3+diRMnEhERwZ49e/D396dnz55s3rz5lhlUVWXUqFEMHjz4hj8fNmwYEydO5IEHHuDXX3/lxIkTfPzxx1hbW/Pmm28a+KqYDtnZoRqs9DpmNfNm3Mk4ZjT1oqWDdZXPdX6sFZ7T4kmY/jM2bX2x79G41nkczFyY32w7n8RP4f24MZwrPMnz/gswU+TXKoQQovaysrLYt28fu3fvvrqzQ2BgIB07drzmWGtra4qLi/HyqrxU17p169iwYQNbt27loYceuvr+8uXLycjIYPTo0fTp0wdbW9sb5vj4448BSEtL48SJE9f8fN26dXz77bds2bKFhx9++Or7jRs3pnfv3rW+G2bKZESump7ydyXIxoK5Z5Kqfa7vO/dh1y2I84+vpSTx1rtFVIWZYs6UgEVMDVjClrSlzDj7MAXleQZpWwghRMNRVFFAVMGRm76KKgoqnWNnZ4ednR2bN2+muLhqk/3+be3atQQHB1cq4q6YNm0aGRkZ7Nixo0ZtX/HNN98QEhJSqYj7Xw15u0sp5KrJQqfj5SZebEzOIroaz8oBKGZ6Gq8bhmKu4/ygr6koKTNYrkfcx/F+s585nvcHk6Lv4VLpRYO1LYQQov6LLYpkdES7m75iiyIrnWNmZsbq1atZs2YNTk5OdO3alVdeeeW6o2I3Eh0dTWho6HV/duX96Ojomn+w/39+SEhIpfcmT558tRD18/OrVfumTAq5Ghju54qnpRkfnK9+sWTuYUfjDU+QfyiBpFd/NWiuDg59WBzyB6klCYyLvIu4otr9hyGEEKLhCLRqzsrQwzd9BVo1v+a8gQMHkpSUxNatW+nXrx+7d++mbdu2VycyGMKVEbP777//avHVokWLGrVxxcyZMzl27BizZ88mL6/h3qmSh6lqwEqvY0ojT2ZFJzEn2BsfK4tqnW/XOQDfefeROH0b9r2b4tgv2GDZmtm0ZlnzA0w/ez/PRd7Fu01/pIVdZ4O1L4QQon6y0tkQYlOzPUGtrKzo06cPffr0Yfbs2YwePZrXXnutSvuhBgcHEx5+/V2OIiIiAGjWrBkAK1eupLCwEABzc/Mq52vWrBmRkZVHE93d3XF3d8fDw6PK7dRHMiJXQ2MC3bHSKSw8n1qj8z2n3o1Dv2Bihq+nNCXXoNm8LYNYErKfAKvmTIruxb6srQZtXwghxO0tLCyM/Pz8Kh07ZMgQzpw5ww8//HDNz+bPn4+rqyt9+vQBwNfXl6ZNm9K0aVMCAwOrnGfo0KFERUWxZcuWKp/TUEghV0OO5nqeC/RgaWwamTV41k3R6Qha8xgoEDNiPWpFhUHzOZi5sCB4B50d72fmuUf4OWONQdsXQgjR8GVkZNCrVy+++uorTpw4wYULF/juu+9477336N+/f5XaGDJkCI888ggjRoxg1apVxMTEcOLECcaMGcPWrVtZuXLlTWesApw9e5Zjx46RkpJCYWEhx44d49ixY5SUlFztY9CgQVeXOfn777+JiYlhz549rFu3Dr1eX+trYaqkkKuFSY08KFVVlsam1eh8c097Gn05mJxfz5C6sGqLIlaHpc6auY3X86Db07wdM5JNqYsN3ocQQoiGy87Ojk6dOrFgwQK6d+9Oy5YtmTVrFs888wyLFi2qUhuKorB+/XpmzpzJggULaN68Od26dSM2NpZdu3YxYMCAW7YxevRo2rRpw6effkp0dDRt2rShTZs2JCUlXe1j3bp1LFy4kG3bttG7d29CQkIYNWoU/v7+7NtnmDVcTZGiNrDFVXJycnB0dCQ7OxsHBwej9/fsiVh+vJhNTO+WWOhqVhfHT/2RtCV/EXp0Itahhr+Xr6oqixNeYF3qh4zxnccTXi8bvA8hhBCmo6CggIiICEJDQ7GxsdE6jriBK7+nmJgYsrKyyM3NZfjw4bi4uFS5DRmRq6WJQR4kF5eyITmrxm34vtUPy0bOxAxfj1pWbrhw/5+iKIz3+4CnvF/j08QZrEh8tUEvjiiEEELcLqSQq6WWDtb0drPnows1X7dNZ21O0JrHKTiaRMq83YYL9z8URWGUzxzG+b7HFylvsSJJijkhhBCivpNCzgAmNfLgn6wC/sqs+To1th398ZrRk6TXf6PgaKIB01U2zGs64/0+4MuUt1meNFOKOSGEEKIek0LOAB70cKSJjSUfXajZUiRXeM/qhXULTy4MX09FseF2ffi3IZ7TGO83n69S5vFp0itSzAkhhLih1NRUxowZQ0BAAJaWlnh5edGvXz/mzZuHoig3fV1ZNLi8vJwFCxbQqlUrrKyscHJy4v7772f//ltP9Dt+/DhDhw7F398fa2trQkND+eijj645TlVVVqxYQZcuXXBwcLi6qPCkSZM4e/asoS+LyZAFgQ1Apyg8H+TOCxEJfFBYgq919RYIvtqOhRlBXzxOZPtFJL22A7937jdw0v8zxHMqCgqLEqaiQ8ezvm8ZrS8hhBD118CBAyktLWXNmjU0btyYixcv8ttvvxEWFkZycvLV4yZNmkROTg6ff/751fccHR1RVZUhQ4awc+dO3n//fXr37k1OTg6LFy+mZ8+efPfddzeduXr48GHc3d356quv8Pf3588//+TZZ59Fr9czYcIE4HIRN2zYMDZv3swrr7zCggUL8PDw4MKFC+zYsYM333zToDtRmBIp5AzkKX83ZkUnsSQ2jbea+9a4HZtW3njPvZekV3/FedAd2LY33v5wgz2nUKGWsyRxOrZ6R/7r9aLR+hJCCFH/ZGVlsW/fPnbv3k2PHj0ACAwMpGPHjtcca21tTXFxMV5eXpXeX7duHRs2bGDr1q089NBDV99fvnw5GRkZjB49mj59+txwLblRo0ZV+nPjxo05cOAAmzZtulrIrVu3jm+//ZYtW7bw8MMPVzq2d+/eDfrOk9xaNRAHcz0j/VxZGZdOSS0X9/Wa3h3rVl7EPrMRtdTws1j/11CvFxjh9SrLEl9iS9qnRu1LCCGEdioKSig4knjTV0VBSaVzrux7unnzZoqLi2vU79q1awkODq5UxF0xbdo0MjIy2LFjR7XazM7OrrRExzfffENISEilIu5//Xsf1oZERuQMaEygO5/EpLElJZvHfJxr3I5ipidw5UAiOy7m4oJ9eL3Yw4Apr/W0z+vklWczP24ctnoH7nUZatT+hBBC1L2iyDQi2n1y02NCDz+PTdv/u6tkZmbG6tWreeaZZ1i2bBlt27alR48eDBkyhFatWlWp3+joaEJDQ6/f3/9/Pzo6uoqfAg4cOMD69ev56aefKvUREhJS6bjJkyezcuVKAJycnEhISKhyH/WJFHIG1MLemq7OtiyLTatVIQdg284Pj8ldSXptB06PtsCqqZuBUl5LURQm+i+koCKXNy88ibXOjq5O1/7LSQghRP1l1dyd0MPP3/KYfxs4cCAPPvggf/zxBwcOHGD79u289957rFy5kpEjRxok25URs/vvv58//vgDuHwL9/Tp05WOO336NP3792f27NlX92f9dxtXzJw5kwkTJrBp0ybefvttg+Q0RQ2mkFu8eDGLFy+mvNy4tyJvZWygO08ei+FMXhHN7Kxq1ZbP633J2nSauLGbabbjaaMODesUHS8GrqCgPIfZ5x/jvabbaOfQy2j9CSGEqFs6G4tKo23VYWVlRZ8+fejTpw+zZ89m9OjRvPbaa1Uq5IKDgwkPD7/uzyIiIgBo1qwZACtXrqSwsBAAc3PzSseGh4fTq1cvnnnmGV599dVKP2vWrBmRkZGV3nN3d8fd3R0PD8PvmGRKGswzcuPHjyc8PJyDBw9qmmOQtzMu5nqWx6XXui29rQWBnz5C7m9nyVhz2ADpbs5MMWN2o7Xcad+DGece5nT+30bvUwghRP0TFhZGfn5+lY4dMmQIZ86c4YcffrjmZ/Pnz8fV1fXq6Jqvry9NmzaladOmBAYGXj3u9OnT3HPPPYwYMYK33rp2lYWhQ4cSFRXFli1baviJ6q8GU8iZCiu9jhF+rnwen05Ree0mPQA49A3G5b+tSZz+M2WXCgyQ8OYsdJa81XgTTa1bM/3M/VwovP6/ooQQQjR8GRkZ9OrVi6+++ooTJ05w4cIFvvvuO9577z369+9fpTaGDBnCI488wogRI1i1ahUxMTGcOHGCMWPGsHXrVlauXHnDGavwf0Vcnz59mDp1KikpKaSkpJCWllapj0GDBjFkyBBef/11/v77b2JiYtizZw/r1q1Dr9fX+lqYKinkjODZQHcySsvZlJJlkPb8PniQipIykmb9apD2bsVab8u7TX/E3cKPF88+QEZpSp30K4QQwrTY2dnRqVMnFixYQPfu3WnZsiWzZs3imWeeYdGiRVVqQ1EU1q9fz8yZM1mwYAHNmzenW7duxMbGsmvXrpuuIQfw3XffkZaWxtdff423t/fVV4cOHSr1sW7dOhYuXMi2bdvo3bs3ISEhjBo1Cn9/f/bt21eby2DSFLWBLa6Sk5ODo6Mj2dnZODg4aJaj559RqMCeu0JueWxVXFy4j4SpPxF6aEKNn3Godp8l8YyN7IyLuRefBO/BRm9XJ/0KIYSonYKCAiIiIggNDcXGxkbrOOIGrvyeYmJiyMrKIjc3l+HDh1daWuVWZETOSMYEurP3Uh4RuYUGac9jQhesWngQN34Lai3XqasqTwt/3mv6E/FF0cy5MIQy1XjbhgkhhBCi+qSQM5JHvZxwszDjUwNMeoDLa8sFLO5P/l9xZKw2/sSHK5rZtOaNxhv4J3s7H8VPbNCrYwshhBD1jRRyRmKp1/GUnytrEjIoNMCkBwD77o0vT3x4aTtlmcaf+HBFJ8d+TAtcxua0pXxz8YM661cIIYQQNyeFnBGNDnAjq7SczQaa9ADg9/4DVBSXkTSretuZ1NZDbqMZ7jWTpYkv8tuldXXatxBCCO2kpqYyZswYAgICsLS0xMvLi379+jFv3jwURbnp68pG9eXl5SxYsIBWrVphZWWFk5MT999/P/v3779l/xkZGdx33334+PhgaWmJv78/EyZMICcnp9JxqqqyYsUKunTpgoODA3Z2drRo0YJJkyZx9uxZY1wakyCFnBEF21nR1dmWz+MNc3sVwNzbAZ+595K29C8KjiYarN2qGO3zBn1dnuCtmOEcz/2jTvsWQgihjYEDB3L8+HHWrFlDdHQ0W7dupWfPnoSFhZGcnHz19fjjj3PfffdVem/w4MGoqnp1WZCJEycSERHBnj178Pf3p2fPnmzevPmm/et0Ovr378/WrVuJjo5m9erV7Ny5k7Fjx149RlVVhg0bxsSJE3nggQf49ddfOXHiBB9//DHW1ta8+eabRr5K2pFZq0b2WVw6o0/EEtP7DgKsLQzSplpaTnibj9E7WBKyf1ydbgZcWlHCtDP9OF94kuWhB/GxbFRnfQshhKgaQ81azcrKwtnZmd27d9Ojx833/R45ciRZWVnXFGbr1q1jyJAhbN26lYceqrz948CBA9mzZw+xsbE3XUvu3z7++GPef/994uPjAfj2228ZOnQoW7Zs4eGHH77meFVV6/TvyqqSWav1wGM+zljrdayJzzBYm4q5noBPHib/QByZ604YrN2qMNdZ8GaTjdiZOTHj7MMUlOfWaf9CCCHqjp2dHXZ2dmzevJni4uIatbF27VqCg4OvKeIApk2bRkZGBjt2VP1xoaSkJDZt2lSpsPzmm28ICQm5bhEH1+7D2pBIIWdk9mZ6HvN2ZnVCOhUGHPy0v6cJjg+Hkvjyz1QUlRqs3apwMHNhXpOtpJTE8mbMcCrUulkORQghRM0VlFdwJLvgpq+Cf03OMzMzY/Xq1axZswYnJye6du3KK6+8wokTVR9EiI6OJjQ09Lo/u/J+dHT0LdsZOnQoNjY2+Pr64uDgwMqVKyv1ERJSed3WyZMnXy1E/fz8qpy3vpFCrg6M8nflfEEJf1zKM2i7fu89QEliDqkf3fphUUNrZB3G7EZr2Ze1hc+S59R5/0IIIaonMq+Idn9E3PQVmVd0zXkDBw4kKSmJrVu30q9fP3bv3k3btm2vTmQwhCsjZvfff//V4qtFixaVjlmwYAFHjhxh8+bNnDt3jqlTp163jStmzpzJsWPHmD17Nnl5hv3715SYaR3gdtDNxY4mNpZ8Fp9OD1d7g7VrFeKO+7jOJL+9C9dR7TF3r9udF7o6/YcxvvNYlvgyja1a0svl8TrtXwghRNU1t7PicLfrj4z97zHXY2VlRZ8+fejTpw+zZ89m9OjRvPbaa4wcOfKW/QYHBxMefv19uyMiIgBo1qwZACtXrqSw8PJC+ubm5pWO9fLywsvLi+bNm+Pq6kq3bt2YNWsW3t7eNGvWjMjIyErHu7u74+7ujoeHxy0z1mcyIlcHFEVhpL8rG5KzyC0rN2jbPrN7oygKyXN2GrTdqhrm+SJ9XIbxdsxIoguOapJBCCHErdnodbR1tLnpy0ZftbIgLCyM/Pz8Kh07ZMgQzpw5ww8//HDNz+bPn4+rqyt9+vQBwNfXl6ZNm9K0aVMCAwNv2OaVeZpXntsbOnQoUVFRbNmypUqZGhIp5OrICD9XCssrWJ+UadB2zdxs8Xq1F2mf/kNhRKpB264KRVF4KXAljaxbMONsfzJL6z6DEEII48jIyKBXr1589dVXnDhxggsXLvDdd9/x3nvv0b9//yq1MWTIEB555BFGjBjBqlWriImJ4cSJE4wZM4atW7eycuXKm85Y3bZtG59//jmnTp0iJiaGbdu2MW7cOLp27UpQUNDVPgYNGnR1mZO///6bmJgY9uzZw7p169Dr9Ya4HCZJCrk64m9tQS83e75MMNzs1Ss8nr8LiwAnEqdvM3jbVWGps+btJpspU0tkT1YhhGhA7Ozs6NSpEwsWLKB79+60bNmSWbNm8cwzz7Bo0aIqtaEoCuvXr2fmzJksWLCA5s2b061bN2JjY9m1axcDBgy46fnW1tasWLGCu+++m9DQUCZPnsx//vMffvzxx0p9rFu3joULF7Jt2zZ69+5NSEgIo0aNwt/fn3379tXmMpg0WUeuDq2Jz2Dk8RhierUk0MbSoG1nfneC84+vpdmOp3G4t5lB266qo7l7mBLdm6FeLzLG921NMgghhDDcOnLCuGQduXrmUW8nbPQ6vk68ZPC2nQbdge1dgSRM+wnVQHu7Vlcb+x486zuPr1LmsS9rqyYZhBBCiNuJFHJ1yN5MzyNeTnyZeAlDD4QqioL/hw9SeCKFjDWHDdp2dQz1fIFuTgN4K2Y4icXnNMshhBBC3A6kkKtjT/q6EJlXxKHsAoO3bdspAOchd5I481fK82q2AndtKYrCK0GrcTJz59VzAymqMPznFEIIIcRlDaaQW7x4MWFhYXTo0EHrKDfV280Bb0tzo0x6APCd14/ySwWkLtDuwU47vSNvNN5IfFE08+OeM/jooxBCCCEuazCF3Pjx4wkPD+fgwYNaR7kpM53CMF8Xvk3KpLTC8AWOZZAL7uO7kPL+XsrSq7bGjzE0tWnFC4Gfsj1jDT+kr7z1CUIIIYSotgZTyNUnT/q5kFZSxi9p2UZp3/uVewBInrfLKO1X1X2uT9LfbSwL4ycQmX9I0yxCCCFEQySFnAbudLChlb01XyQYfvYq/P9Fgqd3J23RAUrisozSR1VN9F9IU+s7mXV+EDllxvm8QgghxO1KCjmNPOnnwtaLWWSVGmfxXI8pd6N3tCJpzg6jtF9VFjpL3miygYLyXObFPCXPywkhhBAGJIWcRob5ulBaobIhOcso7evtLPGe1YuMNUcoDL9olD6qytMigFeCVrMveysbUj/WNIsQQgjRkJhpHeB25WNlwb3uDnyZkMHoADej9OE2phMXP9xH0sxfaPL9cKP0UVVdnR7iMY/JLEmcTiu7uwmxbadpHiGEuB0UFhZqHUHchCF+P1LIaegJXxeGH4shrrCEAGsLg7evszDD542+xDy5jry/4rDrHGDwPqpjrO87nMj7g9cuDGZV6BFs9aa1hZoQQjQUZmZm6HQ6YmJitI4ibkFVVcrLy2t8vuy1qqHcsnI8fj3O6yE+TG/iZZQ+1IoKIlp/jJmHHcE7Rxulj+pILD7HqPA2dHF8kNcarUVRFK0jCSFEg1RSUkJZWRnZ2dn8+OOP2NraYmlp2H2+Re2Vl5dTVlZGYWFhjfZalRE5Ddmb6XnY04m1iZeMVsgpOh3ec+/l/KNfkbvnPPY9Ghuln6rytWzC9MDlzL0wlA4OfXnQ7SlN8wghRENlYWGBhYUFRUVF5OfnU1paKoWcCSsurtmOTFLIaWyYrwsDDp0jPLeQMHtro/ThNKAFNm19SZr1K8F7xmg+CnavyxD+yfmFj+In0tq+O76WTTTNI4QQDZmlpSUODg7k5ORQUlKidRxxEw4ODtUutuXWqsaKyyvw2nmCCUHuvBHia7R+sn+K5Ox/VtPs16dx6NPMaP1UVUF5Lk+Ft8bZ3INFIX9gpsi/KYQQwljy8/NrPOIj6o6lpSW2trbVOkcKORMw+ngMuzJyOXtPS6ONlqmqSlSXJQCEHHhO81E5gFN5B5gQ1Y3h3q8yymeO1nGEEEKIekfWkTMBw3xdOF9Qwj9ZBUbrQ1EUfN7oS/7f8eRsizJaP9XR0q4Lw71fZU3yG5zKO6B1HCGEEKLekULOBPRwtcfb0pxvkoy7hZX9vU2x6xZE0uwdJrPDwnDvVwm17cgbF56goDxX6zhCCCFEvSKFnAnQKwpDfJz5NukS5UYssK6MyhUcSSRr82mj9VMdZooZsxp9RWZZKgvjJ2odRwghhKhXpJAzEcN8XbhYXMaudOOOStn3aIx976aXR+UqKozaV1X5WjZhkv/H/Jyxml2ZG7SOI4QQQtQbUsiZiHaONjS1sWStkW+vAvi83oeiUxfJ/O6k0fuqqgdcR9LDaSDvxz5LWkmi1nGEEEKIekEKOROhKArDfF3YmJxJUblxR8rs7grE4b5gkufsRDVyX1WlKArTAz/FUmfNWzEjqFBNI5cQQghhyqSQMyFDfV3IKatgW2q20fvyeb0PRZFpXFp7zOh9VZWjmSszg9ZwOPc31qcu1DqOEEIIYfKkkDMhze2saOtoY/TZqwC2HfxxfDiU5Nd/Qy2r+Wa9htbe4V4Ge0xlReIrXCgM1zqOEEIIYdIaTCG3ePFiwsLC6NChg9ZRamWYjws/XMwmp9T4xZXPnHspPpvBpW9PGL2v6njG9028LRsxL2YkZWqZ1nGEEEIIk9VgCrnx48cTHh7OwYMHtY5SK4N9nCmpUPk+Jcvofdm08cXxP81JfvN3k3lWDsBSZ80rQWuIKjjM2pR3tY4jhBBCmKwGU8g1FH7WFnR3sauT2asA3rN6UxyVZlIzWAHCbDvyX6+X+Tx5LmcLjmsdRwghhDBJUsiZoGG+LuxMy+FicanR+7Lt6H95Buubv5vMunJXjPSeTYBVc96MGU5pRYnWcYQQQgiTI4WcCRro7YxeUfguKbNO+vOe3Zui0xfJ+t40dnu4wkJnyatBXxBTGM6a5De0jiOEEEKYHCnkTJCrhRn3eTjU2e1Vuy6B2N/b9PIMVhMblWtm05oR3rP4KmUeEfn1+/lHIYQQwtCkkDNRw3xcOJCZz/n84jrpz3tWLwpPpJD9Q0Sd9FcdT3rPoKlNa96KGUFxRZHWcYQQQgiTIYWciXrI0xEbvY5v62hUzr57Y+x6NCL59d9RVbVO+qwqM8WcmUFrSCo+J7dYhRBCiP8hhZyJsjXT09/TsU4WB77Ce3ZvCo4kkvNzVJ31WVWNrFsw3PtV1qa8S3TBUa3jCCGEECZBCjkTNtTXhVO5RZzKKayT/uzvaYJt18DLz8qZ2KgcwBNeLxNk3YJ3YkZRphp/Rq8QQghh6qSQM2H93B1wNtfX2aicoij4zO5N/t/x5O44Uyd9VoeZYs6MwM84X3iStSnvax1HCCGE0JwUcibMQqdjkLcz3yRdqrMRMvs+zbDt5E/SXNMclQuxbccQzxdYnTyXmELTm5ghhBBC1CUp5EzcUB8XLhSU8HdWfp30pygK3rN6k/9nLLm7ztVJn9X1lM9reFkE8W7s05Srxt+TVgghhDBVUsiZuO6udnhbmvNNYt0sDgzg8EAINm19SXnz9zrrszosdda8HLSKU/kH2JS6SOs4QgghhGakkDNxekVhsI8z65MvUV5HtzoVRcFr5j3k7jpP3l9xddJndbWyu5tH3cezPOkVkoovaB1HCCGE0IQUcvXAUB8XUorL2J2RW2d9Og0Iw6q5OynzdtVZn9U1xncejmZuvB/7rEk+zyeEEEIYmxRy9UAHJxua2FiyNrHu1pRTdDq8Xu5J9tYICk+m1Fm/1WGjt+fFwBUcyt3JTxmfaR1HCCGEqHNSyNUDiqIw1NeZjclZFJfX3V6oLsNaYxHgRMo7u+usz+rq6NCX+1xHsCRhOpdKL2odRwghhKhTdVLILVmyhEaNGmFlZUW7du34448/bnjs7t27URTlmldkZGRdRDVZQ31cyC4rZ3taTp31qZjr8XyxB5e+PU7xuYw667e6xvt9gA4dn8RP0TqKEEIIUaeMXsitW7eOyZMnM3PmTI4ePUq3bt24//77iYu7+UP0UVFRJCcnX301a9bM2FFNWpi9Na3sret0yy4At1HtMXOzJeX9vXXab3U4mbkxwX8BOzO/4e/s7VrHEUIIIeqM0Qu5Dz/8kKeffprRo0cTGhrKwoUL8ff3Z+nSpTc9z8PDAy8vr6svvV5v7Kgmb5ivC1tTssgrq7u103TW5nhOuZuMzw9RklR3o4HV1c/lCdrb38v8uHEUltfNmntCCCGE1oxayJWUlHD48GH69u1b6f2+ffvy559/3vTcNm3a4O3tTe/evdm168YzJ4uLi8nJyan0aqiG+DhTWKGyJSWrTvt1H9cZnbU5qR/e+Ja41hRF4YXAZWSUpvBZ8hyt4wghhBB1wqiFXHp6OuXl5Xh6elZ639PTk5SU68+E9Pb2Zvny5WzcuJFNmzYREhJC79692bv3+rf25s2bh6Oj49WXv7+/wT+HqQi0seQuZ1u+Saq7xYEB9I5WuE/oQtqyvynLMN3RLl/LJjzl8xrfXVxAdMFRreMIIYQQRlcnkx0URan0Z1VVr3nvipCQEJ555hnatm1Lly5dWLJkCQ8++CAffPDBdY+fMWMG2dnZV1/x8fEGz29Khvq48EtaNhklZXXar8ekrqgVKqmf3HwkVWtDPKcRaB3Ge7HPyPZdQgghGjyjFnJubm7o9fprRt9SU1OvGaW7mc6dO3PmzJnr/szS0hIHB4dKr4bsMR9nKlTYmFy3o3Lm7na4P9uR1I//pDy3uE77rg4zxZwXA1cQXXCEjamfaB1HCCGEMCqjFnIWFha0a9eOHTt2VHp/x44d3HXXXVVu5+jRo3h7exs6Xr3kaWnOve4Odbo48NW+p3WjIq+E9OV/13nf1dHCthOPuD/HyqRZpJYkaB1HCCGEMBqj31qdOnUqK1eu5LPPPiMiIoIpU6YQFxfH2LFjgcu3RocPH371+IULF7J582bOnDnD6dOnmTFjBhs3bmTChAnGjlpvDPVxZu+lPBILS+q0Xwt/J1yebMPF+X9QUVRap31X12ifN7HW2bIoYarWUYQQQgijMXohN3jwYBYuXMjrr79O69at2bt3L9u2bSMwMBCA5OTkSmvKlZSU8MILL9CqVSu6devGvn37+Omnn3j00UeNHbXeeMTLGQudwro6vr0K4PVSD0pT8shYc6TO+64OezMnJvh/yK7M7/g7+xet4wghhBBGoagNbLfxnJwcHB0dyc7ObtDPyz166BzxhSUc7BZa532fH7yW/IMJtIyehmJmuuv7qarK5DO9SS2JZ3XYSSx1VlpHEkIIIQxK9lqtp4b6uHAou4AzeUV13rfXjJ6UXLhE5vqTdd53dSiKwtSAJaSUxLI25V2t4wghhBAGJ4VcPfUfT0fs9Lo637ILwKa1Dw4PhJA8bxdqRUWd918dgVbNGeo5na9S5pFQdFbrOEIIIYRBSSFXT1nrdTzi5cQ3SZlocXfce8Y9FJ26SPaPkXXed3UN956Jq7k3C+InaHKthBBCCGORQq4eG+rrQmReEcdzCuu8b7u7g7DrFkTyW7tMvjiy0tkwyf8T/sn5hd1ZG7WOI4QQQhiMFHL12L1uDria6zW5vQrg9co9FPwTT+6uc5r0Xx1dnf7D3Y79+SR+MgXluVrHEUIIIQxCCrl6zFyn8LiPC98kXqJCg1Exh37BWLf25uK7e+q875qY5P8RueWZfJY0R+soQgghhEFIIVfPDfVxJr6olD8z634ze0VR8Hq5Jzm/nqHgSGKd919dXpaBjPSezYbUjzhbcELrOEIIIUStSSFXz3V1scPPypxvNNiyC8B5YEssm7iSUk9G5R73mIKfVTDz48ZRoZr2jFshhBDiVqSQq+d0isIQHxe+S86ktKLub68qZno8p3cnc8NJis6k13n/1WWus2BawBJO5f/JtozPtY4jhBBC1IoUcg3AUF8X0krK+C09R5P+XUe0xczdlovv79Wk/+pqY9+Tfi5PsjThRbLKTL/4FEIIIW5ECrkGoI2DNSG2lprNXtVZmeM55W4y1hymJEmbYrK6nvN7nwrKWZn4qtZRhBBCiBqTQq4BUBSFob4ufJ+SRWG5Ns99uY/tjGJlRurCfZr0X10u5p6M8p7L1vTlRBUc0TqOEEIIUSNSyDUQQ31cyC2rYFtqtib96x2t8BjfhbSlf1GWWaBJhup6xGM8jaxasDBugkx8EEIIUS9JIddABNtZ0dbRRrPZqwAek7qillaQtvRvzTJUh5lixuSATziVf4BfL32ldRwhhBCi2hpMIbd48WLCwsLo0KGD1lE0M8zHhR9Ts8kuLdekf3NPe9xGtSd14T4qCks1yVBdbex70sv5cZYmvEh+ef14vk8IIYS4osEUcuPHjyc8PJyDBw9qHUUzQ3ycKalQ2ZCcqVkGzxe6UZZRQPrnhzTLUF3P+X1AQUUuq5Nf1zqKEEIIUS0NppAT4GttQW83e75MyNAsg2VjV5wHt+Li+3tRy7QZGawuTwt/nvR6he8ufkRMYYTWcYQQQogqk0KugXnC15U9l/KIKyzRLIPXSz0oicnk0rr6sw3WYM9peFoE8FH8RFQN9q0VQgghakIKuQbmUW8nrHUKXydqNypnc6cPDveHkPLO7npTFFnqrJjov5BDuTvZm/W91nGEEEKIKpFCroGxN9PziJczXyZc0rSI8nq5B0WnLpKzLUqzDNV1l+N/6OzwAIsSplJUUT+WUBFCCHF7k0KuAXrCz4WIvCKO5hRqlsGuWyNs7wok5Z3dmmWoLkVRmOi/kIzSZNamvKd1HCGEEOKWpJBrgPq4OeBpaabppAdFUfB6uQd5+2LI2xejWY7q8rdqxuOeU/k65V2Sii9oHUcIIYS4qQZXyKWmXl6/7OzZIo2TaMdMpzDUx4Vvki5RVqHd7VXHB5tj1cKTlHd3a5ahJoZ7zcTRzJVFCVO1jiKEEELcVIMr5NLTywDo2jWSJUtS683D9ob2hK8LF4vL2Jmu3SK3ik6H10s9yP4xksKTKZrlqC4bvR3P+b3PH1mb+SfnV63jCCGEEDfU4Aq5sDBrAJ54wpXx4+O5776zJCZqtxSHVto62hBqZ8WXCdpt2QXgMuROLAKc6t2oXG/nIdxp152P4iZSWnH7fX+EEELUDw2ukLti/nx/tm9vysmThdxxRzjffqttQVPXFEXhST8Xvk/JJFfDhXkVcz2eL3Tj0rcnKL5Qf34HiqIw2f8TEorPsDFtkdZxhBBCiOtqsIUcQL9+jpw6FUbfvg4MHXqBIUPOc+lSmdax6swwHxcKK1S+T8nSNIfb0x0wc7bm4vw/NM1RXU1tWvGw+xjWJL9OZmma1nGEEEKIazToQg7AxcWMb79tzDffNOKXX3Jo2TKc7duztY5VJwJtLOnhYqfp7FUAnY0FHhPvIn3VQUpT8zTNUl2jvOcCsCpplsZJhBBCiGs1+ELuiiFDXDh1Kow77rDm/vvP8txzceTn14+9QGvjST9XfkvPJVHDLbsA3Cd0QTHTkfrxfk1zVJezuTsjvV/jh/QVnC2oP1uOCSGEuD3cNoUcgK+vBdu3N2XxYn9Wr06ndesI/vqrfo0QVddAbycsdAprk7R9Ps3M2Qb3MZ1IW3yA8pz6tTTMo+7j8bVsyicJk2/bWdBCCCFM021VyMHlh9ife86DY8fCcHU1o2vXKGbNSqS0tGH+Be1kbsYALydWx2doXoR4TLmbivxS0pb/o2mO6jLXWTDB/0OO5O7ij+wtWscRQgghrrrtCrkrgoOt2LcvhDlzfJg3L4W7745ssIsIj/RzJTyviEPZ2u4fauHriMvwNqR++AcVxfVr0kkXhwfo6NCPJQkvUFJRrHUcIYQQAriNCzkAMzOFWbO82b+/ORkZ5bRuHcHnn6drPnJlaH3cHfCxNOfzeG0nPQB4Te9BaUoel748onWUalEUhQl+H5JSHMN3qR9pHUcIIYQAbvNC7opOnWw5ejSUwYOdGTUqlscfb1jLlOgVheF+rnyTdImi8gpNs1iFuOP0aAtS3tuLqnGW6mpkHUZ/93F8kfwml0ovah1HCCGEkELuCnt7PatWBfHdd4357bdcWrUKZ9euXK1jGcxIf1eySsvZcjFL6yh4vdSD4jPpZG06pXWUahvlMwe9YsaKpFe1jiKEEEJIIfdvgwY5c+JEGMHBVvTuHc1LLyVQUlK/Ro6uJ8TOii7Otqw2gdurth38se/dlJR39tS729iOZq6M8pnLT+mriC44qnUcIYQQt7kGU8gtXryYsLAwOnToUOu2/Pws2LGjGe+848uCBal06RJFZGT9nwjxlJ8rv6blaL6mHIDXjJ4UHEkkd+dZraNU2wD3sQRYNefjeFmORAghhLYaTCE3fvx4wsPDOXjwoEHa0+sVXnzRiwMHQsjPL6dt23A+/TStXv/F/biPCxY6hS8Ttd/z1L5XE2za+5Hyzm6to1SbmWLO834LOJ63l91ZG7WOI4QQ4jbWYAo5Y2nXzpbDh0MZPtyVsWPjGDDgHGlppVrHqhFHcz2PejmzOl77mbmKouD1cg9yfz9H/j/xmmapiU6O/ejs8ABLE6ZTXFH/R2uFEELUT1LIVYGtrZ5lywLZvLkJ+/fn0apVOL/8Uj/3a33K35Wo/GL+ysrXOgpOA1pgGexGyru7tY5SI8/7f0hqSQLrLy7QOooQQojblBRy1dC/vxMnT7agVSsb7rvvLFOmxFNcXL8mQtzjZo+/lblJTHpQ9Dq8XuxB1vfhFEWmah2n2gKsQnjUYwJfprxFemmy1nGEEELchqSQqyZvb3N+/rkpCxb4sWRJGp07RxIVVX9urekVhRH+rnybdIkCE1jHzeWJNph725Py3h6to9TIU96zsVCsWJ74itZRhBBC3IakkKsBnU5h8mRP/vqrOQUFFbRrF8Hq1do/d1ZVI/xcySmr4PvkTK2joLM0w3Pq3Vz66hgl8Vlax6k2ezNnnvZ9g58zVhOZf0jrOEIIIW4zUsjVQps2Nhw+HMpjjznz1FOxPPFEDDk55VrHuqWmtlZ0c7HjMxO4vQrg9mwndHYWXFywT+soNfKQ2zM0tmopy5EIIYSoc1LI1ZKdnZ7PPw/i668b8cMPWbRtG8HBg9pPJLiVZwLc+D0jlzN52t8W1ttb4jGhC+nL/6Esw/Sv3b+ZKWY877+Ak/n7+S1zndZxhBBC3EakkDOQYcNcOHo0DGdnPXfdFckHH6RQUWG6ozODvJ1xMtezMj5d6ygAuD9/F2qFSuriA1pHqZH2Dvdyt+PDfJr4sixHIoQQos5IIWdATZpYsn9/CFOmeDJ9eiIPPHCWixdNc805a72O4b6urI7PoKRC+0kP5u52uI3uQOrHf1Ker/3OEzUxzu890koS2ZD6kdZRhBBC3CakkDMwCwsd773nx/btTTl6tIA77wxnx44crWNd1zMBbqSWlLE1xTTWxPOc1o3yrCIyVhlmd466FmAVwiMez/FF8ltklta/5VSEEELUP1LIGUm/fo4cPx5Gq1bW9O17hpdfTqC01LRutbZ0sKaLsy3L49K0jgKAZaAzLsPuJOWDvailpj9p5HpGes9Gp+hZlfSa1lGEEELcBqSQMyIvL3O2b2/Gu+/6Mn/+Rbp1i+LChWKtY1XybIAbO9JzuVBgGrm8XuxBaXw2l9Ye0zpKjTiauTLCexY/pC/nQuFpreMIIYRo4KSQMzKdTuHFF73Yt685qamltGkTwaZN2q/fdsXjPi44mulZGWcakx6sW3rh+FAoKe/uQTWBZ/dq4lH38XhbNmJxwgtaRxFCCNHASSFXRzp1suXIkVDuvdeegQPPM2mSaWzvZaPX8YSvC5/Fp1NqIrNsvV7uSVFEKtk/RGgdpUYsdJaM832Pv3O283f2L1rHEUII0YBJIVeHnJzM+O67xixa5M+yZWl07RrF+fPa39J8JtCNlOIyfko1jUkPdncFYte9ESnzdtfbBXa7Oz3CnXbdWJwwjTK1TOs4QgghGigp5OqYoiiMH+/Bn3+GkJlZRps24WzcqO2t1jsdbOjoZMPyWNOY9ACXR+Xy/44nb+8FraPUiKIoTPD7kAtFp9mW/pnWcYQQQjRQUshppF07W44cCaNvXwcGDTrP88/HaXqr9dkAd7an5RBrIpMeHO4LxrqVFynv7NY6So01t21PX5cnWJk0i/xy01yCRgghRP0mhZyGHB31rF9/+Vbr8uXpdO0axblz2hRSg32csTPTmcz+q4qi4PVyT3K2R1NwLEnrODX2rO/b5Jfn8HXKu1pHEUII0QBJIaexK7daDxxoTlZWOW3bhrNhQ93farUz0zPMx4VV8emUmcikB+fH7sCikQsp7+7ROkqNeVr4M9TzBdZdnE9KcazWcYQQQjQwUsiZiLZtbTh8OJR+/Rx57LHzTJgQR1FR3d5qfTbQncSiUn5OM41JD4qZHq/p3clcf4Kis6axPEpNDPN6CTu9M8uTXtE6ihBCiAamwRRyixcvJiwsjA4dOmgdpcYcHfWsW9eIJUsCWLEinbvuiuTs2brbgL2tow3tHW1YGmM6kx5cR7bDzM2Wix/8oXWUGrPR2/GM75vsuLSW0/l/ax1HCCFEA6Ko9XV9hxvIycnB0dGR7OxsHBwctI5TY0ePFvD44+e5eLGUlSsDefxxlzrpd3V8Ok8dj+XMPS1oamtVJ33eSvK8XSTP2ckdMS9h7l0/f6flajlPR7TFWmfHkpB9KIqidSQhhBANQIMZkWto2rS5fKv1gQccGTz4As89Vze3Wgf7uOBqrmepCS1F4vFcFxQrMy5+tF/rKDWmV/RM8JvPqfw/2Z21Ues4QgghGggp5EyYg4Oeb75pxNKlAXz2WTpduhj/Vqu1XsfTAW58Fp9BfplpbFyvd7TCfVxn0pb+RXl23d1qNrT2DvfSxfFBlia8SEmFaSzzIoQQon6TQs7EKYrC2LHu/PVXc/LzK2jbNoL16y8Ztc9xge5kl5azNtG4/VSH56SuqMXlpC39S+sotfKc7/uklsSxMfUTraMIIYRoAKSQqydat758q/XBBy/fajXmAsJBNpY85OnIopg0k9kiy9zbAdeR7bi4YB8VhaVax6mxIOtQ+ruP5YuUN8kqq78zcYUQQpgGKeTqEXt7PWvXXp7Vunx5Ot27RxEba5xbdOODPDiRW8i+S3lGab8mvKZ3pyw9n/RVB7WOUisjvV9DVVU+T5qrdRQhhBD1nBRy9YyiKIwb586+fSFcvFhG27YR/Pyz4dd9u9fNnmBbSxaZ0FIklk1ccRnWmpR391BRXH83onc2d2e496tsSVtKbFGk1nGEEELUY1LI1VMdOthy5EgoXbrY8cADZ5k1K5HycsPdBtUpCuODPNiUkklSUYnB2q0t75n3UJqYQ8bqw1pHqZWBHs/jYRHAkoTpWkcRQghRj0khV4+5uJixdWsT3n7bh7ffTqFfvzOkphru+bERfq5Y6nR8Gms6z3JZNffA+bE7SHlnN2qpacyqrQlLnRXj/N7lz+wfOZSzU+s4Qggh6ikp5Oo5nU5hxgxvdu4M5uTJQtq0iWDfPsM81+Zorme4nyvLYtMoKq/b7cJuxvvVXpTEZJLx1VGto9RKT6dBtLS9i0UJ0yhX629RKoQQQjtSyDUQ99xjz9GjoTRpYknPnlHMn3/RIDNOJzfyILWkzKSWIrG+wwunR1qQ8vYuVBNZ664mFEVhgv+HnCs8wfaMNVrHEUIIUQ9JIdeA+PhY8PvvwUyd6skLLyTw6KPnycqq3aSAYDsrHvJ05MMLhikMDcX71V4Un83g0roTWkeplRa2nbjXeSjLE2dSUG46M4SFEELUD1LINTBmZgrvvefH5s1N2LUrl/btIzl2rKBWbU5t5Mnp3CJ2pOcaKGXt2bT1xfHB5qS8+TuqCd32rYkxvvPIK89kbcq7WkcRQghRz0gh10D17+/EkSOhODjo6Nw5klWr0ms8otbD1Y42DtZ8eP6igVPWjvesXhRFppG58ZTWUWrFyzKQxz2n8u3F+Vwsidc6jhBCiHpECrkGrHFjS/78sznDh7syenQso0bFUlBQ/dErRVGY0tiTX9JyOJ1baISkNWPbKQD7Ps0uj8pV1O9RuSe8XsZGb8+KxJlaRxFCCFGPSCHXwFlZ6Vi+PJA1a4JYt+4SnTtHEh1d/Y3nB/s4421pzsLzqUZIWXM+s3tTeDKF7K0RWkepFVu9A6N93uCXS18SmX9I6zhCCCHqCSnkbhPDh7vy99+hFBdX0L59BBs2ZFbrfAudjucbufNlYgapxaaz16nd3UHY9WxM8hu/m9RkjJp4wG0UjaxasChhWr3/LEIIIeqGFHK3kTvusObgwVDuu8+Rxx47z+TJ8ZSUVP2W5JgAd/SKwtJY09m2Cy4/K1dwJJGcbVFaR6kVM8WM8X7zOZ63lz+yNmsdRwghRD0ghdxtxsFBz7p1jfjoI3+WLEmjZ89oEhKqtgWXi4UZI/1cWRxjWgsE29/TBNu7Akl+47d6P5LVybEfnRzuY0nidEorTGdrNCGEEKZJCrnbkKIoTJzowd69wcTFldC2bQS7dlVtaZHJjTxILyljTUKGkVNWnaIoeM/qRf7f8eTuPKt1nFob7/cBycUX2JS2WOsoQgghTFyDKeQWL15MWFgYHTp00DpKvdG5sx1HjoRyxx3W3HtvNO+9l3LLEa1mdlYM8nbmvXMplFWYzuiXQ79gbNr7kfx6/R+Va2TdgofcnmV18utkl5lOwSyEEML0NJhCbvz48YSHh3Pw4EGto9QrHh7m/PJLM1580YuXXkpk4MDzZGfffNurl5t6cb6ghA3J1ZswYUyKouA9uxd5+2LI23Ne6zi19rTPXCrUclYnv651FCGEECaswRRyoubMzBTmzfPl+++b8NtvOXToEMGpUzdeL66tow193R1459ytR/DqkuN/QrFu7U3yG79rHaXWnM09GO49k+9TlxBXVL8ncQghhDAeKeTEVQMGOHHoUCiWlgqdOkWydu2lGx77chMvjucU8ktaTh0mvDlFUfB+tRe5v58jb3+M1nFqbZDHJNwtfFma8KLWUYQQQpgoKeREJc2aWfHXX8155BEn/vvfC0ycGHfdJUp6utrR0cmGeWdTNEh5Y06PtMCqpSdJc3ZqHaXWLHVWjPF9h33ZWzmSu0vrOEIIIUyQFHLiGra2er78MohFi/xZtiydnj2jSUysvBSGoijMaOrN3kt5/HkpT6Ok11J0Onzm3EvuzrPk/nFB6zi11tt5MC1sO7Mofirl6s2fXRRCCHH7kUJOXJeiKIwff/MlSh72dCTUzoq3ziZrlPL6nB5pgfWd3iS/tkPrKLWmKAoT/D7kTOExfsn4Uus4QgghTIwUcuKmrixR0rLltUuU6BSFWc282Zaaw8GsfI2T/p+ro3K7zpO7+5zWcWqtpV0XejkPZnnSKxSWm851FkIIoT0p5MQt/XuJkkGDzpOTc/k23+M+zjS3s2JutGmNyjn2D8O6jQ9Jr+00qZm1NTXW9x1yyy7xzcX3tY4ihBDChEghJ6rkf5co2bnz8hIlp08XolcUZjfz5qfUbNMalVMUfObeS97eC+Tuqv+jct6WQQzymMTalPdIK0nUOo4QQggTIYWcqJYrS5RYWCh07BjJN99cMt1Ruf+EXt7toYGMyj3p/QpWeluWJ83UOooQQggTIYWcqLb/XaJk2LALTJkUzyuNPE13VG5fTIPYg9VO78jTPq+zPWMNUfmHtY4jhBDCBChqQxiq+B85OTk4OjqSnZ2Ng4OD1nEaNFVVWbIkjSlTEmjf0Zq018oJcbTix45NtY52laqqRHVZAjqFkP3jUBRF60i1UqaWMTK8Fc5mHnwcvKvefx4hhBC1IyNyosauLFGyZ08wcTGlpH5capKjct5z+5B/II6cX89oHafWzBQzJvjN51jeHvZlb9U6jhBCCI1JISdqrUuXy0uUtC2wgXgY/vMFk3omzaFvM2zvCiRp9g6TylVTnRzuo4NDX5YkTKe0ouTWJwghhGiwpJATBuHhYc6OX4J5KN+BSPtieo2NvrpEidYURcHn9T4U/BNP9g8RWsepNUVRGO/3AUnF59ictlTrOEIIITQkhZwwGDMzhe+nNcVfNeePxnm07xDO6dOFWscCwKF3U+zvaUzSrF9RK67dO7a+aWJ9Bw+6Pc3nyXPJKbukdRwhhBAakUJOGJReUVjcMYDyFlDSUqVjx0i+/dY0Cg2fN/tReCKFzPUntY5iEE/7vE6ZWsrq5De0jiKEEEIjUsgJg/uPhyPdXOywm6Dn4UccGTr0ApMmxVNSou1ImN1dgTg8EELSaztQy0zjtm9tuJp78YTXDDalLiKuKFrrOEIIITQghZwwOEVReC/Ul9P5Rdw3z4FPPvFn6dI07rknmqQkbR/O932zL8XR6WR8cUTTHIYy2HMKrubeLEt8SesoQgghNCCFnDCKzs52DPRyYnZ0MqPHubFnTzCxsSW0bRvBnj25muWyaeOL06A7SJ77GxXFZZrlMBRLnTVj/d7hj6zNHM3drXUcIYQQdaxeLAisqiq5udf/y7+4uJji4uKrf87NzSUsLIz4+HhZEFhjZ/OK6LA/grnNfJjY2JO0tFKeeiqW/ftzmTvXh+ef99BkQdvCqDQiOy3G7937cR/Tqc77N7QKtYLJ0fdSThmfBO9Gp8i/z4QQoqGwt7e/6d+V9aKQu7JbgxBCCCHE7eRWO1XVi0KuOiNyycnJdOzYkfDwcHx9fWvdd4cOHTh48KDJtGPItgzVTk5ODv7+/tcdBU0tLuXOveGM9nfjjeb/9/v48ccsxo6NxcPDnK+/bkRoqLVBM92qneLYS0S0W4TXi93xerFnrdoyVKaqutH1fvP8cCIK/mFl6GGs9bZ1mul2/X5rlcmQbZlaO3K967Ydud5121ZNrvetRuTMapWojiiKUu0vmL29vUFurer1epNqx5BtGTITgIODwzXtOQDTWzbhnXMpvGBuhb+1BQDDhjnQoYMHjz56jl69kli1KpAhQ1zq7rPd4UDR+B6kf3wIm8m9MXO7ceFTX673pND5PHk6jG2FK3jKZ3adZrpdv9/V1ZCvk1zv+tnOFXK967YtQ1zvK+RhmlsYP368SbVjyLYMmelmpjXxxNFMz8zIxErvN2tmxV9/NeeRR5yuLlEyZswEg/RZlc/mPbMXAMlv/V7rtgyVqTZ8LZsw0GMiay++S3pJUp1mup2/39XRkK+TXO/62Y4hNeTrbei2DKle3FqtjoSEhKvDln5+flrHuS1ceYbxZvfxl8emMeZkHPvvCuEuF7tKP1NVlSVL0pgyJYEOHWxYv74xvr4WdRGd5Dd/I/mN32kRNQ3LIJc66bO2bna9c8uyGHqqKV2dHmZG0GcaJWxYqvL9FoYj17tuyfWuW8a43g1uRM7S0rLS/xXGZ2lpyWuvvXbTa/50gBvtHG14/nQ85f/6t4OiKIwf71FpiZLdu+tmiRKPKd3QO1uTNHtHnfRnCDe73vZmTozymcvPGauJLjiqQbqGpyrfb2E4cr3rllzvumWM693gRuTkXxem66/MPLrsj2LZHQGMCXS/7jGpqaUMHXqBPXtymTfPlxde8DT6EiWpSw4QP2EroccmYtPK26h91YUytZSR4a1wNfdmYbPfNFniRQghRN1ocCNywnR1drZjpJ8rMyMTuVRy/cV4PTzM+eWXZkyf7sWLLyYyaNB5cnKMu52W+zMdsWziQtIrvxi1n7pippjznN8HHMndxb7srVrHEUIIYURSyIk69U6oL6WqyqyoGz+Mb2amMG+eL99/34SdO3Po0CGC06cLjZZJMdfj82Zfsn+KJHfveaP1U5e6ODxAB/s+LE6YRklF8a1PEEIIUS9JISfqlKelOXOCfVgWm8ax7IKbHjtggBOHDoViaamjY8dIvvnmktFyOT92BzbtfEl8aTsN4WkDRVF43n8BKcUxbEj9WOs4QgghjEQKOVHnJgR50NzOigmn4m5ZNDVrZsWBAyE8+qgTw4ZdYOLEOEpKKgyeSdHp8H3nPvL/iiN7S7jB29dCI+sW9Hcfy5rkN7hUelHrOEIIIYxACjlxS0uWLKFRo0ZYWVnRrl07/vjjjxseu3v3bhRFueYVGRl59RhzncInLf3Zn5nP6oSMW/Zva6vniy+CWLTIn2XL0unZM5rExBKDfLb/5XBvM+zvbUrijO2oZcZ9Lu9G9u7dy0MPPYSPjw+KorB58+ZbnrNnzx7atWuHlZUVjRs3ZtmyZVd/NspnLnrFjBVJrxoxdf1V3etdle+3uLF58+bRoUMH7O3t8fDwYMCAAURFRd3yvJt9x8WN1eR6y3e85pYuXUqrVq2uLvbbpUsXfv7555ueY4jvthRy4qbWrVvH5MmTmTlzJkePHqVbt27cf//9xMXF3fS8qKgokpOTr76aNWtW6ee93Bx4wteFaeEJXCwuvWWOK0uU7N0bTHz85SVKdu0y/BIlvu/cR1FkGhlrjhi87arIz8/nzjvvZNGiRVU6/sKFCzzwwAN069aNo0eP8sorrzBx4kQ2btwIgKOZK6N85vJT+ipZjuQ6qnu9r7jV91tc3549exg/fjx//fUXO3bsoKysjL59+5Kfn3/Dc271HRc3VpPrfYV8x6vPz8+Pd955h0OHDnHo0CF69epF//79OX369HWPN9h3W21gsrOzVUDNzs7WOkqD0LFjR3Xs2LGV3mvevLn68ssvX/f4Xbt2qYCamZl5y7ZTi0pU1+1H1SGHz1UrU2pqidqrV5Sq0x1S3303Wa2oqKjW+bdybvDX6nGft9SyvGKDtltdgPr999/f9JgXX3xRbd68eaX3xowZo3bu3Pnqn0srStT/ngpVx0d2N/i1akiqcr2r8/0Wt5aamqoC6p49e254TFW+46JqqnK95TtuWM7OzurKlSuv+zNDfbdlRE7cUElJCYcPH6Zv376V3u/bty9//vnnTc9t06YN3t7e9O7dm127dl33GHdLcxa28OfbpEy2Xcyuci5398tLlLz4ohcvvZTIwIHnyc423K1Q37f7UZaez8X5ew3WprEcOHDgmt9Pv379OHToEKWll0c6zRRznvdbwPG8vezOklEMQ6jK91vcWnb25f/uXVxuvKtKVb7jomqqcr2vkO947ZSXl/Ptt9+Sn59Ply5drnuMob7bUsiJG0pPT6e8vBxPT89K73t6epKSknLdc7y9vVm+fDkbN25k06ZNhISE0Lt3b/buvX5R9F9fF/q5OzDuVBx51Xgu7coSJZs3N+G33y4vUXLqlGGWKLFs7IrHxK5cfG8vpck5BmnTWFJSUq77+ykrKyM9Pf3qe50c+9HF8UGWJkynuKKormM2GNX9fosbU1WVqVOncvfdd9OyZcsbHlfV77i4uapeb/mO187Jkyexs7PD0tKSsWPH8v333xMWFnbdYw313TarVWJxW/j3zgCqqt5wt4CQkBBCQkKu/rlLly7Ex8fzwQcf0L179+u2vfSOAFruCWdmZBIftfSvVrb+/Z04fDiURx89T6dOkaxYEciwYbXfM9Vr5j2kf36IxFm/ErRyUK3bM6br/X6u9/4Ev/kMP92SdRc/ZLj3K3WWryGp7vdb3NiECRM4ceIE+/btu+WxVf2Oixur6vWW73jthISEcOzYMbKysti4cSMjRoxgz549NyzmDPHdlhE5cUNubm7o9fprRt9SU1Ov+VfEzXTu3JkzZ87c8OeNbCx5I8SHT2JS2ZtR/QkMTZta8ddfzXn0USf++98LPP987ZcoMXOyxue13mR8dpiC4zdevFhrXl5e1/39mJmZ4erqWun9AKsQBno8z1cpb5NeYrqfqb651fdbXOv5559n69at7Nq1Cz8/v5seW53vuLi+6lzv65HveNVZWFjQtGlT2rdvz7x587jzzjv56KOPrnusob7bUsiJG7KwsKBdu3bs2FF5Q/kdO3Zw1113Vbmdo0eP4u198z1MJzXyoKuLHSOPx1TrFusVNjY6vvgiiMWL/fn008tLlCQk1G6JEvexnbFs5krCC9tMdpHgLl26XPP7+fXXX2nfvj3m5ubXHD/SezYWOms+TZIROUOpyvdbXKaqKhMmTGDTpk38/vvvNGrU6JbnVPc7Lv5PTa739ch3vOZUVaW4+Pq76xjsu13NCRgmT2atGta3336rmpubq6tWrVLDw8PVyZMnq7a2tmpMTIyqqqr68ssvq08++eTV4xcsWKB+//33anR0tHrq1Cn15ZdfVgF148aNt+zrbF6RarvtiDrmeEytMh84kKv6+R1X3d2Pqb//nlOrtjI3n1IP8ZKa9VNErdqpqtzcXPXo0aPq0aNHVUD98MMP1aNHj6qxsbGqql57vc+fP6/a2NioU6ZMUcPDw9VVq1ap5ubm6oYNG27Yx/epS9W7D6GG5/1j9M9j6qp7vWvz/RaqOm7cONXR0VHdvXu3mpycfPVVUFBw9RhDfMfFZTW53vIdr7kZM2aoe/fuVS9cuKCeOHFCfeWVV1SdTqf++uuvqqoa77sthZy4pcWLF6uBgYGqhYWF2rZt20pT10eMGKH26NHj6p/fffddtUmTJqqVlZXq7Oys3n333epPP/1U5b6WxqSq/HBI3X4xq1aZU1NL1N69Ly9R8s47NV+ipKKiQo3ssUw9FTpfrSgtq1Wmqrgy9f/frxEjRqiqeu31VlVV3b17t9qmTRvVwsJCDQoKUpcuXXrTPkorStXhp+9Qx0Z0ue2XI6nu9a7t9/t2d71rDaiff/751WMM8R0Xl9Xkest3vOZGjRp19e9Kd3d3tXfv3leLOFU13ndbUVUTvWdUTYsXL2bx4sWUl5cTHR1NdnY2Dg4OWscS1aSqKvf9c5ZTOYWc7BGGi0XN5+OUl6vMmpXEvHkpDBjgxOrVQTg66qvdTsGRRCLaLyJgcX/cx3WucR5Tcjjndyaf6c2soK/o6/pfreMIIYSooQZTyF2Rk5ODo6OjFHL1WEJhCa32htPDxZ5N7RvXembali1ZjBgRg4eHGRs3NuGOO6yr3UbMyPVk/RhJyzMvYOZsU6s8pmLWucc4mb+ftS2isNHbax1HCCFEDchkB2Fy/KwtWH1nEJsvZrEoJq3W7fXv78ShQ82xttbRuXMkX3996/1d/8133n2oxWUkz9lZ6zymYrzfB+SVZfFF8ltaRxFCCFFDUsgJk/SwlxOTG3nwQkQCh7NuvS/grTRtasWBA80ZONCJJ56IYcKE6i1RYu7tgPervUhd/BeFpy/WOo8p8LIM5L9eL7Mu9UPiiqK1jiOEEKIG5NaqMFnF5RV0/TOKrNJyjnQLxcG8+s+3/Zuqqixbls6kSfG0a2fDd981xs/PokrnVhSXEd5yARZBzjT79ekGsRhpcUUhT54OI9AqjPeb/aR1HCGEENUkI3LCZFnqdaxr25jUklLGnIw1yFpuiqIwbpw7f/wRQkJCCW3aRLBjR9W24dJZmuG34D/k7jxL9pbwWmcxBZY6ayb4fchfOdvYn/Wj1nGEEEJUkxRywqQ1sbVkRatAvk3KZFV89Z9tu5FOnWw5ejSMdu1s6NfvDHPmJFFefutC0fHB5jjcF0z81J+oKGoYG3Z3cxpAB/s+fJIwWfZhFUKIekYKOWHyBvu48GyAG8+fiuNYdoHB2nVzM2PbtqbMnevD668nc999Z0hLu3lxpigK/gv+Q0l8Fhc/vPUekfWBoihM9P+IlOJY1l9coHUcIYQQ1SCFnKgXFrbwJ8zemv6HzpFabLiRMJ1OYdYsb379tRnHjxfSpk0E+/fn3fQcq+YeeEy8i5S3d1GSmG2wLFoKsg5lkMdEvkh5k9SSBK3jCCGEqCIp5ES9YK3Xsbl9E4orKhh4+DwlFVWfcVoV997rwNGjoTRqZEmPHlHMn3/xps/k+cy+F52tBYkv/WzQHFoa6TMbG509SxNe1DqKEEKIKpJCTtQb/tYWfN++Cf9k5fPcyTiDb2Tv62vB778HM3WqJy+8kMDAgefJyiq77rF6Ryt83+7Hpa+PkfdnrEFzaMVO78gY33fYmfkNx3L3ah1HCCFEFcjyI6LeWROfwcjjMXzUwp+JjTyM0sfWrVkMHx6Dq6ueDRua0KbNtbs5qBUVRHZaglpaTuihCShmtV8eRWsVagXjou6iuKKQlaGHMVNqvkWaEEII45MROVHvjPB3ZWpjD6acjmdHWtWWDqmuhx924siRUJyczOjSJZLly9OuGQFUdDoClg6g8EQKqYsOGCVHXdMpOib7f8L5wpP8kLZc6zhCCCFuQQo5US+9F+pHX3cHHj9ynojcQqP00bixJfv3h/DUU66MGRPHiBEx5OeXVzrGtr0f7s91JmnWrw1m4kOobQcecB3FiqRXySpL1zqOEEKIm5BCTtRLekXhm7aN8LMyp9/fZ0goLDFKP1ZWOpYuDeTrrxuxcWMWnTpFEhFRuXD0ebMvOlsLEqY0nAV1x/i+jUoFKxNnaR1FCCHETUghJ+otJ3MztndshqIo9Pv7DJdKrj8xwRCGDXPh4MHmVFRAhw6RfPPNpas/M3Oyxm/+g2R+d5LsXxrGnqXO5h6M8p7L1vRPiS44qnUcIYQQNyCFnKjXfK0t+KVTMy4Wl/LwwbMUlBt2WZL/FRZmzT//NGfAACeGDbvAc8/FUVx8uT+XYa2x79WE+PFbGsyOD494PEcjqxZ8GPccFarxrqsQQoiak0JO1HvN7az4qWMzjuYUMuTIeUorjDcR285Oz5dfBrFsWQCrVqXTtWsUFy4UoygKAYv7UxKXRco7u43Wf10yU8yZErCY0/l/sS3jc63jCCGEuA4p5ESD0MnZlo3tGrM9NYfhxy5QbsRVdRRFYcwYdw4caM6lS2W0aRPBpk2ZWDX3wPPF7qTM203RmYYxSaC1fXf6uTzJsoSXyC4z3F63QgghDEMKOdFg3OfhyLdtG/FdciZPHYsxajEH0LatDUeOhHLvvfYMHHie55+Pw2VaD8x9HIgbv8XgCxZr5Tm/9ymnjE8TZ2gdRQghxL9IIScalEe9nfmqdSPWJl1i+NEYyox4mxXAycmM775rzKJF/ixfns7d917A7JX7yd1xhsz1J4zad11xMfdktM+b/Ji+ktP5f2sdRwghxP+QnR1Eg7QhKZOhR8/ziJczX7dphLlOMXqfR44U8Pjj50lNLeWH5kdwik+hRcRUzJysjd63sZWr5TwT0QFFUVje/B/0Sv3fxUIIIRqCBjMit3jxYsLCwujQoYPWUYQJGOTjzIZ2TdicksXjh89TbMTZrFdcudX6wAOOPH4wmIKMIuJe2Gb0fuuCXtEzLXApZwqOsiVtmdZxhBBC/H8yIicatJ9Ts3n00Dk6O9vyffsmOJkbf+9QVVVZvjydXRN2Mb3sCNZfjiTsieZG77cuvBf7LLsy1/N1iyhczD21jiOEELe9BjMiJ8T13O/hyM7OwZzIKaTr/ijijLQDxP+6Mqv15X8eJMrKnejhG1j7eYrR+60LY3znoceMJQnTtY4ihBACKeTEbaCrix1/dm1OYUUFnfdFciy7oE76bd3Gln77/ou3UsD+Udt55plYCgrq98K6jmaujPF7h18ufcmx3L1axxFCiNueFHLithBiZ8WBrs3xsTKn+4EodqTl1Em/ru288J/Tm6d0Ufz95Vk6dYq4Zq/W+uZB11G0sO3Mh3HPUaY2jF0shBCivpJCTtw2PC3N2d0lmG4udjzwzxmWxqTVyVpvXi/1wDrMg9VNTqGWVdC+fSRr1tTfxXV1io5pAUuJLYrgu4sfaR1HCCFua1LIiduKnZmeLe2bMi7QnedOxfH0iViKjDyjVWdhRtCqQaiRKWwbksbjjzszcmQMI0fGkJ9fbtS+jaWZTWse9ZjA58lzuFgSp3UcIYS4bUkhJ247ZjqFj1sGsKZ1EN8kXqLbn8afBGHb0R/PF7qT/tZvLJlmxZo1QXz3XSbt20dy6lT9vNU62ucNbPWOLIybqHUUIYS4bUkhJ25bw/1c2d+1OaklZbTdG873yZlG7c9n7r1YNnUlZuR3PDnUiUOHmmNmBh06RLB8ed3c5jUkW70DE/0/Yl/2FvZmbdY6jhBC3JakkBO3tbaONhzuFsrdLnY8evg8zxyPJa/MOLc7dVbmBK1+jIKjSaS8t4fQUGv+/juU4cNdGTMmjscfP09mZplR+jaWnk4D6eL4IB/FPU9Bea7WcYQQ4rYjhZy47blZmPF9+yYsvyOAtUmXaPtHBAez8o3Sl21Hf7xe7EHy3N8oPJmCjY2OTz8N5LvvGrNzZy6tW0ewf3+eUfo2BkVRmOK/iOyyDFYlvaZ1HCGEuO1IIScElwuSZwLdOdotFAczPXftj+TtM8mUVRj+dqf3nHuxDHYjZuR3qKWXR/8GDXLm2LFQ/P3N6d49ijfeSKa8vH7cavW2DOIpnzlsSP2IqIIjWscRQojbihRyQvyPYDsr/uwawvQmXrwalUSn/ZEcNvDonM7S7PIt1uPJpLyz++r7gYGW7N4dwquvejNnThK9ekWTkGD8nSgMYbDnFIKsW/BB7BjK1fo5E1cIIeojKeSE+BcLnY63m/tyoGtzyipUOu6LZMrpeIM+O2fb3g+vGT1Jev038g8lXH3fzExh7lwffv89mPPni7nzznA2b84yWL/GYqaYMz3gU6IKDrM5banWcYQQ4rYhhZwQN9DJ2ZZD3UJ5J9SXT2PTCNt9mu+TMw02u9Rndm9s7vTmwhPrqCioPPLWo4c9x4+H0aOHPY88co7nnoujsNC0t/dqadeFh93GsDzxFVJLEm59ghBCiFqTQk6ImzDXKUxv4sXpni24w8GaRw+fp8/fZzhqgP1aFXM9jb4aTElcFgnTt13zcxcXMzZubMzSpQF8/nk6HTtGcPq0aa85N8Z3HtZ6Oz6Me67eLacihBD1kRRyQlRBIxtLfurYjJ86NCWhsIS2f0Qw9Mh5zuYX1apdq+Ye+L3/AGlL/iL756hrfq4oCmPHunPwYCiqCu3bR7BsmemuOWdv5sTUgCXsz/6B3zPXax1HCCEaPEU11b8RaignJwdHR0eys7NxcHDQOo5ogMoqVFYnZDAnOomLxaWMDnBjVjNvfKwsatSeqqqcfeBzCo4l0+LkZMzcbK97XGFhBdOmJbB0aRqPPOLEypWBuLiY1eajGM2sc49xLG8PX7WIwNHMVes4QgjRYMmInBDVZKZTGB3gxpl7WjKvuS/rkjJp+vspXghPIKEGW30pikLQZ4NQS8uJfXbTDUfbrK11LFkSwKZNjdm9O5dWrcL5/fec2n4co5gc8AnlahmfxE/ROooQQjRoUsgJUUPWeh0vNPHifK+WTG3sycq4dBr/foqRx2I4lVO9Z9nMvR0IXP4oWd+fJn3lwZse+8gjzpw4EUZwsBX33nuG6dMTKC42rYkQruZeTPD7kF8ufcnf2du1jiOEEA2W3FoVwkBySstZEZfOwgsXSSgq5UEPR6Y38aS7ix2KolSpjdgxm8j48iihBydg3cLzpsdWVKjMn3+RmTOTaNHCiq+/bkRYmLUhPopBqKrKtDP9iCuO4ouwU9jo7bWOJIQQDU6DGZFbvHgxYWFhdOjQQeso4jblYK5nWhNPzvVqyZrWQcQWFtPzQDQd90XyWVw6+VVYh85/wX+wbOzC+cFrqSgsvemxOp3C9Ole/PNPc4qLVdq1i2DRolSTmQihKAovBH5Kdlk6yxNnah1HCCEaJBmRE8JIVFVle1oOH11I5de0HOzNdDzh68qzgW7c6WBzw/MKT18kosMiXIe3JXDZI1Xqq7CwghdfTGDRojTuv9+Bzz4LwsvL3FAfpVbWXVzA4oRpLAnZT0u7LlrHEUKIBkUKOSHqwIWCYlbFpbMqPp2U4jI6OtnwTIA7j3k742iuv+b4tBX/EPfsJhqvH4bzY62q3M/PP2fz1FMxlJfDZ58F8tBDTgb8FDVTrpYzLvIuCipy+Sz0KBY6S60jCSFEg9Fgbq0KYcoa2VjyZnNf4nq34vv2TXA1N+PZE7F47jjOY4fPsTkli+Ly/5uw4Da6A86P3UHsM5sovnCpyv3cf78jJ06E0aWLLQ8/fI6xY2PJz9d271O9oufloFUkFp/ly5S3Nc0ihBANjYzICaGRhMISvk26xNeJlziWU4iTuZ5BXs7819eFbq52qNlFRLT5GHNPO4L3jkFnUfU141RVZfnydKZMicff34K1axvRrt3116erK6uSXuPL5LdZFXaEJtZ3aJpFCCEaCinkhDAB4bmFfJ14ibWJl4gpLMHT0owBnk48kF2KZ9/VeI/uQMAn/avdblRUEf/97wWOHy/g9dd9ePFFL/T6qs2gNbSSimJGRbTBRmfP0uZ/oleuvaUshBCieqSQE8KEqKrKX1n5bEzOYlNKJhcKSnCsULl7VyyDOzdi0KDWWOur90RESUkFc+Yk8847Kdx9tx1ffBFEUJA2z6mdyjvAc1FdGe83n8GesliwEELUlhRyQpgoVVU5nlPIxuRM1h+OJdrREltF4X4vRwZ6OfOAhyMO15kocSN79+YyfHgMGRllLFzoz6hRrlVe386QPoqfxI/pK1kTdhIfy8Z13r8QQjQkUsgJUQ9UFJTw838+Z0eIM/sHt+BQXhHmikJvN3sGeDnxsKcT3la3Xm4kJ6ecKVPi+eyzDP7zH0dWrAis82VKCsrzGBl+B14WQSwM/g2dInOuhBCipqSQE6KeKDqbTmT7Rdj3aoL+y8fYmprDlpQs9lzKpVyFTk62DPByYoCXE83trG7a1g8/ZPHMM7GUlaksWxbIoEHOdfQpLjuc8zuTz/Rmsv8nDPSYUKd9CyFEQyKFnBD1SNbWcM71/wLfd+/H68UeAFwqKeOn1Gw2p2SxPS2HgvIKQmwtGeDlRH8vJzo52aK7zi3U9PQyxo6NZePGLIYNc2HRIn+cnas+M7a2Powbz88Zq1kddgJfyyZ11q8QQjQkUsgJUc8kvrKdlHf3ELxzNPb3VC6ACssr2Jl+eaRu68Vs0krK8LI042HPyyN1vVztsfyfyRKqqrJ27SUmTIjHxkbHZ58F0q+fY518jsu3WFvhYeHHx8G75RarEELUgBRyQtQzankFZ/p9RuGJZEIPP4+Fv9N1jytXVQ5k5rM5JYvNKVmcKyjGTq/jP56ODPZx4T53B6z+f1GXkFDCqFEx7NiRy7hx7rz/vi+2tsZfHuRo7m4mRt/DRL+FPOY5yej9CSFEQyOFnBD1UGlaHpEdFqF3tiZk3zj0thY3PV5VVcLzivg+JYv1SZmczC3EwUzHAC8nBnu7cK+7PeaKwrJl6bzwQgLe3uasWRNE1652Rv8sC+Ke56f0VXwedhx/q2ZG708IIRoSKeSEqKcKTiQT1XUpDn2a0XjDf1F0Vb81GZFbyLqkTNYlZxKZV4SzuZ5HvZwY7OOCf5Y5o0bE8vff+Uyf7sncuT5YWhrvtmdheT5PRdyJs5kHn4TsxUypu+f0hBCivpNCToh6LOuHcM71/xKvGT3xfatftc9XVZWTV4q6pEzOFRTjbmHGEG9n1N9g2YtpBDez4vPPg+jY0XhbfJ3I28/zUd152ucNhnu/YrR+hBCioZFCToh6LuWDvSRO30bQl4NxfaJNjdtRVZUj2QV8k5TJ14kZpBSX0czcksIfK0j8upTpz1wenbOyMs7o3KeJr/BNyvt8Gvo3ITZtjdKHEEI0NFLICVHPqapK7NMbuPT1MYJ3P4tdl8Bat1lWofJrWg6rEzLYkpJFWYWKehB8T5jz7YuN6HqXvQGSV1ZaUcKYyE6UqMWsCj2Mpc7a4H0IIURDI4WcEA1ARXEZZ/qspCgqneb/jMcy0HAL/F4qKePbpEt8Ep1GZEkRJEO3Aju+HtkIf8ebT7KorguFpxkd0Y7+7uOY6L/AoG0LIURDJAs3CdEA6CzNaLzxCXS2Fpx7aA3lucUGa9vFwozngjwI7xPG3k7BtLW25o+APAJ/P8l9v57hz0t5GOrfg42sWzDG9x2+S13IoZzfDNKmEEI0ZDIiJ0QDUnj6IpFdlmDfvRFNNj+JYmacteAOnM5jyMrzxLUoBS+4w86ayY09+K+vS6UFh2uiQq1gypk+JBRFszrsBPZmdbt9mBBC1CcyIidEA2LdwpPG3/2X7F+iiRu32WAjZf/WpYUd5z+4g/dzfDF/C879XczTJ2Jp9Psp3jmbQlZpWY3b1ik6XglaTUFFLgviZR9WIYS4mQZTyC1evJiwsDA6dOigdRQhNOXYL5iglQNJX3mQ5Lk7jdaPXq/wwlQvTq1pQZsfrGEcOJ/T81pUEv47TzItPJ74wpIate1p4c/UgCXsuLSW3y6tM3ByIYRoOOTWqhANVPK8XSS98gsBnz6C+7OdjNpXebnKJ5+k8soribiHmNF1nh0/KznklZUz1MeFmc28CbGzqlabqqoy58JQDub8ypqwk7hb+BopvRBC1F8NZkROCFGZ18s9cR/fhbhxm8naGm7UvvR6hcmTPTlxIoxGjpZ8c38m/9noyNxAH37PyCVs92mePHqB6LyiKrepKArTApZgqbNmXsxTVKgVRvwEQghRP0khJ0QDpSgK/h89hNMjLTg/eC15f8Yavc+mTa34/fdgVqwI5If12XzUO5V3Mnz5qIU/v6fnErr7NMOPXuBMFQs6BzMXXglazcHcHaxPXWjc8EIIUQ9JISdEA6bodTT6ajC2Hfw4+5/VFJxINnqfOp3C6NFuRES0oFs3O54cEsP253PY1SyYj1r481t6LqF7TjPyWAxn829d0HVw6MMQz2l8mvgyUQVHjJ5fCCHqEynkhGjgdFbmNNk6AosgZ870WUVRVFqd9Ovtbc6GDU34/vsmHD1aQLs7IuAniO7Rgg/D/Pk1LYfmu08z9kQsyUWlN23rWZ+3aWx9B3PPD6WgPK9O8gshRH0ghZwQtwEzJ2uCf30aMzcbonuvoPjCpTrre8AAJ8LDW/DEEy48/3w8fXqeoXeBPed6teS9UD/WJ2fSdNcpZkclkVtWft02zHUWvNboG9JLE/k4flKdZRdCCFMnhZwQtwkzN1uCd45GZ21OdO+VlCRk11nfjo56li4NZO/eYC5dKqNNmwjeeT2F8b7unO/VkueD3Hn/XApNfj/FoguplFRcO7EhwCqYSf6f8FPGZ/x+aX2dZRdCCFMmy48IcZspicsiqtsyFGtzQvY8i7mnfZ32X1RUwdtvpzBvXjJNm1qxfHkA3brZE19YwmvRSayOz6CJjSXzw/x4yNMRRVGunntlSZJ/crbzWegxvC2D6jS7EEKYGhmRE+I2YxHgRLPfRlORU8SZPqsou1RQp/1bWel4/XUfjhwJw9FRT/fu0Tz9dAzW+To+uzOIE93DaGxrSf9D5+j39xnCcwuvnqsoCi8ELMNO78TcC0MprajZgsNCCNFQSCEnxG3IqqkbzXaOpjQ5l+h7V1KWkV/nGe64w5r9+0NYujSATZuyaN78FJ99lk6YnRXbOzZla4cmnC8oodXecCaeiuNSyeVtv+zNnJjT6Fsi8w/xaeKMOs8thBCmRAo5IW5T1mGeBP/+DKUJ2UT3XklpWt3PBtXrFcaOdScysgX33+/I00/H0qNHNKdPF/GQpxOne4Qxr7kvqxMyaLbrFEtiUimrUGlh15lxfu+xLvVD/sjaUue5hRDCVEghJ8RtzPoOL4J3PXt5ZK7XCkpTtVnaw9PTnC+/bMRvvzUjLa2UNm3CeemlBMqKVKY38SK6Z0v6ezkx/lQ8HfZF8FdmHo97TKab0wDejhlJUvEFTXILIYTWZLKDEILCiFSie63AzNma4N9GY+6t3X87xcUVfPDBRd58MxkPD3M+/tif/v2dAPgnM59xp+I4ml3AMwFuvNLUlunnOuBk5s7ikH2Y6yw0yy2EEFqQETkhBNahHoTseZby7CKieiynODZTsyyWljpmzvTm9OkWtGhhxYAB5+jf/yyxscV0dLbln7ub81ELf75NukSHfYm0tf6OMwXHWZI4XbPMQgihFSnkhBAAWAW7E7J3DGppOVF3L6MwIlXTPI0bW/LTT03ZsKExhw4VEBYWznvvpVBRBs838iCyZ0vudbNnRqRCat521iT+yO7MjZpmFkKIuiaFnBDiKssmroTsH4feyYqobsvI/yde0zyKojBwoDORkS149lk3ZsxIpE2bcHbvzsXbypy1bRuzo1MzyircOZ7+DaOO/8nZgrOaZhZCiLokhZwQohILHwdC9o7BKtiN6F4ryNl5RutI2NvrWbDAn8OHQ7G313PPPdEMGXKehIQS7nV34ET3MF5p5k5s3mO0+yOaHWkZWkcWQog6YdRCLjMzkyeffBJHR0ccHR158sknycrKuuk5I0eORFGUSq/OnTsbM6YQ4l/MnG1otmM0dt2COPvgajI3nNQ6EgCtW9uwf38Iq1cHsXt3LiEhp5k3LxnK4I2QRvzYyQJFSaHv3zGMORFLdun1924VQoiGwqiF3LBhwzh27Bjbt29n+/btHDt2jCeffPKW5913330kJydffW3bts2YMYUQ16G3taDJluE4DWzJ+cfXkrr4gNaRANDpFEaMcCUqqiVjx7oxe3YSLVuGs21bNve7t+Wz1iU0cXiHLxMuErb7NFtSsrSOLIQQRmO0Qi4iIoLt27ezcuVKunTpQpcuXVixYgU//vgjUVFRNz3X0tISLy+vqy8XFxdjxRRC3ITOwoxGXw3GY9JdxE/YQvyUH1DLr93QXguOjnrmz/fn+PEwAgMtePDBszz00FnuyB7BU/42tHF/jGC7UgYcOsdjh8+RUlSqdWQhhDA4oxVyBw4cwNHRkU6dOl19r3Pnzjg6OvLnn3/e9Nzdu3fj4eFBcHAwzzzzDKmpN549V1xcTE5OTqWXEMJwFJ0O/wUP4b+4P6kf/8m5R76kPK9Y61hXhYVZs2NHMzZsaMyJE4W0bBlB7mezCLZ2w9V2ICtaubE7I4+wPadZHZ9OA1s6UwhxmzNaIZeSkoKHh8c173t4eJCSknLD8+6//36+/vprfv/9d+bPn8/Bgwfp1asXxcXX/4tj3rx5V5/Bc3R0xN/f32CfQQjxfzye60LTH0eSu+scUd0/pSQxW+tIV12Z3RoR0YKXX/Zi4fs57Br+FtlFeZwuGs3JHiE86OHIU8dj6fv3GS4UmE4hKoQQtVHtQm7OnDnXTEb49+vQoUPA5f9x/TdVVa/7/hWDBw/mwQcfpGXLljz00EP8/PPPREdH89NPP133+BkzZpCdnX31FR+v7XIJQjRkjveHELJ/HGXp+UR2WkzBsSStI1ViY6Nj7lwfwsNb0DqgKQfHv8mh7N9ZevIVvmzTiG0dmxKdX8wde8JZHJNKhYzOCSHqObPqnjBhwgSGDBly02OCgoI4ceIEFy9evOZnaWlpeHp6Vrk/b29vAgMDOXPm+ksgWFpaYmlpWeX2hBC1Y9PKm9C/x3P2oTVE3b2MoC8ex/nRllrHqqRxY0s2b27Kjh0ezFh/jt+HfMCpNxvz8VPPcqpHGNPDE5hwKp6NyVmsujOQRjbyvyFCiPrJaHutRkREEBYWxt9//03Hjh0B+Pvvv+ncuTORkZGEhIRUqZ2MjAx8fX1Zvnw5w4cPv+XxsteqEHWjPL+E2Ke+I/O7k3i+1APfN/uimOm1jnWN0tIKnto1iAs224kcu4aJj3XlhRc8OVCQz9MnYskoKeP9UD/GBLqhu8ndAiGEMEVGK+Tg8vNuSUlJfPrppwA8++yzBAYG8sMPP1w9pnnz5sybN49HHnmEvLw85syZw8CBA/H29iYmJoZXXnmFuLg4IiIisLe3v2WfUsgJUXdUVSX1wz9IeGk79j0a0ejboZi722kd6xqF5fk8G34XKRnZ7B+0GhcrF+bN8+Whxx15KSqR5XHp9HK1Z9WdgQTJ6JwQoh4x6jpyX3/9NXfccQd9+/alb9++tGrVii+//LLSMVFRUWRnX35oWq/Xc/LkSfr3709wcDAjRowgODiYAwcOVKmIE0LULUVR8JzWneCdT1N4MoWIdp9ovq3X9VjrbXk3+HssnHJ58rfX6dzVguHDY+jb7QzDc135tVMzzuQXcceecJbFpsnMViFEvWHUETktyIicENooScjm/KCvKDiahP+i/rg/01HrSNc4mrubKdF9eNj9WdrHvMPUqQkcPlzAY4858+rbXiwqSGNFXDq93exZ1SqQQBmdE0KYONlrVQhhEBZ+jgTvGYPb0x2Ie3YTMU9voKKgROtYlbSx78m0wKV8n7aE9OZf8M8/zVm9Ooj9+/Po2DIS56/1bGzRmOi8IlruCedTGZ0TQpg4GZETQhhcxprDxI7bjGWQM43XDcP6Di+tI1XySfxUNqZ+zHvNttHRoS/5+eW8995FPvjgIlZWClNneXKuRzGfJ2Zwr5s9K2V0TghhoqSQE0IYRWFEKheGrKUoKh2/Dx/EfVznm64hWZfK1XJePvswp/L3s6z5XwRaNQcgObmUuXOTWLkyHT8/Cx5/x5lv3C6RXVbOB6F+PBPgZjKfQQghQAo5IYQRVRSVkvDCNtIWH8DxoVAClz+KuZdpTFzKL89hbGQXStViPm3+N45mrld/FhlZxCuvJPL991nc0ckK39kWbK/IoY+bPSvvDCLA2kLD5EII8X/kGTkhhNHorMwJWNSfJluGk/93PKdbLODSN8dM4rkzW70D7zb9gbzybF49N5DSiv97nq95cys2bWrC/v0hOJjp2f5gDq03W3P8UiEt95xmhTw7J4QwEVLICSGMzunhMFqcnoJD32ZcGPYt5wd9RWlqntax8LFszFuNN3Eq/0/mxz13TXF21112/PFHCJs3N6Fov0rqY2W4R5nx7Mk4+v59hljZs1UIoTG5tSqEqFOZ350g7rktAAQsHYDzoDs0TgTbM77grZgRPOPzJsO9Z173mLIylc8/T+e115JJ9S/FeroO1Qbmt/DjWXl2TgihESnkhBB1rjQ1j7hx35O16TTOg1sRsKg/Zm62mmZanfwGq5JmMzNoDfe53ng7wPz8cj76KJX3FqWQN7iC8t7Q3dGONe2CZFcIIUSdk0JOCKEJVVXJ/PY4ceO3oJjr8V/4H5yH3KnZyJaqqrwX9yw/p6/mg2Y/097h3psen5VVxgcfXOSD3y9S8qyKmbPCOyG+TA7xkD1bhRB1Rgo5IYSmSpNziHt+K1kbT2F/T2P8Fw/AOtRDkyxlaikvn32Yk3n7WRyyj6Y2rW55TmpqKXPfT2JZcToVfaFJvgVb721KmKt1HSQWQtzupJATQpiE7O1RxE/YSklcFp4vdMNrZi/0tnW/zEdBeS4TonqQVZbKsuZ/4WHhV6XzEhNLGLs0lh8b56A4wKB8J9YMDsLaSm/kxEKI25kUckIIk1FRVErKe3tIeXs35p52+H/8EI4Ph9X57db00mTGRXbBWmfHopC9OJi5VPncE2cKeGzbeaKbFGN5RmGuszfTnvDCzExutwohDE8KOSGEySk+l0HcxK3kbIvCvndT/N6/H5s2vnWaIbYokvGRd+Nn1YwFzXZira/eZIzPD6czITqeAvMK3H4y490ePgx/wk0KOiGEQUkhJ4QwSaqqkv1jBIkv/kxRVDouT7TG981+WAQ41VmGyPxDTIy+h5a2XXin6Q9Y6Ko3KzWvrJxRf8TyXX4mnAL/TebMGevDk0+6Ym4uBZ0QovYaTCG3ePFiFi9eTHl5OdHR0VLICdFAqGXlpK86RNJrOyjPKsJjUle8ZvTEzKluJhMcyd3F9DP309XpYV5r9A16pfrPvO1Kz+XJgxdIKS6l/DMIOm3OzBk+DB/ugoWFrMsuhKi5BlPIXSEjckI0TOW5xVz8YC8XP9iLYm2O96xeuI/tjM7SzOh9/5G1hVnnBvKA2yimB3xao2f28srKmRGZyKKYNFxT9WTMLSdQsWDGDC+eespVCjohRI1IISeEqFdKknJIfm0H6Z8dwtzbHq8Xe+D2TEd01uZG7ffnjDW8HTOS/3q+xFi/d2rczh8ZuTx7Mo6zeUUEn7AifG4R/p7mzJjhzahRrlhaSkEnhKg6KeSEEPVSUWQqyW/v4tLa45i52eA1vTtuYzsbdcmS9RcX8knCFMb6vst/vV6scTvF5RW8fTaFeWdT8DMzp8nPlvz+SS7e3uZMm+bJs8+6YWsry5YIIW5NCjkhRL1WdDadlHm7yfjiCGZO1nhO64b7+C7o7Y2zXdbKxFmsSXmTFwKW0d99TK3aOp1byDMnYjmQmc/jDs7ov4TvVmfi6Khn4kQPJkzwwMXF+LeOhRD1lxRyQogGoTjmEinv7CHjs0Po7CzwmNwVj+e6GHwPV1VV+Sh+EhvTPuGlwJX8x+3pWrVXoaosjU1jRmQidno9r3l6cWpFEStXpmNmpjBmjDtTp3rg41P3iyMLIUyfFHJCiAalJCGblPf2kL7iHwBc/tsaz0l3Y32Hl8H6UFWVD+PHsyVtGS8FruJBt6dq3WZCYQnPnYrjh4vZDPB0Yo63N+uXZrJ4cRqFhRWMHOnKiy960aSJcUYahRD1kxRyQogGqSw9n7QV/5C2+ACliTnY92qCx6SuOD7YHEVf+wkFFWoFH8Y9x9b05cwI+pz7XUfUuk1VVdmQnMXzp+PIL6vg9RAfhru4smJZOgsWXCQ9vYzHH3fm5Ze9uPNOm1r3J4So/6SQE0I0aGppOZkbT5H60X7y/4rDorELHs/fhevwtpi51K4YqlAreD9uDD+lr2Jm0Bf0c33CIJmzSsv+X3t3HiZVded//F37Xr1V7w3dzSbNKiAgKkLiSiYkBkLGZGLiiDExyUQmk2icMfnpb4xGzZjJwhiNDhqNS2bUuK8ooICAAgJCy9L0vlR3VVd17cu9d/6opqAVZOumu+H7ep77nFvNrbqnWh/8+D33nMMtta3c19DJRJeN/5o8khk2OytWdHHPPR3U1ye59FI3P/lJMRdf7DrlW5gJIYYOCXJCiDNGZGMT3t+uxf/XbegMevIWT6Jg6Tm45o9Cpz+xKp2qqdzd8B1e8T3MLdWPckn+N/qtv5uDUa7f3sDGQJSrKwq4q6acPL2R//3fbu65p50tW2JMmWLjX/6lmCuvzJO16IQ4A0mQE0KccVIdIXx/3kzXg5tI7O7CPCofz9KZFFw9A3PZ8f+9oWoqv2pYymu+P/Pz6r9wcf6V/dZXVdN4sLGLn9W2oAF3ji/nOyM96IFVq8L8+tftvPxyD2VlJm64oYjrrvOQmyszXYU4U0iQE0KcsTRNI7K2ga4HN+L/63a0RBr3xWPIu3IquV+ZeFzbgCmawp31/8ib/sf5efVfuCj/7/u1r52JFD+rbeG/m3yck2PnvskjOSc3MyP3o49i3HtvB4895sds1nHttR6WLSuislImRghxupMgJ4QQgBKM43/qQ/yPbyW8ph6dSY97wVnkf30qOV+sOaaFhg+EuTf8f+HGygf7ZTbrJ63zh7l+eyPbQzG+V1nIL88qI8+cqcC1t6f4wx+8/Nd/ddLTo7B4cR433FDEnDkOeY5OiNOUBDkhhPiEZEuQ7v/Zjv+JD4lubELvMJPzpRryr5yK+7Jxn7m/q6qp/Efj9Tzf9QD/POIPLCr6Qb/3L61qLK/38vPdrVj0ev79rDKuHeHBqM+EtUhEYcUKH7/7nZc9exLMmGHnhhuK+NrX8mQLMCFOMxLkhBDiMyTqfPif3Eb3kx8S296O3mHGfelYchbWkPOFszAVuz71Hk3TWN78E57y3sv3yn/FP5TcNCB9a4unuLm2hUeafUx22fjNxAou8hz8e09VNV59tYff/c7La6/1UFRk5HvfK+T66wspKRnYvWmFEKeGBDkhhDhGsZ0dBJ7bSfDFWiLrGwFwzKog54vjyVlYg21KaXYIU9M0VrTdxoq22/h2yS0sLfv/Aza8+X4gwrKPmljbHeHLxTncU1PBWKe1zzW1tXF+/3svjzziI5nU+NrXMsOuM2f2784XQohTS4KcEEKcgFRnmJ6XPybwYi09r+1GDSUwVeRkQt1l43DOH4Ux18bj7fdwX8uNLCr8AT8a8VsMOsOA9EfTNP7a1s2Nu1poi6e4obqIW8aWkmPqe79AIM2KFT5+/3sv+/cnOfdcBz/6URGLF+fK8iVCDEMS5IQQ4iSpyTTh1fsJvriLwIu1JOv8oNfhmDUC18Vj2H5OLfcU/oQ5xV/i59WPYdFbj/6hJyimqPxHXQd37m3HYdBz+1llLB3pwfCJaqCiaLz0UpDf/tbLW2+FKCoycs01Hr77XQ9VVTLbVYjhQoKcEEL0s0Sdj56V+wit3Eto5T7SXRE0i476mmZCM+HyL95A4dwJGPMGbput1niSm2tb+HOzn0kuK78aX8EXityHHd7duTPGH//YySOP+AiFVBYscHP99YUsWJCDwSCzXYUYyiTICSHEANJUldi2dsLv7Kdl1QcE1uzB3ZV5Ls06qRjnBVW45lbjvKAK88jcfr//pkCEG3c1s8oX5sJ8J3fVlHNunvOw10YiCk8+2c1993XywQdRRo40c911HpYu9cjkCCGGKAlyQghxCtXHdnH7qsWUb/awZN+30L3XQ3yXFwBTuRvHzArsM0dk2hnlJ70fLGSen3uts4ebdrWwLRTjKyW53DG+nPHOIw/xbtoU4Y9/7OSJJ/ykUhqLFuVx/fWFzJvnlDXphBhCJMgJIcQp1pVs5Sd7F9CRbORXo59nQnwakXUNhNc3Et3UTOT9ZtSeBACW0QXYe0OdfWoptiklh13y5FiomsbjLX5u+biV5niSa0Z4uHVcKWXWIy923N2d5s9/9vHHP3ZRWxtn/HgrS5cW8K1vFVBUJFU6IQbbaRPkli9fzvLly1EUhd27d0uQE0IMaWElyL/t+wo7wuu4pfoxPpf31eyfaapKYq+PyKbmbLCLbWlFjaYAMBY7sU0pzQY725QSrDVF6M3HtsdqQlG5r6GT2/e0EVVUflhVxE9HF1NoOXIw0zSN1avD3H9/J88+G0BRNBYuzGXpUg+XXebGaJQqnRCD4bQJcgdIRU4IMVwk1URmf9buJ/hO2S+5quTmIw5baqpKYp+f2LY2Yh+2Ed3WTuzDNpL13ZkLjHpsNUVYJxVn2poirBOKsIwpOGLAC6YUfl3Xzn/WedGAf6oq4iejiyk4SiD0+9M8/rifhx7qYuvWGGVlJr797QKuuaaAMWMGbkauEOLTJMgJIcQgOnTh4Evzv8mNlX86ruVJlGCc2I52oh9mAl7sow7iuzpR/NHMBQY9ljEF2GoKM+HuwDHOg8GduU9XMs1/7Ovg9/VedMAN1UX8eFQx+cdQ4du8OcpDD3Xxl7/4CQYV5s1zsnSph8WL87DbZV06IQaaBDkhhBgC3vQ/yZ31/8g4+3TuGP0seaaiE/4sTdNId0aI7/Jmj9iuTuK7vKSag9nrjEVOLGMKsI4twDLWQ2hMPvcVWXkgFsWo17Gsuph/HlVErunogS4WU3nmmW4eesjH22+HcLv1fP3r+VxzjYeZM+0yQUKIASJBTgghhoiPIhv4171XYNZbuHP084yxT+n3eyihBPFaL4m9PuJ7ukjs8WXPFV+miufLtfDYNyfz189XYtY0rvOn+L7bSckYD5axHgyuz14weN++BCtWdPHwwz5aWlKMG2fhqqsK+OY382WxYSH6mQQ5IYQYQjqSTdy890s0J/Zwc9UKPpe35JTdO90dJbHXR2JPJtg1NwdYXmLlqWlFGNIqi1+t4xvP7abUZOyt5HmwjCnoc35guBYyu0e89VaIRx/18cwzASIRlQsucHLVVfksWZJHXt6xTc4QQhyZBDkhhBhiYkqEuxu+w5vdT/CN4hu5rvyOAduj9Vh0JFL8ZmcL97X6iasaS7oSLN3QRsmWdhJ7fQefxwOMhQ4svaHO2hvyLGM9KKW5PP92gkcf9fPmmz0YjToWLszhqqsKWLDALfu8CnGCJMgJIcQQpGkaT3l/w33NP2WG6yL+36gnyDEWDGqfgimF+xo6+U1dB13JNEvK8vjZ6BImKZDY11vJ29uVqer1VvbSXZHs+w0FdqxjPajleewM2Xij1sjaRguRPDdf+HopV12Vz+zZDnmeTojjIEFOCCGGsPd7VnJr3d9jMzi5bdRfmeCYNdhdIqaoPNzk4566dvZHk1xW6ObHo4q5xOP6VAhLB2LZkJfoDXnxAyHPG85eF9KZadQcdDtz8EwrZPKCckZ9rgzrmAIMBTJZQogjkSAnhBBDXHuigV/UfY09sS1cX343S4puGBLBJq1q/LWtm3v2tbO1J8YEp5Ubqov4ZkUBdsPRh0qVnjiJfT7ie3zEd3dR/247vq2dWLzdFGjxgxe6rTgmFGGtKcQ6vretKcJSnY/uGO4jxOlMgpwQQgwDKTXJ/S0385T3XubmXsHNlf+Ny5g32N0CMsPAa/xh/rPOy3MdAfJMBr5bWcgPKgsptx15+68jSSRU3niuizcebmTvW60UJ3qYnh9loj1CTnc3WiQJgM5swDLOk1kAeXzvOnnjM2FPb5Ptw8SZQYKcEEIMI+8EnuOO+qtxGnKGzFDroeoiCf5Q7+XBpi5iisqS0jyWVRczK89xQp8Xjaq8/HKQJ5/089JLQeJxlQXTdSw5R+Hc0hgObzfx2sw6een2UOZNel1mEeQppdgmF2ObXIJtcgmWUfno9FLBE6cXCXJCCDHMtCXquXX/leyObh5SQ62H6kkpPNzs43f7veyLJjg318H3qwr5amkethMcDg2FFJ5/PsBTT3Xz+us9JBIa06fbWbw4l0WL8hhTrBKv7ST+UQex7e2Zbcy2t2fXx9M7zFgnFmObXIx9Smk24Bk9JxYyhRgKJMgJIcQwdOhQ6/k5C7mp8sGT2g1ioCiaxksdQX5X72VlV4g8k4FvVxRw3UgPNS7bCX9uKKTw8stBnnkmwEsvBYlEVCZMsLJoUS6LF+cxdaoNnU6X2eWiPdQn2MW2txP/qAMtqQBgLHFhn1KCbVoZ9unl2KeXYRldMOTCsRCHI0FOCCGGsbWBF/lVwzXo0PGzqv/mvJy/G+wuHdGecJwHm7pY0eSjM5lmbr6T60Z6+GppHtaTmLQQi6m88UYPTz/dzfPPBwkEFEaNMrNoUR6LFuUye7YDvb5vKNPSCvE9vkyw29ZGbFs70S2t2S3MDDnW3mB3INyVYx3nkckVYsiRICeEEMOcP9XBrxqWsj74El/2fI8fVPwam2HoDhcmFJXnOgLc39DFW74Q+QeqdJWFjHdaj/4BnyGZVFm1KszTT3fzt78F8HrTlJebuOKKXL70pVzmzXNisRw5jKW8YaJbWolubiH6QQvRza0k9/sB0NtN2M4uwzGrAsesEThmj8BcnS+VOzGoJMgJIcRpQNM0nuu6nz80/ZhCcwU3V61givP8we7WUe0Jx/lTYxcrmn10JdNckO/k6ooClpTm4Tad3G4WiqKxdm2YZ54J8OyzARobkzidei67zM3Chbl84QtuCguPPrs13R3tDXetRN9vJrKpmWRdJtwZCx04Zo3APqsCx+yROGZVYMyzn1S/hTgeEuSEEOI00hj/mDvqr2ZnZANfLfoR3yn75ZCuzh2QUFT+1hFgRZOP1zt7sOp1LCrN49sVBXze48JwklUvTdPYvj3GCy8EeeGFIBs3ZnacmDPHwcKFuSxcmMOECdZjrq6lOsNENzYT2dhEZEMTkY1NKN0xACxjPThmj8getqml6M2yr6wYGBLkhBDiNKNoCk97f88DLf9KvqmEmyofZIb784PdrWPWHEvyWIufR5p91IbjlFtNXFmWz5VleczI6Z9dHjo6Urz0UibUvf56D9GoSnW1ORvqLrzQeVz7v2qaRmKvLxPqNjQS2dhMbEsrWkpBZzZgn16O84IqnOdX4ji/ElOh86S/gxAgQU4IIU5bzfG93NVwLVvDq/my57tcX3E3DsPw+XtR0zQ2BqI82uzjf9q68SbTjHVYuLIsn6+X5Z3UrNdDxeMqb78d4oUXgrz4YoCmphQul55LLnFz+eVuLrssh5Ejj39hYzWRJra1lciGJsLrGwm/W5+dTGEZ58kGO+f5VVjGeeRZO3FCJMgJIcRpTNVUnuu6n/uab8RlyOWnlQ9wbs6Cwe7WcUurGm/7QjzR6ueZtgDBtMJUty1bqauyW/rlPpqmsW1bZgj2tdd6WL8+jKJATY2Vyy93c/nlmWqd1Xpis1eTjQHCa+sJv1tPeG0DsW3toGmZZ+3Oq8yGO/v0cvQWGY4VR3faBLnly5ezfPlyFEVh9+7dEuSEEOIQ7YkG7m68jk09r/P5vK/xTxW/wWMuG+xunZC4ovJqZw9PtPh5oSNATNWYk+fgyrJ8rijJZeQJbAt2JIFAmpUrQ7z6ag+vvhqkuTmFzaZj/nwXl1+ew+WXuxk71nLC1TQlGCf8XiOR3nAX2dCEGk2hsxhxzKrAeX4VzguqcJxfiTG3fyqQ4vRy2gS5A6QiJ4QQh6dpGm/4H+cPzT8moca4tuzf+UrRDzDqhm/lJ5xWeK49wJOt3bzW2UNK05iRY+eKkly+UpLLBOexT2A4Gk3T2Lkzng11a9aESSY1qqrMXHqpm4svdvO5z7nweE7896mlFKJbWwmvbchW7dLtIdDpsE0twTVvFM551bgurMZYMPQnsYiBJ0FOCCHOMKF0Nw+0/hvPdf6RMbap/NOI/2Saa95gd+ukBVMKL3uDPNse4BVvkLCiMtZh4YriXL5SmsvsXAf6fnwOLRJRWLUqzKuvBnnzzRC1tXEApk2zcdFFbi66yMXcuU4cjhNfRkXTNJJ1fkJr9hNeXUdo9X6S9d0A2CaXZELdvFE4L6zGVCQTKM5EEuSEEOIMtTOykd82/YidkQ3My13M9yvupswyarC71S/iisrKrhB/aw/wXEeAzmSaEouRLxfn8qXiXOZ7XNj7eZeG5uYkb70V4s03e1i5MkRrawqTScecOQ4uusjFxRe7mTnTgcl0cmEy0dCdDXXh1ftJ7PMBYK0pygY717xqTKXy38AzgQQ5IYQ4g6maypv+J7i/5Wd0p70sKVrGt0r/bVjNbj0aRdNY3x3h2fZunm0PsD+axKrXMb/AxYKiHBYUuhl7kjtKfJKmadTWxlm5MhPsVq0KEwwqOJ16LrjAybx5Li680Mk559iPa5mTw0m2BAmv3k+oN9wlPu4EMuvZueZV4+wNduYRuf3wzcRQI0FOCCEEcTXKE+2/5vGOu7DpnVxbdjt/57kGg+7kdlcYajRNozYc55XOHl72BlnjC5PSNMbYLSwocrOgKIf5BS5s/VytS6c1PvggysqVPaxZE2bt2jDhsIrdrmfOHEc22M2e7TjhGbEHpNpDfYZi4x91AGAelY/rwFDsvGosVfn98dXEIJMgJ4QQIsubbOaBln/lNf+jjLZN4YcV93KO+6LB7taACacV3uoK8UpnkJe9PTTGDlbrLvK4uMjjZqrb1q/P1kEm2G3eHGXNmhCrV4d5551Mxc5i0TF79sFgN2eO46SesYPMLhThd+qzwe7AkifmkbkHn7GbV41ldIGsZTcMSZATQgjxKTsjG/l90z+zI7KOWe7LuK78Ds6yTx/sbg0oTdPYFY7zireH1zqDvOsPE1M1CkwGPu9x9wY7F6PtJ77cyJEoSmYLsdWrM8FuzZoQPp+C0QgzZzq48EIn55/vZM4c50nNigVI+6OE39mffcYuurUVVA1TmfvgM3bzR8kixcOEBDkhhBCHpWkaqwPP8GDrLTTEa5mf+1WuLf93Kq3jB7trp0RCUVnfHWGlr4eVXSE2BiIoGoy0mbnI4+LCfCdz812Mspv7PfCoqsauXXFWrw6xZk2Y1atDtLenATjrLAvnnefsPRyMH29Frz/x+yvBOOF367PP2EU/aAFFxVjsPLjcybxRWCcUSbAbgiTICSGE+ExpLc1rvkdZ0XYrnclmLs7/Bt8uvYWR1rMGu2unVE9KYbU/xMquEG91hdgRiqEBpRYTc/OdzM13ckG+k8luG4Z+DjyaptHQkGTdugjr1oVZty7Mhx/GUFXIzTUwZ44jG+xmzXLgdJ74cKwSSmR2n+idQBHZ1AxpFaPHgfPCKlzzR+GcNwrbpGJ0+v59llAcPwlyQgghjklSTfBC15/4S/uv6Eq1clHelXyr9BaqbRMGu2uDojuZZl13hHf8Id7xh9kUiJLSNHKMBs7LczC3IFOxm5ljx9LPkycAQiGFTZsi2XC3fn2EQEBBr4fJk23MmuXoPexMmGDDaDzB3SciSSLrGzJDsavqiGxsQksqGPLtOOdWZSdQ2KaWohuA7yk+mwQ5IYQQxyWhxnnZt4LH2u6kM9XM5/KW8K3SWxhtmzzYXRtUMUVlYyDCO/4w7/jDrPOHCSsqFr2OaW47s/MczM7NHNUDNBxbWxtn7dowGzdG2bgxwo4dmaqd3a5nxgx7NtjNmuWgsvLE+qDGUkTea8wOxUbWN6Il0hhyrDjnVmWXO7FPK0NnPL1mPQ9FEuSEEEKckJSa5BXfIzzWfgdtyXrOy/kiXy/+KVOdc+VZKiCtanzYE+Vdf5gNgQgbAhHqokkACs1GZvWGutl5Dmbl2sk19f9WaZGIwubN0Wyw27gxQn19bx8KjdlgN3Omgxkz7BQVmY77HmoiTWRjU2ZW7Kr9hNc1oMVS6F0WnOdXZneesM8oR28ZvtvBDVUS5IQQQpyUtJbiDf/jPNn+a+riO5jgmM3Xi3/K3NwrTrt16E5WZyLFxkA0G+w2BiIEUgoA4xwWZuTYmZ5jZ1qOnWluO/nm/g8+Xm+KTZsOBruNGyP4/Zk+VFSYmD7d3ucoKzMdVzBXk2mi77cQWl1HePV+wu/Wo0aS6CxGHLMqcJ5fhfOCKhznjcSYZ+/373emkSAnhBCiX2iaxoaeV3m8/W62hFdRYRnDosIfssBzNU5DzmB3b0hSNY29kUQ21G0JRtnaEyOiqABU2cxMPxDu3Jm2xHr8VbPPomkadXVJNm+O9jm6ujKzZIuKjJ8Kd1VVxz4sq6UVoh+2EX63nvC7DYTfrSfdHgLAOqkY5wVV2cM8MlequcdJgpwQQoh+tyuyiac67mVV9/9i1lu4rOBbLCr8AdW2iYPdtSFP0TT2RBJsDkbZEoyyORhlc080W7krsRiZ4rYz2WVjssvGFLeNGqcVaz9ONNA0jebmVDbUbdmSaVtaUgC43XqmTLEzZYote0yaZMPlOnoFVtM0knX+3mBXT3htA/FdXgBM5e4+wc42uUQmUByFBDkhhBADpivVxvOd9/Nc5/340+1Md32exYU/5LzchRh18rzUsdI0jfpYMhvutodibOuJUR/LPO9m0MFYhzUb7ia7M2213dyvu1J0dGTC3Ycfxti2Lcq2bTFqa+MomYzJqFHmTwW8UaMsGAyf3Yd0V4TwuoZsuIu+34KWUjLP2c0ZieP8SpznjsQxeySGnP7dF3e4kyAnhBBiwKXUJKsDT/O09w/siKyjyDSCL3qW8gXPNRSbRwx294atUFphRyjG9p4Y2w9p/b3VO6tex1lOKzVOK+MPacc5+q+Cl0io7NoVZ9u2WO8RZfv2WHYBY7tdz6RJ1mzAmzzZxoQJVgoLjUccRlVjKSLvN2eC3Tv1RN5rROmOgU6HtaYQx7kjMwHv3JFYa4rO6KqdBDkhhBCn1MfRzfyt8z5W+p8gocaY5b6cL3iu5rychVj0Um05WZqm0ZZIsb0nxq5wnF3hOLW9bWcyE650QLXdTI3T1ifg1Tit/TbBwutNsX177JCAF+Ojj2IkEpnYUVBgYMIEGzU1ViZMsFJTkwl45eWfnlyhqSqJPT4i7zUSfq+RyPpGYtvbQdXQuyw4Zo3AMWdkb9VuBEaPo1++w3AgQU4IIcSgiCohVnY/xYtdD7IzsgGnIYf5eUu4LP8qpjgvQK87c6ssA8WXTFN7SLA7cF4XTXAgDBSYDIxxWBnjsDDGbsm0DgtjHFYKTIaTmoyQTmvs2RNn1644O3ceaDPDs/F4pgcul7433Nl6A17mvKrK3GcrMiWcIPp+M5H3mgivbyDyXhNpbxgAc3U+jpkV2M8px3FOBfYZ5Rjcp+f/JEiQE0IIMega4x/zuu8xXvc/RluynlJzFZfk/wOXFVx1xm0FNhjiisqeSIJd4Rh7Iwn2RBLsjSbYG4nTnkhnr8sxGg4Gu96QN9puodpuocxqOuHn8RQlswXZzp2xPgFv58444XBmBq/NpuOss6yMH29l3DgrY8dasm1enjEziaK+m8h7jUQ2NRN9v5no5lbUSOY5QstZhX3D3bQy9Hbzyf/yBpkEOSGEEEOGqqlsD6/lNf+jvN39V8JKkBr7TC7J/wfm5S2myFwx2F0844TTCvuiCfZGDjmicfZGEjTHU9nrTDodlTYzVXYzVTYLVXYz1XYLVb0/K7Ecf9DTNI2WlhQ7dx4Mdrt3x9m9O0Fb28F7ezxGxo2zfCrgja42YWjyZyp3B8Ld1ja0RBr0OmwTizPBbuYI7OeUY5tUgt7Wv8u7DLTTJsgtX76c5cuXoygKu3fvliAnhBDDXEKNsy74Iq/7HuW9nldIaykmOGZzYe4i5uUuosI6ZrC7eMaLKip1kQQNsST1sQT7o0nqownqY5nW1zvpAsCiPxD0MuGu0mZmhM1MhdXMCJuJcqsZ23FMWgiFFPbuTWSD3Z49mXb37jjd3QfvW1FhYuxYK+PGWRg71sroSiPVapCCDi/KjlYim5ozz9ulVTDosY4vxH52Kbazy7BPK8M+tXRIP3N32gS5A6QiJ4QQp5+wEmRd4EVWB55mQ/BVElqM0bYpzMtdxLy8xVRbJ8pCskNQKK1QH82EvL5tJuj5Dwl6AB6zkQqrqU/Aq7CaGWE1U9F7fiyzbX2+9GED3p49CaJRNXtdcbGRUaMsjKsyMNUeYrQSoDjgw9bkRdnVjhrNVP1MFTl9w93ZpZir84fEv3MS5IQQQgwrMSXChp5XWd39NOuCLxJVQ1RYxjIn5++Y7b6cs13zZPbrMBFVVFpiSZriSZrjKZpiSZrjSZpiB88PF/ZGWE1U2MyUW02UWcyUWk2UWkzZtshixHCYkKVpGl5vmn37EtTVJbJtXV2Sffv6Dtc6rBqzypLMcIUYrwtQEfWT29GFMRgBQO+yYJtYjG1SMdZJxdgmlWCbVIyp2DWwv7RPkCAnhBBi2EqqCd4Pvck7gb+xIfgKnakWLDob01yf49ycBcx2Xy5DsMNcJK3QEk9lwl7sQJsJfy3xFG3xFJ3JNIeGGT1QZDH2CXdlVnOf16VWEyUWI2b9wQpfNKpSX9834DU0JGhoSNLQkKS7W6GAOOMIMF4fYJI9zGh6KIkGMKqZwKnm2jGPLyZnegmOqSWZgDexeMAWMpYgJ4QQ4rSgaRp18R1sCL7Khp5X2BZ+l7SWosIyhtnuBZybs4ApzrnYDc7B7qroZylVw5tI0XbgiKdojfd93ZZI0Z5IoXwi9RSYDNlwV9xbzSsyZ9ri3rbIYqLIbCQV1bKhrqEhQX195ryxPk6yzkdOl5/R9DCaIKMJUkkYQ2/EjLqcJEd4cH1lMrNuP7/fvrsEOSGEEKelqBLig9BbbAi+wns9r9CRbMSAkRrHTM52zWeaaz6THOdJsDuDqJpGVzLdJ9wd2nqTabyJTNv9iSFdALdRfzDk9Ya7AyGv2GIiV6cn7YNYm0pXQ5qWfTFCO7xoe73Y23wU9nRjmTWS69+7ot++kwQ5IYQQpz1N02hMfMzm0NtsDa1iS2gV3Wlvn2B3tnMek5xzcBjkvx0CkqpKZyKdDXcdB0Je7886En2DX1LtG6cMuszzfIVmI4VmEx6zEY/JwHluJ9+sKui3fkqQE0IIccY5EOy2hDKhbmtoFf50Bzp0VFknMNE5h4mOc5noOJdKa43sMiE+k6ZpBNNKNuR5Eyk6Emm6kmk6k5ln+DLnab5YlMPt48v77d4S5IQQQpzxDgS7j8LvsTPyHjsi69kf24GKikPvpsYxKxvuzrLPIN9UPNhdFgKQICeEEEIcVlQJURt9v0+4C6Q7ASgwlTLWNo2x9rMZa5/GOPs0Ss3VUrkTp5wEOSGEEOIYaJpGW3I/u6Nb2BPdkmljW/Cl2gBw6N2MsU9lrH0aY2xTqbJNpMpaI8/ciQElQU4IIYQ4Cf5UB3uiW9kT25Jpo1toTuxB6112otBUTpV1ApW2mkxrraHKNoFco2eQey5OBxLkhBBCiH4WV6M0xj+mPraT+vhOGuK7qI/tpCWxF4XMshY5Rg9V1gmMsI6j3DKacssYKixjKLeMxm44tbsDiOFLgpwQQghxiqTUJM2JPdT3Brv6eCbctST2ElaC2evyjEXZYFdmGU2JpZJi80hKzJUUmiow6c2D+C3EUCJBTgghhBhkmqYRVHy0JPbREt+baROZtjWxD3+6I3utDh0eUxnF5pEUmyspMWdCXpF5BAWmUjymMnJNRRh1xkH8RuJUkSAnhBBCDHEJNU5HshFvspH2ZAPtyQY6Eg109L72JptQSGev16Mn11iEx1yGx1SWDXiHnuebSsg1Fkp1b5iTICeEEEIMc4qmEEh30pVqxZdqoyvZiu/Aeao1e3SnOlBR+7zXoXeTayokx+gh11jY9zAdPM8xenAZ8nAY3LLMyhAidVchhBBimDPoDBSYSigwlXzmdYqm0J324ku24ku3E0x3EUh1EkgfPOrjO7M/i6qhT32GDh0OQw4uQy5OQx4uYy4uQ94nznNxGXtbQx4OQw52gwu73onN4JJh3340oL/JX/7yl7z00kts3boVs9lMIBA46ns0TeO2227jgQceoLu7m9mzZ7N8+XImTpw4kF0VQgghTnsGnQGPqRSPqfSYrk+o8UzYS3cSTHcRVgKE0gFCSnfveXf23JtszvxM6SaU7u4z1PtJZp0Fm8GFXe/CZnAetrUbXNj0zmxr0duw6u1Y9DYsva1Vb8eis/X5mUFn6K9f17AwoEEumUyyZMkS5syZw0MPPXRM77n77ru59957efjhhxk3bhy33347l1xyCR9//DEul0zHFkIIIU4Vi95KkbmCInPFcb1P0zTiajQb7MJKkJgSJqqGiCohYmq4TxtVQ9k/96VaiaphYkoo2ya1xDHf26QzY9HbMOsOBj+r3o5Jb8GoM2PW9ba9r006CyZ9b6szY9L3tod7/YnrDn6eCYPOhEFnxKgz9b7+9LkBIzqd7nj/MXymU/KM3MMPP8yyZcuOWpHTNI2ysjKWLVvGTTfdBEAikaC4uJi77rqL7373u0e9lzwjJ4QQQpxe0lqKhBrLHnE1SlKNkdAy5wf/LNrnmoQWI9l7nlITpLQkKa23PfR1n/O+16S1ZHbtv/7wRc+13FT5p377vCE1SL1//37a29u59NJLsz+zWCzMmzePdevWHTbIJRIJEomDSb2np+eU9FUIIYQQp4ZRZ8JoMA3admeKppDWkiR7g13yE+EvraVQtHRvm+rz+pPnI6zj+rVvQyrItbe3A1BcXNzn58XFxTQ0NBz2PXfeeSe33XbbgPdNCCGEEGcmg86AofdZvKHmuOcP33rrreh0us883n///ZPq1CfHjzVNO+KY8s0330wwGMweTU1NJ3VvIYQQQojh4rgrcj/84Q+58sorP/OaqqqqE+pMSUlm2nR7ezulpQdn1Hi93k9V6Q6wWCxYLJYTup8QQgghxHB23EHO4/Hg8XgGoi9UV1dTUlLCG2+8wbRp04DMzNfVq1dz1113Dcg9hRBCCCGGqwFdmrmxsZGtW7fS2NiIoihs3bqVrVu3Eg6Hs9eMHz+eZ599FsgMqS5btow77riDZ599lh07dnD11Vdjt9v5xje+MZBdFUIIIYQYdgZ0ssMvfvELHnnkkezrA1W2t99+m/nz5wPw8ccfEwwGs9fceOONxGIxvv/972cXBH799ddlDTkhhBBCiE+QvVaFEEIIIYYp2fVWCCGEEGKYOu0qcpqmEQqFcLlc/b4NhhBCCCHEUHLaBTkhhBBCiDOFDK0KIYQQQgxTEuSEEEIIIYYpCXJCCCGEEMOUBDkhhBBCiGFKgpwQQgghxDAlQU4IIYQQYpiSICeEEEIIMUxJkBNCCCGEGKb+DxvpD985H+6wAAAAAElFTkSuQmCC\n",
"text/plain": "Graphics object consisting of 4 graphics primitives"
},
"execution_count": 272,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot([ww.subs(Z=1) for ww in w.values()],(r,0,3),legend_label=list(w.keys()))"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:25.572797Z",
"start_time": "2023-06-16T11:53:25.467071Z"
}
}
},
{
"cell_type": "code",
"execution_count": 273,
"outputs": [],
"source": [
"def ff(w):\n",
" return .5877943 - .1371776 * w + .2682367 * w ^ 2 - 2.515898 * w ^ 3 - 2.978892 * w ^ 4 + 8.710679 * w ^ 5 + 16.88195 * w ^ 6 - 4.489724 * w ^ 7 - 32.99983 * w ^ 8 - 14.49050 * w ^ 9 + 20.43747 * w ^ 10 + 12.56504 * w ^ 11"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:26.221629Z",
"start_time": "2023-06-16T11:53:26.217153Z"
}
}
},
{
"cell_type": "code",
"execution_count": 274,
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": "Graphics object consisting of 4 graphics primitives"
},
"execution_count": 274,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot([ff(ww.subs(Z=1)) for ww in w.values()],(r,0,5),legend_label=list(w.keys()))"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T11:53:28.919372Z",
"start_time": "2023-06-16T11:53:28.655789Z"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [],
"metadata": {
"collapsed": false
}
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 10.0",
"language": "sage",
"name": "sagemath-10.0"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.1"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment