{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Photon added states without adding a photon"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Author: Nicolás Quesada "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this tutorial we study how to prepare photon added states following the ideas from \n",
"\"Generating photon-added states without adding a photon\" [Phys. Rev. A 100, 043802 (2019)](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.043802) by S.U. Shringarpure and J.D. Franson."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from qutip import wigner, Qobj, wigner_cmap, qfunc\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib as mpl\n",
"from matplotlib import cm\n",
"\n",
"import strawberryfields as sf\n",
"from strawberryfields.ops import *\n",
"from thewalrus.quantum import state_vector, density_matrix"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ideal preparation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we setup some basic parameters, like the value of the photon-number-resolving detectors we will use to herald and the amount of squeezing and displacement to use. These parameters are taken from the reference cited above."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# the Fock state measurement of mode 0 to be post-selected\n",
"m1 = 1\n",
"# the Fock state measurement of mode 1 to be post-selected\n",
"m2 = 1\n",
"r1 = np.arcsinh(1.0)\n",
"g = 1.195\n",
"r2 = np.arccosh(g)\n",
"alpha = 2.0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Their circuit requires as input a single photon. We cannot prepare single photons directly using only Gaussian resources, but they can be generated by heralding one half of a two-mode squeezed vacuum. We do this by applying a two-mode squeezing gate in modes 1 and 2 and then heralding mode 2 in a single photon event later on.\n",
"Note that the value of the gain `g` is picked to match the parameters from figure 5.(d) of Shringarpure and Franson's paper. However one can change this value to match any other parameter setting studied in their paper."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we setup a 3-mode quantum circuit in Strawberry Fields and obtain the covariance matrix and vector of means of the Gaussian state"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"nmodes = 3\n",
"prog = sf.Program(nmodes)\n",
"eng = sf.Engine(\"gaussian\")\n",
"with prog.context as q:\n",
" S2gate(r1)|(q[1],q[2])\n",
" Dgate(alpha)|q[0]\n",
" S2gate(r2)|(q[0],q[1])\n",
"state = eng.run(prog).state\n",
"mu = state.means()\n",
"cov = state.cov()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Here we use the sf circuit drawer and standard linux utilities \n",
"# to generate an svg representing the circuit\n",
"file, _ = prog.draw_circuit()\n",
"filepdf = file[0:-3]+\"pdf\"\n",
"filepdf = filepdf.replace(\"circuit_tex/\",\"\")\n",
"filecrop = filepdf.replace(\".pdf\",\"-crop.pdf\")\n",
"name = \"added_circuit.svg\"\n",
"!pdflatex $file > /dev/null 2>&1\n",
"!pdfcrop $filepdf > /dev/null 2>&1\n",
"!pdf2svg $filecrop $name"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is a graphical representation of the circuit. It is always assumed that the input is vacuum in all the modes. \n",
"![img](./added_circuit.svg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now inspect the covariance matrix and vector of means. Note that the vector of means is non-zero since we did use displacement gates in the circuit above."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 4.78 2.61694478 0. 0. -0. 0. ]\n",
"[[ 2.7121 3.12724902 1.8504594 0. -0. 0. ]\n",
" [ 3.12724902 4.7121 3.37997041 -0. 0. -0. ]\n",
" [ 1.8504594 3.37997041 3. 0. -0. 0. ]\n",
" [ 0. -0. 0. 2.7121 -3.12724902 1.8504594 ]\n",
" [-0. 0. -0. -3.12724902 4.7121 -3.37997041]\n",
" [ 0. -0. 0. 1.8504594 -3.37997041 3. ]]\n"
]
}
],
"source": [
"print(np.round(mu,10))\n",
"print(np.round(cov,10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now use The Walrus to obtain the Fock representation of the heralded Gaussian state when mode 1 is heralded in the value $n=1$ in the variable `psi`. We also calculate the probability of success in heralding in the variable `p_psi`."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability of successful heralding is 0.02043\n"
]
}
],
"source": [
"cutoff = 20\n",
"psi = state_vector(mu, cov, post_select={1: m1, 2: m2}, normalize=False, cutoff=cutoff)\n",
"p_psi = np.linalg.norm(psi)\n",
"psi = psi/p_psi\n",
"print(\"The probability of successful heralding is \", np.round(p_psi**2,5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now plot the photon-number distribution of the heralded state. Note that the state has zero support on the Fock state with $i=2$ photons."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.bar(np.arange(cutoff),np.abs(psi)**2)\n",
"plt.xlabel(\"$i$\")\n",
"plt.ylabel(r\"$p_i$\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can plot the Q function and compare it with figure 5.(d) of their manuscript:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"grid = 100\n",
"xvec = np.linspace(-5,5,grid)\n",
"Q = qfunc(Qobj(psi), xvec, xvec)\n",
"wmap = wigner_cmap(Q)\n",
"sc1 = np.max(Q)\n",
"nrm = mpl.colors.Normalize(-sc1, sc1)\n",
"fig, axes = plt.subplots(1, 1, figsize=(5, 4))\n",
"plt1 = axes.contourf(xvec, xvec, Q, 60, cmap=cm.RdBu, norm=nrm)\n",
"axes.contour(xvec, xvec, Q, 60, cmap=cm.RdBu, norm=nrm)\n",
"axes.set_title(\"Q function of the heralded state\");\n",
"cb1 = fig.colorbar(plt1, ax=axes)\n",
"fig.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now plot the Wigner function of the heralded state,"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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RJktak53l3ZfzDMKbB2tKWSegOwvCyo1rsQWDK6dPfABuquonrmQsIh8OfAzwgjjpl0TkP1PV3zhmtWNxLzx2TwUbyRbfLka2Ml12cNHrLiUXOB/Co3ym/faJlEGVtNI+HWrdgwOWTgWeSmFecoDJmlxaK+85EaL/VN+LkhQu4+OCvwAezb6/IE47Df428Fuquququ8AvAJ+yzGDuC8Kdqu61QB0ERfCm3xqveVaX2rL3MokJKXwMgvXXbyGZ8LkP0u2rpGMfsbkrcZ6p4vqIFwYujvguJeG+FfgIEflQEamAV5K1ij8Bfw58hogUIlISHGZLSQr3POHO6rVnhcJKCmqnbbto7UIk3h5Cr2aRohjENVP1IZZFr6QbSzr2kbY6iQxYfEt9l0L0ei5v5CtD0KEvH+Gqagt8DfBGAlm+XlXfKSLfLiKfByAinyQiTwBfAPywiLwzrv7TwJ8AfwC8A3iHqv7rZcZzz2q4ObEsWkAkOciE1VbZT8RrUIwp8GJ77SAB0TZRj/EtvscohkS6vRS9UY+Pr/LLnG/fFbcpF9eYo6zQV86CEkOrjA2REEvhYojPi7mUFpqqPgY8NjPtW7PPb2Wi0+bLOODv9zmWe5Jw+yDbsCETPPKrKM81ByneNYWQqa2C1ddjoHuKYnC2Co6vHtr45KS7jCOtz0y0ZR1oyRrtk9q8KiIWZclMxhiKeJ5I52LVjr9QLezGCvdwsejtgSUiVkR+T0R+vq9tLjQOZpMZFoc3RXiV6mlsp96vZlqkLWlj5a6+xtERm2pvuu6EdJcLGcv13GXG1YcDzS5tiU6jr44VFxFipt3YL6ONuz7o8+x9HUsKysuiKz7jXS/hVn1alosgpdUKoEXVS5ZXQiJdce1UbPIyyKMXliJd1dBVY0kN1enkNX4x9J/RNelYseiIpv8/L9xb8cQXh17Onoi8APhbwI/2sb1FkGJs8a437TOlUKYEgtTuJv2dB5K1G1Jrba9hZMEb76YiBPpwWCVLd5kHhPh+6hr4WMtgoXHE1/Z+ZYUlrVyxiMhKitCfhFWkKd9v6EvD/X7gG4CrRy0QM0C+EuDRRx89arGFMCHbFumz/Y06vNqp7ZkZBkiSw6pvgLwjg9py4eSNeRANoWPelsH5taQzLZyPkAasEH6Xs44JDo1pESQH2mIOvdX8qF4VMRbj/ZkqnCmhdsdF9DWDLE15hfEWxhiG28vVxFhnLG3hisjnAk+p6u8et5yqvkZVP1FVP/Hhh/trJb8ysiVcVoWrsdmftOP4F8OsYrymlX7TaOchDyPLkyb6QAodU/qJ1/WZVb6o7hfqLSwvLayqx9ii6ELpzNkKvCdp5CKsW8gzztbjPF5G9HHmPg34PBF5D/A64DNF5LU9bPdErJJsj8JEUtDYmbad6uBbrLjhI0yIF4K163pqh9NlffXUDieRrjfF4g+GHkomJos7ONDOsqHV/YqzBd6P49Bk2bKianNnQUjguHd7qq0aSxOuqn6zqr5AVV9EyOL4FVX9b5Ye2QkIoV9Js73YzgzBs952yQWwuhY4OfKkiX47M7jenGlJngike/aNpXO7bBLCIt1+1ZiVRqkcfmjOGQPhTQZTrKyB6FmQh4dtcHZcyneDFPq1rINM6ffCCU4oH73/oT7Aqi3eZO0q0yFky2CeM20ZLPoK3Y0nS4hYBhOr8uRzFBxEq7fkcolIi0EsYB8IOBWzh7DMRZMtZOnoGyt3IfSa+KCqbwLe1Oc2Z5GSGrwqdkGyVcIFk24o41voOXc+OKJqEIsa27XB6bNGbY7pNudlL8eUO9OWzUxL7Xq8LReKj7Y9ONBmxyE6/+0oVYVLy68a6aEpXa+y6ZjrdSDaHArhusb3GB0eYKww3Cl73eY64VJZuHkG2WLlFbMODVmoUFc8pr+hApmlmFm8ySG1Cot31trto2Zt3k1i2XFPW5hnH0dfBWW6am8m68QhNlwbpjhXss2Rol1CGODkb92wiDyzQcClItxl0nU1Fv5Ojod0UXevdCv0YgfijcQVrXK7Qqmh7/KPIUSrH9JdptiNxFbmfZwzr6F4fBdbagPppnN13mR72ZAiPzbSwtlwaQjXLki2SYvryivO0cJSFk1/5fPmIziA3CHn2irCyWat3WWz1BLpprCxZXTzdLOe3QLX3luEp4du60PXY7emVuW6IUV+EN8ONjgdLgXhTpVYPMN6QastgvXC8YXDldgNYgXlEWeRnGt5ycRiRcSbrN08S21RpLCxVINhGdJNrXrO8iBIbwoXGZGywQQp7K+vjs73A9a+WlgnI/j2TAK9EvL5U0udk6yWSZPEAieraX0zC4FQMjE618RYCnO68Z4FE4IL1i6uhQXawacx29i+xxq78FjTmOwZm1LqJe0ee68iv2+82K7Y/aIQIwx3NplmF4IUa2u8O1MhmZxszxJOkzdJDM4U20tCwUmYdq5N4l/7tHgnunWwSJat6CW+XTpBIrd0TzOeDdGuJ7q3KCbF+jeYj7Ul3C4iwTvQ05fJSzJCItuz3qSJBCBov1qEeMjzKNoxId6mCzDv27F22KG22NZTgkRfpHuSgy+EalXdMWywXsgd0RscjbWVFNINfNbEBjU26JVLZAjlXmrJCsaohtz+UNB6dbavoBTRQZUKhfcZw5uOz0pIRjgqHvXkcQLeBf3bFMAS8oIydZ4lnuO0p6Q9b27o9cbm5zkea0m4C0ckiOk9BTIPSjcS4nhFikgKq00rFkLxHBUTNdN+iTeRnHT629l162TpepYjXTjc8SJHim7Y4N6GMcJw+96VJdZOUjASQobMWS1bJh0aVnFjJuJNcbtduFkKnO9/lx3yiAboN5RsWn9bQmLoQV6YGtPM34ZsN1gUIvJyEfkjEXlcRL5pzvxPF5G3i0grIp+fTf84EXmLiLxTRP6DiHzhsmNZK8KdFKQ5Wx8vhUnO+TncmHlGUBc4H/PgFy52fQLyUDJiycK+9N1cQvGmXOgYJpru8uUUN9igL4iIBV4NfA7wYuCLROTFM4v9OfBlwE/OTN8HvlRVXwK8HPh+EVmq4dpaSQpGmOikZ0Gsgn9ezR5zpF1OtN4CVbsyuSFFCKg6vCk7maGPB81ERy3wevbQuKDptjgxS3fe3WCDnvAy4HFVfTeAiLwOeAXwh2kBVX1PnDdl5anq/5d9fp+IPAU8AtxadDBrY+EunkkWkhWWcZL1gWQltnPlhv5jRyV1fHCTil59yAyHohjO+MhIcbppTBtssGI8LCJvy/6+cmb+84H3Zt+fiNPOBBF5GVABf7L4UNfEwhWCbisLZJI5WwZyWCNrKo2lc/4UNlru/VYlyxMn1BQgZumqXjATxbBA5bGQwtyGJIsLagezweVEYYWHrw3OsspNVf3EVY0HQEQ+GPgJ4FWqy3WWXQsLN5VbPHOXXDExk2w141oWeXEcyKqS9RzTmwguxe/25VRbqvJY/C1X3XZogw1OwF8AeRPFF8Rpp4KIXAP+DfCPVfW3lh3MhRNueu1Mr6GnRYpKOK2UIKy27c1x6CIcZoi37/xzYSIz9JWttkjlsZB8silossFa4K3AR4jIh4pIRehK84bTrBiX/1ngn6vqT/cxmAsl3CQlLBIC5k6RdWQkkE5hJJRDNHIuPceOQk680zpvf8Q7VRhHfRfNsAzyKIbO2p1T00DJfps1aQmzwf0NVW2BrwHeCLwLeL2qvlNEvl1EPg9ARD5JRJ4AvgD4YRF5Z1z97wCfDnyZiPx+/Pu4ZcZzoRpukhKKBaWEo6IS8pqtoh7xedaSmerAAMtrnmeFMpE288SDMFbXi4uti2bwDo0dG5ZNHsgTQNRWWUZY2KOKBC1edaG06g02WAVU9THgsZlp35p9fitBaphd77VArw1xL4xwl5USOEJKmHTyParfmcM4ByIIBh/JF2Jhl3Mm30PZVYXFqWJd0xPxxvbnxoLYpZ1qeeadzGSEKeA3RLvBEiiM4cErZ3KaXSpcGOEuHpVQIcyP8UwkLq451gEXvPsKOKwLtQBSeUQTLd9khZ4XeczG84aeW/1YvCkpQfGhP1kPJSBzK32DDTY4HS5Mw/WqnSf7tFBjj4xKmNTNPZ5s52G6PGJWqSvqvavqQTYPyYKcZLBVvXTihYm1m5eA3AQRbLDB+eHiJIWzWrciIeV0jpSQUoLFtcgSZleKa02Vukh9zmRi+Z6X3nsog62oepEawjE6jJtYu31lqm2wwQbH40IIV86YexV021BB6Cjr1qtiz1A39yQk2UHUoTgQg48Vu8IsPZcKVrlm2i/xpjbusRJZDwkTG2ywLKwRHtp0fLg45CFgR1lhIoI9Y2jZWZBCrQpXI+2404gFzi3MLA8pE8ikhsWRh5ClhImNzLDBBqvDWqT2Hguxx4aAdeRwTh6cJDuI+ig7TNeqXbWzLRGvYZKMEJxriz9wuvoH2bFsYmg32KB/rDXhpsI083TbdUBeyyBoveEvj3RYFWnN1mvQJYl39lgkygznHa2xwQb3MtaWcJVJQ7pTkZbIhcUpHbJ6ETAWxFCs2Nk2n3gXLw05XRCnRIyZ0hg2CQ0bbLA41pdwzelq3AYLTEPjyJ6SBZZBdKmFLC8AsVOZbauyGHPi7VrmxAacZ411VlOgYpA53R82ZLvBKlFY4cEr967TbC0JVzk6BGweDpcSVFbZ5PG0mIRgufDNrD7ELM9cO0sxdEVQY7tmjZussQ026B9rR7ghKuHsNW4T6WqUITSTFyS+7l8UEU+s3kmI2aodbdMpwxa1sVaDukx6ERDBmwKR1evOG2xwv2PtCPekwjTHwUXm6grXxBCn0M03lAtMpGJ7LgZ+Wkw5p87B6j1UDH1e2cRNsZlTIz3IZ1Ob5507mf2cF1VasFnnBpcba0W4JxWmOct2YMaHFom4I2FbdjfPxAI+PwKeZ/X6Gau3T0szz1zLsSHZ+Zh98/DxBM7VtU9w1nbraL582H5hpLsuj9r+BvcO1opwiY6aVTWDzK2SrtpV3G+y/HzMLkslHc/j8p9OKV5thMOGYOcjJ1g3Q665LyER75nOYy5vkZErMZFFQvxd2I9SxI4d9yP5WiPc2Covehgrw9oQbl/W7Vn2N88CNgIqFooi1nt1wSo8J+tXpiIcprXeTeptv8jfJHwkvpx4V3EtHrruwkCm3r6C/g6qvmuXdD+S772ItSHcVVu3p0HK4oK83quFrFj5eVm/04kIMtUSfePYWhzHkewiURnH6biz18dxnDlFxNnDf0O+9xbWgnDP27o9DY66AQ5Zvysm31REZyI3BCfbsnKDcH9ZyxqLy7cLkGweQdJpuukBfEryy51tRTRlhWmJYWp5pp3AiXydV4yJpTU3xHvpsBaEC3Lh1u1JONL6jeR7HpEPckJo2XGnL920szfpvS5VpOPrtFJOzpabkOphYs2JEyaa7kmY0m1VkewqUa+hvKhMqknlP1NOvkbiQ0IEr57SSuhwco/AinB9sCa0tAIsXS1MRB4VkV8VkT8UkXeKyNeddRsuRgxclps+3Yx5Q8gu8qEYxCaL/XbkzZGqfFlXI23d7T9VLjOZ9ZQaaaaykvg2VDtrQyFy6K+t+jpBY6hb4yYPFOe1K+5+ePnwe9ZOaeNnnz3InFfauL7Tyat+KPKjuCP+uvleJ9dMtLSdn4TjpWJBrULjFRfDxmf13vy6C043GLe+ezBscBgi8nIR+SMReVxEvmnO/IGI/N9x/m+LyIuyeR8rIm+J3PYHIjJcZix9PEpa4OtV9e0ichX4XRH5JVX9w9Os3JFVDwO5CBwpPcQsLyCm2K5GehA0K5geQssEMFnd3tRIU2at75QFJxZjC+DyVwg7JB3AkW9OquCZtn7hsAXcOdII/ywiKQCoD51IjExCwSRuU2ItkDTdqeIJby/WCIb5Vm+qk+w8eNGN1DADEbHAq4G/CTwBvFVE3jDDT18BPKeqHy4irwS+C/hCESkITSS/RFXfISIPAc0y41macFX1SeDJ+PmuiLwLeD5wOsLtwrGWHcl6YPb1TwBvLCKr1X3z0LI0Djj5FSalH+MUc8neNGahqtROu1fso6SD3DqdJzNMhYidQVKYtTKFafJLHzuyZrLNLhwsbjx1Pw5kqngRvFfKmbjddL0ZFIkPEGvmy0f3KdMdOKsAACAASURBVF4GPK6q7wYQkdcBr2Can14BfFv8/NPAD0o4eZ8N/AdVfQeAqj6z7GB6FUuiKf7xwG/PmfeVwFcCPProo0C0Dk/56j1Pg1x3/TF/iMzTfVfpdDvr9kR9lwp82drtTOm0zCfapMs2US9NpJqs36noBZ041oDOueY1J+VEdtO/3ez1ma5OJeiTApnDbKLdduFgcb0kDflZ8tUwfzZhIs8oTOeisNxT+u4ReFhE3pZ9f42qvib7/nzgvdn3J4BPntlGt4yqtiJyG3gI+EhAReSNwCPA61T1u5cZbG+EKyJXgH8F/ANVvTM7P56E1wB8wks/Pj7iQyjYSY6H1PpcVRE3seh1TssbXVMCzqWH+eQbOvT2Rb6hGI0BJFT+Ut/FEx+1D1HfFa+5LFANOm2SD+ZdSj6TGGYJuSNrPRy94OeQcL7f8GFCkmFfkwF0kgHh+p0U78wdZj5zmGknB01LCuFNRTkd8WpcpnV66azdwggPnC3x4aaqfuKqhgP8NeCTgH3g34nI76rqv1tmg0tDREoC2f4LVf2Z067nTIGc8Ao72/o8v2xspl3mxb9hvQl4PvkaKOzSlm84Hxaf1UzoztGUrpsSOqIVJiZ0CV7y2M4TPjqy4GirtvaHJYZ0bcwLEfOq+Dgvrdfpws7j03JxerJwjyO02ZAwEemMCCOACSTcWbeaHJ8au2+EB0JygM4Sr1elMnJYZsis3dJeHtLtGX8BPJp9f0GcNm+ZJ6Juex14hmAN/7qq3gQQkceAlwIXR7hR6/gx4F2q+r2nXe80zrLp1ufzl0za5VTxbzGkjrs5Aaf9ZsbJheNky/f05KsI3pYdiRyy9jKnTEromJ1/GbT01GU4D9+anp85w5hEAMwSLXGZZMk2GckCNK3vCK3xfopYtYtAmCQmzF5bnWMsWtYhjjvJCOHqT79TZQ3WCEUk4M66JVi+edsjJRBsTryNV6ykxIgwhtzabdx9IzHM4q3AR4jIhxKI9ZXAF88s8wbgVcBbgM8HfkVVk5TwDSKyDdTAZwDft8xg+rBwPw34EuAPROT347T/UVUfO3YtObnA+Flbn8dbAdQhnWUr6aonkbHJiGadLOFTyQ5ziuzMWrXHxZnm+0gE3G3jEiCXEOb1XVMN5DMrMXjVuUSbywlCINlWYdy67lVcVfEpJMx7XNoWp7UaJ4PMnZKVFawxlAZa73EqjFWxxlCIUJiwfafK2CkDK9goIYSHw8TiDdZuGGOqxZD2nEqXXkaJYVlETfZrgDcCFvhxVX2niHw78DZVfQPBYPwJEXkceJZAyqjqcyLyvQTSVuAxVf03y4ynjyiFN3N2H00gh2OI1Mrk1XdRTAg4eHATAkGld7kJCa+TFXyk7JAX2UE7u/dIq/YU+7ksSGQL80K3JlZtPr+zhuNys0QLUeNtE5H67pW/8UrrPKPWT5GU8x7nE8Fpl63WZic/f5AJRKKULkusMIZaQ9bYKEoWVSGUxqDq8MYwckrpNBKz0CrUTUh2KDKL15pw/CIhDjtZ/7m1m0sMClj0fiLdx4DHZqZ9a/Z5BHzBEeu+lhAa1gsuLKXjJOtWRIJuu4p9Q2SzaUtYxKAzUkRY9GKt4FnyhXAj5SLDOmfp9QGvSpvIdo5Vm7TaZNXm8gHQRSTMEm3jlFHruow955Xae0aNnySLoIxbpfFK7Y6RFsikK6WLSAAwPoR8WZPkBNctW1lDaQVaoTVhG6X1VNZgRNlvfLSEhdJKSNBofGfxpmMqDTgEE+LKgnababvpvFgj1F6p1lDXDZlmm2phvUKZOCrmwXTWrT+X8cxKEfHbXCsYLpaAMzXgvsFJZNvMhIOp6hQBOz+t3SaiHTvXOa7GraNxuewQiK5xvkuM8D44zRofLNvGHS0rdMWOZELas/Mqa0JrKFUab2LUQSBfVaH14GvHVmmp1OG80HhDFS3cJj5ArAQSbbx21q4KnZV+SGLwE133PnamXQguzMI9ji8EDmdFnTPmW8EcGxGRVrmPuHDlOI5sU7hXPq/TapnIB7XTIBkRLMODaNEKgWhrp90bQuM949ZPdGLvaTw03k051bwPyzg/SeFtswHODSEDSmuC9moMbSTDIAc5SmuojNJ64aAJyw4Lw7j1HKgyLAwDqzgvFCYQr9hgyRYQZQZoValMMGys0O0nJ10fJYYN6Z4vLoZwRY610EQEWbNX5O5ynIqIYIqAgUNa8HkdxiEn2j2As5CtxnAul02bOMqCM6zxQaMNRBO02bR8PfO9VaVuXGcpJ4KtXSDk3LJ13uNccqqFrLH8+k7SghHBiscasNZMYstFGBSGqlCayIqVNd34wbFTWWqnjFrPVmkBT+uh8kHjbWPthdzaLUzYcRe3C12K8IZ0LwYXQ7jHyAnZQucwkMUxS8CQyRBiULFdQZlZZ1yfR5bCjeZZVOuchXcS9KxkmzRUJlpt+t60yijKB84Hj3/jwm82S7S1V/Zq11mDzil7bUvd+olj0ilj52njdmbPfZ4BqTqRHbqssqjhwkRCaL1l1DgEYVAaXKHUThDxbBeGvRr2IvGOW89Bo1ytLI0EEr5SWcQKrVcqwnXXZqQ7cd/NJ93arYemawR2qsuVfHMWrHEdtMv3tE0yRIiscFlShnQEPC8aYlFSTIVKvCqmreluKhMI/7J2ipiKRjiCbHPnWGeFdk4v7ci1dkrjQov4UevYr4MzzHnloPUd8TZe2a1dVzlt1Hp2R21HvK1Xxo3joHGHZIXWh79mxqF21LERl6msUFhDaQ22CeMYFIbGGcaFQYDtQUyGaSfEu4/j6sCyWzsqqwwLYb9xDHyIdGji+SmNRMs2WtwZ086SbnK+2ct3210qrCXhaohxmQrluowIBOzjcbi5FnAi4LOSb56BZ6f0bo0pwq5LhOg88JfgfC5KtkmvTQ60JCG4eG5Hjad2QU44aBz7kTidBguxjY6kUeO4O2o74h23nrsHbWeZqlcOnGNv7DJrNckfwVJunY/jC/G1CYJQFMHSLUSoI+Ga6KSrrKUphJENKe/ble1SineqQLym9eyUhtsjZViGEMGxg6sDy9g5vBoGRZAYgMzCjSftSNIND2vxOhWhs0G/WE/CBcRY9Jw76a4ax1nAqVV6WCTrq8U0CScJAcC4BjmGorvSjSKoKbsYzXWG1/khg0eRbe4ca5Ljq1X2o2OsiZpr0leTVSsE4h3Fz63z7DeeNpLyqHGM4neJmm/dppjcIA20LpB465S69dO/X9SQNcULRyOiacND1nTOslzD9YzbQLbD0uC9sl8LW1WIYJBauDoIJDwMTMq49VwbWHbHju3SIqKMx56rAztNulMaAl2Ars3OL9ESLuS+zEg7F6wl4XoNZEEsF9hppHMKq0gqxtKxkzIdobq+mG8BT5xwuQWVbsz0+SSyndpPXN7b9SZdn7RXPZzUkDTbWbJNMahpft3ptVC3jt0oIdSt407tsJlVm87Dfu0YNSHBpnWe/TqTGiJhJw0XhXHbZhazdLrtuHY0rUe9HttWPRxT+D2NEawV2sIEyxaoSkvrLAfGURUG5wsOas92tHKrwgAFY6dcidbulUHBfuNovbJdWe6OHVcri4tWeZmRrkRyBZl6gCdJod040VaGtSRcmBRX7jKsOOJ1O5HwTKJCWt6kKlkoROJe18toQsCZEy5LTQ6RG+HhctZjEALpalGdWDDoIqAZaebGbYqzhYmDLGRNTWSEWbIVgjNsv5mREIDaTUi4aR0HTZATVIPGuzsKlrFTpWk9d0cthTUxG83Res/+2AUpyCfnWSBZ5yaOtXTJOe+CVDSjF4lIlNsFZ4UmarjWCk3rGUfJY2dQMG4cgzJYtge1cHVY0DjlysByV5Xt0rI7bqOFK+zVLVuFYbdx7ACFNTQZ6UqSDwjdLfLkiJQGfFFONCPCVrFxml0I8tfqkxfu6Km7eIRoFc8h4ynLeE2JONqzzKYmJ+jUcqfButFswFG6rSoT2SBOn45EmMgI88hWgIM2SAMCjJ3nIKbpjhvHnajVti5klo2aZBl7Gu85GLuOmFNLnFETtNtR7UJKr1fa1kWiBdf6QLhecY1H5lx7kIWUpekCtjBYa2ijNV1FDdeIcGUYnHLbpcV5z/Yg1NdIOm5lA0m1XoPeS3SyNY4rANZ0UQuqE23XCpGMpzPSgu4/uZc26AdrTbiLYC5JzyHjWct4LhFHskvrrgM0RjxorCU8dRN31vH0uNMnzUo2rhOO1G2ZWLJhuYnkcBayBRhl8bPjaMkmcq3bQLZK+B4syUCs6btqIFvVQNbJam3bIEUEog3jbmvXWbDOTQg4/SzTxAtiBDEG9Q5vwnVnY6nOunYd8RbG4LfAth5FGLeeG1tB9ri2VdJ65WoFWsOVyrKvnu0yWLpXAI3XehlDxlIqsJXwYEslHpMTTRVKOX8r917GPUe4x+EoMj6OiMMiEzIOROwvhIgVwZsyfg6a52FrfppU895bSWtcJzs31S+Ij7dsOlPTc8khhXsFZ5ZyECt71c6zV0cZYQ7ZQnCGpQiDOkYnJLJNy7gY+TBu3ExB8WDtzl5DOrkcOm3WRZkhTWvqaadaFhaLeEi1FQSwpQ26deOwhUF9IN7hsMB5ZWdg8d5zZVDynMK1YcEtbbixVXKndlyrYK+GncqyH8PJ7tauc6QJdKnBZSwFaWMmXrqek55bO2VQbAi3L9xXhHsUjiNimCHjGSKeliZW57BTwNtAtrOv3SeOG7qKVuuG2k2cXwm5bpucZLmO6wnaZxtjYJNTLJHtKGqzwmGy3R1PLFvnlf06WsbtJHxr3ITIhFmyVVUKazpdNll+YgiDggnJZmTbxu25dkLCaZ6PkknSc01hoPWBbG2IVHCtpyhDpEJtHV5Lxm3o5tF6xftg4d4ikO/dGq5WQA1XBgWjVtmuDONW2SqlC52zMU5XJI5zRs+dxOfqJmqhJ2wI9xikW2OK1GbliTkWcfKym5muCotesgo4W01pmWce9xoi3cjzpIRcYsi/5y3HU5xtGy1ea4RR4zpJYRyzyIKM4LtlgkyQWbKtm3oYpdf3qjC0TjvirQpD3XqGlQ3xtq3HWoNzHlsIPrKXqscWBhdJXESmyDZlq6U3ji6W1ylaB4miKC1aBkectSY44FqlHBh2vbK9Fazd69tVN75rwB3g+lYZLNoK9puW7bJg1PquLsOgMLSa2vZMYnDnSQsh449zi1owAlv3sEW9IdwFccgqnrEswyu+nasRn0WWUECNnUtMlxl56u5JUkL6nkcktDGDLEkBTmOsbAzVGjvHXhPCwGrnO6dXSk4AOIhRDLOn9Up8dVcNabaJ5I0IhRWaNvx+xaDAFZ5x42nGLbYwiImWeOMw1uBah8ZkgrBNpY0haHn4GKRgFEFMIOhOUigtzvlAwqoUpbLnleEwnJfrW2W3natxWze2S/ajA8/E6nyhxnSQD0o70XGDZXuMtLDJQusNG8LtEUdZxFOv+HNkiWANH3Z4QbBsU9rqvUO3UcKc8xDJ42tzKSE4y8IyTZvptjGRwStdbG1ItQ1FvlN5xeToatxhgktOJO2mB2ItIkmOmljVyxogWJ5elVHtGClsDw2+MozGjrb1lFWIp3WtR6Ie651irODaWIXM+Y4kVZVmtI90ceaKLSusjR08Wo8tJ5/RIlrTk+SK6zsVjFogXF639wPpWjFI4yiMsFs7rg8s+43jigQHbNJz/RHSQu5Am63ZscHZsSHcc8AhIp6RJY5yeEF47TuuZc5lxHHWbW7J56TsNZVBDIkOnW7beKykerahilvjJyScLFuRsHyO7crSumDJFvbo2M8rw4nTLjWudD60wtkehHCtUeMxYnDeMxpH4rNQjxxFaWjVAaYLJZPMtPbOYWyB+jQ+wTuHdw4decrhICzXesqBZTyCsrKotnSvAgKyXWFrBwIP7Bh2xy2qlkKEO7XjgWHBQevZqQrqVhmW0tXZcKoYnVi5nukstGJj5faCDeFeII6TJfJl7jWcZN122mEWDpYcPa0LDR0DsQYiyJMcGq+dVNDEkKyk2c5KB0aEqgjWbHIqShxbehASrcAuXZeQjaZK9xCoW8+gCC16DuoWaw1N4zgYtQy2hfrAUVSBfG1h0MoG61cCsap3+LZFXZONLljUYgvauqEd15RbQ3SkFFVwlFWDIl+c2yJd9trt/QazU1LYYOFeN8JeHcs8th61QuGlqzBWxi4QAysTizZzoE0STlZr5RqBrXKT+HAuEKYbyYbXmYsazcXgqMOdrSfShSGtdDSrwTzr1s9Yt7mjTAnzWqdde5y6DXothHAwG2UBF6MWkrXbkbs7untIaQ22lGkySVYjqS1OnKy5MylYt6mSWO2UYRHKLB40jqIwjEZtsK5HLYMtYXzQYsvgUDNW8D79sBN5AQ0PihDDJZiiwpQD6oMRRVWF5TyITFvsRoTbgFBSGOHOQRhwuV1xEB14Ax+SIa4by17tuD4UmuhAK2INXog905i2ci9rMoSIvBz4AcLh/KiqfufM/AHwz4FPILRH/0JVfU+c983AVxByVL5WVd+4zFjWhnCNMCnIrD4E9pO6kk4u9PsRJllb+bQ5hW4uw/np4lRnnqTNjHWbJzskfTVos1GnjQR90LRdQkPq1oBkvcx0st8EIZy/VBEshXxVhaE0hiJ1x43WrY3XZiLgdL6dD0XAU2nGg8Yxbjz7dctB7dkdW/ZLy/6oDeOrHVAwPmiphgXjg4aisLRjH4o1uRb1LeraqXPVtg16sEu1fQ0ngmsaBttbqPeT44oXiDHC3VEYe2EMdatd9bMy6rg3hpNQsbrV4Bgk12+Thj6xcjWff4m0XBGxwKuBvwk8AbxVRN6gqn+YLfYVwHOq+uEi8krgu4AvFJEXEzr4vgR4HvDLIvKRqot3tl0Lwg2WrYB3GN+SP/PVWPJKWjB988xqgPOmX2akcyOumerxpsBspbHLQL7JGXZa7TZ9zq3bJtYvcNEINCLU3ncEkcfUJjmgLMwhx4+PJDsobCwIE5YPPcNM7K6biDkWEGdybpOkEKIjEul6DhrL3tixVRp267Bta4S9gwYxgUzHBy3loKCtHbaq8G0b6hg3gURdM+qOwFiLmILm4C7WDTHVFuP9fQbb27QxjExEaIxjX0I3iXHruDtqEAnhbCk87pqRLi556IWRaqihm1m56c2yOCJiIZ92CfAy4HFVfTeAiLwOeAWQE+4rgG+Ln38a+EEJF8krgNep6hj409hG/WXAWxYdzFoQrone0ZxsIeppfqaUYSrmAp0V3G3niDqe8wj6spCziZ5oO9NQU4DpSmOh67A3E/L1a0a8eYhXjpyEj9JuvdfQykaZOMGatpMVUpSCkUlXXgjXxLC0HMQaCEXsKVZYYVDYrhbtwEps6hhKJRYmFAgvbSBLKxJ7kWXx1h6cBiu3cT7E/TaOvabgYOjYHbbcGbWxF1mwnHdNaJeehuidpygLxk2DsSVeRjPnR/GuBddiigrfjHHNmHLnBuP9AwbbWx3ZGiMYK+wfRKK1Qa/dHbeYeFzpfA0KM7FynTIoJlZuozCw0lm0VfSUpd9Hdc4r18XhYRF5W/b9Nar6muz784H3Zt+fAD55ZhvdMqraisht4KE4/bdm1n3+MoO9cMKd1Hatj/0NE8EARxYmn3pplLTW7Oewl3nkvG6WcxqiPUW7eEFBHcY5EIOaoutltS5I1moee6ox6kBnljlKu02aqVO6qmF1fLVO2u0sjAlVtxKqSKKqytAKlQ3dMbZKS2WEQfo/WqZlZuXGq6jTFjxMGk06zyiS7t1xy93KsjMo2CotwzJ0djAmxNlqDP9LSRDloKKtG8TYaGRMbGl1Du8a1Dm0HGCLkmb3OcorDzA+OAC2Qj2GODgTnXZ3Rw3GCFVhaJzjoI7lH22weCFYuQc+9EVLTsj0VtDF5Wa6rTLp+rsKWUFQKl+fZZWbqvqJvQ9kRbhwwhXorUNvJjrEazVcsEdX2oprSP5/+jzxlJ6WnPt2ZKVb7rR1b9M6qMe4Gm+ruYH9F4W5cgLTJJwvkz67qN2mSIMgMTjGzmPicl1SwTEHa2RSVas0wla0cHcqG75XlkG0fJOsUBo6ecFK1DSZXGshVM3Q+qDp1j5kuF0dFOyOW26PWgbWMCwDeRsz8VWo0oWJqSpt3WCqIa4ZY6zFuxbvWtz4IDr+WtrRLuXOdYpqi3bvFuWVBwJRi4Sst9bTjFoOBMrSxpC1UPWssIatyjKOD6VhYRi70KIndfZ1XiltsHaniDdzGqYOyOtj5B6LvwAezb6/IE6bt8wTIlIA1wnOs9OseyZcKOF2ITh+YQ16qX131KgnEXNcY47VnMsas8S8jJSRLnDrzvS0z0cbNN85RdsvAqluwElygp/5HEg2Oo/cJDLBeQ0xynGDjZ/ulDuLwgR5wGtovmhFGBYmWJ9FaEc+LG0nLVTWUJm0HhQiMVXbIXjEe1QEjKBYnLE4tYxbpVbDuDTsJAu3atkqLGXsX5YI13sNCRAu1EvwgwHNOFqOpkDbGjc+AFVcUyMmhIk1+3fDMVVbtKM9RK5grKEeAVHDdW2IB7YmRBwMIvkexNoRAxvkBSXIB43TLta2CwEzoCIxRnfaebZmssJxeCvwESLyoQSyfCXwxTPLvAF4FUGb/XzgV1RVReQNwE+KyPcSnGYfAfzOMoO5WMKN2q0cd6dcME5rNc8l5s5iPr2UkWNW0z4LFOZ2yLgoHCUn5Bl0+TLd59ghV6I2a2KqrtMkPcT0VREaPz/0q8ycYFdLixjhSmmpCstOZdmKhDuIWmtlQjPGgRGsbzDtGGlrcDUk52X3mwlqDLaoUFMyKLdwxYBxYRm0aXvC0AqFnTT+VKWzcL0PNRPaJpR1tMMd3GgPwcRz0AKKeod6jymrSLqCVcUVJaAYG+J7m8YhRqgLx6AqaF0IW9s3QT7ZriytV/YbzwNFrCAmPoSoGXCeLhFknkW7almhT0RN9muANxLCwn5cVd8pIt8OvE1V3wD8GPAT0Sn2LIGUicu9nuBga4GvXiZCAdZAUoDL8qA8HvOI+VgpY67GHP73Em50VDvSVElNNXMTec4OJBCtSkwFXZNnmZ5RTmhi+cVQ4CZWCctkg6TVKpPT4Oecj6TXFkbYsoIxhqtVsDavDCzbpWVQGIZRsx0UYTnra8xoD2lGSDOCZoS0Y6hHqHPgQ5tzxGCshXKIlhVU25hyi6LaYVDtMDSGwpRUhenkBAhxwa0PXSXaxuPbaOW6Eu89LXtIEVpMTQe+Kr6pI+newVx9gPZgF1NMpAVjhaIM5DuuW/asoSxMl5wxbj2FSanLQQapioLWB2s3Oc880hlF2l2nExK+LFDVx4DHZqZ9a/Z5BHzBEet+B/AdfY1lLQj3fkInZRxjLXdVnGw1ZUGcljtzDXRdMK/wTk7Cs3KCCFNygnO+kw1mLdpk187uYopsY9vxq1UI07pSWbargqEVBjbM3yqEgXjMeB+pd5F6Dxnvowd30f1d3GgPHe1D26BtnZgHbIGphjDcxuxcw2xfQ7evUQ6uYbeuUwyHsTZBjFAg9mFTpW5dqMvbOIrG0NQWMQZbDNIJChZxd86UnHTHd59jeP0R2tEeIBRViXehQI6JVm47iN2EfShRWcSHC8DYKSIhc60VoYrkmsZoZz5DHha3glRf75F6r+eNrg82hLuuiB0djqujMO9aXyOO7ZAkk9mx5eFbc+WEWEMhkXGKSEjE6icsdEiWSWRrc7IdFBQ2aKvbpWUYiXZghe1SqLTFjO4i47uY0R66+xxu7xb+zi109zbt/h7uYIQbN/imIUnkYg3F1hA7HFBcuYq5eh1z4xHMtYehHbG1/SC2ugpiQUuU0FIodJrwoYnluKVtPG3lcU2JLyt8O8ZWA1xTd+exjZpuMdxGXYspSlwdYna1chMHWmHQKjjkmsYxalqGpWHUGLbKoN3WsQfbdhk7/IpHMbSqFCpZbHeydLNoBdWgYW9wJmwId03hTRGI5Jhl1pFc5+Eo/TbNm/0/WbHeh3AwpxNyTYVsZrXf/FykZIXCCIPopNoqgsPqSmXZijLCIFq324VQaY0d3UVGd5C92/i7z+Cfexp/+1nqO7epb+1S392n2T3AjWpc3ZI6NEhhsMOKcmtIdWOH4Y2rlA8+h33oDvbBDwTXUu04rg9voN7itaJxyrgNzS33xi37o5Z63NKMDbawiA23ptgSaRtA8C6QKSK0432KaguxlubgLqYc4OoRxthg5fpQ+NwWnrr2jCpP3TpUC7yG1OjSBIs2hbVVRShLGZxnE+uW+PvN6rg+5GP3dJXcH1gLwr1EISbngkRQ90z92xlyTZ9zEk4kC9BmFrGIoH7SVyw5bI7ysxqhC28aFKZ75R2WlmER6sBWJvwNbJARKhx2tIuMbiO7z+FuPYV/9inaZ28yunmL0bN3GD17h/HtfUZ3RrQHLe2oRV24ck0hlNsl5XbJ8IFthg9eYfuRu2zt7VOO9ii8R3BUIlwfXMcp1Fsl+3Ug3DsHFXcOGvYPGurKUVQOOy5oiwpTNLjxfqgupj6cC9dgioq2HoExFNUwLCOCDndwTYsrDM6aEAERz5/zdJZ17TwDH2SFJpRgYyee2zJmmyXrVrMY3O73S8401bV3nK0TLpRwO/E9va9sEHBcW/hLiHTzHjUPmNZvmTjQiJ/bTL8VEfyczLsUZ6saKk4VkQiuVrYL+N+KabxVdJBVRjsZQfbv4G8/jb/5JM3Np9l/6lkOnr7F3lN32H96l/GtMQe3xjTjYI2moAhjoBoUVFsF2w/uM3xol/ruAW7UsN2ECmAFIKaksiVXyi3GreXGVsHduuTGdsOt/ZLbw4LRQUNdBCvXliGzLDx5TEj/RUE9vhljygG+rdGiDBbvcAdfj2glaLldKJ4P3SkS0Y5b3xUQcrHcZGVDAoeLztb0u7TJ0p1xnOW/X690qx4z3mi4K0H3FDXlkZlmk9t0du7069iTFAAAIABJREFUDXwvPWNVzJEEdRkx71Byi7Yj0WjtBqt22pkmzGSkZds0IvhEtsCwDPq3lVAJrLCG7ZjpVdhk3YZQLdvsIeM95OAu/vZN3LNP0dx8mr33P8Pe+26y++Rt9t6/x95T++zdHXProGXPefZa7Sxxi7BT1FwpDDduj7jy7JBmt8GNGlzbgghiLEU5AFuxfXXAeGAZ+Yq7tefGqOLaVsOVrZLd3ZqytNSFDXJClBAOW5EayzqCdy22HOBdg6tH2Go4FefrWk8bW783sVRlSv1udVIvuNNx1XSOsykJQSdTlGzGvXTzrRgXLil0BTFMAb6NU0NsoxfbJUcch5PIqWt5Pr1WNv/wtO67znyf3faxe14MKuaesW5hOtY2YVZemP2smpw6mfygEykhXyfJiKl7g4h01m2qrVrYEBNbRm23FLC+jWFf++jBHfydZ3G3nuXgmdscPHWL3Sdvc/d9u+w+tcezt0bcHDlu1o691lNHwgr7hVJCONkjteMDRg4Xi9BgBDsosYMBsnMVs3UFW+2wPbjBlhWuVIadKoSobVUF1cAyssHCNcaEsLOiwNWO2etPfYuxBb4NEoOrRxgbLFvXOnxrI+nGOF+n+Fj60Wuo6+sLM1W7QoiOSwOaOc66+iWZ42z2d9jgZFw44aYnpzEWNbazdtKrZSfOH4Pj+FggelPnL5SH3CyCebGf3baPIXqZQ+QqgpeQbnrSMV8WHPUwPIqEc0dYUpryOFvNtNwEEcGIkvtwrBAdZ8E51n2PpFxawdQjpDlAxnu4vdv4O88xeu4Wo5u32fvLW+z+5S6779/j6ecOeGK/5ZnGse/mODI1WN8jrxw4Zc9F6zdey+WwpNgaYK9cxVx5ABleYTC4yrAwXKkKrlYFV4cFO1VIxihKEwvRWExRIsaCSChukxcpV0W9x9VjisE2rh5RbV8LdRd8hYtZbCnBImWIJRmh9aE40LZIkBNMTLQgEIPmFq0ekUm50W/PhAsnXMjiLQm/31lbei/19n2SdXzcvJOutWOIfp53d6JfpsItxwsp86y9dcRshMIsZp89iVSFSYxtWu6orRTxfKYatqEebJhW2lD9K5GuNWDxiKuhGaPjEbp3F7e3S3Nnn/GtXQ6eG3HwzIhbd8b85cjxVO0YneIhOPLK+8ctRmBwa0y5vc/wgV0GD9xh+PAt7N3nMNcewbYjhnabYWFCiFpZsFVZqspgCoNYCam8xoY/mU2QiefEO0xR4mOImPce4xyubSk1FivX8KY2ifoIFm96gEFILJk82KbfKg85O2e+b3B6rAXhJgTN7qJHMY3jhrNKok/e9bwGrj+mHOVlqIWboDpDwrmemy2XIhQ0I4bZZfJlE9JpKeNJDOUYo9UoUEhoYU9bI67GH+yi+7s0ewc0d/cZ3d5ndGvE3u0xN0ctT9ftqcg2oVW4OXZs25bt50ZsP7PP6Nm71LfuUt69hR3dhWafamsnREqUJiRelIaqCOU1bZEqixkmzSXnOK28A0p8W2PLKhQw9213llKRnC7MLv1p1nlDp8tmzvstjjz6ni82UYfcw06zXpLtReTlIvJHIvK4iHxTH9u8n5EsNONqjG+7v8LV2PhnXI3EHP9UnFyg62KwLljkfpy90fPv7SnefiR61Q0Ta9eIEHruxpY5rkW07bLGtB7hRmOavRH13Zp6t2avbrnVeA4WyI8eeeW52rF70DK+M2Z854Bm7wB/sIfWB0hbU4jGluUm1N6NscI2piAHq9ZMChDNsXBB0RguBoQSjq7N3hQI0kO0YH1GwEkbT+e565KRnfv8/1lMHGkbnBZLE27WwuJzgBcDXxRbU2ywILqiPsct0/2FlkTGt4GEY+3cdeuueuybQvbZRRP9OCfbSUjaf0p+SDAisWWMBAet9+BaqGt80+DrBle3tLWjHbWMWuXAedoFOEWBfefZbz31fkN70NDuj9B6jI7H4BqMTmoaJL3ZGsFYE9SolA5sMgt37s4U3wZtt+v8O0kJm1i4uQaeHVPg5JkJxxzXBoujDwu3a2GhqjWQWlhscM4QggRhYkbSmnHu+SGLWogVFLPSQHQ1g7u/2EfMty7+eZxTaq80S1hwtULtPa5RXO3jtlvwTSjxiI/xw5OOEkYmbyhmxklw2t+zG/EMscZJh94ajpfNLoFGdYnQB+HOa2FxqA2FiHyliLxNRN528+bNHna7wQYrwoZgNlgRzs1pFvsMvQbgpS996eaSXhEUwduye62+n5HCoHIjbXJOUgNOgRQNkBxrNkgPhUnxvIudyVJi4XIDpohSgbFgLDBJLlA0lESMn7vokwWtaznyy+S7HLPI1OIipzet+4D3MLp7jjs8X/Rh4fbehuJ+R/Lin+Z2CzepoGJxtkKLEAq0bnUYTtKjE2wPN7jqRMfN433TZ6+AKUL1LltAMUDKElsV2EFJMSwoKsvQCENjFtbDh0bYLgzVTkW5XWK3h5iqgmoLNQVeLM6HymFt+ovZYcnJFR4ak9q/cyGCKcrw0dip6SkyceI4PJy1dii56IS49g0WRx8W7mlaWGxwBnQEYasQfaDaFRDpAtGzbg6SOUiOK+d4EVj0Bp3VXNN3a04u6qMoIgbnPUZsliwhMSzKo9agxoT02bLClAPsYIDdqii2CqorJTu3LNdqx+1G2D+jtVkJ3KgsO0NLtVNSXRlQbA2QrW1MOcQXFU6FVkPL9yb+pbAt7z3qNWrMMTRwbiJNPEvxekhteECjhi2dlRqM+aQVp01qd567WOY5v8E8JP15g9NjacI9qoXFotu7LK/CiyZEnHR5plja1MJExXR3x5E90uZkba07UpHxlMwkhC85uXaVqJKlxukIPPFx46G0k+I3qcyjU/CmxNgBWlTIcBvZvkKxs0V5ZZvhjW3Gt8fs3K55eOw4aD1PjluaU55kAzxUWT5oWHD1+hZbD28zfPAqgxtXMVdvoFs7aLlF7ZXaKSOnjJznoHGMG4d3im99F+6lXSz2YQdWSoowsTuE2JiZlp0pSRZu7Dxs4+fCTpJF8pjuee7WI8/7hm/PhF403HktLM6C5EWeym45ZSD/qohv2ZJzx+lv81N+08ygI6bg9LixpcZy0ZgiVw7/LrOaoyDMe8OdtXZzpLY7wyJos6pK6wLjtt7TepNlWgleDGpLpBggg61IuDsMru3Q3NhhfOeArTs1N0YtY6/UqjzXeMYnWNeFwI3C8MFbJQ9erdh+ZIudh3cYPHCN4to1zJUb6GAbXw6pGxg3joO65aBxjGpH3biQBeYJ0kLsY3ZUtIAYi6oPbX4gxO+aInwXMis3WLehc3D432ZFcWxm9RqTPexmzvcRknBvUNfi7z7X81bXBxeeada9lniHeJ8ETLwpwrwloviXKmqjLFXUZlFxXEmtdS49zwLpwXX4QKJhO73szDQlPoy7MKlJqFe+zZQpZUS6ti+eaNV6z7g1DIpQ36CJmmljoCiHaDuE4RXMznX02gNUB/sMD0a04xo3DmQnEra5M3Y82zh22xCbq9m4rQTN9uFBwQcMLB94Y8iN51/l2vOvsf28h9n+wAexD30QcvUh/OAqYykZuVAIZ7fx7I0dB00g3LbxoZuvd7EuQihcM1VHIe5ZjOX/b+/dY2XJrvO+39q7qrrP4947M3wMRyRhGZANQYkTSRkIAgzbREjLjMOE/iNhkMQKZZGRBUSAHCuRKY8BA3YQMGBgC4ESG4RhgLHkREokgYztSKaYCJERS85YkRzITiwpEB3JQw7neR/ndHdV7ZU/1t5V1X36nNOP6tN9zq0PmLndfbqrdld3f7XqW99ay/kMcR6fj+w4ZRnOO/vPyRzxOmn9yam3RBpZlKYJpxFP3aAjecOZe+x2h7ci8hzw48DXA78FfExVL7C9iHwc+HPx7n+mqp+LjxfAjwAfwL5yL6nqT161z70Trosf5NyEWlWyetb+pC6dPtslvv5Ib58QOKjx5n1gGblmIs2InWU/WxHInOmwTYQraSLYvPTUDTqnVeAod3EgouO8CpwWtp1ZZY1rrGmLUOQFko2R/Ag5uY+bPkc+OWc8nVGXNaGs7fzvHD5znDyacX9a8bAKnNU2JcHeCxx7x73M8Y6jjPv3Cu69cMq9997n/vvfwckLz5G/63n8s+9Gj+8Txvc5L21q7uNpzeNpxaNJxeNpxWxaN929Qm36bajKVnvpfM/Fx2ZPmbVxTIQrzuN9hvfWk8F7sdLmTvIsVbh5B6n9o4+J2iQ9NAU4rpsvWPicVvoGHCw+BXxJVT8dK2Q/BfyZ7hMiKf954EXs4P9DEflCJOaXgFdV9feK1V8/d90O9zsmnfgjitVRy/4OWOLgKYJoMOvQXQhxaScwzKGj20IrO0jMzDuxE2aIZBA0XIh2k+SSKqjKoBTe2g1mLvbPrZQ6C5yV4J2jDFbQ4Gu1ngrFCVKXEErc/RKtSopYGiti0WJ+lJGfZIzfmnL/4ZTJWcUsTt0Fi25HhWc0zjl+dszRc2NOv+4+py88x8l738X4696Lf/f74cG70ePnmJDzpKp5PKt5e1Ly9qTi0XnJk0lFWdZUZU1dWoluGhq57GpNXGbNa2JLRpePcA3pmr3Nx0jXZ0KROXIvc8fQi/UHVrVjlkVyXTSLLCbI5MKNW4mPYtEpwOeAn2eBcIE/AnxRVd8AEJEvAh8G/jvgu4FvBFAT2q8tMNh7hAs8dYR6LfRiFHfbIQsayVwGXIQ4TyDa4drbRPLNXGyQTSp7nj86iiUaSwK5d9aCUJTCCWdl4J5zzNJ4cBE8AS8O7xyj0Sku1HBS49VkrcI5xDt8kZOfjCjujZm8fc7s7Smzsxn11CJQASRz5mw4zhk/e8TRO045fvezHD//HMXz7yF7z+9CnnsP4eQ5ZsU9Hk0Cj6cVb56XvDmpePNsxtvnpQ2SnAbqMhDqmlDNCHWd3jQuy+LUB3CZEWt+dGoReDEGwBdH+DxrEmUi4LyQZ9b6sfCOUeYa8kylxRbZOhzpSsLgk44rciG67X6Oe8Q7ReTlzv3PRs//KnheVV+Jt78CPL/kOUsLu0TkmXj/L4rIB4DfBL5PVb961Q73G+EmOWGfizhI6IVE021GknG7FHmVxOBFCJF0k76Y9Ecn1q/VXXI2qoIiBNRZj9xaBKLlCiDzsReu8/gAvjbyKsb3bIMqNg7c50iW44/G5PeOKZ455fjhGbPH59TnM8pJabYtAZ858qMR2fGI0YNTimdPGT33LPk7n8e94z3Icy8QTt9BNX6WR6XyuAq8Oal442zGW2clbz0peXReMp1UVGVNVVZUZUkop4Q6TewNmGbrcHkk13yEz813nY1PrHeuCFmW4XOPz2KEGxNlmUCexgvFqRgicc5bdCz4jjVskWTnIt4kN/QtfdUV4e3X13nFa6r64mV/FJGfA96z5E8vde+oqorIOr+2DKs5+N9V9U+LyJ8G/kvgO6970YADg+m4tV0y3kLL1yIScc49JqChPalIcifEiFYxgk1NxZ1AjRFuESPYOT2zs+0yKM4Js0iyR5nj0bTiwTjjySwl52InMWLLy+yI4kgsRe8tASWjMXJyH3/6FsUzD6nObGpvmFXUZRltbGJTe0cF2fGY/N4p7t4D/DPvxD/zLvTeOwgnz1GPn+FhKTyc1rw5qXjtSclrZyVfezzlzbOZDZCcWMKsruqmCY1WZXQoKM5n1KFu9FqXWbLMFUe4+K/10DXN2eaiOYrc5rj5OME4c8Io84y8xCY/jszZWCefgqAkLbBwNdL9TPv5euwUqvqhy/4mIl8VkRdU9RUReQF4dcnTfodWdgAj2Z8HXgfOgJ+Kj/8PwCeuW89AuAcKCXWc/nDJ36/IECeSPpRis+RUWIzYzVXQkU8WdVxnc8rqeBUU1NoZumDk66OOu+xyd1oFRplrxvSMvePhtOaZsXBeBqBCJIsk4qI7ZEQxdjjJYkHEiOzoPuH0Wdz5I7LzxxTTc5hN0bpuzhTiHIyPcaMx7uQZ5OQ+nD4gHD1Axw+YFfd4XGpDtl97NOW185LXHk154/GMh2czJpOKcpYi3NKGQ6pSzybtcexIByKC+BzVQDY6BhGcz8jHI3zeRrXOC3nubWpxHA+frhYKb9MwVJXcGfG6xi7WuhLa5Nm8Q+HQOtJtgC8AHwc+Hf/9/JLn/Czwn4vIs/H+dwA/FCPi/wkj4/8F+CDwj6/b4UC4e8BcXCbxX6RTTWaE6+oSdY6LF+CKhPktdV5JcL6xKm3QynUncO7i1IcUyRI9nxd03JjUqSPRpuSbEMcyxb9JZ3uLjoVR5phWARTGmeOtiUW66bpBi4wA1AEbLZ7ljI6eIcvHkB+hoxPk+D6uPIfZBC0naFVBXUb7hYMswxUjyMfo6AQt7HVhdJ8JGY8noZERXn005WtPZrz6cMJrj2e8+WTKkycls0lFNQvUZWWWsNnEolyRtuUi7YnWxRLu/OQZkxGO7uGzDOccWe7JC4tu88w3x26UOca5a4ZsOrFR8ebNtRLmdPKy7480eu6yhNktd4WBEe1PiMgngC8DHwMQkReB71XVT6rqGyLyF7GKWoC/kBJoWILtb4jIDwNfA/7EdTs8CMJdZhu6rZgn0y6RyvJy3O5ru5Vk3uPq0pI5ayKr66aJzSIJ7QtWNXcxcZYcCUEhd2InCFUyJ3HUSxvZ+vhY5hy508Yl0B0iuSh6N6RbBxSTF96eVNwfeZteCwT11F7iFFtH5YXCj8mPR2ZPLM+RqoR6ioQaCTVo6jvrQDwh9mTQbEzIj5hJxnmlnJU1j8vA25OK155M+dpZyVcfT/naoxmvP57y8PGM6aSknFZUs4pyVhJqS4yFUJHm+80dy6wAEbLxCVk+wkdJIR8VbXTrHVnuGI08xyOLblPBwzj3jKOckHlrem4uBTenmSfiTRFx87mliPeW/2pV9XUsMl18/GXgk537fx3460ue92XgD66zz/2OSddU2HD4itDVUenVZLqsJDdFe5e9ay8YYV4yPv46pMbk4vxBdOVfJFeIP1zmNcL0HFWa5Fju5mWFzAmlE0TBi1JjtjEvQr3kiE6rQOHNEhbKmuPM8fYUTnJtyn6PMked2XicsrY5aIWDwo/Ix2OcBpxWdgIMgWbamjgbfioZtfOUAaaVleqeVYGzsuat85I3zkveOK949dGE1x7NeO3xlLeeRClhGqJ2G9C6tuhW1WQLTEqwaNfhfGZkOzo2KQFwxZisKCzSzT35KMPnNh7ee0fhHePcc1yYliuYnHCUGcEWUU5I1WdpUm8i3W7VWfqcmkbuPUNDTXj8Vu/bPRTsl3CJZOScRQ17WoMhRaR2W+PttaLS+O91ZLoK6lgxpc5vdGwUW/umLf76Rlcy6CJFtRL1wq6sEOpgAx+DUIVg0Zia/cuLME0kq9oUNFyGWR3IVFAnPJzVHOeW8ZjWSh08ZR2Y1cq4NoIqvDJ1VijhY4bfuxwvOfhWvlDs864icZchMK0tsn0yq3k4rXjrvOStScVrj6a8/qTk9cdT3nw05fysZHYeJ0zMasrplKDB9NtQR0dCQShn+MJKd1WVbHxMNjoBIDt5YHauzFOMM7I4Cy3LHUdHOScjz7jIyJw5EY6LjFFm3+lx9OU655rx8qnMflFOSF/9ZRHvgNWxd0lBAcRjcUqP2wSa2Gnh0r47jPGys/SyQXpdDfImaGzTY6MItc9N4zwEPSGiKxkkdJNlqvMEnHu77Rx4dRACXqCKUW4qcnCYK0H06m5iVbAxM3msQDuvAieZOR5GlTDNlEkmkXCFIvPkUf9Mkxi8tBF5iG+lVqhDoAzKtAqcl4Ens4qH05rHMyPcN57MePNJaZ7bJzOenM2YnVfMphWzSUVdWZFDmE0QEeqQ/LYFIFSTJ2TjY1w2airK8pNncM5RHI3JCm8yQuEpxp5R4cm8uRGOC8/JyDPKLQk7jl5cgFHm4jGxBGaapdbtb3IX5YR9Ye+EG5pILoNuee8SGAElCaIlUJiPRO1pl0ejXQHjpkl0HXSPjcQf4GWwY+OoXWYRSewvcEhIVrBFWeE6t0KKckO0NFWRAbxAGfXdutZGblh836rK40nFKPeIQFmrDW30jidVQKrAUeaYVFY0McpsrPo4swg6i521us1eLHEXbPpt7M8wix2/zsvAk7Li0bTm0aTkrbOKh+cz3nwy49F52US206m5EkIIlJOpXZWk6rLOScllOcXpM7Fngv1k89NncOIoxmOLaDNnEW4eZYTCc2+cc1z4WMZ7MbrNvEQ93Eg2k7bUXpxrb9+QnPA0YO+EC5FYUimrtpfPiUQ0/reKNtps84CJdB1YItyjWsdmO/N/Wzw+iWgP8T1bG0AudSskWcE7+04EobntxSbhpsqoOlikWnUkhibi7RB6UOV8VuOdUNYhZtuVaakxYSSMM8dZPJ/lLpCXMjfcsdtZK0V7Ftna6PEqmBwxq5XzqmZSBh5PSx5PKh5Pax6elzyalDw5L5mcW0Q7m1TUpUkJdVWZnFLOmlLe+ePmcD6PHtsMf3SKiFAcjXHeUxzl5IXHeSErPMfHOSejvDl53D/KOSra6HYcK83GTXQ7X2CS7F5NpHuTckJdUz18e4c72C8OgnAtU2zGblVHKvVV8U2WNmllh0gku4QVMynqcuuxAI0k0oy4vkXHJ7kVpFPQ0U2W1Wo9FOpO8qyOUe4485QhzEW5WUdiqLWVDKaxDjjELmLTsm5IuB0lH6iDcD6ryb1FfIV3zFyrX3blhGattN/ZuhPdzqqas1lgWtY8ntY8mZaczwKPJiVn5yXlrGY2qShnNSEo5dSCi3IyaexfaTS6z8f2O4gnUlXFFUf4YmxJr6MjnHeMjnOy3Kxgo3HGeJSRR/vXvXHG8cj02+PCcxSj26PckzfRrZj/Vuy4pIg2RbdzdrBBTtgaB0G4kCKSWLnTqbC6DSSya9QarU/SVv/c1mOzSK5gP+RsIXlmHmL78TdRrsKkmo9yR5lvLuu7um5KpqWItmsZq4NSY9JCIhoIVEGYlKEhnSwSc2oRar3K0thxqEKwVo91oKqVSYxuJ7OK8zJwNi2ZzgLnk5KqDNH2FQi1Uk5MOqgqcx9otIKJz41kY/IsyQiusGhWnKMYjxARI9vMyLYYm/e2KDz3jwpOR57cO45yx72RBS6Fd5zG5NtRjG4LnyrM2ug2nWxSAUSCayLegXA3xcEQLnT8ogeSWT8kHJgcuzG6BHpllNv5txvlHmWeaV3HCjQjz9zBrFYyESqJWq4X6kqbqCyVBi8iKGbHSuTvpNEpZzQZAotA4/5SZFtF3bislWlVM6sCszpwNq2oauXsvKSuA7NJhQYasjXdVq0XQ0hFH+3xsRE54PKxEW5sw+jznLzIESeNXpvlSbv1jEee+0c549wxyj0Pjk1KyLzjNNrEiljSKyKMM98UPCxGt8CcdNBEvIM9YSscFOE+jTBpoFu9c1GnTvajuwIn7QihK6PcSMwqxHaLpulm6qIVzKLUUeapFGbRb6vY7dxL46kFi0K7xzE1Lp9UgVVmc6XPoqoDtSqzKhhhByPcyawmqDKd1cxmNaEOzCZRNphVNjqntm5gGvXfJCW4LI82voCVC7dymssysjyzqDtqtXnhm8g2yz3HRxn3jwrGueek8Nwbd6SE3ONEOMktqh1l3uQEb9V/ub8+uhWMlIfodjsMhHtDaAmVOf0VOu4JDchCUxZ12Zzn8y5g5SiXVssNahJKciyUITRR7qwKjDPfkF/uhOAEUaEONVki3sxaNCY8mdYWsan5dJcJNJYU0+Z16XMLUU54Mq2aV01nNdOpSQNVWTcarRU1GMHWVWgHRMbtZaMjysmZFTWoyUbOe+tolvumkUwxtkkOeWGNaYoj890eH2XcG+eMc4twkwXswVFuFjcnnI7MvXI68igwipmxwqcKPiWPWi5cjG4XH9sVQh2YvnV3x6QPhNszFonVbs+T6xyxapjryLQIV8+ofXHnSPe6KNehBGQusi2wTmB5JiieWV0z8s6IOygjLzyqg7V6dEJZGilPNZBnjqrWCz5dVWVaX+zHXAdlMqubqqsQo9sQaspaOYvOh6BKWdbMSiNRDTZLrYpkW1eBalaDQOiQvfMO1ThRQoR8HKvGnLNq4Y4FLR95fGaWtmKc4ZxQHGXWlGbkuXeUc5RnPDjKm4j2XnzeUWauhNwJR7nHizDyPnYOa9sxFq4tcug6E2CIbvvEQLhb4Co5YD5qjbPaWL/3rwC+nhEi6R5KM5ptYUkpGgkhva2k2bb3jdRk4TWZgxClhcLBo8oSQCe5ja4ZRWlhWgWKmCCalqEx+KvCKHeUtV4oLC/rQFkFECiruqlgqzokLAKzSLR1FVsphkiwZUu2qctW3YmQs9xTlTU+83PWxq7rxHtnfRG8uRTywjWFDVnuGI8zihjRjjLTa49zb0mycUbuhPtFSpy1jce9CEXWSgndRNgyZ8JNRrdPAwbCXQGJWNvbVxArlsK+KmrdZP+uLgk+X6sDWHf/h8jT3UKI7ntK933n3+TFBYnNbCBTYVZascJpAWdlKy1Mq5Z0k+QAcDarmw5imRPTfbPWRkZ8vmATdbuYlDUiJh2kKDmRbV3Z/ZR4qqqOn1wV1yH6RLqq2hl2Is1YHBfLbQErZMhckyhzTjg5zsm848FxQeGl8dkeR+02j24EEeG0MAlhnFlkfzyK8kSUEtoBkraK3M2X8Q7OhH4xEG7EKlIAcEEOuKlpFYIN2lSf49ELroWrEm8Jh5aAExEyD1V9sfpsmbSQihoSEedeOFLPJLoWEtEe5Uau0yow9g5V4gh1I59JIt0yMM49k9JenxqWF1F+6DjJov/U1prItin/DvPvKdkbNdrRssxRVQGfSFah6boe3++F6DZzuJjMykcW3RaFZzzKmkY0R4VFtKdjqyC7P87IvONe4fHO8SDqtQ9GHkS4F5NnyVYHRrBpYm+cJ9lgcCb0j6eOcDcjVrXuWze60osQDVBkwKlZAAAgAElEQVSXqMsa7S3hsnW3L7auVknDPBTSdTGBtliOmwg4XSmk5yXXQuFMzy0yAcwqNo7G/kS6GpNhyfBf1i0ZT2a1jZmpAqqOWa0UGOlmTiirQJF5ZuV8/7FF7hERcNo0DyOSlM9cmxxz1kxG7RzduBMAUJs55kRwsfEMmD0tyQjeO46PcpwT7o0zisxzOrIZZffHnjzzRrbOItpEtojwIHpwj/JWt01kmzmZlxI6by5Ftd7dbHSrVc30zcc3tr+bxp0k3C6ppvvL7FZWuaVGUBtqrDcN0YBPI+RFYri6goShNa4OaGxcfUhIHtlFuSRJCV3XQhVdC3Si3m4SrUu6x4WHWUu6gt0+zq1B+9mstnaFIig1qmpTIqrAKPdMy5pR7s3+hUW+syowLnyUG6yVYV0rPuqiBJMLQlBEjUQhnhC7zJ2+m53I1kbnOLK4Jp8J41GGd86i2dhe8WQUNdrjnMyZpOBFuBdlhGVkm3sbENlGtPEkdo2UsIpdbsDqOHjC7eqnsBC0db4gdn/VqO/wiTUhvgPa69vmkTtTIHKVtJA7oQw2a6tGmsjW3Fwt6doQxIuke1J4XAmT2KDGCZzHCNiL8HBSUcTHnQiT0uQGH0xSOJ8aKacIPD1nXHiqWqnEotFyVuO9Q52iKjhVNIi1zlV7bPHLK/G1aRRO+v4WuVWMORHGheOoyPDR0pVn5rMtMvPYjqMLYRz73p4UrYyQihty76K3lkY68B1t1ssgJdwUDpZwu2fXbia3+yXotlB0t5hUE5p3eUXDHog/hjUbkyvW0Bw9HDmhiznJoOvNlTQiPZIxYgUPkYS7kW6SF7qkO4nkKiKclWYjcwKPZxbFPuuEs1mNqnAyspaGD88r8jh6JhNhUlnDce+8WdkcPDqvbAJwllEHpcg9ZVlb17IQYsXYat/ApttXnMogwHHhY3cz4aSw3gfjIuNkZER8f2yy0knuyaLly04icBxH6KTIVrCeE5l3TUe1JoplXiZpIl4/2MB2gYMk3PRlIFQ22ys+vkgU115G3wKYNHCRYLu9JNLz0nt1gtnEViRdI1uTEg65RNhJmxhbdC2k8TrEJNpVpCtYIm2cWdnq41loyOi8Coh4HoyESW2R571xFjt8VYwjSU3K2hwNuW8KJqaReI99zijLKOuasgqcB43kmzdJsToEQlCLcLF1Q+uv9Q68bxvTJIJMPWt9rBLLnDCKSTLvhONRFn21jqPMtnUvNqjJnTDOLFw9zq2k16LZlmyLKCn4hnTnj/M+dNsuhsKHPaC5pAnzjbdvO7nCagR7GSemx5OuaaRbIpe8QiGOf7FE0aF7eK3BipXrLtNz7axjNxZJVxBYIN2zqqbIPPdEoh/XSOistIj2OBNmDp7MQtRHhfOyZloqJyPL/E/KmvNSm4m3ZW3EG1QZ5xnjHE7H2jSyqWvrkSs14Nv3tei3Td26stiXFyzIGOeOUSxySETrBMa5abgCTVSbe8dJ7hqCTdLHvZQgYznZmmxj959m3VZEngN+HPh64LeAj6nqm0ue9zPAtwN/T1U/0nn8x4AXgRL4B8CfVNXyqn0eJOECiPY3AWKf2IZgr9pm40/1uR2reHJatr9kB7sNMDJaTrruCtJNiTRxbTXaiXjKoKgTfOGZlDb+5iS3SQ6PZjUj78lHwiQoQYXTUc5RZo3Egwqn45zjwkh2Gr22ReY5CYEqmPOhip9h5kCK+Z9Uk0dYlrQV6+CVeyGPST0nwlHhGeexUXiHaMeZY+QdCJwWWbTCKfejzJCJcDJyjS6bWksukq3CErJt58U9RfgU8CVV/bSIfCre/zNLnvcZ4Bj4kwuP/xjwx+Ptv4kNnvwrV+3wIAlXRKIee/vQEp40/XxhO4K9DKmblriMEKNYaCMq5aLd6jbgqiSag6WkOwtWtivxubNayTOHC4qrhVldc5QbuU2qwEiSdBA4V+U4c4ycME3EO845CoFZFXgy1Uh8Qh0fm1UCdaDI2p9QCBbdhtCe4DS1HE3rd9I0hmlKdyPhjryz54g0Ax+hQ7TAOHccRT/xKCbMUkOaIgqwyWebNNrsCrKFVlYonj7d9qPAB+LtzwE/zxLCVdUvicgHljz+d9JtEfkHwPuu2+F+CHelD/XwP/iug6DPCHYdpCRT95Dexj65izCDfopw9VrSLVw6AdkTClrP7igTXIx2RYyYZ1XgrFRLTmVGwhMVjjPH2AmzAOchEW1GFQLTMjApW/KFOMssFkOEIM0U4O4nIETNVKIeLTayJ/M2eUHVmqbnmZXfGjnbRIYismFyIyQ54ihZx8TW7L0jRLdGilLTvpJMsCgjwJ1Ikr1TRF7u3P+sqn52xdc+r6qvxNtfAZ7fZAEikgPfCXz/dc/dD+HqfORy8c/meJcDY42WYB218wczdSEVLt01OCexq1Yk1g7pJk1Xo7RSYzO5UvlsFpNsoknXNatXWasVScSpB9PKItqTImOcpYm7ysjDyGfWhrG259gwxsw6hQWlrpUqCE7mO4ldhq680NVwE0EK5vUtnE1hUJSjTv/aLI4DypxFtWb5ask1j+W6MB/VdiPdQydbrWomr6+VNHtNVV+87I8i8nPAe5b86aW5/aqqyMaM898A/5uq/sJ1T9ybpHDVx2uX5f1O8t0ETXEBFwlW9kiwTxN8c2aeJ12IE3SjZSzpvSkyTm6H1N+1G+168RaFinBcOIravL7nQTjOHUeZs3HnlaJ14Dh3HOc+TuaFyvpGUviLVYqJ8AMdfzg0dq/uCRqg8K5xGCQpKDWayeM0htxLHGzpmjaKhbfOYt2oVuai2LaowcWrgkMn211AVT902d9E5Ksi8oKqviIiLwCvrrt9EfnzwLu4qO8uxV4IN33xul2iulCNfltp55vtGkl7BYn667wH9pAItvkhxxuLRUx3Dd6Zpt9EswuJtG5xRIikm6dBlNjHGtQqcJO2m6mSRaJVZ5f3yYUwqwEcxcgIcBbH6AQVRh7GkkFumm3A1hNicUP6dqQrDkkOClpveSpAaNwLIoziPLUucabHXEO0Ev3BaSzOfFTrBTKZn8GWxgQlpAQZ3H2yXQFfAD4OfDr++/l1XiwinwT+CPBB1dWIak8Rrja647JLYbtEVmu+vabBf/UVcGn0uswDu290fyiLUVLbs/Uw1roLOGeSQbXEvSCRdGtNBXl2beTFTpSV0iTUCuwYlUpDvFVtUfKsST7F4ZBBqQLkwCjLOMVItgo2z6x2nqDWoDyR6mWFKgnpUt87yOJ4GxcJVNUi3iIzuSF9poVzZJ6GaJM265dEtYnUNRK0DGR7FT4N/ISIfAL4MvAxABF5EfheVf1kvP8LwDcCpyLy28AnVPVngb8aX/f347H8KVX9C1ftcH+SgtbQyawvIsQfybZRbjexdRui1y6ctFcDbZly3fTXdbTvL/i8abd36H7bTeE67oUUzaa3KkLUcDGClfbY5M4iXVUbt5P66ypQhpZ4C7UBlObsCGTeNTJBrbFTmDgQJff+AmGl50JbqJKekdotdp+rEOUAR+aMUCHas8ScC74jNaTIePGx3Lk5Mk2ku+hEaBJnA9kCoKqvAx9c8vjLmMUr3f8Dl7x+bf7cH+GGAFl2uazAZlHudYmt9JxDil67SD+crrXL1aX1g7jk+aD4emZ2NJddIKNFdIk8oYnqD+2ALMB1fbpOmkkM7d8t2p0F6/Mq0cVgOmp7XBLx+khCIVLwKDOSrYM0QyrLEMjFok9gjoSTBaxNXHYGQqZ/o6zQJLCcaaqJhFMkmyX3QodQLQG4nGibqrXO92UxqgXmtNy07UNFqAPnb072vYydYSvCFZHPAP8GMAN+E/gTqvrWSq9Fm3lVl0Vkrbn/+ooqxM8RrHaimEOLXBfRJVmINq8rSPaybaChGcmTol1deM48kVc0tCwOxF3pHjkUpOKIEAnOvkvdv9vMribadS2pemm7KaZcgdNW47XY1rJMWTxWY7UKrkAkWBE0kvCq/RKgPeGHGGkb6cY1LSFZkbYEdxnRduWD9vHOcaCNerPYAnLAfrFthPtF4IdUtRKR/wL4IZZXaiyFjw21r/I0XayoilMVkFi22soDhyoNLMNilGkkW4HWWzXdEWii3eCy+dLoOJViGZGLBipf3AL3s6GJ7FSpapZG9SnaTeSaReLVTsSrtKTs4ouDtttShArrlTCv8duLuxH2/InKvqP2Gaco96JbIW2vO1lhkWS7f0tE20gVaZtLotpG3x0khIPBVoSrqn+3c/cXgX9rvQ2EJglwVVSVKqoQD53Knn16XzfBZXJB35MjUrSb1TOg1RPvIpLEMIsSw6KGLWItDVyHeJskY7xmKny8L9ac3TvB035GmSaibiWrKrZv9CJ4Vvfgpv0nAjYSdu39zncj65BsIu42or047BGYi2pTee9AtoeDPjXc78YaQSyFiHwP8D0A73//++0xLLIyO9bVaEzvnWj40Em2iW64GMneZK+IVfaj8Ud96Md0GUSEUWakWNVtJBuuIN46RrXaEKm9f5/IF4t8U1TaJWBopyYsyjaLEk53jd1Lfuk8nrazGMnCxcTpsoRY2l567W2OakOlTJ5mDfeqSg1V/Xx8zktAhTVzWIpYbvdZgH/lW7+l+V5KqCHzlybPLmxnhefsE4sku8tItosUealzgPVygCgjqMIVBK9RfoDD12+vQop20wCP5FS4jHiTXhtUm6h3GfmmyFbjc6Hbl3k9UusmbjNpI12uINn5aPfiNrtJM+8g43aS7dOAawn3qkoNABH5LuAjmPl37Z+rYBnfq5Jnh45lJGt6aY3obmehpYRhcH7OPtae0Rw4QdUanvhQdWx2rQ4Ot/f4d5G03fR9UrXv2DLiTVGhFSyYNzdFtE3kKtIWlkjzvwvH+bJDJ4u3ZZ4M20h3PZJdlBhcJ/E24HCxrUvhw8APAn9IVc823U6aRrtqlHsI6F7CAR2SXZ6U6hu6kDRU1cu17PiDFLAk5dyfbocdbF2IWKGEabo2b2xZxGvPtWMz8i25KkK9EM12SbZ7Gr3u0M1LC+1jVyXOLuPNxTzAQLS3C9tquD8CjIAvxg/8F1X1e9feSkyeiVxpWNgrlumxQTVKBTcz1deirOg+6ERCq7RgbJ4SI+50rA/0cPeGhnhjYrYO1vP1ssq89hKfqNvSSAogVPH4bTrvq6kOlPnEmVyzvUWZIfWRGIj2dmFbl8I39LEIAVyoUZ81GtkhoGu/WabH3lTViEIzuUEiU24z6lw53BPbrtCVGoLOJ83g8kIR6XwHEglDe/wuS5jFp1+4fR2xdp+/KDM4lyxhd5doh8KHm4LWqPq9Gu8vTXhF/++u9dgu2iTYirLBgJWQiNc3UW5rBYNWYrku+l90G/SyNpaQbJIZhmj2TuBgCHcfUW73Cw4Xo9ib0GIXsY1sMGA9XCTfeSsYzNu+lkW1G+232f8l9rCnIJJ9WnEwhAs0Ue5iN6g+sSyKAJoqtpuMYrvoWza4DsLd12/XwSL5NlGuSNN3Y1G3veAIWbbdhX0se31bWWavGEj27uKgCNei3H4cC90oIt2fdxTUSB1uJNl1GVI0W3dKcHcVzS66Kpo1rHgJ/TQhVXa19bMLdruUSBNpynsvg4tn9+Xfx125sgccKg6KcIG5ct91o9zLumABjWXrphwFV8Gi2azRZpseEDtgvEUbkaSGNaox1I9Na56CnrrboOnX0fxv7q83vJq7C63D011pdtOwKLdEfYFj9fHeqQWdSQORUCKxHsLP4bJodldJsO7Jx+xrs4tySfQOp7Wpy+b0zIF4BwzoFwdHuIBFfKFe+ZKr6fcZyrleC/vGMqfBLqNZ29t8Tb2rZmTXUKcAqbVjl3ihvUJIuAvVaAMG7AsHSbgAEirUF9cm0FIUZ/1jD4MNLnMa7NLStQnRLttGQ7wI6jJkYVLBbaoGHDDg0HC4hEubQFtJWtgz2S5KBjfhNIAlGu0GRLtsq8Hnrfe3JzvUgAHXoQrw5qza9zJ2hoNOk4oGCPXB6LDLoAjBZQRfmLsCI6YqWF/WXUa0ycYEIHUZRxFtvsf2vVi/hbrzHgayHXDXICLPicgXReTX47/PXvK8nxGRt0Tkby08/kER+WUR+RUR+Xsicm3l7UETLpi0AG1T5UU0RHBD3sWUilPx1L5AswIVN0eyu6xRuJRotyjSUCA4T/B58152ebIYMOBA8CngS6r6e4AvxfvL8BngO5c8/leAf19Vvxn4m8Cfu26Hh0+4xN4FXEG6qk2LwV2hJaVIst7UmPoGSBZ2Q7QQo1pfgMsaoh2K2gY8Jfgo8Ll4+3PAH1v2JFX9EvBo2Z+A+/H2A+CfX7fDvWi4Gi98VyUKQRs9d7HDvm0PxHlUrTVif+vkRq1cy5AqkFzjo+2n5Lhb2QbsXGseMGBHeKeIvNy5/9k47GAVPK+qr8TbXwGeX3PfnwT+joicAw+Bb7/uBXtLmqnLGrlgtReEplH5okc0qJHyuiPVl+4Gm5qQiOgmrFzLsKxgoa+xPN0JDzf9vgYMuAq1Km/M1gqaXlPVFy/741UTa7p3VFVFZN1fwn8M/FFV/SUR+U+Bv4SR8KXYn0vBefParhhXCTaNNvhiaRXaqiPVl8EiWaF2+Ryh7aNpzEWi7a+JTqpww3lzUAxEO+CO46qJNSLyVRF5QVVfEZEXgFdX3a6IvAv4l1X1l+JDPw78zHWv25uGq6qWpFnjNdfpuYlAusmfS/dPG+mZw6BoHAa13ryWuSuNFjrv1VuCL/REtunkkP47VCfJgAGX4AvAx+PtjwOfX+O1bwIPROT3xvt/GPgn171obxFu0NiZyXkbJLkiTM+1No7L9Nw0Uj3pvakLWCtCtJLBTRUlXIVdRrQQTyC+sCYqPRFtGloI85Vo3ZaGQ/Q84Bbg08BPiMgngC8DHwMQkReB71XVT8b7vwB8I3AqIr8NfEJVf1ZE/kPgJ0UkYAT83dftcH8aLtZlScSjhPX8o51m5ct+2NZKwfReFQ/ZxbepsShhX1hWGdZnU525ajf6SYqlEd1NExwNdK8j5noyLNHaBww4JKjq68AHlzz+Mh0tVlX/wCWv/2ngp9fZ514rzUKju+ZrJbuStBB8fumEiCQNABdKfvdJAhebypT4nhud6yWVYpsinRwACBUuLE/edUuDa1/gnQzuhwFroVLltTtcabb30t5tpAXRGnHLpYUuDuEHPzcfLfbi3b4Edx67sHp1o9pVk5EpwanZ6KAHgw4YcNPYO+FuIy1IqAlyubSwb1zQZzUgoeo9ubSsWU4fakmj1YYat+66G413+3UMGHBXsHfChS2lhQ165+4ac5fg0KuHdhGLSbGqp4PQ9BeOSbx11xRcDkNnsQED5nAQhAutj7b2BX4d0l2zd+6ukCrCkj67ziX4JujKB30lxWD+ZLHp+jVG2sPgywHrolJ4Y7a6tHjbcDCEC62eizhYI6patXfuLrBUNqhrrnYBb45dyQfQ6rVBda2T3tz6xIHzhCG6HTDgAg6KcBs912VrRVeruBb6xq79s8ugCLXPmyRWnxFkKyFU+A3lDxWH+pzQ40lgwIC7hIMiXNhGz726IKIPLA6p3AfRSs9NzfuQEKCt2uvLhpbkGWCYKjzgzuDgCBc213PRmhALIvo03c9butL037DzumiTDzzB9avTJvQhIcB8M5xtyLZ7QjN5JhmppZkqfIhulAEDVsVBEi509VwPupqIvtjgZhvSvfjj342laxnmEmI967QwH9VuIyHAPNluQ4ZdC9qiBr5YwTaQ7uGij74fd/nzPVjCbfVcjwu6sjXJ9NzNSbdLRkq8zN6xZJCQupYFlzf3++7xMCchbDnluJER2DyynSf/2dL1tBVsN6vTD1gP/iZ+JLccB0u40NFzN0qirU+683rmdn1110G3PWSfTWYW0ZeEANajQn0GW0Tf6x7vXVnsBmyH+ZP43S3L7QMHP2JnruXiGq9LpAsmTVz/Y44lxtw02cpce8g0sqdPCPGSnSgh9ES227R53PTkdlNXGwNWw4XfTY8TV+4iDjrCTZhvLr5uk5uZaX/RG3pZNObEXAfbktGqsMkSvpnFtqsmL92E3/bTMExbxmVbW782IVuFa/scD7g5JLIl1Pgbym/cdtwKwgWTBdwmlWgAoYKoB1/WNlBErAS332VfgC4ULWyjf16HuUTUlj+IbgnxtmTrNyBbg1iXtR4P2GBB2xwm1+lAtmvg1hBuIibrLJbBGh+yJV1qXF03bQNT5j/92FKz8l2uf268zQ7bFs7Z2GKf3W3QJdtt17052WKN43vyWC+rELQ/uMGCtgLS53hTV4R3BbeGcKF1LjjnUXStdo7Q2sYai5GThmjlkh6v264XcXYZHKWDvi1eXXRJpI+oFuIx7+jLvZBtKNcnW6J2vMX+E7rJQ1fNLpRh654saM1JMrlk4r4PjfeTXVLq9T/Hpx23inAhXX4rzmWosnZUmixGvp6hWDJtF9nvhqhuQDqAxWkM63f4Wob0HmD7QpJuFnsTK5r2UFgB813QLmv8LjdsQZs7UdKOLTrUkUVJSsiGBNnauHWECx3S9RnUq3t0F9E30Wra6g0kw7potdrLpzGsC+34gbf9saeTwaYnAkV6SZa1csb1FsPU4J7YzH1XWDxRpgrGZnUHNrIoRbeumu15JbcTvdjCROQHRERF5J19bG8VBLWzbHBZQ277QsqeB1+gWdGQQ73jH4gTyDpTfvuSRSyx1y/ZEuq1OsA1awFqb2vZumxYJDZSX9HPrcEunTff7ZXwzbGpLkxolvRfHFmkrGZv3DWSm+cueKJF5DkR+aKI/Hr899klz/lmEfn7IvJrIvKPROTfWfKc/0pEHq+yz62ZSkTeD3wH8M+23da6SGf8fZCukiIvH320kaCij3bXl6FX/Vg3hR1L376XLd+DXSpvqSeLi3prH+uo1ouwdziuoq2uK6+9KmlyD6Gea2y/L7g1cycHjE8BX1LV3wN8Kd5fxBnwH6jqvwB8GPhhEXkm/TFO+L1A1JehD5b6y8APsqernV2SbiKg4DKCy6h90fyn2ciiWR/7CESi3fVBmI9qZ/1JCJgTIXls+yHbWJ69Idk2n+uWzoQmKjsQokhRv1vjBCDQrH9fpJvkhE2uVA4UHwU+F29/Dvhji09Q1X+qqr8eb/9z4FXgXQAi4oHPYPy3ErZiKBH5KPA7qvqrKzz3e0TkZRF5+bXXXttmtxewM9IVB3GbSSZI/9XBrF3VDRFtt1qsjWr72euiE6GvKb/K5rah5gTAdpF2IyUcUEbdPsP1JZakKzvZzzsRSQm9g5IT3pl4Jf73PWu89nlVfSXe/grw/FVPFpFvAwrgN+ND3wd8obONa3Ft0kxEfg54z5I/vQT8WUxOuBaq+lngswDf+q3f2vsnlgoj1OcQZ4htCxW39wzxol+077LjbnKsr6RMisC28mhGKWHbJuuJ3DbSHJOVb6sVzKOREjaM+iUE1EXveI/rWmnfHGRp9Wuq+uJlf7yGvxqoqorIpYdURF4A/gbwcVUNIvJ1wL8NfGCdxV5LuKr6oUsW8PuA3w38arSzvA/4ZRH5NlX9yjqL6Atd94IGtk4i7TsZN5/B7ncQpXmE2wY0fZ1UtilsaNcmvUkJYOS2GfqnFiOtzT9HQeOU651KzMv3LWK9oG8RLuMvABH5qoi8oKqvREJ99ZLn3Qf+NvCSqv5ifPhbgG8AfiPy37GI/IaqfsNV69nYFqaq/xfw7s6ifgt4UVX71QvWxJxPF1mrIm0RaYKE3PB8rhTVAr1avRL67InQRT9ka42KYLvEY0qUbWPOr53vTbaB7glgu6sv0dBE3zcFgfmKvLuBLwAfBz4d//384hNEpAB+GvhvVfV/TI+r6t+mEzmLyOPryBZuQbewTZAsYzhvCa5NN6S1Xcbf0DVU0ml93KFbIYO9LlJ3skMkW7ATgWzpSoA2UbZpgkfp/7K9r0tyUW2KJG4KzcniRve6c3wa+MMi8uvAh+J9RORFEflr8TkfA/4g8F0i8ivxv2/edIe9FT6o6tf3ta0+EJSGLNftMpYgtMMpd13m2fWrSgg70cqMbFv7Wl9vZ76gYHMkm922UkLKpstW5N9vo5x2TX04JfaTVLhj0S2q+jrwwSWPvwx8Mt7+UeBHV9jW6Sr7vJMRbkK3nDb4wiSGNWHDKU0D3EWk62TefSDRKtS3hBBc1pJtj66K+ch28612TwZ9RLehOxNtk/X02Cgnrek2FwxIHGA6YDvcacIF5mYkBZ9vlAgTDbhgdpy+SLdr80rVRH3LB9BavrrVb32hNxkB5k4G26B1SJRbraevRjkJVuXWlw94X8Q3EO62uPOEm5B+yOpzq6Za8/WidZOA2XZ2k8kH8XY9i+Wm/aJbbgxJ1+5v+32RLVhjmj5025Qoc5vawJoNuWjD2249Ca2efBiFFwP2h6eGcIFYcqsQq8bWJ13rIgWptHbN19NGtcruRvmYCyGbK9Hti2u7J5xeyFY8xGkc266xL2Kre7CkdZE+7/4+65tNXTV7GySFrXEru4Vtg4vJtNWHU0LUdOPYHsSt3MWpa/Xa5cy0OS10lxN/eyFbsauNHtwSbVJq28TdDtwJsdLt9mMg3G3x1BEutLquzUnLTVtbw4wumJleEWqfNzauFBWlES1GAi0Z7KJSbO49xfJc6L+VX+9kC3MVbtuiSUptmUlX53tbE/S3rnncMXPWU4SnknAT6qYcOCOoX7sUVVCy2Mjc+pZ6I6aO1pBIeNlkgb7Q7YXQdWb0BcG8wX2MV4d2vdBPEq/P5F3vyTL6L4fVJJ3cEFIPhadKf9wRnmrChSUSw7ot/DDiRWt8XTdNyFPtpWxkRlsNqWJMpY3K+v4Zdv3BfQwL7EbifZwY+pISbGNuN97b3sthhwj3tuKpJ1yYlxjU5+gW/VslbXHHEUg3StxFVAtdsq36a27ufC/DKBN6kxIwrzJ9Jst2IicwjIq/xRgIt3XYM7YAAAUbSURBVINawaGIOHSDhNpNIDWdCW53US3Mz/7qizCszeX2lWQJrabcX3S7bXeyuU2yAzkh/XtYX8sBK2Ig3AWk31tKqO1qou+66BJtSsDtaqpEO113fXnlMqg4u3road3Jcyv16iNzLl0bO4huSXJC395biU3AB8a9jRh08EvQeFddFiu19ke5ra82Q4Gqhybhl2GuL0JfZBvbLfbZLKffYgLppfBibovN+vrOYPZbcjzgZjFEuFcgdR0zbbfYStvdBN0EkxHC7oh2Vz7hxQbnfaBPKaEpK+6ZxNrou18kKWnA7cQQ4a6AVKHWTOa9gaRFimqdyM6jWidxImzs6dAb2dLfqPWEtnx3eynBNuh6j253VcqrC/8OuH0YCHdFBJ3vx1Bv2H1sFSSyTSWvu5wAPN8Wsr+IbK4VZM9kRqh7kTuSdtv3JXr/pbztlvvs8bAuBqLfHgPhrolarZesYJeimzTCuR5yI2R7oS1kT9vts9ViF41zYuOROQvYQXSb5B/f1xrnNt7/jLVVoMqNNzy/qxgIdwMk326qTDKZoX/i3WUk002O9dkWstFE6bdpTjN9t6cTw86i20ZO6L9Zdx37Ttw0mj3uecbfXcBwBLdAkhkUKw+uXNHTlnWnP6zW9tW/zzgdg76nYzSReG9EZgdhF2XQu+pr3P33prEPor+LkH0cSBH5GvDlHe/mncBeB1r2gLvwHmB4H4eEm3gPv0tV37XJC0XkZ7A1rorXVPXDm+xrH9gL4d4EROTlq+bV3wbchfcAw/s4JNyF93CbMUgKAwYMGHBDGAh3wIABA24Id5lwP7vvBfSAu/AeYHgfh4S78B5uLe6shjtgwIABh4a7HOEOGDBgwEFhINwBAwYMuCE8FYQrIj8gIioi6/j7DgIi8hkR+b9F5B+JyE+LyDP7XtOqEJEPi8j/IyK/ISKf2vd6NoGIvF9E/lcR+cci8msi8v37XtOmEBEvIv+niPytfa/lacWdJ1wReT/wHcA/2/daNsQXgX9RVf8l4J8CP7Tn9awEEfHAfw38a8A3Af+uiHzTfle1ESrgB1T1m4BvB/6jW/o+AL4f+Cf7XsTTjDtPuMBfBn6QW9rsSFX/rqqmTii/CLxvn+tZA98G/Iaq/r+qOgP+e+Cje17T2lDVV1T1l+PtRxhhvXe/q1ofIvI+4F8H/tq+1/I0404Troh8FPgdVf3Vfa+lJ3w38D/vexEr4r3A/9e5/9vcQqLqQkS+HvgW4Jf2u5KN8MNY4NF/V50BK+PWT3wQkZ8D3rPkTy8BfxaTEw4aV70HVf18fM5L2OXtj93k2gYYROQU+EngT6nqw32vZx2IyEeAV1X1H4rIB/a9nqcZt55wVfVDyx4Xkd8H/G7gV2Mvz/cBvywi36aqX7nBJV6Ly95Dgoh8F/AR4IN6e4zTvwO8v3P/ffGxWwcRyTGy/TFV/al9r2cD/H7g3xSRPwqMgfsi8qOq+sf3vK6nDk9N4YOI/Bbwoqreqm5PIvJh4C8Bf0hVv7bv9awKEcmwJN8HMaL9P4B/T1V/ba8LWxNiZ+vPAW+o6p/a93q2RYxw/xNV/ci+1/I04k5ruHcEPwLcA74oIr8iIn913wtaBTHR933Az2KJpp+4bWQb8fuB7wT+1Xj8fyVGigMGrI2nJsIdMGDAgH1jiHAHDBgw4IYwEO6AAQMG3BAGwh0wYMCAG8JAuAMGDBhwQxgId8CAAQNuCAPhDhgwYMANYSDcAQMGDLgh/P8QlxnPS0GGpwAAAABJRU5ErkJggg==\n",
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