{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Two-particle bosonic-fermionic quantum walk\n",
"We provide an implementation of the two-particle quantum walk. The aim is to reproduce the results of \"Two-particle bosonic-fermionic quantum walk via integrated photonics\" by L. Sansoni et al. [[1]] with Perceval.\n",
"\n",
"[1]: https://arxiv.org/pdf/1106.5713.pdf"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# imports\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import numpy as np\n",
"\n",
"import perceval as pcvl\n",
"from perceval.components.unitary_components import BS\n",
"from perceval.backends import SLOSBackend\n",
"from perceval.simulators import Simulator\n",
"from perceval.components import Source\n",
"\n",
"## Use the symbolic skin for display\n",
"from perceval.rendering import DisplayConfig, SymbSkin\n",
"DisplayConfig.select_skin(SymbSkin)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Building an array of beam splitters \n",
"The dynamics of a quantum walk can be achieved by an array of beam splitters (BSs) as in figure. Here we reproduce a four steps quantum walk, we highlight the difference between the optical spatial modes (in red) and the walk positions (in blue)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
""
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# number of steps\n",
"steps = 4\n",
"# spatial modes are twice the number of steps\n",
"n = 2*steps\n",
"\n",
"# BS_array contains the input modes of the BSs at each step\n",
"BS_array = [[[0]*2]*(i+1) for i in range(steps)]\n",
"\n",
"i_0 = n/2\n",
"for s in range(steps):\n",
" if s==0:\n",
" BS_array[s][0] = [i_0, i_0-1]\n",
" else:\n",
" z = 0\n",
" for i, j in BS_array[s-1]:\n",
" if [i+1, i] not in BS_array[s]:\n",
" BS_array[s][z] = [i+1, i]\n",
" z += 1\n",
" if [j, j-1] not in BS_array[s]:\n",
" BS_array[s][z] = [j, j-1]\n",
" z += 1\n",
"\n",
"# build the circuit\n",
"circuit = pcvl.Circuit(n)\n",
"for s in range(steps):\n",
" for bs in BS_array[s]:\n",
" circuit.add(int(bs[1]), BS())\n",
"\n",
"# display the circuit\n",
"pcvl.pdisplay(circuit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Single photon quantum walk\n",
"We can check the functioning of the BSs array as a quantum walk simulator putting a single photon in the first input position (mode 3 <-> walk position 0) of the array. Then we can check the output probability distribution of the photon in the corresponding walk positions."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"output distribution: {\n",
" |1,0,0,0,0,0,0,0>: 0.0625\n",
" |0,1,0,0,0,0,0,0>: 0.0625\n",
" |0,0,1,0,0,0,0,0>: 0.0625\n",
" |0,0,0,1,0,0,0,0>: 0.0625\n",
" |0,0,0,0,1,0,0,0>: 0.0625\n",
" |0,0,0,0,0,1,0,0>: 0.5625000000000001\n",
" |0,0,0,0,0,0,1,0>: 0.0625\n",
" |0,0,0,0,0,0,0,1>: 0.0625\n",
"}\n"
]
}
],
"source": [
"# define input state by inserting a photon in the first mode\n",
"mode = 3\n",
"in_list = [0]*n\n",
"in_list[mode] = 1\n",
"in_state = pcvl.BasicState(in_list)\n",
"\n",
"# select a backend and define the simulator on the circuit\n",
"simulator = Simulator(SLOSBackend())\n",
"simulator.set_circuit(circuit)\n",
"\n",
"#Define a source and input distribution due to source noise\n",
"source = Source(losses=0, indistinguishability=1)\n",
"input_distribution = source.generate_distribution(expected_input=in_state)\n",
"\n",
"prob_dist = simulator.probs_svd(input_distribution)\n",
"print(\"output distribution:\", prob_dist[\"results\"])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the corresponding states of the distribution we have direct access to the output modes. What we want though, is to check the output probability distribution of the photon in the corresponding walk positions. From the initial figure we can define the mapping mode -> walk position. Then, we just have to take care of taking the modes probability distribution and and, for each walk position, sum the probabilities of the corresponding modes."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# function that takes a state and returns the modes of the photons\n",
"def get_mode(state):\n",
" modes = [i for i, x in enumerate(state) if x >= 1]\n",
" return modes if len(modes) > 1 else modes[0]\n",
"# dictionary to map the mode to the position\n",
"mode_to_walk_pos_mapping = {\n",
" 0: 4,\n",
" 1: 2,\n",
" 2: 2,\n",
" 3: 0,\n",
" 4: 0,\n",
" 5: -2,\n",
" 6: -2,\n",
" 7: -4\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"|1,0,0,0,0,0,0,0>\n",
"|0,1,0,0,0,0,0,0>\n",
"|0,0,1,0,0,0,0,0>\n",
"|0,0,0,1,0,0,0,0>\n",
"|0,0,0,0,1,0,0,0>\n",
"|0,0,0,0,0,1,0,0>\n",
"|0,0,0,0,0,0,1,0>\n",
"|0,0,0,0,0,0,0,1>\n"
]
}
],
"source": [
"for state in prob_dist[\"results\"].keys():\n",
" print(state)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mode: 0, Probability: 0.0625\n",
"Mode: 1, Probability: 0.0625\n",
"Mode: 2, Probability: 0.0625\n",
"Mode: 3, Probability: 0.0625\n",
"Mode: 4, Probability: 0.0625\n",
"Mode: 5, Probability: 0.5625000000000001\n",
"Mode: 6, Probability: 0.0625\n",
"Mode: 7, Probability: 0.0625\n"
]
}
],
"source": [
"# get output modes from the distribution\n",
"modes = [get_mode(state) for state in prob_dist[\"results\"].keys()]\n",
"\n",
"# get the probabilities of the modes\n",
"probs = np.array([0]*n, dtype=np.float64)\n",
"\n",
"for mode,prob in zip(modes, prob_dist[\"results\"].values()):\n",
" probs[mode] = prob\n",
"\n",
"# print modes and probabilities\n",
"for mode, prob in zip(modes, probs):\n",
" print(\"Mode: {}, Probability: {}\".format(mode, prob))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Walk position: -4, Probability: 0.0625\n",
"Walk position: -3, Probability: 0\n",
"Walk position: -2, Probability: 0.6250000000000001\n",
"Walk position: -1, Probability: 0\n",
"Walk position: 0, Probability: 0.125\n",
"Walk position: 1, Probability: 0\n",
"Walk position: 2, Probability: 0.125\n",
"Walk position: 3, Probability: 0\n",
"Walk position: 4, Probability: 0.0625\n"
]
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# get the walk positions distribution\n",
"walk_pos = range(-steps, steps+1)\n",
"walk_probs = [0]*(2*steps+1)\n",
"\n",
"\n",
"for i, w_p in enumerate(walk_pos):\n",
" idxs = [index for (index, mode) in enumerate(modes) if mode_to_walk_pos_mapping[mode] == w_p]\n",
" if len(idxs) > 0:\n",
" walk_probs[i] = sum([probs[idx] for idx in idxs])\n",
" else:\n",
" walk_probs[i] = 0\n",
"\n",
"# print walk positions and probabilities\n",
"for w_p, w_p_p in zip(walk_pos, walk_probs):\n",
" print(\"Walk position: {}, Probability: {}\".format(w_p, w_p_p))\n",
"\n",
"# plot the walk positions distribution\n",
"plt.bar(walk_pos, walk_probs)\n",
"plt.xticks(walk_pos)\n",
"plt.xlabel(\"position\")\n",
"plt.ylabel(\"probability\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Two photons quantum walk\n",
"Now we can follow the same procedure as before, but with two input photons in the two input modes (3 and 4)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"output distribution: {\n",
" |2,0,0,0,0,0,0,0>: 0.0078125\n",
" |1,1,0,0,0,0,0,0>: 0.015625\n",
" |1,0,1,0,0,0,0,0>: 0.0625\n",
" |1,0,0,0,1,0,0,0>: 0.015625\n",
" |1,0,0,0,0,1,0,0>: 0.015625000000000007\n",
" |0,2,0,0,0,0,0,0>: 0.0078125\n",
" |0,1,1,0,0,0,0,0>: 0.0625\n",
" |0,1,0,0,1,0,0,0>: 0.015625\n",
" |0,1,0,0,0,1,0,0>: 0.015625000000000007\n",
" |0,0,2,0,0,0,0,0>: 0.07031250000000001\n",
" |0,0,1,1,0,0,0,0>: 0.015625000000000007\n",
" |0,0,1,0,1,0,0,0>: 0.0625\n",
" |0,0,1,0,0,1,0,0>: 0.2500000000000001\n",
" |0,0,1,0,0,0,1,0>: 0.015625000000000007\n",
" |0,0,1,0,0,0,0,1>: 0.015625000000000007\n",
" |0,0,0,2,0,0,0,0>: 0.0078125\n",
" |0,0,0,1,0,1,0,0>: 0.0625\n",
" |0,0,0,1,0,0,1,0>: 0.015625\n",
" |0,0,0,1,0,0,0,1>: 0.015625\n",
" |0,0,0,0,2,0,0,0>: 0.0078125\n",
" |0,0,0,0,1,1,0,0>: 0.015625000000000007\n",
" |0,0,0,0,0,2,0,0>: 0.07031250000000001\n",
" |0,0,0,0,0,1,1,0>: 0.0625\n",
" |0,0,0,0,0,1,0,1>: 0.0625\n",
" |0,0,0,0,0,0,2,0>: 0.0078125\n",
" |0,0,0,0,0,0,1,1>: 0.015625\n",
" |0,0,0,0,0,0,0,2>: 0.0078125\n",
"}\n"
]
}
],
"source": [
"# two photons input state\n",
"in_list = [0]*n\n",
"in_list[3], in_list[4] = 1, 1\n",
"in_state = pcvl.BasicState(in_list)\n",
"\n",
"# select a backend and define the simulator on the circuit\n",
"simulator = Simulator(SLOSBackend())\n",
"simulator.set_circuit(circuit)\n",
"\n",
"# define a source and input distribution due to source noise\n",
"source = Source(losses=0, indistinguishability=1)\n",
"input_distribution = source.generate_distribution(expected_input=in_state)\n",
"\n",
"prob_dist = simulator.probs_svd(input_distribution)\n",
"print(\"output distribution:\", prob_dist[\"results\"])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# get output modes from the distribution\n",
"modes = [get_mode(state) for state in prob_dist[\"results\"].keys()]\n",
"## take care of the case where there is only one mode\n",
"modes = [m if isinstance(m, list) else [m,m] for m in modes]\n",
"\n",
"# get the probabilities of the modes\n",
"probs = np.array([[0]*n]*n, dtype=np.float64)\n",
"\n",
"for m, prob in zip(modes, prob_dist[\"results\"].values()):\n",
" probs[m[0], m[1]] = prob"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# get the walk positions distribution\n",
"walk_pos = range(-steps, steps+1)\n",
"\n",
"walk_probs = np.array([[0]*(2*steps+1)]*(2*steps+1), dtype=np.float64)\n",
"for i in range(n):\n",
" for j in range(n):\n",
" w_i = mode_to_walk_pos_mapping[i]+steps\n",
" w_j = mode_to_walk_pos_mapping[j]+steps\n",
" walk_probs[w_i, w_j] += probs[i,j]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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YtWpVyOfEU5ADXYd//vjH+PfTT/v9m4KmYR8cRNMLL6DphRdAqdVIW7sWmy6+GJ/9xjeQmpMj5pJFR61WIycnBzk5OV4TrMxmM5cRn5yczMWmpTjBihVJsdfFJ4PbV6AJKwciyARBiMRF7Uu4Lmu73Y7Gxka4XC7U1NQgMTEx7OMLGS+NBPb8LocDv73gAvTX14f9XIXTidmWFnzQ0oL3H34YSEpC7pYtqLriCpz5la9AwzNhSkr4m2A1Pz+PyclJWCwWHD9+HEql0qtBiUajifeyufcz1sIXKoOb/btv/JkItLQhgkyIGt/BEJE2PgjHQjaZTGhsbERGRgYqKyt5NaUQUpAdDgcWFxeRnJwcdoYty2RHB544/3wszM5GfH4ZAMzPY/yDD/C/H3yA1/7zP6HOykJJTQ3O+OpXsfWCC3i9B1KzPGUyGVfTPD4+jjPOOINLEBsdHUV7ezsSEhK84s/xmGDF3kDG+/oFy+C2Wq3o6+vD2rVroVaryZAMCUMEmRAV0biofQkmmAzDoL+/H729vVi3bh3y8/PjNgLRaDSisbERFEVBoVBwFltaWlrIucMn//xn/Nd//qfgE5YUAKipKfT84x/o+cc/8JxcjuLLLsMPXnxR0PPEGvZzxV7nQBOsbDYbkpKSvBqUxGKKl1SzwD0FmqIoTE5Oory8nGRwSxwiyISIEMJF7Usgl7XL5UJTUxMWFhZQXV0Ng8EQ8fGjEWSGYdDX14e+vj6sW7cO6enpXN0tW9bjOXc4NTXVy4JvevxxDBw+HPH5w4UGMErTMB4/Htbj453oFoxAaws2waq1tRVut3tZgpgYYiNVQfaErZNmP4ueGdxOp5NkcEsIIsgE3gjlovbFn8t6dnYWDQ0NSExMRG1tbVRuyWgE2fOmYOfOnUhMTITD4eD6PpeUlMDtdnNdq1irLTk5GXqlEq9eey2m+voiXnu4OAEMArADyBL9bLEhnM+W7wQrq9XKCfTAwABkMtmyBiVCfGbjFUPmA9umlsUzOQz4xL1NMrjjDxFkAi9YF7W/XtTR4mkhMwyD4eFhdHZ2orS0FCUlJYJY4JEIMtuKU6/XczcF/rozKZVKL6vNbrej7fBhPHfNNXCe2ujEZB7AMABhneHxJZIMZplMBr1eD71ej4KCAq8JVpOTk+jq6oJGo/EaMRnpBCupxJCD4SvIvgTK4GZroO12Ozckw9eCJggLEWRCWLAlFmy8WIy7ZVYw3W432traYDQasX37dqSnpwt6fD6MjY2htbUVJSUlKC0t5fWatVot/ueaa0DHQIynAUxE8XypCooQ7nR/E6zY+HO0E6xWQuOScFt7svh6vDxLrNxuN/d3MiRDeIggE0LCMAxmZmYwPT2NgoIC0VxXcrkcTqcTx44dg0qlQm1tbcgkKT7wEWSaptHR0YHx8fGArTjDQW63Qw+AwZLl6gLgxlKcVwhoACMAIs/XljZiCJ5CoUB6ejp3o+d0OjEzMxPRBCsxmoIITSgLORR8S6xIBnfkEEEmBIVN/Jifn8fw8DCKiopEO9fi4iKMRiOKi4tRVlYmSvejcATZbrejoaEBFEWhpqYGCQkJ0Z8bS1829gtHY0mY2Z9I7EDPePHpSiwsULVa7XeCFVtiFWyCFV/rMx5EK8i+kB7c4kEEmeAXXxe1QqGIehJTIGiaRmdnJ0wmE9LS0lBeXi7KecIRZLPZjIaGBmRkZGDDhg2ilc7IAahP/QCn4r5aLabtdqixVMYUjNMxXhyIWG/k4UywYt3bKpVK8kIjtCD74tmDG/hEoJ1OJ9dBjBXokydPYt26ddzND8EbIsiEZfhmUbMJHWIIss1mQ0NDAxiGQUFBAVdGJQah6pwHBwfR3d2N8vJyFBQUCLPRymRAGFa5AgDsduRgSWQX8Inlq8GpRiCniDZe7MtKLHuKFaEmWM2eau7S0dHhJdJSQmxB9sV3SAb743A48K1vfQsPPfQQPve5z8VsPSsJIsgEL9g7W98sajFGF05PT6OpqQnZ2dlYv349BgYGuJpIMQgkyG63Gy0tLbBYLNixYwc3nSheKAAYTv0AS3HneSy5qKdx+saL/SG1pCnfCVZGoxHt7e1QKBTo7+9HS0uLV4MSg8EQkwYlwYi1IHvimSAml8ths9mg1+vjspaVABFkAoDQWdRCWsgMw6CnpwcDAwOoqKhAXl4edw4xLSJ/grywsICGhgao1WrU1tZKoj+yLyoAaaf+v5fH8yiKgtVqFazmNl5Iee2sK7asrAzAUoMStha9vb3d7wSrWItjPAXZF7vdHnQ86qcdIsgEvy5q301QKEF2Op1obGyEzWbDrl27uBF7gPjTmHyPPzk5iebmZhQUFIiSRObvnLGEoih8/PHHUKlUXGvP1NTUiGtu44HULGRffLOsNRrNsglWbPx5aGgIAJCSksK9F7GYYCWlTHCbzSZo5cTpBhHkTzmBXNS+hDuJKRgWiwWNjY0wGAyora1dVuspxDmCwYojO7pxeHgYGzduRM4KGmMoQ/gZ2Wq1GmeddRZXczs4OIjW1tZlLlVAulZovGPIoQiWZe05wSo/P5+bYGWxWDA9PY2enp6YTLCSkoVMXNbBIYL8KcWz0D+crlusOzkSi8UzYaqsrAxFRUV+jxELl7XL5cKJEyfgcDiwa9eusEc3rlT81dyazWaYzWa0t7fD5XJBrVZDo9Fgfn4eiYmJkhNnqa3HEz7fB3aCVXJyMoqKikBRFGZnZ2GxWPxOsPLthR4pUhFktm6ZuKwDQwT5U0g4LmpfPGsO+WyQbrcbzc3NmJmZQVVVFTetxx9iW8hOpxOTk5PIzMzE9u3bBdnsQiIxMVGr1V4uVavViq6uLthsNtTV1XElPexPvGPqK8FlHen6FAoFd52BTyZYmc1mvxOsDAZDRMIqFUG2Wq0AQCzkIBBB/pTBFvBTFMWr4xb7hebz5WZ7QOt0OpxxxhkhY5dixVvZvtjj4+NITk7Gli1bJL3Jxwq253NSUhL0ej3WrFnjNXO4o6MDOp2OEw0+LSWFYiW4rIUSO98JVna7nWtQwk6w8mxQEq43QyqCzA6uIBZyYIggf0rg66L2xbMzUTiMjo6ira0NxcXFWLNmTVjnEsNlTVEU2traMD09jVWrVsV8Yg2fmK/QhHtez4lFbEnP6tWrvSw2z5aSrEDHImP4dLaQQ6HVaoNOsJLL5ZxrO9gEK6l0E7NarZDL5XH3ukgZIsifAiJxUfviaSEHg6IotLe3Y3JykncPaKFd1larFQ0NDZDL5aitrcXIyAjnNosZQg/gEPRowfG12DwzhoeHhwF8kjGclpYmWnmVFMQkELG6YQg0wcpsNi+bYOWbTU/TtCSalbAlT1J+P+MNEeTTnEhd1L6wzwtmwbICKJPJUFtby9s1JaSFzDYdWbVqFdatW0dmuQqATqdDXl4e8vLyuIxhs9mMqakpdHd3ewlCWlqaICIgdZd1vEqKPCdYlZSUeE2wYrPpExMTkZqaCpvNJglBZkueyPcwMESQT1M8G74LMbuY7UcbyIKdmppCU1MTcnNzOQGM5BzRbsAMw6C3txf9/f3YsGEDcnNzvY4vZtKYX1bI5hPJzGE2Y9hzpKHZbMbAwABXXuU50jCSz4TUXdZScQf7y6ZnG5SwmdwzMzPc+xFsgpVYsE1qCIEhgnwaIoSL2h/+BJmt6R0aGsLGjRuxatWqiI8frWC6XC40NTVhcXFxWdMR9vixRgqbdSzwFQS2Y5XZbEZbWxuXkMRaz54Tk4IhdUGW6vrUajWys7ORnZ0Np9OJxMREaLVamM1mjIyMcBOsWIEO9/2IBuKyDg0R5NMMoVzU/vAVTLvdjsbGRrhcLtTU1ERd0xuNy3pubg719fVITExETU2NXxddPLtmfdrw7Vi1uLjICXR/fz8UCoWXeztYoo+UN3CpZDAHg2EYaDQa5ObmchOsFhYWYLFYYDKZ0NvbC6VSySWHpaWlidJNy2azEQs5BESQTxOEdlH7w9NCNplMaGxsRHp6OiorKwUph4nUQmYzulevXo3Vq1cH7ZwUc0GWsJjECs+JSWxCkm9DDL1ez4mBZ3mV1G+gpGohe8LenLPIZDIkJSUhKSmJm2DFvh/j4+Po7OyEVqv1alAiRAyaCHJoiCCfBojlovaFFeS+vj709vYKO6YQ/AWTpml0dHRgfHw8rIzueAiytLfqJWItKp7lOmx5FRvvZMurDAYDUlNT4XK5YrauSFgJghwq8czz/QCWmvmw+QBCTrCyWq1ISEiI+HV8GiCCvMKhaRrT09OYnZ1FYWGhqJuDTCZDd3c3HA4HqquruT7IQsHHZW2321FfXw+GYVBTUxPWF/10sJClvfVHhkqlQlZWFje0ni2vMpvNMJlMYBgGzc3NXgMZpIKUBjcEgq9bXalUIiMjAxkZGQCWT7ByuVzcDRNbjx7OvmO328lgiRAQQV6heLqo5+fnMTk5iaKiItHONzs7C5vNBqVSiZqaGlEmBoXrsmbd5ZmZmaioqAj7bl1IQbZarRgfH+dG6gXckCRuPUkRz/KqgYEBzMzMICkpyave1nN6VTxLeqSSZR2MaOPcQk2wIi7r0BBBXoEwDAO32w232w1gKcNVrHIehmEwMjKCjo4OqNVqlJSUiDa+L5RgMgyDgYEB9PT0YN26dcjPz+fdbUwIQZ6enkZjYyP0ej0GBwcBwKv/s6cVIO2temWgUqlQXFy8rLzK053KXvtI+z1HyuloIQcj0AQrs9nMTbBSqVReDUrYhD2bzSYp74YUIYK8wvBM3AKW3LxiCbLb7UZbWxuMRiO2b9+O7u5uwc/hSTCXNTukYnZ2NmJ3ebSCzDAM+vr60NfXh4qKCqSnp0Mmk3H9n9mEGM/+zyvFQpaqlecbo/VXXsVaa579nvmWVwm1PikiZia4v3p0NkFseHgYbW1tsFgsOHjwICwWy4oadRoPpH1rR+Bge1E7nU5QFMU16gD81wdHy8LCAo4dOwabzYba2lqkp6eLch5PWMH0Fc2FhQUcPXoUbrcbtbW1EceuoxFkt9uNhoYGjIyMYOfOnVy9tUwm47olVVZW4qyzzkJpaSkYhkFXVxeoWDciOQ0JJngajQarVq1CRUUFzjjjDFRVVSEtLQ0WiwUnTpzAhx9+iNbWVoyPj8PhcAi+tpVQ9hTLNbITrEpLS7Fjxw6cddZZKCgoAEVROHLkCP70pz+htrYWd911F959910uEdWTp556CsXFxdBqtdi5cyc+/vjjgOd75plncNZZZ3FJabt37172+Ouuuw4ymczr58ILLxT8tQsBsZBXAL4uat8saqGFcnx8HC0tLSgsLERZWRn3ZRa705W/EY8TExNobm5GUVERysrKou42FokgLywsoL6+HlqtloufB4odKpVKr/7P/1YoIOQVk7YtJjx83i/P8irPch62GQZbXuVZzhNJtrDv+laChRyvNapUKlRXV6O6uhr79u2DXq9HdXU13n77bdx0001obm72evwrr7yC/fv348CBA9i5cycef/xx7NmzB52dnVzSnyeHDx/G1VdfjdraWmi1Wjz00EO44IIL0Nrairy8PO5xF154IZ5//nnu31IdcEEEWeL4c1H7IpfL/d5pRnKuzs5OjI6OYvPmzcjOzl52HrEtZOCThLXu7m4MDw/7XUukx+cryGxL0IKCAqxdu3bZxhZqQ46r9STxGt5wiEbwPMt5SktLufIqs9mMrq4uOBwOGAwGr+lVfM+1UgRZCla81WpFaWkprrvuOlx33XV+H/PYY4/hxhtvxPXXXw8AOHDgAF5//XU899xz+MlPfrLs8X/5y1+8/v3ss8/iv//7v3Ho0CFcc8013O/ZxDSpQwRZwlAUBZfLxX3pA33xhYgh22w2NDQ0gKZp1NbW+k2+EGM8oifs67PZbGhra4PT6URNTY1gA835CLJnT+xALUHD2owlvlkD0m++IZTg+ZZXWa1WTqDZbGHP7mHhZARLRewCwYaApLBGtnVmIJxOJ06ePInbbruN+51cLsfu3btx9OjRsM5htVrhcrmW8jc8OHz4MLKyspCamorzzjsPP//5z7k8BClBBFmC+Lqog4kxEL3lajQa0djYiOzsbKxfvz6gG09sC5ndNI4fP47U1FRs375dkA5gLOEKcqie2ITYIaYFymYLs9Or2OQ8PuVVUreQg3nWYk0oQTYajaAoapk3LDs7Gx0dHWGd48c//jFyc3Oxe/du7ncXXnghvvCFL6CkpAS9vb24/fbbcdFFF+Ho0aNRhyyEhgiyxKBpGm6326vrVigiFUpPK3D9+vXIz88P+ngxY8gMw3AzdgsKClBaWir4RheOIC8sLKCurg4JCQkBe2LzPSchcmJlvbPJeWyCnr9uVcnJyV7dqliPkZTfYykJsthlTw8++CBefvllHD582Kv08KqrruL+f9OmTdi8eTNKS0tx+PBhfPaznxVtPZFABFlChOui9oXdGPi4z5xOJxobG2Gz2cK2AsWykCmKQmtrK4xGIwAgLy9PtEH3wTb4yclJNDU1CZJA5nHS6I/xKSZeguevWxXbPay1tRUURSElJYVzkUpVmNnP+0oQ5IyMDCgUCkxOTnr9fnJyMmT899FHH8WDDz6It99+G5s3bw762NWrVyMjIwM9PT1EkAnL4eui9oX9soUryDMzM2hoaIDBYOBlBYoRQ7Zaraivr4dSqURtbS3effdd0ayiQILMMAx6enowMDCATZs2CZr8IbiVL+jRPI4rQTFhkcLa2PKqVatWcdOrzGYzZmdn0d/fj5GRES/3tlSyeFlPmxSuYahOXWq1GpWVlTh06BAuv/xyAEt72qFDh7Bv376Az3v44Yfxi1/8Am+++SaqqqpCrmNkZAQmkymqUbFiQQQ5zvgOhuArxgC4OEgo65VhGAwODqK7uxtlZWUoKiriLfxCWshsBnNeXh7Ky8u5ci6x3OL+BFn0eHEcN0LW7RqPYfRCIcWEM8/yqqmpKeTl5XGzhtlmGGx5FTu9Kl6xSjahK96CzDAM7HZ7SJf1/v37ce2116KqqgrV1dV4/PHHsbi4yGVdX3PNNcjLy8MDDzwAAHjooYdw991346WXXkJxcTEmJiYAgHt/FhYW8NOf/hRXXHEFcnJy0Nvbi1tvvRVr1qzBnj17xH3REUAEOY6wLupoxyV6WsiBcLvdaGlpgcViQVVVFTfZhe95hJi+42mRbtiwAbm5uV7niJWFPD8/j/r6euj1et7x4nDfq3huhOxQBpqmvVp7rqR+wlJ1BbMwDOM1S9i3vKqzs1OQ8qpIkVIWuNVqDfnZu/LKKzE9PY27774bExMT2Lp1Kw4ePMgleg0NDXm9nqeffhpOpxNf/OIXvY5zzz334N5774VCoUBTUxNefPFFzMzMIDc3FxdccAHuu+8+yXgxPCGCHAfYrlusuEV7B8ta1YEEeX5+Hg0NDdBqtaitrY34gyiE9ep0OtHU1ASr1erXIhVzIpPnsdmGI8XFxVizZk1E1z+s58RRTFQqFc4880yu1zCbPczOumXdq1K0QlmkLsj+mm54llcFGsbAXnuxb5CkJMihsqxZ9u3bF9BFffjwYa9/DwwMBD2WTqfDm2++Ge4S4w4R5BgjhIvaH4HcyaOjo2hra4tKeEKdI1zm5uZQX1+PpKSkgBap2C5rmqbR1dWFoaEhwRqOhDpnPPHtNeyZPdzb2wubzQaVSgWdToe5ubmYWm/hIrX1eBLqhsF3GANN09wN0sTEhNcNEmtlCzm9SkrTqMJxWX/aIYIcQ4RyUfvDVywpikJHRwfn9mFbOUZ7jkitKbZ14erVq7F69eqAr11MlzVbTjY5OYldu3YhMTFRlPN4IrWkLt/sYbYJi8vlQkNDA4DAk6vigZStd4C/BS+XywOWV/X19cFms3HTq1JTU6OeXkXTtCRqbSmKgsPhIIIcAiLIMcDTRS1WkoVCoeCsbqvVioaGBshkMtTW1grmEovEQqZpGu3t7ZiYmMC2bds4IQiEWBby/Pw8mpqawDAMampqBG04EhSJWCeB0Ol00Ov1UKlUKCkp4aw3z8lV6enpcUtOWgku62gE0/cGyW63c/Hn0dFR0DTtNb0q0KzhYOuTwvWz2WwAQAQ5BESQRcbXRS1WxiMrlmzmcm5uLtatWydo/IivWLLtOBmGCfvGQIwYMjssIy8vD8PDw7ETY0jb3eoJOz3M03rzl5zkKQ6JiYkxeX1SvoZC3zBotVqv8qqFhQVYLBaYTCb09vZ6zRpOS0sLOZtcKjFkVpBXUkJhPCCCLCIURcFms0Eul4teeiCTyTA0NASj0Riw93K08LGQTSYTGhoaQrbj9HcOoQTZc0DFli1bkJiYyHUDixkSFpNQBEpOMpvNGBgYgFwu93Jvi5G1KnULWcw+0TKZDElJSUhKSkJhYSE3a9izvCoxMZETaH8eDCLIKwsiyCLAuqhNJhNOnjyJ8847T9RNxeFwwG63g6Io1NTUiBYbDUcsGYZBf38/ent7w2rH6YtQLmu2E5ndbucGVNhstpjHJGUS2AxDEc418ZecNDc3B5PJxOUHJCYmcuJsMBgEcW9LPYYcS5cwO2uYHZzgdDo5D0ZHRwecTidSUlI4gU5KSpKUIOt0OknfXEkBIsgC4+miZi1KMT+EZrMZjY2NkMvlWLNmjaiJSqEsZLfbjebmZszOzqK6uhoGgyGic0S7CbPZ3MnJyV7xYs/xjrHaGE7XDUgulyMlJQUpKSlc7S1rPbe3t8Plcnm5t/V6fUTXYiVYyPFan1qtRnZ2NrKzs5d5MAYHByGXy6HRaLi/xdM6JYIcHkSQBYSmaTidTu6uVKlUgqIoUb60npZoeXk5xsfHBT2+P4IJMttkQ6fToba2NmRsKxDRxpDHxsbQ2trqN5s7HoK8kl3WfFCpVF7iYLVaOXHo6+uDSqXyqn3m8/mQ8iYulRuGQOVV/f39mJubw7Fjx7zqz1NSUgQtrwqFzWaLe8Z+JMT6/SWCLACsi9rtdnuVNLEuO6HfVJfLhebmZszNzXGW6PT0tKijEYHA7mQ2aUqIWudIXdZsffHIyEjAMi9PQY4VUit7igUymQx6vR56vR4FBQVesc/BwUG0trZypT2ek5P8IWWXtZRmDfvCJuixwlteXg6LxQKLxcLVn3u+B2K3VxV70pNQdHV14f3338cll1yC7OzsmN9sEUGOkmBZ1Kwgs+5rIZidnUVDQwMSExO9LFGxZxWz5/DcIGmaRmdnJ0ZHR7FlyxZu8LuQ5wgHp9OJhoYGOJ1OLl7sj3gI8qfFQg6Gb+zT4XBwsU92cpJn5rCna1MqFqg/2M+RVNcHfJJ0plQqkZmZyd2o2u12rnsY2141mvKqULAWslSvFWtIdXZ24sc//jHefPNNnH/++TjvvPNQWFgYM28CEeQooGnaK17s+2FjRZiiqKjfUIZhMDIygo6ODr/u2FgJMnsOh8OBhoYGuFyuoCLIF74W8uzsLOrr65GSkoLt27cHLWk6HSzk0wGNRoOcnBzk5ORwpT1msxnT09Po7u6GRqPhhIGiKMlew5UgyIGSurRaLXJzc5Gbm+v1HhiNxojKq0IR7xh2KNhrdNFFF+G1117DM888g5///Oc4cOAAvvCFL+Dzn/88SkpKRH8NRJCjgKbpgGIMfGItRyuUnvOCt2/fjvT0dL/nipUgWywWNDQ0IC0tDZWVlYLW9fKJIbNtQUtLS1FSUhJyYxRakMOx3lZCljUQP1HxLO0pKioCRVFc56r+/n4sLi7C6XTCbrcjPT0dSUlJknERS2nWcCDCybL29x6wIYahoSGuvIqN/0fSIGaluKyVSiXOPPNMnHnmmbBYLPjzn/+MP/zhD/jlL3+JvXv34pvf/KaojYWIIEdBOPXFcrmcc2dHwuLiIurr66FSqVBbWxswMSLa84SDTCaD2+3GiRMnsHbtWhQWFgq+kYfjsmZd5WNjY2F1/2IRUpCHh4fR0dHBjdlLT0/3H4eTsPXEIqU4rUKhQHp6OnfTeeLECej1elitVoyOjoJhmGXu7XjB3gBL3ULmKx6hyqtcLpfX9KpwGsSsxKSulJQUfP3rX8fWrVtx99134y9/+Qv+/ve/Y/PmzfjFL36B3bt3C35OIshREuqDqFAoIrZcJyYm0NLSgoKCApSVlQW90xXbQna73eju7gZN09i5c2dE4xvDIZRHgXWVu91u1NTU8LrrFkKQ2Vagk5OT2LhxI1fuE2jM4UqxkKWKTCZDamoq594ONbkqll3YVorLOtr1+ZZXWa1WTqDZBjGeN0n+hHelWMg0TWNwcBAtLS346KOPcOjQIfT09GDr1q149dVXsXbtWjz11FP42te+hieffBJXXHGFoOcngiwynj2mw8UzWWrTpk1hTSRSKBSCzCr2B2uls24qscQYCG4he8aLo3GVRyrI7M0ARVHYtWsXlEolGIbxanNoMpk4sdDpdIK/J9Ld+sWDFZRAk6tMJhN6enpgt9tjOnd4pQiy0O1z2Qx6zwYxvv3PWYFmb5LCHb0YL9jr9OKLL+KZZ56B0WhEeno6vvjFL+K6667zChM+9dRT6O3tRUtLCxFkKRHOF5GvK9lut3ObPp9kKbEsZLY3dn5+PgoLC/Hee++JmvkaKIbMdoNas2YNiouLI55fHGmds+fNwKZNmyCXy73E1jMOx4qFxWLBhxLerFcCwT5r/iZXsbXPQ0NDnHUt1uQq1vr8NAmyL54NYgBwn3t2vGdrayueffZZqFQq5Ofnw+VyBU1wfeqpp/DII49gYmICW7ZswRNPPIHq6mq/j33mmWfwxz/+ES0tLQCAyspK3H///V6PZxgG99xzD5555hnMzMzgjDPOwNNPP42ysjKvY3m+h7W1tbjhhhuwfv167ne+1/E//uM/sHr16vAvVJgQQRYZPi5ro9GIxsZG3v2fAeEFmWEY9PT0YGBggOuN7XQ6AYg70s3XZU3TNDo6OjA+Ps4rXhwMvoLM1ll7Jo+FOgZbZqLVajEXzWI/5fB5r3Q6HfLy8pCXl8c1xjCZTBgbG0NnZycSEhK8GmNE+xmWckkWS6xbZ/qWVxUWFmJxcRG/+93v0NHRgfT0dJx77rk4//zz8e1vf9vLy/XKK69g//79OHDgAHbu3InHH38ce/bsQWdnp9+SysOHD+Pqq6/mcmseeughXHDBBWhtbUVeXh4A4OGHH8ZvfvMbvPjiiygpKcFdd92FPXv2oK2tzesGjX0v161bh0suuQSZmZlwu93c0BW5XA6TyYSkpCSo1Wp87WtfE+X6kQCXyITjsmbFr76+HuXl5di4cSPvzUJIQXY6nThx4gTGx8dRU1PDDapgNx8xY9WeLmuHw4Hjx4/DYrGgpqZGEDHmU+fMMAw6OzvR2tqKrVu3Bp3jHOSEEayS4Ekkosc2xli9ejWqqqpw5plnoqSkBBRFobOzE++99x7q6+sxODiI+fn5iLwmUm0K4km8e1nn5ubie9/7Hs477zzs27cP7777Ls444wx8+OGHy/a4xx57DDfeeCOuv/56VFRU4MCBA0hISMBzzz3n99h/+ctfcPPNN2Pr1q1Yt24dnn32WdA0jUOHDgFYen8ef/xx3HnnnbjsssuwefNm/PGPf8TY2Bhee+01r2Ox1+jqq6/G73//ewBLNxcKhYL7/FVVVeGll14CIN4eSCxkkQnlsnY6nWhqaoLVasXOnTuRnJwsynnChXXNGgwG1NbWet3Bsh9aMbNyWQt5ZmYG9fX1SEtLi+gGJRjhrN/lcqGxsRE2mw27du2KuEe41C0oFqmuUygrNNTkKoVCgdTUVG72czh1t1KZNRyMeAsyi81mQ2JiIrZt24Zt27Yt+7vT6cTJkydx2223cb+Ty+XYvXs3jh49GtY5rFYrXC4Xlx3e39+PiYkJr2xog8GAnTt34ujRo7jqqqu43w8NDSE7OxtJSUlcVr/dbodCoYBCoeD6gvvrACgkRJCjIJwvYzCX9czMDBoaGmAwGFBTUxNV85BosrlZ2DhtoLpe9ostpoUsk8kwNzeHkZERlJWVoaioSNBNLxwLeWFhAXV1ddDr9di1a1dU78unsXWmkIhx8+ev77O/sYahJlcRl3X4hCp7MhqNoChqWQJrdnY2Ojo6wjrHj3/8Y+Tm5nICPDExwR3D95js39jr84tf/ALd3d3o7+/Hn//8Zxw/fpwTYb1ej97eXigUChQXFwMQ7waWCLLI+LNcGYbB0NAQurq6BBOdaFzWFEVxpTyBGo8AnyRFiSXINE3DZDJhcXERlZWVAdcRLcE2eTaJrbCwEGVlZVG/L/Ese+LjmpcqsRA9tmwnNTUVpaWlXnW3bW1tcLvdSElJ4axntq3kShBkqbjV7Xa7YN38/PHggw/i5ZdfxuHDh3kl77HXZuPGjUhNTUVjYyNSUlJAURTm5+dhs9lAURQMBgOeeOIJVFRUACCCLFlCJfj4xpDdbjdaWlpgsVhQVVUlWAlRpIJss9lQX18PmUyG2trakKUJYgkym13udDqRmZkpmhgHspA9p2exSWxCQOqQoyfWoudbd7u4uAiz2QyTycS1lWTd2lIX5JViIWdkZEChUGByctLr95OTk8jJyQl67EcffRQPPvgg3n77bWzevJn7Pfu8yclJr+/z5OQktm7d6nWM7373uwCAiooKfPWrX43bNSOCLDKeruT5+Xk0NDRAq9WitrYWGo1GsPNEIshsVndOTg7Wr18f1odQiHnFvrCtOFkLxG63C3p8X3zXT1EUmpubMTMzE1Uc3x9EkKMj3ta7TCZDYmIiEhMTUVhY6NVWcnJyEna7HcePHw9rclU8kJIgB2sMolarUVlZiUOHDuHyyy8HAC5Ba9++fQGf9/DDD+MXv/gF3nzzTVRVVXn9raSkBDk5OTh06BAnwHNzc/joo49w0003cY87cuQIKioqYDAYcOGFF6KrqwtyuRwqlcrrR61WizpvHiCCLDqsy5qd0yvEiMJA5wlXkBmGQV9fH/r6+rB+/Xrk5+eLcp5w1jE8PIzOzk6uFWd/f7/oSWOex7fZbKirq4NSqURNTY2gN0ns+eKF0+FAe3s70tPTkZqaGtP5t0IhNbewZ1vJlJQUdHd3Iz8/H2azGS0tLaBpOuDkqnggFUEOpzHI/v37ce2116KqqgrV1dV4/PHHsbi4iOuvvx4AcM011yAvLw8PPPAAAOChhx7C3XffjZdeegnFxcVcXJi9gZLJZLjlllvw85//HGVlZVzZU25uLif6APCTn/wEf/jDH5CSkoLrr78ei4uL0Ol0UCqV3I9Go4HT6cTzzz8vquudCLLIyGQymEwmjI+PB5zTKwThZlmzs5Tn5+cjsgaFEmSaptHW1oapqSlUVlZymZFixqjZ47OCbDabUV9fz8tD4EsowYinhaw8dWff39+P1tZWJCcnc323xe5iJRRSE2RPGIaBUqnEqlWrvLq1BZpcFY+bIikIMpvVHqp15pVXXonp6WncfffdmJiYwNatW3Hw4EEuKWtoaMjrtTz99NNwOp344he/6HWce+65B/feey8A4NZbb8Xi4iK++c1vYmZmBmeeeSYOHjzo5T6/9tpruf3nM5/5DGZmZuByuWC32+FwOOBwOOByubC4uCha/wUWIshREiyGbLVaMTY2Bpqmw4rPRkM4Wdbz8/Oor69HQkICampqIhqpJoQg2+121NfXA8CygRmRdtIKF/b4Q0ND6OzsRHl5OQoLC0U7n9B1yHykSS6XY82aNVizZg03/5bNJGa7WKWnp4s+lCRapCrIvmVPgSZXmUwm9PX1wWazcTdFbGtPscVSKqVZ4fay3rdvX0AX9eHDh73+PTAwEPJ4MpkMP/vZz/Czn/0s4GNuuOEG7v9//OMfhzymmBBBFgk2WzcxMRFqtVr0Pq6hhFIol3m0FqzZbEZDQwMyMzNRUVGx7I5TjBi1LwMDA5ibmxM0qS4QUtgMAe/5t55drEZHRzE3N4e5uTm43W6kp6dLKg4a7xhyMEJZ776Tq3xvigCIOrmKYRhJWMjA0muX6rSnl19+GYmJidBqtVAoFNBqtdBoNFCr1dBqtVCr1dy/xd4viCALDE3T6OnpweDgIDZs2ACKopZlDopBIEH2HFSxZcsWvy3o+J4n0q5GbKlXeXk5CgoK/G5mYrqsHQ4H7HY7GIZBTU1NTJrdS0WQPWG7WLGdrJqamqBQKOB0OtHa2gqKojihSE9Pj+tQACm7rPmKnedNETu5ymQyYWJightG4hmfjnZylZTmNdtsNlFjr5HidrvxyCOPQK1We+1rni0z2RG7Op0O/+///T9R10MEWUAcDgcaGxvhcDhQU1ODxMREjI6OxsQlyAql5ybhOaiitrZWkPFnkbisKYpCW1sbjEZjSKtULAuZ7UAml8tRXl4eM5FZCVnWcrkciYmJKCoq4sp8TCYTFwfVarVcBnxqaqrocTRfpCrI0dwseE6uKikp8RrK0N3dLcjkKvZ7Gm9BpmlastOeZDIZ7rjjDshkMtjtdlitVjidTjidTjgcDjidTrhcLthstpiM9iSCHCXsl8RsNqOxsRFpaWnYvn079+YJ0UErHDy7aMnlcm496enp2LBhg2CbKF9B9qxzrqmpCem2EsNCZt31a9aswdjYmKDHDsVKEGRPPMt8ioqKvEYcskKRkpLCWc96vV70EYenoyD74juUwbO15+DgoNfM4fT09LCqAaQiyDabDQAkOQ9ZoVDgC1/4QryXwUEEOUrYhhI9PT1+XbGRzEOOBFZwKYrCyMgIuru7g7qGI4WPYJpMJjQ2NiIrKwsVFRVhbQxCJnUxDIOuri4MDw9zGe5saUSsWGmC7IvviEOr1bqsBzRrPaelpQmeRSz1GLJYYuc7uYqdOTw2NoaOjg7o9fqQk6ukIshsXwEpCvLMzAxeeukl3HzzzZifn8frr7+O1NRUaLVa6HQ67r9sC02xGhaxEEGOkvb2doyPj6O6uhoGg2HZ34Ua+hAK9kvX2tqK2dlZ7Nixg5tRKvR5QgkywzAYHBxEd3c31q1bh4KCAl7HF2IT9hwO4TlXWuyyKl+EFmSxbMVwb9p8e0DPzMxwVlxbWxuSkpI4Ky45OVmQm0GpWsixymD2nDm8evVquFwuzr3d0dEBl8vFubc9vRZSmddstVoBQJIua6PRiL/97W+4+eabYTQa8cMf/hDp6elwOp1gGIa76bLZbKioqMAbb7whaqIcEeQoKSwsRElJScASoli5rNkPvcPhELwLmCehBJOiKLS2tsJkMkWUxSyEYAYbDhHrzWmlW8jBkMvlnJUGLH322BaTIyMjAMD9PVw3qy+fFpc1H3wnV/nzWnj23I43bIZ1vC11f+Tm5uJXv/oVACArKwu/+93vIJPJQFEUKIriapHn5+e5cIKY15QIcpQkJSXB7XYH/HssLOTJyUk0NzdDJpNh48aNookxENxCZuPFcrk8rHixP6J1WYcaDhFzCznGCVDxRKPReDXJ8HSzdnZ2IiEhgXNvp6SkhLVBS91lHW/Bk8lk0Ov10Ov1KCgo8JpcNTExAZqm8fHHH3u5t2MtjGwf63hfK38kJCRwbTX1ej327t0b8jlEkFcwYsaQ2Rjp0NAQNm3ahNbWVtHFJpCgmUwmNDQ0YNWqVVi3bl3EX/poyqrYdqDBhkMI9WUK1xV4OlvIwZDJZFxpVUlJCedmNZlM3AQlz/nDgeKLUhC9QEilxtcTz8lVGRkZaG5uRmFhodfkKs/a51hY0VarVZLxYxbPz9jc3BwOHjyII0eOYHFxEampqaitrcXu3btF72MNEEEWHYVCwcUihPzgO51ONDY2wm63cyVWHR0doguyr4XMMAwGBgbQ09PDuy+2PyKxYNkJWuEMh4i5hRxHMZHS+EVfNys7QcmzxaRnaZVSqeTWJVVBlvLNArB0w6BQKJCTk4OcnJygk6vESsoDpN0UBPjk8zU7O4v7778fv//977FmzRokJydjenoaTz31FC677DL8/ve/J8MlVjrsHTRFUYLVsc3MzKChoQEGgwE1NTXccYUc/BAITwuWoii0tLTAbDYLlkTG10L2HA5RW1sbsh1ozGPIEt6w44W/CUpsklJPT49XDa6UWQmC7GnBB5tcNTAwgNbWViQlJXE3RsnJyYJ4AKxWq2Rd1sAn1+ntt9/Gn//8Zzz99NO46qqruL8fPnwYN954Ix599FHce++9oChKtFp8IshREupDxr5xQgglwzAYGRlBR0cH1qxZg+LiYq/zx0qQaZqG1WpFfX09J4RCxa35xJDZ4RB83ORCWch2ux1NTU2Qy+Vce0R/VoDQMWRpbmnRoVAovEqrbDYbTCYTTCYTAOD48ePcNRbLiosE1gKVKqFc6p6Tq9asWcMl5ZnNZjQ3Nws2ucput0vaZe10OqHVatHZ2YmysjJcddVVoCgKTqcTarUa55xzDi6++GI0NzcDENejRARZZDwt5Ghgu11NT09j+/btfuvhYiHIMpkMi4uLOHr0aNTx4kDHD6esih3byLesSoi79JmZGdTX1yMtLQ1arZZrfcgmLXn2g/60xpCjQafTIT8/H6tWrcK7776L8vJyzM/PY3Bw0O/UqnjFcVeChcxnfb5JeQsLCzCZTJiamgoYVggHq9UqyZInFvZG+qKLLkJvby8aGhqwdetWbs0mkwlutxtbtmwBQJK6VjRsT9RoBNlqtaKhoQEymWzZdCRPxM7oZjNnLRYLNm7ciLy8PMHPEcpl7Tm2MdKyqmjucEdHR9HW1oaysjJuUAObtMTG5jz7QdsdjojPFUukLCypqanIyspCaWmplxXX1NQEhmG8ksNiGatcCYIc6c2K5+Sq4uJir7BCb2/vsslVwWrOpdo2EwDeeecdvPHGG8jPz4dCoUB7eztuvPFG/PCHP0Rubi4oisJTTz0Fq9WKW2+9FQBE9YoQQY4B0dQiT09Po6mpKSxrVMyaZzZxam5uDhkZGaKIMRDcQnY4HKivrwdN0xEPh4hUkD27fm3btg0ZGRlwu93cWlUqFbKzs5Gdne1lXThWiCBLEX/vk68Vxw5oGB8f50qrWOvZYDCIunlKMcvaEyHX5xtW4DO5ymazSVaQu7q68N///d9ISUnhks/m5+fxrW99CxRFcU1Xpqen8fe//x0/+MEPSAxZyoRzhxyJ5epZxlNRURGWAIrlsrZarairq4NarUZhYSHXm1YMAgkmOxwiNTUVGzdujPgLEYkgu91uNDY2YnFxEbt27eIyLQMdx9O6SM/MxGhEKyWEyrL2HdDgWVrV3t4Ol8u1bGqVkBbt6Wwhh8J3chVbc+45uUqr1aKrqwsWi0Wygnz11Vdjz549AJa6+zkcDrhcLjAMA5fLBbfbDafTidnZWa5emVjIKxy+lqvL5UJTUxMWFhZClvF4IoYgsxZ6bm4uysvLMTQ0hMXFRUHP4Qm7gXhudp7DIXwT2fjCV5DZmxGNRoOamhreCUUroXWmlJtvAOG70/11sGKTw3p7e6FWqyOKgQbi0yzInvjWnLOTqz7++GPcddddmJiYQHZ2Nh588EFccMEF2Lp167J1PfXUU3jkkUcwMTGBLVu24IknnkB1dbXf87W2tuLuu+/GyZMnMTg4iF/96le45ZZbvB5z77334qc//anX78rLy9HR0eH1O/aGTioQQY4BfCzk+fl51NfXQ6/Xo7a2lpcACCnInhb6hg0bkJubC0D8Ol52g2M3k87OToyMjHDDIYQ4Pt8sbvZmJJLNjSR1RU40dcieHazYEh92ahUbA/Xs/5yYmMj7PGIOlxCCeLnU2clVe/fuxd69e3HjjTdifHwcH330Ee6//34kJyejv7+f29teeeUV7N+/HwcOHMDOnTvx+OOPY8+ePejs7PQ7v91qtWL16tX40pe+hP/8z/8MuI4NGzbg7bff9lpXINhrNTk5ifr6eq77olqt5vJUysvLRRdvIsgxINxuXawlWFJSgtLSUt4bhFBJXW63G83NzZidnV1moYs1r9jz+MBSKUJra+uy4RDREq4gDw8Po6Ojg3cW97LzSXjDljpCfs7YqVRsdQI73tBkMnHjDT2nVoWqZwdiN1wiUqQS49bpdKiursYjjzwCl8uF9vZ2L0Pjsccew4033ojrr78eAHDgwAG8/vrreO655/CTn/xk2fF27NiBHTt2AIDfv7MolUrk5OSEtUa5XI6xsTHceeedOHbsGGdJq9VqOJ1OAMA///lPXHLJJWS4hJQJ5wsZymVN0zQ6OjowPj4elSUohIW8uLiI+vp6aDQav402xC6tYq/nxx9/jMTERK/GJ0IdP1QWN/teVFZWRt2cQsob9kpBjGvoO96QbZAxPDzsd2qVvw1Y6i5rqVjwnnXIKpUKmzdv5v7mdDpx8uRJ3Hbbbdzv5HI5du/ejaNHj0Z13u7ubuTm5kKr1aKmpgYPPPAACgsLlz2OTdJ67LHH0NTUhJdffhk333wz9uzZg4svvhi33347KisrcfbZZ3PrEwsiyDEgmOVqt9vR0NDAZQ5HU0AfrViygxkKCgpQVlbm94MntiAbjUYAS5NX1q1bJ/iGF0yQXS4XGhoa4HA4on4vWOQSbhzhiRSFJVatMz37P5eWlsLpdHLWc3NzM1daxQo0W1oldUGWioUcLMvaaDSCoihkZ2d7/T47O3tZvJcPO3fuxAsvvIDy8nKMj4/jpz/9Kc466yy0tLQgKSnJ73MOHz6Mb33rW9i8eTOcTidycnJQWVmJ3/72t7j++uvR09ODbdu2ifq+E0EWgFBWVyAL2Ww2o6GhAZmZmaioqIg6e0+hUMDlcvF+HsMw6O3tRX9/f9DBDIB4MWTPmDUAlJSUiPKhD/Re+Y5sFMoqJy7ryImX4KnVaq/+z/Pz88syiNmZuVKGpmlBvUuREo9OXRdddBH3/5s3b8bOnTtRVFSE//qv/8INN9zg9zlOp5O7cdDpdJiZmQEAlJaWorOzMyYljPF/tz4F+MaQPQcyrFu3Dvn5+YJsPJFYr263G01NTZifnw8ro1sMC9l3OMSRI0dEs8L93VBMT0+jsbEx4MjGqM4Xx9aZlNsNo9GI1NRUSbd4DIQUsr89S6uKi4u5DGKTyQSbzYaOjg5MTk56Ta2SitUslRg328vaHxkZGVAoFJicnPT6/eTkZNjx33BISUnB2rVr0dPTs+xvrBehuroag4ODAIDdu3fj1VdfRVVVFU6cOAG1Wk3mIZ8ueLqsPcVHqIEMnufhI2QLCwuor6/nYizhJLIIndTF9sRWqVRczDrablrB8Dw2wzAYHBxEd3e3VyY5n2OFIp4uQwZLjQ+cTidSUlK4pCbfelwpCJ8/pOgSZjOIMzMzMTs7y31mPKcneSaHxdNClUqv7WAWslqtRmVlJQ4dOoTLL78cwNK6Dx06hH379gm2hoWFBfT29uJrX/vasr+xn7Gbb74Z/f39sFqt+Na3voV///vf3Hzk++67L6rkznAhghwDWJe1pwCGM5mIL3wE2TNevHbt2rA3PiEt5EAzlMXM5GYFmW3BOT09LfiNkdf54rghKpVK1NTUwGq1eo3cY+tx09PTebcejTVSE2RPGIbh+pcXFBRwpVVmsxl9fX1c321WoJOSkmL6eqRiIYfq1LV//35ce+21qKqqQnV1NR5//HEsLi5yWdfXXHMN8vLy8MADDwBYci23tbVx/z86OoqGhgYkJiZizZo1AIAf/vCHuPTSS1FUVISxsTHcc889UCgUuPrqqwOuY/v27di+fTsAICEhAe+88w56enqQlJS0LMYtFkSQBSCURSeXyzE3N4ejR49yblExLKdwyp4YhkFPTw8GBgawadMm3m4hIWLIDMNgaGgIXV1dfsuKxKx1lslkcLvdOH78OCiKQk1Njaj9j+MdQ/asx2VFg3W5stazQqHgEpuk5HKVquXO4mvBe5ZWlZWVwW63w2QywWw2c6VVbGJYuKVV0SCFpC6GYULGkK+88kpMT0/j7rvvxsTEBLZu3YqDBw9yIjg0NOT1OsbGxrBt2zbu348++igeffRRnH322Th8+DAAYGRkBFdffTVMJhMyMzNx5pln4tixYyErWNhyy7m5Oeh0OqxatUqQ/gfhQgRZZGiahsVi4VqviXmnFaq8iu0AxraADJRtGIxoLeRwhkOIaSE7nU5MT08jMzMTmzZtEt2lF29B9sWzJzHDMLDZbNxn4vjx48us53i6PPm6rGMtQKHWp9VqvUqr2PaSvqVVaWlp3HQwIZGCIANLYalQSV379u0L6KJmRZaluLg45P7w8ssv81ojsDQ45pFHHsF7772HmZkZUBSFjIwMfPWrX8W3vvWtmCSmEUEWEYfDgcbGRlitVqSnp4vu9ggmlmwWcUJCQkQtID3PEalYeg6HCDa1SqwY8uTkJEZGRpCQkIAtW7ZEbQmG83ypCbInMpkMCQkJXNbwqlWruG5W3d3dsNvtXrHneFjP4Z7vNeM/8fbQISgXFChLKMPuovNQnlku6tr4CJ5cLkdKSgpSUlKwevVqrrTKbDajpaWFmz3MWs9C9H6WiiBLedqTJ7fffjveeecd/OAHP8DmzZvhcrnwwQcf4I477oDFYsHPfvYz0ddABFkk2Jm5qampKCkpgdlsFv2cgQR5YmICzc3NKC4uxpo1a6LaVCO1kGdnZ1FXV4f09HRs2LAhqOUltMvas6QqJycnprG1eMaQ+SCTyZZ1s2J7QbMxUbVazblchegFHYpwb8r+MP486qbqAQXgMrjRhna0jbWD7qKQwWSgMn07Llh9PhI0wlo40SSd+ZZWsdPBJicnudIq9lqnpKRE5KmQkiDHuuwpXNj30G6346WXXsKRI0e4LmAAcMEFF2DTpk349re/TQR5peCbsTo8PIzOzk6UlZWhqKgIo6OjojbTYPEVS4Zh0N3djcHBQWzevFkQC509B5/NiO9wCCFd1hRFoaWlBRaLBTt37oTZbIbFYhHk2OEg9IYYS/s0ISEBCQkJXglLJpMJPT09XtZzWloa9Hq94Dc5oT5jFE3hV8O/Qf9Mv9+/yxMVMMOCt5yH8GbLW1AtKrFauxrnFZ6DTdmbol6vUFngvrOH2dIqs9mMzs5OOJ1OGAwG3tdaCoLMDvmQqoXMXkelUoni4mIYDIZljyksLIzYo8gXIsgCQlEUWltbYTQavdouCtVjOhSe53G5XJy7vKamhhsZGC3sBziczYhhmIiGQwhlIdvtdtTX10Mmk6GmpgYajQYWiyWmyUIrxUIOhT/rmc3c7uvr48p9hLaeAw69p+x4YOBhGBeMYR1HrpSDMtDoRg+6J3tA9VNIc6dia+oWXFB6AVJ0yzfiUIjVmtKztIqN83t6KlQqlZenIpBYSEGQ7XY7AAjWi15IaJpGe3s7dDod3G43LrvsMtx///247bbbkJKSArVaDaPRiBdeeAFf+cpXYrImIsgCwdbTKhSKZfFRvuMXI4U9j+fEqGjixf7wHI8YDLYNpd1u5z0cQogYMusiz8jIwIYNG7h1CxmfZhgm5LFWQuvMSK4Haz3n5+d7lft4TlJiBTpS6znQTZ/ZZcZDfY9gwR75GFBFggKzmMO71Pt4p/1dKBcUKFIX4TP5Z2FHXlXYFqjYoQ82zu/pqZidnYXJZEJ/fz9XWsUKtGdplRQEmZ2dLkULeXp6GldccQWys7O5jPdDhw7hww8/xJYtW0DTNE6ePInJyUn84he/iMmaiCALwNTUFOrr65GXl+d3TF+4056iRS6Xw+1249ixY4LEiwOdAwjedIBNIIt0OES0Luvx8XG0tLT4dZGL2XTEH6eLhRwM33IfT4uOHbPnWe4T7ufB3/s06BjE471PwOkSrm2lXCEHbWDQjwH0mwbw3MgLMDiTcUnuJThrzRkB1xaPxiUKhYLLzAaWLFDWUzE8PAyZTMb9XUqCLMUYslarxdVXXw2ZTIaFhQXY7XZs2LABFosFMzMzcDqd2LhxI/Lz8/H+++/jBz/4gejXlAiyALhcLlRUVATs9BQLlzVb20tRFLZv3+53jqgQeAqyP9iGI0VFRRHfEETqsmZrrAcHBwO6yGMuyBJIqok1Op0O+fn5yM/PB03TXOyZbZYR7hxiX8FrWmzCs/3Pi/5dUugUGBwcxL96/xlUkIH4dmIDlkQlNzcXubm5nHfMZDJhdHQUbrcbra2tyMjIQHp6uiilVaGw2WxQq9WS6Bjmi8FgwD333MPrOWJfPyLIApCfn88NtPaH2C5rp9PJxYsBiCbGALzcYZ54ZjJH0nDEk0gsZHaG8/z8PHbt2hUwZh5rQV7JSV1CwDbDSEtL46xnzznEnta1v3go+3k7PPMu/j70qujvHcMwmGqYgKnDhNL1q4M+znN9UkAul8NgMMBgMGD16tX497//jby8PMzPz6O1tRUURXlNrYqFG9lms0Gr1UrqOnlCURQYhuG8Nj09PWhrawNN0zAYDCgsLCRJXacbYrqs5+fnUVdXh6SkJFRWVuKDDz4Q1a0ik8mWiRorhnNzc2ENqAjnHHw2XpvNhrq6OqhUKuzatStoByTiso4vvnOI2dizZzyUFWg2Rvuq8X9waPQd0dfGUDTGPh7F7MAsAAS16qQoyJ6w68vKykJBQQFXWmU2mzE1NYXu7m5otVoujCBWExibzSZJdzWL52t+8803cf/996Ovrw8OhwNutxslJSX4wQ9+QJK6TidYl7XQMSc2Vrp69WqsXr2aG70odpzDs7zKczhEuAMqQsHHZW2xWFBfX4+cnByvftjBji2EIHtmsbMCkpKSsuz8KyWpKx7C4mk9r1mzhms1yVrPMpkMx1I/xuDokOhroV0Uhj8YxuLEAvc7pSLw9igVl3Ug2O8P+756llYVFRXB7XZzoYSuri44HA5RythYC1mqsJ/9pqYm3HHHHcjNzcWrr76KrKwsWCwWHDhwALfeeiv0ej0uu+wy0b8rRJAFINQbxN6FCfVm0jSNrq4ujIyMYMuWLZyLmj2P2BndrCAHGg4hxPHDEc2RkRG0t7ejvLwchYWFYR1bCEFeXFxEXV0ddDodiouLMTMzg/b2drjdbq7bEjvInljI4ePbanJwcBAHk/8PemcCXDY33HY3aJfwn2233Y2hdwdhN9u8fq+UB94efQVParDrC/SdVCqVXAtVYHkZm1Kp9JpaFanLlrWQpXqd2D35xIkToGkar776Kue+LioqwoEDB/Dtb38bf/3rX3HZZZeJPkGLCHIMYN9AiqKiFi02XuxwOJaVE4VKuBIKmUyGsbExDA8PY/369cjPzxf8+MFeA1vfPDo6iu3bt3O1seEeOxpBNpvNXEZ9aWkpnE7nsm5L7CB7vV4PUww6tAVE4sMZgiGXy7mEL6VWCaV2aaui3TTcdjcn0IjyJToXnBh6ZwDOheVZ2ypFYBGSuss6lCD74lnG5hlKGBgY4PpuswKdnJwc9uteCRYysHSTrVKp/FYAqNVqzvsodriLCHIMYL8UFEVFlRwwNzeHuro6GAwGbNu2bdmHh43viinINE2DoiiMjo4GHA4RLcFEk3UV22w27Nq1i3fDgWgEmbXI161bh/z8fLhcLjAMA6fTydWL6vV6FBcXw+VywWw2YzIG9eenKwzDgPFRXLlSDnWiGupENRiGAeWgIrae7RYbBg8PgrL7T8hUKpQBwz+sZSV1QY5kfb6hBIfDwZWxDQ8PAwD39/T0dGg0moDHknoMmX1vN23aBJvNhttuuw3f+c53oFQqodVqcejQIRw9ehRXXXUVAPFvwIggxwC5XB61ULLtJ9l4caAPhpglVna7HQ0NDWAYBhUVFaLN0g3ksvZ0Fe/atSuim5tIBNnXIk9LS/PKzmTnK3ted7lcjszMTOTl5+ME71UGWb+Ax+LDn0bncO+JbqyBHVetzsFXK4qhEtkdH+p98rWeHXNOzI/OgXJSUCWqoVAFXt/i5AKG3xsC7Q78nRxbBHIfbYbcPofKLAW+sj0XX64s4KompCrGwCd5JEKsUaPRcKVVDMNgbm4OJpMJY2Nj6OjoQGJiIifQvnkUoWYhxxv2+pxzzjn4zne+g4ceegjHjh1Dfn4+zGYzPv74Y1x88cX4xje+ASB4op8QEEEWgHA+9JEKJU3TnBiE034y2vGIgWCHZaSnp8Plcok6WMDfzQsbr2abr0S60fAVZLfbjaamJiwsLGDnzp1ISEjgStwUCoVXGRjDMKAoCjRNcz/UCnYbs9zbbcJj7aMAlJhGIo72LeCWzpPIp+zYnZWEmzatxroM/q0nQ8H3xkmTrIYmeSkmSrkpLIwtwG6xL1nVSZ9YcbNDsxg7OgKGDn78f3UtwKoFoEzGu2bg3bdn8e2DkyjSOHBOoQ47kwKXOsYbsRI7ZTKZV2kV6wkym81oa2vj8ihSUlKwsLAgeZc1y8DAAC666CJs3rwZ//M//4Px8XHk5+fje9/7Hvbs2ROzdRBBjhGR1CI7nU40NDTA6XSitrY2LNePGDXPo6OjaGtr44ZlHD16VFS3uK+FPDQ0hM7OTkHi1XwE2becyrN8zdddyW5+nol1FEVBIfJEJLH5asM4/jk4tez3jEqDYZUGz88Bz3/QhwTbIrYmyHF1aQ6+sr5IdOs5FAqlAoZCAwyFSzcKjlk75scXMD86j4kT42Edg8by18AotRigtHihH3iBSccP697H1gwFrtqWg6/sKIJKKY0kPrH6bPuiUqmQnZ2N7OxsMAyDxcVFmEwm1NfX4+tf/zp0Oh2ysrLwv//7vzj33HP99gd46qmn8Mgjj2BiYgJbtmzBE088gerqar/na21txd13342TJ09icHAQv/rVr3DLLbdEfEyKoqBQKPDrX/8aGo0GDz74IGpqarweE8sqBGnm7J+G8LWQZ2dnceTIEajVauzatSvsOIyQFjJN0+jo6EBHRwe2bdvGtaEUO07NiiZN02htbUVPTw+qqqrCEmMX7UK/xf/0H89jh2JmZgbHjh2DwWBAZWWl13UNxxUol8uhUqkEKQOLBb6vh6JpnHVk0K8YL3+yHNaEJByBHt/tnUfGqyex8ZX38J+H69FjmYt4TUIm0GgMWmSsywATxEW97Pyh7BWZHIvKZHw4o8d335lHxv0nseHB9/C9V+rQPjYT3YKjRIgEUr7IZDIkJiaiqKgIl19+OQYGBvCZz3wGKpUK+/fvR1paGj772c/C4XBwz3nllVewf/9+3HPPPairq8OWLVuwZ88eTE35/9xZrVasXr0aDz74YMDmQ3yPCSxdL7bNp7/XFStW9u37CoJPcxDWIg13XKEnQgmyZza3b/KUkOMR/SGTyeByuXDixAm4XC7U1NSEFYcyuyy4v+sBzCzOAgsM8hR5OCv3DJy9+mwuYzYcQWbru8vKylBYWMi5nyOJya2Esiff62FxUdj1fj/G5yMb3sCoNRiCBn+YBf7wbi/09gVsT1DgK2tW4arywrDjcGJ8xvgck5Hxe+8YpQbDtAYv9AIv9AxA517AlnQZrtyaja/uLIZGFbvtNlYWcjCSk5NRXFyMwsJC/Pa3v0Vvby+OHTvmlQT22GOP4cYbb8T1118PADhw4ABef/11PPfcc/jJT36y7Jg7duzg5hX7+zvfY7LX6OKLL8YzzzyDv/zlLzj//POhVCqhVCqhUCggl8tj1m2MCLIAhPNGheNKZi3S8fFxbNu2jasR5IMQgsxOi0pMTMSuXbuWxYvFilOzuFwuTE9PIz09Hdu3bw8rXt212I1fdy8NHZDJZECSDGMYxyszf8dLR19BsiMRm1O24DOrzgy4KTMMg97eXgwMDGDLli3IzMzk4sWRiDHDMJgMclceCWJvCV2LTpzzQR8W7I7QDw4HmRyLumS8zwDvd8/h5taTKGLs2JOViAfO2gJljG9YGB4fWzqa7VEmg02VhGNzwLH3FrH/3/XIVdnwwHk5uHzn2siPGyZSGCwBLFm07CCM0tJSlJaWcn9zOp04efIkbrvtNu53crkcu3fvxtGjRyM6H99jsnXFLS0teO211/DGG29g165dyM3NhUajgV6vh9VqxQ9+8ANUVFREtCY+EEGOEaFc1g6HAw0NDXC73aipqYm4VCDaLOvJyUk0NTUFnRYlpiBPTU1hYmICSUlJ2Lp1a1gi+G/zYbzc/0rAJB2FRoFFjQ1H6WM4MnwUtJPC0fc/wmeLzkN1wQ7IZDJQFIWWlhZYLBbs3LkTer2ey6SORIwpilpqJ7qwEPrBEuGw2YorjvbDFaQve7Qwag0GKAV+d+hD/LhqLTKCzOkWxUIOkcjl9VgBt0dGocJofxPe+mjqUyXIdrs9oHfLaDSCoihkZ2d7/T47OxsdHR0RnY/vMdlrpNPp8J3vfAcGgwEzMzOYm5vD/Pw811PgxhtvBCB+PJkIskCEcoUGs5DZDOa0tDRs3LgxqtT6SJO6WOuwv78/5HAIMQSZYRgMDAygp6cHmZmZUKvVYX3wXxj5Iz4cPxL2eWRyGRRpSvRjAM9OPoff9T+DNFcqcpw5qErezpVTsTc1kYgxWx6mVCpRvn496nk9WzjcbjcsFktYU37+y+zC3X29YMSum3bYgZPvATMmKEOsKd6CTMsE2h5pCuj7CDANQr1tpzDHDHVKiZRlrYSyJ4qi8J3vfAcA0Nvbi+npaWg0GmRkZKCgoGDZ48WECHKMCBRDZptNRBIv9kckYuk5HGLXrl1ISkoK+nihBzTQNI2WlhaYTCZUV1djeno6YIIFi4t24eG+RzFgGYzq3Oyg+lnMod3dgVc++BvKdGtwQcn5WJ+9ftnjW+YdePijNnytNAu7i3OXvV9zc3NoaGhAeno61q9fj26jMar1RQs75Ydt4uCvkcPTixq8MjIjfmevxXngxLtL/wXikokdcwuZcgPdHwCzS5ndGnVspgatBAs5IyMDCoUCk5OTXr+fnJyMeFpcJMdUKBQYHR3Ffffdh7fffhszMzNwuVxQq9U499xz8fOf/xxr14rv1QCIIMcMX1cyTdNob2/HxMQE7/aPoc7DR5CtVivq6uqgVqvDHg4hpIXscDhQX18PhmFQU1MDrVYLo9EY9Phmlxn3dz2IWWvkGbz+kCvlcBsotKMT7aOdoDtpZDuzcO+5d0OhUODViXlc91EfKIrBf9dPQnm0D+uVNL5QlIFvbVkD5/wcmpubUVJSwt1cyeNY9qRUKnHGGWdgYWEBt99+BEArzj8/DTk5S0MEMjIycFPfIv5ljkE97awJOP4e4LRzvwolyDRDCx80j6WF7HYAne8BC5/clGmCNCsREqkIcrBOXWq1GpWVlTh06BAuv/xyAEvrPnToEPbt2xfR+fgek71OP/vZz/Dvf/8bt956K8477zwoFAq0tbXhRz/6Eb773e/ir3/9KxcLFxMiyDHC05XMihBN06itrRXUpcNHLNlmG7m5uSgvLw/7CyyUILOtQFNTU71c9cEs8M7FTvym+0k4T/WWFRMn5cSRDz6E6zMuPNA3gwdahrysSLdWj2YAzaMO/HSwEamLFpydpsV+bRJK2Ck7cdwUl9p6unDJJUdQXz8BAHjxxRGkpvZh61YdLrggFf/augtITgUcNsDhQNTNof0xNQbUf7hkLXoQymVNMcJ3nONnIUdhzTqtQMdhwDbr9WttjObqSkmQg+1v+/fvx7XXXouqqipUV1fj8ccfx+LiIpchfc011yAvLw8PPPAAgKWkrba2Nu7/R0dH0dDQgMTERKxZsyasY/rj73//O5599ll8/vOf535XUlKC9evXY/PmzZiZmSGCvJIIJ4ZMUZRXx6sNGzYI3ootnKQuhmEwODiI7u7uiJptCCHIExMTaG5uRmlpKUpKSpY12fB3Lf9t/jde7v8br001UhbG5zHy4TBoF41r6obw+liI5CylEhZDJl6jgNeODkFra8MWHbDHtQhaJoecT3qvQDAMsGXL6xgb8/QkKGCx6PDOO8A771iAt5SAKgnQJy2lIDscp8TZBgjRgnW4D2j52K87PJRgiCLIvMqeItwe7fNAxzuAY3nZ2PTUBHp6epCenh5WbD9SpCLIdrs9aILqlVdeienpadx9992YmJjA1q1bcfDgQS4pa2hoyOt1jI2NYdu2bdy/H330UTz66KM4++yzcfjw4bCO6Qm772zZsgVO5/IBI+zUq1BhPKEgghwj5HI5ZmdnMTQ0xHW8EiNBIFRSF9tsw2g0YseOHUhJSeF9jmgag3gmj3mOjgx1/OdHXsSR8chKIfhi7jJhom6cMxYPDowDan5fSLsuER8B+EiVCO1T/0Bx88coaTiK4qaPoD0VQ40EPp+YqWk7xpgQbn3Pz6BMDmh1Sz8A4HJ9Is7OCMqguluA7mb+zzuFmxHelc4rqUttgJahYKfl3tcpGIsWoPMw4LL7/XNOZgacTuey2H5aWpqgLSalIshWqzWkB3Dfvn0BXdSsyLIUFxeHdVMV7JiesHvwhRdeiCeffBJ6vR5r166FSqUCwzD42c9+hksuuQQKhYIrgRSzbTAR5BhA0zTMZjMWFhZQVVUlqusjmFja7XbU1y/l/LLx2kiItLSKLQWanZ0Nmjzm6W2gaAoP9j6MgZnokrfCgaEZTNSNw9LtPTJRFqV1a09KQUftBeiovQAyyo1VPW0oaTyGksYjyBzqjerYwYg68U6lWvpJTAZoGmrTOJwmI6DVApogmyxNA60ngOHoXpvvpCch4CXIujTYNSWAbQ6YGVuKCWv0gDJAnsXcFND1HkAFDqdkZaShoqLCa1zn+Pg4Ojs7kZCQwCXeRWs9S0GQGYYJaSFLhSNHjuDkyZO4+uqrsXnzZmg0GrS0tGBmZgZXXnkl9u/fzw2zefrpp0UTZSLIIsOKoMPhQEZGhuhxCIVCwc3u9ERIV7lcLvd7jmDY7XbU1dVBoVCETB7zdFnP0DMw6U3QybWCzcD1B+WiMPrhMBbGl7um5QJaaoxCibHyzRgr34wjX7wBG199Hrv/8aJgxxcNuRzOzDwgM2/p39PjgMW4ZLInJAHs5u92Aw0fLsWNoyTeMWRaduozqkte+gGW4uCzY4B1BpApAN2pm0rLKND9IRBizTrNJx3jkpKSkJSU5DWu02QycdZzamoqJ9B8b56lIMiA9Mcvsnz3u9/FzTffDJvNhpmZGVitVlx22WVcb26r1YqFhQXMzc0RC3kl4M/9bLFY0NDQgIyMDGRnZ2N2dtbPM4XFX3zXdzhErEur2JuBzMxMVFRUhNwoPK18lUwFuSLADFybO+j4vHBxLjgx/N4gHLMB3LIixH+VDhsyDr+OSXtk7SnjTuaqpR8AsC0CU6OAdXHJMp41B39umFCyOCd1yfzcNCqUQFrh0g+wlLQ10QV0vY9w7hQTApQ9+Q5pYK1ntjEFaz37G3Hod+0MI/qowHAIVvYkJT772c/GewkAiCCLAsMwGB4eRmdnJ8rLy1FQUIDh4WHR5hR74ulOZkc3sokQkbTi9AefGDI7x5nPzYCnhaySeW9gXjNwU5csW7fNDZfNDcrB//pajVYMvz8Iyh74uTKBLTXdrBm6D9/EBICsuE04FhCdHihauyTER/5PsMPSEP5GiFfrTH+C7IvOACSkIFy3jS6MOmR/1rPFYoHJZEJbW5uX9ZyWluZX8CiKivtgE4ZhVoyFLBWIIAsMRVFoa2vD9PQ0KisrORc1n+ES0cBar57DIaJpxRnoHKHikwzDoKurC8PDw7xvBrws5BClJwqVAgqVAppkDRiagdvuhmvKBZvLDqUm+Md7dnAGY8dGQ1pNMgFd1oaxQVB1H8B8ysJh+A6rEGwlIiBwY5H4u6zDLFHiofJaLf+yJ5VKhaysLGRlZXlZz5OTk+jq6oJOp+Nc26z1LIXhEk6nEzRNE0HmARFkAfFMmqqtrfWK+4gxp9gfcrkcTqcTR48eRVJSkt/hEEKcI9hrcbvdaGxsxOLiInbt2uV3BmowPJO6lPLw1y6Ty6BKUEFVrIKW0mJhYgE2kx0yhQyaJO/uVNPNU5huCW/wg0yg9y2rqxkzXU1wemyU4hdwSZdQcU4xBJlfYxBN6AcBS60xw0Svic5q9bWe3W43F3tub2+H2+1GamqqJFzFVqsVAIgg84AIskCYzWacPHkSWVlZfuOk0Q59CJeFhQXMzMygtLQ04HCIaAkmyGznL41Gg5qaGi4zke/xo80QlivkSM5LRnLeUjKOfcaOhfEFUE4KxnYj5gbDj+fLEf37lnvyfYxPDIHx+VzwtZAFRehT83jPZADef/99pKWlccmOvi09aVl8xy8i3DpkHhZygkbYxiBKpdLLemaTkGZmZjAwMICpqSmv2HMs48ps+1siyOFDBFkgbDYb1qxZg8LCQr9/F9tCZut7R0ZGkJCQgLKyMtHOFUiQzWYz6uvreXf+8iWaOudAaFO00KZo4Xa40XeQZzlONKLJMMh7//9hdGF2qc5XSsTT/y0Dtm3bhqNHh/Hss+9h9+4U5OR80m87OTkZtAA3Qr6E67JmgPDfdx6f1QRtmFZ3BMhkMiQmJiIxMRFmsxkZGRnQarUwmUzo6OiAy+Xyij2LLZR2u52bK0wID3KlBCI/P58rHPeHmDFkz+EQa9euxdhY9CUnwfAnmMPDw+jo6MC6deuWTUiJ5PhiTPphj80XuSEFSM8F7DbAYYfcvtR9KySUG7L6I0tiHADxLWQ3APmpHx/iaiHL8PHHi7j66qWRo88/P4r09AFs26bDnj0pqKhIxWzyLJAi8BLF6PLGw7Wu18Ym0YqmaahUKmRmZiIzM5Ozns1mM6anp9Hd3Q2tVusVexbaemabgkhh6tRKgQhyjBBrhrCvi3h2dlZ017inS5mmaXR0dGB8fNwriU2o4wuNTB7B5kBTS+Uu+qUWk7QrFZgcWppapNYAWj+Wxqkxg8yMKdSK+K8nbOQAcgHQAOYA2LFk+ylEOjWPkiIGuOKKt8Fw7l4FTCYF3n6bwdtvW6BWj2P7522oeljgFYohyDxiyIlRxpDDxTc+72k9FxYWcqM5zWYzOjs74XQ6kZqaynUOE8J6lvroRSlCBFkgQt0FimEh+xsOIZbwe8Kew+VyoaGhQfBMbl8LXAaZYF2bIhHkZVnWKiWQv/qTfxsnAcv0ksrokwDrAnD88FJ9bggYnsuJTEPl8DY1rQAWsWQ9CwifPtE0EzT26nRqMTpOoUqIdfmeV2h4xJDV6thsuaES5pRKpZf1bLVaYTKZYDQa0dPTw1nPaWlpSE1Njch6lkJi2UqDCHKMYGPIDMNE7cIJNhwiFtnccrkcbrcbR48ehV6vFzyTW2oWsiyUBZSRvfQDLDXH+OBgWGIMAExcArkJp34ERuD3TK4SI6kr3EfyeF9iUD3BFz6dumQyGfR6PfR6PWc9z8zMwGQyoaurC06nEykpKZx7O1w3NHFZ84cIcoxgvxw0TUcVq2HrnAMNh4iFhfxfLRbc/q4WCa5ZXLBGhe9nzmJroTDznIHlMWQhLeRTB+RVbxRSkD1J0PNfC8EvCqUY7uVwj8njjRGjPCtKommdqVQqkZGRgYyMDM56Zkurent7oVarOXEOZj3b7XZBB2Z8GiCCHCPYDy1FURELcjjDIcQUZIZh8N1/dOPZhjkACtiUafjrAPDXP/QigWpEVZYC1+8swFXVJVHdFftzWQuJTC4DQ/FIQOK74fJ47fGxkE8htOUitIUswu4kTgw5vO9bLA1FoXpZe1rPBQUFoCiK6xrmaT17xp7Z777VaiUlTzwhgiwQoQSI/XJEGkcOdziEWIJMURTO+UM7jo/Zlv9RJoNVmYT3zMB7/8+EG/53BGUJLnxhYyb2nbsW6Un87pJ9XdaCC7KMn8XNuzEIH0GOa+mR4GnWgh5NLoKFHH7Zk/AWstCf42CI1alLoVB4Wc82mw0mkwkmkwl9fX1Qq9VITU1Fc3MzLBYLsZB5IrHCyNMXmUwWsViOjIzg+PHjKCkpwaZNm4Ja2KyYCSnK4zM2rP5Vi38x9gOt1KHTmYwH6hzIe6QeBfe8jeteOIq6AWNYz2dd1gzDwOl0ghH4BoNvHFnGN/mJl9DFsXVmPPU4jMfKROhhEb6FLHwMeSVayMGQyWRISEhAQUEBtm7dirPOOgvl5eUwm8246667cMcdd6CxsRG//OUv0dbW5jcv5KmnnkJxcTG0Wi127tyJjz/+OOg5//a3v2HdunXQarXYtGkT3njjDa+/X3fddZDJZF4/F154oaCvW0yIIMcQvpnWNE2jvb0dnZ2d2LZtG4qLi8PK5mafKwQf9Jqw7qkOTC44IzuAXIlpmQEvDyhR+3wfUu/8N3b/+l385VhfwGvBvsaFhQUcO3YMgisH38xmPjFknicQsw45KVGBrVtpqFR2/w+IYx1yOMiVYgyXiF8MWR4jRWZvyGPdy1qhUCA9PR1nnHEGOjs7ceONN6KgoACHDh1CZWUlVq9ejcXFT5IdX3nlFezfvx/33HMP6urqsGXLFuzZswdTU/5b2h45cgRXX301brjhBtTX1+Pyyy/H5ZdfjpaWFq/HXXjhhRgfH+d+/vrXv4r6uoWECHIM4dM+0+l04uTJkzCZTKipqQl7OINn8li0PPnBEM7/ywAcLoHKY2Qy2JRJ+MCSgBsOmpB0zxFsvv8Q7v1HvdfD2Nfw0UcfIScnB0q5sKYSbwuZ73CJSGqdRUCvV+LDDz+HmZkv4vXXt+Bzn9MgNdUOsFOU4liHHM7J5cJ2meSVuc/w6aoWtoUcO0EGEHNB9iU5ORlbtmzBG2+8AbPZjD/96U/Q6z9Jenzsscdw44034vrrr0dFRQUOHDiAhIQEPPfcc36P9+tf/xoXXnghfvSjH2H9+vW47777sH37djz55JNej9NoNMjJyeF+UlNTRX2dQkIEWSDC+bKFW5I0Pz+Po0ePQqlUYteuXbwSI4QQZIZhcP1/deKHb08K7i72hFZq0WXV4sGX/s9rsxwdHQUArF27FmVlZaIkdfGC9zWQhoVMURQcjqUZz+ecU4C//vV8jIx8Eb2952H//gysXuMS9oR8LOQ4uKz5JXTxsZDD+3zIY3Sjxn734y3Ino1BdDodzjzzTO5vrMGxe/du7ndyuRy7d+/G0aNH/R7v6NGjXo8HgD179ix7/OHDh5GVlYXy8nLcdNNNMJlCNeeRDiSpK4aEYyFPTEygubkZJSUlKC0t5X1XzcZNIhVkp8uFM57pQPNUADenkNjngc53Afs8bA4XdBoVOjo6uNaf2dnZoCgKMplc0Hwh/hayiEld/I7MC5qm8f777yMpKYlLxElOTkZOTiLuu28XfngPjdzjZhFXEAoGwYRPrhD26vARZF5JXWGGNOQx6mXOfvfjXf9rs9mQnJzs929GoxEURSE7O9vr99nZ2ejo6PD7nImJCb+Pn5iY4P594YUX4gtf+AJKSkrQ29uL22+/HRdddBGOHj0a08EakUIEWUBC9WAOZiEzDIOenh4MDAxg8+bNyz54fIh0stSAcQG1z/XAbBXYcvLH7CTQ/QFALcWmZxetaG/thdVqRXV1NT788EO43e6lGwwRsqx5PV7EsicxC5FVKhU+85nPwGg0wmg0YmhoCHK5nBNnhUFgVx6vGLIMQCqWWnq6Tv3bZ0KawLsTLwuZj3iGecOm+BRayNHsY5Fw1VVXcf+/adMmbN68GaWlpTh8+DA++9nPxnQtkUAEOYYESupyu91oamrC/Pw8du3ahaSkpKjOE0k29/91TOGKv4/CFWRAhmBM9QADJ7w28CPHPkJhVhp27twJuVwOlUqF48ePIzMzEwgvfB4+PPcp3kldvMqexN2k1Wo1cnNzkZubC5qmMTMzA6PRiN7eXkxZ7YB+s3An453UpcYnby4NYB6A7dT/K4VP6hLLZR3m50OhiJ2FzHrK4kmw1pkZGRlQKBSYnJz0+v3k5CRycnL8PicnJ4fX4wFg9erVyMjIQE9Pz4oQZBJDjiH+LFer1Ypjx46BoijU1NRELcYA//aZ4+PjuOGtebiUCYBC4EwaTxgaGKwD+o8v27x1CYnYvn07V7Z1xhlnYN26daBpGpRL2E5I/F3W4mVZ88745vdwL+RyOdLS0rB27VrU1tZiR3V1FEfzRzQxZDkAA4AcLA3ESIJMKayg8Ik8MHy2RglayPG2joElCzlQ/otarUZlZSUOHTrE/Y6maRw6dAg1NTV+n1NTU+P1eAB46623Aj4eWCoZNZlMWLVqVQSvIPYQCzmG+Aql0WhEY2Nj1PODfQnXQmbd5IODg5BrN53aJFMA2g04bYDLBrgcECTSSbmAniPAjP/RkKsKluZIs5uJ5+g4rVkDB+2Ifg2n4G05iGkhx7FTl06XgKUJUALB62MS6nXrIFcIO5iAX1KX8FnWoBmYTCZRRh16L0c6ghxsuMT+/ftx7bXXoqqqCtXV1Xj88cexuLiI66+/HgBwzTXXIC8vDw888AAA4Pvf/z7OPvts/PKXv8TevXvx8ssv48SJE/j9738PYKlM8qc//SmuuOIK5OTkoLe3F7feeivWrFmDPXv2iP+CBYAIsoCEE0OmKMprOERFRQXy8vIEXUc4gszOUGbd5Jph1lWIpeCdNmnph6EBl/0Tgeab4AQA9gWg6z3AFngu8KLNAYqiIJfLIZPJcNddDXjppZOoqUlF2SM0IKDhztdClouZ1BVHr6IIfbAEPZpM6KQuscqewvSgKOQydHR0wOVyITU11WtYg5BIRZDtdnvQCpErr7wS09PTuPvuuzExMYGtW7fi4MGDXNyZzXlgqa2txUsvvYQ777wTt99+O8rKyvDaa69h48aNAJb216amJrz44ouYmZlBbm4uLrjgAtx3333QaDTivliBIIIcQ9gpSc3NzTCZTH6HQwh1nmBJXTabDXV1dVCpVNi1axfUajVU8kDNI+SAOmHph2GWkrCcNihcVlBUGPHm+Wmg633AHdzCtTqc3Jfv8svfwVtv9QOQ4X/+ZwZf/b4dKSWhTxU2vGNrfAVZtAcLiuADtQQue1LEMamLl8s6TA+KRqNGbW0tN+pwamoK3d3d0Ol0nDinpKRELaZSEeRgLmuWffv2Yd++fX7/dvjw4WW/+9KXvoQvfelLfh+v0+nw5ptv8l6nlCCCHEMYhsHo6Ch0Ol3A4RBCEMxCtlgsqK+vR3Z2NtavX899cVXheNBkMkCpAZQaUEgBFszA7PiShaBNAnwbeBj7gb6Pw7KqnS43rFYKNTWvo7fXu26QoeJbhyxuUhe/Q2tUKsAlTBa84BaywAovE7iXtRSyrCmKgk6nQ35+PjfqkJ2k1NbWBoqiuEEN6enpEVl2UhJk0suaH0SQY8TMzAwmJiag0WhQXV0tagwpUFLXyMgI2tvbUV5ejsLCQq+/qSP5/iamLf0ASy5tywjgtC5Z0xMdwFhb2IcaGFrA1y/7G+bmlvfLpgUXZJ5P4F32xOcE/F4bJZAYA+LWQIdCJgMY0AgWq41vHTKP72eYMWSVUgGGYeA+VcnA9rfPyMhAVlYWGIbBwsICjEYjxsbG0NHRgcTERKSnp3M15OHkP4g1WIIP7OAJz85chNAQQRaQQF8WVghTU1OhVqtFL1D3tZAZhkFnZydGR0exfft2pKcvn12sVkQpemodkF229P8LRl5iDAC3/uQY6Dn/Gea8W0mHQPQ6ZIl06oo5PCzklBQ1TvbtxtNPN+Mf/xhDTw8DmlZ7PUbwGLJYLuswPx9qpRJqtRoMw4CiqKUKAo/Qklwuh16vR1JSEkpKSuB0OjnruampCQzDcJZzWloa1Gq13/OwuRjxJljZE8E/RJBFhKZpdHZ2YmxsDNu3b8fc3BxmZwMnNgmFpyC7XC40NjbCZrNh165dAe9YoxZkrwXwv+Ggg0xUYtxxdlmv0E5dpRs2xPbcPARZBhmysxNw7707ce+9SzeNf/tbN/74x14cP76AhQVtfAWZR99OjVKBcGoAlEoFJ5SeXixWnH2tZ4VCgaysLOTk5IBhGMzNzcFkMmF4eBhtbW1ITk7mBDopKYm70ZSChQyEF0MmeEMEWSScTicaGhrgdDpRU1ODhIQELCwsRDwPmQ9sUtfi4iLq6uqg0+mwa9cuqFSBU5U1QhrtkTQhlgXeLGmhe5VISJDFGr9Yfc45eOif/+R17OgJX/Dcbjfa2tqQkZGB9PR0KBQKfPnLa/HlL68FAHR2mvG7/iFhlyeShRzu8BW10vt7wYqmZ/95zx9f6zkpKQkGgwGrV6+Gw+Hg5hAPDQ1BoVAgLS0NGRkZcLlckhFkYiHzgwiyCMzPz6Ourg7JycnYvn07lMqly8y3YUekyOVybnRhXl4eysvLQ7pptXG2kBHEGqKFtpB5j19cWWVPl15zDX7w9NOhzy20jczjcCqlEgqFAl1dXXA4HEhNTUVGRgYyMzOh0+lQXp6GmtxsnHCMCLc8PklnfG4qw4ypqJTBjymXy73EmR2j6M96ViqVyMnJ4Tqwzc7OwmQyob+/H4uLi1AqlRgcHER6ejr0en3Mu3a5XC5QFEUsZJ4QQRaYYMMhIu0xzRer1YqZmRls2LAB+fn5YT1HE29BlgcWPcEFmW/HJN5JXTwOLWDZkwzAN+68E/9x221hnltgeAieQiFHeXk5ysvLsbi4CKPRiOnpaXR1dSEhIQEZGRmwpQk74EQsl3W4grx5dfj9Bjxd2wA4i5kVaV/r2WAwIDU1FWvWrEFPTw8sFgtmZmbQ398PlUrlFXuOxZAFdu4xEWR+EEEWkMHBQbS3twccDiG2hUzTNNrb2zE7O4usrKywxRgAtEJ+EiKZahNDlzX/pC7xxi/yr4n2j1wmw+3PPIPdV18d9nMEr0PmIfGe74Fer4der0dRURFcLhfMZjOMRiMsM2YgRcDV8WqdKawgX3pWJX75rcvCP6YP/qxnNvbM/rCPk8lkSEhIwIYNG0BRFGZmZmAymdDT0wO73e7VlEQswbTbl26miMuaH0SQBSQjIyPocIhAwyWEgI1Zu1yuiDp/xd1lLQ8iyK54W8jSTupSq1R49H//F5vPOovX8+Kox5AHuEYqlQrZ2dnIzs5Gw1wjxpzjAi1ORAuZCX7H+B97avH7734+/OOFQC6XY3JyEVdf/ResW5eEm28+C+Xl2ZwwLywsQK1Wc7FkVoABcE1JjEYjenp6oNVqvZqSCGU922w2KBSKgJngBP8QQRaQxMRELs7jD7Fc1gsLC6irq0NSUhK2b9+OgYEBWK1WXsfQCdnIX2BBpgR2WfNO6uLdqSt2ZU96vR4H3n8fBeXlUR1HGPhlWYc+2gqpQ6YCfz5u+vx5ePSGi8I/VhiMjMyhqupZzM/b8NFH03jxxV4kJLixbVsGzj03BzU1mdi+fdvS0nxc2xqNBnl5eSgoKIDb7YbFYoHJZOJaeno2JYmmqQeb0BXviVMrDSLIAhLqwyeGy3p6ehqNjY0oKirCmjVruGYDfM8jqCADS25rHpalXCU/VfokA3w2Q+EtZJ5P4J3UFf4JGLkcX339dbz39NMY+uADMDMzYTu8M7Ky8NyJE0j2U1ce1rkjelawA4Z/xEAWsicU3xuhEIhnIfu7yZbhJ1+9CHdddW74xwmD3l4Ldu16DlarZ3xdBqtVhQ8/nMWHH85CJmtFcfFRXHRRGW666TMoKEjxShIDPmlKkp6ejszMTDAMg8XFRZhMJkxOTnKxfFacDQYDr8xtIsiRQQQ5hgjpsmYYBgMDA+jp6cHGjRu9xotFIsgJQguyXBHUcvCFppVYGrtHA1gAYMWSZChWXgyZ5/HXnXMO1p1zDgDAODSEd558Eu2vvw7b4CAUPiLHHnl1eTkOHD0KdRRN83llHYdBolaDhTAfG84lYuIpyHy2Rt/Ph0yGX3zjctxyWW34xwiD1lYjzjrreTgczuDLYZTo76fw29924Le/bUNyMo3q6hxce+0OfO5zmwOWVSUkJCAxMZGL5VssFhiNRrS0tICmaV4tPa1WK2mbGQFEkGNIJELpD5qm0dLSApPJhOrqahgMhqjPoxN6DLJcsTRyMezHs5ulHEDyqR8AsIJynr6NQQCgt7cXWVlZSExMREZhIb708MPAww/D5XLhyPPP48Rf/gJjUxMUzqWNuPqcc/DQv/4VtfUhtIW84ObhEQmzBaSQ8Jv2FObW6JvQJZPjye99GdefX8ljZaE5eXICn/3sH+Hi3TpVjrk5Od5+24i33/5/UCj+iTVr9LjkknLcfPNnkJ6u91tW5dvSc35+HiaTiWvpmZSUxImzv5aebJcuYiHzgwhyDFEoFJzbKNLCfYfDgfr6ejAME3BARSSu8QSlwI0E+DYHkQVabwJoVwKA+WhX9MmpxE7q4snM7CwGBgagVqu5WtzU1FSoVCqc/c1v4uxvfhMA0PHuu+hvbsZFAabj8CW+vaxDvwe0wBYyn8YgWWoK065ZLCiTgocgPEReJlfghR9/DV88I3iHNL58+OEILr74L0HzU8KFolTo7HSis7MZv/xlI9LSGJx5Zj5uuGEXzjlnbUDrOTExEcnJyVxLT7YpycjICGQymZf1rFKpSFOQCIl/O5fTiFCbDCvCkbqt5+bmcPToUeh0OlRXVwd0CUViIetVQruseX60YphlzdeCFdtC3rx5M8455xysX78eANDe3o53330XDQ0NGB0dhcOx1Jhx3dlnCybGQHxjyKGaZADxTeo6f00aJm8pRcOVifhG4TwKYILM7cdVfOqzIVco8d/33iC4GL/99gAuuujPgojxcuQwmxX45z/Hcdllf8QPf/g81Go196NUKiGXyznr2el0wuVyQaFQIDs7Gxs3bsSZZ56JTZs2QavVYmhoCO+88w7OOecc/PGPf+TqpgPx1FNPobi4GFqtFjt37sTHH38cdLV/+9vfsG7dOmi1WmzatAlvvPGG198ZhsHdd9+NVatWQafTYffu3eju7hbkSsUKIsgxxLPIny8TExP46KOPUFBQgM2bNwctT4hIkIX2lfDNtA7SGIRyCvsxlZrLmqJpKBQKZGRkYP369TjzzDOxY8cOJCcnY3R0FO+//z4++ugj9PX1YX5+XjBXbrwEWaFU4oGrQpcBCW0h8xFk9h0sy0zAry8tQcd3ymG6ORuPbneiSmeCxjXPHhRKlRoHH/w29mwvE3S9//xnDz7/+b/GoJnQLIBW0PTSDYdcLodCoYBKpYJGo+HEmd1zKIriBJqmaSQnJ6O0tBTV1dWorq7GF77wBa4nQ15eHr7xjW/g1Vdf5W4sAeCVV17B/v37cc8996Curg5btmzBnj17MDU15XeFR44cwdVXX40bbrgB9fX1uPzyy3H55ZejpaWFe8zDDz+M3/zmNzhw4AA++ugj6PV67Nmzh6uJXgkQQY4hbNE+ny8YwzDo6elBc3MzNm/evKz7V6Dz8P0SJ6ri7bIOUvYkdAyZ9+FEFmTfxC2ZDElJSVi9ejWqq6tx1llnIT8/H/Pz8zh+/Dg++OADtLe3w2g0RrVZC98YJDRqjQZv/+Q7uGhjaPGihY4h8xDk6Skjjh49iu7ubszMzIBhGGhUCtxUk4t3v14O8y0leGuvCl9etYD3HtuHM9YXCbrWV15px1e+8rcYtNqdAdAOANDrA3vcVCqVl/WsUCggk8lA0zQnzm63G0lJSdi3bx++/vWv4/zzz8ef//xnpKSk4L777vP6rD722GO48cYbcf3116OiogIHDhxAQkICnnvuOb9r+PWvf40LL7wQP/rRj7B+/Xrcd9992L59O5588kkAS/vk448/jjvvvBOXXXYZNm/ejD/+8Y8YGxvDa6+9JuQFExUSQ44xfKxXiqLQ3NyM2dnZoA1HojkHi14dZ5d1MEGOc2MQUTt1AaCo4ELB1o7m5eWBoihYLBZMT0+jvb2dqx3NzMxERkYGr4H2sbaQExL0OHLnd1GWFV6ZlvBZ1uE/tqigCCUlJTAajWhoaAAAbi5xRkYGVCoVaosNqC02BD9QBDz/fBP27fsXxI/yz0Gp7AHrDQ8kyJ4EaunpW1Y1OTkJiqJw3nnn4bzzzvM6htPpxMmTJ3GbR4tXuVyO3bt34+jRo37Pe/ToUezfv9/rd3v27OHEtr+/HxMTE9i9ezf3d4PBgJ07d+Lo0aO46qqrQr42KUAEWUDCSVQJt/TJbrejrq4OCoUCNTU1vDreRJLUlSh4DJmfhVxYrEIKTaGtzQ2321tUaIFd1nwbg4jZqQsAKB7HZ13bGRkZ3ED76elpjI6Oor29HUlJScjMzERmZiYSExNjnOUaWEBSU1Jw4q7vIccQ3k3l0tHiZyFr1Brk5ORwow9nZ2dhNBoxMDCA1tZWGAwGLgFPyOENAwNz+N73DmOpFl+MuDHLDIBOuN1L1yQhIQH/8R+7gz7DH/5aeg4PD+NPf/oTior8ew1Yz45ve+Hs7Gx0dHT4fc7ExITfx09MTHB/Z38X6DErASLIMSYcd/LMzAzq6+uRmZmJiooK3hnZkVjIggsyT5d1ZpYW7/3lMjAMg3/9qx/PPNOFY8cWsLiogVvoGDLvpC6ewhBBDDkSWNc26952OBwwGo2ccKhUKq+sbd+8g1y1DF+UzeKdeQomnQGItm1igOuUl52Fk3d9D0lafjXTtNCCzON9VCs/qQOUyWRISUlBSkoK1qxZA7vdzg3D6Ovrg1qt5jwU/q4zH8bGFkHTagBqqFQARVlA0y4sRReF+o5aAHSBvYHS6/U4ceIJFBZmRnVUuVyOkZERXHrppbjkkkvw7LPPRr/UTxlEkGNMKOt1bGwMra2tKCsrQ1FRUUR33pEIcpLgLmt+m5LV7oDT6YRarcall67GpZeuBgC0tBjxu4/fCPFsfvDu1MXTQpZrdbycrRQPyy0Y/lzbRqMR7e3tcDqdXFcm1rWtUyjw9OZVqKurA5Vgw1vyFPyvyY4+hR60RpimDhXFRTjyk29DpeS/1cQzqUupCFyYr9VqkZ+fj/z8/GUhBKfT6RVC4Nscw2r9pM54qeQ49dS/3AAWATjBNsyJDDOAbrBinJSUiLq6p5Cbmxbh8T5haGgIF198Mc455xw888wzAW9MMjIyoFAoMDk56fX7yclJ5OTk+H1OTk5O0Mez/52cnPRqkjQ5OYmtW7dG+pJiDhFkgZHJZEHvxAO5rBmGQVdXF4aHh7F161ZkZkZ+t8pa4QzDhC3oWvBtOBBqEfw2DJvdgffeew8Gg4Fzuer1emzcmIGvlq7Dq4vtgi2NdwyZp6XGV0aEjJXu3/8+0tMp3HzzTs61XV5ejoWFBRiNRi/XdnJyMiYmJpCbm4u1a9fibJkMPwdAUTReGpjCH0fmUOdWwp6QHPK8Sy/E+zqduXE9Dn7/+ojduYI3BuEhyCpleJ1yfEMIi4uLmJ6exvj4ODo6OqDX6zlxNhgMIa+F1RrIe6YEwMarGSx1srNh6dMWrvVsBNALVoyTk5NRX/8kcnJSgz4rHAYHB3HxxRfjs5/9LH73u98F9RKo1WpUVlbi0KFDuPzyywEsubsPHTqEfQHK+mpqanDo0CHccsst3O/eeust1NTUAABKSkqQk5ODQ4cOcQI8NzeHjz76CDfddFPUry9WEEGOMf5c1m63G42NjVhcXMSuXbuQmJgY9TkAhC3I8/PzqD9ZB6AcgrnFeLrZ1RotzjzzTExPT2N6eho9PT1ISEhAZmYmnOnBWwXyhbdAxDmpK7xj0PjMZw6ioWEpXnb//d3IyqKwe/cqfPe71di8eRWSkpJQUlICh8OBwcFBDA4OQiaTYWpqCjRNIyMjg5uX+7XSHHytdMnqODE9hyd7p3F4gcK0NhlQBNg2PAT087U78Oevfzmq1yR0DJlPYxBVEAs5EDKZDImJiUhMTERJSQlcLhcXQmATw1jxZhto+LJ+vQEVFUp0dtpAUYHWIAOgP/UDLFnNiwBcp/7m77vnLcYpKQY0NPwWmZlh3mwFYWBgABdffDEuuOACPP3002G57Pfv349rr70WVVVVqK6uxuOPP47FxUVcf/31AIBrrrkGeXl5eOCBBwAA3//+93H22Wfjl7/8Jfbu3YuXX34ZJ06cwO9//3sAS9f+lltuwc9//nOUlZWhpKQEd911F3JzcznRXwkQQY4xvi5rq9WKuro6aDQa1NTU+P2SRnIOAGF1BPMcToEmAd3WPGPIFEVBq9WioKCAm0RjMpkwPT2NkYFhoFC4pfGe9iRiUpdaqYROHd17Pj/vRHX16xgasnj8VoGpKQVeesmEl156AwkJTlRVGXDddRvxmc9kYnh4GBs2bEBOTg43f7ijo8Ova7sqMxkvnNq4p+1O/LZrAq9N29CjSACtWd6N6dt7zsMvvxT9hCOhs6z12vBvdNVhWsjBUKlUWLVqFVatWgWapjE3N4fp6Wn09/ejpaUFKSkpnECziWFlZWl4++0v4eTJk+jpkeFf/xrHxx+bMD+vROAbPfWpH2DJYl4EYMcnru0pAH3co9PSUtHQ8CTS06MX4/7+flx88cW46KKL8Nvf/jbsfJcrr7wS09PTuPvuuzExMYGtW7fi4MGDXFLW0NCQ17Fqa2vx0ksv4c4778Ttt9+OsrIyvPbaa9i4cSP3mFtvvRWLi4v45je/iZmZGZx55pk4ePDgiuqpLWOE9gt9ynG5XEHjtydPnkRGRgaKiopgNptRX1+P3NxclJeXR9xO0xeKovDWW2/hvPPOC5qdPTg4iK6uLmzYsGGpu80T/ovyI6Lhn8B4+G7moqxUtD13u9+/tdhb8aeFPwu1MoweG8XQu4NhP96WmIe2C34T/gnqPgDqPwz5MJVajf/dfyPOWlMc/rF9GBuzorr6f2GxLIb9HLncgdJSBb70pbW4+eadSE1dElU2a5tNWJqbm+OytjMyMpCUlOTlXaAoGv81NI0Xhmdx0qWEY2wId2UrcOsF/OYyB+Ixy68wSQn3mRz9aBRDh8N73++46nbsqdwj2Ll9sdlsnPVsNpuh0WiQkZEBnU6H3t5elJaWemUp9/aa8OSTH+HgwSEMD7vBMOHaUjYA/+b+lZmZjsbGp2Aw6AM/JUz6+vqwd+9eXHzxxXjqqacE278+zRALOcawFvLw8DA6Ojqwbt06FBQUCHoOzzIEf9A0jY6ODkxMTKCqqgopKSmgKAoyCFj5yDNzyh3kJkYtF3byBf8YsvAWsl6vx4d3hF+T64+WFgvOPvsN2O2O0A/2gKY16O4G7r+/D/ff343sbAqf/exy17bT6eTEeWBgAEqlkhNn1rV9dUk2ri5ZsmrmHPlI1gg3kF7wLGseoQGVUrjX4Q+dTsd5gyiKgtlsxujoKIaHhyGTyWCxWLj4tFarRWlpOn71q4vxq18BDocLL75Yj5deakNT0xwcjmBr/eRv2dmZaGx8EklJCVGvv7e3F3v37sWll16KJ554goixQBBBjjFyuRwTExOwWq2orKxEWlr02Y2+yGSygB3BXC4XGhoa4HA4UFNTA41GwxX2y2WAAOHMJXgmdVFBRjWqILQg83wCbydScEHOTk/H8bu+h/TEyDfGt98exxVXvCVAj2MFJie9Xds7dhhw3XWb8KUvbURubi5yc3NB0zSXTezp2mbLqjQajaBiDMR32lNqYoqg5w4G2/XKbDajoqICycnJMBqNXGJYYmIi59o2GAzQaFT45jer8c1vVgMAjh0bwtNPn8C7745jeto3hrz0vVq1KguNjU+F1fwjFD09Pdi7dy8uv/xy/PrXvyZiLCBEkGOIy+WCyWQCTdOoqalBQkL0d6qB8Ff6ZLVacfLkSSQkJGDnzp1eGd9yuTy+ghwk4UYR7ii8MInnPOR1RYU48pOboFFF/pr+9Kc+3HTTe2AEn0Ilg9Wqwbvv2vHuu8fxjW8cxv33r8e+fbu5Yfbp6eleWdue4/hYcfZ1bUdKvBqDXHneldhWuk3QcwdjamoKzc3NXEwfgJeXwmQywWg0or6+HjKZjLvOaWlpUKlU2LWrELt2LSVZmEyLOHDgY/zP//Siq8sGiqKRn78KDQ1PQKeLfHY2S3d3N/bu3YsrrrgCv/rVr4gYCwwR5BixsLCAuro6yOVyZGVliSrGwPLkMd94teeINdai5tvAKhjJSUmY4/H4YM0xVAILMv9OXcI0Bjl3y0b8775rohKrBx5owc9/fhzit1VcBEUdR1vbcovKsyGJr2t7cHAQSqXSSzQibZQRc0GWAV+/6Ou47txrBT1vMCYmJtDa2opNmzYhKytr2d/VarVXYhjbMay3txfNzc1cYlhmZiYSEhKQnq7HHXecizvuOBcMw+CNN9qxe/dN0Ajgvejq6sLevXvx5S9/Gb/85S+JGIsAEWSB8bfZsmUPBQUFkMlkcDqFLePxh6eFPDIygvb2dqxbt45rZsBmYHuuV0hBnnPxrN0NInrCu6z5vtDoLeRrzzsLv/3K53ie15ubb/4IL77YGtUxwmMWwEkA4ZXNqdVqXq7tcBG+l3Xgz5hMJsN3v/BdfHHXFYKeMxisd2HLli3IyMgI+Xi5XI7U1FSkpqairKyMSwybnp5Gb28vlxjGdmaTy+XYu7dCkLV2dnZi7969uPrqq/HII48QMRYJIsgiwjAMBgcH0d3djQ0bNiA3Nxe9vb0xmODySb1zZ2cnRkZGsH37dqSlpQUUYwBQCNmsi2fZU7BropTFV5AzFcBe2oIPbDLM6pJD11h7XleZDHd/8RL8eM9nIljpEgzD4LLL3sGhQwMRHyN8jAAauX/xteZ9Xdtso4xIXNsySi5ct0gEFmSZXIYfX/VjXLwt+lKtcBkZGUFXVxe2bt0acR6Jv8Sw6elptLa2wu12Rzx0xJeOjg7s3bsXX/3qV/HQQw8RMRYRIsgiQdM02traMD09jR07diAlJQVA+MMlokUmk6G7uxsulwu7du2CTqcLKsYAoJAJmGctYAxZaJc1X4+xSg781xlL4wL75mz4TdcE/t+MCyOaJMBfveqpE8gUCjz7jf/AVTs2RbXe8847hI8/HorqGOExCsC7uX80e69vowy+ru2v6K7C25OH0G7vAJPGQB7tiFA/nzG5Qo6ffu2nOHtD5DdMfBkaGkJvby+2bduG1NTou2QBS/sK2+HOs3yN7cyWmJjIiXNycnLYN1ptbW245JJLcO211+KBBx4gYiwyRJBFwOl0or6+HhRFoaamxqswPZJZxXyx2+2w2Wxc8pZKpfJK3gr0ZVQK+V3jmcp8wc7AohVvl7Xb5cbi4iL0ej1WJ+vweFUJHgew6HTj6Z4J/G1iEe0yHSjtqbwAmUyQGmOW+noHgEwsdWKyn/oRmj4A/ct+K+S0qFCubdaiY13b2epsVBjXY4tqM8pSy/Ce8X3ULzZgRjcDRQL/uDTtI8gKpRIP3/AgdqzZIdRLDEl/fz8GBgawfft2GAzCj24EAsf4jUYj13DDs2OYMkCf8ba2Nuzduxdf//rX8Ytf/IKIcQwggiww7BB5g8GATZs2Lbvrj2Q0Ih9mZ2dRV1cHpVKJoqIiKJXKZclbgVAK6bIO20KW4Xtf2o0Hrr0g4CNUArus+U9jonDs2DFotVpOMAwGA/RqJX5YkY8fViy5lV8dMuIPgxaM6TX42737o6ox9rNofNKRKQkABYXCAZpe5F+V5YNePwyrdcDvccQa3xjKta3X6+FwOJCYmIgtW7ZAoVBgb/7F2IuLwTAM6kx1+MD8IUYVY0BSeDdZni5rlVqFX3/rcWws3BjkGcLBMAz6+vowPDyMqqqqsGebC4HvjdDMzIxXYlhqaionzmzb3tbWVuzduxc33ngj7rvvPiLGMYIIssDMzs4iLy8PpaWl/t3CIrqsJyYm0NzcjDVr1nD9iVnxD+cLpZTH1mUtkyvw5PeuxHW7g5eYCC0KfC1khVKBc845h2vl2di4FGNl3a2slXFFUSauKMoEsFbQ9S5HBkAJilIC0AKYh3erRD60Y3FxLPCZYjBP2de1PTs7i/r6eigUCszNzeHDDz9c5tquzKhEZUYlAGBscQxvTx5Cp7sLziRnYNf2KUHWaDU48J2nUZpTKvprA5bEuKenB2NjY6iqqoq6V300yOVypKWlIS0tDWvXroXNZsP09DSMRiMOHTqEBx54AFu3bsUHH3yA73znO/j5z38e45nan26IIAsM24c5EGK4rNm7776+PmzZsgWZmZkwm80YGRkBRVHIysqCTre857Av0YbovAiR1KXWaPDPn30DZ20oFvCk4cF7tgTDQKFQICsrC1lZWdzAeja7tbm52cvdKnTv3ODrVQBI8fj3ApZ6GVOn/hbsyY1YSuIKdF45amrKw12mIMzPz6OhoQG5ubkoKysDwzABXdtsF6tcfS6uWf01AIDNbcM7E4dRv9gAi87i5dpmaAYJCQl45nvPoCA9Pyavh2EYdHZ2YmpqClVVVdDro29ZKSQ6nQ6FhYUoLCxEWVkZpqam8NBDD0Gj0eCJJ57gsquvu+46YiXHACLIAhPqblJolzVFUWhpaYHFYuEmRVEUhfLyckxNTWF6ehrd3d1cUkdWVhYSExP9rvOMDBcGLS4wSgEEJciX12BIxpFf7UNxljAJLXzhayH7dnjyHFhfVlbGuVsnJibQ2dkZ1rUWj8RTPwDgwJL17MRS9yb2PaEB1GGpvMk/MpkcTzxxI7785RrxlurDzMwM6uvrUVRUhJKSEi7EEsy1zV5rNmtbp9Th4vyLcDEuAsMwqDc14APLhxiRjyA1MQ0H9h9AliHy0aZ8YBgG7e3tMJvN2LFjR1g3xfGkr68PTz31FG677TbcfffdaGxsxOuvv44333wTX//61+O9vE8FZLiEwNA0DZcr8Gxhi8WChoYGnHvuuVGfy+FwoL6+HgzDYPv27VCpVJyb2jN5yzO71Wg0QqPRcJtYSkqK153v3MICHnq9EW9OJaCHSoVLFaF7baoHOPnfy35dnL8KHz++D3otv0YFPzbeFtk6/GDps6Djb+EPvkjUJuKN+14P67Ge19pkMkGlUnHXmq0N5Utq6htwOqO9iaMAzGHJtX0cS1a0f+RyJf7611twySWx61ZlMpnQ2NiIsrKysHu7+17rUFnbfOaDRwtbZTE7O4vKykrJTxxqaGjApZdeiu9///u46667iJs6ThALOcYIZSHPz8/j5MmTSElJwcaNG716V/tmUnsmdbD1ilNTU2hqagKwFAvNysqCUqlEc3Mzvro5C/edmj51sNOEp0+YcGxagQVlcvj+Xj9Z1p/ZXoE3fnpdRF92GWSCdW7ibSHzOK/vtWbdrWxtKCsYGRkZYY/aFGZvVABIxVKcObAYq1RqHDx4B3btWiPEScNicnISLS0tqKiowKpVq8J+XqCs7c7OTjgcjmWu7ViKcUtLCxYWFlBVVRVVDXAsqK+vx6WXXor9+/fjjjvuIGIcR4ggxxghkrrYxKLi4mKsXr2aV/KWb73i7Owspqam0N7eDqfTicTERCQlJcHtdkOtVuPC8nRcWL6ULdw0voBfH53E2yM0jLLk4IlbPjHkb1x6Nn79rUuiet1CwXfDidSJxE7rycjIwLp16zA/P8/V4La2tiIlJYV7L4K1Uk1JoTE5GdESeJGQkIAPPrgP5eU54p/sFKOjo+js7MTmzZuRmRm5K9kza5thGM617TmgwdO1LZbo0DSNpqYm2O12VFVVBR1/KgXq6upw6aWX4kc/+hFuu+02IsZxhghyjGFbWkbiPvPs/LVx40bk5OT4dVGHi0wmg8FggMVigdvtxrp16+B2uzE6OoqOjg4YDAYuFpqQkIDNqxLxhy8subAn5hz49ZEJ/KPPjiFXEhjfcXWnbgxkcjke/tYXcPPenbzWtmytAlrICTxjeUJEdWQyGZKTk5GcnIzS0lKvtofd3d1ISEjwKqnyfC97e/fixRebcOBAC7q7VbDbhe+DnpJiwMmT9yMnJ0XwYwdicHAQfX19UXWr8keghiRGo1HQXtu+UBSFxsZGuFwuVFZWhu0BiRcnT57E5z73OfzkJz/BrbfeSsRYAhBBFphwkrqApTtpPhsBTdNob2/H5OQkduzYAYPBELLzVrjHNJlMqK6u5mojS0pKYLfbMT09jenpafT09CAhIQFZWVnIzMxEcnIycpI1eODCIjwAwOZ04/fHJ/HXtgW0LepAqRIAuQJKlRp/v/t6nL8tdu7PcHAygWP8/hB6yAHg3fbQ7XZzJVX19fVc44asrCykpaVhZmYGhYUmvPLKmSgqKsKJExN44ok2vPOOGSaTGt7j9kK/Gl9yc7NQV/cAkpJiE+dkGAa9vb1cS1exGmSw8HVtR4Lb7UZDQwMYhkFlZWXAZhtS4fjx47j88stx++2344c//CERY4lAkroEhmGYoMMjKIrCW2+9hfPOOy9sdxY7w9jpdGL79u3QaDQhLWOapoM2AnG5XGhsbITb7cbWrVuDbkTs2MipqSmYTCbO7Z2VlbUsUYlhGPytyYj/qh/BL3YXoDw/dNP8cLjdeCcoCFMutji9iKbnGkM/8BQalQZv3f9/gpw7FGzjBvZmyG63g2EY5ObmYs2aNcvikRMTC/jNb5rxz3+OY2BABoYJZZXRAF7h/lVeXoyPPvopVFGMg+SDZxnQ9u3b41qT6+naNhqNmJ2djajFpMvl4uqmt27dKpjFLRYff/wxPv/5z+POO+/E/v37iRhLCCLIAhNKkBmGwZtvvolzzjknrLvxxcVFnDx5Enq9Hps3b/aKQQcSXJvNhdraF9HfP4JNm1Lwta9tx/XX13Kb7uLiIhoaGqDX6/12EwsGa2GwJVUURXklKollGdxhvAtuBK7v5oPVZEXjsw1hP16tVOPtB94S5Nx8GBgYQG9vL7Kzs2G1WjE3N4fk5GTOta3X673ef4fDjeefb8df/jKA5mYnXC5/yUSfCHJNzUa89dZPYp55PDMzg8rKSsmVAXm6to1Go1e+RSDXttPpRF1dHTQaDff9lDIfffQRPv/5z+Oee+7BLbfcQsRYYhBBFphQggwA//d//4czzjgjZJMAk8mEhoYG5OXlYe3atVzsGQgsxgMDszjjjBcwM7Pg9fv/3959h0V1pm0Av4ci0hEpUWNBRUXpRaJmV4yxw9iiErsmGteymt0UN1GzpmjcNYmxRF2T2L4YNeoAoiJhLNijFAUBAZUibQCpA9PP94d7zjKKijDlgM/vuvbaKyMyL4Nwz9ueRyBQoXdvS4wb1wuDB9vC3b0H3N3dW/QDyTAMqqurUVpaColEgrq6Or0VyFhVtgZKvNhS89PUP6xH8q6kJn/86z6vY93Mr3Ty3E3BVnYqKCiAn58ft6Qrl8u1rvk86/oaAMTG5mLHjgxcvlyNmhoLPFrafhTI48cPwYEDiw32NanVaqSkpKC+vp5b5eEz9o0n+3o3trStUCiQkJAAKysreHl58b5wxpUrVzBp0iR8/vnn+Otf/0phzEMUyHogl8uf+edisRhBQUGws7N76sewPYw9PDzQpUsXbr9YIBA89Qf/3Lk8TJx4EArF84JLjc6dTTFmjDv+9rfh6NFDNzWX6+rquJlzVVUVbG1tuX3nx2dzL2p12WdQQDd9pGUVMiT9J7FJHzv+T+Pxd+HfdPK8TcHOIisqKuDv7//UN20N2+2VlpZCo9Fw4dxYw4A7dx5i8+YUxMaWYtw4GTZtmmmILwfA//ZXNRoN/Pz8eH/Y6XHs0jYbzlVVVbCysoJCoYCtrW2rWKa+fPkyJk+ejC+++ALLli2jMOYpCmQ9eF4gnz17Fn5+flxLxobYPbaCggLu9GlTDm9t356IDz88DYZ50TvOGjg4MBg2rBtWrBiKwEC3F/z7jVMoFNzM+eHDh1xjBhcXlydOETfFmrJ/Qo5nv65NJauUIWnnswNZIBBgYegCzPjzDJ08Z1Oo1WruysyLzCIblvIsLS3VWqlwcnIy6tIw2/nMzMysVQRXU1RXVyMxMRGmpqZQKpXc0jbboIFvX+PFixfx1ltvYd26dViyZAmFMY9RIOuBQqF45lWZ+Ph4DBgwAB07as9MVSoVbt68CalUioCAAFhZWTUpjJcsicWePdd1MnZLSyWCg13x3nuDERbmrZMfXrVazR0KKysrg0Ag0DpF3JRfYJ+Vr4WM0U3bQXm1HInbE5765yamJlg9YxWGew3XyfM1hUKhQHJyMkxMTODj49OiWWRdXR0XzpWVlQa7g/s4mUyGxMRE7qwC35d0m6Kurg4JCQnc3XK21vbjS9vsuQpjV+i6cOECpkyZgvXr12Px4sUUxjxHgawHzwvkixcvom/fvlqFEOrr65GYmAhzc3P4+vrCzMzsuSep1WoNRoz4Fdeu5ejjy4CZmRJeXvaYPTtA61BYSzQ8RSyRSKBQKLhfXs7Ozk8Nos2FW5Fvmg8T05b/UlfUKJDww41G/6xdu3b4dsE38O7h3eLnaar6+nokJSXB2toanp6eOp1hKZVKrbKpZmZmWgeV9BWSdXV1SExMRIcOHeDh4dEmwpg9YOnq6oo+ffo88TPZ2NJ2c05t60p8fDymTJmCf/3rX1i0aBGFcStAgawHzwvkK1euwM3NDa+88qgiUmVlJRITE+Hi4gIPDw8A4CpvPe3wVnl5HQYN2oOCggo9fAWPe4hx45xx+PBKnX5WhmFQW1vL7TvX1tbCwcGB23d+fKm14GEBDqf/Bom9BEpHFUzbNS+4FFIFErY+GcjW1tb4z7L/GKwTEADU1tYiMTERzs7O6Nevn15/aTa8g1taWgqlUomOHTtygaGrqlK1tbVISEjAK6+80mhwtUY1NTVITEx8ZmvVxykUCu5+eXl5OUxMTAy2tH3+/HlMnToVGzduxMKFC9vE9+BlwO/b621UwxaMRUVFSE1Nhbu7O7p166Z1kvpps4pbtyQYPnw/6up0s4T7bAUA8v97Sle3BAIBbG1tYWtry1WvYsMiMzMT1tbWXMtDhUKBzFuZEHYLQ8+ePaFQK3Cu5Dxu1CY80WavKc/7OOeOzvj5rz/D3urpB+10jW000rC7kT41LC/Zt29f7s1QXl4e0tLSuMps7CG85misY1Nrx+4Zd+vWDT179mzy32vXrh06deqETp06aa0MZWZm6nVp++zZswgPD8e3336Ld999t018D14WNEPWA6VS+cwGEjdu3OBCJicnBz4+PnBycmrSfvGxY3cwd65I5z2VG5cNtl/ua695QCz+lwGe8xF2qZXdd9ZoNHB0dISbm9sTV3wYhsEfZddxseISis2KYWL37OVRZb0SNzb/b8+9V7de2PmXHWj3ePlPPZJIJEhNTUWfPn3w6quGm5E/TcPKbA8fPnxmKc+nYTs29e7dG926dTPAqPWPfYPh5uaGHj166ORzPm1pmw3nlixtnzlzBuHh4fj+++8xf/58g4fx119/jX/84x9Yvnw5Nm3aZNDnbgtohmwEJiYmePDgARQKBYKDg7kexs8L4y+/vIT168+jsfKHuqUBkAmgknvk+VepdMvc3ByvvPIKZDIZysvL0atXL8hkMqSkpDR6xSfYeSCCnQcCALKqsiAuPYP7yAFjxzzR3anh6xvsGYx/zd5g0F9cDx48QGZmJjw9PeHi4mKw532W9u3bN1rKMzk5GQC0Xu/GllolEglSUlLg4eGBzp07G3j0+vHw4UMkJye/UEvIpmhYa7tHjx5aS9uJiYlc6dRnvd6NEYvFePvtt7FlyxbMndu8rmotcf36dezcuRPe3oY7f9HWUCAbmFwuR0VFBUxNTTFo0CCYm5s3KYw///wqNmy4BP2HsQpAGoA67hETE1MsXTpRz8+rTaPRICMjA2VlZQgKCuLqbDe84pOdnY3U1FStYiQWFhZwt3eHu707AEBSL0Fs8e9IV2ZAYauAibkJF9CGvmPMMAzu37+P3Nxc+Pn5oUOHDgZ77hdhZmYGV1dXuLq6QqPRcK93VlYWUlJSnni9CwsLkZGRAS8vL968wWgpdrbft29fdOnSRa/P9byl7Q4dOjy32E5sbCxmzpyJrVu3Ys6cOQYP49raWsyYMQO7du3Cl19+adDnbktoyVoPnrZkzfYwFggE3EnN55XBZL311kmcOpUHgIFAoIKFhRQyma6XrevxKIz/Nxu2sGiPkye/xGuv9dXxcz2dSqVCSkoKZDIZ/Pz8nrm/JpVKuUNhbGnJhsVIGqpT1iGuKA5JtTfRu6ynQe8YMwyDjIwMlJaWws/Pj3uD0dqwtZ/ZpVYLCwsoFAr069cPnTt3bhP7laWlpbh169YL92fWNYZhtK6wNVzadnR0hL29PUxNTXH69GnMmjULP/zwA2bNmmWU78GcOXPg6OiI7777DiEhIfD19aUl62agGbIeNPYDIZFIcPPmTfTs2RMymQwajYYL46ZcCbGyYq8DPWogIJM5AJDjUbN5FR6VRWzJD2IVHi1T/y/kHR074MqVb/GqjhpENIVcLkdSUhLMzc0RGBj43Pu41tbWcHNzg5ubG+RyOXediu1QxRYjsbOzg5W5FYTdhBBCaKCv5hG1Ws01rA8KCuJdDecXYW1tDWtra3Tv3h1ZWVl48OAB7O3tkZGRgXv37nEzucebjrQWJSUlSE1NhaenJ1xdXY06FoFAwL3ePXr00LrCduTIEWzduhV9+vRBcnIytm7darQwPnjwIBITE3H9um5qIbzMKJD1jGEY5OTkIDs7m+thfPfuXeTl5cHExIQLi+f9IFlaNvatsvjv/4BHs9ra//6/AC/Wkk8C4D4aLof36dMDly9vhKWl4WoO19bWIikpCR06dED//v1f+Be6hYUFXn31Vbz66qvcPqhEIuH25dhw1uf928exXbU0Gg2CgoJ437C+KRp2bBo4cCB3BoIt5ZmamgqNRqO1D9oaymUWFRUhPT0d3t7eWjUC+MLc3Jxb2u7bty/kcjm+/fZbODk5YenSpTh27BgmTJiAhQsXGmxM+fn5WL58OX7//XejF0FpC2jJWg9UKhW3L5yWlobS0lL4+/vDzs4OarVa69AM21WGXWZ92szip59u4YMP4qFQNOU9lBqPwlmO54dzHoBCrUfefDMYERGfGvTdNnsFqGvXrk2+59lUDe/fSiQSqFQqrQ5V+goLuVzOdQLy8fHhXUnF5mhKx6aGTUdKS0shlUq19kH5uELAHrTz8fF5ooIeH0VHR2P+/Pn48ccfMW3aNGRmZiI6Oho5OTnYsmWLwcYRERGBiRMnav3bVqvVXM19uVzeJv7dGwoFsh6oVCrU19cjOTkZSqXymT2MG7YzlEgk3AliFxeXJ05YqtVqbN8eh19+yUJmpgYyWVNmWxo8WtZm7yybNHg8C4B2YZGlSydjw4a5Lfr6X1RxcTFu376Nvn376v0KEMMwqKmp4fad2bBg3xDp6l2+VCrlKlU1Z7bPR83t2NTwfnlFRQWsra25cDZ09arG5OXlITs7m9cH7RqKjo7GvHnz8PPPP2PatGlGHUtNTQ1yc3O1Hps3bx769euHjz/+GJ6enkYaWetEgawHVVVV+OOPP2BjY8P1G27K4S32BDEbznK5nKv5bG9vj/T0dCgUCu6g06VLOdi8+Q/Ex5egutoMz99DZvDo9HQ9gNt4NIvGf8dlgu+/X4p33hmhg1egaRiGQW5uLu7duwdvb284ORlur5rFHpqRSCRchyr2DVFzO1RVVVUhKSkJXbp0Qe/evY0eOLrA1llXq9Ut6tikVCq1VofYrYRn9RzWp5ycHNy/f/+pzV74JioqCu+88w727NmDKVOmGHs4jaJDXc1HgawHd+/ehVQqhbu7OxiGeW4ZzMY0LCtZUlICqVQKc3NzuLm5wdXV9YmZXHq6BN99dwWxsQ9QWtqUPeQ44L/dk8zN2yEy8nMMHTrgBb/S5mNPHUskEvj5+T2zFaWhsA3qJRKJVr9hFxcXODg4vFBxjF69eqF79+4GGLX+NezY5OPj80Rrx+Z6Vl1zXZbybAx7BS0vL4/bTuK7iIgILFiwAPv27cPkyZONPZynokBuPgpkPVCr1VAqlU3qYfw8lZWVSE5OhpOTE2xsbLjrD8+63lNYWI3vvruM48fvIz9fA6CxWcdZAHWws7PDpUvfoGfPV5o1vuZglz7r6urg5+fHyz1FtkMVu9QKPL84RlFREdLS0ox+XUaXDNWxiX0Dyr7eNTU1Oinl+bTnys7ORmFhIQICAmBjY6Ozz60vx44dw3vvvYf9+/dj0qRJxh4O0RMKZD2QSqVgGAYMwzyz2MfzFBcXIy0t7YlShAqFgtsDLS8vh5WVFVfz+fH2ejU1Mmzdeg2HD99BVpYCDMPObuLRo4cdrl79Fra2Vi35cl8IO9syNTVtcZtBQ2EYBpWVldxrLpfL0bFjR7i4uHAzudzcXNy9e7fVHApqCmN2bGKvsLGlPNl+2mwpz+aOhWEYZGZmoqSkBAEBAToNen1gGAZHjx7FX/7yF/zyyy+YMGGCsYdE9IgCWQ98fX1hY2ODsLAwCIVCdOvW7YVCuWFFJy8vr2furapUKq2az+bm5lw4P77MqlSqsXt3AvbtS4WLSxWOHl1h0P1NqVSKpKQk2NnZwdPTs1UedGLrELPhXFNTg3bt2kGpVPLi7qqu8KljU2OrFQ2vVDV1CZ1hGKSnp6O8vJzrN85nDMPgyJEjWLx4MQ4cOIDx48cbe0hEzyiQ9SA/Px8ikQgikQgXL16El5cXF87Pa7HHXiupqKiAr6/vC1V0Yu+CsmEBQOvEtjEDkF16b0sHnTQaDVJSUvDw4UNYW1ujurqaO0Hc2GpFa8EeSuvWrRvvOjY1LJ1aWlqKuro6rVKeTzslzzAMbt++/czrWnzCMAwOHz6MZcuW4ddff0VYWJixh0QMgAJZjxiGQVlZGaKioiASiRAXF4fu3btz4ezv768VknK5HLdu3YJGo4Gvr2+Tr5U87bnZZVaJRAKlUsmd2HZyctLZwZymKCkpwe3bt3VepN+Y1Go1bt68Cblczl0BalhJiV2taG2Vq1pbx6bHS3na2Nhwb4hsbGwgEAig0Wi4Smn+/v68L2DBMAwOHjyI5cuX4+DBgwgNDTX2kIiBUCAbUHV1NU6ePAmRSISYmBjY29sjNDQUQqEQ1tbWWLRoEdavX49hw4bp9PpHw7u3EokEdXV1XGN6FxcXvZ5mZfdWvby8eFn9qDmasg+u0Wi0VivYylXsaoUh3xA1VWvv2MSekmfPVpibm8PJyQk1NTVQqVQIDAzkfaU0hmHw66+/YsWKFTh8+DDGjh1r7CERA6JANpL6+nrExcVBJBLh6NGjqKmpQe/evfHll1/izTff1Ou7eHZWIZFIUF1dDXt7e27fWVdLeezhmeLiYvj6+sLe3l4nn9fY6uvrkZiYyN0xb8qsl61cxYYzu8zKnpJvyUqIrhQWFiI9Pb3NdGxi950zMjKgUCi0WhrqszpbSzAMg19++QV/+9vf8Ntvv2HMmDHGHhIxMApkI9u9ezeWLl2KxYsXQyaTITIyEpWVlRg5ciSEQiFGjRql185AbGN6iUSCiooK2NjYcOHc3MIYDZsp+Pn58f7wTFPV1NQgKSkJLi4u6Nu3b7P3Vh9/Q2RnZ6dVjMTQ2EpVvr6+cHR0NPjz64NarUZycjLUajV8fX25f+elpaWora2Fg4MDt53Ah3+fDMNg//79+OCDD3D06FGMGjXK2EMiRkCBbERZWVkYPHgwDh8+jGHDhgF4tNR548YNHDt2DBEREcjJycEbb7wBoVCIsWPHomPHjno7ZKNUKrlfWmVlZbCwsODC2d7evknPq1AokJycDIFAAB8fH94vETYVW2u7e/fuOj3o1Nj1Hnbm3NTXvLkYhsG9e/eQn58PPz+/NrOKoVKpkJSUBIFAAF9f3ye2B+rr67ml7YcPH3JdwQzxmjeGDeMPP/wQR48exciRIw36/IQ/KJCNrKam5qkzYIZhkJaWhmPHjiEyMhI3b97E4MGDIRQKERYWhi5duujtlwe75Mcus7KdqVxcXJ56QIm9t2pnZ4cBAwa0maLyEokEqamp6NOnj15rbTdsOsK+5voqK9lwS6G1FMdoCqVSicTERJibmzepoUdjrzm712+IUp4Mw2Dv3r34+OOPERERgeHDh+v1+Qi/USC3EmwbR5FIhMjISFy6dAl+fn7ciW13d3e9hfPj3ZLUajUXFE5OTjA1NeWuynTu3FmvYzE0tguQp6enQfdW2bKS7BsipVKpVYykJXugGo0G6enpqKiogL+/Py+WbHVBoVAgISEBlpaW8Pb2fuFT7Q1LeTYsAMP+O9f1Xj/DMNi9ezc++eQTREZGcqtk5OVFgdwKMQyDkpISREZGIiIiAmfOnEHv3r0RGhqK8ePHN+uX0Ys8N3tASSKRQCaTwcbGBjU1NejVqxfc3Nz08ryGxi7n5uXlwdfX16hdgBrWNWf3QNl2hi4uLi90ALC5HZv4Ti6XIyEhATY2NjopOsMWgGHDueFeP1vKsyVvOhmGwU8//YRVq1YhKioKISEhLRpvU6xfvx7Hjh1DRkYGLC0tMXjwYGzYsAF9+/bV+3OTpqFAbuXYQgknTpzgrlM5OTlxM+fXXntNb8tubE3g3NxctG/fHjKZrNlBwSds4wu2jzXflnPZdoYSiQSVlZWN3r1tjK46NvGNTCbDjRs34ODgoLdWl3K5XOtKFdt4xNnZGQ4ODi/0nAzD4Mcff8Tq1asNFsYAMHr0aISHhyMoKAgqlQqffPIJUlNTkZaWxvsSoi8LCuQ2pq6uDrGxsRCJRIiOjoaZmRnGjRsHoVCIoUOH6mxGxDAMsrKyUFhYCF9fXzg4ODwRFLa2tlontlsD9oS4VCrlbeOLhhrevWUP4jUWFEqlUuvuNB/vQTdHfX09bty4gY4dO8LDw8MgWyVsRTx29szeMWeXtp/12jIMg507d2Lt2rU4fvw4/vznP+t9vE9TWloKFxcXnD9/3qjjIP9DgdyGKZVKnD9/HkePHkVUVBSkUilGjx6NsLAwjBgxotkzP7Vajdu3b6O6uvqpe5AKhYIL54cPH8LS0pI7PcyHpvSNUSqVuHnzJlcprbWdEG+sdKqTkxM6dOiA3NxcWFlZcf252wKpVIqEhIQWX0NriWeV8nRyctJ6Q8cwDLZv344vvvgC0dHR+NOf/mTw8TaUnZ0Nd3d3pKSkwNPT06hjIY9QIL8k1Go1rl27xp3YLigowPDhwxEWFoaxY8eiQ4cOTfqFplQqkZycDIZhmhxa7ElWtgGGmZmZVp9hPpSUlMlkSEpKQvv27eHt7d3qQ4sNioKCAhQVFYFhGO70sLOzc6t7s/E4tvlF586deVUbva6ujgvnyspKWFtb49SpUxgxYgSSk5Oxfv16REdH4/XXXzfqODUaDYRCISorK3Hx4kWjjoX8DwXyS4it7cvedU5LS8Prr78OoVCI0NBQdOrUqdFfcA2rVHl6ejYrtB4vKckwzHP7DOubVCrl2gzqaw/SGNjQcnV1RZcuXbiuYA17Dbu4uLS6U9bV1dVITExE165d0bNnT96E8eOUSiXy8/Px/vvv4/z581CpVBg/fjwWLlyIYcOGGfWMxV/+8hecOnUKFy9e1OtVPvJiKJBfcgzD4O7duxCJRIiIiMC1a9cQGBjI3XVmf+FdvHgRVVVV6NWrl86WBx/vM6xQKHR2taep2OtabakLFfC/r6ux0GpYtYotjMH37QRWVVUVEhMT4ebmhh49ehh7OM/FMAw2b96Mr7/+Gp9//jmys7MRFRWF8vJyXLhwAX5+fgYf09KlSxEZGYn4+Pg2cyuiraBAJhyGYVBUVISIiAiIRCKcP38e/fr1Q8+ePRETE4N169Zh0aJFentu9mqPRCKBVCrVe73nsrIy3Lp1C7169UL37t11/vmN5eHDh0hOTm5SxyalUsltJ5SXl8PU1JSbOfOtQxVbLa1Xr16tohMVwzD4/vvvsXHjRpw8eRKvvfYa9/itW7fQr18/g147YxgGy5Ytg0gkwrlz5+Du7m6w5yZNQ4FMGsUwDCoqKvD+++/jl19+gampKV599VXurnNQUJBel5fr6uq4mXNVVRXs7Oy4E9u6WGItKipCWloa+vfvj06dOulgxPzAVhXr16/fC3dsYgvAsK+7Wq1u8ulhfWPbQuq7WpquMAyD7777Dt9++y1iYmIwcOBAYw8JixcvxoEDBxAZGal199je3p73twleFhTIpFEMw+CTTz7Bf/7zH0RGRsLX1xcxMTGIiIjAiRMnYGlpiXHjxmH8+PF4/fXX9XpIiK33zJ7Ytra25sL5WfdunyYnJwf37t2Dj48POnbsqKdRG15hYSEyMjJ0UlWMLQDDvu4NTw87OzsbdP+ztLQUKSkpzXqTYQwMw+Cbb77Bpk2bcPr0aQQFBRl7SADw1J+T3bt3Y+7cuYYdDGkUBTJ5qg0bNmDChAlPVPJRKBQ4c+YMV8ZTLpdj7NixEAqFGD58uF4PCSmVSu5wUnl5Odq1a6d1YvtZ4dzw7rS/vz/s7Oz0Nk5DYzs26etNxuMrFuwdc11UrXoWtkezp6cnXF1d9fIcusQwDP79739jy5YtOH36NAIDA409JNKKUCCTFlGr1bh8+TJ3nUoikeDNN99EWFgYxowZo9fuOY/fuxUIBFw4Ozo6au1/ajQapKWlobKyEn5+fq2mUMnzNCzx6e/vb5COTewdc7ZqVfv27bnXXZff76KiIqSnpxu8jnhzMQyDDRs24IcffsDp06cREBBg7CGRVoYCmeiMRqNBcnIyF8537txBSEgIwsLCEBoaChcXF702wGh4YlulUnH3bu3t7ZGWlgaFQgE/P782U7+ZDx2bGnYFKysrg0Ag0Em3pIKCAty5cwfe3t5wcnLS8ah1j2EYrF+/Hjt27EBcXBx8fX2NPSTSClEgE71gw4IN5xs3biA4OJirsd29e3e9hXPD/c+SkhLU1dXB3NwcvXr1gqura6svigHws2NTw25JEokECoWCOxTm7Ozc5Gts+fn5yMrKgq+vLxwdHfU86pZjGAZfffUVdu3ahbi4OPj4+Bh7SDqn0WhgYmKCiooK2NraQqVSoX379tzjRDcokIneMQyDBw8ecNepLly4gAEDBkAoFEIoFOqtBjFbyMTS0hIODg4oLS1FTU0NHBwcuP3P1ni6VKPRICUlBVKpFP7+/rxs4tFYh6qmvO65ubm4d+8e/Pz84ODgYNhBN4NGo8GXX36Jn3/+GXFxcfD29jb2kPQmNjYWn376KUxMTODj44OPPvoIvXv3plDWIQpkI5LL5QgODsbNmzeRlJT0UixzMQyD8vJyREVFQSQSIS4uDl27duVmzgEBATr54a6pqUFiYiJcXV21CpmwRTEkEgkqKipgY2Oj1QCDz0UxgP91bFKpVPDz82s1s3228UhpaSn3uj/eoYrdC/fz8zPIXnhLaTQafPHFF9izZw/i4uLg5eVl7CHpHMMwEAgEuHPnDgIDA/Hhhx/i4cOHSEtLg0QiwaFDh9C3b18KZR2hQDai5cuXIysrC6dOnXppAvlxNTU1OHnyJEQiEU6dOgU7OzuEhoZCKBRi8ODBzarW9fDhQ9y8eRPdu3eHm5vbU0OW7ZTEnthu3749F858rFjVVjo2PX5S3tzcHO3atYNUKkVgYGCrOP2u0Wiwdu1a7N+/H2KxGAMGDDD2kPTm5s2buHHjBvLy8rB27VoAQHx8PDZs2IC8vDwcPXoUffr0oVDWAQpkIzl16hT+9re/4ejRoxgwYMBLG8gNyWQyxMXFISIiAlFRUdBoNBg7dizCwsIwfPjwJi3NlpSUIDU1FX379n2hAhJqtZprY1haWsq7ilVyuZxbfm9LHZtUKhVSU1O5KmGP1zbn45sOjUaDNWvW4Ndff4VYLEb//v2NPSS9KS0txcyZM3Hp0iUsWLAA3333Hfdn8fHx+Prrr1FcXIxff/31ieuR5MVRIBtBSUkJAgICEBERAScnJ7i5uVEgP0alUuHixYvcobCKigqMGDECQqEQo0aNgq2t7RMzWPYwUEuvyTSsWCWRSKDRaLhwNkYDjPr6eiQkJMDBwaFNNb9gGAYZGRkoKytDQEAALC0tuVaGEokEMplMqxgJH07HazQarFq1CocPH4ZYLIaHh4exh6R3Bw4cwLZt21BcXIwrV65o/WxduHABK1euhFKpxMWLF2Fubs67laXWhALZwBiGwdixYzFkyBCsWrUKOTk5FMjPodFokJCQwHWnun//PoYNGwahUIixY8fC0dERa9asgYeHB0JDQ3V6GIhtY8iGs1wub9bJ4eaqra1FYmKiUXv+6gPDMEhLS0NFRQUXxo+TSqXcobDq6mqufCpbjMTQNBoNPvnkExw9ehRisRj9+vUz+Bj0iY2Cxv6NRUVFYf369bC1tcXevXu1ys1euHABnTp1Qu/evQ021raKAllHVq5ciQ0bNjzzY9LT0xEbG4vDhw/j/PnzMDU1pUB+QQzDID09netOlZSUhI4dO0IqlWL37t0YO3asXq9TsSEhkUhQW1uLDh06cCGh69POz+rY1JppNBrcvn0b1dXVCAgIaNLr9nj5VCsrK27VwhD7/RqNBv/4xz8gEokgFovb5PIse4BLLBYjKiqKK6KzcOFCWFlZISIiAt988w0sLS2xf//+JyqnsX+fNB8Fso6wVYuepWfPnpg6dSqOHz+u9Q9XrVbD1NQUM2bMwN69e/U91Dajvr4ekyZNQlJSErp164akpCT4+PhwJ7b79Omj118Q9fX1XDg3bIChixnci3Rsak3YK1t1dXXw9/dv1jK0SqXSKkZiYmLCve6PV2jT1Zg//vhjREVFQSwWo0+fPjr9/Hxy5MgRzJo1C6GhoQCAEydO4M0338S6devg6emJI0eOYPv27ZBKpTh+/DicnZ2NPOK2hQLZwPLy8lBdXc39d2FhIUaNGoUjR44gODi4VXSy4QOGYTBy5EjU1tYiOjoajo6OkEgkiIyMREREBMRiMXr16sV1p/Lx8dHr3qtCoeCWV8vLy7kewy4uLo3udz9LSzo28ZlarcatW7cgl8vh7++vkytb7H4/O3tmK7SxHapauqWg0Wjw4Ycf4sSJExCLxQZvWbht2zb8+9//RnFxMXx8fLBlyxaddY5SKBRa34PCwkIMHz4cS5YswdKlSwEAaWlpEAqFXBibmppi//79OHDgALZv3079lHWMAtnIaMm6+cRiMQYNGvRElSq2UteJEycgEokQExMDR0dHhIWFISwsDIMGDdLr6V2VSsVd6ykrK4O5uTk3g+vQocMzw5ltC+nl5dUq6jc3lVqtRnJyMtRqNfz8/PSy984wDGpqarg3RlKptEVbChqNBn//+98RExMDsVhs8D3SQ4cOYfbs2dixYweCg4OxadMm/Pbbb7hz506L/22sXr0aAwYMQHh4OPfYgwcPMHToUOzatQtvvPEGVCoVzMzMkJKSgsDAQGzfvh3z58/nXmc7Ozu66qRjFMhGRoGsf3V1dfj9998hEolw/PhxmJqaYty4cRAKhQgJCdHr6V2NRsMtr5aWlgKAVgOMhie29d2xyVhUKhWSkpIAAH5+fga7ylRXV8ddY6usrIStrS332j+vCIxGo8H777+P2NhYnDlzBr169TLImBsKDg5GUFAQtm7dyo2pa9euWLZsGVauXNmiz/3uu+/i008/hZubGxeqhYWF8PDwwMaNG7FgwQKo1WowDAMzMzO88cYbCAwMxL/+9S9dfGnkKSiQyUtFqVQiPj4eR48eRVRUFGprazFy5EgIhUKMHDlSrw0aGIbhGmBIJBIolUpueVUqlSI/P7/VlIxsqobFTHx9fY12f/rxIjAWFhZPbdupVqvx/vvvIy4uDmfOnEHPnj2NMl4rKyscOXIEEyZM4B6fM2cOKisrERkZ2azP+/jBq9OnT6OoqAiTJ0+Gra0tVq1ahd27d+PHH3/EmDFjuI8LCQnBiBEj8Omnnzb7ayLPR4FMXloajQbXrl3j7jrn5+dj+PDhCAsL465T6fPENru8+uDBAyiVSjg4OKBTp05wcXFpNSUxn0WhUCAxMREWFhbw9vbmTTETtkMVO3tmFRQUYNy4cVi1ahXOnTsHsVhstD3SwsJCdOnSBZcvX8agQYO4xz/66COcP38e165de6HP1zCIlUolt2UQHh6Oq1evYt26dZgyZQoKCwvxz3/+EydPnsQnn3yCTp064erVq9i9ezf++OMPg++hv2z4VwaHEAMxMTHBoEGDMGjQIGzYsAG3b9/GsWPHsGPHDixduhSvv/46hEIhwsLC0KlTJ52Gs0AggI2NDfLz82FmZgYvLy/U1NSgsLAQGRkZsLe35w6FtcYGGGxlMSsrK3h5efFqn9HU1JR7bdlVi1OnTmHNmjVYtGgR2rdvj7Vr18LW1tbYQ9UZgUCA3NxcdO/eHebm5hCJRLCzs8PBgwcRHh6Or776CgKBAOHh4fjiiy/Qo0cPrFu3Dq6urrC2tkZ8fDzc3d1pz1jPaIZMODk5Ofjiiy9w5swZFBcXo3Pnzpg5cyY+/fTTNjFjayqGYXDv3j3urvPVq1cREBDAhXOvXr1aHM7P6tjUWAOMxxsx8JlMJkNCQgLs7OwwYMCAVvELXK1WY/HixTh79izefvttnDt3DklJSRg6dChOnz5t8BKeul6ylkgkCAgIwKRJkxAYGIg5c+YgJiYGI0eOBAC89dZbSE9Px+rVqzFp0iS0a9cOZWVlaNeuHQQCAWxtbbnrmUR/KJAJJyYmBocOHcLbb7+N3r17IzU1FQsWLMCsWbOwceNGYw/PKBiGQVFRESIjIyESiXDu3Dn07duXu07l6en5woHDnjhuSsemho0YysrKYGFhwc3u7O3teRfObJlPR0dHvbXV1DU2jK9evQqxWMzd+37w4AGuXbuGyZMnG2VcwcHBGDhwILZs2QLg0Zu4bt26YenSpU0+1FVSUgJXV1fu1sGiRYugUCgQHR2N4cOHo76+nluBmTRpEjIzM7Fq1SqEhYVp3aWnoh+GQYFMnunf//43tm/fjnv37hl7KEbHLm8eP34cIpEIsbGxcHV15cJ54MCBz51BsIecTExM4Ovr+0IzL3bvkw1ngUDAhTMfGmBIpVIkJCS0qjKfKpUKixcvxh9//AGxWIyuXbsae0icQ4cOYc6cOdi5cycGDhyITZs24fDhw8jIyHiiSlZj1q9fj4MHDyIhIQFmZmaIj49HSEgIrKyssGTJEq6yoEwm41Zo3nrrLVy5cgXbtm3TmpkTw6BAJs+0atUqxMTE4MaNG8YeCu9IpVLExMQgIiICJ06cgIWFBcaNG4fx48fjT3/60xMzX112bNJoNFonttVqNZycnODi4gInJyeDLy3W1tYiISEBnTp1gru7e6sJ4/feew8JCQk4e/YsunTpYuwhPWHr1q1cYRBfX19s3rwZwcHBTfq7hYWFMDMzg4uLC2pra2FlZYWEhARkZGTg/fffx6xZs7juTXK5nLv+t3DhQqxZs4aKFBkBBTJ5quzsbAQEBHD3EsnTKRQKnD17FiKRCJGRkZDJZBgzZgyEQiHefPNN5OXl4Z///CdWrlwJb29vnc5m2UIobDjLZDJ07NiRC2d97//X1NQgISGhVdXcVqlUWLBgAZKTk3H27Nk2VRHtcbGxsZg2bRoSEhLQs2dPlJeX47fffsOqVaswf/587m7xli1b4O/vjyFDhgAA7RkbAQXyS6CpjS8adq8pKCjA0KFDERISgh9//FHfQ2xT1Go1rly5wl2nKiwshEajgb+/Pw4dOoSOHTvqNbRqa2u5Q2E1NTXo0KEDdyhMHw0wEhMT0aNHj1ZTRlGpVGLBggVITU2FWCzW6lzUFjy+35uXl4fw8HAUFRXh7Nmz6NGjB8rLy3H48GF8+umneOONN+Dg4IBffvkFmZmZvFq2f9lQIL8Emtr4gp1JFRYWIiQkBK+99hr27Nlj9L3J1uzatWsYPXo0BgwYgKqqKty5cwdDhw5FWFgYQkND4erqqvcGGGw4s9Wq2H3nljbAqKysRFJSEnr27Inu3bvraMT6pVQq8c477yAtLa3Nh3FycjLs7e3h5uaGvLw8zJs3D5mZmbh06RK6deuGyspKnDlzBps3b4atrS2+//579OzZk642GREFMtFSUFCAYcOGISAgAP/3f/9HS1YtcPv2bQwePBhr167FihUrwDAMsrOzub7O169fx8CBA7nuVD169NBrOCsUCq0WhpaWls1uYch2o3J3d281MyqlUol58+bhzp07EIvFeOWVV4w9JJ1qGMZbtmzB1q1b8emnn2L8+PGwt7fH/fv3MXfuXNy/fx+XLl3S+r6xB7tomdq4KJAJp6CgACEhIejevTv27t2r9YPZ1n55GYJarca5c+cwfPjwJ/6MYRgUFBQgIiICIpEI8fHx6N+/P4RCIYRCITw8PPQ6S3m8hWHDYhkODg7PfO6ysjLcunWrVXWjUigUmDdvHrKysiAWi5t0Srm12r59O1auXImdO3di9OjRWqVYHzx4gPDwcBQXF+Ps2bNaoUxXm4yPAplw9uzZg3nz5jX6Z/TPRH8YhsHDhw8RFRUFkUiEuLg4dOnShbtOFRgYqNdw1mg0ePjwIdcAg2EYODs7w9nZGR07dtR6YyaRSJCSkoIBAwa0mjdpCoUCc+bMwb179yAWi9tUF63HFRcXIzQ0FAsXLsTChQtRVVWFsrIyxMTEoHPnzpg4cSKKioowfPhwODk54fz58xTCPEKBTAjP1NTU4NSpUxCJRDh16hRsbGy461RDhgzRS+tCFsMwqKqq4k5sKxQK7sS2RqNBRkZGq2oNKZfLMXv2bOTl5SEuLg7Ozs7GHpJelZWVQSgUYubMmQgMDMTevXuRmJjIXYFavHgx/v73vyM3Nxe2trZwdHQ09pBJAxTIhPCYTCaDWCxGREQEoqKioFKpMHbsWISFhWH48OF6rXPNMAxqa2shkUhQWFgImUwGW1tbdOnSBS4uLnptW6kLbBjn5+fj999/b3Nh3NjhK4ZhMHXqVGRlZeHWrVt45513MHr0aISEhOCdd95B3759tW5c0AEufqFAJqSVUKlUuHjxInfXuby8HCNGjIBQKMTo0aNha2url+XHBw8eIDMzEx4eHpDL5SgtLUVVVRXs7Oy4fWcrKyudP29LyOVyzJw5E0VFRYiNjYWTk5Oxh6RTDYP0ypUrqK2thVqtxujRowEAly9fhlwux7Bhw7i/M3bsWPj5+eGrr76i/WKeokAmvLZt2zauUpGPjw+2bNmCgQMHGntYRqfRaJCYmMid2L579y6GDRuGsLAwjBs3Ds7Ozjr5hZuXl4e7d+/C19cXHTp04B5ng5k9sW1tbc2Fs7EbYMhkMsycORMlJSWIjY1Fx44djTYWffvyyy+xdetW2NvbIzs7GyNGjMDf//53jBgxAsD/TtavXLkSFy5cwI0bN9rcm5O2hAKZ8NahQ4cwe/Zs7NixA8HBwdi0aRN+++033Llzp9XsYRoCwzDIyMiASCSCSCRCUlISBg8ejNDQUAiFQnTt2rVZAXn//n3k5OTA398f9vb2T/04tgFGaWkp1yGIvU7l4OBg0HCWyWSYPn06ysrKEBsb26b3SH/77TcsWrQIR44cQf/+/VFRUYEFCxbA2toaH330Ed544w3s2bMH+/bt45pLuLq60tUmHqNAJrwVHByMoKAgbN26FcCjWWHXrl2xbNmyJne7edkwDIO8vDyudeSlS5fg7e3N3XVuStMHtv1kfn4+AgICXqgvsFqt1jqxLRAIuHB2dHTU635lfX09pk+fjoqKCpw+fVprRt8WrVq1Cjdu3EBMTAy3hJ2dnY3JkyfD29sb+/fvh0qlwpEjRzB27FjY2dlBpVIZvJUkaToKZMJLuu4H+zJiGAalpaXcdSqxWIwePXogLCwM48ePh6+vb6OHgrKyslBUVISAgADY2Ng0+/kbNsAoLS2FUqnUaoChy2Cor69HeHg4qqurERMTY7Qw1ldP8cb2fFesWIGEhARcuHABDMNAqVSiXbt2OHHiBKZMmYKbN2/C3d2d+3g6wMV/9N0hvFRWVga1Wv1EAQdXV1cUFxcbaVStC9ue8d1338WJEydQUlKCzz77DLm5uRg7diwGDBiADz/8EPHx8VCpVFCr1VizZg3u3r2LwMDAFoUxAJiYmMDR0RH9+vXD66+/jsDAQFhZWeHevXs4f/48kpKSUFBQAIVC0aLnqaurw9SpU1FTU2P0mXFGRgY0Gg127tyJ27dv47vvvsOOHTvwySefNPtzajQaLoyzs7ORn58PlUqFmTNn4tKlS9i3bx8EAgEX+CYmJujdu7dWQRD2ccJvtHZByEvC3t4eb7/9Nt5++23U19fj999/h0gkwsyZMwEAtra2qKqqwrRp01pc5/pxAoEAdnZ2sLOzQ+/evSGVSiGRSPDgwQOkp6fDwcEBLi4ucHZ2fqGrXFKpFNOmTYNMJsPp06efuddtCKNHj+ZOOgOPasTfuXMH27dvx8aNG5v1OdkgXb16NQ4fPoyysjJ4eHhg4sSJ2Lx5MxYtWgSZTIYJEybA1NQUe/bsgYODA+zs7HTyNRHDoUAmvMT29C0pKdF6vKSkpNVUiOIzS0tLrkxnfX09hEIhrl+/DktLS4wYMQIjR46EUCjEyJEjX2gPuamsra3h5uYGNzc3yGQy7sR2ZmYmbGxstBpgPG3PWyqVYsqUKVAqlTh16pTRw/hpqqqqmnW4rOES87Fjx/Djjz9i+/btkEqlSE9Px5o1azBz5kxs2bIFS5YswZdffgkrKyuYmJjg8uXLsLCwoGXqVoYCmfBSu3btEBAQALFYzO0hazQaiMViLF261LiDa0NUKhVmz56NoqIiZGRkwMXFBX/88QeOHTuGL774AgsXLsQbb7zBXadydHTU+anp9u3bo2vXrujatSuUSiUXzvfv30f79u25cG7YAKO2thZvvfUWNBoNTp06xdvZYHZ2NrZs2dKs2TEbpOfOncPp06exfPly7mehpqYGbm5ueP/99zFq1CikpqYiJSUFpqamePPNN2FlZUUHuFohOtRFeOvQoUOYM2cOdu7ciYEDB2LTpk04fPgwMjIy2nRzAENiGAZbtmzB9OnTn7ifyjAMbt++zd11TklJwZAhQyAUChEWFobOnTvr9UqTWq3mGmCUlpaisLAQsbGxGD16NH7++WeYmpoiOjraIGFsrJ7i5eXlGDRoEIqKivDXv/4VX331FfdnlZWVWLhwIezt7bFr1y6tv0dXm1onCmSicxqNBoBuDpFs3bqVKwzi6+uLzZs3Izg4uMWfl7wYhmFw//597jrVlStX4O/vz4Vz79699RrOGo0GSUlJ+PbbbxEdHQ0AmDx5MqZOnYpRo0bpfM/7ccbsKZ6dnQ2hUAhzc3Ps2rVLqzDOkiVLkJGRAbFY3OzPT/iDApnoRF1dHSoqKtClSxetx6lEX9vDMAyKi4sRGRkJkUiEc+fOwd3dnetO5eXlpZd9y5qaGkyaNAlmZmb47LPPcPr0aYhEIhQUFKCgoOCJU8XGoo+e4llZWZg2bRo8PDywYsUKBAUFoba2FmFhYejevTt2795NP2dtAAUy0Yn9+/dj27ZtmDt3LuRyOYKDg/Haa6898XF0yKRtYRgGlZWViI6ORkREBE6fPg1nZ2cunIODg3USSNXV1Zg0aRIsLCxw/Phx7koWW8SkV69eLX4OXdBnT/H09HRMnToVJSUlCAoKgpWVFbKysnDp0iVYW1vTm982gAKZ6MTUqVMRFRWF0aNHw8LCAidPnsT8+fOxcePGRtsFqtVqmJiY0C+QNkYqlSI2NhYikQjR0dFo164dxo0bB6FQiKFDhzarOEZVVRUmTpwIa2trREVF6X15uiX03VM8MzMT48aNg6urK6ZPn47FixcDeFRIpyWFRwg/UCCTFquqqkJAQAD8/PywZ88eWFtbQyQSYf78+YiPj4eXlxcA4NSpUzAzM+MK37d269evx7Fjx5CRkQFLS0sMHjwYGzZsQN++fY09NF5QKpU4d+4cjh49iqioKNTV1WHMmDEICwvDiBEjmhSsVVVVmDBhAmxtbREZGcnrMDaU27dv45133oGnpyc++ugj9OnTx9hDIjpCa4ekxS5dugRnZ2e899573C9Mf39/9OrVC9euXUNeXh7GjBmDpUuXYsGCBbC3t3/qiVWNRgO1Wq01m+Dre8bz589jyZIluHr1Kn7//XcolUqMHDkSUqnU2EPjBXNzc4wYMQI7duxAfn4+Tpw4gc6dO2PNmjXo3r07wsPD8csvv6CioqLR73FlZSXGjx8Pe3t7HD9+nML4vwYMGIBdu3YhJSUFa9asQXp6urGHRHSEApm02MGDB2FrawtfX1/uMYZhUFVVhZqaGqxZswZlZWX44YcfkJOTg6+//hr79u3DtWvXuI9Xq9Wor6+HiYkJTE1NtZayCwsL4eLiglOnTnGPsSe5jSkmJgZz587FgAED4OPjgz179iAvLw8JCQnGHhrvmJqaYsiQIfjmm2+QmZmJy5cvw9fXF1u3boWbmxuEQiF27dqFoqIiMAyDiooKCIVCODo6IjIy8oWqd70MvLy8sH37dhQXF/PmMBtpOVqyJi1SV1eH/v37o3Pnzrh8+TL3+MmTJyEUCrFv3z4sWbIEJ06cwODBg7lDXe7u7pg+fTrWrl2LhIQEHDlyBBEREWjfvj2mT5+O+fPna/WxTUlJgbu7O9q3b2+ML7NJsrOz4e7ujpSUFHh6ehp7OK0CwzDIzs7mrlP98ccf8PPzQ1FREby8vCASiXj9PTc2uVwOCwsLYw+D6AjNkEmL/PHHH7CwsIBMJkN8fDwA4Pr16/jPf/6DQYMGcTPewYMHcwe5gEeVuNhZ8GeffYb4+Hh89tlnePfdd3Ho0CGsXbsWlZWVAB7dAfXy8kL79u2hVquxatUqLFu27ImxGLPphEajwYoVKzBkyBAK4xcgEAjg7u6Ojz76CJcuXUJubi5CQ0Nha2tLYdwEFMZtCwUyaZFffvkFf/7znzFx4kQsXrwYoaGhCA8Px8OHD7Fz507cuXOHO+TELjMnJyfD3Nwcr776KgDAxsYG/fv3R3h4OJYsWYKIiAiMHz8elpaWKC4uRo8ePXDgwAEAj/arxWIxd51EpVIBAFJTUzFw4ECcPHnS0C8BgEcFGlJTU3Hw4EGjPH9bIBAI0KVLF3z22WdIT0+nMCYvHSp0SppNLpcjJSUFQqEQn3zyCUJCQnDkyBEMGzYMc+bMgZOTEzp37sztqwYEBAB4dDXE0tISPj4+AB5VXPrLX/4CuVyOZcuWISgoiAvrW7duQS6XIyQkBAUFBZg+fToKCwvh6OiIq1evcnedPT09kZ6ezgW0Ie9kLl26FNHR0YiPj+fGTQghL4whpJmuXLnCuLm5MSKR6KkfU1dXx4waNYoZMmQI8/333zNvv/02Y2pqyuzbt49RqVTcxyUkJDDz5s1jhg4dyly+fJlhGIZRKBTM0qVLGS8vL4ZhGEapVDKrV69mXF1dmdmzZzOOjo7MmjVrGIZhmGvXrj3x3BqNRus5dE2j0TBLlixhOnfuzGRmZurteQghLwc61EWarba2FpcuXUJAQACcnJygVCphamr6RCWuoqIibNmyBadPn0b//v0xefJkTJgwAfX19di7dy9mzJgBW1tblJWVYerUqXBxccGePXsglUoxcOBAzJs3D6tWrcL9+/cxd+5c9OvXDzt37oRcLoepqSnS09Ph5+eHAwcOYOrUqY2OVR8VwhYvXowDBw4gMjJS6+6xvb09nQomhLwwWrImzWZjY4NRo0Zx/91YRS4A6NSpE9atW4d169ZBqVRyH5eZmYn9+/cjNzcX8+bNQ7t27dCxY0eu7d61a9dw//59hIeHAwBycnKQmpqK1atXA3i0LG1mZoaIiAgEBQVx5RNramqQlJSEY8eOwcPDAzNmzOBKLbLY96EtWdbevn07ACAkJETr8d27d2Pu3LnN/ryEkJcTHeoiescwDFQqFRiG0QptT09PfPzxx7h69Sr8/f0xZswYyGQyfPDBBwCAEydOwN3dHb1794ZcLseNGzdgbm6ON998E8D/TpiePHkS3t7ecHd3BwC89957CA8PR1ZWFn744Qd4e3vj7NmzWmMSCARcGKvV6mbda2YYptH/URgTQpqDZshE7wQCQaON0k1NTSEUCiEUCqFQKJCQkAAPDw84ODigoqICe/fuxaxZswAA9fX1OHfuHIYOHQoAkMlkaN++Pe7du4e8vDwsWrQIdnZ2+L//+z8cPXoUp0+fxpAhQ2Bubo5JkyZh06ZNCAgIgJ2dHZKSkpCVlYUxY8bA1taW+sYSQniBZsjEqNRqNdRqNdq1a4dBgwZxVYdMTU0RGhqK+fPnAwBsbW2Rm5uLAQMGAAB3JUYkEqFjx47w9/dHVVUVoqOjMXLkSISEhHBBu3z5csTFxUGtVgMAzp49i4ULF2Lbtm2YN28eli9fjpycHMN+4YQQ8hgKZGJUpqamjc5Q7ezs8NNPP6F///7cx02aNAnbt2/HpEmTcOvWLQCPylcGBQWha9eu3N7x2LFjATyaRQPAgwcPYGdnB5VKherqaqSmpoJhGNy9exchISFITU3FrFmzXooa1F9//TUEAgFWrFhh7KHwglwuh6+vLwQCAZKTk409HPKSo0AmvKTRaJ7Y1/38888RGRmJrl274u7duygrK8OZM2fg6+sLBwcHODo6Ij8/H/369QMArh3d0aNHERgYCCsrK9y/fx83btzAwoULsWvXLsyZMwerV69Gdnb2E/vMbc3169exc+dOeHt7G3sovPHRRx+hc+fOxh4GIQAokAlPmZiYaF1TYk9FDxw4EN9//z0mTpwIS0tL/PDDD/jzn//MfUxISAi2bdvGFQa5cuUKoqKiMGXKFFhbWyMxMREKhQLTpk3jPrelpSW6dOmCiooKredqS2prazFjxgzs2rULHTp0MPZweOHUqVOIjY3Fxo0bjT0UQgBQIJNWgj0R3XDmbG1tjffee4+r+GVtbY2PP/4YCQkJCAoKwtSpUzFlyhSMHz8es2fPRm1tLW7cuAEnJycEBgZyn/vOnTsoKSnhqn4ZqsKXIS1ZsgTjxo3jTqi/7EpKSrBgwQLs378fVlZWxh4OIQDolDVpZRqbNTcM0KFDhyIxMRH79u1DRkYGfvrpJy5o09PTkZGRoXVvuKqqCteuXUPnzp25a1NtzcGDB5GYmIjr168beyi8wF5NW7RoEQIDA+lAH+ENCmTSajU2k2UYBh06dMDy5cuf+LPMzEwkJydj1apV3GN5eXlITEzkCpzoo6KXMeXn52P58uX4/fff23yzhpUrV2LDhg3P/Jj09HTExsaipqYG//jHPww0MkKahkpnkjaJbfX4eGg3bEgBPGp08cEHHyAuLg6+vr4GbUphCBEREZg4caLWSXa1Wg2BQAATExOu/GhbUFpaivLy8md+TM+ePTF16lQcP35c6/usVqthamqKGTNmYO/evfoeKiGNokAmLx02dBmGgUgkwrZt2yAWi409LL2oqalBbm6u1mPz5s1Dv3798PHHH7+UvZvz8vJQXV3N/XdhYSFGjRqFI0eOIDg4mDp2EaOhQCbkv9ra7PhpQkJC4Ovri02bNhl7KLyQk5MDNzc3JCUlwdfX19jDIS+xtrNZRkgzsNW7gLZ5upoQ0nrQDJkQQgjhAZohE0IIITxAgUwIIYTwAAUyIYQQwgMUyIQQQggPUCATQgghPECBTAghhPAABTIhhBDCAxTIhBBCCA9QIBNCCCE8QIFMCCGE8AAFMiGEEMIDFMiEEEIID1AgE0IIITxAgUwIIYTwAAUyIYQQwgMUyIQQQggPUCATQgghPECBTAghhPAABTIhhBDCAxTIhBBCCA9QIBNCCCE8QIFMCCGE8AAFMiGEEMIDFMiEEEIID1AgE0IIITxAgUwIIYTwAAUyIYQQwgMUyIQQQggPUCATQgghPECBTAghhPAABTIhhBDCAxTIhBBCCA9QIBNCCCE8QIFMCCGE8AAFMiGEEMIDFMiEEEIID1AgE0IIITxAgUwIIYTwAAUyIYQQwgMUyIQQQggPUCATQgghPECBTAghhPAABTIhhBDCAxTIhBBCCA9QIBNCCCE8QIFMCCGE8AAFMiGEEMIDFMiEEEIID1AgE0IIITxAgUwIIYTwAAUyIYQQwgMUyIQQQggPUCATQgghPECBTAghhPAABTIhhBDCAxTIhBBCCA9QIBNCCCE8QIFMCCGE8AAFMiGEEMIDFMiEEEIID1AgE0IIITxAgUwIIYTwAAUyIYQQwgP/D+0CmG5Z3w5MAAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot as 3dbar\n",
"x, y = np.meshgrid(walk_pos, walk_pos)\n",
"cmap = plt.get_cmap('jet') # Get desired colormap\n",
"max_height = np.max(walk_probs.flatten()) \n",
"min_height = np.min(walk_probs.flatten())\n",
"# scale each z to [0,1], and get their rgb values\n",
"rgba = [cmap((k-min_height)/max_height) if k!=0 else (0,0,0,0) for k in walk_probs.flatten()] \n",
"fig = plt.figure(figsize=(6, 8))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.bar3d(x.flatten(), y.flatten(), np.zeros((2*steps+1)*(2*steps+1)), 1, 1, walk_probs.flatten(), color=rgba)\n",
"ax.set_xlabel(\"position\")\n",
"ax.set_ylabel(\"position\")\n",
"ax.set_zlabel(\"probability\")\n",
"ax.set_box_aspect(aspect=None, zoom=0.8)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Bosonic-fermionic quantum walks\n",
"Moreover, we can select an entangled state as the input state and observe that the output distribution behaves differently with respect to the state statistic."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"bosonic output distribution: {\n",
" |2,0,0,0,0,0,0,0>: 0.007812500000000002\n",
" |0,0,0,2,0,0,0,0>: 0.007812500000000002\n",
" |1,1,0,0,0,0,0,0>: 0.015625000000000003\n",
" |0,0,0,1,0,0,0,1>: 0.015625000000000003\n",
" |0,0,1,1,0,0,0,0>: 0.015625000000000003\n",
" |1,0,1,0,0,0,0,0>: 0.06250000000000001\n",
" |1,0,0,0,1,0,0,0>: 0.015625000000000003\n",
" |1,0,0,0,0,1,0,0>: 0.015625000000000003\n",
" |0,0,1,0,0,1,0,0>: 0.25000000000000006\n",
" |0,0,1,0,0,0,0,1>: 0.015625000000000003\n",
" |0,2,0,0,0,0,0,0>: 0.007812500000000002\n",
" |0,1,1,0,0,0,0,0>: 0.06250000000000001\n",
" |0,0,1,0,0,0,1,0>: 0.015625000000000003\n",
" |0,1,0,0,1,0,0,0>: 0.015625000000000003\n",
" |0,1,0,0,0,1,0,0>: 0.015625000000000003\n",
" |0,0,0,0,2,0,0,0>: 0.007812500000000002\n",
" |0,0,0,1,0,1,0,0>: 0.06250000000000001\n",
" |0,0,2,0,0,0,0,0>: 0.07031250000000001\n",
" |0,0,1,0,1,0,0,0>: 0.06250000000000001\n",
" |0,0,0,1,0,0,1,0>: 0.015625000000000003\n",
" |0,0,0,0,0,0,0,2>: 0.007812500000000002\n",
" |0,0,0,0,0,1,0,1>: 0.06250000000000001\n",
" |0,0,0,0,0,0,1,1>: 0.015625000000000003\n",
" |0,0,0,0,1,1,0,0>: 0.015625000000000003\n",
" |0,0,0,0,0,0,2,0>: 0.007812500000000002\n",
" |0,0,0,0,0,2,0,0>: 0.07031250000000001\n",
" |0,0,0,0,0,1,1,0>: 0.06250000000000001\n",
"}\n",
"fermionic output distribution: {\n",
" |1,0,0,1,0,0,0,0>: 0.015624999999999997\n",
" |0,0,1,1,0,0,0,0>: 0.062499999999999986\n",
" |1,0,1,0,0,0,0,0>: 0.015624999999999997\n",
" |1,0,0,0,0,0,0,1>: 0.015624999999999997\n",
" |0,0,0,1,1,0,0,0>: 0.015624999999999997\n",
" |1,0,0,0,0,1,0,0>: 0.062499999999999986\n",
" |0,0,0,0,1,0,1,0>: 0.015624999999999997\n",
" |1,0,0,0,0,0,1,0>: 0.015624999999999997\n",
" |0,0,1,0,0,1,0,0>: 0.39062500000000006\n",
" |0,0,1,0,0,0,0,1>: 0.062499999999999986\n",
" |0,1,1,0,0,0,0,0>: 0.015624999999999997\n",
" |0,1,0,1,0,0,0,0>: 0.015624999999999997\n",
" |0,0,1,0,0,0,1,0>: 0.062499999999999986\n",
" |0,1,0,0,0,0,0,1>: 0.015624999999999997\n",
" |0,1,0,0,0,1,0,0>: 0.062499999999999986\n",
" |0,0,0,1,0,1,0,0>: 0.015624999999999997\n",
" |0,1,0,0,0,0,1,0>: 0.015624999999999997\n",
" |0,0,1,0,1,0,0,0>: 0.015624999999999997\n",
" |0,0,0,0,1,0,0,1>: 0.015624999999999997\n",
" |0,0,0,0,0,1,0,1>: 0.015624999999999997\n",
" |0,0,0,0,1,1,0,0>: 0.062499999999999986\n",
" |0,0,0,0,0,1,1,0>: 0.015624999999999997\n",
"}\n"
]
}
],
"source": [
"# two entangled input states\n",
"bosonic_state = pcvl.StateVector(\"|0,0,0,{A:1},{A:2},0,0,0>\") + pcvl.StateVector(\"|0,0,0,{A:2},{A:1},0,0,0>\")\n",
"fermionic_state = pcvl.StateVector(\"|0,0,0,{A:1},{A:2},0,0,0>\") - pcvl.StateVector(\"|0,0,0,{A:2},{A:1},0,0,0>\")\n",
"\n",
"\n",
"# select a backend and define the simulator on the circuit\n",
"simulator = Simulator(SLOSBackend())\n",
"simulator.set_circuit(circuit)\n",
"\n",
"bosonic_prob_dist = simulator.probs(bosonic_state)\n",
"fermionic_prob_dist = simulator.probs(fermionic_state)\n",
"\n",
"print(\"bosonic output distribution:\", bosonic_prob_dist)\n",
"print(\"fermionic output distribution:\", fermionic_prob_dist)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# get output modes from the distributions\n",
"bosonic_modes = [get_mode(state) for state, _ in bosonic_prob_dist.items()]\n",
"bosonic_modes = [m if isinstance(m, list) else [m,m] for m in bosonic_modes]\n",
"fermionic_modes = [get_mode(state) for state, _ in fermionic_prob_dist.items()]\n",
"fermionic_modes = [m if isinstance(m, list) else [m,m] for m in fermionic_modes]\n",
"\n",
"# get the probabilities of the modes\n",
"bosonic_probs = np.array([[0]*n]*n, dtype=np.float64)\n",
"for m, (_, prob) in zip(bosonic_modes, bosonic_prob_dist.items()):\n",
" bosonic_probs[m[0], m[1]] = prob\n",
"\n",
"fermionic_probs = np.array([[0]*n]*n, dtype=np.float64)\n",
"for m, (_, prob) in zip(fermionic_modes, fermionic_prob_dist.items()):\n",
" fermionic_probs[m[0], m[1]] = prob\n",
"\n",
"# get the walk positions distributions\n",
"walk_pos = range(-steps, steps+1)\n",
"\n",
"bosonic_walk_probs = np.array([[0]*(2*steps+1)]*(2*steps+1), dtype=np.float64)\n",
"fermionic_walk_probs = np.array([[0]*(2*steps+1)]*(2*steps+1), dtype=np.float64)\n",
"for i in range(n):\n",
" for j in range(n):\n",
" w_i = mode_to_walk_pos_mapping[i]+steps\n",
" w_j = mode_to_walk_pos_mapping[j]+steps\n",
" bosonic_walk_probs[w_i, w_j] += bosonic_probs[i,j]\n",
" fermionic_walk_probs[w_i, w_j] += fermionic_probs[i,j]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot the two distributions as 3dbar subplots\n",
"x, y = np.meshgrid(walk_pos, walk_pos)\n",
"cmap = plt.get_cmap('jet') # Get desired colormap\n",
"bosonic_max_height = np.max(bosonic_walk_probs.flatten())\n",
"bosonic_min_height = np.min(bosonic_walk_probs.flatten())\n",
"fermionic_max_height = np.max(fermionic_walk_probs.flatten())\n",
"fermionic_min_height = np.min(fermionic_walk_probs.flatten())\n",
"# scale each z to [0,1], and get their rgb values\n",
"bosonic_rgba = [cmap((k-bosonic_min_height)/bosonic_max_height) if k!=0 else (0,0,0,0) for k in bosonic_walk_probs.flatten()]\n",
"fermionic_rgba = [cmap((k-fermionic_min_height)/fermionic_max_height) if k!=0 else (0,0,0,0) for k in fermionic_walk_probs.flatten()]\n",
"fig = plt.figure(figsize=(10, 16))\n",
"ax = plt.subplot(1, 2, 1, projection='3d')\n",
"ax.bar3d(x.flatten(), y.flatten(), np.zeros((2*steps+1)*(2*steps+1)), 1, 1, bosonic_walk_probs.flatten(), color=bosonic_rgba)\n",
"ax.set_xlabel(\"position\")\n",
"ax.set_ylabel(\"position\")\n",
"ax.set_zlabel(\"probability\")\n",
"ax.set_box_aspect(aspect=None, zoom=0.8)\n",
"ax.set_title(\"bosonic\")\n",
"ax = plt.subplot(1, 2, 2, projection='3d')\n",
"ax.bar3d(x.flatten(), y.flatten(), np.zeros((2*steps+1)*(2*steps+1)), 1, 1, fermionic_walk_probs.flatten(), color=fermionic_rgba)\n",
"ax.set_xlabel(\"position\")\n",
"ax.set_ylabel(\"position\")\n",
"ax.set_zlabel(\"probability\")\n",
"ax.set_box_aspect(aspect=None, zoom=0.8)\n",
"ax.set_title(\"fermionic\")\n",
"plt.show()"
]
}
],
"metadata": {
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 2
}