{
"cells": [
{
"cell_type": "markdown",
"id": "5cbc8640",
"metadata": {},
"source": [
"### IRREVERSIBLE unimolecular reaction `A -> B`,\n",
"with 1st-order kinetics.\n",
"\n",
"**Adaptive variable time steps** \n",
"compared with **exact analytical solution**"
]
},
{
"cell_type": "markdown",
"id": "b3a6abc4-9625-4eed-9654-8d631fb54b70",
"metadata": {},
"source": [
"### TAGS : \"uniform compartment\", \"chemistry\", \"numerical\", \"quick-start\", \"basic\", \"under-the-hood\""
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6e9d0902-6fc9-4692-ac39-0651d08902ca",
"metadata": {},
"outputs": [],
"source": [
"LAST_REVISED = \"Aug. 29, 2025\"\n",
"LIFE123_VERSION = \"1.0.0rc5\" # Library version this experiment is based on"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1e0ae9a9-9d0c-4edf-a5f2-1c589419e6cf",
"metadata": {},
"outputs": [],
"source": [
"#import set_path # Using MyBinder? Uncomment this before running the next cell!"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a29db1c7",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"#import sys\n",
"#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n",
"# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n",
"\n",
"import numpy as np\n",
"\n",
"from life123 import check_version, UniformCompartment, ReactionKinetics, GraphicLog, PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "af15ecf0-e083-4fef-b68e-abe794dcc86e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"OK\n"
]
}
],
"source": [
"check_version(LIFE123_VERSION) # To check compatibility"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "34d1cefc-f644-410a-9fe4-5204964742ac",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "10c710ac",
"metadata": {},
"source": [
"# PART 1 - VARIABLE TIME STEPS (Numerical Approximation to Solution)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "78077d8c",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 1\n",
"0: A <-> B (Elementary Unimolecular Irreversible reaction) (kF = 3 / Temp = 25 C)\n",
"Chemicals involved in the above reactions: ['A', 'B']\n"
]
}
],
"source": [
"# Instantiate the simulator and specify the chemicals\n",
"# Here we use the \"fast\" preset for the variable steps, trying to push the envelope on speed\n",
"uc = UniformCompartment(preset=\"fast\")\n",
"\n",
"# Reaction A <-> B , with 1st-order kinetics in both directions\n",
"uc.add_reaction(reactants=\"A\", products=\"B\", \n",
" kF=3., reversible=False) \n",
"\n",
"uc.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9fc3948d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 50.0\n",
" Species 1 (B). Conc: 10.0\n",
"Chemicals involved in reactions: ['B', 'A']\n"
]
}
],
"source": [
"# Set the initial concentrations of all the chemicals\n",
"uc.set_conc({\"A\": 50., \"B\": 10.})\n",
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0cc938cc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.0 | \n",
" 50.0 | \n",
" 10.0 | \n",
" | \n",
" Set concentration | \n",
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\n",
" \n",
"
\n",
"
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],
"text/plain": [
" SYSTEM TIME A B step caption\n",
"0 0.0 50.0 10.0 Set concentration"
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uc.get_history()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "54c9beb7-3c05-4088-aca1-6ad5e9ca606a",
"metadata": {},
"outputs": [],
"source": [
"uc.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
" # Useful for insight into the inner workings of the simulation"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "60174ac9-c056-4e2c-a1bf-f68922e471d4",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "987af2c5",
"metadata": {
"tags": []
},
"source": [
"## Run the reaction \n",
"#### Passing True (default) to _variable_steps_ automatically adjusts up or down the time steps"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "43735178-313b-48cf-a583-5181238feac3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"46 total variable step(s) taken in 0.243 sec\n",
"Number of step re-do's because of elective soft aborts: 5\n",
"Norm usage: {'norm_A': 24, 'norm_B': 10, 'norm_C': 10, 'norm_D': 10}\n",
"System Time is now: 1.5586\n"
]
}
],
"source": [
"uc.single_compartment_react(initial_step=0.1, target_end_time=1.5,\n",
" variable_steps=True)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "2d5df59c",
"metadata": {},
"outputs": [
{
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"33 0.776262 4.279344 55.720656 33 \n",
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"38 1.077181 1.581200 58.418800 38 \n",
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"41 1.257732 0.870067 59.129933 41 \n",
"42 1.317915 0.712975 59.287025 42 \n",
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"44 1.438283 0.478760 59.521240 44 \n",
"45 1.498466 0.392320 59.607680 45 \n",
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},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"history = uc.get_history() # The system's history, saved during the run of single_compartment_react()\n",
"history"
]
},
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"cell_type": "code",
"execution_count": 13,
"id": "5d271f6b-a727-4609-9399-342c1a98e7b3",
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EXKcQaDFCAQeuNUEw6uhPr1M1s7+Sd1R835LWPm69QZO/QVokfRQEmoCaXfKuviGsEgxCFQjUAyGt7QWhCCPh6AhkBnoDb17+hZ/8x+/xiOqBgN6kPpQVBf4GDeq2bmTiK9/z/AmtOhjdx2n1igJ/97NyL6he+UK55/Vsyvnuyz8qLcMNtGeaX4MZoUBvcGRmQqCcICm9l0e6L+XsOnZoQ0MG9/NqYka/V+T2wEUFpV8Cf+9rtSF/HMzUlV5/ZKYOQxUKjN7b/vpO5dNjve8WI6tQ/LV1o0KBmQmP1jXxMYa6D1MzCqb+1XnplVOdl1Z5/PVrynyMpDXTL5jZ3y7b5fcaD7Jwo/c+j2OmLHrt0Y6tB/5EdWU/7+87VT2mNdLOjE62jbYHHk9vbG3mvrFSKDBadrN9vxlxKRzjQuQBAkYJtCihQP7S5wMyeZCgdGqjVvx5ByZ7Idd6oqxcDqichGkt91Y7cDHTOcodppaDOK2TENSTWSPLjo02GDleICEgkJBgND/ll7jZJzL8yyPYFQTq8vlbURBoIm70WtXxZDU/VN8HStFFz8FYIEdV6jakJY4o8wlmuSK/fi3OcvvX2/ajfmrBy8qP1ZKXcC9btc5rOamZtmmHUKB1PyufICtPPbDynjeSr8zfH1N/kyetJ116T7/8TQi1/JzI94P6SX0k+1K53pTt3axwKPelel6/tVYmaIk+ehysEArM1GGoQoGyHwjUDs1MzpRxzbQZo4KA8rtR7TxSbrtajhz5UaDy0ZJa16OVVquf1Lsmo2Mc9VZGuSzq1XJafYTRPtVIWjOTczmu8t7R2nagvBb+f63jE/kKDfWKCDNlMdMWrbgn/fWRSh5G+1Ij7cyMUKDVN3JGvD3KJ4Dxv7XajnL5v5Hxj9VCgZGym+377RiHBzu2RDoQMEOgxQkFHI7cIao7U/5FoQzqAZp6nyD/spHP+VUPAOQOVWlP62hF+XO5LIFUfaU9f+fVB+uR3UjjMToQdupyfCPXqI7jb9+skSXGweRplVAg5613Dcp2aWYgoN6fxyfyXFhT7zk0Y1M5SZDLzQdv3PEUD2qxSG8/oXKCoeX4MtCSSOXAUtlPmL0WvXqXB6DKz9Vl0ooT6j1vJF+jTM140lfu05YFn0BPjtV7u/m18wGm+jx0dTsMd1+q1debWYKtN0ELNOFRCwt6HKyYlCi/N/n//dWhFUKBcgKhvoeM3LuBnt6ZaTNWCAVa/Zp8XUa2WGg5olOn07smOR8tXwnK7y6lIKscC2n5UAilTw2UNpjJuZqP3qoovQccge5BPd8PRu5zO1YU6NUp7yPVxyOq713+t15fGqidmf3+09vDr3UcLt/2oRwP86OX1SeQ6H2fWi0U8HyMlN1M329mlVkw40WkAQG7CDRLocAuWLALAiAQGQLY2xcZ7sgVBNxKwIwPBrdeo5XlNrPU28p8YQsEmjsBoytumjsHXJ87CUAocGe9odQg0CwJKLcNyBeIAWyzrGpcFAjYTqA5rWqzGxb6WbsJw35LJYB+qKXWfPO4bggFzaMecRUg0CwI6C17N7I8t1kAwEWAAAhYRkDuT6zyVWNZwRxoCEKBAysFRXI1AeVWP4xhXF2VLbrwEApadPXj4kEABEAABEAABEAABEAABEAABEDAmwCEArQIEAABEAABEAABEAABEAABEAABEAABDwEIBWgMIAACIAACIAACIAACIAACIAACIAACEArQBkAABEAABEAABEAABEAABEAABEAABHwJYEUBWgUIgAAIgAAIgAAIgAAIgAAIgAAIgABWFKANgAAIgAAIgAAIgAAIgAAIgAAIgAAIYEUB2gAIgAAIgAAIgAAIgAAIgAAIgAAIgIAfAth6gOYBAiAAAiAAAiAAAiAAAiAAAiAAAiDgIQChAI0BBEAABEAABEAABEAABEAABEAABEAAQgHaAAiAAAiAAAiAAAiAAAiAAAiAAAiAgC8BrChAqwABEAABEAABEAABEAABEAABEAABEMCKArQBEAABEAABEAABEAABEAABEAABEAABrChAGwABEAABEAABEAABEAABEAABEAABEPBDAFsP0DxAAARAAARAAARAAARAAARAAARAAAQ8BCAUoDGAAAiAAAiAAAiAAAiAAAiAAAiAAAhAKEAbAAEQAAEQAAEQAAEQAAEQAAEQAAEQ8CWAFQVoFSAAAiAAAiAAAiAAAiAAAiAAAiAAAlhRgDYAAiAAAiAAAiAAAiAAAiAAAiAAAiCAFQVoAyAAAiAAAiAAAiAAAiAAAiAAAiAAAn4IYOsBmgcIgAAIgAAIgAAIgAAIgAAIgAAIgICHAIQCNAYQAAEQAAEQAAEQAAEQAAEQAAEQAAEIBWgDIAACIAACIAACIAACIAACIAACIAACvgSwogCtAgRAAARAAARAAARAAARAAARAAARAACsK0AZAAARAAARAAARAAARAAARAAARAAASwogBtAARAAARAAARAAARAAARAAARAAARAwA8BbD1A8wABEAABEAABEAABEAABEAABEAABEPAQgFCAxgACIAACIAACIAACIAACIAACIAACIAChAG0ABEAABEAABEAABEAABEAABEAABEDAlwBWFKBVgAAIgAAIgAAIgAAIgAAIgAAIgAAIYEUB2gAIgAAIgAAIgAAIgAAIgAAIgAAIgABWFKANgAAIgAAIgAAIgAAIgAAIgAAIgAAI+CGArQdoHiAAAiAAAiAAAiAAAiAAAiAAAiAAAh4CEArQGEAABEAABEAABEAABEAABEAABEAABCAUoA2AAAiAAAiAAAiAAAiAAAiAAAiAAAj4EsCKArQKEAABEAABEAABEAABEAABEAABEAABrChAGwABEAABEAABEAABEAABEAABEAABEMCKArQBEAABEAABEAABEAABEAABEAABEAABPwSw9QDNAwRAAARAAARAAARAAARAAARAAARAwEMAQgEaAwiAAAiAAAiAAAiAAAiAAAiAAAiAAIQCtAEQAAEQAAEQAAEQAAEQAAEQAAEQAAFfAlhRgFYBAiAAAiAAAiAAAiAAAiAAAiAAAiCAFQVoAyAAAiAAAiAAAiAAAiAAAiAAAiAAAlhRgDYAAiAAAiAAAiAAAiAAAiAAAiAAAiDghwC2HqB5gAAIgAAIgAAIgAAIgAAIgAAIgAAIeAhAKEBjAAEQAAEQAAEQAAEQAAEQAAEQAAEQgFCANgACIAACIAACIAACIAACIAACIAACIOBLACsK0CpAAARAAARAAARAAARAAARAAARAAASwosDKNlBSXkMlFbVWmoQtGwmkJMZSbEwUFZXV2JgLTFtNoE1mIhWWVFFtXYPVpmHPJgLxsdGUnhJHBUVVNuUAs3YQaJUWT+VVdVRZXWeHedi0gUB0FFGbrCQ6XFhhg3WYtItAWnIcUUMDxpB2AbbJbvtW7F47UcGrDsEGAh2yk2ywCpPBEMCKgmCoqdJAKLAAYhhNQCgII2wLs4JQYCHMMJmCUBAm0BZnA6HAYqBhMAehIAyQbcgCQoENUMNgEkKBvZAhFNjL14x1CAVmaOnEhVBgAcQwmoBQEEbYFmYFocBCmGEyBaEgTKAtzgZCgcVAw2AOQkEYINuQBYQCG6CGwSSEAnshQyiwl68Z6xAKGmnN/+hLeuL5t6W/clpl0KpFL3g43jvzRVq2ap30d98eXWjhrJmezx5//HG674FHPMvGPvtwAQ0cfD51yO3kVQ+/7NhK+/fuposvG+15/1D+flq/djWNHjvR815pSTEtXvQOTbzpNs97DWxt0+yXnqVpdz6gWbe7d26jPbt30LDLx3h9fvTIIVrz9Qq6atwkr/erKito4dzXaPK0u3zszZn1PN0w9Q6Ki4/3+mzRwjdp6CUjKLt1W9329c1/vqDWbdpRzz79feJoXasy0oK3ZtGovAmUlp7hk3bdd6spJjqaBp59vs9nRScL6YtPF9H4G6cFbPcy22nTZ+huPTiwbw9t2riORo4Zp2tv04bvqayslM4dcnHAPOUIxwuO0soVS+iaCVMCplm9chm1ymlDvfsOCBiXt4upt91H0YyP2VBRXkYfLJhDN958p+GkO7dtpvwD++iiS68wnGbl8s8ot1Nn6tajj+E0WhG5ULD4s6WUnJJG/QYMMm1r395dtHXzRhox+hrTaQMl2L71Jzpy+CD9ht0joQR/92YodvXSmmlrZvKX+4Iz+g+M2NYDq9qdmetWx/1q2WI6tXNXOr17r1DMhJR2+ZIPqVvPvtT5tG6G7VgtFHzx6QfUi30vdOrS1XAZrI645ON3qf+Zgym3Y2erTRu2pzc+MGzAT0SjQsHH789l312XUNt2HazINigbRsYTQRk2kei9ebNp+BV5lJmVbSKVtVHfnfsqXT1uAmVlZkVs68E7c16mMdfeSKmpadZenAlr8954icaOn8y+21NNpLI26luv/oOum3wrJSQkGjJsh1CgN/42VCCLIoUyprSoCPTqi0/TzJlN8yyr7MJOcAQgFDBuz7y8gOYs/Jy2rJzjQ5ELCK+89YlHOLhu+uM0aEAPeuD2CVJcCAVNyCAU6N+EEAogFBjpoiEUGKFkLA6EAsEJQoHgAKFAcIBQIDhAKBAcIBQIDhAKBAcIBcbGFy0pFoQCVtt9LppCS+c9RZ1yfZ+Wq4UBtXAAoaDpdoFQoN91QCiAUGDkiwVCgRFKxuJAKBCcIBQIDhAKBAcIBYIDhALBAUKB4AChQHCAUGBsfNGSYrV4oWD12k30xydfo4LCIk+9XzZ0ED33+Azp76FX30O3TR5DE/OGSX/z+NMf/JvX6gP4KHDXLQMfBe6qL7m08FHgvnqDjwL31RkvsdVbD9xJwV2lNrr1wF1X1fxLCx8F7qxjO7YeuJOEPaWGjwJ7uAZjtcULBbJvAuW2A77CYMp1I6TtBfz/j/5uko9QoFyBwI+QwjFSwTS/yKSJj4tmPg+iqIId/4XgHgJ8QFVWWUv19TiPyC21xu+zpIQYKsXxsRGvMu7rJiqKnaFnIHAxtbq2nmrYD4I7CPCqTUuOp+KyancUGKWUCCTGx0jHI1bW4F5zU5PISImnonJ2r2E4Yku1ZaZ6+0mzJRMNo3wVeYd22Z6HxeHK1+p8+Jb6T5ev8fK3F2weEApUPgg4SO68kAe+qsDIigIMqIJtfpFJFxcTzQbMJA2EEdxDIIkNqKpq6gg6gXvqjAsFcbHREFIdUGV17Mbh9WEkJDAxtbaugXgaBHcQ4DWblBBL5VW17igwSikR4P0jDxDl7GkQ9Q31bMwgfuoa+Pih8f/1Tf+vV76v8/96RXxuhz9wqqiqoVpFfC87qvhN5VCUQbM8DayM2nHU16Auk9Z1Ntni/bme3UBl4sx04ij4misPqw+d8jx8waP052GP29IglM7p5QyUq8gjJRTsyz9CI294yOvBdCgAIBSEQk+VVmsrgVIogI8CAcyIl2L4KNBvmPBRAB8FRrot+CgwQslYHPgoEJzgo0BwgI8CwQE+CgQHJ/koSEpNopNllWzSyVbMsQlZbX2tNAGt47/ZTx17X3qP/1/6m0+yGt9jnzXFE2n5RFZ6T+Mz/rmcB4+TuCGKintVUX2cagJN3pNDaRLIHp8rJ6sNUjn4+/JkXDmZZLFVE3Tpb/aSJ4hSelbWkQWX0bKsr6iCyr0m9Sw3kV/jhFKK78mLfaacaLJP+OeVtZXGviBUsR6mh+l59qpkr0iFR+gRepa9qtkrUuExeoyeYC9eT5EKf6I/2XLqAV8hrj7Vjl8jn+fd9duracjgftL/saLAu+Zb/IoCjoOvGhg9/Dxpq4Gs6sx6+n6p0eDUA9FgIBQ03Tg4HhHHI6q/QHE8ojcRHI8oeOB4RMEBxyMKDjge0fh4wspJSkVtBdXUs+lXbRVV19dQdV0V/feTz6n7+f0pNjVB+pt/XsU+r2n8vLoxvvibpa1nn7HfVeyH/+Z/S+/r/F3VGJ+nF3Z53Mb8G/+eXjed5rJXIXtFKob7z1AAACAASURBVNxH99Fr7FXMXpEKv6ff0yvsVcpeVofoqGhq+okR/2evmOgYtrJUfBYTFUPTKm6md5LmU21MnXd8HpvHYfH5b56G/Y8S4mKpju1elf5u/EyyzGzJ+Ul5sJechyc9j99oVxm/27ZOtLfHIYqKjZLK5ImvsOllv7E8SvuSXbk80vXxvBrLoLwG6f1GNor4+5f8TJ1H9qWYmBjVNTddl8d+o13fa27i2nQNGvXQyF5ZDzz+7H89a7lQwB8A/7BpZ8Cl+LJQwNvhslXrpObYt0cXWjjL+7hGHm/z9j2e5qrcji7bOHj4uCeObIPPN2WfeMqVDNyQequ7/J7ynpDzUdqRP1duoceKAqt7ksYKks0qfRLw95RLVdQNBqceNFUGVhToN0ysKMCKAiPdFlYUGKFkLA5WFAhOWFEgOGBFgeBg14qCkupiMZFmE2JpIs0nxdKEWp5Yi4k6nzgf/OYXSu6dRfXJDZ6JuzyR50/SKxsn9vLEXdgVE3V5cm5k4u7v6fIMmkEL2KuAvSIV7qa7PUJBYmwSxUbFUmx0LJugsd9sIif99vzN3298T/EZTyPH4xM2ns47jbDB3+cTPOVn/P+ZPyVRRe86ikponAQrJr3SJFg5SZUmuE0TX/UEzye+YpLO7ajjiwl1DP24+L/Ub/g5lJiS3DTJbpzIek3ENSa+Hpt8+t44cU6MTTRdpTj1QCBrrqceKH3P+WscsgCgnAeq06pXHah93ck25AfO8gNonq880Vc/lOafKYUC+XPZXx7/nOfDA3euz4WCVYte8FwKz5MHWdCAUGC6C7A3AU49sJev1dZx6oHVRMNjD6cehIezlbng1AMraYbPFk49CB/rYHIqryljT7arxA9bal1VV8km4FWUnEx08ERR43tsos4m5vyzysZ4fHLN4xuabPMn7NKT9prGJ+mNE3XpybgQAng53BD4xDEuOp7iYuIpofF3fEwCxbO/43X+TmCf8/j8cx6Pp0+KS2YT52j2N/uM/Z0Qy3/HSX9L8XT+lmzJ+XNbkt0E4uXCqQduaEG+ZcSpB/bWm5WnHmhNyvVKr7X1QLkdXT4pTzlJ57aU/uy0bChXrst5q33gKYUCPtFft3G7z0oGvXKrxQoIBfa2T9PWIRSYRhbRBBAKIoo/6MwhFASNLmIJIRREDH1IGUMoMI+vrJotnK4pIf67rIb/n/2uZn+zybT0Pvtdzt7jy+D55J0/LVdO9PmTd/4EXPqMP41vnOTziT2f6POJObfr1JAclyImzIrJtzzZ5pNpebIsfd44UZYm7oqJs/yZmNA3TtQb4/OJtpiQs4m5NCH3/VvkIT7nE3deJqcHCAVOryHt8kEosLfenCYU8G0E/Gk9n4DPWfi55sXLT//NCAXytnduUCkUGPGVwOOrg7z9AEKBve3TtHUIBaaRRTQBhIKI4g86cwgFQaOLWEIIBRFDH1LGLUEoKKo6KU28pUm9NLlvnNQ3Tu753+U15cSX1Is44nPveFwMEDbCGfiT6IQY9sN+8wkx/z9/LzUhiS0M55Ny/nmC9DmfcEu/+d/sff5UnC9DNzrZVj5Vl56kK57Kp8Wnh/Oym2VeEArcWa0QCuytNyuFAvUk3F/J9VYUKIWCQMcO2i0UyE741dsSnnj+bYJQYG+7DMo6fBQ0YYOPAv0mBB8F8FFgpIOBjwIjlIzFgY8Cwam5+CgorCgQT+mlJ/XaT+350/qSqiIpHn96zwUA/jSfL5EfcvI8+i76e9pe/3PQntH9tTy+xzw1Po1S2FPslLg09v9U9lv8yO+3351DtR2jKD5LMclvnPQn8qfl7Em4LABIE3vlJJ8vU/czMecnX7bJSqLDhRV+bxC7fBQYuytFLCPOkc3YCyauk049yMrMopKKyBxr+c6cl2nMtTdSampaMBgtSTPvjZdo7PjJlJySaom9YIzAR4Gg1lx9FPDJ++FjhZrODPnEmwe9Uw/41gNZKJAn6Urnher2ZoVQoMxTbV9rtQC2HgRz14cpDYSCJtAQCvQbHYQCCAVGuiQIBUYoGYsDoUBwipRQwJ/EF7NJe3F1Ef208ltKOoU9fW4VrfkEn0/k+YSeT+ylCX7jE3z+/smqE8YqPECsyTSZVrPXbvbiIZVN5qVJPZvcp7LJPJ+E86ft0vt8kt840eef8Tg8Lv+MT/r5knb+frIkAqRSenyGoTLi1AOBCUKB4PDu3Ffp6nETCEIBhALeHubMep5umHoHxcXHG+pP7IjUXIUC2U+B+nhEeSuB7Hgw0IoCzpz7FuBB6aeA2zmlfWvJ0aAVQoFcXqVTRdmZIc9buXpALhM/TQErCuy4K0K0CaGgCSCEAv3GBKEAQoGRrgZCgRFKxuJAKBCcghEKMlJjKL/oGB0tKZSW3hezZfrFjb9LqoqpiE3+S9hPERMC+BN8LgYoP+d/8/PP5XA9XU/r2GsHewUT+L5z6ek8m5SrJ/jy+9KTe9WkXprQNwoB277eQD3P6E+nde4hCQKRCBAKBHUIBYIDhALBASsKBAcIBYLDqy8+bfnxiHJ/rz7WkL+vdbThc4/P8HxFaD3d17IjT9KtEAp45srTEuTCyGVVnsbHP+PbELjvBAgFkfhmN5AnfBQYgOSgKPBR4KDKMFEU+CgwAcshUeGjIHIVwSf4x8qPEl+yf7KysHFyzyb5bNLPJ/tics9++ESfCwGN73EBwN+xckaviE/GM9iT9jT20yopm5Jikz1P8OWn83pP7ZUTfP7UPpjjzoyWs7nEM7r1oLlcb3O5DvgocGdNwkeBvfVmtY8Ce0vbvK1HNbDQvC/R/quDUGA/YytzgFBgJc3w2YJQED7WVuUEocAqksLOkbJDVFBxTJr8Hy0/QsfLj9GxiqPSe8fZzwkmCBwuPUgHSw+EnHFWYitpOX56QiZlsJ809mSe/z+98T3+WUaCEAIyE7Okp/ny562SckLOHwbMEYBQYI6XU2JDKHBKTZgrB4QCc7zMxoZQYJaYffEhFFjAFkKBBRDDaAJCQRhhW5gVhAILYYbJFIQC/6D5vvxjZeypf2WB9PSfT/oLFZP/wnIhCHAh4ETlcVO1xp3r5SS1prYp7dkEPkP8xImJf1oCn+TzyT/7m0305c/5pJ+vAuiY3YrKq+qosrrOVJ6IHDkCEAoixz6UnCEUhEIvcmkhFNjLHkKBvXzNWIdQYIaWRlz4KGiCAh8F+o0JPgrgo8BIVwMfBUYoGYsTCR8FfF8+f7LPJ/YFbOK/57ufqSqjho6nnhBP/tl7/HMuCvA4lcxLv9EQHRXNnty3otZJbSQBIDu5NbVObkPZ7P/87xz2/5zGz/jffFk/D8H4KLD6eMQvPv2AevXpT526dDV6uZbHW/Lxu9T/zMGU27Gz5baNGoSPAkEKPgoEB/goEBzgo0BwgI8CwcFOHwVG+2rEayIAoSDE1gChoAkghAL9xgShAEKBka4GQoERSsbiWCUUcM/78sReEgEan/x7BAG2IkASBhqf+iud+F1L19I29trMXlpBfuovJv5tpIm/9H/2o/4/f4+LBWYDhAJBDEKB4IDjEQUHHI8oOOB4RMEBxyMKDs311AOz35uI30QAQkGIrQFCQRNACAX6jQlCAYQCI10NhAIjlIzF0RMK+ESe7/GXJ/d84i/v8ZcEAfmpf+Pe/4qacmMZslhR7MWf+vPJPp/oDyo+k+qyiFLap4sn/41CgPSbrQjgHvztDhAKBGEIBYIDhALBAUKB4AChQHCAUCA4QCiw+xvZffYhFFhQZ/BRYAHEMJqAj4IwwrYwK/gosBBmmEyF20fBvuK9dLDkAOWX7qdDpflsf/9hIQgonvrzlQBmQ/vUXLHkv3Gpfzu27587+5OW/3u2ArQh/n5zCFZvPWgOTJx+DfBR4PQa0i4ffBS4s97go8DeeoOPAnv5mrEOocAMLZ24EAosgBhGExAKwgjbwqwgFFgIM0ymrBQKDrKJP5/8HyzZL3n19/wwYeBgGRMFyg4bvqrMhCzpCX+blLbsd45Y6s8m/Hz5v7TfX/5JaSM5+2tpAUKB+2ocQoH76oyXGEKBO+sNQoG99QahwF6+ZqxDKDBDC0KBBbQibwJCQeTrIJgSQCgIhlpk0xgVCvhyfzHxZ0IA+82PAdxf8qskDOQzYYD/GAltk9tRh7RTqEPqKdQxvbPH2V/blHbUKjFbEgLap3QwYqpFx4FQ4L7qh1DgvjqDUODOOuOlhlBgb91BKLCXrxnrEArM0NKICx8FTVDgo0C/McFHAXwUGOlqmqOPgobYctqUv0sIAY1P/6XfkjAgtghU1lYGxNOKPfnnAkAHtg1A+s0EgdzUjp7/8+0BMVExHjtWOTMMWDA/Eb5atphO7dyVTu/eKxQzIaWFjwKBDz4KBAf4KBAc4KNAcICPAsEBPgoEB/goCOnrtlkmhlAQYrVCKGgCCKFAvzFBKIBQYKSrcatQsL/4V9p9ciftKdpFvxbvoaidNfRr/a/0Te3XVFZdGvDSuVM/eSUA/30KEwDapXag3LRO1CEll07L6hbQhjoChAJBBEKB4AChQHCAUCA4QCgQHCAUCA4QCgQHCAWmhxqWJBh69T1UUFhEW1bOscSelUYgFIRIE0JBE0AIBfqNCUIBhAIjXY2ThYLDbDvA3pO7aNfJHfRr0R7aUfizJArw3+owhsbQAfb6gb146JJ5Onv630ma/J/CJv/8d0f+m20D4MKAHX4AIBSIWoFQIDhAKBAcIBQIDhAKBAcIBYIDhALBAUKBejRj/9+r126if85eJGWUN3IITcwbZn+mJnKAUGACll5UODO0AGIYTcBHQRhhW5gVfBRYCFPH1InK42xlwC/Sz96i3UIUOLmbdpzYxrYHVOgWgG8LOC2zK3XJYMvs2dP/zhmnU+f0LnRqVic6LacDFRRV2V945GAZAfgosAxl2AzBR0HYUFuaEZwZWoozbMbgo8Be1C3JR8EzLy/wwFy3cTstnDXTXrgmrUMoMAlMKzqEAgsghtEEhIIwwrYwKwgF1sCsqCmXBAAuBuxpFAV2Fwlx4GRloW4m/Kk/XxnAxQC+FYD//7TMbtQ1qzvxrQNawagzQ2uuDFasIgChwCqS4bMDoSB8rK3MCUKBlTTDZwtCgb2s7RIKVpSUUmV9vb2F17A+OiNdN0++7eDtfz4ifT7yhodo6bynqFNu27CXUS9DCAUWVAWEAgsghtEEhIIwwrYwKwgFxmFW11UzfwFi8s/FAO47QPIhcOIXOlKuf4xgYmwSEwK4AMBWB7AfeZUA/53DTgwwGyAUmCXmjPgQCpxRD2ZKAaHADC3nxIVQ4Jy6MFMSCAVmaJmPa5dQkLt5Kx2sqTVfoBBTHOzbm9rHxfpYkbcdyKsIrpv+uOO2H0AoCLHy4aOgCSB8FOg3JvgogI8CI12NGR8FdQ11kq8AeVWAUhjgJwrUN2ir5nHRcdSJbQvgKwIGlg6gjFZZ1K13X0kU4CcHRLFXqEHuC87oP5DSU+IisvUAPgpELcJHgeAAHwWCA3wUCA7wUSA4wEeB4AAfBYJDc/dRMOXX/VRYVxfqEMd0+jdP7UhZMU2nMskG7p35Ig0e2Mvjl2D+R1/SR0tXO2r7AYQC09XtnYALBRfOuJd6Upz0wWcfLqCBg8+nDrmdvCL+smMr7d+7my6+bLTn/UP5+2n92tU0euxEz3ulJcW0eNE7NPGm2zzvNTQ0SDfvtDsf0Czt7p3baM/uHTTs8jFenx89cojWfL2Crho3yet9f5ORObOepxum3kFx8fFeaRYtfJOGXjKCslvrL4eBUKDfmCAUQCgw0tWo780GapCOFJRPFOC/dzOHgvz3/uK9VFuvrYxHR0WzEwM6SlsDxAqBpq0CHdNP9RwjuHrlMmqV04Z69x1gpHiG40AoEKhwPKLg8MWnH1CvPv2pU5euhtuQ1REhFAiiEAoEBwgFggOEAsEBQoHg0NyFAqu/V0K11+eiKZomnLT9AEJBiLXMhYI/jRlLD2Zk0z0ZrSAUtGlHPdmAUB20RBFlnAVvzaJReRMoLT3DJ+2671ZTTHQ0DTz7fJ/Pik4WskHoIhp/47SANSmLMNOmz6DYmCgqKqvxSXNg3x7atHEdjRwzTtfepg3fU1lZKZ075OKAecoRIBRAKAjUWLYc+5G2HtlEhd/k09pTf2ArBXbR9sKtfpO1SWnn40SQrwzo0ap3oOykzyEUGMIUdCQIBQIdhALBQe9BQtANTJHQ6NYDCAUCGoQCwQFCgeAAoUBwgFBgRW9szAbfdvDHJ1+jVYte8ErAtx8MGtCDHrh9gjFDNseCUBAi4Nv359MrBcclK+clJtFL2e2oTYzvPpQQs0FyCwnAR4GFMMNoqrn4KNhf/KskAGwp+Im2Hd8i/WgdMSijzUxsRad7VgYI3wF8lUDXVj0pifkUcHKAjwIn145+2eCjwH31ZlQocN+VNe8Sw0eBO+sXPgrsrTe7fBTYW2pz1rkg0KFdNj33+AyvhHz7wStvfeIjIJizbl1sCAUWsJx/tJBuO3iQitme4Az25PsFJhYMT0qxwDJM2EEAQoEdVO236TahoKS6mLYcY2JAIRMDCjaz30IcKK8p04R1Slon6pndh3rnnNG4SuB06p7di/hpA24NEArcWXMQCtxXbxAK3FdnvMQQCtxZbxAK7K23liAU2EvQOusQCixgyU892F5aSXcWHKa1VeKs8etTM+j/MnMoiQkHCM4iAKHAWfVhtDROFgp+Pr6Z+M+2AiYKMGFga8EmOlSar3lp/CjBvm36S9sDemb3pV5cHMjuRynxqUZRuCYehALXVJVXQSEUuK/eIBS4r84gFLizznipIRTYW3cQCuzla8Y6hAIztDTiKk894D7G//3+2zTvtNNpd05rOjU2jma3bk+94hIIzgx9HTcqccJHQRMNM/vGQ9lPVlFeRh8smEM33nyn4btg57bNlH9gH1106RWG01jlfZ4LBYs/W0rJKWnUb8Agw/nLEfft3UVbN2+kEaOvMZ1WmYBvE9hc8CP9dPQH2nRsI/3Ifveq6UmnsNcn7KUMfHVA96ye1CunL1sp0E8SB7iTQb1g5tSDkC6iMbGZtmYmPzgzFLTgo0BwgI8CwQE+CgQHI86RzfQ3wcSFjwJBDT4KBAf4KBAcQhlTBnMfaqV59cWnaebMmVaZg50QCUAoCBGg1vGIKWwS80B8DB2sq6X4qCh6mDk6vOTwITqAUw+8TnhQoodQ0ETDzOQtlE4dQkHgm39v0W5pu8CGw99LwsDGo+uprKbUJ+EFcRdS3/g+FN8zTdou0COrF/Vp7evUM1COEAoCETL+uVUClfEcfWNCKBBMIBQIDhAKBAcIBYLDu3NfpavHTaCszCwqqQj/2e68DBAKRF1AKBAcQhlThvJdqUwLocAqktbYgVAQIkctoYAfj5ja/hR6sPAILS4Xk4qrjxyhUYWFNEJxhCGOR2yCD6GgiQWEAu2b0u4VBfkl+6XVAVwQkH4f20AnKwt9CsOdC57ReiD1b3MmncF++O/S/SfoyOGD9Bt2hGgoAUJBKPS800IoEDyWL/mQuvXsS51P62YYrtVbDyAUCPQQCgQHCAWCA4QCwWHeGy/R2PGT2WrByG2/g1Ag6gJCgeGvyRYT0XFCwdCr76GCwiLNCtiyco4jK4b7KNBTg98tK6ZHC49RGXN0mBUdQ//MbksXw9FhROsRPgoiij/ozK30UXCo7GCTICCJAxvoeMUxn7JxR4L9Wg/wCAJcGDg1o0vQ19DSEsJHgTtr3GqhwJ0U3FVq+ChwV33JpYUzQ3fWG3wU2Ftv8FFgL18z1h0lFOgdFWHmgiIR159QwMuzt6aGbi84RD/VVEnFm5qWQY9ltpa2JSCEnwCEgvAztyLHYIUCLgBsOLLOa6XA0bLDPkVKiUulfm0aRYHWYrVAl8zTKYq9EIIjAKEgOG6RTgWhINI1YD5/CAXmmTkhBYQCJ9SC+TJAKDDPzEwKCAVmaNkb11FCQZ+LptCsp++nIYP72XvVFlsPJBTw7Pjus6dOFtDLxSeogf2/W1w8vZrTXvqNEF4CEArCy9uq3IwIBSfYVoEfmR8B5RYCrdMHEmOTqC/zIaDcPtA1qwdEAasqq9EOhAKLgYbJHISCMIG2MBsIBRbCDKMpCAVhhG1hVhAKLISpYQpCgb18zViHUGCGlkZcPR8FHXI7ecWWTz2IH3oJO0bxCB1jjg67Fx6nG3bupGnjJnnilpYU0+JF79DEm27zvNfQ0CDtG5p25wOapd29cxvt2b2Dhin8H/CIR48cojVfr6CrFPb5+/72Qc+Z9TzdMPUOiov3FjCM7CmUPZ337OPrxE3LH4PyYuCjoIkGfBRo35RqHwUl1cW0ka0U4KLAJuZPgP/eX/yrT+KEmATpxIFzk86n3JL2dO5lw6h7q14UExUT4t3flHz71p/go0BBE6ceCBhwZig4wEeB4AAfBYKDkfGEZZ2zjiGceiDAwJmh4AAfBYIDfBTY3fO4z76jhAK+9SBv5BCamDfMNSTNCgUXXzaaCuvq6HfM0eGuA7/SRdt+pl8vHSH5LuA+DCAUZPjU/brvVlNMdDQNPPt8n8+KThayQegiGn/jtIBtRmY7bfoMio2JoqKyGp80B/btoU0b19HIMeN07W3a8D2VlZXSuUMuDpinHOF4wVFauWIJXTNhSsA0EAq0ER2o2Eqff/457avaRytqltOvRXs0I/ZlPgXObHs29WFHE/IVA/3aDJTiWXU8olamEAq8qUAoEDwgFAgOEAoEBwgFggOEAsEBzgwFBzgzFBz0HtRpjTnseg9CgV1k3WvXUULB6rWb6I9PvkarFr3gGqLBCAXyxb3xyzba/f3/6PULLqScmFiald2O+jJ/BlhR4F39EAr0b4dQOnWnH4/IjyJck/81fZu/mtYe/B8VVxfRCPY6yV7fshcP/AjCvjlNWwgGth2kCwtCgS8aM6KUmU4ZQoGgBaFAcIBQIDhAKBAcIBQIDhAKBAcIBYIDhALBoSUdj6jlwN9pW/AdJRRwHwX+ghtPPfB7QezD7czB4e0Fh9nvasll2vS0LHo4M5vi4OgwELqgP4ePgqDR2ZqQCwPf5n9D/2sUB8pqxNGicmif2p7Obn8endXuPOKCQB8mECTGJtpaJhgPjQB8FITGL1Kp4aMgUuSDzxc+CoJnF8mU8FEQSfrB5w0fBcGzM5Kypfgo4ELB6OHn0QO3T5CwPPPyAvp0+RpHPTB3lFBgpPE4MY4RZ4aByv1I4VF6s1QcC3l2QiL9K7s95cbGBkqGz4MgAKEgCGgWJ6lrqJOOJJRWDBwUKwa4zwFl6JbVkwZ3OF8SB87pcAEN6tSTCkuqqLaOuwNFcAMBCAVuqCXfMkIocF+9QShwX53xEkMocGe9QSiwt95aqlDAV9ZPf/Bv5KQH444TCmRIyibotGUY6tvDCqGA21xRXkp3M98FRfX1UhZ/Ykco3pKeae/d2AKtQygIf6VzYWDjEbZi4OA3TBz4hr4/uIZKa0o8BYmLjqN+zLfAYCYIcHFgcPvzKSuxlVdBjZx6EP4rQ47+CEAocGf7gFDgvnqDUOC+OoNQ4M4646WGUGBv3dklFKzYvYIqayvtLbyG9dHdR2vmqV5RcO/MF6V4zz0+I+xl1MvQUULB/I++pCeef5uWznuKOuW2lcq8L/8IjbzhIXr0d5Mc6eQwFB8FWicB7D1RSIs/nE9PXnqZdP1DEpPp+VZt6bNZz+HUAzgz9LmPneyjYPOxjbT6wEoq2JhPayu+pfX16z3lT4lLZVsIzmGCwHk0OPcCOqvtOQG3EahPPTDbi8JHgS8x+Cgw24rMxYePAsELPgoEB/goEBzgo0BwgI8CwQE+CgQH+CgQHOz0UZD791w6WHLQ3Be5BbEP3n+Q+PZZddDyUXDZ0EEQCvSYc2C3TR7jIwhwAeGVtz5x1J4N+RqsFgpkz/yZ426k/3fiKB1iJyRkMO8F9y7+kG7B8Yg+TQenHjxLU2+7j6LZqRBmg9XODPcV76WV+1bQfw/8hwkEq+hkZaFUpKvZ63DcEcrslMO2EAyRxIEz2GkEZgOEArPEAseHUBCYUSgxIBQIehAKBAcIBYIDhALBAUKB4AChQHCAUCA42CkUTPloChVWiLFpOMObY99kq2SzfLJUryjgEfgJgB3aZTtGLHDUigLuzFBrm4ET92zItW2XUDDxptuopKGe/nqigN4uOUmPfvox/XTdJHokM8fHd8Hundtoz+4dNOzyMV6N8OiRQ7Tm6xV01bhJXu9XVVbQwrmv0eRpd/k0Wr2OysgXu+zpvGef/j52tVZPKCMteGsWjcqbQGnpOB7RzOQtkisKTjAhgK8YWL3/K/qGiQPK4woTY5PoXCYKDO04jNodzKFeXftTtx59QuqXIRSEhE8zsZm2ZiZ3nHogaEEoEBwgFAgOEAoEByPjCTP9TTBx35s3m4ZfkUeZWdnBJLckDYQCgRFCgeAAoUBwsFMosOTGtdCIllDAHRqu27idFs6aaWFOwZtylFDgxhUFHL1VPgr0qnF9VSXdz3wX7GQnI/DAT0W4K917/3bwTaDlpYSPguDqvKK2gjkd/C99s5+tGMhfSZuPbqQG9pJDr+y+NLTTpexnmLRyICEmIbiMdFLBR4GlOMNiDD4KwoLZ8kzgo8BypLYbhI8C2xHbkgGcGdqC1Xaj8FFgL2K7fBTYW2rz1rWEAq33zFu2LoWjhAI3+igIh1DA86hjP7OLT9CzRYVUxlYanB4bT3/PbkuD2AkJCOYIQCgwxquetbMfj/7AhIGv2KqB/9C6w99SVV2VJ3F2Umv6TcdLJHHg4k7DKSe5jTHDQcaCUBAkuAgmg1AQQfghZA2hIAR4EUoKoSBC4EPMFkJBiAAjlBxCgb3gW5JQUFAoTryTA3wUBGhbLfnUAyO33WHms+Ax5rvgM3ZCAg/XpqTTn7JyKCs6xkhyxGEEIBToN4NdJ3dIKwa4ZW0j2gAAIABJREFUOMBPJyiqOumJHB8TT4PanStWDbAtBX3bDGDeM6LC1qYgFIQNtWUZQSiwDGVYDUEoCCtuSzKDUGAJxrAbgVAQduSWZAihwBKMukZailBgL0VrrDtqRYE1lxReK3b6KJCvpKGhgfhe9GkKZ4YrK8roYSYY7K+tpcGHDtLoggK6edQ1XtM2+Cjwbguyo8hp02dQbEwUFZXV+DSWA/v20KaN62jkmHG6DWnThu+prKyUzh1yseHGdrzgKK1csYSumTAlYBoz+8ZD9VHw3vzXKfXC1h5x4FBpvlf5Ts/sLm0l4OLABblD6cCu3ZR/YB9ddOkVAa9DjrBy+WeU26kzfBQYIObPf4iB5KajmGlrZozDR4GgBR8FggN8FAgO8FEgOMBHgeAAHwWCA3wUCA7wUSA4tCQfBeKKnR0gFKjqh+8Nade6lZcTCX6u5bJV66SYfXt08fosUkIBL0sVExBeKC6klT9vom4H82nX+RfS0+woxd7xYm84hALvyoVQQJJPgY1H1tOKvUtp9e6v6KLjF9Kz7CWHzIQsGtLxIralYBhdfOrl1CE11wvizm2bIRRo9Onbt/5ERw4fpN9cMiKkHh9CQUj4vBJbJVCFUiIIBYIehALBAUKB4AChQHCAUCA4QCgQHCAUCA4QCkIZdVifFkKBgikXCXhQCgXqoxn5sRWDBvSgB26fIMWNpFAgF/27bVvoi+2baNbAs4hvQLg5LZMeyMimsmNHcOqBon5bqlBQXlNGX7OtBMv2fEbL9y5hR8MUSFRS2es29lrZfrW0lYCvGjir3Tl+exkIBdp4IBR4c8GKAsEDQoHgAKFAcIBQIDhAKBAcIBQIDhAKBAcIBYIDhALBwSnBEUIBPxbx0d9Noieef9svly0r59jGjQsAeSOH0IFDx7yOpVALA2rhgBfI7lMPjF70h+Ul9H/sOMWjdbXULiaG+S5oQ1cmpxpN3mLitQQfBQdLD9AXuz+VVg6syf/aywlhenwGDT31Uhre+Qoa1nkE8VUEbgjwUeCGWvIuI3wUuK/OeInho8B99QYfBe6rM15i+ChwZ73BR4G99QYfBfbyNWPdEUKBmQLbEVcpBqjPr1Qf2Sg7W1SKFk4RCiTRgnmqf5KJBW+VFlE9+/uChGT6W3Yb6hgbZwc6V9psjkIBP6Fg/eHvJGGA/2w7vsWrbrpkdqVLO4+k4V2uoHPaX0Cx0bGuqzsIBa6rMoJQ4L46g1DgzjqDUODOeoNQ4M56g1Bgb71BKLCXrxnrjhIK+MqCWU/fT0MG9/O6Bq2n+GYu0l9c7n+Ah+cenyH9VgsF8mqHiXnDpM9loWDpvKeoU25b6b26+gbpx0lhQ0UF3Z5/kPjvxKgoeqhNa/p969YUz/7f0kMMZ8D+Oa3OzNZLGdtS8MUvS+njHR+x35/TicoTXiZ+02koXdFtFI3segX1zOll1rzj4scxB5S1ddzLgnMC7ib/dcFvtWg2g6lj9YYQWQI1tfUUFxttqBAxrM7qmQ8c9g/BRQRiY6JZH8kfESC4hQDvH3mot3kMiVvZ2hYR13ivgau1XGVr/CEDgjMIuEIo0HqKbxU+vmJAfYYlt53TKoNWLXqBAq0o4D4Kfv/QH6m8slYq0scfzKdB51xAuad08iriju1bad+eXXTpiCs97x/M309r13xDedde73mvpKSYPnpvHk26+XbPe/zUg1f++QzdfveDmpf9y45ttHvXdrps5FVenx9mztU+/OoL+htzcljMnjh3ZqsKXmjdjgayWO+8+SrdPP1uH3uvvvwcTfntnRQXH+/12bvvzKFLho+knNZCHNEKK7/8nNq0bU+9+/b3+VjrWpWR5r7xCo25ZiKlp2f4pOWMotlWikGDz/f57OSJQlqy+AO6fvItAZuEzPaW29mpB+zLubRC1Jky7P91D21kpxpcmTde197GH76n8rISOv/CSwLmKUfgpx6s+OIzuu6GqQHTrPrPMsrObk19z+A15Rs+Z1sK3t82n/kcWEIP1j5IT7BXPXulJaSzVQOX08jTxtAlpw6n9ARflkpr5eVltHDeGzT1FiGSGQnbf95MB/b/SsMuG2UkuhTnyy8+pVNO7UI9evYxnEYrYlZaAn22ZCmlpKZR/4Fnm7b1K7v/Nv+0gUZdda3ptHoJ5EHCz1uYM8ND+ew0iJEh2a6srKD57N6cqnFvhmRYJ/HXjW2tj05bCzZPuS/o338gpSbF0onS6mBNBZ2Ot7uOrN11D7HdBV0AlnDF55/QqV26sRM/IifUff7ph9SjVx/qclo3JpAak7YyUuKosrqeqmrqQrl8T9qln3xAvfr1p85dulpiLxgjiz9cSAPPOodOYSewRCp8wsYHZ2mMD6woD59vtkpPpIKiSr/mFr37Nl3Avrvatvd2VGtFGYzaeI+NJy4OMJ4waivYeAvefo0uHzWWslplB2si5HTvvPlvunb8BMrKzKKyKmvuNb1C6d35b73+El097kZKTUsP+XqCNTDntX/R+Ik3UXJK5LbKzn7lBbpx6nRKSEg0dBk5GexeK2b3moVKgd7421CBLIrE5xq33nk/E/gjN1F/6YWnaObMmRZdEcyESsAVQgF/yv/p8jXSxN3uoF5REMhHgROcGe7euY327N5Bwy4f44VHPvVgyNUTaSbbjsB9GPBwbUw8nbn0Y7ppmq9QoOdMxYjzIdmBWc8+vkLBISaKrF+7mkaPnahZhQvemkWj8iZQmoZQsO671RTDOq2BZ/sKBUUnC5mjrEU0/sZpAZuGm50ZfsOcEX6883369JdFVFJd7LnWx+gxOjaghC7tMpLOzR0SkIEyQgUTCj5YMIduvPlOw+ngzFAbFZwZenOBM0PBA84MBQc4MxQc4MxQcDAynjD8pRRkxPfmzabhV+RRZlbkhAI4MxSVB2eGggOcGQoOcGYYZKdmU7KICwXyaoFA16e1JSFQmmA+VwsFbjj1IJBQcNW4SRKKb9nTyvsLj9BRNkG866vllDZxCt3ETkhQ6oYQCvbQpo3raOSYcbrNZxNbcVBWVkrnDrnYcBPjKwpWrlhC10yYEjCNfLZ9RU41EwfepcVMHDhadtiTrk1KO7qy69V0VbfxtHHR1zT1tvuCUn8hFASsCsMRIBR4o4JQIHhAKBAcIBQIDhAKBAcIBYIDhALBAUKB4AChQHCAUCA4OCVEXChQgtDzURBOWGqhgOfN/RgsW7VOKkbfHl1o4SzvJTFOcmYYiFU128bwcvEJ+kdxIVWy//eLT6RnWrWWfreU4GRnhj8f38x8DrzHBIL3aF/xXk+VZCRk0hWn51Fe93F0fu5Qio6K3LKwSLUTODOMFPng84Uzw+DZRTIlTj2IJP3g8oYzw+C4RToVnBlGugaCyx/ODIPjZjQVnBkaJWV/PEcJBfZfrj05uEkokAnsr62hhwuP0crKMmlFweTUDHo4K4fSWsAE1GlCARcEPtyxUBIIthdu9TTSpLhk6QjDsd2vo4s6Dad4tmWkJQcIBe6rfQgF7qszXmIIBe6rNwgF7qszXmIIBe6sNwgF9tYbhAJ7+ZqxDqHADC2duG4UCuRL+ay8lPkvOEaH6mqpTUwsPcbEgrHJaRZQca4JJwgFfCvBJ798wMSBd+mHI997YMVFx9HQTpeylQPj6fIuoyk5LsW5IMNcMggFYQZuQXYQCiyAGAETEAoiAD3ELCEUhAgwQskhFEQIfIjZQigIEWCA5BAK7OVrxrqjhIJ9+Udo5A0P6ZZ/y8o5Zq4tLHHd4MxQ9lEgA6livgoWzn2NJk+7S3qror6eni0qpFdKTtAjSxbThjHX0O3ZbekshfdXI3sK4cxQv8lxHwVfLvuEavvH0EdsW8Ga/K/Z8WPiGCu+jeC8DhfSVWxbwaiuY2nzmu+pVU4bdnrEgIBtePZLz8JHQUBKIsK+vbto6+aNNGL0NQZTGI8GHwXerOCjQPCAjwLBAT4KBAf4KBAcjIwnjPe+wcWEM0PB7Z05L9OYa9mpB+w0oUgF+CgQ5OGjQHCAj4JI3Yna+TpKKOBHEY4efh6dd1Yf+uOTr3lOOeAnD+SNHEIT84Y5ix4rTXMQCmSoO2qq6cvZ/6KnLxtB1bGxdFlSCv0hM4e6x8Ub+mKHUODbPMtrytgxhp/R8s2fUvuDrell9pLDgDZnMXFgPOV1G0fcQaEcZGeGEAq8efIVBYs/W8qOUEqjfgMGme4LIBT4IjPT1swAh1AgaEEoEBwgFAgOEAoEBwgFggOcGQoOEAoEBwgFggOEAsHBKcFRQoHszLBTbhuadNdfPEIBPxlBKRw4BR4vR3MSCuSOqvWEm+gvZUW0l/kx4P4L8thWhCErPqdLh42k7NZtdfFDKBBoquuqaeW+5WzlwLuSSFBRU07t2Iu5IqSvWq2ShIGxPSZQp/TOmizNTN6wosB4bwChwJeVmbZmnDQRhAJBC0KB4AChQHCAUCA4QCgQHCAUCA4QCgQHCAWCA4QCwcEpwZFCwZDB/YiLBvJWA/kIRSduPeAV6WYfBf4a4r/Z6QjPsS0JxY1L5H+X0YqmMqeHOcyXgZuDHT4K+DaC/+Wvoo+YQ8Kluz6mk1UnPIg6pp/KjjIcJ/30zunnZnQRLTt8FEQUf1CZw0dBUNgingg+CiJeBaYLAB8FppE5IgF8FDiiGkwXAj4KTCMzlQA+CkzhsjWyo4QCvsVg0IAe9MDtE0j5f35k4afL13hWGNhKJAjjzVUo4CgK6+rob0XHaU5pkUQmMSqKfpuWSXemZ1FGdEwQtCKfxEqhYP3htewow3dp8S+LiDsolEPr5LY0mvkbyOs2nga1PzfyF90MSgChwH2VCKHAfXXGSwyhwH31BqHAfXXGSwyhwJ31BqHA3nqDUGAvXzPWHSUUqAvOVxXIYem8p6hTrv6ydzMXbXXc5iwUyKz21NTQk0UFxE9JaGBvZkRH0/S0LLqViQZJ7P9uCqEKBTtPbKP3t71Dn+x8n/jRhnJIiUulkadfRdf2mEgXdrzETUhcUVYIBa6oJq9CQihwX51BKHBnnUEocGe9QShwZ71BKLC33iAU2MvXjHVHCwVmLiRScZujj4Ibpt5BcfHxXkjlPYVHMzPpryeP05cVZdLnfBvCXWx1wWS2JeG7lcuodZt21LNPf5/qOJS/n9avXU2jx07UrKoFb82iUXkTKC09w+fzdd+tphgmRgw8+3yfz4pOFrL9r4to/I3TAjaB0pJiWrzoHZo2fQbFxkRRUVmNT5oD+/bQpo3raOSYcV6fVdRW0Kds1cC8La9T3KEoSmWvZezFw6jT8ySfAyNPG6NbBn7qwcoVS+iaCVMCltPMvnH4KAiI0xMBPgp8WZlpa8ZJw0eBzAo+CgQJ+CgQHOCjQHCAjwLBAT4KBAf4KBAc4KNAcICPAjOjLfvjOkookJ0Zch8FbgktTSiQnRmur6qkJ04W0NqqCqmqOjDB4I4tm+mc3E7UuxkJBVuO/UhzmTjwwfb5VFZTKl3r+ezVK60P9T/3XBrR5UpKiU8N2FwhFHSmbj36BOTkLwJOPQgJn2ZiCAXWM1VahFAgaEAoEBwgFAgOEAoEBwgFggOEAsEBQoHgAKHA3nGJWesQCswSU8VvqUKBjGFVZRk9xVYY/FhdRWN+3ECV2TmU1/9sGsOOsItSsHLTioKNP3xLJ7qV0zubX6efjm3wXEX7lA40vvdkSSiIrYmhc4dcbLj1QCiAUGCksVRVVtDCua/R5Gl3GYkechwIBSEj9GsAQoHAA6FAcIBQIDhAKBAcIBQIDhAKBAcIBYIDhAJ7xyVmrTtKKOAODPNGDqGJecPMXkdE47cEHwWBAC9lvgueYU4Pt9dUS1F7xyXQg5nZNDwpJVDSsH+u56Ng18kdNGvDP6TVA5Vsq4EchnUeSTf0mUqXdxkd9rIiwyYC8FHgvtYAHwXuqzNeYjgzdF+9wUeB++qMlxg+CtxZb/BRYG+9wUeBvXzNWHeUULAv/whNuusvjj3dQA8shAJBpp79fFhWzE5JKKRfa8X+//7xCfSnrNY0OCHJTLu0Na5aKPhiz6c0e+O/6L/seEM5dEg9ha7vPYUm9JlCfCUBQuQJQCiIfB2YLQGEArPEnBEfQoEz6sFMKSAUmKHlnLgQCpxTF2ZKAqHADC3zcSEUmGdmVwpHCQXKUw60LnjLyjl2cQjJLoQCb3y17M/57DjFF9gKg0PseEUeLkxMpkfZCoO+8YkhsbYiMRcKymtLaNb3r9Lrm16m/cW/SmZbJeXQzf1uk04swJGGVpC21gaEAmt5hsMahIJwULY+DwgF1jO12yKEArsJ22MfQoE9XO22CqHAXsIQCuzla8a644SCWU/fT2pnhvM/+pJeeesTR640aOk+CpSN7Zv/fOF16kFVQwPNKTlJLxafoPRjR+iibT/ToUtH0MOZOdQ9zvtUhXCdevDh+2/RL91204Ktc6m0Wjgn7J1zBt3S/07K634dHc3P1zz1QHmdmzZ8T2VlpfBRYLCnWbn8M8rtBB8FRnDBR4ERSsbiWNXujOWmHQs+CgQX+CgQHOCjQHCAjwLBAT4KBAf4KBAc4KNAcICPglBGHdandYVQsHrtJpr+4N/IiSsKIBQ0NUq1UCB/UlZfT7N/+ZkK1n9Hsy+4kKLZB3nJafQAW2HQKTZOimanUNBADfTV3i/onR9ep54Hu9Lz7BXFXpcy3wO3DLyLLsgd6rkIveMRlbcehIJ9dNGlVxjujayasOHUA8PIDUeEM0PDqIKKCKFAYINQIDhAKBAcIBQIDhAKBAcIBYIDhALBAUJBUMMN2xK5Qih45uUF9OnyNVhRcOcDmg1h985ttGf3Dhp2+Rivz48eOURrvl5BV42b5PW+v6eWeh2VkS92PaGAZ85PPfjuu29oyyWX0etslUElW20Qy96fmJpO96Zn03/emU2j8iZQWnqGzzWu+241xURH08Czz/f5rOhkIRuELqLxN07z+ay8pozmb32T3tj0Cu05+QtlstdU9iodUEkzBt9NOfGn+qSBUOC/r9m5bTPlH4BQoKa0fetPdOTwQfrNJSNC6qyxoiAkfF6JrRKoQikRhAJBD0KB4AChQHAwMp4I5b4zkva9ebNp+BV5lJmVbSS6LXEgFAisEAoEBwgFggOEAlu6m6CNRlwokFcLBLoCrS0JgdKE63P4KDBH+mhdLf2dOTx8m/kxkMMtaZmS00Mrwq9Fe2j2T/+ihVvfptKaEskkd054c//b2ekFN1N7JkzExkRRUZlwuIjgDgLwUeCOelKWEj4K3FdnvMTwUeC+eoOPAvfVGS8xfBS4s97go8DeeoOPAnv5mrEecaFAWVjuzNDJgoAeWAgFZppcU9z97GSE54sLaUFpsfRmYlQU3ZiaQXekZVHbWL7ewFxYtW8FEwheZtsMPmebDRqkxGe2G0y39r+LruiaRzFRMdJ7escjmssNscNNAEJBuImHnh+EgtAZRsIChIJIUA8tTwgFofGLVGoIBZEiH1q+EApC4xcoNYSCQITC97mjhILwXba1OUEoCI3nrtpq+jvbQvBRuXj6z8P1jYJBlzjhw0AvVNRW0Ls/v02vM4HglxPbpWix0bE08vSrmIPCu+gsJhSoA4SC0OorUqkhFESKfPD5QigInl0kU0IoiCT94PKGUBAct0inglAQ6RoILn8IBcFxM5oKQoFRUvbHg1AQImM4M2wCGMhHwfq1q2n02ImaxLkzw4FXXkNvNNTRu2UlxE9M4E4PRyWnUt6O7dSWnZKg9FFwoGQfWz3wEn2x+RO6smY0vcheGQmZdH3vqWyLwR1sq0GuTz6lJcW0eNE7NG36DN2tB/BR4P+GgI8CbT7wUeDNRe4Lzug/kNJT4qigqCrEntZ8cvgoEMyWL/mQuvXsS51P62YYotVCAXwUCPTwUSA4wEeB4AAfBYIDfBQIDvBRIDjAR4Hhr+qwRHScUDD06nuooLBp77qSAk49cLczw0BCgezMkPswmFV8kt4sPUkVTDC4hB2rmMK2Ipx+1jnU++RGen/zK7Ri71Kqb6inHPaaFD2Jsod0pAm9JlNSXLLujQOhwBtNRXkZfbBgDt14852GOxsIBdqoIBR4c4FQIHjAmaHgAKFAcIBQIDhAKBAcIBQIDhAKBAcIBYIDhALBwSnBUULBddMfpw7tsum5x2c4hU/AcmBFQROiUFcUqE89KKqvozfYCQlb2GkJpUXb6OuKd4iKf/FkyI81nNLtVirdeFzz1AN15UEo8CYCoSDg7W04AoQCb1QQCgQPCAWCA4QCwQFCgeAAoUBwgFAgOEAoEBwgFAgOEAoEB6cERwkFcGbolGbhjHIUVZ2kN5jvAe6gsLCiQBQqOp7olJFEp02i81ufQbekZ9HwpBSKMlFk+CgwActBUeGjwEGVYbAo8FFgEJTDolm99cBhl9csiwMfBe6sVvgocGe9wUeBvfUGHwX28jVjHUKBGVo6ceHM0AKIChNHyw7TrI3/oDc3/5sqasqlT7KTWtOkvtOoV/dJtKg2npZXlFF9Yxru8PC3qZk0ISWdkqK5ZwP/AUJBIELO/BxCgTPrxV+pIBS4r854iSEUuK/eIBS4r854iSEUuLPeIBTYW28QCuzla8a6o4QCvvUgb+QQmpg3zMw1RDwuhAJrqmBf8V56af3f6N1tc6mqroqio6JpVNexdM+gh6hXdl+vTA7U1tLs0hO0kB2tWFQvJIMMJhJMTMmg36ZnUocY/eMVIRRYU1/htgKhINzEQ88PQkHoDCNhAUJBJKiHlieEgtD4RSo1hIJIkQ8tXwgFofELlBpCQSBC4fvcUULB6rWb6I9PvkarFr0QPgIh5gQfBU0Ag/VRsOfkLlqycAG9VPMvOslePFzfZyrdMfA+6pJ5Oq37bjXFMBFAeeqBnOuRE8fpk08/oLnDLqdf2DGLPHCJYCQ7LeGWtCw6KyHRU0D4KPBu7PBREOLNr0gOHwXeLOGjQPCAjwLBAT4KBAf4KBAc4KNAcICPAsEBPgoEB/goEBzgo0BwcEpwlFDAfRT4Czj1oHmdepBfsp/+/v1faMHWN+l37DU/Zj5d2fdauuPM+6htSntPU/AnFBSdLGSD0EWSM8NVlWU0u6SIvmLbEhoaU58Zn8gEg0walZJGFTge0ev2glBgXTcMocCbJYQCwQNCgeAAoUBwgFAgOEAoEBwgFAgOEAoEBwgFggOEAsHBKcFRQoFToJgpB1YUNNEyuqKgoPwoPff9X2nOplmexP8v/jEalXcddWzTxQe/UaFATvhrbQ0TDE5K2xJK2RGKPPCtCDdHx1L6ss/o1ukzKDYmiorKanzyOrBvD23auI5Gjhmn2ww2bfieyspK6dwhFxtuKscLjtLKFUvomglTAqZZvXIZtcppQ737DggYd/ZLz9LU2+6jaAO+GdTGIBQExGs4AoQCb1QQCgQPCAWCA4QCwQFCgeAAoUBwgFAgOEAoEBwgFAgOEAoEB6cECAUW1AR8FBiDyE8x+BfzQfD6ppclJ4WxbOJ+Xa/JdP/gP3qtIDBmLXAsLhJwseCN0pO0p0aIAslsQn1jegbdlZNNrarNnJUQOD/EsJcAfBTYy9cO6/BRYAdV+23CR4H9jK3OAT4KrCYaHnvwURAezlbnAh8FVhP1tgcfBfbyNWMdQoEZWjpxIRT4h1hWXUqv/vhPmrXhH1RcXSQ5Kbyq2zh68NyZ1Cm9swU14N8E34bwJduO8DpbZfB1Zbm0LYGfjTCMHat4C3N8eEFCsu1lQAahE4BQEDrDcFuAUBBu4tbkB6HAGo7htAKhIJy0rcsLQoF1LMNpCUKBvbQhFNjL14x1xwkF/OSDzdv3SNcw6+n7acjgfsR9F1w2dBA99/gMM9cWtrgQCrRR85ML3vxpFv3zh2epsKJAinRZl1H0h/P+j7q36hW2+lFmtJutLJhTUUQLiouorPG0hN7xCXQr82NwVXIaxUdhlUFEKsZAphAKDEByWBQIBQ6rEIPFgVBgEJSDokEocFBlmCgKhAITsBwUFUKBvZUBocBevmasO0oo4CJBh3bZkiAw9Op76M8PT5OEgvkffUmvvPWJI09DgI+CpuYm70vu2qsPzf/5TXph7V/pUNlBKcKVrcfSRew14bpbNNvngrdmMR8FEyiNbQtQB7M+CvRuAOWpB+VRDTT76HH6d8kJ2s+OWuShNfdjUFxCHbb/TNcyfwl6AT4K9tFFl15huJ9Zufwzyu3Umbr16GM4jVZELhQs/mwpJTPHlP0GDDJta9/eXbR180YaMfoa02kDJYCPAm9C8FEgeMBHgeAAHwWCA3wUCA7wUSA4wEeB4AAfBYIDfBQIDvBRIDg4JThKKOArB5bOe4o65bb1Egr4sYnTH/wb4dQDZ5968PVXn9N+9nop/wXaW7RbauP925xJfxryNHVs6Ejr166m0WMnarb9cAsFSmeGn/NtCcUn6L9VFdT16FE6d9dO+mrIULo+NZ0mpGZQeyYgKAOEAggF6kYMocCbCIQCwQNCgeAAoUBwgFAgOEAoEBwgFAgOEAoEBwgFggOEAsHBKcFRQgFfRfD2Px/xEQqwooA9/Wbe7afd6VyhYOlutuLjyyW0pWoz/cBevXP6ST4IhncWT54P5e93rFAg34zba6po7vatVLv1J3rr3PM99+glzJfBZCYYDGe/eYBQAKFA3YFDKPAmAqFA8IBQIDhAKBAcIBQIDhAKBAcIBYIDhALBAUKB4AChQHBwSnCUUPDMywvo0+VrpC0G8taDTrltaOQND9GU60bQA7dPcAo3r3K0ZB8Fq/atoKe/fZw2Hl0vMemS2ZV+P/hRuqr7OIpiLyeGlMRY3eMReXm574IPy0ronbIi+rG6ynMJ7WNiaDwTDG5kP/y4RYTwEoCPgvDytiI3+CiwgmL4bcBHQfiZh5ojfBSESjAy6eGjIDLcQ80VPgpCJeg/PXwU2MvXjHVHCQW84PI2A+VFPPq7STQxb5iZ6wpr3JYoFKw/vJYUx/FjAAAgAElEQVSe+N8jtPbg/yTWHVJPoXvP/gON7zVJOvbQySGQUKAs+xYmFMwtLaIPmHBQxo5blMP4lHQakphEI5JSKYUduYhgPwEIBfYztjoHCAVWEw2PPQgF4eFsZS4QCqykGT5bEArCx9rKnCAUWEnT1xaEAnv5mrHuOKHATOGdErclCQU/H99Mf13zGH2593MJf05yG7rrrAdoct9bKD4m3ilV4rccZoQC2VBFQwMtLi+RRIP1VZVe9q9MTqUx7MSEK9hvBPsIQCiwj61dliEU2EXWXrsQCuzla4d1CAV2ULXfJoQC+xnbkQOEAjuoNtmEUGAvXzPWHSUU3DvzRVq2ap2P00InH4/YUk49WPDOv+nblLX0/v751MBeGQmZNH3gPXRr/7soKS5ZanPyvuSeffr7tEE3+CjghT6wbw9t2riORo4Zp3sffbX+W9p8spDm9uxF+XXixAQeUqKiaTQTC65KSaWhicKfgRyOFxyllSuW0DUTpgS8P1evXEatctpQ774DAsblvium3nYfRQexqqGivIw+WDCHbrz5zoD5yBF2bttM+Qfgo0ANDD4KvInAR4HgAR8FggN8FAgO8FEgOMBHgeAAHwWCA3wUCA7wUSA4wEeB4OCU4CihgPsluG3yGJ9tBnBmGDlnhoUVBfT0d/9HKZtj6SP2OhlbRDf1vZXuPvtBykzI8mrHLUUoUDoz5KsLPmYrDRaXl9JRhWjAj1ocnZxCecnpNCghkSAU4HhEI51+VWUFLZz7Gk2edpeR6CHHMSNKmckMQoGgBaFAcIBQIDhAKBAcIBQIDhAKBAcIBYIDhALBAUKB4OCU4CihgK8cmPX0/TRkcD8vPjgeMTJCwb83/IOe+/6vVFxdRLexV33XGLrzNw9I2w20QksUCmQO3HvB/yrL6SMmGCxhwkERc4goh46xsXRNVS3lfvsNXT/x5oD3vpnJG1YUBMTpibBv7y7aunkjjRh9jfFEBmNiRYE3KAgFggeEAsEBQoHgAKFAcIBQIDhAKBAcIBQIDhAKBAcIBYKDU4KjhAI3rijgFdncfBTwow6f+O8jtLdoN0Wz5fR53cbTw+c9TrlpHZ3SbkMqRzA+CsxkWM38GayURIMSWsaEA+7fQA7d4+LZKoM0GpuSRp1i48yYbfFx4aPAfU0APgrcV2e8xPBR4L56g48C99UZLzF8FLiz3uCjwN56g48Ce/mase4ooYBvMXji+bdp6bynqFNuW+k69uUfkY5HdPLJB81FKNhR+DM9sup3tCb/G4n9ZV1G0R/O+z/q3qqXmTbl+Lh2CwVKAOVsZcGyijJ23GIxrWLiQY3iwwHxCdLWBO7ToA2OWwzYbiAUBETkuAgQChxXJYYKBKHAECZHRYJQ4KjqMFwYCAWGUTkqIoQCe6sDQoG9fM1Yd5RQwAuudTyi1nYEMxdpd1y3CwUVNeX09+//Qi/98HcJ1TkdLqA/nv9nOqvdYLvRRcR+OIUC5QWerK+jz9gKg4/ZUYtrqipI3pzAD1c8LyGJCQZpNIo5Q8yMjokIF6dnCqHA6TXkWz4IBe6rM15iCAXuqzcIBe6rM15iCAXurDcIBfbWG4QCe/mase44ocBM4Z0Q1+2nHizZ9TE99s3v6VBpPrVObkszqu+km26+m+LivY86NLKnsCX7KAjUFtXODLnjw4/LmGhQXkwbqqs8yflmhN9u3UJdW7ejqwYOpuQApxnAR0Eg8k2fw0eBLysz/jCMk246AeWM/gMpPSWOCoqa2rgZO6HEXbn8M8rtFLoTzVDKAB8Fgh58FAgO8FEgOBgZT4Ry3xlJ+9682TT8ijzKzMo2Et2WOPBRILDCR4HgAB8FggN8FNjS3QRtFEIBQ8d9IxQUFnkgqlcwyMc28gh9e3ShhbNmeuK6VSiY//YsWt72P7Ry33LJD8GkvtOkbQYfvPE63TD1DggFfo5HVJ56YPTO83fqwb7aGrY1oUQ6PWF7TTWN/mkjHU7PoC1dTqPL2AoD7tPgosRkio+K8skOQoHRGmDbmODM0AcWhALj7SeYmBAKBDUIBYIDhALBAUKB4AChQHCAUCA4QCgQHCAUBDPasC+N44QC9aRdeelbVs6xnAT3gfDcv9+j5x6fIdmW/STIeamPZrxu+uM0aEAPeuD2CVJ8twkF1XXV9Mr3z1HDugp6mr165/Sjv1/yCvVrM9BvR2Xkix0rCvSbp9HjEX+uqaIV/1lG65OTaHmnUz0G+XaEK5hocBX7OZ+JBny7Ag8QCox3CRAKfFlBKDDefoKJCaFAUINQIDhAKBAcjIwngrnfzKTBigJB6505L9OYa2+k1NQ0M/gsjQuhQOCEUCA4QCiw9PYK2ZijhAI+Ce/QLtszaQ/56oIwIDtPlB0qqoUBtXDAs3CLj4Jv81fT/V/dJp1mkB6fQQ+eO5Nu6nertKKgJYVI+Sgwy3h9VaV0csJi5tfgGNuqIIe2TDS4kvkz4D4NzoxPNGvWtfHho8B9VQcfBe6rM15i+ChwX73BR4H76oyXGD4K3Flv8FFgb73BR4G9fM1Yd5RQ0OeiKRRpx4WyM0V5RYH6yEb1524QCo5XHKOZ3zxIH+5YKLUNftzhzCFPUpuUdmbaSrOJ6xahQAn8m8bjFj9jfg1KGmQ3iES94xJoNFtlcA5zhnhuYlKzqSOtC4FQ4L7qhVDgvjqDUODOOoNQ4M56g1DgznqDUGBvvUEosJevGesQClS0uDAwevh5nq0FXLxQHs0oCwXKIxzLKmupvKrODPewxG2gBnrjx1n0l//NpOKqIuqccRq9MHwWnXfKhWHJ36mZJMXHUAwbVZWyenNj+JyJBR8xnwZL2E9lQ4PnEtKY48PLmWgwLDmFhielUnpM81op0io1norKq6muSSdxY/W1qDLHxURRSlIsnSxVHgzaohA45mIbWF8RpeHnRKuA6cmxVFVTL/0guIMAFwqy0hLoeHH4HYe6g5AzS8kfXBC7N8scOIZ0JjFnlConnd1rJVW86hBsINA6I8EGqzAZDAFHCQV8mX/eyCE0MW9YMNcSchouEpzZr5vX1odAKwq4j4JH/99jVF8veot5c9+mIRdeSKee2tmrPFs2b6Zfdu2kq64a63l/375f6etVq+jGSZM97xUVFdHct9+kO2fc7XmPD/Ce/Ouf6Q+PPKp5jT9v3Urbtv9MY8de4/l8w6Ef6A+fPEynFXShubFz6cHzH2Y/D1F8TDxVVFTQKy//i+697/c+9p595im6+557KV516sHs2a/S6FFXUtt2+qsQliz5lDq0z6UBA4W/A2XQulbl5y/96590/Q2TKDMz0yft16tWUnRMDA0Z4itwHD9+nN5/byFNv+2OgPUvs73r7nvYgJmors63h9+9exet/e47mjDxel173333LZWWlNCwS4cHzFOOcPTIEfpk8cc0bdqtAdN8vnQJtWnbls488yy/ccvq6+kfT/2VdjFui0vL6ESdt1g1hAkGV2ak0Ui297Bnom+nW1ZWRq+9Oovu+d19AcskR9j000+099c9dOWVVxlO88knH9FpXU6nvv36GU6jFTE2Npo+//wLSk9Pp8GDzzFt65dfdtIP69fT+OuEfxErw48bN9KB/P00it0joQR/92YodvXSGm1rZvOW+4KBZ54piXK1EVB3rGp3Zq9dGf+jjxZR9249qHefPqGYCSntB++/J917p3XtTnEGxcNYFq+Ofafx7x4rwnvvLpS+F7p1626FuaBszH9nHp173nnUhTmJjVTQGx9YVZ441kfW1PoXd96c8wZdOnw45eaeYlW2pu0YGU+YNmoywb9nvUxXXzOOcnJyTKa0Ljofh/GxRqtWrTxjSOusG7P04j9foMk3TZW+VyMV/vHCc3Tzb29hfhJSI1UE+vvfnqE77ryLEhONbec0cq+ZvRi98bdZO6HE53ONBx/6A0UHOHErlDwCpf3Ln/8/mjmzyWl8oPj43F4CjhIK+NP6Pz75Gq1a9IK9V61hXUsk4NEC+ShwmjPDkupienLNTHpr86vUoaEDXRv//7d3JmBSVOfC/mCYAUEBARVBDaCICogiQRKNuCREE39DzIJGNCSSQBJz1RjNLr/m3qhJ/I1Xc5U/+sRojJL7u0dRML+QYIiKcUHcFQXZBFRkXwbu99Xpmu7p6Z6u6q5t4K155umlzlbvqerpeuec73xZzjjjG7J/13xgvM2bNsq0P94k50z8bgsS5YKpBAk+RDDD8qdt0GCGVkKYAHN+MEP9VJenN2+URzdu0N/18rIGRSzc+tfXyyd3s5EGXXSaQmfR/2HIxg3r5a47b5HxX/9O4OvttZdfkCXvLJLjP/mZwHmiWqbOph488OB06ayxGYYeMSJw/X5Cghm2RBbmXAsD3P8sYHnEB+Qj/Q6SAw8+NAy+SNPOfOgeGXjIEOk3YGDgcqOOUUAwQ4eeYIaOQ5DvE4FP1ioTEszQgSOYoeNw6+/+U8ad803p2DGYKIhj6gHBDF1fEMywyg+1mLJlShTYMP/WtjhWPbD6rN4J405umm5Q2Ia2tOrBh/03ymVzfigrN6yQfbv0kR8ffrnUvdkon/vS2c2wIgrOkw46JHrN+pbDod9ZtFDmPztPTklwecTicz7MzVu5VQ+WavDDRzQI4kyVBv9UgbC54D+DXTV45fG7dZYTde2Ejff9t5xzrlvxI8iGKChN6ZUXn5cVy5fKcSeeHARj2TStXZs1FVwmc5hzLUz9iAJHi1UPHAdEgeOAKHAcEAWOA8sjOg6seuA4IAocB0SB45CVLVOiIA0o/nKIxXWPGT2iaQrChVOulxmz53lJhgzqL9OmNh8Sk/aqB7aKga1mYKsa1LWrk68P+5ZcPPJS6dKQ3jCuNPoyaJ1tMZhh0GMrlW6DTlH4m8qCGSoOZqg4eH97fopCD11BYXBDRxmpFn10py5yVECbXkt7qs1LMMNqyaWXj2CG6bGvpeaoRxTU0hbyBiNAMMNgnLKWimCGWeuRYO2JY0RBsJp3jVQEM8xOP2dOFPjBAgsRpb0SQqXuSksUbG7cLL956kq58ZlrZEvjFjlynxHyyxN+K4f1qm0ueKXjbev7dzVRUNhfNuP42S2bvJEGNkVhwZbmUxS66RSGYzt1VmnQWU7QaQp96mySQjY2REE2+iFMKxAFYWhlJy2iIDt9EbQliIKgpLKVDlGQrf4I2hpEQVBS1aVDFFTHLY5cmRIF/n/3C1cUWLRkhZxy1g+arTwQB4haykxDFMxaNFN+OOvfZPGHb0v3jnvKjz52uZw15OvSTn/YWiewK4uCYjKrdIqCjTb4u8Y2sCUYl+nrwm1Ah3qdptBFRuvyi8eoPNgtxQA3iIK2d2UjCtpen1mLEQVtr98QBW2vz6zFiIK22W+Ignj7DVEQL98wpWdKFBSvMOAfSHGcgDAHGHfapIMZLl+/TH72t+/JQ2/c5x3alw4ZL1/v8w1ZuXiZnPTp05od7rsrlsncvz1KjIIclXVrP5QH7v6TTJy088coCHLelwpm+Ma2LSoNVBxsWi9zVSCs0WkL/tagS0WctnSZHPreKjnmpFNkSEOnQFqKYIZBesOlIUZBcFaVUkZ13lWqp7X9xChwdIhR4DgQo8BxIEaB40CMAseBGAWOAzEKHAdiFNTyrSP6vJkSBRZUsNQ0A386QlzBDGvBmqQoaPx4g1z95H/I+q3r5MDuB8v/OelGGbHvKHnztZdl4ZuvIgoqdCSioDmgSqsemCJ4Tqcp2GiDOTraYJ4+P1SX9Oy3aqXce+RR0lOXrDxOV1AYrYERT9DRBr3KTFOI6oaNVQ9q+aQqnZdghtEzLSwRUeBoIAocB0SB44AocBwQBY4DosBxQBQ4DoiCeL+XhC09U6KAEQUi/s3smV+d3NSX85Y9IU/f9Zhcrj+2/fBjl8l3j7q4aT+i4G758viJFc99REFzRJVEQTHQjbpywqMv/EsWLn5bHhr+UXlBxUHhKuuH1nf0YhuYODhapyp01BEItiEKKp6aTQkYURCcVaWUUZ13leppbT+iwNFBFDgOiALHAVHgOCAKHAdEgeOAKHAcEAW1fOuIPm+mRAExCpp38NotH8oVcy+VP8z/v96OT/Y7RX4x+jfSd4/9oz8TdqESiVEQTWfb6glzNm2UORoU8e86TeHtbfnlJjupJBhlow08cbCbDFKJUOtGjIJaCSafnxgFyTOPokZiFERBMdkyiFGQLO+oaiNGQVQkky2HGAXx8iZGQbx8w5SeKVFgDWfVA9d909+8X342+3uybP1S6drQTS4/7ldePAK22gkgCmpnWKqERSoKZukUhcf11wTCBwXLMI7QZRf31qkJNtJgpMY2OLyKZRgRBfH0W5ylIgripBtf2YiC+NjGVTKiIC6y8ZaLKIiXb1ylIwriIuvKRRTEyzdM6ZkTBWEan5W0Ua568O765d5qBo8s/It3eMf0HS3XjrlZ9u3SJyuH2+bbgShIpgvn69QEEwaP62iDuSoPNunUBX/rrKsnjGzYTUZ07CgjO+0mR+lzG4XQ2oYoSKbfoqwFURAlzeTKQhQkxzqqmhAFUZFMthxEQbK8o6oNURAVydLlIAri5RumdERBGFol0kYZzPDRhQ/Jzx69SE7f/Hn5jf5c/olfy7nDvi079Abr5v/6tUz8Tj4uQWFTiFFAjIL2VSxbGDZGgZ1zr738gix5Z5Ec/8nPBL5ybK74vgf0k3X9DpR/bt6gqylskqdUIKzbkV9RoV5LG6ojDUbaiAMVB0friIPu7eua1UEww8DIAyckmGFgVFUlJEaBw0aMAseBGAWOAzEKHAdiFDgOxChwHIhR4DgQo6CqrxuxZcqEKPBjE/z0grPlzLEnNTvY1vbFRiVEwVGJgh/PvsCLRdBdf77R/pvyua+cLf27H+i1BFEwR+r0RvjIj368Rc+s+eA9/RKKKMi6KOiromDgoMFN/deoz57XEQdzVRj8U0ccPKmPawvEgY0tOKi+wYkDlQb2OKLXHvLAg9Olc5c9ZOgRI0JcpS7porfekBdfeFZOPvULofNWyvDKi8/LiuVL5bgTT66UtNX9BDOsCV+zzAQzdDhmPnSPDDxkiPQbMDAw3KhHFCAKHHpEgeOAKHAcEAWOA6LAcUAUOA6IgsB/qhNJmAlRMG7SZdKnd0+55rLzSh70hVOul6XLV8u0qVMSgRKmklpFwd8fnyE3brtBXnnvRV2Tvp1867ALZMDi/aVw1QNEAaKg3DlpI02+Nvl70tZEQanjeUbFwRMqDR5XafCE/q4vEAeWvk99Bxn7wgtyaPee8pHDh8vgho4VpysU1oMoaEmdEQVhPu3Dp2VEgWOGKHAcEAWOA6LAcUAUOA6IAscBUeA4IArCf9eIM0cmRMHg4yfI1F9eJMeOHFryWP0Ahwtm3RIni6rLrjZGwS3zp8rPH/+RbNq2SXp13lumfvqPMqrvsVW3g4zBCBCjIBintFM9u2WzF9vgn/r7pE5X+LBIHFj7DtPVFIaqMBimow4O18cjdfoCW3YIEKMgO30RpiVRjygIUzdpqyNAjILquKWdixgFafdAdfUTo6A6bkFzEaMgKKn40yEKImAcVhS8t3GVXPDXSfLXt6Z7tZ/wkTFy3adulj079YygNRRRiQCioBKhbO5f3LBDZry3RubpaIPnVSK8VbAcY2GLh6gwGK7CYLBKhGEaLNFiH7ClQwBRkA73WmtFFNRKMPn8iILkmUdRI6IgCorJl4EoiJc5oiBevmFKz4QoGH36+fIfP5zY6oiCn1x5k8y++9owx5ZY2jCi4PEls+U7j0yQlRtWSKcOneRnx1whE4ZOSqytVCSCKGibZ0HxqgcW0+A5HWnwnE5ZMHFgj4u3bWtxcB11NYXDNN7B4SoMhnlLM3aUg1UiNA+V2DaZZL3ViIKs91Dp9iEK2l6/IQraXp9ZixEFbbPfEAXx9huiIF6+YUrPhCj41Q13yrxnXykbg6BSDIMwBxx12qAxCl59eb488vR9ctX7V8gO/Rm45yHyqxHXyYoXF8mpnz+zqVnr1n4oD9z9J2IUFHTUvCeIUVDuvN2ZYhRUujaDrHrwwfZGedaTB5u9YIn2uKzRyYODVyyXEW8tlD8d/TEvtoGNPPDEQe7Rgie2vkBj+RYSzLA5m78/9ojstXdvOXzYkdK1S72sWrO5UvdGvp9ghg4pwQwdh4fu+7MMGz5S+u7fL/JzLWiBxChwpIhR4DgQo8BxIEaB40CMAseBGAVB/6Ikky4TosAO1UYV2FY8asDeX6XDjbManyCIKHhrzZvyi/t+JB0/rJe79edrh0+WS4+5UlYvXyFPPzkHUaD9fuetU+WzY8+QPbp2a3HmIwrKfxggCip/UK5WUfCMCoMXF74mG19aIHeO+ri8m5MHhbm7tGsvQ3W0gScO6k0gdJL+9fWB5AGioHk/IAocD4IZOg4EM3QcEAWOA6LAcUAUOA6IAscBUeA4IAoch6xsmREFBsRGFtwy7eFmbMaMHlF2NYQsQKwkCv780m3y079dJAduHSCHtT9MTv3sGV5MAtuWLVmMKMh1IqIgfzaHiUSPKAj+KVC46oGNMpifm67gT1tY3WiLNjbfupo8sCkLnkCwqQsd5YAO9S3SIQqaI0EUOB6IAscBUeA4IAocB0SB44AocBwQBY4DosBxQBQ4DlnZMiUKsgIlbDtKxSj4cMsaueSx8+SB1+7yijt2vxPkt2N+761uwJYuAWIUpMu/2tqLYxRUW065fEs0vkFhvAMTCDaVoXjr3r7OEwZN0xZ0xYU+dR2ibs5OUR4xCtpmNxKjoO31GzEK2l6fWYuJUdA2+40YBfH2GzEK4uUbpnREQRhaZdIWi4Knlz8pkx8eL0vXvSMNdQ3yo1GXyzeP/LcIaqKIKAggCqKgmHwZcYuCUkf01tatsmDrZnkmFzTRYh6sL7FMo8mDz3fZXXrqo404GKTxDoaw2oIgCpK/TqKoEVEQBcVky0AUJMs7qtoQBVGRTLYcREG8vBEF8fINUzqiIAytCqJgu95AXPvUlXLNU1dI445G6d/9IPndKX+SQ3sOiaAWioiKAKIgKpLJlpOGKCh1hK9u3SIvqDx4YbMKBA2YaM83bN9eEsZhOvLg4A4NclhDg8qDjnKo/vbtsOuMPkAUJHuNRFUboiAqksmVgyhIjnWUNSEKoqSZXFmIgnhZIwri5RumdERBGFol0voxCl5Z+ZZ8Z8YEOWzpwTJLf44dfKJc9olfe0sg2vb6qy/K4rfelBPGnNpUCjEK8kCJUZBnQYyC0hdlkFUPWrucC2MU1HjZt8g+a/6/ZNGyJbJ05MflRRUHLxastlCceHeNezBYBYKtumArLRym8sCWb+zcvr1s3rRRpv3xJjln4nejbmLJ8sKca2EaRIwCR4sYBY4DMQocB2IUOA7EKHAciFHgOBCjwHEgRoHjQIwCxyErG6Kgxp4wUXDw2MEy+aGJYnEJzm0/UT569Cfkfx31pWYlIwpaBm4sBIQoyNMIc/NGMMPgF3CcoqBUMMN1OsJogY46eElHILy8dZP+btFpDFvKjj7YT0caDN0hcvRDD8jgc74hHXW9hYEqELqqQIhrC3OuhWkDosDRQhQ4DogCxwFR4DggChwHRIHjgChwHBAFjgOiwHHIyoYoqLEnTBT8b/2x7eg+x8j4HeNl1KgTpE/fA5qVjChAFMx69CH5whkTKp5xYW7eEAUVcTYlSFoUlGvZ4m1bPWnwko46eElHH5hIeE1/beu8ZYuc9/9nyi9P/mxTdot/MEDjHgxQaWCP/e1Xl208SEci7NauXXAAJVKGOdfCVIQocLQQBY4DosBxQBQ4DogCxwFR4DggChwHRIHjgChwHLKyIQpq7Inxd4+XaQumyfeP/pl8Z/hF0l6HFbNlmwAxCrLdP+Val5UYBXHRW6DiwKYtvK4BFF/Xx4UqFF7JCYSyTHS1hQEqDfprHIQDPYHQoM87ePEQsrARoyALvRC+DcQoCM8s7RzEKEi7B6qrnxgF1XFLOxcxCuLtAWIUxMs3TOmIgjC0SqRdu2WtPP3OC3JwtyNqLInsSRFAFCRFOtp6dnZRUIqWzkSQpbps45vbtnji4E0VB2/ao75erEJhWxnEpistaOIAFQg2AsFGI3iP+np/FQt10XZN2dIQBQmBjrgaREHEQBMoDlGQAOQYqkAUxAA1gSIRBfFCRhTEyzdM6YiCMLTKpC1eHjGCIikiRgKIghjhxlj0rigKWsPZqDvfVlmwUKXBm/6jSgR7bXKh9DoMIvWa7wBPIKhI0NUYbDSCP7VhXx2hUNtkhuYtRhTEeEHEWDSiIEa4MRWNKIgJbMzFIgpiBhxT8YiCmMDmikUUxMs3TOmIgjC0SqT1Vz1Yu9H9b6/cHERiFBCjgBgFg2u62rK86kGpYIbVHGxUqx5s2bGjQCDYCIS8UHi3MT8O4dTnn5XlXbvJvH79veZ20pgHnjjITWfwYiLoc3vspRIh6EaMAkeKGAWOAzEKHAdiFDgOxChwHIhR4DgQo8BxIEaB40CMAschKxuioMaeQBTkAfo3B4cMHtaCaqmlIAsTsepBnkaYAHMEMwx+AWclmGFrLY5KFLRWx8bt2+V1m8qgoxDeeXyWvKui4GkVBSYTPthu4xRKb101/oqTBjoKwQIr5mTCQfpoSz4WbogCRwNR4DggChwHRIHjgChwHBAFjgOiwHFAFDgOiALHISsboqDGnkAU5AEiCsqfTKtXvSuMKGBEQaWPmyREQWEbiqXUe42NLhaCTWfIxURYpELhVX29SUcplNt66MoMB6ow6JebxtDjyX/IiD77y+HDjpSuXepl1ZrNlQ498v2zZj4ofQ/oJwMH1Xbe1dIwRIGjhyhwHBAFjgOiwHFAFDgOiALHAVHgOCAKavnWEX1eREEETIlREAHEBIsgRkGCsCOsihgFEcKsoqjlKhHe0mCKb6g0eEslwqu6SsPbOo3BX9qxXJE2nWFfjYfQtwSnhoYAACAASURBVK5eeuv0hf30uT3ur7+99Xkffb9re1aLqaJLYstCjILY0MZWMDEKYkMba8HEKIgVb2yFE6MgNrRewcQoiJdvmNIRBWFolUmLKIgAYoJFIAoShB1hVYiCCGFGXNQiFQdv6+/rKhJsRIL9LtbfpSoS1utUh0qbTV3oYzJBYyFYQMU+dXXe8z7ec1sCsqFSEeyPkACiIEKYCRWFKEgIdMTVIAoiBppQcYiCeEEjCuLlG6Z0REEYWoiCCGilXwSiIP0+qKYFiIJqqKWbx1Y92NGpTua/v85bicH73Z579J5vlWX62Nq0Bv8IbHqDyQRfHnhiQUcjuPdUMOhjUss+pks1/toRBfEzjroGREHURJMpD1GQDOeoa0EURE20eXmIgnj5hikdURCGVom0xCjIQyFGQfmTiRgFtc8VZ9WDGj+sSmQPEzgzTO1hgxmu0pEHTiI06uNWWaHTHBY3OomwRF8vKVipobV27OPLBB2NMPSJuXLgR/pL94GHeFm66hSInjo6wUYsJLURo8CRJkaB40CMAseBGAWOAzEKHAdiFDgOxChwHIhRkNQ3lGD1IAqCcSqbClGQR4MoKH8yIQoQBUE+atIOZhikjUHShBUFQcq0aQwmDuzRZIL32PS8UQqXfbTyTv/XPHl9r73l+f0PaFF8dxUKPfV37w7u0X730ukOJhJ66fNe+tw9dqgpfgKiwKFHFDgOiALHAVHgOCAKHAdEgeOAKHAcEAVBvhEllwZRUCNrREEeIKKg/MmEKEAUBPmoQRQEoVQ+jcVKsJEJS3Q0wsrZj8oHvfvIoo/0k1XbGmWVTnlYpSMWVutohbCbjULYy8SBTm8wqWDBGPfUAIw9VSiYYOjVXt+34Iz6vHBDFDgaiALHAVHgOCAKHAdEgeOAKHAcEAWOA6Ig7DeUeNMjCiLgSzDDCCAmWAQxChKEHWFVxCiIEGZCRVmMgrSWRyx3iLbI42odiWDSYJVKA+83JxBWeu9t82TCShML+rixlWUhi+top2/YaAUbkWBiwUSCe+4Eg4kG733veZ1YEMcsbsQoyGKvtN4mYhS0vT6zFhOjoG32GzEK4u03YhTEyzdM6YiCMLTKpEUURAAxwSIQBQnCjrAqREGEMBMqKouiIOyhb9BVG0wkrFRpsDonEpqe22sdweBJB/19X9NUXuMh3wJbOrJpmkNOJNjoBG/ag4oEeyycFpGUVkAUhD1L0k+PKEi/D6ppAaKgGmrp50EUxNsHiIJ4+YYpHVEQhhaiIAJa6ReBKEi/D6ppAaKgGmrp5tkZREEYgiYJmo1W8ESCEwzeCAWVCu65G8kQZLUHv36TBDZawU11cKMV9tLpDt7ohOLn+l5nnRpR7YYoqJZcevkQBemxr6VmREEt9NLLiyiIlz2iIF6+YUpHFIShVSItMQryUIhRUP5kIkYBMQqCfNQQoyAIpWBpZs18UPoeUPt5F6y20qkqxShYt2O7rFSR8F5OHqzUaQ/v5aY92KgFG6Hwbk4qvK+PYTZ/tMJpuvrD7gcdItuUhb816ByJbioT9lCZ0FWnP3S1R/3dQ9/rpq/379ZJNmxWkbElXJ3l2keMAkeGGAWOAzEKHAdiFDgOxChwHIhR4DgQoyDMX/r40yIKamSMKMgDRBSUP5kQBbXfsLE8Yo0fViWyZ2V5xOiPTKQtiIKwx70iN83BxIKt8mCxFN7XqRHL7bnJhtx+Ww3C38546gl5dr/95eV9+4Sqbk9fJKhA6NbOpEI7lQl1nlDorr9d9L1unlzIiQZPOLj9PYqCOiIKHHpEgeOAKHAcEAWOA6LAcUAUOA6IglB/qmNPjCioETGiIA8QUVD+ZEIUIAqCfNQwoiAIpWBpdkZREOzIXaoPLbaCioSnH7lfGg4c6I0oWLt9h6xRobBW932ooxk+1OeWzl6vscfce2GmRJRr024af8FEgsmDT86dIysGDJRNKiy6qFDokpMOlsZe767pOtujvt7dpk14j/Za39dHGx1R6/bQfX+WYcNHSt/9+9VaVNX5EQUOHaLAcUAUOA6IAscBUeA4IAqq/hMTS0ZEQQRYCWYYAcQEiyBGQYKwI6yKGAURwkyoqF0tRkFCWGOvptseDbJkw2Z5d9O2JnlgQsHEgicVVCg0yQWTDZ5g8Pfv8NKFCepY6YDqNUEXFQhdcgLByQYnFvz33Wv3vkuXEw6FIkIFhaXZrYb4DZXamtZ+YhSkRb62eolRUBu/tHIToyBe8sQoiJdvmNIRBWFolUmLKIgAYoJFIAoShB1hVYiCCGEmVBSiICHQEVcTRTBDb3RCo41ccHLBftfbr76/Tkc2bLBH7/l2fb5DHxv1tb6vrwvf/yBkbIagKEwY7K53124kg5tCYSMcTDB4ssGTCvbcjXrIiwh7bUtbat6cnLDpFmlviIK0e6C6+hEF1XFLOxeiIN4eQBTEyzdM6YiCMLQQBRHQSr8IREH6fVBNCxAF1VBLNw+iIF3+1dYehSiotu5y+SzIowkEEw3rVTSsVwFhwsG9dnJho4oGExJOPjghsU7TbfAe/bzbQ602EfQ4bHqESYZCgZAf3WCjHJyMaJB23lSKBv3t2PSr0yu0ogbd31H3d7RHnW3hPdd83nOLB6HPy22IgqA9la10iIJs9UfQ1iAKgpKqLh2ioDpuceRCFNRIlRgFeYDEKCh/MhGjgBgFQT5qiFEQhFKwNLt6jAKf0syH7pGBhwyRfhojIOgWtSjIYjBDi9WwXsWCLxncaAc3ssF/30Y6rFXRYGKi6f2cqDAB4QmL3CiJIGwn/GOOzDp4kLzVa68gycumMdHgJIOKB08oqGiwERAd6qSdtskJhnyapuf6fq8Zf5GtR42SDnvvI/U5YdGQkxT1uXw21aNByzOpUW912OtcWstj5dfr/tbERWsHSIwCR4cYBY4DMQocB2IUOA7EKKjpz0PkmREFNSJFFOQBIgrKn0yIAkRBkI8aREEQSsHSIAocJ0SB4xB3MENPOOSkgT+9Yn1OOnijGfQGfvuMB2Td0CNlnd6kb1YJkf/dLlu0jZs0zWaN7rB5h8gWzeP22wgIe+1GT9S6Tfz7bHl48FB5p0ePWotqlt+mYZhYcEJBPAlhAsMeTTx0VLFgIsKkw/CZ02XxyI/Lth49NY2m9aSESY/CvCYp/PJyee21preRF15ZufT2WK/5TYjUa93e+7rf2lRu++/bb5ZPfWasdN+zZ6QcwhSGKHC0EAWOA6LAcUAUhPkUiT8toiAA4wunXC8zZs/zUg4Z1F+mTZ3SlAtRkAeIKCh/MiEKEAUBPmoEURCEUrA0iALHCVHgOMQtCoKclVGtemBxHDaLSQTxRIIJhS0qGLrs3lGWfrhRNptwsPdMNGg6W8XC3rM0ddPvl3XDj5YNOqrBXm/15ITIVq8M/dWyTVpstfJ139bcPhMYXpqctLC01o5qtsmzH5N7jzhSlnfrXk320HlsBIaJBU9eeBKjvXxh5sPyj48dK5u7dnVCwkSFJyx8yeFGTfjyw/JbEMw6Pe4Gze+NvvDkhz/awomO/GsTGZZOJYknMHL1e+W7tPfffpOc/qUzZM/ue8rajfklTUMfYA0Z/nTLDXLaF8fL7rvvUUMptWVFFDh+iALHAVFQ2/UUdW5EQQWid9z7V7nx1vtl9t3XeinHTbpMRhwxSC7+1hlNOQlmGPVpGW95xCiIl29cpROjIC6y8ZVLjIL42MZZctRTD+JsK2U7AmnHKLDglU46qFzISQoTFSYabHSEkxDutUkMExG+lPDS5fLY7fImKys34qJJVOTeM4lh6V0eEyY5yeHXafV7UsQJkraymczooPKhgz7WqczooE2vs/f817pPJ5a4fXpQ9tz2ec9z6Wz8hL328njPLb2fbkcuv19Gvr72yqq9prVFSO08srKtLHvH6rPn7bUc7zH3a+V66XNt8dLn6i1O66Xx01saPTarx+psesy1wb0u1YbitAVlemxcPmtDFMupVjpviFFQiVBt+4lRUBu/KHMjCirQLBYDxeLAsiMKojwl4y8LURA/4zhqQBTEQTXeMhEF8fKNq3REQVxk4ys3bVEQ35HVXrIFuTRZ4UZNqGjwhIWTDXmB4UZheGLDG1WRkxG59N7oC2+EhoqJnIjIC4tcObkRF05gOPmx1Rv14den5eZGZPj1tx2VUXs/pFFCk9zwRYc9ehLGiRBfYrTXPmohL0xa7HCCokme2HPN37G+vTRu26FiIrfPS1soVJxk0ZssT7J4IiMnS0yaeGlz7/mPdZrWREdTmzzxYfUVSBJf3HhyRNPnZIvXvhJtyL+Xb6cJnqY2FAogT+IEbYMdQ0tm7pj9Y3AyyB2DL4cKGOWkUfEx2/EjCtK4WkrXiSio0BejTz9fJp9zmpw59iQv5Zwn58ukS66WBbNuacqJKMjOCR2kJYiCIJSylwZRkL0+qdQiREElQtncjyjIZr+01ipEQdvrM2uxrXqwScXEBxu2yja98WvUG6pGfbSRFfZ8m96MNbbT1/qo96X6nr3O7/PyWHovXy69l9fKcOW5NG6fS+fyuH3utQ2+sIkkls8et2ud6kP0ecGj3vQVptlhbbG0lsZ71N9cfnvfJIiVYeXbo9ai5ebrsDq9fV65hfW4NHq/2SJ/Y64Nfj35+qx0G42CemmbV0K+1d/r1lOuHtC3rR/GTtN+REGFrhx8/AT56QVntxAF02+/Sg7ou49YjIIpU/IxC/7whz/I6NGjpV+/fs1Knj9/vrz22mty+umnN73/9ttvy2OPPSYTJkxoem/NmjXy+9//Xi644IKm9+zD+Oc//7lceumlJVu7YMECeemll+SLX/xis/1LliyR6dOny8SJE5u9v3HjRrnuuuvkkksuaVHeFVdcIRdddJE0NNhMvfw2depU+dznPie9e/cuS+yBBx6Qvn37yvDhw1ukKXWshYmuvfZa+epXvyrdu7ecs2iM6urq5LjjjmtR7urVq+WOO+6Q8847r+JFWYptcaY33nhD5s6dK+PHjy9bnu1fu3atjBkzpmKdfoIVK1bIPffcI5MnT66Y58EHH5R99tlHRowYUTGtnRc/+clPpH0V63ivX79ebrjhBvn+979fsR4/wXPPPScLFy6UsWPHBs5jx33ggQfK4YcfHjhPuYSPPPKIdOvWTUaNGhW6LLv+nnrqKfnKV74SOm+lDM8884wsXrxYTjvttEpJW93f2rVZU8FlMoc518LU39pnQZhyakkb5XlXbTvuuusuGTRokAwZMqTaImrON23aNBk2bJgccsghNZdVbQH2GX3UUUfJwQcfXG0RNee77bbb5JhjjpEBAwbUXFa1BZT7flBtedXku/nmm+XTn/607LffftVkjyRPkO8TkVTUSiG//e1vZdy4cdKrV6+4qypbvn0PO+uss6RHxIElwxzQNddcI+eee6501VgNaW1XX321TJo0SeMk7B55EwoFhic1fJHhC5GcrPi9tuHL3/62dOjYqUl8mEjxBYYvO5rJlJxsaTWNL1MKBEq5NizV79m99H5gR31DQRtyEqZAuPhipknqFO1z7XbHWvKYdV8+b/M0R9x+mzx1xldku36nbJnG8SjLpUD2BGfXsp2X3n9Ps/uqyE8KCgxFAFFQAVelEQWIgjxAREH5kwlRgCgI8smMKAhCKVgaRIHjhChwHBAFjgOiwHFAFDgOO7soCPbXQuSqq66S888/Xzp16hQ0S+Tpyv2jLvKKWimwln8+RdXO4vuqqMqlnOoIIAoqcKsUo4BVD/IAWfWg/MnEqgesehDkI5pVD4JQCpaGVQ8cJ1Y9cBx2plUPSl0BQace3Pf//iijjj1R9undJ9iFFEOqu6fpyMsTT5aee+0TQ+nBimR5RMeJVQ8ch1t/958y7pxvSkcdURBkiyOYIaseOPKsehDkDEwuDaKgAmtWPUjuZEyqJmIUJEU62nqIURAtzyRKI0ZBEpSjr4MYBdEzjbvEoKIg7nZQfjgCFqPAAgSktTxiuNaS2icQhyiAbp4AwQyzczYgCgL0xYVTrpcZs+d5KYcM6i/TpuZjEth7BDMMADFDSRAFGeqMEE1BFISAlZGkiIKMdETIZiAKQgLLQHJEQQY6oYomIAqqgJaBLIiCeDsBURAv3zClIwrC0CqTFlEQAcQEi0AUJAg7wqoQBRHCTKgoREFCoCOuBlEQMdAEikMUJAA5hioQBTFATaBIREG8kBEF8fINUzq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""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(colors=['darkturquoise', 'green'], show_intervals=True) # Plots of concentration with time"
]
},
{
"cell_type": "markdown",
"id": "edb7c015",
"metadata": {
"tags": []
},
"source": [
"### Notice how the reaction proceeds in smaller steps in the early times, when [A] and [B] are changing much more rapidly\n",
"That resulted from passing the flag _variable_steps=True_ to single_compartment_react()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "d36a7f1a-5d3d-4619-88e0-c8cea6a82b0d",
"metadata": {},
"outputs": [
{
"data": {
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",
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""
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_step_sizes(show_intervals=True) # To see the sizes of the steps taken"
]
},
{
"cell_type": "markdown",
"id": "f3ff0273-574d-46b4-a352-88c23b9f7f3b",
"metadata": {},
"source": [
"Why the zigzag? It's because of the **\"fast\" preset** picked for the variable steps, in the instantiation of the class `UniformCompartment`: it's like a \"high-strung driver\" that tries to get away with excessive speeed - and periodically overdoes on acceleration, and then slams on the brakes! \n",
"Other presets (such as \"mid\") are more \"mild-mannered\" and more conservative about going too fast too soon."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2b01d1d8-b442-4754-879f-b4ad88ec80cb",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "bc58e5c8-bd08-41d7-9984-18d000869a69",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "de785658-4ea1-4c2a-b55d-c0798a53ffaf",
"metadata": {},
"source": [
"# PART 2 - Comparison with exact analytical solution"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "9b76b747-71ae-437a-bc20-0dc96240d0d6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0. , 0.03061224, 0.06122449, 0.09183673, 0.12244898,\n",
" 0.15306122, 0.18367347, 0.21428571, 0.24489796, 0.2755102 ,\n",
" 0.30612245, 0.33673469, 0.36734694, 0.39795918, 0.42857143,\n",
" 0.45918367, 0.48979592, 0.52040816, 0.55102041, 0.58163265,\n",
" 0.6122449 , 0.64285714, 0.67346939, 0.70408163, 0.73469388,\n",
" 0.76530612, 0.79591837, 0.82653061, 0.85714286, 0.8877551 ,\n",
" 0.91836735, 0.94897959, 0.97959184, 1.01020408, 1.04081633,\n",
" 1.07142857, 1.10204082, 1.13265306, 1.16326531, 1.19387755,\n",
" 1.2244898 , 1.25510204, 1.28571429, 1.31632653, 1.34693878,\n",
" 1.37755102, 1.40816327, 1.43877551, 1.46938776, 1.5 ])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t_arr = np.linspace(0., 1.5, 50) # A relatively dense uniform grid across our time range\n",
"t_arr"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "e4da456b-1a7c-43fe-9e33-cbe3508d9664",
"metadata": {},
"outputs": [],
"source": [
"# The exact solution is available for a simple scenario like the one we're simulating here\n",
"\n",
"A_exact, B_exact = ReactionKinetics.exact_solution_unimolecular_irreversible(kF=3., A0=50., B0=10., t_arr=t_arr)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "829d1d25-609e-47bd-9147-de5c3e2dd290",
"metadata": {},
"outputs": [
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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig_exact = PlotlyHelper.plot_curves(x=t_arr, y=[A_exact, B_exact], title=\"EXACT solution\", x_label=\"SYSTEM TIME\", y_label=\"concentration\",\n",
" legend_title=\"Chemical\", curve_labels=[\"A (EXACT)\", \"B (EXACT)\"],\n",
" colors=[\"darkturquoise\", \"green\"], show=True)"
]
},
{
"cell_type": "markdown",
"id": "ac108d78-28bb-4f01-aac7-023911bcb221",
"metadata": {
"tags": []
},
"source": [
"#### To avoid clutter, we'll just plot [A], as obtained from the variable-step approx solution and the exact analytical solution"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "821de6cf-2921-4da2-902b-42eb9b5d0f95",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig_exact = PlotlyHelper.plot_curves(x=t_arr, y=A_exact, title=\"EXACT solution\", x_label=\"SYSTEM TIME\", y_label=\"concentration\",\n",
" curve_labels=\"A (EXACT)\", legend_title=\"Chemical\",\n",
" colors=\"red\", show=True) # Repeat a portion of the diagram seen just before"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2c957003-ae4d-4cda-9586-0eec7c274c38",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=A
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "A",
"line": {
"color": "darkturquoise",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "A",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
0,
0.007775999999999998,
0.019439999999999995,
0.028771199999999993,
0.038102399999999995,
0.04743359999999999,
0.06143039999999999,
0.07262783999999999,
0.08382527999999999,
0.09502271999999999,
0.10622016,
0.12301631999999998,
0.13645324799999997,
0.14989017599999996,
0.16332710399999995,
0.17676403199999993,
0.19691942399999993,
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0.22916805119999992,
0.25335452159999994,
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0.2920528742399999,
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"xaxis": "x",
"y": [
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0.39231972947920496,
0.3214859966328534
],
"yaxis": "y"
}
],
"layout": {
"autosize": true,
"legend": {
"title": {
"text": "Chemical"
},
"tracegroupgap": 0
},
"template": {
"data": {
"bar": [
{
"error_x": {
"color": "#2a3f5f"
},
"error_y": {
"color": "#2a3f5f"
},
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "bar"
}
],
"barpolar": [
{
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "barpolar"
}
],
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig_variable = uc.plot_history(chemicals=['A'], colors='darkturquoise', title=\"VARIABLE time steps\", show=True) # Repeat a portion of the diagram seen in Part 1"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "9b746a29-09af-445c-93af-229fe7a128e9",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "VARIABLE time steps
Chemical=A
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "A",
"line": {
"color": "darkturquoise",
"dash": "solid"
},
"marker": {
"symbol": "circle"
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aFJQSAeWOn94mCqLuUlDqPTb4+RH1Wowbr9z0J70Qaan3wWLHcE991pSTAVHvc5qz5qlvM6jFSJLP1ajXTlgiF5uiENVX/7Hge17U6yRPUZDldVrsnEC/byVdgLCUKPDfB8uNFqm8U2d6DAEIQKBvEOjVokCn0L8oKfbhF57/rU8Ejnj3QXLVDQu6DBtNuphh0rjhFeijTjKLfUsSNTc77tzEsEzxT4RsiILgCXZ4f+P21z/xCL48i40I8csEWRab0xm1zoE+ZoL9jLqQj1ogKs7FYbD/foxi9eK0kUYUlLvrgf7mTV+A6y3M2G8vSpwEufv3Ei92S9FieSx2XBZ7W/ZPmoPPRx1TUeXCoziyioKoi4pSHyelRiXE6a9pUVDqxN/fj/C6Dv7jvU0UpHnPinNxVO49u1xOy70PljqGe+Kzppwo8KWA/twNb1Ei1i9T7PNaPx/12gm/x4bXR9DvBavWbvSmjRT7DA72L1wmT1GQ5XVq8vS21BoTcT/XTfaHWBCAAAQgYI5ArxcF5lARqa8QKHeS3lc4sJ/pCFTK8VNq6kG6PU92e8S0bVAPAhCAAAQgAAEIQMA+AUSBfca0UGEEKuVCr8Kw9pnuxrn3uwswEAUuZIE+QAACEIAABCAAATcJIArczAu96kECiIIehF/hTftTJpJOP+mJ3Q5PaYmz0GdUP6Om81TC/vcEc9qEAAQgAAEIQAAClUIAUVApmaKfEIAABCAAAQhAAAIQgAAEIACBHAggCnKATBMQgAAEIAABCEAAAhCAAAQgAIFKIYAoqJRM0U8IQAACEIAABCAAAQhAAAIQgEAOBBAFOUCmCQhAAAIQgAAEIAABCEAAAhCAQKUQQBRUSqboJwQgAAEIQAACEIAABCAAAQhAIAcCiIIcINMEBCAAAQhAAAIQgAAEIAABCECgUgggCiolU/QTAhCAAAQgAAEIQAACEIAABCCQAwFEQQ6QaQICEIAABCAAAQhAAAIQgAAEIFApBBAFlZIp+gkBCEAAAhCAAAQgAAEIQAACEMiBAKIgB8g0AQEIQAACEIAABCAAAQhAAAIQqBQCiIJKyRT9hAAEIAABCEAAAhCAAAQgAAEI5EAAUZADZJqAAAQgAAEIQAACEIAABCAAAQhUCgFEQaVkin5CAAIQgAAEIAABCEAAAhCAAARyIIAoyAEyTUAAAhCAAAQgAAEIQAACEIAABCqFAKKgUjJFPyEAAQhAAAIQgAAEIAABCEAAAjkQQBTkAJkmIAABCEAAAhCAAAQgAAEIQAAClUIAUVApmaKfEIAABCAAAQhAAAIQgAAEIACBHAggCnKATBMQgAAEIAABCEAAAhCAAAQgAIFKIYAoqJRM0U8IQAACEIAABCAAAQhAAAIQgEAOBBAFOUCmCQhAAAIQgAAEIAABCEAAAhCAQKUQQBRUSqboJwQgAAEIQAACEIAABCAAAQhAIAcCiIIcINMEBCAAAQhAAAIQgAAEIAABCECgUgggCiolU/QTAhCAAAQgAAEIQAACEIAABCCQAwFEQQ6QaQICEIAABCAAAQhAAAIQgAAEIFApBBAFlZIp+gkBCEAAAhCAAAQgAAEIQAACEMiBAKIgB8g0AQEIQAACEIAABCAAAQhAAAIQqBQCiIJKyRT9hAAEIAABCEAAAhCAAAQgAAEI5EAAUZADZJqAAAQgAAEIQAACEIAABCAAAQhUCgFEQaVkin5CAAIQgAAEIAABCEAAAhCAAARyIIAoyAEyTUAAAhCAAAQgAAEIQAACEIAABCqFAKKgUjJFPyEAAQhAAAIQgAAEIAABCEAAAjkQQBTkAJkmIAABCEAAAhCAAAQgAAEIQAAClUIAUVApmaKfEIAABCAAAQhAAAIQgAAEIACBHAggCnKATBMQgAAEIAABCEAAAhCAAAQgAIFKIYAoqJRM0U8IQAACEIAABCAAAQhAAAIQgEAOBBAFOUCmCQhAAAIQgAAEIAABCEAAAhCAQKUQQBRUSqboJwQgAAEIQAACEIAABCAAAQhAIAcCiIIcINMEBCAAAQhAAAIQgAAEIAABCECgUgggCiolU/QTAhCAAAQgAAEIQAACEIAABCCQAwFEQQ6QaQICEIAABCAAAQhAAAIQgAAEIFApBBAFlZIp+gkBCEAAAhCAAAQgAAEIQAACEMiBAKIgB8g0AQEIQAACEIAABCAAAQhAAAIQqBQCiIJKyRT9hAAEIAABCEAAAhCAAAQgAAEI5EAAUZADZJqAAAQgAAEIQAACEIAABCAAAQhUCgFEQaVkin5CAAIQgAAEIAABCEAAAhCAAARyIIAoyAEyTUAAAhCAAAQgAAEIQAACEIAABCqFAKKgUjJFPyEAAQhAAAIQgAAEIAABCEAAAjkQQBQYgLxuS72BKITISmDwwP4yavgg2byjMWso6hsiMGHsMOH1YQimgTBjRg6WuoYWaWhuMxCNEFkJDB86UAYO6Cc7apuzhqK+AQI6F2NGDpGN2xsMRCOECQLjxwyTjdvqpa3dRDRiZCWwy4jB6vOjVeobW7OG6vH6+vyEDQIQKE0AUWDgCOFCyABEAyEQBQYgGg6BKDAMNGM4REFGgIarIwoMA80YDlGQEaCF6ogCC1AzhEQUZIBHVQhUIAFEgYGkIQoMQDQQAlFgAKLhEIgCw0AzhkMUZARouDqiwDDQjOEQBRkBWqiOKLAANUNIREEGeFSFQAUSQBQYSBqiwABEAyEQBQYgGg6BKDAMNGM4REFGgIarIwoMA80YDlGQEaCF6ogCC1AzhEQUZIBHVQhUIAFEgYGkIQoMQDQQAlFgAKLhEIgCw0AzhkMUZARouDqiwDDQjOEQBRkBWqiOKLAANUNIREEGeFSFQAUSQBQYSBqiwABEAyEQBQYgGg6BKDAMNGM4REFGgIarIwoMA80YDlGQEaCF6ogCC1AzhEQUZIBHVQhUIAFEgYGkIQoMQDQQAlFgAKLhEIgCw0AzhkMUZARouDqiwDDQjOEQBRkBWqiOKLAANUNIREEGeFSFQAUSQBQYSBqiwABEAyEQBQYgGg6BKDAMNGM4REFGgIarIwoMA80YDlGQEaCF6ogCC1AzhEQUZICXU9VZc+fLhPFj5fr55+XUIs30ZgKIgozZXfqNb8gup3xGdp0wMWMkqmclgCjIStB8fUSBeaZZIiIKstAzXxdRYJ5ploiIgiz07NRFFNjhmjYqoiCa3LW33Ct3Lnqo25PLH7/Te+yeBx6Vq25YIEsWXi2TJo5Liz9WvaSiQPf9wUeekqX331iIv2rtBjnxzMvkigtnyxkzj43VLoV6JwFEQda89usn68aPl42/WiK7HzAlazTqZyCAKMgAz1JVRIElsCnDIgpSgrNUDVFgCWzKsIiClOAsVkMUWISbIjSioDu0i+bdLA8vfVZ8KeCX0I8f8e6Dcr/QNiEKUhwaVOmlBBAFGRP7zEc+Ikc8+qhs3mWMvLHoAZlw+LSMEamelgCiIC05e/UQBfbYpomMKEhDzV4dRIE9tmkiIwrSULNbB1Fgl2/S6IiC7sQOOWaOzJl1glxy7ulFcT7xzDKZe+l1hREF/t/6G3s90sDfbrvmYlm9bmOXx4KjEGaceoGcdNxRXdoKi4Hw37rO5q07uvQtPNIh+KS/L3q/giMK/FEGftnjZ0zrMr3Bb1c/r8WJ3g6dMlkW3Tav5GHmt3Pr3Yu9fu46ZrQsuOnr3ogGzWP6EVML9cN9CtfVBcvlIukx39fLIwoyHgEtLS3y9MdPkqMf/p1UDx8uyxf+UiZNn5ExKtXTEEAUpKFmtw6iwC7fpNERBUmJ2S2PKLDLN2l0REFSYvbLIwrsM07SAqKgOy19IX741ANKrglQTBQEL6T9kQnBC3D92Lr1WwoX22lFQXBagb6g15t/AR819UA/H7woj5qKEN5vHffFFSu7yIU4EkWX0VtQiPjtxREFwbo+53C9JMc4ZbsSQBQYOCLWbq6TV88+S4751X3SOHiwPPuTn8nkj37MQGRCJCGAKEhCK5+yiIJ8OMdtBVEQl1Q+5RAF+XCO2wqiIC6p/MohCvJjHaclREF3Sv76A8FnwtMQiomC4MWxHydYVz+mv2n3L/TTiIJwj8PtxBEFusyzz63oMjrA3ye/v1FTHrTo0FuphRXDowR0+SSiILyOgmZ0zlkn5z7lI87rpxLLIAoMZM2/68Hyyy+R4277vrQMHChP/uBHcsCpswxEJ0RcAoiCuKTyK4coyI91nJYQBXEo5VcGUZAf6zgtIQriUMq3DKIgX97lWkMUlCYUHubvf7OdRRToqQn+xXhaUeB/ax8lM+KIgigJEL6YLyYKgiMioujZEAXh6RnljmueL04AUWDg6AjeHnHZzd+Vj155hbSrRQ7//J3rZPIXzjHQAiHiEEAUxKGUbxlEQb68y7WGKChHKN/nEQX58i7XGqKgHKH8n0cU5M+8VIuIgvj50Bf143cb430L31OiwG83OG8/zYgCREH8vPe2kogCAxkNigId7sW7fiTHfeVCUXDl6Ysvk72+VnohDwNdIIQigChw7zBAFLiVE0SBW/lAFLiVD0SBW/nQvUEUuJUTREHXfOhv1RctfixyIcPgWgCmRIGOOe2wKbEXM4waLZBGFGSZepBmRIGmrEcaxFmjIGrqASMKzL1vIAoMsAyLAh3ypfsWyTH/8SUZqBY7/NvnPi97/O9NImqUAZs9AogCe2zTRkYUpCVnpx6iwA7XtFERBWnJ2amHKLDDNUtUREEWeubrIgq6iwK9Or9eqT+4YKB/MW566oGe8//3Za8W2vLbCS6AGPz2P2rdA396RPjOB8H1EvwLdf8iPO5ihhPGj+2yHkF4McaoIzJq6oEuF14s0V/sMSgGoupGTc8w/0roOxERBQZyHSUKdNgVv3tQ3v/vn5UhTU3y3Ekny+53/Eykf38DLRIiigCiwL3jAlHgVk4QBW7lA1HgVj4QBW7lQ/cGUeBWThAF0fmIWgMgeOFtakSBfwHt3+5QCwL9jX3wAj08TcC/wPZ7rqch3LnoocK6B/px/44F+v9Zb48YXLgwiygI347Rv5UkoiDf9wREgQHexUSBDv3aE4/L4WecJsPr6+WFDx0ru/70lyJDhhholRBhAogC944JRIFbOUEUuJUPRIFb+UAUuJUPRIF7+UAUuJcTegQBmwQQBQbolhIFOvyav/9Vppz2CRldXSUr3jNNRt6/RGT4cAMtEyJIAFHg3vGAKHArJ4gCt/KBKHArH4gCt/KBKHAvH4gC93JCjyBgkwCiwADdcqJAN7H+peUy8bSPybhNm+S1gw+RIQ88JP3HjDXQOiF8AogC944FRIFbOUEUuJUPRIFb+UAUuJUPRIF7+UAUuJcTegQBmwQQBQboxhEFupnNq96QXT5xnOy1dq2s3Xtvaf3NH2Tg+D0M9IAQmgCiwL3jAFHgVk4QBW7lA1HgVj4QBW7lA1HgXj4QBe7lhB5BwCYBRIEBunFFgW5q+/q3ZODME+TAf70qb03cUxp/86gM3nMvA70gBKLAvWMAUeBWThAFbuUDUeBWPhAFbuUDUeBePhAF7uWEHkHAJgFEgQG6SUSBbq5662ZpOeVjcsjyF6Vq1GjZtmCRDDr6gwZ60rdDIArcyz+iwK2cIArcygeiwK18IArcygeiwL18IArcywk9goBNAogCA3STigLdZH1NjayfM0uOfvwxaR44SNZff7MMOGO2gd703RCIAvdyjyhwKyeIArfygShwKx+IArfygShwLx+IAvdyQo8gYJMAosAA3TSiQDfb3NYmf7v4P+TUBXd5vXjr/P+S9v/+H5F+/Qz0qu+FQBS4l3NEgVs5QRS4lQ9EgVv5QBS4lQ9EgXv5QBS4lxN6BAGbBBAFBuimFQV+07++5Ub50rzLpb8SB6uOPV4G3nWvyNChBnrWt0IgCtzLN6LArZwgCtzKB6LArXwgCtzKB6LAvXwgCtzLCT2CgE0CiAIDdLOKAt2Fexf/Us758tmyU55ei38AACAASURBVEODrJ/6TpFF/ydtu48z0Lu+EwJR4F6uEQVu5QRR4FY+EAVu5QNR4FY+EAXu5QNR4F5O6FF8AoccM0euuHC2nDHz2PiV+nhJRIGBA8CEKNDduO+ZJ+XTs0+XcVu2yI7x46VRyYKWQ6Ya6GHfCIEocC/PiAK3coIocCsfiAK38oEocCsfiAL38oEocC8nUT2aNXe+TBg/Vq6ff16Xp+954FG59e7FsvT+GwuPzzj1Atm8dYcsf/zOLmX9x4MPBsvoNl5csdJ7+tApk2XRbfMKRXU7V92wQObMOkEuOff0wuOr1m6QE8+8rFuXg3F1uycdd1SXerqCHzNcOdyG//y1t9wrDz7yVJd97WlR8MQzy2TupdfJkoVXy6SJlfFlMKLAwGvelCjQXfnd66/IkaefJge//po0DhsmNbcvkMaPfsxAL3t/CESBezlGFLiVE0SBW/lAFLiVD0SBW/lAFLiXD0SBezmJ6pF/QRq++NcX99MOm1K4CNflbvrx/V6ImSdO7/JNe/iC/aJ5N8vfl73a5cJbP6a3sJDw2wlfqPui4LZrLpbpR3R8ERqWGuVEQXifimUkShT0dPYQBSkyoO1O0i1srpLWN13epCjQffvj5g2yx+xZMuOvz0hb//6ydd43pek/LjDd7V4XD1HgXkoRBW7lBFHgVj4QBW7lA1HgVj4QBe7lA1HgXk6K9UhfXwUvyHU5/Vjw22x9Me1vzz63osuogPAFe9RohGKiQLejL+jDfYgSBboPwbZNiAL/gjzIRvdHxz7nrJM9IeKLhPG7jSmMjNDTEh5Y8kTh7zC/4CiLYiMZ/DaD17e7jhntCZbwNa8fPzxawpchxfroT53Qz9+56KHCbtqYVtHjIwr8gynuS0/D1EkMDnGJW9dWOdOiQPfzufo6qfry5+X0Xy/2ur3xs3Ok5bqbRAYMsLUbFR8XUeBeChEFbuUEUeBWPhAFbuUDUeBWPhAF7uUDUVA8J0uqqqW1vT33pJ00elRkm+GL+KjrJ33hu+Cmr3v19ZSAoEQIX7BHTWeIEgW6nWf+8bI3yiD8fJQoCF68636YEAU6TtSIgrAo0BfZ/sW6f9HtX2yH6wf3P2o/gkkIj9zQHDSPqBEF4cd02XXrt3jXuX6fwkJBi4TwqBHdp0WLH+s2ZSPrAYkoyEpQ1bchCnS31rW2yGNXf0O+cv11ohIlm97/AWn56c+lfdRoA73ufSEQBe7lFFHgVk4QBW7lA1HgVj4QBW7lA1HgXj4QBcVzMuL5F6VW3b0s7632XYfKTmr0cXgLX0jqi9fg9AJ/2oH/xWv4+fAaBcfPmNZtikGUKNBxzv/Cqd7UAt3G5d+5vTBdodgaBcFvwsuJgvB+JlmjIGpEgb9eQ3jERPBvv99BkRKWAWFRELVGRJQoCDMM5q3YOgtaHOgtj/UOEAUGXtG2RIHuWr0SBD/95c/ksgvPk6GNjbJl8n7S8ovF0rrPZAM9710hEAXu5RNR4FZOEAVu5QNR4FY+EAVu5QNR4F4+EAXFc/KplW9KYw+MKFi87z5FOxW8MA5PO9AXqEe8+6DCugThEQfBC/bgt9zBxqJGDMw+/1vdFkv85le/6ImDYt/EBxcZLCcKsqxRUE4U6AUY/fj+dIDgt/dh0FHyRJcJCxG/XJQoCC4KGYyvpYQeIRBe5yG4D5r/w0ufLVSzsUhij4sC994Gk/fIpijwe/OrJx+XWZ87U3bdvk1qRo+WKnVHBJl2RPLO9uIaiAL3kosocCsniAK38oEocCsfiAK38oEocC8fiAL3clKqR/ob6XXrN3tCIDxtu9gacf7FZviCPeoCPiwKwnPm/b75F8rFREHw23kXRUHUiIK4R0Jwn3Wd8CiAYus86LKlRhT4i0H6/Sgmc+L2s1i5ihAF/sEc1yJlhZK0fh6iQPfp76+9IgecfqpMWfm618XXFv5ShnFHhEK6EAVJj1z75REF9hknaQFRkISW/bKIAvuMk7SAKEhCK5+y48cMk43b6qUt/6nf+exghbWCKKishPnfYOsL9eDogfCUAH+vSl2wR13khy9yw9MXdNzgUPqoGOHHTImC4IgAf//SjijQ9cNrNOj9eupvyyPXBNBl/SkdQcmg4+i1IIKLJBYbZeCvURAcURAUB3r/9OYvbFhKOGQ5ap0VBeEVIG0Mp8gCLlg3L1Gg21y9ZbO0f/aT8j51RwS9vf7Fc2Tod75ralcqOg6iwL30IQrcygmiwK18IArcygeiwK186N4gCtzKCaLArXzE6Y2/1kDwy9aohQl1rOC8/KgLdv/aLHx3AH03Or0uQbE58/4F+tHvPdS7UA5v4TUKNm/d0aWIjq/XV9BTA8JbqbsPBNdZKHbXg+AaBcWmHvhthtdtKHZtGp4SENy/4HPF7nrgj8CIGqHh5zE8vcG/s0KcYyJJGedEQRhu+NYUSXYuTVl9EOhbZQTvqhDsU9StGfMUBXqf6tRiKS9e9GWZufBubxfXvfdI6b/g59K2625pdrnX1EEUuJdKRIFbOUEUuJUPRIFb+UAUuJUPRIF7+UAUuJcTetR7CURNPch7b50RBcG5Mr55iboHqE1AWhJ4H0wBURBeBTNqlcu8RYHP4JF7F8gnL7lQhtfXy/bdd5eGu5Us6MPrFiAKbL460sVGFKTjZqsWosAW2XRxEQXpuNmqhSiwRTZ9XEYUpGdnoyaiwAZVYkIgmgCioJNLsTUI8hQF/ryaNW9tkmefW1EYURAWA2FxoHehp0SBbvvp5S/IQf/+GXnH669Ly8BBsvnKq6TtnPP75GsOUeBe2hEFbuUEUeBWPhAFbuUDUeBWPrwvblijwKmkIAqcSgedgYB1Ak6MKNBCIGpuRV6iICgDtL0JioLgwhc6G+H7kva0KNDtr6zeIdvP/px8/JGHvQNm/b+dKm03/0hk2DDrB5BLDSAKXMpGR18QBW7lBFHgVj4QBW7lA1HgVj4QBe7lA1HgXk7oEQRsEnBCFOgdDE498NclyEMURN3aIygKgvf2DIqC4AIWra09vxzv9tZWufvb35Evf+t/ZEhTk1S94yAZ/n+LRfbbz+bx41bsfiL91Y9awiG/TbXHVpzAAJWQVparduYQ0a8PfZvnnn/HcgZJj3bEe/vozEmPdoTGCwS8zxBeIM4cEf379VP5ICGuJKQ3fYbo8xM2CECgNAFnRIHfzbwXMwyvYOn3wx/hEGdEwXp16x4XNn19fNefHpcz535BJq1/SxpGjJS6H/1EmvrILRQHD+gvI3YaJFurG/NLB+cvJVnrYaPrt7rx+sjvoHC3pZ1HDJb6xhZpbM7TprnLo6d7ttPQgTJQnaxW1TX3dFdoXxHQIwp2HjFENu9ogIcjBHbfZZhs3s7tER1Jh4wePlgaW1qlobHVlS6l7oc+P2GDAAQqTBT43Q3eHtHWLR+i0ISnHri+RkHUPjyyfp2MnztHPvrkE9KubPyWCy6Wpq9fqb5u79+rXw9MPXAvvUw9cCsnTD1wKx9MPXArH0w9cCsfujesUeBWTph64FY+6A0EbBNwbkRB1A4XW+zQBpywKHD5rgel9n95U6M8c/U35Ks3f08GqGkJ26d/UBruWChtY8bawOZETESBE2no0glEgVs5QRS4lQ9EgVv5QBS4lQ9EgXv5QBS4lxN6BAGbBHpcFGgJsPzxO2Pvo75wf2DJE4W7EsSuGLNgWBToasHpEIdOmdyt7Z6860Gp3dqqBMFNv/+NzL/gPBm/ebPU7jFB6hb8XJoPOzwmjcoqhihwL1+IArdygihwKx+IArfygShwKx+IAvfygShwLyf0CAI2CSAKDNB1VRT4u3b1ay/LqV+eKzP+9qy0DB4iNVd/V+pm/7uBPXcrBKLArXzo3iAK3MoJosCtfCAK3MoHosCtfCAK3MsHosC9nNAjCNgkgCgwQNd1UaB38eH6Wtl05dflkh+r2yaqbf2550vb5fNFhg41QMCNEIgCN/IQ7AWiwK2cIArcygeiwK18IArcygeiwL18IArcywk9goBNAk6IgqQ7GDX8P2kMk+UrQRTo/V3V0ix3/WqRXH3Jf8momhqpnryvNPzo7l4zFQFRYPKoNhMLUWCGo6koiAJTJM3EQRSY4WgqCqLAFElzcVjM0BxLE5EQBSYoEgMClUOgx0VB5aAq3tNKEQX+Hly9Yrmcdv458sG//01aBw2S2ksvl5oLvlLxd0VAFLj3akIUuJUTRIFb+UAUuJUPRIFb+dC9QRS4lRNEgVv5oDcQsE0AUWCAcKWJAr3Lv6mtljX/+2254pabZVBLi+x475HS8MO7pHWvSQaI9EwIREHPcC/VKqLArZwgCtzKB6LArXwgCtzKB6LAvXwgCtzLCT2CgE0CiAIDdCtRFOjdXqMEwfeeeFS+ceH5su+aNdI4YoTUffs6qT9jtgEq+YdAFOTPvFyLiIJyhPJ9HlGQL+9yrSEKyhHK93lEQb6847TGiII4lPIrgyjIjzUtQcAFAogCA1moVFGgd71N/dy6fq3sd/kl8u//94BHY8fxJ0rdLT+W9tE7G6CTXwhEQX6s47aEKIhLKp9yiIJ8OMdtBVEQl1Q+5RAF+XBO0gqiIAkt+2URBfYZ0wIEXCKAKDCQjUoWBf7uv9jUIIt+eY9cd/lXZefqaqnbbXepv+0n0vjBDxkglE8IREE+nJO0gihIQst+WUSBfcZJWkAUJKFlvyyiwD7jpC0gCpISs1seUWCXL9Eh4BoBRIGBjPQGUaAx1Le1ybWvviRnfflsef/zz0l7v36y/fNnS/38b1fEbRQRBQYOZsMhEAWGgWYMhyjICNBwdUSBYaAZwyEKMgK0UB1RYAFqhpCIggzwqAqBCiSAKDCQtN4iCnwUj6iFDlde9225/AcdCx3WTN5P6u66R1oOPtQALXshEAX22KaNjChIS85OPUSBHa5poyIK0pKzUw9RYIdrlqiIgiz0zNdFFJhnSkQIuEwAUWAgO71NFGgkG1tb5Pon/iDzLjjPW+hQ30ax6tIrpP6Ci529jSKiwMDBbDgEosAw0IzhEAUZARqujigwDDRjOERBRoAWqiMKLEDNEBJRkAEeVY0TuGjezV7M6+eflyr2IcfMkSsunC1nzDw2Vf2+UMk5UTDj1Atk89YdkeyXP36nkznpjaJAg25XPz/ZsE72VAsdznngVx57l2+jiChw7+WBKHArJ4gCt/KBKHArH4gCt/Khe4MocCsniAK38lGqN8Wup/S1lH7u8KkHdLnAfuKZZTL30uvktmsululHTPVCr1q7QU488zI5dMpkWXTbvG7N+c8Hn9AX3mve2iR3LnqoaPdMXc8lEQXX3nKvPPjIU7L0/hsL/UIUlD+enRIFs+bOlwnjx6Y2Q+V3106J3ioKfFovNzfKfffcJd+a9/+8hQ5rx4yRxquukYZPf8YO0JRREQUpwVmshiiwCDdFaERBCmgWqyAKLMJNERpRkAKa5SqIAsuAE4ZHFCQE1oPFtQw46bij5JJzT4/shb5IDkoBXf6bX/1iQRLoSvriWm/6on/Jwqtl0sRxhVj3PPCoXHXDgi4x9JM6TvBiPOoC3RSWrKLAVD96cxynREH4oK0U8L1dFOg8NLS3y03/XCanXPAf8sG//81LTfX73i/1N/xAWvY/0IlUIQqcSEOXTiAK3MoJosCtfCAK3MoHosCtfOjeIArcygmiwK18lOpNOVGgL/RvvXuxd1Ff7IJbf4F7/hdOlZt+fL9MO2xKF+lQLr7ft7iiQJcLjkIITgnQ/XhxxUov5PEzphW+UA722x8RERQa/oiBvSbs7o2WCG7+yIpzzjq5MPUg2Iddx4wuCA8/9pxZJxT6GOxH5RwVyXuKKEjOrFuNviAK/J1+rK5G/vHDm+WKG6/3Rhe0qbUL6r58gVRd8vUevzMCosDAwWw4BKLAMNCM4RAFGQEaro4oMAw0YzhEQUaAFqojCixAzRASUVAC3pIlIq2tGeimrHrSSZEV41zI6wvw9Zu2elO+w9MB9LSC2ed/y7tYDkoF3Zg/5SA8yiCqI3FEgX8h7vdBx1+0+DFPTITrB/crrijQaxBE9UPH8kVBWDTo2OvWb/GmXPjP+XIgyf6nzKoz1ZwSBfqAnXni9IpbVKIviQJ95G5ra5Ur1G0UP/nNb8iZv/2NdzA3T9xTqq7/vjR++LgeO7gRBT2GvmjDiAK3coIocCsfiAK38oEocCsfujeIArdygigokY8RI0Rqa/NPmG5zp526tVtqjYJg4WLz9P1pB/7UBV3OFwNJLpSTiIIo8RC8mNf9LjYSotSIgjiiIDyqIriPq9Zu9EYkhEcrBKdu5J/4fFp0ShToJF/+ndu7zG3JB0O2VvqaKPBp3VWzQ/7w+4fk1iv/W/Zbs9p7uOETM2X7d74rbePGZ4OaojaiIAU0y1UQBZYBJwyPKEgIzHJxRIFlwAnDIwoSAsuhOKIgB8gJmkAUlID1qU+JNDYmoGmo6OLFkYHijijQlfWw/vCIAl1/wU1fL6xLoC+kJ4zf1fuW37Qo0H3Q8R9e+mxhX/yL8vC0dH9tBN1fkyMK9JfVwekV/j5qGaC3KFHQF+6Y4JQo0AdDqc3UKpmGXpqFMH1VFGgA/2pukv9cv0pm3nqLfO0nP5YhTU3SPmKkVH3tv6X2S+fmeitFRIHpIzt7PERBdoYmIyAKTNLMHgtRkJ2hyQiIApM0zcRCFJjhaCoKosAUSftxyomCUmsU+N/Oh3sZnLdfLr5fN86IgnA7wWH/cUcURMmL4GiJclMP0owoQBTYP457RQt9WRT4Cbxq22Z5+KUX5I758wqLHbYcMlW2fe9WaX7Xu3PJM6IgF8yJGkEUJMJlvTCiwDriRA0gChLhsl4YUWAdceIGEAWJkVmtgCiwitdo8HIX8sGpBLrh4AW5vqhet35zt7vQBb/dN3nXAx1Lb3qKgN6CF+1x1yjQ9aL651/MB0ci+KCTrlEQtVCi32ejyXMomFMjCjSXKIvl+hwQREHHEf1kY51ctHmDzHhwsXz3u/8r47Zs8UYU1H7+bKm64htqpIGav2VxQxRYhJsyNKIgJThL1RAFlsCmDIsoSAnOUjVEgSWwGcIiCjLAs1AVUWABqqWQpdYo0BfUegX/4K0T/esvfc2lh9lHfVse/tY9zjVbnBEF/mgAH0Vw5IJ+LM5dD3S54F0L9MKDeipDcD+CTNLc9QBRYOlgjRvWtz3BRPgHj8vDOxAFb2e4Xt1G8bs7tsg961bLt753g5x9/33Sv63NW7NgxzevlfqZp8U9HBKXQxQkRma9AqLAOuJEDSAKEuGyXhhRYB1xogYQBYlw5VIYUZAL5tiNIApio6IgBHoFAadGFITnofiEw7flcI08oqB7Rl5ubpSLt2yQAc8/Jwv+3+Vy8OuveYUaP3CMbL/xFmmdtLfxNCIKjCPNHBBRkBmh0QCIAqM4MwdDFGRGaDQAosAoTiPBEAVGMBoLgigwhpJAEKgIAk6JgvDKlj7B8P01XSOLKCieEX1nhKvVdITP3/NT+Z9bfiDD6+qkfdgwqb7oUqn5T7WS6MCBxtKJKDCG0lggRIExlEYCIQqMYDQWBFFgDKWRQIgCIxiNBkEUGMWZORiiIDNCAkCgogg4JQoYUVBRx07szm5oaZHLt22U51etlJu/82055bE/eHVb9j9QtqvFDpuOeF/sWKUKIgqMYDQaBFFgFGfmYIiCzAiNBkAUGMWZORiiIDNC4wEQBcaRZgqIKMiEj8oQqDgCTokC1iiouOMnUYefaqiXS7ZtkAOXLpUfXTVf9lq/3qtfd8ZsqZr/LWkbMzZRvHBhREEmfFYqIwqsYE0dFFGQGp2ViogCK1hTB0UUpEZnrSKiwBraVIERBamwUQkCFUvAKVGgKcZZQdM12kw9iJ+RFlX0R1Xb5Acb35LLbvm+/NfCBTJQjTjQkqBq3lVSd+bn4gcLlUQUpEZnrSKiwBraVIERBamwWauEKLCGNlVgREEqbFYrIQqs4k0cHFGQGBkVIFDRBJwTBZVIE1GQPGubW1vkym2b5aWXlsnd/325HPHii14QPQ1BT0fQ0xKSboiCpMTsl0cU2GecpAVEQRJa9ssiCuwzTtICoiAJrXzKIgry4Ry3FURBXFKUg0DvIIAoMJBHREF6iH9vapCvbF4v03/5c7nmxutlzI4d0j5okNR++QKpuuTrIkOHxg6OKIiNKreCiILcUMdqCFEQC1NuhRAFuaGO1RCiIBamXAshCnLFXbYxREFZRBSAQK8igCgwkE5EQTaIbar6XdXb5fY3X5Mrr7tWPvfrxV7Alol7yvabfyhN6paKcTZEQRxK+ZZBFOTLu1xriIJyhPJ9HlGQL+9yrSEKyhHK/3lEQf7MS7WIKHArH/QGArYJOCEK9G0Rr7hwtlx1w4KS+7v88Ttt80gVH1GQClu3StvaWuWb27fIm08ulTvmz5Mpb7zhlWk4+RTZ/u3rpG3c+JINIQrM5MFkFESBSZrZYyEKsjM0GQFRYJJm9liIguwMTUdAFJgmmi0eoiAbP2pDoNIIOCEKKg1auL+IArMZXN7UKBdvXCsn/+hWufzHt8uwhgZpHTFSar4+T2q/eI5I//6RDSIKzObBRDREgQmK5mIgCsyxNBEJUWCCorkYiAJzLE1FQhSYImkmDqLADEeiQKBSCDglCvTIgtuuuVimHzG1Cz9928Rb714sS++/0UmuiALzaWlXIe+t2SELX3pevnXV/8gJf37Sa6R2xoel/itfk6ajju7WKKLAfB6yRkQUZCVotj6iwCzPrNEQBVkJmq2PKDDL00Q0RIEJiuZiIArMsSQSBCqBQEWIAv+WiUw9qIRDymwfq9ra5Jodm6Xuvp/Ld6/7X5mwaaPXQMPxJ0rVld+UlgPfUWgQUWCWvYloiAITFM3FQBSYY2kiEqLABEVzMRAF5liaioQoMEXSTBxEgRmORIFApRCoCFFw7S33yoOPPMWIgko5qiz0c0Vzo1yx+g35yB0/kq8suEtG1tZ6UxDqPv0Zqf7af0urWvgQUWABfMaQiIKMAA1XRxQYBpoxHKIgI0DD1REFhoEaCIcoMADRYAhEgUGYhIJABRDocVHgjxYoxypqSkK5Onk9z9SDvEiL/KquWr6/8lWZe9stcu4vfi6Dm5ulfcgQqf3CXGm89GsycuLusnlHY34doqWSBBAFbh0giAK38oEocCsfiAK38qF7gyhwKyeIArfyQW8gYJtAj4uC4A4WW6PANoSs8REFWQkmq1+npiN8d8dWeejVl2X+92+SM5f8Vvqrx9pHj5a2r1wiG+acKzJsWLKglLZCAFFgBWvqoIiC1OisVEQUWMGaOiiiIDU6axURBdbQpgqMKEiFjUoQqFgCTomCSqWIKOiZzL2uRhNcsW2jbHnxBbn6ezfIx574k9cRfRvFqksvl7rPzhEZMKBnOkerHgFEgVsHAqLArXwgCtzKB6LArXzo3iAK3MoJosCtfNAbCNgmgCgwQBhRYABihhC/q6+VK7dtkr2efUauu/46OXLZMi9ay34HSNUV86XhEzMzRKdqFgKIgiz0zNdFFJhnmiUioiALPfN1EQXmmWaNiCjIStBsfUSBWZ5Eg4DrBJwSBavWbpATz7ysKDPueuD64dRz/Wtub5dF9dVyw/Yt8r6Hfyff/P7NctDK170ONR92uOz45rXSdORRPdfBPtoyosCtxCMK3MoHosCtfCAK3MqH7g2iwK2cIArcyge9gYBtAk6JghmnXiAnHXeUHPWeQ+Ty79xeuMvBrLnzZeaJ0+WMmcfa5pEqPiMKUmEzXknf9WDQTgPl2jUb5PtV2+RTv/y5XHnbrYVbKtaf8kmp/srXpGXKQcbbJmA0AUSBW0cGosCtfCAK3MoHosCtfCAK3MsHosC9nNAjCNgk4JQo8BcznKRWrp99/rcKokDfGSEoDmwCSRMbUZCGmvk6wdsjVre3ya1KFvxk03o5+56fydfvuF12rq72Gm2aPkNqzj1fGj76MfOdIGIXAogCtw4IRIFb+UAUuJUPRIFb+UAUuJcPRIF7OaFHELBJwElRMP2IqaKlgT/VwL+FIlMPbB4KlR87KAr8vdna2irfq9oq//fWajnnZz+TC+5ZKGN27PCebp76Lk8Y1H/6M5W/847uAaLArcQgCtzKB6LArXwgCtzKB6LAvXwgCtzLCT2CgE0CTokCPcVg2mFT5JJzT5fg/6+95V558JGnCiMMbAJJE5sRBWmoma8TJQr8Vja1tshNaoTBL7Zuktn33ycX//Rumbx2rfd06z6TpebLF0jtmZ8TGTLEfMf6cEREgVvJRxS4lQ9EgVv5QBS4lQ9EgXv5QBS4lxN6BAGbBJwSBeEd1aMK/G3Jwqtl0sRxNlmkjo0oSI3OaMVSoiAoDL5fvU0W7tgmJ6tFDy+96yfy7n/+03u6bdfdpPZL50qN+mkfNdpo3/pqMESBW5lHFLiVD0SBW/lAFLiVD0SBe/lAFLiXE3oEAZsEnBYFNnfcZGxEgUma6WPFEQV+9C1qhMEPqrbL3bU75Og/PymX3fkTOfaZp72n24ePkNqz/l1q/uNCaRu/R/oOUVMQBW4dBIgCt/KBKHArH4gCt/KBKHAvH4gC93JCjyBgk4BTosBfzFCvUVBJG6LAjWwlEQV+j7e1tcotakrCndU7ZN9XVsgVP/6RfPLR30t/tbaBDBokdafNkpoLvyIt+x/oxk5WWC8QBW4lDFHgVj4QBW7lA1HgVj4QBe7lA1HgXk7oEQRsEkAUGKCLKDAA0UCINKLAb3aHEga3qhEGd1Rvl7Hr1shXf3KHfP7Xi2VwY6NIv37ScNwJUvOfF0vT+95voKd9JwSiwK1cIwrcygeiwK18IArcygeiwL18IArcywk9goBNAk6JAr2A4cwTp8sZM4+1uc/GYyMKjCNNFTCLKAgKgx8qWXCHkgaDtm2Vixb+VP7zlz+XkZ13Smg64n2eMPBuragEAltpFWN5CwAAIABJREFUAogCt44QRIFb+UAUuJUPRIFb+UAUuJcPRIF7OaFHELBJwClRsGrtBpl9/recvbtBsUQgCmweovFjmxAFfmtVbW1yu1r08HYlDZpra+Wc+34hX/3ZQtlt/XqvSMuB75Ca8y+Suk+e7k1RYIsmgChw68hAFLiVD0SBW/lAFLiVD0SBe/lAFLiXE3oEAZsEnBIFwbscRO308sfvtMkidWxEQWp0RiuaFAV+x2ra2+THanSBHmVQ09QoZy75rVy54G7Z51+vekVaJ0yU2nPOl9o5X5T2nXYyuj+9IRiiwK0sIgrcygeiwK18IArcygeiwL18IArcywk9goBNAs6JgtuuuVjCixne88Cjcuvdi50daYAosHmIxo9tQxT4rdepEQZ31Gz31jHQCyCe9Melco0SBgf97VmvSPvonaX282dLzbnnS9uYsfE73ctLIgrcSjCiwK18IArcygeiwK18IArcyweiwL2c0CMI2CRQEaLgiWeWydxLrxNGFNg8FCo/tk1REBQGd9bskFvVtIQt6s4I015aLt/+8Y/lI4//QdmCdpGhQ6X29M9KzQVfkda9JlU+1Ix7gCjICNBwdUSBYaAZwyEKMgI0XB1RYBiogXDjxwyTjdvqpU19vLL1PAFEQc/ngB5AIE8CFSEKrr3lXnnwkacYUZDnkVGBbeUhCnwsDUoK3FdbJT9WUxJWNDfJ/qtXyZV33CGzlvxGBjY1iQwYIPWfmCnV/3WZtBx8aAXSNNNlRIEZjqaiIApMkTQTB1FghqOpKIgCUyTNxUEUmGNpIhKiwARFYkCgcgj0uCjwRwuUQxY1JaFcnbyeZ+pBXqRLt5OnKAj25E8NdfIjJQz+UF8re2zaKJfddZec/cD9MrSuzivWOOPDsuMb35aWQ6a6ASrHXiAKcoQdoylEQQxIORZBFOQIO0ZTiIIYkHIugijIGXiZ5hAFbuWD3kDANoEeFwXBHdSLGbosBIolA1Fg+zCNF7+nRIHfuzdbmuWHVdvkXjXSYHB1tZyrbqt4ycKFMnbLZq9IywFTpPbfvyR1sz7jrWnQFzZEgVtZRhS4lQ9EgVv5QBS4lQ/dG0SBWzlBFLiVD3oDAdsEnBIFtnfWVnxEgS2yyeL2tCjwe1ut7pRwT/UO704Jb7W2yJd/vkj+656fyX5vvlHYobozPye1Z31emt/z3mQ7WWGlEQVuJQxR4FY+EAVu5QNR4FY+EAXu5QNR4F5O6BEEbBJAFCi6M069QDZv3VHgHB7VcNG8m+XhpR2r2x86ZbIsum1el5wgCmweovFjuyIKgj3+bV2N3KUWP3xCTU845tm/ynmL7pVTHn9M+quFEPXW/K53S+3nviD1p82S9uHD4+9shZREFLiVKESBW/lAFLiVD0SBW/lAFLiXD0SBezmhRxCwScA5URC+aA/uvI27Hqxau0Gu/+Ev5Pr553lN6VsxXnXDgsIdFsK3Zpw1d75MO2yKXHLu6YWuIQpsHqLxY7soCvzev97cLHfXbpdf1FTLThveUqMMfi7n/Oo+Gbt1q1ekfeQoqfvU6VL7hbnSMuWg+DvteElEgVsJQhS4lQ9EgVv5QBS4lQ9EgXv5QBS4lxN6BAGbBJwSBfoifML4sYWLdps7Xiy2FgcnnnmZLFl4tUyaOE7CYiAsDnQcREFPZKp7my6LAr+3+m4J/1dbLXfXbJeXamtk1sO/k/PVKIP3vrissENNRx4ltXO+KPUnnyoyZIgbcFP2AlGQEpylaogCS2BThkUUpARnqRqiwBLYDGFZoyADPAtVEQUWoBISAg4TcEoUuLCYoX8XBn/0gh7hcM5ZJ8sZM4/10hh+HlHgztFdCaIgSGt5U6PcoYTBA0ocvOOfL8tFC38qpytxMFjfXlFtbWPGSt0Zs70FEFv3mewO6AQ9QRQkgJVDUURBDpATNIEoSAArh6KIghwgJ2wCUZAQmOXiiALLgAkPAccIIApCCdFi4KTjjipMLdDy4ooLZ3cTBf6IA129vrFjvjlbzxLo319k0ID+0tjc1rMdSdj6drVewU+3b5fbt22TbWpawtn336fumPALmbhhQ0ekESOk7f1HS8spp0rrqZ8UGT06YQs9V3zYkAG8PnoOf7eWBw/qL62tbaL+scUh0C9OofRlBvbvJ/1UG82t7emDUNMYAZUOGTQw8BlCWoyxTRto6OAB6jO9VdRgPDYHCOgvZFpVMlp7wXuWPj9hgwAEShNwShToYf4zT5xeuCjPO3laEhw+9YAuUx/ijCjYWt2Yd1dpL4LAQGUKhg0dINV1zRXLZ2ldnfykarv8bsd2OWnp42rxw3vkQ3/969v7o6YiNJ3wMWn69OnS9NETRQYPdnpfx4wcIrw+3EnRiKEDPZHWjCmIlxTLFydD1EXQAHV1WtfQEq8/lLJKoP+AfjJy6CDZUdsxqkssiyKrO9NLgu88YojsqGkUyy/FXkLL/m7oUVDNLW3SpH4qfdPnJ2wQgEAFiQI9rP/y79wuS++/Mfe8RUkC3QnWKMg9FakbrLSpB6V2dKO6reJP1d0SfqZ+hq5aJWcu+Y3M/t1DcuBrrxWqte+8i1rH4BS1COIZ0vS+96uTWvfOapl6kPpwtlKRqQdWsKYOytSD1OisVGTqgRWsmYIy9SATPuOVmXpgHCkBIeA0AadGFOhh/qU2G3c90O3pdufMOqHLnQz8fnDXA6eP3y6d602iwN8x/T3jw523WHxS3WLxna+sUNJgicx55Hey27p1hf1v3WuSd4vFutM/Ky37H+BM0hAFzqTC6wiiwK18IArcygeiwK186N4gCtzKCaLArXzQGwjYJuCUKLC9s1Hx/dshhp87fsa0whSEi+bdLA8vfdYrcuiUybLotnldinPXg57IXPc2e6MoCO6ld4tFtfjhopoqqW5rlaOfe07OVsLgk488IsO2bC4UbX7nYVL/ydOl7rRPS9u48T2aHERBj+Lv1jiiwK18IArcygeiwK18IArcyweiwL2c0CMI2CTQ50WBCbiIAhMUs8fo7aLAJ+TfYvHO6u3yQnOjDGxpkY8887Rc8PDD8uE//F4G19R0FFVrNjR+4Bip/9TpUn/STGlXiyLmvSEK8iZeuj1EgVv5QBS4lQ9EgVv5QBS4lw9EgXs5oUcQsEkAUWCALqLAAEQDIfqKKAiiWtbUIL9Qt1e8T/1sV6MMhjY2yif+uFT+85GH5ag//VEGqL/11j5smDSceJI3PaHh2ONFBg40QLx8CERBeUZ5lkAU5Em7fFuIgvKM8iyBKMiTdry2mHoQj1NepRAFeZGmHQi4QcA5UaAXD3xxxUqPzm3XXCzTj5jqrSEQnArgBrq3e4EocCMjfVEU+OT1WgaP1dfKL2ur5Pfqtx51MLq6Wmb94VE59+Hfybue/ov0a+tYpbht7K5SP/M0bxHE5mlHWE0eosAq3sTBEQWJkVmtgCiwijdxcERBYmTWKyAKrCNO1ACiIBEuCkOg4gk4JQq0JJgwfqy3NoC+C8E3v/pFTxSEFxR0jTqiwI2M9GVREMxATXub/EqNMNA/TzfWe0/tvnWrumvCEjlHTU/Y//nnCsVbJ+8rdXo9AyUNWvfdz3giEQXGkWYKiCjIhM94ZUSBcaSZAiIKMuGzUhlRYAVr6qCIgtToqAiBiiTglCjQIweWLLxaJk0c10UU6Nsmzr30OrF114OsmUMUZCVopj6ioDvHNWr9gvvUKIOfq583Wpq9ApPXrpXPLfmtfF6NNNjrX68WKjUfPs2TBvV6EUQ16sDEhigwQdFcDESBOZYmIiEKTFA0FwNRYI6lqUiIAlMkzcRBFJjhSBQIVAoBp0SBHkWw4KavdxMFjCiolMOpZ/uJKCjN/2+NDfLrumpZrEYabFDrGejtXep2i5/93UNylvrZ3b/dolq/oPGYY9UoAyUNPnayiFrfIO2GKEhLzk49RIEdrmmjIgrSkrNTD1Fgh2uWqIiCLPTM10UUmGdKRAi4TMApUXDtLffKg488JUvvv7EwomDSxN3lxDMvkzmzTpBLzj3dSZaMKHAjLYiC+HnQ0uA3dTXy2/pqWa1GHeht+j/+IZ996LfyGTXSYOSOHd5jrftMluZDpiph8AlvMcT2UaPjN6JKIgoS4bJeGFFgHXGiBhAFiXBZL4wosI44cQOIgsTIrFZAFFjFS3AIOEfAKVGg6fjTDIKkrrhwtpwx81jn4PkdQhS4kRpEQbo8vKClgVoA8TdKGqxs7piecOKTT8iZanrCKUuXyk61nbdbVI/r2y02HH+iNHz8ZGmdtHfZBhEFZRHlWgBRkCvuso0hCsoiyrUAoiBX3LEaQxTEwpRbIURBbqhpCAJOEHBOFDhBJWEnEAUJgVkqjijIDvalpkY1ykBJAzVF4ZXmJhmoRhvM+PvfZObjj8kn//hHGb9ubaGRFj3SQI0yaDjh49J82OGRjSMKsufEZAREgUma2WMhCrIzNBkBUWCSpplYiAIzHE1FQRSYIkkcCFQGAadEwUXzbpaHlz7bbdFCbo9YGQdTT/cSUWA2A6+r0QV6TYPf1NfIciUQ9HbYin8qafC4nP7HpTLl5ZcKDbZOmOhNTdA/jUd/UGTQIO85RIHZnGSNhijIStBsfUSBWZ5ZoyEKshI0Xx9RYJ5ploiIgiz0qAuByiPglCjQixmec9bJ3aYZsJhh5R1YPdFjRIE96qvVHRN+rdY00CMNnuuUBpPeekv+benj8pk//Une99SThcbbhw+XhuNOkLozPydjP/kJYcSNvbwkjYwoSErMbnlEgV2+SaMjCpISs18eUWCfcZIWEAVJaFEWApVPwClRoEcO3HbNxTL9iKldyHJ7xMo/0PLYA0RBHpRF1rW2yINq3QK9EOKzan2DdtXsqJoa+YQaZTBHiYMPqvUNBtfVFTqjb7vY8KGPSOMHPyRNR38gn07SSiQBRIFbBwaiwK18IArcyofuDaLArZwgCtzKB72BgG0CTokCRhTYTnfvjo8oyD+/G5U0+G1dx5oGTzfWS8dNF0VO+POTcuZTT8nH1EiDMa+/XuhY+047SdP7PyANMz6sbsH4YWk56JD8O92HW0QUuJV8RIFb+UAUuJUPRIF7+UAUuJcTegQBmwScEgV6isFVNyyQJQuvlkkTx3n7vWrtBu/2iC7f+YCh1TYP0fixEQXxWdkoubW1VZao9QweVFMU/tjw9oiCPTdskPP/8hc57qk/y6F/+bMMqqoqNN82brw0KmnQoKRBoxp10Lbb7ja6RsxOAogCtw4FRIFb+UAUuJUPRIF7+UAUuJcTegQBmwScEgV6R6Nujxg1HcEmlKSxEQVJidkpjyiwwzVN1O1trfKwunvC75vr5JHqGmlq1xMURAYomTBj2Qsy56/PyrFq1MGEZc+LtLUVmtAjDDxp4E1T+KDoEQhs5gggCsyxNBEJUWCCorkYiAJzLE1FYuqBKZJm4iAKzHAkCgQqhYBzoqBSwAX7iShwI2uIAjfyEOyFvuvBvzbVyhNqWsIf1GiDx9RIgzXqlov+tnN1lZz19DPy6aeflsOf/JMMW//W29UHD5am9x7ZOU3h2I5bMPbv795OVlCPEAVuJQtR4FY+EAVu5UP3BlHgVk4QBW7lg95AwDYBRIEBwogCAxANhEAUGIBoOETU7RFfaW6Sx9Rogz8oafCMEgj+aAPd9OGvvyZfeuav8tG/PCX7PPMX6dfQUOhR+867SOP0D6oRB8d60xVaJ+9ruLe9PxyiwK0cIwrcygeiwK18IArcyweiwL2c0CMI2CTgnCjQCxpu3rojcp+XP36nTRapYyMKUqMzWhFRYBSnkWBRoiAYuE5NO/iTkgWeOFA/a9XiiP42tLFRzlm2TD6q1jY44oknZMyrK7r0qXXvfTrWN+hcGLF99M5G+tybgyAK3MouosCtfCAK3MoHosC9fCAK3MsJPYKATQJOiYJZc+fLhPFj5fr559ncZ+OxEQXGkaYKiChIhc1qpXKiINx4qdEG4zdvVndS+LOcqhZGPFz9Hrp929vV1ZSE5ncepu6kcKy3xkHTEUeJqKkLbF0JIArcOiIQBW7lA1HgVj4QBe7lA1HgXk7oEQRsEnBKFBxyzBxxfeHCqGQgCmweovFjIwris8qrZFJREOxXg1oA8W9N9fJMQ7269WKD+n+D6BEI/nbUC8/LqU//RU76y9Pyjn/8rcsute67n7RM2sdb16DxiPd5ax207zImr912th1EgVupQRS4lQ9EgVv5QBS4lw9EgXs5oUcQsEkAUWCALqLAAEQDIRAFBiAaDpFFFIS70qoeWNbUqMRBnfxFTVf4q5IHW9XdFfQ2srZWjlPS4N/U2gYnqNEGu69d27V6v37Ssv+BaqRBhzRoOvIoaTlgiuG9dT8cosCtHCEK3MoHosCtfCAK3MsHosC9nNAjCNgk4JQo0FMPZp44Xc6YeazNfTYeG1FgHGmqgIiCVNisVjIpCqI6qqcqPK2kQceog/rCGgd7v7VOjn7uOfnQCy+on+dl31dWSD91a8bg1qZGGHjSwJMH6uc97xUZOtQqj54Ojijo6Qx0bR9R4FY+EAVu5QNR4F4+EAXu5YQeQcAmAadEwRPPLJPLv3O7LL3/Rpv7bDw2osA40lQBEQWpsFmtZFsUhDu/XsmAPzequymoUQd6usKrSiS0q0I71dfL+5UwOEaJg4+qn6nP/0OG1NR023c9VaHhox+TxvdPl9bxE6R1v/2t8sk7OKIgb+Kl20MUuJUPRIFb+UAUuJcPRIF7OaFHELBJwClRoNcoKLVx1wObh0Llx0YUuJfDvEVBmMB2NTVBC4On1YiDZ5RA0FMX/PsqvPOVV+TDzz8nJ7z0kkx77h8y9s03ugFsHzFSmg6fJs3vfo80qcUStUjQd1uo1A1R4FbmEAVu5QNR4FY+EAXu5QNR4F5O6BEEbBJwShTY3FGbsRlRYJNu/NiIgvis8irZ06IgvJ/1eoFENUXhL0oe6FEHf1cLJOrH9DZ2+3b5sBIGn3jpZTlq+Yuy9/JlMqiqqhuqtjFjPWHQpORB87veLU3q/20TJuaFNFM7iIJM+IxXRhQYR5opIKIgEz4rlcePGSYbt9VLW8fbNFsPE0AU9HACaB4CORNwThTo6QdzL72uCwbX74SAKMj5qC3SHKLAjTwEe+GaKAgT0qMLntfSQMkDvcaBXiBRj0Lwt4NXr5ZTV6iRBytelkOXL5ddl70g/Wq7T1loGzdempQ08EYeKHHQrNY70ELBtQ1R4FZGEAVu5QNR4FY+dG8QBW7lBFHgVj7oDQRsE3BKFNzzwKNy1Q0LZMnCq2XSxHHevq9au0FOPPMyueLC2c4ucogosH2YxouPKIjHKc9SrouCKBYvqekJ+q4KWhzoaQubWv3JCiLqDVO+9NZ6mfHPFXKwGnEw+cVlMupFJQ/UGgjhrXXinh0jD7Q40L+VPGgfNTpP/N3aQhT0KP5ujSMK3MoHosCtfCAK3MsHosC9nNAjCNgk4JQomHHqBXLOWSd3EwJaINx692JnFzlEFNg8ROPHRhTEZ5VXyUoUBWE2q1uaO+6s0LnWwb9amroUGd7WJietWi3Hr/inTFPrHeyjRh2Menm5SGNjd3mwz+S3xUGnQNDrIOS1IQryIh2vHURBPE55lUIU5EU6fjuMKIjPKo+SiII8KNMGBNwh4JQo0IsZRk0z8KcjsJihOweOiz1BFLiXld4gCsJUq5QY+EdTvTynRMBzao0DPXVhQ2C6gi4/tF8/OU1NWThO3ZbxPUoe7K3WPBi57PnIBLUc+A5pnvouTyA0nHyK6JEItjZEgS2y6eIiCtJxs1ULUWCLbPq4iIL07GzURBTYoEpMCLhLwClRwIgCdw+USugZosC9LPVGURBFeZ2anqCFwXNq2oKWBy+o/1e1t3UpquXBLLVQ4rFq5MHhLy335MGIl1+KTFrrnntJ8yFTpeXgQ721D1oOnKJ+3pE5wYiCzAiNBkAUGMWZORiiIDNC4wEQBcaRZgqIKMiEj8oQqDgCTokC1iiouOPHqQ4jCpxKh9eZviIKwuT1At2vqykKzylh8LySB/9Qv19qbpSGzjss+OVHq1EJp7z6qnxErXlwuBIHe766QkYqiVBs02sdNL/jYE8gNB861btlY/vOu8ROPKIgNqpcCiIKcsEcuxFEQWxUuRVEFOSGOlZDiIJYmCgEgV5DwClRoKly14Nec2zlviOIgtyRl22wr4qCYmB8abCsWU9ZaJSXlTyI2r6w8g059vWVnjjYT4062O2fL8ugTRsjy7btPk6alThoPPoD0nTE+0QGD5GWyftK2667dSuPKCh7yOZaAFGQK+6yjSEKyiLKvQCiIHfkJRtEFLiVD3oDAdsEnBMFtnfYRnwWM7RBNXlMREFyZrZrIApKE65XIwy8KQueOOgYffCmWjwxatulqkpmvvovOfrVV2Tqa6/J5Ff+KWPV//s3NESWbx85SgmEQ5Q02E9aDjhQWvY7QIa/62Cp3XeKNDR3nRZh+zggfjQBRIFbRwaiwK186N4gCtzKCaLArXzQGwjYJuCUKLho3s3y8NJnJbxooV7k8PgZ0+T6+efZ5pEqPqIgFTbjlRAFxpFmDogoSI5QL5ao1zlY0dQkr7U0yr+UOHi1uVk2B27TGIz6jpUr5ZjXX5Oj1CiEQ1a+LpPeWClj1GMDGrrfstGv17r3PtKy/4HSPOUgaVWjD5r3P8D7u22PCck7TI3UBBAFqdFZqYgosII1U1BEQSZ8xisjCowjJSAEnCbglChgMUOnjxXnO4cocC9FiAJzOdmh7qzwLyUMXlXTFbQ4eFWtgfBac5OsUiIhPD5AvbHLXuvXy7TVq+T9q9fIO998Q/Z9802ZoCTCsDWrRUJrJfi91LdqbNlvf08atHTKA/27Wf0tw4aZ2xkieQQQBW4dCIgCt/Khe4MocCsniAK38kFvIGCbgFOigNsj2k53746PKHAvv4gC+zlpVBf9Whi85o080BKhyRMKejHF8OKJujdD1EiFd61aJR9YvVreo35PURJhLzUCYRc1GmFg1Y7oDqs7NrROmNghEEIioXWvSSLqebbkBBAFyZnZrIEosEk3XWxEQTputmohCmyRJS4E3CTglChgRIGbB0ml9ApR4F6mEAU9lxM9ymC1Jw86Rh68qv6/sq1ZVjQ0yjY1OiFqm7h5s3xgzRo5Uv1MVSMQ9lUjEHZXAmH4qjdFWlqid2boUGnZV49C6Bh5UBiJoG7n2D5iRM8BqICWEQVuJQlR4FY+dG8QBW7lBFHgVj7oDQRsE3BKFHB7RNvp7t3xEQXu5RdR4FZO/LserGlQ4iAwfUHLBP3zlloHQd/aMbwNVJLgqHVrZfrqtfLu1W/KgW+8KROVQNh55WsyUMmFYpu+I0NBHPgjEdSiivquDDJggFtweqA3iIIegF6iSUSBW/lAFLiXD0SBezmhRxCwScApUaB3lNsj2kx3746NKHAvv4gCt3JS7vaIdWohxX95ow86pi/8S/3WAuEN9RN9LwaRPevq5FglDo5UUxkOVusf7KvuxDD2jTdkJ3VXhlKbvguDlghN7z3S+9Fb+6jR0jpxT2kbM9YtcJZ6gyiwBDZlWERBSnAWqzGiwCLcFKERBSmgUQUCFUzAOVFQiSy564EbWUMUuJGHYC8QBW7lpJwoKNVbLRA67sCg7sSgJYL6/Yr6W8uFYtsJGzbIKes3yvhXVsgENX1hTzUKYRd1h4Yh698qCaZdLZzYOmFPad1zL08ceL/VHRm8/6uflkn79IrFFREFbr0+EAVu5UP3BlHgVk4QBW7lg95AwDYBRIEBwogCAxANhEAUGIBoOASiwDDQjOGyiIJiTa9T0xW0RHjFW0Tx7fUQNhW5naOOM6yhQY58/XV539q1crC6M8N+b62X8UoejFU/I9atkwH1dWX3tH30zh3iQC2y2Dp+j47f48ZLm/6//lFiQU99cHlDFLiVHUSBW/lAFLiXD0SBezmhRxCwSQBRYIAuosAARAMhEAUGIBoOgSgwDDRjOBuioFiXqtRIAz1t4c3WZlmrRh6sVusc6MUVV6u/V6oRCaW2MTt2yJQNG+WwzZvkoI0bZV/1o2/3uJsSCTurtRKGqt/91N0bym6DBkmrkgWeNOiUBwWJEBAK7SNHlQ1lowCiwAbV9DERBenZ2arJiAJbZNPFRRSk40YtCFQqAUSBgcwhCgxANBACUWAAouEQiALDQDOGy1MUlOvqRjXiQMuDNZ3yYI3+v35MSYQ1SiZE3doxGHP/zVvkcLWQ4sFKJuj/T1L/H79hvYxRUmHEhrdksBIL/Yrd7jHUufadduqUCWp6gz86QQmGNj3dwRcMe+9TbpcSP48oSIzMagVEgVW8qYIjClJhs1YJUWANLYEh4CQBRIGBtCAKDEA0EAJRYACi4RCIAsNAM4ZzSRSU2xUtErQ4WOOJgxZZpYTCWk8u6NEJ5UXCe4YMlRFq1MFuShjsvWmT7Kt+9lQyYdymjbKrWjth540bZLgamTBEyYV+aipEnK1t7K5dpjZ0G52gpII33aFfvzjhBFEQC1NuhRAFuaGO3RCiIDaqXAoiCnLBTCMQcIYAosBAKhAFBiAaCIEoMADRcAhEgWGgGcNVkigot6tbtDRobfVGJOgRCHokwmotFvTfanRCbXvxRRbDsfeorpZD1KiEKVs2y75KJkxSMmGPTZtldyUTdlZSYaT6PVT9iGqv7DZwoDfdoctUBy0QgqMT1N96jQVEQVmauRZAFOSKO1ZjiIJYmHIrhCjIDTUNQcAJAogCA2lAFBiAaCAEosAARMMhEAWGgWYM15tEQTkU1UoUbGppFb2o4qa2VtmsLvI3trV4v/Vjwb/LTXPQbfVXay6M27LFEwnvUEJhP/V7n42bZIKa+jBeTXcYo0TCKCUVhmzbWq5r3vP6zg7tShjI+PHStJtaR0EtxOgtxtj52/+/HsUQd4RCrIYpVJQAosC9gwNR4FZShcllAAAa9klEQVROEAVu5YPeQMA2AUSBAcKIAgMQDYRAFBiAaDgEosAw0Izh+pIoSIKqQyoooaAlgpIKXeSCJxXelg1xpMK+a9bIRCUP9lFC4QAlFPbeqtZQWL9B9lCPjVVCYbT6GVRfH7uL+o4OvkAo/FYjEtp23tkbmdDW+X/9W//dPnx47NgUfJsAosC9owFR4FZOEAVu5YPeQMA2AUSBAcKIAgMQDYRAFBiAaDgEosAw0IzhEAUZAarq+m4OWhxs7JQK3v87Ryx4gsH7USMY1GON7e1FGxxVUyN7KImwhxqRoH/vraY+TFZiYZL60X/vptZU2EX9DIu5IGOXhgYP7pAHUTJh512UTBjd+dwu6vfoDtmgHvf+P2p0nx3BgCjI/vowHQFRYJpotniIgmz8qA2BSiOAKDCQMUSBAYgGQiAKDEA0HAJRYBhoxnCIgowAE1bfXhAIHeJAL9C4Vf3eoKdBqP9XqZEMb3Xe+aFUaD1CwRcKWiJM3LZNJlRVyW5KNuxaXSU7q/+PVf/fSd1WcohaXyHr1jFKQckETx7oUQpv/z9yFIMa2eBJid12z9p0j9ZHFPQo/sjGEQVu5QRR4FY+6A0EbBNAFBggjCgwANFACESBAYiGQyAKDAPNGA5RkBGg4erBxQx9qeCNTtDTIPTvTrngTYnofOwtJRjKbUMbG2UXJQ92URJB/95ZLda4tx7BUFMr42qqlVyolrGdj49Sv0eoUQvD1O8hSjQMVM9n2fS0B38KhJYKHaMaIkYxdEoIX0h4UybUbSp7ckMU9CT96LYRBW7lBFHgVj7oDQRsE0AUGCCMKDAA0UAIRIEBiIZDIAoMA80YDlGQEaDh6mnverDNH6mg11PoFAhb1P+3KYmwTU2N2KbEgv69VS3euD7OnRpC+7WrGrGgJcNeSixMrK2RiVU1nmDQIxjGqsfHKKkwSsmGETuqZHjVdhmi/h68Y7sMVPWybm277tZ1FEOnbGjvnBrRpqZGeOLBlxD+9Ar1WNYNUZCVoPn6iALzTLNERBRkoUddCFQeAUSBgZwhCgxANBACUWAAouEQiALDQDOGQxRkBGi4elpRkLQb9VoeqGkOHQKhQyJ4vwN/6ykRBdGg/q/XYii+wkLxHui1F7Rk2EP9Hl/dIRh2r1KjGNTvMeq3fk5PlRilfo9Uv4erUQw76d8mpkx4EsFfb6HrlIn2kSPVnSZ28kYt6DtOtOn/6ztPeH93/H/AiOEyeredZVNz/461Gth6nACioMdT0KUDiAK38kFvIGCbAKLAAGFEgQGIBkIgCgxANBwCUWAYaMZwiIKMAA1Xz0sUpO22XqhRSwU9LWKrN1Kh429PKnT+vUMJiGr1/1r1u7atXWrU7zr1d9ptD72IY2DKRMcUio7pErvpaRNKNoxRv/XjozuFgx7ZMEyNfLCxtY8cVZALvlAoKhx2Gi7tQ4cWxENQQhTqBsSE9xh3qCiZNkSBjaM6fUxEQXp21IRAJRJAFBjIGqLAAEQDIRAFBiAaDoEoMAw0YzhEQUaAhqu7Lgqy7K6+5aQWB7XtrVKjfmt5oCWC96P+3/G3FgutHeX030pA1KvHtHjQ5bzH1N9aQsTZxm7fXpAM/toMHdKhWoar21GOqKuTnRoa1E+993u0WsthhPo9vPNnmPqtf4ao54fW1sZp0kwZJRcKIxwCox6KygUtG8LCQY+SCD/WOXpCr/9QqRuiwK3MIQrcyge9gYBtAogCA4QRBQYgGgiBKDAA0XAIRIFhoBnDIQoyAjRcvTeLAsOo3hYNWjp0ygd/9EKHfOiQEv6oBi0ZtGDwH+/43SEf9O/WmB3UwsEXCx2SIfCj5EPw75GNDTKyoVFGqTIj1P9HqP+P8KREoxdDS4ih+kfV0zJicH2DDFTl8traR6jpF748iJh64YsJTzgMHyHt6jabMkSNkNCjJPyfwN9dnguWMzhtA1GQ19ERrx1EQTxOlIJAbyGAKDCQSUSBAYgGQiAKDEA0HAJRYBhoxnCIgowADVdHFBgGmiCcHtEQFAlaMNT3U6syDOkv62oau4yGCAqJWjXCQdetU7/r9TQL/btzBESC5gtF1UmYJxC6SYjAyIfgc56E8EREh4QY7kmIjlERvozoGBmhRkUoEaGFxBD198Dm5jTdS1+nXz8RJRraB6kfLRwGDfJ+d/w/9Jj6u6NsR5nC8wMHyrBROyneas2Izjq6jB83qk7R5yP6IgM721PtsMUjgCiIx4lSEOgtBBAFMTJ50byb5eGlz3olD50yWRbdNq9LLURBDIg5FEEU5AA5YROIgoTALBdHFFgGnDA8oiAhMMvFs971oDEgDxo8mRAQClpEqOUh61rffkxPs/Blg5YPBfEQqKclRJ2uqx7Leqk/Wq3z4EsHPRXjbQHRdWSEfnyYGukwTMmIYUpEDG3SP00dIyLUb337Tf2c93ijerzw/47H9RSPStwKoyg6pUWk6AhIjZIiZMgQkQEDOuRIMRESIU+CoiMoWDx50sO3D9U5RRRU4pFNnyGQngCioAy7ex54VG69e7Esvf9Gr+SsufNl2mFT5JJzTy/URBSkPwBN1kQUmKRpJhaiwAxHU1EQBaZImomDKDDD0VSUrKLAVD9KxdHioEkJhyYlGbQ4aFQSoVn93az+btS/1d+t6st8XU4/7z2uJYP63aT+buos36Qe0397j3f+6PJNofj6uVYVV4sPr75u16/j1W9T8dXz6ie8abEwWI1kGNzSLIPUbTy9/3s/gf+r595+PPB/7/FgnY4YQ5qbupQvxO0Sv7Oskhq67a7xVczAY1p6VOLWqqeRDBrYfcRGQUp0jNLoX0p6+KM3tNTor0Zt6JEV6qddjbTo+K3+VrKj8H/1+PARQ6WpX3913KmDTJfRdUX9X5fTYkTF8f6v43X+7vhbPddZpvtznWX9cjkJEX1+wgYBCJQmgCgoc4SExUBYHOjqiAI3XmaIAjfyEOwFosCtnCAK3MoHosCtfFSCKHCLWPfe6FESWiR4AqFTRHTIig6xoQVFiyc4AuJBi4/Ov4PiQguRwUMHyPb65k4h0iEqdIyC+FB/t6hyWpjo8h2P63h+ex1/l7sTR1BqBGVGF8GRUWp44iMUo3T8TlHSWadSpYapY7ZFrYPRNqBDKrRr8dC/n/f/tk4J4YkINeXFe76zjC8l2lW9gqzQEkON5tjtz0+Y6hpxINBrCSAKyqR2xqkXyDlnnSxnzDzWK/nEM8tk7qXXyfLH7yzURBS48fpAFLiRB0SBe3nwe4QocCs3iAK38oEocCsfujc2FjPUd+TQIy86RkjokRf+qIrOERbq7xYtILzRFNLxf/278/HWTunRqgZR6Mc6/ta/9d9vl+t4LlC/S7xAG+ri1mursx09gkMP0NC/dfuqq97/9b0/dJlBaqTGADWyon+TGjmhfg9Qoyn03wPU3wPVKIqBSkj0V3JBQqMv/NEdUSM1tLDQPwPVLVAHtrZ2/LTo3/7j/mNvP99RvlUG6B8legaou5b0V53VvweoKTb+7/6KcdG/dT1Vv7/aLz9ObkIkYhSMe68AegSBniWAKCjD/5Bj5sgVF87uJgqWLLxaJk0c17PZo3UIQAACEIAABCAAAQjEJKBHfWjhoCVGW6fM8KSELyR8SaF/d0496ZAUb/8drKuf80VHh9joEBwddTt++5Kj8HictjsljK7bTy3M2aakQrsSF+1KYLTr/ytR0a6kRLuSEvr/4v9fiQdRP+3qp5/+3VlPVDlR9TvMS4vccOZnYhKjGAT6LgFEQZncxxlR0HcPH/YcAhCAAAQgAAEIQAACEIAABHobAURBmYyyRkHlHPJMPXAvV6xR4FZOmHrgVj6YeuBWPph64FY+dG9sTD1wby8rp0fc9aByckVPIWCCAKKgDEXuemDiMMsnBqIgH85JWkEUJKFlvyyiwD7jJC0gCpLQsl8WUWCfcdIWEAVJidktjyiwy5foEHCNAKIgRkYumnezPLz0Wa/koVMmy6Lb5nWpxWKGMSDmUARRkAPkhE0gChICs1wcUWAZcMLwiIKEwCwXRxRYBpwiPKIgBTSLVRAFFuESGgIOEkAUGEgKosAARAMhEAUGIBoOgSgwDDRjOERBRoCGqyMKDAPNGA5RkBGgheqIAgtQM4REFGSAR1UIVCABRIGBpCEKDEA0EAJRYACi4RCIAsNAM4ZDFGQEaLg6osAw0IzhEAUZAVqojiiwADVDSERBBnhUhUAFEkAUGEgaosAARAMhEAUGIBoOgSgwDDRjOERBRoCGqyMKDAPNGA5RkBGgheqIAgtQM4REFGSAR1UIVCABRIGBpCEKDEA0EAJRYACi4RCIAsNAM4ZDFGQEaLg6osAw0IzhEAUZAVqojiiwADVDSERBBnhUhUAFEkAUVGDS6DIEIAABCEAAAhCAAAQgAAEIQMAWAUSBLbLEhQAEIAABCEAAAhCAAAQgAAEIVCABREEFJo0uQwACEIAABCAAAQhAAAIQgAAEbBFAFNgiS1wIQAACEIAABCAAAQhAAAIQgEAFEkAUpEzaRfNuloeXPuvVPnTKZFl027yUkaiWhMA9DzwqV92woFBl+eN3Fq2+au0GOfHMy7o8X6p8kn5QtoNAmPFt11ws04+YGgvPjFMvkPG7jeG1E4tW/EKa6+atO7wKc2adIJece3rJyuEcLll4tUyaOC5+g5QsSSDpZ8WsufPlxRUrY73Hgd48gUOOmSNJ3sfM96BvRtTH/bTDppR9vwq+v2lS5MrO8XLtLffKs8+tSPT57L/XcZ5lJydEhUBPEEAUpKCuL1ZvvXuxLL3/Rq923A+4FE1RJUDAv6DxL2TKfZDpPOntjJnHer/1h9i69VsSffCRgNIE9EnbOWed7DF+4pllMvfS6yTOSYKupzdEgdkjTB/jert+/nne73IXPX7OONk2mwc/WtLPivB7FO9ZdvISFTV4AcrrIT/uQZFWTmzqc4Drf/iLwvub/8VBnM+c/PaoslsKfhmT5Eswnce/L3vVk9Tko7KPAXoPgSABREGK4yEsBsIngylCUiUGgbAYCIuDciHIUzlCyZ6PEgNBcVAsmn79zDxxuqx5a1PibyyS9bDvlQ6LgbA4CBPxc+HLtL5HzO4eJ/2sSFrebu/7XnT/MwVRkH/u9WfHSccdVXZEQbBnSc8B8t+rym0xiaTU52br1m+W0z4+I/aXBZVLhp5DoG8RQBSkyHf4YijJN6kpmqNKJ4Goi55y35gG4ZUbgQDoZASixEu50TXB58lHMt7lSkedNJdjrF8/u44ZXZiqoP/vj5Qq1x7PlyeQ9LPC/yw5fsY071tTRE55xiZLIApM0kwWK40o4NwrGeMkpeOKguBnDPlIQpiyEKgMAoiCFHnSJ9dXXDi7MKTdf3Nkbm8KmAmq6JPmCePHFoYd6qrhXBQLxwlgAtAxi+oThAcfearLhWVUjvxwYdFT7iI2Zjco1kkg6n0oKkc+sKjXhM6f3lhzxcxhleazIixvGMZrJhdxovA5EYeSnTJpREGaOnZ63/uixhEF4S8LEAW97zhgjyCAKEhxDCT9lihFE1SJIJB2RIF/8heUOwDOTiDpiILwIlR+D/gWO3sudISkIwqiyjM9x0wu/ChJPyvCIwi06Llz0UPM+TWblqLREAU5gY5oJulFvy5/+NQDunxx0HO9730txxEFwfUlwgT44qz3HRPsUd8kgChIkXfmkaaAZqBKmjUKkAQGwBcJkXaNAj8cIwrM5ybpGgXh8ogCszlJ+lkRzgej1czmo1w0REE5QvaeTyIKkAT28uBHjiMKwr1gRIH9vNACBPImgChIQTzpStYpmqBKBIFydz0If/vGiu72D6NSdz0oxx9RYD4/5e56oC9EgyuLh08Gk5ysm+9974tY7rMi/J4VnvrhryTOuhH5HBuIgnw4R7VS7L0n/J4V/rvnety7Wy4mCkpNT0MU9O5jgr3rmwQQBSnznvTe2CmboVqIQPDWPfqp4Pzd8El3sWFxTEEwd1j5J9Z+xOBq4YgCc5yTRApO8QjfbizqJFuf+L24YqXXhL+IXpL2KFuaQKnPiqipBcH8MS0nv6MrPDUqya3h8utl72sp6nM6+LkefM8Kf/77NHjfMndcRDEOfq4jCsyxJhIEKoEAoqASskQfIQABCEAAAhCAAAQgAAEIQAACORFAFOQEmmYgAAEIQAACEIAABCAAAQhAAAKVQABRUAlZoo8QgAAEIAABCEAAAhCAAAQgAIGcCCAKcgJNMxCAAAQgAAEIQAACEIAABCAAgUoggCiohCzRRwhAAAIQgAAEIAABCEAAAhCAQE4EEAU5gaYZCEAAAhD4/+3d36sUZRgH8Pc/COyXGAVdRER5UYgQCCeIRClC6sIiDKHAgqJCTgUFYlRUIhUEKRRIEeVNRDdFECR0JVKBRUgXQfTDUIT+g3oH3mXOurtnNued5Tnns1fn7M4+88zn3b14v/vODAECBAgQIECAAIEIAoKCCKOkRwIECBAgQIAAAQIECBAgMJCAoGAgaLshQIAAAQIECBAgQIAAAQIRBAQFEUZJjwQIECBAgAABAgQIECBAYCABQcFA0HZDgAABAgQIECBAgAABAgQiCAgKIoySHgkQIECAAAECBAgQIECAwEACgoKBoO2GAAECBAgQIECAAAECBAhEEBAURBglPRIgQIAAAQIECBAgQIAAgYEEBAUDQdsNAQIECBAgQIAAAQIECBCIICAoiDBKeiRAgAABAgQIECBAgAABAgMJCAoGgrYbAgQIECBAgAABAgQIECAQQUBQEGGU9EiAAAECBAgQIECAAAECBAYSEBQMBG03BAgQIECAAAECBAgQIEAggoCgIMIo6ZEAAQKBBW6+Y+9F3e/dvSMtP/5AWrrvqea1E5++vWKb3/74O+186Lm0fWlLevPgE81rs+rs3ncw/Xjm16lKV2y4rNlH3t/5C/9ctF15Pb9Qtjn6xv60bevmFduWHia9ljc89O4n6djxL2eO1vuHl9Mj+w+t2Oanb441/z9z4J301YlTqfi0NyrH2H6ty/EE/uhonQABAgQIEFiQgKBgQfB2S4AAgbUuUCb745Pe/PyeJ18dhQN58j2+TZ4U58fxowdS1zrFs2w/aTKfJ9b33HV7E1JMe5TJdzukyNt+/NnX6eW3PmzeNi0oGK85a3/5GDdtvHwUhLSDgnZwkZ8vx5T/Hg8KVjuetf45c3wECBAgQIBA/wKCgv5NVSRAgACB/wTKr+vl1/JpKGUC/sVHr6frrrl6NCEv/3et02dQkCffeWVA6SHXzpP+2zbf0PziXzMoyPv67vQv6bGH700P7rqzOay80iA/xlcbdAk+fBgJECBAgAABAvMKCArmFbM9AQIECHQSGA8AZr2pvYIgrzB48ek9o0nyPHXyPvpYUZAn6Se//7lpOZ/68O3J0+mF195Lrzz/aNr37OHqQcHWW29KRz74fMWqixxa5NMxrCjo9PGzEQECBAgQIHAJAoKCS8DzVgIECBCYLTB+Dv2kc+/bk/v89y03Xt+cctB+dK3TJSjoco2CHBRcu+mqJhTIE/Tll46kXTu3jZ6rvaIghxMlMPn9r3Ppz7Pnm8Bi/DQN1yjwDSRAgAABAgRqCAgKaqiqSYAAAQIrBNrn908LA8opBu3l/uOMXer0taIgL/svKx3OnrvQ/LqfVxYMsaIghwLZ49QPZ5qLNBaTSUGBaxT4shEgQIAAAQJ9CwgK+hZVjwABAgRmCpTJ/viv8vOeYjCtTp9BQQkGykqIIYOCjJiDgfYKC0GBLxcBAgQIECAwhICgYAhl+yBAgMA6FMgX4Cu3Nmwf/rTJ9rSgYN46fQYFue+8vL/cvnHooCAf+/13L41u0ygoWIdfJIdMgAABAgQWICAoWAC6XRIgQGA9CORJbr5Kf/vChGXivfHKDRddh2BWUDBPnb6Dgi4hx7Tx/D+3R8y1JgUs+XlBwXr45jhGAgQIECCweAFBweLHQAcECBBYswLlugPtA9y+tGXiRHjWqQfz1FktKOh6McNya8K+g4LSX7tuuYVkuQ3iPEHBasezZj9cDowAAQIECBCoJiAoqEarMAECBAgQIECAAAECBAgQiCcgKIg3ZjomQIAAAQIECBAgQIAAAQLVBAQF1WgVJkCAAAECBAgQIECAAAEC8QQEBfHGTMcECBAgQIAAAQIECBAgQKCagKCgGq3CBAgQIECAAAECBAgQIEAgnoCgIN6Y6ZgAAQIECBAgQIAAAQIECFQTEBRUo1WYAAECBAgQIECAAAECBAjEExAUxBszHRMgQIAAAQIECBAgQIAAgWoCgoJqtAoTIECAAAECBAgQIECAAIF4AoKCeGOmYwIECBAgQIAAAQIECBAgUE1AUFCNVmECBAgQIECAAAECBAgQIBBPQFAQb8x0TIAAAQIECBAgQIAAAQIEqgkICqrRKkyAAAECBAgQIECAAAECBOIJCArijZmOCRAgQIAAAQIECBAgQIBANQFBQTVahQkQIECAAAECBAgQIECAQDwBQUG8MdMxAQIECBAgQIAAAQIECBCoJiAoqEarMAECBAgQIECAAAECBAgQiCcgKIg3ZjomQIAAAQIECBAgQIAAAQLVBAQF1WgVJkCAAAECBAgQIECAAAEC8QQEBfHGTMcECBAgQIAAAQIECBAgQKCagKCgGq3CBAgQIECAAAECBAgQIEAgnoCgIN6Y6ZgAAQIECBAgQIAAAQIECFQTEBRUo1WYAAECBAgQIECAAAECBAjEExAUxBszHRMgQIAAAQIECBAgQIAAgWoCgoJqtAoTIECAAAECBAgQIECAAIF4AoKCeGOmYwIECBAgQIAAAQIECBAgUE1AUFCNVmECBAgQIECAAAECBAgQIBBPQFAQb8x0TIAAAQIECBAgQIAAAQIEqgkICqrRKkyAAAECBAgQIECAAAECBOIJCArijZmOCRAgQIAAAQIECBAgQIBANQFBQTVahQkQIECAAAECBAgQIECAQDwBQUG8MdMxAQIECBAgQIAAAQIECBCoJiAoqEarMAECBAgQIECAAAECBAgQiCcgKIg3ZjomQIAAAQIECBAgQIAAAQLVBAQF1WgVJkCAAAECBAgQIECAAAEC8QQEBfHGTMcECBAgQIAAAQIECBAgQKCagKCgGq3CBAgQIECAAAECBAgQIEAgnoCgIN6Y6ZgAAQIECBAgQIAAAQIECFQTEBRUo1WYAAECBAgQIECAAAECBAjEE/gXEbL/pqiev4MAAAAASUVORK5CYII=",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"PlotlyHelper.combine_plots(fig_list=[fig_variable, fig_exact],\n",
" xrange=[0, 1.5], y_label=\"concentration [A]\",\n",
" title=\"Variable time steps vs. Exact soln, for [A] in irreversible reaction `A->B`\",\n",
" legend_title=\"Simulation run\") # Both plots put together"
]
},
{
"cell_type": "markdown",
"id": "23fa9f49-0370-4ff7-9df9-b15eeb837f3b",
"metadata": {},
"source": [
"### A pretty good overlap!"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a99322ba-2da2-4a70-be13-c29fde3a1581",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}