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"## Macromolecules : Binding Affinity and Fractional Occupancy. Regulation of the rates of reactions catalyzed by the macromolecule\n",
"\n",
"### Reaction `A <-> B` catalyzed when ligand `L` binds to `site 1` of macromolecule `M1`\n",
"\n",
"# IN-PROGRESS\n",
"\n",
"In Part 1 we consider the un-catalyzed reaction `A <-> B` \n",
"In Part 2 we'll see what happens when catalysis is added\n",
"\n",
"LAST REVISED: Dec. 3, 2023"
]
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"name": "stdout",
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"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
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"cell_type": "code",
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"id": "c1ac7763",
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"tags": []
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"source": [
"from src.modules.chemicals.chem_data import ChemData\n",
"from src.modules.reactions.reaction_dynamics import ReactionDynamics\n",
"\n",
"import plotly.express as px"
]
},
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"cell_type": "code",
"execution_count": null,
"id": "8d3de311-5010-4b42-a320-e34607c14a0f",
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"source": []
},
{
"cell_type": "markdown",
"id": "1b3df8ff-f3b2-4d16-a04a-9f3675b79009",
"metadata": {},
"source": [
"# PART 1 - Consider just the un-catalyzed reaction `A <-> B` by itself"
]
},
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"id": "34e5c78b-c23a-47c1-8db0-0e2f997dcff6",
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"Number of reactions: 1 (at temp. 25 C)\n",
"0: A <-> B (kF = 1 / kR = 0.13306 / delta_G = -5,000 / K = 7.5156) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A'}\n"
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"# Initialize the system\n",
"chem1 = ChemData(names=[\"A\", \"B\"])\n",
"\n",
"# Reaction A <-> B , without catalysis (slow forward rate, relative to what we'll see in Part 2)\n",
"chem1.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=1. , delta_G= -5000)\n",
"\n",
"chem1.describe_reactions()"
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"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 100.0\n",
" Species 1 (B). Conc: 20.0\n",
"Set of chemicals involved in reactions: {'B', 'A'}\n"
]
}
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"# Set the initial concentrations of all the chemicals\n",
"dynamics1 = ReactionDynamics(chem_data=chem1)\n",
"\n",
"dynamics1.set_conc(conc={\"A\": 100., \"B\": 20.},\n",
" snapshot=True)\n",
"\n",
"dynamics1.describe_state()"
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"* INFO: the tentative time step (0.02) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.008) [Step started at t=0, and will rewind there]\n",
"80 total step(s) taken\n"
]
}
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"source": [
"# Take the system to equilibrium\n",
"dynamics1.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"dynamics1.set_thresholds(norm=\"norm_A\", low=0.6, high=1.0, abort=1.44)\n",
"dynamics1.set_thresholds(norm=\"norm_B\", low=0.04, high=0.6, abort=1.5)\n",
"dynamics1.set_step_factors(upshift=1.2, downshift=0.7, abort=0.4)\n",
"dynamics1.set_error_step_factor(0.3)\n",
"\n",
"dynamics1.single_compartment_react(initial_step=0.02, reaction_duration=4.0,\n",
" variable_steps=True, explain_variable_steps=False)"
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"#dynamics1.explain_time_advance()"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics1.plot_history(colors=['darkorange', 'green'], show_intervals=True, title_prefix=\"WITHOUT catalysis\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "0977ca98-2038-4122-8109-008b3a908193",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 14.63 ; [B] = 105.4\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 7.20163\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 7.515573071036746\n",
"Discrepancy between the two values: 4.177 %\n",
"Reaction IS in equilibrium (within 5% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics1.is_in_equilibrium(tolerance=5)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9dcb87c0-35f2-4f75-9b25-457383753281",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "d4d1109a-4fd7-408a-89a4-286f7cffed7d",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "24961bae-dc76-454b-b3eb-8fca0433eec3",
"metadata": {},
"source": [
"# PART 2"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "23c15e66-52e4-495b-aa3d-ecddd8d16942",
"metadata": {
"lines_to_next_cell": 2
},
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"source": [
"# Initialize the system\n",
"chem2 = ChemData(names=[\"A\", \"B\", \"L\"])\n",
"\n",
"chem2.add_macromolecules(\"M1\")\n",
"\n",
"chem2.set_binding_site_affinity(\"M1\", site_number=1, ligand=\"L\", Kd=5.0)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "42f86e37-e634-4746-86bd-07036f47301f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"M1 :\n",
" Site 1 - Kd (dissociation const) for L : 5.0\n"
]
}
],
"source": [
"chem2.show_binding_affinities() # Review the values we have given for the dissociation constants"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a9190b2f-aacb-478e-956d-450245338399",
"metadata": {},
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"source": []
},
{
"cell_type": "markdown",
"id": "83fd43d2-6a90-4b24-ae2c-5a65718e416d",
"metadata": {},
"source": [
"## Define 2 reactions, one with and one without catalysis"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "9211536e-74c5-43e5-8c3e-ab619e3c7a0d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 1 (at temp. 25 C)\n",
"0: A <-> B (kF = 1 / kR = 0.13306 / delta_G = -5,000 / K = 7.5156) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A'}\n"
]
}
],
"source": [
"# Reaction A <-> B , without catalysis (same as he had in part 1)\n",
"chem2.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=1. , delta_G= -5000)\n",
"\n",
"# Reaction A <-> B , WITH catalysis (fast forward rate)\n",
"#rxn = chem2.add_reaction(reactants=\"A\", products=\"B\",\n",
"# forward_rate=10. , delta_G= -5000)\n",
"\n",
"#rxn.set_macro_enzyme(macromolecule=\"M1\", site_number=1)\n",
"\n",
"chem2.describe_reactions()"
]
},
{
"cell_type": "markdown",
"id": "e1edaccb-4940-4040-abd9-ccfce973b671",
"metadata": {},
"source": [
"#### Notice the thermodynamics is (as it should be!) the same - and hence the same equilibrium constants - but the kinetics are very different"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "25baaff8-1a2c-488f-bd6a-c351ec75bd5a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "562261e1-3a62-40f5-ac79-5199b3b60565",
"metadata": {},
"source": [
"### Start with no macromolecule ligand `L` present; hence, only the slow reaction is in effect"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "74b8a860-ddaa-4346-a695-5d4b2b334833",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 100.0\n",
" Species 1 (B). Conc: 20.0\n",
" Species 2 (L). Conc: 0.0\n",
"Macro-molecules, with their counts: {'M1': 1}\n",
"Fractional Occupancy at the various binding sites for each macro-molecule:\n",
" M1 || 1: 0.0 (L)\n",
"Set of chemicals involved in reactions: {'B', 'A'}\n"
]
}
],
"source": [
"# Set the initial concentrations of all the chemicals, including the macromolecule\n",
"\n",
"dynamics2 = ReactionDynamics(chem_data=chem2)\n",
"dynamics2.set_conc(conc={\"A\": 100., \"B\": 20., \"L\": 0.},\n",
" snapshot=True) # The macromolecule ligand L is absent\n",
"\n",
"dynamics2.set_macromolecules() # By default, set counts to 1 for all the registered macromolecules\n",
"\n",
"dynamics2.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5666eccd-a621-4749-beaf-999f1ef9bc9c",
"metadata": {},
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"source": []
},
{
"cell_type": "markdown",
"id": "d2aea53b-2a64-425e-8084-9e4e0e67cc8b",
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"source": [
"### Take the initial system to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3fdc370b-1f0e-4d3b-9ab4-7c2c16e33ffc",
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"name": "stdout",
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"text": [
"* INFO: the tentative time step (0.02) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.008) [Step started at t=0, and will rewind there]\n",
"80 total step(s) taken\n"
]
}
],
"source": [
"dynamics2.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"dynamics2.set_thresholds(norm=\"norm_A\", low=0.6, high=1.0, abort=1.44)\n",
"dynamics2.set_thresholds(norm=\"norm_B\", low=0.04, high=0.6, abort=1.5)\n",
"dynamics2.set_step_factors(upshift=1.2, downshift=0.7, abort=0.4)\n",
"dynamics2.set_error_step_factor(0.3)\n",
"\n",
"dynamics2.single_compartment_react(initial_step=0.02, reaction_duration=4.0,\n",
" variable_steps=True, explain_variable_steps=False)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "ef1a4e35-b7d8-41ed-99a1-eb9bacfdd5bf",
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"name": "stdout",
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"text": [
"From time 0 to 0.008, in 1 step of 0.008\n",
"From time 0.008 to 0.0464, in 4 steps of 0.0096\n",
"From time 0.0464 to 0.08096, in 3 steps of 0.0115\n",
"From time 0.08096 to 0.2054, in 9 steps of 0.0138\n",
"From time 0.2054 to 0.3713, in 10 steps of 0.0166\n",
"From time 0.3713 to 0.5305, in 8 steps of 0.0199\n",
"From time 0.5305 to 0.6977, in 7 steps of 0.0239\n",
"From time 0.6977 to 0.8697, in 6 steps of 0.0287\n",
"From time 0.8697 to 1.042, in 5 steps of 0.0344\n",
"From time 1.042 to 1.207, in 4 steps of 0.0413\n",
"From time 1.207 to 1.355, in 3 steps of 0.0495\n",
"From time 1.355 to 1.534, in 3 steps of 0.0594\n",
"From time 1.534 to 1.676, in 2 steps of 0.0713\n",
"From time 1.676 to 2.019, in 4 steps of 0.0856\n",
"From time 2.019 to 2.224, in 2 steps of 0.103\n",
"From time 2.224 to 2.471, in 2 steps of 0.123\n",
"From time 2.471 to 2.767, in 2 steps of 0.148\n",
"From time 2.767 to 2.944, in 1 step of 0.177\n",
"From time 2.944 to 3.157, in 1 step of 0.213\n",
"From time 3.157 to 3.413, in 1 step of 0.256\n",
"From time 3.413 to 3.719, in 1 step of 0.307\n",
"From time 3.719 to 4.087, in 1 step of 0.368\n",
"(80 steps total)\n"
]
}
],
"source": [
"dynamics2.explain_time_advance()"
]
},
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"cell_type": "code",
"execution_count": 15,
"id": "507a0f60-50da-4fc6-9141-31b60b204a97",
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pxViks/GbnzH5ntuczpoY5VF/zSwNtdNrO5Oz/RVWBhJXYbR5i4yIUPZHio/dje8yBJ4+7+4KPrMHhT//SqN9uNtZG64+FLQPS2cPSpGO1tGM2QArHh5W2qXRMhejgdxZH9DOXhj1Uau/GJsJPatlcfbg1+8DEv107uJ1mDp+qOIwQkafN2KrTVfkV/Rf/dhl9qIiXv61s+1GrF3NrKgvzvqXTqvjrd2ZLG9zNSqf1WU6Rg9+dQzXctX/Sm/1xUZtf54+F1zt0dOv4lDT0wo47dhrdF3746DVvm3Wv1yNy3bajFYgaQWc9uVZf13Pw+o7hlWhYFQ+Z2UyWnVidWwzSsvTNi9+wNH/YKNlZucZZDa+i3FFn4bWuZxWeGvrT98n7eTFav1p25Sr8dNVG9eP1WY8rD6ntc9Oo7q3M5YYPW+M2qlR+3TVh7VcrI6H3s673X4ge3WLq3d1s/sBJfTMltiZrQO28jJo5LDESjw7Dxqzlwajh6+zX7BleNA0E8T6gdxZA9QOuO4u0bTbwLUvHVZmdpw5YxFp+yrfdsvpjsg3a5tWf40y8jRqtV2aLTsxsmmWH/1gapb2zr0HERUZ4dThkbMZPf2RGYKblT5mRQTI6PNW0zVyHKTnYNaujMZDV0LPzlJvu+Otvu5lcDXrL6LcuXn56NimuWm31bdrLVftC5e+bVl9sdEKPaOlm1bbrDtCz8hbntmzVn/dat82A+tq3LPz/DXznGznuifvGM7KIpbc9+nZRflhyKxMzpyq6fuH2Vip7zeetHkr47HVZ5AzNvp0jH4s+dv02WjfpjmysnIcP0zr68pqXpw9m81+KNM7N7LjAM9VH3HlddPZ2KN3WKhtZ956lqtld9U+3fW66WxGz9Wz29V7iJp3u/3ATv3afdfzJHyNFnquvAtqZzyM3N8bVbbZMhbti77ZoK6tCDsPGrOHsdmvLWYPdDsvVFYbjZVlRq5suSP0zOrBimgT+XFX6BnNVKp5Eff87bw8Vy88RnXj7MFmJOCNli4Iu9pfSZ09HPS/5Bq1UzPxaPQQ0A+m6i+y7ixftiv0rPQxKy/XMvq8lXTNxi49U1dCT9tPPBF6Vsbb6h5L1THQbEmSlR+5VM/GwtYrs5ZAXWL5+JQRiidLfb14U+hZabO+FnpW26EroWd2rI2dNmNH0Bm9U5jF1z6HnL2Um8086cvu7KXTzN2+XiyYjdP69uZJm7cyHlt9Bpm9kAs2ehv6ehD3t/y8C2J58f+8Nh//eHoSUurXVVY0aD2NW82LN4We0XuG3r6rutK3KVfPaavtzM6z3OyHT23/PnE63XS7j5V3aW0/0q4KsCv09O8hVvKuLkG3OvZT6LlSAzbumy1rEFP5+rXzZo1fm5wqHtQBSivq9BVndbrZzoPGrGOJPFr9Rc7KLKMNxI6g6lS4UVyrjV+Nq60LWTNk2jSs7KFR8+aqXq3MlrjD19M46sPN7tJNo5c/ozKq9a9laXdGT5uWWVvX23Q1wyq4aduQ2ne1PK3Uvwyh56w/q/mT0eddpWuHqS+EnpXx1uiFTlvHVsdHT8dSoz1HVscwrQAXS3fFR/yiLvIuPmIpr3j57NmtvWOJdCALPVFms+OR1Lp1xdaZuLLbZjwVenbeMczGe6O+qd+H5kqQmNnW2rE6/gpbnrZ5vZ8CV8tftWmq72TOnrtmzyvx4+DTD4/B9NcXKn3q1n49Hf3rhl5XYupTr0H9gcVZW7HzzLc7o+dK6Dl7HzESv1af01bamVWh5+zdUJRP/eFVFUtGP9JXl9Czmncxk26nH1DoefpGq4lv1gmsNnajrLh6sdH+AmSlcdoRejJ+3fcGbme/1NsZBPV5kSH43BV4doWeFfHgDfZ2bIj2aOdcKFcvDOqAbFb/ngg9s7ZuZ0bPFRvtw8zVDLAMoWdlZk1Gn7eSrpWxS/B1NR5qX1TcmdFzZd/KL+5G4k0GV6P2ZvSsMWuX6qyK+AVezOapL5nq7J74LpbTan+hD2Shp+5PtbJky4ypq5UMdp6/ngo9V6LT1XhldF+tf+0hzO7M6Oltu5olcuZkzU6b16ZrNB7bfQYZzYga2VD7v+hTr8z8SJnFUz1Ni9m9wTdfg+dfm1/piAqreXFWj94WeurYZtRHjJaoGjnIs9IujdqZVaFn5XkjyuFsVtbq88jqeOjtvNsd+yn03BntTOKYCT2jAcXVTI2ahNnLip09IyLs11u2Y0DfHsqvAGaHaOsbo7f2lVhZomOnGpw9LN2ZSZIh+LwlGl21E0+ErR3m7oRVGTg79Fu7X83qg81Vu9Qum7I6wNqxaXWWWru/wFV/NmuD2hccq2Vx9mJvtodVzavZr5xGL7BW8+OsjarpGnlQdOeHL63Qc/ZC4erlVP9iaTTeVvdY+vWWXxUnQ7XjYx2oXAkNLVM1bHxsNC5lZjuWf2tt6JfjGz2P7HBQ07fah5y9oJgtkfJkj57VfJn1MSvjtdXnr6dCz1VeXI3pIn3h9KhPzysqBdUzMqt/O23RbCzR2/akzVsZj60+g5yVzagsar8R4k70N9VhnLhutF9PALeaF18LPVdjpyp+rT5TrbYzbzxvjMY//X5FZ2LWynPabFyysrXJ6vuc3X7g7EdPV+OAzPs1eo+e9mVDhaQODOnnLzl+tVHh6w9SFwP0y28vxphhNznWbmttmu0tU69rvSHpH5TOKtyoI+lnZYzSUDuGlYbsaaOx8vDy9GGtfyl3JlSMyqN2VlfLfKywsLJUQt9+rNh1FkZNU3uYubs2VRb6fWpGaVh9sBk9ZNVr4sXEnT16Rpy1/Uxr0xkfUQbxEd5AjfqT1bYpY0ZP7af6WVb9r5cy+rzR7K42XZE3sWzOqM1pmbqacTMaJ43GY7N6cNUOjDxSGs02+GIsNSqD1RcFtT+rsyH6scrsulG7tPtMcfYSazTOWH3Bc/aCZvYLvf661b7tbDx01sftsPJU6Ik8WnnHEOLD6GPU14z6h5UVNvr2JWyLJYxiKaP4ocKZONI+fz1p81bGY6vPIMFL7WtGHlH1KzZcPUuEXwejI26sbmUwa48yZvRcPX/VsrsKp5bXajuzOw4ID9WuPCqbzb6K5b1W9tZ7e0ZPHcNc5d1uP3D2Y5y773beiBdwQk876IqzfdQGaLQ2WYQ12o+nOnkRa9vVs1W0S4n0D2/1u77B6tf2evMcPSOvQt6c0TMaXPUNzl9/vXCnY5i1D9WWjCWb3hR6Ip9mZdC3SzsPWa2wE2mImQ3VkYQ7M3pG+RT9TF3WZuRcQeRXv99Duz/UqNxW94/KEnrqS7Y231bOKXR2dqbVPq/nZSVdtW71Z4uZeY3Tizp9OzE6R0//oquvN2fjbXWPpaogU8cDo7MkXYkSvTt4s5dY7TNML27d4WD1uaCvDyvn6OmP2LEq9FRWrvq2M6aunj9WWXlD6Dkbf638EKldmaKW2SieWZlEHH0fNHp26duxs+ebu23eynhs5xmkf6cT3531P6Mfu7TjsV6U2M2LUZuUIfSM6lSM5UZLva0+p620MztCTzuGabkY1Y++r4t3qkNHT8HKEm4ZQs9q3q32AyuTI+68m3ojTo0Uet4oOG2QAAn4DwFn6/j9J5fMCQmQgD8RMHsp9ac8+lNeyMufaoN5CSQCdld5+LLsFHq+pM20SIAElOVDva/urLiVVz9mMwHERQIkQAJmBOzsTyPFql68yYQESMBzAv4+DlHoeV7HtEACJGCDgNHyISvLm2wkwaAkQAKXCQGz/cmXSfFtFZMzerZwMTAJuCRg5LnUZSQfB6DQ8zFwJkcCJEACJEACJEACJEACJEACsglQ6MkmTPskQAIkQAIkQAIkQAIkQAIk4GMCFHo+Bs7kSIAESIAESIAESIAESIAESEA2AQo92YRpnwRIgARIgARIgARIgARIgAR8TIBCz8fAmRwJkAAJkAAJkAAJkAAJkAAJyCZAoSebMO2TAAmQAAmQAAmQAAmQAAmQgI8JUOj5GDiTIwESIAESIAESIAESIAESIAHZBCj0ZBOmfRIgARIgARIgARIgARIgARLwMQEKPR8DZ3IkQAIkQAIkQAIkQAIkQAIkIJsAhZ5swrRPAiRAAiRAAiRAAiRAAiRAAj4mQKHnY+BMjgRIgARIgARIgARIgARIgARkE6DQk02Y9kmABEiABEiABEiABEiABEjAxwQo9HwMnMmRAAmQAAmQAAmQAAmQAAmQgGwCFHqyCdM+CZAACZAACZAACZAACZAACfiYAIWej4EzORIgARIgARIgARIgARIgARKQTYBCTzZh2icBEiABEiABEiABEiABEiABHxOg0PMxcCZHAiRAAiRAAiRAAiRAAiRAArIJUOjJJkz7JEACJEACJEACJEACJEACJOBjAhR6PgbO5EiABEiABEiABEiABEiABEhANgEKPdmEaZ8ESIAESIAESIAESIAESIAEfEyAQs/HwJkcCZAACZAACZAACZAACZAACcgmQKEnmzDtkwAJkAAJkAAJkAAJkAAJkICPCVDo+Rg4kyMBEiABEiABEiABEiABEiAB2QQo9GQTpn0SIAESIAESIAESIAESIAES8DEBCj0fA2dyJEACJEACJEACJEACJEACJCCbAIWeFwhn5hYhM6fQC5ZoQksgrlYYSkpLkZVbRDBeJhAcBNSrHYVT53O9bJnmBIGEmHAUFBYjJ7+YQLxMICQ4CHXjI3D6Qp6XLdOcIJAYG66027wCtl1vt4iw0GAkRIfh7KV8b5umPQB14yKQkVuIgsIS8vAygYiwYMREheFchvttN6VOlJdzRXNWCFDoWaHkIowQeULs8eNdAhR63uWptUahJ48thZ5cthR6cvlS6MnjS6Enj62wTKEnjy+Fnjy2si1T6HmBMIWeFyAamKDQk8NVWKXQk8eWQk8uWwo9uXwp9OTxpdCTx5ZCTy5bCj25fGVap9DzkO7f//53dOrcBQl16uOnLd+gT78B2LF9K+om1Ud0TBx2bP8JQ4bfgzUrPsSgoaOwbvUSDBg8HJ+tXYGbBw7FiWNHcOF8OnpdfzNmv/ESJj34JDanfYbEuvXQIKURNq5fjeGjJ2DtysW4sse1yMvJwcED+3DjgCH44L03cNfoCdi1YxtKAXTs3BUfLXgX4yY+pNhU4x47clDJ061D7sL+PTtx/NgR9L1pILZt/R5FRUXo3rM3tmz+Uslvpy5XYeP6VWjeqi1atGqDT1Z8iO49+yA5pREWz5+llCE2Lh5zZ76KsRMfRklJMRbNm4nxkx9RSH739ReIT0hEh85dkZuTjeWL5+GeCX9R7n21cZ1SptbtOiHj0kWFxcixk5V7aZ+vRcMmzZDapoMj7xMmTlGWbq5cvhSpbTuiWYtUpJ85hW82bcAdI8cr8YqLi/H+OzMwYerjjppcuvA9hW1C7TrKNW15xHdtucX3wwf/wN5dv6H/oGFK+KzMDKXcd49/wGFz3qwZGHPfNISFhzuuzZ/9OkaOm4yIiEjHNbVOIqNqOa4tnPsW7hgxDrWiYxzXPpz3ttIuYmJiHde0fNWLRtfEPX0Z1fDLF83FDf0HI7FOUqWWveKj93F9v1tQJ6m+cl0VejNnzkKvvv2RVC+5UvhVyxag53X9UD85pUoP0bYV/c0D+/c42qf+nhFXbRgjJtr7p08exw/fpWHInWOq5Em94CxvahhX6ajhfvnxW6VfdevRyzQ9cSM7OwurlszH6PumOcKZLd3csGY52nW4Ak2at3JqU71ppcx6Q+pYkdKwiaU0tIGc1bsrY/o25iq89r5ZezayoRd6SxbMVsbU+ITadpKsEtZqu3CViNEY4CqOq/vacdtVWDv3P14yv0r/lyH0ZDDRl7OgIL/Ss8gOB2+EVZ/fzmz5Wuh5MhZ4g4ldG0bPczs2/HVGT7xfnD51An363WKnOH4V1lOhJ/rHc88951dlulwyQ6HnYU1T6FHoUehVdCIKvTIWFHr2BlYKPee8KPRctycKvaqMKPRctxtfhKDQgzKRQaHni9ZWNQ3xesqtAAAgAElEQVQKPQ+5U+hR6FHoUehxRg/gjF5ZP5Axe0Wh5/pBTaFHoccZPdf9xN0QnNFzl1z1x6PQ80IdcI+eFyAamOAePTlchVXu0ZPH1tmMntxULw/r3KMnt55lLN2Um+OaY93XSzdrDhnv5NRfhZ53Sle9VjwVeiL39LpZPXVIoecF7hR6XoBIoScHoolVCj25uHm8gjy+FHry2ArLFHry+FLoyWMrLFPoyeNbk4Rebl4Bnnt5Dnp2a49hA/vIg+IDyz9t34NXZi3B2y8+htrxFT4d7CRNoWeHlklYCj0vQKTQkwORQs+nXNXEKPTkYafQk8eWQk8uWwo9uXyNhF5+cR6KSopQXFKM4tJiFJUWKU7klGviv5IiFJUUl10rLVLCiGvqv+Ke8re4Vx6vpNyOYrM8nnLNkU65TU04Nc1SlKIEJSgtLUGJ8n9p+b8lZXcc18v+VsJprpfFq4hT2VZF/Mq2ysI70iy3V5GH8nhO8iXCirwrrExtVeRLcNd+/uPqZ/HyLc97rQEIAXTvoy9WstepXQtFEEVGRFSb0FNFZnK9RPx1ygiPy0uh5zFCzw1wjx736HGPXkU/ojOWMhZ0xmJvbKUzFue8uEfPdXviHr2qjDx1xpJdmIXC4kIUlhQgvzhf+Vd8L1D+LUBBcT4Kyu8XiO8l+ab3i4oLkVecWzm8sKmxJ8L0OXYt1id/USa6ygVXhTirEF1CVFUWZ0KAFCO3KNd1Y/FxiK7oikZohNVY7eOU/Se5/8Z/e80Zy6uzluDTL3/ArJceR8umFZ7BV3z6NQ4dPYWp44dWm9DzNnEKPW8TdcMehR6FHoUehR6dsdAZi9oL6Iyl6oNUBhN9KjVN6GlFlCuR5Oq+mYhqdqQRjiYcx7nw84oIU0WZEGmKcDMQaSJf1fUJRSiewlP4H/yPV7MQFVoLIUHBCAkORUhQiPJvqPp3UChCgkMQGhyCYIh/xffya0GhCA4quxcq/lbClV8rj1cWNxQh4r/yeCHiXnk8ca3WuXCEZoWgoKXYHx9c9j+CEaT+HRTkuB4k7jiul/3tCFd+r+x7RZzKtiriV7UVZGJLk6ZJviLDQhETFY5LWUUVedWUpSKfFfmKCKk4espbXjeF8Hl6+uwqIk/bYLRLN4Xwe2/Rp8rtQTf2xN+fmICoyIpjsoQ4fPalOY7o82Y8he5d2irfxb0tP+9C5/YtMf3fC5Vr6qzh3MXrDO2aLRsV4lTNh7DzwpMTlGWl+vQb1K9TqWwUel4dCtwzRqFHoUehR6FHoUehR6Fn/gz1J6EnhIwQOflFeRDLy/KL8pWZprzyv8W1vKJc5bpyX/ku/s1HblFOWXhxXxu+OBc3HOmN1cmfKjNdehElZsKEWPO1iLoX9yINaTiEQ2694ESGRCE8NBzhweEICwlHWHA4Isr/Fd/FdXFfXA8vvy7+VcNXuh8aURZeE06xoQkfGhSGP9duR6c7rlWElSrKFDGlCCtxrUKwVRZdoagXH4XionAUFJa4VV5ZkXi8gveOVxCC6dSZ81UEm5HQW7txC1ThduFSJqY+9RpG3NbXsW9PFXKq+Pvz8AlMefIVTH96kiL2VBGmijJVxAm7+mvqfkAjoafPs8jLpxu3YMywm5U0GqfUqyQul3yS5tiTR6Fns1eq07r6dbNqA9ix+4BiUavoVVWvKn6jXwS4R89mRVgMTq+bFkG5EYzOWNyAZiMK9+jZgGUzKPfo2QRmM3h1O2MRYiqrMAs5hVnILsxWxFF2gfi7/HuBuJet/J9RkFE5XGF2uUgrE2YO0Vac73OR5Qq7N0SUQyiVi6iwkDCEB0eUiSmtMCv/HhEcARGmkjDTCDlViGlnYlyVw5/u0xmLvNrwB2csVve/OZtVE4SEBhDv/U//czaemDaq0vJPIcrUMHohqOoBMcunnRnUhhNhtI5ghHj82/TZ+MfTkyqlY1ZT+nxR6Fls09pNm/ffPbDSBkl9g9BXih6ythGoyVPoWawIm8Eo9GwCsxGcQs8GLDeCUui5Ac1iFAo9i6DcDGZH6AlRJsSYKsqyCjPLvivCLBtZBZkOUZap/J2liDgh2nIKRdxMZJWLOPWem9m2HE0IrIjQCAgxExkahcjyv8u+RyrXI5R/IxAproVFlf8d5fi7IkwkokTY8niVZqvKZ7u0s1vREZGoHxeLs5fyLeeXAa0ToNCzzspuyEATeurs3cnT56qgUHWCN4Se0BBLP0lzOgOpX9YpMqROOFHo2WypRjN6orJffmsxpj8zSXFdqhd+ogKaNU52TPUaQafQs1kRFoNT6FkE5UYwCj03oNmIQqFnA5bNoBR6NoGVBxfLE5UZsoIyMVY2Uyb+rfguZslKgnJxPucSMvI018UsW0GGI54QZUK4yfrUjkxETHgsaoVFIzosBtHKv7Hl/5Z9j4mIc3xXw8WGxyozWqrwUoRbaKQi2GLD42Rl17Jdet20jMqtgBR6bmGzFMkfhJ7IqJ2lm/rjFbQTNVZm2mQLPXU1YZOUeg4hqF57fMoIZTknhZ6l5lkRyEjoGUFUG4OR5x594+AePe7R4x69ij5Gr5tlLOh1097gTK+bVXkJISZmxMTyxEP79uLC6XTEdqhTIdLK76uiTYg0ZQZNzLIpYq5s9syZKJuMyViDNTiBE/YqTBNaiDIhxlSxFRMuhFjFdyHK6u+sDXSNQHQtId5iIMLEhIm/a5V9V8RcDOIi4t3OR01zxuJ2QW1E9NTrpo2kvBK0uLgY778zAxOmPu6WPX8Vetyj5709es6csah734YNvN7Q66ZW6OkFlVGD84bQcyYo9RNNIg8Uem51fddCTz+tqhd6d93W17FR0kjoXdG6IRKbdMaWb79Cv5tvxfZffkJSvfqIiY1T/h4+8h6sWLoQQ+8cjdUrFmPwHSOwdtUyDLxtGI4dPYzz59Jxfb/+eOO1F/HgY08hbeMG1E2qh5SGjbF+7ccYPW4iVi77ED2uvg45udk4sH8fBgy6He/NfB2jx0/Ejl9/AUqBzld2w4K572Di1EcUm2rcI4cPYvvPP2LIsJHYs2sHjh09gpsGDMLWH79DUWERevbqg81fbVTy26VrdyVeq9S2aNW6LVYsWajcF3mZP+dtpQxx8fGY+e9/YeLUR1FSXIx5772FydMeU0B/velzJNROROcu3ZCTk43FH8zBhCkPKfc2frYWKQ2boF2HTrh06SJWL1+MsRMeUO59vn4NmjRthjbtOjryPnHSA8q5LcuXLUXbdh3RolVrnDl9Cpu+WI+RY+5V4okHwztvvoqpDz/hqOiF789W2NZOrKNc05ZHfNeWW3w/+Od+7Pr9NwwacqcSPjPjElYs/RDj75/qsDnrzVdx36QHER5e4a1p9tszMO6+BxARWeFZSq2TqKhajrhz33kDI8bci+joGMe1ee++pbQLwVz9aPk6uybu6cuohl/0wXvof+sQ1KmbVKm3fLRwLvrdPFBpl+ITFATUjonAzFnvoO+N/VGvfoNK4Zct/gDXXd8PyQ0aVul12raiv7l/325H+9TfM+KqDWPERHv/5Ilj+O6bNNw58p4qeVIvOMubGsZVOmq4H7dsVvpVj2uuM01P3MjOysSSRfNx36S/OMLFRIWhsKgE+YXFleKuWbUMHTp1QfMWrZzaVG9aKbPekDpWNGzcxFIa2kDO6t2VMX0bcxVee9+sPRvZEN7m4mPCcCGzQLm9YO4sZUxNSKhtJ8kqYa22C1eJiDFgyN0jURBSiIz8S8jMz1D+FYIts0D8nYFL+RfLrheImbPy68q9S8gsEP9nKmdyqZ8u6IJmaIaP8bGr5E3vh4dEIMYxQxaDmIgYXH+uNw4nHUdQXJAivIQoS4yOR2RINCJDaimzatHh6qxauSArF3Ji9kx42rPyMRoXrcSzE6YgP7/Ss8hOXG+EVZ/fzmyFhAQjJjIUl7LL2q7sjydjgey8Gdk3ep7byUd8rXBkFxShqMi/nLHs2vkbTp08pjyDa+pHzEZHhYciI8e9tiv6x3PPPeeV4hsdr6AuxRzY72rT4xX0W6+M7AghefTEGYdHTGf78VTvnc726KmrBEXB1X19qiDt2a1DJecvIoy6jJNLN91sKrJm9LqG/YLkDjcgbV8hbh14G376cQvqJycjLi5e+fuecfdh4YL3MXr0WCxevBAjRtyNZcs+wrBhd+Hw4UNITz+L/gNuxYv/fAFPPfMsNqz/FPXq1UfjJk3w8YrlmDj5AXy48ANcd11vZOfkYN+e3bj9jjvx+oxXMHHyVPzy81aIN9JuV/XAOzPfxCOP/YdiU4178MCf+PHHHzBy1Gjs2PEbjhw6iEG33Y7vvt2MoqJC9Ln+Bmz84jMlv917XI2PVy5H27bt0LZdeyz84H306XsDGjdugrff+rdShviEBPzrpel49K9PKELrrTf+D489/qRSK59/th6JiXXQ7aruyM7Oxpx3Z+GhR/6q3Fu7ZjWaNGmKTp2vwMULFxQWD0x9ULm3ZvXHaNaiJTp27OTI+wNTp6K0FFi6dIlyvXWbtjh16iTWf7oW906YqMQT6b/6r//FE//5jKNVzH7nbYVtnbp1lWva8ojv2nKL7/v37cVvv/2KO4eXHW556dIlfLjgfUz9y8MOmyKNBx9+rJLQm/Hqy3hg2kOI1Ag9tU5q1aoQem+8/hrunTAJMTEVQk8wE+0iLq5C6Gn5qgkbXRP39GVUw783exaGDL0DSUn1KvWSue/NxsDBt6F+/WTlehCAsLBgzH5nNvrfcisaNKg4i0bc/+D9ueh3081o2LBRld6mbSv6m7t373K0T/09I67aMEZMtPePHTuKtC834p5xZSLf6OMsb2p4V+mo4TZ/87XSr67rfb1peuJGZmYm5s97D3956FFHuNCQIJSWlqJY976xbOlH6NLlSrRKbe3UpnrTSpn1htSxQvxwYvfjrN5d2dK3MVfhtffN2rORDfEjRVhIMArKX+ZmzXxTGVNrJybaSbJKWGft4mzOGZzNSce5nHScyT6Ns7lncTbrLMqun0V6zlmczT6rXL8/ZwLewBvIQY5H+RGRk2rVQ3xEPDqUdkCDwmQcSzmuiC911kz8GxcpBFrZLFm0+C6WNIZGKwKtbOYsBrWjjNm8P/e9Kv0/LCQIxeJAZi++KxuNix7D0RnIz8+v9Czytn1X9tTnt7NwYsm8GBsKikpdmfPKfU/GAq9kwKYRo+e5HRNhoUEoLhaHdtuJJT/sb79uhxjLBw66TX5iklIQbTckJAiFbrZd0T+8JfREEY0OTDfzhKkiMfKx4ex4A2/M6Im0td461byoedWX49X/noa5H60Hl2662ZCl7NFbOxrYs0jJUXabSbh0zf+5mTtG0xPgHj15bYJ79OSxFZa5R08eX0/36IlVAhfyzivi7HzeWZzLTVf+PpcnhFyZaFP+zj2jCLsL+edRUmpP9QjhJfaECdEVGx6P2LBYxEbEO67FRSQgVtwLE/dFuIp7Inx8RILiWr46PnacsVRH/mpymtyjJ7f2/HXpptxS+8a6v+zR801pAyuVoFLxs/Nl8jESet7wupn/3YuI+P5vAEpQkNQD529ahpKIstkkftwnQKHnPjtXMSn0XBHy7D6Fnmf8nMXWCz1VuAnBpogz5d90pOee1Qm3su92hVsQghQhVicqCXWjkpAYVRd1ouoqf9etlaRcL/u/7Jq4X10izRvUKfS8QdHYBoWePLbCMoWePL4UevLYyrZ8WQg9oyle7Vl53jhHr+DARiR+OQJBhZkojkrG+ZuWo7DOlbLrL6DtU+jJq14KPXlshWUKPff5aoXb+dyzZYJNFW85Z3A+Lx2XCs7hZOZpnM9NV2bniksr74V0lboQbnWj6qFOZF3UqSWEW5Lyd1J0vTIhF6mKuLJ7NVm4uWKhv0+hZ5eY9fAUetZZuROSQs8datbiUOhZ4+SPoS4LoScTvNbr5tbv0zA46jP8mNEUDULOILxlf/x8tBhDht+DNSs+xKCho7Bu9RIMGDwcn61dgZsHDsWJY0dw4Xw6el1/M2a/8RImPfgkNqd9hsS69dAgpRE2rl+N4aMnQPWelZeTg4MH9uHGAUPwwXtv4K7RE7BrxzbhMwIdO3fFRwvexbiJDyk21bjHjhzEju1bceuQu7B/z04cP3YEfW8aiG1bv0dRURG69+yNLZu/RHRMHDp1uQob169C81Zt0aJVG3yy4kN079kHySmNsHj+LKUMsXHxmDvzVYyd+DBKSuh1k143K3oYvW6WsaDXzaqjrnDvfzLrOE5nn8Tp7FPKv2dzTivXWh1ohk3Rm3Aw/6CybNLO52E8jJVhHyOkVpgyoyZm1oRYSxJCrlzEJdWqD+EdUtyvH13Z8ZCa1ofz3lbG6piYWDvJVwmrjsuRGodMHhkU+4g147antrTxP14yH7369kdSvbK9u+IjQ+jJYKLnQK+bVVsGvW56s7e4b4teN73nddP9Wrh8Y1LoeVj3+uMVrr++L3Z9vRgNC3chPugivsPNGDzqAaz5eAmF3sZ1inht3a4TMi5dVETvyLGTlRpI+3wtGjZphtQ2HRwidcLEKSgpLcXK5UuR2rYjmrVIRfqZU/hm0wbcMXK8Es/IHbPeVbtWuIo4WoErvh8++AfEQNx/0DDFZlZmhiJw7x5f5hFUfObNmoEx901DmMbr5vzZr2PkuMmg0KvoRBR6ZSwuN6F3NPMwvlq1BpHt4nE+5DxOZZ3EmRzx/2mcyjqhiDrh6t/s8yAexGIsRjrKRJ7w6Fgnqp4i1oQjEXVppHBOklQrCS2TGiGoSISpi69XrlV+PIv30OsmhR6FnievA+oPtc5s+HpGj0LPkxr1XlwKPQo977Um+5Yo9OwzqxTD7By9BqWHkJT+Ob4vvBZjG23F/Iu3Y9AdozmjR6GntB+jl0rtjKnayIyuiXtm544tXzQXN/QfjMQ6lY9XWPHR+7i+3y2ok1R2vIK6dHPmzFlVftEX91ctW4Ce1/VD/eTK3jjFPe3sr777UOgFntATRwEczzqK45ll/5/IOoZjGUdwIvMYhMA7lV12BtsDeEBx/38Kp0xH1ZSYRsqMmvg/Wfwfk4J60cnI23IB7ft0Q6N6zdAgpuqRHlqD+j16SxbMptBz8znGGT03wRlEo9DznCXP0fOcoSwLni7dFP3Dm143ZZUzEO1S6HmhVjNzCpGZW3HmkWoy8tg61N40DkHF2WX79vqvQmHtTl5I8fIwwT168uqZe/TksRWWa9IevWOZRxziTQg6IeIUUZd1FCcyjzqdiVMpipm3xvHNUK9WfYeQU8ScEHLl18QeOG98PPW66Y08BLINGUs3A5mXnbL5ekbPTt4CISz36MmrRU+FnshZSp0oeRmkZVMCFHpeaBxmQk+YDr20H3U+vw0hWUdQGhyBi31mI7fZcC+kGvgmKPTk1TGFnjy2/iT0xAHd2tk4IeqOZ5TPzmUdVZZUunJkEhkShZTYRmgY2wiNYpqgYVwTNIxtjIYxjcuuxTZBaHCYXKAa6xR6clFT6MnjS6Enj62wTKEnjy+Fnjy2si1T6HmBsDOhJ8wHF1xC7S9HIeLUV0pqWW2nIePq/wWq6ZwkLxTZJyYo9ORhptCTx9ZXQk+c7SaWTSriLfOYMvtW9rcq5I4gsyDTaUHF0QHCQUmKEG7l4q1RXGNFvKnXvDUT5y3iFHreImlsh0JPHl8KPXlsKfTksqXQk8tXpnUKPQ/pmu3Rq5tUX/FiuWP7Tw6vmyNbHsWKX4swJnIBPiy8HzfePh7Hz16i1006Y1FaIffoOfd6ePrkcfzwXRqG3DnGtNc62z+oRrLqdOOXH79VvNl269HL6SiRnZ2FVUvmY/R90xzhvOWMZdv+Ldj5088o7RyOoxmHlX1xwkul2Bsn9soZfe7FvUhDGg7hkHK7WXxLNI5rgpRoMSvXWJmRaxzbFA1iUtAiIbWSCWd7M10Nlfp9oK7Ca++b7Tk1ssE9enbIOg/LPXreY8k9ep6z5B49zxnKsuCp0OMePVk149ouhZ5rRk5D2BF64miC9cvn4p6g17E4ZziGJ3yJXS3/G+l5ETxegV43KfRcuLcPVKGXX5yH/Rf2Yv958f9u/HFhH/68sA97zv+OJmiCm3AT5mCO4TgkZtvE3rjk6BRlKaWYjYvcHYzmndqibcvOitdKOx8KPR6vIGNGj8crlPVCX8/o0eumndFPXlh63bx8vG6u+PRrPPvSHGjP6pbXsqxZptCzxsk0lF2hJ44UGNynEzZ8uhojwxfgQElrHE8ejqsHP8Bz9Hi8guOcQrXB0etmRder6UJPHC+wdvViFCQV42DwIey/sEf5X8zUmX06R3bBDSV9cbJlurI/LiWucflsXEO01M3GqTY8ebmj0KPQo9Bz76WAM3rucdPG4oye5wxlWeCMnmuyuXkFePntxUrAmFqR+OuUEa4j+SAEhZ4XILvao2eURHDeeSRuHIbwsz8qt7PaP4SM7v/kvj0NLO7R80LjNDHBPXry2OYW5eBY7j7sPLUTv53eiX3nd2PPud8dxxAYpdw0rgVSE9sgtXYbpNZph9SENkhNbKecJ8dPZQLcoye3RcgQenJzXHOs+3pGr+aQ8U5O6YzFOxyNrHgq9ITNQPe6+efhE1i44gsMG9gbb8xZienPTELt+Op/hlPoeaFfuCP01GTjtzyG6D2zlK/59a/DuVs/80KOAsMEhZ68eqTQ85ytWHK59/xu7Du3G3vP71LEnBB1wiGK2adtYgekJrZF6zrt0Kp2a7Sq3Qbt6/DIFTu1QaFnh5b9sBR69plZjUGhZ5WUe+Eo9NzjZiWW3wm99J1AbrqVrHs3TN2OQJTxUUFi2ab43NqvJ557eQ7uuq0vundp69303bBGoecGNH0UT4SesFVr//tI+HaqYrYotiXO37wCRXGVnSR4IZs1zgSFnrwqo9CzzrawuAB/XNyniLm96bvK/j2/G0cyDkJ4vtR/QoJC0KJ2S7St0x6tEtqhTZ32aJPYXnF8Ehocaj1hhjQkQKEnt2FQ6MnjS6Enj62wTKEnj6/fCb1Vw4A/VsorsJnlISuA1Duq3FWXbY4ZdhNaNk2BEH1bft6Fvz8xAVGR4b7PpyZFCj0P8buzR2/A4OH4bO0K3DxwKE4cO6J43byhfQLe/GgTnov5b6wtHIpanUahXutrsXH9agwfPQHqvpu8nBwcPLAPNw4YAnWD+64d2xTvgB07d8VHC97FuIkPKTbVuMeOHMSO7Vtx65C7sH/PThw/dgR9bxqIbVu/R1FREbr37A2tt8KN61eheau2aNGqDT5Z8SG69+yD5JRGlZyFzJ35KsZOfBglJcVYNG8mxk9+RCH53ddfID4hER06d0VuTjaWL56Heyb8Rbn31cZ1aJDSCK3bdULGpYsQ+xVHjp2s3EujMxY6Y6lmZyxFJUU4cPEP7LtQJugy/zyPczlnsbpgFcQ9/Sc4KBiNY5uhU8IVuPJkJ9S/oQXalC+7TIqPQUFhMXLyiytF27BmOdp1uAJNmreyNPJY2ZeoN8Q9epbQVglk1RurK+syHI9ox21X6du5T6+bdmg5D8s9ep6z5B49zxnKsuCp0PO6181vnwWOb5ZVXHO71z4PNOpd5f5P2/dg6SdpDmEnlnH+bfps/OPpSYrwq84PhZ6H9L0l9Hpdf7PijOXJDr/iy32FqB98Cklt+mDVsRYUesuXIrVtRzRrkYr0M6fwzaYNuGPkeKXmjB4MelftWuEq4mgFrvh++OAfEF6x+g8aptjMysxQBO7d4x9wtI55s2ZgzH3TEBZe8cvM/NmvY+S4yYiIiHSEM3rJWzj3LdwxYhxqRcc4whm9VPJ4Bd8dr9Dl5l44kn9ImZnbk/479l7YhT8v7EdRSaGjjvqir/L3V/hKOZagdWI7ZZauTWIHZellm8R2iAiJhMzjFSj0qg7QPF7Bw4eWJjqFnvdYUuh5zpJCz3OGsiz4ndCTVVA37b46awneW/RpldgvPDkBwwb2cdOqd6JR6HnI0dtCb9KDT+KH1W+i0ZmVaBb8B5YUjMFdo8Zh1aZtuLLHteCMHoWeaLJm544tXzQXN/QfjMQ6SZVatv6MM3Xp5syZs9Crb38k1UuuFN6Z90VnZ9Ud2L/HMeOs71pGAlobxtWMihXRo81bKUpxNKNMzO09V7GHbkD6TXgX7yIDGVV6vzimQMzKta7dHi0ym0IcX3BDn0GoFRptOlJQ6JWh4Tl6ZRw4o1e1q8hgok+loCC/0uoSDx/ttqNT6NlGViUChZ7nDGVZoNAzJ3vhUiamPvUaHp8yotKePP0sn6y6cWWXQs8VIQv3Pd2jZ5RESNYR1P7qXoSf3YLS4EhkXvU8sto/aCE3gROEe/Tk1WWg7dHLLszCb2e2YcfZbfg9/TfFQcq+83uQV5xrCLFuVJIyQ9euTie0rtPW8be3vFyaHZgur0YvH8vcoye3rrlHTx5f7tGTx1ZY5h49eXw9FXoiZ4HqdVMIuldmLcHbLz5WycumEIBP/3M2npg2qlqXb1LoeaFfyBB6SrZKSxC741XEbH8BQSWFyG/QFxf7zEVxVH0v5Nr/TVDoyaujmiz0coqysUMRddux/fRW/HpmGw5c3G8IKyGyNtrUbq8stWxbp4PiFKV93U6Ij0iQBxcAhZ48vBR68tgKyxR68vhS6MljS6Enly2Fnly+Mq1T6HmBrjShV563sIu/o/bGuxGa+QdKwuNxqddM5Da93Qs5928TFHry6qcmCb39F/Zi68nv8ePJ7/DrmV+UZZhGn9aJbdG5Xld0TLqibKYusS3q1aq8JFUe0cqWKfTkkabQk8eWQk8uWwo9uXw5oyePL4WePLayLVPoeUhYxh69zWmfIbFuPcVDZYXXzQ/RO+Y3FB/+EruL2mJgh3D8e98VuGv0/aDXzRmYMPVxR03SGUvN3qP3e8av+OnkFvx08nvl/0v5F5W6bYImuAk3YQ7mKCKuQ90rcEX9rriiXjd0SrzFpMoAACAASURBVOqCqNBalbzHmnVtV3sB1Xi//Pit4s22W49eTkcJ7tErw8M9emUcZOxHo9dN1w9q7tGrysgTD7yuiXs/BPfoeZ+ptyx6KvS87nXTWwW7DOxQ6HlYyb4TeosVZyxFJ7bi6LZ1uCt8IV7OeQqjhtyAX08E83gFCj2lJdc0ZywX8s7jhxObFUEX/1sU3i5+q4qTlNjwOHRLvho9Y69F4sm4Mg+mJs5RnDmKUbs6hZ75oOfMCY+roZJCj0LPrI3IEL/6tCj0KPT8dUZPePU+feoE+vS7xdUw6rf3KfT8tmpcZoxCzyUi5wF8LfSE181D+3diePhi/HtvR/yl1pvYnPgwCpKvR4cruvMcPQOPlDxeoepsS3V53Vy57H2EXh2rLMP86cQWHLz0h6OD/RV/VbxhJsTVQfcGPdEj5Vp0T75G2V8XhCDY9bpp1nMp9Cj0jAhYbReuHhkyRA1n9FxRByj0KPQo9Fz3E3dDUOi5S67641HoeaEOZO/RM8tirT8+QPyWxxFUlIXChA640G8RiuKsHcTshWJLN8E9evIQ+2KPXkFJPrad3oqtJ7Yowu7nUz9AzOBpP6HBYcqeOiHoeqSI/3tBeMSs6R/u0ZNXg9yjJ4+tsExnLPL4co+ePLbCsr8KPbml9o11T4WeyGWget30TQ24n4pUoaeeLbFj94EqOezUrkUVV6TuF6N6Y1aX0BOlVo5hSBuD8PSfURoShYyr/oHsdhUHfVcvGc9Sp9DzjJ+z2DKEXtkyzG/xk5itO7kFv53dhsLigkrZiIuIR7f6V6NHw7LZuq7J3ZVDxwPtQ6Enr0Yp9OSxpdCTy5ZCTy5fCj15fCn05LGVbVmq0BMnxYvPX6eMkF2OarVfnUJPKXhpMWJ3vIKY7f9wHMNw4fr3URJZs2dGKPTkNWtvCD2tN0z9Mkw1503imhsuw5RXMv+wTKEnrx4o9OSxpdCTy5ZCTy5fCj15fCn05LGVbVma0POXgwJlA6yOPXoHD+zDjQOGOLy7qV43uzSOwKIVn+LJ6BdxOrQVlhTfjzvHP4JjRw5ix/atuHXIXdDu9di29XsUFRWhe8/elbwVave0fbLiQ3Tv2QfJKY2weP4sDBo6CrFx8Zg781WMnfgwSkqKsWjeTIyf/IiC+ruvv0B8QiI6dO6K3JxsLF88D/dM+Ity76uN6xRPoq3bdULGpYtYt3oJRo6drNxL+3wtGjZphtQ2HXDhfLribXTCxCkoKS3FyuVLkdq2I5q1SEX6mVP4ZtMG3DFyvBLPyEsXvW7K8bp56NKfSDvyBQ5v24u92XvwVXFale41KP42dAjqiNbXdEb3lGsrLcPMysyAaE93jzeecXa1R4p79KyNZp542qMzlnsQExNrDbRJKO7RqwpGBhN9KtyjV5W7J2OBR53Azcj0uukmOB9E81To0eumDyrJJAkKPQ/Z+5PQ69i5Kz5aMBsPdfgTObtXYWnecNzbOQu/N3wEv+3YSaHXqo1S21qBK74fPvgHhFes/oOGKfeNBMm8WTMw5r5pCAsPd7SY+bNfx8hxkxERUbH00OiFZuHct8o8RUbHOOIaiRqtkFYDGl0T9/RiVg3vTa+bXXr2xN7CvUg78jk2Hf4cRzIOKsncgltwERexM2wnuje4Ft1TrkH3BtegW3IPHD9wCOoPEfquRaEHbFizHO06XIEmza3tpbUibvWcPXm5o9Cj0JOxR49Cr6yX+npGz5OxwMNXI7eiU+i5hc0nkSj0fIJZSiLShJ7IrVi62axxMoYN7CMl8/5g1P+E3rsYN/Eh5Oz+BJ+lbca0qH9jf9g12BxxNwYMn8gZPQo9pduYed3cdW4HNh36DDk/n8OygmU4hmOObpYUVQ9Xp1yH7nnd0Kx+K9x07W1VuuCB/Xso9ACYLd2k0DMetc1+uDAKrV+6uWTBbAwYPBzxCbU9eiS4mlG2alyGqKHXTdf0OaNXlRGFnut244sQPF4BCPQZvRWffo1nX5pTqTm98OQEv9A/UoXen4dPYOGKL/DE1FGIiqyYCfFFx/JlGtW+R8+ksMH555CweSoij65BSURt5LQYg8yu/w+lYRUzS77kZDct7tGzS8x6eFXoHTiTjm+ObsKmw5/hi0PrcDLruMNIo9gmuCq5J3o2vE4ReOKQcn6sEeAePWuc3AnFPXruULMeR8aMnvXUAzukr2f0Aptm1dJxj568Gvd0Rk/kLJC9bgqht+XnXfj7ExMUvSP0z9+mz8Y/np6Elk1T5FWMBcvShJ4zj5siX/S6aaF2vBQket8cxP34lHIMQ0lkPVzo8y7yU27yknV5Zij05LAVZ9d9eWg9vj72Ob4+/DXEMQjiExociquSr0H/FgNxc7OBaJGQKicDl4FVCj15lUyhJ4+tsEyhJ48vhZ48tsIyhZ48vhR6ztnqhZ6qgR6fMgLdu1Tvj+TShJ685uZ/lv11Rk9LKiTrKBI2T0LEqa+Vy/kN+uLSNf+Hojj/fZmn0PNOWxdHHHx3/BtsPLQeGw+vh3Cqon7iIxLQr2l/3NR8IG5segtiw+O8k+hlboVCT14DoNCTx5ZCTy5bCj25fCn05PH1N6G388xOpOekyyuwieWO9Tqibq26Ve4azei9/NZiTH9mEmrHe+bgy9NCUuh5SNBf9+ipniuHj55QyevmkS9n4NT+XzA0Yhm+KeiD7KReuGLIE/j+++8QHROHTl2uAr1uVvUOWdOcsRREFipLMYW423w0DeOKxuJjfIxTOIWWCano33wgRnYehp3rduO6vv2RVC+5Uk9w5pRjy+YvHW1F3324R6+MCPfo2RtYuUfPOS/u0XPdnrhHryoj7tFz3W58EYJ79Ly/R2/YR8Owcs9KX1RfpTRWjFyBO9reYSj09Hv0/GXlonSh99P2Pbj30RcrQZk346lqn8r0VuuoaUJPvDCcPLwXt0d+gq17T6GwNBTXJ+7H2uj/QETKlRR6NdTrZnFpMbae/B6/rNuMz8M+xw8Z3zuaeGhwGB4JeQSxHetgQOfb0SS2makzFjUShR7wy4/fohRAtx69nA4X2dlZWLVkPkbfN80RjkLP3ghLoUehZ6/FVA1NoUeh568zehR63hd6z256FpuPbPZ02LAd//kbnkfvJr1dzuiJAPpZPtuJeSmCVKEnRN4rs5bg7Rcfc0xdig2KU558BdPG3+4X3mg85VgThd7xY0fQ96aB2JG2GCGH1uImLMeG/FsQHV8HrQc9jQ3f7kDzVm3RolUb5dwznqMH+OOMXo8b++Kniz8oM3dfHf0CGfmXMA3TsAzLUBhZhBua9kf/5oPQt0l/fL5yBa7vdwvqJNVXmryZ100KvYoRgULP3ui44qP3K7UxO7Ep9Cj07LQXo7AUehR6FHqe9iLz+J4u3bwcvG5qnbEIkkLv+MPyTWlCLzevAM+9PAd33da3yuydEIBLP0lzeKeR1zR9Y7km7NEzJVFShJjdbyJ22z8UZy2lwRHI6vgosq74T5SGVJwP5xuSlVPhHr3KPEpRit/O/IKNhzfgi4PrlL/FNfUjvGLe1OxW3Nx8kOItMzgo2LTaVKF36nxudVRtwKfJPXryqph79OSxFZbpjEUeX+7Rk8dWWPZXoSe31L6x7qnQE7m8nLxuivIG/Iye8Djz9D9n44lpo6q4FvUXleut7lGjhV45hJDc04j74QlEHVqmXCmOaYpLV/8LeY0HeQuTbTsUekBmQYZyYLnYayeOQEjPPevgGBYSjp4pvZRZu/7NB0Mch2D1Q6FnlZR74Sj03ONmJRaFnhVK7oeh0HOfnauYFHquCHl2n0LPM37OYlPoOWdrdI7eoBt7+sWEFmf0vNAvAkHoqRgiTm9G/Ld/QWjGfuWSOIbhYq9/ozi6qRdI2TNxuQq9Py/uxxeHPsXnB9fhp5PfoaikyAEuMbIO+jUbUL4k82ZEu3kmIoWevbZoNzSFnl1i1sNT6Fln5U5ICj13qFmLQ6FnjZO7oSj03CXnOh6FnmtG/hpCmtATBRYKd8knadyjN/werFnxIQYNHYV1q5dgwODh+GztCtw8cChOHDsC4SGz1/U3Q6xhnvTgk9ic9hkS69ZDg5RG2Lh+NYTnTNV7Vl5ODg4e2IcbBwzBB++9gbtGT8CuHduUBXwdO3fFRwvexbiJDyk21bjHjhzEju1bceuQu6D13rZt6/coKipC9569ofWkuHHdx2gX+Se6HXsR87JGol/E10jsdjdm/1obg4bejdi4eMyd+SrGTnwYJSXFWDRvJsZPfkRp4999/QXiExLRoXNX5OZkY/niebhnwl+Ue19tXKeUqXW7Tsi4dFFhMXLsZOVe2udr0bBJM6S26eDI+4SJU1BSWoqVy5citW1HNGuRivQzp/DNpg24Y+R4JV5xcTHef2cGJkx93NHH9Pt9tF5ERSBtucX3wwf/gNgs3X/QMMVGVqbvvW7+euYXfP/xZ1gWvhy7s353lOVRPIqvEzajV8sbcGPzW9A9+RrlntmepuWL5uKG/oORWCep0pij3z/FPXr3ICbGuctj7tGz99jiHr0yXuq4HBlVyx5AJ6HpddM1Su7Rq8qIXjddtxtfhKAzFu87Y/FFvQVKGlKFnoBEr5s/YUhNE3rrVynOWFJT4rBm8UzcXPoRmoQcwf/lPo4hN/VEROogCj0A82e/jpHjJiMiomIvo9FL3sK5b+GOEeNQKzrGMW58OO9tXDdoAFYdWY6Pdn0AcYi5EHXzMA8lEaW4rdWduD31Lhz9co/yA4EQ19oPhZ7xEOzs6Ac1hmAv+iSFXlWGzrytunroUehR6Jm1ERniV58WhR6Fnr/O6FHoUei5en7KvC9d6MnMvD/YrsleN01n9MqFnup189rUOLTb+xTePDME4yPnIbJZb7yytwfGTnqEM3o2hV5ecS4+2b8CpzYdwFvFbyIDGY5m/HTYM2jZuxNubX+749ri+bMo9MppnD55HD98l4Yhd44x7foUenDM/qc0tL5nUwVKoef6BwBXzx0ZooYzeq6oAxR6FHoUeq77ibshPF26GeheN93l6ot4FHpeoBxIe/TMcAQVFyDm99cR8+uLCCrOQWlILWR1+U9ktX8EpSHhXqBY1USg7NETnjG/P/4Nlu5ZgLV/fIzswiylsMIrZs+U63Bn29EY3GoYYtzcb+cOfO7Rc4ea9Tjco2edld2Q3KNnl5i98NyjZ4+XndDco2eHlv2w/ir07JfE/2J4KvREiQLZ66b/1VhFjij0vFA7l4PQUzGFZB9D3I9PIOrwKuVSUUwLXOr1JvIbXO8FkpVN1HShd+jSn8qyzOX7FuF45lFH4domdlDE3Z1tRqF+dAOvc7NikELPCiX3w1Douc/OVUwKPVeEPLtPoecZP2exKfTksRWWKfTk8aXQk8dWtmWvCz1xrMLUp17DfSNvwdyP1mPH7gOGZejUrkUlJy2yCyrT/uUk9FSOESe+QPx3jyA066ByKafFKGR2/W8Ux9hfLmZWNzVR6InjEFbu+whLdi/AttM/OYrWIKYh7mg9AiPajUNq7TYym6Ml2xR6ljC5HYhCz210LiNS6LlE5FEACj2P8DmNTKEnjy2Fnly2FHpy+cq07nWhp2bW2Tl6gXRg+uWwR697zz5ITmkE7X4x1etmrV//hXe/L8BTMS8qVb865m+IatUPHbpcc9l43QwJC8XGw+uxdM9CdPqzDd7AG8hBDmLD4zCo5VB0PNgGI+6ehGidMxa9QxCj/Xjco1cx/HGPnrVHgSee9rhHj3v0ZAg9GfsW9b2Be/Sqjg+ejAXWRhvvhjLyom0nBX+d0aMzFjpjsdOOvR22WoReIB2YfrkLvbLjFd7CI+12otafi7AufyASokPQvtsNSG86NqCPV5j7zms42Oo4Vh74COfzzil980k8id+b7MPtHe7Czc0HIjw4AmZeNyn0Kg9nrrxhUuhZG/49ebmj0KPQo9Cz1s/0odTjkZzF9vWMnidjgXsUPItFoecZP5mxPZ3RozMWmbXj3Ha1CD1xvt6Wn3f5xYnxnqKn0Ks4Ry8s/Rf8+Ol7SMr7HT3Cf0RGZCvMyhiLMZOfUDAHwjl6F4suKDN3wrHKsPNDMQMzkI98XJXcE3e2vRulW3IwYsxEaM/QotAr62VG5xNq+x+FXtXRyIq41cfy5OWOQo9Cj0LPvbcCCj33uGljUeh5zlCWBQo9WWTl2/W60BOzdVOefAUnT5fNcBh9GtSvg1kvPY6WTVPkl9AHKVyOe/ScYY08/jlif/k7ws79ogQrimmOrC7PIKflKCAoxHKN+MsevZyibHx2cC0W/T4Pm4+lOfLfMiG13KnK3WgU6729iZYBeRCQe/Q8gGchKvfoWYDkZhDu0XMTnMVoMoSexaQDPpivZ/QCHqiugP66dDMQ6sFToScYBLLXTX+ewPK60FMbtLM9eoHQ6LVloNAzrtHII2sQu+0FhF3YUSb44lKReeV/Ibf5cABBLptBdQu9Lw9vwKr9S5Vz7/KL85T81omsq4i7oa1H4Ip6XV2WwV8DUOjJrRkKPXl8KfTksRWWKfTk8aXQk8dWWKbQk8eXQs8528tS6Mlrbv5nmULPWZ2UIurwSsT+8gJCL+1VAhYmtEfWlc8it2nFweBGFqpD6J3OPol3f30Di3a9jwt55x3ZGtxyGEZ3uA/XN7nR/xqgGzmi0HMDmo0oFHo2YNkMSqFnE5jN4BR6NoHZCE6hZwOWG0Ep9NyAZjEKhR6FnsWmEnjBuEevYo+eqN3vvv4C8QmJ6NC5a2Wvm6Ul+HbV22iR+Rm6FX+OCyWJ+KBgAu4ZfC3yGt2CtM/XomGTZkht0wEXzqdj4/rVmDBxCkpKS7Fy+VKktu2IZi1SkX7mFL7ZtAF3jByvNCajNf1LF76HmwcORULtOkqYjetXoXmrtmjRquxYg21bv0dRURG69+ytfD988A/8sO1rbKqVhtV/LEMCEnAv7sXCqA8xpsMEjO00EesXLMGY+6YhLLzicPj5s1/HyHGTERER6WjYRt7luEevDA/36AEb1ixHuw5XoEnzVpYGQ+7Rq4pJL/SWLJiNAYOHIz6htiWmZoFc7RG1alyGh8n9e3bi+LEj6HvTQKvZsBTu4yXz0atvfyTVS3aElyH0ZDDRF5BeN6tWuSf7dS01IC8H4h49LwP1ojlPhZ63nbHs3JmO9PRcL5bQmqmOHeuibt2oKoEv2xk9Z/v1AuUcPQo9i0JPdcbSIAVdwn9F0c9v4MP0fng4+nUUJPXAiuKxaNCmp8+F3sf7l2DND0sRfzEWi7FY6bxX1b4aQ3IH4/6Jjzs687xZMyj0ymls2fwlomPi0KnLVVUGuwP79+DggX24ccCQKvco9Cj0zB6l+h9nnD1yKfSsvZBYCUWhZ4WStTB0xmKNk7NQFHqeM5Rlwd+E3rBhq7By5X5ZxTW1u2LF7bjjjlQKPUEgN68Az708Bz27tccVHVph4Yov8MTUUYiKDMers5ag99Wd0b1LW59XkrcTpNCzKfRSGqF1u07IvJiOdcvn4aHYmQjJOYGVecPQtHYQmtwwFadDW0ud0duyZRO2n9qKdy++g5NZx9EWbXElrkROahHuv2Ia2kS3wycrPsTd4x+g0Euu6jCJQq/yKJKdnYVVS+Zj9H3THDfMlm5yRs94BKbQc/5k4oye6yc3Z/SqMuKMnut244sQPEfP++foPfvsZmzefNwX1Vcpjeef74XevRtR6AkCWmcs4vvLby3G9GcmoXZ8LALpwHRRNu7Rc7+vBZXkI3rvu4j59WUE551RDOWn9ENG1+cR1eRqZelmVm6R+wloYv55cT9mb/83lu35ELlFOcqdulFJyvLM+zo/gKRa9b2STk0wwj16cmuJe/Tk8eUePXlshWUZSzfl5rjmWOcePbl1xT168vh6OqMnckavm/Lqx5lln3jdTEyIxfTXF+Lph8coQi+QDkyn0PNOww0qzkX07lmI2fEvBOeXOUEpajoI+T1fwKUoz2Z+045+gdnb/o2vjnyBUpQqtjsnXYn7r/gLbk8djrCQin133imN/1uh0JNbRxR68vhS6MljS6Enly2Fnly+FHry+FLoOWd7We7R0y7dHDawj7Jcs1njZIi//RmIO92EM3ruUDOOE1SUhZhdbyJ65wwEF1xSjmEQ3jkzr/x/KEqwLvjyinOVmbt3t7+B/RfKvH2GBodhUMuhmHDFVOWA88v5Q6Ent/Yp9OTxpdCTx5ZCTy5bCj25fCn05PGl0HMt9J59aU6lQP7ii0TajJ4eiVjKOfWp17Bj9wEE0oHp3KPn3h69jEsXsW71EowcO1lpKlW8bq77GA90Po2wX1/HkqxBuCL0VzRN7YQDTR9E2g+/m3rdFMcjrFz0PhaULMDBggOK7XtC7kFy08a4p+9kZXmmkddNsYa+/6BhSngjpyF0xlLRo7lHr/Loxj16ZTxWfPQ+ru93C+ok2V8CzT16zl8iuEfP9Qss9+hVZcQ9eq7bjS9CcI+e9/fo+aLeAiUNnwm9QAGmLweFniShV368QmneOaxe8G90zV2NdiE7cLIkBauCJmDYsLtQFJ/qOF6h25034J1tr2PNnyvwQMkDigfNlKTGyvLM+INRaJna3unxChR6Fe7VRRtftWwBel7XD/XpjAXdevRyOnxR6FHoaRuIjKMEKPRcv0FQ6FHo+euMHoUehZ7rEUxeCGlCT+uMpWXTqp775BXJt5Yp9OQKPfUcvdYtGqNTxjJk7lyGT/IGY3Ktd5Bb71osir8Sh7Yl4gW8oFR8aHAo/iP0CVzZtxeua91PuWblHD0KPQo9/cjxy4/fKjs6KfSsjamc0SvjRKFXtb3IYKJPhUKPQo9Cz9pY7U4oT5duevscPXfKcLnGodDzQs1zj54XIBqYiKsVVsXrZkjuKRRv/18s+P09vJFfhKNlvlWQFB6jeM+898rHLivvme6S5x49d8lZi8c9etY4uROKe/TcoWY9Dr1uWmdlNyT36NklZi+8vwo9e6Xwz9CeCj1RqkD2uumftVaWK2lCTxgPpPPynFUihZ6cJq4Xeufy0vH6Ty9hwc73IJytiE+HkGA8EVaC8aFlechpORbZnR5GYUIHOZkKEKsUenIrkkJPHl8KPXlshWUKPXl8KfTksRWWKfTk8aXQk8dWtmWpQk8co6A9KF12YarLPoWeHPKq0Dt47jhe3/oy5vz2liOhIa2GY0KXqehRtzNq/TEf0b+/hdDMPx33C+r1Qna7SchtPkJO5mq4VQo9uRVIoSePL4WePLYUenLZUujJ5UuhJ48vhZ48trItSxN6Wi+bRoXwF7ejngLmHj15e/SGjBmGl76bjgs/n8V2bMce7MG45vejS0ZnjLx7klJ1xcXFeP+dGZgw9XFEnNiE6D0z8d6ephgZuRh1g9NRXKshlpRORtPO/dCsXTclDr1uAqrQmzlzFnr17Y+ketyjpx8LuEfP3ujIPXplvGTsR6MzFtdtkXv0qjKi103X7cYXIeiMhc5YfNHOzNKQJvSqs1C+TJtCz/tC7+ipg1izZjFeKfoXcotyMQqjEN0oHhP7PYxaeVH4ZtMG0+MVRN0vWzALtzc7icZH5yI4/yyW5o1A+7C9aN66s7Ks88c/MlBUVITuPXsrTeXwwT9AZywUehR6zr2tuhpXKfQo9MzaiAzxq0+LQo9Cz19n9Cj0KPRcPT9l3pcm9Jx53fxp+x4s/SQNf39iAqIiw2WWT7ptCj3vCb26Kcn4LGcDlv+yEAMLb8XbeBu3tx6Gm3MHoEunq9GsRSrSz5xyKfTUM7lqx8Ui6vBKbPhqCzoVf4P2obuU9pAWfg9y6nRHl/4TgKAQCj3O6BmOE5zRszd8UuhR6FHoPem00/h66SZn9OyNYbJCU+hR6MlqW1bsVovQE3v3Xn5rMaY/Mwm142Ot5NOvw3CPnmfVk1uUgzm/vo23tr2Ki3kXFGP9mw/C8zf8D9rV6YCs3CLPEgAQdvF3RO/8N6IOLkVQuSOX4uhGyGkzGdlt7kdJRG2P06hJBrhHT25tcY+ePL7coyePrbBMZyzy+Ppa6MkriX9a9tcZPf+kZS9X3KNnj5c/ha4Wobfi06+x5eddATGjJyqTQs+9Jl1Qko/3d7yDN7b+C+m5ZxUj1ze5Ec9c+z/oWPcKGB2v4F5KFbGCCy6h1v55qLV7NkKzDig3SoMjkdtiBLI6PoqihLaeJlEj4lPoya0mCj15fCn05LGl0JPLlkJPLl8KPXl8KfTksZVt2etCT8zWTXnyFZw8fc407w3q18Gslx5HoBykTqFnr5kWlRTiw13zMOOnF3E6+6QSuUeDa/Fsr3+ia3IPhzEZQq8ip6WIPP45au2aicjjnwEoUW7l178OOe2nIrfJEGVZZ6B+KPTk1iyFnjy+FHry2FLoyWVLoSeXL4WePL4UevLYyrbsdaGnZtjZHj3ZhfKlfe7Rs75HL+2LtTgadAxvHHsNOZlZuAf3YHPyFjx59XMo3pODhk2aIbVNB1w4n46N61djwsQpyoHpK5cvRWrbjrb36CXUrqM0hY3rV6F5q7Zo0aqN8l3vdfPoru+xf9tGjA5+G8H5F3CpNAFzc+/H/b0TkN16grKsc96sGRhz3zSEhVfsKZ0/+3WMHDcZERGRjiZn5HRg4dy3cMeIcagVHeMI9+G8tzFk+D2IialYurx4/iwMGjoKsXHxjnBG18RNdR+iWkY1wvJFc3FD/8FIrJNUqRvo90/R62Zl9kZjBvfo2RtJuUevjJcMxyP0uum6LdIZS1VG3KPnut34IgT36HGPni/amVka0oRedRbKl2lT6LkWeqPvm4pV+5diS9qX2FmwQzkq4era1+K2/MG4b8KjSnWlfb622oSe6nVzwC0DlT18RTvmY8GJ7ng0ekb5ss6RmPF7Ksbc9yCFHoAtm79EdEwcOnW5qkpXO7B/Dw4e2IcbBwypci8rMwOfrPgQd49/wLCLGolfbcDTJ4/jh+/SMOTOMaZd3Fne1Eiu2B0neQAAIABJREFU0lHDUejZG0kp9Cj0zFqMDPGrT4tCj0LPX2f0KPQo9Ow9Tb0bmkIPwKuzluC9RZ9WIvvCkxMwbGAf5ZrYU/jsS3OUvwfd2LPS3kIKPXOhl5OThUULZmFBzELsO78HQzEUudH5GN5nLHrVvR7rVy/FyLGT/Ubo9R80TMmLECRrls7DA6m/otafi5Rr07OfwV9a/oySVnchp9Vo5Rpn9Cj0RDvIzs7CqiXzMfq+aY4xxGzp5oY1y9GuwxVo0ryVpZHcirjVG/LkV/xVyxag53X9UD85xVL+tIEo9Cj0KPToddP2wKGJoD0X1x07FHruULMWx9Olm7PfeAnPPfectcQYyqsEpAo9Z4em+9OB6ULoic9fp4yoAlccBfHKrCV4+8XHFA+hRmG5R69qm/z80Kd4ecvz+D39N+Vm8/hWePzq/8LtqcMRHBRsqRHL3aNnKQsIzk9H9L65qLV3DkKyDiuRSsNikdNiFLLbTUNRQtly0Jr24R49uTXGPXry+HKPnjy2wjK9bsrjyz168tgKy/4q9OSW2jfWPRV6IpcpdaJ8k1mmUomAVKHnTED5Uz04y6e416xxsmN2Ty/8RDko9Cpqc/OxNPzzu//Cr2d+US42im2Cv179N4xsO9Z2lfuD0NNmWjhvido3B1GHV5UJvuBIFCRfi/xGA5Db/C4UR1U+dNx2gX0YgUJPLmwKPXl8KfTksaXQk8uWQk8uXwo9eXwp9OSxlW1ZmtCrSc5Y9Es31WWbuXkFeO7lOejZrb1D6Amvon+bPhv/eHqSw2sohR5w4OJ+PPfNk/jy8AalzdaPboBHuz+FcR0nud2G/U3oqQUJzjuL6P3zEbV/PkIz9jvKl5/cB3ktRyG3yVCURCS4XW5fRKTQk0uZQk8eXwo9eWwp9OSypdCTy5dCTx5fCj15bGVbptDTEVaPh5j+9CR0bNtCEXp33db3/7f3JmBOFPn//zvHZO6DY4b7EFBBQFHERVFkQW5BVEBEFEQRQdf1WPiDu/tHd/0uLAjirnKIcgmCgyAgIqi4eCN4oCgqKnIM93DPPTl+T3WmM0kmRyfpSjLDO8/Dw0y66lPVr67u5DXV9Wl06uB8vpq36Ik1eld0uBJ1cxrgs4+34qbe/fD1l9uRU68+0tMz8M1X2zHkznvwxuvLcPuQ4Xhz9UrccutQvLX2DfS/5TbkHdiPkyfz8ccevfH8zH/hz088if+9vwl1snPQqHFTvPPWGowY9QBW5y7HH669HkVFRfjtl5/Q9+Zb8dKc2bj73gfw3c6v4HAAHa68GksWzsPYhx5TYqp19+/bq/Rj0O3D8OMPu3Dw4D706jMAO774FOXlVlx3/Y34aOv7Sn+v7HgNNr71Ji6+tDUuvqQNVq18Fdfd0A2NGjXBopfnKPuQkZmFF5+fjrEPPY7Txaew7JWX8A/bPxQ+t5gGoWOLa/CngX9BUVEhli95GWPG/VnZ9t7mDWjUqCkua3c5zp45rbAYdd84Zdvmd9ajWbMWaH1ZO1ffx4wdB4fDgTdWrUKbtu3QstWlOH7sKLa8txF3jhit1BP39M/977N4+NH/z3UkX130ksK2du26ynvu+yN+d99v8fve3/bgh13fYcCgwUr58+fOYtXryzB6zEOumKKN+8Y+Aotb1s15L87Cfbdej/T9q2HZuwrGgjzMKJyIh1LnI6HZDShvNQzlzQdgwcsLcOfdo5HqlnVz4UsvKONCMFdf7nwDvSe2ee+jWn75kgXo3X8Q6tb1zLr52quvoGfvm5GdU08pajAAGakJmD//JfyxRx/Uq9/A40zIXbEEN9x4Exo0bFTlGuQ+Vrw37vn5R9f49N7mi6t7GV9M3LcfPpSHTz/6QOHm7xWob2qdYO2o5b74/GPlvOp83Q1+2xMbCgrO4/Xli3Hf2D+5yqUkmWC1OVBW7nxsh/pav3YV2rfvgItaXhwwprpRyz57B1KvFY2bNNPUhnuhQMc9WDDvMRasvPt2f+PZVwyjEUhLTsC5wnJls7jmiWtqVq3aoTRZpazWcRGsEfW6nJycEqyo5u3u123NlTQUXLl8UZXzPzXZhLJyB8qtnmNXQzi/RWQw8W6stLQUCxe8gHEPPxFJV8Ouq35+BwpgMhmQkmjC+SJr2O2EUjGSa0Eo7ehV1tfneSix05PNKC63wWp1hFJNetkfvv8WRw7l4abe/aW3JasBs9mApAQTCorDG7vi/OAaPVlHJ3BcaaInmvW+7TE2uxh6q2q/+3bvHHRGT4hehyuvVL4of/zhVvTu2x9f7vgC9YToZWQqP981YiRWLH8Vdwy/C6tWrsDtQ+/Am2+swi233Y4D+/fjZP4J3NSrD2ZM+z9MmPRXvLf5HeULeeMmTfDW2jdx7/0P4PXXluHa629AUWEhftnzMwbccite/M9zuPf+sdj59VdwwIGrOnbCKy/NxcN/fhz5+Sdcdff9vhc7tn+BIXfcqQjN/gP70a//AGz77FOUW8txQ9du+N+W95T+Xt3pGqxfuwaXtm6j/FuxfClu6PpHpS8vzX1R2YfMzCw89+y/UatHNv754RSMKhmFaZiG+zqMQW9HbzTIaYSrOl6NwsJCLF64AA/9yZlZ8523N6BJ0yZo1/4KnDlzWmEx5kFnAouNG9ajWfOL0LZde1ffHxj7IMTl+o1Vucr7F19yKY4dPYLNmzbinlH3KfXEB8Pzs2bg8QmTXAd64YL5Cts6dZyi574/4nf3/Ra///rLHuz67lvcevsQpfy5s2ex4rVXMXbcw66Yoo1xD//ZQ/T+O3smxjz4EJKSxOMVHDAd/hT/WfE/jE9fiNSyPGddcypmFj6GUf2uQPKl/QFjgvL2vDn/VcZFekal6LnzVRv29Z7Y5r2PavnFryxA/4G3IDs7x2PgL1n0Cvr266/8AUK8DACSLGa8tOAl9OzVF/UbeIre8lcX44/de6Jho6qi5z5WvM+un37c7Rqf3tt8cXUv44uJ+/ZDeXn4cOsWDB8x0u9JHahvaqVg7ajlPvvkY+W86nK9MymTv1fB+fN4dekijHvoEVcRi9kEu90Oq93zC8eaN3KVPwy1bKVN9LTss3e/1GtF06ahi16g4x4QghAurzEWrLz7dn/j2VcMAwxIshhRXGZTNr88f65yTa0VoehpHRfB9ku9Lqek6Cd67tftYO2Hsv3VJQurnP+JZhOsdjtsXmM3lLjeZWUw8W5DiN78Of/FI4/9JZKuhl1X/fwOFMBoMMBiNqKk3Dl2Zb8iuRbI7puv+L4+z0PpR2KCSfkDhXgsUzy9dn23E4fyDqFPv+oreiaDAWazEaVhjl1xflD0YjMqpYqemP1avuZ9TBg3DMlJlc8fi82uam/VXVCDrdG7ELNu5pUfxIcr38JUx1SYYcYThifQ/c5BaF27LT776H1kZtVG28uvQnFRIVavXIwRo50zYx9ueQcNGjbGJW3a49zZM3hnfW7cZt30fgxASM/RGzYSWWc+R9Le15G8/y3MOvsgxibPQ0pyAoqb3YqSFndg0abv+Rw9r1My2GMPtGSg5OMVAGbd1H6tdy8ZbPxpjSrjUQJ8jl5w+ny8QlVGkVwLghPXvwSzburPVK+Ikd66yaybeh2J0ONIE71AGTdFN+Ml66bo58Yt23DXbT0Vet63ZjLrZuWgOl92Hv/eNgVLdy2AzWFDnaS6eLLLM7ijzd0Qf2XX+xWva/RC2U+DrQRJeRuR9FsukvI2w2AvVarbUhqiuPlgFLcYivK6V4USUpeyXKOnC0a/QbhGTx5frtGTx1ZEZtZNeXy5Rk8eWxGZa/Tk8Y1U9ETPmHVT3vEJFFma6MVmd0JvVU248vaWba7Ki2dPcq3JE28Geo6e2H4hJGNZ9dNyPPPpk8gvPqE8HmFE2/sw+dp/ICMxM3ToGmvUBNFz31VDeQGS97+J5L2vI/HIh4DDefuONb0VilsMQXHLYbBmaLulTyNCv8UoepESDFyfoiePL0VPHluKnly2FD25fCl68vhS9OSxlR35ghc9PQDXZNETDzqf8MF4fHnUKcLtsztgRvc5yv+yXzVN9Nx5icydyfveQPJvubCc+MK1qbz2FShucYfyz5biuW5OT94UPT1pVo1F0ZPHl6Injy1FTy5bip5cvhQ9eXwpevLYyo4sVfTcZ8sa1KuD+dOfQMN6daskOJG9kzLj19Q1eg2aN8PK48vh+K4Y7+N9nE8qwKOGxzB0yH3IyMjConmzcPf9j8But2HF4nkY+YAzsybX6L2AIcNHI8kt497yRXNw69B7kOKWddN9PZCp4ABSfn8dCz8twEjLAmQZzygsy3K64MUjfdBvyP1Kohz316rlr6Bnv0HIqlXH4/3VKxbhj71uRu06nlk317y+BDd274M62c6sm6rozZs3H1269UJ2juczANe9sQydr++OevUbVjl9Aq2D2/vLT/h97x706D2wSr2C8+fgvfbRvVCwNVJco6ftShbJupxAxz1Y695jLFh5LePZVwxv0ctdtgC9bx6MzKxaoTRZpWyw8ac1ONfoVSUlg4l3K1yjV5V7JNcCreNdz3Jco6cnTX1jRSp6XKOn7/EIJZpU0XPPXjlj7krcddtNyrPnxLq3VW9txdMTRlerJC2+wNZE0Vuy6gWsP/0mtpV9jtEYDTS3YELPKdj4+kr0HzRMkQ6KHrB0wX9wxz0PIDFRZN10vnx9oQkmemrdlUvnY2D3Tqh3bL0ifqaC/Xi+6FGMTFqMlJyWKG3UC6WN+6AsuxMoer4vc0zGwmQsoXwAhvKHBq1xZUgNk7EEp0/Ro+jF64zez7u/w7Gjh9G1e5/gAzlOS1D04vTAaOiWNNFzf2C6mMVzFz2R8GTGnJWY+uQY1MpM19DN+C1Sk0SvyFiM5w/PRIujTfE9vocp24JRuBfdbuiL+g0bQ4gIRa8ye6wM0VP5ihFvObEdy9Z+gLvTc1Gn5CfXSWBPrI05hePQp2snpDXvDLul8hENnNH7AKlpGWjf4Wq/Fw2tMzdfb/9UebxHx2u6BLwAFRYWYF3uUgy/1/moEPHyd+vm5g2r0abtFWh6UStNFzUts5jegSL5Kz5n9EYgLS2yzySKXtWhLYOJdysUPYoeRU/Tx0pYhSh6YWGLi0oxEb2aNKMnjmJ1X6NXWF6AGdv+iUW75sJqtyIzMUtJtDKi3X1SsmlqHfk1eY2eVgZqOcuJbUjatw7Jv6+CqeiwR/Wy7GtQ2vAmlDbqibKcP2gKzTV6mjCFXYhr9MJGF7Qi1+gFRRRRAWbdjAhfwMpcoyePrYgcr6Ind6+jEz1S0RO9ZNbN6Bwr71akiZ5oSGSr3PbVbkx+5C78d+Gbyq2btbPSMW7Scxg6oBtu6xf4QcSxQRJ6q9VZ9N7ck4t/fDIJx4uOKlInHpXwty7/Qq2k2qGD0LkGRc83UMuJHUg8sB5JBzcj4cz3HoXsliyUNuiOskbdUdx0AOxJnmv11MIUPZ0Hq1c4ip48vhQ9eWxFZIqePL4UPXlsKXpy2VL05PKVGV2q6ImOi9m7UY9O89gH78cXyNzBaMSujqL325lfMOGDh/DF4U8URG3qtMOz3eegQz3/t7xFg6V7GxS94MSNpfmK8CXmvYvEI1tgLD3lUak8qy1KG/dU1veV1esChzFB2U7RC842khIUvUjoBa5L0ZPHlqInly1FTy5fzujJ40vRk8dWdmTpoid7B2Idv7qt0fv+h6+w5duNmHVmBq6zX4cUUyqu79ITrc9ejLT0TGVt05ZN63BRq9Zo0epSJUtip85duUZv/mzcde94JFiit0ZPjG33dZHuY91nMhaHHWuWzUP/lmfR6PR7sOTvcD2rb37RgxiYsgm1GrdRbvEsb9ITtZu2A7Nu+r+CcI1eaFdXZt108pKxHo3JWIKPRa7Rq8ookvW6wYnrX4JZN/VnqlfESEWPWTf1OhKhx5EqeiLr5tHjpzyya6qPXOjc8bIacetmdRK9zI718OI705FVkoG1WIsH6z6EGxv1QNcb+sA9WyFFr+pjABZXB9ED4J6MRTygPenwe0g8+C5e/T4DtySsQn3T0cqrRGYLzD9zJ7p2bI2stn3hMKW4tvHxCgBFL7QPFIoeRc/fiJEhv95tUfQoevE6o8esmwBFL7TPUz1LSxM9VeiGDOiGTh1ae/S5JiVjqQ6it3ffz9iwNRf/LpiKDuiAyy1X4LaB98CcB1itVnTqfANFb/d36NX/NmWc+nreW3UUPfeTTnwJ79HpUjQq3o7EQ+/CcvRTGOylWFD0APonbkCDhHyU5XRGaePeKG10E97Y8i2fo8esmyF91lD0KHoUvYkBz5lo37rJGb2QLmHSClP0KHrSBpeGwNJEz/3xCuLZee6vmvR4BbFf8bxG7/v8b/HgO3fj97O/IsmUjCf+8DeMv+oxDUMj9kW4Rk/eMTDZS5BTsA2Fuzcos37mc794NGZLro/SRj2cz+5r1At2i+cD2+X1rGZE5ho9eceRa/TksRWRmYxFHt9oi568PYnPyPE6oxeftELrVaS3borWmHUzNOZ6lZYmehfKjF48i97zX/4b07c9rYyVPzbthZk95qJeagO9xo70OBQ9eYi9k7GYCg8hKW+TMtuXeGQrDOXn3Ro3oqzuVcraPpHYpazuNYDBKK9zNSAyRU/eQaToyWNL0ZPLlqInly9FTx5fip48trIjSxM90XFxi+bkqQswf/oTUGf1xGze2IkzMX7kLTVijV48il7e+QN4aPMofHl0mzKL9/9fPxUj2z8geyzpHp+ipztSV8BgWTcTj30MS977SDzyASz5X3l0xJGQjsJLRsOe1hilOV1QXqeDvI5W08gUPXkHjqInjy1FTy5bip5cvhQ9eXwpevLYyo4sVfRE51WxO3LspGtfatLjFeJtjd6rS17ADMxASnkK7jKNwO3DRyHhrAm7dn6JvgOHwD172zdffs41egD2//4rxD30NX2N3o3d+6BOdj3lPFRFT0vWTWPJKSSJmT4x43f4A7x37mpkGs6gs2WbEsthTkNpvS4oa3Ajdpe2wi/5dvToPbDKtcvX2kf3Qq8tnouBg0cgLS3d53Xv2JFD+OKzrRh4+11+r4vuSYX8FQrWjlqPyVhC+/jhGj0nLxmJR5h1M/hYZDKWqoy4Ri/4uIlGCa7R4xq9aIwzf21IF71Y7lw02o4X0Su2FmNR/stof6A1Zhpm4k9t/oLmRxtjyPD7kHfgd4pexeMixJhwF1zxO0WvF7Jz6nucLoGybm5/byWybIfQ2fw5LMc/hbHsrKvuD9Z22I2rMbDpAZTVuRLWup1QWu9a5cHtFD1g84bVaNP2CjS9qJWmy5MWufUOFMmXu0DHPViHKXoUPX9jRIb8erdF0aPoxeuMHkWPohfs81PmdopehHTjQfQ2ffom3v71TWy1bsUjhkdw7e290NLSCls2rcfg4aMpem7PBaTohT6j532KeM+aJZz5EZajnyj/fj1wBD8X1cfgpDc8qtnSmiE/63q8tu8S3D2oO8prX+56eLtaMNhMmxbp4YweQNEL76IebPxpjSpDajijF5w+RY+iR9ELfp6EWyLSWzf5eIVwyUdeT6roicyb4yY9h10/7q3S0/ZtWmDutMdQK9P3bVqR71r0IsQq62aprQT/+GQyFu+ar+zs0DYj8EzXWUhNSIvezktsiWv05MENtkYvkpZNBQdgyd+OhGNfwHJiOxJOfQuDvcwjpMOYpKztK8v5A8pzrkFZdmfYUqpPoqBgfLhGLxih8LdzjV747LTUZNZNLZTCK8M1euFx01orXkVPa//juVykoif2jVk3Y3OEpYqeeGC6eD0+dmhs9i5KrcZC9Nwfm5CRmIn/9HwFPZv3i9IeR6cZip48zjJFz7vX4nl9Cfk7K+UvfztMhXlVds6W0ghl2RXil3MNyutcCYcxUR4EiZEpevLgUvTksRWRKXry+FL05LEVkSl68vhS9OSxlR1ZmugFeo6e7J2Kdvxoip7dYceLX8/Es188A6u9HNc37oYXei1Cdorzlrya9KLoyTua0RQ9X3thKjoCy/EvkHBCzPrtQMLJb2CwFXsUdRgtyi2e7vJnS20mD4qOkSl6OsL0CkXRk8eWoieXLUVPLl+Knjy+FD15bGVHpuhFSDiaa/Qat2uFeV/MguWMGW+ZNmCycTLuvuch7N71DRwA2l1+FV5f9jLuuf9POH0qn2v0atVRju4WrtGDd6KMULJuep8igdbB7f3lJ/y+d0/oWTftVqxYPAd3XGlGnXPbkXBiB8wFv3s0fdDWFO+V98XwSw6jLKczyrM7oaxuRzhMya5yXKPHNXrhXtK5Rs9JTsaMnox1i97HmWv0qo78SNbrhnseRVLPZrNhyUuzMXrcE2GFiVfRYzIWJmMJa0DrVEma6In+iVs3mzepX2Oel+eLebREb9Hy57H83FKYbCZ0slyDkUP+hG1r3sOQ4aMpel4fDKuWv4Ke/QYhi6LnGrJxL3oAvL9oG0vznbN+x51r/Y4dPYb3i7pgdMrCylPRYEZ5rXYoE7d6ZnfG//YnIqV2E7TvcLXfS6TWL/R8vEJonzLMuunkJUNqmIwl+Fik6FH0KHrBz5NwS0Q6o8dkLOGSj7yeVNETz9BbvuZ9TBg3DMlJlsh7G4cRZIveu++8iXcyN6PRvhx8iA8x6KIh6GDqgJv6DHJ9oeCMnudfACl6N6N2nWyPs6U6ip736S6ybm7/aCOGXeFAwontyi2f5nO/eBTbXNoHaenpuLrOCVgzWsGW1Vq5/bO81uWwWzKUshQ9/xdSPl7B/3MctX78UPSqkpLBhDN6wUckZ/SCM4pGCc7ocUYvGuPMXxvSRC9Qxk3RGWbdDH7YP8nbioffvRcnio6hfmpDzO+7DFfX7xy8Yg0pwTV68g5krNfo6bVnxtIzsOSLWb/tsBzfBkv+lzCUn/cZ3pZcH9Zal6G8VntYa7WBNbMNymtdBoc5Va/uuOJwjZ7uSF0BuUZPHlsRWcatm3J7XH2ic42e3GMVrzN6cvc6OtEjndETvWTWzegcK+9WpIlebHYnNq3qnYxFPDbhmU/+ikW75sEBB267dBj+dePzSLdU/0dRhHKEKHqh0AqtbE0Rvap77YCpYD8STv+AhDO7YT71A8ynf4D53B4Y7OU+IBlgS2uC8sw2igRas9qiXEhgVmuPtX+h0QUoeqES016eoqedVTglKXrhUNNWh6KnjVO4pSh64ZILXo+iF5xRvJag6OlwZPQUvd0nd2Hcprvx6+k9SLdkYGaPuejf8lYdeln9QlD05B2zmit6/pklnN4N8xkhfrudEnj6R5jP/+q3gi21uSJ95bXawpblnP0rr32FpoNC0dOEKaxCFL2wsGmuRNHTjCrkghS9kJGFVIGiFxKukApT9ELCFVeFpYvejp0/YdSj0zx2evHsSejUoXVcgQi3M3qv0XsKT+Fm3IzkzDQ81H0Cvv3wcwwePhrqvfYlRUWurIbqugeu0eMaPXX8rl6xCH/sVXPX6H3x2VYMvP0uv6drqFk3xTP+zGf3OKVPmQX8EWbx7/zv+LCsq5LNtptlq1t7RljTWyi3fiqzgLUvw1lLC7zx7nYMv3e8q5w/0du8YTXatL0CTS9qpemSI9YlBttn70CRrMvhGj2u0ZMhelyj5zxLoy16kVwLNF2gdC7ErJs6A9UxXKSix2QsOh6MEENJFT0heTPn52LutMdQK9N526FI0DJ24kyMH3lLjcjGqYfoHc8/gsWFC9Fl3zUQovdY7b+g3+W3oUHDxq5HJFD02qF5i4uRf/woPv7fZtx6x0hlPPn6YGAyFopepFk3DbYSfPPJ2zAWn0CXunmKACac/hGmwv2Aon+Vr/OODCwouh+PNNyA8ixx+2cbJDa4HKUZrVGQ1AIOY4KrMEXP9yeU9zkb6HPMe0Yvd9kC9L55MDKzaoX48edZXGuSnmCNyJAaZt0MRh1g1s2qjCh6wcdNNEowGQuTsURjnPlrQ5roFZeUYcqMhRgyoFuV2TshgKve2oqnJ4yu9tk4IxW973/9Gut25uK10uWK5CXcmIlWJy9C7bo5FL37x8LucODN1atwcWuKnvtJ7O+LMWf0PkBqWoa0xysYbEWK8JnP/uhc/3fmR5Sc2o+F+f3xeOosn9fZ8qy2sGZeqsz+vbknC23aXIZG7bppuu5zRq8qJoqepqGjqdDa3KXo0q0XsnPqu8pzRk8TuiqFxIzFmIcnBqzMGb3AbDmjF97Yi0YtzuhFg7KcNqSJnsi6OflfCzBh/DC0bNbQo/diVm/GnJWY+uQY10yfnN2LTtRw1+h9mvch7ts4FOfLziMjMRMv912JLo1vjE6nq0ErXKMn7yBdiGv05NEEDNbCits+RQKY3Ugu+AmGkz/AWHjId7MGM6wZLVCe2VqRQGUNYNalsGZdCocpRWZXq31srtGTewhliJ7cHlef6NEWvepDRp+eco2ePhx9RYlU9ERMZt2Ud3wCRZYmehfKjJ6AG47ozfn6OUz9/O+wO+y4pHYbvDrgTTRObxqbURCnrVL05B0Yip48tiKyukavuOAsEk7vQsKZn2ASSWDETKD4ueiw3w7YUhvDmtlakUBbrdYoadQbttRGcjtcjaJT9OQeLIqePL4UPXlsRWSKnjy+FD15bGVHliZ6ouNrNn6E3Le21ug1eqGKXpm9FOM3j8I7v61Tjm3flrfghV4LkWRKln2sq118ip68Q0bRk8fWXfSKSm0+GzJYC5Bw5men9J39uWI28OeAWUBFIFtKI9jSmin/W9ObwZ7aGLb05rClNIQttQnslky5OxYH0Sl6cg8CRU8eX4qePLYUPblsKXpy+cqMLlX0RMeZdXMHBg4egQ1rXkOnXt2w/s3lWGhbiOEYjswO9dAtsztOn8pHlxt7Qr3H/5Ot73KN3qb1GM01eli5dD76DxqG9AzPL/Bco+f7shhq1s1AF9evt3+qpF3peE2XgNfgwsICrMtdqlvWTeU2loJhAAAgAElEQVQxEOd+gfnMbhw7dAAfHsrEvWkrYCw9EfSzwGFOw5Lie3Bdzgk0ysmEPbWp8pxAa1pT2FIaKz8HejHrJrNuyhA9GQlqvMcxk7FUPbOZjCXoJTMqBZiMhclYojLQ/DQiXfRiuXPRaFtrMpbVqxZhnnUuBpXegrWWtRiX+BAGDhyOw3kHKHoAtr73Nho1bY6LL22r8NhC0VOGL0Wv8izWkpikJoie+3XLfZ8NtjKYCg/AVJgHU+FB57/z4vcDMBWI9/JgsJdgSfEo3GjZiuamfVUvgQaTa/ZPuUU0rSnsQgLTmsCW0gSr3/8Sf7jhJtSr77muWsu1dM3rS3Bj9z6ok11PS3GPMsy6GRgZs24GH1IUPYpevN66SdGj6AW/gskrIVX0Zs3PxdHjpzyya6pr9zp3vOyCebxCSVsHTn6Rh8VYjPtM96H/wGH4bus29Ow3iKJ39wPK6Kbo+ZY6ih5FL5Tn6BlLTmDD+rX4Q8s0NEvOh/H8QZiKDsJccBCmgoNBZwVfKb4fPVM+QoNMi1P+0poos4LWtMbKraE2MUOY0gAwGKt8KlH0nEhkzF5R9IJ/CaLoUfQoesHPk3BLRHrrJp+jFy75yOtJEz0mYwHKbWV44oNxWP3zCuVI3dS8L+b3Xcb1eBrHLdfoaQQVRjGu0QsDWghV/D0wPYQQ0oqaz/4CU9EhmAr2w1QgZgTF7GCeMjtoLtirqV0hfda0ZrCnNHTNClrTm8OeXE8RQXtiXU1xwinENXrhUNNeR8atm9pbr9kluUZP7vGNV9GTu9fRiR6p6IleMutmdI6VdyvSRO9Cf7zC8aKjGPnW7fjuxDcwGoyY2HkK/tRxQmyOcjVtlaIn78BR9OSxFZHjWfSC7bmx5LhrBlDcFmoUs4GFB2EWQqjMCuYHCwGH0eKSPltyfdiF/KU2VCRQ/d2W1AD2pNpBY3kXoOiFjCykChS9kHCFVJiiFxKukAtT9EJGprkCRU8zqrgrKE30LuQZPSF3I9bdgpMl+Ui3pGNe3+Xo1uSmuDv48d4hip68I0TRk8e2uoueFjLms3tgKjwEc+F+GMU6wSIhgXnKYyNMRUcgsopqfSm3hKY0hD2prjITaEvOhiM5G/akHNiSchQZtCdlK2XEi6KnlWx45Sh64XHTUouip4VS+GUoeuGzC1aToheMUPxulyZ6YpdFxs3JUxdg/vQnXA9NFw9LHztxJsaPvKVGrtEzX5KCH779CkdwBKZkM24wdsWtQ0YqWTdF9sR31uei982D8e7ba7hGb30u7uAaPdfVwdd6PK7Rq7x4XujJWLR+jESSaU+vrJsGW7FL+ozFRxX5MxYehvqzqeI9Q/l5ZbdeLHoYdyStRF1j4NlC8fgIR2I2jGk5KE2oA1tiXbz8YxPcemUq0mvVU4TQnlwhjEnZgNGsFRteWzxXyZCclpauuY6vglyjV5WKDCberXCNXlXukVwLIjoJwqxss9mw5KXZGD3uibAixKvoMRkLk7GENaB1qiRV9EQfVbE7cuykq8uLZ09Cpw6tddqF2IZRs25m1M7GR59sRq71dVyLa2HJSMKAdoPx03ffuh6vQNF7Bw0aNsYlbdrj3NkzivRS9Cq/VFL0An/Rpuhpu9ZF8uVOL9HT1lNAEcLCQ1i59h30vyoHdc1nYSw9CWPxcRiLTyi3iZpKxM/5fm8Z/W/RI7graRlqG09VadaekFEhf/VgT6wNmyKCOXAk1amYLazrnElMysaruWspegBkzOhR9JxDM9ozepFcC7Sew3qWo+jpSVPfWJHO6DEZi77HI5Ro0kUvlM5Ux7JC9C5p2wa5B1/HJedaYR3WYWj6MHRo2QmpaRnYtbPyOXoUPYqeOsZ9zR5Q9Ch63tdALXLrXSeSL3fRFj2179oer+CAsfQUEkrzUct8FmdPHFIEcPGnp3B7yxOo4zimZBUVmUdNQgzLTgEO3w+s9/VZ81zh47g3MxdpKcmuW0hVCRS3ktoUIRS3kjrlUEgjDKYqoWRIDbNuBv92wBk9zuhxRi/4eRJuCYpeuORiX4+iF+Ex+PbYt+i3vD8Onz/E9XgRsvSuzjV6OgN1C8c1evLYisjVORmLXDKRRw9ljZ6YERQyaCoRs4MnKmYJ3WYMS/Jhcns/1N6JW0kV+Uusq9wyqswYJmXDYcmCw5IBu/IvEw5zuvP/ivfEg+3j9SVjRi9e9zXa/Yr2jF609y/W7cWr6MWaix7tRyp6og/MuqnHkQg9BkUvdGYeNWr/uzZOl5xGy6yLsXTAGjTPbBlhRFZXCVD05I0Fip48thQ9uWxDEb1Qe6LcKlpxy6hy+2iJEEXnLKHyc+lJmIqPuX4ONb57ebsig5mwCwlMrAVHQpoihsp7CRmAJQv2BDdBTEhXyij/zGmwJ6Qq/+v9oujpTbQyHkVPHlsRmaInjy9FTx5b2ZEpehESXv/zevz3ixfxQs9XlRk9vvQjQNHTj6V3JIqePLYUPblsZYpeqD1XbhMVAqiIYKUMGkrOwFh2FgbrOeV/Y9k5GMrOwVju/N9gLwm1Kb/lHaZU2F0CmOoUxgoZdJgrfrdkAOZU2C1OOXQokpjukkXxu5BKUb5WrVooKrWhpEz7ba+67UwND0TRk3uAKXry+FL05LGVHZmiFyFhNRlLVp162LHtY3Tt3hu7dn6Jutn1uEavqBCrVy7GiNEPKZQ/3MI1eupw4xq9qidesKyHWtarbfvkA+W8a9/har9ndrB21Ipfb/8UDgAdr+kS8CpRWFiAdblLMfze8a5y/m7d3LxhNdq0vQJNL2ql6cqjZZ+9A9XcNXrOPfUWvdxlC5RMxplZtTQx9VdI67gI1ojWNXrKbaVCBhUBLIChTMih+Nn5nkHdVnYOP5xMxIGCVAzI+gzG8kLl8RUGUSdCYVxQ9AD6J25AQ9Nhj91SZgwVSRSziKoEpihyqPxeIYsQt6KKchYxy+iUSHfpVH9eunghhgwfjaTklGD4wt7ONXpV0UVyLQj7QERQkclYIoAnuWqkosdkLJIPUIDwFL0I2VP0bFixeB5GPvBnheRnH72PzKzaaHv5VSim6ClMli+ag1uH3oOU1MrbrCh6FD0tlx6KXlVKNUX0tBx/tYz/ZCwORfgUUayQP6Pyv1MGlfeVbYVA2XkYrYUQj7QQv4ttS/Zfjj6ZO9DIkOesL7bbikPpmqayMwonYnzGIiRZzK7bTxVZVGcc1RnIhFRA3K7q9rtSTsxEivcryiv1TMkebVP0KHrxOqPHxyvw8QqaLpSSClH0IgRL0aPoJSYmuUaRr7/mU/SceArOn8Nba17DnSMf9HnWBZtR0SI9nNEDIvkrfnxn3XQOG4pehB9abtXX5i5Fl269kJ1T3/WuWKNXfP4kygrPOcVPiKStEIYyIYhCHtUZRbHtnEsqhVwaKyRSqVMhlSJTqhC9h1JeQIqhSL/OAxXy51y3WGLMwguHe+GxVl/AYUpy/jNX/G8UPycC5hTlfZgSK8okK+87xHaljng/GVDqqu9XlDGnBuy7mLEY8/DEgGWifetmJNcCXQ+UxmCc0dMIKgbFOKMXA+g6NUnR0wHk+aJynC+26hCJIdwJcI2evPHANXry2IrIzLopj288rdGTt5exiywrGYtym2rFDKMy62gtcs4uKlJYOfOovlcpi+o2VR4LlMdsxOqlrHF0SWQyHMZEl1DCZIHDYIHDZAGMzv8dRgvU940JiUhMTkVRucHjfX/lYUpwxlfjGZ2/K/GU+AlSEvLEim2k7cbrjF6k+xUP9SMVPbEPzLoZmyNJ0dOBO0VPB4g+QlD05HAVUSl68thS9OSypejJ5StL9GT02lh6puKW1UKnLFbcemqwlgC2UmUNo8FaDIOtBAZbKWAV/1f8LsqI7aKcWxln2WIYrKUV20WMkojXQ8rYf++YTgn1lEtPiRSSmBBQRpXyyqynkMpKSfUno+7vu+TWUFFPld0gs6F6saHo6UWyahyKnjy2siNT9HQgTNHTASJFTw5EP1EpenJxc0ZPHl+Knjy2InJ1Ej25JHxHVzKoinWMikSWOiVSiKK9DLCL38uUf7CXweCo+Fm8Zy+FCVYkm6woLCxSyrvKVWyHvdwZp+J3g60cqIgh6sPm3O6sJ0S2XMqaSplcq8iomLE0JrjNgCYCBiNgNMNhMAEGM2A0wSH+N5jhMDq3ASY4xP8VZcTPyYkWlNoNsNkrypgS3Mp5xlTqGk0AfMR0b9sg2qnoh/Kzs01nf0xufRM/i1hqzIptJnkJiGQeJ+/YFL1o0ta3LYpehDy5Ro9r9LhGr/Ik2vvLT/h97x706D2wypnFNXoAs276vuCuWv4KevYbhKxadYJekblGLygizQX8rdHT+/EKWjORau64j4IXejIW50ylpxiu3/Q/XN2uJRrVTVdEU4ihIqCqWApxVGXUJanOGMrspyKSFdJasV2VUWWGVImln4zaYMbUgkn4W9ozkQyFuKv7TflVOGhrjIFJ6z365kwoZAQMBjiE3Kr/lPeMnu+JbQ739wyVZSrKq/WVWOp7HrGcdZR/qIjlVtfVB4/3nHVMRhPMZjNKyx1V+6XGcu2DAQ6P9g2Y9VkypkyZEnfH5kLoEEUvwqNM0aPoUfQoeny8ArDm9SW4sXsf1MmuF/JVlaIXGJn/rJsho/aoQNGLjJ97bSZjCc7Sl4yqs5RiFtNuLcaCNZ9h3KCrYXBYAYcNsFthsIscCOJnGwziPYfV+b94X2xXtlmRmmhAaWkZbFYhtOI9IaEVdZS6IqaoY3PFVGI77M6Yys8VbVbENIg43m0qMdU44nmTnjGdfXbWE7cP+xO94MRqTomnC56i6MXocFL0IgRP0aPoUfQoehQ9ip56FsiYvaLoBf+gvtBn9HwRYtbN4OMmGiV8PV5Buf1XEUwHDMr/Ff8Mzv893hPb4P6ew1kGzvdddb3rVWxTyjmcdZR/HrG82qto39mHyjoJJgcSzQYUFpd5xKkay21/1L7Bjlkfmyl60RhsPtqg6OkAnmv0dIDoIwSTscjhKqJyjZ48tiIy1+jJ48s1evLYishcoyePb7QfryBvT+IzMpOxyDsuXKMnj63syBQ9HQhT9HSASNGTA9FPVIqeXNwUPXl8KXry2FL05LKl6MnlS9GTx5eiJ4+t7MgUPR0IU/R0gEjRkwORohdVrmpjFD152Cl68thS9OSypejJ5UvRk8eXoiePrezIFL0ICXONHtfocY1e5UnErJtOFv5Ej1k3fV9wmYwl8AcR1+gF/6DmGr2qjLhGL/i4iUYJX2v0otGunm1EKnoiWRGzbup5RLTHouhpZ+WzJEWPokfRo+gxGQuTsahnAZOxVP2olMHEuxWKHkUvXmf0KHoARS9C2YigOkUvAniiKkWPokfRo+hR9Ch6FD3/H6YUPSebaN+6yRm9CL/g6VSdokfR02kohRWGohcWNs9KXKOnA0QfIZh1Uw5XEZXJWOSxFZG5Rk8eX67Rk8dWRGbWTXl8oy168vYkPiPH64xefNIKrVeR3ropWmtYRzwgnq9oE6Do6UCcoqcDRIqeHIh+olL05OKm6MnjS9GTx5aiJ5ctRU8uX4qePL4UPXlsZUem6OlAmKKnA0SKnhyIFL2oclUbo+jJw07Rk8eWoieXLUVPLl+Knjy+FD15bGVHpuhFSJhr9LhGj2v0Kk8iZt10smDWzdAurMy6GZgXs24GH09MxlKVEdfoBR830SjBNXpcoxeNceavDYpehPQpehQ9ih5Fj8lYmIxFPQtkJB6h6AX/oKboUfTidUaPokfRC34Fk1eCohchW4oeRY+iR9Gj6FH0KHr+P0xlyK93axQ9ih5FL8IvtAGqR3rrJh+vIO/YBItM0QtGSMN2rtHTACmMIsy6GQY0jVWYjEUjqDCLcY1emOA0VOMaPQ2QIijCrJsRwAtSlWv05LEVkeNV9OTudXSiRyp6opfMuhmdY+XdCkVPB+4UPR0g+ghB0ZPDVUSl6MljKyJT9OTxpejJYysiU/Tk8aXoyWNL0ZPLlqInl6/M6BQ9HehS9HSASNGTA9FPVIqeXNwUPXl8KXry2FL05LKl6Mnlyxk9eXwpevLYyo5M0YuQMNfocY0e1+hVnkTMuulkwayboV1YmXUzMC8mYwk+nrhGryojZt0MPm6iUYLJWJiMJRrjzF8bFD0N9Nds/Ah/n75QKdm/R2c8PWE0kpMsyu8UPYoeRY+ix2QsTMaingUyEo9Q9IJ/UFP0KHrxOqNH0aPoBb+CyStB0QvCdsfOnzBzfi7mTnsMtTLTMWt+rlLj8bFDKXr3PwK7naJH0aPoUfQoehQ9/x+mMuTXuzWKHkWPoidPFiK9dZNZN+Udm2CRKXpBCAmxa96kPm7r11Up6S1+4j2u0Qs2zMLbzmQs4XHTUotr9LRQCr8M1+iFzy5YTa7RC0Yosu1MxhIZv0C1uUZPHlsROV5FT+5eRyd6pKInesmsm9E5Vt6tUPQCcC8uKcOUGQvRueNlLtH7bf9h/HXqAvzf5DFo2ayhUpuiJ2fwUvTkcBVRKXry2IrIFD15fCl68tiKyBQ9eXwpevLYUvTksqXoyeUrMzpFT4PoDRnQDZ06tFZKeoveU099hqef/kzmMWJsEiABEiABEiABEiABEqiWBKZMuQ5PPXVdtex7de80RU+D6AWa0RPJWL7+2oy8PCNuuqkc69Yl4tpry3D0qAlnzhhw3XXlePnlJIweXYLFi5Nwzz2lWLYsEcOHl2LlykS0aGFD3bp2bNyYiKeeKsRTT6Xi5ptFfQMOHDBh8OASzJmTglGjSrB1awLS0hxo3dqKN95IwsSJRXjhhWRcc40VgAPbtyfg4YeLMH16KnJy7K66rVrZ0LlzOZYtS0KHDlY0b27D2rWJ6Nq1HGazAx98YEGfPmVKf7dtS8DQoaX4/nsTdu82K/1+//0EpS+PPlqk7MOZM0b87W+FmDYtBWYzlPenTUtVSPbrV4b8fIPSF9HXBx8sxrPPpijbBg0qxb59RuzcmYDate0YMaIE//mPc9ttt5Xi119N+O47s0ffxbZhw0qwc6cZP/1kRsOGdtx8cyleeilZqSfanzSpEM8842xfvB5+uFhhm59vVH533x/xu/t+i99bt7ahQ4dyrFyZpJTPynJg1KhizJ7t7Jt4PflkEZ59NhllZQbXe5MmFWH27GSUlFS+px6ToqLK9/7ylyLMm5eEggJnf8Tr8ceLlHFx7lzle+581XK+3vO1j2r58eOL8cYbiTh+vDKu2CaOw9q1FmVcur8eeKAYGzZYcPiw5/v331+MTZssyMvzfF/UdR8rHsEAtGtndY1P722+uLqX8cXEfXvTpjbcdFMZFi50Hntfr0B9C8TeV6xu3cqV82rrVmfiJX+vjAwHBK9ZsyrHi7+yw4eX4MsvzdizxxwwprpRyz57B1KvFfv2VT12wRoNdNyD1fU3xoLVCzSetdR95JFi5Zp66pTnmNdSN5TxpzWer2uA1rr+yrlftyON5V7f3/mvZxsilgwm3n1MSnJ4fBbpvQ/B4qmf38HKRXN7JNeCaPZTbcvX53ks+qF3m1ddZUXjxjasX5+od+hqE0+cH1OmTKk2/a1JHaXoBTmawdboMesmk7EwGUvlScTHKzhZ8PEKoX1M8vEKgXkx62bw8cRkLFUZ8fEKwcdNNEow6yazbkZjnPlrg6IXhD6zbr6GTp27on7Dxli5dD76DxqG9IxMLJo3C3cz6ybuuOcBUPQoesy6yayb6lkgI8MkRS/41ySKHkUvXpOxUPQoesGvYPJKUPQ0sA30HD1RnclYNEAMowiTsYQBTWMVJmPRCCrMYkzGEiY4DdWYjEUDpAiKMBlLBPCCVGUyFnlsReR4FT25ex2d6EzGEh3OMlqh6OlAlaKnA0QfISh6criKqBQ9eWxFZIqePL4UPXlsRWSKnjy+FD15bCl6ctlS9OTylRmdoqcDXYqeDhApenIg+olK0ZOLm6Injy9FTx5bip5cthQ9uXw5oyePL0VPHlvZkSl6ERJmMhYmY+EavcqTiMlYnCyYjCW0CyuTsQTmxTV6wccT1+hVZcRkLMHHTTRKcI0e1+hFY5z5a4OiFyF9ih5Fj6JH0WMyFiZjUc8CJmOp+qEqg4l3KxQ9il68zuhR9Ch6EapGRNUpehHhAxTRu+JKZNXOwY5tH6Nr997YtfNL1M2uh9S0DOzauQMDB4/AhjWvKRkr31mfi943D8a7b69Bz36DcDjvAE6fykeXG3tiwQvTMebhifhk67uoXTcHDRo2xpZN6zF4+Giof5krKSrC73v3oEfvgVA/PHfv+gYO8Qyzy6/C68texj33/0mJqdbNO/C70qe+A4fA/S/D33z5OaxWKzp1vgHbPvlA6W/7Dldjy6Z1uKhVa7RodSneWsOsm2KILJ4/G3fdOx4Jlspnqi1d8B9m3fQ6fzijxxm9Otn1Qr6qckaPM3ohDxqvChQ9ih5FL9KzyH/9SG/dFN9v+Rw9eccnUGSKXmy4s1USIAESIAESIAESIAESIAESkEaAoicNLQOTAAmQAAmQAAmQAAmQAAmQQGwIUPRiw52tkgAJkAAJkAAJkAAJkAAJkIA0AhQ9aWgZmARIgARIgARIgARIgARIgARiQ4CiFyb302fPY9yk57Drx71KhMWzJ6FTh9ZhRrtwq63Z+BH+Pn2hAqB/j854esJoJCdVJjxxJ/Pb/sMYO3Emjhw76Xq7fZsWmDvtMdTKTL9wIYax52L8Tv7XAkwYPwwtmzUMIwKrCAJi/O47eBSPjx0aEIj7OFcL3ndnv6D1SLmSgPf5z3M/vNExa34uXlmx0VX5nxNH47Z+Xf0G49gNj7N7Le/vCxy74TH1Hoscu+FxDLeWeg0eP/KWgNeMcOOznhwCFL0wuBaXlGHKjIXo3PEyZbCLwf/XqQvwf5PH8EtzCDx37PwJM+fnukRNfAERL39fmsk5BLh+iqpj9+0t29CgXh3Mn/4Ex2wYWMXYHfXoNKWmFmETX1C2fbU74B8ywujGBVVFMD94+LjrC4a4Xhw9fopMQxgF4vyfu2Qt7h3WV/njmPrFberkMX7/UMmxGwJgP0W9xy6Zhs7Ue+yq8vzE2KEcu6HjDLmG+x/aggl2yMFZQSoBil4YeMWAnzFnJaY+OUb5sPQWvzBCXpBVxBe15k3qu764eYufNxSKnn7DhDN6+rAMZUaPoqcPczVKsOuFvq3VzGhaPrsoJfofe47dyJly7EbOUGsE9fvCw6NvxdLcza5JDq31WS62BCh6YfD3dZEONhsVRjM1uoqvi3QwkeOtW/oNCYqePixDET31FmXRspZZQH16WHOjUEAiP7ZaZ0U4diNn7R6Bs9GR89Q6G82xGxlr92tEu9YtPO5miywya0eLAEUvDNJC9Fa9tdXjliGKXmggVdEbMqCb67aLYKLn3QI/LENj7l6aohc+O/eaWkXPm71Y3zt0QDeucwjzMIR6rQizmRpfLdTPLfVLH8dueENDXWPGNXrh8RO13Nc7hnILIcdu6My9v6dpmUUNvRXWkE2AohcGYc7ohQHNq0o4M3rerXrfQht5ry6cCBQ9fY51OKInWg63nj69rt5RtPwlv3rvYXR6H+4fyjh2Iz8+vHUzcobhSAfHbmjcvZMIudcORbJDa5Wl9SZA0QuDKNfohQHNR5VQ1+hR9PThrv5VlFk3I+cZ7heHcOtF3uPqHYGSp8/xC1fy+EcKffjzD236cAz1OhpqeX16WXOihCPXNWfvq++eUPTCOHbMuhkGNB9VgmXd9P4ysnnrdrS6qLErS2Sotx3p0+uaEYVfNPQ5jv6+OLiPXdHS6rc/xO39b1QeHaJlXZQ+vatZUXi7pj7HM9h1k2NXH87uUcR1oknDHNcyBfF77ltb+WigEFCL6+aile9g3MhBHtdR9TZi71szxfc0XndDAKyhKEVPA6Q4LELRC/Og8Dl6YYLzqhboOXreouee0l6ECfbcPX16WLOiuD9eQd0zcgz9GHuPRRHB/Vma3mM31GeXhd6jml/D1/PcvLnXfAqR7aG/W7HcrwEcu5Ex9lWbicT0YRroOuprDR6vu/pwV6NQ9PTlGa1oFL1okWY7JEACJEACJEACJEACJEACJBAlAhS9KIFmMyRAAiRAAiRAAiRAAiRAAiQQLQIUvWiRZjskQAIkQAIkQAIkQAIkQAIkECUCFL0ogWYzJEACJEACJEACJEACJEACJBAtAhS9aJFmOyRAAiRAAiRAAiRAAiRAAiQQJQIUvSiBZjMkQAIkQAIkQAIkQAIkQAIkEC0CFL1okWY7JEACJEACJEACJEACJEACJBAlAhS9KIFmMyRAAiRAAiRAAiRAAiRAAiQQLQIUvWiRZjskQAIkQAIkQAIkQAIkQAIkECUCFL0ogWYzJEACJEACJEACJEACJEACJBAtAhS9aJFmOyRAAiRAAiRAAiRAAiRAAiQQJQIUvSiBZjMkQAIkQAIkQAIkQAIkQAIkEC0CFL1okWY7JEACJEACJEACJEACJEACJBAlAhS9KIFmMyRAAiRAAiRAAiRAAiRAAiQQLQIUvWiRZjskQAIkQAIkQAIkQAIkQAIkECUCFL0ogWYzJEACJEACJEACJEACJEACJBAtAhS9aJFmOyRAAiRAAiRAAiRAAiRAAiQQJQIUvSiBZjMkQAIkQAIkQAIkQAIkQAIkEC0CFL1okWY7JEACJFCNCJw+ex7jJj2HXT/u9ej1PyeORt/unTFlxkLl/acnjEZyksVV5rf9hzF24kyMH3kLbuvXFYHiiO2z5ufilRUb/ZJp36YFZj31EGa/tApvb9lWpVz/Hp2VPoiX6JMos3j2JHTq0NpVtrikzO82tdCajR/h79Od++Tr1aBeHUz/+4OY/uIKFxPRt7nTHkOtzHTXfgg+Yr/cX+o+qtvc++Pdlro/7kyr0bBhV0mABEiABOKIAEUvjg4Gu0ICJEAC8UDAW9bUPon3l695H2n7SlUAAAbnSURBVBPGDUNJaakigkMHdPMQGyE14vX42KHQEsddaFQpfGLsUJ+iVj+nthLX18tdnu67s59HuR07f8KoR6cp1bwlMFCszh0vqyJtajvefVFlzlvUVAZHjp2Et+gF2p94GAfsAwmQAAmQQPUmQNGr3sePvScBEiAB3QmI2a3ct7a6Zqv8NSAEavLUBZg//Qm0bNYQ4veZ83Nd9bTGUePrIXqtLmqEr3f9ggnjhyl9UsXs8staYnHuJkydPMZDIvUUvYKiEhQUFGHIgG6uNoQApqUm44NPv3FJsT9Z1P1AMiAJkAAJkMAFTYCid0Effu48CZAACVQl4C1wgRgJkTl6/BQee2AIHnvqRY8ZvlDiiDb0ED0xC7fv4FGly+qs4ow5KyFm+YSUyhQ90WbzJvWx7avdyu2kYtZz8r8WKG0LAVZnPyl6POtIgARIgASiQYCiFw3KbIMESIAEqhEBX2vIfK09E7vkfmui922LocTRInpa1ugJ0buibSv8deoC/N/kMVi36RNFvsR7Yu2gbNG7d1hf5ZZWcfvpwcPHFelU3/MWvUD7wzV61eiEYVdJgARIIE4JUPTi9MCwWyRAAiQQDwTc17eJ/nivfxPviVs05yxZ57qF01e/tcTRa0ZPTfKy/ZsfkZWZjqlPjsGpM+ejInpiFlG5ZXX9/xQMQjZrZ6V7rGfkjF48jGz2gQRIgARqPgGKXs0/xtxDEiABEtCFgL9bMb3X5gVrzF8cPUXPOxGM+rvsGT0heup+XNOhtXL7qPo7b90MNjK4nQRIgARIQE8CFD09aTIWCZAACdQAAh9t+xbi0QHisQHuLyFL6i2RItGJ+vIneqHG0VP0RN+Wr3kP/Xp0VvYjmqIn2t68dTtaXdRYSQhD0asBJwV3gQRIgASqIQGKXjU8aOwyCZAACcgkoD5Tzv1RBOrthqJd72fn+RO9UOPoLXrekhqNNXq+Hv9A0ZM5WhmbBEiABEjAHwGKHscGCZAACZBAFQK+HiDua32eqBjo1s1Q4gQTPa3JWLwfWC76qMeMnvfD370fmC7aCUX0mIyFJx4JkAAJkIBMAhQ9mXQZmwRIgARIgARIgARIgARIgARiQICiFwPobJIESIAESIAESIAESIAESIAEZBKg6Mmky9gkQAIkQAIkQAIkQAIkQAIkEAMCFL0YQGeTJEACJEACJEACJEACJEACJCCTAEVPJl3GJgESIAESIAESIAESIAESIIEYEKDoxQA6myQBEiABEiABEiABEiABEiABmQQoejLpMjYJkAAJkAAJkAAJkAAJkAAJxIAARS8G0NkkCZAACZAACZAACZAACZAACcgkQNGTSZexSYAESIAESIAESIAESIAESCAGBCh6MYDOJkmABEiABEiABEiABEiABEhAJgGKnky6jE0CJEACJEACJEACJEACJEACMSBA0YsBdDZJAiRAAiRAAiRAAiRAAiRAAjIJUPRk0mVsEiABEiABEiABEiABEiABEogBAYpeDKCzSRIgARIgARIgARIgARIgARKQSYCiJ5MuY5MACZAACZAACZAACZAACZBADAhQ9GIAnU2SAAmQAAmQAAmQAAmQAAmQgEwCFD2ZdBmbBEiABEiABEiABEiABEiABGJAgKIXA+hskgRIgARIgARIgARIgARIgARkEqDoyaTL2CRAAiRAAiRAAiRAAiRAAiQQAwIUvRhAZ5MkQAIkQAIkQAIkQAIkQAIkIJMARU8mXcYmARIgARIgARIgARIgARIggRgQoOjFADqbJAESIAESIAESIAESIAESIAGZBCh6MukyNgmQAAmQAAmQAAmQAAmQAAnEgABFLwbQ2SQJkAAJkAAJkAAJkAAJkAAJyCRA0ZNJl7FJgARIgARIgARIgARIgARIIAYEKHoxgM4mSYAESIAESIAESIAESIAESEAmAYqeTLqMTQIkQAIkQAIkQAIkQAIkQAIxIEDRiwF0NkkCJEACJEACJEACJEACJEACMglQ9GTSZWwSIAESIAESIAESIAESIAESiAEBil4MoLNJEiABEiABEiABEiABEiABEpBJgKInky5jkwAJkAAJkAAJkAAJkAAJkEAMCFD0YgCdTZIACZAACZAACZAACZAACZCATAIUPZl0GZsESIAESIAESIAESIAESIAEYkCAohcD6GySBEiABEiABEiABEiABEiABGQSoOjJpMvYJEACJEACJEACJEACJEACJBADAhS9GEBnkyRAAiRAAiRAAiRAAiRAAiQgkwBFTyZdxiYBEiABEiABEiABEiABEiCBGBCg6MUAOpskARIgARIgARIgARIgARIgAZkEKHoy6TI2CZAACZAACZAACZAACZAACcSAwP8DtZVcru9TKSAAAAAASUVORK5CYII=",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics2.plot_history(colors=['darkorange', 'green', 'darkblue'], show_intervals=True, title_prefix=\"WITHOUT catalysis\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "af8fec87-0f53-4491-b742-e909182781b9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 14.63 ; [B] = 105.4\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 7.20163\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 7.515573071036746\n",
"Discrepancy between the two values: 4.177 %\n",
"Reaction IS in equilibrium (within 5% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics2.is_in_equilibrium(tolerance=5)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9d774e6b-8952-4664-837c-08ba42f8be48",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"jupytext": {
"formats": "ipynb,py:percent"
},
"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": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}