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"## Coupled pair of reactions: `S <-> P` , and `S + E <-> P + E`\n",
"A direct reaction and the same reaction, catalyzed\n",
"### Re-run from same initial concentrations of S (\"Substrate\") and P (\"Product\"), for various concentations of the enzyme `E`: from zero to hugely abundant \n",
"#### Given the initial [S]=20 and P=[0], the times at which [S] = [P] are computed for various concentrations of `E`\n",
"\n",
"1. No enzyme `E` \n",
"2. [E] = 0.2 (1/100 of the initial [S]) \n",
"3. [E] = 1 \n",
"4. [E] = 5 \n",
"5. [E] = 20 \n",
"6. [E] = 30 \n",
"7. [E] = 100 \n",
"8. [E] = 2000 (100 times the initial [S])\n",
"\n",
"LAST REVISED: June 14, 2024 (using v. 1.0 beta33)"
]
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"name": "stdout",
"output_type": "stream",
"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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"id": "087c0d08",
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"from src.modules.chemicals.chem_data import ChemData\n",
"from src.modules.reactions.uniform_compartment import UniformCompartment\n",
"from src.modules.movies.movies import MovieTabular\n",
"\n",
"import pandas as pd\n",
"import plotly.express as px"
]
},
{
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"execution_count": 3,
"id": "23c15e66-52e4-495b-aa3d-ecddd8d16942",
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"name": "stdout",
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"Number of reactions: 2 (at temp. 25 C)\n",
"0: S <-> P (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n",
"1: S + E <-> P + E (kF = 10 / kR = 2 / delta_G = -3,989.7 / K = 5) | Enzyme: E | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in the above reactions: {'E'}\n"
]
}
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"# Initialize the system\n",
"chem_data = ChemData(names=[\"S\", \"P\", \"E\"])\n",
"\n",
"# Reaction S <-> P , with 1st-order kinetics, favorable thermodynamics in the forward direction, \n",
"# and a forward rate that is much slower than it would be with the enzyme - as seen in the next reaction, below\n",
"chem_data.add_reaction(reactants=\"S\", products=\"P\",\n",
" forward_rate=1., delta_G=-3989.73)\n",
"\n",
"# Reaction S + E <-> P + E , with 1st-order kinetics, and a forward rate that is much faster than it was without the enzyme\n",
"# Thermodynamically, there's no change from the reaction without the enzyme\n",
"chem_data.add_reaction(reactants=[\"S\", \"E\"], products=[\"P\", \"E\"],\n",
" forward_rate=10., delta_G=-3989.73)\n",
"\n",
"chem_data.describe_reactions() # Notice how the enzyme `E` is noted in the printout below"
]
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"source": []
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"id": "0e771dda-1c0f-4fc0-ab21-049740643897",
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"# 1. Set the initial concentrations of all the chemicals - starting with no enzyme"
]
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"id": "5563e467-a637-44fa-9ba1-d35ddd82c887",
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 0.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
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"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\")\n",
"dynamics.set_conc(conc={\"S\": 20.},\n",
" snapshot=True) # Initially, no enzyme `E`\n",
"dynamics.describe_state()"
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"id": "651941bb-7098-4065-a598-e50c0b641ab3",
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"### Advance the reactions (for now without enzyme) to equilibrium"
]
},
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"execution_count": 5,
"id": "76f24d9a-a788-41d8-90a4-db87386f91aa",
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"35 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 20, 'norm_B': 20, 'norm_C': 19, 'norm_D': 19}\n"
]
}
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"dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# Perform the reactions\n",
"dynamics.single_compartment_react(duration=4.0,\n",
" initial_step=0.1, variable_steps=True)"
]
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"#dynamics.explain_time_advance()"
]
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bWns6O7NFn6ysdX/ldT8cNDaSl9t84r6oPLRzPphyeyBl/076t5//wfrOk4fb/ZDbOefWFjcN4/ZgvRAekhW8WOWJwIfzht3rS83+RWsfNLcnnTzQ44Q11v6E3W19t3zPeUF0u1l2E9deT5Q5v1uZ9oun202qqoD3ulDxTaVKX4IY208yPhn4JJTj5DZuXu/xiev1hWEPbuE2NsyWb5Sl75qbn5CzXvuFwE2c2i8KfpZVvxtF/qzjYW1qLRd0Gze/G2s3sarKVWfOeo2zlxjUbQOXH9Yy6Se0nC4AuqLMT1Am0V75EEGKOp06TIvVrzZ9U8sq7Va//UbZfs743Zw5b1KS8KeR7UrCRzItYjUJkeonWnUeMDV0sern6+930+j3fe32/cjjpfO9aR9D1fPObQm1c3z9LKuyv27ttIuaoGuJve3OBx6qD+zc0jn7p3Nv4Fae23tu4yrPXzsXJ0edtnh995m+B2RjjlOscqAi+/27ypzi/ji/c+xi1i5O3e6hVOed1wO0oNU5zocV9kCGfmKV8znPQ77/tfNxWy3ldk11uw/zexiY5kBQzKXgxaruk1ivZWWqT9vdgroEWbjkTaffRdt54+/VTmf9XnXz5D1qSD/fbT38nqp5WeuCbqBVlvzo+Ot4nUDOfqssx/UaY2egGb8bBuc4qYjVIGbywuZsh/2C7HYzqMrArT+qc9ZP4LmJVZ2x9WpDVFHp5OksT3dJrP0JsepYRu2D18MEr3K9vjx1vlSjttm5LNxrLrhdI7zO8ySWAXM/vYIZRR3fOMSq1zio+BTZb+p1BGSUsfd6ABx0g+y0dviJ2KD2xWFZ9asj6rywl828/vXxctcH7GHEqvNmluvyOp+c7/t9f6m4efh9p3740afWg36/ewK/+xcWMXIOB7XTacl1s6RxW/0iN/vVIfPq3Bt4Xbuc9biVKceJH1zKuSfzSSY6bQk6F+0PE6PeG+jc53q1yxkgz+9+mMtgF7+gFQv2733Veac6hn7XDl3Lqn0rPrc56WUksF9X/OaG13ngd10Kuv6a+BxiNUvZ66LrXEYjB8V+MVQ9uf0EsXMCBvm0yPrdnsCpTpwkxKqK6Pe7AXX2W1WsqtzU+okj+xezzpdAFLGqsgRGx7Kqw1V1zuqK1TjaoDp/ddK5LYdRufm3PzDgv1VvWt2WyupY8uIQq3J+6dSrytRryaKbNcS5PMnLQuD2EEHlvFZts1s6r3NQReh5LYd2q0elPNUVMX79DSNW3b7jdJZNxiFW5XxSqddr7rlxUXkwZTrAkvNG3N7uuMSq1/Xd+X7Q9ToogJ597nhdG8OIF+dDeb/vWXuf7HNDZYmmnb39WuB1vurcGwTdwznFE7eFV4DJdjBPvi+x3+ut37g5t0pMpy0mxarOfa5sl3OZLb9vvxbIMv2uDzpi1UvwOeed1xiqGEfsfVO1rDrnnbMev3PJuWJDLmdXcQnktkKsRrmTUMjrtlTWL5uOZdVtDyK3yaJ64+/3xeA8eZx+E84+2S90blYClS/pJMSqys2ln2h0Ll1QFasqVjq3C6Kdq7zR1vkSCCtWZVvsFxK/5SEqllUdrqpzVlesxtEGhdM+chIpBnVuaOyCV1W06jY0bB1ewkn1i0qnnbKNzmuM6qoD5zXU7wtY5Xqi0/agtFEFfhyWVRVhG9SPQlgG7PedFtQ/5+dxWFZVvjN12+WWPk1i1e0hnr3NKg+63B52+C1fleWrPHSQ1y9Vscple5Wrcs12e3hlF0g69wZegshtKbBdaPC5ywcH/+O/pUB1Xlt02mJSrOrc58p+O+eZ232E23ecm/+r8zvPyUln3nmNYb7EqpfxzD6+ziXxzrH3+n6BWI3j6u5Thu7TaFWxqrOETfXGX+ck5gtT0FNNLyyqvnpJiNW0W1aZmd/ei/YvO7ebF9Ubci7Hb+kKB8MIuqhyGbCsJnMBibLkMKyg9OuJvcwwYsXUcl+dGyTVa2iaxCqPkZuvj+osTItYle1NQrTay9R52CPbFOXc8xqHQhKrJpYB61hWvZYkq855Zzo5P+T3Z5BlVeUhgZ84CPK1k3lVhLezL/K6GuZBto5l1W7R4+XPHFCSl1Dbl/6yv6fb1mQq9ylpFauqxgi39svvTHkfpWtZVZl3aROrbm6IquepzOtlnYZYVSUZMp3Kk3A+4XmA/LaucYoCL5EQxbKq6nfhJ3Tcvhic22+o+I1yOUmI1aBlCuwz4sXBz3fDKTCdX8Yq/iYqQlpXrPpdPHT9Hdz67/RTsY+/KoOG6LPKfX75jfc8fZRU54KqwFR5au/3hcufhRGpskxTYjXoxjPMMmDug58fDkfNDsvXjTmfl35bFkWJIp02sRqnaI0qUiFWMwScy/Wcc9TLV1Tn+1pVrOpYiHTOJbeotW6rPFRWRHndq7h9V9vv9fy+K936wuNyxinH1YnzYRdUOg/rdL//ZfwVu5+qvDbKHSPs10GdtpgUqzr3uV7XWrfl6s5rtrP/OmJVdd55pdM5b0z5rNrHmFm4bb8WtOzfvlw5pCRLLFvB+6zaL2RuTwycVkZVy6qbH4t9iUgYn1Vuq9tTe/mEyOlD57XEmdPzkzcW37J/9ouYqrVZ58tPZzme7I/95tv51Mat3W5sdJ68uZXpXHLllobHhdt35IBe1tNM3S8B3Rttt2VA9qUp9id+fm1xu5CqclVdDeB35fGLBuzcbsRr3rsFB4njaufnuyTnvarPalB7JHNdsel2ngTV5fW5KbFqv3myP0CSbgthxapb++3LvuIWqyyAvbbK4jmpO5ZyXNIqVmX7wix/l9dHZhbGkuqcsw3dshr0MFnnBllVlNrH33nN9boO8fnHh19QInlf4BYh336PFGRl9DoXeTtADjjjNWec3ysyndt3aND1Xl5v7O123gfq3BvItEGRjp3nptcWf05GOm0xKVa97nPl96S9f3Lu2a/v8j37/bzbHHV+Z+iIVbexsV/D5bwL0gEq18O4xarbHJcPbuSOG7LdbprC7Vzzm0th70nizlcvxKp9ktn3J+L3nQOjKlY5r9N/gcuS+32GFavyRLa3kyc8Lwt1W5bg5lPitq2Mc2Ko3NwlJVa5LW7+Bc42OX1t/fZZDbKsyv47y3R7gOHm42ud7CKggTzpecmN6vIa5zxx22e1zvgIy59zT165T6/XHnOyjDj3WQ0b9Znb4meBUhlb1aebUS56Xn7KYcVIlLYkmdekWJVjb++PDAYSVqy6XTP4POAtcuK2rHJdXr4/QTe0QWMYh1j1qiNq24LaburztIpVv/6rfJ/q8AtaumqPWaGyz6rzOq4rYr183lWuk273KM6beKefYNA+q857Nzln5L7LkrXbPYNbX1SWfHKZbvcGQXElZFuCHt7KdF5t8bqGuwmmMPcpbvMzyXtA53cvzyXn1jXcJuf84bnD2w06H6q4fZfb56eOWJUs3Mp0zik3HcBbWvJy7XyIVfvYO8fUbatFe5qgfZZVzned61ycaeuVWI0TjMmy5IU8iWAoJvuBukAABEAABEAABPwJ6CwjBEt3lyVwAQEQiE7AbaVf9FLjLwFiNX6mviXal5vKhCYsTIa7iepAAARAAARAAAQ8CLgtgQQsdwIQ95gZIJAMgUK5DkGsJjP+nqW6LTMJE6XOcLNRHQiAAAiAAAiAQEwE7Etj07z8LqbuRioGYjUSPmQGAVcCbttzphUVxGpaRwbtAgEQAAEQAAEQAAEQAAEQAIEGTABitQEPProOAiAAAiAAAiAAAiAAAiAAAmklALGa1pFBu0AABEAABEAABEAABEAABECgAROAWG3Ag4+ugwAIgAAIgAAIgAAIgAAIgEBaCUCspnVk0C4QAAEQAAEQAAEQAAEQAAEQaMAEIFYb8OCj6yAAAiAAAiAAAiAAAiAAAiCQVgIQq2kdGbQLBEAABEAABEAABEAABEAABBowAYjVBjz46DoIgAAIgAAIgAAIgAAIgAAIpJUAxGpaRwbtAgEQAAEQAAEQAAEQAAEQAIEGTABitQEPProOAiAAAiAAAiAAAiAAAiAAAmklALGa1pFBu0AABEAABEAABEAABEAABECgAROAWG3Ag4+ugwAIgAAIgAAIgAAIgAAIgEBaCUCspnVk0C4QAAEQAAEQAAEQAAEQAAEQaMAEIFYb8OCj6yAAAiAAAiAAAiAAAiAAAiCQVgIQq2kdGbQLBEAABEAABEAABEAABEAABBowAYjVBjz46DoIgAAIgAAIgAAIgAAIgAAIpJUAxGpaRwbtAgEQAAEQAAEQAAEQAAEQAIEGTABitQEPProOAiAAAiAAAiAAAiAAAiAAAmklALGa1pFBu0AABEAABEAABEAABEAABECgAROAWG3Ag4+ugwAIgAAIgAAIgAAIgAAIgEBaCUCspnVk0C4QAAEQAAEQAAEQAAEQAAEQaMAEIFYb8OCj6yAAAiAAAiAAAiAAAiAAAiCQVgIQq2kdGbQLBEAABEAABEAABEAABEAABBowAYjVBjz46DoIgAAIgAAIgAAIgAAIgAAIpJUAxGpaRwbtAgEQAAEQAAEQAAEQAAEQAIEGTABiNYbB375rP23fXR1DSSgiiEDrFqW0b38N7dpbE5QUn8dAoElpMTUrK6Yt2/fFUBqKUCHQpV1TWrd5t0pSpImBQNuWpdb1ZM8+XFNiwBlYBF9PShsX09YduKYEwoohQaOiIurQpow2bNkTQ2koQoVAu/Iy2rF7P+3df0AlOdJEJNC8SQmVFBfRtp37I5bknp2/k3HklwDEagz8IVZjgKhYBMSqIqiYkkGsxgRSoxiIVQ1YMSSFWI0BokYREKsasGJICrEaA0TNIiBWNYFFTA6xGhFgAWSHWI1hkCBWY4CoWATEqiKomJJBrMYEUqMYiFUNWDEkhViNAaJGERCrGrBiSAqxGgNEzSIgVjWBRUwOsRoRYAFkh1iNOEh33nkn3fCTn7kuA35v7pvUvEU5DR56tGctLz47nY4aPoI6d+1hpalcuZyWL/uYTj3jvFye6Y89SGdOmEgty1tZ7y1e+AHt3FFFx408OZfm4T/+J1157U25/511b6/aRi/NmE4TJ1+dS/P6y89Sn/6DqKJXH+u99V+upg/nz6OzzptYq73THr6XJk2eQqVlZbn357zxCnXu0o36DhhcK61XGZzI2Q97Rr989nTcz+tvvMV3GfAz06fSSWPPoHbtOwSOrk5aWZjKuPpV7OQe2EifBF7jEKZMt7LiEqvOeR6mfV55/OZV1Hqc51XU8vzyy3k17pRRiS8DdrseJNk3t7I3f72R5vzjZTp/4mWmq87Vx9fbyhVLafxZ56dyGXCS503S0D/7ZDGtX7eWTjrl9FpV1SexumD+O1bfhg0/IWmcocs3KVbTcE6HBhVjxqhiVfV+KMYmF3RRSYpVvge4/fbbC5pPfWh8gxerP7jh1/TPBZ/UGssls6fW+v/cy26lFZVfWu/1ruhKz029O/c5xCrEqu6FAGJVl5h/eohVfZ4QqxlmEKv6c0c1B8SqKqlk00GsJsvXrXSIVbPMIVbN8s5HbQ1erI6acB29PeO+HPtbfvEQzZ2/OPcei9nNW6pyApWFa7u25fTne2628kCsQqzqnrgQq7rEIFbjJUYEsQqxGveccpYHsZo0YbXyIVbVOMWZCmI1TprBZUGsBjMq9BQNXqw6B3DxJytp4jV30fT7b6PBA3oRi9kbp1xME8aPtJLOeHUu/e6BJ2oJXPismjsN4LNqjjXXFNcyYLOtLuza4LNqdvzgs2qWd31aBmyWXLjaTIrVcC2sf7miitX6RyTZHiUpVrnliAac7PiplA6x6qB036PP0JMvzLLEqFO4clK39yBWVaZaPGkgVuPhqFoKxKoqqfjSQazGx1KlJIhVFUrxpYFYjY+lSkkQqyqU4k0DsRovz6DS6ptYda7gDOp/mj5300hxtA9i1UZRQr77p1dYllQVsbpW5P9LzQH6Efb9jGM+BpbB4qnmwEHaX439y0g1kggAACAASURBVAJhxZCgpLgRNS4pot2Y3zHQVCuiZbPGxA/AcJgh0FTs+7m/+iBVi+s4juQJNC5pRMWNilIZ0Cr53puvoUjss9q8SbHY9xN7wZui37SshPZV11BNzUFTVTboevia0khcU/YmtFc2fyfHebjFymnbumVuxWY+xCqvGr31V4+Q1D9h+wuxGpacYj4JeMr3z6HrLj/fyqUiVtln9Q4RKexiIZ7uEydKE1t9s2f9g8pbltOwo4d7tuKp6X+l404YSd2797TSrFj+GS1dsojOmXBBLs8jD/2JLrr4EipvlYkGvOCD+VS1vYpGjxmbS3PPb35hRSWWh7Puqm3b6Mkn/kJXXPWjXJrnZzxNRww8knr36Wu9t2bNKnrvnbl04cTv1Wrvn/5wD11x9Q+prOxQ72a+8iJ1696DBg46slZarzI4kbMf9ox++ezpuJ833/JzX7H6l2mP0mmnn0UdOnQMHH2dtF5sAytxJHBy181vT+81DmHKdCsrLrHqnOdh2ueVx29eRa3HeV5FLc8vvzxnTzrxhMTFqtv1IMm+uZW9ceNX9Jq4jlxy6eWmq87Vx9fbT0XU2nPPuzCVYjXJ8yZp6Es+XkRr16ymceJabD/qk1h9d97bVteOHzEqaZyhyzcpVtNwTocGFWPGqGJV9X4oxiYXdFFJilW+B4gzGvDA0ZeRXZhK8CxgO7ZvQ7/82VWUD7Ea1wSAWI2LpEs58omC9FO1J3HzWeWnDzJiMIvVqbfdRpXi6eVZQqxeI55eDs1a/VS2OMHWNRnaqqHasXVN7QmMrWv8t0SKetnA1jVRCXrnT8M2F4gGnNz4IsBScmx1Sja5DDgN57QOm6TSRl0GrHo/lFT7C63cJJcBx7l1DQvS5SvX1op548ZailX+TO5W4iVw7buZ2DUMa5eRwwdbAWO3bN1uVcPGuO5dO1gWVHnIPG4i02kBlsY8v11UIFYTOnvcAibZq1KJBnz4T39Ovy8uogViKcLx+w/QlD3VNFYIV4jV2oOGfVYzPBANON6TGVvX6PNENOAMM4hV/bmjmgNiVZVUsukgVpPl61Y6xKpZ5oUiVtmqes5pIyzrqd8ht8u0r/Rk8dmnV7fcTiRObcLxdh54/PmcIY3Ts0iVYlR+7lxuzO3g7TidItMprPnz3z/8lFU/f/bjKy+0gtDywe31KieumdCgfVbl4LjBtK/b9ttnlfOyf9kbQqTe37SEXhM+lX2En8KU3ftpIvz84pqnuXIQYCl2pL4FIsCSWd5cGwIsmWWOAEtmeSPAklneJsWq2Z6lt7aoYjW9PUtny5IUq/I7OWrPnTFxgsSqfYtMTsvbai79bJWrsJRlsUC96OwxliujtKxKYexm8bRv1Wn/nMvjXVFU/VeDAtNGZcf5G7RYjQOgFKvbxfLflcK6yoL1b8K5vvXBg9aS4CniVRJXRSiHIFbNTgKIVbO8IVbN84ZYNcscYtUsb4hVs7y5NohVs8wbmliVrotulKU11kus2gWol8j8fNU6a6mwdHd0q0dabu2fcXosAzY797Vqs29dUyV8V1mw8ovjeV4plgSzaO0oItjiiE4AYjU6Q50SIFZ1aMWTFpbVeDiqlgKxqkoqnnQQq/FwVC0FYlWVVHzpIFbjY6lSUiGIVe6HzjJgP8uqFKtBYpJ9Vp2W1TjEKvfj2GEDckuS7UuQIVZVZmwe0nCAJY7Cy5ZV+/FokxL66O036cvWrajzt4+ha4RoHeiy3QoCLGWoqQYUQICl2pMcAZYQYCnMZQ8+qxlq8FkNM3vU8sBnVY1T0qlMilUEWMqMZlSxqno/lPTcKZTykxSrJgMs8bJcr2jAbsuA/ZbpRrGs8rh7LQN2E8oQqwVwpniJVW76X9+dRe+1bUPPjDieRgmf1muEH+tJ4rf9gFiFWI0yzSFWIVbDzB+IVYjVMPNGJw/Eqg6t5NJCrCbH1qtkiFWzzAtFrDIVt61rpACUwZfctq6xi1UuR0bktVtXOc2xw46gCeNHevqsqlhWOXASt2HL1qpc5GIZYIkDKzmFLPeJDywDNjvvtWrzE6scDXij2Bv1qROOpzcbF9MAsek8+7BeYAu8BLEKsao14RyJIVYhVsPMH4hViNUw80YnD8SqDq3k0kKsJscWYtU8W7caC0ms2oWmvS/OoK5+y4BlPr8tZKJYVu1RfldUfplrpmwji+LnX5uXe5/9ZGUkYiwDTsc54doKu8+qW4JlxY3oAeHD+lRZMXUQvqu8tc3VjmXDKe5eqpoGn1WzwwGfVbO8uTb4rJplDp9Vs7zhs2qWt0mxarZn6a0tqmU1vT1LZ8uSFKvyOzmdPW84rUI04BjGOkischVfNyqiB4QfK4vWIvE/W1hZtLZD4CWtEYBY1cIVOTHEamSE2gVArGoji5QBYjUSPu3MEKvayCJlgFiNhC9UZojVUNhCZ4JYDY2uYDJCrMYwVCpiVVbDYpVF6yYhXi8Sy4FZtPYTy4NxqBGAWFXjFFcqiNW4SKqXA7GqziqOlBCrcVBULwNiVZ1VHCkhVuOgqFcGxKoer6ipIVajEkx/fojViGMU5LPavEU5DR56dK1anhbLgXlrG14e/OP/mUpDjj2BTu3YzUrD0SmXL/uYTj3jvFye6Y89SGdOmEgty1tZ7y1e+AHt3FFFx408OZeGI5Zdee1Nuf/ZX9Zet5uP2usvP0t9+g+iil59rHxeEeimPXwvTZo8hUrLynLle/lK+kWxc/bDDkU1+h2iAdeesPBZhc9qmEsYfFYz1BANOMzsUcsDn1U1TkmnMilWEQ04M5pRxarq/VDSc6dQyk9SrMYZDbhQeKaxnRCrEUcljFjlKmeLgEssWHv/7XFaPfJEurBDVzpnXw3E6nkTfUcEYhVi1TlB/B6CRDy9yfkQKGp5fvnlA6Zxp4yidZt3J1kVQaxCrCY6wUThEKtJE1YrH2JVjVOcqSBW46QZXBbEajCjQk8BsRpxBMOKVa7245JG9Pozf6enx4ymfT16iq1tqunkpZ/AsuozJhCrEKsQqxEvWiI7xCrEavRZ5F8CxGrShNXKh1hV4xRnKojVOGkGlwWxGsyo0FNArMYwgjo+q87qNnDgJWFhfVj4sZYeFIGXRNClHwrR2vKg+AdHHQLwWTU7KeCzapY31wafVbPM4bNqljd8Vs3yNilWzfYsvbVFFavp7Vk6W5akWJXfyensecNpFcRqDGMdRazK6v8oBOtvmjWmavHGmWI58H079lEZ9CrEagzzM0oREKtR6IXLC7EajlvYXBCrYcmFywexGo5b2FwQq2HJhc8HsRqeXZicEKthqBVWHojVGMYrDrHKzfhHaTH9sEUp7RR72wysPkAPCcFaUQPFah8iWFZjmLAaRUCsasCKKSnEakwgFYuBWFUEFVMyiNWYQCoWA7GqCCrGZBCrMcJUKApiVQFSgSeBWI04gFF8VrnqF5+dTkcNH0Gdu/awWvJu5QqauXwJPTxxIjUXOvU3O/fR7of/G9GAs+MEn9XaExbRgBENOMwlDD6rGWqIBhxm9qjlgc+qGqekU5kUq4gGnBnNqGIV0YD1zookxSqiAeuNRVKpIVYjko1brPLN00effkwLLriIHhV+rI2FYL353v+iU8+bRIeLbXD4wNY1t9AusUet1/HM9Kl00tgzqF37DoGjq5NWFubcFiiwEkcC55ZBuvnt6SFWIVbDzB+IVYjVMPNGJw/Eqg6t5NJCrCbH1qtkiFWzzCFWo/MeOPqyWoX0ruhKz029O3rBMZUAsRoRZBJiVe6z+qTYj/XnzUvpyj/cSx9c8n36baNm1P3AQYjVGyFW5bSFWIVYDXMJg1iFWA0zb3TyQKzq0EouLcRqcmwhVs2zdasRYjXaOIyacB2NHD6Yfvmzq3IFnXvZrRCr0bCmL3dcPqtuPVtW3IguKy+lNSJqMC8LvmPnfvruXg7D1DAP+KyaHXf4rJrlzbXBZ9Usc/ismuUNn1WzvE2KVbM9S29tUS2r6e1ZOluWpFiV38np7Hn0Vi3+ZCVNvOYumn7/bTR4QK/oBSZUAiyrMYBNUqxy8z4rLqLHxJJgfvHiVxark/fU0GARhKmhHRCrZkccYtUsb4hV87whVs0yh1g1yxti1Sxvrg1i1SzzQhOrCwWerWYRWbUNFa/WLvWyZbVt6/JUWVKdzYRYjWHCJC1WZRP/IsTq42Jp8McljWioEKqXij1ZL/Lx3Yyha6krAmLV7JBArJrlDbFqnjfEqlnmEKtmeUOsmuUNsWqed6GJ1TEC0WzzmGiWqHO0R71On9Up3z+Hrrv8/Dy00r1KiNWIQ5Gkz6ps2vTHHsxFA14ghOqLiz+kVTu30+zTxtFkYWVl0fr6vb+mK6+9KdcbZxAgNx81Z6Afrwh00x6+lyZNnkKlZWW58r18Jf2i2Nn74cSuGv0O0YBrk4PPKnxWw1zC4LOaoYZowGFmj1oe+KyqcUo6lUmximjAmdGMallVvR9Keu4USvlJitUkogH/WIBl66rp4/eiQrauBh33PfoMPfD483T3T6+gCeNHBiU38jnEakTMpsUqN3fBRx/QB7t30NTx42mVWCJ84v4DdPIv/h1iNTuWOhF+ddLKqYJowPonjXOLJv0SvHP4PQSJWg9/UdkfAkUtzy+/nFfjThlF6zbvTrIqgljN4IVYTW6aQawmx1anZIhVHVrxpIVYjYejaimFJlZV+5XPdLw0+KKzx6TGugqxGnE25EOsyq1r9ow5lR5vUkyvlhbTHXfeSdt/8jNhaa2h9iJiMCyr2LpGd2q7WWnjWgYMsRo8GhCrwYziTgGxGjfRQ+VBrCbHVqdkiFUdWvGkLWSxWn2gmtbv+DI0iLXbV4XOu6YqXN6yxsW0dsdq2rvPe0tDv0at2b7a8+MjPjmcbr/99tB9SnvGGa/Opf+Z/kotf1V+79ZfPUJLZk9NTfMhVmMYClM+q25N/UpECc4EXyqmLUVFdKY4WSeLZcEjhbW1Ph7wWTU7qnGJVbOtLuzaEA3Y7PjBZ9Usb/ismuVtQqxu2b2Zdu7fEdixmoPhhVAUEVV9oIY27AwnwKoP1miLt7LGjai65gDtq66mdSGFX75YBQ5iA0tw4/Bb6ben/0e97jVvU7Oisvb5kSahyvAhVmOYgvkUq7L5Lwrr6jQhWueJi2SvmoOWYL1U+LOWiu1u6tMBsWp2NCFWzfLm2iBWzTKHWDXLG2LVm7eXINu5fyd9s+frOhk37vqK9lbvqfP+WpulqEg8xG4uHmZ/VbWNtuzZXCftlt1fC6G506WMulYurovrxFG/CXQv7xm6g91ahs8btt4S4Q5X0boitGW1W8senv0deNgQOrXfsaF5IGM8BCBWY+CYBrHK3ViR3eKGRSvvxDpRLAn+vhCtHDm4vhwQq2ZHEmLVLG+IVfO8IVbNMk+bWLUvPazat42q9h7aVIKtYjViWSQfGcF4SOxZQrFmbw4ep3OzonF5XK7z2LiT89cVmmZHI57aystaUasyt00xapdfXFRCnVt0DVVpSaMoeYupc/Nw9RYXibyabW7RtDHtEavcDh5sRF0080o4UVhxGWGFX6jByXOmJH1W5XdynrvY4KuHWI04BfLps3rcyJNzrbcHgvm72N5m4dtv0oo2rWn30cMtK+uZm7bQSzOm08TJV+fyIBowEQIsHToB4LNa92KAAEsRL5A+2dMQORQ+q8mNbxifVV5KyktK5cG+c7wcUopFtgLKg8XivqxYZNFot/jZrYXO5ZTbWDzurSsew5AYnd0IYnaMG1G4iYzmjZtTmybt6zSxbdN21Lxxizrvd7dZiqRldd++YurQrKNLGe1FGc3rvM8CjQWT/SgraeJahkyThnM6zDjGnaeQfVbjZmGivCTFahLRgE0wqW91QKxGHNE0ilXu0vPvzKKP2ramB0aOsJYC/2DjZqr42+P0fYjVWiMOsQqx6ncJgFiNeIGEWI0EMMnAZGEaZl+myktKdwlxWfe9ncR+frvXVlGz3U1pTcd1tSyOO/az9XIbHTiY8VEJG1QlTPvd8rAoY6sdH05RyFax4uxnZcVltYTaYSz8Vu+38pV9q4WVzs2K1kyIybZN2tWpukPzjlRW3CSubniWY8JnFWK1Nn6I1cSnda0KIFbN8s5HbRCrEamnVaxyZNGyluX0/rHHWb6sW7dvoylTp1Gvy6+xgjDxAcsqLKv26Q/Lat2LAcRqxAskxGokgFHFqo64lBFApVXSbpFUDaBj7+xQsaNfhfiZIX5UD7YSsrVQHnbrXpOSMjqsWafcZ2wlZAHJh3OpZtumta2Fdj86Xq7Ky1bjOBbMf8cqZtjwE+IoLpEyIFYTwepbKMSqWeYQq2Z556O2vIhV3r9ny9btrv1NWwQqlUFJi8+qV1vfEkGXOGLwKyIIE29r833hy8pLgzuIvwvtgM+q2RGDz6pZ3lwbAiyZZZ5Gn1UWjrwkdpNY6upluYxbXKpSl8tUy0tbCdGX8VOU77USIpDf58MetMS+tLVDi7bUXryqdmasknbLpmobkE6dgEmxqt6q+p0yqlit33Ti712SYlV+J8ffapSoQ8C4WOUQye3altOf77lZp52pTpt2scrwNsktboQ/69fi79OzW9ycWGBb3ECsmj0VIFbN8oZYNc87abHKy1xlNFf2q9y5b6e1jQa/x0tpN+3aYP3N4jNOf0pJUldcsgBl0ZkRnJnInnFaI9MWYMn8jDNbI8SqWd5cG8SqWeYQq2Z556M242J14OjL6O6fXkETxo/MR38TqbMQxKrs+IKSRnRdi1KqFJGDmwvD6h3i6fZ3xRY3hXJArJodKYhVs7whVs3zVhWr0sIpI8Zy5NddQmSy9ZNFJwtOFqYc4dV6T3HvSbcey8A5Uiz6WS6TFpdxjwjEatxE/cuDWDXLG2LVPG+IVfPMTdcIsZolvviTlTTxmrto+v230eABvXLjMOPVuXTrrx6pMy5yuXKafVabtyinwUOPttq+XeyxJqMB7ywi+vdmjWn/c/9LC4cMoTaH96Xf7txHZatX0Yfz59FZ502s1d9pD99LkyZPodKyjH8QH27+jfz++i9Xu5bBn01/7EE6c8JEalle11/IL5+9MexDeP2Nt9AusZTZ69AJmqSTVtbH/sB2tronrdNXWDe/Pb3XOIQpEz6rdanBZzXMTFLLk6/IoTUi+M/Wvd/Q1j1bqPLz5bR59ZfU5Mhy2rhjc+79rXvE53u3iK1KOF3mb/6te7APZusmbah1mXg1aWv93cb2d+33M5/zq0lxU6uqqD6ruu2NM32YaMBx1m+iLPis1qacr3PaxFjr1BHVsqp6P6TTpvqcNkmximjA6Zg5xsUqLwMeO+oouu7y89NBQLTC7kPrJlZ/98AT9PaM+1zbW4hiVXbk8Vdn0NPDhtIHAwZQmbCy/vizFVTx9tt0NsSq79yEWNU/dZO86fZ7CKLf0to5IFajEvTOH8eN7f6affRNVnhmRGVGhPLfufet97Lv7xPvi8+3762yGtZf/HAgoOniJ+hoWVYutg8RgrL0kPCUYjMjQLPv2/7m9xsXlwYV7fl5kudN6EYpZoRYVQSVcDKTltU4zumEcRgpHmLVCOZcJRCrZnnnozbjYpUtlX7iLx8QuE4/y2p9Fats4es2YDD9efAA+ltZCVVUVtIZs2fTqedNouHVB3JDActq7VkJsap/liZ50w2xqj8e9pUW+rnjyeG8sd1TszsrKlloZgSnJTxtYjMjQGu/z4GIdI+MtbMtDSgaQH3296J13TdSy9LWGetnVmxawtQhQjnqrMkjyfMm6X5ArCZNWK18iFU1TnGmgliNk2ZwWRCrwYy8UkjtY/+8beuWnga68DVFy2lcrLLPqt+Rr2jAOsuAnW0sJJ9VL/bviojBP21eSiuELysf54pltv//rv3UOWURg+GzGu2E180Nn1VdYtHT17dowNLXc+32VdZ+mxxI6OvdG62/2a+T32fByX+HOeR2J7zvJe9byf6dvF8m723J7zUTf/P+l+zbyZFqndFnVX1Ww7QNeeoSgM+q2VlhUqya7Vl6a4sqVtPbs3S2LEmxyj3m7+T6erhpnx/c8GtavnJtqgSrcbGa1gH3EqvO9vIgbt5SRc9NvTutXQndrg0i52PiNU28lopXb/G6VLwmi1eP0KUiIwiAQH0lsGPfDlpbtTb3WrVtFW3YsaHWe1/v+lq5+62bsHWzNXUr70YtSltQpxadqH2z9tbfXVt2rfNeResK5bKREARAAARAAARA4BABN+2jqodMcoRYzdJWHRyZzm5drQ+WVfukWygiBj8ttrh5SiwN3iEMrceL7W0uEhGDLxDW1kYmZ6dLXbCsmh0AWFbN8uba0mJZZUvnerHFCltC+cURbtdsX537X+4FqkKIrZ1s0WRLJ1s5OzXvYv3fQfzP77F1lP/PxwHLqlnqsKya5Q3LqlneXBssq2aZF5pldeGGhcKdZatZSKK2oZ2GWg+D7QfEqs8wuEXYzfd2NqpiVba9kKMBy6FxRqV1RqB7uZQFazEN+/1v6b+uv57OKmosBGs1jRLiFdGAD0Va1r3iIBqwLjH/9PBZ1ee5dtMqeuPF56j9qO7Wclxelsvik//mZbn8Ny/fDTp42W2H5h2t/ThZhLLgZCHKIpT/li+3ctIQjKVy5XKqXLGUxp91Pu0Re0+n7YDPatpGpHZ7EA24No80nNNpmDFRxSqiAeuNYpJiNYlowGOmjaHZlbP1OhlD6lmXzqLRFaMDxSoHwuUjTStIjVtW73v0GXrg8edrbREjheKU75+TtyjBXmKVIwXbIwHzILZrW05/vudmazALORpwkFjl/lUVFdETD91Lz117Hf2rRTPqJHxYLxQW1kEvPk99O3ejviJAk/3A1jXBVxSI1WBGOikgVuvSYqFZue1zse/nauv3WmERzfy/SvxeSY33l9Bl4ue/xI/XIa2dUnB2b9nDsoLmRGjzrsT7gYY90nBjC7EadvSC8yHAUjAjEylMWlbTcE6bYBpUB8RqEKF4Py80sfrjmT8mtq6aPn4/7veWddV+uAVYOnbYgJzGMd1Gr/qMi1UWfxedPaaOKGUR++QLs/Li0GvfuoZB2SNhsThdUflljp9zEOu7WOWOczTgYf/nGnq2vDk91aSYtggB+4NnZ1CvLt3p4j5HUDOx7Y08IFaDT22I1WBGOikaqlit2ruNvhACVIrQVVUrc+KURanf0a20O02qmUT/6r44txy3mxCjdmsoi9UkjzTc2EKsJjfCEKvJsdUpGWJVh1Y8aSFW4+GoWkqhiVXVfplIp7qq1ERb/OowLlY5GrDbkl/n8tp8g9Gpv775rPr1/Y3s0uAXxG8+zhRL59jSeqqhJXTwWdWZmdHTwmc1OkPdEqTP6vZ9VfTl9rViae4ayzL65fY1mZf4X/7tVTbvCdq1RTexNLe7CEyUeXUR/1t/Z99rVJRvD3RdMsmkh89qMly9SoXPqlneJsWq2Z6lt7aoYjW9PUtny5IUq9zjhhYNOI2jbFysptGyGnVgGpJYZVZ7RNAlDr70pPBnXSCCMbU6eFAEYKqxAjANsu3PGpWrW36I1SSoepcJsZo8b7aMrvjmM/H61Fqiu2nPWlq2abnlO+rnN8pLcLsLX9GKVodb27WwZbSiVS/rb34PhxoBiFU1TnGlgliNi6RaORCrapziTAWxGifN4LIgVoMZeaWAZdWDTFp9VsMPNVFDE6uS1UqxJ6sUrRsaFdGAmgOWlZVFa7uE9meFWI0yU/XzQqzqM3PLwaKTBennQpCyKP10yyfWb35vb80e10pKGpVkhSiL0MMtMWqJ09ZCnIrf5WWt4mlcAy8FYtXsBIBYNcsbYtUsb64NYtUsc4hVs7zzUZtxyyp3Mo3RgMPCbyg+q5MmT6HSsrIcJns04LmNG1milbe7qaispPNmzaa+F3yXznEsDfbzLVSNfseR2a6/8RbaJQSx1/HM9Kl00tgzqF37DoHDqpNWFvbe3DepeQtEAw6Ea0uQZFTTNPms7ty/w7KOshBd+vXirLU0Yzn1spL2btOPerfpS0N2HkltytvRsSO+TS2LuiW6lcv2qm300ozpNHHy1TrDGGta+KwG40zyvAmuPVoK+KxG4xdXbpNiNQ3ndFzcopQTVayq3g9FaWN9ypukWE0iGnB9Ym+qL3kRq6Y6Z6IeiNVMNOAD4sXb3Lyx4Us67J236O+TLxVW1mrL0np0dmkwxGpmRiLAUrxnZj7EKgcw4oBGlVvFS4hTXspbmf1/d/WuOh1s16S9ZRHlZbr86ile3xLWUv7drml7K718CDLulFG0bvPueCE5SoNYzQBBgKXkphnEanJsdUqGWNWhFU9aiNV4OKqWArGqSqpw00GsRhw7iNXaW9csWreG5r0/jx679FJaJZYJV9TwVjcZ0fr21AfozAkTqWV53eWLqk8SYVmtPWG99rsNM63dyoprGXCSFqKkxeqg846jZZuX0udb2a/0M/p08xLauOsrV8QcQZetpP3aDaTDW/cRf2espvw76IBYDSIU/+cQq/EzlSVCrCbHVqdkiFUdWvGkhViNh6NqKRCrqqQKN50xscpRgHkfVd5j1e9YMntqwdFsqD6rfgM1XwRe4m1unhTLg6tFwuP3HxBBmKotf9YoMUjhs2r29IhLrJptdbjaeCuYDzfMp0UbP6RFm/5FH21cQOt3HNq2yl4qBzdiP9KB7Y8UojQjRvu3OyKWpbsyGnC4XiCXLgH4rOoSi5YePqvR+OnmNilWddtWX9NHFav1lUtS/UpSrHKb63M04KTGJO5yjYnVuBuepvIgVr1H423hz/rz5qW0QlhZ+Rgr/Fhv2l1NA0NGDYZYNTvz66tYZd/SJZsW0YKv5ovX+9bfvJTXebAoHdJhmCVGe5b3sgRpv7YDid9P6oBYTYqse7kQq2Z5Q6ya5Q2xapY31waxapY5xKpZ3vmozbhY9dpnlaMEP/nCLHp7xn354BCpyzMGRgAAIABJREFUTohVf3xsWf2fJiV0T7MSqirKiNbvCAvrDbv3W8uEdQ6IVR1a0dPWB7G6afdGa+nusq+X0mdbltIy8fpMROPlfUztR4/yCiFEjxCCdCD1bTcg87vNAOKovCYPiFWTtIkgVs3yhlg1yxti1SxviFXzvCFWzTM3XWNqxKqMEFxoy4Dhs1rbZ9XP9/Txxx6k9ZO+T892aEurxVY3HcT2NucKS+u5Qrh2WlVJH86fR2edN9H3HIDPam088FklsvusbtuzVWwLszT3Yl/TT7csoS27N9cC16lFF0uY9hOW0v78O/t305JmtdLxfLvy2puMXJfhs2oEc61K4LOaHHP4rCbHVqdkk2IV0YAzIxPVsqoaw0NnHtTntEmKVUQDTsfMSY1YveUXD9Hc+YsLzrIKsaouVqWoWNG2DT0nIgfPKC2mTUK09hTW1e+sWEnd575FF4kATH4HxCrEqiTAUXc/FWL0wxfm0PrDN9MnOz62rKcbdq6rBYmX7PLS3X5tM9ZSS5iKV6smrQOvwhCrgYhCJ0jDjS3EaujhC8wIsRqIyEgCiFUjmGtVArFqljnEqlne+ajNiFh121fVrbN3//QKmjB+ZD44hK4TYlVfrMpowJXCj/Wepo3pf7P7s46dM4daXfhdumJPDZUfdF8eDLHaMMVqzcEay1q67Osl1hLeZWJZL/9eVfUF/V/xM1X8bBU/LRq3zFlL+7LVlH1MhUA9rGnwnrtuFwGI1dCXxsCMEKuBiCjJKNrBtUdLAbEajV9cuSFW4yKpXg7EqjqrOFJCrMZBMd1lGBGrdgRePqvpxuTfOvisRhu9JSJy8C+FP+usxsVWQSxUrxRBmNxEK3xWo7HWzZ0vn9UV33xqWU3Zv9Ra1iv+5vfsR2lxmWUtZTGaCXyUeXVt2V23m6lKD59Vs8MBn1WzvOGzapa3SbFqtmfprS2qWE1vz9LZsiTFKve4PkcDXvzJSpp4zV2uA8s7uFx3+fmpGHTjYjUVvY65ERCr0YFyEKYXhYX1ZbE0+CXx4qOXWB58lvBpPVO8BmWjB0OsRmetU4IJscrWUbu1lK2nLFDZmmo/WJD25QBIln9pZlnvt1r31ulOQaSFWDU7TBCrZnlDrJrlDbFqljfXBrFqljnEanjeUqxOv/82GjygV/iCEs4JsRoDYIjVGCBmi+DFvyxWXxLClX+zXGGf1rOzovVEEVV43/4a2iWCMuFInkDcYpX9Se1ReaXVlP1P7ce3WvW2rKXWUl6bOE2+x/mvAWLV7BhArJrlDbFqljfEqlneEKvmeUOshmcOserBzs/kzFkQDXg5LV/2MZ16xnk5gvZop/zm4oUf0M4dVXTcyJNzaZy+dTKy6OChR1tptldto5dmTKeJk6/O5Xn95WepT/9BVNGrj/WeVwS6aQ/fS5MmT6HSsrJcXq8otH5R7Jz9sE8Rt3yvZq2sL4rf+8SONz1E9OAf/PtdNOonP6P+Ypmw1/HM9Kl00tgzqF37YD9FnbSyPidb3cuEk7tufnv6tEcD3rjrK5q96jXa8N4X9M+S+TR3+1tUfaD22DVv3IIGHnYkDes4XLyOsf6uaHW4Mha/eaVciEdC+KxGJeidHz6rwWzhsxrMKJ8pFsx/x6p+2PAT8tkM37pNitU0nNNpGIiollVEA9YbxSTFahLRgGs21NCBPQf0OhlD6pJOJVTUJLN9pDwgVj3AjppwHY0cPpiOHXYE/e6BJ3LRf8+97FYaO+qo1KyPVp0XCLAUPsBSkFiVn/9DiFUWrGxpvemuO+nR226jM0QQJl4iPCy7PNhelo4A1UkLsRp8VlTt3UbzvnyL5q4VeyavmZXzM72MLqPZ4md98QbLYjqs03D6NgvT9kOs/6McEKv69NweXumXEi1HGm5sEQ042hj65UaApeTY6pQMsapDK560EKvxcFQtpdDE6vbHtlP1Km+Di2q/ddO1+H4LalzR2FWsupXVoH1WZYClw3t2oR/e8vucWOWIwXbxqjsI+UoPsZq8WJVjywGYVvz+l3TPbbdTlXg41FlYWlmwniWWBB9tE606AlQnLcRq3bNsb80emr9unhCnsy2RumjjglqWU7aaDu9yPJ209UQaeNRRNLz/SCppVBLr6Qqxqo8TYjXDDGJVf+6o5oBYVSWVbDqI1WT5upUOsWqWeaGJ1d2v7abqDebFarPTmlFxp0xMGHnAsuoxV+3RgPlvuexXbm9TaMuAuZvwWTV3YeIAS68Jkfq/QqyyX+s3RUXU0SZah7tYWs21rv7V5PRZ3bZnKy3c+AF9tPFDWviVeInfX+1cn+s4bxEzpONRNLTDUeL30dZv3ucUhzoB+Kyqs4ojJXxW46CoXgZ8VtVZxZHSpFiNo731oYyoYrU+MDDZhyTFKvejIUQDRoAlx4zl5b5H9O1Jv/zZVWT/+5ZfPERz5y/OWVpNTvSodUGsRiWont8eDfjdxo2s5cEcQXhjoyLqIEQrRw7m1/H7zfsDqPeicFIWNaqmT7b8i96ufC8nTiu3fZ7rAO9rekicZkRqoW8dk+/RgVg1OwIQq2Z5Q6ya5Q2xapY31waxapY5xGp43rCsKrJj66o80q7svboEsao42DEkc9u6prK4iB4QUYKfLCuhvcLiyotMxwrBerUIwgRLqz70xZsW5iynizZ9SEs2Lc4VUlxUXEec9m7TT78S5PAkALFqdnJArJrlDbFqljfEqlneEKvmeUOshmeOfVbDsyuonPBZNeezyhODI7Ndf+MtrlvXsHX1v5uWUMm0R+nZc8+lDZ06WQGYpgjROk6IVzdPSfisErHf6by1b9O/5r5Di/cuotd2vVrrHOzYvBON7DZGvEbT8V1PpO7lPbXP0SSjmsJnVXs4XKOD65cSLQcCLAXzS/K8Ca49Wgr4rEbjF1duk2I1Ded0XNyilBPVsopowHr0kxSrSUQD1usdUjMB4/us2n1W68MQQKymR6zK+fSXJ6bR2jPPppe6daGVwurKB1tYWbDy61ti31Z5NFSxun7HlzRr1ev0xqpXrKi9O/fvoAnip1L8rCz7gkYIUcoCdWyvsTSk8xG0Zfu+SKdrkjfdEKv6Q4MASxlmCLCkP3dUc0CsqpJKNh3EarJ83UqHWDXLHGLVLO981AaxGpE6xGr6xKoUoFs6dqSZwp+VXwtKGlkj3VcIVSlavy0EbEMSqx+JSL1vVL5C/xAv/lseHJ2Xt5IZXz2ODu85gEYfMz4XsdcZYCns6QKxGkxO7t877pRRtG7z7uAMEVJArEKsRpg+SlkhVpUwJZ4IYjVxxHUqgFg1yxxi1SzvfNRmXKwW6n6qfoMDn1VzU9fNZzWo9k1iebAlWkVApjfFbz44GNNplqX1AJ28vyaoiIL8fG3Vavrgq/fo/XXv0vvr36UlXy/K9aOi1eF0TOfjrRdvLdOnTX/XPsYlVgsSYJ4aDZ9Vs+Dhs2qWN3xWzfI2KVbN9iy9tUUVq+ntWTpblqRY5R7X52jA6RzRuq0yLlbZmde+v2qhgIJYTcdIhRGr9pZzBGEOxvSPrGjlz3iJ8KQ91XSuEK9lh1YIp6PDmq1YtOlfGXG64V36YP17xMt95fHtjsfQMUKYHtMpI1IPa9YhsHSI1UBEsSeAWI0dqW+BEKtmeUOsmuUNsWqWN9cGsWqWOcSqWd75qM24WLVH/3XrMPZZzcc0KJw6o4pV2dMVwpf1EVsEYX6//OBB+s7eGrpkTw31rymMrW927N8uxKmwngrL6QcbMlbUfQf2Wt1sWVaeE6ZSpPKSX50DYlWHVjxpIVbj4ahaCsSqKql40kGsxsNRtRSIVVVS8aWDWI2PpUpJEKsqlAo7jXGxWti46rYePqvp9Vlt1z7Ycjj9iam04/SzaXa3zjSrcWaJMMu5McLKOkbs1cq/e4glw/ZD+hYOHnp0qOn8+svPUp/+g6iiV59Q+av2bqN31s6heV/OoZpPd9NHexcS//DRo7wit7yXLaj92w9UrmPOG69Q5y7dqO+AQ2Mal1iFz2rwMMBnNZhR3CkQYCluoofKg89qcmx1SjYpVhENODMyUcUqogHrzHCiJMUqogHrjUVSqY2LVa9owPc9+gw9+cIsenvGfUn1NZFyIVYLW6zKAEtthbBlsTqrtJH1+4tsFOHDRUAm9mkdLXxbR2d9W/MlVuevm0cvr5xBL654Nre8lyP4bi3bRt37HE7jvnU2jeg2isqKm4Sa6xCrdbHxF9WV194UiqduJohVXWLR00OsRmfoVQLEanJsdUqGWNWhFU9aiNV4OKqWArGqSqpw06VGrM54dS7d+qtHqNCWAUOs1g+xarfCVgqhyoL1TeHfOlv4tvKCYN4AR1pbu73xGnVuXk5JW1b31+wTFtS3LAvqO+K18KsPclea4V1GiO1lTqKKjd1oSO+ja1lDw16OIFYhVsPOnTD50mCFgVgNM3JqeSBW1TglnQpiNWnCdcuHWDXLHGLVLO981JYasXrLLx6iufMXF5xllQcN0YDNTd24fFZVWzxHCNZZQrCyeGU/Vz4qstZWuUw48248x0HhN2uJ06xIZV9UefD2MicIgTqi24mWUNX1Pw3TwriWAYepu6Hmgc+q2ZGHz6pZ3vBZNcvbpFg127P01hZVrKa3Z+lsWZJilXuMaMD5H3cjYlVaTYO6e/dPr6AJ40cGJUvkc45SPPGau2j6/bfR4AG9atXB2+2sqMxEVe1d0ZWem3p3rc8hVhMZEtdCTYtV2YjVYvsbtrKytZXFa3X2A14aPEYsER4jfvOS4bDHP9e9Q/OEH+o7X75F74qXPI487NtCnJ5EJ4jXiK4nUpOSpmGrCJUPYjUUtkiZIFYj4dPODLGqjSxSBojVSPi0M0OsaiOLnAFiNTJCrQIgVrVwFWRiI2LVTsbLZzWf9EZNuI62bN1uNcEpVn9ww69p85aqnEBl4dqubTn9+Z6bc02GWDU3evkSq/Yevs2C1fJvLabPstbWnkKoWsI1G5RJJebugg3zreW987JW1OoDGQl8RLvBdEJ3FqcZK2qLxi3NAXbUBLFqHj3EqlnmEKtmeUOsmuUNsWqWN9cGsWqWOcSqWd75qM24WM1HJ1Xq9LKsspC9ccrFOYsvW4l/98ATueXK8Fmtfz6rQfNFBsJpO+yY7BLhjHjdm10PPEoI1pNFFGEWr30d1taNu76iGc89TgsOLqAXtszIVdW2aTsa3+tsOqf3BXS8sKCqLvF18zMNar/X5/BZrUsGAZbCzqbgfPBZDWaUZBTt4NqjpYDPajR+ceU2KVbTcE7HxS1KOVHFKqIB69FPUqwiGrDeWCSVGmI1S9ZNrKq8B7HacMWqPcDSvKy19U0RTXhZcSNrVnUTW96MFqL1ZCFeG614lZ5aOpVmrnyBLjhwgbXVzJrGay2BemH/72kJVPvFAGJVrIZ47EE6c8JEalneKvbrJMRq7EhzBabhxhYBlpIbX4jV5NjqlAyxqkMrnrQQq/FwVC0FYlWVVOGmy4tYtS+7daLLVzRgFWHKbXWmY7H605/9nPYJQeI8Zs/6B5W3LKdhRw/3nCFPTf8rHXfCSOrevaeVZsXyz2jpkkV0zoQLcnkeeehPdNHFl1B5q8zN+IIP5lPV9ioaPWZsLs09v/kF3fCTn+X+d9ZdtW0bPfnEX+iKq36US/P8jKfpiIFHUu8+fa331qxZRe+9M5cunPi9Wu390x/uoSuu/iGVlR3aEmXmKy9St+49aOCgI2ul9SqDEzn7Yc/ol8+ejvt58y0/p/3VdXnLdH+Z9iiddvpZ1KFDx8AzUyetLMxvXNcVFdHrYmnwP8Rr5u6NtGfhVKIPHyTaWmllL25UQtc2vdbiNmHEBcIHNdw2M7ItXuMQ2HGXBG5llQjh3bikiHbvrQlTZC6Pc55HKsyR2W9eRa3HeV5FLc8vv5xXJ514ghW0LcnD7XqQZH1uZW/c+BW9Jq4jl1x6uemqc/Xx9fbTTxbTueddSNU13teUfDUwyfMm6T4t+XgRrV2zmsaJa7H9aFzSSFwHi2iPeJBX6Me78962unD8iFGp7UqR+E5q3qSYduyWkRaSa2oazunkeqdectOyEtpXXUM1IeNYqN4Pqbeofqfka0ojcU3Zm8A1he8Bbr/99voNsAB6Z1ysuvl8poFTWLHKbd8rlnu6idU09Ku+tYF9KGuExdJPrOazz9v2bqXXP59Jr1fOpJlfvEZbdm3MNKereGDR+3Qq7T2ezuk8nK4UDzeOF/1I+xGXWE17P9PUvpbNGicuVtPU33y3pWlZsbieHEylWM03myTqr09iNQk+cZdpUqzG3fZCLS+qWC3Ufuer3UmKVe4TfyfjyC8B42I1jQGWeAh0fFad+8EiwJK5SZyGAEtuveU9UGeteo3eXP0aceAkPto0aUsn9xxHJ/Y4lQ70OZ2eb32Y5dsqj85CrJ4lngSeIayWw30sxebo1q0JAZbM00eAJbPMEWDJLG8EWDLL2+QyYLM9S29tUZcBp7dn6WxZksuAucfYuib/4w6xmh0DL7GKaMD5n6T2FqRJrH6zewvNWvMazaoUL/Gb/+fjqE7H0hghUMdUjKOhHY6qBXCNWKry9yYl9JywEFdmIwlzAhau5wrRer4QrwNTJFwhVs3Pf4hVs8whVs3yhlg1yxti1Sxvrg1i1SxziFWzvPNRm3GxysuAx446iq67/Px89Ne1TqcPbdvWLXPRfjmD3z6rCLDU8AIsPT/zb1S5t5Jm7n2V2KLKR/umh9EYYUUd0/NUy5rasrTcc36//vKz1Lv/IPqyXz96R1haOTjTB8LnQh7HCLE6QiwTPkEsL+ff2SDDruUhwBICLIW5kG6v2kYvzZhOEydfHSZ7LHkQYCkYI6IBBzPKZ4oF89+xqh82/IR8NsO3bpNiNQ3ndBoGIqpYRTRgvVFMUqwiGrDeWCSV2rhYdW79klTHTJULsdowxOrXuzfRbLHMd9bq1+nA53tpY81X9J74Gd5lRMaKKgTq4MOGKk07Fqt9hFit6NXHSr9PqNF3SjKi9R3x+sgmXI8XYnUEi1YhYI9zCeIFsQqxqjTpHIkgVjNAEA04zOxRy4NowGqckk4FsZo04brlQ6yaZQ6xapZ3PmozLlbZZ9XvyFc04LDwIVbrt1h9f/279KYQqSxUF236lzVNzm/8HerYtgsN/faxNFoI1RalLbWmj1Os2jPvFMJ1nrC2smidJ0TrkqxwZU9XtrJawlX8Pjq7VBhiFWJVa/JlE0OsQqyGmTc6eSBWdWgllxZiNTm2XiVDrJplDrFqlnc+ajMuVvPRyaTrRIClpAkfKt+Ez+rGXV8JP9SZwg/1dcsfdcf+7VYDju86yhKnY3qeRgPb196yJwkC28SWA5ZotSyuxfRZ1se1VAQRPkGExc+I1wM0NEEfV/isJjGy/mXCZ9Usc/ismuUNn1WzvE2KVbM9S29tUcVqenuWzpYlKVa5xwiwlP9xh1iNYQwgVmOAqFhEkmL1vXVzhQX1dWFJnUlLvl5ktahzi66WH+qYHhl/1KYlzRRbGm8y3iHvbSFYnxXbbLwqgjOxBVYeHJBprBCto0VwprijCkOsxjuOKqVBrKpQii8NxGp8LFVKglhVoRRfGojV+FiqlgSxqkoqnnQQq/FwTHMpeRGr9oBFd//0CpowfiTx8uBjhw2gP99zc5p5ubYNYtXckMUtVjfsXGdtOWO9hD/qrv07rc6M6HoSnVxxmhCpp1H/dgPNdVChpg0ionDG4prxc10t/pdH/5oDdIwQrixa+Xf3iHu5QqwqDEjMSSBWYwYaUBzEqlneEKtmeUOsmuXNtUGsmmUOsWqWdz5qMy5WWai2a1tuiVKOwnvjlIstsXrfo8/Qky/MqhWFNx9AdOuEz2ph+qzyUt8H/3UvFX9UTf974GnaIH7KipvQuX0vpIv6f08s+T3Rcyq8N/dNat6inAYPPVp3uljp/XxWdQuc+eYrVNW9By0ZOpTeF/6tC23BmToJocqRhVm08u8jA5YLu/m/xiVWk4xqOv2xB+nMCROpZXkrXXyB6TkS4JXX3hSYLo4Ecl6NO2UUrdu8O44iPcuAz2oGDQIsJTfN4LOaHFudkk2KVUQDzoxMVLGKaMA6M5woSbGKaMB6Y5FUauNilS2o0++/jQYP6FVLrHKU4Ft/9QghwNJyWr7sYzr1jPNyY+68GV+88APauaOKjht5ci6N86baKajcbk6dosnrAjnt4Xtp0uQpVFpWlqvPK7CP30XWT1SoXpy5n9ffeAvtEnuSeh3PTJ9KJ409g9q171AnCS/vZZH63PKnqPpANU0RPwtbLaKzhlxA3+k3icrLggVPmsSqfRx4qfD7wtLKopVfH4i/q4TfKx9lws/VEq6WeK2xfjcT79kPiNW6MwpiNamvHqI03NhCrCY3vhCrybHVKRliVYdWPGkhVuPhqFoKxKoqqcJNZ1yssjX1v3/54zpiFZbVHtYs4psniFXvEyqMWN25fwfN/OJFmrlSvMTv/TX7qEXjljSu11k0bP2RdMa4C6lDxy7KZ3FaxaqzA58WC9Ga3cOVxWtlNkATpxskhWvW8tpFWGEhViFWlU+CGBJCrAZDTHJFQnDt0VJArEbjF1duiNW4SKqXA7GqziqOlBCrcVBMdxnGxeotv3iI5s5fbC33lcuAD+/ZhSZecxedc9oI+uXPrko3MZfWwWfV3JDp+Kx+uX1NRqSK19w1s6xGdmvZwxKp4751Fp3QbbS5hue5Jra6viuE6xsiONPrwtfVLlzZ6jpKWFvH7WNf1xrqXXPI5BrXMuA8d7+gqofPqtnhgs+qWd7wWTXL26RYNduz9NYWVaymt2fpbFmSYpV7jGjA+R9342KVuyyX/Nq7P+X759B1l5+ffyIhWgCxGgJayCwqYpWX+s5c+YIlUj/e9JFV06D2QzIitdfZRradCdk9Y9lWCCsrRxWeLYQrW19ZzMqjs7CyjhJ+rscLATueiqiitBFt2b7PWNsaekUQq2ZnAMSqWd4Qq2Z5Q6ya5c21QayaZQ6xapZ3PmrLi1jNR0eTrBNiNUm6tcv2E6tVe7fRIx/9kR4QPqm89JeP3m360dVDr6fv9J9oBVDCUZcA+7W+LgTpHCFc3xbCdaMtujCn7icMrSP2VtPI7L6u5Qcdzq6AGisBiNVYcQYWBrEaiCjWBBCrseIMLAxiNRBR7AkgVmNH6lsgxKpZ3vmozbhY/cENv6Z/LvikTiClQt26BtGA8x8NWEb2/dvS/yEWrBw0aXXHdXTxMZfS2IrTfc8rv2BMXhkLxWdV94LCPqvtunaj7YOH0EfZyMKLxO9VNvHKQnVoNb8O0BDx4t8cdTjoSNL3DtGAg+jX/RzRgDNMEGBJf+6o5oDPqiqpZNOZFKtp8ENPlqZa6VHFqmrASbXW1P9USYpVRANOx/wxLlbZT/Wis8fUWfKLAEsIsPTh/Hl01nkTfc8Me4ClhRs/pJdWPGu9VlV9YQVNOrP3eTR03UA68/SLXaMBOwuHWD1ExC3A0s6yYlrapITm7quxtsVhEbvJJl47CqHKgvWQeD1IrVwsrxCrwRd8bF0TzCjuFBCrcRM9VB7EanJsdUqGWNWhFU9aiNV4OKqWArGqSqpw0xkXq2xBvfunV1h7q9oPbF0DsaoqVkd8dww9/cn/WiKVgyjxdjNnCZF65uHn0+geY0lHgOqklfO1PltWO3fpRn0HHLKWOwMsfSmEqhSt/Jstr9szu+NYR4UIzlRLvNYcoFJheIVYDf6SgFgNZhR3CojVuIlCrCZHNFzJEKvhuEXJBbEahZ5+XohVfWaFlsO4WK1vllUecPismpn2762bS2+sfoGeWfY0bdixnlo3aUNnHc4i9Tw6sccpZhrRwGoJigbM/q7s58qvd4XPKwdush8dssGaRopgTcOFBZbFLA5/AvBZNTtD4LNqljd8Vs3yNilWzfYsvbVFFavp7Vk6W5akWOUeIxpw/sfduFjl5b4PPP48Tb//NmuvVT4Wf7LS2rqmUCMCQ6wmO5HfWTubXvp8hmVJ/Xr3JmrXtD2dcfgEOrv3+Q1q+5lkKbuXHiRWnbnWCMsrb5Ez1yNYE/u8DheBmgYK0Xpk1u+Vow/jOEQAYtXsbIBYNcsbYtUsb4hVs7y5NohVs8whVs3yzkdtxsUqd9Jt6xq3pcH5ABKmTojVMNSC88xZ/Q96WYjUFz9/lrbu+YbaNz2MvjPgQmvJ77AOJwQXgBSRCeiKVWeFbGl9WwjXuULAsr/rekekYU7PYpWDNbF4PVIEbzpK/G7IEYchViNPW60CIFa1cEVODLEaGaFWARCrWrhiSQyxGgtG5UIgVpVRFWzCvIjVgqXl0nBEA44/GvCbq2bmLKnb91VRh+adMst9hUhd/Mw8uv7GW2jX3hrPaaTjh6qTVlbYkH1Ww5670md1Z4+e9GlxI/EqomVCvPLfzqXD7OPaT/i69hPW1/7Z3/2EgO3qYYFFNGD9UUE04Awz+Kzqzx3VHAiwpEoq2XQmxSqiAWfGMqpYRTRgvXMiSbGKaMB6Y5FUaojViGQhVuMTq/946wX64LCF1nLf3dW7qFPzLtnASefR8C4jrJGyRwP2GjodAaqTFmI1/MniFWCJHzl8aonWIku4LhO/PxO/Vzl8X1sKAdtXCNf+QrT2tYnYw4SAhVjVHxeIVYhV/VmjlwNiVY9XUqkhVpMi610uxKpZ5hCrZnnno7a8iFUOsrRl63bX/i6ZPTUfHELXCbEaXaxWbvucHpz9X9RoTQ1NFT9lxU1o8uAr6IfDbqQOzTrWGhuI1dpT1W27mbCT2a2sqMuAZVt0ogHvFjGa7NbXz9gKKwTsBscS4rbC/7WfWDZ8yp/+QM0vuoT6N29pWWPdts4Jy4Tn25XX3hQ2u1Y+RAPWwhVLYlhWY8HoWgjEanJsdUqGWNWhFU9aiNV4OKqWArGqSqpw0xkXq+dediu1a1tOf77n5sKl5mg5fFbDDeXGXV/RPfPB5ITrAAAgAElEQVTvpr8vnUrVB6p9RaqsoXWLUtonIsv6LQMO1xrkciMQl1iNSpejDrPVVVphWbx+WlJEW8T79qOTsLSyYOVlxGyFlX83LaAYTvBZjTpb9PLDZ1WPV9TU8FmNSlAvv0mxqtey+ps6qlitv2SS6VmSYpVbjGjAyYybTqnGxarXPqs6jU5bWohVvRFZtnkJPbf8KXrus6doVdUXdFjTDnRu3wvp3D4X0rBOw30Lg1jVYx01dVrEqls/NglLq1w+LH1geQmxfd9XzteDBawQrv2FiLWWEvNv8X9JVDgJ5YdYTQisR7EQq2Z5Q6ya5Q2xapY31waxapY5xKpZ3vmoDWI1BuoQq2oQV1WtpBmfPmkJ1U+3fEItS8uFQL3AEqojup6kVAjEqhKm2BKlWay6dfJLS8BmrK5sfZVLiPfVNsBS76z11QriZPnBHqA+KdkDFmI1tumrVBDEqhKm2BJBrMaGUqkgiFUlTLEmgliNFWdgYRCrgYgKPoFxscrLgMeOOoquu/z8gofHHYDPqprP6t+WTKUNsz+nRw8+SlvFz9iK0+mm426nge2PtOaBavQ7+KzWPm3qo8+q7oUhKMBSZdbnNWeFFUKWBa19ZXCxqJStr7klxFkr7Gv3/ho+q7oDopg+DZFD4bOqOFghksFnNQS0BLKYFKtpOKcTQKhdZFSxqno/pN2wepohSbGKaMDpmDTGxSrvsfq7B56gt2fclw4CEVsBseovVj/auIB+/tYNtGDDfPq/4mdRp6X0w+NvoOO7nliLvOrFGWIVYtV5ygaJVbdTfKOwwC4QUYgXidcSIWbni31g2S/Wedxx5530/i0/z1li2SLbW1hhyxLwgUWApYgX4xDZIVZDQFPMArGqCCrhZBCrCQN2KR5i1SxziFWzvPNRm3Gxyj6rfgeiAS+n5cs+plPPOC+HyXkzvnjhB7RzRxUdN/LkXBpn1FLnXqBuW1W8/vKz1Kf/IKro1ccqx0swTnv4Xpo0eQqVlpXl6vOy6Mkyeo7sT08t+ws9+clfiPdKHdrxaDpv2zl0zvnfow5tO9eZAhCr4U5/WFYptq1r2AK7RFhcWcR+lBWyP7nrTrrj9tvrDA6L1gohWu3Lib8l3isXEYrDHhCrYcmFzwexGp5dUE6I1SBCZj6HWDXD2V4LxKpZ5hCrZnnnozbjYjUfnUy6TvisHiK8ec/X9JQQqE99+lda9vUS6ti8M13U/xK6oP93qXebfpGHAj6rkRFqFVBoPqtanVNIvEII2BVCwPLvpeI3C1r+f2ddI6xVWgcRzGlgVsQenrXC8vY6vM2O6gGfVVVS8aSDz2o8HFVLgc+qKql40pkUq/G0uPBLiSpWC5+A2R4kKVa5J4gGbHY83WqDWI1hDCBWMxCf/+xpS6S+uWqm9f93+k2iC/t/j0Z1P2QBjoobYjUqQb38DV2sutHifWBXNWpEXwjhukq8vhBLildlhewax16wMn9PIVy/deAAWb/Fq6cQtWyZrRC/Sx06FmJVb45GTQ2xGpWgXn6IVT1eUVNDrEYlqJ8fYlWfWZQcEKtR6BVG3ryIVfZbvfVXj9QidPdPr6AJ40cWBjVHKxu6WP1wwz+t5b5PLfsr7a3ZY/mjXtjvu3ThgEuoUVGjWMcUYjVWnIGFQawGIqqVgH1hP88GdLL/5vfdjuZCqLIPrAzsVCGE7LCWpdR8y27iz3AkTwBiNXnG9hogVs3yhlg1y5trg1g1yxxi1SzvfNRmXKze9+gz9MDjz9P0+2+jwQN6WX1e/MlKmnjNXTTl++cUXJTghhxgqWm7FvRe9TwhVP9KX2xbQT3Le9GkrpdQl2860XcuuKzOfPYLhAOf1XCnP3xW4/NZdRsBpy94uFEiK3gTLyVeInxhK4Vw5b8/FX/bLbHjZ86kra1a0XvHHWdVw0uHu1u+seK3sMCyVba7sM7K/8O2hfO5+bBHKS9M3jREDoXPapiRU8sDn1U1TkmnMilW03BOJ81TpfyoYlX1fkilLQ0hTZJiFdGA0zGDjIvVUROuo4vOHlNHlLKIffKFWQUXJbihitXHnvkjLdi9gJ76ZjqVNiqjiwZ8T/ilfo+6HehKH86fR2edNxFi1eMcdwa2inIpgFgtDLHqNcbs+8o+sOwLu2rOG7RZiNWFI0fQSiFUt7hEJ7aXI0UrLyfuJsQsLy/m3yxwg3xkIVYzJCFWo1x9/PNCrCbHVqdkiFUdWvGkhViNh6NqKRCrqqQKN51xscrRgN2W/MqlwYgGnO5owPPWzhF+qX+jfZ9sp0rx07ZnB+GXegmd0+cC6yzweyIIy2rmQgGxGu8FM8zWNaotiMuyqlKfMxrwemGB/VK81gohy79zL/H/WvH/dh8x20WIVn51FcK1K/+W/2ffK962lV6aMZ0mTr5apWmJpEmDFQZiNZGhtQqFWE2OrU7JEKs6tOJJC7EaD0fVUiBWVUkVbjrjYrXQLKtu/rU83HZR3RB8Viu3fS58Uv9mbUfz5fY11L/dQCt4EvultmvS3tgZAJ9VY6itiuCzapY316YaYImtsbyMuFJYZlm8csAnXmK8Rvx22zPW3pPOVoCnjKDlvztlf3M0Y/6fXw3lgM+q2ZGGz6pZ3ibFqtmepbe2qGI1vT1LZ8uSFKvyOzmdPW84rTIuVgvNZ5XF6u8eeMJ3eXJ9Fqv7a/bRkyLCL29H8/76d6lVk9YieFJGpA5qP8T4mQKxahY5xKpZ3jpi1a9lvISYRasUtBy1eI2IYMy+smyxVTnYT9YSrkLUdhDLkqWg5f+loC1RKSjlaSBWzQ4QxKpZ3hCrZnlzbRCrZplDrJrlnY/ajItV7mQhRQNuyGJ11qrXLUvqc8ufsubmmYdPsPxST/vWmfmYq1adEKtm0UOsmuUdl1j1a3W1+JBFLItWfrFVdn32/41C5PLfQf6ysny7JZYF7GFZgZsTuuL/spQbaSFWzc5xiFWzvCFWzfKGWDXPG2LVPHPTNeZFrJruZJT63IS1fQlwfQyw1OekIZYl9WmxFc2m3Rvp1qJbqfmI9nTBoO9R88YtLJxegX3gsxo82+CzGsxIJ0V99VnVYaCbNijA0l5hfJVidl1W1G7I/uZteORnKvWWC6usXG4sLbWdDohox19toG9mvkQjJ11mRTvOxwGf1eSow2c1ObY6JZsUq2nwQ9dhk1TaqJZVRAPWG5kkxSqiAeuNRVKpIVY1yf7ghl/T5i1V9NzUu62cLFZvv/1211Jmiq0oWononsdlt6JwSzRt2jQ66aSTqKKiwvp42bJl9NFHH9HFF1+cS37vvffSpZdeSq1bt7bee++992jbtm00bty4XBpnO5x1b926lbiu66+/PpfniSeeoCFDhlD//v2t95YuXyqs3jPo2SbP0gfrPqAuLbvQ5CGTqeX7LemG/3sDNWnSJJf3ueeeo549e9LQoUNrdauyspLmzJljtdd5OPth/9wvnz2dH2+Z7sEHH6Rzzz2XOnXqFDi6OmllYSrj6lexk3tgI30SeI1DmDLjLMtZv3Oeh2mfVx6/eRW1HpX5FrWOuOaVTjvcrgc6+WXaSvHHWvHakP39pe1/+Rlbct2OThs20ARxHXng6kyQJ34Mxt7v/OK/K2zvdcz+3U385qsgv/jsPnRFCtN69+ttuJKSyZXkeZNMiw+VunDhQlq1apV1La6vB3/X8cHf4TjEdUCc0/w9cnX2nAaTcARU74fClY5cOgRM3gPotKuhpTUmVqWvqtteqn6fpW1A5J6w0rpaXyyrH21cQP858zaq2NaDpoqfMT1PpTtG/if1btOPpj18L02aPIVKy8pywwHLajkNHnp0qOkJy2oobJ6ZYFnV5xlkWdUv0TuHtMRusllk2TK7ddNX1P/FF+ipq65S9qN11sI+s2ytLeeXMM6yBbeZsOTy8uQ24v/m4m/+vLn4m5co85Y+/Lc8YFmNc6RrlwXLanJsdUqGZVWHVjxpYVmNh6NqKbCsqpIq3HTGxOq5l91K7dqW05/vudmVltNimVakblvsFHKApZ37d9A9839Bj3z0R6o+UE3dy3taInV8r7NTOQTwWTU7LPBZNcuba1ONBmy+ZcnVuF8U/Q0LWLH8eKvwm91q+zv3vvVeNo34+xuR1m/7Hq/WthSClYVsayFeW4vfHYSPbrkIGtWi+gC1sd7LvJ/5PPM3v984ue43qJLhs2p2uE2KVbM9S29tUcVqenuWzpYlKVbld3I6e95wWmVMrHrtrypRp3WfVd5q5+0Z9+VmhJvoLlSx+vaaN+kns35Ea6pWUUmjErpiyLV003G3UVlx1MV1yZ1AEKvJsXUrGWLVLO+GKlbDUK4Rmeyilv9mAesUu1sbCSFsiVwWwZnPdQ+2xlrCNStw+e+MsHV7P/ueSNMkP664ut0zmh5i1Shuglg1y5trg1g1yxxi1SzvfNQGsRpAncXpikr2xMocxw4bUMc6XGhilS2ov3z3tpw1dUiHYfSbk/+bBrY/Mh9zUKtOiFUtXJETQ6xGRqhdQEO0rGpDipDBLlpZxFY3K6GvhGV1U82BrPjNil6HJZfFsc7BQjVjmWVhK/+ua7GV1ttWWUtui3oucCFWdWZR9LQQq9EZ6pYAsapLLFp6iNVo/AohtzGxyhbKG6dcTBPGj3TlorJFTBqBFprP6tAzR9G/vf4DWvL1IppUNIl69e1PV53yY8uy6hWBDj6rtWfee3PfpOYt4LOqcz6++Ox0Omr4COrctYdONqW08FlVwlQrkUmfVa/WpSFyqI7P6hohXncKcfuNsM6yH+5OKqIN4m9+b4v4f1P2b/bH3SaMt1UhLLjMiqMntxKClX1tR/zlMdp6wom0q0dPyw+3THxWKtLw33wcJkRwE8psD8Q+uXzwnrhp2C4IPqv652USOUyK1TSc00kw1C0zqlhFNGA94kmKVUQD1huLpFIbE6u3/OIhWvrZqlwUXWeHgnxakwIQtdxCEasbNn9Jzz/zV3q09M+0dvtqGt1jLJ2x93Q64aixVNGrj4UBYlVtNkCsqnGyp4JYDWYm59W4U0bRus27gzNESAGxmoGnI1bD4GbhulMIVw4utU2I16rslkC7xN8seLeI/1nsrhV+s5zOub/tZSKC+2wRabYyGy1epw0sWFm4ZkRtRsCysGWBa4nahMUvxKrOaCWXFmI1ObZeJUOsmmUOsWqWdz5qMyZWuXNsXeXD7gMq39+ydTvZ9y/NB4wwdRaCWH1//bs0fcFU6vRFO3q48SM0edCVNHnwlfTp3H9Rn/6DIFbHnkHt2ndQHn6IVWVUuYQQq8HMIFaDGcWdImmxGqa9LFhZuLKAXfH036j4+FFU0r2HFTGZlyJLSy6Xze/x1kC7WOiKv+3vhanbL4+u+N23ZBGVrllN3U870ypWWn+blhVT45JG1GTHvlRYgKNwWjD/HSv7sOEnRCkm0bwQq4nidS0cYtUsc4hVs7zzUZtRscodZAvr86/Nq9VXNz/QfMAIW2eafVYfW/wwTfv4IVq2eQkd1elYS6Re0O+7Ybua93zwWTU7BPBZNcuba4PPqlnmbVuW0q69NbRnn65Xqtl26tZmt9RaQjdrxWVrLh/5Fr/2/sgtiOR7ba0tiA6l6J5d4szvtBLWYt6qSB6dhKW4RFiM+eBAWLw9kTx4KXVx9l/eeE0un9ZlWcjpTYrVQuYUZ9ujitU429IQykpSrMrv5IbAMc19NC5W0wwjbNvSKFZZnE5b/BA99vHDVrcuGfgDIVSvKoggSn7jALEadpaGywexGo5blFwQq1Ho6eetr2JVn4R/jijil0uW1l/WykXCerxB/N6rH5g5tm5Zy6CzpbGgZWErD+d+vN1F8C15tBTJWDDLwy6k5Xt2H2J7g53lxtYZn4IgVk1Qrl0HxKpZ5hCrZnnnozaI1Riop02sPvvZE5ZInb9uHvVrN0As+73KWvrbqEhEACnwA2LV7ABCrJrlzbVBrJplDrFqlrdbNGAWrRttAal4STOLWz54mTNbgeXBvr/bbSJ3TfGh7zX2CebP5SEtyvy/m0+w2Z5718ZCma3L9sNL8FqWZZeI0VYZNhHNZRXz9USkLRcRr7ft5N2MMwfntwtu+b70bba3w2n1TguzNLcDYtXs6ECsmuWdj9ogViNST5PP6umTJ1oi9bElD9MJe0dQt8Mq6PRR59NxXUaSW0CV119+Fj6r06fSSfBZtc6COW+8Qp27dKO+Awbnzoq4xCp8VoMvNPBZDWYUd4o0+qza+5jkeRM3S2d5aQ+wxAGu9mYbzWKZg2DJQ/oN8//V2ajP8rOqbLAs/v+wuW9ZUZ9XjDqxVvftPsT2D+zlJs0/6fKdS665vnYbNtCY55+n9y6/MlT1USzPvHS8uUOsqzaijRDvYfO2dclb3qyUdu+rpv3Vhyzybm3hLa3c6t2ydjWtEP7Qw8+f5NmFKKxUuRRKuiTFKqIBp2MWQKxGHIc0idW3er5Lb66aSZ1bdKXLW15JR/c8no45epTVQ4hV94F+BmI1BwZite4c4S+qK6+9KeJVQi07xKoapzhTQazGSbN2WWkXq3H0PK4AS7wtkvNwCmj5uZfglT7I9nL2CiHNIryJCGq1W/hly8NpgZbv2y3R8j2nZduPWychVic89xw9cPXVceBtsGVUVFbS6DlzaOqllybCQG6PFaZw9hd3s+yrlOW1KkA5r22pvj0PB2xrxA+fPOIOOJfuq9Qn02z73S/p9ttv18mCtAkQgFiNCDXfYrVq7zYrgFKTdw/SHeLn5J7j6FLhm9pibVmtvUAhViFWg6Y6xCrEatAcifPzNOzJCLEa54hCrCZHM3zJSfmsskWZ9xO2H1WbNtLCf7xMvS75P6EaHMXybC0dD1VrJpI2R9kOc8jtp2qLJxHQrOYgeWirXFLes9mt3s6rKunbc96ilydP9mxSFFZh+tlQ89xx550QqykYfIjVGAYhXz6r/1z/Dj226GGasfxJallantuSplvLHjH0Kp1FwGfV7LjEtQzYbKsLuzb4rJodP/ismuXt5rNqtgUNq7akxGrDoqjX27T7rEYRunZ/cj0qGX9ytuqHOZy+6rUfDvhbVu1L93XrHiestT8QEeNx5JcAxGoM/E2L1QMHD1i+qY+L17LNS+mYzsdbW9Kc33diDL1JdxEQq2bHB2LVLG+uDWLVLHOIVbO8IVbN8oZYNcuba0u7WDVPJNkak/RZld/JyfYApQcRgFgNIqTwuUmxunTzYpq26CH6y5JHrZaxSJ088Eoa0H6QQksLPwnE6v9r716A5KrqPI7/Jz4gSiaYYCmEJa+JkmCokLAEIUFKwwKShZCyNGjhhodsxtrwLhFTQhVlWFiLgKY0CY84u6DGBzFEeSxmFU02mGggEiDuEiNIhsjykkkkgjizfe54Oz13uvve8+zbt78ztWUtc8//nPs5Z6bnl9vnTNg5JKyG9SashvcmrIY1J6yG9SashvUmrIb3JqyGNw/dI2HVUjzkntUHd98XPVF9626RcUPHy+Tpx0Vv/VUfyYNg4sNaJk85Nvo6e1arTzQHLO13Yc/q4DXCAUuWPyDrNGfParotpwGnGzXyClcHLPm8h5BhNQ/f0z4ts9a2fbK6u/v3smXzRpl9dvHfLZfVtN51PsMqpwG7mCH7GoRVS8MQYfWurq/JrjHPyzf+d4XsfWOPfObdnTJl+FSZc9qnyqMnrO6fSJ0AqnNt3EPyHwJ0l1DyTwbptq+8vlrANK1HWCWsmq4dk3Z5+MWWA5ZMZi5bG04Dzubk+yrCqm/hwfUJq2HNCathvRvRG2HVUt13WH225xm5+66VclvvbbLvLX+Wzx1/jZzYNkP+tLdHjp/xYcJqlfnTCaA61xJWzb9ZfD4hWvUfK+SMOfNkWPtw8wHWaMmTVeek5YKE1XRbn9836b3bXUFYtfNz1Zqw6koyex3CanYrF1cSVl0o5rsGYdXB/Pjas/rAzh/KZf91kag/T3PUIUfLzbNujf63lT/Ysxp29tmzGtZb9cYBS2HN2bMa1ps9q2G9Q4bVsHeW395sw2p+7yyfI/MZVuPX5HzeeeuMirDqYK5dh9X/+9Mf5I7Hvi53/Prrsu/N1+S8oxfIBUd/VsYe3OFgtM1dgrAadv4Iq2G9CavhvQmrYc0Jq2G9CathvVVvhNWw5oTVsN6N6I2w6kDdZVjdvbdbPvvgP8nm5zbKAW85UL500hL55FHzHYyyGCUIq2HnkbAa1puwGt6bsBrWnLAa1puwGtabsBrem7Aa3jx0j4RVS3GXe1Yf7v653HDvF6XjjfHyi+G/lFtP/2b0tt/knrxtW3/FntXX/1pz5nT2oepcG3fIAUv63zQ+996xZ1V/PqqdDq5fxa4Fe1bT/Xx+36T3bncFe1bt/Fy1DhlW8/A97crNpo7tk1VOA9bT9xlWOQ1Yby58XU1YtZR1FVZ/+sefyNU/u1g6ejvkI0NPkUs+/UV559sOikZHWN0/SeoHxyVXXC2vEVYjFE4DHvz9YfktPaA5Byy51BxYKw+/2HIasL/5Jaz6s9WpTFjV0XJzLWHVjWPWKoTVrFLNex1h1XLubMPqmrvvlB3DdsrSHTfJm71vyiVjr5RJvZNk9j/u//tahFXCaq1lSlglrJr8COPJar8aYdVk9WRrQ1jN5uT7KsKqb+HB9QmrYc0Jq2G9G9EbYdWBuume1R2v/I8se/QWWfXkv8vIoYfIgmMujf5vSNsQB6MqZgn2rIadV/ashvVWvXEacFhz9qyG9WbPaljvkGE17J3ltzfbsJrfO8vnyHyG1fg1OZ933jqjIqw6mGuTsPpw93pZXgqq656+X94/cqIsmHKpfHziuQ5GU+wShNWw80tYDetNWA3vTVgNa05YDetNWA3rrXojrIY1J6yG9W5Eb4RVB+q6YfVHO1ZHT1S3Pv8rOWHUh6Rz6qXy4dGnOhhJ8UsQVsPOMWE1rDdhNbw3YTWsOWE1rDdhNaw3YTW8N2E1vHnoHgmrluK6e1a7tq2Inqg+2/OMnDnhY3LyqzPlpBNPlUNHHRGNRO2heuo3j8spHz27PDL2rO6fJA5YGrhg2bPKnlWTH2HsWe1XY8+qyerJ1oY9q9mcfF8VMqzm4dA0355Z6ts+WeU04CzK+6/xGVY5DVhvLnxdTVi1lM0aVve+sUeWb/2KLNtys/z5r/vk/KM7S09UL5NHfrxBph13AmG1+/eyZfNGmX32/oOlqk0NYZWwmlwX/Oka/R9ihFXCqv6q0WtBWNXz8nU1YdWXbO26hNWw5oTVsN6N6I2waqmeJay2jxshyx65Re58/HYZ9vZ26SwdotQ57TJ5+5ADJPl39HiySljVWZI8WeXJqs56ia8lrBJWTdaNThvCqo6Wv2sJq/5sa1UmrIY1J6yG9W5Eb4RVB+r19qxu+cOmUlC9We7fuVbGDu+IQuqnJp3noNfWLMGe1bDzzp7VsN6qN04DDmvOntWw3uxZDesdMqyGvbP89mYbVvN7Z/kcmc+wGr8m5/POW2dUhFUHc10rrP7n734UBdVf7n5Y/v7QD0Zv+z117GwHPbZuCcJq2LknrIb1JqyG9yashjUnrIb1JqyG9Va9EVbDmhNWw3o3ojfCqgP1amH1ridWyvLSW39/9+oO+ej4s6K/nzrtvdMd9NbaJQirYeefsBrWm7Aa3puwGtacsBrWm7Aa1puwGt6bsBrePHSPhFVL8eSe1Td6X48OUVq29RY58fUTpOO9R8onT7lQRg8fV7Un9qz2s2Q9/Y4DlgYuI/assmfV5EcYe1b71TgN2GT1ZGvDntVsTr6vChlWOQ24fzZtn6xm/X3I99pplvo+wyqnAedjFRBWM8zDWfMXyY6nu6MrO8aMknu6FpdbVYbV7j3PRn+WZuVjy2ToW98hlx1ypRw/dqZMm3ZizV4Iq4TVDEuw5iWEVcKqyfohrBJWTdaNThvCqo6Wv2sJq/5sa1UmrIY1J6yG9W5Eb4TVFPXzL79RXnq5pxxQVXAdOaJdVi65KmoZh9UNz2yOgurap74vf9c+Onrb75GvTpB3HtQuk6ccS1gtCdT7EyNZ/yWRJ6sDlxJhlbBq8sJBWCWsmqwbnTaEVR0tf9cSVv3ZElbD21brkbCaj3nwOQrCaoruzDkL5YoFn5A5p82IrlzzwAa5afl3ZP2apeWWdz++VpZsWiIbd/1MprznWOmccqnMnjDX57y1bG32rIadevashvVWvXEacFhz9qyG9WbPaljvkGE17J3ltzfbJ6v5vbN8jsxnWI1fk/N5560zKsJqnbnetn2nzOu8TlYtu0YmT+zfc5r8b11bu+Tf/vvLsv3FJ2XWmNOjE3+PP6w/2PLhXoCw6t60XkXCalhvwmp4b8JqWHPCalhvwmpYb9UbYTWsOWE1rHcjeiOsWobVJTctkfNe4++mNmLx0icCCCCAAAIIIIAAAj4Ehn5oqBx40oE+SlNTQ4CwahlW1Z7Vi4dcXLXK+r71clDp85i2Y2r2srpvtRxX+jy87fDomt/2/VZ+U/o8o+2Mcpuu3i6ZO2SutJc+1cejfY/K3tLnzLaZ5Wu+2vvVAeNI9t0jPbK6d7XMHzK/3ObevnvlyNLn+Lbx0X/b1bdLNpc+57YNfAvzit4VUbsDSp/xx7q+dXJY6XNS26QB91arhrooeR+VDeu1q7wueZ/VYL/d+22ZNWSWvLv0mfahc21cK8u81us36Z42xnpfrzUPJjVd1kr2n1znJuOr1abeurLtJ8t6s+3D1brSGUe1nwc67V1c+4K8IOt618k5Q85xUc6oRrWft0aFPDXy+X3jacjlsk/2PSnPlT5ntc3y3VXD6m/q2xT1Pb2NP0unHPLwPd2wxeCw46y/DznsklI1BNTvANdeey0+DRYgrKZMQLU9q4tuuF2eeKgrapn80zWV5X6x4SccsFQBwgFL/Rg/vu8HMuHID8iYcROsv/05YIkDlkwWEQcs9avxp2tMVk+2NhywlM3J91Uh38CibUUAAA4SSURBVAbMn67pn03btwFnPXDS99pplvo+3wbMn67JxyogrKbMQ9bTgPfse3NQJcLqQBLCKmH10FFHOP/JV29d2XamXqg+8y+fsy2TqX388+LUj8yU517al6mN6UWEVcKq6drJ2o6wmlXK73WEVb++1aoTVsOaE1bDejeiN8JqBvV6f2dVNd/z2l+kWljNUJpLNAU4YEkTzPJyDliyBDRozmnABmgWTThgyQLPoCkHLBmgWTQJGVYthlmoprZhtVAYAW7GZ1hVw1evyXw0VoCw6sCfsOoAMWMJwmpGKEeXEVYdQWqUIaxqYDm4lLDqAFGjBGFVA8vBpYRVB4iaJQirmmCWlxNWLQGboDlh1cEkEVYdIGYsQVjNCOXoMsKqI0iNMoRVDSwHlxJWHSBqlCCsamA5uJSw6gBRswRhVRPM8nLCqiVgEzQnrFpOEgcsTR4gWO9gAPas9lNxwJLlN12iOXtW9T3Zs9pvxgFL+msnawv2rGaV8ntdyLDKAUv9c2kbVjlgSe97wmdY5YAlvbnwdTVh1VKWsEpY1V1ChFVdsfrXE1b1PQmrhFX9VaPXgrCq5+XrasKqL9nadQmrYc0Jq2G9G9EbYdVSnbBKWNVdQoRVXTHCqlux0qFwPa/KvWtWybxP/7Pr0pnr5eEpDE9WM0+X9oWEVW0yLw0Iq15Y6xYlrIY1J6yG9W5Eb4TVRqjTJwIIIIAAAggggAACCCCAQF0BwioLBAEEEEAAAQQQQAABBBBAIHcChNXcTQkDQgABBBBAAAEEEEAAAQQQIKyyBhBAAAEEEEAAAQQQQAABBHInQFi1mJKz5i+SHU93RxU6xoySe7oWW1SjaSyg47rmgQ2y6IbbB+E98VAXoA4Etm3fKfM6r5NVy66RyRPHOahICSWQ1ZX17W+9nH/5jbLpke0DOuDnhr23ritr3N68WoWrr79V1j64kfXtgVfXljXuYRISJeM54XcV/9aN6IGwaqiuXpBfermnHFBVwBo5ol1WLrnKsCLNlICuq3oRuGn5d2T9mqUAOhaYOWehvPzHPVFVXgDc4eq4sr7duScrqXmo/LmhftnZsHkbP0ssyXVdWeOW4DWaq99JvnTVBeV/ZFx6x2r57g9/yvp2wK1ryxp3gF6nhPL9xqr7o4dH/K7i17pR1QmrhvLqBfmKBZ+QOafNiCrww8gQMtFM1xV3N+61qmR9Auh3FMWrntWV9R1u7rPOSbgRFaOnNFfWeJh5TpuHMKMoZi9ptqxxv/N+1Mnzo5DKu8D8OjeyOmHVQL/aD6a0H1YG3bRcExPXam+v4a187pYO69qdZWWlrK6sbz/+1ary5MmPdZora9yPe7KqetfSUzt38WTVA3eaLWvcA/rfSqqn3OfNO13Gjz6MsOqPueGVCasGU2ASqgy6abkmLlyTbyNuOUTHN5w1VDnutvDlTF1Z336WRjwfiz9/YfndMn56aq2qJq6scbdrpHLbAf+Qmw9b1ribeVBbN55/8ZVo+53pa6qbkVDFtwBh1UDYRagy6LbwTVy4xjV4UXazXHgBcOOYrGLqyvp2Px+x6YJzz5SFF8x130GLVjR1ZY37WTDqCffyO9cKr43ufXVtWeP2c5B8a7Xpa6r9SKgQQoCwaqhcbW+lOpWWFwJD0L81s3WN327DPNjNQ9yaFwA3jq7CKuvb7XzEnhzKkR9X1rjbuaisFu/t42R398Y6tqxxe/9aJyyryvzDo71v3ioQVg1nRPfUWsNuWq5Zmqvan6A+4j8TlDx5klOZ3S4Zwqpbz7R/BGB9+/GuVpVDT/xYp7myxv24J6vqnsocZlTF6CXNljUefp75XSW8ecgeCasW2jp/D9Sim5ZrWs81+SJQea2Cmj51In8+yNGKqdzrpEqOOHgYh3M4sK3nyvp2AJyhRPyLTbVL2beaAbDGJVlcWePmvjotk6+Nqi3vONIRrH1tmi1r3I2zThXCqo5W811LWG2+OWPECCCAAAIIIIAAAggggEDhBQirhZ9ibhABBBBAAAEEEEAAAQQQaD4BwmrzzRkjRgABBBBAAAEEEEAAAQQKL0BYLfwUc4MIIIAAAggggAACCCCAQPMJEFabb84YMQIIIIAAAggggAACCCBQeAHCauGnmBtEAAEEEEAAAQQQQAABBJpPgLDafHPGiBFAAAEEEEAAAQQQQACBwgsQVgs/xdwgAggggAACCCCAAAIIINB8AoTV5pszRowAAggggAACCCCAAAIIFF6AsFr4KeYGEUAAAQQQQAABBBBAAIHmEyCsNt+cMWIEEEAAAQQQQAABBBBAoPAChNXCTzE3iAACCCCAAAIIIIAAAgg0nwBhtfnmjBEjgAACCCCAAAIIIIAAAoUXIKwWfoq5QQQQQAABBBBAAAEEEECg+QQIq803Z4wYAQQQQAABBBBAAAEEECi8AGG18FPMDSKAAAIIIIAAAggggAACzSdAWG2+OWPECCCAAAIIIIAAAggggEDhBQirhZ9ibhABBBBAAAEEEEAAAQQQaD4BwmrzzRkjRgABBBBAAAEEEEAAAQQKL0BYLfwUc4MIIIBA/gSW3rFalt+5dtDAFpx7piy8YK7MnLMw+tr6NUsHXaO+NuLgdrmna3H0tbRaR508vy7AiIOHRf2cf/mNsumR7VWvXfz5C2XOaTPkrPmLZMfT3RL///HFax7YIItuuF06xowqjytZKMs4Zhw3WdY+uLHc9Mx/OEH+9QsXafWb5T7ytyIYEQIIIIAAAoMFCKusCgQQQACBoAJxmFq17BqZPHFcuW8VOtet31IOeyrcTZ86UVYuuap8zdXX3yobNm8rh9istZKhMhk21ddVrZde7qkZNtU1cVhNjiv+7/XCaiVyHG6rjaPa13T6zXIfQSeczhBAAAEEEDAUIKwawtEMAQQQQMBMQIXQ+IlhvQrJ0LZt+06Z13ndgKeaWWu5DKsjR7RHT2DjsB2PSwXYtLCbZRy1wmrWfgmrZuuSVggggAAC+RMgrOZvThgRAgggUGgB9TbeCeMOH/DEtNYNq+D11M5d0ZNU9XRRBbbKJ606tVQf9Z5oZgl5agyT3jdann/xFXnPIe+K3qKrnvaqD/XffIbVrP1muY9CLzBuDgEEEECgMAKE1cJMJTeCAAIINIdAHBjj0cZ7RmuNvnKv5xMPdQ24TLdWWljNsmdVhcbpUydFe1TVeNT41FPWm2/7nvewmqVf9qw2x/cBo0QAAQQQSBcgrKYbcQUCCCCAgCeB+C20cflqbw+OA2Z8+FKtoejUstmzqsJqfOiRGkv8tFfniabJntWs/eqMw9O0UhYBBBBAAAEnAoRVJ4wUQQABBBCwFVBvp1Un4Safnlbbq5rWV61aaU9W097GG78NWIXV+BTiOPjqhESbsJrWr8440hz5OgIIIIAAAo0UIKw2Up++EUAAgRYTUMHzWz9YFz2ZTH7EISx5SnCtsGpSy2VYVeNXe2bjP6+jExJtwmpavzrjaLHlx+0igAACCDSZAGG1ySaM4SKAAALNLFD5Vt3KJ6iVJ+pWHqCk7rVeWFWnA6uPrLVch9XKudAJibZhtV6/OuNo5rXE2BFAAAEEii9AWC3+HHOHCCCAQO4EKg9NigdXa09q2tuAdWqlhdWsByxVezKsExJrjSN++3JsEu/hrXz7cXIyk/1ywFLuljsDQgABBBAwFCCsGsLRDAEEEEAAAQQQQAABBBBAwJ8AYdWfLZURQAABBBBAAAEEEEAAAQQMBQirhnA0QwABBBBAAAEEEEAAAQQQ8CdAWPVnS2UEEEAAAQQQQAABBBBAAAFDAcKqIRzNEEAAAQQQQAABBBBAAAEE/AkQVv3ZUhkBBBBAAAEEEEAAAQQQQMBQgLBqCEczBBBAAAEEEEAAAQQQQAABfwKEVX+2VEYAAQQQQAABBBBAAAEEEDAUIKwawtEMAQQQQAABBBBAAAEEEEDAnwBh1Z8tlRFAAAEEEEAAAQQQQAABBAwFCKuGcDRDAAEEEEAAAQQQQAABBBDwJ0BY9WdLZQQQQAABBBBAAAEEEEAAAUMBwqohHM0QQAABBBBAAAEEEEAAAQT8CRBW/dlSGQEEEEAAAQQQQAABBBBAwFCAsGoIRzMEEEAAAQQQQAABBBBAAAF/AoRVf7ZURgABBBBAAAEEEEAAAQQQMBQgrBrC0QwBBBBAAAEEEEAAAQQQQMCfAGHVny2VEUAAAQQQQAABBBBAAAEEDAUIq4ZwNEMAAQQQQAABBBBAAAEEEPAnQFj1Z0tlBBBAAAEEEEAAAQQQQAABQwHCqiEczRBAAAEEEEAAAQQQQAABBPwJEFb92VIZAQQQQAABBBBAAAEEEEDAUICwaghHMwQQQAABBBBAAAEEEEAAAX8ChFV/tlRGAAEEEEAAAQQQQAABBBAwFCCsGsLRDAEEEEAAAQQQQAABBBBAwJ8AYdWfLZURQAABBBBAAAEEEEAAAQQMBQirhnA0QwABBBBAAAEEEEAAAQQQ8CdAWPVnS2UEEEAAAQQQQAABBBBAAAFDAcKqIRzNEEAAAQQQQAABBBBAAAEE/AkQVv3ZUhkBBBBAAAEEEEAAAQQQQMBQgLBqCEczBBBAAAEEEEAAAQQQQAABfwKEVX+2VEYAAQQQQAABBBBAAAEEEDAUIKwawtEMAQQQQAABBBBAAAEEEEDAnwBh1Z8tlRFAAAEEEEAAAQQQQAABBAwFCKuGcDRDAAEEEEAAAQQQQAABBBDwJ0BY9WdLZQQQQAABBBBAAAEEEEAAAUMBwqohHM0QQAABBBBAAAEEEEAAAQT8CRBW/dlSGQEEEEAAAQQQQAABBBBAwFDg/wGqS76jWpUojQAAAABJRU5ErkJggg==",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With ZERO enzyme\")"
]
},
{
"cell_type": "markdown",
"id": "9a793ebf-f544-43ad-a1d3-059f74f3c02b",
"metadata": {},
"source": [
"### The reactions, lacking enzyme, are proceeding slowly towards equilibrium, just like the reaction that was discussed in part 1 of the experiment \"enzyme_1\""
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "7b253509-903b-4c1a-8771-cd283e7fbf4c",
"metadata": {},
"outputs": [],
"source": [
"# To save up snapshots of crossover times at various Enzyme concentrations\n",
"crossover_points = MovieTabular(parameter_name=\"Enzyme concentration\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "4677fcaa-e90b-4975-a567-cb55b66f91f2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.7435259497128707, 9.999999999999996)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=1.0)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "d684e2c3-c717-4c95-8852-62729914e48f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: S <-> P\n",
"Final concentrations: [S] = 3.372 ; [P] = 16.63\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.93068\n",
" Formula used: [P] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 5.00001\n",
"Discrepancy between the two values: 1.387 %\n",
"Reaction IS in equilibrium (within 2% tolerance)\n",
"\n",
"1: S + E <-> P + E\n",
"Final concentrations: [S] = 3.372 ; [E] = 0 ; [P] = 16.63\n",
"Reaction IS in equilibrium because it can't proceed in either direction due to zero concentrations in both some reactants and products!\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(tolerance=2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "15085e98-f3cd-4c99-95cc-4db5c2e99e40",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "cf52d120-927e-44bb-893d-1673e9fd8bd6",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "27401e5d-8f3e-4c27-8438-129d3e3408a2",
"metadata": {},
"source": [
"# 2. Re-start all the reactions from the same initial concentrations - except for now having a tiny amount of enzyme (two orders of magnitude less than the starting [S])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "3d00754a-1fcf-4296-8fd5-4240f6590ec7",
"metadata": {},
"outputs": [],
"source": [
"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\") # A brand-new simulation"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "373ce459-3b57-4ab2-a136-4eb8bedcdd91",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"E\": 0.2},\n",
" snapshot=True) # A tiny bit of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 0.2\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system (now with a tiny amount of enzyme) to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "dde62826-d170-4b39-b027-c0d56fb21387",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"33 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 19, 'norm_B': 19, 'norm_C': 18, 'norm_D': 18}\n"
]
}
],
"source": [
"dynamics.single_compartment_react(duration=1.5, \n",
" initial_step=0.05, variable_steps=True)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "b0543cac-f3cd-453c-ae9b-c00f01e61fa8",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With a tiny amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "e4632751-75db-40d8-95ee-6ddede100b41",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.24710707675961718, 10.0)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "3171fd78-a103-4523-8c43-6e29695f49d2",
"metadata": {},
"source": [
"## Notice how even a tiny amount of enzyme (1/100 of the initial [S]) makes a very pronounced difference!"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: S <-> P\n",
"Final concentrations: [S] = 3.34 ; [P] = 16.66\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.98745\n",
" Formula used: [P] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 5.00001\n",
"Discrepancy between the two values: 0.2511 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"1: S + E <-> P + E\n",
"Final concentrations: [S] = 3.34 ; [E] = 0.2 ; [P] = 16.66\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.98745\n",
" Formula used: ([P][E]) / ([S][E])\n",
"2. Ratio of forward/reverse reaction rates: 5.00001\n",
"Discrepancy between the two values: 0.2511 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "07ae53db-dbe3-4389-a77b-fdffe77a2c47",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "b116cbea-f62a-4072-9255-24e109f894a2",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "fe1c77c1-0e3e-4f6a-b774-d86398cde6aa",
"metadata": {},
"source": [
"# 3. Re-start all the reactions from the same initial concentrations - except for now having a more substantial amount of enzyme"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "7c3d57f9-00cc-4377-ad12-a3d9af0fac18",
"metadata": {},
"outputs": [],
"source": [
"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\") # A brand-new simulation"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "61deddc2-1435-4261-8e40-66043b73365e",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"E\": 1.},\n",
" snapshot=True) # A more substantial amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "b4377e1a-8c8e-41a3-8087-2f4d617a2c2e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "4c4616a5-4cd6-44b9-82bf-2e46689f512b",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system (now with a more substantial amount of enzyme) to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "a4dd3c4e-06b3-4823-9c62-7528460f7d4a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"39 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 2\n",
"Norm usage: {'norm_A': 24, 'norm_B': 23, 'norm_C': 22, 'norm_D': 22}\n"
]
}
],
"source": [
"dynamics.single_compartment_react(duration=0.5, \n",
" initial_step=0.02, variable_steps=True)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "12ed7017-11b0-460d-8c53-34dd3962d9a7",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "50c6521a-7c67-437d-9666-fef5782cf4ef",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=S
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "S",
"line": {
"color": "cyan",
"dash": "solid"
},
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With a more substantial amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "11d21c1a-bf34-4572-a5ff-d360617380c0",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.06769827987210066, 10.0)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "f01eaeb0-e3e6-40fc-9e3e-c79a9fe54285",
"metadata": {},
"source": [
"## Notice the continued - and substantial - speedup of the reaction, over the earlier runs"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "aa2f5b84-0a08-42e1-8b26-0b953806a900",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5e6c18d4",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "90c86d7d-cff3-40dd-829f-083a3fc71f85",
"metadata": {},
"source": [
"# 4. Re-start all the reactions from the same initial concentrations - except for now having a good amount of enzyme"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "4d585598-f502-409d-be2c-992808f3177e",
"metadata": {},
"outputs": [],
"source": [
"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\") # A brand-new simulation"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "d505b176-3c55-494a-8e72-74dff8a741db",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"E\": 5.},\n",
" snapshot=True) # A good amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "db20d234-bd14-4df4-b803-ae8d47ff1093",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 5.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "45a4f23a-e9c3-423d-b2bb-f9e48464dcc7",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "99099e14-885d-4a75-a3f5-0dc69709a608",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"36 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 2\n",
"Norm usage: {'norm_A': 24, 'norm_B': 21, 'norm_C': 21, 'norm_D': 21}\n"
]
}
],
"source": [
"dynamics.single_compartment_react(duration=0.2, \n",
" initial_step=0.01, variable_steps=True)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "cc595321-b1d5-4188-a47c-bce6e6b682e2",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "02d64d04-0373-4235-b2dc-44bc24b549fe",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=S
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "S",
"line": {
"color": "cyan",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "S",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
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0.0024000000000000002,
0.0032,
0.004,
0.0048000000000000004,
0.005600000000000001,
0.006400000000000001,
0.0072000000000000015,
0.008000000000000002,
0.008800000000000002,
0.009760000000000003,
0.010912000000000003,
0.012064000000000004,
0.013446400000000004,
0.015105280000000004,
0.017095936000000003,
0.019086592000000003,
0.021475379200000002,
0.0238641664,
0.0262529536,
0.02911949824,
0.03198604288,
0.035425896448000004,
0.038865750016000004,
0.04299357429760001,
0.047946963435520004,
0.053891030401024005,
0.061023910759628805,
0.06958336718995456,
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With a good amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "193fcaa3-b936-4221-bedc-d4c0e516b1ac",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.014494267066104415, 10.000000000000002)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "9c8cc734-7144-4a60-bdfe-a1e707a8899d",
"metadata": {},
"source": [
"## Notice the continued - and substantial - speedup of the reaction, over the earlier runs"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "8bc8ff02-307d-4842-a34a-58b458850264",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5b82371b-1364-4d3f-89cd-820333200c7f",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "ff8b0763-358c-4765-a134-274a843b959a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "711d3422-71b5-42dc-a121-5c4fba686ea3",
"metadata": {},
"source": [
"# 5. Re-start all the reactions from the same initial concentrations - except for now having a lot of enzyme (same as the initial [S])"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "bbae7051-3d61-45ea-b4be-a79dad90342a",
"metadata": {},
"outputs": [],
"source": [
"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\") # A brand-new simulation"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "a1abec42-c74c-4adf-8580-914df5188021",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"E\": 20.},\n",
" snapshot=True) # A lot of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "52260372-0585-4c38-abf8-c4764cb45368",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 20.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
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"### Re-take the new system (now with a lot of enzyme) to equilibrium"
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"id": "29c08e79-d275-41b1-a2a0-c4db6521dfe7",
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"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"39 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 3\n",
"Norm usage: {'norm_A': 27, 'norm_B': 23, 'norm_C': 23, 'norm_D': 23}\n"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With a lot of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "e0869320-aee5-4273-a6e3-dd46d173d80d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.003687634618431487, 9.999999999999996)"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "ae56f399-c58b-4c2c-b994-5ef3e7d498ac",
"metadata": {},
"source": [
"## Notice the continued - and substantial - speedup of the reaction, over the earlier runs"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "6594d68a-ff8b-428c-b42f-f1b5fa22b5d2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f55639f8-4e01-4ce8-ad48-cc9fe8a71c4f",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "5f165e29-6c26-47f7-9f0c-143305a11c67",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "3a3c7ae9-3a86-4afa-8e2a-17a2cb8e5b6c",
"metadata": {},
"source": [
"# 6. Re-start all the reactions from the same initial concentrations - except for now having a very large amount of enzyme (more than the initial substrate concentration [S])"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "cce1bc79-60e5-459d-842e-f5f722d0f637",
"metadata": {},
"outputs": [],
"source": [
"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\") # A brand-new simulation"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "84b38ef9-cdbd-4169-b76c-58ca3557371c",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"E\": 30.},\n",
" snapshot=True) # A very large amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "5ba56162-8c48-47b4-b105-5fe2376d1797",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 30.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "74d8f3bc-49c7-4d39-a04d-95400f5d819f",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "a99f0ac6-14e7-4138-86f4-3873d6bf2bb9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"36 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With a very large amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "1fde8290-ac8a-4d02-80c3-14a5ee801b5a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.002465868124424963, 10.0)"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "d69fe48c-8f70-43ad-9cdf-4c2530bd6c49",
"metadata": {},
"source": [
"## Yet more speedup of the reaction, over the previous run"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "b49cc4ba-b349-43c1-9e0d-9b5969653d88",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a566fe13-4b57-40f5-ac0d-15f240f14196",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "50b3aa69-81a6-4cfb-8de6-a88d4e64470a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "e998b386-e0ae-4342-a18b-493fc80695b9",
"metadata": {},
"source": [
"# 7. Finally, re-start all the reactions from the same initial concentrations - except for now having a huge amount of enzyme (far more than the initial [S])"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "7979df61-ab06-4a86-ae67-62a12561e4bd",
"metadata": {},
"outputs": [],
"source": [
"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\") # A brand-new simulation"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "9fa2865e-ccf0-4f3f-8f63-3c54692c541f",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"E\": 100.},\n",
" snapshot=True) # A lavish amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "f430f845-821d-4e35-b015-cb3e09012d7d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 100.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "2ffda9ba-42c0-40fa-bd3f-fabb689a43f6",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "9bdb8454-4e1d-4a04-ae00-c178a0a799b7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"40 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 2\n",
"Norm usage: {'norm_A': 28, 'norm_B': 25, 'norm_C': 25, 'norm_D': 25}\n"
]
}
],
"source": [
"dynamics.single_compartment_react(duration=0.02, \n",
" initial_step=0.0005, variable_steps=True)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"id": "a30fa6b8-d788-43bf-8203-0fe90ab853cf",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "5bcb8653-ebf6-41da-9b68-298931d91359",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=S
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "S",
"line": {
"color": "cyan",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "S",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
0,
8e-05,
0.00012000000000000002,
0.00016,
0.0002,
0.00024,
0.00028000000000000003,
0.00032,
0.00036,
0.0004,
0.00044,
0.00048800000000000004,
0.0005456,
0.0006032,
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0.0016192087039999996,
0.0017912013823999995,
0.0019631940607999993,
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0.0030711020979814394,
0.003499074919497727,
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0.005368460203880872,
0.006255904646577046,
0.0073208379778124544,
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0.010132261972273935,
0.011972466768648722,
0.014180712524298466,
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"xaxis": "x",
"y": [
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With a huge amount of enzyme\")"
]
},
{
"cell_type": "code",
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"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
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"source": [
"## Yet more speedup of the reaction, over the previous run"
]
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"id": "d73a6b89-2b43-4ca2-b8fd-56d04c39de5c",
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"True"
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"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
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"execution_count": null,
"id": "20ed8cfd-4bed-43ef-abc2-3c8c2490c889",
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"source": []
},
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"source": [
"# 8. Finally, re-start all the reactions from the same initial concentrations - except for now having a LAVISH amount of enzyme (two orders of magnitude more than the starting substrate concentration [S])"
]
},
{
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"source": [
"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\") # A brand-new simulation"
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"dynamics.set_conc(conc={\"S\": 20., \"E\": 2000.},\n",
" snapshot=True) # A lavish amount of enzyme `E`"
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},
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"execution_count": 61,
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"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 2000.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'P', 'S'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
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"dynamics.describe_state()"
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"### Re-take the new system (now with a lavish amount of enzyme) to equilibrium"
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"name": "stdout",
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"text": [
"48 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 33, 'norm_B': 33, 'norm_C': 32, 'norm_D': 32}\n"
]
}
],
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"dynamics.single_compartment_react(duration=0.0015, \n",
" initial_step=0.000005, variable_steps=True)"
]
},
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"cell_type": "code",
"execution_count": 63,
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"source": [
"#dynamics.explain_time_advance()"
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CIAACIAACIAAC6UcAspp+bYYSgwAIgAAIgAAIgAAIgAAIgEDGE4CsZnwTo4IgAAIgAAIgAAIgAAIgAAIgkH4EIKvp12YoMQg0agJrPt1I5192a4LB3IdvpZ5dOzVqHn4qn6m7EpuvB/rByYPonpsv94MGeUDAlYC5C7lItGbZLNACARAAARBgJtDoZNW8mcGXDHPPQvhGQcA8n8zKpvK8EsIFKfHfzU45/xpq16YV/fWBm/wHYc7p53ptvooGDzKYG6cRhzcfmE0aP5J+eXmpLxJ46OYLW6SZwmj3SCsQ8cE5v7PNh0jXXXEBTTjvDNaaznn6Zbr7wSfpD7+5gk4/aYDrseL8PZtOD60zSlZ/9LPbadVHG5I6jrgZWzJ3Wv3P/Nz8sPb6CIObN3WpOLkjrCbroXUuWn4K4nbjLS6CX2/bGdnTfbNsqRRUK0Pzy8nrC8O8IFvzZto7Nc22sPcxN5k3b7zifP77vV6L7wLxcRNxJ2Ze/cnPeaySx/7gR6ctVeLHJY15zbSXJ6pz0jpS6sRIdo0z6+H3oYjs+u0mQ+n6fZ1KieDu45kmq6nuU5BVIvN8iMuDdtOborqPUz1nM0JWzS8Nu5gKCOYXgnkD4vfmRxVoOqVL9YUqndiolrUxy6o4t47r1SW20y3NtrF/KZhfFrLrhWq7W9OZ1xjdm1bzS0I3n6yM5rlsFS3zxiqsevphEzQP1/Xaqc3MNvEr8CLuyBEDfY22mXUNoz84cTfrpyvkZtl088nKYZ6XdsbmQyU/N02i/7+0dGXSg2nVvmdeD4KMkqoey0zn9L0BWdUlmdr0kNVgvCGr8ZNVs0/HRZ6deljay6oKaPFFdmyP7yaG67lufoKdwsidrgSilNWomYkvnlTe4OnWV5TPbbRGXAuCrGu0zuTwc4Mt6mONEURSZLIq4pv9M87t5NauHNdrJ1ZmOYS8iBkLfqaSxVVWraO2fvuZNUYQaXWS1SAjDukmq05TAzNNhsQ5hZFV3W+uzE0PWY1n26bD0pm0l1Xdp9HWmx/79ED7DadsWrHoarJ04ubmvtuvqt/4RaRzGtGwTz8TN9Ri+rLsyYa9DLI0smlVKiMDMtESx9Opi9OpJyuTvez2aW8ysTC/1CcaaxCuvuXB+sM5SYhsap/9Rt3ruNYbBnHAWU+9VH9cayyn6WxmGmtfM0dyRCBxo/fK8ndp8ev/aIDPeiPpNE3RbFuzrazT3EVAr/qZkuS3na1rrawVsPY5nTKI8lvPRb8303aYXF+MYUiqvaxBpdVJwFQe5ul+fapOn7VeX2Yba3ysSzRksiPrV+IaGvZUd84v5rjJahiSau8fQaXVSVbFcbweMDn11XSSVSd5c7qumt91bt/X4tor+360f0c5jZ7Yz2md2RiycpvHcZpibS+H9ftRtLH9O1v3WmKPp1Mf+32h9V5D9d7A2k+96iZ7IOfUR6zfaX7KYj9/OO8BZX1KXMutbe/UP2QPV2VpremszD5c91nS/ZXT/bBX25i8ZP1J1EXloZ39wZTsgZT1O+mqm+5LfOeZH9n9kOyck5VF5jCyB+vp8JAs7WVVdATxsd+wO32pWb9orY0me9IpGvoMYzTW+oRdNr/b/Jn9gii7WZbJtdMTZZFfFtN68ZTdpKoKvNOFStxUqtTFi7H1JBMngzgJzXaStZvTz8SJ6/SFYd3cQtY2gq24UTbXrsnWCdmPa70QyOTUelFwG1l1u1EUv2t7eMuk6YKydnO7sZbJqipXnT7r1M5OMqhbBhHf78ikm2jZlwDoSpmbUHKU13yIYEqdzjFSLatbv/lP0qi07PjWG2XrOeN2c2a/SeFYT2OWi2ONZFxklUNS3aRV5wFTY5dVt7X+bjeNbt/Xsu9H0V4635vWNlQ972RTqO3t6zayatZXVk6r1HhdS6xltz/wUH1gJ0tnr5/OvYEsnuxnsnY1z18rFztHnbI4ffel+h5Q7OJvl1WxUZH1/l2lT4n62L9zrDJrlVPZPZRqv3N6gOY1O8f+sMK6kaGbrIp89vNQ3P9a+chmS8muqbL7MLeHgXHeCEpwSXtZ1X0S6zStTPVpu2xTF68RLvOm0+2ibb/xdyqn/fhOxxadt/+x33N9rYfbUzWn0TqvG2iVKT8663WcTiB7vVWm4zq1sX2jGbcbBns7qciqFzPzwmYvh/WCLLsZVGUgq49qn3UTPJms6rStUxmCSqWdpz2e7pRY6xNi1bYMWgenhwlOcZ2+PHW+VIOW2T4t3KkvyK4RTuc5xzRgUU+nzYyCtm8YsurUDipriqw39ToCGaTtnR4Ae90g20c73CTWq3xhjKy6HSNov7DGFrz+9dF66QN2P7Jqv5kVx3I6n+w/d/v+Ulnm4fad+t4HnyQe9LvdE7jdvwiJMfuwVzntI7mykTRRVredm92OYebVuTdwunbZjyOLabaTeHBp9j0zn8lEpyxe56L1YWLQewOd+1ynctk3yHO7HxYxxBI/rxkL1u991X6n2oZu1w7dkVXrq/hkfdJpkMB6XXHrG07ngdt1yev6m4rfQ1a/pex00bVPozEbxXoxVD253YTY3gG91rSYx5c9gVPtOByyqiL9bjeg9nqryqrKTa2bHFm/mHW+BILIqsoUGJ2RVR2uqn1WV1bDKINq/9VJJ5sOo3Lzb31gIP5f9aZVNlVWZyQvDFk1+5fOcVWZOk1ZlI2G2KcnOY0QyB4iqJzXqmWWpXM6B1VEz2k6tOw4KvFUZ8S41dePrMq+43SmTYYhq2Z/UjmuU9+TcVF5MJXqDZbsN+LWcoclq07Xd/vPva7XXhvoWfuO07XRj7zYH8q7fc9a62TtGypTNK3srdcCp/NV597A6x7OLk+iLGIGmFkOwVPcl1jv9bZs21E/S0ynLKmUVZ37XLNc9mm24ufWa4EZ0+36oCOrTsJn73dObagyOGKtm+rIqr3f2Y/jdi7ZZ2yY09lVlgSKskJWg9xJKOSVTZV1y6Yzsip7B5Gss6je+Lt9MdhPHvu6CXudrBc62SiBypc0h6yq3Fy6SaN96oKqrKqM0skuiFau5o22zpeAX1k1y2K9kLhND1EZWdXhqtpndWU1jDIonPaBk5gyqHNDYxVeVWnVLajfYziJk+oXlU45zTLarzGqsw7s11C3L2CV64lO2b3SBhX8MEZWVcTWqx7pMA3Y7TvNq37234cxsqrynalbLln6OMmq7CGetcwqD7pkDzvcpq+a8VUeOpjXL1VZFbGd4qpcs2UPr6yCpHNv4CREsqnAVtEQ5674iM3/xP+bgmq/tuiUJZWyqnOfa9bb3s9k9xGy7zjZ+lf7d56dk06/c2rDqGTVafDM2r72KfH2tnf6foGshnF1d4mh+zRaVVZ1prCp3vjrnMTiwuT1VNMJi+paPQ5ZjfvIqmDm9u5F65ed7OZF9YZcxHGbuiI2w/C6qIoYGFnluYAEmXLoVyjdamKN6UdWUjXdV+cGSfUaGidZFW0kW+uj2gvjIqtmeTmk1RpT52GPWaYg555TO6STrKZiGrDOyKrTlGTVPm9PZ/YP8/vTa2RV5SGBmxx4rbUz86qIt70u5nXVz4NsnZFV64iemP4sNpQUU6itU3/Fek/Zq8lU7lPiKquqgxGy8pvfmeZ9lO7Iqkq/i5usypYhqp6nZl6n0WnIqipJn+lUnoSLE140kNura+xS4CQJQUZWVddduImO7IvB/voNlXWjIg6HrHpNUxBrRpw4uK3dsAum/ctYZb2JikjryqrbxUN3vYOs/vZ1Ktb2V2XQGNesijovWvKO4xol1b6gKpgqT+3dvnDF7/xIqhkzVbLqdePpZxqwqIPbOhyxa7ZfvjLm4rx0e2VRkF2k4yarYUprUEmFrB4iYJ+uZ++jTmtFdb6vVWVVZ4RI51yS7Vorm+WhMiPK6V5F9l1tvddz+66U1UW0y6hTBjfY58MqVDoP63S//839V6zrVM1ro/nGCOt1UKcsqZRVnftcp2utbLq6/Zptr7+OrKr2O6d0OudNqtasWttYsJC9fs1r2r91urJPJWPLlvZrVq0XMtkTA/soo+rIqmwdi3WKiJ81q6Kssqf25hMi+xo6pynOIr148ibk26yf9SKmOtqs8+WnMx3PrI/15tv+1EZWbhkbnSdvspj2KVeyNKJdRPn6dO+ceJqp+yWge6MtmwZknZpifeLnVhbZhVSVq+psALcrj9tuwPbXjTj1e9nmIGFc7dzWLpn9XnXNqld5TOa6sik7T7yO5fT7VMmq9ebJ+gDJXLbgV1Zl5bdO+wpbVoUAO70qS/RJ3bY02yWusmqWz8/0d/P6KJj5GUm199nGPrLq9TBZ5wZZVUqt7W+/5jpdh8T5Jz5umxKZ9wWyHfKt90heo4xO56J4HaDYcMapz9i/V8x0su9Qr+u9eb2xltt+H6hzb2Cm9drp2H5uOr3iz85IpyyplFWn+1zze9JaP7PvWa/v5s+s9/OyPmr/ztCRVVnbWK/hZr/z8gCV62HYsirr4+aDG/ONG2a5ZU4hO9fc+pLfe5Kw82WErFo7mfX9ROLn9oZRlVWR175+QcQy3/fpV1bNE9laTtHhxbRQ2bQE2ZoS2Wtl7B1D5eaOS1ZFWWTrC+xlsq+1dXvPqtfIqll/e0zZAwzZGt/EyW5saGCe9GLKjer0Gns/kb1ntUH7GCN/4hjmR5TTfE+v0zvmzLRhvmfV767PoixuI1Aqbav6dDPIRc9pnbJfGQlSFs68qZRVs+2t9TE3A/Erq7JrhjgPxCtywh5ZFcdyWvvjdUPr1YZhyKrTMYKWzavsqfp9XGXVrf4q36c6/Lymrlr3rFB5z6r9Oq4rsU5r3lWuk7J7FPtNvH2doNd7VgVL6/2A2WfM9y6brGX3DLK6qEz5FDFl9wZe+0qYZfF6eGumcyqL0zVcJkx+7lNk/ZPzHtD+3Sv6kv3VNaJM9v4j+o543aD9oYrsu9zaP3Vk1WQhi2nvUzIPEK+0FNO1o5BVa9vb21T2qkVrGq/3LKuc7zrXuTDTZpSshgkmlbHMCznHZiiprAeOBQIgAAIgAAIg4E5AZxohWMqXLIELCIBAcAKymX7Bo4YfAbIaPlPXiNbppmbCVIwwpbiaOBwIgAAIgAAIgIADAdkUSMCSE4Dco2eAAA+BdLkOQVZ52t8xqmyaiZ9d6lJcbBwOBEAABEAABEAgJALWqbFxnn4XUnUDhYGsBsKHzCAgJSB7PWdcUUFW49oyKBcIgAAIgAAIgAAIgAAIgAAINGICkNVG3PioOgiAAAiAAAiAAAiAAAiAAAjElQBkNa4tg3KBAAiAAAiAAAiAAAiAAAiAQCMmAFltxI2PqoMACIAACIAACIAACIAACIBAXAlAVuPaMigXCIAACIAACIAACIAACIAACDRiApDVRtz4qDoIgAAIgAAIgAAIgAAIgAAIxJUAZDWuLYNygQAIgAAIgAAIgAAIgAAIgEAjJgBZbcSNj6qDAAiAAAiAAAiAAAiAAAiAQFwJQFbj2jIoFwiAAAiAAAiAAAiAAAiAAAg0YgKQ1Ubc+Kg6CIAACIAACIAACIAACIAACMSVAGQ1ri2DcoEACIAACIAACIAACIAACIBAIyYAWW3EjY+qgwAIgAAIgAAIgAAIgAAIgEBcCUBW49oyKBcIgAAIgAAIgAAIgAAIgAAINGICkNVG3PioOgiAAAiAAAiAAAiAAAiAAAjElQBkNa4tg3KBAAiAAAiAAAiAAAiAAAiAQCMmAFltxI2PqoMACIAACIAACIAACIAACIBAXAlAVuPaMigXCIAACIAACIAACIAACIAACDRiApDVRtz4qDoIgAAIgAAIgAAIgAAIgAAIxJUAZDWuLYNygQAIgAAIgAAIgAAIgAAIgEAjJgBZbcSNj6qDAAiAAAiAAAiAAAiAAAiAQFwJQFbj2jIoFwiAAAiAAAiAAAiAAAiAAAg0YgKQ1Ubc+Kg6CIAACIAACIAACIAACIAACMSVAGQ1ri2DcoEACIAACIAACIAACGo6ZscAACAASURBVIAACIBAIyYAWW3EjY+qgwAIgAAIgAAIgAAIgAAIgEBcCUBW49oyKBcIgAAIgAAIgAAIgAAIgAAINGICkNUQGn/v/irae6A6hEgIYRIoyMum5k3yaMeeCkAJmUBJszyqrqmj8oPosyGjpbYtC2n77gqqqa0LO3SjjpeXm00tjH77jcEWn3AJNCvMpdycLNpdXhVuYESj1sUFtO9AFVVU1YJGiASys7KoTcsC+nrnwRCjIpQg0LQgh/LzcmjXvkoA+ZZAh9ZNwCJiApDVEBoAshoCRFsIyGr4TM2IkFU+tpBVHraQVR6uIipklY8tZJWHLWSVhytkVc4VssrX31QjQ1ZVSbmkg6yGABGyGj5Eh4iQVT7UkFUetpBVHq6QVT6uIjJklYcvZJWHK2QVssrXs4JFhqwG40e/+c1vqKi4mPaXl1NNTU0iWpYxRSUnJ4dy8/KprraWsrKNKa1FxVRTVWVMv6ym/PwC6tGnH234ZC117daTtnz1JfUbMIReXFBGpRMm0+xHptMFE6bQju1b6b2VK+jMc0rpnTdfp2bNi6l33+OpbM5MGj221DhuCS1fspjadziCunbvTatXvUvl+/bQ4KEnJ8phzSP+/eqi+dSlWy/q1LlL4veVFRX05JwZNPHSqUkU3l/5VuLf/Qae2IDOvLJZdNKpo6j1YW2k5Lx+LzLt2L6Nlr+2iMaVTnKkbx1ZtdZRp7lemF9G/QcOofYdj9LJVp9WpZw6gbds/ry+PXXyqabd+Nl6Wv/xR3TaqHNcs4Qpq/Y+plrWsNPt3bO7/vwJO7ZOPC9ZDdondcrClTYK1lHKalz6OFd7BhlZjaIvcHHgiOtXVj9dtzpxX3DSKT/gKFbax4xSVu33WWkP01YBTANOBvLIA7+jW265JdOaOe3q0+hl9aJr7qZ/vL8uqeHWLJuV9O+zJ91IGzZuTvzsmE4d6blZd9T/HrKa3Ochq87XAMgq3/UxLjfNkFWeNoas8nAVUSGrfGwhqzxsIas8XEVUyCpkla93+Y/c6GV12Ngr6Y0F99cTvOHOh+nNlavrfyZkdsfOPfWCKsS1datienzadYk8kFXIqurpB1lVJaWfDrKqz8xvjihYQ1b9tpZ3PsiqNyO/KSCrfsm554Os8nCFrDbkipFVvr6mE7nRy6od1up1n1Hp5bdR2UM3U+/unUnI7LVTxtPYkUMTSRe89CbdO+OpJMHFmlWdLqeWFhssqXHykyrMacB+jp/JebxGVjO57px1i1JWOesVh9hBZDUO5Y9zGfzKapzrFIeyRSmrcag/ZxkwstqQLjZY4uxxarEhqzZO9z82j+Y+vzQho3ZxFUllP4OsqnU2nVSQVR1aemkhq3q8dFJDVnVoqaeFrKqz0k0JWdUlpp4esqrOSiclZFWHll5ayGr0smqfwanXgtGmljlSGCWCrFoompDvuP6SxEiqqqzuqKqhfLxHLYz+WB8jx3jvX35uDh2owLtAQwVrBCvIz6Fa4z2gVdV491/YbJs1yaX9B2uorg7vWQ2TbXZ2FhUa/XY/3g0cJtZELPEgQPCtqDy0QSA+4RFoUpBLldU1xuaLuB6ER/XQJpbNCnOMd9ji/iBMrub1IMe4HhzE9aAebVHTvFAxy/bKadWiqH7GZhSyKmaN3njXo2T6j98KQ1b9klPMZwKecuEYuvLicYlcKrIq1qzWlJRQ/j6xG/ChC6e5G3B+fn5CCsSNQFFRCVVXVxmCUEWFBYV07HH96eO1a6hHr9705Ref0wlDhtHcp/5Cl1x2BT143zS6ZPJPadu2rfTOW2/SeaU/omVLX6NiY0fhfscPpEcffpDOH/9jKjaO+/LiF+iII4+inr360PvvrqQ9e/fQ8BGnJsphzSP+vXDBM9SjZx86pkvXxO8rKg7SozP/RFdcdU0SpbdXvJH4tyiT/fOX2Y/R6T84k9q0aSsl6/V7kUnU6xWj3D+eeLFj61hl1VpHxeZMJHu67K80+MShdOSRR+tkq0+rUk6dwF98sam+PXXyqabdsP5TWrvmQxoz9lzXLGHKqr2PqZY17HR7du+uP3/Cjq0Tz0tWg/ZJnbJwpY2CdZSyGpc+ztWeQWQ1ir7AxYEjrl9ZXfPRh4n7gjOM71p8GhKIUlbt91mZ1j7iegBZ/W+rTvv9naHuBtxz+CSyiql5JCGwbQ9rSb/99WUUhayG1Y8hq2GRlMQxnyiY61StSWRrVsXTB3PHYCGrFYY0Nt23D6+uMcBhN2DnjooNlvhO4ig2/ZHVxmsaMF5d468PRDkNGK+ucW6zuJx3/noVfy6/04Dx6hr3tolyGjBeXcN/3sTpCGFusCSEdP1nXybteSOrqymr4nfm20qcBNf6NhOrwwh3GTqwd2LD2J279iYOIwbjjuzYJjGCan7MPDLJtI8Am4N5bm9Rgawy9V7ZhknWQ6nsBrzfkNUiyGoCG2QVssp0qrqGjctNM2SVp/UhqzxcRdQga1bjct7x0QkWGbIajJ9TbsgqD1cRFWtWk9mGKatiVHXM6UMSo6duH/N1mdaZnkI+u3Q+ov5NJHY3EfvtzHhiYf1AmkgvJNWUUfP39unGohzidZx2ybSLtfj9Hx55OnF88burLz0vsQmt+IjyOsUJq6c26jWrZuPIYFrnbbu9Z7WTkfkr4++K/xykDsaUX3zCIYANlsLhKIuCDZb42HrJKt+RMztylLKa2WSDyWqmswlaP7+yGvS4mZ4/SlnNdLaQ1YYtHMZuwPY9cbxk1fqKTJFWvFZz7aebpGJpxhKCev5ZIxJLGc2RVVOMZSOe1ld1Wn8v4om3oqiuX/XamDaMc6ZRy2oYAEcYQZYZf5/ZU0EnYJOlMJAmYkBWQ0PZIBBklY8tZJWHLWSVh6uIGmRkla9UmREZssrTjpBVHq4iKmQ1/rJqLl2U9QJzNNZJVq0C6iSZ/970VWKqsLncUXYcc+TW+juRHtOA+c7NQJHFFkGPG3+n7auk8RXYTTEQTEtmyGpYJBvGgazysYWs8rCFrPJwhazycRWRIas8fCGrPFwhq3KuYYysisg604DdRlZNWfWSSbFm1T6yGoasinoM6te9fkqydQoyZJXv3AwUWWywtNtYs1pi7AZMtt2Ac/Pyqa62lrKys6m5sZNvTVUVVRtp8vMLqEeffrThk7XUtVtP2vLVl9RvwBB6cUEZlU6YTLMfmU4XTJhCO7ZvpfdWrqAzzykl6yYfZXNm0uixpVRUXELLlyym9h2OoK7de5N94b99Y5BXF82nLt16UafOXRJ1rqyooCfnzKCJl05NYvD+yrcS/+438MQGbLzWpHr9XgTcsX0bLX9tEY0rneTI3iqr1jrqNFbQzWxUyqlTHmywpENLL21c1s55yWrQPqlHhSd1FKyjlFVssOTcj6LoCzy9mieqX1nFBkvu7RGlrGKDJZ5zJa5Rw1yz6rXBkpiW67QbsGwasNs03SAjq6ItnKYBy0QZshrX3msplymrxeXllFWd/OoayKq8AVUkELKq3/k3frae1n/8EZ026hzXzGGOrMblRj4uN82QVf1+q5IDsqpCyV+aINOA43Le+as5fy7IKg9jyCoPVxEV04CT2YYpqyKy7NU1pgCamy/JXl1jlVURx9yR1zq6KtIM6teDxo4c6rhmVWVkVWycJMqwc9ee+p2LzQ2WxMZKdpEVdRIfTAPmOy8DRzZltciQ1WzIKnYDdulRGFkNfLo5BojLTTNklaeNIas8XEVUyCofW8gqD1vIKg9XyGpDrmHLqlU0rUezb+rqNg3YzOf2CpkgI6vWXX43bNxcX0yzjEKKF76yov7nYp2suRMxpgHznZuBIm8zcn9HfOEbOwGv2HWQmmJD4EA8zcxYsxoKRmmQMEdW+UqZnpG9ZDU9axV9qaOU1ehrz1uCILLKW7L0j+5XVtO/5rw1iFJWeWsWfXSMrDZsg7DWrEbfuulbAuwGHELb9TREdW12Fi3ZVUHdampDiIgQkFW+PgBZ5WMLWeVhC1nl4SqiQlb52EJWedhCVnm4iqiQVcgqX+/yHxmy6p9dfc7RhqAuysmmx/dW0hmV2BE4BKR4dU0YEB1iQFb54EJWedhCVnm4Qlb5uIrIkFUevpBVHq6QVTlXjKzy9TfVyJBVVVIO6cSa1RpjV17aX045WLOKNasu/QlrVgOebC7ZsWaVj609chSso5TVuGwixtXCQUZWo+gLXBw44vqVVewG7N4aUcoqdgPmOFPiG5NjzWp8axvfkkFWA7aNkNUsQ1arIasJknh1jXOHgqwGPNkgq3wANSJHISiQVY0G0kwKWdUEppEcsqoBSyMpZFUDlmZSTANOBgZZ1exATMkhqwHBClnNKy6mg/v3Y2QVsuramyCrAU82yCofQI3IkFUNWGmQFLLK10iQVR62kFUeriIqZBWyyte7/EeGrPpnV59z5cFqGlSYS11q6miZsSMwPsEJYIOl4AydImDNKh9brFnlYRvlyCpPjeITNYisxqcW8SyJX1mNZ23iU6ooZTU+FHhKAlltyBVrVnn6mk5UyKoOLYe02/ZXUW9DVndlZdHbhqy2M3YHxicYAchqMH5uuSGrfGwhqzxsIas8XEVUyCofW8gqD1vIKg9XERWyClnl613+I0NW/bOrz7nXkNWT83Po3dxsmrenggZV4fU1QbFCVoMSdM4PWeVjC1nlYQtZ5eEKWeXjKiJDVnn4QlZ5uEJW5VwxssrX31QjQ1ZVSTmkE2tWi4w1q3uMNatZ2A0YGyy59CesWQ14srlkj2Idpaw4XrL6wvwy6j9wCLXveBQfDObIUbCOUlaxG7Bzh4qiLzB371DD+5VV7Abs3gxRyip2Aw71FIl9MGywFI8mgqwGbAdTVveW7yeqqU5EyzKmA+fk5FBuXj7V1dZSVnY2NS8qppqqKqo20uTnF1CPPv1owydrqWu3nrTlqy+p34Ah9OKCMiqdMJlmPzKdLpgwhXZs30rvrVxBZ55TStYbprI5M2n02FJDkkto+ZLF1L7DEdS1e2+yX0TtN1mvLppPXbr1ok6duyTKWVlRQU/OmUETL52aROH9lW8l/t1v4IkN6Hjt9uv1exFwx/ZttPy1RTSudJIjfevIqrWOOs0VVAxUyqlTHsiqDi29tHG5aYas6rWbamrIqiop/XRBpgHH5bzTr3VqckBWeThDVnm4iqiYBpzMtrHIas/hyffjx3TqSM/NuoOvo2lGhqxqArMnN2V1nyGrdZBVjKy69CfIasCTzSV7XG6aIas8bQxZ5eEqokJW+dhCVnnYQlZ5uEJWG3JtDLI6bOyVNHRgb/rtry+rB3D2pBshq3ynWTSRxZrVV6pr6dziAhpg/HfB7opoCpJBR8WaVb7GxJpVPrZessp35MyOHKWsZjbZYLKa6WyC1s+vrAY9bqbnj1JWM50tRlYbtnAmr1ldve4zKr38Nip76Gbq3b1zbLs3RlZDaBohq59U1NAJLQuplbETsNgRuBAbAgciC1kNhM81M2SVjy1klYctZJWHa9CRVb5SZUZkyCpPO0JWebhiZFXONWxZXWUcZhdfEzpG7mv8poXkt2JktVWL4liNpNqLCVkNocMIWd17oJqGtiik/8vJotd3VdD3arAjcBC0kNUg9NzzQlb52EJWedhCVnm4Qlb5uIrIkFUevpBVHq6Q1dTI6gjjMMv4mtAx8lLjN8MdfmtfszrlwjF05cXjIiil/JCQ1YBNYa5Z3V9eTjU1NYeiGRss5WKDJUeyKhsXYYMl/Y658bP1tP7jj+i0Uee4Zg5TVuOyUyrWrOr3F785omAdpazGpY/7bS+vfFiz6kXI/+/9yip2A3ZnHqWsYjdg/+dDOubkWLN6tQFCjK6m+vMH44BidNXrc/9j82jGEwvpjusvobEjh3olT8nvIasBMUNWkwFiN2DnDoUNlgKebC7ZoxAoWXG8RlaD7lDNR1A9chSsIavq7aObErKqS0w9fSpltaLmIG0r36peuDROKWS1dUk+fWPMYkv1Z+PaT+ng/nLqdvxxqT50So7XpCCHxPV2T3lVSo4X94O8NOcpuuWWW+JezNDLJ6YGn3/WiNiMrkJWAzaxTFbrjAtpHkZWHcmKkdUlry6kE0afRjsP7qD9Vfvq05ZXldPOA9uNkelsKszPoV3lB2nXR19TTfM6qjr80NTqLeWbqbr221Fs498ivchnfkQ8EXfU/h/Qv/L/RVtyv/bVyq1rWtEJ+0+gh+r+5Cu/PVMn6mRMwRhOs4w/HJ9u1M14ataXyow/qfqMpJHG2otd9I7xJ8pPC2MlxiTjzx+NP3H+iDIuM/5sNP6k6yddWIfFNy59PKz6hBmnsfWFMNm5xRLXcfF9scD4g0+8CAymwca3TQt6yfiDT+YTuJVuzWhZXfDSm/TnssVJ61XFz26861Fas4znXtVPr4Gs+qFmy2OuWX3RkKvLivLptMoamrW3MoTI6RdiT8VuQxS305Z9m+mLPZto2/6t9HX5V4n/fmP8NX+efjVDiUEABEAABEAgngQKcgqpTbO28SwcQ6lysrOoxtjQEp9wCWQZ4bKMAZfaOrAVZC/ucwXdcsovw4Ucs2jiNTUbNm5OKlWcRFUUDLIaQqcxZXW1MXViZElBYnMlsclSpn+EjK7Z/iGtNf6K/4q/4mden9zsXGrfvGMiWXF+CRUX/Hd/ssLcAjq8aTsyBlYTo6sVVbV0ZNFRSSHbNetIudk59T9r1eQwapbXrP7fTfOaU6vC1l7FUPp9qyatjdjNldKmS6Iw16ymS51TVU6vacCpKkemHSfKacCZxtJenyDTgDOdTdD6+Z0GHPS4mZ4/yjWrmc4Wr65p2MJh7wac6X2Io36Q1RComrK6x3gaNbhlAVVQVuL1NW0y6KmfWA+z4ss3aMmmxfTxjrWGmH5AYhTV/ikuKKHvlHzXEM62iae87Q2xPMKQTSGgQlDbGD8XAuj1wW7AXoT8/x6y6p+dV07Iqhchf7+HrPrjppILsqpCyV8ayKo/bl65IKtehPz/HrIKWfXfe/hyQlYDspWtWa3NzjZG/rIpPy+f6mprKcv4/+ZFxVRTVUXVNdWUn19APfr0ow2frKWu3XrSlq++pH4DhtCLC8qodMJkmv3IdLpgwhTasX0rvbdyBZ15TilZd6QsmzOTRo8tpaLiElq+ZDG173AEde3em+y71Nl3sXx10Xzq0q0XdercJVHryooKenLODJp46dQkCu+vfCvx78O7HUGvbVycEFQhqkJYpxh/xDqar40/Qj6PbdOPvte6J/U5/Djq1roHvb/4DTrp1FHU+rA2jmSxG3BpwF4nz47dgA+dP1F+vGQVGyz5a50oZRW7ATu3WRSbbfnrQdHk8iur2A3Yvb2ilFXsBhzNuRTVUTl2A46qLul8XMhqwNZzktUcQ1AL0lBWxdrSp1/+M328cy3NO/BMEh0hpmP2nUXfHdiTBnUZZkzfLWlAD7sBO3co7AYc8GRzyR6Xm2bIKk8bQ1Z5uIqoQUZW43Le8dEJFhmyGoyfU27IKg9XERUjq8lsIat8fU0nMmRVh5YkrZOsitHUJmkkq+9/vZIe/eBBevHf82lo7aH3Kv0z710afvRpNPzI02iE8V8xkuolo16/F3ExsoqR1YCnXYPscblphqyG3bKH4kFWebhCVvm4isiQVR6+kFUerpDVhlwhq3x9TSdyJLIq3t+zc9deaTnjtgOVCkxzzapI+5fCXLquWR6dW1FD0/fFe0fg6tpqmvfJkzRr9Uz6YNv7iaqKzY/O6HwW/aT3ZBrQfkji31F8sGaVjzrWrPKx9ZJVviNnduQoZTWzyQYbWc10NkHr51dWgx430/NHKauZzhYjqw1bGBssRd/rUy6rYovk1q2K6fFp10Vf+5BKYJXV5XnZ9MPiAhpk7GI7b098dwReuulVuunv19DG3f9OUBBTen/Y4yd0ybFX1O/UGxIeX2Egq76wKWWCrCph8pUIsuoLm2cmyKonIt8JgkwD9n3QRpIRssrT0JBVHq4iKmQVssrXu/xHTrms9hw+ie64/hIaO/LQVNNM+FhldWNOFp3YopDaGTsBrzB2BC6I2auqhJwKSRWyKj6djJ17haD+sOckEu9pi8sHssrXEpBVPraQVR62kFUeriIqZJWPLWSVhy1klYcrZFXOFSOrfP1NNTJk9VtSq9d9RqWX30ZlD91Mvbt3rue34KU36ca7Hm3A05yu7LRmtSYnh5rl5lFWTHYDFjv5PvLkvbRw9wJaU7cmMZI6te911GRVluNuwP0Gntig3l5rUr1+LwJizSrWrKpeoFTTYc2qKqng6aJgHaWsYjdg5z4TRV8I3oNTF8GvrGI3YPc2ilJWsRtw6s6fOBwJa1bj0ApEKZdVMQ341GH96cqLx8WDgFEK6xpamazeO+MpemPB/dLyymS1znjfanVurrEbcB7l1UT/6pq2XY+kixeNp65fd6bVWatpYO9h9KtBt1Ch8cft1TWQ1W20/LVFNK50Uih9FbsBh4JRGiQuN81eI6t4dY2/PgBZ9cdNJVeQkdW4nHcq9YwiDWSVhzpklYeriIppwMlsIat8fU0ncsplVYxUusmfTuHDTOs2supXVvMMWS2IWFb3Zu2jG9ZfS1v2baaf5F1EPxg8jk489uQEOq/3rEJWIate51hcRp3ictMMWfXqMf5+D1n1x00lF2RVhZK/NJBVf9y8ckFWvQj5/z1ktXHJquk+1lq3alHkOEDnv2cFy5lyWRVrVt0+Ue0GrDMN2F5G65pVUbcX83PosqJ8GllZQ4/tjW5H4L+u/TPNeP+P9Nmu9TSmy7k0ue9U6tu2f7Aek6LcWLPKBxprVvnYeskq35EzO3KUsprZZLFmlbN9/coqZ5kyIXaUspoJ/NzqAFltSCeT16zK3Oeia+6m9Z99GSthTbmsxvVEd5JVe3lFI+7YuYeem3WHY1XeNX4zwPjb2/j7YQQVPlB9gO5ZcU/i756KPXTVoKvoF0N+QUcWHxlBaXBIEAABEAABEAABEAABEACBOBGQuY+qD6WyHpDVb2mrNo6Zzjq6ah9ZrcgiOrmkkMTOwEt2VVA3Yypwqj6f795IMz+YTrM+nEktm7RKjKZeftzPjfel5qWqCKEcByOroWCUBsHIKh9bjKzysMXIKg9XETXINGC+UmVGZIys8rQjRlZ5uIqoGFltyDbskdVVX6+iXQd38TWiQ+S+7fpSi8IWSb+FrLo0g2yH3ahfZ6Mqq2bZ3XYDzjI2WBK7AR8sKKDmNTWUn5VNzYuKqaaqiqprqik/v4B69OlHGz5ZS1279aQtX31J/QYMoRcXlFHphMk0+5HpdMGEKcauuVvpvZUr6MxzSsm6NrBszkwaPbaUiopLaPmSxdS+wxHUtXtvWvzGPHpv09v00K4HqWur7jSp+UXU76hB1Lvv8YnWeHXRfOrSrRd16twl8W+sWXW/VqjsWqxztcEGSzq09NJizaoeryCpo2AdpazGZV12kDZzyxtEVqPoC1wcOOL6lVXsBuzeGlHKKnYD5jhT4huTY4OlEbNH0LKNy1Je6aUTl9LwTsM9ZVVshCs+bjNIU134lI+s3v/YPJrxxMKkV8SYojjlwjGR7RLsJKtip2DrTsCiEVu3KqbHp12XaCvZbsBCVmsNWT1gyGoTY1S1ifFvblltcXQbuuFvPyU6WEcfl6yn2Wc+Q9vXbKZmzYshqx2P8nVeQVa9scXlRj4uN81eI6vYDdi7T8lSQFb9cVPJBVlVoeQvDWTVHzevXJBVL0L+f4+R1WR2HLJ69ctXkxhdTfXnD2f8gcToqvUj22BpUL/u9Y6T6jI6HS/lsirk7/yzRjSQUiGxc59fGsmCXuurawQo605YQk43bNxcz8/eiE6ySoaslhuymm/IanNmWW3V9nC6bu3Pqcm2fOrWvDtdO/42atWkddJorKgARlb1TjvIqjcvyGoyI8iqd5/xkwKy6oeaWh7IqhonP6kgq36oeeeBrHoz8psCssovq37bhiOf6qxSjmPrxEy5rIrdgGVTfu3Ta3UqEXVa+5pVUZ5PcrLplBYFdFRNHb22+yA1reMp5fYD39CdK/4fPbVuDn3/qFPohsG3UZ82x/EcLIVRsWaVDzbWrPKx9ZJVviNnduQoZTWzyWLNKmf7+pVVzjJlQuwoZTUT+LnVAbLakE7Ya1bj1Icgqw6tEceR1aAdRyarIqaQ1Y8NaX1hdwUdV82zydL1y66iJz56lNo0bUtPn/MSHdPye0GrE4v8kFW+ZoCs8rGFrPKwhazycBVRg4ys8pUqMyJDVnnaEbLKw1VEhaxCVvl6l//IKR9ZjeuaVf8IiZxk9Yrm+bSgIIfu2VdJF1TUBDmENO/cdU/Q1UsmU7O85lR29gvUr93A0I8RVUDIKh95yCofW8gqD1vIKg9XyCofVxEZssrDF7LKwxWyKueaySOrfD0p3Mgpl1VR/DjuBuwXq9Oa1RxjzWpVfr6x31EdFRhrVtsYGx2FuRvwgNNH0JnPn0QnV4yg4b3PoPNOmkj2Xers6wmxZlWvlbFm1ZsX1qwmM/KSVWyw5N2nZCmilNW49HF/5LxzBRlZjcvGZt61jCaFX1nFbsDu7RWlrGI34GjOpaiOyrHBUlR1SefjRiKr6QzMXnY3Wa0zZHWfIau5hqy2D1FWn5w9g/7VdjX9dcOf6ZoWv6DR/c+lbt37QFZtjRNUDCCr3mdqXG7k43LTDFn17jN+UkBW/VBTywNZVePkJxVk1Q817zyQVW9GflNgGnAyOciq354Ubj7IakCebrKanZdPe6iO6gxZ7WC8Z5Uqw3nP6iOP3kN/PDiNOh52FF3e/Arq+d2+ifesYmQ1uTEhq/LOHeY0YMgqRlYDXkKVskNWlTD5SgRZ9YVNKRNkVQmTdiLIqjYy5QyQVciqcmdJYcKUyarYBVi8R1W8Y9Xts2bZrBRWP5xDOa1ZFdFHlxTQqtxsmrungk6sCr7J0j+3vE3XYiaiDwAAIABJREFULf0ZfbJzHf12+HSa0OvScCoRsyhYs8rXIGHKKl8p0zOy18hqetYq+lJHKavR1563BEFklbdk6R/dr6ymf815axClrPLWLProkNWGbYA1q9H3y5TJavRV5SuBm6xea2yyVGZssnRbeRVdfLA6UCEOVO+n65deRc988je6oMckunvE/ZSTlRMoZlwzQ1b5WgayyscWssrDFrLKw1VEhazysYWs8rCFrPJwFVEhq5BVvt7lP3LKZdXpPatil+C5zy+lNxbc7782EeV0k9VHCnPp1mZ59CNDVH9nCGuQzyOrHqBb3/wV9TysD/1uxAPUt+3xQcLFOi9kla95IKt8bCGrPGwhqzxcIat8XEVkyCoPX8gqD1fIqpwrRlb5+ptq5NjIqrlDcLpNA3Zbs5prrFmtqqulPdnZVFVSQt85WEnVNdWUn19APfr0ow2frKWu3XrSlq++pH4DhtCLC8qodMJkmv3IdLpgwhTasX0rvbdyBZ15TinNf+kJemnzi/TCgYX0m8LbaPz5l1JRcQktX7KY2nc4AmtWJT0ea1bll4EwZRVrVpMZe8lq0D6pemHnTBfFZlZRympc+jhXmwYZWY2iL3Bx4IjrV1axG7B7a0Qpq9gNmONMiW9MbLAUj7aJjazecOfD9ObK1Wk3suolqzXfyuruFi3omIMVlFXtT1ZvmnUlrdu3hlof055O3vZ9Gj22FLLqcQ4FFQPsBux9kYrLjXxcbpohq959xk8KyKofamp5IKtqnPykgqz6oeadB7LqzchvCkwDTiYHWfXbk8LNlxJZlb1XVVaNO66/hMaOHBpuDZmjeclqXW0t7c3Jpu2GrB5dUUmFVVXaI6u5xzajpxf9mSrzqmj6hFn0ytPPQFYV2hWyipFVhW4SahLIaqg464NBVnm4iqiQVT62kFUetpBVHq4iKmQVssrXu/xHTomsWovntGbVfxWiz+m2ZlWU7tfGmtXZxtrV6/dX0ZUH9DZZ+s/BnXT5yxPojS9ep5tOvIMuP+7q6CucghJgzSof5DCnAfOVMj0je8lqetYq+lJHKavR1563BEFklbdk6R/dr6ymf815axClrPLWLProkNWGbYA1q9H3y5TLavRVDr8EXrI6xxDVGwxhPaeihh7YV6lVgFmrZ9KNy6+mQR1OpAdPn0Xtm3fUyp+uiSGrfC0HWeVjC1nlYQtZ5eEqokJW+dhCVnnYQlZ5uIqokFXIKl/v8h8ZsuqfXX1OL1n9R142jSsuoG41tbRkV4XyEbfs20w/fWUirfxqRUa/U1UGBLKq3E20E0JWtZEpZ4CsKqPSSghZ1cKllRiyqoVLKzFkVQuXcmLIqjIq7YSQVciqdqdJQYaUy+rqdZ9R6eW3OVYt03YDFmtWydgN+EtjzSpVV9GRxrrVZoq7Ac9+ZwZtXP0J/fOw9+nWjrdTUVEL6t33eCqbMxNrVhVODqxZlUMKU1axwVIyYy9ZDdonFbo9e5IoNrOKUlbj0se5GjaIrEbRF7g4cMT1K6vYDdi9NaKUVewGzHGmxDcmNliKR9ukXFaHjb2Shg7sTYP69aB7ZzxVv/vv2ZNupFOH9acrLx4XDzKKpVDZYCnLkNWtLUqo0tgJuL0hqyWKsnrB30ZTt/KuNGzUD6jFV82oWfNiyKpiu4hkQcUAuwF7w47LjXxcbpohq959xk8KyKofamp5IKtqnPykgqz6oeadB7LqzchvCoysJpODrPrtSeHmS7msmhssfffoDvTTG/5QL6tix2CrvIZbTb5oqrJabrwTdWdtNbWqrKQ2ed7vWS0e2pbuWXIbjck/m3466QZas/JdyGr33loNCVmV48LIqlY30koMWdXCpZwYsqqMSjshZFUbmXIGyKoyKq2EkFUtXFqJIauQVa0Ok6LEkcmqeEWNEFdz2q/5ept0mwYs2slrzapIsyQ/hyYU5dMJVbX0zB7vdas/e+UnNP/TpxrVDsDWPo81q3xXgDBlla+U6RnZS1bTs1bRlzpKWY2+9rwlCCKrvCVL/+h+ZTX9a85bgyhllbdm0UeHrDZsA+wGHH2/TLmsium+PboeTb/99WVk/f8b7nyY3ly5un6kNXo06iVQkdWt2Vk0sqSADmRl0Uu7D1KnmjrHA/xjy1s08fn/oVaFrWn2Wc9Sl5bd1AuTISkhq3wNCVnlYwtZ5WELWeXhKqJCVvnYQlZ52EJWebiKqJBVyCpf7/IfOeWyai+qGF01P2UP3Uy9u3f2X5uIcqrIqijaucaOwG8bOwM/treSRlbWOJb2jhU30Z/en0aXHHsF/WbY7yOqVbSHhazy8Yes8rGFrPKwhazycIWs8nEVkSGrPHwhqzxcIatyrhhZ5etvqpEjl1XVgsY1neqa1eZFxbS1ppr2Gn+bGhssndLrONrwyVrq2q0nbfnqS+o3YAi9uKCMhow9g55/4q/0YPYD9IfBM6hq4wE685xSsm5kg92A1XoD1qzKOYUpq9hgKZmxl6wG7ZNqPZ83VRSbWUUpq3Hp41ytGmRkNYq+wMWBI65fWcVuwO6tEaWsYjdgjjMlvjGxwVI82iblsmpusCTWrGbCR0dW9xi7AW8zNlnKLiik0T37SmV1f99aKv/7N7S28wa6+djb6b2VKyCrSxZT+w5HUFdssOR6ymz8bD2t//gjOm3UOa7pIKt8Vx7IKg9byCoP16Ajq5BV93aBrPL0W8gqD1eMrDbkClnl62s6kSGrOrQkaXVktdJ4z+qW2hraW1hIA42R1ap1a5JGVl+Y/yQ933IRnfD58dR2eCca1nI4ZNXYjGo5ZFWpl0JWy6h0wmQlVlyJIKs8ZCGrPFwhq3xcRWTIKg9fyCoPV8gqZJWvZwWLnHJZTdf3qbphVl2zKmJc3Tyf5hbk0K3lVXTpweqksIs/W0iXLCql/u0G0ewzn6WWha2CtW4a58aaVb7GC3Nkla+U6RnZS1bTs1bRlzpKWY2+9rwlCDINmLdk6R/dr6ymf815axClrPLWLPro2GCpYRtgzWr0/TLlsrp63WdJ71eNHkHwEujI6l8Kc+m6Znl0prHB0kxjoyXr59rXL6eytbPpusG30lXH/yp4wdI4AmSVr/Egq3xsIas8bCGrPFxFVMgqH1vIKg9byCoPVxEVsgpZ5etd/iOnXFatu//Kip2p71k167ouJ5vGGK+waVFXRwt3V1D72kOvsFm17T3jdTXjqCC3kGaPfpa6H9bLf6tmQE7IKl8jQlb52EJWedhCVnm4Qlb5uIrIkFUevpBVHq6QVTlXjKzy9TfVyCmXVdWCpUs6nTWrNVVVVG3sBvxVkya0dOAAOm/VBzS466HdgP+Z9y7VfXiAtvXcRb02fI8umDCFdmzfijWrWLOqfCpgzSrWrCp3lgAJo9hUJ0pZxW7Azp0lir4QoOumPKtfWcVuwO5NFaWsYjfglJ9GkR4QGyxFir/+4CmXVafdgO9/bB7NfX4pvbHg/niQUSyFH1ndZWyw9OKggTTygw/ptC49ErJ666YbadT+kXTSuDNp3Yv/hKwa76Nt3iSPdkBWFXsiEWQVsqrcWQIkjEJQIKsBGswja5BpwFH0BT4S4UeGrIbPVESErPJwxchqQ66QVb6+phM5NrK64KU36ca7HqV0mwbsR1YrDFl9xpDVEz/8kMYd04Pe+/Qduv2LW+iynMvooouvoXmz/wxZhazqnMeJtJBVyKp2p/GRIQpBgaz6aCjFLJBVRVA+kkFWfUBTyAJZVYDkMwnWrCaDg6z67EghZ4uNrN5w58P05srVaTeyKtpDZ4Mlkf4/WVmJdav/l5OVWLf6/PJf0cP/uo8uP+5quunEO0Ju4vQMhzWrfO2GNat8bLFmlYdtlLLKU6P4RA0iq/GpRTxL4ldW41mb+JQqSlmNDwWekkBWG3LFmlWevqYTNSWyao6aehXsjusvobEjh3olY/m92KW49PLbqOyhm6l3985JxxCv29mwcXPiZ8d06kjPzUoWSl1ZFXGmGq+wecZ4hc31O7fTi2Wn0epvVtFfznqORhx9Gkv90i0oZJWvxSCrfGwhqzxsIas8XEVUyCofW8gqD1vIKg9XERWyClnl613+I6dEVq3Fc1qz6r8KwXMOG3sl7dy1NxHILqsXXXM37di5p15Qhbi2blVMj0+7rv7AfmT1CeMVNtcbr7AZ8NF8+uez42hA+xNo7thFlJ9TELxCGRABssrXiJBVPraQVR62kFUerpBVPq4iMmSVhy9klYcrZFXOFSOrfP1NNXLKZVW1YKlO5zSyKkT22inj60d8xSjxvTOeqp+u7GfNan6+8eqavv1p6YZ1tCZ7LbX/7FP6Tp/udMTGNlQ6YTLNfmQ61qxizar2KYA1q1izqt1pfGTAmlUf0GKcJcjIahR9IcYoGxTNr6xiN2D3Vo5SVrEbcDqdgcHLijWrwRmGEQGy+i1Fmayq/MyvrPbo04+e27CW/v7149Sp8jC6dMw19PGy9yCr37aHdWR1+ZLF1L7DEdS1e2+tPv/C/DLqP3AIte94lFY+M/GO7dto+WuLaFzpJF/57Zm2bP68/lVEoQS0BYGsQlY5+pU9ZhSCEuXIKl5d49yrougLqejjYR0DshoWyeQ4kFUeriIqpgEns4Ws8vU1nciRyKp12q29sFHtBqwipqKs9nRCVouLS6i8vJxqjHeoik+WsYFSTk4O5efnU21tHWVnZ1FRUQlVV1dRlfG3sKCQjj2uPy341xv06rYnqHvTAXT3j26nZ+b+jS657Ap68L5pdMnkn9K2bVvpnbfepPNKf0TLlr5GxUXF1O/4gfToww/S+eN/TMUlJfTy4hfoiCOPop69+tD7766kPXv30PARpybKYc0j/r1wwTPUo2cfOqZL18TvKyoO0qMz/0RXXHVNUjO8veKNxL9PGDKsQV/6y+zH6PQfnElt2rSV9jOv34tMol6vGOX+8cSLHftqjrH5VH5uDh2oqE6qo07nfrrsrzT4xKF05JFH62SrT6tSTp3AX3yxqb49dfKppt2w/lNau+ZDGjP2XNcsBfk5iX5ZVV2rGtoxnb2PBQ7oM8Ce3btp7lN/SZw/UX6aNcml/QdrqK6uTlqMoH0yyrqZx46CtbiGFhr9dv/BQ9fYVH7i0se56iweBAi+FZU12oeIoi9oFzLCDE0Kcqmyusa4N5BfD5yKtuajD+nLLz6nM4zvWnwaEhD3WM0Kc2jfgdRfD+z3WZnWPuJ6kGNcDw76uB5kGgtRn2m/v5NuueWWTKxaWtUp5bIqW/MZB2J+ZVWUvaKqhiqr9G/8f7LiNnr2rdup3aCf06ff/10cMMSmDFZZjU2hMqQgYcpqhiAJrRpeshragRpZoChlNdNRB5HVTGcTtH5+ZTXocTM9f5SymulsIasNW7ioaV6mN3vs65dyWY3jBkuilXTWrNrfB+tngyVxzPHPnUlvfvE60bll9FbHs6mT5tPX2PeuAAXEBksB4HlkxQZLfGyxwRIP2yinAfPUKD5Rg6xZjU8t4lkSv9OA41mb+JQqymnA8aHAUxJMA27IFRss8fQ1naiQ1W9pOckq127AH+9YS2OeGU51BcW0/5K36dq89nRNBFNadDpLKtNCVvloQ1b52EJWedhCVnm4iqiQVT62kFUetpBVHq4iKmQVssrXu/xHTrmsimnApw7rT1dePM5/qUPOaV9D26pFUf1uv+JQbu9Z9bvB0t7DDtCnH6+m/7TNoaz2Z9GeE4fRqCfmGLsAYzdgwRwbLOl3cmywhA2W9HuNfo4oNtWJUlaxwZJzH4miL+j32Ohy+JVV7Abs3mZRyip2A47ufIriyNhgKQrqDY+Zclm1v/olHhj8l8KvrH6Ut5Yqtuyjdl260JamPei54cPpl3+eRZMgq4nGgKzq90nIKmRVv9fo54hCUCCr+u2kmiPIyGoUfUG1XnFIB1nlaQXIKg9XERUjq8lsIat8fU0ncsplVaxZdftEtRuwDjRrWj+ympuXR4sPLKJ2+9vQ948/ndZVFNIjJ4+gq2bNoskXYmQVsuqvN0JWIav+eo5erigEBbKq10Y6qSGrOrT00kJW9XippoasqpLSTwdZhazq9xr+HCmXVf4qpf4IuhssLfv8NfrRwjHUt+3x9Py5y+jlgjy6pCif+hmvEpm7p4Ka6O1yn/oKp+CIWLPKBxlrVvnYYs0qD9soZZWnRvGJGkRW41OLeJbEr6zGszbxKVWUshofCjwlgaw25IoNlnj6mk5UyKoOLYe0urJ678o7aJrx95Jjr6DfDPs9iTeFHdeqkHYa7w57fndFQlob+weyytcDIKt8bCGrPGwhqzxcRVTIKh9byCoPW8gqD1cRFbIKWeXrXf4jRyKr1g2L7rj+Eho7ciiJ6cGD+nWnx6dd5782EeXUldUfGqOqy43R1T+dMZvO7nJeotS3NsujRwpz6ULjpfd3lVdFVJP4HBayytcWkFU+tpBVHraQVR6ukFU+riIyZJWHL2SVhytkVc4VI6t8/U01csplVYhq61bFCSkVu/BeO2V8Qlbvf2wezX1+adIuvKqViDKd7prVA5UH6PP9m2ht/loa1/I86t2zP2356kvKO2EovT3vSXr2Z1fRpb+/m340YQrt2L6V3lu5gs48p5SsO1KWzZlJo8eWUlFxCS1fspjadziCunbvTfZd6uy7WL66aD516daLOnXukkBWWVFBT86ZQRMvnZqE8P2VbyX+3W/giQ3QziubRSedOopaH9ZGit3r9yLTju3baPlri2hc6STHpsMGS/q9GmtWsWZVv9fo58CaVX1mcc4RZGQ1ir4QZ5b2svmVVewG7N7KUcoqdgNOpzMweFmxwVJwhmFESLmsihHUsodupt7dOyfJqtgl+Ma7HqVM32Bp94Fd9NXBzXTg8Eoakj+UunbrmZDVfgOG0BPPPUV3/Hwq3XrX3TTR2BUYsppHO4w1vFYh1+n0L8wvo/4Dh1D7jkfpZKtPqyLVOoG3bP68/uGDTj7VtJBVyKpqXwmSLgpBiXJkFa+uce4tUfSFIH031XkhqzzEIas8XEVUTANOZgtZ5etrOpFTLqtiNPVPv726gaw2lpHVbfu20o6q7dTmmCOo44EOSbL69IIy+n9X/5xuuvtuOt8YWa385muMrEJWlc9nyCpkVbmzBEgYhaBAVgM0mEdWjKzysYWs8rCFrPJwhaw25ApZ5etrOpFTLqs33PkwvblydWK6rzkN+LtHd6DSy2+jMacPod/++jKd8scireqa1X2Ve2nMM8Ppk53raP6412hghyFJ5T+QRTSxqIDeysum+/dV0riKmljUL4pCYM0qH3WsWeVjizWrPGyjlFWeGsUnahBZjU8t4lkSv7Iaz9rEp1RRymp8KPCUBCOrDblizSpPX9OJmnJZFYUzp/xaCzrlwjF05cXjdMoem7Sqsvr3L5bQBc+dRX3b9KeF5y2jnKycBnV42Nhk6TfGZktjDVF90BDWxvqBrPK1PGSVjy1klYctZJWHq4gKWeVjC1nlYQtZ5eEqokJWIat8vct/5Ehk1X9x45lTVVbF62rEa2su7HUJ3TX8PmllPsvJSoyubsvOoll7K+iEqsb5GhvIKl9fh6zysYWs8rCFrPJwhazycRWRIas8fCGrPFwhq3KuGFnl62+qkVMuqxddczf94/11DTZSStdX1+jsBrxp57+pqrqK2hS3o0HHD6cNn6xNWrP6orFmtdTYWGnmI/fR74yNli7dtJl6vfF37AZs2fFYtWOLdNhgSU4rTFmNy+YzUayjlNH1ktWgfVKn/3OljYJ1lLIalz7O1Z5BRlaj6AtcHDji+pVV7Abs3hpRyip2A+Y4U+IbE2tW49E2KZdVsU71/LNGNJjym+kbLBU2a0L/t3MDZddlU8cWR9Fxx53gKKuPG7J679Sp1HPLFjp/6TI613hNDV5dc+j1PDqfoGKA3YC9acflRj4uN82QVe8+4ycFZNUPNbU8kFU1Tn5SQVb9UPPOA1n1ZuQ3BaYBJ5ODrPrtSeHmS7msihHUO66/JPFuVesn019dU5dP9OXuTdQ8pzkd0fJo6tGnn6Oszn5kOq386ZW0auc3NOn1ZXTp2eMhq9++S1an+0NWMbKq01/CSAtZDYNiwxiQVR6uIipklY8tZJWHLWSVh6uIClmFrPL1Lv+RUy6rmTayKtCrrFm9793f0d3v3EoXH/tTum3YPZ4t9kxBDk1tnk8nGmtWZxtrV5vUeWbJqARYs8rXnGFOA+YrZXpG9pLV9KxV9KWOUlajrz1vCYLIKm/J0j+6X1lN/5rz1iBKWeWtWfTRIasN2wBrVqPvlymXVTHdd8YTC6nsoZsT71oVn9XrPku8uiZddwRWkdVz5p1KK79aQX86Yzad3eU8z5avNlIMbVlIXxgbLZUZ7xod1sg2WoKsenYR3wkgq77ReWaErHoi8pUAsuoLm1ImyKoSJl+JIKu+sHlmgqx6IvKdALIKWfXdeRgzplxWRV1kr66RTQ1mrHeoob1kdV/VXjr5b8fT5r1f0GulK6n7Yb2Ujv+I8RqbW43X2BxbXUuLdlco5cmURJBVvpaErPKxhazysIWs8nAVUSGrfGwhqzxsIas8XEVUyCpkla93+Y8ciaz6L278cqrsBlxDNfR5xSZqZqxX7dj0SCooKPBcs3rBhCm0dsc2WvzeCnpgkrHO94XF1L9Jc+rd93gqmzOTRhubLhUVl9Byy0659l3q7JvfvLpoPnXp1os6de6SAFlZUUFPzplBEy+dmgT2/ZVvJf7db+CJDYDPK5tFJ506ilof1kbaGF6/F5lUNi6yyqq1jjo9AGtW5bTClFVssJTM2EtWg/ZJnf7PlTaKzayilNW49HGu9gwiq1H0BS4OHHH9yip2A3ZvjShlFbsBc5wp8Y2JDZbi0TaQ1YDtoCKrlbUVtLlqM7XKb02HF7ah/Hw1Wd2xfSu98O7bdOtFk+iixS/R6ILmNPjY/pBVxTYLKgYqUq1YlESyLZs/p/dWrki8iojjs/Gz9bT+44/otFHnuIaHrHLQPxQTssrDFrLKw1VEhazysYWs8rCFrPJwFVExsprMFrLK19d0Ikciq2KTpZ279krLuWbZLJ3yR55WRVYP1Oynr6u/pnZNOlBJXomWrL7zzxX01wkTqeT1V2mwMbJ6ac9+kFXFVoesykFBVhU7kI9kkFUf0BSyQFYVIPlMAln1CU4hG2RVAZKPJJBVH9AUs0BWIauKXSWlyVIuq2dPupFatyqmx6ddl9KKch7Ma83qefN/QCs2L6fHRj1FIzufpV2UucbOwFcbOwO3qa2j5bsqqLgu87cGxppV7W6inCFMWVU+aCNJ6CWrjQRD6NWMUlZDr0zMAgaR1ZhVJXbF8SursatIzAoUpazGDEXoxYGsNkSK3YBD72baAVMuq07vWdUueYwyuMnq9gPf0Ml/7U/lVeX0+o/+SUcXH9oBWecjdgYeU1JAH+Rm0/kVNfSHfZU62dMyLWSVr9kgq3xsIas8bCGrPFxFVMgqH1vIKg9byCoPVxEVsgpZ5etd/iNDVv2zq8/pJqtvfbmMzl8wivq26U8vnv+G76P9PS+brm+WT1/mZNHdhqxeYEhrJn8gq3ytC1nlYwtZ5WELWeXhClnl4yoiQ1Z5+EJWebhCVuVcMbLK199UI6dcVsU04FOH9acrLx6nWsZYp/Nas3qw6gCVV++jnCa51L6wA1XXVGutWTU35BE7Uv6rZQu6/fsn0q/+OJ2G/c8F1K9pEXYDdukdWLMqhxOmrMZlp9S47ErqJatB+2QcLoZRsI5SVuPSx7naPsjIahR9gYsDR1y/sordgN1bI0pZxW7AHGdKfGNig6V4tE3KZVW8Y/XeGU/RGwvujweBgKXwktXyyn10sOYANWteRC3zWgaS1dyiEnp06An03YceoD2lP6b/zW0KWYWs1hPAbsBlVDphcsAzOlh2yGowfk65Ias8XIOOrEJW3dsFssrTbyGrPFwxstqQK2SVr6/pRE65rIo1q26fTNsNeG/FbqqsraTWLQ6nJllNAslqs+bFtGfAQFr55xn054kT6QZDVjsseoHadziCunbvTXjPanLPCjqKhVfXeF9K4jLqFJebZsiqd5/xkwKy6oeaWh6MrKpx8pMKsuqHmnceyKo3I78psGY1mRxk1W9PCjdfymU13OLHI5rTmtUv935Opzw5gPJz8mnJBe9Sm6ZtQynwDGNK8f82zaO+1bX0u/Iq6mn8N9M+WLPK16JhTgPmK2V6RvaS1fSsVfSljlJWo689bwmCyCpvydI/ul9ZTf+a89YgSlnlrVn00SGrDdsAa1aj75eQ1RDawElWl2x6iSY8P46GHHESPT12cQhHOhRiXxYlNluab7zSZsLBavqtIayZ9oGs8rUoZJWPLWSVhy1klYeriApZ5WMLWeVhC1nl4SqiQlYhq3y9y3/kSGRVrFu98a5Hk0p9x/WX0NiRQ/3XJMKcTrL64Pv30p0r/h9d1Ody+t/v3xtqCb/IzqJTWhRSuSGus/dW0qmVmbU7MGQ11O6SFAyyyscWssrDFrLKwxWyysdVRIas8vCFrPJwhazKuWJkla+/qUZOuaze/9g8mvHEQip76Gbq3f3QO0dXr/uMSi+/jaZcOCbtdgl222DpIFVQVXUlNc1rSq1btqWaqqrAa1Z79z2eyubMpNFjS+mZNq3p3dcW0ZajjqY7v9Odqt5bSeX79tDgoScnuNrXE766aD516daLOnXukvh9ZUUFPTlnBk28dGpSf3l/5VuJf/cbeGKDfjSvbBaddOooan1YG2kf8/q9yKSyFtQqq8uXLK5fl6vasUU6rFmV0wpTVrFmNZmxl6wG7ZM6/Z8rbRTrg6OU1bj0ca72DDKyGkVf4OLAEdevrGI3YPfWiFJWsRswx5kS35hYsxqPtkm5rA4beyWdf9aIBlIqJHbu80vTbpdgN1ktry2n2tpaKioophYlrUOX1aLiEvrt31+mN7/Tib7qcywX0qOUAAAgAElEQVT9adlblLV3N2T123MrqBioSLXOabxl8+dkvopIJ59qWuwGjN2AVftKkHRRCApkNUiLueeFrPKxhazysIWs8nAVUTENOJktZJWvr+lETrmsit2AZVN+zanBmbIbcFZONu2r2Us5xp/ighYkxDLskVURc/Hri+ltQ1YfO74fTXhrBQ3bsYtGnTgi0QcwslpG/QcOofYdj9I5J+rTQla9scVl1CkKgZLRwciqd5/xkwKy6oeaWh7IqhonP6kgq36oeeeBrHoz8psCsgpZ9dt3OPOlXFbTbWRVtr5WNIhVqmVrVl/cMJ8ue+lHdGqnH9DsM5/lbMPEutVRJYW0ISeLBho7A/9lTwU1q2M9JHtwrFnlQxzmNGC+UqZnZC9ZTc9aRV/qKGU1+trzliCIrPKWLP2j+5XV9K85bw2ilFXemkUfHbLasA2wZjX6fplyWU23NatCVu+d8ZTr9GSZrN678g6aZvz9Wf9f0A0n3Mbe0luMDZdGlRTQNuO/3WpqadaeSjqyNn2NFbLK12Ugq3xsIas8bCGrPFxFVMgqH1vIKg9byCoPVxEVsgpZ5etd/iOnXFZFUdNpN2C/snrZ4h/Si/9eQPef9jiN+16p/xbSyLkiL5seKsyl1/NzqI8xwjrFeK3N2RXpuUswZFWj4TWTQlY1gWkkh6xqwNJIClnVgKWZFLKqCUwjOWRVA5ZGUsiqBizNpJBVyKpml0lJ8khkNSU1C+kgMrG2TgF22mCpiqqosq6SivNLKDcnj5oXFbOsWbXulCt2qfuyfA+9dsZIKjPewfo/L71MvZs2p0t79kvQwG7Aep0Ca1a9eWHNajIjL1kNuumXd4vwp4hifXCUshqXPs7VskFkNYq+wMWBI65fWcVuwO6tEaWsYjdgjjMlvjGxwVI82gayqtkOF11zN+3YuYeem3VHIqeQ1ZKSEiovL6fq6urEz7KyshKiWptdSy2MzZXEv1u0aEFVxqtrxN/CwkIaMGAArV69mo499ljatGkTnXTSSTR79myaOnUq3X333Yn/fv3117R8+XKaOHEivfzyy4njDB48mKZPn574mYj53HPP0dFHH019+/ald955h3bv3k0DzjiD7jHK8aGR5z9GnmFGnl8Y/17y1FOJ43Xr1i1RzoMHDyZiXXfddUkUxDHFR5TJ/pk5cyadffbZ1K5dOyk5r9+LTKJeotyTJ09Wom+to1KGbxMJnqIOnTp10slWn1a3nF4H2bhxY317eqX18/uPP/6YPvjgAxo/fryf7L7yWPulrwAhZdq1a1f9+RNSSJYwQfskS6E0g6YLa81qOSaPSx8Pqz5hxmlsfSFMdm6xVq1albgvEN+1+MSLgHmfdYZxn4VP5hMQ9/i33HJL5lc05jVMmayaa1Vl71J1+13c+JnvhDVHV2Ujq2RseFRVV0VZxoZHzXKbU1Z2dspGVq3vWX307WW0onULevmEE+g8Yzrw95+eS/2+1xPvWVXsVBhZ9QYVl1GnuIzwYGTVu8/4SYGRVT/U1PJgZFWNk59UGFn1Q807D0ZWvRn5TYFpwMnkMLLqtyeFmy9lsnr2pBupdatienxa8iieWR37iGW41QwvmuwVO/YNln73j9to+j/vol8NupmmDrg+vIP7iLQyN5smF+UnNl46pqaOZu+toE7Gf+P+wZpVvhbCmlU+tl6yynfkzI4cpaxmNllssMTZvn5llbNMmRA7SlnNBH5udYCsNqSD3YCj7/Upk1Wn96uaCOL6nlXxqp03Ftxf31Iy6bbL6uUvT6CF65+hh86YQ2O6nBt5K39hiOqk4nz62Hj3a4HhqWLjpSsOVMX69TaQVb5uA1nlYwtZ5WELWeXhKqIGGVnlK1VmRIas8rQjZJWHq4gKWYWs8vUu/5Ehqx7shJxu2Li5PtWgft0bjA7bZfW4x79D2/ZvpbcuXE2dSr7rv3VCzCnexXpTs3yaZ2y8JFbWtjFea3PD/io6P6a7BUNWQ2x8WyjIKh9byCoPW8gqD1fIKh9XERmyysMXssrDFbIq54qRVb7+pho5ZbIqRiivnTKexo4cKi2byitiVCuVynSyNau1ZPzJqqXmhUVUZ0hhVGtW7esJxW7AeT170/Q+PUlMDy40Nli61thgqeMVV9NoQ1pzvwX3/sq3Ev/Xb+CJDVDOK5tFJ506ilof1kaK2ev3IpPKWlCrrFp3PNZp26A7r6qUU6c8WzZ/Tu+tXEFnnsPzKqONn62n9R9/RKeNOse1WGHKKtasJqP2ktWgfVKnv3GljWJ9cJSyGpc+ztWeQUZWo+gLXBw44vqVVewG7N4aUcoqdgPmOFPiGxNrVuPRNimT1RvufJjWfrqpfhdde/W91rTGA1fDUjjJal1WnTG9SshqbaxktUu3XokNlp41Rljvza6hC+6/j+4ydgMWI60XG9ODf3iwhjb+403IqqJU6/RLyKoOLb20cblphqzqtZtqasiqKin9dJBVfWaqOSCrqqT00kFW9XjppMY04GRakFWd3sOXNmWyKqogRlfFx7oG1Pz5zl17yfr+Ur4qhxvZSVbFjsBNC5vHVlYFhb2VFVQ2eybN+uWvaKOxc7H4JNa0vr6UelXX0qjjhzSA5TVy6vV7EVBlxBIjq/r9FCOrZVQ6Qe11SPp01XJAVtU46aaCrOoSU08PWVVnpZsSsqpLTC09ZFWNk59UkFXIqp9+w50npbIqKiNGWBe+siKpXrJ1oNwVDzO+dc3qb9++mR547x66euCv6RcDbwrzMKyxXsvPoVmFObQ0L6f+OGK09dSqGhpeWUvDjf82S+EmwlizytfcYU4D5itlekb2ktX0rFX0pY5SVqOvPW8Jgsgqb8nSP7pfWU3/mvPWIEpZ5a1Z9NEhqw3bAGtWo++XKZfV6Kscfgmssjrl5Qvp+fXP0h9PfZjO6/bj8A/GHHGDMcI6qzCXXjTkVbzuxvyI9awDqg5J6wjjv8fU1CZGYbk+kFUuskSQVT62kFUetpBVHq4iKmSVjy1klYctZJWHq4gKWYWs8vUu/5Ehq/7Z1ee0yuroucNo1bb3aN7/vEqD2jfcoCiEw6UsxAfGJkzL8oy/hri+b/y/2EXYKq/fM6YKdzPe2do78d9aOra6jorrwjFYyCpfM0NW+dhCVnnYQlZ5uEJW+biKyJBVHr6QVR6ukFU5V4ys8vU31ciQVVVSDumc1qzm5eZTXl5+rNesVlZU0JNzZtDES6cm1U62G/DOrCxamp9NW/7yOP39rDH0j44dkuTVDHDlzJn0yeizqMXhbRObNrUz/or/Hm78bW/8PdL4izWr2A044GnXIDs2WAqbqHO8KFhHKavYDThefSF1PT34kfzKKnYDdmcfpaxiN+Dg50U6RcAGS/FoLchqwHaQyWod1VFebh7lZpCsmpjMDZRKjFfXfGKMtq4xpg2vNf77UY7x/7lZ9MOHH6YFZ59NX7dr50i2x1db6IyFC+mdiy+tT9PMGJFtZRmULcgmOjo7mw5UVFPh4heo5sijqG2P3kkxD68lKjRYm59i43+LDRk2P+/Oe5IGDxhC7Tse5auVVaRaJzB2A9ahpZc2CoGSldBrZBWvrtFrVzM1ZNUfN5VcQaYBx+W8U6lnFGkgqzzUIas8XEVUTANOZgtZ5etrOpEhqzq0JGkbq6w6vWf1qadmUcfTR9Putu0Sa16/Mf5uMf5+8e3/bzMktOnWrTT2uedoxmS1nVtF2o1HH02r+vbVaq1Js2fTspNOoo2dOmnlMxO3+/prrXJ6HaTTxo00fPlymjVxoldSX7/v9vHH1PeDD6hs/Hhf+f1kGvnyy7SrpITeGTzYT/bQ8rTYtYtEe/9xavIsgdAOEFKgoH0ypGIEChMGazHDQvcjblBrQ1pmoHPswa+8QntLimnNoGj7uE6ZddIaWMXm9QZbnVyH0jY3zrvRT8yhp668Sj9zI8gh+myd0Wd10Xb5YBW13/Q5/X3MmEZAyV8Vc4x7iho/ndbf4epz9fzHO1S0ew+9c/rpASPFM7u4FmRFdK2NI5GL//c2uuWWW+JYtEZVJshqCM1trlmduWo63fbmDfSTPlPo9u9PCyFyZoYoN66GnxgjsRX/3b+JdhsXxz2Wf9cYo7W7jJ2Jxciq+fnCyGP9fGP882DiNuvQR+TfY9kUShxHTF/GBwRAAARAAARAAARAAAR0CFy7v4ruaZqnkwVpGQhAVkOAasrqjcuvplmrZ9KtQ++mS/seeqcsPv4IYIMlf9xUcmGDJRVK/tJ4TQP2FzXzcomZFjofMQ24uGku7dhTqZMNaRUINC3IpRxjOYf4HsMnXAIti/Kp/GA1VRo76OMTHgExYt26JJ++2VURXlBEShBoUpBjLGPLpj3luB4IHiXGtIhurQrROyImAFkNoQFMWb3w+bH0+qZX6PHRc+mM75wZQuTGGwKyytf2kFU+tpBVHrZRrlnlqVF8ogZZsxqfWsSzJH7XrMazNvEpVZRrVuNDgackWLPakCt2A+bpazpRIas6tCRpZWtWxXz/nJycjN5gyWnNqrkBk9PvBUKVjYussrp8yWJq3+EI6to9eYMlr6YLupmNSjm9ymD9PTZY0qGllzYuG714yWrQPqlHhSd1FKyjlFXsBuzcj6LoCzy9mieqX1nFbsDu7RGlrGI3YJ5zJa5RscFSPFoGshqwHUxZLS8vp9qamkQ0yOoogqw27FiQ1YAnm0v2uNw0Q1Z52hiyysNVRA0yshqX846PTrDIkNVg/JxyQ1Z5uIqoGFlNZgtZ5etrOpEhqzq0JGnrZXXfPqqtPbQuBbIKWZV1K8hqwJMNssoHUCNyFIICWdVoIM2kkFVNYBrJIasasDSSQlY1YGkmhaxCVjW7TEqSQ1ZDwCzWrD7+r1n089cuo3O6jqcHTv9zCFEbdwisWeVrf6xZ5WPrNbLKd+TMjhylrGY22WAjq5nOJmj9/Mpq0ONmev4oZTXT2UJWG7Yw1qxG3+shqyG0gZDVW5f/hqatvIOmDriefjXo5hCiNu4QkFW+9oes8rGFrPKwhazycBVRg4ys8pUqMyJDVnnaEbLKw1VEhaxCVvl6l//IkFX/7OpzClm9aOEkeuaTv9G0U2bQ+O4TQojauENAVvnaH7LKxxayysMWssrDFbLKx1VEhqzy8IWs8nCFrMq5YmSVr7+pRoasqpJySGeuWd29dxdl12UnUmHNKtasyroL1qwGPNlcskexjlJWHC9ZxW7A/vpAlLKK3YCd2ywu552/XsWfy6+sYjdg97aJUlaxGzD/eROnI2CDpXi0BmQ1YDsIWW1eVES79+2mHMgq4dU1zh0KshrwZIOs8gHUiByFoEBWNRpIM2mQacBR9AXN6kWaHLLKgx+yysNVRMU04GS2kFW+vqYTGbKqQ0uSVshqYbMmVF6+j3KMP+KDkVWMrMq6FWQ14MkGWeUDqBE5CkGBrGo0kGZSyKomMI3kkFUNWBpJIasasDSTQlYhq5pdJiXJIashYH72o4V07rNn08mdTqcnzlwQQkSEwJpVvj6ANat8bL2mAfMdObMjRymrmU0WGyxxtq9fWeUsUybEjlJWM4GfWx0gqw3pYM1q9L0eshpCG9z75nT6xZKf08Tel9GdJ/0xhIgIAVnl6wOQVT62kFUetpBVHq4iapCRVb5SZUZkyCpPO0JWebiKqJBVyCpf7/IfGbLqn119zp+9+HN68N3pdPPQ39LkvlNDiIgQkFW+PgBZ5WMLWeVhC1nl4QpZ5eMqIkNWefhCVnm4QlblXDGyytffVCNDVlVJOaQTa1Yr8yopp0qsWMWaVWyw5NyhsGY14Mnmkj2KdZSy4njJKnYD9tcHopRV7Abs3GZxOe/89Sr+XH5lFbsBu7dNlLKK3YD5z5s4HQEbLMWjNSCrAdtByOqBnAOUX5MPWTVYQlYhqwFPKV/Z43LTDFn11XyemSCrnoh8JwgyDTgu553vyjNnhKzyAIas8nDFyGpDrpBVvr6mExmyqkNLklbI6t6svdTU+JNTh5FVyCpkNeAp5St7XG6aIau+ms8zE2TVE5HvBJBV3+g8M0JWPRH5SgBZ9YVNKRPWrCZjgqwqdRv2RJDVgIhXbl5Jgx4dRMe1HUAvnLc8YDRkNwlgzSpfX8CaVT62XrLKd+TMjhylrGY2WWywxNm+fmWVs0yZEDtKWc0Efm51gKw2pIM1q9H3eshqwDYo+6iMLnj2Ahrb9Xx68P+3d3exchWHHcAHaCkPtXFM1NIQyS4BhKEU5IaAUhCRmgINFXZ4wa2U4JI0mAeKRKQ6wRK0SAT8ECrEA5AQaojUmlZKbKomkBIViosIUhDUpVBBLSNBChUQPhQg5SNllp7L3vXunXPO7uzuHP9uFEXxmZkz85vZPed/z8c9c9uYrakurOZfA8JqPmNhNY+tsJrHNbY6zpXVfL3qRsvCap55FFbzuMZWhVVhNd/qat+ysNrerlfzml3XhMt/eHn4s4//edh86l+M2Zrqwmr+NSCs5jMWVvPYCqt5XIXVfK6xZWE1j6+wmsdVWB3u6spqvvVWt2Vhta7UiHLxmdVX3vvPigNXhF+8+4teqQMOOCAcdNBB4Zd++eD3/u3dcMCBB4ZfXbY8vPPWW+Htd94OBx/8K+G4314bnvrP/wjHHHt8+O+fPBPWnvzJ8I87tocNn78o3PbN68MffX5TePGF58OPH3og/OFnN4T+N1Juv/3mcM76DWHZ8kPDfT/8fviNj3w0HLPmhDD4lrrBt1j+0/e+G44+9rfC6iOP7vXzf3/+8/C3t98ULvjTxX9u5+GH/rW3fe0nfnefUaeeSU1tjw2++ML/hPvu+V44b8PGkfr9twH3j7HJdI375tU6/WzSH28DbqLVrKxnVpt5jVN6FtazDKveBjx6tcxiLYyzdqddt21Y9TbgpWdqlmHV24Cn/Sma7f48szpb/2rvwmqNeVi3cUt4au+zvZJHrT4i7Nx29UKtKqx+6MAPhXffC6bxR1j9TDjsw782UrZOCBRWayzMgSJ79zwZnnzi38Pvf+azS1ae5JXVeTmRn5eT5tSV1XF/gdJ8VUy+xiyshdXJz2PV4ji3Ac9iLeSTmHzLwurkTWOLwmoe19iq24AX2wqr+dZak5aF1YTWhZdtDS++9OpCQI3B9bCVy8Ot123u1VwIqwetDO++846wun1bOOPTwuqwZeXKapOvpmZl5+WkWVhtNm91SwurdaWalxNWm5vVrSGs1pVqVk5YbebVpLSwKqw2WS/TKiusJqRPX39J+PKm88P6s0/rldxx167w9ZvuCPfvuOH9YPqXB4SPrTwq/Msf/9u05my/2I+3Aeeb5kleWc3XyzJbToXVMkc1+17PMqzOfvR5ezBOWM3bs/JbbxtWyx953hHMMqzmHdnsWxdW950Dz6zOfl0Kq0vMwe7H94QNF18Vtt94RThhzZG9koP/FsPq7/3mmeH2c3bMfjY71ANhNd9kCqv5bIXVPLbCah7X2Kqwms9WWM1jK6zmcY2tCqvCar7V1b5lYXUCYXXTxzeFG8+5sf0sqEmAAAECBAgQIECAAAECiwSE1THDanxmddnyZeGN198Ib7/9dq+1A997+298G/DBBx/ce+lSfOHSihUrwlvvvQ04/veQQw4JJ598cti9e3c48cQTw9NPPx3OOOOMcNttt4VLL700bN26tfe/zz33XLjvvvvCBRdcEO6+++5w6KGHhlNPPTVcf/31vX+Lbe7cuTOsWrUqnHTSSeHBBx8Mr7zySjjrrLN6/eivE///HXfc0dvfscce29v+5ptv9travPn952+rn7jP+BP7NPhz8803h3Xr1oXDDz98qFxqe6wUxxX7fdFFF9X6OPaPsVaF/y8UPeMYVq9e3aTaQtmm/UztZO/evQvzmSrbZvsTTzwRHn300XD++ee3qd6qzuAaa9XIBCq9/PLLC5+fCTSXrYlx12S2jjVouBTrBkNasui8rPFJjWeS7exva2GSdku19cgjj/TOC+Kx1s98CQyeZ81X7/Rm0gLxHP/KK6+cdLPaayggrCbAhj2zuuXaW8Jj927r1Xw/rC4Pr//sZ+EdL1gK/nTN6AXlBUsNv50aFPeCpQZYYxadhfUsbwOelzdejzltI6uPcxvwLNZCLocc7ba9Ddifrll6NmZ5G7A/XZPjkzK/bXob8HzMjbCamIc6bwMWVj9AFFaF1Vl8tc3LSXPqmVV/uqbd6hBW27nVqSWs1lFqV0ZYbeeWqiWspoTab/fM6mI7YbX9WppkTWG1huZSf2c1Vn/t9bfCa2+8fwuwn8kIeMHSZByHteIFS/lsU2E135673fIsw2q3Zb1gKef8tg2rOfvUhbZnGVa74LfUGITVfXW8DXj2q15YncAcCKsTQBxoQlidvGnVorCaz1ZYzWMrrOZxja2Oc2U1X6+60bKwmmcehdU8rrFVYVVYzbe62rcsrLa3W6gprE4AUVidPOKIFoXVfNTCah5bYTWPq7CazzW2LKzm8RVW87gKq8NdXVnNt97qtiys1pUaUc4LlhbDeGZ19ILygqUxP2xLVPfMaj7bwZZnYT3LsOoFS6PX1izWwvRW+vh7ahtWvWBpaftZhlUvWBr/c1FSC55ZnY/ZElbHnAdhVVitu4SE1bpSzcvNy0lz6sqqFyw1n9tYQ1ht51an1ji3Ac/L567OOGdRRljNoy6s5nGNrboNeLGtsJpvrTVpWVhtojWkrLAqrNZdQsJqXanm5eblpFlYbT53dWoIq3WU2pURVtu51aklrNZRal5GWG1uVreGsCqs1l0r0ywnrE5T274IECBAgAABAgQIECBAoJaAsFqLSSECBAgQIECAAAECBAgQmKaAsDpNbfsiQIAAAQIECBAgQIAAgVoCwmotJoUIECBAgAABAgQIECBAYJoCwuoY2us2bglP7X2218JRq48IO7ddPUZr5Vdt6pEqP872Cy/bGn708OOLUB+7d1uxyCmLwYGlyo+7vdrfV7/2jXDnDx4I22+8Ipyw5sgifVMWs7A9/lMbF3a76XPnhku+cF5xtvPmevr6S8JLL7+24Fjy90HTNdm0fJ252/34nrDh4quK/uwP+1DVGXt/vVT51PbY1ijLLh3H6jhMy7V/P45h+5671pmr1Oe/C8ew4g66He6wsNpycuNB5MWXXl0IqPHDfdjK5eHW6za3bLHsak09UuXH3R5PTO/fccMCajwg7Xpo96J/K0U8ZTE4jlT5cbdX+9tx167w19u/3/uFTalhNWUxbdvqBODqr3wxrD/7tFKW6D79nDfX+P183DGrwjWXf6nX18H+FQs9ZCypY1FqblLbo1V/8C/1sz9szuuMvb9eqnxqe8qyK8exOg7TdHUMG33uWmeulvr8d+UYVvIxoYt9F1Zbzmr8sH550/kLJ5TxxP3rN91RZBhqSbCoWlOPVPlxtw+OKfVbwEkY5GojZTG431T5cbdX+4u/OY0nqiVfXUlZTNs2Bo1Pn/47RV5J7beaN9em/cn1Wc7RbtOxpcqntldjKPk7ddQ81B17VT9VPrW9qWWp5nUdpu3qGBbC4Llr3bkatRa7cgzL8V2tzfYCwmoLu2Ef0lIPIi2Gv0+Vph6p8nEHgwGov05q+7DbUW/41nfC3/3DPxf3y4SU1eBYU+VTdqnt1f7iAelPNvxB+NiqjxQbVlNWs7CNJ08rVyxbdLtqaVeu5tG1utWvuvW3KydU07bu/0x07ZhXgmWJx7F5dXUMe/+xnbbnVqM+/104hk3ivFgbkxUQVlt4Nv3ybbGLoqo09UiVTwWm1PZRIaPEWytTVrMIVPHE//kXftq75b3kE9Z5s63Wdf86HQxZJXwxzJtr/IxUfer368Izq9O2FlY/WEEp+ybHqTrfo6XeXplymvQxrM4adQz74B0Tkwyrw9ZoicewEo6z+1sfhdUWM970y7fFLoqq0tQjVT51kE9tH3awKvUlNSmrSR/oU7b/9fRPFt3uXucka14X87zZDrOP/xZ/U13SL1rmzTV+Rqrb/arPS7xCddO37wylB9ZpW9cJAvP6eU/1a54tq76VeBybN9fB214dwz54UVrq+J/6/C91tbWkY1jqu8L26QsIqy3Nh93Xv+XaW4o/+WnJ0XvhxuAzvEt5pMqPuz2OIx6UYh9Ku41ycA5SFk3Lp9pbantlOmydlHgilbKYpu2oYFpaWI3jmCfX6gSqP5iWfILadE02LV937rpkWBnVHXvd8nXbW8qyC8exug7TcHUMW/pcre5cNQmmJR7D2p4Lq5dHQFht6VrnjWktmy6yWsojPh8Sf6o/75MqP+72Lr3wKmUxbdv+BVr6Ceu82cb+PLnnmYVnq0t9i/W8ucaTpVPWrll4W3uprsMODtO2rvpQ+me/BMuuHMfmeY2Wvo7nzbYrx7AiT8Q73GlhdYzJrfO3qMZovriqS3kMBqo4uJRf2+3Dnk+rMEu9FWVebAcXZekH+tQ6nOa6rWz75zq+bKn/TzCV9KUwb2u2/+/+lew6bA1M2zpefen/m7Vd8pwXy64dx+bF1TFs/HOv1Oe/K8ewko63Xe+rsNr1GTY+AgQIECBAgAABAgQIFCggrBY4abpMgAABAgQIECBAgACBrgsIq12fYeMjQIAAAQIECBAgQIBAgQLCaoGTpssECBAgQIAAAQIECBDouoCw2vUZNj4CBAgQIECAAAECBAgUKCCsFjhpukyAAAECBAgQIECAAIGuCwirXZ9h4yNAgAABAgQIECBAgECBAsJqgZOmywQIECBAgAABAgQIEOi6gLDa9Rk2PgIECBAgQIAAAQIECBQoIKwWOGm6TIAAAQIECBAgQIAAga4LCKtdn2HjI0CAAAECBAgQIECAQIECwmqBk6bLBAgQIECAAAECBAgQ6LqAsNr1GTY+AgQIECBAgAABAgQIFCggrBY4abpMgAABAgQIECBAgACBrgsIq12fYeMjQIAAAQIECBAgQIBAgQLCaoGTpssECBAgQJZ7zi8AAAa3SURBVIAAAQIECBDouoCw2vUZNj4CBAgQIECAAAECBAgUKCCsFjhpukyAAAECBAgQIECAAIGuCwirXZ9h4yNAgAABAgQIECBAgECBAsJqgZOmywQIEChd4IZvfSfc9O079xnGps+dGy75wnnh9PWX9Lbdv+OGfcrEbStXLA87t13d25Zq6/hPbVySa+WKZb39XHjZ1vCjhx8fWvbqr3wxrD/7tLBu45bw1N5nQ/X/q8I77toVtlx7Szhq9REL/RpsqE4/TvvECeHOHzywUPXcMz8Zrrn8S432W2ccpa8f/SdAgACB/UNAWN0/5tkoCRAgMDcCVZjafuMV4YQ1Ry70K4bOe+7/8ULYi+HulLVrwq3XbV4o89WvfSPsemj3Qoit29ZgqBwMm3F7bOvFl14dGTZjmSqsDvar+velwmr/BFThdlg/hm1rst8645ibxaAjBAgQIEBgCQFh1fIgQIAAgakKxBBaXTFcaseDoW3343vChouvWnRVs25bkwyrh61c3rsCW4Xtql8xwKbCbp1+jAqrdfcrrE51OdsZAQIECGQUEFYz4mqaAAECBPYViLfxHn3kRxddMR3lFIPXk3ue6V1JjVcXY2Drv9LapK24j6WuaNYJebEPxx2zKjz/wk/Dr3/4Q71bdOPV3vgT/y1nWK273zrjsC4JECBAgEAJAsJqCbOkjwQIEOiQQBUYqyFVz4yOGmL/s56P3bttUbGmbaXCap1nVmNoPGXtcb1nVGN/Yv/iVda/+ubfZw+rdfbrmdUOfVgMhQABAvu5gLC6ny8AwydAgMAsBapbaKs+DLs9uAqY1cuXRvW3SVvjPLMaw2r10qPYl+pqb5Mrmm2eWa273yb9mOXc2zcBAgQIEEgJCKspIdsJECBAYCoC8Xba+Cbcwaunw55VTXVoVFupK6up23ir24BjWK3eQlwF3yYhcZywmtpvk36kHG0nQIAAAQKzFBBWZ6lv3wQIENjPBGLw/Jvv3tO7Mjn4U4WwwbcEjwqrbdqaZFiN/Y/PzFZ/XqdJSBwnrKb226Qf+9nyM1wCBAgQKExAWC1swnSXAAECJQv036rbfwW1/426/S9QimNdKqzGtwPHn7ptTTqs9s9Fk5A4blhdar9N+lHyWtJ3AgQIEOi+gLDa/Tk2QgIECMydQP9Lk6rOjXomNXUbcJO2UmG17guWhl0ZbhISR/Wjun25Mqme4e2//XhwMgf36wVLc7fcdYgAAQIEWgoIqy3hVCNAgAABAgQIECBAgACBfALCaj5bLRMgQIAAAQIECBAgQIBASwFhtSWcagQIECBAgAABAgQIECCQT0BYzWerZQIECBAgQIAAAQIECBBoKSCstoRTjQABAgQIECBAgAABAgTyCQir+Wy1TIAAAQIECBAgQIAAAQItBYTVlnCqESBAgAABAgQIECBAgEA+AWE1n62WCRAgQIAAAQIECBAgQKClgLDaEk41AgQIECBAgAABAgQIEMgnIKzms9UyAQIECBAgQIAAAQIECLQUEFZbwqlGgAABAgQIECBAgAABAvkEhNV8tlomQIAAAQIECBAgQIAAgZYCwmpLONUIECBAgAABAgQIECBAIJ+AsJrPVssECBAgQIAAAQIECBAg0FJAWG0JpxoBAgQIECBAgAABAgQI5BMQVvPZapkAAQIECBAgQIAAAQIEWgoIqy3hVCNAgAABAgQIECBAgACBfALCaj5bLRMgQIAAAQIECBAgQIBASwFhtSWcagQIECBAgAABAgQIECCQT0BYzWerZQIECBAgQIAAAQIECBBoKSCstoRTjQABAgQIECBAgAABAgTyCQir+Wy1TIAAAQIECBAgQIAAAQItBYTVlnCqESBAgAABAgQIECBAgEA+AWE1n62WCRAgQIAAAQIECBAgQKClgLDaEk41AgQIECBAgAABAgQIEMgnIKzms9UyAQIECBAgQIAAAQIECLQUEFZbwqlGgAABAgQIECBAgAABAvkEhNV8tlomQIAAAQIECBAgQIAAgZYCwmpLONUIECBAgAABAgQIECBAIJ+AsJrPVssECBAgQIAAAQIECBAg0FJAWG0JpxoBAgQIECBAgAABAgQI5BMQVvPZapkAAQIECBAgQIAAAQIEWgoIqy3hVCNAgAABAgQIECBAgACBfALCaj5bLRMgQIAAAQIECBAgQIBASwFhtSWcagQIECBAgAABAgQIECCQT0BYzWerZQIECBAgQIAAAQIECBBoKSCstoRTjQABAgQIECBAgAABAgTyCQir+Wy1TIAAAQIECBAgQIAAAQItBf4PaMHH/cb4sAQAAAAASUVORK5CYII=",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(chemicals=['S', 'P'],\n",
" colors=['cyan', 'green', 'violet'], show_intervals=True, title_prefix=\"With a LAVISH amount of enzyme (NOT shown)\")"
]
},
{
"cell_type": "markdown",
"id": "7faa3d9f-f2b3-4031-9bb5-ebb18dfb5345",
"metadata": {},
"source": [
"_Note: NOT showing the enzyme (concentration 2,000) in the graph, to avoid squishing down the other curves!_"
]
},
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"execution_count": 65,
"id": "fb5f2c87-acbe-42e7-867f-15a42e0c726e",
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"source": [
"new_crossover = dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
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},
{
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"id": "7cf81e1a-dd35-4075-95d0-a7f014dc02e5",
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"source": [
"## Yet more speedup of the reaction, over the previous run"
]
},
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"execution_count": 66,
"id": "859e65f6-873e-4126-88f3-24ef0cfb8030",
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"text": [
"0: S <-> P\n",
"Final concentrations: [S] = 3.313 ; [P] = 16.69\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.03748\n",
" Formula used: [P] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 5.00001\n",
"Discrepancy between the two values: 0.7496 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"1: S + E <-> P + E\n",
"Final concentrations: [S] = 3.313 ; [E] = 2,000 ; [P] = 16.69\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.03748\n",
" Formula used: ([P][E]) / ([S][E])\n",
"2. Ratio of forward/reverse reaction rates: 5.00001\n",
"Discrepancy between the two values: 0.7496 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
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],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
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"execution_count": null,
"id": "5de0f238-e027-42ca-bbed-a4a7b3e54e79",
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"metadata": {},
"source": [
"## Now, let's look at the time of the crossover points (for the [S] and [P] curves to intersect), as a function of the Enzyme concentration"
]
},
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's plot just the first 4 data points, to avoid squishing the graph\n",
"px.line(data_frame=df.loc[0:3],\n",
" x=\"Enzyme concentration\", y=[\"crossover time\"],\n",
" title=\"Time of crossover of [S] and [P] , as a function of Enzyme concentration (first 4 points)\",\n",
" labels={\"value\":\"Crossover time when [S]=[P]\"})"
]
},
{
"cell_type": "code",
"execution_count": 69,
"id": "42894206-49cb-4880-857c-e831fd8800bb",
"metadata": {},
"outputs": [
{
"data": {
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"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "variable=crossover time
Enzyme concentration=%{x}
Crossover time when [S]=[P]=%{y}",
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"line": {
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"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "crossover time",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
0,
0.2,
1,
5,
20,
30,
100,
2000
],
"xaxis": "x",
"y": [
0.7435259497128707,
0.24710707675961718,
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0.014494267066104415,
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0.002465868124424963,
0.0007383445224719487,
3.7174487975074336e-05
],
"yaxis": "y"
}
],
"layout": {
"autosize": true,
"legend": {
"title": {
"text": "variable"
},
"tracegroupgap": 0
},
"template": {
"data": {
"bar": [
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"error_x": {
"color": "#2a3f5f"
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"error_y": {
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"marker": {
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"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
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"barpolar": [
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"pattern": {
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"solidity": 0.2
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"linecolor": "white",
"minorgridcolor": "white",
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"baxis": {
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"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
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"type": "carpet"
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"choropleth": [
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"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "choropleth"
}
],
"contour": [
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"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
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"heatmapgl": [
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same plot, but with log scales on both axes (all data points used this time, \n",
"# but the value E = 0 is automatically dropped by the graphic function because of the log scale)\n",
"px.line(data_frame=df,\n",
" x=\"Enzyme concentration\", y=[\"crossover time\"],\n",
" log_x=True, log_y=True,\n",
" title=\"Time of crossover of [S] and [P] , as a function of Enzyme conc - log scales on both axes
([E]=0 value skipped)\",\n",
" labels={\"value\":\"Crossover time when [S]=[P]\"})"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1bb12fdd-1c93-4cf3-a302-13da5339e82a",
"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
}