ProyectoModulo1_EscotoU_TinajeroC_SaveyedraJ.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Código de deformación de Vigas\n",
    "\n",
    "## Hecho por:\n",
    "- Héctor Ulises Escoto González\n",
    "- Jorge Diego Sayavedra Godinez\n",
    "- Carlos Adrian Tinajero Velazco"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objetivos\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### General\n",
    "\n",
    "Determinar de qué manera una viga simple apoyada en un punto A se deforma cuando se somete a un esfuerzo P en el extremo contrario al cual en el que se apoya.\n",
    "\n",
    "### Específicos\n",
    "\n",
    "* Hallar una expresión matemática, en forma de ecuación diferencial, que nos permita analizar y simular el comportamiento de una viga sometida a esfuerzos.\n",
    "* Definir qué importancia tiene esta clase de aplicaciones en el campo de la Ingeniería Civil.\n",
    "* Simular el comportamiento de una viga particular dadas las condiciones propuestas por el modelo matemático.\n",
    "* Graficar y hallar los resultados numéricos que solucionan el modelaje del comportamiento de la viga."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importancia de este modelo\n",
    "\n",
    "Dentro del amplio campo del conocimiento, entre las incalculables aplicaciones del desarrollo matemático, producto de la razón y de la ilustración del pensamiento del hombre, encontramos los métodos de matematización que nos permiten resolver problemáticas variadas, y así, dar solución a los obstáculos que se interponen entre el hombre y el amplio camino hacia el progreso.\n",
    "\n",
    "En el nombre del progreso y de la incomensurable capacidad humana para innovar, por el desarrollo de la tecnología y el descubrimiento de nuevas formas y métodos para salvaguardar los derechos inalienables, imprescriptibles e irrevocables del hombre, damos justificación al presente proyecto, cuyo objetivo principal reside en fomentar la aplicación de la tecnología y la ciencia en beneficio de todos los hombres y de todas las sociedades del mundo.\n",
    "\n",
    "Por lo anterior, nos vemos en la necesidad de realizar el presente proyecto fundamentado en la imperante obgligación y con ella en la responsabilidad de nosotros, como ingenieros y ciudadanos del mundo, para presentar y profundizar en las aplicaciónes que darán solución a las problemáticas constructivas y urbanas, y permitir así la seguridad y la integridad física estructural, la cual debe garantizarse a todas las personas por igual.\n",
    "\n",
    "Así, exponemos el presente trabajo y describimos la metodología utilizada en la realización del mismo, que tiene como finalidad utilizar el código **Python** mediante la plataforma **Jupyter** para resolver una problemática común en el ámbito de la <font color = blue>Ingeniería Civil</font>, la cual consiste en el **análisis estructural mediante el momento flexionante.**\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "En esta ocasión nosotros definiremos una problemática conforme a una viga de 20 pies de longitud que se le aplica un momento en una fuerza de 15k en uno de sus extremos"
   ]
  },
  {
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"
    },
    "2.PNG": {
     "image/png": 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quVdfFjlB/0Zs9LIZJlOufBi0g4uRgCf3ge8mV9VH2JlNpe8YT6RNtfl61lnnlJ///Odlafueju98vTZ4/vziXu2ntuyccw8Jsf+zjBtSj269twrhnyNv7C+WU087s/u78fGpcsEFF5VvPP10uf0v/lfZtrRD2t3rD8rRMb963OrEqowlUX/DX4zFa2y5bYvOkmzpY2WojcwMeAvQJa0KO/12ITMcHK9LWjVliY4uO0pg2BKHo+MAXV2Kp02O3AM2dAAzJU/uARvaw0zJk3ug7dgw27PlwJWBDb6mfuo7R2cI8mxmiCzFs1Tu6jholnIi/qb9JGO0j0h6W6r0ddqg7ayqMIOt8p3o8Hz9niioqh82+E5m/iRKtb8FxFvUxt6Kx+raA0SP/iTha8tBjxk9sUAdq+w6vqM91LHa3/JszaNAfANsuuOJIx+C6NFHxCo/uzotUDfaA6HpPekVdtSHMYGBVuOnpizR0c9TQup8L47UT+M7ZLNWJx7swfHkHmg7E2TywpN7oG6MJ12eqKif2bB8z/6Een+T37Spto96B9QsP9bxXPqPb/DN7/h/luKJvX5dymR3/G/ljd3Oi+/YyO9P0Y11z5X9+08e0KdcVg6++tWv6qa66elpLYtyySPiVLlF/r9rdxhQJi+B1fkqaGKVCcTqN891bGz939frB3rNkjKV8HQ80CglAKm0J/eA7uo3z/GN3ddpg3KYkUc3c5HwdIB9G/H1+oHvwpvnOn3U+8bu6DggQPED/vDkHprNc7E+skEsEgvo6jd2/F0dd32b5yrr1/ibASlSP+LNbCr7SEBOMCmK2NCf5ERt3Xg2NoPf2H3dftCfTPqpY60NesRpxAZAnHwyqs0J9Jgcsx/Elw9D6yb9w+pNxHeMCfihPif6vrGrTa3vjKQj+cqz7Rv70dg8JyQdHPM1J8Su1kZ9p+PJ/93Nc/x+ZGRUibr5HX3T3hUPqOu5555bfv/736t+f90pyzt5TtsqfcCfv3FQDQfh9P6m/WhtnrNYZSxePbFLZ+WueOuwSCLSdiYDvBlX+05sclc8vutsLgolSO6K59ldYpd21drRn7krvp/Y6+NnkNh9nTaoX5zYc1d8LbFDuJ/+9Ke7f29Of7Z3xbOznfPkOWzmxz/+sfh28Bz55Yi9AZfTnH322fq38Jxsl5fALIMkdoHYJLHjuyR2kMRuSGI3JLHXEfvOnTv1b86/8IUvlIWFBe2bfmKnjug88sgjesEMf8LW7vOViB1gc84555TnnnuufOpTn9INdWFukboksbeQxA6S2AE2SexJ7EDrlsSubX8jEzvP4s2YPzHjDZxLV/71X/+1fPFLd5VPfvKT+n28fQKc1WVD2b9/v5L7k08+WW6//fbyhS/eUz77v/6y3Hbbbfr//OkapA7B8/berjf2TzzxlbJr1+6B37fBhTJMAigHcud0O/YieboeKDeJvYUkdpDEDrBJYk9iB1q3JHZt+xud2DkR7uMf/7huVLvjjjv0LRxi/8xnPqNL4csdFgO58x2cu9w/97nPlbvvub98/vNf0ENmeA5/sna4w2YgbHa9b9myctzxDCYC11zzbh23bMz3ddugjUnsLSSxgyR2gE0SexI70LolsWvb3+hL8fQFb+UQNW/vGzdukn6dl583an4sVx6/R44dNtu28+dunDdgz4GMD2ePbMuI+LtisyLPoI48kzE/xC1im8TeQhI7SGIH2CSxJ7EDrVsSu7b9ePrGDtA1nqj3N/3Z3jy3EsiJjZuJ78jbt/FEEnsf6Kgk9iR2gG4SexJ7gyR2QxK7tSmJPYl9CJQTdr6Ug00SexI7SGK3+E5iT2IHapPErnULcwuxemTELsnbJfb65G1srNCV7dAj+CA167Casuyg/t4lMJ7OMNDl5Dlrk6/TBjbm/PoOM5vVH1BT22Ho0RYj9rpgb/poNQfU9C6B8XXaUBsJptjkC2KHnCin1g9G7JRX57vmEhgj9tr6mb8bYq9vE30UJXbigIG53sZI2oi9Lo94dpfYuznr63YhOviLQS8aq1wCA7HXt0mIXWyq6wZED2InlyLxA7HrATUaCyvbUR8GcXJPc6KmfqLTJfbDfK8dhF380SX2Khur3zF/QI2MQ2azsh16J8oYjB9q+6jxnfKE+NvXGQb9acQ+eEDN4UBOWHwHiF1thFvYkBfwXZTY0aNeSuwQGYXyEAiKW6BWQvNW17WpsRMdOpgOo8xaGwYVzmlmoHB1HKDLudhaP0fuARsSBEd6cg9qI0QTsukELb6o8gEQPdrCLFZ95+m0gY300czcTj3e09VxQFuoH3735B6wgWgIKk/uwfrVLj/x5B5oO+dOq78r44fnc/42qC5L/c0Zz3YxkqvjgD5qJnqe3ANxgO+qbUSPQVx9F4gFSLAZxKrKEh3im0EiEqs2yRvTFb1aG0DuVdcNiB76SoTVdZNBT/rHjlkW39XYiQ7xhh80JyptmqOCq22A1Alyoq/qbex4YSaUrtwBbecCGHLCk3vAZuOmEYnveB/BFWpTYyc6Np5MWr5WlkX94Alyw5N7IL5Z2SVePbkH6kS/anw7cg9mI2N+7bgl0FiVmIvmBPViPFmD0/WweQkoHlKDfpuG4FcCehTYu2DE12uDxhGETSNrwI04egnMaHMhx8rARg/qlw7w5B4YxMfGZ4M2dnGM2QR8J75mhh3xHcnBLXcR31GvsQkutgnaaL/W2/B8vcgkYIMug5GRQK3vRnXpdUreViNlcaHLqMR4yN/SR4OXhawMVi04t5tJmCf3wEDUuxjJ1+kHevTR3OLuYM5ykcmU1rHahkuOxAfkesQP5J5dFlJvgz5x58k8UB/GrdmFXbr07+kMoeM72sSkwNUZgt0MSJssj+r7yS6BaS4LqYHZ4G9fPgz6lXwAntyD+k7GU3xe6zuzkZzgMiX52dMZhvhOxyAOdYmMDSNhnkB3ftte6ScugfF12tCc6I7fvk4b2NiYX9+vtEfzKJCv+I4XTcbvNSz78M3AviFxaP3K0GUmeRCzRJY+PJ0hiJ7OfKVx2Ls6DngDsLeT9a7cAzOXWd7YqZ8j94ANHW2XV/g6bWBDBzMr9+QeaDs2+KLed+vU10w+Ir6jT3lLY8boyT00bxoRfzNLpk34w5N70H6VoGWm6ck90HYCnfI8uQeez+QLRMriLRWSCvmbPpIkpL88uQd7O5mojwUB/UlOVNdN9IjRGb0Ehpyts6M/aY/FaqWNtIM84ttqpE06IAfyFdgKIBfo+PI28Bft4ZNEve/40yg7kz4U39JHEDRvXp7chdRJ4zuQr4D40T5yZB5oO5MBJpSe3AM2Rh6BPsJG+hS72vgBjEG0qbqPBOT2qnhC3tg1Zx25B2w0vkP+tlUs4siTe6DtNpGsz9cmVrfKWLyGbxMkCBWt+55ha/mNja3/r2yHHoMLsxfKrP12QoUJdv71dYaBbn5jP46/sa+v/MYuOm+Ib+xCTvU2q/3Gvj72jV1zL/qNnW+dq/3GbhOIahvRU8KVuIvET/cbe8B3kLSSEzlRUT9s6CMlDBls69p0FL+xS7/qN3Z5U/XkHqibfmPf+Kf+jb3DExITntyDfWPnFlB4ot531CuSE+jZhDJ3xXfR7bAISWuH5a74ZhZriejrtMHzIWkbYH2dNnTgE5voRKoh9khZkEaUpG0Qi9nYd+zcFZ+74q1+XWJ35Mshd8Vbm4wn6v3NWHfa6eeWQ4cukPirqyM5kX/uNoAkdkDbk9iT2BsksRuS2K1+SexHj9g5Hvbqa95f7rrrbj1Glrzy9PqRxD6EJHZA25PYk9gbJLEbktitfknsSexAYzWJfRBJ7CCJHWCTxJ7EDrRuSeza9iT2JPYhqE0SexJ7B0nshiR2i+8k9iR2oDZJ7Fq3MLcQq0nsg0hiB0nsAJsk9iR2oHVLYte2J7EnsQ9BbZLYk9g7SGI3JLFbfCexJ7EDtUli17qFuYVYTWIfRBI7SGIH2CSxJ7EDrVsSu7Y9iT2JfQhqo8QuNrWFit5xS+zr/rDEjs1qiJ1+PZrEHuuj1RO79VGt7/qIPVC/o07sAZsesde1h/ocKbFX24heQ+wRP/SIvd4GfQ5T8mQetG7SP70Dany9AYhNj9gDOXHUiB0bIfbIATXS9iMi9sp+7dk0B9T4eoM4tomdMe7YJXaLVSV2HNEQOxWoAY1jAFMb+dnTaQMbjgpsgt3T8UCQ02H868k9oMvJc7TLk3toEpEO8+QeOOWo6TBP7oG2G7Ez8Pk6beA7fE1HR3xHH9mFF/X1o/20KeJvDSZpk52y5eu0wfMh6Uh70NXjbiN9JDacsMX5zpH66YAk/ovUT206b3ae3AMDsg5iARsGPk7tq60b9aGPpmeXdJCtrR/+gtDsCF9fZwiix8BnRzM78mUAsdubnS/3wNsgserJPOAvcmhqZpv+7OkMAd9JvGEXHYP0wpSADXVSYg/kKzBiZ8Lmy9ugHM5ih9w9uQdsGE91TK2NH9GjT7GJxIKRkx0V7Mk9oBvliU2bNguxv6/cdfc9ZX5+Qcpd2ZbjXYm52Pjd4YnguEXuMaZEfEe9lNibSyjoZIKqCjIgN4HhypcBM8TxqXkdlDy5By4ymZxe1H89uQeOFlzcfiBUP4KCSwQ4b9iTe1AbaQ+XHHhyF51y8IUr9yD+hpi4NCXiO8rQy3ACNrSf+uFDT+6B9uOHSDk83/o1EgsTahPtIwiNoyMjZam/JcYj/ibe9JIa6S9P7oFJx+TUQsim8V113eTZ+GxBL7yQnKgsC38RcxqrtfUTPbWRdkXahE10PEGfuPNkLqQ93Bkwv7jHl3vo+K65aMXVcUAfcVFPJI+o3+T0gt6h4MqXweTUovnbkXmgHeQD8OQu8B1j/kSQJ6SPsIvEAuMJORHyt/pOxpOA7yan58p73vuhct/9D5bde/ZLP69sSznR8buxiYxb+JuY05wI+I56TYjv7BIYmRnorEpm6DXot2H5wtNpAz1mH8wmsPd0PPC2iWP415N7QJc3dpbdPLkHbHQmxtuJI/fQLEEzS/LkHmg7Niwj1vtunb5pNW/Snk4bPJu3DC7+YNnf0/Ggb5Dy9h3xdzNLxB+e3APPJ2AjNrQdm1gfrdPBnASJlEVsN29pntzDamz4xMIbV20sAN5oyIlILBAD07M7NCeq7cRftCcaq8RpxAZgExlPADlB3HkyD03d+CQR8p3EGysKtTmBja18WR5FfEd8Y+vJPfBs4gd/e3IP5ISShhCuJ/dA3VjB0lUsR+7BbMiJ+pgD+BuSithwFwI3MnIeuyf3sHnzFn1jv/uee8vCwqLkyMq25EQT357cA/7mAq/QuCVt11WsYE5Qr86nPZZsm2/s9d9OGpva9X/0IACCnTI9nWE0l8DEvp2ge3QugeHbSV4CozYMsOIPT+6B5zMr/YNeAqPx0/vGXls/83fzjb2+TfSR2dS1BxAHDMz1Nva9HGK3uq1sx7Ox0W/s1Tm7mktgrKzVXQIT/J4oejqISS7Vx0/7G/vKdtg0S/GaExX1w0YHZvJIBtu6Nh3FS2CkHCa6sUtgyImjdQmM3ZrJkr+nM4zVXQKzUdqi39jvvif0jd3iO/CNXW1Yio/sDYp/Y0fPPmPkrvguesS+is1zAeKk7dHNczqI5a541W3e8j25B2waYo+UBWlESdoGsVVunqvOo/7Nc/Wx0CV2aVetHf2Zu+L7N8/Vx0+X2AN5RP26xO7Il0Puirc2GU9EiD13xQ9AbZLYk9g7SGI3JLFbfCexJ7EDtUli17qFuYVYTWIfRBI7SGIH2CSxJ7EDrVsSu7Y9iT2JfQhqk8SexN5BErshid3iO4k9iR2oTRK71i3MLcRqEvsgkthBEjvAJok9iR1o3ZLYte1J7EnsQ1CbJPYk9g6S2A1J7BbfSexJ7EBtkti1bmFuIVaT2AeRxA6S2AE2SexJ7EDrlsSubU9iT2IfgtoksSexd5DEbkhit/hOYk9iB2qTxK51C3MLsZrEPogkdpDEDrBJYk9iB1q3JHZtexL7cU/skrwdYrcHrAyz6VwCg02FHXoEH6SmHVZpQ0fpiULaYb5eG+jqJTAahL5OG9iY8xvCXRlqI060DvN12qDtgyfPrQz08LURO8Hu6/UDG/q1d/Kcr9cGbemdPOfrtKE24odQHzXkFLAhqSD23slzh4fFD8Rug1ht/Rp/G0nX+RtYHzXEXgfioHfy3MpAj/7k7oRILHDkphJ7k7OOXj/QwV/EXHWsig56nMwViW9A7vUIYGWgB7F3BjFXpw38BbFz8pySdIUd5TCI4wf8UVM/dLrELnFe36bOxFVs622YDAix66TI12mDPOI4WTt5ztdpg7rxMseYEqmb5VHHpsIOvRNlDGaCoy8K1WUZTxg5+zptNCfP3a0nz81X2RID9Cvx7ck9EGvwHnFU7zuxGSD2lYEeL4yaE1wSsm37yXppCpdE1GFfWdpxsthFbPZKGfvF7qD8vG9Idjhs33Wq/Ftvs7i0r+zZf7a2y5P7kDbtPCi2+x3ZcjCbhaDN9nA5e8u2pQNh39Gnu/edpf7w5B6oV7gcsdm+8xT5OdKv+OHUMu/KlgP+PiXku0Wx2bHrtLJz9+n6s6fjAd9tkxiPtIl4i9osSr+a73y5C+lPciLiO8rZJbEQzQnaE83zbRI/lOfJlgMxFx9PTtZ48GQ+aM/BsmvvmWHfYRfpV/qINkVilTppewL5Coif6Pi9c/cZZeee0x3ZclgNT3RyIhRz+FvGIO3Xej/guyhP7Np9annv+64rDz/yeDnjzAuknjV91fRrzN+r4YlV5UTHd2uYfYzI2ww36vBzLXgDitrwhsZMkTdWT+6B2Qe31fCvJ/eALjc4cUuSJ/eADctTW2XG7Mk9qA03F8ns0pN7oO3Y4AtPvhxoC/XjbdqTe6B/5hZ26Yzek3vgjUH7KOBv2s9NaNE+4sYjZrKe3ENjE/K32LD0yltapH74m7yI1A9/kxeebDkQB9xs5smWA/1JTkTqhs9mJRaiOcFbXTRWiVPuAfBkywGbSN2A5oTEnSfzQO7QP3ymi4xBjAn4IRI/9JHm65b63APcCBfJV0D8RPqIdnB1LfDky4H45oYyT7YcVpMTNp7Mh/xNLkR5Ynxiulx99fvKffc9UHbu5Ma/lf3O840nYv7mIirGVk/ugVi1nIhzLGPxGl1i6X5j55XeX7vvB6/8w8v3vm4DWyboW4qvKsuWPnpL8Z7OMNA9OpfAYJOXwPSW4uvqBnj+H/wSGNGxpXj7xl5bP/N38429vk30UfQbO3HAgFJv0yzF47u6POLZw0vxvm4P5js+LdTHqi0Hru4SmJFA3Tp91CzFB+KnWYqP+K5/Kd6Whn3dBtgML8X7uj3Y8iukpvlaZWNlET+hS2CkXyGN2CUwa6V/+pfifb1+oGc5Eb0Epm8pvqpvzXervQTGluLrvrF3eSLyjV3aAU/oJTAB3xFz0ZygXpoT/E+P2H2DNtQmN891Oiw3z+XmOYMNYjGb3DxnyM1zVr8usTvy5ZCb56xNxhMRYrfNcxFiJydyV/wAktgBbU9iT2JvkMRuSGK3+iWxJ7EDjdUk9kEksYMkdoBNEnsSO9C6JbFr25PYk9iHoDZJ7EnsHSSxG5LYLb6T2JPYgdrk37Fr3cLcQqwmsQ8iiR0ksQNsktiT2IHWLYld257EnsQ+BLVJYk9i7yCJ3ZDEbvGdxJ7EDtQmiV3rFuYWYjWJfRBJ7CCJHWCTxJ7EDrRuSeza9iT2JPYhqE0SexJ7B0nshiR2i+8k9iR2oDZJ7Fq3MLcQq0nsg0hiB0nsAJsk9iR2oHVLYte2J7Ef98QuydsQuz5gZfTbWKErAz2CD1KzDvP1+oENHbXaS2C0TY7cAzbm/IZwV4baiBONaHydNmh7XgIjvpMk0pPnAjYkFcQevwTGiN0GZl+3H+bvhtjrbAB91CP2OhAHvZPnKiB69OcxeQmMAL3Bk+fqQO5FxxOIvTOIuTpt4C+IvXsJjKPTBuUwiOMH/FFTP3S6xC5xXt8mie8OsdfbMBkQYtdJka/TBnnEEafRS2B4UWBMidTNcuIILoFxdDxQv9VeAnPXKi6B0YmrI/dAO+A94qjedxKrA8S+MtDjhVFzAmPOXGa2w6yUgWkloIcTGxuSxdPrB3p0FgMsZdba4MTmLG1PxwO6HKJP/Ty5B2yoGzNFT+6Bt4zmDGlP7oG2Uw7JGPEdbeGcZuw9nX7wzMZmbmFPyHe0hTatzmblujXg+eMTc1LPunKsTVs7Z9Kb7zy9fmj8iA1vaAzmNfVrfMekg3Oaa/zdQPtIbXy5B3KCQbbWRtskgwQ5UVs3bOijuYXd3Zz19Pph5TA2TGkdq2yA6BGntTYAu1Gxqa0bQE/HE4m7ehtrD5N+bCjX0+sHesSbndkt41ZFWeg04wn/RupnZ9+PBmy2aPzgC0/ugXLIB86K9+QesFnNmG85MWk2FW1Ch1i1nKjjCYBulCfGxifLNe/5YLn3vvvLjp27pNyVbYmBZvz25B6om/GEjFv8f0vuARtiLupv6sVqzBpmUxgTGMwOasAyfNQG0GEkffO2XwMqqwQgFffkHmgkt/1E6sfzLXntzaEGlGMXhURsNncmEKOu3AP+pi0kln0C8fXawIbBnCDx5B5sQBJyCvjbbKbVH57cA/3KIBaJBXTHJmbC/uZyiMmpxVD9SBBiPFI/7SN5k470kU2KZlzZcqA/1XeV5aC3SSZQzYVA1XbiL9pDHVlO9XTaQI+BPBLfwCYQY65sObAETax6Mg+0mz7lM12kj4g3JadQfNvAHBq3pE4MypF8BdhAGp7MAzE9Ob2o8OQeqBvxHRlTuzbkUdDf5ER0bLAXhXp/j45OlHe/59pyz733l6XtOyVHVra1MX8qNn5L3ZrLczy5B/zFeI//Yr6T8UTG4jW8vjcO9NbsPaiNFpbf2LGJfBOj7Tg/v7HnN3ZATjAo1+dRfmNvkN/YDfmN3dpkPFHv79w814LaJLEnsXeQxG5IYrf4TmJPYgdqk8SudQtzC7GaxD6IJHaQxA6wSWJPYgdatyR2bXsSexL7ENQmiT2JvYMkdkMSu8V3EnsSO1CbJHatW5hbiNUk9kEksYMkdoBNEnsSO9C6JbFr25PYk9iHoDZJ7EnsHSSxG5LYLb6T2JPYgdoksWvdwtxCrCaxDyKJHSSxA2yS2JPYgdYtiV3bnsSexD4EtUliT2LvIIndkMRu8Z3EnsQO1CaJXesW5hZiNYl9EEnsIIkdYJPEnsQOtG5J7Nr2JPYk9iGoTRJ7EnsHSeyGJHaL7yT2JHagNknsWrcwtxCrR0TsJG+H2HlAHbCx4/f42ddpY61eVACpUaavMwwuUeBoPTrMk3tAl/Ogm4CqAeWo86XDPLkHyuESGDrMk3tgcOi/BKYOXMBgx1RGfEe/2iUw9fXTwGBAEn94cg9NMEX6qCGnWL8asUf7aHSMQWwmVJYOYpB0xN8ykYIA6nPiBMmJ5hKYehsG/uYSGE8+jLU6WE7PCrEHchZ/EXPUMVIWeWTxXd8mbCL5CiANnVA6MhfSl/SPXQJTGwtrNd6YeETipyF2/vXkPiS+IfZ1ERubDDC2ejIP5BFHEkPuntyHjPkS34wpvtyDjVtmUx8LjCe0iXp6cg/0DTwR8ffGTXYJzN1331Pm57kEZmVbyunFt6/Thtn0LoGpg+SRxJzlRL0fqJcSO4MXAyyO1I6rgXRU10Z+dnXaED0KtLPit/g6DhhYCEL+9eQeSF47K97OKK4Bz2/OivfkHpj9R21oOzb4IuQ78TXnVVfbCOif2c5Z8Z7cA23RM66jNjL7xx+e3IP2qwwsERt8xxnS6u9KP+gbGmfFTy/WlyXP7p0VX18//G02vtwDcdCci+3JPZjv7Jx9Tz4E0cNn3BsQyVn81T0rPlBWc1Z8tY0Am9B4IqCPdDxxZC60PZ2z4gPtYVDGD4wrro6DZjzRPAqUpTkRyD1siB/ecF25B/HDVOeseFfuQcqhf7SPPLmHxkYm4xEfEKuWE7Gxobk4xpU7GB2bKNe8+9py7733l+3bd0m5K9sSA93x25F7II/iPAHHBnNC9Hhp5P4EvQTGOixwiYA8BBuCyZMvB95uG3Ly5B5wSkMAntwDnTy/GLsEBhvqhvM9uQfaoR0mweTJPZgN5cQuycDXdDS+9+QeWKJrbrLy5B7sRq/VXXgR6lep02ouejBij/nbLoFZCJW1WfJBL68I2JBDduGFL/dATrAk6smWA74jJyKxgM+IBepYWz/aDhFSR0++HNQmGN964UVwPEGfWPVkHpr2zMxxCYyv44ExwSZssZygTZHcoz/ttrr6+AbED0TjyTzgh9VfAhPhiU5OQE4t2eHAUjdtiuQeujYpqvc3l8A0xF5/CYxdzhLniaCN+JuYC3OslMFY3PeNvf77ltowqAS+1/G9bbXf2BksI9+30F3NN3YSKvIdhHJoD0tnntwDbcfGvtHU+QEbfA3Z1vvO+ojvqiwx+TrDWO039uYTiyf3oP0qCc8ykyf3gC42+o290g/YMEiASP3wN3kRiVX9nhjqI76xdze7uHIPfMYgJ2p9R32Igeg3duKb9jRLiJ5OG+hpHgVsQO8be70N+sSqJ/OgdZP2sBQf8R05gV1kDMLfzfK9J/dAWRrfgXzFXwz+R+sbO6jtV7WRPorYHPE3dskNT+7BvrG/L/SNnRg4et/YbaIR8Z19FpWcwMiI/U998xzOjxE7REF7IolI27E5epvnjg6xQ05hYs/Ncx1iPx43zwXiW9Ajdl/uYbXEfrxtnjvaxO7JPahNePNcM57k5rlm5Sbiu2a/UxJ7B5QTdr6Ug02c2HNXPM9PYofYc1c8SGK3+q2G2HNXvLUpiT2JfQiUE3a+lINNEnsSO0hit/hOYk9iB2qTxK51C3MLsZrEPogkdpDEDrBJYk9iB1q3JHZtexJ7EvsQ1CaJPYm9gyR2QxK7xXcSexI7UJskdq1bmFuI1ST2QSSxgyR2gE0SexI70LolsWvbk9iT2IegNknsSewdJLEbktgtvpPYk9iB2iSxa93C3EKsJrEPIokdJLEDbJLYk9iB1i2JXduexJ7EPgS1SWJPYu8gid2QxG7xncSexA7UJold6xbmFmL1iIhdk9eInQfUQWwkQWI2XHhBIhoBeHIPdNRRuQRGbNT50mGe3AM2OJEO8+Q+1qoNiejLPfRdAiM/+zrDYMK2uktgYhe60H4SMWLTkFPEhoEVYo/20RFdAhPxt0ykIICITe8SGF/ugYGfnIiUw2B5ZJfA+DoeyKNYfJtNJF8BpKETSkfmQwZl6R+7BKbed8QbE49YfK/Ty5T415P7IL4npK+On0tg6FOzCfhbxiDaFOkj+oaciPh748b2JTAr9y/lROPbbFZ5CUzQd9RrC8TODBaHMMjyEO28FaA2HFAfsGGQZPBnloi9q9OGPJuBZXxyXv91dRygu7Btn7XJkXvAhroxUHhyD2ozPq2d5sk90HYrZyzkO3zNGcAR35EcXPyhAeLpOLBLBOy8ak/uAZ8xSERsqNP45FzIhraPy4CkfVTjO40f3tAWdTCvLqvjO/Ki2t8C4q05Z9+TeyAOQhe6CBhY1HfVsbBFY7R3CUyFnfrO7gCwWK2POy6hCNkIiLnIGNT0EXau3AH+ogyd9FeXw7jFHReBC11EZ9OmEa1bMzi7ei1YfM9p/9bXb7OSNJdEuXIHlEM+AE/uofFdrI/6berjR8cTLv6qtRGo74QnImPd6Nhkefd7Phi8BKbhifpLd6ib2dRfjIQNMRf3HePJTFnDL3gL4tILZvM1UJutdkA9MzJPpw1sGFwY+PjZ0/FAo6go/3pyDzglegmMOTJ6uL85n8725B5ou5XDZMDXaQMbfB25BIZnk+x2CUx9/RiQGnLy5B7UpnNrnyf3oMGu/RqJBS56YLC0tztPpx/2trClcwmM3e7m6bWhvlN/28TQ0/Ggk4GgDXHQkJMn98BkRXOiOhaMaGYXuATGCMDTawPfMaFksldfll0CE7EBTKJCF9QI6CNi1ZN7oD7UbWZuR3Xd0GNMwI74qakfOuRcb2Lo67VBWc0lMBE/NKThyT2QR0dyCUykPb1LYOrjB3Lmtsjw2DCxuktg7lFi5xKYlcdJG/MndTXGk3ugbmFuEX8Rc+bvgO+kDDhpjS6XdBzIq7x96zs8zMYc2CwBeHr9sGWCzlK82NfaNEss/OvpeEAXQqN+ntxDs8TCMpAn99BdYtFvJ75OG7SdQa9ZyvF02kCPtpDw2Hs6bWBDv9pSPN/sfL02dFld/BDxty3F2/K9J/fAZQ2QRsSGTzi6FC/l1ccP39h7S/GeXhvm7+Ybe52/gSZX0EaXziR5a9oD0NOlePFdJBYGl+J9vX6gg7+IudpYRQfonQuB+AbNoFdrgx7f2Im7epu1SrT9S/GeXj/QYQkVP+CPWhv6iDYR55H6QYLNcrKn0wZ6xA+fSzy5h2Ypnom1J/dA3dizw5hCmTX1Q8dyImbTLMU3n2w9vTZOOKFZiq8fT5ql+LvuvqfMzdlSvKfXD2KA+CYnPLkH/K3c0lmK93Ta0FjtTDTqbWw8ISdWv3luYDLg6w1A9Hqb5+o3ReBIBjGc48k9oLv6zXP1myKsw0aDm7lO6BK7dYiv1w9sVrV5boDYPZ1hQJo6IIk/PLkH2+wCscf6FWKPxIIOfB1ir/dd3+a56voZaRhJ1/r7yDbPRWwGid3X6QfPxsY2z9XnLP3ZbJ6rtUGPOI3YAAZL6lbbr0CJXWLVk3nQunWIPeI7xgTeBOtzoo/Y1abedw2xe3If/cTuyYdB21nxISc8uQfqpsQeGPPNxt4+a23UdzqeHJub52zMP1Y3z1msHhmx6/JA7orHJpKItJ3JQO6Kz13xoCH2+jzKXfEN0CdWPZkHrZv0T+6Kz13xIP/crQW1SWJPYu8gid2QxG7xncSexA7UJold6xbmFmI1iX0QSewgiR1gk8SexA60bkns2vYk9iT2IahNEnsSewdJ7IYkdovvJPYkdqA2xzixX3X1+5LYG6hNEnsSewdJ7IYkdovvJPYkdqA2xyCxUxf6ctOmTeXt77iy3HbbZ5TY13UOBvJsGiSxDyGJHdD2JPYk9gZJ7IYkdqtfEvsfltg3bNhQ3v/+95cvfelL5aGHHy6vfPPb5bXXXiuPPfZYeeihh8qtt96q/bxcfZPYh5DEDmh7EnsSe4MkdkMSu9Uvif0PS+xbtmwpH//4x8v3v//9cvPNt5RPfur2ctNNt5Qbb7yxfPKTnyw/+clPysLCwrL1TWIfQhI7oO1J7EnsDZLYDUnsVr8k9j8ssbPcvm3btvLd7363XHzxxWX33lPKxORMGR8f17f2L37xi5pfni14AxG7JG9D7PqAlUFBjY0VujLQI/ggNRIE0ND16zlFjA707eioY/3kOSMaX6cN2ponz5nv9ICagA1JBbGv05jxdQYgOsRZQ+w2MDt6LZi/G2KvswH0UY/Y60AcRE6eo030pxF7fXu4CEiJvTZnRYc+gtCisXq0T56rH7dkUJb+0QNqArHAIE7uaXxXlIVNl9iFJOrbJPHdEHu1DZMBIfbAyXO0nfsJOL7Wk3ugbrwoMKbUt6fJiY5NhR16J8oYjB9q+whQP+UJJWVfB/B8xivezr/2tafK0o59MjZMlDPOOKP86le/KgcPHrS6OraAGFCe6L6YrQzaAU+oTYUPgMbqALGvDPR4YdScICA4J74puAZqI8Y0kJ89nTYYHKgoAxKVnZ6ZLZ/4xCfKnj17peM3uTYMDiQvRx/yr68zDAblucU9WkdP7gGbrUIaDMye3AM3KtEeAteTe8Bf2OALfOLptIENvibYI/7eJO1vVi48HQ+0pekjT+5BbSSpYn1kZ1zjQ0/uAV07k35zpe9OUhsuTOGCiNr6qe/E37w11PobqE1nkPXkHiBOzpGujQXNCXwng3Kt76gPPpuRWKjPWfMdPgjFqugRpxEbwIRN6xYoB31i1ZN7oN2Q4PTc9kofWDmMCdhZ/Kxshw19xMSVf6vbJM/X+BYCrSkH8Gy920H87ck9UA73J0xITnhyD/iL8RTUt6fJI7FRf9f5Dn9z3nltfAN0lScqxi3KOPW008vf//0/lIsufkvZvmNPefjhR8rNt9xaxicOn4vEALFK3npyD9TNeMImyZ5OGxarnZwIxGoznqzB6QwSBBQPqYHayKBsNkbwK2NUB3/OKGbp4x3vuLz8/Oc/LzfffKvMHpcvm4QiCPnXk3tgMFpY2h9s05jWjQ7w5B6w4TamZlCqAb7TcsQXEd8R6Myysfd1hkEHcxmOTdx8nTZoP20K2wh54g9P7oELaiam5kPtQRcb66M6O+o0NbNNz0mvr5/4W2KHvAj5W2xY4ozYEAf4rj4WJCck3siJSHvwGbFAHEV8x2DJ5UPV9ZO2E6chG4G+QcqYUm9jfTTWuQ2tBvQLZeiNh4Fy8B1+iPibQZk22bhV62+JbyHbyHjCs4kfG088+TBoByt5wJN7aHzH5SwR32keYVOdE+bv8HiC75Qn6nw3PbNQPvWp28oTTz5VrnnP+8v3vveDsmPnbsmPw4//1IkbJpsxiP7lhRC75cAtclMzi+qL2rEBveZzScTf5B3j95pmuY0ZPa//NVAbmX2ozVpfZwiix8wFR8zNz5cHH3yw3HvvveX1118vC4uLxf7UYNiOZSkIin89uYe1ottczejJPdjSWbNE7uu0QTl0NLMlT+4B32HDzK/Wdywh0xY6D3tPxwMzRF2KX2efO2rQLOVE/E376Vf84ck98HwGo7VrA/0qbd8qiaL+rvbdiZogwJZFfb0B4G+Z+fMWFPO3XetIf3lyD5YTtuzoyT2wlGi+q28PNsQCb4O19aM/+Z5IHSOxSpxGbEBzG1zEhj4ilzyZB/xF/0zNLIV8x5hAmyI50ew7CY1bUicIg77y5C6kfsSPjiee3AHlQE7khCf3gA3jCYjEAn0asUGPN3tuD63uIwG6TFpr/c0n4KWlpfLaaz8uL7zwUvnYxz4mMWif3g4HcmLTFnuLpsyxsfFy2WWXlXe+8/Jy5ZVXlquuvlr+/+3y/+/U34HLL3+X/P7d5cKL3lS2bKkbU9Ah5hhTqscT0eOiNcbiNazLY8wShvcx3kO/ja3/+3r90PV/cQazGzYtPPvss+XQoUPlkUce0e8dW7dude1oIIM5jfPkHtDtfWP3ddpoHGnf2H2dNmwQi14C0/7G7uv1Az3awqAUsaGPet/Yfb02GFSaCYQn99AMYrE+6nxjF394cg/o8jZDHe1bla/Xg/eN3dMbhPm7/xu7r9cGfWQ2dX0EiAMjp3obnRQFfMezsRn8xu7r9mC+G/zG7ukNAr3Bb+y+Xht6CQz5Wm3T+cYuserLh0F9ut/YA77rbZ5rvt/6uj0MfmOvbZPGt5C05WulH+TZDOSMra7cAeU0b4Oe3AN+0G/s1fHT2PR9Y3d0hiB6jCc62Q3kHro62T3Mxrd+UJ+RkZHy6KNPlO9+93vl9NNPV7L3dPthY7599mCT3aK8lN55553lvvvuL88991z5j//4j/L5z39eX1ob3HfffcJzj5YfvPpque666/Tv51fyB3LG+/p8NZu+zXOrJHbpZAa/6gAkEUV/fmGb/r3gDTfcUCYnJ8spp5yif0d46qmnOjZGAAxiMdLIXfHm79wVj01D7JGyII0oSdsgFrOBACH2+jzKXfEN0CdWPZkHrZv0T+6K/9PdFd+Pk046Sd6i31wuvfTPlORr+pecaHbFo88zRkdHy/T0tDzn0vLrX/9a/1wObmswNTVdlrbvLG996/9TXnzxRf3TOmwO5xNkUWIHR53Ym3Iuu+yd5a/+6odldnZWKiHBL7MXZjx33HGHzpjajaCjktiT2AG6SexJ7A2S2A1J7NamKLHTn6xo0ree3EM/sff/nmedffbZ5cc//vHQGzl1Y4/B1q0juvuev6G/9tprxTfN/ey95/Rs3iDETsMnJqfK93/wg/LBD35QSZ3nQOY45Ctf+Yq+vbeXQ+ioJPYkdoBuEnsSe4MkdkMSu7VpNcQ+M3eUiF1iYcMGyfXNvNxeVn7605+Wc889d4jvejZvEGLnwP0rrriyfPOb39LvEk1lGaRYrrjtttt0A0P7WzsdlcSexA7QTWJPYm+QxG5IYrc2rY7Ydxw1Ymdshch3795d7r///nLeeeeJfwaf07N5gxA7OxCfeeaZ8s53vktsCcKeHU5hQ93zzz9fdu3a1f29yZLYk9gN6CaxJ7E3SGI3JLFbm94IxE7u7tixQzfUnXPOOeKfNyixo0tjrrrqqvLVr36t7Ni5xw3cqamp8uUvf7l84AMf0Lf7pjF0VBJ7EjtAN4k9ib1BErshid3a9EYgdoj8zDPPLE8++aT++4ZdiqfB7BjkNp3rr7+xTE3PuRWFzC+44ILy6quvlu3bt6ud2SexJ7Eb0E1iT2JvkMRuSGK3Nh3rxH6ScBzXw8KFbBhnAzm53P+cns0xTuzMUN72trfp36vv3XdAT+LxKopj2Fjw+OOPl9tvv707k6GjktiT2AG6SexJ7A2S2A1J7NamY5nYGR93796jl8ywDM9yPHm8nF/4/R+H2Ds2hytUnb11q5I1f5i/ZasdwYdzsGuDhvLdgb9r37Nnj1RynXbU0SX2wQ47HCgHko4SzeoOqIkRO3r0EYP5H5rYsSGYYn0EsUNOseSF2Cmvzg+DB9TUTjwafxtJ19dPB75VEnu9jZG0EXt9e3rEXjtQrP6AmobY69skxC6DZX3dAKTRHFATqNsAsa9sh02P2MmJmrLM3908qmyTxneX2OvbdPQOqImRdM+mOaCmwk70jNjjk/7IATWAvonuiteccIi94a6//du/LW9+85sH8Ja3vKVcddW79dKZu+66S/eR2T6zwWf3A39FiR29LrFTQWbLNA6H1kBtJGixYZD1dACXu1xw4YU6iznl1NMkkCb0nPgtWzkDfusQto6MlPn5hXL99TeUD1z7QXm7t5noyIgdzO+V4YEgh9i3SAP5E4MaUFdOxdskbfLkHghyViDwgyd3IYSBjb6hyM+uThuit3kLZ7KPh2yYSM3MLslgJpMwT8cBbRkR0sAfntyD2khSRWyYdIyOceFFwEZ0sdE+qvQDNhyfCarL6vibAbPa3wISKmoDoXGWdMSG/hwbn663ET36yM7Ll5yotKM/aY+dCldfluZRxEbARCVStw0yMKJPLrlyD526Tc9sk1iob8+mzVvkBYULourjhz6iTWoTKIv43riJlyZH7kFtOCeeiZEjd0DbJ/RipFlX7kJsGE9jfUQeBXNC9HQ8CY8NGzUn9IXTkXugb2Zmt2sdPR7xYBNx8YGU0/97+uvQofPLv//7/6enzL3yyjfLt771LcW3v/0d4cCflJ+9/roQ/Z9JbNhFNf32bRjHjoovZBIhZO3ptAEXM4licriGiyEWtx8oi0v7y/zinkrsLdu2n9yx2duS9bDvwBnl//yf/7e8/vNfykzm78ovf/mr8su//lX5hfz7i1/89TB++deq88QTXym/+Zu/LW97+5XynL1laecp+q9XxjD2lt17TyvPPv9y+dpTz5SvfvXrdfjaN0z/a0/7cg+NzVe/MSxbDmLzlJaDTaWdlvN0p361ZX2jfEX+/frXnw3YCLSsSDkCbL4et3lKbKijK/fQsbFyasoSHeom7enZeXrD+JraSSxEbLSPYjZav6jvpF1PSb9W+44yJK6x0XKqyjI9bRM5UVk/6tT1QaUNICe0nKp+BZ02Eauu3EGnTqvxXa9fa+pn5cRsGt/Rnnob9FaVe5oTEg+e3APt0Th4OuY79UHjB0dnCKLXqV+9jfmuG98t2XLA5q57HiwHTz3P4ZFlsE24b8fJeslY/+/hwrdddkX51a/+phw4eHbZu/8MwZmKfQfOLCefck755KduL3/9q98or+3cc+qA/TDqOHYQe8vCtn1lacdB3tjtgoNmGboKasONM7Yk4eoIuOzlF7/4pR5Ic+j888v5F1xYLnrTJeXc884r557r4dxy1tlnl0svfbPOdM4440x5+7arDHkL98oYgtRndnau/Po3f1M+9vFPyNv/9VXgiNuPfPTmcuONH3blLjo2N9wQsLn+hvLRaDmCD3/4I1LWTfLzDUOy5fDhj3xUfPBpqd+NrtwD9bI21ZdzQ8cGf3hyF6J70023ys8BG3x3861ani/3cEO5+ZaPl5tv/pj+7OsMA39/+CNBf3/4o2GbG2/8SPnoTbe4suVAf94kfoiUgw2xQB09uQ+Jb2kPdfTlHpo8ithcrzaxulkfkUuezIe159aPfSoU35oTYhfKCfE3dYvkHvX7qOREzOZ6jZ8bxReezEd/TnhyDzdYfIf7KG5DfltO1PsbXXIi4jvi53vff1X45i0+lziAh1iB4JNb/+9ZaTjvvEN68MzISOe68MZG+JLVm5mZufKhD/15efrpZ8rFF19StnQuk+l/The6MmC32x2OY9tgxYKy1vBtovleHvmu09gc7tsJu+F/9KMflQsvvFD0N+rSSvMNiW8hfK/wwMYCLonhJDq+g9glMHXfTqgPB9786Eevif2p+u2jBixjNEtGntwDNro8Lp3jyX2ss2U98YUv98HylC4Zib0n98DEi08SbNTz5B5oy1bxg35iceQe1Eb8ELFhcyTLjhEb9lyM6LJ1vb+xaZbi+dnT8cByKEkV8rf2ETa+3APLgSwne7LlQH9ypWykbgwus/O2UciTe6BviDnq6MmXA5+AovGtS/6BugFb7mY88eXD4DbGEV1+jcQCYwLL0LH43qB5RJx7ch8W3+s31OcrIH4Yjz2ZB9o+MTVXJiZtV3Yd1unnQ8YUX+6DPo3asHeCT3uRPmIpmpyI+Jvz2l966Zv6IulxiQd4qCHb/t/zvLPPPqezeW7w0hv29vAizDg5NjYmE6qb9cKYAwcOaBv7n9O1EftVfWOXepGzq988V7Ernr9Nh9jPl7d1Ar1ZHVipovy5G8R+8OBBI3aZgUD4nm4bPBti/6EQ+8li7+l46HaYBIgn92AdlrviSSqCqXZzGuD5uSu+t3muOhYEDCLkRCQWiIHcFd/ePOfrDSJ3xQPqpvEd5IljeVc8G7ujxE5OHOnfsXPh2WOPPab6b8i/Y09iHwb1S2JPYm+QxG5IYrf6JbEf38TOG3pz8hyfnt+QJ88lsQ+D+iWxJ7E3SGI3JLFb/ZLYj39i37t3r548By8msVcmFc9OYgdJ7ACbJPYkdqB1S2LXtiexH31ib76xf/zjHy9PPPFE96yW/uf0bI5xYv/hD3/YIXb7G0AauFJFuTDm6aefTmJvIDZJ7PguiR0ksRuS2A1J7NamPxax0zZykgNqIHZOUCVW+D2gToyPnNPCX1Z8+9vfVl1IfTm/8PtjlthZZuAMeBpAQ2uJHX2cjj1OSWJPYgfoJrEnsTdIYjcksVubjjaxEw+cIDcxMaFnwHPC3K9//euybdu2MjMz0wV/fr1z1155U/9E+dnPflZOPvlk5cXD+QTZMUvsg5AEqST2ftBRSexJ7ADdJPYk9gZJ7IYkdmvTH4PYFxYWyr333lsefvhh/Xz8+uuvl7vvvrs89NBDXSD7yle/Vl555ZVy+umnS1+tfCQ28iT2PvDsJHaQxA6wSWJPYgdatyR2bXsS+/8dYucZZ511VjnvvPPKoUOHFPzcD373posvlbf23VWkDtBJYu8Dz4bYf/Sj/x06oAaHc6AEZw57cg+QYPSAGv3MIDYEuyd3ITYc9MAhHti7Og66B9QE6kf7qR/+8OQeiAMOyVgXsOH5o+PxA2o41IbyPLkHnm/nYs+FymoOmwn5WxKRpIrY9A6oCRyYssEOqKkvZ53GKAfU0K5aO/qT9tgBNZU28mw9mUvju75N5F70gBr0IwfUUDfaw8Uf9bGwTnOCA2oiOcHEfesIhBs4bEbqp/Et/evKlwGHuXBYjyfzgB8mp+Y1Lzy5B2wYTyKHzaiN9JHayM+ejgcbT2IH1NCfnBUf8TcH1Lz88rdWTexwDc8hLliSXw6cDT8mYx1xVMt96B0ZsUtFmZU3s6o6SONk5muF+je1DWOtEIzMsKVQSNrXGQYn1DW39njyYayVoJ0qP/3Zz8vll7+rnHHGGVU480xmXRcUTg/y5B7U5tAFMmM725V74HJ9bM4++1xX7uPMcs45zP7OV3tfZxgc03vxpW8N1Y8jfakfbfPkHnj+IbWprxvPP3T+RUGbM9XmrFAfnVkuuPASRaRN+Pvccw+F6ncOxyKfd0h+rrch3g6df6ErWw74+/zz31TOCNQNm4sveau2q7Z++Iv2RHKCZ58rcRqzOUNj2+rmyz1oTkjceTIP9CV1e9Mlbwn1K20591xyL5YTmq/yNufJfXTiO5CvgPg5+5z68YS2X3jRpeWCiy5x5R6wIb5jfWTj1jmSR5Gc0PFE2hTpI3TPv+BNIX9fcMEF5dvf+V65RIjd55Jh8KLJyykrJJ7cg9oI7zWTgSoIR/KiwEt3PceeoPViErqG2XWzLAPT16DfhmUgT6cN9EZGp8r4xJzaezoeWJqanF7UJVhP3gaNmp1bLK+88m29TOb551+owgsvvFhefOll/deTe0D3pZdeKc+HbF6Qcl6Rf19y5cvhhRdf6tTPl3t4UWxe+eZ3wm2y+kVtVuG7l/GdL/ew2rq99PI3y8uvfCtkh+9oU6R+avNizIY4oE2ebDl0fefIlgPx88o3v63/VtcPf0t71MaTLwONhVXY4D9PthyanPBkHiz3XtaxwZMvBy0HPwTjTv0QsAGMJ1EbzYmA73g++fCy5IUnd4HvxAehPhIb853YhHJiFb6T55PnERt0n3zyKZ1MeVziAT6Cw1hR8OQe4DtWDKM2UY7l8wUvwazErOHVnRkIr/182zjxxJXBskdjY0taKwM9Zh84hjI9HQ/MQPQSGPnXkw9ByuGc7/0nn1mWlnbqNbA1WFzcpjsXty1td+UeFhaw2Ve2bVty5R4WFhbLLrFZWtqhP3s6baC3fceusnPnnoDNgtocPOUsaVt9/bZt265+wB+e3AM2u3bvKwsBG56/e8+B6vYAdLGhvBo7fIDe3n2nKEK+276z7Nixu9oG4O8dO2M2xMGu3ftDNvhuz96TA+1Z1BggFmhXlR2+k3J2SMxFY3Xnrj2SR/U2gJirrpuAPloS/V1i58k98Gz69OSDZwbKWdQxgdzTnJByPb1+UDf83eRRpCzi22x8nTaw2bVnv/aRJ/eAzb79lhOe3AM2xDeI1G37dskJtQn4W8eTWE6gS05oHzlyH/jhNCFq7l1wuMQBS/2QLp+iPbkH+A7eY4Xbk3uALyHrCMfCfdSLz1PH3Td2gC7fliNtapZYcKIn96DLJWLDdzhP7oG25+a53DzXIDfPGXLznNUvN88dvc1z9OfMnF2M5Mk9kBPtv2NfCdQtzC3EKjkR8t1xvHkOJLGDJHaATRJ7EjvQuiWxa9uT2JPYh6A2SexJ7B0ksRuS2C2+k9iT2IHaJLFr3cLcQqwmsQ8iiR0ksQNsktiT2IHWLYld257EnsQ+BLVJYk9i7yCJ3ZDEbvGdxJ7EDtQmiV3rFuYWYjWJfRBJ7CCJHWCTxJ7EDrRuSeza9iT2JPYhqE0SexJ7B0nshiR2i+8k9iR2oDZJ7Fq3MLcQq0nsg0hiB0nsAJsk9iR2oHVLYte2J7EnsQ9BbZLYk9g7SGI3JLFbfCexJ7EDtUli17qFuYVYTWIfRBI7SGIH2CSxJ7EDrVsSu7Y9if04J3YuV6FhkDsNrQM2dkA9P/s6bXAr1SbtsLUSuL7OMDgqjzN2CXZP7gHd2YVdOsh6cg8NOXETmif3QDm0B5L25C7E39gwKEV8h691oBB7X6cN69fpWW6yqq8fAwR+wB+e3AM2HLMY6iN5PucaR/uV5LU+qvMDNgxioL4s8zcxXu9vIUGJN7Wp7te1GgcM5hEbBgi9GGltfXsYiIiFSM7iL2IuGqtxm7Uac9HxhJcLHU9cuQPpSyYQUzLBicQC8UabGIvq6sdtYzbAWh7Vt4n4pq8iNsQPBODLh0HbOe98bHzWlbsQ32l865ga6CPNo5iNjSd246GvMwx07Ua4+nELm5m5nTauOnIP2HChCxeaeXIP2ChPBLhFY1XqFc0J6sVYvAZjLmfBKfxcC85vZ3DxZMuBoGWAxTGe3APJMTE5r/96cg/oLizt13Z5cg/YUDeSxJN76NmMufLlgA2+8GTLgf7hqk5Pthy2jkyW+cU9Id/RfhL+D22D7rj0K6sXntyD2XCJUKyPpuQNjcE8Uj9ie0TeaDzZciDeeAvyZMtBc0IGWU+2HDZLvJETnmw54DNiIZLn+Iv2RGOVOI3akBORfAX0EXHnyZYD49acTPo92XLAd/ghEj/0EW1iQPfkywHCxdaTLQdsIv6mHazeTM8uufLlsCqe0DyK9Sv+Js8j/mYcMZ6o9x3Pn9+2V+JVOMmRe9CcCI7f2ES5BRBzUX9TxtjEbFnTvKHxS2aZNRiwkdmlpzME0eNtBodg7+o4YAaCI/nXk3tAd04GsVCbmOlI3ZgheXIPzMBoD0tNntwDbceGmW/Ed02nVfuuYzPT+STh6jig/dSPNy5P7oE3JwbZSB/xfAI3FAuiC9lqH9X4TnToIwYJJhHV9ev4TmfZgfoxuERteJthwKxqDxA9+lNzIhAL9NFs5+2EFSZXrx+ig78gGepYWz+eTZzydlfdJgEXV2i+1tqIHvrEan3d7LPHzOyOmO+kLbRJc6KmLNGhj7p5VFk/Pl8Q35qv1TYbNH4YW125A9o+MbWgROjJPWBj8W3Xj3o6bRALlkf26bHKTnTIb9pU3UcCdMmJ0Lgl5WzfeUDGIck/R+7BeGLcxm9H7qHLE7XjloD2NBOBWhv0qBeTgeP0G/uJOiuPfA/CRp24Lr+x0yb84ck9NJ8x8ht7fmPn2UoyARuQ39itfgzmkXwF+Y3d2mQ8Ue/vjRs3lpdf/pb4QojQkXt4w3xjx+h4I/b169eX8y98c9m6VRroyD1QTtj5UidsktiT2EESu8V3EnsSO1CbY5jYyaOFbbuNCB25hyT2IRxNYt9QPvmp2yVJktiT2N8gxB6weaMQe8QPSexWvyT2o0fs9Gf+uVsf1OYYJnZ0dVd8oE2UE3a+lINNEnsSO1gtsbP5kphtY7nneMTeb9eva+gROzmB7/v1lwM2HrFTrqffYJMMfHyL5OdaXySxW/2S2JPYgcZqEvsg0M2/Y09iB9gci8SODti3/0D56U9/Vp577rny7LPPdvHiiy+WL3zhC2VkZJi4esS+VuU333yz2jz//PPlhz/8YTnvvPMkvtb31cOIfeeuA+Vzn7uzfOMb3yjPPPPMQHltPP300+Xzd95ZRkbZnDZI7DfeeGNXj+c8+uij5Re/+EX5wQ9+oO14/oUXy3NSF+Q33XRT1+5wSGK3+iWxJ7EDjdUk9kEksYMkdoDNsUjsEO+ePXuUGJ948ivlQx/6UPnABz7QxS233FJee+218p73vKds3rx54JkQOzt5R0fHlGRfffXV8tGPflSf8dBDD+mk4MCBA33kbsS+78Dp5bHHn5AJwxfL+9///oHy2njve99b/uwtbyljE+zYHyR2Jg6NXvOc119/vdx7773l2muvLdddd0P54If+XH9//vnnd+0OhyR2q18SexI70FhNYh9EEjtIYgfYHGvETnxCvE8++WS57bbPlO3bdwmxMQCe1AVv4m9961vL17/+dSVPdvA29rrpZ3F7uUne1J944oly9tlnK/mjMzY2Vj72sY+Vb33rW+XQoUP6LB0sIfb9p5eHH3m0XHHFFUPltbFhA3+mY3+u1Cb2devWDehu2bJFy7v66qu1HmPjU/K7EZHxp0d1sZfEbvVLYk9iBxqrSeyDSGIHSewAm2ON2JGfcsopQuq3lR07dkndJodsIG8I8+1vf3v5+c9/XpaWlro6kOXZ5xwq3/ve98rFF1+sZNrkBzpTU1Pl+uuv1+X0+fl5+X0fsT/8aHnHO97R1T8c6M+azXPU56WXXirvete7tN7E6Uo2bSSxW/2S2JPYgcZqEvsg0E1iT2IH2BxrxA5YJh8dHRWisWNRl4uFhYUF/X69f/9+JU1+h+1FF12iS+6zs7NDNpSPHd+89+7dK79LYgf4JYndciKJPYl9CGqTxJ7E3kESuyFC7OhAgpRzOGJfXFx0if1CIXY2p83MzAzZ8Oy5ubny3e9+N4m9D/gliZ1yktjBcU3sOILkhaipAA9ZCTiEBKFQfq6xQ48/gYHUKLOuLPuTGzqMf32dYaA7O88lMLbpqAZNIkK4ntwDB/XjRJzpyT3QdmxIRILE02kD3+FrBj/zna/XgzxXbCAZuwTGNlHVgIDdLH0U8bfaSJvwhyf30PQrF5nUxgJth9gpr853ZsMgBurqZ77D38R4nb8N5BDJaDnh67ShR1R2/tyt//cQJEvsV155ZfnJT35SlrbbBE3rtuGkAWLvt7M2r+0Q+/eE2Pfp/xMDbJ6D2N/5znfK/9sFG4O2/SD3jKT7/3TN0+Nb/MsvvyzEfoWWo3l0WJs2bOBTAgjY0Ec6oZSffZ1B0Je0Z2pmm/5cY0cbyFVyz3KioiyxafzQ9JmrN4BOfAuxW75W+kGeTfwwyXHlDihnfGJWc8KTe8CG8RRYv9b5jj6N2KjvJL/xQ20fNb7jbozIuIUuxE7fenIP5ITFt53TUAPqZi9z2NT7jnr1fOfrDUD0KEOJnf8wc7OD+usO3e/ajE7pzzV26OF4Dqg3G19vAKK3WTqYc40jF62gu7i0X+oYuARGbKgbZOPJPWBDgnDGvCf3QNux0Qt0Kv2ADb4mESO+w2Z+ca8miavjgPbjh5C/xSZ6eQXPX82lDRNT81rHKj+IDs/nAhgmONX16/iOy0yq/S0ghzivOmJDHHCOfdtmfGK6XC5E+eyzz5UPXPvn0m7LG8BZ0Jdc+lb9s7IlNt712QF0tu/YVX7wg1fLqaedqf+Pzw6eek559MuPlyuvukb+f2yozAFoWWPaHuq4rK4+e7x881vfLte8+736M3F6WBsHxBznpFfbiJ7mhNjxs6vTAs9m3Jpb2C3/X2+jOSFt0pyoKUt0yLluHgXqR05ovgZsiJ/IZSH0K/kAPLmHxnc6pgbqpjnR9GuFHXr423KCfK0tS8YT5Yn6sY6+Wdi2T/q2/iKhLk8E/a1jvrQrEnfEHP5T3zk6bXR9J2PxGt42OVCCmSxLIDUwm5GOzYYhuQ87dJ9GYu/rDIMZCE7kX0/uAV1N3k0yY3bkHmymIzNfmWF6cg8sNxIcLDd5cg+2VDKmb3e1vsOGt0fepCO+o/164YXM5j25B30LkjZF/E37SSj84ck9WL/aBR6e3AO6BK71UaXvpBwCHdTXz5ZeifGIv8mHiA16C4tL5aM331puuvmWAXzu83fKW/Ar5YorriyTk1P6RtbYkUcXvelS/Zvxubn5gWcCfe7Com6u27//ZP1/+mjfgTPKffc9UB566OFy8y29Mj96083luutvkLpvGXyO+IuBiFg9XJtO2ripvPzKK+XKK6+SvtmoA/hKNm0wKOHz+vFE/E1OSC55Mg/Uh3I4qKe2buo7iTf8EBqDpL+oW8SGsojvSL7iL2xYnfPlw9CcEOIkJzy5B+pGfEd5orGp9TfA37QpYoMukxvepD25B/qGT7ahGBKb3vjt67RhK5pBbpH2EHMx33HZk43Ff6Rv7PXfTmyJ5eh8YzcnHo1v7DL4iy8ivmNgp37Y+zpt2DcxBrFI/ZolRPzhyT0QVAyY+MOTe+D5R/aNvc4P2NibRuQbu/mbvKj3N99867+xs6TH7vX77ru//PRnPyuPPfa44DHD44+Xr3zlK+WOO+7QP18btD1BBqT15cILL9al+Onp4e+klM+muuFv7KfpUvx3vvOd8riU0ZTHATP33HOPLv33+5X+pD0rxar7jV0GmcPZtNH7xh7x97H6jd383cujujZRPwblSL7y7GYC4cuHQdt5GyQnPLkH6sZ4YmNqfXvICfb68LOnMwzxnY4nR+Mb+4nH2Td2i1XG4tw81wHlsHJxtIg9N8/96W6eQ86muC996UvlwQcfKvsPnKKkyt+htwFptu1XT+z2jZ3v9u3yeCakPPAc6c8j2jxXPTbk5jlA/VZD7Edz81yUJ3Sye8wS+/G2eS6JfQiUE3a+lINNnNhzVzzP/1MkdmQc/nLrrbeWr33ta+W0088oE5Mzofg+UmLPXfG5K361xJ674vPP3VpIYge0PYn9T5fYiU3+fv2+++7TI1dHx9gIGLu2NYndkMRuSGK3NiWxJ7EPgXLCzpdysEliT2IHEWK/++67dUncdqevgtgvukQ3zx3u79jZPJfE3gN+SWK3nEhit1xMYu+D2iSxJ7F3kMRuiBD7XXfdpUS4dav9WVl9Hhmxn3foQn0jP+uss6TP7G93GznnwPO36q+88krZvn27/C6JHeCjJHbLiSR2y8Uk9j6oTRJ7EnsHSeyGo0Xs9OfOXfvKnXd+QYj64bJ79275nfUXJMvNbN///veV3Ldu3Sq/T2IH9EsSu+VEErvlYhJ7H9QmiT2JvYMkdkOE2B944IHyiU98olxyyaXl4kverFehLgfeyhviBvTnxNScvI3vKLfffrte9nLRRReVCy+8UJ/Jn7O96U1vUlKHdHWwFJsk9iR2QNuT2C0Xk9j7oDZJ7EnsHSSxG2qJHcLl78d///vfl7//+78vf/d3f1d+85vfLAtud2MnffMMyJOcoD18S+etHT2e9W//9m/lsssu0z9n69XDiH3PvlPLXXfdo9fB1uRThNifeuqp8ra3vU3rlsSexA7UJold6xbmFmI1iX0Q6CaxJ7EDbI4lYgdKfhvt7nROlZudW9S3eO5g98D1rf3x30/sfG/nmzp6PGN8fFyfjU6vTCP2OckJduFDxDXtqiV2nsXEA/BzEnsSO7C4SGKnbmFuIVaPiNg7yds4vw7SOEmQptBa2DGLRgCe3AMXd3CkLB3myT2gq5fABOpHOep86TBP7oFyaA8d5sldSNuxIRFduYvOpSQQe8B3TNg4D/rEE+OXwEQudLFg4iKTepuGnGL9CrHbMbSe3APPHx1jEONvxevL6pJ0xN8ykbLJV70NOcFgHimHgZ+cqC9nrQ6W07NLnZyts8NftMcuvKgvizyy+K5vEzaxMcj6SMcTR+ZDxi0Z63qXwHg6wyDemHhEbOijzdIm/vXkPiy+T+xMvGpB/BBHnswDecR555C7J/chPCHxzZjiyz1gQx5hUx8LjCe0iXp6cg/0DTkR8Tc2Ruz2wlQDbHrx7eu0YTbCE4FxC38Rc1HfUa8tEDuJwUUPzN42bRmpQs+mc0C9ozMMu7xCLwuptulcFjLduQTGkXvgrPPFpQN6qYQn94BN96B+R+5BbSbnYjbSdrURX+ilCI5OG+pv8TXJGPV39xIYV2cYtIX60TZP7mE1NtSJSxuYEFT7QZ6Pjfm7xmZUbQYugXH12uhcXiExHolV4i1qQxxwsU2tDwCrFuREJBbwGbHQvVTC1euH+Y7BPxqr3UsyKm0ANjYG1beJnCDufPkwqBtldC+BcXSG0bsExuKnznfEt14QpblX7zu9yKQ6voFdjKSXwLjyYZBz3UtgHLkH9d048V3fR9g0ORFpj14qNdmMDZ7OMNCdmF4MjXX058LSPok96ufrtKE5IRxm8e3rtEHd1CbQr5pH430XIzk6w5BYlXqRE2uYjathZxbCrGIlDNjIz1zb6On1Az1mRlu22iUHtTbMyhmMWIr2dPrB8jY2XGaxb/8Z4pip7u/417NpwPMJClt69HXawIbOYlblyT3Qdmx4c6Benk4b1iab5NTYNG3mzXt2bqfOmj09D7SF+uF3T+7BbCar+qjBYL/WtmmjDmC8SVf5QXR4PjdmgZr69WLIEpIyPT0PPZu6fgXkRHN5hSdvw9pkvrO61fmBPpqZ58ILy1lPrx9Wjl1kUhur5DR65FHzpu/ptYHPdUDujCeeThvoaU5IrEZsyKEZITR+rh2DGBO4ZRK/15SFDrpMwGpt6MdefG+utLGylNTF357cw3pyQiYQTAg8uQfKMVIa1Z9XGk+B2mhOdGwEnl4/0KH9tIlPLTV91PWdjif14xY8sWf/6TI2zLpyD+SExXeMJ4jTZtyq9Z2+zPLZNmBD3jF+21K8OBKH8Cqv38VWgC6x9C3FezptNMsEVJQyPZ02sGmWWPjX02kDm7Hx8fLCiy+Xc887VPbv318uvfRSPZubb5DLYWxsXBJegn1C3tQcuQds+D46PjHpyl2MjanN5KTMZD35MpianpH6zcvPY0Oy5TA1PVt27j5YxscnXLmHCWnL7NyCts2TezCbxZANfTS/sD1mI76bX1jS8jy5B2wWt+1SRMqampop0zNz2l+e3AP+np6J9RFxMDe/zZUtB/oT30XKwWbn7pO1XbV2+Iv2TIRiFeKUPJqszyOAjdXNl3tAv9mfUAXpS/p0x64DGheujgPaQu5F4gd/ax5JnHtyH2NlTuI7kq+A+Jmcqu8j2r5taXdZXNrlyn2MaXwDX+4BG8mjacmjypgD5Pfc/FKoj+ib+UUZTw7jb/ahLCwslPPPP78cPHiw7Nq9uzz55FPlggsucrnEQ7MU391DUgE+KZiNLcV7Om3AsZB0nGOPdPNcY8NDHZ0hiB7OoIFU2tVxoMQuMxCc48nboG4cs/nb3/5z+fGPf1L+4R/+ofzP//xPeeaZZ/QYz+Vw//33l4ceeqQ88MCDrtyD2jyMzQOu3MNgOfcPyV2IDZeFcN0m9q6OgwcffLg89tiTofqhS/0i5aiN+CFic//9D+ifXsVs7lebqL8feeSx8sijXw6V9YD4+8Gwv+M2xAFtqo4FgfrukYDvRA+ffVligTry/65eCzyf9misVrdpNTb3aWxr3QJ+sJx4xJV5oD2U8+UvPxH03YPhfr2/m0f1sUpZlhMBG/GX5sSDsXHr0UclJyQvPLkHjQXiW/vI1xlC1ybiO/P3qsYGzYnlfccNhk8++WT57//+7/K73/2uvPbaa+UnP31dXvz+zOUSD0bSx+rmuWa/03G4K55ncx3m97//V+Xee+/TjuTPhTi+kz8DWg5vf/s7yruuuKq8452Xu3IP2FxxJTbvdOUe3v72t5crpJx3Sjn87Om0gd7ll18h9buy2uYybN51RXnPe68t73hHff1oC/WjbZ7cg9pceXXIBt0rr7qmvj0CdLGxPqr33dVXv0cRqd/ll7+rvOtdAX8LtI+CNsSB+a7ehv686qp3V9ughw2xQLvq7SQnpD2RWKVfyKOYzWUac/ivtl8BbbniiqtdmQfqQ3ve/Z4PBHzwdm2L9Wtt/OBvGRvII/k3Eqsa34F85dlXXnmN1PFdjswH5Vx9zXsVntwDNownINIe+hQbfvZ0hmGxemUwJ9C96mrJCfW3r8OfY6LHJJdrkT/72c+W559/SYj9zS6XeGC1Of/cbQBHj9hZyvre935QTj31dP1TIcCfAPGM5YDTcciGDSe5cg/82ZB9997gyj2wGxybk8R3/OzptIHexk2btX61Nuxq37h5i+76ZHnG1XFA+6kf/vDkHvi2s3VkXP3hyT3w/JEx28XqyT2ga9/e6KNa363TTUygviz+HG2zzsyr/S3gL0WI74gNOUR8R2z4Ezc2jtXaoEcMzMxt13ZV20l/simHsSFSluZRIL4BO3mpW22/AvS3Sqx6Mg/Uhz7lrwNqYwEbvvWyNyES3/i7l0f1vtP9FtK/ntyHjY/so/Hlw6DtE5NzmhOe3AN147syiLRH80gIip89nWFIrOp4Qk7ExgZyYqVxC99yxgNgyf/Z514sb3rTxS6XeEhiH8LRIXZAAm7feUDsSKx1CgKLcpfD0fpzN9qBTeTPJQD9Q4IQWJ7cA/1qf+5W/ycgtJ/6xf7czSZF+MOTe6A/rF/rbfAdG5KifWR/sxv/czcbxAL+7tiQyJ7cQ7NJxpMtBwiXfSeRcpo/d4v8SRn+YnChjp58OZBH0fjGJlI3wPhD3HkyF9KX9I/9uVvkT4jyz92oG+MJ8OU+6NOozZH9udvh+4hnogN4Qdi+Y7/yhMcjHpLYh3D0iB3dPKAGmzygBhv+xAlEyvpDHlDTD3KCnef1edR/QE19LBAD0zNL2q5aO/qz5oCafvBs4jRiAyBO6ubJlgP6xKon86B1k/7JA2rygBpAf+bJc31QmyT2JPYOktgNSewW30nsSexAbZLYtW5hbiFWk9gHkcQOktgBNknsSexA65bErm1PYk9iH4LaJLEnsXeQxG5IYrf4TmJPYgdqk8SudQtzC7GaxD6IJHaQxA6wSWJPYgdatyR2bXsS+3FO7DSO5IXceUAVaJwkiBVau3ORP4uyXayU6esMY60EuZ48J4OZJ/dA59olMPVtohx1vnSYJ/dAObSHDvPkHmg7NiRixHf4mvrhe1+nDelX6dNVXQIj9WNw8eQeLJiil8BIv3YS0ZN7QBcb66M6P2Cjg5ggUhb+JsYjsUq82eSr3sZ2xdsEx5N76O6Kr27PWh0siQUbZOt9R3tsx3Vl/cRfxGksvpnsNrvi623oI2LVk3mgL2lP7BIY/kRKXkjEjgmVr9MGO6+FnGQCb3lU2yYmrty+F7hUChuJn9iueMmJ6K548R3jifFEfXvoU5vs1tuQ37Qpkq/o2q74+nELGyN2e2GqATa9+PZ12lAbHfMj3CJ5JPWK+pt6MdFbwxnfHBqvFzdIUNVhNTYTOrhyRvGI2HtyD/xd56QkIv96cg/ocrh/c6lLDUZGp7RuzGI9uQfK0faIrSf3Ie2hHPGFL/dBEnLeOfae3AMX7nDxB3/f6ck90P5om7ChTbE+mtJ+JRk9uQeNBXnbivZRc+FFpH5cDEGMR/xNPowH+4g4mJxedGXLgf5U30XKEZ/NLe6ROIrkBHk+r7HnyZcDNtH4JrYjdQP4m1j1ZD4kX6UcLoGJ+o5YiMY3ZcXGhgmNhUi+AmwifcT4C6GRE57cx6T4Oz7m2xkSdgFKLWw8WQzxBPVjwhbxN7oL2/Z2xlVfpw1iYGISngjENzaM+YFxi/ZY7gU5VsqgrDU4kE7mYgR+UQNsuFxkenaH/uzptIEegcSbdK0NQHdeBiSC15N7YPDfsfs0bZcn94ANdeMmME/ugTqZzTZX7oH2zM3v1nIgQ0+njZ7vdlb7jmfT/u07TylT0jZPxwP10j4K2jBYRvtI+zUSC/J8yAl/V/tObBa27SuLS/tDbcLfMxLjkfppHgVt+FSivgvY0J/mO1/eBs9mGZ5YCOWs+I724ItI/YhT2hWz2SVjEHXz5W2gpzmxsMuVe6A+jFtLOw5W1w09fIddbXxTN/pIxwb5N9KmuQWJ70CcNjb4wpN7oB3kA/DkHvCD8URgTMVG9LGr9zfjyTZtU62/Ac/nJSY0bonujl2naj95cg/UCX3i25N7oG4aCxJHntxDYzM9V59H5jsbi9ewdMHSAssRLHezbLASejZb9GdPpw30+ObbfEPydDywzMsshOUpT+4BXRpn38V8nTZ0OXnrmH638+QeKKdZBvPkHmg7NixRsfzv6bSBDW1hubvad2qzVQdmlmdcHQe0307M4rQ6X6cN2s9sMdZHG/Q2JpYsPbkHdPUGJymvyg+iwxI0bwx68lxt/fDdxuYUufpYxd/sn4jYsJyM7+r71U6RIydqfceziQEGWNpV6zv6kyVE6lhbP/SI04gNIOb000etjeihr0u2wXELEtRYqLDDhnhrPrlV1U90dElU6qZ5VGMjoCzeIunfiB94I2TJ1pU7IG5YgSAvPLkH6kZ8g9p+bWw2berkUU0/iZ6NJyyrx8YG44n6cYv+ZBJKznpyD9goTzB+O3IP1I1YiHAL/iKPIv7Gd814ska/g0hQ8AvvY7wH1vMbG372dNpAj2DHiZTp6XigwltHo5si7Bt7pE3YkPQEhif3oN9BGMilsz25B9rOtzd8EfEdbaGTIzb0kQ5i0uGejgcNXPFDxN9qIwMf/vDkHng+3xNPOIFyattkm+cor84P9q2KhAe19TN/N5vn6ttEH0U3zykBSALX2/T2J9TWjWdjo5vnqnPWfMeEMhqrdklGvQ3AJjKeUD8lXMml+vixzXO8qZnvVrbDhm++5J7lRJ0N/mY8gcxq26TxLQRg+VrfJiZF7NXw5B4oR/edSE54cg+Uw4tZZCOc2ZATttfJ0xmC6DGe4odI7qHLBAd/e3IP9KdOdqVvPbkHG/ODm+fUxiaGoViVekVyAj34i7FY/Ji74gHlGLHnrngdkHQQ83XaIBF1E1Ooj3JXPMhd8YbcFW/16xG7r+Mhd8Vbm4wnIsSef+42ALVJYk9i7yCJ3ZDEbvGdxJ7EDtQmiV3rFuYWYjWJfRBJ7CCJHWCTxJ7EDrRuSeza9iT2JPYhqE0SexJ7B0nshiR2i+8k9iR2oDZJ7Fq3MLcQq0nsg0hiB0nsAJsk9iR2oHVLYte2J7EnsQ9BbZLYk9g7SGI3JLFbfCexJ7EDtUli17qFuYVYTWIfRBI7SGIH2CSxJ7EDrVsSu7Y9iT2JfQhqk8SexN5BErshid3iO4k9iR2oTRK71i3MLcTqH5XYKwvF5tgndumwiPOlHNrDpRye3ANtjxI7NmFix0b69WgSe6yPVk/s1ke1vusj9kD9jh6xk4hC7AGbHrHXtYf6dIk9MFD0E3u1jeg1xB7xQ4/Y623Q5zAlT+ZB6yb90zugxtfrBzZHTuz1vosT+wkaP0eX2OvbY8QeOKBGnn0sEzs2xy6xW6wqsetALg+gcRAUQbUSujaSJGpTYYcNHUyH8bOnMwR5Lg7keEH+dXUcQJpzC7u0jp7cAzY4BAL15B6aQZkjED25B9qODR1W6wf1nfiaQazed+s1MAhcTqVydRzoYKkDRb2/sdFjaEN9dJImYsSGtnNaHeVVxWonfuwiitn6Nokd/m6S0dVxQD5EbRgoGczr+7XxneREpQ16+Iz7IJR0a+w6vqM91LG+fhLfMnEl16ttBORedzxx5EPo9BGxWmtDfShnenbJ6lZhhx65qv1K/NSUJTr0EWXxb6R+5ITma6UNesQPfeTKHaxb3xwpO+vKPVA3YifKE/RpN+Zq7ETHxpNOTlSXZTyh/nbkHhgPeAGknzy5B2LAeCLib+MJJjme3ANtJ+bwt/rB0WljnfiKOODI2zWcBc3MjTOKeVAdRstI12a0JVsOoxq03A5Emb7OMHAIt+/wryf3gO7C0v5Qm7DhJh2Iw5N7UBtpD0HoyV1I25sbe1y5C/G3tIVZdsR33I7EZSER39EW2vSHtkGX24tIEk/uAV1seGv35B4oh0slWLmI1I9bnMiLkL+lj9SmOidGNA44sztiQ+KSE/V1G9W4JhYiOYu/RsftRqpI/Zqb3aI2kXwF9JGOJ47MhfiL/uEeCVfuwnyHXSR+mOiSrxEbyoJwsfXlPvQWQvGFJ/NAHjG54bhpT+5CbLinAbhyFzZumU19LDCe0Kbo2DAxJeNJwHf0DRdE6bjqyD1gg35k/KZu3BYZGbc0ViX3IvkKqBc5sYaD45kVsBzPMkYtVmNjb4Ojeli9J/fAAfoELTMST+4BXc6KZ0bvyT1QDg5kxufJPVAO7WFG5slddGzwhStfBviajvNky4HZMsnLbNaTe2jeNHjz8uQezCZwQY2A5xOEERt8hw1vNK7cAc9nIgUiZeFv3jQisdq1cWTLoXk78WTLgRm8nou9tr5uxCixEMlZ/LVRYi4aq8Rp5GIkgA1v+Z5sOejbCeOJI/OxTlfxuAErEgvEN/WLXErSLIlG8ggwiaB/PdlyIH54g/RkHmg7k0lywpMvB8bT6JhvOVE/DgM+42hOBPqINpETEd/Rn1ySFRlXKQfSjV78RSxExi2gORH0N/ViYnjk39grv7fo+n8nQeq/Gdi3WAbz2Pfb3DzHs3PznNnwtgUiZUFmDGSRWCXeojbkBJOi+jzq/8ZeHwvEQG6es2/suXkuN8+B1XxjJydyV/wAktgBbU9iT2JvkMRuSGK3+iWxJ7EDjdVVE/to+f8BMP9RWRSpZ1wAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determine la pendiente y la deflexión conformela fuerza aplicada en el punto B de la viga en cantiliver por le método directo que está en la imagen: \n",
    "\n",
    "![2.PNG](attachment:2.PNG)\n",
    "\n",
    "La fórmula que nos permite determinar el ángulo de flexión de la viga es:\n",
    "\n",
    "$\\theta = \\frac{dy}{dx} = \\frac{F}{EI}(Lx-\\frac{x^2}{2})$\n",
    "\n",
    "La fórmula que nos permite determinar la flexión de la viga se obtiene integrando la fórmula anterior y está dada como:\n",
    "\n",
    "$y=\\frac{F}{EI}(\\frac{L}{2}x^2 - \\frac{x^3}{6})$\n",
    "\n",
    "Y se comenzó por dividir la viga así:\n",
    "\n",
    "![1.PNG](attachment:1.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es importante denotar que en las ecuaciones anteriormente presentadas y que permiten llevar a cabo este modelo, las variables significan lo siguiente:\n",
    "\n",
    "$F$ = Fuerza aplicada al sistema (viga)\n",
    "\n",
    "$E$ = Módulo elástico del material \n",
    "\n",
    "$L$ = Longitud de la viga (en *ft*)\n",
    "\n",
    "$I$ = Inercia del sistema\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para nuestra simulación, usaremos una viga simple de 20 *ft* de longitud total con un módulo de elasticidad de $29000(12^2)$, una inercia de $\\frac{758}{12^4}$, sobre la que se aplicará una fuerza equivalente a $-15$ unidades."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ángulo de deflexión de la viga"
   ]
  },
  {
   "cell_type": "code",
<<<<<<< Updated upstream
   "execution_count": 27,
=======
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.019652442907833682\n"
     ]
    }
   ],
   "source": [
    "L= 20 #longitud de la viga\n",
    "F= -15 #fuerza aplicada\n",
    "E=29000*(12**2) #Módulo elástico del material\n",
    "I=758/(12**4) #inercia\n",
    "y=(F/(E*I))*((L*x)-((x*x)/2))\n",
    "print(Pendiente(x,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
>>>>>>> Stashed changes
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.019652442907833682\n"
     ]
    },
    {
     "data": {
      "image/png": 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dqrdbva3I/ZGqM7qOuk7tqk2/b/I6HgAAQLKjFAJAIrL7Z9c/Gv1DOwbt0Iu3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\nL2jql1PVaXwn7T2413ckhBhKIQAAABDm7rjyDmV2ztSC7xa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      "text/plain": [
<<<<<<< Updated upstream
       "<matplotlib.figure.Figure at 0x20b076e1cf8>"
=======
       "<matplotlib.figure.Figure at 0x1f9e90a6128>"
>>>>>>> Stashed changes
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Parte 1 \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "%matplotlib inline\n",
    "\n",
    "L= 20 #longitud de la viga\n",
    "F= -15 #fuerza aplicada\n",
    "E=29000*(12**2) #Módulo elástico del material\n",
    "I=758/(12**4) #inercia\n",
<<<<<<< Updated upstream
    "def Pendiente(y, x):\n",
    "    return (F/(E*I))*((L*x)-((x*x)/2))\n",
    "\n",
    "print(Pendiente(y, x))\n",
=======
    "def Pendiente(y,x):\n",
    "    return (F/(E*I))*((L*x)-((x*x)/2))\n",
    "print(Pendiente(y,x))\n",
>>>>>>> Stashed changes
    "\n",
    "x0 = 1\n",
    "tt = np.linspace(0, L+1)\n",
    "xx = odeint(Pendiente, x0, tt)\n",
    "\n",
    "plt.figure(figsize=(15,10))\n",
    "plt.plot(tt, xx, 'g', label = 'Ecuación de la Viga')\n",
    "plt.grid()\n",
    "plt.legend(loc = 'best')\n",
    "plt.xlabel('Distancia $(ft)$')\n",
    "plt.ylabel('Pendiente $(rad)$')\n",
    "plt.title('Pendiente de la viga')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El resultado de aplicar la fórmula nos indica que la pendiente de la viga, en este caso, está dado por *-0.01965 radianes*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deflexión de la viga"
   ]
  },
  {
   "cell_type": "code",
<<<<<<< Updated upstream
   "execution_count": 28,
=======
   "execution_count": 23,
>>>>>>> Stashed changes
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.26203257210444914\n"
     ]
    },
    {
     "data": {
      "image/png": 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AqQO0ae8mryMCAJAjUAQBADlOaFCoesT30IK7F2hm75lqHtdc/5nzH8UNilPn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\nAABJRU5ErkJggg==\n",
      "text/plain": [
<<<<<<< Updated upstream
       "<matplotlib.figure.Figure at 0x20b062d18d0>"
=======
       "<matplotlib.figure.Figure at 0x1f9e9070048>"
>>>>>>> Stashed changes
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L= 10 #longitud de la viga\n",
    "F= -15 #fuerza aplicada\n",
    "E=29000*(12**2) #Módulo elàstico del material\n",
    "I=758/(12**4) #inercia\n",
    "x=20\n",
<<<<<<< Updated upstream
    "y=0\n",
    "def Deflexión(y, x):\n",
    "    return (F/(E*I))*((L*(x*x))-((x*x*x)/6))\n",
    "print(Deflexión(y, x))\n",
=======
    "def Deflexión(y,x):\n",
    "    return (F/(E*I))*((L*(x*x))-((x*x*x)/6))\n",
    "\n",
    "print(Deflexión(y,x))\n",
>>>>>>> Stashed changes
    "\n",
    "x0 = 1\n",
    "tt = np.linspace(0, L+1)\n",
    "xx = odeint(Deflexión, x0, tt)\n",
    "\n",
    "plt.figure(figsize=(15,10))\n",
    "plt.plot(tt, xx, 'g', label = 'Ecuación de la Viga')\n",
    "plt.grid()\n",
    "plt.legend(loc = 'best')\n",
    "plt.xlabel('Distancia $(ft)$')\n",
    "plt.ylabel('Deflexión')\n",
    "plt.title('Deflexión de una viga')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El resultado de aplicar la fórmula nos indica que la deflexión está dada, en este caso, en *-0.262 ft.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusiones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos concluir bastantes cosas tras la realización de este trabajo. Esto debido a los múltiples ejes en que nos basamos para determinar los aprendizajes que esperábamos lograr. Por tanto, los agruparemos en un pequeño listado, como sigue a continuación:\n",
    "\n",
    "* Los modelos que permiten representar esta clase de fenómenos en el ámbito de la ingeniería son aparentemente sencillos y pueden transformarse a sistemas de ecuaciones no diferenciales; pero siguen partiendo de la base de las mismas.\n",
    "\n",
    "\n",
    "* Una viga simple sometida a esta clase de esfuerzos se comienza a flexionar de manera cóncava y **a medida que la fuerza se aplica en el punto más alejado respecto al punto de apoyo de la viga, ésta sufre una deformación más extrema.** Por lo que, en función de las características físicas propias de la viga en cuestión, puede llegar el momento en que no soporte la tensión y sufra de un desgarramiento.\n",
    "\n",
    "\n",
    "* Finalmente, en lo que se refiere a la importancia de la solución de este tipo de problemas dentro del campo de acción de la Ingeniería Civil, resulta evidente que tomar en cuenta estas propiedades, no solo de vigas sino de todo elemento estructural que deba soportar esfuerzos de esta naturaleza, es imperioso para poder lograr que el diseño propuesto por el ingeniero sea óptimo para resistir las fuerzas que experimentará a lo largo de su vida útil. Esta responsabilidad se hace aún más evidente en estos tiempos, cuando los recientes sismos en nuestro país nos recuerdan que **el hacer caso omiso de esta clase de comportamientos naturales puede ser la diferencia entre la vida y la muerte de todos aquellos quienes usarán las edificaciones que nosotros diseñemos.** Es una responsabilidad demasiado grande como para dejar que sea hecho a la ligera."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Referencias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kassimali A. (2014). Análisis estructural (5° Ed). México D.F.: Cengage Learning."
   ]
  }
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