Sistemas_de_ecuaciones_lineales.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       " <div style=\"background-color: #023324; \"><p><br></p>     <img src=\"https://www.uexternado.edu.co/wp-content/themes/externado_theme/images/logo-uec.svg\" alt=\"Universidad Externado\" width=\"150\" align=\"left\">  <h1  style=\"color: white;font-family:Lucida Sans Unicode, Lucida Grande, sans-serif\" align=\"center\">Sistemas de ecuaciones lineales</h1> <p><br></p></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.core.display import HTML, display\n",
    "encabezado=display(HTML(' <div style=\"background-color: #023324; \"><p>'+\n",
    "             '<br></p>     <img src=\"https://www.uexternado.edu.co/wp-content/themes/externado_theme/images/logo-uec.svg\" alt=\"Universidad Externado\" width=\"150\" align=\"left\">  '+\n",
    "             '<h1  style=\"color: white;font-family:Lucida Sans Unicode, Lucida Grande, sans-serif\" align=\"center\">Sistemas de ecuaciones lineales</h1> '+\n",
    "             '<p><br></p></div>'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Profesor: David Andrés Franco Quintero**\n",
    "\n",
    "**Materia: Fundamentos de matemáticas (Pre-Cálculo)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sistemas de ecuaciones lineales"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aproximación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El recurso previo a esta lección es el de resolver este pequeño problema (encuentre el valor de la manzana y del banano):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0+vwqSi5gEdQQT/YLMhb7O0aF5DfE4MY3fA93+vSyGUI9pdKcemVKneRzRe7PhPtfSOjmmOwjcSNdgQj5jOyRB2X+pn18LDoxnfJ6WE6BXbjnZtWfygVWM6ULdxD48aYGGiXK/5D+oES//P2f/6Q9gqh5DkiXSMe4m1ClG8eB0nxdAVjDNLCqBwSwyhSwgl6sGUpy84VecxI8iFQ9IzGUECJ6v3WFkLEvMYQ/kz6OBlYqRYHMBhb+uIZ7ZsKlqAZWVAHL4ZW4smJTDrBqgXoBFvukpjDSjyPHllSST6eeEzmTfToBm+YIsfTnXiVNUO6FcmuhLl/Z+QhXP2yYBVbRywUsbQrm3DHn6R+wL/iTTpffkn6lRb/+A8ab8gjIGyBLnpFhBSwPeFWWt5y7NLtK0bOH8ndUmJbKiBsowFKJHww5veI59bpJzLTiMccj7re//epXX71HMiFU2NfQQvCCqVSShKClUkGfszyEY4X4oboJ6f1R1eoVVY5P4YotVzFGLxdYtbKEgTWHXk3NqAe1Kf0zJx/F6itKPo6bRO4Pmva/MG14dloOsAB55I8QKFoG1PQILI8LWNX8MsGzwCo6aWBFIlwQOkONcSUDDax67+X3XlbitPnDH9zjTbkEsgkhVRISr7B+Xo53yNqAwqusXP+7AVaVAKtk4AGrNGimtrDw42ld0LC3+h8VQRpyFLxXSC+/TKMva+CJV6WyEsCiVzDFwArmACtQV4N2jDTzoerqBgEWyiGv1+8UigMAWKEoeMXAklV+MUV6Af3vf89PSsTttddee0UC97LgXj8wfyPT1vzEJI+fByxZtVBNxOoZWGhd5DosHT0LrKKTXmcciXIZE6tXzzcYA8Oql19+9tln8R0/KWb96rd6vIFZ8pBLxGKyhI8IWEKPUAJWTZbFqlO8GuYqdaAqDSyXRRgIwFI9bp8vGIJPqL9Dli6oUlC8FQ+5l2XE3ffufe++8u4rz0oMjc1CaYiFIrXekMzO6o3o2nvq/9evN9QpNVUDWQ36t2UqeNUNqq9VbL1kN7DKykLe2jSv+ZClfXN02/S/1bNSwYrC9sp9pGdNAkryZT0wKQOb5POvcOWXwIdXibqmLHIap8OGVSH53A6rWs34WGAVnTSwMKMlMzP8fKNaEAmDkfbyK88++8qzuaKskQfdn82DDsRKaGCBV1EuCWGxcvyVWT+kR1KVSpmSgHomDgxg8TKCKuzGIWJhLn4O8eoHLlzBIbxHAXxFJAPvFRVOwyyKIY07TNXXKmClCgNLeFXLXpgqoAbuYYFXqsSKan/V0DAQgFULYDGp7sALrQgHV6AV+dH7OGb33qf07LPMLTJa+ZVhkxA7H1i8nK2kqiCw9Dz2sGFuh6UdqgVWkSnAx/JiyV1Uep2cMX/6MxuD915GeqgXBpvDrcucNfyg+x9Gluq/M7AqfT6VJFGzx1dJ5aqe3jJDaliVLNnS6TKQgFVZip01ABbPVLjKaaYV4YrCZ4Q4mifAK1QbfsUx5BDOmYOFpGKw+NwntRDSOaaaYslgamhoiDKtGthMVUdU2PTEYYMmVklxxdEBFiAbUsDiOvoONc3DnSvF+fs0q+697957NbUus9dCbag8vu4CNkVDZbI9sILYwwgye5uygaXTsZSbt8NKHGCxw2owCWiBVWQywArFVPvqF7/5059+L7h65RVnoOlR9+zjwqvLJEHWb9WcoW7DpLF8D9u1moRYaXp5vTUaWPJsdRY8yohyPw+rTdO4eAZarnRJGBBiwWKFsHmExtwPxF2xReBamh3Cvffe54YWonmZXs++8tpr7/3qq99yCLG2TYCVVsBSp2IUBla1Ubza4Xy1wpguCosrjoWBNQfuispp18PyVy8T0xlRYBXLsVkcuWd1ZehMWMd4MkIcljgnCUu0ms1XlYtWcnCu8lcl6q1VBrrWtpVZYBWPAgF9dhM21iiDRbxC70rc+CsyvF55HL9+HL9+BK9Hnn2EoUU/P/74y4ws9Zybw1vlYjgehDssTeoclVq1uDKEBgwf68F5waPKOAE9uHTXtJgGWq6cFfpo3qaqqiojUSxpUP2/3/+ePMJ776EUzK5ojMArNfBe4frmf37/pz9xJ6u+1mtO1TRnkOlFjxLHaFTTCj4qEmF7GqnOkbskHJYVz/5eOGoOM+Qd4fW8TUl4BVyRuwLolb8Cp+51qGXAdfnZbGTxzgFON25XKXmqdEWIY0SqqgLqYC3xV3ph87BhaIrImveSrJTUs6/9FS8rl/jLWlnJwELLWBoIKGWkGNR6HN/4h0f4eXf5EWIV6Vn6BX5+DchSScO5x4c5YJ89ZoBkSwT/5Bp4vJidKxcFrWxulbgHWDGeW+oCVin2/lVWAVhYPiQ1zW+/eu81NqjPcvzuy7EIIP99j+APLt/LPouRhRCiLJRQmWPICgHLlM4lJQEudTDN61SIMBXRogaWHMdey8CSlSAq+aSMRs2MrKP0uvfxe/GN4yc/IGwuZEkviytqPpcmGgz6fApYpaV1AbUhkzsR+littF4ST8DCVjIDrEAgIrko3ffqqAVW0QjddnUEUQjA0rjCA051iR+/z40tGmIsgIpRRT/96DK5rNfkOaeJRS4hyees8fkp+qX2JpodEnwwvKxRbuBVf3q1MmWSmcpXH2fRISvHYREwItE5DvG/eo8c6msqho/fl13U3EseFT7VWAYQCy5LhXBOrDYUUyfVUZnZhBpRn1ugNloHAwrqXJLyjmkiVtwBv27Aa0gVHbC86qxQBhalzNPtMKYSOc6+Zx9H5IhUEqfH780RuVN0Ul9Wkz+KWLw4ghx+kLc4Jel7UC4gkPjJeZHSKKytlWnVCA5ZxDCQgpGAFW9ocD88+ytWVtniQ4iwFwQLtWlwzMFgE1zhAffaa689Tt/uw3h7hE35IzLufsQSXD3yo0fwy8fFmnPS3HHHHLXVPhnDpLUZZ25geWtqavi4P8CqoVlBKxwLxxLStskFVrEhy+2wUlwTAljtzKs/SKtdRZB+eFwD65F7H+EoXqaX4dWPQDIqHl82IZxTX6uOSiTT1lRPUUzXuoiVsxJXne9AxMIxEXH4BQCrJEq1YqTIgQWHxXMVLb9YAl5x5F5+Ba9XHqfA0cPwkVxY/Uix//J9aE088uzjjCyqqFEV3qGYlU5i/W2GvqM9oRqDco6pPumHjyfDrGI4HOfntpxF5vNFKIrGYVlgFYvUoWlhXzDs9cYSc9pb0UD4w29Bq3eZVzzg8JR7hK3VI1wR3vujt3/0o8vCLP7+CL5dBrL+oJNGHfqUwRAL4hBAShuMboJWLI21gvgDPrlGOsiygzHBW6hxUgQ9IJ0TKEXuxZP9HTko22EBF3EKIQ86IN+JYDaw7mNfyvED+QX/6MeTo+CFIsYpaPHIymQy9RzCtOI+797xkLVKJFNalZXq8ECMOaxy4FInIHsQI0rYhd7/wDJHI/MZoqikW/97U/fvOXIvYwLwvdfek8gRsB4Rg/U4s4oTTzELxDILszSx5hCyMvWJdIhPn6TAZZKZtDg5QAu5aE4koz/y4hy3sHO4D8cxHne1KXjrflWx5N13WIIrnBca89YmGtuXdGxD92o/BtuzZrg9LknzONNK1TYOspTZovJQVsZI0twhytTXU6YkMy2kTDKNJdqUMOn6jChp7BbOwuW9v7EEnxqIgwODAw5Y4WYO4R9++9WvXv4SIXzNRazHH1e4evzxZ58Fsd6+9+0f8QA0xMJCBxl3/80zXnfIWYnYhZ5paW9voYjxjGvSrUxGnUejkSW7EfnOnqAKYKCIgcXEqqeHZce208uO/IVJ/+6Xr7wsvNLEYsFr6YwzVSE6qY9jCghNCYnc0xI1sCnDuUfZl6ECkM2Wglg9XnLOsrrIIOUSRgVmXuM8+2qBVRQKaF6F4XRiczDYTpM5OMQF4ct6uD2uiMX99sdfeQ1egRLmbeWvlNGCwxKDwEnzA0MsyphVrZuXbG7dsYqyhtNn1aod0CoSp5LAK4m3rVcmHpmlL8QYGMBCDyvW2Lpl25kL5BL++StZzODmlQw8+vFlQtYjlwlX74hREMPAHUIarDqETP05d5BZJfvR3r658/DmHYihRNAlFcNkUhGLgaWOsqus5BLIV+zAouTr3AReqXb7yy+/J8QycePIaWK97RDrXjVhLcRCCxAGH/M+yTRwRbm2GYFb5cRtB77hRfpBC4dO5AJWItFsHVaRKRAQXsXCwRABiwbbpu4zF47wVhzZiMP9F84T/IgZGx589znO3LFY9z7y+LPYbvKrr/6ApPkBIQvUopTZsflwB+kwDTgm1eHDp1iH6U82C7eQTvzUS5rk4ZqHgJUsXmCZdTnisDw+GKzuZUeI+b/9y69k2uJxF67Epz7y2mu8jO0yxfDtH+lQ8iKtV9RqSA7hb56Ww0mJWu00nDvOfnT2FJgFbT4MqRjiD5SLSGpgwXShg5MKyzouX6WaMut/YPkLA6uTI/chmVO9ZfW1lylyL5uwCbEeecRlsShyl++9/Aimg57F6kD2WA6x6snar9p8+CxJRW7z5sMculMcv58e/ulmRTKEyg0smP1IDrCqiiTvvsNSDqsyFIzF5jQuAbCW/c+y/7nwB+4kYGHofY84gw3Nd1cHOQ9Y3DV++b330Df+zX+BVvV31HPGfHSOdBoD7tSps2efeuqJJ849AT31FKXSKc2tFjS80k69oyocUxIW64yN2h9Z54kI8xFCbIJT60LImXLkZOBBNBQff/bxy/eCVz8ycxiqjfUy2jdfUQj/+xfcCKQwrmrt7Dh9mkL40VMIl46hCuFTzC12Xy0ZKrr90Wg4iU3TPAST4FV5kO92ULf5YGlk/wBLr3uV00DNQthQbM4cRO40hY4jp56XsE1glUnAZ1U/CxZLt9/f4Tr72cd1B5Dc6W+4I5GprfW2rDp86qlzOnIUuKdM4J7421N/43BuZmhlkjWeUsOrZJhPJsPcIalaAavK5yvmS1G+AzLACoVizY00LLZ1/7m7m48f+sOvfsXEunyvbh88zk8yVw85C1j3PnIvaMa7omm4/UmIdccPdmymjPnkQ9Jbn3xy7gnKnTc+ef0t6PXXX3/jjXOf05hD4vCIU+Y8ldVFHjjAijbu69zU3f37bj5s7n9kXxNWh0rlojsxz5J1ePllRX38BTqCbzOxHufDCL5ECH//59+ITf3BDzYf/ogjSCE8xyE898Ybr+sgvvHG5xh8Pzz1n4e5YkwmsbqJW/JJfUgNellhuK5UZb8Dy1sIWIn21i0dH3X//fSf//z336s5C16WrNbOSAo+outDmSZEJ55w9TZ7LKoGyM3y8ls0UbGdkypATr63Pnzrw9ffOMehe+MNHTqOHIeOkw/9CndVKAfyA1cNDXFypZURvmnSAqtfJTUhoBAKJRr3Lenc8t8dcgyymiu8LMjCqMI0IZpY3NN6TfoKWNjgGHR0uPCce4UMwu//9NOf/td//XTzqbN/J1x98Snpi8/evPTWW5feJL168OCr0JtvXrr0usocyht+1CWT4cpKdYgdfWyUMQMEWP7yWGP7ki0dm7AXlzfvymo2DuG9wn3+EbWL1DtAFvdljMd65ZXX3sPCLQ7hf/+GQvjTn579++lPPkMIt3/xKoXwQ44hBU9CiAj+iwLIETx8mEKYgbfwkrMSYmEulpvvTH8aecUJLJV7P5VtzyZyP8IqP01647UUv2QC6DJvecIU0ctw+Dxn8V+/+SkVfIcJV29+8en6Tz89SLmmk49E6ffNNxS6fwvw4VIVs1IgPDmsJM6rhsNq4G98C1vEAqufpZpYXCwkGhvb9y1Z8pslv5BjBjhpLhs9ohYN8TYdacVrz/Aj49BlV/0rkjT/63/9/e9//7/0gPvs04/ff//9Dz7++NPtBw8e3E5aD9HPxwhc30A06v71+d+eOnWYPYK67imhHnEDA1h+P7nU9l8s6fxN52/49PY/6eUNMux+pNcPXX7k2WepKhSnep/2DIZYfOrTu0ysv//pT39CDD/5I4XwA9LHG9dvP7j94BeI4HYEUEKoBx+G3ll2C7y1JxjixgyQJSVhCiVhpOiAFUI/or2Vc++/fvGL//qNPC8lcm/rFX/G6GeJ1wW+c+9llZVw+LIp8+8f/f3vT/ydk++DD6ZJ5Cj5KP0Qt/WLtx87dmzFq5J7JnJsUNOpICx+MqXSD7yKA1e2JOx3BTwySyhqJD3dKDd5yZJjbmS9LY85Hm3vKCxlTTfrCRus4eaZLoy2//m///f//u///ckf/0je4OO7bv/+7bfTePt4I14sEOsYsoZ0cMWxFd8gbZ5QyEqVlgZ8kUhcMgbwyj72t7j2F/JBcLwVs3lOO+6aeLpdH3jxe90MNGtAsBzk8n3PPv64mT58TbeSOYbqDBoK4Vf/GyGkCH74ly8+/eCu22+/664PPji5UQcQEVy/eDHG3YqDK2AbgP03zlEM2Sx4PZ6alCaWVDm427VSgNU/16dlA0v/Ie4vmTPnaSp+cSqPnMujIkfAevttE7vLUiCqRqpMXuuN0ZyUWGtKT8vfUvb9zyd//JCKQUSOcu/2uyhyHLj1G2evnz17tkROtIJw/xYxi5DF3SzeauWrZIfV3NxA3+IEqwhbLJwNf+vjZqUU8PDXhYow+to0hBtkk0wzDpj5zW+UyZKy8G1kDukdEvZwyeossVj0/NPbTRhYNNre++qPf/zLX/75z3/8czs94e76PnQ7xhu0tm1jW9vs2YtltPELo241mKWfdMm0t6wMt5EOEGDxRloclvn0nEY++lIdmamtwttK6Fa9fS8OuXg8Z7nDI2q5u9rNgxD+9i+I4Re/+/TTvxLyEcFp0ySCazdSDGcjhhy6FSsQSMLWN6+CWaiuV2WSNTWeGlUWJuVCnng8UnzA8oQBrBaK2xxZCoPQadiDWD9yQvejt1FcP24mr7F1Byn3jqoJX8EC+V999dVvETgKHZLvdkm+aR8gbm1tSD2J3O7dKvdeXbFCaP/EE8SsHS3JFD8x5XbJ5jgDi2ppOCwLrP6WWKyUeN/quBw5mjvcQKx3gCuFLK4MpYslfl1OcVCLtdCH+eqrr7789a//Cp2klJmrc0ZljcIVKLV69eoV9P3Y7mP0B5Q3r7NHWNVCRU1ZwMd3l2PvkOIVtpzIzYbFI/SveM1YTF+GAG4Zq8BGVQVQoP/2O5cv34tTejhej5t6h6puVRK+8sqXFMJ//vNLCaHw6vvfv+uuacIrHcLdu1cgeBRChtZilIivvslWFdTHnGFQz7lyExlXUhchsOYkZEG/2gKtD2RzsZ6pxb/+Eff9BFRom6q9rq8IsIhY7yF0X+rkE9SD9R/ww1I4vxuRW0GZxz9S5JB8b4JZZzlyyVSwPOAjXJHDamiOR3i3kwIWUrG4MvC7JEJCUhfr8YYG3oM8p/lp13CTouadt50RhyH3DnqdZk8h9650O+ZxAtZ7X733JeXL++9/8MEHzmjjlFmrUga4Wv2Q0uoVu3cvXkxWffvBN98ij3Bqc3smHfTX6evLfaUOsIotXRhY5eXeqAFWM/GqoeHphl+46sLLl99B2AD8t/lF1Hr2vkeceVjp0Whg4aKK93797l/fp3rmfccmTHPxajcsgg4hoLV7MZsHCiFhX5CFJcG8CTiZCVNNSG61qp8dlj+vJAxjR5bZKzOn/ml1bINTF7LF/9Fl7VOx2V7vauWmqgOs1yR0XxKv3n//dko/Bhbzapo8K7tmrxFcrXZCt2LF4sVdFFFOPoI9d1JTwUBVVRgOC5sziVlVFlj9K04f3ExPr2Z+NYSb9N1UeP2CD8ZSRzdcfueyyRiWexc0Vu45ayPJsUvO3M7tg9sdU75WeIUnHHj10EPfPPTQgxCItWZNFw3E9Spr0Mzy0UdZ6vNV8gOvrLpaVmrzJl7iRFHET/Vgy8vkXj0pquc0z2l4+umGp7ONKi8TeefyO4b8Mp0haxqEV/dJtYMV8sT8L798l0K4lUJHww6iQbd2reEVakGMuZUrEcCHhFgI4Ww98FAYeumjK03hi5xKVYZ5sgvQr5DLM/ojbHrBqL5cg81pIqaueb6DdyTVz9F9VIOsy8x6wyysZ4DXv1cbLG6s4gegnpLv6FaQ6vbbFbDYmk5t6+pas1vx6qGHXI/LNV2uyGHmoiVT40EBIo/yCH/zBTSw4PPNvdr+4r0xOtDDnYxXc1zO9bzvDZUDrGaUC83xsO5iNc1p0EeP/reDLB5xjstivc2zOPfe58w4Y/KQkwYPudslZcSVO55cahmdMw+ufHAlJc1uJM0EyZpXZbyh/e4pLfWlkqlQKKq3lmDlcYWnXwZbfvz4iwe/IsCag1Px0QYki8UvXd2Ys0eZWqq6drqDl390Lx83o1eYvqKH3fscOqb+7agIhVc5wFrJEdwp445Gnttlofvu8VBBmKDKnzsxwziGDKx+2TXQA7AEWWoDpbSyXEcdkd69/K5DLCSgZKE6sOcVs9PcRO7o91XgFLDYYK1ZQ8Ta4PirB8Vj7V4zv2vyhKltFLlvLsHi70AXkIgVj4crI9nAklbqAAOWufH66oHlOg9KLHJ/AyuRaE40g1sNTYmmmLqIQm5bmmOyRq4klPXvb+Np9+677wqz3nkbJ6VcNpsnsB4efQQmFia35CnHDmvt2o3uHoKkDQ02Gm0bTnDOTJi6tm3jeikMyWVlfJQP5byp0BdBFx6bJYoOWGUaWI7Lgs2a42Cfl0Ni34mm1oF33mXf8I48BC6/fa+s1hJgYdx9xeNOtWAYWLqs0RUhIrhz505G1sqVOzdICCmGbRh4r17i8qYlmfLQlzkUloW4pXBY9I0HWAUeALc6buU5wtc2JneGy3WOskfCdbSYJN/LHDqJ1uV3pLrmjuo7ruU2Aqyvsh6XIP00qaS7uuYDWK7ke0gDaw2ANZUit/gYIocpw0yqzlOFSZ+4nJeFwV9WJlt2voXA6uGviw9Y4eYENnuSyWpqkiEXa6pXPdA7nv5Fa6dcCvCHP7gyh3Ln3XcVs2AXLqvVMkwsLmi48fm+AhYXNAws7mBxG4HShhJnw+qdGHSrebTxU26qQtYlLgxbUvxhErIqzaEf2NxVTMAqU8CaI9EL4+QJtLKa5jS5naq+j9YdQybWO3gCvK3Wbz+iiIWJi/d0XQ1iaWDBpHbNlgie2LBhw84NO0UrNpygGE6cTOLimo0qDbyWTIhvZy1N8Ur3Ku4hR8vgDFHu3Oq45QILu7OFV/pix0ymhU9SUNcLmOSTHZoa+e9kSS8efU2S7z39uMwGVtvs+WyxTuw+seKEohZBfzUiN3HiRHpcEu1nL1aFISGrtK4KpbQsVxRg6fuIPN8yYPX098UHrGZxWKBWLFbLr3ppKeAkSKpqWuXyYh5ySBx4BUqJL9/VzFKNBT7ITxzWV1/9lon1geGVOKw2Hm1da2av0TpBgw7fTixdM2/+fBpvlDVtbVjo9+pb59ghpD2MLAUsPk95WJVzT19/KRdYUUF9oiksJqu5SYjVZC7ac8dQ9pgT9Qla79Dgk2L7R2pNvAKWA30ZeLqwkXmLNbvpdYK1AQGkQXdiDVGfuI9eFpCFgYe6MO318xF/laWIIhozUVViYzFk/8TNDSwcAh1mnzVnDvHqjpY7MvVySpYO3O/NdfW/5ROUKfEuv/Ouwysm1uOCLA4dR+4uB1hSEXY5iYfgcfgo/U7s5sBN7CKD2sb+FNPVZw+TySpNeUoFWFW44bcsqu4jiugLeARY0epiuX/AffGu/F4Osb8SsPD2AwdYvNET68rlBHY+UI2ApU4Nzdxxx9Ptv2j9jR5xMuj+wOsWfv3rwsSSnPnLP//5u6//+sFd2paPU0nT1mU0ceL8+ZI986D5PNq62qaiVQOX9fo5SpqWID7YIG/wapYT4COULv0StNz4GWCVMLASTQmiVaLJTSyexmikGCKEFEOMvu7f//7M//zxL1/++t1fv/uly6m+wwen8OLI93jYffXPX3/9Vxp2CliI4RgQC8Gb3cXxmr9mHoWPcD9vjQ4hxZCpvxFNZJTWLUlPjTpGGfVNWAMLOwj6K25ZwAKvQliQlYixwcpkcIIxr2z7hRO4vwu4/vDb99TDEpHT1JLdYY8ri4XI/RXPy7uAe+NNndSjGFGcOHzzkH/z548iYiFyaGVh7ud1jlymlGctUgksziopicoFag15wIp+S4GleVU8wBJYhcK4nCWqWzFziFgxOUk2jVYojTjOHKQO+a2//98//hO4UszSyPoRbzp8/D5eifXHP/7xLyDWXdL2xGgbN27MmDFTp8J4i+gXkydOHD169Ch8HzVKBtvkNioL155cu3H7q5feQPM9VeP3+BlYyJUwA6uqX4KWGz8W321AkUNBTcQias2hVyIWjjG/6A+j6j4i3rTzm06MPwrhX77kGH5pkIW+DE5weITb7l8hhgihtqkMLAnh1AltFD7yAxMnSgARPgreKBXEidzJauPa+pMnEEKs3yZmEbAohASssOCq/4ClB0KotpaAVVlJyEqglk7jHKtMEocZR5ucuCFwv/nNT//7p5x8hHpivYL9uy5i8TLA97767R+/Usl3l35YjjlJgZO0mzxhshYVghQ+ihhCiJ+UxSdkvarsqQ+wD/Nq0rKovvCxujoHWEVzldrVAks/PMwXJJtPxQcsdfVdUO4NBrJqm8hfkcPCQw5HiQdrkTjN/LTD1pP/+ikD669//SsNuC+BrHc0svTSGBltNNzIYsnEMpbCTGNi8YATIYMkbdSYw3Djma6pbWPGnGxD1tBzblVLwu+n0RaOOw6r2IBVZhxWQnpZeBKoLrzce8BX6rDafyEh/B0WNwJZGvvMLNkFzQsgKYR4K8elOjGUIMr4U2OPQ6iCSCCbPGHqmLWg/lvnpLipq/P5qippwCmH1b/AMtfmMLBYvCTL603jWLSgAKsJS+DlOvIf/OAHv/jBf/3XT/+Xk3wqctpkXZYzet4zj0sVOfOwdCInD01FLkB/ojwxRxHryWS1oY9KkXviLK8jVee5BnEdpNzz1OAAyyM9rGIDlnN+XN+A5fUWJlYewfz9CSw/N7SD5jA1HFccw60AnEY4o5+vbuESh0dcU6z+jh/89O//+y882L7++neOyVJPOc6ZV94zwJKle2LMebwpn0W4GsMjbjIPuYkCLTYIXdx8p7c6uXY9PecoaZIAFpUyDQ3NDXzNQv8Dy7kCnr/gCvb0wo/ReFDOJ1Fzhg3RshCu35szp54iWP+D/0II//H1X7PGnQohr4N3ht0/xKRK752DiAhqozXVAZZyC6O1WZ3YNZliuBYhBPSTNLRKfL5KrN1uCDfF0BLsj1lCI/dwYGTJdWbB8mAoiMcoOS5Ebg7bLNVRveMOjtzvTOR+/eWvdSf18mU+uUFF7isXsG5XeedAy6E9ojfBST/6jgcmkKVZvyNTWuepSyXJ9PGVKaBVg3FYVfyZyNGzRSF9H6OGluqwRsuUcpeyKGCpp0gwVF7urNtyT47o3+vzEm75Bb3uD8pNUzSwarn3Xq8ummqKoRODG3pjtV5v/Q82P/W/36SUOSnE+p1qZekB9+59777y3pfcxOJ6Rha6y2hzWYSpKmf0YHOlDP2KZ+fBrLVU07xBwy1TEyytJGDxq5iA5RFgeb0KVoKraFCAVR1vkCvM4LJimHuNRSnCqw7//Y03//E1VjNSCCWGvzbVzWW59Ou9fyKEGJzYjakm6Q2yNPUV7R1kTRRgDYdXJY81ZhyFkCprqm1SnpISH5jf1BCOhXkSg8xq/0VQZRxsFv2ItSvy6PTLWgdc7NuAFz8t5Z6b+lU/feqNN4VXX//1619z4LTL4nUiClhIvn9+/YHemSMPy2njTOAUq1TcJo/WJp9F+YfsI5OFngQRSw5wrec1Kw2KWMMUsDBdXYzA0qec9AFYDgEKAEsbmkLAKulvYPHlS7WCq1p1NV4sxp1jrnNqvemWHYefeuOb7V+vPTnu5MmvIRltvzZt0Hdf+fKVL7/851f//KdqYX1fjTc92MZgvYvufbJ0ojgZw0MQ420tZc3rT1DSJMvL4/EGPqWI93bdskD1oAqzQ0MBK8thBfnWn7jUDyhkeW1WDFd21XMI39y+nqpeMkAcQoMs6PK7zz775Zfv/fM9RPB3UlQr6Ov6ZswYs5F3zZr5mOFi0HPoRnN1M5ygNZEjSCHcTtDHhKsnGiGCUk2Ik/yFWJH+O/fX7bDkJ52JqGtCmG3l8BG0mqSheseqw0+8/iaS7+S4v0ry/e7XzhPzMj0s3yXUf4nIfUmRMw/L242/l8jxBmjMGKLfN1Eyb6KEbqLKvqlSUL/5uixmS2VcwILDGlZlHFZRAMvvhI5Vqa4Ov15g4d/oEVi3cpNSj8AKqTpQfgrNSfAayKYYDUNvbcuOs0+8/s362Wvp0T1m6tq2r41B+PWv//ruX4GrXxOu3vvyS2zO4dV7jCtTFVLKqHzhDdBYjLX7BGYJR40a7X7GIW0w3saNOwliUdKky8uimOIK93Mpo1Rh/HBhh+UC1tMNc5rFZxHz61s2UwhfXd+mG3ltQiyXWcC1MRxCbCB/XyFfmSwO4VodQj4fBSHkGM43MWRejRqNRha+UGs5hKsy3rIS3jEaFofFVWF/A0uuf5Z+lgMsXJkUV8HjS3ZjZEwzm09R5LZvPHlyzF/h0l3EMrR/92XOPqTjX03gzMOSt1qsXyy5dwwLSFecoLipYtA8NlXuMesRuc0tGZ4JIGIxrqASIVbRlIR6DGtg6WOjegeWGwD5wMK/0TOwSm49sNzQKtR8i8aamkk01kLwV2fPvfXq+rVTZaIKm0kpZ752hhtmDjHSZKy5rYHQCktH18thRHx2H7YTrl6NlXtLwaxRaBo7meMQ6yneZRKNyg1y2FJ4ywLVs1w9rCyHxZeb84WcahJc2axo1OOtRwgvHQSvJkyegM1IX3d9PZuM1O++dpD15bsA/u9+/TVWYTmjTiF/7dr1OJhBnX9oVmufWHNiHsdw9OjhzCsEUpA1pm39m2RTVyU9HnxAlHAhdWEFJZ+vvy5XcDksV2MXJSEGlQYWu1M8K5n0bx1cvxYzpVMpkb5u+3q2Yv3XFLYDwNWXLHfyOd2IcSepyFvPkTv26jerdeSw4HaeeWCOGq391uSp2uCfo8clFrNmYjHjsMhjVVZK093DX//+BpbuNelSMORyWFrITX2hi5YbUB5/KOzuaSM/sOzJ4UMwpEEY58tmb+GBmj0CK5T1IlvD20yaMX3TsuMUDbbZ0i7nkg4P+t8xsVTeMK/kAfe+duQ6X06uRcLQQPtG9G/Sv/71L2ze3blzAyFrOI204aNcyCJijRs37eTGV7kJ4w/F0skE0ZN41e8OC8oClnZY2cASk/B0czPW7vj9aRp15y5t3wh/OlmvCUJ5gvgRtIRZv2ZcwSPoUacr6pMncXbfMT5n9BKOy0QA//Wvf/MG8g0Uw5kIIqSjKAOvDR4LkxcV1XE8Ifn48iIFluwzrDLAIkcYDKbTGTwsD7atRU+hjdeizUbkfud6Xv66EK+Mudq4cft2Pp0bkfs3J98L/1r+4EpOPmIWYmbCNlqZrLXiTvkEh0w6HWtqMIorYPHXv9/PyXIDS449D/PLzas4va4ELH+5rBjQ4qlbt8NyeFU8wMpSMBgoiTSwxWqoE15tR+uF3EHX/C5e9Al7/bvfLf6doy+BLjYHYqx41/NGfriRJ3hT5cq//vX5vz7//Mc/fu655156gdKGkTVz0nDlDkbJs478ARql698EsXAldDIRbm4eFi/CprsqBzWwcK92XDksPriSUqVG8YoH3eT5es317+i12ITwS3nxkU4qhHxA8sdyUCvjngL4OkD1Oem5z5/78XMv0cjDwNuwdOnMkZMm0Tc99LDjBK33jWRTD69KVMTjlb5KdalV0QILN5LFNbDICZamMuxMt7ehaz6VUMXbAmdL9h3TcYP+SajXkZNjWtdu1MmHM/Df+vfrKnQUNsq+l5br5JtHyTeJ0w82n/tYY3jS4tW3QKxMOkMJGHWAVS3AUh9z/8TQkSqNuEmOr2tIbXYqy1EWsHw5wAoKsLQ7y226E69iuiTkUywixQQs/oR8AFYDgOUJqpQBryZPnK/XqO/ezQXeP4794x+/0y966n39179+wNKoOsiXTki2fM76299+8ref/OQnPyNovSRJM4OH23AtbsKgKJx2konVkkwKsOJFAyyJZDmfh5XtsCh4EQEWaN/cFI2FUknDq3FjumSNumxP2r179z92UwgRO4Tvd/8E9DEX9oEcjLz+UxVCjqHAniKoYvizn0kIV+5cuGHGDIrhyJEcPm0VEEMad288dbgdmzINsFL9DqxsZqkcDChgCbHgB0tTknwcuQmwVib7dh+jwEnQEDeep9CR++tJUH67YdVbr+PenDck+X72s5/8zEROJ99IpJ/4LN3HGiceazOf+J52gFVdVMDy614OAIPNK7EY9jqFsoCF+PrcxMoDVjCkgUfIC7mZgF8rXvUvsNx8ypKeH40wr6LBzI5TT2heKVydOIEtpKRvVtBj/x/f/EOLkfX110Kqg3y9i7pa6Q090Gik/fCHP/zPH/6QiPXcc+yxaLQtnTlz5uCRGHD8rJOFxxhu2988d3ZHJh0MyVaiygDOyuqnM52ypPbA+nVSaGsa4dMlePcjG9QoFkRSCKmqwaiDv1q6RvYC8rmXKyh8+K6C+M/f6RjqCOLocZLQniNIMfzhTyiIPwT1YVM5hnfPmD59pjgspyrkzvubb3AIAwKspNyjhqTr10WPilo6H5F6vM1RzVjguIRkSiK3kSI3dWpXl+b8iQ0bKHYUNjwuRa/+4x9f/O5363+3/utPf7f94BcH/yGRk2vlPj/3Od/thcj9hOPmJhayj/IP7lT6Eib51svSmkx9WjZbyAemS0L5JPotfh69OFRnHrbbhWUlW6jgh6WBpdglf8gVnziskCwnF0jlvKvQCldbqcmvW/a06w1YYBVfxxbBVycayqw6jJShzJ8AXs2fpzJm9U7seP/moW+0/vH/yqCjXGFDYG6B4+ca6SkyBRhm/8kSYr30AvwB2YPp06ePmDlixODBXNVI13gq5Wnbwbcwz5UOhpOJ5oQCVmlxAIvvJSwvDCwwCxVhU5m3VkLIvJpA8ZMIYufyBj414JvVOoT/7zf/+Au9MP5kuDGqtDVg2P/kh8J7Vwi5tlkIjwWzIKW1040B9C+d4xASsPTd9kUALE/PwIoLr0KZzCrFqzHkr7rmd61xhQ75p6L2JusbuQHtVVfy8b2E6vrUv/3wKU4+PCwZ9T9+yTwuETiSPCwl98aoyJ2FxUqHiFjNYrDilcUJLOaVlHblPX1UVwZWUMrAfFzpd2VmFSOwqnCmbqQh3OD3K15hQ9bkLhQz85YuXUoZgwOZcG7ovx/89/J/Z+n1f/9LKCUPNUqVnyBTOFnO/qejn7hG290zGFkErelA1nBpJXAfa+NBnirEXTCZRBg7SlCw3qpo9SwDrJzmH7e0sI0wjhZgU9TvTa86/NQbr7bRJzN1ggohj7mdq3eq0+Q4jKz/8+//89b/4fpZBRCj7QnxpUL7HzoRdAFrARHrbiHWvOHKKPAsPYi1kaDPm3TCPEnvAKt/D/3NBhaix3U1UB9uiCaTwTSS73X2V8yrNfPVw5KSb+VOPlDtwX///yRsnHiUeq//6w12VIZTpB8+dRbJd8odODewEDjY05ncl1C5N1WS7y2eKkySxQo3NWuHFQgUH7CEVwo4WIHruhlLDhx3Oli+ylxgOR0r1b/Kfn/9/6krOoCs3GUSN019c1hI6IZwwpukwfb6QbQQUA9i3RQVNIpXK/mY4+Wkf73Ac1aqwyJm4G/yRDslrDpl8mUzvyhpxGC5Bpsga6YhFrrGlKobX8UmnQxfXZUKVDCwioBYxKvCwIpHw01U80ejmNfEvPyqzWffeHP9GK4HYbDmrRFe8Rl8HMN/cwhVEP+3y08hdBTFsy5KQT/9z//8/9K3H6KwkZJwwUIZd0shmfgSYE0mm3qSoM/EyrCKHFgAflNTCH3Lls1E+vXjpsHdY7Jn/rwTSzfcvWHhggUL+MBVCZ5MmP4rK/fwkPwbxe0sZR79ePY/T51yBU+ApSZ9xJtS6DSyRok3JWJNG7cerN+BTdnhRLhJAStehMAKhvgsgyBw5QklEri9r70xS4lEb8DSX4nGHDWzUfAE+g1YuT32PGDJ5cvhRDKzA4ONJ7cmUr7MI391YgYDC/lCrLrzJei5l577/LnnPv/xj7lL8JMfKilInfrPfKmU4f4LOay7Z9w9YxG9GFkkWIT5MldIvhxFoY83ovpKPBWRolhACmBBjpUW8aIsclhRnOfn9aa9GZ5jXTtmDHi1Zv48x6LuxKBbvvwFEgeRJEPuJyqG//lDCR0XMlqHc0MoXXeB/gkubchmzVPIglM4qdpYAizjsARZ/RdBB1g6drz+jwKH7YWpumDLqlPn3pSp1QnsrxC8DRsWPgBe3fPoo/eb2D333I8///HP/vYzihvaDmf52yl5TJ4y+XeYaeVqR1DoFix4QLKPUo+RhSagXkDKPVR+XKbTSfSduVhtiJcEnOHef/FDU0rnHRwRspCJE/I07luSq9bW9ubKgHlHUxT6FbHYpfFvw42NrUuWdOp37FzS2t4YVu/JF4dyTaiBddPB1RdgRfi67mjY1UOYjDOs5sNgoZ5ZuHPngofvuf/+5XeSZKhRzvz4Z6Sf5FUu2dbAVc3ohrEC1owZi6Yvmi42i8fbfOkay8Q89nWlfL5IRUk1H5jc31vkHWDV8MsBFp/VEw0JsJIZeNRXdQ8Qx3+tmQeHtVCAdQ8cqsYVhVANO038/5Rhl6v/j8MrMVgPLEQM4bDm0YuJNU9NXmDGa6N0AjPGYhUvsHg3dCyWDqYyqzY/9RaWro3j1TQUvPkE+xkLHyBgPfzwPY/ef/8sjSsO3M9+5n5WctgYVof1t5xS+gU2WOAVdySAK4LWUpwuJn13idwlbLfIpOWSRyZWHJdR6M+h/+LnAhbWSQW1QUo0Ny7p2NSdo22btixpbPZ5+CMPyIyhfAYOsOi35cHEviVbzHtvw/dtW8CshLw97rCKFBOwYBn5/ttoKN2yij05BtvELhx1Jg4Lo+2BlQDW/bPAKzzgkDJOzihb0JN0D0Fa7mLK4bCIWNPJmqMDOhyH0uHgAZmsIX9QWsMnTFRUVzcUFbBqHIclDoGXwWCTUyIGYJFHfXX9SdTUEzHk0ARUfZidC1be86ATQ9eo+8kPr0B9iaCE8LkXXiBePbwTwKIQoh4kWuFHPhpRFojQwOMluC1MqwwuZC8+YPHcPDaFpdPpWH19LJhEKc2k54KQcg/pN+NuGKwFTz5MBmvWrBfuVP7KjatsQ3qqQOBU5NztCHj7mQQtSj1kHjfe4U7VOrZMMmMsVoNr4WRxAAv1YMhf7vf4YwkyV52bTh9Zd/HQRdKhi4dI+OniumWnN20h8DTjPQM+AU12e8jvT7S3dm47fYHee796N/pp3YUz2zZ1tkplWFEhyCoiYPkYWNFgjFMGnlwKwtGjRrmA9bAGFvScIMtxWIUH2w9likYPNu4hoOvJ7oDqQbzwpFvKDgHEmoiisE2KwqACVkNxASsYNA7LARYOFUsTsGqTq06pdUQTJrK/gsVayiEkk7rynnto2AFYd7qBZYaeK3JZUZQQik14EDFUPmEp26t53MnCyGNidbWN0ctDxGAlU8nKSl9RAMsZMA6vatP1sfpkkEj/xCVOvqnCK25ICLCeZIc1a5bD+uzA9cB6lXsqcsuXP/rwgoXaYM2Av5qO3FvKyMKxyXzUEWYK0XdP8omX2J9TfMBKJBJBRBHmagsB5+LxA3v37n1Mv6C9B44fOnJm05bOfY1hj5ov1DQI8lEZ5d7Gxn2dm7rpvXftPcrvwz/Ie3YTsqg09JUQsYYxsHyqsXULgOWW/k9101it8K8MmRnCtWNwQOj8UcphoYuwkLLmYRpsPNqYV885FuFnecPNGWV4ccZgEZZpuS9EOaib7uywKGmW8sG/XUSsMbMxU9iSIr+aCpbIUbUlJTc7UL0IDfdSl4JBPeRw0gWNuGS6psbrbdn81OsHN57UTUDVBqSiGpXNw04MX7pTAvgzPfR+mIsskcTvJ3rUUQjvv8fxCUs5dDO58y4eax4ORuTShidbsQxLSkKqrgVY6vO4VXFz550WcIX4Ca9wdqRXZgjh7plXo+fzw5KBBWJR4AhYd8rzki2WTj1TFGZPqLK1+mFW8s26/56HpYM1Q3VP2WXNVA9LBA4ea+OrPGORCYewzAmnIMb7O/cgDFnM5smxYuEE0SPsb1/SsW3ZukP7DxydO/c/cjT3KIGHvFIHVYaV6uP3q0Ef5FZ9Y+uSDoIdvfdW573w/TF6z3UXTm9aQrCLkFOoGBaJI4Pwj+Sej1Xo63td6h1YlQpYQZmkaYMlnziRj+FVDkuPtvs1sfKKGudB90NHzlCDv4I7eJRTZiH7K6fjjjEHXs3D2U54zJHF+vzUjgwX27KssLrkls1S9KDegZWq8XjSO9A3Pol5ed4lwGXNCXZYCliPmhi6XJayCz/MkyuECvn3P6qGnVoaMpNLQiEWYrhGQkh19blTOOEpxUtHDbACdcUBLIwaCh/5UhDL68WWnDcurYfBmjB59HzOPU4+sViOw1Jd1B//+Me5FXXB2HHg4O5fmkWop8A9Q5FbpCrCmfLEXGouGsCsTxub05ZMKog7pprQw+rv3IMwYrH6QM7oCWHpQaixk3C1f9fex/bk0oq15+iB88cvLtvWua+5UnaMmJOv6AuS2Idi8NDxXY9tzXvPrY/t3UXMImS1h4EmIhYWS4BY/Q4s2VGEn5Mth2WJO5sDnCOrTbnLHihffudzhlh5TzrHFfxMiXGFpieZgwULNbCmG2DRM04/5mCxiFg4t6HF6ymL6i0St25atQflA8tBFvEqlkwGPXU1GTZY46ahb+yYVBp2YlIBLBp4XFk/h5czeZGDrJ8Y/Y0jyDF8wfDKrGTTBksqwnlL1zCw0Anc/haFsNRjgBUpDmDpklCQn05LFNMt4u5lflqOJpxHn9iMGRuMxbrfEMv9tNSBy3q50g8Zytk3636qCB945hnmlZrsEYdlPBbP+oxRy9io7A8nmpubwmFX073/5AALyCoPUT3Y3tl9ZP+Bx/bkuysDnj2P7T1+pHsLEatOnUAoxTh67R303rv27tla8L237jm6d9ehC9voXeGxSiK8kiASKB5gpciUc9MTPYSJo0c5DzkFrAVPKnsgWaNn5n+sypqf/Y3nmP/mjDQZZ07GvHA/efIH8Ixjf6VqQkWsmfMmscMyFuvcqVVJf1lUbSpu6PenXE/AUsRiYCXQwXpz/UleSDRxIm47YJM6Ay5VO6xHXR4re+Rh0xsi+DcTRjPkJIYYdPeYuma62ARVVWN9g3FYWAW5/lV0serCamuOrFcuGmAFxKTqICZa1FwF2fuJ8/nAegBrBhFrhgMsTr5Z+cj62U8KyIkdJx9C9+SC55+5exGIBWANmj6EXkwsc5nTxAkwp4hcS6omGI3GEk1ErOICFjOr3B8Gr47v7RFWWkfPrztN2OHNIgwsvH8w3NpxZt15MldXeP+te4+vO9PR2tg8zFMRqeKTG/oRWHo9EU7NhHjZ3utYPzR1wkRkzLxRpo3AD7knHxZiyYPuheV6hvk5Zc55tDG0HGOlRtpzJmUWLHiGgEUJo1Y0KFjhNW/4PLlOBxPzfDRWS7CipBoHIOC4X/dezhsWnKuQvgHYDSy90j0aqyVglftLXQaL7zabP1zagDMQQ6ls2GO5K+uXXAPvZ3/72d+0VAx/5grhrFmPssF6ADZh0SJjEtA7lmG3VIiFXU5rySiQxSplXFWq5X8RXzEAC7+TGKbTKQphuSe1SiI3Zgxu2SBakSYRgRG4u2VhAxPLuCwTOPW8/PHffmbEj0kNqx+7Qvfk889I5ECsQS5iIf1GIf1GY2EN+n+Hd2Q8wWg4GkMTKzJMmu79lXsyNQZc4XjNUIhNUuOSbRf2984rItbxdd2dzXFPnSegeodUDy7pOHNx12O9vOfco7sugli4PLyqsjJMDzy+RTzimrq5pcDic3AArHLKnJZVp564tJ7vSKKUmacfcjzaFj7zwAPPE7K0QVg+a9ZyhSx3YehOGT3ONK6YV+LJkTFmBZZB1qTho4RYOIpOWSwAqwm3KTRFixdYnEQMrFTL4XNvbd8oKx8nIooy1QWLpSobEIuRdb+7GfhjR39Trx//P/TSIw4hxKBDCDWwpiOIQ2nU8fS8qa15wqsLy0fXoxeTLPWFfcAVN2PiRQIsjwDLF8QdNcEoDSBZbcvAwkGq4NXImbCOd28wkbvfQRZl3536eamjZzJPvpkElIfl/fewwXrmmUXO85J4NWSIOKzhTKxR8ydO1VOsLbg9B3sKixBY5d5abzsh50B++6kAdqgq3NbaHHeA5Q3hnXcd7f1dmVj7qisqSmCxsB21pD+BFeZrVTHwvAQstNzbuOk5UZ29S+mPli7bAwLWw/BYcFk03rD+EeuOX3ohZ8CpTDHJQunCuOIn3MPEKwFWLq8mUcoQsQRYymLtaCn1lMBh0auIgQWF0ul0uT+z4+zrb65XLXcGFjFfQ18ZhScFWfdLCO/kpZDGp0rkPn/u/8FGAq1/vcTAB/ERQtWHYegPEqMwfcRM+AQqqiep6a42HJeyHRYr5fN5fDjBhe95LIKSUF14x8DyYTNDoMTjb9z81CevyuQqZ9/w4SOJV+QdZ4i/RzmNwN0v0sln1jDnZqBg/iXJPyY9npbEq0UiRv0g4Gr6CF7uzv5+FNeEsp/18KqktyxKtoKAVa2WNdzKuLmVCyw/ASvR2b1uV+Fmex52Htt/YdO+5ioBlt9bG2vsPN0XXpGO7qKCsrGhuqTCUxmOl0T6D1j0+UdxaX0iht3eBCx0PWUNlgEWRttMsVgAlkoa0oOP0ktljZM2GHXPaUsgjzYZajzWaLA9+aThlbZYM2ciMScRsoazKZ83f3QXTqLbyBYr5SmJc0lYzA4rHI2Tw0qHgjXEfNU4lotjwfxJbmDJGkjGPo+9WRTBO1/AGoeXZKEIdus85/r5pZcUrRSvKIbPG+gPWgReTdeNGFf3mCzW1DEnN76KUxt8Hg9WP4YbigRY6tcCLMxSB6gibEfLXc47VCUh5wWIZWpC7U7NA1McPm8UU9hyKyty9zx8z8NPPq+BBdJT+OCvRsj2HAaWXFcIYMlarLQ/IqcVFAewfKiIBFj+UG17x7Ljj/WhIASw5h74+ZktjXEDrMYl3UeO91YPqvc9en5d95LmBgJWVWW8GvM2NxlY2f+0169aV5QtcT5GG7tKME2DLXBv8iL3yfoKKXbmlDQYbc88I8PtYege1IYPPrr8UY2sF1Te8LB7yT3MoEfJXTGvHsZge1HGGpsDGmojgCu4A3XoAF9nzGf9vkEFjac6TiXhnIaGaH/CqpDko8FV0NIFLPf7k6sOm71wZqprEg+76Q6xyGPhm6sfKEscZOJVRt9LAntnyM3SIXwSfRiJIdeDymAN5tNS5o0Ui8U3sXMvBoeleDyRBpzXhcu+SgJA7U1LsatQVRWNwQja2WXlXhyL/Ob6tWxNkX4UuEkg1uCZDCxKvgXP4/Xwk0/e8yRDC8yaNctJPo2ul1TgVOotnyWhA+iffEADaygxayhFbsj0ERy6ecIrvuZxMlfT3ELNBANVOPyQgYUN0Ihdf8RKttCVlIT5CtooAStGzPmwbx4J2rNrHRWFVbC3BKxYa8ey/Qf65s6ooGR7Fq+oq6siYMUrUB5GysxC2psNLK/aCldaWsVX12lgccsdZzi5gTWPgcVJs/AZjawFD6un3aPErEcfXT7LIROKP6kAlWa98OgLjwqvaKgteJ57CBpYGG8j9FhTrhwXifN+uKmzpWdcEonigr2mogcWxVZ25YxTw45jSKXN4MEjNLGe4VYgPJbyWdLMMh34F9wvE0M15jiEz5Oe+eUzi16UYTdoECa7RoD6sKqTUFhrYuEITdkx4MEdOtgtUB0JKGD120XkJnxVVWqzUKCMl9tS5NzAGoUe1uCZI6YvWoS4PfP8A/SZo49KUlMXvDBrljv3coS4zXpUeLUAoXtGAjdIxQ7+asTgmTi2lYGFCyrmywZ83lGYSeKeQgWsEgWs/jiYzQEWj9dgnT/R3nn6s4/70sFibd37cyrsqurq/N6gN02wW3f+aCF3VujP9uy62L1lX4MG1jAi1q0FlnZYVThxrinRpIDVfko2RoyZoC5D51s6h7NBkMHGxHr+gQUKW5w1QBanzazsVMHrUZeeZG/wvC4Ih4JYpCEjmFjErEnm/Mf5E3mesI1XPiY9PvTd1Tqs4gUW9mWlW6So5s27k+eLw5o0aSSGncQQQXzgGYrh88ytJ+8xc4bErNwYGl/lCiFFkGL4IkbdbUOBq0EobOifHzwSvJo3EmtDeHHIROzK5JN6WtKwWLiwigubYgNWWVkZThB7Qp6WUyfo6+TnTZoEYDGxnmGROydqSVXtWiAyKzdsLlfvhI5x9YziPPIPwRvC2TcSD0uZZZo/GsnHFzi98dTmTIYQlUyEw9Vssaqq+htYkQjfJxD0BBtbOz754v18vszdc/To0T35q94fO042iYFFBqu980yh6cW5Wx977GgBBh7F+zZ7PHVV1dWYgLjVwMpxWAws7Q5wKIoGlppcHqkaCc9I2jzwAHNLVYfizlmzluNppp5pWbDiSkY94V68+0XlyYciZYaAWMgajLZJbMtHz+dp+TFrZ7MtT5ViM2FTdURte/TdhMBck/KBJYuw1poWlgB/krZYXNwoZIFYjCzFLBU0DL7l6vXo/a4oPqlw9fwvn/nlL8GrKYtuI2QNgklVNmESXCoK63k07Aj6XVPHTUPb/fCqjNcfQE1YTMAKuIFVK4ca4Wk5dXKXAhZFbtLgESOGOMCS/CNkq+y7x8m+WY++4HplPSnVs5JST0BPmaeyD6ETYvGVKMPn8ywhb8+ZZs5ATOH6JgZWiQCrf6IlwCopqTbA+ujIp9/PZw7Wtp/flb/ynWrC7iXhUgZWon3bkfP5BeGexw4cP36+QKW4FRarkYHVUB2XpQ394LAoYarlouJoudcfbD/81Ft8iNPUHIc1khsJbA904txtmPXkw/c8ec+jPepJrQVSyTgZM2goUmbIIGTMzMGD+VaASXIOnUqaqdgCfRiLR8uqo028W5xP9bkJgbkmCbD4mRdF893jb9l81tQ1E3n1I8/OE7HgsKYvmrEIIbzbGXrErCfFZxWI3SwNe8K9xhU8wosoa6bcdtvQoUPFJ8AmUPxmTmLo02sUJi7UygY0AjPJmroI36YgnZhiABZ6WBiAuPczWot2BJ/TgHNlJvJ9pwgcIjdiEKcMZ51xWoysJx9+uIfQZaWeJv2L0vibMvQ2oJ7Tj7Nv8OCRqh0hd9Jy4HhlA26CBrDQdUc5HakK9DuwkG1eeuq0L/nowwLA2rNr/7plFy4e35uLnT3cdi+tq/ES7DpPXzyQZ7C27j1/8cKFI4d25dWKc/fuX7ZpX5y+ZOSwqvkx0x8OC8Cq5st2ywi76fbDT1xaL+ZgsrpKfpRZDkOjjXT3i3ePxSoW8QnPPKMLmycxovjlfq45KfO86rywNSBvMJSeb0DWIO4ijOCD3WHMR0pRqDYUTm2TU2Zq/LgYUgGrsrKy98/z1qgAsPh835O8lqhLCkKO30iMO3gstGMIWgjhi88Qv5lZT0oEAX68sgbdPbmjjkL44vgXpxCvGFiM/ekcQOWwuIuFk8UmdvGlXweleVyDLlZDkQKrtt5cI8AbmlQPC6inyA0RYhGl6XW3dlvks4T2iJw771Qm5geOePXii1NuY2eKDFzEDYnBgzl2bLFwozas6YQxfEUmnzKDHlZzXDUAI1gM1B+xcpWEVBAxsDq7P/w4H1hHjx/p7th0et353PlDbp03VgFY6faOZfkV4dyj5y+e2bZpW6FuvEwUUi2M4/dvPbBcDqu6IdpA443+NNF69tybG6dNGzMVN8FxQSjA4h7MdCEWDbix3LVUyHoeI27B80/2pOcdPQNasTNYRN+GDlWPOA0sXKAzE1cvjeK5ZVmK1Xbw9Sc2t9R4/eXBogcWYrsKF1Sd5Kn5LjVHSOEbDmANnjlYhVAtBAKxgCweec/3HELGPQfyl4KrRS+OnzKFDdZtbLHUxAVHjxdiGWLxKeVoBK7KJP2eajnXqfiA5ffW1u9QJ43y05IrwuHisBhYilhapjmBqFwp+zhwv+TIMa0o+5CAKv8k+QazuxdeqR4WmljTpvG5tzsypaXYkdIgZ7JFSsr755ovDax4vEmAlSrcc5+792L3ksb2LflAwuqEbfuqqCSsSSw5feR83vwibNSWfe1Ltq0r8Hdsz6pwnTgFYdgtBBauLCuXJUQCrGq+Xa/c68VWroPYA0fAomecMlicN+jB0GgjU7RobFbemEcdRhxeTz5vEoV/J/ol14KUMTTOpiBpkDGLNLBArMHyoMuxWGPa1l86d3aVFysxQkUNLO5geWpWPfUGVo2qVe6mIuQIUgyHUBDvXrRILUODXxBkqRhKzAryHqxiWjGuxo8fz8Tiumao+AQuCakonIR1DcOliYUt0NM2HkTbPVnjKanGim0fT84Xy7IGEIuBtVmfeeiaXRWHNXLwECIWuk4uvbjItLR08mWTKid0SL8pL0rcmFiqJByiUo+BJbOE0o8Yh7Y735CZImCJw8L3srL+uapeA4uPiox6vZ5k65Yzn+X3zbfuutDR6PHs676YY5Pmzj164Ofd+7CuoSbReeZQvovCwod9Hk+iAOzUyoa4AhY7rJJbAayKkhKZ7MDWZ/rJF4njmNGgvxyrRnH3xDS+rWSimuDirOG0GTGCHuSgzCK21DzaSM/IkPvl8wUlwwwj7ZecMFPYGSBbdMIMGjLIdN0pc2YOFmLNVysbxqAmXJX2+AlUuLQ04NN3gdyE4Fy19Kyl3pPpT3Ij5qQ2WGrUMbKo5B2MfSC8iW3RdFPkLJIYvmiYlRU+LmV+qVkFXI2XUScloaoKeaaVLSrugZbiBtcq8IZCMgqoCZNBT4nP54vIWiJcpuH393bl101MRBZ9GFVVVcNKMFmx+QmJnKxpMEsApZoeUgBZYBbF7pcaWTlx+6WJnA7eeE4/nYKAvZqklsgN1xYLx+J3ye1NMudDH2el9LCq49W8LYZCcqtxrxeOxmK1DCx/urVjWQFg7Tm/bEujp65927pdOe5r7p4D+8+0hunr7m3suHB8b54523OcSkaPp5lolv/vPnb+yLZ9DRUVhCuKw7AIIQQflizsvJnAQtsVZ7grYBEAQgCWP81nuW9fq05FmWgaMMpiYbKGnPlQdkf0msKDbZEaR8/8ktj0vPZablSZsaaGmQBLHnGKVwIsyhv8oO+2nM93go6RuWU/DbbKYNEDy5vZLPejoXE82kRwODms4WjSDcF0HlZNYaSgoJuyaLwB/y85hIXi5+BqLMFq/Njx4zX3s4cd30o7iYk1bziQP5+BdZLnCQlYAdkp4AJWLzfo3AJgEbGGDfN4MzukhTVmTNdE7CRkYOkeFnvTIRyyQdK1u81paT2DhyEmTiV8HDcndi/qyCF2MKaK9exN8W8NGaKINUluIR8lqJcLMrF3/HCLD8AKxyNMrH4GVhDAqo/VGmDllW57ji/rVMDK67rv3X9mSRjrGho7juS1uKhkPA5zVte85HQBYHETq0E5LMw+MLCkxXTTgaUHmhtYSV5pvF0OIs+yB7omHEEZA2KJFlFpN2URd6Uw5Mhz//JFzpBf5o607+FFGv89SRdFLWXJtcMazN9GDB6pLNYoOZhoNudMkL5gBKzych/fRFuswEq3HD53aTtO55ngiiBwNWkSHBY+QTYLg6bz0EMsKYwUwPFC/l8W0vd++T0twZUG1lCxWIOGSggdYM3jRuBEAyysHSVgVV0rsHrS9cZPXzju8bZsPqUip5c0qAUhqpZG2BA3UEtlIcdtiuJ9Xt4ZyKvsG280Zbyer9BdLKfprpZiOfOEvP3eU2eAxXtGiwJYXgDrUD6wHjt+RoB1JBdYc+nvlm0J48sKYOXPBD62f9mWhMcTXtJ9sQCwsCiiuaJiGImnS/k4wH4EVqZl89lPuP/C6/bmu4ElC4lGsC1n3cZDjSVJYJ5jL/JTjZKFxhn9JKhiWAmxxruJBYPFzzhG1kzde5+kHBb2E86WK4z9DrCK2GHxKqztfFxrdkUoERwMJPPxABzIRUJ+CiFH0cSPqS9BRPQcXH3ve2OdIAqvhmrs5zgsuYBoNLru08bJkQ3ButJiBhZWYSFyEyfq5WtqvoeJNXiIQyymFnw+so8i96KTfb98UQfuly+a3FPpN3aswZa7mDahE4s1Creqjh49mYE1jvcTZlIGWA3VRQ4sgtL+noDFS0cZWN7GTUcKLF0AsGhshVu7Cyx52LMLXfcSAlbJrQaWWoAZkMJQAasmIyeRY9XoxK4sXA3Xw03ZcuYViDUU4BFq0bcXx784Fs4br7FjVbpQklCijNdZo55w2pQzr3TXnQe0ARY7LD5jhpcRBUsCfPi+jwxW2LnPtp/BpT+GcnUtZZJX3rbJUiLjrxSveOANYYc1ZJAK5NDbFPjHy9BD8L7nHmlZuOIYjh07/ntTTMvddN3V9PxgVw/L3KQtu+KSpXUAlt64XQzAImJVVlXVeTxefTI3zmEzcz0uYA2RsA3RHovrQnKn4+HzkXzaTlHoXvxeQSF0YykhxzsOa5AilgocN7FkMyvmKzhy6Lp7SuuqKt0l4U0coFcUMi1UW1vPB0oDWPvz6zoBlqd9U940IMHs/AWs/vT7qWA8UBhYzR5fuHVbIWDxNGE1thGShg27RcAqcYBVlQMsffuEnP8/3yln9OTyCJUuTCxBVo7PGjtlLOvF7yEzvqd+ykoap42gHZazrkHxShyWBtZ6XkaULIGPKQ/mXMBdXMBKZ3Y89ToNu6lyNrKb+Bh2I1RFKONO4+o2A33WWOHViz0Mu/HfkyHnrGowa0M4doPFYw1nnzARF1eZa+uTpaVFCaxSAlaQL3KcjcjxWe65j0pDrEHG5DOwVOhIY1XYJG6/zIubPDPHqgTU3tSgfqSriyU1IVA/Rp0xU1pabMDyamDlcoXLPjisfGCJwwKwvABW3iRhMQIrIMDim77cwPLW1KDn/ub2jVNx4e58tUR7Es86jWRgoWAbNMSVL05V6Iy3seMZWOMLP+OYV9/jOfnbeMCJvdI9rMG6qOEeljpduw23Wh7GGTMVDKyw7mEVHbD8wTSbVAYW31FlGu4jxSeMGKxbWIZXHIgpxmWNz0N8gQCOdUpC7bCGOA5r5Eg1bYFlKQCW2pK5KpPyXCuwvIV13QlaMSxCwCr1eHgjIYA1YTK2EA6fJ2uwdAvL4ZW03XVbYuhtU1y4v1LU5Mex3AFUtHdX01lt91Gq7e40sehDrCpKYBU4H0aAVchhZQErd9FDr8DaqoDluZXACgiw+PqZKhewQt4adUc4Btt8XLA0ipIGKx45b2Shts6ZQQWRNV4za6yMuoLjTleFKmVUQWhWjmpeqWlC2PK1bbxBIuOpqCCLFSpih0XA4jN+edgJsObpjrsUhGKx3P5qinopZiE2V0YW40oC6Dw59LAbKaXNyEluYmExG1Zi7WhJ5gOrj8saegLWdWZoBa6OgsPCoTzY+dw2AcCahzMIR86bpDOPcEWhE9Ln8MpkoMwA9sys701ha6qC51rBZopp7UyHa3vPN5DLvqZUnacqElFL3fXl8P0GrFitBtaFAsA6eiVgoSSEoW3/qMBBpUUILEwhU9xL0OnH4q9KplUo5vUGMwys9UgZXJswnwfbJLWuR075gMMSfyAdBKeeuc1xWcDVeKlcpGWQTyy1FGZo1rrRwSMcf6VmCWWacK3kDG6fjfAcIa4acumGB+kqJLAqLy8r50NncevLpe0AFt+fihOfeQxMGqkn53VFqALorApyjToeWT17BccjYOMzxtx0p4cF5A+eNNKcejGRQ4g7YFBW+0vVAYh4UPXlQtCeSkGh1fUkqRQWGP/83yR3nHri0sHZuAtz9PB5M2fO4yVlM0eONAaLI+fyV/qBOdRBPU/rXMlmadZPGWpmKzhyQ9TsNPc/VORGTzQ14WbyphpY/bc1B+Js83prOf6hwg5LgOXv0WE10yMq1HoFYAUIWOvy/xaLuLbsq+Y2OPhRVYWH3c0HFmHKDSzmlQBLGsY82DDchs/j59tIec6pKflBqvXpNN7FG4x3ykLODHTa5VsBh2V4pYGle+6DXf5Klo5OHXPy5MZXP9HAAqygIgUWqupLMKmTBVg4+HmSMQozBViDhujC2g0spyi8kk343ve+5zaoQ1ULepC76T54pN4Xxw4L84Rj5LqvpD9QlMDyA1hnz106pgzWzHl8ONpM9CEGy1zMEDVLmEUr6aNKUaim/753BWYJsaZoc8pxc+1ldYClLNbE4gSWXD6LvR+tBfcDcknoDxZuuov7qksCWD2VhFWFgbWV9+30C7BKCgNr89nXD25cqwYb/IFs/+cO1kxKHeOwnLJQLwFVSxWQN8gKIZZiVuHxNsWZVSYNdvVfHGAhZcaMO7nxi0/Obm4JMLDEYYWvCVhZ5eONKSWzgOX3tuyQqnpC1/w1a+bh+nMwSwFLQV/PzrtaWLeZuUJpxfTYAnQqao4fnyYmi1Cnq7mukW5gjdLAGqeBRR9wUQILVzm+QZGbMGEibmnCPYszcdqoMVgjJE+GunvuZnXNbaaFqprqroiJz/9eVi19mykH3Q6LZ6clbhw6bA0bN6aNvWkxAQsjVoDVvuX0xfN795COKu05+therO9M+MM9LGsAkTyl1wIsOa+hgUrC6lsJrEgBYElJuIrPIidgEa/W4K4o+APs7ZuEDWpm0SMv9NRpoz3WFJmvuU0cFqa6xo8VZmV7LPTkx+esGyVcDRk8xKxomKR4JXt3sRZm7RefUM74rtth3XRgBeVsGQUsDLulfMS6TFqMZIelPFZWEyuL+xK9HktC96AzY47jOD3bYY3SwJo8VV9FUcTAasEk4XpMrsoNQ0v58FQDrMHO5OqgrKpQSkITOFn04ZgseWqK1x/rTE9nxc61955XoAjq+dzRqePGtW3PBRbOl7m2z/n6hWwLh2IaWJ3bLlzcv+u8o13njx9ad6ajMRhMtHfnQYcdVieVhMH0lUrCnoDF5/81lBCw4rfSYZGygSUXM6Z5VcP2k2Om0mBbOk/dIyznFk9S60bVY26IXo51m7uRpUuasfmSJ933FMGkYaw7WNpimbUwqv0ySo5JVg7rKeWwcMPPtQJLl0N6Cd6NaNgbYJUxsNBzf3X92gmT5685wTE0VgHMN3W1mZxXqDJO4TY17MYWLmyk2nYGnR5z03nuQp/Ro6bouRMzauJ8dlgn1zOwyvWGtGsFFj7XmwGsIJ/KM5uANV+lHicfIK+Wjap5Qr1sNMtjOfOEJuPGalw5SWjWuDv7mdRGVh067rpPkt05crL7OH3rkBtYVf1zCQUkDisWixG0/OWNrVu2nblwxK0LF5Z1b2pNBP3NS/L3A87dc+DQ6SXNJQBWd0/ACgNYhXHGh46WeDzRW1oSuoEVzwHWpfUnx8AdLMXLMEsZhJHcwxoxxFXTOHM1U5yKZuzYbGh9L+cX493+QAFwxBA2HyNMSThatT2nGmCV3yxgXQ+4soElu8dns8E6cWLp0ulyGTMO1ON+jIw9h1jaWpkGsnIKY8fLtEWhJoyzj1DNsbp8gnJYg9XZAwJ9lNVjTkpJGLzRwCq/5qNWsoGV1MDqImd6wmTeCGlhDXavdR+SS6wpLnPqSrrvyVS1k3pO4MzqtSGmIBwxAg1+HHMxSW8oxH2q7LCKD1hAVsxPLqq1s2ObaBNe+NaxZUmjzxPaV6ghv+fAxe7WcIX/ysAK9AKsimi/OawsYGGeBsDCYDtxYsYJec4t5etNZd0jDTW8hoxQA073sdQKvtvMU66QzeLVWWrAmY7xEFMSDuE5fz6TXB/rPppnlscMDGCVC7AwN49hdwLAmjFj6Yzpjscamb0Wy/B+aD6wuKAe7+r/SWuGUeZadStDjm/NcR3Ro3cLKGJNGKN7WOmgp8ITKClGYGHfPQFLSH9iBogl978hYCM1sfSkj1nu7nSxZL37WEV7PeXjTj4H9I45HSInJEvTfaa85qk90Aws9LCKEVjpWKic6r7GxvZ9rftY7fS9tXXJks7O1vbGxn2FLlid+9j5I5vaI35/IrHk9KFrA1ZDfwCL/zcSt4NCuPzZAGscA2spE4vGGzsEPmKJieUuCU3SmBZMtivPx9VYMyU/xbWkQeEKRSE5LDQuJs1TNaEG1sGbCqzrmWnMc1hUVbdN7WJgnSBgEbEQQG4HTtIWS3dkHINqiGV6MeOzoY++FgYg/tiUhKaoGeScTI4NmfziNhava3CAlQyVgRKRGwIs/3UDix6cNP4p9v4aAOvSMQLWGkQOUZuxVG6spM+FF/BrjyWIHmo6WVJKm8a7hCjL2JsQjs81WHojK/MK9edIviJtngtY47jp7lqHVRTAgsUKBTFyE1AYL1Is1Ni+ZEvHli1bOrYtu5i/uVnWqpf5vYlGnMdwpWUNha6T1sDy3MJZQr3SsUoOIqqKk/g2WZzeB2CtlYfcBmjGBuSNdBMGj3RtK3H2oKrEcVZk9cwryRmTNWaGcIR0sPDL6XxRFa9yRk0op6OMWWuApTbmXNssYSD3bRWw5JD4a/RYEk2fjy/58qQArGOz2xBCxO/uuzeAWUvV/aYjtVNwdvLqtUQG+T04VFlBNN7tsFw9rEEqeDjXfeaI6SP4HmOzg3yyWdaQ9pexqZHFo7hMtbfPr9CSUQ2ta4uYIzj9CH8svGkcDquta41KPXpazpjByNJloRM3tawmr4c1RSKXxXqnKnSIlXVOCEcO8RoxU19Abm5UhcPiFWyZ0jpPgIEVEWD1tmj5Rg9g/f/Jxb1656r+Spj/q7x9S/eZM8uWLbuwbv+uArsMiTitYY9c+vzZ1QJLOawKbO+75cDic4gqK6vi1RpY/nxg8WibridsnJXu8mhyup+3OcjqHVj6/D7DK368EbBwiIG5utiZkx+jgeUtq9Abc67eYQUKnVQqbov//PqBRaV1NrBObLh7w913383EEmTxOkinj2WIpYbdIow7GWz5URRWwV+NzV3HNkguUqUwTucr1/ED0E9WYR42OAFYGxWwojhvoEiB9boB1gxk3owZi2bwveAzVQ9LTSVnbx0f6qxrkOZfbuxcnSzAPgtYsgRwEAVuBC5h08CaOU+uHeKmu6zDAqKuBljlStcbI62+AKvcn2jvOL3u0P7jx4+f37U3f2szzofB1c/e2vorAqs8dgVgYdlpybBbByyPA6xKQlakOtthbV/bBlfOuLpbiKUcwkjXNjhHQ3VNqJ5zV6gIs4ClVzTIMVjwbtP5vnXk53R12TpWuneJw3qdgVV27Q4LqQXT7KtMNJN7JhetSsLAjQYWDztxWBvuXrgQxEL3nTvII01tM8J1vhMPvEWI36IpuaVglskS78DHOmQDaxCmQkZI8LQY+6Pm690CbmBVXzWwansD1rXkax6wXl3cpRzWQqD+biAr22INcTfeXU9KF6/yceVoijke2QHWIHWmIm7enDkTvbN5Clrz5ksP62qApQeuzs0btXXsSsDSX4/yYHvn6XXn9z6GBVlb5+by6uhjuy6e2YIzjslh8aWE1wSshn4EVpXbYdU4wFI5Q1kjTzplEGR2K99hmUVE9O1KwPqesxDG2RShpmjIXA2aPlSYJaZO/MHECVOnKmBxY/vaHZbHQ6hKoEfZumRJa2t7c6LS4zivGwqs2bOF+YSrhRREJhZjmA2WtliD3SZLLx1V8csrC7W/wmkY7pW32a3j6W4J9bMdlvfagFXbq8O6loR1ASuVDSzk3kIgaxGXhSMGZxNrkC4KnWJagDWlQM45zJqStQSQ993ziztl6kmpp8YFWF0T+KCLawBWZaWzXvBqYtKTegIW/06DK7Fvy7JDe/MvUBXa7Np/5DTxaljco29RvQKwrtB09/QbsFAVAljhynL6L9MaWLORMztJGGx3G481Um0r0d2XIa5FfM5irB5LQjEHWTNcQ5yScPoQvk4Gt/ZNpxyVnEHKkD0wwKqoCPiupunuPOXk96WJxsYlW3gaeFPHltZ9jdJ+5xMBry+agQB6WH6ckULDbv1sGXcLFy58ABaLYzhzulgsrRHaK0gYDfQ18QsUhTLmZNjlOyzB1VJFKxrnWE9BEcSwE4d1mIBVJsBKXYfDCmF4eEOxcKKxuTIcbm6urKoK6BKot1LJEW4OxorpQKCuzs8nhRhgLVy4E6xnkwWPJRZrhIqbnvlxpnucnax5Qfslf9MGa4o5ptVcJjAEpymqmOFJOUOIBWCtWZMLLBLPVuUDS/9exwF5h7zqa/ms39/tzAopKBuvQaqQOjMyZCDWXHhvIcPm6K5DF7qJVzh2j9B27cAKe25tD6uvwFqIl/ZYalHMCD3EXPOEzkosdd5AT/6KT08zR5G714xyygxaBGRRfuIbhhs97OQhN3XMDQJWKtzYuun0siPr1q07sqy7o1WA5eMa8/qimQsscVg7H3iAgMVFITGYH+BO130w9+3MDIZT2ugzerLrmymKVa5JQhewhvCN62rYSfeHqc8RXMNltQDLX3JNwAKvQkIrb4iBlcCEeitp3772xrBDLGdo9fYv9wCsxSfAq50Ls4iVVRMaYJn+n+uImbGLxuJbYVEQ3YHjwA/RqBfG09NZrwKbt2YegCXLGhSwhkUilX0CVlCAFeorsHw5ujKwmFcMKt6nopCVYmDlXc8lvDqwH7wqiRBiAp7yRON1AauiCIAVVMBqa5u9+wQbrJ0PcNpsUE3jkSOzlrqbx5xrXYN6zgFLY3PB5T6JSBYaG2ZhV8kgdlgzFknrYoY85+gZ5wZWSYmv8lqApZHlC+/bcnrd/vMHDhzYtX/d6S3tiIYcEV95rZ2GLKuuSkIAazeFEPdiG2ItnS6LDQYbZOku1hBVVy+S6fkp48erLdDcYR/L/XY13sbqvdJDzTos3XUfIsCaMZ1G+N2L7lal/NI17BOmjjm5/tIT1w4sEEuGBn5iYGH6fBO86pbOfY3hcKAcNNMPfQHXlf/lbGDpkhBPS0m9DQsFWDxVOMJNLN3G4h2tWQ4fxELICiPLuPusPRYKV0tniNDwl2VgSyn7xGE5wCJiVRUsCQ2wtA0FSyhX+wosdwnZG7A0qPjnML0UsIKJgotFhTW7Lp7ZtKTRI8AKDFxgVecDa/5uqQi5KBRizZCVDYPVErvcHTquSULenUO4wsPMDS3ebpLTQ3BaYegjLMKVyAwsHm3TJWdcwAoGsJXwOoBVmWjddOQ41fhz527diwlen0d8+w0F1lsErMUMLEGWdLFgE6aPcDmsEebkhkF5h/WMV/tzVCdr/HhtrxSyspY+qiBK+4+c1d0z7tZBPLH0BNmENV1dU9cqYJVFqxuuElh+xSzeEBILCbC8ja0d3bwp5MIZeNVmBazQ1QGLAJADrC48LRea3FMOy0wUMrEwwZC9tsaNrCmFXf74LF6pk0YHYePGCMeYEq/ulilKlX0T5N4cB1joYF0BWOXsQdmHcrhibmBdyXuGZSFVuC/ACoUcX+V2WADWmfwjk4U159ed2da5r/nGA+smX/OlP3GkKv1UQryKh+NlLmB18TNuwcoFCxbsfICzRprGch6W2v7BSeMmlnv/7nhDLZM6agCOd83S6KectMOEV1piD04sXbMUwFq78eAbClhxfFGxdkx/4fXAg/BrV1JwsSdffrwNAat5idnTuXXXkW374p6I/HuRSG5iXG08kTJlDrB2r6AhRxFcYCzWUm7qGqcgBaEz7eryCeZERJfT0uGUs8ey9gnoocsmlcbd3U4UCVhr1sClTl27loC1GcCKNjQ0UPnaV2DJlavZT3Ucb9Le2X3k4vHzu3YdP3Sku7O9EqeeyLkfURYeAlW9/dt8NybHWgNr9myO3E5KPZV8bLF49SjvKhxiVi8PchoTbt6rKGV3s8ZPcbwpR06X0gQscViUcHdjGcqGGTw5foLzj4A1RjusAPpLwBUbrKCTKeVZUv4qVFsLXGUS/qAj+jwLDugADFZYpB/G+pBFnWMlRmVliG+wkBhY+Rhi1hw4vu7CmU2d7WH8i74rAytIwPqwF2Dxx6IPf8xaC3ZjlQ2skpJ4dUMhYC1YuXPlygU7BVlS0MhCLGSMs1Z7iHtBjMuXq++KWboxM9a9CivrpAFc0Mr2Ctf4LjTIOsEOa0KbHOBXUxq4PmClGh1g8RW3twBYC9hj3a081oiZM9XmHKcbM8gpbLKwrw94wmDD9NdtVOhkjTp1vLRxWIvYXyk9czes8QmKIJeEa9UsYVn11QKLhw3mkXOA1bHs0K6jW7fueezA/gsd+8IuYMXpFWFg9UIsV6zrNLA4cpR9SD2ETk0UUuBGuGpCZwGzItYiZ33D+DyXxY2IsU7o9AFiuu0uwOKwbUDY9HoeOKwx6jwsB1g40TmYAyyZOZVfib8iYNUn6mMxPYh7GcqUqtntjqsFVg1992X2FTofS2Cz9eiBXcePdC9p5v+uMLDmKmCVhosXWLi6XAOLT8sEsHYSrR5e+bB2CBvUaBvhcliD9UkzeqbQvYJP54wLWXrwTZHDgG9zP+dI8Fd87f3ChVKGUs6cOHFiDZrubbNxRPIqHO/LvDKAwefTF2BVKmJVErD0mWZHz/O12yX638s14Vcbz2AwFQz6U+0OsAj4FEH69oC4VK5szLCTDYXOAQS6sNan9SiHpW4YGsvfx05ZNPa27DuLBw3Rmwm5CYhh98xCeSGKFEMNLKmqjcPq6+dYaoBFNAq7gLXpyHnulsw9en7dttZwwOMvlyKIDVYED5V4ZNgVj192AytlgLWaIgd7T49LIZZa7272SZrdrHqKNWuzhXanZn2NunaWNxsumuJ+VKoZH21MNyw0krkmBtZaXDy+I2mAVVnVC7DEYQHdyUQiE8bkRK72qR/3qU2A7Y2NuAeKkXUdDgvrRnsCFr5Sewg49KWix0jwyg6rqIHlclgaWDBYD69cKXlDHutu3sJLxBoywpxbNcK19FEBK6eiGa+5NXaK6cpkbY1wSkL4q0XKXz3wzAMqZe4+wQ5rMgELl1AAWJXhhnDT1QFLHlkuYElTErtAKfbZwHL1Dq42ngSsVC6wVj4MuYg1U6+BHGG2QLu38t7mOq9Hn5Cva2s4rNuMS3AuI9RHVhOy0G2/e+FCDuEzUooKsYj5bFIJWN5o01UBq05CqoDlclit5h70rQcIWM0AViyWIGCFY9GYAhYRqy+x8yhgvXWQgfWQTj1+XN6tIocHpsthuSZY8bxzVjg42Td+isCK03CRy2G5DpYZIt0I9leMqgdkdhz5t0GAtd0NLB9Kwr44rBiCkUkkWjt5amLbtm5+6V/K77qVtm3a0tqIawp8lVftsFxfFQCrh5JQ6agiTui6gVXSj8AiAkTLvN5gy47DT721ffbsNRhs9zx4zz33yHB7YOHdjsVySsLBfHSD2yBgoivrGh0edPpn56RM18I9tXF3qMGVElKGRhv6L12zF7/61hObVyWrSqsqFV6uDCzdtFRLYeQIeHqzVGOry2Ed2dQar3ADK2tK+WrjWc7ACuIYOgYWDbuH75EQPrwgqyh0lzZZl4OazXHZa4uMVyVi5VxP7/AONTW3200EEcQNbFN3A1i4+2VHxutpIkWry68CWHU8eeE8x9FEJmCZ83f37DqyDStE/H7MikWjsURzom/A0vHD/1PTIgtCBFj34PXwAm2xZLk7wX6EWnLLgXM1AJ0n5hTjTuFI+SmpqkFypzrzXN1TnlvlyWnQ6oGd+LaAiUUFNaEeWwlxaXapyityWJW9OywvHwCTSCf2dXYvO3LxUJ4uynf+m/2HLh7p7tjXGPbofa19Bxbb3nAyRK9g0JPACaQH9vRMLBxy3NHYaw8L55EWL7DCGliZVQSsgwpYD97zIDPLPOXgsFwtLJfH0sga5FgscQjjs0ecawXRbc6iBn4+GoPljLadC9keAFjH3nz9qR0tqTpsfrxKYPn0ZDHeKpVo3XRBDTOOPZWEPKzk3/PpEvJagFWmgMUH+Mmwu0cEYD1gLNZMKW145LnnWt3Eci/e1mGEw8LIu8010TXItfKUKkJ2CQ+4gSXE2t01daq6lzBIwGpoaoj2GVgexDUfWH5ve8eF4w769zVXCbBC0XCsubk5do3AIoe1QgHrnntWMrGeyUX9iMHueWqXxcquCQEs3njpJGCWtx+igMXtiBmKVw8swIsbtxsWblDAev2Jwy01pfoBWNqXHhaVg3BY6UTrtguHzh/Ya/SY62f59WOPPbb3AA41viZgBcPssMIhrM5KJRqXdB85fgB7c3pY7n5018XufT6PJzyAgdXQDGARseTiZ56nWbny/vsfvJ+Hm8tiZTksp6jRvHKmufLtgeO29B3hZtXokEFDXbjiQmCBfsgBWG2zj106d3ZVptTjAKukpDdg8eK9cmcbAzeYU41b9MI6Poy/wqPCXlGh+XbNwCpPpVJ+P9+3vh3AWvng/ZAhlmu6yzgstahoUA6xshpZ+Q5rkXP8nKmLsOqWRx1A9Tx9w5dtJ3ZYrQCwxsjNz2m/nx0WgKU+714/QQprKgdYdXV+r7nCc66UGQAWAl0WJWCRw5Ib/Kr7DCw/eVOK3GIGlnpacuBM5GaaLtYQNveuWR/34a1m1kcSbqz8Wk2uOncR6mYEnOkig3runOEH8IqBtZZvfs7468wDsLR3hyX+Kpb0J5Z0rzu/d+vc/5irpYb+f6jf8I/qcvmE5xqApfMbsKgrDTdu2XZh3cVD+4+f31vQaMkRyfRvDmRgNTUQsKIMrLMMrNU7abTp8aYtFvc9XQ4rqw3jGPNF+lqFKVMKUes21/Fp+myPIbwj5270XhY8Ty/OmAd27typgXXwEpnyVN3VAEv8smsvu8yINXfqhXXqOu+IKzI3AFhlLTvOnntz+/rFu1c8JAF8NBtYqhOj2oAG2XryYlCWxbpNn5SvDMMUtVJblt26jmuVcecaddIAgkmlGO7uGjNmNhoxmbTXD4cVVQ6roqIvyBJgmTWhAiw/edX9ewVY5zWwIAZWM5WE1fF4Q7wPwELa42LPls0CLPKmD9KzUpHehfrBrjUhI3Q7wukAOpW0mbHQz0lx/KZ5yrEbYs4Rk9XKC5+h2Amt0O1HI2vDCawHkZ570OPsmvH1Biw5ryoRC3kbO09f3FVw6Xm29hw/s6SvwCpxAct9VgPDItXM63m7zyy7eL5gM4v8cAcWTDOw8lxY34F1C5vuElgdiGGRhoamcCxc7veqa74w2Nge0HfKG9OCyXNYaq4wi1kul3WbOrpWP/VcK4jM9alqmobXZsNgPf+A6lMv2EkJs3MFnnFyU32mBocP+uKCq/xh5gBLbwwlu1zuD/lDiebGxsbmRKKZfm7t0J0X+spsam0ONyuFw81hn6zKc7by9C2e+B/LygCsNK75OvzEpYMKWLPo9ahyqVwTyuLREe4ADnFa79nThe76RtaNcs89qw2jNkmNUDEUg7UAU5McRAYWO6w2nrbIpMvkEt0Sj8QqK+l6+tzKzUJFche8PIRC7ef5KJ3FW3iSS6UtV06+KvJYBC2qsXv61+XEUVixkgqqMTOE+rcOHoPDImAt54clZ4J6XM50TlMdYqDlXlpz21B3tuU8J9XctF4PYppY9G0Ro/4ZLgd5Vpf+150PbFi4E8BqwwHJh1cF/e5lyHoLknwe2CiTC6xQKA0F0wWPycvX3PN9dVjDIvFwJIKt9jIT6QknsEsqwVnM+6WwV6p93xaqDQv9z3sOrNu2L+oh73edwGLdkoWjHFYDrCoCVkNDLBxkYJ1SD7mVkjIqa1QLxu2wzIptTaxBehFpDq70xcZT5FRIc9Cos/OZ9z0jZZ55/gFky8Pc68fqwdUbBFgoZ5I0TqqqIvTU7guw1Agr9/PxDEugTvzQ0b1O3Xz02Pl1pzvwp52d+Jt9jc3NlTcAWAlZiLX4GAFr+SyStlgLtUvN5pU6WmdEdl2YdbeHcgmKWDLqBpk+jMRwhCwkWij26mHRAnhUMliLCVjEfAJWbZTrNLI0Glj4TS/ACvIsFJ7l7nVbiS1nDLCouHZWXPG9PJicjVeDV70BSwBa5vczsF7dLsBaPkvlngtYfM+ccfeDnbXL6pZHsZ4ubypPSeVSb3Nmewa5F2KpBYDPuEO3Eqyn2O3ugr3nFpYHS6WuBlixdEIDq3de/cfcXRTDsItXfQKWN0aAakVud3Imy6tzSWtjItyIYrTAove5mNNN3Ehg3eStObnAYofVkCBg+ZO4+fmSAtby5cvvn6V6MC6LpYhl7uOV9ViOOx861GFVlpz1V4pXQqzBvJVrES8foox5csGTqk8NYG1YsZuBBVMeBK+qcHpX34CFFUGUOs3tSzo2nT595szp093d3afPHNmvLmPbc2D/kTPd3Wfob+jbto4l7c3hANow1wiscuWwWjY/gWGXBSyxWDLspsMojByZBSwVvyyPZS5hNxWh0zgeNNS9kEgdK0MxXMijDsTn2cmVC3ZuWA1g8aKGpzavqvdGG7KBVd07sNRyUV186FgnOs8ccgGrjh+14HZQBjaV7g19BVY1AcuDA7pfV8BC5NTD0iTfzJluWOX03p09+NnFtHL1i0xCZt/uZWrpZ1TkELuV9yjWr1gDg4XIteDzls9L9416AxZZrFiyzw5rq3JYVwMsb8hLT+MlHdu6Ob2VkOjbtrQTsbYUONMdwLrIi0cHMLDiBCxyWDXeZEbZAwbWrOWzFLHMLJdZvDdypHNypnP5+pCsPRLu1HEhLOuUBh5t2APHPXcZbGpqbQEDaw3lzEbMyK+q8eD8rqsBFu5arG1c0nF62UWeRL7IzcgDj21Vwd91fP/Fiz8/9HN8O7JsW2f7dQIrSMAqy2QwTaiBdSfGnWOxZOnozMGuk5L19swh+qxyxHBR9j4dU+GMdR3W6tw4xCMXc/MMLB50Av2VGHYrGFiL3/z81I6WdG1TAxsaKQnZYPUGLLVeFCsWwlRaN8pCx/Z2LBDRPax1m5bwWkheBUlWFUtE8PZ9A1ZDAwMruerUU25gIXSu/t/0meZAfFcrSyzWiEEuYrmOnFFnveupiqzzeJxzkmTCh4ClI4fpSfj7EwysN8+d3ZzxXD2wkrEYHBZZ+se2bp279Urac3TvodPoYTm86hOw/In2JZtOH6G03s+rJC7Kaol1F7o79/l8PI+bd+jo3L0ErEb/wHNYejYNO+bj8WgoWOMHsJAzs9GAWU7DjccbpY0YhBmLpg8RYI0c7ABLEUuqGlMTDr3N3CNupJrtpnmlWxHTVf/lAY0rjPCVK1dSyuzePXs2KkIy5aUKWDhBDV+43M+rUElIudPY2X1k/64DB/buPQDt3XtUfRnmbj3Kf0Q/7MU+qzMd+5oR+1BI2u59DackMTdB4bDSmR1PveEA605ilsN8OXdg5oiRLoPqQlb2EaSuWS9VGGqn4Aw6aWApXs2QilAj/x6EcPVqMqmzpa7ZkUnGmrgmjJQEeHIigpMbrgAsjwIWOazyUKKxtbNDFkFu2rSpo3vZxV3Gq17oxgVTctlUR2d7Y9xT5akSh9XzwYgOsBqqCVi4Ie2NSwclcmyxDLFU/2+6m/M5bawhZi2W2S7gOHtXAt42aGjWA5MrQvfD8kEGFrN+9xqyplgOsiPTu8PCYOWRFVILsdKxBDms1o4z646fpwTc1bMO7Dp/CEcP9wlYsgE7Go1F/R5/qH0Lp7fKbk5m+tf2X9jU7oOHyruXELc3Hzrd2RgINF8nsOTjwOSXYPrWAquBgRXOyEzN7MWcM8sBrFkOsGAQsNSdb5Aa6UaWSpsRzvWq6sxk/rYIx/+6nm/GWsndqdx/4X4xp8yjjz4qM0QMrMWzZ2/c/ibmlWvqSlNVVw2s2vaOM4fOH6VH3Fx5yGV9ieZuxYv+bCv2LCxpvHpgBdzACqaDANbZN948CKPgAOtRVwS5tHH5UxeyGD1m50D29IXpHC9yHdOgcTVzxExlsGTY3X8Pf9XA/J0rKIbcBUTPnYCFsxoivtKrAxaGaOO+Ld3LLhy5uA6niR05gjsOjFfdfxF/so5M7LoLpzfJiqK+AatagBUt86SRfJcObj+mki/bYsnCBhfoR2bV01k3kTu30hqDj6Ug/Bh1tf542S5KQnTcn1egl74tEeshitxsqaUPr0rW9B1YpDS9QulEJhFMt3du6pYD2HJ0wbz4xIttnY3NYRevegFWXIAVxI7OA0f1kglO8Ll7jh4gJiU84cL34uzF9HhVoHHAAqsaDqspCmAlMSnPc1zImTudpHEBa4QMt0kGWCNcZ87oG9hv0wtehuobrJyrldQoM0/JmbpfzObgUWn1P3gP7MEKBtbBt6giDNaUErAqrw5Yfm+ofdOF4z1urnK058BFeu4IsHDUTB+BFcgBFiwW+oAErGMGWAhh1rCjmnBStska4SDL1chSVtVAa5HUNbc5g06942BVEaKs0YPu/vvJYT2EGM6moprqGqoI07GoA6wSAAu/K7nCwgYBFkaov3HJtguHcDzDrl3nd50n0/CYTui5j4mBwI/n9x85w8tI++ywwCsCVoU/s/msiRxX07ohocrppdNnmgOm1c8jBmfdk2lIn23tlb1yLXE3vBoyZDpvYaXAPWmS7/4HsTWIItfFu1jP7sgEg1ftsLzYSJhON7d2biHv+RFcKfnSTYWEu09xplhl34ElDssTMqvhsnQUXcVSX09XpZ7Z0j7wgMXE0sBqoJow6PeHU2QPeCvcbuWw7jRJw8CimnCIAGuSslgj3QZhhL4f9DY10aWyZ5FzVeggvk99iHt9hJngcvEKDzkFrI3reZomVVp19Q4LwNp2pC/rYP5j76Eznc1XC6xAAWDVthzmrjv6gApYs1zMZ2KJRVVDL6suNFWhagYOzcKVHnmaVyNGyPvBYXFFyMyn6MmX7cGVD1FJuLirbSMWsu1o8RKwmpochyX9IyoQr/QZBtWBfaH2ztMXz+89uoeEOw72bDX5TA91+SP66bG95FX3YdJwGIAV76vDihKwdkjkGFg6+Vwrl9WZ+DxBzZk3coR7zsLMsea2Im4zS231YgbFK55n1O1Tk3zL6YVymuw95gjfoshl0sEyT0WkB2B5AKrCDiuZbm5vb+3s3LKls6CW8I/0t5ilDmddrNInYIVb6XmcB6y5R88DWKXt5miSHGB17Kv0XAOw5vYLsLBSltfKlpWXI22r+D+mtA1U+HhnyRuvMrAeRMo4Fosfcny8NkbbpEm5NaELWewOBrmmY4YOWmR+yy1iVxti5GBxWAsFWBhraF48+KAAa/bGjdtxtEzS4ylNpTBVHhFemYWjdS7hC8wPOSWPnw8V6AOwuLLndTDYLt/XgtBnFppSVMt5N6EXCyBff1M1se6UGPJMIY27u82w07wfmeW0dAid9Q3ZboEPUXHGnKkn1ekoD6hhpzrWDxpgoSI8tSrjTYeivGy0JFBXx4vSo70DC58ffuVvxMIrB1I9RRLH9ixprKqqKHFvoQoUWIwLYEXFYTXQ19Sf1EtHVftPR06b06XqEg9X3FzPS71MQdv624xBdS9uz+6fYhXcdF7SgIrwUaybowp+OVush1bL7Cpq6WTQXxFXwgDNX3Ykv8l1WIlErLmxlajU0eEQawu/zC/BKwJWOxmscKCA5KvgarrzxR0AVpnHH2rdVOiE0T0AlsdPwFJtRrcISQBWYsnp63JYfJ8sD0YYhFsBrCgDq4r/VwArUlHi9zdiZwkBazWAJcjKbmKN4JxhYk1yXQHjjDh9vpNZ7JJ17tUQZyOd6URMd9zBo/fLaMMzDuUMGywy5avCLmCVXB2wlvWpJNx1sRsL368WWJUOsMoYWEFvgptY67mJpYGlejEuYE3KHnrZTtVZvS2tLPXjIq54+KqhIe6jFMH86e4Q3skhZGCRSUVd8/lTm1clAaxo0zUCK9HecaEv6P8PTHg19xlY0eoGHNlM2ecJtuw4+zkaEjmof9jtsPSDMi9uzoTFIN3HMv2Ioeqp6TTbzVIuBA4G60n1sETkJHSI3EY+qQFXd5QQV93A8vYILK86r4EdVhIzFeZQho/oxYczOOc0sE53b+tsbbxGYOWXhHO5JOwdWIVa8lcBrCpeZtRvwJL1xolWrMSavXi1kzO6BaOm5ZXBMiZLdT8dZum00Zo+yMUrp3llxupMV/tF5ww7rNXouZPBeosqQp8DrJIrA0uu8pa1QwDWljMXd1GxsnUrCpY97q77XMwno8LZOnfPXmm649j3cN9v0HE2SwuwcCSWJ91+6hwvHQWwXnjJPe6ygDUpn1g5Dstcxg4tMgNvkLpoaISeqxVe3e14VOmcaWDNnr0ddQ0Nu1AoGm5qiFYrYJVHGwgYvZWEap9aYt+mCwXSP1+P7TfAAoh6BRaXpdWRYR5/ktt//LhcfudL6mmJyKnNrEtzvam7A+haCei0TwGs6UN1Fuq70HQOjmR3qpOPnSm+WMuXI/seoqfl7PXcP6XIVeCjjDf0BVjGYcUSCW+6vXPbmSPrLl68uO7DdTxfAV00P+An/OWF7i3t4XDA2enVI7BkZtUNrHzsoE3VE7DmKmBVtl7hqvorAau1ua5IgBUhYCVx6OhBNU3o+APX3DKPtknDDbEGZ5ssZbHyNCSbVyPdwILBWuC4gzvZHqx86CEB1pvYtVuHHW0MrJJegWXWOhKwyts7uy8cOq4awvhJL2v4Dyxr2MU95AN7d/GyBkqYgO9qHFZlFrCCAiwvH+zEa90x7F5yejEaWIjgcDP0XP33EQ6xnJNcjU9YxAu0pju8GjySvwY8bzFdAQvD7k5undG4Y2Bh2oJCuCpDwEIPy3FY5eSw+gysGDus3r0qFddndEnYN2DpXdL+dMspOUxs9UOSezpyqiRUoZPEM49L1XzXiwFdcRNzBac/XdXRPEGhUxDvPUKellwRzjLAItY/tJqBhRU1q3BOK7aDNFydwyJg+UPtm85cPH7ApV38ytauXfuPbGrtK7CqcUqwBlZHgU4UJgIJWMErOqzK1u6rBdZcBSxPPwMLC8AkFB5Pig9s4NV7yx1imSYW1sJgtImcugZZo32CWPMhg8zCPL7RZRDuoWdgzXRgNRI+A8DaoAabjDb0EfgZt1s/45LYR4hzLyPVsvuNT1fIA5beOiJL+PD3/sbWLZhWVpPx6y7uP6AGnZqMV0+5C2c6sHDUJyeo9bXp7lyUWVFBMQ0FQ0kqQ7kPuB2VzfLlL7BTUGU1V9Uy1+XU1E47cOTgEXqnzhCniyzbcIa6KmtFfVOa0/s5RbWK4J13wicQ848dmy3ntTKwuIfVFK3wMLCC5fRBF5rAcKR2nvr5PBnMoPP6EMyf56Ty3K1q6QjOHyWHRXkmjkQ33QsBC1FjWmGu0uP3ZMyqGhfq8biUpyUqwkmSeC6Lr3CfPWchnQh3NwL5N91pn46UsnzmdD5CjK2pihw7rAf5abl++6VzT+1oSaajAiw81fvksLBsOZQOef3pJd1Hzu/NXzi6h79pkcM/pI6X8fR0iGSuw2oiYHnCBKx87MjKBX+w9aMCTXccU0LAqkv1NIfYa0mIXVgaWPhoCFg3c+FoT8Di9c+eoByP4moZS0HjWqmtk2Y42yyn/6nBZcz5EHNAn74vgMuYwTOdohL/wMylANZOxx3wAFemfKMcixIEsFJ9BlbAmcbBcsdN0jHYRj+ddm/NWXdmm+4lbOpYsq9ZjlNmCPUNWOEsYIUpSZMhvyep1oagJnzhBQw8bbHU7hxm/iRGVVZxPXiwC1muzdCD9NkMztyg4hV/IRhYi7IMFhMLwFpxjIbdQWx8pmGXDoXhsKoNsILl5WV9AlY5HFbn6XXHd+mjnQ7sfcwcX7J1z2OyBhfa9fNlWNZQUcLXmzTEI70BSxaPErA8dVjDpiNnHBb7e75YgIppNvcMLPWTsfkqdG7WD8pZ1j4i29/D5TKwHnBH7gUpCQlYbLAI9Rlu/WEDG28T6N1hhQCstALW6YsHdOevsD3Fn87devy0bH7uA7AoYtXEK/oqetKt9BQp6LB6BNZcBla4rvQagLV1734FrGHV/Q4sxoBH1YSLFx9zAWvW/bIBmktCKQiNx3I/6GTYuW8uxIwzG6sh03UZo/0FsIcfZxKw2B3wM04Da7l5xr157mwLGayrcljy5a7iOxCwPRT7Q5e00k+dzuZncgLdW/bJvmhsfm5vTKhp5fxk6Uk5DivGSyLIpfIGp/WoCZlX+IQeVWtDxGHpmtpQO6cu1Kdpuq+ykqsHhwj0xV4NV8CaKS2sh10GCw7rIQALBuuNp3ZkMul0Ihniw2XKGFg1fG9Bea/AUi2ZWGPrpjN6FwiOyTxvvOrRA+f3//ziz39Of/fzQxeXdXc2wmHxeoXegaUsA5GAd+dgO+FsrqbvdK9seCDbYansG541XT0ia5eYE7rpQnlVRYuznyRpzPYewDLJB14J6hfLkmWst/XyQfgNfQOWclhpLFz2pwu2tgtQ6/yZzua+AYstKdXyDRXssAr0sPoELE/7tp6BVVcYWHv4vNKqulxg3dStOQysKC9rCAiwqlzACqb4jF8shnlouSaWkzNYRDTJSZpJbmSZzBkxRO+iHzLE2TqhV4tqXmngjWRg7XSZ8lkvaGDNbluPwz2SQZzUUMrrsCJXBSwQKxzCHrhEY3MiTHarQ69b4XI8HG7EqRwRnMwR1pvx+w6scCFg1ZXKdsL17FJfeimrD8hNLIlAFrKMTx080ykLs3nFZc0QNerEm8m4ZZ+wiIadtgkvGYP1DYB1EFsx02SwYuEQt7DKXA6rz8CqTWDR9ukzy85Ap08vW3dcedWte4+vW3YGG8zxd904nrw5HpFFXr0Dq0xWj9KDiIDFCxuOqd058rCc5USOHdZw4++1yx85idsRI7K679m4QvLRI3OmWvNsHpjisBaq5KPQvQDSo/n3EPqniNzmlkxSHFYWsHpe1uB1AcvbV2D9x/llhHn8S86JbD2XhCXVTY7DugKwCnsoDayPLh4o2JIHsBI9AmtLIyVPFS8rIHLcAmB5AqAVfcJlzmWqaLozCDxlwSRs+fasueVZDrCWcs5IpkjWOMNtkgtY2l6xpg8xj7iRaBTP0wYN7w2HJYuwHqWMeQEpo5ruaGHxtHIacShNpUorKUQVSu4vKH7tBpZZ0ulqn/v9Nf5gGCeOamAt29KOoVpXVVcRUJdW+AKBvh7fl90YRVM0EseJ80H6SGW2S1U25LGyfAIDy00rHUNXL5iXcA9Rp12JXcAE1xDX5KCi3nBuxHAnRuqaO10V4WrilWwuaalJErF42FXj64wJimAQpytc+Qg/AKu2ls92ivGKoi2sziVLNp1ep67zOIo7hbcsWaL+rrW9MR6mYpDHd0O8xNU4zvqn/Y7K6A3Rw0rhxIa3XsVxIa61o05DAhZLc0r7LHdVyNenjXDtL+SJnukj8OLsG2nqcPlnRs6cOSO7lpaK8EGerOBFWDsy6WSMON+g2u56EiLnM3EWjtaKeOFysBklYR/mVrfiAD8GluPas1VB+YXpMcY8X0xEX7YYAeuzfGDxLCGAVbAPJU13AtaHVw2sA4fQzadyh9dvR2B0bv7NzwHMDTUYYKWYWBpYFeVpfaCT6iPMcppYGG1LZ86bNGm4eb4NdyqaLIfleCyl6caSuypK/BPzGFiqIuRHHOUMmu68kZDdQVCAVYoblqquBli53Sh/iIE1NwtYzj/iu1ZgQdjgBWBFSzyl+ogZvTjkhWxgzRzp7sFIGEeaRUV694BBlYrmiEGG+Wq6QjmFmSP5tIsHsoCl5ghREV46d3ZzS00qlU7zee4NbmBF+wAsLwGrNh2rT87B8XCNLfCr4SBOHNXXfF3A9sE4zkmEYa2uJmCF4w1xdlg9AUsnOPkRAhZ6WGV+vlUAFmu3maWW5FOPS6wIcfyVrgqdCUO9xEHt1tETPxy26XpaFe9iJo1mTlfA0hXhnS9wC2v17jU8WXF286okA0uVhIWA5QzYfGAllmy7sP8A7wHAN/dLfsJf4bQGHKEAYPkq1c2EuV8JDSzt5hlYSQDr/Vxgbb1BwMpzhnsO/PzMFnyUw5hXtw5Y4FW147AEWIIss9hdLcWapZcRqTmupTMnmaan08ZS4ye7JJRtXmr2xqx/Qc7Mo/cbRS+8+8ylBCw92GCwXphFo+3+lStXUMosVocR0QOMPkzczBnoCVg5n2RA3ymhn1cIZjDhXJ0AZwxgGeKYcrCPYXRJNpFH4rg1MRbxlErzWJZso0B7wd3EonGneOUiFrsEfSwijzzlEZyDWV1dGJc5G85twOmOT1DAmgVgrUAjRo7uSylgNVw1sIhYZK9wq0KSE7OMvtPfEPqlGJn72PkLHe3cf/HQE6/KM6yCLyKCH6EB3juw/H4+5abEjxPZNp/9/NKxxe5lNU41vVQclsvhD3c7fNV455JaXawNfyW5qJyp043gYhoGC80/3Y544U5pYRGwushgvcVrGlzAaohHewWWPl4GwCJobJLTGq50WIOcryC35vjC6pKn3K+EC1iqp9Orw2r/qMd1WPErA8vTG7Bki9CtAxZaWBpY5FyUw+JiIUi2nE8lR8684NoMx65cAcs0Pt1dLKckHOFYLLktwFmu5/TsmViThhOw1DPufjZYL7zAS/dW7jyxZjHfPrFDAYv91VUDq1KeWFhPBGA5l1PBF7TTl1/Sw+fqX/UxjC7hf9DAaooG6nCuGB+KtXolRt1LWX1ABSwTOtOKGan3yRmHpWrC6TzsRqjDyFQTxjSf6R2n5wOLPCoM1mK5NLslkyTF2GE5JWF5n0pC9JHThKt0LB2ivETjC3s12zWw/kOOSKYRptwtX51GBivMjiTQG7Aox/ng04gHwOJT/ORg95xVNXfL3pzhLhlmIffMUQ7qUm1XaThdPyxHumpJBtb0whUhPS27eLJic0sm7U3GFLGq6UF/dcCqad+y7cwFXhuKpaNuXXR+dXHdke4t7c2V6irNXhxWmQOsZCFgzTXA6nnhaC/AuoLD6mz2VN1aYNF/gE+4zO2w1Dos3rfPS7F0QbN8Vk5NuHTmyEmThmdVdc6EjWrFjHBLNRYG53bcR5Hop3lqklCABYc1i5OGn3GLZSeXNxj0BuVGuEA5BpheOOoeDM6ACOhZFl6lINd/BwLssHBurD7FCZdT0deN/johF4Rf/RVfnmxg8dVWsaivLiULihj6LyjH8yjvJtQu1TVqjFF1zbSabU7aWGXNcemKUt6TIohGzEL3WiJeGMLTrLiDdrPwKhnmXowCFi6SQCb0Biy9cyCdlqFaVyefMxyWlIQAVnvC53HOT5Zddw3xZjJY7n8pOwtFuM5hGJpdERqkVBNudmpCvYaNz3PE41L1sIxGuaLnzBa6zsI1z0pjTXXUkHyTsKImh/RqjnADAevg60+cWtWSySQTYW2xmghY5c6dCPozcR/gJwLSKWJ+P44E3WTuUf1o20fqBlXXZapYW4OZCmK+uas8H1i63w5gieOgL1uonYD1cd46LAFWTfu2DwsC68yWfQ09A+tMZxwOq7sQsHZdPM3AqnC2Cd0SYFGA3Q7LARalcikXNNiD6t41nwOsHLFZGO4Qy0AKTzvHNphW8STxV0gaDax7NLBekIfcQ1QRLj526XPs5CrDlz/oY4N11cDSDgvBTGcBa902bItiorEPD189sNR/7QZWOFYZ4E0mvLJhtWnF6JJwgwKWDBoeN6aynpR7ztgQZ8AJ7xXyDe942BnmP8obBbjxqIC1Hhd47KBBF8Ze3DBWYV0DsLBzIK1uzZHblgJV7c58K5eEAfNVKJFAUE0Yboj0DqzSwLBhao2pp45qQkxYuCwWOyy1hs0AiwM3Stn0Uaa8dgdPxU/LWQmik08Ba6Fj72GwJPl27l4zW9Y0EOsTGSr0CVjN5K+aouV9BlYMwEok2vfta23FohpI/9zq/j39sK+ReKWWLfcFWNUCLG/7ltNXANZHBYF16MyW9mpPafumHhwWASuQWNJ9MQ9Yc/fsWtfNwPIMu8XACnq9bocVwLZ5A6xkCy5+0RZLasJCwFI543LnMujMJVZ6kZ5+uYA1apRyWNzCWriT3AGZOdBqFncRuOu5WC7/9Ebx5Y/yqRI9A0svd3ABK+Au9RDMkAtYR88fYWD5yGFVhn2+a3JY6j93AysUqpRTLz55db17rlVPdlEIl2KadJSWy2JNyh11DqvM/kunfzhKRt48B1iyjVA5LF54K1vHU6nKcIKIFePDZQRYenKrd2DJ9hws2eAYlcqfOgebyEWqfOJI3BFXyPHegUXsGzYsAj8WrxrmCcqht6qL5QaW1IQjTeA0dkaJ0ZqUFzsdvpkjsLdi5kjX0rXh2cnn2iAgybdzA3lTbLFQtXQ4FouF4a+ammJ9B1aaGO8HshrxSMTZDfwz/yqRaOaX/tNwQqVguDdgcX0U0cBq7DxdYAsNX2EHYK3bVeAAv593dzZSZdnYcWRX/gnK7LAqPM2FgIWLW7qXxPHRVNxaYMkaZwMsGu1qAR/lsi+ValEFzbHVcsiM2ryrgGUM1qjh2WPObDAcnCPjrlwGS73jpHmcM05FOOsF4RWmlRdjxWNLWgErei3A4rcIBHyOwzLXfB13AavyOoBF/2E2sMKVuFGBV7uvd9Zsy2TXwoXKYdEnP3r06FGjzYhzqmo98BT1Zw6e6VqebdZfjcoJ4QMI4XJXRbgSu+G2YzNcxuOJyIAhYlXLgfh1Ghl9BVZSAQtH8iFES1xX1ZNXbayQvTgNYe64i/oGrGEKWJHKiIfb7m+g7b5bLQTUJaFME450pZ1y6Sb9XA5VgQsOHzfXMq4maVzJ++LdsoDFWzDVDswTa2av1wYLwErGEjHY0x6BlSt1i3zQz0f/QWqs1dVVVdTRyyP1M35ZVQE6SfeiV4dVBmAh18rKyhhY5KLyoCTA8rcXXIe19+fbljRGKj2ZjiPnHyvIOpSES05fLLCpGtuuBFgV2cBydJVjp28K5MusSQv4UuouCuzpemj5C7x6TzowAiwzWEbrQTPfMQruHYYj9XSzi1Vug8Ul4dKlspHw/uXLZylcoSDkbYSXPj+1KlPr9QZToVB5iRtThZX7OfrURjb9N75m7G7H/mdyt4eWbRJgJRKVgcKri/saSzVLCPmCyVQqWJPkEG53rQ5x9Y6Xzps3nHk1euLo0Wr4uMyq09AabEg/qSCsJIZc2Dyw82FczTbLNKpX4ohfvr9jR7KUJ58wFCKRK52IXEg5QzDkY2B5PPs2HVEOa88ucljhSAXawvF4lO9OD+ICyXgifqWN1SI/FpAOwzaeeGVVwJ/Cave3Xl0/W5+K5V7DtnTppOzPXYPLtLPMBJCaBeK4zXRNqrrezQBr5T0SONkxTgXhBnL3HDnV/MMatmA0GkfnSK2jNWjqMW9w19lVZJPeFkbQyoKVA/Zy1dP3+5FuZWVcMrR+dOTTvMJuz/llnQlPkFxSPnS24l7CZvqyZLYsK3D1M5ruYcwBn9mfd0eYc7oMf37XNl6uSYUGuwFWKeUMPeVe3b5+NheFL8yS1XsLHnhggww2+arDH8AkEK6Gzx81b5TuSk3KedRpY2AGI6eNvOsoBtaGnQsw2ACs5XrdHtrFfDVV2lsbSqVCQfkIrxJYuXOHCT60//yBAwfO7z/SLTfBUbV0o4GVqvFmeE+m6+QBs/8ZDkuANZEkYdDP/FHOwMuC/iTXhLx2GOzP6J1VFxDAknP4eYyvZIPFV9C2pAMGWL6rGUMsN7BS9F170FZ99vRclIStzQysSHVEX2LLdjNypVX0IvZ4aGJVR+gDrAkm9b0Cu2X/vTrfSDUkKHCjJXn4c+dvo92V9XCNJpdd1WtHckjPyXdiAwFr5f249EKdIoZthPPVfI/mlQArGo6WlclRDA6xrpA3VxVqA6wczGUDy6uB5RNgYdr707xTyrbSI6Qx7Kw5zILZrnWbcC6JJ1noUuq5R48f2dTe3Miz6QVW0C/bsi9uPr1bhategZVqMRaLDyafpTswG04od6BGC2v+KHm5ykNXP8FxBs7KreG6HKKUmScpcw/cwXK1kUvtPOVzGjI4cfZagZUXz0r6Spw+cwTzyMu2bdnXzF48HPb18G/0NZYuYEVwY30q6E23qBAee4hPSsb5VLi7jEvCeZM0ryaqQBibpR2D00Q2O6SdgkbxnsMPk+oAa5Y+RH4l3z6xHuc01NeW3yBg6evRsRljX8eyQ+iBzOUNZvsaBVj0+au3RYEcueK2H5EGFre9fMGaGl7tfnC2XN006wW1O0d7U507o50QOE7fNQmUXWO7mhg6cenN5zGwdhKwcK/YnbN09sl8D85yT9XUEKvSGljEK+2w+gKsq5IGVu61aFcEVnmsveOTAmck4+7BfUsKr2o4f2FLI31ValJkzvKBhonALa2tHacLVZO80H2Y+dBuFa6uCCzwKtnCd9Zri2XWNexkYA2fN8rASjRq/igXtZzHnPZaqgwcblaLqmfkaM4ZpMwCXE6+nA2WPjxN3f2ZpHqQPqJQ6MqoKgys/E+8eZ9cCrBpUwfuxyVrhSOwbiiw6ONNpry1jsXi9bezeDGsBtY8BtZkek3MHnKuIie7q+XqFo8a5Y4+QojjeXjYqRiKTeDjUZ4ggxUKVFTdMGDJ7/z+xi2n1+0/sPfo3gPHL57Z0t5cwsDinWX8xmjpXXmfokgDq5p4VVkp1fRTOPVWLBbm7VBNm2I6K/N0DIxPNcySX1A1MG/SPPxEJcC87MhRuqrso8clRW75rOX6YBmsWMaahmSN348L55MhXN/BvCpTp13dNGDlfoF6AlY0qg/9+SL/aunH9l/Ytqn7wv7CWwk7sfYzWNPacaHQPsTjR053bDq9roA5m6uP5S0mBXwYb0mni6WvA2VgEbHmuXKGhtvE0fMnzs9KnhxkGWfl9OgN7ihlKGP4GYez/6EHZUvJ4rbZfHFCJl1TCsuS4lNA63r76HtXJZrPje28vQTWyocHxfUAi4PmAL+kPEgVRMoLi/XU66+u3yghVA/vlS5gTZw4mTSRY5gdPw2tUZpbBVg1cbR6RwLWCZhUAOtBCSFWPnJByMfhZ7xBdLWvcULBDJjctnLjEhzesH///kPrzuAS2hI1GaL/XuaRem+YGYfVEIlU+VLB0lTLDiy7Xawvm8NOrUd5XQNHLhdWTvxM4PQP+GleVh2Y9Z7zR81boxwW4+pBlrOfaUdLyuNXZ0GGGFZlLod1M5rMhb4+zv8js3H4n/GElLu4vY0FNyvu2XVoHX1x8q9fmbvnwM9PL8F6y2BNC2rC/Hfde/zikSMXzxc43O/o8QubloQ9WNZQPCI8hBJJNVE4W1ksOWSdgXWCBtt8M2RcGq2xldM/Vute3Emj+80A1hoBljzj+KxHSpnVaorw8KpMEAaLEBrGB1d3A4glCphTHfDzDQVWiniVTJPFkolC2eOUB6zRCliMrIlZyBqd5beG6296wEncJ4s/I6mqeqfmFbsEPjBzu1oW4sdCpxsFLOWyvLwiEpek4yyx9uaw+fw1sIhfV56B1P++cVj0MeKrndH7c3gtlmQFgCWRmz9affZZyUcBnD96/qh8OZk3nzPUnbDIPl0SStxWyvYAddJoJmiAFS06YKkjwBNU2BU4an/P3gO7DjyW/+dzeTUPgOWvwbsWuBoa7+q6w83R1r0/5/t2qooJWHWlqcpQIoGJwqdMFwuPH753C8BaM2/+/NH6K4/E6ZqIb0ia+fKs0zUN/PgoZQ6Ga2vFvJIxR+9ggEWj7UEZ01zNYOfpJVyuHkRFiK5nCB9d6Q0DlhKvdpRZxBsErEAwnUxmkmlcn2NKm5UKJLjZdMMGDSzBlWvsjZaXFDmjcgvF+aOcuCte4T0phiekc/ygHnbMq904Swy7cmq9ZYEbBywyG4Ks5mbcYAXta28MhyvlyoksYFVcHbDiAqxkhrdAf7N49uwVD/HnpOYrJHKjXZ/9ZBe3dXFYAFpMq9Gjs3BFgRs9fw0Ba/XOh1aq3MMBYg+tPiYnjZI1Tfo95cGQ1xvV5WBxAYsdFta6F5js+w+cC5v3h5gjxIlWAqxg45YCx5Wq64ULvO8eYl2xVYSBUgJWLNEcTONKVbZY4svRFlHAmj9/vv7C84CDR+iaOHn+RJM3rgeby1pl2XhJM04ZBhZly/0P8pBWBks/40KhZDqJHhY+vBsGLEmMwM0CFqaVvF6cPMrQl8NSDLC4rJ6P6E2YrJRrGLKc1nxh/ShnyE2eONm852gXsB7Uw05sAu8tydR6o4GqG1cShsLhUHmwHOuL/L6wz4MGIPYgoGue47D6CCwPAStCxGKHxcRq2XzqideVOcUnJfMVDCwxWFnKItZoEykDffMHWaGjpC0ILIrcRolcMu33RKMh5lVTLrBuyrqjq3VYAFZjZ/eHfbp5U6Cza133kuYKTwX9a95ka/e6q3jXA4dw78GN/HyvV9w/rgw3NTc2R2MZvl4Pt1URsahSY4e1QoClceUaN12T3WNN5cko7ascVI2eONGphbrcwJIOAkbb7q629XyuTEuKR384FA6FAryL6Po/x7yBe4PmOtSCVg2spN8L6EvfXaBvgEVlNaBPIZgwYYJ73Dlea/5oKbFH0U96uGlaZQ1W5bBUC+vBB//NEeQLFLZfIoNVX5+ujfp81w4stzg/eAsTWaqA+4/pL1RTXg/sPsZM6vyArJGPyOrJZGYVz1jMni1FIT3MVnI1jTkfyr7JOZK4zadXboMr6yGZEzyK3Jo1u1dQfqvsWymkX7+RDdbmTCqlDwpwO6ybukCygFxrMhUry8p4vVuUnhp+f7DwKck9SK59bqDIB+pK/Vgnf6jAqe+F35WPR242Hxd/zW/dPGFByZl3YeJVc1NUFvBtX7wbxHpQ7o7fueHEGg2syTljZ2JOB1kPudx212TnKWeA9dDKlS5erVjc1ibnymRQDibokU4Jc0OApWb0biKwyhlYmWSSasJaObRBdQIxJFxlNTssAMtts1zUUjFkZM2XYtE15CZMVu9IA9UB1oMuf0U2AR2s+mQ6FMWc0o0CFp/XU8kTFvoPeWV28NqAxdsaBVg4jQD/cIwsFkcOi0JW43NaTtn3MIAlkZPAuYI3UbcCTWGdm38FWD+Zs2/FagCLXyslcuvFYO1IllZ6fMUELMFVSAErrIAVbO/c1qe7gv9DdbCWNFd7PCW+0jp0sTYd6cutnRDetbXZMcxFAyxfvIGI1VTmlabxYmyc57EAYK04sds4rMkTJ092DbfJXc5Y427WfMmaidlSsOJs6xJgrdi5k3PmIcUrMlhtvAYrlSpNpXGWAi6MulHAyiv9biiwcJtqOp1IZBKJWG0tTuq5dHB9G1msfz9ogLXhxDw17iQMrhi6KhyN/uxOsR5zDKwJYP7E+WtcwEIEvwGv1B2gmdo0AwsLPm8ksIRYAb2m43qAxf+wrzIex+FlzKtkJtOy49Q5PU3NzlEBSzusCSoCjkV1twJN9CY6sHIyVrGuq6trze7dDCzQinmFGcKNG/ngvpbS0spApOiAVZvlsLBXMdm+pfvirj19OTgeZ8NuaSwpqSijmiXIc4zd+tzYXsTrs5ojFR5fwNkOVxzACjOwqv3uJccPPqgc1ooTjsOaPFE95CZ0aWbpdgIMOtqaE+ePzh1qhleSMmt2nwCwHnpI8QqnkLet3ch35dSVlobC4QQOpq2ODCBgJYlXRKxab3qV7MrkTuC/eYXZSgYWSkLlFCZPyOb+ZO0W5iufxQZL5jXYngqvZOQZl7pTuVSOINowFEKeIryJwAr73LoRwKrkXcBErHo5Zmb7RjanCvULVQuV42ZMlotZkx3UG6eV+6ycYF6TFbCQdfR1Wak67hsJWIhcpqYuHNHAqm4qEmDVmpIwrIGVTrRuwQVsvRPr6PmLZzpawxUlZdFwIoHLBOvbO/tGLNw22bEvTsDSN0wWA7C4wRMhh9Xc3NBcFuQthbweRiUNuZ8N2mJN1gbBcedd6kHXJROHXdm5gsa88z5T6TWBHRZ3ER5iWl166JvVaL+0teEmvR2Z0tIqpHBDmIhFoySVugE9rLxP+UYs+oP0oYK85Q678eckqDBEaUPEwrENFMOHdBPLXRNOKGCznMhlzW2JPZ0w2WUuutCJIZOKMcfAXy0F4cb1bLBwWqgDrBsRLMFTpQ87dXOBhWb7tQJL9tGhg4WKur5lB09Tt5nk40W3J8icukvCnNIwO3T5vnSym3MuhyWhk8i1beQjDzMZf6C5Oi68asCtWtF4tP+BRcQKyebnaFQeEF6/N7GvY9nFXb1hZ+5j53FbcPOwipJEjBI0Rh7Lm2Ri9Qo7bMrpwPYrqiV9Pl+Bx37/KIB7tBqIVg0NzeEgEYsqmmOGWCsf2rkaXXdKmS5jlIg7bRMmuNw5/oqJNXmiRhda8pPl22RFKwgWix3Wan7KIWXgDohXvAVuVbLOU0W4asZRSZU3BVg3MuxuYNG3RHNjIpFMy60K6zeul9qGhgYagRpYWSYhZ+w5BY6ZGeQQCtsca0HQP7F7gzKpTkG4kTtYGS87LHxINxxYlZU3BVgxJlY91jZQOT2b51gVsMD6NVk9rKn8LdtnaSuaxStjr1wRN8ASUXIj+VTvz5+sCYSrcWIfwaqJLxuKFgGwlMNyA8vrDWX2dZw5cnzvlcrCuXv2Hse9dtXEq3iMj7WJpQl2scbO7t7ede7RA8yraJm/LJoNrP6uCQlYJQ0NDU+TyaLRxkXhpWOzu+jLulImUVATrlnDwycvY/RQ65rMg0smDplf8oddxlyJJrR1dc12cuabb4hXx44tbkP7BTvlU56S6nC4qaEhHA9HBgSwMK0v4zkUjjXH0gmEEMtDyPBwbbNSZi6kFcMDzzXeJrgwxFMTLo+K33dpg+WMu8mTlUtdvfOhnWKwXgWv1m7EIvdVbLAYWNJ0vxHx0oCqvEHAYmaV+nSdSV9tEKu+njwWisI23lP4oJlhpcdl18TJKo1UMrnTT8/n6FnXydmtP8M5dliLHWDtXA1eLZ69li8j3IzNgxE5YrRJiFUcwMp3WLhMzN+4b0v3hUPn9/ZklebueWzXoQvbOvc1YwkJCu+mxJxk0uv34BTebUfoXfcUXHuFVVlH9x6/eGaT4hX/r8UFrOoGdljky1Mtqzb/7fVvFnPjHV1x+rJuEIvljJupesy1qT+hH7s0uRS7uibgNbmN3sbgairXhLO5JFyNrBFescGSNVgpD+5faWoGsQaGw+LTeVhlYVxWHkol5Xj39Rs3SlG40jisidphyYBzNVc0sXLaLzLouiZk+QR2WGxSdz5kypq2tWvZJmRuJrByHZbvOoBV5wCLyv/KECxWbf2qU0+99eps8fcrGfVqlrpLe/sJUzW4suvCicpRqblsHTwTNdWQcDms1eDVCramvIsw4w0HcLMig6oaxOp/YLmWNbiBhQu9E437lnScBneOFlqlsPWx8/upHFzS2FxdDV7JEYKxZDLo95QnGju3naF3PfBYAWTNnfvYgeOHLnSzv/LgbOYcYPUvsfABRHABZnNzA9YSYbLmiX8fPDYbxFLjYYMGlgw2AdCEXHWpRjyYNUF41abeARozZszUqW1tXXD8uxlYqw+CVtvXz15Lzzg+6zEZJGDJ7cEoCXH6me+GL3W/cZJz8svRPWZFoyEahKVBNd+1kU8X42e5A6zJuVWNa+QZe2CGX1fWmJOouxwWgvgqXEJb28m1mOjakUl70/RElpLwRiWXG1oMLiJXVWlpVSBwLRdqVqilWKWlqRSQFacveTyKtnst2lhPXNq+mGd9HnrIAVaXWNOpOvn040/X0pMLy0UrvOMEY++/4fxbgdMtYLD4HKykN4jTveTuVL5qOaqA3NcFsTdKTjzlZFOcE4GvgbNVKhQMptJB3HN75sLF47v27uGbw0Rbt27d89he4AqHk0SG8R0GUFOMgIU9R3w1yxZC1rr9hDu8w1bnXY/u3bV/3YXThLqwRx0zqvOoeIAViTCxEtgSl2rZcfbzSweRNNwaX71zBc/UdJnmuU6bPGRNaCNH1aXNF3+b6uAKQk3IwAKx4K62H1u/cS25A3jyVZlQwBepjsvlSpGBAqygAhaGHU6SL5U9A5ihn32MQ0gmVXyCgb5i1lRXce22Cq4hOMGpaaYqZ2EcFsbcapTUs2GwcJpTS5IvQL25wKqkL01lChcD3CBgURnWkEhkMrW1mZZVp869eVARC8Ba7XJYU91m3Xlo5q0RcQUu6x1gsTj5VoBYK4RX3HHHAsAk8wrnoCpgRYJFCyyRJ9zY2rmp+8y6Q+fPu64Qo9fxQ0dw0W17M19CrIAVTsQSlBrBaBAnb7S3dnbAZh3f5bqQ7MCu83jXbR2drY2V5ojmogMWDkqpjjc1o5OQ5D2F2Igqzpwt1u7dAJbLLrmSQMHL4VdbliUgZK1ld4Xva8liwWEdo2RBs/3Y9u3Eq5Mn0S4mT54s9YQpfWGxwg2RquIHVrS6gR7DGljxSDQSYWChE3ju0nZNrNUy7OapVsyE7PjlIcvFKmNq3WMUDkuZ1BUrNK8wMU8hTGMBq7484mY5rKoqdZXJdQKL/gkAqyHejKclEQvLsfi45NltYvBlVQ0lX5dxWOb552aWqq8ZXer7hKzQUf5JB5WAdYxyjyO3G7PTG9cfvPQEn9vnj+C8Zz5DQlTswKIvSnOinb3SkXXr1h3hb9CRZeSQ2hubw8Micoy3lN6hkHPAGf1BY+O+TlxIhtvHjvAL73rh9CaiVSMOnNd7RYsQWEyscEKI1YKNqK8eWz978WIZFRt2n1DAovE1xrglPeAMuUCntqkT1KtN/mCMsVdjxihgMbFWC6/Wbzz5wUmej29JpUp9BKxq4IocVvEDqyHagArfpyrCagCLYplKp3kv76uKWFJ8rHF6x1nDboJ74KmdO9lLjpyimked04lxeHXyJBmss5uprMlg2N9kYGHDfOkNcFgKWNXh5oam5jlYeptMykXQ2zdKS0KhHsBy+SWOA/+QR/0cud39GIRu9prFx1Ycw+PyGEWO5ypkSUMynAoyrxpkmA4EYOGSc08gDGTxBWL49lF3d/fpbWAO/1PDegBWEH9ZGW5u7djUDW1jdZ/u3obbxyqxUjFQKScsFhmwINxJQcSqxvRyKhVMqUtBsU1ChtsJGm5dXfL1H+Pwx8GWW22uX41hd7UWb3iSXmPWthGxFi9G0hzk/hXxatoHH3/BCx6Rvsph4X6CKk/2VfRFpwperlMdVAf5cRUBYAW93iQf8PSmhHAFyIIQ8rhzRtC43PjljjXzMFAOVd4eE63kE+AUKIRUUretHXcSTUAcK5MGsFLBGwssk6k+meDWuClVA+ragMX/hg/2FOtYmvk6mWRQiPXq+tncklit5qgZWC7Mq1hoaOlnpOkNTjXlo+ut6XHZJU/LYysOCukJ9bwYpCVZWgVHgXJQzqTXgMDn1Z/A0puf3X/rPkgQh4BTebckS7hDLIxLuYVY+gbOkDp1w8kLnG65pJPfp5Nf9L7tjQmfRMDHTsbny1nWUBzAgsdqioWIWMFUEkuJ1HBD9YaSkIHlGm003MblEavN0GotV4L8xmv16BxHv1yrgMWiepD81bSTn36Ipmcp3yICh1VdPVCA1QCLRaEbRi8BFhIjSNxoUSFcr4iFEGrom/iNyyG/aWpltV6ctxk3RgobhFBiuH3xeuLVBye3qzWjMd7TeKOBpc8U4LuI8HsBVt0NAFYKNSGaWE18xw/OvlWPy8WLlYt0PS2nZj8tcxIwv2GRnas856OTjyoIqqT1XEWKgIWKkGxyyYACFi9AT4T5Tje8yHNQGIU4kWEVnophwyK+HoHl4XnahO5x4StQqfeB6GZREQJL0juKpSexEJ9nLdeHg1iUNVQSUs7MFmCZZ33OgBNEGVrxT5pW9IaiMSfXSk24+Nh2qgcXw1/dRQbrk7M7VmVKA3rOiDwWeVHPwABWg9yeGBlWLeelAFjBNBkFDX1YBYG+22EB4ONcEdReYYJpC+YNz3FCrAk807p49+JjwBZ6gNM+2Mgd97TfG0tgOVFQyoYbmFyB7J9vBLD4GqwUAyuMZTXNTQ0AVoqT7603hViUfDCnAiwVBpVL45xHZgGfP9UVNvUeJ9GQWMzE2i7mnv5sI9/ZQR8GT5WTwypxyp8BASx8tOCTvnC0tKq0VB1VSawaRsAaJmvofL5sZ+ZRn6bzL/PFeOp/yG4EBAJFBawaF7BiBKxEDS9+xJ1VMtx2YzrFuANBlcoax5qPmapclYLW2ql5GUMeSxFr+2LNq7tgsA6vIlNugFXdEGmoxnxsUfNKlYS4PBEGix1WNS7mqwyFQjh9ACEk6LcJsSiGXXrcmfiN08F0MastZ8Q5bzOO32ztBGE+44p5Ne1jsQlef5SqKjxHbziwciTAUj2W8usCFhEr3IBLlvE9nKok2CNyfOTF4jXCejwtNehzpGi/Vp6NBl15tOLkU09LZJ+K3EmJXCbBPo8elCXFBixvb8AKeCrDzsPdPWQoKYcNKwQsn/vGqIDP9f/iu/m3na5lkQHL40F+x/jSSFx4WxIo5aS55BALwGprM7jSzzjkgUoawRa/9E/St3IlGTksVROSPVg/e+Na4tW0jz8jg5Wp8QeDVCFUwqbwwKdYl6iE6e/o9KCKkuqSEnwfVoW0qI7IGrKmMA1BzHepcYf1WMeO7T62G+NOQjgub9xpp7U2Z8S57YR6OzVxQUMOEVw7bRoZrM8+eWpzJu0lXiVCwfKchL45CaYvkr7Gr48qCfns/rgsvePld1SX1FM9fZaPeJ+N9WYnduN52SbEogjQJzxumjtyJ1XyjcmtF8dlB/okEWs2LBZFbiPjatrJjVxKJ/FBEK/4HvR8yX6G3i/XuFHyOzKHnea/hbTfcxyTOVLcdUAldlW5sWMO0NGTClrmf1WNff1eaBndqs+9j9LAivEWyXhVqY+H2yU85tDhxYSKjLa8kZZVGq7VuaP67PxD1rDkp9z6xeuZVzBYG7+gwdbCd1MLsDDs0cPim277vIK6PyS4KimpEmDJRx5ublLbeTPaY6EXuJuHXVebMlj5yMpqaI1R4TNDzrz5mJMqhMCVRPCDjw9+8tHhVV5vNNbcnIhGy24JsDxuJ3D1EmDxZSMpbgOEKXT0AxopST7i/fVvKF7ksTC9gP64Aywwi+VC1lqVfvLtZLYXm8bvNE43JNZL7/QuIv1BXrwGaoYFWIU+Vt7QUF3dP8Cq5c2EOUHuC7CMCgArzC83sPSRqu6ZyAEALFYi7ivl2Zqzn+M+XiCLgdXWtjYbWJwHBcebbjecdN5S3oodFv7N9W1r4a/uOrn9LRpsSQ86aZg0ilRzbsgd3cUPLLWwDj9WywRnMxU24TAWFXFVyH2sjRgmKoauJ/+0HLfA4+ykghX9fLKAE5MYbqQhRzpJvLr9g48//RCXDXlj0URzM6+9L5fEK3pg8d4rbh/JegIcoZJoSmS4Kvz83zjjXSYYEDlpRwisnB/1g3CcCpyBvZOi8qbjPhh3kom1XqrBu0D67XwPJgErnLgCsMRj3Xpg4VfmdOa8tygMLK1AFrGyyjoCVgyvcBaw+KpYrzeE7WX0Kzewig5XDKyo5hUcAl+rwAbh4PqNKOK2kyOaTcDSacAI4lT4YNoHBS0CDblxUjEqXOH7SYw2whV5A8mZk5++yZcrlVdUDHhgscNqagg38YwLVkE6xJLmSTb0p7m8gh54xChVSONHd/jML2jYrd0ovCKXcPtdH3xKNfXmlrSX7HFzc4yt/sBwWBgO2cDimaoYlryDWOROZyNbVOTEYU3LE6cZA16i5uL8NP3iWEvkxF/dBWB9+iFfPJFM8ZGRDVco+7gqvI5QXZVccdU995woXy+wCjssKDYQgFVRQZ9+mSEWVYbhNHlRqQqJWPREJ1e0nnLm5LjcjPnAGW0nXT1kVyGIvzZOTA02hau7PpbBliyljwHH9VVS8kqZhSZnsQPLUYWqGqrlpB4eeVwWylzhQfRMMFQALEN91l3KKhijelIKxpNO9Ph1UkohjLqTJx1c3X77+xTCjzZjT06IgJWIRfUWWWfD6s36rK8HWFCp7ulGIrhGJ0JhaybkJuoz9bW6np69sQ2PuPVMLAKWzru7+IXHpYoduypTP4/RsXP8GBbQnOTs+/iDD0zkDreka5JUhSaxB5syr6dg4et7rZ/n1codV70wV8CEqz/0dICjXr7GgUBO07xQD0vdFesVXMkt10WKq0LAiqXpo65PqqRhYm0UW6QG2l06a+7irCGX9cE4bajGGV65HISMu5P8kKN/BrXM7e/DHDzFvAKwAgpYJQMXWA3V4FWYiZXCMtxMRhOLSY3hN+akE5q7VCAdk3VSfBb/6mROCJUohh9TIHnU3SWjbhXu7QiHYwBWOCr36g0AYDnEMsDiUxAz9UIsXlqzESUw4aoN5bREDVnH3+V5qU2WWuqg0zAvdCc/YNYLr97/mEm/Kun1glcIXzweKekxWrd+ltD8Bj/eSGDFo/LKdVgaVl51y3XRA6uBadXAvXfcspeWiS6c7bSxjX0RAUulwV2ONI8+cHda9GD7IDdjIHou3nXX+5QyH5776HB7WCKCHWoaWJIcAwVYfr98nNjhL2chhtVBmsEUjm544g0mFkzWWu2w3EE0RHc4ZYacu8d8FzvaDz74gGCFmkaPus72DLkE8nSop8jvDxRg6XKFJ6g8AV8k3twc5k2FmQy2NzmsR/OpbepargjvyhGHxfW0dDcIp2WFDpFD6IhXd73/8RcfgleZVHmCgZUMhbATpedw9ROwPApYZHquEVieQI4KOiwNLNXLwp/JTsJb5yz7LAUsTSxZjZVM1+o+Foi1lsWwoUEjqXI7CzmDYUTVyrSTTtY4xeNd08yo5KH2AScdjbUvPjxNvEoEKobR10EDKzJQgVWCo4O4696EThaUStVgHeTZJ95AZX1yLRtMx6XefpcKoPZZ4z6Y5mr7TXMX4HepmPOwA65uZ3uFUdfR2pIO4kR5EIuAFRqQwPIzsBKoaolX9Une33TqHEUOkwsnOf1cwLrdJN9dTluCKukxQvxpTofwLqcSkNChGiRjSpHrJF6VhhoFWEkAK+7rMV79Biz+AUQxTcnrBFZfHBaIFS1WYKmSBusgoShyPlZfn6mtTYsxV485wZVOmO+LZMQBRiCWKv0w7PRIU29unob4HezVF599eGbTEvJXFVWVOJYlwDfgyebagSE9YF1grcDpOM1oxTQ3x3HgnQeLcA8/9cZbr36Kcyk+YKarsGDEfV8zXxtVdPx08LS9UjHkbxh3ClcYdWc+WtLekkIbhqopkj5kD1PRRWnnXQqY3YmikricM5fMJDPpoN8Lj/UUz/tQ5o0TXpm46eS73TjUccabTstOPokdB/l9fmc2pjjQIJEqTfGmFmz6D/IGluKMmSzJcq13cE+q9P51dpYruOWsnRC5+++1rqtjb82neFWSHky0Icq8wkl0ABYRC2eqUUmD1UQbxR0ZXGlifV895/hBd9I9zrQxwLBUZFPD7gPKGCoHO9pbwnWeEswNfQuA5ccamEgch01gMy+vg6wsLQ0mZdH7m19wo1zFRQ+62/Woc3wWv81JieUHZti5LAX/WhU1Ha2ZoPAq0wxmAVg4Z6oI187kKXf+SgMrhmu0g15vWRAHh5yT5BPjNE0H4vsqeN93I0v86clsa6+fCsJ7/BqRW0aFdKKyrg7ASshBcDg6okiB5caKuwl/NcAyQOoNWOVq7VcPi1aLQgpYvNWkOorDWGNszIlYOHgAjayDQiznCXe7yRz3c05a8PxNP9wM2b6vcgdj7TMaazvayZHX+cJotX6bgIUbiDSwsDuuNImL2Km42S7EMkFBLG7PQpEO4QcGXXeZQff9203MVVFz+uzmVRn6MEI06DLNsFjhAQUsXyFgNTfHwuFkml7ooraQw/+EC2oVutvN40/9Sh6Ymliu1pV6WLpKAX4PZa9aG8PYCxkMofcXwtpRPk7QAstZ4pALrCJy7Po6Bcxz8VEpBCz0PpO19bjhcjP3jbd/fFJVI4pS73/w/vt33e4851SXJYtXt7t4pfLm/Y/ZGxzegVMe6wKYy04kOG0HNrDKPHWeChyy29ygiNUU505WTSmo/9QbH372xacfqwaUsqamq+J0ZO5SzXW0Ck3pqNwEf+c35VF3ikIYxJgLJxONNNQbBpbDyt2pxsDiwFHQ0olYJu3lI7thsj7d+PFJ4ZXKtvff5+QzXYm7jDnNTz/DrO8rXsGYlobpK+j18mEFoVAwlcK6IwusKwCriMambO4sGQZkyTbeJrQSeLamFnu7yJm/fomG28cfqM4LuaSPP/3ii08//fj992/PQZZ+tOlHIP6W3op+motffUoZg9nBZA1CEcCgFlAVEcH7pEI9LESvmWcKWVhEGgrW1IhP/eRDDqEMNCb3p58ihPgTgEhZLt124SJGl463v88NGHlSGOQna2pozMW4lGpuamKD5eOTFIp2z3i2pCxU9/myEDYKWjiRmZOIBYPJzI7Dp5745MPPOPkEUaCOSj5THd6uE89ETz9Y76LA6UcET/Wc+2hzeyZJbjgSjTUnwup/L5UDdIoyBfOB1ZfekgMzeX9/D8r9d3PAVe7+927u59lnCbCGMbBkE288xht4YbJCQZ4tfOLcW3AIDCg84b/47MO33vrwQydtTMXiFIvaU+39GKL3xFqGz2SspTyY/AjwWYhyXk8RBaRPygdWBQMrroDVjAlDLIsiYgUz6L0zssB4jsTHEsI3P/sCsXGaLTlhvF0x6mMO/vvyjp98dGozQljqx+pkVkLf5jiQgOW03gVYzU0StUpmcKjcH4TJAuw5+TjVJHKkzwhaH8uj0DSpnBpbcez9j1Xy3aVBf6o1k6LRXjGsBJuZwpESBU1PUY1Jt/oJWLLIoeiBJciqDvL+nCRljd9TyknzxCeffChpw7j65ImPPjp3Tv6ITYPuhLq7Vt9nH/HZZxc/++z4px8fwAPuk9Mdm1uSSb+Hl96ENbCKf1YrV7nAQgy5oI7zufTKYjUxsSgrCFmnPpJ4IYafgtznPvroiXOfvMV/pCsc6Va5Oy/vS8A/+4zfDr8kk7CqBVeg1QFYTdXRBvqOor7SN9CA5WGbBdAag0VRQ6NgTiJIg6UkVIrn5UeffKgjB16fk8ip7LvdhMqUz5KIQNQXn6nA8TuexjYmXitA5TvRsamhOlpmTmMo0gy0DitHeQ6rurqkPBhM8fqUcNDjqcEO+sNnMd7wXPsMLuns4c2bD5/66COpdN7P6VVR+UcF4PeVpVp2+swnRz78bD+94+mPOtozqZrSAN9Rom/00J2M/o7E1agwsIap45J54PHFnFgWRdT3J1vaN3d8dJpDePwLHcLOU2Re3QMvR7dLHfPJJ+dOc/Q59h1LWjJ+UKkuWE4OSxYCYvmabyACS90DzQ4LJ/k1Y76imWASLectMXWpltbDZ0+r5JPInTp8mIJJ0TxCBvX99wsE7vu88oMjJ89VfsdTO1q8Hk8QHZA4Oo3hhuqSqAXWAAOWiBvv1cOqcVQKkj+gDlgLCroyq3YQn05/8smRI598chpVXXtLe/uOTh6DX3yqellZIlzt+uKzI8Sozi30Zss+WbaMftnemEI96MFmiEq4q7D4q/7+/K9W+gusE0P6gMNKAjhvRjwWNg40VFYSsXxUvqWSja3ksroJ3hRDXE/S3kIh3Ly54+xp7tKAWFvzQsiu9KOOjsM0QJd9gthTCBNRbxAzW8HycmJVXIAp+/OIV4jlLVvoeCMkh8zF4xGJG19/UN0ULQsEIr46Zn0rMoiS78MjxOvNO9pbMvRnOzo6VOTyYH+7ity5p86e6pB35ZC3oGulSgk+3laezyX89dNrlotMhYHVV3D1BKq+6lZ8htckfVAZ9h9j8GEQ4mkdDHLAalI4fqCzY9NHHxF1uOHrq/FlMi2tnUAWW4QsSSGz7PQ2GZit9K4dHVjnWMqHIVXhAoJKPqxn4LkrqCCwKPMxQ0dR5BXv2D0AYNFnSXaIkNXSQojfxiFsb0ymPDXBZLJl1Q6qec4VCOFeKb4/OtvZuqqF3nVJR8cmDLpkCOdeJVOpEJ8VS7+pFmDhzBaZISzKkdej9C7oiL4UkFdZR8v4j+v8uPuzsZ2Sr0Mi15IM0shNJzPt7Z2CLN3gy04+wtVhKp4pwMhbXLeX8PtLceVKg/Q+UL3j1xpYxRk1C6yCEodVbU5LUHcoBgCsmhr6XlqKDGnF1RotydI6/rMaf5p8A7LmCHqguz7+9NPzn+7i1/HPPjxy5jTuDUonajzJRnrX1sZMCofj+rArqmiPr+ijegFWNd8Q2hCtrkwleZ1PCscKUwyJ3STgSiVDXQprRzo+OnMEzJLwnceLqxg2FC2ZdE3KR+9K79ueCdZgvAbDoVCSD0TWJenABhZ93CUglj62pyQgG3DBelKKP3u+1yUZ0tH3plval3R8tIwjp/QFUlAihzoAJ1lQ3q5q3dG+KuHjQ4HjcW2tGuR7iQFWfweioCywCqpCEcsFrBIBFtWENOgSyZqgP5lItDQ20q+lTgwH/d5Eoh7IQj/hw88+vIj5m4uYxTmyDLVge3NjzEvMC2LapzHBnWLYf9nGqe9hGYi6ErBo6FVjbyHcT2UqJcACsuCzEplEJpyqhDsKBf2eZJLMKw4oJWRRCD+8eFEFUYWQLAKv/aaQJ5KJxpZE0usPenHBczocygUWEWugAgt9N5gsfYZ6wACL23IpD8URn36Cks5frje+kfXi5FsmkftwnTty5OwzybTfn0rhBJlMoo6eJBG5+VaIFRdiGWD1dxwKywKrB6mzYF1HvGAgluOkMN5Oi4OMg6lgqiblF4YlQyE0nb1ezppNH50mdZ8WdXdv6lzS3hgqo8+5DGPJV1qDvhjvOa+qqqzq26K34lXuF1T7AowuIAsQ4ZtWic/CK6ykpoc4VcRVNDiDoRCKuTIProsOBiszLUtQb5/W8Tvd/dFH3OdK+mpqYGehYCgRpp+w2JEvx4yGueHO269LpIQfiMDKF1yqvmRKiFVqZhP8fvqUw7FoGQ9gsvjt3CN1AneaCsctre248qwGy/34APnK0lIcZh1H71RwZVwWl4K38qKJq5MFVg9SwCrJA1Z57oH1+BOeQ0wGMUvm96cTjepCx81LWpd0dnayd2/kK9Lwz1ap/4KShhWp+lYDq5TvRTZnY6dS4aQiFs5ckotZ+NjHaFSdWlpK7jUjIdzMMeQLMdsbE2EuJOvq/EFpJpYztkCrWCyGYYud9992YIFYVTqHPP6yaCwcjSli0RciycmHuG1u5eCh5KaKgDEv+8DxT2A2BCtp4g3V2bLAGtDAcroIXBbqgacvYhTHFQoxr1LJGr+YBqp2eBloZWWKXHs4EeY113giiqGqwgEyWpVVlZX6dJ/+/qyvVb0AqxR/J+U0rttTZaFZ1I/7C0Mh/BbDCLGhf4LeINGc4KstU3ykHH0pKuRfwzuHw6X8PwV8WA8Sa2pK4DSgb5PDqlPXKEhDQl8aH+GeZ9UwQUppSp/oHYuqe5X85N8rQ2F+JeN8c2hAzmFGpOO4rp3/DYozUlS32qv1DxZYAxVYFSUuqd+iR8KECknHBMDCEz6ZYmAFAzhZNmfhj74crY6fjFVyW3aqVF5CrKpvG7C0YxS+5ADLtLEQCHEOAqxKBSwdsro6hX/6hYzaKnlHPvA87Cv10CCM8HXJTeGmpniT47AC3w5gSeYEAu6b8cSV43aiiqpS3L6qSI18BLA4i+hnjoN86hX6nwH4Ibx3RJZ7Nehuu17UYIE1gICV9YFVuKT+Xu6EkUWefMgZr5kJq4GIkRQO+3h5Wnkw9xOsVOczkaOqAqw0r0pLdW3oGP2BptwvqbFWLocFpZQ/os+dMaUHIUIcV6ooiVT69CXhOf+P0J4sV4qcF5wDQSwejsswjJRUGDgV903ZfZW5DlTHUfJNRYFSkMjF63L1HgnzZVDj2fxLBHzYM1majD4733gZh91iTg2TVdLDqqX90Y+fcy8qDKyree8BBaTelPuB5950y1OHxCu1oi9uEsgFrHBlpIRb8+XZt8ZialDevlS/eUp6p3V13zZglRYGFu7fkxtDq3xZwMKDQAMLCEJL3r3Mw5TPvLaWo4xFj54KAEsroia26pyR3j/RuHHqGVgSBYWb6lxgeeXQzFBQRZDjFImY3RS4mweLr5hY2JIgl3WbWfH+/rx7lgVWlnr7BEo0sdwOK8xr1PWzn/8qqrrIzlONh1iiUo9QVROV6q7zt6Tp3huwqiqlJKbKmIEVVGdqx12SYSVnXmKlhxv6EmkJphtYlfLm5uP5tgBLR7Unh8VS+Yg/07cEgVfYBR5SnVbYK9n+JXevIcooCzlsEfJponjxH8VtgZWlvgALX3qmUtjlsJwkEkWbwjE1EPm4XpSKEZ8z06PeL/BdA1apJpY4rKg6UztsRh+PqmZxquKy8mJsgOX7DgNLOSyuhsNm23xICf4qFkvEwupM+4gBFiLXzLGGkVJtigiIRQyLWmANMOV+ArmJjy8y7grVg0fDRw019afxOOxVAgnjki5pGEx1kncDmFFZ6g1YsnLNz6WNzJLifDi1zDMajYUZ6vEIESiih5+yVGYw6ngH1B/S7yp1b0avT9IXlH8rgeWrzI5DoGSYMKjZOHida7BX+A5gwWFpYOHt0fCKqBaE00PVi3bUXGPRygIrS70DS1bF8BOOXvnAwp8SsGLssZoolxJ8/THVilmuygCrPz/bG6erARZMVlXE5wJW+BqBVamB5fuuAotnHJyOAwWSGRWSDlbIlIRR7bDUd178Z4H17QGWjkcBYNWVBvIdVmWW4nHnJtamZjQ4dVJhJ4Qc38HvYnoGAzZgSn0FllqGVlnFG3p59TupqQnAShhgNfUKLP3rHoBV920Blk4PWe/ZI7AShljELOlhec1dVQwspYg02SPoJTKwpOVVqmjl1evY+vvz7lkWWFkyH3lPwMJyKvrq5jqssPq9cVjYLkEvpJK78R7XwKoQh/5dBBaGSqQAsK7GYelfV2QDK/AtA5Y5X6y8MLBKhvGjMJnlsFznN2UBC71C6a2XlCiDFVDACppTnxSwijcRLbAK6kqfgJ61cjss/UUPqDXJvOdEzjwOG6gR3zD3Duknnt6bMuADppTzSej5+Cxy8EJtdxSaaDAx6tWMYNbUhMRZz365/4wdlmuyotDi24Ea15wRxL90f/7m88Szs7LSYF3vGTPNd6+6D7S2FoYrqCcx1B0TOnZuBlwTCG6dcoB1De9dCFDF+/n2UdcKLL2JIqCA5X4b+DHFq5JoSbQaF4kFvo3Acn0eGljut9HAqna4zWc9YR1o9ppuHbd8YIWNy/h2A8v9+4LAUhPMcKK4c0P3oBxgwWfRSwEr6HPi647dAAXWVX98Fli9ACvLKdB3xSt9esG3H1gFSjN8zsOG6SiI1MgJFAJWIYflHnBXWhoyUON6FcASBcQyaWDpeLmP+NW/1jHOAlYPusWfdh8kwLrWj88Cqxdg5Q7AEgusPGA5bx/w9dVhWWDlzS/z594TsMpDFlj6vb+TwMqVTgZzQKRL7iTTf+9Ont7+v4Gkq/s8rj6+hf6uwOC9xo+neNTTgLrS55r7doXih7fp7d8o9P8XjxSwruO9LbAssIwssG6MLLB6EgPrmj+u7yywcsFkgSXq7fPI/uu+Ayur11VAPf2/AzWuNxpYvYG9t/+/eGSBVVAWWNcmC6wbIwusnnR9H9e3Flg3Uu5kyW0a9/fHVozqabBdSf39MRebbJysrlkWWFcnC6zrl42T1TXLAuvqZIF1/bJxsrpmWWBdnSywrl82TlbXJZ0sNoF6lwXW9cvGyeq6ZIHVd1lgXb9snKyuSxZYfZcF1vXLxsnqumSB1XdZYF2/bJysrks2WfouC6zrl42R1XXJJkzfZYF1/bIxsrou2YTpuyywrl82RlbXJZswfZcF1vXLxsjKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrKysrqJsmv1N8fh5WVlVWvssCysrIaMLLAsrKyGjCywLKyshowssCysrIaMLLAsrKyGjCywLKyshowssCysrK6at1sbvh70U37j79TCvj6+yMY6KqrQzaWldl8LXLd7C+ETYBbIQus65UF1gBRT1+IG/UFsglwK2SBdf1CNnq9Nl+LXBZY3wZZYF2/LLAGhCywBr4CpJw/8UGBwm9uVUCBQDnJAqvoZYE18GWBdf1iYAUtsIpePX1ByB1DFlhFqkCOcv7WAusqVVJSRsAKWmAVu3r4gvg1sK73K2QT4ObI55IF1vVLgGUd1gAQvgzOF6pc6UZ9ofT7e3NkE+D6ZB3WtQvx8uVI97B6kE3U4lFhYOVC63r+dQusG65cXllgXYWuBVj9/TFbGVlgDUD5LLCuXVcAVsgCq+hlgTXwFLDAug5ZhzWg1TOw3NDq7V8pPHB6B1ah97HqTRZYfVFPOVn4ba3DGiDqf2BdTWJZQRZYfdE1AMs6rOKXBdbAkwVWX2Qd1rdTDk4ssAaILLD6Iuuwvp3y09epNhqtra3N+SpFSRoqbgcmPwcCVSQMjGAwGo3wz8GoAzr1jxcAlSs16FdlrBKl/g1F8etKDxBncKqe8necWNcCrNxKw04OFZ/8XmJVjL6na9PeYNDrTXvJGpcLSzSw9JfOAEt4pYilgRWKOmSqY/UCLK8AKxq1wOqbrgpY33FiWWB9G+VnXtXWg1gkAAsKlpaWBgIEEIJOaWkwmOOW/WUlwyDFrGAwAn8VCql/hcxaEP9CaWlPwHLEwCqxwMpW3jjxZ6vQ++QD67tNLAusb6HQXQKv6utr6zWwyGGVl7qAFWSKST8ypH5WwBrmBlYoVGuAFQoFgz5flc8vFV9ZL8CKllTzywJLKXeg5PCqr8D6Tp+TZYH1LZQAi2glwEqDVl4GVgC8Kvn/t3cugFFV1/qfvOdOkskIJowIOsZG8cFEk5RBjFBRTEiugqkaLjFCIDUIAsFAkdhLpLxEIFjkIRSwoZdaQB6iPC5FsahULPjHtnrro2pbkKJYpL2W9mrrf31r7X3OmUceJMFM9KwzeU1mJjM7Z//mW2uvvVYM/SMJRBk+sgyLedPFUlPhL7ri47BzNCHDayisBNFYkYBlPQG0wkpW1pFjEU3WFmDhq62wxM4UWK1ddLLtyzJxCbM0jrSIInmUnp5G5vV6CwqKsmA+U0Bl0NUCLPynGXEJocACsVxWd9DNobGIwPLapAo2G1jtYzawvnomQSwIrDxDYbl9hCllRbAsHzMLOoy1mA9LiGlp6QQb9ilBKwYW39stfqPLFQQstSzIpuW6VlgOidF39FhEjRnlfbQ1olCtZgMr3GxgfQUN/yivNwG80grLxBXz6lGGli9LlBYMv/Eqs6gqWSXUwEoIA5bJKw7Jx8p5Eh+ngWUTS1kooBpzqa1mAyvczgxY4WYDK4oM/0xe5jOy5nQqltdXUERHQXZRCbHq0TArEoCxwU/M0sDC47hMQ+g9Sb7NZZOlw3BzKl51ww8muL6+J0qoC9g6l/Dry6umE2sbvX0YsL6M52pbCw2ndAqZBM5BLAUsN/MqWx2PErFeehQfLykTYvnkEGdRgBUfAVgGr1x05DYCrFgbWMFmA6tt1kpghRHry3iutrXQACtPZqZHq6yEBOXb+XzsCxKzGFaw18neUfb662CWyKwsHIhqkdIiYMlcocdFUoMVWNpi1YmRKpwCKllh6efkFBkuP3yNpXi7AOsrzKvmXDUbWF9B8yhLVcRyuTWv4A8yj4ArRtUHH/zJYh8QtbTQKpLIFnKvCFJOpGURsGTLTjiw9ImRmqr/KohlnlBG3ECdkx05Ph1pNrCaNhtYXztzpmhgZbJbSIBR+Vbi63Hs6qXXFap+//s/kv2Bjz/+/ve//9OfFLMeHSDEIoXldqcEmdvt87lzgg8plhYOLJ3oaA10dnZghU6aM7G2Ait0orZ04kajRRqfUKA0N54t/RM2sKLVFK9K6EhJSQewXISqLJ+KSYm6YlwJqv7wP6b94Q9/IGiRziLnkInFCsvnBvzYPDjI/D4NRY9bjhYCy1gR6+hhaou1ilTKbGCZFml8bGB9zYx55cfh9xCvkAPqZWAhKKVp9Q7TilH1K9jPfvX0r8QArT+ayDKABVqlZCrzeCDXPL4cT06OW1ki/SEk0HdXhlx6shidIhGHD5UZbwPLBhYs0viova02sL4upnlV4ofCIo2V7iVgZUFeFRUNKCqCuCJHEMqKUfXWWz/72dM/e/rxp3Fhbv0PfEOEs8gzHEDIgjepFVamKCw/GTRWjsdPrPJ4vSawrIYtQF5vGh2ZXrWTx4s0VBtYNrBgEYZHl/uIT2r8NkHW0j9hAysqzcnpDEbQPTGFYCICq6goS4WuRFz96mc/e/z7bE9///HvP66MqQVmKZn10qPkFmJpscQkFnhVUARk+SG0/Pi1j13CTN7zk5ZGt6LPAJj8nM1XMMPidBHUjh6p1lrrUWVOnDMFVkv/9pc1Bu1lkVCixyEUME295qZevw5VfLmvzLYWWiiw3B43oMI57EUDXnrpdeDqD3AEn3788fvuuw+swnHffY8bZkXW66/ziiGIlV0ivMomYBVAYgmz/Jwq4fMhLk9YykxLF0SlpQuwsg0TZMW1YGJGs9nAOnNr7FmaI2JulbCB9bWyIGCVpLqAqxzZc1MEefWn34srSD7g9+97/D5oLKLWzUSsm28ORRa5hr9nkfUoEyubkEUGd5AetACsUjKLhRaUFqHLm53GkMr0el2u+DgvA6uADkFWWkxnrdzQOjyF29cRWKGNt8JHxAbW19SCFVa8y5BXAxhXf4Iv+NbTP3v6Z4/fDIFFRtQiYhGv8L3VOXzLRNZLjKxsf3ZmiQdYAgUBqyBe+YVkCLAX0MHJWUQsb7bXCiwmVkePUmussel2pvZ1BFZwUkwoumxgfc0NGekeFRknhqAkVhbH2n//e6irt55+5pnHHydA/fuvBVn3ff8++oHsZsM9vE8h6++GyoLGIlD5S4RReewLGqDKyeOVwjxfXh5RKt7l9nhyyHJzXV4QSwNL+YVcHrAznUROGVCP35MSdPK3Flihk9M6SZt6Hs0B8+yPROtMj582YAvPV7BlbvUKhVRLgNVSa/L5Rfn4fcWNz4MUj/LdkClK7iC8QZFXTz/z9M+eeeb7RKybCVLEq5tJYRGt8AOuvO/X9/2aLo8//swzb72FJUNE30GsogIknYobmIPHlt2JPn+h36+AlZeX63IlYVe0m3AFYLmgsQoKirKDiYV01s5zgtjAapuFAstjA8s20+Q8SPFABPlRRQaLgx8wrn719NNP/wz2zPe/T8giN1CIdR8rLCCLP9/8azpArKcVsphYAF9RYVZRVqEvy5+T5ctI4Loz7rycnLw8SHr2Arup54B90YSrOHeC21tgSKw0jmMJsDpPmV8bWG0zW2HZ1oSp8yDT5yvhfTgvvfTOO3PIG/w74epvBCxkXmlk3ceqCgrr3/9TMevff40PItfNNz9DyPoZkPX7PzGxOJNrQGGRD/4e13/gisnkB1oq0tEzQFEG/aMbHSwQsxde2cCygWUDy7YgozMhNTUlxestIX316Etl73zw+wqSV0Qr4hVE01tKZcExvPnm7yPmfh8j6z/5It+AWDc/w9D61R/++KcPOI10QCGS3wtzSFXha2Ehyytdza8rnXR5uV2TunZN4kJ1DgfXzHLn+XwFXhV01y5hZzpBaL759VSzPm8rgPT1zU2cSMBqamJaa+K3ZVJ2pOG5aVBpWOnrpZA2Uo/djXRnbjusYHrLWGPPL5rH76tuClgecsVKHq0sq6vdAl79inj1OBHrLUgsC7LoYLEFYikDsf5diMUy661fSez90QEDsgCsBFdXV2FpJay0kOnl9xcWlhpG1zHGkrpKW548t5u358RI8mhM99TOBSxnosZVYpjCsoHVvOG5Cao8fFjHKhhY7giHDayvurHWTknJ9BZ4iwL1NbVztv3xD/9z8iRHsB5HzF3ZM3QhY24xsf7zP3/5S+YV7P8Jsp4hkfX0W38nt/CDd7BTh+v5uXIKS8dNX726avX0ueOAqHHj5s6dPr2ML9Pn8nVErdzc2K40HdFlB9MzDhMPO3ZSU7l3T+c5QcinEXcsuDSvFUDWSdiUfV2BBWtWYbkTMuLOksJqaoyiffy+6mYAi5zCyvK6Wdv+WNHwhz/84QiiWI//9vFnHn+cIAVc8WfC1TOssVhh/VJJLPmCVAcQ66233gKxXh85YAD65+T5Syunrz56dMuWo0d3bF49ndC1efOOHUcX07Hj6I4dm3EdY6uw0EXAstQexckRi3e62E51gjgNZWU9sfG9DazmTT+35hSWKot7VhRWU2MU7eP31TcnmJXujSNgldXNmrPl97/fQscf//iHv78FZN38+OPw9G4mWiFIdTPg9f2fKWQRp+77d4UsFchCHOutvzOxRg4oKiqqrCxfvWP3R++RfbR799Gjix95ZPfu5z76iC7PfvTcc7t3P7J48Q7i1nTor8LcJJeBrNhusbEkr3JjY3UAWScRdvSQNWfWSWb9vi3AimSht4cLDWC1djJGk0V6zsyrTKWwvAkR4ljtC6xIY9ZZxu+ra06AgBsPkktYVVv7QdUH73zwwWmkNhCxfv3/fv3rxzmgDlqxfZ+JxTKLc7Pu0/Esg1iPv/U/f/zTO4cOPfroS4cO1VQd/ei9Tz79+ONPP/nkvRdffPbZF198AbaTP7/84rNMrUceWUxSa25pYY6rK2ClgJUbi64VNrBaDiwgq6WTL5ot0nMWfRUcdD+bCivSmHWW8fvqmhNJUbxJpiRQXvNODYq1v/Q6dj6zxvr1b39NdvNvmVWS4072MxDr+yr7/b7/NCLw3/8+gPXbt34FYu16Z1dV1dGjuz/65NMPP3z77Q8//PjTTz/d+elSunw6++PZuCxduvOFl8meffbZ50hqbV4NmZUjT4ybUXCbnRSSgJiKnQlYkU70LwdY5jg1N/mi2SI9Z9ZXmUYM66wprMbG1/q8Onp8vr6mgJXpKygpqa+vL0cS1QAkZH3wpz/+Dwo1/PrX/0/s3+kDOuo+JtbPBFowE1j38SLiM8/AKfz96dOnTp0iZ/DTjz+87sYbb7zuunc3ffjhtGl0UTZ16mxm1tKdZC+Q1tq9eAeYVZiru+cYvBJTEzHatxjihFaVU4NOdCtp9HVnOIdaBCw1WukxTTxgx45Q8+YMf6FGgUfX2VRY/Ac1/CwlcZ02sKLG8A+g8xv1q/w+H/dELXqUd+hgg87jv2Vikc765S/V0uB9Nz+jVg8ZWKbEuu8+Bay3/n6E7OTJTz4lXL19443FxTcW33jd9e++++6mTZsmTpw4beLoaYOnTh02+wk2+rr0iaUvvAydpVzDXGWoXarPVG8KF6aJiUH4tWWbgDvAnLrZhnrS6c5UAMxswsFpG6rMKkz3ZUxVFVhTQ0yKsqqqhuq+1tqH8ZxIGRen/6LUGeMyY+nmo+DvcM+iqF911S9UV6h167H0eD2ZmenGSJq6KoTjwZxxRhhPNqORrxpIaRuVkcFl4Xz0jyNT/49EDdCOHpuzYWeyqT4qjIEVI3kn3Ogrz+dD2jtEFrJIH/8tE+uXMF4b/Pdf//szz1iAdZ8VWCDWW0Ssv3/+t9/85i8f/uXdd6+7sfjfiFcErOuvvvrqTZcQsEaPHjx42LBhT2gbxvbE0v97+bm/ksyaDpklvPJkZ3p9Hq/UepBqpjEx3rg4ow9yQpQNsNMEFupRZHrTpYmQ0T3IbUAnmFgaWKHzK1XKSIcByxAFLguwMr3ZDCzJvVXA0o0feYq7OgWwrN3EwSwEWf00ngysrrl0SXRpjRWmPJsDlkrx0+MeEwYsry8D/zulVPmxlOrq6LE5G9YpgRUTo36Ixz9Lirq/JNugf/X0079FKOuXphG/OL5+s9oUbQCLkx6QP/q3t/72t7/85e3rCFLXwSG8UXh1CesrodXDY8bca9iYh4cNHjxl8LAndorMUiorNpHe7eidtcDnKUDp+QLRDl5vUrQCyxkCLDrtdRkfLRg0dOK0hXh4RitsZUpgGTozRjYAGA1oeaNKnFVhZaYVeAsyNbDM2zGwXJ0EWBnoc4me4nhNeLcqCFJYXbvm5aHihyscWCGgCvX6jF4CcnOjuYBqzJmgFZaX3Y7MFgMr2se1MWsOWFH3ugRYrLBSnTTNfKrTIO+EZr/w6ccRywom1m9h/8/MedcCiwPvbxGvfku8QujqOiHWdSSvmFakrohWDz8MXN0Fu4M+7r334fFTrujVi5i1dOfLz+3WyOLNY+i1g+rzJSUl2BINJzHJJFZUAUsrHiuwJPfd79eKQQPLaLqhLIRXQcDSvCooKPBii6WFV0Qi8MoLYCEonQ1vsIBvCGClpOZ2SmBlaIXFgJcSakphubrSketSwArbWBgxNhUJWDLsRjMU1f08gQWWCazMlgKrMywIRbLmgBV1r0u/H/H39P9iYIFZXHpU/EJOfSdo/ed//vo/fylB+N+yp/j/fhkGrO8/8zMA6zd/eZtj7dddz9AifbUJtGJ5pXh1zx333MFGyBrz8FACVu/exKzZLLM2r54+rrSwMC/B7cnx5Pj9Jf6SAsIVtkVnezITDWJFFbBgeuJgvzdOe7iEABb6EUEyAFEMLHUYwIoNNj3B0M1IeFVAyikblVrTrcBysr7yxjG2eJ5BI0BqCbCQHYIUEQJWRkanAJZX2gtIdVrBPl5RpkQxkUULTlmB5XSGr+7pJhWhwNLKSw18stVdxN34b2fwQHbPTBdgpaC/Jjn1TT3vaB/XxqxTKiwrsNDwmUvE6HJ+Uh9LQYuo9WvWV/xBwPpluMIiYP39LSLWX64TVjGvrr9EgDVl8HgC1hgtsO65i3hFxHpozMPjL2Nk9SZkLX3hxedIZY0bV5jTFSKL5nuAgYVKDp5seqON60TAcjoTGVjoK0QKS3gV6hLGx4aaASyvxaCw0rACGMwrA1hpXmxmFz3CwEpJMUJYGXkgVtSdgCGm1KQvz+eWyCWRClFMSFHsinbFJ6md8qZLGAFYCEfBwomlbyADp5WtEfoidafq4XLYPT2FoG8DK4osBFgJPi6M9agUibG2z/kfRa2nn/7bb8VYYpnIImD9jBXWz976O0fdEcUSZF3PCssiscaMUTGsuwRc944hYg0lZPXu1Xvi6GlTl77w7O4dnP+ek+fKzfEXlvj9nmyjU0VaZwCWm4GF60AsCAb01fbGcdgkJmQvnPYkTWCpx7HiSusNE3PxuiuaobDQC7LEX+TzZguwNLNcPIM7C7B8XuJVjiKW1+vy+Tz0+jI9mZkkqXiLkk4gDQWWMf6RVxHjE0IsNFiPUc4oEGAld0/uDl6lqOXKpp53tI9rY9ZJgSVPCv9O+ISPFjGx2B59SXUo/L3Z/Zlo9DeNLBXX4lx3BN0BrL///cjfj3z+ORPrekgsrBDK+iBJLCwJklf48MYxGx++fwzgdT+OjeOZWL16X3zxxROnTd358nOLd0guaW5Ojr+UgOWxACs5WrvqWIDldnnc7P87nS4PaEUXxavu3eMTVPpjHh9ccsdKLP04ilUZOHwqMGa1cGChUVFRlo8D/qazo4EV7XsztcLK0QqrAHX/3T6E6ryeTK8OWilgGaoqFExmdlYwqzIsZuWWBpaLXUIsTrr4fycKywZW1Jj23fVJgG5c7BM+KtF3RtZLr6MLNGOLwHXqD0dOamT91kDWL6VqA8ewSGEdOXny/X/85d3rlUd4tSisXiDW4MHjp4wnGzpe28bxG4lXQ4ZeJm7hJRdPHD119gsIZcEvzMstLCwsKQwBlmWzbzSZ/IMRY3OT0hF1gzwscmEy2NlQ+T1GdF5Znliu3o6kSZXAK1emxTvJnYTfouJhWmRhjZ+bH5Hzyf85n7RUS0mnGcfAkolJT6dbR49R45aUxPhlLrtljdhrZrdzfMkrL0TD2uLiNamwDFbh/6C+M8FFdELADwFHF67x5RGgeBt+bC5d6XK78Rh4fpGetfVNP9otgmtsWDQKgDATYMk/2ABWUcmjgSLDMAECIrUIW1UfnD517MjJv/0Gpj1DnQ/PdWaYWMgc/RzEuk4JrEs2XTyxd+/eQNYUuvSacgUOsssuu2wo2ZAh9Im+mzLlChJZE3uPnvrEzmcfWbx6emkhjCRWSbbFJUyOfmCR1OFqMykpOblMI58JrNRYXu3iUoZyBBPLFRcBWPRNnACL0JeVYQVWPP/7fEiiQ++jAQPQ2DbPDZdQK6w8PFLnAJY4hQBWgcfnUW0A1Ph5RTk1B6x4d7BH6FLAwuNkJOSZ2DKAlRKbkpLoSnTl+bLysjLy3Akid3NT8XZjAytaTC/nwj0RYElmAyGKSOXDG7UvISOBVDLHtl566dChXadPHfn8N7/5C4ilXENNLdkCLcA6cuSz9//BwFLEuuSSiy8hfw/U6s3Wq3evXr1IUwFaF4kBXVPYMew9evTUpS8/98iO6eNQ6C+nsCQIWB09bo2ZVWF5sJs7NzeHrZAIUmQFlsrYtiRI8sRkYqHKfbCZpxVmdAaWHDHT2B9CwjtSfmlGZxUxrqSCYl5ebGxqanqqzjHqFArLrRWWxOzUqND4FfoLcS4mSOwqFFiNTUT9s0sTSymvYLeQ5FQsESs11+3KQ/eovCzxn7FBDLwS8tnAigIz9ZUJLF9JUUmgqKTI76cpVoDTBh5HBkBGU2HcodOnTn7+F9hvPv7N30RmaaH125t/+8wzf+PdOSeOnPzsH3+5/robBVgwhtbFAi1tvWCitC4ibA296KLLLtPIGjwbwffV40pzaNp7TGKlRZ2wMswCrDx3blKSAIskYlZhKc2EMIWFxTscBrDY3O7GeJWQIMCCwmJiqfOOZyD37R5QSv+kkWBWRkIS5qEGFoSJK8qBlYBXznVkvBKxozFBqdrCHNbZhT4RTuEKqxFiGT/GKmIZQUNTXeEgYpFPyDqX23PiU0Ye3m9ycjlaZgMrSkzpK9HOHAQp8BGpCFmEqwIJe3q9LKm99KaeVTpu7ubdL372/l/eJWD94zfv/8ZwDUVq3fzb3z7zt7+99feT2E7IwNISSyNL8apXrykAFXmFClfMKzb6jq5G9H00gu9ELEisEGB1i02EYu/o8bMaTgCplMCSlWaBP8D1ocnoC9y0LK8E3U2FFWm1kL6JC94yqPMYyDnxcqZVli9LSSz831ioZSlxNVJs3IDCwjyHI1ZiWOo9KfqBleGOk2wyr9fvRQpbSUBGcFzluMrKQji2GbxjAK9dgBW2nynC1pxYRayE0HF3S4sUoB/UV2MI4pciExDL1AmypdEVCVj676gKGR0xaGdkkYCl828jAivaXpTWVyawELfl1OICnweL5PQlM9Ep/+KswnHTd+x+cSf5emR/+cc//vE+WTC0wKvPP//85MnPPheX8EaV2nD19Uws9gmn9JoyZTAu44dOIVZddoWFV+waIv7O64XkFi5mYqV4zJ6FnQNYDlegvGZ1zfS5mG3lNO3ojTtDlgmdLiOGJTF39cavkyFDeWUkXrlc6ZwbqrKMLPEZnmoKVqvIcT90iCZcVxWljJep2ZmAlZ7uj0sk4pfX1NSUoSztuLmV40oRn0gQYMWfKbBc/I6glK2uUJOR4MX37BzSIOohXDVy5KFD5XMrS0mn5rUYWB0xZmdmnR5YagFFvdtwR9UsX44/x4OWSm7dzj6THPkEV0JO6dzVi597YenUiZve3fSXTZv+MQ3I+o1ClsYVGQHr8/ffVzF3lY3FKusSxKYGD1YJ7088PIY+jx8/dOhFQQZ4XXZFMLFyY2OytcSK6QzAoskRKKs6evRo1eq54+bOPXSociSAJVEnY5Gwq3bptMRC3kFISYYYSxq8KreDTAd2B2XS5Sl5RRPtpVVkz+/atX3HjtVzK3NimVhYWPTydI12YGUoYGEvpDcupYSGcNYcHsJx46aXzy31q9CFhO9kF3jLgCUaK9QF0gsavA1IeLVKbNeuzTs2ry4nYpGL7moRsDpiyM7QWgKsoBYqEYDVoe6vAIuIxa68jxMcc/zqLQXr4h5UnvFkQgUUls7d/MizO2dP3CT7mFF34R9KZf2DkfWb3zKuCFjv/+YvEr8ygUW42mSWahgz5t7/owN7n8c8vHH8kCEXBBMLqqtX74snErFeYGJ1dcSYXaGjHlh4Nw+U1275qOGjLTtWTz80ffr0Q+OYWBnsyoQEheONHNBQWKVZPUIDWOl4BMxGldKtcUWswrFr14HTZDTd/N2wSVRW3jqDwrICKynOQ7zaUkFDeHT1XLQvOVRZ6EvAGl8QsCISK8R474DJKmOyxhm8kkHkIaQRfP75XdvVEGZgzbAlwOqIETsTC3FfGwVWSorl1USAUwe/1iTLXmKJvLiAgtxuqoReSia2HKNz8zji1Ys7p05EHArZCYNxDH5f2T/EM2SF9bffmOrqeiWuwLhpU2fPfmLpzv+D/Yvsn//61x3/QqL7/Rs3Dhly/vkXXIAPTS3WWJdsmjb7heewVtgtOU1prLSYZL2drkNpbzHryQCjQfVXVm1579OPP/loy+LNq1fv2kVO2qEBjCzsVbOW+kIydzrKwmRyK9k0KWfF+Vqq5ZmzmzJXYqJlGmIh3q1mmky1XbteffX5V1/dfuDUsSOnTleVl/q68Y5iSYHgRh8Yr+hctUhKkAIvXmlM6XB66uu2VC/6+NP3Pjq6GT1MVs8tryzEAObpjdxOVASzTMDGpFZsbGr39BAzt5Vn+DjUjkEkVNEA0icM4bFTp3ccGsm7qnxud1NVb6M5hiVnpbUprVl23M3bjkwDvJC+h9tLh0h8R/dNVB2hHB2+yGACS62X0P/fBFZsSjoDy50Lf5D01dSJiJojBDV+MKd+klzSzPrN+7/5G4hFLqLmlQq3E62mTeMSo1IXmVj1z3/+9Z9P/vVH/7z7n3fccde9D92/8c47+11+/uWXC7IuwGqhEGvixNkv7yZiuZJiYjI9mdwUulMAq/xow6cfvv3hJx/tXrx58/Yd28EsNBTCpERFhTRsaObdcpmsKcwYnQVYMcHASmRipShcCbBoqilcEarYth9449iRI0dOHa2p9Lu6IbkpRoAVjxEjXkUdsPi9PQxY/vLaikVL3n770/cwhDvIRVs9HcjKYmLF6yFXLcEiAUtfT7zqjlFNU5auPWvNKw5eYQxp+F6h41UZwmOnd0EXZ7UMWF/yoLXQBFeim/T3VmDBBFdSBUk1szX6b+uf5TGc0QMsUVgKWNwHIjc2F8BiXhWOI14tBa+AK52iPp5w9cT7D7//GR3vv//5+397H9ErCCyy6999F6Digsgo4f4Cwepfz4JVBKu//vWH/0vHj3705D/vvuOeu4hYG+/s169fT0HWBSKxsFZIGmspEWtuYW4SmitnQ3MkW0/IDhq4IAsDliPOXzZn/4frbnz74/c+emTxjsVwMLaTyuKejbrqkjc7k+uDpuHbgmzoKwWs7iawMN8MYJFht0gsUqzoBHLn6cDL88yr7a9sf+Wpp55649iJL06e/IgkVpHLkRQnSQCdDlgOGsLqeetuvJGhjyHcsb1q++q5nGOWYRYyTgkDVIRYFolVjKvJq+4CLPpHaHUlyMf4YQgPnvjis5NHTm0+NKClCutLHrOWmupNa0AqBFhuv4EsrufkNrhmUVgmvkw120EvpxGFxVm+RKzU9DT2BwvHTV/83M4gXm2EPfzwE589QZfPyAhahCu6fPw+Ylv/mPYPlG5fyrrqBW438c/n/gr737/+7//+9//+139997/+67//+4c/evLuO+6456H777/mGiCrXxCxel18ySWbpi598ZHNCLx3o4GjidwpgOUp2/LJghuLaba9+Nwjp0+/cYoMyJLzXwGrQACFwjHZ2QWRFRYcGguwkL4eiz25sYkpvgzTk2Ft8MorT2HCvXn4C8y201U1RXmOhDhUsumEwOpaUjOnegkN4dvvH6EhfITGjy6neQjzMkxihQMrrIAfSo0KrhAeSxNeiTsdjCsawqf27Hlq69Y3DxOwPjtyasehcS0E1pc8ZC02pZAaA5YPKQFuC7DU3Zy6yybfFkXpFLKiBlgqGTpeXgy3BCRqIeael8e8emH2xEsUr4aOv5Nodf/9DyFs/n/KXvhMjs8+W4pjp2rn9fKLzz773HMKVY/8L4xY9d3v/sd/0CdNrHseeujbRKxr+tzJxJJQFpIbehOxJk7d+ezi6aW5SETCll6zlnC0Ais+KcldTgoLs+3jk8+e+uupYzBNrCxdz6+ggL1DLnVVwEckhWWuEqpq9/gmx5WXY8418WQw27Zu3fDmweMMrFM7dj2alZSgQjWdDFjdHY5A2ayGefMBLBrCU6eOPXfsoyPHTm0/NFINYQLHr6yw0K8sArDwkKKyaHB5w02eJXdtlQb+nj0YwQ0HDxOwvvjiCP01jju6jT+VGOmci1qF5UwUly7RXN2zvg4NLL9P4lcSeE8MaruEe9JHimJWCj9sx028EIVlACtRgJXq8ftZX+3YTbxifTV06NDx4++8c+M193/72w899BCAdde/EER/+eUTLxv24r9IUAFUjKpHFKoWg1TfZVqxQWMBWCDWt799g4VYCllCrE1TX3hux9zS3G5J8Sm5kPfp0Q+s+MpZDR+/feONb//jsyOA1YkTCCsRsUYiCx3zzZfhK9CWRofwioHVPT3YJdSm9xvm5OTkZQR7Mq8IrsZu2LBixeHjmGzHTtPczkpI4EpZnRBY3fzlVRWf0hBeJ0N4Avsnjnx0WhELGHH7XCrlQKxpYKXFpGWmZUK9KnFlZNryGL4ivBrbd8PaFStewxB+gSHs/MDyBwHLktugFFZRk8DSr1arLP6+415vYwpLGcqVkL6au3n3y7OnTWR9RbgaQry6k3h120MPcaHjf93xL1n1++c//ymY0q7fX/9X2eLvfneHxpRhhsK6+yYDWPALh4hbOPSCochtgMaa/TI5hTndsNklNrZ7jHaZohVYKDRXWVXxyYfX3XjdX97/7ATh6sSRL46QPjjNkfcs5YwgZb2oyFfklTg8DJ0kMqECNLDQ5Ew3schTG3jzTHW1SuOK5tqeDRtksmG2neC/lZVBwILP2dmAle5wELC2ffKXG2UI/3XiX0cwhmoIlUz1qS02qjyKSg5J1v8M/T/pzsCKiWFye93KF1SwMpHPuFq+du2K1147/uc/f3GCh3BAls/XEmBFJbEALL8orLBfGcCSGBaSGxhYTkuE3vJ6EdUCsfAzu5Vf9msRSwqWWPHBwMLeiEISWJsfeXHptIm9RV8NGTKEFBZ4deutt95zD0od3333P/+pgun//KvY/yJOxf7fd1lW7SBZFUosFlg//NFPSGDdetu3bwCwrrmTNNaQfkPOP38IkHWRSKyLB+98bvHq0pyuSdAZdPZFO7Dovaq0Zst7H7593fU02+jU/9eJE/T5xLFTB3aNHMkSi6u6YrsytpnDiFZFvHqYnaZen+41yPsMUGOAKZeVAVxlWde1XtnDvgxNthErJrz22p/Jvjj2xvZDqwAsL3CFUg/xrmgFFlswsNIcDndlzZaTH1533XV/+cdnJ5R9cYJel0Bfm6W2VZzaY6hPYqfKM9JZbSrnKkupK0kTfT6IV33zRwyf8MDvfkdDyH9qJIBl4VXnAxZhJlKEDQMUCViBysr6+krzCPhNYDH8JAbfUcBiY2rplDpcoap8oAFETk5p6erFz+6cSv7gFVIJRjmEt91263e+I7j6yT9/8uSTPyL74Q9/yPF0mOn7ffc/wlj1HxLCMjxCA1jX3HknEYvsAnzIJh0iljiFriSW+8ZST7QAyxEOLJe/suqjTz7EFiYAS+zIiVMy3YzZNkArLe0eegvMOcvLh16UsOOCWpY7FZrqSk+1q/rm568dMWLChAmYbccPHzywaxXQyG2rCINpMZIIEq3ASkqS/ckuLECkZWfGYG8TDeHHf6EhfN8YwhPHNLEGZBUZyJJ3XCOvLUE4JVFk1a5ICodx2pqZaGtZrmBc5U+aNGL4gxMeIGIdN4YwywtcoVxW5wGWav6qPUJkI/hL0M0lEED93kQ+V1PcHnYJM2T3gC8QqK+pqqqdBauF8deqsvqAP9GDx0vRsXfCVoe+PA0spwVYmV4P94AoLJy747kXpo6W+NUQCKwhG+/cSMB6iIB100233E3A+hbx6knm1Q//+7+FVv8VFK36j3BmCa9++CQE1ndMYHEYa4jYBSjfcAU01ujZL++GU+jACmF6ZwBWXun0oy9++o+//INmG023w4cP83wLIhZ0woBC0VrosUYuTgGvGSK3VPOKXRgDVwMKuSKDRV2xM0jKgCbbpOHDh09gZB0//OaB53m2+Xz0cORpxnQmYKFDUky8v7Lm9JHP//EXzfzjh09gFIVYI6WKTha0qi4XI4UNRUbJqFkMIDP2N480c0G0R31VXxnBZcsefJCG8DiGcNcq+is+b2JnBhbxCgKrJFAZqK8vJ6uvJNmUooBFAovGinfmBcprquZs29dQvb+6urqhmj81NOzbNouRxQ8oxPL7IzqZX6JpYFlKmiBHhRQWBNb0R15EAAu8ugC8Ig208f774RF+56Z7brpbgPUtKKwf/kgDKwxXQcqK7b9YXxkCC8C6XWksDawh9AeHssa6eNpSrBRic1xKqpFOE83AcuWM27z75Pv/eJ9dwsNsWiCsGjlAm1AL0w6zLStDHLg0bopKyoidxSyVij1AeTJBy/CvmLgidTBckPXaaxpYGazdvJ0NWNmZ/pgkN71XnjryOY0hDeHhw68ZYwhiGWMoo8dEyuAKx6pLWBaPqDQs0jwzdl0awJflilcMebWMbPgaGkQeQgZWnrtTA4vZkhIoL6urYtVUW1VXU06aCTEsKCzUwiN1VVleV7ulYv+ivfOWLFkyz7T1KxsIWXQPDx6RiQVoRR+wuF8JVgjnbt69EwH3K6aIRyghLFNhXXvttd/6FkksQ2FZkaV11XfVhY7v/ocGFkfcIbAArMcYWLezxCLTxCK74oreyG14ARIr1qEVVpQDK9flKpy++NSRzz6jyXZcAeswAll6uo0cYEw5JbhYK/jQHgdHtuKVllbKZLIdev75XaHyatIaOiaDW5htBw+8qoCFR+t0wCrxZMYT81fvUEOI0aNXtYJ16rE3DrDIGjnSMnzAkc8YyCzDYQw2C6704qoaRAzhGsLVmjVrJg8aMYKHkF3Czg0sXiF0YBv5top9+/aRZKrYNqeqPKCBxeoqgX/fsH/RvAXr5s+cOX/mfLGZ89fNWLJ3ZXXFnNqy+hK4gSqHNKVjM/vDgRWP2kteX0ZC6bjVJLBGX3xxrysuu2joBQgtWRUWAUsRi0SWBLH+WyHru5pY8uW7hrQSdaV40MmNUQAAfYJJREFUxWmjt95222OP3UC46nP7NX2u6dPH4BW7hUOniMR68ZHVJLFiU50xmTilC9JiohdYKMWQN2716VNYINS4OniCl++IWEDWqlUoY4JJN3KAJYbMS4e+LKWt5AorrVTkZZfpDm4QXJEthE2ePIL0weGDEjEWhUX4S0tHnkpnAFYaB7E8mc74hKyRu7brIXztteMAFnI2sHixfdfzh9QQDrByy2pFVmwZQ7hqlVWf8hDqMVyzZiFdFi4cNGiEDCG897wkTo1oAljOqDkRYXIm8mcs+MUmpjj85bXbqhet38tGmmlLXSAl1elEU3JXfEJCoLJuzr7qlXsJVzOL/02Z+mbmfELW+pX7ttSWkchyqm07kcfhS7OIwPKg51HGuLkqxf0KAtYFQy9giIjCuo0VlkmsMGRpaAXZf2laYYHwRz9hgfUQIlg33E4GYvVBwjv+DJYLIbIALEgsxN1jCVhxAFZJdnQDi6ZfKU23N04dO3js8D9pnjGzjvN0e+M0thbSpMHcGamVAubcAD3RLJogy5RWI1cFRV6s8opwNWlhfzoWisKCQ8M7gXySLUG86jzASstUwBpwiIbw2LHDByGwjr/22orDQiwWWcysQ3oMTS97QLAFidORoZH2q/ZcddVVNIhrJ61l4q9h6rPCOnyKhzAvKbZzAgtp7YndHN1iA2W1FSv3zhDxNHPdkkX7ausFWMSrJB9+Xb0oiFbBtm7Ggr0r982qC3hoHFISGVgduntSA0uvssTFuWRpJS9HC6zeilfni8K6htMavkPE+t73mFjaLXyS/ULTMVR8stp//xcTDbwih/BucghvhUNIuLqGiAUTYhGvBFhDp/TWEmscASuGgYXKWFFznoQDqysqHmK6HXjjjYMHQSpBFickynTb/iqgtep5xSzTRdR+ojHRWFnpjKHnzbgLR4pNedV/IBlNORJY9OeQ1zBSA6ugkwELCisGwBq5CkP4pgzh8ddWrFBDSC+PkbXreQP8q8LGMHgAV0mxq2DeC602rF27Nn9t//4LxdZMBvOPn5AhTOjEwEKoKbGkvKpi5ZJ1xUo2zVy3t3pWPfw7AlZ8kqcSOJu3YH4jtBK5BcrNqgl4kpO7p6dLolbHveSkUGB5vWpBOKNw7uJnOYIFj/CCCxhYhCwC1g2GxPre976nNZaILCOWpaFlQZXA6r9xC+HV975zK0ewbr9dFBYhqweA1ZMObC1UEutijmLtmBsbmxgfVyAKK3rOk7DEUS5rmZE18pBMN5ltryFwjJTEL04cfPPAgaeeemo7zRxzvgULBT3RlCywCgM12QhXNNmgDFgbDBzYty8Baw3yiOjPHT51ehcBS6ekehlY0VtexgIswhUUVrrXnUFjoIfwteN/hsQCsZBnduLwwTffoEF8FWOIQXxeSu+N1DZgpNVWGUNowRXR6qpRA0dhCNcuz1+eP3DgqFHg1Rph/okTp7bvGleYkOTqrMDi0Dj8QcUrgc/8JfvnlBOwnG63KymJ5deSdTObwJXcaVEDESvTkdyBwEpOFv8PwEIdL7dKufbpnggo0vDybPCqF2oYE7CGXN4PEksByyCWFllqudDiGgYbriVU/RC3ePLJn1x7y/du+o5EsG5gWt1+Tp9zzu1zLiOrXxdRWuj+xU7h0pd3by4tzHPFuTkwe/aWVtFCTNfQa9EdnKbFWwqta2IxsGS6rTiO6UZi6+Cbb259Yysx6yk131hrrRpphLaM6pernjfcQMkSxUzbw8pAq6tJNNcGjqKP/P5rlj2IvMfjnOpeSQqrAG2QCFiksVJjUcyu5Sdac40229E4f5n3PDo5WRZ1LLxuTkfHEEJi0Qj+mTUWDeEXf0aeFGH/KRrCp155hcfwVZNaoqaMETTFqUpiMHEFV3rSpA35G5b37XvVVTSKCyfTEE547XcGsDKSJA8rfJGnvcYn9HHa8rj6jZPrPdJnT6BsFgFpvgU+MwGszO7OxHR66wqU1+5btKAZXPG9ZqyHxiJgdcd/B36ELvz3JZwfYgIsb4ICFgfawSsuN4H2SqVzNz+3cxr2PPeaAl5dcP7l58NVI2LdIMT6wXd+wMSCZ3iLwawndZKDxfRPPxJYEa7Aq+995wcq5E523nnngFh09OjSrwdMJBYBqzdLrOcWzy3McSXluRGXdZ61iqOCq7S0tgAL+2gSMmi6bd8OYH1BnMJsw84ZfHd4xUGyN9988ykttIRagi3BlCKVIQtEXPFEo6lmxVU+1NWogX3z+08mXjGwThyj2UbAkr5t8AnTU1NzWwcslUh+Fk/IJA2sOJlwNCU8mZleH5cBVRKLSa+GEPbaYRnBDW9u3bpVoPWqHkQZxed1EVYT+KY6xRiSnppEeopGsO/YsbgOLvXkNQ8+yJmjAqwsUn2dBFhWlS8VeRP99XVzGhYF8ap45jxyCQlYzszkJGzYbBGviFgLFu2rLevePTP6gOVnYLkgsBY/K0UayCMUl/ByhJYIWNcQsB677ccg1g9+IMhiofWTb/3kySdVOIuV1o+C7MknhVU/EV7d9APi1WMGr24/h2jFwOrRpQvhqodWWBLFki2FBCw0gk6LOWuStK3AUhv/fADWrl0A1gnMtt9htvFmv9dYbK04uAITbitDS6bbq8+H2quKVa9qTxDzbBSpKWHVBProT7i6qu9VA/sOzB80/EEDWKe3HyoVYGHPjxel/1qpsDoAWJgT2QBW1shVzytgMbFWrNhAIyhLhhjAFW8e3HBww4YNWmgZWktKh6qLJePqFQNXAxdiXXAZASu/71WIvrNLDYElqe7HeW9OVoa7swIr1l9ZVrWten0IkOYDWFBXMQ5fZc2WlUtaxCu635L922pKaFqAWFEFLDLyB115KOP+8lTyxnpfMYWBdf75l5NPSAaFdcNjRKxbb/0xaaxQZCH1XWTWj8J59RPYtaKv6J4/fgx2+0/hD8K0wiJgdSFg9RRijWaJtfO5xdMLXUk5OemMk7M3Lu0CrAwEjbVLiA1+hKm12J/MtBJirWCRQBqBJ5yacaH2Cm8XNJTBKI60IC170hqEr8Ar8RBHDB/+APOKnM43ZJUwSwks5lXnUVg0JbJFYQ0IAtafMYRrZfQOqyEk28A6Sw1hhFF8xZpyxbgi91l4pYGFFVcLr5DqfuwA7x/3dVZgBerrZlXs3zsjGEjFAizcAf5iw975kfkUZsXr9u6rrS/pQGChrrUVWAkCLL/Pl5Pnz3MVlqJs37RLrr6495Qpl4lHOOTyngaxiDO3PfZjqCyRWewcyprhT0CtnzwZYpBV9Av6PfmPwBvd6zYAiwPuF553znkcw+IgVhcyRLFkmRASi4g1+8VHNpcmJOTlOmNkR79ZNkMDoy3joR+jXYDly8oCsA6Z/gxm24axY8eiqAIO0gpq6h08uGGrMOspnlZ6emlT2UKyCD+QXcHhk4avGS64GtWXDOuFgxhYNNl+9+fDBw8giSgjwefDlmqac7G5sSjS3xmAhXmH4tzSycZYJzSAReO3loZu7UE6NPtXQGexa6gHsZEhZFz15UFcM3z4suFrMIQqKNi/P/FKCyzkYT2/ipifI8AKPxe+LGA1fV7jdyElrLBXGT3SkH21JIxHBKza+sxkR5LDU1+1bdGMFvKKiLXg53Nq6rOxUhhlwMrx+XPYI3zkRfIIr76YFRYDi6wfiHVnH0SxWBwRsXCwc6iQxdC6FjIqxPh6JcZYXv34x1pe3U60uv08kljgFSssEKvnkPMvYGCNNhYKcxLyXCaw9MpNtAOLZ9vxCWvHsm3dsIGxRZNOiy0SCaAW5pyU6eVJZiUVz7S+ilcThg8HryYNHCXX0vX9R4wYLurgz2ojXBYBy59Fgll4FZub0ikUlgZWuhVYSqUeB/T7AvtjeQw3cFBLRCv/LGO4h8aPPr+yxzqIe9QQ9s3vLxsvycCrUWps8/sPgsBSCgvMfx7bMfOiHVg6UVRuRp8S/diKU7tl3/554fGpYgNYySVls6rnhQusYmS6zywOy3MoXre+oq48EBM9wEpQwPLn+PPQiHDz7hemoVhCL/EIobB6Xn55TyQc9LlGNBYTi+02hpaE4AGtu29hZl0rlBJUGbCCG/kDAOuxX/yUeXUlKSwVxAKvuvTswsTqR8C67DIVdt80beezi1eTxEqSOlEwXWA/CoHl0y6h5DVIFGv52D1j92wlZInU2mBKhBUHjQm3Z+seq/Ekw8fA/HyFqwnDRV6NGnXVqKuwPJjfvz8ElgLW7w6/yZMtI8+XRYLZC2BxV5HOAiwnN/sygXXwoKlS1yJAvoeGUYjFI/jaaxMmIEK4lodwLA3h2KBhvErDKh8jNWnSiBFCKyywjuo7St4JmFfLOOTOzH+Kt2MW5uV2HmA5HU6P31NSX1M7Z1vD/vVLImRXaWA549Mrq7atXBLOpfkzlsybt2RGOMngTJYFMiGxogJY8Qkq6E6WQMCavuPZpdMu4UKjOoTVk/QVE6tPn9tvuOF2zSw4h+TcKWTdpCNa3xNKWUAljuD3fvADzauf/lTJK+YVFFafHgBWFziF/ejPXXARA2t0bzRWhU84LichKTkGvNL18XWd6vYDVrLuCthWhWUkYr3G0+13K9YSsfgdX6SWkgiG8YSTX42Vmwiq8nmi9R+EDboTJkyYhEN4JfEY+u0kAtYECbn/7jUNLB8pLL/b5UJLkbYqrLNILPk7upRVI8DSEmvtBk0sBX0M4QQi1oQVExSzeOBw0I2u2oMlCbjNGCfstVS4Gk7f5edzABA5IbyvSXuE5BIefOPV57H5OavTAAvfp/gDgfryKhJXi/ZGzq4q5hgWASsuu7523/oFYTeYuWDvyurq/esXhBFr5oKfb6urL+neUcCS6WXtiAtgEa8Kff6EpLzS1YtfnIo+hL20Rwi7/PzzOaWTiHU7Eeuxnz6Gy2O/oA8WWj+QcNb3bvpeuBmkUrj6xWPA1YVs59GFPcJzEcHq15Pt8stJYV009DJSWCg+Opr35xTSzHGmms08PDrQ2FZomfdXeVgqsI+8rBbd0Rm8SpiRoYGliPW71+DQQGLtUTgau3z5WpTdE6MJNwJJ18vzl/fFkc+iajlQRapg8mSkNEJdEbFIYOVDGowahXnYn2HGwOLic8c5hJWVlZGTk5WT54qVJki5uWjZ0PJ9YKHA0h2r9XjrSsSOdjphMcq6gRvXLwwC1gqBPmmpIGL1RVHjtRNMG4EhXLt2OVJBgfrlAnt2AyVwNXwZ42rSoP75fVl3KVyRwCJgaaf64IFXpUJPju592NbX15g1BStrp+rG7oczTp6fBzWt6mpnYavNjPmNbLVhYKUlx3hLyuZU750ReqPiGXurt82ataVh/YLwXyGzoSTZkdwdYqfRFvdny0KB5Uz0FmTzGqHPl5CE+igvTLuEkxpMYF2Oo2e/Hj0ArNvJm7vh9p/e8FMw6xestBSytFnklAVUsF/8+Be/+AXpqyuJU4IruoBXSL8ij7Dn5WwAFmks9gnRu/7ZR1aPc305wDIUVuuAhULIBrAOYin+td/xOqGWT3tMYnHlPRYJZMPpxxGDDJs8eQSjCqUE6P1/Gc9JuDKSjkWTrT/zagRrrwdIX8EjRKUBVCfNysnJUR0sEHQnp7D9gdVe77BNA0uIxSkhMoZ7ACvWUctpBIlCJI5kAHkEzUGcTEOIAeTiMbAJy4avmYzsq77iKDKvJi+kYV4mTvWfVRRwpBHD6hTAcvora2q3VcAXnNF4roIGVnqgZtvK8Jj8zCX7t1WV16NnUdhjrNvbMCvKgFXg8/hQfzDBVTp3x3M7J159Ca8RXjaUeQVYASM9u2hiafspYYu59WNlP/hxKKh+YHBKG+Hq9kuv1AKLFRYDC9F2yKuewCMU1mXGOiGqzJDCiu0UCksD682DEmchdQCfZaw2UlG4LF/OtHkAKQkPPPAg2bJlw5WtwUQUVD24DL/BdASuaK5BXwmvaFZOkocQgXX4DYkXk8LKy2Ngccw9Fj3CUtoMLM0t/Zq/DGAx9HkIMYhrNyxnl++qsXD1NmCFdPJkGi0EzAlaD0KF6hFcZnDqQTHUkBk+qb8QHx5j34H9pc4F9uSoCNZxXiPkWszcq97q/rT1dYZac8AK9cgj3UZ62/A+m/XYx9worpRLGJOcnllZVRGuohhK5f7EQNW+vevCWLdk/5aaAP2bogNYiQCWV/Eqp3T64meXErDQemLK0IsuEHF1ec/zFbDOJf+No+UaWbffztB67Mc4NLYYVHQAVFZWiby69NJLr7zyPAHWeecxsERg9QtWWFMgsQhYFyMVay796xI7gcLKswDr4IYVksPAoWFCVN+xgipy/HjZapAiFpD1gFALU+tBY5rp2UbqoX++uDJXwR1kXvWfBGBBpGmP8FWJudOzyHFL4532U1javmxgyYrqBDjQ7PMtX84KS0XSBVkPiD34wIMR7QEewjWTB/UfKEN4lSxmKIUFh/sBs8b0Kml30dHAagQMYcBKJIG1pXrejMaqLgQDy+urr23Yuy7stjPWV1RVehz+mm3rw4DFQayOA5bDAiyR+l4sEfrcCUldXYXj0CtnE/civGKKeIQkeXoq60LA6kOAIcpcePuFjK2fyoV0FqTWLx77RSP2TRxshCsClmis81QIyxBYTCzu+DWUJRbXSp629MXF0wsdjlzu1a7MGcHOfCys9227wrLuJcT+EbLlCK3whFPTbfnA5RJh4SgUCoayQjDswdCJB20wSQVekEA6UIWviFdYIrRMtu0cLyZgob0APcNuTCxWWC0He0uBpSfVGY95iJnAQvfJmKCguwyhrAm+pmJ9y5fnj6XR2yALEv0XYpUPQ/jgAxZsBQ8hV+ibvHDhQOUNksBCOfz+CwctnCwBQvLbjSQsFlg5vg4HViP/K+tt8LPTX1+3bVEYZcJkkgDL7a+vjeD1FS9YSSLKERlYxTPW76sKZEYNsFJ8spOQgJVTOHfH7hembhKPcAp7hMho6Hk5w6SLklhsWN+78Morb7/ySnz+qbZgSGlWWYz1FZBFdzxPEUsUVhetsLhHIaLuQ6dwOwqsE64uTRJgedRxloDVJoXFwPIFA4vjVStWcJhqLUi1nGnTH1uXBw5c2B9eHQuqYGoZc20NqstBGXC+O/bisL6aRApLRbBewza7E2qycbFzmmxeBQICVkpqyhko0Q4Hls8KrDc3CLNoCHmBYoQKrOdPIob3H9ifB0OQFTSED1qHELgyVleNtKz8/rxCuEaG8DXhFVeyJlz5OhxYjf2vIgGrollgaYXlKSmftb9RYHUrqakIB9a/zUCye8cByxEOLH+BKKycUlSWAbDgEV42lHlFwEKCFHhlAus8HJBZF14IYF0pYuunuPz0F3J886cKUUG8uvLSb15Jn0xiaWCFK6yLGFi9VTeKUlfzCuuMiXVWFdaGDWOX6xC7rMDDsesv0adB/Wmy8Ua2/P6TaMKFOoEc0VrDtFrIM00la0s2A8evdMSdxMFrerKhWKnP5/Wmp+Ppk1eYmJubeEY5a40BS/WiccWH2JkOeag1ASxG/tYNW8eO3UBDyF4hVgP7A1dIVejPxcAEWcNJbC4zPUA9hhjBNZOI+AsVrlS2w1gAa5IhsGCHD6L8IUr9FGblcSkAt6V5Z7S4hBZgye/OFFhlc/aHh7BmcpjK4QjURQLWfAJWeQcCSyQWTzIkYXo82dlaYZVOX/zi0mnSnf6yoQSsIYpXchBXzj33nHMNjUW0uhIqib5c+k1C0E8v/ek3f0oXdbC2CsIVI4t4RcAC6AxgnauysAyFRc7oRajtfhkDa+oLz20el9OVnBtPkwqrHYDVrgrLiLNjCV6INQnaaNCkhYN0ALivmb2oDWH3EbwcDyE2SqbaHuEV+5LiEI5QAusBEgfYRagEFnjFLUST0Vw08Uxjfc0Ay302gZWeHgysrVu3CrB4DIfrBIZJ/ddKugJkqoY+UjyMZVWxNbqC9EBWV6OEV2KcxMb5DsIr1P45IA4h8cpdUIBOa6h8fpaI1RSvgoCV1Mj9WgssUljhwCoWYHWLCKzi+XsbasuzOw5YmJf4w07UPkUCZiaZl56Fq3DcdG6fKt0nVNYos0r0VRfiFYB1rnYKOXQuEutKBtGll2paNWqXMrNYYl0ovCKF1aVLF5WDhSi/agJ90dApaJ9z8eipO9E+h7ybxBR3uyksmsz6LviqG2+CWM3CKuhhEIAOU1gHDtBsM1YGx4JYD6jcBJpokwhZgJFsYJb8RtnbzIX5OMQFnxFrgleZjgxy28kNYo0GXLHA4lKjb2pvhruooi8rb7BPR4dDna8jSqu51xMKrFBwmYs1Ymcy5FZLViY/YYM2gJVmAdaBrQd4yw0nM+whjTVCEWsEu8TC8/y+fUfJhoC+ylXWpaMBKiyoos4FNg0wstSN+8rugclrhmuHEP1ydAArq6CgINOTGSNtDZW130Q1gWS1UGC5XOFJmhEA5nB4Kuu2LApLrIoArFoDWOEuIQOrGyus8G2GUFjYTRijz6emFOBZMADLy8BKFWAxseiv50rtvmlIwoK84aQGCV4ph1ArrHM1sJhYCljMq29+45u4fLMJZF3JcaxLr7QKLAuwekJiXTDkgvMvGHoR9/u6uDcqJW+eW+hCo+2UdlBYfFtJmk/RP4s3mKa0SeuB5QsH1h5FLF55Z2ItHNR/EAMLKe143xdvb+CogZIXGgwqjSvhlTiEjCvxCOHNoEzDSCuwUHKYTzCvu23AcqvjywJWmg8NrlfpIaRB3Ape7enbVxNr+IhBAFN/HkKmvR4hHBhFq6nfCa76DlS57/kbJpktHUVgqc6HcKoLCrIBrGQBlvssAMuauN00sELfOEKfQLcUrr6wYN26dfPp0kjiqAArOdnjh0vYCLBiIwOruMOBlWwFFlchEmDxIuELDKwpmlfGCmG/LoZHCJmliGUILImk03HpN9i+qbgVSWFJ3F0JLFNh6cRRIRaLLALWFb0JWLwBujDJEeNqF4WlNyQy+BxWhdV2YInC2v7UU09ZFNaevmOX02xDuhCINWjhoIUceM+Xmgt86FkV2TDNBuYrdTUJ8mqETDYGFqkD1fgwKyPD65OuWYRfbxo3lT4bCkv/3NJxCrVGgVWgKo4+dQBDyMAC87lphNZYCAFiCPPzDWL1bWTgZFyhq65iFcZbMyGv1opCVbySRVbuZYSeQ5mZHukbzQpLu8JRAaxQwYVm2dsaVi5aD9s7L3xvjagkAVYKgBUedJ/ZFLBEYWUmO7pHE7BSACze+YyGzxBYQ4YGAUstEvYQlxCHIbAuVLASkfUNbd/8RkRkXWoIrCBedTFi7j1lnfB8hLEIWL16I9kd3XMcAqy2KyxBHotLtPRuV2BlGcB6ygAWKYS+fScxsR4AsRZOYnnAE255X8MsU4w37u65yqjXQMoATiLW8QdNHjQZuBJv5gEQ66DZZZSj7t4C6aSMTVdtBVZjCutsAmukAayn9giwyK4yNRY51oNYZQFYOAzqR8DWKCNwBV7xBk2uic8jqDxCRNyfelV7hJBYBT4LsLARJGqBleSvLKuds2Xbtm0V27btq14fnsZuKCw68/01kYClXMJuTSiszJgOAxY2QAcDC5uK6W8Xlk7f8dzSqaN797pMuqeqRULx1HoqiYU4lmgsRSxxB1ld4dM3LBZBZX3jUiWwLtTAOldXalDIwqfzzx8ChXXRZewTbmJgkcJKjne1yRXhLpNO+QJYpatgdCLKx6Wn62oNLQWWumuiPsHQUiFrQJjCIpfwKjQZljRRElmTeL7157nTV6WRWoi1x+CVwlVfzMqBkniEFoSq1zNPtt+xwMJk0z1GEYORFkNozcrdc9IxXi0bt+YUlg6+qxO31SesFVg4E+lcTDFjWAbztWPNu3FArOGyjwkDiEAfDYwQKwL1DWNlxSZlG4CrCUKrCRNWoI/YQRZYq8SrBvIN06+3sRDSmVvkGJYGgPXNoHFgWSHn8gTKy2rY6mpn7bP2nogArPJZkfKwJOgeS8CKUCpLAyuZJHuUACtVgDUOee7TJva+4rKhQ8Zzl0AWPLJ2ZxDrXE0s8Oo8K7BCeaV8QxNWEF3hDqFWWAaw9ErhRWcDWJ5EJpa1RE3i2QWW7NcVYsEtHD6cgZXfn+QVE8uAVshEk1QG5prSV9gjx13VFbAgsVasEHUwUnc7LPIxsNBKWvrntAVYoQrL45ZDTtzWn7ChwEpPTcGpKMBapRTWU9olHCu7cgxiDR8xmRND+gqx9PiNjUAsWdJgV1BwNWmSXrDQ0D+8QgSWhj7nhvgEW9EMLJcL3+d5/P5AZSAQKA0QuWorImwVNIHljpjproDlCtREAtaM9Qys5CgBVmYaA6urw4Vy7i/OHt0bHiHx6s4haLnVT23wE2Bx4B2OYYjCutQAVhixlM4CrPCtwStjX44CVs9ghSWpDQKsS6Yt/Yhcwq70z25bsJdA5UfLbYfTWOp3nBVgPRUcwxormT/5k4brQJahsDSuDJ1gcWt4PWsDsrqXS/LVZN6JMnz4g8MRwJ/wGg7i1VaebapPH4hFEou9Gq/qT9iOCsunTOUptRlYPP2ciakpqelQWJlBCotdQl3hQog1SBFr+GQCVj4Tq68UaOBKFzyMZvYCPGlGlSTA8WYmyQbhNRAaRGTQE6/0EDKyuJlthg+bbH3tBSwzYtE4sLQ1Baxwc/vy8hJyWGu5cgLltQ2h9dxZJQFY6Y7YpMpIDSgkhpWITPdwYBXPWFRRV5+mgBUK2NaOxxkZA4t1eEomV3k0gIVqowhhcevUfndy5y3GCF80sFR2wzkqrSGIWBFgJV++oYGl/EGV0nCOUbtPLxT2VEEsKKyLNLCebT9gCbEsIa9EE1gxZ0VhoYQT4yh/kg69T1bE6qumGWYWvskftUEfkwhUaznikr98klSgY3U1fBlNtGVKHdB027DhqVde1X13xKvxQVtBIfjaXWHl+WiC0IdOrGzV/0EMwxwnegFVIIhX6VLTnWNY25XC4mFcjoORxcR6YMKDGMGBMmSQn+wyQ2qxmy2hrXxVU0x2MjGuFK+GK2CJT4gyilv1EJqetc8XAViteqHBIdbGgaUh1Tyw5H+Sx9/n+Xx5Lqlv53DkBGq2RApSqQJ+SUmBugjVGkhhbasLpEQGluwl1MCK6wBgJcXFeeNU2CCVW5WQg5pEwJorHQl7kUd450Yi1p19+vWRBqeisbowsrqwwrJILDOxgSySvmJaKZEVFL7iBAkAqwfTqovK+VLZWJBYF1kUVhIaaLQm5Uob+ILoFV0s909US446E6tlwNLPQ5Qas4CAlRAGrOWc7r5BZNRyTazhTKyBPMvylTDgHyYxqejzWvqaP6kvfY+UobVGBboHSRcMV7ySuuY02V5RXQ7ZHkWJmYQ8YorL7SsAu9Ce0KFUZbMnRyMKy5gqZJjGWBBtE7C64a8gqC3F6phX6bqmu6GwMIgbZBjpAonFxMIgcPEFDJpEpwbmC7PEg0Z5MT7Q3JlIhUMPoYSvlqk0kxEooLj1qVd0h8NDDC2SqUXcrjNDzB28t+/M+waGQsui2Pj0sYJKxQqbF1cJ3Ig2Q98UFTn95XOqwysuFKsCfo6EQNmc98J/DxHFCitC4ijddU5NCWYFPJA4C6y+JGAlWYBFpwnhKpPwScDihjmzJ/buNXTIeODqmmuuUT3k2TMkYPXr0rOH7NDRxLpQ5Y6ayLo0VF8pXgm6Lg3iFT8Ib8zRrDKSG4ZcLhpLxbA+QgwrOabtwErUBR/8bPTFI2Etp8ZVq4GVGB8BWODVBgLWhuVj8xE2HsTEenDZ8MmoJcdRY1m+UgtYowhW+CSkyuf1xElSMhNzbdkEEljLeMrRTONKm1u36v58jK1Dqw6RU5OHFkgELB+vE6antglYbusRMpNa83+AdQsFVmr39O7paekuA1hWhQWXcLmUahCN9eADD3LBaGZWf42sgUL+fNlezp/XwpeWrUx6vUIvWXDVnhFrl28Yu3WP6suqBpCFKndK82XIEXXA0v8PAZbcGPfLrUSQKpJLOAv7ARNKyms/CvcJ56O8TElKZVWE+6KZalmJvJt7OxhYRKxMTmtIp7+sOnxNhEd458ZrNl5zjYVY/S6XzAYUMe6hVgqVxDrPku0exKtv6mVCdgvVEqH2BpU7eK5aJOTqMv2ka04XSW8YwhLLANb0UldbgKX5gpPDX4LwJFZWysrKA36P3KDNCssCrFcVsJYvR+1eHLqgKKYbb89dtmayhLEGwhscyDmN4swgaDVq0qhJmldMrBHomLNGSmZNRrE6ptXYsShhLj13uNXVrl27Xt/1+kuPFmWgohMBKwOhY9Iu7aGwZFLpk7WtLoH+K6bCUsCyMt/wq5cLskyv8AEga82khWobOYDFq4HKS1TMyle86i81/YRZksa2ZvjkEZNRB2OsGsJXZfye3wU79JL0zm6Twmo08yYYWLhdOLBaJLAEXrAcdUcUvIqw0qeB5SOf8b15ocAqXrCoYlZNWdW2cHeyeAmXSOZ8H/IJ41TI/8sGljfeqRQWN9zF0zCANWXo+I0bhVfXXHOnJhZpLMEVI4vtvBCnUMXfgxTWL775DcvxTQUssI4dwnNV9T6WWEwtIKtnv55DCFjnK2BNtABL74w701cdBKxAec2sOchb2TKntqbSL7ew4qrdFNaGDcsFWKjbwBILGkuIpd1CmCKWRF1G9Z0ksSsVfBkkEms4b5ZbM3nSZPZwMHu52YKlsdX2V7eT7XinvDIrL4GB5W0HYOl3c51vJrfik/ZM/w0hf8kCrFTilQKWimEdsCBruZZYfceONaEP6oNYCwcaJhm22jEkXi1Xu811IdJBI0YgloWdOZMGSfIuxnCPHj+CFsbwnV3llQQsd7QCK1j1SqyN71dZWxG+U6fYAqyyo+EyqnjdvJX7tmyp2B++gjhzXsOssoBs9orxdiSwQKz0zJT0lJRE/vMmsMaP33j/NdfccP8NLLHu5ECWimHJjsIu5+Ji3Z5zpRZZjS0QKu/wUmsAS6q5M7FQ0v3cPl369ejTQ0u6y5GLNfQyBtbOjxYTsBwxcV5JRkhMbDmxnImhJ42nsmbWtupF6xctWlm9rbbcw7PYKU5hcEJjM49sMRV8B7BWPc+L8gIsddCE28DzjYg0SJXAenA4zzYdhiFijZJDIjED8xf254R43o9DYgtbphcOWsj7p/VE22P2s+I2YU89deCNU6dPV5UFCFjxCV5Znk+XhqAtUaZNKSw6VREIdqlHaaVjbv1LJrC6i8XEZ+gh1GkNQQpLnEJNLOhUIAvlGAYqbPVV8B/YV2mt/lI3ayFzSzJ21aIhXEmsy6pxfIXHj5hFQ0hjWFNZ5AUKuMOwO7hkcosmasiIR27Iar19YoqZ49ZSgRW6sugKQGGFZWIZwKI366ot4fufi2fMW79y5aKwDmHF8w2BxcBSiyQdASxJa8hEPpILae4JwcAiuwEGZGmF1RMhLFJDoJWkNojGul1rrAuDFdY3zaC74pUBrHOMkLuBrB59+gBXEujviXaqUFgWYLkdRHjpl9M2YGEzw/55C9bNWLBkffWcusp2BFZCVpaebVslYMwtqKCweLahXqZJrGXD1zCPlM4adRXzatRAOaRilvZ3pOIfT02+DhlHwY3BuDnfgTeOHTtybEtVZWFCEoCVUdR6YLl1tQJ5I6cHVLPJpce/LciKCCynuISreD9mkFMoxVrZKezb1yQWkMUlGUZZZJaZKcrlw/JBq4UDmVr5nJLVV/uRKvtNDaF0tn0KQ3jkVG1ZgHSLLyvHl5fRGmCFjnjLgKVz3FoJrK6RgWUqLL9/XM3RikULQpRU8cx1M5YsCC2zTNfO+3lFbX1JtgJWXEcCK15Xa3BbgTV74mgNrPvvv0aJLMbV5Zx6AO8NwOohuVjnoE8Xaazbr1Q6i3BlVVkqX1SnNlxq3ZJzjmYWu4V9LAY+DulHCmsoK6yLySVsH2DJQAfKZu3DP7W4eD757gAWDbwCFic3xLQeWMonPMDEGrtVCSylEMZyfuPA/ppYHMlaqEqgDBxlbNulb4RbAy3zCr0nRpm3kOrkllahG/qi1N2bB098cfLksdNllW4GFkfd04kErVRYQUF2n98fCFRWlpfX11cGSjwI5bfWJKMhGFgxMd2dkhmySvuEBq4MhcVLhUSs4Q/qutJqDEctlPES6PMnrtQwCiM7cJRxSL/Hq9Qv8cMe2V4g/cO2bsUQfnHyCCRWhisvr7UKq+kRb05htZBXwcDqSpdmFJY3I6uy5ui+RfNCO1YUF88M6aNaPHMGvaFvqy0rkY0T2TExZnLrlx50xx+VRX53MLBGE7A2AljfpgMK65o7GVlKYAFXuPSwboHWVRtuvzAohPXTIIVlZLlz54nzTGBJtjtAdQ5f+sANhcIaQsTSQXcGVnI7AatmTrWKO67b21BbbwEWb61saW/CCMCKd2coYB1QadpchA5OoZpumlgPmAphslG1KajOgEaTkUuqr7JWItC7DWWL3NoVKw5/8cXnn2O25QmwEDpuBbCSlLSCS2RETHz+osrymqqqqtqq2pry+kBJ65ElwOrKf0oDi4SgN4EVFso1mNufzWXCQboifn7/yQb0uVDfQsX9UTKMV6lPV+k3AMuwqk3m8judq8vhQ1l2ffPwcQzhKfKriVUZorASWwms5sbZeodEzxkAS90/XhV/bYnCyiZgxSVklBKxGlaG9/oKteIF837eMIdGQfHKE+MUVH3JwOLtz8l6kmVmKpVvAosF1kMPffuhb5OxxLqTgKXqy/QQkdXl3HONWn7nnWPUmbnwQiDJpNU3fmHii1B2qZnVYMKKH0FAdbs05UHgDHmrQ4aIwlLAynUkS7WGMwlimeFNiRgjFa/EbGeE4mT1frpVjCSOxiSqtKyWjqUGobaEvKyRhw6ZEZgNkkdkrHKp5p6Yb9J8gpGl3ZqB4g+qGadmnfCKyRRCNJR34tbGRrfVFa8d/+IzzLa6Sj+d1Rm+oqwCnzeme2pjwGrsxNMay60SYsXQUmrOtoqG6oZ922rrykoyuzc54hHMekvdfAILHoyrdKzKZXFBLJXYoPbmLLcqrL6qhceaB03qm8ga1bRxPYxRmv59BzKxiIEoAshDuGLFiuNf/Pn9z08SsB7NSshw5/nocGNzNmqiSsAgLq7p8y3esn3FVUKitLISu2eMS7DxrwOBkkzOt5E9jAmN+IShA9mNTEZRBe4DTa4SJtEA5xWOq5mzb1GkDtFBvFo3b9G+WWX1JZmOmLRsyQUyE1vPZI602ZoB1mAB1kO3MbBu0MkNkn/VQ3jFxDonrDIWao9e+Q1r7P2bxgf0lamwggSWEOt23UMMqo5sCIiF3oTtDKyMQJ2hsBhYniBgnVkmfRiw9Dohz7Y9hk9oTLiBUuWk/whNrAdU3XGecQND5hyapppKKkRiIRyD2dZf9uxwO9Djf/7is8/Yn/GzPioq8hV4Y1JbDSxXELCKKqu2NKxcP2/Jkr0rK+bUBBSwUq1KS+RZa4CVSYJQAYuHcPsBrbA2bFCj119LrIEDFw5as0yXcVfV7xW0ghRVOLCUylJDyFujuAHPGnSsR7meP/+ZgEUKq7woi4hNuMrLaQOwAvXlNXXNW019IJOIlZlJXgQdja0Sho5jy4BVHASshMLy2m37m5NYxTP27t9WV5+dTC4ZAysFwMIMigpgJSTkFQqwBg97eCN4RQrrNoNYd/bpEQwsKdtgAZbeV3ipMCtktfBSZUZdmXMspUvPIVwJqW6//bHHONJPyNp458bx7Q8s/NPJJWyYJ9sT1u3dh/5GFmA52wwsFJjZZaYRqS7qMuEkT5REkyKWEYcxNQJi6kFTTnSUVV8txGWhLCEuxx5DLmgu7Yv//MUXXxw5dbSs0scuYQEDq/GISvPAcrs1r3wZvvJZ9NY8Y/7MmevmrayoqsxM5xu3E7C8Hg0sc3fOVpGpy7HIupZdwnxdo5UgE4ysZSaymhBaBvb1lujlnKRlNKxHz7T3dQwrg+ZFji/H12pgxbsr62bNqWja9u2r2Darrr4kOV2o7ff7fb7IyGodsCwKy5uRl1dadrRi/7xmgDUTwKolhzBZFFZKlAJrmgbWQ7feRmZoLJJYvI1QK6wuusoM51QZ6Q1XGsyyGDmDGlmmwpJwu1JYIBbh6gYiFoBFf3IjIQvEuqL3RJ042l7A8pXV7tsrwJqxvqIu0L7A0hJru07Uxkqh4dBwUXYQq2/+pMnDzUYvQW6N9m4GqmCxhFosvGJcLeQ9J4PWmn13eLIBWKd3lAfc3ZzxXBGrTcByu9w6F8mXlVFkNDovXsB7+DP5xu0FLK/X5xZgqYXCp7RjvYFotdYYQ16CuAo6VYbwd1bsWwaRR2qU+hJqXGwmf1J/bsJNQ8jIlyH8M5h/+vXKrAw39uoRsVoNLJe/vLaiYeWiRYtWWo8go18uqt43B83/kgEsf0lJCSOr/RVWAjJhC8urtqFwVnMu4ZJF1duqygJpxKs0OIS50QCs9HSJ1tF7qQmsMcDVQ7feeuttt6kw1p19+umdzz2UxLIUxlLIutCs54eA1TcutewlNHClK7mfq3KwGFm3i8K6gQTWY6yx7idikcYaPx7Amjh153M7oLBiLMBqIVT4n4h/r0Gt+Hh/eZXaM1U8Y9G2mkBKojveoVMZnIlnBMRgYMXEeY1VLiONaAM7NIwsTgHilOyruPeEVSEEuzUstXjhS619CbhAqlH45SRUgOdayYNGTA4C1mcnjp3aMb0yJ7ZbqjMO9RrSvDHm4kDo828OWAniD/KeuiIG1jw1cuul+VOYNYaqpoCVnIw1Qo/HRxory5BYQTKVQ+441PaAvtxRdiCpSwv0FbLMgJagCtSyQAtDSrzn6u9rsU8T6e/LHjSB9fkXJ46dfoc8wowEV25uTi5Zt254xjrppVlgqT0BZIGaLdXr5y1YsGAGHQv4I9Rm0JV7V26rC3R3JMeky64xnx+LHe2usACsLGT17I1UNiuUWAv27q+YVRdASkM6gJUSbcBabQLrnlvvufVWhSyWWP369eRNOVgiFOuhA+/nnWfNeTd0lkCK9ZUSWFeaAutcBSwl0hC/uoF4dQPx6tuP0Z8EsTYSsYZe0Wv0RC6RTMBKd7cKWCF1m5w59VZglZXQaWb5rcpbbx2wQKwsnTyqt8Jt2KBiMIOALCbWQElqHzTZ0kdV5pvMuMnoSmyx/hLd0ibdKtDqaxADa/gyEQissE6cOr1rHI1Wt9TUGK83zZsW0yZgZbizfBlZdGRAYRm1ANatb2h/YBX4SM4wsUpHWotikUIVhTUIUSxFLK4ik99/EnYWmirrwWXGIC5syiYZvFo7YtKINWtYYj04QQ3hsdO7Dj1axLwiYLlaD6yugap96xdIpXVWpsX/hnwa+aIOXIvl6kA6A0t2ubYrsEyF5fMVIXO0sVLKIfeasWRRAym/7Oy07qnkEUYVsJJcqgcFAev+h+65557vfOc7DKzbRGKRS9hP6atzOR/r3C5GFOu8c3QUyyjpd+mVlwabbDW8UBYJJWG0h0o/PfcchNtJVzGv2A/99rfvv5+IRQpryujRg2e/sHvzuEKXs9XAkteoS/YFIigs0yV0qP02LRvLYGA5nSyxslS2uwaWBGAw2yTBOl9lLGKty4KsBy3zDTMOe9/QTZ3hBUm1ho6Fa1RznUn9J61lzYENJ5ifw4dP+B1PtgO7VpXmxMJTi0kjNZ/dRmCJN5gRBqx2V1gIOLu1xBqgJZYIVQV8HPlaYylkDbK0zza7pyqpFYStNXTw0E3WuMqflL8WnXbUbWkIEXL/4tgb2w+ho4fLBVjl5rpiWwuspMpIrZbDbeaSagIWPTQUVgEUlv+sKCw31k3em9esvNJPa8F67MwpSaOzKaWjgRWrgcWxnaQEqYcFYN3LwDKQxcTq169HPynepxVWF7PMjI67h5ebCeaVlO6TEFYfVW5ZYljkDt4AXIFXgqz777+fiMXAWvryI6vH5bgSM1sJLJcbYYESvaBcWTerQWJYxTTtquqtS8wpunJUa4Dl1MCi2fb8q4ZDs0FCMDTZ1ObA/vmSqY7YO5C1LEhmBamEyWtCjbHF060/dsrh6D+ImIa6v68d//PxE6cw2fKIB91S01WGcptcwgQjiJXgN1zCfzsLLiFaP7jdeUws7VdvN4C1VvFKsK+IddVVe4AsA/tGNumDJvcjGI3gZCHWhknYsgmMrQHM1o6gISSNemDXoQH0il057A/mulytBlagtjq8EWAENbOgepYC1tlUWPFuJGFFIFrjxFq0r7YMKVyxqSkdAyzpcEy8is1NRNaR1+uNR+lIVSJ5KoAFXt1EBmIBWDdccydJrB49+vToYfiDiL/3MAPvxlrheayirgzTWZEUliKeFljfBq5+rIL9AJYoLNWXkEDFO7UzoYVaOl6yUuMP1JeV1dVVVdXV1dTVVM2pUDqheN286i21dTU1+B39sqy+skTqkbZ0NJ0Wi41NdfIGaJpw4hNyRaetLLFALGn5LKX71HyDypo0efhw6VlsSATVuVhNOpl4avoxrNTW3r59ZfeJ8nJGoOX6sTd2rcrKc9FpnJqSnsbtc2LiXWcCLD3lrM0SGFwJCZWzVIVdrkNZ4ugeOXU0MqAijZ0JLE7ESseO7ayswgFGVSy1j1zFsFhQ9tcth64ay9XvgazJnJXwYJDSsjZV1YOoeTWJW1gMzB81EIsZA9UiR37+2hXHjx8/zAIrAwIrV+/R02PXBICtZgVWSxRW8RIAKyYmOSaTI3kFPunbIwGNxsFvBRaub0ph0b/KVVBfVbEywhMqnr9uxrp1EZ7o/CXVc7CA6ZA2Jk5VYPzLBxa9yNxcBpbH640ArJvuYGCBWBzF6qMkVg8jhKWLj55rNq+3bIXWu6GlOcWlqhWY5I2iCBYO/sQhLMirG779beBKDFmrpLAeJmANnr0TJd1DgdWiFyvvOu5AfR3KM5Dxp4b9Ohl45pJF1fsq0HJkn6wtlwU8TKyWjmYYsIRYOoolNegIV+CVEEu3+MrXxIJjOEjFUMxO61bnxugJrXDFvOo7UNV30MTqz8A6fPDArpEZXbvxO2KmNChsE7AwV1OdXKApKSFQ26BWCcmZJmA1soWpLcBysVPIwHreIBaGUPSVlliKWNywo68o1TXLjG71JvmDBpCYNXwyO9ZK5fbV2SK8lIH6WSteO35CPMKEBFcsA6srHc2BI9Q0sDxcY6p5iSUxLAGWx+Mjl9B7NoAVy7s8wgv8zZwxD13CQrcYwqQeFhLuogVYPq/HzcBC15ydAqw7brrjlltuMYgFidWHcNXP5NW5nPKuKmOZOetGyrvVLzS8QV1cRm137iI7ErXAgrK69dYf3ApHFHkV99//8PjBU1QIC42fkYVx5sBKcrsDNbMqqldy67ZFi7h9m3ovKV63ZO96LCvzr/bvm1VXiWqkrQMWzMXdviCxDu16Vdd2h0u41gDWoEEmsRSyuFs9SjQheC7Hg8u0ztJzTqkrpc76Wu6tAvPkEmpgJXRDPdmUzExxCdlbbR2wOPYnVQ9dSfGVIcBKl8K1vFmKH10+R5pi4X8nFFiSuAtgFTKyOIqlxxAKi/WVRab2Hdt3zx7Vq2PgQDh23Ko+SKWa42cEBjFY+QNVvwrJypKl1/6D1q5FI+1jBwhYGQaw0OyhtcByB+qwJLdgBtuCGWqx0LJEiFXCGQuQpBlITxNgYT9UwVkBViIa24e7qMi52ldRUb0oQgOLmajXEAgCVtA2pbNuocBCXq3PTf+SwtK5JrDAKxALXqGSWH1EYil91UXKJZtLhVplXWhqrCsvDKaVqt6neKVq1SiBRQ4hePUdZSDWvQAWeYRLX969ujTW0Y2erwmslrxUpzORTpskt6eSzpr1S0jzynlj0b7F80kLL+Dr1i2Yt7JiVrkHd2w1sLoqYrE+ePUVVRdrwwZSWMSrEZMHTbYgC41epPUzJ0IiGjxCktZxBJvgyuJL8mzj1X2OJ6+ZPGIC2tafALCyElx4G0xnYKW3BVhcmsko0OoPdgkD6SX0K4QHPVK3tY3ASkf1+UR3HiErxyQWL7eqZVblFfbXXQn79jW6oV11FXJJJ01m53kNkz9UXa2RGlgLVbELPYgAFmzy5BEjVhjAQk5D24EVX1I+a99+9DnFuyJfwgy/o/fKmgBK/6axwvJ52lVhFStgxSbWRyoqSn7f/orauqo5DetD90TLf7q2HsBydjSwJIgFheVzxyc5/KVzNz/3wuzBw8YQsG65xSCWAtadAqwupgmxepjJCUF13lXhZDPgLteep4AlzGOJ1QcJ7sIrBtZNwquHHtoowNr54iPTC0nO5uaaIfeWDJiTRhg7u91uOmnWL5ivlpGDt6RbrqH3mepZZR5HW4DFsU8p5LfqeS2xWGFBYI0Aj6yRLAt8uHYfF22aLMUx0dHLjLtM5nrAfYN66nB+FvFqMgsL4tXvCFjHAKyMBAj3VPTNSo/BUzoTYKmwVRI6sqCFVGU5Wz19Uzdnv3Io1sFToKvq5VeBQInfGeFxzwRYMBJsRKycnJw8hr5eKeT9hMwqkalYI5WmQ2P7mh0cCd6owyNu84g1OKyRdpgktVkabCtcMeKGo+nXcXEJRzKwyLqxnRmw8EYpwHK4KuvmzNlWQfplX1PJ7ltm1ZWXZGJRNy0TG6C9qpFrc+N4Bgor0M0R66+vrZ4XrqKwglIeqKzZsj+sGCkvTNXWl6h/mLy6jgSWB3uXfD4CVq60qp/KCotgdS19fI+BdZsorD6GwuppEEsFss5REiskH8vqF4q+koi73kXNdwawOH4lAotV3T3fAbDGCLBeeHbx9Fzw6kyBBf3oFmBFcNzDrHjmkv1zykoS2wIsjC2dZ9486a6nd5dwXgOSPAdpjcXMWm60WlcQukqqX0mhUYLXwsm8Fs95pCQLLPUZ6MacUtp/oY7dcNYjA2vVgKyEeHrxmenKfW4DsALldVW1s2bNmUVWWzunYZFkHNJ79s/3zakl419U1ZVVBtoMrMzMTLiYHjchK8+VpzY5bTd8QtZYa3GRvA6jc3ZwH0K15waVDoVdCychk22hFOxTmzNVG7VRAw1cyU7C48e/OC7AcsfHtwOw4kvqa2qqMFBVuFRJrYugg6+tKQ+UeIhW2WmZKWcRWOWzInZ+XrmlJpCSW1m1L5L84oLv3R1OXdOr44DFiQ1eTwEBy+VyxBaOW737xaWzCVh3EbCuhRGxxCfk3NE+PYIUlhl67xGksExiWU3z6rzz2CPsqe+OXTk3cDoD9NVNN8nq5D2isIYNHj1t9su7d8ylwUbKsaf1wGpRMkwbgRWjLc6oi3VATbe1+f0hsEhiDdIaS5K2wzuoquJXUr+PN0RzmaerTFyxD5lPsJK5JmtjspNQgJWRkASnEAAQ0ddaYKFAZUVD9f791dXVDQ0N+xctUcsVxTPmLcJV1fhdQ8UWeoeOBKzQVfnQsQsGVrqKiblJYrkSErIG6G4USmItH8G4GqQS0fpL8fbIHZ/7GlX8ZJfAQGxwGhX2eyuuMITIajCAZQ5Y64HlD9SXl2krxyX4kGvK6usDnkxsgskkYLlc7QusYrT5YmCVzVkZIYQFhzHW4cgti9DmS9rmBNIdidhCZT3nWzpH2mhmWoMAy8P9bRWwHnlx5+wnHh5z1x13333ttd8iYN1iDWL1MVzCnoZL2EWSs6ybmc8zypBeacBKO4QXnnfOeaqxFx6EHvBcCCw4hLcKsL7HxLpHFNaw0aOnLX3xkdXjunYjhZXTOoXlcpXPiuS5R/rXkEvobB2w8JykGRKARZNtJBehU8RCDAabQARZWmMxspR02rNHN6k3PZxR5gZCU4RJn1CSYQuDeCWz7Tjy3EcOyMpIQrA8PdMZ2zpguTiC5fNX1m1pWITyDGTz9u5dsmSGdijmz8AVe/fOm7dk3vpFDVvqKi3FNZ2NACuIWBGBlSKWm5voTCiqPLR9++nTB4yWHsSstSRTuSS7EEva0QbFpKSuoTFcclwV3hJ6ILvgGMNlxr4c8qk5hrXr0IAstys9pl2AJQ1PYGU1mlw1lg/+VM7AwqJuZuYZAMshwHI2r7BqAw5HIgMr/I0aXQtTYh2J5Vsi4Kx4XvWWukAmFqKSY6zv0C2dI200DIMXiW/d8DJTU3GeMAFic0qnL37uhaUA1j133333t4hY34LEUuuEhKweRkv5MIll3WhjySGV6n6cAH+edHu2eoQ9u6Aq8jXX3HDbY1pgSeDsHg5jPTyes7CeWzy9MImBpcv3MbCafaW4nduV5Ehy1dfui9QPV/4f5v9txnoSv54WKaxgZaVTWZGVlJqC3ydklE6vOn361Kk3iFivPKVXCoGsSSOscSxrDqR87AmdWsE2VvUH7S8J2npTjtQZ4PgLYlgZCZxkm6jyWRs9wSJNPIAe841Of2y7XLlk3fyZM+fPnL+ObKY5XFivIMMvZixZVFFVbx0aa/5WhMRHB/LwcSutDqCs0tkpTEdX9GRHcvfMuED5OzSEb7xBI/iKEGvtWh5EOtYIsYy0NgNZTKsQ9KuafRYb2Jcd74X9J0+26isWWIffOLBrZGFebCLvfpAXFQqsxs4L+a1sreD7+AM1VbPmbKGjcaPfzaqqqSxJj+ElJU7mVn9P/+8a5xY0FpEkRsbc3SSwUgI1W1ZG+K0UWXL4y+eEl3uXvjmVmQ46t5O76yTkZidf+5kBLIdTAQtrM04G1twdu19eOmwYAQsS61sAlkgsIVafHmZ75i49lcyS5vU9JK2qh4pm6Q5g5ylW6aRSDSxpvkMXtJ245oYbbrPwSuVTPPTQvQDWtNnYSJiXhPKonlwLsJp9oU4TWJV1FSjiLjMM007Dq7i4GNfNmEG/m79g3v4K+se1Elh4XgSs1BQPnbYJ/sqyqqOnTh0DsZ5iYmGpUCoDYPufIbGCMhwMZO1pDFt9Na7Iw1zIK2LCKymMcpw3EiJgnJHh87lTEp3xCa0DlpvXxtz+slkN65tII9K/4VPeGJpEqb7aBLCSGgeWVICIicksqSyrq/39qVPGEAJZWG3FEOrNlHQoZg20LJ82MoCW4JV0p+BdTcuUwMIYQmCdOHiAPMLC3NiUzLQ0XSy7tcDyBMpmVVTv54oMKxsx/Kq6YlZZIDOGVeaZACs5BFh5TawSOhweAlYkp09VhWsCWPXZyQKs9C81fgVrHFi5qNfw7M6pwx5mYH0Ldq1VYlmBJU1PjcD7uUb4/dxz+hCybldbC4OApdun9tDEMhUWO4Q33aSD/aSx7iGPkJMayCMsdSTFphCujALJLRkx1jw07UiVV9bMqti/iLyXvci32jtvgZGHRZSS6+iX61fuI+3bMpcwIrCcSG31lHhKAqgkPGfbR0cajhwzptsGIdYkQRaApfbqDOxPwBobMRIjteb68lTra9JKgvImr7TAUuGXAQIsn9vFqZ+tB5aL9+K0bCvcrHJjaBKbVVhJunR1KLA4NT8tzVNSUl9fVztrW0XDETWEqs6Mpv6aEWsmjRhkIkuHA2kMx4brVF0ZuS8X6snXC7KTLbwSgUXIP0EaddWALFdqYnpamu5K0jpgJSV5KkmiqvdKebucsS7M6JeQqIFMRzIvlaZzz4VWAatxhQVg+QJ12xZFDKs3BawFP6+oK+dcd/oz0QWscasXIxMLUXcFLCKWzmy4IRRY3Eqwi4EryV3Xee+qx6pyCTWspLOXit0rhdXndgEWAu4c6heNpYFFHuHcHFcsBJahsFoyYE6WYjLtsB6/paIBto9Dx7rcYvGCvfur98Eaqqsbts2qUpnuKc0+egRgpdA3xKuSQH09aYM52/Y1vHfEmG57jOm2loE1Qq3Qq8mG1a6xIcjStBJS6baFy5Uukz3PXHZOBBbx6rgGVgJ4JQWV2qiw5lQvaclWOANYzrYCKzM7UBKgIayRIaw+aQzhU+YQToJnTQfcQ1NkaWQhA75v3z3yRXDPY8m4GijdaqVd4eTJRgBLAesEhvB5BpZshxdrLbDiI3diDhu/mfMaaglYjrYCqwmFFUgmhdU0sMoiA2tRRa3kuncwsGCpqei8IE/ClVu6esfuF6YOHnbvHSHAulUyG0IVVrDK0sEsSxVSFbcy9RXvIZSgfU9cAKxrkNRwK/uD117Lwf5bbrkDCks8wud2zM1xAFiisBITcZI3/zolsISzxuVHp2deW65i27JvpbGXcP+2WXV1VXSh39aVlVf6PX7Ap9lHDzFGltORSOqqvqyGNwJhbW3lyZM83Q68ojTWBk55H7F2BKLHnJvFc205kJVv5K/jIkmhulchN9vLt+orzStjsqHu3IljpyWFiImVgYqZrQIWt0Og6eZv8fpqdW2ldViaBxZunJoqwJIIYDopmpLskkAJgM9DuA9jqIZQZKoewxESDeQIPIusQcq3HijkH9vXaqPUsmtf1eTLyHgLDmAxr04cO7X90KEBWXHd0VYX+wSAELcrhBSNmAksBbhAxMSncGJxtQZHTLoyDSw9ou2gsAIOh7+yTtUpiQQsh78sQstClTmqFFZ6VAHLVTp9swDLqrAkF8sCrMvRVVVbUEIWtkfrJNLzwu2c885RvNIhsH49+jGwkIJ10/cIWN+StclbbrnnrofGDBsMjxD7chwssDy5rQFWvBu96fG2HeBmAI+S3FIlkjkprky3AsBt/Px3PK0Clsfp9AcqyxBk3cZT7ecr969cedIQCIKs5RpZI0awxpo0qD+qPOVLM3u1n5nnnbUxKGcWIS1yuSRoDeLCyMOXGbj63Z/JnfmC/tbpd156FPvg3O0CrLLafYsWoP9TsbKgU1ldVTxzxt59HMNy6h5FLQJWqhVYKSnpXFwCxCdnELiq3v/z/QjykMjixQs9hBbfGquuI/Siq+wIXz6Qy76P7bvc3GtpmNkQepApsLRGPa6AxcWwvDECLCzbYeGudcByndHmZ0d6GLAc7aewUglYVRGBNa8pYM2MWmDFuXK4JNbgYWPuIon1rSCfEMTqQ8QShWUAy8gh1QJLxbFCiKXTtACsLkqmMbSUwkLKKAssXpoUhXUvsrBmc6WGbg4WWLketwBLin00bQIsftchAmGyuGi+YM74y3WJZKOAX1dMJbmTx0+8akEWfSSF5QmUc1uZfdU/F1v5P+HTjVe6gCziFX2SvvNMLMOksWq+HPyz/qQar7PACuIVIu4ErCOnttTWlBf5HNiU524HhVW1pXr9EmP/2wzrpqYZCzjbYQEa0u7fVndGCovFQxiwyPfKDtTX1SpxxSNIQ3jy5EmLW7iVh1AUFn3WebgisRSReDT7LldjKeNpDm/+pHzVuH54sL4Cr+CBVtWUP1qQBleQq222RWFVnpHCSo/hhVIrsBztpLBqmwTWLPSOImBFSmtYYACre1oUAMvJMlROsrxx0xe/uBSbcyJKrD59+inWXG64hf2ArB5mUhbqXOmCM+dYpJVqkiPAMojVEwpLCSwOYPFfZGDd9RABiz3Ccr/DIcJHu4RnBCyXizsvGhPGQbPQBFZFTUCqPyWpexGwmudVRGA5HX6abFtoqilc/Zw01spf0ZQTtzCIWEAW0iARf18rG+SYWtxHXdKLjDQjLQvQxLj/oEFKHEwe/uCEBy28IoV15AiIVVVW6acn6HK3PoalgeWrrKnd0sCLXFCLixbNWzBfJ44uWb9ov1y5cn/DtlllAccZAis1ArDSSuoJ+eROyxiuBLGgsUJ1qlpvhcIaYSgso9yYppblHaA/hk9GtH/+JDWCuhSZhVcErCMfEfTRnr0VwHKEAgsuYQtSAJEK1QiwHE0Dy4HJ0AKF1TiwiqMZWCg+ZgUW6Awl3j3VGRsf7+P9z8OGBUXdddhdFBbnYcEpZJV1ufh21rSsoPINwfJKQlgGr2CksHQICwuE+i/CJbz34cGDZ3PWaA6ABWGOmHvLe6gCcJwEyTt4dauqjIRAmaWAH5pQ8LzCBlenU6jYkph+uDkcJWXEKwNXMuUIWXq6HdAuzXJDZUElDNI75Dj7vf9yc+Kpw2KDOE+e59rw4Sav/szhlyMkRYgdc+rqC+Lo1UjTc1kib/wkw3kfnIFO883Nvaa8Xl9RZRk8XFTg2UJWsX+vWmCdjxYFSC6i32ybM6eqph7ASnU4k+ItPWPCgKW5FZfMyaJG+zHZRARglRGvqoNH8Fd0YAhPKZ26wZohIvudgollgGt5vnDKMP5B82q4lVcSwDry8smT7zVUzKlS/dljYpDCqVL/mwJVkMW7dM8bR6CuYv2SdTOLmzIsVq/fV4XyMly7pYnyLRHfYCxvSE0ljipgheu9IGCF/TbqgOUQYMUysMZt3v3yE8jEMoD1rVuCgNXT0FiXs8iS2HlPvb9QpzZIMtY5quC7OqSMOwNLx8G69JAQlvYIDS8UMffBUyGwphfmupzEq2wi1pnwyoF/fARg5RUFAauq0hOfoIHF5Ss8LfkbEYFFKNxW/fNFi4Lm269IgdB0O6Y1limyjGDWCF14Bp6NHMGGrXCDFg6avHCyYQDWBMtsU8A6eQSzLRBHL8etiNUCYAURi4Hl9aGfp88XqCwvr0GFQ07VrtqmNj8Xr9tbTZRCmjb9qqysPlDicUQEVgYfocBKFmAZHakTFbBKAmW12xpoCI0x3K801koSj6eCZCrjSozrjPHFGMdBwcPXX194c/mIyZO588Rw06d+7fjhwzKEEIy1qAvcJmAJslyBsjn79i/a26TN27t+UcOcmhJsVG8jsCK7hC1QWOWdDFjJjthYlyuvsHT64mf/DxLrjrv/GaqwbuijlwkvN31CHXdXQsvcDC1u4HnnqW90mxzlEF5+uWi0fsjC+naQRwhE3nKPAGvpy7s3l9KcS2SBRXYGvHJo14RnrZs7v3BtclNhoeZAELDEu2vJ34gELCdnCf48iFeMLLg0yqfR2UTLTWQNUmlZIaaD6wKqSZMnoVTm5Mlrhq+hqTYZuJrwwGvKm3kNk+2Lkyc//3xldQUpLKyQOxI9KYktBlaQxbuEV14v15WRVQmsWpTr8jL/NgO57Vx4Gr8q8Xjg4OGPtBRYcZY9rbGxqtZScoECljF41WoEf8WxQPGstVO4ltctRqiqPbrIBX2zMHgk+ZcLB2k/kGAP3A/nOq+GQ4ghPEa8+vxTA1ic0OCNwQaZ1gALmSUuNMvesq2ZxoQVFdtmVZXTOR7jSJTM6LOosCLHsMr9zs4CrGQLsHIKp+94TkusCAqrn0mbnlbrIsGsnl3UUmEPYzN0MK+kq6E8wvl4EBNYd9xyrf6Ld99yxz3Icx88e+eLi1cXdnXFJ6IOVib592c6UgawXIbEynvUBNZ81HS3AsthFNFoxiIAy5kSqKHZtv/nocBaJEEYiCwznUhDa8RaRpaxw3BQ6GTjKbaGcYU+CWtkrg2fgGIoaFRM6urwYQCLxMHnnyCcRC4hp7+m6CrcrQCW1+v2oimEJ56kKoFfpgh6wKi+hCul4mgstrJ1i+1mDEoIsCLyKiEhjs5DC680sBwxcAnhVVuRtfLn0srvPUBfUV+ltCmFylUwLPIzaDTxi0HqwFBO1iM4gSWqSsACr0hgffL5Jyv379tCIjU7pjsDy9taYLl9bl88kgBrmrG6mrqysvIAgOVsI7Bao7CaBlZxRwfdk5KALMsVyWhKQWdeLk3q3Jxxmx95dulg8QmfNBTWPZLrTsQCbM5n2FiwdbnKyuqpiNWjzznBpnYaqp3TeAg2Atadwqt7broJGVjfetIA1pjxUwZzEpYrqZszRkKR3dObG6xQhuiJI1WqxND5WS01F/OCbpKuXX5m/4hwYpWUV83a1lAdAqxf/RzAYmQZS11CLHEN1eq8nmSTzRI0ShDoik7Llg230EpwRca0Ymfm809OVldsqSqrL4jpnpwsu0SNkuTGSR16PkRqfAqFpQvI6ZJ8ziBgScXR4IcKYpUClgochgKLLdmhgSW+K03EkvK6WdvMOGC1EQkkp/Dk/iNwrd/YqkWWyFRhlgyU5tVCGU2jtFiQK71McDV8wgN6EI8flnj7yU/IIQTzEXTvnuqMSUvzYnI02qwjsvESD0ssvCxOmuG0mYDugxJkuK6SRCrieE5ja7/5v7J+39jz0P/fJlcJY5uIYZWXcFpD40F3JI5GBbCSg4EFn3Dn1MFP3GskNnDJBhNYzCvBDWukYL3VxWCWlGxnYcX9vFShB8mKOF9ZPwLW/QKsW7DfWgHr7jvuQlKDbMvp2s0Rky64Sm89sJxGBBjAqj47wPJWlgVNN0vk/RNG1pFjb1hW54OQxZPOkAFWU61zuAopTzZIgwkrJhi4Em1wkmbbew3b5tTW1AcIWFIRr9XAIoGlgRWvhpHubK04isK56dZHkWYxjQHLzUcIsJL181LLA3HJJfUyhNXVPzelqlosVK71G2+8eUAPoOFZY/SGh9EpjFaTBVcPCvI18xn5RzgE+F51w75tc6rII0xPTY11ErC8rQRWAkSWVGxV9Vo9fk+JH+4z1o885DSglKunxOOnaz2Sf5XYRmD5G1dY9Y0Bq1gDqzASsIrpX70veoCltko5HAwslys2B2H32YMtYfdrb7nDANad/RC/Ot80q9K6XKc6WBPf1S5DtYioYle45wV0nN9vCID10K33AFgqgkXguuOOu8YMGzyY9z3nEK/S0gq8dP6ke73NDZYJKCuwgr8vKZNqM8XFM9fthUvYbsBC8SMkYu2rDmLWr36OdKxPPpd8IsRhDhzY+ubWNzcYe3XW6vhxOK+WTR6+RmomD1824cEJYiteW/EaLqDVYfI1jyGh4b33Giq2zKoi56IArXJi1C4Pb0uAFWpeZfyDWrYg37AeLQwEWOsrqgLdu4cWvopX23bDgOVOyIgLU1jsFkqkSCwus6SkslxtygG0WGKtxIH8kM9Xfs5C9Q1gf6tVpw4SjTVcAC8fJvCXAfqThfYGroZPeA3MP45oOw/gyfdoBPdVbJlTW1dWX5IZkxoLYAGrbQGWdiaTkrolSzFA7novmTnd8E231G7s5sSkmzhof4WFEsmeJlzCliismOgBFiksfi92QGK9uHTqsCfuvUuAhYoNdwQrrCAzHMSeFqUlye9GBryZyXC5KdCIV5cPYYX10D3fUeUhnvzWk3dDYN1x7xglsMblgFf0Poc3n7YDC9tBSrhmCrajLpiHUoseOr/aB1guTxIRi/MA9u3TQutXyqWh2fY5KwQEYqwTTiHLsOEWqTBcx4dJGUwwgLWCiXX4sObVs8c+OkLHR1uOVtWUVwYKvBwvbg9gKXXkFmB5yrfsnzdfAYvedtO7h/AqoXGFxVPYAix3MLDScBQUcIV4gr4aQs7HWikiC3UNfnXSMoRbVdfH5WisvVZ5hUpI8RAaY2eMoXan8WnFBOYVC9RjRxj5DUz8GsIVCSwngBXTZmAZGVmW+0ZOI2wPYDWusFoArJzICmvBz7dVSQyrQ4AV/iKl9KnLBTGKkg07nts5e+oTkFg/YWLdLS7h/Teg/7MA6wIRSMHcCnINrdbTiNQzrOjjAhg9Qr8779wIYEFgsbxSvLrnXhJY6Ec4tzDWwZWu0+AOSjWelrymCLdz6tKu/vq6OQ0reTF5/75ZZQEPnQataQ5pHT+9H87hLKkv11tLjGjWSlma/wQCQS0YErK2mlvjOPauA8gjho8ImmSTLXEr0GoF0erwCqHVCcgrUm0ffXRqi+CqxINgeXqINT4uwcBSQfd4TDf2n834E+HcT8BaolJuASxPagTWJbgs0PKGmBVw9CVOZ5OjQ3VadjZJw8zsghLenDNrTvAYQmIt+vxzTX1yDEmk8hCqxo9o8mHgarjgKghVbCvAqxUT+BBnkCXqH4798aOKbcAVEd/v4dIbibGxjuTkRlqZNWIWtzoknBevr4t0IuHU1FXVQv9HLTkvW6aw+LfhwFrHewkTk+jf+0m4wpov5WXwV2JIOEQJsBBFYGCJT8gSS/uEHMN6CFVHDWCJQApmliDLLD1jZJQqZWUqswsM4A25c+PG++8nYN2hgCUO4T3wCKfOfnn35nHkETKv0tIxUO0CLE+grGoOTQWW/3X1JR5n67rZRgSWI0aqNdCM27INKosn3H4yhI1Xfk5T7qTUcKAJ9+abG940VJaBLRBLPg1X8DIWtTDLCFcrNK4OH6PZdmr3qd2njx49uoPnmisJmqp9gcXfJilgzbSc5A7zrhlKQ7kT9MpkC4CVJMDibmT0paCkADWoMmkIa+rqZAxZq7J3iOwGKFWNrGOMrA1bjSVX7lU7Gc1vOAEeYwjjMRyh4uwrJkxQtFpxmHB1XLnUp06d2nL69NHaqjIaQnci/p28pwI+yJmcE0mtApaq9mEWp2w1sJpWWASsbZHysOh/WUmnbk7E8jLc56s+DX8lSoCFiiCYsokisTjsriSWTjxXeQ0ErH5BCouJBbFkDWn1tOZoaXWlUGU18OpO8Oqhe+64CXCEugKv7lBZ7s8+Mp0EFgpd0yU9UVWCbTOwEv2B8hqaDFyfoT7gSUkR6d52YOFrckwBijkxszgPvELCMdVcvIGm20o13w6+ycgiaB2USIzG1ooRK2iuqQ/9RU2y11heHWRXkGcaSbXTp3dUba6qAa6KfF5Aop2ApT04+opavQDWnMaAZUleOHNgKcvO9mRnZ2Ymo3ofqC9Sdcs27R1iCPeflPULThM5pgbwTSv0lVJl9K8QbvE4ygCyqa9qFE/RCJ7+YPs779SUlZdX+n0J2FpD7lzLyhiFj2ZzwApz6QRYnhRP24HVtMJyNVLAj5eenKiHFbHiOxoTpjmcJIi9UQgsVyHXHRWJZVkmfOjb3LAeIfcLFKUuUFIplFhGREsUlxFmD7HzhwwhYt0vCkupOYm436sElg65Q2JxlYZ2AVaKx48syEq+lPh5Nw6Q1U7AovmWhppO9agzw64NT7h9+yoapFrKfnYLMeEO6gmnldaGFYIsOvAJ02ztCvpkscMHD9Ll4MFjOEinnd6+Y9f06YcOVVYWFXERLDdq9Eup3TYrLFnai8vgGB+RvnxWtSolJi6hAayMtiisTHUQrjwF2NFAV5VkZ6OyGJhVVQvvUA1iQ8N7+7EcihGEP3xKhvAgD6Bm/grLCBqXESssyCKjcTx87CBGkGzXLhrBR4uKAv4MFX360oF1FhWWCazGarrPKg/4/ZELKM/kJhQxjsSoAZZU5gSwUlMTnSjZgMyGqVxkRkmsO0yJpSJQF2lWnW8KptAwPNkQXJS4wi0v0hcBFissAOsWxNzv/pYSWGMeHjxs9s5nH1k9LtchCistxsmNX9swWDonTwor8OtOxmZnlGfwtKb5thUA5lhKkRSebgFMONJypLS2bNmyjaQCJlzDERxCrGOnDh5UE+4gPjZsOKhm2wpcgg1xqxVMqzfffEPZ6e3baa6NKx1QmpWFNH6Ojrs9btkXYAKr8VcRCVh0jTsoRs7ASkz0VNZWrNy7YN18LFfQ226Kw9gsaFFY5rqYLPBYLRxYaUaRPBRywf6rNLmqe1q2FEMsg1iVMdwCuYVKjEc+OvLesY8wggffUCMow4eDLmuJXTyC6mOtMYYcAFwhw/7Gm8AVDeGhQy+NHDAgK8PrjoMbLOBvG7BCcRVsQadRommR3lRadmY2l+nOnZ89aPMVXpBxwcptNYGUpEBNRaTyfgSsshKaKvEErMyoA1aii0u7v0ASa4wiFnzCe+6Rklj9+rE/SMi5yFBK8r3AywItZtXl5w8hz+98fUOTWPjeorBuufvau791LX0CsJCDxUmj00vjHTExiMfGxKBTdW77ACvoIYCspnZvNT9+wWMpwKJJl6aYBaFVxdUDobYw5bb9fhtKlR87xchCKOZNaCZ8khlHE0pPtg3QAnQcZl5pXB1448CB0wdoru2CNBg5IGsA4yrD6NTMuT5tABbnISiBpVVTSoonUDNrW/X+ResXreTdK6kELHcor84QWECWHFxulJtV848wHkJ2sGtQY7FKjyHZqS2nTqlRVCqLB5HHUJtFTgnwVxxWv3nzzQNsAvxDlcBVFifLCrDcFmAhC6Gl50RHA6tpl9CRV17b0Eiv1PJAoDxidVQNLEc8BFbUASvFlVMoUaxhiGJxAQVrEGuIElgmsS7S3xv+IVikwGXBlULbRepy0UVQWBslhgVgkcK61sjBGj2VBVZeEjtYLLA6EbAw18g1TI/x+Hm7HWZcWX2ZmnYf1NZ+8AH8EJ5wopTeNOzgm9YpF2qA1YED28l2AVag1UiwKouOvDzZg+T2+NoMLPoWOVhG7hRq9HgSUzyctEG4mDOrqqzSk9rOCosbiaalGVehYByqvHPNZFg5JCv4v4OOo3oMQ4bwoIzim40OIdHqKYzgf+xavWvX9EPjFPB9DKwkAlZWkMLqTMBqRmG5kdcwI0JcfWXFrLq6WRUrI/SWQiNVBlZcnDc6gu4hwMor5JoN6KgqxGKFxYkNpLCGKF4p6Ci1ZMotwRWBawgfzKshJq8MA7WgsFTQHQrr2mvvvoVTGsYMG81Jo9NLE3BGdzZgSd0BfQo5HGmZskWY5Ra6ar5eVvN6zTvv0HT702k2nm/B0LJMOH0tHJg3mFa7nn/+EGzkSFYGqIhMuMqTf2KKKpoqr7aVwHIzf7w6isVRaHpIT0klI6OmDO3pM02FZbUzVFhaYPFaYXamBVh062T00UxjaIH8CD3W01NA/9HpNat5DGEkNw8cEGxpZ9kiuXgMZUTfxAgeeOoA66pDh+YyrVicZvgykLma1LmB1fheQgEWirpHgNKMeSSZKxpWzovQIWndItWqPg4Ky9WBwDJeKlYo5PSmz56cwsJSRLEk3f0W8tSwnZCBdf+ddyq9ZAXPRReZeuuiC4aaQfULTFaF4EqxbsgQVli3AljYmnPLLWqJcPTgpS8+snlcYZKcrGnpqmFkC0ojN/4yrXBJjGCtftAQ0yee7JLjRh/cDSZbtILUY6489NLru97Z/s72D0groeMqw+iAzDsFL3yW2UfXHuBfw4PZ9fyhVatGAlalNNl4ujGr8CmROyeLxeoOD07dXS+SCT6SQkxPLJcy7rLmwVoWfLQS1GdIIYHVbIPRSL+z/o2YENOKEHl3UHfI1EoWnnk82VLEEQNYGiitrCw/NL2mBmO4yxhDHqc3DGi98aZBMGOAAfxdAP44sgGFWTmcuIGwFc3HeFdCAqE/Dx2HNFjaMkH1OdHcJnR1Qga9+Vkfo6V/L7FphZUYKJuzP0IF1OIZS/YuWrR3Sbj4ki5fAZxAMZbyGq0dj3YxK7A8AFYO+n0h3f3he++54+5rOXX0pntuJWBtvJNUkZVXVsmkr7Uwy0DV0Aj3uGjokPGssO656Q7BFQJYd0hp5BeeWzy9NC+O31s7ObBisRcjHQFlsBfbyGhy+ItKK1+iWVN+6PVDr+/i+bb9gHxmahnzTiYZe4E81Q6tOrQKwmqAwCovgy+KK4mpKQavUmINYrUbsJwOXbBJZEeq8ywCK4nVGj13ECumO1f+TElPSURfaE+u319YVPpoJQ3gIRrCQ7t4DJV9sP1PB06fPqBVl3onkEEErJ6HNh1ZSkNYmJOHlFi9NYiA5Upw5+WhlNiXCiyH05T+bQFWSnPAKkdP4Qh9kOaj/9j8CL9YRx5hTQClTc2O8VEELDotc3LyEHd/7oXZw4aNuZf3zKjEhvvvv+ZOzavLLrqMLpEwJOzig8llZdVlViNgDTHyRqGxgCteIlS7cgoTktgVyE6L6bzAUoYJ3j3ZzJtOyMjKGlD66ICRj44cCeeE1NYuZdstpuaYsueVF8iw4pRO4IqOBBdKtJClpsSeNWD5U9SM4h1x+Cb1rAMLPq4jWWKCyd2T1evohtLK9OuMrKKiosCjNIQYQxqgd+jjdR7DD6yjaI4gOYKrZAiB+xy40QnxZi5YujMWzm8HAAvEcrYdWM7IuewaWM6Sypot7zVSZD5iO7fiJfu31dWX8F7HKAWWJy8hj53CpcM4inU3i597vvMQAWsjCayhrKQuM+AThK3LLMwaqvIXLmJ9NdRyF7IrGFjjxytg3UHIugOtJ+7SS4SL55bmJcWXsHV+YOG2xj5ztqQEIk1WVl4hgWvAyErRCSSfnt/1/K4QO6Rs5CpjqnEKg5tmmzKuKZWYnpgam5J6FoEV3ABNeHW2gOWVGi34i8kCrOBtMog25fl8GMQBRTSEIw+Z9vohgZey1xH0U2E/Q5tmqW1H8TFBwIpViSFfNrCCz8/WAisxIrCKDWBlYiNtRInViM3gvlJp3elfw7yKBmBZJy2yvklhkcQy4+5MrDtuugfAGj9kKNlFBnSMy2WKRya+eDFwqOaYCSo+8OmyoUPHq0VC0nHELPp6111jhk1RS4Q5SUnpzCulsPT7ejRZJGBpswIrxrL2hd/htSS5VImuLGZWKdyUVSNXrSKfzzL3SBHgUGaIqwzs7Ut16omfKJ1I4RHGBhsDq4ntJU0DSxv374rQcbsxGDX3+8aAZbE4pK+6XCxOUU25u6ppyuMatFbgTpAxxBCWjhw3slKzS8ZxFeylVdbxoxFMQIwd25PTpfsgGyqFx+JtwAqYtgArdBza+jjNmRMVyyIrrEqePLmBmqMtae1q3HH/HG7IkZaZCT5Y34A7zKzA8hCw3Dk5OVnjpi9+7mVTY3HRYgBrvOIVoCMm9LnC4uoBUxcoz1CYpXFm3An3u4wU1saNYx566C6WWHewviKBNXo0F+4rzU1yZBKtvgrASo2xLH7p3xGyeM4JsrIGsI2EVggyODwDcBjagAwLWqh5layqtKQSqqBM4BKGA6up/XBnBqxI9z4bwEqLibMCKzUUWPKs9CPFxbkV9tUYlo4skjFTmNfDN2CAcqXdvOQFS0+z/G8YWCBWZwUWKax9EXA0c8l+tKoni/WX1+kd7M3bzCVcCTs7JmqBlZjoZomVx23rEcaSDjqgCfmEG0ViTQlGj2DLQqzLDKfwomBehQCLFNbGe+8FsGB3aV5NW8oCq6sjvYAFVsFXAFg8HbrjEmP+zhQJeQItE1w0tRSgBhi/UL4gHCVMNesEl07vaREkFmZbewAr8sQ9W8DSrR8iAYufEAfk9d9J1sQSg5ddqMZvgB46rUxp/BhxAFYBfahaESrbl4EVG9xtqDMByxEZWPOX7J9TrqpxBcq5lUhLvELi1b5Z4FUMusnqUEd7jEebLBhYHjfi7gk5RKxHnl06dRgnvHN4CcAazxJLwNMLdkWvIKElJo7gUPURFLrS98PdCFgPbxxz77133XUHwYrsoXvhEI6eisJ9pV0dIrCMVcIo5FWLgKUmGsNKN7biYokKWGaOuCoeJVyS6ZUlnzDh1PUZqCYVBKy0mO7p4FV3UlihAouIRU+zGWBFhklHAktXO9Xjl6qBFa9xFQIsGTwanjyMkxq0DBkwYzAx0q54J7oHYwgL+DBxZQArttMCKzWyS8gKCxMoNdbhCqA77t4ZzfajLp6/ZFHDrLoAGmBjC0J6tAALJhOMPiXyOmGOqys2QZPEmopsrLvgrxFOSGFtJGBNmWIBT69ewUpLu4WRlgYtd6K7TZkydPz4hxlYYvfeO+bhwaMnTpMlQpcjjWlVUpDtSW+k5lmHWxOqynDIxP1TbRpUZhSNrzKZfNhqzPMpw6CWunDHeaQuaPN5zWqd/BWuoExnZSRCBIhsZ3XkkkKC7m1+PGV6PFM1sNQri1NVUN06z9X46zR0eXl5MlZ5luEyh5OuTXCKWIOGK4DRw2WzwlKgxHNQQi7I2j5SX44lBaoqFoUX4Zu/pHoWmtE7UlKdLof0814QKYnBCrkZ8xY1oPwSvSGkZ6alG+UFo2I8rMDy+/1ErNjYcSp99GHWWCSBHhoDn3A8eYRThDy9e1n4w+CacoXhFeITaTG64ObKesndeguxBgNY9Oj3Mq2IV08MG9179NSdiGDledMkp6GkwJOZIvP9DIupfQl2BsDiV6CvcxGxuipqYeZJPEXVoEow55nXV+AzfmAVYfAqTvHKAJap5nT05+zHG846sILNaVZBVcSyrGbm5eTlZOXkZCHx00osHw5pmpQAWokTiPqmIBZ9k+Y1gu54DqkRiNX2kfpyzBOo27ZyybqZYvPxqfjfitctWM/FgOi1pbjiHUklRKyG9UtmNI6smTPXLdi7f9+smkoSC+BVdAKLTm4UX8nxoAVn18Jxm3e/KMQijUXAupeA9TB8QlJYvazoEZtCByHLdAwZVpcFRejlPnzpNWXKlPHDACzSWIyrMU88MXjiRFUZOcGLlNES6CtPSqcGFkxPRANYhsIS10OVNI8Ldg6lO6BMNV1lWLrZmI5THAffTWA5hVcJXC4n9mz70aRwvhxgyY80Thlea9Fl2efI0He783w5TKwcIVYe69IEC/4zEmIYWOlcdFtLLF7AsCisMHkVDRO0heYO1MxqWLl+HgwdWvF1yZK9i6q3VTGwElO4N5G/smZWxf5F8xbMmD8zHFoz181YMm/9/oYttWWBzJj0mHSPR29LtY5Th1oQsPy5Ho+H3rFKuTIWiHXvXfcEKSwhD6wXf5g66wq9ZjiFL/i4QgmsXkqVqTsRsAYPU8D6PzrGPPzEsGEELOwiHFeakEBnEwssz1cSWBaFJcCSMHAQsBIsjSC0nnBZZlcjwJIQj6rvdZbjfl8WsJwGsKzjoWiljZBFKgsXtztkiyOuoEt8jFZYJLEIWT4hVtxXBlhdSTzNqVAVI6sbqhu46mE119ZAr0rsGkaPyW6B8totFQ2L1s9bsA7BrGJl/1ZMumzBvPXV1fvoLpUl6ehYlRmFwHIgvIJly0SPJyc3x+PzeTPy0JDiuZeXDhaNJTEmUlgIYfUOs169R1sCWlNEVU25Yor4g720JDNv32s0A+uJMWP+j6BF6opwBYHFOViFCd4C5Q96sBUjCuPtQXYmwOKobldTXcEwY9K9spRvWLw0vTUW8Lvh78hqoyRSmsACyqGmtL5CeMeRfKYFyc/cdPS8vYHV2O+tG6hlTNTaVyxn+ustlcpwg6C918rxwwCydvVyfggNVlufd7SYn7RTXe2cLXPIZpHNYZtVW1UW8KdI5Xi1W8GPwhvb9pHMWrJgxowFYvhKemx/Bd2lrjzg4ce01laLSmDl5uZ6EDqh9yrJbQCxODROEgsu4ZQpV7BQCmdWbzMKP+WKK8zQ1WjtQFpvzcB64gki1pilxCsC1uiJE6fNfvmRzXML8zIKijhpFPoq9ysILKWwNLBwEtD54I2PN0pQAWMcqFLAYrEEYEnUuDFgcbVQBpbe0XL2XnPHA6tbN5NYqOam+zBGApZeUpViWyxoiVhKu7b1iUeJ+Tz+SpQ8tFgNfaD0M+9TALD4ht0SPYHysrpZW/ZVr1wEQ1Mi/rq/oWJLbQ06UTt5/2B6uqVQUVQCK4c8Qn8BESvBgV3Qz+58YthgrOZBYY3RwBL2XNz7Yjb6xoCWdeVQvtPRrqB79B49mkBIxAKrWF8RrzZtmroTu54LM3xwCLNLvMzP3Nyzu9bVdmuLwsLvFbDSgRszlQBqwOwUBGCppG9GVHKyTEe9aYWBxfoKkRsAixMivxrAUteHKSwDWgSsFCBLmpHK/8J8m9P/Bz16MU7dgkwvNwZbW19HRxn9L9x+VcuopEQqawS4EDhvY0kxaivROegpKaksI5mFkpLKKuhjzqyqmkDA7+ebZWYG166NPmBhIzwBq6AEAUmHqxR1G3Y+MZiJpYA13gCWpg+IdXHvEGbJ0uHoYFeQbyhH7ymjRWGxsT94yaZpUlYmI4N49agIrM4MLGejwHK5TIVlAisxXraFGMDC5GoUWHHhwBJ/kHkV91UClr4+zqIYu1kMTwfZ/pLun9oosGI0r5yG8x3Kqs4NLPw7khxJOGEYTjwycv5Ikwt1LsXSz4ndEh3QWTU1uKDMWR0qnZG28qQ4hGuhtWujCVgOmW+5sWipTbwoKinwJuSVTt/x139pjXXvmI0SxJoCBF0cZlpo9eKI1uhewZ7gxZZ74GeWWIKr2fQHRo+++JKJU7kwck6ez1dShCVC5ISBVx09Nu1temIYU8Yhe4kNb0ZtWm4s4IvzMMmYbZbHTTBcnGTtEp7NUNbZmuCNPa41z8F6vaR2SIYVoBT50YIfsNFrOjGwdLzTvEa/pcTHY+1fgztRLSXQd55AkFUGSjxyzuE+marctoZVVC1CMLByY3Nz6CmWCLHcOYXjpi/+68tLCShY0BuDqPuwoaHAuoSOCNAyYHWxASvL7QyfcPYTs4cNmzp64sUQWM8uXj23NM/t87PA8ndWYCWHgCL05yBgqRgKgKVXvWLPCFiWzHILr0Cs0L/b3vZlAyu1MWBZNpczp0MeLSFETjX9Vzs3sBhaDlXlQXAla6huV3wosHArj984yNK5bonGXDo5W57MKAYW+1+5fu4YTsTy5RSWjltNxNqpiPUwEWvwYAKWyatLLgGv6JOFRhMZW6OVsrJg7RJluA2ANXUYH1MHT5u46epLkNKweW5pIQusEggsd04uAauDN1u2wsKApeZRsnh2yZF8EKvCag5YsIjAMn7+agLLaTHr9Ya7orbYhAIrwnA38Vc7N7B0bNSIkfIGYeaVCSxLoWM1mkFjqsGXnkkYi2JgORMZWFBYRIxASUlCXp5orJ2zh0nE6eFh4wcPJl+vdwiGNLgutlCr92iLG3hJkNEVBKypg6eyTQOvrn532ifP7ZhbWJiT5/dzGV4ACwor2iNY4daYwlLACp9CDg0sWT1sAbCSbGCZZo2v6Iz18Ef7egDLrUyalblcqHKneBUCrMaqn5r1u9LTPUysqAQWTAOLiUHmR7EZJDe8vBTbCodJeFwrLBZWQRi6xEDWxIt7R0LV1VdffcnV9HXTpokTR08jXg0GrqZtmvju1e9++Cl3yinM8ZOV0DChriDWYjufwmrOwkCjvlhyihL1ilfjD9Gci3P2E22/bGA1Zk1PokhAb+qvdl5g4bnr7V5KVrmkyp10N7dWXGgEWnydASxSWNkeM+geVbCCJWpiaWT54xNchVIcazZJISLWsMGksEb3FmkVopuUbbp408XqcvEmy22uBq9gfCMQa+o0kVfvvnv91e9+/N5uElh5eQQsWZuwgdU4sJJsYFlMTyTLqmHQo7Xscb86wNIuoYKU2/K9BVgRO+DwL0xgZRpB96gElsuVm0teWA6qxIJZfn9uUtfcnNLVi3cLsaYOGzYVLmHviw1aKc0U7PExri7ZxGRiVPHNTFMSi414df3117/78Scf7SgvdNOIo6MU+mHIQmzrihdHtzUGLHzSJ1MkYIU7N18vYDX2+nVybWOP1rLn+xUClj6HLPtV8TurS90UsIwYVrplI2H0Ais3l2mMXYUcQorNJY1FxCIxhKATCazRvbWrZ2HQ1SKhFKM20XHxJmGWFVXEJv66iZCleIXr3v3wk48Wry5NRXJPYian5aaoSvM2sMLu1zJgnX2LMmA1CqKWPd+OH8+2mgaWeQ61GVgkr8xa+1EHrCTuyoZmIolcjAjbYpBXUChxLISbpg2mC5IQLtYcup4vV19tkVpGHJ7h9a4FV+oQYE0kWm169+rr370O+uqR1aW5iekxbpeUskhMyczEZoKOHhPbbOvM1hhkGgugy3KPLNjoBIjGFjs63ACsnLwcH7xdrp6Wwi5ibo4iFukhkUUgFgPrepZMWjZdYjBrk+XzJRZY8YXs3U3K3r3+uutYXyHFHbLC64XPDIlFwPoKqivbbPsy7SsPrLw8nwJWKtcsYWCxxtr9ImmsiUDWaPqsOKR4Jci6xCSWhpURahde8Q2vf/fqdw2jKz4kfbV489zCHKkqL93WsZ/e1le22dY2aw2wdDpMGK2iE1g5JrBSU1JIXiEOXzpu9Q4U9Js6UWyTwavrSCNdh0/XK40VEoUP5dX17BNqWF3/9rsff/re7h2oipzESxpuj8dHh99HwLIVlm22tcm+4sDC5ltUDODiaSnp9MHLhmTj5k7fvBuBLPhxcOaYVsSpG2+kCxkRS1SWEX7fZJFXVytcXcfH9UQrgd27H376wkeP7Jg+rjSvq2wh8HAzd5/XA2BF1/jY1jEWaeJE3eSJEmuPseq8wEqX7vVkhYWl4+Zu5kDWpnfh0om6uk5gJcxSyBKJpQJaRlxe6Ma3hyCTH8AryCtsyElw5bpYYPmwg6kAPqGtsGyD2cBquX2NgdUdq5opHpZYhVmMLASyds6explTxB7QpxgEevvt64JklmGbjGQGBbfiG2/UiLvuurc//PiTFx/ZPHdcYQ7anuQkEiQ5V82jFVZHj4ht0WA2sFpuX3dgZUJh+fy+PBT3Lx03fccjz7248+MP371eEaq4eCZxB/a2FluErE1XSy7Du1dvIjWG6JWIq2J1CLjeJnn10VHIK9JXXnee2wSWhxswRNfo2NZRZgOr5fb1ApbOlI2X0tdpaWnAhy/Hl0UfviwSWXNXE7Je+PTDD999mwF0I8ukT9775NOPPwySWRyhuv76d01xBUF2nSnGbnz7408+Orp5emlOBj08DBnuhCyPVOHxpHiia3RsO9sWaWLon9EyU6cSq6/26dGMtS9oogxWMA0sV7z0OiBeZWKPjr/I7/dl5WRl5RGxpm8mvxB8+pDY8/bbSz7+5L2PKj766CNiloGsG68Ljm6pb0mKfQx7G/dkebV5LvGKd5aTinNbgYWTMvpGyLazac0BS58X2LlllPu1rVGLWmXUXsbA4tq9qjlLWma2x1PiLyopImb5fAhmlY6DyNoNPn388Ycf7/3kvYo5R6uqdhw9StexzDIJJb4fHWTwAIltDUS29z799ON5H3/SsKV29bjCHHJBfWJ+BlaqDayvq7UEWPrcSPyqTsJ2tK8HsCwKS4iFcvZFOPyyXMgqawf49N7+9xq2Ha2qKS8tHTcO1xHGGFkcpypmUjGvlOdIkuookW0LoNVQcbSusjAHvEIHPo/PU+BLYWLZwPq6WnPAQuEh49z4qk7CdrSvB7CsCgvEKigpKQoQskpKfHl5Lp3hMH11FZFnyxbgKlBaCOlVies0soIMtGJc0Y0ry8tq6K5Hj1aVlRfmcBs5P3f0UkVl8Dxwdn4VgdXeJ89X7URsFlg4mFl2/KoJCxrDr2b5AGVaYFmBlZ2N8p9FKJlc4nbnunJZZOWUMniq0MHMn4v6Dl1zCgOV5cSibQ3sGZq24MMPP/70vQZmW2XAX0o3m47+HJWBHNSFyCQJV0AH+Z6eTI8NrDN8vPZ6rCgwZzPAUpXH6WJvim/CgsfwK3aOBJsWWBpYHHjPZlahEXNBZkpKbiz2Q7tduf7CQKASTTYSpewc3d3j8xOM6sjle++TTxet/3QRH598sgjdGatq5tKtU1K60YmXEwgUBuitMjG2W2yKp4SYSIcn24MlSTwPG1gtf7z2eqwosOaABVSVMLRsYDVuX3U30GqGwJK0BslsyC4RXNElWxEr15XE7qPDKKfAg5Mc541zAVm1W7ZUfFRRsY0v9EnEVWmulIKMTXXE0rfd6MINHT3Z/OB0kMDy8KPZwGrx47XXY3W8BfGqUZfQVlhNW6Qx/EqbUzUAlZ+SlVPIQCHLzCSXOFf1A0UDGLpNTFpmJop8OZ1xcUnxSS5/ZXl5TU0dG5ozkpH754h1GB1GHahmi+7i9IEganYBPTTanei/64xYXKzTW3ufR1/FMQo1p3lOpGRKIQ/P1+F129ZCC6EzESs9M9u0zLT0xEQ0MFTASk4G0Yg2AJZqAdzVTa4huYuVpfKpNOBnKdZNAwviqhs3F+f65emZmfS4Xxtgte/jtd+jRaeZr1GKaNorhLZZTBoG6xOCm+glo0JqZlp2GgMLZEoU6NBvk1mBlbA8So+JQet0fpgkr05NyI1NSdV9uqTDQqzqLa5LtKLrOpluJcS3tIHV4sdrv0eLTrO8RnENI5f2te3raaHA6qavQjBLgJUmwGLXTvMqm/URA4uRlRQXp86obqLE2JwaWPxDoqT+oVUC7hXzdQFWOz9eOz5cVFroa/xaxWdsa86ETvqnbrFGyySQKS1bWoI7NbCckvfAwML9BFher6G0HNJ6SZ9klhiWM5GTleU2DKyYpjsd22abbbaFWBCwumn3jcwJiZWWbQKLpblFeGlgocpCJGDh9mHAUrdB3xP7ndM222w7MxPvzwIsiVUBW2BTWlokYBkgOyNgOS0ZuEiniA1anbTNNttsa84ArDSrS2gCKxU5WTECJqcClhHaEo45w4Cl7hwbGVgGnBSwYm1g2WabbS03UVhGx2Cj9Td9pKbqzToSa4JJMF50FwJe+nrdkDI2giWqNUYrm2xQ2WabbWduTQIrNVV5jEHAihFeOTlnIQxYuXxow/c2sGyzzbZ2MimNGuk3DKxkM+3BqrFiGgWWXk40FwkBrFA82cCyzTbbWmFnCixnjBZdTbmE1rQGG1i22Wbbl2YWWPG2QyCMCWdkQEhdLZjhUioLBVhHPH/bbLPta2ShwHIYiswGlm222RZlFgwspCiEu5AaWMYVytN0htiX+sRts822r5+1BliN9Tn7cp+5bbbZZpvFGgvYm2aDyjbbbIsSax5Yttlmm21RYjawbLPNtk5jNrBss80222yzzTbbbLPNNttss80222yzzTbbbLPNNttss80222yzzTbbbLPNNttss80222yzzTbbbLPNNttss80222yzzTbbbLPNNttss80222yzzTbbbLPNNttss80222yzzTbbbLPNNttss80222yzzTbbbLPNNttss+2sWFKj1tHPzDbbbLMtxGxg2WabbZ3GbGDZZpttncZsYNlmm22dxmxg2WabbZ3GbGDZZpttncZsYNlmm22dxmxg2WabbZ3DwKWExpFlg8s222yLGmNe2cCyzTbbOoPZwLLNNts6jdnAss22MHOGWEc/H9u02cCyzbYws4EVrWYDyzbbwswGVrSaDSzbbAszG1jRajawbLMtotnAikazgWWbbRHNBlY0mg0s22yLaDawotFsYNlmW0SzgRWNZgPLto63/w//lztu3qVRSgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=P size=1200x660 at 0x2016E6DA080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "im = Image.open('sistemas_de_ecuaciones.png','r')\n",
    "display(im)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si no ha resuelto el acertijo, lo invitamos a hacerlo en este momento."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hecho lo anterior, ahora resuelva este sistema de ecuaciones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 x = 30$$"
      ],
      "text/plain": [
       "3⋅x = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + 8 y = 18$$"
      ],
      "text/plain": [
       "x + 8⋅y = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.core.display import *\n",
    "import sympy as sp\n",
    "from sympy import *\n",
    "from sympy import init_printing\n",
    "from sympy.plotting import plot\n",
    "init_printing()\n",
    "x=sp.symbols(\"x\")\n",
    "y=sp.symbols(\"y\")\n",
    "ecu1=sp.Eq(3*x,30)\n",
    "ecu2=sp.Eq(x+8*y,18)\n",
    "manzana=sp.symbols(\"manzana\")\n",
    "banano=sp.symbols(\"banano\")\n",
    "f1=sp.Eq(manzana+manzana+manzana,30)\n",
    "f2=sp.Eq(manzana+banano+banano+banano+banano+banano+banano+banano+banano,18)\n",
    "display(ecu1)\n",
    "display(ecu2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Algún problema?\n",
    "\n",
    "Si le parece extraño que tan abruptamente se le mande a resolver dos ecuaciones después de haber calculado con frutas, no se preocupe. Vamos por partes (como dijo Jack):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuando usted resolvió el problema de las frutas, solucionó un sistema de ecuaciones lineales (así como lo oye); lo único que cambió fue la forma en que se le presentó el problema. Si se le muestran frutas en vez de las tétricas $x$ y $y$, la gente tiene a ser menos reacia a solucionarlo. Encuentra fascinante resolver acertijos con objetos (como frutas), cosas visualmente estimulantes; en cambio, con $x$ y $y$ ya se encuentran ante un problema de talla mayor al cual pueden responder que no tienen los conocimientos para resolverlo (aunque en uno u otro problema se haga exactamente lo mismo). Lo anterior, valida la idea de que para conocer y aprender, es tanto o más importante el mensajero que el mensaje (ese es uno de nuestros retos como profesores, entender esa idea)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Volviendo a las frutas, se entiende que cada manzana equivale a $10$ $(30/3=10)$. Luego, el banano equivale a $1$ (a $18$ se le quitan $10$ de la manzana, quedando $8$; hay $8$ bananos que se están sumando entr sí, por lo cual cada banano equivale a $1$). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Piense en un momento en que las manzanas se van a representar con la letra $x$ y los bananos con la letra $y$... entonces la primera línea de frutas quedaría:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 manzana = 30$$"
      ],
      "text/plain": [
       "3⋅manzana = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 x = 30$$"
      ],
      "text/plain": [
       "3⋅x = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f1)\n",
    "display(ecu1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y la segunda línea de frutas quedaría así:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$8 banano + manzana = 18$$"
      ],
      "text/plain": [
       "8⋅banano + manzana = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHEAAAAWCAYAAAD3j3MyAAAABHNCSVQICAgIfAhkiAAAA3NJREFUaIHt2EmIXFUUBuAvcYK4UJyIURSMYlYGRYmCkYoTaERbiYLBoRbBAQWbBFRcZaWJxOAQEIdFN7oyoiG40HbRDhhiAhrFCYJNg4JxbFEwGBLLxblFV7+urnrvdSXVhPfDo6hz7rn3/+95991zLxUqHAGsxAh+xH6MYSuu6CepgliFF/Ax/kIDr3eJORp0g41C8G94FRvwJg7gP9zVP2qFsEfo+Bvf6p7EOae7ngjVCsYtxCHswxkZ34rU59gsuR0prMAFmCfmoVMSC+uen2k0khrdlrHPw1DybShAfjY4V/D7FL9kfKPirT49Y18nOK6boc8L8S8+6h3NXBjFXsGtG8ronoKl4i34Bse02J9JBF7ORXkq6sqtxFPEhP+E0zK+q1Kfb2fsy5J96wx9juAgLirIpZeo6bwSC+s+NtPoC7yGe3G3WH1PYC3ewANlmZfAH3gMm8VLtQ2/YzFuxvu4PxPzmSgClrXp73Zch+fxZYdxB3FyAZ57ErdeoYzuaThbTMQ4HhaZfxfHlyRVV24lNjEghDVanr1YPUP7D1ObRS22E/EDfsZJXcYbz4zV7RkqJqfrSmyiqO5peKol8BMsyBk3rrcT8Kj4/G3GeYnHJXgvxT/dJuZJ0/f1ZrVXz6njcKKmexLL6J6GtSYnekkBgoNYn3m2mUxY1jfQoa9ainurjW+BOD8dEiJbsTLFbUz/l4jSfIco0PqNms5JbPpz687uiXAnNokSdyEewYM5CT7bxlbHLSKJH+TsB25Kv6NtfP9gF27FxaaW3DvEJFye/m8RRdpD8lWH/d4TC+vOJvFGDONrXC1K8TV4Dt/1kGgenJB+Zyqnm/YDGfuEOFBfKvaPa/AiPs857qAo8/NiWG+TWFY3uFJkegxnJtsq8fbOhmRducLmjhS3D2dlfDeIm4v9OLVN7Esmb0h+FWX7XEFN589pad1L8ac4myzO+HanTpeXJF1XLonzRTndEPeNw2Kf2y6ENMSnvh3uMbmnrylK+DBgQGwnQ6LSb+D7FtumlraldJ8vsj6h/SH42hS4s6SAuvJHjOPE522nEHRQ3GK8g+s7xC1PY+4yN4qZ9TpX6eOZ9mV1H1XYLiq4y/pNpEI5rBZv95Z+E6lQDOfgcbwi7h2/kv+CosIcwX1i9U2IO95FnZtXqFChQoUK0/A/X7o2cn8yTGUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$x + 8 y = 18$$"
      ],
      "text/plain": [
       "x + 8⋅y = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f2)\n",
    "display(ecu2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y hallando el valor de cada manzana y el valor de cada banano, se está hallando el valor de $x$ y $y$, respectivamente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI8AAAASCAYAAABim40OAAAABHNCSVQICAgIfAhkiAAABE9JREFUaIHt2FuoVVUUBuBPywuoqZlWkF00hUosj4EaFCdDsXrIB58kBKGXgsKohyICi8qiC12kG3irtB4yI4JKu5diaaUFpechjwWZlwyzu5fTwxybvc5q7XP2XnlOPuwfFmvP+Y8xx7/XGmuOOSdNNNFEEwWYgyfwEX5BB16ow+8MLMUP+AvteBTDe0RlE8cltkgJcxDfqC95xmJ32L6K+/FutLdhRE+JbeL4wuUYhz5oVV/yvBV2N+b6H4n+p7sK1oGH0CJl3n4cwBqcFnbnYxX2BPc6ziwYby5Wok3K/p+xCfMLbGdE7EWYEOPvxq/YgCkFPuvDp9b1QUktZfU0GqM30ar75BkTNjvQN8cNkf77bxgEJ+YMWuI+Hh/jDSzBLMzGADyFF6WpbEWIuhrPxe9ssBXYLNXcPRiFa6R6OgoPZOwnZWJvwrrwvwBX4TWcK72UCtaEXR7zpWR+r6SWMnrKxDjeMD3ua3E0xx2UPtaZmIp38s4rpcz7ERMz/UOkr+gwdmFahuuP7yLYwEz/YNWZKovTQ8i2XP9LEXuPahJXsDq4SwvGy+PBsF2m+vU0qqWMnjIxsliAhQ1cs7sZL49W3c88lWd3Sw1+cfDXF5GVRdWsAu6L4K4t4NYFV+9iarv0UvJ9HdIslsc9wc3oYsw+eDLsFke7rJZjoaeeGFm067oE56/ldcauoFX3yfNs2FxXg783+NvzxCAcwbc1HPfjJ/Qr4NqkrWAWw3EnNkqz1hGd//znGdvBwe9U/NJXhc+YGtpOkEpGh+LS0IiWsnoajdHbaPXfk+e+4G+j85rnQmmaL1pDnC09nFdwKMcNlrZ36zN9E6W6eSo+lUrA/vA9B/OwNWN/UcReG+LyaJEW5jsKuH7Sy5wjTed35fhGtZTRUybG8YgDcR9agz8pa5dNnkpd31zgNLkLbpL0oLNf1vMYJu3e3s/Z310wViX2ZwXjD5G2mx/694sciJel0nIrHi7wb1RLGT1lYuSxIMaoF1uk3fCxxPa4j6/Bj4t7W55YKj2M/OKQ6nQ1s4C7Kbh50R4d7TcLbIfh++CnZvqXRd/FBT6XqR4fZDFIWvEfVWMBV1JLo3rKxsij3f+/5hmr+63672KrnsUW6Si6f8GglYOjUwq45cFNiPbIaLfpvD4akRnnkM47s61dxL45fOZm+oZKZfKwatIWoYyWRvWUjdHbaHWMDwkrZWuAdPD3Jf4uGLBFWjzuq8H9Ie3UYK90BjQdn+Btabt6pXTuchRf489M7PPwVY3YlZKZLSGrcIm0vhgjrXXyWFRCSxk9ZWL0FmarbukrxwjTVGetfVK5z+IG6RD0cVwhvdcpUkluwx35IJOlrHqmQMBZwa0u4AZIX9XGXP9I6dBwr3TGsUGaISbFWEvqjC3EH1SdRvtGu6spfXdJLWX0lInRW1io6+fUXsNvtFS6d0kf0E48hpN7VG0TTTTRRBNN9Bz+ARLi0Jf2SfHkAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$manzana = 10$$"
      ],
      "text/plain": [
       "manzana = 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x = 10$$"
      ],
      "text/plain": [
       "x = 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$banano = 1$$"
      ],
      "text/plain": [
       "banano = 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$y = 1$$"
      ],
      "text/plain": [
       "y = 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sp.Eq(manzana,10))\n",
    "display(sp.Eq(x,10))\n",
    "display(sp.Eq(banano,1))\n",
    "display(sp.Eq(y,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora tenemos todos los ingredientes para la caracterización de los sistemas de ecuaciones lineales:\n",
    "\n",
    "## Caracterización\n",
    "\n",
    "1. Un sistema de ecuaciones es el conjunto de dos o más ecuaciones (las cuales comparten las mismas variables, explícita o implícitamente). Ejemplo: _las dos líneas de frutas, las dos ecuaciones_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 manzana = 30$$"
      ],
      "text/plain": [
       "3⋅manzana = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$8 banano + manzana = 18$$"
      ],
      "text/plain": [
       "8⋅banano + manzana = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 x = 30$$"
      ],
      "text/plain": [
       "3⋅x = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + 8 y = 18$$"
      ],
      "text/plain": [
       "x + 8⋅y = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f1)\n",
    "display(f2)\n",
    "print(\"--------\")\n",
    "display(ecu1)\n",
    "display(ecu2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Un sistema de ecuaciones lineales consiste en un sistema de ecuaciones en el que el máximo exponente de las dos variables que tienen las ecuaciones es 1. Ejemplo: _$x$ tiene un exponente 1, $y$ tiene un exponente 1_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Resolver o solucionar un sistema de ecuaciones lineales consiste en hallar los valores de las dos variables que hacen que se cumplan ambas ecuaciones al tiempo; en otras palabras, se trata de hallar cuánto valen las variables a fin de que se cumplan las igualdades expresadas en las ecuaciones. Ejemplo: _hallar cuánto vale la manzana, hallar cuánto vale el banano; hallar cuánto vale $x$, hallar cuánto vale $y$._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$manzana = 10$$"
      ],
      "text/plain": [
       "manzana = 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$banano = 1$$"
      ],
      "text/plain": [
       "banano = 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x = 10$$"
      ],
      "text/plain": [
       "x = 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$y = 1$$"
      ],
      "text/plain": [
       "y = 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( 10, \\quad 1\\right )$$"
      ],
      "text/plain": [
       "(10, 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sp.Eq(manzana,10))\n",
    "display(sp.Eq(banano,1))\n",
    "display(sp.Eq(x,10))\n",
    "display(sp.Eq(y,1))\n",
    "display((10,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. La manera de saber si las soluciones halladas son correctas, es reemplazando los valores obtenidos en las ecuaciones iniciales y verificando que se llegue a una premisa verdadera. Compruébelo: reemplace el valor $10$ en $x$ y $1$ en el valor $y$; resuelva y verifique si hay verdad en las igualdades presentadas (\"True\")."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 x = 30$$"
      ],
      "text/plain": [
       "3⋅x = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + 8 y = 18$$"
      ],
      "text/plain": [
       "x + 8⋅y = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\mathrm{True}$$"
      ],
      "text/plain": [
       "True"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\mathrm{True}$$"
      ],
      "text/plain": [
       "True"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(ecu1)\n",
    "display(ecu2)\n",
    "print(\"------\")\n",
    "display(sp.Eq(3*10,30))\n",
    "display(sp.Eq(10+8*1,18))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Métodos de solución de sistemas de ecuaciones lineales\n",
    "Existen múltiples maneras de solucionar sistemas de ecuaciones lineales (*Regla de Cramer*, *Eliminación Gauss Jordan o por matrices*, etc.). En esta lección nos centraremos en 4: de forma gráfica, por igualación, por eliminación y por sustitución."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### De forma gráfica"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si graficaramos las ecuaciones anteriores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 x = 30$$"
      ],
      "text/plain": [
       "3⋅x = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + 8 y = 18$$"
      ],
      "text/plain": [
       "x + 8⋅y = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(ecu1)\n",
    "display(ecu2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tendríamos una gráfica así que tiene dos líneas. Ambas se cruzan en el punto $(10,1)$ (compruébelo). Pues bien, encontrar la solución a un sistema de ecuaciones de forma gráfica consiste en encontrar el punto exacto en que las dos rectas se cruzan. La limitación de este método está en que hay sistemas que tienen su intersección en números decimales difíciles de estimar (este método es muy inexacto e impreciso)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una recomendación de graficación, que es fácil de usar, es Geogebra. Te dejamos el siguiente enlace para que grafiques tus sistemas de ecuaciones (sólo debes escribir en el módulo la ecuación como la tienes): https://www.geogebra.org/graphing Dándole clic en el punto de intersección te dará la respuesta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Por igualación\n",
    "Este método consiste en despejar en ambas ecuaciones la misma variable (por ejemplo la $x$). Como esa variable debe valer lo mismo en ambas ecuaciones, entonces es posible unir ambas nuevas ecuaciones por intermedio de esa variable (igualarlas, de ahí el nombre del método). Te dejamos un video que muestra el procedimiento. Te animamos a que hagas lo mismo para las ecuaciones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 x = 30$$"
      ],
      "text/plain": [
       "3⋅x = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x + 8 y = 18$$"
      ],
      "text/plain": [
       "x + 8⋅y = 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(ecu1)\n",
    "display(ecu2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "F:\\Python\\lib\\site-packages\\IPython\\core\\display.py:689: UserWarning: Consider using IPython.display.IFrame instead\n",
      "  warnings.warn(\"Consider using IPython.display.IFrame instead\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/lTRANviJWEY\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/lTRANviJWEY\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Por eliminación\n",
    "Este método puede ser un poco más complicado. Consiste en multiplicar (o dividir) a todas las ecuaciones por factores que permitan llegar a tener (para la misma variable) un coeficiente positivo en una ecuación y el mismo coeficiente, pero negativo, en la otra (ejemplo: $3x$ y $-3x$). Te dejamos un video en donde se explica tal método. Anímate a resolver las *ecuaciones de las frutas* con este método."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "F:\\Python\\lib\\site-packages\\IPython\\core\\display.py:689: UserWarning: Consider using IPython.display.IFrame instead\n",
      "  warnings.warn(\"Consider using IPython.display.IFrame instead\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/v6iKv3QXqNs\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/v6iKv3QXqNs\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Por sustitución"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Este es el método más intuitivo (tanto como para ser el que uno usa para resolver los problemas de las frutas). Consiste en despejar una variable en una de las ecuaciones y remplazar la expresión equivalente en la posición de la misma variable en la otra ecuación. Te dejamos un video a continuación. Intenta resolver las *ecuaciones de las frutas* con este método."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "F:\\Python\\lib\\site-packages\\IPython\\core\\display.py:689: UserWarning: Consider using IPython.display.IFrame instead\n",
      "  warnings.warn(\"Consider using IPython.display.IFrame instead\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/3FHhPLVUt9o\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/3FHhPLVUt9o\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Terminología"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este punto ya sabemos resolver sistemas de ecuaciones lineales. Vamos a hablar de los últimos tres términos que necesitas saber: sistema consistente determinado, sistema consistente indeterminado y sistema inconsistente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sistema consistente determinado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En las *ecuaciones de las frutas* vimos que sólo cuando $x$ vale 10 y $y$ vale 1 es que el sistema cumple las igualdades. Pues bien, eso es un sistema de ecuaciones **consistente** (que tiene solución) **determinado** (que tiene una única solución). Su gráfica (la del sistema) son dos lineas rectas que se cruzan en un único punto (el punto que representa la solución)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sistema consistente indeterminado "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grafica este sistema de ecuaciones lineales:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$4 x + 5 y = 30$$"
      ],
      "text/plain": [
       "4⋅x + 5⋅y = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$8 x + 10 y = 60$$"
      ],
      "text/plain": [
       "8⋅x + 10⋅y = 60"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sp.Eq(4*x+5*y,30))\n",
    "display(sp.Eq(8*x+10*y,60))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Notaste que ambas ecuaciones se superponen? Pues bien, quiere decir que técnicamente son la misma ecuación (tanto como que la segunda es el doble de la primera). En este caso, al ser la misma ecuación, el sistema comparte todos los puntos entre sí (la línea de la ecuación 1 toca todos los puntos de la línea de la ecuación 2). Por esta razón se dice que tiene infinitas soluciones. El sistema es pues uno **consistente** (tiene respuesta) **indeterminado**(no hay una única y puntual solución, sino infinitas)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En los métodos no gráficos de solución se identifica un sistema de ecuaciones consistente indeterminado por cuanto las simplifaciones son absolutas (incluso de las variables) y llegamos a expresiones sin variables que son verdad (tu profesor explicará más este punto)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sistema inconsistente"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grafica este sistema:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$4 x + 5 y = 30$$"
      ],
      "text/plain": [
       "4⋅x + 5⋅y = 30"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$4 x + 5 y = 20$$"
      ],
      "text/plain": [
       "4⋅x + 5⋅y = 20"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sp.Eq(4*x+5*y,30))\n",
    "display(sp.Eq(4*x+5*y,20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Ves que no se cruzan? Pues bien, por nunca cruzarse se dice que ambas rectas son *paralelas*. Cuando las dos líneas rectas de un sistema de ecuaciones lineal son paralelas, el sistema no tiene solución (no hay puntos de cruce entre las ecuaciones del sistema). De ahí que se le diga al sistema **inconsistente** (no hay solución del sistema)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En los métodos no gráficos de solución se identifica un sistema de ecuaciones inconsistente  por cuanto las simplifaciones son absolutas (incluso de las variables) y llegamos a expresiones sin variables que son falsas -no tiene sentido- (tu profesor explicará más este punto)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Video resumen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aquí te mostramos un video resumen de la anterior terminología. (Nota: aquí usan la palabra *dependiente* como sinónimo de *determinado*, en otros videos usan la palabra *compatible* como sinómino de *consistente*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "F:\\Python\\lib\\site-packages\\IPython\\core\\display.py:689: UserWarning: Consider using IPython.display.IFrame instead\n",
      "  warnings.warn(\"Consider using IPython.display.IFrame instead\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/GV1H_ac5QSw\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/GV1H_ac5QSw\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solucionador de ecuaciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En https://www.geogebra.org/graphing puedes graficarlas, y si pones la palabra \"interseca()\" y dentro de los paréntesis los nombres de las ecuaciones, él automáticamente te calcula su punto de intersección."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fuentes de los videos\n",
    "\n",
    "Caneles de YouTube:\n",
    "1. [julioprofe](https://www.youtube.com/user/julioprofe)\n",
    "2. [profezuluaga.com](https://www.youtube.com/channel/UCPW6RPrqFQMHzUZlhnctnNw)"
   ]
  }
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