{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Zm_gfqcWRMKr"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/IrisFDTD/OPTICS-UNIZAR/blob/main/Topic_9/chapter9_twyman_fourier.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tYZjdh8TvE7-"
   },
   "source": [
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"><img alt=\"Licencia Creative Commons\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\"></span> The following notes written by  <span xmlns:cc=\"http://creativecommons.org/ns#\" property=\"cc:attributionName\">Sergio Gutiérrez Rodrigo (<sergut@unizar.es>) </span>. Distributed under  <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\">License Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j2H5UHGe1Uf8"
   },
   "source": [
    "```\n",
    "Departamento de Física Aplicada\n",
    "Universidad de Zaragoza\n",
    "Instituto de Nanociencia y Materiales de Aragón (INMA)\n",
    "C/ Pedro Cerbuna, 12, 50009, Zaragoza, España\n",
    "```\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D7vYGeB21ZQU"
   },
   "source": [
    "---\n",
    "# **Óptica - Tema 9 - Interferómetro de Twyman - Interferometría por transformada de Fourier**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pHK91d3vcJ9L"
   },
   "source": [
    "# Cálculo de $g_p(\\nu)$ numérico (usando la integral)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pmL024TIcaqO"
   },
   "source": [
    "![image.png](data:image/png;base64,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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OkU24WATUiRr"
   },
   "source": [
    "![image.png](data:image/png;base64,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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "duBQ0vPgc1Ny"
   },
   "outputs": [],
   "source": [
    "# Define the functions\n",
    "def gamma(t, v, v0, Dv):\n",
    "  return np.exp(1j*2.0 * np.pi * v0 * t) * np.sin(np.pi * Dv * t)/(np.pi * Dv * t)\n",
    "\n",
    "def gp(t, v, v0, Dv):\n",
    "    return  np.cos(2.0 * np.pi * v * t)*np.real(gamma(t, v, v0, Dv))\n",
    "\n",
    "def gamma_r(t, v, v0, Dv):\n",
    "  return np.cos(2.0 * np.pi * v * t)*1/Dv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 256,
     "status": "ok",
     "timestamp": 1702324764720,
     "user": {
      "displayName": "SERGIO GUTIERREZ RODRIGO",
      "userId": "07959720391705098820"
     },
     "user_tz": -60
    },
    "id": "WkxdCQXFA56y",
    "outputId": "eca1f603-7208-4de4-f1f1-b3707d8adc93"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For v0= 80.0  the value of g(v) at v 80.0\n",
      "g(v) analytic= 0.2\n",
      "gp(v)= 0.10402044326282249\n",
      "2*gp(v)= 0.20804088652564498\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import simpson\n",
    "\n",
    "# Parameters\n",
    "v0 = 80.0\n",
    "Dv = 5.0\n",
    "\n",
    "# Integration limits\n",
    "t_min = -np.inf\n",
    "t_max = np.inf\n",
    "\n",
    "# Perform the integration\n",
    "t=np.linspace(-1.0,1.0,10000)\n",
    "v=v0\n",
    "gp_num=gp(t,v,v0,Dv)\n",
    "integral_gp=simpson(gp_num,t)\n",
    "\n",
    "# Display the result\n",
    "print(\"For v0=\",v0,\" the value of g(v) at v\",v)\n",
    "print(\"g(v) analytic=\",1/Dv)\n",
    "print(\"gp(v)=\",integral_gp)\n",
    "print(\"2*gp(v)=\",2.0*integral_gp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BTUPWQ3q91br"
   },
   "source": [
    "# Compare $Re(\\gamma(\\tau))$: numeric vs analytic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Fiyjn5DI96fR"
   },
   "source": [
    "![image.png](data:image/png;base64,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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 293,
     "status": "ok",
     "timestamp": 1702324782990,
     "user": {
      "displayName": "SERGIO GUTIERREZ RODRIGO",
      "userId": "07959720391705098820"
     },
     "user_tz": -60
    },
    "id": "kSS8RYSa9O7r",
    "outputId": "697c8e7c-1963-47d3-8e65-3bd33feb0aa2"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-2-452f911f85e7>:3: RuntimeWarning: invalid value encountered in cdouble_scalars\n",
      "  return np.exp(1j*2.0 * np.pi * v0 * t) * np.sin(np.pi * Dv * t)/(np.pi * Dv * t)\n"
     ]
    }
   ],
   "source": [
    "t_0=0.1\n",
    "int_gamma_r=[]\n",
    "t_num=np.linspace(0,0.1,200)\n",
    "for i,t_0 in enumerate(t_num):\n",
    "  # Integral nu>0\n",
    "  nu_gamma=np.linspace(v0-Dv/2.0,v0+Dv/2.0,1000)\n",
    "  gamma_r_num=gamma_r(t_0,nu_gamma,v0,2*Dv) # Factor 2 for gp definition\n",
    "  integral_gamma_r=simpson(gamma_r_num,nu_gamma)\n",
    "\n",
    "  # Integral nu<0\n",
    "  nu_gamma=np.linspace(-v0-Dv/2,-v0+Dv/2,1000)\n",
    "  gamma_r_num=gamma_r(t_0,nu_gamma,v0,2*Dv)# Factor 2 for gp definition\n",
    "  integral_gamma_r=integral_gamma_r+simpson(gamma_r_num,nu_gamma)\n",
    "\n",
    "  #print(\"Integral gamma_r=\",integral_gamma_r,\" at tau=\",t_0)\n",
    "  analytic_gamma_r=np.real(gamma(t_0, v0, v0, Dv))\n",
    "  #print(\"Analytic gamma r=\",analytic_gamma_r,\" at tau=\",t_0)\n",
    "  int_gamma_r.append(integral_gamma_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 484
    },
    "executionInfo": {
     "elapsed": 923,
     "status": "ok",
     "timestamp": 1702324789146,
     "user": {
      "displayName": "SERGIO GUTIERREZ RODRIGO",
      "userId": "07959720391705098820"
     },
     "user_tz": -60
    },
    "id": "T6kV4SKNTPij",
    "outputId": "f8c9ac68-8b91-4cf3-9920-0e129c97ecde"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-2-452f911f85e7>:3: RuntimeWarning: invalid value encountered in divide\n",
      "  return np.exp(1j*2.0 * np.pi * v0 * t) * np.sin(np.pi * Dv * t)/(np.pi * Dv * t)\n"
     ]
    },
    {
     "data": {
      "image/png": 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aLGKR3W+Xd+bQxMTE5GSYwVOZUju2AUEQ8KZidEVTpZ7OsDh64Ch//+bTrNr+IvYT2/UdDhxBPwBdRzpO8uryoHefpHBva2iA48Q+XV53//Ed3n+0JHNTi+372gimYvhddqqnSkuTlTMlc862LWdX8JTNF+mOZ86KbKGJicnwMYOnMsVWEcLtdmIRi7Qdbiv1dIZF90EpaPAHPAMCCwV7TTUAfUfKV0k91iwdo+eEbkIAT610fEcPlefnp7D3HcmGIdBQA7K9wtiFkrJwdH8zhTLNjJ5ILpvjjvue4cp/foaLvvUybZHyvGkxMTEZOWbwVK4IAtYqqd29q7k8g4uwHFg460/uG+iqrQIg2la+dV3tsSxxh5vguNHvey5QLwVP5fr5KbTtPABAxeRjBfFjli7gmYVX8+S05bT0JUs1NVV59X/+wPw//46Pb3mBj7z8OH/59/8p9ZRMTD6Q3HvvvcybN6+kczCDpzLm4GXX8R/nfpQ9PoOYFg+RxFFpOc43+uTz9zdI2uKJzvKteXq+Zjr/vfgjBC9Y+r7nKhprAYi1l7cFTeawpNVVM/VY8GT1evCPbwJBYH9XeQu5gmQjtOElSXphVEjKrrX+9S3iaf0NSU1MPuh8+ctfZs2aNSWdgxk8lTFVTXVkbfayvbNPdUhBgyK7cCKOpefy08Uf4cUxC/Sclmoks3k6Y1Kn4Lhq3/ue900ax96qMeyxvP+5ciFfKGJtl5Yd66dPHPDcxFrpuPZ3lr9K/PbDPTg72nDYLFz98DfZsPw6/mP+tbywrbyzhiYm5YQoiuTzeXw+H1VVVSWdixk8lTGjK6Q74Ja+8qy9yPRJtiU1DSd3r2scVU3S4eZoOK3ntFSjuVcKaoNuO0HP+40qKxbO5fnpF/BX7+iyLUBu6U3y/ORlvDl5ETVTxg14bn6+j5W715F77a+lmZyKbH97J7ZigZq6SjyjGph//lyKFisbD50dCvEmH2yWL1/O//t//4+vfOUrVFZWUl9fz7333gvAoUOHEASBLVu29G8fDocRBKHfr27t2rUIgsDLL7/M/PnzcbvdXHLJJXR2dvLiiy8yffp0AoEAf/M3f0Myeexmv1gscv/99zN+/Hjcbjdz587lN7/5Tf/zyn5ffPFFFi5ciNPp5PXXXz/pst2jjz7KzJkzcTqdNDQ0sGrVKq3eLsA0Bi5rRpPh0n0bqO/xwqeXnPkFBqJYFCnGYliB6obKk27TKC+PxDJ5IqkcQbf2Ttlq0rFlF59663fYJowDLn/f842yPEM8kyeazpfd8QEc6ElwNFiLf+pELK6BBtUTnQXiXQfJ77OWaHbqsXtXCz6rncrpk0EQWDROspPYdLivxDMzKQuy2VM/Z7GAzTa4bQUB7PbTb+sYniH3Y489xurVq9mwYQPr16/nk5/8JOeddx6TJ08e9D7uvfdefvKTn+DxePjoRz/KRz/6UZxOJ7/61a+Ix+N8+MMf5sc//jFf/epXAbj//vt54oknePjhh5k8eTKvvfYat956KzU1NVx00UX9+/3nf/5nfvCDHzBhwgQqKireZzL8n//5n6xevZrvfOc7XHnllUQiEd54441hvQ+DxQyeypg6l8Ds9n2IEc+ZNzYYvfE0uyub8ObSVDdUn3Qbj8PGyo73sPf20HZ4DsFpTTrPcmSE27sIZOIEbSc3yPU4bFR67GT6IhztjhNsKj9/pwOycfOEGu/7nhs1rp53gVQZ16yBVO/020Il8XNv5PcfXwjAgko7l+7bQGB7gu7PLaXa5zzDXkw+0Hz726d+bvJk+PjHj/37+9+H3Clq6caNg09+8ti/H3wQkieUbcgZo6EyZ84c7rnnHnlKk/nJT37CmjVrhhQ8fetb3+K8884D4NOf/jR33XUX+/fvZ8IEyX7rxhtv5C9/+Qtf/epXyWQyfPvb3+ZPf/oTS5dKNaETJkzg9ddf57/+678GBE/33Xcfl1122WnH/cd//Ee+9KUv9T92zjnnDP7gh4EZPJUxVXXymm8qRTqTw+Usn8xFRzzLH6dIFx2723XK7ebF28j0dNB7uBXKLHiKdUpLOu7KUwdFn3v3eZIdXXTvmwxlGDxFtu1kRscBpi96f/1B0zhJCNQaj9ITS1PlP/XnbGT2dMSIpfP4XA6mT5Dq80IhHxfGW+iLp9nyXjMrlgz+AmNiYkTmzJkz4N8NDQ10dg7NIeD4fdTV1eHxePoDJ+WxjRs3ArBv3z6SyeT7gqJsNsv8+fMHPLZo0aJTjtnZ2UlrayuXXnrpkOY6UszgqYwJVPqxWCwUi0W623sZPbZ8uu46olIdU13g9HfslspKaOsg1l5+cgXxbmlJx1cTOuU2rooAyY4u+o6Wp42J451NXL53FzNSE973nLu6Aq/TTiKTo+VIJ1UzxpRghiNnd5ukAD+jIYDNKpeJOhwExo2ib/t+Dr+zE86S4EkURd5tiTCxxovfVT43Y4bnX/7l1M9ZTig9/qd/OvW2J+rh3XnnsKd0Inb7wM9bEASKxSIWeX7H12XmTpEZO34fgiCccp8A8bjUhfv8888zatSoAds5nQOvC17v+zPbCm5ZW05vzILxMkawWrH6pY6mno7yWhrp7I1jK+SpC5w+G+GqDAIQ6w7rMCt1SfeGAQjUnLymC8AlC4FGyjA4BEjJAWLd6JMU/Vut2Cqkz6/7aHkeH0By7Wt88u3fszx6cMDjvklSwJjYe/BkLytLfvfDX/Krz97D9V99kt++01Lq6Zw9OByn/rPZBr/tCcHISbdRmZoa6bfd1nZMzPf44vHhMmPGDJxOJ83NzUyaNGnAX1PT4FcZ/H4/48aN0126wMw8lTn2gJ9cJEpfV7jUUxkamzazav1vqbIsBk69Nu2pCNIHJHsjuk1NLbJ9ERxARf2pgyevvPSaKMPgqVAUKUakrEztqNqTbuOoqoT2bnrLNLMGkNx7gFA6xpjgwLvhqumT4LlXyB8+XKKZqcv+rjj3HXVxvt3JtZte5KW+Fq746ZdxmxmoDzRut5tzzz2X73znO4wfP57Ozk6+/vWvj3i/fr+fL3/5y/zDP/wDxWKR888/v7/QOxAI8IlPfGLQ+7r33nv53Oc+R21tLVdeeSWxWIw33niDL37xiyOe56kwM09ljiMk+aNFusqr6yfeEwbAHzx1OhbAVyVlLlLh8jLPFUWRQlSac1XdyQviASoapbu6dFf5tbx39sVxZVNYBIGqUwRPntpKRITyC+6PI90maTnVTR24NNk4R/Lvs3Z0kkuVp5zG8fz01QMksDChqYqA2870A9t4/amXSz0tEwPw6KOPks/nWbhwIXfeeSff+ta3VNnvN7/5Tb7xjW9w//33M336dK644gqef/55xo8ff+YXH8cnPvEJHnzwQf7jP/6DmTNncs0117B3715V5ngqzMxTmeMKyctaveUVXKTkJS1f1emLpP3V0vOZSEzrKalKXyJLr91LoAhVjacWc/M3SnVqYl9Yp5mpR0eLlC1zelxYPSevO0iuWMmPM+O4pLaRz+o5OZXIZHPkesMIwJgJjQOeqxtdS9HpwpJJ07L/KONnTTz5TsoAURRZu6eTjN3Jws99ir4/vEz02RfY8upmLvvENaWenonGnNj6D/Dcc8/1///06dNZt27dgOePr4Favnz5+7TqPvnJT/LJ4zsDkTJE9x7XDSgIAl/60pcGdMkdz8n2e7L9APzd3/0df/d3f3fS/WiBmXkqc6IXXcJ/nPtRNo+aVuqpDIlMnxTsBWtOHzxVVIcAyEbLy+KjLZrmmTmX8buLP4rzNN12SuZJiIQR5ULKckGpY7KFAic1dgZorKugaLFyNFyeQq7NhzoQikXsNhu1owZmEAVBwF5XQ8Tl43B7uDQTVIldrRGWvPlHzu3YzTmj/Cy9XFpKzx46TDR1Gt0hE5MPKGbmqcypqqkga7PTFS+vE1wuEsUGhGpPHzyFpk7g4SU3UHC6+EdRRDjFRdpoHOsmPH1BfHVjDbtqxpGyu4jEUoTOsIxpJMJyndbpgsNRsgp+a5kGT0cOSkWyzuoKBOv7xT4PfugWnt3SSrU1yHKd56Ymm17fyoTeFi5wJnG5HLimTsDvcUIyxdYdRzh/Yflm1UxMtMDMPJU5tXKrf2c0U+KZDJ58oYgot6lW1J/en6gm5CVtd5ErQl+yfExY2yJS8NQQPEM3ocvB+nnLeXXCQjrT5ZV52u2r47czLya25LxTbtPohJW717Fi40tlaaLbIxe6u2tO/j2dWCfVHO7vLK/M6Im0btgCQNX8mVLrvN1OYKzUPr5/084SzszExJiYwVOZU59PsmLvBqZseq3UUxk0vfE07qwUXFTUnroTDcBhs1Ah+8J1xsqnKLe4+R0+9dbvWHZg8xm3rfFLAXBXrHwCYIDDaYHDFY34pp46K+HzuZnX10xTpJ3W1vKS0wBoS+Tp8FXhHN140uebKiV1/3L1l+xn7x4AGhbP7X/Ic9F5rJm4mNdS5SluamKiJWbwVOZUOARmdeyjsfUAhWJ5mMv2hJPsqJtAd/0YrL4zL1Nd1r6Dq3f+ld5DrTrMTh0yXT0EMnEqB7EwXue148mm6C4zLatj2bXTiNTZbFJNFNDV0qHHtFTlHV8Dv553BfnL3u9NCDAu3cctW15ixtr/03lm6tFztBNHXy9FwcLYxccUoietOJ9tDZNZ150vm3OLEShXk+8PEmp8RmbwVOaE5IJqVzZDX7w8MjM9WXhl8rlsPO/K96vrnoTpsTYm9zSXlZBkRu4mdFeFzrjtip2v89mNz1J8511tJ6UywR3vMqPjAI3O0y83WiukmqhYW7ce01IVJaOk1G6dSEOFh/p4D86udvKF8lp2VTiw6xAA1uoqPAFf/+OTan04bRZSuQJHepOneLWJgqKmnTzRa87EcCif0YkK6EPBLBgvc2x+H067jUwuT19XH9WB0kjVD4WehLQ8VeUdnJmqIyDVlSTKSCgzJ+tS+eXg9nR4KgJEgHgZHV82X2Tmrrdx5zI0CNefdltbVQXshXhneQVPoijSIgcNoytObr5d1ViLVRBwZ1K098YZXRPQc4qq0LLvKAD+xoFaXVaLwHxXjvi+gxzaM5Fx1eXV0Xsyirk8T3/3F+y1+rn1jmsYX61eg4bVaiUUCvX7wXk8nrJpcPmgIIoiyWSSzs5OQqEQ1pM0gQwWM3gqdywWBJ8X+iKEu/pg4slrM4xEb59kzVLlG5yVgCMoBU/lpDKej0rdhP7TWLMoeGULmlRf+Wh19YTjuHMZLIJAsO70Rf+uKuk9SHWWV81TbzzD7X99krjDTaP9gpNuY/F6cPncJGJJOpo7yjJ4OtIRIWexUdXU8L7nrmzbSt++HfRubYJl5R88PfGzF+h96c/4gS8d7uPfv/W3qgZQ9fWScfRQDXVN9CUUCvV/VsPFDJ7OAqx+H/RFysb/zfn2Rlatf5Ea9/nAgjNvL9fMpMtJZTwqiXoGa08fWAD4leApUj7H19MqZZEcHheWUwhkKigWNJme8lLBbz3SiaOQY7QITr/v5BsJAraKEMSSdLd0wMLyMwh+MTiRnUur+e+r5r/vOe+EcfS9u4Po3kP6T0xljoZT/GB3ik/J/77ovdf53W/Hc+cdK1UbQxAEGhoaqK2tPaV5rklpsdvtI8o4KZR98PTQQw/x/e9/n/b2dubOncuPf/xjFi9efNJtly9fzquvvvq+x6+66iqef/55QFJFfeyxxwY8v3LlSl566SX1J68StjJb1krLGRaPf3B3fJ4KKXjKlonKeDKVwZaWlntO52unEFCEQMvk+ADC7VLwJAROLZCpEKgOISIQT5ZXN6FS4G6rCJ22Ns9ZXQnNrfSVYU2XKIoc7kmAIDChIfi+56snj6UFSLa2vf/FZcaL29qIOn2su3UV92R28Mozf4anniL9sQtw+U6+LDtcrFarKhdoE+NS1gXjTz31FKtXr+aee+5h8+bNzJ07l5UrV54yZfrss8/S1tbW/7d9+3asVis33XTTgO2uuOKKAdv9+te/1uNwho2yrBUvE4uWbEQK8jyVoUFtryxrlYvKeG9PjFZ/DXFvAF/FmZdxKqql48vHElpPTTVinZIXn63i/RfcE/HMnsm/n/cxnpm2XONZqUuPrKDuqDp9AOyVs4uxMmpoUOiKZ0hmC1iEk9d1NcmWNKmuvrLvInthmxQAXj2nkemf/wSWUAjSaV5fu6Wk8zIpT8o6eHrggQe44447uP3225kxYwYPP/wwHo+HRx999KTbV1ZWUl9f3//3yiuv4PF43hc8OZ3OAdtVVJxeBbvU9JwvWbS8N3ZGqacyKHJyhsVbExrU9n7ZHDgfL4/gqbNo5em5l/PixR9FGEQ3YVD277OkkuTKpGMrIRsZOypCZ9y2NugGQaArlimrC3CiQ6rRcp2hbs3XWEfE5aM9VR6f3fEcPdjOre+8wMeaN+Kwvj+D2DSuAUEQsKaTdHSXT2b0RNr7ktT86QUm9rZwxYxaLA57v7HzgS27Szw7k3KkbIOnbDbLpk2bWLFiRf9jFouFFStWsH79+kHt42c/+xm33HILXu/A5aO1a9dSW1vL1KlT+fznP09Pz+kLXTOZDNFodMCfngSrgmRtdnrLRIG7KL8/gerBBaXeaVP4zyU38tiMy7Sclmp0y2KX1f7BdRMGayvZUzOOHbUT6IuXx9JWqlsKnlxnMHaGYyKg2UKRSKo8vqMAqW7pd++prT7tdu4Lz+fni67j1bryK6huP9RKdaKPycX4SZdfHT5P/5JW6+F2vaenGjtee5vpnQf5eOe71Mnfx1EzJ5O3WDnQ0lvi2ZmUI2UbPHV3d1MoFKirqxvweF1dHe3tZ/6Rb9y4ke3bt/OZz3xmwONXXHEFjz/+OGvWrOG73/0ur776KldeeSWFQuGU+7r//vsJBoP9f01NTcM7qGGidK11l4O/nShCTMoghc5gCqxQGfSQsTtJ5Iqkc6f+HIyC8jnUDLKb0OJ2sWHBxbw6YSE9ZRIAb2qayW9nXow4e/YZt3XZrVx/cAM3bvsT3a3ls7SV75Euqv660wdPxyySykNn7Xh6jkjnSvdpjtEmB8jlKHKq0PGuZDFjmz0L5FqkyVddxH+cexNPhqYRTpbBudPEUJRt8DRSfvaznzF79uz3FZffcsstfOhDH2L27Nlcf/31/N///R9vvfUWa9euPeW+7rrrLiKRSP/fkSNHNJ79QGpzCVbs3cCkt41v0ZJMphHlLpSKM5gCKwRcNuzykkJPwvgnOduG9Xz6redYfGjroF+jBMA95RAAA81FB4crGgmcpL39ZExN9zI60kFvW/nc5TcLHjp9lQRGn76luVY2f46m86Syxg/ujyd6VAqIfA11p9ym69wL+d9Zl7LPEdJpVurTfVDSsqqfOq7/seoKH+NqpZrETYfLqxPUpPSUbfBUXV2N1Wqlo2Pg3VBHR8cZ9RsSiQRPPvkkn/70p884zoQJE6iurmbfvn2n3MbpdBIIBAb86UmlXbJoqW0+9RyNQk80zY7aCRyuHoPPP7gOF0EQuKJtG1fv/Cvho8bXT0n3hvFnElQ4Bi+QV+W24c0k6SsTracueXmxxj843zO7rFwd7i6Pi5Qoivy+cS6/mnclldNO7d0H4HdY+Zv3/sQdG56l62h5ZWdSHVImMDTq1MGTZ/pUjoTqOZwsv5ougEJRJHlUyrBNnD5+wHMLx0o3cJsPl09Qb2IMyjZ4cjgcLFy4kDVr1vQ/ViwWWbNmDUuXLj3ta5955hkymQy33nrrGcdpaWmhp6eHhobB3WGXgpCcwRGTSQp5Y9/5hgsW/jhlKesWrxhUMbXCjIhk0RLtMH47eFouiPcET6ENdBKuePfP3PHWbyns2KXVtFRDFEVG7dzCzPZ91DoHFyAqHaGxnrCGM1OPaCpPJi8FCzVnqF0TLBbqLTm8uRR9R8tnWRIg2yX9nmrGnvr8Nlq2pilX8+ODLT04k3HsVgvjpo0d8Nz5iaPcuvl5LH/+c4lmZ1KulG3wBLB69WoeeeQRHnvsMXbu3MnnP/95EokEt99+OwC33XYbd9111/te97Of/Yzrr7+eqqqBAobxeJx/+qd/4s033+TQoUOsWbOG6667jkmTJrFypXpCamoTkrvRBFEk0mfsjpg+ubagwjO4eiAFqyxSWA4WJrm4JDngCQ0+A6lY0KT6jH98sWSGc/e+zWX7NlDtHpxUXL9KfJkInXZEpUAh5LHjsp9Zr8cakm5gwmUkV5DO5rGFwwDUjzu1M8EYp8jMjv14tpeX96LCvh0HAfBVV2D1Dsx2j61wUZ0Mkzt0uBRTMyljylok8+abb6arq4u7776b9vZ25s2bx0svvdRfRN7c3IzlhOzG7t27ef311/njH//4vv1ZrVa2bt3KY489RjgcprGxkcsvv5xvfvObOJ2D65wqBTa7DZxOyGSI9EaoHKQEQCkIR5PYCnlCnqEZMirLPoky0LLKxSSBTO8gNJ4UnCE5eAobO/gF6OmUlt5sNhvuwOCETt2KSrzBg3uF8I49fGHdU4ijRwOXn3F7R0WAHBDtNn7wq9DRGSHi8lGdT+JvOHXB+Gghw2V73yTl9FAofharpbz82joOSfpO7lHvL+cYNUdShLd1tJPO5HA5h28UaxReeupP7H78f3F/+EN85lNXYCmzz6tcKOvgCWDVqlWsWrXqpM+drMh76tSpp9SacbvdvPzyy2pOTzesHg+FTIaYwS9OwtatrFr/FL7UbOD0y6vH4wyWT2amGE9gAQIV/kG/RlFRz5SByni0R/oMLF73GdXFFTxycFgOxwcQ7gpjL+bxuAanEu0JBUgA8d6wpvNSk9YMPLHgaiZUe7jTdupLQU1TPRZBwJVJ0dEbp7F68N9rI7DRP5o1S27gXy6d8L7nqsc0YnG5sKXTHNx5iOnzys9e53h+s34/LT+WdA6Tv/gf7g9U87WPnlPiWZ2dlPWynckxLHI6Om7w4Ckle745vUOzQ3CEZJVxg/u/iaJIISllngJVg888eWSl7lzU2J8fHMuuWHyDr+nyVQYpChYSqfLQsYrKtVnO4OA+Q6+8dJ4sk4J/gLaItDTZEDq9N6HV58XtdSEg0tpcXgXxAPu74qTtLkZPeP/SpGC1Yh0l1Xu17zyg99RURRRFHvvTTtr81YyrkjLCXU/+b9lox5UbZvB0lmDzST+WRMTYKtwpeX6uQS73KLjlzEXO4BYtyUyeLqefsMtPSPasGww++eKbixk/eIrLAYL9VGa5J8GxYB4/WnYL/zf1PK2mpSrK8vBgl14D8udXTubVbRFJl6o+cPrgCUHAGgoB0Ndq/G7X4ykWRQ71SDWIE6pP/n31jZaCp47m8hUBBdhwsJdtCYH/W3Qll93/ZaqCHsZ1NvOX36w584tNhowZPJ0l7L3gch5a+lEON74/NW0kMnI9kDsw+AsvgFvuXFOKsY1KXyrH03Mv51fnXt9f5zMYlEBLLAN/OyV4cgzS2Bmgyi8t8ZWLjlWqV/FfPLN3H0Coroo+d4D2QvnUzLj/+ioff+cF5vYcPOO2dlkoM9pu/G7X42ntjnLFljVcfHgzowMnb1KpHlULlF9geCJPvy3pC35o/mi8M6ZSd7XkyHDkebOTUAvM4OkswRsKkLPaCafypZ7KacnK6uLuIbTxA9inT+c/z72J3801tkVLX0ISAK30OBAGWQ8EEKyrYlfNON4JNZE3uL9dSs6uuIKDr32plEVAk9lCWQhJZmQLId8gg6fA7Ok8tvBafjdmoZbTUpVcewc1ib5ByU24aqTOZMXvr1xo2XOEcX2tLI0dlRprTkLVuEa6vBU058sn8D0RURRpXbeZimSEa2dLhfGLP3wJALmODrr6jH9TVm6UfcG4iURIbv3vM7jNQD4hd6KFhhY8BYMeMjaH4YPDXkWKwTs0KYZgbSUvyUtakVSOKp9xuzt3NkzijZkFPjP3zNYsCn6HlWv3vI4zk6anZymjG05vtltq8tE4Vo6ZUp+JKq/0eUXTebL5Ig6b8e9L03LzRWgQSv9u2Rw51VNeYpId+5sBcNTXnrK5oXrRXH45P4LfaePbojikmx6j0NLcxblv/4mlFgvzGz4MQKi+mk2Xfpg3k3ZmtES5qmJopRImp8f4v3CTQdEU6eCyvW8S2rq51FM5LQV52c1bMbiLkoKiCxVOGTs4zO7cxaffeo7Ld78xpNfZrBb8Luleps/g/natopPmigbcTafWBjoRwWJheqKT0ZEOIt1h7SanEs12P23+agL1p/e1Uwi67f0t/Ea/gVHIyZ2PVYM4Rsec2fzvrEt5Y/TgA2YjEG2R6pg8o08nAio1r8QyecIG/+2divc27wbAU1+L2yfXsAkCExZMJ2e1s/FgeQW95YAZPJ0lVOcSzOzYj/vIoVJP5bTs9tZyoHI0/kGaAisE7XDpvg1csu010mnjXpwSPRHJmkUYeoasymXFm0kSNXjRf6/sL1g5xOyaxStlG40ePOULRX7XtJCn5q4kNHHsmV8AWCwCn9j1Zz698bf0loGBbjqbh7gUPNU2VJ1ha6gaU8+RUD0HcuW1WJFulT4Lb+OpLbtcdiu1fieIIkd6y3N56+C2vQBUTR74fV08XvpsN5jBk+qU1y/B5JQoViDKspgRyeaL/LFpHgD/OoSsBYDf42ROx35EUSTSE8U1anAZAb1JyXfzziF0oincsPUVCs1HSO9ugMmn92csJdV7tjMzlqFamDuk19kCPujsItZjbK0uJTi0CMeWwwdDrZghnU3KweHggq5S0dUdxVYsYLUIBAZxI1Mrexh2RjOIZbS0le2WarRCTaf/PX1s/xvk9h+g66JqaDpXj6mpStfewwSAMTMH+jAurrGzfP/b+HaliH9uKT6neclXCzPzdJbgkzu78gnj+k8pS26CAAH30IozBasVi0s6gRvZgiYtSyk4h9hNCMfLTRj3+ACm75SsWaoKQ9OPscsWNAmDW+x0xzIgilR6HUNS07bJAXM5+Pf1dEiZCIfXjeA4c4BYF3Axs30f8w5tpa/X2N/P48n1hQGoHV1z2u1qPTYchRw9ZWbsDJDOFaBNUlEfO2vSgOdqKnyc17OfSd3N7D1UfsdmZMzg6SwhIBdgF5PGzTyF4xnJmsVlG5bFg8UjreUbWUU9Iy+5DVWKAcDhk2ovUgZetktmctgykj7QYAqNj0dRiTe6kGTswGG+sP5pPr79T0N6neLfFzd4Zg2gN5Kk1x2gUHnmJTsAh83C5a3bWXb4XbrKxPw4kUiTk5f460fXnnZbT52UyY60lpcUA8D+w10E0nGcNivVk8YMfNLlwtEgHXvLtn0lmN3Zixk8nSX4K6XMkzWTluoZDEjsSCur1j/FZzb9flivV0w94wbOzGRknSbPEKxZFBTV9ZSBtZ56emJYxCJWi4A3NLRjVLJxRldRj/ZEsBfz+B1DC/AVNfKEwYNDgKOuII8vvJYtK28a9Gts8ufX21kecgVH4zkeWvpRfnnRLfjP8F0NNUqZqURH+QVPR2RldFdtFYLn/c4N3nFSQNWzu7wV1I+nUBTZ3V7a84gZPJ0lBCr8CIKAVSwSiRoz+5SUM0Y21/Da8O1yZiZp4MxMISEHT0MQyFRQgotM1LjBU0TOqthcLgT70JZeXaEARcFCKmlsu4i4vOzm8A8tOHRXKObOxg+eumLSZ1DjH/xv0Sl/p8OdYS2mpDotfUkQBGpqK87owVjZKGVnsmUmxQCwLe/mD9MvJH7eRSd9vmLKeABi+w/rOS3NWLu7k5UPvsaN/7mOcAk7W83g6SxBcDiwO6RiwIhBa0qScj2QdYi+dgr2MqgJ6hYchF1+vIMUVzwejxw8ZQ2soq7U81iG8RnmFi7iR8tu4dVpgzeELgVK5sgxxMyaV/ZfzJytwVP/smRYiympztE+qf5zVMUZ7GeAKnlZr9gXPqVxvFHZ3pdjf1UTFUsWnPT5UTOlOqhCSwti0dgCvGdif1ec//jWY3Q2t2OxCOxsK921wCy9P1sQBJ6/+KPsieQ4zz684ERrUnLwpBRGDxWnnHlKx4yZWQP43cSlJJoKfHLyxDNvfAKKf1/WwMt2ybB0srIO4zOs8LtAEIikjK2lo4hHDsVeB8BbW0mfO4AgGl+puu6NP/Px7XuYNPd6YMqgXuOS349knzFvzk4k884WPrRjHTPqlwCLTrtt9eg6AJzJONF4hqDcXVgO7OmQfpPT6k8e7I+bOUHKvCWTdLX3UttozE7lwfDcz/7AsoPv8OHUYa6+934CQ7zBURMzeDqLsIWC5OIRomlj1jxllOBpmJmnvmUX8Z/JRq6bMF7NaalGNl8kIVuPhDxDv4C6GmrZWTseb8C4MgVKVsY6DCmGkFsWOjW4EGFGzmx6K4cWPLnmzeGxhTFGhdzcq8G81ETs7qYm0UelY/CLD4rPXzps3Mzv8eQOtzCht4Wm4pmFPV2hALGqOjpFO+3dkbIJnpLxJGO2vYXLV8mkmpPf0LjcTmyhIJF4huYjXWUbPLU2d8ALLwCw+GNXlzRwAjN4OqtQ2v+jaWNenJRi6qEYyh6PL+Q3tEWLklERBPC7hh48eceP5eUpy2gMGvfEfaR6FP8761Kunj/mzBufQMha5Jqdr+ET8yBecsY6lFKhFLR7QkNbeq2SRUO748bXQiqEo9iA4BA6Jn1VIaA8liUB0r1hBMA/mGMUBNZf8hF2tEX5SEZgquazU4ejB1tZ2rwV0e0h5P3sKbfb9KFb+cv+PiYK3jPk4IzL5r9swlos4B47mokfuaLU0zFrns4mZrTv57K9b1Lca8yW1Jxcy+McZvCkBIcxg2bWYu1dfPqt5/jbHWuGJcWgZKuMbM/SJTo4EqrHOqZpyK8N+l1M6jlCfW8b6bhxl16POiRrFl/d0O7Qq2Tz48xxGUgjIooixZgUIFYMIXhyTZvCb2ZdyprxJ6+tMRp5WeMpWDs4OYbGkHTT0hZJazUl1Wk/JNnPOKpP7xU5plbKoh7qMe7v7kwc2LQDgIYFMw1x42Vmns4iRkc7cHfsp9g2s9RTOSnt7hDtlaOZVF83rNdXJfq4dN8GauOVgPFUgON9kjWLbYgCoAohjwNrsYAlniSdzeNyGO/nqXS3KEtwQ8HvdVGw2rAW8kR7o7iGGURrzUuj5xGrnsVnpw6tbs1ts/C3W1/CkU4R6VqM7wzCjKUiGs/gyEoBQmXd4AILgMqGalpC9UQLxvtenogoihQiUexI8x4M9UEXiCIdZSQC2i2LenpqTh88ja2SfmuHe4xbT3k60rkC0T378QEzlxjDX9HMPJ1FOLzSD8SoBcfvNkzlDzMuQpg2fVivDxZzzG7fR02LMfVK4vJJ1+IbXk2X3wr/b92T3PHWb4mEjSnH4Nm7m5nt+6gpDP0OVhAEcEudT1GDCp3mCsX+zGbFEKxZQDI/rium8GeTRA0slNkt6zTZ7TZcwcHXjSidedF0nkzeuJk1gFgqiyMtfUerGwcXxM7p2M/fv/kMlX/+o5ZTU5VwqyRY6j9DlnRqPsxHtq+h8c8v6jEt1dn0XjO+eASv086EBdNKPR3ADJ7OKhwBOXgyaKu7UosVHGZmRhFlFJPGtKBJyoXG1pMI1Q0Gi8OOzSldsI0aXDTu2sJl+zZQkwgP6/WKTEXMoEKS4UQWRBFBGN73VPAa36Klt6MPAMHvG9LyR9BlY37nPpY0b6On15jBvUJnWw8WsYjdbsNdMbjC/8qAB0chR6o3rO3kVCTeIXv3jTq9gvqokJsx4XbsR4+UnRQDwO7dR4k6fQTHjTqpEGgpMH7+1WTQKGa0eYPWk8TjKRBFAu7hfe18QXmZJ52mWChisRor9k/J2SLbCJajBLcbMlnDalkV49Ix+gd5QToRm8dNHkhEDBrgH2lj1fqnyAZCWC1XD/n1Fp8XOoytMh6Jp+jxBKmvGPySHUiZtcuObiWbSNHb3kNj7dC1zPSipzNMzmLDHfCDZXDnCaX+K1smBfEAqe4eHEBt0+lLIRrG1iMAzkSc7kiKmpAxApDBsj7j4pVzruOey4cuAaMVxrr6mIwIl5x5yicMeGESRT665lesWv8Uodzwgjvlgm0tFognjVfUmZa7tOzDaONXsMr+fQmDLtuJCemz8w2xjV9B0fhKGjQ4jPaEsRUL+OzDOzXaZFXytIG1kFr9NfzPgmvYtuL6Ib9WkaiIdBpbifuII8BDSz/Km1feMujXVNVLwaTR7YMUsvkixV4pi9gw5vTBkzMUxONxISBy5FCbHtNTlW0t0u9p1oTTZ9j0xAyeziI8cv1CIWG8Za1cJksxl8NWLOAfQp3F8bi8bixWKwCxXuPdHSq1Zs4RBE+Kcreixm4kCvkCYloKWgNVw8s62H0eioKFpAG/owAJWZ1/OCKgAPagYtFi3AtwT1wq+q/0Db3o3xaQji9q4GVJgI5oGgSByiEE+VX1UtG1JZUimTK2hRBAeyTN/868hJdnXUT12MbTbywIWKuk4+tuLq/gqTOcpD2SwiLAjIbh3bRpgRk8nUV4gtJFW0wZb9kuJtfwFAQL/sAwU8aCAG6pnThuwGWfcNFCnzuAo2L4yxlKvVTagP59x9dhBYdhfAxw9LxL+dGyW9g9wRgdMycSV5ZefcMLgB1y8JQxaGYNoCchBQaKLtVQcMjmx3EDF8QDdEalIL8+OHj7GV/Ij9VqRUCkW64LMzJHwym6fJWkJ01FcJz5s3TKkg3htvIyP963YRuf3/Abbu3aitdpnEojM3g6i/A0jeJn51zPL+YNvVZDa+Jypkh0ubHZrMPejyB3a8UNeGf/1sT5PLbwWnILFg57H/Z+CxrjBYcRuY5HcDix24d3Egv63CAIhlUZV5YTnf7hBfjOqgp63QH6ROOc5E9k1GuvcOs7LzC+p2XIr1W685IGrukCCLz5Oh/a8SoTox2Dfo1gtWKRs8Z9Bl+WBGiLSNlbRZ/qTLhrpY68WFuXZnPSgtYd+3Hms0wIGMv2yLi/cJMhE/C7iDm9WPJQLIpYhiHUqBUJOdgR3CNTz153wbVsbo0zvXJ4WlFaoiiMh4bZTQiQG93EztouHC7jpKcVYspn6Dmz0eqpqPBK700kVTo39NOhZPxcgeFlngpz5/H4XgvLJ9bw92pOTE16eqhO9FExBGsWBZdcd5iJGDt4crQcYUJvC7XWoUkqJBubOGLxMytpTCHe44nu3s+Clp1MHzu4LG6goYak3UUmbszf3qkIH5GWGUPjRpd4JgMxg6eziIBsCVIUIZ7N9//bCMTlGh7LCNtMnRVBMp1ZQ/r3RZIjk2IASM2ay8tHXQSqjHWiAOhx+nh25iVMqxt+TVddrJtrdr7G6GQ9fHz4GTqtSMXk4Ck4vGNUAmcjq8Tn5aymfxhF/27ZsiZv4GVJgEJUCu4CtacXjzyRAxeu5MXt7Sx0GO/m5UTyu/Zw4aHNjJk+uDIB1/nn8dM9dibX+viqxnNTk0RrJwC14xpKPJOBmMHTWYTLbuWClm24UgliHQsJjDWOwWxKPmHbPCPLPCkBoRGDp0v++juWprNUpGYCQ2sDVwga2J+wt2CluaKBMWOGbywashSZ1HMEm8N4nx9Al81Dr7+GaTXD+/wq5DqiSNK4d/cFuWMyMIzgyTptKr+ZdSlNExqNm1kTRZCDp9AQFNThmBBoZ8x43bwnku6WapcC9YP7PTZWSBnj1nDK8N6LCsWiSLarCzswaoKxbijN4OksY25fM7ZImERnLxgoeOqzuthfOZox9WfoCjkDE3qPcOm+t7HvEOH88SrNbuSIoogn0osvn8M/jEJchYDbjrVYIGnAgnFlWTLoGX5mzSdndApJ4zU1ALw5ehZbxNGsmD28gvbKYppb33kBnxX4p4vVnZwKFAtFxGQSAaioHnpjQ6BesmhBHHwhtt4kYknISd/VwVqzKNT6nSCKdIeN+f08nmx3LxYg2Di49v3GkCyDki0QSeUIDVFBvxS0tvViz6SxCgKjJo4q9XQGYAZPZxkWtwsikDSYVklr1Sj+MOMibpg3sruH+ngftO/D1mKcwBAgk8lhyUsnbH9oeJ1oAHWdR/jiuiexHmqEVctVmp06FJtbmNW+j9ETh3/hDMhdemLKmFIFfXLGqGKYAXDQ76E6IXVqFbI5rA7jLJ0DhMNxBLEIQGgYchOV8vvSlzBuZq1XLvYW7Q683qFluie37uUL65/GE5sONxvbALnYG8YCVJ9BXVzBZbdy86E3cXd30r53CqG5k7WdoAoc3i81NTgqg9hGWC+rNma33VmGzaPoBBnrzmmk1iwKShdU1mA6QUobvwB4h9mpBeCVhU6LBgwunPt2s2LfBiZ0HBr2PgKKjEM2SyZjvAuw0gU43KL/UIUfEWk5JGJAi51wtxTYWZ0O7K6hB8GVLhuz2/Yya98WMiljLm31doYBsPi9Q16aqgh4sRfzhlcZj8ZT2FJSKUTdGQQyj6dJyBBKx+g5MvguxFJyuDtBc6gey7ixpZ7K+yj74Omhhx5i3LhxuFwulixZwsaNG0+57S9+8QsEQRjw53INjGZFUeTuu++moaEBt9vNihUr2Lt3r9aHoRqKQnUyaqxW92giMyJrFoVjFjTGOr64sszmciFYhy/F4O3X6jJe8JSVbX+cvuF32/lDx/zUogYTOi0WRT629td8euNvCeWG9/7bbFZEl/T+RHqNp4XUG03T4wmSCw2tkFrB77Zz8aHNLG3eSqTTmFpIkXCMnMU2LKX/oGzRkjdY5v5E2pul4MfqcvaLIw8GV2UIgD7ZE8/obMPPs7MuJXr19aWeyvso6+DpqaeeYvXq1dxzzz1s3ryZuXPnsnLlSjo7O0/5mkAgQFtbW//f4cOHBzz/ve99jx/96Ec8/PDDbNiwAa/Xy8qVK0mnjXmXdSIOOXhKJ4yVeZq49kW+uO5Jxh/ZM6L9eOTMTMFgx5dQuglHmFru94xLpykazLk+J7/nzhF491msFgT5hiXaa6wLVCyewpXL4M8mpSBvmFi80m8w1me8urVOV4D/WXAN6y+7cVivt1gtiHJ2O9IdVnFm6nG4chQPLbuZLZd9ZMivrayTgkoxHqdQNK6Bbu9R6RonhEJDMnd2V4UAiBn0szuRI73SOWds1fDPOVpR1sHTAw88wB133MHtt9/OjBkzePjhh/F4PDz66KOnfI0gCNTX1/f/1dUdS3mKosiDDz7I17/+da677jrmzJnD448/TmtrK88995wORzRy7PKJOxMzVnCRSySxikU8npEVmioq6kWDFRwrRrcW9/CzMsCAi3bMYEXjeTl4cg9TA0nB6nFTFCxEDZYdVVTwLVYrLu/wP0erbLGTMODSj1LTNZJiYYusvh4zqMp4d0xWUB+Gk0GFLG3gyGfpDRvr+3k8R3zV/HLelew/95Ihvc5bJWXWkj3GzBqeyNEu6Tc5ptJ4RsZlGzxls1k2bdrEihUr+h+zWCysWLGC9evXn/J18XicsWPH0tTUxHXXXcd7773X/9zBgwdpb28fsM9gMMiSJUtOu89MJkM0Gh3wVyqcskJ1xmDmwHm5PsI7gqwFgFdOURcNVm8RzxbocwfIB0fmNO90OhDt0oXNaCrqhaS0lOUZYfD0l0tv4kfLbqErMHzJAy2IHS/kOoI2bsX8OGHEmie5pqtiBB2TNp8SHBrv+AC641LwpMgODAWbx43NKf3+wl3GDTDakwW6fJXYx40Z0usC1SEA0gZcUj6RfL7AFX/8JXdseJaxFuN5DZZt8NTd3U2hUBiQOQKoq6ujvb39pK+ZOnUqjz76KL/73e944oknKBaLLFu2jJYWqaJfed1Q9glw//33EwwG+/+amppGcmgjIj53IT8753q2TFtSsjmcDKUAeqQXXq+SmUmlJT0Xg9BR3chjC6/lvQuuGvnOPMqyj7EuTkq2zxMcWQDs98sWLSljaVnFlczTCIVcLRWSRUskZ5zvp4J30wZufecFZjbvHPY+lFqiuEGFMis2ruNDO9YyIdw69BcLAoKcWYsYOHjqkHWo6gJDKxMIycuS2T7jB0/t7X04cxkChTQ19cPTXdOSsg2ehsPSpUu57bbbmDdvHhdddBHPPvssNTU1/Nd//deI9nvXXXcRiUT6/44cOaLSjIeOtyJAzOml11jXJYpJ6cfuG0EtCYC/KsSji67jRwuvN1RNQjQliT4GRthNCNDVOJ6dteOJFo318xTlbJ9vmOrbCkonW8RgKtwJORiwjjB4al12MY8vvJYDDcbRIVModPdSnegjaBl+PZ1S85YyaObJ3trChN6jVAvDE2KNNzZxoHI0fdmiyjNTD8e2rSxo2UlTcWjlCxX1NSTsbjqLw29q0Yu2g0cBsIWCWJzG06QqW52n6upqrFYrHR0DWy47Ojqorx+cBpDdbmf+/Pns27cPoP91HR0dNDQck4Lv6Ohg3rx5p9yP0+nE6TSGaJzSzWYkhWqxWKSYTiMAvmHUIRxPwOsk6pJrLjJ5wwi9Ke+33zXyn9TuBeez6XAfH/YYxyKiUBT530nLcOcy3Fo3suW2qZ0HuWbnBhxjsnDhBJVmOHJSco2ZUrM0XJTvpBHNj7Oy0r97CB1aJ+KUX5uOGqsmTyEXi2Pj2BLVUDm4bAUvvdfOIvfwXq8Hod3bufDQYUZlzxnS62omj+GRJVIh/dczebxO44YA3YclTzt7bU2JZ3JyjHVrOwQcDgcLFy5kzZo1/Y8Vi0XWrFnD0qVLB7WPQqHAtm3b+gOl8ePHU19fP2Cf0WiUDRs2DHqfpaYyk+DCA5sYt3VDqafSTyqVQShKd7qKSOJwsVsteBzSXZOS7TEC1W+9wcffeYGJLSOXtei3aDHQ8cXTeVpC9eytGUsgMLJlu9p0jEk9R6CtTaXZqUNYtNLqr6FYM7KTtVJPZMTgKR+XAp6RLJ/nZ8ziN7NXsG3c8FTYtUaUZUwCwxABBaj0ScFvt4ENdBVvwYohevf5nDZ8csDUETVW3eiJhI9KiRF3nTGDJ+OGnYNg9erVfOITn2DRokUsXryYBx98kEQiwe233w7AbbfdxqhRo7j//vsBuO+++zj33HOZNGkS4XCY73//+xw+fJjPfOYzgNSJd+edd/Ktb32LyZMnM378eL7xjW/Q2NjI9ddfX6rDHBJBcixo3YUlGSr1VPqJxNMcqByNq5jDPYIuJoUL2neR7+0l0TYDqoyxNCL29lGT6CMojFxeIOCyYS0WiBmoG02xZnHbrThsI7vncsnBl9E6Qg/VjuHpuZfzqSUj+06N6m3l1ndeoCo8Gj5uLJXqotwx6RnBTYynoZaWYB1HBWMpPgNkcwUsKekYg3Jb/lCp8jpAFAkb6Pd3PMWiSDEWwwJU1g9dr6s24CTelac9mmZCzciW4LUk0SoFT/5RgxcB1ZOyDp5uvvlmurq6uPvuu2lvb2fevHm89NJL/QXfzc3NWCzHTvR9fX3ccccdtLe3U1FRwcKFC1m3bh0zZszo3+YrX/kKiUSCz372s4TDYc4//3xeeuml94lpGhUjKlRHRRu/n3ERlV4HgmXkyc6Zvc0U29tJdXTBLGMET3m5E801AnVxhXl73mbcur8QrLgULp024v2pQbynj1nt+3BVjqybEOgX9csZTOg0KgeIoRF0ogEEHFaqE31Yekd+o6A2xUQCAQiM4HNUMmtGtGgJ98WwikXpGIe5bDexdT9fWP80lYlpcMN8VeenBj19cWyyFVTVEI2PAa489DbxXftILA3AxAvUnp5qpLslm52K0WbwpAmrVq1i1apVJ31u7dq1A/79wx/+kB/+8Ien3Z8gCNx3333cd999ak1RV/yKQnUmS6FQxGot/cqsWtYsClaPmyKQNFDmQtFAco1QigHAJdfcKPUpRiB1tJ0V+zZgrR2cj9bpULr18gYTOu03Ph7h99QvZ3WMpkUmFosgv+f+EWSeKq0F5rTtoT5qB85XaXbqEJbFHy1u17B9Bf0BD/Zivn9pzGj0tHUDYHe7sA9DlLdOyGFPRYm2G1tlfLc9hD2UZWVTw5k3LgFlHzyZDEQxpRUQiUXihCpLX3Qcke9QAyoUUwPY3C5yQMpAaXVFd8ozwnogAJfPeP59Cfm9Vux/RoInYExz4Blrn6dhfzON5waAccPeT0BWiS8mjXV88WSGXpcPdy5DaJhZGYAqS5FL9r+FYDeW6TFAJBwna7Xj9Q7/dxiokYQkCzFjBk+9HVJGxhoYXgDsli1a4t3GlWLI5ov8X8NsxHr4l8lD07LSCzN4OstwuBxYbDaK+TyxSMIQwRPvbWfVuidxT5+KGneqdq+bFJCMG+fOXlkm9Y5QxwqOLf3lDXTxTcteXyPtRINjchWigY4PQIxGJWsW1wiX7aqk35wlmyGdyeFyGiPICGdF/mfBNThtFv5lBLWHQbkQW8zlSCfTuDzGKWno9FXxH0s/yrlNAb4wzH0oheZFA51fjkfRn7IPs2NSsWhJG1jrqSOaRhTBYbNINWgGpPRrOiaqI8ip3LhB7D2SsSS2YgG3XZ2vm0O+gGcMdHJTNJC8I9RAAvD2B0/G6YZJyUukdhUK/r1ydrSQyUhLSQZByRR5K0aoRRb0IcgK5WED+fcdUxcf2cUoEPQiyrWLkR5jWdD0yvYzwcDwv6cVclYun05TyBivrutQRQO/nHclLecuH9brfdVSZi0bNm7w1Nodw1os0Bh09f+WjIYZPJ2FCLKre8Igy1rp/guvOv5E/RY0Bgmecrk8YZuLpN01IkNZBaWN3EiZp4z8XbL7Rr4s6a+p5KGlH+Un536URM44wZMo1yj5QiOT0xCsViz95sfGCS7CKcXXbmSZMMFiwSIv34YNdHwAvbK8QOUIshUVlX4KghIcGi/A6MoKdPkqcTaNHtbr/cqyZMRYn93xxLbt4IvrnuSmna+WeiqnxFy2Owt567wr2Xw0ylSDeIdl5SJVhwpZCzgWPOUMUhMUyxZ5bOG1AHxlhBdeOK5jMm2czJPyGSrv/UhwOazgcEBBJJbO9evOlJJCLg8ZyT/LXzHype5sqIIIdiIG+Y4C5N7bya2bn8czfTJw4Yj2ZfF4KcQTxA3mkebdvJEP7djCpPEXAXOGtQ+7zYro9kAyTrgnQmWjsXSGFO++at/wAsRgjSRvUCyhB+uZCHdIxey+EVpBaUnpz1omqmOtriLWXSBiEHuBnJxBUSt4ys6Zy6N7RZZOG82nVNnjyFBa3H1OGzYVuht9VSEOVI4m7zaOk3g2rgRPIz+ZCYJAwGWnJ5ElmsrTMHL1gxETO85qJDhCIVeAdZd8hE2H+1hqIJXqTHcP1ckw3sLITVZtPi+FzoHvmxEQ2tqY0HuUmuLIbjyiDU2E+2L0pgsYRwNfwr/jXRa2dFFfGF4hdUVdJXGHm7jgIpcvYLcZz6olKhfFe+UsmRExg6ezEMUiJJ4xhkL1seBJnWDAGwoQdfnoLRhjLVxNaxYAf3UFv59xESB1nYxUlFINto6ZwXtRD1+YPFmV/V3Qso18ewep5vFQP+PML9AYZXmt6HRht4/8c+xXiTeQTVIqIi29OlToCLX7PGSAhMGCp5zc2OAZoR7ZjnMv5e3DfVzhMkDDzQnU7d5OTWsrdbnhZQ8raiv5+bk3UCiK3JnIUR80XvCU6pGK4oNDVFDXk9KflU1UZ1z3ES48sAnr/n2lngoABXnpwqmCBhIcM99VdHlKTebAIT7+zgus3KeOJY7vuCDMKBffI64Qe2vG4moYuc4TwMR4J5N6jpDqNIbWTDSdp9VfQ7xSnSUaI1rsKF50Dv/IM2udC8/lN7NXcKjaWG3khZh0jL4RLr0qNVM9BhQCVSQUgtXDy8pYLEL/8SlLgEYjLQdPoWGIgOqFmXk6C2ns60Bo3YXtyKhSTwWATneAeKCW+ZXqpGAr8inOP/gOgS4ncJEq+xwJ6d4INYk+7LmQKvuzWgT8LhvJZIZoIkO1r/Sm00qgGhhhG7+Cze2iAKQMUvTf6w7w9NzLmVY/8sACYMah7XjfWY+nLmYY8+OsfNF1qdARahs1ipa9abpEY11CirJqvX+Emacqn2TR0hM1Ts0aQCFfAPkYK2qHfz6t9jnpimXoMmjwVAhHsAKVDcaqNzseY33zTVTB4VNa3Y1xYVo3bj673ZO4fvIkVfbnJ8+iozsouIxhf5GS73ZtKghIKnxq0x8Q+npJ3DQJ6kq/rFV3YBdCqkDQuliV/dm8bjIc68QsNWqpiysEhQLViT6KfcYRIszJgapHheBJyVz0JQ2UmRFFxIQUWARHIAIKMPvQdqrWv0iVYylcbgyLJIBwTwRBLCIijCh4uvDIuyx+dzu52VaYeoWKMxw56Wwea1wK9KsNVqx/PGbwdBbilAuzcwZpdVdqr9TqqlKEKIVMxhAWNEoAYFOpIB4ksdMckDSC3IQosnj764j5AkHhw6rs0uaR5SYMYkETVjl4Umx6sgby71OWtDwqdBPW5hLMaduDxxMBjOH/lozGKRYkY+5QTWhE+/J5XdiKBTJRY9V09XXKwbjHg20EtXk1liLxVJRUlzGWzY+nqy/BrtrxVORTBEYQIGqNGTydhSjt5AWDBE8xuW7Hp1JBtVduX7WIReKJNMFAabvSFL0ptQri4ZgFTTJS+otvJpVGzEsXJX9InQJaJTuaNkgrv3fDOj69cQ017qXAohHvz6VodRlkWRKgT7Qh2l141Qiekn2SRUuuCfibkU9OBfp6o2StdqwWAa9nZEvdivdfLmoMoWGFqFwjaBmmNYuCqzJIHEj1hkc+KZXpSBV4ZfK5jKn0INiMG6IYd2Ymw8blkzIg+VTpdYLEYpFP/PkJMlY7/uJSVfbp9LixWCwUi0USkXjJgyeljd+hggaSguIhlzRAZibWJ11AioIFv1+d7JpLyY4aJLjIRmRrFps6HZxuOXgqGMj8+JmZl9A7LsuNE8aOeF/ekGxhYpAbNIBeu4//WPpRGr02/nGEqtQ+2dYqb4Df3/FEZeNj2whtoLwVAbqBtAHNj9uj0nWrPmAc25+TYXbbnYW4/dIPywgntmQsibVYwJNL41ep2w5BQHBKd5ZGUFFXU0BSwWYgCxrF5kd0ubCotESqdF4aZWk5Ky+9Ov3qfIbukPIbLP3nB1AsioTl+qSQCkuTSmZGNFBweMyaZeSfYUAuOM8nSn9+OZ7DtWP45bwrOXLOBSPaj0/278saMHjq6o5iLRaoDZS+UeZ0mJmnsxCPfAEQDaBQnZAvvEWrDZdbPYNHwe2CVIqkAdLq8YJA0u7CqYIpsIJDNlvNGmBZKy5r+Vjc6tV05WfP4aGlIudOrefTqu11+CgBsFulAN8nF2UrhtGlJpbJUxSl/w+O0J4FwC9nZoRUyhB1hwB9CcWaZeTHF5LNc0kkKRaKqt00jJTOLJI1S2PDiPYTkI/PaMuSAM4N6/niuleo8V0MLCj1dE6JGTydhbhGNfDE/Kuwut3cWeK5JKLynanTqarBoyB7hyVjpb84/XX6Uja6pvLQnHmq7VPxAcwa4M5eye5Z3eql0X0+DzmrnWjaGDpIOfl99qgUAPuCfhJ2N3mklndKbG4abe3g1ndeIOPx4bRdPeL9BZTgCZFoOE5FVenFJMV33+VDO9Yyyj8POHdE+wrVSJkZoVggEklQUamOhMVI6ZG9+0YqXxKSuxGLMeMFT8luqSg+oEJtnpaYwdNZiN/vptsrmz8WRayW0p24k/KPUwl21OKdpZez8XCYiVX1qu53OCj2LAG3ej8noa6WA5WjKBpA4TgpLx3aPOp9hoF+BW5jBE/5lKR341HJSytQV8kjSz4CwFfzRVz20qo4x3oiVCf6wC6qsj+704FgtyPmcsR6I4YInvLtHUzoPUplduKI9+V0u+iubiBStNIbTRkmePJu28KilnYaCk0j2k9FbYiYw0PK5iafy4+oc09tMnIRu8/A6uJgBk9nJcd3tcUzedXar4dDWs48CSpmLQCEqiqiHXliBrj2xuQAwK+SgCRAdsZsfr8bVjTWqbbP4dIRquX5qeezeFqjavsMFtNctvdNAs1WYLlq+x0uSn2gTwXrEgCfw4YgSEmnaDpX+uCpT1p6tXpUbK7weCASMYy/XUqu33GNsBMNAEHg9fOu4VBPkr8VbYw8HFOH6l3bOL/lKHWFkdU8VVaHeHTJhxFFuDOdp9ZAwVMhLJlNV9QbV10czODprMRps7K0bSe2dIpE37kE3aX7EqZknRs162UA/LJmVMwA9iWXrP8/UnmRYH4BEFJln8f8CUt/fD1WN3trxjJv3GjV9hmwW5nZsR+sVsRiEcFS2pqSNrsXu6c4YlsPBYtFMj+OpHJEU3lqS5y4SMi1LWpqkb2zcDl7u5IscJc+6wSQlTvjPCF1ll4rvQ4O9STpTRhHhbsgi0cGq0amoG6zWqj0OOhJZOmOZan1G6ezrRiRg6eG6hLP5PSYwdNZypL23ZBIkOjpg8bSBU8xbBwN1FJbpe4PYWxfK+cffAf7PgtcVLr7wmK+QFVPOwD+EWrLHI+SPYwbQMFZ8dcLqJjB9CnLY4UCmXQWl4pLgkMlVyjy5FTJ5me1ipm+a/etg84ukofGQ21pVeKTYdnXzqdSxyuQHj2Go9lewgVjFFMrwZMvpE6kWuGR6tX6jGJhIooU5SX0kYqAglQ31ZPIGsrfLhFLQlau6zIzTyalQHC7EBOJfif1UtFeP4Zn5lzGNXNG1h1yIvXhDhYd3YGjubR3J7Hj7EX8KtXLAFT1dbBq3ZM4KkJwZ2n9+4QjR5jcdZiarDqmwABenwdlXSvWFytp8BQ9zmBazQCxLpegkOgj2RdVbZ/DJSUHFnYV5TRCcvdsxAABPkBBlhXwqxQ8Ld31JtPXb8Q5Ng3njlNlnyMhGU9SzEslApU1I1fevvTwZs59bxeZRW6YcsmI96cGvR2y4rnDgVelJXStMMYtg4nqWJRutBLrBMX764HUjdOdcjdaqXWC4kqrr9WK06meFIPH68FWLFA0gNxE5c6tXL37dZo6D6u2T4vVAvJ3NBYpbcePUrTuc9pUba6wyXV+RpDTSMsdky4VL0ijU33Mbd1N8eBB1fY5EvJyx+RITYEVPC4HtmLBMEKSijWLaLfj9Y78ZqNGyFGRihLv7B3xvtSiO5lnR+0EOpuMUmV2aszM01mKxe2mAKRLrJCrtq+dQr/5cYl1kBQpBovLpWo7ev9dlwGCp4L8HqspAgpydjSV6q/HKRWJljY+vfG3WCorgJWq7dfu9UjmxwYQco3miyTsbpxB9eqTJnQ34zvwNo49HuBi1fY7HERRJJvJ4QSCleoco0vW6soYIPgF6JPVxa1eryqyL65ggAgYIjOq0GFx8ccpS1k41riedgpm8HSWYvNI3mjpeGmDi9Gv/ZHPbniXceOuA9Sr+zhmQVPa40vFlOBJXTVc73E1QelUBpe7dGq7ynvsUrFeBsDqcpOnj2S0tNnRVCSOP5vEUVA3OFS0ulIGsPjYNGkhf8438d1zZqu2T6fsZJA1gAp+NJ3nPxffgLVY4HMqFRq7g9LyX9YgwVOkRwpyrH51CuI9cpCZChsneOrq17FSL4uvFWbwdJZik73RMiV2dS/GE3hyaTwOdVu1FSXoYon9+5TgSW0dK5/fi4iAgEg8Ei9p8KS8xx6VfO0UrB4XeUrv36csq1k86h6fQ+5syxhAJb5fi0xFOQ23nB01gpCroi7udDlwOdS5rHlkE+x8ic+hCkeDtfxy3lVcMEmdQmqvvLyZMciyJEBvTxRbIT9iEVA9MGuezlKOKVSX9sRdkL29XCq2SAO45SxIqWuCEpksSbsLvOpmZSxWC4JcQ5UocU2QEjy5VbSfAXjvvCt4aOlHOdo4QdX9DpV0TBEBVfc7qvj3ZQ2QeVI6JtXUfPPIy1p5AwRPETk4VMO3T8ErSx4UDBI8dWWhy1eBbbQ6emsBWe4gFzVO8BRa9yqr1j/FvINbSz2VM2Jmns5S+uYs4IkeLx+eOK2k8yjIys1ulQxXFRQlaLHEmaf2ujH8dMkNXD5DfTFLweVCzGRKvqwlptMIHPNMVAtXyE/OGiGaKa3SaUoDBXUAZ8BHwu7GWiytNQvAsnUvMjeRpiI9A1BnWcsjZ54MYUB+6AjXvfcX3E2jgEtV2afi3ycaxBy4KyadS9XKyij+dsW4MZYlATJy/ZXX4NYsYAZPZy2Oykq6vRX0iqVTFwcoyJkhl8oXXnddDb+cdyU4nfw/Vfc8NJRuQp/K3YQAvbWj6LP6iBdV3/WgKRSK/boraqlvKygdmLESW7Rk+oMndb+j+YWLeGSvjWUTq/iiqnseOsHudkK5rKoq+H65JqhggMxTqquH8X2tuCrVW+4JVFdwNFBDxulBFEVVvTmHg3PXDha1HGRUWp3g118dJObwkMBpiOMDyEWk4CkwQhFQPTCDp7MUoyhUi3Lw5FG5Uyvgc9Plk7yPsvkiDltpVqCVbkK/yt2EANvOuZjNzWGu9pWu8ySeyfPilGU4Czk+r1IXk0JTTyuX7X0TX3UcrihdhjQrL8s41P6OuhT/vtL+BrOZHEJODoBVUt8G8FVIwVOps79wrOjZ5lVRx6q2kmfmXA7At7MF1TuGh0pw307OP7SL+vgsVfZXObqBny3+MABfy+RVDayHS15eQgyooGOlNWbN01lKZTrGkuZt1O4q4dqxKCJmZMPVgLoXJq/zWAF6vITLPsEtb3Pjtj8xvnWf6vv2ySezUmZmYpk8e2vGsmfUFJwqdxTWpKPM7NiP8+gRVfc7VCLY6fEEsYXUvdtVBDcjqdIGT8d7z6klIAnSBe4P0y/kmekXkcmVNnuYlov+7Sp1ogG47Jb+mzKlIL2UFOTaOa9KNzFuhxW37LnYa4DjE4vF/iXEyjpjmwKDmXk6awml4yxt3oqjqJ6Z61ARCwUOe6qw2bN4VTypgeTNdG7nHqzJJInuc6j0qqd+PRSs3V2MjnQQyql/992fPUyV7sTWn1nTYFlSWcrNlbipYeu4WfwxWcPUherc0StUZOPctPUVnE47UDoF57jScOB0YrWp1/Xq97o4UN2EKEKkxOayGTmwcPjVW1oWBIEKj52OSJpwIktTpbo3gENFUVD3VqgX5Fd6HRwNp+hNZBlbVVpF73gsiZCTbjSqao0fPJV95umhhx5i3LhxuFwulixZwsaNG0+57SOPPMIFF1xARUUFFRUVrFix4n3bf/KTn0QQhAF/V1xxhdaHoToeA7TyZ0SBp2at4JfzrzrmZaYiS9r3cE7LeyS6elTf92BRFM6dKncTAszf/Tar1j1JYMMbqu97sCR6I0zqbmZiSv332CUvkykdmaUippEKvt9lZ1S0k4qedopFUdV9D4WEnHkS3Ope/C0Wob97L5Is8dKknHlyqhg8Adz43l/44ronSe/arep+h4UcPAVUXD6/cv8GPvn270nu2qvaPodLb4esdO5w4Papfz5Vm7IOnp566ilWr17NPffcw+bNm5k7dy4rV66ks7PzpNuvXbuWj33sY/zlL39h/fr1NDU1cfnll3P06NEB211xxRW0tbX1//3617/W43BUReluK6ZLZ/qoXJQEATx2dXWeAAR5GSlVQpG+QkqbgniQ0uq2YqGkmZlsSyvX7PorF+17S/V993drlbhmJpZR3/gYji2RWYsF4snSHaOSeRLc6vsHzoy3M7d1N/GO0t3AAOTkc4ArqN6yJIDHYcUqFvsD0FKRzeRALoEIVodU2281WULpGImu0lu09KQLvFc3ka4xk0o9lUFR1sHTAw88wB133MHtt9/OjBkzePjhh/F4PDz66KMn3f6Xv/wlf//3f8+8efOYNm0a//3f/02xWGTNmjUDtnM6ndTX1/f/VVQYv3jtRLxyjZGYKeFJW7FmcdiwqOgZpmB1S3cnqZgBgieVi40BHAbQ6lLeW5sGF16vrBtVLLFK/LLXn+fWzc9TFelSdb8unweLRTrFxvpKd/FNpLIk7G4ElZfOAZYd2c7FB94m1dKq+r6HQka+SVS0p9TCLuvJJUscPEVkaxZRsBBQsW7NEZD2ZQSLlnbBxSuTz2X3EmOYFJ+Jsg2estksmzZtYsWKFf2PWSwWVqxYwfr16we1j2QySS6Xo7Jy4Prq2rVrqa2tZerUqXz+85+np+f0d1WZTIZoNDrgr9QobeVivkAuU5qamcy+A9yx4Vk+sutVTfZvk1W30yVsle6XYtAgeFKWAktpQZOW7+itKgtIAvjlzq9SC526wr1UJ8N4XSpbQghCv0F3Kc2P2+rG8siSj/DuRdeqvm/le5EosX/f/81dwY+X3YJ1urpdmw75PJoqsVBtpCcCgOBxS6baKuGUg810pPTXrO64FADX+I2vLg5lHDx1d3dTKBSoqxsoTlhXV0d7e/ug9vHVr36VxsbGAQHYFVdcweOPP86aNWv47ne/y6uvvsqVV15JoVA45X7uv/9+gsFg/19TU9PwDkpFvMctI8UjpTmxpaJxvLkUQVGbegibnHlKl3DZTuy3LtEgeJLrN/IlFCFMayQgCcfMjy3ZLNlsabq1RFHsl9PwqtwRCmCR37dEuHTBhRbq4gp2+aYhXeLgIpzMUbBYCalcK6P496VjpT2+bpefX867ivWLL1N1v27ZgiZT4swalJc1C3yAu+2+853v8OSTT7J27Vpcx/mS3XLLLf3/P3v2bObMmcPEiRNZu3Ytl156cuXau+66i9WrV/f/OxqNljyAstttiHYHQi5LMpagolb/pcd+01wNlnzg2AW9lObHqQI4BIvqApJwrG6tUMKaIGXJ0KFF5qkyyM/OuZ6M1cGtmTzVKnmSDYV0Ooe1IBeMq1wvA2CRA/x4CS1a+n3t3Oq/v4o2VqrEFiaKHITaAWK/f1+JLXbC2SJdvgrGNKp7HvfISt5GMD+ufGMtq9a/yajGawB1O1+1oGyDp+rqaqxWKx0dHQMe7+jooL6+/rSv/cEPfsB3vvMd/vSnPzFnzpzTbjthwgSqq6vZt2/fKYMnp9OJ02m8aPlP56ykI1XgcruHUSUYPyMvp1k1Cp6UC3quRJmZfKHIfy34EACfqqtRff/9/n0lzDwppq92FcUHFaxWC0V/gGy2QCxToFr92OWMRJViakHQJHto8UsWLYkSyk1UvrWOm7ZuZfzEy4CZqu7b6St9cJFJprh8y59I25wEnSvO/IIh4JED6myJg8M+uZuxwqNucOiRZQ/yBig1SctCp75K46uLQxkv2zkcDhYuXDig2Fsp/l66dOkpX/e9732Pb37zm7z00kssWrTojOO0tLTQ09NDQ0ODKvPWk1RdA93eCmL50rRJKxkhuwZLPgDhOQv45byr2DWhNHcpicyxpVyvBuq87ooARwO1tHjVcVEfDkpg6tBAigHoVzWOlUiFOyE7ygsOB4JN/XvJ9y75EI8s+QitNaNV3/dgsXZ1MiraSRD132OXvKyVKWVmrSfC+L5WpvQ04/eoW7fmqqniaKCWVkdpvdYKe/eyqOU9xiXV7WoM1ISIOb10C6W/+c/Kv0W/yk4GWlG2mSeA1atX84lPfIJFixaxePFiHnzwQRKJBLfffjsAt912G6NGjeL+++8H4Lvf/S533303v/rVrxg3blx/bZTP58Pn8xGPx/nXf/1XbrjhBurr69m/fz9f+cpXmDRpEitXrizZcQ4XxTKkVArcWfnCa1dZX0bBUVVJl6+CPlQu9B0kSou702bRxB7G3VDLM3Muw++y8W3V9z44djVMZuckC5+aqE378LltO0m0dpA+OgFGhzQZ43TEo8rSsjYXD2UZKVpClfG80savsgYSHFtazpUwMxNX6nXcbtW7et1TJvLMnMsYV1VagUz73r2cf2gL1TPU8bVT8E8Yy8/OuR6/y8Y3VN3z0CnIS4ehEpSYDIeyDp5uvvlmurq6uPvuu2lvb2fevHm89NJL/UXkzc3N/a3CAP/5n/9JNpvlxhtvHLCfe+65h3vvvRer1crWrVt57LHHCIfDNDY2cvnll/PNb37TkMtyZ2JyXwvOI4fJHmmA6XVnfoHKKPUydq82madSG8sm2zu5YdsahKAfuFL1/R/zJ8yXzLiz2VvF9noB+yhtlOqn9LaQ7Wgm09EFTNdkjNMRT+XodQcIBbRRNFb87Upp0VKQuzXVbuMHsEyexB+mX8iYcY18TvW9D454r7TcI2iwtBySg9++EouAZmTPN1dI3axMpZypi6XzJfUIlaxZYghInoLlQFkHTwCrVq1i1apVJ31u7dq1A/596NCh0+7L7Xbz8ssvqzSz0jO1/SCjD29DbJkOLNB9/IjVSbe3gppQSJP9V2RinHNkOzWWGuAcTcY4Ham+GE2Rdiw2bU6sfqd04hZFSJTImFQJTH0a2LPAsVb3Uml19QSreXzhtSwZr80Je1zrPm7a+grVrjlwXWmWl4uygruiq6Um3voa9lc1ITpKZ+2hLL1aPBoET3JwEU1lKRSKWFWUCRgKebnbz6Ny8BR027EIUBQhnMxSG9DmRvdMxKIJhLx0rqkuA187OAuCJ5NTo3SjZUoksrh90jyei9fy9dnaZBRC6TjnHX4Xa640/n3KBV+rgniX3cKnNv0BdyZJom0+vnH6H2fg6CHGRDIEhVNLdYwEJXgqVcfkMWsWbRzlA8Uso6KdWLvVFeAcCkVZ3dyrQTehEZYlk2EpsLBpkXlyWfnMxmdx5zJEes+nsiak+hiDIa+YAleoGzxZLAK37HsDR18P4UNTqZ1TGnXvHsWaxenEpVGNrNqYwdNZjF2+MGVKpIPUrzCuUcbE7VMsaEpz4VVsYSwubX7sgiDgtRSxFvMlEyFc/O5rWBIJgpnlmuz/2He0NMenFKpr0cYPxzomS6bVVSz2uwz4Qupnh0J2mNp1CHdHHlFcUZKlZUVjSlEDVxO73YZPKIJYJNobKVnwVJR97XwaFFPXiWnEdIxYV5/q+x4sPSnJmqVUma/hYAZPZzGKQnWpWvm1XvLxygWwYon8+/oFJDXKPIGskZWIkyzBspYkICnbXmjQxg/HdIKyJVKJ977zFrdufo3xFUuBearvX9EJKpToN5hOpIhaXTjJ4q/QIPNkgyt3S8bViVQWn0f/2tCkokWmQUE8gODxIGYyREtlsSOKiPLvI6BBG7/N5yUHxEpo0dJldfPK5HNZNLY8isXBDJ7OapT28nyJTEmXrX2Oqd0RKq8ZC6i/5NTv35fOlKSgWrnga6G+rWBxuRGhJMHT8QKSPg2KjeG4AL9ES8vFcITqZJhgUZtlJ49fMT8uzfFFsfLIko8gILJag45Ct9+LRRAoiiKxvlhJgqftMxbzeG8VXzhnvCb7t3k95Pr6iJcoeCqmM2SzsgioBpknh99HDkiGSxc89SQkHbRKb2k6p4dD2eo8mZwZxW8tW6LgyRENU5mK4tXAFgKO2XsIxQKZtP4ihMpyqF0D9W0FpYW+FBY0seNUh70a3dU7lVb3EgVPOTkAdmjgTQjgDSrBU2l+g9GUFPwG3A5NzLkFqxWLS/qOxsKlUakOJ7MULVb8GmVHrXItVaJEFjSxgsAT867iN7MuJRRU/3folBsJEiU0rw73xrEV8lT5yid4MjNPZzHOEtcEHVvy0ebC6z3ugheNJnBppNVzKlKZPEXBgl0jAUmQBEYLlCZ4UuqsBIcTi82qyRj5mbP42TlZ5k9t4A5NRjjD+HLQpoUGEhyXsctkKBZFTQKY0xHR0JpFweJxQyp9TG9JZ5RjDLm1ufA6fF7SQDJSmuPrTefp8lXgdVg1kRJwyd/RTImODyC0/lVWrX+d+pqVwOldP4yCGTydxQgTxvP0nMsYN6aWz+s9eD5PISed1Dwa+L4BWGxWBIcTMZuRLvQ6t7hum7aI38Tr+OriqZqNoZgfl6JjMiEbSiuZBS3wBvzEnF7Cef0LjeG44EmjzJMv5KMgWMhabMRSWYJefQP87J693LT1FezjxwGXaDKGxeOBnj4SJfJHm7RxLY72CFUZbZbtlFqqUpkf9yWlrHpIZfV0hX5z4GjpgidlbI8GHaFaYQZPZzHeiiCtgVqcNv01WDLJFIWiZAvj0yidDrD2nMtoSRS4xK5d9udUxNN5EAR8Gp3UAIrVNRwN1FBl1b+WpN/YWaNuQii90GlerkVya7Ys6eOnF32cTL7IbZkCGqy6nJZMV48klZDR7sbCKgf4yRIFF5Uth/D2hQnZtLGhstTWcjRQi91SGqHk5KEjnHNkO5V2bczmvVUhok4fuYI22eXBkJMDby26CbXCDJ7OYnwlvDAl5PqHrNWOT6N0OkCifhRdHXHiJbj2KlIMfg3FK/vmLeKZcAX+UdrcVZ+OsMvHnyYtYcoo7TpgAoUMFx7YRKDNDizXbJxTUUylEQCPVlGNIBBw2+mKZUryO0zLAbBNw6Vlm5y1S5VIToOUdIxaNTVkFi7imVYPVzeWxt80e/CwpGfn1+b7Y58zi0fPuY5p9X7+SZMRzowiAuovE1NgMIOnsxqfUGRe6248QhFQ1238TPR3hzkcWDWs81A0pGIl8O+b8varVLR2UxltAkZpMsaxzIz+IoR9Njfb6ydRPalGszH8VpEFrbso2rRpKjgTvRYHTodbE+sShYDLRlcsQ7QEn6Gin6VVQTxAz+yFvJgK8ZFqbX4Dp0PM5cjJHpMBjbIWIY9ssVMii5aUXIvk8GvzHVU63JSOt1JQkL+ngSozeDIxAH6bheUH3gYgm8nhcOp3gYpn8nR7KzQRrjueSeFWLC0HybU0wMx6Tcc6kVDHUQK9Xfg1Ut+G0po7KwGpVurbAH6508eSz5HJ5nA69PuOFosiT8y4FFGEz47WLqtw0f63WXCohcyhRphQpdk4JyMj38Q4NFDf7mfMGPbvz9Jp1X/pPBmJUxRFRASCIW2CC6UQPZwqTXCRljN6To2WlpXgqS+RLYnkS7FQ7NexClWbOk8mBsDrP3YyS8SSOJz6RfXhUDVPzL+KiTXaBk9T2/bTeGgrtExFb/++YlpqP9dKQBKgvvMId2x4lsruJrh1oWbjnIxcRwdN4XaqcyHNxvAdt1wWiyRw6qjgnMjmEeUymYCGAWJjKkw82kmmN6zZGKdC0SLT6sILxzr5SmF+HJWFHfMOJ26HNpezqlgPd2x4FnfQC1+8QJMxTkdaMQXWwJsQoNJt4+Z3X8adyxANX0BQAzHV0xHti4JYBCBUUz6ZJ1Pn6SzG5rCDXbooJGL61iPE+9XFtc0kKOre2VLoBGUkKQatNJAAPA473lwKMaF/PYlvx3Zu2L6GqYd3aDaG1W7D4pDufPXW0VFqkBxWC04N3eRt/ebH+n+GeTl40qqbEKA6n2Rq1yFchw9qNsap6NeWcrs1y5gE/W68uRSUyEIoJ39vPCFtghqnw05DJkooHSPSHdZkjNPRG8/wXt1Emhsn4HSaOk8mBkFwuRBzORJRfXWC9CimhuO80RL6ihAW8gXISml8raQY4FhWqxQK1Yqtj1PDYmMAweWEbJZ4ROcAv62DWzc/D4EAgnClZuMowVO6BCrxyXyRvMXabxOjBbXhLq7c/QbW/ATgI5qNczLicsBt1XBZMiCb8QrpNLlcHrtd38umEjx5NQqeAASvFzGbJdobAbTp6jsVPdh5ZfK5jKvScGlZA8zg6SzH4nRSiMX62871wvHOJm7b9AIhy3xgiXbjyNYo2aTOweFxF3rFJkYL3MdZ0OiNEjxpWi+DFOATjZHUuVsrGY5RnQxjc2lb49Hv31eCzMXLcy7h3cqF/Gz6dM3GUDoVS2F+3Fk/hh8tu4XFo7ULLJRCdAGRSDhOtc7mwEr20FehXRu/zecl19dHrFd/i5aeuHRuKydrFjCDp7Mei1tSqE7pfOLO90WoTEXxoW2hs9NXGv++uNxaK9psODUUkfQFSmd+rJjZOjVc8gFJJyiP/staSmu94NY2s+Ysoflxv8K4hlpkXlnYUCxB8BRO5iharHg0qgcCaWlZcDolc+DeqO7B0++nX0isLsKK0er7gyoo5sCl8O/rC8exF3JU6iwgO1LM4OksR1GHTuls76FkgrT0fQNwyvvP6+wdloynKAoWrBoGTnCsnqqYz5PPZLHpWBOgvKduv7af4bZll/HX2h5G1YzWdJwTUX4TWho7w7HgKRfXP7iIynVdWhbEK/pKpVhaPmbNom1tpcXroZDJEOuNaDrOyThg8ZIJuQlWaBcg2gM+UpTGHNi5YQNfWP8CQdsyYJHu4w8XM3g6yzk4dylvuCZQX6OvBktOzgQ5NK6X6c886Rw8RXwV/GjZLUyscPElDcfxHbckGI8mCNXoFzwV5PdUK983BWtlJTFnmkheG4XoU6FknqwaZ55cfi8FwUIqp6/chJjPc9mGF0hZ7ARs2nWJ+eXuLFs2QzqTw6WjJIpr6xZW7t7M+DFLgXmajWP1eCj09hHX2fw4lS2QyUudaBUaLms5ZQ2pdAmCJ0XHyq2h1poWmMHTWU6+sZGj7SIR9BUh7K+X0TjzZJkwkd/MXkFTUw1f0HSkgcQykjWLW+NUs91uoztUQ6YI8WSWkKajDUSU1be17CaE0lm0KGbLdo1rusT5C/jxeUVmjwryD5qONJBULEFDuAOAgFe77Jov6EcARCAajuOq00+rx9bSzPSug9TmZms6Tqa2jtZojik6y631dfZyzpHtpN1evA7t7FOcskWLuwQek4ohsVvDgngtGFHwlMvlaG9vJ5lMUlNTQ2WlvsasJmemVCKL/VkLn7bBk6cqSEuwDqtd304N5ULv07ibEODlpdfSFctwu87+fa+Nno0lmeAjtdoKOzb1tXLhgU04mwpw2RRNxzqerLyMpnXw5JeXlPRWGFfa+HM2Bx4Nl+0sdhtWp4N8JkssHKNWx+ApKwfAWnkTKhxceim/97QyNVSn6TgnEmvt4LzD75IPVWgqXplZfC6PHvVx+Th9jw8gJ+tYlZOvHQwjeIrFYjzxxBM8+eSTbNy4kWz2mCrp6NGjufzyy/nsZz/LOeeco8V8TYZIXaKXua27sR20AFN1G1cJnrQuNvbJSwRxnbMWwp49XLvjVRrs04Glmo7ld0r2HnoGwPlCkXcqx0IleDX2m6qPdLOgdReuI/qqC8cLIgm7G7uGxcYAASV40llEUllisrhdmqtGvzX3QlpiWS7QOcOdl4MnLe11ACpki5awzhYt8V4psLB6tD2PVsoNBX1J/VXUc3Lzja8qpPvYI2FIynAPPPAA48aN4+c//zkrVqzgueeeY8uWLezZs4f169dzzz33kM/nufzyy7niiivYu3evVvM2GSQNPW1cfOBtAvt36zpu2OIk5vRqqi8D4LMUmdO2h0n7t2o6zokUu7qY2NtCfbJP87FK4W93fKCmpT0LgEuui8vp3K21deI8HlnyEaKLl2k6TjCf4UM7XuXit19BFPWr60rITvWCW9uCeIDe8VPYX9VERNRXd7kgN6Z4NLJmUQh6SmPREpeXtGwa21yF5OPrLYG/XVHuBA+WkSkwDDHz9NZbb/Haa68xc+bMkz6/ePFiPvWpT/Hwww/z85//nL/+9a9MnjxZlYmaDA9F4FDvVv7nZ1/MwYYEK8eN03QcnxUu2f8WgK7eaMpygV3jTi2Ai3at45wduxEWuWC6Pmn1WCxFU7gdnE4cGqpvw7GCdL11gpRgVAlOtcLnsjGhtwURgVQ2j0enguqkLCBp0ThrARCUs2t6W7QochregLb1MhNa9nLHhmepzs6E67WtrzqelFzArbVHaHUhxc3vvkzALsA/Ltd0rOMRi0VEOQAOVod0G1cNhnTW+PWvf93//1/72tf42te+huckP0yn08nnPve5kc/OZMQod/V6d6PpVRPkO85XLhFL4azSKXiST9paSzEA+CliyaZI62hfkuzo5obta7B4vcCtmo7lLpFWV0yHNn6QFOgFQQBRJBpO4KkLaTqegqKbZdMheBqTDjOt8yCZo7UwXyfJCVHsv/D6NfZj87tseHMpilF9u9FS8m/eqfGyZDDgpiHWjYDknmC1aVecfjzReJptNRPw5NJU6KyfNVKGfUu5Zs0aJk+ezC9+8QsVp2OiNoqnVSGts4hkRp+7eqvDjsUmjZHQUaFa8dJzaFwQD8d0iPT071PUvi0a61gBuAOl0Qmat/6P3LT1j1RFuzUdR7DbJZ9JIBHRT4QwmcxQECzYNZYLAZh+ZCdX7FmHZd9+zcdSKGRz5GX5B7/GnVqKNUpeZ6HTtBwAa2nsDFBRJS2ZiUBUR5Xx3qzInyYv4c/zL8XlKi+F8WEHT2+++Sbf/e53ufvuu1m4cCF//etf1ZyXiUq4S+CNlosn+Oibv+OWLS/hd2hfAyHIF3g9zY+VLIlLh8zTMf8+/U7cioCkRYd6mX7/Pp0DfF9PJ6OiXfjs2t9lK3VHcR2zh/snzOLH532Mw+ddqvlYigVNRsffYKwAP1p2C/+1+AaCQW2DCyV4KugcPGWjigaStsGh3W5DdEnnmXBPWNOxjqdcrVlgBMETwK233sru3bu59tprufLKK7nhhhs4cOCAWnMzUQG3T7kw6WfvkYwmqExFqU6G8bq1/1EowVNKR/NjvboJAZxy5imn47KWsuRj0VhAEsAbLJEFjRysaelNqKAEoXr69yndfX6P9tlDJTOipwVNJCVZswg+Lw6NA2C/XJCutwXNhokL+c2sS2Gq9hIeFvlcFuvRMfMUTkjWLB59uzTVYMRpAbfbzb333svu3bvxeDzMmjWLr371q2zfvp1CoaDGHE1GgLcExrJx+QJRdDiwW7XPPFld0oVJTwuafEZ6P906BE/9xrI6nrgVAUmbDpknb201T8y/isfmXUk6p885I58vgPwZ+nQQ57O4pc8wqaNBt6IrFdDYugTA5dffv0+RDdDamgUgoHSCpdPk8vpd145a3LSE6vHVVms+ltUrBYh6WtCIW7bwhfVPs3Jn+a1cDbsgJZPJ8MYbb7Br1y52797N7t272bVrF5lMhh/84Ad8//vfx+l0MmPGDDZt2qTmnE2GgKeqgt/NWE7Wauf/FUWsFu0VZJULhODU/sILx+7q0zqeuH87fyWHG6M8MUX7blIlu6VnvUVGrq+yaSwgCeDzuuj2ShpPsXQelw7LaPFYEgFJNsCvcZs7gM3jpiBYSCb0yx6Oeut1PrTzMA2Lg8AkTcdS6tbyOhqQpw4eZuXudXjGjgK0XZoMyAXpAiKRvphu5sB9coBY6dU+QLT7veSBRJ9+maekPJbWFlBaMOzg6eKLL+add95h7ty5TJkyhQsuuIBPf/rTTJkyhSlTppBOp9myZQtbt+qrv2MyEJ/fzcFKydcukc1r3lkExzJAWpvmKuyfu5R1zvHUVTboMh5ALFMgb7Xh02NJJBSg2xPCZ9NPYTyjSDHokHmyWgR8ThvxTJ5YOkeNX/v3VKk9EmxW7DqYLe+6+BqeDi3gnxonaD6Wgrv9KBN6WwgK2mdKvHLwVNAzO9rWwfSug9gqtFf5tznsRCpqiRcgEk9TXaP5kCCKjNu1mWDBSsiurRYZgKVCsmiJZPTLrKWV4ClYXuriMILgqaenh/Xr1zNv3ryTPu92u7n44ou5+OKLhzuEiQo4bVYcVgvZQpF4Wp/gKR3Tr9gYIN84ipZ2iFj0KzpURCS17iYEEKZO5YkFVzOjIcA/az6aREtVI2+Om89VE7TNWCgs69xDqjdMoms21GifCeoPnlz6BKR+2QNRT/8+RTfLo7FQLRxT+C7qGDylZBFQrQUkFdZccB3NvUlu0ek8k0tnWLBHWrWpcH9G8/E6z7+ER8Xx/N1o/QL8tFIQX1F+wdOwC1J27959ysBJTx566CHGjRuHy+ViyZIlbNy48bTbP/PMM0ybNg2Xy8Xs2bN54YUXBjwviiJ33303DQ0NuN1uVqxYUfZK6XOiLcxt3U1Cp7XslLzko9QiaU2/f59OF6ZCvsAl7/6Fy/esx2fRXjFaUfjW057lqL+GTaNnUJwwUZfx5rfvZeHRnaS7enUZL57IEHe4KXr1ufAqNy16+tspHbYeje1nALyN9fxx8lJeGbtA87EU0nLw5NApeArpbNES6ZbO10WLhaAOTQ0VXv1VxhVfO6/GOl1aMKTgqbm5eUg7P3r06JC2HypPPfUUq1ev5p577mHz5s3MnTuXlStX0tnZedLt161bx8c+9jE+/elP884773D99ddz/fXXs3379v5tvve97/GjH/2Ihx9+mA0bNuD1elm5ciVpnduo1eTCw+9y8YG3SXV06TJeMlck5vSCxqq/CnXJPma37cXWfEiX8eLRBJN6jjCj8wA+j/Z3oUp2S8/gScmQ6JFZg2NZSr3kJnqD1fz34o+w9pIbdRlvVGczH9rxKtVb3tJlPABR7gj1h7QPLgJVQXbUTWCnr45coaj5eAAZOcPt9OtjCq6oqPfpFDxF5SUt0e3BqkPjTSn87fJRxdeuvKxZYIjB0znnnMPf/d3f8dZbpz4BRCIRHnnkEWbNmsX//u//jniCp+OBBx7gjjvu4Pbbb2fGjBk8/PDDeDweHn300ZNu/+///u9cccUV/NM//RPTp0/nm9/8JgsWLOAnP/kJIGWdHnzwQb7+9a9z3XXXMWfOHB5//HFaW1t57rnnND0WLbHo3I3WPHYqPzvneg4u0WfJtrGzhUv3bySwd5cu4ykXeNFmw6lDvUygkOG2TX/ghteeQSzqc2GydrRTG+shYNGn/sGqFP3r9B3VOzisyKeY0NuCs6NNl/GK2RzFjHQR9GmsEQQD30e9DJCz/QKS2mfWAJbtfYs7NjyLbdPbuowXk8Uq9bDXAaiP93DLlpeY/uoLZ95YJQoJ6TMMVelrCq4GQzpz7Nixg//v//v/uOyyy3C5XCxcuJDGxkZcLhd9fX3s2LGD9957jwULFvC9732Pq666Sqt5k81m2bRpE3fddVf/YxaLhRUrVrB+/fqTvmb9+vWsXr16wGMrV67sD4wOHjxIe3s7K1as6H8+GAyyZMkS1q9fzy233HLS/WYyGTKZY1IAUZ0l/M+ExS3VW6Rj+tQjKBkSn04XJqes8p3TSQhUUTLXq5vQ63VRmZK+U5lMDpdb+4LqWZtfY8bRo1T3TgXGaz6eYiGS1inzFNOxjR/Arfj36fYdjSMCIgIBPboJrRamJzopJpNEwnGqfNp/R3NyZ5/W5uMKfptAJpciE9Hn/B4PS0taVp2WJYMuG/XxHmw9+phXi6LIdn8jTnuSYG35BU9DyjxVVVXxwAMP0NbWxk9+8hMmT55Md3d3f03Qxz/+cTZt2sT69es1DZwAuru7KRQK1NUNNEqtq6ujvb39pK9pb28/7fbKf4eyT4D777+fYDDY/9fU1DTk49ESm5x5yiT0ujDp42un4JLb6Qs6+fcpYpyCDkEMgPc4LalYRJ/PUKmXceu0JKIYLKd1sqBxbnuXm7b+kZnNO3QZT7nA69WNFo0mKAgWCnYHTh2kHwCu3r+BK3e/QbJDW7sbhVxSv5ouOCYEmtFJ6DQpW/nYddCSAwhWSUXbRZ3kJuKZPC9POIffz7iIyjIMnoZ1dXO73dx4443ceKM+9QJG56677hqQ0YpGo4YKoGyyvUc6rs+Ju3HDa9z87k5Gz7gGmKb5eE7Zu0uv4CmpWJfoVBBvsVrA6YRMhmQ0DvWVmo9ZTGewAF69gif5M8zo9B0Vu7sZFe2iIqfPeIpYbVGn72jEFeDH532MOreNLwvaa7sBWDwuiEZ1s6D5/fzLOVTTw0+n6NMR6pKDtIxOwUVSzjw5dNJAClaFAChmMuTTGWwaS830xKVlZY/Dqou2m9poX4WmEdXV1VitVjo6OgY83tHRQX19/UlfU19ff9rtlf8OZZ8ATqeTQCAw4M9I9BvL6nTXa+/poiHWjV8HfRk4lh3RK3hK6xw8AQguxd5D+5ogURT71be9Ot3VO+TsYU4nIVBlHIcOIqBw7H0UdVq2U7r6vDosnylY5Zu0pE7BU1+mSNLhJqBDJxock2PQSwh03+jJ/GbWpURm69PBGAz5KApSSBDRwRy4J5LEkS9PaxYYQfAUiUT47Gc/y6RJk5g+fTptbfoUQio4HA4WLlzImjVr+h8rFousWbOGpUuXnvQ1S5cuHbA9wCuvvNK//fjx46mvrx+wTTQaZcOGDafcZzmgGMtmdVoSUYIYl07pZsUiRS8LGiWDZ9PB903BIt8FJnWoCUqlMlgK0tKrV2PDVYX03Hk8Mf8q3p04V5fxcvJvwaVTZk0p2rZms2Ry2ndNKkXbeui6KShq9MmoPsHTMXsWfXSXvCEleNInwO8QHbSE6nGM0kf812azgnytiPRoL2uTeW8nf//m09z43l80H0sLhh08feELX2Dbtm1873vf4/Dhw6TkO6p/+Id/6O9e05rVq1fzyCOP8Nhjj7Fz504+//nPk0gkuP322wG47bbbBhSUf+lLX+Kll17i3/7t39i1axf33nsvb7/9NqtWrQJAEATuvPNOvvWtb/H73/+ebdu2cdttt9HY2Mj111+vyzFpQXLqDH4//SL2NU3VZTwleNLD9w2O8+/L6BM8NY+byk+W3sy+Zdq71Svo6d+n1FUJgNenT4Dorq6k21tBj6jPxV6pl9ErwPcpxrJATIfGjeKu3Xxox6vMb9WnAxXALhf961ETlEmmuGj7ayzf/xZBpz5LPl5ZBbuQ1Cd4UiQRQjrIoShYZN2zqA7BU6JPGkMPc3UtGHZF74svvsif/vQn5s+fj9V67Mu7cuVKvvGNb/QHJFpy880309XVxd133017ezvz5s3jpZde6i/4bm5uxmI5Fh8uW7aMX/3qV3z961/nX/7lX5g8eTLPPfccs2bN6t/mK1/5ColEgs9+9rOEw2HOP/98XnrpJVw6LtGojbWhngNVvUx36qO7VJQ1sfQqNvZUV/KH6ReSsdr5kg7+fXHZmkUvfRmAfKiC7q4ocR2knpRuQpxOBKs+Fyal1V0vBe7+7KhO9SRWp4NfXHwr4ZzIR4oWtLZ5zXV0MqG3BU+q7swbq4RdKajWYVkr2htlWtchihYLfp06Jn3VQbo9IbI2nUQ5d29ndluYanGKLuMBiKEQ0WiSaFL7G1HFQ8+pU2mA2gw7eBJFEb///RfjyZMn66rIvWrVqlMGamvXrn3fYzfddBM33XTTKfcnCAL33Xcf9913n1pTLDk+RaFapwuTkgHy6NRi6wt42F8lFejHM/l+MTutiPVbs+i3JLL7vMt43t/GpNrRmo8Vxcpfx82n1qffHW8om2RJ8zaq4j7gfM3HK+poXQKAIOD1ugiHU7roICnehHrVdMGxLF5Gh+yo0sYvutxSQ4UOBEc38MSCqwH4dqGITeNxx+7YzKiubqpzyzUd53jeu+ga/rSzg8lV2p9nUvJn6AqVn7o4jGDZ7sorr+SXv/zl+x5PJBIIOnV3mAyOYD7NtM6DBA/t034wUeyvPfLqVMip+PeBPircFdvf4fI962nsadV8LIV+Cxodji8qONg0egYHp83XfCyFQC7F0uatjD+gj3RAogh5ixWvjm7uSnZND4uWrJz90atTCyA/ZSp/nLyU3fXaW/rE+qQLr0XH4DBwnG5dRIcAWJSlZfw6+r5VehUVde1VxjOyFINbBxFXLRh25un+++9n0aJFgJSFEgSBdDrdr9ptYhwqEmGu2LMOa7QO+BtNxypksvRaXTiEvG5t7gCzo0fJRuMkehdBSNs6HU9LMzM6D1CZWazpOMej57KW3urbAF45AySm0/3nEy35xewryOSL3DxmlKbjHM+5zduYsu8wuUP1MLlG07GU5hC9aroAHGNGs6Oum5ArpPlYCbmjT5Fh0QOb1YLfZSOWzhNO5TQVAhULhX57nZCO1iV6+ttl5eDJW4bWLDCC4GnMmDGsW7eOL3zhCySTSRYvXkwsFiMQCLzPbNektCi1R3p0oyWw8LPFHwbgTr9+J7blhzZT6AuT7loBE7St8zjWTajf8Y1v3sPfbn6ZWvcCuGq6pmOle/uojfVQI+p34fXKbeC2XJZMroDLoV3gls0XyeQlm5uATp1aAGNinYR6W8h09Wg+Vl6WYtCrmxD0NT9W5BCsOmaeAG7e+ReEzi4SB8dDzQzNxolF4hRFSelbEa/UgwldR/jYlpeoZwpco93xAeRj0mfor/yABU8AkyZN4uWXX6a5uZl3330Xu93OkiVLqKgoP7XQsxmPfAIt6mBurGQtHFYLTpt+wmcWl4sCkNRBZDHf302o45KPUKAqGUEMa98FY9u9i7959yWC9nmAPv6EPnl5ySIWicZTuCq1S+XHjru462UhBGDtt6DRvpU/n1QU4vUrxg0KBcb1HiVQ6AYu0HSslJJ50jl4qhTyZHMp4hrrIEW6wwAUHU5cTv1qK0MOgbp4D3RrrxK/219HMWPjsnqt2ye0YVhnjsOHD7N7927mzJlDfX09Y8aMYcyYMf3Pt7a20tjYqNokTUaGcmEik0EsFhEs2hU6KkXpel6UACxupZVfhzbwtNKppd+JW/Hv08PeQyn41XNJxOJyYrdZyeULxCNxarUMnjp7uGnrK+S9PqyWqzUb50T0VFHPyQG+bgXxQEUuyfU71lLweIFPaDqWIlSrd5u7EgAn5CUnrYgqNV06mQIreENSliuvcYAviiIvNs4hW1vkq6NPLUBtZIZ8Ff31r3/NpEmTuOKKK5gwYQL/8z//A0iyAN/5zndYvHjxgEDKpPT0Cx2KIqmkttmnzMFD3Pzuy6w4oI/zuEK/f19M+06fYlrpJtTvxOaW77DzOqioK/Uydj3v6gWhXwg0obGKerI3wqhoJ+OS2i+fHY+jvxtN+1b+Jxdew4+X3YJzovamzgp+eelVSKcoFoqajvXe5Pn81+Ib6F2kr3ixIseQ1NhjMiZntvQsiAfwV0k3LUWNlf7jmTxZeem8yqufCr6aDDl4+uY3v8kXv/hFtm3bxmWXXcbnP/95vvGNbzBx4kR+8YtfcM455/DMM89oMVeTYeL2uEAuwE1o/KNP94ZpiHXTkNHHeVxBsaDJ6KCiLsqZJ6+Od/V6WtAowZPTq6+22TELGm2/o8mYYq+j70lbyZLkdPiORlM5ChYrAR0FFv1yttBSLBKLa/s9DWeLpBwuvDp2ogE4fIo5sLaZp45QDb+ZdSn7FyzTdJwTCcj1R2IiAXLNlRb0RlM48jk8dgtuR/n52sEwlu3279/Pl770JcaOHctDDz3EmDFjeOONN9i6dSvTp2tbyGoyPASLbCybThOPJahBu04fxbpEWUbTC5tbn+Apn81BTvYN0zN4ksfSo25NqZfRe0lk87mXsflojKnekKbjpGSLG6uO9joATvnCq7V/X6Eo9muRBXQSkARwetxYrFaKhQKxvijBoHbfn7DcSq+XNYuCIuiY1ti/r6dgoyVUz9wmfaxZFCqqQwDkc3myyTQOrza/keieg/z9m09TqK4BrtRkDK0ZcvCUy+Vwyyed0aNH43K5+MEPfmAGTgZn45wLaI9lucSm7QVDqZex6xw8KfUkWpsfJ3IiDy39KI58jr/XUdxNT/++fEr/NneAfH0j3eFOIhqrMaTkzJZVx5ouOBYA51Lafobx3ijX7niVjM1BwHmFpmMNQBAQ3C6IJ4hpHFw0vbuB5Ud7qEqP03ScE3HJwVNW46VXJTis1DFzCBDwe8hbbdgKeSLdYWo0Cp5ivVLji71MrVlgmCKZv/rVr9i1S/JMslqtZnddGdDTNJEDVaOJoW2KNCMHL8oyml4kp83kD9Mu5ECDtgJ90UyenNVO3uvDYdcv3ewP+og5vfRYnYgaptPhOCkGvestdNKyUvwB7ToHT8ycyY+X3cILcy7RdJhYb4SJvS1MDbfq+h2FY9m8uMbBU82hPcxr20OFoI9rgoKzqkLyYBS0DWqEfXuZ3baXxqy+5Q8Wi0A+ECTi8hHWsH40LgdPDh27QdVmyJmnCy64gHvuuYd//Md/pKKignQ6zb//+7+zbNkyZs2axZQpU7DZ9O20MjkzPp0uTEonkU3nJRFLQwP7q/uY5tK2BiKe0V9AEsBbU8HPzrkegH/JFfBoqIO0rXYi8YKfCxr080UDGNvXxuIj2+GwG5ig2ThZpZtQo7vqUxHwuSlYrJrbsyiBi95L5yAXOHdBMqxtTRDyTZpPZ2sP6+xZPDE/zZzR2moTBXZt59L9WxkVHqfpOCfjTxffyL7OOJe5g0zWaIxEWAoKHYHyVBeHYQRPr776KgB79+5l06ZNbN68mc2bN/P4448TDodxOBxMmTKFrVu3qj5Zk+HTlOgh0XmYbEcTzNKuNTSXUoqN9b0wKf59MY3tS9Kt7Vy2901cddXAZZqOdTxuuxWrRZDqWdJ5TYOnzVXj6XY28rVGfYOnpq5mLIffxd5cq+k4qUyevMXa3/2mF0r9kdY3MMlo6YKnlhkL2GwfxWifdqsRYrFIUc6OKh1+ehGSl9G0ti/JycuC3pB+dZUKylJhX0K7ID9d5r52MAKRzMmTJzN58mRuueWW/scOHjzI22+/zTvvvKPK5EzUY9aRHYzb8y6W/aPg0jmajZPKiWStdt0vTMF8mildhwg4o4B2tinpzm5mduzHZte+9uh4BEHA57QRSeWIpfPUaZhgi2ekk2ZAR+NjOBZwZzUu+t86ZQG/idXylXP1c6sH8JPn8j3rsRfyFIqXY7VoY0GTLFFNF0By4hR2RL30WLUbOxlLIopSm7ue6tsAIY/0mwgntc0e5uUlM0V3SU8qZH+7Xg0DxLSceSrF8amFqrev48ePZ/z48dx0001q7tZEBexufQqq3561jOfF8fzrvJmajnMilfFertr9BkK0AfiYZuMo9TJWt/7aJNfvfo1idw+pI5OgdqomY+TyBQK9XThtDvxOfetlnHKNVU7j76iiMO7XuVPL77Ixo/MAAPF4mmBAmwCjVAXxcCy7pqVxbrRPuvAWbTbcOv8OQ2KO2zb9AUchRz6/AptGLgrFpHSe8eksxQAwu20vlVvW4WqIwbljNRkjK2dHPZVm8GRicOw66SApy2Y+p75fLaUbrahxN5ry/und5g5Qm02QS0ZIaahuHIsk+Jt3XwLAa/uIZuOcDEWxPa/1d1ReNgvoXLfm9HqwWi0UCkVi4Zh2wZOctdBV5FSmtpBiXO9RikddwDRNxoj1SRdewe3W3ED6RIJBL5UpKXiLRhJUapT5EmU5i6CGSvunolLIk4/3kO/UzqJlv7eGVGWac3Suq1QTM3j6gKDodWh9Vx+X7+r1tmfx+PXRQeoviNe5pguO1bAo1hRaEJfvCAWbHbtT38yMIo1QSGv7HZ321l+obu+lOjYWGKXpWAMQBASnC5JJ+X3WprYrI1949V46B2hqO8j1O9bi8UaBSzUZIy7Xy1hKcANjczqwOBwUs1kivRFNgqd0Mo2Yl86jQVl3SU88ch1SRkOLltcaZtDuncBnJ2iT2dIDM3j6gOCQU/h5je1ZFq5/mTHhJBWpKYB+nkVexWcuk0EURc3uSJXMk946VnAs25WKaRdcKAr0gs7q23DM7kZrFfVQRyuB3h78Fm0tRE6G4JaCp0RYO52g7dMW8URPJV84Rz9rFgVFyyqv4U1aZ1U9/7X4BhaNLk2xseD1QDbbb6GiNmHZFBiLBb+O/pkKHrkOKadR8CSKIj0JaYWg0qfvDZqaaOcQa2IoXD4leNL2rr6iq5Vxfa14Hfp+tRT/PmuxQDKp3dJdXrmrL0HmSVFRT2u4rFUq6xIAjyxAWNQ4wBcV01ydO7XgWB1SUsO7+mg6T8FixRcowYVX/gzzGqqoRzIFUg4X9srS6AsqZr0JjeQYekU7v5m9gr/Ov0RTE/dT4ZOXCgtxbb6jsVQWSyYDokiVt3yDJzPz9AHB6ZXvCLVc1hLFfgVsj853TG6vGwEQgXgsiVcjXzal4N5ZgnoSpW5NS3XjVPRYPYneuJsaeWb2ZeScLr6iUfZQLBZBXhb0BfVvAz+WPdQuuFB0pPTulgTwBpUAWLsAX+l0C+loPXM8Nq+HHNoFT+GcSEuwDldtaQQk/RWShlVBo/KAvuY2Pv/mM+RdHlz2azQZQw/MzNMHBOuY0bw8ZSkbx87VbIxiJksuXwD09X0DEKxWBKeULUloaCy7ccYyHjnnwyRna/c+ngq7Dq38SjehrQTLkv6Qj6PBWjpdAdI5bZbU0qmsFEABvhJknpRaOcVfTwvGbn6DlXvWUZ0MazbGqVCCp4KGwZN953ss3/8W4/paNRvjtOPL9ZVamaz3ycGh3tYsCsEqKXgqJlNQVP93GO2R1MVLUTeqJmbm6QOCu6aKnbUTSGhYRJqUL7wiAv4SFKtunH0+bfEcF1u0O+mE85BwevovEnpiC/iJOTy4i9p1GCnehHrb6wB4HTYEQTJzj6VzmritK8XGCAJen/4n74PnX8avXDP44hhtOtEAKlsOEujsIoS+1iUAvgr5d5FKaVZ7aGs+zLy2PTQkJqm+78EgVFbS7a2gqqDN/lPNLcxp28OEOq30vU9PqDpI1monZXeSiqf669jUItoTBsDmK19rFjCDpw8Mip1IXEMFbiXjk7PbcWlw4TsTXWMns78jRkzUbuxS2bMAJBady89a/Vw9STun9S5fJRtHz+SccfpfmCwWgXO791NIpohGl1IbUD+AUwxrRaerJPUknoCPvNVGVMPfoaK+7Q3of3EKyJ1a1kKeZCqL16N+7Zyivu0qwfEB9C69kCdSjdzWqE2nmPD/t/fmcXKVdb7/u/Z96ep9S7qzJ5A9JIRdEiGCgooCijD4Y+A6I8NV0VFnRmdGRx1HrneuXB3Ge0WvMyijjgsog6AgIIQkBEJCls7anaT3rfa96vz+OOdU0mTprq5TXafSz/v16pfSderJc6qq63zO9/k+n8/hQ1x7ZAeBpsosDHmcNr57+W1k8xL35o1ofYsRHZdvYCwVev+0QoinWYLbBJ1jvbhGsyBthjLcEcaVpQiDzT7j/itwyh5BdcguB4v2bCMQjOFLzawJKJzyzipnBM2Ap45XOlaxdMnM79QCuOb4myRiCeJjQWgLaD5+LJYgazRVZLcknBLd5cy3k5S+xkpEezg8Ll6ev5aY0cqtiUyZxJO8JKh1RWSq+BzldRlPKALfWqHoEoPBQI3LynAkxXg8TYtfW/kUH1dCgX3VG80Coudp1uA2w837/sDm/X8kmSyP7X4sliJtssjbsStAe2yURcPdJAfLZ+7WfryL1X0H8MxwmjucuvCqDtnlIFLByhqAwS5/duLh8jSrjvnq+d+X3c4z11YmBaE5OCD3I+15vSzjZ1JppIzioF6Bi5PBaOTYwhXsa5xHKF2evrWc4r7trFDlotz5dqmwXJlxVLAyU858u7jiEG8X4klQDbhO60GKlqmheqyume9svJXfXfW+sow/GSt63uKGrpcxdh8t279Rqd2EADWhEW598xnWbn2mbP9GdnQcXyKCzySV7d84H6oRaLxMn1FVeJajIjIVAqkYS4eO4e47Xpbxw8qSiIQBTwV2E0L5I1pyMTW6pDIX3+bxAe7a+SQrX3qqLONnlAq+s4KhuZef3MOHdj1NZvduzcdOqdEsFYie0RIhnmYJJrMJrPLdRLkuTIV+oAptIVaXYtLR8uz0SacyGBTnX3cFlgzcFiMtkWFcY8Nl+zc6d7zAR3c+QduJw2X7N86HussvUSY7hlPRLJX5jDo8qolkeSprUWXJB5utbLlrk9GejtAx1kt0ZLws4+cT8t+3x1+ZyozXYSGQCGMeHyvL+FnFA6ySobkNUpLG6GhZqvg99gCHa9uxV3E0CwjxNKtQXaPjZfKYKQSuVujCZHaWN/z49IpdJcST6qIupcpnAqq6e9srsFsSTplIJsrkMWPau5eb9r3Asr6DZRl/MpxKNahcRqCxkOrTVZmlc4DLD7/Ge/f9gdzRY5qPnc1kQenp8laocuFWRI1Upu+ZXEz+nnFXMDTX6pGrXuXI0dzetIhfL70K+9LyhJvPFKJhfBZhsNmRiJRNPFne2sN79z5Pq2c1cElZ/o3zYS2zeCr4R1ksmC0z/6dT8M5Kpcjn8hhN2t/7qDu1KtWMa1Hew1S58vsGB5k3dpLaRGUa4tUdcFKiPJ/REV89/3vjbSyrtfOJsvwLk2NRhHcypL1DdTiV41/X34I9m+L+CokLrxrWm0iQzeY0r/AVQoEVv6VK4PB7CFOe93BMiWapZndxEJWnWYWxsCRSpgvT0BAd433UpcrjvDsZhfDjWHnu6gu7Ce2VuatXHbGNUp5omSoXBfFUgZ4uOPUelssINF3B0Fw4zYFbyWDUmnAqS9Zkxl7BJR+r4r6fLMPSazCRIWG1kw3UVuQGBsCniDYDEmGNjTLT2Tw/XXQVTy65Cl9jraZjF4Pab5UOa/tdLuXz8tKyJBGocvEkKk+zCLPdThZIlkk8qRe8SuS+wWn5fWUKlo0pFbtKiSeb04HRaCSfzxMLxfCWQeBIySQGwOWpTOUptGodPx10cFXz/LKMn1GqkpVallT7dMzZTFl8kNQmbW+F+g7hlDBNlaHCHVTOz++s3PmZbVaMViv5dJrwWIhArXZCNRhP0+trwGigLH/fU0VdMlSbu7UiPB7h3pd/Qs5gJGC/TtOxZxpReZpF9C1dxW8XbWTE31CW8TNKNcTmrIx4UvPmcmUST2P+Bv7vJe/j1Y1byjL+pBgMGGzy3Vo5dkzmc/lCP5WrQju1LE2N9PoaGDGWR6BmlMqTrULiyeF2YlQ80CJliPcwHtjPdQe3sni4W/Oxp4pNEd6ZmPbnl+jp5ZojO1g3XL4dtVPBoHzHRTTOtxtT7A/8TitG48x75an4AvKSYVbj6uH4sLyJwGi1YrdXd+WpasXT2NgYd9xxB16vF7/fzz333EP0PCnQY2Nj/MVf/AWLFy/G4XAwZ84cHnjgAUKh0ITjDAbDGT+PP/54uU9nRoh3zGN/wzxGbeW5MGaUPo5KXZhMc+fw7MJLeW1OeQwso1mJqM2JoUJp7gBZtxzREi/Dsl0snsQoyd48ngrEz0D5vazUqqS9QpU1g8nET66+lf+98TbChjIU/nt7WTZ0lJboqPZjTxG1X64cu16Tff2s6j/I4rETmo9dDOmaWkZcNYQ09noK94+wov8gF8WHNB23WHx1flJmK8GctgIuPCJfb40V+vvTkqpdtrvjjjvo7+/n2WefJZPJ8NGPfpT77ruPH/3oR2c9vq+vj76+Ph566CGWLVtGT08PH/vYx+jr6+NnP/vZhGO///3vs2XLqeqC3+8v56nMGKpDdTRZHoPHrFp5qtSyXUMdexvn016mzLLCbkJb5ZYMfveOD7C3L8yVHu3dtyOJDDvaLsKRz2CrQLYdQCAZZWVfFwFqgY2aj6/ucqtUTxeAyeclOxonXIa/w7SyJG+r4MVJtWPIlaHyFA/KN8iWCt2gqey65j28dGiENZ46TcdN9pzg2iM7sEodmo5bLDXtTfzLpbKR7GdzecwabU4JKbl2pirPtYMqFU/79+/n6aefZseOHaxbtw6Ahx9+mBtuuIGHHnqIlpaWM55z8cUX85//+Z+F/54/fz5f+cpX+MhHPkI2m8VsPvVS+P1+mpqayn8iM0xdNk7nWC+GfgegfTBpPlnZC1Mhv69M4tB45DBXHd1JZ9MKYG1Z/o3JOFWZ0f4cI3kjL3esosZpqUjuG0BNdIx3HH2NVLy1LONnUmkMgLtClTU45TFVjvdQbYh3VFBcWOe08WLnGrwt2vv4JBQPJKu7spWLckW0xIKy+3alQ3NrnNZCSPdYPE2DR5ubqZiaa+epbndxqNJlu61bt+L3+wvCCWDz5s0YjUa2bds25XFCoRBer3eCcAL4+Mc/Tl1dHevXr+fRRx+ddFdMKpUiHA5P+NEjbf3d3LzvD9S9tass46fT8sWgUl/cbhN0jPXSdPJIWXYymU6cYE3fAVrHBzQfe6q4lapXOQKe1UzASvl0wanIjVyyPH1rj655Nw9fdjuOOW1lGX8qrO7v4rqDW0l392g+dkbZtOGoUM8agLO5kddbl7LXo32AtdrAbPNUVlyoDetBjV3UE0oPlbXC52cyGgoRLaNR7ZYm1Vw7W5WHAkOVVp4GBgZoaJjY9Gw2mwkEAgwMTO3CNjIywpe//GXuu+++Cb//0pe+xLXXXovT6eSZZ57hz//8z4lGozzwwAPnHOtrX/saf//3f1/8icwwNmU5K1OmhuofrX03g6E4mzrKkzY+GW6TxHv3/QGAVOoezRsSVf+oSi1LAqzo3kPgzV1YFgPr52g6diQcw5eIEDBUJroEwOVVjECTSSRJ0jRgOpeX5GqP0YTXVblznDs+QGDoKNmBQc3HVqNLnBWsrKlVmXKEH6eVBmZ7hXzIVJYc7+Kunb+jxr0e3rlIs3FV8WSroPhVuaHnNXIne4kebIXmVZqMmVBz7SoYPaMVuhJPn/vc5/j6179+3mP2799f8r8TDoe58cYbWbZsGX/3d3834bEvfOELhf+/evVqYrEY3/jGN84rnj7/+c/zqU99asL47e3tJc9Ta9SLfq5MBn3RVBbJYKxYPMvp2+uj4Zjm4knt6aqUFQNAbTpGPjJMflT7aIj8oSN8dOcT2MY7gc2ajz8VXEpYqCWTJpHJ4bRq9xV1+nJupYKPASzKTUyyDFv5c4rAd1Xwzt5nN9EcHsaWTZNMZbBr2COYUXq6HBUUhwA+c55AIkxuTNsImrSyLOnwVl5ctGTjpKJjRIa123zQa/dxvLadtlbtq5Izja7E04MPPsjdd9993mPmzZtHU1MTQ0MTdyNks1nGxsYm7VWKRCJs2bIFj8fDL37xCyyW8/9hb9iwgS9/+cukUilstrPfrdpstnM+pifU5bRcQvt4j1xeKiwluSt0YSrk96XTcn5fg7a74jKFylPl+knMinBLlcFFPaWYgJorGO3h8jgxANZchkg8ral4igyPcdO+P5C1O7CZb9Rs3GKxKJ+fVBlMJKV4Qu7pquCdvdti4vbdzyAB4fEPYG/SbnNDVq2sVdAEFMChiPyMxp55qnhyVij0+HSsXhcpIDKmnR3Dmw3zeHmpj03LL9ZszEqhK/FUX19PfX39pMdt3LiRYDDIzp07WbtWbtx97rnnyOfzbNiw4ZzPC4fDXH/99dhsNp544gnsUzA73LVrFzU1NVUhjibDoTRZ5svQTxILRXjv3udJmSy4rddrPv5UMdhtSKp40phT29wrJ55U4ZYpgwN3SrkwWSpYWTM4HFjNRlJZ2Ym40a/dax0dCzFvrBdThftJVAdurbfy5/MS31n9HqyZNB8uQ7P2VDFazBhsNqRUikgwQoOG4unJZVczVDvOFQvmaTbmdFB787Ia7yhUxVglQ4FVHD4PESAe1K6HV+2fqq3gsrlW6Eo8TZWlS5eyZcsW7r33Xh555BEymQz3338/t99+e2GnXW9vL5s2beKHP/wh69evJxwOc9111xGPx/n3f//3CY3d9fX1mEwmnnzySQYHB7n00kux2+08++yzfPWrX+XTn/50JU9XM9RdcPmk9pWnaDBCx3gfebMVu4bVgmIpZ36fKjor5U4Np9ybc+UQT8rF3Fwhk1MATCaMNhtkE0TD2r6HsUK8TgXPj1NO+Om4tucXSWXJGM1kbGa87spVDwGMDgf5VEqO4tCQwZyJoNOHz19ZAexWKkNqj5lWPNe5lpCzk6s7K9/2oVbXEhoagUaCF0Y0C1SpeAJ47LHHuP/++9m0aRNGo5FbbrmFb33rW4XHM5kMXV1dxJUvqNdff72wE2/BggUTxjp27BgdHR1YLBa+/e1v88lPfhJJkliwYAHf/OY3uffee2fuxMpIoRk3pX3lKa5e6OyVvaMwOh3kgURE+8qT6lzurGDlSRXA2TL0rRVy31yVvfC+um4TB8dSrDFq+wUbVxy9TZUUh5wy6NRaAKsN2jazEbtF27DaYjE6HRAMEtdQPOXzUiF+xlfBeBYAT43swC1pLJ4OWXxE6lz46rX3cSsWp3KOqZA2lScpn+eDz/2InAR1f7FekzErSdWKp0AgcE5DTICOjo4J29WvueaaSbevb9myZYI55oWGq8bHH+atI22ycH82h0XDNHBVrBgrLJ5Man6fxl9qAD9bvplEKMq72srjQTQV1KpXrgw9T+puwkp76MTaO+nNjRHOaTtuXAc9XXBqp1hW68pT/zDXH3wFQ00AeJemYxeL2eUkjbycrxWRUIyrD+8gZbbhs1euNQDAG1B6khIJcrk8Jg1MJDO5fMH7q8ZZ+cqMu1YWTxmN3sPgaBjyeUxAoM6vyZiVpGrFk6B4XG4Hu1oWAxBL5/BrKJ7U0FxjhUJzVfoXr2BnPkBzGfL7hiQraZcft7dylSe7x0XaZCGd1z73KlvhbEKVchmBJlXxVMGeLgDzokX8n0veR3NzgL/QcNz40AhLh45hQvuqa7GYlb6uhIaVp/DoOKv6D4LVis1S2UuXt9ZH1OogYbETDsWoCZTe4D0+HmFF/0GSVntFg51VvEpESzqrjWfe2KC8Q9jgcGCt8lw7EOJpVmE1G7EpzbiRZBa/hnc3SaXR0VThu/p453z2jtkYtWnbE5HM5EjnlNy3Cm5zt82fx3c23kq9x8Zfajz2sZpmBptTLGup7DbiueFBVvYdJNtbC2jnZZVSPqOWClfWPF4XMZuTUEZbI9dYWB/LkgBmZWkyqWHfWlhxpzY4Kn9+FquFx6+8lWgqyz05A1rs640MjHDtkR1IThemCoYCq3gWL+BfLv0gTquJL0x++KSo4smoAxsGLRDiaZYxPzVOIhQlFoxAQLsKSkrp36j0kki58vui4RhXHd1J2mzBZanckkg5I2jeapzPW9l67urs0HzsYljUewjv0dcwdrcAl2o2bjKmLkvqo7KmtYlkQlleMVfQSkMlvmARL55Mc1WtdkJcjfYwuCpvIAmyy3g0lWVco4iW8JjcW2SscG6fSq1HbsGIp3PE09mSbUPCI7InlsUnxJOgCrn+0FakkVFS/ZfCPO22MyeVJZ+K7tQCanMJ5o73aZ7fFx8Ps6bvAAaLRZP+humiXngTmRyZXB6LhnNRl8kqWVmDU1YJaY371nYtuYRfRRv53HrtHKGng9dq5OqjO7FnU6SS12LTqE8wqVSeKl1ZA8jPX8Drh3LMc2rX+FzIfdOBOAQIuKycHE8wHtMmviSquG9bdCIO3TYzVrORdDbPaDSNM1Da90JUCQW2+nwazK7yCPE0yzDa7eSAhMZb+Y8sWMHDl9v5kw2V3WLb1t/N+/Y+j98ZBK7VbNyYsvxgqHBPl8tq4ua9z2PLZoiNX45fw8ZLaTyIPZPHbavsTi21YV1rA8JwIkvOaMJdwd2SAB6HlZX9BzFKeaLjEWzNGomniCqeKi8u1IiWkIbVtYSSa2fx6ENcXNG9i1VvvkVuhQWWXVfyeGplzVThUGAVg8HA+3t2YBoaJHR0Pu2B0m5GY4p4ctT6S5+cDhDiaZZhcijiSeO7+nBSjmZxOisrLmzKhTET19aOIa44/xoqvCxpMZuYGxvBmE4TGw9rJp4kSeK9r/wCYzaLN7URqNzdoc2tvocab+VPyhdybwWDjwGMJiPY7ZCIExmPUNtcp8m4au6bTQfiImCSaA4PYz6ZBtZNevxUSChWE5XeDapSa8hgTYRJjGgTlaSaUdoqnNt3Oq3ZKLnYOJGh0iNaTlo89NTOoa21cruVtUSIp1mGSTEITGrsblzpaBYVu+qirrEPUkInuwkBsDsgnSaqoYt6Kp3FmFXewwp/easXf6238i96/SVqhkPUJuYBlW2KNyjiSUsTyYwamlthB3WAhtg4t+1+BnN/PfA+TcZU44P0IA7hNAfu8ZAm4yWVnjVbBXMJ347Z6yEHREeCJY+1q7aDV5Z6eOeqFSWPpQcq17whqAgWpTKkdT9J067tvOvAH2ka1z4pvhicHlkcqlEqWpFQxGaldxMCGJU5JDQUT5HgqYt4JUNl4ZQPUl7j6mF9bw9Lh47hNeQ1HXc6GJW+nZiG7s0vXnQF/+eS95FZvlyzMaeLu0aOF5E0jC/ZNX8V/2/Nu4mvWqPZmKXgUE0kw9oIYFU8OWsqH82iYvPJc4mNBUseazgiJ1vUe6o/mgWEeJp1mFXxpHE/ibv/OItHevBltXcvLwY1c0rSuPJUyH2r8LIknBJwcQ1d1FUzQ4PVJgcsVxCntzzVQymh5oZVfreP2vQc1+jCCxBMS8RsTjw6OD9frXzRzSeSSDlt3E5HckbGnT5cddoGfk8X9XOU1shEcmfbMp5cchWmxYs1GU8L7IqQS4yX7jIeHg+DJNFwgYgnsWw3y7Aqu+FSGt/V5xLyXYWjws2qqoFlTuP8vrROrBgAzE6n5k3/MaWfBB2cn72tlSeWXo3Z6+ZBjcbMZrKQkj8Tbl/ll0WsbgcZtK0eFqJLdGCw6FfcqSUpTyQcw6tBNSUYl3e1+Rz6MFh0B+Rzyka1eQ+PmjwcqWvH017ZJeXTcQSU6lqJ4cCpZIoPPf9jcgYj9X95pRZTqzhCPM0yUvMW8Id541zSOFfTcdXQXEeFdzK5FA8RKZVCyucxGLUprh6Zs5jHV9/I7Wsqm+YOskN2ilO7q7SgEK+jA/HkDng5WtuGyWhAkiQMhtINA0/vD9NDZUa1E0hqWHlasesl5mbAL2nToF0KdrsVyWLFkEkTHglpIp7m7tmBLZggkL9IgxmWjlcRiDmNxNNoVBb3tToKzXUF/ABkwqVV10YHZY8nk9GAr6byf39aIMTTLMMwp51dLWGaPfWajptXKj2VFk8ev5sXO9eQMln401QWt0Z3qUHJzKjLj7m2VpPxSsHicpI2WYhpaJSpiic9uDeru+FyeYl4OofLVvrXVFTZBi5ZrFhtla/MjK67jEfjjdw+fzHv12A8KZ9n3vGDIOXxVdhqQsXgckIwTWg8TJsG43UeeYu58Tg1xts0GK10fHU1RKxOUpT+ecrn8rQd2oPPZKPOfrUGs9MGjxLRkkmX5oY/PqREs7jdmt3QVhohnmYZBQfulLYO1ZJSear0Ti2H3cru9mVk8xKRdA6tzKT1YiAJMHDZO3gkO5d7FnRqNmbQ4uTN5kXMr2DosYrTamLZSDeWdIpI+Epc9aVXLdRdbUYdiEMAV8BHzOZkPK1N83o0HANJHsurkzt7k9NJLhgkMl56T5CUz5NXNoFoUcXSgprWBr63Xt5J+FclOnCHgxGuOrwDgIDrTzWZnxZ4Fs3nXy79IHVuG58pYZygEs1i8unjvdOCyl8JBDOKlywt4SFs/dr1BGXSGcjI/RauCm8jNhgMeOxmxuMZwokszRrZFQW63mLD8V7q4pXvR/A65TtdLeM9hrx1PD//ElzLK39+BoOBLcdeI59KERu9BTQQTzFVPOmg4R/Ar5pIahTtEVF27eXNFuw66QnqX7KC/bZmFthL7zGLhKIFcag2o1cal9VUyAot1YF7bEhe1jLY7boKzW3wys3dY7EUubw07cy9iGJ1YL2AxNOFUT8TTJmayBi37n6Wla+/oNmYsdP6SdSG7UrSkY0wd7yPmEb+KwANRw+w8fhuamKl7zopFXVZSzV91IKwjpqN4ZQZaUyjhurhhlYevux2tl55kybjlUp9KszVR3fS8uZ2TcaLjp0KzdWiR0wLwksu5o3WJQyZSr+hCo0qf8tWK3adiAuDwVDoTxotMaIlpIgLow48uk6n1mXDaIC8dKonazpER2VxaPNfOOJJVJ5mGU6lUVXScDdaxGjlf13+IbyGHJ+wVv7iu+ngVrIn+0j1XAxLtei2gJyybd6hA3HYEBri5r3P0xJrgTu1aQ6OB8PYM0m8eumXcTggGNJsK78azWLXwU47gJp8htV9BzBntOk9PLUsqY/KGkCNUxYW4/HSs9+Camius/J/f6fzrqPbyHYfJ36gHtrXT3uc8IgsDs0efSy5qpiMBt53Yif24UHGDs2nYe30IlriY/L5XSjRLCAqT7MOp3Lx11Q8KdEsFp1kMpmUvpaEhrvRJKXfwqGD6ASfIU/neB+uwT7Nxmx99Q98bNt/sqh7r2ZjlkLhPQxrY8dwKppFH/eLqkdQTiMvq7ginkw6Cc0FqDdmaA4Pk+7rL3msiFJZM+sgt+906qU0NYkw0aHSIlqiigmlRUfu4ipzcjHqY+OEBkamPcZxq49DtXOwt7VoOLPKIsTTLMOp9CRJ6RT5rDbmdWrzuV4uTGanKp6080FSG+KdOoiGUAWwliaSGcVB3a6T3DCT0puklR2D9a09XH/wFeaNnNBkvFLx+pWLZDyOlC+9aTyhGDWqn3090Nl/jNt2P0P9G6UvTUYUk0azSx+fTxWrYo0SL9EpPqacn82nr8oTnDrHUAkRLTvr5/GbpVdiW64PmwktEOJpluHxnfryiWnkMp4+fpx3Hfgj60/qo2phUS4gyZg24iKfyyMpBot68AhS41NUby0tyCohvE6d3PmqDtwpjT6jpv5elg4dozEe1GS8UlGbnqV8nnis9PexZ85i/s8l7+Pope8oeSytUKtrmUjpS6/HG+bwg7Xv4cSl15Q8lpbYlb+XRIkmkkmlP9Ouw54guxJDU0q+3YUWzQJCPM06bDYLklHua9GqGTc9NMLikR46wgOajFcqVuXCq1UETSwSA0n2OSlUDCqIR51DMkk+p81W91xcPz1dcEoAayWeMoVQWX2cn8NpB5P8dxgaK30TQjCdJ2ZzYldMDfVAQTxp8B6OpCWCDi/W5saSx9ISu1KVSZYY0fJm61KeXHIVLFumxbQ0Rc3am24AspTPEx4LgSRR775wxJM+1lkEM4bBaMRgt0E8TlyjfpKUsjymFw8dq2LulNKo8hRR+knyZgs2Hez08ahNz5JELBo/9d8loC4B6iG6BCCybAVPDJi4rmW+JuOplTW7DpZdQfk7dDiQolHCwQgtc5tKGi+YkJuy/c7Kfz5VPIrflBbhwGNR+fwCOnLfBnAr8SXpEjc2HDc6OFLXjmtO5X3W3o5LafJOTlM8hYNR/r+XfypHszjeqeHMKosQT7OQfQtXMxxOco1Zmy+ipBJPYNVJs6pNmUc2po04DJns/NvqG2lwGPmUDraB2512DCYTUi5HJBTTRDxJOhNPppZmjtaGGLRqM59sTK2s6UM8AZicDrLRKLES+2UAvLvf4Oqj3bReGtBgZtrgVYRFPl76TYx37y429vTSkixNZGqNW6nKlBxfoohDPUWzqHiVIObUNKtrowOjAJhsVuwOUXkSVDHHFy7nwECEsFGbD7JaebLoZSdMx1xe7FzD/EZtcuhC6TyjLj++ep1ceA0GDHY7qWSaiAbVw0w6g6SYnOqhpwvAo3hZRTTyssrH5dfJ6dXH+QHsuPxdvHYywmJ/6UtRnmOHWN13hPrURg1mpg1epa/LkEmTTKZL8meqOXyADSd6qEtfrtX0NMFd5ydidZKTSrNoaezajTlvotZ2mUYz0w5/Qw0ps5XwNEMpCtEsOvrb0wIhnmYhWpssppUKj00nO2Es7e283roUvH5NxlMNJNXXTQ/8avOHODKa4Cpn6Q2m4ViKN5sXYc+kJmwoqCT+fIolQ8fw2ELAJSWPpy5LunRyfgCWulpiwzmCqdJ3vWaUyppbJ9ElIC8vGwxGJClPcCRIU1vDtMfKReVlMTWMVy94F87je+vfh9Nq4u+mOUY6mWbD/lcBqLN/RLO5aYV/4Tz+5dIPYjUb+cI0grpDSjTLheQuDkI8zUoapSQt4SGSI2NA6b4bGVU86aQZ1+uQP9ZhjYJz08dPsOH4HuZ6tem/0QKP0wajCU0iWsI5A8/PvwS3zYzZoo+vhEA8yJaDr2AJNwIfLm0wSSr4dLl0siwJ4FNiVIIaRLSolTVPjX7Oz2A0smfxWkZTea5LS5Sy4JaPxjEA3hp9iaeAW34P4+kcyUwOu6V4k9lxJZpFMprw6qTyezoNPtk2JJ3NE0pkiu6rCw/Ky3a2Ov0sKWuBPr4pBTPKmsNvMH/3a5iXueDai0seT73rdeikGddrgqbwCK5cUJPxpOMn2Hh8N+4GfbhvA3gdavWwdIEYSujLQBJOs2PQwMsqm5f45/UfwJZNc1e9fr7AO4N9XH10J6auPFxTmjDPxeKYQHcX355lazg0FGU8P/2/nUw6gyEpfw789X6NZqYNHpsZi8lAJicxGkvT6i9+08z4sJJr53ZhNOlvA7zdYiLgsjIWS9MfShYtnmJDsnhy6uhvTwv0820pmDHU3iStDAifXrmJ/b4VfFsn22z9qRi37/4tOZsduKPk8VJKQ7xFJw3xACtP7KNm71sYlttgbWkRNJFwHHsmic+mD/EL4FV2amnRbBxOytEscasDr452o7VERljddwBLT2kXlUQygykjNxx7A/paGtEioiWo5toZDLo7P4PBwO2H/4hxbIxQ92JaVy0oeoywcn5GnSQ0nI139e7GcPQIod210HxpUc9NjMjLdp7GunJMrWII8TQLsSniKa3RbrRwKkfKYsPj0YdVgUvZUWVIp8lkc1jMpVWMkkpDvE0vDfFAQyKEabyP3PBQyWNlD3TxsW3/iXV+J3BNyeNpgVpBkTIZ0qkMVtv0+83UC7fHbsasozt7h1Jdy0RLu4lRxYXBaMSts8pTszFFc3iY6NAo020RCCrmjAaHE1OJf8vloCmfJJMIEx6eXkRLZDQI6DOaRaXNmCIVDxLuHSz6uQeddcRq57Cm/cKJZgFhkjkrUUVARiMfpEJumEMfDdWqiaRRyhOJlH6OhZ4unUSXwClbiJQG56daTVh0FLp6uhlpaLy0beDRE/1cf/AVrh7YX+q0NMVeEE+l3cSElNBVo0O2sNAT6w6/wW27n8H01lvTHuNUZUY/n8/TMSmN0NN14I4p759Vh9EsKvZa2a4govQvFcPztQv5zdIrCSzWZvezXhCVp1mIXanMaOGDJOXzXPrGC8QNJnwGfWyzNdttmMwmctkc0VCEQIlNtKrItOvEfRvAphiBalE9TChO83oKXTWZTRjsdqRkkkgwTH3T9Je2YoPDLB06hsWmze5SrVCb17MlLk2OWD18d/37WVZj4S+0mJiGWJXt6ckSTCQHvPX8YO17WNeqryU7FYvPQxKIKxWkYlGdu+063o3maqglBCRGxot6XiaXZyQqR7M0KY3nFwqi8jQLUcNtMxr0k6SSaRYMHmXFwCH99JMYDKC4ncfGS8/VUkWmXkJzAeyF6mHp4kmNQNGLyamKySF/2UaCpb2HceX5Jp2dn1upruVLfA/Hk1niVgfGhulbAZQL1ZQ0XUK+3VgqT9DhxdysL4NMFVuNH4DEWHHCQmVfyyKeXHoV6YtL37xTLrwNtQCkijzHobEojlQCq9FAQC/XB40QladZiBr+WuqXNkBEXVIxGHC59dHzBGCwOyASJV5ibAJATtnm7tSRR5C65KNF9TBdyH3Tz/kB7Ft1BQcGIqwo0WU8pnwG9CYOPYWm+NLew6DS06XHi5PDrzpwlyCeYnLFsEaH7tsAzkJ8yfQyCo8bHBypbcfVXtrGj3Lib5abvTPjwaKeN763i/u2/5xUYzNG4w1lmFnlqNrK09jYGHfccQderxe/388999xDNHr+P9BrrrkGg8Ew4edjH/vYhGOOHz/OjTfeiNPppKGhgc985jNks9r4BekFR3M9r85ZzvaWJSWPVagK2O0YjPr5OBldspCLlxjYCfDU4sv5yYp3Yp/bXvJYWqE2G+c0qB5mCpU1fYmLaOcCjta2MVrCNnc4tatUTw3/cMqzyJhKkUpPf0kxf6CLq4/uZGGoV6upaYYqLHIlxJeY973Fxp43mRufXkN2ufHU+QFITTP7TV3WqnXrUxwC1LXWA5ALhSE/9TDy8f4RAGx+/S5JTpeqrTzdcccd9Pf38+yzz5LJZPjoRz/Kfffdx49+9KPzPu/ee+/lS1/6UuG/nac1yeZyOW688Uaampp45ZVX6O/v56677sJisfDVr361bOcy03gaanl1zgqs5tLFTlS5o9RLKLDKwMKLeYs6Opz+ksc6aXQS8Vp1E10Cp/pl0qnS+3hU8aSn3DcAv7IBIVSiEWhCp5U1T8DLv6+5kbjZxh3JLA3W6W24MPb0sLrvAM1h/YXKuhVrgfwkN7bnw37kEBtOvEVLbKlW09IUb2MtEauT+DRFfmD/HhalJBqtpTvpl4uG5loSFhsjFgfxcBTnFMVQeEART7UXlscTVKl42r9/P08//TQ7duxg3bp1ADz88MPccMMNPPTQQ7S0nHtLpNPppKnp7GvnzzzzDPv27eN3v/sdjY2NrFq1ii9/+ct89rOf5e/+7u+wWs9+Z5BKpUilUoX/DoenV76dKdRdcelsftquuCrxkHxhMjr11QwYXHQRrydquNFemuDJ5SUiKbnyqJfdhAD2eR1867LbcTttfKbEsbq9DYTrUqxtqNdkblrRmg6zZOgY2eMeYPo7ddRlSb2JQ6PZRKa2nngiQziZpWGaN+fpiFzVsetwt5ZHqTwRi4Ekyf2IRZJVqlYuHbmnn45vkRzRUuO08FdFPjeXzbF6zysYpDyNtg+WZX5a4HFY+fcrbyOWznF32shU3azU3XmextryTa5C6GedpQi2bt2K3+8vCCeAzZs3YzQa2bZt23mf+9hjj1FXV8fFF1/M5z//eeKn9Rts3bqV5cuX09h4Kqjz+uuvJxwOs3fv3nOO+bWvfQ2fz1f4aW/Xz/LO2XBbzdQmQrSEhwhHS1v2iSuNoCadVZ48ilt2qfEl0XCcDcf3sKqvC69NP/caXpeVvNFEJJUln5dKGmtb81L+a8kV2Od3aDM5jZg/cIwtB1/B0XXuv72pkInos7IG4HfKgryUiJaMIg6dOqqMqtQ0BNjWfjG/b1tJOjO9DD/VB8utCjGd0eCRbxzH4xnS2akvaQGMDY5hkPJgMBBo0q/AMBgMtNXIqzS9walfM+KK95XaM3UhoZ+rQREMDAzQ8LadJWazmUAgwMDAwDmf9+EPf5i5c+fS0tLC7t27+exnP0tXVxc///nPC+OeLpyAwn+fb9zPf/7zfOpTnyr8dzgc1rWAMhoNfGTv7zEkE0QH3kFDCXd0SXWbu448ggBqDRmawiPkBn3AommPExkLsvH4brBYsJZQodMaNaRYkiCazpYUWqxGvOgp+BhONcWnS3TC/+3FV3LEvYRvr1ihxbQ0ZfVoN51HjpM41god01vayCo3MC4d9pX4vE62d64il5cYS2RpshZ/yZHUUGCd5dqp+B0WzEYD2bzEaCxFs2/qN5KjA4pvksejSwPQ02mtcdA1GKF3fOriKa3szqtt0VdVWwt0JZ4+97nP8fWvf/28x+zfP32ju/vuu6/w/5cvX05zczObNm3iyJEjzJ8//Wwpm82GzWab9vMrgdFpR0omiAZLa6g+1rGURzbcwgdW66vfouPkYW7f/Vv8znXwkSumPU5UaYg3OPS1LGm3mNhydDu2RIzI4Fq8c6e3jVuSJJLhKAajGZ+OliUBHKoPUokO3KOJPDGbc4Lxpl5YNH6SdH8Xqd4+YNW0xsjFlMqMzqJLQL5RC7isDEdSjERTRXv9SPk8ecVnzaezXDsVo9HAB47vwD7Qx/jedpovm7pIH1d6gow+fQrD01k33k3LG3/A6BuCDR+d9HgplyOrNNE3tDdOcnT1oSvx9OCDD3L33Xef95h58+bR1NTE0NDEWIpsNsvY2Ng5+5nOxoYNGwA4fPgw8+fPp6mpie3bt084ZnBQtqMvZtxqwOhwkGOceLi0C1M4lSNpseOo0dcXt11pDlYvLNMlFlIa4u36WpYEWBwZxBAJExsNwTTFUzye4r6tPwXAa3iHltMrGZdfG/GkNpzX6HArv8XtJs30t7kDSErDv0eH4gmg3ZjGEh4iODgGrcWJhFgoipSXl/tqlF1teqTJkIZkhHCRDtzhIXlZy+LXv3hqdppIx8ZJ9k0toiUUTbK9YQGeVJzWNlF5Kiv19fXU10/+Im/cuJFgMMjOnTtZu3YtAM899xz5fL4giKbCrl27AGhubi6M+5WvfIWhoaHCsuCzzz6L1+tlmU5Cb7XC7HSQg5J9kNQLk96WfNSdVdkSI2jiypKRyak/8WRwOiASJlaCHUNY8ekyGI04dLaV36lcUHIleFllsjku3/0iSYsNv+lqraamGVafmxjTd+DOpNKgbFbx67Qn6Npjr5Pdt4/M3npY01nUc4PDQQByVjsOh/7Er4rF5yMDRefbRZXj7Tp9706nprmeHiA5RaPMk9EsL85bS53bir2EbEq9UpUN40uXLmXLli3ce++9bN++nZdffpn777+f22+/vbDTrre3lyVLlhQqSUeOHOHLX/4yO3fupLu7myeeeIK77rqLq666ihVKL8R1113HsmXLuPPOO3nzzTf57W9/y9/8zd/w8Y9/vOqW5SZD7VFKllh5Crz1Otce3k5TeFiLaWmGamgpJUozIEwozcZ6FE9G5T1MhKYvgKNqZc1m05VPF4BH7cUrQTwFR8MsHT7G6r4DeN36WnqFUzvkktMUwOOpHN9d/37+fc2NeGv01zAOYFUa2WNjxVfXRqwuvr/2Jl649F1aT0tT7LWy0C82oiU5KgsRR12N1lPSnHqlbykzVfGk9Ea11ujrpkwr9PVtWQSPPfYYS5YsYdOmTdxwww1cccUVfPe73y08nslk6OrqKuyms1qt/O53v+O6665jyZIlPPjgg9xyyy08+eSTheeYTCZ+/etfYzKZ2LhxIx/5yEe46667JvhCXShYlCpDssRQUs/xblYMHCKQLk2EaU3BRT2eLGkc1SPIojN3ajgVN5IooaFa7eky6lAc+tS78VSSTGZ6RrURpefCYLdjsuiq0A5Q8MtJT7PyFEzI0SzZunpMJn1+nduVc4wHixdPY8ksIYeHvE6jWVScAT8A8bFgUc/b0X4xTy69CtMyfXpYnU7THLlvKReJkkqmJjkaBnqHcaYTtPn1d9OiBfr7NpkigUDgvIaYHR0dSNKpLdzt7e288MILk447d+5cnnrqKU3mqGfUqIpSdzLl4vrcBu5Wmo2lRGLa/jJwyp3aqrMlLZCXXjNAooSl15hSedSbySmAt8bDMws3kjRbuTORoXYa4icyJld0jDoUvwBupVqUnWb223hMjmbRYz+XirPGyxiQmoZ4GonI51fv1nfl31NfwyDFu4wfRY5m8bc1l2diGhKo8yFZLBgyGQZODDF34fl3lJv/+BL3bf8jDfWbgbUzM8kZRJ+3KoKyk+mcx6tzlnM8cG5D0amQS8ilWZdXXzuZ3EoDezaTRcpM30PncPtifrLinYSWr9FqapphUfq6UiUsvSaU5SK9heYCmC1mTsxdxNHaNoKp6XkERZVGbINLX+JexaNULHLTbIqPH+3mmiOvsXqsW7tJaYxbsRhIh4oXT+kDXWzseZNFMX21BbydQKNsM1GseBoKyxWcBo++xSHIfZHGWtmLaujo5FFA0X55U1egTd9Vw+lStZUnQYnMn8+rc5IEfCVuIVWWxdS4EL3g87nY1r6clNnC/5fK4jmHO/xkjBhs9HkbsDTpb7eI3esiDKRKyLdLKj1PJh1W1kA2kYwks9M2kYwpVhx6XHYFcM9t4d9W34jd7+HPpvH89Mk+VvV3Ya/Tb0Oumv2WnU6F9PBhNpx4i+aIvi/AgaY6IlYnQWnq3zPZeIK2/W/gsTpp9m0q4+y0w9LSTF8kRe94jMnCZLIDsnhqmKdfz8NSEOJpluJ1qA7c0w89lvJ58skEBsCjM/Fkt5p5ff4qUtk8oSxMt5VWdSjXmwcSQHz1er416OWmi9r58DTHGLE66aqby4oWfSa6L0iO4xrqJ9q/AOYW31SrVtYsOsu1Uwn4XIy6/BizkM9LGI3FLS8nlKUwi84qv6fjrZfft+nk2yWV83MF9L2Vv7Gjhe+tfx8An5ti5NXwiQGuOPY6KZuDOvd0pPPME9rybv7deRSzs4n3nue4dDROLhgEoG2S5b1qRSzbzVJ8JqiNBTEOnds5fTLisSQGJWHbo8PcKVXwlBJ9ETi0l1V9XQTSpTXWlwOv10HeaCJYQgTN8bo2/mvJFYRX6rMnYf3xPWw5+AqZo93Ter66i83q1edONL/Sq5SXpheArFoc2HQsnvyNtWxrX87vmy9GyhcXX5IOystgHp3vRvM7LdiUoHV1KW4yRnrlpUijz1u0aK4UnXXyTcixkfMvM/cePoEEpJ1u6uv1LXyni6g8zVLqImPc+cZvMB6vBW6e1hgR1Z3caMShs2BggBZDCmN4hOhosGhzPpX2rt20DgwQSF6p7eQ0wK+BOAzpuLIGYPG4SXGqglQsuxeu4Rfrvfz5uoXaTkwjrGYjl40cxhoKEuxbQU2Rd+kpZdlVj6HAKnUBD1vnynYw0XQOj33q9+w5pU9K78GyBoOBZp+d7tE4/aEEc2onXyYe65fdxa01/jLPTjs6VPE0HD3vRpyhIycAMDY2YJjmZh29I8TTLMWleK/kE9PvlwmZHTyy4RYabQY+oTOPIIBNh7aRO3SYzMFWWDF3WmPkEkkMnLI+0BOBXJLru16hsd8GH798WmPEwzEMUl53JqcqVrf8ZT1dE8nxVI641VHYQKBH1o51YxoaJNo7CEWKp4yyS0+PocAqDqsJl9VELJ1jOJLCM9XPmiSBIp5qGqeX+zeTbDnxBql9B4hd4oB51056fEgxyHRUgUGmyrxaJ7fvepq6RIjUvauxBc5eERztlhvKHS367lUrBf1d8QQzQmErfzJZdCldJZzKkrTYMdTos6RudpVuIokiLt0+/TUc++0mlg4fo+Hk0WmPseq5X/HfX/4xraOT756pBDbFAmPaPkhKVa7Gpd+t/GalHys8DRNJNbrGpWPxBNBpydIaGmJEqbZMhWQkRk7ZKVvbpO/KE0CDKY8vGSU8MLWIlqgSzeKq178wVKn32vEYcphzWfoPHz/ncfscdbzesgT7En1WfLVAiKdZiupGbMjniUenV31Sm6m9el3yUbanJ6fpZZVJZzCk5f4Fjw4bVr3KBTOXSpNPpac1Rl4NldXpso9d6VVKT3Mrf+cbr3DNkdeo1ZmJ6+lY3PKNTLzIbe5wyh9Kj5/P07n+2A4+uOdZ4vsPTvk5o4rQyljteNz68yF7O06lLys6NDXxlFDcyH0N+heGKgaDAXOTHF02cPjkOY/bZqzhxXlrCay6aKamNuMI8TRLsTusYJJ3hKj5ZsWSPtrNO47sYPnQ9Csf5cTmLi2CJqK8LhKGQqVOT3j9bvIGIxIQCU6vMnMqVFZ/5wfgUMKBM9M0kWzq7mJVfxd+kzT5wRXCqgjXeLD4v8MfXnw9P1zzbnwdrVpPS1PsSk5hZCQ45ecM2jw8uu5mXrr0XVXRN+NqlkVFemhq1bW0EnNS01RXtjmVA3ervBQ3cuzs1WpJkjjQL3+Wlzbrd7m8VIR4mqUYjEawy03e0WkuieT6+lnZf5DO8T4tp6YZdmXJJzXNbLSIYrAo2e2YdRjtYbeayVtlc73wNKoWUiZDVqlY+XTad+FWoj2mFQ4sSaA44Htr9fslPt18u2Qmx5BkZszpo86vT/Gr4lB6zmJFZL8NxzKE7W6MraUZ+c4U/hZFPI1MrfL0i85LeXLpVdQsmFPOaWlO43y5L2+s5+ziqffEMJ7hPtz5NPPr9f25LAUhnmYxarBsLDS9yoyai6fH6BIAu9JLkpnmkk/BnVqH0SUqaiZdZBrVw/BYGEmSyBuM+HR68XW0N/PMwo38oaN4h/dULE4uKzuT+2r0u6ylNnunihRPo0o0i9VkLPi26RW3sqwYH596X9dwRF4yr9N5NItKQ4ccsZIbHYNJ+kiTmRwHjW6O1LbT3FQ9PU8A7YvkzTfx3rPb3BzfsYdbdz/LR3t3YNFp3qIWXLhnJpiUk/OW8eqc5QRN07MZUHPxrDp1b1Zdz7PTrDwNu2v4yYp38ubaq7WclqYYlb6u6DSW7cJjcrUqZ7Njt+rz4uupC7CvcR77HcUvbYRH5PPLmsx4PPoVwOpOwFSRFeDxE4Ncc+Q1rho7rPtlLdVlPFVEREv+jV1c1r2LhenxMs1KW1rnNpEzGMmkM4Qn6Xs6OS5/J7ltZvxOffaMnosFyzqQMJAMRYiOnVnxHlBsCrxz9J/XVwpCPM1i+pet4tU5Kxi1Ts99OR3Td+XJ2trEtvaL2dO0YFrPD2aN9HkbyLTp1yFX3VEYm0ZfVyE016lfYaFeWMLJLLl8cX1Lhd1rDqeuTQjtSxfxwzXv5tdLryrqeZG+AVb1d7F6tLs8E9MQvyKeMkVU10wH9rP+5F46s9PryZxp3A4r0bpG+jz19A2fXyT2d/Ww7uRe1kkh3Qvft1Nb4ybc3Mbh2nYOnxw74/ExxaagvlO/35taoM/bTcGMoO6SCyenZ7KoLofp1d3Y2dLE1rkraauZnjgYj8vLIn4dJ9Z3XXEdv6ldzd/NKX5LcFAycaC+gzodGxD6HBbmjPfjzCQJBaMEAlPfFaj2rBl1WhlVqa31Mub0YUwXdy8bGZYrMma/fvu5VAKK1UCuiMqTGrLrqaKt/K9veh9vngxxrcHFkvMcF9zbxRXdu3DW6Hcjw/noufEDPHdgiPUxA6tO+72UzxPrkXfhtS+qrl6uYhGVp1lMrTFHbSxIcmR6ZfGssmzn0OmXt+rAPZ3YCwDp8BFW9XXRntDvsoHb55IjWqbhMj7kquHpxZdzbN30DDZnAovJyE3HtrHl4CuE+oaKem5MyUUzuvWZa6dSr/T0jMVSRVXXYmNBACw+/fZzqQTaGtnedhHPtS4nmZ5anmZGiWYJVIHHk0pbQBbq6rLcuYiclPuFXC0lBrNXiOVKYsOO7onfjX37jiGFQuTMFpauX1aJqc0YQjzNYpYe3cOdb/wG7xs7pvX8vM4N+nx2MzXxEK6hgULjcDHYu/ZxzdHXmBucfv5fufE55KqYWiUrhkJlzaHfyhqAWRE/oSK2uQN0t8znu+vfz+GN+k6sDzgtXHpiD1cd3sF4EUaZiVFZXNh17vEE4PU62blgDXuaFzIcncJnNZ8nG5aX6+paqkc8tdfI4unE6PmX0ZP9gwD4q7Qv6LL5tSBJHNzVhXRaSsWhF7bL/2fBApw6jOzSErFsN4tRd6NN14Dw8ZXXER4Ls6lzetEn5cbnsHDX67/BgERo9D0Eiox4SEfku0eHV7+Vi/bQINd3vULAMQTvKc6QLhSSo1n03rBqdrvIDhW/o3A0npWjWXS+7GM2m9g4fBgpHmd8YJS6uqmJobSSWu84R0SGnjAYDDR4bZwYSzAQTtIeOP9Samw0SCabI28w0lBFladF2SAffe1XdAzUwXuXn/O47KAsnup07s91LlbPqeGDXS/SOnKS7lfa6dwkV69Hd+4GoHbdykpOb0YQladZjFPZjZaehgO3JEkMZgyEHB78OowuAfmiZLArPkhn2RUyGdmovPtJr8uSAHX5JEuHj2E90VP0cxtf+j3//eUfs6x7bxlmph1WReRHitjmDjAalbe617r1XVmDU9W14HBwys/JKMuSnimKrUrTYZNoCw0y0jO5L9yw4i6edTjxOKvDqgCgucGPLxklOzQs+4ydhXw0VthZ2TK/bSanpxlWs5HAog4Ajr30GgD5vMS/tqznxY41LLhidQVnNzMI8TSLcaoGhNHit7knM3nSWdnLRM+VC9XLKjyNrfw5pSLnrtHnsiSAR5nbdOwYVNHs9OhT/KrYlQ0JsSLfQ/ebO7nmyGu0x/Xbs6Zi9Ml/i5EpRnsA5JXma71X1lSu6N/PB/b8juxrr0967Hi//DqYfPq9cTkbbZ0tSBiIReKF6Jy3M9zdSy4vEbO7aK6vrvM7nfaNawHo2/kWUirFS4dHOJi1cnjBctYtrg5j01IQ4mkWoxrX5aexbBccHOXaw9vZeHIvbpt+V39Nyk6r6DRMJHOKO7Vbx5WngniaxnuoRp44a/R7fgAORTwli9ipBeA+dphV/V00ZPWba6dirvEDECti88YPV27h31bfiHdudVQvXEqGW2wKAvFYoIVH193Mocv03a/2dlrrPKScbvKSxMmjZ3fg7jss+yBR34C5ik0kr9+0kpjTw8h4jK5fP8evf7sTgPevacNuMVV4duWnet85Qcl4lMiK/DSqFuGBYVYMHGLteLeufUrUxPposfElkoQUlxshPTqO9vApwicXLz7cWX3f9Zjbdzp2xR08FSxOPGWUypq3Chqqbco5xkenJp4yuTx9aQOjLj8Ntfp+/1R8SoZbcvhMb6C30x+Vo1mcrdXVUG00GrA1yOfZe+Ts4ukNfzuPrbqB4GVXzuTUNKfea6dx/SoAtj7yOOanfsPSoaN86JIL299JRYinWYy3Vqk8JZPk08VtdY8plRyTU99LPhaPXJlJFBm6mo3FyWTkLdV+nea+Afjq5WZhYypJMpEq6rnZmCIuavUtLsyLFvLMwo283nI+55wzySnn5wvoV/yqOGrl9zE9xd68kWgKSQKz0UBAxz5kpxNolbPfMmOTC8T+kHwz0Oyrvh1bHiXjbuj42XfpHhxNMuyuoXlx50xOqyy880/eTdhfRzcOTPk8t81zs/gCDgM+Hf2utwjKjr/Gy67mxSQsNu5OpPFbp967FFPEiEnnHjpqYn2x4imUM/CTFe/Els1wv0u/DatevxvJaMKQzxEcHqdpTtOUniflcoVqlZ7FIYCnvYV9jfPIWqdeYcnl8qAsZfrr9b8bzd0g9y2lg1MTT6OHenjHkR1IjU26dk8/nbq2egCyoTDkcmA699KOffurXNY9xHxD9e1GC7Q1EgXGT/Sf9fGuQfm7aFGTfnspp8rche3c+9jX+ednD7Gw0c2fXFH9gnCqCPE0i7FaTLy27FKiqSzjGfAX8dy4ErOgLovplXxHJ9vah1ntn5qoUBlP5enzNuC1m3Xdl2AwGsHtgnCY0GhoyuIpHorKAgMI1Ou78qTulhuLTd3LKjg8jkHKI2HAX6RFRSVwLZrPv62+kZY5DdwzhePD3SdY2X+QvKt6HKqbW+rIGk2QyRIfGcPZWH/OYz0H9rJ+aIg55utncIba0NjRwk5XDSekM78bpXSalhefxWBxs7j+igrMTnuafQ6+/oEVlZ7GjCPE0yzH77TI4imeppOpC6GkIp6sHn33WxgWLWTrvhQeT3FOvqGEfKGucel/SeT5q9/PW6NJ1roDLJ7ic8ZjaQ7Ud+Agj9Ou392SALVOC3PH+3APJcmnr8E4hQppUIkukVxOLBb9f801NPgZdfnJJaYmhiJDct+QTefN/qfjdVjJuDyYI0GGTgzRcQ7xJOXz5MaDGIGmtoaZnaQGtFy2lsdeiWC3GPmnvITptMpg/7FeFp48SIfFSke9vr87BedH/98qgrLSZM6TiAUJj4zDnKkvb6jiyebTd+lZ7QcpNr4k1t3Lqr4u6u3638nkrPGQH88UVZkZwcLTiy+nxWfXdcM/yAL23ftfwpLPEhr8IDXtk1fXwoq4MLj1/flUafLKvT3BeIZkJjfpbqWY4rbuDPjLPDNtObFsNSdGYlxidNBxjmNGeocxZtJIBiONHdXVMA4wJ+DEbTMTTWXpGoiwrOWUwO3pOg6AqaEBi/nC35F2IaPf9QjBjHD1oW3c+cZvyO8pzihR3clk1/myXY3NiD8RxtA/uTHf6WQOH+Gao6+xcvhomWamHQGlOjZehHgai8nN5YEqMJC0mE3kXYqJ5NDkO7UAeuta+df1t7D7supY9vE5LKwbPMS1h7czfOzkpMfHlVw7d53++7lOJ3HxSvY0L6Qnc+779oFu+W9VqglgKaIPUy+YjAZWtfsx57K8tefYhMe698rfJ4GOC98H6UJHVJ5mOVaPmwSQCBXXUP3Hi69gqzSXv1p2cXkmphG1+SR373wSq90G3DLl58VCsgeSzav/0vrCYB9burZiaU/C5VNr2BwNxjHmc9TquBn+dAxeD0RChKbowD0ay5Cw2rE31pV3YhphMBhYHzmJdaCPse4+2hedP/IorVhveKqgGf505ta6gGF6zpP9NtYjb/E3NVTHe3c23mEOs/rVn2IIdsD1p6JKom++BUDLqgs7NHc2ICpPsxxrwYCwOPfmESWaxRvQ97KIT7kzz6TSSKmpb+VPKIaMDp0vSwI0ZWIsGe7GcHzqES2W13bwwCuPc+WBrWWcmXZYvPLSR3h4ag7cQ5EkAPWe6hCHABbF6yk0ODLpsdmQLJ78jdWT+wYwz2OiLTRIdG/XOY8JK7vU7M3F9SnqiYXL52OS8kR7ekEJzk32DZDoHSBnMLL4yrUVnqGgVIR4muXYFXGQjhRXeRqLy0tEfp17zPh9TrJGE5IkER6dulFmUsmecvr1L54cStNwtgg7BnW3pNNVHT46qlFmdDQ4peOd21/lmiOv0ZkpzlizktiVgN/I8CQ+SJJELiy/f7VVFJoLsCgf5QN7fkfL1ufPeUysfxgAd2txO2T1xMql7Yw5vITiKcb2Hwbg6AvbyUsS481zmNOq/x2ggvMjxNMsx6G4S2fCRVSeJImLXn+Ry7p3Uatv7YTdaiZrV/LtihBPau6bqwrEk0vxacqEpy6eVLduRxWcH4BDOcfYFN9Dx+GDrOrvoonijEMriUtZgotNIp6SmRz/vPq9/NvqG6mrMvHU2iELoszYOHnFKuPt/GLp1Ty67mY8Ky+ayalpis9pwTxfXkLf+Qc5y2/PwT7yBiOuVct1v0lDMDlVK57Gxsa444478Hq9+P1+7rnnHqLnCbjt7pZjRM7289Of/rRw3Nkef/zxx2filCqCW6laqA3gUyEbizO/5wDrT+4l4NF/5cKgGHmGp1i1AAqhnp4q2Arur/MDnDOI9GyklWVJV1113AG7FRf05BRjdtRlLV9DdZwfnGr+Tk3iwN0fTpGy2Ij7a/G7q2dZEqC5vRGDwQjZLIP9Z1+CPTQSJ2x3M2/OuX2gqoGLL5N7nY5s200qlebrxvl8d/37uOSGC8PfabZTteLpjjvuYO/evTz77LP8+te/5sUXX+S+++475/Ht7e309/dP+Pn7v/973G4373rXuyYc+/3vf3/Cce9973vLfDaVw6Pc0eeKCJYdV7ZJZ0wWarz6jmcBsKj5dkVUntSgXU8VRHvUNMgX3VwsDvmz382/nbwqnmqro+HYvqCTZxZuZFv7FDYoSBJ5pZJaTctafqW5PTWJQOwdl3to2mocVVfBMFstGJXPXH/XsTMeH42mGIulMRhgfpX7IF35zkvAYCTZ289zH/trYqEovlof1yyvPtd0wZlU5W67/fv38/TTT7Njxw7WrVsHwMMPP8wNN9zAQw89REvLmdtATSYTTU0T19B/8YtfcOutt+J2T/wj9fv9Zxx7PlKpFKnTmpHD4erps/A21vJGyxLMPi/nlp4TCY3J52dwOicYwOkVq9dDFohMMTcM4D8XXI4xHuf9VdB3UVtfg4SBdCZLKhzB5p/cMTyvLPF56v1lnp021LQ1s69xHmnL5BfUTCRKMp1BwkBdFbiLqwRaZPGUC4ZAkuAcwmj8rQO848gOWlxTtUTVF4bWVhgZZfRQN2xaP+Gx49t3864DfyTZ0YnDWt0+SPXNtaTf/R4yTz/Db0ckUo1WPrx+rq4TCwRTpyrfxa1bt+L3+wvCCWDz5s0YjUa2bds2pTF27tzJrl27uOeeM8MQPv7xj1NXV8f69et59NFHkaTzu/5+7Wtfw+fzFX7a26snVbq2oYYX5q3l+bqF5PNTczcOj8riSe+5diqJeQvZ1r6cXs/UlgHi6SzdjgBHa9sI1Oq/J8jnspG22ZEwMD6FrfxSJoOkhObWNFRHZaZB2TU3FE5Oeuxov7xbLWW1U+NxlHVeWtIyp5F/W30j/3Ple8icox8IIH7kGCv7D7I0MTyDs9MOZ6dswxA6fObu0OH9h1k80sMqitv9q1ce+NQHOPThe/jdgg38yca5/Nk18ys9JYFGVGXlaWBggIaGibb9ZrOZQCDAwMDZk6zfzve+9z2WLl3KZZddNuH3X/rSl7j22mtxOp0888wz/Pmf/znRaJQHHnjgnGN9/vOf51Of+lThv8PhcNUIKDV+JC9BMJEpGC6eD7WCo/dcO5X80qVsHbSy2Dk1oTAalXcSWs1GXFVw92s0GnjqyvdzPJHnWruPyWplkViSPXUdODIp6hv9MzHFkmnw2Jkz3o8nHScZvRK7+9zLxWODspGm0eupmtBcgHq/k6gvQCqbpy+UVDyRzqSwG+082XB6pnnpPMK/hFj38TMeG++RDTJr2qvPWfxs2C0mvv+nGxmNpamrsv40wfnRlXj63Oc+x9e//vXzHrN///6S/51EIsGPfvQjvvCFL5zx2Om/W716NbFYjG984xvnFU82mw2brTr/MCwmI02mHNlwmLGxMAHX5MZ00XG58lQNBpIAtYogHJ2iA3dwYITVvQew1dVUTU+Jt9aH1BtiJDr57rKhtIHfLroMj92M3aqrr4Bz4nWYueHINuzJGKPHb6R12bnv4EOKC7l5CsuXesJgMNAecHJ4KMrxsfg5xVN6cAgAX5UKjPkrF/Kv89YRqannzlwe42nLWLHeQQDqLyAHboPBIITTBYiuvjkffPBB7r777vMeM2/ePJqamhgaGprw+2w2y9jY2JR6lX72s58Rj8e56667Jj12w4YNfPnLXyaVSlWtQJqMW7v+gHFggOjBRdA+uXhKKH5CtiqpPNXbTfgTYbK9AKsnPT7W08vVx3ZiSlfPF3idErMyHJmCeFIMJBuqyEDSYDBg8rohGWN8cPS84ulI60L+df0tbF5cHUuSp3NprI85hw8wvtsLC89SWZIkpGG58lRbpQJjXrOfA3OXkszk6R6LM09pDM9nc8T6ZfHUsfj8DusCQaXRlXiqr6+nvn7yUvTGjRsJBoPs3LmTtWtlp9bnnnuOfD7Phg0bJn3+9773PW666aYp/Vu7du2ipqbmghVOABaPm9zA1Buqd89bya/WOvjTdYvKPDNtaE6GuHvnk9h7AvDpGyc9PjoqbxU3+fS/005lWbgP+4FtGF5Pw/o55z12ZCyCKZ+joQpsJk7H4vXC0CDBofNv5R+KpEhY7XirpJ/rdJYmR6kbOETs8DzgyjMez4TCpGMJJAw0dVaneDKbjCxp8rLrRJC3+sIF8XSk6zi5dAaj2czCxfoP5BbMbnQlnqbK0qVL2bJlC/feey+PPPIImUyG+++/n9tvv72w0663t5dNmzbxwx/+kPXrT+3oOHz4MC+++CJPPfXUGeM++eSTDA4Ocumll2K323n22Wf56le/yqc//ekZO7dKoObbxcantktwOC3J0Sz11bGTyVcnL9/korHz7mJSiY/IF2dLFYmnlkwMy0gP+Z7JK6+mP/6Rv3jlv7CYrwQuLf/kNMIe8JOESfPt+kNyZa3JW13iEGRX7WEgcbL/rI8PH+tFAmIuD/X+6qj8no3VdRbSrx1l7PcRWHk7AMde3AGAZV4HZktVXpoEs4iq/YQ+9thj3H///WzatAmj0cgtt9zCt771rcLjmUyGrq4u4vH4hOc9+uijtLW1cd11150xpsVi4dvf/jaf/OQnkSSJBQsW8M1vfpN777237OdTSaw+jyKepuZQrfYO1bp1bi+uEFCcmzPJFNlkCrPj/BdVNbHeUSUeSCCbSA4DqSlEtMQVs1C3rzp61lTcdT6SQFjpaToXNa+8wDUnx+m87vwVOD3i75Q3mmTPsfGlv0f+vbG+vmr68c7GJX4TvkNbkUY88MnbwGDg6IlRskYTtetF7ptA/1SteAoEAvzoRz865+MdHR1ntRj46le/yle/+tWzPmfLli1s2bJFszlWC06/hxCQDE1NPLXt2oZ5PEZ9fml5J6YRNX4XOaMJUz5HcDhI3ZzzV2dSyvKlq656xJNqdpoJTV49TI4HAXArzuTVgr8+wAiT59t5Dx9g1XiQFnv1iYuGBfJyVX50DDIZsFgmPP5mXSffufRWblhUPZ/Ns3HpxmXsN5oIjUfoP9ZLU2cr/+ZdzMj6Jv7vlZdUenoCwaRUpc+TQFtcfnl5KjnFbLSOw3tYf3IvtebquDiZzSZwyUscwSlEtGQUceGpr54LlE8xu8xMIaIloyzPeqpk2VUloLiFJ5XK4NnI5/LklJuAhpbq63lqn9NI3GInmc4SOt57xuOHh6OkzRZa5zZWYHbaEfA6cM6Rnbb3Pvk8W4+O0htMYHY6WLOgYZJnCwSVR4gnAS4lvy0dnjyiJR1Pkk/I8RA1TdVz8TUrhp7B4cmb4nNK9cbfWD0XXzUgNhuOIE0S0ZJTHPBrqsh9G6BmwRyeXbCB37StOucxI0PjSPkcBqCxZfKdo3rDbTOTr5M3spzY333G44eHZHG8oKG6llzPRv01lwMw+PRz7Hr4BwC8d3UrLlvVLogIZhFCPAlwtTXxRssSdgcm7xEZHZDdm3NmCzU1+nffVjF75bmGR8+/UwvgPxZdxZNLr6KmXf/RLCqNzbJ4yudyhfics5LNFnL7AlWU+wbQMreFvU0LOGDykszkznrMwEnZwsTkcWOxWs56jN5RKzJ9x9/W95TJsPSZX3DNkR0sCOg/U3Iyrrr1nbyxaC3DkRTp117nw7v+izs2CIsCQXUgxJOAQEcbL8xbyx/9HZMeO64moXu9E8zt9E580VK2tS/npO38xomJdI6jVh9Hatupr4JoFhW73YrB6SRnMDI0GDznccmxIKlsnqzRRF2V5NqpeB3mguN7bzBx1mPGj8sO1cb66qs6qUhXXMF3Lr2VF1sumvD70Il+agZPsnikh3lN1bMT9Fw0eO3c/skP88rclRiAFVeuZllL9Z+XYHYg6qMCGr2yh1UkmSWezuI8j+t0UKk8marMvTm7YgVbx90sNp//y1k1kLRbjHiqbPngpc0fZOdomtUmB+dy4BqIptnf0InNZMTrqK7KjMFg4GJTnNjACUa65jC/fvkZx4SPy1v8zY3V2zczr6OB9LZ+Dg5M7F87cegEAPlA7QWztPWu5c00fe0+/LkUnR3V3cclmF1cGH+BgpJw28wEDBlMkQhDw2E6Ws/dCxNRPZBq/DM0O21QPX9UcXQuxo+eYE3vfiwtzVW3FdzfGEAaGyr4HJ2Nkzkrv110GQsa3FV3fgAbx47B4Z3EdjfCFWeKp+iQXBl1tlTvhXhxoyzwuwYjSJJUeJ9OHJSz4Fyt1bOcPBVWz6mejRkCgYoQTwIMBgN3dr2AYWiQYNcSOI94Ug0k7YHqqjw1ua34EhEy3Wng3D4ysYNHuOrY6+Rs1WHDcDpNPlkg9gfPLZ76lOWuVr9jRuakNY7mBhJApPfsPkjPLNrIq6k2/nbNxTM7MQ2Z3+BiQ+9e2sf6GXyrg6blch2x97BceWpdUB2h4wLBhUz1NK0IyopRqSSFBkfPe9yOhWt5dN3NpFavm4FZaUdrJsJHdz7Bqj/+13mPiw7LBoy2KhOHAAvSId514I94XnzunMf0DwUx5XO0VKl4qp0jJwioAbJv5+hIjITVzty26u15splNXGKO0xYaZP/OA/IvJYnY4WMAzF/WUbnJCQQCQIgngYIt4AcgOjhy3uMG4jnCdjc1VbZTq65NXsbJRWPkk+cOz1Xdt52B6ltKaLZJLB7pwdp99JzH+P7wO/7ilcdZ239gBmemHc3zZRPJ1NCwHLVzGslMjhNjcqLA/IbqjS4BaF3SCcDRvUcAGHhjL1IoRNpiZcnGFZWcmkAgQIgngYKjTl6qS0yylV/tGWrwVFdQcn29j5TZSl6SGOsfPudxajSLq8oMJAECbc0A5MfGzxAWKuqya01d9VXWAOYuaCVnMBKJJMiOTfys9r7+Fu9563kuHzlMvbu6Pp9vZ9FKeakuuWcfUizG3qNDRKxO4kuX43RVZ9VQILiQEOJJAIBbSaBPjpxHPOXzLH31OTb2vEmDo7ra5SwmI3mfLBjGFC+gs5FUKk+1zdVVWQOob2tAwkAilkCKnN0tPq24p9c1VeeyVkuNi7jLS16SGDg60YF7cP8xOsf7WGGMVWUz/Olc9I51jHsCZKIxen/2JN8Punj0kpvxbHlnpacmEAgQ4kmg4FHcprPj5xZPuVCYtp4u1p3cR0NN9Zn0mWvkpbhg37nFUyYoO5DXVaF4aql1E7W7yOYlRpUt+6eTT2cwKNWa+s7WmZ6eJhiNBiyKDUH/kZMTHhvrkcWU5wLYjWa3WUhdJ+dsPv3Dpzjy+n4MRiO3XbmgwjMTCAQgxJNAoaZZjoTIB8PnXPIZ6x9GAuI2J7VVuCxiqZXFU+QcfV3ZRJJUTN6N1tRafT5BVrMRQ60sgvu7zxRPo8f7kPI50hYrDVUYXaISu+RSfrZ8M7trJzriR0/K51zTUZ3C8O3c8+GrOdA0n0gqR3NkhM1LG2mrwpsWgeBCRIgnAQB1LfXsal7M75uXIeXOHn0x1CeLDrPPi7mK3MVVnPVyNSlyjh2Fg4kcj624nqcuvoaGuup0OnY2yKJo5CyVp0GlUpML1MlhyVVK7ZJ5nPQ1sm88e+qXkkSyX64oNs27MMTTwkYPS+58H3G7k83GIF+4sfrsMwSCC5XqalwRlI3mgIs/zJftB4KpPDVn+WSM9smN1rba6tuJBuBaNJ/n5iwnXDuX957l8d5QiiFPLfaAE6OxOntmvK2NhHcZGRqNnvHY8BHZZNHWUt3LWivb/AC8fvzUEnN0eIxQMEreYGTpRZ0Vmpn2fOLmNUhb/jcGoxEs1eUILxBcyFRf+UBQFuwWE/XKDrqT42fPDVM9oFx11Sme6hZ38uqcFey0nn3Jqjcob3Nv8dtnclqaYrp0Aw9fdht/6FxzxmMHTF72NczDvri6+2bWtPu5aPAIrTv+yMioHIK8f88RJIBAgKZAddsUvB2DzSaEk0CgM4R4EhSY5zZSHx2jv6fvrI9HhmQDSW9D9W3jB5ijJNEfV7yA3k5430HWnNzPRdnwTE5LU+Y2+ZAMRo6NxM54bIetgWcWbcS7bnUFZqYdPpeVG0JHWNe7j0O/ewWAXf0xYhYHtRdIv5NAINA3QjwJClzTv487dv0X6Ve3n/Vx1UCypkq3ubcHnHiTUdx9JwiPnymQjLvf5Kru11mcOLcPlN7pqJWrLj2jcaS3Nf4fHpKX8hY0uGd8XlpjWH8JAOEXXgZJ4g9JB99fdxOuG66r8MwEAsFsQIgnQQFvo9xQHT1HQ/V/LLmGR9fdjHd5dTauum1mPnzkj9zy1u8Z2HemC3dGyUvzzG2b6alpRnvAyaajr3HTa08xcPh44ffJcJRYbz/GfI759dUvnlqvuZS0ycLA4ROM7dnPa93jZE1mVqyq7iVJgUBQHQjxJCig2hXElXy305EkiRORNGG7m9Ym/wzPTDusipP68Mm3ZaPlcmQG5N1azYs6ZnhW2mExGVlujNEcGeHwvu7C7/t27ObOnb/mjoMvUue2Vm6CGrFpdQfdbQsYj6f5xae+TiqTY0Wbj4UXQFVNIBDoHyGeBAXqFW+j5NiZRpmjsTTJTB6DAZp91RsP4VLsCsZ6JxplRk72k0imSJssdC5oqcTUNCPQLu+m6z3QXfhd36EeABwtjVXvvg1yFXHxzZsBiCQz3P7mb/nY1fMviHMTCAT6R4gnQYHGdlk8ZYPhM7ye+vce4oYDf+Sq8Ams5ur92HiV6lrobfl2JxWhkaqtx+es7spM3YolACR3v1X43ckueQmveUF7ReZUDj78rjWMtc8DILPuEq6/qLotGAQCQfUgfJ4EBZpb65AMRvK5HMN9IzS0NxYeG9pzkEUjPRgbq3sbeNOcJgaB8b6J4mlYqczY2qq76gQw97K17P/uj0j09pMfHMLY2MDoMdkgc8HF8yo8O+2o99j4+x98gfzwCKY2sctOIBDMHNVbQhBojsVixlQnL2v17Ds24bHxI7K4cHfOnfF5aUmnYqCYP3mSbDJV+H2wWxYXnrnVfxFe1FFPf20LqWye/ldfZ2RwjPSI3Md28aqFFZ6dthhsNiGcBALBjCPEk2ACidVrebFzDfuyE40iEz2yuKhb2FGBWWnHnIVzSDk9SLkcJ3btL/z+10uu4kcrt+BfdXEFZ6cNFpMR83L5PA79/lVO/Pt/YkDC0NxCTUN1GpwKBAKBnhDLdoIJOC7fyOvxg3Sc7rGYSJAalJe5Wi+q7mUfo8nIyLqN7B6M0Sm56ETeSbh7KM6Qp5bOzgujb2bDlo3s3vpH/jCSZWn3DvIGI9z47kpPSyAQCC4IhHgSTGBxkweAroFI4XeR7uNEU1lCdjcL5jZUamqa4diwjq6tPewZzXAz0D0aZyCcxGoysqrdX+npacKWS+bxxcveTySdw5uM0hkd5l/eu6HS0xIIBIILArFsJ5jAkiYPvkQE8+43yQ6PANC7VzaUTNY34nNUf8bWxS0+4FSw7L5nXmHT4W1cb49it5gqOTXNcFhNfHyT3N8UtrtZc/M7aPFXr8WEQCAQ6AlReRJMoL3GyXXH36B1+AR925cw58bNHDs+TN5gxNU5p9LT04QrF9VRGwtievkthi8PMPTqTpYPHKZl46JKT01TPnb1fK5b1si+/jDXLbswliMFAoFADwjxJJiA0WjAubAThk9wZOcB5ty4mf+oWcJLG/381bUXxk6tZp+Dm4wj+Hre5NB3xkgflIOQF6yv/mbxtzOv3s28CyCORSAQCPSEWLYTnMGSdRcBMPDWQVKZLK8eHSVnNHH5xRfOlvBll68CYPveEyQyOfatuIyLN66o7KQEAoFAUBVUrXj6yle+wmWXXYbT6cTv90/pOZIk8cUvfpHm5mYcDgebN2/m0KFDE44ZGxvjjjvuwOv14vf7ueeee4hGo2U4A/2y/oqLyRmMDPePsu97/0Fbfzf1HhuLGz2VnppmXHvdOswuJ3mDkWcWbuSD93+wqp3TBQKBQDBzVO3VIp1O88EPfpA/+7M/m/Jz/umf/olvfetbPPLII2zbtg2Xy8X1119PMpksHHPHHXewd+9enn32WX7961/z4osvct9995XjFHTL/JYa8k3N5CWJVx9/mosHj3DVwvoLKjes1u/iQ//ny2T+9F7e9ZEtvHNZ4+RPEggEAoEAMEiSJFV6EqXwgx/8gE984hMEg8HzHidJEi0tLTz44IN8+tOfBiAUCtHY2MgPfvADbr/9dvbv38+yZcvYsWMH69atA+Dpp5/mhhtu4OTJk7S0nD26I5VKkUqdcqsOh8O0t7cTCoXwer3anOgM89sfPcP27/2Ufk8dfS0dPPwPd9IecFZ6WgKBQCAQlI1wOIzP55v0+l21ladiOXbsGAMDA2zevLnwO5/Px4YNG9i6dSsAW7duxe/3F4QTwObNmzEajWzbtu2cY3/ta1/D5/MVftrbqz989foPX8ecL/81B664nv/+wPuEcBIIBAKBQGHWiKeBgQEAGhsnLs80NjYWHhsYGKChYaIJpNlsJhAIFI45G5///OcJhUKFnxMnTmg8+8rwJ5d18Nynr+EdS6rfGFMgEAgEAq3QlXj63Oc+h8FgOO/PgQMHKj3NM7DZbHi93gk/AoFAIBAILkx05fP04IMPcvfdd5/3mHnzppet1tQkmwQODg7S3Nxc+P3g4CCrVq0qHDM0NDThedlslrGxscLzBQKBQCAQzG50JZ7q6+upr68vy9idnZ00NTXx+9//viCWwuEw27ZtK+zY27hxI8FgkJ07d7J27VoAnnvuOfL5PBs2iFwwgUAgEAgEOlu2K4bjx4+za9cujh8/Ti6XY9euXezatWuCJ9OSJUv4xS9+AYDBYOATn/gE//AP/8ATTzzBnj17uOuuu2hpaeG9730vAEuXLmXLli3ce++9bN++nZdffpn777+f22+//Zw77QQCgUAgEMwudFV5KoYvfvGL/L//9/8K/7169WoAnn/+ea655hoAurq6CIVChWP+8i//klgsxn333UcwGOSKK67g6aefxm63F4557LHHuP/++9m0aRNGo5FbbrmFb33rWzNzUgKBQCAQCHRP1fs86ZGp+kQIBAKBQCDQD8LnSSAQCAQCgaAMCPEkEAgEAoFAUARCPAkEAoFAIBAUgRBPAoFAIBAIBEUgxJNAIBAIBAJBEQjxJBAIBAKBQFAEQjwJBAKBQCAQFIEQTwKBQCAQCARFULUO43pG9R0Nh8MVnolAIBAIBIKpol63J/MPF+KpDEQiEQDa29srPBOBQCAQCATFEolE8Pl853xcxLOUgXw+T19fHx6PB4PBoNm44XCY9vZ2Tpw4IWJfyoh4nWcO8VrPDOJ1nhnE6zwzlPN1liSJSCRCS0sLRuO5O5tE5akMGI1G2trayja+1+sVf5gzgHidZw7xWs8M4nWeGcTrPDOU63U+X8VJRTSMCwQCgUAgEBSBEE8CgUAgEAgERSDEUxVhs9n427/9W2w2W6WnckEjXueZQ7zWM4N4nWcG8TrPDHp4nUXDuEAgEAgEAkERiMqTQCAQCAQCQREI8SQQCAQCgUBQBEI8CQQCgUAgEBSBEE8CgUAgEAgERSDEU4X59re/TUdHB3a7nQ0bNrB9+/bzHv/Tn/6UJUuWYLfbWb58OU899dSExyVJ4otf/CLNzc04HA42b97MoUOHynkKVYGWr3Mmk+Gzn/0sy5cvx+Vy0dLSwl133UVfX1+5T0P3aP15Pp2PfexjGAwG/vmf/1njWVcf5Xid9+/fz0033YTP58PlcnHJJZdw/Pjxcp1CVaD16xyNRrn//vtpa2vD4XCwbNkyHnnkkXKeQtVQzGu9d+9ebrnlFjo6Os77nVDs+1cUkqBiPP7445LVapUeffRRae/evdK9994r+f1+aXBw8KzHv/zyy5LJZJL+6Z/+Sdq3b5/0N3/zN5LFYpH27NlTOOYf//EfJZ/PJ/3yl7+U3nzzTemmm26SOjs7pUQiMVOnpTu0fp2DwaC0efNm6T/+4z+kAwcOSFu3bpXWr18vrV27diZPS3eU4/Os8vOf/1xauXKl1NLSIv3P//k/y3wm+qYcr/Phw4elQCAgfeYzn5Fef/116fDhw9KvfvWrc445GyjH63zvvfdK8+fPl55//nnp2LFj0r/+679KJpNJ+tWvfjVTp6VLin2tt2/fLn3605+WfvzjH0tNTU1n/U4odsxiEeKpgqxfv176+Mc/XvjvXC4ntbS0SF/72tfOevytt94q3XjjjRN+t2HDBum//bf/JkmSJOXzeampqUn6xje+UXg8GAxKNptN+vGPf1yGM6gOtH6dz8b27dslQOrp6dFm0lVIuV7nkydPSq2trdJbb70lzZ07d9aLp3K8zrfddpv0kY98pDwTrlLK8TpfdNFF0pe+9KUJx6xZs0b667/+aw1nXn0U+1qfzrm+E0oZcyqIZbsKkU6n2blzJ5s3by78zmg0snnzZrZu3XrW52zdunXC8QDXX3994fhjx44xMDAw4Rifz8eGDRvOOeaFTjle57MRCoUwGAz4/X5N5l1tlOt1zufz3HnnnXzmM5/hoosuKs/kq4hyvM75fJ7f/OY3LFq0iOuvv56GhgY2bNjAL3/5y7Kdh94p1+f5sssu44knnqC3txdJknj++ec5ePAg1113XXlOpAqYzmtdiTHfjhBPFWJkZIRcLkdjY+OE3zc2NjIwMHDW5wwMDJz3ePV/ixnzQqccr/PbSSaTfPazn+VDH/rQrA0DLdfr/PWvfx2z2cwDDzyg/aSrkHK8zkNDQ0SjUf7xH/+RLVu28Mwzz/C+972P97///bzwwgvlORGdU67P88MPP8yyZctoa2vDarWyZcsWvv3tb3PVVVdpfxJVwnRe60qM+XbMmowiEMxSMpkMt956K5Ik8S//8i+Vns4Fxc6dO/lf/+t/8frrr2MwGCo9nQuWfD4PwM0338wnP/lJAFatWsUrr7zCI488wtVXX13J6V1QPPzww7z66qs88cQTzJ07lxdffJGPf/zjtLS0nFG1EugbUXmqEHV1dZhMJgYHByf8fnBwkKamprM+p6mp6bzHq/9bzJgXOuV4nVVU4dTT08Ozzz47a6tOUJ7X+aWXXmJoaIg5c+ZgNpsxm8309PTw4IMP0tHRUZbz0DvleJ3r6uowm80sW7ZswjFLly6dtbvtyvE6JxIJ/uqv/opvfvObvOc972HFihXcf//93HbbbTz00EPlOZEqYDqvdSXGfDtCPFUIq9XK2rVr+f3vf1/4XT6f5/e//z0bN24863M2btw44XiAZ599tnB8Z2cnTU1NE44Jh8Ns27btnGNe6JTjdYZTwunQoUP87ne/o7a2tjwnUCWU43W+88472b17N7t27Sr8tLS08JnPfIbf/va35TsZHVOO19lqtXLJJZfQ1dU14ZiDBw8yd+5cjc+gOijH65zJZMhkMhiNEy+7JpOpUP2bjUznta7EmGegSdu5YFo8/vjjks1mk37wgx9I+/btk+677z7J7/dLAwMDkiRJ0p133il97nOfKxz/8ssvS2azWXrooYek/fv3S3/7t397VqsCv98v/epXv5J2794t3XzzzcKqQOPXOZ1OSzfddJPU1tYm7dq1S+rv7y/8pFKpipyjHijH5/ntiN125Xmdf/7zn0sWi0X67ne/Kx06dEh6+OGHJZPJJL300kszfn56oRyv89VXXy1ddNFF0vPPPy8dPXpU+v73vy/Z7XbpO9/5zoyfn54o9rVOpVLSG2+8Ib3xxhtSc3Oz9OlPf1p64403pEOHDk15zFIR4qnCPPzww9KcOXMkq9UqrV+/Xnr11VcLj1199dXSn/zJn0w4/ic/+Ym0aNEiyWq1ShdddJH0m9/8ZsLj+Xxe+sIXviA1NjZKNptN2rRpk9TV1TUTp6JrtHydjx07JgFn/Xn++edn6Iz0idaf57cjxJNMOV7n733ve9KCBQsku90urVy5UvrlL39Z7tPQPVq/zv39/dLdd98ttbS0SHa7XVq8eLH0P/7H/5Dy+fxMnI6uKea1Ptd38NVXx+IPKQAAAeNJREFUXz3lMUvFIEmSpE0NSyAQCAQCgeDCR/Q8CQQCgUAgEBSBEE8CgUAgEAgERSDEk0AgEAgEAkERCPEkEAgEAoFAUARCPAkEAoFAIBAUgRBPAoFAIBAIBEUgxJNAIBAIBAJBEQjxJBAIBAKBQFAEQjwJBAKBQCAQFIEQTwKBQCAQCARFIMSTQCAQCAQCQREI8SQQCASTcPPNN2MwGM7688QTT1R6egKBYIYRwcACgUAwCaOjo2QyGaLRKAsXLuSpp55i9erVANTV1WE2mys8Q4FAMJMI8SQQCARTZOvWrVx++eWEw2HcbnelpyMQCCqEWLYTCASCKbJ79246OjqEcBIIZjlCPAkEAsEU2b17NytWrKj0NAQCQYUR4kkgEAimSHd3N4sXL670NAQCQYUR4kkgEAimSD6fp6enh97eXkS7qEAwexHiSSAQCKbIAw88wMsvv8zixYuFeBIIZjFit51AIBAIBAJBEYjKk0AgEAgEAkERCPEkEAgEAoFAUARCPAkEAoFAIBAUgRBPAoFAIBAIBEUgxJNAIBAIBAJBEQjxJBAIBAKBQFAEQjwJBAKBQCAQFIEQTwKBQCAQCARFIMSTQCAQCAQCQREI8SQQCAQCgUBQBEI8CQQCgUAgEBTB/w9JIhFgPDH4fAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "v=v0\n",
    "t=np.linspace(0.0,0.1,400)\n",
    "plt.plot(t,np.real(gamma(t,v,v0,Dv)),label='analytic')\n",
    "plt.plot(t_num,int_gamma_r,color='red',linestyle='--',alpha=0.5,label='numeric')\n",
    "plt.xlabel(r'$\\tau$')\n",
    "plt.ylabel(r'$Re(\\gamma)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "authorship_tag": "ABX9TyM9OmxJzZLQBVjeTV5R62Ev",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
