L10.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lecture 10 - Optimization\n",
    "\n",
    "C&C Problem 13.10-13.11. Find minimum of: $$ f(x) = 3 + 6x + 5x^2 + 3x^3 + 4x^4 $$ using:\n",
    "- Bisection with initial bracket $x_l=-2$, $x_u=1$\n",
    "- Newton's method with $x_0=1$\n",
    "- Newton's method with finite difference estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "\n",
    "def f(x):\n",
    "    return 3 + 6*x + 5*x**2 + 3*x**3 + 4*x**4\n",
    "\n",
    "def fp(x):\n",
    "    return 6 + 10*x + 9*x**2 + 16*x**3\n",
    "\n",
    "def fpp(x):\n",
    "    return 10 + 18*x + 48*x**2\n",
    "\n",
    "x = np.linspace(-2,1,100)\n",
    "plt.plot(x, f(x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the simplest case, we can just use our existing root finding methods to find the minimum, $f^\\prime(x)=0$. For example bisection from L8, where `f` is renamed `fp` to reflect that we are optimizing instead of root finding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of minimum: x=-0.5867, f(x)=1.0690\n",
      "Iterations: 31\n"
     ]
    }
   ],
   "source": [
    "def bisection(fp, xl, xu, tol=1e-8):\n",
    "    \n",
    "    # check for valid initial bracket\n",
    "    assert fp(xl) * fp(xu) < 0, 'Choose xl,xu such that f(xl) * f(xu) < 0'\n",
    "    err = 9999\n",
    "    errors = [] # store errors to plot later\n",
    "    \n",
    "    while err > tol:\n",
    "        xr = (xl + xu) / 2\n",
    "        test = fp(xl) * fp(xr)\n",
    "        if test < 0:\n",
    "            xu = xr\n",
    "        elif test > 0:\n",
    "            xl = xr\n",
    "        err = np.abs(fp(xr))\n",
    "        errors.append(err)\n",
    "    \n",
    "    return xr, errors\n",
    "\n",
    "xb, errors_b = bisection(fp, -2, 1)\n",
    "\n",
    "print('Estimate of minimum: x=%0.4f, f(x)=%0.4f' % (xb, f(xb)))\n",
    "print('Iterations: %d' % len(errors_b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Newton's method, modified for optimization by renaming `f` to `fp`, and `fp` to `fpp`. Note this function is only for the 1-dimensional case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton(fp, fpp, x, tol=1e-8):\n",
    "\n",
    "    err = 9999\n",
    "    errors = [] # store errors to plot later\n",
    "    \n",
    "    while err > tol:\n",
    "        x = x - fp(x)/fpp(x)\n",
    "        err = np.abs(fp(x))\n",
    "        errors.append(err)\n",
    "    \n",
    "    return x, errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of minimum: x=-0.5867, f(x)=1.0690\n",
      "Iterations: 6\n"
     ]
    }
   ],
   "source": [
    "xn, errors_n = newton(fp, fpp, 1)\n",
    "\n",
    "print('Estimate of minimum: x=%0.4f, f(x)=%0.4f' % (xn, f(xn)))\n",
    "print('Iterations: %d' % len(errors_n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Newton's method converges faster than bisection.\n",
    "\n",
    "In the last part of the problem, we substitute finite (centered) differences for the first and second derivatives in Newton's method. This is a similar idea to the Secant method for root finding. The difference formulas are defined with a step size proportional to the value of $x$, for example $\\delta=0.01$ is a 1% change. Note these functions are not specific to this problem and will work for any $f(x)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fp_cd(f, x, d=0.01): # f prime centered difference\n",
    "    return (f(x + d*x) - f(x - d*x)) / (2*d*x)\n",
    "\n",
    "def fpp_cd(f, x, d=0.01): # f double-prime centered difference\n",
    "    return (f(x + d*x) - 2*f(x) + f(x - d*x)) / (d*x)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test these against the analytical derivatives at $x=1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First derivative analytical:  41\n",
      "First derivative numerical:  41.00190000000019\n"
     ]
    }
   ],
   "source": [
    "print('First derivative analytical: ', fp(1))\n",
    "print('First derivative numerical: ', fp_cd(f,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Second derivative analytical:  76\n",
      "Second derivative numerical:  76.00079999996012\n"
     ]
    }
   ],
   "source": [
    "print('Second derivative analytical: ', fpp(1))\n",
    "print('Second derivative numerical: ', fpp_cd(f,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use them in Newton's method. Only `f` is required as input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of minimum: x=-0.5867, f(x)=1.0690\n",
      "Iterations: 6\n"
     ]
    }
   ],
   "source": [
    "def newton_cd(f, x, tol=1e-8):\n",
    "\n",
    "    err = 9999\n",
    "    errors = [] # store errors to plot later\n",
    "    \n",
    "    while err > tol:\n",
    "        x = x - fp_cd(f,x) / fpp_cd(f,x)\n",
    "        err = np.abs(fp_cd(f,x))\n",
    "        errors.append(err)\n",
    "    \n",
    "    return x, errors\n",
    "\n",
    "xcd, errors_cd = newton_cd(f, 1)\n",
    "\n",
    "print('Estimate of minimum: x=%0.4f, f(x)=%0.4f' % (xcd, f(xcd)))\n",
    "print('Iterations: %d' % len(errors_cd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The iteration count is the same as the analytical Newton's method. However, note that each iteration of the finite difference version is performing more function evaluations to estimate the derivatives. It would be possible to make this more efficient by computing the `f(x +/- d*x)` terms only once and using them to calculate both `fp` and `fpp`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 16.20\n",
    "\n",
    "Find location (2-dimensional) of peak pollutant concentration in a channel: \n",
    "$$ c(x,y) = 7.7 + 0.15x + 0.22y - 0.05x^2 - 0.016y^2 - 0.007xy $$\n",
    "\n",
    "Over the domain: $-10 \\leq x \\leq 10$, $0 \\leq y \\leq 20$. Solve with:\n",
    "- Gradient ascent with $\\alpha=0.01$\n",
    "- Newton's method\n",
    "- `scipy.optimize.minimize`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def c(x,y):\n",
    "    return 7.7 + 0.15*x + 0.22*y - 0.05*x**2 - 0.016*y**2 - 0.007*x*y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First look at the function using a filled contour plot. The `meshgrid` function creates the set of all 2D `(x,y)` points from the ranges of `x` and `y`. These are assigned to temporary variables because they are not used later in the optimization. Last, the concentration values come from calling `c(x,y)`. The `contourf` function has many options, see docs [here](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contourf.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wtW+88UbB8xQaGhqioSHZUC2V8e/SpUvjkEMOKXgYRd++feMPf/hDjBs3rtPvu8022xRs/+1vf4vGxuI7S6ZMmdLu+3XV2u/36KOPlnR8petLAym00QjFMrql8ozSyj+BAgCUzvUz/9wHQ3roJ6IW/OlPfyrY3muvvZIp5ENS1+u2bNmyOPTQQ2Py5Mkt+3r37h2/+93vYs899+zSe2+88cax3XbbtWw3NTUVBBcd+XBNEREHHnhgl+pZ27777hvdu3/wdPUnn3wyFi9eXNSxixcvjqeeeqplu76+Pvbdd9+y1gdZIVCoPA2p/NMhAgCd5zqaf+6HK0+7rjgGHkL+XXvttQXbX/7ylxOq5AOpOkOvWLEijjzyyLj//vtb9vXq1SsmTZoUn/70p8vyGUcccUTB9vXXX1/UcS+88EI89thjLdv9+vWL/fbbryw1rTFo0KDYY489WrZXrFgRt956a1HH3nLLLbFy5cqW7T333DM23HDDstZH8twsANWgIwQAus5zFvJPsFB5ggWKYbYCefaXv/ylYFD8mDFjzFT4sKampvjsZz8bd999d8u+Hj16xK9+9avYf//9y/Y5xx13XMFsgDvvvDNeeumlDo/7wQ9+ULD92c9+Nnr37l22utY4/vjjC7Z//OMfx/Lly9s9Zvny5XHZZZcV7Bs/fny5S0uciwTFcNNZeRpP+abzAwDKy7U139wbkwYGIEI+NTY2ximnnFKw73vf+15C1RRKRe/bqlWr4rjjjovf/va3Lfvq6+vj9ttvj0MOOaSsn7XFFlsUdLivWLEiTjjhhFi2bFmbx/z2t7+NG264oWW7Z8+eMWHChA4/a+LEiVFXV9fyXzEp0vjx42PMmDEt29OnT4/zzjuv3WPOPffcmD59esv2VlttFccdd1yHn0W2uEkgDTSa8k2nBwBUhmtsvrlHriwDx4pT630GBqKSBU1NTUW/dsmSJXHwwQfHc88917LvqKOOiqOOOqoSpZUsFWfmk046Ke64446CfRdffHHsuOOOMXPmzJL+ay8cWOP888+PgQMHtmw/8sgjsc8++8QLL7xQ8Lrly5fHT3/60zj66KML9p999tmx6aabduFP3Lbu3bvHD3/4w6irq2vZd+mll8ZXv/rVePvttwteu2DBgjj55JPjxz/+ccu+urq6+NGPflQwGwNqhZtN6DydHQBQWa610HnaekAeXHXVVbH33nvHDTfcEPPnz2/1NUuWLIkbb7wxttxyy4Ln+44cOTKuvPLKKlXasfqkC4iIuOmmm9bZ961vfSu+9a1vlfxeDz74YIczAkaMGBF33nln7L///rFixYqIiJgyZUpstdVWsfPOO8dmm20WixYtiqeeemqdf+BDDjkkLrzwwpLrKsUhhxwSF110UXznO99p2fezn/0sbr755thtt91i2LBh8eabb8bjjz8eS5cuLTj2kksuiQMOOKCi9SWh1hPnWh9xQDoYgZVfOjkAoDrqhzdG05y+SZdBBTSOWB19Z+n4JlmLR/WJ9V5d2vELc6pp84aof3l20mVAm5qbm+PBBx+MBx98MOrq6mLUqFExZsyYGDhwYDQ2NsbcuXPjqaeeaumvXmPUqFFx7733xpAhQxKqfF2pCBWSsNdee8VvfvObOOGEE1qCg+bm5pg6dWpMnTq11WM+//nPx9VXX12VWQDnnXde1NXVxYQJE1oewLx06dKChOrDevToERdeeGGnghjIAyNXKkugkF8CBQCorjXXXuFC/ggWKmtJQ7foP1u7hPYJFsiK5ubmeOWVV+KVV15p93WHHnpoXHPNNTF48OAqVVacmr7aHXTQQfGPf/wjTjnllILlkNb28Y9/PH71q1/FrbfeGv369atafeeee2489thjcdhhh0XPnj1bfU3Pnj3jsMMOi8cffzzOOeecqtVWTbU+SwGgUgQKAJAc1+F8Mhinsgwm65iVDiC99thjjzj66KPb7YeOeP9ZwwceeGDcd9998dvf/jZ1gUJERF1zc3Nz0kWkwYoVK2LKlCnx2muvxdy5c6Nfv37R0NAQO+64Y4waNSrp8uLdd9+NRx55JGbPnh1vv/12bLTRRtHQ0BDjxo3r8BcxCc8991xss802Ldu7b/jZWK9+w069V62HCm4IOubGsrI0jPJJRwYApIMZC/lkxkLlmK1QnFpeBikiYun0v8eUdz54fus//vGP2HrrrROsKL3W7sP7w/2DYosxPRKsqHxemr4yDt5nQct2Wn4Pmpub48UXX4xp06bFrFmz4p///GfU1dXFgAED4qMf/Wjstttusd566yVdZrtqdvmjtfXs2TM+9alPJV1GmwYOHBgHH3xw0mUANUagkE8CBQBID89ZgNJYBgnIurq6uhgzZkyMGTMm6VI6TXROqpmlYJZCR8xSgNIIFAAgfVyf88fgnMrSDuxYrfcnrNokPQ+0hTxyFgagVRpC+aPDAgDSy3U6f9xPA5BXQgVIqVofVVAMo1MqRwMof3RUAED6uV7nj/vqytEe7Jh+BaBSnIFJrVpf+gigXHRQAEB21A9vdO3OGcFC5QgWAJLh7AtkkpvHytHoyRedEgCQTa7hQDmYrQBUgl45UqnWZym46APloDMCALLNtTw/DNypHAPOOqaPASg3Z14gc9w0Vo7GTn7ohACAfHBNzw/32pWjjQhQXc66kDJGEJAUjZz80PkAAPni2p4f7rlJir4GoJyECqROrS99RPuMQIH26XQAgHxyjc8PwUJlaCsCVI8zLgAaNjmhswEA8s21HtonWGif2QpAuTjbQoq4wLfPDWJlCBTyQScDANQG1/x8cA8OQJbpoSNVLH0EUDqdCwBQW1z780GwUBkGo7XPYEagHJxpISVc2NvnxrAyNGSyT6cCANQm9wD54H6cJOh/ALpKLx0AZJTOBACobfXDG90PQCsMSgOoLGdZUqOWlz4ySqB9bggrw6iobNOBAACs4b4g29yXV4Z2ZPv0QwBd4QwLUIM0XAAA8kWwkG3uzwHIEqECqVDLsxRon9ElsC6dBgBAa9wjZJtgofy0J9tntgLQWc6ukDAXcapNYyXbdBYAAO1xrwCFBAsA5efMCqSWm7/yEyhkm04CAKAY7hmyy/061WagI9AZeuxIXC0vfeTiDRRL5wAAUAr3DtklWCg/A9YAystZFUglN33lp3GSXToFAIDOcA+RXe7dy08bs20GPAKlckYFgBTTGQAAdIV7CaAYggWgFPVJF0Bts/QRrTGCpPyMdMomnQBQe8YOe6sqn/P83KFV+RwgHeqHN0bTnL5Jl0GJGkesjr6ztI3KaUlDt+g/W9sIoKuECgA5J1DIJoECZF+1AoLO6ExtggjINsFCNgkWqKbFo/rEeq8uTboMIAOECpAAsxSA9ggUIBvSHBpUQjF/XsEDpJtgIZsEC+VltgJA1wkVSEwtL31E2yx9VF5mKQB0Ta0FB13V3t+XwAHSQbAAgoX2mK0AFEOoAAApYpYCJEN4UHlt/R0LG6D6BAvZY7YCAGkiVIAqs/RR28xSKC+zFLJHoADVIUBIl9b+PQQNUHmChewRLJSX2QptM1sB6IhQgURY+gigkEABKkeIkD2CBqgOwUL2CBbKS7AA0DlCBagisxTaZpZCeZmlkC0CBSgvIUI+rf3vKmSA8hAsAK0xWwFoj1ABIGcECtkiUICuEyLUJiEDlI9gIVvMVigvsxUASidUoOosfcTazFIAoBRCBFojZICuESxki2CBajBbAWiLUAGqxNJHVINZCtlilgIUR4hAZ3z490bAAMURLGSLYKF8zFZom2ABaI1QAUiUWQrUKoECtE+QQDmZxQDFEyxQqwQLAMUTKlBVtbr0kVkKVINZCtkhUIDWCRKoFrMYoH2ChewwW4FqMFsBWJtQAUiMWQrlI1DIDoECFBIkkDQBA7ROsJAdgoXyMVsBoDhCBQCoEoECvE+QQFoJGKCQYCE7BAtUmtkKwIcJFagaSx9BZZilAGSBIIGsETDA+wQL1BqzFQA6JlQAEmHpI2qNWQrUIkECeSFgoNYJFrLBbIXyESy0zmwFYA2hAkCGmaWQDQIFao0wgTwTMFCrBAvZIFgAoBqEClTFqk2GJF1CIix91DqzFKglAgVqhSCBWiRgoNYIFqglZiu0zmwFIEKoAJBZZimkn0CBWiBMgPet+S4IF8g7wUL6ma0AQKUJFaBCzFJonVkK5SFQAJIkSIC2mb1ALRAspJ9goTzMVmid2QqAKwwAVIBZCuTR2GFvCRSgBL4z5Jl7nfQzEKk8DIwDWJeZCkDVuBkrD42D9NPIJm90ikLXmL1AXpmxALXLbAWobXr4oAIsfQS1S6BAnhhlDeXne0XeuPdJNwOSysMAOYBCZioAVeEmrDw0CtJNo5o80NkJ1eHBzkC1eL4ClWK2AtQuoQKUmVkKAGSRMAGSYWkk8sAySNQCD21unWABapOoGiAjzFJIN7MUyCpLsUB6+D6SZe6F0k1bojzMwAd4n7MhUHFuvMg7jWiySOclpJfvJ1nlnijdBAtUihUboPZY/gjKyIWUStEASC+NZ7JGRyVkh+cukEWWQiLvLIMEYKYCUGFmKQCkg5HPkF2+v2SNQRfpZbASlWKQJdQWMxUAUs6Nf3ppMJMFOiIhPzzUmSwxYyG9Gkesjr6zDP7qCrMVgFrnKgJlIpVfl1kKXSdQSC+BAmlnZDPkm+84WeB+iTzT3l2XfhGoHWYqAECJNJBJM52MUFs8d4G0M2MhncxWAKArXEEAUsosBaBUAgWoXWYukGYGZKST9kbXma2wLrMVoDY4+0EZuGiuy80VeaVRTBrpTATWcC4grdxDpZNgAYDO0OsHkEJu7tNJY5i0ESYArXFuAKgeA+rWZeAl5J9nKkAXuViuy00VeSRQIE10FgLF8LwF0sbzFdLJ8xUAKJWrBkDKmKUAtEegAJTKzAXSxECNdNIG6RoD69ZlACbkm5kKQFm5mSKPNH5JAx2CQFeZuUBamLFAHi1p6Bb9ZwtngNqg9w+6QPJOuRkhlD4CBZJmhDFQbs4rpIF7rPTRFqHc9JlAfgkVAKANGrskTacfUEnCBZLmXit9BAtdY+Y+UCuc7YCycQPVNW7ggTV09AHV5HxDkgQLkG9mK0A+6QGETnJhhHzTwCUpOveAJAgzSZL7rnQx2KlrDLYDaoEzHVAWbpy6xo17umjYkgQdekAaOBcBEdonlJdBmZA/9UkXAABQy3TeAWm05tz0/NyhCVdCragf3hhNc/omXQaUxZKGbtF/tmAGyC9Di6ETpOyFzFLoGqOA0sUsBapJoACknfMU1eQ+LF20U7pGO7mQfhTIFzMVAOD/aMhSLTrpgCwxa4FqMmMhXRpHrI6+s3SOA1DIlQFKJF2nnIz+SQ+BAtUiUACyyvmLanFfRl6YrVBIfwrkh5kKQJe4SQIojs44IA/MWqBazFhID7MVAFibqwJAQsxSSA+j4ag0gQKQN2OHveXcRsW5R0sPbZfOMxCvkNkKkA/ObFACF79Cbo7IA41VKk2nG5BnznEAALVHjyBAAoz0gfwziheoFc53VJIBIOmhDdN5BuQVMmATss9ZDYCapZFKpehcA2qRcx+V4p6NPBAsAHnijAZFkqQXckPUeUb4pIPGKZVgtC5Q65wHqRT3bumgLUO56GOBbNMrCABQBjrRAD4gXKASBAvpIFjoPIPzgLxwNgNK5kao89yAp4MGKeWm4wygdc6PALTFbAXILj2DUAQXOsgPgQLlZCQuQMecJykn93LpYLBU5xmkB+SBMxlAlbjxhnzRSQZQPCEs5SRYSAftG8rBIE7IJqECUBKjKsgyDVDKRccYQOc4f1Iu7uvIMu1qIOucxaADUnPKwSie5Gl4Ug5G2gJ0nXMp5eL+LnnaOZSDfhfIHqECUDSjKYBapgMMoLycVykHwULyBAudo30NZJkzGECFuclOnsYmXaXjC6AyzFoAIMJsBcgaoQK0w0UNsk+gQFfo7AKoDudausL9XvIMpOocsxWArHL2AoriZqdz3FxDdungAqguQS5dIVhInrZP52hrf8DATsgOZy4Ackvjks7SqQWQHOdgOsu9HwBUh1AB2iAh/4CRE51jpE6yNCrpLJ1ZAMlzLqaz3AMmSxuoc7S5P6AvBrLBWQsA4P/oxAJID8shAQCkk1ABoAKM0EmWEWqUSscVQHo5P1Mq94LJ0hbqHLMVPmC2AqRffdIFQBq5gH3AjQ2QdzqrANJv7LC34vm5Q5MugwypH94YTXP6Jl1GzWocsTr6ztKWBOjI0qVL45lnnonnn38+3n333Vi2bFmsv/76MWTIkNhpp51i9OjRUVdXl3SZ6xAqAJSZkTnJMjKNUggUALJjzTlbuECxBAtkzZKGbtF/tvZkxPuDPdd7dWnSZUDFPProo3HZZZfFpEmTYsWKFW2+rqGhIb70pS/FGWecERtuuGEVK2yf2Bhok1kKZI1AgVIIFACyyfmbUrg/TI7BVgDrampqitNOOy123333uOOOO9oNFCIiZs+eHRdccEFstdVWcc8991Spyo7pMYS1WPqIrnDjDNmgQwog25zHIRu0j0pncN8H9M+QN83NzfH5z38+rrjiimhubi742ZZbbhlHHHFEHHvssbHvvvvGwIEDC37+1ltvxWGHHZaaYMHyRwDkglFoFEMnFEB+WA6JYlkGCYA0uOaaa+JXv/pVwb4999wzrrjiithmm20K9jc1NcXNN98cZ555ZixatCgiIlasWBHjx4+PF198MTbYYIOq1d0a8SfQKqMjSmcUTnIEChRDoACQT87vFMP9YnK0k0qnPf4BsxXIk4svvrhge88994z7779/nUAhIqK+vj5OPPHEuP/++6NXr14t++fNmxf/7//9v4rX2hFnKfgQFyuAfNLhBJBvzvMUQ7AAQFL+/ve/x8yZMwv2/eQnP4kePXq0e9wuu+wSX/nKVwr2/f73vy93eSUTKgCQaRqHdERHE0BtcL6H9DJboXRmK3zAAFDy4JVXXinY3mSTTWL77bcv6tjDDjusYPull14qW12d5QwFrMPNS+ncJEM66WACqC1jh73l3E+7DEhJjjZT6bTNIT/ee++9gu0RI0YUfewmm2xSsP3uu++WpaaucHaC/yP5huzRKKQ9OpUAapdrAO1xDwnZo8+GrBs2bFjB9rJly4o+du3XbrjhhmWpqSuECkABIyFKZ8RNMjQGaY/OJABcC2iPe8lkaDuVThsd8mHXXXcteODy888/H0uXLi3q2CeffHKd90qaMxMAkCs6kQBYw3JIAEAarLfeenH88ce3bC9btiyuvfbaDo9btWpV/Pd//3fBvvHjx5e9vlIJFSBMo6PzjLRJhpFltEXHEQCtcX2gNe4pk6ENVTqzFd6n74asu+SSS2LkyJEt29/61rfi/vvvb/P1K1eujJNPPjmefvrpln177713HHXUUZUssyj1SRcApIcbFbJA44+26DACoD1jh70Vz88dmnQZpEz98MZomtM36TJqTuOI1dF3lvYnUF0zZswo+ZjBgwfHkCFDyvL5G264YTz44INx5JFHxtNPPx1Lly6N/fffPz7zmc/EZz7zmdhyyy2jT58+sWDBgnj00UfjqquuiunTp7cc/7GPfSx+9atfRV1dXVnq6QqhAkAnGWED6SBMAKBYggVaI1ggC5Y0dIv+s7VBF4/qE+u9Wtw69LC2ww8/vORjJkyYEBMnTixbDSNHjozHHnssbrjhhvjZz34WTz75ZNxxxx1xxx13tHnMRhttFGeddVZ885vfjB49epStlq4QKlDzTJ+D7DBLgbUJFAAolWAB0sFsBUinPzduHi8t6Z90GWXxZuOSiFiQdBnrWLVqVaxatSp69eoVdXV10dzc3OZrN9lkk7jgggvimGOOSU2gEOGZCsD/sfRRacxSgOQJFADoLA9wZm0Gr5AF2u3vMziULJsyZUqMHTs2vva1r8WUKVNi9er2+5feeOONOPHEE+MjH/lIXHPNNVWqsmOpnanwyiuvxBNPPBFTp06NJ554Ip566qlYvHhxy8833XTTmDlzZknvOXPmzBg1alTZarz++uvjhBNOKNv7RURMnjw5PvWpT3X6+M78vQBkgYYeH6YjCIByMGuBD7MMUvWZrQBU06RJk2L06NElHTN48OCyff6f/vSnOOSQQ2LZsmUt+xoaGuLf//3fY//9949Ro0ZF375945133olnnnkmbrvttrjllluiqakp5s+fH1/5ylfi8ccfj6uuuirx5yqkKlSYPHlyfP/734+pU6fGO++8k3Q5HerTRzKaddLt9xntQNoJFPgwgQIA5SRY4MMEC9UnWCiNZyu8z7MV6IzRo0fH1ltvnchnz58/Pz7/+c8XBAr/+q//Gj//+c9j/fXXL3jt0KFDY//994/9998/TjnllDjkkEPi7bffjoiIq6++OjbffPM455xzqlr/2lJ11n7mmWfi3nvvzUSg0Ldv3zjwwAOTLgNIgKWPIDkCBQAqwfUFAKikSy+9NObPn9+yveWWW8Ydd9yxTqCwto9//ONx++23F+w7//zzY968eRWps1ipmqnQll69esWIESPi5Zdf7tL7jBgxIl599dVOHfuFL3whpkyZ0rJ99NFHd/iPXg5nnHFGfP3rXy/69fX1mfgnBSiaWQqsocMHgEoyY4E1zFaoPrMVSmO2wvvMViBLfvnLXxZsn3POOdG7d++ijv30pz8d//Iv/xIPP/xwREQsXbo0fvGLX8Tpp59e9jqLlboe6B49esTWW28du+yyS+y6666xyy67xLbbbhtTpkzp0rMGIt7vcB85cmTJx82ePTv++te/Fuz70pe+1KVaijVgwIBO1QzFsvRRacxSgGQIFACoBsECawgWACiX9957b53B8p/+9KdLeo999tmnJVSIiHjsscfKUltnpSpUGD9+fJxyyilFpzTVcsMNN8SqVatatrfYYov4l3/5lwQrohw8TwHSzywFIgQKAFTXmuuOcAHBQnWZrVAasxXeZ7YCWbBw4cJ19g0bNqyk91j79QsWLOhKSV2WqrP1wIEDUxcoNDc3x/XXX1+wr1qzFIB0MUsBqk+gAEBSXIOg+rS5gDwaMGDAOvvee++9kt5jyZIlBdv9+/fvSkldlqpQIY0eeuihgukp9fX1MX78+AQrgvKx9BFpZpYCOnMASJprEe5JSTNt+vdZiYK069ev3zrP5n366adLeo8nn3yyYLvUmQ7l5uzTgWuvvbZg++CDD078H42uc8GhVEbMVJfGGzpxAEgL1yTcm1aXtheQR3vttVfB9s9+9rOij507d2787ne/K9iX9NL8QoV2LFq0KH79618X7LP0EQBUls4bANLGtQnBAmlltgJkw+c+97mC7dtvvz1+/vOfd3jc8uXL44tf/GLB8kf9+/eP/fffv+w1lsKZpx233XZbLF36wcNeNt544zjwwAOrWsODDz4YRx55ZGy22WbRv3//6NOnTzQ0NMTOO+8cp512Wvz617+OlStXVrUm8sGNB2mlwVbbdNoAkFauUVA9ZitQKitSkHbHHHNMbL/99i3bzc3Ncfzxx8cZZ5wRb775ZqvHPPjgg/Hxj3887r///oL955xzTgwcOLCi9XakPtFPT7m1lz4aP3581NdX96/sz3/+8zr75syZE3PmzImnnnoqrrjiihgxYkR8+9vfjlNPPTXq6uqqWl8WudBQKje0UB06awBIu7HD3orn5w5NugwSUj+8MZrm9E26jJrROGJ19J1lMFwxljR0i/6ztVshzbp16xa/+tWvYvfdd4958+ZFxPvBwk9+8pP47//+79huu+1is802iz59+sQ777wTTz/9dMydO3ed9znooIPinHPOqXb56xAqtOHvf/97TJ06tWBfWpc+mjVrVpx22mlx9913x89//vNWnyjeFfPmzYv58+eXdMyMGTPKWgNQG8xSqF0CBQCyQrBQ2wQLkF6LR/WJ9V5d2vELISGjR4+Ohx56KL74xS8W9DuvXr06nnnmmXjmmWfaPLauri6+8pWvxGWXXRY9evSoQrXtEyq0Ye1ZCp/85Cdj9OjRVfv89ddfP/bZZ5/45Cc/GVtvvXUMGTIk+vTpE++++268+OKLcd9998Xtt98ey5YtaznmD3/4Qxx++OFx7733Rs+ePctWy5VXXhnnn39+2d6P5Fn6qHhmKQAAsDbBAlSH2QrFM1sBsmHLLbeMRx99NG699db4f//v/8Vf//rXaG5ubvP1ffr0iSOPPDJOO+20+PjHP17FStsnVGjFihUr1nlQRrVmKQwbNiyuv/76OOaYY6J3796tvmbXXXeN4447Li655JI46aST4u6772752UMPPRTf/va349JLL61KvVlj6SNIL7MUapdZCgBk0Zrrl3Ch9pitAOlltgJZUF9fH8cff3wcf/zxsWjRopg6dWq8+uqrsXDhwli+fHmst956MXDgwNhmm21i2223rfpy/MVIX0Up8Nvf/jbefvvtlu0NNtggPvOZz1Tls7fccsvYcssti3rtsGHD4g9/+EN87nOfi1/+8pct+6+44or493//9xg1alSlyiTDzFIonlkK1SNQqF0CBQCyzqyF2iRYqB6zFYpntgJkzwYbbBCf/vSnky6jZEKFVqy99NHnP//56NMnnSPc6+rq4oYbboi//OUvLU8KX7FiRVx77bVx0UUXleUzTj311Dj66KNLOmbGjBlx+OGHl+XzAcgngQIAeSFYqE2CBUinxaP6RN1zSVcB+SZUWMsbb7wR9913X8G+L3/5ywlVU5y+ffvG6aefHueee27LvnvuuadsocKQIUNiyJAhZXmvJFn6CNLJLIXaJFAAIG8EC1A5ZisUz2wFoBqckddyww03xOrVH5x8t99++9h5550TrKg4BxxwQMH23//+94QqIc0sfVQ8Sx9B5QgUAMgr17jaY4BM9WijUYr3Glp/TilQHnoYP6S5uTmuv/76gn3VekBzV40cObJge8WKFbFo0aJkigEokkZY7dHZAkDeudbVHve0pI0BhUClOct8yAMPPBCvvvpqy3avXr3iuOOOS7Ci4rX2zIelSz3tHjrDCBioDJ0sANQK1zyoDG01gHQQKnzIddddV7B95JFHxoYbbphQNaVZsGDBOvs22mijBCpJJ89TMFKB9DGiq7boXAGg1rj21Rb3tqSNPgCgkpxh/s/ChQvjzjvvLNiXlaWPIiIee+yxgu3BgwdHjx49EqoGAD6gUwWAWuUaWFsEC9VhtgJA8oQK/+eWW26JZcuWtWyPHDky9t577wQrKs2tt95asL3XXnslUwhknBvU6tDgAgBqhWABSIrZCkClOLv8n7WXPjrppJOirq4uoWpKM3ny5HVmWRx22GEJVZM+lj5yIwEkR0cKALge1hKDZ6rDYDCAZOlpjIhnnnkmnnrqqZbtbt26xQknnNDl9504cWLU1dW1/NfR7IF77703nn322ZI+47HHHoujjjoqmpubW/aNGTMmPve5z3WmZKhpbkyrQ0OrduhAAYAPuC7WDve71aH9VhyDDIFKqE+6gLXNmjUrmpqa1tk/d+7cgu2mpqaYOXNmq+/Rv3//GDRoUNGfee211xZs77///rHJJpsUfXy5PPLII3HBBRfEfvvtF8ccc0wcdNBBMWTIkFZf+8Ybb8RPfvKTuPzyy2PlypUt+3v06BFXXnll1Nen7p8WQAOrhug4AYB1jR32Vjw/d2jSZVAF9cMbo2lO36TLAICKSF3P8x577BGvvfZah6+bPXt2jBo1qtWfjR8/Pm644YaiPm/58uXrPI8gyQc0Nzc3xx//+Mf44x//GBERDQ0NMWbMmBgwYED06dMnFi1aFC+++GK8+OKL6xzbvXv3uO666zL1LAgqz6iE4hjlAuUjUACAtgkWoHwaR6yOvrO0eTuypKFb9J+tzQuUT+pChWr7zW9+E++8807L9uDBg+PQQw9NsKJCs2fPjtmzZ3f4us022yxuuumm2H333atQVXZ4ngKkh1kKtUGgAAAdEyzUBrMVAMirmo9z11766Itf/GL06NEjkVoOPfTQOPXUU2PbbbeN7t27d/j6+vr6GDduXNx4440xbdo0gQIAiRIoAEDxXDdrg4E1lWfWeXGsYgCUU+pmKrT1nIRKue+++yr23hMnToyJEycW/fqddtopdtppp4iIWLZsWUybNi1ee+21ePPNN2Px4sWxcuXK6N+/fwwcODBGjRoVu+yyS/Tta9QDbXPTUBw3oZWnMZV/OkYAoHRmLAAAWZS6UIH39e7duyBkoHSWPgIAANJOsJB/lkGqPM9WKI5nKwDl4owL1DSzFCrPLIX8M0sBALrGtTT/3BMDkCdCBcgpSx8B1aATBADKwzUVusaAseLoKwDKwZkEgIoxIivfdH4AQHm5tuabe+PKEywAVIdQgVzyPAWK4YYTOk+nBwBUhmtsvgkWSAOzFYCuchaBHHKDQBpoMAEAdI5gATrP4DGAytPzCNQkN5rQeTo6AKDyXG/zy+Ab0sBgRKArnEHIHUsfQfI0lPJLBwcAVI/rbn65X64sg8gAKkuoADljtAFQKTo2AKD6XH+BStF/AHSWswdQc4xaqSyjrvJJhwYAJMd1OJ/cN1eWdh9A5QgVAAAAIOUEC/kkWCBpZisAneHMQa7U+vMU3Ax0zGiVytIoyiedGACQDq7JUBrtP4DK0AMJALRJ5wUApItrc/4YmEPSDFAESuWsAUBZaAzlj04LAIDqcC9dOWYrAJSfUIHcsPSRr3NH3ExC8QQKAJBertNQGm1BgPLSCwlAlxlZBQBQXYKF/HFPTZIMVARK4YwBABTQSQEA2eCaDcUzWwGgfIQKkANGFHTMDWTlGFGVLzonACBbXLvzxb01SdK3ABTL2YJcqPXnKQCUg04JAMgm1/B8ESxUjsFmAOUhVAByz41j5WjwAACkg2ABKAezFYBiOFNAxrngA+WgIwIAss/1PD8M3qkcg84Auk5vJJln6SNIhoZOfuiAAID8cF3PD/fbJMXgRaAjzhJArhmFAu3T8QAA+eP6Du3TTgToGqECACUzagoAIN0EC/ngvpukmK0AtMcZAjLMRR7oCp0NAADpJ1ioDLMVADpPjySZ5nkKtMdNYmVo1OSDQAEA8s/1HugKAxmBtjg7AECN0cEAALXDdT8fDOypDAPRADpHqAAZZcRA+9wcVobGDABA9ggWgM7S9wC0xpkBAGqITgUAqE3uAbLPAJ/KMCANoHRCBTLL8xSgujRisk9nAgDUNvcC2eeeHIA0ECpABpl+2D4jTQAAoHWCBViXNmT79EEAa3NWAIAaoAMBACAfzFYAIGlCBQA6pOGSbQIFAODD3Btkn/vz8jNboX1mKwAf5oxAJtXy8xRcyNvnRhAAADomWAAAOkvvJADtMgoq23QYAABtcZ+Qbe7Ty88gtfYZ5Ais4WwA5IYbQCikowAA6Ij7BQCgVEIFMqeWlz6CajP6CQAg/wQL2eV+vfwMVmuf2QpAhFABMsXFGyiWzgEAgNogWCg/wQJA+/RQArngpq/8NE6yS6AAAJTK/QMAUCyhAgDkiA4BAKCz3EdklwFB5WfgWtusogA4C5Aptfw8BRdtqkmjBACgNgkWAICO1CddAEBXGUEC79MJAOw96IWyvt8DC7Ys6/sB2TB22Fvx/NyhSZdBieqHN0bTnL5Jl5ErjSNWR99ZBvi1ZklDt+g/W1scapVQAYACZilkk0AB8qfcAUE1ahBCQH4IFrJJsABANQgVIAMsfQQA+ZOG0KDc2vszCRwAyCKzFdpmtgLULqECmVHLz1OgbZY+ArMUIO3yGB50Rlt/D8IGSC+zFbLJbAUAKk2oAEALSx9lj0AB0kWAULrW/s4EDZAeggUwW6E9ZitAbRIqAABAJwkRKkPQAOkiWMgesxUAqCShAqSc5ym0zdJH5WWWQvaYpQDVJ0RIztp/90IGqC7BQvYIFsrLbAWADwgVyATPUwAAkiBESC8hAwCkgyWQoPYIFQAwSyGDzFKAyhEkZJOQASrPbIXsMVuhvMxWAHifUAFSzNJHbbP0EbVMoADlJUTIpw//uwoYoHwEC0BrzFaA2iJUAACg5ggSaouAAcpLsJAtZiuUl9kKAEIFMsDzFKCyLH2ULWYpQOcJEogQMEC5CBaAtZmtALVDqABkjqWPqFUCBSidIIH2CBiAWmG2AgDlJFSAlPI8BarBLAUgr4QJlErAAKUzWyFbBAvlYwmktpmtALVBqAAAGWCWAnRMkEC5CBigeIIFAKg9YlVSzfMUWJulj8rHLAUgL/Ye9IJAgYrx+wUdM/ghO7QBykfbFKhlZipACln6CPgwDXVYl05eqs3sBQAojiWQIP/0XAJAigkUoJBR46SB30NYl3uW7DBboXzMVgBqlZkKQGa4YSsfDQkga3TgkkZmL0Ahz1cA1jBbAfLNTAVSy/MUgFpnxB8YEU52+F2F97l/yQaDjMrH4DegFpmpACnjeQpUmgZENmiQU8t0zJJla35/zVwA0q5+eGM0zembdBnkmNkKkF96L4FMMPoDoDYIFMiLNTMX/E5TiwyOoNZorwK1RqgAUEPMUsgGDXFqkc5X8szvN7XI/Uw2aB8A0BlCBQAAEqOzlVri951aI1iglpit0DpLPEM+eaYCqVSrD2l2sW2dmzNqicY3tULHKrXMcxeANPFsBQBKpQcToEaY2gykgZHa8AHfB2qBARPUEgPiWmcAJeSPbzUApIRGN3mm8xTa5vtB3rnHST8DkAAohVABUkJy3zojPcpDIyH9NLbJK52lUDzfF/LMvU76aTOUhzZs6/R5QL74RpM6tfo8BQDIG52j0DnCBQAA0kyoAAAJM3KPvNEhCuXhe0TeuOdJP7MVysNsBSDvhApAarkRKw8NA6BahAlQfr5X5I1gAWqXJZAgP3ybIQVcWKF2aViTFzo9obKEC0C1GJRUHgbJAXmmJ5NU8TwFKC8NAqDSdHRCdfnOkQcGVUDtMqgS8sE3GUglozqoBRrUZJmOTUiW7yBZ5z4o3QxOAqA9QgUASICGNFmmIxPSw/eRLHM/RN4ZLAfklVABEmbqH5VidBFQbkZGQzr5bgKVoD1BpegHoRadcMIJUVdXV5b/Ro4cmfQfR6hAenieAmsYzUHeGZVHFumwhPQTLpBF7ovIO+1boNz69Em+D1WoAJBDRhUB5aKTErLHd5asESykl3YFlWK2AnTeUUcdlXQJUZ90AVDLXESh9mg0kyU6JiG71nx/H1iwZcKVAFlXP7wxmub0TbqMTGscsTr6ztL+h1r2wx/+MCZOnFjycVOnTo2jjz66Zbuuri5OOumkMlbWOUIFIFVMDQVInjAB8mPvQS8IFsiEscPeiufnDk26DKCKljR0i/6z9QFQGwYNGhSDBg0q+bhLLrmkYPtTn/pUbLbZZuUqq9PEpAA5Y4pyepmlQBYIFCB/LGNGVrhXSi9tjK4zgA4o1dKlS+MXv/hFwb4vfelLCVVTSKhAKnhIM5B3GslkgU5HyDffcbLAPRMAvO9Xv/pVLFq0qGV7wIABceSRRyZY0QcsfwQJ8TwFANJCRyPUDs9aADrLsxW6zrMV1mUJJGjbtddeW7B93HHHRe/evROqppAzGZAapoN2nWnJ6WTEHWkmUIDaZEkk0sy9EwC17uWXX44///nPBfu+/OUvJ1TNuoQKAAA1Soci4DxAWgkW0skgpq4zmG5dVnKAdV133XXR3Nzcsr3TTjvFDjvskFxBa/GtJXGepwDl4QY/nTSISSMjlIEPcz4AAEiPVatWxY033liwLy0PaF5DqAAJkMKvy2gNgOrQeQi0RthIGhmckU4GMwFU1j333BOzZ89u2e7Tp08ce+yxCVa0Lg9qBoAK0RAmbXQYAh3Ze9ALHuJMqowd9lY8P3do0mVAWXlg87o8sJlqmDFjRsnHDB48OIYMGVKBatp23XXXFWwfddRRMWDAgKrW0BGhAkAOGC0EtEeYAJRizTlDuAC0pX54YzTN6Zt0GQAlOfzww0s+ZsKECTFx4sSy19KW+fPnx+9///uCfWlb+ihCqACkgKWPyCOzFEgLgQLQWWYtkBZmK5BHZiusy2yFdHhs4ahYf8FGSZdRFv9c+HZEPJZ0GSW56aabYuXKlS3bm2++eXzyk59MsKLWOXuRqFp8SLPnKQBQLQIFoKs8a4G0MGAjfcyWBii/66+/vmD7pJNOirq6uoSqaZuZCgAZ52Y+fTR6SQOdgEA5mbUAUH5mK0B1TZo0KUaPHl3SMYMHD65QNev661//Gs8991zLdvfu3eOEE06o2ueXQqgAAJAjwgSgUgQLJM0ySOnj2QqUmyWQqKTRo0fH1ltvnXQZbbr22msLtg888MAYPnx4QtW0TxwKJMrzFLrGLIX0MUuBJAkUgEqzHBJJc69F3mgTAxER7733Xtx+++0F+9L4gOY1hApQRZ6nAECl6OQDqsk5B1jDQCfKTd8JteiXv/xlLF68uGV76NChccghhyRYUft8S0lMLT6kGcg3I+dIis49IAnOPSTFPRcAebP20kfHH3981Nen98kFQgUgMaZ5do0RQUCETj0gWc5BJEWwkC7aJl2jbQy17cUXX4y//OUvBfvSvPRRhFABAMpCw5Yk6MwD0sBzFgAoN0sgUUuuu+66gu099tgjxowZk1A1xfENhSpxQQSgnHTgAWnjvES1GdSRLmYrdI3ZClCbVq1aFTfddFPBvrTPUogQKpAQz1OArnHDni4atFSTEcFAmjk/UW3uw9JFO4VyMjiTWnDXXXfFm2++2bK93nrrxdFHH51gRcXx7QQSYRQGQOl01gFZIPwE6BztZKg9az+g+Zhjjol+/folVE3xhAoA0AVGx1EtOuiArHHeolrcj6WL2QoAxXnrrbfiD3/4Q8G+L3/5ywlVUxqhAkDGuEmH2qNjDsgq5y+qRbBAXpitUMgSSOTZTTfdFE1NTS3b22yzTXzsYx9LsKLi+WZCFbgIFnKTRF5ovFINOuSArHMeg9pjIBRAx6677rqC7Sw8oHkNPZ1UnYc0Q+e5OYfaoiMOyAvnM6rBgA8AsmLKlCnxwgsf3B/17NkzvvCFLyRYUWnqky6A4ixcuDAeeeSRmD17dixYsCAGDRoUDQ0NMW7cuBgwYEDS5QHUHI1WKk0HHJA3a85rDyzYMuFKyLOxw96K5+cOTboM4v0BUU1z+iZdRiY1jlgdfWcZB7zGkoZu0X+2FQ/Il9133z2am5uTLqPTUhsqvPLKK/HEE0/E1KlT44knnoinnnoqFi9e3PLzTTfdNGbOnNmp966rq+tSba+++mqMHDmyS+9RrKeffjouuOCCuOuuu2LFihXr/LxXr15x4IEHxoQJE2KHHXaoSk0AQGUJFIA823vQC4IFAIAMS1XsOXny5Nh///1jo402is033zyOOeaY+OEPfxgPPfRQQaBQKy655JLYbbfdYtKkSa0GChERy5cvj0mTJsVuu+0W//mf/1nlCimG5ykU8jyFzrP0UXqYpUAlCRSAWuBcRyW5V0sPbZjO03YupG8F0iVVMxWeeeaZuPfee5MuIxUuvvji+M53vlOwr0+fPrHrrrvGxhtvHHPmzIknnngili1bFhERK1asiHPOOSfq6urim9/8ZhIlAwBdpJMNqCVmLAAAZFOqQoW29OrVK0aMGBEvv/xy2d97t912i1/84hclHTNixIiy1/Fh//u//xvf/e53C/adfPLJ8b3vfS8GDRrUsm/+/Plx3nnnxTXXXNOy75xzzoltt902DjjggIrW2Fke0gxknZFvVIpAAahFggUqxbMV0sOzFTrPsxWAtEpdqNCjR4/YeuutY5dddoldd901dtlll9h2221jypQp8alPfarsn9e7d++qPR+hGKtWrYpvfOMbBQ/qOPPMM+PSSy9d57WDBw+Oq6++Ovr37x+XXXZZREQ0NzfH2WefHfvuu2907969WmVDUUzf7DzThiHfBApALfMAZypFsAD54oHNkB6pijvHjx8f//znP+Ppp5+Oq6++Ok4++eTYaaedokePHkmXVjU33XRTTJ8+vWV7zJgx8f3vf7/dYy655JIYM2ZMy/a0adPilltuqViNFM+af5AvZilQCQIFgPc5H0J+GSQFkC+p6vEcOHBg9O7dO+kyEnXTTTcVbJ955pnRq1evdo/p1atXnHHGGe2+DwCQPjrQAAo5L1JuBoWQdWb8FzJ4E9LBNzFF3n777Xj44Ydbtnv27BnHHntsUcced9xxBTM6HnrooXjnnXfKXiNQfUb1pIMGKeWm4wygdc6PlJv7uHTQrgHID6FCitx3332xatWqlu2dd9451ltvvaKOXX/99WOnnXZq2W5qaor77ruv7DV2hYc01zajKwA+oMMMoH3OkwAf0J4G0kaokCL/+Mc/CrY/8YlPlHT8uHHjCrafe+65LtdE55mSB/lhdBvlpKMMoDjOl5ST+znID/0tkLya/xa+/vrrceKJJ8bWW28dAwcOjJ49e8bQoUNj6623ji984Qvxs5/9rGrLCE2bNq1ge/To0SUdv/nmm7f7fkD2mCIM+aKDDKA0zpuQL9o3APlQ86HCq6++GjfccENMmzYtFi5cGCtXrox58+bFtGnT4pZbbomvfvWr8ZGPfCTOPPPMWLJkSUVrmTFjRsH2Rz7ykZKOX/v1L730UpdrAqh1RrVRLjrGADrH+ZNycV9HllkCCUiT+qQLyIL33nsvLrvssrjrrrvizjvvjK233roin7Nw4cKC7SFDhpR0/NqvX7RoUVdLioiIefPmxfz580s6Zu2AhNrm5geodTrEALpm70EvxAMLtky6DHJg7LC34vm5Q5Muo6bVD2+Mpjl9ky6DjFvS0C36z9bXAEmp2VChvr4+9thjj9hnn31iu+22ixEjRsR6660XS5Ysiddffz0efvjhuOmmm2LevHktx7z44ouxzz77xF//+tfYdNNNy17T2jMh+vQp7cHGa79+8eLFXa4pIuLKK6+M888/v0vv8V5D73DLAKUxNRjyQaAAUB6CBaDWNY5YHX1n1fyiI0AK1GSocNFFF8VXvvKVNmcC7LDDDnHooYfGhRdeGOeff3784Ac/iObm5oiImDt3bhx55JExderUqKurK2tda4cKvXv3Lun4tUOFSi/XRNs8NAjywRR5ukqgAFBea86rwgW6wmyF5JmtQDmYrQDJqcmez+985ztFLS3Uu3fv+P73vx8//elPC/Y/9dRTcdttt1WqvBalhhblDjmgHCx9BABAuQltgVqljQ2kQU3OVCjVv/3bv8W9994bv/vd71r2XXnllXHssceW9XP69+8f7777bsv20qVLSzp+7df379+/LHWdeuqpcfTRR5d0zIwZM+Lwww8vy+dDLbL0UfLMUqCrdHgBVJblkOgKsxWSZ7YCQHYJFYp07rnnFoQKf/3rX2PhwoUxYMCAsn1GWkOFIUOGlPzQaACoZQIFgOoQLNAVggXIPksgQTJqcvmjzvjYxz4WAwcObNletWpVTJs2rayfscEGGxRsz58/v6TjP/xQ6Ygoa+BB8TxPAbLPLAW6QqAAUF3Ou5BdZmh3jiWQgKTp/SxSt27d4iMf+UjBvlI7/TuyxRZbFGy/9tprJR2/9uvXfj+oNjc6nePGGrJLxxZAMpx/6SyDSQCgdEKFEvTp06dgu9TliToyduzYgu0ZM2aUdPwrr7zS7vsB0DENSzpLhxZAspyHIZsMquocg/g+YMUIqD7fuhIsWLCgYHvQoEFlff9tttmmYPvRRx8t6fgpU6a0+34AQGXoyAJIB+djOsOgEgAojVChSAsWLFhnJsDw4cPL+hn77rtvdO/evWX7ySefjMWLFxd17OLFi+Opp55q2a6vr4999923rPUBlWeUTrI0KOkMHVgA6eK8TGe4D0yWdhBdZbYCVJdvXJF+8YtfxOrVH0wtGzp0aNmXFxo0aFDsscceLdsrVqyIW2+9tahjb7nllli5cmXL9p577hkbbrhhWeujYy5iHzAVEwCApAgWgFqg3Q0kRQ9oEd5666246KKLCvb967/+a9TV1ZX9s44//viC7R//+MexfPnydo9Zvnx5XHbZZQX7xo8fX+7SAIC16LQCSC/naEpltkKyzFYAyI6aChWmT58ev//970s6Zu7cuXHIIYfEW299cHPRs2fPOPfcczs8duLEiVFXV9fy31577dXhMePHj48xY8YU1Hzeeee1e8y5554b06dPb9neaqut4rjjjuvws4B0cROdLI1ISqWzCiD9nKuBvDNb4QNWj4DqqU+6gLXNmjUrmpqa1tk/d+7cgu2mpqaYOXNmq+/Rv3//Vh+i/Oabb8ahhx4a2267bXzhC1+II444IrbYYotW32Px4sVx4403xkUXXVQQKEREfPe7343NNtusyD9Rabp37x4//OEP49BDD43m5uaIiLj00ktjyZIlcfHFF8dGG23U8toFCxbEeeedF1dffXXLvrq6uvjRj35U8GwGAKC8dFIBZMfeg16IBxZsmXQZZMTYYW/F83OHJl1Gzaof3hhNc/omXQYAHUhdqLDHHnvEa6+91uHrZs+eHaNGjWr1Z+PHj48bbrihzWP//ve/xznnnBPnnHNObLDBBrHNNtvEoEGDYr311oslS5bEG2+8Ec8++2yr4cbJJ58c//Ef/1H0n6czDjnkkLjoooviO9/5Tsu+n/3sZ3HzzTfHbrvtFsOGDYs333wzHn/88Vi6dGnBsZdcckkccMABFa2P1knEP2CkBFljlgKlECgAZI9ggVIIFsiaxhGro+8sfRJA9aQuVKi2RYsWxZQpUzp8Xb9+/eLHP/5xfOUrX6lCVRHnnXde1NXVxYQJE1oewLx06dKYPHlyq6/v0aNHXHjhhfGtb32rKvUB5WXpI8gGgQJAdgkWIBvMVqArljR0i/6zDXSESqupGHPs2LFx3nnnxe677x59+vQp6piPfvSjcfHFF8fMmTOrFiisce6558Zjjz0Whx12WPTs2bPV1/Ts2TMOO+ywePzxx+Occ86pan0AeWCWAgDUDuEwxXKPCABtS91Mhbaek1AOQ4cOje9973sREbF69ep46aWX4uWXX47Zs2fHwoULY9myZdGnT58YOHBgbLzxxrHrrrvG4MGDO/15EydOjIkTJ3ap5h133DEmTZoU7777bjzyyCMxe/bsePvtt2OjjTaKhoaGGDduXAwcOLBLnwEAdExHFAAAaWUJJKCaUhcqVEu3bt1izJgxMWbMmKRLKcrAgQPj4IMPTroM6JDnKQB5JFAAyA/LIFEsz1ZIjiWQ6IolDd2i28Kkq4B8E2FCGXhIM13heQrJMa2dYggUAPLHuR3II4P8gGrREwoA0AadTgD55RxPMQxCSY7BV3RF41BdnlBJvmEA1CQNRABAsEAx3DcCQCGhAlA2plqWzugbSC8dTQC1wfke0kt7qXTa5UA1CBUAANaigwmgtjjv0xGzFQDgA0IF6CIPaYbs0SikPTqWAGqT8z+kk9kKAOmjNxQgIW6OAQDSRbBAewxMISssgQRUmlABKAs3LWSFxiDt0ZkEgGsBpI8BWQDpIlQAAAidSAB8wDWBthigQlYY+AdUklABAKh5Oo8AWJtrAwBA64QK0AUe0kxnmb6bDCPLAADoKveUydCGAkgPPaJAl5lWCWSZkagAtMU1grYIFsgCbXWgUoQKANQEDT9ao7MIgI64VkB6mK0AkA5CBYAqcyMMAJAtggVaY9AKWWC2AlAJQgUAoCbpIAKgFK4bkA4GaQEkT6gAneQhze8z6oEsMIqMtekYAqAzXD9Ym/tMAGqRXlGAKjKqBpKnQwiArnAdgeRpV5XGYECg3IQKAOSa0WMAAFSS+00Aao1QAQCoGUaXAlAOridA1pitAJSTUAEAqAk6gAAoJ9cVPsxsheqzBBJAcoQK0Ake0vw+Ix1K46a3+jTuAIBKEiwAALVIzygAkHs6fQCoFNcY1jCgpfoM3CqNgYFAuQgVAMgljTrW0NkDQKW51rCGe1AAaoFQAaAKjKABAAAoP20tgOoTKgCdYtokkAVGjgJQLa45rGG2AmmmLQ+Ug1ABSuQhzZB+GnJE6NwBoPpcewCAWqB3FAAAAMpEsECEQS7VZgmk0pitAHSVUAGgwtzgVpcGHBE6dABIlusQAJBnQgWgZEY1AGmmIwcASAODXarLYC6A6hEqAAAAQJkJuYE0M1gQ6AqhApTAQ5oh3YwGQwcOAGniuoT70+oyWwGgOvSQAlSQm1qoHh03AKSR6xMAkDdCBQAAAKggwUJtM1uBtLIEEtBZQgWgJG46SCuNtdqmswYAgAizxQGqQagAUCFuZgEAWEMAXtsMgCGtDBwEOkOoAEXykGaAdNJJA0BWuGZBdRjgBVBZekkByDwjv2qXzhkAssa1q3a5ZwUgL4QKAAAAUEWCBag8sxWKZwkkoFRCBaBobjSK5wYWKk+HDACQNWYrAJAHQgUAMk3DrDYJFADIOtcyACCrhAoAAACQAMFCbTIopnrMIC+elQmAUggVoAhLGnxVII00yGqTDhgA8sR1DQDIGj2lQFGMWiie0TAAAEB7DI6pHu0zgPITKgAAmWE0JwB55PoGpIHBhECxhAoAZJLRXQBAnggWao/7WQCySqgAAGSCzhYAADrDEkjFM1sBKIZQAaCM3KxCZQgUAKgFrne1x2wFALJIqAAdWNLga2KkAmmj8QUA5JVgASrDADCA8tFbCgCkms4VAGqNa19tMWCGtDGwEOiIUAEAAAAAACiKUAGgTEynrQ4juWqLkZoA1CrXwNriHrc6tNkAykOoAAAAACkkWACSYgkkoD1CBWiHhzS7kQCSoyMFAFwPa4nZCtVhtgJA1+kxBSAzNLRqhw4UAAAASCehAkAZGO0CAEClCNtrh0E0pImVC4C2CBUAgFTRcQIA63J9hPIxKAyga4QKAGSCUVsAANQC970ApJ1QAWiTqY5AtRmFCQBtc52E8jFboTj6BYDWCBWgDUsafD0ojptRAACqRbBQG8xWACDN6pMuAAA6olFVG3SSAABA+jSOWB19Zxl4CZX2wgsvxLPPPhuzZs2KpUuXRu/evWPIkCExevTo2H777aNfv35Jl9hCqAAAAAAZsvegF+KBBVsmXQYVNnbYW/H83KFJl5Fr9cMbo2lO36TLAGrYwoUL4/LLL4/rrrsuXn/99TZf171799hhhx3iM5/5THz729+uYoWtEzMCAIkzSwEASuPaCQDZ9stf/jJGjx4dEydObDdQiIhYtWpVPPnkk3HZZZdVp7gOmKkAtMrDmIrjeQqVZ+mj/NMpAgBAUsxWKI4lkKC8zj///Jg4ceI6+z/ykY/ERz/60Rg8eHAsW7Ys3nzzzfj73/8e7733XvWLbIdQAQAAADLIMkj5ZwkkgPz50Y9+tE6g8PnPfz7OPffc2Hbbbdd5/erVq+PRRx+NX//61/HHP/6xSlW2T6gArVjSIH0HqAazFACgawQLAJAdzz77bMEzEXr06BG33nprfOYzn2nzmG7dusXuu+8eu+++ezQ1NVWjzA7pOQUgtSx9BABArXNPXHmWtS2OZZKha5qamuKkk04qCAauuuqqdgOFtdXXp2OOgFABoJPceELXmKUAAOXhmgoA6ffLX/4ynnrqqZbtT3/603HiiScmWFHnCRWAdRh9AAAA2SJYyDezFSrPoDGg0q666qqC7fPOOy+hSrpOqAAAVJ2ODwAAyB6DEKFzZsyYEQ899FDL9siRI+NTn/pUghV1jVABgFQyGgsAoDRC+3xzfwyQXQ8++GDB9qc//emoq6tLqJquEyrAWpY0+FrQMVNjofN0eABA5bjOQudp5wGV8vjjjxdsf+ITn4iIiObm5rj//vvjxBNPjK222io22GCD6NevX2y66aaxzz77xCWXXBIzZ85MoOL26T0FAAAAyACzFUgDSyBB6aZOnVqwPXbs2Jg5c2bss88+se+++8YNN9wQzz//fPzzn/+MxsbGeP311+NPf/pTnHvuufHRj340/u3f/i0aG9MTfAoVgAJuDkgDjaX8MnoSACrP9RYA0uXNN98s2G5sbIxdd901HnjggQ6PXblyZVx55ZWxxx57rPM+SalPugAAAACgvPYe9EI8sGDLpMugAsYOeyuenzs06TJyq354YzTN6Zt0GUAFzJgxo+RjBg8eHEOGDOnyZy9cuLBg+8QTT4wFCxZERES/fv3ilFNOiQMPPDBGjBgR7733Xjz77LNx3XXXxV/+8peWY55++uk46qij4qGHHooePXp0uaauECoAAFVh1CQAAORD44jV0XeWBVDIlsMPP7zkYyZMmBATJ07s0ucuX748li9fXrBv1qxZERGx1VZbxT333BObbLJJwc932mmnOPHEE+NHP/pRfOMb32jZ/+ijj8YPfvCD+O53v9ulmrpKqABQIg/vqixLHwEAlIfZCtA5ZitQy15ZMCh69en6yPw0WL6gLukSIiJi1apVre7fYIMNWg0UPuzss8+O2bNnx49//OOWfT/+8Y/j61//evTv37/stRZLpAgAAAA5ZaZgPhmIA5Adffv2jW7d1u2GP+uss9oNFNa48MILY4MNNmjZfuedd+Luu+8ua42lMlMBPmRJg5wNoBJ0aAAAQL5YAomsmTRpUowePbqkYwYPHlyWz+7Xr18sXry4YN/xxx9f9LFHHnlkXH/99S37Jk+eHEcffXRZausMoQLQonHE6qRLAAAAyswySPnkgc2VZQkkyJ/Ro0fH1ltvnchnDxgwoCBUGDp0aIwcObLo4z/+8Y8XhArPP/98OcsrmTgRoASep1BZpnHnk1kKAAAA1LKPfvSjBdsbb7xxSccPHz68YPvtt9/uck1dIVQAAACAnBPy55NBOSTNigdQnLVnSPTq1auk49d+/bJly7pcU1cIFQCAitGBAQDp4boMpTFTHSiX7bbbrmB74cKFJR2/9us32mijLlbUNUIFAFLBKCsAACid+2iA9DvwwAOjrq6uZfuVV14pabbBP/7xj4LtESNGlK22zhAqABFhyiJQfkZDAkD6uD5DacxW6Jj+BOjY8OHD4xOf+ETL9sqVK+NPf/pT0cffc889Bdv/8i//UrbaOkOoAP9nSYOvA+1zMwkAAABAZ5x44okF25deemlRxz388MPx+OOPt2x369YtDjrooLLWViq9qAAkzpTt/DEKEgDSy3U6f9xPA6TfiSeeGGPHjm3ZfuCBBzoMFubNm7dOGPHZz342Nt9884rUWCyhAgAAANQYwQIUz6z1jlkCCTrWvXv3uPzyy6Nbtw+65M8+++w444wz4t13313n9ffff3/svvvu8fLLL7fsGzhwYFx88cVVqbc9QgUAoKx0UgAAVJ/ZCgDpt++++8bll19esO8nP/lJDB06NPbcc8/4/Oc/H4cffniMHDky9t1335gxY0bL63r27Bm33XZbjBo1qtplr6M+6QIAssDIFAAA8mbvQS/EAwu2TLoMAKgpp512WnTv3j2+8Y1vRGPj+/1NK1eujIcffrjNY4YOHRp33nlnjBs3rlpltstMBcA0RRJlRFW+mKUAANni2p0v7q0rx0CzjulbgOJ97Wtfi7/97W/xhS98IdZbb702Xzds2LCYOHFiTJ8+PTWBQoSZChAREUsa5GsAAAAAQHVsvvnmcfPNN8fSpUtjypQpMWvWrJg7d2707NkzBg8eHNtvv31st912SZfZKqECAAAA1DDLIAFAcvr06RP77LNP0mWUxPBsAKAsLJ8AAJA8SyBVjiWQOmYJJKgNQgWADrhxrBwNHgCAdDA4AAAollABAOgyHREAAOlh8E7lGHQGIFSAmmdqIgAAEGGQAABQHKECAIkweio/dEAAQH64rueH+22SYvAi5J9QgZq3pMHXAAAAACiOJZCAWqc3FaAdbhYBAKg1ZisAAO0RKgAAnabTAQAgvSyBRFIsgQT5JlQAoOo0bgAA0s3AAWifWe1ALRMqQA0zcgDoCp0NAADpZ0APAOUmVAAAAADWYQAB0BUGMkJ+CRUA2mA6K7RNJwMA1AbX/HwwW6EytBmBWiVUAKCqNGgAAAAAsqs+6QKS9u6778Zzzz0XL730UrzzzjuxbNmyGDBgQAwePDh23nnn2HzzzZMukQpa0iBXAwAAaM/eg16IBxZsmXQZQAY1jlgdfWfpe4G8SW2o8Morr8QTTzwRU6dOjSeeeCKeeuqpWLx4ccvPN91005g5c2bJ77ty5cp44IEH4ve//31Mnjw5nnvuuXZfP3z48PjSl74Up556agwbNqzkzyvV5MmT41Of+lSnj+/s3wsAFMsyCAAA2TN22Fvx/NyhSZeRO/XDG6NpTt+kywCoqlSFCpMnT47vf//7MXXq1HjnnXfK/v6PPfZYHHjggfHuu+8WfcycOXPiwgsvjJ/+9Kfx05/+NL7whS+UvS5IggcmAQAAxTJbAQBYI1WhwjPPPBP33ntvxd5//vz5rQYKPXv2jG233TaGDRsWG2ywQbz99tsxderUePvtt1tes3DhwvjiF78Y8+bNi7POOqtiNQLp4IFbleF5CtlnlgIAQHaZrQBAOaQqVGhLr169YsSIEfHyyy+X7T379+8fn/3sZ+PYY4+NcePGRZ8+fQp+3tzcHJMmTYqvf/3r8frrr7fsP/vss2PbbbeNfffdt2y1tOeMM86Ir3/960W/vr4+E/+kAAAAZIzZCtA6SyC1z3MVIH9S1wPdo0eP2HrrrWOXXXaJXXfdNXbZZZfYdtttY8qUKV161sAaQ4YMiW9961txyimnRL9+/dp8XV1dXRxxxBGx5557xr/8y7/E888/3/Kz008/PaZNmxZ1dXVdrqcjAwYMiJEjR1b8cwAAAKAjggUAIFWhwvjx4+OUU06J3r17V+T9d9ttt3jllVfaDRPWttFGG8Vtt90WO+20U6xe/f4a9C+88EJMnTo1dt1114rUCQBpZOkjAIDsswQSAF2VqrlHAwcOrFigEBExePDgkgKFNbbffvvYY489CvY9+OCD5SqLhCxpSNWvP+Se5ykAAOSDgQawLs/la1/jiNVJlwCUkV7VIu24444F23PmzEmoEqDS3AzCunQeAADkhwE/AHSFUKFIaz8AecWKFQlVAl1nhAAAANAVBhwAQO0SKhRpxowZBdsbb7xxQpUAAAAAkDZmvbfPAEfID6FCEf75z3/GfffdV7DvYx/7WFU++8EHH4wjjzwyNttss+jfv3/06dMnGhoaYuedd47TTjstfv3rX8fKlSurUgtAZ5lenW1GIgIArXGPkG3u0QHorPqOX8JVV10VjY0fpM0bbLBBfOpTn6rKZ//5z39eZ9+cOXNizpw58dRTT8UVV1wRI0aMiG9/+9tx6qmnRl1dXVXqAgAAAACg9pip0IGZM2fGhRdeWLDvjDPOiJ49eyZU0bpmzZoVp512Wvzrv/5rLFy4MOlyAAAAqBFmK2Sb2QrlZwmk9lkCCfLBTIV2rFixIj73uc/F4sWLW/aNHDkyvvWtb1X8s9dff/3YZ5994pOf/GRsvfXWMWTIkOjTp0+8++678eKLL8Z9990Xt99+eyxbtqzlmD/84Q9x+OGHx7333lvW0GPevHkxf/78ko5Z+xkUkBVuAKGQjgIAAADgw4QK7fjyl78cjz/+eMt29+7d48Ybb4x+/fpV7DOHDRsW119/fRxzzDHRu3fvVl+z6667xnHHHReXXHJJnHTSSXH33Xe3/Oyhhx6Kb3/723HppZeWraYrr7wyzj///LK9XxosaTBJB6rF6CcAgHzbe9AL8cCCLZMuAwCoEj2rbfiP//iPuPnmmwv2ff/7348999yzop+75ZZbxgknnNBmoPBhw4YNiz/84Q9x9NFHF+y/4oor4tVXX61UiWScqYZAscxSAADIP4OAys8MeCDvhAqtuOyyy+Kiiy4q2HfWWWfFN7/5zYQqaltdXV3ccMMNsfHGG7fsW7FiRVx77bUJVgUAAEAtMRgBKJbBjpB9lj9ay9VXXx1nnXVWwb6vfe1r8aMf/SihijrWt2/fOP300+Pcc89t2XfPPfesE4x01qmnnrrObIiOzJgxIw4//PCyfD4AAABQOWOHvRXPzx2adBkAZIRQ4UNuvvnmOOWUU6K5ubll34knnhhXXHFFglUV54ADDigIFf7+97+X7b2HDBkSQ4YMKdv7QVqZolp+plJnl9GGAECpPFsBPlA/vDGa5vRNugyAirD80f/5xS9+ESeeeGKsXv3BFKzjjjsurrnmmqirq0uwsuKMHDmyYHvFihWxaNGiZIoBAAAAgDZYAgmyTagQEb/+9a/ji1/8Yqxatapl39FHHx033nhjdOuWjb+iPn36rLNv6dKlCVQCAABArTLbMbvMMgagWNnoMa+g3/3ud/H5z38+mpqaWvYdfvjhceutt0b37t0TrKw0CxYsWGffRhttlEAlAGSdzgAAAOg6S+wCeVXTocJdd90VRx99dKxcubJl38EHHxy333571Ndn63ETjz32WMH24MGDo0ePHglVk25LGmr31970QqrJSCcAgNpkgAIA5FvN9q7ed999cdRRR8WKFSta9u23337x61//Onr27JlgZZ1z6623FmzvtddeyRQCAABAzRMsZJOBQVSTgY+QXdkajl8mDz30UBx22GGxbNmyln177713TJo0KXr16pVgZZ0zefLkuPPOOwv2HXbYYQlVA9lkWiq8TwcA1J6D+k+ryufctWSrqnwOAKRJ/fDGaJrTN+kyAMqq5kKFRx99NA455JCChxjvueee8fvf/77Vhx13xcSJE+P8889v2f7kJz8ZkydPbvP19957bwwdOjS23377oj/jsccei6OOOiqam5tb9o0ZMyY+97nPdapmAADypVqhQUfaq0PgAPm096AX4oEFWyZdBiUaO+yteH7u0KTLACDFUhcqzJo1q+ChyWvMnTu3YLupqSlmzpzZ6nv0798/Bg0atM7+p59+Og488MBYsmRJy74xY8bEFVdcEfPmzSupzt69e8ewYcNKOqYjjzzySFxwwQWx3377xTHHHBMHHXRQDBkypNXXvvHGG/GTn/wkLr/88oJnQvTo0SOuvPLKzD0TAoDkmaUA+ZCWEKEUrdUsaACA/GscsTr6zqrZ1dkhs1LX87zHHnvEa6+91uHrZs+eHaNGjWr1Z+PHj48bbrhhnf2//e1vY9GiRQX7pk+fHttuu23JdXY066Czmpub449//GP88Y9/jIiIhoaGGDNmTAwYMCD69OkTixYtihdffDFefPHFdY7t3r17XHfddbH33nuXvS6AUliLFaB6shgiFEPQAPlgtgJYAgnIn9SFChSaPXt2zJ49u8PXbbbZZnHTTTfF7rvvXoWqAABISl5DhGJ8+M8uYACoHEsgAdAeoUKKHHrooTF//vx4+OGHY9q0abFq1ap2X19fXx8f+9jH4qtf/Wp87nOfy+RDpqmexhGrky4BSDFLH0G61XKQ0Ja1/06EDJBeZisA7bEEEmRP6kKFtp6TUA4TJ06MiRMnVuz9u/p5O+20U+y0004REbFs2bKYNm1avPbaa/Hmm2/G4sWLY+XKldG/f/8YOHBgjBo1KnbZZZfo29f0Oeiq+uGNSZcAAOsQJJTGLAYA0swSSECepC5U4H29e/cuCBkojyUNkm+oNM9TAOgaYULXCRggfcxWyB5LIAHQFqECANQ4Sx9B8gQJlbPm71a4AAAA5SFUAACAhAgTqsfsBYDSma1QXpZAapvnKkC2CBUAAKCKBAnJM3sBkmEJJADIB6ECANQwSx9B9QgT0sfsBQAAKJ15RVADGkesTrqE1Kof3ph0CbniIc0A6zqo/zSBQgb4d4LqMKAhe9zjl5c2KJAHZioAAEAF6KDOJksjAUAyPFcBskOoAAA1ykhBqAxhQj4IF6ByPFsBALJN/AcAAGUiUMgfyyIBWAIJgEJCBWrGkga/7lBJGhpALdPxnH/+jaG8zJiklnmuQts8ExKywfJHAFCDNOShPHQy1x7LIgEAUOsM3QZqltEhAHSFQKG2+feHrjPIIVvMTAZgDTMVAACgBDqTWcOsBQA6q354YzTN6Zt0GQCdYqYC5Jz1CIG1GRUInWNNfdridwM6z30JsDb9GJB+QgUAusxUaCDvdBhTDL8nQN657wcgQqgAAABtMgKdUvmdgdKZrUCt8pw/IKuECgAA0Aodw3SFcAHIK7MVqAZLIEG6CRWAmmRECLXKSEAojs5gysXvEhTHPQoAZIdQAQAAPkQnMOVm1gIAbTHgDcgioQI1YUmDX3WoFNOfgbzQ8Uul+f0C8kIbAKC26WkFgBphWQFom85eqsXvGrTNvQrwYZ6rAOklVIAccwEGgI7p5KXazIoBACDLhAoAANQkHbskze8frMtsheywBFL5eK4CkDVCBQCoARroUEhnLmnhdxEAgKwRKgA1xyiQ8jE6CcginbikjVkzUMhgCGANyzpDOgkVAACoGTpuSTO/n0DWGGRUPga/AVkiVAAAoCbosCULzFqA95mtAADpJVQAgJzTKAeBAtnjdxYAgLQSKgAAkGs6Z8kqv7tAFlgCqXwsgdQ6z1WA9BEqkHtLGvyaA0Ct0ilL1vkdppaZbQkA6aS3FXJKkk+lGZGUDRrj1Crr0pMnfpcBAEgToQJQU0wnBcg/HbDkkd9rapUBEtlgwBGVZuAkpItQAQCA3NDxSp6ZgQOQfwbCAVkgVAAAIBd0tlIr/K5Ta8xWAIB0ESoAQE5pgFNLdLJSa/zOA2ljCSSA2iFUAKBkGgxAmuhcpVb53QfIJ0sgtc5zFSA9hAoAAGSWTlVqne8AtcIMTABID6ECAOSQhje1QGcqvM93AUgLM5oBaoNQAQAAIOMEC9QCgyYAIB2ECpBD1hlsnXUpAfJDByqsy/cCID+0X1unvwPSQagAAECm6DiFtvl+kHdmK6SfJZAA8k+oQK4tafArDuWmkZB+GtvkmQ5T6JjvCQAAlaTHFQCATNBRCsXzfQEAoFKECgAApJ4OUiid7w15ZVZm+pndXB6eq9A6z1WA5AkVAABINR2j0HkH9Z/mOwQAQFkJFQAgR4zcI290hkJ5+C6RN+55ACA5QgUAAIAaIFgAqskSSOVhCSQgjYQKQE1wI1YeGgZANekAhfLzvQIgDzxXgSyaOHFi1NXVdfq/E044Iek/QguhAgAAqaPjEyrH94u8sAQSACRDqAA5I62H2qVhTV7o8ASAfDDTGSCf6pMuAAAA1hAoQHUc1H9a3LVkq6TLgC7be9AL8cCCLZMuAyqqfnhjNM3pm3QZQJnddttt8fGPf7zo1/fv37+C1ZRGqAAAAFCDBAsAZFnjiNXRd5ZFWMiuYcOGxciRI5Muo1N88wAASAWzFKD6fO8AACiVUIHcWtLg1xvKyXqo6eZ5CmSdjk1Iju8fWec+KN20IwDyR68rAACJ0qEJyfM9BEi3+uGNSZcA0EKoAOSemy8AgI4JFsgysxWgNjWOWJ10CVCThAoAACRGJyaki+8kUAmWQALIF6ECAGSckXlklc5LSCffTYB0Mgsf8uWqq66KffbZJxoaGqJ3796x3nrrxciRI+OTn/xkfOc734mHH3446RLbJFQAAAAAMs9ACwCy5Be/+EX86U9/ijlz5sTy5ctjyZIl8dprr8Wf//znuPjii2PPPfeMXXfdNe6///6kS11HfdIFAJB+pisD5WYkNKTbQf2nxV1Ltkq6DCBHxg57K56fOzTpMsihxhGro+8s46bp2IwZM0o+ZvDgwTFkyJAKVFOcqVOnxn777RfnnntuXHTRRVFXV5dYLR8mVIAc8YAiALJAoADZIFggi/Ye9EI8sGDLpMsAIIUOP/zwko+ZMGFCTJw4sax1NDQ0xEEHHRQf+9jHYuzYsbHhhhtGt27d4u23346nnnoq/vd//zf++Mc/try+ubk5Lr744li9enV8//vfL2stnSVUAIAMM82frBEoQLYIFgDSpX54YzTN6Zt0GeTYqnm9o6l7Pn7HVs3rnXQJBT72sY/FH//4x9h3333bnHEwbty4OO2002Lq1Klx7LHHxksvvdTys0suuSQ+/vGPx2GHHVatkttkbhAAAABtEgYC5WJZVaCWHXTQQbHffvsVtYTRLrvsEn/961/jox/9aMH+b3/727Fq1apKlVg0MxUAAKgKHZOQXWYskCWWQAKgNZMmTYrRo0eXdMzgwYMrVE3HNtxww7jttttil112iebm5oiIeOGFF+LBBx+MffbZJ7G6IoQKQM7VD29MugQAQqAAAEDleFgzxRg9enRsvfXWSZdRkp122in222+/gmcs3HPPPYmHCr5tAAAAdEg4CJAOBs9BbTnggAMKtv/2t78lVMkHhAoAtMu6p+nlIc1khY5IyA/fZ7LCfVJ6aV8AlGbkyJEF2/Pnz0+mkA8RKpBLSxr8agNAGuiAhPzxvQYAqJ4+ffoUbC9dujShSj6g5xUAAICSCBbIArMVoLY0jliddAlQEQsWLCjYHjRoUEKVfECoAABAReh0BABaYwmkrvNcBagdjz32WMH28OHDE6rkA0IFAMggI+8ASJrgEACgspYtWxZ33nlnwb699tormWI+RKgAAEDZ6WyE2uC7TtoZiAFAlv3gBz+I2bNnt2x37949Dj744AQrep9QAXLC2oFUgmnJQGfoZITa4jsPdIa2BpWgb4S0uvnmm+Ott0o771199dVx/vnnF+w74YQTYtNNNy1naZ0iVAByyxqTAAAA5JU2L2THtddeG6NGjYrx48fHH/7wh3jvvffafO3UqVPjyCOPjJNPPjmam5tb9jc0NMRFF11UjXI7VJ90AQAA5IcRy1CbDuo/Le5aslXSZUCr9h70QjywYMukywCgxi1dujRuuummuOmmm6Jbt26xxRZbxMiRI2ODDTaI7t27x9tvvx3PPvtsqzMaNtxww7jnnnti2LBhCVS+LqECAGSMtYEBSCPBAgBAcVavXh3Tp0+P6dOnd/jaT3/603HDDTfEiBEjqlBZcSx/BABAWZilADgPAKXwXIWuswTSujxXgTQ644wz4thjjy36eQj9+vWLI444Iu6///64//77UxUoRJipAABAGehIBCDNLIEEQJKOOOKIOOKIIyIiYuHChfHcc8/FG2+8EW+99VY0NjbG6tWrY8CAATFw4MAYO3ZsbLfddtG9e/eEq26bUAEAAICysQwSAEDbBgwYELvvvnvSZXSJ5Y8AAOgSsxSAtTkvkEaeS5VOlkACyB6hAgCtcnOfThrDAGSFYAEAIJ+ECgAAdJpOQwCAZHlY87qWDfWwZqgkoQK5s6TBrzUAAKSB4JG0MesTALpO7yuQS0ZqAFSezkKgGM4VQEcsvQqQLUIFAAAAAACgKEIFyIHGEdYKhFpguj5pYuQxUArnDNLEPRV5ZLY+UE1CBQAASqJzEOgM5w4AgHwQKgAAAACQKM9VAMgOoQIA63BDD7TFSGOgK5xDSAtLIAFA5wkVAAAAqBrBAkBleK4CUC1CBQDIAKPpSAMdgQBAJZkxDZANQgUAAACqSkhJGhi0AQCdI1QAAACg6gQLAADZJFQAAKBDOv8AANLPcxWAahAqALnjJgoAIBsEliTNEkjp47kKAOknVACAlNPYJWk6/YBKco4BAMgWoQIABYwMAgAAAKAtQgUAANpkBDFQDc41JMmsUPLGksBApQkVAAAAAEgNs6cB0k2oABnXOGJ10iUAkFNGDgPV5JwDAJANQgUAAACgplkCCQCKJ1QgV5Y0+JUG8kUDl6QYMQwkwbkHWMMSSADppQcWAACA1BAsAHSdhzUDlSRUAACggA49AGqRGaIAUByhAgAAAKki3AQASC+hAgAtrFsKAACkhfYJQDoJFYBcsW4keWIKPkkwOhhIC+cjkuD+izzRPgYqpT7pAtJi5cqVMWXKlHj99dfjzTffjP79+8fw4cNjxx13jJEjRyZdXixcuDAeeeSRmD17dixYsCAGDRoUDQ0NMW7cuBgwYEDS5QEAAJTdQf2nxV1Ltkq6DAAAPiS1ocIrr7wSTzzxREydOjWeeOKJeOqpp2Lx4sUtP990001j5syZXf6c+fPnx4QJE+L222+Pd955p9XXjBs3Ls4666w46qijuvx5pXr66afjggsuiLvuuitWrFixzs979eoVBx54YEyYMCF22GGHqtcHAOSHUcEAAAB0JFXLH02ePDn233//2GijjWLzzTePY445Jn74wx/GQw89VBAolMvdd98d22yzTfzP//xPm4FCRMQjjzwSn/nMZ+ILX/hCvPfee2Wvoy2XXHJJ7LbbbjFp0qRWA4WIiOXLl8ekSZNit912i//8z/+sWm0AAADVIPCk2iyBlC6eqwCQPqmaqfDMM8/EvffeW5XPmjx5chx++OEFnfV1dXWx0047xWabbRYLFy6Mp59+OhYsWNDy81tuuSX++c9/xqRJk6Jbt8rmMRdffHF85zvfKdjXp0+f2HXXXWPjjTeOOXPmxBNPPBHLli2LiIgVK1bEOeecE3V1dfHNb36zorUBAPmj0w4AIH/qhzdG05y+SZcB5EyqZiq0pVevXrH55puX7f1mzZoVRx55ZEGgsPvuu8dzzz0XU6dOjTvuuCPuvffemDVrVlx++eXRo0ePltf9/ve/j+9+97tlq6U1//u//7vOZ5x88snx+uuvx0MPPRS/+MUv4s9//nO8/vrr8eUvf7ngdeecc07cc889Fa0PAACgmgSfAADpkbpQoUePHrHDDjvEl7/85bjqqqviySefjMWLF8c111xTts+YMGFCvPvuuy3b48aNi/vvvz/Gjh1b8LpevXrF6aefHnfccUfB/ksvvTRee+21stXzYatWrYpvfOMb0dzc3LLvzDPPjKuuuioGDRpU8NrBgwfH1VdfHV//+tdb9jU3N8fZZ58dq1atqkh9AAAAAADUrlSFCuPHj49//vOf8fTTT8fVV18dJ598cuy0004FMwW66qWXXoobb7yxZbtnz55xww03RO/evds85vDDD4/x48e3bC9fvjzOP//8stX0YTfddFNMnz69ZXvMmDHx/e9/v91jLrnkkhgzZkzL9rRp0+KWW26pSH0AVIe1fKkmI4CBLHCuoprci6WL5yoApEuqQoWBAwe227lfDrfeemvBKP4jjzwytthiiw6PO+eccwq277jjjpbnGZTTTTfdVLB95plnRq9evdo9plevXnHGGWe0+z4AAABZJ1gAAEheqkKFavjNb35TsH3iiScWddzYsWNjt912a9l+7733yv5Q6bfffjsefvjhlu2ePXvGscceW9Sxxx13XMGMjoceeijeeeedstYH5JvRP1CbdNABAORb/fDGpEsAcqamQoW5c+fGs88+27JdX18fu+++e9HH77XXXgXbd999d7lKi4iI++67r2AWxc477xzrrbdeUceuv/76sdNOO7VsNzU1xX333VfW+gAAAJImDKVaLIEEAK2rqVDhH//4R8H2dtttF/369Sv6+HHjxhVsP/fcc2Wpa4216/vEJz5R0vGVro/0aRyxOukSAAAAoOLMrAZIj5oKFaZNKxzRMnr06JKO33zzzdt9v65Ke30AQL4Y7QtklfMXAEByaipUmDFjRsH2Rz7ykZKO33TTTQu233777Xj33Xe7XNcaXa1v7de/9NJLXa4JgOoz1R4AIB3cl5EXnqsAlFN90gVU08KFCwu2hwwZUtLx/fv3j969e8eyZcta9i1atCgGDhxYjvK6XN/ar1+0aFFXS4qIiHnz5sX8+fNLOmbtgASqwU0SAEDtOKj/tLhryVZJlwEAUHNqKlRYsmRJwXafPn1Kfo8+ffoUhAqLFy/ucl1rdLW+tV9frtquvPLKOP/888vyXgBAOlg6BADImrHD3orn5w5NugyAmldTyx+t3Wnfu3fvkt9j7Y77td+zK7paXyVrAwAASBsBKdVgCSQAKFRTocLa6urqqnJMZ5X6WdWsDQDILp1wAAAAdFZNLX/Uv3//gu2lS5eW/B5rH7P2e3ZF//79Cx78XGp9lart1FNPjaOPPrqkY2bMmBGHH354WT4fAACgLZ6tAFCc+uGN0TSnb9JlADkgVChRLYYKQ4YMKfmh0QAAAAAA5E9NLX+0wQYbFGzPnz+/pOOXLFmyTsf9gAEDulpWi67WN2/evILtctaWBUsaaurXGcpq7LC3ki6B/2PNXirN0kdAHjm3UWnu0dJD2wUgeTXVC7vFFlsUbL/22mslHb/26zfccMMYOHBgl+tao9z1rf1+AAAAAADQFTUVKowdO7Zge8aMGSUd/8orrxRsb7VVedftLHd9a78fAABAXpmtAABQHTUVKmyzzTYF23/729+isbGx6OOnTJnS7vt11drv9+ijj5Z0fKXrAwCyTYcbAHSeJZDIg/rhxfeDAbSlpkKFjTfeOLbbbruW7aampvjLX/5S9PGTJ08u2D7wwAPLVVpEROy7777RvXv3lu0nn3wyFi9eXNSxixcvjqeeeqplu76+Pvbdd9+y1gcAAJBmwlOoDZ6rAJCsmgoVIiKOOOKIgu3rr7++qONeeOGFeOyxx1q2+/XrF/vtt19Zaxs0aFDsscceLdsrVqyIW2+9tahjb7nllli5cmXL9p577hkbbrhhWesDAAAAAKC21VyocNxxxxXMBrjzzjvjpZde6vC4H/zgBwXbn/3sZ6N3795lr+/4448v2P7xj38cy5cvb/eY5cuXx2WXXVawb/z48eUuDQDIMKN3gVrhfAcAUFk1FypsscUWBR3uK1asiBNOOCGWLVvW5jG//e1v44YbbmjZ7tmzZ0yYMKHDz5o4cWLU1dW1/LfXXnt1eMz48eNjzJgxLdvTp0+P8847r91jzj333Jg+fXrL9lZbbRXHHXdch58FAAAAFM9zFQAghaHCrFmzYubMmev8N3fu3ILXNTU1tfq6mTNnxoIFC9r9jPPPPz8GDhzYsv3II4/EPvvsEy+8UHhzsHz58vjpT38aRx99dMH+s88+OzbddNMu/klb17179/jhD38YdXV1LfsuvfTS+OpXvxpvv/12wWsXLFgQJ598cvz4xz9u2VdXVxc/+tGPCmZjAJANGqkAUB5mK0D+ea5C53lYM9BV9UkXsLY99tgjXnvttQ5fN3v27Bg1alSrPxs/fnzBzIK1jRgxIu68887Yf//9Y8WKFRERMWXKlNhqq61i5513js022ywWLVoUTz31VMyfP7/g2EMOOSQuvPDC4v9AnXDIIYfERRddFN/5znda9v3sZz+Lm2++OXbbbbcYNmxYvPnmm/H444/H0qVLC4695JJL4oADDqhofQBAtuhcAwAAoFxSFypUy1577RW/+c1v4oQTTmgJDpqbm2Pq1KkxderUVo/5/Oc/H1dffXVVZgGcd955UVdXFxMmTGh5APPSpUtj8uTJrb6+R48eceGFF8a3vvWtitcGAACQdgf1nxZ3Ldkq6TIAAHIndcsfVdNBBx0U//jHP+KUU04pWA5pbR//+MfjV7/6Vdx6663Rr1+/qtV37rnnxmOPPRaHHXZY9OzZs9XX9OzZMw477LB4/PHH45xzzqlabZA2pm8CAADVYMlKAGpd6mYqzJw5s6qfN2TIkPif//mfuPzyy2PKlCnx2muvxdy5c6Nfv37R0NAQO+64Y5vLLHVk4sSJMXHixC7Vt+OOO8akSZPi3XffjUceeSRmz54db7/9dmy00UbR0NAQ48aNazcQAeiItUgh3yx9BNQysxUAAMovdaFCUnr27Bmf+tSnki6jTQMHDoyDDz446TIAAAAAUmHssLfi+blDky4jk+qHN0bTnL5JlwFkVE0vfwQAAABQKksgAVDLhAqQUY0jViddAgAApJ5l4AAAykuoAAApYLQblaAjDQAAgHITKgAAAJBrQlbIr7HD3kq6BICaI1QAAAAAKJGZpmRd/fDGpEsAMkqoAACQQ0blAhRyXgQAKA+hAgAAAAAAUBShAgAAADXBbAUAgK4TKgAA5IxOMwCoDs9VSAcPawaoLqECAAAAANQgD2sGOkOoAAAAQM0wmwsAoGuECgCQMNPmAQAAgKwQKgDUMGuPQv4YgQvQMedKyskAkXTQtgGoHqECAAAAAABQFKECAAAAANQoD2sGSiVUAAAAoOZYAgkAoHOECgAAOaGDDACS4bkKANQSoQIAAAA1SRgL+eJhzQDVIVQAAAAAAACKIlQAAAAA6CJLIJFlHtYMlEKoAACQA5bwAOgc508AgNIIFYDMM6KCLDOiDQAAAMgSoQIAAAA1zWwFyA8PawaoPKECAAAAAABQFKECAEDGGWELAOlgaUsAaoFQAQAAgJonoAVqnecVAsUSKgAAAAAAAEURKgAAAECYrQB54WHNAJUlVAAAAAAoE89VACDvhAoAABlmVC0AAADVJFQAAACA/yOsBWqZhzVDso455pioq6sr+G/kyJFJl7UOoQJAjbLOKAAAAEA6/O53v4vbb7896TKKIlQAgIRYbxcAIJ/c5yXPICogSxYuXBhf+9rXki6jaEIFAICMskQHQGU4vwIA1XT22WfHnDlzIiJivfXWS7iajgkVAAAAAAAgAffff39cd911ERFRX18fF1xwQcIVdUyoAAAAAAAAVfbee+/FV77ylZbts846K3bYYYfkCiqSUAEAAADWYgkkuspzFciq+uGNSZcANePcc8+NmTNnRkTEZpttFhMnTky0nmIJFQAAAADIHQ9rBtLskUceiSuuuKJl+6qrroo+ffokWFHxhAoAABlkBC1A5TnXAgCVsHz58jjppJNi9erVERExfvz42GeffRKuqnhCBQAAAAAAqJKJEyfG9OnTIyJi8ODB8aMf/SjhikojVAAAAAAAgCp46qmn4oc//GHL9mWXXRYbbbRRghWVTqgAAAAAbbAEEl3hYc0AfFhTU1OcdNJJ0dTUFBERBxxwQBx77LEJV1W6+qQLAAAAAIBKGDvsrXh+7tCky8ic+uGN0TSnb9JlQFnNmDGj5GMGDx4cQ4YMKVsNl1xySTz77LMREdGvX7/4n//5n7K9dzUJFQAAMsaoWQAAgNIcfvjhJR8zYcKEmDhxYlk+f9q0aXHRRRe1bF944YUxcuTIsrx3tQkVAAAAoB0H9Z8Wdy3ZKukyAKDier/VLXqvyseK+d0WpOfPsXr16vjSl74Uy5cvj4iInXfeOU4//fSEq+q89PzNAgAAAABAzlx++eXx17/+NSIi6uvr45prronu3bsnXFXnmakAAAnw0D4AgNqw96AX4oEFWyZdBkDNmzRpUowePbqkYwYPHtzlz33llVfiu9/9bsv2WWedFTvssEOX3zdJQgUAAADogCWQACDbRo8eHVtvvXVVP7O5uTm+8pWvRGNjY0REbLbZZmV7RkOSLH8EAAAAQG6NHfZW0iVkUv3wxqRLgMy7+uqr44EHHmjZvuqqq6JPnz4JVlQeZioAAGTIQf2nJV0CAAAARZgwYULL/x900EExevTomDlzZrvHzJ07t2C7qalpnWOGDx8ePXv2LFeZJRMqAAAAAFSQ5yoA1KalS5e2/P9dd90Vo0aNKvk9Zs+evc5xTz/9dKLPZbD8EQAAABTBbDEAAKECAAAAAABQJKECAAAAAACU2cKFC6O5ubmk/x588MGC99h0003XeU2SSx9FCBUAAACgaJZAgmwaO+ytpEvIpPrhjUmXAKSQUAEAICN0ZAFAdu096IWkSwCAshAqAAAAAAAARREqAAAAQAnMHAMAaplQAQAAAAAAKIpQAQAAAIDc87BmgPIQKgAAAECJLIFEZ3hYMwAd2WuvvaK5ubnlv5kzZyZd0jqECgAAAABAq+qHNyZdApAyQgUAgAwwIhYAAIA0ECoAAAAAAABFESoA1CAPKAMA6DqzyACAWiRUAIAq84A+AIDa5V4wWQZYAXSdUAEAAAAAACiKUAEAAAA6yRJIQC2oH96YdAlAiggVAAAAAACAoggVAABSzihYAAAA0kKoAAAAAAAAFEWoAAAAAF1gRhml2nvQC0mXAACdJlQAAAAAoGaMHfZW0iUAZJpQAQAAAAAA+P/bu/P4qqq7X/zfkAASIgKGQWIrCig4PaJoFa1aVFC0irMVq9XaPnVovfa21f7aW4dWrW2vbW3tvfaps9ZavWqtA1YBpyLUqWoFZBAHgowOEOYk5/eHjyknYThJzsk+w/v9euWPvdh7nw8556y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      "text/plain": [
       "<Figure size 1920x1440 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_temp, y_temp = np.meshgrid(np.linspace(-10,10,100), np.linspace(0,20,100))\n",
    "plt.contourf(x_temp, y_temp, c(x_temp, y_temp))\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we write gradient ascent, we will need the gradient function. This could also be defined using the numerical derivatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def c_grad(x,y):\n",
    "    dfdx = 0.15 - 0.1*x - 0.007*y\n",
    "    dfdy = 0.22 - 0.032*y - 0.007*x\n",
    "    return np.array([dfdx, dfdy])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use vector norm to measure error in gradient\n",
    "from scipy.linalg import norm\n",
    "\n",
    "def gradient_ascent(f_grad, x, y, alpha=0.01, tol=1e-8):\n",
    "    err = 9999\n",
    "    errors = []\n",
    "    \n",
    "    while err > tol:\n",
    "        grad = f_grad(x,y)\n",
    "        x = x + alpha * grad[0]\n",
    "        y = y + alpha * grad[1]\n",
    "        err = np.abs(norm(grad,2))\n",
    "        errors.append(err)\n",
    "    \n",
    "    return x, y, errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of minimum: x=1.0346, y=6.6487, c(x,y)=8.5089\n",
      "Iterations: 54405\n"
     ]
    }
   ],
   "source": [
    "x, y, errors = gradient_ascent(c_grad, 5, 15)\n",
    "print('Estimate of minimum: x=%0.4f, y=%0.4f, c(x,y)=%0.4f' % (x, y, c(x,y)))\n",
    "print('Iterations: %d' % len(errors))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial point $(x_0,y_0)$ should not matter for this problem, because it looks concave. The local maximum will be the global maximum. Our function converges to what looks like a reasonable point, based on the contour plot. However, it takes quite a few iterations to get there. This is sensitive to the choice of $\\alpha$. For example, $\\alpha=10$ will converge in ~50 iterations instead.\n",
    "\n",
    "Can we do better with Newton's method? First we have to define the Hessian for the two-dimensional problem. This is the analytical version, which we would probably not do for more complex problems. Instead finite differences or another approximation could be used. For this problem the function $c(x,y)$ is quadratic, the Hessian contains constant values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def c_H(x,y):\n",
    "    d2fdx2 = -0.1\n",
    "    d2fdy2 = -0.032\n",
    "    d2fdxdy = -0.007 # equal to d2fdydx\n",
    "    return np.array([[d2fdx2, d2fdxdy], [d2fdxdy, d2fdy2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.linalg import inv # matrix inverse\n",
    "\n",
    "def newton_multivariate(f_grad, f_H, x, y, tol=1e-8):\n",
    "    err = 9999\n",
    "    errors = []\n",
    "    \n",
    "    # group x,y into the same vector to do matrix math\n",
    "    x = np.array([x,y])\n",
    "    \n",
    "    while err > tol:\n",
    "        # our gradient function is still set up for separate x,y inputs\n",
    "        grad = f_grad(x[0],x[1]) \n",
    "        H = f_H(x,y)\n",
    "        # the -inv(H) holds for all min/max problems.\n",
    "        # the second derivatives take care of the sign, unlike in gradient ascent\n",
    "        x = x - inv(H) @ grad\n",
    "        err = np.abs(norm(grad,2))\n",
    "        errors.append(err)\n",
    "    \n",
    "    return x[0], x[1], errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of minimum: x=1.0346, y=6.6487, c(x,y)=8.5089\n",
      "Iterations: 2\n"
     ]
    }
   ],
   "source": [
    "xn, yn, errors_n = newton_multivariate(c_grad, c_H, 5, 15)\n",
    "print('Estimate of minimum: x=%0.4f, y=%0.4f, c(x,y)=%0.4f' % (xn, yn, c(xn,yn)))\n",
    "print('Iterations: %d' % len(errors_n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function is quadratic, so Newton's method converges quickly. In general, there is still a risk of diverging, just as in the one-dimensional root finding problems. \n",
    "\n",
    "Other notes:\n",
    "- This problem only has one global maximum. For a multi-modal function, these methods will return the first optimum they find. It's up to us to compare their function values and possibly second derivatives to determine which one is the global optimum.\n",
    "- We did not use the range constraints because the methods are following the gradient, and will not run into the boundary. For a general problem we may need to incorporate these.\n",
    "\n",
    "Last, built-in Scipy `minimize`. \n",
    "- We have to modify our function `c(x,y)` to take a vector input instead.\n",
    "- We want to maximize, not minimize, so return the negative of `c(x,y)`\n",
    "- Full docs [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html). If no gradient function is given, it is estimated numerically. The default method is BFGS, which estimates the inverse Hessian so it is not needed as an input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "def c(x):\n",
    "    c = 7.7 + 0.15*x[0] + 0.22*x[1] - 0.05*x[0]**2 - 0.016*x[1]**2 - 0.007*x[0]*x[1]\n",
    "    return -c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  message: Optimization terminated successfully.\n",
      "  success: True\n",
      "   status: 0\n",
      "      fun: -8.50894953977536\n",
      "        x: [ 1.035e+00  6.649e+00]\n",
      "      nit: 8\n",
      "      jac: [ 1.907e-06 -1.431e-06]\n",
      " hess_inv: [[ 9.964e+00 -1.817e+00]\n",
      "            [-1.817e+00  3.088e+01]]\n",
      "     nfev: 33\n",
      "     njev: 11\n"
     ]
    }
   ],
   "source": [
    "res = minimize(c, x0=[5,15])\n",
    "\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result object contains all of the information we need: whether the method converged, how many iterations it took, the objective function, and the decision variables. We can access these using `res.fun` and `res.x`. In this case notice we are maximizing the negative, so the optimal objective function value is `8.509`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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