{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Multi-step methods\n", "\n", "Our goal is to implement Adams-Bashforth methods for solving linear differential equations. We focus on the 2nd-order method, but include code for the 4th-order method. Adams-Bashforth methods are called linear multi-step methods because they use a linear combination of function evaluations at multiple timesteps (i.e. a weighted average of values of f at previous time steps). These methods are worth implementing because they have the accuracy of the R-K methods but require less computatation at each step. The drawback is that their regions of stability are quite small, so we may need to take small steps in the interest of stability, rather than accuracy." ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.integrate\n", "import numpy.linalg\n", "import matplotlib.pyplot as plt\n", "\n", "def degradation_model( t, y, params ):\n", " y1 = y[0]\n", " y2 = y[1]\n", " dydt = np.zeros( (2,) )\n", " dydt[0] = -params[0] * y1\n", " dydt[1] = -params[1] * y2\n", " return dydt" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [], "source": [ "def forwardEuler( fn, t, y0, params ):\n", " \"\"\" [t,y] = forwardEuler( fn, t, y0, params )\n", " Given a function handle fn for dydt, find the value of\n", " y at timepoints t, given y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (NY,NT)\n", " \"\"\"\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[:,i-1],params);\n", " y[:,i] = y[:,i-1] + h*yprime;\n", " \n", " return (t,y)\n", "\n", "def explicitTrapezoidal( fn, t, y0, params ):\n", " \"\"\"[t,y] = explicitTrapezoidal( fn, t, y0, params )\n", " Given a function handle fn for y', find the value of\n", " y at timepoints t, assuming y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (NY,NT)\n", " \"\"\"\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[:,i-1],params);\n", " yhatFE = y[:,i-1] + h*yprime;\n", " yprimehatFE = fn(t[i],yhatFE,params);\n", " y[:,i] = y[:,i-1] + h/2*(yprime+yprimehatFE);\n", "\n", " return (t,y)\n", "\n", "def RK4( fn, t, y0, params ):\n", " \"\"\"\n", " [t,y] = RK4( fn, t, y0, params )\n", " Given a function handle fn for y', find the value of\n", " y at timepoints t, assuming y(0) = y0.\n", " fn takes t, y, and params as input.\n", " Uses a 4th order explicit Runge-Kutta method\n", " \"\"\"\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " f1 = fn(t[i-1],y[:,i-1],params);\n", " f2 = fn(t[i-1]+h/2,y[:,i-1]+0.5*h*f1,params);\n", " f3 = fn(t[i-1]+h/2,y[:,i-1]+0.5*h*f2,params);\n", " f4 = fn(t[i],y[:,i-1]+h*f3,params);\n", " y[:,i] = y[:,i-1] + h/6*(f1+2*f2+2*f3+f4);\n", " return (t,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implement the method\n", "\n", "Use the explicit trapezoidal method to compute the value at the first time step after the initial condition. \n", "\n", "Then, use the Adams-Bashforth method to compute the remaining time steps. Write the code so that the ODE function is called as few times as possible.\n", "\n", "\\begin{eqnarray*}\n", "f_b &=& f(t-\\Delta t,\\widehat{y}(t-\\Delta t))\\\\\n", "f_a &=& f(t,\\widehat{y}(t))\\\\\n", "\\widehat{y}(t+\\Delta t) &=& \\widehat{y}(t) + \\frac{\\Delta t}{2}\\left(3f_a-f_b\\right)\\\\\n", "\\end{eqnarray*}" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [], "source": [ "def adamsBashforth2( fn, t, y0, params ):\n", " \"\"\"\n", " [t,y] = adamsBashforth2( fn, t, y0, params )\n", " Given a function handle fn for y', find the value of\n", " y at timepoints t, assuming y(0) = y0.\n", " fn takes t, y, and params as input.\n", " \"\"\"\n", "\n", " h = t[1]-t[0];\n", " if abs(np.mean(np.diff(np.diff(t)))) > 1e-8:\n", " print( 'The time steps must be evenly spaced' );\n", " return;\n", "\n", " # We need the first two steps. And they need to be computed\n", " # by a second order method so that the results from this\n", " # function are second order.\n", " # So let's use the explicit trapezoidal method\n", " (tstart,ystart) = explicitTrapezoidal( fn, np.array( [t[0], t[0]+h] ), y0, params );\n", "\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0:2] = ystart;\n", " f_a = fn(t[0],y[:,0],params)\n", " for i in range(2,t.size):\n", " f_b = f_a\n", " # Compute f at i-1\n", " f_a = fn(t[i-1],y[:,i-1],params);\n", " y[:,i] = y[:,i-1] + h/2*(3*f_a-f_b);\n", " \n", " return (t,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run and plot result from AB2.\n", "\n", "Run the AB2 method on the degradation model with degradation rates (2,5) and initial conditions (1,1) with time beginning at 0 and ending at 2.\n", "Stephanie\n", "Then plot the true solution (solid lines) and the forward Euler's solution (dashed lines), explicit Trapezoidal's solution (dotted lines), and AB2's solution (dash-dotted lines).\n", "\n", "Then plot the difference over time between the true solution and each of the other methods." ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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PHTq0c8eOHaM6d+4cdffdd1dfRLbJkuTlTNr3A2uxMWW6fV8oPAZ7Vtbp0kAvZ56d2INtKTn8vucYs4Z3wWrTjHr1dwpLrPUcuBBCiJamcm+jyq/w8PBSMPY2qnp+woQJJ/0v+c0330x+/fXXA1NTUy3l5eXMnDmz/euvv57k6OioH3jggaP79+/fsX379vh169a5L1q0yLPmpzctkrycSfBF4NcFSnKg29XGuX531Pnykd0CuaZve975bS8xHXzo6O9KabnmtoUbZAaSEEKIBhEcHGydMWPGkZkzZ7b7z3/+ExAZGVl4+eWX53t4eNjGjh2bB+Ds7Kx79OhRmJyc7NjY8dZFfa+w27x5tIZ7Nhiv844Y3/f878TCdXUwe0xX/tp/jJdX7uG7ewYx6Pmf+SPxGG/+ksiMYTWv2CuEEKKJe3fYqbv1dh2byaD70ynJNzF/7Kn/wEdPyaDfncfIO2Lh02tCTyq7/edaN2osKSkxRURERAIEBweXrFy5ci+c2B6gst4XX3yxNyoqqqTqtQ899FB6r169/NauXeuxcePGU3amzsjIMK9cudL7oYceOlpbHE2BJC91oTW4t4ZWkbDq/+BoPFz9QZ0udXW08P70Pvi5O+LqZOHzO/pz+cu/8sKK3XT0c2N0j2axjYQQQohGVtltVP18bGxs/s8//5x4pmvNZjM333xz+oYNG9wCAwPLq5aVlZUxceLETrfffvvRyMjIUnvHXR8keanNnpXw5W1w2yqIGA1p8XB4y1ndoqO/GwAl1nJyikp5aGQ4z36fwJs/J0ryIoQQzdGZWkqc3G1nLPcItNalpcXeTCYTJtOpo0WmTZsW0qlTp+LHHnssrYbLmiQZ81Ibz7bGDtPJf0GXy41zmfuhOOesb/X0dzu59v11XNa1NTcN6ED84Ty+2tzs9sMSQgjRQsycObNtbm6u+YMPPkhu7FjOhiQvtQnoCk6ekPQnBPU2Xuty2PntWd/qb8M64+poYeanW3hwRDh9O/rywOI4rpUF7IQQQpyjyjEvlV8ffvihT12u27t3r8Prr7/eZs+ePc5RUVGRERERkS+99JJ/fcdrD9JtVBuTCdr1MVpeTGYIu9xYefeXZ6DXtWd1q1aezjx3VQ9uW7CBl1fu4bVrenLxM6tYs/cYablFtPJ0qac3IYQQorkrLCzcXP3cmDFj8vLy8rbU5fqZM2ceA47vFhwaGlqmtd5ovwgbjrS81EX7i4yxLkXZEDbSOJefBuVlZ32r4ZGtuf6iDry/ej+7j+TzznW9Afj3sniZPi2EEELUgSQvddH5Mrj4HiNZCb0EUFBeAgfXnNPt/jm6K2N6tKGNlzPDo9rw6KiufL/9CIOe/5mcwmYx0FsIIYRoNJK81EVQbxjxJLgHgKuv0Y2Egk0Lzul2zg5m3pjWmy6tjRWcbxkYQkc/Vw5lFXHNe+tkB2ohhBDiDCR5qauyYmN9F4DwkYCGHV+BzXbOtywuK+fezzbz33VJLJ0xAC9nB+IP5/LgkjjpQhJCCCFOQ5KXulr5GLx/KZRbT0yZ7jTMmHl0jhzNJrILy3jqu50czS3h8zsuwtGs+HJTCjd/tF4SGCGEEKIGkrzUVXBfKCuEo9ugdRR4BoGjC5gdzvmWJpPihUnReDhbmPnpZkL83fjvrf0A+Dkhned+2GWv6IUQQogWQ5KXump/kfE9+S9QCroMN1bf/fqe87ptgIcT/7k6ml1H8njuh1306ejHW9f2QgFzf93Hm2de8VkIIcQFwmw2x1Rdz+XRRx8NHD58eGhERERk+/btu3l4ePSsLFu5cqVb5XUvvvii/+jRoztVHmdmZpqCg4O7xcfHO86bN8+nc+fOUSaTKea3335zbZx3dvYkeakrr3ZGa0tSxYJyXUaAtRg2L4Cj59dCMiyiFTdeHMJXm1PILChlVPe2vHWtMYX6PysSeO77necbvRBCiGaucm+jyq+nn376yMqVK/fu2rUr/q233joYGxubX1k2fPjwgsrrZs2alZGamuq4dOlSD4AHH3wwaNq0aRmRkZGlPXv2LPriiy8SY2Nj8xvvnZ09WaTubAT3g+R1xuuOQ0BZoOtYaHXq5qJn65ErIrhjSCd83YzdyK/o3oZ/j+3KnG928uGaA9x3WRhODubzfo4QQogLi8lkYu7cuQevu+66Tr6+vvtXr17tsXXr1p0AvXv3Lm7s+M6FtLycjQEz4ar3jV2mndyh4yA4ut3oRjpPzg5m2ni5oLVm3ur9ZBeWctOATjx0eRjFZTYeXLIVa/m5z2wSQghhP+PfWB3+4R/7/QBKrTY1/o3V4QvXHvQFKCixmsa/sTr8s7+SfACyCkvN499YHb5k4yFvgLTcYsv4N1aHf70lxQsgNbuoTg0JJSUlpqrdRu+9916dtgEA6NevX9HQoUNzRo8eHfbSSy8lOzs7N+sZIdLycjba9jr5OOxy+OEReDkKbvvFWAfmPO1Nz+fZ73exfNthPr61H38b1gWzycSz3+9ixfYjPHdVd67s3e68nyOEEKJ5qew2OtfrZ82albZq1SqvMWPG5NkzrsYgLS9nK/FH2LXceN1lhPE95xD8+ZZdbt+5lQcvT+nJxqQsZn66mXKb5s4hoYyPbktpuY3/rkuSKdRCCNHIvp4xMOGmAR2PAThaTPrrGQMTru/fIRPAzcli+3rGwISpfdtnAfi4OpZ/PWNgwtUx7bIBWnk6W7+eMTBhfM+gHIC23i7WhojZbDZjMrWMX/v1+i6UUiOVUglKqUSl1COnqTNZKRWvlNqhlPqkPuOxiz9ehV+fNV77hYJ3R3Dygi2fQFmRXR4xukcbHhsTyf/ij/LvZdvRWvPK1J5c1689Gw5m8dpPieQWnf2+SkIIIURLUG/Ji1LKDLwJXAFEAtcopSKr1ekC/AMYoLWOAu6rr3jsJrgfHNkOJRUDsyOuMNZ/yT8Cq1+x22NuGtCRO4Z04rO/kkk4modSiifGd+Oq3u14+cfd9Hzif2w6mGW35wkhhGjaqo95ufvuu4PO954LFizwbt26dY8tW7a4XXnllV0GDhzYxR6x1jdVX10QSqn+wONa68srjv8BoLV+pkqd54HdWuv3z+besbGxesOGDfYMt+72/Aj/vQpu+Bo6DYV9v8KCceDsAyU58Pd94FLnMVRnZLNpdh3JI7Kt5/Fz1nIb495YTfzhPNwczXw9YwCdW3nY5XlCCNFSKKU2aq1j7XW/uLi4A9HR0Rn2ul9LEhcX5x8dHR3SkM+sz26jICC5yvGhinNVhQFhSqk/lFJ/KqVGnu5mSqnblVIblFIb0tPT6yHcOgqu2JQxqXLK9GBo3Q3MFtA2WPum3R5lMqnjict3Ww+zatdRLGYTX/1tADEdfCgoLeeqt9eyL71ZTc8XQgghzktjj9yxAF2AocA1wHtKKe+aKmqt39Vax2qtYwMCzn9Wzzlz9oJWkXBkq3GsFAy6HwrSjd2m/3wbCo7Z9ZHlNs27v+3lb//dzOakLJwsZj6+pR+RbTzIKSrjild/JzW70K7PFEIIIZqq+kxeUoDgKsftKs5VdQhYprUu01rvB3ZjJDNN2w1LYfLCE8eRE8CvMxRlQ1kBfHe/XR9nNinen96HAA8nbv5oPfvS83FxNPPZHf3xcXOgxGrjqrfXkp5XYtfnCiGEEE1RfSYv64EuSqmOSilHYCqwrFqdpRitLiil/DG6kfbVY0z24d4Kqk43M5lh4Cw4tgfMzpCw3G4zjyoFeDix4Oa+mJTihnl/kZZXjKezAz/OGkKQtwuHc4qZ+NYfZBeW2vW5QgghRFNTb8mL1toKzABWADuBRVrrHUqpJ5RS4yqqrQCOKaXigZ+Bh7TW9u1zqQ9lRbDsHtix9MS5HlPAKxh8O8G928DBxe6PDfF3Y96NfTiWX8q3cYcB8HN34ou7LsbXzYHkrCJGvvK7rAMjhBCiRavXMS9a6+Va6zCtdajW+v8qzj2mtV5W8Vprre/XWkdqrbtrrT+rz3jsxuIMu1cYLSyVzA4w4F5I22G0wFjLoMT+ixhGB3vzv1mDuXlgx+PnAr2c+fKuATiaTeSXWDl4TMa/CCGEaLkae8Bu86QUBPc9sUljpV7XgVsr+HEOPNsOPr2mXh4f7GvsWh6fmssT38Rjs2lC/N34buZAHMyKa99fxzu/7aXEWl4vzxdCCNHwzGZzTNV1Xh599NHA4cOHh0ZERES2b9++m4eHR8/KspUrV7pVXvfiiy/6jx49ulPlcWZmpik4OLhbfHy84x133NGuY8eOUWFhYZHDhw8PzcjIaBY7AEvycq6CL4KsA5B39MQ5Bxe4eAakrAePQAiy2xIDNVqdmM68P/bz7A+7AOjS2oMFN/cjPa+YZ5bv4sHFcfX6fCGEEA2ncm+jyq+nn376yMqVK/fu2rUr/q233joYGxubX1k2fPjwgsrrZs2alZGamuq4dOlSD4AHH3wwaNq0aRmRkZGll19+ee7u3bt37N69O75z587Fs2fPDmy8d1h3krycq+B+xvfqrS+xN4OztzGdevjj9RrCbYM6cUP/Drz72z4+WL0fgO7tvPhgeh9MCnYdziUtt1nudi6EEMJOTCYTc+fOPfjQQw+1/+2331xXr17tMWfOnKMAEydOzHVwcACgf//+BSkpKY6NGmwdSfJyrtpEQ0AEWKtNT3bygH53GuNhkv6EpXfBoY31EoJSin+PjeKKboE8+W08y+JSARgUFsBHN/UlJbuYMa+vZuh/fibxaLPfRFQIIZqOd4eFs26uHwDWUsW7w8JZ/74vACX5Jt4dFs7G+cZy64WZZt4dFs6WT7wByDti4d1h4Wxb7AVAziFLXR5ZfXuA9957r87Luffr169o6NChOaNHjw576aWXkp2dnU+Z2fHRRx/5jxw5Mqeu92xMkrycK4sj/G0d9Jh0alm/O8DRHb570NiwcfmD9RaG2aR4eUpP+ob48vXmlOMzjQaHBbDojv7kFZdx4FghY9/4gz/3Nf2JXEIIIWpWvdvotttuO6sN7mbNmpXWqlWrsjFjxpzyv9mHH3440Gw26zvvvDPTfhHXnzple+IMtDa+qq774uprdB+teR16TIWtn8G+X4y9kOqBs4OZ92+MxdliRil1/Hy3IC9W3j+EKe+sJSW7mGvfW8dzV3fn6pjgM9xNCCFErW7/OeH4a4ujPunYyd120rGrb/lJxx6B1pOOvdpZ6zlaAMxmMybTqW0Wr732mt+KFSu8f//99901lTdFzSPKpiplI7wQBklrTy3rPwPMjqBM4NkOfnrCSHLqiaezA44WE8fyS7htwQYOZRnTpdv5uPL9fYPp19GHcq15cPFWnvhmh6wFI4QQgiVLlni++uqrgcuXL0/08PCwNXY8dSXJy/nwDoGCNEj+89Qyj9bQ+wbYthgCuxuJzq7v6j2kzIJS1u07xg3z/iKrwFht19PZgYW3XMSQMH8A5v1xgFmfx1FqbTY/p0IIccGrPubl7rvvrr7Z8Vm7//772xcUFJgvueSSsIiIiMhp06a1t0es9U01x/+Bx8bG6g0bNjR2GIbXY8EvFKZ9fmpZdjK81hPa9IT0ncYKvHetMbYTqEd/7c/kug/WEdnGk/k39cXL1RhJrrXmtZ/28PKPewAIa+3Oojv64+3aLAaXCyFEnSmlNmqt7bZeRVxc3IHo6OgMe92vJYmLi/OPjo4OachnSsvL+Wrfz5gubauhFcM72BjzcmQbXP4MpO+CbUvqPaS+HX1545pexKfmcvXcNaRmG/ssKaW497IwXp4SjQJ2H83n0S+31Xs8QgghhD1J8nK+gi+CoiwjManJwFlgK4Nje421X1Y9Adb63zxxRFQgH93cB4vZhMWkTiq7slc7PrqpL05mxbr9mWw9lE25rfm1wAkhhLgwSfJyvjpfBjE3grNXzeX+nSFyAqz/AHIOGV+7vmmQ0C4O9ee7ewbSytMZa7mNHaknpu8PCQ/gu3sH4eJo5uq319Dt3ytYuvlQg8QlhBBCnA9JXs6XZxsY+yp4nWHc1KAHoCwfOl0CE+ZC1MQGC89U0ery+qpErnxzDd9tPXy8rHMrD766ewABHk4UlZWzeo905wohhGj6JHmxl+T1EL+s5rLAbhB2BRz4FbqONTZ2LC9r0PBuGhBCj3ZezPh0Ex/9sf/4+QAPJ368fyjDwgNYsimFJ76JZ/GGZMrKZSaSEEKIpkmSF3v59Tn47n4oK6q5fPCDxtiYP16F+WPhle5Q3HCrMHu7OvLxrf0Y3rU1j38TzzPf78RWMc7FxdHM+9P7cNOAEOb9sZ+Hlmxl0ty15BY3bIIlhBBC1IUkL/Yy4F4oSIe4T2subxcLHYfAhnmQsgk8254+0aknzg5m3r4uhusuas+CNQdJyiw8XmY2GfskzbqsCwBbkrO58s0/SMlu2BiFEEKc3sKFC72VUjGbN292rjyXkJDg6Ozs3DsiIiIyPDw8slevXhFxcXFOAF999ZVnVFRU17CwsMioqKiuy5Yt86h+z3vuuSforrvuOj72Yffu3Y7t2rXrnpGRYX766acD2rdv300pFXP48OEmsyq/JC/2EjIQ2vaCNW+ArbzmOoMegMIMGPoPuG0VeDT8zuNmk+LJ8d34/t5BhPi7AZy0WN29l4XxzvUxOJgV+9ILuOylX4lLzm7wOIUQQpzqs88+8+3du3f+ggULfKueDw4OLtm1a1d8QkJC/LRp0zLmzJnTBqBVq1Zl3333XeLu3bvjP/roo/233nprx+r3fOaZZ1K///57n02bNjkD3H333cH//Oc/U/z9/cuHDBmSv3Llyt1t27at/2myZ0GSF3tRCi6eCZl7jR2la9JxMLTrA+veMca8HFwLW07TUlOPlFLHE5cFaw9w5Vt/kJZXfLz88qhAFt95Mc4OJopKy7l67hpW7DjS4HEKIYQ4IScnx7R+/Xr3Dz/88MBXX33le7p6ubm5Zm9v73KAAQMGFIWEhJQBxMTEFJeUlJiKiopOWj/D3d1dP/fcc8l33313+88//9yroKDAfNddd2VWXh8eHt6kEheQjRntq+s4o/Wl6DQbfSoFgx6ET6fAN/dC3GfGarsdB595tlI9CvZ1ZV96AVe9vYb5N/WlU4A7AD2DvVlx32Cmvvsnh3OKuWPhRq7pG8y/x0bh7FC/KwQLIURTN/6N1eG11RkcFpD9wIjwo5X1J/QKyrhpQMdjabnFltsWbAitWvfrGQMTar7LCZ988on30KFDc3r06FHi4+Nj/f33310HDRpUCJCcnOwUERERWVBQYCouLjatWbPmlMXH5s+f7xMVFVXo4uJyysJeU6ZMyZk3b57/nXfeGfLLL7+cZuGypkNaXuzJbIHbfjb2NDqdsMuhdXc48Af0nm5s1vjb8w0XYzXDwlvx2e0XUVhSztVz17I56UTi1d7Pje/vHUyfEB8APv0rmSnv1LAJpRBCiHq3aNEi32uuuSYL4KqrrspcuHDh8daXym6j5OTk7U8//XTyzTff3KHqtRs2bHB+7LHHgt57772Dp7v/3/72t7QePXoUREdHl9Tfu7APaXmxN6WMrQJSNkJwn5rLB90PS26CToONhGf9B0aXk1/oqfUbQHSwN1/cdTE3zPuLa99fxy8PDqWVpzEWzMvVgU9uu4inl+9k3h8HSM0pYuPBLLoHeWExqePryAghxIWkLi0lp6vfytPZerbXHz161Pznn396JCQkuMyYMYPy8nKllNI2m+2U1UWvueaa7JkzZ4ZUHu/du9fh6quv7vzBBx/sj4qKOm1iYjKZMJmaR5tG84iyuVn3NnxwGaSf5mczcjz4dYHfXoTQy8Bkgl+eadgYqwnxd+OLuy7mqQndjiculSxmE4+NjeKLu/rjZDEzae4a+j79I2NfXy3rwQghRANYuHChz5VXXpmZmpq6LSUlZduRI0e2tmvXrnTFihXu1euuXLnSIzg4uAQgIyPDPGrUqC5z5sw5NGLEiIKGj7x+SPJSH3pMAYszrHm95nKT2djz6Og2WPu6UXfbEjiyvWHjrCbAw4mJvdsBsHbvMV7/aQ9Vdx2P6eDL9/cO4vKoQLILy0jOKuRwdvHpbieEEMJOFi9e7Dtx4sSTBlSOHz8+6+OPP/aFE2NewsPDI2fPnh00d+7cgwDPP/98q6SkJKdnnnmmbURERGRERERkSkpKnXtdnnrqqVatW7fucfToUcfo6OjIKVOmdKj9qvqnqv5yai5iY2P1hg0bGjuMM/v2fti8EO7bVvOU6PIyeK03uPrBlIXw9gDocDFM+6zhY63Bv7/ezvy1B7mmb3ueHB+FxXxynrtkYzKPL9sBKIZ3bUVRWTkvTO6Ju5P0RAohGp9SaqPWOtZe94uLizsQHR0te6jUIC4uzj86OjqkIZ9Z7y0vSqmRSqkEpVSiUuqRM9S7SimllVJ2+2FrVP3/BjYrrJtbc7nZAQbMhMObIWu/8Xr395D8V8PGeRqPj4vib8NC+fSvJO78eBNFpSevXXN1TDA/3DeYrm08+GpLKj/sOMrIV35j48HTzLQSQggh7KRekxellBl4E7gCiASuUUpF1lDPA7gXWFef8TQov1BjH6PEn4wZRTXpdT24t4Zfn4fdK8DB1dhmoAlQSvHQ5RE8MT6Kn3YdZcq7p24X0M7Hlc9u789dQ0MxAYezi5k0dw1PfxePVcbCCCGEqCf13fLSF0jUWu/TWpcCnwHja6j3JPAc0LIGUIx5xZg6rU4zI8fBGfrPgAO/G9sF9LkNxp1mnEwjuaF/CO9cF0NEoAceNXQJmU2Kh0dG8NXfBtDOxwWbhnd/38+Vb63h4LEWMzZMCCFEE1LfyUsQkFzl+FDFueOUUr2BYK31d2e6kVLqdqXUBqXUhvT0dPtHWh9cfY2p0GXFp99FOvZmcPEBawmMeMJIYmzlkHPK7LdGMyIqkOevjkYpxf6MAh5YFEdO0cnvJzrYm+X3DmJkVGsAdqTmMPKV31m8IZnmOK5KCCFE09Wos42UUibgJeCB2upqrd/VWsdqrWMDAgLqPzh7ydxv7CC9/cuay53cod9dxniXw1th5zfw5e0w7wooyW/YWOtgc1IWX29JYdSrv/PX/syTytycLMy9Ppa51/XG3clCcVk5Dy3Zyj2fbG6kaIUQQrRE9Z28pADBVY7bVZyr5AF0A35RSh0ALgKWtZhBuwDeHYwWmDWvnX7sS9/bwNEdfpwDS24xpk4PftBIbJqYib3bseSui7GYFVPfXcuL/0s4Za2Xkd3a8L9ZQ4hqa2xeuv9YPlkFTW5rDCGEEM1UfScv64EuSqmOSilHYCqwrLJQa52jtfbXWodorUOAP4FxWusmPg/6LJhMxuq5R7fD3p9qruPqC31uMconvg/jXoOY6UZZYWbN1zSinsHefDdzEBN7t+P1VYm8//v+U+oEejmzbMYgHr0igt1H87n8lV+Z8OYf/POrbZTbpBtJCCHOxcKFC72VUjGbN28+vppoQkKCo7Ozc+/KdV569eoVERcX5wTw1VdfeUZFRXUNCwuLjIqK6rps2TKP6ve85557gu66667jQzp2797t2K5du+4ZGRnmcePGdQwJCenWpUuXqEmTJoWUlJQ0iWXV6zV50VpbgRnACmAnsEhrvUMp9YRSalx9PrtJ6T4JPNrAH6+dvk7/GWBxgj0rjEXsinOMbQNe6Q57VzVcrHXk7mThhUnRvHdDLDdeHAJAVkHpSeNbTCbF7UNCWfq3ATg7WNiSnM3ybYcpKy8/zV2FEEKcyWeffebbu3fv/AULFpy0q3Tl3kYJCQnx06ZNy5gzZ04bgFatWpV99913ibt3747/6KOP9t96660dq9/zmWeeSf3+++99Nm3a5Axw9913B//zn/9M8ff3L7/22msz9+3btz0hIWFHcXGxeuWVV/wb5p2eWb2PedFaL9dah2mtQ7XW/1dx7jGt9bIa6g5tUa0ulSyOcNFdsP9XOBpfcx33VsaGjls/g9Qt8M198NOT4BkEX9zapAbwVjU8sjUujmYKS61MfHsN93y6+ZTBvFFtvVhx32Am9GxLVmEZY17/g+d/2MW17/8pM5KEEKKOcnJyTOvXr3f/8MMPD3z11Ve+p6uXm5tr9vb2LgcYMGBAUUhISBlATExMcUlJiamoqOik1hN3d3f93HPPJd99993tP//8c6+CggLzXXfdlQnGbtOVex7FxsYWHDp0yLE+32NdyXKoDSXmRmjbG1p1PX2dIQ/Dru/g8+thyn+h7+3g5g/vDoVF0+Gm741EqAlyspi5qncQL/+4h81J2bw8pSd9O574u+XiaOaVqb0Y3yuIOct28NYvewG47KVfuXVQJ2YM64ybrM4rhGgu3h0WXmudzpdlc8k/jx6vHz0lg353HiPviIVPrzl5J97bf651o8ZPPvnEe+jQoTk9evQo8fHxsf7++++ugwYNKoQT2wMUFBSYiouLTWvWrNlV/fr58+f7REVFFbq4uJzSdz9lypScefPm+d95550hv/zyyynXlpSUqM8//9zvpZdeSq5e1hhkb6OG4uwFHQedfs0XMBKVyQsh/wj8OBva9QH/LjDsn5CyAf73r4aL9yyZTYoZl3RhyZ39MZuMwbwv/S/hlMXqhoW3YsWswcy8pAtOZkW5TfP2L3u56JmfWLJRplULIcTpLFq0yPeaa67JArjqqqsyFy5cePx/iJXdRsnJyduffvrp5JtvvvmkPYg2bNjg/NhjjwW99957B093/7/97W9pPXr0KIiOjj5l5+np06e3v+iii/JHjhzZJKbByt5GDUlrWDkbTBa47PHT19u0AJbdAwPuM3ag/mA4hAyCfT/DVR9A96sbKuJzkl9i5d9f7+DAsQI+v/2iU/ZFqpSWW8yzP+ziy00nJqD1bu/N4+Oi6NHOu4GiFUK0RC1tb6OjR4+aQ0JCevj4+FiVUpSXlyullE5JSdm2Z88exzFjxnTZs2fPDoD8/HwVEBDQs6ioaDPA3r17HS699NLwd999d/+Zdpb+9ttvPV588cXWP//8c2LV8w888ECbuLg41xUrVuw1m82nXNci9zYSVSgFBcdg3TtnnkXU+waIuQn+eAWyDsAl/4KJ70HwRbBsJqSd0qLXpLg7WXhxcjQf39IPi9nEsfwSvt6SckqrSitPZ16a3JMv7+pPJ39XALYeymH8G39w9383ciz/lORfCCEuSAsXLvS58sorM1NTU7elpKRsO3LkyNZ27dqVrlix4pQ1NVauXOkRHBxcApCRkWEeNWpUlzlz5hw6U+JyOi+99JL/qlWrvJYuXbqvpsSlsUjy0tAuvgfKCo2ZRGdyxXNGt9HXMyBsJLgHwNUfgIMLLLoeSvIaJt7z4OJo/KB/+McB7v1sC/d+tuWU/ZEAenfw5cf7h/LCpGg8XSxo4PttR0jNKWrgiIUQomlavHix78SJE0/a+Xb8+PFZH3/8sS+cGPMSHh4eOXv27KC5c+ceBHj++edbJSUlOT3zzDNtIyIiIiMiIiJTUlLqPMDw73//e4eMjAxLbGxs14iIiMgHH3ywjX3f2bmRbqPG8N9JkLIJZm03kpHTyU2Fd4aAkwfc/rORyBxLhOyDcM1n0HFww8V8Hsptmrd+TuSVn/YQ6OnMC5Oi6R/qV2PdvOIynv1+F5/9lYSLo4VbB4awbn8mdw0NZXBYqwaOXAjRXLW0bqOmTLqNLhQXz4TCDIj79Mz1PNvC5PlGsvLlHdB1nDED6b7tzSZxAWMw7z2XdmFxxWDea977k4//rHnMmIezA/93ZXdW3j+Evh19eeWnRNbuy2TRhqY5VVwIIUTDk7mpjSFkIAx5BDoMqL1uh4thxP/BDw9D214w9GHjfHkZbFsMvqHQvl/9xmsnvdv7sOK+wXyweh+XRwUCkJxZiI+bI+7Vpkl3CnBn3o19+GnnUf751Ta+3XqY/JK/8HZxwMPFgb9fHo6Hs0NjvA0hhBCNTJKXxqAUDPtH3ev3uwNSN8Evz0DbnuDqB4unG7OXOgxoNskLGONgZlzSBQCtNbM+38LBzEIeujycq3u3w2Q6eSr5pV1bM6hLAPPXHODVH3eTX2qszrt862EeviKixmuEEKIe2Gw2mzKZTM1vrEU9stlsCrDVWtHOpNuoMR3ZBqueOv2GjZWUgjGvQGA3+OI2sFmNFpcr34EJbzdIqPVBKcW/xkQS7OPC35dsZdybq0/ZqRrA0WLitsGd+PmhYYysaLHJKSrj70u2Muj5VSzdfOiU9WSEEMLOtqenp3tV/LIWGIlLenq6F7C9oZ8tA3Yb01/vwfIHjZVzO1xce/2sA8Zqux5t4JaVJ3adzk+DPf+DXtfVZ7T1RmvNsrhUnv1+F4dzinn72t5c0f30A9q3Hsrm319vZ3NyzvFz7X1duWtoKBN7B+FkaTrT+YQQjcPeA3Y3btzYymKxvA90Q/7jX8kGbLdarbfGxMSkNeSDJXlpTKWF8HIUBPeDaZ/V7ZrEn+C/V0PkBGPtl58eh0MbIGmtMQMp/Ir6jLheFZWWs/DPA9zQPwRnBzM7D+cS7Ot6yngYMBKepVtSeel/u0jOKsbBrCgr13g6W/hu5iCCfV0b4R0IIZoKeycvommR7LExOboas4d2f1/3hec6XwqXzIYdX8KfbxnTqVtHQZtoY0ZS5v76jbkeuTiauX1wKM4OZqzlNm5bsIFhL/zC4g3J2GwnJ9lKKa7sFcSvD13Cu9fHEN7a2OW9sLSc77cdJr+4jF8S0k7ZJFIIIUTzJy0vja0gA17uBt2vgvFv1u0arWHRDbDrW7j2C+h8idGl9M5g8O4At/zvzOvHNBObkrJ44pt4tiRn0z3Ii8fGRtInpOaNVLXWrEnM4I1fElm7NxNXBxOFZTYGdvbj41svauDIhRCNTVpeWjZpeWlsbv5w0Z3GOJa6UgomvAV+XeDLWyE72Uho2vSCI1th+UP1F28D6t3ehy/vuphXpvQkPa+ESXPX1jigF4yWmAFdAvj0tv58dffF9Aj2BmD9gUz+77t4Pl+fxMNfbCUlW1btFUKI5k5aXpqzjD3w3iXg2wkGzoJv7jUWstu8AMa9Ab2vb+wI7aaw1MpXm1OY1rc9Sin+2p9JVFtP3GoYD1Mp4Ugeb/+SyLK4VCp7ncwmxVW9g7hzSCidAk7ZEkQI0UJIy0vLJslLU6E1JP5oDN519qz7dbu+g8+mQc/r4PKnwMkTFl4JyeuM7qM20fUXcyPJL7HS/+mfcHE0c88lnZkUG4yzw+lnGB08VsDzKxL4YdthbNpouLJpGBYewEOXRxDZ9iw+byFEsyDJS8sm3UZNxZFtxiyiTfPP7rqI0TD4IdjyMWz/Akxm6DrGmEb92bVQlFX7PZoZdycL82/pSzsfF2Z/vYOLn13FKz/uJqugtMb6HfzceHNab9b841JuHdQRS8Widr/uTmfUa79z84d/sfHgGXb5FkII0aRIy0tT8uFoyNoPM9aDo1vdr7OVwydTYN8vcO0SWDYDArpCm+5w6WP1Fm5j01rz1/5M3v1tHz/tSuO7mQOJauuFzabPuOpuVkEpb/6cyOfrk8grKcdU0RLzjyvCuWNI5wZ8B0KI+iItLy2bJC9Nyf7fYcE46DTMWLPF4lj3a4uyjAXsyoph6sfG4F1zxXiQI9th5zIY8rDRMtMCJWcWHl/b5cHFcRSWWrl9cCg9Kwbu1iS/xMqn65J45cfdFJSW09HPjev7dyCrsJT9GQU8Ob4bPm5n8WcghGgyJHlp2aTbqCnpOMjYBmDvT8bg27Ph4gNT/gslubDiX6BtxiJ4X9wKGz+CTQtaZBdSpaqL0rX1cub3PRlMePMPJr+zllW7jp6yTgwY3U+3De7ExtnDeXZidzxdHXji23heX5XI99uPEJecjc2m2ZyURXZhzV1SQgghGp60vDRFa96A1pEQesnZX7ttCXxxi7H4Xa/rYeEEGP82BPUG9wAot0JOkjFDqQXLL7Hy2V9JzFu9n9ScYh4cEXZ8Q8gz2Xk4l/d+38f/dhwhv6ScQE8njuaWYDYpRnVvw9S+wVzU0U82gxSiiZOWl5ZNkpemLm0XtIo4u2tW/BPWvgET5lYM3jVWn+VovNF9tOZ1Y0PHyHH2j7eJKSu38e3WVPp29CPI24X1BzLZcCCLaf3a4+XicNrrisvK+V/8UT78Yz+bk7IBsJgUVpvGz92R6f07MLVPe1p5OjfQOxFCnA1JXlo2SV6asr2rYOFEGP0i9Lml7teVW40Wl6S1MPwJuOhuYwXet/pD31vh4BpI2WjMUhr6KJgunN7DF1Yk8MbPibg7WbimbzA3DehIW+8zr0acdKyQRRuSWbQhibS8E91HJgXDIlpxbb/2DAlrhVlaY4RoMiR5adnqNXlRSo0EXgXMwPta62erld8P3ApYgXTgZq31wdrue8EkL+VlxnTnPf+DSR9B1IS6X1ucA1/dBQnfGQvXjXsDti0yNnR08oDlD8Dmj6HLCGODRxfv+nkPTdD2lBze+30f3249jAJuGhDCP0dH1nqdtdzGzwlpzPvjAOv2HTPWjAE08NGNfRga0QqtNUpJEiNEY5PkpWWrt+RFKWUGdgPDgUPAeuAarXV8lTrDgHVa60Kl1F3AUK31lNrufcEkL2AMul14JaRugmsXQ6ehdb9Wa6OL6MfHwScEJi+AwG7G+WUzwewImz4y9kOa+snZd081c4eyCvlg9X6CfVy5eWBHSqzlfLUphSu6tcHL9fRdSgBpucUs2XiI937bS1aRFXcnMxN6BrFufyb+Hk58cms/SWKEaESSvLRs9Zm89Ace11pfXnH8DwCt9TOnqd8LeENrPaC2e19QyQsYs4Q+HA3ZB401YDzbnt31B9fA4pugOBtGvwQRo2D+WOh2NQT3NTZ5LCuCK98xxshcoH7elcZNH63H0WLisq6tmNirHUPCA3Awn75bTWvNuv2ZfL4+me+2plJarnF1NDPz0i4M6uLPaz/tYUCoPyO7B9LKQ8bHCNFQJHlp2eozebkaGKm1vrXi+Hqgn9Z6xmnqvwEc0Vo/dZry24HbAdq3bx9z8GCtvUstS+5h2P0DxN50btfnHTVmIR343ZiFNOJJcPY21srf/xv8719wOM4YyNtzml1Dby601mxPyeWLTYf4Ji6VYwWl+Lo5smzGANr5uNZ6fU5RGYvWJ/F1XCrbU3JPKlNAr/bejOwWyKjubep0PyHEuZPkpWVrEsmLUuo6YAYwRGtdUtu9L7iWl+oObwVXP/AKOrvryq3wy9Pw+4vQujtMng9ewfBGjLFDdesoGHCvsdP1Ba6s3MZvu9P5JSGdJ8ZHoZTizZ8TAZjQK4igWgb5Hsoq5JstqSzZdIi96QUAx1fyBegW5MkV3dpwRbdA2SBSiHogyUvL1ujdRkqpy4DXMRKXtLrc+4JOXqwl8FpvY/uAm38AV9+zv8fuFfDl7cZCdhPeMjZzdPE+sYljeRl8cx8MmAkB4faMvlm7df4Gftx5FKXgoo5+TOwdxBXd2+B+hp2tATLyS/gx/iifrk9ia3IOmhPTrgHeuyGG4ZGBlJXbsJiUjJURwg4keWnZ6jN5sWAM2L0USMEYsDtNa72jSp1ewBKMFpo9db33BZ28ABxYbUyhDuwO05ed3T5IlbIOwuLpkLoZLr4HLv03mB2MVpn8NNj+JYx8Brpfbf/4m7GkY4V8tTmFLzcf4uCxQq67qD1PTeiO1hqbptbp0rnFZfy8K40VO46wYvsRyjV4OJkZHhlI3KFs8oqt/PLQUFwdz5wQCSHOTJKXlq2+p0qPAl7BmCo9T2v9f0qpJ4ANWutlSqkfge7A4YpLkrTWta6cdsEnLwA7v4VF15/bPkiVrCWw4lFY/z607w9XzYNVT4LNCqNfAGcvo97hOKOb6QJaD6Y2Wms2JWXj4+pApwB3NiVlcefCjUzoFcSVvYKICPSotQWluKyc3/dk8MP2I6yMP0JusRUFjOwWyPDI1iz88yBhrTwY2S2Qvh19caulhUcIcYIkLy2bLFLXnG1aAMvugRFPGa0n52rrYvhmptGCM/F9CBlgtMLkHYG0ncaO1R36G88J7G6/+FuQ7Sk5vPrTHn7elYbVpmnv68qw8ABmDQ/D27X2xLKs3Mafe4/x/fYj/LjzKGl5xtCvynVkzErRKcCNy6MCGRoeQHSw9xlnQQlxoZPkpWWT5KW5S/geOl9mJBvnI22X0ZJzLBGGPQoDH4DPrzNW4h14P/zyf8bCd92uMlbl9e9sn/hbmMyCUpZvO8yqXWlsPZTDmkcuwdFi4ouNhyi2lnNJRCvaeJ15sK/NptmcnM1n65NYt+8YSZlFp9RxdjAR2caTO4eEMiIqsL7ejhDNliQvLZskLy1Ffjrs/h5633Du9yjJN1pgtn8BnYfDZf82plh3ucxYa+b3F2H9PLAWQ69rYcjD4NXOfu+hhbGW27BUtI7cMO8vftudDkBEoAeXRLRiRFQgPYO9a73P4ZwifklIZ/m2w+w6nEt6/oktCqLbeXHTgI6gNEs3p/LIyAgi2njWy/sRojmR5KVlk+SlpfhxDqx+qWIfpFvP/T5aG2NgfvgHeATCpPnQLgZ2fQdL74LJH0PCctjwAaCMZw26X6ZX10JrTWJaPj/tSmPVrjQ2HsxiZFQgb17bG4D/7ThC346+tXYxaa3Zl1HAqp1H+TE+jZ1Hcsktth4vHxvdhrE92pJwNI996fmM7NaGizr5nXETSiFaIkleWjZJXlqKk/ZB+hCirjy/+6VshEXTjXEvI5+BDhcbSc0V/wGzBfashK2LYPsSiJ4GE960z/u4QOQUlpFbXEawrytJxwoZ/J+fMSno3d6HYRGtuCSiVZ0G/ZbbNPGpufyw4zC/70kn4UgeJdaT/04rBR393BgcFsDAzv70bO+Nv7tTfb49IRqdJC8tmyQvLUlpIXw8EQ5tMPZBCh12fvcrzISv7jASovBRMPQRYy0Ymw3e7APugTD2FbA4g3cwHNkGiT9BvzvA4czjOsQJNpsm7lA2P+9KY1VC2vHVeV+/phdjo9uSVVBKYVl5rQvjAZRYy9mclM13camsP5jJnqP5lNfwV9zLxYG+HX1557oYTCYlG0qKFkeSl5ZNkpeWpnIfJLMD3Pbz+U9vttlgzavw24tQmmdMzR54n7G1gLUE2veDsmJY9zYU5xrdSfduvaB2qba3tNxifklIZ3hka3zcHPnwj/3M+Saetl7OxIb40ifEh9gQX8Jbe2CqZV2Z/BIr6/YdY9mWVHak5rA/o+B4MmMxKUZEtSastTv//TOJ7u28mXdjH8BYWM/PzVESGtFsSfLSskny0hLlHQGTxRiHkp8Gju7geJ576RRlw4Z58OfbUJAGbXoaSUzXcZD4I3wyGW74GgIijLEyNpsxWylyHHSfBCazHd7YhelARgG/JKSx/mAW6/dnkpZXgknB1scvx93Jwl/7M9FaEx3sjbPDmT/n4rJydqTm8vuedHYdyWNHag7JFbOZFBDRxpN23s78uCsNDycLfTv60bu9N73a+9CjnZesNSOaDUleWjZJXlq6z641xq8M+6ex4eL5JhFlxRD3Kax5DTL3gW8nY42Zdn2NvZGUgnXvQFYSHPgNjmw1EppL/gURY4xycc601hzKKmLXkTyGR7YG4Nr3/+SPxGM4mBXdg7yIDfGlf6gfw8Jb1emex/JL2JyUxZbkbOIO5bBh/zGKKsbNVK4zU/k6tJU7PYO96RnszaAu/nTwO4fVnYVoAJK8tGySvLR0B9fA/2ZDygYI6ArD50CXEeefRNjKYec38McrxhYDbq3gojsh9hZYOdto8Zn6Kez8GlY9Zawf07Y3XPoYdBoqSYwdZReWsvFgFusPZLHhQCZbD+XQp6MP/731IgBe/XEPQT4uxHTwoYOva61dTTabZv+xAuKSs9mSnM0vCWk1rjUzqLM/U/u2Jy2vmG+3HmbOuCi6BXlhLbdhUqrW5whRnyR5adkkebkQaA07l8GPjxutJVf8B/rdbr97H/gdVr8Ce38CRw+IvRH63AY+HaDgGLw9ALqONjaEzEk2upyiroSoCeATYp84xHHFZeVkFpTS1tuFEms5/Z9ZRWaBsTaMu5OFrm08mNavPVf2aofWmhKrrc7dTXHJ2ayMP0L84Txyi8qo+q9HR383erX3ZufhXHYfzSeyjSfdgzwJa+1BVJAX4YEeeDrLlG3RMCR5adkkebmQlJfBpvkQNdHYjfrwVnByN7p+7OHwVvjjVdjxJSgz9JgCPSbD+vfgktlGorL2LdjxhTEzKaAr/O1P49rCzHPbIVvUymbT7EnLZ3NSFjsP5xJ/OJfxPYO47qIOHMoqZMh/fqFzgDuRbT2JbONJZFtPurfzqjXRKC4rJzEtn81J2cQdyuJobgkJR/KOb21QE393R9p6uxDdzpv7h4fh43YOe3IJUQeSvLRskrxcyOaNNKZV97kFBv8d3Pzsc9+sA7DmDdi80FiNN3y0Mbg3uC989wBs+RTu+NVIWNr2NFpv/tMZLp5hTMcWDSYtt5iFfx4kPtVIag7nFAPw2jW9GBfdlsS0fJZuTjme2LSvQ7dTVkEpu47ksftoHjsP5/JLQhoZ+aVYbSf/WzO4iz9RQV58G5dKUVk5P9w3GD83R37bnY7FbKKjvxuBns7S/STOiSQvLZskLxey3MPwyzNGkuHobiQY/e46/5lJlQoyjMG7f70LxdnQ/mLoNtHYALLnNKPOx1cbg4hDBkFwPwjuY4yh+foeiBoPkVfKPkoNKLOglJ2Hc4kI9MDP3YllcanM+nwL5RWJh5ujma5tPHlxcjQd/Nw4mltMcVk57XxcMZ8hyTg+0PhwLr8nZnDgWAFHcorZm3byOjQeTmbySsqPHzuYFW6OFiLaeNC7vQ8d/d2Of/nJQnviDCR5adkkeRHGpow/zTGW/R/9ktESY08l+cYO2GvfhNxD4BVsbCbZ+TJjIK+jG/S9zWiBWTgBAqMhaS0c+su4vnU3iJxgjJHx72Lf2EStisvK2XM0n/jDOcSn5rIjNZd5N/XB09mBl1bu5rWf9uBoNtHez5WO/m508ndj1vAwnB3MlFjLcTSbTrteTKnVRlJmIfvT8zmYWcietDz+SMwgr6icnOKy08bk4WzhqQnd8Hdz4uN1B+nXyY8bLw4BjJYfb1cHWaPmAifJS8smyYs4IWkdtO0FFkfY+a2x0J09ZiZVKi+D7V8ag4f3/QKl+cZ6NMEXQedLjZaZ1S8Za8P0ug4y9sBXd0J5iTFGBqBV5IlEJiDcPnGJc5aYls+mpCz2pRewPyOffekFpOeXsHn2cJRS/H1JHN9vP0Infzc6BbjT0d+NLq3cuaJ7m1rvXVxWzqGsQnYdziMps5DkzEK2pmSTmFZAidV2Ul2LSdG9nRdujmZWJx7DbFL4uzsS4O6Eu7OF2A6+dPR3I8jHhSBvF9p4OR/fNFO0TJK8tGySvIiafTgaDq42unOGz4GgGPve31pqtKzsWWlsKXC0Ijlxb13RKnMpuPjB4htgysfg1xk2fmTspXRsn7EA3wMJRpdT8l/g0cbYokA0OptNHx+n8v22w6zZe4z9GQXsS88nNaeYTv5urHpwKACzPt9CanYRQT4utPN2IcjHhc6t3InpcObB28Vl5SRnFpJwJI9NSVnkFpeRml1M4tE80qrsun06kW08uX1wJ0rLbXy89iB/GxbK5d3aUGI17hvk7YqLoyys2JxJ8tKySfIialZeZiQLvzwLhRnQebgxJiZkYP08L/cw7F1lrNa7d5UxRkaZjJagzpcZLUDJ62DFo8a2B6UF4BVkfP/0GiO5mjzfuNfaN6FVV2NdGdmmoEkpKi0nI7+EYF9jXNXTy3eyOSmLlKwijuQWY9MwoLPf8TVqrn57DWXlNoJ8XGjrZSQ3lQvxnY7NpsnILyElu4i9aQVsT82hzGrjwLEC9qTlcyy/pMb9ntp4OVNu08dnSzk7mHBxMOPkYKZ7kBfBPi74uTkR4OnEwM7+tK3DXlOi8Ujy0rJJ8iLOrDgX1r4BcZ8Zu0tHjIYj241BuKGXQKch4OJj32fayiFlEySuNJKZlE2ANvZTatcHul1lPHvVE8ZCedd/bbTAZO2H3FT4ocqMJb8u0C7WSG6CYozxMxaZntsUlZXbOJJTTFm5jU4B7gA8vmwHe9PzSckuIjW7iOIyG1fHtOOFSdForenzfz/i4+poJDfeLrTxdOaiUD/6hPiitSY9rwRfN8dTuoiKSstJzSlif0Y+8am5WMs1KdnFxCVnk5xViLVcU36Gfxs7+bvRta0niWn57Dmaxx1DQrmokx+bDmay83AufTv60drTmVYeTrT2dMbP3RF3J4uMw2lAkry0bJK8iLqz2YyNHnd8BctmQkluRetIbyOZ6H+3/RMZMBa62/ezkcgk/ggF6cZ5/wjw62i0zLSKhN/+Y+zBdMNSI+H55Wnj2pLcE9eYnYydsYf8HboMN96TUrLibzOgtSazoJRym6aVpzMl1nKe/X4XqdlFpGQXkZJVRFZhGTMv6cz9I8I5ll9CzFM/YlLg6+ZEgIcTrTycuLZfe0ZEBVJQYuWXhHRaeToR4O5EK08nXB2NvZtsNk12URlpucUkZxWSW2QlLa+YjQeySM4qxM3JQnZhGcmZBZTZagm8gkmBxWTC2cHE/cPD6N7Omz8SMziUVcg/R3fFy8WR1KwiCsus+Lo54e3iINPEz4MkLy2bJC/i3JRbjT2T9q4yvo7ugIcSjWnWWxcb3T6hlxgL4NkzMbDZjPExiT9C4io4HGfsdl3JvbWRyLSKNLZE8GgL416H4iz4YCS4+oCTBwx+yOhSyjsCy+6B674wuqiO7YXsg+DT0ZgVZZaNCJuTEms55TaNq6OFvOIylm5JJT23mPT8EtJyS0jPL+HmAR2Z0CuI7Sk5jHl99UnXuztZePaq7ozp0ZZ96fm89/t+fN0c8HF1xMfVEV83R6KDvfF1c6TcpjEpKCorJz2vhPS8EhKO5pGSWUhJuY3kzCK2p+aQX2xFAwUlVmyn+efWrMDHzYnMgpLjdRRgMilcHMy09nTC180Rq03TxsuZ2WMiaeXhzIaDmZSU2RgcFgAYs7cczEpaeJDkpaWT5EXYR2nhifVhPrsWdn1rvPZqD6HDIPwK48vetIbcFEjbCWnxFd93QnoCWKvsx+MVDBZnY6p11JXg2xk+HGnMWjI5wPAnjO6x4mxj92wwZkJ5BRsrA/t2NBKayu8BEZLYNHPFZeUcOFZgJDV5JaTllZCWV8xVvdvRLciLP/cdY8Ynm8gqLDu+zg3A/Jv7MiQsgB+2H2HGJ5vwdnU8KcH5+8hwOgW4k5iWT1xyNj5uDni5OODhZMGhYtp4bnEZmQWl7DqSy7H8UhzMiqxCK2v3ZlBYWo5NawpKrBTVsVmnaxtPPJ3NbDyYjdWmj4/XKbXa8HUzVjX2dnGgsKyciEAP7h8ejqNZEXcoB2cHM5FtPYGWlfxI8tKySfIi6kfmvopWmZ9h/2/QYQBM+8wo++kJYyPHykTApwNY7LzgmK3cWOn3eDJT8T1jN9isFZWUkZy07Qne7eHPt43F89pfZAwg/vkpo0us8v0UZ5+4/wMJRjK061s48AdMeMtoYco6aJx38z//HbxFk2CzafJKrGQVlJJZWEpogDteLg7sPJzLN3GpZBWWkllQSlZhGVkFpbx9XQydW7kzf80B/r1sxyn3+/nBoXT0d2Ph2gO8v3o/ns4OeLpYjO/ODvxzTFc8nR3YkpxN4tE8LGaF1mDTmtTsIpwdzJhMJnIKS1mdmIFNa/zdnckpLGVbag5aQ7lNn7KicXUWE1htRqtPl9YeOFlMbE0xrnc0m3AwK6w2jberA96ujjhbTBSWltMtyIvbBnXCbIL/7ThKZBtPLo1sTblNk5iWh4uDBVcnM26OFpwdTr/GT32T5KVlk+RF1L9yKxRlgXsAlBXDf0KNNV6OU0Y3ziX/BGuJ0QJStZXDnjOGrKWQufdEUlPZWpO5D6j2d8FkAbfWRnLl4GKsTRN2udES49cZvrsfuk0yupkmvA3r5kL6LmOjSmUyBhh7tDYSNfdW4BZgfHkFQ49JxjMKM417O8jMlZamqLSco7nFZBWWkltsJbeojLxiK+N7tsXNycLK+KN8E5dKXnHZSeU/PjAEdycLT30bz/ur959y371Pj8JsUjy+bAdfb0nB1dGCm5MZNycLPq6OzLuxDwCLNySzIzUXs0mhMBKa7KISQvzdcTSb2ZdurNHj6mDGz8OJ3MIydh7JxWRS2GzGhp215D/HVSY7BaXlp5SZFDiYTZhNCmu5Jqy1O2Oj25JfYuXrLalcHOrHyG6B5JdYWbophbuHhdK7lqnydSHJS8smyYtoeFobWwdk7YfM/cb3dn2MtV2O7YXXe59c39kbrngOoqcaA3ATlp9IbNxb26f7pqwY8g4bY2DyUo2Wl7zDJ87lphpf5TVsOujiY+ymnZcKQbFG91neUUjbYUzZ1jbITzcSOLSR+Ix/E3YsNbZCUAqufMf4HDZV7AdVmei4BYCzpzFOx8kDnDwrEqCg83/PoknLq+hayi2yViQ4RnIzKdZYz+ibuFTWH8gkv8RKYUk5BaVWlFIsuLkvAPcv2sK3cYcpLT/R9dTWy5k1/7gUgBvm/cVvu9NPemaXVu6svH8IAH/77yYSjuThaDHhaFGYlaKVpxNXxwRTarXx5aYUDhwrwNXRjKujhcJSKynZRfi7O2GrmOmVX2zFwWLCZtOUldtqnKJeXaCnE38+etl5f36SvLRs9Z68KKVGAq8CZuB9rfWz1cqdgAVADHAMmKK1PnCme0ry0sKV5BtdPseTmwPG7tTtLzK6oRZOOLm+owdM/siYdXRog7GztYu3kVQ4V3wPH2W0ghRlG90/zt5GImA6i1VWtTaurUxmKpOb3GpJT0GakbCcicXZaGXybGvsK6VMRteWdwiUFUBxDpSfZrG1DgOg9w2QugX2rDDed4+pRuvR5gXg4Ga0GlmcjO4wJw/jGc5e4OAMvqEQ2M2415HtxgJ/bn7GYOjyEiO2FjDmQRhKrTYKS63kl1gpK9d09HcDYN2+YxzJLaaotJyiMuPLw9mB6y/qAMBLK3eTmJZXpdxG5wB3XpwcDcDY11cTfzj3pPFAQ8MD+OgmI3m66OmfOJJbfFIso7u34bVrelFUVs5FT/9EfokVswmcLGZMaCLaeHHb4I5cHlX7Csy1keSlZavX5EUpZQZ2A8OBQ8B64BqtdXyVOncDPbTWdyqlpgJXaq2nnOm+krxcwMqtkJN8IrEpyDASipibICDMWK13xaNGK0dR1okE4LZVxjovG+fDNzONc5VdOy7ecO0S8As1tkWI+9ToxrE4n/g++EHjl/+hjXAkzjh3vNwJQgYbLUD56VCSZ7SelBUZi+iVFRhjcIpzjOSpJNd4XZxjxF6cY7yPokyjBajq7Km6UBYjCSsvNWIC47W2YcxZqfZ3vHU3Y5By4THISTJmhYHRqnUkruKeZuOeju7G+yu3GgmRR2tjewZHDygvMraU6D7ZeFZJrrGNg8URCrOMz8a7vXF9UbZx7BFobMBpcTYSpcx90KYnmB2NrsTcFOM5ymxsT6HMxtghk6Xiy2z8mVkcjZh0uXGtJFuNpqzcRmFpOaVWGybF8Q0ztx3KoaDUSonVRklZOSVWG609nenb0egSeu+3fRSUWikus1FiNcpj2vtwVUw7u8QlyUvLVt/TJfoCiVrrfQBKqc+A8UB8lTrjgccrXi8B3lBKKd0c+7NE/TNbjC4j344QWkN550uh8zrjtdZGAlGcDa5+xrmQgTD+LSOxKc6uSHKyjVYYMM4d22skH5UJiLUYBtxrlCd8B7+/eOpz/3nEiO33F4yxL1UpE/w7y3j99d9g83+NX8RmB+O7iw/ct9Uo/+5BYxq4MlX8QlZG+bBHjVg2zDPG7ICRMGhtJBjt+hixp8UbyZC1xBiYrExGAqAUlBUaSdTReKBKy9DeVae+H10O5eUVXV1V5B8xpqdXVTmzrK6U2bg/JiMORw8jNpP59K1NVTn7GImS2cH4s/ELMxJaB+eKeCsTtor1e5TJeN+qopXNs62x7o/FyZglFxQLmYlGElSQYVxrs56cRFmLjDWCtA08gyD/qHFsLTJ+ptJ2Gc8qzDD+TKzFxv1NFiNRK80Hi4vxvj3aVlzvYMTV4WJjdpytzBgDZSs3rnd0NZ7v4Gq8X0c34/kufsZzTBVJa3A/Yx+w0nyjXnmZ8edf2aLn6GYsNunoanwmTm7G56QsRkIZ2AOyDxjnSguMa8tLK1omzRWfU4HxPkwWI/EtzTc+JxdfHHw74VWQbrQ8WkuNn1NbGd2dPI0kU5mM8yaz8TxtA2sJt9ms4NUOXP2N1tbsA3DACnnXwdBHav6zF6JCfScvQUByleNDQL/T1dFaW5VSOYAfkFG1klLqduB2gPbt29dXvKIlUcr4B7tyCjcYrSt+NWU9FXpdZ3ydzqAHoe/tJ5KasiLjH3tzxWypHlOMRfDKy4xfgLbyk7uQwkcZv7xsVuOXla3c+CVWyb+LkYTYrBX3KDcSr9BhRvmhv4wWC62N+9rKjT2dxr1qlC/9GxzZWlFe8exWkTDpQ6P8v5OMGVeV12ttJD5jXjKe99+rjV9CNhugK8pj4eKZxi+gZTOMX5CV1ypltGh1Gmoc//FKlfdd8WcQ2A08g41r9nxv1ENhJFDK+AXm5GGUp9TQourRxrifyWLEVlyRUFkrBoeWV/yiPt4FqE9819pIGig1rrcWGYkOGH9+YCSDJXnGL9mqY5oqEymbteLLZnymx/acHN/BtcYvc6WqzGQDSitf5xqxlBYa36snhLtXnIilaitZUbXxVZWz3fIOn3w+JxW0lVOUFZ58XHhqFcD4eajeOgfVBtWfRk7yida66kpy63Z9dZvmS/IialXf3UZXAyO11rdWHF8P9NNaz6hSZ3tFnUMVx3sr6mTUdE+QbiMhhB1VJmFV/y2s+rpyBWatTz5fvbwy4Tul3GSn8vKan28yn7m8ckB7fZeX15BA1Vau1IklBSrLlensxqKdhnQbtWz13fKSAlTd6rddxbma6hxSSlkAL4yBu0IIUf8qx8tUHTdT0xia2raRqO0X7nmX17JuUGOX1zbr73zLhaji/NPbM1sPdFFKdVRKOQJTgWXV6iwDple8vhpYJeNdhBBCCHE69ZrqVoxhmQGswJgqPU9rvUMp9QSwQWu9DPgAWKiUSgQyMRIcIYQQQoga1Xs7ndZ6ObC82rnHqrwuBibVdxxCCCGEaBnqu9tICCGEEMKuJHkRQgghRLPSLPc2UkqlAwftcCt/qq0n04xI7I1DYm8czTl2aN7xN9fYO2itAxo7CFE/mmXyYi9KqQ3NdR0Aib1xSOyNoznHDs07/uYcu2i5pNtICCGEEM2KJC9CCCGEaFYu9OTl3cYO4DxI7I1DYm8czTl2aN7xN+fYRQt1QY95EUIIIUTzc6G3vAghhBCimZHkRQghhBDNSotMXpRSI5VSCUqpRKXUIzWUOymlPq8oX6eUCqlS9o+K8wlKqcsbNHDqFPv9Sql4pdRWpdRPSqkOVcrKlVJbKr6qb4DZIOoQ/41KqfQqcd5apWy6UmpPxdf06tfWtzrE/nKVuHcrpbKrlDXaZ6+UmqeUSlNKbT9NuVJKvVbxvrYqpXpXKWvsz7y22K+tiHmbUmqNUiq6StmBivNblFIbGi7qk+KrLf6hSqmcKj8bj1UpO+PPW32rQ+wPVYl7e8XPuG9FWaN/9uICp7VuUV8YG0DuBToBjkAcEFmtzt3A3IrXU4HPK15HVtR3AjpW3MfcxGIfBrhWvL6rMvaK4/xm8NnfCLxRw7W+wL6K7z4Vr32aUuzV6t+DsdFoo3/2wGCgN7D9NOWjgO8BBVwErGsKn3kdY7+4MibgisrYK44PAP6N9bnXMf6hwLfn+/PWGLFXqzsWWNWUPnv5urC/WmLLS18gUWu9T2tdCnwGjK9WZzwwv+L1EuBSpZSqOP+Z1rpEa70fSKy4X0OpNXat9c9a68KKwz+Bdg0YX23q8tmfzuXASq11ptY6C1gJjKynOGtytrFfA3zaIJHVQmv9G8aO7KczHligDX8C3kqpNjT+Z15r7FrrNRWxQdP7ea/LZ3865/N3xS7OMvYm8/MuBLTMbqMgILnK8aGKczXW0VpbgRzAr47X1qezff4tGP+jruSslNqglPpTKTWhHuKrTV3jv6qiK2CJUir4LK+tL3V+fkVXXUdgVZXTjf3Zn8np3ltjf+Znq/rPuwb+p5TaqJS6vZFiqov+Sqk4pdT3SqmoinPN5rNXSrliJLVfVDndXD570UJZGjsAcW6UUtcBscCQKqc7aK1TlFKdgFVKqW1a672NE+FpfQN8qrUuUUrdgdECdkkjx3S2pgJLtNblVc41h8++2VJKDcNIXgZWOT2w4jNvBaxUSu2qaE1oSjZh/GzkK6VGAUuBLo0b0lkbC/yhta7aStMcPnvRgrXElpcUILjKcbuKczXWUUpZAC/gWB2vrU91er5S6jLgn8A4rXVJ5XmtdUrF933AL0Cv+gy2BrXGr7U+ViXm94GYul5bz87m+VOp1oTeBD77Mznde2vsz7xOlFI9MH5Wxmutj1Wer/KZpwFf0bBdvHWitc7VWudXvF4OOCil/Gkmn32FM/28N9nPXrRsLTF5WQ90UUp1VEo5YvzFqz77YxlQObPiaoyBaLri/FRlzEbqiPE/pL8aKG6oQ+xKqV7AOxiJS1qV8z5KKaeK1/7AACC+wSI31CX+NlUOxwE7K16vAEZUvA8fYETFuYZSl58blFIRGINb11Y51xQ++zNZBtxQMevoIiBHa32Yxv/Ma6WUag98CVyvtd5d5bybUsqj8jVG7DXOmmlMSqnAivF0KKX6Yvybe4w6/rw1NqWUF0br7tdVzjWLz160bC2u20hrbVVKzcD4R9iMMSNkh1LqCWCD1noZ8AGwUCmViDFgbWrFtTuUUoswfvFYgb9V6xpoCrH/B3AHFlf8m5iktR4HdAXeUUrZMP6BfFZr3aC/QOsY/0yl1DiMzzcTY/YRWutMpdSTGP+oAzxRrZm6KcQOxs/KZxXJbqVG/eyVUp9izGrxV0odAv4NOABorecCyzFmHCUChcBNFWWN+pnXMfbHMMajvVXx827Vxg7HrYGvKs5ZgE+01j80ZOx1jP9q4C6llBUoAqZW/OzU+PPWxGIHuBL4n9a6oMqlTeKzFxc22R5ACCGEEM1KS+w2EkIIIUQLJsmLEEIIIZoVSV6EEEII0axI8iKEEEKIZkWSFyGEEEI0K5K8CCGEEKJZkeRFCCGEEM2KJC9CCCGEaFYkeRFCCCFEsyLJixBCCCGaFUlehBBCCNGsSPIihBBCiGZFkhchhBBCNCuSvAghhBCiWZHkRQghhBDNiqWxAzgX/v7+OiQkpLHDEEII0URt3LgxQ2sdYMf7tbJYLO8D3ZD/+DcEG7DdarXeGhMTk1a9sFkmLyEhIWzYsKGxwxBCCNFEKaUO2vN+Fovl/cDAwK4BAQFZJpNJ2/Pe4lQ2m02lp6dHHjly5H1gXPVyu2SPSqmRSqkEpVSiUuqRGsoHK6U2KaWsSqmrq5zvqZRaq5TaoZTaqpSaYo94hBBCCDvrFhAQkCuJS8MwmUw6ICAgB6Ol69Ty832AUsoMvAlcAUQC1yilIqtVSwJuBD6pdr4QuEFrHQWMBF5RSnmfb0xCCCGEnZkkcWlYFZ93jXmKPbqN+gKJWut9AEqpz4DxQHxlBa31gYoyW9ULtda7q7xOVUqlAQFAth3iEkIIIUQLZI9uoyAgucrxoYpzZ0Up1RdwBPbaISYhhBCixbDZbMTExIQvWrTIs/LcvHnzfAYNGtRl0qRJIb6+vtFdunSJOpd79+3bNzwkJKRbREREZEREROSHH37oA2A2m2Mqz0VEREQ++uijgVWve/HFF/1Hjx7dqfI4MzPTFBwc3C0+Pt5x3rx5Pp07d44ymUwxv/32m+u5vu/TaRIDdpVSbYCFwHStte00dW4Hbgdo3759A0YnhBBCNC6TycTcuXMPTpkyJXTMmDHxZWVlas6cOUHLly/fk5SU5HDvvfem3XTTTR3P9f4LFizYN3jw4MKq55ycnGy7du2KP901s2bNyvj444/9ly5d6jFhwoS8Bx98MGjatGkZkZGRpcXFxaYvvvgi8bbbbgs515jOxB7JSwoQXOW4XcW5OlFKeQLfAf/UWv95unpa63eBdwFiY2NbZr/jxvmw8xsY9xp4tm3saIQQQpzG+DdWh1c/d3m3wMy7h3ZOLyixmqa992eX6uUTegVl3DSg47G03GLLbQs2hFYt+3rGwITantmnT5/iESNG5MyePTuwoKDAPHny5GNRUVElUVFRJQkJCY7n947OXmVCdd1113Xy9fXdv3r1ao+tW7fuBOjdu3dxfT7bHsnLeqCLUqojRtIyFZhWlwuVUo7AV8ACrfUSO8TSvBWkQeKP8PFVcNP34OLd2BEJIYRoQp5//vnUHj16RDo6Otri4uJ22uu+N9xwQydnZ2cbwC+//JIQGBhYXlJSYoqIiDg+AeeBBx44fNttt2VVva5fv35FQ4cOzRk9enTYp59+utfZ2blBGhfOO3nRWluVUjOAFYAZmKe13qGUegLYoLVeppTqg5Gk+ABjlVJzKmYYTQYGA35KqRsrbnmj1nrL+cbVLJQVw+8vQNteEDEaBt4PQbHw30nw6TVw/Zfg4NLYUQohhKjmTC0lbk4W25nKW3k6W+vS0lITT09P24QJEzLd3d3LXVxc7JYonEu3UaVZs2alrVq1ymvMmDF59oqnNnZZ50VrvVxrHaa1DtVa/1/Fuce01ssqXq/XWrfTWrtprf0qEhe01h9rrR201j2rfG2xR0xN3oHVMHcA/PYfSKroLTOZIXQYTHwHktbC0rsbN0YhhBBNjslkwmSq+69vq9VK5aDb++67z+5jEsxm81nFYw9NYsDuBaUwE1Y+BpsXgk8IXL/USFiq6nYVFOeAf1hjRCiEEKIFsVgs1KUFpTmR/Rka2t5VsOUTGHAf3LX21MSlUuzNEDLQeH14a4OFJ4QQonkZO3Zsx4EDB0bs37/fqXXr1j1efvllf3vct3LMS+XX3XffXedlUBYsWODdunXrHlu2bHG78soruwwcOPCUAcznQ2nd/CbuxMbG6ma1t1F2EhzZDhGjQGvI3Ad+obVfBycG8F7xH+h3e/3GKYQQLYRSaqPWOtZe94uLizsQHR2dYa/7ibqJi4vzj46ODql+XrqN6lO5Ff56B1Y9BU4eEHoJODjXPXEB6DgUwkfB938HN3/oNrG+ohVCCCGaBek2qi+H4+D9S2HFoxAyCG79yUhczpbZAlfPg/YXwZe3w75f7B6qEEII0ZxI8lIfspPhvUsgNxUmfQTTPgfv4FovOy0HF7jmU/DrDJ9dB3lH7RaqEEII0dxIt5E9ZSSCf2cjURn/FoSNABcf+9zbxcdY92XvKvBobZ97CiGEEM2QtLzYQ0GG0aXzZh9I3WKci55iv8Slkmdb6HWd8Tplk7TACCGEuCBJy8v5yjkEcwdBSR4M/ju06lr/zywthE8mg0cg3LgcnD1rv0YIIYRoIaTl5Xzt+wWKMmH6NzDsH2Bxqv9nOrrChLmQthM+mwbWkvp/phBCiEZjs9mIiYkJX7Ro0fH/rc6bN8+nf//+Yf369QsLDQ2N6ty5c9STTz7Z6mzv3bdv3/CQkJBuleu5fPjhhz4AZrM5puo6L48++mhg1etefPFF/9GjR3eqPM7MzDQFBwd3i4+Pd7zjjjvadezYMSosLCxy+PDhoRkZGebzef/VScvL+UrbCWYnCO7bsM/tchmMfxO+ugO+vA2u/tDYXkAIIUSLU7mD85QpU0LHjBkTX1ZWpubMmRP03nvv7Xd1ddUDBw4szMrKMvXq1Sty1KhRuTExMWe1q/O57G00a9asjI8//th/6dKlHhMmTMh78MEHg6ZNm5YRGRlZevnll+e+8cYbhxwcHLjrrruCZs+eHfj222+nnOv7r06Sl/PV7SpoFdk4iUP0VChIh//9y9huIObGho9BCCEuRO8OCz/lXNexmQy6P52SfBPzx566omz0lAz63XmMvCMWPr3m5AW/bv+51o0a+/TpUzxixIic2bNnBxYUFJgnT558bMSIEQWV5T4+PrbQ0NCipKQkx7NNXs5FZUJ13XXXdfL19d2/evVqj61bt+4EmDhxYm5lvf79+xcsWbLEroNAJXk5X0G9ja/GcvE94N0ewkc3XgxCCCEaxPPPP5/ao0ePSEdHR1tcXNzOqmUJCQmO8fHxrkOGDMk/2/vecMMNnZydnW0Av/zyS0JgYGB55fYAlXUeeOCBw7fddltW1ev69etXNHTo0JzRo0eHffrpp3udnZ1PWbb/o48+8r/66qszzzamM7FL8qKUGgm8CpiB97XWz1YrHwy8AvQApmqtl1Qpmw78q+LwKa31fHvE1CBKC+HgHxAUA66+jRdH5Hjje94RY4fqqAmNF4sQQlwIztRS4uRuO2O5R6C1Li0tNfH09LRNmDAh093dvdzFxeV4opCTk2OaOHFi6LPPPpvs6+trO9v7nku3UaVZs2alrVq1ymvMmDF51csefvjhQLPZrO+88067Ji/nPWBXKWUG3gSuACKBa5RSkdWqJQE3Ap9Uu9YX+DfQD+gL/FspZef5xfUoLR7+ezUkrW3sSAw/Pw1LboKd3zZ2JEIIIeqJyWTCZDrx67ukpESNHj06dNKkSZnTp0/Prl7farVSOej2vvvua2vveMxm80nxVHrttdf8VqxY4f3ll1/ur6n8fNij5aUvkKi13geglPoMGA8cz9a01gcqyqpng5cDK7XWmRXlK4GRwKd2iKv+pVW02AVENG4clUY+A0d3wJKb4fqvIGRAY0ckhBCiHtlsNqZOndohLCys+PHHH69x8S+LxUJdWlDsacmSJZ6vvvpq4O+//57g4eFx1i1BtbFHKhQEJFc5PlRxzq7XKqVuV0ptUEptSE9PP6dA7S59F1icwSeksSMxOLrBtYvBpwN8eo2RyAghhGixVq5c6b506VK/1atXe1S2rnz++ede9rh35ZiXyq+77767rr/buf/++9sXFBSYL7nkkrCIiIjIadOmtbdHTJWazYBdrfW7wLsAsbGxpwwIahRpO8E/rGlNUXb1heu+hA9GwHcPwk3LQanGjkoIIYSdvPTSS6mVry+//PJ8rfXG87nfX3/9VeP4m/Ly8jrdNzw8vHTPnj0n/W85KSlp+/nEVBt7JC8pQNVdB9tVnKvrtUOrXfuLHWJqGOm7IGRgY0dxKu9guPFbcAuQxEUIIUSLY4/kZT3QRSnVESMZmQpMq+O1K4CnqwzSHQH8ww4xNYxrF4OpiTZe+VUsIVBWDEe2NvwiekIIIUQ9Oe8xL1prKzADIxHZCSzSWu9QSj2hlBoHoJTqo5Q6BEwC3lFK7ai4NhN4EiMBWg88UTl4t1loHQUBp65T1KSs+AcsmADH9jZ2JEIIIYRd2KXZQGu9HFhe7dxjVV6vx+gSqunaecA8e8TRoJL/MqZKR08Di2NjR3N6gx6E7V/CF7fCLf8Ds0NjRySEEEKcF9mY8Vxt/xJ++EfT7Taq5BUEY1+F1E3w63ONHY0QQghx3iR5OVfplTONmsFHGDUBel4Hv78IB5vIgnpCCCHEOWoGv3mbqPQEaNW1saOouyuehYgx4OrX2JEIIYQ4SzabjZiYmPBFixZ5Vp6bN2+ez6BBg7pMmjQpxNfXN7pLly5R53Lvvn37hoeEhHSrXM9l5MiRnR5++OHAymOz2RxT+fqpp55qVXndhg0bnENCQrrl5+cfn9Y6dOjQzu+8847v5s2bnXv27Bnh6OjY+7HHHmt9fu/+VE28z6OJKsqGvMNNZ2XdunDygCkLGzsKIYQQ56ByB+cpU6aEjhkzJr6srEzNmTMnaPny5XuSkpIc7r333rSbbrqp47nev6a9jZ577rkjAK6urr1qWqE3Nja2eNSoUVmPPvpom9deey114cKF3mVlZeqOO+7ITElJsbz66qtJ9t5NupK0vJyLjD3G91bVt3BqBkryje0Dti2pva4QQogajX9jdfiHf+z3Ayi12tT4N1aHL1x70BegoMRqGv/G6vDP/kryAcgqLDWPf2N1+JKNh7wB0nKLLePfWB3+9ZYUL4DU7KI6NST06dOneMSIETmzZ88OfPjhh9tOnjz5WFRUVMkVV1yRHxAQYK2XN1qL55577vCyZct816xZ4/LYY48FzZ07NwkgKCjIOmTIkEIHB4d6WVRWWl7ORXAf+Pt+cHBp7EjOnsUZcg7Bt/dDcD9jQTshhBDNwvPPP5/ao0ePSEdHR1tcXNxOe933hhtu6OTs7GwDGDJkSO4777xzqC7XeXh42J5++unkESNGRNx+++1Hu3fvXmKvmM5Ekpdz5erb2BGcG7MFrnwH5g6Cr+6E6cua1vYGQgjRDHw9Y+DxJfUdLSZd9djNyWKreuzj6lhe9biVp7O16nFbb5c6t5p4enraJkyYkOnu7l7u4uJit1aNmrqN6mratGk5DzzwgPWBBx5Is1c8tZFuo3Pxy3OwaUFjR3HufDvCqOfh4Gr449XGjkYIIcRZMJlMmM5ipqvVaqVywO19993XtinEdL6k5eVcrH8fugyH3jc0diTnLvoa2L0C1s2FfncYO1ILIYRocSwWCzUNuG3OJHk5W4WZUJDWvGYa1UQpGPuKsfeRJC5CCNFsjR07tuOff/7pkZWVZWndunWPRx55JHXWrFkZZ3OPqmNefH19rWvWrNl9PjElJSVZ+vTpE1lQUGBWSul33nmn9c6dO7f7+vrazue+lSR5OVtpFeOjmtMaL6fj4gMugM0G+3+B0EsaOyIhhBC1eOmll1KrHn/zzTf7z+d+f/31V8KZygsLCzfXdo+UlJRtVY/bt29vPXr06NbzietMZMzL2UqvSF6ae8tLVZs+goVXwq7ltVYVQgghGptdkhel1EilVIJSKlEp9UgN5U5Kqc8rytcppUIqzjsopeYrpbYppXYqpf5hj3jqVUkeuLcGrxr3mWyeel4Lgd1h2QzIO9rY0QghhBBndN7Ji1LKDLwJXAFEAtcopaqv3nYLkKW17gy8DFTuEDgJcNJadwdigDsqE5sma+AseCDBGDPSUlic4KoPoLQAvr4bdL2sKSSEEELYhT1aXvoCiVrrfVrrUuAzYHy1OuOB+RWvlwCXKqUUoAE3pZQFY/RFKZBrh5jqV0tKXCoFhMOIpyDxR/jr3caORgghhDgteyQvQUByleNDFedqrKO1tgI5gB9GIlMAHAaSgBe01pk1PUQpdbtSaoNSakN6erodwj4HBcfg/eGwd1XjPL++9bkVYm4yupCEEEKIJqqxB+z2BcqBtkBH4AGlVKeaKmqt39Vax2qtYwMCAhoyxhPS4uHQXy23W6Vy+nSHi43jlvo+hRBCNGv2mCqdAlTdIKddxbma6hyq6CLyAo4B04AftNZlQJpS6g8gFthnh7jsL32X8b0lTJM+E61h5WPG6xFPNm4sQgghsNls9OnTJ/zhhx8+PHny5FyAefPm+bz33nsBNpuNjIwMB6UU06dPT589e/ZZLdPft2/f8LS0NIfKdV5CQkKKo6OjC7/++mtfgD179rh06dKlCOC6667L+Ne//pUGsGHDBuerr7668/bt23e4u7trgKFDh3a+5pprMm02Gy+//HIggJubm+2tt9462L9//yJ7fR72SF7WA12UUh0xkpSpGElJVcuA6cBa4GpgldZaK6WSgEuAhUopN+Ai4BU7xFQ/0naCkxd4tGnsSOqXUsbg3Q0fGGu/hA5r7IiEEOKCZjKZmDt37sEpU6aEjhkzJr6srEzNmTMn6L333tvv6uqqBw4cWJiVlWXq1atX5KhRo3JjYmKKz+b+Ne1t9Nxzzx0BcHV17VXTCr2xsbHFo0aNynr00UfbvPbaa6kLFy70LisrU3fccUfmypUr3f7444+EgICA8kWLFnnecccdHbZu3brr/D6FE86726hiDMsMYAWwE1iktd6hlHpCKTWuotoHgJ9SKhG4H6icTv0m4K6U2oGRBH2ota63RW3OW/ouY2BrSxywW92Ip8A/DJbeZawqLIQQ4oR3h4Wzbq4fANZSxbvDwln/vrFjb0m+iXeHhbNxvg8AhZlm3h0WzpZPvAHIO2Lh3WHhbFvsBUDOoTo1JPTp06d4xIgRObNnzw58+OGH206ePPnYiBEjCgYOHFgI4OPjYwsNDS1KSkpytO+bPb3nnnvu8LJly3zXrFnj8thjjwXNnTs3CWD48OEFAQEB5QDDhg0rOHLkiF1jsssKu1rr5cDyauceq/K6GGNadPXr8ms632T5dATPetnTqulxdIWJ78H7l8E398LkBRdG0iaEEE3Y888/n9qjR49IR0dHW1xc3M6qZQkJCY7x8fGuQ4YMyT/b+1bdHmDIkCG577zzzqG6XOfh4WF7+umnk0eMGBFx++23H+3evXtJ9Tqvv/66/7Bhw3LONqYzke0BzsaENxs7gobVtidc8i/4+WnI2G20OgkhhIDbfz6xpL7FUZ907ORuO+nY1bf8pGOPQOtJx17trHV9rKenp23ChAmZ7u7u5S4uLsdnVeTk5JgmTpwY+uyzzyafy/5BNXUb1dW0adNyHnjgAesDDzxwylibb775xuPjjz/2X7Nmjd26jKDxZxs1HxfqzJuL74G710riIoQQTYTJZMJkOvHru6SkRI0ePTp00qRJmdOnT8+uXt9qtRIREREZERERed9999VL90H1mADWrVvncvfdd3dYunRpYmBgYLk9nyctL3X113vwx6tw1x/g4t3Y0TQckxn8Qo3X25ZAxyHg3khT1YUQQpzEZrMxderUDmFhYcWPP/54jfu7WCwWahpwW5/27NnjOGnSpNB58+bt79GjxyldSedLkpe6SouH0nxw9mrsSBpHTgp8/Tdo2xtu+BosDTYeTAghxGmsXLnSfenSpX5dunQpioiIiASYM2dOypQpU85qjEnVMS++vr7WNWvW7D6fuP71r3+1yc7Ottxzzz0dACwWi96+ffvO2q6rK6WbYXdIbGys3rBhQ8M+dN5I4/vNPzTsc5uSrYvhy1sh9hYY81JjRyOEEKellNqotY611/3i4uIOREdHZ9jrfqJu4uLi/KOjo0Oqn5cxL3WhtbHGS0BEY0fSuHpMggH3Guu/bJjX2NEIIYS4QEnyUhf5R6E4u+WvrFsXl/4bOl8Gy/8O2UmNHY0QQogLkIx5qQttMzYtDO7X2JE0PpMZrvoADvwO3u0bOxohhBAXIEle6sKzLYx+sbGjaDpcvKHrWON16mbwDzcWtRNCCCEagHQb1UV+OpTXeQ2hC0feEWMg89d/u3DXwRFCCNHgJHmpi8+vhYUTGjuKpscjEIY+Aju+hNUvN3Y0QgghLhCSvNRGa0jbZWxSKE414D7odjX89AQkXMDTyIUQoh7ZbDZiYmLCFy1a5Fl5bt68eT6DBg3qMmnSpBBfX9/oLl26RJ3r/Q8fPmyxWCy9n3/++ZNWIQ0KCuoeFhYWGRERERkWFhb58ccfewMkJiY69OvXLyw0NDSqc+fOUU8++WSr6vf86quvPHv27Blhsxm7FVitVrp27Rq5cuVKt++//949MjKyq8Viifnwww99zjZeuyQvSqmRSqkEpVSiUuqRGsqdlFKfV5SvU0qFVCnroZRaq5TaoZTappRytkdMdpN3GEpyZKbR6SgF416HNj3gi1sh60BjRySEEC2OyWRi7ty5Bx955JHgwsJClZOTY5ozZ07Q3Llzk26++eaMZcuW7Tmf+y9YsMAnOjq6YPHixb7Vy3799dfdu3btil+8ePHev//978EADg4OvPjii4f27t27Y/369Ts/+OCDVhs3bjzp9/eVV16Z265du9JXXnnFH+Dpp59uFR0dXTB8+PCCTp06lX744YcHxo4de+xc4j3vAbtKKTPwJjAcOASsV0ot01pXXYr4FiBLa91ZKTUVeA6YopSyAB8D12ut45RSfkDZ+cZkV2kVb+NCX+PlTBxdYeonsOVT8Apu7GiEEKLejX9jda0bvg0OC8h+YET40cr6E3oFZdw0oOOxtNxiy20LNoRWrfv1jIEJNd/lhD59+hSPGDEiZ/bs2YEFBQXmyZMnH4uKiiqJiooqSUhIOK9lzxcvXuz7wgsvJE+fPr3T3r17HUJDQ0/5XZydnW329PQsB+jQoUNZhw4dygB8fHxsoaGhRUlJSY4xMTHFVa958803kwcOHBg+ePDg/Pfff7/V+vXrdwKEh4eXAqfsh1RX9pht1BdI1FrvA1BKfQaMB6omL+OBxyteLwHeUEopYASwVWsdB6C1PqcMrF6lVWyEKS0vZ+bVDoY8ZLzOOwpu/sa0aiGEEHbz/PPPp/bo0SPS0dHRFhcXZ5fl9hMTEx3S09Mdhg0bVjhu3LisBQsW+M6ZM+f4PklDhgwJ01qrQ4cOOc6bN29f9esTEhIc4+PjXYcMGZJfvaxDhw5ld955Z9rQoUO7Pv3000mtW7e2ywaN9khegoDkKseHgOoLohyvo7W2KqVyAD8gDNBKqRVAAPCZ1vr5mh6ilLoduB2gffsGXF+k4yAY8ZTxy1jULj8d5g6E6CnG5yaEEC1QXVpKTle/laez9Wyvr+Tp6WmbMGFCpru7e7mLi4tdpnkuWLDAd9y4cVkA119/feYtt9wSUjV5+fXXX3e3adPGumPHDqcRI0aEjRo1aoeXl5cNICcnxzRx4sTQZ599NtnX19dW0/0feeSRtKeeeipo5syZdmugaOwBuxZgIHBtxfcrlVKX1lRRa/2u1jpWax0bENCAuxq3iYaL72m45zV37gEQOQ7WvA5xnzd2NEII0eKYTKaz6m6xWq1ERERERkRERN53331tq5d/8cUXvp9//rlfUFBQ94kTJ3ZOSEhw2bZtm1P1elFRUSV+fn5lmzZtcgYoKSlRo0ePDp00aVLm9OnTs0/3fLPZjNHZYj/2aHlJAaoOdGhXca6mOocqxrl4AccwWml+01pnACillgO9gZ/sENf50xr2/wqBPcD1lDFM4nRGPmt0ty27B/w7Q1BMY0ckhBAXLIvFwq5du+JrKtu6datTQUGBOS0tbWvluVmzZrWdP3++7wsvvHC4at2UlBTLoUOHnDp37lxqs9mYOnVqh7CwsOLHH3/86Kl3rl/2aHlZD3RRSnVUSjkCU4Fl1eosA6ZXvL4aWKWN7axXAN2VUq4VSc0QTh4r07hyDsGC8cY6JqLuzA4weT64t4bPrjUWsxNCCFEvxo4d23HgwIER+/fvd2rdunWPl19+uc7jHObPn+87atSorKrnpk6dmvXll18e/x/7kCFDwiIiIiKHDBkS/thjjx0KDg62rly50n3p0qV+q1ev9qhs1fn888+96vrcX3/91bV169Y9li9f7jNr1qwOnTt3Pqtp3krbYWVUpdQo4BXADMzTWv+fUuoJYIPWelnF9OeFQC8gE5haZYDvdcA/AA0s11r/vbbnxcbG6g0bNpx33LXasxL+ezXcuBxCBtT/81qaI9vg9xdh7Gvg7Fl7fSGEsBOl1Eatday97hcXF3cgOjo6w173E3UTFxfnHx0dHVL9vF32NtJaLweWVzv3WJXXxcCk01z7McZ06aYnrWIgt8w0OjeB3WHSR8Zra6nRImPnfk8hhBAXnsYesNu0pe8Ct1Yy3uV8FWXBB8Phr3cbOxIhhBAtgCQvZ5K2E1rJ4nTnzcnL2Jn7h3/Avl8bOxohhBDNnCQvZzLuNbj08caOovkzmeDKd8C/CyyeLlsICCGEOC+SvJxJYHdoJ9N87cLZ09hCQNtgwQTIOtjYEQkhhGimJHk5nfQE2PIJlJyy2rE4V36hcO0X4OINllPWPxJCCCHqRJKX00n4HpbeBbamtU9ksxfcB277GTwCodxqJIlCCCHOyGazERMTE75o0aLj607MmzfPp3///mH9+vULCw0NjercuXPUk08+2epc7n/48GGLxWLp/fzzz5+0hH1QUFD3sLCwyIiIiMiwsLDIjz/+2BuM/ZBqe+5XX33l2bNnzwibzdg1wGq10rVr18iVK1e6Pf74461DQ0OjwsLCIvv37x+2e/fus9pYUpKX00nfBR5twMWnsSNpeSqnS696Et67BPb/1rjxCCFEE2cymZg7d+7BRx55JLiwsFDl5OSY5syZEzRnzpyUF1988dDevXt3rF+/fucHH3zQauPGjc5ne/8FCxb4REdHFyxevPiU6bW//vrr7l27dsUvXrx479///vdgAAcHB2p77pVXXpnbrl270ldeecUf4Omnn24VHR1dMHz48IKYmJjCLVu27Ny9e3f8hAkTsmbNmtXubOK1yzovLVLaTgiQmUb1qt+dsHsFfHw1TPoQIkY3dkRCCFE37w4Lr7VO58uyueSfR4/Xj56SQb87j5F3xMKn14SeVPf2n2tthu7Tp0/xiBEjcmbPnh1YUFBgnjx58rERI0YUVJb7+PjYQkNDi5KSkhxjYmKKz+btLF682PeFF15Inj59eqe9e/c6hIaGntLtkJ2dbfb09CwHY7foDh06lNX23DfffDN54MCB4YMHD85///33W61fv34nwNixY/Mq6wwcODD/888/9zubeCV5qYnNBhm7IebGxo6kZfNsAzctN1Yx/vx6GP8m9LymsaMSQogm6/nnn0/t0aNHpKOjoy0uLm5n1bKEhATH+Ph41yFDhpzVYM3ExESH9PR0h2HDhhWOGzcua8GCBb5Vd5UeMmRImNZaHTp0yHHevHn7ql9/pud26NCh7M4770wbOnRo16effjqpdevW5dXrvPPOOwGXXXZZztnELMlLTXKSoKxQWl4agqsv3LAMPpsGyx+CLsPBrc7bcgghROOoQ0vJaet7BFrP+voKnp6etgkTJmS6u7uXu7i4HN/fJycnxzRx4sTQZ599NtnX19d2NvdcsGCB77hx47IArr/++sxbbrklpGry8uuvv+5u06aNdceOHU4jRowIGzVq1A4vLy9bXZ/7yCOPpD311FNBM2fOPFa97K233vKNi4tzfeedd87q85DkpSbeHeCB3eBw1t2G4lw4ucO1i42uOklchBDijEwmEybTiSGrJSUlavTo0aGTJk3KnD59enb1+larlW7dukUCjBw5MvuVV15JrVr+xRdf+KanpztUbsaYlpbmsG3bNqfu3buXVK0XFRVV4ufnV7Zp0ybnYcOGFdb23EpmsxlVw9YwS5cu9XjhhRfa/P777wlVE7G6kOSlJkqBR+vGjuLCYnGCtj2N1+vegcx9cPkzxgJ3QgghamSz2Zg6dWqHsLCw4scff/xoTXUsFgu7du2Kr6ls69atTgUFBea0tLStledmzZrVdv78+b4vvPDC4ap1U1JSLIcOHXLq3LlzaV2eeyZ//PGHyz333NNh+fLle4KCgqxne71dfjMopUYqpRKUUolKqUdqKHdSSn1eUb5OKRVSrby9UipfKfWgPeI5b+vfN75E48hJhnVzjanq5TJVXQghTmflypXuS5cu9Vu9erVHREREZEREROTnn3/uVdfr58+f7ztq1KisquemTp2aVdkKA8aYl4iIiMghQ4aEP/bYY4eCg4Ot5/vchx56KLiwsNA8adKk0IiIiMhLLrmkc12vBVBan1VLzak3UMoM7AaGA4eA9cA1Wuv4KnXuBnpore9USk0FrtRaT6lSvgTQwDqt9Qu1PTM2NlZv2LDhvOI+o7mDwC0Arv+y/p4hTk9r+P0FWPUUhI+Cqz+ULjwhxFlRSm3UWsfa635xcXEHoqOjM+x1P1E3cXFx/tHR0SHVz9uj26gvkKi13geglPoMGA9UbaIaDzxe8XoJ8IZSSmmttVJqArAfKKApsJUbM406Dm7sSJqEpGOFrN2XwdHcEsrKbZRabZRYbdx3WRe8XR35YfsRlsWlHD9fWWf+zX3xcHZg7q97WbDmAKUV50vLbTiYTfz16GW4OJpZ+OdBft+djpeLA54uDnhVfN0w6EGUszd6+UMUfXgleZOX4OnqjLODqca+UyGEEBcOeyQvQUByleNDQL/T1dFaW5VSOYCfUqoYeBij1eaMXUZKqduB2wHat29vh7BPI+sAWIsvmJlGWmuOFZSSmJbPnrR8Eo/mkZiez5Pju9EpwJ3fE9P551fbAWMokKPZhKPFxC0DO+Lt6khmQSl7jubjUHHe0WLCzcmCraJBL9jHlYs7+xtlFXXKym04O/x/e+cdHlWV/vHPmZZkMumVJCSBFDrSpCMgUhQUCypWbGvvq6u79rqsW3T96a6LWLArCooiCCKKDek1tFCTQHpPJlPP748zKSCYIAkpnM/z3Gfuuffce9+5mcx873nf877KY1lud7G/qJoyu4vyGhfVTg82PxMzhifD4D/w1vpS9u4/wJszvwXU9ZMjrSy5ZzQAs7/fQ06pnfjQABLCAogLDSAhzEp44HEla9RoNBpNO6K1A3YfB56XUlY29jQtpZwFzALlNmoxiwq2q9foHi12idZASklueY0SKXmVjEyLJD0miG93FnDtG6vr+gVajKTGBFHpUPFT5/TuxKjUKDqF+mMyiF+Nelw+JJHLhxxbTE7u24nJfTsdc/9tY1O5bWy9q9Pp9lLlqI/dGjjlRiKKqkizu7DmruGgjMRhja3bvzmnjKUZeVQ761MHdI8NYvHdauTsmYUZVDo8JIQFEB8aQHxYAEnhVqKDtRtKo9EcF16v1ysMBkPL/f5oDsPr9QrgqNOvm0O85ACdG7QTfNuO1idbCGECQoAi1AjNNCHEc0Ao4BVC1EgpX2oGu34flflg9IOoxpMntlWklLg8EovJwMFSO7e+u47M/Mo6QQLw5NRepMcE0SsumEem9CQt2kZajI3YYP/DBEpYoIWwkziKoUZv6q/XOz6E3vEh4HbAvx8GgxGu/qxu/7+n90dKSWm1i5xSO9kldgwN9NWegirWZ5VSXOWs23Zm92hev+Z0AG57bx3+JiPxYQF0ibTSNdJG16hAgvzNLf9mNRpNe2JLQUFBz6ioqDItYFoer9crCgoKQoAtR9vfHAG7JlTA7jiUSFkNXC6l3Nqgz21AnwYBuxdKKS854jyPA5VtImDX4wZjaw9KHT+Hyux8tuEg89flMKZbFH8+pwd2p4fr56wmLdpGarSN1Ogg0mJsRARa2l/syMEN8M6FIAxw5Tzo1LfJh1Y73Rz0iZtAPxOnJ4cjpWT6rJUcKK4mr7ymztV12eBE/nphHzxeyeMLtpIcGUhKVCApUTbiQgMwGtrZfdNoTkGaO2B37dq10SaTaTbQG10X8GTgBba43e4bBg4cmH/kzhMWLwBCiHOAFwAj8LqU8hkhxJPAGinlAiGEP/A20B8oBqbXBvg2OMfjtBXx0s5YsPEgH64+wE+7i5ASBiSGMmN4MlP7xbe2ac1PwU54+wJwVMDlH0LSsGY5rdPt5UBxFbsLqogJ9qdf51DyymuY8PwKyuz107UtJgOPTOnJVUOTKK9x8c22fLpGBdI1yobNr/0JXo2mo9Lc4kXTtmgW8XKyaTHx4nGrJ/vBf4Ae5zb/+ZsJt8fLmv0lDO2q6ljd9cF61h8o5YL+8VzQP57kyMBWtrCFKc2Ct8+HpOFw3v+16KWklBRXOdldUMWegkp2F1QyoVcspyeH88ueIi6dtbKub0ywH10jbdw3sRsDk8KocripcXmIsPm1qI0ajebXaPHSsdGPig0p2Qt7v4O+lzbe9yQjpWRLTjnz1mfz+caDFFY6WXLPGaTHBPH0+b2x+Znanxvo9xLaGa5fCn5Bqp2XAbboFiktIIQgwuZHhM2PwV0OrxQ/ICmMr+89g8z8KvYUVrKnoIrdBZWYjerv8PW2PO76YAORNgtp0UGkx9hIjw1iSp84Qqw6pkaj0Wh+L1q8NCTfV6Azum1Nk96RW8Ft76mgW4vRwJndo7lgQDzJEWqE5ZQMLrX6hISU8MkNUJkLZz8HvS9Sc7pPAmajgdToIFKjg466v098CA9P7sHOvAp25lXy8dpsqpwezuweTQhm3l91gC83H6JbTBDpMUGkxwaRFm0jULufNBqN5jfR35INqZ0mHdm6M43Ka1ws3pxLcICJSb07ER8WQEywH9eN6MLkPp30U3tDhIBpr8Fnt8En18OWeTDlXxAU2/ixLUzXKBtdo2x1ba9XklNqJ9Y3TVtKKK5y8vbK/Tjcajag2SjY+sQkLCYDX2fkUV7jIj0miNRoG/5mY6u8D41Go2lraPHSkILtEJqoqhy3AjtyK3jxm118nZGHw+1lUq9YJvXuhM3PxLs3DG0Vm9oF0T3guiWw8j+w/Bl4eTBcuxhiera2ZYdhMAg6h1vr2rU5cjxeyYHianbmVZBfXoPFpCYyzPl5H9/vUtnIjQZBcoSVYSkRPH1+HwAKKhyEB1r07CeNRnPKocVLQ6wR0GV0q1x6zk/7eHphBlaLiemnd+b8/vH06xzaKra0S4wmGHGnqoX0y3/r8/S0g2nvRoOgS2QgXY4ItH79mtPZV1jFjrwKduSqxeGqz9c0fdbP5JTaSYsOoltsEN1ighiYHMaAxLCT/RY0Go3mpKJnG7UyUkqEEKzYWcC8ddk8em4vndq+uagqhNfGw4i7YMCMkxYLc7L4eG02GQfL2ZlXwfbcCgorHUwbmMA/Lj4NKSXXvrmapHAr3WKD6RZrIz0m6NSMj9KckujZRh2btv1I2oGpcrj5x5IdBPmZuHdCN85Ij+KM9KjWNqtj4XZAcDx8fpeKhTnvRQhLbm2rmo1pAxNgYH27qNKB06NGZspr3JTZXXVBwrU8MKk7t4xJocrhZvGW3Lp4mgCLjqfRaDTtBy1eatn2OSx5BK6aB+FdW/RS3+8q4M/zNpNdYufaEcl1oy+aZiYkHq5eAOvehCWPwn+Gw1mPqzw+HfB+N8wnExJgZv6tI+qChHfkVrAjr4LBXZRLaXtuBX+cuxFQtyIp3EpaTBC3jkmhf2IYDrcHgaiLv9FoNJq2hBYvteRlqIrStpabpVJW7eLphRnMXZtN18hAPrpp2K9yh2iaGYMBBl0HqePVCMy+FUq8nCLUBgl3DrdyVs+Yuu2nJYSw7I+j2ekTNbXTuT2+GgnLtuVz5/vr6RIZSLovniY9xsbItCidSVij0bQ6+luoloJtEJYEFmvjfX8nh8rtfL7pILeOSeHOcWl66uvJJLQzXPkJuOxqqKEwE3YugqG3qmKPpxgmo4GUKBspUTbO7vPrqt9dowK5aXRXduRWsiWnjC83H0JKWHH/WGx+Jj7bkMOybfl1BT1To20kRQRiNuqRGo1G0/Jo8VJL/naI6tH8py2vYdGWXGYMT6Z7bDA/PnCmThffWghRL043fQgrnoOtn8LUl9tcYsLWpntsMN1jg+va1U43mfmVJIQFACo/zdr9JSzYeLCuj8VkYPPjE/AzGfluZwGl1U5So5VA0kJdo9E0J1q8AHhcUJQJ3SY12ymllMxdk83TCzNwuL2M6xFNQphVC5e2wti/qOnUX94P/xsFox+A4XeCSc/0OhpWi4m+CaF17WtHdOHaEV2odrrZnV9FZkEFuWUO/ExKpMz5aR/fbFeFYIWAxHArA5PC+Ncl/QDYX1RFeKBFz37SaDS/i2YRL0KIScC/UVWlZ0spZx6x3w94CzU3ogi4VEq5TwgxHpgJWAAncL+U8pvmsOm4cFZBv8sgeVSznO5AUTV/nr+JHzOLGNwlnJkX9iEhrOXcUZrfgRDQZ5rK6/PlffDNU2C0qFwxmiZjtZjokxBCn4SQw7b/98oB7CusZld+BZn5lezKr8TYIEj6prfXsj23gthgf1KjbXSJDGRI13Cm9I0D0EHsGo3mNznhPC9CCCOwExgPZAOrgcuklBkN+twK9JVS3iyEmA5cIKW8VAjRH8iTUh4UQvQGvpJSxjd2zbac58Xp9nLGc8updLh58OzuXD44EYPOgNr2yVwGcf1VzaRtn8Oe72DoLRCR0tqWdUiWb89nW245mXmV7C5UFbvHdovmxcv6AzDk2a8JCTDTNdJGl6hAukYG0j8x9Jh1pDSaI9F5Xjo2zSFehgGPSykn+tp/BpBS/rVBn698fX4WQpiAXCBKNri4UI9ZRUAnKaXjt67Z7OKlphwsNjUz5Xeyt7CKpHArBoNKOJcabSMuNKD5bNScPL7/Jyz/K3jd0H0yDLsNEod1yOnVbQUpJQ63F3+zEbfHy3Nf7WBPgarWfaCoGrdXctMZXfnzOT2odrq56rVVdI0M9AkbG12jAkmKsNa5rTQaLV46Ns3hNooHshq0s4Ehx+ojpXQLIcqACKCwQZ+LgHXHEi5CiBuBGwESExObwewGfHYbFO+BW3487kPdHi8vLc/k5eWZPDm1N5cNTtTJ5to7o/4I/a6A1bNh9Wuw/QvoPU0VgNS0CEKIuqBek9HAX86pD553ebxkl9jx8+WcKbO7MBsF3+0sYO7a7Lp+j5/bk2tGdCG7pJqXl+8mOcJKUoSVxHAlbHS1bo2m49Am/puFEL2AvwETjtVHSjkLmAVq5KVZDSjYDpHpx32Y1yu5/+NNzF+fw9R+cUxokEdD084JioUzH4aR98KmDyDAl4/HUQlr34D+V0FAaKuaeKpgNhoOq/vUKSSAD24cBkClw81e3whNbUBxblkNX23NpbjKedh5Xr9mEGd2j2FHbgWLt+QqYRNhJTkikDCrWcfYaDTtiOYQLzlA5wbtBN+2o/XJ9rmNQlAuIoQQCcB84Gop5e5msOf4cDugaDf0OO+4DpNS8tCnW5i/Pof7JqRz+5lpLWSgplWxWFWSu1p2L4MlDyu30oCrYMjNEN6l9ew7xbH5/TpgeFByOOseGU95jYsDRdXsL6pmf3FV3dTvzTllvLBsJw095kF+JubdOpy0mCA2ZZeScbCczuFWEsIC6BQSoDMNazRtjOYQL6uBNCFEF5RImQ5cfkSfBcAM4GdgGvCNlFIKIUKBhcCDUsrj99k0B0WZID0QfXw5XrYeLGfumixuHZOihcupRM+pcNP3sPI/yqW0apaKi7nwVTDrGKe2RLC/md7xIfSOP3wm1LSBCUzp24nsEiVs9hVVc6CoitgQfwCWbM3jpeWZdf2FgNhgf5bccwZB/mZ+zCwkq7iahDCfuAn117E2Gs1J5oTFiy+G5XbgK9RU6dellFuFEE8Ca6SUC4DXgLeFEJlAMUrgANwOpAKPCiEe9W2bIKXMP1G7mkz+NvUadXxJynrHh/DFnSPpFqNnP5xydOoLF7wC4x6D1a+q0hK1wiVnLcSeBsY24ZHVHAN/s5HU6KCjzl66Z3w6l57emewSO9kl1WSX2Mktq6krizBvXQ6frKuPtamtDbX8vjEIIVi85RAl1S4SwgJICLMSp8WNRtPsnPBso9agWWcb5WVAxmcw6l4wNZ5AbtaK3cSHWpnc99cp1TWnOJUF8HwvCIxSIzTpEyBxuE5818Fwe7zkltf4xI0SOA63lwcmqQegK2av5MfMosOOGZAYyrxbRwDw5o97sbu8xIX6ExvsT1xoANHBflrgNDN6tlHHRj8exvRUSxOY89M+nv1yOxf2j9fiRfNrrBFwyRzlTlr9Kqx8GSxBapSmx5TWtk7TTJiMBp/L6OiJJ+dcO5i8CgfZxdXklNrJKrZjtdQLk0/W5bA5p+ywY0akRvDuDUMBeGj+ZowGQWyIP3EhAcSG+JMcEVjn1tJoNFq8QPZalYiskZkjH63O4rEFW5nQM4a/Tet7cmzTtC8MBuh2tlqcVSrR3a6vVBkCUHWUfnwB0iaqUZlO/U8ot5CmbWIyGogPDSD+GHmePr9jJFUON4fKasgtq+FgmZ3QgPoyCVsOlrO3oJLyGnfdtmkDE/jHxachpeT8l38k1GohOsiP6GA/YoL96d85jD4JIUgpcXq8ehRH0+E5tcWLqwZeOwtG3QdnPnTMbgs2HuSBeZsYnR7F/13eX1fO1TSOJRC6n6OWWkz+qgTBd3+D72ZCYDSkjYfJ/9TBvqcYgX4mUqNVNe4j+ew25V6qFTiHyuyEWZXr0eH2EhXkR165g+255RRWOvF4JXecmUqfhBBKql0MeGopIQFmYoL9iA7yJzrIjwsGxDMqLQq708Om7FKig9V2nftG0145tT+5RbtAehutKLztUDmDk8N55cqB+olG8/vpNkktVUWQ+bUalcnPUKIG4IcXwGCC9IkQkaoz+p7iHE3g+JuNzJ5xel3b45UUVzkx+UqQGIXgj+PTya9wkF9RQ36Fg1/2VjG0awQAuwsquXTWyrrjA8xGImwWHju3F+N7xnCgqJoPVh8gwuZHpM1CRKAfETYLSRFWrJZT++dC07Y4tT+N+dvVa9TRp0m7PF7MRgN/mthND8Vqmo/ACDjtUrVIWS9SMr+Gfd/DkocgrIsSMX0uhgQdc6g5OkaDICqofqJBiNXMHeOOnbohKcLK29cPJr/cQV5FDcWVToqqnETa1MjO/uIqZq3Yg9t7+ESOOdcNZnR6FN/uyOeZhduIsFmUwAlUr5ee3pmYYH8KKx0UVDgIs1oItZrrsiZrNM3NqS1eCrapJ92I1F/t+mVPEfd9vJHXZ5xOWkyQFi6alqHh6Mo1X0DpAdj5FexaAmvfBGFQ4sXthI+vhZheENsXYvtAaKIendEcF0H+ZkalHbt8yai0KHY9czbldjeFVQ6KKp0UVTroFacS/NWOBhVVOtl2qJzCCgflNW4m9Y4lJtifhZsO8diCrXXns1qMhFktfHjTUBLCrHyzPY9vdxQQZrUQZjUTFmghzGphaNcILCYDbo8Xo0HobMeaRjm1xUv+dghP+dVU1vUHSrjuzdXEhvgTFqinuWpOIqGJMPgPanFWg6NCba/Mg8JdsONL5eoE8A+Bc/4JfS9WZQtK96syF0bzsc+v0TSCEIIQq5kQq5mUI3TO6cnhnJ4cftg2p1sJDoAzu0cTFeRHSbWT0moXxVVOSqqdBPsCknflVfLZhoOU2V2HnSPjyYlYMDBz0XZmDE+mc/jRZ3JpNLWc2uJlzANQXXzYpoyD5cx4fRURNj/evWEokbbGc79oNC2CxaoWgNDOcPsqJWjyM+DQRsjdXF+aYP9P8N7FYPRT2aJj+0Cn01S+GVt0670HTYenYemEzuHW3xQeN41O4abRKbg9XsrsLkqqXZRWOwnwuZdGpEYe5gbTaI6FTlLXgL2FVUz770/4mQx8eNMwrf417YfKfDU1O9cnag5tAnsx3PKTcjVlLIDNcyEsCUI6qyW0s4r30tmANR0QnaSuY3PqfmuVH1RPq6njICAMgJhgP0amRXLXuDQtXDTtC1u0ch/1vVi1pYTyHLDFqra9WI3Y7FoC7pr64x7MAmMwrHwF9iyHkIR6YROSqOJtdPyBRqNpY5y64mXv9zD/Rrj1F3KdAdj8Tdj8TPx7ev/WtkyjOXGEUEKkloHXqEVKqCqA0iwlbvxVICZeF5TlwIGfocaX/dUSBH/OUutLHlGuqlpRExynltRxar+jUuWqMejAdo1G0/KcuuKlYBsYzBRYErj81ZXEhwXw9vVDWtsqjaZlEUKN0tiigYH124ffoRaAmnIoy1LxYLWjLmaryhq8a6kKHgblcqoVL+9cBFm/qEzVAeGqVELCIJj0V7V//btKIFkj1BIQrmywHh78qdFoNE2hWcSLEGIS8G9UVenZUsqZR+z3A95CfVsWAZdKKff59v0ZuB7wAHdKKb9qDpsaJX87nvAUrnxjHYfKanhOp/zXaBT+weDf6/BtY/+sFlCZqSvzwOOs33/69dB1tBI81UXKTeV21O//bqaaBt6Q9Elw+Ydq/b8jwVWtMhNbbOo1dRwMvUXt//ZvahZV7T5LoJpZFdNTjSaV7FX7zAEqaNlo1u4ujaYDc8LiRQhhBF4GxgPZwGohxAIpZUaDbtcDJVLKVCHEdOBvwKVCiJ7AdKAXEAd8LYRIl1J6TtSuxvDmZfCTPZG91VW8cc3pDErWT4AaTZMw+6vA34b0veS3j7n1FyVoqovqBU5gZP3+pOFqm7NSjfBUF9bPBJQSVvxdjdw0ZMgtcPZMFcPz4pHuXgGjH1CCq6oIXh2jRI3JX6VGMPkrwdX7IhXsvORhVVXe6KdeTX7QfTLED1TVwjd9qASRwaQWo1nZHJas7MxerVxmBnN9v8g0FU/nqIDyQ2q/MPhejer9m/yUyHNVq221+wxGdQ4twDSao9IcIy+DgUwp5R4AIcQHwFSgoXiZCjzuW/8YeEmoLERTgQ+klA5grxAi03e+n5vBrmPjrGJ+UQIfukczvk80ewqryMyvoMrpYXByODHB/tj8jIQEmDHownkazYlTO+27YRxOQ8557tjHCgGPFKgfeWcVOCvUq58vXkcY4fxXlPBx1/gWJySqKs0YDJA00rfdAR6HGj2qzZfjrFLB+x6nWtxOcNlVHp34gcqFtuQotc8mPAPDb4e8LfDeUcTbxL/CsFtVfN0Hlx3lPf9D5fPJWADzbvj1/kkzlbja+D4sfbyBoDGA1w1nPgwj7oRVr8LSR9U+S6DaX1OuarYlDlYFQTe8Vy/aEOAohzPuV8f/8IIqGGoKAFuUEotlWTD0Vgjvqo7f9z2YA5VwlV4lyEbdC8Nug6+fgLVzlFALiVf3sHgP9LtcBYxvWwB5GWpEz2hRItRVo64/+Ab44m51jeAEFVM19WXtTtQ0SnOIl3ggq0E7GzgyeKSuj5TSLYQoAyJ821cecWz80S4ihLgRuBEgMTHxxCw2W+njl88I48tcvCWChZtjjtn1neuHMDItkpmLtjF3TTaf3zGSuNAA3v1lPz9lFjK+ZyzhgRbMJgNWs5HTOocCKnGTySAwGPSTk+YUwO1Ugb4BYWrqdXUxlOyD6J7qB6/0ABzcoApRmgMgb6ua2j3wGiVqDqyEHYtgzINq/66vIWM+TH5e/ehmfAqbPoJL31XlFdbOgY0fwHWLwGRBVhUgNr6PvOl7ajwCy/InMH5+F/LyDymvrCLQacd04Ee8579CSUUlIRtmYfryftyJI9nnjiIxsgeWg6tx3rKanRUWui26FPP3z+Mu3k9xeSURtk4YXVW4E0dQUmknvGQjxu9mUpEymZ/LO3NmSBKmqnxKps7h+0NGzll/M6Zlj+P56SWcjhr8hQGBwGu04PF6MXmdiC/vJ7vzFBbnJHKdyYrBbWf30GdYfCiQW7Luw7D4QVj8YP099noPH336+nHWJlzF5zs685jLjjCY+DnhOhYUxPKs80HEsscO/xs5D2/y/T/5Imgai9bG8rK9BEx2PvGbyjelMbzsfhyWP3N4/5rSw9urZ/NfxyQy14bzT3sReBw8XzOZXLuBv8mf4Yfnjzi+5PD2lo954MBgAneG8KizBLwe7iw8j4fL7ETryZ6aRmg3AbtSylnALFB5Xk7oZEKQfuHD8OmtrAj9F0WXfMoeZxjbcyuICfan3O5iS04Zm3PKSIkKBKDK4aHa6SbQT82m+GhNFhuzyli4OfewU8eHBtA5PICiSicHiqvZ8OgEAixGnlu8nTX7ivno5uEAzPlpH3sLq3j8PBVbsGjzIUqqXVw+RAmzlXuKqHF5GNNNJRjbdqgcr5T0igsB4FCZHYMQxASron41Lg9Gg9AVr9sgUko8XlmX9tzp9lLj9hDkZ0IIQZXDTaXDTXSQH0IISqudlFS76BKpPnt55TUUVjrq/vZZxdXkVzgYmKSm+O/Kq6CgwsHwVOWG2ZxdRn5FDeN6KFG+el8xhWUVnJ3ghsAovjvgoLK0kMnBeyB+IIv3g6s4i3P5FnpfxLx9FszFOzm39F04437e3hNAeNE6Jh/4B1zwCq/ssJJctIJJW/8EN3zNPzf707v0GyZmPAi3ruSJX7wMrVzGxB2PwB3ruP+bSsY7lzJh11Nw+xru/3wf53uXMiLrf5A4lCsWOfmDcSFjDrwM3adw3mcO7vdfwqi8+SCMLN6URT+/g8S6cuCtc9m8L49kSylB3grY+ikp71p4u+s+hudn4N2zgh6v2ZnfNZ/+pfsR/xlKSIO/heHdC4lo0K7K2shZ73j4vEcifexLKM3PYsrsQyzunkJ3z0bE1nlgl7j8DBgtAXjzd1Bc4iQgKBibv4VDJeXc+H42iwdfQvfib8my9uTObzbRa/DVpNg3U+wN5usdRZyVEkBUsI1cZwBfbs1nancbUSE2dhc7efq7Qs6a8DTJniwy4y7i79+u5byJM+lsLGVDAXy07iD3jIolKiyEH7OdzN+Qy/VDorEF2vghs4C5mTDhjDcIMTpZXt2XL/dk8eDFnxBicvPRxgKWbS/kXxd1IzAgkNdW5vB9ZjHnndYJrzGApRsOsq4igtf7zUUi+K4omF3lFXD7GvC4eWLRDnbmVvDuH4aDENw7dxN7CqrpGRdCDWY2r8+m1NWDm2I/xCmN7K4wYQwUcMvtgODSWSvxAnNvHg4Iznp+BRUON1aLGUeOgZK9B/HKoXxqeBtXtaDKbeAOQzA6raKmMZpDvOQAnRu0E3zbjtYnWwhhAkJQgbtNObZl6HU+hCUh5kwl8sPziJz+HoOH9avbffGgzod1f+r83jx1fu+69vt/GEpOiR0hBEWVDtbuL2F7bjlGg4EDxdXkVdT4CjuqkZe1+0vIOFRed/yKnQXsL67mx8xCEsOtzFufzYEie514eXXFHvIqaurEy7NfbqOixs2nt40A4J4PN+D1wkc3DwPg8ldXYrWYeOcGNeh12ayVRAX58eJlKhbgqtd+ITHcyjMX9AHg+jdXkxYTxINnq4rat7yzlt7xIdw2VtV5uuuD9fTrHMq1I1QG1/vnbmRQchiXnq7su2/uRkakRnBBf+UG+ONHGxnbPYopfeOQUnLf3E1M7BXDhF6xuD1eHpq/hUm9YxnbPZoal4fHF2zlnD6dOCM9ikqHmyc/38rUfvGMSI2krNrFk19kMG1gAsNSIiiqdPD0wm1cNjiRwV3CySuv4ZmF25gxPImBSeFkl1Tz7JfbuGFUVwYkhrG3sIpnFmZwx5lpnNY5lJ15FTz1RQZ/mtidPgkhbMkp48kvMnjs3J70igth3YESnvw8g79d1JdusUH8vLuIJz7fyv9d1p+0mCC+3ZHP4wu28sa1g+kSGcjiLbk8tmALc28aTmKElU/X5/DYgq0sumsUcaEBvL/qAI99tpUfHhxLdJA/b/y4jye/yGDDo+MJtVp448e9/HXRdjKenIjVYuL1H/byz6U72fXM2ZiNgtd/2MuL32Syb+ZkAF7/cS9zftzD9juSwRrJGz8WsWBNJmsm50HnIbz1i4EfN+3gmx6fw4CreWd9JDt2bGGc3+Mw6a+8vzWFgj0bONtxF0x7nbmbuuDI2sBk+z1w6TvMX98Jv7yNnFv5NMT0YeGmCEJL93OuYR3UlPHdjkpiqu1MDk0CRxWHMnfi58yH9LOhIo/dBRG4ZGcmpoyD/B0UViax15CkRl0+upo/FZdgk5UqHuSlQfy94T/WziUkRUymKHQK7H8R8rcyIPF0HNaxkPc2bP+CoQYzRkMgRKSA10tgSAR2WzJB4WEQGMkdZ0Zjjk6EtE4QlswfJ3gQUbeCZzQOaWLJzhK6xUeSHhdBmUvw+dYiYsOCiQwNpkRGcdNoOxuD08nucxuVJUauGe5H1WlPQdLL7DpUzps/7ePqYUn0jAth7e4i3l+1n0A/MyaDoGazh7N6RPOi/WxEwDk4fshlSJdwnMPuhk7BrNx4kLeKMxlz4ekQEsDC73cz58B+Xs+SeA5IXBt2EuRv4pxv43F74nB71wLgN/BKCPZn2ZIdvO/N5NlJ6rOwIGsTH7uy+PiH2hu4S/3/L7UAFmAPAME9zwEhWLdlExtM+QT2OguAH75bxbfVBXz7M4AE1MyxJ1cq75zJUESnkAAVrwMU+dVgjHapew9UBBRTEVDJ2jIDRoMgwCywhZsokmqUOSFMqCrYvnim3mldiLBZ6nJpDe/VlWqnB6MQGI1CvRrUUjtSHe17INNofovmEC+rgTQhRBeU8JgOXH5EnwXADFQsyzTgGymlFEIsAN4TQvwLFbCbBqxqBpuaRlx/uOwDePMceONsuGtjk1OpWy0m0mKCAEiNtjGka8Sv+tidHky+kZBrR3RhT2Fl3b5Su4vM/EqumP0LACaDIC40gCtmr6yryNo7vv6Z8YL+8Yel4b51TAqSepfUlUOT6q4FMLpbFDa/+j9vn/gQohuk3Y4PC6irJAtgNhowNXBxldldVDvr46YzCypJiqgfy804WE5KlK2uvT6rhG6x9e2Ve4ro6Svm5pGSb3fm06OTul9ur2T5jnz6JKj35/Z4+X5XYV3QtNPjZeWeIs5IV1+ADreXtftLmNBTjSQ43V4255RRUuWqa+/Kq6TK4a4736GyGmpcyn6PV1LpcOP2euvsa+jMMxsMBPmbqH37VouRxHBr3ShWSICZvgmh+Pnuf0ywH2PSo/G3qHZihJUL+sfXpTjvHhvE9aO61LUHJIXxx/HpdcU9h6VE8PDkHpgProHAcMZ2jyEi0ILxqwcheSSTeo8hJcIP+fc0xNCbuWjAjQyOt8J/+8K4x7hi6I1MSLPCB6fB+Kf4w6gbmN4nCL78K1QXc/f4YdiHRMD6SRCcwF8m98BVHQ8H/SB+EM+mxuF1pEB5HwiK4cXL4sHbF3ZFgSWQ1645HeQgmPstLHuC2VWFKpg2vxh2LOSJ2huXBxXSj7vG/QuXJxXv69dzMLAXlwwaQYwlEpaFIP2CsZuSMASHERAeidNkY+VBN3aDlWoRSG5pEv4mIxtL/dnZ7WNKdwZRJR3Yk06Dhw5RXOXklnfWcsOorozvGcPOvApufmctrhIvrgKJe5sdp3sv//NIXJ5euBdtAyD8gt70G3IZO7JLuePDH5ndZxDpXWNYsy2Ph1etAWp8Sz5HY4RvFCun1M4Hq7PqHioOFFexJCMPs8GAySgwGQ1YjL5138hn7TqAzc9EVJB/3d8+PtTKwKQwTAb1/2Yyirr/PZOxfpvV9787tns0kTY/pJQIIbh0cGeGp0ZgMhh8I621P/z11zU2+D++d3w6t4xJqWs/f2k/PF6pjm/Q3yiO7uKuffip5dWrjy9h7SNTeh7WfnJq72P01GiOj2YpDyCEOAd4ATVV+nUp5TNCiCeBNVLKBUIIf+BtoD9QDExvEOD7EHAd4AbullIuaux6zV4eYNVsFZAX3hVmfKF86i2MxyvJLa/hQFE1B4qrOFBczf6ianJK7ZRWuyipdpISZeOTW5SbadILK0gIszJ7hvryGPLs1zjcXkIDzITWVmi1WgjxvYZZzaTHBNWJqo1ZpUQF+REXGoCU6sc8wGw8TPBoTpDivSqQ0vfUynd/h6AYGHC1ar8ySgWRnuMbe3iuK7LH+bjP+QcujxfXS8Nw9boE19Db8UqI/+kxSBvPvrDh2J1uepQsh9g+rK4Io6jCgbO6DJfBH5c04PJ4cXqkenV7CbOauSqhAIr38MvGTYQ48+geWAVVhRTmH8TqKsEqq8iw9OYvIc/h8nj5b+nN7BGJPGS+n9OTw3ih4j4wWvg224t/SDRD+3QDayR3fZ5FsbRRIa3kyTAO1TliJLWy8JJBCTw37TQAUv7yJbeMTuG+id0orHQw6OmvAep+fM0GAxaTAbPRgNmk2lcNS+LaEV0oq3Zx49truH5kFyb0iiWruJqZi7djMRrUsUZ1nMWkfvhrzzM6PYre8SEUVzlZmpHLiNRIEsKsFFQ42JRdisl3vBIeh5/LbBRE2vzwNxtxe7w4PV78TUYdv9bO0OUBOja6tlEte75TMwaskXDtQjUFspWpfdoC2JJThtEg6NFJjWa8uGwXBRUOSu0uX4yEk5IqtV7lGzE597Q4/s/35NTr0cVMH5zII1N6UuVw0+sxlU7HYjTgbzZgtZgIsBgJMBsJsBixWoxM7tOJ6YMTcbg9/PXL7UzsFVvnxnnr5/2+pz5D/dNf7ZOj7+mxT3woqdE2qhxuVu0tpldcMNHB/pRVu9ieW/6r9yuOmBaaEhVIhM2PMruLnXkVdIsNItjfTGGlg32FVUjA65V4JXilxOuLLZFSicNByWGEWi1kFVezPquUcd2jCfQzse1QOZuzy/D4+nulxOuVuH2Lx6tEwLXDuxBiNfNjZiFfb8vjoUFgclUwvyiBFTsLcedsxO0Fd3Qv3B4v7v2/4DYG4I7qicsjmWt5AnN0Gv8OvJul23L5otd3EJHKvdu7s3hrLi63B5f3V7cBgFCrmQ2PTgDg5rfXsqewkiX3jAavhxte/oKig3vpJIoIEnY+9IwF4DHTHJJEHte5/kR6jI0l1kfh0AYAKg3B2CI7Q2AkK/MEBV4blcZQ8i2dWWMbi8VoIFbm4zHbcFlC6dEpiBtGdQXgf9/tJinCyqTenQB4++d9GAzqh79OdNStq+3RQf4k+kbqDhRVqyrFAWaklDjcXsxGw2EjBBpNc6PFS8em3QTstjhdR6sn4gV3wNxr4cblrW3RYT/mDV1IAHeOSzvmcU63l1L74VML/nPlQDqFKF+y0SB4eHIPqp0e7C4PdqcKRra7vNidbuwuD5UO9QrK/TVvXTYp0TYlXqqc/HvZrkbtf3RKT1KjbeSU2rn2zdW8dHl/pvSNY8vBsjp32W9R1z9H9f/opmEM7hLOip0F3PvRxkaPr+2/am8xf5y7ke/uH0Ogn4nlO/J5bvGORo8/3z6fkPK1bEucycdrs/lT2VuYKvaxP+0N1uwvxmy3YhReTCV2JdiCUzEZjZgMBvzNAs/VizCbjSSszaZPfKia2goMc2URYbP4nvgNWHzuh4brVosRMpfB3hXMZC8Gvxx4Ph8qDjLb6wafB1AaLNx95xOYTSYC1+3BVJVL5oSzlTDIe1nlEQmOw2YJrHtfQxt954dz0+iUw9pXDUs+ruMTG7gbhRD4m3UJAY1Gc2LokZcjWfMG9DwfrGEtc/4Ogtcr8UiJ2yNxe72+18PXw6zKpVXj8rA9t4KkcCthgRZKq51kHDx85OVon8L0mCCigvworXayJaecPvEhhFjN5JXXsDOvAgCDEAhBXeCf8L0aBHSNsmHzM1Fmd1FQUUOi1YWlZDflUf2oqHFj2PAexu0LMFz5EQYhMH39MKaM+Zju36GCB3/5DxTuhHP/rQzK86Uuiul5FGuP+waqXBqFuyBpmMrPsXYOLH8W7t6spgcvegDWvO6rI5TgK5oYD8Hxaj04XrX9Q3UyM43mCPTIS8dGi5djUZYDH1wBV83TCZPaEx6XL0OpAQ78AuveUiNqFit8/y9Y9gT8ORv8glSekO0L4aLZaoSi/CB4PSpRVnPhqoGiTCWCCndB4Q7feia47arPDctUHaDd38CWeTDhKV9mVl3sUKP5vWjx0rHRbqNjsW4OHFqvslsOu621rdEcjYpcVSgwfZLKDLrtC5g7A275CaK6qarJmUuhMlcFY/ecCjG91ZRdgNOmq6WW4LgTs6emXF0vYbASQNsXKgFcN64k1PbIdEg+QwX2RqZDdA+1O+VMtdTiZzvyChqNRqNBj7z8NtlrIWFg4/00LYuUyi1SmgXLnoQhN6u/y4Ff4PUJcPlcSJ8ARbthw7sw8FolEmqPawkq8uDgOshZp0ZN0ieqlOgv9ocpL8Cga9Xso43vK4ESmQ4RqWoESKPRtDh65KVjo8VLU1g+Eza+B7etUqnONS1HZb6qnRIU6yuoN1bVUBl4DVQVqunGZ/8Nep6n6tSU50BoUsu6VmrK4eB6n1hZCznroTxb7RMGGHkvjHtEiaXcTSo5m9HccvZoNJpG0eKlY6PdRk0hbzOU7of5N8K0N3QMQnOyfaGKP+lyBnjc8HxvGHIjTHhaxRolDlPBqqCydv5xW/2xJj/lDmpO3A6oKlABsVLCrNFwaBN1rp+wLpA4BOJuUUX7OvVVwbagRnk6nda89mg0Go3mV2jx0hSmvwvfPacKlS24A859URWf0xw/3/9LvY66V70ufUy5VLqcoe7pef9XHwMiBFz4v5a1p6ZcVQVOUskAeeciVVH4D8vU9buMhu5TIH4AxA3QwdsajUbTBtC/wE1l9J/UyMCKvynXwS0/qxktml/j9dbfm+/+rsTBJXNU+9AGNRuolivmKhdRLadd2sK2eVR1493L1OyerFXK9fPgfjWCMvxOlSW3lglPtaw9Go1GozlutHg5HsY8CHuWQfYa+OovMOmvOr8GQGWBmu0DamRl9Wy4Z6u6N0YTGC31wbMXzzn8noV3aXn7yrKVUMlcBnu+hZpSQEBcPxh5t5rhY/RlfUuf0PL2aDQajeaE0OLleDAY4LqlSrj88l8VWDpp5qk1AuN2Qu5miO2tYk5WvQpf3gf371YxKdE91ZRkl13NrBl5z+HHnwyx56xSr5ZA2PwxfHK9agd1Ui6glLHQdUxd5VuNRqPRtC+0eDleDAY14lJTBqv+BwXbYcaC1raq5agpV6MWiUOVe2fXEvjwCrhuiQpcTR4JE59VrheAbpPUcjLxesFZCf7Bajr1i/1h8j/UDKWk4cq+lDMhqrseKdNoNJoOwAkNGQghwoUQS4UQu3yvR82pL4SY4euzSwgxw7fNKoRYKITYLoTYKoSYeSK2nFSE8AWW9oKuY1vbmualpkwFJ2etVu2KQyrxW6aqBEzScOX6ieqm2tE9VBK/kx3Iai+BjR/CJzfAP9JUKn1Qs4TOuE8F14JKPDfsNmWnFi4ajUbTITihPC9CiOeAYinlTCHEg0CYlPKBI/qEA2uAQaj5pmuBgYADGCKlXC6EsADLgGellIsau+5Jz/PSFN6ZBtHd1RRfaNkEac1BrX0eN3x6s5pVM+Aq5e6ZmQjjHoXhd6hRjUPrVWZak1/r2lx+CLZ/oZZ9P6jAWmukGlXpeR70OLd17dNoNG0GneelY3OibqOpwBjf+hzgW+CBI/pMBJZKKYsBhBBLgUlSyveB5QBSSqcQYh2QcIL2tA57VyjXii1GtaVUrov+V8AZ96ttrprWS3DncYO9GGzRqj3nPIhIgSnPq4Dashw1kgGqls4D++pzlxgMKp9Ja7LxAxVbk+MTrBGpMOx2JVbiBpxaMUcajUajOWHxEiOlPORbzwVijtInHshq0M72batDCBEKnAv8+1gXEkLcCNwIkJiY+PstbgniB8GQm2C0T7e5HSpdfKTPtWIvVa6Ns59TaeO9HuWeaU5Xi8ddn3sma5UqMtjrfNV++3x1zet8g1oJpx8+Pfm6Iwa7aoVLa1G8Fza8p3LBmAOgZL8aZTnzYeh+rnJZteVRLY1Go9G0KI2KFyHE10DsUXY91LAhpZRCiOP2QQkhTMD7wItSyj3H6ielnAXMAuU2Ot7rtCgWqwriBeV2KT+oUtjX4nWrkYK4fqp9aKNKe3/5R0rk1JSDo1zFaxyNilwo2aeCZgG2fqrcJpP/odpf3q+KEtZmn137ppoSXCteBt+oZkbVMu6RE33HzYvHDQd+hpB4lTG3ZC98/0/lDkoapkavxhw5oKfRaDSaU5VGxYuU8qxj7RNC5AkhOkkpDwkhOgH5R+mWQ71rCZRr6NsG7VnALinlC00xuM3z6S1wYCVcv1QVBwQ1Jfesx+r72KLhzEcgrr9q71wM8/6gqiHH9IJ1b8EPz6taSkYzrH4Nvv8HPFKoShMU7lQBtLVxK13HHj6ScuYjKmallp7ntfz7Pl5cdti9XMWv7Fik3Foj74GzHofkUXDfLgiMUH21W0ij0Wg0DTjRgN2/A0UNAnbDpZR/OqJPOCpI1zf9g3XAQCllsRDiaaAHcLGUDYcGfps2GbBbS95WeP1sCIqB675qmmuoZL8SMKffoMTJjkUqP8mU59X038JMVQgwaWT7LkvgqoEdX8LW+SphnKsK/ELU6FOPKZAyDvxsrW2lRqPpAOiA3Y7NiYqXCOAjIBHYD1ziEyWDgJullDf4+l0H/MV32DNSyjeEEAmoWJjtqJlHAC9JKWc3dt02LV4A9v0Ib1+givRd/ZlyK53qLHtKZd6tKVWBzd0nq4RxyaPAZGlt6zQaTQdDi5eOzQmJl9aizYsXgIwF8NHVkD4JLn2nfY+Y/B6qimDbApUoTghY+qia1dT/CjUtW1fm1mg0LYgWLx0bHUzQUvQ8TwXU7lwEX9yt4lM6Oh63imUByFyq3vfB9ao9/kmY9poKwtXCRaPRaDQnwCk2HHCSOf0GNVNoxd9VXZ0zH2r8mPZIwU7Y8I7KxzLsdhhxJ/Q4D2L7QkzP1rZOo9FoNB0MLV5amrEP+QTMcypFfe8LW9ui5qGmDLbMgw3vQvZqEEYVeNvpNLXfYtXCRaPRaDQtghYvLY0QMOUFCEtWP+7tGa8X9n2vBEvGAnDbVbHD8U9B30vVDCuNRqPRaFoYLV5OBkaTKhYI4KiAot31CevaOl6vEmBCqBiWdXPU9OZ+l0G/KyF+gM52q9FoNJqTihYvJ5vP74Y9y+GujeAX1NrW/Bp7KQiDyi+TuQzmXgPXL1Eur35XqKnNPaaotP0ajUaj0bQCWrycbM56HAovaxvCxetV2XqzV6l6SFmroHCHcnMNulYVb+wzDYy+PCyJQ9Si0Wg0Gk0rosXLySa0c33ZgF1LVcXm5izQ+Ft4XCpmJWs1ZP2iqjTXlKl9AWGqYGOfi+trKIUlqyy/Go1Go9G0IbR4aS0qC1QSu5jeLZuFd/PHYDCpIo3SC+9dqkRMdA/oeT50HgKdB0NEqo5d0Wg0Gk27QIuX1sIWBRe8Ah/NgI+vO7EsvFJCeQ7krFNJ4ZxVcM5zat+qV8Hsr8SLyQ+uXQSRaeAf0mxvRaPRaDSak4kWL61Jz6lwzt/hy/tg4T1w7otNG/2oLFAi5eC6esFS5SvobTBB3ID6itPT31MuoVoSdLZsjUaj0bRvtHhpbQb/ASrzVBZeW+yvs/DWlCtxkjwKDAb46iH4+SXfTgFR3SB1nBIs8QOUG8rsX398YMRJeysajUaj0ZwMTki8CCHCgQ+BZGAfqqp0yVH6zQAe9jWfllLOOWL/AqCrlLL3idjTbhn7EFQcUll4jWY1E6n7FBXYm/EpLLgDbl8LkamQepaqyhw/QGWzbQuzljQajUajOYmc6MjLg8AyKeVMIcSDvvYDDTv4BM5jwCBAAmuFEAtqRY4Q4kKg8gTtaN8IAVP+DVWFsPwZtc0aqcRL2gS4ch4Ex6ntKWPVotFoNBrNKcqJipepwBjf+hzgW44QL8BEYKmUshhACLEUmAS8L4SwAfcCNwIfnaAt7RujCS55W01fDusCwZ3U9qBYtWg0Go1GowFOXLzESCkP+dZzgaMVt4kHshq0s33bAJ4C/glUN3YhIcSNKJFDYmLi77W3bWOyQNLw1rZCo9FoNJo2TaPiRQjxNXC0R//DIkullFIIIZt6YSFEPyBFSnmPECK5sf5SylnALIBBgwY1+ToajUaj0Wg6Fo2KFynlWcfaJ4TIE0J0klIeEkJ0AvKP0i2HetcSQALKvTQMGCSE2OezI1oI8a2UcgwajUaj0Wg0x8BwgscvAGb41mcAnx2lz1fABCFEmBAiDJgAfCWl/K+UMk5KmQyMBHZq4aLRaDQajaYxTlS8zATGCyF2AWf52gghBgkhZgP4AnWfAlb7lidrg3c1Go1Go9FojhchZfsLHxk0aJBcs2ZNa5uh0Wg0mjaKEGKtlFKnFO+gnOjIi0aj0Wg0Gs1JpV2OvAghCoD9zXCqSKCwGc7TGmjbWwdte+vQnm2H9m1/e7U9SUoZ1dpGaFqGdilemgshxJr2OqyobW8dtO2tQ3u2Hdq3/e3Zdk3HRbuNNBqNRqPRtCu0eNFoNBqNRtOuONXFy6zWNuAE0La3Dtr21qE92w7t2/72bLumg3JKx7xoNBqNRqNpf5zqIy8ajUaj0WjaGVq8aDQajUajaVd0SPEihJgkhNghhMgUQjx4lP1+QogPfft/aVjVWgjxZ9/2HUKIiSfVcJpk+71CiAwhxCYhxDIhRFKDfR4hxAbfsuDkWl5nQ2P2XyOEKGhg5w0N9s0QQuzyLTOOPLalaYLtzzewe6cQorTBvla790KI14UQ+UKILcfYL4QQL/re1yYhxIAG+1r7njdm+xU+mzcLIX4SQpzWYN8+3/YNQohWSbndBPvHCCHKGnw2Hm2w7zc/by1NE2y/v4HdW3yf8XDfvla/95pTHCllh1oAI7Ab6ApYgI1AzyP63Aq84lufDnzoW+/p6+8HdPGdx9jGbB8LWH3rt9Ta7mtXtoN7fw3w0lGODQf2+F7DfOthbcn2I/rfAbzeFu49cAYwANhyjP3nAIsAAQwFfmkL97yJtg+vtQk4u9Z2X3sfENla972J9o8BvjjRz1tr2H5E33OBb9rSvdfLqb10xJGXwUCmlHKPlNIJfABMPaLPVGCOb/1jYJwQQvi2fyCldEgp9wKZvvOdLBq1XUq5XEpZ7WuuBBJOon2N0ZR7fywmAkullMVSyhJgKTCphew8Gsdr+2XA+yfFskaQUq4AfqvY6VTgLalYCYQKITrR+ve8UdullD/5bIO293lvyr0/Fifyv9IsHKftbebzrtFAx3QbxQNZDdrZvm1H7SOldANlQEQTj21Jjvf616OeqGvxF0KsEUKsFEKc3wL2NUZT7b/I5wr4WAjR+TiPbSmafH2fq64L8E2Dza1973+LY7231r7nx8uRn3cJLBFCrBVC3NhKNjWFYUKIjUKIRUKIXr5t7ebeCyGsKFH7SYPN7eXeazooptY2QPP7EEJcCQwCRjfYnCSlzBFCdAW+EUJsllLubh0Lj8nnwPtSSocQ4ibUCNiZrWzT8TId+FhK6WmwrT3c+3aLEGIsSryMbLB5pO+eRwNLhRDbfaMJbYl1qM9GpRDiHOBTIK11TTpuzgV+lFI2HKVpD/de04HpiCMvOUDnBu0E37aj9hFCmIAQoKiJx7YkTbq+EOIs4CHgPCmlo3a7lDLH97oH+Bbo35LGHoVG7ZdSFjWweTYwsKnHtjDHc/3pHDGE3gbu/W9xrPfW2ve8SQgh+qI+K1OllEW12xvc83xgPifXxdskpJTlUspK3/qXgFkIEUk7ufc+fuvz3mbvvaZj0xHFy2ogTQjRRQhhQf3jHTn7YwFQO7NiGioQTfq2TxdqNlIX1BPSqpNkNzTBdiFEf+B/KOGS32B7mBDCz7ceCYwAMk6a5Yqm2N+pQfM8YJtv/Stggu99hAETfNtOFk353CCE6I4Kbv25wba2cO9/iwXA1b5ZR0OBMinlIVr/njeKECIRmAdcJaXc2WB7oBAiqHYdZftRZ820JkKIWF88HUKIwajv3CKa+HlrbYQQIajR3c8abGsX917TselwbiMppVsIcTvqS9iImhGyVQjxJLBGSrkAeA14WwiRiQpYm+47dqsQ4iPUD48buO0I10BbsP3vgA2Y6/tOPCClPA/oAfxPCOFFfUHOlFKe1B/QJtp/pxDiPNT9LUbNPkJKWSyEeAr1pQ7w5BHD1G3BdlCflQ98YreWVr33Qoj3UbNaIoUQ2cBjgBlASvkK8CVqxlEmUA1c69vXqve8ibY/iopH+4/v8+6WqsJxDDDft80EvCelXHwybW+i/dOAW4QQbsAOTPd9do76eWtjtgNcACyRUlY1OLRN3HvNqY0uD6DRaDQajaZd0RHdRhqNRqPRaDowWrxoNBqNRqNpV2jxotFoNBqNpl2hxYtGo9FoNJp2hRYvGo1Go9Fo2hVavGg0Go1Go2lXaPGi0Wg0Go2mXfH/PNBxYmalnJ4AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "params = (2,5)\n", "y0 = np.array([1,1])\n", "dt = 0.1\n", "t = np.arange(0,2,dt)\n", "(tFE,yFE) = forwardEuler( degradation_model, t, y0, params)\n", "(tET,yET) = explicitTrapezoidal( degradation_model, t, y0, params)\n", "(t,y) = adamsBashforth2( degradation_model, t, np.array([1,1]), params)\n", "tru_y1 = y0[0]*np.exp(-params[0]*t)\n", "tru_y2 = y0[1]*np.exp(-params[1]*t)\n", "tru_y = np.vstack( ( tru_y1, tru_y2) )\n", "\n", "plt.figure( figsize = (8,6) )\n", "plt.subplot(2,1,1)\n", "plt.plot( t, tru_y.T )\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( tFE, yFE.T, '--' );\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( tET, yET.T, ':' );\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( t, y.T, '-.' );\n", "plt.legend(['Y1','Y2','FE Y1','FE Y2','ET Y1','ET Y2','AB2 Y1','AB2 Y2'],\n", " bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0., )\n", "\n", "plt.subplot( 2, 1, 2)\n", "plt.plot( t, tru_y.T-yFE.T, '--' );\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( t, tru_y.T-yET.T, ':' );\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( t, tru_y.T-y.T, '-.' );\n", "plt.legend(['Y1 - FE Y1','Y2 - FE Y2','Y1 - ET Y1','Y2 - ET Y2','Y1 - AB2 Y1','Y2 - AB2 Y2'],\n", " bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0., )\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Determine how the error depends on the time step size" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# range from smallest timestep that doesn't take way too long to run to largest time step with qualitatively correct answer.\n", "dts = np.linspace(1e-4,0.2,10)\n", "errFE = np.zeros( (dts.size,) )\n", "errET = np.zeros( (dts.size,) )\n", "errAB2 = np.zeros( (dts.size,) )\n", "params = (2,5)\n", "y0 = np.array((1,1))\n", "\n", "plt.figure(figsize=(8,12))\n", "for i in range(dts.size):\n", " t = np.arange(0,4,dts[i])\n", " sol = scipy.integrate.solve_ivp(fun=degradation_model, t_span=(0,4), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", " (t,y) = forwardEuler( degradation_model, t, y0, params)\n", " plt.subplot( dts.size, 1, i+1 )\n", " plt.plot( t, sol.y.T )\n", " plt.gca().set_prop_cycle(None) # this resets the color cycle\n", " plt.plot( t, y.T, '--')\n", " errFE[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " plt.gca().set_prop_cycle(None) # this resets the color cycle\n", " (t,y) = explicitTrapezoidal( degradation_model, t, y0, params)\n", " plt.plot( t, y.T, ':')\n", " errET[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " (t,y) = adamsBashforth2( degradation_model, t, y0, params)\n", " errAB2[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", "plt.tight_layout()\n", " \n" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot( dts, errFE, 'C0.-' );\n", "plt.plot( dts, errET, 'C1.-' );\n", "plt.plot( dts, errAB2, 'C2.-' );\n", "plt.legend( ['FE Error','ET Error','AB2 Error']);\n", "plt.xlabel( 'Size of Time Step');\n", "plt.ylabel( 'Error');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implement AB4\n", "\n", "Use the RK4 to compute the value at the first three time steps after the initial condition. \n", "\n", "Then, use the Adams-Bashforth method to compute the remaining time steps. Write the code so that the ODE function is called as few times as possible.\n", "\n", "\\begin{eqnarray*}\n", "f_d &=& f(t-3\\Delta t,\\widehat{y}(t-3\\Delta t))\\\\\n", "f_c &=& f(t-2\\Delta t,\\widehat{y}(t-2\\Delta t))\\\\\n", "f_b &=& f(t-\\Delta t,\\widehat{y}(t-\\Delta t))\\\\\n", "f_a &=& f(t,\\widehat{y}(t))\\\\\n", "\\widehat{y}(t+\\Delta t) &=& \\widehat{y}(t) + \\frac{\\Delta t}{24}\\left(55f_a-59f_b+37f_c-9f_d\\right)\\\\\n", "\\end{eqnarray*}" ] }, { "cell_type": "code", "execution_count": 112, "metadata": {}, "outputs": [], "source": [ "def adamsBashforth4( fn, t, y0, params ):\n", " \"\"\"\n", " [t,y] = adamsBashforth4( fn, t, y0, params )\n", " Given a function handle fn for y', find the value of\n", " y at timepoints t, assuming y(0) = y0.\n", " fn takes t, y, and params as input.\n", " Uses an explicit 4th order Adams-Bashforth method\n", " \"\"\"\n", " h = t[1]-t[0];\n", " if abs(np.mean(np.diff(np.diff(t)))) > 1e-8:\n", " print( 'The time steps must be evenly spaced' );\n", " return;\n", "\n", "\n", " # We need the first two steps. And they need to be computed\n", " # by a fourth order method so that the results from this\n", " # function are fourth order.\n", " # So let's use the explicit RK4 method\n", " (tstart,ystart) = RK4( fn, np.array([t[0], t[0]+h, t[0]+2*h, t[0]+3*h]), y0, params );\n", "\n", " a1 = 55/24;\n", " a2 = 59/24;\n", " a3 = 37/24;\n", " a4 = 3/8;\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0:4] = ystart;\n", " fc = fn(t[0],y[:,0],params);\n", " fb = fn(t[1],y[:,1],params);\n", " fa = fn(t[2],y[:,2],params);\n", " for i in range(4,t.size):\n", " fd = fc; fc = fb; fb = fa;\n", " # Compute f at i-1\n", " fa = fn(t[i-1],y[:,i-1],params);\n", " y[:,i] = y[:,i-1] + h*(a1*fa-a2*fb+a3*fc-a4*fd);\n", " \n", " return (t,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compare AB4 output to RK4 output" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "params = (2,5)\n", "y0 = np.array([1,1])\n", "dt = 0.01 # 0.1 is unstable for AB4\n", "t = np.arange(0,50,dt)\n", "(tRK4,yRK4) = RK4( degradation_model, t, np.array([1,1]), params)\n", "(tAB4,yAB4) = adamsBashforth4( degradation_model, t, np.array([1,1]), params)\n", "\n", "tru_y1 = y0[0]*np.exp(-params[0]*t)\n", "tru_y2 = y0[1]*np.exp(-params[1]*t)\n", "tru_y = np.vstack( ( tru_y1, tru_y2) )\n", "\n", "plt.figure( figsize = (8,6) )\n", "plt.subplot(2,1,1)\n", "plt.plot( t, tru_y.T )\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( tRK4, yRK4.T, '--' );\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( tAB4, yAB4.T, ':' );\n", "plt.legend(['Y1','Y2','RK4 Y1','RK4 Y2','AB4 Y1','AB4 Y2'],\n", " bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0., )\n", "\n", "plt.subplot( 2, 1, 2)\n", "plt.plot( t, tru_y.T-yRK4.T, '--' );\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( t, tru_y.T-yAB4.T, ':' );\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.legend(['Y1 - RK4 Y1','Y2 - RK4 Y2','Y1 - AB4 Y1','Y2 - AB4 Y2'],\n", " bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0., )\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Determine how the error depends on the time step size" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# range from smallest timestep that doesn't take way too long to run to largest time step with qualitatively correct answer.\n", "dts = np.linspace(1e-4,1e-2,10)\n", "errRK4 = np.zeros( (dts.size,) )\n", "errAB4 = np.zeros( (dts.size,) )\n", "params = (2,5)\n", "y0 = np.array((1,1))\n", "\n", "plt.figure(figsize=(8,12))\n", "for i in range(dts.size):\n", " t = np.arange(0,50,dts[i])\n", " sol = scipy.integrate.solve_ivp(fun=degradation_model, t_span=(0,t[-1]), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", " (t,y) = RK4( degradation_model, t, y0, params)\n", " plt.subplot( dts.size, 1, i+1 )\n", " plt.plot( t, sol.y.T )\n", " plt.gca().set_prop_cycle(None) # this resets the color cycle\n", " plt.plot( t, y.T, '--')\n", " errRK4[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " (t,y) = adamsBashforth4( degradation_model, t, y0, params)\n", " plt.plot( t, y.T, ':')\n", " errAB4[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", "plt.tight_layout()\n" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot( dts, errRK4, 'C0.-' );\n", "plt.plot( dts, errAB4, 'C1.-' );\n", "plt.legend( ['RK4 Error','AB4 Error']);\n", "plt.xlabel( 'Size of Time Step');\n", "plt.ylabel( 'Error');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus Code\n", "### Illustrate the trapezoidal rule and AB2 in terms of numerical quadrature\n", "\n", "Plot the method computing the area under a known curve (not an ODE)." ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.patches as patches\n", "\n", "fn_f = lambda t: 5 + -1*t**2\n", "\n", "h = 0.1\n", "eps = 0.2*h\n", "t0,t1,t2,t3 = 0,h,h*2,h*3\n", "tru_t = np.linspace( t0, t0+3*h, 40 )\n", "tru_f = list(map( fn_f, tru_t ));\n", "\n", "plt.figure( figsize=(10,4))\n", "ax = plt.subplot( 1, 2, 1 )\n", "plt.plot( tru_t, tru_f )\n", "plt.plot( t0, fn_f(t0), 'C0.', markersize=16)\n", "plt.plot( t1, fn_f(t1), 'C1.', markersize=16)\n", "plt.plot( t2, fn_f(t2), 'C2.', markersize=16)\n", "plt.plot( [t1,t2], [fn_f(t1),fn_f(t2)], 'C3')\n", "yb = plt.ylim()\n", "poly = patches.Polygon([(t1,yb[0]),(t1,fn_f(t1)),(t2,fn_f(t2)),(t2,yb[0])],facecolor='0.8')\n", "ax.add_patch(poly)\n", "plt.title( 'Trapezoid Slope from Current Step\\n(Trapezoidal Rule)')\n", "plt.ylabel( 'f(t)')\n", "plt.xlabel( 'Time')\n", "\n", "\n", "ax = plt.subplot( 1, 2, 2 )\n", "plt.plot( tru_t, tru_f )\n", "plt.plot( t0, fn_f(t0), 'C0.', markersize=16)\n", "plt.plot( t1, fn_f(t1), 'C1.', markersize=16)\n", "plt.plot( t2, fn_f(t2), 'C2.', markersize=16)\n", "slope = (fn_f(t1)-fn_f(t0))/h\n", "plt.plot( [t0,t2], [fn_f(t0),fn_f(t0)+slope*2*h], 'C3');\n", "yb = plt.ylim()\n", "poly = patches.Polygon([(t1,yb[0]),(t1,fn_f(t0)+slope*h),(t2,fn_f(t0)+slope*2*h),(t2,yb[0])],facecolor='0.8')\n", "ax.add_patch(poly)\n", "plt.title( 'Trapezoid Slope from Previous Step\\n(Used by Adams-Bashforth)');\n", "plt.xlabel( 'Time');\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Examine steps taken by AB2\n", "\n", "Use the slope at previous steps to get the final slope estimate for the current step." ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fn = lambda t, y, params: -params[0]*y\n", "params = (5,)\n", "y0 = 1\n", "h = 0.1\n", "eps = 0.2*h\n", "t0,t1,t2,t3 = 0,h,h*2,h*3\n", "tru_t = np.linspace( t0, t0+3*h, 10 )\n", "tru_y = y0*np.exp(-params[0]*tru_t)\n", "\n", "# use explicit trapezoidal to get first two points\n", "yprime = fn(t0,y0,params);\n", "yhatFE = y0 + h*yprime;\n", "yprimehatFE = fn(t1,yhatFE,params);\n", "y1 = y0 + h/2*(yprime+yprimehatFE);\n", "\n", "# Compute f at i-1\n", "fim1 = fn(t1,y1,params);\n", "# Compute f at i-2\n", "fim2 = fn(t0,y0,params);\n", "y2 = y1 + h/2*(3*fim1-fim2);\n", "\n", "# Compute f at i+1\n", "fim0 = fn(t2,y2,params);\n", "y3 = y2 + h/2*(3*fim0-fim1);\n", "\n", "plt.plot( tru_t, tru_y.T, 'C0' );\n", "plt.plot( [t0,t1], [y0,y1], 'C1--' );\n", "plt.plot( [t1,t2], [y1,y2], 'C2--' );\n", "plt.plot( [t2,t3], [y2,y3], 'C3--' );\n", "plt.plot( [t0-eps,t0+eps], [y0-eps*fim2,y0+eps*fim2], 'C4', linewidth=3)\n", "plt.plot( [t1-eps,t1+eps], [y1-eps*fim1,y1+eps*fim1], 'C5', linewidth=3)\n", "plt.plot( [t2-eps,t2+eps], [y2-eps*fim0,y2+eps*fim0], 'C6', linewidth=3)\n", "\n", "plt.plot( t0, y0, 'C0.', markersize=16)\n", "plt.plot( t1, y1, 'C1.', markersize=16)\n", "plt.plot( t2, y2, 'C2.', markersize=16)\n", "plt.plot( t3, y3, 'C3.', markersize=16)\n", "\n", "plt.legend( bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0., \n", " labels=['True Solution','Explicit Trapezoidal Step','First AB2 Step',\n", " 'Second AB2 Step','Slope 1 for first AB2 Step',\n", " 'Slope 2 for first AB2 step\\nSlope 1 for second AB2 step',\n", " 'Slope 2 for second AB2 step']);\n", "plt.xlabel( 'Time')\n", "plt.ylabel( 'Y');" ] } ], "metadata": { "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }