Skip to content

Instantly share code, notes, and snippets.

@MasonProtter
Created November 30, 2017 02:09
Show Gist options
  • Save MasonProtter/d30451d9564220d845bd366647280604 to your computer and use it in GitHub Desktop.
Save MasonProtter/d30451d9564220d845bd366647280604 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Physics 580 Assignment 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Initialization cell: Import libraries, define functions to be used"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"from functools import reduce\n",
"import time\n",
"\n",
"def num_div(f,x,h,deriv_type='asym',exact_h=False):\n",
" if exact_h is False:\n",
" if deriv_type is 'asym':\n",
" return (f(x+h)-f(x))/h\n",
" elif deriv_type is 'sym':\n",
" return (f(x+h/2)-f(x-h/2))/(h)\n",
" elif exact_h is True:\n",
" temp = x + h\n",
" hs =temp - x\n",
" if deriv_type is 'asym':\n",
" return (f(x+hs)-f(x))/hs\n",
" elif deriv_type is 'sym':\n",
" return (f(x+hs/2)-f(x-hs/2))/(hs)\n",
" else:\n",
" print('Error: Parameter exact_h must be Boolean')\n",
" \n",
"def num_div_comparison(f,x,fp,precisions,deriv_type='asym',exact_h=False):\n",
" def plot_deriv_and_diff(f,x,h,fp,deriv_type,fignum):\n",
" plt.figure(fignum)\n",
" \n",
" plt.subplots_adjust(hspace=0.4)\n",
" \n",
" plt.subplot(211)\n",
" plt.ylabel(\"f'(x) with h = {}\".format(str(h)))\n",
" plt.plot(x,num_div(f,x,h,deriv_type,exact_h),'orange')\n",
"\n",
" plt.subplot(212)\n",
" plt.xlabel('x')\n",
" plt.ylabel(\"f'(x)-cos(x)\")\n",
" plt.plot(x,num_div(f,x,h,deriv_type,exact_h)-fp(x),'b')\n",
" plt.show()\n",
" \n",
" sq_error = reduce(lambda a,b: a+b, \n",
" (num_div(f,x,h,deriv_type,exact_h)-fp(x))**2)\n",
" print(\"Error in numerical derivative: {}\".format(str(sq_error)))\n",
" fignum = 1\n",
" try:\n",
" for h in precisions:\n",
" plot_deriv_and_diff(np.sin,x,h,np.cos,deriv_type,fignum)\n",
" fignum = fignum + 1\n",
" except TypeError: # This is in case only one h is passed instead of a list of h values to try\n",
" plot_deriv_and_diff(np.sin,x,precisions,np.cos,deriv_type,fignum)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 1\n",
"Write a script that calculates and plots sines and cosines for $100$ points between $0$ and \n",
"$2 \\pi$."
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njBcE55xzAPwf40hCGpcgofgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1068a90b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_sin_and_cos():\n",
" \"\"\"Write a script that calculates and plots sines and cosines\n",
" for 100 points between 0 and 2 pi.\"\"\"\n",
" x = np.linspace(0, 2*np.pi, 100)\n",
"\n",
" plt.figure(1)\n",
" plt.subplot(211)\n",
" plt.xlabel('x')\n",
" plt.ylabel('Sin(x)')\n",
" plt.plot(x,np.sin(x),'orange')\n",
"\n",
" plt.subplot(212)\n",
" plt.xlabel('x')\n",
" plt.ylabel('Cos(x)')\n",
" plt.plot(x,np.cos(x),'b')\n",
"\n",
" plt.show()\n",
"\n",
"plot_sin_and_cos()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 2\n",
"Calculate and plot the numerical derivative of the sine function over the same interval and still for $100$ points using the finite difference equation:\n",
"$$\n",
"f'(x) \\approx \\frac{f(x+h)-f(x)}{h}~.\n",
"$$\n",
"\n",
"Use value of h that range from $0.1$ to $10^{-13}$ by powers of $100$. For each value of $h$, plot the difference between the numerical derivative and the analytic derivative as a function of \n",
"$x$ for the $100$ points you are plotting. \n",
"Also calculate the squared error for each graph."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEKCAYAAAA1qaOTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10698cc50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 0.123684042186\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaAAAAEKCAYAAABUsYHRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10698ccf8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.23749993419e-05\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAa0AAAEKCAYAAAChTwphAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnIsMT1rOOeci4/8Bo5w0N4m5rVkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1067ec518>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.23749812468e-09\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEKCAYAAADuEgmxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nocEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1065dd400>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.25170204982e-13\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106337b38>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 4.71593441557e-13\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaYAAAEKCAYAAABZr/GWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106612080>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 2.15532198135e-09\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZoAAAEKCAYAAAArYJMgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1061aeb38>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 0.000216404832215\n"
]
}
],
"source": [
"x = np.linspace(0, 2*np.pi, 100)\n",
"precisions = [10**-(2*x+1) for x in range(7)]\n",
"num_div_comparison(np.sin,x,np.cos,precisions,exact_h=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 3 \n",
"\n",
"Repeat (2) for the symmetric derivative:\n",
"$$\n",
"f'(x) \\approx \\frac{f\\left(x+\\frac{h}{2}\\right)-f\\left(x-\\frac{h}{2}\\right)}{h}~.\n",
"$$\n"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAacAAAEKCAYAAAC2bZqoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106ad1da0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 8.76516953837e-06\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106188630>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 8.76736722357e-14\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1052673c8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 6.80260997035e-20\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEKCAYAAADuEgmxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4ZxzLmqeNJxzzkXt/wFSXaAf8K/vswAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10642b278>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 7.36189641427e-16\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\naI6ilAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1062152e8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 4.50195971758e-13\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaYAAAEKCAYAAABZr/GWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nk3POuYTiick551xC+X/UbiV+BQYNhgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10631c358>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.10704220314e-07\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZoAAAEKCAYAAAArYJMgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnHMuof4fUds/jlExo/IAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1063f0c88>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 0.00071449267395\n"
]
}
],
"source": [
"x = np.linspace(0, 2*np.pi, 100)\n",
"precisions = [10**-(2*x+1) for x in range(7)]\n",
"num_div_comparison(f=np.sin,x=x,fp=np.cos,precisions=precisions,\n",
" deriv_type='sym')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 4 \n",
"Repeat (2) again using $h$’s that differ by exactly representable numbers."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAacAAAEKCAYAAAC2bZqoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1064c75c0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 8.76516953827e-06\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7Mr3dY1inwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10673dcf8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 8.76733852897e-14\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1063482b0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 4.64042731936e-20\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEKCAYAAADuEgmxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106315c50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.6488589995e-15\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnXecVOX1/99nl96VLr2JNBHFgiAqWDASu0YTOxETS+LP\n2PUbW2JMoolGE3uPJbGgRlFBUQQNCEiTBem9I4h02D2/P87czGyd2dmZvTO75/16zWt27p2598zs\nvc/nOec5z3lEVXEcx3GcnLANcBzHcTIDFwTHcRwHcEFwHMdxIrggOI7jOIALguM4jhPBBcFxHMcB\nXBAcx3GcCC4IjuM4DgA14r1BRDoDZwHtgHxgPvCKqm5Ns22O4zhOJVKmIIjIr4DhwOfA4cB0TBgm\nichVqvpZ2i2MoVmzZtqxY8fKPKXjOE7WM23atI2q2jze+6Ss0hUiMhs4RFXzRaQeMFpVjxOR9sA7\nqtqvIkaKyLOY4KxX1d7x3t+/f3+dOnVqRU7pOI5T7RCRaaraP977EhlDCLyI2kADAFVdDtRM3rz/\n8TwwLAXHcRzHcSpIvDGEp4EpIjIZOAb4I4CINAe+q+jJVfVzEelY0ePE5fs82LEKcutATm2oUQ9q\nN4PaTSEnFbrmOI6TIvbthN0bYM939nfBbsjfDfsfBnWapfXUZQqCqj4sIh8DPYAHVXVeZPsGYHBa\nLYsgIiOBkQDt27dP7iDzH4UFj5W8r3ZTqN8JGnSBhl2hycGw3yH2t3gSluM4aSB/F2z5BjbPgO+/\ngR8WwfbFsH0Z7Nte8meO+wAOSG9ApcwxBAAREeAIoE1k0yrgK01R3eyIh/BeWscQti0xDyFQ2n3b\nYPdGU+Gda2z/tkWwfSlovn2mRgNoNgCaHwMtBtvfubXKf27HcZzd38H6z2D957B+AmyZGW1rcutB\nwy7WKa3fEeq0jEYwcutCbm2LbDTuAbX2S+r0iY4hxMsyOgn4B7AAEwKAtkDXSJbRmKSsq2wadLJH\nPPJ3W3hp8wz4bipsmAiz7wTUBKLVidDmVGhzGtSJO2DvOE515vs8WPk2rB4NG/8LWmBh66ZHQc9b\nYL9+Fo1o0CljohHxxhAeBk5Q1aWxG0WkEzAaCyVVHXJrw/797NHlMtu2Z7Op+uoPYPX7sHIUSC60\nHAodfgLtz4GajcK123GczGDbYlj6Ciz7l4WCwGL/vW6H1ifD/odndKQhXtrpAqCHqu4rsr0WkKeq\nXSt0cpFXgeOAZsA64E5Vfaa094eedqpqrt6yf8Pyf9k/P7cetD8XuoyA5oNAJDz7HMepfPJ3wYq3\nYNHTsO5T29Z8ELT/CbQ/G+q2Dtc+UhQyAp7FsoxeA1ZEtrUHfgKU2nAniqpeUNFjVCoi5uLtdwj0\n/T1smgKLn7UewZIXoHFvOOg66PBTqFE3bGsdx0knO1bBgn/Awidg9yZo0NnahY4XQf12YVuXFIkM\nKvcATqfwoPK7qpqXZtuKEbqHUBr7tpuL+O3DsGWWDQZ1uwa6/wpq7x+2dY7jpJItcyDvD3bPaz60\nPQMOvBpaHp8xYwFFSdRDiCsIJRz4UFX9OmnLKkDGCkKAKqwfD/P+Aqv+YwPR3a6Cg66Hui3Dts5x\nnIrw3TT45vc2jlijPnS5Arpfa55BhpOqkFFJPA0cmsTnqj4i0PI4e2yZDXPug3kPwIK/Q/froMcN\nUKtJ2FY6jlMevp8Ls+6wcYKaTaD3byPef9OwLUs5yfg3PmqaCE36wMBX4dQ8OGA4zPk9vNsZ8v5s\n6a2O42Q2O1bBpMthdG9YMxb63AVnLIOD766SYgDJCcLdKbeiKtOoOwx6DU6ZbvnHM26C93vC8jct\nxOQ4TmaxbwfMvhv+cyAsfdm8+9MWQ587q3yKeUKCIMaFIvJbVX1bRNqLyBHpNq5Ksd8hcPxoOH6M\npapOPAc+Od4GqBzHCR9VWP46vNcdZt9lk1CHz4NDH0x7DaFMIVEP4R/AACBIE/0B+HtaLKrqtD7R\nvIXDH7Nxhg8Ogek3wt5tYVvmONWXrfPh05Nh4nlWNuKECTDo34lVOKhCJCoIR6rq1cAuAFXdDGTu\ndLtMJ6cGdPsFDP8WOl8Ccx+A93vAqvfDtsxxqhf5e2D2vTC6D2z6Cg57BE6eCi0GhW1ZKCQqCHtF\nJBdQ+F/564K0WVVdqNMMjnwaTvzSshfGD4cvLoBd68O2zHGqPhsnw4eHwezfQruzrIPW/RrIyQ3b\nstBIVBD+BowCWojI74GJwH1ps6q60XwADJsGfe6x1Lb3e1p5DMdxUk/+LgvTjhkAe7fAsf+xjECf\nK5TYPARVfVlEpgFDsbTTM1R1blotq27k1oI+/2e1T/57KXzxE1jxJvT/e7UZ0HKctLNpCvz3Etg6\nF7qOhH5/rvKZQ+Uh4YlpkcVx5gWvRaSBqvpIaKpp3BNO+hLm/skyHdaPh6OegwNOCdsyx8leCvbB\nN7+DOb+DOq3guA/hgJPDtirjqEjhjUqvZVRtyKkBvW6Dk6dA7ebw2Y9g6rW2nJ7jOOXjh0Uw9hj4\n5m7ocAGc+o2LQSnEWyDn+tJ2AQ1Sb45TiP36wrApMOMWK5y3bhwMfM1mQTuOE58lL8GUq2wNk6Nf\nhY7nh21RRhPPQ7gP2A9oWOTRIIHPOqkgtw4c9hAc/5GV2P3oCFjwhM9ydpyy2LvNxgr+e7GtTPaj\nWS4GCRBvDOFr4G1VnVZ0h4j8PD0mOSXS+iQ4ZaZd4FN+Aes+gSOeglqNw7bMcTKLzbPgi/Nsslnv\nO6H3HRaGdeISr5d/GbCslH1xS6k6KaZuSzj+Azjkj5ae+mF/W//ZcRxj0bMw5kjYuxWGjoOD73Ix\nKAdlCoKqfquqG0vZty49JjllIjnQ8yY4YTzk74SPjoKFT3sIyane7NsBky6DySOg2UA4ZYaVoXfK\nhY8DZCvNB1pNpBaD4asr7EbwLCSnOvLDIptktvgF6P1/Nt5Wp0XYVmUlLgjZTJ3mcNwHdhMsfg7G\nDoJtS8O2ynEqj1XvWfmJHSvguNFw8D3VuvRERXFByHZycu0mGPwubFtkN8easWFb5TjpRQtszYLx\nP7aKpMOmwQHDwrYq60lYEETkwthnJ8No+2ObyFb3APhsmFVQ9XEFpyqydyt8fqbN5O90sRWHrGZl\nqtNFeTyE64s8O5lGo25w0n+h7ZlWvOvLn9lgm+NUFbZ+Cx8dCavfh8MehqOehxp1w7aqyuBrKlc1\najaAQa9D39/DstdsXGH7irCtcpyKs/oDE4PdG2HIx7bQvXhzlEp8DKEqImK1kI79D/ywED7qDxu+\nDNsqx0kOVZj7oK0XUr+DhUY9pTQtuCBUZdqcCidPhhqN4JPjYNFzYVvkOOUjfzdMuhSm32Ch0BO/\ngAYdw7aqyuKCUNVp3MNEocWxMPly+PoGKMgP2yrHic/OdfDJ8bDkRStBMejfFhJ10kZ55nTPjzx/\nmw5DnDRSe3/L0Z72/2Deg7B1Hgx8xRcGcTKXzTNh/Gmwe4MJQftzw7aoWpCwh6Cq58c+O1lGTk04\n/FE4/B+w5kMYM9AnsTmZycp3YexA0Hw4cYKLQSXiIaPqRrdf2tT+HSutlLYPNjuZgqrNn/n8DGjU\nA07+CvY/LGyrqhUuCNWRVkPh5ElQs3EkRvty2BY51Z38PVaTa/qN0P4cK95Y74Cwrap2uCBUVxp1\nN1FodjT890KY9Vuf2eyEw+7vbHb9omeg1x22KmCNemFbVS0pT+mKXBE5QETaB4+KnlxEhonItyKy\nUERuqejxnHJSu6mFjzpfBt/cC19c4BVTncpl6wKrVLrhCxjwIvS910q8O6GQUJaRiFwL3AmsAwoi\nmxU4ONkTi0gu8HfgRGAlMEVE3lXVvGSP6SRBbi048hlodJCt3bx9KQx+xxbjcZx0sm48TDjLBGDI\nJ9BiUNgWVXsSleJfA91VtZeq9ok8khaDCEcAC1V1saruAV4DTq/gMZ1kELFFd455E7bMshWntswJ\n2yqnKrP4Bfj0RFu34KRJLgYZQqKCsAL4PsXnbhM5bsDKyDYnLNqdCSd8DgV7YOzRsGZM2BY5VQ0t\ngJl32Ozj5oOtGGPDLmFb5UQoM2QkIkFl08XAZyLyPrA72K+qf0mjbYENI4GRAO3bV3jYwolH0/5w\n0mSrM//Zj6D/I5aq6jgVZd9OmHQJLH8dulwBh//d5sc4GUM8D6Fh5LEcGAvUitnWsILnXgW0i3nd\nNrKtEKr6pKr2V9X+zZs3r+ApnYSo384mBLUeBlOushnOXu7CqQg711o9reVvQL8H4IgnXAwykDI9\nBFW9O43nngJ0E5FOmBCcD/w0jedzykPNhja4PP0G+PYh+GEBDHzVtjtOedgyGz4bbmWrj3kL2p0R\ntkVOKYSW36Wq+4BrgI+AucC/VdVHMjOJnFw47K/RchdjB8L25WFb5WQTq96HMUeD7jOv08Ugowk1\n4VdVR6vqgaraRVV/H6YtThl0+6UVx9u+zMpdbJwctkVOpqMK8x6Gz0+DhgdGylAcGrZVThx8BoiT\nGK1PsoyQGvXh42Nh6WthW+RkKgV7Ycov4OvroM3pcOLnUM8TCLOBRCemNQeuADrGfkZVL0+PWU5G\n0rinZSBNOAu+vAC2zoU+d/kyhk6U3d/BxHNh3TjoeYst5eozj7OGRNdDeAeYAHwMeLpJdaZOMxgy\n1nqA39xjaysc9ZzXnnFg67eWrrx9GRz1AnS+OGyLnHKSqCDUU9Wb02qJkz3k1oYjn7USxTNugW2L\nYPDbUK9t2JY5YbFmDEw8z1JJvQxF1pKoL/eeiPworZY42UVQ7uLYd61n+OHhPthcHQkGjz87Beq3\nh5OnuBhkMWUKgoj8ICJbsVpG74nIThHZGrPdqe60GW61aGrUs8HmxS+GbZFTWeTvhsk/jwwe/xhO\n/BIadAzbKqcClCkIqtpQVRtFnnNUtW7Ma1+Q1zGa9LK0wuYDrTTBtOuhYF/YVjnpZOca+Pg4WPys\nrWFwzFtQs0HYVjkVJKGQkYh8ksg2pxpTuykc/yEc+Cv49q8WQti9KWyrnHSw8Sv4sL9Vxh30uq9h\nUIWIFzKqIyJNgWYisp+I7B95dMQrkzpFyakJ/R+29RXWf26NxuYZYVvlpJJFz8DHx0BOLZuX0v6c\nsC1yUkg8Wb8SmAocBHwNTIs83gEeTa9pTtbS5XI4YYJNUBpztK/ZXBXI3w1f/cLGDFocB8OmwX4V\nXRLFyTTijSE8rKqdgBtUtVPMo6+quiA4pdPsCGs0mh5uazZP/ZUtpO5kH9tXWMLAwidsstlxo6H2\n/mFb5aSBeOshDFHVccAqETmr6H5VfSttljnZT92WMORjmH6zjStsmgLHvO7zFbKJtR/bWtv5u2HQ\nG9D+7LAtctJIvIlpxwLjgB+XsE8BFwSnbHJqwmF/geYDYNLl8EE/OPoVaH1i2JY5ZVGQD3Pug9l3\nQuNetrxqowPDtspJM6KqYduQMP3799epU6eGbYaTLFu/hQlnw/d50Ot26HMn5CQ6Wd6pNHauszDf\n2o+h44VwxONW1NDJWkRkmqr2j/e+RNNOF4nIyyLyCxHpVXHznGpJo+42X6HzZTDndzDuBNhRbJE8\nJ0zWfQofHAIbJsKRT8OAF10MqhGJJg/3BJ4AmgJ/jgjEqPSZ5VRZatSDo56xhmbTFPigL6x8N2yr\nnIK9MOM2+GQo1Gpswt1lhFeyrWYkKgj5wN7IcwGwPvJwnOTodBGc8jXUaw+fnw5TrrZF2J3KZ9ti\nGHsM5P3BUoaHTYMmfcK2ygmBRAO4W4HZwF+Ap1TVp6A6FadRd5vcNPN2mPeghSuOfgn2Pyxsy6oH\nqlZ6Ytp1ILkw8F/Q4bywrXJCJFEP4QLgc+Aq4DURuVtEhqbPLKfakFsbDn0Ajh8De7fCR0fBN7/z\nWkjpZuc688wm/9zmivxolouBU74sIxE5CDgFuA5ooap102VYSXiWURVnz2YLHS17FfY/HI56Fpr0\nDtuqqoUqLPsXTLsW9v4Ah/wBuv/aaxFVcVKdZfSmiCwEHgbqARcD+1XMRMcpQq39YOArFrrYvgQ+\nPBS++b0NeDoVZ+fa6PKnDTrbGM5B/8/FwPkfiY4h/AGYrqq+fKaTfjqcBy2Ph6nXwqw7YPnrcMQT\n0OzIsC3LTrTAitJNvwnyd8IhfzIh8DkgThES6hqo6lQXA6dSqdMcBr0Gx4yC3RthzAALJ+35PmzL\nsostc+DjwfDVSNivL/xoJvS80cXAKRH3FZ3Mpt0ZMHwudP8VLHwc3jsQFj1nvV6ndPZ8bwsVfXAI\nbJ0HRz0PQz+1zC7HKQUXBCfzqdkQDnvIJks16AKTLzePYeOksC3LPAryLTz03oHw7UM2r+DUedD5\nEp9k5sQl0UHlHBHpJyKnisgQEWmRbsMcpxj7HwYnTrRZztuXmyhMPA9+WBi2ZeGjCqs/MI9g8s+h\nQVcYNtXGXuo0C9s6J0uIV/66C3AzcAKwANgA1AEOFJEdWDmLF1Tdf3cqCcmxWc5tz4C5D8LcP8OK\nUdD1Suh1K9Srhgv5bfivDb6vG2fZQwP/Be3PdY/AKTdlzkMQkVeBx4AJWuSNES/hp8BmVX0hrVZG\n8HkITjF2roHZd1uYRHKh60hbxKXeAWFbln42ToJZd8LaMVC7OfS+A7r+AnJrhW2Zk2EkOg/By187\nVYNtS2yG85IXTBg6XQw9bqh6g6iqsOZDyPsTrP8MajeDHjfBgVd5VVKnVFI9Me1eEakR87qRiDxX\nEQMdJ6U06GRVVH8836p0Lv0nvNcDxp8Oa8Zmf1bSvu2w8CmrDvvZj2DbQuj3AJy2xNJIXQycFJBo\nMnINYLKIXAa0BB4FHkmbVY6TLA06w+H/gD53wfxHYcHjsOpdaNjNxhk6/gzqtgrbysRQhS0zLc12\nyfNW66nJwXDUC9DhfA8NOSkn4ZBRpJjde8BmYLCqVnpqh4eMnHKTvxuWvwEL/gEbv7RwUquToNOF\n0GY41GwUtoXF2bbUZmcvfQm2zLZlSNudCwdeDc0G+GCxU25SOoYgIoOxweV/An2wOkYjVHV1ksad\nC9wF9ACOUNWEWnkXBKdCfD8Xlrxk4aQdKyCnFrQcapPfWp8M9TuEY1dBPmyZAatGw8pRsHm6bW96\nlGVUdfgJ1G4ajm1OlSDVgvAVcKmq5kVenwXcp6oHJWlcD2yhnSeAG1wQnEpFC2DDl9b4rhhlhfTA\ncvdbDYVmR1vdpIbd0lP4LX83bJ4BmybD+gmWLrrnO0Cg2VHQ9kxodyY07Jr6czvVklQLQm7RWkYi\n0rSiC+WIyGe4IDhhogrf59mC8ms/hvXjYd8Ptq9mE2jSCxr1sEeDjlC3DdRrC7X2h9w6JYdvtMAG\ngXethx0r7bFtEWyda17K1rxoBdd67aDVCfZoORTqtqy0r+5UHxIVhHgT0y4EXimpsJ2qbopMXGut\nqhOTN9VxQkTEGv0mveCgX1v4Zutc671vmmJisfJt2P10CZ+tYWMQOTUjGxTyd9k6A5TQ0arf0YSl\n9cnmgTQ9snpOpHMylnhZRk2B6SIyDZhGdKZyV+BYYCNwS0kfFJGPgZLSOW5X1XcSNVBERgIjAdq3\nb5/oxxwnOXJybVGeJr0tfTVg10Ybd9i5ynr8e7ZY1s/eraAxq7vl1rXaSzUb2RyBem2hbluo3x5q\n1Kv87+M45SBuyEhEcoEhwECgNbATmAt8oKrLK3RyDxk5juOknZSEjAAi4aKxkYfjOI5TRYk3hnAn\nFgzdpqp/SdVJReRMbGJbc+B9EZmhqien6viO4zhO+YlX3O6SyJ87VPX1yjGpdERkA7AsyY83w8Y8\nspls/w5uf/hk+3fIdvshnO/QQVWbx3tTvJDRCap6kYj8OkVGVYhEvlBpiMjURGJomUy2fwe3P3yy\n/Ttku/2Q2d8h3qybw0TkAOByEdlPRPaPfVSGgY7jOE7lEM9DeBz4BOiMpZ3GzsLRyHbHcRynClCm\nh6Cqf1PVHsCzqtpZVTvFPLJNDJ4M24AUkO3fwe0Pn2z/DtluP2Twd8iqBXIcx3Gc9JGGyl2O4zhO\nNlItBEFEhonItyKyUERKLLWRyYjIsyKyXkS+CduWZBCRdiLyqYjkicicTMlaSxQRqSMiX4nIzIj9\nd4dtUzKISK6ITBeR98K2JRlEZKmIzBaRGSKSdSULRKSJiLwhIvNEZK6IDAjbpqJU+ZBRpPTGfOBE\nYCUwBbggKOWdDUTWo9gGvKiqvcO2p7yISGusCOLXItIQS1A4I1v+ByIiQH1V3SYiNYGJwK9VdVLI\nppULEbke6A80UtXhYdtTXkRkKdBfVbNyHoKIvABMUNWnRaQWUE9Vt4RtVyzVwUM4AlioqotVdQ/w\nGnB6yDaVC1X9HPgubDuSRVXXqOrXkb9/wGphZU2ZTzW2RV7WjDyyqiclIm2BU4ESyrY66UZEGgOD\ngWcAVHVPpokBVA9BaAOsiHm9kixqjKoaItIR6AdMDteS8hEJt8wA1gNjVTWr7AceAm7CFqbKVhQY\nIyLTIlWQs4lOWLXo5yJhu6dFpH7YRhWlOgiCkyGISAPgTeA6Vd0atj3lQVXzVfUQoC1whIhkTehO\nRIYD61V1Wti2VJBBqnoocApwdSSUmi3UAA4FHlPVfsB2Slk6IEyqgyCsAtrFvG4b2eZUIpHY+5vA\ny6r6Vtj2JEvEzf8UGBa2LeVgIHBaJAb/GjBERP4ZrknlR1VXRZ7XA6OwcHC2sBJYGeNZvoEJREZR\nHQRhCtBNRDpFBnLOB94N2aZqRWRQ9hlgbiqr5lYWItJcRJpE/q6LJSjMC9eqxFHVW1W1rap2xK7/\ncap6YchmlQsRqR9JSCASajkJyJqsO1VdC6wQke6RTUOBjEuqiLseQrajqvtE5BrgIyAXm3U9J2Sz\nyoWIvAocBzQTkZXAnar6TLhWlYuBwEXA7EgcHuA2VR0dok3loTXwQiRjLQf4t6pmZepmFtMSGGV9\nC2pgS/t+GK5J5eZa4OVIx3QxcFnI9hSjyqedOo7jOIlRHUJGjuM4TgK4IDiO4ziAC4LjOI4TwQXB\ncRzHAVwQHMdxnAguCI7jOA7gguA4juNEcEFwHMdxABcEx3EcJ4ILguM4jgNkoSCkcjlJETk+shxf\n8NglImekwk7HcZxsI+tqGaVrOUkR2R9YCLRV1R2pOq7jOE62kHUeQknLSYpIFxH5MLKS0gQROSiJ\nQ58DfOBi4DhOdSXrBKEUngSuVdXDgBuAfyRxjPOBV1NqleM4ThaR9eshRJZlPBp4PVIrHaB2ZN9Z\nwD0lfGyVqp4cc4zWQB9szQTHcZxqSdYLAublbImsd1uIyFKNiSzXeB4wSlX3pto4x3GcbCHrQ0aR\nxdqXiMi5YMs1ikjfch7mAjxc5DhONSfrBCGynOR/ge4islJERgA/A0aIyExgDnB6OY7XEWgHjE+9\ntY7jONlD1qWdOo7jOOkh6zwEx3EcJz1k1aBys2bNtGPHjmGb4TiOk1VMmzZto6o2j/e+rBKEjh07\nMnXq1LDNcBzHySpEZFki7/OQkeM4jgO4IITGwoUwc2bYVjiO40TJqpBRVeLmm2HuXMjLC9sSx3Ec\nwz2EkPj+e1iwAPb63GjHcTIEF4SQ2LED9u2DxYvDtsRxHMdwQQiJnTvt+dtvw7XDcRwnwAUhJHZE\nVl1wQXAcJ1NwQQiJQBDmzQvXDsdxnAAXhJDwkJHjOJmGC0JIeMjIcZxMwwUhBFTNQ2jYEDZuhE2b\nwrbIcRzHBSEUdu2y576RZXzcS3AcJxNwQQiBYPygXz97dkFwHCcTcEEIgWD8oGdPqFnTBcFxnMwg\nVEEQkWdFZL2IfBOmHZVN4CE0bAhdu7ogOI6TGYTtITwPDAvZhkon8BDq1YPu3V0QHMfJDEIVBFX9\nHPguTBvCIBCEunXhoIOsFPa+feHa5DjZTH5+9L5ykidsDyEuIjJSRKaKyNQNGzaEbU5KCEJGgYew\ndy8sWRKuTY6TzfzpT9CnT9hWZD8ZLwiq+qSq9lfV/s2bx10SNCuI9RC6d7e/PWzkOMmTl2eVgzdv\nDtuS7CYhQRCRHBHpJyKnisgQEWmRbsOqMkU9BEi9IKjCH/8Iq1en9rgVYd8+eOghd+2d5Pn4Y3j3\n3eLbg+CBl5OvGGUKgoh0EZEngYXA/cAFwFXAxyIySUQuE5GM9zIyjVgPYf/9oXnz1Be5W7oUbrkF\nnn02tcetCF98Af/v/8Hbb4dtiZOt3H473HZb8e2BIFQ09LplC3TsCJ9+WrHjZCvxGvPfAf8Euqjq\nyap6oaqeo6oHA6cBjYGLkj25iLwK/BfoLiIrRWREssfKJmI9BDAvIS/PevWpYt06e549O3XHrChL\nl9qzh8ecZCgogG++iV7bsaTKQ5gxA5Ytg6++qthxspUyBUFVL1DVz1WLN1Wqul5VH1LVF5I9eeT4\nrVW1pqq2VdVnkj1WNhHrIQAcfTR8+SUMGADvv58aYchkQfCS304yLF5s986mTYWz8lRTJwhz59rz\n2rUVO062kugYwr0iUiPmdSMReS59ZlVtinoI994Ljz9uF+Hw4faoKOvX2/P8+dHaSWGzbJk9u4dQ\ndfkujUnks2bZs6oVhQzYvj16jVc0ZJSXZ88uCGVTA5gsIgeLyInAFGBa+syq2uzYATVqWNkKgFq1\n4MorYcECuPpqGD062qAnS+Ah5OdHez1hE3gI8+eb+18a+fkwcyY8+ihccAEcdxwcdpiF1v72t8qw\ntGqgCmecAb16wZFHwtChcNVV8OqrsHJl6s83fryNh82cmfpjQ2FvNzZsFHgHOTkV9xBcEBJAVW8F\nbgImAy8Ap6rqo+k0rCqzY0c0XBRLzZp2A0O0N5QssYJS0WOVl02b4Pe/t4Y9lqVL7abdubP0BknV\n8skPOQSuvRYmTrTtrVvDtm3w0ktpNb1KsXYtvPMO1KkD++1nv/s//wk//Sm0awc335za833xhQn9\nqFGpPW5A7HUce30HgtCrl3mhRa+78uAhowQQkcHA34B7gM+AR0TkgDTalfGsXQudOpWcAhePnTuj\n4aKiBCWxK9rLWrcOunSxxqCyxxH++U+44w6YMiW6LT8fVqywniqUHjZavdpuyquuMvd/+XL47DN4\n7z04/3wSf45rAAAgAElEQVQbVPRZ3YkRXEN/+Qt8+KGNU333HUybBoceaimcqSS4zt57L7XHjT1+\n7972d0kewhFH2CTPVauSO/6WLbBmDeTm2nN1JNGQ0QPAuar6B1X9KfAUMC59ZmU+d91lPd7YRi9R\nSvMQwFzu1q0r3qtftw4OOMAqqla2h/D11/YcG6pavdoa8pNOstelCUIw4Hz22Zb+JxLd17evxYoX\nLEi5yVWSQBAOPji6rUYNE4NjjrH/QSoz24LrbNq01Deo27dbiZcTT7TXJXkIQWcj2bBRcL0ecQR8\n/310rK86kaggDFDVvOCFqr4FDEyPSZlPXh489ZT9nYxrWZaHAHYDV9RDWL8eWra0Y4UlCHl50W3B\n+MGAAdCgQemCEGw/6KDi+0rznr79FqZOTdrcKsvMmdC+vYWLinLQQdbIJtubLsru3fZ/CBIiRo9O\nzXED5swx8Ro0yMbcSvIQKioIwfU6ZIg9l5TeWtWJNzHtQhHJUdViUTlV3RSZuDYofeZlJjfeaKWr\nO3dOridUlocA1vDl5Zn7myzr1kGLFiYI69ZVfJA6UXbujPa0Yj2EQBA6diy7wuu8efbbtm5dfF+P\nHjbOMmNG4e0jR1pc3CnMzJlRES1KILipSgGeN8/Cgj/7mY1PpDpsFISj+va16zq2sV6/3kKjPXrY\nGFVpmUbr1sENN5SedTd3rh0nEJbqOI4Qz0NoCkyPrFtwtYicJyIXi8g9IjIe+BOQtTq6fbtlRpSH\njz+23s/tt9tNlQ4PoW9fE4Nkb9a9ey1W3LJltOBXZY0jzJ5tDUOjRoU9hCDltH37+IJw0EGFQ0UB\ntWpZCCzWQ9ixAyZNsnBCNpfEeOMNywLasyc1x9u5037jyhKE4Prq0wdOPRXGjjWvIVXMmgX169u4\nXcuWxUNGzZtbZ6F9+9I9hH/9Cx58sHSxysuz36VNG3tdUUFYvtzGvLKJeBPTHgYOBV4FmgNDI69X\nARep6tmqmrUR3XvusZTGFSsSe39BgXkHHTpYBkyrVsldNDt2xA8ZQfJho8CFDjwEqDxBmD7dns8+\n27yCoJFeutR+r6Cg3/LlJTfggSCURt++hX+XSZOsEVXN3vkN+flWZmTcOPj3v1NzzDlz7LilCULL\nltC4cWoFoWZNOPBACxsl09mKd/zevc0DKOohBIIAJhilCULgWZZWOiUvz7yMwDutiCCowllnwckn\np3acJt3EHUNQ1XxVHauqd6nqlap6nao+oarLK8PAdLFvH7z4ov39xReJfSYvzy6q224z17JVK7sw\ny8qpL4mdO8sOGXXvbr3hZGP/wc3SsqXdPC1aVN44wtdfW8z6lFMKN9JLl5qQQrSgX9HB4W3bTJzj\nCcKaNVHR++yz6L5YjySbGDUKFi2yTsJf/5qaBiQQzdIEQcR+51QKQhDSO/54uz/efz81x1a16zfw\ndkvzEMDCuKWFjILOynvvFQ/Hbt9uXmzPnnYskYoNjH/+uQ2ur16dvnkZ6SDRtNM/RWYn1xSRT0Rk\ng4hcmG7j0smYMdEewJdfJvaZoOfRr589t25twrJpU/nOHc9DqFnTcqqTvZCCm6VFpCbtwQdXrofQ\nr5/ZD9FGetkyGz+A0iu8zp9vz/EEAaK/zfjxtq1GDesVZxuqVsu/a1f4859NUBPtoJTFzJkWYunS\npfT3pFoQAm+0Xj0Lf733XmrEbe1au8eC47doYdd4cOyigrBunTXwsezZY9dHr16WQVTUewl+h549\n7Vpq3rxiHsKDD0KTJvb3hx8mf5zKJtEso5NUdSswHFgKdAVuTJdRlcELL0DTpjBwYOI3YCAInTrZ\nc6tW9lzeCyfeoDJULNMo1kMA61l9803FJuwEjBljcwxKYu9e68n162cNXG6uDdQVFBQWhAMPtOei\nghDclIkKws6dFjI66STo1i07PYTx4y11+YYb4NJLzbt66KGS3zt/vl23ifwfZ860/3tOGXf4QQdZ\nltEPPyRl+v/YvNkmGsYuUDN8uN0vqQjjBd5trIewZ4817FA8ZATFvYQgSeOGG0ywioaNggSIHj3s\nOdlwMNh3/s9/4Ne/tgmWH3yQ3HHCoDylKwBOBV5X1e/TZE+lsHmzXRA/+5m5tzNnWrgiHosXWwZM\n06b2OhCE8rqW8QaVwRq+deuSS30LPIRAEA4+2DIrFi2KvmfHDhv4u+02GDECLr7YMnXeeKPsY7/w\nAtx3H2zdWnzf3Lk2kHjooRbyChrpNWvsZgxCRvXq2eBfSYKQm1t2r7ZZM5tfMXNmdPzg2GOtZ1eW\nIOzebaKYafHcP/3JerwXX2y/y5VXWggpyMratct+88GDzbO69NL4oRjVsjOMAgLhrWijHTugHDAw\nkpReVqdG1ZIzLrzQvtfPfw4PPGBeZmwYtujxg+t63Tq7l7ZvL+whQHFBCMJFAwZYB+LttwtfC3l5\n5hl07Wqv4wnCWWeZrSXx179C7do2ufKUU6zD+X2WtJiJCsJ7IjIPOAz4RESaAxlSMq38vPaaNSSX\nXmqVRvPzEyt3u3ixXXBBBkyyg0+JeAjBzZxM7H/dOovhNmhgrwNX+3e/s5tu4EDriZ50koUpxoyB\nCRPMtb3yyuLudizLl9uNFMw1iCW46YKQWo8edqPFppwGlJRpNG+e/b61a5f9/YKB5c8+sx7woEEW\nCli0qPSUwscftwalf3/7/2fCbOdZs6z3+KtfRa+Hq66y6+u+++z/1aGDXadr19q22rXjD9YuX24N\nUKKCUNGwUUmCEIh/kF1WEmPH2ncaPz46G/3GG61D0aKFNaa//rV1Utq0iXbEglDounXRsaSiglB0\nYHn6dAuhdetm5WFWrbIYf0Benu0L6ouVJQgrV5po33df8cSIDRtMwC+6yOwcNszal08+Kf13CNi+\nPfwFrRKtZXQLcDTQX1X3AtuB0yt6chEZJiLfishCEbmlosdLlOeft0bykEOsxwCJjSMsWRK94CDa\nUymPh1BQYL3VeB5C0IgnIwjBpLRAuHr2tDTQl16ymy4317KkRo82b2nFCvtu779v6apPP136sYMb\nvKSJYF9/bd8rCAn17GnpoMHgcUmCENtLmzcvOr5QFn37mjcyZow1Ho0b27kKCkrv7eblWYOwbZsV\nzOvVq/xjP6lE1byz+vXhl7+Mbm/XDs45xyY+/t//WVG/Tz6x73XrrXDUUTZgWRbxBpQDOne2ayEV\ngtCkSTRdE+x6a9KkbEH44x/N21u40DoNa9daY/viixZyWr/eFniaPDl6n0L0vlu/vrggNGtmv2lR\nD2HGDPs9cnLs2Dk5hcNGc+faNRTQurXZU5JHOXasPW/ebJ2LWB57zDol119vrwcMsN+itLDR7Nlw\n3nl2zzRsaL/hFVeEtxRoooPKNYELgX+JyBvACKBCt5OI5AJ/B04BegIXiEjPsj9VcebMMW/gkkus\nwWzSxBqHeOMIqlEPIaBBA3uUx0MIpsPH8xBiQyPlJZiUFlCnjtm+ZYvZ+vnn5u6eckrUiwC7eAcP\ntgGxkvLhY+vElFSyY/p0u+lyc+11z57WOwpuoPbto+/t3t1i18Fvl59vMfKyxg8CgnkakyZZ2nBw\nLig9bLR0qb1n7lxL7Vy40ArwJcLy5TZ7NchKKw979liv/4orCnslr75qAnzvvbZqXiz33Wc95Vmz\nTLSHDImK++DBJrwlhewCgmsm3qLztWpZeC4VgtCnT/G5Ix06lC4IX31labbXX1/YI2zTxnrXzz9v\nPfitW+2aiy1qWJaHIGL3aKyHUFBggnDIIfa6aVP7HQNB2LnTrodg/ADMQ9izp+SGeexY29+rl1Xk\nDURj5Uq7r047LXqsmjWt3MYHHxQXl/nzbfB93DjrAN51F1x3HTz3nF2r//53xSanJoWqxn0AT2NV\nTodEHs8BTyfy2TKOOQD4KOb1rcCtZX3msMMO02SYOlX1rrtUBw9WrVlTtVYt1bVro/tHjlRt3Fg1\nP7/0Y6xerQqqjz5aeHu3bqrnn5+4LRs22HEeeST+e085RfXggxM/dsAhh6gOH17+z6mqjh5t9j3/\nfPF9S5bYvtxc1c6dC+/Lz1dt0ED16quj277+2t7ftKlq8+aF3z9mjO379FN7vWiRvX766fg25uXZ\ne0H1vfds265dZtftt5f8mW7dVM87L/r68svtOliypOxzbdig2r179Hz33KNaUFD8fTt2qD75pOq/\n/qW6d69t27JFdejQ6GdHjLDPrltnv8lRR6nu2xf/+8Yydqwd64MPSn/P2WerdumS2PFOO021V6/o\n65Ur7fdNlIIC1UaNVK+6quRj9+5d8ufOOku1SRPVrVsTP1fA3r2qIqq//a3qiy/a7zF/fnT/6acX\n/k4LF9p7nnoquu2hh2xb8+Z2LFB97bXo/ldftW1z5hQ+d36+arNmqhdfrPrYY/aeL7+Mfqc6dexa\njuWpp+x9s2dHt61cqdqhg53/228Lv3/aNNV+/ewzDRva7/jII9YGJQswVRNplxN6E8xMZFt5HsA5\nsaKCLcX5aAnvGwlMBaa2b98+qR/jmmvsn37YYao33qg6ZUrh/c8/X/wfVpSJE+09o0cX3n7MMarH\nHpu4LcuW2XGeeSb+e2++2QTsu+8Kb58/X/UnP1GdPLnkzx1wgDV4yVBQYCLUo0dxgfzsM7P9hBPs\nedOmwjYVbdC3b4/ebIcfXvhYa9ao5uREG5L337f3TZwY38a9e+3Gy8mxRjege3fVM88s/v78fGv8\nb7opum35cjvGRReVfp6tW83uOnVUP/7Y3guqV1xhN+f27aq7d6v+4x/2mwcNf8eOqg88YL9jjRp2\nff3f/9m+m2+2/12tWsUbm0TYts2Oeeutpb+na1drnBLhppvMlr17VXfuNCFp1MhEKxGWLrXv9dhj\nxfdde601aEUFdO5cuy5KE+9EaNZM9corVR980M6/eXN033XXqdarp7pnj71+/XV7z9Sp0fds3GiN\n+i9+oXrnnXbd7toV3f/pp/aZTz4pfN5p02z7Sy+p/vCD/VY/+5nqO+/Y9j/8obitK1bYvj/9yX6L\n+fNNsBo2LGxTLHv3qr75pn3Hzp3t82PGJPNLGakWhK+xdZWD152BrxP5bBnHTEgQYh/JegirVxdv\nVGNZsMB+iSeeKP09QU9k3rzC28891xqiRJk3z47zyivx3ztzpt04118f3VZQEO115uRYA7NzZ3R/\nfn78BiMeL79sx3/77cLbX3jBtj/+uD1/9FF0X9Cj+vrrwp8JLuZzzil+nmuuse8wbVr0xt64MTEb\nBwxQPeKIwtvOPLPk/8XKlSU3WjfdZL/vjBnFP7N3r+qJJ5rX8e67tq2gQPW226INP0QFb9Aga0Te\nflv16KNtW4MG0d+ooMAan+Bz996b2PcsiaOOsnOUxPffm013353YsZ591uxZsMBsCq6rESMS+/x/\n/lO6kD/wgO0reu9dfrmJbKKiUxK9eqmecYbqLbdYpylWdILOxcMP2+vbbrP/Y+x9Eo+5c+0YL79c\nePsf/mDb16yx19dea+dv08ZsCkSoKH36qLZsqdq6tX2+Vi3VceMSt2fRosKCVV5SLQhDgeXYWgjj\nsbkIxyfy2TKOWWkho3gUFJjrdvHFpb/nrrvsRit6UV17rYWbEiUIoxRtbEvj8svtglu40F6/9ZZ9\n/ve/V/35z+3vnj0ttKFqvXYwlzhZ9u61Xu4JJxTefs89duy1a6M2BJx7roVBit4Qp55q773hhuLn\n2bxZtUULa+BGjLBeX6IsXlw83HPHHXbjF71xAu+uaJjlu+9U99tPddiw4scPfufHHy++b9w48wru\nv996uR9+WLwXPHly4TCGqoWHLr9c9bjjzLNIlsBz3L69+L6PPjK7x45N7Fhffqn/C2HWqWP/x9/8\nxq710nqvsfzqV/a5bduK7wt65tOnR7dt2WK2lxRiKg9DhpgojhhhjWwsBQUm5o0bq65fr/qjH1mD\nXB62bDHbH3yw8Pbjj1ft2zf6OhCOeN7t3/5mnaOf/tSunaJhpXSTUkGw41EbODjyqJ3o58o4Xg1g\nMdAJqAXMBHqV9Zl0CYKq9Ta6di19/yWXqLZtW3z7fffZr7hjR2LnCRqn2N51WaxapVq/vsWFd+yw\nhrp372icetQoLeTdBPH1RDyQsrjySmssYxu6ESNUW7Wyv7t1s99M1cSoZk1z1Yty441a4thLQOB1\n1KljveyK8MordqxZswpvf+kl2z53bvHP/PnPtm/ChMLbhw+3MFDwO2cSQQ+4aDhD1UJTubmJx+aD\nDkSdOnadrVhhjWGLFuaFlTReEpCfb/fE6aeXvP+rr4p3fiZMsG3vv5+YfaVx/vkW3jrttJLH2fLy\nzFMeOdIEo6zOXkkUFNhvcuON0W3bttl1HrtN1e6V224r/3eoTBIVhESzjK4G6qrqLFWdBdQTkasS\n+WxpqOo+4BrgI2Au8G9VDa34wNFHW6ZBaRlDRTOMAso7WznIMoqXdhpwwAFw003w5ps2kW7pUnj4\nYZtEA3D66faecZHliorOUk6W3r0twyI2pXbZsmh++eGHR1NPX37ZsiEuv7z4cYLsn+BzRbnoIptH\nsGtXYhlGZVFaplEwD6IkG375S8s6+fOfo9tWr7bsnksuif7OmcTAgZY2WVL66cSJlk3TsGFix9p/\nf8va2bULfvtbaNvW0njvvx/++1+bOPf007bW9w03FM6UmTrVMmvOOqvkYwdZZbGZRkH1z2Dls2QJ\n6hnFzlKOpUcPuOYaS99dsyaaYZQoIsXnIowfb9d5sMhTwOOPJ56xlukkOjHtClXdErxQ1c3AFRU9\nuaqOVtUDVbWLqob6kwYrMZU2C3Tx4ui0+FjKKwjBRJZ4aaex/OY31uiPGmU3X7CAB9iFO2QIfPqp\n3axF6xglS0lls2MFoX9/awzWroVnnjGBKCnNcdgwszmYuVoUEfj73y09L5jQlizdu1tDWbSmUWyl\n1aLUr28Nx7vvRoXkxRctVbEkgcsEGje2Bq7oBLUgFXdQOVcoOfRQE9Prrotuu+QS+5/ecoulzD7z\njKUjxy67+eabJpg//nHJx23RwlKeYwVh9mzLy2/Xrnw2lnTsH36wlOCSBAHgzjstfRuSu7ZatSrc\nIRozxr5PeX/fbCJRQcgViWYZR+YQ1EqPSeHQt69NnCppgfBduywXuiQPIZitnOjktPJ6CGCN1sMP\nW854SdPlhwwxIcjLS52HEBSnC3p0BQV28wW9vv797fmJJ+wmL63xbNXKGo6SVu0KOPhgm0g0cmTF\nbK5Tx36joh7CkiUli3nANdeYWDzwgInqs89annpQxiATGTzYGv/YNQemT7frq7wN1quv2jycWjF3\ndE6O3QtvvWWe85Yt1im5/37br2r7hgwp/X8rYtdLUQ+hd++S17soD8H1vWpV6YLQpImVkWjb1kSv\nvMR6CKrw0UdWJqVOneRszgYSFYQPsUlpQ0VkKLY+QhbV8IuPiE1pHzu2eLGvIOSQipBR4CGURxDA\nZq8uWFByw3b88fY8bpwJQ05O8clO5aVZM/tugSCsX2+NT+Ah9Otn57n/frtBLrigYudr0yY14Zle\nvYovSrJ0aeFZ0kVp1szqOf3zn7aIyoIFmesdBBx7rHVUJk2Kbps40Z5L88ZKo0mTaGXOWNq0gTPP\nNJGtU8cmkY0bZ5PKZs82oSgtXBQQOzlNNSoIFSXWAy5NEMDCrCtWmFdSXoLZymCzxefNs9+jKpOo\nINwMjAN+GXl8AtyULqPC4swzbXZi0XK1wTT4kgSheXNrGMs7hlCekFFAab2qjh1NKMaNMw+hefPo\nbOGK0KdPNGQU3NSBIDRoYHHaXbtMrBo3rvj5UsGhh9oM0O++s9f5+ebZlOUhgDV2+fkmBA0b2nfK\nZIYOtUbu8cej2yZOtMa7pOVHU8HIkeYN3H+/eQdBJ6osYgVhzRr7v8SbQZ0IsR5wWYJQEVq1go0b\nLRR3990mkJdemp5zZQqJ1jIqUNXHVfUc4D61BXJSUEw5sxg40HqLRcNGwTT4kgQhN9d6K4mGjJL1\nEOIxZIgVCFuzpuLhooDevS38kp9fXBAgGjYaMSI150sFgwdbTzQoRbJqlZWMKMtDABOM884zwT7/\nfAvTZTING1ps//XXowUHJ05Mb3y7YUMLr40aZYO1gwbFv9Y6dLCB3x07UjegDJUnCGBe48SJcPPN\n8QsvZjuJegixlFH6LLvJzbU6JO+/X7iWz+LF1qMv7eIvT+30ingIZTFkiMV5x4+v+IByQO/eZu+S\nJSULwogR8ItfWCOcKRxxhA1QT5hgr0uqtFoat91m8earr06XdanlV7+y54cftjDXhg3pH/C89lq7\ndlevjh8uguj1smJFagUh0ZBRRQgE4aabzOu6osJpNJlPMoJQweGgzObMM62g1qefRrcFGUalhWzK\nEoS//Q3eeSf6escOG7xLRUgnlmAc4YcfUuchxGYaLVtmYaHY0NAxx1h1x7IWYals6ta17JhAEIJw\nX7yQEdj3XbEifpXQTKF9ezj3XOutjx5t29ItCM2bW8OYk1M+QVi2zK6jVq2imT8VoW7daGptugVh\nzRoThao8mByQzK18d8qtyCBOOMHCBbFho9LmIAS0bl1yyGjvXitZ/MQT0W2JrIWQDK1bRysspspD\nCPL6v/mmcMpppjN4sOXIb99uHoJIxdMcM5Xf/MY6Ab/9rc2nSKR8eEW5/34bWI6tXlsasYKQqgHl\ngOA6T5cgBGMxLVtWPAMuW0h0YlqOiPQTkVOBrSKSoiYn86hTx8pCv/OOpVqqxheEVq1sMDd2lSew\nMsQ7dhT2HhJZLS1ZgvkJqfIQ6te3751tgnDMMTZuMHmyeQht2lTd2G///iaAP/xg3kFF0zkToW5d\nW6chEdq0MW94yRKbH5JKQWjZMjUZdaXRqpWJ3j33pO+ezTTKFAQR6SIiTwILgfuBC4CrgI9FZJKI\nXCYiGRQwSA1nn22NeOfONpN127b4grBvXzSzJSAY2IwVhHR5CBANG6VKECCaaZRNgnD00dYwfv55\n/JTTqsBvfmPPmThhqkYNE4XPPrPOUCoyjAJatjSvKF0hy5o17fqpLt4BRNdKLo3fAY8BV0bqYfyP\niJfwU6xK6QvpMS8cfvITy7l/4w1bqAMKL55RlNjJabHx0SAvfP16y9TJzU2vh3DyyZYWd8IJqTtm\n7942i1c1ewShSRMbB5gwwXqmxx4btkXpZfhwW7bx9AqvYZgeOnSI3gup9BAuu8zEP51UhseVSZQp\nCKpa6nQjVV0PPJRyizIAEZu6f8klFof+5hvLXimN2MlpQQ8oSH3MyTEx2LTJYp47dqRPEBo0sNWW\nUkmfPtH6NdkiCGBho6efNmGv6h5CTg5cfHHYVpROhw7RQf5gBnwq+PGPSy+b4SRHomMI94pIjZjX\njUQkxU1PZlK/Phx5ZNk9hZJmKy9dah5DsMRjsG/nzvSFjNJBbI8u2wRh504b10kkw8hJH8F107lz\n5s/vqO4kGn2rAUwWkYNF5ERgCjAtfWZlF0HIaPXq6LZg/ODss+05EIR0egjp4MADLZYK2ScIAVXd\nQ8h0gusmleEiJz0kOlP5VqxUxWRsvOBUVX00nYZlEw0aWMP52mvR8MrEiVZaYOhQe52tHkLNmlaW\nunbt1KWzVgatWkG3bva3C0K4BOmpqRxQdtJDoiGjwcDfgHuwVdMeEZEDkj2piJwrInNEpEBE+id7\nnEzitttgxgz4z3/s9Rdf2IBXmzb2Ols9BLDv0bdv9g2wDR5sgta2bdiWVG969rRso3QPADsVJ9H6\nkg8A56pqHoCInIUVu0t2SZNvgLOAJ+K9MVv42c8sX/nuuy1cMWeOZSs1aGBx02DiWjrTTtPFww/b\nJLts4667rEhdEPJywqFdO+sQNW0atiVOPBIVhAGxxexU9S0RGV/WB8pCVecCSLZ1OcugRg24/Xar\n73PHHRY6CvLCY0tbpDPtNF3Urp2dE7vatnXvIFNwMcgO4k1Mu1BEckqqbKqqmyIT19I6HUZERorI\nVBGZumHDhnSeqsJcdJHFq//xDxOIIFU1VhCy0UNwHKd6EM9DaApMF5FpWFbRBqAO0BU4FtgI3FLS\nB0XkY6BVCbtuV9V3StheIqr6JPAkQP/+/TXO20OlZk0bSxg50haQCTyBVq0shLRvn4Vess1DcByn\nehBvYtrDIvIoMAQYCBwM7ATmAhep6vIyPpvC+bLZwyWXwCOPFF44pHVrW3EpmeUzHcdxKou4YwiR\ncNHYyMOJQ61aVtQudnikVStbq2DzZnvtISPHcTKRMgVBRH4b+XObqv4lVScVkTOBR4DmwPsiMkNV\nT07V8cOm6Fh5MJM5qM3vHoLjOJlIvHkIVwDLgJQu56Kqo1S1rarWVtWWVUkMSqKoILiH4DhOJhJP\nEH7AQkUXish+IrJ/7KMS7KsSBIIQrM3sHoLjOJlIvDGEx4FPgM5YllFsMEQj2504FBUE9xAcx8lE\nyvQQVPVvqtoDeFZVO6tqp5iHi0GCBDWA3ENwHCeTSbS43S/TbUhVpmZNWzjHBcFxnEymyi1/makE\n6y6Dh4wcx8lMXBAqiVYxc7bdQ3AcJxNxQagkYgXBPQTHcTIRF4RKIlhVDdxDcBwnM3FBqCRiPYQ6\ndcKzw3EcpzRcECqJQBDq1IEc/9Udx8lAvGmqJAJB8PEDx3EyFReESiIQBB8/cBwnU3FBqCRcEBzH\nyXRcECqJ/fazGcseMnIcJ1MJRRBE5M8iMk9EZonIKBFpEoYdlYmIeQnuITiOk6mE5SGMBXqr6sHA\nfODWkOyoVNq1g8aNw7bCcRynZOIuoZkOVHVMzMtJwDlh2FHZPPWUp5w6jpO5hCIIRbgc+FdpO0Vk\nJDASoH379pVlU1ro2TNsCxzHcUonbYIgIh8DrUrYdbuqvhN5z+3APuDl0o6jqk8CTwL0799f02Cq\n4ziOQxoFQVVPKGu/iFwKDAeGqqo39I7jOCEjYbTFIjIM+AtwrKpuKMfnNgDLkjxtM2Bjkp/NFLL9\nO+CtFc8AAARISURBVLj94ZPt3yHb7YdwvkMHVW0e701hCcJCoDawKbJpkqr+Is3nnKqq/dN5jnST\n7d/B7Q+fbP8O2W4/ZPZ3CCvLqGsY53Ucx3FKx5MgHcdxHKB6CcKTYRuQArL9O7j94ZPt3yHb7YcM\n/g6hjCE4juM4mUd18hAcx3GcMqgWgiAiw0TkWxFZKCK3hG1PeRGRZ0VkvYh8E7YtySAi7UTkUxHJ\nE5E5IvLrsG0qDyJSR0S+EpGZEfvvDtumZBCRXBGZLiLvhW1LMojIUhGZLSIzRGRq2PaUFxFpIiJv\nRAp7zhWRAWHbVJQqHzISkVysgN6JwEpgCnCBquaFalg5EJHBwDbgRVXtHbY95UVEWgOtVfVrEWkI\nTAPOyJb/gYgIUF9Vt4lITWAi8GtVnRSyaeVCRK4H+gONVHV42PaUFxFZCvRX1aychyAiLwATVPVp\nEakF1FPVLWHbFUt18BCOABaq6mJV3QO8Bpwesk3lQlU/B74L245kUdU1qvp15O8fgLlAm3CtShw1\ntkVe1ow8sqonJSJtgVOBp8O2pToiIo2BwcAzAKq6J9PEAKqHILQBVsS8XkkWNUZVDRHpCPQDJodr\nSfmIhFtmAOuBsaqaVfYDDwE3AQVhG1IBFBgjItMiRS+ziU7ABuC5SNjuaRGpH7ZRRakOguBkCCLS\nAHgTuE5Vt4ZtT3lQ1XxVPQRoCxwhIlkTuhOR4cB6VZ0Wti0VZJCqHgqcAlwdCaVmCzWAQ4HHVLUf\nsB3IuPHM6iAIq4B2Ma/bRrY5lUgk9v4m8LKqvhW2PckScfM/BYaFbUs5GAicFonBvwYMEZF/hmtS\n+VHVVZHn9cAoLBycLawEVsZ4lm9gApFRVAdBmAJ0E5FOkYGc84F3Q7apWhEZlH0GmKuqfwnbnvIi\nIs2DZV5FpC6WoDAvXKsSR1VvVdW2qtoRu/7HqeqFIZtVLkSkfiQhgUio5SQga7LuVHUtsEJEukc2\nDQUyLqkiExbISSuquk9ErgE+AnKBZ1V1TshmlQsReRU4DmgmIiuBO1X1mXCtKhcDgYuA2ZE4PMBt\nqjo6RJvKQ2vghUjGWg7wb1XNytTNLKYlMMr6FtQAXlHVD8M1qdxcC7wc6ZguBi4L2Z5iVPm0U8dx\nHCcxqkPIyHEcx0kAFwTHcRwHcEFwHMdxIrggOI7jOIALguM4jhPBBcFxHMcBXBAcx3GcCC4IjlMB\nRORwEZkVWTOhfmS9hKypc+Q4sfjENMepICLyO6AOUBerV/OHkE1ynKRwQXCcChIpRTAF2AUcrar5\nIZvkOEnhISPHqThNgQZAQ8xTcJysxD0Ex6kgIvIuVla6E7ZU6DUhm+Q4SVHlq506TjoRkYuBvar6\nSqQa6pciMkRVx4Vtm+OUF/cQHMdxHMDHEBzHcZwILgiO4zgO4ILgOI7jRHBBcBzHcQAXBMdxHCeC\nC4LjOI4DuCA4juM4EVwQHMdxHAD+P0rCKp3ShlkGAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1063482e8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 2.53276755801e-13\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaYAAAEKCAYAAABZr/GWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWvHE5JxzLq14YnLOOZdWPDE555xLK/8P8ZVjLfio6U0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1068dd278>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.13521655133e-07\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZoAAAEKCAYAAAArYJMgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106215860>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 0.00158629990076\n"
]
}
],
"source": [
"x = np.linspace(0, 2*np.pi, 100)\n",
"precisions = [10**-(2*x+1) for x in range(7)]\n",
"num_div_comparison(np.sin,x,np.cos,precisions,deriv_type='sym',\n",
" exact_h=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 5\n",
"\n",
"Finally, try to calculate the numerical derivative of $10^{15} + \\sin(x)$. Compare it to the analytic derivative."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAacAAAEKCAYAAAC2bZqoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106a92da0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 8.76516953827e-06\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7Mr3dY1inwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106644f28>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 8.76733852897e-14\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1067434e0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 4.64042731936e-20\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEKCAYAAADuEgmxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnXeYlNX1xz9nC73KolKkWRERC6JiAREVezdqMEaNmkSN\niTFRk/w0aowxMcYSjbFFk9iNxt6xRiHSFCkqIiBIXXqH3fP748ybHYYp78zO7Duzez7PM8+0O/c9\nszvv/b7nnHvPFVXFcRzHccJQFrUBjuM4TungouE4juOExkXDcRzHCY2LhuM4jhMaFw3HcRwnNC4a\njuM4TmhcNBzHcZzQuGg4juM4oam3aIjIj0Rku3wY4ziO4xQ3Ut8V4SKyHFgNfAk8CjypqovyYFtO\nVFVVaa9evaI6vOM4Tkkybty4xaraOVO7ijwcawawNzAc+BZwrYiMwwTkaVVdWZ/OReQB4Bhgoaru\nlql9r169GDt2bH0O6TiO0+QQkVlh2uUjp6GqWquqr6nqeUBX4C5gBCYo9eXBWF+O4zhOxOTD05D4\nJ6q6EXgOeE5EWtW3c1V9V0R61befjNRuhPlvQnlzKGsO5S2gWQdo3hkq2oBI5j4cx3EaAq2F9Utg\n/WLYtBJq1kPteqhoDVX7FfTQ+RCNb6V6Q1XX5KH/jIjIBcAFAD169Mitkw1L4e0jk79X1hxadYc2\nfaDN9tC+L3TcAzoMgGbtc7TacRwnDaqwdi4snWi3lV/Aqi9h1QxYt8CEI5FO+8IRowtqVr1FQ1U/\nFxEBBgHdYi/PBf6rDVR3XVXvAe4BGDhwYG7HrOwAh31gal2zHmrXwYZlsH4RrFsIq2fbP2z24yYw\nAW13gq0Pgs4HwTaHQOscRctxnKaN1po4LHwHFr4Hi9638SegVXe7aO0yAlp2gxadLRJS2Q7KmlmU\npFnHgptZb9EQkcOxHMYXmFgAdAd2EJEfqupr9T1Gg1DeDDrvn7mdKqybH1P/CbB4NMz+F3x5v73f\nfjfodjR0Oxaq9gfxpTCO46Rg02r45hX45gX45mXzIMCiGl2Pgk6DoOMA6LA7VLaN1tYY+QhP3QYM\nV9WZ8S+KSG/gJaBvHo5RPIhAyy526xoLZ2ktLPsU5r8O37wIU/8IU26yK4Mep0HPM2CrvT0v4jgO\n1GyAb16CWY/B3OehZo1FOrqOgC5HwraHQqtumfuJiHyIRgUwJ8nrc4HK+nYuIo8CQ4EqEZkDXKOq\n99e337wiZdBxd7v1/SlsXAFzX7Afxed3wLRboEN/2P570Ovb0LxT1BY7jtPQLJ9qEYmv/m5hp+ZV\n0Ps70PM0C2+X5WM4Ljz5WNx3FXAa8BjwdezlHliC/AlVvbFeB8iSgQMHalGt09iwDGY9bj+WJR/Z\nrKxeI2HnS6FDxmUnjuOUMloLc1+Ez26FBaNAKqD78bD9ebDtYUUlFCIyTlUHZmyXj1y1iPQFjmfz\nRPhzqjql3p1nSdGJRjxLP4Yv/mJXGjVrYdvhsOtVlkD30JXjNB5q1sOMB2HqzbBquoWqd7wItj8X\nWmwdtXVJaVDRSHLwvVR1fN47DkFRi0bA+mqYfi98dpsl1TvtB7v9yhJfLh6OU7psWgPT/2pisfYb\nS2Tv8lPY7kQoq3e0vqCEFY1CTe25r0D9Ng6ad4J+V8LxX8E+d8G6efDOMfDaYFjwVtTWOY6TLTUb\n4PO74LntYfxlNhV/2Otw+GjLWRS5YGRDoUTDL5fDUN4CdvwBHPsFDLoH1s6BN4fBqMNtSq/jOMWN\nKsx8DF7sC2MvgrY7wPB3YfhbFn5uhJGDQonGtQXqt3FSVgk7nG/isecfYck4eHkvGPM9WDs/ausc\nx0nG4tEWHfjgDKhoC0NfMsHY+qCoLSsoeRMNMUaKyNWq+m8R6SEig/LVf5OgvAX0vQyOmw47/9gS\n5s/vaPHR2o1RW+c4DtiF3Affgdf2h9UzYd8HYMQ4W7fVCD2LRPLpadwF7A+cEXu+Ergzj/03HZp1\nhL1vgaMmw9ZDYcLP4OU9YeG7UVvmOE2X2hr47M/wws5WTqjfLyw6sP05UFYetXUNRj5FY19VvQhY\nB6CqS4Fmeey/6dFuRxj6PBz8LGxaBW8MgdHnbl77ynGcwrN0Iry2L4y7xIoCHjUJBtwAlW2itqzB\nyadobBSRckABRKQzkKQMo5M13Y+Do6fArldayOqFvjD7KUvCOY5TODathYlXwSsDYc0cOOBxOORV\naLdT1JZFRj5F43bgGWBrEbkBeB/4bR77b9pUtII9boQRY63C5funwvunWAVex3Hyz+Ix8MqeMOV3\n0Ptsu3DreVqTyFukI29r2FX14dg2r4diU25PUNWp+erfidFxDzhiDEz7I3xytZVQ3ucv0OPkqC1z\nnMZBzXqY9GuY+nto2R0OeQ26HBa1VUVDXgufqOo0YFrwXETaqOqqfB7DwerV7HoFdD0aPjzbPI5e\nI2Hgn31TKMepD8smwQfftvvtz4O9brH9Kpz/UejNHhq89lSTosNutkvXbtfArEfg5QGw8P2orXKc\n0kNrYdqt8Mo+tqfFkBdg3/tcMJKQj02YLkv1FtD0phY0NGWVsPuvocsR8OFIeHMI9Psl7HZ1UVXQ\ndJyiZe0C+PA7MP816HoM7Hd/0RYVLAby4Wn8FugItE24tclT/04YOu8PR06EXmfBp9dbOZI1ybY5\ncRznf8x73Tz0Re9aHbghz7lgZCAfl6LjgX+r6rjEN0Tke3no3wlLZVvY/0GrefPR9+GlAbD/Q9Dt\nmKgtc5zionYTTLoGJt8I7fvCsDd8f5uQ5MMTOAeYleK9jGV2nQLQeySMGA+te8I7x8KEK+wkcRwH\n1s6DUcNh8m9tf4sjPnLByIJ6i4aqfqaqi1O8t6C+/Ts50m4nOPwD2OFCmzr45jBY803UVjlOtCx4\ny0ryVH8E+//dkt0VraK2qqTwnENjprwFDLob9v+nVc59ZS+vX+U0TVRhyk3mYTTrCEf8F3qfFbVV\nJYmLRlOg97ftJKlsbx7HtD95CRKn6bBxha1lmnglbHeynQsd+kVtVcniotFU6NDPTpZux9rOYh+c\nCZtWR22V4xSW5dPg1X1hzrOw581WO6qybdRWlTR5FQ0RGRl/7xQZzdrDQf+CAb+FWY/DawfAqq+i\ntspxCsOc5+DVQbC+2mZH9f1pk68blQ/y7WlclnDvFBtSBv2ugqEvwupZVr1z/htRW+U4+UNrYdJ1\n8O7xNiFkxFjYZmjUVjUafI/wpkrXI2HER9CyC7w1Aj673fMcTumzcZVVgJ50jS10Hf4etO4RtVWN\nCs9pNGXa7gCHf2iL/8ZdCv893yp8Ok4psmomvH4AzPk37PlHW9ha0TJqqxodLhpNncq2cNDT0O9X\n8OX9MOpQ36PDKT0Wvgev7mMh1yEvQt/LPH9RIFw0HMtzDLjeZpYsGW/Jw6WfRG2V44TjywfsYqdZ\nR9trpuuIqC1q1ORbND6P3X+W536dhqDnaTD8XajdCK8PtmmKjlOs1NbA+J/CmPNg66EmGO12jtqq\nRk9eRUNVT4+/d0qQTgOtFk+7XeHdE2HK7z1B7hQfG1fY7Khpt8BOl8DQl8zTcAqOh6ecLWnVFYa/\nAz1OhYlX2JVczYaorXIcY9VMW2M07xUrZz7wdt87pgHxv7STnIqWcMCj0G4X+PQ6WPWlJcybd4ra\nMqcps3i0eRg162Hoy753dwS4p+GkRspg92th8MOweAy8uh+s8HSVExEzH4M3hkJFWzh8tAtGROS7\njEi5iHQVkR7BLU/9jhCRz0RkuohcmY8+nSzodSYcOgo2LjfhWPBW1BY5TQlVW+H9wRnQaZAJRvtd\noraqyZI30RCRS4AFwOvAi7HbC3notxy4EzgS2BU4Q0R2rW+/TpZ0HmyzU1p1hVGH25oOxyk0Nevg\nw7NshXfvs2HY69CiKmqrmjT5zGlcCuysqtV57BNgEDBdVWcAiMhjwPHAlDwfx8lEm95w2Afwn2/B\nmO/Bis9hjxstjOU4+WbdInjvRFj0HxhwA+x6lS/YKwLyebZ/DSzPY38B3WJ9B8yJveZEQbP2MOQF\n2PEHtiPg+6fCpjVRW+U0NpZPg9f2s83DDnwC+v3CBaNIqLenISJBRdsZwNsi8iLwvwJGqnpLfY8R\nwoYLgAsAevTw4mQFp6wCBt4JbXeGCZfBG0NgyHNW/NBx6sv8N+G9k6G8ORz6NlTtG7VFThz58DTa\nxm6zsXxGs7jX8rHbyVxgu7jn3WOv/Q9VvUdVB6rqwM6dO+fhkE5GRGCXS+Ggf8OKqbHSIx9HbZVT\n6ky/16out9rONg1zwSg66u1pqOq1+TAkDR8BO4pIb0wsTgfOLPAxnbB0PxYOex/eOdYqjA5+1F5z\nnGyorbGFpNP+CF1GwIGPQ2W7qK1yklD0GUxV3QRcDLwKTAWeUNXJ0VrlbEbHPeyqsN0utvBq6i1e\nesQJz8ZV8N5JJhg7XgRDnnfBKGJKYkW4qr4EvBS1HU4aWnaxYocffgcm/BRWTIN97oSyyqgtc4qZ\n1V+bl7p8Eux9B+x8cdQWORkoek/DKSEqWtXNdPnyXnjrCFi/JGqrnGJl8X8tF7b6K9sDwwWjJMib\npyEinYHzgV7x/arqufk6hlMCSJnNqW+3i63leG0/m6LbbqeoLXOKiZmPwZhzoEUXGPYGdOgXtUVO\nSPLpaTwLtAfeoG5F+It57N8pJXqfZaVHNiyDV/eF+W9EbZFTDGgtfPJrKwmy1UCrMuCCUVLkM6fR\nSlWvyGN/TqnT+QBLkL9zrE2j3OtW2OkiX6TVVNm0Gj48G77+l5UEGfRXW4vhlBT59DReEJGj8tif\n0xho0wsO/wC6HgXjLoGPvu97czRFVs+G1w+Er5+GPW+G/f7mglGi5GNF+EpAAQF+ISLrgY2x56qq\nPneuqVPZFg7+N3z8K5hyo82sOvBJaLF11JY5DcHC9+H9k6344JAXoJtfW5Yy9fY0VLWtqraL3Zep\nasu45y4YjiFlsMdvbW+O6v/CK/vAkglRW+UUmun3wqhhUNneSpq7YJQ8+SyN/maY15wmTq8zbQU5\ntbaCfOZjUVvkFIKaDfDRRfDfC2CbYZbwbt83aqucPFBv0RCRFiLSCagSkY4islXs1guvRuskY6u9\n4Yixdv/BGTD+cqjdFLVVTr5YO9+8iy/ugr4/szUYzTpGbZWTJ/Ixe+pC4MdAV2B83OsrgD/noX+n\nMdJyGxj2Joy/zMpHLJ0ABzzuG+yUOos+tPzFhuVwwGPQ81tRW+TkmXzkNG5T1d7A5araO+42QFVd\nNJzUlDeDff5sM2kW/Qde2ctWCTulhyp8fie8OQTKW8IRo10wGin5CE8Niz2cKyInJd7q27/TBOjz\nXTj8PyDl8MaB8MVfvOBhKbFptW3JOvZi2PZwGDEWOvSP2iqnQOQjPDUEGAUkq4etwNN5OIbT2Nlq\nbxgxDj4YCR/90DyPfe6GyjZRW+akY/lU271xxdTYlqxX+va/jZx87KdxTez+nPqb4zRpmm8FQ1+A\nyb+FSdfAkrG2nsOvWouTGX+Hj34AFa3hkFdh2+FRW+Q0APmccvuliDwsIt8XES8m4+SGlMFuv7Ii\ndhuWWxXU6fd5uKqY2LQaRp8Ho8+GTvvAkRNdMJoQ+fQjdwX+CnQC/hATkWfy2L/TlNjmEBuMOh8I\n/z0f/vMtK37oRMuSCfDK3jDjb9DvlyburbpGbZXTgORTNGqw8iE1QC2wMHZznNxouY2FPfb4HXz9\nDLw0wEpSOA2P1sK0W63U/cYVJhYDfgNlJbGPm5NH8ikaK4Bbga+As1V1f1W9MI/9O00RKYNdr4DD\n/mO7AL45BCb+woseNiRr5tiGWuN/Yvt3H/kJbDss8+ecRkk+ReMM4F3gh8BjInKtiByax/6dpkzV\nIDhyAvQ5x4oevrYvLPs0aqsaPzMfhRf7w6IPbDbbwf/2BZhNnLyJhqo+q6o/w1aIvwR8F3ghX/07\nDpVtYd/74OBnYc1ci61PvtFLkBSCtQvgvVPggzOtZtRRH8OOF/peKE5eZ0/9S0SmA7cBrYDvAF5w\nxsk/3Y+Doz+FbsfBx7+wOPuySVFb1ThQhZmPwIu7wtwXYMCNMPxdaLtD1JY5RUI+s1g3AhNUtSaP\nfTpOclpsDQc9CbOfssWAr+wNfX9uM3oqWkZtXWmyaiaMvQi+eQk67Qf7PeCVaZ0tyGd4aqwLhtPg\n9DgFjp4CPc+EyTfAS/1h3mtRW1Va1G6EKX8w72Lhu7DXn6x8vQuGkwRf7++UPi2qYP8H4dBRVr/q\nrSMsHr9qZtSWFT/z34CX94CJP4cuR5gA7/JjKCuP2jKnSHHRcBoP2xxiCdvdr7cQy4t94ZNf2wpm\nZ3NWzYD3ToZRh9k2rAc/Cwc/A623i9oyp8jJZyK8TET2FJGjRWSYiPgG0E7DU97CypAc8xl0Ox4+\nvRae39FKkfgsK1hfDeN+Ai/sAt+8YkUGj55skwscJwT1ToSLyPbAFcBw4AtgEdAC2ElE1mClRR5S\n1dr6HstxQtN6OzjwMVh0CUz4mZUi+exP0P862O7EpleJdeNK+PwOmPJ72LTS1rv0vxZa+eaaTnaI\n1rMQnIg8CvwFeE8TOot5G2cCS1X1oXodKCQDBw7UsWPHNsShnFJBFeY8Y9NzV3wGHXaH/r+G7sc3\nfvHYuAo+/zNMu9m8jK7HwB43QofdorbMKTJEZJyqDszYrr6iUWy4aDgpqa2BWY/Cp9fByi+g/a62\nh3XPM20XwcbE2gXmWXxxF2xYCl2ONKGsGhS1ZU6RElY08pnTuF5EKuKetxORv+Wrf8epN2Xl0Huk\nzRDa/58gFTD6HHiuN3x6gw20pc7SiTDmfHi2p+1LsvVQOHw0HPKSC4aTF/Lpm1cAY0RkdxE5DPgI\nGJfH/h0nP5RVQO9vW+n1oa+Yx/HJr+DZ7eA/Z8L8UVbVtVTYuApmPASvDYaX94SZD0Ofs+GYaXDw\n01C1b9QWOo2IvK0IV9WrROQNYAywFDhYVafnq3/HyTsi0PUIuy2fBtPvhhkPWgirVXfo9W3oeYbl\nQIqt5lLNBljwpgnE189AzRpouxPsdSv0+Q408wo+TmHIW05DRA7GEuL/BPpjdafOU9Vv6tHnqcCv\ngb7AIFXNmKzwnIZTLzatgTnPwcx/wLxXQWugdW+bcdXtGKgaDOXNo7FtfbUtxpvzLHzzou1rUdkB\nep4Gvb9jthWbuDklQ9icRj5rT90MnKqqU2IGnASMAnapR5+fAidh03Ydp/BUtIJep9tt3UIboL9+\nJjYD6RYobwmdD4JthkKnfaHTQKhsVxhb1syBxWOgerSFzJZOABSaV8F2p5iQbTvc1qY4TgORT0+j\nPLH2lIh0UtXqPPT9NnC5expOZGxcAQvesSv9BW/A8imxNwTa7mh1mtrtao9bbwctu0HLbaGiXeqS\nHDUbbGbT2m9MINbMhhXTYPlUWD4Z1s23dmXNoGp/E4htDrV9uX3HPCfPNJinISIjgUeSFStU1erY\n4r8uqur7dDqlS2U76H6s3QDWL4Hqj6B6DCz72ERk7ougSVadV7S2G7HQkdbYYrva9UnatoF2faHL\n4bDV3ubNdNwjupCY4ySQj8uVTsAEERmHzZYKVoTvAAwBFgNXpvpwLHm+bZK3fqmqz4YxQEQuAC4A\n6NGjR1bGO05ONN+qLokeULsRVs+GtXPNc1g731Zfb1yxef0rKYOKtiZEle2hVVdo2d2S7y27eF7C\nKWryEp4SkXJgGHAA0AVYC0wFXlbV2Xno/208POU4jlMwGjQRHgtNvR67OY7jOI2UfOQ0rgEUWKWq\nt9TfpM36PhG4A+gMvCgiE1X1iAwfcxzHcQpEPgoWnh17uEZVn6y/SfVDRBYBs+rRRRWWhylVSt1+\nKP3v4PZHT6l/hyjs76mqnTM1ykd4ariqniUil+ahr3oT5kunQ0TGhonrFSulbj+U/ndw+6On1L9D\nMdufj9pTe4tIV+BcEekoIlvF3/LQv+M4jlMk5MPTuBt4E+iDTbmNny+osdcdx3GcRkC9PQ1VvV1V\n+wIPqGofVe0ddytFwbgnagPqSanbD6X/Hdz+6Cn171C09je6TZgcx3GcwtHI97p0HMdx8omLRgwR\nGSEin4nIdBFJWfakWBGRB0RkoYh8GrUtuSAi24nIWyIyRUQmF8tsvGwQkRYi8l8R+Tj2Ha6N2qZc\nEJFyEZkgIi9EbUu2iMhMEZkkIhNFpCRLQ4hIBxF5SkSmichUEdk/apvi8fAU/yuD8jlwGDAH23Xw\njKDMeykQ289kFfB3Vd0tanuyRUS6YIUtx4tIW2xSxQkl9j8QoLWqrhKRSuB94FJVHR2xaVkhIpcB\nA4F2qnpM1PZkg4jMBAaqasmu0RCRh4D3VPU+EWkGtFLVZVHbFeCehjEImK6qM1R1A/AYcHzENmWF\nqr4LLInajlxR1XmqOj72eCVWu6xbtFZlhxqrYk8rY7eSuioTke7A0cB9UdvSFBGR9sDBwP0Aqrqh\nmAQDXDQCugFfxz2fQ4kNWI0JEekF7IltHVxSxEI7E4GFwOuqWmrf4Vbg50AJbZK+GQq8JiLjYtWv\nS43eWKXwv8VChPeJSOuojYrHRcMpKkSkDfAv4MequiJqe7JFVWtUdQ+gOzBIREomVCgixwALVXVc\n1LbUgwNVdS/gSOCiWNi2lKgA9gL+oqp7AqtJs7VEFLhoGHOB7eKed4+95jQgsTzAv4CHVfXpqO2p\nD7GQwlvAiKhtyYIDgONieYHHgGEi8s9oTcoOVZ0bu18IPIOFnkuJOcCcOA/1KUxEigYXDeMjYEcR\n6R1LPJ0OPBexTU2KWBL5fmBqvqslNxQi0llEOsQet8QmVkyL1qrwqOpVqtpdVXth58AoVR0ZsVmh\nEZHWsUkUxEI6hwMlNZtQVecDX4vIzrGXDgWKajKIbzQMqOomEbkYeBUox1a3T47YrKwQkUeBoUCV\niMwBrlHV+6O1KisOAM4CJsVyAgC/UNWXIrQpW7oAD8Vm45UBT6hqyU1bLWG2AZ6x6w8qsG2oX4nW\npJy4BHg4dgE7AzgnYns2w6fcOo7jOKHx8JTjOI4TGhcNx3EcJzQuGo7jOE5oXDQcx3Gc0LhoOI7j\nOKFx0XAcx3FC46LhOI7jhMZFw3EcxwmNi4bjOI4TGhcNx3EcJzSNVjTyvf2piPw+toXnVBG5PVZg\nz3Ecp0nRaEUDeJA8laUWkcFYQb3dgd2AfYAh+ejbcRynlGi0opFs+1MR2V5EXont6vWeiOwStjug\nBdAMaI5t47kgrwY7juOUAI1WNFJwD3CJqu4NXA7cFeZDqvohtqHOvNjtVVWdWjArHcdxipQms59G\nbBvRwcCTcemI5rH3TgKuS/Kxuap6hIjsAPTFdvQDeF1EDlLV9wpstuM4TlHRZEQD86qWxfZv3ozY\n1qLpthc9ERitqqsARORlYH/ARcNxnCZFkwlPqeoK4CsRORVse1ERGRDy47OBISJSEdvHegjg4SnH\ncZocjVY0YtuffgjsLCJzROQ84NvAeSLyMTAZOD5kd08BXwKTgI+Bj1X1+QKY7TiOU9T4dq+O4zhO\naBqtp+E4juPkn0aXCK+qqtJevXpFbYbjOE5JMW7cuMWq2jlTu0YnGr169WLs2LFRm+E4jlNSiMis\nMO08POU4juOEptF5Go7jOI2Nt96CxYthl11gxx1hwwb47DO7LV0Kqnbbdlv41rcKa4uLhuM4TpFz\n0kmwbJk9FjGBSMa++7poOI7jNGlUYcUKOPtsGDECpk2DFi3M69hlF6iqMiERgYoGGNFdNBzHcYqY\nDRugthZ22glOPz1qazwR7jiOU9SsXWv3LVtGa0eAi4bjOE6BUYVZsyyZnW0RjjVr7L5Vq/zblQsu\nGo7jOAWkpgZ+8APo1Qs6d67LR8wKtSqiTjSKxdPwnIbjOE6eUIXly6FDB3u+di2ceSb8+99w8cWw\nww4wcSI8+CBMngw9e2buMwhPFYun4aLhOI6TJx58EM4918TgoINg+nQYMwZuvx0uucTaTJpk7QIP\nIhPFFp5y0XAcx8kTM2fa/T77wOuvw8qV8PjjcOqpdW1at7b71avD9VlsiXAXDcdxnDyxerWJwpNP\nWqhq0yaorNy8TeAxlKqn4Ylwx3GcPLFqVZ0nIbKlYEDpexouGo7jJGXmTDjhBKtt5IQj8DTS4Z6G\n4ziNkvffh2eftZi8E47Vq6FNm/RtysuheXP3NBzHaWQEBfKefDJaO0qJMJ4GmNfgnobjOI2KQDTe\nfhsWLozUlAblxRdh3LjcPhuf00hH69bhPY1iW9wXqWiIyAgR+UxEpovIlUne/66ILBKRibHb96Kw\n03GaIoFo1NbC009Ha0tDsXSpTY+94YbcPl8IT2PtWkuqN2+em035JjLREJFy4E7gSGBX4AwR2TVJ\n08dVdY/Y7b4GNdJxmjBLl0LXrlZdtamEqB56yAbpQDCzJUxOA7L3NFq1MuEoBkKJhoiUicieInK0\niAwTka3zcOxBwHRVnaGqG4DHgOPz0K/jOHlg2TLo2NGuvJtCiKq2Fu66yx4vX55bH4XyNIolNAUZ\nRENEtheRe4DpwO+AM4AfAm+IyGgROUdEcvVWugFfxz2fE3stkZNF5BMReUpEtsvxWI7jZMmyZVZD\n6bTTbEB95pmoLSosb74JX3wBbdvapke5UKicRrEkwSGzp/Eb4J/A9qp6hKqOVNVTVHV34DigPXBW\nAe17HugVO97rwEPJGonIBSIyVkTGLlq0qIDmOE7TIRCN/v0tRPXEE1FbVFjuvNOq0J5ySm6ehqp7\nGqjqGar6ruqWFeBVdaGq3qqqSQfyEMwF4j2H7rHX4o9RrarrY0/vA/ZOYec9qjpQVQd27tw5R3Mc\nJ3+MHg0nnww//CH89rfw0kvhP7tihVVFXb8+c9tCEoiGSOMPUc2eDc8/D9/7Hmy9dW6isX69eWRh\nPY1sptyWkqcBgIhcLyIVcc/bicjf6nnsj4AdRaS3iDQDTgeeSzhul7inxwFT63lMx9mCbAfn9est\njDFzJsydCxs3btnmqacsnPPEE/DLX8LRR2deWT11Klx0EXTrBieeaH2EZd267Df3yUSQ0wA4/HAb\nECdOzO+ne5KMAAAgAElEQVQxioW//tXuL7wQ2re3LVbXrcuujyDcFCYR3qpVdov7SsbTiKMCGCMi\nu4vIYdiAn+NMZkNVNwEXA69iYvCEqk4WketE5LhYsx+JyGQR+Rj4EfDd+hzTcRLZsMFmCJ1+et3K\n20yMHGnhmt69oXt3G1ATqa629xYvtjLYAOkip599BrvtBvfdB8ccY6/Nn5/ejkcesXzDzjvbIHTZ\nZenb//rXUFUF11+feXaQap2nAfY5aFwlRVQtj3HKKXDTTXDssVbSvF07ez9bb2PVKrt3TwNQ1auA\nnwNjsLzC0ar65/oeXFVfUtWdVHV7Vb0h9trVqvpccFxV7aeqA1T1EFWdVt9jOo2biRMtBv/VV+Ha\nL1wIS5ZYqYxhw8KFX6ZPh732ggcegCFDYFqSX2V1NXTqZI+DiGl1deo+v/rKruRfecXEoKLCBCcd\nP/iBhYz69YNtt4UpU9K3Hz/eQl9XX22D4513pm67apXZE4hGcJ/rVNRi4auv4N574bvfhT59YPhw\n+xtedpm9DuZpQPaiEXgOYXMaq1eH8w7XrClBT0NEDgZuB64D3gbuEJGuBbTLcXJi9Gj49FMLCYUh\nEIlzzoGPP4b99oMZM9J/prrahOmcc2D//e154sm/ZAlstZU9DsRjyZLUfQYC0a2b5RA6dUovMuvX\nmwBceqktvBswIH3/YJ7O0KEwYYJ5NT/+sW1FmoxAHAKxCMJUpexprFoFffvCBRdYjmmPPeDvf4c5\nc+D3v68T90A0sp1Bla1o1NQkD20msnZtCXoawM3Aqap6o6qeCdwLjCqcWY6TG/Pm2f2jj8LYsZnb\nByGj886zK865c9NfgYMN8IEQVFXZib9y5eZt4j2N4D6dCATvBWGgTKIR2B22PZhAdu5sg+UZZ9he\nD6m8mUTRaNECmjUrbU9j7lwT2zvugAULLOd01ln23eLJ1dMIwlNhF/dBuLxGSYangP1V9X/Or6o+\nDRxQGJMcJ3fmz7eBrqoKfv7zzO5/4Gl07gyDBlkeIl0uYe1au2UShHhPI7hPN6gvXgxlZXWDdCYR\nCAb74Op4q60yi8aiRTYzCKBLbIpJILKJJIqGiHkbpexpBP/XXXZJv7q6ocJTEC6vUVKJcBEZKSJl\nqrqFE6uq1bHFfwcWzjzHyY558yxef/XV8NZbliNIR3DFHgymnTunT1gHA3M60VA10Qje69DBBCFd\n+Ki62gblstgZWVWVPqcR2BiIRqdOFk5JFe5Yt868oaB9tqIRPC5lTyMQjW23Td+uIUSjlD2NTNu9\ndgImiMg4bLbUIqAFsAMwBFgMbFFo0HGiYt48GxQuvBBuuw2uuMJmN5WXJ2+/cKHtrhYMFJ07W4w7\nFYlhpOA+foBfudJCP4GHUVZmgpDJcwj6gvDhqXjRAPMEtk5S5CdRHLvGMpLZiEZj8TQyiUaus6cK\n4Wmolpinoaq3AXsBjwKdgUNjz+cCZ6nqyar6RcGtdJyQzJ9vV9HNmtkU00mT4IMPUrdftMgG3iBc\nkQ9PI7ENZA4fxedAgs8mS7DH2x3YG/SfaEc88WE4qBs4v/kmeftAHPLlaXz1VfReyvz5Nist+Ful\nor5TbvOZ0wjWipSSp0EsNPV67OY4RUttbZ1oAOyzj93Pnp36MwsXbn5lHoiGavK4dxjRCMJQ8YNT\np06Zw1M9e9Y9j0+wB4NYPIsW1Xkw8XakOkaip9GihX02k6cReGBg7adPT/0d0nH44Xbs996rC8E1\nNPPnwzbbZD5+RYUN6oWePQWZPY1i20sDwk+5/X1sFXiliLwZ2+NiZKGNc5xHHoGjjoJbb808YFVX\nW1gouIoOQjCprqahztMI6NzZFvwlzoYKCMJQ8fkKkcyeRpjEdmL7+L5StQ8GwEztEz0NMHFNJxpt\n2tgAGpCrp7FxI3z5pXl8D+VadChFv++8E779/PmZQ1MB7dvnFp4qKwu370VYTyNYcFpMnkZYzT9c\nVVcAxwAzsZzGzwpllOME/POf8Oqr8JOfwI472mKsVAQDYOBptG1rA1860UjmaUDqEFWiIJSXm0cR\nn9PINjylmjw8Fd9XIoliFzY8Ff9dM4lGfGgK6nIa2ZYrmTvXPtOsmc1oy1de5I9/tHUnU0MWF2oI\n0WjdOty+F43e06AujHU08KSq5lht3nGy46uv4IQTbMHdmWda2YdUV2dBorNLXMWyrl2z9zSC15NR\nXW0DQ/zVZKIXkW14as0ai13HJ8KTJdjT2R0mPNWsmQlpQNeu6UUjCH0FdOhgC9LC1kwKmDXL7m+4\nwewLu/AyHRs3wp9jNSkmTAj3mUKLxqpV4fIZ0DQ8jRdEZBpWZfZNEekMZFnOy2lojjkGLrkkaity\np7bWRKNPH6vzFNRkmjkzeftETwPSi8batXaiZ+tpxA/usKVoBI8TRWPVKgt9JeszaBPfPv69RBJF\no107CyWl8zS23nrzq+DA00jmOaTyNCB7TyHIKR17LFx8Mdx9d+57cAc8/bR5MGAVADJRU2N/g/jf\nRjratcvd0whDtp5GyYmGql4JDAYGqupGYDW+y17WbNpkV8ypSjfkk9paW6fwxhuFP1ahmDfPVvD2\n6WPPg/tUZT4C0Yi/muzWrW5wSSRxBlL843SiET+4w5ZrKpYsqRvEA9J5AonTeOPbpxON+PYi6UNg\niSIDNoBu2JDcpmSikWv9qcDT6NEDrrvOktHHHZddPiKR22+H7beHXXe1GXKZWLzYzomGCE+FIVtP\no+TCUyJSCYwEHheRp4DzgAzrT514Pv8c9t3XfugdOlgs9oc/hHPPtSqbZ54Z7oopLF9/bVcpn38e\nvnprlDz88JY7wwVFB3v33vw+VTHCefMs/BJ/4gaeRrKr6WRx/lxEI5mnkdgmXc4hMbkOdlWfmGAP\nqKmxgT5RBLbaKnV4KjF3A+kX+OXb0+jc2Qa+9u1twWXr1lYg8tprs7+IGjvWkuqXXGI1t8KIRtg1\nGgHt2+c2eyqsaDRrZknzRutpAH/BQlN3xW57xV5zMqAKf/ubVUWdOdMKo519tg3kjz0Gr79u1Ulf\nftna/OY34YqYZSJIDtbWbln99Be/sP0dwrJsmYUDEk/umhqr15SNvQsXbrlPgSr89Kd2FRpP4FEE\nHkbnznZSpvI04qfbBnTtat5KsoEumafRurUNbvURjfgSIvFtgs8n6zO+DViCvWPH5DmNJUvsb5Yo\nGulmaMWXEAnIVjSC59mKxqxZm08nHjDAwlNnnmlraQ47zGpBheW22yx38N3vWuHIWbMyD/C5iEYh\ncxoi4bZ8LVlPA9hHVc9W1VGx2znAPoU0rJSpqTHX+6qrrDjcuedaXaNPPoGf/cwSeGPG2Mn/9dc2\nqH/+OZx0Evzf/5lHkqmOUCbiZ5R88snm7z31lFX5/O9/M/czZw4cdJDtQnf88XUn59KllmM45BAT\noPiQxYYN8OSTW171zpxpM6B+/vMtbV2wwEqMxwvTjBl2cgUDjoh5G+k8jWSiAcnzGsk8DUi/wC9x\naizY8zVr6k7wVMICyT2BQBgy5UoCkolduvZQV6wwnlSrwmtrbcBM5WlkG56aPdtCU/G0bWsVZh94\nAD78EPbcE95/P3Nf8+dbGftzzrGBfbfd7PVMXnouorFmTXYXRNl4GhBuy9dS9jRqRGT74ImI9AHq\nHZkXkREi8pmITBeRLcqRiEhzEXk89v4YEelV32M2BBdfbOGnm2+2E+3OO82j6NYt9Wc6dzbP46mn\nrET3TTfVz4apU+1qt1WrzUWjutp2nYPM1VynTIHBg+1K7vLLLawweLB5RYMG2UymCy80b2PwYBvk\nn3zSyk+fdpqJSuBV1NbalWGwlWl8uOitt+x+3brNvYivvrK/WfxMpT590uc0EgeFdKKRavBNJRqb\nNtmAmSynAXUDdnX1lp5GuvBUssQ5ZC8aqcJTq1fb4JPK00j82yTupRGQi6ehaqIR72kEiNjgP2aM\nDbZDh1oF2lS88QYcfLDZFkzw6N/f7jOFqALR2GabcHbnUh49W9EI42mU8pTbnwFvicjbIvIOVhb9\np/U5sIiUA3cCRwK7AmeIyK4Jzc4DlqrqDsCfgHoOpYVn8WK7eho50k74t9+23EWq2keJnHyyue13\n3lm//ZinTrUk4W67bS4aY8bY/R572BVbssFx8WK46y448EC70nr3XfjDH2y9xNy5tthu5Uob7O++\nG157zU7KnXc2sWjVCq65xq4gv/c9Gzj+9CfzvoYNq/OuAt5+u+7vM3ly3eszZtSFpgICTyNZjiJV\neApSexrNm28+DRVSi0YwWCbzCKBugI8vVpiqTTzV1TYgVyTUZ0hVtDCxLHr8MbIRmdat7bsnehrJ\n6k5B3UCajadRXW0DX6KnEc/uu1ue4phj4Ec/gr8kBL4XLoRvf9vCWKp28bLjjvZez572HcJ4Gm3a\nhA8f5VJKpBCeRslOuVXVN4EdsS1XLwF2VtW36nnsQcB0VZ2hqhuAx9hyRtbx2E6BAE8Bh4qEWTqT\nPRs22KD4xhs2GI4aZYuHjj3WTsb+/a1y6vjx6Rc3Pfig9XXllcnLP4ThV7+yq+6bb87t82Ci0bev\nnZAff1xn8+jRloC75x6L9d9/f91nxo+3E7dLF9uruk8fSzjusYe9f+ihJjo/+Ymd5AfEiuMPHWr9\nHnWUbVc6caLFqn/zG0twX3ih5VGOP75uRfBLL9l9ba2JxrHH2vN40fjqq7rkd0CfPnZyJg7qq1bZ\nLVE0Ul1NQ12cP/EXlUo0kuUe4p9XV1t4benSLb2G1q0t+ZkqPJXYZ9BvtuGpoHR7svbJChkmW+CX\nSjTKy+03nY2nEUy3TScaYIL05JP2+7voIrugAfNKd9vNPPBrrjGPIn6Bp4i9H8bTCBuaCuyB7EQj\nm5wGNHJPQ0QuAlqq6ieq+gnQSkR+WM9jdwO+jns+J/Za0jaxPcWXY5V3E+27QETGisjYRemqzaVh\n2TIYMcKuZoYNswHy8stt7+bjj7cT8oYbYO+9bc+F886zH3lQpAxsALz7bssB9OuXkxmAXbGfcYZ5\nG7l8ncWLbbDZZRcTjerqOvd89Gh7bZ99LB9x9911Ce0hQ+Cjj2zry48/NmFIHLR32gluucX+Bomv\nP/us/V0Cr+EXvzCP6957bQC65x77XP/+FuICE4nFi20KZs+edaKxbp15Nck8Ddgyr5Fsui3Yydax\nY2pPI3HghdxFY/FiG2RUt2yTbkpssrUfQb/pZlslfiYQqkRhSlZCJCCZaCQrVhjQsWN2nkYw3TZZ\neCqRykp44gnzcM86y867E0+E7bazBXy//vWWGyaB/Z4mTUp/MZeraIQNT9XW2gBfCE+jvNz+NsVC\n2PDU+ar6v5+Kqi4Fzi+MSdmjqveo6kBVHdg52ZkRgg4d4D//sVDM22+bpzF3riWoH3jAXluwwB4f\ncIDNJjrtNNvuM7gaefNNq7Hz/e/X/zvFexvr1tkV+ymnhEteB0nwwNMAC1HV1pqnsN9+9trFF9tJ\n/ZOfmGD26GEn50031X2uPoiYYFx8sQ0GwZXuUUdZ4boVK+ryGYccYkIbiEawgC9RNFKt1Ui2sC8g\n1VqNZDOKwAbXNWu2PKFTiUZ8TiNVm+C1VCKQrH1V1eYJ9ni727c3zyWx/3g749tD8u+abFV4Kk8j\neK0QnkZAy5bw/PP2W3jxRZsY8uGHFmpNRf/+JpSpVrdD4T2N4H9UiJxGq1bhSpM0FBmr3MYoFxFR\nNS2P5SOaZfhMJuYC28U97x57LVmbOSJSAbSnQOtDmjWzZG46qqoscXfOOZYUffZZOP10E48XXrBY\nbFWV5SXqyy67mLdx++0W8lmyxK44/vMf8wDSJdXjRSMIkU2aZFdsK1bUicZxx9mV/x13wMCBFitO\nNnjVhxYttkxuHnmkCdObb5oY9+plt379LDy4adOWazQCevWy+0RPI1kJkYBUq8IXLrS/cyLxazXi\nr5CTraeAzZPcyUqIBKQqJVJdndwzjReBeM8u2UK9xPbxZPI0gnUswcCUTjSy9TRmzzYhSOZJpaJ9\ne7uoWLDA1jVlIphBNWlSXQ4rkfnz09ctS2YDhBeNbCrcBoT1NIopNAXhPY1XsIV9h4rIodj+Ghn2\nRMvIR8COItJbRJoBpwPPJbR5Djg79vgUYFQgXFFTUWHi8Ne/WiJ45Eh47jmbXhumymUYrr7aTrbh\nw20wnTjRwmEnnJB+wd7UqfaD7NHDBq/u3c3TGD3a3g9Eo6LC1o2MHGkDeL4FIxWDB5uYvfiiJccP\nOcRe79fP8kFffrnlGo2A1q1tBkw2nkYq0UjnaQTvx5Ns5TbU1XTK5GmkCk8lbsAUkM5zSNY+VXhq\n0SIbeJINaF262G8pPgwTiEJi7SnI3tOYNct+h9leKbdpE04wIPMMqnXr7DsV0tPIZi+NgGw8jWIi\nrKdxBXAB8IPY89eB++pzYFXdJCIXA68C5cADqjpZRK4Dxqrqc8D9wD9EZDqwBBOWouLcc20K6+9+\nZyfGhRfmr++ddrKZRvE8/LDFes8/H/7xj+Qn49SplhcJymbvvruJRrCHQjDzBMybOeOM/NkchspK\nyx09/LCd0EOH2uvB1fbkyeZJtGiR/ETv0yd5TqOyMvkVfhCCqa2t+5sE01BT5TQguWhUViYfGIKZ\nTpk8jWD2WsD69WZLqvBUcNx4Ej2g+P6TtQ9yN8l+K/EL/BJnRyWbyJGLpxE2NJUrnTrZ90g1gypY\nOJiNaGQ7e6opeRqhRENVa4G7gbtFZC9VHZ+Pg6vqS8BLCa9dHfd4HXBqPo5VSG64wX5cZWVbXhnn\nm+OOg+uvt1jvu+/CDjvY7fLLTWTAROPAuJ3b+/e3dSLr19vCwag2wYnnqKPgX/+yx4Gn0bev3U+e\nbJ5E797JB7revbfcjS9Yo5GsfdeuluxftKhunn66OH860ejUKfkxgnxFppxGsJo76COV9xLfR+K0\n28WLLZyYqn0y0Uj2PWFz0QhCdcuW2aCZbJp4Lp7GgAHh2+dKkAxPRrYL+8CiBc2bF1Y0StXTyGX4\nqJeH0RgpK7N1DUGp5kLzy1/asYYMsSuRhx+2tR21teYmz55dNwCDeRobN9qK6yA0FTUjRtj99ttb\nrgXsJOrdu040Uglwnz7mgcWv1k22RiMg2VqNdHH+TKKRjHjRENl8x7uArbYy4Y6/ukyVJ4l/LV4E\nVFPnNFq2NO8smWeSan5IslXhyUqIBHTsaANdmJXSa9fa37nQngaYaEyZkryOVS6iAdnVn8rV01i/\nPn3trTVris/TyEU0iiiP3zQRsbns//iHzSz5y1+sls9TT9kUYdhSNAKKRTS6djWvaWTC/o/BDKpk\nazQCeve2Ey0+dJeshEj8sSC5aCS7Am/XzsJQuYjGkiU2sCa7Sg+7n3i69itW2ICdSgSSJdvDehoB\n6UQjm0q3c+bYfZjptvVlt90s1Dk+SQykPqJR6JwGpA9RrV3bODyNa/NuhVMvvv1tO2l++cu61d/x\norHzznXzvAcNanj7UvHsszb3Pp5+/eyKccWK9J4GbJ7XSFZCJCCZaKRaIAcmysnWaqSaGgt1OY1k\nJUQCktWfSrXmAuoS7PHhqXR2B8cI65mACWTLlpv/bTJ5GkGbTMSXRC80I0bYdzz99C0rKQSikUo4\nU5GNaOTqaUB60ShZT0NEykRkTxE5GlghIln++Z1CUl5uifjp063UdHm55TkCKittnvvOOyefEVNM\n9OtnYTZILRqBBxLMoNqwwQbWVJ5GkOuIX6uRztOA5KKRahEe2GC9fLn1m0pYktWfSudpBK/Ht09V\nQiT+GPHtV62yK/BU31NkywV+YTyNMHmNYI1GQ3ga225r6zvmzTMPNn4gnj/f/l7ZLpArtGiE2VOj\n5DwNEdleRO4BpgO/A84Afgi8ISKjReQcESmCtKpz1FG2En3WLBOMxIVft91mq7+Lnfj1CqnCU927\n23ThwNMIBCCVaFRW2qCZ6Gm0apX6JE8UjWT7eMcTvP7FF5k9jXyIRtjwVLqEf0A2opHNnhqzZpko\npVtTlE/23RceecQWwI4cWZcryHZhX0A2u/cV0tMoKdEAfgP8E9heVY9Q1ZGqeoqq7g4chy22O6vQ\nRjqZEamrjBsfmgoYMqRuamsxs8sudTOLUolGebldvQaeRqoSIvEkrtVIVUIkIFE0Vq60RYfpwlNg\neZZMwpIYnmrTJvXanqqqzUUjCFWFDU+lS/gHJK4Kz1dOY/ZsE6TEC5hCcsIJVhzzmWdshiHkLhq5\n5DQK4WkUW3gq7ZRbVU05g19VFwK35t0iJ2f239/qQu25Z9SW5E6rVhaWWr58y+qz8cSXSE+3sC8g\nUTRSLewLSBSNMB5BssfxpApPpVtU2alTXSn7wO7AvlTt46f1hvU0Xn3VHqfaSyMgW0+jIUJTiVx6\nqU2muPFG29hs/vzNp6CHJdvZU5WV2QlkY/U0ABCR62NlPILn7UTkb4Uzy8mVn/ykNDyKdAwdaqGG\ndPTubQnzQw+tW5yYWEQxnlw8jRUrbEokZCcaqcJTzZvb1WWi55CuxEay8FSq1d3BsTdtMs8Iwnka\nvXvbdx0/3u5V8+dpNEQSPBl33GEzBb/7Xctl5epprFxZl2NLR7Zl0SGzp1Fba7+/YvM0wuYjKoAx\nIrK7iByGlQAZVziznKbMPfdYSZZ07Lefue5Ll9qeHS++mNnTWLiwbn1BGE8D6sJB+fA0gvfiw1OZ\nPI2qKrvyj7c7k8jE25vJMwEbWKuqbMvddBVuwQawZs0yexq33GLlYBpiYV8ymje3xaNt29rfLlfR\nUK0T4HTkIhqZPI1i3EsDwq8Iv0pE3gDGAEuBg1V1ekEtc5osYVasn3OOlc9O3LgoFV272gCwYIEl\nZsN4GmCDbrdu6afGJr6eytOALT2HxYs3n+mWrD2Y0GyzTfrps/Htq6vNg1i40AazdANPhw426+6i\ni+r2O0klGiL2XjpP46abbD+ZU0+1SgVR0bWrCceIEblVbY6vP5VssWY82e6lAZk9jWLcSwNCioaI\nHAzcDlwH9AfuEJHzVDVJGTjHaRjCCgbUzeB5/HH73Pr14TyN4Eo9k6fRqpWtxl63Lr3nkDglNkxO\nI2i3zTYmMulEI7FoYSaPKuCCC6zKwI032vN0U7M7dkzuaahaSZ3/+z9bL/GPf2T3PyoEgwebrWF3\nzownm/pT7mlsyc3Aqao6BUBETsK2fE1SWNpxio9gJlZw5duqlW1ElYpkoiGSfjDt1Mni55k8jWCl\n9MaNNiBlCk8Fxw/s2Xnn9P0H7VessAR3mAWdFRW2U+VRR9nzVJ4GJC9auHatFev8xz9suuvf/ha9\nYATkIhiQXaXbQuQ0itXTCJvT2D8QDABVfRo4oDAmOU7+2XVXK/A4ZozNtlq50qYhpyKZaHTokH4A\nCgbsTJ5D/F7iEC5HMXeuTSOdNy98eOoPfzD7r7kmdft4RoyAww+3x+lEI7Fo4cyZtjHZP/8J111n\nIa5iEYz6kM3ufbmIRiAGjcrTEJGRwCOqukVJLVWtFpHtgS6q+n6hDHScfHHQQeHbBvWj4kUj034j\nweCfztPYaisTi9razCGv+PfOPNPCP1tvbZtYpbMbrEz43/9uYaJ0HlU8IjYJ4e9/Tz9VtmNHqz4A\n9h0GDbJV+c8/D0cfHe5YpUA2nsaqVdlPLy4rM+HI5GmUlGhg+3FPEJFx2GypRUALYAdgCLAYuLKg\nFjpOBJSV2RX9Aw9YnmLKlMyi0amTXWEn24civk1trfUb1AlL52l06WIewNZbW42xYcPSX8VXVtrx\n77vPvsNvf5ve5kR69qxbFJeKeE/jnntMWMeOhb33zu5YxU6hw1OQfk+NwNMotvBUpsV9t4nIn4Fh\nWDhqd2AtMBU4S1Vn53JQEdkKeBzoBcwETovtO57YrgYIquTPVtXjcjme4+TCXXfZzox33GFX0scf\nn7799tun3gMkICgDf/75dr/ttslX8AdUVsLLL2dnd6dOFlL50Y9Sr6qvD0FOY8MGS54fdljjEwxo\nGNFIt6dGqXoaxEJTr8du+eJK4E1V/Z2IXBl7fkWSdmtVdY88HtdxQnPiiXZbuRJGjbK8SDquvtoW\nV6bjhBNsA6mOHW1GV7pV77nSqZN5Ar/6Vf77BvM0amrgwQdtweS99xbmOFHTsqWFKKPyNIo1EZ4p\npxHsordKVW/J43GPB4bGHj8EvE1y0XCcyGnbNrOXAXZyZzrBKyqs3EshufFG83bS5VbqQ5A3ueEG\n2y0y2FCrsRFsppVJNGpqLISZ7ToNSO9pFGsiPNPsqfOBWdge3vlkG1UNSqTNB7ZJ0a6FiIyNVdQ9\nIVVnInJBrN3YRYn1rB2niTF8uJVXKRTBzKrZs63OUzFsH1wowtSfyqXCbUCj8zSAlVhY6mURuY+E\nXftUdUnSTwGxFeTJFu//MqEPFRFN0U1PVZ0rIn2AUSIySVW/TGykqvcA9wAMHDgwVV+O4+SBwNPo\n0AG+851obSk07dtvuRNiIvURjcRaZPEUq6eRSTTuBt4E+mCzp+JFQ2OvJ0VVh6d6T0QWiEgXVZ0n\nIl2Ahcnaqerc2P0MEXkb2BPYQjQcx2k4AtE4//zcQjKlRP/+tmDxZz+zcFyyKrb19TTity2Op1g9\njbSOparerqp9gQdUtY+q9o67pRSMEDwHnB17fDbwbGIDEekoIs1jj6uw2VtTEts5jtOwDBgAv/+9\n1Zdq7Pz1r/CDH8DNN1t59S+TXLLmsj94QKacRmVl8S2UDBWNVNUf5Pm4vwMOE5EvgOGx54jIwFgY\nDKAvMFZEPgbeAn4XvyrdcZxoKC+3K+9CJdqLiZYtber1U0/B559b4cNbbrHy8wGFzGkUW2gKwpcR\nySuqWq2qh6rqjqo6PMiNqOpYVf1e7PEHqtpfVQfE7u+PwlbHcZyTT7bFmIccYiXk990XJkyw9+qb\n00jnaRRbaAoiEg3HcZxSo0cPK5XyxBO2PuWQQ2xXwHx4Gppk+o57Go7jOCWOiO0T8s475glcfnlu\n+4WDe44AAAVoSURBVIMHtG5tgrFu3ZbvrVlTnJ5GkaVYHMdxip+ddoIrroDrr6/bVTGXRHj8nhqJ\nArF2rXsajuM4jYarrrLaXk88Yc9z9TQgeV6jWD0NFw3HcZwcaNnSCjYG5JrTgOQzqNzTcBzHaWQc\ndRScdJIVicxlh8BS9DQ8p+E4jlMPHn7YdlbMBfc0HMdxmhgtWtheKrmQydNw0XAcx3H+RyAap55q\nJfhbtYLvf9/2QynWxX0ennIcx4mIXXeFn//c1no0b24Vde+9F/79b9v8qxg9DRcNx3GciKiogJtu\n2vy1Sy+FCy+EBQvqtpwtJlw0HMdxiog994QPP4RXXoHBg6O2ZktcNBzHcYqM8nI4+uiorUiOJ8Id\nx3Gc0LhoOI7jOKERTVaTt4QRkUXArHp0UQUszpM5UVDq9kPpfwe3P3pK/TtEYX9PVe2cqVGjE436\nIiJjVXVg1HbkSqnbD6X/Hdz+6Cn171DM9nt4ynEcxwmNi4bjOI4TGheNLbknagPqSanbD6X/Hdz+\n6Cn171C09ntOw3EcxwmNexqO4zhOaFw0YojICBH5TESmi8iVUduTLSLygIgsFJFPo7YlF0RkOxF5\nS0SmiMhkEbk0apuyRURaiMh/ReTj2He4NmqbckFEykVkgoi8ELUt2SIiM0VkkohMFJGxUduTCyLS\nQUSeEpFpIjJVRPaP2qZ4PDyFnSTA58BhwBzgI+AMVZ0SqWFZICIHA6uAv6vqblHbky0i0gXooqrj\nRaQtMA44ocT+BwK0VtVVIlIJvA9cqqqjIzYtK0TkMmAg0E5Vj4nanmwQkZnAQFUt2TUaIvIQ8J6q\n3icizYBWqrosarsC3NMwBgHTVXWGqm4AHgOOj9imrFDVd4ElUduRK6o6T1XHxx6vBKYC3aK1KjvU\nWBV7Whm7ldRVmYh0B44G7ovalqaIiLQHDgbuB1DVDcUkGOCiEdAN+Dru+RxKbMBqTIhIL2BPYEy0\nlmRPLLQzEVgIvK6qpfYdbgV+DtRGbUiOKPCaiIwTkQuiNiYHegOLgL/FQoT3iUjrqI2Kx0XDKSpE\npA3wL+DHqroianuyRVVrVHUPoDswSERKJlQoIscAC1V1XNS21IMDVXUv4EjgoljYtpSoAPYC/qKq\newKrgaLKsbpoGHOB7eKed4+95jQgsTzAv4CHVfXpqO2pD7GQwlvAiKhtyYIDgONieYHHgGEi8s9o\nTcoOVZ0bu18IPIOFnkuJOcCcOA/1KUxEigYXDeMjYEcR6R1LPJ0OPBexTU2KWBL5fmCqqt4StT25\nICKdRaRD7HFLbGLFtGitCo+qXqWq3VW1F3YOjFLVkRGbFRoRaR2bREEspHM4UFKzCVV1PvC1iOwc\ne+lQoKgmg/gmTICqbhKRi4FXgXLgAVWdHLFZWSEijwJDgSoRmQNco6r3R2tVVhwAnAVMiuUEAH6h\nqi9FaFO2dAEeis3GKwOeUNWSm7ZawmwDPGPXH1QAj6jqK9GalBOXAA/HLmBnAOdEbM9m+JRbx3Ec\nJzQennIcx3FC46LhOI7jhMZFw3EcxwmNi4bjOI4TGhcNx3EcJzQuGo7jOE5oXDQcx3Gc0LhoOE6B\nEZF9ROST2H4brWN7bZRMTSrHiccX9zlOAyAivwFaAC2x2kI3RmyS4+SEi4bjNACxkhAfAeuAwapa\nE7FJjpMTHp5ynIahE9AGaIt5HI5Tkrin4TgNgIg8h5Ub741ta3txxCY5Tk54lVvHKTAi8h1go6o+\nEquA+4GIDFPVUVHb5jjZ4p6G4ziOExrPaTiO4zihcdFwHMdxQuOi4TiO44TGRcNxHMcJjYuG4ziO\nExoXDcdxHCc0LhqO4zhOaFw0HMdxnND8Pyb6KT3dwjRiAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1068957f0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.6488589995e-15\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nC4LjOI4DuCA4juM4EVwQHMdxHAD+P0rCKp3ShlkGAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1066da518>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 2.53276755801e-13\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaYAAAEKCAYAAABZr/GWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWvHE5JxzLq14YnLOOZdWPDE555xLK/8P8ZVjLfio6U0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106625240>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 1.13521655133e-07\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZoAAAEKCAYAAAArYJMgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnXeYlOXV/z9nF5CyKLL0uoDYUBRcib2DoMZubNhiooma\n17xqLK/+LLFEE6PGrlFjjV0RC9iwYBQEVFREFCkCgkvvsLB7fn+cebLDMH139pnZPZ/rmmt2nrnn\nmTO7O/f3OeU+t6gqjuM4jpMrisI2wHEcx2nYuNA4juM4OcWFxnEcx8kpLjSO4zhOTnGhcRzHcXKK\nC43jOI6TU1xoHMdxnJziQuM4juPklCZhvKmICHACoMALwEHAUcC3wP2qWh2GXY7jOE7dI2F0BhCR\ne4EOQDNgBbAFMBI4HPhZVS+sT3vatWunZWVl9fmWjuM4Bc+kSZMWqWr7VONC8WiAfVV1ZxFpCiwA\nOqtqpYg8DXxW25OLyCPAEUCFqu6UanxZWRkTJ06s7ds6juM0KkRkdjrjwsrRbARQ1Q3ABFWtjDze\nCNRF2OxRYGgdnMdxHMepJWF5NAtEpERVV6nqfwVBRDoBlbU9uap+KCJltT1PSpZ/A2t/gqIt7Nak\nFTRvD81Koag452/vOI5TCIQiNKo6LMFTK7GQV84RkXOAcwB69OiR3Um+uxu+vy/e2WGLdtCqDErK\noKQ3bLUTtOkPW24Pxc2yNdtxHGdzVGHldFj1AxS3gCYt7djqWbBqBqyeDesrYN1CqFwCVeuguhKq\n18Pez0DHA3NqXlgeTVxUdbWIdAcq6uG9HgQeBCgvL8+uImKHP0HPk+2PVbUeNq6yP+T6hbB2vv1x\nl34Bc0dA9QZ7TVEzaFsO7feBDvtBxwPME3Icx8mEVbNg/ihY8C4s/AjW/Zx47Bal0LyjXQC33tbE\nqDgSidkiZS6/1uSV0ER4C8jSxahnSnrZLRXVG2DFd7DsK1j6mf1TTLsdpv4ViptDpyHQ7WjodhRs\n0Tb3djuOU5hUrYNpd8HMRy10D9CyB3QabBevW/UzT2XjakBtfmrVC5qWhGl1aOto7kz0FNCmPm2p\nF4qaQpt+dis7yY5tXAOLPoa5I83jmTcSPm0CnYdAz5NMeJq2Dtdux3HyA1X48Tn44jKLlHTYHwbe\nBl0OMw9FJGwLkxLWOpqVwMXA+jhP/11V29Xy/E8DBwDtgJ+Ba1T14UTjy8vLNdTyZlXzdGY/a7c1\nP5pr2+1o6HWaXa0U5aPz6ThOTlm/GGY9BT88DMu+hDa7wMC/Q6eDw7YMABGZpKrlKceFJDRjgKtU\n9eM4z81U1TTiUXVH6EITjSos+gRmPgE/PguVS6FVT9j2D9DnbGjW8Bw+x3GiUIVF4+C7u2DOixYK\na7sbbHsBlJ2WVxWt+S40bYF1qrqm3t88DnklNNFUrYd5r9k/XMUHVjTQ5zew/cXQqnvY1jmOU5dU\nb7CIxrR/wJKJ0HQr6HW6XWBuvUvY1sUlr4UmHiIyUFVr3RUgG/JWaKJZ8jlMuwNm/dvisWWnQb8r\noPU2YVvmOE5t2LgWZjwCU/9m+Zctt4ft/se+4yEn8VNRiELzmaoODOO9C0JoAlbPhqm3wg8PQfVG\n83B2vhpadA7bMsdx0qV6I1S8bx7MnJdsbUu7veziscvheZ/cD0hXaPIpw1wYv9mwadUTyu+CflfC\n19fD9Adh5mMWTut3ua/JcZx8Rqst/zr5Slg7D5qU2LKGPr+1dXUFIjCZkk/70VwXtgEFRYtOsPs9\ncMRU6HokTLkBXt0OZj5lyUTHcfKLRePgzT1g3JnQshvs8wIcWwF7PQkd92+wIgMhC40Yw0XkalUd\nISI9RGRQmDYVHK23gX2egcEfmfh8Mhze3geWTg7bMsdxANYvgfG/gbf2NC9mz8dhyMfQ4zho0iJs\n6+qFsD2ae4E9gZMjj1cC94RnTgHTfm849FP4xSOw8nsYvRtM+l/YsCJsyxyncaIKMx6H17aDGY9a\ny6ojptnaOAl76q1fwv60v1DV84F1AKq6FNsMzckGKYI+Z8ER31rMd9o/4LUdYM7LYVvmOI2LFdNg\nzMEw7gwo2QaGfgYD/pr3VWS5Imyh2SAixdiWzohIe+pmP5rGzRZtYdB9MGScNcwbeyx8eCys+Sls\nyxynYVO9Ab68Ft7ob0sSdr8fhvwHtu4ftmWhErbQ3Am8DHQQkRuBj4CbwjWpAdFuEAydALv8xbq8\nvr4j/PAvLxZwnFywfgm8NxS+vg66H2+Rhb7nNrowWTxCX0cjItsDB2Plze+q6tT6tqGg1tFky4rv\nYfzZsHCsNeIb9CC07Bq2VY7TMFjxHXxwhK1zG/RP6H162BbVCwWzjkZVvwW+DR4HO2+GaFLDZMu+\ncMj71mJ88hXw+k6w+3013aQdx8mOua/AuLNAiuGgd6HDPmFblHfko0/3TdgGNFikCLa/EIZNtjYX\nH58MH58GlcvDtsxxCo/KZfDJGfDh0baQ+tDxLjIJCGs/mosSPQU0zrKM+mTLvjB4LEy50boLLBwL\nez0N7fcM2zLHKQx+fg8+Od120t3p/0G/q3yL9iSE5dHcBGwNtI65lYRoU+OiqAnsfI0t9ETgnf3g\nm79ZiwzHceJTXQVfXgPvHgzFLWHwx9D/zy4yKQgrR/MZMEJVJ8U+ISK/CcGexku7PWDY5zD+t/DF\npXaltufj0LxWe885TsNjzU/w8Sm2ZUevM6D87ka7LiZTwvIezgJmJ3guZQWDU8c0awP7PAe73ws/\nvwujB8DCzfakc5zGy/y3YNSutk/MHo/Bno+6yGRAKEKjqtNUdVGC536ub3scrKFf39/DkE+gqBm8\nsz9M/buvuXEaN9VV8OXVtj6meQc4dGKjKV2uSzwf4mxK24HWLqPrL+HzS+CjE2DDyrCtcpz6Z9VM\nePdAK5jpfab1Etxq+7CtKkhcaJzNabYV7PsiDLgV5o6AN38By79N/TrHaQioWgeNN/rDssmWs9zj\nEWjSMmzLChYXGic+IrDDxXDQ27B+Ebw5yJtzOg2fjavhPyfD+F9D293gsC+t27JTK0IXGhEZHn3v\n5BkdD4Shk2CrHaw55xdXWNzacRoaq2fbXk4/Pge73AQHj7GFmE6tCV1ogIti7p18o1V3OORD2OZc\n+OZmeH8YrF8ctlWOU3f8/AGMLre8zAGvQ78rvBlmHZJPv8mGu49pQ6B4Cxh0P/ziIaj40EJpy71b\nkNMA+P4+GHMIbFFqbWS6DAvbogZHPgmNUwj0Oduac25cbVvT/jQqbIscJzuqKuHT38GE86DzEBgy\nHrbcLmyrGiQuNE7mtNvDSj1Leltr9G9v9/U2TmGxfgm8NximPwA7XgH7jbRqSycnuNA42dGqh/VJ\n63Y0fHYRfPpbu0J0nHxn1Qx4ey9YNA72egp2vQmKisO2qkGTD0LzXeR+WqhWOJnTpBXs8zz0uxJ+\neNiuENfFbfjgOPnB4gkW8l1XAQe9A2WnhG1RoyB0oVHVk6LvnQJDimCXG+zKcNF4KxJYNiVsqxxn\nc358wVorFbeyVksd9g3bokZD6ELjNBDKTrES6Kq1dsU47/WwLXIcQxW+vtHaKW09AA4d50n/esaF\nxqk72g2CoROgdV/44Jcw9TYvEnDCpWq9bVD25VVQNhwOfteaYzr1iguNU7e07AaDP4Tux8HnF8OE\n30H1hrCtchoj6yrg3YNg1pPQ/3rrWVbcPGyrGiWhC42IFItIFxHpEdzq4JxDRWSaiEwXkcvrwk4n\nA5q0gn2ehX7/B9MfhPeGQeXSsK1yGhPLplgz2KWf2V5LO11l/fucUAhrh00AROQPwDXAz0Cwh7AC\n/WtxzmLgHmAwMBeYICIjVdWXsdcnUgS73Aitt7XS57f2hP1fh9Z9wrbMaej8NAr+c5JttXzIh1C6\ne9gWNXrC9mguBLZT1X6qunPklrXIRBgETFfVGapaCTwDHFVrS53s6H2GlZGuWwhv/QIqxoZtkdNQ\nUbW84AdHQEkfW1TsIpMXhC00c4DldXzOrpHzBsyNHHPCosN+1kOqWSmMORhmPB62RU5Do6oSxp9t\necFux8DgsdYM1skLQgmdiUjQqXkG8L6IvA6sD55X1dvqwYZzgHMAevSodVrISUXrbaysdOzxMO4M\nWDnNErTeIdepLZXLYOxx8PMY2Olq2Pka/7/KM8L6a7SO3H4E3gaaRR1rXctzzwOiL2W6RY5tgqo+\nqKrlqlrevn37Wr6lkxbNtoYDR0Of38KUm+CjE2HjmrCtcgqZ1T/aHjILx1pVWf/rXGTykFA8GlW9\nLoennwD0FZFemMCcBHifiXyhqCkMesAWzH3+J9tsav9XoEXnsC1zCo3FE+HDI+1i5YDR0OmgsC1y\nEtDgpF9VNwIXAG8CU4HnVNV7ouQTwTbR+70My6dY25qlk8O2yikkfnwR3tkPippZc1cXmbymwQkN\ngKq+oarbqmofVb0xbHucBHQ7yiYJVXh7b5j7atgWOfmOKkz5C3x0PGy9q1WWtdkpbKucFDRIoXEK\niLYDbLLYcnv48CiYequ3rXHiU7UOPjkNJv8f9DwFDh7j7WQKhLAXbLYHfguURduiqr8OyyYnBFp2\nsYV1n5xheZvlU2D3+237aMcBWDsfPjwGFo+H/jdY1wlf6V8whCo0wCvAWOAdoCpkW5wwadLS2tZ8\ndR18/WdYOR32fQmae0Vgo2fJ55b0r1xq/xPdjwnbIidDwhaalqp6Wcg2OPmCFFl56lY7wrgz4c3d\nYf9Xoc3OYVvmhMWcEfDxqbBFKQz+D2y9S9gWOVkQdo7mNRE5LGQbnHyj54kWSquuhLf2grkjw7bI\nqW9U4ZtbYOyxdqFx6KcuMgVMKEIjIitFZAXW6+w1EVkrIiuijjuNndLd4dAJtt7mw6Ph6xtAq1O/\nzil8KpdbU8wvLreLjoPfgxadwrbKqQVhLdis7ep/pzHQsqt5Np+eA1/+P1j6OezxKDT1f58Gy+IJ\nJjKrZ8OuN8MOl3rSvwEQauhMRN5N55jTiGnSEvZ8Agb8HeaOsO0GVk4P2yqnrlGFaXfZeqrqjXDI\nWNjxMheZBkJYobPmIlIKtBORrUWkbeRWhndadmIRgR0uggPfsjLX0bvDT6PDtsqpKzauho+Hw6T/\ngc7D4LAvoP2eYVvl1CFheTTnAhOB7YHPgEmR2yvA3SHZ5OQ7nQ6GoROhVU94/zCYcrMv7ix0Vk43\nL3X207ZR3n4vW/NVp0ERVo7mH8A/ROQPqnpXGDY4BUpJLxjyse09MvkK26r3F49A05KwLXMyZc7L\nVsYuTeCAUdDl0LAtcnJEWPvRHKSqY4B5InJs7POq+lIIZjmFQpOWsNe/YeuBMPlyWD4V9hvh20QX\nCtUbrI3M1Fuh7e6w7/PmpToNlrAWbO4PjAF+Gec5BVxonOSIwI5/ssaK/znRFncO+if0OC5sy5xk\nrP4RPj4FFv4H+p4HA2/zVkONAFGPcVNeXq4TJ04M2wwnW1bNgI9+BUsmQdmpUH6Xx/nzkbkjLVRW\nvQEGPQhlJ4dtkVNLRGSSqpanGhd2efMPIvKUiPxORPqFaYtTwJT0hiGfwM7Xwuxn4fWdYcE7YVvl\nBFRXweeXWnfuVr1g2OcuMo2MsFvQ7Ag8AJQCf4sIz8sh2+QUIkVNba/4Q8dB0y1hzGD47BKoWh+2\nZY2bDSuts8PUv1mobMjH0HqbsK1y6pmwhaYK2BC5rwYqIjfHyY62u1kJdN/z4Nu/w1t7wIppYVvV\nOFn9I7y9D8wfBeX3wO73eD6mkRK20KwA7gBmAmeo6p6qem7INjmFTpOWNqnt/yqsmQujy2HW02Fb\n1bj48XkYtSusngUHvAHbnhe2RU6IhC00JwMfAucBz4jIdSJycMg2OQ2FrkfAsC+sMu3jU+DT39su\njU7uqFwGH59mxRkl21hj1M5DwrbKCZlQhUZVX1HVP2GdAt4AzgReC9Mmp4HRsqtt+bvDpTD9fhi9\nmzVudOqeOSPg9Z1slf/O18KQ/8CW24ZtlZMHhF119qKITAf+AbQETge8LtWpW4qawoBb4IDR1oL+\nrT1h8pVeKFBXrJlr2yyPPcY2KBvyiRVmFDUN2zInTwh7h82/AJ+rqm/j7OSeLofC4V/DZxfBlJss\nb9P/eiu1lbCjyAVIdRV8f4+JtlbBrrfA9v/rAuNsRtihs4kuMk690qwN7PGIdYJuthV8MhxGDYT5\nb4dtWWGxZJJV9E26ENrvbQK+46UuMk5c/DLOaZx0HgxDJ1nPtI0r4b0hMPY423DLScyyr2HsCVbJ\nt2YO7P2MNcQs6R22ZU4e40LjNF6kyMJmh38Du9xke9y8tj18fSNUVYZtXX6x4nv4z8nwRn+Y/yb0\nuwqO+Na2WvbNyZwUhJqjEZEiYBegC7AW+FpVfcGmU78UbwH9roCy4Za/+fIqmP0M/OKf0G6PsK0L\nl7Xz4avr4IeHoLg57Hg57HCxJf0dJ03C2iagD3AZcAjwPbAQaA5sKyJrsLY0j6lqdRj2OY2UVt2t\nZf3cV2HiefDWXrDNubDTVVYm3ZioWm+dFb6+EaorYZvfwU7/D1p0DNsypwAJpXuziDwN3AeM1RgD\nRKQDcAqwVFUfqw97vHuzsxkbVsDkq+D7+0CKTXB2vAxadgnbstyiCj+NsiT/qunQ7RgY8FfvT+bE\nJd3uzb5NAC40ThJWzYSvb4CZkWueToNtK4JuRzesXT2rq2Duy/DNX2HJBNhyO9jtTl/V7ySlULYJ\nuF5EmkQ93lJE/hWmTY6zCSW9YI+H4ZffWXeB5d/AJ6fBy52tpc3SyWFbmD2qsPQL+PJqeG07+OgE\nqFwKu98Hw750kXHqjLAXbDYBxovIWUBH4G7grnBNcpw4lPSGXW+CXW6w3SFnPAIzH7W2Nu32gh3+\nBN2OLIyFn8umwKyn4MdnbdM4KYL2+8KuN1uorKg4bAudBkboobNIE83XgKXAfqo6vb5t8NCZkxXr\nl1hIbdpdsHombLk97HAJdD/OFobmExtWwawnYPqD5sVIMXQ6BLofbwLZvEPYFjoFSEHkaERkP6wo\n4ElgZ6zP2dmq+lOW5zsBuBbYARikqmmphwuNUyuqN1pb/G9ugWWTbXV8x4NtAm/TH1pvC1u0q//1\nJtVVsPRza3L5w8OwYTlsPRB6nwE9TvQKMqfWpCs0YYfObgVOUNVvAETkWGAMsH2W5/saOBYrj3ac\n+qGoiS387HkSLBpnSfU5L8GEqD1Ymm1tm7KV/sLW5rTf11rg1AVV62Hld1a4sHY+rFtgK/h/HgOV\nS0CaQI/jYdv/sff2BZZOPRO20OwZ3etMVV8SkQ+yPZmqTgUQ/yI5YSAC7fe02663WDhtxTRY8R2s\n+AYWfwrf3GwNKKXYJv1Og6FZKVANWm2btjVpbdtRt+gELXva4kgRe37jaitIWPQxLPzYwmCrZ9hz\n0bTsAd2OsvBYp0M8NOaESlgLNocD/47XUFNVF0cWdHZW1Y/q3zrHqQNErICgpDd0GVZzfOMaE5wF\n71grl6+uA1KEr4tbmFeycdWmY1uVQdty86a23MHWurToDM07enNLJ68Iy6MpBT4XkUnAJGo6A2wD\n7A8sAi6P90IReQfoFOepK1X1lXQNEJFzgHMAevTokZHxjpM1TVpCxwPstssNsGGlhb6kyMRp41pb\nLLphBaz9Cdb8aI0+tRqatjZvp6SXVbo19MWjToMhtGIAESkGDgL2Bjpjvc6mAqNU9cdanvt94BIv\nBnAcx8kdeV8MEAmbvR25OY7jOA2UsHI012DB5lWqelsdnvcYbMFne+B1EflCVQ+tq/M7juM4mRNW\nU80zIj+uUdXn692AGERkIZDtjlftsJxSIVPon8HtD59C/wyFbj+E8xl6qmr7VIPCCp0doqqniciF\nIb3/JqTzi0qEiExMJ0aZzxT6Z3D7w6fQP0Oh2w/5/RnCasy0m4h0AX4tIluLSNvoW0g2OY7jODkg\nLI/mfuBdoDdW3hy9wlIjxx3HcZwGQCgejareqao7AI+oam9V7RV1KzSReTBsA+qAQv8Mbn/4FPpn\nKHT7IY8/Q+jdmx3HcZyGTQFsnuE4juMUMi40tUBEhorINBGZLiJxW+bkMyLyiIhUiMjXYduSDSLS\nXUTeE5FvRGRKvlQxpouINBeRT0VkcsT+68K2KRtEpFhEPheR18K2JRtEZJaIfCUiX4hIwbUIEZE2\nIvKCiHwrIlNFZM+wbYrFQ2dZEmmh8x0wGJgLTABODrY8KAQi+wGtAh5X1Z3CtidTRKQz1nz1MxFp\njRWWHF0ofwOxNuOtVHWViDQFPgIuVNVxIZuWESJyEVAObKmqR4RtT6aIyCygXFULch2NiDwGjFXV\nh0SkGdBSVZeFbVc07tFkzyBguqrOUNVK4BngqJBtyghV/RBYErYd2aKq81X1s8jPK7FeeV3DtSp9\n1FgVedg0ciuoKz8R6QYcDjwUti2NERHZCtgPeBhAVSvzTWTAhaY2dAXmRD2eSwFNcg0NESkDBgDj\nw7UkMyJhpy+ACuBtVS0o+4E7gEuB6lQD8xgF3hKRSZGu7oVEL6z7/b8i4cuHRKRV2EbF4kLjFDwi\nUgK8CPxRVVeEbU8mqGqVqu4KdAMGiUjBhDBF5AigQlUnhW1LLdlHVQcCw4DzIyHlQqEJMBC4T1UH\nAKtJsMVKmLjQZM88oHvU426RY049EsltvAg8paovhW1PtkTCHe8BQ8O2JQP2Bo6M5DieAQ4SkSfD\nNSlzVHVe5L4CeBkLixcKc4G5UZ7wC5jw5BUuNNkzAegrIr0iCbiTgJEh29SoiCTTHwam1mUX8PpC\nRNqLSJvIzy2wwpJvw7UqfVT1ClXtpqpl2P//GFUdHrJZGSEirSKFJERCTkOAgqnCVNUFwBwR2S5y\n6GAg74phQtuPptBR1Y0icgHwJlCMdTmYErJZGSEiTwMHAO1EZC5wjao+HK5VGbE3cBrwVSTPAfB/\nqvpGiDZlQmfgsUgFYxHwnKoWZIlwAdMReNmuWWiCbTE/OlyTMuYPwFORC94ZwFkh27MZXt7sOI7j\n5BQPnTmO4zg5xYXGcRzHySkuNI7jOE5OcaFxHMdxcooLjeM4jpNTXGgcx3GcnOJC4ziO4+QUFxrH\ncRwnp7jQOI7jODnFhcZxHMfJKS40juM4Tk5xoXEcx3FyiguN4ziOk1NcaBzHcZyc4kLjOI7j5BQX\nGsdxHCenuNA4juM4OcWFxnEcx8kpLjSO4zhOTnGhcRzHcXJKk7ANyAfatWunZWVlYZvhOI5TUEya\nNGmRqrZPNc6FBigrK2PixIlhm+E4jlNQiMjsdMZ56MxxHMfJKS40juM4BcT06fDUUzB1KlRVhW1N\nenjozHEcp4C46ip49ln7uaQEBg2CwYNhyBDYdVcoykP3IQ9NchzHcRKxfDlsvz08+iiceSYsXgxX\nXAG77QYDBoRtXXxcaBzHcQqINWugY0c44wy46y744guYPx+GD4cvv4SNG8O2cHNcaBzHcQqINWug\nZctNj3XqBLvsYj+vXVv/NqXChcZxHKeAiCc0AC1a2L0LjeM4jlMrEglNcGzNmvq1Jx1caBzHceqR\npUvh8MPhgw+ye70LjeM4jpOQ6mpL2r/xBnz4YXbncKFxHMdp5KxYkfi5G24wkQFYtSrzc6umztG4\n0DiO4zRgJk+GrbeG99/f/LlRo+Daa+G006C0NDuhqaw0ryiZR+PFAI7jOA2YWbNMCG69ddPjFRVw\n6qnQvz/cfz+0bp2d0ATeiofOHMdxGilB2Oz11+H772uO33STPffMMyYIJSWwcmXm5w9EpFWrzZ9z\noXEcx2kEBOIhYqv2AWbPhvvug7POstYxYELjHo3jOI6TMYHQHHcc/Otf1pfsuutMeK65pmZcLoTG\niwESICJDRWSaiEwXkcvjPL+FiDwbeX68iJRFPXdF5Pg0ETk06vgsEflKRL4QEd/NzHGcemPlSuue\nfPnlJiSXXQaPPQbnnw/dutWMy6VHk4/FAKFtEyAixcA9wGBgLjBBREaq6jdRw84GlqrqNiJyEnAL\ncKKI7AicBPQDugDviMi2qhrsznCgqi6qtw/jOI6D5WG23NI6Ke+zDzzwgInK5TGX0bkoBmjefNMx\n+USYHs0gYLqqzlDVSuAZ4KiYMUcBj0V+fgE4WEQkcvwZVV2vqjOB6ZHzOY7jhMbKlSYiABdeaPcX\nXwzt2286LhcejYgdz0ehScujEZEiYBfMe1gLfK2qFbV8767AnKjHc4FfJBqjqhtFZDlQGjk+Lua1\nXSM/K/CWiCjwgKo+GO/NReQc4ByAHj161O6TOI7jsKnQHHssvPQSHHbY5uNyITTB8YITGhHpA1wG\nHAJ8DywEmgPbisga4AHgMVWtzrWhGbCPqs4TkQ7A2yLyrapu1uwhIkAPApSXl2t9G+k0LlatspJU\nkbAtcXLJihU1QlNUBMccE39cSYnlUqqqoLg4/fOnEpoWLfIzR5MqdHYD8CTQR1UPVdXhqnq8qvYH\njgS2Ak7L8r3nAd2jHneLHIs7RkSaRN5vcbLXqmpwXwG8jIfUnJCZOtUmnx49rMT1mWfib071+OOW\nND7mGNhrLxg5Mvl533oL/vhHuOUWeOKJTddtxOM//7G8wbffZv9ZsuWRR+C882xle0Nm5UrL0aSi\npMTuV6/O7PwN0qNR1ZOTPFcB3FGL954A9BWRXphInAScEjNmJHAG8AlwPDBGVVVERgL/FpHbsHBe\nX+BTEWkFFKnqysjPQ4A/18JGx6k1331n9336wCuv2Ba8zZpZaCVg7VrbMbGkBMrK7DWvvgpHHpn4\nvDffDO+9V/N4++1N1BIxdqyJzb77wptvwsCBtflUmfHcc/aeP/4IL7xQk7huaKxcCV26pB4XCM2q\nVekJU0ChCk1axQAicn3Eowgebyki/6rNG6vqRuAC4E1gKvCcqk4RkT+LSPD1ehgoFZHpwEXA5ZHX\nTgGeA74BRgPnRyrOOgIfichk4FPgdVUdXRs7Hae2LF5s948+WiME8+fHH3PbbfDVV9C3b82xZOc9\n6iib3H79a/jpp9TjmzWzyejAA7PvHpwNS5ZAu3bWUPKIIzK/ki8UonM0yQiEJtPuAIGIBGtmYilo\nocE8n/HMn6hWAAAgAElEQVQi0l9EBmPeyKTavrmqvqGq26pqH1W9MXLsalUdGfl5naqeoKrbqOog\nVZ0R9dobI6/bTlVHRY7NUNVdIrd+wTkdJxlTptjq7UxQtSv0Qw4xT2LDhsRjA8EoLbUbwKJF8ce0\na1czNh2hKS21SatnT8sPJLNj0SLo0MG8mi5dYOhQ68GViOXLzbv6V60uKY0lS2DIEFtT8t57sPvu\n1pZlyhT7XTYUgvLmVER7NJmwZo15g0UJZu4WLQpYaFT1CuBSYDxWbny4qt6dS8Mcp7446SQoL4ev\nv05v/NSpsOuuNlF/8AFMmwY//5x4/OLF0LSpTS5NmkCbNpuLSCA8gRC1bZue0LRtu+nrlixJPr60\n1BYO3n67heuCsF48pk83AT73XAu71YYlS8zW006DESPsd3HllbDTTrbmJJU3VgioZu7RZCM0icJm\nYM8VYjEAACKyH3Anlu94H7hLRNKIRDpO/jN7tk30Bx1kV9ipuO8+E5d//QuefNKOLVyYeHwwwQcV\nZ+3aJfZoAsEoLU0uGmvXwrp1m46PPk8yOwA6d7b7ZAK5YIHdt2hh+aRZsxKPTUZVFSxbViOKv/wl\nfPopzJsH99xjRQwHHlj4YrNunX3WsIWmYD0a4FbgBFX9i6qeAvwTGJM7sxynfli9uibH0aSJic03\n3yR/TUUFdO8OZ55Z01YkWQhq0aKaCR7ih8UC4YkNnSUKK8UTpujjiV4TnL9TJ7sPxCQewXMvvGBV\nckcemV3H4WXL7HNE/w7AwnfnnQejR5vIHHBAYYtN8LtxodmcdIVmz+jWMKr6ErB3bkxynLpjyZLk\nOYAgKb///rZZlSpcdFHycy5caLkOqFnxnY5HE5DMo4kOhVVWJk6ax44PBCT2vNFEC167dhbnTyY0\nwe9m333h2WetSOHhhxOPT0TgmQW2xrL33pbvmj/fcl7xSr8LgWCLgHRyNIEYudAAIjJcRIqieoj9\nF1VdLCJ9RGSf3JnnONnz1FPQsSM89FDiMcFk2rkzbLutXVWnKgyoqKgRmuA+mUcT7UlAfI9m8WLY\naivL5UDNpJzIQwkm73Q9mupqWLq0ZlxxsdmeyqNp08aSz0OG2AQ6c2bi8YlIJTRg64ZuucXyX3Pn\nZv4edcmSJfDDD5m/Lh88mnwtBkjVgqYU+FxEJmFVZkFngG2A/YFFREqOHSef+Pvf4ZJL7Ocvv0w8\nLgjVBDmLjh3h7beTn7uiwiZGqBGH2no08cJrYJNez57xzxk9LpXQLFtmYhP9Hp06pfZogt8LWJgw\nGxFIR2gAttvO7mfNsmq3MFizxrzbykrLw2VCJkITbFyWC49m/Xr7WyeqTAuDVAs2/yEidwMHYaGy\n/livs6nAaar6Y+5NdJzMuPRS+Nvf4PjjLbmf7Co82qMBm3yXLbPEbrxFhVVVJgpByEzEfk7k0ahu\nLjSlpRYSi36PeGOC4/GIDZ21bAlbbJF4fGwOKPisqTyaIJcD0LWrJfAzJdbWRASCmmmpeV3yxz9a\n9WGzZva3y6RlUCZC06yZ3bIRmui/YSzRWwXE24UzLFJqnqpWqerbqnqtqp6rqn9U1QdcZJx85Pvv\nTWTOPttavWy3XWqhadasZhIMJtZE1VhLltjVYhAyA/s5kUezcqXlHGI9GthUFBYt2jy8Fjsm1o7o\ncSLJ197EekCQntDUpUcTWwwQS/fu9jmyrW7LlCeegD//ueZ38/TT8M9/muBVViav+otHJjkayK6x\n5urVqT0ayL/wWbrlzX+NdANoKiLvishCERmea+McJ1OCdSFnn215iN69TWgSFQQE4aHgyjVVNVYg\nKNFCk8yjiTfBxxORWI8mEL5Ek93ixTapRHtd2QjNzz+bcMaiar+baI+mWzc7lmmyPvgMbdokH7fF\nFva3qC+hueIK2/WyrMwKQM45xwoTbrrJns+0Ai4TjwayE5p0QmfBuHwi3SjeEFVdARwBzMJyNH/K\nlVFOclSt/fiECWFbkn/MiPSO6N3b7nv1sjBCIg8lNg+RSmgCQYn1aBIJTbyQVbwKsWxCZ7GhqHSE\nJtqOjh2tk8DSpZuPX7nSfm+xQlNdndwLiseSJSYy6XQpLiurn9DZ/PkWBjzvPDj8cLjjDvNsn37a\nPKtgTCZkIzTZtKBJVQwA+bdoM5MWNACHA8+r6vIc2eOkYOlS+NWvbE/ygw6Czz4L26L84ocfLDYd\nCEEgODNmxB//00+bCk3HjnafSJjiCU379olDZ8k8mkBoKist7BItAs2a2USUTDhiQ1HJhCa28wAk\nF9XY3BVYjgYyz9PEE8VE9OxZPx7NxMgm7yefbCHWadNsEWn37jVNMTP1aILQWVBRlgr3aDbnNRH5\nFtgNeFdE2gPrcmeWA3a12b8/7LCDLSi87TbYZRdr4XH11fblPeyw7EpOGyozZpi4BKGwXr3sPtHv\nKNajCQQkU49m1ar4V5HxhCY2R5Moh5FMOJYsyWz84sW2IDU6f5BMaIJjsR4NZJ6niWdrIsrKYM4c\nK7rIJRMmWFXWgAH2uG9f664NNf8P2Xg0JSXpV3tlKjRVVVZR1mCFRlUvB/YCylV1A7CazbdddlKw\ndi3ce29NLLisDCZPTjx+zBhbJLfVVtZe/uKLLY798cdw3XW2orqyEg49NPlCvcbEDz/UTBhQUyYb\nz6NZt848xGihadbMJsVkQhMk3gOSLdqMJzTB1X3wN4sXXgvGJcvRxE7e7dol7iYQeBXRVVTpCE1s\nMQBkJzSZeDQbN+a+Q8CECdCvX/zKrJYt7TuXTY4m3bAZZC40wYVMgxUaEWkKDAeeFZEXgLOxDcic\nNFm71lp4nH++5VeaNLEJ5o4kO/o895xdgb7/vo2dOdNKL3ff3Z7fYQfbs2TOHDjhhPhJ3bpmwQIY\nNCj1plxhoFrj0QS0aGGTZTyPJt5kCsmrsRYutAk+Ot+QbNHm4sU2uW+9dc2xZs3s7xqIUDwxCh5n\nmqOpqrKuy7HEVrVB8gq74Go+2qNp29YudDINnWUiNMGFQS7zNKomNMH3KB6dO2fn0eRSaFLtRRP9\nXEEKDXAfFja7N3IbGDlWK0RkqIhME5HpIrLZwk8R2UJEno08P15EyqKeuyJyfJqIHJruOcNgzRoT\nmXfftUaMCxda19/hw621x7Jlm79mwwZ4+WV7XfPmNlmVldkXPZq994a77zYxuvfezOyaOxeef97a\niiRrLx/NJZfYl/Tcc+NPaGEyf755KdEeDVj4LJ5HE0wksRtVJROa6K4AAcHjRB5NvER4aWmNJ5Op\n0KgmDp1Fny/WjtjxW21l/0+JPJqmTTcVCJHsSpwzzdFAbvM0s2ebTcmEpkuX7HI0mWxi1rp13QtN\noRcD7K6qZ6jqmMjtLCDJnyk1IlIM3AMMA3YEThaRHWOGnQ0sVdVtgNuBWyKv3RHbkbMfMBS4V0SK\n0zxnvbJmjW1OFYjMmWfWhC/OPdf+IZ54YvPXvftuTeI/Fb/+NQwbBpddll7rjIcftgmje3c7/29+\nY915U/1zvv++tXU57ji7Cr7qqsRjV6yw3RSDUlhV++K++SY8+KCVkF50kd1Hf6HXr4d//xtuvHHz\nbX/HjLH3TjTRxVacBQQlzrHEdgUI6NgxeTFArNAEobN4Hk08TwJqwlzBmOBYNImEZsUK81xqKzQi\niUU1KG2OXbCYqdAEnZvTzdFku2hz40a7CEpnm+qgWrO8PPEY92jqllQtaAKqRKSPqv4AICK9gdqm\n6wYB04PNzETkGSzvE9079yjg2sjPLwB3i4hEjj+jquuBmZEdOAdFxqU6Z72xZIm1RP/kE9td8fTT\nN31+wAC7qnrgAbjggk2/1EHYbMiQ1O8jYpP3TjuZ6Lz3XvyEZFWVidHf/26NEi+7DPbYw754F1xg\nuZ5XX7Ur2ffegy++gBNPhG22MY/n/PPNq3r8cZuE7r3XhHO33TZ9n48+ss+9bJldyXftal+o2HxD\nq1a2AO3qq+GYY0wQAo8PrBXMSy/Z1fDzz5sHGLQGGTt203AU1IhsPI/m3/+21zZrVnM8XmUV1Ey+\n8VaGV1TYXjTRpAqdxZtk0/Fo2ra1i43YdiKJVtqnEppf/GLz44mEJrYrQEC3bpYjTJfly+33mK5H\n06KF/T4z9WjGjLH/65kz4cUXk4+dMMH+D/r3Tzwm8Ggy6Q6wcmX8dkGJKCmx//9028U0BqH5E/Ce\niMwABOgJnFXL9+4KzIl6PBeI/Sr8d4yqbhSR5Vj/ta7AuJjXRoovU56zzrjySiuN7NrVbn37mvcy\ncKDFsQ891DaPeu45a4cSj3PPNY/i448tDAY2Ib78Mhx99OahskQEm1n9+tfmDVxxheWBApYvN6Eb\nOdJE5fbba57ffXebpE47DXbc0QRhXaSm8LrrbK1B69bWPn/kSPtnvuEGax//+9+bkAahoVdesY3E\nevQwb2XePLs6bdkSdt7Zbn362NV78+YmDvffD488YqLyy1/a+1VU2KLLPfYwu665xvqLXXSRlaQe\ndZR5R9Fb2s6YYV/Y2C977972Zf7xRxPNgPnzze7AIwno1Mm+qKtWbX6FWlGx+fiSEvs7JQqdxdtD\nvl27ml5aixaZ6Ma2vCkttYkuei8XSF6lFrxnNKqJPatOneKHFRcsiN9vLGhDk+4EnG6fs2iyWUvz\nzDN2P2JE6l5pEyZY9Wb0RUcsnTvb93Dp0vRtz8ajAftfS6ckOhCPZK1lClpoVPVdEekLRNreMS3i\nTRQsInIOcA5Ajx49sjrHjjvaVeK8efbP+/zzcP319k9eWWkT1ejRtqlTIk46ySbPBx6oEZp33rHJ\nJZ2wWTRnnmkT/dVXWyuN88+3bYafftqOV1bCXXeZ0MRy4onmIfzlL/YlPPxwE86bbrLXVFebCPzy\nlza+TRsrtz71VBs/YIB9Ie++20ISr7+evCdTQJ8+1jLm+uvt6i568iwrM7G9+mrbZ/7ZZ+2L9MQT\n9ns79VT7nQci98MPFg6MnUCiS5xjhaZjx82vJqOrsaInjspK+7vEhs5EEi/aXLzYxDWWWI8mkdcT\nPB892SXL6UQ/H7BqlXmk8d6jU6f4Hsr8+SbysXTrZr+H6H5vyUi3z1k0PXuaN50u69fbRcohh5gn\nfs899j8Vj+pqmDTJLl6SEb2WJl3bM83RRHdwzkRoknk0wcVKvglNulVn5wMtVPVLVf0SaCki59Xy\nvecB3aMed4sciztGRJoAW2HVbolem845AVDVB1W1XFXL26fzjYnDqadaSOaDD8xz+flny3/ssIN9\ngT/4ILnIgF2dDB9uXs/nn9uX5rnnLFE7eHBm9ohY2GDECBOJyy+3ifqdd8zTCUJkiRgyxL6od9xh\n711WZiG5yZOt2WBsscHJJ8Ott9rk/sEHcOedlisaMyY9kYmmefPNJ8J99rFFdPfeax5e8AX71a9s\nInn5ZXjrrZrxsRVnAYkWbcauoQlIVPYbCEOs0ATHEnk08Sb4du3sCriyMrXQxIYcE03ebdrY/0C8\nLQiizxdNp072uaKLQTZssGPxfjeZljin2+csmrIy8z7TraIcPdo89ksusVzjQw8l3sfnu+/s956s\nEACyW0uTrUeTbp4mHaEpKrLvUqEWA/xWVf9bG6WqS4Hf1vK9JwB9RaSXiDTDkvuxRbMjgTMiPx8P\njFFVjRw/KVKV1gvoC3ya5jlzRmmpTehvvGFXTbGx/ET87nf2pRo40P6JnnzSchbJXPtEFBfXFB98\n/bXlOebPt6u8gQMzPx9Y7uf222smmQARW9szapRNDGvWwGuv1W3X2N69LTzXJMb3Pv98C5u98UbN\nsdg1NAFduljeKbYg4Kef4oe1EglNvMWaAfH6na1bt7mXFhDtfSQKayXakyaRcBQXm1eaaHy89+jY\n0cJg0SJZUWHH4uVoMu0OkE3orGdPu+BKts10NE8/bZ/toIPgwgvN63z88fhj0ykEgMy7A1RWms3Z\nCE26bWjSEZrg+YL0aIDiSBIe+G/FWBbTYA2quhG4AHgT23bgOVWdIiJ/FpEjI8MeBkojyf6LiOx9\no6pTgOewJP9o4PxIl+m456yNnfXBzjubKDz5pOV9Tj3VJvDa0q+fhROCzbRyTXS+JNc0b24Ty6hR\n9njVKpsg43k0xcV2lZyuR5OoDU0yoYnn0SSb4KO7A6QTOosmmLxjiyGC88bb6yb6fNHEE9V4XQEC\nsvVoMs3RQE2eZsOGmtBvLKtWWd7whBPs/3yvvaw45c4743tEEybYhdAOOyS3IVOPJtM+Z5AbjyZ4\nPt+EJt1igNHYYs0HIo/PjRyrFar6BvBGzLGro35eB5yQ4LU3Ajemc85CYNtt7eakz7Bhlgv6/vua\nUEE8jwYsTxPt0WzYYMIQT2iCBZmJPJp4kdZ4Hk2ykFV0v7PYHThjxyTajTPWywtek2noDOILTSIR\nLi7OXGhSdW6OJnotzR57mDd92WW2IdmLL276OV591f72J51kj0XMqzn9dLj5Ziso6djRRGrUKBs/\ncGDqBp+tWlm+JV2PJhCabHM06VDIQpOuR3MZMAb4feT2LnBproxynHQYNszuR41KvIYmIHYtTeCt\nxJtME21zHG+LgIAOHWzCi84NJJvgA2GpqNh0i+VogpxLvBxNopxHXQhNvK4AAcXF9jtLN3SWTBQT\nEb2WZt06E5q+fWHcOCu+iV4r8/TTFs7bJ2pD+RNPtBzMlVearXvsYWOOPtr+Rn9Ks+98Jmtp8smj\nycftnNPtdVatqver6vHATZGNz3Lc9s5xktO7t3mBo0YlXkMT0KuXTXpBh91Ea2gC4q0vqaiwCTPe\n1Xm8RZvpeDTff2/5kHhjiori51ySNamMJzSLFm3eBicgCBOmGzqDzBZtZtJQM6B1awu1zZpluZYF\nC6wE/r33bEIvL7ew8K672t/+xBM3rRxs1gzGj7fKtWuvtWMHHGD5w7lzayonU5FJd4D6Epri4tSh\n8JYt868YIIPrjP/yENaCxnFCZ9gwKw3v1MkEIN5kCjWezsyZVo4dTCDxigEgsdB06BB//Uj0os2g\nnDodoQnW0iSq0kvkoSTKeSQa36ZNfK+iZUsL90TnoxYssN9jojVc3bpZTjEdMulzFk1ZmV08vP22\neScHHmi/908/tVL4Zcss/NmrlxWGxCJif+dddrHy+Gzo3NnWiKVDcAGTa6Fp2TL1+qV8DJ1lIzQZ\n7KLtOLll2DD4xz9sPc322yceF0z+M2bY5JPKo+nYEb78ctNj8drPBMTrd5ZMaJo3tzxAsCNopqGw\nvn0Tj1+zxkJOwZqKZKE22FxUY3fWjKVbNyspTodshaZnTysAqK6Gv/61ZnLt2dPKl+uDTLoDZJOj\nCUQpU6FJRcuWiZuxhkW6OZporqtzKxwnS/bf32LSq1cnzs9AzXPBxD5/vk0eQegolk6dTFiiK5eS\nCU280FmiFf8B0d0Bknk0sTmaVKEz2Hyb6GTrmmKFZsGCxAIMNS2Fgqv4ZGTSUDOasjL73W+3neVW\nwqBzZytZjtf0NpZsQmfNmpmXmQuhyTePJt0Fm0UiMkBEDgdWiEiCr5vj1C/Nm9csik2UnwELBQ0c\naJ0PpkwxoWnfPnGSulOnzbc5Xrgw8Wr4eHvSpPIkSktrJrFE49q23VQ0Nm7cvCVN7DmD9w5YtKju\nPRpIL0+TTY4GakqcL700/Y3E6ppM1tJkIzQimTXWTFdoWrTIvxxN0j+hiPQRkQeB6cDNwMnAecA7\nIjJORM4SkZD+DRzHOOwwu0/m0UBNd4HDDrNuB8mu2uNVYyXzaFq1snPHFgMkm2SjvYx0Q2eB8GXq\n0aQrNKqpPZp0haa6OrNeYdEcf7z1txs+PPPX1hWZrKXJJkcDuRGaQvRobgCeBPqo6qGqOlxVj1fV\n/sCRWEuYFF2DHCe3HHuslb0ecEDycT162LqbxYstqZyJ0KxebbdEQgObL9pMx6MBS7on6qZQWmoT\nUbBYMVneB2rEK3rRZjpCs2KFTU4rV9rVcDKPJro7QFWVnT/e4shMOzdH06WLVYxl0x2jrsjUo2ne\nPPPF0SUlmXUGaJBCo6onq+qHkbYvsc9VqOodqvpY7sxznNR07mxrLBIlyKMZMMB6yRUVWY+2RMSW\n/SZbQxMQu2gzXY+mtDRxsjm231mqlfaxHk3QBidVjgYsyR6sMUkmwsEEfN55NrG2a2d9xmLJpqFm\nPpGJR5Npn7OAXHk0a9fWz4676ZJW1ZmIXA9cF2nxgohsCfwjsgGa4xQUhx1me+Yka9odu81xsvYz\nAR06bDoppUrCB6KQbEx0v7NOnVJ7NLFCk2o81AjuhRfaVfm++9otEVtsYavuZ8822996y9r033rr\npvmUbBpq5hMlJSYe6Xg0K1bkj9AEraDWrUtvfH2QbnlzE2C8iJwFdATuBu7KmVWOk2P23DP587Hb\nHAceTbJG3x06WO4HLKSUaMV/QLRHk4hMhSMIw2UiNAceaG32y8qsgWo64Z/LLqv5edttre3+hAmb\nbq6WTZ+zfCPd7gArV2ZW2hxQUpJ+l4VMPBowr6aghEZVrxCRd4DxwFJgP1WdnlPLHCdEYrc5Tsej\nCUJnqiYyiVb8BwTPpTMm3dBZ8JpYoUnmNRUXW7fwbDn8cDvHiBENU2jSzdHki0cTvflZvniT6ZY3\n7wfcCfwZeB+4S0QSrKl2nIZBp04wZ44JRrqhs8pKe006nkQ6obN4Hk1xsXlcyV4TjE/Wubmu2Hpr\nK8R45ZVNjxd6jgYsHxXsKJqMfBWafCHd0uRbgRNU9S+qegrwT6zJpuM0WHr2hPffNwG59177Aifb\na2fPPc0T2m472zUVah86i92TJlgAmWylejyPJtdXtkcdBVOn1iyIheTbGRQKu+5qPdeOPbYmX/fD\nD9Ytulevms+Y6xyNauMQmj1V9Zvggaq+BOydG5McJz+45x6rxDr8cFvYuf/+ycfvtZdNtqeeaj26\nIHHnAagRmmQeTatWVuIbCEY6LV1KS21yvOgiuPFGE6X6EBrY1KtZsiTzzs35xsUX226uo0ZZ/uqs\ns2wvmxEj7Hf88ss2LtscTevWJjSpPKYNGyzvl0kxQMEIjYgMF5GieJ2aVXVxZEHnPvFem+K8bUXk\nbRH5PnIf95pHRM6IjPleRM6IOr6biHwlItNF5M5gUzYRuVZE5onIF5HbYZna5jgB7drZfiaPPmpX\nsdG7eSZiu+1MnGbOtP5ryXZZ7dbN+rQFe6nEIxCJp582ARs3LrVodOliuaV774X+/W278UQNMuuK\nHj2sdHzEiJpj2fY5yyeKi610+7PPrFji8cdNbIJtw59/3sbVJnSmmnolf7pbBESPyafuAKmuNUqB\nz0VkEjAJWAg0B7YB9gcWEdn1MkMuB95V1ZtF5PLI48uiB4hIW+AaoBxQYJKIjIxsI30ftpX0eGyT\ns6FAZK9FblfVW7OwyXHqjK5dbXV7MkTgf/4n9bkuush2kRw/3nIuxx2XfPzll8PgwVaiHHQIrg+O\nPtoWWf78s1Wufftt4QtNwI47WifnJUtq8nQnnGAl3QsX2lqlbIUGzKtJJiLZCE3BeDSq+g9sS4Cn\ngfbAwZHH84DTVPU4Vf0+i/c9CggWej4GxGubdyjwtqouiYjL28BQEekMbKmq4yILSR9P8HrHaRBc\ncgl8+CFMn24T2u23Jx/foYN1ta5PkQELn6mah9ajB0ycGF5DzFzQpMmmxSC/+pWFs554wh7XVmiS\nUehCkzJ6GgmbvR251RUdVTWoTl+Arc2JpSswJ+rx3MixrpGfY48HXCAipwMTgYsjIrUZInIOcA5A\nj2Qr9xwnj0jVrj5M+veHbbaxxbCnnGICufPOYVuVOwYMsPDZww/b42zX0UDqNjTBzq0NUmhEJNgy\naJWq3pbJiSPrbuJ1TLoy+oGqqoikSIWlzX3A9Vio7Xrg78Cv4w1U1QeBBwHKy8vr6v0dp9EiYlV6\nIok3lGtIiJhXc/PN9jhfPJqgGCCfcjSpqs5+C8wGijM9saoeoqo7xbm9AvwcCYERua+Ic4p5QHQ3\nqm6RY/MiP8ceR1V/VtUqVa3GSrAHZWq34zjZ07Vr4xCZgBNOqPk5X4QmHz2aVEKzEguZDReRrSPV\nYv+91eJ9RwJBFdkZwCtxxrwJDIm879bAEODNSMhthYjsEak2Oz14fSBeEY4B0txw1nEcJ3MGDKjZ\nBylfhKbgypuB+4F3ge2xqrPo28RavO/NwGAR+R44JPIYESkXkYcAVHUJFv6aELn9OXIMbE+ch7B9\ncn6gpuLsr5Gy5y+BA4H/rYWNjuM4SRGp8WryRWiKi62cPZ+EJmmORlXvBO4UkftU9fd19aaquhir\nYIs9PhH4TdTjR4BHEozbKc5x3xvHcZx65YILLFnfr1/mr81UaJJ1pogm3/akSbepZp2JjOM4TkOi\na1e4887sXpsLjwbybztn34bZcRwnJFq0sD18UnWIzlRo8s2jcaFxHMcJCRE49FC4667kXlEgGkGi\nPxUuNI7jOM5/efFF66Bw4YXWPiheg801a2z306I0Z2wXGsdxHOe/tGhhzTl/9zu45RbrqhB0AghI\nd4uA6HO60DiO4zj/pbjYum3/5S/w7LO25cSMGTXPZyo0LVt6MYDjOI4Tg4iFzt54A378EcrL4bnn\noLo6O6Fxj8ZxHMeJy9Ch1vm6Rw848URrVvrZZy40juM4Th3Sp4+JzVNPWXHAd99l1nkg34SmgDdZ\ndRzHabg0aWKFASedZOG0zp1TvyYg3xZsutA4juPkMUVFcMQRmb0m8GhU82MPIxcax3GcBkbLliYy\n998PPXvaltpLl9pW4CtXQqdOdrxnTygtzb0YudA4juM0MHbe2UJv552XeuyIEbYNdy5xoXEcx2lg\nHHGEhc4WLIC5c2HJEvNq2rWzRp7z51sJ9ezZMHBg7u1xoXEcx2mANG0K3bvbLZbOnetHYAK8vNlx\nHMfJKS40juM4Tk4RjdcqtJEhIguB2Vm+vB2wqA7NCYNC/wxuf/gU+mcodPshnM/QU1XbpxrkQlNL\nREmO6YIAAAQpSURBVGSiqpaHbUdtKPTP4PaHT6F/hkK3H/L7M3jozHEcx8kpLjSO4zhOTnGhqT0P\nhm1AHVDon8HtD59C/wyFbj/k8WfwHI3jOI6TU9yjcRzHcXKKC00tEJGhIjJNRKaLyOVh25MpIvKI\niFSIyNdh25INItJdRN4TkW9EZIqIXBi2TZkgIs1F5FMRmRyx/7qwbcoGESkWkc9F5LWwbckGEZkl\nIl+JyBciMjFsezJFRNqIyAsi8q2ITBWRPcO2KRYPnWWJiBQD3wGDgbnABOBkVf0mVMMyQET2A1YB\nj6vqTmHbkyki0hnorKqfiUhrYBJwdKH8DUREgFaqukpEmgIfAReq6riQTcsIEbkIKAe2VNUMG9qH\nj4jMAspVtSDX0YjIY8BYVX1IRJoBLVV1Wdh2ReMeTfYMAqar6gxVrQSeAXLcA7VuUdUPgSVh25Et\nqjpfVT+L/LwSmAp0Ddeq9FFjVeRh08itoK78RKQbcDjwUNi2NEZEZCtgP+BhAFWtzDeRARea2tAV\nmBP1eC4FNMk1NESkDBgAjA/XksyIhJ2+ACqAt1W1oOwH7gAuBarDNqQWKPCWiEwSkXPCNiZDegEL\ngX9FwpcPiUirsI2KxYXGKXhEpAR4Efijqq4I255MUNUqVd0V6AYMEpGCCWGKyBFAhapOCtuWWrKP\nqg4EhgHnR0LKhUITYCBwn6oOAFYDeZcvdqHJnnlAdAPubpFjTj0SyW28CDylqi+FbU+2RMId7wFD\nw7YlA/YGjozkOJ4BDhKRJ8M1KXNUdV7kvgJ4GQuLFwpzgblRnvALmPDkFS402TMB6CsivSIJuJOA\nkSHb1KiIJNMfBqaq6m1h25MpItJeRNpEfm6BFZZ8G65V6aOqV6hqN1Utw/7/x6jq8JDNyggRaRUp\nJCESchoCFEwVpqouAOaIyHaRQwcDeVcM4xufZYmqbhSRC4A3gWLgEVWdErJZGSEiTwMHAO1EZC5w\njao+HK5VGbE3cBrwVSTPAfB/qvpGiDZlQmfgsUgFYxHwnKoWZIlwAdMReNmuWWgC/FtVR4drUsb8\nAXgqcsE7AzgrZHs2w8ubHcdxnJzioTPHcRwnp7jQOI7jODnFhcZxHMfJKS40juM4Tk5xoXEcx3Fy\niguN4ziOk1NcaBzHcZyc4kLjOHmIiOwuIl9G9qxpFdmvpmD6oDlONL5g03HyFBG5AWgOtMD6Wf0l\nZJMcJytcaBwnT4m0FJkArAP2UtWqkE1ynKzw0Jnj5C+lQAnQGvNsHKcgcY/GcfIUERmJtd/vhW1Z\nfUHIJjlOVnj3ZsfJQ0TkdGCDqv470t35YxE5SFXHhG2b42SKezSO4zhOTvEcjeM4jpNTXGgcx3Gc\nnOJC4ziO4+QUFxrHcRwnp7jQOI7jODnFhcZxHMfJKS40juM4Tk5xoXEcx3Fyyv8HjWG7acDPgPIA\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106b60e48>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error in numerical derivative: 0.00158629990076\n"
]
}
],
"source": [
"x = np.linspace(0, 2*np.pi, 100)\n",
"precisions = [10**-(2*x+1) for x in range(7)]\n",
"num_div_comparison(f=lambda x: 1e15+np.sin(x),x=x,fp=np.cos,\n",
" precisions=precisions,deriv_type='sym',exact_h=True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"Repeating all the steps in (2) but adding $10^{15}$ to $\\sin(x)$ seems to have very little appreciable effect on the numeric derivative and hence is a fairly good approximation of the analytic derivative."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"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": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment