Lab04_Q2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2: Asymmetric quantum well\n",
    "The system we want to work with here is a finite segment of the real line from $x = 0$ to $x = L$ with a variable potential $V(x) = \\frac{ax}{L}$ where $a$ is a constant with units of energy. In order to impose boundary conditions for the wavefunction $\\psi$ such that $\\psi(0) = \\psi(L) = 0$ we also demand that this potential blows up at the boundaries. We can then give the Fourier representation of the wavefunction as follows:\n",
    "$$ \n",
    "\\psi(x) = \\sum_{n=1}^{\\infty}\\psi_n \\mathrm{sin}\\frac{\\pi n x}{L}\n",
    "$$\n",
    "where $\\psi_1, \\psi_2,...$ are Fourier coefficients. These coefficients, in particular, are the components of the eigenvectors of the following eigenvalue equation for the Hamiltonian operator (obsevable of this measurement is energy):\n",
    "$$\n",
    "\\mathbf{H \\psi} = E\\mathbf{\\psi}\\\\\n",
    "\\mathbf{\\psi} = (\\psi_1, \\psi_2,...)\n",
    "$$\n",
    "$E$ being the energy eigenvalue. $\\mathbf{H}$ is the infinite dimensional matrix representation of the Hamiltonitan operator $\\hat H = -\\frac{\\hbar^2}{2 M}\\frac{\\mathrm{d}^2}{\\mathrm{d}x^2} + V(x)$. Different eigenvalues $E$ correspond to different discrete energy levels the particle can be observed in.\n",
    "\n",
    "It can be shown that the matrix elements of $\\mathbf{H}$ are given by:\n",
    "$$\n",
    "H_{mn} = \\frac{2}{L}\\int_0^L \\mathrm{sin}\\frac{\\pi m x}{L}\\big[ -\\frac{\\hbar^2}{2 M}\\frac{\\mathrm{d}^2}{\\mathrm{d}x^2} + V(x) \\big]\\mathrm{sin}\\frac{\\pi n x}{L} \\\\\n",
    "       = \\frac{2}{L}\\int_0^L \\mathrm{sin}\\frac{\\pi m x}{L}\\mathrm{sin}\\frac{\\pi n x}{L}\\big[ \\frac{\\hbar^2}{2 M}(\\frac{\\pi n}{L})^2 + V(x) \\big]\n",
    "$$\n",
    "The second line comes from acting the Hamiltonian operator on $\\mathrm{sin}\\frac{\\pi n x}{L}$.\n",
    "\n",
    "The following few blocks of code is to evaluate $H_{mn}$ for arbitrary integers $m,n$ (row and column of $\\mathbf{H}$, respectively) with $L = 5\\times 10^{-10} m$, $a = 10\\ \\mathrm{eV}$ for an electron whose mass and charge are $M = 9.1094\\times 10^{-31}\\ \\mathrm{kg}$, $\\mathrm{e} = 1.6022 \\times 10^{-19} \\ \\mathrm{C}$, respectively. In SI units, $a = 1.6022\\times 10^{-19} \\ \\mathrm{J}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Q2 \n",
    "#Code for end of Newman 6.9 b)\n",
    "#for H_mn\n",
    "#define constants\n",
    "M = 9.1094e-31 #kg (mass of electron)\n",
    "L = 5e-10 #m (Length of well)\n",
    "from scipy.constants import e #electron charge\n",
    "a = 10*e #J (energy constant in potential)\n",
    "from scipy.constants import hbar\n",
    "#define assymetric 1D potential \n",
    "def V(x):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "    x [float] : position of particle in well\n",
    "    Output:\n",
    "    V(x) [float] : potential at position x\n",
    "    \"\"\"\n",
    "    return a*x/L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define a function for computing the element of H in the mth row nth col\n",
    "#use Gauss quadrature for numerical integration\n",
    "from gaussxw import gaussxwab\n",
    "import numpy as np\n",
    "#import some particular numpy \n",
    "#atributes to make code loop nicer\n",
    "#without np. everywhere\n",
    "from numpy import pi, sin\n",
    "\n",
    "#define integrand function for H\n",
    "def Integrand(x,m,n):\n",
    "    \"\"\"\n",
    "    Inputs:\n",
    "    x [float] : position of particle in well\n",
    "    m [integer] : row index of Hamiltonian (>=1)\n",
    "    n [integer] : column index of Hamiltonian (>=1)\n",
    "    Output:\n",
    "    Integrand(x, m, n) [float] : The value of the integrand in the\n",
    "    integral that defines elements of the Hamiltonian\n",
    "    \"\"\"\n",
    "    out = (2/L)*sin(pi*m*x/L)*sin(pi*n*x/L)*\\\n",
    "    (hbar**2/(2*M)*(pi*n/L)**2 + V(x))\n",
    "    return out\n",
    "    \n",
    "#define a function for H_{mn}\n",
    "def H(m,n):\n",
    "    \"\"\"\n",
    "    Inputs:\n",
    "    m [integer] : row index of Hamiltonian (>=1)\n",
    "    n [integer] : column index of Hamiltonian (>=1)\n",
    "    Output:\n",
    "    H(m,n) [float] : the element of the Hamiltonian for an\n",
    "    electron in the assymetric well with potential given by V(x)\n",
    "    above, in the mth row, nth column.\n",
    "    \"\"\"\n",
    "    N = 100 #steps for Gaussian quadrature. \n",
    "    #get points and weights for integration from 0 to L\n",
    "    xp, wp = gaussxwab(N, 0, L) \n",
    "\n",
    "    # Perform the integration\n",
    "    s = 0.0\n",
    "    for k in range(N):\n",
    "        s += wp[k]*Integrand(xp[k],m,n)\n",
    "    return s "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part c) from Newman 6.9\n",
    "As mentioned in the intial preamble, $\\mathbf{H}$ is an infinite dimensional matrix. So, we cannot calculate all of its eigenvalues in practice, but we can calculate the first 10x10 block of $\\mathbf{H}$ and approximate the first ten eigenvalues by calculating the eigenvalues of this block. Newman tell's us the value should be 5.84 eV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#let's get the first 10x10 block of H\n",
    "Ham_10 = np.empty([10,10])#preallocate empty 10x10 array\n",
    "#imbedded for-loop to fill entries using above function\n",
    "for i in range(1,10+1):\n",
    "    for j in range(1,10+1):\n",
    "        Ham_10[i-1,j-1] = H(i,j)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#eigh returns eigenvalues and eigenvectors\n",
    "#of Hermitian matrices. H is of course Hermitian\n",
    "#because Quantum Mechanics\n",
    "from numpy.linalg import eigh\n",
    "#get eigenvalues and eigenvectors\n",
    "eigenvals_10, eigenvects_10 = eigh(Ham_10)\n",
    "eigenvals_10_eV = eigenvals_10/ e #convert to units of eV\n",
    "ground_state_E_10 = eigenvals_10_eV[0] \n",
    "#^ array index ought to be 1 less than algebraic index.\n",
    "#ground state is n=1 so array index is 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 10x10 block...\n",
      "Ground state energy eigenvalue estimate is: 5.8363731\n",
      "The magnitude of diference between theory value is 0.0036269\n",
      "This is 0.0621041% of theoretical value of 5.84eV.\n"
     ]
    }
   ],
   "source": [
    "print('For 10x10 block...')\n",
    "print('Ground state energy eigenvalue estimate is: {0:.7f}'.\\\n",
    "      format(ground_state_E_10)) \n",
    "theory = 5.84\n",
    "diff = abs(ground_state_E_10 - 5.84)\n",
    "print(\\\n",
    "'The magnitude of diference between theory value is {0:.7f}'\\\n",
    "     .format(diff))\n",
    "print('This is {0:.7f}% of theoretical value of 5.84eV.'\\\n",
    "     .format(100*diff/theory))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ground state came out to be ~5.84eV, as expected. Now let's do the same method of approximation but for a 100x100 block."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-05T14:25:10.471272Z",
     "start_time": "2018-10-05T14:25:10.377939Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'H' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-fcb02bf8f233>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m         \u001b[0mHam_100\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mH\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'H' is not defined"
     ]
    }
   ],
   "source": [
    "#part c\n",
    "#let's get the first 100x100 block of H\n",
    "Ham_100 = np.empty([100,100])\n",
    "for i in range(1,100+1):\n",
    "    for j in range(1,100+1):\n",
    "        Ham_100[i-1,j-1] = H(i,j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-05T14:25:10.764320Z",
     "start_time": "2018-10-05T14:25:10.749905Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'eigh' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-f75fac2b8c90>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0meigenvals_100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0meigenvects_100\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0meigh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mHam_100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0meigenvals_100_eV\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0meigenvals_100\u001b[0m\u001b[0;34m/\u001b[0m \u001b[0me\u001b[0m \u001b[0;31m#convert to units of eV\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mground_state_E_100\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0meigenvals_100_eV\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'eigh' is not defined"
     ]
    }
   ],
   "source": [
    "eigenvals_100, eigenvects_100 = eigh(Ham_100)\n",
    "eigenvals_100_eV = eigenvals_100/ e #convert to units of eV\n",
    "ground_state_E_100 = eigenvals_100_eV[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100x100 block...\n",
      "Ground state energy eigenvalue estimate is: 5.8363727\n",
      "The magnitude of diference between theory value is 0.0036273\n",
      "This is 0.0621109% of theoretical value of 5.84eV.\n",
      "Percent error for 100x100 is 6.210e-02 higher than for 10x10.\n",
      "Diff between 10x10 and 100x100 approximation is: 4.0067710e-07\n"
     ]
    }
   ],
   "source": [
    "print('For 100x100 block...')\n",
    "print('Ground state energy eigenvalue estimate is: {0:.7f}'.\\\n",
    "      format(ground_state_E_100)) \n",
    "theory = 5.84\n",
    "diff1 = abs(ground_state_E_100 - 5.84)\n",
    "print(\\\n",
    "'The magnitude of diference between theory value is {0:.7f}'\\\n",
    "     .format(diff1))\n",
    "print('This is {0:.7f}% of theoretical value of 5.84eV.'\\\n",
    "     .format(100*diff1/theory))\n",
    "print(\\\n",
    "'Percent error for 100x100 is {0:.3e} higher than for 10x10.'\\\n",
    "     .format(100*diff1/theory - 100*diff/theory))\n",
    "diff_est = eigenvals_10_eV[0] - eigenvals_100_eV[0]\n",
    "print(\\\n",
    "'Diff between 10x10 and 100x100 approximation is: {0:.7e}'\\\n",
    "     .format(diff_est))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still quite close, but our % error is oddly slightly higher for the 100x100 case. The difference is negligble, but we can conclude that larger matrices do not have a large impact on the error once you reach a certain threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-05T14:26:15.254208Z",
     "start_time": "2018-10-05T14:26:15.247840Z"
    }
   },
   "outputs": [],
   "source": [
    "#6.9 part e) in Newman\n",
    "#define a function for the wavefucntion psi(x) for this\n",
    "#particle in this potential well\n",
    "def psi(x, m):\n",
    "    \"\"\"\n",
    "    Inputs:\n",
    "    x [float] : position of particle\n",
    "    along the real line\n",
    "    m [integer] : integer greater than or equal to 1\n",
    "    denoting energy level of particle\n",
    "    \"\"\"\n",
    "    #the eigenvector for mth energy level is\n",
    "    #the m-1 element in eigenvects_100 b/c of\n",
    "    #algebraic vs python indexing\n",
    "    the_vector = eigenvects_100[m-1] \n",
    "    wave = 0.0\n",
    "    for n in range(1,len(the_vector)+1):\n",
    "        wave += the_vector[n-1]*sin(pi*n*x/L)\n",
    "    return wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-05T14:26:16.046485Z",
     "start_time": "2018-10-05T14:26:16.030371Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'L' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-b75662d750bf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#a range of positions between 0 and L\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;31m#wave functions for energy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m#levels 1, 2, 3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mpsi1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpsi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'L' is not defined"
     ]
    }
   ],
   "source": [
    "#a range of positions between 0 and L\n",
    "x = np.linspace(0,L,100)\n",
    "#wave functions for energy\n",
    "#levels 1, 2, 3\n",
    "psi1 = psi(x,1)\n",
    "psi2 = psi(x,2)\n",
    "psi3 = psi(x,3)\n",
    "#corresponding probability densities\n",
    "dens1 = psi1**2\n",
    "dens2 = psi2**2\n",
    "dens3 = psi3**2\n",
    "\n",
    "#plot probability densities\n",
    "font = 12\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure()\n",
    "plt.title('Probability density vs $0\\leq x \\leq L$',\n",
    "          fontsize = font)\n",
    "plt.xlabel('Position x in meters',fontsize = font)\n",
    "plt.ylabel('$|\\psi(x)|$', fontsize = font)\n",
    "plt.plot(x,dens1, label = 'ground state')\n",
    "plt.plot(x,dens2, label = '1st excited state')\n",
    "plt.plot(x,dens3, label = '2nd excited state')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, \\\n",
    "           borderaxespad=0., fontsize = font)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For some $x$ the probability amplitudes exceed 1! This is a clear indication that the wavefunctions aren't normalized. Let's now do this and plot again. The reason these weren't normalized is because previously we didn't pay any attention to the 'length'(modulus) of our eigenvectors, which ought to be normalized to one for a valid wavefunction. Thus, the manual normalization was required after computing the probility amplitudes. I could of course go back and normalize the eigenvectors and pretend like this didn't crop up,but I figured it would be more transparent to explain by this conrete example of what happens when you don't normalize eigenvectors. The normalized plot is below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x28a62af0908>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjsAAAEbCAYAAAA8kkXwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3Xlc1NX++PHXYYadYd9kBHFlUVkErTRNTVOzrmtqpVY3Wyyvdcu2X4vfbrbcm7Zo5q28tz2XrLS01Mot01wRxQVFBEEEWWRfZ+b8/pjBSwgKCgzgeT4e84j5fM7nfN6fj8S855zzOUdIKVEURVEURWmvbKwdgKIoiqIoSnNSyY6iKIqiKO2aSnYURVEURWnXVLKjKIqiKEq7ppIdRVEURVHaNZXsKIqiKIrSrqlkR1EURVGUdk0lO4qiKIqitGsq2VGumhAiRQgxzPLzYSHE4Cau/xMhxLymrPMS57pwLU19bM1709z3rMY5m/3eNWf8iqIoTUElO22A5YMxSwjhXGPbDCHEFiuGVScpZU8p5ZaWPKfl/pQJIYot9+ljIYRLS8bQEPXdm9rbrybhsoaa8beG2IUQnkKI74QQJUKIVCHEXdaM53KEEN5CCCmE0Fs7FkVpr1Sy03ZogceuthIhhLYJYmmNbpdSugB9gL7AC7ULtONrV/5sMVAJ+AF3A0uEED2tG9IlRQM5Usoz1g5EUdorley0HW8Cc4QQ7rV3CCHChBBbhBD5li6Fv9TanyKEeEYIcRAoEUJoLdueEkIctHwD/o8Qwk8I8ZMQokgI8YsQwsNy/LNCiJOW7UeEEOPqC7L6m70QYrKlpaX6VVGzJUoIESCE+EYIkS2EOCWEmF1jX7QQYr/lfCsAh4beJMsHxk9Ar0tc+yXvF9DXcp3nLa1EF87fgHtxqWPrbPWo1aX1ORAE/GC5b88IIb6pVX6REOKduq7/cvfuMvc9RQgxx/I7USCEWFEr/meEEGcsdScKIW6uGX8dsT9t+R1rUPyWe7uq1rZ3hRALL3X+WuWdgQnAi1LKYinlduB7YFpd96vWse5CiDuEEP8VQnxdT5l/CSG+q/H+TSHEr0II26uoNwo4cLn4FEW5ClJK9WrlLyAFGAZ8C8yzbJsBbAFsgSTg/wF2wFCgCAipdfwBIBBwrLHtD8zffvXAOWA/5m+Z9sAmYK6l7B1AAObkeDJQAnSoHV/tn2vsdwWOAg9Z3tsA+4CXLDF3AZKBEZb3qcDfLdc2Eaiqvu5L3R/Lz4HAYeCVuq79cvfLUj7BUt4T+L3muS91LxpwbJ33qfY9q7Wvg+Uc7pb3Wsu/VUwd9+GS9+5S973GeXdbrs/T8m/2sGVfCJAGBFjeBwNdG3AtjYm/E1AKuFrea4CzwPWXOn+tOqKBslrb5gA/1PO7Ewk8C2wDCoC1wCNAp3rKewH5mBOUh4FDgNvV1At8Cbxp7b8z6qVe7fmlWnbalpeAvwkhfGpsux5wAd6QUlZKKTdh/sN6Z61jF0op06SUZTW2LZJSZklza8hvwC4pZZyUsgL4DvMHB1LKr6WUGVJKk5RyBXAC6NeQgIUQNsBXwBYp5QeWzX0BHynlPywxJwMfAVMs12MLvCOlrJJSrgL2NOBUq4UQ+cB2YCvwWj3X3pD79Z6lfB7was19DbgX9R57JaSUZzF/YN5h2TQSc5fHvjqKX+7eXeq+V1toub484AfMH+oARsxJcLgQwlZKmSKlPNmU8UspUzEn3GMtm4YCpVLKPxpxfhfMyUVNBYCudkEhxPeYE+FxwBuAn5TyNinl+5ZY6rqeXOAd4DPgOeBWKeWfzncF9aqWHUVpZirZaUOklAmYP5ifrbE5AEiTUppqbEvF3FpTU1odVWbV+LmsjvcuAEKI6UKIA5Zun3zMXUTeDQz7VcwfNLNrbOsEBFTXZ6nz/2FuZQoAzkgpZa3ruZyxUkp3KWUnKeUjtZK6mtfekPuVVmtfQPWbBtyLeo+9Cp8CUy0/TwU+r6fc5e7dpe57tcwaP5di+R2QUiYBjwP/B5wTQiwXQjT02hoaP5gT4+oE8S7L+8acvxhzS2JNrphb72p7GfPvp9YS43+FENOEEL6XuZ44oDfwnJSyrv+vGlyvpZswxFKnoijNRCU7bc9c4AH+9+GcAQRaWlCqBQG1BztKroAQohPmb/+zAC8ppTvmrhrRgGOnYP7gmiilrKqxKw04ZUlOql86KeWtmLst9EKImvUHXUnsNdS89obcr8Ba+zIs19OQe1HnsVcRL8BqIEII0Qu4DXO3R10ud+8udd8vH5SUX0kpb8ScNEngnw2IvTHxA3wNDBZCdMTcMvJVI89/HNAKIbrX2BaJuWuz9vXsk1K+IKWMwZy8bARuB44KIT6rKzghRG9gCeYk5q91lWlkvb0xD6ZOrKsuRVGahkp22hjLN9wV/K+lZBfmMRFPCyFshXm+k9uB5U10SmfMHyzZAEKI+7AM/r0UIUQ0sAhzi0t2rd27gULLgFNHIYRGCNFLCNEX2AkYgNnCPJh4PA3sMmughtyvR4UQHYUQnphbPlZYtjfkXtR3bGNkYR5PA4CUshxYhfmDf7eU8nQ9x13u3l3qvl+SECJECDFUCGEPlGNu+TNeLvZGxo/ld2UL8DHmxOxoY84vpSzBPLbtH0IIZyHEAGAMl25NQkqZKaX8REo5CfDF3DJT+x7oMXftPYx5/E1vcZn5hRpQbxRwBLAVQjhYXvaXqlNRlMZTyU7b9A/MH7xIKSuBvwCjgBzgfWC6lPJYU5xISnkEWID5gzQL8zfR3xtw6BjAA9gu/vdE1k+WOo2YE4wo4JQl7qWYB3pWAuOBe4HzmAcBf9sU12I5d0Pu11eYv40nW17zLMc25F7UeWwjvQ68YOlqmmPZ9qnlfPV+aF/u3l3qvjcgJnvM409yMHd1+WJO5hoSe4Pir+ErzAPyv6qxraHnB3Mi4oh5IPQyYKaU8qKWHWF+Ik/WfmFOGP9Tq6wr8CPwlpTyeyllKeYnJOtKihpcL+ZWpxjMyVv160i9d0ZRlCsi/ty9ryhKaySECAKOAf5SykJrx9NYbT1+RVHaNtWyoyitnGV80RPA8raYKLT1+BVFafvUjLKK0opZJsnLwvxU1Ugrh9NobT1+RVHaB9WNpSiKoihKu6a6sRRFURRFadeu+W4sb29vGRwcbO0wFEVR2pR9+/blSCl9Ll+yfvv37x+h1WrnSin9UV++lStnBLYbDIYHYmJiKusqcM0nO8HBwezdu9faYSiKorQpQoiGzGxer/3794+wt7d/Lzg4uNLR0fG8jY2NGlOhXBGTySRSU1NvzM/Pnwm8W1cZlUkriqIoLU6r1c4NDg6udHZ2LlOJjnI1bGxsZEBAQLFGo7m33jItF46iKIqimEkp/R0dHcutHYfSPtjZ2VVJKeudIFUlO4qiKIo12KgWHaWpWJYErDensVqyI4QYKYRIFEIkCSGerWO/vRBihWX/LiFEsGX7cCHEPiHEIct/h9Y4ZoulzgOW1+VWL1YURVEUpZ2zSrIjhNAAizGvTxQO3CmECK9V7H7gvJSyG/A2/1vhOAe4XUrZG7iHi9fauVtKGWV5nWu2i1AURVEUK3jiiScCxowZ09nacbQl1mrZ6QckSSmTLYsXLse8cGRNYzAvHgjmFZNvFkIIKWWclDLDsv0woFYJVhRFUZTL0Ov1vVevXq1raPkJEyYEz549O6A5Y2op1kp29EBajffplm11lpFSGoACwKtWmQlAnJSyosa2jy1dWC8KSydebUKIB4UQe4UQe7Ozs6/mOhRFUZRrXFVVlbVDUC7DWslOXUlI7YFqlywjhOiJuWvroRr777Z0bw20vKbVdXIp5YdSylgpZayPz1XNiaUoSh2KKwwcSi9g7cEM3t+SxIfbTvLNvnS2Hs/mXJF6AEdp/bZv3+4UFhYW7uzsHD1q1Kguo0eP7lLdyrF27Vqdn59fxPPPP+/v7e0deccdd3QGWLBggXdQUFAvNze3qKFDh3ZLSUmxBUhMTLQTQsTUTIr69esX8tZbb3kDLFy40CsmJibkwQcf7Ojq6hql1+t7r1y50rW67LFjx+z69u0b4uzsHN2/f//uOTk59c6Rd/bsWe2QIUO66XS6KDc3t6iYmJgQo9HI2LFjO589e9ZuypQp3Z2cnKJfeOEFP4BRo0Z18fb2jtTpdFGxsbEhe/fudQCYP3++95o1azyXLFni7+TkFD106NBuACkpKbYjRozo6uHhEanX63vPmzevTYyNtdakgulAYI33HYGMesqkCyG0gBuQByCE6Ah8B0yXUp6sPkBKecby3yIhxFeYu8s+a66LUBTlf8oqjfxyNIs1BzLYevwcVca6H7QRAmKCPBjZy5/bIwPwc3Vo4UiV1uipVfGBxzOLnJrzHD38daVvToxMu1y58vJyMWnSpK4zZ87Mevrpp7OXL1/uNmPGjC4zZ87MrC6Tm5trm5eXp0lLSztoNBr5/vvvdfPmzdP/8MMPJ2JiYsoefvjhjhMnTuyyd+/exIbEFh8f73zXXXfl5uXlHViwYIHPrFmzgidOnHjQxsaGKVOmdImNjS3etm3b8S1btjhPnDix+7Bhw/LrqmfevHl+HTp0qMzJyYkH2Lx5s7MQgtWrV5/S6/UuixcvThk7dmxRdfkRI0YUfPXVVykODg7y0Ucf7Th16tQux44dOzJnzpycnTt3uuj1+sqFCxdmABiNRkaPHt1t1KhR+WvWrElOTk62veWWW0LCwsLKJ0yYUNiQ67QWayU7e4DuQojOwBlgCnBXrTLfYx6AvBOYCGySUkohhDuwDnhOSvl7dWFLQuQupcwRQtgCtwG/NP+lKMq1rbzKyCc7Uli8OYmicgN+rvbcc0MwscEeBHk6E+TlhJSSnOJKzhWW80dyHusPZzJv3VHmb0zkgYFdeOimrrjYX/MTuiutxObNm50NBoN4/vnnz9nY2HDPPffkL1y4sKRmGSGEXLBgQYajo6ME+OKLLzwnT56ce+ONN5YCLFy48IyXl1dUYmKiXUPOGRAQUPnkk0/mADzyyCO5zz77bFB6erq2oqLCJiEhwXnbtm3HHR0d5ahRo4qHDh1aZ6IDYGtrK7OysmxPnDhh16tXr4qRI0cWX+q8jz/+eG71z//6178yfHx8onJzczVeXl7G2mW3bt3qnJeXp50/f/5ZgPDw8Mpp06ZlL1u2zFMlO3WQUhqEELOADYAG+K+U8rAQ4h/AXinl98B/gM+FEEmYW3SmWA6fBXQDXhRCvGjZdgtQAmywJDoazInORy12UYpyjZFS8n18Bv9an8iZ/DKGhPjw4KCu9Ovsicbm4l5onYMtnb2dua6LF48N605ydjHv/HKCRZuSWLY7jedHhzIuuqMVrkRpDRrS4tJS0tLSbP38/KpsbP430iMgIOBPay55eHgYnJycLjRfZmZm2kVHR19IQtzc3Ezu7u7G1NRU206dOl12UI+Pj8+FMjqdzgRQWFioycrK0up0OoOrq6upen9QUFBlenp6nUnU3LlzM59++umAkSNH9gCYPn169muvvZZZV1mDwcDs2bP1P/zwg8f58+dthRDSci3aupKd5ORku+zsbDudThdVvc1kMonY2Nii2mVbG6t9lZJS/gj8WGvbSzV+LgfuqOO4ecC8eqqNacoYFUWpW2F5Fc99e4h1B8/SM8CVNydG0L+bd6Pq6OLjwsI7o7lvQDCvrD3C31fEsz81nxdvC8dOq+Y7VaxHr9dXZWVl2ZpMJqoTnoyMDLvOnTtfeBim9vMv/v7+lampqReeDC4sLLTJz8/XdOrUqao6eSkqKrLx9PQ0AWRnZzfo8zcwMLCqqKhIW1hYaFOd8KSlpdnV8/wNHh4epo8++igdSN+7d6/DLbfcEnLdddeVjBkz5qKE5IMPPvBcv369+88//3y8R48elXl5eRofH58oKWWd1xgcHFyp1+srUlNTExoSe2ui/qIoitIoh9ILuH3RdtYnZPLMyFB+mHVjoxOdmqKDPFj50A08NKgLn/+Ryt1L/yC7qOLyBypKM7n55ptLNBqNfP31132rqqr44osv3A8ePOh8qWPuvvvuvBUrVnjt2LHDsaysTDz22GP6yMjIkpCQkMqAgACDr69v1YcffuhlMBh45513vNLS0ho0ZUqPHj0qe/bsWTJnzpyA8vJysWHDBpdNmza511d+2bJlbgkJCfYmkwl3d3ejRqORGo0GAG9v76qkpKQL5y0qKtLY2dlJX19fQ3Fxsc3jjz/+p6eifX19q06dOnWh/ODBg0tcXFyMzz//vH9xcbEwGAzs2bPHYevWrc061qopqGRHUZQGW3swgwlLdlBpMLHiweuZObgrNnV0WTWWVmPDc7eGsfDOaA6dKWDs4t85k1/WBBErSuM5ODjIFStWnPz888+93dzcor/88kvPIUOGFNjb29e7vMWYMWOKnnvuuYzJkyd39ff3j0xJSbFfuXJlcvX+RYsWpSxatMjfw8Mj6vDhw47R0dEl9dVV27Jly5L37dvn7OnpGfXyyy93GD9+fG59ZY8fP24/YsSIHs7OztEDBgwIu/fee7Nvu+22IoCnnnoqc8GCBR10Ol3USy+95Ddz5sxcvV5fERgYGBkaGtrz+uuv/1NMM2fOzDlx4oSjTqeLGjZsWFetVsu6deuSDh486BgcHBzh6ekZNWPGjODz589rGnot1iKqm6uuVbGxsXLv3r3WDkNRWr0vd6XywuoEYjt58OG0WDycGzTustEOpudz99JdeLvYs+Kh6/HVqae1WiMhxD4pZeyVHh8fH58SGRmZ05QxNaeIiIjQ+++/P/uxxx6rN9FQrCs+Pt47MjIyuK59qmVHUZRLklKyeHMSz3+XwJAQXz7763XNlugARHR055P7+pJVWM7UpbvIK6m8/EGK0sTWrVvncvr0aW1VVRWLFi3yOn78uNPYsWNb9RNHSv1UsqMoyiUt3pzEmxsSGRsVwAfTYnC0a/4W65hOniydHktKbin3fryb8qqLHgxRlGZ19OhRh+jo6J6urq7RixYt8vvkk09ONuSpKqV1UsmOoij1+nJXKvM3HmdctJ63JkVhq2m5Pxn9u3mz+K4+HEwv4MXVCVzrXe5Ky5ozZ05Obm5ufFlZWdzx48ePTJkypcDaMSlXTiU7iqLU6cdDZ3lhdQJDQnz418SIJhmI3FjDw/3429BufL0vnRV7Ws00LIqitDEq2VEU5SK7knN5fPkB+gR58P7dMS3aolPb48N6MLC7Ny99f5hD6erLtaIojaeSHUVR/uRMfhmPfLmfjp6O/Peevi0yRudSNDaCd6dE4+Niz8wv91FUroZNKIrSOCrZURTlgvIqIw99vpdKg4mPpsfi5mRr7ZAA8HS2Y9Fd0WTkl/HP9cesHY6iKG2MSnYURQHMj5g/9+0hDmcU8s6UKLr6uFg7pD/pE+TBXwd05os/TrPzpJrqRFGUhlPJjqIoAHy2M5Xv4s7w5PAe3BzmZ+1w6vTkLSF08nLi2W8PUlapHkdXFID169e7BAcH92qq+p544omAMWPGdG6q+loDlewobZeUcOo3+PFp+HISLL4eFoTC5+Ph11fg+AYwqQ/EhjiSUcir645yc6gvjw7pZu1w6uVop+GN8RGk5payYGOitcNR2rHXXnvNp1evXmF2dnZ9JkyYENzQ4/R6fe/Vq1frmjG0i4wcObI4JSXlwuKc1ojhSs47YcKE4NmzZwc0Z0zVrLbqudI2nC8/z4aUDRRWFlJSVYKtjS3TwqfhZu9mvaCMVXD4O9j5HpyNB1tn8OwMnl3AXgdZh2H72yCN4BsOw/4Put8C9awSfK0rrTTwt2X7cXey5c07Ii9a6bi1uaGrF3dfF8R/fj/F2Gg9vfRW/F1U2i29Xl/1zDPPnF2/fr1reXm5ahho49Q/oFKvpPNJ3LnuTl7d9SqL4hbx+ZHP+ejQR9zxwx3EZ8dbJ6j80/DfEfDtA1BVBre/C0+fhJm/w51fwfgPYOZ2eC4dJn4MhnL4ahJ8erv5WOUir6w9QnJOCW9PjsKzGZeBaEpPjwzF3dGWeeuOqMkGlWZxzz335E+bNi3fy8vLUHvf2bNntUOGDOmm0+mi3NzcomJiYkKMRiNjx47tfPbsWbspU6Z0d3Jyin7hhRfq7A9etmyZW2hoaLhOp4uKjo4O3bVrlyPA4cOH7d3c3KK2b9/uBJCSkmLr4eERuXbtWh1AVlaWZuLEicG+vr4Rrq6uUcOGDesKsHbtWp2fn18EUG8Mv/76q3N0dHSoTqeLCgkJCa+uE+DYsWN2ffv2DXF2do7u379/95ycnHobQhp77aNGjeri7e0dqdPpomJjY0P27t3rADB//nzvNWvWeC5ZssTfyckpeujQod2qr3nEiBFdPTw8IvV6fe958+b5Xsm/X22qZUep0/Yz23lq61M4aB34bNRn9PLqha3GloScBOZsncO9P93LY30e456e97RcS0DievjuIXPX1PiPoNdEsKknX7dzgl7jIfQ22PcJbJoHS4fD1FXg37tl4m0Dfjp0lmW705g5uCsDunlbO5wGc3O05YnhPXhxzWE2HsliRE9/a4ekXK3VjwZy7ohTs57DN7yUsYuvenbKefPm+XXo0KEyJycnHmDz5s3OQghWr159Sq/XuyxevDhl7NixRXUdu337dqdHH300eNWqVUmDBg0qWbJkidf48eO7JSUlJfTs2bPipZdeSp8+fXrn+Pj4o1OnTg2+4447cqtXLZ88eXJnZ2dn0+HDhw+7urqafvnlF+fa9dcVw6lTp2wnTJjQ/YMPPjg1ceLEgu+//9516tSpXY8cOZIQEBBgmDJlSpfY2Njibdu2Hd+yZYvzxIkTuw8bNiy/Ka59xIgRBV999VWKg4ODfPTRRztOnTq1y7Fjx47MmTMnZ+fOnS56vb5y4cKFGQBGo5HRo0d3GzVqVP6aNWuSk5OTbW+55ZaQsLCw8gkTJlzVumSqZUe5yMaUjTz666PoXfQsG72MaN9obDXmR5B7efdi5e0rGRI0hAX7FvDNiW9aJqjf3oJlk8E9EB7aChGT6k90atLawXUPwl/Xg7CB/46C5C3NHm5bkFtcwfOrE4jo6MYTw3tYO5xGu7NfEN19XXjtx6NUGNTYLKXl2NrayqysLNsTJ07Y2dvby5EjRxbbNOTvEbBkyRLvadOmZQ8dOrREq9Xyt7/9LdfW1lZu2rTJGeDJJ5/MCQ4OroiJiQk9d+6c7bvvvnsGIDU11Xbbtm1un3zySaqPj4/R3t5ejh49urgh51y6dKnX4MGDCyZPnlyg0WgYN25cYa9evUq++eYbtxMnTtglJCQ4v/XWWxmOjo5y1KhRxUOHDq0z0bmSa3/88cdzPTw8TI6OjvJf//pXRmJiomNubm6dk3dt3brVOS8vTzt//vyzDg4OMjw8vHLatGnZy5Yt82zIdV6KatlR/uR8+Xle+eMVwj3D+c+I/+Bke/EXLVc7VxbctIAZG2ewYO8CBuoH4ufcjE/v7FwMv75sbskZ8x7YOja+Dr9wmPELfDkRvpgIdy6D7sObPtY25KXvD1NcbuDNiZFWnSH5Smk1NrxwWzj3/Hc3n+1I5YFBXawdknI1mqDFpaXMnTs38+mnnw4YOXJkD4Dp06dnv/baa5kNOTY9Pd3u22+/9frvf/97oXvGYDCI9PT0C33IM2bMyL777ru7zZ8/P9XR0VECJCcn27q5uRl8fHwandmnpqba/fTTTx46ne7CADeDwSAGDRpUdPr0aVudTmdwdXU1Ve8LCgqqrBnPlV67wWBg9uzZ+h9++MHj/PnztkIICZCZman18vK66DqSk5PtsrOz7XQ6XVT1NpPJJGJjY+tsJWuMtvcXTmlWb+17i+LKYl4e8HKdiU41IQRzb5iLwWRg3h/zmm/cxN6PYcP/g7C/wLgPrizRqeamh/t+Ap9QWHU/5CQ1XZxtzI+HzrLu4FkeG9adEP8Wf2ijydzUw4fBIT4s3HSC8yWV1g5HuUZ4eHiYPvroo/T09PRDq1evPvHvf//bb82aNQ36H0mv11fNnj37bFFR0YHqV1lZWdxDDz2UB1BQUGDzzDPPBE6aNCnnn//8Z0BWVpYGoEuXLlUFBQXanJycRk9pHhgYWDlu3Ljc2ud87bXXMgMDA6uKioq0hYWFF/KBtLS0egfvNebaP/jgA8/169e7//zzz8cLCwvjTp06dQi48HlRewhEcHBwpV6vr6gZZ0lJSdzWrVuv+o+1SnaUC/Zk7mF10mqm95xOD4/Ld2sEuQYxK3oWW9K3sCFlQ9MHdGgVrP07dBsOE/4DmiZoiHR0hylfmutafieUX3trLeUWV/Di6gR66914qB20hjx/axjFFQY+/C3Z2qEo7UhVVRWlpaXCaDQKo9EoSktLRVWVeamSZcuWuSUkJNibTCbc3d2NGo1GajTmHMTb27sqKSnJvr56H3744exPP/3Ud9OmTc4mk4nCwkKb5cuXu50/f94G4IEHHgjs3bt36YoVK1Jvvvnmgvvuu68TQKdOnaoGDRpUcN999wVlZ2drKioqxE8//VTnzJ+1Y7j//vtzf/nlF/dvvvnG1WAwUFpaKtauXas7efKkbY8ePSp79uxZMmfOnIDy8nKxYcMGl02bNrnXF39jrr2oqEhjZ2cnfX19DcXFxTaPP/64vmZdvr6+VadOnbpQfvDgwSUuLi7G559/3r+4uFgYDAb27NnjsHXr1qsey6WSHQWASmMl/9j5D/Queh6OfLjBx90ddje9vHrx+u7XyS+vt5u38bKOwJpZEHQDTP7cPPamqXh0gjs+hdyT8O2DYDJd/ph25B9rj1BYXsX8OyLRtsHuq9q6++m4PSKAT3ekkFtcYe1wlHbimWeeCXB2du7z/vvv+69Zs8bT2dm5zzPPPBMAcPz4cfsRI0b0cHZ2jh4wYEDYvffem109iPipp57KXLBgQQedThf10ksvXdS/P2jQoNL33nsvZfbs2UFubm5RXbt27fXpp596AXzxxRfuW7Zscfv4449TAf7973+nJSQkOC1ZssQTYMWKFadsbW1laGhoLx8fn8i33367zvEDtWPo1q1b1cqVK5PeeOONDl5eXlF6vT5i/vz5fiaTSQAsW7Ysed++fc6aVvJUAAAgAElEQVSenp5RL7/8cofx48fXO0V5Y6595syZuXq9viIwMDAyNDS05/XXX19Ss66ZM2fmnDhxwlGn00UNGzasq1arZd26dUkHDx50DA4OjvD09IyaMWNG8Pnz5696gT5xrT+2GRsbK/fu3WvtMKxu6aGlvLv/XZYMW8KN+hsbdWxiXiITf5jIzMiZPBL1yNUHU1EMHw2Bsnx4eDvommk80O6P4Mc5MOxluPHx5jlHK/PbiWym/Wc3s2/u3iYHJdcn6VwRw9/exoODuvDcqDBrh3NNEELsk1LGXunx8fHxKZGRkTlNGZNybYuPj/eOjIwMrmtf2/9ap1y1KmMVXx79kgH6AY1OdABCPEMY1HEQKxJXUGm8ynETUpq7rnKTYOJ/mi/RAeg7w/xo+pbXIa/9d4GUVxl5cXUCnb2deWRwV2uH06S6+er4S2QAn+1IVa07iqJcRCU7CutT1pNTlsO0sGlXXMfdYXeTV57HT6d+urpg9n8Gh1bC4Oeg86Crq+tyhIBb3wQbW/jhcXOi1Y69vzmJlNxSXhnTCwfbq24VbnVm39ydCoORD7e1/8RVUZTGUcnONU5KyRdHv6CzW2f6B/S/4npu6HADXd268uXRL6/8yaz8NFj/HHS+CQY+ecWxNIprAAybC6e2QvzyljmnFSSdK2bJ1pOMjQrgxu5tZ/LAxujq48KYKD2f7UwlR7XuKIpSg0p2rnEHsg9wJPcId4fefVUzIQshuDv8bo7mHWX/uf2Nr0BK8/gZJPxlEdi0YMtD7P0QeJ35EfeS9jeEQErJ3O8TcLTV8PzocGuH06xmDe1GucHIpztSrB2KoiitiEp2rnFfHPkCnZ2O27veftV13dblNtzs3fjy6JeNP/jIGji+HoY8b35aqiXZ2JjX2KooNC8r0c5sOJzJ70m5zBkRgo+u3idi24WuPi4MD/Pj8z9SKa28aEkjRVGuUSrZuYadLT7Lr6d/ZWL3iZecQLChHLWOTOw+kV9P/8qZ4jMNP7AsH356GjpEwnUNf+y9SfmGQcx9EPe5+ZH0dqK8ysgra48S6q/jrn5B1g6nRTx0UxfyS6v4em+6tUNRFKWVUMnONWxF4gokkimhU5qszimhU5BS8v3J7xt+0K8vQ0m2uXWlKSYOvFKD5pgHK295w3oxNLEPtiZzJr+Mubf3bBdz6jRETCdP+gS5s3R7MkZT+x50rihKw1wbf/2Ui5ikiXWn1jEgYAABLgFNVq+/sz/RvtFsTNnYsAOyjphXJe/3IAREN1kcV0TnD9c9BIe+hqzD1o2lCZzJL2PJ1iRG9+7ADV29rB1Oi3pwUFfS8spYn9Cg5YoURWnnVLJzjYrPjiezJJNRnUc1ed23BN9CUn4SyfkNeAT455fAXgc3PdPkcVyRAY+BvStsetXakVy11348CsBzt4ZaOZKWNzzcj2AvJz7cdrL51m1TlAZauHChV0xMTEhLne/EiRN2Tk5O0QZD04xba+n4m4PVkh0hxEghRKIQIkkI8Wwd++2FECss+3cJIYIt24cLIfYJIQ5Z/ju0xjExlu1JQoiF4moeL2rn1p9aj52NHUMChzR53cM7DUcg2JB6mfWyTm6GpJ9h4Bxw8mzyOK6IkycM+BskroP0tjuz9r7UPNYdPMuDg7rS0ePqx2O1NRobwYyBXYhPL2D3qTxrh6O0MWVlZWLSpEmdAgICejs7O0eHhYWFr1y50tXacTVU9+7dK0tLS+O0WvOwgH79+oW89dZbLT7nRGPP+8QTTwSMGTOmc3PEYpVkRwihARYDo4Bw4E4hRO1nYu8HzkspuwFvA/+0bM8BbpdS9gbuAT6vccwS4EGgu+U1stkuog0zmoxsTN3IwI4DcbGrcx25q+Lr5Hv5riyTCX5+EdyDzF1Yrcl1M8HJC7a9ae1IroiUknnrjuKrs+fhm9r+Qp9XakKfjrg52vLZH6nWDkVpY6qqqkTHjh2rNm/enFhYWBj30ksvnbnvvvu6JiYmNuEifUpLslbLTj8gSUqZLKWsBJYDY2qVGQN8avl5FXCzEEJIKeOklBmW7YcBB0srUAfAVUq5U5rbrT8Dxjb/pbQ9+8/tJ6csh5HBzZcLXujKKqinK+vgCsg8BDfPBVuHZovjiti7mBOw4+sh+7i1o2m0tQfPEnc6nzm3hOBkZ8UB31bmaKfhjpiObEjI5FxhubXDUdoQV1dX01tvvZUREhJSqdFouPPOOwv0en3Fzp07nQDWrl2r8/Pzi5g7d66fp6dnpI+PT8S77757YWBcZmamZujQod1cXFyie/fuHXby5MlLzvnw66+/OkdHR4fqdLqokJCQ8LVr1+oAsrKyNH5+fhFfffWVG0BBQYFNUFBQr/fee88LoLi4WDzwwAMdAwICeut0uqiYmJiQ4uJikZiYaCeEiKmqquJvf/ubft++fS7PPfdckJOTU/T06dODAOLi4hz69+/f3c3NLSo4OLjX0qVLPa4k/tLSUjFmzJjO7u7uUTqdLqpXr15haWlp2vrOe9999wX6+/tHuLi4RPfs2TNs/fr1LgCrVq1yXbRokf+6des8nJycokNCQsIBcnNzNZMmTerk4+MT4evrGzF79uyAK+mes9ZfQj2QVuN9OnBdfWWklAYhRAHghbllp9oEIE5KWSGE0FvqqVnnn5aTryaEeBBzCxBBQdfG47g1rT+1HketI4M6Nt9yDMOChvHP3f9kY8rGi1dRN1TA5lfNA5J7jm+2GK5K3xmw/W34Y7H5KbE2oKCigGO5J3h94xlC/T2YENPR2iFZ3dTrO7F0+ym+2n2ax4e1n4VP26MXf38xMOl8UrP2uXbz6Fb6yoBX0i5f8s/S0tK0qampDpGRkRey5tzcXNuCggLN2bNnD65evdr13nvv7XLXXXfl+/j4GGfMmNHJwcHBlJGREZ+YmGg3evToHoGBgXVO633q1CnbCRMmdP/ggw9OTZw4seD77793nTp1atcjR44kBAQEGJYsWZLy4IMPdr7pppsOP/nkk/rw8PDSWbNm5QLMnDkzMDEx0fH3338/FhgYWLV582ZnjebPE7IuWrTozK5du1ymTJmS+8QTT+QAFBYW2owaNarHc889d+aRRx45sWvXLqfbb7+9e1RUVFlsbGx5Y+JfvHixV1FRkSYtLe2go6OjaefOnU7Ozs6mus4L0Ldv35LXX389w8vLyzhv3jy/qVOndj19+vTBiRMnFu7YsSPz5MmT9mvWrDlVXX7y5MnBvr6+hpMnTyYUFRXZjBw5svvbb79d+dRTTzVqBlhrtezUNZam9ijCS5YRQvTE3LX1UCPqNG+U8kMpZayUMtbHx6cB4bYfBpOBX07/wqCOg5pkbp36+Dn7mbuyUuvoyjrwFRSkwdAXzBP6tUbO3hA5xbyERCueVdloMvLqH69y89c3c+PyG5nx830UeL7GlIFGNDZqyFqwtzM39fDhq12nqTKarB2O0gZVVFSIyZMnd5kwYUJudHT0hWRHq9XKN998M8Pe3l5Onjy5wNHR0XTw4EEHg8HA+vXr3V999dUMV1dXU9++fcsnTZqUW1/9S5cu9Ro8eHDB5MmTCzQaDePGjSvs1atXyTfffOMGMH78+MLRo0fnDRkypMemTZvcPvnkk1QAo9HI119/7f3uu++e7ty5c5VWq2X48OEljo6Olx2Rv2LFCje9Xl/x2GOP5dra2nLjjTeWjho1Kn/ZsmUejY3f1tZWnj9/XnvkyBF7rVbLwIEDSz09Pev9n+2RRx7J8/f3N9ra2vLyyy9nVVZWivj4+Dqb99PS0rTbtm1z+/DDD0+7urqa9Hq9YdasWVmrVq1q9CBPa7XspAOBNd53BDLqKZMuhNACbkAegBCiI/AdMF1KebJG+ZpfZeuq85q3O3M3eeV5zdqFVe2W4Ft4Y/cbJBck08XNMnbEUAm/vQX6WOh6c7PHcFWuf9T8WPyepTD4ojH0rcLb+95meeJyhncaTlfXMP79y3kcfTey8MiT+Hi8wuguo60dotVNv6ET93+6l42Hsxgd0cHa4Sj1uJIWl+ZmNBqZMGFCZ1tbW9PHH398uuY+Nzc3g62t7YX3jo6OpqKiIpuMjAyt0WgUXbt2raze16lTp4qdO3fWOUAyNTXV7qeffvLQ6XRu1dsMBoMYNGhQUfX7Rx99NOezzz7znTVrVqa/v78RIDMzU1tRUSHCw8MbvRBcamqq3cGDB511Ol1UjWsV48aNy21s/DNnzsxLS0uzu+uuu7oUFRVpxo8fn/fuu++esbe3rzPpmjt3rt/nn3/unZ2dbQtQUlKiOXfuXJ25SFJSkp3BYBAdOnSIrN4mpRT+/v6VdZW/FGt9rd4DdBdCdBZC2AFTgNqz0H2PeQAywERgk5RSCiHcgXXAc1LK36sLSynPAkVCiOstT2FNB9Y094W0NRtTNuKkdeJG/Y3Nfq5hQcMA+DX11/9tPLgcCk6bHzVv7Q/L+fSA7iNg90dQVWbtaC7y7Ylv+fTIp9wZeidvDX6LgswbKT7fkyVDPybCJ4Jnf3uWzw5/Zu0wrW5wiC8dPRz5bGeKtUNR2hCTycTkyZODs7OztevWrTtZ34d3bQEBAQaNRiNPnjx5YTDz6dOn6x3zEhgYWDlu3LjcoqKiA9WvsrKyuNdeey0TwGAw8NBDD3UaN25c7meffeaTkJBgD+Dv72+wt7eXR44cuewaMEKIP8UeGBhY1bdv36Ka5ywtLY378ssvTzc2fnt7e7lgwYKzJ0+ePPzbb78d+/nnn93ef/99r7rOu379epdFixb5L1++PDk/P/9AUVHRARcXF2P19BC1y3fp0qXKzs5O5uXlXYizuLg4LikpqdEToVkl2ZFSGoBZwAbgKLBSSnlYCPEPIcRfLMX+A3gJIZKAJ4Dqr9azgG7Ai0KIA5aXr2XfTGApkAScBH5qmStqG0zSxNb0rQzsOBAHbfMPCvZz9iPUM5QdGTvMG4xVsG2+eaxO9+HNfv4m0X8WlOaYB1S3Insy9/DKH6/QP6A/T/d9mjP5ZXyyI4Xx0R3pGxTIh8M/ZHDgYN7Z/w4Zxdd2A6fGRjD1+k7sOpVHYmbR5Q9QFGDq1KlBJ06ccNi4cWOSi4tLgydr0mq1jBgxIv/FF18MKCoqstm3b5/DypUr653V8/7778/95Zdf3L/55htXg8FAaWmpWLt2re7kyZO2AM8991wHgJUrV6bMnDkzc9q0aZ0NBgMajYY77rgj54knnghMSUmxNRgM/PLLL85lZWUXfYv08fExJCcnX0hYJk2alJ+SkuKwePFiz4qKClFRUSG2bt3qtH//fofGxv/DDz/odu/e7WgwGHB3dzdqtVqp0WhkXectKCjQaLVa6e/vX1VVVSXmzJnToaSk5MIgIz8/P0N6erqd0WgEoFOnTlUDBgwoePDBBwPz8vJsjEYjhw8ftl+3bl2jHyO22oAJKeWPUsoeUsquUspXLdteklJ+b/m5XEp5h5Sym5Syn5Qy2bJ9npTSWUoZVeN1zrJvr5Syl6XOWVLNJvYnx/KOkVOWw0D9wBY75w0BN3Ag+wAlVSVwcCXkp7aNVp1qwQPBvzfsXmpemb0VKK0qZc7WOQTqAnnzpjfR2mh5+2fzU2NP3GIehGunseP5655HIFh8YLE1w20VJsUGYqexYdnu05cvrFzzjh8/brds2TKfY8eOOXXo0CHSyckp2snJKXrJkiUNGivy0UcfnS4pKbHp0KFD5L333tt5ypQp9Q7869atW9XKlSuT3njjjQ5eXl5Rer0+Yv78+X4mk0n89ttvTh988IHf559/fkqr1TJv3rxMIQTPP/+8P8CSJUvSwsLCyvr16xfm4eER9eyzz3asThRqevzxx7PWrl3r4erqGnXvvfcGenh4mH766afjX3/9tae/v3+En59f5DPPPNOxvLxcNDb+jIwM20mTJnXV6XTR4eHhvW644YaimTNn5tZ13gkTJhQMHjy4IDw8vHdgYGBvBwcHU80uqenTp+cBeHh4RIWHh4eBOcmrrKwUYWFhvdzd3aMmTpzY9cyZM7Z1R1M/ca3nA7GxsXLv3rY7eVxjfHjwQxbFLWLzpM14O7bM/FK7zu5ixsYZLBr8LoPXPAl2zvDQb20n2QHzmJ11T8IDm0AfY+1o+PLol7yx+w0+H/U5Ub5RHMssZNS7vzHjxs48P/rP01W9tfctPjn8Cav+sooeHtf200izvtrPbydy2PX/bsbBVnP5A5RLEkLsk1LGXunx8fHxKZGRka139L/S5sTHx3tHRkYG17WvlT4KozSH7We2E+4V3mKJDkC0bzQOGgd2HFkGeckw8Mm2legA9L4DbJ1g36eXL9vMqkxVfHr4U/r49iHK1zy28M31ibjYa3lkcLeLyt/f+35c7Fx4d3/beHy+OU3pG0RBWRUbj2RZOxRFUVqYSnauEQUVBcRnx7fIwOSa7DR2xPrHsjNrD7h3grC/XP6g1sbBzTwf0KFVUGHdMR8bUjZwtuQsf+31V8C8LMSvx87x8E1d8XC+eHJXN3s3ZvSewbb0bezJ3NPS4bYq/bt60dHDkRV7VFeWolxrVLJzjdiZsROTNLXoeJ1qAxw7kiKMnImZDjZttPsg5h6oKoGEb6wWgpSSjxM+pqtbVwZ2HIiUkn+tT8TbxZ77BgTXe9xdoXfh5+THe3HvtVywrZCNjWBSbCC/J+WSlldq7XAURWlBKtm5Rvx25jfc7N3o7d27xc/dP3U/ADu82vAcJx37gk+YVbuyfs/4nePnj3Nfr/uwETZsT8ph16k8/ja02yWXhXDQOnB32N3sP7ef04XXdqvGxJiO2AhYubfVTemiKEozUsnONcAkTfx+5nf6d+iPpqVbVnJP0vn4r/hrHNmR1YYHggthbt3J2A9nD1olhI8TPsbPyY9bO9+KlJI3NySid3dkSr/Ayx47qvMoBIJ1yetaINLWK8DdkUE9fPh6bzpG07X9cEYrYDSZTG1sAJ/SWll+l+qduVklO9eAo3lHyS3P5caOLTteB4A/3kdobOnf8SZ2nd2FwdT4BdxajYjJoLGH/S3fupNamMruzN3cFXYXthpbNhzO5GB6AY8P64699vIJrL+zP/38+7E2eS3X+hOYU/oGkllYzrbj2dYO5Vq3PTU11b2iosL2Wv+dVK6OyWQS2dnZbkBCfWWu3SWRryHb07cDMCBgQMueuDQP4r6E3pO4Ifhmvk1dT0JOwoWniNocJ08Iu808bmfE66C9eEBwc/k59WcAbu18K0aTZMHG43T1cWZcdJ1r3dZpdJfRvLTjJQ7lHCLCJ6K5Qm31hob64elsx6p96QwJ9b38AUqzMBgMD+Tn588sKiq6V0rpifryrVw5E5BgMBhm1FdAJTvXgN8zfqenV0+8HOudBLN5HPgSDGVw/cPc4BGEQLAzY2fbTXYAek8yJzsnf4WQUS122o0pG4nwicDf2Z/VcWc4ca6Y9+6KRqtp+OfDsE7DmPfHPNYlr7umkx07rQ1/iQzgq92nKSirws2x0fOTKU0gJiamEnjX8lKUZqUy6XautKqUQ9mHuL7D9S17YpPRPBlfUH/w742bvRuhnqHsy9rXsnE0tW43g6OneTboFpJWlMbRvKPc0ukWDEYT7/xynFB/Hbf2atyAb52djsGBg1mfsp4qU1UzRds2jO+jp9Jg4sdDZ60diqIoLUAlO+1c3Lk4DNJAP/9+LXvipF/gfAr0e+DCpj5+fYjPjqfK2IY/aDW20Gs8JP4I5YUtcsrqLqzhnYbz7f4zpOSW8uQtIdjYNH5s521dbiOvPI+dGTubOsw2pbfejW6+Lny7P93aoSiK0gJUstPO7c7cjVZoW77raPeH4OIPYbdf2NTHtw/lxnKO5B1p2ViaWu9JYCiHY2tb5HQ/p/xML69eeDv48+6vJ4js6MawsCsba3Kj/kbc7N1Ym9wysbdWQgjGRevZk3Ke07lqzh1Fae9UstPO7c3cSy/vXjjZOrXcSXNPmlt2Yu8zt4RY9PHrA8D+rP0tF0tzCOxnng26BbqyzhSfISE3geHBw1mxN40z+WU8cUsI4gqX3LDV2DK803C2pG2h0lh5+QPasbHReoSA7+LOWDsURVGamUp22rGSqhIO5x6mr3/flj3xnqVgo4WYe/+02dvRm2DX4Laf7AgBEZPg1FYoat51ln5J/QWAQfqbeW/TCWI7eTCo+9WtbTZQP5AyQxkHzh1oihDbLL27Izd08eLbuPQrehy/ylTFdye+Y0n8EnLK1HqWitKaqWSnHduXtQ+jNNKvQwuO16ksMT9uHj4GdP4X7e7j14f95/ZjkvXO/dQ29J4E0tTsy0dsTN1ImGcYvx0xkVVYwRPDe1xxq061fv790Aotv2f83kRRtl3jovWk5pay/3R+g4+pTnJu/+52XtrxEu8feJ9R34zizT1vqqRHUVopley0Y3sy92BrY0uUTwuO10n4FioKIPb+OnfH+MVQWFlIUn5Sy8XUHHx6QIdIOPR1s53iXOk5DmYfZEjgzby/5STXdfakf7erX7Hexc6FSN9IdmTsaIIo27ZRvTvgYGvDd3ENG6gspeTJLU/y0o6XcLN3472h7/HD2B8Y3mk4Xxz9gnFrxpFVolZVV5TWRiU77djuzN1E+ETgoHVouZPu+wS8e0Cn/nXu7uPbTsbtgHkl9Iz9kN886039cfYPAPJzupFdVMHfh/dosroHBAzgWN6xa74lwsVey7AwP348lEmV8fKtjWtOrmFz2mZmR89m+ejl3BR4E8Fuwbw28DVW3LaCckM5L+98+ZqfpVpRWhuV7LRThZWFHMs71rKPnGcegjN7zWN16ulq0bvo8XXybfvz7QCE/8X83yPfN0v1f2T8gbu9O6v+MNC/qxfXd2m6SSH7683J6LX+CDrAmCg9eSWVbE+6dOKXWZLJP3f/kz6+fbi/9/0XdSeGeobyWJ/H+O3Mb6xOWt2cISuK0kgq2Wmn9meZx8W06ODkfZ+a146KvLPeIkIIYvxi2J+1v+1/+/XsAv4RcGRNk1ctpWTX2V34aHuRW2xo0lYdgDDPMDwdPNW4HWBQD29cHbT8cCCj3jJSSv5vx/9hlEbmDZiHjaj7T+ddYXcR6xfLv/b8i7PFasJCRWktVLLTTu3O3I2djV3LLQtQWQoHV5gHJjt5XrJojG8M58rOkV7cDiZ0Cx8D6buhoGkfXz5VcIpzZedIPt2Bgd296Rt86XvaWDbChus7XM/OjJ1tf7D4VbLXahjVqwMbDmdSXmWss8x3Sd/xe8bv/D3m7wS61r/KvI2w4R8D/oFRGpm7Y27bT+gVpZ1QyU47tTdzL1G+Udhr7FvmhIe/g4rCix43r0uMXwxAO+nKGmv+79EfmrTa6vE6Bec78/iwpm3VqdY/oD955XkcyzvWLPW3JX+JCqCk0sivR89dtM9gMrD4wGL6+PZhcsjky9YVqAvksT6PsfPszvbxO64o7YBKdtqhosoiEs8nXkgqWsT+T8Gre70Dk2vq4t4FN3s34s7FtUBgzcy7G/j2bPKurN/P7ASDJwM7hxDTyaNJ667WP8D8b3VNPpVlMkLKdvjxaXgngv4bb2eh41IKtr0PRZl/Kro1bSvnSs9xb8976+2+qm189/G42rmyPHF5c0SvKEojqWSnHTqYfRCTNBHtG90yJzx3FNJ2Qcw99Q5MrslG2BDhHcHB7IMtEFwLCB8Dp3de9CF5pQwmA39k7KayqBuPD+veJHXWxcfJhx4ePa69ZCcjDt6Ngk9Gm5N0v54IVz03a/ZzV85CTIuvg2PrLhRflriMDs4dGNRxUINP4ah1ZGy3sfya+ivZpdnNcRWKojSCSnbaobhzcWiEpuXG68R9YZ4x+RIDk2uL8IngZP5JiiuLmzGwFhI+BpBN1pW1L/MQlbKUHm7R9AlqnladagMCBhB3Lo4yQ1mznqfVOLIG/jvK/PPEj+Gpk3DnMpi6iuPT4ril4p/k2wfA8rtg3RySc46x6+wu7uhxBxobTaNONSlkEgZpYNXxVc1wIYqiNIZKdtqhuHNx9PDogbOtc/OfzFAJ8cshZBQ4N3zCuwjvCCSShNyEZgyuhfiGgndIk3VlfbhnAwBzBo5ukvouJcYvBoPJQEJOO/h3uBQpYdt8WDkd/HvDA5vMq9fbu1woEhXkQblHCE/o3oQbZsGej/h67V/R2mgZ3318o0/ZybUTAwIG8PXxr6kyVTXl1SiK0kgq2WlnqkxVHMo5dGHRzWZ3YgOU5kD0tEYd1sunF0D76coKux1Sd0Bp3lVVU1xhYE/mLhxlIDd169xEwdUvytc8u3a7GD91KXFfwKZXoPcdcM8P4OJzUREhBKMjOvBbciHnb5xL6e3vssZUwC22Png5XtkcR1NCp5Bdls3m05uv9goURbkKKtlpZxLzEikzlF34EGt2cV+Aiz90vblRh7naudLFrUv7SXZCbwVphBMbr6qapdsTMdmdYnDQgCYK7NLc7N3o6ta1fSc7WUfgx6eg8yAY9wHY1j+j+OjeHTCaJBsOZ/KjzoUijQ1TTsXB/s+v6NQD9QMJcA5QA5UVxcpUstPOVH9oRfu0wODkokw48TNE3QkabaMP7+3dm0M5h9rHXCQdos1JX+KPV1xFcYWBj/dtQdgYua3HwCYM7tKi/aKJPxffPufbqSiGr+8Bex2MXwqXGXfTM8CVYC8n1h06yzfHv6G7e3eiAm6AdU9A2p5Gn15jo2FSyCT2ZO4htTD1Sq9CUZSrpJKddibuXBx6Fz1+zn7Nf7L45ebWjKipV3R4hE8EeeV57WNyQRsb87ilpF/BUHFFVXy6I4UycRKg5VrmgGjfaIqqitr+4qx1+XEO5JyACR+B7vL/T1R3Ze1MPUlCbgKju4xG3PEJ6DrAN/dDVXmjQ7i1860AbDq9qdHHKorSNFSy045IKYk7F9cyj5xLae7CCrzePNfMFYj0iQTa0bidkFuhshhO/dboQ4vKq/jot2R8fDLp5t4NV2jX/4oAACAASURBVDvXZgiwbtW/L3FZ7awrK3E9xC+Dm56GLoMbfNjo3gEI5yMADAkaYp4R/C8LIT8Vdr7X6DA6uHQgzDNMJTuKYkUq2WlH0ovSySnLaZlkJ2035J6A6Ctr1QHo6t4VR60jh3IONWFgVtR5ENg6Q+K6y5et5bOdqeSXVmCwPXUhCWwpHV064uPow/5z7WAl+mpGA/z8Inh2hYFzGnVoWAcdOs9E7KQfXdy6mDd2GQyht8Fvb0Fh/Wto1Wdo0FDis+Ov+VXmFcVarJbsCCFGCiEShRBJQohn69hvL4RYYdm/SwgRbNnuJYTYLIQoFkK8V+uYLZY6D1hevi1zNa1DXLb5m3mLdIHEfwW2TtBz7BVXobXR0tOrZ/tp2bF1gG5DIfEnc8tXA1W36twQaqTUUNxyk0FaCCGI8o3iwLkDLXreZrX/U8g5DsP/AVq7Rh1aXFWM0S6J4rxQcoprdEmOeBVMBvjl/xodztCgoUgkW9K2NPpYRVGunlWSHSGEBlgMjALCgTuFEOG1it0PnJdSdgPeBv5p2V4OvAjU93XtbilllOV18UI37dj+rP3obHV0c7+ybqUGqyqDhO/Mj1vb666qqgifCI7mHaXCeGXjXFqdkNFQdNY8S28DmVt1qugXWgi07Hidan18+5BRkkFmSdPMAm1V5YWw+TUI6g+hjZ+raPuZ7ZgwUFUUzvqEGvfDIxj6/8284G3a7kbV2d29Ox1dOqquLEWxEmu17PQDkqSUyVLKSmA5MKZWmTHAp5afVwE3CyGElLJESrkdc9Kj1HDg3AEifSMbvH7PFUv8ESoKGjVjcn0ivCMwmAwczT3aBIG1At1vAWHT4Keyisqr+HBbMkNDfckxJOLp4EmQLqiZg7xYdWtSu2jd+f0d89xPI+Y1aPmS2jad3oSngyfBLqGsO3j2zzsHPgG6AFj/bKNa74QQDA0ayh9n/6CkqqTRMSmKcnWslezogbQa79Mt2+osI6U0AAVAQ2b2+tjShfWiEHX/pRNCPCiE2CuE2Jud3T7WrSmoKOBkwcmW6QKJXw6uevMYlavU26c3QPsZt+PsBUE3wLGGJTuf7kihoKyKx4d1NyerPpHU82vbrEI8Q3DUOrb9cTsFZ2DnYvPkgfrGL4RbZaxi+5ntDA4czOjeenadyiW3ZleWnbN5wPOZfXBqW6PqHho0lCqTuX5FUVqWtZKduv6a1/6a1JAytd0t5f9n77zDozqv/P95RzPqQr0hCVDXqCK6KcYYDLjgEncndpL1b51kk91ks5s42Wyyu9lNNm2TbDbVJXESO+5xxxgMtjFgOupCBSEhhNqMepdm3t8fV4MlUB3dOzOC+3kenhG3nPeAQPfc93zPOTIH2DD6a8K2vlLKx6SUK6SUKyIjL++kOh9xtPvXXNza3ayUV+feO23PkpkQ5R9FTEDMlaPbAUjbDi2l0FE/5WVdA8M8/uFZtpijiAu3ca77nFtSWKDop3Ijc+d/c8HDvwbbMFz/r07dfqzpGD3DPVyfcD3bs2OwS9hd1jz+orz7ISBK2UGaBUsjlxLqE6qnsnR03IC7gp3zQMKY38cDl5Y4XLxGCGEEgoEpe/FLKRtGP7uBv6Cky64KClsLEQiyI7K1Xaj4hdHeOg+oZjInIodSa6lq9txO2jblc5puyn88qOzqfHlzGgWtSvrI1eLkseRH5VPZXjl/0ywDnXDij4poPnSJUyb21e/Dz+jH6tjVZMYuYHG4P2+XXKJjMvnCms/DmX3QOPMg3cvgxXUJ1/Hh+Q8ZtumzsnR0XIm7gp1jQKoQIlEI4Q3cB7x+yTWvA58e/fouYJ+cotWuEMIohIgY/doE3AJc4dMNP6aotYiU0BRth39KCQXPQtwKiEhVzWxmeCb13fV0DnaqZtOtRKRByGKlu/QkdA0M88SBs2wxR5MTH0xhSyEmg4nM8Et1+q4jNyIXu7RTZi1zmw9z4uSfYKhbGeLpBFJKPjj/AWsXrsXX6IsQghuzYzlUbaGjb2j8xSseBu8gOPi/s1pjU8Imuoe75/8Omo7OPMMtwc6oBudLwDtAOfCClLJUCPFdIcSto5c9CYQLIaqBrwIXy9OFELXAT4HPCCHOj1Zy+QDvCCGKgAKgAXjcVX8md2KXdopai7RPYTUVK+mZpXMXJo/FsRt1xezuCKEIlc9+MGnH3acOfqzVAaXzdWZ4Jj5ePq70dByO78O8nIBuG4bDv4ElGyDOuSG49d31NPU2sXbh2ovHbsyOYcQu2XNpKssvBFZ8BkpfgfbaGa+xMmYlXsKLw42HnfJRR0fHOdzWZ0dKuVNKmSalTJZSfm/02HeklK+Pfj0gpbxbSpkipVwlpawZc+8SKWWYlDJQShkvpSwbrdJaLqXMlVJmSSm/LKW0uevP50pqO2vpHu4mNyJX24UKnwODCbI+oapZc5gZYP7uKExE2jYY7oPay8Wonf1KX52tmdFkxwUzZBui1FrK0kj36HUchPqGEhcYNz+DndJXoavB6V0dgCNNRwAlIHGQGx9MXIjf+BJ0B2v+Tqm8++hXM14j0DuQrIgsjjbNrnRdR0dnbugdlK8AClsLAciL0nBnxzYCxS8qD3H/MFVNB/sEsyhoEaWWK2RnB2DJejD6Tajb+f2Bs3QPjPCVLWmAEuQN24fdJk4eS1Z41vwLdqSEQ79Q0oepW502c6zxGFF+USxZsOTiMSWVFcOHVRa6Bi7R2SxYCLn3KGNTBrpmvM7qmNWUWErmrzZKR2ceMu2oaiHEd2Zp830p5exqMnXmRGFrIUHeQeN+SKtOzfvQ2wJ592liPisi68rSMZj8lNL8qndA/vBiv5fOvmF+f+AsN2bHkLlQmX/lKLvPjdR4Z24G5ETksLtuN20DbYT5qhvUakbdQWgqgh3/qwxkdQIpJUebjrJm4ZrLSv9vzInhiQNn2Vfewu35l3TIWPEwFDwDJS/Bir+Z0VqrY1fzePHjnGg+wbXxc2/foKOjMz0z+ckgZvlLx8UUWYrIjczVtplg0XPgGzKnN+epyArPoqm36cqaHZS2VdFzWKouHnriQA3dgyN8ecvHAu8SSwlRflFE+bt/uklWRBYwz3Q7J54C32ClHYKT1HTWYB2wsjpm9WXn8hNCiV7gw87ixstvjFsG0dlKFdgMyYvMw9vgzZHGI077q6OjMzum3dmRUv6HKxzRcY7e4V6q26u5YdEN2i0y2A3lbyrCZKM2AtqscOUhW2Ytu3LedlO3Af+kpLIi02jvHeL3B85yc04sGTEfTzUvtZZeDDLcTWZ4JgJBqaV0fnwf+tuh7HVY9pCym+YkjsBjrF7HgcEg2J4Vw/PH6+kbGsHfe8yPTSFg2afh7a9BYyHETp9K9jX6sjRqqa7b0dFxIbpmZ55TbClGIrVNgZS/ASP9kKtNCgvGP2SvGEISICpTSWUBj31YQ9+wbdyuTtdQF3VddeRE5LjLy3EEmAJICk6aPx2ti14E26AS7MyBY03HiAuMIz4ofsLz27JjGBi280HFBB3Xc+8Go++sdndWx67mdNtpOgY6nHVZR0dnFsw42BFCRAshHhRC/EQI8cTo54NCiBgtHdSZGkfnYcfYBU0ofA5CEyFBux6N/iZ/koKTrpzycwepN0DdIaxWC08drGVH7kLSoj8enuoI7jxlZweUEvRSaylTtLXyDKRUeuvE5kGs88G+Xdo51nyMVTGT//tetSSMsABvdpVOUJXlFwqZtykC/qGZiY4da+m7Ozo6rmHaYEcIYRZCvASUoYxfMAFNo58PAqVCiJcmmFqu4wKKWotICk5igfeC6S92hs4GZQZQ7r1ODVWcDVkRWfPjITsbUm4A+wh7d77E4Mj4XR34WBvjSON5AtkR2bQNtNHYO4FGxZNoLIDm4jnv6lS2V9I52DlhCsuB0cvADeZo9pW3MDgyQUeLZZ+GwS4oe21Ga2ZFZOFv9NeDHR0dFzGTnZ2nUKaSL5RSbh3tX/Ovo59bgVjgeZQmgDouREqpfTPBkpcAqZTYakxWeBaWfgvNfc3TXzxfSFiN3TsQe9Ue7siPJzkycNzpEksJixcsJtgn2E0OXo6juaDHp7JO/llJH2XfNSczDr3OVDs7ANuzY+geHOHQGevlJxevhfCUGaeyTAYTK2JW6CJlHR0XMW2wI6VcLaV8SUo5KIS4bPKjlHJISvmilPIabVzUmYz67nraB9u1TWEVvQDxKyE8Wbs1RnGkcq6oVJbRmwq/ZawXBXz5+pTLTpdYSzxqVwcgLTQNk8Hk2fqpoT4lbZR5m9LNeA4cbTrKkgVLiA6InvK6tSnhBPkYeWeiBoNCQP6DUH8YrGdmtO6qmFXUdtXS3HsFBfc6Oh7KbAXKu4QQgdNfpuMKiiyKXkezzslNJdBcMqeS3tmQHpqOURg9+yE7Sxo6+vlLWxrxwsIiZU7tRVr6Wmjpa9F+eOss8fbyJj00nRKrB5efl7+hpI3mmMKy2W2cbD45ZQrLgY/Ri+vNUewua2bEZr/8gpzRHaaSv85obcdO0rHmYzP2V0dHxzlmG+wUAAeFEAsdB4QQ1wohPlTXLZ2ZUGIpwc/oR3KIRrsuxS+AwQhZd2hj/xJ8jb6khKZcUTs7v9xXxYf20WC0+t1x5xx6HU+pxBpLVkQWpZZSbHYPnbhS/CIEL4JFa6e/dgqqO6rpGe5hWfTM5mltz4qhrXeIY7Xtl58Mjlf8KX5REU9PQ1poGv5GfwpaCmbrto6OziyZVbAjpfwa8BuUgOc+IcQe4AXgVS2c05ma4tZiMsMzMRqmbZc0e+x2paw3ZQsERKhvfxIywzMpt5ZfESLlWksvLxw/z8ZVy5VRBtXjp6CXWErwEl6kh6W7ycPJyY7Ipm+kj9quWne7cjm9Vqh5D7I/4XTHZAeOUSsznUu2MT0SH6OBdyaqygLIuRMsFcqO6DR4GbzIjczVgx0dHRfgzE+KQ0AX8AxQDyRKKf9HVa90pmXINkR5W7l2Kay6A9B9wSXC5LGYw8y0D7bT1DvJw2Qe8fN3KzF5Cb54fYpSlVV7UNGajFJqLSUlJAU/o/PN8LQiM1wprixvK3ezJxNQ9irYRz5OG82BUy2niPCLIC4wbvqLAX9vIxvTItlV0oTdPkFAnnmHshta/NKM7OVH5VPVUUXPUM9s3NbR0Zklswp2hBB/Bd4HXgY+AWwDrlffLZ3pqGirYNg+rJ04ueh58A6EtBu1sT8JjofsfJ+AXtHUzWuFF/j02iVEBflCymal+V3dQUCppCuxlHicXsdBUnASPl4+lFs9MNgpeRki0pUxDXOkoKWApZFLL5uHNRXbs2No6hqgqKHz8pMB4ZC0SdHt2CfQ9VzC0qil2KX9Yr8sHR0dbZjtzk4VkCKl/K6U8jVgO/BLIcQX1XdNZyoc4mRN9B7D/UoLfvOt4O2vvv0pSAtNw0t4zXvdzk/3VBDobeTz147qqRavU6agj+p26rvr6Rrq8thgx2gwkhaa5nk7O53noe6Qsqszx75Pln4L53vOz3ra/OaMaIwGMUUq6y7oPAfnp++hkxeZh0EYONV6BQ3B1dHxQGar2XlUStk25vfFwHrgb9V2TGdqii3FRPlFEROgQQPryl1KpYuLU1igiJSTQpIoa5u/OztF5zt4p7SZhzckEhrgrRw0+cKS9VCl6HYcwZynBjugpBTLreXY5fQ7FC6j5K+AhOw752yqsEXR68y2T1Wwv4lrksN5p6RpYm1Zxs1K/58ZpLICTAGkhabpuh0dHY2Z82wsKWUDsEEFX3RmQXFrsYYprBcgMAYS3TMIMjNsfouUf/xOBaH+Jh5enzj+RMoWaDsDbWcptZTibfDWrpJOBczhZnqGe2jobpj+YldR8hIszFel71NBawEmg+li6nQ2bMuKocbSS3XLBFobnyBI2w6lr4BtZFpbeZF5FLUWMWKf/lodHR3nmMm4iH8QQkw36npICPEPKvmkMw0dAx2c6z6nTQqrr03Zfci5CwyX9ZB0CZnhmbQNtM3LTsqHzlj4sMrCFzelEORrGn8yZbPyeWYv5W3lF5v3eSrmcDOA5+yyWaqVyeJz7JjsoKClgKzwLLy9vGd979bMaISAXRM1GARl56nPAucOTWsrPyqfvpE+qtqrZu2Hjo7OzJjJzk4MUC2E+J0Q4gEhxHIhRNro5/1CiN+haHmitHVVx4Gjjb8mk85LXwH7sMsaCU7EfBUpSyn50a4KYoN9+dSaxZdfEJ4CwYuQVXspt5Y7taPgSlJDUjEKo+eIlEv/Cgil5HyODNmGKLWWzlqv4yBqgS/LFoXyTtkkwU7KZkWjVf7GtLbyo/IBpTJMR0dHG2YyLuJfgHyUgOZvgJ1AMfAW8FngNJAvpfxXDf3UGUOxpRiB0OZhWfQCRJohxn2N7tLD0jEIw7wLdnaXNVNQ38FXtqTia5pgV0wISLme+vqDdA93e3yw4+3lTUpoiueIlMteh4TVsGDh9NdOZ8paxrB9eMb9dSZiW1Y0JQ1d1Lf1XX7SO0AJeMrfnLYqKzYglij/KF23o6OjITPS7EgpLVLKnwDXAVbgFeAXwH8Dv5BSTjAZT0criixFJIckE2AKUNdwe60y2yf3bs0nnE+Fn9GPpOAkz3nIzgCbXfKTdypIigzgzmXxk1+YvJkywzCAxwc78LFI2e36qbYaZcJ55q2qmHM0E8yLcn6I7rYspThg0qos861Kr6qGE1PaEUKQH5WvV2Tp6GjIbAXKUcAXgAPAYuDnQK0QYvrBMjqq4OjPokkKq/hF5TPnbvVtz5LM8Mx5tbPzyqkGqlp6+Oet6Ri9pvhvlbSRMh8fTBhICbl8MKinYQ5Xmjy6XT9V9vqoQztUMVfQUkB8YDwRfs53B18cHkBGTNDkwU7aNqXBYPnr09paGrmUpt6mK6KZpo6OJzLbYCcfKJdS/lJK+TkpZR7wOeA5IcTsVX46s+Zc9zk6BzvVFydLqaSwFq+DkEXq2nYCc5gZS7+Flr4Wd7syLQPDNn62p5Lc+GBuzJ6mFYBvMGVB4aTZBSYvzxUnOzCHjYqU3R14lr8BsUtV+bcppaSgtcBpvc5YtmfHcLyundbuwctP+oVA4kbF92l2xhy6HT2VpaOjDbMNdn6MspPTLIR4VwjxcyAW6EZJcelojEOcrHqw01gAlkq39NaZiPkkUv7zR3U0dPTzje0Z03bilVJSZoTMnk5lxpOH49BPuTWl2NkADcdVS2E19jZi6bfMur/ORGzPjkFKeLd8kp0v8w5oPwvNUzfJTAtLw8fL52KzUB0dHXWZbVPBZUAgcC3wW6ATuAlYBOwUQlQKIWY2FEbHKYpbi/Ez+qmfAil6Aby8IfM2de06SUZYBgLhOZVAk9DZN8wv36tmY1oka1OmT4mc7zlPt32IzKFBZZilh3NRP+XO78PpN5VPszrBzsXu4yr0qUqPDmJJuP/kJegZNwNi2qosk8GEOcxMcWvxnH3S0dG5nNnOxvo+cC9gAl6VUv4b8BBK0HM78ABKlZaORhRbiskKz8JLzR44thGl22vaNvALVc/uHPA3+ZMYnOjxOzu//qCaroFhvnFjxoyud/x5zPjCmX1auqYaDpGy2yh7XakQjEhVxVxJawneBm/SQtLmbEsIwbasGA6dsdDZP3z5BYFRsOiaGZWg50TmUN5WzrBtAjs6OjpzYrZpLF+UcvM9QK8Q4gzK5PM6YKeU8riU8g8q+6gzypBtiNNtp9XvnFzzPvS2uLW3zkSYw80eHexc6OjnDwdruSM/DnPsghndU2Ytw2gwkpqwXgl23F3lNAPM4WZa+luw9Ftcv3hPq9KYT6UUFigvDBnhGappprZlxzBsk7x3ehJ9mXkHtJSC9cyUdnIjcxm0DVLZXqmKXzo6Oh8z2zTWV6WUW6WUscBC4D5gq5TyOik9aYDOlcnpttMM24fJjVC5EqvoefANgdSt6tqdI5lhme57yM6An+6pBAlfvWHmOwRl1jJSQ1LxTrkBuhuhxXODOQcZYcqulVt2dyreAmlXrQprxD5CeVu5qv+HlsaHEL3AZ4pU1k3KZ8XbU9px+KTrdnR01Mfp2VhSSquU8piU8riaDulMjibi5MEeRRORdQcYp5sK4lo8WaRceqGTl0+e5zPrlhAfOrPJ8FJKyqxlyp8r+XrlYPVeDb1UB0ewc7rttOsXP/0WhC6BaHUGpp7pOEP/SL+qA1gNBiWV9UFlK/1DtssvCF0CUVnKgN0piA2IJdw3XNft6OhogHG6C4QQ35mlzfellPud9EdnCopai4jyiyI6IFo9o6ffhOE+yLtPPZsq4XjIllnLuDbePUNJJ0JKyfd3lhPsZ+KLm2YuFG/oaaBrqEsJdoLjIDJDSWWt8+yxckHeQcQHxru+ImuwB2o+gJX/T7Uml1pVM27LiuFPH9Wxv6r1YrPBcaRvhwM/V2bP+YdNaEMIQU5kzkUfdXR01GMmOztilr90NKLYosGk88LnlN4lCavVtasCgd6BLFmwxOMqst6vaOVgtZUvb04l2G/mug9HsJAVnqUcSN4MdYdgaIJxAx6GOdzs+p2dM3vBNgjpN6pmssRSQrBPMAlBCarZBFiVGEaIv4l3Jktlpd8E0gbV705pJzcil9quWjoHO1X1T0fnamfanR0p5X9osbAQYjvwv4AX8ISU8geXnPcB/gQsRxlRca+UslYIEQ68BKwEnpJSfmnMPcuBpwA/lBleX5Zu73OvDu0D7dR313Nn6p3qGe1qhLMfwIZ/cut4iKkwh5k9qo3+iM3O93eWkxgRwCdXTzDscwrKrGUYhZHU0NGqouTr4fCvFAFuyhYNvFWPjLAM9tTtoXuomyDvINcsenqnUh246BrVTBZZisiOyJ62H9JsMXkZ2GKOZndpE0MjdryNl7xHLlwGAVFQsXPKXlaOl5kSSwnr4tap6qOOztWM05qduSCE8AJ+BdwIZAL3CyEuHRT0MNAupUwBfgb8cPT4APBt4J8nMP0b4BEgdfTXdvW9dw+aTDoveVkRf3pYFdZYMsMzaeptom2gzd2uAPD88XqqWnp4dHvG5Q+0aSizlpESmoK312iz8cVrwcsHqj2/BN2RUqxoq3DNgrYRqHoHUreB17TvZDOib7iPMx1n1G/IOcr2rBi6Bkb4qGaCZpEGg5LKqnoXRoYmtZEdno1A6CJlHR2VcUuwA6wCqqWUNVLKIeA54NJudrcBfxz9+iVgsxBCSCl7pZQHUIKeiwghYoEFUsqPRndz/oTS++eKoMRSgkEYPk6BqEHRc8obp0r9S7TAIVL2hFRW18AwP9tTyaolYWzLmp1uSkpJubV8/PBPb38l4Dnj+SJlx9gIl6Wy6g9Df/vHlUwqUGYtwy7tmgU761MjCPD2YldJ48QXpN8EQ91Qd2BSG4HegSQFJ+kiZR0dlXFXsBOH0p/HwfnRYxNeI6UcQWlcGD6NzfPT2ARACPGIEOK4EOJ4a2vrLF13D45J5/6mmVX+TEtTCTQVQ9796tjTiIzwj0XK7uaX+6qx9g7x7VsyZ50Gaepton2w/WLQcJHk66H1tDISwYOJ9I8k3DfcdSLl0zuVjt6OqjUVcOyOqlmJNRZfkxfXm6PZXdqMzT5B9jxxIxj9pi1Bd4iUr5AMvI6OR+CuYGeiJ8Wl/7Nnco1T10spH5NSrpBSroiMjJzCpGdwcdK5mv11ip5TJjJnq6gB0oAF3gtICEpw72wmoNbSyx8OnuWuZfHkxAfP+v6yNiVYG7ezA5CyWfmcB92UM8IzXLOzI6XSXydxI/iopw8qthQTFxhHmO/E1VBqsD0rBmvvEMdqJ0i7evtD8iao2DVlM8mciBw6Bjs4331+0mt0dHRmh7uCnfPA2HKIeODCZNcIIYxAMDCVcOP8qJ2pbM5LVJ90bhtRZmGlboOAqTbLPIPM8Ey37+x8b2c53l4GvrYt3an7y6xleAkv0kIvaUAYlQmBMfMmlVXTUcOQbXLNiSq0lEN7raopLFBSwVqlsBxclx6Jj9EweYPBtO3QeQ6aSya14dDl6bodHR31cFewcwxIFUIkCiG8UToxv37JNa8Dnx79+i5g31SVVVLKRqBbCLFGKDmGh4DX1Hfd9RS1Kj/0VBMnn30fepohz3OFyWMxh5lp6GmgY6DDLesfrLawp6yZv9uUQtQCX6dslFvLSQpJwtd4yf1CKKmamvfBPkFDOg8iIyyDETlCVUeVtgtV7FQ+09QrObf0W2jsbdQsheUgwMfIxrRIdpU0YZ8olZW2TfmsfGdSGykhKfh6+VJimTwg0tHRmR1uCXZGNThfAt4ByoEXpJSlQojvCiEcQ3CeBMKFENXAV4FvOO4XQtQCPwU+I4Q4P6aS6wvAE0A1cAaYOjk+TyhsLSTAFEBScJJKBp8H32DlLXMecFGk7IZU1ojNznffKCMhzI+H1yc6ZeNi5+SwSwsOR0nZrIhxLxTMwVPtuShStmqcyqp4WxHOL4hVzaQjcNB6Zwdge3YMTV0DFJyfIDgPioGF+VMGO0aDkczwTL25oI6OirhrZwcp5U4pZZqUMllK+b3RY9+RUr4++vWAlPJuKWWKlHKVlLJmzL1LpJRhUspAKWW8lLJs9PhxKWX2qM0vXSk9dopald4gqkw6H+xWJjBn3+lx4yEmw51jI/58uI6K5m6+dZMZX5Nzf/+t/a1YB6yYw80TX5B0HSA8PpUVHxRPgClA26CzpwUaTqjaSBA+rmZ0lNBryWZzNCYvMXkqK3UbnD8GvROUqI+SHZFNubWcYbs+AV1HRw3cFuzozIy+4T4q2yvJi8xTx2DZ6zDS7/FVWGMJ9gkmLjDO5cFOa/cgP91dyYbUiIlHAMwQh9+Ttg0IiICFS6ftrutuDMJAemi6tiLlyncAqfquY4m1RN1qxikI9jOxNjmCt0saJ66oStsGSKjeM6mNnIgchuxDVLVrnDLU0blK0IMdD6fMWoZN2tQLdgqfhbAkiF+pjj0X4Q6R8o92nWZgxMa/zNm5MwAAIABJREFU35o1p467ZdYyDMJwuTh5LClblLf9/nan13EF5nAzle2V2LTSF1XuggXxEKNeuklKSamllOxwbfU6Y7kxO4b6tn5KL3RdfjJ2KQRGTzkY1KEt0nU7OjrqoAc7Hk5hayGgktagvRZqP4S8Bzx2PMRkZIZncr7nvMtmBp08186LJ87zN+sTSY4MnJOtcms5iQsSp95VSN6sdLOu+WBOa2lNRlgG/SP91HXXqW98eEApwU/bpuq/z4aeBjoGOzQXJ49la1YMXgbBzuIJGgwaDJC6VemcbZs4TRUXGEeoT6ge7OjoqIQe7Hg4Ra1FLApaRKhv6NyNFT4HCI+ccD4djhSQK3Z3bHbJv71WSlSQD39//dy7S5dZyybX6ziIXwk+wR6v23GIlDXpaF37IQz3aaLXAciKULH7+DSEBXhzTVI4O4unSGUNdsK5wxPeL4QgKyJLFynr6KiEHux4MFJKiixF6qSw7HYo+AskbYQQdSc+uwKHSLnUWqr5Ws8cqaO4oZNv3Wwm0Gduc5ks/RZa+lsubyZ4KV5GSLoWqvdO2XDO3SSFJOFt8NYm2Kl4G0wBsGSDqmZLLCWYDCbSQqZII2rATTmx1Fr7KGucIJWVdJ3SIXqKVFZORA5nOs7QO9yrmY86OlcLerDjwTT2NmLpt6jTX+fcIeiog6WfnLstNxDsE0xCUILmOzst3QP8eFcF61MiuDVv4ZztOfy9bEzERKRsga4GZXyEh2IymEgLTVO/IktKRZycvAlMzvUymowSawnmMDMmL5OqdqdjW1b05KksnyBYsn7KEvTsiGwk0u0NNXV0rgT0YMeDceh1VAl2Tj0D3kGQccvcbbmJrPAsSi3a7ux8761yBkfsfPe2uYmSHZRZyxCImZU8J4+Ojqj28FRWuJlya7m6s5uaiqHrvOpVWDa7jTJrmUtTWA7CA31YkxTGzuKmSVJZ28FaBdYzE96vi5R1dNRDD3Y8mKLWIny9fEkNnaNuZLAHyl6D7DuU+TzzlKzwLC70XqBtYKqpIc5zoMrCawUX+Px1ySTNUZTsoNRaypLgJQR6z8BeSAJEpHt8Cbo53Ez3cDfne1Sc3VS5CxAfdxhWibOdZ+kf6XepOHksN+XEctbSy+mm7stPpm5VPqt2T3hvmG8YcYFxum5HR0cF9GDHgylqLSIrIguTYY7b72WvwXAvLP2UOo65CcfbuRa7OwPDNr7zWgmLw/35u+uSVbNbZimbvL/ORKRshrpDMNSnmg9q4+gErapup+JtiFsOgVHq2URJYQEuLTsfy7asGAyCiVNZYYlKcDtFKisnIkff2dHRUQE92PFQBm2DlLWVqZPCKngGwpIhYdXcbbkRc5gZgdBEpPyr96qpsfTyX7dnO90p+VJa+lpo6W+ZfbBjG4S6g6r4oAUpoSkYhVE93U5XI1w4Cenqjy8psZQQYApgSfAS1W3PhIhAH1YnhvPWpFVZW6H2gNLZfAKyI7Ivavd0dHScRw92PJRyazkj9hHyIuZYiWU9ozw48z8573rrXEqgdyBLgpeoHuycburiN++f4RPL4tiQGqma3Yudk2ejF1m8Dox+UDV5d1134+PlQ3JIsno7O1WjOxvp6k45ByXYyQzPxCDc96PuptxYalonSWWlbQf7MJx5b8J7Hf219N0dHZ25oQc7HkpBizIUMi9qjsHOqT+D8FIaCV4BZIVnUWZRrzrFZpc8+nIxwX4mvn3zNOXhs8SpeUwmP0i8VgkAPLgEPTM8k/I2lUTKFbsgeBFEqfv3P2QboqK9wm0pLAc3ZisNBt8sunD5yYTVSn+lqolTWeZwM17Ci6LWIo291NG5stGDHQ/lZMtJEoISiPCLcN6IbUTprZO6VdUJ0u4kKzyLlv4WWvpaVLH3x0O1FNZ38J0dmYQGeKti00GptZTkkGT8jH6zuzH1BqXb9SRVOp6AOdxM20AbzX3NczM03A817yspLJV3HivbKxmxj7ilEmssEYE+rE0O543CCVJZXiYldVm5W+mFdQl+Rj9SQlL0nR0dnTmiBzseiJSSwtZC8qPy52aoajf0NMOyB9VxzANwPLjU6D1S39bHT3ZXsCk9UpWeOmORUumPMiu9joOULcrnFIMi3Y1qnZRrPlAG06pccg5crGLKjVBB9zZHduQu5FxbH8UNE4w7SdsOvS3QWDDhvTmRikjZLi8PhnR0dGaGHux4IHVddbQNtM092Dn5J2XgoKPE9QogPTQdgzDM+U3Xbpd8/aUiDELwX3fkqNJTZyxNvU20DbQ5F+yEJUJE2qQlyZ5AWmgaBmGYu0i5YqfS/2nJenUcG0NxazERfhHEBDg/sV4ttmXFYPISvFE4QSorZQsgJq3Kyo3IpXu4m9quWk191NG5ktGDHQ/kVMspgLkFO91NysMy735lq/wKwd/kT1Jw0pxFys8cqeOjGiv/erOZuJBZpplmgKPk2algB5QAtfYADHnmqAB/kz+JCxLntsNmtysP+JTrweijnnOjFFuKyY7IVj2QdYZgfxMb0yJ5s6gRu/2SVFZAuFIpOYlux1GRqet2dHScRw92PJBTLacI9gkmMTjReSMFfwFpg2UPqeeYh5AdkU2ppdRpcWx9Wx///fZpNqRGcO9KbeaElVpKMRqMpIelO2cgZQvYhuDsh+o6piKOTspO01gAPU2Qpu7gT4DOwU5qu2ovVjN5ArfkLqSxc4CT59ovP5m6FS6cUl5SLiExOJFAUyDFrXpzQR0dZ9GDHQ/kVMsplkYudb5c1m5XqrAWr4Nw9RrkeQrZ4dm0D7bT0NMw63vtdsnXXirEIAQ/uDNXs7f+UmspqSGpeHs5KXpevFYZiunBqSxzmJmW/hbne8BU7gJh0CTN6tj586RgZ0tmND5Gw8SpLIdmaYLvt0EY9AnoOjpzRA92PIz2gXZqu2pZGrXUeSNnP4C2Glj+GdX88iQc2/rO/PB/6lAth2vaNEtfgSJOLrWWzq0KyOijTMau2uOxJejmcEWk7HQqq2InxK9S0jgq49gFcXcl1lgCfYxsNkfxVnEjI7ZLxMbRWbAgXinDn4DciFwq2yvpH+l3gac6OlceerDjYTj668xJr3PiD+AXBuZbVfLKs0gNTcXXy3fWGobK5m5+sOs0mzOiNEtfAdR319M91O28XsdB6g3QeQ4sleo4pjJz6mjdcU4Z/pmhfiNBUHocJQYnssB7gSb2nWVH7kIsPUN8VGMdf0IISL8RzuxTyvEvITcyF5u0qTuiQ0fnKkIPdjyMU62nMBlMzg8u7G6C02/B0gfA5Kuucx6C0WAkMzxzVsHO4IiNrzxXQJCPUdP0FXycQlEl2IHRIZmeR6B3IInBic7NKqt4W/nMuEVdp1B21ootxR6VwnKwKSOKIB8jr56aIJWVvl0pwz+7/7JTjj+LnsrS0XEOPdjxME41nyIzPBMfLyerU079GewjsPyz6jrmYeRF5lHeVs6QbWhG1/90TyVljV384M5cIoPUr/wZS4mlBG+DNymhKXMzFBwP0TmTpjY8geyIbEosJbMXi59+UxmCqYGmrLG3EeuA1SODHV+TFzflxLKrpJH+Idv4k0s2gHfgx4HgGML9wokLjNMrsnR0nEQPdjyIQdsgpdZS51NYdhuc+KMybiBijg9aDycnModh+zCn205Pe+1HZ6w8tr+G+1YmcENmtOa+FbUWkRmeOfdp9aCkNuoPQ1/b3G1pQHZENtYBK029l1cRTUp/O9Qe1CyF5dj98MRgB+D2/Dh6h2zsKb+k+7TRB5KvV3byJggecyJyKLLowY6OjjPowY4HUWYtY9g+7HywU70XOuthxd+o65gH4uiKO92brrVnkK88f4rE8AC+fYu6s5cmYtg2TJlVpWn1oKQ2pN1jq7Icc6ccfYVmRNUepS1C+s2a+FTcWoy3wZu00DRN7M+V1YlhxAb78uqpCaoJ02+E7sYJuynnRubS1NtEa1+rC7zU0bmy0IMdD+J403FgDuLk47+HgCjNHiKeRHRANNH+0VO+6Uop+ecXC2nvHeb/HsgnwMeouV8V7RUM2YfUC3Zi8yEwZsLUhieQHpaO0WCcnZbk9FtKZ++45Zr4VGwpJiM8A5OHNtM0GAS3LY3jg8pWrD2D40+mbgXEhKlLx06VvrujozN79GDHgzjWdIzU0FRCfUNnf3N7ndKBddmDYFR3oKWnkhuZO+XOzpMHzvJeRSvfutlM1sJgl/hU2FoIKJoiVTAYIG2bsms3MjN9kivx9vImPTR95iLlkUGoflfZwTCo/+NnxD5CeVu5R8zDmoo78uOw2SVvFjWOPxEQoUxCr9h52T3mcLMSWOrNBXV0Zo0e7HgIw7ZhCloLWBm90jkDx54AxFWRwnKQG5FLQ08D1n7rZecK6zv44a7T3JAZzUPXLHaZT4WthUT5R6k7jyn9JhjqhroD6tlUkeyIbEqtpTMbVHl2Pwz1aLb7eKbjDP0j/c5XM7qI9JggzLELeGXCVNZ2aCqCzvHnfLx8MIeZKWideGCojo7O5OjBjodQai2lf6SfVTGrZn/zUJ8y9NN8i1LBc5WQEzlxOW577xB/98xJooJ8+fFd2paZX0pRa5F6uzoOkjaC0c9jq7KyI7LpHe6ltrN2+otPv6V0hk68VhNfHH2qVEsjasgd+QspqO/grOWS+WeO8RmVl6cul0YtpcRSwrBt2AUe6uhcOejBjodwtOkoAMujndAxFL8AAx2w6nMqe+XZZIZn4iW8xqWybHbJl58voLV7kF9/chkh/q5L6Vn6LTT0NKifQjH5Kd2UK972yG7KMxYp2+1KeiZls2Y9oApaC4jwiyA+0POD/tuWxmEQ8PKJ8+NPRKZDWDKUv3nZPflR+QzaBilrm8MAVh2dqxA92PEQjjUdIy00jRDfkNndKCUceQyis5V5SlcRfkY/0kLTxgU7v9hbxf7KVv7t1kzyEmb5dzlHHFqKvCiVd3ZA0bh0noMWz3vIJQYn4m/0n15LUn8Eepoh8zbNfHHMlfOESefTEb3Al2vTInnpxHlsYyehC6Hs0tZ+qJTpj8FRvODYwdLR0ZkZerDjAQzbhiloKWBljBN6nbqD0FIKqz+n/JC8ysiNzKXEWoLNbmPf6WZ+sa+KTyyL44FVi1zuS2FrIUZhxBxmVt+4Y1Dk6bfUtz1HvAxeZIZnTj82ovx18PLWZPAnQGtfKw09DXObK+di7lmRQFPXAAeqLxmmar5VaQ5aOb7lgGPX6lTLKRd6qaMz/3FbsCOE2C6EqBBCVAshvjHBeR8hxPOj548IIZaMOffN0eMVQohtY47XCiGKhRAFQojjrvmTzJ0SawkDtgHnxMlHfgd+oZBzt/qOzQPyIvPoHe5lX00BX362AHPMAr53e45b3uyLLEWkh6Xja9QgRRMUrVTplL+uvm0VyInI4XTb6cm1JFJC2euQvBl8tZlX5RDuzmmunIvZbI4i1N/EC8frx59YuAyCYif8fi+LXsapllOz71qto3MV45ZgRwjhBfwKuBHIBO4XQlza8e1hoF1KmQL8DPjh6L2ZwH1AFrAd+PWoPQebpJRLpZQrNP5jqMbRxqMIBCtiZulye53ypr/sIUXXcRWyIlr5O/v2O2/gbTTw+KdX4OftNc1d6jNiH6HEUqKtMNZ8qzI8s+2sdms4SVZEFsP2YSrbJxla2nASus5DpnbDaU+1nLpYsTRf8DF6cdvSOPaUNtPRN6a1gMGgzA2r3qsUIIxhadRS2gbaqO++JEDS0dGZFHft7KwCqqWUNVLKIeA54NJE/m3AH0e/fgnYLJTX9duA56SUg1LKs0D1qL15y7FmRa8T7DPLXjCHf6Okrq4yYfJYovxjMMkwumQlv31wOXEh7gn6HCXPqldijcW8Q/n0wN2daRvelb0KBqOiPdKIwpZCssKzPLaZ4GTcsyKBIZud1wouGQ5qvkUZDHpm37jD+ZHKzpWeytLRmTnuCnbigLGvJedHj014jZRyBOgEwqe5VwK7hRAnhBCPTLa4EOIRIcRxIcTx1lb3tl4fsg1R2FI4e71Of7tSbp5zNwRf+ld39fCfb5bR17WYBSH1rFjsRDNGlXA0E9R0Zyd0McQuhbLXtFvDSWIDYonyi5pYOCulEqAlblRSrhowMDJAWVvZvNLrOMhcuIDsuAWXp7IWrwPfECh/Y9zhpJAkgryD9GBHR2cWuCvYmUhQcWkCerJrprp3nZRyGUp67ItCiAmbeUgpH5NSrpBSroiMjJypz5pQYlH0OrNOYR3/PQz3wjVf0saxecCTB87y1KFa1ixcSa+tg7quOrf5UthaSJhvmPYlz5m3QsMJ6Dw//bUuRAhBfnT+xA/gpmJor9W0CqvUWsqIfWRe6XXGcvfyBEovdFHS0PnxQS+T0lCy8m0Yo4UyCANLI5fqwY6OzixwV7BzHkgY8/t44MJk1wghjEAw0DbVvVJKx2cL8ArzIL11uPEwBmG4qD2ZESODijA5+XqI8exOsVqxq6SJ/3qrjO1ZMXxns9KN90TzCbf5c7zpOMuilmkvjDaPBgyXvO17AvlR+TT2NtLYc8kIhLLXQBggQ7uZbY4Hv6ZpRA25belCfIwGnj16bvwJ8y0w0Am147tn50flU9NZQ+dgJzo6OtPjrmDnGJAqhEgUQnijCI4vFSK8Dnx69Ou7gH1SKT94HbhvtForEUgFjgohAoQQQQBCiABgKzCLUczu4WDDQbIjsmen1yl+UelXsvYftHPMgzl5rp2vPH+KpQkh/Py+pSSGJBLmG+a2YKehp4ELvRdmvzvnDBEpEJWpVDZ5GMuilgGXaEmkVIKdJeuVuU8aUdBSwJIFS5ybK+cBhPh7syNvIa+eaqB7YExFW/L1SsfpslfHXe9I1+n9dnR0ZoZbgp1RDc6XgHeAcuAFKWWpEOK7QghHucaTQLgQohr4KvCN0XtLgReAMmAX8EUppQ2IBg4IIQqBo8BbUkrP7K8/SsdAB8WWYtYvXD/zm+x2OPR/EJ2jdNW9yqhs7uZvnjpGVJAvjz+0Al+TF0IIlkcv52TLSbf45JhW71SfJGcw3wrnPoLuZtesN0NSQ1MJMAWM/z40FYG1CjJv12xdKSUFrQXzNoXl4FNrFtM7ZOPVsfOyTH6KqLvs9XGprOyIbIzCqKeydHRmiNv67Egpd0op06SUyVLK740e+46U8vXRrweklHdLKVOklKuklDVj7v3e6H3pUsq3R4/VSCnzRn9lOWx6Mh81foREsj5uFsFOxU5oPQ3r/uGqayJY39bHg08eweRl4OmHVxMR6HPx3PLo5TT0NFyeQnEBx5uPE+wTTEpIimsWzLwVkHDas1JZRoORvMi88cFO8YtKFVbWHZqte7brLJ2DnfNSnDyWvPhgcuKCefrwufE9dLLvhP42qPng4iE/ox+ZEZkcaz7mBk91dOYfegdlN3Kg4QAhPiFkhl/aYmgSpIT9P4LQRMj6hLbOeRit3YM8+OQR+ods/PnhVSwK9x933pFCOdHi+lTWsaZjrIhegUG46L9TVCZEpEHxy65ZbxbkR+VT3V6taEnsNsXHlBvAP0yzNU82K8HVfA92hBB8as0iKpq7OVY7ZkxEymbwCYaS8d/v1TGrKbWU0jPU42JPdXTmH3qw4ybs0s7BhoNcs/AavAwzbIJXtRsaC+HafwYvo7YOehBtvUM8+OQRmroG+MNnV5IRc3kH3rTQNAJNgRcffK6isaeRhp6G2QnM54oQkHsPnDsEHeemv96FLItahkQqpfh1h6D7AuTcpemaRxqPEOkXSeKCRE3XcQW35sUR5Gvk6cNjKguNPkqPpdNvwvDAxcOrY1djkza3CvN1dOYLerDjJirbK7EOWGeewpISPvgRhCyC3Hu1dc6DaO8d4oHHD3PW0ssTD61k+eKJdwi8DF7kR+W7/Af/8WYX63UcOMaDFL/o2nWnYZyWpPgFRVybfpNm60kpOdp0lNWxq+fF8M/p8PP24u7lCbxd0khr9+DHJ7I/AYNdUP3uxUNLo5bi4+XD4cbDbvBUR2d+oQc7buJAg1JKunbhDCeVn9kHDcdh/VeV/htXAR19Q3zyiSPUWHp5/KEVrE+duppnefRyajprsPZbXeShEuws8F5Aamiqy9YEIHQJJKyBoheUQNhD8Df5Yw43c7LphFKFZb4FvP2nv9FJqjqqaBtoY3Xsas3WcDWfXLOIYZscX4aeuBH8w8elsny8fFgatZQjTUfc4KWOzvxCD3bcxMGGg5jDzET4zaAcV0rY/2NYEAdLH9DeOQ/A0jPI/Y8fobq1h8cfWsG1adM3f1wTuwbApW+6x5qOsTx6uev0OmPJvUcRqzcVu37tKciPyqfEUszQQKfmA2qPNh4FFP3KlUJyZCCb0iP500e1DAzblINeRqWirXIXDPVevHZN7Bqq2qtcGuDr6MxH9GDHDfQM9VDQUsC6uHUzu6HmPaXUeN1XlPz9Fc6Fjn7u+e1HnLX08MRDK9g4g0AHwBxuJtQnlIMNBzX2UKGpt4n67nrXp7AcZN2hVDoVPe+e9SdhWdQyhuQIZcFRmrdHONJ4hEVBi4gNjNV0HVfztxuSsPQMjS9Dz74Thvug4u2LhxxB3tGmo652UUdnXqEHO27gSOMRRuQI6xbOINix2+Hdf4fgRbD809NePt+ptfRy928/orV7kD8/vHpGOzoODMLA2ri1HLxwELu0a+ilgkOv41Jx8lj8wyB1q5LasNvc48MELF2QBMCJ+BxNU64j9hGONx9nVazHN0qfNdckh5O1cAFPHDiL3T6aplx0DQQtHBfcmsPNBJmCONKop7J0dKZCD3bcwL76fQR5B5EXNYPW9mWvKBVY13/rit/VKajv4M7fHKJ/2Mazj6xh5ZLZlyuvW7iOtoE2Tred1sDD8RxvOk6QdxBpoWmarzUpufdAdyPUfug+Hy4hvHIPqUNDfOTrrek6ZdYyeoZ7rii9jgMhBI9cm0R1Sw/vV7YoBw0GWHq/IlLuUqbrGA1Glscs10XKOjrToAc7LmbYNsx79e+xKWETJsM0b722Ydj7nxCVpbn2wd3sKWvmvsc+wt/Hixc/fw3ZcbMYnzGGaxZeA6B5KktKycELB1kVs2rmrQO0IG07+CyAgmfd58NYpISTf2SdIYiTHZX0DfdptpRjN2NVzJW3swNwU04sC4N9eWx/zccH8z8F0g4Ff7l4aE3sGhp6Gjjf7VnDYXV0PAk92HExhxsP0z3UzbYl26a/+MRT0H4WtvwbuPOBqiFSSp46eJbP/fk46dFB/PUL60iODHTaXoRfBOYw88VqN62obK+kqbeJjfEbNV1nWkx+SiBc+gr0tbnXF4CGk9Bcwrqkmxm2D3OsSbsOv0caj5AWmkaYr3YNC92JycvA36xP5HBNG0XnO5SDYUmwZAOcelpJcfOxbkdPZenoTI4e7LiYPXV7CDQFXqwcmpTBHqWvzqK1ii7jCmRwxMY3/1rMv79RxvUZUTz7yBoig+aeqlsft57C1kK6h7pV8HJiPjivtO7fEL9BszVmzIrPgm0QCj1gd+fEH8Dkz7JVf4+f0U+zoHPQNsipllNXZAprLPeuTCDI18gv91V/fDD/U8pL0LlDACSHJBPhF6GnsnR0pkAPdlzIsH2YffX72JSwCW+vafQMH/4P9LbADf9xRc7Aauke4IHHj/DcsXq+uCmZ3z24An9vdbpCr4tbh03aNH3T/eD8B+RE5MysdYDWxORA/Co4/nv39twZ7IaSv0L2J/AOiGBlzEoOXTikyVIFLQUM2Yemf2mY5wT5mvh/65PYXdZMSUOnctB8q5K6PPlnQNH3rF24loMNBxkeMyxUR0fnY/Rgx4UcazxG52AnNyy+YeoLLdXKZPPc+yDhytMjHKmxsuP/DlB2oYtfPbCMr23LwMugXkCXG5lLoClQs10Fa7+V4tZiro2/VhP7TrHyYbBWu1eoXPwSDPfCss8Ailj8XPc5znWpP9Ji//n9mAwmlkcvV922p/HZ9UsI9jPx83crlQPe/soIjrLXYEAJgDYv2kz3cLemaUMdnfmMHuy4kN11uwkwBbA2boquyVLCrkcVLcYN33Wdcy7AZpf8394q7n/8MP7eRl7+wlpuzlW/P4rJYGJN7BoOXjg4fnq0SnzY8CES6X69zlgybwO/UDj2pPt8OPGUIqaPV0rxHaNQDl5QVywupWTvub2siV1DgClAVdueyAJfE49cm8S75S0U1I9qd/IfhJH+ix2V1y5ci5/Rj331+9zoqY6O56IHOy5ixD7C3nN72Ri/ER+vKXQpFTuV0tLrvglB0a5zUGMaO/t56PdH+J89lezIW8gbf7+ezIWXD/RUi7Vxa2nqbaKqo0p12/vP7yfKL4qMsAzVbTuNyQ+WflIZFtnd7Pr1649BYwEs/8zFtOuiBYuID4xXvTKuor2Chp4GtizeoqpdT+bTa5cQ6m/iZ3tGd3cW5kN0Dhx9AqTE1+jLuoXr2Hdun0t6TOnozDf0YMdFHGs6RsdgB1sXTyE2Hu6HXd+ASDOs+lvXOachUkpePdXA1p/t52RdBz/4RA4/v3cpgT7aTm3flLAJgzCw6+wuVe0O24Y52HCQaxOu9bzBk8s/A/YROPUn16998OfgG3LZOJN1ces42nSUIduQaku9W/cuBmHguoTrVLPp6QT6GPncxmQ+qGzlRF2bElCu+QK0lCpz84DrF11Pa38rxRbPGh+io+MJ6MGOi3ir5i38jf5Tj4h473vQcQ5u+vEVMeyzpWuAv3vmJF95voC06CDe/vIG7lu1yCVBQoRfBKtjVrPz7E5VU1nHm4/TN9LnWSksBxGpkLQJjj4OwwOuW9dSBaffUgJ0n/FtA9bHrad/pF+Zgq4Se8/tZVnUsiu25HwyHrpmMRGB3nx/52nl33TOXRAYDR/9EoBr46/FKIzsPbfXzZ7q6HgeerDjAjoHO9lVu4ubk27G1+g78UXnDsOhX8Lyz0KiB5QzzwG7XfL04TomLzd1AAAZPklEQVQ2//QD9p5u4dHtGbzwuWtYEuFafcVNSTfR0NNAkaVINZv7z+/Hx8vHc0ueN/wT9DTDqT+7bs1D/wde3rDqc5edWhWzCqPByP7z+1VZqrazluqO6qsqheXA39vI17dlcKKundcKLigd1Vd/TtnZaSoh2CeYlTEr2XdunyZaNR2d+Ywe7LiA16pfY9A2yL3p9058wVAvvPoFCEmArf/pWudUpvh8J3f99hD/+moJ2QuD2fXlDXzhumRVq61myuZFm/E2eLOzZqcq9mx2G7vrdrMmdg1+Rj9VbKrOkvWQsBoO/i+MqJc6mpTuJqW/T/4nIfDyOWb+Jn/WL1zPrrO7sKkwv8uxa3F9wvVztjUfuWt5PHnxwXx/Zzk9gyPKy5HJHz76FaD8m6/rqqOms2YaSzo6Vxd6sKMxUkperHyRvMg80sPSJ77o3f+Athq47dfgE+RaB1WipWuAr71YyK2/OkCdtY+f3J3HX/52NUlz6IY8V4K8g9iYsJFdtbsYsY/M2d7BCwdp6WvhtpTbVPBOI4SAa78GnfWumYZ+5LfKWJNrvjTpJTuSd9DS38KRprn3Pdp3bh9Z4VlX3JTzmWIwCP791ixaugeVRoP+YUqTweIXoauRTYs2AeipLB2dS9CDHY052nSU2q7ayXd1zrwHR38Hqz8/L9NXXQPD/HR3BZt+8j6vFjTwyIYk3vvaddy1PN4jBLw3Jd5E20AbRxuPztnWK1WvEOYbxnXx183dMS1J2QKxeXDgp9pOQx/ohGO/h8xbITx50ss2JmwkyDuIN868MaflmnqbKLIUXZUprLHkLwrlruXxPHmghprWHkWoLG1w5LdE+UeRG5nLO7Xv6KksHZ0x6MGOxjxf8TwhPiFsXTJBFVZHPbz8MERmwOZ/c71zc6BncIRfv1/Nhh++xy/2VXNdehR7/nEj37zJzAJfzxFXb4jfQKApkLfOvjUnO5Z+C+/Xv8+OpB2YPF08LgRs+Gdlt7D0Fe3W2f8TGOxSdEJT4OPlw/Yl29l7bi+9w71OL/du3buAUnV0tfPo9gx8jV5865US7CGJkHk7HH0Muhq5PeV2KtsrKWgtcLebOjoegx7saEhrXyvvnXuP21Nuv7y3zvAAvPCQkgK492mlK+o8wNozyE93V7DuB/v40a4Kli8O5c2/X8+vPrnM5QLkmeDj5cOWxVvYe24vAyPOVyi9ceYNRuQIn0j9hIreaUjGLUoQ/d73YWRQffvWM3D4N0pvn9i8aS+/NflW+kf6LwYss8Uu7TxX8RzZ4dkkBSc5ZeNKIjLIh2/dbOajGitPHjgLm7+ttB3Y91/cnHgzQd5B/KX8L9Mb0tG5StCDHQ15sfJFRuQId6XddfnJt78GF07CHb9VSoY9nIqmbv7llWLW/XAfv9hXzZqkMF794jp+/5mVZMcFu9u9Kbk56WZ6h3t5++zbTt0vpeSvVX9laeRSkkLmyYPWYICt34O2M3DoF+rb3/MdpQJr87dndHleZB4JQQlOp7IONBygrquOBzMfdOr+K5F7VyawNTOaH79TQdlABKx6BAqewd9SzR0pd/Bu3bu09LW4200dHY9AD3Y0wtpv5U9lf2JTwiYWL1g8/uSR38HJPymphoyb3ePgDBgYtvFG4QXuf+ww236+n5dPnOfWvIW8+9Vr+d2DK1iaEOJuF2fE6pjVZIRl8ETxE04JlU+1nKK2q3b+7Oo4SN2ijJHY/xNor1XP7tn9SqfmDV+FoJgZ3SKEYEfyDo42HaWxp3HWSz5d9jRRflHcsGSauXJXEUIIfnBnLsH+Jr7y/CkGrvkq+IXA7m9xb9o92KSNlypfcrebOjoegR7saMSvC37N4Mgg/7j8H8efOPUMvP11SL8ZNv2Le5ybAiklp86182+vlbD6+3v5+2dPca6tj0e3Z3D4m5v50V15pETNr4oxIQSfz/0857rPObW783LVy/gb/dm2ZJsG3mnMtv8G4QU7v67ORHS7DXZ9E4IXwTVfnNWttyTdgkTyRs3sdneq26v5qPEj7jffj8ng4XopFxMW4M1P7s6jsrmH/9x7AbnxG3B2P4uaylkft54XK1/UJ6Hr6KAHO5pQ3V7NS1UvcU/6PSQGJ358ovQVeP1LSpfbu/8ABi/3OTkGKSVF5zv44a7TbPjRe9zx60M8e6yejWmRPP3waj78+ia+cF0yoQHe7nbVaTYt2kRaaBqPFT02q34vZzvPsvPsTnYk78DfND90VeMIjoNN34Sqd5S5a3Nl/4+huQRu+A9lHtcsSAhK4JrYa/hz2Z/pGuqa8X1Plz+Nj5cPd6VOkA7WYWNaJJ+7NolnjpzjiYHrIDwFdj3KA8m3Yem3sKduj7td1NFxO3qwowH/c+J/CDAG8Pm8z398sOx1ePn/KQ3f7ntG6X7qRnoHR9h3upl/fbWYa/57H7f+8iCP7a8hKTKQH9+Vy7FvbeEX9+ezPjUCgxsaAqqNQRj4XO7nqO2qZXfd7hndI6Xkh0d/iK+X7/jv5Xxj9echKhPe/EfobHDeTvVeeP8HkHsfZN3hlImvrvgqnYOdPFb42Iyubx9o582aN9mRvIMQ3/mRNnUHj27P4ObcWL636wz7zf8OHfWsPfxHFgUt4k9lf9KHg+pc9Wg7jfEq5NCFQxxoOMA/Lf8nQn1DldTBhz+Bff8F8SvhgefB2/VVSwPDNgrrOzh6to2DZyycqGtn2CbxM3lxbVoE/5yZzvUZUYTN492b6diyeAvJwcn8rvB3bFuyDYOYOtZ/r/49Dl44yKMrHyXCL8JFXmqAlwnufBKe3ArP3guf3XXZDKtp6TyvBOtRZrjlZxcnm8+WjLAMbk+5nWdOP8O96feSsCBhyuv/WPpHBm2DfMr8KafWu1owGAQ/vScPa88gD7/Xzjurv07Syf/m82s+zb80v8fTZU/zUNZD7nZTR8dtiKu98dSKFSvk8ePHVbF1oecCD779IN4Gb167/TW87TZ47YtQ8jLk3AO3/mLWW//OIKWkvq2fwvMdFNQrv4rPdzJkU97uzLELuDYtgg0pkaxYEoqvyTPSaa7g7bNv8/X9X+fRlY/yqczJH6ADIwPc/trt+Bn9eGHHC1eGVqTqXfjL3ZC2XWl3MNM06sggPHUztJyGR96HiJQ5udHa18rNr9zMuoXr+Nmmn0163eHGwzyy+xF2JO/ge+u/N6c1rxa6Boa557cfUdPaw76EJ4hr+YB/WH4jh9rKeWHHCySHTN78cbYIIU5IKVeoZlBHR0P0YEelYKdtoI1Pv/1prP1W/rD9D6Rb6xUhclsNbP4OrP9Hp9+GJ0NKSVvvENUtPVS19FDV3E15UzflF7roHlSqjnyMBrLjglm2KITVieGsWBJKiP+Vu3szHXZp5yvvfYX369/nZ5t+xuZFmye87jeFv+HXBb/mya1Psip2lYu91JAjjyltD1b+LWz/AXhNs7nb0wovPAjnPoK7n3I6fXUpvyv8Hb8s+CW/3/Z7VsasvOy8pd/CXa/fRbBPMM/e/Oz81Eu5ifbeIb707EmKq8/xfvD/b+/Oo7Oq7zyOvz/ZCCQQkSVssiMe5SiioI4ijgsuuDCOHnEqY08BF2rrHGyrdpwOM5ZhOGNb6VjPFNSpStW6VEsLlVqrbVFQwQFlUUQECZtCCCEkIdt3/rg/NOY8AbI8ueR5vq9z7uEuv/u7399NePJ97v3d+5tJXVYl1/YtpHeX/iy4YkGrJe6e7Lj2JLZkR9JlwFwgE3jEzP6zwfYOwBPAGcAe4AYz2xy23QtMAWqBb5vZkqOpM5HWSHYOVB/gG0u+wcclHzNv9L8w6t1fwYeL4PghMOFHMORvm1WvmVFaUcPO0kp2llaybW8FRXvL2bq3gi17DvDJ7gPsr/zyUeq8nEyG9+rMKX0KOLlPF0b0KeCk3p3JzvSuWfVV1FQwdclUPtz7IY+Mf4SRPUd+sa3O6pj33jweXvUw4weO54FxD8QYaZK8/H1Y/jPoNyZ6z1NjQz3sWA1P/wOU74GJP4MRf99qIVTWVHLVS1dRXVvNnPPnfGUU+dq6Wm555Rbe+/w9np7wNEO7tuxKUjqqqa1j9u8/4NU33mRBpwdZn1vMjJ7dmDpiCt8edWerDOXiyY5rT2JJdiRlAhuAS4Ai4B3gRjNbV6/MdOBUM7tN0iTg78zsBkknA08DY4A+wB+BE8Nuh60zkZYkOzsP7GTRxpd4ccOvKSrfyU+r8zm/aC1k58G478LZ07HMHA7W1FFRVUt5dS3lB2s4UFVLWWUN+yurKa2spqS8mr3l1ew9UEVxeRW7yw5G0/4qKqq/+uRQVobofVwuA7vlRVP3PIb2zGdYz3x6F+QeE+NRtQfFlcVMXjyZ0qpSbj/tdk7udjKFnQqZuWwmb25/kwmDJ/CDs3+QmlcUzOD952HxXdEbvMfdDYPOjzoxZ2TC5qWw/rew6qlooMlJT0GfkUeut4k27t3IjD/PYPO+zdx62q1cf+L1vLHtDRZ/spjlO5Zz/7n3M3HoxFY/bjr5zaptzF20krsr5/KXwk0s7JzPsA6FTD/9Di468ZoWfV54suPak7iSnXOAmWZ2aVi+F8DMZtcrsySUWSYpC9gJ9ADuqV/2ULmw22HrTKQ5yY6Z8Y/zR7M6pxKTGFl5kGkl+yis7MPLGeezyM5lR20BB2vrqKo5uqcgsjNF1045dO2UQ/fOOfTI70D3/A70KsilsEsuvQpy6de1Iz0755KZAk9HHQs+Lf2UW1+5laKyoi/W5WTkcM9Z93DdsOtSP3Hcty3qU7bptWhZmZDdCar2R/8Ovzy61ZXfM2khlFeXM+utWSz8eOEX6wo7FXLD8BuYduq0pB03nVRW1/Lcik/Z/8c5dM19mSe75rI1O5uBVTD3imcY3PeUZtXryY5rT+J6GqsvsLXechFwVmNlzKxG0j6gW1i/vMG+fcP8keoEQNItwC0A/fv3b3LwkuiecTxXVNRyUu0wMrIG8Uav4ezuOIisDDE6U+RkZZCTlUGHzAxyczLpmB1NeR2yyO+QRV6HLLp0zKJLbjZdOmaTl5OZ+n9cjzH9u/Rn8bWL2VW+i3V71rFp3ybG9h3L8OOHxx1a2yjoC5NfjPqV7VoDO9+PblkNvRiGXNgmnek7ZXdi1nmzGNdvHFtKtzC231iGdx3u/xdaUW52JpPPGUTV6Id5f+se7tywjFVFz7C+biMDeqXJ77pLe3ElO4k+yRpeYmqsTGPrE3VMSXjZyszmAfMgurLTeJiN+8nUo3tXizu2SaJXXi965fXiQtJwNG0p6rPTbUg0tERMxg8cH9ux00VOVgZnDOoBg67mUq6OOxzn2lRcPVeLgPov2OgHbG+sTLiNVQAUH2bfo6nTOeecc2kmrmTnHWCYpEGScoBJwMIGZRYCN4f564A/WdTBaCEwSVIHSYOAYcDbR1mnc84559JMLLexQh+cO4AlRI+JP2ZmayX9O7DCzBYCjwJPStpIdEVnUth3raRngXVADfBNM6sFSFRnW7fNOeecc8cWf6lgK75B2Tnn0oU/jeXaE3/bnHPOOedSmic7zjnnnEtpnuw455xzLqV5suOcc865lJb2HZQlfQ5saebu3YHdrRhOe+BtTg/p1uZ0ay+0vM0DzKxHawXjXDKlfbLTEpJWpNvTCN7m9JBubU639kJ6ttmlL7+N5ZxzzrmU5smOc84551KaJzstMy/uAGLgbU4P6dbmdGsvpGebXZryPjvOOeecS2l+Zcc555xzKc2THeecc86lNE92mkHSZZI+lLRR0j1xx9MWJD0m6TNJa+KOpS1IOkHSa5LWS1or6c64Y0o2SbmS3pa0OrT53+KOqa1IypT0f5J+F3csbUHSZknvS1olyUdCdinP++w0kaRMYANwCVAEvAPcaGbrYg0sySSdD5QBT5jZiLjjSTZJvYHeZvaupM7ASmBiKv+cJQnIM7MySdnAUuBOM1sec2hJJ2kGcCbQxcyujDueZJO0GTjTzNLtRYouTfmVnaYbA2w0s01mVgU8A1wTc0xJZ2Z/AYrjjqOtmNkOM3s3zO8H1gN9440quSxSFhazw5Ty34Yk9QMmAI/EHYtzLjk82Wm6vsDWestFpPgfwXQnaSBwOvBWvJEkX7idswr4DHjFzFK+zcCDwPeAurgDaUMG/EHSSkm3xB2Mc8nmyU7TKcG6lP/2m64k5QMvAP9kZqVxx5NsZlZrZiOBfsAYSSl9y1LSlcBnZrYy7lja2LlmNgq4HPhmuE3tXMryZKfpioAT6i33A7bHFItLotBv5QXgl2b267jjaUtmVgK8DlwWcyjJdi5wdejD8gxwoaQF8YaUfGa2Pfz7GfAi0e1551KWJztN9w4wTNIgSTnAJGBhzDG5VhY66z4KrDezH8cdT1uQ1EPScWG+I3Ax8EG8USWXmd1rZv3MbCDR/+U/mdlNMYeVVJLyQqd7JOUB44G0eMrSpS9PdprIzGqAO4AlRJ1WnzWztfFGlXySngaWAcMlFUmaEndMSXYuMJnom/6qMF0Rd1BJ1ht4TdJ7REn9K2aWFo9ip5lCYKmk1cDbwCIzeznmmJxLKn/03DnnnHMpza/sOOeccy6lebLjnHPOuZTmyY5zzjnnUponO84555xLaZ7sOOdcO9PaA/NKellSScOBUMMrNt6S9JGkX4XXbTjX7niy49KapP6SysIAr42VKZM0uC3jShDDWkkXxBmDO6b8gtZ94eN/Eb1qoaE5wE/MbBiwF0j1V064FOXJjmtXJG2WVBESkF2S/jcM6dAsZvapmeWbWW2o/3VJUxuUyTezTS2NvSXM7BQzez3OGOCL839x3HGku0QD80oaEq7QrJT0V0knNaG+V4H9DeoTcCHwfFj1ODCxZZE7Fw9Pdlx7dJWZ5QOjgNHAfTHH446CIv6ZkzzzgG+Z2RnAd4CHW1hfN6AkvEgVfNBj1475B49rt8xsG/B7YASApD6SFkoqlrRR0rRDZSWNkbRCUmm4IvTjsH6gJJOUJWkWMBZ4KFw5eiiUMUlDw3yBpCckfS5pi6T7Dv0Bl/R1SUslPSBpr6RPJF2eKPbwLbxY0qh6se9u7FZV/SsqkmZKejbEsT/c4jqzsfMU4p8e+l3sl3R/OP6ycD6erd8XQ9KV4Y3RJZLelHRqWP8k0B/4bTg/3wvrzw7lSiStrt+GcKVslqQ3gHJgcDhPm0Isn0j6WuM/ZXc0wtXNvwGeUzRq/c+J3oiNpGslrUkwLTlStQnW+VtoXftkZj751G4mYDNwcZg/AVgL3B+W/0z0bTYXGAl8DlwUti0DJof5fODsMD+Q6AM8Kyy/DkxtcEwDhob5J4DfAJ3DvhuAKWHb14FqYBqQCdxONEisGmnLNKIhRzoRDT/ywFG2eyZQCVwRjjMbWH6YfY1o/LYuwCnAQeBVYDBQAKwDbg5lRwGfAWeFum8Ox+7QMI6w3BfYE2LJAC4Jyz3qnc9Pw3GzwvFKgeFhe2/glLh/r9rjFH7/1oT5LsCOFtZ3AfC7essCdtf7v3EOsCTudvvkU3Mmv7Lj2qOXJJUAS4kSnP+QdAJwHnC3mVWa2SrgEb7sdFkNDJXU3czKzGx5Uw8aOjHfANxrZvvNbDPwI77asXOLmc23qA/Q40R/zAsT1Wdm84GPgLdCuX9uQjhLzWxxOM6TwGlHKD/HzEotGsdtDfAHM9tkZvuIro6dHspNA35uZm+ZWa2ZPU6UHJ3dSL03AYtDLHVm9gqwgij5OeQXZrbWotshNUAdMEJSRzPbYWkwtlyymVkp8Imk6+GLW4ZH+p04Up0GvAZcF1bdTJToO9fueLLj2qOJZnacmQ0ws+lmVgH0AYrNrH4nyy182cdgCnAi8IGkdyRd2YzjdgdyQr2JjgGw89CMmZWH2cN1oJ5PdBvuv83sYBNi2VlvvhzIlZR1mPK76s1XJFg+FOMA4K5wS6okJJUnEJ3fRAYA1zcofx7hFkqw9dCMmR0gShhvA3ZIWtSUjrQuosQD834NmKJogM+1wDVNqO+vwHPARaG+S8Omu4EZkjYS9eF5tDXb4VxbOdyHo3PtyXbgeEmd6yU8/YFtAGb2EXBj6F9zLfC8pG4J6jlcn4TdRFeIBhDd+vnKMZoq9LN4kOgPyExJL5hZ8RF2S7atwCwzm9XI9obnZyvwpJlNS1Q40T5mtgRYIqkj8EOihG9sM+NNS2Z2YyObmvU4upklPP8WPYU4pjl1Oncs8Ss7LiWY2VbgTWC2pNzQqXYK8EsASTdJ6mFmdUBJ2K02QVW7iPqyJDpGLfAsMEtSZ0kDgBnAgmaGPRdYaWZTgUXA/zSzntY0H7hN0lnhVkiepAmSOoftDc/PAuAqSZdKygzn/gJJ/RJVLqlQ0tWS8ohuj5WR+OfgnHOtxpMdl0puJOq0uR14EfjX0IcEom+8ayWVESUZk8ysMkEdc4HrwtNUP02w/VvAAWATUZ+hp4DHmhqopGtCTLeFVTOAUXE/mWRmK4j67TxE9BK5jUQdrw+ZDdwXbll9JySZ1wDfJ+oQvhX4Lo1/tmQAdxH9jIqBccD01m+Jc859SVEfNOecc8651ORXdpxzzjmX0jzZcc4551xK82THOeeccynNkx3nnHPOpTRPdpxzzjmX0jzZcc4551xK82THOeeccynNkx3nnHPOpbT/By6EvuzBMeQhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dens1 /= np.sum(dens1) #normalize\n",
    "dens2 /= np.sum(dens2) #normalize\n",
    "dens3 /= np.sum(dens3) #normalize\n",
    "#plot normalzied probability densities \n",
    "plt.figure()\n",
    "plt.title(\\\n",
    "'Normalized Probability density vs $0\\leq x \\leq L$',\\\n",
    "          fontsize = font)\n",
    "plt.xlabel('Position x in meters',fontsize = font)\n",
    "plt.ylabel('$|\\psi(x)|$',fontsize = font)\n",
    "plt.plot(x,dens1, label = 'ground state')\n",
    "plt.plot(x,dens2, label = '1st excited state')\n",
    "plt.plot(x,dens3, label = '2nd excited state')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2,\\\n",
    "        borderaxespad=0.,fontsize = font)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.5"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}