Linear_Algebra-project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CompMech04-Linear Algebra Project\n",
    "# Practical Linear Algebra for Finite Element Analysis\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this project we will perform a linear-elastic finite element analysis (FEA) on a support structure made of 11 beams that are riveted in 7 locations to create a truss as shown in the image below. \n",
    "\n",
    "![Mesh image of truss](../images/mesh.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The triangular truss shown above can be modeled using a [direct stiffness method [1]](https://en.wikipedia.org/wiki/Direct_stiffness_method), that is detailed in the [extra-FEA_material](./extra-FEA_material.ipynb) notebook. The end result of converting this structure to a FE model. Is that each joint, labeled $n~1-7$, short for _node 1-7_ can move in the x- and y-directions, but causes a force modeled with Hooke's law. Each beam labeled $el~1-11$, short for _element 1-11_, contributes to the stiffness of the structure. We have 14 equations where the sum of the components of forces = 0, represented by the equation\n",
    "\n",
    "$\\mathbf{F-Ku}=\\mathbf{0}$\n",
    "\n",
    "Where, $\\mathbf{F}$ are externally applied forces, $\\mathbf{u}$ are x- and y- displacements of nodes, and $\\mathbf{K}$ is the stiffness matrix given in `fea_arrays.npz` as `K`, shown below\n",
    "\n",
    "_note: the array shown is 1000x(`K`). You can use units of MPa (N/mm^2), N, and mm. The array `K` is in 1/mm_\n",
    "\n",
    "$\\mathbf{K}=EA*$\n",
    "\n",
    "$  \\left[ \\begin{array}{cccccccccccccc}\n",
    " 4.2 & 1.4 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 1.4 & 2.5 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 8.3 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 4.2 & -1.4 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & -1.4 & 2.5 \\\\\n",
    "\\end{array}\\right]~\\frac{1}{m}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.16666667,  1.44337567, -0.83333333, -1.44337567, -3.33333333,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 1.44337567,  2.5       , -1.44337567, -2.5       ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-0.83333333, -1.44337567,  5.        ,  0.        , -0.83333333,\n",
       "         1.44337567, -3.33333333,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-1.44337567, -2.5       ,  0.        ,  5.        ,  1.44337567,\n",
       "        -2.5       ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-3.33333333,  0.        , -0.83333333,  1.44337567,  8.33333333,\n",
       "         0.        , -0.83333333, -1.44337567, -3.33333333,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  1.44337567, -2.5       ,  0.        ,\n",
       "         5.        , -1.44337567, -2.5       ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        , -3.33333333,  0.        , -0.83333333,\n",
       "        -1.44337567,  8.33333333,  0.        , -0.83333333,  1.44337567,\n",
       "        -3.33333333,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        , -1.44337567,\n",
       "        -2.5       ,  0.        ,  5.        ,  1.44337567, -2.5       ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        , -3.33333333,\n",
       "         0.        , -0.83333333,  1.44337567,  8.33333333,  0.        ,\n",
       "        -0.83333333, -1.44337567, -3.33333333,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  1.44337567, -2.5       ,  0.        ,  5.        ,\n",
       "        -1.44337567, -2.5       ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        , -3.33333333,  0.        , -0.83333333, -1.44337567,\n",
       "         5.        ,  0.        , -0.83333333,  1.44337567],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        , -1.44337567, -2.5       ,\n",
       "         0.        ,  5.        ,  1.44337567, -2.5       ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        , -3.33333333,  0.        ,\n",
       "        -0.83333333,  1.44337567,  4.16666667, -1.44337567],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         1.44337567, -2.5       , -1.44337567,  2.5       ]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from __future__ import print_function\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "\n",
    "fea_arrays = np.load('./fea_arrays.npz')\n",
    "K=fea_arrays['K']*1000\n",
    "K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this project we are solving the problem, $\\mathbf{F}=\\mathbf{Ku}$, where $\\mathbf{F}$ is measured in Newtons, $\\mathbf{K}$ `=E*A*K` is the stiffness in N/mm, `E` is Young's modulus measured in MPa (N/mm^2), and `A` is the cross-sectional area of the beam measured in mm^2. \n",
    "\n",
    "There are three constraints on the motion of the joints:\n",
    "\n",
    "i. node 1 displacement in the x-direction is 0 = `u[0]`\n",
    "\n",
    "ii. node 1 displacement in the y-direction is 0 = `u[1]`\n",
    "\n",
    "iii. node 7 displacement in the y-direction is 0 = `u[13]`\n",
    "\n",
    "We can satisfy these constraints by leaving out the first, second, and last rows and columns from our linear algebra description. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Calculate the condition of `K` and the condition of `K[2:13,2:13]`. \n",
    "\n",
    "a. What error would you expect when you solve for `u` in `K*u = F`? \n",
    "\n",
    "b. Why is the condition of `K` so large?\n",
    "\n",
    "c. What error would you expect when you solve for `u[2:13]` in `K[2:13,2:13]*u=F[2:13]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The condition of K is: 6.640986594413608e+16\n",
      "The condition of K[2:13, 2:13] is: 52.2354\n",
      "\n",
      "(a) The error of u is 6.640986594413607\n",
      "(b) The error for k is so large because tit is ill conditioned.\n",
      "(c) Error of u[2:13]; 5.223542514351013e-15\n"
     ]
    }
   ],
   "source": [
    "#1\n",
    "cond_K = np.linalg.cond(K)\n",
    "print('The condition of K is:', round(cond_K,4))\n",
    "cond_K2 = np.linalg.cond(K[2:13, 2:13])\n",
    "print('The condition of K[2:13, 2:13] is:', round(cond_K2,4))\n",
    "print()\n",
    "#a What error would you expect when you solve for u in K*u = F?\n",
    "print('(a) The error of u is',cond_K*1e-16)\n",
    "#b  Why is the condition of K so large?\n",
    "print('(b) The error for k is so large because tit is ill conditioned.')\n",
    "#c  What error would you expect when you solve for u[2:13] in K[2:13,2:13]*u=F[2:13]\n",
    "print('(c) Error of u[2:13];',cond_K2*1e-16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Apply a 100-N downward force to the central top node (n 4)\n",
    "\n",
    "a. Create the LU matrix for K[2:13,2:13]\n",
    "\n",
    "b. Use cross-sectional area of $0.1~mm^2$ and steel and almuminum moduli, $E=200~GPa~and~E=70~GPa,$ respectively. Solve the forward and backward substitution methods for \n",
    "\n",
    "* $\\mathbf{Ly}=\\mathbf{F}\\frac{1}{EA}$\n",
    "\n",
    "* $\\mathbf{Uu}=\\mathbf{y}$\n",
    "\n",
    "_your array `F` is zeros, except for `F[5]=-100`, to create a -100 N load at node 4._\n",
    "\n",
    "c. Plug in the values for $\\mathbf{u}$ into the full equation, $\\mathbf{Ku}=\\mathbf{F}$, to solve for the reaction forces\n",
    "\n",
    "d. Create a plot of the undeformed and deformed structure with the displacements and forces plotted as vectors (via `quiver`). Your result for aluminum should match the following result from [extra-FEA_material](./extra-FEA_material.ipynb). _note: The scale factor is applied to displacements $\\mathbf{u}$, not forces._\n",
    "\n",
    "![Deformed structure with loads applied](../images/deformed_truss.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.linalg import lu\n",
    "def LUNaive(A):\n",
    "    '''LUNaive: naive LU decomposition\n",
    "    L,U = LUNaive(A): LU decomposition without pivoting.\n",
    "    solution method requires floating point numbers, \n",
    "    as such the dtype is changed to float\n",
    "    \n",
    "    Arguments:\n",
    "    ----------\n",
    "    A = coefficient matrix\n",
    "    returns:\n",
    "    ---------\n",
    "    L = Lower triangular matrix\n",
    "    U = Upper triangular matrix\n",
    "    '''\n",
    "    [m,n] = np.shape(A)\n",
    "    if m!=n: error('Matrix A must be square')\n",
    "    nb = n+1\n",
    "    # Gauss Elimination\n",
    "    U = A.astype(float)\n",
    "    L = np.eye(n)\n",
    "\n",
    "    for k in range(0,n-1):\n",
    "        for i in range(k+1,n):\n",
    "            if U[k,k] != 0.0:\n",
    "                factor = U[i,k]/U[k,k]\n",
    "                L[i,k]=factor\n",
    "                U[i,:] = U[i,:] - factor*U[k,:]\n",
    "    return L,U\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L:\n",
      " [[ 1.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    1.    0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [-0.17  0.29  1.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.29 -0.5   0.12  1.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [-0.67  0.   -0.18 -0.1   1.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.   -0.19 -0.72 -0.08  1.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.   -0.43  0.13 -0.24  0.33  1.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.25 -0.79  0.18  1.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.   -0.57 -0.09 -0.25 -0.22  1.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.   -0.23 -0.87 -0.33  1.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.   -0.54  0.24 -0.59  0.29  1.  ]]\n",
      "\n",
      " U:\n",
      " [[ 5.    0.   -0.83  1.44 -3.33  0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    5.    1.44 -2.5   0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    7.78  0.96 -1.39 -1.44 -3.33  0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    3.21 -0.31 -2.32  0.41  0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    5.83 -0.48 -1.39  1.44 -3.33  0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    3.02  1.01 -2.38 -0.27  0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    6.18  1.14 -1.54 -1.44 -3.33]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    2.55 -0.55 -2.23  0.61]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    2.57 -0.84 -1.53]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    2.43  0.7 ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    1.11]]\n"
     ]
    }
   ],
   "source": [
    "#a  Create the LU matrix for K[2:13,2:13]\n",
    "L,U = LUNaive(K[2:13,2:13])\n",
    "\n",
    "print('L:\\n',np.matrix.round(L,2))\n",
    "print('\\n U:\\n',np.matrix.round(U,2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "#b Use cross-sectional area of  0.1 𝑚𝑚2  and steel and almuminum moduli,\n",
    "#𝐸=200 𝐺𝑃𝑎 𝑎𝑛𝑑 𝐸=70 𝐺𝑃𝑎,  respectively. Solve the forward and backward\n",
    "#substitution methods for 𝐋𝐲=𝐅1𝐸𝐴 𝐔𝐮=𝐲 your array F is zeros,\n",
    "#except for F[5]=-100, to create a -100 N load at node 4.\n",
    "\n",
    "def solveLU(L,U,b):\n",
    "    '''solveLU: solve for x when LUx = b\n",
    "    x = solveLU(L,U,b): solves for x given the lower and upper \n",
    "    triangular matrix storage\n",
    "    uses forward substitution for \n",
    "    1. Ly = b\n",
    "    then backward substitution for\n",
    "    2. Ux = y\n",
    "    \n",
    "    Arguments:\n",
    "    ----------\n",
    "    L = Lower triangular matrix\n",
    "    U = Upper triangular matrix\n",
    "    b = output vector\n",
    "    \n",
    "    returns:\n",
    "    ---------\n",
    "    x = solution of LUx=b '''\n",
    "    n=len(b)\n",
    "    x=np.zeros(n)\n",
    "    y=np.zeros(n)\n",
    "        \n",
    "    # forward substitution\n",
    "    for k in range(0,n):\n",
    "        y[k] = b[k] - L[k,0:k]@y[0:k]\n",
    "    # backward substitution\n",
    "    for k in range(n-1,-1,-1):\n",
    "        x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "#constants/given\n",
    "A=1e-7 #area\n",
    "E_s = 200e9 # Youngs Mod for steel\n",
    "E_a = 70e9 #Youngs Mod for aluminum\n",
    "F=np.zeros(11) #forces\n",
    "F[5] = -100 #given force\n",
    "\n",
    "#Steel\n",
    "u_s = solveLU(L,U,F/E_s/A)\n",
    "#Aluminum\n",
    "u_a = solveLU(L,U,F/E_a/A)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "#c Plug in the values for 𝐮 into the full equation,𝐊𝐮=𝐅,\n",
    "#to solve for the reaction forces\n",
    "\n",
    "u1 = np.zeros(14)\n",
    "for i in range(len(u_s)):\n",
    "    u1[i+2] = u_s[i]\n",
    "u2 = np.zeros(14)\n",
    "for i in range(len(u_a)):\n",
    "    u2[i+2] = u_a[i]\n",
    "\n",
    "F_s =K*E_s*A@u1\n",
    "F_a =K*E_a*A@u2\n",
    "u1=u1*1000\n",
    "u2=u2*1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Each displacement for steel:\n",
      "---------------\n",
      "u_1x= 0.000 mm\n",
      "u_1y= 0.000 mm\n",
      "u_2x= 1.949 mm\n",
      "u_2y= -2.125 mm\n",
      "u_3x= 0.433 mm\n",
      "u_3y= -4.000 mm\n",
      "u_4x= 1.083 mm\n",
      "u_4y= -5.375 mm\n",
      "u_5x= 1.732 mm\n",
      "u_5y= -4.000 mm\n",
      "u_6x= 0.217 mm\n",
      "u_6y= -2.125 mm\n",
      "u_7x= 2.165 mm\n",
      "u_7y= 0.000 mm\n",
      "\n",
      "Forces for steel:\n",
      "---------------\n",
      "F_1x= 0.000 N\n",
      "F_1y= 50.000 N\n",
      "F_2x= 0.000 N\n",
      "F_2y= 0.000 N\n",
      "F_3x= -0.000 N\n",
      "F_3y= -0.000 N\n",
      "F_4x= -0.000 N\n",
      "F_4y= -100.000 N\n",
      "F_5x= 0.000 N\n",
      "F_5y= 0.000 N\n",
      "F_6x= -0.000 N\n",
      "F_6y= 0.000 N\n",
      "F_7x= -0.000 N\n",
      "F_7y= 50.000 N\n"
     ]
    }
   ],
   "source": [
    "#Steel\n",
    "xy={0:'x',1:'y'}\n",
    "print('Each displacement for steel:\\n---------------')\n",
    "for i in range(len(u1)):\n",
    "    print('u_{}{}= {:.3f} mm'.format(int(i/2)+1,xy[i%2],u1[i]))\n",
    "print()\n",
    "print('Forces for steel:\\n---------------')\n",
    "for i in range(len(F_s)):\n",
    "    print('F_{}{}= {:.3f} N'.format(int(i/2)+1,xy[i%2],F_s[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1BCKSJCIzRWSeiOSIyCPueD0R+UJElrk/6/otc7+ILBeRJSJyXvCqN8YYY8JXSDUEQD7QR1UzgW7AABHpBdwHTFPVDsA09zYikgEMAboAA4DRIhIblMqNMcaYMBZSDYE69rk3492LAhcDb7rjbwKXuNcvBsapar6qrgKWAz2rsWRjjDEmIoRUQwAgIrEiMhfYCnyhqj8CjVR1E4D7s6E7ezNgnd/i692xQPc7QkSyRSQ7Nze36p6AMcYYE4ZCriFQ1UJV7QY0B3qKSNdSZpdAd1HC/Y5R1SxVzUpLS6uMUo0xxpiIEXINgY+q7gK+wtk3YIuINAFwf251Z1sPtPBbrDmwsRrLNMYYYyJCSDUEIpImInXc68lAP2AxMBEY5s42DJjgXp8IDBGRRBFpA3QAZlZv1cYYY0z4C6mGAGgCTBeR+cBPOPsQTAZGAueKyDLgXPc2qpoDjAcWAp8Bt6hqYVAqD0fPARnAyUBfYE1wy4kI7+FsyMoOdiERYDzO+7MLMDTItRgTBeKCXYA/VZ0PdA8wvh3nIyvQMk8AT1RxaZGpO84HVwrwInAP8G5QKwpve4FRwGnBLiQCLAP+CnwL1OXoRkJjTJUJtTUEpjKsBjoDN+B8u+oPHAww3y9xmgGAXjh7ZJhjrcbbawnwJ5ymKqlaKgtPq/H2er4C3ILTDMDR44qMMVXGGoJItQznH2oOUAd4v4z5XwPOr+qiwpSX13IOzgGwA6uxrnDl5fVc6l5Ox2lWP6u26oyJWiG1ycBUojY4WY8APXC+mZXk3zibDmZUcU3hqqzXsgi4AxhbfSWFNS/vzQKcxuErnDVXZwILcBoIY0yVsIYgUiX6XY+l5NXcU3H2wJhRbJky9Lt5MtNmHj3Cs2/PpkwdHaFfj8t6LffifFid497eDAzCOQYmy9tDdLliPAtX7jpyO6NtHXLGX1GhckOel/dmc5w1A/E4DUQnnAbhVG8PcfPIbxjzwWIKi5TYGGHEZemMvu/MEyrbmEhnDUE0mwPciLM6thzbaH3NQEod6DEQls+Ehbs2cs4f3ubGgR0BiImJjK1RKZsSOOtAOz77ZhEAnVY2JO5gLDnfbDp2xg+PXv3lbR2Ye/MGdh48AN+U/Rgj3/mZnXH5nNQPataD1XNhJ7vofvOb3HfVSZX4bILP6+vZuH0tWo6ry8x2a0jYFct5P3dmypZFHPqm7IOI3vt6Nd/mbKP5SbAuBwoLlBffcx7PmgJjSmYNQTT7A7APGOzebonzrbYMvjUDg+6GWmnQ+cj/2H18xexKLzOY6ifX5BRpypcpznGEsQknk1gQz5cps0pcpltMY7KTFrImZZunx+h5/bG3TzpyPE0+X0bY8YueX89zYPCcXpw5rA0ao/zn9m/IbrLC02PUGwAXDXCu566BD//iXB/zwWJrCIwphagGTPqNaFlZWZqdHVn/aKuTZI0hsQYMeQISk52xyX8DLYK7Vu1EC5QWz/UPbpFh5I4Xs+naB9q4B9zu2wHT33Cu/+0mj9scDAC7P1vOwyt30neEkFLLGftoJGxd5VzX7BHBKy4CiMgsVbU3ZYSyNQSmQnoMhPgEWDXH+SBr2wP+92/lnNl5ADSavIPmT/YLcpXh4df3ZtPyJCg8DAf3Qo26cDgftq2BK888JdjlhZWi007myVtfIzkVtq2DlFrQ61cw8WmIjQl06hNjjE9kbOg11ers0+uScbay+H/wxRjnwyv9dOXUovwj82x9/vsgVhhe+v0GYuNgzmcw7VVnrO/1SkZb26W+vIpi4IyhAMrnL0L2RGjcHtp0V0Zclh7s8owJadYQmHJr3XMvBYdg1iSgCH78QImJFdoNPzqPHipi01897FEX5eatWE+LbkrePmX2JGXLciV3tVKrIdx4jaXxlNd94yeQlCps/qGQA9uUJd8qOzYovS5RnrndIiSNKY01BKZc3v92LonpBTRc15CN9/Vh9qJtvPXsZg7mFpJ6WiJz2x7dCrXp0a+DWGl4eHrOJyBw+Lva3LphD9mzN3PV77aCwuwaiykoKAh2iWFjz4E8drXZRtFh5Q//yGfm7M38lL2Z7iN3kto4hpGTPg92icaENGsIjGcFhUV8uHkmB7cVcf9FA6hzXnu673+AtNt60vlh5xj6L/96dDW35hWw9R928smSvP/dXFJaKwe3KJ3qt2ds4xoo0G5zEfu+zCOxVgz3jv8o2GWGjTvef5fYBCFpeW3S7z77yPi53+dzYGkMaxusZ8O2XaXcgzHRzRoC49k/Pp1BjdZwcn576tRMPjLe8u/nc8/Uu9i/ooAabeP4+MyjyTMb7psahErDw4TdPwBwVUPnULh9cUfXrgx/eBeFh5Xdbbaz50BeUOoLJ0vXbSU2PY/D+4v425BfUf+6bkiy83rG1U7kNxlnkVBT+OtnloFsTEmsITCe7D2Qx+zYJexfo9x+YZ/jpsfWTODmk5yTIaz4Y+0j40X7D7Pt3/Orrc5wMfLDz0luGMOBlcIFp3Y5Mp7v7ghfOw+SFqUSmyDc/oGdgrIsj373ERIjdNjehri4OGJiYqg7OAOAxLZ16ZPZEV2STF673cxeti7I1RoTmqwhMJ78ddIUkhvGcGH9LOJiA79tTs9oS97SWJLqx/KfPzcD98Nt3a2fVGOloa+goIAl9VaiRcofew06ZtqmhNgj1+/MrsmhfUXEdcpj8drN1V1m2Pg0O4eUdsrB3CLuv/S8I+PNnj4XgBo9mwJw51n90UJ44cdpQanTmFBnDYEp05otO9jUeBN5S2K56uwepc47sv8VFBUou/sXkr7zD6T0aELR7nx2friomqoNfXeMe5+EmjEULEkivWXjY6Z9Wefo5pb9n64ifUdbJEZ4/AcPEZJR6u3NztEsF9Xsecx4QsOaJHdrTK3z2gPQuWVjaq+tT0LnQ0z88edqr9OYUGcNgSnTk198RlySMCLznDLnbdqgFrHLahKXJNwx8X06Z4+g0/fXsf+HDVVfaBjYtmcfB9vvovCQ8vxlVx43/Q13x0KAwxv2cu+l/Tm4tYiUtsonPy2o3mLDwAsfzyC5sXBgjTD4jONDnJo9cy61z+9w5PaDA88nb2cR49d+T1FRUXWWakzIs4bAlOqHxas53GEvsctqcnqXdp6Wef6KKyk4WIR2OsCazTuo2auFpRa67p70X2Ljhdqr6lMrJem46Xl+OxbqIedEPhfX7gXAO1v+Vz1FhomCggJmpSwChbtOPj/gPLX7tiUm6ehrWr9WDdL3tqFGW3hpir2exvizhsCU6qVZX1J4CO7pe17ZM7uSEuJovqk5MbHCH6d/UIXVhZd5K9aT0PEQ+XuKePKKS0qc75BfxG7e+l1c/otuHFgjJDcWRk3+qhoqDQ/3jZ9AYq0YDi2Np3uHFp6Xu+uivhxYr3xftJADeYeqsEJjwos1BKZE//3fHBLTC0hb35C2TRqUa9lHBg8kb0cRyR0KmTF/aRVVGF58IUSn7E8nLq7k04hsqxF/5PqWJ5xvsX/odoGFFfnxDyF65qIryrVsQlwc/Wp2I8XCiow5Rkg1BCLSQkSmi8giEckRkd+74/VE5AsRWeb+rOu3zP0islxEloiI96+xplQFhUVM2PLTkRCiiugT45y+75VVX1ZmaWHJP4TotoHnlDrvj81Tj1zf/elyADrVqEP+kngLK3L5hxA1qFWz3Mv/3y9P5eAyCysyxl9INQRAAXCXqnYGegG3iEgGcB8wTVU7ANPc27jThgBdgAHAaBGJDXjPplxKCiEqj2F9T+PAekhpJoyZ8m3lFhhmiocQlebj9HpHrh/euJdtY+eS0/RZnrrwMgsr4vgQooqIiYnh2s4WVmSMv5BqCFR1k6rOdq/vBRYBzYCLgTfd2d4EfBtgLwbGqWq+qq4ClgPHHntkyq2sEKLyuKVTfwC+jY3ew7xKCiEq7oJt+5k2dzPXztpydPBwEWt+MwEUGtWtQ8ryOlEfVlQ8hKiiLKzImGOFVEPgT0RaA92BH4FGqroJnKYB8J0Grhng/5e83h0LdH8jRCRbRLJzc3OrquyI4CWEyKvends4YUV1Y3hg3IRKqjB8lBZCVNwnDWqQWqicuXZPifM8N+TyqA4rKimEqKIsrMiYo0KyIRCRmsD7wO2qWvJ/xyNZeMfQAGOo6hhVzVLVrLS0tMooMyKVJ4TIK19Y0ZYWm8k7FF07xJUWQhTIuLQSNs+4Rx7ExcVFdVhRSSFEFWVhRcYcFXINgYjE4zQD/1FV3zFrW0SkiTu9CbDVHV8P+B9v1BzYWF21RqLyhBB55R9WdNu771Ta/Ya6skKIAnmuZR0KA7S5En/0TzVaw4rKCiGqKAsrMsYRUg2BiAjwGrBIVZ/zmzQRGOZeHwZM8BsfIiKJItIG6ADY+XYrqCIhRF49f8WVHPYLK4oGZYUQleTdrsevwYpJjj/mdrSFFXkJIaooCysyxhFSDQFwOvB/QB8RmeteLgBGAueKyDLgXPc2qpoDjAcWAp8Bt6hqYXBKD38vzfqSwnzlnr4VO8ywNEkJcbTwhRV9FflhRV5DiAKZkt4ASTz2YJnYOsc2FJf/ohsHVkdPWFFFQ4i8uvuivuxfZ2FFJrqFVEOgqv9TVVHVk1W1m3v5RFW3q2pfVe3g/tzht8wTqtpOVTup6qfBrD+cHQkh2tCItk3qV8ljHAkrah/5YUVeQ4hK0vrflx1zO75p6nHz/KG7G1ZUM7LDik4khMir+Lg4zk21sCIT3UKqITDBURkhRF5FQ1hReUKISlLvVxnE1Eo4cjux0/FNWma75hxakkBiamSHFZ1oCJFXFlZkop01BKZSQoi8Gtb3NA6si+ywovKEEJWmw2e/PnK9Zq+AR9Py7MWDIzqsqDJCiLyysCIT7awhiHKVGULk1S3pkRtW5DWEyIuavVsQ16gGAKkXtA84T/3UmhEdVlRZIUReWViRiWbWEES5v0ysvBAiryI1rKigoICl9b2FEHnV6YfhACQ1r1PiPJEaVlTZIUReWViRiVbWEESxNVt2sLlJ5YYQeRWJYUV3jHuf+BreQ4i8SGpdh7pDu5Y6T1xcHOk7Iy+sqLJDiLyysCITrawhiGJVEULkVdMGtYhdGjlhRRUJIfKq7X8uL3Oeey+JrLCiUZO/qpIQIq8srMhEI2sIolRVhhB59fyVkRNWVNEQosp0JKxoa3iH6xQUFDC7xuIqCSHyysKKTDSyhiBKVWUIkVeRElZ0IiFElelIWFEj4e+TpgetjhNV1SFEXllYkYk21hBEoeoIIfIqEsKKTjSEqDL5wormpC4Jy7Ci6ggh8srCiky0sYYgyviHED0wKHhrB/yFc1hRZYQQVaZwDyuqrhAiryysyEQTawiijH8IUe0aVRtC5FU4hxVVVghRZQrXsKLqDCHyysKKTDTx3BCISFMRuVFEHhWRp4pdnqzKIk3lCEYIkVdHworiwucwr8oMIapMx4QVvT8u2OV4Vt0hRF5ZWJGJFp4aAhEZAqwCXgCuBwYHuJgQF4wQIq96d25D3rJYkurE8MC40F/VXRUhRJXpSFhRen5YhBUFK4TIKwsrMtHA66fCE8D7QANVbaaqbYpd2lZhjaYSBDOEyKuR5/rCiraEfFhRVYQQVaZwCysKVgiRVxZWZKKB14agPvCaqu6pymJM1QlmCJFX4RJWVJUhRJUpXMKKgh1C5NWDA88nb4eFFZnI5bUh+AA4pwrrMFUoFEKIvAqHsCJfCFGdVQ2CFkLkVaiHFYVCCJFX9WvVIH2fhRWZyOW1IbgVaC8ir4rIUBG5oPilKos0JyYUQoi8SkqIo8XG0A0r8g8hGnnFxcEup0z+YUXPh2BYUaiEEHllYUUmknltCDoCPYHrgH8Dk4tdJlVJdeaEhVIIkVePXDGQvO2hGVYUSiFEXvnCiuaGWFhRKIUQeXVMWNHEKcEux5hK5bUheAPYA1wIdALaFLvYToWV7E8v/nTC9xGKIURe9YkNvbCiUAsh8ipUw4pCLYTIK19Y0bq0DZUSVjTp6zWVUJUxJ648awjuU9VPVXWZqq4pfqnKIqNNQUERI8fOZduuEwuV8YUQZYZQCJFXoRhWFIohRF6FWlhRKIYQeeULK4qvpLCih8fMYmPu/kqozJgT47UhmAm0rMpCfETkdVJkAuoAACAASURBVBHZKiIL/MbqicgXIrLM/VnXb9r9IrJcRJaISOgdwFwB4z5fTkGhMmpcxQ9v8g8h+n2IhRB5FUphRaEaQuRV/dSa1FgROmFFj34fmiFEXlVWWNGGrfuZvXgbk79ZW4nVGVMxXhuCO4FbReTXbmJhSvFLJdY0Fii+fvs+YJqqdgCmubcRkQxgCNDFXWa0iMRWYi1B8epHiwH479RVFb4PXwjRwAahF0LkVaiEFYV6CJFXz14ZGmFFn2bnkNI2dEOIvKqMsKLJ3zgrVyd9YytZTfB5/aSYBZwEvAmsA/YGuFQKVf0aKH682cXuY+P+vMRvfJyq5qvqKmA5zs6PYW1mTi4AS9furtDxzv4hREPOCs0QIq9CIawo1EOIvAqVsKJQDyHyqjLCiia5awamztzAgbzQ2eHTRCevDcF1wG/cnyVdqlIjVd0E4P5s6I43w2lQfNa7Y8cRkREiki0i2bm5uVVa7InIXpjLwfxCAIqKlLc/W17u+wiHECKvgh1WFC4hRF4FO6woXEKIvDqRsKIDeQVM+2kDAHn5hXzpXjcmWDw1BKo6VlXfLO1S1YWWQAKMaaAZVXWMqmapalZaWloVl1Vxf3t7/jG3fZsPvAqnECKvghlWdPek8WETQuRVsMKKwimEyKsTCSua+uN68tzmH+xoAxN84bJxeYuINAFwf251x9cD/mkmzYGN1VxbpZo689hvCT8t3Fau5cMphMirpIQ4Wm5qUe1hRU4I0eGwCSHyKlhhReEWQuRVRcOKJv9v7XG3VQN+nzGmWng922GCiNwjIt+LyFr3KIBjLlVc50RgmHt9GDDBb3yIiCSKSBugA84REWFp2648tu449pCwA3kFzF7sbRNHOIYQefXw4AurPawoHEOIvKrusCJfCFFhGIUQeVWRsKKiIj3uyIKNuQeYvbh8XwCMqUxe1xC8CDwKrAX+BfwzwKVSiMg7wPdAJxFZLyLXAyOBc0VkGXCuextVzQHGAwuBz4BbVLUw8D2Hvr+/E3jHpOf+U/YOS+EcQuRVdYYVvfftHCeEaHN4hRB5ldmuOYeWVl9Y0e1uCFFymIUQeXVNn57lCiuavXgbm7YdOG7cNhuYYPLaEFwG3K6qV6rqg6r6SPFLZRWkqlepahNVjVfV5qr6mqpuV9W+qtrB/bnDb/4nVLWdqnZS1U8rq45geG/ayoDjX/y4vsxlwzmEyKvqDCuauOdHAK5qFH4hRF49N+iKagkrWrpuK3FhGkLklYiUK6yopMMMi29GMKY6eW0IduCsHTBVpKioiKVr99CwXhJJCU6UQmys0LJxTbbuyCs1tTASQoi8qo6wonAPIfKqXmqNagkrCvcQIq/KE1Y0+Zu1nHVKE07PbARA7ZoJ3HBpOvOX7bDUQhM0XhuCR4G7RKRGVRYTzdZt2c/rfzqLLZ9fQ2qNeAAS4mJYM3koE547j9UbS456iIQQIq96d25D3tKqCyuKlBAir6o6rChSQoi88hJWdLigiOfu6MWMMRfRuY0TupqUGMuYB89i6QdXsv+g5RGY4PB62OGbQDawVkQ+F5HxxS7vVm2Zka9Vk1SGXdQp4LRBZ7UiKyPwoZKRFELk1cj+VRdWVN0hRCPfmENeCYE0j72SXeWPX9VhRZESQuSVl7Ci+LgYzu7RNOC01k1T6dCydlWWaEyJvB5lcBfwByAfqAGkFbs0LHlpU5UiKYTIK/+wot9VYlhRMEKIxny4iOQzXmfUuzlHxlas30tM1hgef31utdRQVWFFkRZC5NWJhBUZE0xe1y/fB4wCmqnq6ar6y+KXKqzRlCASQ4i8+vsQJ6yISgwrCkYI0eM3ZwGwY3f+kbG8Q4Uo0Ouk6uuzKzusKBJDiLw6kbAiY4LJa0MgwGS11IyQEokhRF4lxlduWFGwQoiGDuhY4rTX/nRWtdVR2WFFR0KIlkRWCJFXFQ0rMiaYvO7yOxa4HJhadaWY8vCFENVZ1oi2Z0VWCJFXDw++kGGfv0Rye2XG/KWcfXLJH65leXrOJ6S0Dk4IUZ2aCezad+yHRoxA+xZ1qrWOP3S/gH/u+NgNKzqzwq+DL4SIw/DMoMgKIfLKF1b0XZ15jJw4hUevuCjYJVWZWbNmNYyLi3sV6Er4pN9GoyJgQUFBwfAePXoEDBP0+he/HrhTRKYCXwLFkzdUVV+seJ2mPHwhRDE1i3jqouhbO+CvT2x3vmUur6z6ssINQbBDiK4a0I4X31t0zFjrpqnVXkdmu+Yc+iGBxPTD3PvuRzx7dcUyA25//13iM4SERbVo0CvyQoi8uqZPT6a9+zPrGjlhRc0aVG+DV13i4uJebdy4cee0tLSdMTExthY5RBUVFUlubm7G5s2bXwUCHkLltZt7Duc8AX2Ax4F/BLiYavLCJ19FfAiRV5URVhTsEKJRd/c+buwJd9+C6nYkrKhtxcKKFq/dHPEhRF6VN6wojHVNS0vbY81AaIuJidG0tLTdOGtyAs/j5Y5UNaaMS2ylVW1KtfdAHnPil0ZFCJFXJxJW9NcPpwQ9hCguLo6E+GP/FIec1yEotZxoWNHjP0yMihAir8oTVhTGYqwZCA/u76nEz33b3hNm/jJxCslp0RFC5FVFw4oKCgpYVn9VSIQQ+R9RUCc1IYiVVDysKNpCiLzyElZkTCiwFj6M+EKIipbEM2RodIQQeTWy/xU8tOIdtrTYwsH8QyQnlv2hese494nvHMPhRYmkn1r1IUSlee1PZ9Hh0vEA/HpA+6DWEhcXR+edbVlRczWP/zCRf7cc4Wm5tzd/Q3JjiZoQIq86t2xM7f/VZ3/nHUz88WcGnXZSsEuqUpI1plL/OWn2iFmVeX8lGTVqVP3s7Owab7311tqnnnoqLSUlpejWW2/d7nX5lJSU7gcOHJhTfPzxxx9v+Prrr6d17dr1wMSJE1dVbtWVy75ihpFoDCHyyj+s6LbxZQdnBiOEqDTtW9RBxLn+t7t6BbcY4J5L+nOgHGFF0RpC5JWFFYWXe+65J7c8zUBpXnvttbRPPvlkmddm4PDhw5XxsBViDUGYiOYQIq9GlSOsKBghRGVp3aQmCfExIbPt/RKPYUXRHELklYUVVZ1+/fq169KlS+f27dt3eeaZZxr4xlNSUrrfcMMNzTMyMjr37t2748aNG+MAevbs2em6665r0b179/QOHTp0mT59ekrx+7zzzjub/vnPf24EkJOTk3jmmWd26NKlS+cePXp0mjNnThLA4sWLE7p165betWvXzr///e8DZlEPHTq05fr16xMHDRrU/pFHHmm4ZcuW2H79+rXr2LFjRmZmZvqPP/6Y7Hu8q666qtXpp5/e4bLLLmtTUFDAiBEjmnfs2DGjY8eOGU888URDgG+++Sbl1FNP7dSlS5fOZ5xxRoc1a9bEg7MWol27dl06duyYMXDgwLYVfS2tIQgT0RxC5FWCx7CiYIUQleUvt5xK75MbBbuMI7yGFUV7CJFXFlZUNf7zn/+szsnJWTR37tyFL7/8cqPNmzfHAhw8eDDmlFNOObBw4cJFp59++t777rvvyIf2gQMHYubMmbN41KhRa0aMGNGmtPsfPnx4q9GjR6/NyclZ9PTTT6+/6aabWgLcfPPNLYcPH567YMGCRY0bNw74tf7tt99e27Bhw8MzZsxY+tBDD2295557mmZmZh5YunTpwscee2zDsGHDjjz2/PnzU6ZMmbJ80qRJq5599tm0NWvWJObk5CxcunTpwuHDh2/Pz8+X2267reWECRNW5OTkLBo2bNi2u+++uxnAqFGjGi9YsGDh0qVLF44dOzbwubU98Houg4EiYs1DkPhCiNI2NqJtk+gMIfLq4cEXkre9iOT2hUyftzTgPE/P+QQkOCFEpRlyXgc++3tofcP+Q/cLQHHDio4/CZMvhKjwsEZtCJFXvrCilMYxjJw4JdjlRIwnn3yyUadOnTJ69OjRefPmzfE5OTlJADExMQwfPnwHwHXXXbd95syZR0Ixhg4dugPg/PPP37dv376Ybdu2BTxSbvfu3TFz5sypOXjw4Hbp6ekZN998c6utW7fGA8yePbvmDTfcsAPgxhtv9LR5YebMmanXX3/9doBBgwbt3bVrV9z27dtjAQYMGLCrZs2aCvDll1/W+u1vf5sbH++c+bZRo0aF8+fPT1y2bFlynz59Oqanp2c8/fTTTTZu3BgP0KlTp4OXXnppm9GjR9eLj4+v8BEfXj/kJwAbRORJEelc0Qcz5ecLITq4rYgHojyEyKu+cd0BeG31l8dNC3YIUVmSkkKnQQE3rGhJAompMdw7/vgjOG5//11iE4Tk5bVpUCt6Q4i8Gtb3NA4ujWFdmhNWZE7M5MmTU2fMmJGanZ29eMmSJQs7d+588ODBgwE/18S3k06x64Fu+xQWFpKamlqwePHihb7LypUrj5yJrLyHWwZK/xcRBahRo0aR/3y+cb8xad++/UFfHUuXLl347bffLgOYPn36sltuuSV31qxZNTIzMzMquh+C14agHTAGuAJYICLfi8gNIlKrQo9qPLMQovK7pk/JYUXBDiEKR89d7IYVtTk2rMhCiCrm2oyoCCuqFrt27YqtXbt2YWpqatGcOXOS5s2bV8M3raioiDfeeKMuwNixY+v37Nlzr2/aO++8UxdgypQpNVNTUwvr169fGOj+69WrV9S8efNDr7/+el3ffX7//ffJAKeccsq+V155pR7AK6+84mnVba9evfa+8cYb9cFpZurWrVtQr1694/Yy7dev356XXnopzffBvmXLltiTTz45b8eOHXFTp06tAZCfny/Z2dlJhYWFrFixIuGiiy7aO3r06PV79+6N3b17d4WygTx9HVHV1cBDwEMi0gf4DfA34HkR+QB4XVVP/IwoUWxh95ep0bs5Td0T2tQ/XMhfVm3nu7jDFKyJ4fcXWwhRedyS3p839n/Ot3E/M4LTATeEqGUM+1fABVcEJ4QoHPnCivLSd3P7++N4/f+uBZwQohrthA7bW4fUppdQ1yezI+/8+wfy2u1m/9Ka1D9cyMifNnJ48z7iG4f/WpbqOkwQ4PLLL989ZsyYtI4dO2a0a9cuLzMzc79vWnJyclFOTk5yly5dGqemphZ+8MEHK33T6tatW9i9e/f0ffv2xY4ZM6bUvf/feeedlTfccEOrJ598sklBQYFceumlO3r37n1w9OjRa4cMGdJ29OjRjQYNGrTTS71PPvnkxqFDh7bu2LFjRnJyctHYsWMDPvYdd9yRu3Tp0sT09PQucXFxOmzYsNwHHnggd9y4cStuu+22lnv37o0tLCyUm266actJJ52UP3To0DZ79+6NVVW58cYbtzRo0CBgg1MWqegJDEWkKTAOOANQYC3OKZJfUNXjNzaGkKysLM3Ozg52GceYJY8gCbEQI0yqn4weLKD5wBh+uq0Wv9zfgyFnWe5AeV3z9qskdyqi/rKGPPqrgYz47lXikoU7G11Mesvg5g6Em4KCAm749lXiU5zXb9XW7XzI/8jLVd46/7fBLi/sLFq7mWfWTmDbfOWUP+3mgh15pF3fjdavhs5OroGIyCxVPSZXe968easzMzO3BaumkpSUC9CzZ89OzzzzzLqzzjrrQDDqCrZ58+Y1yMzMbB1oWrl3FBSRs0VkLLAEJxP5n0B/4L/AI8BbFa60gkRkgIgsEZHlInJfdT9+ZdFDhWheAf037qVfYR5zr6tJ86/z+GmKp+bTFDOy/xUUFSpbWm3h9KdeJ75GDGuyxZqBCvCFFUmMcM93E3nTPRTx54mhcchmuOncsjG119an8WkxZDYrJAbY+PpcRp06hi3Pfkfe0ko5BN6YcvF6lEErEfmziKzAOdthC2AE0ERVf6eq01T1HmAYUK0trojE4jQl5wMZwFUiklGdNVS2BIXZI1IpSBJ6jdpLz2d/4K4H7MzT5XXuzZ+xcIYQlyBk9oeCwzD1TehyxfhglxaW3nx7F3u3KY3bQ62GQu4aYe5Ph+z1rKDOKenI9iJm3V4LBQTYsmoXrzzxDTmd/sGCTv9g/d2fs/er1WiBhRmVV6C1AwAzZ85cEq1rB8riaZOBiBQCG4GxOPsLBNzuISIdgZdV9ZeVWWQZtfUGHlbV89zb9wOo6l9LWiZUNxn4rOiXxLSRdQFI3HX0H8EhcS72r8EbjREQIanG0bG8fQCKFNm5WMpLY4TYeCE+0b1dBPkHwF7PihERkpKgKF4YOGI7TWcfIk9geMf6/HvJsWsIYuskUev89tS7sgu1B3Uqca/4aqg5bDYZmMBK22TgdU+gi4DPVLXUzyJVXQpUWzPgagb4n0ZsPXBa8ZlEZATOWg1atmxZPZVVUI2tzv4gbT8/SPLOoy+5AgdrxLOmXd0gVRZe5m929i9q2hHqNYOc6c5rCMLJEbDzVnXzvZ7pp4PEwKJvfFPs9ayI+KU7aJNXQEK+UneVs9tVDHDx9mO/vMY3S6X2wI7UuagjqX3aBK0ZMJHP61EGn1R1IScg0F/HcV9XVHUMzqGTZGVlhfTXmcbzDzMia9MxYwo0GJZJs5H9ImJP5OogWWNKnPZt9tXVWElk8L2e3wU4K7K9nuVzeNNefhr2NxKLrVlJUBi0/SDJmY2oc1ln6lzUkeRuja0JMNUiEtIH1+Ps0+DTHGfzRkQpjAGpEW/NQDlktK1TrnFTuoCvm6q9nhWw8bGviY8J/CEfHxtDjdNb0PTPZ5PSvYk1A6baRMLBwz8BHUSkDbABGAIMDW5JlS+uCLa/MZemfzrbmgKPcsZfQZcrxrNwxdGjNDLa1SVnvEXsVsSR13PlLnD3PWp78DDzRl8Q5MrCy+FNe9n+xlxiSthRMKagKKz/1mfJI5V6jHQPfahcuQZ33nln05o1axbu2bMn9pxzztl7ySWX7C17qaMmT56c+uyzzzaaPn368vJVWv3+9a9/1cnIyMjr0aNHXtlzly3sGwJVLRCRW4EpQCzOTo85ZSwWngqVjY/NoNU/Lwx2JWEjZ/wVzKn9V4r2OCeT6TIh+Kc6Dme+ZurnNn/n0GonendJ33/RZd5NwSwrrGx87GsoaydM+1s/Yc8//3zErSku7qOPPqpTUFCwu7IagkjYZICqfqKqHVW1nao+Eex6KkI8ZNjroUL2f7e+GqqJLLF1j0Y+7/5wcRAriRwdPju6z0De/K1BrCT87P9+PXqo9CA5+1svn3vvvbdx69atu/7iF7/ouGzZskSAyy+/vLUvuvjmm29u5js98IgRI5r7pg8dOrRljx49OrVu3brrO++8U7v4/U6fPj2le/fu6Z07d87o3r17+rx58xLBCeoqz+mJe/bs2en6669vkZWV1alt27ZdZsyYkdK/f/92rVq16nrbbbcdOQvj6NGj65100kmd09PTM4YOHdrKd0KxlJSU7r/73e+aderUKSMzMzN93bp1cV988UWNqVOn1vnjH//YPD09PSMnJyfxRE+DHPZrCCLFKQcfDHYJESuxVW0Or9kNwL7/raPR73oFuaLwl9SpAVIjHt3vZK2vum4CbV4P7ZS9UJEx58ZglxBRvvnmm5QPP/yw3s8//7zw8OHDdOvWLaN79+5HDtXYsmVL7CeffFJ35cqVC2JiYvA/s+G6desSZ86cuWThwoWJ/fr163TxxRf/7H/fmZmZeTNnzlwcHx/PRx99lHrPPfc0nzJlygr/0xPHx8ezZcuWWN/piT/++OPlTZs2LXjllVfq3n333c3++9//rgZISEgoys7OXvLYY481HDx4cPuffvppUcOGDQtat2590gMPPLBl48aN8e+991697OzsxYmJifrrX/+65UsvvVT/1ltv3X7w4MGY3r1773vhhRc2/Pa3v23+wgsvpD311FOb+vXrt2vgwIG7f/Ob3+wE+OUvf9l4zZo1PycnJ2tJZ3AsjTUEJuIld2/Cvq/XApC32A6Xriwt/j6AtcMnAbDjrXlHGoKCvALiQuysjSZyTZ8+veYFF1ywKzU1tQigf//+x5xGsl69eoWJiYlFQ4YMaXXhhRfuvvLKK3f7pl1++eU7YmNjOemkk/JbtGiRP3fu3GOiN3fs2BF75ZVXtlm9enWSiOjhw4cFAp+e+KeffkrynZ4YnBMhpaWlHTnt4KWXXroLIDMz82D79u0PtmrV6jBAixYt8leuXJnw1Vdf1VywYEFKZmZmZ4C8vLyYhg0bFgDEx8frkCFDdgP06NFj/9SpUwOeWNB3GuRBgwbtuvrqq8t9Os2I2GRgTCB57jbu2he2PzJ2eNM+cl+bzeyafwlWWREj7fpTINbdA75Q2fb2fHZOWMSCJs8EtzATdUo7EiM+Pp65c+cuuvzyy3d99NFHdc4555wOJS1X/Pa9997b7Oyzz967bNmynEmTJi0/dOhQDJT/9MQASUlJChATE0NiYuKRZWNiYigoKBBVlcGDB2/3Lb969eoFzz333EaAuLg4jYlxPq7j4uIoKCgI+IRP9DTI1hCYiLXmugnMkkdYO+LjI2OFuQdYO3wSmhfS598KG3UGH00JXztiMisvGU/h7vwgVmSiTZ8+ffZ9/PHHdfbt2yc7d+6M+eKLL445Dnb37t0x7jf93S+99NK6RYsWpfimffDBB3ULCwvJyclJXLduXWJmZuYxO+ft2bMntnnz5ocAXn755Qa+8fKcntjr8xgwYMCeyZMn192wYUOc7z6XLl2aUNoy7tEUMQCVcRpkW69XFb4Gbgfm45wP0k4VX3Ev4ZypIhaoiRMt5fFMFe0+uZp5yU8c2RveX2zdKD0pz1jgDzj5ngC3AsPLfzd5y7dzePN+Wr0ykF3jnIN6fPsTHB8LFsHuAHwnfj8AbAXKvaI2spT3MMETdcYZZxy49NJLd3Tt2rVLs2bN8nv27LnPf/quXbtiBw4c2D4/P18AHn/88SPJtu3bt8/v2bNnp+3bt8c///zza1JSUo559957772bhw8f3mbUqFGNzzzzzD2+8fKcnjgrK8vTEQA9evTI++Mf/7ihb9++HYuKioiPj9dRo0at7dix46GSlrn66qt33HTTTa1feumlRuPGjVtx3XXXtT6R0yBX+PTH4azKz2WwGtgDPAMMwhqCE7EH8G0tmwiMBj7zvvi8Js9QsHn/ceM1+7ah09RrKqHAMDMWyAb+cWJ3s3/+ZhZnvlzi9MyDD0bffgQvAHOA14NdSNWJpHMZXH755a39d8iLFpV6+uOothroDNwAdME56fPBAPO1Bk7GXt3SrMbba+m/68x+AgdVl6LNu4G7sbTfZgUcD1ur8fZ6VpIaJzem1RslH1Ww55OlVffg1WE15X893wGuqtqyjKlK9pFVXsuAW4AcoA7wfnDLCWteX8t/Au2Ae4BR5XuIWme1RhKO34xW71dhfYbswLy+nu/jNKy/4tjTgpVTg2u7Uf/67gGn7fkk5EPeylaev/U1wCqgTzXUZSrF+++/vzra1g6UxRqC8moDdHOv98D5JmEqxutreQuwAngSeLz8D5N266nHDkRqNLyX1/Mid3w+0A8YdmIP2frVQSSf0vi48QPzNp/YHYeC8vyt+/YVKveR3xGhqKioKFL/qiKK+3sq8azF1hCUV6Lf9VjAdlavuPK+lkOAj8r/MC2ePe+Y25ISX/47CQdeXs/6fvPdAFTC7l8Zs248bifNw+v3lDB3GCnP+3Mc0by5YEFubm5tawpCW1FRkeTm5tYGFpQ0T5Tt9WPCzjLAd9Twx37Xyyn5lMYcnO18a01oHcVn59sENHGvT8TZTl4Jum69i3lJf4FCZyflwl1RdOjhEmAn0DvYhQRHQUHB8M2bN7+6efPmrtiXzFBWBCwoKCgo8bgiawiqwk/ApTj/JCYBD+FshzTl9w9gKhAP1AXerNjddJxyNfPSngWgzqCOlVRcGBqF0wjEAfVwjjqoBHFxcXRZfhs5bf4OgB6KolVn7+CsvYrS78c9evTYinM8lQlzdtihiRpz6z5J4a48MnfeS1ydKM0hqGI7Jyxi5SXjAeihDwW5GlPZAh12aCKHrd4xUaPlKxcBWDNQhepe3JlG9/wi2GUYYyrAGgITNer9KoNaAyu4E4LxrPmT51Kzbxvy1kd5ZJ8xYcb2ITBRpcOkocEuISpEZQqkMWHO1hAYY4wxxhoCY4wxxlhDYIwxxhisITDGGGMMIdQQiMhgEckRkSIRySo27X4RWS4iS0TkPL/xHiLyszttlIhEaTSIMcYYc2JCpiHAyVe+DPjaf1BEMnBywLoAA4DRIuI7hciLwAicQNsO7nRjjDHGlFPINASqukhVlwSYdDEwTlXzVXUVsBzoKSJNgFqq+r06cYtvAZdUY8nGGGNMxAiZhqAUzTj2rO3r3bFm7vXi4wGJyAgRyRaR7Nzc3Cop1BhjjAlX1RpMJCJTgeNPng4PquqEkhYLMKaljAekqmOAMeCcy6CMUo0xxpioUq0Ngar2q8Bi64EWfrebAxvd8eYBxo0xxhhTTuGwyWAiMEREEkWkDc7OgzNVdROwV0R6uUcXXAOUtJbBGGOMMaUImYZARC4VkfVAb+BjEZkCoKo5wHhgIfAZcIuqFrqL3QS8irOj4Qrg02ov3BhjjIkA4uygH12ysrI0Ozs72GUYY0xYEZFZqppV9pwmHIXMGgJjjDHGBI81BMYYY4yxhsAYY4wx1hAYY4wxBmsIjDHGGIM1BMYYY4zBGgJjjDHGYA2BMcYYY7CGwBhjjDFYQ2CMMcYYrCEwxhhjDNYQGGOMMQZrCIwxxhiDNQTGGGOMwRoCY4wxxmANgTHGGGOwhsAYY4wxWENgjDHGGKwhMMYYYwzWEBhjjDGGEGoIRORpEVksIvNF5EMRqeM37X4RWS4iS0TkPL/xHiLyszttlIhIcKo3xhhjwlvINATAF0BXVT0ZWArcDyAiGcAQoAswABgtIrHuMi8CI4AO7mVAdRdtjDHGRIKQaQhU9XNVLXBv/gA0d69fDIxT1XxVXQUsB3qKSBOglqp+r6oKvAVcUu2FG2OMPDA1gQAACJtJREFUMREgZBqCYq4DPnWvNwPW+U1b7441c68XHw9IREaISLaIZOfm5lZyucYYY0x4i6vOBxORqUDjAJMeVNUJ7jwPAgXAf3yLBZhfSxkPSFXHAGMAsrKySpzPGGOMiUbV2hCoar/SpovIMGAg0NfdDADON/8WfrM1Bza6480DjBtjjDGmnEJmk4GIDADuBQap6gG/SROBISKSKCJtcHYenKmqm4C9ItLLPbrgGmBCtRdujDHGRIBqXUNQhn8AicAX7tGDP6jqb1U1R0TGAwtxNiXcoqqF7jI3AWOBZJx9Dj497l6NMcYYU6aQaQhUtX0p054Anggwng10rcq6jDHGmGgQMpsMjDHGGBM81hAYY4wxxhoCY4wxxlhDYIwxxhisITDGGGMM1hAYY4wxBmsIjDHGGIM1BMYYY4zBGgJjjDHGYA2BMcYYY7CGwBhjjDFYQ2CMMcYYrCEwxhhjDNYQGGOMMQZrCIwxxhiDNQTGGGOMwRoCY4wxxmANgTHGGGOwhsAYY4wxWENgjDHGGEKoIRCRx0RkvojMFZHPRaSp37T7RWS5iCwRkfP8xnuIyM/utFEiIsGp3hhjjAlvIdMQAE+r6smq2g2YDPwZQEQygCFAF2AAMFpEYt1lXgRGAB3cy4Bqr9oYY4yJACHTEKjqHr+bNQB1r18MjFPVfFVdBSwHeopIE6CWqn6vqgq8BVxSrUUbY4wxESIu2AX4E5EngGuA3cAv3eFmwA9+s613xw6714uPl3TfI3DWJgDsE5EllVR2VWoAbAt2EVUkkp8b2PMLd/b8AmtV2YWY0FGtDYGITAUaB5j0oKpOUNUHgQdF5H7gVuAhINB+AVrKeECqOgYYU/6qg0dEslU1K9h1VIVIfm5gzy/c2fMz0ahaGwJV7edx1reBj3EagvVAC79pzYGN7njzAOPGGGOMKaeQ2YdARDr43RwELHavTwSGiEiiiLTB2XlwpqpuAvaKSC/36IJrgAnVWrQxxhgTIUJpH4KRItIJKALWAL8FUNUcERkPLAQKgFtUtdBd5iZgLJAMfOpeIklYbeIop0h+bmDPL9zZ8zNRR5wd9I0xxhgTzUJmk4ExxhhjgscaAmOMMcZYQxCKRGSAG9O8XETuC3Y9FSEiLURkuogsEpEcEfm9O15PRL4QkWXuz7p+ywSMqA5VIhIrInNEZLJ7O5KeWx0ReU9EFru/w94R9vzucN+XC0TkHRFJCufnJyKvi8hWEVngN1bu52Nx8NHNGoIQ48Yy/xM4H8gArnLjm8NNAXCXqnYGegG3uM/jPmCaqnYAprm3y4qoDlW/Bxb53Y6k5/Z34DNVTQcycZ5nRDw/EWkG3AZkqWpXIBan/nB+fmM5Prq9Is/H4uCjmDUEoacnsFxVV6rqIWAcTnxzWFHVTao6272+F+cDpRnOc3nTne1NjsZNB4yort6qvROR5sCFwKt+w5Hy3GoBZwGvAajqIVXdRYQ8P1cckCwicUAKToZJ2D4/Vf0a2FFsuFzPx+LgjTUEoacZsM7vdqmRzOFARFoD3YEfgUZuhgTuz4bubOH2vJ8H7sE5TNYnUp5bWyAXeMPdJPKqiNQgQp6fqm4AngHWApv4//buJUSrOozj+PcXXUSFbhtJoVy0LxGKdFHZojRKqI1kzFS0CEIUg+hCELQqkhaBGJhoNwiTEFsUZK6KKEkiiCwzyG5qMUIKFfS0OP+hYS46F2tmXr8fOLzn/N/zHM4z7ywezuX5w4mqeo8eyW+IieazkAm0g1fvsSCYeSbUknmmSzIfeAtYP2wCqxG7jjI2I/NOcjtwtKr2jzdklLEZmVtzPrAE2FxV1wInaZebxzCr8mv30u8EFgNXAPOSrD1dyChjMza/cTgr7eDVeywIZp6xWjXPOkkuoCsGXquqXW34l3ZpkvZ5tI3PpryXAXck+Y7uls7NSV6lN3KD7nyPVNXHbXsnXYHQK/ndAhyuqmNV9RewC7iB3slv0ETzsR38Oc6CYOb5BLg6yeIkF9I9/LN7ms9pwtrTyVuBL6tq05CvdgN9bb2Pf9tNj9qi+v8634moqseqalFVXUX3++ytqrX0QG4AVfUz8H3rHAqwgq5TaE/kR3er4Pokc9v/6Qq6Z1x6Jb9BE8rHdvCiqlxm2AKsBA4Ch+hmgpz2c5pEDsvpLjd+Dhxoy0rgcronnr9un5cNiXmi5fwVcNt05zDOPG8E9rT1nskNuAb4tP1+bwOX9lh+T9PNl/IF8Apw0WzOD3iD7nmIwWnhH5hMPsDS9jc5BLxI62brcm4sti6WJEneMpAkSRYEkiQJCwJJkoQFgSRJwoJAkiRhQSBJkrAgkCRJWBBIkiQsCKRJS3JJkiNJdgwb353kYJK5p4mtJBuSPJ/k1yTHkzzSvutL8m2SgSQvJ5kzJK6/xS5Jsi/JqSQH2va8JNuSnGjxa/677CX1GgsCaZKqaoCuRey9SVYDJLkPWAX0V9WpMxxiIzAfWAO8DjyX5FmgH1gHPA7cA6wfJXY7Xbvau+hmqdtJN3fEj8DddFNN70iyaJRYSRrB1sXSFCXZAqwGbgU+ALZU1aNniClgX1Xd1LbPA34A5gBXVpsqOsmbbfu6tt0PbKMrOLa3sZXAO8C2qrq/jV0MHAfWVdXms5uxpF7kFQJp6jYCJ4GP6CaWeWqcce8PrlTV38BhYP9gMdB8Ayw8XWzbB2DvkOOdAI6NEStJI1gQSFNUVb8De+hmzNtaVX+MM3Rg2PafY4zNYaSBYfuMdbzRYiVpBAsCaYqSLAUeAj4DnkyyYJpPSZImzIJAmoL2BsAO4F1gOfAb8NK0npQkTYIFgTQ1zwALgAfbWwV9wKr28J8kzRoWBNIkJVkGbAAerqqfAKrqQ2AT8IKv/EmaTXztUJIkeYVAkiRZEEiSJCwIJEkSFgSSJAkLAkmShAWBJEnCgkCSJGFBIEmSgH8AX01uyIWsB3IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#d Create a plot of the undeformed and deformed structure \n",
    "#with the displacements and forces plotted as vectors (via quiver). \n",
    "\n",
    "\n",
    "#nodes\n",
    "l = 300\n",
    "nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],\n",
    "                  [4,1.5,3**0.5/2],[5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
    "nodes[:,1:3]*=l\n",
    "elems = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],\n",
    "                  [6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\n",
    "\n",
    "ix=2*np.block([[np.arange(0,5)],[np.arange(1,6)],[np.arange(2,7)],[np.arange(0,5)]])\n",
    "iy= ix+1\n",
    "r=np.block([n[1:3] for n in nodes])\n",
    "\n",
    "#plot time\n",
    "plt.plot(r[ix],r[iy],'-',color=(0,0,.5,1))\n",
    "plt.plot(r[ix],r[iy],'o',color=(0,.2,.6,1))\n",
    "plt.plot(r[0],r[1],'^',color=(.8,0,.5,1),markersize=10)\n",
    "plt.plot(r[0],r[1],'>',color=(.8,0,.5,1),markersize=10)\n",
    "plt.plot(r[-2],r[-1],'^',color=(.8,0,.5,1),markersize=10)\n",
    "for n in nodes:\n",
    "    if n[2]>0.8*l: offset=0.1\n",
    "    else: offset=-l/5\n",
    "    plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='magenta') \n",
    "s = 5\n",
    "plt.plot(r[ix]+u1[ix]*s,r[iy]+u1[iy]*s,'-',color=(0.4,.8,.6,1))\n",
    "plt.quiver(r[ix],r[iy],F_s[ix],F_s[iy],color=(0,.2,.6,1),label='applied forces')\n",
    "plt.quiver(r[ix],r[iy],u1[ix],u1[iy],color=(.8,0,.5,1),label='displacements')\n",
    "plt.axis(l*np.array([-0.5,3.5,-1,1.5]))\n",
    "plt.legend(bbox_to_anchor=(1,0.5))\n",
    "plt.title('Steel : Deformation scale = {:.1f}x'.format(s),size=15)\n",
    "plt.xlabel('x mm',size=15)\n",
    "plt.ylabel('y mm',size=15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Each displacement for aluminum:\n",
      "---------------\n",
      "u_1x= 0.000 mm\n",
      "u_1y= 0.000 mm\n",
      "u_2x= 0.000 mm\n",
      "u_2y= -0.000 mm\n",
      "u_3x= 0.000 mm\n",
      "u_3y= -0.000 mm\n",
      "u_4x= 0.000 mm\n",
      "u_4y= -0.000 mm\n",
      "u_5x= 0.000 mm\n",
      "u_5y= -0.000 mm\n",
      "u_6x= 0.000 mm\n",
      "u_6y= -0.000 mm\n",
      "u_7x= 0.000 mm\n",
      "u_7y= 0.000 mm\n",
      "\n",
      "Forces for aluminum:\n",
      "---------------\n",
      "F_1x= 0.000 N\n",
      "F_1y= 50.000 N\n",
      "F_2x= -0.000 N\n",
      "F_2y= 0.000 N\n",
      "F_3x= 0.000 N\n",
      "F_3y= -0.000 N\n",
      "F_4x= 0.000 N\n",
      "F_4y= -100.000 N\n",
      "F_5x= 0.000 N\n",
      "F_5y= 0.000 N\n",
      "F_6x= 0.000 N\n",
      "F_6y= 0.000 N\n",
      "F_7x= -0.000 N\n",
      "F_7y= 50.000 N\n"
     ]
    }
   ],
   "source": [
    "#Aluminum\n",
    "xy={0:'x',1:'y'}\n",
    "print('Each displacement for aluminum:\\n---------------')\n",
    "for i in range(len(u2)):\n",
    "    print('u_{}{}= {:.3f} mm'.format(int(i/2)+1,xy[i%2],u2[i]))\n",
    "print()\n",
    "print('Forces for aluminum:\\n---------------')\n",
    "for i in range(len(F_a)):\n",
    "    print('F_{}{}= {:.3f} N'.format(int(i/2)+1,xy[i%2],F_a[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r[ix],r[iy],'-',color=(0,0,.5,1))\n",
    "plt.plot(r[ix],r[iy],'o',color=(0,.2,.6,1))\n",
    "plt.plot(r[0],r[1],'^',color=(.8,0,.5,1),markersize=10)\n",
    "plt.plot(r[0],r[1],'>',color=(.8,0,.5,1),markersize=10)\n",
    "plt.plot(r[-2],r[-1],'^',color=(.8,0,.5,1),markersize=10)\n",
    "for n in nodes:\n",
    "    if n[2]>0.8*l: offset=0.1\n",
    "    else: offset=-l/5\n",
    "    plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='magenta') \n",
    "s = 5\n",
    "plt.plot(r[ix]+u2[ix]*s,r[iy]+u2[iy]*s,'-',color=(0.4,.8,.6,1))\n",
    "plt.quiver(r[ix],r[iy],F_a[ix],F_a[iy],color=(0,.2,.6,1),label='applied forces')\n",
    "plt.quiver(r[ix],r[iy],u2[ix],u2[iy],color=(.8,0,.5,1),label='displacements')\n",
    "plt.axis(l*np.array([-0.5,3.5,-1,1.5]))\n",
    "plt.legend(bbox_to_anchor=(1,0.5))\n",
    "plt.title('Aluminum : Deformation scale = {:.1f}x'.format(s),size=15)\n",
    "plt.xlabel('x mm',size=15)\n",
    "plt.ylabel('y mm',size=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Determine cross-sectional area\n",
    "\n",
    "a. Using aluminum, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
    "\n",
    "b. Using steel, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
    "\n",
    "c. What are the weights of the aluminum and steel trusses with the chosed cross-sectional areas?\n",
    "\n",
    "d. The current price (2020/03) of [aluminum](https://tradingeconomics.com/commodity/aluminum) is 1545 dollars/Tonne and [steel](https://tradingeconomics.com/commodity/steel) is 476 dollars/Tonne [2]. Which material is cheaper to  create the truss?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) minimum cross-sectional area for aluminum: 7.9e-06 m^2\n",
      "Aluminum Displacements:\n",
      " -------------\n",
      "u_1y= 0.000 mm\n",
      "u_2y= -0.077 mm\n",
      "u_3y= -0.145 mm\n",
      "u_4y= -0.194 mm\n",
      "u_5y= -0.145 mm\n",
      "u_6y= -0.077 mm\n",
      "u_7y= 0.000 mm\n",
      "\n",
      "(b) minimum cross-sectional area for steel: 2.8e-06 m^2\n",
      " Steel Displacements:\n",
      " ---------------\n",
      "u_1y= 0.000 mm\n",
      "u_2y= -0.076 mm\n",
      "u_3y= -0.143 mm\n",
      "u_4y= -0.192 mm\n",
      "u_5y= -0.143 mm\n",
      "u_6y= -0.076 mm\n",
      "u_7y= 0.000 mm\n"
     ]
    }
   ],
   "source": [
    "#a Using aluminum, what is the minimum cross-sectional area to keep \n",
    "#total y-deflections<0.2 𝑚𝑚?\n",
    "\n",
    "A_a = 0.0000079\n",
    "u_a = solveLU(L,U,F/E_a/A_a)\n",
    "u2 = np.zeros(14)    \n",
    "for i in range(len(u_a)):\n",
    "    u2[i+2] = u_a[i]\n",
    "F_a = K*E_a*A_a@u2\n",
    "\n",
    "print('(a) minimum cross-sectional area for aluminum:', A_a,'m^2')\n",
    "xy={0:'x',1:'y'}\n",
    "print('Aluminum Displacements:\\n -------------')\n",
    "for i in range(len(u2)):\n",
    "    if (i % 2) != 0:\n",
    "        print('u_{}{}= {:.3f} mm'.format(int(i/2)+1,xy[i%2],u2[i]*1000))\n",
    "\n",
    "print()\n",
    "\n",
    "#b Using steel, what is the minimum cross-sectional area to keep total\n",
    "#y-deflections  <0.2 𝑚𝑚 ?\n",
    "\n",
    "A_s = 0.0000028\n",
    "F = np.zeros(11)\n",
    "F[5] = -100\n",
    "u_s = solveLU(L,U,F/E_s/A_s)\n",
    "u1 = np.zeros(14)\n",
    "for i in range(len(u_s)):\n",
    "    u1[i+2] = u_s[i]\n",
    "F_s = K*E_s*A_s@u1\n",
    "\n",
    "\n",
    "print('(b) minimum cross-sectional area for steel:', A_s,'m^2')\n",
    "xy={0:'x',1:'y'}\n",
    "print(' Steel Displacements:\\n ---------------')\n",
    "for i in range(len(u1)):\n",
    "    if (i % 2) != 0:\n",
    "        print('u_{}{}= {:.3f} mm'.format(int(i/2)+1,xy[i%2],u1[i]*1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(c)\n",
      "Weight of steel: 761.413 N\n",
      "Weight of aluminum: 756.08 N\n",
      "\n",
      "(d)\n",
      "Cost of Steel= $ 36.95\n",
      "Cost of Aluminum= $ 119.08\n",
      "The steel truss is the cheaper option.\n"
     ]
    }
   ],
   "source": [
    "#Part c What are the weights of the aluminum and steel trusses\n",
    "#with the chosed cross-sectional areas?\n",
    "\n",
    "rho_s = 7700 \n",
    "rho_a = 2710 \n",
    "l = 300 #m\n",
    "nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[4,1.5,3**0.5/2],\n",
    "                  [5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
    "nodes[:,1:3]*=l\n",
    "elems = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],\n",
    "                  [6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\n",
    "\n",
    "for i in range(0,len(elems)):\n",
    "    n1 = elems[i][1] - 1\n",
    "    n2 = elems[i][2] - 1    \n",
    "    ix1 = nodes[n1][1]\n",
    "    iy1 = nodes[n1][2]    \n",
    "    ix2 = nodes[n2][1]\n",
    "    iy2 = nodes[n2][2]\n",
    "    l += ((iy2-iy1)**2 + (ix2-ix1)**2)**0.5\n",
    "m_s = A_s*l*rho_s\n",
    "m_a = A_a*l*rho_a\n",
    "weight_s=m_s*9.81\n",
    "weight_a=m_a*9.81\n",
    "print('(c)')\n",
    "print('Weight of steel:', round(weight_s,3),'N')\n",
    "print('Weight of aluminum:', round(weight_a,3),'N')\n",
    "price_s = 476/1000 \n",
    "price_a = 1545/1000\n",
    "\n",
    "cost_s = price_s*m_s\n",
    "cost_a = price_a*m_a\n",
    "print()\n",
    "print('(d)\\nCost of Steel= $',round(cost_s,2))\n",
    "print('Cost of Aluminum= $',round(cost_a,2))\n",
    "print('The steel truss is the cheaper option.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Future Predictions using past data\n",
    "\n",
    "The data from the price of aluminum and steel are in the data files `../data/al_prices.csv` and `../data/steel_price.csv`. If you're going to produce these supports for 5 years, how would you use the price history of steel and aluminum to compare how much manufacturing will cost?\n",
    "\n",
    "a. Separate the aluminum and steel data points into training and testing data (70-30%-split)\n",
    "\n",
    "b. Fit the training data to polynomial functions of order n. _Choose the highest order._\n",
    "\n",
    "c. Plot the error between your model and the training data and the error between your model and you testing data as a function of the polynomial function order, n. [Create the training-testing curves](../notebooks/03_Linear-regression-algebra.ipynb)\n",
    "\n",
    "d. Choose a polynomial function to predict the price of aluminum and steel in the year 2025. \n",
    "\n",
    "e. Based upon your price model would you change your answer in __3.b__?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "steel = pd.read_csv('../data/steel_price.csv')\n",
    "aluminum = pd.read_csv('../data/al_price.csv')\n",
    "t_s = steel['Year']\n",
    "P_s = steel['dollars/MT']\n",
    "t_a = aluminum['Year']\n",
    "P_a = aluminum['dollars/MT']\n",
    "\n",
    "#a) Separate the aluminum and steel data points into training and testing data (70-30%-split)\n",
    "np.random.seed(100)\n",
    "s_random = random.sample(range(0,len(t_s)),len(t_s))\n",
    "a_random = random.sample(range(0,len(t_a)),len(t_a))\n",
    "train_per=0.7\n",
    "np.random.seed(100)\n",
    "\n",
    "t_s_train = np.sort(t_s[s_random[:int(len(t_s)*train_per)]])\n",
    "P_s_train = np.sort(P_s[s_random[:int(len(t_s)*train_per)]])\n",
    "t_s_test = np.sort(t_s[s_random[int(len(t_s)*train_per):]])\n",
    "P_s_test = np.sort(P_s[s_random[int(len(t_s)*train_per):]])\n",
    "\n",
    "t_a_train = np.sort(t_a[s_random[:int(len(t_a)*train_per)]])\n",
    "P_a_train = np.sort(P_a[s_random[:int(len(t_a)*train_per)]])\n",
    "t_a_test = np.sort(t_a[a_random[int(len(t_a)*train_per):]])\n",
    "P_a_test = np.sort(P_a[a_random[int(len(t_a)*train_per):]])\n",
    "\n",
    "#b) Fit the training data to polynomial functions of order n. Choose the highest order.\n",
    "max_N = 46\n",
    "Z_s_train = np.block([[t_s_train**0]]).T\n",
    "for i in range(1,max_N+1):\n",
    "    Z_s_train = np.hstack((Z_s_train,t_s_train.reshape(-1,1)**i))\n",
    "a_s_train = np.linalg.solve(Z_s_train.T@Z_s_train,Z_s_train.T@P_s_train)\n",
    "\n",
    "\n",
    "Z_a_train = np.block([[t_a_train**0]]).T\n",
    "for i in range(1,max_N+1):\n",
    "    Z_a_train = np.hstack((Z_a_train,t_a_train.reshape(-1,1)**i))\n",
    "a_a_train = np.linalg.solve(Z_a_train.T@Z_a_train,Z_a_train.T@P_a_train)\n",
    "\n",
    "\n",
    "f, axes = plt.subplots(2, 1,figsize=(10,10));\n",
    "axes[0].plot(t_s_train,P_s_train,'o',label='Steel');\n",
    "axes[0].set_ylabel('Price (usd)',size=20);\n",
    "axes[0].plot(t_s_train,Z_s_train@a_s_train,label='Order Fit: {}'.format(max_N),lw=3);\n",
    "axes[0].legend(prop={'size':15});\n",
    "\n",
    "axes[1].plot(t_a_train,P_a_train,'o',label='Aluminum');\n",
    "axes[1].set_ylabel('Price (usd)',size=20);\n",
    "axes[1].plot(t_a_train,Z_a_train@a_a_train,label='Order Fit {}'.format(max_N),lw=3);\n",
    "axes[1].legend(prop={'size':15});\n",
    "\n",
    "plt.xlabel('Time (years)',size=20);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "1. <https://en.wikipedia.org/wiki/Direct_stiffness_method>\n",
    "\n",
    "2. Aluminum and steel price history on <https://tradingeconomics.com>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error steel\n",
      "---- n = 1 ----\n",
      "the coefficient of determination for this fit is 0.635\n",
      "the correlation coefficient this fit is 0.797\n",
      "\n",
      "---- n = 2 ----\n",
      "the coefficient of determination for this fit is 0.730\n",
      "the correlation coefficient this fit is 0.854\n",
      "\n",
      "---- n = 3 ----\n",
      "the coefficient of determination for this fit is 0.730\n",
      "the correlation coefficient this fit is 0.854\n",
      "\n",
      "---- n = 4 ----\n",
      "the coefficient of determination for this fit is 0.729\n",
      "the correlation coefficient this fit is 0.854\n",
      "\n",
      "---- n = 5 ----\n",
      "the coefficient of determination for this fit is 0.729\n",
      "the correlation coefficient this fit is 0.854\n",
      "\n",
      "---- n = 6 ----\n",
      "the coefficient of determination for this fit is 0.729\n",
      "the correlation coefficient this fit is 0.854\n",
      "\n",
      "---- n = 7 ----\n",
      "the coefficient of determination for this fit is 0.728\n",
      "the correlation coefficient this fit is 0.853\n",
      "\n",
      "---- n = 8 ----\n",
      "the coefficient of determination for this fit is 0.728\n",
      "the correlation coefficient this fit is 0.853\n",
      "\n",
      "---- n = 9 ----\n",
      "the coefficient of determination for this fit is 0.734\n",
      "the correlation coefficient this fit is 0.857\n",
      "\n",
      "---- n = 10 ----\n",
      "the coefficient of determination for this fit is 0.735\n",
      "the correlation coefficient this fit is 0.857\n",
      "\n",
      "---- n = 11 ----\n",
      "the coefficient of determination for this fit is 0.712\n",
      "the correlation coefficient this fit is 0.844\n",
      "\n",
      "---- n = 12 ----\n",
      "the coefficient of determination for this fit is 0.716\n",
      "the correlation coefficient this fit is 0.846\n",
      "\n",
      "---- n = 13 ----\n",
      "the coefficient of determination for this fit is 0.674\n",
      "the correlation coefficient this fit is 0.821\n",
      "\n",
      "---- n = 14 ----\n",
      "the coefficient of determination for this fit is 0.690\n",
      "the correlation coefficient this fit is 0.831\n",
      "\n",
      "---- n = 15 ----\n",
      "the coefficient of determination for this fit is 0.670\n",
      "the correlation coefficient this fit is 0.819\n",
      "\n",
      "---- n = 16 ----\n",
      "the coefficient of determination for this fit is 0.715\n",
      "the correlation coefficient this fit is 0.846\n",
      "\n",
      "---- n = 17 ----\n",
      "the coefficient of determination for this fit is 0.127\n",
      "the correlation coefficient this fit is 0.356\n",
      "\n",
      "---- n = 18 ----\n",
      "the coefficient of determination for this fit is -0.925\n",
      "the correlation coefficient this fit is nan\n",
      "\n",
      "---- n = 19 ----\n",
      "the coefficient of determination for this fit is 0.249\n",
      "the correlation coefficient this fit is 0.499\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:22: RuntimeWarning: invalid value encountered in double_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": 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cGU/XnrkbMVEaacbZodabvihmD7Hee8B2Y6nTmmYNsdx0nGM5HtO20UKIwa7Gh9p+pBhGYkocLXFlbIopVwiRNcZ9ZgGoMV9h7B7xwBiSOCFEIRFVQbpBwBVS0rAK0uDWvEG2fxPAm8ZtEyF1lz4C4J9EFD5wvMcEM70XTwkhto9yn2chjU2JE0KUm68gopcxSKuiEOJjAB8bWxMXQRoo/gSAj4hooVnXr8FYjq0QYmDLzWAXNVeqGGL5dDs/cozlXzWm0Vj3KnyXYI3ENO7ymu8EYwwDXc/7NNXO5RvfMC0/E2Xw6w+JQqG4anzvEC2REEKguLi4fLCESKlUDhwjfMWlS5dky5cvD3rmmWfOmxIyS5gOY5Qmi6lL57Yh1puWD3nr7hQVQ0TOgyy/zfhzLF1ZR40/bx3l9qaykwcZb2Eew7CM40hOAJhFRAtH2h7S1TQweOvbKUiJV4Lxrp3RMP3OB+smvBXXd8HxBqQr/R9CGrzvCWCPEOKa8RsmQoh2IUSeEOIxSK0O7hj978JSxnoOANJdjicHSZJkGHzM3xVCiE4hxOdCiBwA/w2py2652Samu1p8B9k9bgwxmky38yPI+PPvg5QxYre2mbG+j9fzPl0xRc5lNgFSU1O1eXl5rhqNRtbR0SHLy8tzW7JkyTXDP1JSUjqPHj3q3NTUZNPb20u5ublXhpUkJyd3bN26dabpdWFh4cDu5Gv09PTQihUrgh544IGLjzzyiEXudjPhROk7BZBucU0moh+YrzC+ToE0pcARK8Q2HjMAPGO+gKQ5hx6EdFWYO4ayXoP04fgbIrpmUDkRychsTirjmJJPIE1R8JMB296NsX2Qm1ovXqYBc9MY6/U2W2Tq6rhmgLCx1eEFSC2E24nomj9AIvI2DUg3et3489+JyN1sOwcAvxvDMZh7E9JV/FrjP/N6zGPJIKLBvmhNHyJd11n/dTF2j+QDyCKiRwbbhogWENFMs0W1AIKJyMdsG4LUZRMxYHcQUdpgvxd81zJpfsym8XRXdQcTURqkVpgxmW7nB757OsFtA2JMB7B+DPUVG+vLJqIrY1qMx/P7gRtfz/s01c5lNjGSk5O7srOzL8bExITHxsaGr1mzpiUpKemaGzP8/f11GzdubEhISAhPTk4OiYqKuvL737FjR/2xY8eUISEhEYGBgZEvvvii18D9B3r11Vfdvv76a6c9e/Z4hoWFRYSFhUWMJsEajSnf9TbEgFGTvUKI48OsHzUhhCCihyB9sb9DRB9AumoKBXAPAA2AteLaqQGmusMA1hPRIkjJoGkeJRmkO8gGTg0wJCHERWPSmAvgKBF9BqAM0gesH6SBuh6Q7noy+TGkqQieJ2kywhJIV8H3QppL5c5RVv8KpNaHtQCqjL+fFgA+kKZneBXAJuO2X0L60H3a+EFvGjvygvGOuWcBRAP4EYA7iehzSF0jMyGNuUiCdOvzSeNxFxDRC5DuvDtBRO/hu3ly2jD0uLYhCSHqieggpAG4/QC+HWKg+tsAeojoCKQvRYJ05R0PaQD2p2Ot2wKyId3c8Bci+hdI00K0Qxr0HQVp4P33AZi6Uf4IaWqLb4jo75DeuyRISdJg58D/AgggaYLDWkjddrGQfs91kN4Tk9cA/BLAvxrvyDsJaaDxckjn6X0Yu+l0frwE6a67vxnf2/OQ3v8MAO9C+lsfTX2NRLQb0rxHx4noY0hTpWRC+gwZrCV3TO8Tpua5zCbApk2bmjdt2nTVmL3Q0NC+qqqqMvNlTz311MWnnnrqmjF83t7e/R9//HHNwOXPPfdcw8BlJk8++eSlJ5988tJQ68djyidKGH6gYC2unlBwXIQQRSRNOvn/IM0tcyekcQF/BfCsGNtEj1PFGUgfZFuMP+0hdRVsFkL8c6yFCSE+I6IoSHO8pEP6oOuDdPfU5xjQBSCEqCJp9uUtkN7T2yDdbXQPpDukRpUoGQfePkREBwA8DuB+47E0Qmrh+NBs2zYiug/SubMO0mSIALALwGXjHYT3QJqX5mFI41+cICVeZwD8B6Q7dMw9BalF8ceQBhdfhPRF/G+Qkr/r8TqkL0JbXHvnocmvIb3PMZC+tHogJQsbAfxpuK66iSKEOGe8C+unkBKRByF1czZB+lJ8AcC3Ztu/TES9kAbvPgTpbqh8SL+b+3DtOfDfkBLpOEjnjAHSHXH/DeB5IcSVZnUhxAUiWgzgD5BafRdDah1ZCqklc8yJ0nQ6P4QQpUS0BMBvIZ0ftsb6siAlr6NKlIweg3RRsQrScZyF1JL7B0h/bwPrHuv7NOXOZcZGg4YbeMWmL5IePXEGwBtCiIetGgxjjLFJUVJSUhsdHc3zUl2HkpISz+jo6ICBy3mMEmOMMcbYEDhRYowxxhgbAidKjDHGGGNDmA6Dudl1EELUQrqrhDHGGGPXiVuUGGOMMWZV27dv91i7du1gD8celcrKSnlkZGR4WFhYRFBQUOTvf//7EedeGq2bskXJ09NTBAQEWDsMxhibVtRqdasQwmJfQOzmZDAYIITAeJ7FptPpYGf33aTwfn5+uuLi4lOOjo7i8uXLsoiIiMj777+/PSAgYNzTTtyUiVJAQACKi/n5i4wxNhZEVGftGNjUt2nTplm7d+/2BIA1a9a0PPPMMxcqKirky5cvD05MTNSo1WqnDz744PT+/fud//jHP3p7eXnpAgMDe+RyuQCAhoYG23Xr1vmfP39eDgDPPffc2WXLlnXm5OT4NDY22p09e1bu7u7ev2/fvjOmOh0cHK7MddTd3U0Gg+Xmhr4pEyXGGGPsRvcfBf/he7rttGLkLUcvyC2o69mkZ4d82G5+fr5iz549Hmq1ulwIgdjY2PC0tDSNp6envra21mHnzp21u3btOltXV2e3ZcsWH7VaXe7u7q5PTEwMValUXQCwYcMG35ycnOb09HRtVVWVPD09PbimpqYMAEpLSxVFRUWnBntg7unTp+0yMzOD6+vr7Z955plzlmhNAjhRYowxxpiFHDp0yCkzM7PdxcXFAAArVqxoO3jwoPPKlSvbvb29+9LS0joB4PDhw8qEhASNj49PPwBkZWVdqqysdACAgoICl6qqqivPadNqtTZtbW0yAMjIyGgfLEkCgKCgIF1lZeXJ2tpauzvvvDNo9erVbb6+vv3jPSZOlBhjjLEb0HAtPxNluKd9KBSKq/rDpGdjD15GcXFx+WAJkVKpHLFPLSAgQBcaGtr96aefOq9bt65tpO1Hwne9McYYY8wiUlNTtXl5ea4ajUbW0dEhy8vLc1uyZIlm4HYpKSmdR48edW5qarLp7e2l3NxcN9O65OTkjq1bt840vS4sLHQcuP9A1dXVdlqtlgCgpaXFpri42CkyMrLHEsfELUqMMcYYs4jk5OSu7OzsizExMeGANJg7KSmpu6KiQm6+nb+/v27jxo0NCQkJ4V5eXrqoqKguvV5PALBjx4769evX+4WEhETo9XpatGiRJjEx8exw9ZaWljpu3LhxLhFBCIGf/OQnTd/73ve6LXFMN+VDcePi4gTf9cYYY2NDRGohRJy142BD44fiXj9+KC5jjDHG2BhxojQGhw8fxu7du60dBmOMMcYmCSdKY6DX63H69Gn09FhkfBhjjDHGpjhOlMYgICAAQgicPTvsmDLGGGOM3SA4URqDOXPmQCaToa6OZ/FnjDHGbgacKI2BXC7HnDlzUFtba+1QGGOMMTYJOFEao4CAADQ0NKC3t9faoTDGGGM3hO3bt3usXbvWb7zlXLp0STZz5swoS5RlwonSGPn7+0MIgXPnzlk7FMYYY2zaMRgM0Ov14ypDpxv8ebc///nP5yxatOiamcDHgxOlMfL19QURcfcbY4wxNohNmzbNCg4OjgwODo7cvHnzTACoqKiQz58/P3L16tV+kZGREdXV1fJt27Z5BAQEqOLj40MLCwudTPs3NDTYpqenB6pUqnCVShV+4MABJQDk5OT4rFq1yj8pKSk4Kytr3sB68/PzFS0tLXZLly7tsOTx8CNMxsje3h7e3t48oJsxxtiU1vBv/+7bW1WlsGSZ9sHBXT7//V9DPmw3Pz9fsWfPHg+1Wl0uhEBsbGx4WlqaxtPTU19bW+uwc+fO2l27dp2tq6uz27Jli49arS53d3fXJyYmhqpUqi4A2LBhg29OTk5zenq6tqqqSp6enh5cU1NTBgClpaWKoqKiUwMfmKvX6/Hzn//cd8+ePTV5eXkuljxmTpSuQ0BAAIqKiqDT6WBnZ2ftcBhjjLEp4dChQ06ZmZntLi4uBgBYsWJF28GDB51XrlzZ7u3t3ZeWltYJAIcPH1YmJCRofHx8+gEgKyvrUmVlpQMAFBQUuFRVVV15EK5Wq7Vpa2uTAUBGRkb7wCQJALZu3eq1bNmy9qCgoMH75MaBE6Xr4O/vj8LCQpw7dw7z5l3T+scYY4xZ3XAtPxNluOfHKhQKg/lrIhqyjOLi4vLBEiKlUmkYbJ+jR486ff31106vvfbazK6uLplOp5M5OTnpX3rppfNjO4Jr8Ril6+DnJw2m5+43xhhj7DupqanavLw8V41GI+vo6JDl5eW5LVmy5JrB1SkpKZ1Hjx51bmpqsunt7aXc3Fw307rk5OSOrVu3zjS9LiwsdBy4/0AffvjhmcbGxm/Pnz//7X/+53+ey8rKumiJJAngFqXr4ujoiNmzZ3OixBhjjJlJTk7uys7OvhgTExMOAGvWrGlJSkrqrqiokJtv5+/vr9u4cWNDQkJCuJeXly4qKqpLr9cTAOzYsaN+/fr1fiEhIRF6vZ4WLVqkSUxMtNojMWi4ZrKphIhCAbxjtmg+gGcAuAJ4DECLcfm/CSHyhisrLi5OFBcXjyue/fv3Q61W49e//jVsbTnfZIzd+IhILYSIs3YcbGglJSW10dHRrdaOYzoqKSnxjI6ODhi4fNp0vQkhKoQQtwghbgEQC6ALQK5x9R9N60ZKkizF398f/f39aGhomIzqGGOMMWYF0yZRGiANQLUQwmp9X/7+/gB4nBJjjDF2I5uuidIDAP5q9vonRFRKRK8SkdtQO1mSUqmEl5cXTzzJGGOM3cCmXaJERHIAdwH4m3HRnwAEArgFQCOA/x1iv8eJqJiIiltaWgbbZMz8/f1RX18/7qnYGWOMMTY1TbtECcByAMeEEM0AIIRoFkLohRAGADsBfG+wnYQQO4QQcUKIOC8vL4sE4u/vj76+PjQ1NVmkPMYYY4xNLdMxUVoFs243IvI2W3cvgBOTFUhAQAAAcPcbY4wxdoOaVokSESkALAXwvtni3xPRt0RUCmAJgJ9NVjzOzs7w8PDAmTNnJqtKxhhj7Iazfft2j7Vr1/qNpwwbG5vYsLCwiLCwsIjU1NQgS8U2rSYAEkJ0AfAYsGyNlcIBAAQFBUGtVvNz3xhjjLFRMBgMEELAxsbmussY7DvX3t7ecOrUqZPjjW+gadWiNBUFBQWhv7+fpwlgjDHGAGzatGlWcHBwZHBwcOTmzZtnAkBFRYV8/vz5katXr/aLjIyMqK6ulm/bts0jICBAFR8fH1pYWOhk2r+hocE2PT09UKVShatUqvADBw4oASAnJ8dn1apV/klJScFZWVmT9qDVadWiNBX5+/vDxsYGp0+fRlCQxVr6GGOMsXH57M1y30vntQpLluk+x6krbW34kA/bzc/PV+zZs8dDrVaXCyEQGxsbnpaWpvH09NTX1tY67Ny5s3bXrl1n6+rq7LZs2eKjVqvL3d3d9YmJiaEqlaoLADZs2OCbk5PTnJ6erq2qqpKnp6cH19TUlAFAaWmpoqio6NRgD8zt6+uTqVSqcBsbG/GLX/yiac2aNe2WOGZOlMZJLpcjICAAp0+ftnYojDHGmFUdOnTIKTMzs93FxcUAACtWrGg7ePCg88qVK9u9vb370tLSOgHg8OHDyoSEBI2Pj08/AGRlZV2qrKx0AICCggKXqqqqKw/C1Wq1Nm1tbTIAyMjIaB8sSQKA06dPlwYEBOhOnjwpX7p0aWhMTEx3ZGRk73iPiRMlCwgKCsI///lPtLe3w9XV1drhMMYYYxiu5WeiDPf8WIVCYTB/TURDllFcXFw+WEKkVCoNg+0DAAEBAToAiIiI6EtISNB89dVXCkskSjxGyQJMXW7cqsQYY0r9TI4AACAASURBVOxmlpqaqs3Ly3PVaDSyjo4OWV5entuSJUs0A7dLSUnpPHr0qHNTU5NNb28v5ebmXnmqRnJycsfWrVtnml4XFhY6Dtx/oJaWFpvu7m4CgMbGRtvi4mKnqKiobkscE7coWYCnpydmzJiB06dPIy6OH6zNGGPs5pScnNyVnZ19MSYmJhwA1qxZ05KUlNRdUVEhN9/O399ft3HjxoaEhIRwLy8vXVRUVJderycA2LFjR/369ev9QkJCIvR6PS1atEiTmJh4drh6jx8/7vDjH//Yn4gghMDTTz/dFBsb22OJY6LhmsluVHFxcaK4uNiiZe7btw/ffvstNm7cOK5bHhljbKoiIrUQgq8Gp7CSkpLa6OjoVmvHMR2VlJR4RkdHBwxczl1vFhIUFIS+vj7U1096lzBjjDHGJggnShYyb948yGQyHqfEGGOM3UA4UbIQBwcH+Pr6cqLEGGOM3UA4UbKgoKAgNDU1QaO5ZoA/Y4wxxqYhTpQsyDRNQHV1tZUjYYwxxpglcKJkQbNmzYJSqeTuN8YYY+wGwYmSBclkMgQFBaG6uhoGw5CThzLGGGPMzPbt2z3Wrl3rN54yqqqq5ElJScHz58+PDAwMjBw4d9P14kTJwoKCgtDd3Y2GhgZrh8IYY4xNOQaDAXq9flxl6HS6a5Y9+OCD837xi18019TUlB07dqzc9By58eJEycKCgoIgk8lw8uRJa4fCGGOMTbpNmzbNCg4OjgwODo7cvHnzTACoqKiQz58/P3L16tV+kZGREdXV1fJt27Z5BAQEqOLj40MLCwudTPs3NDTYpqenB6pUqnCVShV+4MABJQDk5OT4rFq1yj8pKSk4KytrnnmdarXaQa/X49577+0AgBkzZhicnZ0t0rXDjzCxMEdHRwQGBqKsrAxLly4d8qF/jDHG2ET655+e922tr1NYskxPX/+u9CeeHnJm5fz8fMWePXs81Gp1uRACsbGx4WlpaRpPT099bW2tw86dO2t37dp1tq6uzm7Lli0+arW63N3dXZ+YmBiqUqm6AGDDhg2+OTk5zenp6dqqqip5enp6cE1NTRkAlJaWKoqKik4NfGDuyZMnHVxcXPTLli0LrK+vt09JSen4v//7v3O2tuNPc7hFaQJERkbi8uXLOH/+vLVDYYwxxibNoUOHnDIzM9tdXFwMM2bMMKxYsaLt4MGDzgDg7e3dl5aW1gkAhw8fViYkJGh8fHz6HRwcRFZW1iVTGQUFBS5PPfWUX1hYWMSdd94ZpNVqbdra2mQAkJGR0T4wSQKA/v5+Ki4udnr++efrS0tLT9bW1tq/8MILnpY4Jm5RmgChoaGQyWQoKyvD3LlzrR0OY4yxm9BwLT8TZbjnxyoUiqu6wobqcRFCoLi4uHywhEipVA7anebn59cXHh7eHRER0QcAd911V9vRo0edBtt2rKZVixIR1RLRt0R0nIiKjcvciegTIqoy/nSzdpyOjo4ICgpCWVkZ3/3GGGPsppGamqrNy8tz1Wg0so6ODlleXp7bkiVLrpmFOSUlpfPo0aPOTU1NNr29vZSbm3vluzs5Oblj69atM02vCwsLHUeqd/HixZ2XL1+2aWhosAWAgwcPukRERHRb4pimVaJktEQIcYvZE6x/DeAzIUQwgM+Mr60uMjISHR0d3P3GGGPsppGcnNyVnZ19MSYmJjw2NjZ8zZo1LUlJSdckLP7+/rqNGzc2JCQkhCcnJ4dERUV1mdbt2LGj/tixY8qQkJCIwMDAyBdffNFrpHptbW2xZcuWc7fddltISEhIhBACP/vZz1otcUw0XDPZVENEtQDihBCtZssqANwmhGgkIm8Ah4QQocOVExcXJ4qLiyc01p6eHvzhD39AfHw8MjIyJrQuxhibDESkNrtIZVNQSUlJbXR0tEUShJtNSUmJZ3R0dMDA5dOtRUkAOEBEaiJ63LhslhCiEQCMP2cOufckcnBw4O43xhhjbJqbbolSkhAiBsByAD8mopTR7khEjxNRMREVt7S0TFyEZiIjI6HRaFBfP+nj6RhjjDFmAdMqURJCNBh/XgCQC+B7AJqNXW4w/rwwxL47hBBxQog4L68RuzstIjQ0FLa2tigrK5uU+hhjjDFmWdMmUSIiJRE5m/4PYBmAEwA+BPCQcbOHAHxgnQivZW9vj6CgIJSXlw97yyRjjDHGpqZpkygBmAXgCBGVAPgKwMdCiH8A2AJgKRFVAVhqfD1lhIWFQaPR8LPfGGOMsWlo2kw4KYSoARA9yPKLANImP6LRCQ4OBhGhoqICc+bMsXY4jDHGGBuD6dSiNC0plUr4+vqioqLC2qEwxhhjU9L27ds91q5d63e9++/bt885LCwswvTP3t4+5q233nK1RGycKE2C0NBQNDc3o7293dqhMMYYY1ZlMBig1+vHVYZOp7vq9Z133qk5derUyVOnTp384osvKhwcHAz33HNPx7gqMeJEaRKEhkrzX3KrEmOMsRvdpk2bZgUHB0cGBwdHbt68eSYAVFRUyOfPnx+5evVqv8jIyIjq6mr5tm3bPAICAlTx8fGhhYWFV57L1tDQYJuenh6oUqnCVSpV+IEDB5QAkJOT47Nq1Sr/pKSk4KysrHlD1f/WW2+5LV68+LKzs7NFJjGcNmOUpjNPT094enqioqICixYtsnY4jDHGbgKX3qv01TV1KixZpt1sZZf7D0KGnBwwPz9fsWfPHg+1Wl0uhEBsbGx4WlqaxtPTU19bW+uwc+fO2l27dp2tq6uz27Jli49arS53d3fXJyYmhqpUqi4A2LBhg29OTk5zenq6tqqqSp6enh5cU1NTBgClpaWKoqKiU4M9MNfkvffec3/qqaeaLXXMnChNktDQUHz55Zfo6emBg4ODtcNhjDHGLO7QoUNOmZmZ7S4uLgYAWLFiRdvBgwedV65c2e7t7d2XlpbWCQCHDx9WJiQkaHx8fPoBICsr61JlZaUDABQUFLhUVVVdeRCuVqu1aWtrkwFARkZG+3BJUl1dnV1FRYVjVlaWRbrdAE6UJk1oaCgKCgpw+vRpqFQqa4fD2JSn0+lQU1ODzs5OzJ49G7NmzYKNjY21w5rWhEGAZGTtMNgkGa7lZ6IMN2egQqG4qiuMaPBzUQiB4uLi8sESIqVSOWx32ptvvumWkZHRbm9vb7HJCzlRmiRz586FQqHA8ePHERERAZmMh4exm5cQAq2traivr8e5c+eg0WiurCMi6PV6nD179qoBm3Z2dvDx8YGvry/8/f3h5+cHe3t7a4Q/LfW3duPirnK43R8CuY/TyDswdh1SU1O1jzzySMCzzz7bJIRAXl6e2+uvv14zcLuUlJTOjRs3+jY1Ndm4ubkZcnNz3SIjI7sBIDk5uWPr1q0zn3322WYAKCwsdExMTOweTf3vvfee+29/+9vzljwmTpQmiUwmQ2JiIj799FMcO3YMcXH8AG528xBCoK6uDmfPnr2SHHV3S597Dg4OcHNzu2af6OhohIWFwc3NDQ0NDTh37hzq6+tRWFiII0eOQCaTYc6cOZg/fz7mz58PPz+/Ia9Qb3aGnn60vlkGg1YHmT23yrGJk5yc3JWdnX0xJiYmHADWrFnTkpSU1F1RUSE3387f31+3cePGhoSEhHAvLy9dVFRUl16vJwDYsWNH/fr16/1CQkIi9Ho9LVq0SJOYmHh2pLorKirkjY2N8szMTM1I244F3YyP1oiLixPFxcWTXq8QAq+88gq6urrw05/+lFuV2A3PYDCgoqICX3zxBZqamgAAXl5e8PX1xdy5c+Hr6wsPD48x/S309fWhvr4eZ86cwZkzZ9DQ0AAhBGbPno2UlBSEhYXx35YZYRC4+EYZeqra4fmoCg6B1z+1DBGphRB8lTeFlZSU1EZHR7daO47pqKSkxDM6Ojpg4HJuUZpERISkpCS8++67KC8vR2RkpLVDYmxCGAwGnDp1Cl988QWam5vh7u6Ou+++G2FhYXB0dBy5gGHI5XIEBgYiMDAQANDT04Py8nLk5+fj3Xffhbe3N5YvXw4/v+ueu+6GcjnvDHoq2uB6b9C4kiTGblacKE2ysLAwzJgxA9988w0nSuyGo9Fo8M0336C0tBStra3w8PDAvffeC5VKNWEDsR0cHLBw4UJER0fj22+/xaeffopXX30VCxYsQFpaGlxdb97koPPrJmiPnIfy+95wWuRt7XAYm5Y4UZpkMpkMUVFROHLkCLRaLZyceFAluzFUVVXh/fffR3d3N/z8/JCVlQWVSjVp3WAymezKuKYjR46gsLAQZWVlWLBgAZKSkjBz5sxJiWOq6K29jLa9p2Ef5ArXOwKtHQ5j0xYnSlawYMEC5Ofn48SJE0hISLB2OIyNi16vx+eff46CggLMmjUL69ats2pSYm9vj7S0NMTFxaGwsBDHjh1DSUkJwsLCkJqaelMkTP2XenDxrXLYujnAIzsMZEPQ6S6j6vTvEBz0a9jZ3bytbIyNFY94tIKZM2fC29sbpaWl1g6Fseum1+tx/PhxvPTSSygoKEBcXBzWr18/ZRKRGTNmYPny5Xj66aeRkpKC2tpavPLKKzh9+rS1Q5tQhl49Lr5ZBqE3wOOhCMgUdtDp2vDN8TVoavoAGm25tUNkbFrhRMlKoqKi0NDQgJaWFmuHwtiY9Pf3o7i4GC+88AL27t0LW1tbPPDAA7jjjjtgZ2dn7fCuoVQqkZqaiieeeAJubm7YvXs3rHHX62QQBoFL71RA19wFj+xw2Hkp0Nd3Ece+WY3OzipER/0Z7m7ft3aYjE0rnChZyYIFC2Bra4sjR45YOxTGRkWv1+Orr77C9u3b8dFHH0GpVGLVqlX40Y9+hLCwMGuHN6IZM2bgkUceQWBgID766CMcOHAAvb291g7LojoO1KLn5EXMuGM+HELc0NvXimPfPIiurjOIitoJD4/F1g6RsUFt377dY+3ateO6VfVHP/rR3KCgoMj58+dHPvzww74Gg0WeictjlKzFyckJcXFxKCoqQkpKCjw8PKwdEmNDOnXqFA4cOIBLly7Bz88Pd911FwIDA6fdBI/29vZYtWoV9u/fj8LCQhQXFyM+Ph5paWnTfu6ljkP10Bw6B+Wi2XBK9EFv7wUc+2Y1enoaEB39F25JYlOGwWCAEGJcd8LqdLqrWrA/+eQT5VdffeV06tSpMgCIi4sLy8vLc77jjjvGPfnk9P5kmOaSk5Mhk8nw1VdfWTsUxoakVqvx9ttvQyaTITs7G+vWrUNQUNC0S5JMbGxscMcdd+DRRx9FSEgICgoK8NFHHw37jKqpTpN/Hh3/qIVjtBdc7w5Cb28T1MdWobe3Cbfc8honSWxSbdq0aVZwcHBkcHBw5ObNm2cC0qzZ8+fPj1y9erVfZGRkRHV1tXzbtm0eAQEBqvj4+NDCwsIrt4A3NDTYpqenB6pUqnCVShV+4MABJQDk5OT4rFq1yj8pKSk4KytrnnmdRITe3l7q6emh7u5uWX9/P/n4+OhgAdyiZEVOTk4IDg5GWVkZ0tPTp/0VLbuxaDQa/POf/8SJEycQEBCANWvW3FAPpfX19YWvry/c3NyQn58Pe3t7LFu2bNolgNovG3D54xo4qjzgfn8oevsacezYg+jTXcItt7wG1xmx1g6RWcnevXt9L1y4oLBkmTNnzuy65557hnzYbn5+vmLPnj0earW6XAiB2NjY8LS0NI2np6e+trbWYefOnbW7du06W1dXZ7dlyxYftVpd7u7urk9MTAxVqVRdALBhwwbfnJyc5vT0dG1VVZU8PT09uKampgwASktLFUVFRacGPjD39ttv70xKStJ4e3tHA8DDDz/cEhMT02OJY542iRIR+QJ4E8BsAAYAO4QQ24hoE4DHAJhGRf+bECLPOlGOnUqlwqlTp1BXV4d58+aNvANjk+DkyZPYt28f+vr6sHjxYiQlJd1QSZK51NRU9Pb24ssvv4RCocCtt95q7ZBGrbvsIto/qIZDuDvcHwhDT985HPtmNfr7L2PhwjcxwyXa2iGym8yhQ4ecMjMz211cXAwAsGLFiraDBw86r1y5st3b27svLS2tEwAOHz6sTEhI0Pj4+PQDQFZW1qXKykoHACgoKHCpqqq6MoW/Vqu1aWtrkwFARkZG+8AkCQBOnDhhX1lZ6XDu3LlSAFi8eHHI/v37nZYvX64d7zFNm0QJQD+AnwshjhGRMwA1EX1iXPdHIcT/WDG26xYSEgI7OzucOHGCEyVmdT09Pdi/fz9KSkrg4+ODrKwseHp6WjusCUVEyMjIQHd3Nz777DM4ODggPj7e2mGNSPQb0J5XA9tZCng8GA5N1wmUlv4IekMPFt7yFlxcFlg7RGZlw7X8TJThurAVCsVVo6uHar0VQqC4uLh8sIRIqVQOOkL7nXfecY2Pj++cMWOGAQBuv/32ywUFBUpLJErTpq9HCNEohDhm/L8GQDmAOdaNavzkcjlCQ0Nx8uRJ6PV6a4fDbmJ1dXX485//jNLSUqSkpODRRx+94ZMkE5lMhnvuuQchISH4+OOP8e2331o7pBFpixqhv9iDGZnz0Nz6EdTHHgCRDWJi9nCSxKwmNTVVm5eX56rRaGQdHR2yvLw8tyVLllwzoDolJaXz6NGjzk1NTTa9vb2Um5vrZlqXnJzcsXXr1isTshUWFo74gEg/P7++goICZ51Oh97eXiooKHCOiIiwSNfbtEmUzBFRAICFAIqMi35CRKVE9CoRuQ2xz+NEVExExVNt7qIFCxagu7sblZWV1g6F3YT6+/vx6aef4rXXXgMRYd26dUhNTb1hu9qGYmNjg5UrV8Lf3x+5ubmoqqqydkhDMvT2Q/PZWciDXHDe9lWUnfwZXJyjEB+fC2enqT9VA7txJScnd2VnZ1+MiYkJj42NDV+zZk1LUlJS98Dt/P39dRs3bmxISEgIT05ODomKiuoyrduxY0f9sWPHlCEhIRGBgYGRL774otdI9a5bt64tICCgNzQ0NDIiIiIiMjKyKzs7+7Iljomm250eROQE4AsA/yWEeJ+IZgFoBSAAPAvAWwjxyHBlxMXFiak04Zxer8fzzz+PWbNmYfXq1dYOh91EWlpa8P7776OxsRELFy5ERkYG7O3trR2WVfX09OD1119Ha2srHn74YcydO9faIV2j85sLaHunAt33f4Wz7S/Bx+eHCA3ZBJlMPqH1EpFaCBE3oZWwcSkpKamNjo5utXYc01FJSYlndHR0wMDl06pFiYjsAPwdwG4hxPsAIIRoFkLohRAGADsBfM+aMV4PGxsbxMbG4vTp07h06ZK1w2E3ASEEioqK8PLLL+Py5cv44Q9/iLvvvvumT5IAwMHBAatXr4aTkxP+9re/obv7mothq+v+thV6r0s4d/kVzJyZibDQ/5rwJImxm9WEJUpEpCQii7XdkzTq6y8AyoUQz5kt9zbb7F4AJyxV52SKiYkBEUGtVls7FHaD6+jowK5du7B//37MmzcPTzzxBMLDw60d1pTi5OSEH/zgB9BoNNi7d++UmmPJ0KtHd+UlXFiwBySTIyT4/027KQ0Ym04sligRkYyIsonoYyK6AOAUgEYiKiOiPxBR8DirSAKwBkAqER03/ssE8Hsi+paISgEsAfCzcdZjFS4uLggNDcU333yD/v5+a4fDblAnT57En/70J9TV1WHFihXIzs6Gs7OztcOakubOnYulS5eioqICzz//PC5cuGDtkAAA3aUt6HaqRIdtMebPewr29rOsHRJjNzRLTg9wEMCnAP4VwAljVxiIyB1SArOFiHKFELuup3AhxBEAg102TZs5k0YSFxeHU6dOoby8HAsW8F0rzHJuxtv+LSEhIQHNzc04fvw43n//fTz22GNWHeRu6NPj8id16AxRQyazh4/P/VaLhbGbhSUTpduFENdMFy6EuARpXNHfjWOM2BDmz58PNzc3FBcX33SJkl7TB72mD3azlej4tA7d37bCxtUetm4OsJlhDxt3B9jPmwFbV2kMjdAbYOjRw0bJp9RIGhoa8O677+Ly5ctISUnB4sWLb7o72q4XEeGee+5BaGgo3nnnHRw5cgSLF1vvwbKdXzZCr+mGxrMInp5psLV1Gnknxti4WCxRGixJup5tbmYymQxxcXH45JNPcOHCBcycOXPknaap/tZutOedgY2zHfTtveipbgf6BWTOchi6dLD1dIShux/djRdh0H532tjNcYKhpx/6th7AAMj9XaCMnw3HKE/I5PzlP1BJSQk+/PBDKJVKrFu3Dn5+43o4900rPDwcKpUKX3zxBUJDQzF79myrxNFd1oqe0AroDG2YNesOq8TA2M3GYokSEWkg3aIPfNdFJox1yIUQ02kWcKu55ZZb8Pnnn6OoqAh33nmntcMZFyEEOg7UoaeyDfK5TrCfNwN2Pk7oq9eg40AtDD16wCBg42oPp0XesPVyRG/1ZXS1noPtPQYovHxhbz8bMoMc/Rd70F12ET2n2yD3cIJtlBfIVoau4xfQ9l4l2vdVQ3GLF5Tf84Z8Dl9lA9IEknv37oW/vz9WrlwJpVJp7ZCmtczMTJw5cwZ79+61ShecrrkTPedb0ZT6FhSKefD0uG1S62dsIm3fvt2juLhY+eabb5693jKeeOKJOZ9++qkrAPzqV79qeOyxx9osEZslW5SuGhFqfMzIkwA2AMi1VD03OqVSiZiYGHz99dcICAiYVl1wQmeQUmQi9Ld0QZN/Hl3qZtj5KNF1vAWdRU1XtrVxs4frY/Pg6OMFne4Smpv3obunHh5BKWg88yI01SeAamlbW1sX2NvPhuvceHhG34bevou41FmF3r4WeGSnwL3r++gpvoxO9QV0FjXBbo4TlPGzoYjyhExxc3bNdXV14e9//ztcXV3xwAMPwMHBwdohTXsKhQJ33HEH3nnnHeTn5+O2226btLr1nTq0vnES7UGfoY8aoQrdA5mMp3Jg05PBYIAQYlwXGzqdDnZ2332+v/322zNKSkoUJ0+eLOvu7pYlJiaG3nfffZfd3d0HfeTJWFi8lYeIXAE8DWAtgD0A4oUQFy1dz40sPT0dzc3N2LdvH0JDQyGXT935UfSdOnQfv4DO4mboGjuvXikjOCS7wDZZDw9lDAwt/dCd18LOW4lmfICjlatgU62AXn9lQlacO/cWAMDf/wkoFYHo7W1Gb18TurvPobHxfZw/v1sqWmYPGxsnNDd/CBsbBbwWpGNWyl2wr5mHrq9b0L73NNr3noatlyPkvs6Qz3WG3NcZdj5OIJsb+1ZqrVaLt99+G1qtFo8++ignSRYUHh6OBQsW4PDhwwgNDYW3t/fIO42T0BtwaXc59B296Er6FjPsF8LNbdGE18vY9dq0adOs3bt3ewLAmjVrWp555pkLFRUV8uXLlwcnJiZq1Gq10wcffHB6//79zn/84x+9vby8dIGBgT1yuVwAQENDg+26dev8z58/LweA55577uyyZcs6c3JyfBobG+3Onj0rd3d379+3b98ZU51lZWUOycnJWjs7O9jZ2RkiIiK63n///Rnr168fd6uSJbvePAH8HMAPAbwKYKEQwiLTh99sbG1tkZqaitdffx2nTp1CVFSUtUO6QvQb0Neghb69F90nWtFddhHQC9jNcYLL7X6ADQEGQKa0AwX34XjFGvQcOw+ZTA4Xl1vg4roAHRdOoL29CO7ut8LR0R8ODj7w8FgMpWIe2tq/RmdnFebOefCaCfT0+i50dJTC3n42HB19ARDaL6vR1Pg+mi/koakpF/b2szHrjrvgiWWwOeuBvnoNeirb0HVMurXbxs0eTklzoIyfBZn9jdcb3NDQgLfffhtdXV247777MGfOtH8c4pSzfPnyq7rgbG0n9jxq31eD3prLEPc2obOzHEFzfzWh9bEbx8nyjb6d2kqFJctUOoV0RYRvHfJhu/n5+Yo9e/Z4qNXqciEEYmNjw9PS0jSenp762tpah507d9bu2rXrbF1dnd2WLVt81Gp1ubu7uz4xMTFUpVJ1AcCGDRt8c3JymtPT07VVVVXy9PT04JqamjIAKC0tVRQVFZ0a+MDchQsXdv/2t7/10Wg0zVqtVlZYWOgSHh5ukWe9WfIvvA5AC4DXAHQBeNR8EjTzSSLZyPz8/ODq6oqSkhKrJ0r97T3oOnYBPVXt6KvXAP1SS6ZMYQunBG/YL3RGu20hmjQfQ0ZyyGT26O6pR8uJTwAA4WG/Q2fnabS1f4X6c69DqQzGvHlPI8D/8Wu6Dzzck+HhnjxoHDY2Cri5JVy1zM01Hm6u8QgJ+Q1aWz9DU9Ne1Nf/BWfFDjg6BsA5JhzKW4PhSIGQX/JG/9c2uPxRDTo+qYNy0Ww4JfrA1vXGaHE5ceIE9u7dC4VCgUcffXRSWjtuRqYuuLfffhv5+flYsmTJhNXVW3sZnUcb0Z9Qj5quZ+HiEo05cx4c9f6dl3tRXX0O1TXn0FzfgZ5mA25fFwlVaNCExcxubocOHXLKzMxsd3FxMQDAihUr2g4ePOi8cuXKdm9v7760tLROADh8+LAyISFB4+Pj0w8AWVlZlyorKx0AoKCgwKWqqurKg3C1Wq1NW1ubDAAyMjLaByZJxv07ioqKFPHx8WHu7u66mJgYra2trUVmirVkovQHfDeYm2ewGyeZTIaoqCjk5+ejo6MDLi4uVonD0KvHhRePw6DVwW6OE5wWzYY8YAbImaB1PI5zrS+g5fSnMBi6IZM5QAgDhOiDra0zZs5cDj/fdXByCr1SnhB6WHDC9itsbBwwa9YKzJq1An19rWhu/ght7UXQaE/iQss/YDo1FbfMw+zELChOxkN75Dy0R87DcYEXnG+dA/nc6XnaGgwGHDp0CIcPH4afnx/uv/9+ODnxgPaJFBYWduXvMywsbEKSUu1XjWj/oBo9vlWon/E/UCqDcEv0a9dMCdCt6UNLaxuaWlrRevEyms5fQkdDH3BRDrve7xoThEEHp94GXKoigBOlm8JwLT8TZbhZ7BUKxVXjhYaanP3JiAAAIABJREFUUV4IgeLi4vLBEiKlUjnkmKOtW7c2bd26tQkA7rzzznkhISG9o417OMMmSsZHkLwhhBjxSa1CiE2WCIh9Jzo6GocPH0ZpaSmSkwdvZZloXcVN6O/SwvbBLmgcv0SD5gQ07SfR39oBIfSwtXWFt/e9mD3rbsyYEQMiGYxzjYLo2onfJyJJGkgu94Sv78Pw9X0YAKDXd6OzswoaTRkam95HTev/QjbbHl5hy+HWkIbuIhm6S1ogD3CBc8pcOIS5g2TTYxyTTqdDbm4uTp48iZiYGGRmZk54VxCTZGRkoKamBrm5uXj88cct9r4LnQFtH5xGV3EzbEIJdf6/g6ODHxbe8gbs7GZ8t50QePWlXPR86zqgADs4d1+Ea8d5KLRnIe9ugJ2uBX32QLezAjN1T1okTsYGk5qaqn3kkUcCnn322SYhBPLy8txef/31moHbpaSkdG7cuNG3qanJxs3NzZCbm+sWGRnZDQDJyckdW7dunfnss882A0BhYaFjYmLisA9d7O/vR2trq83s2bP1RUVFjqdOnVJkZWWdGW6f0Rr2L1sIoSciLyKSCyH6RlMgEXkBeAxAgHn5QohHxhPozcjDwwO+vr4oKSlBUlLSpD/PSegFOgrP4uytm9Hbch5EdnByCoGX51LY2jrDzS0B7u7J14wlGixBmggdPTo429uO+L7Y2DjCxSUKLi5RmDNnFTSacpw/vxtNzR+g2WEvnDIj4dmzAlQUjotvdsB2lgIut/nCMcprSg/81mq1+Otf/4rz589j2bJl+P73v8/P/JpECoUCd911F/bs2YNDhw7h9ttvH3eZ/e09uLirHH3nNOhPPY0axz8BOiAsdDPkcvcr2xn0Brz8P++i/zRBfmkX5H1tgOgDoR96Gz10djKcl9tA52G6MPG4su/FY58g7N77xh0rY4NJTk7uys7OvhgTExMOSIO5k5KSuisqKq76ovD399dt3LixISEhIdzLy0sXFRXVpdfrCQB27NhRv379er+QkJAIvV5PixYt0iQmJg47bUBfXx8lJSWFAYCTk5P+jTfeqDG/K248aKSHPRLRy8D/Z+/N46Msz/3/9/3MvmZfCSRA9gQQEgHDJqKAQF2LIq61VlvbnvbQxe8551eP59hvv9r2WJcuitVqFVyqRxALroAsEYQoO4RACGTft9lnnuf+/TFhDxAgrM779ZpXMjPPc9/3JJPM57nu6/pcjALeBw6VNZ0o50gIUQqsBsoA9Yjj3+2H9fYLxcXFcuPGjRd6GX1i48aNfPDBBzz44IOkpqae17k9W5rZt/KvNBT+ldzc35CSfNN5KUmuanGzfl8rAVUSCGkEVY2QqjEgxkKy08KaPc18uK2Bvc1uYm1G8lOc5Kc6D30dEm9Drzu1WAuFumloWExN7QLc7t3odQ7i9ddj3zwW3YFYdLFmHJPSsI1KQhjOj/jrK42NjSxcuBCPx8Mtt9wSaWp7AVm8eDGbNm06a0NPX0U7bW/swm9opG3CP+gIrMPpGE5u7q9xOAqOOvbDDz5h93sHCHUvRieCmAwqQhC+6UAa9ARNJjwWG91WJ22OOJqiEqmNGcAtHTv52Xf/44zWKIQok1IWn/GLjHDO2bx5c9WIESNaLvQ6LkU2b94cP2LEiIxjH+9LrLiu56bQt9wjq5TykdNbXoQTUVBQcFSPrvOF5gnSsWwv7YXLsNvySE257ZxGK8obutnV0EVOsoOfvb6BtpZmfNKAXxrxCwX1iKl1imBMRjQzM6NoCirsaOjmldIqAj1J5ka9Qm6ygySnmZCqETwouDSNlCjzEcIqigED7mTAgDvp7CyjpvZ1GpveoyH3bZzDiojaN4nQIhddnx7AMWEAtjHJF0Wl3J49e3j77bcxGo185zvfOe8COsLRTJs27VAV3Pe///0zsvNwlzXS9u4OOgqW05L6LkI1kJ39n6QNuLPX7eqKRdsIupZjN/gpnXodOKxoQkEVAoPUsMsQdp2OWJuNrKQUEqLjiTZaiTbaGOSY0R8vO0KEbwyn/K8vpfwvOGQgKaWUrlOc8oEQYoaU8rJpVnshsVgs5OTksHXrVqZOnXpe3IClJmn7x266jF/it9SSmf7zfhdJLn+Iv63Zh0GvsG5vM/W7dxOj+dmnRHFbaztGaQehRwgJQoeUIM2tBBNUjO0CNgZB8zJAZ2JQfBf3jEohLbeAhoCOHfVdbK/rpLrNg1GvYNApGHUKRr2e7XVdLN162Pjy6IjUL8jJ/ldMgaXU179JddpTGAbFEdN6Df7PxtK1Igl7SSr2ktQL1mNuw4YNLF26lMTERObOnUtUVNSpT4pwTjGbzdx000288sorfPbZZ1x//fWndX6gupuGj5bTMHE+PuMBEuKnk539K8ym3tukfPbZGkL+WoSEimvG8be7f4aiXFwRzwgRLidOKZSEEIXAa0Bsz/0W4B4p5fYTnPIT4N+FEH4gSNirWUopL0zZ1mXAiBEj2LFjBxUVFeTm5p7z+Vyra3BXVNM65V3MpoEkJp75FWh1QzsbduxjUnE+cc5wGX6XL8gvn3mH/EorLuFmlGaHUACpdTBO7yDoKSOg1h09kAS9iEbXnoYWrCOktYEAIRXUrmRqawZTv6wJ9Abi0vzcc9VQrigsxGmzY7LoUY7Yiuv2BdnV0M2Ouq7wrb7rqIiUSZ9BXvLjjB+0lzznpwRj3qFp0v8S5RmLs2wi3atzsY9JxTFhADrn+XFH1jSNjz/+mHXr1pGdnc2tt96KyRRxZr5YyMjIoKioiA0bNjBmzBhiY2NPfRLhyG3926uoGfV7FJuB4XnzSYifcsLjP1+9jh1v1KAFyrE64bff+VVEJEWIcI7pyz7CfGCelHIFgBDiauBFoKS3g49tZRLh7MnMzMRqtbJ58+ZzKpRCHX585W10fFRJ0/hX8NPAqPwFKMqZbTdt3FZB6dMbEGgsfLOWDlMTjYkG7C0+8rsg5HkXA0ZU6UEToaPOtToFTWmpGAMBjMEABr8fa2sj7kArNkMIb1wUHTExxDU3o2vbh8tXBz4QUofaPYBde+op15UjhIGDb3MhVDCHcGSZyBs/jDuvzENvCEfogqpGZbObHfWdh8TT65sG0OGZS5x5GpMHruHqgV/QOXotwptOYuUUnOuuwj5yIM5JaejjLMe+/H7D7/fz7rvvsnv3bsaOHcvUqVMjH44XIZMmTWLz5s18/vnn3HzzzX06p23lLg5k/T8wq4wc9SZ2W9ZJj9/6SilBVyl6QrQOvyLyPogQ4TzQl09A20GRBCClXCmEOK67phAiQ0pZdaJBRHjvZoCUsuaMVvoNRqfTMXz4cDZs2IDH48FqPXujVSkloRYvgX1d+Pd14q/qRG0PW060D19Gl3kD2Vn/SXT0ifM2uzrdrCvbTNWGffgO6BBBB1LnRjX6kCEFg99IyLUIKT0IqeDUpeLsHgrBBoLB3Vh1AYx6iWo2UDdoIC2pySQdqCWqswP7qKv4wT3zDs2laiqLl79NRUMNI+OTuG/qXPSKHm/Ax4J/vkxtayNRdQ0k19YhO/fgDvVeICG69LS1pfJF2T7W6b5AZwNntp38SSO4Ij+HnGQHN488/DNq6PL1RJ6u4sOGZvSBTxgZ+wmy4GVqs94iruZq4p69htZQHLsNkvKBVhKHRB/azkt0mBBCsHZPCy0uP/kpTgb3MdkcoLOzkzfeeIPGxkZmzJjB6NGj+/gbjnC+cTqdjB49mi+++IJx48aRmJh40uPV7gAHmp4nMLCBUSMWnlAkBYMhPl5eSuXHNYT8VQgC7L26iD889F/n4mVEiBDhGPpS9fYe8BXh7TeAu4BiKeVNxxz3D8IJ34sJV7w1A2YgE5gMTAH+U0r5SX++gDPhUqp6O0h9fT0vvPDCWX9YSinxbmuh85/7UDvCwkjYdIihPkJpzfice6lue4nk5JvJz/sdQgjefPldWre40fxG0PQITUEqArQQWqgWGayGwH5UfOgwoQgbEpUQnRjQ6MpJIa65Gdp9eKQRAyoWp6C26EoKc/IYPnQE2YMOV22pmobuDK+U3T4PC5b+jd3NDRi7u9GFQugP3oIBYpraULuDeDRDeFMYBaFLQtEPQNEloLMqROVFMWzyKApzs9H1Imi6vAG2V31Oa+PrmNVShNCQ/lisXYOIrb6aDS15vEqQPWjE2YykRJvZVtt16HxTT7J5ZqKDNrefyhY3dR1eBsZYyeup3hMCGurrMVSVIjSVm26+lcL8nOPWEuHiwu1288wzz5CVlcXs2bNPeJxUJXULP6M85Yckxn2LwpG/p7Ozm/auLjq7XXR3e3C5Pbi63DQsU9ECe5G+rYTUWmxRgofmv39BrCAiVW8XP5GqtzPnRFVvfRFKMcB/AQcdD1cB/yWlPK7RnBAiH7gTGAekAF5gJ/BP4B0pZb/0XTlbLkWhJKXkhRdeIBgM8sMf/vCMQu6hDj8di/fgKW/AnfcVofRavIb9eAJ7UdXDDW1jYq5ixPC/otOZ+XLtOkqfX4wWqEBKP4jj3y8mQpit4ImyY3Z7UXxhy62uxDgaMofwxEO/pqmzkb/+8zWafG5MRgtzrpxMUd75b+ypaiofLH+bLyt3YmxqIrGmDtEZwKPqkT2fO0KJ6xFO8SgWhbiCBIZdeyX5WZlH5ToBeL01NDYuwe3eQ1vbFwSCjRg8ScQcuJZg6FpWRNkp9fiYnJPAlLwkdtYfzouqaHIRbzcxJMHGgGgLB1o9bK/vpLrNS4rSxRRDBT70fBrIohMrg+Nsh4RUfqqTghQnic7Lo/3K5cSnn37KmjVrePjhh3uNKkkpaX6/jHLxr4Ts7cTH/5kVf1iNpvZmIqyh+jcBYBFBgkkOlBFF/Pj+fwNgZXkTSzbXkxFnDRckpDpJdprPmYiKCKWLn0tVKD377LNxGzdutP39738/qV/SyZgwYULWpk2bbMXFxa4VK1bsOfj4rl27jLfddtuQzs5OfWFhoefdd9/dZzabj/swOyOh1OPM/YSU8hdnuvCecQxSyuDZjHGK8acDzwA64K9SyidOdvylKJQAduzYwdtvv83NN9/MiBEjTnm82h3As6UZtSuA2unHu6OF7oR1tBS8R4AGDIYYbLZs7PZs7LYc7PYcbLYs9PrDaWbP3vefBL1lOIwhAtE2gkY9qt6A2e2mKyaGttRknI5obp/0LXIG5tHq6WDdppUEg0G+NeEWdMq5r9I7W7aVb2Dx6qUEW5qIr6lH3+bBq+o55JOvOFD0A9ApcShGQUx+MoVTihlWkH+UcNK0IM3NH3Fg/yt0ub5GCZmJqp1Agu4mfFo1BqOD5KumYx4c3es6DnKgoZmFr7yM0+nguhtnU9Wp9YirTnbUd1HddtigNt5uOspD6uDWnk4RSCnZWttJSJPkJjuwGi+8tcE3AbfbzdNPP01ubi633nq8sWPb59vZ3vEwQXszrXuvp+bzAFpoH0IKxMEuUEdckAgkpDjwjRnND256kCiLg6Cq8R/vbeXtjTU4zHq6fYdz/KxGHQOiLQyIsRz1NS3GSlqMhQS7CeUMnecjQuni51IQSpqmIaU8qor7dIVSMBjkWEPJxYsXO9xut/Liiy8mHCmUZsyYMeSmm25qf/DBB9vnzp07aMSIEd5HHnmk+dgxz8hHqceZu6gviz6WnpykycBc4FtA0pmM04d5dMCfgOuAGmCDEOJ9KeWOczHfhSQ3N5ekpCRWrVpFYWHhcVYBancA/54Ogi1eQi1eunftpjtpA5ouhLAK3CVf4TFWYLfnU5D5W2JiSk565blu1VpCgRp06NHP+Dbfvf1edKf4BxtnjWZmyU0nPeZiozDnSgpzrjx0v72zlYVL/kZzQw2xNXUYWzrxBVwEkeCDhnVGmjZ+yUolAUUHlgFRCKmBgOzJxRRPWEDQX86Bqpdp0i+lncO7zdVb/kLC+m8xsOhOrJnJx/38W1paeO+thUipMWfOHGJjY8kaANflH/7z6fQG2VUfjkodjE69tKaSoBr+cDUbFHKTnXT5glQ2hyOFQsDgeNtx5pyJjkhEqr+x2WyMHj2a0tJSJk2aRHx8/KHnunfsZ0f7jwk6GrGZf8bmlRvR1HqM0UasE8Zji4rFE/DjU4P41RA+qaEBD0ydQ1L8Yb+stzZU8/bGGh6aNIR512UTVCXlDeH3Q1Wrh9p2LzUdHjZXd9DuOfoa9W/fuZLJOSfPn4oQ4Wx47LHHkhYsWBAPYWfuRx99tKm8vNx4/fXXZ5WUlHSXlZXZFy9evGfZsmWOP/zhDykJCQnBoUOH+oxGowSoq6vTf+c730mvra01Ajz11FMHpk6d6p43b15qfX294cCBA8bY2NjQkiVLjmpRcuONN3Z/8MEHRxWUaZrGF1984Vi8eHElwP3339/62GOPpfYmlE5EXy4xvxZCvA/8g6Oduf+3t4OFEGMIi6ObCVsK/BA4q4jUKRgN7JFSVvbM/yZwI3DZCSVFUZg0aRJvv/0227ZtOxRVkqpG+5qdHNj7Mh7nLjS9DxnlJzCp/qjzTaYU8of8juTkm07ZZqTL5ebLlz5Hqo2QbOP+O+47Vy/roiMmKo4f3vXzQ/c1TWPJh6+xpXwr1vp6rA2dBP21BAlf+AT2HD73y71fsvFv76ITZjDpGDjmYTKKfWx672sMxiBJhbXUJv6F+r1/J3bTdUTFDMccnYwlfiBt0sJbb72FoijcddddJywxj7IYGDMkjjFDDrelCIQ09ja7Dgmn7XWdWI1mvj9xKNFWwyFRtam6gw+2HH5fnCwiFeHMueqqq/jyyy95//33ueOOO7BYLIRcAXbs+Dn+6BoOrBhNe+UXSLUJfYydHz//Zp/H9gVV/rh8D8XpMfyf6bkIITDpoSg9lqL0498zbn+I2g5vj3jyUpAacWr5pvDTnQcG7nL7zr765whybWbP03mDTthsd/Xq1daFCxfGlZWV7ZRSUlRUlDdlypTu+Ph4taqqyvziiy9Wvf766wf2799veOKJJ1LLysp2xsbGqiUlJTmFhYUegIceemjgvHnzGqdNm+aqqKgwTps2LauysnI7wJYtW6zr16/f1VvD3N5obGzUOxwO9WD0KSMjI9DY2HharrB9EUqxQCtwzRGPSeAooSSE+L/AbcAB4A3gv4GNUspXT2dBZ8AA4MhfWg1w/pNf+plX5/+G+qZqxo+bzvjJNx56/GBU6fPPP6ewsBBvZTV7Nz5Ha9yHyAwfDvMwjNYkdHo7er0duy2b1NTbEUKHEIY+5S54/X5emfciQf8mDAjiJ99yLl/qRY+iKNw4415uPMJOqqF+P2+//yqeugPYGluRegURAtEdIhSqI4gfglD5WTmVy20gw9cYjdvicaREkT5SpSVtMS1iEXQBXeDqjiHOnotrm57/fezfUQIS1S6wZKRw8z0/ITFlwAnXaNQr5KU4yUtx0lsXr6kFh80LO73Bo3KldtR18dLe4yNSB4XToFgruxu7SXSaI0Kqj9jtdqZMmcKHH37I8uXLmXH9DCo+/T2u2K9oWz+MtooOFEwo8TYe/P3LfR63us3Dj974moYuH3+4/Yo+/T3bTHqykxxkJ0WcWyKce1auXGmfMWNGh9Pp1ABmzpzZvmLFCsfs2bM7UlJSAlOmTHEDrFq1yjZ27Nju1NTUEMAtt9zStnv3bjPA2rVrnRUVFYc8V1wul669vV0BmD59ekdfRRKEcwKPRYhekm1PwkmFUs+21hYp5R/6MNaDQDnwF+ADKaXvdBdzhvT2n+K4eYUQDxJe41n1YzofrFv1Tzo/K8OAnw1b/8aml17DP8DO1NsfIC4+GXfjHvwGPcteuQProK3IxCD+A4OpLkvD3xGNiDZwzUN3k5tTiNvjRac72uPH6/OxsWwLGmB32HHYbDjtdpx2OwaDjr/+9M8Eu75Ep3lpK87kxzfedmF+EBcxySnp/MtDj/b6XEtbA++8+QLuyr0YW3zgB81pRxmcQqi6CX8L7FoGGOyYnQrGeAfBAQHSkvcyJP8LRKaVUH0ifq+gZrvA9VU7r3/1Q3SY0enD4imU5CRj2Ghm3HAXFtPpbZ9FWQyMHRLH2GMiUnuaXEds53XyweY6Fq4/Pl3gWCGVn+ok2mJgX4ubymY3qgznREVZDD29+iRBVUOTkox4Gxlx3wyhNXbsWD7/8H127ViGvf1lQimbUaszqN6kQx9tYdJ3H+KK0VcDYQFU0dRNVqKDtBjLCQXQr/+5g71NLp67YyRXDY3r9ZgIEQ5yssjPueJkec9Wq1U78v6J3udSSjZu3LizN0Fks9m03s45EcnJyaHu7m7dwZymqqoqY2Ji4mnlTPclR+kGoC9CKRmYCtwBPC2EWAFYhBB6KWXo5KeeFTXAwCPupxHuTXcUUsr5hM0zKS4uPh8Crk88/9azdPn9mISkraWJqLpaTDVugmgYDAWo0oc/uB+qWvjkyadQ9CoFJSr67AqEoqLuH8qeLwWedj3QAjRDM3z0myf5SJgBBb0+GUOCHXtqPB07mtBCKpraBAiEsIBiDn8VFoQwEfKWoWguOooG8/D3/1+kI/1pEh+bzPcf/s9THic1jZraWl555RXSDGlcO/VOqksX0dD+JvqEOvSmTrJzA6itiTRuT6Z1rwV/oAM6gtDhoqp8EfPfWYZOAawSb6ITJSWVCSVTKR41kV07NvLe+39HSg1jbByjhl/FpLFTMeiO/7M36pVDVVP0ZCVKKant8LKrvpuBsVZUTfZJSJ0Ko04h1mYkxmYkzmYk1mYkLcZySHhlxNlQepLR9za78ARUspMcmA0Xb2HAsiWvsWPVJ+hdAaTQIYVAH4RRk+tQkvYTDBnx78pk77ookicMZ+6Pwk1pq9s8/J//3cLaPa2HxnKa9eT1CNC8FCef7mikzR2gssVNmzvAD64eyrdGRPr7Rbg4ueaaa1z3339/xuOPP94gpWTp0qUxr7zySuWxx02cONH9yCOPDGxoaNDFxMRo7733XkxBQYEXYPz48V1PPvlk4uOPP94IUFpaaikpKfEeO0ZfUBSFsWPHdv/tb3+LefDBB9tffvnluFmzZnWczhh92XorFUL8EXiLo3OUvjryICmlCiwDlgkhzMAswArUCiE+k1LOPZ2FnQYbgCwhxGCgFphDOEfqoqbiwHZefftFkjeUY0BBQ+AkHArzCTMGYzb3PvdLzBYrH7/5NlWrS7HFtJExYS/S1k6oroBNdUMRbSrW+CBJVwykeMK1rFm+BPe2nSidPgJa+L0QVOsI1oCnxkC4qwwYCFfYqIAqOSouJyR0jhjE7ff8OlJ+fg7p7OrizTffxOl0cvvtt2M0Gxl6zW0MkbORPhX33hqqty6g1fYhqRO3MHCiHYNuAjtWCDxVRkRIoEo/Ia0FXN0orhaobGHN2m18KZ5GlRIzas9sB9i2chPlz/0ZvUklEGWjIyGOUFQU8XEpTCm5jtz0/KNsJ4QQPZVSh1McehNSO+q66PQGGZJgY0i8HUUIdjZ04Q2oh3vt6RWklOxpcrGn2UWbK0CbO0CbJ0B1u4elW+sJaeHrF6tRR2aineo2z6FEZEXA0AT7IfEwINoSFln2sNCKsRox9NHE83RpaWrgT6/9FhEMgk5B0Rsw6gyEAn5s+2vQtYQIaCqgcvCKUCgaGWMEStJ+mipHsbdmCNamRq770X0MG3M1UoZF548Wfk2Ly8+867IZPTj2qDyzN7+sxhtUD61jzpUDyU5yMHfMxR0Rj/DNZvz48Z65c+e2jho1Kg/Cydzjxo3zlpeXH5UXlJ6eHnzkkUfqxo4dm5eQkBAcPny4R1XD7c/nz59f/cADDwzKzs7OV1VVjBkzprukpOSUV2VFRUU5lZWVZq/Xq0tKShr+5z//uerWW2/t+p//+Z+a22+/feivf/3rAQUFBZ6f/OQnp1UV2BcfpRW9PCyllNf08nhv5zuBm89lrpIQYgbwNGF7gJellP/3ZMdfSHuAZR8t5Ks1n5JcXUunx4BUHOiMmYCGUGLRGSF2WAITb7mSUHAl3a6ddHdsx+vfD0Ki98WSaf0VKRNnMX/+fAKBwCFfpb3NLrp9IXKSHZj1Ci+9/Fu6fS78rk6i9h5A+FVcA2LwJqdRbRhBsw+SqcGm82LQ+1FCfpRQEE1nYsq0f2VKXu9NOSOcPW63m1dffZXOzk4eeOABEhISej1OSolvbwcN65bRrCyhO7EMFJVox1gGpt+NwzGBrVu2s/2TL+je1wQBBY0gmtoGQkGvT+tpKiyRWhea2obU2uAISzMhwaRoGA0qAaeVzvgY3NHR6JzR5KSkc1XxRP6+7G2cRjOjC0dRnDcas77vfeZcQS9VLfup2LOd3KzhDEnIQK/oUTgceveHVPY0udje03+voqmb1CgLmdGt+Dy1dBoy2N9sYle9i9qO4y8sFQFDEuyHPaZSneQmOzHqFbp9QVz+EO0eL3F2M5nxThRF0NHVxpMLnsLQ2Y6m06NoGkLT0GkqiqqhSA0RUrG1dhJsDZz4BQoben0awiBwZASJSd2DI+0AmDyY2/JIGfksf3/t78yaNYtB2YW8tHYfH25rYH+rB6tRx2vfHd1rEraqSapa3exrdjN2aBx204W3d4jYA1z8XAr2ABcrZ2w4eboIIVIIR3WGAE3AW1LK3f06yVlyoYTSutKP2PzKc7g6QcEKhnQMtsEMu28MJqOBKwpyMJtNSCnZ8OUcut0bMfgTMHUMxOQaiM2cS3LRdCw5aexrcbPuq63sXf8xrfEjWNNmO3T1fbAU/GBp+MhB4ZYaLn+ID7c14A9pZCXayUy0YzHqsBp12Ix6LD1fh6dFHVVRFaF/aWpqYuHChbhcLu644w6GDh3ap/MCtS7a1myhsfM9OgZ8TsjSilGfwIC0OaSm3o7ZnAKA3x9g245dICWjRg5HCIGmalTV1FG+ZSeNO2vxVHejusJ5Q1JrR2ptSLUNqXVxZIqfERWTEsKlGtEJiUUJIsx6PFE2up3RuKMcBKOdSAT2YWfsAAAgAElEQVSW5hbimlowBAK4HA4EErPPi8njQ+8PQEgijQoBixmpKEghkD1CKWQw4LbacNvt+Jx2QmYT0XUNDKqqQvEF0Ux6/GYzXqsVn8WKqtMhNA1F09Bp4ZQFv8mEz2IhaDWjmg2oihl9wIOjvQNnaxtR7R0ICUGjnoDZjMXlxtOuHVrDyRC6RPTGPIRUw3FYqSJQkTbQFQ8nNCCRZPUZ4i1fg6bD3jISp/lGnq5PR7UYGNS8DiFD/MOTjyegUZIZz/SCZKYWJBFvv3SaG0eE0sVPRCidOactlIQQT0spf9rz/U+klM8c8dwrUsr7ejnnX4CZhH2NdgOJwDzgj8ByKeVpJWGdK86XUNpXV8GTKxcRUFX0mkpGxR5MFc3oTKPQOXJwFhj49n3fwmY9Otm6pXUVmzd/h/idd7K3ZjJ7ovT4BjsYlBbFtroulm2txx1QAcm3jDuw6iVa7lSuHBxPlNVwqKLpqwMdtLj8jB0Sy466cAuNG65IZXbRQIanRUVyjy4AFRUV/OMf/8BoNDJnzhzS0tJOe4xQm4/uNQdorPyYjpTPcMdvBaEQHz+ZAam3Exs7sc+NjP3+ILv3VbFnWwWt5U34GkJID0gZQqptaD0CSijRCGFGqm2gtqFJzwnLKAQCebCOQ4IOAwITQpiQ0ouGn4NiTB78eoK6D0Xq0GNHkz5UETjhcb1z9J6yIg2AgiSIFOF/RYoxH50xH9AABYEGPWIofNMAlSqHStfIieyo66Khy3fUHGOSN3Jf3juYFJXoym+xpnYsrwbMtCLRKYLB8Ta01v1MNFRSEzWMf79rGkMS7KfxOi4eIkLp4icilM6cMzGcnHjE9/cSdr4+yPBjDxZCzATGAtOB2YT9jSCct/TvwGAhRIWUcuVprfwSZNOeL/nDV6Vkb97KiMpqPNoRW7PCjjV7MN/7j7m9CpWOzm18/fUvMfrjKFems3tcdNgXZ1cTnV/XYjPqmDk8hbFD4shNdqJ1DOGdt9/mxiwYOTKc0z6t4PgtMyklUnLGjrwRzg4pJevXr+ejjz4iKSmJO+64g6ioqDMaSx9rJuaGbKI8g3Gtu4G2sk20x35Ce2gtLS2fYjQmkZpyK07nMNzuPZjMqSQmTEWnO95OxWQyMCw3i2G5Rzdk7e72sH33Hqp27qOrsh1zih2T3UznvnaCLRLNbQZVIGUnUu0ANIQuEaGLAyERUhD2lNYjdF6k3g8GFeE3olNtgAJSARSEUMLCTHOB5kJKF1JzI3QJCF08mNzoQhYU1YIQIaTm4aCwOXg+SKTmQ0ovSA9S8yKlFyGsCF0cihKD1HsReg1UHVJVAJXYYj03z52FXqdHb9Qd9ffhCYSo6/Cxp6mbGQn2Q+X1rS4/O+u7aeqoIjr4J6RvFeb2TAa2/pTU2yaTbhCMqu9me10ng2KtXD8sBY8/yEsvvYSlew8J5qln9HuPECHCheFkQkmc4PsT8S/AfVJKKYQoJtwM92PCjtnrgfeAl4GVZ7bUC89P33yK3Y54bKoPeyiAQwsRpYOOkKTBZKddZyG+uYVhFVu5al81btWIqsViMeaj6YyoihGdEsW9v7jzKJEUVMNmgSs3vUm67ikMQTuxW35CyU9HY7CEf0VSShq7/ERZDFiMh6t/ZEoeXwwYwPLlyykoKMBo7N1HSwhBJIB04fjkk08oLS0lNzeXm2++GZPp7LdbFKsB5zWDcExII/7rK+letZ8OZR1dGWuoCjwPh5uwUK6zkRB/HUlJM4mNHY+inNxvzeGwMrZoOGOLjrsmOkTQH6KyuobKqhoCgSD5OUMZkj4AnV6H3xtECIHRfOrIlpQSnydAbWMzdY1NNDe109XqYtDQZCaMHYXRFDaK01SN7i4vDc3NaFJiMBgw6g2YDOEGxx3d3bR3dtLZ6aKr24233U1UQhQ52YPJzBiI3nh6VXNWo57Mni3qgwQCrQRda4kJriLoWoZUJQl7biMt8V5i7s9G6BXigPFZJsZnHXbktpoMzJl9Ky+88AJLlizhjjvuiER0I0S4RDjZfzGlpyGucsT3B/+ye/uPkyilPGj5WwJM6BFNLwCrpZT/JoQ4sWPeJcDQzV8yvKODkKJH1elQdQZUnY6BHjdXePy4fHpCMvyjUUMOTI5rkcYhaAPaMTh1WO0GCoszMZnCH1LVbR6+++oG9jZ3csOQZcwa8jFKZyYZm35E/C1jDokkCAud5KjjK9CEEEybNo2XX36Z0tJSrr766vPys4jQdw4cOEBpaSlFRUXMnDnzjBoanwxhULCPTsFWnEz0zky6V03GvbmKkLkNo2sA/qgDuPM20qx9RkPjIvR6JwkJU0lKnElMzFUoiuHUk/SCwaQnJzODnMyM454zWfo+phACi81E5pA0MoeceCtS0SlExdiIirH1+nxScu9O5meLpgXZv/8Fmls+obt7OyDRSyeOxiuJ33cLCdPGYCs+dYemhIQErrnmGj7++GMqKirIzs4+J+uNECFC/3IyoRQFlHFYHB1pB9BbooBLCBEvpWwBOoFZQoiPgGlAtxDCBvh6Oe+SIbotRHenRJUhNFRUQkgEPqliDUBcwAj6FNxRVxCMzkImt3DjAyMYNPDorbBASGP5riaeWLaTeMMWnp2yGLPYT1TbNSRumkvCnGFYCuNPsIrjGTRoEPn5+axdu5ZRo0bhdEZaFFwsuN1uPvjgA5xOJ9OmTet3kXQkQhFYCuKxFMTj3z+YUKMHXZQRX2UWng0FxHtvx5tejidrE02Ny6ivfweDIYbEhOkkJs0kJno0YY/ZCAcJhVwcqH6Zffuewa4UktQ8B9PeLMzdGViy44j+/lD0cZZTD9TD6NGj+fLLL1mxYgVZWVmRqFKECJcAJxRKUsqM0xzrFcK5SPMI5zT9O/ADYFfP/XmEW5tcsqSb0pG19YR0ZlS9mZDORFBvodORTnfSYPxCjyREKL6Tq25IYszoKceNUdPu4Y4X11Hd5qU4tZYfFD6H2ZRGQvnPsFQOJ/7ufCw5p39lfO2111JeXs7y5cu56aZLqynt5UpdXR1vvfUWLpeLOXPmnHBb9FxgSndiSg8LZnNOLFHXpuPd0YJ7QzzWTwqI1c0mMGwfroEbqW9YRG3dGxiNCSQmTicpcRZRUaNO2Q/wckTTgnR1baatbS1t7Wvp6tqElCrWtgJSN/4MY7IN67gkLFckoI86/e1TvV7P1VdfzaJFi9i1axd5eXnn4FVEiHDp8eyzz8Zt3LjR9ve///30XWx7mDBhQtamTZtsxcXFrhUrVhzqwvmb3/wm4fnnn0+qrq421dXVbU5JSTktE+z+NOZ4GVgghPgN8Bsp5TwAIYSdcN+3dODb/Tjfeeer5BEYCmYe9ZimBAlFeYjNVBk2Ip1hwzMxnCAXwu0Pcc9LX9LpCfLi3cNwuP5I0JvAwOW/QheyEHdfHubMmDNaW2xsLKNHj2bdunVMmDCBuLhIef+FZPPmzSxZsgSr1cp3v/tdUlMvrJOyMChYRyRiHZFIqM2He2MDnjI75k05xDvmEBy1jy7nOurq3qam5jVMpmQSE2eQlDQLp2P4ZRv5UFU/XV2bcbl20NZeSnv7elTVBQgctkJS9HMxlqdjrBlM0o9HYRxw9tVqw4YNY/Xq1SxfvpycnJxzGmWMEOFiRNM0pJTodGcewT7YkuRIfv7znze43W7lxRdfPMqYbtKkSa5bb72185prrsk5k7n6TSjJsM/AXCHEvcDinj5xB21l3wR+JvvbtOk8c+/3bkULSIwWPQaTDqNZh9IHN2ApJU3dfhas209li5vX7svF6nmEDvduBnz9U0yxccTNyTmtEH5vjBs3jg0bNrB69epIVOkCoaoqn3zyCevWrSM9PZ3Zs2djt19cpeD6WDNRUzNwXpuOv6Id98ZGWKMnTs0kMf0+AsMraLeuoqbmNaqrX8ZgiEPKAHZ7HnGxE4iNm4jDnn/JR5y6urawfcc8PJ59AFgsg0iMnYm9sxDDrnTUvRpI0MeZcd6c3i8iCUCn0zF58mTeeecdtm/fzrBhw/pl3AgRLhYee+yxpAULFsRD2Jn70UcfbSovLzdef/31WSUlJd1lZWX2xYsX71m2bJnjD3/4Q0pCQkJw6NChPqPRKAHq6ur03/nOd9Jra2uNAE899dSBqVOnuufNm5daX19vOHDggDE2Nja0ZMmSfUfOe+ONN3Z/8MEHx3V/Hjdu3Bm1PznICYWSEGIp8LCUsup0Buxx4D5nLtwXkpiE3pNIT0S7O8Dj/9zBR9saenyPYOxgG8bOH9PpqWRg3Tzs3iISfliI0ofqoFNht9spLi5m/fr1TJw4kdjYc5PcGqF3XC4X77zzDlVVVYwZM4apU6ee1RXTuUYoAnNOLOacWFRXAM/Xzbg3NKBbMpgE41BShz+ML2c77doqEAp+fz17K/+HvZX/g8EQR1zcBOJiJxEbOw6jMQ4pNYLBDhTFgF5/8XSql1Kju3sbLS0rcHv24vc3EvA34fXVYDIlkZv6O0zNGWibdQT2d4W9oBJNOCbHYxmWgCHZ2u8Rtfz8fBITE1mxYgW5ubnHXRlHiNAf/OKdzQN3N3Qf7wtyFmQnOzy/+/aIEzbbXb16tXXhwoVxZWVlO6WUFBUV5U2ZMqU7Pj5eraqqMr/44otVr7/++oH9+/cbnnjiidSysrKdsbGxaklJSU5hYaEH4KGHHho4b968xmnTprkqKiqM06ZNy6qsrNwOsGXLFuv69et39dYw91xxsk/nV4CPhRCvAr+VUp60264Q4gvgP6SUy3t57jMp5fEJO5cxy7bW86vF2+j0Bvl2URp5KU6GxNuJ52/UVpeTGfoNum2pRN2S0S8i6SAHo0pr1qzhhhtu6LdxI5ycxsZGFixYgMfj4eabb2bEiBEXekmnhc5uxDFhAPbxqQSqu/FsaMSzuRllYwaJ0TkIvYJxoANdvsAdu432jjW0tq6ioWERIDAa4wkG2wn3vxbY7TmYTEdXggmhx2odjN2Wjd4QjV7vRK93YNA7MRji0OmOz/nxB1rw+xsw6KMxGKLR6WyHRIumBQkGOwgG2wiGupBaECnVsCeTDKFqPjo6vqSl+TP8gUZAwWIZiMmUjDPqChKjZ2JbdRVqlYYPN4ZkG85r07EUxmFIOr2LotNFURSmTp3K66+/zrJlyyJ/qxEuG1auXGmfMWNGh9Pp1ABmzpzZvmLFCsfs2bM7UlJSAlOmTHEDrFq1yjZ27Nju1NTUEMAtt9zStnv3bjPA2rVrnRUVFYe2WFwul669vV0BmD59esf5FElw8mTut4UQ/wQeBTYKIV7jCGMWKeVTx5wyCPhjTyTq344RVt+I0IamSb6ubuevq/exbFsDhQOcvP7AGHKTw0m1Pl8dpV+8RBxT0S1PxTYmGeuVpy4rPh0cDgdFRUVs3LiRiRMnEh0d3a/jRzie5uZmXn31VXQ6Hffff/8Fz0c6G4QQmAY5MQ1yEjVrCN6tzXi+akKGNLy72pBfhxDGZJJzvkd63i8JpdXR7l6Lz1eH0RgXFkyhbjo7ywgG2o8aW9P8tLauRsre+6aZjEmYLWlhMWNMorPzKzo6N3Jkka0QBvR6J5rm78klOjk6nZXY2InEx08hWhuNbDISavYQavHiq+hA0yTRNw3FnBVz1lvfp0tmZibjx49nzZo15Ofnk5mZeV7nj3D5c7LIz7niZBk2Vqv1qO4cJ4rUSinZuHHjzt4Ekc1mO+8dPk4VyggCbsAEODjSwe54GoHxwLPAeiHEHVLK8p7nLuncpJMhpWRbbRdLttTxzy311HZ4MekVfjEthwcnDjmqo3lj4xKkDOJcfS2WEQlE35h5TpJkx40bR1lZGWvWrGHWrFn9Pn6Ew9TV1fHGG28ghODee+8lPr7vtg4XO4pJh604GVtx2N5ChjR8ezvwbW/Fu7MV79YWUMCeMYmYgQ6kX0XzhVBMOpKHzEGfYgadgtCJ8M2gAxv4/XWEQl2EQt09ty78/ia8vmq83mo62r/E52/AbsticMaPsTtyCQW7CIY6eiJIHSiKCaMhBkPPTW+IQhFGhKJDCD2K0COEHoM7Ef/WLjyfNNPW1JPOIEAXY8Y0JIro6wejjz+/AulIrr76arZs2cKqVasiQinCZcE111zjuv/++zMef/zxBiklS5cujXnllVcqjz1u4sSJ7kceeWRgQ0ODLiYmRnvvvfdiCgoKvADjx4/vevLJJxMff/zxRoDS0lJLSUnJWeUZnQ0ny1GaDjwFvA+MklJ6TjVYzzEPCCFuBj4RQvxGSvk8fXP2vujZ1RDuoXagzUN1m5fqNg/7Wt00d/vRK4KJ2Qn8bGo21+Un4TAfzjmQUlJbu5DKfc9i9eZiVlKJuTkTcY7aiURFRTFy5Ei++uorJkyYcMatMiKcGE3TWLduHZ9++ik2m4177rnnshJJvSH0CpacWCw5sURrmQRquvHtaMW7oxX/6loUiw5h1qO5grjXN/Q6hmLVY0i2odgNKLYkTNY0LFY90Q4j+jgL+sFmFLMeKTWkLxzFUqt8KBb9oZuw6pF+FbUjiNYdQHUF0FxBtICKFtCQARUZDKB5PahtTSDAmOEk+qZUTEOi0ceaEfqLIxFdr9dTUlLChx9+yP79+0lPT7/QS4oQ4awYP368Z+7cua2jRo3Kg3Ay97hx47zl5eVH+aOkp6cHH3nkkbqxY8fmJSQkBIcPH+5RVVUAzJ8/v/qBBx4YlJ2dna+qqhgzZkx3SUnJKW0DioqKciorK81er1eXlJQ0/M9//nPVrbfe2vXrX/868bnnnktubW01jBgxIn/y5Mmdb7311v6+vqaTNcVdDXxfSrm9TwMJ8ZWUctQR9wcQznPyAnlSyqwTnXu+OdOmuI+8s4W3NlYjBCQ7zQyMsZIWa+HKjFimFyQTYzveJycQaGHHzv9Da+sKoi1XEbfsduKnF2EvObfbMx0dHTz99NMAPProo5ES5H7E5XKxaNEi9uzZQ25uLjfccANWa7/mS17SSFUSrHOhdgeQqgRVQ6oS6VcJ1rsJNrrRPCFUdxDpCx0Xb1asenRRJoJNHlD7EIzWC3Q2I8KkQxgVFKMOYQx/bxzoxDo8Ht0ZeB6dLwKBAE8//TQpKSncfffdF3o5JyXSFPfiJ9IU98w57aa4UsoJpzlH0zHn1wLXCSF+AVwWXSB/ODmThyYNYUCMBZP+1NVMoZCbr76+C693P9lZj2LfVIJbbcQ6MvGcr/XI3KRt27YxfPiJe3ZF6Dt79uzhvffew+/3M3PmTIqLiy9bj6EzRegExoF9q3qTmkTzhlA7/ahtPkKtPkJtXkLtfuxZ0VgK4zGm2NF8ITRvz80XQjHoUBwGdI4egXQJ/w6MRiNjxoxhxYoVtLe3ExNzZl5qESJEODf0p4/S9BM8/jvgd/01z4VkUFzfowZSSnbufAS3ey8jr3gFw/YMOtdWYhmRgGLpT5/PE/OrX/2KZ555huXLl5Ofn49ef37mvRwJBoMsX76cL774goSEBO655x6Skvo3Ef+biFAEOpsBnc0AqSf2KdIZjOgc58/Z/HwzfPhwVqxYwbZt25gw4XSvUSNEiHAuOaf7MUKIr0591OXJ/v0v0NS8jMyhv0QpTaHzn5VYCuOI/fb5a4Sp0+m48cYb6ejoYMOGDedt3suNffv28Ze//IUvvviC4uJiHnzwwYhIitCvxMTEkJaWxrZt2y70UiJEiHAM5zpx5dKNh58Fra2fs7fy9yQlzsLx9dW41tRiL0kldm4ewnB+c4WGDh3KkCFDWLVqFT7fJd2T+Lzj9XpZvHgxr776KlJK7r77bmbNmhUxB4xwThg2bBiNjY00NTWd+uAIESKcN/r9U1sI8SMhxMEEmX/29/gXOy7XbrZt/1fstmwy+AWedQ3Yxw8g6ltDzlmV26m49tpr8Xq9rF279oLMf6khpWT79u388Y9/ZNOmTZSUlPCDH/yAoUOHXuilRbiMyc/PRwgRiSpFiHCRcS7CG8mEDSrfBtaIfsiyFEL8TgixSwixRQjx3kEhJoTIEEJ4hRCbem7Pn+1cZ4PLVc5XX9+JopgoGPocXYtqMKTYiJqecUGTTVNTUyksLGTt2rXs3bv3gq3jUqCzs5M33niDf/zjHzgcDr73ve8xdepUjMbLNz8mwsWBw+EgIyODbdu2ndS0L0KECOeXfhdKUsr/D8gCXgLuAyqEEL8RQpzN5fgnQKGUcjiwG/i3I57bK6W8ouf2/bOY46wIi6S7UISBUSMX4FvmR/OGiL0956LwbJk5cybx8fG89dZbNDT07nHzTUZVVdavX8+f/vQnKisrue666/je9753SbtsR7j0GDZsGG1tbdTV1V3opUSIcF559tln4+65555BZzPGhAkTshwOxxWTJ08+yr31hhtuGJyRkVGYlZVVMHv27Ay/339akYtz8gkuw5dDDT23EBADvCOE+O0ZjvexDDeRAlgHpPXLQvuJbteusEhSjIwatQB22fBtbyVqagaG5HPbM6qvWCwW7rzzTkwmEwsWLKCzs/NCL+miQFVVvvrqK5577jmWLVtGWloaDz/8MOPGjbuoG9pGuDzJy8tDUZTI9luEyxpN01BV9azGCAaPbz/785//vOGFF17Yd+zjd955Z1tlZeW28vLy7T6fTzz99NOn5Q58LnKU/kUIUQb8FlgLDJNS/gAoAm7thynuB5YdcX+wEOJrIcTnQojzXlfb3b2Trw+KpJELMHqT6Xh/L8YMJ/YJA873ck5KVFQUd911F4FAgNdffx2v94I5wl9wVFVl06ZN/PGPf+T999/HYrEwd+5c7r77bmJjvxGtCSNchFgsFjIzM9m+fTuadt5bWkWI0C889thjSVlZWQVZWVkF//3f/50IUF5ebhwyZEjBXXfdNaigoCB/7969xmeeeSYuIyOj8Morr8wpLS095A9SV1ennzZt2tDCwsK8wsLCvI8//tgGMG/evNQ77rgjfdy4cVm33HLL4GPnvfHGG7sPNuM9kttvv71TURQURaG4uNhdU1NzWrkU58JYJx64RUp5lD24lFITQpyw8ZgQ4lPC+U3H8h9SysU9x/wH4QjVgp7n6oFBUspWIUQRsEgIUSCl7Opl/AeBBwEGDTqr6N4h2trWsnXbj9DpbIwauQCzMoCmVzeBIoi9LeeCJW+fjKSkJObMmcNrr73GO++8w9y5c79RkRNN09i6dSuff/45bW1tJCcnM2fOHHJyci5p08IIlw+FhYXs3r2b6urqSEuTCGfHoh8OpGlH/7YNSMz3cNOfTthsd/Xq1daFCxfGlZWV7ZRSUlRUlDdlypTu+Ph4taqqyvziiy9Wvf766wf2799veOKJJ1LLysp2xsbGqiUlJTmFhYUegIceemjgvHnzGqdNm+aqqKgwTps2LauysnI7wJYtW6zr16/f1VvD3FPh9/vFW2+9FffUU0+dVrPgfhdKUspHT/LczpM8d+3JxhVC3AvMAqb0bO0hpfQD/p7vy4QQe4Fs4Lj+JFLK+cB8CLcwOfUrOTm1tW9QvvsxrNbBjBj+V8ymAbS+up1Qi4/47xaijzWf7RTnjMGDBzNz5kyWLFnCZ599xtSpl4Vx+kk5WMm2cuVKWlpaSEpK4vbbbyc3NzcikCJcVOTk5KDX69m6dWtEKEW45Fi5cqV9xowZHQcjOzNnzmxfsWKFY/bs2R0pKSmBKVOmuAFWrVplGzt2bHdqamoI4JZbbmnbvXu3GWDt2rXOioqKQ92qXS6Xrr29XQGYPn16x5mIJIB777130NixY13Tp093nc55l4RVc0+D3keASUc25xVCJABtUkpVCDGEcBL5cV2K+xMpVSr2PEF19cvExU2isOAZ9HoHHR9U4itvJ/rmTMxDo0890AWmqKiIhoYGSktLSUpKYsSIERd6SeeMxsZGli5dyv79+0lISGD27NmHckEiRLjYMJlM5OTksGPHDq6//vpvVMQ3Qj9zksjPueJkFZtWq/WobbETXaRKKdm4cePO3gSRzWY7oz3pn/3sZyktLS36jz766LRLvy+VT4o/Ag7gk2NsACYCW4QQm4F3CDfxbTtXiwiFXGzZ8n2qq18mLe1ehg+bj17vwL2h4ZCppH1Myrmavt+ZPn066enpvP/++9TW1l7o5fQ7Pp+PDz/8kOeff56mpiZmzZrFD37wAwoKCiIiKcJFTWFhIR6Ph337jstLjRDhouaaa65xLV26NLq7u1vp6upSli5dGjN58uTuY4+bOHGie926dY6Ghgad3+8X77333qEmh+PHj+968sknDzVFLS0ttRx7/unw1FNPxS9fvjxq0aJFlWdy4XFJRJSklJknePxd4N3ztY6du/6N1rbPycn+L9LS7gLAX9lJ+6I9mLKiiZo55HwtpV/Q6XTcdtttzJ8/nzfffJMHH3wQh6NvzUwvVqSUtLS0UFFRQWlpKS6Xi6KiIqZMmYLV2r9b9REinCuysrIwmUxs3bqVzMxe//1FiHBRMn78eM/cuXNbR40alQdw9913N48bN85bXl5+VAJ1enp68JFHHqkbO3ZsXkJCQnD48OEeVVUFwPz586sfeOCBQdnZ2fmqqooxY8Z0l5SUHDjV3EVFRTmVlZVmr9erS0pKGv7nP/+56tZbb+365S9/mZ6SkuIvLi7OA5g1a1b773//+/q+vibxTTQ2Ky4ulhs3HpfGdEo8niq83mri4sLFdcFGN80vbEGxGUh8+Irz1uy2v6mvr+ell14iJSWFe++996jmuZqm8fnnnxMVFcXIkSMvynwel8tFTU0Ne/bsoaKi4pD1QVpaGtdffz0DBlxc1YcRIvSFRYsWsXPnTn7+859fNG1zhBBlUsriC72OCCdm8+bNVSNGjPj/27v3uCjPM2/gv2s4iMNJzkKUGcFBhpmAdaBOOXWBJEPgNaYY02CFplnf2u62ry1ra3f3zdalaavbJl2saxNo+7bW2iRNYpJtaGOTDxZXhDqTOKhBRMiAgppf6S4AACAASURBVBAPEIaDHGbu9w9mUkRARgaGwev7+cwnzDPPcz/XlUG4uJ97nuuaq+NwR0ajMTQpKUk+cbt7/mZ3EalUDqlUDgAYvXETV39xFvAghD6pctsiCQAiIyPx6KOP4pVXXkFlZSU2bNgAIoIQAm+//Tbq6uoAAGfPnsUjjzyCZctcvwarra0NJ06cQEdHB8zmsVldb29vxMTEICMjA6tXr14QcTJ2t9RqNU6fPo2LFy9CqVS6OhzG7lnu+9vdhSy9w7j6izMQI1aEb0+EZ8isLp8uCGq1Gl1dXTh+/DgkEgk8PT1x/fp1NDU1Yf369QgLC8PRo0dx4MABPPjgg0hOTnbJ7NLg4CDeffdd6PV6+Pn5ISYmBpGRkYiMjMSKFStumQ1jzJ2tWrUKUqkUZ86c4UKJMRfi3yoOsg6M4Novz8BqHkbotvsXzJ23nSErKwvXrl2DXq+Hl5cXAgICoNVq8dBDD0EikSA2NhZvvvkm3nrrLVy8eBEPPPAAQkND56RgslqtuH79Orq6uj7pqN7f34/r16/j5s2b0Gq1yMrKwpIlS5x+bsYWAg8PD6hUKpw6dQr9/f3w9V08P2sYcydcKDnAOmTBtV+dw8jVQYR+SYUl0QGuDsmpJBIJHn/8cQwPD8Pb2/u2AigoKAjFxcWoq6vD22+/jcbGRgQFBSEuLg5xcXGQyWROmdGprq5GdXU1RkfHutYQEUJCQuDv74/Y2FikpqZyDzZ2T1AqlTh16hSeffZZ/Nu/TXmLOsbYHOJCyQHdrzVh+JIZIV9Qwmd10J0PcENENO0sDRFBq9VCqVTiwoULuHDhAvR6Perq6rB06VKkpaXh05/+NLy9xz7g0Nvbi/7+fkRG3n7bhIGBASxZsgQff/wxTp06hY6ODoSEhKC+vh4rVqzA2rVrERERgdDQ0AWzmJWx+SSXywGMzbBarVa+rQVjLsCFkgMCcqKxNCEYS9UO9dNblAIDA5GSkoKUlBQMDw+jpaUFer0e77zzDk6ePImkpCR4enrir3/9K27evAm5XI7U1FSsXr0aEokEJ0+exNtvvw0vL69PmhuGh4fj/PnzEELg4YcfRkREhIuzZMy1JBIJPve5z+HIkSPc0oQxF+FCyQFe4VJ4hfO9eCby9vZGfHw84uPj0dbWhmPHjqGmpgYAEBUVhejoaJw7dw6HDx9GUFAQRkdHYTaboVAoEBgYiKCgICQkJCAoaGyWjv9yZuxv4uPjuaUJW/T27dsXotfrfQ8ePHjH+yVNJSMjQ3H69Gnf5OTkvqqqqov27Y8//rjMaDT6CiEQExNz86WXXjIFBgbO+A7fXCgxp4qOjkZxcTGEELBYLPDw8AAR4cEHH8S5c+dw+vRp+Pr6Ijo6GuvWrZu0PQMXSYz9zZIlSxAfH49z585xSxO2KFitVgghZvW9PDIyctuSjJ07d3b29/dLKioqwsZvf/755y8FBwdbAWDbtm0r9u7dG/6DH/ygc6bn4t9IbE4QETw9PT9ZEO7h4YHExEQUFxdj06ZNSElJ4R/4jM3Q/fffj8HBQTQ3O9ymirF5t3v37giFQqFSKBSq0tLScABobGz0jomJUW3dujVapVIlNDc3e5eVlYXI5XJ1SkrKmpqaGj/78R0dHZ46nS5WrVYr1Wq18ujRo74AUFJSElVYWChLS0tTFBQUrJp43o0bN5rtzXjHsxdJVqsVg4ODEkc/qc0zSowxtsDFxsZi6dKlOHPmDOLi4lwdDnMTT594euXF7otOXS+yOmj1wPfSvjdls93jx49LDx8+HGIwGBqEENBoNMqcnBxzaGioxWQy+VRUVJgOHTrU1tra6rVnz54og8HQEBwcbElNTV2jVqsHAGD79u0rS0pKunQ6XV9TU5O3TqdTtLS0nAOA+vp6aV1d3fnJGuZO57HHHpNXVVUFrl69evD555+/7MixPKPEGGMLnKenJxISEnD+/HkMDQ25OhzGpnTs2DG/vLy8noCAAGtgYKA1Pz+/u6qqyh8AIiMjh3NycvoBoLq62ler1ZqjoqJGfXx8REFBwScN7U+cOBGwY8eO6Pj4+IQNGzas7uvr8+ju7pYAQG5ubo+jRRIAvPLKK6auri6jQqG4+ctf/tKhj63zjBJjjLmBxMREGAwGvPPOO8jPz3d1OMwNTDfzM1em6x8rlUpvuSw21SUwIQT0en3DZAWRr6/vjBdhT+Tp6YnCwsIbP/7xj5fv2LHj+kyP4xklxhhzA9HR0Vi7di1OnTqFrq4uV4fD2KSys7P7Kisrl5nNZklvb6+ksrIyKCsryzxxv8zMzP7a2lr/zs5Oj6GhITpy5Mgnszzp6em9e/fuDbc/r6mpues+YVarFWfPnl1i//qNN95YplAobjoyBs8oMcaYGyAiPPTQQzhz5gwMBgPy8vJcHRJjt0lPTx/YsmXL9XXr1ikBoKio6GpaWtpgY2Oj9/j9ZDLZyK5duzq0Wq0yLCxsJDExccBisRAAlJeXX9q2bVt0XFxcgsViofXr15tTU1PveNsAjUazpqWlxWdwcNAjIiIi8cCBA6ZHH320t7i4eFVfX59ECEFKpXLgV7/6VasjOdF002SLVXJystDr9a4OgzHGHPbqq6/iwoUL+OY3vwkfH595PTcRGYQQyfN6UuYQo9FoSkpKuubqONyR0WgMTUpKkk/czpfeGGPMjXzmM5/B8PAw3njjjWnXgzDGnIMLJcYYcyNRUVF48MEH0dDQgA8++MDV4TC26HGhxBhjbkar1SIwMBDvvfeeq0NhbNFzi0KJiHYTUTsRnbY98sa99s9EdJGIGolI58o4GWNsPkgkEiQlJaGlpQW9vb2uDoexRc0tCiWbnwgh1toelQBARAkAngCgApAL4AARcV8Mxtiit3btWgghYDQaXR0KY4uaOxVKk9kI4EUhxJAQ4kMAFwF82sUxMcbYnAsODoZMJsPp06d5UTdjc8idCqWvEVE9Ef2SiOw3proPwPg7j162bbsNEX2ZiPREpL969epcx8oYY3MuMTER169f5xtQMre3b9++kOLi4ujZjJGRkaHw9/dfm5WVtXqy17/4xS+ulEqln3J03AVTKBHRO0R0dpLHRgA/AxALYC2AKwCetR82yVCT/mklhCgXQiQLIZLDwsLmJAfGGJtPCoUCANDS0uLiSBibOavVCovFMqsxRkZGbtu2c+fOzhdeeOHDyfavrq6Wfvzxx3d1k+0FUygJIR4QQqgnebwhhOgSQliEEFYAFfjb5bXLAFaOG2YFgI75jp0xxlwhICAAYWFhaG5udnUojH1i9+7dEQqFQqVQKFSlpaXhANDY2OgdExOj2rp1a7RKpUpobm72LisrC5HL5eqUlJQ1NTU1fvbjOzo6PHU6XaxarVaq1Wrl0aNHfQGgpKQkqrCwUJaWlqYoKChYNfG8GzduNAcEBNzWC250dBTf+ta3VpSVlV2+m3zcooUJEUUKIa7Ynn4OwFnb128COExEzwGIAqAA8FcXhMgYYy4RGxsLvV6PkZEReHl5uToctoB0/Mu/rhxqapI6c8wlCsVA1A++P2Wz3ePHj0sPHz4cYjAYGoQQ0Gg0ypycHHNoaKjFZDL5VFRUmA4dOtTW2trqtWfPniiDwdAQHBxsSU1NXaNWqwcAYPv27StLSkq6dDpdX1NTk7dOp1O0tLScA4D6+nppXV3d+cka5k7lhz/8YXheXl6PTCa7fRpqBtyiUALwH0S0FmOX1UwAtgOAEOIcEb0M4AMAowD+UQgxu/k8xhhzI7GxsaitrUVbWxtiY2NdHQ67xx07dswvLy+vxz6zk5+f311VVeW/efPmnsjIyOGcnJx+AKiurvbVarXmqKioUQAoKCi4ceHCBR8AOHHiREBTU9MnjXD7+vo8uru7JQCQm5vb40iRZDKZvF5//fWg2traxrvNyS0KJSFE0TSvfR/A9+cxHMYYWzBkMhk8PDzQ3NzMhRK7xXQzP3Nluk9gSqXSWy6LEU22zHhsDL1e3zBZQeTr63vbpbXp1NbWSltbW33kcvn9AHDz5k1JdHS0uq2t7eydjrVbMGuUGGOMOc7b2xsrV67kdUpsQcjOzu6rrKxcZjabJb29vZLKysqgrKws88T9MjMz+2tra/07Ozs9hoaG6MiRI/ZPsyM9Pb1379694fbnNTU1SyceP1NPPPHEx9euXTO2t7efaW9vP+Pj42N1pEgCuFBijDG3Fxsbi66uLvT19bk6FHaPS09PH9iyZcv1devWKTUajbKoqOhqWlra4MT9ZDLZyK5duzq0Wq0yPT09LjExccD+Wnl5+aX33nvPNy4uLiE2Nla1f//+GX1UXaPRrCkqKoo5efJkQEREROKrr74a4Iyc6F68UVlycrLQ6/WuDoMxxpyio6MD5eXlKCgoQGJi4pydh4gMQojkOTsBmzWj0WhKSkq65uo43JHRaAxNSkqST9zOM0qMMebmli9fjqVLl/LlN8bmABdKjDHm5iQSCWJjY9Hc3MztTBhzMi6UGGNsEYiJiUFfXx8++ugjV4fC2KLChRJjjC0C9lsD8OU3xpyLCyXGGFsEAgMDERoayn3fGHMyLpQYY2yRkMvlaGtrm3XDUcbY33ChxBhji4RcLsfw8DCuXLly550ZW0D27dsXUlxcHD2bMTIyMhT+/v5rs7KyVo/fvmnTJvl99913f3x8fEJ8fHyCozewdIsWJowxxu5MLpcDAEwmE1asWOHaYBibgtVqhRACHh4edz3GZE2gd+7c2dnf3y+pqKi47QaVzzzzzOUvfelL3XdzLp5RYoyxRcLPzw9hYWEwmUyuDoXdw3bv3h2hUChUCoVCVVpaGg4AjY2N3jExMaqtW7dGq1SqhObmZu+ysrIQuVyuTklJWVNTU+NnP76jo8NTp9PFqtVqpVqtVh49etQXAEpKSqIKCwtlaWlpioKCglUTz7tx40azvRmvM/GMEmOMLSJyuRxGoxEWi2VWf7Ez9/fuwYaVN9r7pM4cM/g+v4GcYuWUzXaPHz8uPXz4cIjBYGgQQkCj0ShzcnLMoaGhFpPJ5FNRUWE6dOhQW2trq9eePXuiDAZDQ3BwsCU1NXWNWq0eAIDt27evLCkp6dLpdH1NTU3eOp1O0dLScg4A6uvrpXV1decna5g7nX//93+/74c//GFkRkaGef/+/ZeXLl064+N5RokxxhYRXqfEXOnYsWN+eXl5PQEBAdbAwEBrfn5+d1VVlT8AREZGDufk5PQDQHV1ta9WqzVHRUWN+vj4iIKCghv2MU6cOBGwY8eO6Pj4+IQNGzas7uvr8+ju7pYAQG5ubo+jRdJzzz3X3tLSctZoNDZ0d3d7PP3008sdOZ5nlBhjbBGRyWQAgA8//JDXKd3jppv5mSvT3RleKpXeclmMiKYcQ6/XN0xWEPn6+jp8aU0mk40AwNKlS8VTTz11/dlnn41w5HieUWKMsUWE1ykxV8rOzu6rrKxcZjabJb29vZLKysqgrKws88T9MjMz+2tra/07Ozs9hoaG6MiRI0H219LT03v37t0bbn/u6KfUJmptbfUCxhaRv/baa8uUSuWgI8fzjBJjjC0ycrkcp0+f5nVKbN6lp6cPbNmy5fq6deuUAFBUVHQ1LS1tsLGx0Xv8fjKZbGTXrl0dWq1WGRYWNpKYmDhgsVgIAMrLyy9t27YtOi4uLsFisdD69evNqampbXc6t0ajWdPS0uIzODjoERERkXjgwAHTpk2bej//+c+vunHjhqcQghISEgYOHjzY6khOdC82UExOThZ6vd7VYTDG2Jw4d+4cfv/73+Pv//7vsXLlSqeNS0QGIUSy0wZkTmc0Gk1JSUnXXB2HOzIajaFJSUnyidv50htjjC0y4++nxBibHbcolIjoJSI6bXuYiOi0bbuciAbHvfa8q2NljDFX8/X1RXh4OBdKjDmBW6xREkJ83v41ET0L4ONxLzcLIdbOf1SMMbZwyeVyvP/++7xOibFZcosZJTsa+yzh4wB+5+pYGGNsIZPL5RgZGUF7e7urQ2HMrblVoQQgA0CXEKJp3LZVRPQ+Ef2FiDKmOpCIvkxEeiLSX716de4jZYwxF7LfT4kvvzE2OwumUCKid4jo7CSPjeN2K8Sts0lXAEQLIT4FoATAYSIKmGx8IUS5ECJZCJEcFnZbvzzGGFtUeJ0SY86xYAolIcQDQgj1JI83AICIPAEUAHhp3DFDQojrtq8NAJoBxLkifsYYW2jkcjkuXbqE0dFRV4fC2LT27dsXUlxcHD2bMTIyMhT+/v5rs7KyVo/fbrVa8fWvf/0+uVyujomJUT3zzDPhU40xGbdYzG3zAIDzQojL9g1EFAbghhDCQkQxABQAWlwVIGOMLSSrVq3CX//6V3R0dCA6ela/gxhzGqvVCiHErD5kMDIyAi8vr1u27dy5s7O/v19SUVFxy2Wjn/70pyGXL1/2am5uPuvh4YH29naHap8FM6M0A0/g9kXcmQDqicgI4BUAXxFC3LjtSMYYuwfxOiXmCrt3745QKBQqhUKhKi0tDQeAxsZG75iYGNXWrVujVSpVQnNzs3dZWVmIXC5Xp6SkrKmpqfGzH9/R0eGp0+li1Wq1Uq1WK48ePeoLACUlJVGFhYWytLQ0RUFBwaqJ5924caM5ICDgtl5wP//5z8O/973vXbEXZvfdd59DU6xuM6MkhHhykm2vAnh1/qNhjLGFTyqVIiIiAh9++CEyMzNdHQ6bZ2//7D9XXrvUKnXmmKErZQO6r35jyma7x48flx4+fDjEYDA0CCGg0WiUOTk55tDQUIvJZPKpqKgwHTp0qK21tdVrz549UQaDoSE4ONiSmpq6Rq1WDwDA9u3bV5aUlHTpdLq+pqYmb51Op2hpaTkHAPX19dK6urrzkzXMncqlS5eW/OY3vwl66623goKDg0f/67/+q+3+++8fmunxblMoMcYYc5xcLofBYMDo6Cg8PflHPptbx44d88vLy+uxz+zk5+d3V1VV+W/evLknMjJyOCcnpx8AqqurfbVarTkqKmoUAAoKCm5cuHDBBwBOnDgR0NTU9Ekj3L6+Po/u7m4JAOTm5vY4UiQBwPDwMPn4+IizZ882/PrXv1725JNPyg0GQ+NMj+d/NYwxtojJ5XLU1dWhvb39k0tx7N4w3czPXJmuf6xUKr3lstjYrREnH0Ov1zdMVhD5+vredmntTiIiIoa3bNnSDQBFRUU9X/va1+SOHO9Oa5QYY4w5iNcpsfmUnZ3dV1lZucxsNkt6e3sllZWVQVlZWeaJ+2VmZvbX1tb6d3Z2egwNDdGRI0eC7K+lp6f37t2795NPptXU1CydeLwjHn744Z4//vGP/gBQWVnpL5PJZnzZDeAZJcYYW9Ts65RMJhM++9nPujoctsilp6cPbNmy5fq6deuUAFBUVHQ1LS1tsLGx0Xv8fjKZbGTXrl0dWq1WGRYWNpKYmDhgsVgIAMrLyy9t27YtOi4uLsFisdD69evNqampbXc6t0ajWdPS0uIzODjoERERkXjgwAHTpk2bektLSzsfe+yxVQcOHIiQSqXWiooKkyM50XTTZItVcnKy0Ov1rg6DMcbmxZ/+9Cfo9Xp85zvfmdU6JSIyCCGSnRgaczKj0WhKSkq65uo43JHRaAxNSkqST9zOl94YY2yRk8vlGB0dxeXLl++8M2PsFlwoMcbYIme/2SSvU2LMcVwoMcbYIieVSrF8+XIulBi7C1woMcbYPcDe921kZMTVoTDmVrhQYoyxe4BcLofFYkF7e7urQ2HMrXChxBhj9wCZTIb8/HyEhIS4OhTG3AoXSowxdg9YunQpUlJS4O/v7+pQGLvNvn37QoqLi6NnM0ZGRobC399/bVZW1urx2zUazZr4+PiE+Pj4hPDw8MQHHngg1pFx+YaTjDHGGJs3VqsVQgh4eHjc9RgjIyPw8vK6ZdvOnTs7+/v7JRUVFWHjt4/v66bT6WI3bNjQ48i5eEaJMcYYY06ze/fuCIVCoVIoFKrS0tJwAGhsbPSOiYlRbd26NVqlUiU0Nzd7l5WVhcjlcnVKSsqampoaP/vxHR0dnjqdLlatVivVarXy6NGjvgBQUlISVVhYKEtLS1MUFBSsmnjejRs3mu3NeCfT3d0tOXnypL+979tM8YwSY4wxtgjdeOXCypHOfqkzx/Ra7jsQ/FjclM12jx8/Lj18+HCIwWBoEEJAo9Eoc3JyzKGhoRaTyeRTUVFhOnToUFtra6vXnj17ogwGQ0NwcLAlNTV1jVqtHgCA7du3rywpKenS6XR9TU1N3jqdTtHS0nIOAOrr66V1dXXnJ2uYeye//e1vg1JTU3uDg4MdaqzLhRJjjDHGnOLYsWN+eXl5PfaZnfz8/O6qqir/zZs390RGRg7n5OT0A0B1dbWvVqs1R0VFjQJAQUHBjQsXLvgAwIkTJwKampo+aYTb19fn0d3dLQGA3NzcnrspkgDg5ZdfDn7qqaeuOnocF0qMMcbYIjTdzM9cma5/rFQqvWUmh4imHEOv1zdMVhD5+vo6NBtk19nZ6VFfX+/7+OOPX3T0WF6jxBhjjDGnyM7O7qusrFxmNpslvb29ksrKyqCsrCzzxP0yMzP7a2tr/Ts7Oz2GhoboyJEjQfbX0tPTe/fu3Rtuf15TU7N04vGOOnjwYHB2dnaPVCp1eDaKZ5QYY4wx5hTp6ekDW7Zsub5u3TolABQVFV1NS0sbbGxs9B6/n0wmG9m1a1eHVqtVhoWFjSQmJg5YLBYCgPLy8kvbtm2LjouLS7BYLLR+/Xpzampq253OrdFo1rS0tPgMDg56REREJB44cMC0adOmXgB45ZVXgr/97W9fuZucaLppssUqOTlZ6PV6V4fBGGNuhYgMQohkV8fBpmY0Gk1JSUnXXB2HOzIajaFJSUnyidvvyRklg8FwjYha5/GUoQAW6zfuYs4NWNz5cW7uyZW5yVx0XsZc5p4slIQQYXfey3mISL9Y/wpbzLkBizs/zs09LebcGFuIeDE3Y4wxxtgUuFBijDHGGJsCF0rzo9zVAcyhxZwbsLjz49zc02LOjbEFhwuleSCEWLQ/2BZzbsDizo9zc0+LOTfGFiIulBhjjDHmUvv27QspLi6Ons0YGRkZCn9//7VZWVmrx29/4403/BMSEpTx8fEJGo1mzdmzZ5c4Mi4XSneBiFYSURURNRDROSLaYdseTER/JqIm23+DbNtDbPv3EdH+CWMdI6JGIjpte4RPds754uTcvImonIguENF5ItrkipwmxOSU/IjIf9x7dpqIrhHRf7oqL1tMznzvConoDBHVE9GfiCjUFTmNi8eZuX3eltc5IvoPV+QzIR5Hc3uQiAy298dARNnjxtLYtl8kon00VY8IxlzIarXCYrHMaoyRkZHbtu3cubPzhRde+HDi9h07dsgOHTr04fnz5z/YvHnzje9+97uRjpyLC6W7Mwrgn4QQSgBaAP9IRAkAvgPgXSGEAsC7tucAcBPA0wB2TjHeF4QQa22Pj+Y49jtxZm7/CuAjIUQcgAQAf5nr4GfAKfkJIczj3rO1AFoBvDZfSUzBKbkRkSeAMgBZQohEAPUAvjY/KUzJWbmFAPgRgBwhhApABBHlzFMOU3E0t2sANggh7gfwRQC/GTfWzwB8GYDC9sidnxQY+5vdu3dHKBQKlUKhUJWWloYDQGNjo3dMTIxq69at0SqVKqG5udm7rKwsRC6Xq1NSUtbU1NT42Y/v6Ojw1Ol0sWq1WqlWq5VHjx71BYCSkpKowsJCWVpamqKgoGDVxPNu3LjRbG/GO1FPT48HAHz88ccekZGRt1dZ07gn76M0W0KIKwCu2L42E1EDgPsAbATwd7bdfg3gGIBdQoh+AP9DRKtvH21hcXJuTwGIt41lxQK4AeBcvHdEpAAQDuD43EV+Z07MjWwPXyK6DiAAgMONJJ3JibnFALgghLB3EH8HwCaMFSIucRe5vT/u8HMAfIhoCYBgAAFCiJMAQEQHATwK4I/zkAZbgF5//fWVH330kdSZY4aHhw88+uijUzbbPX78uPTw4cMhBoOhQQgBjUajzMnJMYeGhlpMJpNPRUWF6dChQ22tra1ee/bsiTIYDA3BwcGW1NTUNWq1egAAtm/fvrKkpKRLp9P1NTU1eet0OkVLS8s5AKivr5fW1dWdn6xh7lSef/55U0FBgWLJkiVWPz8/y6lTpxocyZlnlGaJiOQAPgWgDkCE7Yee/YffTC+j/T/b5ZunF9JU+WxyI6Jlti+/R0TvEdHviShiDsN1mJPeOwAoBPCSWED9gGaTmxBiBMBXAZwB0IGx2cBfzGG4Dpnl+3YRQDwRyW0zZ48CWDl30TrmLnLbBOB9IcQQxoqry+Neu2zbxti8OXbsmF9eXl5PQECANTAw0Jqfn99dVVXlDwCRkZHDOTk5/QBQXV3tq9VqzVFRUaM+Pj6ioKDghn2MEydOBOzYsSM6Pj4+YcOGDav7+vo8uru7JQCQm5vb40iRBADPPfdcxGuvvdbU1dVVv2XLlmtf/epXHfo3zzNKs0BEfgBeBfANIUTvXdY4XxBCtBORv22sIgAHnRjmXXFCbp4AVgA4IYQoIaISAD/GWH4u56T3zu4JLJC8gNnnRkReGCuUPgWgBcBPAfwzgGecHKrDZpubEKKbiL4K4CUAVgA1GJtlcjlHcyMiFYC9AB6yb5pktwVTvLP5N93Mz1yZ7u9FqVR6y2Wxqb7HhRDQ6/UNkxVEvr6+k15am0pHR4dnQ0PD0uzs7H4AKC4u7s7NzVU4MgbPKN0l2y+TVwH8VghhX5vSRUSRttcjAdxxvZEQot32XzOAwwA+PTcRz5yTcrsOYADAEdvz3wNYNwfhOsxZ751t3yQAnkIIw5wE6yAn5bYWAIQQzbZZspcBpM5RyDPmxH9z/y2EWC+E+AyARgBNcxXzTDmaGxGtwNi/rWIhRLNt82WM/XFitwJjM4KMzZvs7Oy+ysrKZWazWdLb2yuprKwMMQFP5gAACEdJREFUysrKMk/cLzMzs7+2tta/s7PTY2hoiI4cORJkfy09Pb137969n8yg1tTULL3beMLCwkb7+vo86uvrlwDAH/7wh4DVq1ffdGQMLpTugu3y2C8ANAghnhv30psYW1wJ23/fuMM4nvZPE9l+UP4vAGedH/HMOSs32y/Y/8bf1ljkAPjAqcHeBWflN04hgN85L8K758Tc2gEkEJG9J+KDABy6pu9sznzfyPbJUtunyP4BwM+dG61jHM3Ndln7LQD/LIQ4Yd/ZdnnOTERa25jFmPn3MWNOkZ6ePrBly5br69atU2o0GmVRUdHVtLS0wYn7yWSykV27dnVotVplenp6XGJi4oD9tfLy8kvvvfeeb1xcXEJsbKxq//79M+rPqtFo1hQVFcWcPHkyICIiIvHVV18N8PLyQllZWetjjz0Wu2bNmoTf/e53IT/5yU8cmmmjBbSswm0QUTrGFu6ewdj0PQD8C8bWFbwMIBpAG4DNQogbtmNMGFsU6w2gB2PT5a0AqgF4AfDA2MLSEiHE7D43OQvOyk0I8QERyTD2iZxlAK4C+JIQom3+srmdM/OzvdYCIE8IcX4e05iUk9+7rwDYAWAEY9+nTwohrs9fNrdycm6/A5BkG6NUCPHifOUxGUdzI6L/i7FLoeNnwh4SQnxERMkAfgVgKcYWcX99Ia2dY3PPaDSakpKSXP7BGXdkNBpDk5KS5BO3c6HEGGOMLRJcKN29qQolvvTGGGOMMTYFLpQYY4wxxqbAhRJjjDHG2BS4UGKMMcYYmwIXSowxxhhjU+BCibG7RGNd3z8komDb8yDbc5kTxu6bfYSMMeYe9u3bF1JcXBw9mzEyMjIU/v7+a7Oysm7p8fjmm2/6JyQkKBUKhaqgoEA+MuJQT1wulBi7W0KISxjr1r7HtmkPgHIhRKvromKMsYXNarXCYpnd7QInK3Z27tzZ+cILL3w4fpvFYsGXv/zlVS+++GJLU1PTuejo6OH9+/eHOnIuLpQYm52fANAS0TcApAN4duIORLSXiP5h3PPdRPRPRORHRO/amgafIaKNkxz7d0T0h3HP9xPRk7avNUT0FyIyENHb49pd/B8i+oCI6onIpTdTZIzde3bv3h2hUChUCoVCVVpaGg4AjY2N3jExMaqtW7dGq1SqhObmZu+ysrIQuVyuTklJWVNTU+NnP76jo8NTp9PFqtVqpVqtVh49etQXAEpKSqIKCwtlaWlpioKCglUTz7tx40ZzQEDALb3gurq6PL29va2JiYlDAJCbm9v7+uuvL5t47HS4KS5jsyCEGCGibwH4E8bujjw8yW4vAvhPAAdszx8HkAvgJoDP2RqghgKoJaI3Z3InZVvLm58C2CiEuEpEnwfwfQBPAfgOgFVCiCFbuwvG2D3og4ZdK/v7LkidOaavX9xAgnLvlC1Ajh8/Lj18+HCIwWBoEEJAo9Eoc3JyzKGhoRaTyeRTUVFhOnToUFtra6vXnj17ogwGQ0NwcLAlNTV1jVqtHgCA7du3rywpKenS6XR9TU1N3jqdTtHS0nIOAOrr66V1dXXnJ2uYO5nly5ePjo6OUnV1tTQzM3PgpZdeCrpy5Yq3IzlzocTY7D0M4AoANYA/T3xRCPE+EYUTURSAMADdQog2W7HzAyLKxFjrivsARADonME519jPZ+vA7WGLAQDqAfyWiF4H8PqsMmOMMQccO3bMLy8vr8c+s5Ofn99dVVXlv3nz5p7IyMjhnJycfgCorq721Wq15qioqFEAKCgouHHhwgUfADhx4kRAU1PTJ41w+/r6PLq7uyUAkJub2zPTIgkAJBIJDh482PLNb35z5fDwsCQrK+tjDw8Ph3LiQomxWSCitRhrGqsF8D9E9KKtOelErwB4DMByjM0wAcAXMFY4aWwzUyYAPhOOG8Wtl8jtrxOAc0KIz0xyrnwAmQAeAfA0EamEEKMOJ8cYc2vTzfzMlekmxKVS6S2XxWx/5E06hl6vb5isIPL19bVOdsx0HnjggX6DwdAIAK+99lrAxYsXJ/6cnRavUWLsLtk6tP8MwDdszX5/BODHU+z+IoAnMFYsvWLbFgjgI1uRlAVgsk/LtQJIIKIlRBQIIMe2vRFAGBF9xhaLFxGpiEgCYKUQogrAtzHWkNhvknEZY8zpsrOz+yorK5eZzWZJb2+vpLKyMigrK8s8cb/MzMz+2tpa/87OTo+hoSE6cuRIkP219PT03r1794bbn9fU1CydeLwj2tvbPQFgcHCQfvSjHy3/yle+ctWR43lGibG7978BtAkh7JfbDgB4kog+K4T4y/gdhRDniMgfQPu4GaffAvhvItIDOA3g/MQTCCEuEdHLGLuc1gTgfdv2YSJ6DMA+WwHlibF1UBcAHLJtIwA/EUL0ODdtxhibXHp6+sCWLVuur1u3TgkARUVFV9PS0gYbGxtvWRckk8lGdu3a1aHVapVhYWEjiYmJAxaLhQCgvLz80rZt26Lj4uISLBYLrV+/3pyamtp2p3NrNJo1LS0tPoODgx4RERGJBw4cMG3atKm3tLR0+Z///OdAq9VKTz311EePPPLIbYXbdGgG60YZY4wx5gaMRqMpKSnpmqvjcEdGozE0KSlJPnE7X3pjjDHGGJsCF0qMMcYYY1PgQokxxhhjbApcKDHGGGOLh9VqtU7+uXs2Jdv/s0lvPcCFEmOMMbZ4nL169WogF0szZ7Va6erVq4EAzk72Ot8egDHGGFskRkdHt3V2dv68s7NTDZ4MmSkrgLOjo6PbJnuRbw/AGGOMMTYFrjYZY4wxxqbAhRJjjDHG2BS4UGKMMcYYmwIXSowxxhhjU+BCiTHGGGNsCv8f1pNcGEdMlZAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#c) Plot the error between your model and the training data and the \n",
    "#error between your model and you testing data as a function of the \n",
    "#polynomial function order, n. Create the training-testing curves\n",
    "\n",
    "#Steel\n",
    "Z_s = np.block([[t_s_train**0]]).T\n",
    "Z_s_test = np.block([[t_s_test**0]]).T\n",
    "Z_s_train = np.block([[t_s_train**0]]).T\n",
    "max_N = 20\n",
    "SSE_s_test=np.zeros(max_N)\n",
    "SSE_s_train=np.zeros(max_N)\n",
    "print('error steel')\n",
    "for i in range(1,max_N):\n",
    "    Z_s = np.hstack((Z_s,t_s_train.reshape(-1,1)**i))\n",
    "    Z_s_test=np.hstack((Z_s_test,t_s_test.reshape(-1,1)**i))\n",
    "    A_s = np.linalg.solve(Z_s.T@Z_s,Z_s.T@P_s_train)\n",
    "    St_s=np.std(P_s_train)\n",
    "    Sr_s=np.std(P_s_train-Z_s@A_s)\n",
    "    r2_s=1-Sr_s/St_s\n",
    "    print('---- n = {:d} ----'.format(i))\n",
    "    print('the coefficient of determination for this fit is {:.3f}'.format(r2_s))\n",
    "    print('the correlation coefficient this fit is {:.3f}\\n'.format(r2_s**0.5))\n",
    "    plt.plot(t_s_train,P_s_train-Z_s@A_s,'-',label='order {:d}'.format(i))\n",
    "    SSE_s_train[i]=np.sum((P_s_train-Z_s@A_s)**2)/len(P_s_train)\n",
    "    SSE_s_test[i]=np.sum((P_s_test-Z_s_test@A_s)**2)/len(P_s_test)\n",
    "    \n",
    "plt.legend(loc='center left', bbox_to_anchor=(1.3, .5));\n",
    "plt.title('Error in predicted vs measured values',size=20)\n",
    "plt.xlabel('X values')\n",
    "plt.ylabel('Y Error \\ny-Z@A(nN)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error aluminum\n",
      "---- n = 1 ----\n",
      "the coefficient of determination for this fit is 0.843\n",
      "the correlation coefficient this fit is 0.918\n",
      "\n",
      "---- n = 2 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 3 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 4 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 5 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 6 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 7 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 8 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 9 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 10 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 11 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n",
      "---- n = 12 ----\n",
      "the coefficient of determination for this fit is 0.858\n",
      "the correlation coefficient this fit is 0.926\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Aluminum\n",
    "Z_a = np.block([[t_a_train**0]]).T\n",
    "Z_a_test = np.block([[t_a_test**0]]).T\n",
    "Z_a_train = np.block([[t_a_train**0]]).T\n",
    "\n",
    "max_N = 13\n",
    "SSE_a_train=np.zeros(max_N)\n",
    "SSE_a_test=np.zeros(max_N)\n",
    "print('error aluminum')\n",
    "for i in range(1,max_N):\n",
    "    Z_a = np.hstack((Z_a,t_a_train.reshape(-1,1)**i))\n",
    "    Z_a_test=np.hstack((Z_a_test,t_a_test.reshape(-1,1)**i))\n",
    "    A_a = np.linalg.solve(Z_a.T@Z_a,Z_a.T@P_a_train)\n",
    "    St_a = np.std(P_a_train)\n",
    "    Sr_a = np.std(P_a_train-Z_a@A_a)\n",
    "    r2_a = 1-Sr_a/St_a\n",
    "    print('---- n = {:d} ----'.format(i))\n",
    "    print('the coefficient of determination for this fit is {:.3f}'.format(r2_a))\n",
    "    print('the correlation coefficient this fit is {:.3f}\\n'.format(r2_a**0.5))\n",
    "    plt.plot(t_a_train,P_a_train-Z_a@A_a,'-',label='order {:d}'.format(i))\n",
    "    SSE_a_train[i]=np.sum((P_a_train-Z_a@A_a)**2)/len(P_a_train)\n",
    "    SSE_a_test[i]=np.sum((P_a_test-Z_a_test@A_a)**2)/len(P_a_test)\n",
    "\n",
    "plt.legend(loc='center left', bbox_to_anchor=(1.3, 0.5));\n",
    "plt.title('Error in predicted vs measured values',size=20)\n",
    "plt.xlabel('X values')\n",
    "plt.ylabel('Y Error \\ny-Z@A(nN)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost of Steel in 2025   : $ 1246988.53\n",
      "Cost of Aluminum in 2025: $ 304499017.75\n"
     ]
    }
   ],
   "source": [
    "#d)Choose a polynomial function to predict the price of aluminum and steel in the year 2025.\n",
    "\n",
    "for i in range(0,47):\n",
    "    price_s=a_s_train[i]*2025**i\n",
    "print('Cost of Steel in 2025   : $',round(price_s,2))\n",
    "for i in range(0,47):\n",
    "    price_a = a_a_train[i]*2025**i\n",
    "print('Cost of Aluminum in 2025: $',round(price_a,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(d) The steel is still the cheaper option.\n"
     ]
    }
   ],
   "source": [
    "print('(d) The steel is still the cheaper option.')"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}