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{
"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": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"fea_arrays = np.load('./fea_arrays.npz')\n",
"K=fea_arrays['K']*1000\n",
"\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",
"\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": "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": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Condition of K = 6.640986594413607e+16\n",
"Condition of K[2:13,2:13] = 52.23542514351013\n",
"\n",
"a) Expected error of u: 6.640986594413607\n",
"b) The condition of K is large because it ill-conditioned, meaning it is very sensistive to small changes in the input\n",
"c) Expected error of u[2:13]: 5.223542514351013e-15\n"
]
}
],
"source": [
"condition1 = np.linalg.cond(K)\n",
"condition2 = np.linalg.cond(K[2:13,2:13])\n",
"print('Condition of K =', condition1)\n",
"print('Condition of K[2:13,2:13] =', condition2)\n",
"print()\n",
"error1 = condition1*1e-16\n",
"error2 = condition2*1e-16\n",
"print('a) Expected error of u:',error1)\n",
"print('b) The condition of K is large because it ill-conditioned, meaning it is very sensistive to small changes in the input')\n",
"print('c) Expected error of u[2:13]:',error2)"
]
},
{
"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": 3,
"metadata": {},
"outputs": [],
"source": [
"#a)\n",
"L,U = LUNaive(K[2:13,2:13])\n",
"\n",
"#b)\n",
"A = 1e-7\n",
"E_st = 200e9\n",
"E_al = 70e9\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"u_st = solveLU(L,U,F/E_st/A)\n",
"u_al = solveLU(L,U,F/E_al/A)\n",
"\n",
"#c)\n",
"u1 = np.zeros(14)\n",
"for i in range(len(u_st)):\n",
" u1[i+2] = u_st[i]\n",
"u2 = np.zeros(14)\n",
"for i in range(len(u_al)):\n",
" u2[i+2] = u_al[i]\n",
"\n",
"F_st = K*E_st*A@u1\n",
"F_al = K*E_al*A@u2\n",
"\n",
"#Calculations done in SI units. Converting back to mm\n",
"u1 = u1*1000\n",
"u2 = u2*1000"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Steel\n",
"\n",
" Displacements:\n",
" ---------------\n",
" u_1x : 0.00 mm\n",
" u_1y : 0.00 mm\n",
" u_2x : 1.95 mm\n",
" u_2y : -2.12 mm\n",
" u_3x : 0.43 mm\n",
" u_3y : -4.00 mm\n",
" u_4x : 1.08 mm\n",
" u_4y : -5.37 mm\n",
" u_5x : 1.73 mm\n",
" u_5y : -4.00 mm\n",
" u_6x : 0.22 mm\n",
" u_6y : -2.12 mm\n",
" u_7x : 2.17 mm\n",
" u_7y : 0.00 mm\n",
"\n",
" Forces:\n",
" ---------------\n",
" F_1x : 0.00 N\n",
" F_1y : 50.00 N\n",
" F_2x : 0.00 N\n",
" F_2y : 0.00 N\n",
" F_3x : -0.00 N\n",
" F_3y : -0.00 N\n",
" F_4x : -0.00 N\n",
" F_4y : -100.00 N\n",
" F_5x : 0.00 N\n",
" F_5y : 0.00 N\n",
" F_6x : -0.00 N\n",
" F_6y : 0.00 N\n",
" F_7x : -0.00 N\n",
" F_7y : 50.00 N\n",
"\n",
"d)\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": [
"print('Steel\\n')\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print(' Displacements:\\n ---------------')\n",
"for i in range(len(u1)):\n",
" print(' u_{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u1[i]))\n",
"print()\n",
"print(' Forces:\\n ---------------')\n",
"for i in range(len(F_st)):\n",
" print(' F_{}{} : {:.2f} N'.format(int(i/2)+1,xy[i%2],F_st[i]))\n",
" \n",
"print()\n",
"\n",
"print('d)')\n",
"l = 300\n",
"nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[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],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\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",
"plt.plot(r[ix],r[iy],'-',color='k')\n",
"plt.plot(r[ix],r[iy],'o',color='b')\n",
"plt.plot(r[0],r[1],'^',color='r',markersize=20)\n",
"plt.plot(r[0],r[1],'>',color='k',markersize=20)\n",
"plt.plot(r[-2],r[-1],'^',color='r',markersize=20)\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='b') \n",
"s = 5\n",
"plt.plot(r[ix]+u1[ix]*s,r[iy]+u1[iy]*s,'-',color=(1,0,0,1))\n",
"plt.quiver(r[ix],r[iy],F_st[ix],F_st[iy],color=(1,0,0,1),label='applied forces')\n",
"plt.quiver(r[ix],r[iy],u1[ix],u1[iy],color=(0,0,1,1),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=20)\n",
"plt.xlabel('x (mm)',size=15)\n",
"plt.ylabel('y (mm)',size=15);"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Aluminum\n",
"\n",
" Displacements:\n",
" ---------------\n",
" u_1x : 0.00 mm\n",
" u_1y : 0.00 mm\n",
" u_2x : 5.57 mm\n",
" u_2y : -6.07 mm\n",
" u_3x : 1.24 mm\n",
" u_3y : -11.43 mm\n",
" u_4x : 3.09 mm\n",
" u_4y : -15.36 mm\n",
" u_5x : 4.95 mm\n",
" u_5y : -11.43 mm\n",
" u_6x : 0.62 mm\n",
" u_6y : -6.07 mm\n",
" u_7x : 6.19 mm\n",
" u_7y : 0.00 mm\n",
"\n",
" Forces:\n",
" ---------------\n",
" F_1x : 0.00 N\n",
" F_1y : 50.00 N\n",
" F_2x : 0.00 N\n",
" F_2y : 0.00 N\n",
" F_3x : -0.00 N\n",
" F_3y : 0.00 N\n",
" F_4x : 0.00 N\n",
" F_4y : -100.00 N\n",
" F_5x : 0.00 N\n",
" F_5y : 0.00 N\n",
" F_6x : 0.00 N\n",
" F_6y : 0.00 N\n",
" F_7x : -0.00 N\n",
" F_7y : 50.00 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": [
"print('Aluminum\\n')\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print(' Displacements:\\n ---------------')\n",
"for i in range(len(u2)):\n",
" print(' u_{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u2[i]))\n",
"print()\n",
"print(' Forces:\\n ---------------')\n",
"for i in range(len(F_al)):\n",
" print(' F_{}{} : {:.2f} N'.format(int(i/2)+1,xy[i%2],F_al[i]))\n",
"\n",
"l = 300\n",
"nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[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],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\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",
"plt.plot(r[ix],r[iy],'-',color='k')\n",
"plt.plot(r[ix],r[iy],'o',color='b')\n",
"plt.plot(r[0],r[1],'^',color='r',markersize=20)\n",
"plt.plot(r[0],r[1],'>',color='k',markersize=20)\n",
"plt.plot(r[-2],r[-1],'^',color='r',markersize=20)\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='b') \n",
"s = 5\n",
"plt.plot(r[ix]+u2[ix]*s,r[iy]+u2[iy]*s,'-',color=(1,0,0,1))\n",
"plt.quiver(r[ix],r[iy],F_al[ix],F_al[iy],color=(1,0,0,1),label='applied forces')\n",
"plt.quiver(r[ix],r[iy],u2[ix],u2[iy],color=(0,0,1,1),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=20)\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?\n",
"\n",
"![Mesh image of truss](../images/mesh.png)\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"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 : 0.00 mm\n",
" u_2y : -0.08 mm\n",
" u_3y : -0.14 mm\n",
" u_4y : -0.19 mm\n",
" u_5y : -0.14 mm\n",
" u_6y : -0.08 mm\n",
" u_7y : 0.00 mm\n",
"\n",
"b) Minimum cross-sectional area for steel: 2.8e-06 m^2\n",
" Steel Displacements:\n",
" --------------------\n",
" u_1y : 0.00 mm\n",
" u_2y : -0.08 mm\n",
" u_3y : -0.14 mm\n",
" u_4y : -0.19 mm\n",
" u_5y : -0.14 mm\n",
" u_6y : -0.08 mm\n",
" u_7y : 0.00 mm\n"
]
}
],
"source": [
"A_al = 0.0000079\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"u_al = solveLU(L,U,F/E_al/A_al)\n",
"u2 = np.zeros(14) \n",
"for i in range(len(u_al)):\n",
" u2[i+2] = u_al[i]\n",
"F_al = K*E_al*A_al@u2\n",
"\n",
"print('a) Minimum cross-sectional area for aluminum:', A_al,'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_{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u2[i]*1000))\n",
"\n",
"print()\n",
"\n",
"A_st = 0.0000028\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"u_st = solveLU(L,U,F/E_st/A_st)\n",
"u1 = np.zeros(14)\n",
"for i in range(len(u_st)):\n",
" u1[i+2] = u_st[i]\n",
"F_st = K*E_st*A_st@u1\n",
"\n",
"\n",
"print('b) Minimum cross-sectional area for steel:', A_st,'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_{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u1[i]*1000))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c) Mass fo steel : 0.0776 kg\n",
" Mass fo aluminum: 0.0771 kg\n",
"d) Cost of Steel : $ 0.04\n",
" Cost of Aluminum: $ 0.12\n",
" The steel truss is cheaper.\n"
]
}
],
"source": [
"rho_st = 7700 #kg/m^3\n",
"rho_al = 2710 #kg/m^3\n",
"l = 0.3 #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],[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],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\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",
"\n",
"m_st = A_st*l*rho_st\n",
"m_al = A_al*l*rho_al\n",
"print('c) Mass fo steel :', round(m_st,4),'kg')\n",
"print(' Mass fo aluminum:', round(m_al,4),'kg')\n",
"\n",
"price_st = 476/1000 # $/kg\n",
"price_al = 1545/1000 # $/kg\n",
"\n",
"cost_st = m_st*price_st\n",
"cost_al = m_al*price_al\n",
"\n",
"print('d) Cost of Steel : $',round(cost_st,2))\n",
"print(' Cost of Aluminum: $',round(cost_al,2))\n",
"print(' The steel truss is cheaper.')"
]
},
{
"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__?\n",
"\n",
"**Answer:** Yes, based on my price model, I would change the answer to 3b. This is because at this high of an order (46) the function can be unpredicatable when extrapolating. In this situation, the function of the highest order is predicting a value way to high."
]
},
{
"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": 23,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import random\n",
"\n",
"steel = pd.read_csv('../data/steel_price.csv')\n",
"aluminum = pd.read_csv('../data/al_price.csv')\n",
"t_st = steel['Year']\n",
"P_st = steel['dollars/MT']\n",
"t_al = aluminum['Year']\n",
"P_al = aluminum['dollars/MT']\n",
"\n",
"# Part a\n",
"np.random.seed(100)\n",
"st_rand = random.sample(range(0,len(t_st)),len(t_st))\n",
"al_rand = random.sample(range(0,len(t_al)),len(t_al))\n",
"train_per=0.7\n",
"\n",
"np.random.seed(100)\n",
"t_st_train = np.sort(t_st[st_rand[:int(len(t_st)*train_per)]])\n",
"P_st_train = np.sort(P_st[st_rand[:int(len(t_st)*train_per)]])\n",
"t_st_test = np.sort(t_st[st_rand[int(len(t_st)*train_per):]])\n",
"P_st_test = np.sort(P_st[st_rand[int(len(t_st)*train_per):]])\n",
"\n",
"t_al_train = np.sort(t_al[st_rand[:int(len(t_al)*train_per)]])\n",
"P_al_train = np.sort(P_al[st_rand[:int(len(t_al)*train_per)]])\n",
"t_al_test = np.sort(t_al[al_rand[int(len(t_al)*train_per):]])\n",
"P_al_test = np.sort(P_al[al_rand[int(len(t_al)*train_per):]])"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Part b \n",
"\n",
"max_N = 46\n",
"\n",
"Z_st_train = np.block([[t_st_train**0]]).T\n",
"for i in range(1,max_N+1):\n",
" Z_st_train = np.hstack((Z_st_train,t_st_train.reshape(-1,1)**i))\n",
"a_st_train = np.linalg.solve(Z_st_train.T@Z_st_train,Z_st_train.T@P_st_train)\n",
"\n",
"plt.plot(t_st_train,P_st_train,'o',label='data')\n",
"plt.plot(t_st_train,Z_st_train@a_st_train,label='Order Fit: {}'.format(max_N),lw=3)\n",
"plt.xlabel('Time (years)',size=15)\n",
"plt.ylabel('Price (dollars)',size=15)\n",
"plt.title('Price of Steel',size=20)\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 25,
"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": [
"max_N = 46\n",
"\n",
"Z_al_train = np.block([[t_al_train**0]]).T\n",
"for i in range(1,max_N+1):\n",
" Z_al_train = np.hstack((Z_al_train,t_al_train.reshape(-1,1)**i))\n",
"a_al_train = np.linalg.solve(Z_al_train.T@Z_al_train,Z_al_train.T@P_al_train)\n",
"\n",
"plt.plot(t_al_train,P_al_train,'o',label='data')\n",
"plt.plot(t_al_train,Z_al_train@a_al_train,label='Order Fit {}'.format(max_N),lw=3)\n",
"plt.xlabel('Time (years)',size=15)\n",
"plt.ylabel('Price (dollars)',size=15)\n",
"plt.title('Price of Aluminum',size=20)\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"---- n=1 -------\n",
"the coefficient of determination for this fit is 0.643\n",
"the correlation coefficient this fit is 0.802\n",
"---- n=2 -------\n",
"the coefficient of determination for this fit is 0.751\n",
"the correlation coefficient this fit is 0.867\n",
"---- n=3 -------\n",
"the coefficient of determination for this fit is 0.751\n",
"the correlation coefficient this fit is 0.867\n",
"---- n=4 -------\n",
"the coefficient of determination for this fit is 0.751\n",
"the correlation coefficient this fit is 0.867\n",
"---- n=5 -------\n",
"the coefficient of determination for this fit is 0.751\n",
"the correlation coefficient this fit is 0.867\n",
"---- n=6 -------\n",
"the coefficient of determination for this fit is 0.743\n",
"the correlation coefficient this fit is 0.862\n",
"---- n=7 -------\n",
"the coefficient of determination for this fit is 0.751\n",
"the correlation coefficient this fit is 0.866\n",
"---- n=8 -------\n",
"the coefficient of determination for this fit is 0.751\n",
"the correlation coefficient this fit is 0.866\n",
"---- n=9 -------\n",
"the coefficient of determination for this fit is 0.750\n",
"the correlation coefficient this fit is 0.866\n",
"---- n=10 -------\n",
"the coefficient of determination for this fit is 0.794\n",
"the correlation coefficient this fit is 0.891\n",
"---- n=11 -------\n",
"the coefficient of determination for this fit is -0.029\n",
"the correlation coefficient this fit is nan\n",
"---- n=12 -------\n",
"the coefficient of determination for this fit is 0.705\n",
"the correlation coefficient this fit is 0.840\n",
"---- n=13 -------\n",
"the coefficient of determination for this fit is 0.859\n",
"the correlation coefficient this fit is 0.927\n",
"---- n=14 -------\n",
"the coefficient of determination for this fit is 0.838\n",
"the correlation coefficient this fit is 0.915\n",
"---- n=15 -------\n",
"the coefficient of determination for this fit is 0.889\n",
"the correlation coefficient this fit is 0.943\n",
"---- n=16 -------\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.928\n",
"---- n=17 -------\n",
"the coefficient of determination for this fit is -1.348\n",
"the correlation coefficient this fit is nan\n",
"---- n=18 -------\n",
"the coefficient of determination for this fit is 0.889\n",
"the correlation coefficient this fit is 0.943\n",
"---- n=19 -------\n",
"the coefficient of determination for this fit is 0.861\n",
"the correlation coefficient this fit is 0.928\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:19: RuntimeWarning: invalid value encountered in double_scalars\n"
]
},
{
"data": {
"image/png": 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j+ljuOc+BnI9n3clKqd5qJ32tf6QyHInnBsYXNQVPmV5VSi0Y4DZjgN3eL7ibLaMZwM2EUmqNiBRhDGSMwAheV2IMKFvRy/rLgeXudWdjdGNcD7wrIhN79m0PMs97catS6qF+bnMPRj/8dKXUNu8XRORv9NLKopR6C3jL3boyE2NA2/eBN0VkileXjMu9H4tSqmdNtreb6wOH6GP5SPt83Obe/0FjXtzHvpJvAv2ReILlIfHCXYaeGgFsNlvb9OnTjb/p9Kd6We1gAe6v7u5uc1NTU0h9fX1EfX19jNlstuXm5m7u2bd9JP5Mr1lXV2eaN29e+l133VXquTHwhZHehz1UPE2tp/bxumd5n49cDFNTRSS0l+Wnur8PpIn5c/f3k/q5vmffc3vpj/Muw2G5+xk3A2NEZMqR1seoXUDvrRHbMW4AZrlHA/eH52/eW/P9SRzdTfEzGDWfyzEGGcYAzyulDumr9lBKNSilViilbsSohUXR/7+Frwz0MwDGUwFbewnWJnofE3KAUqpVKfVfpdRtwO8wmtLnea3iGZmb1Mvm0wdQRo+R9vlId39/pZd9HLG7yctA38ftQIPD4bC5XK6BdltisVicUVFRjWlpaXsjIyNrnE6nuampKeTIWx7MX+k1Ozo65Pzzz0+/4ooraq+//nqfjA730AG7f1ZjPMIxV0S+4/2C+/eTMR4F+9QPZTsW4cBd3gvEeGb5Koy75FcHsK+nMC5mvxKRQwa/iYhJvJ5pd/c5vo/xaNktPda9kIFdUDy1ub9Jj2db3cdN8FrkaYI8ZCCTuxb2MEaLyUMicsg/p4gkeAbOuT3t/v4LEYnyWs8O/N8AzsHbcoxazTXuL+/jeJflXBHp7YLvucC0HeXxj4q7CX4VsEBEru9tHRGZJCJxXouKgQwRSfRaRzCanHN6bI6InNHb34VvWmq8z9kz3uKgbhoROQOjVjogI+3zwTezPZ7ao4znAEsGcLwC9/EWisiBGRjd5/P7nit73ieXy2UuLi5O8qSq9NbZ2RnQ2tpq9/xeV1cX5nIdWmHt7u4OADCZTANuEvdOrzlt2rSJnvSaPdfzTq85d+7czPz8/AOfoWXLlu1ft25dcGZmZk5aWlruI488csRnwp988snIr776KuT555+Pyc7OzsnOzs7xVR7tEd0kfpjHusB4bGf9YV7vN6WUEpFrMQLMSyLyGsZdZBZwEdAMXNPLI13D3SfAEhGZiXFT4nkO24Qx4rrf+VuVUrXum5dXgc9F5ENgC8Y/ejLGgKJojFHCHj/AeITsz2JMqrEBo1ZwMcazrvP7efi/Y9TGrgGK3H+faiAR47G6J4Gl7nU/w7io/8h9wfH0LT7sHmF+DzAZ+B4wX0T+i9FkGYfRdzkH49Gere7zXi0iD2OMVN8sIi/zzXO29fQ97qFPSqn9IrISY6BQN7CpjwF1LwIdIvIpxsVZMGptMzAGin0w0GP7wEKMQZhPiMgPMR7na8AYnJaPMUDwRMDTVP8AxiOJX4vIKxjv3RyMYN3bZ+BPQIoYE3UUYzSnT8P4O+/FeE88ngLuAH7mHsG+FWNA1DyMz+klDNxI+nw8ijFK/V/u97YU4/0/F/gnxv96f45XLiLPYTxfvl5E3sJ4xPU8jGtIby1b99hsttvr6upim5qaIkJCQpoCAgIc3d3dls7OTntbW1tIfHx8aXBwcAVAcXFxqslkUkFBQc1Wq7ULoLW1NbS9vT3Ibre3RURE9DY49oiWLl1auXTp0oPGD2RlZXUVFRVt8V5266231t56662HjCdISEjofuutt3b3XH7//feX9VzmcfPNN9fdfPPNdX29fixGdMDm8AM/ijl4YoxjopT6QozJU/4fxrOp8zH6jV4A7lEDm7BkuNiDceG51/3dhtGEd7dS6t2B7kwp9aGI5GM8I3oORvDowhht/F96NM0ppYrEmM3qXoz39FSM0bkXYYwo7lfAdg8QulZE3gNuAi5zn0s5Ro3vda9160XkEozPzmKMST0A/gE0ukfcX4TxXOt1GP2jIRg3AHuAX2KMVPZ2K0YLyw8wBkHVYgSEn2PchByNpzEuyBYOHanv8VOM93kqxsWzAyNo3Qn89XBN6INFKVXiHrX8PxgB8SqM7ocKjCD2MLDJa/2/iUgnxoC5azFGWa/C+NtcwqGfgd9h3NBNx/jMuDBGkP8O+LNS6kATpFKqSkROAf6A0Qp2CkZt8SyMlp0BB+yR9PlQSm0UkdOA32B8Pizu4y3AuInqV8B2uxHj5vZKjPPYh9Gy9QeM/7eex3Zs2LChKiEhwVVbWxvT3Nwc4XK5TGazudtqtXbGx8eXxsTEHAiQiYmJpU1NTWHt7e3Bzc3N4SaTSQUEBHQlJCSUjBkzptpkMg3nsUBDRg7XMa+NTmJMKbkHeEYpdZ1fC6Np2qi0YcOG4smTJ/vy2fjjxoYNG2ImT56c0nO57sPWNE3TtBFAB2xN0zRNGwF0wNY0TdO0EWCkDzrTjoJSqhivWYY0TdO04U/XsDVN0zTN7aGHHoq+5ppreks40y87duyw5ubmTszOzs5JT0/P/f3vf++zfN66hu0lJiZGpaSk+LsYmqZpI8ratWtrlFI+C0xDZTDSayYnJzsKCgq2BwYGqsbGRlNOTk7uZZdd1pCSknLMj1nqgO0lJSWFgoKB5EvQNE3TRKS/Ob2H1NKlS8c899xzMQCLFi2qvuuuu6oKCwut8+bNy5g9e3bz2rVrQ1577bWdb7/9dugDDzyQEBsb60hLS+uwWq0KjPSaixcvHl9aWmoFuP/++/edffbZrbfddltieXl5wL59+6xRUVHdb7zxxh7PMe12+4Fnpdvb26W3GdyOlg7YmqZp2qD65epfJu2s3xl05DX7Lz0yve2eOfcMy/SaO3fuDDjvvPMy9u/fb7vrrrtKfFG7Bh2wNU3TtFHIn+k109PTHTt27NhaXFwcMH/+/PSrr766PikpaUDZxnqjA7amaZo2qA5XEx4s/kyv6ZGSkuLIyspq/+CDD0IXL158zJm79ChxTdM0bdTxV3rNXbt2BbS0tAhAdXW1uaCgICQ3N7fDF+c0YmrYIvIkxkT7VUqpPPeyKOAlIAUj2cdlnsn/ReRnwA0Y+Y9/eDTJLDRN07SRyTu9JhiDzubMmdNeWFho9V7PO71mbGysIz8/v82TEnTZsmX7lyxZkpyZmZnjdDpl5syZzbNnz953uONu3Lgx8M477xwnIiiluOWWWyq+9a1vHZLW82iMmOQfInIy0AIs9wrYvwfqlFL3ishPgUil1J3ufLQvAN/CSLH4AZCplHIe7hjTp09XepS4pmnawIjIWqXUdO9lOvnH0RvxyT+UUp8APXOMXsg3qeWewUjL6Fn+olKqUym1B9iJEbw1TdM0bUQaMQG7D2OUUuVgJFnHSCIPMBbwHuRQ4l42KLr2N1P50Dq6ylsH6xCapmnacW6kB+y+9Dbkr9e2fxG5SUQKRKSgurr6qA5mCrLgKGulq7jxqLbXNE3TtCMZ6QG7UkQSANzfq9zLS4Akr/XGAWW97UAptUwpNV0pNT029uhm1jNH2TGFBtC5t+mottc0TdO0IxnpAft14Fr3z9cCr3ktv0JEbCIyAcgAvhysQogItvFhdBXrgK1pmqYNjhETsEXkBeAzIEtESkTkBuBe4CwRKQLOcv+OUmoL8E9gK/AO8IMjjRA/Vtbx4TgbOnE2dg7mYTRN07Tj1IgJ2EqpK5VSCUqpAKXUOKXUE0qpWqXUGUqpDPf3Oq/1f6uUSlNKZSml3h7s8tlSwgB0s7imadoIdqzpNT3q6upMcXFx+b7Yl8eICdjDXUBiMBJg0s3imqZpI4TL5cLpPLbGV4ej97weP/7xj8fOnDnzkJnVjoUO2D4iZhMB40J1DVvTNG2YWLp06ZiMjIzcjIyM3LvvvjsOoLCw0Jqampp79dVXJ+fm5ubs2rXL+uCDD0anpKTkzZgxI2vNmjUhnu3Lysos55xzTlpeXt7EvLy8ie+9914wwG233ZZ45ZVXjp8zZ07GggULJvQ87qpVq4Kqq6sDzjrrLJ8GhBEzNelIYEsJo/nj/bg6nZhsR58QXdM0bTQp+/kvkjqLinyaXtOWkdGW+LvfDrv0mk6nkx//+MdJzz///O4VK1aE+fKcdcD2IVtKGM0roWtfE/aMyCNvoGmapg0Kf6XXvO+++2LPPvvshvT0dJ/kwPamA7YPWceHgUBnsQ7YmqZpHoerCQ8Wf6XX/Pzzz0O++uqrkKeeeiqura3N5HA4TCEhIc5HH320dGBncCjdh+1DJruFgIRgPeOZpmman/krvebrr7++p7y8fFNpaemmX//61yULFiyo9UWwBl3D9jlbSjitX1WgnC7ErO+HNE3T/MFf6TUH04hJrzkUfJFes21jNXXPbyf25snYkn063kDTNG1Y0uk1fWvEp9ccKWwTwgH089iapmmaT+mA7WPmUCuWaDude3Q/tqZpmuY7OmAPAmtKOF17m1Au3d2gaZqm+YYO2IPANiEMV1s33dVt/i6KpmmaNkrogD0IbClGP3an7sfWNE3TfEQH7EFgjrZjCg2gS/dja5qmaT6iA/YgEBFsKeG6hq1pmjbC+CK9ptlsnpadnZ2TnZ2dc/rpp6f7qmx64pRBYk0Jo31TDd0NHVgi7P4ujqZpmtaDy+VCKYXZfPTJmhwOBwEBAQcts9lsru3bt2891vL1pGvYg8TTj921R9eyNU3T/MFf6TUHy4ivYYtIFvCS16JU4C4gArgRqHYv/7lSasVQlSsgIRixmeksbiRoStyRN9A0TRulPly+LamutMWn6TWjxoa0nXHNxGGXXhOgq6vLlJeXN9FsNqvbb7+9YtGiRQ2+OOcRH7CVUoXACQAiYgZKgVeBxcADSqk/+qNcYhKs48N0P7amaZof+Cu9JsDOnTs3pqSkOLZu3Wo966yzsqZOndqem5vbeaznNOIDdg9nALuUUnv7Spc2lGwTwmh6dy/OVgfm4IAjb6BpmjYKHa4mPFj8lV4TICUlxQGQk5PTNWvWrOYvv/wyyBcBe7T1YV8BvOD1+y0islFEnhSRXhNUi8hNIlIgIgXV1dW9rXLUDvRj79W1bE3TtKHkr/Sa1dXV5vb2dgEoLy+3FBQUhOTn57f74pxGTcAWEStwAfAv96K/AmkYzeXlwJ96204ptUwpNV0pNT02NtanZbKOCwWz0KnzY2uapg0p7/Sa06ZNm+hJr9lzPe/0mnPnzs3Mz88/MEXlsmXL9q9bty44MzMzJy0tLfeRRx45YpBYv369ffLkyROzsrJyTjnllMwf/ehHFdOmTevwxTmNmvSaInIh8AOl1Nm9vJYCvKmUyjvcPnyRXrOnqsc2gFMR94MTfLpfTdO04UKn1/St4yG95pV4NYeLSILXaxcDm4e8RBjN4l2lLbi6nP44vKZpmjZKjIqALSJBwFnAv70W/15ENonIRuA04H/9UTZrShi4FF37Duk60TRN07R+GxWjxJVSbUB0j2WL/FScg9jGh4FAV3Ej9vQIfxdH0zRNG6FGRQ17ODMFWgiID9bPY2uapmnHRAfsIWBNCaNrXxPKOToG+GmapmlDTwfsIWCbEI7qcuEoa/F3UTRN07QRSgfsIeCZQEU/j61pmja8+SK9ZlFRkXXOnDkZqampuWlpabmFhYVWX5RNB+whYA6zYo6206kzd2mapg0bLpcLp/PYHrl1OByHLLvqqqsm3H777ZW7d+/esm7dum2eecqPlQ7YQ8SWEk7X3sbDzm+raZqm+Y4/0muuXbvW7nQ6ufjii5sAwsPDXaGhoX3OOz4Qo+KxrpHAlhJG29pKuqvbCYjzaZY5TdO0Ye3dv/45qWb/Xp9e+GKSxred8/0fDbv0mlu3brWHhYU5zz777LT9+/fbTj755Ka//OUvJRbLsYdbXcMeItaUMACaPy7RtWxN07RB5p1eMzw83OVJrwnQV3pNu92uFixYUOfZx+rVq8NuvfXW5Ozs7Jz58+en9ye9Znd3txQUFIT8+c9/3r9x48atxcXFtocffjjGF+eka9hDxBJjJHlpW1tJUH4M9qwoP5dI0zRtaByuJjxY/JVeMzk5uWvixIntOTk5XQAXXHBB/eeffx7S27oDpWvYQ5JudcgAACAASURBVEREiLnByD3SsUuPFtc0TRtM/kqvecopp7Q2Njaay8rKLAArV64My8nJ8Ul6TV3DHkL2jEhjEpU9OmBrmqYNJu/0mgCe9Jo9H7HyTq8ZGxvryM/Pb3M6nQJGes0lS5YkZ2Zm5jidTpk5c2bz7Nmz9x3uuBaLhXvvvbfk1FNPzQSYNGlS2//+7//6JGvZqEmv6QuDkV6zp8Z3i2n+uITEX52IyWYe1GNpmqYNBZ1e07eOh/SaI4JtQrg7e5d+JlvTNE3rPx2wh5h1fCgIdOpmcU3TNG0AdB/2EDPZLASMDdGznmnaALk6nTR/vJ+u4iYQwGzCEmHDHGXH4vmKDcRk05c1bXTSn2w/sE0Ip+WzMlxdTkxW3Y+taX1xdTnpKm6iY1cDbeuqcDV3YU0KBbOgOhy0lzbjavWa9dEEAWNDsaeFY8+MxDo+DDHrhkRtdNAB2w/smZG0rCqlc2cDgTnR/i6Opg0byqnoKm2mc2eD8bW3CZwKzIJtQjhhiyZiSw47aBtXRzfddR046zroKmuhc1cjzZ+U0vxRCWI3Y8+IxJ4dhT0rEnOIT3IwaJpfjIqALSLFQDPgBLqVUtNFJAp4CUgBioHLlFL1/iqjN1tqOGI3076lVgds7bjnau+mbVM1Hdvr6dzdgOowkjEEJAQTMjsRe3oE1gnhfbZGmewWrIkhkBhCYJ4xoZSro5vOnQ20b6+jo7CO9k01YBFCZo8l7NRxmIIChuz8NM1XRkXAdjtNKeX9CMFPgQ+VUveKyE/dv9/pn6IdTMwm7FlRdGyvQ7kUYup9lh1NOx7ULN9K155GzJE2gvJjsaVFYEsLP6basMluITAvhsC8GJRL4ShvpeXTUlpWldD6ZQVhZyQTMidR/+9ph3jooYeiCwoKgpcvX37Y56378sYbb4TecccdSZ7f9+zZY//73/++e9GiRQ3HWrbRFLB7uhA41f3zM8BHDJOADRCYG037hmq69jUdyJetaccL5VJ07myg5bMyuoobCcyNJurqiX1OEXksxCRYx4YQdXkWISeNpfGdYhrf2k375hqiLsvEEn3Eyau0UcrlcqGUwmw++rFEDoeDgIBvWmzmz5/fPH/+/K0AlZWV5szMzEkXXXSRT0YZj5bRGAp4T0TWishN7mVjlFLlAO7vcb1tKCI3iUiBiBRUV1cPUXGNfmxMQvu2uiOvrGmjhKvTSfOnpVTev5aaJzfTta+Z0FOTiLgofVCCdU/WxBBiFucSeXkWjspWKh9cR8sX5Tohzyjlj/Sa3p599tnIU045pVGn1zzYHKVUmYjEAe+LyPb+bqiUWgYsA2Oms8EqYE8muwVbajgd22phXp9/b00bNbpKmql7YTvdtR1Yk0OJvDyLoEkxiGVo6w0iQvCUOGwTwql/eQcNr+6kY1sdUVdkYbKPlkvi8FL38o4kR0WrT9NrBsQHt0V9J3PYpdf09vLLL0fdeuutlb4651Hx6VRKlbm/V4nIq8C3gEoRSVBKlYtIAlDl10L2wp4dReObu+mubdfNctqopVyKltWlNL5TjDkkgJgbJ2FPi/B3sbBE2Ii5Po/Wz8poeGsP1Y9vImZxrh5JPkp4p9cE8KTXvPTSSxv6Sq8JsGDBgrodO3bYwUivWVRUdODi3J/0mh579+4NKCwsDFywYIHPJt0Y8QFbRIIBk1Kq2f3z2cDdwOvAtcC97u+v+a+UvQucaATs9m11hM4d6+/iaJrPOVu6qP/XDjoK67HnRBP1nYxhNUJbTELInLGYowOpe24b1Y9tJOb6PCxRdn8XbVQ5XE14sPgrvabH8uXLI88999wGm83ms5bb0dCHPQb4VEQ2AF8Cbyml3sEI1GeJSBFwlvv3YcUSHYglLshoFte0UUQpRdumaiofXEfHrgYiLkwjetHEYRWsvQVmRxGzZBLOFgdVj23AUdHq7yJpx8hf6TU9Xn755aiFCxf6dJDSiK9hK6V2A5N7WV4LnDH0JRqYwIlRNK8qxdXRrfvPtFHBu1YdkBBMzPWTsCYE+7tYR2QbH0bc9/KpfnIzVY9tJGZxLrbxYUfeUBuW/JVeE4yBbeXl5dbzzjvvkBuEY6HTa3oZivSaPXUWN1L92EairswmaHLskB5b03ytq6SZ2me34WztIvzcCYScmIiYR9azzt11HdQ8uRlnYydRV00kMDvK30UadI/8t4js+DDOzBlzVNvr9Jq+pdNrDlPW5DBMwRbdLK6NeK0FFVQ9tgEE4r43mdC5Y0dcsAawRNmJ/V4+lrggapdvofWrCn8XaVCt3VvHn97fwSdFQ/dYq3Z0dMD2MzEJ9qwo2gvrUU7d2qGNPK4uJ/WvFFH/chG2lHDibjkB67hQfxfrmJhDrMTeNAlbWgT1rxTR8PoulNMnj9IOKx0OJz95eSOJ4YH85NxsfxdHOwIdsIcB+8QoVHs3XXt1yk1tZOkqbaHq4a9pLagg9NQkYhbnjZrHokw2CzHX5REydywta8qoeXIzrjaHv4vlUw//t4hd1a38bsEkQnRa0mFPB+xhwJ4RCWahXTeLayNI61cVVP11ParTScySSYSfmzIim8APR8xCxLdTibw0k87iJmpf2I5yjY6WsC1ljTz28W4umTqOUzL1+JmRQAfsYcBkt2BLi6B9S62eIlEb9lS3i/p/F1H/irsJ/Napw2IilMEUPG0MkRel01nUQNO7xf4uzjFzOF385OWNRAZZ+eW3J/q7OFo/6YA9TARNisFZ14GjTD//qQ1f3Q2dVD22gdYv3U3g1+dhDh6ez1b7WvCMeIJnxtP8cQmtBZUj+ub64Q+L2FLWxG8uyiUiaHR0YRwPdMAeJuw50WCC9o16pKY2PHXsbKDq4XV0V7cTffVEown8OEtPGTE/DWtKGPUv76D22W0jcqDoR4VVPLxyJ9+ZNo5z8xL8XZxh56GHHoq+5pprko9lH9/73vfGpaen56ampuZed911SS6XbwYs6oA9TJiDA7ClR9K2qWZE37lro1PL52XUPLEJU7CVuFtOIDAvxt9F8guxmIhdMomws8fTsbWW5o+GfMbNY1LW0M7/vrSerDGh3HNhnr+L43culwun03lM+3A4Dh6I+P777wd/+eWXIdu3b9+yY8eOLevXrw9esWKFTx6b0AF7GDnQLF7a4u+iaBpgJO5oeGs3Df/ZhT0rirgfTCYg1qdJl0YcsZgIOz2ZoBNiafpwLx076/1dpH7p6nbxg+fX4XAqHr1qKoHWo88BPVL4I72miNDZ2SkdHR3S3t5u6u7ulsTERJ88XqDH8Q8jgbnR1L+6k7ZNNSP+OVZt5HN1Oal7qZCOLbUEn5hAxPy0464J/HAiLkqnq7yV2ue2M+aWE4Z9xr17397O1/sa+MvCqaTGhhx5Ax/6z3/+k1RVVeXTO724uLi2iy66aNil1zzzzDNb58yZ05yQkDAZ4LrrrqueOnVqhy/OWdewhxFTUAC29AjadbO45mfO5i6qH99Ex9Zawr+dSuSF6TpY92CyW4i5JgcRqH12K6p7+E6s8v7WSp5cvYfrZqdwfv7x0W/tnV4zPDzc5UmvCdBXek273a4WLFhwIGHH6tWrw2699dbk7OzsnPnz56f3J73m5s2bbTt27LCXlJRsLCkp2bhq1arQt99+2yd3SLqGPcwETYqh/pUiHKUtupat+UV3bTvVT2zG1dxF9NU5BOZG+7tIw5YlOpDI72RSu3wrzZ+WEnZqkr+LdAinS3HfO9vJiAvh5+f55xGuw9WEB4u/0mu+9NJLETNmzGgNDw93AZx55pmNq1evDp43b94x93XqGvYwE5gbDSahbaOeM18beo6KVqoe24Dq6Cb2pnwdrPshMCcae240zR/uo7vOJy2fPvX25nJ2VrVw65kZWC3HzyXfX+k1k5OTu1avXh3qcDjo7OyU1atXh+bk5Ogm8dHoQLP4Zt0srg2tzn1NVP1tIyJC7HfzsSbpFp7+irggDURoeG3nsPq/dbkUD3+4k/S4EOYdZ49weafXnDZt2kRPes2e63mn15w7d25mfn5+m+e1ZcuW7V+3bl1wZmZmTlpaWu4jjzxyxCnhFi9eXJ+SktKZlZWVm5OTk5Obm9u2cOHCRl+ck06v6cUf6TV70/JlOQ3/3kncD6dgTRzawSHa8amjqJ7a5Vsxh1mJuWESlii7v4s04jSvKqXxrd1EXZVN0KThMdXnxzuqufbJL/nz5Sdw0ZSxg3YcnV7Tt0Ztek0RSRKRlSKyTUS2iMit7uVLRaRURNa7v87zd1n7KzAnGgTaN+vPujb42jbVUPP0FizRgcR+b7IO1kcpZHYiAQnBNLyxG1dHt7+LA8A7m8sJtpo5Ny/e30XRfGDQAraIBIvIUDzo1w38WCk1EZgF/EBEctyvPaCUOsH9tWIIyuIT5hArtgnhtK2vHpUp/bTho219FXXPb8M6LpTYmyZhDtXTVB4tMQsRF6fjau6i6cN9/i4OTpfi/a2VnJodhz1g9D9zfTzwWcAWEZOILBSRt0SkCtgOlLtrvX8QkQxfHcubUqpcKbXO/XMzsA0YvLafIRJy0licdR20fV3l76Joo5RyGpOiWJNCibkhD1PQ8TEn+GCyJYcRNHUMLWvK6K45pLt0SH29r56ali7OydW169HClzXslUAa8DMgXimVpJSKA04CPgfuFZGrfXi8Q4hICjAF+MK96BYR2SgiT4pIZJ8bDkP27Cgs0Xba1o/eucWLKpt59esS9ta2DquBOseL5o/242p2EHpqEqbjYNaroRJ+jpFmtGHFHr+W482N5VjNJk7NGh796dqx8+Vz2GcqpQ6Zfk0pVQe8ArwiIoN2Cy8iIe7j/Egp1SQifwXuAZT7+5+A63vZ7ibgJoDk5GOa792nRITA/FiaP9qPs6ULc8joaqp0uRTff24dO6uMRxNjQ23MnBDFyRmxnJQZQ0K48fSEUgqlwKQn7fCpppX7aXp/L0EnxGLPjvJ3cUYVc5iV0NOSaHp3L53FjdhSwoe8DI1tDt7YUMYZE+MIs+uWk9HCZwG7t2B9NOscDfeNwCvAc0qpf7uPVen1+uPAm32UaRmwDIxR4oNRvqMVmB9L88r9tG+uJWTWyH4kQylFfZuD3dUt7K5p5Y0NZeysauGn87IJsVkoKK5jza5a3txYDkBGXAgnZcTy5Oo9mE3CpdPGcU5uPCemRev+uGPUtHI/Te8WE3RCLJGXZekZzAZByJyxtHxaRtOH+4i9YdKQHrur28V3/1FAU4eDG09OHdJja4PLZwFbRJoxarMAniuAch/DqpQalFnVxJii5glgm1Lqfq/lCUqpcvevFwObB+P4gykgPghLbCBt66tGTMDu6naxq7qFPTWt7KlpPfDz7upWGtu/uV8Ls1u469s5LJ6Tgohw9azxKKXYUdnCJzuq+aSomn98sRcwBs+8saGMF7/aj81iYkZKFLPTo5mTFkPe2HDMOuD0mw7WQ8NkNRN6yjgaV+yhc28TtvFhQ3bs363Yxue763jg8slMTR5RPYHDwkMPPRRdUFAQvHz58qMeOfj9739/7AcffBAB8JOf/KTsxhtv9EmGGF/WsA+aZUFEQoGbge8Cr/rqOL2YAywCNonIeveynwNXisgJGDcNxe5yjCgiQtC0MTS9U0x3TTuWmOGdXADgysc/Z+3ebz6b8WF2JsQE8+38BCbEBJMaG0xqTAjjIgOxmA8eQiEiZMWHkhUfyo0np9LhcLJuXz3pcSGEBwawZlctq3bUsGZXDb9/pxAoJMxu4ZSsOC6fnsTstGjddH4YOlgPreBZCTR/XELTB3uHtJa9bl89c9KjuXjKuCE75kjlcrlQSmE2H32rncPhICDgm26HF198MXzDhg1BW7du3dLe3m6aPXt21iWXXNIYFRV1zI/8+LzWKyIRwI+Aa4DngRlKqVpfH8dDKfUp39TovY2Yx7gOJ2hKHE3vFtO6rpLws1P8XZzDqmnpZO3eei6fnsSiE8czISaYYNvRf8TsAWZmp32Td/m0rDhOyzJmCaxu7mTNrhpW76zhva2VvLGhjKSoQC6fnsSl05MYE6afJfamg/XQM1nNhJ48jsa3h66W3dXtoqyhnRPTjs985T0tXbp0zHPPPRcDsGjRouq77rqrqrCw0Dpv3ryM2bNnN69duzbktdde2/n222+HPvDAAwmxsbGOtLS0DqvVqsBIr7l48eLxpaWlVoD7779/39lnn9162223JZaXlwfs27fPGhUV1f3GG28cGGG4ZcsW+9y5c1sCAgIICAhw5eTktP373/8OX7JkyTHXsn3ZJB4D/Bi4HHgSmKKU8sl0bMczS7gNW3oEbeuqCDtz/LC90D760U6eXl0MwBXfSiJv7OAOtIkNtXHhCWO58ISx3O1w8u6WCl78cj9/fG8HD3xQxGlZcSyYOpaTMmIIPc4H3ehg7T/BJybQ/Ml+oy/7+rxBP95bm8qoaenikqnD68nWrdvuTGpt2eHT9JrBIZltORPvG3bpNadMmdL+m9/8JrG5ubmypaXFtGbNmrCJEyf6ZC5xX9aw9wLVwFNAG3CDdwYU7/5lbWCCp42h7sVCOvc0Yk+L8HdxDvHq1yX8/p1CZqREck5uPPnjhraM9gDzgeC9p6aVl77az8trS/hgWyUBZmFGShSnZ8dxWnYcqTHBfWbmGY1aPi/TwdqPvqllF9O5rwlb8uDVspVSPPlpMamxwZycoR/l8k6vCeBJr3nppZc29JVeE2DBggV1O3bssIORXrOoqOhAX2R/0msuWLCg6YsvvgiaMWNGdlRUlGPq1KktFovFJwOafRmw/8A3g8501gAfsudEIzYzbWsrh13A/npfPXe+solZqVE8e8NMAsz+ne12QkwwP52Xze1nZ7J2bz3/Lazio+3V/OatbfzmrW2Mjw7i1MxYcseGkzUmlIwxIQRZR2eW2Y5dDTS8vht7dpQO1n4UPCuR5k9KaPpgcGvZL321n02ljfz+O/nDbizH4WrCg8Vf6TUB7rvvvor77ruvAmD+/PkTMjMzO/tb7sM57JXKPbXoM0qpI054opRa6osCaYcyWc0E5cfStqEK14XpmGzD47Gm8sZ2bnp2LWPCbDx61TS/B2tvFrOJmanRzEyN5mfzJlJS38bKwmpWbq/inwUltH9mjEAXgeSoIDLHhJI1JpTM+FCmj48kMWL4D/A7nO66Duqe34Ylxk7UFTpY+5PJZibkpHE0vTN4tezKpg5+u2Ibs1Kj+M5UPdgMjPSa119/fco999xToZRixYoVkU8//fTunuudfPLJrXfeeWdSRUWFOTIy0vXqq69G5ubmtsM36TXvueeeSjDSa86ePfuwU9h1d3dTU1Njjo+Pd37xxReB27dvD1qwYIFPZtE5bMBWSjlFJFZErEqprv7sUERigRuBFO/9K6UOmbRE67+gaXG0flVB++YagqeN8Xdx+HJPHbc8v462zm7+ccMcooKH98Qu4yKDWDRrPItmjcfpUuyra6Owopkdlc0UVjazo6KZ/26vwulSWEzCJVPHccvp6SRF+bTbbUg4Wx3UPL0F5YToa3Ix2UdnC8JIEnJiIi2flND84T5si31by1ZK8cv/bKar28W9C4Zf7dpfvNNrgjHobM6cOe2FhYUHXay802vGxsY68vPz25xOp4CRXnPJkiXJmZmZOU6nU2bOnNk8e/bswz7u1dXVJXPmzMkGCAkJcT7zzDO7vUeRH4sjptcUkb8BU4HXgVbP8r76pEVkDbAKWAs4vdZ/xQflHVTDJb1mb5RSVPyxAEu4jdib8v1alqLKZs59cBVJkYE8etU0chKH7hnTwdTZ7WRnVQv/Kijh+S/34XIpLpk6znjmOz2GmBCbv4t4RK72bqof34ijqp2YxbnDrgvleNb00X6a3ikm7gcn+DTX+IpN5dz83Dp+Oi+b752S5rP9DoROr+lbfaXX7M+td5n7y0T/+qaDlFJ3Dqx42pGICMFTx9D0/l666zr8mgLxjY3lOF2KRxZOHTXBGsBmMZObGE7uBeF875Q0Hv1oJy9+uZ+XCvYTZDWzaNZ4UmKCiQwK4MyJYw55jtzfXJ1Oap7egqOyjehrcnSwHmZCTkyg5RPjuewYH9WyG9q6uOu1LeSNDWPJ3AkD30FTGez/AvZ/BbFZMO1an5RLGxxHDNhKqV/DgYlQlFKq5QibvCki542kdJYjRdDUOJre30vb11WEneGfec//snInD31YxLm58eQkjJ5g3VN8uJ27L8zjZ/MmsrOqhWWrdvO3T77p/kqLDeYn52Zzds6YYTHqXDlc1C7fQtf+JqIXTiQwS88PPtyYbBZCThpL07t76drf7JNa9m/e2kZ9WxfPXD/j8DeQtbtg40vQUgVtNdBaAw37oKnUeN1ih+k3HHN5tMF1xIAtInnAs0CU+/ca4Bql1JY+NrkV+LmIdAIOjElNlFJq9F7dh4gl0o4tNZzWdZWEnp40pIHC5VL86f1C/rJyFxedkMgfL518XPSVBVrNTBoXzsNXTuHuC3Lp7HaxoaSB37+zne8+u5Zp4yP5+XnZTBvvvwCpnC5qn9tG565GIi/LJDBPT5oxXIWcmEjLqlKaPtxHzHW5x7SvVUXVvLy2hJtPTSM38TDzHhR/inphIXQ24TAHub+CaSeUKtsJ1NoDaYoQugv38Z1zj6lI2iDrT5P4MuA2pdRKABE5FXgcmN3byj2nKNV8K2jaGOr/tYOu4iZsEwY/C5BSio93VPPH9wrZXNrEFTOS+O3Fk3wyf7fTpejqdhE4QlI7RroH1sWHx3NGdhz/LCjhgQ92cMlfP+Oc3DH85Nxs0mJDhrRMyqWoe6mQju11RFyUTvBU/w9I1PpmslsImTuWpvf20lXSjHXc0V0uu7pd3PXaFibEBPPDMzL6XrHsa1zPXEBrgIWNMyLoCDRjPH3b4v4y2B022lwj+8mI40F/AnawJ1gDKKU+EpHgniuJSIpSqrivnbiTdIxVSpUcVUk1AAInxdDw2i5aCyoHPWBvLWti6Rtb+HJPHeMiA/nTpZNZMHWsz2r2Dz79HC27Pqc4dAqWhElkJYSTOSaU7PhQUmKCCTCbWLOrhn21bWTGh5I5JpSQY5jq1JcsZhMLZyZz0ZREnli1h799spuzH/iEK2YkceuZGcSFDs0Yg8Y3d9O+sYbw8yaMmAQxx7uQ2Yk0e2rZ1x5dLfu5L/ayp6aVJ6+bftjsdQ0v3EyQWfHo1LP4oOsiguq7CXZ2ENzdgc3ZjcscjiV6LLZxqUzN142gw11/rn67ReSXGM3iAFcDvT1T9gcRMQGvYYwQrwbsQDpwGnAG8CtAB+xjYLKaCZrsfib7glRMgxDA2rq6+fMHRTzx6R7CAwO4+8JcrpiRjNXim0FWTpfinY17uWHvTwgPaIWOZ2nYE8rqnTmsduXxB1ceFaZ4UmND2FNRiwkX7RgBMCbEypgwu/vLRlyonfhwO4kRgWSOCSE+zH5UNxRKKRraHOyvb8OljPSevc2D3t7lZHdNCynRxjzpQVYL/3NGBlfOTObhD4t47ot9vPp1KUtOSuWmk1MH9QajbWM1LWvKCJmTSOjJ+tnbkcJktxA6dyxN7x9dLbuwopk/vlvI3PSYA3Pr96psPRHNW3lu/Jk8aLmNXGcrZdGR1DoVbc5v5vwIECG0vgWb9fiewnck6M/V5Hrg18C/3b9/AizuuZJS6lIRyQGucm+TALQD24C3gN8qpXwyn+pw1NnWhi1oaJ7ZDZo+xngme2MNwTPij3l/3U4XJfXt7KltZVdVC0+tLqa0oZ0rZiTx03nZRAQN4Bnr0rW4StfT5nDS0NxKU3MTrS0ttLW10NneiqOjBVdXOyewg3BTK//JnEaClDK2tpnT67/mfOcXADRY49noOIGT7e8AUBcznZ1BU9hizmKjI4nCBsXGkgZqWg6eHiDMbjmQ8SshPBCbxYQtwGx8t5iwWcyIQFlDO/vr2tlf38b+ujZK6ttp6ew+aF9JUYGkRAezr66NYKuFhHA7n++upbXLeFoxOSrIONYY43hXzxrPohPH88D7RTz0YRHPf7GXW8/M5MoZST4fUe6oaaf+lSKsyaGEn3cUo4M1vwqZk0jzpwOvZde3drFk+VcE2Sz88dLJvd+c7vsCdn1Iy+fPIBYbz3dfyCsP/pzg9mIs9XYCx6djSU9HJSVhDw0hICgIU2Ag1jAF6Bs/X6TXPOmkkzLWr18fPH369JaVK1fu9Czfvn279bLLLkttbGy05OXltb3yyit77HZ7v6ct7c9MZz9XSv2wPztTSm0FftHLfgKUUo5eNhkVqop38/z/+zEZ35rN5LPmMW7i4E7yb00OxRIbSGtB5VEH7A6Hk48Kq3ltfSn/3V5FZ/c3d9zZ8aH863snMiNlgAOplKLt8fMJop0QwLs314kJp8mEU0w4bSY6bfCT6Fv4snMKO5ImEBtTRy5fc0rnak5s2EhcTTOzmj44sL20bmFGTQHf8hwqKAZJnoQzLpem8Gz22zLY0DGG7ZUtFFY089rXZTT3CMA9BVnNJEUGkRQVyKzUaJKigkiKNPrxCiuMCVX21LQyMT6MdoeTPbWtXHBCIrNSo9lb20ZhZTOFXhOuAFjNJtLiQjglI4bdNa388j+beWLVbu76dg6nZcf5pDtBOZzUPbcNMQtRC7ORYfZ4mXZkB9WyS1uwjj3y2Ifq5k4WP/0llU2dvHTTLOLDe+92qX/mKiKd1QSYLfzJfCW//vQ3NN7gpC0MXM4WXFWbCNq9laCvnJjrBVOTYG6E4LPPJ+X3f/L1qQ5rg5FeE+D222+vaG1tNT3++OMHTep+2223jbvlllsqb7rppvqFCxcmP/jggzF33nlndX+P1Z+ZzqYNqPRu7j7r04CFwHxg1I6GsQUFM+n0c9j26Uq2r/6YCVOmc8rVNxA9LmlQjiciBM+Ip3HFHhxVbQTE9b9mX9faxVOr97D8s700tjuICbFy+Qwju1ZqTDATYoKJCrYOkn3nWgAAIABJREFUPLCUrqXlqxcIoZ2X02azKSYZh8lCu8lGuykQBwF0KysOZcGpAthDKr949V4uCf8npndtlAbk8vGEE3gqcwlLE8aSFFdKvhSwu2MSJfYxpKpdTOdzprdsIq21hMimNkLKPid090dEoogE8uyRSOopyLS5qJST6IxIp9Op6Ox20tXtorPbRafDhUsp4sPtRB/mPM/O7f+NUIfDya7qFnZUNrO9wgjiOyqaKWs0GpSKa9u4/pkCwuwW5mbEcGJqtLuvPgwxQWVjB8nRQazeWcOqohpSY4LJig8ja0wo4UGHNlM2vLEbR3kr0dflYonQaURHqpA5Xn3Z1+Qcdt3imlauefJLqpo7eOzqqUxJjux9xa5WLKZmNkck8YuJ3+d7bzxB47VOGjoiaKudiTW0BhlTjIqvo2vOwRW7qq6vSPHRuQ0X/kivCXDhhRc2v/nmmwf1dbhcLj777LPQ1157bTfA9ddfX7t06dJEnwVst69F5HXgXxw809m/e1tZRGZiBOmLMR4F+wFwR38LNBKZA8JpbvgWsy49k7b6Aja892+eueMHTD7rPE78zpUEhX0zOKy+vJSIMQmI6dhqRUFT4mh8Zw+tBZVE9KNJtLyxncc/2cMLX+6jo9vJOTnxLJyZzOy06GNurlW7VuJ89hJCcNJUa+fz7hlU748GwOxyYXY5CXS5CFAuAlxOrMrBBWUvEnJhDS2hLqCd0O4CFuxZy5XrTKiSIHaFTOXDtElcv/kZIjoaKUqexcdp3+KV5CuoHxtOZHwjY1UJKVLElI4tTGouIrW+kugdbxG49T8IYDXbsIaMISx8LBKWCKEJEJYIQTFQ3godTdDRCJ1NuNrqcbXW4myphYBgrFmnI+Nnw9hpxjqBkRBgh/YGqN8DsRON3zGyheUmhh/yaE1ju4Mdlc1sKWvkzQ3lfL2/gRWbKlixqeKQ99BsEpwuRYBZcDi/uZDGh9nJijcG4mWOCSW/rJ3ALyuwzkmgPNpKbXEdSkHmmJCBdV1ofmfUshNp+mDfYWvZG0saWPzUV7iU4vkbZzG1r2DdVkfL05dhqevmOfNFpH5Uiu20Zhqbotm0fh7BwSG0tsYBOYwdm0Byqg17aCfK1kCnq4qUkPRBO9cfbduXtL21w6d9htnB9rY/T0weduk1+1JZWWkJDQ11emrjKSkpXZWVlQP6p+1PwI4CaoHTvZYpvunTBkD+P3vnHSdHdabr51RV5zg5jyYrj7IQEiIH2QRjTDYGg21svLtmjbG99t7d67z2GnMBhwXsxQlsg8EGG5NzkoQCytIojjQ5dE/nWFXn/tGjBEojRrmf36+mu2eqq073dNd3wve9rxDfB64GdgB/BL4DLJVS/nYkDToRiYcypOI6i5/aAZQyZtq/IuS7rHzhGda/9SpzrriWaQsuoXvjBh779jdoPm0uH/niHVjshz86Uj1W7OOKSCzvw3fRmH1Oi0opWb4jxO8WtvPM6h5MCZdPreK2sxtoKh2l6rstr2D8/hMEnS6+Pe4Wrl7yGJfV/QGxc2lZAApIsfs+ArKnS6Qd1qw+DyQUFPfhrerE0xRCiChlqde5efMbpD+X+y5MDTzBaZsULM8JZMhGWKliu7eJ1SWVPFt+GT+vqiFe5qTB2MT87NucGVrGmEQvrvQA9mA/tt6l2LM66vukeE0gq6pkNJW0ppG0WHEkshS9tmiv/QwU4qoftzGEgsREEFKLUevPxDv1EkTtnFxnYA98Dguz6gqZVVfIp+fWE0pkuO/lTfx24XYsimB2fSFTa/zUFbvYMhCj1GPnutm1DMbSu6bb23pzo/aFWwJ8xFA5DQcvk+Xbb7dhvt221/nKvLZdWfZjy72UeGxkdRNVETSUuKgpcB6XtfOGniUdj2N1utAOoLkc7O5i+bN/I9i5A6e/ANe+toJCHG7Ph+4QHy3c86qIvtVN9NUdFN3wwVF251CC6x5chN9p5Xefmb3vssFsChbfT/blH+CUaV6WNVyWfRSzQJLySjrWnY6z6my2dguc1ZIyLUQk0sPCN9t3t8NdwfTpY+EAFWInGsfKXnN/7EsGXAgxItvNQ1nDXiWl/H+HcKxbgTbgf4CnpZSpkTbmSCCEWADcC6jAr6SUPxztc5TVe7n2P2YTCSRZ/04Pq1/tJJ1opWbqeLKx13n99//LyheewV1UCgg2vbuQ7rbP4SkuoXZiK40zT6OiaeyILzKumWWk1gVItQ3hmFC06/eprMHfVnTzu0XtrOmK4LFp3DBnDLfMqx89MwvTgJV/RH/qXxhwebnT8lVm/X0Z2at1UmknaXNnZ0Qgh6O1HN5AoMcddK0bT5E8l4JyJ3EjwKZ1HWQyQ/h8fRSU9OJt6sRFHCkFfWo13hm92OZkgQQKm6hPbaKlV6D1CrQNAj3gZpttAgurJvD9hvPYXlVJwu7AKZN4ZBSPDFNp9FCuDzCoFNKlVTFAEWocCkNhikNBSoIBENBXVkyTp53p+loGZCGV+gBjk9tZnZlB71Ax1Y4+Jlo207z1ScTmnEx+QjgIWavxTr0cd+tHoLwV1N0ByO+08p+XTuRTp9fxw2fX8/zaPt5tD9Ja7efL57dwWn0hhpRU+h1U+h17ZQBHl/US+vMmwpVOIuM9fMOmUeyxUuy2YZhyr+n43y7cTkb/oPOfw6LSUuYeTsrLTbn/Y3UP724LDCfPeXcl7NUWOkel1n7Xx8U0iPT3E+jaQTwUwmK3Y7XbsdgcPPPTHxMPDQGgWizYnK7hzYlqsZKMRkhEwqSiERRVw1VYQ6Crj0wygp75YB6rUBScXh+qxYqqaSiqiqJp2BxO/OUV+MsqKKioxF9eib+8Aqv92NUfKw4N12nlxN7sxAinUX1769X/z2tbyBgmf7p1zge/u6YJqx8j+dSdOMwo2wtL+HblF7kh8ysS5bn/f1fXWKLbZuOPSyYhyfbCaouL5bY6YmoVhSJBkZKgMJwgsDHEuedyRDjQSPhIcSztNfdFeXm5Ho1G1Z1r3u3t7dbS0tIR5XYdyhr2ZcChBOxy4ELgOuAeIcSrgEMIoUkpD5z9c4QY7nD8HLiAXDnZEiHE34aT40aNZDLJpk2bKCkpYdpF1Uw7v5Y1b3Sx4qUdJKPnU9bcSmLoFTrXrUSolWiO01EsbUSDCZb8/S+8+9TjWGx2JGCx2aloaqasoZnIwAC+0jJqJ7VSUlf/gQuLfWwhisdCfEnvroAdjGe49Kdv0RVKMrbMw/c/PonLp1bts0TpsAl3kX7wQmzxTro8xdyV+CS3KfeQ/oQEFbbvOBPMCcjh8AyAAJH7AYCmWFE7EsSiS4ltqEbRaij0zKGwUQFvlEhygNVbOoAIum6lrLSKtv5eNC2J0xnG6Qrj9EZwFAVxVIawWzNAmHJzIVd1LeKT7QJtqYC0QDesZLCREg5iwk1S2CggiEcNY7MlkQUSo0CiF4LRlGur1g2WLYJMxMIYXxaZEfRnrFQ1r6K01UQZUgj0Qn+yjGjKQcpw4DUMJtKP4427YPGP0YVCUCkkZquj5Iwb8bR+FNwl1Be7eOBTM3l3W5Dn1vTy/NpervvlItw2DVNKvnBWI5+b37BLUCa5NkD4iU3YG3xU3zyRifuouz17j+CuGybtgQShRAarppA1TDb3x9gw7E72yrDFKEB9fBuz6CS1FVakTZYjMIWCoqr4XXYK3HaKPXaKvQ5K/U48DhuqqiJUFVXVEKqCoqgoqoppGMSCAWJDAeJDQ0hpIoRCqLebYE8XRvbA1yZPydkIJYsQGUyZJhnLIM0UiubH4alEsTgxjBayugsU0FygOjNIMw4ygWZJolnSKGoSQRIwkNLA0A103SQVi9PfvphMMrLXeV3+AgoqqiiqGUNxdS3FNWMoqh2Dw733LJRpGCjDyUmZVJJoYJCCikqQuQv+4Y7q3bPLib3eSXxJL97zx+z6fU84yZ+XdnLVzJoPButEkMD/O4OibBcD7mK+V/UlYh0uPvn0I4jrdfr769i2dQZ6ogxHYBs430I1UxSVz8PaV8f0jB1rdSFKnYtMmZ0kknHlJ5fm1bGy19wfiqIwZ86c6K9//euCW2+9deihhx4quuSSS0IjOcahXMXfEUL8DHiUvdewl++5k5TSAJ4FnhVC2IFLACfQJYR4WUp5/UgaNkrMBjZLKbcCCCH+BHwMGNWA3dPTw1/+klshUFWVlpYWJk+ezPXfns3GxQO894KNjH41mnc9qdIsDU11DK1vRkqJbkQx9W2Yeg+gkk4laV+5ha3Ll2BqudGZ+PMjADi9JRRUjKGsoZHJ586npHYMzullud55NIPitvDNv6xmIJrmNzfP4qyWkiMiX9r20D8xNt7JQ00LWLGpmasq/kiqWRII1CCQpDdMx5quArSc4fQwe3ZRM2YMor8nayaBFYBAoYqeFdUYRjWKVklNSQOBoe0oOujd5TRWTMJRIBGONIaWIJmM0jcYYig0BMTweAfx+gJ4fH24Tx/Eou00i9OBBBpD+IGdlhjZ4U3PaqQzLlIpN+mwC4HEWRLCNWYIzZImpWsowkRRk0QSHkL9lVhtCRyNERyOKC4ljItw7r1Jq7QFKpCDCkYE1LiJP7gZ5U9fx/LEl4n7XQS0YjJaNY1n3cIdE2v5pNjAq/Yz6HvrN1SZK9jwfDNXvzadmz/2ET7i9RD4w3osVR6KbpqA2CNYJ2NRti5bycD2TlSLima1oFlVLFYLmlUjMxigfeMWwv09IKBWUalTFRaoKiaCtCmJDGxEqnYUUyCQgImUZu52KHebRtIFdB3i50O1ONCsHoSigjRQND9W5zSyWR+KWoQQbiQ6yAzILKZIg6WQyokNZJOQSeqkE7lNNwxsVgsOt4XCAoFSHiQrhrBZHVgUO5rwoBiFyIwFM6WSjUMymiUZzWIaJqYhMU2JNCW6YaDYTWy2DNIIIc0QFmsUoUYI9gTp2fwyRnb3iN1VUEhRVTXZVJrwQB+JcAhPUTFlDc10ta0nGQnlPt9SYrE5qBo3gZqJk6mZMJnS+kZU7dA6yVqRA1tLAbF3uvGcU4tQc9+ZhxdtRzcNrkn9nS0P/ASLChZFIPvXUpzegseQ3Cevwt3ezad7/xd9okH2Rkki4aVn6wX4M+NJdS5BJldQWDsBITx0rXsST1EpFeMvINBTTfytARRV0DKhkLFFJ5dZzLGy1wSYMWPG2K1bt9qTyaRaVlbW+otf/KL9E5/4ROQnP/lJ5zXXXNP4ve99r2rixImJ22+/fURuZodir/nqPn4tpZSHNHkihPACHz8Wa9lCiCuBBVLKzw4//hRwmpTyn/e1/+Haa2YyCQYGtjM0lGbHjm7Wrl1LPB7HZrMxfvx4Jk6YSKbfwRsvv0Om4AUi4TKKiqpIp9M47E6sihMzI4inh8iYQ6gC9BQUV72HouogBaqqo6g6ijDQ0xrpsJVM2E2JcyqzBk/Dd1EDjylZ7nv2Pf7L8iDl9igOZw2NH7kNZ8NpYB2FqfDkEJm//gvWjX9nld7Im/3NTDp9OdkaSVvbPFT9TAY6N+LoWIfY+bkSAkVREYqKEMqu22w6gRBwzbf+Cylhx+oVbF/9Hj2b2nIjGc2CwzOG+FCuhFG1OrC7apAUkU27QPEjFB9C8WBzWXAUS7SCFLo1RiwdZDDYh5RJNC2DqmXR1AyalkXVMiiKQSbjIJ1yYRh+7JYirMKJyNjQo2BmdRSPwLQkMdUgMulDChNhCZPtF6jRIFK1YFptSE3B4k1i84Wxu0PYnWEcjggORwS7PbHX22dmVIyIFTOiIqOgxHUMiwXDb8dMgqU+jcOTG/3pukYm5YK0DzPlIRwxSSesmBk3wvBiMIjFG8PuT6FaDLIpG5mklWzCktviGhKB5lbQ7AI9bUVP5DZpSIQhEYaBZYyOt6KfbNaOnnVh6G6k7kUaPhTDiYKG1FUMXcHMCmRWQeoCRVewmApCKmDsDPYKKE6kpmLYTDShoaGieAykS8ewpTHUFCgGPocTn92BRVhYsv71Xe+Roig4nc5dm9VqJZVKkUwmCQYDOF29eP1xUgkr6ZSNTNZBNmNHSnX44yZwu904nU4URcmNfIc7jRbNgtPpxqY6UKUdMlbMuEomohIdyBAPZUDGMI1BpBFAs4TADIKwYhguTNOJIAyyH8N0oVhawIyBEEgzgdQ7kUYw93m12KhoHk/TzJnUTZ1BYWX1ATvPybWDBH6/HrXQTsXXZvH82l6+/OgKvmT+jkZ1ORZdpyiepjabImOzsVQ2YXP2w4ws0m8iJUSjRQQCNfR1NmPbFkeTxRipJUy68GIu+sxtSCnZvuo93vrT7+nbuomCyiqaZl0IyljaV0Woay3mzGtbDuvSkLfXHF32Z6950IA9UoQQFcC1QAPQDzwqpdw4qic59LZcBVz0voA9W0r5L3vscyu59Xdqa2tnbN++fcTnWdr+KOGt3wQgaaoktGrs6nSygSY2rg+STmdwuVx4/O00Nz5HOmthKNKIxRZCGhpG1oqCgc/bg9W6txCI1HPTyDKrILMqUioIh45q2b3KoOsW0pFS+tv8+BwhfJN6MXWNbLuTwo4gk/UQps+BgYaBBQMbUnPjrJ6Mr3kWwj8Gak/LZULviZGFnpXQtRzZvZzM6qewmAn+YptFZXI7ybkmpqqwYcNZZLfOQR0KoSdfo2n2mVQ0NaBnMpiGgWkamLqeu28YmIaO1eFk6oUX4y/fW04zk0zQsW4N21e/R+fa1QzsaMfh9dE863S6N64n2N2Faex+7UJRsToKULUCDKMQUxYi1BKE6sfu1UAzEZqJUE1QJSgGpjRJD5nokThkg0gjADK3Gdmd06UCRXWBsGHqQfacH/CVVmLoOqlYFD2ze3ZMAlLVkBYrpsUGdg2rz8DmzWL1pLG7kticcRz2GHZHFEXJLYFlszYsljSplJOeDY2omoHdlcXlMhH2CJotitW2b80hI6thpC1ojjSKemhLatmsjUzGTibjwOMJoGn7nqrWdZVs1k424yCTte+6n83ayWTsw7e5x1nDgYGKIrOowkBVdQxDQ0oVVc1gsyWw2eJYbAmEmsHMOtCzNjJZO40NS/H6BoilrSSzdtK6A0N3YupOMGyolgyqlsLl6KPAGdlnWzO6StqwkzWd6LoLQ3cOZzruRhoqmaSDZMxOOu0gnXaSyTgABavVis/nx2X3YFWcKIYNM24lExUoNh1pT5IVcTA0zLiFqNiBoe4A6USzhFAUAyNbipkowoxkIRVGJPpQkn0IaeLwFjGmdQZjTz+N2kmtH1jekoak69/fAuC9q+v50p9Xcpm2iHPrXsBdP7jHfgKZVBEOA6FKgoEqBgdriUWb8NjGoKU8DK16EkXPzbS6yqv5zI/u2SvBVUrJ5iULWfzXx+jbuhmrw8nEs85j0jkfobTu8FwA8wF7dBlxwBZC3COl/Nfh+7dLKe/d42+/kVJ+eh/P+RJwMbl1441AKXAH8DPgFZmbaztqCCFOB74lpbxo+PE3AKSU/7Wv/Q93hL1l2d/o/Nt3MWwGWX8GozaFzZl7X6OmjZRZTzbUhMhuoLx0C7YtkG6UWLpFLoPaJkGAdbOC2auRFhaE1SCRtuO2OKlPd1OmhFBtJlmbhYBw02tY6LM6iLiKsBXacJR1Y3NEAQj2V2CYKoUlvbkLZ9qCucWK7DewJAQFGZMye4pSRwiryE0bSyBsKcc98zo0l4/kqqex9K9AIxccU5rKDm8J3y/4AgvW/JXSi7oY6B9DR8c0lPY6ROBldqYqfPon/zNqNeiZZAKLzb5rfdA0c+ukod5eQn09hPt6CPX3MdTVQaCrc1cwF4qKZnWTU8tVhqfmBUiBlCbZdBCGP46KqlFYVU1JbR3FtXXYXW6iwQCxYIBEJERpXSM2h4N0Ik7jzDmUN+5OpTX0LMlolFQ0QjIaIZWIk0kkSCcSxMNRkpEYyWicVDxOOh4nk0qSzmbImDo4UiiqlfLiSWTNNBVj6jn3+qvQB5IMPLASYVHx3DKJB95ZxdJFLzBNXUWNvRubpuPIpvCZJi6LFatq4osMIZNJgoqVmKqRsFgxUFEzEsUUJFUrUgPNomOxmyhOiekDYUh2rKknqPqxywR+M4yPKC4thdWaRXrA8EhMDxhekG6Zy/R/H6YpMEwFVTFRlN3XFMMQqOqhDQocixVMj8TwgO6VSDeI3Kw6IgHakMD1tkKyw49djaE5DQyvxPQOt9ErMbyg+8B0S3j/gNaSO96eSAnprJW07iSru8mmXaQTTtJJJ+mMg2zGgd0ew+0O4PSEMLIWMmknpaVbsTvivB/TFKRSblIpD6mkh2TKQzrmJROykQmmUBJJ1HSawrI6iqvrMHWTlG5QWFZGbGA7BbYkg9Z1SMcgFmsab0U/29ePI9LlxVZi4ihIYLFkyGZthAO1pLdVoyVNRDaDIIMhI5BpxzJ5PhedN5fq8ZNw+fddBialpGdTGyuef5q2hW/RNPt0Lv3Xrx/S/+r95AP26HI4AXu5lHL6++/v6/Hw7y4mJ0v6SeAqYGeXzgFcQ67Ua5OU8rUP/WoOESGERq7jcB65JbglwPX7swY93ICdamuj97vfBd3AGBoivb0doxRS40yiUwR6g446nPypbhW8t/E6Jm3fyPIxLYRUC1ndIG21sralibn2JcyNrKQ52klzpJuYcBLRSrGN+yiFc69HlE0ERWFTX5TbHlnO1oEYXz27iY+81cN7nqfoTQ9y7qX/Rse6Nla//Qy26hD+MUMUFvVgsaR3tVmGNdR2QaLfQW+mHKvPxRznGhpjPSjAgNPNGn8Db/mm86ZtFuG4j9ltS7km9SdS5xvo0sK2tf9Ecn0aGXmN0vpGzr7xM6QTCZpmnjbi93A0MHSdoe5OBrZvo3/7NpKRCNI0cmpGpolpGkgzlwhVUFm1K0AXVFQd8nrjkUYPphi4fyXSlJR8YQqW4txIrC+S4icvtPHnZZ34HRYunVLJOWNLOb2xaLf5QzpKun0JXa88hBJch1UmkCio0sAjw7jM3bMBMWGjXVRQHg1Q7Mp19CQwZHfR5Sxhq7OKDbZ6tpi1dGYrsSayFIWHKAoNUJ7spjzbT6GM4BYxrFoK6ZFIG4g0iLRAZEDawHRI1KhAhAXZrJsUhWQVJw49hM0Mo6lJTJdkKFjEo2d8ipp4jPJ4hJJoBG9oEC0dIWPxkHB56fAX8rtZZ9BRXgVS4kinKIiEKYqEKIuEKRoK4Q0O4R0awhePokiJOdxRk0LgMFOUyCA+LYTNEkf6JIZfYvjBHL7V/TKXefN+TFAHhl+TH9R+gfqGHalIhgwvSdVGgRbC5UxCoUm2TGAUmYg9VCelhHTamQvmCTdIE6c7itOVy3/Yc6Yjk7ajWdIMdNUypeEHqKrB0qefoXfLKqSmgZQIQ9/VJzGESlpYyahWvJPncMdXbhvRZzoeGkLPpPGVHp5yYj5gjy6HE7Dfk1JOe//94cf7CtjPA5+WUvYIIf6bnOnHC+QytDcCPwEeklJeNkqv6ZAQQnwUuIdcWddDUsrv72/fww3YXakMT/aHCGR0MtJkTCZN47ZNlG7cgHP9OjJrV5L2hEi3SLZlqvjhFd+g31LERH0tJaKbhkwnpw+u4dyOVdh1AwOVmFaEbPko/qvu2StxC+DJ97r4xl9W47Kp3HftNOY2FRN8fCPJVYNsuaaRLz62glhaR8FkWmYH0wLLsKgplAILjlIFe2EUtyeIxzuI3T48ShhUYbmFxeZp7PA2Uz20jabURsqVARzODEZhblbALJT099fRvmk29q0pzMQm6qbO5LIv/9uHqivPA0YkQ//9KzGTOqWfb8VS/gFTPNZ2h7nv5U28sXGQZNbApimcN76UL5/fQnPZQbJ8U2HoX4/Zs4rg8n8gAuuxmglsl/8cq2LA4EYSWxZh9KzGqQdR2T0hlrRoBJwuepxFtDsraHOOYbVjPBsszYREIc5YEncyQdpqJW2xkrFYcKWSeGNRwm4PQ14/pqLgNJJYpE5UdeWy0Q0DXyxK2OPlbP0VQrKYEAWEFR9h1Y2uaCjSxGGk8ZshzlOfYbqxjIBWQFj4GTKLGDJKCJuFhPETET4iioeYkuvoKEgUaaIg0YVKarjnrJgmvmiEosgQReEQRaEhyiNhyiMhypJ9FJoDOAlhURMkpIf1lnGsqRyPJZulJNJDR2k1equKRyaYF1lOeXqQjLCREjYyGQt6VIOYiZFKoYkYVksSiz2LKBCIQqBARyLQQw70iIWsakPxZjF76pg6eCPq/AqWb3iHkvGTeaTfgd2iMrbcQ71DR/Rto7+zk9e6dBZmijEtduY0lbFgUjnnjy+jxGPb13//iJIP2KPL4QTslcDZ5CbAXhm+vzNyvCqlnPK+/fcM8G8B86WUclii9E0p5RnD/9TDkjo9GhxuwF4WjnPx8k3YFIFFCGLG3jP/XlUwPTKEb9Vi5luX0Vq5EFMVVHVk8SXSWM3ctHS64jRsF/w71M4B7YNfOikl33l6Hb9+u53aQidzG4oIJjJ0hZJUJwz+I6TyXyLJ1nIHV8+sZiiRZSieYSiexuhrp7i3DU/fBpRUENNmx3DXoBbb8FR0Ula2BZ+/HylBJAU4d38uTFMMjwy8dHZOwhycgLn5ZewOJ1Mv/Chzr7p+V7lLnsNn8HfrSG8aouTWVqw1Bw6+qazB4m1BXt3QzxPLOolndK6eWcO/nt+yX43pEWEaENoOAxthsA0GNpLpXIEIbMIid8/U6IpC3K4RcVoJ2x3DfUsTBIStTgZsBbjMBH49ikePY82aCBNSDoWA3UOfrYhxHQHqwgMkVDspm0LaAVmnScouSFhs2IwMmiFxR02qurPYjUwuy12xklY10haNjFWQsUHWbmLYTTIWJVfxb0oUCYopkUBa04hoboKaj4DmZ1ArJKgUEKaAiFlAWPqJ4iUqvEQVN0nFQbExyBnptzg3sghFShI4uGTHYgpTuaRCCSSkHSEkCpJcDr5EYe/rgCR3ATXrAzq1AAAgAElEQVQlGCmFmNVFl6uGaN1VfLdrMm0DSR64fgaTntqBtcaDeUUjV96/kEAsjd9ppSu0dzVRhc/OHRe0cNGkcrz2Y+u0lQ/Yo8v+AvaB5kx85GwydwbpPcu49hXlY0KIYinlIBAGLhkedV8ERIc9tE9Kty6x8Gnu2vgmDmcfiiNOwvAwqBQzKIoJqIUMagUMal7q6mLcsPH53HwDYPrrUKadAxVToHoWtvJ9m4b0RVL8fWU397++ZZc71Y5ggsFYmiq/g6oCB8Kv0B1NcIvFRcvnZuH5gEzl7n5SoKuDjYveZu1rrxFu20R8o8qmwrPRahQKytdhtSZI9PhJJHykEgWoSil2ixuRsSG3xhDxdxGmyQ0/uPsDSWN5Do90e5jUugDeC8ccNFhDTg71rJYSzmop4UvnNfOzVzbz+0XtPLmii1vm1fOFsxs/3EVcUaGwIbeNXQCAFXLzurE+GGiDwY1ogxvxBbbgGdhIVbAXIU1ADt8GgL31MqRqBaEg9AQQA3p2/c05ZgqEO5F93Qhz5/RwdO92NV0ADWejJIM4Yn04YgMQ74fYAHKwH2HsnbS5b0Ls6fJrIMgqGrqiYqgCXRUYGhgamKrEFzFwp/c+bgwnK2f/mCG8mBXTSKreYXW6CG29UbYHE+wcC9ktCs2lnj1U6HKbXVPZsLaX//zbGqyqwQUTKnhiZTebyXDZhiCfvauLfmnwp1tPZ2qNn0gqy8beKKFEliK3lXHl3l21+nlODUYtS1wI8RlgopTyDiFEMfBNYBywAfgh8HlgSEr5s1E54RHgcEfYf7/vqzgn/QXTVNDTToSqo6hZVNXYa7+WzTEqejJotzwPySFoPA/UffeZDFNy/+tbeHVDP8t2DO368k+r9fN/Lh5PQ7Ebv9OyV6lIcs0ggYfX471wDN5zDy3bc3BHOytfep5VLz+HoWeR7nEIeyVCN1F0HfQ0QmaRMo2QQYxsH4VVNZz5yZtpnDH74CfIc1CMSIaBB1ZiZk3K75yJcpgX4Y5ggrteaOOpFd34nRY+M6+eS6dUUlf8wan1I45p5gJ7pAssTnD4we4Hy3B2dCKQG8GHOiDcAfVnQUXr7ufGB3LPTQRyz7e5wV0GngOssUqZm/aPD0AiCIqWU5pTrblbaQ7rxw/l9kuFc9rwO+9nYpCJQzoKmRgyFUVm4ojyiYim83NttLlzUqC+KrDu/31NZPRdYjU7JWbb+qIMRNP7fc5OLm8u4Y7Nad4t0nBcWMfFrcd/p/hkGmEfSXvNH/zgByX3339/WUdHh627u3tlRUXFPkXFDmeEPVIeAh4RQvwA+IGU8g4AIYSbnK74GODKUTzfccPM86+k8+lt1PkEnmw/GGmEngZjeNPTCDODJjOkCyag1ew/0EVTWV5Y28dza3t5cV0fU6p9nDuulJfX93NJawX3Xjttv5KRjknFOFqLiby8A8eEon2ugb6f4to6zrvl85x+5bUs+8eTLH/2afTYBiCnsy2EwOJwYXM5cXh8TLnwGiaeeV5+CnyUMGIZBn61CiOaofgzkw87WAPUFDq599ppfG5+Az96bgM/eXEjP3lxI5OrfHzx7EYumlh+9LTEFQW8FbltX7iKc1vVPlbIFAU8ZbltJAiR6xg4RkcAZKf8/eHgtGq0Vvtprd67LYFhnfjn1vTyp3c78Dst3H31VPxOC9sG48xvLsbvtDL427XM7YxSMQLXuDwj52jba5511lmxT3ziE+Fzzz137OGca9QCtswN1a8XQtwEPDUsC7pziPkn4CtytIu+jxMqnFkqEi9C1gnlk8FalFuD1myg2va4b8Ux8eP7PEY4meWu59t4dGkHGd2k0GXl82c2ML3Wz22PLGd+czF3Xz31oPrO/ssaSW0KEX5xO8WfOrBl3544vT7mX3cTp11+FdFAAJvTic3pQrPZjohaWp5cTkLwsY3owTQlt0zENsY7KsedVOXj9585ja5QkmdX9/CHd3dw2yPLmVDh5Y4LWjhv/Oj4cucZOWnd5NElHTy1opuGEhd//Nwcyry5nINJVbvd3lwzykitD5LeEsLesh93rjwH5Xiy1wSYN2/eYcma7mS/AVsI8QzwRSll+0gOOKxodtI7dO1F9Sy45XmonA7aobul6YbJex0hXlrfxxPLugjG01wzq4arZtYwrcbPa20DfP73y2it9nP/DTOwagfXKlbdVtxzKoi+1oEeSKIVjczYwOpwUlQ9qi54efZD7I0u0huH8H+sEVvD6MtCVvkdfHZ+AzfPq+epFV3c89ImPvu7pUyp8fOVC1qY31ycD9xHiURG54HXt/LAG1swJfzzOU3cdnbjfjX+7eMKUZwa4RfasdX7EJYTw31sf3z18ZU1G3ujo3phaSn3JH585ZQTxl5zNDjQCPs3wAtCiN8C/y2lPKByvxBiIfDvUspX9vG3l6WU532olh7PaLZcZvdB0A2Tx5Z2Uuy2siOY4BevbSEYz6ApgrlNxXztorG7etldoSSff3gZLeVufnvz7BGZd7jnVBB9vZPYO934L2087JeV58gRfbuL8LPbcEwqwjXnyK5RqorgiunVXDqlkieWdfLTVzZz40PvMquuAIuqDM/mNDK52nfwg+UZEaYpeWplFz96to3eSIpLWiv4t4+Mo7rgwLFLaAoFVzQTeHg90Tc68Z53eApkpzLHm73maLDfKCClfEwI8Q/gP4GlQojfw+46BSnl3e97Si3ws+GR+TfeF+ALR7HNJyyvbOjnm39dvevx/OZirplVw5ktJXtl9EopuefFjbnEsxtm4HOOLNtX9dlwthYTX9qH94IxKPbjQxQkT47om12E/7EV+8QiCq8dd9RGuRZV4drZtXx8ehWPLengvlc270qCenpVD2e2lPDP5zQxuz7/dR0Nlu8Y4jt/X8eKjhCTq3z89PppzKo79Pd2V07Kqx04p5WiFZ64OgcHGgkfKY43e83R4GDzLFlyDl02wPO+7f30ATPJmSEtFkLsuah+Uq5dj5TlO0JYVMGfv3A6f/7C6fzultlc0lr5gfKbu1/cyJ+XdfLZ+fUH7YnvD/cZVci0QXxp32g0Pc8oEX2jk/A/tuKYVETR9eMQh7DMMdrYNJVPnV7Hm187h8e/cDqrvnUhX1swlrVdYa5+YCFX37+Q1zcOHPCCl2ffSCl5Z/Mgn/71u1zxi3foDiW566opPPVP80YUrHfiu7gBTJP4uz0H3znPXpx77rmxZ555xh+NRpVIJKI888wzBeecc070/fudeeaZ8UWLFnl6e3vVdDot/vrXv+5KGthpr7nz8TvvvHPszNM58Br2AuBu4G/AdCllYn/77mR4n88KIT4OvCiE+IGU8n4OP9nyhERKyUAsTUcwSedQgo5ggo5gklfa+plQ4T3gF/fPSzv46SubuXZWDf+2YNxht8Fa7cE6xkvsnW7ccysRRys7OM9+ib7eQfjZdhyTiym8dixCPbbrknaLyszhz+IXz27i5rn1/GnJDh58Yys3PfQuEyu9fG5+Axe3VmA5xm093skaJs+s7uHBN7aytjtCsdvKVy5o4ZYz6j+UF73ms2Fr9JNYNYj3orp8zsEIOB7tNb/3ve+V/vSnPy0PBAKWKVOmTDjnnHPCjz766CE7Th1I6exN4Av7093ex/7v1xuvIrcOngTGSymb9/fc44XDrcOWUrKiI8RTK7p5e/MgHUMJUtm9Z0uK3TZqCh3cMlwbuy+WtAe5/peLOK2+iF/fPOtDXyQTqwcJPrKeohvG45hU/KGOlefDEXm1g8jz7Thaiym8Ztwuz+PjkbRu8NflXfzyza1sGYhT4bNzy7x6rpldc8wVtY43TFPy2NIO7nt5E93hFI0lLj43v4HLp1Xt1nj/kMSX9DL0xCZK/3kq1uqDi+ocC06mOuzjgRHXYUsp54/wHP3ve34XcIEQ4qvAhSM81gnFaxsHuPnXS7BqCvMaizirpYSaQic1hQ5qCpxUFzgPqkgUTWW5/Y/vUeV38PPrp4/KiMYxoQjVbyP6dlc+YB9DIi/vIPLidhxTSyi8auxxHawhN2V+7exarp5Zw6tt/fzyza18/5n13PvyJj4xvYob5ow5uG75SY5pSpa0B7nnpU0s3BpgxpgCvvfxSZzdUjrqte6OiUUMPbmZxKqB4zZg5zk6jGYd9oL9/P7HwI9H6zzHI/Mai7nrqilcOLHssEcg3/77OnojKR6/be6Ik8z2h1AF7nmVhP+xjUxXDGuVe1SOm+fQiby0nchLO3BOK6XgqpYTamlCUQTnjS/jvPFlrO4M879vbeWP73bw24XbmV1fyA1zxrBgYvkhlRueTJim5PZHV/D3ld147Br/dcVkrp1Vc8SmqxWnBXuTn+SqQXwfqc9Pi5/CHNFvmhBi+cH3OvGxagpXzqg+7GD9x3d38PiyTr54dhPTa0dXJME1qxxhVYm91TWqx81zYKSUhF9ozwXr6SdesH4/k6t93HPtNBZ+41y+vmAcPeEkX/rje8z94cv8+PkNdA4dNMXlhCeVNXhxXR+ff3gZf1/ZzZfOa2bxN8/jutm1RzyIOlpLMEJpMh0fyJnKcwpxpOt9Ttwr1FFiRUeI//vUWuY3F/PlC1pG/fiKXcM1s4zY4h58C+pQfUffeu9UQ5qS8NNbib3TjXNGGQWfaD6hg/WeFLlt3HZ2I58/s4HXNw3wyKLt/M9rW/if17Ywr6mYuY3FzKorYHK1D5t2csjXZnST3y1s596XNhFN63jsGv96fjO3n9d81Ea7jolFDP1FkFw5gK12dBTx8px4jHrAFkL8M/CwlDIE/GO0j38yMRhLc9vDyyjx2LjvABrhHxb3GVXEFvUQebWDgsubjsg58uSQhsnQ45tIvNePe14lvosbTppgvSeKIjhnbCnnjC2lK5Tkj4t38OyaHn70XE6H3qYpzG8u5pLWSsaWe6gucOA5wRLWIqksi7YE+NFzG9gyEOfssSV85ox65jQUHfWsecWuYW8pILl68KT9TOU5OEdihF1OTmhlOfCQEEKcrBriHwbdMPmXP7xHMJ7hidvmUuA6dEnTkaIV2nHNLif+bi+e+VUjlivNc2jIrEHgDxtIrQ/ivXAMnnOO3Lrm8USV38GdF43lzovGEoilWdI+xKKtAZ5b08tL63fnovocFqr8DhpKXJzRVMyZLSVU+h3sCCQIxNNMqvIds/KxUCLDmq4Ia7rDrOnKbe2B3DR/XZGThz49k3PHjdCMZJRxTikhuD5IZnsEW31ele5UZNQDtpTy/wgh/oNcZvjN5NTPHgP+V0q5ZbTPd6Lyyze3sXBrgB9f2bqX6P+RwntuLYllfURe3E7htYdf351n35hJncHfrSXTHsF/eSPuOfsu3TvZKXLbWDCpnAWTyvnPSyawtjvC9mCczqEkXUNJukJJlrQHeXpVTgikqdTN5v4YkPONnlzlY2qNn2m1BUyt8VPhs+/q9CQzBs+t7aEjmKTS76DSZ8fntOBzWPA6LLit2gcytJMZg55wkp5wioFomnAySySZZTCWpjucojuUpDuUZCixW5ixusDB5CofV82sYWKll9Mbi46L6X37+ELQFBKrBvIB+whyJO01L7vssvpVq1a5LBaLnDp1avzhhx/ebrPZDnlAe0TWsKWUUgjRC/QCOlAAPC6EeFFK+bXROo8Q4sfApUAG2ALcLKUMCSHqgPVA2/Cui6SUXxit835Ytg7EuOeljSyYWM5VM2uOyjlVrxX33Eqib3TiObvmkKw38xwaejjN4ENr0AeTFF47FueU0oM/6RRAUQSTq30f0CiXUrKxL8YbGwd4Y9MAm/tjlHhsXNJawYqOEL99Zzu/fDNnfuR3WnBYVBQhCCUyxDPGvk4F5Nw1PTYNr8OC06oyEE3vFYj3xGPXqPI7qPQ7mFbrp6bAyaQqHxMrvfidR26268Og2DQcYwtIrhnEf2ljflp8FDja9pqf/OQng08++eQ2gI997GP199xzT/HXv/71gUM915FYw/4ScBMwCPwK+KqUMiuEUIBNwKgFbOBFcrrluhDiR8A3gK8P/22LlHLqKJ5rVFi2Pcjnf78Mm6bwrcsmHtVze86qJra4h/Dz7RTfdHTPfbKS6Yox+Nu1yLRB8c2TsDeNvuvWyYYQgrHlHsaWe/jcmQ1kDRNNEbtG0hndZH1PhBUdIdr6omR1E0NKXFaNi1srmFrjpyecoiecJJLMEknqRFK5kXMkpRNJZolndGbVFVLpd1Dhs1Pus1PqseN3WvDaLSdsKZpjSgnJtQHS28LYG/OftYNxvNlrXnPNNeGd92fOnBnv7OwcUe/wSIywi4ErpJR7ya1JKU0hxCWjeSIp5Qt7PFwEXDmaxx9ttg3Gue7BxVT67fzq1pmU+46umL/itOA5q5rI89tJb4+Mmv/yqUpy7SDBP7WhuCyU3DYlP2txmLx/3dqqKUyp8TOlZv8Bqb7YRX3xqfd+28cVIiwKyVUDJ1bAfvKfauhfN7q+vaUTElz+8xPSXjOdTotHH3206O677x6RKcqodzOllP/5/mC9x9/Wj/b59uAW4Nk9HtcLId4TQrwuhBipatsR4d1tATKGyf9+ehZNpcdGscg9rwrFbSH8XHve3OEwkVISfb2DwMPrsZS7KP2nqflgneeooFhV7OMLSa4ZRBr57++B2NNe0+fzmTvtNQH2Z69pt9vlFVdcEdx5jLffftt7++23144bN27CpZde2jRa9po33XRT7Zw5c2ILFiyIjeR5x73vohDiJXKZ5+/n36WUTw3v8+/k1sofGf5bD1ArpQwIIWYATwohJkopI/s4/q3ArQC1tUfWc3Z9TxSnVaW+6Nhd3BWrivfcWkJ/20Jq4xCOsXkrxZEgdTMnE7m0D8eUEgqvbEaMkmZ0njyHgrO1hOSqQdJbQ9ibR1do6YhxgJHwkeJ4tdf8yle+UjE4OKg9//zzI07CPu4XcqSU50spJ+1j2xmsbwIuAT65s3xMSpmWUgaG7y8jl5C2T1USKeWDUsqZUsqZJSUl+9pltF4Hq7vCjC33jLrW8EhxzS5HK7IT/sfWfC99hISe2kJiaR+e82pzjlv5YJ3nKGMfW4CwqiRWHHKu0inJ8Wiveffddxe/8sorvieffHLr4SS6HfcB+0AMW4B+HbhsT/tPIUSJEEIdvt8ANANbj00rczy8eAfLtg9xwYRjW8sJIDQF30cb0PuTeZ/dERBf3kd8SS+ec2rwXTDmlKixznP8ISwqjtZikqsGMFP6sW7Occue9pozZswYv9Ne8/377WmvecYZZ7S0trbuiiUPPvhgx/Lly10tLS0TGhsbJ/7sZz87pFHdjBkzxn7qU59qWLhwobesrKz1iSee8AJ87WtfGzM4OKjNnDlz/Lhx4ybceeedFSN5Tfu11zwREEJsBmxAYPhXi6SUXxBCfAL4DrlpcgP4v1LKvx/seIdrr3kwFm8N8MlfLWZ+czG/umnWEVM0GwlSSgZ/tZpsT5zyO2eijJLhyMlKckOQ4CPrsVR7KPns5OPecSvPyU2mM0r/z1bg/1gj7tOPfc1/3l5zdBmxveaJgJRynzqbUsongCeOcnP2SVcoyRcfWU5toZN7rzty8qMjRQiB7+IG+n/6HpFXOvBf0nCsm3RcIqUk8tIOoi/vwFLhoui649vLOs+pgbXag6XaTXxx73ERsPMcHU7oKfHjnWTG4PO/X0pGN3nwxpmH7eZ1pLBWunHNKif2TjfZgZPfbelwiL7WSfTlHThnlFH6xSmo3uNTVCPPqYdrehnZ3jjZ3vixbkqeo0Q+YB8hpJT8219WsbY7wr3XTaWp9Pj0ovZeMAZhUQg/s+3gO59CmGmdoSc2EXm+HcfUkpzjVj7BLM9xhGNyMSiQWJlPPjtVyAfsI8Qv39zKUyu6ufPCscfcNOBAqB4rnnNqSK0Pkto0dKybc1yQ3h6h7973iC/txXN2NYVXnthe1nlOTlSPFVtTAYmVA3lNhVOEfMA+Ary+cYAfPruBiydX8MWzG491cw6KZ14VaoEtV+ZlnrpffCklkdc6GLh/JUhJyedb8S2oR5ygMpZ5Tn6cU0owgikyHR+oVspzEpK/Eo0y7YNx/uUPy2kp8/Djq1pPiNIfYVHwfbSebG+C+JLeY92cY4KUkvCz24g8146jtYSy26djq8s7IuU5vnFMLAJNkMzXZJ8S5AP2KBJL63zud0tRFcEvb5yJ03riJOE7JhVjrfMSeWH7KVfbKU1J6MnNxN7ownV6BYXXjEWxnzj/uzynLopdwzGukMSqgbwI0ihx3333Fd14440fSvZy/vz5zR6PZ+o555yzVyXT1VdfPWbs2LETWlpaJixYsKAhHA6PKAbnA/Yo8u2/rWXrYJyfXz+dmsLR1bk/0ggh8F/SgJnIEnlxn1LwJyUyaxD84wbii3vxnF2D/7K8bWGeEwvn1FLMWJb01tCxbsoJh2maGMb+LVsPhWz2gxaud955Z+8DDzzwgUze+++/v6OtrW3dxo0b11VXV2f2VFE7FPIBe5R4a9Mgf17Wya1nNjC3qfhYN+ewsFZ7cM0uJ/Z2N7F3uo91c444RiRD/4OrSa4ZxPfRenwL6k6IJYw8efbEPrYQYctLle6Lb33rW2XNzc0Tm5ubJ37nO98pBWhra7M2NDRMvOGGG2onTpw4YcuWLdZ77723qK6ubtKsWbPGvvPOO7tKerq7u7WLLrqocdKkSeMnTZo0/oUXXnAB3HHHHZXXXXfdmHnz5jVfccUV9e8/78c+9rGo1+v9gNZ4YWGhCbmOQjKZVEZ6vcnP+40CyYzBN/+6mroiJ7ef13ysm/Oh8F/WiBHNEvrbFoRFwTVrX74rJz6Z7hiB367FTOgU3TAhtxaYJ88JiLAoOCYV5xy8Lm9CWI6/cdh/vP0fNZuHNo/qtGNTQVPiu/O+e8LZa1555ZV1r776qq+pqSl5//33d47kucfff/YEZPmOIXojKX5wxWTsJ3itrlAViq4fh62lgKG/bCKxov9YN2nUSa4L5DLBgZIvTMkH6zwnPM6pJci0QaotePCdTxGOV3vNxx9/vL2vr29lc3Nz6qGHHhqR3Vp+hD0KzGsq5u2vn0uJx3asmzIqCE2h6IbxBH6zluBjbUBunexEx4hkiLy0nfiSXixVbopvnJhXLstzUmBr8KO4LSRW9OOYdPwtyR1oJHykOF7tNQE0TeO6664L3nXXXeW333574ODPyJEfYY8SJ0uw3oliVSm6aSLWMT6Cj7YRW3TirmmbGYPIS9vpvWsJ8WV9uOdWUnJraz5Y5zlpEKrI+WRvCJ5yVR7743iz1zRNkzVr1th23n/qqaf8zc3NqZEcIz/CzrNfFJtKyS0TCfxhA6Ent2DGdTzn1IAAI5xG9dp2ZVTroTRCFYSfa0emdHwfqUcr/lDWsR8aaUoSy/oIv7AdM5rBMbkY30V1x7xdefIcCRxTSoi9001ybQDXjONXXfFosae9JsBOe822tra9eup72muWlJRkW1tbE4ZhCMjZa372s5+tbWlpmWAYhjjttNOic+fO3XGwc8+YMWPs1q1b7clkUi0rK2v9xS9+0X755ZdHbrzxxvpYLKZIKcX48eMTv/nNb0ZUknNC22uONkfKXvNERxomQ49vIvFeP4rLguLU0AeSCKuCramAbFcUI5xBWBRkdniWSBW4ZpbhnluJpcx1VNtrxDKkN4eIvtZBtjeBtdaD7+IGbGO8R7UdefIcTaSU9P73ErRiByWfmXxUz5231xxdTkp7zTxHB6EqFFzVgn1CIck1AZLDZgOq14beF8da58Na6yGxtI9sT5ziz00muXKA+LI+4ot7sTX7cU4pxT6uANW9u3ObWNFPuj2Cc2oJ1jHewyqpklJixrJkumKkN4dIbw7tci9SC+0UXj8Ox+TifLlWnpMeIQTOqaVEX+0gtrA7b7t5EpIP2HkOCaEInJNLcE4uQV7VghHJoBXa99rHNbMMvT+JtcaDvdGP98IxxN/tJb64h6HHN4LI1XrbxxWilTgY+utmZNogvqgHtciOc3Ixtnof1jHeXUpjeiCJHkgh7CqKTcWIZsj2JdD7E7tuzcTwmp0msI3x4r1oDLZGP9YqT967Os8phXNKCdFXOwg9tSUfsE9C8gE7z4gRmvKBYA2g2DSsNZ5dj1W3Fe+5tXjOqSHbHSe1IUhyQ3CXkprislDy2clk+xMklvURfaOL6GudIMBS6cZa4yG+qGffbXBoWMqcOCYVo5U5sZS7sNV68haYeU5pLOW7l5/0oRRawf9v786jo6zvPY6/v1kmIWSBaAgYsyAEQlCkNx61HPVWpRW9F7UB3HpwodZqq6UL2lqvp9altrVirRQr2HsrakWqFK1LPeqxcsuVtuCCAYQgJkgkEAhhCZBtvveP5xkdyTrJM5nt+zonh8kz8zz5fZ3E7/ye7dP579TErphu2CJyB/ANIHCLnx+r6kvuc7cCXwc6gO+o6isRGaRBRPAVZOIryCT73CI6DrTS3ngE3/GZSHISvsIshlbk42/poHXbflpq9tOydd+n14D7irLIOrcIPdJB0tAUUvOHkpSZaru5jelC3rdOpmHhe7RsaSIlTm98lKhiumG7HlDVXwUvEJFy4DJgInAc8JqIjFPVgd001ngiOctHclbnS6qS0pJJLx1OeqlzVYWqoofbkfQUu7+3MX3kK8wiKSuVI1ua4vZOhYkqXq/DvghYqqotqvoRsAU4NcJjMiESEZIyUq1ZGxMCESF97HBatjQldL59PIqHhn2jiKwTkf8WkcAF7wVA8J11trvLOhGR60RkjYisaWiwm+cbY2Jf2thh+JvbPr1iwvRdOOM1A6666qrCjIyML4S63ahv2CLymohUdfF1EfAwMAaYDOwA7g+s1sWmuvyoqaqLVPUUVT0lLy8vLDUYY8xgSh87DIAjG+3e4j0Z7HhNgJUrV2bs27evX4ejo75hq+pUVT2xi6/nVHWnqnaoqh9YzGe7vbcDhfZPlnYAABQ6SURBVEGbOR6I3XtrGmNMCJJz0kgbO4yD/9iBtvf7ltcxL9riNdvb27n55puPf/DBB0NK6QqI6ZPORGSUqgau+/kqUOU+fh74o4jMxznprBT4ZwSGaIwxEZH178ez+/dVNP+znswpkb0m+5Mf31bYUl3tabxmWmnpoeN+dk9MxWvee++9Iy644IKm4uLiztPyPojphg38UkQm4+zurgG+CaCq60VkGbABaAe+bWeIG2MSSdrYYfhG57D/jW1knJJPki+x7lEQHK8JEIjXnDVrVlN38ZoAlZWVjZs3b04HJ16zurr60/CBgcRr1tTUpK5YsWL46tWrN/W3pphu2Ko6u4fn7gHuGcThGGNM1BARsqcWsXvx+xzZsCeiEbk9zYTDJdriNVevXp1RW1ubXlJSchLAkSNHkoqKik7ctm1bVW/rBkT9MWxjjDH9kzY6h6TMVA5v6HPkctyItnjNyy67bN/u3bvfq6ure7+uru799PR0fyjNGmJ8hm2MMaZ7kiQMKT+GQ+81oO1+JCVx5mjRFq85Y8aM/QOtyeI1g1i8pjEm3hz+oJE9f1jPsddMJH18blh+hsVrequ7eM3E+bhljDEJKH3MMMSXlJC7xeONNWxjjIljkppE+vhcDm/Y0+OJWCb6WcM2xpg4l146HP+BNtobDkd6KGYArGEbY0yc843OBqClZl+ER2IGwhq2McbEuZRjh5CUmUrrRwM+UdlEkDVsY4yJcyJCWnG2zbBjnDVsY4xJAL6SHDr2ttC+ryXSQ4lq4YzXnDFjRklBQcFJZWVl5WVlZeWh3ojFbpxijDEJIM09jt1as4+UkyN3m9Jo4vf7UVWSk/t/n/W2tjZSU1M/t2zevHn1zc3NSYsXL+6U2Xz33Xdvv+aaa/b252fZDNsYYxJA6qhMxJdMSwIdx462eM2Bshm2McYkAEkWfMVZtNYMfsN+fcnGwsa6g57Ga+YWZB4698oJMRWvCfDTn/604N577x115plnHliwYMH2IUOG9Hl9m2EbY0yCSCvOpm1nM/7D7ZEeStgFx2vm5OT4A/GaAN3Fa6anp2tlZWVjYBurVq3Knjt3blFZWVn59OnTxw4kXhNg/vz5dVu3bq167733Nu7duzf59ttvHxnK+jbDNsaYBOEbnQMKLbX7GVIWnvuKd6WnmXC4RFu8JjhBIwBDhgzROXPm7Ln//vvzQ1nfZtjGGJMgfIVZkCy0JsDlXdEWrwlQW1ubCs7JbsuXLx82YcKEkG49ZzNsY4xJEEm+ZHwFmQlx4lk0xmteeumloxsbG1NUVcrLyw8tWbKkNpSaYjpeU0SeBsa73w4DmlR1soiUABuBTe5zq1X1+t62Z/Gaxph41/TSVg6u+oSCO6Ygqd7sZLV4TW91F68Z0zNsVb008FhE7geC9/N8qKqTB39UxhgTvdJKcji4so7W7QdIG50T6eGYEMTFMWxxzhi4BHgq0mMxxpho5iu2IJBYFRcNGzgT2Kmq1UHLRovIOyLypoic2d2KInKdiKwRkTUNDQ3hH6kxxkRQ8tBUUkZkJMRx7HgT9bvEReQ1oKtr1W5T1efcx5fz+dn1DqBIVfeISAWwQkQmqmqn31BVXQQsAucYtrejN8aY6JM2OptD7zagfkWSur6kyUSfqG/Yqjq1p+dFJAWoBCqC1mkBWtzHa0XkQ2AcYGeUGWMSXlpJDs3/qKetvhnfcZm9r2CiQjzsEp8KfKCq2wMLRCRPRJLdxycApcDWCI3PGGOiSuA4dmut7RaPJfHQsC+j88lmZwHrROQ94BngelVt7LSmMcYkoOThaSRl+Wixht1JOOM1/X4/N910U0FJScmJJ5xwwsS77747pNi0qN8l3htVvbqLZc8Czw7+aIwxJvqJCGnFWQk/wx7seM2HHnromO3bt6d++OGHVcnJydTV1YXUg+Nhhm2MMSZEvuIcOva20LG/JdJDCZtoi9d89NFHR9x11107Ah8QCgoKQkphifkZtjHGmNCllbjXY9fuJ+OkvF5ePTCvPPzrwt0f13oar3lsYfGh8274bkzFa3788cdpjz/++PAXX3xxeG5ubvtvf/vbbSeddFKfPzFZwzbGmASUOmoopCTRWhP+hh0JwfGaAIF4zVmzZjV1F68JUFlZ2bh58+Z0cOI1q6urPw38GGi8Zmtrq6Snp2tVVdXGxx57bNjVV19dsnbt2k29r+mwhm2MMQlIUpLwFWYOyolnPc2EwyUa4zXz8/Nbr7jiir0As2fPbrrxxhtLQlnfjmEbY0yCSivOpu2TZvytHZEeiueiMV7z/PPPb3r55ZezAF566aWs4uLikE4gsBm2McYkKF9xNvi307b9AGknDIv0cDwVjfGad955Z/3MmTNHL1y4MD8jI8O/ePHimlBqiul4Ta9ZvKYxJpF0NLex467VZJ9XTPbZ/b/02OI1vdVdvKbtEjfGmASVPDSVlLwhtNZ22lNsopA1bGOMSWC+4mxaavejftvbGu2sYRtjTAJLK85GD7fT3nAo0kMxvbCGbYwxCcxXEggCsd3i0c4atjHGJLCUY4eQlJFiQSAxwC7rMsaYBCYiDLtwDMnD0yM9FNMLm2EbY0yCy5g8gjQ3IzvRhTNes6KiYnxZWVl5WVlZ+YgRIyZNnTp1TCjbtRm2McaYhDTY8ZrB9w0/77zzxkyfPr0plJ9lM2xjjDFxKdriNQP27t2b9NZbb2UF7iveVzExwxaRWcAdwATgVFVdE/TcrcDXgQ7gO6r6iru8AvgDMAR4CZirdls3Y4wZdI3PbC5sq2/2NF4zdeTQQ7kzx8VUvGbAk08+OXzKlCn7c3NzQwoQiYmGDVQBlcAjwQtFpBy4DJgIHAe8JiLjVLUDeBi4DliN07CnAS8P5qCNMcZERjTGawYsW7Ysd86cOQ2hrhcTDVtVN0KXEWgXAUtVtQX4SES2AKeKSA2QrapvuestAS7GGrYxxgy6nmbC4RKN8ZoA9fX1yevWrRt6ySWXbAl13Vg/hl0ABP8ibHeXFbiPj15ujDEmAURjvCbAkiVLcs8555ymjIyMkGfnUTPDFpHXgJFdPHWbqj7X3WpdLNMelnf1c6/D2XVOUdGAzuQ3xhgTJaIxXhPgmWeeyb3lllt29KemmIrXFJG/AfMCJ525J5yhqve637+Cc3JaDfCGqpa5yy8HvqSq3+xp+xavaYwxobN4TW91F68ZNTPsfnoe+KOIzMc56awU+KeqdojIARE5HfgHcCXwUG8bW7t27W4RqQ3riD/vWCCef6HjuT6rLTbFc20QufqKI/AzE05MNGwR+SpOw80DXhSRd1X1PFVdLyLLgA1AO/Bt9wxxgBv47LKul+nDCWeqmtfba7wkImuO/lQaT+K5PqstNsVzbRD/9SW6mGjYqvpn4M/dPHcPcE8Xy9cAJ4Z5aMYYY8ygiPWzxI0xxpiEYA07shZFegBhFs/1WW2xKZ5rg/ivL6FZw44gVY3rP654rs9qi03xXBvEf32Jzhq2McYY4wpnvOZzzz2XVV5ePqGsrKy8oqJifFVVVVoo27WG7SERKRSRN0Rko4isF5G57vJcEXlVRKrdf4e7y49xX39QRBYcta2/icgmEXnX/RrR1c8cTB7X5xORRSKyWUQ+EJEZkagpaDye1CYiWUHv2bsisltEfh2putwxefm+XS4i74vIOhH5q4gcG4magsbjZW2XunWtF5FfRqKeo/Wjvi+LyFr3PVorIucEbavCXb5FRH4j0s39OBOI3++no6Oj9xf2oK2trdOyefPm1T/yyCMfHb187ty5xU888cRHH3zwwYZZs2Y1/uQnPxkVys+yhu2tduAHqjoBOB34tjgBJT8CXlfVUuB193uAI8DtwLxutvc1VZ3sfu0K89j7wsv6bgN2qeo4oBx4M9yD74UntanqgaD3bDJQCywfrCK64UltIpICPAicraqTgHXAjYNTQre8qu0Y4D7gXFWdCOSLyLmDVENPQq1vNzBdVU8CrgIeD9pWIBCp1P2aNjglRE40xms2NTUlA+zbty951KhRnbt9D2Lisq5Yoao7gB3u4wMishHnHuYXAV9yX/YY8Dfgh6raDPxdRMZ23lr08bi+OUCZuy0/Eb6ZRTjeOxEpBUYA/xu+kffOw9rE/RoqInuAbCDkAAMveVjbCcBmVQ0kKL0GzMBphhHTj/reCVp9PZAuImlALhEMRFqxYkXhrl27PI3XHDFixKGLL744puI1f/e739VUVlaWpqWl+TMzMzv+9a9/bQylZpthh4mIlABfwLnTWr77hxf4A+zr7u3/cXer3h5tu68GUp+IDHMf3iUib4vIn0QkP4zDDYlH7x3A5cDT0ZTDPpDaVLUN54ZE7wOf4OwZ+X0YhxuSAb5vW4AyESlx9yRcDBSGb7Sh60d9M4B33DTDhAtECo7XzMnJ8QfiNQG6i9dMT0/XysrKxsA2Vq1alT137tyisrKy8unTp48daLzm/Pnz85cvX169c+fOdVdcccXuG264IaTfMZthh4GIZALPAt9V1f397LVfU9U6EclytzUbWOLhMPvNg/pSgOOBVar6fRH5PvArnBojyqP3LuAyoqCmgIHWJiKpOA37C8BWnLsP3grc7fFQQzbQ2lR1r4jcADwN+IH/w5l1R4VQ6xORicAvgK8EFnXxskH7INnTTDhcoi1e85NPPknZuHHjkHPOOacZ4Morr9w7bdq00lC2YTNsj7n/U3sWeFJVA8cud4rIKPf5UUCvx6NVtc799wDwR+DU8Iw4NB7Vtwc4xGd3r/sT8G9hGG5IvHrv3NeeDKSo6tqwDDZEHtU2GUBVP3T3GiwDpoRpyH3m4d/cX1T1NFX9IrAJqA7XmEMRan0icjzO39aVqvqhu3g7zofkgONx9pLErWiL18zLy2s/ePBg8rp169IAXnjhheyxY8ceCWUb1rA95O62/j2wUVXnBz31PM4JILj/dhcXGthOSuDsW/eP9T+BKu9HHBqv6nP/Z/8XPjsGdy7O/eAjxqvaglwOPOXdCPvPw9rqgHIRCdxz/8tASMfgvObl+ybulRjuGdffAh71drShC7U+93DTi8Ctqroq8GJ3t/kBETnd3eaV9P13OSYFx2tWVFRMCMRrHv264HjNM844Y9ykSZMOBZ5btGjRx2+//fbQcePGlY8ZM2biggUL+pQ3UVFRMX727NknvPXWW9n5+fmTnn322ezU1FQefPDB2pkzZ44ZP358+VNPPXXMAw88ENKeh5iK14x2InIGzglG7+PsVgP4Mc4xp2VAEbANmKWqje46NTgn7/iAJpxdWLXASiAVSMY5Aeb7QcEmEeFVfaq6QUSKcc5gHQY0ANeoaq85s+HiZW3uc1uBC1T1g0Eso0sev2/XA3OBNpzf06tVdc/gVfN5Htf2FHCyu407VXXpYNXRnVDrE5H/wjlMEbx34CuquktETuHzgUg3hfP8CovX7L/u4jWtYRtjjPGcNez+665h2y5xY4wxJgZYwzbGGGNigDVsY4wxJgZYwzbGGGNigDVsY4wxJgZYwzbGY+IkLH0kIrnu98Pd74s92PbBgY/QGNOdcMZrPv/881nl5eUTSktLJ1ZWVpZ0lfTVE2vYxnhMVT/GSUb6ubvo58AiVa2N3KiMMUcbzHjNjo4OrrvuutFLly7dWl1dvb6oqKh1wYIFIcXTWsM2JjweAE4Xke8CZwD3H/0CEfmFiHwr6Ps7ROQHIpIpIq+7wSjvi8hFXaz7JRF5Iej7BSJytfu4QkTeFCcP+ZWgW1h+R0Q2iJP5HPGbghgTbtEUr7lz584Un8/nnzRpUgvAtGnT9q9YsWLY0ev2xMI/jAkDVW0TkZuBv+Lcaaq1i5ctBX4NLHS/vwQno/gI8FU35OFYYLWIPN+Xu1K5t7J9CLhIVRtE5FLgHpw40x8Bo1W1JSgxzZiw27Dxh4XNBzd7Gq85NHPcofIJv4iZeM2RI0e2t7e3y8qVKzPOOuusQ08//fTwHTt2+EKp2Rq2MeFzPk6W8YnAq0c/qarviMgIETkOyAP2quo2t+n+TETOwrkdZQGQD9T34WeOD/w8N4Eo2R0DwDrgSRFZAawYUGXGRLngeE2AQLzmrFmzmrqL1wSorKxs3Lx5czo48ZrV1dWfBn4MJF4zKSmJJUuWbP3e975X2NramnT22WfvS05ODqkma9jGhIGITMYJxzgd+LuILA3kFx/lGWAmMBJnxg3wNZwGXuHO1GuA9KPWa+fzh7QCzwuw3k2cOtp/AGcBFwK3i8hEVW0PuThjQtTTTDhcoi1eE2Dq1KnNa9eu3QSwfPny7C1bthz9d90jO4ZtjMfcNKSHcbKLtwH34eR9d2UpTm72TJzmDZAD7HKb9dlAV2eX1+IkZ6WJSA5O4hk4sZB5IvJFdyypIjJRRJKAQlV9A7gFJ3Qls4vtGhMXoi1eE6Curi4F4PDhw3LfffeNvP766xtCWd9m2MZ47xvANlUN7AZfCFwtIv+uqm8Gv1BV14tIFlAXNAN/EviLiKwB3gU6JX6p6scisgxnN3c18I67vFVEZgK/cRt5Cs5x8s3AE+4yAR5Q1SZvyzYmegTHawIE4jU3bdr0uePGwfGaeXl5bZMmTTrU0dEh4MRrXnvttUXjxo0r7+jokNNOO+3AlClTek0VrKioGL9169b0w4cPJ+fn509auHBhzYwZM/bfeeedI1999dUcv98vc+bM2XXhhRd2+gDRE0vrMsYY4zlL6+o/S+syxhhjYpg1bGOMMSYGWMM2xhhjYoA1bGOMMeHg9/v9XV8vZbrl/jfr8pIxa9jGGGPCoaqhoSHHmnbf+f1+aWhoyAGqunreLusyxhjjufb29mvr6+sfra+vPxGbHPaVH6hqb2+/tqsn7bIuY4wxJgbYpx5jjDEmBljDNsYYY2KANWxjjDEmBljDNsYYY2KANWxjjDEmBvw/Ps/4tWrNpRAAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Part c\n",
"\n",
"Z_st = np.block([[t_st_train**0]]).T\n",
"Z_st_test = np.block([[t_st_test**0]]).T\n",
"Z_st_train = np.block([[t_st_train**0]]).T\n",
"\n",
"max_N = 20\n",
"SSE_st_train=np.zeros(max_N)\n",
"SSE_st_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_st = np.hstack((Z_st,t_st_train.reshape(-1,1)**i))\n",
" Z_st_test=np.hstack((Z_st_test,t_st_test.reshape(-1,1)**i))\n",
" A_st = np.linalg.solve(Z_st.T@Z_st,Z_st.T@P_st_train)\n",
" St_st=np.std(P_st_train)\n",
" Sr_st=np.std(P_st_train-Z_st@A_st)\n",
" r2_st=1-Sr_st/St_st\n",
" print('---- n={:d} -------'.format(i))\n",
" print('the coefficient of determination for this fit is {:.3f}'.format(r2_st))\n",
" print('the correlation coefficient this fit is {:.3f}'.format(r2_st**0.5))\n",
" plt.plot(t_st_train,P_st_train-Z_st@A_st,'-',label='order {:d}'.format(i))\n",
" SSE_st_train[i]=np.sum((P_st_train-Z_st@A_st)**2)/len(P_st_train)\n",
" SSE_st_test[i]=np.sum((P_st_test-Z_st_test@A_st)**2)/len(P_st_test)\n",
" \n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 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": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"---- n=1 -------\n",
"the coefficient of determination for this fit is 0.885\n",
"the correlation coefficient this fit is 0.941\n",
"---- n=2 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=3 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=4 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=5 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=6 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=7 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=8 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=9 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n",
"---- n=10 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.947\n",
"---- n=11 -------\n",
"the coefficient of determination for this fit is 0.897\n",
"the correlation coefficient this fit is 0.947\n",
"---- n=12 -------\n",
"the coefficient of determination for this fit is 0.898\n",
"the correlation coefficient this fit is 0.948\n"
]
},
{
"data": {
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gVSlsEYkRkY9EZJuIbBWRUSISJyLzRSTb/Ix1S3+fiOwQke2mOT6NRqPRaFolrUphA08D3yql+mKYvdsK3Av8oJRKwbCocy+Aaaf2SgxLR1OAF7w4mdBoNBqNpsXTahS2iERhONl4FUApVaGUKsCwyevyA/smhtk9zPD3lFI2pdRuDFN61ZxSaDQajUbTGmg1ChvoheHQ4XUR+VlEXjH94XZUSh0Cw0g9p7y7dAX2uZ2/Hw8+k0XkJhFZIyJr8vLymrYGGo1Go9E0kNaksAOAocCLSqkhGI4C7q0hvXgIq7bpXCk1Wyk1XCk1PCFB70rQaDQaTcukNSns/cB+pdRK8/dHGAr8iMvfsfmZ65be3eF6NwwvORqNRqPRtDpajcJWSh0G9olImhk0GcOX6jzgOjPsOgxXkZjhV4pIsIj0xPDBugqNRqPRAIZ75Q9W76O0otLfomjqQGsznPIH4B0RCcLwm3o9xkvHByLyK2AvcAWAUmqziHyAodQrgZuVUg7/iK3RaDQtj62Hirj74w0Ultu5cVwvf4ujqYVWpbCVUuuA4R6iJntJ/zCGY3uNRqPRVOFIYTkAi7LytMJuBbSaIXGNRqPR+JbcIkNhr9x9nLIKPQDZ0tEKW6PRaNopuYU2ACoqnazYdczP0mhqQytsjUajaafkFtmICA4gJNDCoixth6Kl06rmsDUajUbjO/KKbHSKDuGigZ3pGR/ub3E0taAVtkaj0bRTcovKSYwM5vazU/0tiqYO6CFxjUajaafkFtlIjAz2txiaOqJ72BqNRtMOUUoZCjsqpEnyz8zMTAwICHgF6I/uHNYVJ7CpsrLyxmHDhuVWjdQKW6PRaNohhWWVVFQ6m6yHHRAQ8EqnTp36JSQk5Fsslmp+HDTVcTqdkpeXl3748OFXgEuqxuu3Ho1Go2mHuPZgJzTdkHj/hISEQq2s647FYlEJCQknMEYlqsc3szwajUajaQHkFhl7sBMjm2ZIHLBoZV1/zGvmUTdrha3RaDTtkDxTYTdhD7tV8swzz3SYOXNm98bkMW7cuJTIyMjBZ511Vh9fyQVaYWs0Gk27xDUknhjVfhW20+nE4WicSVa73V4t7K677jr80ksv7W5Uxh7QCluj0WjaIbmFNkICLUQGt921xw8++GDHlJSUjJSUlIx//OMfiQDbt28P6tWrV8Y111zTPSMjI33nzp1BTz/9dIfk5OT+I0aMSFu2bFmE6/yDBw8GnHfeeb379+/fr3///v2+++67cIA77rijy1VXXdVjzJgxKdOnT+9ZtdypU6cWRUVFOX1dn7Z7pzQajUbjFWMPdggi0uRl/emj9UlZh4vCfJlnaqfI0icuH7TPW/ySJUvC5s6d2yEzM3OrUophw4b1mzx5clF8fLwjJycn5OWXX855++239+7Zsyfw0Ucf7ZKZmbk1Li7OMXr06LT+/fuXAvzmN79JuuOOO46cd955xdnZ2UHnnXdeyq5duzYDbNiwIWzlypXbIiIimm2eXitsjUajaYe4rJy1VRYuXBhxwQUXFLh6uhdeeGH+ggULIq+44oqCzp07V0yePLkEYPHixeFnnnlmUZcuXSoBpk+ffjwrKysEYOnSpVHZ2dmhrjyLi4ut+fn5FoApU6YUNKeyBq2wNRqNpl2SW2Sjb6fIZimrpp5wU6GUd10aFhZ22nC1t1EGpRRr1qzZ6kkxh4eH+3zIuzb0HLZGo9G0Q/IKbU25pcvvTJo0qfjrr7+OKSoqshQWFlq+/vrr2LPOOquoarrx48eXrFixIvLw4cNWm80mn376aawrbuzYsYWPPfZYouv3smXLQque35zoHrZGo9G0M8oqHBTZKtv0lq6xY8eWzpgx49jQoUP7AVx77bV5Y8aMKdu+fXuQe7oePXrY77nnnoNnnnlmv4SEBPvAgQNLHQ6HAMyePXvfjTfe2D01NTXd4XDIyJEji0aPHr23trKHDRuWtmvXrpCysjJrx44dB77wwgs5l112WWFj6yQ1DRu0N4YPH67WrFnjbzE0Go2mSdl7rJTxTyzg8csH8ovhSY3OT0QylVLD3cPWr1+fM2jQoKONzrwdsn79+vhBgwYlVw3XQ+IajUbTzji5B7sN97DbIlphazQaTTujGcySapoArbA1Go2mnZFbqK2ctUa0wtZoNJp2Rm6RjQCLEBcWVHtiTYtBK2yNRqNpZ+QW2YiPCMZiaXorZxrfoRW2RqPRtDNyi2x6OLwVohW2RqPRtDPyimx6hbgXGutec9myZaGDBw/u26dPn4zU1NT0l19+Obb2s+qGNpyi0Wg07Yy8onIGJ0X7Wwy/43Q6UUphtVobnIfdbicwMPDk74iICOecOXN2DxgwwJaTkxM4YsSIftOmTSuMj49vnB9PdA9bo9Fo2hWVDifHSipIaAdbuvzhXnPgwIG2AQMG2ACSk5PtcXFxlYcOHfJJ51j3sDUajaYdcbS4AqWa2WjKZzcnkbvFp+41SUwv5dLnW7R7zQULFoTZ7XZJT0+3+aLKWmFrNBpNO+JYiaE74iPa9pYuf7vX3LNnT+D111/f69VXX93dmCF3d7TC1mg0mnbEiTI7ANGhzaiwa+gJNxX+dK95/Phxy/nnn9/ngQceOOB6MfAFeg5bo9Fo2hEnSl0KOxClFP+c/x1F5eV+lsr3+Mu9Znl5uVx44YV9rrzyymM33HBDvu9qpBW2RqPRtCtO9rDDApn7+Sdcs+QWHnvmCT9L5Xvc3WsOGzasn8u9ZtV07u41x44dmzpw4MBSV9zs2bP3rV27Njw1NTW9d+/eGc8991xCbeW+9tprsatXr46YO3dufN++fdP79u2b7is/2tq9phvavaZGo2nrvLRoJ//6Zhub/n4es5/9K3cUv8gbAVOY9df3G5yndq/pW7R7TY1Go9FwosxOgEUID7IiDmOEuL99V41zvpqWgVbYGo1G044oKLMTHRqIiBCqjPVQA9jFgjWr/CyZpja0wtZoNJp2xAlTYQNEmT3sYKlkxcIv/CmWpg5oha3RaDTtiMIyO1Gmwo5xFnKUKABiK/b7UyxNHdD7sDUajaYdcaLMTly4sQc7wVHATmtXTlgiSAna62fJNLXR6nrYImIVkZ9F5Evzd5yIzBeRbPMz1i3tfSKyQ0S2i8h5/pNao9FoWgYFpaeGxDuqfI5ZonAEx3Jmjy5+lkxTG61OYQO3AVvdft8L/KCUSgF+MH8jIunAlUAGMAV4QUR8Yx9Oo9FoWimuOezjhYV0pICCgEhSb/mGiF+87W/RWgSNda+ZlZUVlJGR0a9v377pffr0yXj88cdr3btdV1qVwhaRbsCFwCtuwVOBN83vbwKXuoW/p5SyKaV2AzuAM5pLVo1Go2lpOJ2KwnJDYS9Z/D3BYqfEEg4h7dPVptPpxOFonNdLu91+2u/u3bvb16xZs23btm1bMjMztz799NOdcnJyAr2cXi9alcIGngLuBtxtuHZUSh0CMD9dZuS6Au72a/ebYachIjeJyBoRWZOXl9c0Ums0Gk0LoMhWiVKGWdI9uzYCUGFpu242/eFeMyQkRIWGhiqAsrIycTq9mhyvN61m0ZmIXATkKqUyRWRiXU7xEFbNMoBSajYwGwxLZ40SUqPRaFow7nbET9gMM9dBFp9YzayR+5fen7Qjf4dP3Wv2ie1T+tCYh1qke80dO3YEXnDBBSn79u0LfuCBB/YnJyfbq6ZpCK1GYQNjgEtE5AIgBIgSkbeBIyLSWSl1SEQ6A7lm+v1Aktv53YCDzSqxRqPRtCBOeeoKJMBpmMzuHJNY0ymtFn+61+zTp489KytrS05OTuDFF1/c55prrslPSkqqbGydWo3CVkrdB9wHYPaw71JKXSMiTwDXAY+an5+bp8wD5orIk0AXIAXQpnw0Gk27xV1hRzgNK2dnnDGpycutqSfcVPjTvaaL5ORke1paWtn3338fef311zfac1drm8P2xKPAOSKSDZxj/kYptRn4ANgCfAvcrJRq3OoCjUajacW4FHZMWBDRjiLyiCKx7/Bazmqd+Mu95s6dOwOLi4sFIC8vz7pmzZqIjIwMn/gvbTU9bHeUUguBheb3Y8BkL+keBh5uNsE0Go2mBVNQVgEYPex4ZwG5EkuC1ScLmFsc7u41AVzuNbdv3x7kns7dvWZCQoJ94MCBpQ6HQ8Bwr3njjTd2T01NTXc4HDJy5Mii0aNH12hhZsOGDaH33HNPNxFBKcUtt9xy+Iwzzqjm1rMhaPeabmj3mhqNpi3zwsIdPP7tdrb+Ywo7HxnKMWs0E+5f3Oh8tXtN36Lda2o0Gk0750SZnSCrhSArdFTHOR4Q5W+RNPVAK2yNRqNpJxSW2YkOC2TrzmwSpJBCa7i/RdLUA62wNRqNpp3gsiOeufQHAMotPt0arWlitMLWaDSadsJJO+LHDVeaTmm7Vs7aIlphazQaTTvBpbBxGLubwoMi/SyRpj5oha3RaDTthBNldmJCAwk2rZylJvX2s0Sa+qAVtqbJyFy3nhdefc3fYmg0GgxlfehEOd1iQ4l0FlGuAhky7gJ/i9XiaKx7TRfHjx+3JCYmDvRFXi60wtY0GZu+/he/2ns3//jnn2o0E6jRaJqe5TuP4nAqxqYkEOsoJFdiCI7r5m+x/EpTuNd0ceedd3YdOXJkNctqjUErbE2TEecsIFjs/MX+Mv96+HZ/i6PRtGsWZR0lIjiAId1jiHeeINcSC15saLcV/OFeEwxPYXl5eYHnnHNOoS/r0ypNk2paB5HOUnbQhaNB0fypYg5ffTaKCy+90t9iaTTtDqUUi7PyGNW7A4FWCx2d+WQFJdV+oo84+Oe/JNmys326hyw4JaW0yyMPtzj3mg6HgzvvvDNp7ty5u77++mufWqbRPWxNkxGpSsm1xLA1cjSB4iBr2yJ/i6TRtEt2Hy3hQEEZ41MTKC4tIZF8Cqxte4W4u3vN6Ohop8u9JoA395ohISFq+vTpx115LF26NOq2227r3rdv3/SLL764T13caz722GMJ5557bkGfPn184gPbHd3D1jQZ0aqEXdYubI27jIPHP2OAbZu/RdJo2iVLsg2T3uNT4lm2Ygnnio1iS/NZOaupJ9xU+Mu95ooVKyJWr14d8frrryeWlpZa7Ha7JSIiwvHCCy8cqF8NqqN72JomI1qVUGwJ5YNNBSwL7c9Y50Yyly/xt1gaTbtjcVYePTqE0aNDOLu3/QxAudTqKbJV4y/3mvPmzdt96NChjQcOHNj497//ff/06dOP+UJZg1bYmiairKSUaIops4QwuncHDlk6EyJ2Fi760N+iaTTtiopKJ8t3HWNcSjwA5WX5RoQl2I9SNT3u7jWHDRvWz+Ves2o6d/eaY8eOTR04cGCpK2727Nn71q5dG56ampreu3fvjOeeey6heWtxOnpIXNMkbNm0mmHioMwSwu8m9ua2l0dzbdgXpNiz/S2aRtOuyNyTT2mFg/Ephq5xOssBCLK2fbOkDz744JEHH3zwiHtYWlpaRXZ29mb3sNtuu+3Ybbfddqzq+Z07d6786quvdlUNf/LJJw/Wpfxbb731GFAt34aie9iaJmHn9g0AVBDMiOQ4SoMTWRo8gAmV69izq1r712g0TcTi7DwCLMKo3h0AsCobALERsTWdpmmBaIWtaRKO5ecCYCeQkEAro3p1YE9gEtFSygcfvehn6TSa9sOS7DyGdo8lMiQQgCCnobB790jxp1iaBqAVtqZJqLCXAKAwHhIT0xL58lh/ylQQSRU7/CmaRtNuOFpsY9OBQsanxp8MC1HlVCoL6cPH+VEyTUPQClvTNJhv8RarsahyQmoCW1QKy4MymGBfx5bNWzyeppTi088/5al//JpP/nYh2zevbzaRNZq2xtId5nau1FNrpcKcZZwgnOCYTv4SS9NAtMLWNAmuebKQUGOeLDk+nB4dwsgO7UVnOc76j/9KRUV1uwL/98/fM3nt77nd+QHT5Se+/lwPn2s0DeW299YBkNEl+mRYhLOMExLR5s2StkW0wtY0CUFUABDfrd/JsAmpCTyVfzkfR07gKucPPPnEHaedU1iQzx8qP2RnQBfe6zidDZZeXGb7nn27dzar7BpNW6CswnBqERpoxWo5pZyjnKWckOYzmqLxHVpha5qEUGc5FWRN9mIAACAASURBVMpKcr+RJ8MmpCZQZleEj7yfVYF9ub3iXR77v3+ejF/03aeEiJ3Vwf258nevszJqKN0lj/ff/Y8/qqDRtGpW5xgWNv977bDTwqNUCYUWn5r1blP4wr2m1Wod1rdv3/S+ffumT5o0qY+vZNMKW9MkhKkyCgmnY0LMybBRvTsQZLWQeSKc4n7Xkm+JZEbRG8z79AMA9h4w9mhXmA+TK2Y9wnZLN6bafiQv73DzV0KjacUs3XGUQKswIvn07VvRqphirbCBpnOvGRwc7Ny2bduWbdu2bfnxxx99tsq2yRS2iISLiLWp8te0bKzKSSVWYkIDT4aFBQVwRs84FmXlMWn6LczvMIVE8olZ/ywHD+ynwm5YDQwOMubbYmI6sjhyBClygNdeedQv9dBoWitLdx5lSPdYwoJOt48VSzEllrZtltSFv9xrNhU+s3QmIhbgSuBqYARgA4JFJA/4GpitlNJmrtoRCiEs6PR3trP7JfLgF1tYnJXHzFte5K2n85mZ/w2vvXoXwYGG5aWU3hkn01961YPsfmk5F5YvoLAgn6gYbexBo6mNgtIKNh8s5I9np54WvvfgAbpLKWWW5rVy9sNbW5OOHyj2abc+rmtE6eSZ/Vqce02AiooKS//+/ftZrVZ11113Hb722msLfFFnX/awFwC9gfuATkqpJKVUIjAOWAE8KiLX+LA8TTOzavdxPs7cT9aRavbzvVLVC86VZ3SnZ3w4D3y+iXK7g1/89lW+iBjFDc5v+EX5D5SpIEZOmn4yfUKnZBZEnUF/yeGFFx/2WV00mrbM8p3HUArG9OlwWvjGzKUA2KRt2xEH/7nXBNixY8eGTZs2bX333Xd33XvvvUmbN2/2yQX3pS3xs5VS1QbzlVLHgY+Bj0UksPppmtZAsa2SX85eTrAqJsii+OWYQdx5biohgZ5nPQSFp5YcEmjloan9uebVlby4cCd/PCeVsTe8xsdv/obLTixmF53pFRqOw6mwO5yEBFqZdNGdHHhnGWfbFlJptxMQqJuRRlMTS3ceJTzIysBuMaeFHzpgmAWulKBmlaemnnBT4S/3mgDJycl2gPT09IozzzyzaNWqVWEZGRm2usruDZ/1sD0p64ak0bRMSm127gj7mGXBd5AZ+HsuXnkVnzxyBQ/+628e0wsK5eVPMDYlnksGdeHFhTvZlVdMbFwXpv7hY97ucD6LY4dx9pOL6Hf/twz/5/fkFdlIThnMdxEjGU42r730f01ZTY2mTbB0xzFG9upAoPX0R3xJqTEyq5pZYfsDf7nXzMvLs5aVlQnAoUOHAtasWRMxcODAal7CGoLPFLaIFIlIoXkUuf0uFZFKX5Wj8Q8/L/mKPzg+JiegE/Oix2ILDuIStZQ/lb/IurVrvJzl3TDDXy/qR3CghQc+34xSioCAIK66+V0eOnI1ARZhxsjuFNsqeW/VXgBiEgcA4Cja7uuqaTRtioMFZew+WsLo3h2qxTkdhufIQGvbHxL3l3vNdevWhQwaNKhfWlpa+oQJE1Jvv/32w8OGDSv3RZ18NiSulIp0/y0ikcDvgd8An/qqHI1/sNuMNrwqaAC/veMNAF7492/5fdG7zJ8/h8FDh5+WXsDjkLiLxMgQ7j4vjfs/38y89QeZOrgrRwrLcTgV147qwdUje7Azr5h3Vu7ldxN7M/Wae9jy0LsMt3k2aarRaAxc5kjH9ImvFmdRhkGjqLCoZpXJX/jDveY555xTkpWV1SQPKp9v6xKRGBF5EFgPRAIjlFJ3+rocTfPi9LBX8ewLb+EE4aRWVF/8b8xh12z6cMbIHgzqFs0/v9rKiTI7BwuMl9+uMcao08xRyRwuLGf+liNYLBbWhqYxVGXx1cfv+KBGGk3bZNnOY8RHBJHWMbJaXJBpMji5a6/mFkvjA3w5JB4vIv8C1gKVwBCl1F+VUj5z3q3xP+695tS+/fkpaADjK9ezb++eGtN6wmoRHp42gGPFNh77dhsHTIXdLdZQ2JP6JtI1JpS3lht528OSsIoiK/snX1RFo2mTrNh1jDN7dcBiqf7CHOIsx6mE9CGj/CCZprH4soe9B7gKeBMoBX4lIne4Dh+Wo/EDTuXqYZ/+ENgT3INYKeb9956tckZt6tqgf9dofjW2J3NX7uXVn3YD0MXsYVstwjVn9mD5rmNkHSni8mv/yiHiyKjIakxVNJo2zdFiG0lxnrc8h6lyCgkjqnPvZpZK4wt8qbCfAF43v0d6ODStGKfDtYPhdIXdZ+A0jz6uRVHrkLiLu6f0ZUyfDmzYf4LYsMDTLDP9ckQSQQEW5izfQ2R0HMtDMhjj2Mi2dasbVR+Npi3idCrsDkWQ1fOjPdxRSoFEgEVbpW6N1LjozDQt+qZSqlaDJ0qpB30llKblcWpP4+k957MnT2HBqv5MqFhH/vECYuNO7fusq8IOtFp4fsZQpr2wjPiI07ebxIUHcfHALnyydj93T0kjN7gb4eVL+PJ/79J38IhG1UmjaWtUmC/WQQGeFXKk0p66WjM1vmYppRxAgkjdN+2JSIKI/FlEZovIa66j0ZJq/IpLYVfdW22xCFnBPekk+bz+2uMnw6WOQ+IuYsKC+PyWMbx07fBqcTNH9aCkwsEnaw9w9gW/oliF0MOuXW5qNFVxKexgLwo72llCoUUr7NZKXcZFcoClInJ/HeekPweige+Br9wOTStGKa9GfYjoPAq7shLvNixel1XiVYkKCSQuvPq74aCkGAYlxfDm8hx6pw5nRVAG4+zrKcrX6xk1GncqKmvuYUerEu2pqxZ84V4zOzs7aMyYMSm9evXK6N27d8b27dt9YqmmLgr7IPClmbYuc9JhSql7lFIfKKU+dh0+kFXjR5w1KOzzp85kZUA/xtnWUVpy0uZAvRV2TVw5IoldeSVkHSlmZ0gynSSf117TfrI1GndOKmwPc9gfz/+GLhyjMFD3sF00lXvNq6++uuddd911ZNeuXZvXrl27tUuXLj4xHlarwlZK/V0p9XfgSeDfbr+98aWIXOAL4dwRkSQRWSAiW0Vks4jcZobHich8Eck2P2PdzrlPRHaIyHYROc/XMrUnvKtriI8IZmtob3rKEV579d9ATTbOGsbENMPA0KKsXFJTx+FQQqStmj0DjaZdU1MPe8eabwgWO5VBcc0tlt/wh3vNzMzMEIfDwbRp0woBoqOjnZGRkTU9QutMrZbORKQ/MAeIM38fBWYqpTZ7OeU24M8iYgPsmEavlFKNNa1TCdyplFprWlHLFJH5wCzgB6XUoyJyL3AvcI+IpGO4+8wAugDfi0iqOS+vqSfiZZW4i4qQdJxF8wgpdpkO9ez8o6F0jg4lrWMki7LyuOnG61m97kXOtG1CORyIVbtd12ig5kVnw2wbOUQc0y+6obnF4n8vPpV0dN8en47Fxyf1KD3vd7e3OPeaW7ZsCYmKinKce+65vfft2xc8fvz4wueff35/QEDjDYvWZUh8NnCHUqqHUqoHcCfwsrfESqlIpZRFKRWqlIoyfzfaDp5S6pBSaq35vQjYCnQFpmLs/cb8vNT8PhV4TyllU0rtBnYAZzRWjvaK02k8CLwp4ZEX3cTP1j6Mtm1AKWWaJvVtP3tCWgKrd+dTYqtkY2gK6bKHOa8959MyNJrWjLch8Xe/+pxxagNLwwYQ2nu0P0RrdvzlXrOyslLWrFkT8dRTT+3bsGHDlpycnOBnn322up3YBlAXlR+ulFrg+qGUWihSfV+AiCQrpXK8ZSKG/7KuSqn9DZK0SlnAEGAl0FEpdciU7ZCIuDyrdMXww+1ivxlWNa+bgJsAundv1DqDNo2i5h724KQY3gxL41fFX/Lqy/8hSdV/0VltTEhNYPbiXazYdYzQ6D5QDIXHNvi0DI2mNePqYQdW6WHv3/AdwVKJPbATePGi15TU1BNuKvzlXrN79+4V/fr1K0tPT68AuOSSS/JXrFgR4SltfalLD3uXuUI82Tz+Cuz2kO4JEflYRGaKSIaIJIpIdxGZJCIPAUuBfo0VWEQiMPxr366UKqwpqYewahddKTVbKTVcKTU8IaFWRyztlhraPgABVgsFGC88tmMbjXN8LMPw5FjCgqws3J7HZdf9hR3ShSG2bT4uRaNpvbh62MFuPWyn08kI20b2SQLTp/3GX6I1O/5yrzlhwoSSEydOWA8ePBgAsGDBgqj09PRmc695A5AAfGIe8cD1VRMppa4A7gfSgOeBJcA84NfAdmCSUmp+Y4QVkUAMZf2OUuoTM/iIiHQ24zsDuWb4fiDJ7fRuGCveNQ2idvWbNP53bJEejLRtNEN8+yYfHGBldO8OLMzKJTAwkNWh/TjDuZWfvpvn03I0mtaKp0Vn73z2EWPUJpaFDSA4eZi/RGt2/OVeMyAggEcffXT/xIkTU1NTU9OVUvzxj3886os61cXS2Z+VUrfWJTOl1BbgLx7yCVRKVV/7Xg/MIfVXga1KqSfdouYB1wGPmp+fu4XPFZEnMRadpQCrGiNDe6a2OWyA8WmJfLeoH9cU/4+fHX2aRI4JqQl8vzWXnGOlFAV3I7DUwcq13zH23EuapDyNpjXhSWHnbV9AoDiQwI7+Estv+MO9JsC0adMKp02b5nMXm3WxdNagVzIxmCQir2D0dhvLGOBaYJKIrDOPCzAU9Tkikg2cY/7GXMX+AbAF+Ba4Wa8Qbzin5oO895o7RYeQ5+iMRRRD1A6fD4kDTEg1RqcWbc9l+pV3c5Qo0qrYMddo2itVV4k7nU7OsG1gj3Tk0itu9qdoGh9QlyHxn0VknohcKyLTXYe3xCIyUkSexvDeNQ9jaLxvYwVVSv2klBKl1ECl1GDz+FopdUwpNVkplWJ+Hnc752GlVG+lVJpS6pvGytCeqesmwvK0meyWTljE94vOALp3CKNnfDiLsvKI79iN5cH9GedYz94dei5bo6m6SvyND99hlNrMsrABBHUd4E/RND6gLgo7DjgGTAIuNo+LqiYSkYfNXu4jwEaMVdx5Sqk3lVL5vhNZ4w+kBktn7pw1oDsrQjIA32/rcjEhNYHlu45RbndwICSJaCnlw09eaZKyNJrWRNUh8crN32IVRWBQJ3+KpfERdZnD3qCUqosNyJswFpe9CHyplCoXkaYYFdX4gZPOP2pJNzw5jpWqU53SNpQJaQm8sSyHVbuPM3rMFZR/9Qmd7Z42Lmg07Qub25D4wWN53GT5EoBpV9/pT7E0PqIuc9h1Xc3TCXjYTL9DROYAoSLSePMuGr9zym5Zzb3moAALW+Iu4xBxtaZtKGf27EBQgIVFWXkMPOMcVgamM7ZiPeXF1XZsaDTtilPbuqzMeeN5AD6LGos1vpc/xdL4iLoMiS8TkedEZJyIDHUdVRMppRxKqW+UUjOBPhirtZcBB0Rkro/l1rRgxg/sw7cxo1kb0+ilCx4JDbIysmcci7LyANge2ovuksdrr2pnIJr2jfuQeGL5NiqVhe6dR/lZKo2vqIvCHo1hj/sfwL/N4/9qOkEpVa6U+kgpdRnGdqr/NVZQjX9RzrovsJ+QksDfD8/gHflDk8kzITWBHbnF7M8vpWuS8f4YUJLdZOVpNK0Bl8K22csYV7Ge1QF9GXq5Hg6vD411r/nFF19E9u3bN911BAcHD50zZ06ML2Sri7euszwck7ylF5HOIvJHEXlWRO4HOiml3vSWXtM6qM98dPcOYfSKD2+iAXGDiWnm9q6sPC78xa2st/RiRMVmlNMnTnE0mlZJhcOB1SK8+vpz9JGDbAnrDYG1GudqtzSFe82LL764aNu2bVu2bdu2ZdGiRdtDQkKcl156aU1WOeuMV4UtIk+5fb+tStwbXs65FXgD2Ilh7WwR8LiInC0idenNa1oqqmZb4lW59/y+3DiuZ+0JG0jvhHC6xoSyaLsxLL4uNI0h7OSzuV790mg0bZ6KSidBVgsRhYbNjp5xyf4VyM/4w72mO3PmzImdMGHCieZwrzne7ft1wNNuvwdWTSwiFwJnAlOAKzjlGesb4M9ATxHJVkotbIzAGv9Q3xXf52Y07TYSEWFCWgLz1h2kotKJhHWHEti7b22TlqvRtGQqKp0EWBWjbBtZb+3FpKvu9rdIABz/KCvJfrjEp+41AzuFl8Zdntri3Gu689FHH8XddtttR7zF15eaer3i5bs3bsXwV62A4RhuLsOAczG8an0K3NFAOTX+xmySqvkd/XhlQmoCxbZK1u7N5/Lr72cvCQyo0AZUNO2XCoeTMbKWgbKLn0P7QkijPRu3WvzlXtPFnj17Ardv3x46ffp0nwyHQ809bIuIxGIoddd31+Pa6iF9osvNJcZCtXFKKSUiLwFLlFL3iUg195aa1oHTZeusBe2sH927AwEWYVFWHmf26svKkAwuLlvK+mULGTR6or/F02iaHVulk4ygXWCD2LDO/hbnJDX1hJsKf7nXdPHWW2/FTpkypSA4ONhnT82aetjRQCawBogC1pq/M4FID+mLRcTlpPsEcJGIBGFYRSsyfWiX+0pwTTNzssm1nC52ZEggw5NjT85jHwvuRojY+X7xp36WTKPxDxWVTkbYNpMtXbn42nv8LY5f8Zd7TRcfffRR3IwZM47XnrLueFXYSqlkpVQvpVRPD4enXfhvYMxVgzHnfRbwmfl5HcZw+Lu+FF7T/Hh5EfUbE1IT2XKokNzCci689GYKCaOnfae/xdJo/EJFpZOBahc/B6ViiWp/3rnc8Zd7TTAWth06dCjoggsu8Kk1J19aIXsNeEdEHgEeUUrdASAiERh7uHsAl/uwPE1zUkfTpM3NhNQEHvt2G4uy8rhieDrfBvVnvG09xw7uo0OXpNoz0GjaEGVlZYRQQbkE+1uUFoG/3GumpaVV5Obmbmio3N7w2VYrZTADw5745yKyUER+wLB4thW4XNU0qaBp0SjV8uawAfp1jiQhMvik1bOc4O7ESyFvvfO8nyXTaJofVX4ciygqxdMyI01rp6Z92F+LSHJ9MzS9c01WSk00PycrpV7Wyrpt0FQeuBqKiDAhNYEl2UdxOBUDh5yPXVmJqzCdgVTaWPz5W7w7+xnjt70cyrTzOE3bJLziKAAOj+uCNa2dmobE3wC+E5E3gceVUvYa0iIiy4G/KKV+9BD3g1JqcqMk1fgVZwt+3ZqQmsBHmftZv7+A0ZMuZ/nSJxldsZFH/vV3etjWc7FazmAUa3/qy/xFX5Fu38720JHcccutWMI7+Ft8jcZnhFQaO4gc2k5Vm6SmRWcfYPi0jgLWiMhdInKH6/BwSnfgORH5PxEJrBIX5zuRNf7Abprva1n9a4NxKfFYBBaaq8U3h/YmRQ7wZ9uTXM5itgT3IErKWPDTl5xVuYKLWc4fS5/mkydm8fZz/wJHje+iGo1f2XKwkPdW7aXSUbuxrBCnsV7KqXvYbZLaXsPsQAkQjLGVy/2oyhEMgykxwEoRSXOLa8H9M01dKLObCrulLRMHYsKCGJwUc3IeOzllPAtDB/Fu3GR+HHgnXa9+nULC6FOxg/7O3XwTPJIvosZwCUuZnvcfHvvXHZQfzfFvJTQaL7ywcAf3frKR6S8uI/tIzYuOrcoGgNJz2G0Sr0PiIjIFeBKYBwxVSpV6S+vCTHOjiEwD5ovII0qp/9IyO2ZtDodTYRHfK1WlFCEYQ21RoZ7e1fzPhNREnvohi+MlFZw99dcw9denxX8blMH5thUEiYOcwO789o6Xef+1O+h9eCn32N/ivRf2c/mf3iKghdZP0345fKKcLtEh7M8v48JnfuLuKWncOM6zf+tAqQDA6bv1xJoWRE139S/AFUqpe+uirN1RSn0KjAIuE5F5QEQtp2gaSUWlk/OfXsydH6z3ed5ZR4rpXrmfAhXO5dfc5fP8fcGEtASUgiXZeR7jc4J7ECTGKEFkdDdEhCt/9R9ir3qJz8LHcqXzR55+5qHmFFmjqROHC8sZ0TOO7/44nnEp8fzzq63VetplFQ7sDicBVJohWmE3lMa61wT47W9/261Pnz4ZvXr1ypg1a1aS00deBGuawx6nlNrsLd4DuVXOP6CUOgdYAugNsU3M8wt2kHWkmE9+PkB+SYVP816clcsQezbrAlMIj6mT3YBmZ0DXaGLDAk8Oi1elb8YkKpWFAhXOpVeecj7Xp9cQek6+izyiObPsJxxlxc0lskZTK0opcgttdIoOIT4imH9c2h+gWju//L/LeODzTVgtpmLQQ+J1oinca86fPz981apVEdu2bduclZW1ed26deFff/21T4bufLkPe4qX8CeUUiG+KkdTnc0HT/D8gh307WS0ic/XHfBp/ruWf0ZPOcyuoG4+zdeXWC3C+NQEFmfl4fSwpH3ilKtZGjKA1aH9iIiMPS1u0NCz+DJyLGPYrHvZmhbF8ZIKKhxOOkUZj9CuMaGkJEacXGAJkFtUzuaDhXy76TAWXItDtcIG/7jXFBFsNpuUl5dLWVmZpbKyUrp06eKTla2+tHRWDRFZq5Qa2pRlaODtFXsICbTy3k1ncs2rK/lgzX5mjfGNL+qKSidxyjD04whKrCW1f5mQmsDn6w6y5VAh/btGV4vvdtV/wOL5HXXw2Os4+s0SRpQtRVWUIkE+9QSo0TSIw4WG+wWXwgajnb+1fA+lFZWEBQWwerdhVyC/1I41xuhhSwvrYX/22WdJubm5Pv1TJSYmll566aUtzr3m2WefXTJmzJiizp07DwKYNWtW3tChQ33iR6OpJzr0YrNmwFbpJCYskJiwIK4YlsSWQ4VsPnjCJ3nvOVZCN8chSlUwF0/7jU/ybCrGpRjD9d6GxXsnD6N39yEe44aMPI8vI8cyjo089dQ/mkxGjaY+HD5hPOc7Rp9S2BPTEqlwOFmxy7CkuTrnOMEBFkRATK96FkvLUtj+wF/uNTdt2hSclZUVsn///g379+/fsGTJkshvvvnGJ+u4fN7DFpFbgLeVUgXAV77OX1MzUwd34eGvtvLhmv1kXFK9l1lfdh8tYaB9B+sDejOqR18fSNh0JEQG079rFIu253HzWX3qfX76qBkc/24xQ8uWoirKkKA6O+bR+ICN37zEtuwlXHHzG2Bt0sG/VoOnHvbw5FhCA60s2p7HpL4dWbX7OMN6xFJiq8RSYijsAGuQX+T1Rk094abCX+4133///ZgRI0aUREdHOwHOPvvsE0uXLg0///zzG71Apil62J0wDK18APwkLXHjblvDrSnFhAVxTkZHPl93AFtl4xZTAGzOXEI/tZfsoEYtmmw2JqQmkLk3n8Ly+k8ZnTH6Yr6IGMcEtYFnntZz2c3N+o3fc8XxL3jz2Zv9LUqL4ciJckSMl1EXIYFWRvXuwKKsPArL7Ww7XMjw5DgmpCViNXvYQQHa+Ye/3Gt27969YunSpZF2ux2bzSZLly6NTE9Pb5lD4kqpvwIpwKvALCBbRB4Rkd6+LktzCvfXoiuGdSO/1M4PW3O9n1BHKg5mYhFFoTW29sQtgIlpiTiciqXZRxt0furwX5JPBANKl6Hs2n17U7Pj+7f48b+Ggu5pMxwgjSxcSsEu329PfPfFO9nxUDrfz33C53k3FYcLy0mICCbQevqjekJqAjnHSvns5wM4FZyRHMeE1ISTQ+KhwXqdr7/ca15//fX5ycnJtrS0tIz09PT0jIyM0hkzZvhkjrJJxp2UUkpEDgOHgUogFvhIROYrpe5uijI1pxiXkkCnqBA+XLOPCwZ0blRegWIYTAkNavzwenMwJCmGyJAAFmXlcX4D6j5q4jTeWvMeM4u/5dmnH+IPdz3cBFJqXKxY+wWXlP7EgY1X0s+Rwx6VSF/nPt747DFm3TG31vNXffA45WWFjL/un7WmDc7Poo/jAMv2r/GF6M3CYXNLV1Umphl6459fbsVqEYZ0jyE00MpKMRR2eFh4s8rZUvGHe82AgADmzp27pzFye8PnPWwRuVVEMoHHgaXAAKXU74BhwGW+Lk9T3e6r1SJcNqwri7LyOFLYuF5ipDJGkAYPGdeofJqLAKuFsX3iWZSVR6XDya68Yr7bfNirQRVP9BxyGYWE0bdkOcpua0JpNcGVFURRyjffvUIcxcwLncBiBjC98EcWzX2s1vOLsr8mcc9nJ/2114TdXDk9sDwb5SNDFk3NkRPldIyqrrB7dAjnlZnDGZ+awDUjuxMeHIDFIliVaRwoSju1aYs0xRx2PDBdKXWeUupDl5cvZThUvqgJytN44PJhSTgVfLK24XuyyyocxDkKOKYiGTau9dy6CakJHDpRTr8HvmXSvxdx05xMrnttFceKbeQV2dh0oObRqXGTf8G88LGcozJ5Qe/LblJcc67ji41erzO4I5mJlxGs7JTu/R7lqKzpdLrZ8+jr3Mf8D56utazOlUYHarBzJ3P/e08jJW8eDp0oO23BmTtnp3fkleuG8/ep/U+GufZhd4jv2CzyaZqXppjDfkAp5XE4QCm11dflaQykyg66nvHhnJEcx4dr9tW4WrImco6V0LnyGPssLXv/dVXOH9CZK4Z144axPXni8oH83xWDcCr4acdR/vnVFi569if+9c1W7DV4P+o2YCqFKpTexStOefNyOsn86ElK929pppq0fSzKuAepaj92ZeXs867kj7//I3MCz+P88lW8+czvvZ6rnE46KWMP8s59G2stq5sjjxX0w6YCCCrK8k0FmpCyCgeF5ZUeh8S94ephd07yjR0GTctCG5xtA3hTyJcP78auoyWs3ZvfoHxzjpaQ5MzlYEB8Y8RrdqJDA3niikHcd34/rhiexPQhXYkLD2LR9jxW7z5ObFggLy3axYyXV5zc51qViVOu4YuIsUxRq3nRXDH+ytN/I2Xj47w+59/NWZ02TQCndjJslyQy0gcAkHbObexX8YwqWsrxXetRZQWo0tPb8aZl3xItJQB0th+qsZxjB3aTpHLJCu7BD9ZhnF22hj2bVvi4Nr7FtaXL05C4N6w4cCghJrHlWiXUNBytsNsQL89+jDlvP3fy94UDOhMWZGXuPWt6hAAAIABJREFUyoZtgdyWtY0uHOVoQIyvRPQLFoswLiWe/20+zMET5fxhUgpPXzmYzQcLueCZJazbV+DxvMR+F1GsQhhQ+APfvvIIows+J0rKGGnbUKc5U03tuHqEAFkBp1wOjBs5krdDLibNuZ+PPn2Oz56/hi+fn3Haues3GArXpgIYY9vIB09NY+6zv2RP5v+qlfPD1+8QKA4KLFFkWgcQSzHffvdyE9XKN7heJjvXo4cdoBxUEIglQO9jb4tohd1GiLHt5dcHH2F69j8oKjFWdocHB/DLEUl8vHZ/g+yLl+1chFUUJZbW73JyQmoCJRWGchjaI5apg7sy75axhAdbufrlFazcVW2BKOdcNIsPYiYzWm1m3L6nSJc9rLamMURls2jenOauQpskACc5qiOZzhS2B/Y7Le6yX/yBEhVMT9suLixaxvnFK1j8wbMn40+UGT3udwPOplJZ+UXBj8w49i2LfnytWjl5Jw4DUOKM4IOScexVCQwuqY9vo+bnSAN62C6FrWmbaIXdBlDAecGLAQgXG6/894GTcfed348zesbxp482kLnnuJccPBPoNB6Iytr6FbbLbGlwgIX0zlEA9EmM4MPfjKZTdAg3vrmGE6XVja3MvPUtXutwOQWWCN6LmERm1Disovh52/Jmlb+tYlEOSiWY3vcu5Z4/PX5aXErv3qyxpHFOxRqCxEGAOMneu/LUuU5ju6x0GkHJzRt4ZfSXbFE9SCvPqVZOgDKMTNmCkrhmfF++CR7NSMdWPpp9f9NVro7kFpazOqf6f/OklbN69LADlZ2KpnUR0ebxhXvN3/3ud11dTkdefvllnxmx0Aq7DeAs3sfU0oVskmQOEseY4mVU2A0Xm0EBFl66ZhhdokO46a1M9h2vu2vzMDG2dPXo2PoXsCREBjOkewzDesQSFHCq2XeKDuGZq4ZQZKtk7qq91c4LsAZw462vUHLDx1x48xtcdvWdHCWKlIpqWzM1DSBAOXGIlZiwYCwWqbYeY2tQLwAySWGz6sGI0s0o0x1iiKmwD4Zn0DsxihvPHcfaoDQGV+5g97olp+UTW1lAiQomut9krh+TzOqyflQqC/YC//ayV+w6xvlPL+EXLy0nr+j0LYSHT5QTERzAnDnP8MgT99Vp8WigclAhuoddV5rCveZ7770XvX79+rAtW7ZszszM3Pr00093On78uE90rVbYfmJ/vmGlaPbinfxnfhbFtpq3r9REyvEv6MZRFoaO48uw8ZyhtvPiM385GR8bHsSrs0ZQ6VTc8MbqOpntLLZVEuMopFwFMumiaxssW0vilZnDeW5GdedxGV2iGdsnnteX7vZqzjU1aQiRodEkxHdhRWAGoys3kb83u6lFbvME4KDSdAX5UeZ+Rj7yA/vzT71U2sLTcCphQfBIFoUMY6BzFx/NNtp2tKOYoyqKN7dCud24b4cDuhEslfzvx/dOK6dj5XH2SEf6dE0gMTKETsMuYpFlMGeXruHwnubfvKKU4rWfdnP1KysJsApKweIqTmsOnyinY1Qw3Q7P5+7i//L4v++tNd8AKnUP2w1/uNfcvHlzyNixY4sDAwOJiopypqenl37yySc+sTyl76yfuPHNNWw7fMqs7fGSCh66tH8NZ3gn2b6fXBXDjb/6Mwd2bOLo1z8ypGQFSqmTRu17J0Tw4jVDmfnqKh76YgtPXDGoxjxzjpbQ0XGMvZJIanRcg+RqaXSI8G5f+abxvZj52irmrTvIFcOTvKYD2BPSnYvsy3nm/dnc+qfWY+ayJWJ1U9hLsvPILbJx+3vreO+mMwmwWrj1D/fx0AsduGXm1Xz1xYc4tv8/e+cdn1V1PvDveWf2XoSEhJEEwt6bgIBbUFFBcVdR61Zqa/XXqrWt1tZq1dpaFReKGxeoqCwZsleAJAQCJJC91zvP74/7Zr9ZkJAEzvfzySfJveee+7znvfc+9zznGZ9jLU8HINhRQrYIotrmZGtGIVPjQhk38TLsP76Fr71hWt5oRy5p+t7EBGsVHhdN7c97+4cz07qD/376PHc8dGYd0P6z9jDPfnuQ2Ynh/P3q4cz8x1rWpuYxb3Sdd3d2aTUR/h6ElxdgEE5uKVvGm+/149brm6+aZ5LdU2HvP/Db6Iry1A4tr+ntE1+ZOOjZbldec+TIkVVPP/10ZFlZWU55eblu48aNfoMGDeqeucQVrXMkv4KD2WU8NDuevU+cz82TYnnvl6NsP3pq4VcCsAgjHsGR9B9/Pl96T2Wacw8vv/h4g3aT+ocwd0Rvvt+fg8PZsnkto6CCKEceWfpWU+eeFUyNC2FghC//W3+4VdPjkOGzsEsd/ramJnRF+zBIB3ZXBrL9J0oJ8TGx7WgR//rpEKBVUfrD3XcQ5OvDDdfdwibdYKZW7KS6JI9QZxG5Oi2CYU2KNjudNHk6e0Q/EqvrliwKszKIkrnkGIKJCdJSdvYJ9uJE+ByyZSCDKg+eyY8MwI5jRfQL8ea/14/G39PItPgQ1qflNbgvc0qrifDzJEIWslv0x4cqhh56g92p+5rt1yjtyiTuoqvKa1555ZWls2fPLh47duzAefPm9R01alS5wWDokLCS7vcq1sEIIS4EXgT0wOtSyme6WCTWpmhv/1eM7I2vh5HFFyTwXXI2v/9sL1/fN6VJov/2MnLE5ZRuWM3AsqaOUdMTQvl0Rya7M4sZ1ad5X4i047nMkLnsNrS/TGVPRAjBomn9eOij3axJzWNGQvPJYpJmXcPWjX9nrPWAllRFrx6Qp4oBB9WYKLfYSc8r554ZA8gsruLln9KYMiCEcX0bWne2mIczpXopb775JJc7C0l2rXF/uiOT1Sm5HMmv4AnfAVxnWUXyz18xeMpl/LDyPa4RDop1/vh71X1Xd188hhVvTuIm6wq+eucZLruxdZNzR+F0SrzMenQ6zQKWFB/KZzuy2JtVwojoABxOSW6ZhUBTJRGykHUeI9liGM7t5Z+x9KM/MuT3H6F3U/PaiL1beom3NBPuLLqqvCbAs88+m/3ss89mA1x22WV94+PjOyTH8Vk9wxZC6IFXgIuAROBaIURi10qlJfQ36XVEBWqV2nzMBp6aO4SUnDJeW9d+ZybRKJv4yPOvYbnnVGY7tvPqK0812Dc1LgSdgLUpLefWLjm4Bm9hoVjfM4p+dASXDoskws+D/7XhO9jrEUciR/ns7VfOgGSdx/J/PcT7f2/exNrZGKRmEl+25RhOCYmR/jw1dwh9grx4YNnOJp77Y6YuoEqaCK9OI0iUU6L35bLhkfh5GOkf6kOoj5ks0RujcLD+l2+A+iFdDaMdBvXy45AYggCKcnackc9bg90p0ddTElPjQhH17suCcgsOp8Tn5FZMwkGZzofbF/2FzzymsdD+A28vecltvyZpxyrO+nlYm+iq8pp2u53s7Gw9wC+//OJ58OBBryuvvLJDqnWd1QobGAccklIellJagWXA3C6WiaIKK4HexgZvdbMTw7loSAQv/phGRn5Fu/ts/PrXN34WldJMdNHGBtsDvEyMiA5gTWrLCtvDopl7bTqfFtudTZgMOm6ZHMvG9IJW843jEwtAVl73juVtDY/Svcws/5bqwmaLD3UqejQv8dfXHwFgcKQfPmYDLy4YSW6Zhd99tgcpJZsPF7AuNY9pk6fxo34U51dvBaAcb341pS/rHpnB/24cw6XDIvmxLBGr1OPvWsc2OLWQrkp9ZJPzX3HdnWzUDWZmxXaKc8/cGDilRK+ru/+DvE0MjwpgTaomc01Il7MiEwC78AS/XlR4JQBQVuDejG/Eju3sN5y2ia4qr2m1WsXkyZMH9u/ff/CiRYti3n777cNGY8dYPc52hd0bqG+KyXRtq0UIsUgIsU0IsS0vr+0VnU6HwkorgV6mJtufmDMYs17HY8v3timEo6TS1myWrqlXLuJLzylcaPuFN99omEozKT6MPZnFFFZYm+3bQ6+9NPh796y0pKfLteP74GM2tGrpmH/z78gkhERLz/YUN0gH4RTz0Xt1xTMc5YUs+cf1HFzZ+Y5YBhw40JFdWo2/p7HW6jQ8OoDFFySwcl8269Lyefij3dy3bCfVNgfJ5iEYheYVXuX0bFAcIykhlHRnL3aJOIZYtO8wwF5ChTRjjjuvyfnHxgax0TSK3uTz0dKnmuzvDI4XVrLzWDG9/BtO1pLiQ9l9vJiiCmttljOd62XDw6jlDrjq6jspkd70sWa67dskbdjUDLuWJ554IictLS05LS0t+Q9/+EMuNF9eMyMjY9/WrVtTlixZcvydd945BnXlNVNTU/enp6cnv//++8dAK6/51FNP5TQ9I3h5ecn09PTk9PT05N27dx+cNGlSk5eEU+VsV9juFiYaaEIp5WtSyjFSyjGhoWfGwaqowkqQd1OFHe7nwSMXDWTDoYI2Vdm6b9lOLn9lA03n1xoBvSfhQEfkiZXs2r+7dntSQihS0mzJydJqG36yDKcUTEma07YPdZbg52Hk2nHRfLP3ZIPwosZ4e/nyi3kwEx37ObJrY7PtTgu7BfZ/2alpUGuWU6zVdbPLT95/mVvKvmLT3p867bw1GLHXOp0l9vJrYHW6eVIsHkYdz3+fQlZxFcWVNlbuO8nV1z1IvtQUWJHVixCfuntpfN8gzAYd+0z9GezIYMt3S4mwF7hCuty/fPYdu5AC6Uv/ypRO/KQadoeTBz/chQAevXhgg31JCaG1RWqOuKxsHlK7Bgf209p69hrATsMAhtsO4XRTItSEXSnss5izXWFnAvVjdKKArrH91aOw0kqgG4UNsHBcH0bHBPLXlQew16smlXyihMQ/fMuBk6W12+onWpBu3k0uvGExH3nP5ELHVrw+vJa/Pa95jQ/t7U+gl5G1zZjFM/IrCLUXclIE0Tdx9Cl9xp7MLZP7IoA3f85osd1JUzRewsIX33/UKXK8/e+n2PPxH1m9rDPXyTWFPdBSZ1HIK9OcZBOrj3R6zvQakzho5vD6eBj1TOwXzO7MEswGHdFBnizdfIx+0VF8ZxyPVepJox+Gek6aHkY9E/oFc4JIdEKyfd86ohy5HNeH0SfYfVTRVTPHs8I0kWnW3az6uHN9Et7edJRtR4v40+VDiApsKM/wqAACvIy8u+koL/6YxojoAPycZVRLI2NnXF7bLt3ch37iJB9/8k7ttif+8huefO4JTKgZ9tnM2a6wtwJxQoi+QggTsAD4sotl0mbYbkzioBWquGVyLPnlVnZn1q2j/rA/l0qrg4teXM+xgkpsDifpeeVcO67lmOEb7nud//rMx0dU8XDJy7zz52vYumMzU+NCWZeah9NNeNeR/AoiHflk6c6NkK7GRAZ4ctnwSJZtPeY2XWkNSbOupUqaiLCfQnhXlfuljPpUVp1gmDzM/mO72t9/OxljT+H4jh+0f5yaBW+kI5WUT/6KM/9Qp53XIDWT+B1J/bhmbNNrOSleuwZnJYZz44RYth0t4mB2KeHnLeZ3hgdwhg5ye8wXpYOpkibCbCeJdoV09Qlyr7CFEJzwGI5ROMjK+LljP2Ajvk/OZnCkH3NHNF1P1+sEU+NC2ZJRiK+Hgf/eMJogRwknRTAevnUFeJyu6nknMrQa4nuSk/mN5W3Or/wOk7TXxrUrzj7OaoUtpbQD9wDfAQeAj6SUXeol5HBKiqtszc6wAaYMcHly15sB11gKvU16Fry2iVX7c7DYnUzsH4JoaRLk4ccdi1+jaPz/8ZXnZG60fUf+yieYnhBKfrmV/fVm7DVk5FcS7czjpCH4VD9mj+f2qf2otDpYusVtaXcAhg6fwhbDICZY9mEvyGhz35m71/PW83ey5oOXW2zn79S+mzjrkTb33V5q7DIewsZXq5cDYJTa+qlJOEhIfpZP3vpNp53fgB2H0PHoRYOID2+as35WYjjeJj3Xju3DvNFRmAw63v/lGLMmTWCvdxIRfk2T4SQlhJJHGDt08cyo3o5JOCjS+TdZM67PQ/c/yhYSSKrcQVVphzj0NsHmcLI7s5hxfYOaDSO6ZGgvfD0MvHbDGML9PAhzFJOtaxjadsWFC6iUZnrZNWPhdyvexltYGOE8hCeW2iUGxdnHWa2wAaSUK6SU8VLK/lLKP3e1PCVVNqSEIK/mvQZrPLnrK+zcsmoCvYx8fOckqmwO7nlfC0MZHtW2sKvBF93K5Ys/4xNzErPs2/Er0bxM16TkNmmblbqdMFFMgb5nl9U8HRIj/ZgaF8JbGzKaTVcKcNCzP7Eih9f/80dkaXab+v70uw+52baStKMt12MOdmiKY4J9PwWH97Zd+HZyhAgs0kCgTVMAPo4KrLLuoX9N+U/gPL18y81hdDmdNUdUoBf7nryAKXEhBHmbuGRoLz7bkUWFxa5lAnNTyapfiDfRQZ4km/oRhMtD3OnbwCu7iRwGPT97jKavzObt1x89/Q9Wjy92ZfHXFQfYf6KUapuTMTHNZw68cEgEu/9wPsOjtXsvwllAXqP7MGTQePYY+jPUqlk+wm0ZAHgKK76iSpnEz2LOeoXd3ajxzG5phg0wPUHz5C4o19apc0sthPl6kBjpxweLJhDoZSLEx1Rr5nO3ht0Eg5l8cywewsberZ8xqk8Ay3edaOKR7lusmWCrzqGQLnfcPrUfuWUWvtilKbKc0mouenE93+w5WdvmkuseY6V5HHfalvPyS48jK5qW6WxML5vm4TvcktriGnGEowCr1OMnKvnw8yWn+WncI5BUYWaHLo7hljRw2PFzlpNHIKWyzoS87pPOWdutv4bdrIz1ZqMLx/eh3GLnw63HKau2E+6mkpUQgqT4UE44e9VuKxG9mrRrzJTzbqZUehFT3XAJwOGUbYraaI5v92Xzv/WH+fGg9nI8OqZhwiIpG/Zfk0zlZE4m4RRRrG+4to8QpJj7MEge49sfvmaM9SCpoi6laWvjqei5KIV9hqlR2O68xOuTFK95cv98KB+AnDILYS7z38AIP76+bwpLb5vQrGmtOW5Y+BtyCSDRksKCsX04lFvOtkYpUT112qzEYPBz18U5w9S4EAb18uPv36WwJ7OYRe9u58DJUj7dURdSExU5gAHz/8aPplHca/uYF158rMX1aWmtYqxNKzYxypnGtpUfum/odBLpzGeNcSR2qcPb1nm+khLBPnMcifIYP334EkGOMvJ0/vxgqHM4TD7aOTN8I3ac7XgMjY4JJCHcl3+v0fKJu5thgxa6+FHxMMqkJxXSjC52Wqt9jxs3npXG8cyw7OCrj7Wa2naHk/6/X8Hfvz91D/Jyix2nhCUbjtA7wJMIfw+OHk/jpRce5rW/3cjqp2fw09MzKCpp+LK39vvP0QtJuZsX5yp9KDoh2b/lKxI5ys+ewzlChCazUtinRUeU15w6dWqcr6/viBkzZjRIFXnw4EHTsGHDBsbExAy55JJL+lVXV7frAa4U9hmmdobdjNNZDUN7+xPkbarNfJRXWk2ob916XS9/TxIi2l+n2js8mvXm4Uy17yXacQwfs4EP6pWVLK604ouWDGhwQtPKVucSQgj+OV8rkjLn5Q3sPl7M4Eg/NqUX1FaHAojrN5LwOX9mvWEo91uW8fwLjzXXJR+/9QJ9yWaVYTQG4WTDvnVu26Xt2kioKOW4IYLdugGMtBwEx6lXdGuOmqdFlUcsAClZyQQ7SyjQ+RE950me9LiLIulDlM193O/pYsCBQ7T9MSSEYOGEPuS7LE/NKeyJ/YOxmYLYoBvCARFDv95tc6A86TUcD2Ej56gW0maxOwHJK6u1F4TGs+G2UFZtr/1dM7ve8t5i7i1+nUWVXzDcfoiZjp189M6LDY7Ly9PuS4euqbPcRZMuIIcA7rdoL3xGcwR7Tf0BcCqnszbTGeU1ARYvXpz93//+t4nzyUMPPRR1zz335Bw9enSfv7+//cUXX2xXogulsM8wRZVtm2HrdIKpcSGscxUEyCu3EN7Mw6m95Jj64CUsbF73AXNGRLJi70lKqrSL7kh+BUGOYkqkN+NmzuuQ8/VkBkb48dmvJzE2NpDHLh7Ew+fHU2VzsC2joVViyJBJmGf/H9v18dxZ/TGHtq52219ekfbgzwicQKn0ok8zBUQ2bloFQKXem90ecQyTR1j9SeckMpHA/Jvuo0D6Em3NJFQWU6T3Y+zw0fzxd8/wi2EQY6wHsZS2bu5vD1Xl5RiEs90K5vKRvfE0ase4M4mDlu53TEwQf7Vex2Lr7c16iDfm3vv/yB76MaViF6nH8yjKz2aV9yP8IeJ9dh8vZsbf1/Dst+2bbZfVK2c7JlZT2MH2Eo4Qzupe97E69EYAnFUN0207HeWuz9LUTyVmwqVs851JrgjkBEFcs+AuTpq0GbYyidfRFeU1AebOnVvm5+fXIFDe6XSyadMm31tuuaUI4NZbby346quv2uUopLwTzjBtnWGDKzxl1wk2HMrH5pCE+bovD9k4l3hrXLdwMfn/+YKBlhRmje3D+78c44tdWdw4MZaMggoiHAUc14UyxNx8OcpziahALz6+cxIAlVY7JoOOtam5TIlr+HI8bvwFvLzhK8aWpvD16uU8MHZGk77irEfIIpjrbvk9G57/hQnWZKoKTuAZ3DDMp6TS9UKg96XKFARVsO/oLpr2COWHt7H0k1e4ZOoVRE1sZ6IbKZFCEB4YygpDIhNsyQSLMsp03rVN0kz9uLBqKx+8+w+uvfsv7eu/BYoKT+IJONvif1EPPw8jc0dE8vH2zGZn2KB5iz9zOByAmGDvZtvVR6/XscY8lvssH/LKsicZNX4uEx1ZxBVnMeDVhdidkuU7s5g5KIzEXn54m1t/hJZb7Ph7GimpsjGhnxZ5oZNOKvBkxh1/wmmpIuuvy+hrbaiwPZ1a8pShiSObdioElzzwX1LeuIP8CgeR4XFE+ffGUSaQ+u6nsB84cCz6YEV1h5bXHOjtUfnCoD7drrxmc+Tk5Bh8fX0dNWlKY2NjrTk5Oa0rgnqoGfYZpqjCiqdRj6ep9ZtqmisG9ePtmjkyzLdjZtgBEbGsM49gmn03zsJUBkf68cGW40gpOZJfSZQzjyz9uZWStK14mQyM7xtUW86xMTMvuEELubE1DQcrOHKA8fb9bDUNwtvLh0PmvvQShbz3btPwLoPUZlfhoTFcc8ODFEhf+lrdh5i99ekS7qj8jK/Wf9Huz1NfVaaZ+hKCFkpWWc8M6x06GIDyyo41i+dmasla7Kfg1fzoxYN499ZxLSrM6Ql1ZvDooFZrNtQyetI1VEozUfbDFJWX127v46vnvvMGkF1azdX/2cS1/9tMcWXz6X1rKK+2M29UFKsenFYbulbf2U5n9mSXMY7RtlQqKurO5+8oo0x6Mrq5bIN6IwmL3mTyg28DcMn1D7PaaxrzJsxu82c9m+mq8prN4W4pRYgWg3KboGbYZ5jCSvdpSd0R4mNmaG9/vkvWwoXC3MSc1tAmL/F65Jhi8Las48dv32HBtMX83/J97Mks4fCx4/SWeWwwDGtXf+cSSfGhPP3NAbKKq+gd0FARDBo8ntWGQUywJuOoLEHv5c+KN57lYPZRzGYv7haVHDdpHr1hUSMg5WOobjpJ8HWWY5N6pl9wFaFB4XxjGswEazKV2YfxiujXoG2YTUtjO+AU47VrnhjBkSMhfRkANlH3uW66+R6OPPkKcdUZp9R/c2RlpDICsJ1C/WZ/TyOTBrT8UpkQ7ku4nxmn1F602srkpFl8tm4cF1Rv4d8HxnGxa/sNPisQBwpZ5BvIa2UXsCezhAWvbea928YT4uP+3nQ4JRVWB36eBuJcyrqwJA8/WdkgnO2oMYpLbJt5870XufUOzQci2FHCSRFEvKGN4+MZwKzfdnleKLe0NBPuLLqyvKY7IiIi7GVlZXqbzYbRaCQjI8MUFhbWfGYmN6gZ9hmmuTzizZEUH4rVrl0XHWUSB7jmmvspwJeR1XuYM7wXnkY9H2w5hn/2eq2cn779Dm3nCjXZt9Y1k9o1xaMfMSKXd954HgDdiR94yLaUuMqdOKUgIWEqAPMW3M1++jDMTXhXkF17WIeFaabyw6YYQkQp733wasOT2aoZbdVi6sfbDlB0xOXNnXsQdr7Xavx0/WvnuoWLSEF7mTAY6jyT9To920yDGGNPITd1e4v9tYd8l1e0XXZO/WYhBLdN6ceVo3q33rgRRzyH4S0shDjr1quvz3+Xm4u+ZIrcCcDlIyLJKKjgmv9uqi3W0ZhSl2+Ir4f2Gfcf3MbmlxcyXKaz2xRX287PWxv3qpK6l64wZxE5uuZjthUt01XlNZtDp9MxYcKEsiVLlgQCvPnmm8GXXnpp6ykP6/dxqidXNKTa5sDhJs1nYworW85y1pikema9jjKJAwRHx/GN12RmOHex5LU/c+mwXny5+wS+Ou36cZ7jMdgtMSDMh0h/j2ZrigeGaekyrRUZAFTrte/7fOc2knWxnH/Z9YCmUHZ4DGSUM43tqxrmI49wFHBSVzeDjO43EQCDpWFRmC/e+Sf9Ocl2EYefqGTZZ2/y/X9+z4rX7+PoF0+x9J8PtJoPvMY6o9Pp2G7SikyEhjRME3rc2AcfUc3nX7/dYl/tobJaM/86OtHQd/u0fjx6UdP0pa1x552PkSKjOK9iW+221WIk68RQRtrSCHAWMjo2iLdvGUdOSTULX9/sNs1vRoG2Dl3j9LZr+V+52PYL/zPP4fo7/l7b7qrr7yNP+jWowtXLWUD+OZy86HTpqvKaAKNHj0644YYb+m3atMkvPDx82KeffuoH8I9//CPzpZdeiujTp8+QoqIiw/3335/fns+kTOIdwKb0Am5esoUPFk1gVJ/AFtsWVVjp20wRAneMjA7A10P7mlpa926vSRwgcfjllG5cy6CSn5l6+QN8vD0Tb2/X2mlg+2cl5wpCCJISQvl690lsDidGfcP33qtvWEzqU28zpjoZR3kBRbo6L9+DphiG1mtbZIrCWO3g513rGH3+fG2jlEQ6C9hqqqvmNPfKm9m770UtuYnTCTrtnJmL6r9eAAAgAElEQVQF2jrwep/pDC9Nx8eWRUjuYQY6jlGFiRllX/Pja77MvKMlZ7G6a6c8PIl/Z/uy8IobGrQYMvICHD+/i5etbdnc2oLDqa3/OuicGfbp4O3jzQ8e47nb8ikA//acx12PvMGLf7ubaVV72eV1D//ZeBXjH3qDP84ZzCOf7CH5RClDG2UeTM+r4N6gbziy4kPkoLcZV72f9bqh3L74NTDWTdY8/INZZ4xnlC0Nq83KsYw0BogSig3K0nU6PPHEEzlPPPFEgzKYzZXXvP/++5uEQdSU12y8/fnnn28xMcL27dvdhhIkJiZa9+7de6Bt0jdFzbA7gIERvtgczmZnXPUpqmi+Upc7DHodsxPD6R/adMa75M1nePW5WzDLdi2D1DLmgmv50nsqFzi3sfGLl4kP9yHAWYpV6pl56fWn1Oe5QlJ8GGUWOzsaJZ0Bbaa61nsUo0nj5VeeRkfdUleBvuEL3WXz7qRUehJdz0ktK20v4RRRqK97+Ash2GlOYIQzja0rl9Zu95TaDG7B9Q+wW9efeVVrGOVM43WvK3gn6Gb8ZCWR2V+R+mXbMpUt+tV9/Pqxt/D3aZg05/zZl7JH9Gdo9aGOq+Dl1K5bJ90zGmHA0IuxSNecRmjfQd+YMbX7rytZwfL3/sZ5AzWL6drUpml+D+eVM8Sayo1lK1j65rMM4AQHzP0aKOvatqZoeot8Pn7vFTat+waAStE273bFuYFS2B1AoLeJ4dEBrNh7skWzuNXupMxib7ZSV3P85YqhvPurcU22J2R+wV0Vn3GeY2e7Za4hLvFiyqUH/YvXc/2EGELthWSJUALD1Ay7JSYNCMagE82WKB17/iJyCGBC9UaErFPYJv+YBu1iYxL4xZjIRGsyVUXa7HXdmq/RCUlFIz+CYnMUeiHZnFxXf9sgHdiljvCw3uwxx+MlLGwT8cy//U88eP/TvOpzHXHOTHJ3v0/RrpVN5BRIJE0ddGri8uuzyxzPUOdhdqx8t+XBaSMCLaGI1J/ysmCncsGlV/GDoUZBa1aIOfNvoUJqLxh+opKII59htJcytLe/22shPa8cb2cVHsKGV45WCUya3d9bJrOWPrUw7wBFxdqkUOqUwlbUoRR2B3HblH6k5Zaz9JemoTevrD7Eh1uP1YaANJ5h25wtz5A9jPpap5X6mKUdu9TxvX4Mm82DT0nu8ZfewpdeU7jQsYXyHcuIcuSRqT83y2q2Bz8PI6NiAptV2COGT+VL72mMlwcZZjlEtTSy4+YV3HrHk03aprnCu95/5yUA8ku1mZqz0cN6zry7KJVeRNdLtmKQdqwYEUJg9R9MClFsCryY8CBt1rd48fO87HUNUxz7+Gnlq83Ojg9m1/niFJRbGPvnH/hqd0OrX7Gxj/bCsH9Da8PTJgwuy5DDo/tebwfMWqY7u8tsL4Rghy4egG3EM8FxgE/feICk+FB2HCvmldWHOJxXF5p1OK8CH6ktm15m2UiR9GHhwvvcnmv+gjspkd5E2U4gXElT/L2U05miDqWwO4iLh0YweUAwf/8upbZgB0CV1cGLP6bxf8uT2XFMM5/WeInbnXaWvHI7P/39It76z/3tOl9hUR4JzmN8ak7i/Pvf5bq7Xzpl2aMGzKYaE1GFa+kjc8kxqIdEW0iKDyX5RCm5Ze49hMedfyc5BDCCdOzoGRU72W270N4jAHBWa4pY59Qe1gEBDZOpxPYZwGZDIuOt+6l2zcYN0oHFpUzuuOsxgn+7lnvvq3spEELw68Uv8ZlhKpdUb+Tw5m8b9KnNsEWDuPJjhZVY7U6+3ddwvXrOVbdTLj2I6KC85kapvcDaA+Naadl1/PqeJ3natIhxE+fXbks1xQJwyBzFT2Ik15V+h3/qmzickue+S+G8f6wFtDzkGQUVeLvKlRqFg62GgfiEui9E4h0eww5DHFOsu5lf8S1l0pOJE6Z36udT9CyUwu4ghBA8OWcwlVYHz357sHb75sMFWO1ObE4njy/X/BwCvUxkZO/nw5cXcF3eZ1xQuZVLsz/jzVfubrb/7NzjvPrivRS4qkF99fH/8BHV5BlCwS9S+zlFps27k6+8JnOpfRN+opIifdtKdp7r1IR3rU917+g5fPhkvvRJAmixhORV197DAfowrDoNpMTbWY5TCqZOn9ukbc1sfNm72gtasKOEIlFnOg/xbBqbbNKbOOoxAA9hY+WGrxvsq3E3q7/+mlemvXCuT8vD7qgz5/ePHcBW/UBGWVJwWps427Ybs7RSLY14BEW13riL8PLy5PHfP8eEqXU55oL6ziLd2Ytsj5GUDbyRcjyZUPQdnrq6EDqnU5JZVIXNIfGVtU7HHDLHtni+Q6YYQkUpObpAlvtcyYCRrRctUZw7KIXdgQwI8+VXU/ry0bZMtruckdam5uFh1PHYxYNqCxYEeZvYvvS3LCxcxSY5mL+K27FKA/PyPud//7rDbcD/Z+88yV1F71D09ym8/PwiSkszADCagjtE9uDY87C6ggYsOuWZ2hYSe/kR4mNmTTNmcYDxs+8gh4AWFbYQgu3mgYxyprJz1ScEOUrIJhCvsBie+DK5QaGRoF5aQhtb1XFw2BjoOEaKIbq5rmtJOu8aqqWRYNvJJvskgm0ZRZRbtDXlPNd1WlptJ+H/vuWV1XXlJg+Y+hNLDl+8/bdWz9kaHk4rZXg28bLv7lyx4Gb6PXmABx78A3Pn38qHnrMZ6jzCTf519c33nywl3WUa96WSA/ShSpoICoxvse9LZsznNa8F9J3zJ274zb+hndX4FGc3PetO6QHcOzOOCD8P/vjlPhxOyZqUXCb2C+aWyX0Z7gr5qC44zOzSbXwrxjIo6Toefewv/OQ9jyLpw7WFy/nfvxY1Udo6p/YwjXbmck/ph/y67CNsUs+FMy/vELlnzb+Xr700k62fR8uhaQoNnU6ru7w+La82uU1jhg2fzCd+F7LCZ1KLfRWbozAKB+t3rSHcXshJXQg/HcjlrY0ZrD5YN/tdcP29pBLFYEsa6758m97kc9zYeq3nUaMmsU2fwCjLQbDXT6epOZ3ZnZKNrlKuNTNsoNbMW4ufZr7OKclo9Zyt4emsplx4YuhhChsaZsYy+WiOhH66uiWEtal5fJ+cg68swltY2OwxhOJL32DBbY+02G/kuEtY9Mh/8Rl5WecIrmiVziyv+Ze//CW0T58+Q4QQo0+ePNnusOqed6d0c3zMBh67ZBD7skp5ZuUBMgoqSYoPRa8TvLBgJL+5IIFffnwLP1HJfnMC4efdCQYT1y9+ll2BV3BCBnNj4ee89q/bG/Tr6azGIQUFEx7nX+YbWG0YyVemycQMndBhsieMvZ63Ai5j/q2PdlifZztzRkRSXGnj0c/2NpsK8e6H/sv1v/m49v9Kq51HPtlNVnGdWfniK++gVHoSZTtGpCwgRx9IZpG2v75jmxCCreZBjHaksjtNyzpW1Uafg2Rzf+LJ4pul/2yyz8dsqLUU5JZZCPY2YTLUPR5yS7V12Btvuo8TMoj+1e7zmrcHL1lNBZ4Y9D17FnntjQ+SL/3oY61b21+yIYMPtx3nxmjtJcgizPQaO0fNmLsZZ7q8ZlJSUvmqVatSIyMjW09C7walsDuBS4f1YlL/YP63Xvu+pidoHrt9Q7y5e8YAdBbtJk6ISqw7SKfn8vuf4WiveRyiNwsLv2LLpu9qd/s6yinEj8iLHuS+R19m1l3/48o7mj54T4eh513NzQ+8h9lLZTlrK0nxoTwwK45Pd2Ty0k+HWj8A+OlgLh9ty+STbXVZrfrFDmSLMZGJ1n1EyELyDQG1Cn1tal6Dl4E8UzRmYWdSlZaFa/DQpDad1+ap5SA/mptau01LTSqY1D+YtSnaefLKLIT6mmvX6GtkAPDx9maLMZGxtoOUZqZyOng5q6kQHvi0oeJVd8bHz4/thnhG2tJYfuc4bp4US365hSG9/fC0ZABg0fm13ImiU+hO5TUBJk+eXJWQkHBKyhpUprNOocYB7aIX19M70JPYkIbhOZ6OKizSwOzLr2t8ILPv/BMvPFvBA1VvsHXjp4ybeAEAgc4y8oQ/tY/QkAEougf3z4zjWGElz69KJTrIkytGtuxEVZODfG1qLvfPqvOQTjX3ZZZdmzWX63zJLNKclU6WVJOWW15b6en8i26k8sOljCaVo4Qxc3bblkVuvOlBcp5fQj9L09lxUkIo3+/PIT2volZh/+Oa4axKzuGZbw+yNjWPq8doa+VHjDFcbv+ZNz/+NwO9IbeijMsfeL3h7FFKKDwMwf2blcdHVpOjD+zxChsg3RTDBVXb+P7LJ7goaRE7jvnzz/kjWPXWGwD0Du3XSg9nN7/5ZHd0anZZh5bXjI/wrXzuquE9prxmR9Dz75RuSly4L89dPQwfc9P4aW9nFcX4EO7jfq34lgW3kfPmpwysSqvdFuQspUCnvLe7I0IInrlyGCeLq3nkkz308vesrXvcGCkla1PzEAJ2HS+muNJKgCuRTkjv4ZD6CQA2vTdZRVVM7BfMpsMFrEnJrVXYiYkjWa0fxAznLlL0fYhpo5nVz9+fNcbBTLXtpjIrlaztK4l0FpAjAmtn02tT88grs9AvxBs/DyPzRkexMb2AHw7k4HBK9DpBn7jJsGcpsVW7GViSyghpY9PHLzLxmgdY+vzt2LES4t+XoJzvEAOvZ8KV7qMfvKmiUvQ6KxS2wTMaquCWwvdY+/VevnxsHQA77YWUSk8unndLF0t47lG/vCZATXnNq6++uri58poAV155ZWFqaqoHaOU109LSajP7nE55zY6g598p3ZjmZlq+zkqKhS/hzRznH5PIStNoLreuY93qz5k24wpCZClH9RGdJ6zitDAZdPzn+tHM+89G7nl/B5sfnenWmSo1p5ycUgvzx0Tz4bbj/Hwon0uHaSF5V197LweffI2BHMfXK5Ts/GquGh1FQYWFtal5LJpWN1s96NGfGZW7OGZq3eGsPkdMMcyxb+C19//BmKrtDJN5fOBxEY8GejEgzIc1Kbm1M+wapieE8umOTHZnFjOqTyDzrlxI8p5nOc+6gwwZTgC5HMn4mYk8QGL5Dvo4c3jfcRmXWPfzn/TtNOdl4SOrqNJ5EHgWKOxrb3qA0udfw09UkmTbXbu9jy2HdF1vRvqe2y/bLc2EO4vuVl6zI1Br2F2An7OC4lZyBOcZ++MhbOzb/g0V5aWEyGJK9WptuTvj72XkwVnx5Jdb2Z3pvmpejTn8nvMG4O9pbJCwRAjBVo9EqqWR/sPPwymhd6An0xPC2HqkiApX2BWAf+QojhCOxavJ8lmLxMZNxikF15d/zjBHOn/3vIEN3lcB2nr8xvQCrA5nA4U9ZUAIOkGDXPnfmJP4XExh87hnWaUbw6UVG9j43l8Y7DhCMGUEOjU/jfrVp+ojnU58qKJKmPDx6PkK29c/kB36uuWNA3s2Y7Va6e/IIsPQvpcqRcfQ3cprdgRKYXcB/s5ySlvJEXzLjb8mU4YwuCqVbRtXYRZ2KnQdugSk6ATcKbf6rEvLY0CYD9FBXkyNC2niUBY/axFvht6GMTwBgKhAL60musPJ5sN1xYSuu/4ejA//xK/veQopJd/u0yqHtcacyxeyT/TFhI3nvW7gYPhChCt9SlJ8aG0u/PoKuyZXfn1v9UcefYkr/vgNCy65gr3+U/ATlTiOrsQkNI/b4dXacs5Y20EsJU2LYmSm7cUs7FiE6awwiQOkmeryxP/0wwes/uZ9gkUZufqOyZWgaB/dsbzm008/HRYeHj4sJyfHNHz48MT58+fHtNZXfc6OO6WHESjL2deKwvaJ6Mty80iusfzE68k/kwRYdN2zSIKiDn8vIyP7aDnGHzo/ocG+KquDX44Ucv147R5Nig/l6z0nOXCyjMRIzYt4/JhZjB8zi4+3aRbE3gGe9ArwwNOoZ01KHjMH1S2kRPlqSy5rU/O4870dPHfVsFrHsOYQQvBj8DxWWKv47UNPc+tbW2t9xcb1DcLDqKPa1nCGXSPriz+mUVhhrU2tW8ND9/2BtX/6kSTbHgCyZSCDZQYICKWE9955juvvfa7BMYcO7CQasJ4lM2yAamMvcGWp9bHlkHp4JxcA1XqV16Cr6G7lNR9//PHcxx9/vOkbbBtRM+wzTEVFCQGUU9EG5VtqHoBJOIip2g+AwKOzxVN0AEnxoezJKqnNKb8xPZ+5L/9cm2BlWnxIbTvAbQGRrOIqhIBeAR6YDXom9Q9mTWqu23W59a7jW8q4Vp8H732c3z38Z4TQgrpq8DDqa53lwtwobCm1dKWN0el0bPaeCkCGDGe1aRQ6UddzdXXTGtrZedrzzo7xrJlh33TTYt4yXESlNJNoOUyMRQt7i+nVcnYzhaKtKIV9htm7dS1G4aBStK6wb73lPjJkOLMtWwHw8lSxnD2BGuX2sytz2D9XpbI7s4Rnvj2I2aCrU4p+HiT28nNbRzmzqIowXzNmg17rMyGU44VVZBRUNmlbc56f0/Jrc39LKRusebdEfXebS4ZqXtu9/Bten8OiAgj0MjZbneyhB57iSzGJ703jOGGsm+VXSjNxbsLIyiq1pUS7NOJp1LdJzu6OX0gYNz++jOXmqYx1pjDHupH3DLOZe+2irhZNcZagFPYZ5sgRbbZsFeZWWoJHUCRrPUbWrgsOiE1s5QhFd2Bob3+CvE21KUVHxWgm0cN5FYyJDcSjnoJKSghlW0YRZdUNsyVlFVURFVjnszA9XvN7WZvSULnnlVk4mF3GkN5+lFTZ2J1ZQlpOGVe+upERT33PD/sbWAObICUN4qevGh3Flsdm4t1o1qvXCabGhbIuNR+nm5rvRoOBpEc+4YZH3mDU+MuwS+3RskU3kDG2g+Qealiz3WbXbMc2aWjWQ7enkmPsi03qecU0jwUPLUHozw4LgqLrUQr7DFNSWgiAQ2dqpaWG1VML5bFKPWOnnt9pcik6Dp1OcMHgCFbsyya3rBoPQ52CHhYV0KBtUnyolsc7veHyWWZxJb0D6ma5fYK96Bvi3WSGuzFdm13/9sKB6ASsPpjL/ct2cbSgkn4hPvz6/R1sSm+yNNcsQgi8TO4VTFJ8KPnlFvafLHW739/TG0+jmRlJs9gltMQ+yaYBeAsLX3y5pEFbZ01pTXn2KbMHFz9H2vlLuft3r2PwUoV0FB2HUthnGJtNM2nq2+hAdutti0mjNwX44+Wv6lT3FO6Y1g+7w8kb64/grLfuHBvc0NN/dIyW6au+InY4JSeLq4kKbHiNJMWHsulwQYPqXcdcJvIJ/YIZER3Aa+sPs/9kKU/NHcyyRROICfLi9ne2sTezxK2cWmLStjHVtfbenFm8PntMrhAnv3gcUmC2aTP9qhNpLH3xWjzRlL5VnoV+GUKQOPki0KnHq6JjUVfUGUaHNrPw9mjberTeJ4ivzbP50OOCzhRL0cHEhnhz6bBI3tt8lPxy7TufOyKSC4c0jMk16nVMHlCXxxsgp7Qau1PS243CrrY52XKksHabxe5EJ7R+pieEYbU7mdgvmEuG9iLQ28S7vxqPv6eRm5Zs4VBu+Wl9pjBfDwZH+jUbslYfv+HzedZwA7ffsZi9oh+DLengdPLuB8+xsGgFN5StAKBa5dhWKNqMUthnGKNT8xyOiWp7+N2Di5/hgQdPv/6w4sxy94wBVFgdLN+ZhadRz4sLRuLv2TRVbVJ8GFnFVaTnVQDUFv2obxIHbRZtMugazHCtDmdtVa1Lh/ViYIQvT80dXLsuHOHvwdLbxqMTgnve39Hk3FLKdhWQmp4QyvZjRZRWN61QVJ+rLpnLbx9/GZPBwE5TPMMd6Sz71z3EWtIpk57U+KeXerScd12hONN0ZnnNOXPm9I2NjR0SFxc3+Oqrr461WCztcuBQCvsMY3ZW45SCUaOntv0goye0cUau6D4kRPgyOzGcKpsDva75+7ImzGuNy6GspuhHfaczAE+TnvF9gxoqbLuz1pO8X6gP3z4wjbjwhuumsSHe3D2jPwezy2pN6PVpzxMjKT4MR73a2W3BY9CV5OPP+JIfmWbZzTfGifzVfBvLOA/p175MbQpFR3Kmy2suXLiw8PDhw/tSUlKSq6urxQsvvBDSnnMphX2G8ZLVlOJFYO/YrhZFcQa42/WC3ZLCjnLl8a5RxFlF7mfYoJnFD+WW1yr1vHKL21m7u+MA1rqJo24PI/sE4Ntozb01rr3iGl73uo4YZw4ewsZxz8H88fd/4wXTPfj5t5xASKE4Hbpbec358+eX6HQ6dDodY8aMqcjMzGyb97GLs89Fs5vj46ikSPgQcJaFsijcMyI6gKlxIa2uHyfFh/Lu5qNUWR1kFVcR4mPC09Q0Pnl6QihPf3OAtal5LBwfQ3JWCYm9Wre+9A3xJjrIk7UpudwwoW45RsrmCx+4Q1tzD2GNa829uWNtDicbDuWTFB+KEILHHvkzLzydzyD7YW6/47cAlFvsbqvZKc5Clt8dTe7+js2tHJZYyeWv9MjymhaLRXz44YfBzz//fLuKoiiFfYbxc1ZQIlQRj3OJF+aPILu0usU20xNCeePnI2w+UkBmUZXb2TVA/1Afegd4sjYlj8uGR5JRUMlVo1tfBxZCkBQfymc7srDYHbVm9FMhKSGUb5OzScst52hBJRn5Fdw+Tav3/HNaPsVVVrzNBm5ZspX3bxvPpAEhCCG4/7H/Um614OfhgdMpqbDaz5q0pIruR3cur3nTTTf1mTBhQvmFF17YLk9QdbecYfxlBQXi3C61d64R7GMm2KflRDljY7U83mtT8sgqqmJQM7NmIQRJCaF8uesEu49rFcEG927b9TQ9Poz3Nh9je0YRkwZoS2cS2a41bKgzr//p6/1sOJSPU2qm8jGxQTz3fQpH8sr5y5VDAS1das25dDqBn4cWxlVpcyAl+J4laUkVrdDCTLiz6K7lNR9++OFe+fn5hu+++y69vceqNewzTIAsp1RV3VI0wsOoZ2K/YNak5JJZXNUkpKs+SfGhlFvsvLNJS/k5JLJtCnti/2CMetGu9Wd3RAZ4Eh/uw/q0fMbEBhHiY+Zv36VgsTs4cKKU0mo7248WAXWOdI0pr9bSpjbOqKZQdBTdsbzm888/H/LTTz/5L1++/LBe334rV49Q2EKI54QQB4UQe4QQnwshAurte1QIcUgIkSKEuKDe9tFCiL2uff8S3SD/oZSSAFlOuVLYCjckxYeSUVCJ1e5skjSlPpP6B2PQCVbtzyHCz6NJZa3m8DYbGBsbVFuDu9rmILukukWHuOa4bWo/5gyPZMnNY7lv5gC2HCnk1TXpWF25zGvOkZpTzoniJhUNKbdonrXKJK7oLLpjec1HHnkkJj8/3zBmzJhBAwcOTFy8eHG7iqX3lLtlFfColNIuhHgWeBT4rRAiEVgADAYigR+EEPFSSgfwKrAI2AysAC4EVnaJ9C6OpO+jn6imUpXJVLghKSEMvtJyzTe3hg3g62FkdEwgvxwpZEjv9oX7JcWH8teVB8ksquTprw+QnlfBg7PbX03qmjHRXOMq5blgbB/+t/4w//pRq4EdG+zFkfyK2rbrUvNYMK5hWGu5RQulUSZxRWfS3cpr2u327W2T3D09YoYtpfxeSllTemgzUONlMxdYJqW0SCmPAIeAcUKIXoCflHKT1BYy3gEuP+OCNyJ5xwYAqsVZmI5Rcdr0DfEmxpW6tCWTOGiOXwCD22gOb3zcTW9u4dvkbP7v0kQuHRZ5CtLWYTLoeHBWPE4Jvfw9mDeqzgmuORN8jUlczbAVirbTIxR2I26lbqbcG6jvzJDp2tbb9Xfj7V3C0aIUcstPkpuriWRvQ6UuxbmJFgbV8gwb4PzEcIx6UVuqs60khPsS4edBel4Fd03vz6+mdEzikrkjejMsyp+pcSG1LwUA4/sG83NaPjZHQ/+cGpO4dzOFRhQKRVO6zd0ihPgBiHCz6zEp5ReuNo8BdmBpzWFu2jdXz8Cty6AQYhGa6Zw+fU4rG12z7F1yHzqdgyqnK0udUtiKZrj3vDgmDwjB16Pl+OQBYb7s+sP57XbaEkLw0PnxnCiu4v6ZcacjagP0OsGnd01C73IVCfY2UVBhZXpCKD8fymfX8WLGxgYhpeSHA7lkFWthbr5qhq1QtJluc7dIKWe1tF8IcRNwKTBT1vnrZwLR9ZpFASdc26PcbHd33teA1wDGjBlzSjF1WSWHWLfiT0yf/SS9QmIb7Nu+/TvOL9mKSTjIFFqmOrNJZXdSuCfU18wFg929tzblVD2sa9aeOxqjvs5gNy0+lM93ZjEtPhT9yoOsTcljbGwQGw4VcPs722od3XzUGvbZjNPpdAqdTndKz9VzFafTKQC3IWM9wiQuhLgQ+C0wR0pZPxnyl8ACIYRZCNEXiAO2SClPAmVCiAku7/AbgS86S77v33qJuakrWfXhX5vs27b+C0zCwUo5liip5V8OCwjvLFEUim7BvFFRWna1QC9G9wlkTaoW3vXN3pN4mfQEeZvQ64QK6zq72ZeXl+fvUkCKNuB0OkVeXp4/sM/d/p5yt7wMmIFVruiszVLKO6WUyUKIj4D9aKbyu10e4gB3AW8Bnmhr3p3mId47ejz6wqX4VWVSWl2En0dtGB+eNs3x0Bg9jT9lDWGaYztTps3uLFEUim7BlLgQVi+eDsCsxDD+suIgH249xnfJ2cwcFM7/XTqIQznltZXGFGcfdrv9tuzs7Nezs7OH0EMmh90AJ7DPbrff5m6naCkbzLnGmDFj5LZt29p9nKwu5atn5nMxm/ms1xRm37iEQE8tu9OGpycRbCsl4fe/QMEhKg6swue8h2lXTUOFogdjtTu59a2t/Oyq8PXqwlFcNLRd4aeKbo4QYruUckxXy3G2o956OgDh4YczbCzbnAnMO7meH965hYKKHI4d28dwezp7jAMQZm9E5HB8Zi5WylpxTmEy6Hj1+lEMjPDF12xgekJY6wcpFIom9BSTeLfn8kWPseLVMjbkGbj65Do+fjSMkmQAAAlQSURBVPdXlNr78SuqydR3WUSZQtEt8PUw8uldkyissLqtQqZQKFpHzbA7CoOZi3/9N2TvCfzkHMHV2esZXfozAL1D+3excApF1+NtNhAdpNLyKhSnilLYHYneSNLtz+LddwLfyTGMsKaTKUO48pobuloyhUKhUPRwlMLuaHR6xt/8DBEJU3jTeSEf6C/A6NemfPEKhUKhUDSLWsPuDIRg+LVPMGjrEpxeKuZaoVAoFKePUtidhRCYxt3a1VIoFAqF4ixBmcQVCoVCoegBKIWtUCgUCkUPQClshUKhUCh6AEphKxQKhULRA1AKW6FQKBSKHoBS2AqFQqFQ9ACUwlYoFAqFogegFLZCoVAoFD0AVQ+7HkKIPODoaXQRAuR3kDgdSXeVC5Rsp0p3la27ygVKtlOlLbLFSClVDuZORinsDkQIsa07FnHvrnKBku1U6a6ydVe5QMl2qnRn2c41lElcoVAoFIoegFLYCoVCoVD0AJTC7lhe62oBmqG7ygVKtlOlu8rWXeUCJdup0p1lO6dQa9gKhUKhUPQA1AxboVAoFIoegFLYCoVCoVD0AJTCdiGEiBZCrBZCHBBCJAsh7ndtDxJCrBJCpLl+B7q2B7valwshXm7Ul0kI8ZoQIlUIcVAIMa+Zcz4qhDgkhEgRQlzQHeQSQsQKIaqEELtcP//p7DETQvjWO98uIUS+EOKFUx2zrpCtK8bNte9aIcReIcQeIcS3QoiQ7jBubZWtrePWwXLNd8mULIT4Wwtj0RVj1qpsnXytzRZCbHd9b9uFEOfV62u0a/shIcS/hBDidMZNcQpIKdWPto7fCxjl+tsXSAUSgb8Bv3Nt/x3wrOtvb2AKcCfwcqO+ngSedv2tA0LcnC8R2A2Ygb5AOqDvBnLFAvvO9Jg16nc7MO1Ux6yLZDvj4wYYgNya79F1/BPdYdzaIVubxq0D5QoGjgGhrv/fBmZ2kzFrq2ydea2NBCJdfw8Bsur1tQWYCAhgJXDR6Yyb+mn/j5phu5BSnpRS7nD9XQYcAHoDc9FuHFy/L3e1qZBS/gxUu+nuVuCvrnZOKaW7LEFzgWVSSouU8ghwCBjXDeRqMx0sGwBCiDggDFjvZnebxqyLZGszHSibcP14u2Y7fsAJN6fsinFrq2xtogPl6gekSinzXP//ALizgHXFmLVVtjZzCrLtlFLWfE/JgIcQwiyE6AX4SSk3SSkl8E7NMY1o87gp2o9S2G4QQsSivWn+AoRLKU+CdvGjPbBbOjbA9eefhBA7hBAfCyHC3TTtDRyv93+ma1tXywXQVwixUwixVggxtaV+O0K2RlwLfOh6KDSm3WN2BmWDMzxuUkobcBewF00ZJgJvuGl6xsetHbJBO8ftNL/PQ8BAl1nZgKZ0ot2064prra2ywZm51uYBO6WUFrTPnllvX3PjcUrjpmgbSmE3QgjhA3wKPCClLD2FLgxAFLBBSjkK2AT83d2p3GxrNsbuDMp1EugjpRwJPAS8L4Twa6njDpCtPguAD5o7lZttLcYlnkHZzvi4CSGMaEpxJBAJ7AEeddfUzbZOHbd2yNaucTtduaSURS65PkSzlGQAdnencnd4S32fQdk6/VoTQgwGngXuqNnkTmR3h7axneIUUAq7Hq6HzKfAUinlZ67NOS5zEK7fua10UwBUAp+7/v8YGOWmXSYN356jaMZkeCblcpmyClx/b0dbg4pvrtMOkq2mr+GAwXVed7R5zM60bF00biNc50t3zfo/Aia5adcV49Ym2dozbh31fUopv5JSjpdSTgRSgDQ3zbrkWmuLbJ19rQkhotCeEzdKKdNdmzPRxqCG5sajXeOmaB9KYbtwrbO9ARyQUj5fb9eXwE2uv28CvmipH9fD6StgumvTTGC/m6ZfAgtc60N9gTg0p44ulUsIESqE0Lv+7ueS67C7PjtKtnpcS/Mz2Jp+Wx2zrpCti8YtC0gUQtRUSZqNtkbZmK4YtzbJ1tZx68jvUwgR5vodCPwaeN1Nsy651toiW2dea0JbOvsGeFRKuaGmsctsXiaEmODq88ZmPk+bx01xCshu4PnWHX7QvDYlmulul+vnYjTPzR/R3nR/BILqHZMBFALlaG+Wia7tMcA6V18/opmvAOYAT9U7/jG0t+MU3HhcdoVcaOtWyWienjuAy87EmLn2HQYGNjpHu8esK2TrqnFD8zQ+4OrrKyC4u4xbW2Rr67h1sFwfoL2s7gcWdKdrrS2ytXXMTkU24HGgol7bXUCYa98YYJ9rTF6G2kyZpzRu6qf9Pyo1qUKhUCgUPQBlElcoFAqFogegFLZCoVAoFD0ApbAVCoVCoegBKIWtUCgUCkUPQClshUKhUCh6AEphKxQdjNAqJB0RQgS5/g90/R/TAX2Xn76ECoWiJ6IUtkLRwUgpjwOvAs+4Nj0DvCalPNp1UikUip6OUtgKRefwT2CCEOIBtOQV/2jcQAjxrBDi1/X+f0II8bAQwkcI8aPQirTsFULMdXPsdCHE1/X+f1kIcbPr79GuohDbhRDf1UtBeZ8QYr/Q6i0v6/iPrFAoOhNDVwugUJyNSCltQojfAN8C50sprW6aLQNeAP7t+v8a4EK0sotXSClLhRAhwGYhxJeyDVmOXHmjXwLmSinzhBDzgT+jlVb9HdBXSmkRddXbFApFD0EpbIWi87gIrbLSEGBV451Syp1CiDAhRCQQChRJKY+5lO5fhBDTACdaecJwILsN50yoOZ+W8hm9SwbQ0lMuFUIsB5af1idTKBRnHKWwFYpOQAgxAq3gxQTgZyHEMumqP9yIT4CrgAi0GTfAQjQFPto1U88APBodZ6fhklbNfgEkS63aU2MuAaah5X7+PyHEYCmlu/KNCoWiG6LWsBWKDsZVzehVtNrDx4DncF97HDQlvQBNaX/i2uYP5LqU9Qy0oi2NOYpWDcsshPBHq74GWsGFUCHERJcsRiHEYCGEDoiWUq4GHgECAJ/T/awKheLMoWbYCkXHcztwTEpZYwb/N3CzECJJSrm2fkMpZbIQwhfIqjcDXwp8JYTYhlYt6WDjE0gpjwshPkIzc6cBO13brUKIq4B/uRS5AW2dPBV4z7VNAP+UUhZ37MdWKBSdiarWpVAoFApFD0CZxBUKhUKh6AEoha34//bqgAQAAABA0P/X7Qj0hAAMCBsABoQNAAPCBoABYQPAgLABYCD2bWYZaY+QeAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Z_al = np.block([[t_al_train**0]]).T\n",
"Z_al_test = np.block([[t_al_test**0]]).T\n",
"Z_al_train = np.block([[t_al_train**0]]).T\n",
"\n",
"max_N = 13\n",
"SSE_al_train=np.zeros(max_N)\n",
"SSE_al_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_al = np.hstack((Z_al,t_al_train.reshape(-1,1)**i))\n",
" Z_al_test=np.hstack((Z_al_test,t_al_test.reshape(-1,1)**i))\n",
" A_al = np.linalg.solve(Z_al.T@Z_al,Z_al.T@P_al_train)\n",
" St_al = np.std(P_al_train)\n",
" Sr_al = np.std(P_al_train-Z_al@A_al)\n",
" r2_al = 1-Sr_al/St_al\n",
" print('---- n={:d} -------'.format(i))\n",
" print('the coefficient of determination for this fit is {:.3f}'.format(r2_al))\n",
" print('the correlation coefficient this fit is {:.3f}'.format(r2_al**0.5))\n",
" plt.plot(t_al_train,P_al_train-Z_al@A_al,'-',label='order {:d}'.format(i))\n",
" SSE_al_train[i]=np.sum((P_al_train-Z_al@A_al)**2)/len(P_al_train)\n",
" SSE_al_test[i]=np.sum((P_al_test-Z_al_test@A_al)**2)/len(P_al_test)\n",
"\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 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": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d) Cost of Steel in 2025 : $ 3825162.46\n",
" Cost of Aluminum in 2025: $ 2829867039.6\n"
]
}
],
"source": [
"# Part d\n",
"\n",
"for i in range(0,47):\n",
" cost_st = a_st_train[i]*2025**i\n",
"print('d) Cost of Steel in 2025 : $',round(cost_st,2))\n",
"for i in range(0,47):\n",
" cost_al = a_al_train[i]*2025**i\n",
"print(' Cost of Aluminum in 2025: $',round(cost_al,2))"
]
}
],
"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
}