{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "ChEn-3170: Computational Methods in Chemical Engineering Spring 2020 UMass Lowell; Prof. V. F. de Almeida **12Apr20**\n", "\n", "# Laboratory Work 11 (14Apr20)\n", "$\n", " \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n", " \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n", " \\newcommand{\\Cmtrx}{\\boldsymbol{\\mathsf{C}}}\n", " \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n", " \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n", " \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n", " \\newcommand{\\Qmtrx}{\\boldsymbol{\\mathsf{Q}}}\n", " \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n", " \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n", " \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n", " \\newcommand{\\yvec}{\\boldsymbol{\\mathsf{y}}}\n", " \\newcommand{\\zvec}{\\boldsymbol{\\mathsf{z}}}\n", " \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n", " \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n", " \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n", " \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n", " \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n", " \\DeclareMathOperator{\\rank}{rank}\n", " \\DeclareMathOperator{\\abs}{abs}\n", "$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Name: `your name`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rubric for each assignment: \n", "\n", "| Context | Points |\n", "| ----------------------- | ------- |\n", "| Precision of the answer | 80% |\n", "| Answer Markdown readability | 10% |\n", "| Code readability | 10% |\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Guidance:\n", " + \n", " Save your work frequently to a file locally to your computer.\n", " \n", " + \n", " Before submitting, `Kernel` -> `Restart & Run All`, to verify your notebook runs correctly.\n", " \n", " + \n", " Save your file again.\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Use the material covered in Notebooks 13 and 14." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "### Table of Contents\n", "* [Assignment 1 (20 pts)](#a1) Single reaction, 3 species in closed reactor vessel.\n", " - [1.1)](#a11) Produce a plot of the equilibrium function as a function of the normalized extent of reaction.\n", " - [1.2)](#a12) Demonstrate the quadratic convergence of Newton's method.\n", " - [1.3)](#a13) Plot the normalized extent of reaction at equilibrium on the equilibrium function plot.\n", " - [1.4)](#a14) Find 3 different initial mole fractions of $A$, $B$ and $C$ that produce the same equilibrium molar fraction.\n", "* [Assignment 2 (40 pts)](#a2) Single reaction, 5 species in closed reactor vessel.\n", " - [2.1)](#a21) Produce a plot of the equilibrium function as a function of the normalized extent of reaction.\n", " - [2.2)](#a22) Demonstrate the quadratic convergence of Newton's method.\n", " - [2.3)](#a23) Plot the normalized extent of reaction at equilibrium on the equilibrium function plot.\n", "* [Assignment 3 (40 pts)](#a3) Single reaction, 6 species in closed reactor vessel.\n", " - [3.1)](#a31) Produce a plot of the equilibrium function as a function of the normalized extent of reaction.\n", " - [3.2)](#a32) Demonstrate the quadratic convergence of Newton's method.\n", " - [3.3)](#a33) Plot the normalized extent of reaction at equilibrium on the equilibrium function plot.\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assignment 1 (20 pts): For each item below respond in a separate notebook cell.\n", "\n", "\n", "Find the equilibrium molar fraction for the following reaction:\n", " \n", "\\begin{equation*}\n", "\\text{A} + \\text{B} \\overset{K_x}{\\longleftrightarrow} \\text{C}\n", "\\end{equation*}\n", "\n", "taking place in a closed reactor vessel.\n", " \n", "At some initial time, the charge to the reactor vessel was:\n", "\n", "Name | Parameter | Value | \n", "----------------------------|--------------|----------| \n", "initial mole fraction of A | $x_{A_0}$ | 0.21 | \n", "initial mole fraction of B | $x_{B_0}$ | 0.38 | \n", "initial mole fraction of C | $x_{C_0}$ | residual | \n", "mole equilibrium constant | $K_\\text{x}$ | 38.7 | " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[1.1)](#toc)\n", "\n", "Produce a plot of the equilibrium function as a function of the normalized extent of reaction. How many roots are there? What is an initial guess for Newton's method to find the appropriate root? Justfiy your answer.\n", "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "'''Parameters for chemical equilibrium of A + B <-> C'''\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "'''Equilibrium function at values or array values'''\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "'''Function: plot equilibrium function'''\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "'''1.1 Plot equilibrium function'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Comment on roots:** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[1.2)](#toc)\n", "\n", " Demonstrate the quadratic convergence of Newton's method.\n", "" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "'''1.2) Equilibrium function derivative'''\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "\"\"\"1.2) Newton's method\"\"\"\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "******************************************************\n", " Newton's Method Iterations \n", "******************************************************\n", "k | f(e_k) | f'(e_k) | |del e_k| | e_k |convg|\n", "------------------------------------------------------\n", " 1 +2.678e+00 -2.342e+01 +1.143e-01 +0.000e+00 0.00\n", " 2 +5.191e-01 -1.434e+01 +3.619e-02 +0.000e+00 1.53\n", " 3 +5.198e-02 -1.147e+01 +4.532e-03 +0.000e+00 1.63\n", " 4 +8.153e-04 -1.111e+01 +7.338e-05 +0.000e+00 1.76\n", " 5 +2.137e-07 -1.111e+01 +1.925e-08 +0.000e+00 1.87\n", " 6 +1.477e-14 -1.111e+01 +1.330e-15 +0.000e+00 1.93\n", "******************************************************\n", "\n", "Equilibrium mole fractions:\n", "\n", "x_a = 6.494e-02\n", "\n", "x_b = 2.662e-01\n", "\n", "x_c = 6.689e-01\n", "\n" ] } ], "source": [ "'''1.2) Find root and equilibrium molar fractions'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[1.3)](#toc)\n", "\n", " Plot the normalized extent of reaction at equilibrium on the equilibrium function plot.\n", "" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "'''1.3) Plot equilibrium function with root'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[1.4)](#toc)\n", "\n", " Many values of the inital mole fraction $x_{A_0}$, $x_{B_0}$ and $x_{C_0}$ exist for a given equilibrium molar fraction $x_{A}$, $x_{B}$ and $x_{C}$. Find 3 different initial mole fractions of $A$, $B$ and $C$ that produce the same equilibrium molar fraction. Show the results and explain your choices.\n", "" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "******************************************************\n", " Newton's Method Iterations \n", "******************************************************\n", "k | f(e_k) | f'(e_k) | |del e_k| | e_k |convg|\n", "------------------------------------------------------\n", " 1 -6.472e-01 -9.471e+00 +6.834e-02 +0.000e+00 0.00\n", " 2 +1.854e-01 -1.490e+01 +1.245e-02 +0.000e+00 1.63\n", " 3 +6.149e-03 -1.391e+01 +4.421e-04 +0.000e+00 1.76\n", " 4 +7.760e-06 -1.387e+01 +5.593e-07 +0.000e+00 1.86\n", " 5 +1.242e-11 -1.387e+01 +8.953e-13 +0.000e+00 1.93\n", "******************************************************\n", "\n", "Equilibrium mole fractions:\n", "\n", "x_a = 6.494e-02\n", "\n", "x_b = 2.662e-01\n", "\n", "x_c = 6.689e-01\n", "\n" ] } ], "source": [ "'''1.4) Alternate initial molar fraction 1'''\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "******************************************************\n", " Newton's Method Iterations \n", "******************************************************\n", "k | f(e_k) | f'(e_k) | |del e_k| | e_k |convg|\n", "------------------------------------------------------\n", " 1 +2.926e-01 -1.456e+01 +2.010e-02 +0.000e+00 0.00\n", " 2 +1.604e-02 -1.296e+01 +1.237e-03 +0.000e+00 1.71\n", " 3 +6.076e-05 -1.286e+01 +4.723e-06 +0.000e+00 1.83\n", " 4 +8.856e-10 -1.286e+01 +6.884e-11 +0.000e+00 1.91\n", "******************************************************\n", "\n", "Equilibrium mole fractions:\n", "\n", "x_a = 6.494e-02\n", "\n", "x_b = 2.662e-01\n", "\n", "x_c = 6.689e-01\n", "\n" ] } ], "source": [ "'''1.4) Alternate initial molar fraction 2'''\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'1.4 Alternate initial molar fraction 3'" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "'''1.4) Alternate initial molar fraction 3'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Explanation of choices of initial molar fractions:** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assignment 2 (40 pts): For each item below respond in a separate notebook cell.\n", "\n", "Find the equilibrium molar fraction for the following reaction:\n", " \n", "\\begin{equation*}\n", "\\nu_A\\,\\text{A} + \\nu_B\\,\\text{B} + \\nu_C\\,\\text{C}\n", "\\overset{K_x}{\\longleftrightarrow} \n", "\\nu_D\\,\\text{D} + \\nu_E\\,\\text{E}\n", "\\end{equation*}\n", "\n", "taking place in a closed reactor vessel.\n", "\n", "At some initial time, the charge to the reactor vessel was:\n", "\n", "Name | Parameter | Value | Name | Parameter | Value |\n", "----------------------------|--------------|--------|----------|-----------|-------|\n", "initial mole fraction of A | $x_{A_0}$ | 0.40 | stoic. A | $\\nu_A$ | 1.8 |\n", "initial mole fraction of B | $x_{B_0}$ | 0.38 | stoic. B | $\\nu_B$ | 2.3 |\n", "initial mole fraction of C | $x_{C_0}$ | 0.11 | stoic. C | $\\nu_C$ | 1.5 |\n", "initial mole fraction of D | $x_{D_0}$ | 0.02 | stoic. D | $\\nu_D$ | 2 |\n", "initial mole fraction of E | $x_{E_0}$ |residual| stoic. E | $\\nu_E$ | 0.6 |\n", "mole equilibrium constant | $K_\\text{x}$ | 101.7 | . | . | . |\n", " \n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[2.1)](#toc)\n", "\n", "Produce a plot of the equilibrium function as a function of the normalized extent of reaction. How many roots are there? What is an initial guess for Newton's method to find the appropriate root? Justfiy your answer.\n", "" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "reaction: 1.8 A + 2.3 B + 1.5 C <=> 2.0 D + 0.6 E\n" ] } ], "source": [ "'''2.1) Parameters for chemical equilibrium of A + B + C <-> D + E'''\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "'''2.1) Molar fractions function'''\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "'''2.1) Derivative of the molar fractions funtio wrt normalized extent of reaction'''\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "'''2.1) Equilibrium function'''" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "'''2.1) Gradient with respect to molar fractions of the equilibrium function'''\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "'''2.1) Function: plot equilibrium function'''\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "'''2.1) Plot equilibrium function'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[2.2)](#toc)\n", "\n", " Demonstrate the quadratic convergence of Newton's method.\n", "" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "\"\"\"2.2) Newton's method\"\"\"\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "******************************************************\n", " Newton's Method Iterations \n", "******************************************************\n", "k | K(e_k) | K'(e_k) | |del e_k| | e_k |convg|\n", "------------------------------------------------------\n", " 1 -1.625e+02 -1.687e+04 +9.630e-03 +0.000e+00 0.00\n", " 2 +3.259e+01 -1.234e+04 +2.641e-03 +0.000e+00 1.28\n", " 3 +5.571e+00 -1.311e+04 +4.249e-04 +0.000e+00 1.31\n", " 4 +1.274e-01 -1.326e+04 +9.604e-06 +0.000e+00 1.49\n", " 5 +6.345e-05 -1.326e+04 +4.783e-09 +0.000e+00 1.66\n", " 6 +1.583e-11 -1.326e+04 +1.194e-15 +0.000e+00 1.79\n", "******************************************************\n", "\n", "Equilibrium mole fractions:\n", "\n", "x_A = 3.618e-01\n", "\n", "x_B = 3.062e-01\n", "\n", "x_C = 3.553e-02\n", "\n", "x_D = 1.511e-01\n", "\n", "x_E = 1.454e-01\n", "\n" ] } ], "source": [ "'''2.2) Find root and equilibrium molar fractions'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[2.3)](#toc)\n", "\n", " Plot the normalized extent of reaction at equilibrium on the equilibrium function plot.\n", "" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "'''2.3) Plot equilibrium function with root'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assignment 3 (40 pts): For each item below respond in a separate notebook cell.\n", "\n", "\n", "Find the equilibrium molar fraction for the following reaction: \n", " \n", "\\begin{equation*}\n", "\\nu_A\\,\\text{A} + \\nu_B\\,\\text{B} + \\nu_C\\,\\text{C}\n", "\\overset{K_x}{\\longleftrightarrow} \n", "\\nu_D\\,\\text{D} + \\nu_E\\,\\text{E} + \\nu_F\\,\\text{F}\n", "\\end{equation*}\n", "\n", "taking place in a closed reactor vessel.\n", "\n", "At some initial time, the charge to the reactor vessel was:\n", "\n", "Name | Parameter | Value | Name | Parameter | Value |\n", "----------------------------|--------------|--------|----------|-----------|-------|\n", "initial mole fraction of A | $x_{A_0}$ | 0.03 | stoic. A | $\\nu_A$ | 1.1 |\n", "initial mole fraction of B | $x_{B_0}$ | 0.05 | stoic. B | $\\nu_B$ | 1.3 |\n", "initial mole fraction of C | $x_{C_0}$ | 0.02 | stoic. C | $\\nu_C$ | 2.5 |\n", "initial mole fraction of D | $x_{D_0}$ |residual| stoic. D | $\\nu_D$ | 2 |\n", "initial mole fraction of E | $x_{E_0}$ | 0.3 | stoic. E | $\\nu_E$ | 1.8 |\n", "initial mole fraction of F | $x_{F_0}$ | 0.4 | stoic. F | $\\nu_F$ | 2.2 |\n", "mole equilibrium constant | $K_\\text{x}$ | 187.9 | . | . | . |\n", " \n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[3.1)](#toc)\n", "\n", "Produce a plot of the equilibrium function as a function of the normalized extent of reaction. How many roots are there? What is an initial guess for Newton's method to find the appropriate root? Justfiy your answer.\n", "" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "reaction: 1.1 A + 1.3 B + 2.5 C <=> 2.0 D + 1.8 E + 2.2 F\n" ] } ], "source": [ "'''3.1) Parameters for chemical equilibrium of A + B + C <-> D + E + F'''\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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pnarDd5yn5jyChlncECZHrofQGCmX/W+2A+igp201/ytVsv/JDQiNkLkA7A10HZrUfUfp2CgAiRAeJitl9f8RwLv6/Ca03HeUU1oD626Iln9dNhKAIA11m9pQXTr8T+pdPyZTxOFwOBwOp4XQJCZxcTgcDofDeX5w58/hcDgcTguDO38Oh8PhcFoY3PlzOBwOh9PC4M6fw+FwOJwWxosc4e+FwNHRkVxdXRvbDA6Hw3mhOHv27EMialY7IzYluPM3Mq6urjhzpj477HI4HE7LhTF2s7FtaM7wbn8Oh8PhcFoY3PlzOBwOh9PC4M6fw+FwOJwWBnf+HA7HYJSUlMDW1haMMWRlZdVbz6lTp9CvXz+0atUKbdu2xYIFC1BSUtJg+54+fYrw8HB4eHjA0tISdnZ2ePXVV7F7926ddWzduhWenp6QSCTo0qULNm1Sv+fVwYMH4efnB3Nzc7i4uGDVqlWoqqpqcB2Uqa6uxkcffQRXV1eYm5uje/fuiI+PV8lz7949fPDBB+jVqxdsbW3RunVrhISE4PvvvzeoLZwXC+78ORyOwfj222/x5MkTAMCuXbvqpePixYsYNGgQnJyccPToUaxatQo7duzA1KlTG2xfeXk5TE1N8cEHH+Dw4cP4+uuv4enpicmTJ+OTTz6p8/ytW7di5syZGDt2LJKSkjB+/HjMnj0bX3zxhUq+Y8eOYezYsejduzcSExMRFRWFVatWYcmSJQ2ugzLLli3D8uXLMXfuXCQmJsLf3x/jx4/Hv//9x+Z6Z8+exb59+zBq1CgcOHAAO3fuhLm5OYKCgnD06FGD2sN5gTDEDlQ8aU49e/YkDqelMGjQILK3t6dXX32V2rRpQ5WVlXrrGD16NHl4eFB5eblCFhsbSwDo7NmzhjRXgb+/P3Xt2lVrnoqKCmrdujVFRESoyCMjI8nBwUHFXl9fXxowYIBKvpiYGDIzM6N79+4ZxObffvuNxGIx/e1vf1ORDxw4kLp166b4XFhYSBUVFbXq8vLLL1P//v0NYosxAHCGmsA9vLkm3vLncFowxcXF8PT0RJ8+fVBRUaGQHz9+HCKRCBs3btRZ1507d3DixAm8+eabePvtt/Hbb7/h2LFjetlTUVGBpKQkhIeHw8zMTCEPDw+HWCzGoUOH9NKnKw4ODirlqSMjIwMPHjzApEmTVOSTJ09GQUEBTp06BQC4desWLly4oDZfRUUFEhMTVeTffvst/P39YWFhATs7O4wfPx6//vprnTYfO3YM5eXltcqZNGkSLl26hNzcXACAnZ0dTE1VV3WbmprC19cXd+7cqbMcTvOEO38OpwVjaWmJPXv2ICsrC8uWLQMA5OfnIyIiAmFhYZgzZ47Our766itUV1cjIiIC4eHhMDc3R2xsrF723LhxA6WlpejatauK3NzcHO7u7rhy5YpCRkSorKysM1VXV9cqR35uQUEBtmzZgmPHjiE6OlqrbdnZ2QBQyzZvb28AUNimKZ+bmxssLCxU6rBp0yaMHTsWXl5eOHDgADZv3ozLly8jMDAQT58+rdMeiUQCDw8Prfaoo7y8HBkZGXjllVe0lsFpvnDnz+G0cPz8/LB69Wp8/PHHSElJQUREBExMTLB9+3a99OzatQtdunTBq6++ChsbG4wePRqHDh1CUVGRzjoePXoEAJBKpbWO2dvbK44DQGxsLMzMzOpM06ZNq6Vr48aNMDMzg6OjI+bOnYv169cjIiKiXrbZ29urHNdWB6lUqjj++++/Y/HixYiMjMT27dsxbNgwTJgwAYmJibhz5w6+/PLLOu2xs7MDY0yrPepYvnw5bt++jcWLF2stg9N84RH+OBwOoqOjkZycjLCwMJSXlyM5ORmOjo46n//TTz/h559/xqpVqxSyKVOmYO/evdi/fz9mzJihkx5hqBe1HJryMTkjRoxAZmZmnTrV1WPChAnw9/fHw4cPcfjwYcybNw8mJiaYOXNmvWyrTx0yMjLw5MkTTJw4EZWVlQp5hw4d4Onpie+//x7R0dGorq5W6b0QiUQQiUQgIp2uU02+/vprrF69GsuWLUP//v215uU0X7jz53A4YIxh8uTJSExMhK+vL0JCQvQ6X969P2LECEVLv3fv3mjdujViY2N1dv7aWq2FhYWKLm15Xltb2zp1ikS1Ozhbt26N1q2FsPFDhw7Fs2fPsHDhQkybNk3j2L+ybS+99JJCLrdVflxbHYqKihTH8/PzAQChoaFqy5P3HEybNk1l+GTKlCnYuXMn7O3tUVhYWOshoLCwUMUOZY4cOYKpU6di+vTpiImJUVsup2XAnX8TpboaKCtrbCuMSx0NqOemV1N+bXqUj+lyPmPGq68huH//PqKjo9GjRw+cP38e69evR1RUlE7nlpeXY+/evQCA7t271zr+4MEDXL9+vdbYtDrc3d0hkUgU4+ZySktLkZOTg/HjxytksbGxiIyMrFOn3Flqo1evXoiNjcVvv/2GDh06qM0jf/DIzs5Wcf7ysXUvL69a+fr27avIl5eXh2fPninyOTg4AAB27typ8lAjx9raGgAUS/nkyHsyvL29UVZWhhs3bqhc25r2yDlx4gTGjx+PMWPGYPPmzVqvB6f5w51/E+Xnn4Ea84U4zRB1DxHKDwry98pJk1yeRCLt70Ui1cQY4e7dKSgvF0MqTYa9/SrMn78YmzYFw8rKByYmUJtMTYX0229H8OjRI3Tt+iHatw9SOV5e/hsSEt7EtGm7MHjwCojFUCSJBDA3F5L8fatWYvj7D8Xu3fsRGbkcNjamsLQE4uMPoKysDCNHjlRcr4Z0+9ckPT0dVlZWcHJy0pinb9++cHR0RFxcnEprfffu3bC3t0dAQAAAwNnZGd27d0dcXBzefvttlXxmZmZ4/fXXAQD9+vWDtbU1rl+/jilTpmgs19XVFep2Bh06dCjEYjHi4uLw4YcfqpTTtWtXuLm5KWQZGRkYNWoUQkJCsHv3brW9IZyWBXf+TZQ2bYDVqxvbCuNRx7Dkc9OrKb82PcrHdDmf6I/Pms5VPl7zvXLSJFdO1dXa31dXq77Pzl6HkpIUBAaehL29PaqqViMtLQ23b7+Ffv3OAGiFqiooUnm58FpZKaScnFiIRFYoLl6Iq1etUFEBlcTYJ/jhh1344YcYALp0fywH0BceHuEA5gDIA7AIJibjEBbWE9bWgLU1YGPjAFtbB9jaAnZ2gFQK2NsLr46OfyRlf75582b85z//QWhoKDp06ICCggLs378fBw4cwOrVqyEWixV5PTw84OLighMnTgAAzMzMsHLlSsyePRvt27dHaGgoTp48ie3bt2PDhg0q5/7jH/9AWFgYZs6cibfeegvnz5/HqlWrEBUVhbZt2wIAbGxs8K9//Qtz5szBgwcP8Prrr8PW1hZ37txBeno6goKC8Kc//UnjVXJycsL8+fPx0UcfwdraGj169MC+fftw8uRJlSWRV69exfDhw+Ho6IhFixbh7NmzKnr8/f11+E44zY7GDjTQ3BMP8sNpypw7d47EYjEtXbpURX716lWysLCgWbNmaT0/Pz+fTE1Nadq0aRrzbNmyhQBQSkoq/f470aNHRPfuEd28SfTLL0QXLxL99BNRejrRsWNEBw8SLVuWTp06+ZOpqYSsrJyoT58omju3mN5+m2jCBKJhw4j69yfy8SFycSGytdX+SGRlReThQdS9+2l66aXXydKyLZmYiMnevh316RNCe/cerWW3i4sLBQYG1pJv2rSJOnfuTGKxmDw8PGjjxo1q6x0fH08+Pj4kFoupY8eOFBMTozboUUJCAgUFBZG1tTWZm5uTu7s7RUZGUnZ2ttZrT0RUWVlJK1euJGdnZxKLxdStWzf65ptvVPLs2LGDAGhMTRXwID9GTUy4xhxj0atXLzpz5kxjm8HhNHuqqoCiIuDRI+DhQyE9eADk5wP37wO//QbcvQvcuSOk0lLV8+3tAQ8P4OWXgVdeAby8AG9vwN1dGB7hPF8YY2eJqFdj29Fc4d3+HA6nWWBiAjg4CKlzZ+15iYCCAuDmTSHl5AA3bgDXrgFpaYDyPj9WVkC3bkCPHoC/P/Dqq8JDQlOewMnh1AVv+RsZ3vLnvMjUXGNeE8YYTExMnrsuY/P0KXD1KnDpEnDhgpDOnQOKi4Xjjo5AUJCQQkKALl34w4Ch4S1/48I7szgcjkbk6941JX3iAaxYsUKrLnd3dyPWRD+srYHevYFp04D/+z/g+++Bx4+BixeBLVuAYcOA//4XmDtXGCJwdxfeHzsmTHLkcJo6vOVvZHjLn/Mik5eXh4cPH2o8bm1tjS5duuik6+7du7h7967G4xKJBN26ddPbxsaCCMjLA44fBxISgJQUoKREGHZ44w3grbeAwEA+X6C+8Ja/ceHO38hw58/htAxKS4UHgX37gEOHhCECd3fgnXeAqVOF5bsc3eHO37jwZ1IOh8MxAObmwMiRQFycsMIgLg7o0AF4/32gY0dg+nTgl18a20oOR4A7fw6H02CCgoLAGFOkVq1awdPTEytXrkRZPeJUnzp1Cv369UOrVq3Qtm1bLFiwACUlJQax1dXVVcVWeTp48KBO5x88eBB+fn4wNzeHi4sLVq1ahaqqKpU8FhaAs/MplJf3g0TSCqambREbuwCeniUYOxaoEb24QWzduhWenp6QSCTo0qULNm3apHL8yZMnWLFiBfr16wcHBwfY2dmhX79+OteX00xp7EADzT3xID+clkBgYCD5+PhQRkYGZWRk0IkTJ+jDDz8kExMTmjt3rl66srKyyNzcnEaNGkUpKSm0detWsrOzo/DwcIPY6uLiQkOGDFHYKk+PHj2q89ykpCQSiUT0zjvv0MmTJ2nt2rUkkUjovffeq7MOtrZ25OUVTra2RCIR0dtvE92927C6bNmyhRhjtGTJEjp58iQtXbqUGGP0+eefK/JcunSJ2rRpQ++//z79+9//pqSkJJoyZQoBoM8++6xhBhgR8CA/Rk2NbkBzT9z5c1oCgYGBFBAQUEs+ceJEcnJy0kvX6NGjycPDg8rLyxWy2NhYAkBnz55tsK0uLi40ceLEep3r6+tLAwYMUJHFxMSQmZkZ3bt3TyHTVocTJ85SdDSRmRmRhQXRv/5FVFGhvy0VFRXUunVrioiIUJFHRkaSg4ODouzff/+diouLa50/cOBA6tixo/4FPye48zdu4t3+HE4Lpri4GJ6enujTpw8qlNaoHT9+HCKRCBs3bmyQfhsbGxW9dVFRUYGkpCSEh4erbK0bHh4OsVisErP+eXPr1i1cuHABkyZNUpFPnjwZFRUVSExMBFB3HdLTD+GTT4TNu0JCgEWL0mFvHwJLS2tYWlpiyJAhuHz5cp32ZGRk4MGDB2rtKSgowKlTpwAAlpaWsLCwqHV+r169tK6+4DRvuPPncFowlpaW2LNnD7KysrBs2TIAwj7zERERCAsLw5w5c/TSV1lZicrKSjx58gRHjx5FXFwcJkyYoPP5N27cQGlpKbrW2NLS3Nwc7u7uiu1qAaHXUl6etqQusNCRI0dgYWEBiUQCf39/nca/5dsM17TNzc0NFhYWCtt0rYO7OzBjRgJEohCUlVmhtHQ3xo37Gk+fPkX//v1x69atetkj3x5Y+Vqp4/vvv4enp6fWPJzmC3f+HE4Lx8/PD6tXr8bHH3+MlJQUREREwMTEBNu3b9dLz+nTpxUBe2xtbTFixAgEBgbik08+0VnHo0ePAABSqbTWMXt7e8VxAIiNjdUaNEiepk2bpqJnxIgR2LBhA44dO4a4uDiYm5tjzJgx2K0c01dP26RSqeK4PnWIjo5CUFAg7t49hDfeGIVdu0bBzi4JIpEJ1q5dWy977O3tVY6rY8uWLfjPf/6DDz74QGsZnOYLj+3P4XAQHR2N5ORkhIWFoby8HMnJyXB0dNRLR/fu3bFt2zYAQFlZGS5duoTly5dj/PjxOHz4MJgO8W+FoV6ozSs/JmfEiBHIzMysU2fNemzYsEHl85gxY+Dv748PPvigVhd6fWzTNd+1a9dw48YNLFmyBLa2lfj6a6BfP2DRIguIxX1x7Nj3AGqHRZaHQdZWjjbS0tLw5z//GZMnT8bEiRP1OpfTfODOn8PhgDGGyZMnIzExEb6+vnqF7ZVjZWWFXr3+iMlfecmTAAAgAElEQVQSEBAABwcHhIeHIykpCa+//nqdOrS1WgsLCxVd2vK8tra2deoU1RFiz8TEBOPHj8fixYtx7949vPTSS3rbVlRUpDiuax3y8/MBANOnT8f06dNV8pWUAL/84oy0NCAtbQViYmIUxwIDA5GWlqZSjrLN8nLlx5XJzMzEyJEjMXDgQHz55Zdq68lpGfBufw6Hg/v37yM6Oho9evRAVlYW1q9fbxC9ckd38eJFnfK7u7tDIpEoxrPllJaWIicnB15eXgpZfbv91aFLK1pel5q25eXl4dmzZwrbdK2Dg4MDAOCjjz5CZmamSjpyJBOurkcwZAjQvv0MlWObN2/Wao98rF/5WgHApUuXMGTIEPj6+iI+Pl5lMiKnBdLYyw2ae+JL/ThNnerqaho8eDB16NCBCgoKaP78+SSRSCgrK0tnHZqW+u3Zs4cA0JdffqmzrlGjRlHnzp2pQmn921dffUUA6MyZMwrZw4cPKTMzs86Um5urtbyKigrq2bMnOTs712lb9+7dKSgoSEW2cuXKWkv9dKlDdXU1ubq60qRJk9SWVVBA1LcvEWNE6i5feXk5OTo60tSpU1Xk06dPJ3t7eyorK1PI/ve//1GbNm2oZ8+e9Pjx4zrr2RQAX+pn1NToBjT3xJ0/p6mzZs0aEolElJaWRkREZWVl5OfnR15eXvTs2TOddNQM8pOenk4bNmwgJycnat++PRUWFupsz/nz58nc3JzGjBlDKSkptG3bNpJKpTRu3Lh61U+Zr7/+miZMmECxsbF08uRJ2rNnD7322msEgPbs2aOSd+DAgeTu7q4iS0hIIMYYzZgxg1JTU2ndunUkkUho4cKF9apDQkICmZqaUnh4OB04cIDS0tJo3759FBUVRWvXrqXiYqLBg4WgQN98U7s+X3zxBTHGaOnSpZSamkrLli0jxphK8J7ffvuNXFxcSCqV0tGjR2sFNyotLW3gVTUO3PkbNzW6Ac09cefPacqcO3eOxGIxLV26VEV+9epVsrCwoFmzZumkJzAwkAAokpmZGXXq1IlmzJhBt27d0tuu9PR08vf3J4lEQk5OThQVFaU2UI2+ZGRkUHBwMDk5OZGpqSnZ2NhQSEgIJSUlqa2Ti4tLLXl8fDz5+PiQWCymjh07UkxMDFVWVta7Dj/++CMNHz6c7OzsSCKRkIuLC02YMIF+/PFHIiIqLiYKCBCCAh0/XrtOmzZtos6dO5NYLCYPDw/auHGjyvHU1FSV76ZmqqtnpLHgzt+4ie/qZ2T4rn4cDqehFBUBQUHAtWvAiROAv39jW2R8+K5+xoVP+ONwOJwmjp0dcOwY8NJLwJgxwL17jW0R50WHO38Oh6OR6upqrdHzau5m97x0tUTatAEOHQKePAHGjwf0iJrM4dSCO38Oh6ORadOmaV1Gp088gBUrVmjV5e7ubsSaNA+8vYEvvwROnwbee6+xreG8yPAxfyPDx/w5LzJ5eXl4+PChxuPW1tbo0qWLTrru3r2rdSMZiUSCbt266W1jSyQ6Gli/HtizB3jzzca2xjjwMX/jwp2/keHOn8PhGJqKCmECYHY2cOUK0K5dY1tkeLjzNy6825/D4XBeMMzMgJ07gbIyYPZsgLfhOPrCnT+Hw+G8gHTuDKxYIUwC3L+/sa3hvGhw58/hcAxCRUUFPv/8cwQEBMDOzg4SiQRubm6YNm0azp07p5eu7OxsDB48GFZWVnBwcEBkZKTWLWp15d69e/jggw/Qq1cv2NraonXr1ggJCcH333+vs45Tp06hX79+aNWqFdq2bYsFCxagpKTkudVBmfnzAXf3g5g0yQ/m5uZwcXHBqlWrVFZOVFVVYc2aNRg4cCDatGkDa2tr9OjRA19++aXKboGcFkZjRxlq7olH+OO0BH7//Xfq378/mZubU3R0NB09epTS0tJo27ZtFBQURHZ2djrrunPnDjk6OtJrr71GiYmJtGfPHurQoQP17duXqqqqGmTnkSNHyM3NjVasWEHHjx+no0eP0rBhw4gxRkeOHKnz/KysLDI3N6dRo0ZRSkoKbd26lezs7Cg8PPy51UGZpKQkEolExNg7NGjQSVq7di1JJBJ67733FHmePn1Ktra2NG/ePDp48CClpKTQggULiDFWKyxxUwI8wp9RU6Mb0NwTd/6clsD06dNJLBYrQtLW5Ntvv9VZV3R0NNna2qrsB5Cenk4AKD4+vkF2FhYWqmy2QyRs7PPyyy9T//796zx/9OjR5OHhQeXl5QpZbGwsAaCzZ88+lzoo4+vrSwMGDKAPPhDu5pmZRDExMSobDVVWVlJBQUGtcyMjI0kikei8f8Pzhjt/4ybe7c/htGCKi4vh6emJPn36oEIpaszx48chEomwcePGOnXcu3cPO3fuxDvvvIO+ffuqzTNmzBidbTp8+DCGDx8OOzs7hWzAgAFwdnbGoUOHdNajDjs7O5iamqrITE1N4evrizt37mg9t6KiAklJSQgPD1fZDjc8PBxisVjFNn3qkJWVhZEjR0IqlaJVq1YICAjADz/8UGddbt26hQsXLmDSpEl4/33A0RFYvBiYNGkyKioqkJiYCAAwMTGBvb19rfN79+6NsrIyrUs5Oc0X7vw5nBaMpaUl9uzZg6ysLCxbtgwAkJ+fj4iICISFhWHOnDl16khNTUVVVRVGjhzZYHtKSkqQm5uLrl271jrm7e2t2KseEHottUUM1DVyYHl5OTIyMvDKK69ozXfjxg2UlpbWss3c3Bzu7u4K2/Spw7lz59CvXz88evQIW7duRXx8PBwcHBAaGoqzZ89qtSc7OxsA0LVrV9jYAMuWASdPAv/7nxssLCxUylFHeno67Ozs8NJLL2nNx2mecOfP4bRw/Pz8sHr1anz88cdISUlBREQETExMsH37dp3Ov3XrFgDAxcWlwbYUFhaCiCCVSmsds7e3V5kwl56erjVioK5RCJcvX47bt29j8eLFWvPJy67LNn3qsGjRIjg7O+PkyZMYN24chg0bhu+++w6dOnXCypUr9bJn1iygUyeh9S+VSrVOLjx27Bj279+PhQsX1uoJ4bQM+LfO4XAQHR2N5ORkhIWFoby8HMnJyXB0dHzudghDvQBjTOMxOT179kRmZmadOq2trTUe+/rrr7F69WosW7YM/fv3N4htuuYrKSlBeno6lixZApFIhMrKSsWx0NBQxMXFKc5R7r1gjMHExKRWOWIx8I9/CBH/7Ow0L/y/cuUK3nrrLQQFBdX5wMNpvnDnz+FwwBjD5MmTkZiYCF9fX71i9nfs2BEAcPPmTZ1D/WpCKpWCMaa21VpYWKgydm1lZQVfX986dapzwgBw5MgRTJ06FdOnT0dMTEydeuRla7LN29tbrzo8evQIVVVVWLlypcZWfnV1NXbt2oXIyEiFzMXFBXl5eWrtGT8eWLMGOHu2CHZ2tcf5c3JyMGjQILi5ueHgwYO81d+C4d3+HA4H9+/fR3R0NHr06IGsrCysX79e53ODgoJgYmKCI0eONNgOCwsLuLq6Ksazlbly5Qq8vLwUnxvS7X/ixAmMHz8eY8aMwebNm3Wyzd3dHRKJpJZtpaWlyMnJUdimax3s7OwgEokwb948ZGZmqk0ikQgjRoxQkcmvs/xhQ7kckQiYOTMPRM9QXOylUvbt27cREhICGxsbJCUlwcbGRqd6c5opjb3coLknvtSP09Sprq6mwYMHU4cOHaigoIDmz59PEomEsrKydNZR11K/7777TmddUVFRZGdnR0VFRQrZDz/8QADowIEDCtmTJ08oMzOzznT16lUV/T/++CNZWlrSsGHDVJbs6cKoUaOoc+fOKssFv/rqKwJAZ86c0bsOgYGBNGDAgHqv/e/evTsFBQWpyFasWEmAGXXrdo+qqwVZfn4+denShVxdXenWrVv1Kut5A77Uz6ip0Q1o7ok7f05TZ82aNSQSiSgtLY2IiMrKysjPz4+8vLx0XgP+9OlT6t+/P7Vq1Yrmz59PCQkJlJ6eTjt27KDQ0FC9gvzcvn2bHBwcaMCAAZSYmEh79+4lZ2dn6tOnT4MD5Pz8888klUrJxcWFUlNTKSMjQyUpM23aNDIxMVGRnT9/nszNzWnMmDGUkpJC27ZtI6lUSuPGjatXHc6ePUuWlpYUGhpKe/bsobS0NDpw4AAtWbKEFi9eXGd9EhISiDFGM2bMoNTUVFq3bh1JJBIaNGghAUSpqUTPnj0jPz8/kkgkFBcXV6vOjx8/rv8FNSLc+Rs3NboBzT1x589pypw7d47EYjEtXbpURX716lWysLCgWbNm6ayrvLycPvvsM+rbty9ZW1uTmZkZubq60vTp0/XqRSAiunjxIoWGhpKFhQXZ2dnRlClT6OHDh3rpUMeOHTsIgMakzJQpU2rJiIRgPf7+/iSRSMjJyYmioqKouLi43nW4cuUKTZgwgVq3bk1isZjat29PI0aMoISEBJ3qFB8fTz4+PiQWi6ljx44UExNDT59WUuvWRMOHE+Xm5mqtc2pqqm4X7znDnb9xE9/S18jwLX05HE5jsGIF8OGHwpa/dYQwaJLwLX2NC5/wx+FwOM2Q2bMBc3Ng3brGtoTTFOHOn8PhaKS6urpB0fOUIao7Ih/HcDg6AlOnAl99BRQWNrY1nKYGd/4cDkcj06ZNa1D0PGViY2PrXJbHMSxvvw2UlQH79ze2JZymBh/zNzJ8zJ/zIpOXl6d14xdra2udA/sUFBQgNzdXa55evfgQryEhAnx8ACsrICOjsa3RDz7mb1x4eCcOh6MRV1dXuLq6GkSXg4MDHBwcDKKLoxuMCV3/CxcCV68Cnp6NbRGnqcC7/TkcDqcZM3EiYGICxMY2tiWcpgR3/hwOp8EEBQWBMabYdEYqlcLX1xfz5s1TG+ZWFwoLC/H222/D0dERlpaWCA0NxaVLlxpsa1VVFdasWYOBAweiTZs2sLa2Ro8ePfDll1+iurpaJx23bt3CuHHjYGtrCxsbG7zxxhv49ddfn1sdapKdnY3BgwfDysoKDg4OiIyMVMT8b9sWGDoU2LnzNubOnYe+ffvCwsICjDHk5eUZ3BbOiwF3/hwOxyD4+PggIyMDp0+fxr59+xAREYHU1FT4+vri888/10sXEWHkyJFISkrChg0bEB8fj4qKCgQHB+P27dsNsrOkpASrVq1C165dsWXLFhw8eBDBwcF45513dNrl7tmzZxg4cCCuXr2K2NhYfPXVV7h27RqCg4NRXFz8XOqgzN27dxEUFISSkhIcOHAAGzduREpKCsLCwhQPM1OnAvfvX0dc3H5IpdI6dzDktAAaO8pQc088wh+nJRAYGEgBAQG15OXl5TR27FgSiUT0008/6azv4MGDBIBOnjypkBUVFZFUKqV58+Y1yNbKykoqKCioJY+MjCSJRFJnSONPP/2URCIRXbt2TSHLyckhExMTWrt27XOpgzLR0dFka2tLhYWFCll6ejoBoPj4eCIiKi0lsrOrorfeEo5v3bqVAFBubq7B7DA04BH+jJp4y5/DacEUFxfD09MTffr0QUVFhUJ+/PhxiEQibNy4sUH6zczM8Pnnn8PU1BT/93//p/N5hw8fRrt27RAcHKyQ2draYsSIETh06FCDbDIxMVHZGlhO7969UVZWpnV1g9w2f39/eHh4KGRubm4ICAhQsU2fOjx8+BDvvvsu2rdvD4lEAk9PT2zZskWn+hw+fBjDhw+HnZ2dQjZgwAA4OzsrypFIgIkTRfjuO+D333VSy2nmcOfP4bRgLC0tsWfPHmRlZWHZsmUAgPz8fERERCAsLAxz5sxpcBlOTk7o1asXTp8+rfM52dnZ6Nq1ay25t7c3fv31V/yu5MHqChykawCh9PR02NnZ4aWXXqq3bVeuXNG7Dk+ePEFAQAASEhKwfPlyJCQkYMSIEXj33XexYcMGrbaUlJQgNzdXJ3vGjwdKS4Fjx7Sq5LQQ+FI/DqeF4+fnh9WrV+Mvf/kLQkNDsWbNGpiYmGD79u0GK8PZ2Rnnzp3TOf+jR4/ULjGUt9gLCwthZWUFADoHBxJ6ktVz7Ngx7N+/HytXroSpqfbb4qNHjyCVStXaVqgUSk/XOqxfvx43b97EpUuX0LlzZwBAaGgoioqKEBMTg3fffVejTYWFhSAijfb88ssvis8BAYC9PXDoEDBggNYqcloA3PlzOBxER0cjOTkZYWFhKC8vR3JyMhwdHQ2mn4jAGGtwfnUOPDMzs0G2XblyBW+99RaCgoJ0mvAHQCfbdK1DUlISXn31Vbi5uan0UAwZMgTbtm3DlStX4OPjU6v3wtTUVKFLl3JMTYHhw4GEBOFBgNOy4c6fw+GAMYbJkycjMTERvr6+eoXt1YVbt27V2Z2ujL29vWKpmjLylrVyS9fX17feduXk5GDQoEFwc3PDwYMH62z1y8vWZJuyXbrWIT8/H9evX9fYg1FQUIC8vDy4ubmpyHNzc+Hk5ATGmMZyas5tGDVKiPV//XodleQ0e7jz53A4uH//PqKjo9GjRw+cP38e69evR1RUlEF05+fn48yZM3jzzTd1Psfb2xvHjx+vJb9y5QqcnZ0VXf5A/bv9b9++jZCQENjY2CApKQk2NjY626YudsGVK1fg5eWldx0cHBzg5OSE9evXqy2vS5cukEgktXo42rVrB7FYDFdXV432BAYGqsiGDBEm/124UHc9Oc0b7vw5nBYOEWHKlCkQi8VITk7GqlWrsHjxYgQHB8PHx6dBuisqKjB79mxUVlbiz3/+s87njRw5Ejt27EB6errCgT158gRHjhzBn/70J5W89en2f/DgAUJDQwEAycnJaN26tV62LVy4EDk5OejUqRMAYQ+E06dPY/Xq1XrXYejQodiwYQOcnZ3h5OSksVxN+x6MHDkSsbGxePz4MWxtbQEAp06dws2bNzFy5EiVvFZWQEgI8NNPOleX01xp7LWGzT3xdf6cps6aNWtIJBJRWloaERGVlZWRn58feXl51bnmXU5gYCD5+PhQRkYGZWRk0PHjx2nt2rXUtWtXMjMzo02bNullU1VVFfXt25c6dOhAe/bsoaSkJAoMDCSpVEq//vqr3nVU5tmzZ+Tn50cSiYTi4uIUNsvT48ePFXljY2PJxMREcW2IiH7//Xdyd3enrl270sGDB+nQoUPk4+NDbm5u9PTpU73rUFRURJ6envTyyy/TF198QSdPnqQjR47Qv/71Lxo5cmSd9bl9+zY5ODjQgAEDKDExkfbu3UvOzs7Up08fqqqqUsn7zTff0DvvfEPALAJAn3/+OX3zzTcq9WsqgK/zN2pqdAOae+LOn9OUOXfuHInFYlq6dKmK/OrVq2RhYUGzZs3SSU9gYCABIADEGCMbGxvq3r07zZ07ly5fvlwv2woKCigyMpKkUim1atWKBg4cSBcuXKiXLmVyc3MVtqpLqampirw7duyoJSMiunnzJr3xxhtkbW1NVlZWNGrUKLUBc3Stw6NHjyg6OppcXV3JzMyMWrduTa+99hp98sknOtXp4sWLFBoaShYWFmRnZ0dTpkyhhw8f1sqnqc6BgYE6lfM84c7fuIlv6Wtk+Ja+HA6nqfHqq8J2v025+59v6WtceJAfDofDaWGMGgVkZgL37ze2JZzGgjt/Doejkerqaq1R86qqqvTWWVckPt4baXwGDRJe09Ia1QxOI8KdP4fD0ci0adNgZmamMekbDyAvL0+rPjMzM6SnpxupNhw5fn6AjQ2QmtrYlnAaCz7mb2T4mD/nRSYvL0/rRjfW1tbo0qWLzvrKy8tx8eJFrXm6dOkCa2trnXVy6seIEcAvvwD/+19jW6IePuZvXPg6fw6HoxFXV1e18enri1gs1rhenfN8CQoCjh4F7twB2rdvbGs4zxve7c/hcDgtEPlOw3zcv2XCnT+Hw+G0QLp3B+zs+Lh/S4U7fw6H02CCgoLAGFOboqOj9dKVnZ2NwYMHw8rKCg4ODoiMjFS7cU19iIyMxCuvvAIbGxtYWVmhe/fu2LBhg86rFg4ePAg/Pz+Ym5vDxcUFq1atUnvuqVOn0K9fP7Rq1Qpt27bFggULUFJSYpA6KLN161Z4enpCIpGgS5cu2LRpU6088nDCL7/8MkQiEYKCggAAJibC1r7c+bdM+Jg/h8MxCD4+Pti8eXMtuT67+d29exdBQUHw9PTEgQMHUFRUhEWLFiEsLAynTp2CSNSw9kpJSQnmzZsHd3d3MMZw7NgxREVF4fr16xo31pFz7NgxjB07FtOnT8e6detw/vx5LFmyBE+fPsU///lPRb6LFy9i0KBBGDJkCI4ePYrc3FwsWrQId+7cwb59+xpkvzJbt27FzJkz8cEHHyA0NBQnTpzA7NmzQUR49913FfkOHjyICxcuwN/fH6WlpSo6goOBw4eBX38FnJ0NZhrnRaCxQww298TD+3JaAoGBgRQQENBgPdHR0WRra0uFhYUKWXp6OgGg+Pj4ButXx5tvvklWVlZ15vP19aUBAwaoyGJiYsjMzIzu3bunkI0ePZo8PDyovLxcIYuNjSUAdPbsWYPYXFFRQa1bt6aIiAgVeWRkJDk4OKiUrRzfPyAgQCWU74ULRABRbKxBzDIo4OF9jZp4tz+H04IpLi6Gp6cn+vTpg4qKCoX8+PHjEIlE2Lhx43O15/Dhwxg+fDjs7OwUsgEDBsDZ2RmHDh0ySpkODg4wNdXeCXrr1i1cuHABkyZNUpFPnjwZFRUVSExMBCDsYpiUlITw8HCVrYbDw8MhFotr1SE9PR0hISGwtraGpaUlhgwZgsuXL9dpc0ZGBh48eKDWnoKCApw6dUoh09Zb0q0bYG/Pu/5bItz5czgtGEtLS+zZswdZWVlYtmwZACA/Px8REREICwvDnDlz9NLXkIh9JSUlyM3NRdeuXWsd8/b2xpUrVxSfiajOSIGaIhDKzy0qKkJ8fDxiY2OxYMECrbZlZ2cDQC3b3NzcYGFhobDtxo0bKC0trZXP3Nwc7u7uKnVISEhASEgIrKyssHv3bnz99dd4+vQp+vfvj1u3btXLHm9vbwBQKUcbIhEQGMidf0uEO38Op4Xj5+eH1atX4+OPP0ZKSgoiIiJgYmKC7du366Xn9OnTaiP2xcfH63R+YWEhiAhSqbTWMXt7e5VJf+np6XVGCtQUgTAhIQFmZmaQSqUYP3485s2bp3jw0YS8bHW2SaVSxXFt+WrWISoqCoGBgTh06BBGjRqFUaNGISkpCSYmJli7dm297LG3t1c5rgvBwcDNm0Bens6ncJoBfMIfh8NBdHQ0kpOTERYWhvLyciQnJ8PR0VEvHd27d8e2bdtqyd3d3XU6X95DwBjTeExOz549kZmZWadOdZEC+/fvj8zMTDx+/BgnTpzAmjVrwBjD3//+9wbbpmu+a9eu4caNG1iyZAkqKysVcgsLC/Tt2xfff/89AGFvherqasVxxhhMTEy0lqMv/foJr//9L2DAeE6cJg53/hwOB4wxTJ48GYmJifD19dU7Zj8AWFlZNSh6n1QqBWNMbau1sLBQ0aqVl+Xr61unTnXO0dbWVmFnSEgIxGIxVq5cidmzZ6O9hlB32lrURUVFiuPa8hUWFiq65fPz8wEA06dPx/Tp02vldZZNvV+xYgViYmIU8sDAQKSlpamUo7yaQl6u8rWqi27dALEYOHMGmDBB59M4Lzjc+XM4HNy/fx/R0dHo0aMHzp8/j/Xr1yMqKuq52mBhYQFXV1fFeLYyV65cQWBgoOJzeno6guUh6rQgd5ba6NWrF6qrq5Gbm6vR+cuddnZ2Nvr27auQ5+Xl4dmzZ/Dy8gIg9HJIJJJadSgtLUVOTg7Gjx8PQJhkCAAfffQRQkNDa5UnFosBADNmzEBYWJhCLu/JULZH2fnLx/rl9uiCWAz4+gpb/HJaDtz5czgtHCLClClTIBaLkZycjFWrVmHx4sUIDg6Gj4/Pc7Vl5MiRiI2NxePHj2FrawtACJhz8+ZNjBw5UpGvId3+NUlPTwdjDJ06ddKYx9nZGd27d0dcXBzefvtthXz37t0wMzPD66+/DkBw2kOHDsX+/fuxfPlyxSqCAwcOoKysTFGHLl26KB503n//fY3ltmvXDu3atasl79u3LxwdHREXF6fy8LB7927Y29sjICCgznor07s3EBsLVFUJwX84LYDGXmvY3BNf589p6qxZs4ZEIhGlpaUREVFZWRn5+fmRl5cXPXv2TCcdgYGB5OPjQxkZGbXS1atXdbbl9u3b5ODgQAMGDKDExETau3cvOTs7U58+fVTWq9eHo0eP0tixY2nnzp108uRJOnToEM2aNYtEIhHNmjVLJe/AgQPJ3d1dRZaQkECMMZoxYwalpqbSunXrSCKR0MKFC1XynT9/nszNzWnMmDGUkpJC27ZtI6lUSuPGjaulz9TUlMLDw+nAgQOUlpZG+/bto6ioKFq7dm2d9fniiy+IMUZLly6l1NRUWrZsGTHG6LPPPlPJl5eXR9988w1988035OnpSV5eXorPeXl5RES0YwcRQJSdrevVND7g6/yNmhrdgOaeuPPnNGXOnTtHYrGYli5dqiK/evUqWVhY1HKKmggMDCQAatPw4cP1sunixYsUGhpKFhYWZGdnR1OmTKGHDx/qpUMdP//8M40ZM4Y6dOhAYrGYnJycKCAggHbv3l3rwSIwMJBcXFxq6YiPjycfHx8Si8XUsWNHiomJocrKylr50tPTyd/fnyQSCTk5OVFUVBQVFxfXyvfjjz/S8OHDyc7OjiQSCbm4uNCECRPoxx9/1KlOmzZtos6dO5NYLCYPDw/auHFjrTw7duzQ+N3s2LGDiIguX6YmF+yHO3/jJiZcY46x6NWrF505c6axzeBwOByNVFUBtrZAZCSwYUNjWyPAGDtLRHz/ZyPB1/lzOBxOC8fEBOjZk0/6a0nwCX8cDkcjNdeZ10S+7rwuiKjOnfPqCrHLMS69ewOffQaUlwsrADjNG97y53A4Gpk2bZreEfTUERsbW2c0Pk7j0gTg3t8AAB+7SURBVLs3UFYGqFlpyWmG8EdtDoejkeXLl2Pu3Lkaj+uylA4ARowYodPSPE7jIY/PlJkJ+Pk1ri0c48OdP4fD0YirqytcDRDz1cHBQRHYhtM06dRJ2OEvMxOYMaOxreEYG97tz+FwOBwwJrT+eQdNy4A7fw6Hw+EAEMb9L18GSkoa2xKOseHOn8PhNJigoCAwxmqlDh066KXn1q1bGDduHGxtbWFjY4M33ngDv/76q8HtzcnJgYWFBRhjuH79uk7nZGdnY/DgwbCysoKDgwMiIyPVbuDzvOpw6tQp9OvXD61atULbtm2xYMEClNTw2pcvX8bMmTPRs2dPiMXiOncB7N1bWPN/4YLBzeU0MfiYP4fDMQg+Pj7YvHmzikwikeh8/rNnzzBw4EBIJBLExsaCMYa//vWvCA4OxsWLF2FpaWkwW2fPng1bW9tazlITd+/eRVBQEDw9PXHgwAEUFRVh0aJFCAsLw6lTpyASiZ5rHS5evIhBgwZhyJAhOHr0KHJzc7Fo0SLcuXMH+/btU+Q7e/Ys/v3vf6NXr16QSCTIyMjQqle+lcPly4DS/kWc5khjhxhs7omH9+W0BAIDAykgIKBBOj799FMSiUR07do1hSwnJ4dMTEx0inWvK3FxceTk5ESffPIJAVApTxPR0dFka2tLhYWFCll6ejoBoPj4+Odeh9GjR5OHhweVl5crZLGxsQSAzp49q5Aphy1eunQpCbd8zVRVEVlYEEVHG8zUegMe3teoiXf7czgtmOLiYnh6eqJPnz6oqKhQyI8fPw6RSISNGzc+N1sOHz4Mf39/eHh4KGRubm4ICAjAoUOHDFJGYWEhFixYgDVr1sDOzk4v24YPH65yzoABA+Ds7Kximz51yM3NxcSJE9G6dWtIJBL4+vriu+++q9OWiooKJCUlITw8XCU+Qnh4OMRisUo58h4JXRGJAC8vvta/JcCdP4fTgrG0tMSePXuQlZWFZcuWAQDy8/MRERGBsLAwzJkzRy99lZWVKklowOlGdnY2unbtWkvu7e2t2KdeUznqkrqIgu+99x48PT0xefJkne0qKSlBbm6uTrbpWodbt27h1VdfRVZWFj755BMcPnwYPXr0wNixY3H48GGt9ty4cQOlpaW1yjE3N4e7u3uta6Uv3Pm3DLjz53BaOH5+fli9ejU+/vhjpKSkICIiAiYmJti+fbteek6fPl0rat+XX36p8/mPHj2CVCqtJbe3t0dhYaHic15eXp3RAs3MzODu7q6i59SpU9i1axc+//xzvepVWFgIItJom/KkP13rsHz5chAR0tPTMWnSJAwZMgTbt29HSEgI/va3v2m1R16eLvbUB29v4O5doKioQWo4TRw+4Y/D4SA6OhrJyckICwtDeXk5kpOT4ejoqJeO7t27Y9u2bSoyfQMEqZuNXrP3oF27djpFC1SebFheXo6ZM2di/vz58PLy0ssmefm62KZrvqSkJAwbNgy2traorKxUyIcMGYJFixbhyZMnsLa2rtV7YWpqqrc9+uLtLbxmZwMBAQ1Wx2micOfP4XDAGMPkyZORmJgIX19fnWP2K2NlZYVeveq/A6tUKlXbai0sLFRp5YrFYvj6+tapT9k5fvrpp3j06BH+/Oc/o0jWpH327BkA4OnTp3j69KnGUMVSqRSMMY222dvb612H/Px87Nq1C7t27VJbZkFBAc6dO4fg4GAVOREpytNUjrfce9cT7vxbBtz5czgc3L9/H9HR0ejRowfOnz+P9evXIyoq6rna4O3tjWw1g81XrlxRaa3n5eXBzc2tTn0uLi7Iy8tT6Lh//z7at29fK1+PHj3QvXt3XNCwuN3CwgKurq4abQsMDNS7Dg4ODujfvz8WL16stsx27drB0dFRbQ+Hu7s7JBJJrXJKS0uRk5OD8ePHq9WpK87OgKUlH/dv7nDnz+G0cIgIU6ZMgVgsRnJyMlatWoXFixcjODgYPvKF38+BkSNHYuHChcjJyUGnTp0ACI7+9OnTWL16tSJffbr933//fUydOlXleFJSEv75z39i9+7d6NKlS522xcbG4vHjx7C1tQUgzCG4efMmRo4cqXcdhg4dioyMDHh7e6NVq1Ya7VfXkyIWizF06FDs378fy5cvV2yFfODAAZSVlanYUx/kM/7/v727j66qvvc8/vnmCQgkkChBgQohvRV5FAGlWmWA1JlqCxWcUh/mSsFR2moZ1njHEVevUtZt7R07y85cS2fBFbnUVRSs0ArYudImC9EloDxUGCotD4K0oAQQEIGQ7/xxktyE5EByHrLPPvv9Wmuvk+zsc/b3nLXgc36//fv9dpLjBpHpgp5rmO0b8/yR6Z5++mnPycnxqqoqd3c/c+aMjxgxwgcNGuSffvppm14jFfP8T5486RUVFT5kyBBfsWKFr1y50ocNG+bl5eV+4sSJpF67NYsWLWp1nv/cuXM9NzfX9+7d27jvwIEDftlll/ktt9zia9as8aVLl/pVV13l119/fbO59G19D/v27fNevXr5qFGj/Pnnn/eqqip/5ZVXfN68ef6tb33rkrVv3rzZO3fu7HfccYe//vrrvnDhQi8pKfE777yz2XGnTp3yZcuW+bJly3zKlCkuqfH3jRs3xn39adPcr7zykmWklZjnn9Yt8AKyfSP8kcneffddLygo8Mcff7zZ/p07d3phYaHPnDmzTa+TivB3j4Xi5MmTvaioyLt16+aTJk3yPXv2JP26rYkX/k888YRLanHebdu2eWVlpRcWFnqPHj38vvvu848//jjh97B//36fMWOG9+7d2/Pz8/2KK67wyspKX7JkSZvqr66u9jFjxninTp28rKzMZ82a5adOnWp2zJ49e1xSq9t9990X97X/8R9j6VBT06ZS0oLwT+9msc8Y6TJq1CjftGlT0GUAQJutXi3dfru0bp30pS8FU4OZvePuiY8gxUUxzx8A0EzTEf/ITgz4AxBXXV2d6urq4v7dzJSbm3vR13D3Vlfba6ph0Boyw1VXSd26Ef7ZjJY/gLimT59+0VX02rIeQHV19SVX42uYkofMYMaI/2zH120AcT355JN66KGH4v493sI4TY0cOfKSU/N69+7d7tqQXoMHS2vWBF0F0oXwBxBX//79271E74WKioqSWvkPwRg8WFq0SKqpkZosYogsQbc/AKCFhgUJue6fnQh/AEALAwfGHt9/P9g6kB6EPwCghc99TsrLk/7856ArQToQ/gCAFvLypP79pd27g64E6UD4AwBaNWAALf9sRfgDAFpVUUH4ZyvCHwDQqooK6ejR2IbsQvgDAFo1YEDskev+2YfwBwC0qqIi9kj4Zx/CHwDQqvLy2CPX/bMP4Q8AaFVRkVRWRss/GxH+AIC4mO6XnQh/AEBcTPfLToQ/ACCuigpp/37p7NmgK0EqEf4AgLgGDJDq6qR9+4KuBKlE+AMA4mK6X3Yi/AEAcTUs9MN1/+xC+AMA4rrySqlLF8I/2xD+AIC4zGKtf7r9swvhDwC4KOb6Zx/CH4AkacGCBTIzvfPOO832v/HGGyorK9PQoUO1Z8+eDqvnwIEDevjhh/XFL35RhYWFMjPt3bu3zc9fv369br31VpWVlam4uFjXXXednnvuuYSPS7f9+/frzjvvVPfu3VVcXKzJkyfrgw8+aHbM8uXLNWXKFPXr109dunTR1Vdfrccee0wnTpxIa20VFbGWv3taT4MORPhLMrMvmNkdZvagmT1Q//PfBF0X0JG2bNmivLw8DRkypHHfc889pwkTJmjMmDF68803Vd6w2HsH+NOf/qSXXnpJJSUluvnmm9v13G3btqmyslLnzp3TggUL9PLLL2v06NGaMWOG5s+f3+7j0u3TTz/V+PHjtXPnTi1evFhLlizRrl27NG7cOJ06darxuKefflq5ubn64Q9/qNdee03f/va3NX/+fH35y19WXV1d2uobMEA6dUo6fDhtp0BHc/dIbpKukfRTSQclna/f6uq3ht8PSnpG0jWJnmfkyJEOhMGNN97ow4YNc3f32tpanz17tkvyRx991M+fP9/h9TQ954IFC1yS79mzp03Pfeyxxzw/P99PnDjRbP8NN9zgY8aMafdxyejXr58/8cQTFz3mmWee8ZycHN+1a1fjvt27d3tubq7/5Cc/adx3+PDhFs9dvHixS/K1a9empN7WrFrlLrmvX5+2U7QgaZNnQFZk6xa5lr+ZVZjZcknvSZohaaukuZL+VtJtkm6v//kH9X+7X9J7ZrbMzAYEUzWQXu6ubdu2acSIETp+/Lhuv/12zZ8/X0uWLNFTTz2lnJyO/68imXOePXtW+fn56tKlS7P9PXr0aNZCbutxkrR161ZNnDhRJSUl6tKli2666SatW7cu4Rqb+vWvf60xY8bo85//fOO+8vJy3XTTTVq5cmXjvp49e7Z47ujRoyVJH374YUpqaU3DdD8G/WWPyIW/pB2S+kuaJqmXu3/F3X/g7i+4+2vuvqb+57nu/hVJvSRNlzSg/rlA1tm1a5dOnjyprl276oYbbtDWrVtVVVWle++9N6HXc3fV1tZecjt//nyK30nMtGnTJEnf+973dPDgQR07dkwLFizQ2rVrNXv27HYf9+677+rGG29UTU1N4+WByy67TJWVlS3GSCRi+/btzS63NBg8eLB27Lj4fzvV1dWSpGuuuSbpOuK56qrY4/79aTsFOlrQXQ8dvUma1JHPpdsfYfDiiy+6JJfk5eXlfuDAgaRe7/e//33j611sGzt2bJter73d/u7uGzZs8D59+jSeKz8/3xcuXJjQcePHj/eBAwf6mTNnGvfV1tb6wIEDfdKkSY376urq/Ny5c822fv36+fe///1m+2pra5u9fn5+vj/66KMtanv88cc9Nzc37ns8cOCA9+zZ0ysrK9v8uSSqtNT9O99J+2kaiW7/tG55HfpNIwO4+8pLH5X65wKZbPPmzZKkb37zm1q+fLn++Mc/qk+fPgm/3siRI7Vx48ZLHldUVJTwOS5m165dmjJligYPHqyf//zn6tKli1auXKmZM2eqc+fOuueee9p83OnTp1VdXa05c+YoJydHtbW1jeeprKzUCy+80Ph7dXW1xo0b16KeefPmad68eY2/jx07VlVVVc2OMbMWz4tlYOtOnjypSZMmKS8vT4sWLWrzZ5Oovn2lAwfSfhp0kMiFv5n1cPdjTX7Pdff09D0CIbFlyxaVl5dr8eLF2rt3r77xjW9o48aNCY/u79atm6699tpLHtda4KXCnDlzlJ+fr1dffVX5+fmSpAkTJujIkSOaNWuW7rrrLuXk5LTpuJqaGp0/f75FgDdVV1ennJycVr/0TJw4UV/96lf1wAMPNO678EtPSUmJampqWrzu0aNHVVJS0mL/Z599pokTJ2r37t2qrq5W37592/cBJaBPH8I/m0Tqmr+Z3Sdp5wW7XzGzXwRRD5AptmzZohEjRqigoEAvv/yy8vPz9fWvf73ZNDNJevDBB/XII49Ikg4ePKhBgwbp9ddfb/F61dXVys/Pv+Q2YcKEtLyfP/zhDxo+fHhjoDe4/vrrdeTIER2un7PWluN69OihnJwcPfzww9q4cWOrW8PgxKKiIo0aNarZVlBQoN69ezfbd/XVVzc73+DBg7V9+/YW72PHjh0aNGhQs33nzp3TlClTtGHDBq1evVpDhw5N+vNqi759pTSOKUQHi0TL38y+IGmBpHJJ/+mCPw+T9C8Xee4Lkl5z9yXpqxAIzqFDh/TXv/61saXeu3dvLV++XOPGjdO0adP00ksvNbbQ582bpyFDhujuu+/W9OnT9eMf/1iVlZUtXjPobv8rrrhCW7Zs0dmzZ1VQUNC4/+2331bnzp1VWlra5uMKCgp08803a+vWrbruuuvSMvNh4sSJeuSRR7R7924NqB9av3fvXq1fv15PPfVU43F1dXW65557tHbtWq1atUpjxoxJeS3x9O0rHToknT0rNfmoEFZBDzroiE3SE5KOSerfyt9OS7q//udiSUslDWjy9/8pqTrRczPgD5luzZo1Lsl/85vfNNv/7LPPuiSfN29es/1z5871zp07+4svvpj22pYtW+bLli3zmTNnuiT/2c9+5suWLfOqqqrGY6qqqjw3N9cXL17c7HmS/NZbb/UVK1b4b3/7W//ud7/rknz27NntPu6dd97xrl27emVlpf/yl7/0qqoqX758uc+ZM6fVgXpNtWWe/8mTJ72iosKHDBniK1as8JUrV/qwYcO8vLy82RoEDZ/D448/7m+99Vazbf/+/W39WBPyz//sLrm3Y8xlUsSAv/TmYtAFdMiblL4g6Q1JH0gaf8HfPpb0YP3PPRVb5Gd8k79/V9KhRM9N+CPT/ehHP3JJrYbH9OnT3cx85cqV7u7+8ccf+/Dhw71Xr17+5ptvpr02tWGWQMPMgkWLFjV77urVq33s2LF++eWXe7du3Xz48OH+7LPPthhp39bjduzY4VOnTvWePXt6QUGB9+nTx7/2ta/5qlWrLvoe2hL+7u779u3zyZMne1FRkXfr1s0nTZrUYnZDv3794n4mbTlHMl57LZYY69al9TSNCP/0bhb7jKPBzO6X9A/u3qvJvjckfejuU81stKS3JX3D3Zc3ec7P3D2hjq5Ro0b5pk2bUlA9EKzjx4+rsrJSs2bNUl5enn7605/qrbfeCrosdJDt26UhQ6SlS6WpU9N/PjN7x91Hpf9M0RSpAX/uvlDSoAt2PyfpP5rZfEnPSvqLYqv8NRgs6ZOOqRDITKdOndJtt92m+++/X/fee6+mTp2q2tpaLV26NOjS0EEaJhQw4j87RGLAX1PufuSC358zsxsk/WdJxyVNkrTKzD6RtEuxJYDXd3ihQAbp2rWr1q//t38GZtamAX3IHsXFUrduhH+2iFz4t8bdHzSzv5N0zt1Pm9l0Sc9L6irplGLr/ANAZJkx1z+bEP713P2TJj+/bGZrJQ2V9L67HwquMgDIDMz1zx6RuubfHu5+zN3XEfwAEMMSv9kjcuFvZgkvKWZmLVczAYCI6NtXOnhQStPNGNGBIhf+kl4zs9+Z2VfNLPdSB5tZvpndYWbVklZ3QH0AkJH69IkF/yH6Q0Mvitf8Ryi2at+vJX1sZv8qaYOkP0uqkWSSSiX9jaQxksZLKpH0fyVd+k4lAJClGqb7ffih1Lt3sLUgOZELf3d/T9KtZvZFSd9RbGrfXYqtktWUKTa//1eS5rs785oARFrTuf6jRwdbC5ITufBv4O5vSXqrvut/pGKL//RU7EvAR5Lek7TZ3euCqxIAMgcL/WSPyIZ/A3c/r1i3/4agawGATHb55bE7+hH+4RfFAX9tYmbfMbObzCw99xwFgJBpWOiHuf7hF/mW/0X8B0nPSMo1s72StkraVv+41d13B1gbAASCuf7ZgZZ/fB9JWijpS5L+i2LL/P53Sf9D0i4zO25mrPkPIFII/+xAyz++OyWVNBnw9xsz26zYZ/a/Fbvb34V3CASArNa3r/SrX0nuscsACCda/vH9RdLAC/bNl/SQu592903u/i8B1AUAgenTRzpzRjpy5NLHInMR/vE9LWmZmY1ssu8LkhgACCCymi70g/Ci2z8Od19oZp0lrTWzI5IOSxou6X8FWxkABKfpXP/hw4OtBYkj/C/C3f/JzBZLGqfYAkA76hcHAoBIYqGf7ED4X0T96n+9JG10978EXQ8ABK1Xr9hAv4MHg64EyeCafxxmdoukDyVtkrSrfl8/M+sVaGEAEKC8POmyy6SPPgq6EiSD8I/vnyT9V3fvIelc/b4rJS0KriQACF5ZmXT4cNBVIBmEf3yfc/cX6n9uuOPfFknXBVQPAGSEsjLp0KGgq0AyCP/4dplZQ9CbJLn7Z5IKgysJAIJHyz/8Ihf+ZvakmfVvw6E/Umye/82qb/mb2b+TxDAXAJFG+IdfFEf7/72k9yXtlSQzmyLpd+5+tOlB7v6KmZVJelVSNzP7naSRkr7XseUCQGYpK5OOHZPOno3d4hfhE7mWv6Sjat51/5Kkr7R2oLv/H0mfkzRZ0i8k3ezui9NeIQBksF71c54Y8R9eUWz5vydphpmtcfcPVX89Px53/0TSyg6pDABCoKws9nj4cGytf4RPFFv+cxUbsf+Bme1U7Hr+bWb2FebwA8ClNQ1/hFPkWv7u/jszGyrpfkk3KXaznrsl3SVJZnZI0ruSNjc8uvveYKoFgMxD+Idf5MJfktz9fUn/TZLMrE7S30nardiAvhGK9Qzcpn8b5X/U3S8PploAyCyEf/hFMvwv8ANJ69x9g6RXGnaa2ZWKfQkYKenagGoDgIxTVCR16kT4h1nkw9/dn4yz/y+SVtVvAIB6Zsz1D7soDvgDACSJJX7DjfAHALQbLf9wI/wBAO1G+Icb4Q8AaLeG8He/9LHIPIQ/AKDdysqkM2ekEyeCrgSJIPwBAO3WsL4/Xf/hRPgDANqNhX7CjfAHALQb4R9uhD8AoN0I/3Aj/AEA7dazZ+yR8A8nwh8A0G4FBVKPHoR/WBH+AICEsMRveBH+AICEsMpfeBH+AICEEP7hRfgDABJC+IcX4Q8ASEhZmXTkiFRbG3QlaC/CHwCQkLKy2I19jhwJuhK0F+EPAEgI6/uHF+EPAEgIq/yFF+EPAEgI4R9ehD8AICGEf3gR/gCAhPToIeXlscpfGBH+AICE5ORIpaVSTU3QlaC9CH8AQMJKSgj/MCL8AQAJKy2Vjh4Nugq0F+EPAEgYLf9wIvwBAAmj5R9OhD8AIGG0/MOJ8AcAJKy0VDp+XDp/PuhK0B6EPwAgYSUlscdjx4KtA+1D+AMAElZaGnvkun+4EP4AgIQ1tPwJ/3Ah/AEACWto+TPoL1wIfwBAwmj5hxPhDwBIWEP40/IPF8IfAJAwWv7hRPgDABLWqZNUWEjLP2wIfwBAUljiN3wIfwBAUljiN3wIfwBAUmj5hw/hDwBICi3/8CH8AQBJoeUfPoQ/ACAptPzDh/AHACSltFQ6fVr67LOgK0FbEf4AgKSw0E/4EP4AgKRwW9/wIfwBAElhff/wIfwBAEmh5R8+hD8AIClc8w8fwh8AkJSGlj/d/uFB+AMAktK9u2RGyz9MCH8AQFJycqQePWj5hwnhDwBIWkkJLf8wIfwBAEkrLaXlHyaEPwAgabT8w4XwBwAkjZZ/uBD+AICk0fIPF8IfAJC0hpa/e9CVoC0IfwBA0kpKpPPnpZMng64EbUH4AwCSxip/4UL4AwCSxvr+4UL4AwCSxm19w4XwBwAkjdv6hgvhDwBIGi3/cCH8AQBJo+UfLoQ/ACBphYVSfj4t/7Ag/AEASTOLtf5p+YcD4Q8ASInu3aXjx4OuAm1B+AMAUqK4WDpxIugq0BaEPwAgJYqKpE8+CboKtAXhDwBIieJiwj8sCH8AQErQ7R8ehD8AICVo+YcH4Q8ASImGa/7uQVeCSyH8AQApUVwsnTsnnTkTdCW4FMIfAJASxcWxR677Zz7CHwCQEkVFsUeu+2c+wh8AkBINLX/CP/MR/gCAlCD8w4PwBwCkBNf8w4PwBwCkBNf8w4PwBwCkBN3+4UH4AwBSgm7/8CD8AQApUVgo5eTQ8g8Dwh8AkBJm3NY3LAh/AEDKcHOfcCD8AQApU1TENf8wIPwBAClDyz8cCH8AQMoQ/uFA+AMAUqa4mG7/MCD8AQApw2j/cCD8AQApQ7d/OBD+AICUaej2dw+6ElwM4Q8ASJmioljwnzoVdCW4GMIfAJAy3NwnHAh/AEDKEP7hQPgDAFKG8A8Hwh8AkDJFRbFH5vpnNsIfAJAytPzDgfAHAKQM4R8OhD8AIGXo9g8Hwh8AkDK0/MOB8AcApEynTlJBAeGf6Qh/AEBKsb5/5iP8AQApVVTENf9MR/gDAFKKln/mI/wBAClF+Gc+wh8AkFJ0+2c+wh8AkFK0/DMf4Q8ASCnCP/MR/gCAlCoqIvwzHeEPAEip4mLp9GmptjboShAP4Q8ASKmGJX4Z9Je5CH8AQEqxvn/mI/wBACnFnf0yH+EPAEgpWv6Zj/AHAKQU4Z/5CH8AQEo1dPsT/pmL8AcApBSj/TMf4Q8ASCm6/TMf4Q8ASCm6/TMf4Q8ASKncXKmwkPDPZIQ/ACDliou55p/JCH8AQMpxZ7/MRvgDAFKue3fp3Lmgq0A8eUEXAADIPm+/LZkFXQXioeUPAEg5gj+zEf4AAEQM4Q8AQMQQ/gAARAzhDwBAxBD+AABEDOEPAEDEEP4AAEQM4Q8AQMQQ/gAARAzhDwBAxBD+AABEDOEPAEDEmLsHXUNWM7OPJO0Lug4ACJl+7t4z6CKyFeEPAEDE0O0PAEDEEP5ARJnZ1Wb2pJldHXQtADoW3f5ABJmZSVonaZikrZJucf4zACKDlj8QTTMk9Zd0raRySfcFWg2ADkXLH4gYM7tc0v+TdLe7/6uZ3SrpF5IGuntNsNUB6AiEPwAAEUO3PwAAEUP4AwAQMYQ/EDEWM93M1pvZETP7zMz2mdmrZpYfdH0A0i8v6AIAdLifS3pA0suKDfQ7L+kqSQPc/VyQhQHoGAz4AyLEzLpLqpG00N0fDLoeAMGg2x+IlnOSPpE00syuN7Oy+i8EACKE8AcixN0/lTRRUm9Jb0s6JGlBoEUB6HBc8wcixMymSFokaYWkVxW7BLA3yJoAdDyu+QMRYWYlkvZLet7dHwq6HgDBodsfiI6hkrpKej/oQgAEi5Y/EBFmdoWkP9X/ulDSdkmdJFVIusLd7wqqNgAdi2v+QES4+1/N7N9L+ntJfyupWNJRSTsV+zIAICJo+QMAEDFc8wcAIGIIfwAAIobwBwAgYgh/AAAihvAHACBiCH8AACKG8AcAIGIIfwAAIobwBwAgYgh/AAAihvAHACBi/j+ZnPt3MclgQgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "'''3.1) Plot equilibrium function'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[3.2)](#toc)\n", "\n", " Demonstrate the quadratic convergence of Newton's method.\n", "" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "******************************************************\n", " Newton's Method Iterations \n", "******************************************************\n", "k | K(e_k) | K'(e_k) | |del e_k| | e_k |convg|\n", "------------------------------------------------------\n", " 1 +4.809e+01 -3.465e+04 +1.388e-03 +0.000e+00 0.00\n", " 2 +6.665e+00 -3.564e+04 +1.870e-04 +0.000e+00 1.30\n", " 3 +1.079e-01 -3.578e+04 +3.015e-06 +0.000e+00 1.48\n", " 4 +2.753e-05 -3.578e+04 +7.694e-10 +0.000e+00 1.65\n", " 5 +1.592e-12 -3.578e+04 +4.448e-17 +0.000e+00 1.79\n", "******************************************************\n", "\n", "Equilibrium mole fractions:\n", "\n", "x_A = 5.130e-02\n", "\n", "x_B = 7.548e-02\n", "\n", "x_C = 6.742e-02\n", "\n", "x_D = 1.665e-01\n", "\n", "x_E = 2.724e-01\n", "\n", "x_F = 3.669e-01\n", "\n" ] } ], "source": [ "'''3.2) Find root and equilibrium molar fractions'''\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[3.3)](#toc)\n", "\n", " Plot the normalized extent of reaction at equilibrium on the equilibrium function plot.\n", "" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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