diff --git a/notebooks/contrib-dev/Modeling_Isomerization_of_1,5_cyclooctadiene.ipynb b/notebooks/contrib-dev/Modeling_Isomerization_of_1,5_cyclooctadiene.ipynb new file mode 100644 index 00000000..01b13476 --- /dev/null +++ b/notebooks/contrib-dev/Modeling_Isomerization_of_1,5_cyclooctadiene.ipynb @@ -0,0 +1,1378 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Modeling Isomerization of 1,5-cyclooctadiene\n", + "\n", + "Prepared by: Feng Gao - fgao2@nd.edu and Sam Zhang - szhang32@nd.edu\n", + "\n", + "__References:__\n", + "\n", + "Based on Problem3 HW3 of Chemical Reaction Engineering Class of Prof.Hicks (2023), with permission.\n", + "\n", + "Nishiguchi, T., H. Imai, and K. Fukuzumi. 1975. Catal. 39 (3): 375- 382.\n", + "\n", + "Yanlong, Q., and X. Weihua. 1986. J. Mol. Catal. 34 (1): 31-38.(https://colab.research.google.com/drive/1K0twABdh7iWOVkRLfqNJHRxa1fsiHLDf?usp=sharing)\n", + "\n", + "\n", + "## Problem Description\n", + "This problem is meant to provide practice for undergraduate students in using simulation to model and understand chemical engineering reaction kinetics, and specifically to have a better understanding of the kinetics of isomerization.\n", + "\n", + "Aditionaly, doing this project is a chance to learn and practice solving ODEs and using nonlinear regression to predict reaction parameters.\n", + "\n", + "After working on this project, the students also be more familier using Numpy library which help in constructing array, matrix, and multiple mathematics functions, Scipy library which help in solving integral function more efficiently in this project as well as nonlinear regression, and Matplotlib which provides visualization when they graph." + ], + "metadata": { + "id": "OO4YuBxPk_0s" + } + }, + { + "cell_type": "markdown", + "source": [ + "##Useful links to review library\n", + "1. Numpy\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/NumPy.html?highlight=numpy#getting-started-with-numpy-arrays\n", + "\n", + "2. Scipy\n", + "\n", + " https://docs.scipy.org/doc/numpy-1.15.0/user/quickstart.html\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/04/Linear-Algebra-in-Numpy.html?highlight=scipy#scipy\n", + " \n", + "3. Matplotlib\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html#matplotlib-basics\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html#customizing-plots\n", + " \n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html#plotting-multiple-lines" + ], + "metadata": { + "id": "uFObEFzXmecR" + } + }, + { + "cell_type": "markdown", + "source": [ + "##Import libraries" + ], + "metadata": { + "id": "xLw4HZ1grSES" + } + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "id": "OuZjhFGbknjk" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import integrate\n", + "from scipy.stats import t\n", + "from scipy.integrate import solve_ivp\n", + "from scipy.optimize import least_squares" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# 1. Background: Modeling isomerization of 1,5-cyclooctadiene\n", + "\n", + "In chemistry, isomerization or isomerisation is the process in which a molecule, polyatomic ion or molecular fragment is transformed into an isomer with a different chemical structure. Enolization is an example of isomerization, as is tautomerization. When the isomerization occurs intramolecularly it may be called a rearrangement reaction.\n", + "\n", + "1,5-cyclooctadiene is a cyclic hydrocarbon with two double bonds located at the 1st and 5th positions in its eight-carbon ring structure. Isomerization in the liquid phase typically involves the conversion of this compound into its isomeric forms, such as 1,3-cyclooctadiene, through the rearrangement of the double bonds.\n", + "\n", + "The process is often catalyzed by transition metal complexes, such as those containing palladium or platinum. These catalysts play a crucial role in facilitating the movement of double bonds and promoting the formation of new isomers. The choice of catalyst, reaction conditions (temperature, pressure, and solvent), and the presence of co-catalysts can significantly influence the efficiency and selectivity of the isomerization reaction.\n" + ], + "metadata": { + "id": "0j0-u_h3mkQ5" + } + }, + { + "cell_type": "markdown", + "source": [ + "## 1.1. Learning Goals\n", + "**General goal:**\n", + "\n", + "•\tMathematical Modeling: Using ordinary differential equation (ODE) to model and analyze species' concentration variation against time.\n", + "\n", + "•\tSimulation: By writing up Python code, the translation of theoretical models into practical simulations is strengthened.\n", + "\n", + "•\tVisualization: Creating plots to visualize the reaction process interpret data to validate mechanism.\n", + "\n", + "\n", + "**Specific goal:**\n", + "\n", + "•\tAnalyze the reaction kinetics for series reaction, understand how to apply rate constant and species balance.\n", + "\n", + "•\tModel the reaction kinetics of liquid phase isomerization of 1,5-cyclooctadiene transition metal catalyst.\n", + "\n", + "•\tFind intermediate maximum concentration by solving the ODE with integrate from scipy ($t_{opt}$ for intermediate).\n", + "\n", + "•\tVerify the right mechanism by applying experimental data.\n" + ], + "metadata": { + "id": "RwBh9u7IYBZq" + } + }, + { + "cell_type": "markdown", + "source": [ + "## 1.2. Problem Statement\n", + "The liquid phase isomerization of 1,5-cyclooctadiene with transition metal- based catalyst. Researchers have attempted to model the reactions in two ways:\n", + "\n", + "Case 1. As a set of consecutive pseudo first-order reactions of the form:\n", + "\n", + "$$\n", + "A \\xrightarrow{k_1} B \\xrightarrow{k_2} C\n", + "$$\n", + "\n", + "Case 2. As a set of competitive pseudo first-order reactions of the form:\n", + "\n", + "$$\n", + "A \\xrightarrow{k_3} B \\xrightarrow{k_4} C\n", + "$$\n", + "$$\n", + "A\\xrightarrow{k_5} C\n", + "$$\n", + "\n", + "\n", + "\n", + "Where **A** refers to 1,5-cyclooctadiene, **B** to 1,4-cyclooctadiene, and **C** to 1,3-cyclooctadiene.\n", + "\n", + "\n", + "\n" + ], + "metadata": { + "id": "dJFUYT8BYFx-" + } + }, + { + "cell_type": "markdown", + "source": [ + "#2. Analysis" + ], + "metadata": { + "id": "6qkMPT1tZft4" + } + }, + { + "cell_type": "markdown", + "source": [ + "## 2.1. Visualizing the dimensionless concentration of each specie verses time (Case1)" + ], + "metadata": { + "id": "xcxeq9UioC9G" + } + }, + { + "cell_type": "markdown", + "source": [ + "The first mechanism involves 2 steps and 3 species.\n", + "\n", + "__1. Rate of species A__\n", + "\\begin{equation}\n", + "r_A = \\frac{d[A]}{dt} = -k_1 \\cdot [A]\n", + "\\end{equation}\n", + "\n", + "__2. Rate of species B__\n", + "\\begin{equation}\n", + "r_B = \\frac{d[B]}{dt} = k_1 \\cdot [A] - k_2 \\cdot [B]\n", + "\\end{equation}\n", + "\n", + "__3. Rate of species C__\n", + "\\begin{equation}\n", + "r_C = \\frac{d[C]}{dt} = k_2 \\cdot [B]\n", + "\\end{equation}\n", + "\n", + "Note that to have the $[B]_{max}$, the external condition is given: at t=0, dB/dT ≥ 0, thus for\n", + "\\begin{equation}\n", + "\\frac{d[B]}{dt} = k_1 \\cdot [A_0] - k_2 \\cdot [B_0] ≥ 0\n", + "\\end{equation}\n", + "Therefore\n", + "\\begin{equation}\n", + "\\frac{k_1 \\cdot [A_0]}{k_2\\cdot[B_0]} ≥ 1\n", + "\\end{equation}" + ], + "metadata": { + "id": "perBJlBEfPqj" + } + }, + { + "cell_type": "markdown", + "source": [ + "###2.1.1. Setup Function: Define rate constants and initial conditions." + ], + "metadata": { + "id": "FVDMpKles_vC" + } + }, + { + "cell_type": "code", + "source": [ + "def setup_case1(A0, B0, k1, k2):\n", + " \"\"\"\n", + " Sets up the initial conditions and rate constants for the isomerization reaction.\n", + "\n", + " Args:\n", + " A0: Initial concentration of species A\n", + " B0: Initial concentration of species B\n", + " k1: Rate constant for the reaction A -> B\n", + " k2: Rate constant for the reaction B -> C\n", + "\n", + " Returns:\n", + " initial_conditions: Initial concentrations for A, B, and C\n", + " rate_constants: Rate constants for the reaction\n", + " \"\"\"\n", + " C0 = 0.0 # Initial concentration of species C is always 0\n", + " initial_conditions = [A0, B0, C0]\n", + " rate_constants = {'k1': k1, 'k2': k2}\n", + " return initial_conditions, rate_constants" + ], + "metadata": { + "id": "wxRZzJHYq7Ql" + }, + "execution_count": 44, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "###2.1.2. ODE Function: Define the system of ODEs for the concentrations of A, B, and C." + ], + "metadata": { + "id": "VC7P9w4gtGy9" + } + }, + { + "cell_type": "code", + "source": [ + "def case1_kinetics(t, y, rate_constants):\n", + " \"\"\"\n", + " RHS of differential equation for reaction kinetics.\n", + "\n", + " Args:\n", + " t: Time\n", + " y: Values for differential equations, [A, B, C]\n", + " rate_constants: Dictionary containing rate constants for the reaction\n", + "\n", + " Returns:\n", + " dydt: First derivative of y w.r.t. t\n", + " \"\"\"\n", + " A, B, C = y\n", + " k1 = rate_constants['k1']\n", + " k2 = rate_constants['k2']\n", + "\n", + " # Define the ODEs\n", + " dA_dt = -k1 * A\n", + " dB_dt = k1 * A - k2 * B\n", + " dC_dt = k2 * B\n", + "\n", + " # Return the derivatives\n", + " dydt = [dA_dt, dB_dt, dC_dt]\n", + " return dydt" + ], + "metadata": { + "id": "vokOEYsEkYxj" + }, + "execution_count": 45, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "###2.1.3. Solver Function: Use scipy to solve the ODEs and get the concentration of species A, B and C at time t." + ], + "metadata": { + "id": "Iq6bQ9O_tOxJ" + } + }, + { + "cell_type": "code", + "source": [ + "def solve_case1_ode(initial_conditions, rate_constants, tmax):\n", + " \"\"\"\n", + " Solves differential equations for the isomerization reaction.\n", + "\n", + " Args:\n", + " initial_conditions: Initial concentrations for A, B, and C\n", + " rate_constants: Rate constants for the reaction\n", + " tmax: The amount of time to simulate\n", + "\n", + " Returns:\n", + " A: Concentration profile of species A\n", + " B: Concentration profile of species B\n", + " C: Concentration profile of species C\n", + " t: Time array for the simulation\n", + " \"\"\"\n", + " t = np.linspace(0, tmax, num=int(tmax*100)+1)\n", + " tspan = [t[0], t[-1]]\n", + "\n", + " # Solve the ODEs\n", + " soln = integrate.solve_ivp(case1_kinetics, tspan, initial_conditions, args=(rate_constants,), t_eval=t, method='RK45')\n", + "\n", + " A = soln.y[0]\n", + " B = soln.y[1]\n", + " C = soln.y[2]\n", + "\n", + " return A, B, C, t" + ], + "metadata": { + "id": "O7MPbNl2kYdF" + }, + "execution_count": 46, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "###2.1.4. An example with specified variable values and find $t_{opt}$:\n", + "Given that $A_0$ = $1.0$ $M$, $B_0$ = $0.0$ $M$, $k_1$ = $1.0$ * $10^{-3}$ $s^{-1}$, $k_2$ = $0.5$ * $10^{-3}$ $s^{-1}$, $t_{max}$ = $10000$ $s$\n", + "\n", + "We hope to determine the time at which the concentration of species B reaches its maximum. This specific point in time is defined as $t_{opt}$.\n", + "\n", + "To find $t_{opt}$, we need to find the time at which the derivative of B with respect to time is zero.\n", + "\n", + "That is to solve:\n", + "\n", + "\\begin{equation}\n", + "\\frac{d[B]}{dt} = 0\n", + "\\end{equation}\n" + ], + "metadata": { + "id": "II-pbh71tTfv" + } + }, + { + "cell_type": "code", + "source": [ + "# Example\n", + "A0 = 1.0 # Initial concentration of A\n", + "B0 = 0.0 # Initial concentration of B\n", + "k1 = 0.001 # Rate constant for A -> B\n", + "k2 = 0.0005 # Rate constant for B -> C\n", + "tmax = 10000 # Total time for the simulation\n", + "\n", + "initial_conditions, rate_constants = setup_case1(A0, B0, k1, k2)\n", + "A, B, C, t = solve_case1_ode(initial_conditions, rate_constants, tmax)\n", + "\n", + "# Plot the results\n", + "plt.plot(t, A, label='[A]',linewidth=3)\n", + "plt.plot(t, B, label='[B]',linewidth=3)\n", + "plt.plot(t, C, label='[C]',linewidth=3)\n", + "plt.legend()\n", + "plt.xlabel('Time (s)',fontweight='bold',fontsize=12)\n", + "plt.ylabel('Concentration (M)',fontweight='bold',fontsize=12)\n", + "plt.title('Concentration Profiles over Time for Case1', fontweight='bold',fontsize=14)\n", + "plt.show()\n", + "\n", + "### Find the t_opt for species B\n", + "# Convert B to a numpy array for differentiation\n", + "B_np = np.array(B)\n", + "# Calculate the gradient of B with respect to time\n", + "gradient_B = np.gradient(B_np, t)\n", + "\n", + "# Find where the gradient changes sign\n", + "max_idx = np.where(np.diff(np.sign(gradient_B)))[0]\n", + "\n", + "# If max_idx is not empty, we have found a local maximum\n", + "if max_idx.size > 0:\n", + " t_opt = t[max_idx[0]]\n", + " B_max = B[max_idx[0]]\n", + " print(f\"The time corresponding to the maximum concentration of B (t_opt) is: {t_opt} seconds\")\n", + "else:\n", + " print(\"No local maximum found for the concentration of B within the given time frame.\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 494 + }, + "id": "un7YQeWZkgv6", + "outputId": "eb7142d7-8d36-4273-b09f-4ebf429fd85a" + }, + "execution_count": 47, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": "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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The time corresponding to the maximum concentration of B (t_opt) is: 1386.19 seconds\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "##2.2. Visualizing the dimensionless concentration of species B verses time (Case2)" + ], + "metadata": { + "id": "mTpJIAlGo1qu" + } + }, + { + "cell_type": "markdown", + "source": [ + "The second mechanism involves 3 steps and 3 species.\n", + "\n", + "__1. Rate of species A__\n", + "\\begin{equation}\n", + "r_A = \\frac{d[A]}{dt} = -k_3 \\cdot [A] - k_5 \\cdot [A]\n", + "\\end{equation}\n", + "\n", + "__2. Rate of species B__\n", + "\\begin{equation}\n", + "r_B = \\frac{d[B]}{dt} = k_3 \\cdot [A] - k_4 \\cdot [B]\n", + "\\end{equation}\n", + "\n", + "__3. Rate of species C__\n", + "\\begin{equation}\n", + "r_C = \\frac{d[C]}{dt} = k_4 \\cdot [B] + k_5 \\cdot [B]\n", + "\\end{equation}\n", + "\n", + "Note that to have the $[B]_{max}$, the external condition is given: at t=0, dB/dT ≥ 0, thus for\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\frac{d[B]}{dt} = k_3 \\cdot [A_0] - k_4 \\cdot [B_0] ≥ 0\n", + "\\end{equation}\n", + "Therefore\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\frac{k_3 \\cdot [A_0]}{k_4\\cdot[B_0]} ≥ 1\n", + "\\end{equation}" + ], + "metadata": { + "id": "RGdLCuPEkn1a" + } + }, + { + "cell_type": "markdown", + "source": [ + "### 2.2.1. Setup Function: Define rate constants and initial conditions." + ], + "metadata": { + "id": "LrwYMbO-yUti" + } + }, + { + "cell_type": "code", + "source": [ + "def setup_case2(A0, B0, C0, k3, k4, k5):\n", + " \"\"\"\n", + " Sets up the initial conditions and rate constants for Case 2 of the reaction.\n", + "\n", + " Args:\n", + " A0: Initial concentration of species A\n", + " B0: Initial concentration of species B\n", + " C0: Initial concentration of species C\n", + " k3: Rate constant for the reaction A -> B\n", + " k4: Rate constant for the reaction B -> C\n", + " k5: Rate constant for the reaction A -> C (competing reaction)\n", + "\n", + " Returns:\n", + " initial_conditions: Initial concentrations for A, B, and C\n", + " rate_constants: Rate constants for the reaction\n", + " \"\"\"\n", + " initial_conditions = [A0, B0, C0]\n", + " rate_constants = {'k3': k3, 'k4': k4, 'k5': k5}\n", + " return initial_conditions, rate_constants" + ], + "metadata": { + "id": "Ku6mj4-lq7uP" + }, + "execution_count": 48, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "###2.2.2. ODE Function: Define the system of ODEs for the concentrations of A, B, and C." + ], + "metadata": { + "id": "PkC2-YMoyYmc" + } + }, + { + "cell_type": "code", + "source": [ + "def case2_kinetics(t, y, rate_constants):\n", + " \"\"\"\n", + " RHS of differential equation for Case 2 reaction kinetics.\n", + "\n", + " Args:\n", + " t: Time\n", + " y: Values for differential equations, [A, B, C]\n", + " rate_constants: Dictionary containing rate constants for the reaction\n", + "\n", + " Returns:\n", + " dydt: First derivative of y w.r.t. t\n", + " \"\"\"\n", + " A, B, C = y\n", + " k3 = rate_constants['k3']\n", + " k4 = rate_constants['k4']\n", + " k5 = rate_constants['k5']\n", + "\n", + " # Define the ODEs\n", + " dA_dt = -k3 * A - k5 * A\n", + " dB_dt = k3 * A - k4 * B\n", + " dC_dt = k4 * B + k5 * A\n", + "\n", + " # Return the derivatives\n", + " dydt = [dA_dt, dB_dt, dC_dt]\n", + " return dydt" + ], + "metadata": { + "id": "Vo34AnJtp7r2" + }, + "execution_count": 49, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "###2.2.3. Solver Function: Use scipy to solve the ODEs." + ], + "metadata": { + "id": "V5pHDJFEyewI" + } + }, + { + "cell_type": "code", + "source": [ + "def solve_case2_ode(initial_conditions, rate_constants, tmax):\n", + " \"\"\"\n", + " Solves differential equations for Case 2 of the isomerization reaction.\n", + "\n", + " Args:\n", + " initial_conditions: Initial concentrations for A, B, and C\n", + " rate_constants: Rate constants for the reaction\n", + " tmax: The amount of time to simulate\n", + "\n", + " Returns:\n", + " A: Concentration profile of species A\n", + " B: Concentration profile of species B\n", + " C: Concentration profile of species C\n", + " t: Time array for the simulation\n", + " \"\"\"\n", + " t = np.linspace(0, tmax, num=int(tmax*100)+1)\n", + " tspan = [t[0], t[-1]]\n", + "\n", + " # Solve the ODEs\n", + " soln = integrate.solve_ivp(case2_kinetics, tspan, initial_conditions, args=(rate_constants,), t_eval=t, method='RK45')\n", + "\n", + " A = soln.y[0]\n", + " B = soln.y[1]\n", + " C = soln.y[2]\n", + "\n", + " return A, B, C, t" + ], + "metadata": { + "id": "Zp5y8sytp7Ox" + }, + "execution_count": 50, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "###2.2.4. An example with specified variable values and find $t_{opt}$:\n", + "Given that: $A_0$ = $1.0$ $M$, $B_0$ = $0.0$ $M$, $C_0$ = $0.0$ $M$, $k_3$ = $1.0$ * $10^{-3}$ $s^{-1}$, $k_4$ = $0.5$ * $10^{-3}$ $s^{-1}$, $k_5$ = $1.0$ * $10^{-3}$ $s^{-1}$, $t_{max}$ = $10000$ $s$\n", + "\n", + "To find $t_{opt}$, we need to find the time at which the derivative of B with respect to time is zero.\n", + "\n", + "That is to solve:\n", + "\n", + "\\begin{equation}\n", + "\\frac{d[B]}{dt} = 0\n", + "\\end{equation}\n" + ], + "metadata": { + "id": "r68jZYXYvxgU" + } + }, + { + "cell_type": "code", + "source": [ + "# Example\n", + "A0 = 1.0 # Initial concentration of A\n", + "B0 = 0.0 # Initial concentration of B\n", + "C0 = 0.0 # Initial concentration of C\n", + "k3 = 0.001 # Rate constant for A -> B\n", + "k4 = 0.0005 # Rate constant for B -> C\n", + "k5 = 0.001 # Rate constant for A -> C (competing reaction)\n", + "tmax = 10000 # Total time for the simulation\n", + "\n", + "initial_conditions, rate_constants = setup_case2(A0, B0, C0, k3, k4, k5)\n", + "A, B, C, t = solve_case2_ode(initial_conditions, rate_constants, tmax)\n", + "\n", + "# Plot the results\n", + "plt.plot(t, A, label='[A]',linewidth=3)\n", + "plt.plot(t, B, label='[B]',linewidth=3)\n", + "plt.plot(t, C, label='[C]',linewidth=3)\n", + "plt.legend()\n", + "plt.xlabel('Time (s)',fontweight='bold', fontsize=12)\n", + "plt.ylabel('Concentration (M)',fontweight='bold', fontsize=12)\n", + "plt.title('Concentration Profiles over Time for Case2',fontweight='bold',fontsize=14)\n", + "plt.show()\n", + "\n", + "### Find the t_opt for species B\n", + "# Convert B to a numpy array for differentiation\n", + "B_np = np.array(B)\n", + "# Calculate the gradient of B with respect to time\n", + "gradient_B = np.gradient(B_np, t)\n", + "\n", + "# Find where the gradient changes sign\n", + "max_idx = np.where(np.diff(np.sign(gradient_B)))[0]\n", + "\n", + "# If max_idx is not empty, we have found a local maximum\n", + "if max_idx.size > 0:\n", + " t_opt = t[max_idx[0]]\n", + " B_max = B[max_idx[0]]\n", + " print(f\"The time corresponding to the maximum concentration of B (t_opt) is: {t_opt} seconds\")\n", + "else:\n", + " print(\"No local maximum found for the concentration of B within the given time frame.\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 494 + }, + "id": "8kGUQZwvp7Ch", + "outputId": "c8375b25-6a8f-448a-b9f4-41b2f4f74340" + }, + "execution_count": 51, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": "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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The time corresponding to the maximum concentration of B (t_opt) is: 925.6 seconds\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 2.3. Validate the mechanism with experimental data" + ], + "metadata": { + "id": "UDdqXaqfq5jR" + } + }, + { + "cell_type": "markdown", + "source": [ + "### 2.3.1. Let's look at the plot using the given rate constants $k$ and experiment data first" + ], + "metadata": { + "id": "4YGWbDEsZZnK" + } + }, + { + "cell_type": "markdown", + "source": [ + "Consider the situation in which only reactant A is present initially. Prepare plots of the dimensionless concentration of species B (i.e., $B$/$A_0$) verses time (180 minutes) for each of the two cases noted above using the following values of the rate constants (in $s^{-1}$) at 160 °C.\n", + "\n", + "$k_1$ = $0.45$ * $10^{-3}$ $s^{-1}$, $k_2$ = $5.0$ * $10^{-3}$ $s^{-1}$, $k_3$ = $0.32$ * $10^{-4}$ $s^{-1}$, $k_4$ = $1.6$ * $10^{-4}$ $s^{-1}$, $k_5$ = $4.2$ * $10^{-4}$ $s^{-1}$, $t_{max}$ = $180$ $min$\n" + ], + "metadata": { + "id": "Z85fvyymrCjZ" + } + }, + { + "cell_type": "markdown", + "source": [ + "|Additional Information || |\n", + "|-----------------------------------||---------------------------------|\n", + "|**Time(min)** || **B(%w/w)** |\n", + "|0 || 0 |\n", + "|20 || 2.3 |\n", + "|30 || 3.5 |\n", + "|60 || 4.2 |\n", + "|90 || 3.2 |\n", + "|120 || 2.4 |\n", + "|180 || 2.0 |\n" + ], + "metadata": { + "id": "z1yfFLQjqsl1" + } + }, + { + "cell_type": "code", + "source": [ + "# Given rate constants in s^-1\n", + "k1 = 0.45e-3\n", + "k2 = 5.0e-3\n", + "k3 = 0.32e-4\n", + "k4 = 1.6e-4\n", + "k5 = 4.2e-4\n", + "\n", + "# Initial conditions: only A is present initially\n", + "A0 = 1.0 # Assume 100% A initially for dimensionless concentration\n", + "B0 = 0.0\n", + "C0 = 0.0\n", + "\n", + "# Time span (convert 180 minutes to seconds)\n", + "tmax = 180 * 60 # seconds\n", + "time_points = np.linspace(0, tmax, 300) # Create 300 time points for smooth curves\n", + "\n", + "# Rate constants in dictionary form\n", + "rate_constants_case1 = {'k1': k1, 'k2': k2}\n", + "rate_constants_case2 = {'k3': k3, 'k4': k4, 'k5': k5}\n", + "\n", + "# Solve ODEs for both cases\n", + "solution_case1 = solve_ivp(lambda t, y: case1_kinetics(t, y, rate_constants_case1), [0, tmax], [A0, B0, C0], t_eval=time_points)\n", + "solution_case2 = solve_ivp(lambda t, y: case2_kinetics(t, y, rate_constants_case2), [0, tmax], [A0, B0, C0], t_eval=time_points)\n", + "\n", + "# Experimental data converted to seconds and dimensionless concentration\n", + "experimental_time = np.array([0, 20, 30, 60, 90, 120, 180]) * 60\n", + "experimental_B = np.array([0, 2.3, 3.5, 4.2, 3.2, 2.4, 2.0]) / 100\n", + "\n", + "# Plotting both cases and experimental data\n", + "#plt.figure(figsize=(12, 6))\n", + "\n", + "# Case 1\n", + "plt.plot(solution_case1.t, solution_case1.y[1] / A0, label='Case1: Simulation', color='blue',linewidth=3)\n", + "\n", + "# Case 2\n", + "plt.plot(solution_case2.t, solution_case2.y[1] / A0, label='Case2: Simulation', color='green',linewidth=3)\n", + "\n", + "# Experimental data\n", + "plt.scatter(experimental_time, experimental_B, color='red', label='Experimental Data', zorder=5)\n", + "\n", + "plt.xlabel('Time (seconds)',fontweight='bold',fontsize=12)\n", + "plt.ylabel('Dimensionless concentration of B (B/A0)',fontweight='bold',fontsize=12)\n", + "plt.title('Comparison of Simulation and Experimental Data',loc='left', fontweight='bold',fontsize=14)\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "id": "NFQ0vwKyq8Jx", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 477 + }, + "outputId": "b1b39203-f20c-414b-cbaf-395023c3b08a" + }, + "execution_count": 52, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnIAAAHMCAYAAABRBkUNAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAADXdUlEQVR4nOzddVhU2RsH8O8MXQLSIIIoiiKCidhYoOLa3bl2oGvsuuqqu+ra7c+ONbETg8VYscVaYw0wkFAkJKTm/P4Yuc6dIIaBId7P88yj99xz731nmBlezj0hYIwxEEIIIYSQEkeo7gAIIYQQQohyKJEjhBBCCCmhKJEjhBBCCCmhKJEjhBBCCCmhKJEjhBBCCCmhKJEjhBBCCCmhKJEjhBBCCCmhKJEjhBBCCCmhKJEjhBBCCCmhKJEjajV48GAIBAIIBAK0aNFC3eGo1X///Yfu3bvD0tISGhoa3Oty//79QrleSXjtHR0duRjnzp1bJNds0aIFd83BgwcXyTVLKnqt8qckfOaKm+zXSyAQYMeOHeoOp1iiRE5J0dHRmD9/Ppo3bw4rKytoa2vDwMAArq6uGDZsGM6ePQta/YzkVUpKCtq3b4/Dhw/j48ePEIlE+To+NTUVf/75Jxo2bAgTExNoaWnB3Nwc1apVQ4cOHfDLL7/g33//LaToSw5KPNTv0qVLvF/Oih708yk5wsPDeT+7S5cuqTWeuXPn8uIRCoXQ0dGBmZkZqlevjs6dO2Pjxo348uWLSq+rrqRTs8iuVIqsX78eU6ZMwdevX3nlGRkZePLkCZ48eYJt27YhLCwMjo6O6gmyhOjduzdq1qwJALC3t1dzNOpz+/ZtvHr1itseMGAA3NzcIBAIYGdnl+Ox8fHxaNasGR49esQrj42NRWxsLP777z+cOXMGFhYWcHV15fbTay/f6NGj4efnBwDc60OIKtBnTj0YY0hPT8fnz5/x+fNnPHv2DMePH8cvv/yCrVu3onPnzuoOsUAokcunP//8E9OnT+e2NTQ00KFDB9StWxcCgQAvX77EuXPnEB0drcYoi7/ExESUK1cOvr6+8PX1VXc4avfmzRve9vbt26GhoZGnYxctWsRL4jp16gQPDw9oaWnh7du3uHHjBh4+fChzHL328vXq1UvdIZQpvXr1Qr169WTKS1MSTd936vXzzz/D2NgYHz9+xOXLl3H79m0AwOfPn9G1a1fs3bsXvXv3VnOUBcBInv37779MQ0ODAWAAmKWlJbt3755MvfT0dLZp0yYWHR3NK3///j2bOnUqq1mzJjMwMGA6OjrMwcGB9evXj928eVPmPHPmzOGu5eDgwD58+MAGDhzIzMzMmJGREfPz82PPnz9njDF29+5d5uPjwwwNDZmJiQnr3r07e/v2Le98wcHB3PkAsFevXrEVK1aw6tWrMx0dHWZra8smT57MEhMTecfFxsayn376ibVs2ZI5ODgwQ0NDpqWlxSwtLVnr1q3Zrl27mEgkyvFaL168YEuWLGEuLi5MW1ubderUiTHG2KBBg7g6zZs3553j4cOHrF+/fszBwYFpa2szXV1dZm9vz7y9vdmMGTPY+/fvZV6zQ4cOsfbt2zMrKyumpaXFTExMmJeXF1u6dClLTk6WqS8Z4/bt29n58+dZixYtmIGBATM0NGS+vr7s8ePHMsfl5uLFi6xbt27Mzs6OaWtrMyMjI1a7dm02e/ZsFhsby9ULCwvjxSD9cHBwyPVatWvX5uoPHjxYbp3w8HCZ55HTay/9uuzatYu5u7szXV1dVrlyZbZ8+XLGGGMZGRls/vz5zNHRkWlrazMXFxe2adMmmes7ODhw55szZw5vn/T7PC/HZWRksFmzZrF27doxJycnZmxszDQ1NVn58uVZkyZN2OrVq1l6errcayh6hIWFMcYYa968OVc2aNAgmefy/PlzNmrUKFa1alWmp6fH9PT0mLOzMxs5ciR7+vSpTH3p1/nDhw9sxIgRzNraOsfXLCdbt25lPXr0YC4uLszMzIxpamoyIyMj5u7uzqZNm8Y+fvwoc4z0a3nnzh3WoUMHZmxszPT09FiTJk3Y1atX5V7vyJEjrH79+kxXV5dZWlqyoUOHsujo6FxfK3mkvxu2b9+eY/0vX76wypUrc/W7du3K2z9ixAhun7W1NYuJiWGMyb6v4uLi2IQJE7jPZPXq1dmaNWtkvrsYYywrK4vt2rWLtWnThllYWDAtLS1mbm7O2rdvz06fPp3rc1Lm+07VnznGGPv69Stbs2YNa9q0KTM1NWVaWlrM2tqade/enYWEhMjU3759Oy+Or1+/sgULFjBnZ2emra3N7Ozs2JQpU9jXr1+5YyTfV/Ieks/zzz//ZJ06dWLOzs7M1NSUaWpqMmNjY1a/fn22YMEClpSUJBNTft4r2aQ/79mf7WzHjh1jOjo63H5DQ0PufcMYY69fv2YTJ05kTZo0YRUqVGD6+vpMW1ub2draMj8/P3bixAne+SQ/B7l9jyvz2c0NJXL5MGrUKN4P5/Dhw3k+9vLly8zU1FThD1ooFLJly5bxjpF8M5YvX545OjrKHGdhYcGOHj3Ke1NmP5ydnVlqaip3Pukvm5YtW8qNpX79+rzjHj16lOsvwSFDhvBil75W06ZNedu5fbH9+++/TF9fP8drnj17lqufmZnJevbsmWP96tWrsw8fPvDilNzfuHFjJhAIZI4zMzPjfchz4+/vn2McdnZ2XFKlikTOzc2N9xomJCTkKc68/lKpW7eu3Nh+/fVX1qlTJ7n7tm7dyjufqhO5L1++5PqebN26NcvMzJS5hqJHXhK5gwcPMl1dXYXn0NHRYfv27VP4Ojs5OTEbG5s8vWY5UfQzkXyPRUREKHwtGzRowLS0tOTG/+TJE95xGzZskHuNSpUqsRo1aih8rRTJbyLHGGM3b95kmpqa3DHZr3FgYCBXJhAI2Pnz57ljJH/mFhYWrGbNmnKfx/jx43nXSklJYa1bt87x9fX398/xOeX3+44x1X/mYmJimIeHh8LnIBQK2cqVK3nHSCdyTZo0kXvsgAEDuGPyk8iZmZnlWNfNzY19+fJF4euiqkSOMcaWLFnCq/PHH39w+06ePJnr98Vvv/3G1c9PIqfMZzc3dGs1H4KCgrj/m5qa5vm+enx8PLp27Yq4uDgAgJ6eHoYMGYJy5cph3759ePPmDUQiEaZOnYq6deuiefPmMuf4/PkzUlNTMXHiRCQnJ2PLli0AgI8fP6JLly4wNDTEuHHj8ObNGxw6dAgA8OLFCxw7dkxhk/Hff/+NTp06wd3dHWfPnuWam2/fvo0///wTs2fPBgAIhUJUr14dDRo0gLW1NUxMTPD161eEhobi5MmTYIxh+/btGDVqFBo0aCD3WlevXoWrqys6duwIxliutw137tyJlJQUAECFChXQv39/GBgY4P3793j8+DFu3LjBq//HH3/g4MGD3HbDhg3Rtm1bPH36FAEBAQCAp0+fol+/fvj777/lXvPatWtwcXFB165dcf/+fZw5cwaAuK/Z1q1bMWPGjBxjBoDdu3dj+fLl3Larqyu6dOmCDx8+YOfOncjKykJERAS6du2Kf//9F+XLl8eSJUtw584dHDhwgDtuyZIlAABjY+Ncr1mnTh3u1urly5dhbW0NT09P1K1bFw0aNEDLli1hbm6e63kUuXv3Lry8vNCmTRscOHAAz58/BwDMnz8fANC8eXM0a9YMmzdvRlRUFABxF4ShQ4cqfc3cCAQCODk5oWHDhrCzs4OpqSkyMjLw7NkzBAQEIDMzExcvXsThw4fRs2dPtG3bFoaGhtiwYQNev34NAKhXrx7vNmr58uVzvObLly8xYMAApKWlAQDMzMwwaNAgCAQC7Ny5E58+fUJaWhoGDRqEunXrwtnZWeYcr1+/hq6uLkaPHg09PT1s2LABqampAPL3mllaWqJjx46oXLkyypcvDw0NDURERODAgQOIjY1FREQEFixYgPXr18s9/tatW6hQoQL69euHd+/eYe/evQCAtLQ0rFq1Chs3bgQAvH//HpMnT+aOMzIywrBhwyAUCrl+wAUVGBiIT58+yZT36tWL60fWoEEDzJs3Dz///DMAYNy4cahduzaGDRvG1ff390ebNm3kXuPjx49ITEzEqFGjYGJigr/++gvv378HAKxZswbdunXjvncnT56MixcvAgC0tbXRu3dvODs749GjRwgICABjDMuXL0fdunXRt29fudfL7/edNFV85gYMGMCNeDcyMkLfvn1RoUIFXLt2DYGBgRCJRJg8eTLq1auHxo0by43jn3/+QZcuXVCjRg3s2bMH4eHhAIA9e/Zg0aJFsLW1xS+//ILw8HD88ccf3HGjRo1C5cqVAfD7AlaoUAHe3t5wcHCAqakpGGMICwvDgQMHkJycjEePHmH9+vWYNm1avl4vZQwdOhTTpk3jBiUGBwdj5syZAABNTU14eHigXr16sLCwQLly5ZCcnIxr164hODgYgPhnMWzYMNjZ2XH9an/66Sfu/JJdBiS/xwv62ZUrX2lfGSfZQuTp6Znn41asWMHLuM+cOcPti46OZoaGhjJ/uTEm+1fFX3/9xe3z8vLi7QsICGCMMSYSiZitra3cvxyl/2ocMWIEty89PZ25urpy+ypUqCDzPN68ecMOHTrE1q5dy5YuXcqWLFnC7OzsuGPmzZun8FoNGzbktfJlU/QX6oQJE7jyhQsXyhz3+fNn9vnzZ8aY+DZI+fLlufpeXl5cSwxjjE2bNo0XS2hoKLdPstze3p53W1nylqX07RxF3N3duWMcHR1ZSkoKt2/9+vW86x09epTbJ/2XcH6Eh4czExMThX/haWpqsv79+7NPnz7xjstr60CNGjW425Tnzp3j7XN3d+de640bN/L2Sb6Wqm6RyxYdHc2OHz/O1q9fz70nJVtehg4dyqufl1uBiupMnDiRKxcKhezRo0fcvkePHjGhUMjtnzhxotzXGQA7duwYt2/lypUKX7PcJCcns4sXL7JNmzax5cuXsyVLlvBaa5ycnBS+lgYGBry/+jt37sztq1OnDle+cOFCXnwXL17k9l27do23T9kWOUWP4OBg3nFZWVmsRYsW3H7J783atWuztLQ0Xn3p7889e/Zw+8LCwngtkv369WOMibuRSLb8bdu2jXfOMWPG8K6p6Dnl9/uOMdV+5h48eMAr//vvv3nXat++PbevS5cuXLn099CkSZO4fffv3+ftk7y9KH1nQfpnJyk+Pp6dOXOGbdy4kS1btowtWbKENWvWjDu2ZcuWCl8XVbbIMcaYpaUl7zWX9vz5c7Z//362Zs0a7vtFMg/YtWuXUrHm97ObG2qRKwLXr1/n/m9hYYF27dpx25aWlmjXrh3XaiRZV5Kmpiav9cDR0ZGrq6WlhS5dugAQt1RUqlQJHz58AACuFVCeAQMGcP/X0tJCz549MWfOHADiv8Sjo6NhZWWF2NhYDBo0CKdPn87xeWb/hSvP1KlToaurm+Pxkpo2bYrVq1cDAGbNmoUTJ07AxcUF1apVg6enJ5o2bcr9lfv8+XN8/vyZO7Z///68v4AHDRqEP//8k9u+fv06PDw8ZK45YMAAGBkZcdtVq1ZFaGgogJxfx2wpKSm8QQU9evSAnp4etz1w4ECMGTOGF4cqRks5ODjg7t27mDNnDo4cOcK1ZGbLzMzEX3/9hYiICAQFBUEgEOTr/D179oSWlhYAyIzC7tq1K/daZ/8Fni0uLo73eqpSamoqxowZg127duU4VUtO78n8kvxs1q1bl9cZv2bNmqhbty7Xqq3oc2xra4tOnTpx29WqVePtz+trtnz5csyZMwdJSUkK6+T03Dt16gRbW1u5cUi+1+/cucP938rKCq1ateK2GzVqhEqVKqmkVS4vhEIhdu/eDXd3d3z+/Jl77vr6+ti3bx+0tbUVHqulpSXz/dmkSROudeXu3bsAgJs3byIzM5OrN3ToUIWtpPfv30dKSgr09fVl9uX3+05aQT9z165d45W3bNlS4bVCQkIU7pP8vpL3Xs0PkUiEGTNmYNWqVUhPT1dYT5Wf2dwwBVOEhYeHo1+/fjm+NoBysRb0sysPzSOXD5LTQPz33395nidOMsmwsrKS2S9ZpujDYWlpCU3N73m35JdW9gSy2STr5fRLztLSUmEcgPiWMAAMGzYs1yQOAHfLSR4XF5dcj5fUvXt3TJ06FTo6OsjKysL169exfft2zJgxA97e3qhcuTI3L5rk6yvveUhvK3qNpb8wdXR0uP/nZV63uLg43ntC+roGBgYwNDTMNQ5lODk5Yffu3YiLi0NISAhWrFiBDh06QCj8/hEPDg7mEtP8kPyFL/3LUnKf5PsOUPyaSX9ucnrfKDJz5kzs2LEj15+LMudWRBWf45zeY0De3mfHjh3DlClTcvxFACDHX5Z5fa9nfwcAst8XgPzXIb+2b98OJu6vzXvImzC3QoUKMn/8tG7dWibJkGZmZiZze1My9uznKf1dkhPGGGJjY+Xuy+/3nbSCfuby8zw+fvyocJ/k+0SZ96qk1atXY8mSJTm+LwHVfmZz8vnzZ94tfcnf7507d841iQPyH6sqPrvyUItcPrRq1QovXrwAIP6iPn78eJ5aVCT73siblkSyzNTUVO45sv86k0f6w5xXMTExvC9A6dhMTEyQnJyMU6dOcWWtWrXCpk2b4ODgAA0NDTRo0IBrhciJgYFBvuNbsmQJZs2ahZCQEDx79gz//fcfTpw4gQ8fPuDNmzcYM2YMLl++LNO3Sfp5SG/n9TXOb8uVqakpBAIBl6hIXzc5OZn3AVYUR0Foa2vDy8sLXl5emDRpEnbv3o2BAwdy+1+8eIE6derk65yqeO9JJpTZfcIkY8ovyf6Ebm5u2LdvH6pVqwZNTU307NmTa+FWpcL4HOf3PQbwn7uhoSGOHDmCpk2bQldXF+vXr8fYsWNzPUde4zAxMeH+HxMTI7O/qKdZunz5ssxEqydOnMCxY8dy/C6OjY1FVlYWL5mTjD37eUp/l0yePJmXOElT1IdVme87SQX9zEk/j3nz5vHuDigThzLvVUmS71tbW1scPXoUHh4e0NbWxrRp07h+wUUl+w+IbNmtls+fP8eDBw+48r59++LPP/+Era0tBAIBLC0tc0x+c6KKz6481CKXD+PGjeN9EYwePZr3A8+WkZGBLVu2cF98jRo14vZ9/PgRZ8+e5bZjYmJ425J1C9vu3bu5/2dkZPAGC9jZ2cHKygoJCQnIysriyjt06AAnJydoaGjg+fPncucnU4WwsDDEx8fD2NgY7dq1w+TJk7FhwwasXbuWq3Pv3j0A4iZ/yS+uv/76ixfzzp07eecurNdYX18f7u7u3HZAQAAvadm1a1ehxDFr1iycOnWKd0som2QLIMD/xVyUJK9769Yt7gv00aNHOHnyZL7PJ9kS4u3tDVdXV2hqauLjx485ziov+YtJ+hZ0biR/Xnfv3uWtlPH48WPu9px0XVWTfO5OTk5o06YNdHV1IRKJuIFOqiI5v1t0dDRvwFdISEiR3VYFxH88DxgwgGsJql69Ordv+PDhXHcSeTIyMni/RMPDw/HPP/9w23Xr1gUAeHp68r7jtbS0MHXqVJlH9+7d4ebmhnLlyqns+amS9PvP3Nxc7vNo164dGjZsWODrSSee8j5bku/bevXqoUGDBtDW1sbXr1+V+g4oiFOnTmHWrFnctpGREYYPHy4TJyC+O2RnZ8etWJFTEieZZOf2Gqjys0stcvng6uqK+fPncyOnoqKiUK9ePfj5+aF27doyEwK3bt0agLiP1vz587kfYrdu3TB06FCUK1cOe/fu5VppBAIBJk2aVGTPZ/Pmzfj48SNq1aqFs2fP8n4xjRgxAoD4doqJiQl362HBggWIiYlBZmYmtm3bVmjN4AcOHMCcOXPQokULODs7w8bGBsnJydi3bx9XJzs5EAqFmDx5Mn799VcA4v5JTZo0Qdu2bfHs2TNegurt7c1LtlRtypQpXN/D8PBw1K9fnzdqNVvVqlXRoUMHlVzzn3/+we+//w4zMzM0b94c1atXh4GBAcLCwrB//36uXrly5Yr0DwVJ9evX527rXr58GQ0bNoStrS0uXryY79sIgDh5f/z4MQDx+1goFEJfXx+7d+/O8YtW8vbJ6dOnMWPGDJibm8Pc3DzXJaHGjh2LDRs2IC0tDSKRCM2bN+eNWs1OMLS1tZX+yzovqlWrhgsXLgAAHj58iD59+qB69eo4e/aszGjugurXrx/mzp3Lfc67dOmC4cOHQyAQYNu2bSq5hqJRq8bGxtz3EACMHDkS7969AyD+Lr558yZatWqFmzdvIjY2FgMHDsSFCxcUthwNHToUV69e5UatZmRkcPuyf4mXL18eQ4cOxebNmwGIR4LeuXMHjRo1gq6uLiIiInDjxg2EhoZi0KBB8PHxUclroGru7u5o06YN9z4ZN24czp49i7p160IoFOLNmzcICQnB06dPMWfOHDRp0qRA17OwsICWlhb3mv7yyy948OABtLS00KJFC9SrVw/VqlXjWt9PnTqFH3/8EdbW1jh06BCePXtWsCeci82bN8PY2BifPn3ClStXcPPmTW6fQCDA1q1buZH9VapUgVAo5D7PEydOxP379xEbG4vt27fneB07Oztucvdly5YhNjYWenp6qF27Nlq1alV4n918DY0gjDHGVq1aJXfeNumH5EiZy5cv5ziyUCgUsqVLl/Kuk9NoPsnRT9L7FI26kx5Z1aFDB7mx1K1blzfactGiRXLr1axZkzcnTk7XUjRqSNEoLunRcvIeq1ev5upnZmayHj165Fi/evXqMvPzSO6XHmWU0wiznOQ2j5ytra3M5LwFGbWa2xxG2e+v3bt35/n5KXpdpEenSe7L6Wf+77//yv3M6Onp8UYi5nXU6r59++Q+TxsbG9amTRuFz+v48eNyj3N1dZX7eqp6HjnpePL6OZH04sULZmRkJHNtTU1N1q9fP4XvI2VHDq9du1bh+9jZ2Vnha6VIXketSk+iml2upaXF7t69yxgTjyqUHEX4559/yn1OVlZWCufvGjNmDC++5OTkXOeRk36+Bf2+Y0z1n7no6Ogc55GT917I7XtIURyMMdalSxe551+yZAljjLGrV6/yRgRnPwwNDVnXrl0Vvv9yuqYieZk3EhDPESo9uS9jsnPGZj9atWrFm6lB+nM0efJkuceNHTuWMab8Zzc3dGtVCRMmTEBYWBjmzp2LJk2awMLCApqamtDX10f16tUxevRoXLp0CQ4ODtwxzZo1w+PHjzFlyhS4urpCX18f2traqFixIjc6ZsqUKUX6PNasWYO1a9eiRo0a0NHRgY2NDSZOnIi///6b159i+vTpWLduHapWrQotLS1YW1tjxIgRuHz5ssytO1Xp3LkzZs+ejdatW8PR0RH6+vrQ1NSEjY0NOnTogBMnTmD8+PFcfQ0NDRw8eBABAQFo3749NzjE2NgYnp6eWLJkCW7fvp1jfxdVWbZsGS5cuIBu3brB1tYWWlpaMDQ0hIeHB3799Vc8fPiQt+ZpQe3atQtbtmxB37594e7uDhsbG2hpaUFPTw/Ozs4YPHgwbt++jf79+6vsmvlVo0YNXLx4EU2bNoWenh7KlSuHjh074ubNm3LnTcxN7969cfDgQbi7u0NLSwtmZmbo1asXbty4kePP+IcffsDatWtRvXr1HEc5KtKjRw/cv38fo0aNQpUqVaCrqwtdXV1UrlwZI0aMQGhoaKEv9VOlShVcuXIFbdu2hb6+PgwNDdG8eXMEBQVxdwFUaezYsTh06BDq1q0LHR0dmJubY8CAAbh582aRfJ5evnyJCRMmcNu//PIL18+zatWqWLx4Mbdv1qxZXJcLSbq6uggODsbkyZNRoUIFaGtro1q1ali1ahWvuwYg7iJx7tw57N27F+3bt4eVlRU0NTWhp6eHypUro3v37ti0aRNvvsjiyNLSEjdv3sSGDRu4uSQ1NDRgYGAAFxcX9O/fH3v27OHNfVYQmzdvxqBBg2BlZcXrE5utSZMmOHfuHBo1agQdHR0YGxujffv2CAkJgZubm0piyImmpiZMTU3h4uKCTp064X//+x/evHmDjh07ytRds2YN5s2bBwcHB2hpaaFixYr46aefcPLkyRz7KP7++++YOHEiKlSoIHfuwML67Aq+ZbykDLh06RK8vb257bCwMJnRa4QQUhrMnTsXv/32GwDxFD3Zk9kSUtpQixwhhBBCSAlFiRwhhBBCSAlFiRwhhBBCSAlFfeQIIYQQQkooapEjhBBCCCmh8j0hcHx8PE6fPo1r167hyZMn3ESO5ubmqFGjBho3bowOHTqobQZ5QgghhJCyIs+3Vm/fvo0lS5bg5MmTuc7ErqOjgx9++AFTp07lLfFSUolEInz48AFGRkYFXm+OEEIIIUWDMYYvX77A1tZW7vx2pUGeErmOHTvizJkzAMBbZFZbWxumpqZgjCE+Pp6X4GUnPH5+fjh+/Liq4y5S79+/h729vbrDIIQQQogS3r17hwoVKqg7jEKRp0QuO4u1s7ND586d0aZNG9SpU0fmRXn37h1CQ0Nx4cIFHDt2DBERERAIBLwFzEuihIQEmJiY4N27d8V2kWRCCCGE8CUmJsLe3h7x8fEwNjZWdziFIk+JXNu2bTF58mS0a9cuXyc/c+YMVq5cifPnzysdYHGQmJgIY2NjJCQkUCJHCCGElBBl4fc3TT+SB2XhjUAIIYSUNmXh93fp7PlHCCGEEFIG5DuRe/z4MSZOnIg6derA1NSUG/BQp04dTJw4EY8fPy6MOAkhhBBCiJR83Vr9448/MHfuXG7wguSh2aNUNTQ08Ntvv2HmzJkqDlV9ykLTLCGk7MnKykJGRoa6wyBEaVpaWtDQ0FC4vyz8/s7zhMABAQGYNWuWwv3ZSV1mZiZmzZqFqlWrolu3bgWPkBBCiEoxxhAVFYX4+Hh1h0JIgZmYmMDa2rrMzvOa50Ru1apVAAAjIyP8/PPPaNSoESwtLaGtrY309HRERUUhJCQECxcuRFJSElasWEGJHCGEFEPZSZylpSX09fXL7C9AUrIxxpCSkoKYmBgAgI2NjZojUo88J3IPHjyAQCDA6tWrMWjQIJn91apVQ/PmzWFtbY1hw4bh4cOHKg2UEEJIwWVlZXFJnJmZmbrDIaRA9PT0AAAxMTGwtLTM8TZraZXvwQ70lxshhJRc2X3i9PX11RwJIaqR/V4uq/0989wi5+7ujpCQEEyYMAHR0dHw8vKClZUVtLW1kZaWhujoaISEhOCPP/6AQCBArVq1CjNuQgghBUB/lJPSoqy/l/OcyI0fPx4hISH48uULZsyYobAeYwwCgQATJ05USYCEEEIIIUS+PN9a7dWrF2bPng2BQADGmMKHUCjE7Nmz0aNHj8KMmxBCCCnVwsPDIRAIcP/+/UK/lkAgwLFjx4rNeUje5auP3Ny5c3H37l2MHj0abm5uMDIyglAohJGREdzc3DB69GjcuXMHc+bMKax4SR5kZADv3wMJCeqOhBBCVCsqKgrjx4+Hk5MTdHR0YG9vj44dOyIoKKjIYrhy5Qo6duwIW1vbAiUuYWFh6Nu3L2xtbaGrq4sKFSqgU6dOePbsGQDA3t4ekZGRqFmzpgqjV425c+fCw8NDpjwyMjLf67KTgsnzrdVs7u7uWLduXa710tPToa2trVRQRDmpqcD06cDWrUBKirisZUtg8WKgXj31xkYIIQUVHh6Oxo0bw8TEBEuWLIGbmxsyMjJw7tw5jB07lkuACltycjLc3d0xdOhQdO3aValzZGRkoE2bNqhWrRqOHDkCGxsbvH//HmfPnuXm99PQ0IC1tbUKIy98JS3eUoGpUGZmJjtz5gwbOHAgMzExUeWp1SohIYEBYAkJCeoORaHYWMYaNWIMkH0IhYz973/qjpAQUhykpqayJ0+esNTUVMYYY1lZjMXEqPeRlZW32Nu1a8fs7OxYUlKSzL64uDju/8uWLWM1a9Zk+vr6rEKFCmz06NHsy5cv3P7w8HDm5+fHTExMmL6+PqtRowY7ffo0t//Ro0fM19eXGRgYMEtLS9a/f3/28eNHuTEBYEePHs3bE5AQGhrKALDw8HCFdcLCwhgAFhoayhhjLDg4mAFggYGBzMPDg+nq6jJvb28WHR3Nzpw5w1xcXJiRkRHr06cPS05O5s7j4ODAVqxYwTu3u7s7mzNnjsLnMW3aNObs7Mz09PRYpUqV2KxZs1h6ejpjjLHt27czALzH9u3b5Z7n4cOHzNvbm+nq6rLy5cuzESNG8H4WgwYNYp06dWJLlixh1tbWrHz58mzMmDHctfJC+j0tqST8/i6ofE8/Is+lS5cwatQoWFtbw8/PD3/99RcSExOVPt+6devg6OgIXV1deHp64tatWznWDwgIgIuLC3R1deHm5oYzZ87w9gsEArmPJUuWKB1jccIYMGAAEBIif79IBPz4I7BzZ9HGRQgp/mJjAUtL9T5iY3OP8/PnzwgMDMTYsWNhYGAgs9/ExIT7v1AoxOrVq/Hvv/9i586d+PvvvzFt2jRu/9ixY5GWloYrV67g0aNHWLx4MQwNDQEA8fHxaNmyJWrXro07d+4gMDAQ0dHR6NmzZ75e17lz58LR0VHhfgsLCwiFQhw6dIhb9jI/5167di1CQkLw7t079OzZEytXrsTevXtx+vRpnD9/HmvWrMnXOaUZGRlhx44dePLkCVatWoXNmzdjxYoVAMR95qdMmQJXV1dERkYiMjISvXr1kjlHcnIyfHx8YGpqitu3byMgIAAXL17EuHHjePWCg4Px6tUrBAcHY+fOndixYwd27NhRoPjLFGUzwBs3brBJkyYxOzs7JhQKmVAoZAKBgHsIhUKlzrt//36mra3Ntm3bxv799182YsQIZmJiwqKjo+XWv3btGtPQ0GB//vkne/LkCZs1axbT0tJijx494upERkbyHtu2bWMCgYC9evUqTzEV94z+zBn5LXHSDw0Nxm7eVHe0hBB1km69iInJ2/dHYT5iYnKP++bNmwwAO3LkSL6fc0BAADMzM+O23dzc2Ny5c+XWnT9/Pmvbti2v7N27dwwAe/78uUx9KGiRW7NmDWvZsmWOca1du5bp6+szIyMj5u3tzebNm8f7vaSoRe7ixYtcnYULFzIAvON+/PFH5uPjw20r0yInbcmSJaxu3brc9pw5c5i7u7tMPcnzbNq0iZmamvJaUE+fPs2EQiGLiopijIlb5BwcHFhmZiZXp0ePHqxXr14KY5FGLXL58PDhQ/z888+oXLkyGjVqhNWrVyMyMpIbsSoQCFC7dm2sXLkSL1++VCqxXL58OUaMGIEhQ4agRo0a2LhxI/T19bFt2za59VetWgVfX1/89NNPqF69OubPn486depg7dq1XB1ra2ve4/jx4/D29oaTk5NSMRYnmZnA1Kn8MhMTIDAQkJ4BJisL6NcPSEoqsvAIIUQl2Lf1vPPi4sWLaNWqFezs7GBkZIQBAwYgNjYWKd86D0+YMAELFixA48aNMWfOHN5KRA8ePEBwcDAMDQ25h4uLCwDg1atXeY5h3LhxuQ7AGDt2LKKiorBnzx54eXkhICAArq6uuHDhQo7HSc7TamVlBX19fd7vMysrK27ZKmUdOHAAjRs3hrW1NQwNDTFr1iy8ffs2X+d4+vQp3N3deS2ojRs3hkgkwvPnz7kyV1dX3ooMNjY2BY6/LMlzIufq6oratWtj8eLFCAsL45I3bW1tdOzYkas3bNgwTJgwAZUqVcp3MOnp6bh79y5at279PUChEK1bt8b169flHnP9+nVefQDw8fFRWD86OhqnT5/GsGHDFMaRlpaGxMRE3qO4OnoUePKEX7ZiBeDjI/7X35+/7+VL8YAIQggpSZydnSEQCHId0BAeHg4/Pz/UqlULhw8fxt27d7kBeunp6QCA4cOH4/Xr1xgwYAAePXqEevXqcbcik5KS0LFjR9y/f5/3ePHiBZo1a6by52VkZISOHTvi999/x4MHD9C0aVMsWLAgx2O0tLS4/wsEAt52dplIJOK2hUKhTCKc0yoI169fR79+/dC+fXucOnUKoaGh+OWXX7jXT9Vyi5/kLM+jVp8+fcr9X1dXF76+vujevTs6duzITUNSUJ8+fUJWVhasrKx45VZWVgo/vFFRUXLrR0VFya2/c+dOGBkZ5TjSaOHChfjtt9/yGb167NnD33Z3F/eXAwCBQDxiNSQEuHHje52NG4GRI8V1CSFlm5kZoO7Gj7ws+Vq+fHn4+Phg3bp1mDBhgkw/ufj4eJiYmODu3bsQiURYtmwZ93vp4MGDMuezt7fHqFGjMGrUKMycORObN2/G+PHjUadOHRw+fBiOjo7Q1Mz3xA4FIhAI4OLighBFHZ6VZGFhgcjISG47MTERYWFhCuuHhITAwcEBv/zyC1f25s0bXh1tbe1c+/ZVr14dO3bsQHJyMvfzunbtGoRCIapVq6bMUyFy5Cv7yh4k0K5dOwwdOhQ9evSAkZFRYcVWKLZt24Z+/fpBV1dXYZ2ZM2ciISGBe7x7964II8y7uDhAalwHJk4EJNcM1tQE/voL+LauMADx4IdJk8S9UwghZZtQCFhYqPeR13aAdevWISsrCw0aNMDhw4fx4sULPH36FKtXr4aXlxcAoEqVKsjIyMCaNWvw+vVr7N69Gxs3buSdZ9KkSTh37hzCwsJw7949BAcHo3r16gDEtzs/f/6MPn364Pbt23j16hXOnTuHIUOGcIlLUlIS11IHiOeDu3//Pu/W49q1a9GqVSuFz+X+/fvo1KkTDh06hCdPnuDly5fYunUrtm3bhk6dOuX1x5cnLVu2xO7du3H16lU8evQIgwYNynFxeWdnZ7x9+xb79+/Hq1evsHr1ahw9epRXx9HRkXvenz59Qlpamsx5sn/XDho0CI8fP0ZwcDDGjx+PAQMGyDTAEOXlK5HLbpo9duwYOnXqBAsLCwwYMEBlszibm5tDQ0MD0dHRvPLo6GiFc9NYW1vnuf7Vq1fx/PlzDB8+PMc4dHR0UK5cOd6jODpyRDz5bzYdHUBeQ2PlyoD0qmqXLskmgYQQUpw5OTnh3r178Pb2xpQpU1CzZk20adMGQUFB2LBhAwDxXKfLly/H4sWLUbNmTezZswcLFy7knScrKwtjx45F9erV4evri6pVq2L9+vUAAFtbW1y7dg1ZWVlo27Yt3NzcMGnSJJiYmHAtfHfu3EHt2rVRu3ZtAIC/vz9q166N2bNnc9f49OlTjn3qKlSoAEdHR/z222/w9PREnTp1sGrVKvz222+8ljBVmDlzJpo3bw4/Pz906NABnTt3RuXKlRXW/+GHHzB58mSMGzcOHh4eCAkJwa+//sqr061bN/j6+sLb2xsWFhbYt2+fzHn09fVx7tw5fP78GfXr10f37t3RqlUrXh92UnAClscepDdv3sTevXsREBDAu22ZvVht9mCH0aNH448//lA6+fH09ESDBg24/goikQgVK1bEuHHj5K7x2qtXL6SkpODkyZNcWaNGjVCrVi2Zv8IGDx6Mx48f486dO/mKKTExEcbGxkhISChWSV3r1oBkX9ouXcTJnTypqUD16oBk63i9esCtW+JbsISQsuHr168ICwtDpUqVcrwzQUhJkdN7urj+/lalPLfIeXp6YtWqVYiIiEBQUBCGDx8OU1NT3ohVANiwYQMsLCzQpk0bpQLy9/fH5s2bsXPnTjx9+hSjR49GcnIyhgwZAgAYOHAgZs6cydWfOHEiAgMDsWzZMjx79gxz587FnTt3ZOapSUxMREBAQK6tcSVFaipw5Qq/rE8fxfX19IB58/hld+4Ap0+rPjZCCCGEFI18j1AQCATw9vbGpk2bEB0djZMnT6Jv374wMDDgkrqMjAz8/fffSgXUq1cvLF26FLNnz4aHhwfu37+PwMBA7n7627dveZ02GzVqhL1792LTpk1wd3fHoUOHcOzYMZm16fbv3w/GGPrklO2UIDdv8m+rCoWAr2/Ox/TtCzg788sWLKC+coQQQkhJledbq7n5+vUrTp48iX379uHs2bNIT0/P92zVxVVxbJqdNw+YM+f7dt264ha23OzeDQwcyC/75x+gcWPVxkcIKZ7o1iopbejWah49fvw4x/26urro0aMHjhw5gujoaIUT+BLVkL6tmtfpjfr0ASpW5JctW6aamAghhBBStPKcyNWqVQtOTk4YP348zp49K3eocbZy5cph0KBBKgmQyMrIAKTnO85rIqepKbviw7FjwOvXKgmNEEIIIUUoz4lc//79kZSUhHXr1sHPzw9mZmbo1KkTNm/ejIiIiMKMkUi5dw/4ttIMp0mTvB8/fDgg2cLMGLBpk2piI4QQQkjRyXMit2vXLkRHR+P69euYOXMmnJ2dcfLkSfz444+oWLEiN4fODcklBEihkG6Nq1EDMDfP+/HlygHfBgFztm8HCmn1FUIIIYQUknyv7ODp6YkFCxYgNDQU79+/x8aNG+Hn54eXL19yixBbWVlhyJAhCAgIwJcvXwor9jLr0SP+doMG+T/Hjz/yt2NigOPHlY+JEEIIIUWvQAuk2traYuTIkTh+/DhiY2Nx9uxZjBkzBoaGhti5cyd69+6NFStWqCpW8o30uBM3t/yfo3p1oGlTftn//qd8TIQQQggpegVf6f4bbW1t+Pj4YM2aNXj16hX+/fdfLF68mFu/jqiGSAT8+y+/TGrKvDyTbpULCgJevlTuXIQQQlTr0qVLEAgEiI+PL9TrhIeHQyAQcGvHqvs8JH9Ulsilp6cjJiaGW4+1evXqmDp1Knr06KGqSxAA4eFAcjK/TJkWOQDo1g0oX55fRoMeCCHFWVRUFMaPHw8nJyfo6OjA3t4eHTt2RJDkeoWFbOHChahfvz6MjIxgaWmJzp074/nz5/k+z4MHD/DDDz/A0tISurq6cHR0RK9evRATEwNAPOF9ZGQkjI2NVf0UCmzw4MHo3Lkzr8ze3h6RkZEyE/KTwpWvRC48PBzz5s3DmDFjsH79eqSlpSEuLg7dunWDgYEBbGxsYG5ujlWrVhVWvGWedP+48uUBa2vlzqWrC0jPErN9O5DDzDKEEKI24eHhqFu3Lv7++28sWbIEjx49QmBgILy9vTF27Ngii+Py5csYO3Ysbty4gQsXLiAjIwNt27ZFsvRf2Tn4+PEjWrVqhfLly+PcuXN4+vQptm/fDltbW+482trasLa25pbALO40NDRgbW0NTU1NdYdStrA8evr0KTM2NmZCoZB7tG3blvn5+TGBQMB7CIVCdvjw4byeuthLSEhgAFhCQoK6Q2ELFjAmnjBE/GjevGDne/qUfz6AsYAAlYRKCCmGUlNT2ZMnT1hqaipjjLEsURaLSYpR6yNLlJWn2Nu1a8fs7OxYUlKSzL64uDju/8uWLWM1a9Zk+vr6rEKFCmz06NHsy5cv3P7w8HDm5+fHTExMmL6+PqtRowY7ffo0t//Ro0fM19eXGRgYMEtLS9a/f3/28eNHhXHFxMQwAOzy5ct5eh6MMXb06FGmqanJMjIyFNYJDg5mALjntn37dmZsbMxOnjzJqlatyvT09Fi3bt1YcnIy27FjB3NwcGAmJiZs/PjxLDMzkzsPAHb06FHeuY2Njdn27dsZY4yFhYUxACw0NJQxxlhmZiYbOnQoc3R0ZLq6uqxq1aps5cqV3LFz5sxhAHiP4OBgmfMwxtilS5dY/fr1mba2NrO2tmbTp0/nPefmzZuz8ePHs59++omZmpoyKysrNmfOnDy/jozJvqclFaff34Ulz2nzwoULkZiYyCu7ePGiouQQ//vf/9C1a1clUkuSE+kWuYK2YLu4iCcTllwpYtcuoHv3gp2XEFIyxKbEwnKppVpjiJkaAwsDixzrfP78GYGBgfj9999hYGAgs9/ExIT7v1AoxOrVq1GpUiW8fv0aY8aMwbRp07B+/XoAwNixY5Geno4rV67AwMAAT548gaGhIQAgPj4eLVu2xPDhw7FixQqkpqZi+vTp6Nmzp8I1xBMSEgAA5SX6qgwePBjh4eG4dOmS3GOsra2RmZmJo0ePonv37nludUtJScHq1auxf/9+fPnyBV27dkWXLl1gYmKCM2fO4PXr1+jWrRsaN26MXr165emc0kQiESpUqICAgACYmZkhJCQEI0eOhI2NDXr27ImpU6fi6dOnSExMxPbt27nn/uHDB955IiIi0L59ewwePBi7du3Cs2fPMGLECOjq6mLu3LlcvZ07d8Lf3x83b97E9evXMXjwYDRu3Bht2rRRKv6yJs+J3D///AOBQAAbGxv07dsXly9fxu3btyEQCNC2bVvs2rULIpEIQ4YMwblz5xAaGlqYcZdZqhixKm3wYH4id/aseDoSS/V+txNCCOfly5dgjMHFxSXXupMmTeL+7+joiAULFmDUqFFcIvf27Vt069YNbt++QJ2cnLj6a9euRe3atfHHH39wZdu2bYO9vT3+++8/VK1alXctkUiESZMmoXHjxry+YTY2NhCJRApjbNiwIX7++Wf07dsXo0aNQoMGDdCyZUsMHDgQVlZWCo/LyMjAhg0bULlyZQBA9+7dsXv3bkRHR8PQ0BA1atSAt7c3goODlU7ktLS08Ntvv3HblSpVwvXr13Hw4EH07NkThoaG0NPTQ1paGqxz6Nuzfv162NvbY+3atRAIBHBxccGHDx8wffp0zJ49G0KhuHdXrVq1MOfb4uHOzs5Yu3YtgoKCKJHLozz3kYuMjAQArFq1Cn/++SdOnDjB7Zs0aRIsLS1hbW2NCRMmAADi4uJUHCoRiYAXL/hlrq4FP2/37oCe3vftzExg376Cn5cQQlSFfRtIlxcXL15Eq1atYGdnByMjIwwYMACxsbFI+bYkzoQJE7h5T+fMmYOHDx9yxz548ADBwcEwNDTkHtnJ46tXr2SuNXbsWDx+/Bj79+/nlS9cuBC7du3KMc7ff/8dUVFR2LhxI1xdXbFx40a4uLjgkfStFwn6+vpcEgcAVlZWcHR05FoUs8uyB0woa926dahbty4sLCxgaGiITZs24e3bt/k6x9OnT+Hl5cVrbWzcuDGSkpLw/v17rqxWrVq842xsbAocf1mS50Tu69evAMQvMADeXwzlJNZ7yv5/Tn+JEOV8+CC7+kKVKgU/r5ERIH0XPJfvH0IIKVLOzs4QCAR49uxZjvXCw8Ph5+eHWrVq4fDhw7h79y7WrVsHQDy7AgAMHz4cr1+/xoABA/Do0SPUq1cPa9asAQAkJSWhY8eOuH//Pu/x4sULNJNa1HrcuHE4deoUgoODUaFCBaWel5mZGXr06IGlS5fi6dOnsLW1xdKlSxXW19LS4m0LBAK5ZZK/gwUCgUwinJGRofAa+/fvx9SpUzFs2DCcP38e9+/fx5AhQ7jXT9Vyi5/kLN9DS0JDQ5GZmamwLKe/JEjBSC9sr6cH5NACny8DBwJ79nzfvndPfBuXRpETUrqZ6ZshZqp6Wz/M9M1yrVO+fHn4+Phg3bp1mDBhgkw/ufj4eJiYmODu3bsQiURYtmwZd+vu4MGDMuezt7fHqFGjMGrUKMycORObN2/G+PHjUadOHRw+fBiOjo4KR18yxjB+/HgcPXoUly5dQqVKlZR41rK0tbVRuXLlfI1+zQsLCwvurhoAvHjxgmudlOfatWto1KgRxowZw5VJt0Zqa2sjKysrx+tWr14dhw8fBmOMa5W7du0ajIyMlE58iax8J3LZt04BcD8YyTJSeMLC+NuOjoCqRqW3agXY2opb/bLt3g0sXqya8xNCiiehQJjrQIPiYt26dWjcuDEaNGiAefPmoVatWsjMzMSFCxewYcMGPH36FFWqVEFGRgbWrFmDjh074tq1a9i4cSPvPJMmTUK7du1QtWpVxMXFITg4mJu8fuzYsdi8eTP69OmDadOmoXz58nj58iX279+PLVu2QENDA2PHjsXevXtx/PhxGBkZISoqCgBgbGwMvW/9VGbOnImIiAiFt1dPnTqF/fv3o3fv3qhatSoYYzh58iTOnDnDDSBQlZYtW2Lt2rXw8vJCVlYWpk+fLtMKJsnZ2Rm7du3CuXPnUKlSJezevRu3b9/mJayOjo44d+4cnj9/DjMzM7lz3Y0ZMwYrV67E+PHjMW7cODx//hxz5syBv78/l2STgsv3K8kY4x7yyvLTj4Hkj3QiJ9E/t8A0NID+/fllf/0F5PIHFyGEFBknJyfcu3cP3t7emDJlCmrWrIk2bdogKCgIGzZsAAC4u7tj+fLlWLx4MWrWrIk9e/Zg4cKFvPNkZWVh7NixqF69Onx9fVG1alVuIIStrS2uXbuGrKwstG3bFm5ubpg0aRJMTEy45GPDhg1ISEhAixYtYGNjwz0OHDjAXSMyMjLHPmU1atSAvr4+pkyZAg8PDzRs2BAHDx7Eli1bMGDAAJW+bsuWLYO9vT2aNm2Kvn37YurUqdDX11dY/8cff0TXrl3Rq1cveHp6IjY2ltc6BwAjRoxAtWrVUK9ePVhYWODatWsy57Gzs8OZM2dw69YtuLu7Y9SoURg2bBhmzZql0udX1glYHjMvR0fHfE9KGCadeZRQiYmJMDY2RkJCAq8/YFEbNIjfd23cOOBbtw6VePxYdhTsuXNA27aquwYhRL2+fv2KsLAwVKpUCbq6uuoOh5ACy+k9XVx+fxemPN9aDQ8PL8QwSF5I95FTUbcMTs2aQJ064v5x2XbtokSOEEIIKa7oJnUJIt3AqepEDpBdsuvIEeDLF9VfhxBCCCEFl6dE7t27d0pfQHKuGKK8tDT+QARAtX3ksvXuDUgO1EpNBQ4fVv11CCGEEFJweUrkKleujN69e+PChQu5DjcGxHPIBQUFoU+fPryJC4ny3rwRr4QqqTBa5CwtgXbt+GU7d6r+OoQQQggpuDz1kcvMzERAQAACAgJgamqKFi1aoE6dOqhSpQpMTU3BGENcXBxevnyJe/fu4fLly4iLi+PNHUMKRrp/XPnyQGH12xw4EDh58vv25cvA+/cATftDCCGEFC95SuQOHDiAuXPn4unTp/j8+TOOHj2Ko0ePKqyfPRDW1dWVWz+NFExR9I/L5ucHGBsD39aBBmPA/v3A1KmFd01CCCGE5F+ebq326NEDjx8/xsmTJ9G1a1fo6OjIzB2X/dDR0UG3bt1w6tQpPHz4EN27dy/s51AmRETwtx0cCu9aurpAt278sr17C+96hBBCCFFOnqcfEQgE6NChAzp06ICMjAzcvXsXT58+xadPnwAA5ubmqF69OurWrZvjjNFEORKrqwAQr8JQmPr2BbZt+74dGgo8fQp8m/ycEEIIIcVAvpfoAsQL3DZs2BANGzZUdTxEAekRqzY2hXu9Fi3E15BMIPfsARYsKNzrEkIIISTvaB65EqKoW+Q0NIA+ffhle/fKjpwlhBAiNnjwYHTu3FndYRSIo6MjVq5cqe4wSD5QIldCFHWLHCC+vSopLAy4caPwr0sIIfIMHjwYAoFA5uHr66vu0AAAq1atwo4dO9QdBgBxd6hjx46p/Lxz587lXndNTU2Ym5ujWbNmWLlyJdLS0vJ1rkuXLkEgECA+Pl7lcZYlSt1aJUUrIwP4+JFfVtgtcoB4ua5q1YDnz7+X7d0LeHkV/rUJISVAVhZw9ar4loGNDdC0qbg5vxD5+vpi+/btvDIdHZ1CvWZusrKyIBAIYGxsrNY4ioqrqysuXrwIkUiE2NhYXLp0CQsWLMDu3btx6dIlGBkZqTvEMoVa5EqAqCjZsqJokRMIZFvlDhwQJ5aEkDLuyBHA0RHw9hZ/UXh7i7ePHCnUy+ro6MDa2pr3MDU1BSBu4dHW1sbVq1e5+n/++ScsLS0RHR0NAGjRogXGjRuHcePGwdjYGObm5vj111+5abMAIC0tDVOnToWdnR0MDAzg6emJS5cucft37NgBExMTnDhxAjVq1ICOjg7evn0rc2u1RYsWGD9+PCZNmgRTU1NYWVlh8+bNSE5OxpAhQ2BkZIQqVarg7NmzvOf4+PFjtGvXDoaGhrCyssKAAQO4gYXZ550wYQKmTZuG8uXLw9raGnPnzuX2Ozo6AgC6dOkCgUDAbb969QqdOnWClZUVDA0NUb9+fVy8eDHfPwNNTU1YW1vD1tYWbm5uGD9+PC5fvozHjx9j8eLFXL3du3ejXr16MDIygrW1Nfr27YuYmBgA4vXbvb29AQCmpqYQCAQYPHgwACAwMBBNmjSBiYkJzMzM4Ofnh1evXuU7zrKCErkSQLp/nJYWYGZWNNeWTuQ+fgSCgorm2oSQYurIEaB7d/FM4ZIiIsTlhZzMKdKiRQtMmjQJAwYMQEJCAkJDQ/Hrr79iy5YtsLKy4urt3LkTmpqauHXrFlatWoXly5djy5Yt3P5x48bh+vXr2L9/Px4+fIgePXrA19cXL1684OqkpKRg8eLF2LJlC/79919YWlrKjWnnzp0wNzfHrVu3MH78eIwePRo9evRAo0aNcO/ePbRt2xYDBgxASkoKACA+Ph4tW7ZE7dq1cefOHQQGBiI6Oho9e/aUOa+BgQFu3ryJP//8E/PmzcOFCxcAALdv3wYAbN++HZGRkdx2UlIS2rdvj6CgIISGhsLX1xcdO3bE27dvC/zau7i4oF27djgi8bPPyMjA/Pnz8eDBAxw7dgzh4eFcsmZvb4/D39Z/fP78OSIjI7Fq1SoAQHJyMvz9/XHnzh0EBQVBKBSiS5cuEIlEBY6zVGIkVwkJCQwAS0hIUMv1jx1jTDzMQPyoWLFor9+gAf/6/fsX7fUJIaqTmprKnjx5wlJTU5U7QWYmYxUq8L8UJB8CAWP29uJ6KjZo0CCmoaHBDAwMeI/ff/+dq5OWlsY8PDxYz549WY0aNdiIESN452jevDmrXr06E4lEXNn06dNZ9erVGWOMvXnzhmloaLCIiAjeca1atWIzZ85kjDG2fft2BoDdv39fJr5OnTrxrtWkSRNuOzMzkxkYGLABAwZwZZGRkQwAu379OmOMsfnz57O2bdvyzvvu3TsGgD1//lzueRljrH79+mz69OncNgB29OhROa8in6urK1uzZg237eDgwFasWKGw/pw5c5i7u7vcfdOnT2d6enoKj719+zYDwL58+cIYYyw4OJgBYHFxcTnG+PHjRwaAPXr0SO7+nN7T6v79XRRU1kfu5cuX+Pz5M6pUqYLy5cur6rQEsgMdiqJ/nKR+/YBbt75vHz0KpKQA+vpFGwchpBi4elW2JU4SY8C7d+J6LVqo/PLe3t7YsGEDr0zyd462tjb27NmDWrVqwcHBAStWrJA5R8OGDXnLR3p5eWHZsmXIysrCo0ePkJWVhapVq/KOSUtLg5nErRBtbW3UqlUr13gl62hoaMDMzAxubm5cWXZLYfYtxwcPHiA4OBiGhoYy53r16hUXl/S1bWxsuHMokpSUhLlz5+L06dOIjIxEZmYmUlNTVdIiB0BmWc67d+9i7ty5ePDgAeLi4rgWtbdv36JGjRoKz/PixQvMnj0bN2/exKdPn3jH1axZUyWxlib5SuRu3LiBTZs2ISoqCm5ubpg2bRoSExPRo0cPhIaGAgCEQiHGjRsn98NDlCN9a7Uo+sdJ6tkTmDwZyG7VTk4GTpwAevcu2jgIIcWA9BdSQevlk4GBAapUqZJjnZCQEADA58+f8fnzZxgYGOT5/ElJSdDQ0MDdu3ehITVwQzK50tPTy9Na4tIT5AsEAl5Z9jmyk5WkpCR07NiR19csm43El7+88+Z263Hq1Km4cOECli5diipVqkBPTw/du3dHenp6rs8jL54+fYpK39aPTE5Oho+PD3x8fLBnzx5YWFjg7du38PHxyfV6HTt2hIODAzZv3gxbW1uIRCLUrFlTZXGWNnlO5G7evIkWLVog41tP93PnzuHixYvQ09PDvXv3uHpZWVlYvXo1atasiWHDhqk+4jJI3S1y1tZA69bA+fPfy/bsoUSOkDIpr39JFvVfnN+8evUKkydPxubNm3HgwAEMGjQIFy9ehFD4vUv4zZs3ecfcuHEDzs7O0NDQQO3atZGVlYWYmBg0bdq0qMNHnTp1cPjwYTg6OkJTU/mbZlpaWsjKyuKVXbt2DYMHD0aXLl0AiJPG8PDwgoTLefbsGQIDAzFz5kxuOzY2FosWLYK9vT0A4M6dO7xjtLW1AYAXZ2xsLJ4/f47Nmzdzr/8///yjkhhLqzwPdli6dCnS09N566qGhobi+vXrAMR/qWT/tcIYw86dO5UKaN26dXB0dISuri48PT1xS/KenhwBAQFwcXGBrq4u3NzccObMGZk6T58+xQ8//ABjY2MYGBigfv36KmtKLgrqbpEDxLdXJQUGArGxRR8HIUTNmjYFKlQQD2uXRyAA7O3F9QpBWloaoqKieI/sEZ1ZWVno378/fHx8MGTIEGzfvh0PHz7EsmXLeOd4+/Yt/P398fz5c+zbtw9r1qzBxIkTAQBVq1ZFv379MHDgQBw5cgRhYWG4desWFi5ciNOnTxfKc5I0duxYfP78GX369MHt27fx6tUrnDt3DkOGDJFJzHLi6OiIoKAgREVFIS4uDgDg7OyMI0eO4P79+3jw4AH69u2r1ACCzMxMREVF4cOHD3j06BHWrFmD5s2bw8PDAz/99BMAoGLFitDW1saaNWvw+vVrnDhxAvPnz+edx8HBAQKBAKdOncLHjx+RlJQEU1NTmJmZYdOmTXj58iX+/vtv+Pv75zvGsiTPidzNmzchEAjg6uqKtWvXomPHjty+vn37Ii4uDp8/f0bfb8McHz9+nO9gDhw4AH9/f8yZMwf37t2Du7s7fHx8FN73DwkJQZ8+fTBs2DCEhoaic+fO6Ny5M+/ar169QpMmTeDi4oJLly7h4cOH+PXXX6Grq5vv+NRF3S1yANC5MyD5kmVmAgEBRR8HIUTNNDSAb6MLZZK57O2VKwttPrnAwEDY2NjwHk2aNAEA/P7773jz5g3+97//ARDfity0aRNmzZqFBw8ecOcYOHAgUlNT0aBBA4wdOxYTJ07EyJEjuf3bt2/HwIEDMWXKFFSrVg2dO3fG7du3UbFixUJ5TpJsbW1x7do1ZGVloW3btnBzc8OkSZNgYmLCa1XMzbJly3DhwgXY29ujdu3aAIDly5fD1NQUjRo1QseOHeHj44M6derkO8Z///0XNjY2qFixIlq0aIGDBw9i5syZuHr1KtegY2FhgR07diAgIAA1atTAokWLsHTpUt557Ozs8Ntvv2HGjBmwsrLCuHHjIBQKsX//fty9exc1a9bE5MmTsWTJknzHWKbkdVSEjo4OEwqF7NSpU4wxxuLi4phAIGBCoZBduHCBq3f+/HkmEAiYhoZGvkdeNGjQgI0dO5bbzsrKYra2tmzhwoVy6/fs2ZN16NCBV+bp6cl+/PFHbrtXr16sfwGHWap71IuVFX9Q2NmzagmD9ezJj0Nq0BQhpAQo8KjVbIcPy45etbcXlxdjzZs3ZxMnTlR3GESFyvqo1Tyn99mdDLMnXjQxMeH26UsMX8z+P8vnopzp6em4e/cuWrduzZUJhUK0bt2au30r7fr167z6AODj48PVF4lEOH36NKpWrQofHx9YWlrC09OzUJYtKSwikeyqDtbW6olFek65f/4B3rxRTyyEEDXr2hUIDweCg8VLvgQHi9fx69pV3ZERUqbkuyfl2bNn8fLlS4VlkhMm5senT5+QlZXFm7QREA/NfvbsmdxjoqKi5NaP+rYUQkxMDJKSkrBo0SIsWLAAixcvRmBgILp27Yrg4GA0b95c7nnT0tJ4a8YlJiYq9ZxUIT7++2jRbBYWagkF7doBpqbAt+4WAID9+4Hp09UTDyFEzTQ0CmWKEUJI3uU7kfvjjz+4/2cPm5YsK06yO3F26tQJkydPBgB4eHggJCQEGzduVJjILVy4EL/99luRxZkTiVVZOEW1qoM0bW3xpO2bN38v27OHEjlCSMkhudQWIaVBvpfoYhKjVhU9lGFubg4NDQ1uPbxs0dHRsFZwL9Ha2jrH+ubm5tDU1JSZeLB69eo5jlqdOXMmEhISuMe7d++UeUoqIZ3IGRjwBx0UNenRq48eiR+EEEIIKXp5bpFr1qxZniY/VJa2tjbq1q2LoKAgbtFhkUiEoKAgjBs3Tu4xXl5eCAoKwqRJk7iyCxcuwMvLiztn/fr18fz5c95x//33HxwcHBTGoqOjAx0dnYI9IRWRTuTMzdUTR7bsmQckJ3bfuxdYuFB9MRFC8k/ZP7oJKW7K+ns5z4lcUTRH+/v7Y9CgQahXrx4aNGiAlStXIjk5GUOGDAEgHjJuZ2eHhd+yhokTJ6J58+ZYtmwZOnTogP379+POnTvYtGkTd86ffvoJvXr1QrNmzeDt7Y3AwECcPHmyxDSvF7dETigE+vQBJEeD790L/P67eB8hpHjLXhEgJSUFenp6ao6GkIJLSUkBILvaRVmhsrVWVaFXr174+PEjZs+ejaioKHh4eCAwMJAb0PD27VvePDqNGjXC3r17MWvWLPz8889wdnbGsWPHeGuxdenSBRs3bsTChQsxYcIEVKtWDYcPH+bmHSruilsiB4hvr0omcm/fAiEhQAl5SQkp0zQ0NGBiYsLNz6mvr1+od1sIKSyMMaSkpCAmJgYmJiYyS6qVFQJW1tsk8yAxMRHGxsZISEhAuXLlivTa06bxk6Z+/YC//irSEGQwBtSsCTx58r1s1ChAah1rQkgxxRhDVFQU4uPj1R0KIQVmYmICa2truX+QqPP3d1EpVi1yRFZxbJETCMQJ5S+/fC87eFA82fu3pfMIIcWYQCCAjY0NLC0tufWzCSmJtLS0ymxLXDZK5Iq54pjIAeJ+cpKJ3OfPwPnzgJ+f+mIihOSPhoZGmf8lSEhJR93Ti7nimshVqgQ0asQv27NHPbEQQgghZVWeErmHDx/i4cOHSE1NLex4iJTYWP52cUnkANk55Y4fB5KS1BMLIYQQUhblKZHz8PBAnTp1EBoaKj5IKISmpiZCQkIKNThSfFvkAKBHD/EKPdlSU4EStIwtIYQQUuLl+dYqYwyZmZm8bVK4MjP565oCxSuRs7AAfHz4ZXv3qicWQgghpCzK02AHU1NTxMfH4+eff0abNm248m3btuHixYsKj5s9e3bBIyzD4uLEU31IKk6JHAD07QucOfN9+/x5ICYGsLRUX0yEEEJIWZGneeRatmyJS5cucXO0ZB+S2ySSWVlZKghR/dQ1D83Tp4DUMrFITweK0+TVSUmAlRXwbWJtAMDatcDYseqLiRBCCAHKxjxyebq1unjxYlhYWIAxBsYYBAIBBAIBty3vQQpOun9cuXLFK4kDAEND4NvSuBwavUoIIYQUjTzdWq1fvz5evnyJW7duISIiAoMHD4ZAIOCWxSKFozgPdJDUty+/b9z168Dr14CTk/piIoQQQsqCPE8IbGRkhFatWgEQ930TCATo2rUr6tSpU2jBlXUlJZFr2xYwM+NPlbJvH3/CYEIIIYSonlITAoeHhyMsLIySuEImPYecmZl64siNlhbQsye/bM8e2YEahBBCCFEtpVd2yMzMxJIlS1CnTh0YGhrC0NAQderUwdKlS3nTlBDlSa9nbWqqljDyRHpy4KdPgfv31RIKIYQQUmYotdZqRkYG2rRpg6tXrwL4Por1wYMHePDgAc6cOYNz585Bq7j1zC9hpBM5ExN1RJE3jRoBjo5AePj3st27gdq11RURIYQQUvop1SK3fPlyXLlyRWaEavb25cuXsXLlSlXFWGaVpEROIBAPepD0119ARoZ64iGEEELKAqUSuX379gEAHBwccPLkSURHRyMmJgYnTpyAo6MjGGPYQ3NQFFhJSuQAYNAg/vbHj0BgoHpiIYQQQsoCpRK5Fy9eQCAQYPHixejQoQMsLCxgbm4OPz8/LFq0iKtDCiYhgb9d3BO5qlUBLy9+2Y4dagmFEEIIKROUSuRyWtEhr6s+kNxJt8gZG6sljHwZPJi/ffKk7OhbQgghhKiGUomcs7MzGGOYNm0azp49i9jYWMTGxuLs2bOYMWMGBAIBTRSsAiXt1iognoZER+f7dkaGeE45QgghhKieUolc7969AQDv3r2Dn58fLC0tYWlpCT8/P7x58wYA0Fe65zvJt5KYyJmYyC7ZtXOnOiIhhBBCSj+lEjl/f380bdpU4RqrTZs2xaRJk1QZZ5mTlgZ8/covKwmJHCB7e/XOHeDff9USCiGEEFKqKZXIaWlp4cKFC1i4cCFq1aoFXV1d6OrqolatWli0aBHOnz9Pc8gVkPRAB6DkJHJt2gA2NvwyapUjhBBCVE/AGC2klJvExEQYGxsjISEB5cqVK5Jr/vcfUK0av+zrV37/s+Js+nTgzz+/b1tbA+/eAZpKTUFNCCGE5J86fn8XNaWX6CKFS7p/nK5uyUniANk55aKigAsX1BMLIYQQUlpRIldMlcSBDpJq1ADq1+eX0ZxyhBBCiGpRIldMlfREDpBtlTt+HIiLU08shBBCSGlEiVwxVdJWdZCnd29AW/v7dloacOCA+uIhhBBCShtK5IqpkriqgzQzM6BjR34ZjV4lhBBCVIcSuWKqNNxaBWTnlLtxA3j2TC2hEEIIIaVOgSaD+PLlC8LDwxEfHw95s5g0a9asIKcv00pLIufjA1haAjEx38t27AAWLVJbSIQQQkipoVQiFx8fjwkTJmD//v3IysqSW0cgECAzM7NAwZVlpSWR09IC+vcHli//XrZjBzB/vngfIYQQQpSn1K3VUaNG4a+//kJmZqbcZbokl+siyikNgx2yDRvG346OBk6fVk8shBBCSGmiVIvcmTNnIBAIoKWlhZYtW8LMzAyaNGW/SpWGwQ7ZatQAvLyA69e/l23dCnTurLaQCCGEkFJBqewrO2lbtWoVfvzxR5UGRMRKy63VbMOH8xO5M2eAiAjAzk59MRFCCCElnVK3Vjt06AAAMC7JzUTFXGlL5Hr2BAwNv2+LRLTSAyGEEFJQSiVyS5cuRaVKlTB16lScPHkSCdIdukiBlaZbq4A4ievdm1+2bZs4oSOEEEKIcpRK5GxtbREWFoYPHz6gc+fOKF++PDQ0NHgP6jOnvKwsIDmZX1bSEzlAdtDD69fApUtqCYUQQggpFZRK5LJHpAoEgkIZtbpu3To4OjpCV1cXnp6euHXrVo71AwIC4OLiAl1dXbi5ueHMmTO8/YMHD4ZAIOA9fH19lY6vsEkncQD/tmRJ5ekJuLryy7ZuVU8shBBCSGmgVCJXsWJF7uHg4CD3UbFiRaUCOnDgAPz9/TFnzhzcu3cP7u7u8PHxQYzkjLISQkJC0KdPHwwbNgyhoaHo3LkzOnfujMePH/Pq+fr6IjIyknvs27dPqfiKwpcvsmVGRkUfh6oJBOJBD5IOHwY+f1ZPPIQQQkhJJ2DFbMI3T09P1K9fH2vXrgUAiEQi2NvbY/z48ZgxY4ZM/V69eiE5ORmnTp3iyho2bAgPDw9s3LgRgLhFLj4+HseOHVMqpsTERBgbGyMhIQHlypVT6hz58fw54OLCL0tL4y9AX1J9+gTY2gIZGd/LVq8Gxo9XX0yEEEJKp6L+/a0OxWqt1fT0dNy9exetW7fmyoRCIVq3bo3rknNXSLh+/TqvPgD4+PjI1L906RIsLS1RrVo1jB49GrGxsQrjSEtLQ2JiIu9RlKRb5LS1S0cSBwDm5kCXLvyyLVuA4vXnBCGEEFIyKJ3IZWZmYsmSJahTpw4MDQ1haGiIOnXqYOnSpUovzfXp0ydkZWXBysqKV25lZYWoqCi5x0RFReVa39fXF7t27UJQUBAWL16My5cvo127dgqXF1u4cCGMjY25h729vVLPR1nSiVxpuK0qSfr26sOHwN276omFEEIIKcmUGlqakZGBtm3b4sqVKwC+D3548OABHjx4gDNnzuDcuXPQKiaLafaWmPfCzc0NtWrVQuXKlXHp0iW0atVKpv7MmTPh7+/PbScmJhZpMpeUxN8ubYlcq1aAgwPw5s33si1bgHr11BcTIYQQUhIp1SK3fPlyXL58WWZ0avb25cuXsXLlynyf19zcHBoaGoiOjuaVR0dHw9raWu4x1tbW+aoPAE5OTjA3N8fLly/l7tfR0UG5cuV4j6Ik3SJXGkasShIKgaFD+WX79skfrUsIIYQQxZRK5LJHfDo4OODkyZOIjo5GTEwMTpw4AUdHRzDGsGfPnnyfV1tbG3Xr1kVQUBBXJhKJEBQUBC8vL7nHeHl58eoDwIULFxTWB4D3798jNjYWNjY2+Y6xKJT2W6sAMHiweBRrtsREICBAbeEQQgghJZJSidyLFy8gEAiwePFidOjQARYWFjA3N4efnx8WLVrE1VGGv78/Nm/ejJ07d+Lp06cYPXo0kpOTMWTIEADAwIEDMXPmTK7+xIkTERgYiGXLluHZs2eYO3cu7ty5g3HjxgEAkpKS8NNPP+HGjRsIDw9HUFAQOnXqhCpVqsDHx0epGAtbab+1CgAVKwLSL/+3QcaEEEIIySOl+sgJJJtSpEhOFqyMXr164ePHj5g9ezaioqLg4eGBwMBAbkDD27dvIRR+zz8bNWqEvXv3YtasWfj555/h7OyMY8eOoWbNmgAADQ0NPHz4EDt37kR8fDxsbW3Rtm1bzJ8/Hzo6OkrFWNhK+63VbCNHAoGB37dv3gRCQ4HatdUXEyGEEFKSKDWPXO3atfHgwQNUrFgRGzZsQIMGDQAAt27dwpgxY/D27VvUqlULoaGhKg9YHYp6HpopU4Dly79vDxpUOheYz8wEHB2BiIjvZSNGAJs2qS0kQgghpQjNI6dA9ijQd+/ewc/PD5aWlrC0tISfnx/efBuK2LdvX9VFWcaUhVurAKCpKU7cJO3ZAyQkqCceQgghpKRRKpHz9/dH06ZNFa6v2rRpU0yaNEmVcZYpZeXWKiCeU05D4/t2Sgqwe7f64iGEEEJKEqUSOS0tLVy4cAELFy5ErVq1oKurC11dXdSqVQuLFi3C+fPni80cciVRWRi1ms3ODujUiV+2YQOt9EAIIYTkhVKDHQDxVCHTp0/H9OnTVRkPQdlK5ABg9GjgyJHv20+eAFevAs2aqS8mQgghpCQoVmutEjHpPnKl+dYqALRsCTg788s2bFBPLIQQQkhJkqcWuUqVKkEoFCIgIAB16tSBk5NTrscIBAK8evWqwAGWRWWtRU4oBEaNEo/WzXb4MBAdDUgto0sIIYQQCXlK5N68eQOBQICvX78CAMLDw3OdS07ZeeRI2UvkAPFKD7/8Anx7iyEjA9i2DZCY+5kQQgghUvJ8a1V6ujl5I1al114lyilrt1YBoHx5oFcvftn//gdkZaknHkIIIaQkyFMiJxKJIBKJ0KhRI952To8s+g2sFMbKzjxy0kaP5m+/eQOcPKmeWAghhJCSQKnBDleuXMGVK1fwRfoeICmw5GTZqTfKSiLXoAFQty6/bNUq9cRCCCGElARKJXItWrSAt7c3Hj16JLPv2rVr0NDQgKam0jOblGnSrXFA2bi1CgACATBxIr/s0iXg4UO1hEMIIYQUeyqffiQrK4v6yhWAvEbOstIiBwA9e8qOVKVWOUIIIUS+PDebvX37FuHh4byy0NBQZGZmctsikQh//fWX+MTUIqcU6UROUxPQ0VFPLOqgoyPuKzd37veyPXuAxYsBc3O1hUUIIYQUS3nOtrZv34558+Zx24wxTJgwQW5dgUAABweHgkdXBskbsVrWZnL58Ufg99/FU5AAQFoasGkT8PPP6o2LEEIIKW7ydWtV+pZpTlOQjJYegkjypCzOISfN2hro3Ztftn7998SOEEIIIWJ5bpHz8PDAoEGDAAA7d+6EQCCAr68vLC0tuTpCoRCmpqbw9vZGhw4dVB9tGUCJnNjEicDu3d+3IyLEqz1IJ3iEEEJIWSZgSoxKEAqFEAgEuHr1Kje3XGmWmJgIY2NjJCQkoFy5coV6rS1bgBEjvm83aADcvFmolyy2mjQBrl37vt2wIXD9uvriIYQQUrIU5e9vdVFq1GpYWBhev36NevXqqTqeMo9a5L6Tnorkxg3g1i31xEIIIYQUR0oNLc0eyPDhwwfcu3cP8fHxEIlEMvUGDhxYsOjKoLK4PJcinTsDFSoA799/L1uxAti3T20hEUIIIcWKUolcVlYWfvzxR+zYsUPhfHECgYASOSWkpPC3DQzUE0dxoKUFjBsHzJjxvSwgAFi4EHB0VFtYhBBCSLGh1K3VlStXYtu2bRCJRDmOXCX5J53I6eurJ47iYuRIfjKblUUTBBNCCCHZlErk9u7dC4FAAE9PTwDfW998fHwAAI0aNcLs2bNVF2UZQokcn6kpMHw4v2zzZiAuTj3xEEIIIcWJUoncf//9BwCYPn06VzZy5EicPXsWEydOxI0bN1CrVi3VRFjGJCfzt8vyrdVskyYBQol3anKyeIJgQgghpKxTKpHL+DYzq5mZGbcU15dvwy3bt28PkUiEuZJrLJE8oxY5WY6OQI8e/LJVq4D0dLWEQwghhBQbSiVy5cuXBwB8/foV5t8WwNywYQOePHmCnTt3AgBevnypohDLFkrk5Js6lb8dGUmjVwkhhBClErlKlSoBAOLi4uDp6QnGGE6ePAk3Nzfs27cPAoEAzs7OKg20rKBETr569YDmzfllS5cCNKaGEEJIWaZUItewYUNoa2vjxYsX+Omnn6ClpSUzWnX+/PkqDbSsoEROMelWucePgfPn1RNLsZaVBVy6JG6yvHRJvE0IIaRUUmqJLmm3b9/Gxo0bERERAQcHBwwfPhz169dXRXzFQlEu8VGtGvBtLAkA4NAhoFu3Qr1kiSESAa6uwLNn38tatQIuXlRfTMXOkSPiJTEkZ1GuUEHcqbBrV/XFRQghalAWlujK94TAqampCAgIAAC4urqibt26qF+/fqlK3NSJWuQUEwqBKVP4a9EGBQF37wJ166ovrmLjyBGge3fZ+80REeLyQ4comSOEkFIm37dW9fT0MHz4cAwZMgTh4eGFEFLZRolczvr3B6ys+GULF6onlmIlK0vcEievgT27bNIkus1KCCGlTIEGO2hra6s0GEKJXG50dcX5iKQjR4Dnz9USTvFx9Sr/dqo0xoB378T1CCGElBpKJXL+/v5gjGHjxo0QiUSqjqnMEomAr1/5ZZTIyRo9GpDs6sAY8Oef6ounWIiMVG09QgghJUK++8gBQFRUFJycnBAYGIgqVarA19cXVlZWEAgEvHq0TFf+SLfGAbSygzzGxsDYsfxbqrt3A7/9Ju7XXybZ2Ki2HiGEkBJBqVGrQqFQJmmTJ6uU9McpqlEvMTGy/b+iowFLy0K7ZIkVEwM4OPBbMCdNAlasUFtI6pWVJV4CIyJCfj85gUCc5YaFARoaRR4eIYSoQ1kYtarUrVUAvHnj5D1I/slrkaNbq/JZWgLDhvHLNm0CPn1STzxqp6EhnmIEECdtkrK3V66kJI4QQkoZpW6tbt++XdVxEMhP5PT0ij6OkmLqVGDjxu8DMVNSgDVrxLdYy6SuXcVTjMibR27lSpp6hBBCSiGVTAisauvWrcOSJUsQFRUFd3d3rFmzBg0aNFBYPyAgAL/++ivCw8Ph7OyMxYsXo3379nLrjho1Cv/73/+wYsUKTJIe/qhAUTXN3rkDSE7Hp6MjO/iB8A0cKO4fl83UFHjzBjAyUl9MapeVJR6dGhkp7hPXtCm1xBFCyiS6taqAk5MTKleujHv37snse/nyJYYOHYph0ve98ujAgQPw9/fHnDlzcO/ePbi7u8PHxwcxMTFy64eEhKBPnz4YNmwYQkND0blzZ3Tu3BmPHz+WqXv06FHcuHEDtra2SsVW2KRb5GigQ+6mT+dvx8UB//ufemIpLphQiKxmTZHVqyfQogUlcYQQUooVaLDD1atX0ahRI96+a9euoWnTphAIBEoNdvD09ET9+vWxdu1aAIBIJIK9vT3Gjx+PGTNmyNTv1asXkpOTcerUKa6sYcOG8PDwwMaNG7myiIgIeHp64ty5c+jQoQMmTZpU7Frkzp4FJBsSK1QQT/1FctapE3DixPdtKyvg9euS279QxESISorC67jXeJvwFtFJ0YhKikJ0cjSik6MR/zUeX9K+4Ev6F3xJ+4LkjGSImIh7SNISakFfS5/3MNA2gJmeGSwMLGCh/+1hYAFLA0tUKFcBDsYOMNY1VtOzJ4QQ1SkLLXJK9ZHLJm/k6ps3b5Q+X3p6Ou7evYuZM2dyZUKhEK1bt8b169flHnP9+nX4+/vzynx8fHDs2DFuWyQSYcCAAfjpp5/g6uqaaxxpaWlIS0vjthMTE/P5TJRDkwEr55df+IlcdLR44EMe83S1yRRl4r/Y//Aw+iEeRj/E45jHePn5JcLiw/A1UzX31DNEGUhIS0BCWkK+jjPRNYGDsQMcTBzgYOyAqmZV4WLuAhdzF9gZ2eVp1DohhJDCl+dEbtWqVViVPSrum+7du0NHR4fbFolE+PDhAwDAwsIi38F8+vQJWVlZsJKag8PKygrPJFdKlxAVFSW3flRUFLe9ePFiaGpqYsKECXmKY+HChfhNDT3mKZFTToMGgK8vEBj4vWzxYuDHH4vXYJF3Ce8Q8i4E199fR8i7EDyMfoi0rLTcD1SD+K/xiP8ajwfRD2T2GWoboppZNbiYu8DN0g21bWrDw9oDlgY0Tw4hhBS1PCdy8fHxCA8P5/4SZ4zxkqVs2Xdqvb29VRRiwdy9exerVq3CvXv38tyKMHPmTF4rX2JiIuzt7QsrRA4lcsqbPZufyEVFAVu2AOPHqy+mj8kfcfH1RZx7dQ5BYUF4n5jDElolSFJ6Eu5G3sXdyLu8chtDG3FSZ+WB+nb10bBCQ1gbWqspSkIIKRvyfWuVMcZL5iQJBAKUL18e3t7eMq13eWFubg4NDQ1ER0fzyqOjo2FtLf8XgrW1dY71r169ipiYGFSsWJHbn5WVhSlTpmDlypUIDw+XOaeOjg6vpbGo0GAH5Xl5AW3aABcufC9btAgYMUK8PmtRYIzhYfRDHH56GGdenMG9yHtgUH5QuI6GDhxNHGFrZAsrQytYG1jDytAK5fXKw0jbCEY6RjDSNoKBtgE0hZoQCoS8B2MMqZmpSMlI4T2+pH3Bx5SP+Jj8Ufzvt/9n98NTVmRSJCJfROLMizNcmaOJI7wqeMGrghcaVmgID2sPaGloKX0NQgghfCof7FBQnp6eaNCgAdasWQNAfLu2YsWKGDdunMLBDikpKTh58iRX1qhRI9SqVQsbN25EbGwsIqXWl/Tx8cGAAQMwZMgQVKtWLdeYiqqz5IIFwK+/ft/u1AmQ6OpHcvHPP+KZNiStXy9em7WwMMbwIPoBAv4NQMCTALz4/CLf57AzskMtq1pws3RDdYvqqGxaGU6mTrAxsoFQoPSc3Ur5mvkV7xLe4U3CG7yJf4M3CW/wOu41nsc+x7NPz5CUnlSg8+tq6qK+bX00d2gO70re8KrgBT2tYnT/mxBSqtBgBwXmzJkDALxWLlXx9/fHoEGDUK9ePTRo0AArV65EcnIyhgwZAgAYOHAg7OzssPDbQpsTJ05E8+bNsWzZMnTo0AH79+/HnTt3sGnTJgCAmZkZzMzMeNfQ0tKCtbV1npK4okS3VgumSRPA2xsIDv5etnAhMHSoeE4+VfqU8gl/PfwLW+5twb8f/83zcaa6pvCy90KjCo3gZe8FD2sPlNcrr9rgCkBXUxfOZs5wNnOW2ccYQ8SXCDz79AzPPj3D45jHuB91Hw+jHyI1MzVP5/+a+RVX317F1bdXseDqAmhraMOrghe8Hb3RwrEFGlZoCB3Nom8NJ4SQkqpAiVxh6NWrFz5+/IjZs2cjKioKHh4eCAwM5AY0vH37FkLh91aKRo0aYe/evZg1axZ+/vlnODs749ixY6hZs2ahxVhYKJEruDlz+Incu3fAzp3AyJEFPzdjDEFhQdh8bzOOPTuG9Kz0XI8x0DKAdyVvtHVqi1ZOreBi7lLkrWyqIhAIUKFcBVQoVwGtnVpz5VmiLLz4/AL3o+4jNDIUdyLv4FbErTy13qVnpePym8u4/OYycFmcSDat2BS+VXzRrko7uJi70AhZQgjJgdIrO2zbtg3/+9//8PLlS8THx8ueWCBAZmZmQeMrFoqqaXbkSGDz5u/b48cDq1cX2uVKrebNgStXvm87OAD//Qdoayt3vrTMNOx7vA/Lri/D4xjZiaalORg7oFv1bvCr6odG9o3KZAtTligL/378F9ffXceNiBu4/u46nsc+z/d5KhpXhG9lX/hW8UUrp1Yop1M6b40QQgpHWbi1qlQi9+uvv+KPP/4AIDvggTuxkhMCF0dF9Ubo3x/Ys+f79owZ4luDJH/+/hto1Ypftm4dMGZM/s4TlxqHjXc2YvWt1YhKkh2hLcnRxBE9avRAjxo9UM+2HrUiyfE59TOuv7uOK2+uIDg8GHcj78pMYJwTTaEmGts3hm8VX7R3bg83Szd6nQkhOaJETgEbGxtupKi+vj5MTU2hqSl7lzYsLKzgERYDRfVG6NKFP7hh3jz+4AeSN4wBzZqJBz9ks7EBXr7M2+3qL2lfsPLGSiy9vhSJaYong9bR0EH3Gt0xvM5wNHNoVmJvmapLwtcEXH17FcFhwQgOD8b9qPv5GuVbyaQSOlXrhE4undCkYhNoCgs0vzkhpBSiRE4BAwMDfP36FRMmTMDy5ctL/V/FRfVG8PEBzp//vr10KTBlSqFdrlS7ckV8i1XSkiXA1KmKj0nNSMW62+uw6J9FiE2NVVjPxdwFY+uPRT+3fjDVM1VRxCQuNQ5/h/2Nc6/O4ezLs/mad6+8Xnl0cO6ATtU6waeKDwy1DQsxUkJISUGJnALe3t64cuUKjh8/Dj8/v8KIq1gpqjdC06b8VqTCnjqjtJNOjM3MxGuwSv8IRUyEXQ924eegnxGZxJ+qRpK3ozemeE1BO+d21PpWyBhjePLxCc6+PIvAl4G4+vZqngaXAOKW0lZOrdDFpQu6uHSBmb5Z7gcRQkolSuQUuHPnDpo3b4569erh8OHDMDc3L4zYio2ieiPUrQvcu/d9e8cOYNCgQrtcqXf7tnj5Lklz54pHtma78+EOxp8djxvvbyg8T0/XnpjWaBrq2tYtnEBJrpLSkxAcFozAl4E49eIU3ia8zdNxGgINtHJqhR41elBSR0gZRImcAi1btsTz588RFRUFbW1tuLi4wNSUf4tJIBAgKChIZYGqU1G9EapXBySXlA0IALp3L7TLlQnS/Q6NjICwMECk+xEzg2ZiW+g2hf2yOlXrhHne81DLqlbRBEvyJHsS5uPPjuP48+MIjQrN03HZSV3PGj3R2aUzJXWElAGUyCmQvbIDwF+yK1t2GY1azZ+KFcXznmU7fRpo377QLlcmPH4M1KolHgAhxtBh5l5cN5mAz6mf5R7TxqkNFrRcgAZ2DeTuJ8XLm/g3OPH8BI4/P47Lby4jU5T7tEeaQk20qiRuqaOkjpDSixI5BSQn5FV4Ykrk8s3cHIiV6GMfHAy0aFFolysz+vUD9u4FYBgJ+I0CXE7Iredc3hmrfFehnXO7og2QqExcahzOvjyLI0+P4MyLM3lacUJTqIm2lduin1s/dKrWCQbatMgxIaUFJXIKvHnzJk/1HBwc8h1QcVRUbwR9fSBV4vfOzZuyfbxI/r14wVCt519gPhMBvTiZ/QZaBvi12a+Y1HBSmZy8t7RKSk/C6f9O4+CTgzjz4gy+Zn7N9RgDLQN0qd4F/dz6obVTa5rShJASjhI5AqBo3giMAdINnQ8fAm5uhXK5MiP+azxGnByBQ08Oyd3f07UnVvisgK2RbRFHRopSUnoSTv13CgFPAvKc1FkaWKK3a2/0q9UP9W3rl/pplggpjSiRy0VERAQOHjyIp0+fIiUlBdu2bcONG+LRfw0bNoS2smsiFTNF8Ub4+hXQ0+OXvXgBVKlSKJcrE25H3EavQ70QFi9nYuokS9SP2YBbO7sWfWBErZRJ6pzLO6OfWz/0q9UPVcrTh5KQkoISuRxs3LgRkydPRnp6Om9wQ+XKlREeHo59+/ahZ8+eqo5XLYrijRAfD0gN/MX794CdXaFcrlRjjGHljZWYfnE6MkQZshUe9gXOrgZSzXDlinj+PlI2fUn7gqPPjmLPoz24+PpinpYMa2zfGEM8hqCHaw9a+5WQYq4sJHJKzWoaGBiIMWPGIC0tTWat1S5duoAxhsOHD6skwLLiq5xGAV3doo+j2MrKAi5dAvbtE/+rYCBNYloiOh/oDP/z/jJJnKlueRidPgoc2QOkikcpTp0qOaKVlDVGOkYY6D4Q5/qfQ4R/BFb6rEQ923o5HnPt3TUMPzkc1kutMeDoAAS9DsrXmrGEEKJKSiVyixcvBiBec3WM1Erkbt86dT148KCAoZUtqXIG11Ei982RI4CjI+DtDfTtK/7X0VFcLuHV51douKUhTjyXHZXapGITPBz9AH8M7Mwrv3ULOHiw8EInJYe1oTUmNpyI2yNu49nYZ5jdbDacTJ0U1k/NTMVfD/9C692tUWlVJcwOno1Xn18VYcSEEKLkrVVjY2MkJSVh165dcHR0RNOmTblbq0FBQWjTpg0MDAzw5cuXwoi5yBVF0+zTp0CNGvyyzExAQ6NQLldyHDkinhVZ+m2a3fH80CGga1cEhwWje0B3mbnhBBBgZpOZ+M37N2gKNZGRAbi6ivsfZqtUSfz669CAVSKFMYabETex5+Ee7P93Pz6lfMr1mKYVm2Kwx2D0qNEDRjpGRRAlIUQRurWqQEaG+JaVmZnsJJqfPom/6GgwbP5I31rV0qIkDllZwMSJ8u99ZpdNmoT/3VyPtn+1lUnizPXNEdg/EL+3+p2bRkJLC1i0iH+qsDBg3brCeAKkpBMIBGhYoSHWtF+DCP8IHO11FJ2qdcpxWpKrb69i2IlhsF5mjUHHBuHKmyv0fUgIKTRKJXKVK1cGAKxfvx7p6d8Xsk5JScHq1asBAFWrVlVBeGWHdCJHt1UBXL0qHvGhCGPAu3fYt2GszGz+bpZuuD3iNtpWbitzWJcuQOPG/LIFC/iTMRMiTVtDG51dOuNY72OI8I/A8rbL4WapeH6glIwU7HqwC813NEf1ddWxNGQpPiZ/LMKICSFlgVKJXLdu3cAYw+nTp9FeYg0pGxsb3LhxAwKBAN1pkdB8ke4jR4kcgMjIPFWzSeJv/1DtB1wbeg2OJo5y6wsEwJIl/LK4OGDOHCViJGWSpYElJntNxoNRD3Bv5D1MaDABZnqKl/l6HvscP134CXbL7dAzoCfOvzpPAyQIISqhVCL3008/oWbNmmCMIS0tjZso88uXL2CMwc3NDZMnT1ZpoKUdtcjJYWOTp2qRht//P7PJTBztdTTXvkleXoD07DgbNgCPHuU3SFKWCQQC1LapjVXtViHCPwKHex5Gx6odoSGQ3y8iQ5SBgCcB8PnLB5VXV8aCKwsQkRhRxFETQkoTpRI5AwMD/PPPPxgzZgxMTU3BGANjDKamphgzZgwuX74MPenZbUmOpBM5evkgnuCtQoXvAxukiAC8LQdcdRCvl7mr8y780eoPCAV5e1v/+Sc/YRaJgEmTaDoSohwdTR10rd4VJ/qcQIR/BP5s/SeqminuYhIeH45fg39FxZUV0XFfR5x4fkKmiwAhhOSmwEt0Mca4AQ7m5ualchmbohj1smcP0L//9+1atQCawQXfR60CvAwr+6ZU957AOXd9HO55GL5VfPN9+jlzgHnzZC/ZpYuS8RIigTGGq2+vYvO9zTj05FCuq0jYGtliiMcQDKs9DJVMKxVRlISUXmVh1CqttZoHRfFG2LoVGD78+3aDBsDNm4VyqZLnyBFkTRgHjYjvfebelgMm+QKX6pjidN/T8LL3UurUKSlAtWr8MRWVKgFPntDtbaJacalx2PNoDzbf24yH0Q9zrd/aqTVG1R2FH6r9AC0NrSKIkJDSpywkckrdWh01ahQ0NDTQsGFDmX2NGjWChoYGRo8eXeDgyhK6tarYR5+mqD3DFC0GAX26AS0GAZUmAbc87XB1yFWlkzgA0NeXHfgQFgYsX16wmAmRZqpninENxuH+j/dxa/gtjKgzAobahgrrX3x9Ed0DuqPiyor49e9f8TbhbRFGSwgpKZRK5P7++28AwMiRI2X2jRgxAowxrg7JGxrsIN+nlE9otasVHsU+weVKwH434HIloJJZZVwbeg2ulq4FvkavXrLTkfzxBxBBfdBJIRAIBKhvVx+bOm5C5JRIbOm4BZ52ngrrRyVFYcHVBai0qhI67uuI0/+dRpZI/hJ1hJCyR6lE7v23+1D29vYy+ypUqMCrQ/KGph+RFZsSi9a7WuNRDH8oqZOpE4IHBcPBxEEl1xEIgNWr+WMqkpOBn35SyekJUchQ2xDD6gzDjeE38HDUQ4xvMB4muiZy64qYCKf+OwW/fX5wWu2E36/8jqikqKINmBBS7CiVyGlrawMA7ty5I7Pv9u3bAABNTcUznxNZ1CLHl5SeBN89vngQzR/x4WjiiOBBwbA3lv0joiDq1AGGDeOX7dsHUMMyKSpuVm5Y3W41Pvh/wO4uu9HYvrHCum8T3mJW8CzYr7BHz4Ce+Dvsb1o9gpAySqlErkaNGmCM4Y8//sDWrVsRFRWFqKgobN26FQsXLoRAIEAN6YVDSY6oj9x36Vnp6HawG+584P+hUNG4IoIHBaOiccVCue7vvwMmJvyysWMBicVLSGmTlQVcuiTO2i9dEm+rmZ6WHvrX6o9/hv6Dh6MeYmz9sTDSlj8vYqYoEwFPAtBqVyu4rHPB8uvLEZtCS5QQUpYolcj1/zZPRkpKCkaOHAk7OzvY2dlh5MiRSE5O5tUheUMtcmIiJsKwE8Nw/tV5Xrl9OXsEDwpWuFqDKlhaivvGSXr2jAY+lFpHjgCOjoC3N9C3r/hfR0dxeTHhZuWGte3X4sOUD9jccTPq2NRRWPe/2P8w5fwU2C23w8CjAxHyLoRa6QgpA5Qetdq2bVtuImDJBwC0bt2aRq3mE/WRE5t5cSb+evgXr8xMzwwXBlyAk6lToV9/5EigXj1+2bx5wJs3hX5pUpSy5yeU7ssbESEuL0bJHCDuSze8znDcHXkXt4bfwlCPodDTlN9sn5aVht0Pd6PxtsZw3+iO9bfXIzEtsYgjJoQUFaUSOaFQiFOnTmHJkiVwd3eHnp4e9PT04O7ujiVLluD06dMQCpU6dZlFt1aBlTdW4s+QP3ll+lr6ON33NKqZVyuSGDQ0gPXr+QMfUlPFKz6QUiIrC5g4Uf4SHtllkyYVi9us8tS3q4+tnbbiw5QPWO27GjUsFHdjeRTzCGPPjIXtMluMPDkSoZGhRRgpIaQo0ITAeVAUEwp268ZvBPjtN2D27EK5VLF05OkRdDvYjVemIdDAiT4n0N65fZHHM2aMeO1VSSdPAn5+RR4KUbVLl8S3UXMTHAy0aFHY0RQYYwz/vP0HG+9uxKEnh5CelXOnTk87T4yqNwq9XHtBT6sM/sVIyhSaEJgUmbJ8a/VB1AMMODpApnzLD1vUksQB4oEPFhb8sgkTZH9OpASKjMy9Tn7qqZlAIEBTh6bY03UP3k9+j8WtF+fYDeFmxE0MOT4Edsvt4H/OH88/PS/CaAkhqqZ0Irdt2zZ4enrCzMwMGhoaMg+afiR/yupgh5jkGPyw/wekZKTwyhe2WojBHoPVExQAU1Ng6VJ+WVgYsHCheuIhKmRjo9p6xYiFgQWmNZ6GF+Nf4Fz/c+ji0gUaAg25deO+xmHFjRVwWeeCVrta4dCTQ8jIyijiiAkhBaXUrdVff/0Vf3wb3qfocIFAgKxi2sckv4qiabZRI+D69e/bmzYBI0YUyqWKjfSsdLTe1RpX317llQ+rPQybO26GQLKjmhowBjRvDlyVCE9bG3j0CKhaVX1xkQLKyhKPTo2IkN9PTiAAKlQQZ+4a8pOgkiQiMQJb7m3B5nubEfEl5+VKrA2tMbz2cIyoO6LQpvkhpCiVhVurSiVyNjY2iI6OBgDo6+vD1NRUbgtcWFhYwSMsBorijVCnDhAq0Q951y5ggOzdxlKDMYYfT/2Izfc288ob2zdG0MAg6GjqqCkyvsePAQ8Pfr93b28gKIg/IIKUMNmjVgF+Mpf9Qz10COjatejjKkSZokyc+u8UNtzZIDO9jzShQIgOzh0wut5otK3cFhrCkp/QkrKpLCRySt1aTUxMhEAgwMSJE/Hlyxe8e/cOYWFhMg+Sd2Wtj9y62+tkkjj7cvY43PNwsUniAKBmTWDyZH5ZcDCwbZt64iEq0rWrOFmzs+OXV6hQKpM4ANAUaqKzS2ec638OL8a/wE+NfoKZnpncuiImwsn/TqL93vaosqYKFv2zCDHJMUUcMSEkL5RqkfP29saVK1dw/Phx+JWBYXxFkdFXqgSEh3/fLs0jJK+/u45mO5ohU5TJlelp6uHa0GuobVNbjZHJl5QEuLoCb99+LzMxAZ48KZHdqIikrCzxvfPISPEPs2nTUnE7Na++Zn7F4SeHseHOBlx7dy3HulpCLXSv0R2j6o1C04pN1d71gZC8oBY5BZYsWQJdXV0sWbIEnz59UnVMWLduHRwdHaGrqwtPT0/cunUrx/oBAQFwcXGBrq4u3NzccObMGd7+uXPnwsXFBQYGBjA1NUXr1q1x8+ZNlcddEGVlsENsSix6HerFS+IAYGfnncUyiQMAQ0Ng40Z+WXw8MH68WsIhqqShIZ5ipE8f8b9lKIkDAF1NXfSr1Q//DP0HD0Y9wOh6o2GobSi3boYoA/se70PzHc1Rc0NNrLm5BglfE4o4YkKINKVa5Fq2bInnz58jKioK2tracHFxgampKf/EAgGCgoLyHdCBAwcwcOBAbNy4EZ6enli5ciUCAgLw/PlzWFpaytQPCQlBs2bNsHDhQvj5+WHv3r1YvHgx7t27h5o1awIA9u7dC0tLSzg5OSE1NRUrVqxAQEAAXr58CQvpOSbkKIqM3tRUnBxku3oVaNKkUC6lNiImwg/7fsDpF6d55T83+Rm/t/pdTVHlXf/+wJ49/LIjR4AuXdQTDyGF4UvaF+x9tBcb7mzAg+gHOdbV19JH35p9MareKNS1rVtEERKSd2WhRU6pRE4oFHLN6owxmSb27DJlRq16enqifv36WLt2LQBAJBLB3t4e48ePx4wZM2Tq9+rVC8nJyTh16hRX1rBhQ3h4eGCjdDPKN9k/2IsXL6JVq1a5xlQUbwRdXSAt7fv27duyS0WVdEuuLcG0i9N4ZS0cW+DigIslojP1p09A9erif7PZ2IhvsZqYqC0sQgoFYww3I25iw50NOPD4ANKy0nKsX9+2PkbXG41eNXtBX0u/iKIkJGdlIZFTeh45ybVV5a23qoz09HTcvXsXrVu3/h6gUIjWrVvjuuTcHBKuX7/Oqw8APj4+Cuunp6dj06ZNMDY2hru7u9w6aWlpSExM5D0KE2P8JA4ofUt0XXt7DTODZvLKLA0ssbfr3hKRxAGAuTmwciW/LDISmD5dLeEQUqgEAgEaVmiInZ134sOUD1jWdhmcyzsrrH/7w20MPTEUdsvtMClwEp59elaE0RJSdimVyMkboSr9eP36db7P++nTJ2RlZcHKyopXbmVlhaioKLnHREVF5an+qVOnYGhoCF1dXaxYsQIXLlyAubm53HMuXLgQxsbG3MPe3j7fzyU/pJM4oHT1kfuU8gm9D/dGFvveQiuAAHu77oWNUckaLdC3L+Dryy/btAm4fFk98RBSFMrrlYe/lz+ejXuGiwMuolv1bgonGo7/Go9VN1eh+rrq8N7pjYP/Hsx12TBCiPKUWn7BwcFB1XEUOm9vb9y/fx+fPn3C5s2b0bNnT9y8eVNuv7uZM2fC39+f205MTCzUZE7esk+lJZFjjGHEyRF4n/ieVz67+Wy0csr9tnZxIxCIBz64ugLJyd/LR4wAHjwofS2phEgSCoRo5dQKrZxa4cOXD9h6bys23dsk8/nOdin8Ei6FX4KVgRWG1R6GkXVHwsGk5P3+IKQ4K9Baq7dv34a/vz/8/Pzg5+cHf39/3L59W+nzmZubQ0NDg5tsOFt0dDSsra3lHmNtbZ2n+gYGBqhSpQoaNmyIrVu3QlNTE1u3bpV7Th0dHZQrV473KEzSI1aB0pMQ7HywE8eeHeOVtazUEr82+1U9AamAgwPwbWETzosXwNy5agmHELWwNbLFr81/RdjEMBzvfRy+VXwhgPwpSaKTo/HHP3+g0qpK8Nvrh9P/nUaWqHSs/EOIuimdyM2cORMNGzbEqlWrcPbsWZw9exarVq1Cw4YN8csvvyh1Tm1tbdStW5c32lUkEiEoKAheXl5yj/Hy8pIZHXvhwgWF9SXPmybvnqYayEvkSkOLXHh8OCacncArs9C3wJ6ue0pMvzhFxo4FPD35ZUuX8pdZI6Qs0BRq4odqP+Bsv7N4OeElpjeeDnN9+d1WGBhOvzgNv31+qLy6MhZeXYjopGi5dQkheaNUInfo0CEsXrwYgOxAB8YYFi1ahMOHDysVkL+/PzZv3oydO3fi6dOnGD16NJKTkzFkyBAAwMCBAzFz5vdO8xMnTkRgYCCWLVuGZ8+eYe7cubhz5w7GjRsHAEhOTsbPP/+MGzdu4M2bN7h79y6GDh2KiIgI9OjRQ6kYVU1eIqdTfBY3UIqIiTD42GB8Sf/CK9/UcROsDeW3rpYkGhrAli2Altb3MpEIGDQISElRX1yEqJOTqRMWtV6E95PfY2/XvWhasanCum8S3uDnv3+G/Qp79D7UG5fDLxdosBwhZZVSidy6desAiG9BTpkyBQcOHMDBgwcxZcoU6OnpgTHGTR+SX7169cLSpUsxe/ZseHh44P79+wgMDOQGNLx9+xaRkZFc/UaNGmHv3r3YtGkT3N3dcejQIRw7doybQ05DQwPPnj1Dt27dULVqVXTs2BGxsbG4evUqXF1dlYpR1aT7yGlplfx5SVdcX4HLb/gjAIZ4DEFnl87qCagQ1Kwpezv1xQvg55/VEg4hxYaOpg76uPXBlSFX8Gj0I4yrPw7ldOR3UckQZeDAvwfQYmcLuK53xeqbqxH/Nb5I4yWkJFNqHjlTU1MkJiZi+fLlmDhxIm/fqlWrMHnyZBgbGyMuLk5lgapTYc9DExICNG78fbtcOSChBE+Y/jjmMepuqssbqeZo4ogHox4o/DIvqTIzxT876cVHgoPFCwUQQsSS0pOw79E+bLizAaFRoTnW1dPUQ5+afTC6/mjUsy1lE2qSIkXzyCmQ+q0JqUqVKjL7sstS5Q3FJHKVpuW5MrIyMODoAF4SJ4AAOzvvLHVJHABoagI7d8r+zIYMAb58kX8MIWWRobYhRtQdgbsj7+Lm8JsY7DEYupryv+xSM1Ox7f421N9cH/U21cPWe1uRnJ4sty4hZZ1SiVyFChUAACtWrOC1usXFxWHFihW8OiR30jlvSU7kloYsxf2o+7yyKV5T0MyhmXoCKgIuLrKjWMPDgalT1RIOIcWaQCBAA7sG2N5pOz74f8AKnxWoZlZNYf27kXcx/ORw2C23w4SzE/Dk45MijJaQ4k+pRK59+/ZgjCE4OBh2dnZwc3ODm5sb7OzsEBwcDIFAgA4dOqg61lKrtLTI/Rf7H367/BuvrKZlTcxvOV9NERWdiROBplL9ujdtAiRWjiOESDHVM8WkhpPwdOxT/D3wb/So0QOaQvnTmyakJWDNrTVwXe+KFjtaYP/j/TTRMCFQso9cdHQ0PDw8uPnbJNddBQAbGxvcu3dPZsWFkqqw77Hv2SNekD2buztw/77KL1OoGGNouaslLoVf4sqEAiFuDLuB+nb11RdYEXr1Svyzk5wo2NwcePhQvCYrISR3UUlR3ETDbxPe5ljXQt8Cg9wHYUTdEahqVrWIIiQlCfWRU8DKygrXr1+Hj48PBAIBN+2IQCCAr68v/vnnn1KTxBWF0tAity10Gy+JA4AJDSaUmSQOACpXBpYt45d9+gQMHCiemoQQkjtrQ2v80uwXvJ7wGif7nER75/YKJxr+mPIRS68vRbW11dBiRwvsebgHXzPlzOdESCmmVIucpLi4OLx48QKAeKBD+fLlVRJYcVLYGf3atcD48d+3mzcHLl1S+WUKTVRSFKqvq86bMsDB2AGPxzyGobah+gJTA8aArl2BY8f45UuWUJ85QpQVFheGzfc2Y2voVsQkx+RYt7xeeQyoNQAj6oyAq2XxmGKKqE9ZaJErcCJXFhT2G2HpUuCnn75v+/oCZ8+q/DKFptehXjj470Fe2Zm+Z9DOuZ2aIlKv2FigVi3gw4fvZVpa4lUf6tZVX1yElHTpWek4+vQoNtzZIDNPpTyN7BthRJ0R6OnaE/pa+kUQISluykIip9St1Tlz5sDJyQnt27eX2dehQwc4OTnht99+k3MkkUf61mpJWtXh1H+nZJK4PjX7lNkkDgDMzIC//gIEEneDMjKAPn2ApCT1xUVISaetoY1eNXvh0uBLeDb2GaZ6TVW4HBgAhLwLwZDjQ2C7zBZjT4+VGVFPSGmgVCJ3+PBhvHnzBn5+fjL7OnbsiPDwcAQEBBQ4uLKipPaR+5r5VWYt1fJ65bHSd6V6AipGvL2BGTP4ZS9eiNdopTZwQgqumnk1LGm7BO8nv8eB7gfQ2qm1wroJaQlYf2c9av+vNhpsboDNdzfjSxpN9EhKB6USufDwcACAs7OzzL7KlSsDAN68eaN8VGVMutQI+pLSIrc0ZCnC4sN4ZcvaLoOlgaWaIipefvsNqC811mPXLvEarYQQ1dDR1EFP1564MOACXo5/iZlNZsLKQPFgu9sfbmPkqZGwXW6LkSdH4nbEbVrjlZRoSiVy2dONPHv2TGZfdhl9MPIuLY2/XRISuXcJ7/DHVf4suE0qNsEg90Fqiqj40dIC9u0DjIz45ePHA/fuqScmQkqzyuUr449Wf+Dd5Hc40vMI2lVpp3DEa1J6Ejbf24wGWxqgzqY6WH97PRK+luC1EUmZpVQiV7VqVTDGMG/ePAQFBXHlQUFBmD9/PgQCAapWpTl98ko6kdPWVk8c+TH1wlSkZn5fkkIoEGJNuzVckk/EKlcGtm3jl6WlAd26AaVkKWJCih0tDS10qd4FZ/qdQdjEMMxuNht2RnYK69+Puo+xZ8bCZpkNBh8bjCtvrlBjBCkxlErkunXrBgD4/Pkz2rZtC319fRgYGKBt27b49OkTAKB79+6qi7KUK2ktcpfCL8kMcBhZZyQ8rD3UE1Ax1707MGkSvyw8nOaXI6QoOJg44Dfv3xA+KRwn+5zED9V+gFAg/1dfamYqdj7YieY7mqPq2qpYeHUhIhIjijhiQvJHqelHvn79Ci8vLzx48EDufnd3d1y/fh26JaXXfi4Ke/hyv37A3r3ft2fOlF27s7jIFGWizv/q4FHMI67MVNcUL8a/gJm+mRojK94yMoAWLYCQEH75H3+If96EkKITkRiB7fe3Y8u9LXiTkHN/bqFACN8qvhjqMRQdq3WEtkYJuGVCODT9iAK6urq4cuUKxo4dy5sA2NTUFGPHjsXly5dLTRJXFEpSi9zGOxt5SRwALGi5gJK4XGhpAQcPAhYW/PJZs4Bz59QTEyFllV05O8xqNguvJrxCYL9AdKveTeEaryImwpkXZ9A9oDvsltvB/5w/Hsc8LuKICVGswBMCM8a426nm5ualso9UYWf0HTvyF1cvrq00sSmxqLKmCm8Fh1pWtXB35F2FX4KE7+JFoG1b/hQkJibA7dtAlSpqC4uQMi86KRq7H+7G1tCtePZJdiCftPq29TG09lD0rtkbJromhR8gUQq1yOWBQCCAhYUFLCwsSmUSVxRKSovc71d/5yVxALCm3RpK4vKhdWtg/nx+WXw80KkT8IWmtSLFWVaWeO3AffvE/2ZlqTsilbIytMLURlPxZMwThAwNwfDaw3NcYvD2h9sYfXo0bJbZYMDRAQgOC4aIUadXUvQKnMiRgisJ88iFx4dj3e11vLJerr3QzKGZmiIquWbOFI9alfTkCTBgAA1+IMXUkSOAo6N4puu+fcX/OjqKy0sZgUAAL3svbP5hM6KmRGF7p+1oWrGpwvpfM7/ir4d/oeWulqiyugrmX56PdwnvijBiUtZRIlcMlIQWuVl/z0J61veMU0uohYWtFqoxopJLKAR27ADc3Pjlx4+LJxEmpFg5ckQ89Pr9e355RIS4vBQmc9kMtA0w2GMwrgy5gufjnmNmk5mwMbRRWD8sPgyzL82Gw0oH+Pzlgz0P9yAlI6UIIyZlUYH7yJUFhX2PvU4dIDT0+/bOneKpKYqL0MhQ1NlUh1c20XMiLcVVQGFhQL16wOfP/PJDh2Rb7AhRi6wsccubdBKXTSAAKlQQv5k1NIo0NHXJFGXi/Kvz2Bq6FSeen0CmKDPH+kbaRuhRowcGeQxCk4pNFE59QgoH9ZEjRaK4t8jNCOIvGlpOpxxmNZulpmhKj0qVgIAA2d9/gwYBjx7JP4aQInX1quIkDhCP2nn3TlyvjNAUaqK9c3sc7nkYH/w/YHnb5XC1cFVY/0v6F2y7vw3NdzRHldVVMCd4Dl59flWEEZPSjhK5YqA495G7+Poizr86zyub3ng6zPXNvxeU8k7QhallS2D5cn5ZcrJ48MPHj+qJiRBOZKRq65UyFgYWmOw1GY9GP8Kt4bfwY90fUU5HcatPWHwY5l2ZhyprqqDp9qbYfHczLQtGCkzpRE4kEvGWMLlx4wZmzJiByZMn4/r16yoJrqwori1yIibCtAvTeGW2RraY1HDS94Iy1Am6sIwfDwwZwi8LCwO6dAG+flVPTIQAAGwU9wdTql4pJRAIUN+uPjb6bUTklEjs6boHbSu3zfE26j9v/8HIUyNhvcwafQ73wdkXZ3O9TUuIPEr1kZsxYwaWLFkCV1dXPHz4EEFBQfD19YXo/+3deVxN+f8H8NdpvZF2bSqF0oxSRMkyGJlskzAkS5gZhsEwmBnLWOY3YyyzfGcYgzFjGTuJCSP7LkspRPaIuGVrEVru/fz+ONOtU/fW7XaXlvfz8TiPOp/zuee+70G9fdb/ptzp6enhwIED6Nq1q9oD1gVN97Hb2QEZGcXnhw4B3bqp/W0qbdOVTRgaNVRQtur9Vfi49cf8SdEg6NJ/hYqWoYmMBPr310KkNV9eHr/zw9mzwvIhQ4ANG4ofKSFaVTRGLi2t7L9zoE6OkauMtOw0bLyyEesurcO1J9cqrG9vao9h3sMQ4RMBbzvvCuuTitEYOQVOnz4Nxhj69esHAPj9998hkUjAGANjDBKJBIsXL1ZroLVZdWyRK5QWYu6xuYKyt2zewkjfkfyJRAJMmiT/h3tR2eTJ1M2qJGNjYOdOwNlZWL5pU9l15wjRGn194Ndf+e9L/2+i6PyXXyiJU6CRWSN82eFLJI1LwoXRFzDRfyKsTRTvgiN+KcaPsT+i5YqWaL2yNX6O/RmPc+pmtzVRnkqJ3O3bt8FxHLy8vADwiR3HcYiMjMTo0aMBAHFxceqLsparjmPkNlzegNvPbwvKFgYtLF78lwZBq529Pb/Dh2mpNUjnzhXuxUuIVvXvz7euN2okLHdyolZ3JXEchzaObbCk5xI8mvoIO8N2ItQzFIZ6hgpfkyBOwNQDU+H0Pyd0X98daxPXIjsvW4tRk5pCpa5VY2NjFBYW4vDhw2jZsiVsbGxgYWGB58+f48iRIwgKCoKBgQHyS2coNZSmm2b19YULwV66BLRsqfa3UVqhtBCev3nizovimVX+jfxx9qOzxbt3bN7M9/tVZNMmIDxcQ5HWTv/+y2/bVvLvhJERcOQI0KGD7uIidZxEwv/H7PFjfkxcp07UEldFT189xZakLVh3aR3iHlXc+CEyECGkeQiGeg9Fj2Y9YKRvpIUoazbqWlXAxMQEAHD+/HkcO3YMAODp6QkAyM3NBYBa+8DUrbCw7Gr+Rjr+t7n+0npBEgcA8zrPE27BRoOgNaZXL763qqT8fCA0FLh7VxcREQI+aevShf+PWZculMSpgU09G0zwn4ALoy/g6qdX8VWHr+DYwFFh/TeFb7Dt6jb03dIXDj85YOyesTiVeoq2BqvjVErkvP9bkn7GjBkYOHAgOI5DQEAAACA1NRUA0Kh0MzyRq/T4OEC3XasFkgJ8e0I4KCugUQB6NOshrNipE9+1omgUPsfxA746Kd7ahig2cSIwYYKw7OlToHfvsgsIE0Jqvrcbvo2FQQuROjkV+4ftR4RPRLl7vT5//Rwr41ei05pOaPJrE8w8PBNXM65qMWJSXaiUyE2ePBkcx8kmNxgZGWHMmDEAgL179wIAOlAfkFLk9T7rMpFbf3k9UjJTBGXzupRqjQNoELQW/O9/QM+ewrLr14GQEOD1a93ERAjRLH09fbzX9D2sC12H9Gnp2DJgC973eL94fLIc97PuY8GpBfBa7oVWK1vhxzM/Ii07TYtRE11SeYuuEydOYPfu3TA0NMTQoUPRogW/svXixYtRUFCAXr16oVWrVmoNVlc02ccuFpftfXz6FLBWPLFJYwokBWj+W3NBItfOqR3OfHimbCJXJCqKn71acuKDszOfxNEg6CrLzgY6diy700NoKD/OnPJkQuqGp6+eYvvV7dh4ZSNOPzhdYX0OHLq4dsFgr8Ho/1Z/4SLudUhdGCNHe60qQZN/Ee7f55dpEr4f0KCBWt9GKX9e/BOjd48WlMUMjUFws+DyX0iDoDUqNRVo355fyqukceOAZctojTlC6pqUFynYnLQZGy5vQPLT5ArrG+gZIKhJEAa3GIxQz1CYi8y1EGX1QImcAjk5OXjy5Ak4joObmxsAYNu2bYiKikJeXh6GDBmCgQMHqj1YXdHkX4SbN4HmzYVleXnan/CQL8lH89+a417mPVlZoFMgTn94WnFrHNGaK1f4/Dir1G4+330HzJqlm5gIIbrFGEOiOBEbr2zE5qTNeJTzqMLXGOkboWeznghrEYb3m79f7ji82oASOQUmT56MpUuXok2bNjh37hwiIyMxaNAgwS/8bdu2YcCAAWoNVlc0+RchKQnwLrWAt1Sq/VaWtYlrMeof4T5RB4YdQPem3bUbCFHo2DEgOLjsuMrVq8tu8UUIqVskUgmO3TuGjVc2YkfyDqXWnDMxMMH7zd9HWIsw9GzWEyaGJlqIVLvqQiKn0mSHor1UQ0NDAQCrV68GANnkB8YYli5dqp4Iazl5uzpoO4mTMikWnxbuxNHeuT2CmgRpNxBSri5d5G/XNXo0v/YcIaTu0tfTR7cm3bC672qIp4oROTASA98eCBMDxcnZ68LX2HZ1GwZsGwC7H+0wfOdw7L25F/mS2rEGbF2hUiKXksIPhi9aO+7cuXPgOA4XLlzAzJkzAQCXL19WU4i1W+lEThdryO2+sbvMOIuZHWdSl2o1NHBg2TXmJBK+/NQpnYRECKlmTAxNMODtAdg2cBsyvsjApv6bENI8pNwFhHPyc7Dh8gb02dwH9j/a4+Poj3Ho7iEUSgs1G6xEwnc3bN7Mf6VtHStNpUQuMzMTAGBpaYn09HS8ePEC1tbW8PPzQ7f/dnt/+fKlykEtW7YMrq6uEIlECAgIwPnz58utv337dnh6ekIkEsHb2xv/lmieKCgowFdffQVvb2/Ur18fjo6OiIiIwKNHFY8l0AZd77PKGMOi04sEZV62Xujl3ku7gRClffYZ8OWXwrJXr/iFhGlnPEJISaZGpgj3Dsc/g/9B+rR0rOm7Bj2a9YA+p3hC2os3L/BXwl/ovr47HH5ywOjo0dh/ez8KJAXqDS4qip/t17Urv1NQ1678eVSUet+nllMpkWvw35TK6OhobNu2DQDw1ltvAQCy/huNbWlpqVJAW7duxZQpUzB37lxcvHgRPj4+CA4ORkZGhtz6Z86cQXh4OD766CMkJCQgNDQUoaGhSEpKAgC8evUKFy9exOzZs3Hx4kVERUXhxo0bCAkJUSk+ddP1PqunUk8h9mGsoOyrDl9Ra1w1t2ABMGyYsCwnhx9DV3qpEkIIAQALkQVG+o7EvqH7IJ4mxso+K9HVtSs4KP55//TVU/yZ8Cd6bOwBux/tMOqfUdh7cy/yCuWsZl8ZUVHABx+U3bM7LY0vp2ROaSpNdujevTuOHDkiKPvqq6/w/fff43//+x+mTp0KPz8/XLhwodIBBQQEoG3btvjtt98AAFKpFM7Ozpg4cSKmT59epn5YWBhyc3OxZ88eWVm7du3g6+uLFStWyH2PCxcuwN/fH/fv34eLi0uFMWlysGR0NNC3b/F5kybAnTuK66tbn019sPfWXtm5i7kLbk+8DUN9xZs5k+qhoAAYMADYvVtYbmsLnDhRdjY0IYTI8zjnMSKvRWLL1S048+CMUq8xMzZDSPMQDHhrAIKbBlduooREwre8lU7iinAcv3NQSkqVl7KiyQ4KzJo1CyKRSDaxwcrKCuPGjQMA7Nq1CwDQSYWtmfLz8xEfH4+goOJB9np6eggKCpJNsCgtNjZWUB8AgoODFdYH+FZDjuNgYWEh93peXh6ys7MFh6bocozclfQrgiQOAKYGTqUkroYwNAS2bQO6l5pYnJEBdOvG/wwkhJCKODRwwMSAiTj94Wncn3wfP3T/AX4OfuW+JjsvGxsub0C/rf3Q8IeGGBw5GJHXIpGbn1vxG548qTiJAwDGgAcP+HqkQiolcl26dEFCQgKWLl2KFStWICkpCc7OzgCAsWPHYv369ZhQeqNIJTx9+hQSiQR2dnaCcjs7O4jFYrmvEYvFlar/5s0bfPXVVwgPD1eYnS9YsADm5uayo+izaYIux8gtPiOcqWptYo2PWn2kvQBIlYlEwM6dZbe0TUsDOncGbt3STVyEkJrJxdwF09pPQ9yYONz97C5+6P4DAhoFlPua3IJcbL26FQO3D0TDHxrig20fYEvSFuTk5ch/wePHygWjbL06TvHmbRXw8PCAh4dHmfLw8PAqBaRJBQUFGDRoEBhjWL58ucJ6M2bMwJQpU2Tn2dnZGkvmdDVG7n7mfWy+sllQNtF/Iuob1ddOAERt6tcH9uzhW+ZKzgt68IBP5g4fBv4bwkoIIUpzs3TDtPbTMK39NDzIeoCo5ChEJkfidOppMMgflfW68DV2JO/AjuQdMNY3RnCzYPTz7If3Pd6Hdb3/9p4svS+lIsrWq+NUTuQAfqzZhg0bkJycjFevXuHQoUOyyQ/9+vWTTYpQlo2NDfT19ZGeni4oT09Ph729vdzX2NvbK1W/KIm7f/8+jhw5Um5fubGxMYy1lFHpqkXu59ifIWHF07zrGdbDBP/Kt6KS6sHMDNi3D3j3XeDSpeLyx4/5ZO7QIaBlS93FRwip2ZzNnTGp3SRMajcJj3IeYWfyTkQmR+LE/ROQMqnc1+RJ8hB9IxrRN6Khz+mjU+NO6OfZD6Et34eLkxPfdSBvmH7RGDkVhmjVRSp1rQLA9OnT0a5dO/z22284dOgQYmNjIRKJ8OOPP2LUqFGIUmHGiZGREfz8/HD48GFZmVQqxeHDhxEYGCj3NYGBgYL6AHDw4EFB/aIk7tatWzh06BCsdbEjvQK6GCOX9SYLqxNXC8o+bvVx8f+WSI1kZcW3vvmVGtry5Ak/qz8+XjdxEUJqF8cGjhjvPx5HRxzF46mPsbLPSnRv0r3cJU0kjN95YlLMJDRe2gRf9Dbix9mXXiGh6PyXX2jPbiWplMht3LgRixcvlk12KCkkJASMMezYsUOlgKZMmYJVq1Zh3bp1SE5Oxrhx45Cbm4tR/+1BFBERgRkzZsjqT5o0CTExMfjpp59w/fp1zJs3D3FxcbIxegUFBfjggw8QFxeHjRs3QiKRQCwWQywWI790v6YO6KJrdXXCarzML17nT4/Tw5TAKeW8gtQU1tZ861vp//c8f8631p04oZu4CCG1k219W4zxG4MDww8gfVo6/gr5Cz2b9YShXvmT5n50uIsBg4CHDYQ5BHNyAiIjgf79NRl2raJS12rR9luenp4YMmQI5syZI7tWtJ7ctWvXVAooLCwMT548wZw5cyAWi+Hr64uYmBjZhIbU1FTo6RXnn+3bt8emTZvw9ddfY+bMmXB3d8euXbvg5eUFAEhLS0N0dDQAwNfXV/BeR48eRZcuXVSKU1203bUqkUqw9Lxw+7R+nv3Q2KKxZt+YaI2FBbB/P9CnjzBxy84G3nsP2LpVuOQNIYSog3U9a3zY6kN82OpDZL7JxO4bu7Hz+k7E3I7B68LXZervfBv4xxPodB9weAk8NgUe+Ojhet/3QWsnKE+ldeRMTU3x+vVrREZGwtbWFp06dQLHcZBIJDhy5AiCgoJgYmKC3FwlpiHXAJpch+brr4H584vPBw/mdyrRlOgb0ei7Rfhb/MTIE+jUmMYi1DavXgGhocDBg8JyPT3gjz+Aj2iCMiFEC14VvMLBOwex8/pO7L65G89fP1dYt0ezHtg3dJ/a3pvWkauAvpz+64f/rQ1jaEj5tDK0PUbu13O/Cs5b2bdCR5eOmn1TohP16vELToeGCsulUuDjj4GFC+WPMyaEEHWqZ1gPfT37Ym3oWqRPS8fhiMOY6D8RTmZOZer28+yngwhrNpUSOU9PTwDAokWLBOu13b9/H4sXLwbHcbIuVlI+bY6Ru5J+BUdShDtyTAqYRNtx1WIiEbB9O5+4lTZjBjBlCp/YEUKINhjoGeBdt3expOcSpE5OxYXRFzCz40y8ZfMWOHDo25zGfVSWSmPkhgwZgosXL+Ls2bMYNGiQLBFo0qSJrM6w0htBErm0OUZuybklgnPb+rYY7DVYc29IqgUDA74r1dYW+P574bVffuFnta5erd1dRQghhOM4tHFsgzaObTC/23ykZqXCztSu4hcSAZVa5D777DO8++67ZWatFp1369ZNtmUXKZ+2Erlnr55hw5UNgrKxfmNhbKDFrSSIznAcPxbzl1/KXtu4EejZE8jM1HZUhBBSzMW84r3PSVkqJXIGBgaIiYnB4sWL4ePjA5FIBJFIBB8fHyxevBh79+4VzCwlimlrjNyqi6vwpvCN7NxQzxBj24zVzJuRamvSJGDDBr6VrqQjR4COHYHUVN3ERQghRDUq7+xgYGCAadOmYdq0aeqMp87Rxhi5AkkBll1YJigb1GIQHBrQ9id10dCh/HpzAwbwM1uLXL0KBAQAe/cCrVvrLj5CCCHKo2YzHdNG12r0jWg8zH4oKJsUMEn9b0RqjB49gOPHAbtSw1HEYuCdd4B//9VNXIQQQipHqRa5kpMYlMVxHO7cuVPp19U12kjkVsSvEJy3c2qHto3aqv+NSI3Spg1w9izQqxeQnFxcnpsLhIQAy5YBn3yiu/gIIYRUTKlE7t69e5VaooIxRktaKEnTY+RuP7+NQ3cPCco+bfOpet+E1FiursDp0/xuOMeOFZdLJMDYsUBKCj/TlYa8EkJI9aT0j+eiGanKHER5mh4jtyp+leDcUmSJD97+QL1vQmo0S0sgJoYfO1faokX8biMlx9IRQgipPpRK5KRSaaUPiUSi6dhrBU12reZL8rEmcY2gbITPCJgYmqjvTUitYGwMrF8PzJpV9tr27UCnTsDDh2WvEUII0S3qMNExTSZyO5N34smrJ4KyMX5j1PcGpFbhOOC774BVq4DSu+9dvAi0bQucO6eb2AghhMin8vIjAJCcnIzbt28jMzNTbpdqREREVW5fJ2hyjNzK+JWC83cav4O3GtLWaaR8H38MuLgAgwYBWVnF5WIx0Lkz8OefAG3cQggh1YNKiVxqaiqGDRuG06dPK6zDcRwlckrQ1Bi5m89u4ui9o4KyT/xoCiJRznvv8a1v778P3LpVXJ6XBwwfDiQl8TtFlG65I4QQol0qda2OHTsWp06dokkPaqCprtU/4v8QnFubWGPAWwPUc3NSJzRvzidzQUFlry1aBPTpAzx7pv24CCGEFFOpRe7YsWPgOA7m5uYYPHgwrK2tYVB6zx+iFE0kcm8K32Bt4lpB2UjfkbSvKqk0S0tg3z5gyhRg6VLhtZgYfgeIbdv4HSEIIYRon0rZV4MGDZCXl4dly5YhPDxc3THVKZoYIxeVHIVnr4VNJTTJgajKwABYsgTw8gLGjwcKC4uvpabyM1p//pm/RstHEkKIdqnUtTpo0CAAQG5urlqDqYs0MUaudLdqV9eu8LD2qPqNSZ02Zgxw+HDZbb0KCoCJE/n15jIzdRIaIYTUWSq1yI0ZMwb79u3DtGnT8Pr1a7zzzjuwtLQsU8/FxaXKAdZmEgkglQrLqtoid+f5HRy/f1xQRpMciLq88w6QkACEh/N7tZa0bRtw5gywbh3w7ru6iY8QQuoalRI5X19fAPxuD5MnT5Zbh+M4FJbsgyFllG6NA6qeyP196W/BuZWJFUI9Q6t2U0JKcHAADh0CZs8GFi4UXnv4EOjWDfj8c35rL5FINzESQkhdoVLXaskZqTRrVXXqTuSkTIp1l9YJyoZ4DaFJDkTtDAyABQuA3bv5CRGl/e9/QJs2wKVL2o+NEELqEpVa5N555x1wNKq5ygoKypYZGqp+vxP3T+B+1n1B2UjfkarfkJAK9OkDXL4MjBzJj58r6epVfjeIb78Fpk2jNecIIUQTVF5+hFSdulvkSi854mXrhdYOrVW/ISFKcHICDhzgZ7ZOny6ciV1QwJdFRQGrVwMtWuguTkIIqY3Ustfq06dP8fTpU3Xcqk5RZ4vcy/yXiLwWKSgb6TOSWk6JVujpAZMnA3FxgI9P2evnz/Nrzs2fL//vPSGEENWonMhlZWVh/PjxsLGxgZ2dHezs7GBjY4MJEyYgq+QGjUQhdbbIRV6LRG5B8XIw+pw+hrYcqmJkhKjGy4vfDeKrr8quKZefD3z9Nb94cGKiTsIjhJBaR6VELjs7G+3bt8eKFSvw4sUL2eSG58+fY/ny5ejQoQNycnLUHWuto84WudLdqj3de8Le1F61mxFSBcbG/GzWkycBDznLFyYk8GPn5swpuyA2IYSQylEpkVu0aBGSk5NlCVy9evVQr149APws1uTkZCxatEitgdZGpVvkDAxUWxn/7ou7ZdaOG+EzogqREVJ1HTrwLW9ffMF3vZZUWMhPgvDzAy5c0El4hBBSK6iUyEVFRYHjOPj4+ODKlSt4+fIlXr58icuXL8PX1xeMMezYsUPdsdY6pVvkVG2NK712nKXIEu97vK9iVISoj4kJsHgxEBsrf6LD1atAu3bAl18Cr15pPz5CCKnpVErk7t27BwD45ptv0KLET2cvLy/MnTsXAHD//n15LyUllG6RU2V8nJRJyyRyQ7xp7ThSvfj7A/Hx/Bi50suQSKXADz/w4+tiYnQTHyGE1FQqJXKG/zUdyZupWlRmYKDSyiZ1ijpa5E7eP4mUzBRBGa0dR6ojY2O+O/XCBeC/zWEEUlKAnj357b/EYq2HRwghNZJKiVyLFi3AGMOXX36J5cuXIz4+HvHx8Vi+fDmmT58OjuMELXVEPnW0yG28slFw3qJhC/g5+FUhKkI0q1UrfjmSb7+V/5+XLVsAT09gxYqyexETQggRUimRGzVqFADgxYsXmDBhAvz9/eHv748JEybg2bNnAIAPP/xQfVHWUlVtkcuX5JdZO25Yy2G0dhyp9gwN+W7WxESgY8ey17OygHHj+GtXrmg9PEIIqTFUSuTGjBmDsLAwhfurhoWFYfTo0WoNtDaqaovcgTsH8OLNC0FZuFd4FaMiRHvefhs4fhz480/5e7bGxvILCU+dCmRmaj08Qgip9lReEHjz5s3YvHkzQkJC4OnpCU9PT4SEhGDLli3YtGmTOmOstaraIrfpivA5t3duj8YWjasYFSHapacHfPQRcP06MGxY2euFhcDPPwPu7nx3a2Gh9mMkhJDqqkozEsLCwhAWFqauWOqcqrTI5ebn4p8b/wjKhngNUUNUhOiGrS2wfj0wYgTfrXr7tvD606d8+bJlfGLXvbtu4iSEkOpELXutEtVUpUUu+kY0XhUUL7ylz+ljYIuBaoqMEN0JCuLHxc2ZI/8/N0lJwHvvAd268V2vhBBSlymVyOnp6cHAwABnzpwBAOjr61d4qLr8yLJly+Dq6gqRSISAgACcP3++3Prbt2+Hp6cnRCIRvL298e+//wquR0VF4b333oO1tTU4jkNiNdrksSotcpuTNgvOuzXpBtv6tmqIihDdE4mAb74Brl0D+veXX+fIEaB9e6BPH9q7lRBSdyndIlc0kaHoe2WOytq6dSumTJmCuXPn4uLFi/Dx8UFwcDAyMjLk1j9z5gzCw8Px0UcfISEhAaGhoQgNDUVSUpKsTm5uLjp27FgttwxTNZF7/vo5Ym4LV06lblVSGzVtCuzYwSdtPj7y6+zdyy9pMmgQP86OEELqEo4pkXG5urqC4zjs2LEDrVu3lp1XJCUlpcI6JQUEBKBt27b47bffAABSqRTOzs6YOHEipk+fXqZ+WFgYcnNzsWfPHllZu3bt4OvrixUrVgjq3rt3D25ubkhISICvvNVIy5GdnQ1zc3NkZWXBzMysUq8tz88/87Pxirz3HrB/f8WvWxW/CmP2jJGdG+sbI+OLDJgZqy82QqobiQRYswaYNw9IS5NfR08PGDwYmDWLnxFLCKnbNPX7uzpRqv+zaEsuRefqkJ+fj/j4eMyYMUNWpqenh6CgIMQqGAgTGxuLKVOmCMqCg4Oxa9cutcenCaq2yJXuVu3t0ZuSOFLr6esDH3/Mz2xdsQL4/nvgyRNhHakU2LQJ2LwZGDiQX6vO21s38RJCiDZUm8kOT58+hUQigZ2dnaDczs4OYgX79YjF4krVV1ZeXh6ys7MFhyaoMtkhLTsNx+4dE5RRtyqpS0QiYPJk4O5d4LvvAHPzsnUYA7ZtA1q2BAYMoDF0hJDaS6VELikpCatXr8bGjfz2UPn5+fj0009hb28PS0tLjB8/HhKJRK2BatOCBQtgbm4uO5ydnTXyPqq0yG27ug0Mxb3hDYwaoJd7LzVHRkj1Z2rKd6GmpPBfTU3l14uK4sfQ9e0LxMVpN0ZCCNE0lRK5n3/+GaNHj8bmzXwX35IlS7BixQpkZGQgKysLK1aswA8//FCpe9rY2EBfXx/p6emC8vT0dNjb28t9jb29faXqK2vGjBnIysqSHQ8ePKjS/RRRpUWudLdqv7f6wcTQRI1REVKzWFryLXP37wOzZwOKhsFERwNt2wK9egEnTvCtdoQQUtOplMidO3cOANCrF98SFBUVBY7j4ObmBlNTUzDGsHXr1krd08jICH5+fjh8+LCsTCqV4vDhwwgMDJT7msDAQEF9ADh48KDC+soyNjaGmZmZ4NCEyrbI3c+8jwuPLgjKaEsuQnhWVsD//R+f0H3zDWBhIb/evn1A58780iW7dvHj6gghpKZSKZF79OgRAMDNzQ2MMVy6dAkAn+D98ssvAIBbt25V+r5TpkzBqlWrsG7dOiQnJ2PcuHHIzc3FqFGjAAARERGCyRCTJk1CTEwMfvrpJ1y/fh3z5s1DXFwcJkyYIKvz/PlzJCYm4tq1awCAGzduIDExscrj6NShsi1yO5J3CM6tTKzQza2bmqMipGazsOAXE75/H5g/n0/w5Dl7FujXj5/d+uefQF6eVsMkhBC1UCmRy83NBQAYGBjg3r17eP36NVxcXGBjY4MmTZoAAApV2BAxLCwMP/74I+bMmQNfX18kJiYiJiZGNqEhNTUVjx8/ltVv3749Nm3ahD/++AM+Pj6IjIzErl274OXlJasTHR2NVq1aoXfv3gCAwYMHo1WrVmWWJ9GFyrbIlU7k+jbvC0P9Sm7QSkgdYWYGzJwJ3LsHLFwI2NjIr3fjBjB6NODqCixaBGRmajFIQgipIqXWkSutUaNGEIvFCAoKgoODA/7++2/07NkTe/fuxdatWxEeHg5HR0c8fPhQEzFrnabWofnwQ35drCJTpgA//SS/blp2Gpz+5yQo2ztkL010IERJubnAX3/x/8ZSUxXXq1cPGDIE+PRTfpIEIaTmqgvryKnUIte5c2cwxnDo0CGsX78eHMeh+387WBd1YXp4eKgvylqqMi1yO6/vFJybGZtRtyohlVC/PvDZZ8Dt28DGjfzSJPK8esV3tbZuDQQGAuvXA2/eaDdWQghRlkqJ3IIFC+Du7i7biqtjx44YM4bfaWDbtm0AgC5duqgtyNqqMmPkIq9FCs5DmofA2MBYA1ERUrsZGvItbomJQEwM0LWr4rpnzwIREYCTE78Ly9WrWguTEEKUotLO9o0bN8a1a9dw/fp1GBoawt3dXbZl16FDhwAAVopGGBMZZVvk0l+m42TqSUHZgLcGaCgqQuoGjgOCg/njwgXgxx/5NefkDe999ozfUu/nnwF/f35YxODB8hcjJoQQbVJ5Zwd9fX20aNECHh4egn1XGzVqhEaNGsHEhNY2q4iyLXK7ru+ClBWvkVDfsD6CmwZrMDJC6pa2bYGtW4uXLnF0VFz3/Hlg7FjA3h4YPhw4epSWMCGE6I5KLXIAkJWVhU2bNuH27dvIzMxE6TkTHMfhr7/+qnKAtZmyLXKlZ6v29uhNiwATogGOjvzSJTNnArt3A7//DvzXyVDGmzfAhg384eYGjBzJd8O6umozYkJIXadSInf06FH069cPOTk55dajRK58yiRyz149w5GUI4Iy6lYlRLMMDPg15vr1A27e5GeXr1sHlFj9SCAlBZg7lz86dgSGDgUGDgSsrbUbNyGk7lGpa/Xzzz9Hdna2bLKDvINUTJmu1egb0ZCw4n1rRQYiWnKEEC3y8AAWLOCXLNmzB+jfn0/0FDl1Chg3DnBw4Pd33bYNeP1ae/ESQuoWlVrkrl+/Do7j0LJlS8yYMQPW1tYwKO8nG5FLmRa50t2qPZr1gKmRgt3BCSEaY2AA9O7NH0+e8F2qq1cDSUny6xcU8Pu7RkcDDRoAAwbwLXVduwL6+tqNnRBSe6mUfTk5OSElJQXfffedbMcEUnkVtchlvcnCgTsHBGUfvPWBhqMihFSkYUPg88+ByZOB+Hg+oduyBXjxQn79nBxg7Vr+sLUFQkP5lr2uXSve0YUQQsqjUtfqhAkTwBjDmTNn1B1PnVJRi9yem3tQIC3O9gz1DNHHo48WIiOEKIPjgDZt+EkRYjHwzz/82DiRSPFrMjKAP/4AevQA7Oz4CRK7dvELERNCSGWp1CJnYWGBJk2aYOHChUhOTkbnzp1haWlZpl5ERESVA6zNKmqRi74ZLTjv3rQ7zEW0cBUh1ZGRERASwh9ZWfyadBs3AkeOAIqGDWdm8jtHrF/PJ3/vvlvcfdu4sVbDJ4TUUCrttaqnpweO48AYE6whJ7gxx6FQ3sqaNZCm9mpr3Fi45+PevUCv/+Yx5EvyYbPYBjn5xTOD/+jzB0b7jVbb+xNCNC8tje923bgRSEhQ/nVeXnxC16cP0K5d+RMsCCHy0V6r5SjK/2jmqurKa5E7fu+4IIkDQN2qhNRAjRrx23tdvAjcugUsXswnZhVJSgIWLQI6deLH1Q0Zwk+wEIs1HzMhpOZQ6f94c+fOVXccdVJ5Y+Sibwi7Vf0b+cOhgYMWoiKEaEqzZsAXX/BHWhqwcyewYwdw8iQgkSh+3YsXwObN/AEALVsC773HHx07ArSRDiF1l0pdq3WNpppmzc2B7Ozi89Ongfbt+VZO119dkZpV3O/6XdfvMOudWWp7b0JI9fHiBbB/Pz+8Yt8+fm9XZYlEfKtdUWLn7c1PwiCE1I2u1Soncs+fP8f169eRm5uL7t27qyuuakVTfxFMTPhtfopcuMDPgLskvgTflb6CupfHXoa3nbfa3psQUj1JJMC5c3xSt2cPcPly5V5vbw8EBQGdO/MJnocHJXak7qoLiZzKY+Tu37+P3r17w9bWFp06dULPnj3x5s0btGjRAk2bNkV8fLw646yVFI2RK92t6mrhCi9bLy1FRQjRJX19vmV+/nzg0iV+QtTy5fzacw0aVPx6sZgfSzd6NODpySd2AwcCS5fy95NKNf4RCCFapNIYubS0NLRv3x5isVgwqUEkEqFly5bYunUrtmzZAj8/P7UFWttIpWXHxBSNkSu97EiIR4jC2cGEkNrN2RkYO5Y/CgqA8+eBAwf44/z5ihOzjAwgMpI/AMDCAggMBAIC+EkX/v6AnNWjCCE1hEotcvPmzcPjx4/5sVyuroJrHTt2BAAcOXJEzitJkdKtcQDfIvco5xHiHsUJykOah2gpKkJIdWZoCHToAHzzDRAbCzx9yk+W+OQToNSPYoUyM/lxePPm8YsSW1nxLXcjRwIrVvBLpNSSlaMIqRNUapHbt28fOI7Dl19+iT59+qBTp06ya0WJ3cOHD9USYG1VesYqwLfI7bm5R1BmbmyOdxq/o6WoCCE1iaUlv9VX//78osN37gAHDwInTgDHjwOPHyt3nxs3+GPdOv68Xj1+vG5Rq13btoCTE421I6Q6UimRe/LkCQAgKCiozDX9/3aDzsrKqkJYtZ+8Fjkjo7Lj43q694ShvmHZyoQQUgLH8cubNGsGjBvHJ3Z37/JJXdFx965y93r1qvg1RRo2BPz8hIezMyV3hOiaSomctbU10tPTERcXJ+tKLXLw4EEAgJ2dXdWjq8XktcjlIxeH7h4SlIV4ULcqIaTyOA5o2pQ/Ro3iyx4+5Jc5OncOOHuWX6Q4L0+5+z15AsTE8EcRG5vipK51a/5r48aU3BGiTSolcp07d8bWrVsxZ84cwZIjH374IdatWweO49C1a1e1BVkbyUvkTj8+iDxJ8U9VAz0D9GjWQ4tREUJqMycnICyMPwD+59ClS8WJ3dmzfPessp4+5de/27+/uKxBA+Dtt4EWLfhtxoq+OjhQgkeIJqi0jtyVK1fg7++PfDnZCGMMIpEIcXFxePvtt9USpK5pYh2aO3f4LpCSInZ8iL+vrJGdd3XtiiMjaNIIIUR7njzhZ8MWJXfnzwPqGCljYVGc2Hl68kfz5oCLC7/kCiGaUBfWkVOpRc7b2xtRUVEYOXKkbLxckYYNG2Lt2rW1JonTlDI5MCfFvjvCiQ40W5UQom0NGwK9e/MHUDyJ4uJFID6++MjMrNx9MzOBU6f4oySRCHB3FyZ3np78QsbKrJtHSF1XpZ0dXr9+jQMHDuDmzZsAAA8PD3Tv3h316tVTW4DVgSYy+suXAR+f4nPO6QLYx/6COrcn3kZTq6ZqeT9CCFEXxoCUFGFiFx/PbzWmTo0aFSd2JZM8JydAT+Xl7EldQi1yFTAxMUHfvn3VFUudUrpFTr/5PpRcusnD2oOSOEJItcRxQJMm/DFwIF/GGJCWBly9yh9JScXf5+aq9j5pafxRellSY2N+3bwmTQA3t+Kj6NzCoiqfjpCapUqJXHJyMm7fvo3MzEzIa9iLiIioyu1rtdLLj0ib7hOc92zWU4vREEJI1XAc31Lm5AQEBxeXS6X8NmNJSfxx/XrxoerYu7y84rXv5LGw4BM9Fxd+iRRn5+LvXVwAR0fAoEq//QipPlT6q5yamophw4bh9OnTCutwHEeJXDkELXImzyB1OCe4TokcIaQ20NPjkypXV6BPn+Jyxvjtw65f5xOykl9TUvjrqsrMBBIT+UNRTA4OwuSudMLXsCHNsiU1g0qJ3NixY3Gq9IhVUimCFrmmBwGu+KeWiYEJOrt21n5QhBCiJRwH2NnxR+dSP+7evAFu35af5OXkVP29pdLibtvYWPl1RCK+dbEowXN05GO1ty8+7Oz41j9K+IguqZTIHT9+HBzHwdbWFh988AFsbGzUHVetJ2iRaybsVu3q1hUiA5F2AyKEkGpCJOKXKvHyEpYzBojF/A4Vd+/yLXcpKcXfP3xYtZa8koqSydu3y69nZFSc1JVO8uzs+Ja9osPKipZaIeqnUiJnaWmJx48fY+XKlQgJoSUyVCFrkeOkQLMYwTXqViWEkLI4ju8SdXAAOnQoez0vjx+Pl5LCf33woPhr0fdv3qg3pvx8/r6pqcrFb2UlTO4aNuR3yChdVlRubKzeeEnto1IiN2bMGMybNw8XLlygRE5FshY5+wTANENwjRI5QgipPGNjfk06d3f51xkDnj0TJnilE71HjwCJRDPxFb3/s2d8N7Ey6tfnu28tLSt/UBJYN6iUyM2ePRtpaWn4/vvvcfLkSbRp00bu+ixz5sypcoC1laxFzl3Yrepu5U7LjhBCiAZwHN/KZWMDtGolv05hId99WzLRe/gQSE/ny4sOdex2oYzcXP5IS6v8a01M5CeB5uaAmRm/4HLR15Lfl/xavz6NAazuVErkrl69it27d4MxhpMnT+LkyZNy61Eip5isRa7U+DjaW5UQQnTHwKB4GZXyvHkjTO5Kf//4Mb/d2ZMn2kv6Snv9mj8eP1b9HhwHmJrKT/KKEsD69fk69euXPRSV01hB9VEpkfv0008hFovBcZzc9eMAfvkRolhBAQCT54DTWUE5dasSQkj1JxIBjRvzR0Xy84GnT4sTu5LflzyKyp8942fWVgeM8TOF1TFbuCRjY/lJXp8+wLRp6n2v2k6lRC4+Ph4cx8HLywsRERGwsrKCHu2XUin5+YCe2wF0ui+Fw0vgsSlwoakxurh20XVohBBC1MjIiF++xNFRufoSCb/d2ZMn/NeiIzNTeC7vUHUXDW3Ly+OPZ8+E5R4euomnJlMpkXNxccHNmzexaNEi9Oih/q7AZcuW4YcffoBYLIaPjw+WLl0Kf39/hfW3b9+O2bNn4969e3B3d8eiRYvQq1cv2XXGGObOnYtVq1YhMzMTHTp0wPLly+GuaESsFrjEReHe3Y/gfK247IkVYNJiH9C/v87iIoQQolv6+sVj+SorP19+wleyLDubP4pa2oq+L/qal6fuT6S8+vV19941lUqJ3LfffouwsDDs2LFD7Ync1q1bMWXKFKxYsQIBAQH45ZdfEBwcjBs3bsDW1rZM/TNnziA8PBwLFixAnz59sGnTJoSGhuLixYvw+m8RosWLF2PJkiVYt24d3NzcMHv2bAQHB+PatWsQiXSwXltUFPqs/QAMwm5pm+d5wAcfAJGRlMwRQgipNCMjwNaWP1SVny8/wVNUlpsLvHxZPDFD3qFsVzElcpXHMUWD3MoxatQonDhxAvfu3YOzszP8/Pxgbm4uvDHH4a+//qp0QAEBAWjbti1+++03AIBUKoWzszMmTpyI6dOnl6kfFhaG3Nxc7NmzR1bWrl07+Pr6YsWKFWCMwdHREVOnTsW0/zres7KyYGdnh7Vr12Lw4MEVxpSdnQ1zc3NkZWXJnZ1bKRIJ4OoK9vAh5I4iLNqwMCWFRoMSQgip8RjjW/mUSfjatAHatVPfe6v193c1pVKL3Lp162STGR48eIAHDx7IrVfZRC4/Px/x8fGYMWOGrExPTw9BQUGIVbCPSmxsLKZMmSIoCw4Oxq5duwAAKSkpEIvFCAoKkl03NzdHQEAAYmNj5SZyeXl5yCvRtpydnV2pz1GukycBRUkcwP+Nf/CAr9eli/relxBCCNEBjuMnh4hEgLW1rqOpfVSeocAYK/dQxdOnTyGRSGBnZycot7Ozg1gslvsasVhcbv2ir5W554IFC2Bubi47nJ2dVfo8cik7D7wq88UJIYQQUieo1CJ39OhRdcdRrcyYMUPQypedna2+ZM7BQb31CCGEEFJnqZTIde7cWd1xAABsbGygr6+P9PR0QXl6ejrs7e3lvsbe3r7c+kVf09PT4VAiOUpPT4evr6/cexobG8NYU3ubdOrEj4FLS5O/u3PRGLlOnTTz/oQQQgipNarV4m9GRkbw8/PD4cOHZWVSqRSHDx9GYGCg3NcEBgYK6gPAwYMHZfXd3Nxgb28vqJOdnY1z584pvKdG6esDv/7Kf1960eSi819+oYkOhBBCCKmQUomcnp4eDAwMcObMGQCAvr5+hYeBgUqNfZgyZQpWrVqFdevWITk5GePGjUNubi5GjRoFAIiIiBBMhpg0aRJiYmLw008/4fr165g3bx7i4uIwYcIEAPzs2cmTJ+O7775DdHQ0rly5goiICDg6OiI0NFSlGKusf39+iZFGjYTlTk609AghhBBClKZ0tlVyAoOqkxmUERYWhidPnmDOnDkQi8Xw9fVFTEyMbLJCamqqYBeJ9u3bY9OmTfj6668xc+ZMuLu7Y9euXbI15ADgyy+/RG5uLsaMGYPMzEx07NgRMTExullDrkj//kDfvvzs1MeP+TFxnTpRSxwhhBBClKbUOnKurq7gOA47duxA69atZecVSUlJUUuQulYX1qEhhBBCapu68PtbqRa5e/fulXtOCCGEEEK0r1pNdiCEEEIIIcpTeR25zZs3IzExEVlZWTA3N4evry/CwsLQrVs3dcdICCGEEELkqNReq7m5uRg+fDj++ecfhXVCQkKwYcMG1K9FO9/WhT52QgghpLapC7+/K9W1OmTIENkepoq25oqOjsaQIUM0ESshhBBCCClB6a7V/fv3Y/fu3eA4DowxBAUFITAwEA4ODkhLS8Pp06dx7NgxMMawZ88e7Nu3Dz179tRk7IQQQgghdZrSidzatWsB8LsvREZGonfv3mXq7Nq1C4MHD0ZBQQHWrVtHiRwhhBBCiAYp3bV66dIlcByHTz75RG4SBwChoaEYPXo0GGO4dOmS2oIkhBBCCCFlKZ3IPX78GAAQFBRUbr333ntPUJ8QQgghhGiG0l2rubm5AAArK6ty6xVdL6pfGxRN7M3OztZxJIQQQghRVtHvbU1uLaprSidyhYWF4DgO33//PWxtbRXWy8jIAABIpdKqR1dN5OTkAACcnZ11HAkhhBBCKisnJwfm5ua6DkMjlF5HTk9PT6n9VQE+8+U4DhKJpErBVRdSqRSPHj1CgwYNlH4GysrOzoazszMePHhQa9e40RZ6lupFz1N96FmqFz1P9antz5IxhpycHDg6OkJPr3ZuZlWpnR1qc9NkefT09ODk5KTR9zAzM6uV/4h0gZ6letHzVB96lupFz1N9avOzrK0tcUWUTuTmzp2ryTgIIYQQQkglUSJHCCGEEFJD1c4O4xrE2NgYc+fOhbGxsa5DqfHoWaoXPU/1oWepXvQ81YeeZc2n9GQHQgghhBBSvVCLHCGEEEJIDUWJHCGEEEJIDUWJHCGEEEJIDUWJHCGEEEJIDUWJnA4tW7YMrq6uEIlECAgIwPnz53Udks4tWLAAbdu2RYMGDWBra4vQ0FDcuHFDUOfNmzcYP348rK2tYWpqigEDBiA9PV1QJzU1Fb1790a9evVga2uLL774AoWFhYI6x44dQ+vWrWFsbIxmzZph7dq1mv54OrVw4UJwHIfJkyfLyuhZVk5aWhqGDRsGa2trmJiYwNvbG3FxcbLrjDHMmTMHDg4OMDExQVBQEG7duiW4x/PnzzF06FCYmZnBwsICH330EV6+fCmoc/nyZXTq1AkikQjOzs5YvHixVj6ftkgkEsyePRtubm4wMTFB06ZN8e233woWnadnqdiJEyfw/vvvw9HRERzHYdeuXYLr2nx227dvh6enJ0QiEby9vfHvv/+q/fOSCjCiE1u2bGFGRkZs9erV7OrVq2z06NHMwsKCpaen6zo0nQoODmZr1qxhSUlJLDExkfXq1Yu5uLiwly9fyuqMHTuWOTs7s8OHD7O4uDjWrl071r59e9n1wsJC5uXlxYKCglhCQgL7999/mY2NDZsxY4aszt27d1m9evXYlClT2LVr19jSpUuZvr4+i4mJ0ern1Zbz588zV1dX1rJlSzZp0iRZOT1L5T1//pw1btyYjRw5kp07d47dvXuX7d+/n92+fVtWZ+HChczc3Jzt2rWLXbp0iYWEhDA3Nzf2+vVrWZ0ePXowHx8fdvbsWXby5EnWrFkzFh4eLruelZXF7Ozs2NChQ1lSUhLbvHkzMzExYStXrtTq59Wk+fPnM2tra7Znzx6WkpLCtm/fzkxNTdmvv/4qq0PPUrF///2XzZo1i0VFRTEAbOfOnYLr2np2p0+fZvr6+mzx4sXs2rVr7Ouvv2aGhobsypUrGn8GpBglcjri7+/Pxo8fLzuXSCTM0dGRLViwQIdRVT8ZGRkMADt+/DhjjLHMzExmaGjItm/fLquTnJzMALDY2FjGGP9DTk9Pj4nFYlmd5cuXMzMzM5aXl8cYY+zLL79kLVq0ELxXWFgYCw4O1vRH0rqcnBzm7u7ODh48yDp37ixL5OhZVs5XX33FOnbsqPC6VCpl9vb27IcffpCVZWZmMmNjY7Z582bGGGPXrl1jANiFCxdkdfbt28c4jmNpaWmMMcZ+//13ZmlpKXu+Re/dvHlzdX8knenduzf78MMPBWX9+/dnQ4cOZYzRs6yM0omcNp/doEGDWO/evQXxBAQEsE8++UStn5GUj7pWdSA/Px/x8fEICgqSlenp6SEoKAixsbE6jKz6ycrKAgBYWVkBAOLj41FQUCB4dp6ennBxcZE9u9jYWHh7e8POzk5WJzg4GNnZ2bh69aqsTsl7FNWpjc9//Pjx6N27d5nPS8+ycqKjo9GmTRsMHDgQtra2aNWqFVatWiW7npKSArFYLHgW5ubmCAgIEDxPCwsLtGnTRlYnKCgIenp6OHfunKzOO++8AyMjI1md4OBg3LhxAy9evND0x9SK9u3b4/Dhw7h58yYA4NKlSzh16hR69uwJgJ5lVWjz2dWVf/vVHSVyOvD06VNIJBLBL0cAsLOzg1gs1lFU1Y9UKsXkyZPRoUMHeHl5AQDEYjGMjIxgYWEhqFvy2YnFYrnPtuhaeXWys7Px+vVrTXwcndiyZQsuXryIBQsWlLlGz7Jy7t69i+XLl8Pd3R379+/HuHHj8Nlnn2HdunUAip9Hef+uxWIxbG1tBdcNDAxgZWVVqWde002fPh2DBw+Gp6cnDA0N0apVK0yePBlDhw4FQM+yKrT57BTVqa3PtrpSeq9VQrRt/PjxSEpKwqlTp3QdSo304MEDTJo0CQcPHoRIJNJ1ODWeVCpFmzZt8P333wMAWrVqhaSkJKxYsQIjRozQcXQ1y7Zt27Bx40Zs2rQJLVq0QGJiIiZPngxHR0d6loRUErXI6YCNjQ309fXLzA5MT0+Hvb29jqKqXiZMmIA9e/bg6NGjcHJykpXb29sjPz8fmZmZgvoln529vb3cZ1t0rbw6ZmZmMDExUffH0Yn4+HhkZGSgdevWMDAwgIGBAY4fP44lS5bAwMAAdnZ29CwrwcHBAW+//bag7K233kJqaiqA4udR3r9re3t7ZGRkCK4XFhbi+fPnlXrmNd0XX3wha5Xz9vbG8OHD8fnnn8tajulZqk6bz05Rndr6bKsrSuR0wMjICH5+fjh8+LCsTCqV4vDhwwgMDNRhZLrHGMOECROwc+dOHDlyBG5uboLrfn5+MDQ0FDy7GzduIDU1VfbsAgMDceXKFcEPqoMHD8LMzEz2izgwMFBwj6I6ten5d+vWDVeuXEFiYqLsaNOmDYYOHSr7np6l8jp06FBmKZybN2+icePGAAA3NzfY29sLnkV2djbOnTsneJ6ZmZmIj4+X1Tly5AikUikCAgJkdU6cOIGCggJZnYMHD6J58+awtLTU2OfTplevXkFPT/jrR19fH1KpFAA9y6rQ5rOrK//2qz1dz7aoq7Zs2cKMjY3Z2rVr2bVr19iYMWOYhYWFYHZgXTRu3Dhmbm7Ojh07xh4/fiw7Xr16JaszduxY5uLiwo4cOcLi4uJYYGAgCwwMlF0vWjLjvffeY4mJiSwmJoY1bNhQ7pIZX3zxBUtOTmbLli2rlUtmlFZy1ipj9Cwr4/z588zAwIDNnz+f3bp1i23cuJHVq1ePbdiwQVZn4cKFzMLCgv3zzz/s8uXLrG/fvnKXfWjVqhU7d+4cO3XqFHN3dxcs+5CZmcns7OzY8OHDWVJSEtuyZQurV69ejV8yo6QRI0awRo0ayZYfiYqKYjY2NuzLL7+U1aFnqVhOTg5LSEhgCQkJDAD7+eefWUJCArt//z5jTHvP7vTp08zAwID9+OOPLDk5mc2dO5eWH9EBSuR0aOnSpczFxYUZGRkxf39/dvbsWV2HpHMA5B5r1qyR1Xn9+jX79NNPmaWlJatXrx7r168fe/z4seA+9+7dYz179mQmJibMxsaGTZ06lRUUFAjqHD16lPn6+jIjIyPWpEkTwXvUVqUTOXqWlbN7927m5eXFjI2NmaenJ/vjjz8E16VSKZs9ezazs7NjxsbGrFu3buzGjRuCOs+ePWPh4eHM1NSUmZmZsVGjRrGcnBxBnUuXLrGOHTsyY2Nj1qhRI7Zw4UKNfzZtys7OZpMmTWIuLi5MJBKxJk2asFmzZgmWuqBnqdjRo0fl/pwcMWIEY0y7z27btm3Mw8ODGRkZsRYtWrC9e/dq7HMT+TjGSiylTQghhBBCagwaI0cIIYQQUkNRIkcIIYQQUkNRIkcIIYQQUkNRIkcIIYQQUkNRIkcIIYQQUkNRIkcIIYQQUkNRIkcIIYQQUkNRIkcIkevYsWPgOA4cx2HkyJG6Dkeh3Nxc2NnZgeM4zJ8/X9fh6FTRn5erq2ulX7tx40ZwHAeRSISHDx+qPzhCiEZQIkdIHeHq6ir7RV/RcezYMV2Hq7SlS5ciIyMDIpEIn3zyia7DqbEGDRoER0dH5OXl1fmEmJCahBI5QohcrVq1wsmTJ3Hy5EnMmjVL1+HIVVhYiF9++QUAEBoaChsbG90GVIMZGhpixIgRAIDVq1fj+fPnOo6IEKIMA10HQAjRjsjISLx580Z2PnDgQIjFYgDAkiVL0KpVK9k1b29vmJubo2PHjlqPszL27duH9PR0AMCAAQN0HE3N179/fyxYsAD5+fnYtGkTJkyYoOuQCCEVoBY5QuqINm3aoGPHjrLD2NhYds3b21twzdzcXOEYuZEjR8rK9+3bh88++wzW1tawsrLChAkTkJeXh9TUVISEhMDU1BT29vb4+uuvIZVKBfEwxrBmzRp06NABZmZmMDExgY+PD3799dcydRXZuXMnAH5sWPfu3QXXnj17hrFjx6Jx48YwMjJCgwYN4OHhgfDwcBw/flxQNyUlBaNHj0bjxo1hbGwMW1tbhIWFITk5ucx7SiQS/P777wgMDIS5uTlMTEzg7u5epls3Ozsbs2bNwltvvQUTExM0aNAAAQEBWLlyJUpvcV1ybNutW7dkz87Kygpjx44VJOAA8PTpU0RERMDc3BwWFhaIiIjA06dP5T4jqVSK+fPnw8vLCyYmJhCJRHBxcUHv3r3x119/Ceq2adMGlpaWgmdLCKnmGCGkTmrcuDEDwACwo0ePlrl+9OhR2fURI0bIykeMGCErb9q0qez7omP48OHMzc2tTPmqVasE94+IiChTp+gICwtT6jN4eHjI4ijt3XffVXj/WbNmyerFx8czCwsLufVMTU3ZuXPnZHXz8/NZcHCwwvsWef78OfP09FRYb/DgwYJYi8rNzMyYtbV1ufHm5eWxVq1alanTsmVL2feNGzeW1f+///s/hXF06NBB4XOrX78+KywsVOrPgRCiO9QiRwhRmVgsxh9//IE///wTenr8j5P169fj9evX2LJlC+bNmyeru3LlStn3kZGR+PvvvwEAzZs3x+bNm7F79260a9cOALB161Zs3bq13PcuLCzErVu3AADNmjUTXMvJycHRo0cB8GP9oqOjsW/fPqxYsQIDBgxA/fr1AfCtgiNGjEBmZiYAYOrUqThw4AAWLVoEfX19vHz5EqNGjZK1oC1ZsgT79+8HANSrVw/ffvstYmJisGrVKrRt21b2/jNnzsT169cB8K2dUVFR+PPPP2WtXVu2bJH7+bKzs9GwYUPs2LED3377rdxnt2bNGiQkJAAArK2tsXr1amzfvh0vX76U+5z++ecfAICFhQU2bNiAQ4cO4e+//8bYsWPh4OBQpn7Rs8zNzcX9+/fl3pMQUo3oOpMkhOiGOlrkZs6cKStv0aKFrPyvv/5ijDEmlUpZgwYNGABmYWEhq9u3b19Z3SVLlrCTJ0+ykydPslWrVsnK+/TpU2786enpClu4Xr16xfT09BgA1r17d3bt2jVWUFBQ5h4JCQmye/j6+sriOHnyJAsMDJRdi4uLY4wx5uPjIytbuXKl3LgkEgmztLSU1bty5Yrs2tKlS2Xlffv2lZWjRCtZQkKCrLxkq15mZiZjjLGePXvKypYtWyare/DgQbktcu3atWMAWKNGjVhsbCzLzc0t97l+9dVXsvuUbI0khFRPNNmBEKIyf39/2fdWVlay79u0aQOAH/tlZWWFnJwcWasXANy8eVP2/WeffSb33vLGpynCSo05MzExQXh4ODZu3IiDBw/i7bffhqGhIVq0aIH3338fU6dOhbm5uSCOxMREdOrUSWEsfn5+gvp9+vSRW/fJkyd48eIFAL7VzsvLS3at5PMqea8iZmZm8PX1lZ1bW1vLvs/MzIS5uTnu3r0rKyvZCljy3iV99NFHOHv2LNLS0hAYGAiO49CkSRN069YNU6dOhYeHh6B+6WdJCKneKJEjhKjM3Nxc9n1R1yrAJyRVlZubW+51KysrcBwHxpgscSppzZo1eOedd7B3715cvXoVKSkpSExMRGJiIs6fP4+YmBi1xaIIx3HlnpdW1PVaxMCg+Ed0RQmWont//PHHcHJywqZNm5CQkIBbt27hzp07uHPnDqKjo5GcnAwLCwtZ/ZLPkpZzIaT6ozFyhBCtK9kKdPToUTDGyhx37twp9x4GBgZwd3cHANy+fVvu9TFjxuCff/7B7du38eLFC7Rv3x4AcODAAeTm5gri6Ny5s9w4cnNzZTNSS9bfu3ev3LgaNmwoS4xyc3Nx9epV2bVz587JfQaV0aRJE9n3cXFxcu9dEmMMPXr0wN9//40rV67g5cuXmDx5MgB+jOOZM2cE9YueZf369dG4cWOVYiSEaA+1yBFCtG7o0KGyQfjDhw/HrFmz4O7ujidPnuDWrVvYu3cvevbsiblz55Z7nw4dOuDmzZtISUlBVlaWoIWwadOmGDBgAHx8fODo6IiMjAykpKQA4JObvLw8+Pj4wMvLC0lJSTh+/DgiIiIwcOBAGBoa4t69ezh//jx27twpa6UaNmwYLl26BAD4/PPPkZGRgbZt2yItLQ1//PEHYmNjoaenh8GDB2PFihWyzzp37ly8ePFC8HnCw8NVenYhISHYt28fAGDOnDkwMTGBqakpZsyYIbf+Bx98gAYNGqBTp05wcnJCYWGhIAHMy8sT1E9MTAQABAQEQF9fX6UYCSFapP1heYSQ6kAdkx1Kvq5z586y8pSUFLnvU1J5y48AYHPnzq3wM+zevVtWPzIyUnBNX19f4b2Dg4Nl9cpbfqR03Pn5+SwoKKjCes+ePatw+RGpVCqrX1RecpKComeal5cnmHRRdLi7u8u9T7du3RTGYWdnJ5tEwRhjFy5ckF377bffKnz+hBDdo65VQohOrFu3Dn///Tc6d+4Mc3NzGBkZwcXFBd26dcOSJUvw6aefVniPHj16wN7eHgAQFRUluPb9998jODgYTk5OMDY2hrGxMZo3b44vvvgC27dvl9Vr3bo1EhMTMXbsWDRp0gRGRkawsLCAl5cXxo4di8OHD8vqGhoaYt++fViyZAn8/f1hamoKkUiEZs2aYfTo0bJ6VlZWOHv2LGbMmIHmzZvD2NgY9evXR9u2bbF8+XJs2rSpwvFyihgZGeHgwYMYOnQozMzMYGZmhkGDBincH/fTTz9FWFgYmjZtClNTUxgYGKBRo0YYOnQoTp06JWjFLHqGxsbGKrcYEkK0i2OMpigRQmquRYsWYfr06TAxMcGDBw8EMz2J8goKCuDq6opHjx5h3Lhx+P3333UdEiFECdQiRwip0SZMmABbW1u8fv1aNi6NVN62bdvw6NEjGBsbY+bMmboOhxCiJGqRI4QQQgipoahFjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhqJEjhBCCCGkhvp/D2CkJecjHGMAAAAASUVORK5CYII=\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 2.3.2. Using nonlinear regression to predict the vaules of rate constants for Case1 and Case2\n", + "\n", + "We esimate the unknown model parameters, i.e., rate constants from data by solving a nonlinear regression problem." + ], + "metadata": { + "id": "RqJ2UE6hZnAL" + } + }, + { + "cell_type": "markdown", + "source": [ + "### Main Idea\n", + "\n", + "The core of our approach lies in solving an optimization problem: minimizing the sum of squared differences between the observed data ${y_i} $ and the predictions from our mode ($\\hat{y}_i$),expressed as:\n", + "\n", + "$$\\min_{\\hat{\\theta}} \\quad \\sum (y_i - \\hat{y}_i)^2$$\n", + "\n", + "computationally. This works even if $\\hat{y_i} = f(\\hat{\\theta}, x_i)$ is a nonlinear function, where ${\\theta}$ encapsulates the model parameters - in our context, these are the rate constants of the chemical reactions. The independent variables ${x_i}$ , could include factors like reactant concentrations.\n", + "\n" + ], + "metadata": { + "id": "VCTQmzsnbLAM" + } + }, + { + "cell_type": "code", + "source": [ + "# Experimental data (time in seconds, B/A0 as dimensionless concentration)\n", + "experimental_time = np.array([0, 20, 30, 60, 90, 120, 180]) * 60 # Convert minutes to seconds\n", + "experimental_B_A0 = np.array([0, 2.3, 3.5, 4.2, 3.2, 2.4, 2.0]) / 100 # Convert %w/w to fraction\n", + "\n", + "# Time span for solving ODEs\n", + "tmax = 180 * 60 # 180 minutes in seconds\n", + "time_points = np.linspace(0, tmax, 300) # Create time points for ODE solver\n", + "\n", + "# ODE function for Case 1\n", + "def case1_kinetics(t, y, k1, k2):\n", + " A, B, C = y\n", + " dA_dt = -k1 * A\n", + " dB_dt = k1 * A - k2 * B\n", + " dC_dt = k2 * B\n", + " return [dA_dt, dB_dt, dC_dt]\n", + "\n", + "# ODE function for Case 2\n", + "def case2_kinetics(t, y, k3, k4, k5):\n", + " A, B, C = y\n", + " dA_dt = -k3 * A - k5 * A\n", + " dB_dt = k3 * A - k4 * B\n", + " dC_dt = k4 * B + k5 * A\n", + " return [dA_dt, dB_dt, dC_dt]\n", + "\n", + "# Objective function for least squares fitting\n", + "def objective_function_case1(params):\n", + " k1, k2 = params\n", + " sol = solve_ivp(case1_kinetics, [0, tmax], [1.0, 0.0, 0.0], args=(k1, k2), t_eval=experimental_time)\n", + " B_A0_predicted = sol.y[1] / 1.0\n", + " return B_A0_predicted - experimental_B_A0\n", + "\n", + "def objective_function_case2(params):\n", + " k3, k4, k5 = params\n", + " sol = solve_ivp(case2_kinetics, [0, tmax], [1.0, 0.0, 0.0], args=(k3, k4, k5), t_eval=experimental_time)\n", + " B_A0_predicted = sol.y[1] / 1.0\n", + " return B_A0_predicted - experimental_B_A0\n", + "\n", + "# Initial guesses for the rate constants\n", + "initial_guess_case1 = [1e-4, 1e-3] # Guesses for k1 and k2\n", + "initial_guess_case2 = [1e-5, 1e-4, 1e-4] # Guesses for k3, k4, k5\n", + "\n", + "# Perform least squares fitting\n", + "result_case1 = least_squares(objective_function_case1, initial_guess_case1)\n", + "result_case2 = least_squares(objective_function_case2, initial_guess_case2)\n", + "\n", + "# Optimized rate constants\n", + "optimized_k1, optimized_k2 = result_case1.x\n", + "optimized_k3, optimized_k4, optimized_k5 = result_case2.x\n", + "\n", + "optimized_k1, optimized_k2, optimized_k3, optimized_k4, optimized_k5\n", + "\n", + "# Print the optimized rate constants for Case 1 (Consecutive Reactions)\n", + "print(f\"Optimized rate constants for Case 1:\")\n", + "print(f\"k1 = {optimized_k1:.2e} s^-1\") # Scientific notation with 2 decimal places\n", + "print(f\"k2 = {optimized_k2:.2e} s^-1\")\n", + "\n", + "# Print the optimized rate constants for Case 2 (Competitive Reactions)\n", + "print(f\"\\nOptimized rate constants for Case 2:\")\n", + "print(f\"k3 = {optimized_k3:.2e} s^-1\")\n", + "print(f\"k4 = {optimized_k4:.2e} s^-1\")\n", + "print(f\"k5 = {optimized_k5:.2e} s^-1\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "4Q-kfzzs7i3N", + "outputId": "0dafe040-0fef-4109-ddb6-b8c018b56075" + }, + "execution_count": 53, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Optimized rate constants for Case 1:\n", + "k1 = 4.90e-05 s^-1\n", + "k2 = 1.25e-03 s^-1\n", + "\n", + "Optimized rate constants for Case 2:\n", + "k3 = 3.36e-05 s^-1\n", + "k4 = 1.44e-04 s^-1\n", + "k5 = 5.17e-04 s^-1\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Discussion:** Why do we need to redefine the reaction kinetics of ODEs here rather than using the previous ones?" + ], + "metadata": { + "id": "5ilc2trrIGrG" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer:** When performing nonlinear regression using `scipy.optimize.least_squares` or similar methods, we need to pass the parameters (in this case, the rate constants $k_1, k_2, k_3, k_4, $ and $k_5$) as arguments to the objective function. This function then uses these parameters to solve the ODEs and compare the results with experimental data.\n", + "\n", + "In the original definitions of the ODEs, the rate constants were defined as global variables or were set within the function but not as arguments. This works fine for initial simulations where the rate constants are known and fixed.\n" + ], + "metadata": { + "id": "F53tyPUWIomO" + } + }, + { + "cell_type": "markdown", + "source": [ + "###2.3.3. We can plot nonlinear fit models of Case1 and Case2 as well as the experiment data" + ], + "metadata": { + "id": "zcp6VYM4bcVF" + } + }, + { + "cell_type": "code", + "source": [ + "# Solve ODEs with optimized parameters for Case 1 and Case 2\n", + "solution_optimized_case1 = solve_ivp(case1_kinetics, [0, tmax], [A0, B0, C0], args=(optimized_k1, optimized_k2), t_eval=time_points)\n", + "solution_optimized_case2 = solve_ivp(case2_kinetics, [0, tmax], [A0, B0, C0], args=(optimized_k3, optimized_k4, optimized_k5), t_eval=time_points)\n", + "\n", + "# Extracting B/A0 for both cases\n", + "B_A0_optimized_case1 = solution_optimized_case1.y[1] / A0\n", + "B_A0_optimized_case2 = solution_optimized_case2.y[1] / A0\n", + "\n", + "# Plotting the results\n", + "#plt.figure(figsize=(12, 6))\n", + "\n", + "# Case 1 with optimized parameters\n", + "plt.plot(solution_optimized_case1.t, B_A0_optimized_case1, label='Case1: Optimized Model', color='blue',linewidth=3)\n", + "\n", + "# Case 2 with optimized parameters\n", + "plt.plot(solution_optimized_case2.t, B_A0_optimized_case2, label='Case2: Optimized Model', color='green',linewidth=3)\n", + "\n", + "# Experimental data\n", + "plt.scatter(experimental_time, experimental_B_A0, color='red', label='Experimental Data', zorder=5)\n", + "\n", + "plt.xlabel('Time (seconds)',fontsize=12,fontweight = 'bold')\n", + "plt.ylabel('Dimensionless concentration of B (B/A0)',fontsize=12,fontweight = 'bold')\n", + "plt.title('Comparison of Optimized Models and Experimental Data',loc='left', fontweight='bold',fontsize=14)\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 477 + }, + "id": "iCxa314jH-pi", + "outputId": "9c514665-6f60-4d7d-8ec5-5c6d04458019" + }, + "execution_count": 54, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": "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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 2.3.4. Residual analysis" + ], + "metadata": { + "id": "q2tGHGLIbr3x" + } + }, + { + "cell_type": "markdown", + "source": [ + "Mathematically, if ${y_i}$ is the observed value and ($\\hat{y}_i$) is the predicted value for the $i$ observation, the residual ${e_i}$ is given by:\n", + "$$\n", + "\\underbrace{e_i}_{\\mathrm{residual}} = \\underbrace{y_i}_\\mathrm{observation} - \\underbrace{\\hat{y}_i}_{\\mathrm{prediction}}\n", + "$$" + ], + "metadata": { + "id": "ppcAaG23veHI" + } + }, + { + "cell_type": "code", + "source": [ + "# Calculate residuals for Case 1 and Case 2\n", + "residuals_case1 = experimental_B_A0 - np.interp(experimental_time, solution_optimized_case1.t, B_A0_optimized_case1)\n", + "residuals_case2 = experimental_B_A0 - np.interp(experimental_time, solution_optimized_case2.t, B_A0_optimized_case2)\n", + "\n", + "# Plotting residuals\n", + "plt.figure(figsize=(12, 6))\n", + "\n", + "# Residuals for Case 1\n", + "plt.subplot(1, 2, 1)\n", + "plt.scatter(experimental_time, residuals_case1, color='blue')\n", + "plt.axhline(y=0, color='gray', linestyle='--')\n", + "plt.xlabel('Time (seconds)',fontsize=12,fontweight = 'bold')\n", + "plt.ylabel('Residuals (B/A0)',fontsize=12,fontweight = 'bold')\n", + "plt.title('Residuals for Case1',fontsize=14,fontweight = 'bold')\n", + "\n", + "# Residuals for Case 2\n", + "plt.subplot(1, 2, 2)\n", + "plt.scatter(experimental_time, residuals_case2, color='green')\n", + "plt.axhline(y=0, color='gray', linestyle='--')\n", + "plt.xlabel('Time (seconds)',fontsize=12,fontweight = 'bold')\n", + "plt.title('Residuals for Case2',fontsize=14,fontweight = 'bold')\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 607 + }, + "id": "is4YUR8K74B8", + "outputId": "3fb82a48-1b1c-4252-e50e-3fdec782c433" + }, + "execution_count": 55, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": "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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 2.3.5. Uncertainty analysis\n", + "\n", + "$$\n", + "\\Sigma_{\\theta} \\approx \\hat{\\sigma}_e^2 (J^T J)^{-1}\n", + "$$\n", + "\n", + "where $J$ is the Jacobian of the residuals w.r.t. $\\theta$:\n", + "\n", + "$$\n", + "J_{i,j} = \\frac{\\partial(y_i - \\hat{y}_i)}{\\partial \\theta_j}\n", + "$$" + ], + "metadata": { + "id": "FOp0Add0b2vl" + } + }, + { + "cell_type": "code", + "source": [ + "# Assuming nl_results is the result from scipy.optimize.least_squares\n", + "# For Case 1\n", + "jacobian_case1 = result_case1.jac\n", + "covariance_case1 = np.linalg.inv(jacobian_case1.T @ jacobian_case1) * result_case1.cost / (len(experimental_B_A0) - len(initial_guess_case1))\n", + "standard_error_case1 = np.sqrt(np.diag(covariance_case1))\n", + "\n", + "# For Case 2\n", + "jacobian_case2 = result_case2.jac\n", + "covariance_case2 = np.linalg.inv(jacobian_case2.T @ jacobian_case2) * result_case2.cost / (len(experimental_B_A0) - len(initial_guess_case2))\n", + "standard_error_case2 = np.sqrt(np.diag(covariance_case2))\n", + "\n", + "# Printing the standard errors for both cases\n", + "print(\"Standard errors for Case 1 parameters (k1, k2):\", standard_error_case1)\n", + "print(\"Standard errors for Case 2 parameters (k3, k4, k5):\", standard_error_case2)\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "HPIoHNKAuire", + "outputId": "80b4f86b-ee67-4a1f-e0cb-37065eac073a" + }, + "execution_count": 56, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Standard errors for Case 1 parameters (k1, k2): [9.29231266e-06 2.15044313e-04]\n", + "Standard errors for Case 2 parameters (k3, k4, k5): [4.55894840e-06 5.02493690e-05 1.77319869e-04]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "####Now let's convert it into covariance matrix:" + ], + "metadata": { + "id": "EgMvHjx-cH44" + } + }, + { + "cell_type": "code", + "source": [ + "# Assuming nl_results is the result from scipy.optimize.least_squares\n", + "# Calculate the residuals (e)\n", + "e2_case1 = objective_function_case1(result_case1.x)\n", + "e2_case2 = objective_function_case2(result_case2.x)\n", + "\n", + "# Calculate sigma_e^2\n", + "sigre_case1 = (e2_case1.T @ e2_case1) / (len(e2_case1) - len(result_case1.x))\n", + "sigre_case2 = (e2_case2.T @ e2_case2) / (len(e2_case2) - len(result_case2.x))\n", + "\n", + "# Calculate covariance matrix\n", + "covariance_matrix_case1 = sigre_case1 * np.linalg.inv(result_case1.jac.T @ result_case1.jac)\n", + "covariance_matrix_case2 = sigre_case2 * np.linalg.inv(result_case2.jac.T @ result_case2.jac)\n", + "\n", + "print(\"Covariance matrix for Case 1:\\n\", covariance_matrix_case1)\n", + "print(\"\\nCovariance matrix for Case 2:\\n\", covariance_matrix_case2)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "7NxMCuM1Nxq9", + "outputId": "36faa646-0b4b-47d0-bb47-98fdac38f919" + }, + "execution_count": 57, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Covariance matrix for Case 1:\n", + " [[1.72694149e-10 3.76535904e-09]\n", + " [3.76535904e-09 9.24881132e-08]]\n", + "\n", + "Covariance matrix for Case 2:\n", + " [[ 4.15680210e-11 -3.09765719e-10 1.41498128e-09]\n", + " [-3.09765719e-10 5.04999817e-09 -1.66221176e-08]\n", + " [ 1.41498128e-09 -1.66221176e-08 6.28846721e-08]]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 2.3.6. Fit statistics for Case1 and Case2\n", + "\n", + "We use SSR, MSE and $R^2$ to evaluate the fitting results." + ], + "metadata": { + "id": "KQrqU-uqWoP6" + } + }, + { + "cell_type": "code", + "source": [ + "def calculate_metrics(experimental, predicted):\n", + " residuals = experimental - predicted\n", + " ssr = np.sum(residuals**2)\n", + " mse = np.mean(residuals**2)\n", + " total_variance = np.sum((experimental - np.mean(experimental))**2)\n", + " r_squared = 1 - (ssr / total_variance)\n", + " return ssr, mse, r_squared\n", + "\n", + "# Calculate SSR, MSE, and R^2 for Case 1\n", + "B_A0_predicted_case1 = np.interp(experimental_time, solution_optimized_case1.t, B_A0_optimized_case1)\n", + "ssr_case1, mse_case1, r_squared_case1 = calculate_metrics(experimental_B_A0, B_A0_predicted_case1)\n", + "\n", + "# Calculate SSR, MSE, and R^2 for Case 2\n", + "B_A0_predicted_case2 = np.interp(experimental_time, solution_optimized_case2.t, B_A0_optimized_case2)\n", + "ssr_case2, mse_case2, r_squared_case2 = calculate_metrics(experimental_B_A0, B_A0_predicted_case2)\n", + "\n", + "# Print the fit statistics for both cases explicitly\n", + "print(f\"Fit statistics for Case 1:\")\n", + "print(f\"SSR (Sum of Squared Residuals): {ssr_case1:.2e}\")\n", + "print(f\"MSE (Mean Squared Error): {mse_case1:.2e}\")\n", + "print(f\"R-squared: {r_squared_case1:.2f}\")\n", + "\n", + "print(f\"\\nFit statistics for Case 2:\")\n", + "print(f\"SSR (Sum of Squared Residuals): {ssr_case2:.2e}\")\n", + "print(f\"MSE (Mean Squared Error): {mse_case2:.2e}\")\n", + "print(f\"R-squared: {r_squared_case2:.2f}\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "EyMewskuxYQf", + "outputId": "39d653f0-2858-4dc5-bb78-fc30cc1d79cb" + }, + "execution_count": 58, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Fit statistics for Case 1:\n", + "SSR (Sum of Squared Residuals): 1.51e-04\n", + "MSE (Mean Squared Error): 2.16e-05\n", + "R-squared: 0.86\n", + "\n", + "Fit statistics for Case 2:\n", + "SSR (Sum of Squared Residuals): 6.04e-05\n", + "MSE (Mean Squared Error): 8.63e-06\n", + "R-squared: 0.94\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "###According the fit statistics, Case2 has lower SSR, MSE and higher $R^2$, therefore, we can conclude that Case2 fits better for the experiment data." + ], + "metadata": { + "id": "ioUQNKC-cTTE" + } + }, + { + "cell_type": "markdown", + "source": [ + "## Discussion Question" + ], + "metadata": { + "id": "wZ8zqKhBnvSG" + } + }, + { + "cell_type": "markdown", + "source": [ + "**1. Discussion**:\n", + "\n", + "Why is nonlinear regression preferred over linear regression for estimating rate constants in chemical kinetics?\n" + ], + "metadata": { + "id": "0ixvdJLjEPcK" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + " **Answer**: Nonlinear regression is preferred because most chemical kinetics follow nonlinear models, especially when involving complex reactions like consecutive or competitive reactions. Linear regression could oversimplify these models, leading to inaccurate parameter estimation. Nonlinear regression, on the other hand, can directly fit the nonlinear models to the data, providing more accurate and meaningful estimates of the rate constants.\n", + "\n" + ], + "metadata": { + "id": "dR1w53q_HT4Y" + } + }, + { + "cell_type": "markdown", + "source": [ + "**2. Discussion**: How can the residuals of a fitted model inform us about the model's adequacy?\n" + ], + "metadata": { + "id": "UFhzEdoDHfCs" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + " **Answer**: Residuals, which are the differences between the observed and predicted values, can reveal patterns or trends that the model fails to capture. If the residuals appear randomly distributed around zero, it suggests that the model adequately captures the data's trend. Systematic patterns in the residuals, like trends or cycles, might indicate model inadequacies, such as missing variables or incorrect functional forms.\n" + ], + "metadata": { + "id": "oEG4enPvHh8l" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "**3. Discussion**: What does a high $R^2$ value signify in the context of reaction kinetics modeling?\n" + ], + "metadata": { + "id": "1DVYcq52HkI3" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + " **Answer**: A high $R^2$ value, close to 1, signifies that a large proportion of the variance in the observed data is accounted for by the model. In the context of reaction kinetics, this means the model effectively captures the relationship between the reactants and products over time. However, $R^2$ alone should not be the sole criterion for model adequacy, as it does not necessarily imply causation or correctness of the model." + ], + "metadata": { + "id": "BWS8OWJ_HoR0" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "**4. Discussion**: Why is it important to understand the uncertainty in estimated parameters in chemical kinetics?\n" + ], + "metadata": { + "id": "xh6r84ncHvpe" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + " **Answer**: Understanding uncertainty in estimated parameters is crucial for several reasons. First, it helps in assessing the reliability of the model predictions. Second, it aids in comparing different models or reaction mechanisms by providing a quantitative measure of confidence in the parameter estimates. Lastly, it is vital for practical applications, like designing reactors or optimizing conditions, where precise control of reaction rates is necessary." + ], + "metadata": { + "id": "7QA03MTrHyGb" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "**5. Discussion**: Discuss the limitations of using the proposed kinetic models (Case1 and Case2) for the isomerization reaction.\n" + ], + "metadata": { + "id": "WmUYjlVRHz7D" + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + " **Answer**: The proposed models assume pseudo first-order kinetics and simplified reaction pathways, which might not capture all complexities of the actual reaction, especially in the presence of catalysts or under varying temperature and pressure conditions. Also, the models assume constant rate constants, which might vary with changes in reaction conditions. Furthermore, the models do not account for possible side reactions or the formation of unexpected intermediates, which could be significant in real-world scenarios." + ], + "metadata": { + "id": "riWt-svgH1Sj" + } + } + ] +} \ No newline at end of file