{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Second Order Model\n", "\n", "In this notebook we will fit a higher-order state space model to the step test data. The learning goals for this notebook are to \n", "\n", "* Review the two-state model for the temperature control lab\n", "* Reformulate systems of first order differential equations in state space\n", "* Simulate the step response of state space models\n", "* Fit a model to step test data using multiple fitting criteria." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Step Test Data\n", "\n", "Using a Temperature Control Lab device initially at steady state at ambient room temperature, the following device settings were used to induce a step response in $T_1$ and $T_2$. \n", "\n", "| P1 | P2 | U1 | U2 |\n", "| :--: | :--: | :--: | :--: |\n", "| 200 | 100 | 50 | 0 |\n", "\n", "Data was recorded for 800 seconds and saved to a .csv data file. Some noise and data dropouts are evident in the data. The data file is accessible at the link given in the code cell below. \n", "\n", "The challenge is to develop a first-principles models that reproduces the system measured response shown below." ] }, { "cell_type": "code", "execution_count": 198, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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T1T2Q1Q2
Time
0.0021.54320.89850.00.0
1.0021.54320.89850.00.0
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" ], "text/plain": [ " T1 T2 Q1 Q2\n", "Time \n", "0.00 21.543 20.898 50.0 0.0\n", "1.00 21.543 20.898 50.0 0.0\n", "2.01 21.543 20.898 50.0 0.0\n", "3.01 21.543 20.931 50.0 0.0\n", "4.00 21.543 20.931 50.0 0.0" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "data_file = \"https://raw.githubusercontent.com/jckantor/cbe30338-book/main/notebooks/data/tclab-data-example.csv\"\n", "data = pd.read_csv(data_file)\n", "data = data.set_index(\"Time\")\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Pandas library includes a highly functional method for plotting data." ] }, { "cell_type": "code", "execution_count": 199, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 199, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data.plot(y=[\"T1\", \"T2\"], figsize=(10, 3), grid=True, ylabel=\"deg C\")\n", "data.plot(y=[\"Q1\", \"Q2\"], figsize=(10, 3), grid=True, ylabel=\"% of power range\", ylim=(-5, 105))" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## Two-State Model\n", "\n", "For this model we no longer assume the heater and sensor are at the same temperature. To account for differing temperatures, we introduce $T_{H,1}$ to denote the temperature of heater one and $T_{S,1}$ to denote the temperature of the corresponding sensor. We further assume the sensor exchanges heat only with the heater, and heat transfer to the surroundings is dominated by the heat sink attached to the heater.\n", "\n", "This motivates a model\n", "\n", "$$\n", "\\begin{align}\n", "C^H_p\\frac{dT_{H,1}}{dt} & = U_a(T_{amb} - T_{H,1}) + U_b(T_{S,1} - T_{H,1}) + \\alpha P_1u_1\\\\\n", "C^S_p\\frac{dT_{S,1}}{dt} & = U_b(T_{H,1} - T_{S,1}) \n", "\\end{align}\n", "$$\n", "\n", "where $C^H_p$ and $C^S_p$ are the heat capacities of the heater and sensor, respectively, and $U_b$ is a new heat transfer coefficient characterizing the exchange of heat between the heater and sensor. Where the temperature measured and recorded by the Arduino is given by\n", "\n", "$$T_1 = T_{S,1}$$\n", "\n", "The following cell creates a simulation of heater/sensor combination." ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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TH1TS1T1
Time
0.0021.00000021.00000021.000000
1.0021.31684721.00781621.007816
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801 rows × 3 columns

\n", "
" ], "text/plain": [ " TH1 TS1 T1\n", "Time \n", "0.00 21.000000 21.000000 21.000000\n", "1.00 21.316847 21.007816 21.007816\n", "2.01 21.630650 21.030852 21.030852\n", "3.01 21.935475 21.067561 21.067561\n", "4.00 22.231957 21.115691 21.115691\n", "... ... ... ...\n", "796.00 52.948664 52.946492 52.946492\n", "797.01 52.949058 52.947023 52.947023\n", "798.01 52.949466 52.947455 52.947455\n", "799.00 52.949892 52.947773 52.947773\n", "800.01 52.950354 52.947967 52.947967\n", "\n", "[801 rows x 3 columns]" ] }, "execution_count": 200, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp\n", "import pandas as pd\n", "\n", "# known parameters\n", "T_amb = 21 # deg C\n", "alpha = 0.00016 # watts / (units P1 * percent U1)\n", "P1 = 200 # P1 units\n", "\n", "# adjustable parameters\n", "CpH = 5 # joules/deg C\n", "CpS = 1 # joules/deg C\n", "Ua = 0.05 # watts/deg C\n", "Ub = 0.05 # watts/deg C\n", "\n", "# initial conditions\n", "TH1 = T_amb\n", "TS1 = T_amb\n", "IC = [TH1, TS1]\n", "\n", "# input values\n", "U1 = 50 # steady state value of u1 (percent)\n", "\n", "# extract data from experiment\n", "t_expt = data.index\n", "\n", "def tclab_ode(param):\n", " # unpack the adjustable parameters\n", " CpH, CpS, Ua, Ub = param\n", "\n", " # model solution\n", " def deriv(t, y):\n", " TH1, TS1 = y\n", " dTH1 = (-Ua*(TH1 - T_amb) + Ub*(TS1 - TH1) + alpha*P1*U1)/CpH\n", " dTS1 = Ub*(TH1 - TS1)/CpS\n", " return [dTH1, dTS1]\n", "\n", " soln = solve_ivp(deriv, [min(t_expt), max(t_expt)], IC, t_eval=t_expt) \n", "\n", " # create dataframe with predictions\n", " pred = pd.DataFrame(columns=[\"Time\"])\n", " pred[\"Time\"] = t_expt\n", " pred = pred.set_index(\"Time\")\n", " \n", " # report the model temperatures\n", " pred[\"TH1\"] = soln.y[0]\n", " pred[\"TS1\"] = soln.y[1]\n", " \n", " # report the prediced measurement\n", " pred[\"T1\"] = pred[\"TS1\"]\n", " \n", " return pred\n", " \n", "pred = tclab_ode(param=[CpH, CpS, Ua, Ub])\n", "pred" ] }, { "cell_type": "code", "execution_count": 202, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pred[\"T1\"].plot(grid=True, ylabel=\"deg C\", title=\"Model Prediction\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's compare the predicted measurement to the actual measurement. How did we do?" ] }, { "cell_type": "code", "execution_count": 203, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 203, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = pred.plot(y=[\"T1\"], ylabel=\"deg C\")\n", "data.plot(ax=ax, y=[\"T1\"], grid=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## State Space Model\n", "\n", "Our two-state model for the temperature control lab is given by \n", "\n", "$$\n", "\\begin{align}\n", "C^H_p\\frac{dT_{H,1}}{dt} & = U_a(T_{amb} - T_{H,1}) + U_b(T_{S,1} - T_{H,1}) + \\alpha P_1u_1\\\\\n", "C^S_p\\frac{dT_{S,1}}{dt} & = U_b(T_{H,1} - T_{S,1}) \n", "\\end{align}\n", "$$\n", "\n", "The initial steady state is $T_{amb}$. So let's write the dependent variables as excursions from the ambient temperature.\n", "\n", "$$\n", "\\begin{align}\n", "C^H_p\\frac{d(T_{H,1} - T_{amb})}{dt} & = U_a(T_{amb} - T_{H,1}) + U_b((T_{S,1} - T_{amb}) - (T_{H,1} - T_{amb})) + \\alpha P_1u_1\\\\\n", "C^S_p\\frac{d(T_{S,1} - T_{amb})}{dt} & = U_b(T_{H,1} - T_{amb}) - (T_{S,1} - T_{amb})\n", "\\end{align}\n", "$$\n", "\n", "Then divide by the heat capacities.\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{d(T_{H,1} - T_{amb})}{dt} & = -\\frac{U_a+U_b}{C^H_p}(T_{H,1} - T_{amb}) + \\frac{U_b}{C^H_p}(T_{S,1} - T_{amb}) + \\frac{\\alpha P_1}{C^H_p}u_1 \\\\\n", "\\frac{d(T_{S,1} - T_{amb})}{dt} & = \\frac{U_b}{C^S_p}((T_{H,1} - T_{amb}) - \\frac{U_b}{C^S_p} (T_{S,1} - T_{amb})) \n", "\\end{align}\n", "$$\n", "\n", "The two-state model can be rewritten using vectors to collect the states, inputs, measurable outputs, and arrays to collect the coefficients of the differential equations. \n", "\n", "$$\n", "\\begin{align}\n", "\\frac{d}{dt}\\underbrace{\\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix}}_x & = \n", "\\underbrace{\\begin{bmatrix} -\\frac{U_a+U_b}{C^H_p} & \\frac{U_b}{C^H_p} \\\\ \\frac{U_b}{C^S_p} & - \\frac{U_b}{C^S_p}\\end{bmatrix}}_A \n", "\\underbrace{\\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix}}_x + \n", "\\underbrace{\\begin{bmatrix} \\frac{\\alpha P_1}{C^H_p} \\\\ 0 \\end{bmatrix}}_B \n", "\\underbrace{\\begin{bmatrix} u_1 \\end{bmatrix}}_u \\\\\n", "\\\\\n", "\\underbrace{\\begin{bmatrix} T_{S,1} - T_{amb} \\end{bmatrix}}_y & = \n", "\\underbrace{\\begin{bmatrix}0 & 1 \\end{bmatrix}}_C \n", "\\underbrace{\\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix}}_x\n", "\\end{align}\n", "$$\n", "\n", "In other words, we can write the temperature control lab model as a **state-space model**\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{dx}{dt} & = A x + B u \\\\\n", "y & = C x\n", "\\end{align}\n", "$$\n", "\n", "where the state space variables are the deviations of temperature from the ambient $T_{amb}$\n", "\n", "$$\n", "\\begin{align}\n", "u & = \\begin{bmatrix} u_1 \\end{bmatrix} && \\text{inputs} \\\\\n", "\\\\\n", "x & = \\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix} && \\text{states} \\\\\n", "\\\\\n", "y & = \\begin{bmatrix} T_{S,1} - T_{amb} \\end{bmatrix} && \\text{measurements} \\\\\n", "\\end{align}\n", "$$\n", "\n", "and parameters are embedded in the arrays\n", "\n", "$$\n", "\\begin{align}\n", "A = \\begin{bmatrix} -\\frac{U_a+U_b}{C^H_p} & \\frac{U|_b}{C^H_p} \\\\ \\frac{U_b}{C^S_p} & - \\frac{U_b}{C^S_p}\\end{bmatrix}\n", "\\quad\n", "B = \\begin{bmatrix} \\frac{\\alpha P_1}{C^H_p} \\\\ 0 \\end{bmatrix} \n", "\\quad\n", "C = \\begin{bmatrix}0 & 1 \\end{bmatrix} \\\\\n", "\\end{align}\n", "$$\n", "\n", "By using the notation and techniques of linear algebra, **state-space models** provide a compact means of representing complex systems. This example consists of $m=1$ inputs, $n=2$ states, and $p=1$ outputs." ] }, { "cell_type": "code", "execution_count": 174, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pi = 3.142 isn't that nice\n" ] } ], "source": [ "print(f\"pi = {np.pi:8.3f} isn't that nice\")" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ua=0.05\n" ] } ], "source": [ "print(f\"{Ua=}\")" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "A=array([[-0.02, 0.01],\n", " [ 0.05, -0.05]])\n", "\n", "B=array([[0.0064],\n", " [0. ]])\n", "\n", "C=array([[0, 1]])\n" ] } ], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp\n", "import pandas as pd\n", "\n", "# known parameters\n", "T_amb = 21 # deg C\n", "alpha = 0.00016 # watts / (units P1 * percent U1)\n", "P1 = 200 # P1 units\n", "\n", "# adjustable parameters\n", "CpH = 5 # joules/deg C\n", "CpS = 1 # joules/deg C\n", "Ua = 0.05 # watts/deg C\n", "Ub = 0.05 # watts/deg C\n", "\n", "# array parameters\n", "A = np.array([[-(Ua + Ub)/CpH, Ub/CpH], [Ub/CpS, -Ub/CpS]])\n", "B = np.array([[alpha*P1/CpH], [0]])\n", "C = np.array([[0, 1]])\n", "\n", "print(f\"\\n{A=}\")\n", "print(f\"\\n{B=}\")\n", "print(f\"\\n{C=}\")" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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x1x2yTH1TS1T1
Time
0.000.0000000.0000000.00000021.00000021.00000021.000000
1.000.2989180.0155680.01556821.29891821.01556821.015568
2.010.5876240.0597840.05978421.58762421.05978421.059784
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4.001.1239650.2150410.21504122.12396521.21504121.215041
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" ], "text/plain": [ " x1 x2 y TH1 TS1 T1\n", "Time \n", "0.00 0.000000 0.000000 0.000000 21.000000 21.000000 21.000000\n", "1.00 0.298918 0.015568 0.015568 21.298918 21.015568 21.015568\n", "2.01 0.587624 0.059784 0.059784 21.587624 21.059784 21.059784\n", "3.01 0.862058 0.127671 0.127671 21.862058 21.127671 21.127671\n", "4.00 1.123965 0.215041 0.215041 22.123965 21.215041 21.215041" ] }, "execution_count": 179, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "# input values\n", "U1 = 50 # steady state value of u1 (percent)\n", "def u(t):\n", " return np.array([U1])\n", "\n", "# extract data from experiment\n", "t_expt = data.index\n", "\n", "def tclab_ss(A, B, C):\n", " \n", " IC = [0, 0]\n", "\n", " # model solution\n", " def deriv(t, x):\n", " dxdt = A @ x + B @ u(t)\n", " return dxdt\n", "\n", " soln = solve_ivp(deriv, [min(t_expt), max(t_expt)], IC, t_eval=t_expt) \n", " \n", " # create dataframe with predictions\n", " pred = pd.DataFrame(columns=[\"Time\"])\n", " pred[\"Time\"] = t_expt\n", " pred = pred.set_index(\"Time\")\n", " \n", " # get the state variables\n", " pred[\"x1\"] = soln.y[0]\n", " pred[\"x2\"] = soln.y[1]\n", " \n", " pred[\"y\"] = pred[\"x2\"]\n", " \n", " # convert back to model temperatures\n", " pred[\"TH1\"] = pred[\"x1\"] + T_amb\n", " pred[\"TS1\"] = pred[\"x2\"] + T_amb\n", " \n", " # report the predicated measurement\n", " pred[\"T1\"] = pred[\"TS1\"]\n", " \n", " return pred\n", " \n", "pred = tclab_ss(A, B, C)\n", "\n", "pred.head()" ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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krJKIpOJw+FAqldDpdNe9rlKpbnidiNyXsa4J/9hfgPXfFaDiJxu3RQf7YtqQcNwRr8PI6CD2chB5OIfDR15eHiIiIqBSqTB27FikpKSgb9++9usZGRkICwtDYGAgJk2ahFdeeQVhYWHXfT2z2Qyz2Wz/2GQyOVoSEUmsuKoe7+8rwEf7L6D26oqjkUFqzB0bjamDw9E/zJ+rjBKRnUyIn+7zeGPbt29HXV0dBgwYgLKyMrz88sv44YcfkJubi5CQEGzatAn+/v6IiYlBfn4+nnvuOVgsFmRlZUGlUrX5mm3NIwEAo9GIgICAjreMiLqVEAJHLlbhg+8LsO14CSxXn5EdpNPgiaR+mJmgh1Ihl7hKIuopJpMJWq22Xe/fDoWPn6utrUW/fv2wYsUKLF++/JrrJSUliImJQVpaGubMmdPma7TV8xEVFcXwQeSEhBA4UWTC1uPF2Hq8pNUmbuP6BuP/3doXkweGsZeDyAM5Ej469aitn58fEhISkJeX1+Z1vV6PmJiY614HmueIXK9XhIicw5XaRmw8cAGfHinC+fJa+3k/bwXuGKrDwomxiO+tlbBCInIlnQofZrMZp06dwi233NLm9YqKChQWFkKv13fmyxCRROobrfj7d/n4a8Y5VJubH5H18ZJjyqBw3JWox+RBYfDx4jLnROQYh8LH008/jVmzZiE6OhoGgwEvv/wyTCYT5s+fj5qaGiQnJ+Pee++FXq9HQUEBVq9ejdDQUNxzzz3dVT8RdQOrTeCTI5ewZtcZ+w6yQyMCsGBCH8xI0HPXWCLqFId+g1y6dAkPPvggysvL0atXL4wbNw779+9HTEwM6uvrkZOTgw8++ABVVVXQ6/WYPHkyNm3aBI1G0131E1EXstkEvjxRgv9NP4Nzl5uHV3oHqrFi+kDMSozg7rFE1CU6NeG0OzgyYYWIuoaxrgkfZxVi44GL9jkdgb5eWDK5Px4aF8OhFSL6RT024ZSIXJfNJrA/vwL/PnwJX54oQUNT8yqkGpUS/3lLLBZOjEWAj5fEVRKRO2L4IPIwQgh8nl2MNelncPFKnf38IJ0GD42LwewRvTmng4i6FX/DEHmQ3GIjkrfk4lBBJYDmXo67hkXgvtGRGBEVyPU5iKhHMHwQeYCqukasST+DD/dfgE0Aai8FltzWHwtvjoXam/M5iKhnMXwQubFGiw3/OlyINelncOXqRm8zE/V49s7BiAhUS1wdEXkqhg8iN9TQZMW/DhfirxnnUGxsXqdjQLg/kn81FBP6hUpcHRF5OoYPIjdS12jBxgMX8bc953G5unnPpDCNCk8k9cND42LgxY3eiMgJMHwQuYEaswUffF+A9/bmo+Lq8EqE1gdPJPXDfaOjuE4HETkVhg8iF7fjRCle2HICZabmno7oYF8sntwP94yIhLeSPR1E5HwYPohcVJmpAS98nosduaUAgJgQXyydEodfDYuAksMrROTEGD6IXIzNJpB2qBCp20+husECpVyGxyb1xZO3xXF4hYhcAsMHkQs5d7kGqz7NwcH8KwCAYZFavHpvIgbruQ8SEbkOhg8iF2Csb8JbX+fh/X0FaLIKqL0UePqOgVgwoQ8U3GmWiFwMwweRE7NYbUg71HqRsKSBvfBfd8cjKthX4uqIiDqG4YPISe3Nu4yXt57C6bJqAED/MH88O3MwJg8Mk7gyIqLOYfggcjKlxgb88bMc7D5lAAAE+nrhd7cPwNyx0VwkjIjcAsMHkRPZdrwEqzfnwFjfBKVchkfG98HSKXHQ+npJXRoRUZdh+CByAqaGJiR/notPjxYBABIjtVjzH8PQP0wjcWVERF2P4YNIYgfzr+B3m7JRVFUPuQxYPLk/npoSxyEWInJbDB9EEmm02PC/u8/gr5nnIAQQFazG2vuHY1RMsNSlERF1K4YPIgnkFhvxzMfHcbLEBAC4b1QkXvjVUPir+CNJRO6Pv+mIelCjxYa3vs7DXzLOwWITCPL1QuqcBEyP10tdGhFRj2H4IOohxy9V4ZmPj9vX7ZgRr8NLd8ejl0YlcWVERD2L4YOomzU0WfG/6Wfwzt7zsAkgxM8bL90dj5mJ7O0gIs/E8EHUjbIuVOLpj48hv7wWADBrWASSZw1BiD97O4jIczF8EHWTjw5cQPKWXDRZBcIDVHhldgJuHxIudVlERJJj+CDqYo0WG178IhcfHbgIALgzQYfUOYnQqrlKKRERwPBB1KUuV5ux6KMsHCqohEwGPD1tIBYl9YNMxm3viYhaMHwQdZEjFyux+KMjKDE2QKNS4o0Hh+O2QRxmISL6OYYPok4SQuDdvfl4bccPsNgE+ob64e1HRqN/mL/UpREROSWGD6JOqKprxNMfH8PuUwYAwF2JeqTOSYDGh/M7iIiuh+GDqIOyLlTiqX8eRVFVPbyVcjx/1xDMGxvN+R1ERL+A4YPIQT8fZukT4ou35o5EfG+t1KUREbkEh/bsTk5Ohkwma3XodDr7dSEEkpOTERERAbVajaSkJOTm5nZ50URSqWu04P/9IwuvfHkKFpvAXYl6fPHkRAYPIiIHOBQ+AGDo0KEoKSmxHzk5OfZrr7/+OtasWYO33noLhw4dgk6nw9SpU1FdXd2lRRNJoaLGjAffOYD0k2XwVsrx8ux4/N+DIzi/g4jIQQ4PuyiVyla9HS2EEFi7di2effZZzJkzBwCwYcMGhIeHY+PGjXjsscc6Xy2RRC5W1GH++oPIL69FoK8X3ps/BqNigqQui4jIJTnc85GXl4eIiAjExsbigQcewPnz5wEA+fn5KC0txbRp0+z3qlQqTJo0Cfv27bvu65nNZphMplYHkTM5UWTEnHX7kF9ei96Bavz78QkMHkREneBQ+Bg7diw++OAD7Ny5E++88w5KS0sxYcIEVFRUoLS0FAAQHt56UaXw8HD7tbakpqZCq9Xaj6ioqA40g6h7fJtXjgfe3o/yGjMG6TT4dNEErt9BRNRJDg27zJgxw/7/CQkJGD9+PPr164cNGzZg3LhxAHDNY4ZCiBs+erhq1SosX77c/rHJZGIAIafweXYRnv74GJqsAuP7huBvj4xCAOd3EBF1msPDLj/l5+eHhIQE5OXl2eeB/LyXw2AwXNMb8lMqlQoBAQGtDiIpCSHw52/OYmlaNpqsAjMT9Xh/4RgGDyKiLtKp8GE2m3Hq1Cno9XrExsZCp9MhPT3dfr2xsRGZmZmYMGFCpwsl6glmixXL/3UM/73zNABg4c2x+L8HRkClVEhcGRGR+3Bo2OXpp5/GrFmzEB0dDYPBgJdffhkmkwnz58+HTCbDsmXLkJKSgri4OMTFxSElJQW+vr6YO3dud9VP1GXKa8x47B9ZyLpQCYVchhd/NRQPjYuRuiwiIrfjUPi4dOkSHnzwQZSXl6NXr14YN24c9u/fj5iY5l/QK1asQH19PRYtWoTKykqMHTsWu3btgkaj6ZbiibrK6dJq/OeGQ7hUWY8AHyX+Mm8UJsaFSl0WEZFbkgkhhNRF/JTJZIJWq4XRaOT8D+oRGacNWLLxKGrMFvQJ8cV7C8agXy8+0UJE5AhH3r+5twt5tPSTZVj0URaarALj+gZj3bxRCPLzlrosIiK3xvBBHmv3T4LHXYl6rPmP4fBWdmoONhERtQPDB3mk3SfL8MRPgsfa+4dDqWDwICLqCfxtSx7nq1M/Bo+ZDB5ERD2Ov3HJo3z9Qxme+PBIc/BI0OMNBg8ioh7H37rkMb75wYDH/3EEjVYbZibosfYBBg8iIinwNy95hG9+MOCxf2Sh0WrDnQk6rH1gOLwYPIiIJMHfvuT2dp8sswePGfE6vPHACAYPIiIJ8WkXcmvbjpdgadpRWGwCM+J1ePNBBg8iIqkxfJDb+iTrEp759zHYBDB7eAT+575hnONBROQEGD7ILX104AKe3XwCAPDAmCi8ck8CFHKZxFURERHA8EFu6O/f5uOlrScBAAsm9MELs4ZAJmPwICJyFgwf5Fb+lnkOqdt/AAA8PqkfVk4fyOBBRORkGD7Ibfwl4yxe33EaALB0ShyW3R7H4EFE5IQYPsgtfHy40B48fj91AJ6cEidxRUREdD2c+k8u77uz5Vj1aQ4AYFFSPwYPIiInx/BBLu1MWTUe/zALFpvAr4ZF4OlpA6UuiYiIfgHDB7ksQ3UDfrP+EKobLBjTJwj/fV8i5HyclojI6TF8kEuqa7TgP98/jKKqesSG+uHth0dDpVRIXRYREbUDwwe5HIvVhic3HkVOkRHBft5Yv2AMgvy8pS6LiIjaieGDXIoQAslf5OKrHwxQKeV455FR6BPqJ3VZRETkAIYPcil/23MeH+6/CJkMeOOB4RgVEyx1SURE5CCGD3IZW44V49Wrq5c+N3MIpsfrJa6IiIg6guGDXML+8xV4+l/HAAALb47FwomxEldEREQdxfBBTu9ksQmPbjiMRqsNM+J1+OPMwVKXREREncDwQU6t8Eod5q8/iGqzBTfFBuN/7x/OtTyIiFwcwwc5rYoaM+b//SAuV5sxSKfBO4+Mho8X1/IgInJ1DB/klOoaLVi44TDOl9eid6AaGxbeBK3aS+qyiIioCzB8kNMRQmDFv4/jWGEVgny9sGHhTQgP8JG6LCIi6iIMH+R03t2bj63HS6CUy/C3h0ejf5i/1CUREVEXYvggp7LvbDlSt58CADx31xDcFMtFxIiI3A3DBzmNoqp6LPnnUdgEMGdkbzwyPkbqkoiIqBswfJBTMFuseOLDLFypbUR87wCk3JMAmYyP1BIRuaNOhY/U1FTIZDIsW7bMfm7BggWQyWStjnHjxnW2TnJzL31xEscvGRHo64V180bxkVoiIjem7OgnHjp0CG+//TYSExOvuTZ9+nSsX7/e/rG3N7c7p+v79MglfHSgebO4tfcPR1Swr9QlERFRN+pQz0dNTQ3mzZuHd955B0FBQddcV6lU0Ol09iM4mJMGqW0/lJqwenMOAOCp2+KQNDBM4oqIiKi7dSh8LF68GDNnzsTtt9/e5vWMjAyEhYVhwIABePTRR2EwGK77WmazGSaTqdVBnsHU0IQnPjyChiYbbh3QC09NiZO6JCIi6gEOD7ukpaXhyJEjOHToUJvXZ8yYgfvuuw8xMTHIz8/Hc889h9tuuw1ZWVlQqVTX3J+amooXX3zR8crJpQkh8MzHx5B/dQXTtfcPh4J7thAReQSZEEK09+bCwkKMHj0au3btwrBhwwAASUlJGD58ONauXdvm55SUlCAmJgZpaWmYM2fONdfNZjPMZrP9Y5PJhKioKBiNRgQEBDjYHHIVb+85h5Qvf4C3Qo6PHx+PYVGBUpdERESdYDKZoNVq2/X+7VDPR1ZWFgwGA0aNGmU/Z7VasWfPHrz11lswm81QKFo/paDX6xETE4O8vLw2X1OlUrXZI0Lu68D5Cry24zQA4LlZQxg8iIg8jEPhY8qUKcjJyWl17je/+Q0GDRqElStXXhM8AKCiogKFhYXQ6/Wdq5TcgsHUgCX/PAqrTeCeEb3x0NhoqUsiIqIe5lD40Gg0iI+Pb3XOz88PISEhiI+PR01NDZKTk3HvvfdCr9ejoKAAq1evRmhoKO65554uLZxcj8Vqw5J/HsXlajMGhmvwyj3xXEiMiMgDdXidj7YoFArk5OTggw8+QFVVFfR6PSZPnoxNmzZBo9F05ZciF/Q/u87gYP4V+KuUWPfQSPh6d+lfPyIichGd/u2fkZFh/3+1Wo2dO3d29iXJDX11qgx/zTwHAHj914no24s71RIReSru7ULdrvBKHZb/6xgAYMGEPrgzgfN/iIg8GcMHdauWeR7G+iYMjwrE6jsHS10SERFJjOGDutW6jHM4VliFAB8l/jxvJLyV/CtHROTp+E5A3Sa32Ig3vmpe3+Wlu+PRO1AtcUVEROQMGD6oW5gtVizfdAwWm8D0oTrcPTxC6pKIiMhJMHxQt1i7Ow+ny6oR4ufN9TyIiKgVhg/qclkXKvG3q4/VpsxJQIg/l88nIqIfMXxQl6prtODpj4/BJoA5I3rjjqE6qUsiIiInw/BBXer1HaeRX14LXYAPXpg1VOpyiIjICTF8UJfZd7Yc7+8rAAC89utEaH29pC2IiIicEsMHdYnqhiY88+/jAIB5Y6MxaUAviSsiIiJnxfBBXeK/tp5EUVU9ooLVXMWUiIhuiOGDOu2rU2X41+FLkMmAP903HH4q7lZLRETXx/BBnVJZ24g/fJoDAPjtxFjcFBsscUVEROTsGD6oU577/AQuV5vRP8wfv582UOpyiIjIBTB8UId9cawYW4+XQCGX4U/3DYOPl0LqkoiIyAUwfFCHGKob8NznJwAAi5P6YVhUoLQFERGRy2D4IIcJIfDHzSdQVdeEoREBWHJbnNQlERGRC2H4IIdtyynBrpNlUMpl+J/7hsFbyb9GRETUfnzXIIdU1jbihc9zAQCLJvfHYH2AxBUREZGrYfggh7y09SQqahsxINwfSyb3l7ocIiJyQQwf1G7f/GDA5qNFkMuA13/N4RYiIuoYvntQu9Q1WvDs5ubFxBbeHIvhfLqFiIg6iOGD2uX/vj6LYmMDIoPUXEyMiIg6heGDftFZQw3e3XseAJA8ayjU3lxMjIiIOo7hg25ICIHkLblosgpMGRSG24eES10SERG5OIYPuqEvc0rx7dlyeCvleGHWUKnLISIiN8DwQddVa7bgv7aeBAA8MakfokN8Ja6IiIjcAcMHXdebX+eh1NSAqGA1nkjqJ3U5RETkJhg+qE1nDdV4b28+gOZJptyxloiIugrDB11DCIHnP8+FxSZw++AwTBnMSaZERNR1GD7oGluPl2DfuQqoOMmUiIi6AcMHtVJjtuDlbc2TTBcl9UdUMCeZEhFR12L4oFb+76s8lJnMiA72xWOT+kpdDhERuaFOhY/U1FTIZDIsW7bMfk4IgeTkZERERECtViMpKQm5ubmdrZN6QF5ZNd779uok018N4SRTIiLqFh0OH4cOHcLbb7+NxMTEVudff/11rFmzBm+99RYOHToEnU6HqVOnorq6utPFUvdpPck0HLcN4iRTIiLqHh0KHzU1NZg3bx7eeecdBAUF2c8LIbB27Vo8++yzmDNnDuLj47FhwwbU1dVh48aNbb6W2WyGyWRqdVDP23q8BN+fb5lkOkTqcoiIyI11KHwsXrwYM2fOxO23397qfH5+PkpLSzFt2jT7OZVKhUmTJmHfvn1tvlZqaiq0Wq39iIqK6khJ1An1jVakfnkKACeZEhFR93M4fKSlpeHIkSNITU295lppaSkAIDy8dZd9eHi4/drPrVq1Ckaj0X4UFhY6WhJ10t/2nEOxsQG9A9WcZEpERN1O6cjNhYWFWLp0KXbt2gUfH5/r3ieTyVp9LIS45lwLlUoFlUrlSBnUhYqr6vHXzHMAgFV3DuIkUyIi6nYO9XxkZWXBYDBg1KhRUCqVUCqVyMzMxJtvvgmlUmnv8fh5L4fBYLimN4Scw6vbf0BDkw039QnGzAS91OUQEZEHcCh8TJkyBTk5OcjOzrYfo0ePxrx585CdnY2+fftCp9MhPT3d/jmNjY3IzMzEhAkTurx46pzDBVew5VgxZDLg+VlDrts7RURE1JUcGnbRaDSIj49vdc7Pzw8hISH288uWLUNKSgri4uIQFxeHlJQU+Pr6Yu7cuV1XNXWaEAL/tbV5JdP7R0chvrdW4oqIiMhTOBQ+2mPFihWor6/HokWLUFlZibFjx2LXrl3QaDRd/aWoE3acKMWxS0b4eivw+2kDpS6HiIg8iEwIIaQu4qdMJhO0Wi2MRiMCAgKkLsctWaw2TFu7B+cv1+KpKXFYPnWA1CUREZGLc+T9m3u7eKB/Z13C+cu1CPL1wqO3xEpdDhEReRiGDw/T0GTF2t15AIDFk/tD4+MlcUVERORpGD48zIZ9BSg1NS8o9tC4GKnLISIiD8Tw4UGM9U34S0bzgmLLbo/jgmJERCQJhg8P8vaeczDWNyEuzB9zRkZKXQ4REXkohg8PYTA14L1v8wEAz9wxEAo5FxQjIiJpMHx4iDe/zkNDkw0jowMxdQiXuiciIukwfHiAgvJapB1s3i145fRBXEadiIgkxfDhAf6UfgYWm0DSwF4Y2zdE6nKIiMjDMXy4uRNFRnxxrBgAsOKOQRJXQ0RExPDh9l7feRoAcPfwCAyJ4HL1REQkPYYPN7bvXDn2nLkMpVzG/VuIiMhpMHy4KSEEXt/R3Osxd2w0YkL8JK6IiIioGcOHm9qZW4bswiqovRRYclt/qcshIiKyY/hwQ1abwJ92Nfd6/PaWWIRpfCSuiIiI6EcMH25o6/Fi5BlqoFV74dFb+0pdDhERUSsMH27GYrXhjd15AID/d2tfBPh4SVwRERFRawwfbubz7GKcL69FkK8X5k/oI3U5RERE12D4cCNNVhve/Lq51+OxSf3gr1JKXBEREdG1GD7cyOYjRbhQUYcQP288Mj5G6nKIiIjaxPDhJhotP/Z6PJHUD77e7PUgIiLnxPDhJj47WoRLlfXopVFh3lj2ehARkfNi+HADVpvAXzPPAQAevSUWam+FxBURERFdH8OHG9hxohTny2uhVXthLns9iIjIyTF8uDghBP6ScRYAMH9CHz7hQkRETo/hw8XtyStHbrEJai8FfsN1PYiIyAUwfLi4P3/T3Osxd2w0gvy8Ja6GiIjolzF8uLCsC1dwMP8KvBQy/PaWWKnLISIiaheGDxf2l2+an3CZMyISeq1a4mqIiIjah+HDRZ0qMeGrHwyQy4DHk/pJXQ4REVG7MXy4qJZ1PWYk6BEb6idxNURERO3H8OGCiqrqsfV4CQDgiUns9SAiItfC8OGC/v5tPqw2gZv7hyC+t1bqcoiIiBziUPhYt24dEhMTERAQgICAAIwfPx7bt2+3X1+wYAFkMlmrY9y4cV1etCcz1jch7eBFAMCjt/SVuBoiIiLHObQcZmRkJF599VX0798fALBhwwbcfffdOHr0KIYOHQoAmD59OtavX2//HG9vrj3Rlf558CJqG60YGK7BpAG9pC6HiIjIYQ6Fj1mzZrX6+JVXXsG6deuwf/9+e/hQqVTQ6XTtfk2z2Qyz2Wz/2GQyOVKSR2m02LD+u3wAwG9viYVMJpO4IiIiIsd1eM6H1WpFWloaamtrMX78ePv5jIwMhIWFYcCAAXj00UdhMBhu+DqpqanQarX2IyoqqqMlub0vjhWjzGRGeIAKdw/vLXU5REREHSITQghHPiEnJwfjx49HQ0MD/P39sXHjRtx5550AgE2bNsHf3x8xMTHIz8/Hc889B4vFgqysLKhUqjZfr62ej6ioKBiNRgQEBHSiae5FCIEZb+zFD6XVWDl9EJ7g2h5ERORETCYTtFptu96/Hd4CdeDAgcjOzkZVVRU++eQTzJ8/H5mZmRgyZAjuv/9++33x8fEYPXo0YmJisG3bNsyZM6fN11OpVNcNJvSjvXnl+KG0Gn7eCswdGy11OURERB3mcPjw9va2TzgdPXo0Dh06hDfeeAN/+9vfrrlXr9cjJiYGeXl5na/Uw7295zwA4P4x0dCqvSSuhoiIqOM6vc6HEKLVsMlPVVRUoLCwEHq9vrNfxqPlFhvx7dlyKOQyLJzYR+pyiIiIOsWhno/Vq1djxowZiIqKQnV1NdLS0pCRkYEdO3agpqYGycnJuPfee6HX61FQUIDVq1cjNDQU99xzT3fV7xHe3dv8hMvMBD0ig3wlroaIiKhzHAofZWVlePjhh1FSUgKtVovExETs2LEDU6dORX19PXJycvDBBx+gqqoKer0ekydPxqZNm6DRaLqrfrdXXFWPL44VA+CiYkRE5B4cCh/vvffeda+p1Wrs3Lmz0wVRa+/vK4DFJjC+bwgSIrmUOhERuT7u7eLETA1N2HigeSn1/3crez2IiMg9MHw4sU0HC1FjtiAuzJ9LqRMRkdtg+HBSFqsN7+8rAAD858RYyOVcSp2IiNwDw4eT2n2qDEVV9Qjy9cLsEVxKnYiI3AfDh5P6+3cFAIC5Y6Ph46WQthgiIqIuxPDhhE4UGXEw/wqUchkeHtdH6nKIiIi6FMOHE1p/tdfjzgQ9dFofaYshIiLqYgwfTuZytdm+qNhvbu4jbTFERETdgOHDyXx04AIarTYMjwrEiOggqcshIiLqcgwfTsRsseLD/c2Lii2cGCtxNURERN2D4cOJbD1WgvIaM3QBPpgRr5O6HCIiom7B8OEkhBBYv69599qHx8fAS8E/GiIick98h3MSRwurcKLIBG+lHA/eFC11OURERN2G4cNJfLj/AgDgrkQ9gv28Ja6GiIio+zB8OIHK2kZsPV4CAHhoXIzE1RAREXUvhg8n8O+sS2i02DBEH4ARUYFSl0NERNStGD4kZrMJbDzY/HjtvHHRkMm4ey0REbk3hg+J7TtXgfzyWvirlJg9nLvXEhGR+2P4kFjLRNN7RvSGn0opcTVERETdj+FDQqXGBqSfKgPAiaZEROQ5GD4klHboIqw2gTF9gjBQp5G6HCIioh7B8CERi9WGtIOFANjrQUREnoXhQyJf/WBAqakBwX7emM59XIiIyIMwfEikZaLpfaMjoVIqJK6GiIio5zB8SOBiRR325pVDJgPm3cQhFyIi8iwMHxL41+HmuR4T+4ciOsRX4mqIiIh6FsNHD7NYbfg4qzl8PDCGu9cSEZHnYfjoYZlnLqPMZEawnzduHxImdTlEREQ9juGjh6Udau71mDOiNyeaEhGRR2L46EGG6gZ8/YMBAHD/mCiJqyEiIpIGw0cP+iSrCFabwKiYIMSFc0VTIiLyTAwfPUQIgU2HLgIA7h/NXg8iIvJcDB895ED+FRRU1MHPW4GZiXqpyyEiIpKMQ+Fj3bp1SExMREBAAAICAjB+/Hhs377dfl0IgeTkZERERECtViMpKQm5ubldXrQr2nR1oumvhkfAT6WUuBoiIiLpOBQ+IiMj8eqrr+Lw4cM4fPgwbrvtNtx99932gPH6669jzZo1eOutt3Do0CHodDpMnToV1dXV3VK8qzDWN+HLnBIAwP1c24OIiDycTAghOvMCwcHB+O///m8sXLgQERERWLZsGVauXAkAMJvNCA8Px2uvvYbHHnuszc83m80wm832j00mE6KiomA0GhEQENCZ0pzGP74vwHOf52KQToPtS2+BTCaTuiQiIqIuZTKZoNVq2/X+3eE5H1arFWlpaaitrcX48eORn5+P0tJSTJs2zX6PSqXCpEmTsG/fvuu+TmpqKrRarf2IinK/yZgta3vcPyaKwYOIiDyew+EjJycH/v7+UKlUePzxx7F582YMGTIEpaWlAIDw8PBW94eHh9uvtWXVqlUwGo32o7Cw0NGSnNqJIiNyi03wVsgxe3hvqcshIiKSnMMzHwcOHIjs7GxUVVXhk08+wfz585GZmWm//vN/2QshbvivfZVKBZVK5WgZLuOTI5cAAFOHhiPIz1viaoiIiKTncM+Ht7c3+vfvj9GjRyM1NRXDhg3DG2+8AZ1OBwDX9HIYDIZrekM8RZPVhi3ZxQCAX4+MlLgaIiIi59DpdT6EEDCbzYiNjYVOp0N6err9WmNjIzIzMzFhwoTOfhmXlHH6MipqG9FLo8ItcaFSl0NEROQUHBp2Wb16NWbMmIGoqChUV1cjLS0NGRkZ2LFjB2QyGZYtW4aUlBTExcUhLi4OKSkp8PX1xdy5c7urfqf2SVbzkMvs4RFQKrieGxEREeBg+CgrK8PDDz+MkpISaLVaJCYmYseOHZg6dSoAYMWKFaivr8eiRYtQWVmJsWPHYteuXdBoPG8fk8raRnz1QxkA4N5RHHIhIiJq0el1PrqaI88JO7MPvi/A85/nYmhEALY9dYvU5RAREXWrHlnng26sZcjlXk40JSIiaoXhoxucNVTj2CUjlHIZ7h4eIXU5REREToXhoxv8O6sIAJA0MAwh/u67hgkREVFHMHx0MatNYPPR5iGXX4/iiqZEREQ/x/DRxb47W44ykxmBvl6YPChM6nKIiIicDsNHF2tZTn1WYgRUSoXE1RARETkfho8uVN3QhJ25zcvLc20PIiKitjF8dKEdJ0rR0GRDv15+GBaplbocIiIip8Tw0YW2HGveRO6eEb1vuJMvERGRJ2P46CKG6gZ8d7YcAPCrYXzKhYiI6HoYPrrI1mMlsAlgRHQgokN8pS6HiIjIaTF8dJHPs5sXFps9nL0eREREN8Lw0QXyy2tx7JIRCrkMMxP1UpdDRETk1Bg+ukBLr8fE/qEI5XLqREREN8Tw0UlCCGzJbn7KhZvIERER/TKGj046UWTC+fJa+HjJMW2oTupyiIiInB7DRyd9dnXI5fbB4fBXKSWuhoiIyPkxfHSC1SbwxdWFxfiUCxERUfswfHTC/vMVMFSboVV74dYBvaQuh4iIyCUwfHRCy1Mudybo4a3kt5KIiKg9+I7ZQQ1NVmzPad7BdjafciEiImo3ho8Oyjh9GdVmC/RaH4zpEyx1OURERC6D4aODtuWUAABmDYuAXM4dbImIiNqL4aMD6hut+OpUGQBgZgKXUyciInIEw0cHfHPagLpGKyKD1EiM1EpdDhERkUth+OiAbcebh1xmJuohk3HIhYiIyBEMHw6qa7Tgqx+ah1xmJfIpFyIiIkcxfDjoq1MGNDTZEBPii6ERAVKXQ0RE5HIYPhxkH3JJ4JALERFRRzB8OKDGbME3pw0Amud7EBERkeMYPhzw1akymC02xIb6YYieQy5EREQdwfDhgK1Xh1zu4lMuREREHcbw0U7VDU3IPH0ZAIdciIiIOsOh8JGamooxY8ZAo9EgLCwMs2fPxunTp1vds2DBAshkslbHuHHjurRoKew+VYZGqw39evlhYLhG6nKIiIhclkPhIzMzE4sXL8b+/fuRnp4Oi8WCadOmoba2ttV906dPR0lJif348ssvu7RoKfy4sFgEh1yIiIg6QenIzTt27Gj18fr16xEWFoasrCzceuut9vMqlQo6na5rKnQCxvomZJ5pHnK5i0MuREREndKpOR9GoxEAEBzcekv5jIwMhIWFYcCAAXj00UdhMBiu+xpmsxkmk6nV4WzST5ahySowINwfAzjkQkRE1CkdDh9CCCxfvhwTJ05EfHy8/fyMGTPw0Ucf4euvv8af/vQnHDp0CLfddhvMZnObr5OamgqtVms/oqKiOlpSt9l2vBgAMDOBy6kTERF1lkwIITryiYsXL8a2bdvw7bffIjIy8rr3lZSUICYmBmlpaZgzZ841181mc6tgYjKZEBUVBaPRiIAA6dfSMNY1YdTL6bDYBHYvn4T+Yf5Sl0REROR0TCYTtFptu96/HZrz0eLJJ5/Eli1bsGfPnhsGDwDQ6/WIiYlBXl5em9dVKhVUKlVHyugRO3NLYbEJDNJpGDyIiIi6gEPhQwiBJ598Eps3b0ZGRgZiY2N/8XMqKipQWFgIvd41J2puzflxYTEiIiLqPIfmfCxevBgffvghNm7cCI1Gg9LSUpSWlqK+vh4AUFNTg6effhrff/89CgoKkJGRgVmzZiE0NBT33HNPtzSgO1XWNuK7s+UAgDsTGD6IiIi6gkM9H+vWrQMAJCUltTq/fv16LFiwAAqFAjk5Ofjggw9QVVUFvV6PyZMnY9OmTdBoXO8pkZ25pbDaBIboA9C3F4dciIiIuoLDwy43olarsXPnzk4V5Ezse7kMY68HERFRV+HeLtdRUWPGvnPNQy4zOeRCRETUZRg+rmP7iVLYBJDQW4uYED+pyyEiInIbDB/X0bKXC59yISIi6loMH20wVDfgQH4FAGAmwwcREVGXYvhow/ac5iGX4VGBiAzylbocIiIit8Lw0YatV/dy4ZALERFR12P4+JkSYz0OFVQC4JALERFRd2D4+Jkvc0oBAGP6BEGvVUtcDRERkfth+PiZH4dcIiSuhIiIyD0xfPzEpco6HL1YBZkMmJGgk7ocIiIit8Tw8RMta3uMjQ1GmMZH4mqIiIjcE8PHT2zLaVlYjEMuRERE3YXh46qC8locv2SEQi7DjHgOuRAREXUXho+rPj1aBACY2D8UIf4qiashIiJyXwwfAGw2gU+PXAIAzBnZW+JqiIiI3BvDB4DDFypxqbIe/iolpg3hkAsREVF3YvgA7L0edybooPZWSFwNERGRe/P48NHQZLU/YjtnZKTE1RAREbk/jw8fO3NLUW22oHegGjf1CZa6HCIiIrfn8eHjw/0XAAC/HhUJuVwmcTVERETuz6PDx8liEw4VVEIpl2Hu2GipyyEiIvIIHh0+/rG/AABwR7wO4QFcTp2IiKgneGz4uFLbiM1XFxZ7ZFyMxNUQERF5Do8NH2/vOY+GJhviewfgplhONCUiIuopHhk+DKYGfPB9AQBg2ZQBkMk40ZSIiKineFz4EELgj5+dQF2jFcOiAjFlcJjUJREREXkUpdQF9KRaswXv7s3HrpNl8FLI8OqcBPZ6EBER9TCPCR+FV+qQ9D8ZsNoEAOCZOwZisD5A4qqIiIg8j8eEj8ggNQLVXvDxUuDxpH54iOt6EBERScJjwodMJsPu5ZMQ5OctdSlEREQezaMmnDJ4EBERSc+jwgcRERFJj+GDiIiIepRD4SM1NRVjxoyBRqNBWFgYZs+ejdOnT7e6RwiB5ORkREREQK1WIykpCbm5uV1aNBEREbkuh8JHZmYmFi9ejP379yM9PR0WiwXTpk1DbW2t/Z7XX38da9aswVtvvYVDhw5Bp9Nh6tSpqK6u7vLiiYiIyPXIhBCio598+fJlhIWFITMzE7feeiuEEIiIiMCyZcuwcuVKAIDZbEZ4eDhee+01PPbYY7/4miaTCVqtFkajEQEBXIeDiIjIFTjy/t2pOR9GoxEAEBzcvDFbfn4+SktLMW3aNPs9KpUKkyZNwr59+9p8DbPZDJPJ1OogIiIi99Xh8CGEwPLlyzFx4kTEx8cDAEpLSwEA4eHhre4NDw+3X/u51NRUaLVa+xEVFdXRkoiIiMgFdDh8LFmyBMePH8c///nPa679fL8UIcR191BZtWoVjEaj/SgsLOxoSUREROQCOrTC6ZNPPoktW7Zgz549iIyMtJ/X6XQAmntA9Hq9/bzBYLimN6SFSqWCSqXqSBlERETkghzq+RBCYMmSJfj000/x9ddfIzY2ttX12NhY6HQ6pKen2881NjYiMzMTEyZM6JqKiYiIyKU51POxePFibNy4EZ9//jk0Go19HodWq4VarYZMJsOyZcuQkpKCuLg4xMXFISUlBb6+vpg7d263NICIiIhci0PhY926dQCApKSkVufXr1+PBQsWAABWrFiB+vp6LFq0CJWVlRg7dix27doFjUbTJQUTERGRa+vUOh/dget8EBERuR5H3r87NOG0O7VkIa73QURE5Dpa3rfb06fhdOGjZRl2rvdBRETkeqqrq6HVam94j9MNu9hsNhQXF0Oj0Vx3bZCOMplMiIqKQmFhoVsO6bh7+wD3byPb5/rcvY3u3j7A/dvYXe0TQqC6uhoRERGQy2/8MK3T9XzI5fJWa4d0h4CAALf8C9XC3dsHuH8b2T7X5+5tdPf2Ae7fxu5o3y/1eLTo1N4uRERERI5i+CAiIqIe5VHhQ6VS4YUXXnDb5dzdvX2A+7eR7XN97t5Gd28f4P5tdIb2Od2EUyIiInJvHtXzQURERNJj+CAiIqIexfBBREREPYrhg4iIiHqUx4SPv/zlL4iNjYWPjw9GjRqFvXv3Sl1Su+3ZswezZs1CREQEZDIZPvvss1bXhRBITk5GREQE1Go1kpKSkJub2+oes9mMJ598EqGhofDz88OvfvUrXLp0qQdb0bbU1FSMGTMGGo0GYWFhmD17Nk6fPt3qHlduH9C8G3RiYqJ9QZ/x48dj+/bt9uuu3r6fS01NhUwmw7Jly+znXL2NycnJkMlkrQ6dTme/7urtA4CioiI89NBDCAkJga+vL4YPH46srCz7dVduY58+fa7585PJZFi8eDEA125bC4vFgj/+8Y+IjY2FWq1G37598dJLL8Fms9nvcap2Cg+QlpYmvLy8xDvvvCNOnjwpli5dKvz8/MSFCxekLq1dvvzyS/Hss8+KTz75RAAQmzdvbnX91VdfFRqNRnzyySciJydH3H///UKv1wuTyWS/5/HHHxe9e/cW6enp4siRI2Ly5Mli2LBhwmKx9HBrWrvjjjvE+vXrxYkTJ0R2draYOXOmiI6OFjU1NfZ7XLl9QgixZcsWsW3bNnH69Glx+vRpsXr1auHl5SVOnDghhHD99v3UwYMHRZ8+fURiYqJYunSp/byrt/GFF14QQ4cOFSUlJfbDYDDYr7t6+65cuSJiYmLEggULxIEDB0R+fr7YvXu3OHv2rP0eV26jwWBo9WeXnp4uAIhvvvlGCOHabWvx8ssvi5CQELF161aRn58vPv74Y+Hv7y/Wrl1rv8eZ2ukR4eOmm24Sjz/+eKtzgwYNEn/4wx8kqqjjfh4+bDab0Ol04tVXX7Wfa2hoEFqtVvz1r38VQghRVVUlvLy8RFpamv2eoqIiIZfLxY4dO3qs9vYwGAwCgMjMzBRCuF/7WgQFBYl3333XrdpXXV0t4uLiRHp6upg0aZI9fLhDG1944QUxbNiwNq+5Q/tWrlwpJk6ceN3r7tDGn1q6dKno16+fsNlsbtO2mTNnioULF7Y6N2fOHPHQQw8JIZzvz9Dth10aGxuRlZWFadOmtTo/bdo07Nu3T6Kquk5+fj5KS0tbtU+lUmHSpEn29mVlZaGpqanVPREREYiPj3e674HRaAQABAcHA3C/9lmtVqSlpaG2thbjx493q/YtXrwYM2fOxO23397qvLu0MS8vDxEREYiNjcUDDzyA8+fPA3CP9m3ZsgWjR4/Gfffdh7CwMIwYMQLvvPOO/bo7tLFFY2MjPvzwQyxcuBAymcxt2jZx4kR89dVXOHPmDADg2LFj+Pbbb3HnnXcCcL4/Q6fbWK6rlZeXw2q1Ijw8vNX58PBwlJaWSlRV12lpQ1vtu3Dhgv0eb29vBAUFXXOPM30PhBBYvnw5Jk6ciPj4eADu076cnByMHz8eDQ0N8Pf3x+bNmzFkyBD7D7Srty8tLQ1HjhzBoUOHrrnmDn+GY8eOxQcffIABAwagrKwML7/8MiZMmIDc3Fy3aN/58+exbt06LF++HKtXr8bBgwfx1FNPQaVS4ZFHHnGLNrb47LPPUFVVhQULFgBwj7+fALBy5UoYjUYMGjQICoUCVqsVr7zyCh588EEAztdOtw8fLWQyWauPhRDXnHNlHWmfs30PlixZguPHj+Pbb7+95pqrt2/gwIHIzs5GVVUVPvnkE8yfPx+ZmZn2667cvsLCQixduhS7du2Cj4/Pde9z5TbOmDHD/v8JCQkYP348+vXrhw0bNmDcuHEAXLt9NpsNo0ePRkpKCgBgxIgRyM3Nxbp16/DII4/Y73PlNrZ47733MGPGDERERLQ67+pt27RpEz788ENs3LgRQ4cORXZ2NpYtW4aIiAjMnz/ffp+ztNPth11CQ0OhUCiuSW0Gg+GaBOiKWmbc36h9Op0OjY2NqKysvO49UnvyySexZcsWfPPNN4iMjLSfd5f2eXt7o3///hg9ejRSU1MxbNgwvPHGG27RvqysLBgMBowaNQpKpRJKpRKZmZl48803oVQq7TW6cht/zs/PDwkJCcjLy3OLP0O9Xo8hQ4a0Ojd48GBcvHgRgPv8HF64cAG7d+/Gb3/7W/s5d2nbM888gz/84Q944IEHkJCQgIcffhi/+93vkJqaCsD52un24cPb2xujRo1Cenp6q/Pp6emYMGGCRFV1ndjYWOh0ulbta2xsRGZmpr19o0aNgpeXV6t7SkpKcOLECcm/B0IILFmyBJ9++im+/vprxMbGtrru6u27HiEEzGazW7RvypQpyMnJQXZ2tv0YPXo05s2bh+zsbPTt29fl2/hzZrMZp06dgl6vd4s/w5tvvvmaR9zPnDmDmJgYAO7zc7h+/XqEhYVh5syZ9nPu0ra6ujrI5a3f0hUKhf1RW6drZ5dOX3VSLY/avvfee+LkyZNi2bJlws/PTxQUFEhdWrtUV1eLo0ePiqNHjwoAYs2aNeLo0aP2R4VfffVVodVqxaeffipycnLEgw8+2ObjU5GRkWL37t3iyJEj4rbbbnOKx8SeeOIJodVqRUZGRqtH4erq6uz3uHL7hBBi1apVYs+ePSI/P18cP35crF69WsjlcrFr1y4hhOu3ry0/fdpFCNdv4+9//3uRkZEhzp8/L/bv3y/uuusuodFo7L9DXL19Bw8eFEqlUrzyyisiLy9PfPTRR8LX11d8+OGH9ntcvY1Wq1VER0eLlStXXnPN1dsmhBDz588XvXv3tj9q++mnn4rQ0FCxYsUK+z3O1E6PCB9CCPHnP/9ZxMTECG9vbzFy5Ej7o5yu4JtvvhEArjnmz58vhGh+hOqFF14QOp1OqFQqceutt4qcnJxWr1FfXy+WLFkigoODhVqtFnfddZe4ePGiBK1pra12ARDr16+33+PK7RNCiIULF9r/7vXq1UtMmTLFHjyEcP32teXn4cPV29iyHoKXl5eIiIgQc+bMEbm5ufbrrt4+IYT44osvRHx8vFCpVGLQoEHi7bffbnXd1du4c+dOAUCcPn36mmuu3jYhhDCZTGLp0qUiOjpa+Pj4iL59+4pnn31WmM1m+z3O1E6ZEEJ0bV8KERER0fW5/ZwPIiIici4MH0RERNSjGD6IiIioRzF8EBERUY9i+CAiIqIexfBBREREPYrhg4iIiHoUwwcRERH1KIYPIupSycnJGD58uNRlEJET4wqnRNRuv7St9vz58/HWW2/BbDYjJCSkh6oiIlfD8EFE7fbT7bg3bdqE559/vtVuqGq1GlqtVorSiMiFcNiFiNpNp9PZD61WC5lMds25nw+7LFiwALNnz0ZKSgrCw8MRGBiIF198ERaLBc888wyCg4MRGRmJv//9762+VlFREe6//34EBQUhJCQEd999NwoKCnq2wUTULRg+iKjbff311yguLsaePXuwZs0aJCcn46677kJQUBAOHDiAxx9/HI8//jgKCwsBAHV1dZg8eTL8/f2xZ88efPvtt/D398f06dPR2NgocWuIqLMYPoio2wUHB+PNN9/EwIEDsXDhQgwcOBB1dXVYvXo14uLisGrVKnh7e+O7774DAKSlpUEul+Pdd99FQkICBg8ejPXr1+PixYvIyMiQtjFE1GlKqQsgIvc3dOhQyOU//lsnPDwc8fHx9o8VCgVCQkJgMBgAAFlZWTh79iw0Gk2r12loaMC5c+d6pmgi6jYMH0TU7by8vFp9LJPJ2jxns9kAADabDaNGjcJHH310zWv16tWr+woloh7B8EFETmfkyJHYtGkTwsLCEBAQIHU5RNTFOOeDiJzOvHnzEBoairvvvht79+5Ffn4+MjMzsXTpUly6dEnq8oiokxg+iMjp+Pr6Ys+ePYiOjsacOXMwePBgLFy4EPX19ewJIXIDXGSMiIiIehR7PoiIiKhHMXwQERFRj2L4ICIioh7F8EFEREQ9iuGDiIiIehTDBxEREfUohg8iIiLqUQwfRERE1KMYPoiIiKhHMXwQERFRj2L4ICIioh71/wGMqz190iSGPQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pred.plot(y=[\"T1\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## \"Least Squares\" Model Fitting\n", "\n", "Fitting a model to data is a basic task in engineering, science, business, and a foundation of modern data sciences. For engineers the goal is to validate hypotheses about how a device works, then to enable simulation and design. In the data science model fitting may be almost completely empirical using black box models to develop predictive models of complex systems.\n", "\n", "In this case we wish to find values for a small number of parameters that cause a model to replicate a measured response. One common measure of fit is the sum of sum of squares of residual difference between the model and data. For residuals modeled as independent and identically distributed random variables from a Gaussian distribution, minimizing the sum of squares has a strong theoretical foundation. So strong, in fact, the term \"least squares\" has become synonomous with model fitting and regression.\n", "\n", "The SciPy library includes a well-developed function [`scipy.optimize.least_squares`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html) for this purpose. The name is a misnomoer because the function allows other common \"loss\" functions in addition to sum of squares. The simplest use of `least_squares` is to provide a function that, given values for the unknown parameters, creates a vector of residuals between a model and data. \n", "\n", "This is demonstrated below." ] }, { "cell_type": "code", "execution_count": 185, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 185, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DzUg+at9jfe1q2baGl5IHXAZ5auqsm9FKkYmg0YFiVWNzFVdnoU2jF9uH9JkKF/y66XJ1r7nl/fplDn4PwLnIDKJ1gZtlJcmHECKkVdZY+N/B0/ywv5jV+09x6JT7lEKjXsvQLomMyOrAyKwOjOiaSFJs/S0dRK1T+8Baoy7lXbC13voQGrOZXie/Qrfw73Bsff3nJ/eB4n2QOghm/ge0DaxP8sNLsOGfns8V73Peb6oVw7WMPrL2cRPJh32QZ2R8w/VrCa1Wbf2oOFX/XEyd7hStTk0WTGX1y85eCls/UH+G3gTX/qN5r9+cRKpoJwBlkZ0J5NatknwIIULOiZIqvt1TxLe7T7L24GlqXGag6LQahmUmclHvZC7qnczgzolE6GXVz2Y5scXZEtHncti3rF4RPTDQ03NTBsB1b0FyX9jxkTreoLEpr11HO5OPkb+AmE7qWI21f3WfLWJtxvgLa52WD6WJ5MO+8qcvu1zsopM8Jx+exqHojeC6wG2n/nBnjjpNNrk39LwYBlzT/Nf2ojWlwhjYLU8k+RBCBD2bTSH3eCnf7j7JN7uL2FXg/m2xS4coJvTpxEW9OzG2ZxIJUbJol9cKd7h3gdgTj7h0t6W5FRROV0GHPmPQxaXB6LudYx3sht7Y9Ov1nQYDpkPWhTD6LvXY+tpkpPSYs5ytGcmHvaVDXzsttqnWksOr1Vv7AFNfck1oul2kLiy24S0YcVv9snV3oo1Jdi6/Hpvi/Zocdcd89J4Cl/xOHW9yare6AmqtvKSJ9PTu6j4lyYcQIihV1Vj58UAx3+w+yXd7iigqd35F1GhgRNcOXNI/hUv7p9I7JVbGa9R1fDPkr1d3NjVXwKg76icJdoqirg3hyc8WQJZzsKPFbObHpUuZNnUautbsiGqIgp+/537M0zoZVm+6XSLcHzfk0Er1ts/lTV/bWxkj1EGvoK5+Ov4RuHRu/R1noX7yYfBiTRFPXFs+5uRCYlfn49hO0PcKOPAN5ju/p3rDgda9VitJ8iGECBony6r5drfanbLmQLHbgl4xETrG9+nEJf1TmdS3k4zbaIiiwL9v9NBlooHxD3t+jqUaTC7LfP/8PfjyQdAamh7s6UtxtclHeYHzWLPGfNi7XZo55sO+50lztrP31pTnYNhNaktS/6s8Jx12vk4+9C7/JzyN/7j+XXUMjyEOkORDCNFOKYrCzhNlfLP7JN/uLiL3uPs+F50To7i0fwqX9E9ldI+OsiV8c+z5r8exGh7HIdi57vtx1V+h/9XOZb1b+4HojYgY9dZ1fESzul3sLR/NnO1i3yul7oe/L2i17muGNKbu6+tb+7t2SXQiYuuf1keAvmPL1zHxIUk+hBB+ZbbByn2nWLnvNN/uLqKwzPlBo9HA0C6JXNo/hUsHpNI3NU66U+zOHIaNb6lN+paahsvZp7ymD4NZX6jP+fbZxnc1tZ8zRDtW+Ky3e6o/2D+MXZOHZg04rTvbpanWEsX99QKl7r/t1iZ6SS4rl/pyFk8bkORDCNHmzpksfL+niGW5BXyzS4dp/RbHuSiDjot6J3Np/1Qm9UuhU5x0p3j0xQNw5IfmlY1Ogts+V5ve7d+ATY0lH7UtH/aWh0CxJwOKy2qzTbViQP2ptk3NdmnLlg9v1Ot2aeXk14494JaPnSutBjFJPoQQbeJMRQ3f7DrJsp2FrDlQ7DIdVkNqvJHJA1K5pH8qY3skEWkI7m9pfmOzQVWdVUGrzsJ/f+NMPCY8DpnnN36dlP7OFTTtCUVNBRzbBPu+hvGPuu+QGizJh9aefLjsqeNVt0szWz4U57/FgDrvTljxtPOxLxb96nVp66/hB5J8CCF8pqrGSs7uk3y25Tir9p1y2y+le3IMk/t3IvbsAe6+XnZ8rcdmg7cuVtfaaMiQG2HSE95d197yUVmsXh/UWRB7l8GpPXD3Kme3i6dxAv7kaPnwstul3piP+hsCulGCpNtlzL3q+ijvz1AfW0yNlw8jknwIIVpFURQ2HD7Df346xrIdBVTUOD84BqTHM3VQGpcNSqN3SiwWi4WlSw/Ixmx12Wzwr+mNJx4DpsPUP3p/bXtC4XrtvLXOXWB3f+lcWyLQLR8aTy0fLVnhtJktH4FOPrQ66HWJ87G5ouGyYUaSDyFEi5RXm/lsy3H+tS6PfSed4wm6dIji2uGduWZ4Z3p2CvA36VCx6o/Oha+G3QzXvOa7axs9vAfb/u28/9XDMO1F9X7Ak4/a7jfX5MOrFU69TT6CLAk2VwW6Bn4jyYcQwit7Csv41//y+GzLcUcrR5RBx/RhGfxsZBdGZnWQGSreOLUXVr3gfHxptm+v31RCYa6Ag9+p91s74LG1PM12aclU26YGnAbLbJd2TJIPIUSTFEVh1b5TvPnDIX48cNpxvGenGG4dk8W1I7q0vyXNzdXqQM2YpAbOV4JFcd863ZPTB533H96vLqvtS67jOCJiYcyvYPWf3MtUFNcvGwieul2aNebDvrx6c1s+7MlHkCTJl82Hda/DpCcDXRO/keRDCNEgk8XK51tP8NYPhxxdKzqthssGpnLrmG6M6dGx/bVylB5Tu0l2/1cdqHn/T9Ahy61It1PfYnjxNnVPlDu/heReDV/PPrul16W+TzzAPaHoOxUGXls/+TCV15YN9GwX+6wn16m23qxw6uUiY4Ge7WI39j71px2R5EMIUU9JZQ0frD/Ku2uPcKp2T5WYCB03nd+V2Rd0o0uHADfPt5WKYlj2hDoN9epXPX8z3vQubHbZk+TkTvfko+wEQ48tVO9Xl8DqF2HGGw2/ZtVZ9TaqgX1XWst1zEffaerOqQOuUT/UT+2F0/tdZrsEesyHh24Qr2a7NHN59WCZ7dKOSfIhhHDIO13B22sO8+FPx6gyq3/A0+Ij+cUF3bjx/K7h37Wy7HHI/VC9P/EJSOhSv0zdxbpcly3P/Qj9sjpTYc/mOe9bzWorw5qX1Kmu5/8SKmtbPtpie3dQP5AHXqsmOf2uVNfS+HltcvRm7dRbR8tHoLtdPCR7zelCqTfVNkRmu7RjknwIIdiUd4Y3Vx9m+a5Cx5fCAenx3DW+B1cMScegC/I/0oW5cHQdrP8HVJW08CIKVDrHszg+kOuy1lnavKJIvc37H3x8R/2GfNfk5O0pcGKz8/HXj8LQmer9hnacbS2NRt1QzOO52vfVFCwtHx4Wm2sqkXBt5fB6hdMg6XZphyT5EKKdstkUVuw6yRurD7L5aInj+MS+nfjlRT0Y1zMp+MdzHPtJbalY/w/fX7uh5KPu7ItztcnF1vfdiw3+Odrc/zgHc4J74mFXclS9bauWj0bVvr81QTLmw1NLxJ7/Qv5GyDzP83NckxODPfmwqWunaBtKmqXbJdAk+RCinamx2Phs63H+ueogB0+pixpF6LRcMzyDOy/qQZ/UuADXsAGWGnVFztgUqC4FrR7euqR+uXvWqOdaIiIG/j0TTuaCqcxzGfsYhLgMKD+htnyUn4T9Oe7FzrtbTT5MperKldoGuqzy1qi3bTXmozF1P3wD3u3SQDLw9qWQXer5nGsyqHPZF0ixAg1cT7pdAk6SDyHaiQqThX9vOMrbaw5TUKruJBsXqefWMVnMvqAbKXGRAa5hE/51rfODuiEdezZvK/PG2Ff7bLDbpfbDLqGzmnzs/FT9sZ++7EV+PFzB2LQhahJks6itH54W+3IVE4DNwOq2bAW65aMlO7G6tnzoXZIPm7XhvVKCbbZLOyTJhxBh7kxFDe+uPcLCtUcorVI/ODvFGbnzwu7MHN2VuMggHkRadRZyP4LUQVC0s+FyEXHqdNar/tr612wy+agd89GpHxzb6H4uNg3bqNs5W7RU/WCP6QTlBeq4j8bGIQy4BrIuaHXVvVav5SMIu12aYnVNPlwS6MbGishsl4CT5EOIMHWipIo3Vh9i8cajVJvVb3rdk2O4a3wPrh3eOfA7yVpq1DEQpw/AoOvAEKUeP/AtHN8Mx3+CI2uc00Ab8sBmdaM0X+wICi7Jh8vrbnlfnVJ72Xxny0eXUeqS6CUus1mS6qznkZCpJh+F2yF9WMOv+bN3Wvatv9XqtnwEabdLQ6pL4dO7ap+rc+9uayzZk+Qj4CT5ECLMnCip4rWVB1iyMR+zVf0jO7hzAr+a2JPLBqahC4ZN3RQbLL7Ruay3tQZG3a5OO/3g+mYsj+0iOsl3iQd4bvn4vHYBqD6XOccY6CIgc7R78tGxm/u1el0KxzbA+jcaGfxIgBIPgq/bxdtk4H+vOf8N6QzuyUdja33IbJeAk+RDiDDhKekY06Mj90/qzQW9gmjmiqKg2bbI+aEBzrUuKs84E4/xj0K3CyF/PXw/r+Hr+TLxAJfkw8OAU9M5Z7eLLkId9+EqLsP9cbfarpSTufWvpTOCNcBbqAdd8qFBbY1Rmiqpqi5x3tfq3RO8RqfoBtny6u2QJB9ChLiismr+9p2adNRY1W90Y3sk8eClvRnTo4F9R/zh8GpY8xe3FSp1isLkgj3otxa7l7WXsagDYYlJgYufUu9njWs8+WhoFklLGePV2zOH1Gm0ES6rueqNzjEGWj3E100+Ut0fxzSyXLpWH/jko163S4CTD1BbP5rb8hWX5rxvb82wD/JtVsuHdLsEilfJR3Z2NnPnznU7lpqaSmFhIQCzZ89m4cKFbudHjx7NunXrWllNIURdlTUW3lx9mH+uPkhl7e6yY3p05MFL+jC2ZwCTDlBbMD78BVS6JxlawPFR3utS9cN780Jna4L9w9h11kJT02Z93fIRmaDe7l2q/nTq514X15aPyET358aluz9uaAbLfRvg9QAMMK0r2KbagnfJhz1RBHUjP6hdqMzSxIBTST4CzeuWj4EDB/LNN984Hut07n2Vl19+OQsWLHA8joiIaEX1hBB1WW0KH23K588r9lFUu+/KsMxEHru8X2CSjrp7byg2+HaumnhEdVQHaerVvwMWq5VNW3cwYvqvMCSmw4pnaq9R+4Fu8ZB8NNUU7+um88zz3R+f2uPyQHFJPgz1l1+PTXN/XDc5AbhgDnTqq069te/rEiiuvzut3vE+BZRWV38hN1AHidZ9rz0lGPYWpebMdpGptgHjdfKh1+tJS0tr8LzRaGz0vBCi5TblneXpz3awu0Adj5DZMYrHLu/HFYPT/T+mw2aF96bDkR8aLjPjTeh9qeOhYjZTeMTobBHQ1X7YObpd7MlHnTVHtLrm7W7qC+lDGz5nNTvroTNA1zEw6g746W31WN0l0j0NMk3MVG9vXASf3A1T/9j6OreU6zf/li7M5msNtUbYrKCrU8e6S92DMw7HWh4eSMtHwHn9r23//v1kZGRgNBoZPXo08+fPp0ePHo7zK1euJCUlhcTERCZMmMC8efNISWm439NkMmEyOfs9y8rUP6pmsxmzuRm7GXrBfj1fXzdYhHt8EP4xNhRfSaWZ/8vZx5KfjgMQH6nnvok9uHl0V4x6LRaLnz6YXWh2fIi+gcRDMcZhm/QMtm4TwCWWuvFpNTp0gNVcjbL/W3Qf/wINYNMasLo8T4/zO6qi0aFxaZZvk38Ld3yH5vQBdMsfR2Pf8h6wmKrQWUxoAIuiRbFYYMoL6E5sRWOtwRKTXi/Gup1CltgMFLMZMs6D+zfbg/B9DM2gU5xrgCoaLZZm1KOt/w/qNRqP7RHmmqp6SanWbMLe9m4bditWsxm9VosGMNdUN/h71Ss2tYzV6rFMe/0746vrNodGUZRmDiuGr7/+msrKSvr06cPJkyd57rnn2LNnDzt37iQpKYklS5YQGxtLVlYWhw8f5plnnsFisbBp0yaMRqPHa3oaRwKwaNEioqPDdNtuIZpJUWDDKQ2f52mpsKh/ks/vZGN6lo3YAK4Nlnl6DSOOqtvE70m7loOdpridt+qMKJqmv9v0LvySAQUfktdxPKll24m0lABQHNOXH/s85Sh31ZZfoEVNOL4e/Hem5t7nOPf58PdoK66vC7Cx270MOPEhMTWnWN3nd5yNqV3Xo5Fv0tO33Ob2eGXfZymN7tZWVfbK6IN/Jq1sGwAWrZGvhr4Z4BrBtO33YLBW1jv+3yFvYNW5Jx99Cj+jf8EnHEmayLautwNwWe79RFrK+K7ffMqjPOxKDFy9ZRYaFJYN+ismQ6LPY2ivKisrmTlzJqWlpcTHxzda1qvko66Kigp69uzJo48+ykMPPVTvfEFBAVlZWSxevJgZM2Z4vIanlo/MzEyKi4ubrLy3zGYzOTk5TJ48GYMhiFd1bKFwjw/CP0bX+E6Um3ny051sOKKOC+idEsPcqwZwXrdAbEDmojQf/asj0KCgxKZi+dX6Zg9UrPv+ade/hu6b32EbdD3aHR86ytm6T8A682PHY/3z6WhqxwGYf3sIw5+dra3mp+rMnPEhwzz3AaOWq19D9/0f0JQXYL79W49dNPVi3Pwu2h//gqZMbbUyP5IXHLNKAN2SmWgPrABAiYjB8kheE89o+/+D+j/3QuM6hdb+ug8dgKhEt2PaVc+jW/NnrCPvwHa52n2lf2UQmnOFmO/4vsGl9u3vq/nBXepeQXVfqx39nfFlfGVlZSQnJzcr+WhVJ19MTAyDBw9m//79Hs+np6eTlZXV4HlQx4h4ahUxGAxt9qa35bWDQbjHB+Edo02BRT+d4P9y9lNtthFl0PHgpb2548LugdnaPm+tumeKfRpp+XFAAY0WzT0/YojxPhlyvH+1u5Bq6www1Bqi0Dbw/hoi3P9etOm/g84j4fgmx0O9YnGMTzEYo6CR13bEOPqX6k/lGbBZMcQktl19veUyhkKj0Xn1u2yz/4MNjMMw6DT1f9+13W86QyQ6+7naMR8GLZ7fH5fv24YIY/PewzDl6/i8uVarkg+TycTu3bu56KKLPJ4/ffo0+fn5pKenezwvhHCXd7qSV3fqOFi+F1DX63jxZ0PI7OiHLsiaCvjxFXXJarvd/4WyY9DzYri1dvM0+6DQ1EEQ26l1r2mfJrvrszrHG5l14c/VQK97G/46zPnYWuO+wqk36g5GDQqaBu4HUEPvb91ZVeAy+Nflo8z+/IYGnLo19gdJzO2QV8nHww8/zFVXXUXXrl0pKiriueeeo6ysjFmzZnHu3Dmys7O57rrrSE9P58iRIzz55JMkJydz7bXXtlX9hQgLNpvCu2uP8OLyPVSbNURH6HhiWn9uPr8rWn8sh26zwX9/A9uXeD5/8DvnVEdLlXrMvhdLazT4Ad5Ib7DGj8lHx+7ORatA/QC0fwgGy+yQ1nCdIRUsn8MNznbxMKja8V64fOO2Jx8NzY5yTUpkhdOA8ep/z7Fjx7jpppsoLi6mU6dOjBkzhnXr1pGVlUVVVRW5ubm89957lJSUkJ6ezqRJk1iyZAlxcXFtVX8hQl7+mUp++59tbDiizqroHW/jjTsvonuKb8c8NeqHPzsTj8HXQ2IWoMCuL+B0bbfpuSK168XTWhwt1VDyUXd1SrcPST93Pd3ysTqlGGDbIudiVt62fASjQP5eG+JV8uGy4JudPSlsVvIRJDG3Q14lH4sXL27wXFRUFMuXL291hYRoTz7dcoxnPtvJOZOFmAgdj13eh/iiXLp08EGrgieb3oX1/4SiXerjpF7q7rKlR9XHV74Mo37hLH/xM/DKECg5Cn/uA/euA3Nty4feFy0fDfQR11u4zKUlxN+bsPWYCMNvhS3/gkKXPVrCIvlw/fANklaAhlq2PCUTji4wl48y+/MbXF7d5d+StHwETBi0GwoRekqrzDzz2Q6+2HYCgFFZHfjLDcNIizOwdKmHTch84cRW+PJB92OnDzjvj7oDRs52P6/RqGM7SmqTk6WPwIDaVoA2bfloZN2SQHxg1F30DOoveBWSXFs+guSD2KuWD/s+Oy5JrOP5DXTdSctHUAiH/z1ChJT1h07z0H+2cbykCp1Ww5xLevOriT3R67S+XfRHUaDsuPoNsPQYfHqPejxlIHQdrTZZD/qZmkREJkLqAM/XyRiu7nEC6i6i9s3ffD3mwxDt7NKo+0ET6A9GT0lSuLV8BMsHcUPvtacBp566XexxNDjgVJKPYCDJhxB+YrbaePmbfby28iCKAllJ0bx8wzCGd/Xhuh1HfoR/36R+eMckQ4mHdRvOvxNG3d78ayb3dt4vzIXo2v1jfNHy4Tpo84IHYeXz6n1PHzSB5Kl7yNe76QaCJoRmuzS726U2juYkH8ESczskyYcQfpB/ppL7/72FbfklAPx8VBd+d9VAYo0+/i+Y8wyYaqfKllSot/pI0BmhQ1f1A3PANd5ds8/l7o8Pray9ro9bPlwXKvPXPi7N5bHlIxySD9eWjyD5IG5sb5e6Gut2aWj9TNfj0vIRMJJ8CNHGlu0o5JGPtlFebSEhysDzMwYzbbAP1r5RFDURsLduWM1uC2IBYEyAxw63bpCmIQpu+QTer7NKscHDOAhvuX6oG11mxXna1TSQPO32Giwf1q0SSrNdGut28ZR8SLdLMJPkQ4g2UmOx8fzXu1nw4xEAhndN5NWZI+ic6IMWA5sVPr4Ddn5a/1xsqrpQmKVa3VHWF7ND7F0trjwNwvSW64eGMQ6S+0DxPhhYd22gIBrzMfM/kNLA+JhQE4zdLt4MOPW04JtXyUeQxNwOSfIhRBs4erqS+/+9me3H1C6Qu8b34JHL+vpuefTdX6iJh1avTgW1//E1xsG4X8OpPVCwDSY+4ZvXa7Pko07Lxy+WQf466D2lTsEWb0HlG65jULLGubfShLKg7HbxYoVTR7eL65iPJpIPt9eSlo9AkeRDCB9btqOARz7aTnm1hcRoA3++fiiX9E9t2cVsNlj3GuSvdx6rOqsmFqAO0rzkd/WflzYIBv+sZa/piYfNt9ok+YhJgn5XtP66vua60VkzN9ELDaHU7eJhzIej5UO6XUKNJB9C+IjZauP5pXt458fDAIzomsjfWtvNsuU9WPGU53O6CDj/7pZf2xt6I/x6C7w1GSprd5H1yZiPOt0uwaqqxHk/WFoIfCEoFxlroB6NjvmQbpdQI2mfED5QVF7NzW+tdyQed4/vwZK7x7Yu8bBZIfcj9X73CXDFn92bpG9f5txp1h869oBrXnM+9vUKp422KAT4Q8K+tkm4CcIhH15NtW1Jt4tjtkuwBNw+ScuHEK20Ke8s936wiZNlJmKNev7886FcNjCtxdfrU/gZ+v+7T+3jtn/oTfs/6NQHVjzjXIgrqZcPau+lrmOc92vOtf56rt+8g7k7Y8JjcOAbGHtfoGviW0G5yFhLBpy6drs0c52PYIm3nZLkQ4gWUhSF99cf5dkvd2K2KvRKieWft46kZ6eWf4hqDq2kf8EnzgNRHWDSU2riUVcgPqwjE5z3fbHImGsMwdztktwbHjkE2nD7wArCpo+GkoKSfDh9EJJ6Oo/Zu128WudDko9gIMmHEC1Qbbby9Gc7+GjTMQCmDU7jxZ8N9X7RsJoKOLVX3T/l1B70/3YZJPrAZojv3PDYCn9vsGZ362ewbzkM/nnrr2WMhbtWqs3mntbSaMjFT8N3z8HEJ1tfh+YKu8SD0Jrt8s3vYdUf4aHdEJWoHrN3u3gz4NQ+cypY4m2nJPkQwkuFpdX88r2fyD1eilYDj13ej7vG90DTkj9m702HYxvrHVYSuqJx/YYXTHpOUn98JWO498+56GEYcgMkZPquHu2RJoRmu4Da5Xj6IHQZ6XwM7jOvmjvgNFjiback+RDCC9vyS/jlez9RVG6iQ7SBV2eO4IJeyS27WFmBx8QDwHLDIsJg8e62o9FAYtdA1yL0BeVslyaSgtKjavJhtUDVGfVYTCeX58uYj1AgyYcQzfTlthM8/OE2TBYbfVJjeXvWeWR2jG7+BWw22L4YUvpD6XFYcnPDZTv1a32FhWiSa8tHkCQfDXVvJWapWwmU5KuPTx+oPaGB6I7Ocs3e2yVI4m2nJPkQogk2m8Ir3+7nlW/3A3BxvxReuXEYcZFetk1s+zd8fm8b1FCIFgqV2S7n3w0RMbDmJSjNVxP510ar5wzR7uOfpNslJEjyIUQjqmqsPPzhNr7KLQDglxd15/Gp/dFpvfzWZLU4t4sX3guWb+XhJpT2dkmsHd9TchQsVc7j5grPz29qnQ9JPgJKkg8hGnCmooY7Fm5ky9ESDDoN864dzM9HeTHA0VQO25fA9g/VJmL7yqCtoYtwDrITorVCabZLQu0Yn5J8z0utO57vIfk4fRDyfoShM3HOdml1TUUrSPIhhAdHT1cya8EGDhdXkBBl4I1bRzK6h4fN1RqiKPDeNXD8p6bLGqLdEoqSqCxiGip74weweCZM/VPz6yJEg0Jotou95aM03/OCY47nexhw+rcR6q3FBN3HN/46wi8k+RCijtxjpfzi3Q0Un6uhc2IUC28/j14pzVwAy2YDFDi82j3xuO5t6DoWcn4HOz5yf47LwDjr+MdZfzqNixu6frcL4bG84PmWKkJbKHW7JHRRb01l6uaKdrd84l6usW6X7UvUgauNvY7wC0k+hHCxcm8R936wmcoaKwPS43n3F+eREt/MDdT++xvY/h/1j5qpzP2cfYdZo4dVSXURjj5s20UPU710aeOvI4mH8BW3dT4CVw03DSUFETEQnQSVp+HModqyOuh1iefne5rtcmwjLLreXtAn1RUtI6mfELU+3XKMOxf+RGWNlQt7JbPk7jHNTzwAfnpH3e/EnnjYlw6/+GlnGU9LoveqbefoM7VlFReixYKw26WxlWTt63lUnq4t62F8SJMrnNYpJwJCWj6EAN5fl8fTn+0A4NrhnfnjdUOI0Dfjj5PpHOxfDoW57se7nA93rKjfShHhYTTH1X+DMfdC51FgbWQgnRC+FjKLjNW2Yuhql+CvqZ3hovXwESbJR0iQ5EO0e2/9cIjnvtoNwOxx3fjdlQPQNmcq7Y5P4KNfeD7XqY/n7pG6LR9JvdUN1TLPVx9L8tGAIPlgDDeaIFxkrLGkwL6Mun2AtiQfIUuSD9FuKYrC3747wEs5+wD41cSePHpZ3+bv0fLdcw2fS+zm+bhry0d8Z7jp3817LSHaQlAuMtbIhon2nZQdLR+t6XYJkmSrnZLkQ7RLiqLwx2V7+ceqgwD8dnIf7r+4V9OJh6LA1g8gfwOcOdhwucQG1gNx3QDrl99BXJqXNRfCl0Jotgs4///UnKstK2M+QpUkH6LdURSFZ/+7iwU/HgHg6Sv6c+dFPZp+otUCS26BfV+7H5/wOKx6wf1YTAObzblOEYxNbX6lhWgLQbnIWGPJh73lo7FulyY2lqtbTgSEJB+iXVEUhflLdzsSj3nXDuLm0VnNe3Lx3vqJB0AHD8+PbiD5cC0rf/xEoGmCcbZLM7pdfDHmI1haetopST5Eu6EoCn9avpc3fzgMwPxrBzNztBfbsptqm3rjO0NUBzipzo4hNqV+2egGVkPtewVc9rxzgKkQgRQqs13sa3bU7XZpdMxH7XMaWoo9WJKtdkqSD9FuvPLtfl5bqY7TeHb6QO8SD3BuYBXVAQxRzuMRHlY/bSj50GphrOxsK4JFEM528TQd3a4lA04tJs/XkuQjoLz67WdnZ6PRaNx+0tKcA+YURSE7O5uMjAyioqKYOHEiO3fu9HmlhfDW378/wMvf7AfUMR63je3m/UXsf/AiYtyTD0+rlkZEe399IfwtGGe7GD0k8/bESNecMR91kg9rQ8lHkCRb7ZTX/9oGDhxIQUGB4yc317m40osvvshLL73Eq6++ysaNG0lLS2Py5MmUl5f7tNJCeOPN1Yf40/K9ADw+tV/zBpd6Yk8+DNEw7Gb1fqf+nv9YCt+SD4q2oWnwQeB4+v/k6Hap2/LRnOTD7Pl1giXZaqe87nbR6/VurR12iqLw8ssv89RTTzFjxgwAFi5cSGpqKosWLeLuu+9ufW2F8NJ/fspn3lJ1AbGHJvfhngk9W34x15aPITeoSz2nD5MPRhG6gnG2S2PJvGORsdr/ix7XBKkz20W6XYKS18nH/v37ycjIwGg0Mnr0aObPn0+PHj04fPgwhYWFTJkyxVHWaDQyYcIE1q5d22DyYTKZMJmc/zjKytR9McxmM2ZzAxlrC9mv5+vrBotwjw+8izFnVxGPf7wdgDsv7Mavxndr1e9GW12GDrDpo7BaLJBVuzW31YzBtY73rIMWvk64v4ctjU+vKI7v5cH+uwml91BrU7B/fNsAazPq3NbxafTR9T6YrDYbNrMZrUaPDlBM59AANo22Xp21CugAq9WCZvEtaE5s8dimowCWBmIIpfewJdoqPm+u51XyMXr0aN577z369OnDyZMnee655xg3bhw7d+6ksLAQgNRU97ULUlNTycvLa/Cazz//PHPnzq13fMWKFURHt02/eU5OTptcN1iEe3zQdIz7SzX8Y7cWm6JhdCcbgywHWLr0QKtes2/BVvoBeYWn2V5n59nJhiSizadZ2Xcupev3Afta9Vrh/h56G98VVqvjj9XSpnb9DRKh8B72OrmPgbX3TxefZq0Xv9u2ii+1dC9j6hzLy8sjd+lSehQdYjBgqSrDAJSUneOHOnUeeOwIvYBDB/bSu8jD1PhaZeUVrGwi3lB4D1vD1/FVVlY2u6xXycfUqc5dNwcPHszYsWPp2bMnCxcuZMwY9Z9L3RUiFUVpdNXIJ554goceesjxuKysjMzMTKZMmUJ8fLw31WuS2WwmJyeHyZMnYzAYmn5CiAn3+KB5Me48UcaT72zEoliZ3D+Fv94wBL2uhU2sVSVod36MbcgNaH9YD4XQtVd/ulwyzb3c2P6YzVVckDKgZa9TK9zfw5bGp7VdD9s+wJY+nGnTpjX9hAAKpfdQ+7+DcEK9n9SpU7N+t20dn+ZoBzj0ktuxrKwsMi+fhnZTIRxfhN6mtpYndkyuV2ftN+vgFPTIyoSihl8nPj6hwXhD6T1sibaKz95z0RytmmobExPD4MGD2b9/P9dccw0AhYWFpKenO8oUFRXVaw1xZTQaMRqN9Y4bDIY2e9Pb8trBINzjg4ZjPFxcwR3vbabCZGVMj478beYIIg2NLFrUlK+yYev76JY/5jikM8ahq/vaKX1a/hoehPt76HV8V/wf9BiPtvcUtCHyewmJ91DvrJ9Wq/Pqd9tm8cV0qHdIp9Wq/+eM6jRcTe0ut1qdvn6dderHmk6xNPoyGq2myfqHxHvYCr6Oz6svFK15IZPJxO7du0lPT6d79+6kpaW5NePU1NSwatUqxo0b15qXEaJZTpWbuO2d9ZyuqGFQ53jevG1U6xIPgNwP6x9rbB0C0TYiomHojRDdMdA1CTNBuLdLYwNOdXW+qDa2zoelpvHXkQGnAeXVb//hhx9m1apVHD58mPXr1/Ozn/2MsrIyZs2ahUajYc6cOcyfP59PP/2UHTt2MHv2bKKjo5k5c2Zb1V8IAKpqrNz53k/kn6kiKymad39xPnGRPsjok3rVPybJhwgXmiBcZMzYSHe7vm7y0chUW6skH8HMq26XY8eOcdNNN1FcXEynTp0YM2YM69atIytL3a/i0UcfpaqqinvvvZezZ88yevRoVqxYQVycrIMg2o7VpvDg4i1syy8hMdrAgtnnkRxbvysPgMoz8N1zMPQmyDyv6YtXl9Y/JsmHCBfBuMhY3QTDlevifoDH1prmJh/B0tLTTnmVfCxevLjR8xqNhuzsbLKzs1tTJyG88txXu1ix6yQRei1v3TaKHp08rDhq9+EsOLwa9n4Nv93d+IVtVigvUO8PvxW2/Eu976k1RIiQFITdLo0lQV3HQtYFkPej+tjmYVyHtHyEBPnti5D2zprDjh1q/3z9UEZ1a2BMgMWkJhyHV6uPy0/UL3M2D6prR2ubq+C96aBY1YWMIhOc5dKG+C4AIQIpGBcZ87hwWO0Kp8ZYuO0L52FJPkKW/PZFyFq+s5A/fLULUJdNv2pohueCigKf/BL+faPzWN3N4EqOwitD4O+j1ceb/wVHflDvJ/eGwder97ucB/oIH0YhRAC5jfkIko+Dpuqhc2mwbyz5aGhl0+a+jmhTsqutCEm7CsqYs3grigIzR3fl7vGN7NeSvx52fa7eT+yqJho15WA659wU7tBK9bb8BNhssPNT5/O1BsgYBveuh4TObRGOEIGhCcJuF08zWBriad8WR8tHE6ttBktLTzslqZ8IOWU1cM8HW6kyW7modzLPXj3Q80J2e5dBzu/hiwfUx0Nvgjm5ztH0ZbVdL1UlUJLvfN7n98HRtc7Hw29Rb1P6ySZyIswE4WwXb+ph85R81D5ful2CmrR8iJBisth4Z5+OgvJqeiTH8OrMEZ5XL604DUtudmmW1aiDRgHiM+BUGZQdh449YMFUKNrlfO62Rerteb+ErLEw4No2jUmIgAn1D2CrjPkIVZJ8iJChKArZX+7mcLmGuEg9b84aRUJUA2t57F+uJh4JmTDwGuh5CXS7QD0XnwGn9qgtHz+945542PW7Eqb9KXi+DQrRFoJxzIc3WjPgVASUJB8iZLzz4xE+2nwcDQqv/HwIPT1Nqd3wJmx+DwrV3WwZehNc/JR7mfjagak7PoIjazy/2PXvSuIhwl8wznbxZORsz8c9drtIy0cokN++CAmr9p1iXu3MlulZNi7qnVy/UE0F5PzOmXjEZcCYX9UvF187aPTgd+ofqB4T3c8PuQF04bufgxBOQTjg1FVkIjx6GNIGez7fWLeLLK8e1KTlQwS9o6creWDRZmwKXDcig4sijtYvVHlGnaFiroTELLjyL+ofLE97gcTXmZI7/hEYdQes+Qv0ngxj72+bQIQINsG4wqkrjabx/Xxa1fIRhMlWOyLJhwhqVTVW7n5/E2XVFoZlJjL3qgF8u6JO8rHyj7ByvvPxyFnQ65KGLxrfxf1xxnB1yfQBV/uu4kKEgmDc28WVYmv8fGum2gZjS087EoSprhAqRVF46rNcdheUkRQTweu3jMCor/NPtuos/PiK83HqIDj/7sYvnDVOXe8DYMRtsleLaL/cWjuC8MNYURo/3+iA0yYWGfO0KZ3wG/nti6D1wfqjfLL5OFoN/O2m4aQnRGE2136bsVlg19fqoFFzBaQMhF/92LxvbxHRcMunsPcrdTqtEO1WkM92aVHy4WGdj6tegS8fdC/nzWJmwuck+RBBacvRs8z9cicAj17ej3G93AeYanOehp/ech64cI53zcbJvSD5wabLCRHOgn22S4u6XTTuz826EDp0r19Oko+ACsJUV7R3p8+ZuPeDzZitCpcNTK23dHqM6STan95WH6QPhal/cu69IoRovmBcXt1VQ8nHqDvU20lP1j9XtwVHp/ecaHjcwE74i7R8iKBitSk8uHgrBaXqCqZ/un6oc+l0Sw3a755l7IElaFCg12S45aPAVliIcBGM3S400O0y7U9w/l3QqW/9c3Xj0Oo9j++QMR8BJb99EVT+/v0B1hwoJsqg4x+3jiQ+0mW9jR0fo/vf34gBFF0EmvGPBKyeQoSFUO120erUvZY8aXbyIS0fgRSMqa5op9YfOs3L3+wD4A/XDKJPap1N3PZ+BUC1PgHL7d9A19H+rqIQ4SVUu10aUzf5sFk9t+pIy0dASfIhgsLZihoeXLwVmwIzhnfmZyNd1uLYnwN/6g27vwRgXc+HIGVAgGoqRBgJ+paPJma7eFI30bBUgy6i6XLCryT1EwGnKAoPf7iNwjJ1nMcfrhnkPGk1w9JHoKIIANvQmynVehi5LoRogRBfZMwTT8mHIap+OWn5CChJ/UTAvfPjEb7dU0SEXsvfZg4nxlj7R8FSA9/Ph7OH1W8ud63COu2lwFZWiHAS7IuMNTTgtDGekg+9sX45GfMRUJL6iYDafqyEF77eDcDTV/RnYEaC8+SSm2H/CvX+5D9AxjAwN7VkshCi2TRBvshYS9RLPkygl5aPYBMm/9pEKDpnsvDAv7c41vO4dUyW82TRbmficd6dcL6sRCqEzwX7mI+WqBuHpRoMkR7KSctHIEnyIQLmD1/uIu90JZ0To3jxOpf1PA6thE/vUe/3uxKu+LM0kQrRJoJ8tktL1G35MFeD3kPyoZWPv0CSdicRECt2FrLkp3w0Gvjzz4eSEF27nkfRHvjXtepAM40OJj4e2IoKEc7cWj7C5MPYU7eLpy8v0u0SUGHyr02EklPlJp74JBeAuy7qwZgeSc6Ta/+qJh66CJj1BaQNDlAthWgHNEE+26UlPA049VhOWlMDSVI/4VeKovDEJ9s5XVFDv7Q4HprSRz1hKocvHoCdn6qPb/scssYFrqJCtAfBvshYS9RNPqwmz+Wk5SOgpOVD+NWSjfl8s7uICJ2Wv9wwDKO+9tvHzs+ciUeHbpA5JlBVFKIdCcPZLnWNvd/zcRlHFlCS+gm/yTtdwbP/3QXAw5f1oX96vHpCUeDYBvV+QleY/ZUMBhPCH8JxtovFpaXj5o+gx0TP5ST5CChJPoRfWG0KD/1nG5U1VkZ378gdF/ZQT5zaB/++Ac4cUh9PngsJXRq+kBDCd8Kx28Vc6bzf69KGkyoZ8xFQ8vVS+MU7aw6zKe8ssUY9f/75UHTa2j8Iq/7oTDxiUqD7hMBVUoj2JhxbPsxVzvuNxSRjPgJKfvuizR0uruD/VuwF1FVMu3SIVk8UbIcdH6n3r3sbBkwHnSFAtRSiPQrD2S41Fc0rJ90uAdWqlo/nn38ejUbDnDlzHMdmz56NRqNx+xkzRgYPtlc2m8JjH23HZLFxYa9kbjgvUz1RsA3+eZF6X6OFPpdL4iGEv7n9nwuT5KOhqbV1SctHQLX4t79x40beeOMNhgwZUu/c5ZdfzoIFCxyPIyI8bGcs2oV/rctjw5EzREfoeH7GYOcqpnuXOQtd8jswxgamgkK0Z67JR7jMdhl1O6z/Jwya0Xi5cIk3RLUo+Th37hw333wzb775Js8991y980ajkbS0tFZXToS2/DOV/HHZHgAen9qPzI613S17v4a1f1PvX/kX9Y+FEML/tK7JR5i0fMSmwCMHmu5WkW6XgGpR8nHfffdxxRVXcOmll3pMPlauXElKSgqJiYlMmDCBefPmkZKS4vFaJpMJk8k5NaqsrAwAs9mM2cc7mNqv5+vrBotgik9RFB77SJ3dMiorkRtGZKj1KjmKfsmtaGxmlKgOWHpe5tVOtcEUY1uQ+EJfSMWoaLGnH1abgq0ZdfZHfK6dQS1+HavN7aFmxjvoP3F+0bEoGpQGrh1S72ELtFV83lxPoyiK4s3FFy9ezLx589i4cSORkZFMnDiRYcOG8fLLLwOwZMkSYmNjycrK4vDhwzzzzDNYLBY2bdqE0Wisd73s7Gzmzp1b7/iiRYuIjo72pmoiiPzvpIbFh3QYNAqPDrWSUruj9bC8N8k68wMWbQQr+82jwpga2IoK0Y7FVBdy6e5HAdibejV7Mn4W4Bqppm+5zXH/8+Hv+ey6I478g8yzawHY3PUu8pMu9Nm1BVRWVjJz5kxKS0uJj49vtKxXyUd+fj6jRo1ixYoVDB06FKBe8lFXQUEBWVlZLF68mBkz6vfBeWr5yMzMpLi4uMnKe8tsNpOTk8PkyZMxGMJvcGOwxFd8zsRlr/xIWbWFxy7rw50XdoOaCnQf3oL2yA8AWGYvQ+k8yutrB0uMbUXiC30hFWNpPoZXhwNgveC32CY+0eRT/BGfYV6y8/WeKvbZdXVf3Is29z8AWKb/A2WQ52QrpN7DFmir+MrKykhOTm5W8uFVt8umTZsoKipi5MiRjmNWq5XVq1fz6quvYjKZ0Onc+9HS09PJyspi//79Hq9pNBo9togYDIa2+4fdhtcOBoGO74/Ld1BWbWFgRjy/HN8TvU4LO76C2sSD0b9C321sq14j0DG2NYkv9IVEjBFRjrs6nQ6dF/X1V3w+fQ2XGS56QwQ0ce2QeA9bwdfxeXMtr5KPSy65hNzcXLdjv/jFL+jXrx+PPfZYvcQD4PTp0+Tn55Oenu7NS4kQtWZ/MZ9tPYFGA/OvHawmHjYr/O/vaoHBP4epLwS2kkIIla6dzUR0HVQrU20DyqvfflxcHIMGDXI7FhMTQ1JSEoMGDeLcuXNkZ2dz3XXXkZ6ezpEjR3jyySdJTk7m2muv9WnFRfCpNlt55vMdANw2JouhmYnqvi1vT4GinerI+kt+F9hKCiGcXKfa2iyBq4e/uCYfsrx6QPk09dPpdOTm5vLee+9RUlJCeno6kyZNYsmSJcTFxfnypUQQen3lQQ4XV5ASZ+S3l/VVDx7bCMd/Uu+PfxgSMwNXQSGEu3aXfLis7SEtHwHV6t/+ypUrHfejoqJYvnx5ay8pQtDBU+d4feVBAH531QDiIw1w5EdYcrNaYNgtMPHxANZQCFGPa7eLzRq4eviLW/IhLR+BJKmfaDVFUXjmsx3UWG1M6NOJKwanw9kjsPBKUGrn2p93R0DrKITwwPUD2Baea1q4keQjaMj6sqLVPtt6nLUHT2PUa/nD9EHqEupHfnQmHpfOhc4jAltJIUTj2lu3i4z5CChJPkSrlFWbmfeVuoT6ry/pTdekaHX59K/VhYu44EG4cE7gKiiEaJ72lnxIy0dASfIhWuVv3+6n+JyJ7skx/PKiHursli/nQM05tcCAawJZPSFEc7W7MR8y6iCQJPkQLXag6BwLfjwCqINMI/RadazHuUK1wC+/l+4WIUKFtZ2N+ZBul4CS5EO0iKIoPPvfXVhsCpf0S2FS39qNAz+9R73tcp4kHkKEEul2EX4kyYdokW93F7F63ykMOg1PXznAeeLYRvV25C8CUzEhRMu0i+TDdYVTST4CSZIP4bVqs5Vn/7sLgDsu7EH35Bj1hNUCSm2/cd+pAaqdEKJFgin50LTRR5OM+Qga8tsXXnt7zWGOnqkkJc7I/Rf3UvuKD3wLCZ2dhfSRgaugEMJ7wZR8oGm6SIsuK2M+goUkH8IrhaXV/P37AwA8Ma0fsUY9/Hsm7P0KErs6C+rr71QshAhiwZR8aLTOVlRfUhTnfYN8QQok6XYRXnnh691U1lgZ0TWRa4Z1hq2L1MQDoOSoeqs1SH+qEKEmmJKPy+art2Pu8+11S/Kc9xNkn6lAkpYP0Wzb8kv4bOsJNBqYe/UgNDs+hs9+Vb+gdLkIEXqCaZ2P0Xep48YSuvj2ukV7nPflC1JAScuHaBZFUZi3dDcA1w7vzOAuCbDjE8+FpctFiNATbOt8JGa6z07xhaSe6q0+yrfXFV6T5EM0S86uk2w4fAajXsvDl/aCz+93drdc+0/3wtLyIUToCaZul7Yy9UU4/264Z02ga9LuSbeLaJLZauOFr9Xmyjsu7E5G+XbY8i/1ZOdR0Hmk+xOk5UOI0BPdMdA1aHsJnWHai4GuhUBaPkQzLN5wlEPFFSTFRPCriT0hf716IjIRfrG0frIhLR9ChI6blkC3i+DKvwS6JqIdkZYP0aiyajN/+WY/AHMu7U1c+WH4Jls9ecGv1cSj7mI90vIhROjoe7n6I4QfScuHaNQ/Vh7kTEUNPTrFcOP5XWHd350n+12p3moN7k+Slg8hhBCNkORDNOhESRVvrzkMwBNT+2Mo2gGb3lVPzvoSOvVV7+uk5UMIIUTzSbeLaND/rdiLyWJjdPeOXNonEV4Yqp7o1F/tI7aTlg8hhBBekJYP4dGewjI+3XIcgKeu6I8mby1YqtSTU/9YZ3dIafkQQgjRfJJ8CI/+vGIfigJXDE5nSEQBfHKXemL4LdBjgnthnbR8CCGEaD7pdhH1bDl6lpxdJ9Fq4DeT+8Dy26CiSD3paa8FrQ51F8raTZuk5UMIIUQjpOVD1PN/K/YCcN2ILvTqaIC8H9UT0/4PUgd4fpJr14skH0IIIRohyYdw8+OBYn48cJoInZaHzo+Cv44ASzXEpMB5dzb8RNeuF0k+hBBCNEKSD+GgKAovLldbPWaO7kp6/lIoO6aenPxs45s8uc54McS0YS2FEEKEOkk+hEPOrpNsyy8hyqDjvkm9YE/txnFj7oVhNzX+ZNftqSOi266SQgghQp4kHwIAq03hzyv2AXD7hd3odOgzOLZBPdl3atMXcO12MUjyIYQQomGSfAgAvtx2gr0ny4mP1HPXRT1h27/VExotZI5u+gKu3S4R0u0ihBCiYZJ8CMxWG3/5Rm31uHtCTxL2/gcOfa+evG9D8waQui6xLi0fQgghGiHJh+DTLcfJO11JcmwEt/ephs/vVU90uwiSejXvIq5TbaXlQwghRCMk+WjnLFYbf//+AAB3je9BVMFG58kZbzQ+w8WVVsZ8CCGEaJ5WJR/PP/88Go2GOXPmOI4pikJ2djYZGRlERUUxceJEdu7c2dp6ijZib/VIionglpEp8N856okLfwPxGc2/kGu3i8x2EUII0YgWJx8bN27kjTfeYMiQIW7HX3zxRV566SVeffVVNm7cSFpaGpMnT6a8vLzVlRW+ZbHaeNWl1SP62I/Ok1kXencx124XWedDCCFEI1q0t8u5c+e4+eabefPNN3nuueccxxVF4eWXX+app55ixowZACxcuJDU1FQWLVrE3XffXe9aJpMJk8nkeFxWVgaA2WzGbDa3pHoNsl/P19cNFt7G9+mWE+SdrqRDtIEbR2Vg2bfB8Q/CnDUevPg96TR6RyZr1kZ49VxvyHsY2sI9Pgj/GMM9Pgj/GNsqPm+up1EURfH2BWbNmkXHjh35y1/+wsSJExk2bBgvv/wyhw4domfPnmzevJnhw4c7yk+fPp3ExEQWLlxY71rZ2dnMnTu33vFFixYRHS3N923FqsD8rTqKqzVc1dXKpZ0Vup5exfCjb1MYP5T1PX/r1fUu2vcsHSvUVpSlg1/DrI9ti2oLIYQIUpWVlcycOZPS0lLi4+MbLet1y8fixYvZvHkzGzdurHeusLAQgNTUVLfjqamp5OXlebzeE088wUMPPeR4XFZWRmZmJlOmTGmy8t4ym83k5OQwefJkDAZD008IMd7E99nWExSv20GHaAN/uO1iYox6tD8VwlFIyejKtGnTvHptXcGfoUK9P3na9Dbb30Xew9AW7vFB+McY7vFB+MfYVvHZey6aw6vkIz8/nwcffJAVK1YQGRnZYDlNnRkSiqLUO2ZnNBoxGut/UBkMhjZ709vy2sGgqfisNoXXVx0G4Jfje5AYG6WeUNQmM60hCq23v58a55geQ2RM82fJtFB7fw9DXbjHB+EfY7jHB+Efo6/j8+ZaXg043bRpE0VFRYwcORK9Xo9er2fVqlX89a9/Ra/XO1o87C0gdkVFRfVaQ0TgfLntBIeKK0iMNnDb2G7OE5Yq9dbQcGLZoDOHnPfbOPEQQggR2rxKPi655BJyc3PZunWr42fUqFHcfPPNbN26lR49epCWlkZOTo7jOTU1NaxatYpx48b5vPLCezabwmsr1bEZd17YnVijS+OXpXbgr74FyYcQQgjRTF51u8TFxTFo0CC3YzExMSQlJTmOz5kzh/nz59O7d2969+7N/PnziY6OZubMmb6rtWixb/cUse/kOWKNem51bfUAsFSrty0Zr9F1LBz9H4y5r9V1FEIIEd5aNNW2MY8++ihVVVXce++9nD17ltGjR7NixQri4uJ8/VLCS4ribPW4ZUwWCVF1+uccLR9R3l/85+/Bwe9g4IxW1lIIIUS4a3XysXLlSrfHGo2G7OxssrOzW3tp4WPrD59hy9ESIvRabr+wW/0C5toxHy1p+YhNgaE3tqp+Qggh2gfZ26UdeW3lQQCuH9mFlDgP4zpkzIcQQgg/kOSjndhxvJTV+06h1cDd43t6LtSaMR9CCCFEM0ny0U68vkpt9bhqaAZdo2vAZqtfyJ58GFow5kMIIYRoJkk+2oHDxRV8nVsAwBMdvoc/ZsE7l0HdlfUdLR/S7SKEEKLtSPLRDryx+iA2BS7ul0Lagf+oB49tcI7xsHOM+ZBuFyGEEG1Hko8wV1RezcebjgPw4HlRcGq382RN7WYsR9fBGxMhf736WFo+hBBCtCGfr/Mhgst7a/OosdoYkxnF0OU/dz9Zcw5ikuA/s+Ccy5L4knwIIYRoQ9LyEcaqaqy8v17dTfjJrrug7Lh7AXvLR9UZ9+My4FQIIUQbkuQjjH20+RgllWa6doxmcNlq9eCExyExS71vTz7iOzuf1H08pA70b0WFEEK0K5J8hCmbTeGdNYcB+F2fo2j2L1dP9JsGEbHq/Zpz6iDTs2o5ZrwFt30hLR9CCCHalCQfYerbPUUcLq4gPlLPRHNtq8fQmyB9KBjtyUcFfPmg80l9LweNxv+VFUII0a5I8hGm3vzhEABP9z2GfudH6sGhN6m3ETHqbU0F5P3ofJJRNv8TQgjR9mS2SxjKPV7KhsNn0Gs1XF39pfNE5mj11p58fHqX89z01/xXQSGEEO2atHyEoXd+VGe4XD8onshja9WDt68AQ+0UWvuYD1edR/ipdkIIIdo7ST7CzBkTfL3zJACPKu+A1QTxXaDLec5C9pYPV9HJfqqhEEKI9k6SjzDzQ4EWq03h8iwNHQ5+rh685jXQurzVHpOPjv6poBBCiHZPko8wcs5kYW2RBgMWXqyZBzYLdDkfekxwL9hrMkQmuh/T6vxWTyGEEO2bJB9h5LOtJ6i2avhl/Abiz+5QD553R/2C3S+Cx/Pgmtf9W0EhhBACme0SNhRF4V/r8gG4JukoFAARcTDoZw0/aciN6pLrXcf6p5JCCCEEknyEjTUHijlUXEF/7XH6FHyhHpzxBugaeYu1Whj/iH8qKIQQQtSSbpcwsXDtEQAejV3qPOg6w0UIIYQIEpJ8hIGjpyv5dk8RACOUnerBi5+G2E4BrJUQQgjhmSQfYeD99XkoCjydtp4Es5qEMMrDQFMhhBAiCEjyEeKqaqws2agONL1e8w0AtkHXy7odQgghgpYkHyHus63HKa0yMyqxgoSzapeLddLTAa6VEEII0TBJPkKYoiiOgaavRL0JwLmIFIjvHMBaCSGEEI2T5COErT98hj2F5fQwnKXz2Q0AbO0qYz2EEEIEN0k+Qpi91SM79QcAbF3HcTqufwBrJIQQQjRNko8QVVBaxYpdJ0nhLBee/RQA27gHA1wrIYQQommSfISoxRvysdoUHkteg9ZqgszRKD0uDnS1hBBCiCZJ8hGCLFYbSzbmE0U1U60r1YPn3wUaTUDrJYQQQjSHV8nH66+/zpAhQ4iPjyc+Pp6xY8fy9ddfO87Pnj0bjUbj9jNmzBifV7q9+25PEYVl1Twe9TnRVQUQ1QH6Tg10tYQQQohm8WpjuS5duvDCCy/Qq1cvABYuXMj06dPZsmULAwcOBODyyy9nwYIFjudERET4sLoC4IP1RwGF63WrwAJcNh8iYsBsDnTVhBBCiCZ5lXxcddVVbo/nzZvH66+/zrp16xzJh9FoJC0tzXc1FG7yz1Syev8p5urfJdpSAmigz+WBrpYQQgjRbF4lH66sVisffvghFRUVjB071nF85cqVpKSkkJiYyIQJE5g3bx4pKSkNXsdkMmEymRyPy8rKADCbzZh9/E3efj1fX9efPlh3BEWBacbtYAVbl/OxGuLA5fcVyvE1JdxjlPhCX7jHGO7xQfjH2FbxeXM9jaIoijcXz83NZezYsVRXVxMbG8uiRYuYNm0aAEuWLCE2NpasrCwOHz7MM888g8ViYdOmTRiNRo/Xy87OZu7cufWOL1q0iOjoaG+qFvYsNvj9Zh09LQf53Pg7AL4a8g8sOvk9CSGECKzKykpmzpxJaWkp8fHxjZb1Ovmoqanh6NGjlJSU8PHHH/PWW2+xatUqBgwYUK9sQUEBWVlZLF68mBkzZni8nqeWj8zMTIqLi5usvLfMZjM5OTlMnjwZg8Hg02v7w9c7Cvn1ku38L/LXpFOM0rEHll9tcJwP9fiaI9xjlPhCX7jHGO7xQfjH2FbxlZWVkZyc3Kzkw+tul4iICMeA01GjRrFx40ZeeeUV/vnPf9Yrm56eTlZWFvv372/wekaj0WOriMFgaLM3vS2v3ZYW/3SceCpIpxgAzaSnPMYRqvF5I9xjlPhCX7jHGO7xQfjH6Ov4vLlWi8d82CmK4tZy4er06dPk5+eTnp7e2pdp9w6dOsfag6f5q6F2JlFiFgz+WWArJYQQQrSAV8nHk08+ydSpU8nMzKS8vJzFixezcuVKli1bxrlz58jOzua6664jPT2dI0eO8OSTT5KcnMy1117bVvVvN/694SipnOFq3Vr1QNYFga2QEEII0UJeJR8nT57k1ltvpaCggISEBIYMGcKyZcuYPHkyVVVV5Obm8t5771FSUkJ6ejqTJk1iyZIlxMXFtVX924Vqs5UPNx3jenviAXDZvMBVSAghhGgFr5KPt99+u8FzUVFRLF++vNUVEvUt31lIZWUld0cuVQ9c9QpEdwxspYQQQogWkr1dQsB/fspnpHYfyZRATCcYOjPQVRJCCCFaTJKPIJd/ppIfD5xmivYn9UCPSaCXJeuFEEKELkk+gtyHP+WTqTnJLH2OeqDPZYGtkBBCCNFKknwEMatN4aNNxxioyUOLDTp0h4GeF2sTQgghQkWr1/kQbWfNgWIKSit5M/IL9UDaYNBKviiEECK0ySdZEPvPxnzu0n3FQA6pB+IzAlshIYQQwgek5SNInamoYcWuQlbrXaYvx6YGrkJCCCGEj0jLR5D6bMtxzFaFBG2V86DF8zL2QgghRCiR5CMIKYrCf37KByBCY3Oe6Ds1QDUSQgghfEeSjyC0/VgpewrLMeq16BSzevCWTyBjWEDrJYQQQviCJB9BaEltq8e0gclolNqWj4zhAayREEII4TuSfASZqhorX249AcANw9OcJ/TGANVICCGE8C1JPoLMsp0FlJssZHaM4vzMWOcJnSypLoQQIjxI8hFkPtl8HIDrRnRBax/vgQa0MitaCCFEeJDkI4gUllaz5kAxADOGd3FOrdVFgEYTwJoJIYQQviPJRxD5dMtxFAXO79aRrknRYK1RT8h4DyGEEGFEko8goSgKn2w+BsCMEZ3Vg8ufVG91hgDVSgghhPA9ST6CxI7jZewvOodRr2XakHQoPQ77lqknFVvjTxZCCCFCiIxiDBIf17Z6TBmQSvypraBYnSetlsBUSgghhGgDknwEgRqLjS+2qWt7/DJtH7x9t3sBm9nDs4QQQojQJMlHEFi17xSdK/fwu6iVDD5YWr+AVZIPIYQQ4UOSjyDw9cY9fGl8GhTguIcCrl0wQgghRIiTAacBVlJZQ83+7wNdDSGEEMJvJPkIsC+3F3A+OwJdDSGEEMJvJPkIsE82HyNTUxToagghhBB+I8lHAB08dY4tR0uI0tQEuipCCCGE30jyEUCf1m4ilxIpi4gJIYRoPyT5CBCbTeHTLWrykWyU2SxCCCHaD0k+AmTd4dMcL6kiLlJPrE5WMBVCCNF+SPIRIPYulysGp6O1VHkupNGpt6mD/VQrIYQQou3JImMBUG22smxHIQDXDO8M++okH5EJ8ItlEJcGW96HwdcHoJZCCCFE2/Cq5eP1119nyJAhxMfHEx8fz9ixY/n6668d5xVFITs7m4yMDKKiopg4cSI7d+70eaVD3fd7iig3WchIiOT8bh3BXOleoLoUUgdAdEe44NcQnx6YigohhBBtwKvko0uXLrzwwgv89NNP/PTTT1x88cVMnz7dkWC8+OKLvPTSS7z66qts3LiRtLQ0Jk+eTHl5eZtUPlR9tlXtcrlqWAZaxQK22jEfGcPV2wHXBKZiQgghhB94lXxcddVVTJs2jT59+tCnTx/mzZtHbGws69atQ1EUXn75ZZ566ilmzJjBoEGDWLhwIZWVlSxatKit6h9ySivNfL/nFADXDOsMZpcul1s+gctfgCnPBah2QgghRNtr8ZgPq9XKhx9+SEVFBWPHjuXw4cMUFhYyZcoURxmj0ciECRNYu3Ytd999t8frmEwmTCaT43FZWRkAZrMZs9m3u7nar+fr63rjq+3HqLHa6J0SQ8+kSMwVRRgABQ0WfSyMvNNeWa+vHQzxtbVwj1HiC33hHmO4xwfhH2NbxefN9TSKoijeXDw3N5exY8dSXV1NbGwsixYtYtq0aaxdu5YLLriA48ePk5GR4Sh/1113kZeXx/Llyz1eLzs7m7lz59Y7vmjRIqKjo72pWkh4daeW/WVaruxqZXJnhWhTEZN3PYxFa+SroW8GunpCCCFEi1RWVjJz5kxKS0uJj49vtKzXLR99+/Zl69atlJSU8PHHHzNr1ixWrVrlOK/RaNzKK4pS75irJ554goceesjxuKysjMzMTKZMmdJk5b1lNpvJyclh8uTJGAwGn167OQrLqjmwbjUAD18/kc6JUVC0G3aBLjKOadOmter6gY7PH8I9Rokv9IV7jOEeH4R/jG0Vn73nojm8Tj4iIiLo1asXAKNGjWLjxo288sorPPbYYwAUFhaSnu6cnVFUVERqamqD1zMajRiNxnrHDQZDm73pbXntxny98yiKAud160C3TrWJlaI2U2kMUT6rU6Di86dwj1HiC33hHmO4xwfhH6Ov4/PmWq1eZExRFEwmE927dyctLY2cnBzHuZqaGlatWsW4ceNa+zJh4fOtJwC4elhn50H7NFt9ZABqJIQQQvifVy0fTz75JFOnTiUzM5Py8nIWL17MypUrWbZsGRqNhjlz5jB//nx69+5N7969mT9/PtHR0cycObOt6h8yDhSVs/NEGXqthisGu6zbYaptpopMCEzFhBBCCD/zKvk4efIkt956KwUFBSQkJDBkyBCWLVvG5MmTAXj00Uepqqri3nvv5ezZs4wePZoVK1YQFxfXJpUPJZ9tUVs9JvTpRMeYCOeJqrPqbVSHANRKCCGE8D+vko+333670fMajYbs7Gyys7NbU6ewoygKn29TFxabPryz+0lJPoQQQrQzsrGcH2w+WkL+mSqiI3Rc2j/F/WRViXoblejvagkhhBABIcmHH3xeu5z6ZQPTiI6o09gkLR9CCCHaGUk+2pjZauO/2wsAmD4so34BST6EEEK0M5J8tLE1+4s5U1FDUkwEF/ZKrl+gukS9jUz0Z7WEEEKIgJHko43Zu1yuHJKOXlfn122zQekx9b60fAghhGgnWryxnGhaZY2FFbtOAh5muRz4Bt6/Tr2vj4L0oX6unRBCCBEY0vLRhnJ2naSyxkpWUjTDMxPdT25613l/yh8gPh0hhBCiPZDkow3Zl1OfPjSj/uZ6J7apt/2uhPPu9HPNhBBCiMCR5KONnKmoYfW+U0CdvVwATh+E0qOg0cG1/4BGdv0VQgghwo0kH23kq+0nsNgUBnWOp1dKrPvJHZ+otz0mgFGWnhdCCNG+SPLRRj6r7XK5pm6rB8C+ZertwGv9WCMhhBAiOEjy0Qbyz1SyKe8sGg1cNbTOwmKVZ+DEZvV+z0v8XzkhhBAiwCT5aANfbFNbPcb2SCI1PtL95KGVoNigU39I8NAqIoQQQoQ5ST58TFEUx8JiHrtcDn6n3va82I+1EkIIIYKHJB8+tqewnH0nzxGh03LZoLT6BU5sUW+7X+TfigkhhBBBQpIPH7Ov7TGpXycSogzuJxUFzhxS7yf19nPNhBBCiOAgyYcP2WwKX25rZJbLuZNgrgSNFhK7+rl2QgghRHCQ5MOHfso7y/GSKuKMeib1S6lfoGC7epuQCfoI/1ZOCCGECBKSfPiQfaDpZYPSiDTo6hdYOV+9TR/ix1oJIYQQwUWSDx+psdj4KrcAaKDL5cwhdbCpRguT/+Dn2gkhhBDBQ5IPH/lh/ylKKs0kxxoZ2zPJ/WTVWfjvQ+r9rAugY3f/V1AIIYQIEpJ8+Ih9lstVQ9PRaetsFLf8KTj0PWj1cOEc/1dOCCGECCKSfPhAhclCzq6TgIcul+oy50Zy1/4Tel3q59oJIYQQwUWSDx/4ZvdJqsxWuiVFM6RLgvvJXZ+BpQqS+8Cg6wJSPyGEECKYSPLhA59tUWe5XD2sMxpNnS6XXV+ot0NvhLrnhBBCiHZIko9WOn3OxOr9xQBMH1ZnB1tFgYKt6v3uE/xbMSGEECJISfLRSkt3FGK1KQzunEDPTrHuJ9e9BhWn1PspA/xfOSGEECIISfLRSp/XdrnUa/Ww2dRZLgAJXSEi2s81E0IIIYKTJB+tkH+mkp/yzqLRwFVD6yQfJ3MBRb1//QK/100IIYQIVpJ8tMKX29W1Pcb2SCI1PtL95NH16m2vydBllJ9rJoQQQgQvST5aSFEUxyyXel0uAEU71dv0oX6slRBCCBH8vEo+nn/+ec477zzi4uJISUnhmmuuYe/evW5lZs+ejUajcfsZM2aMTysdDHaeKGPfyXMY9VqmDk6vX+DEFvU2pb9/KyaEEEIEOa+Sj1WrVnHfffexbt06cnJysFgsTJkyhYqKCrdyl19+OQUFBY6fpUuX+rTSweCjTccAmDIwjfhIg/vJXV9AwTb1viQfQgghhBu9N4WXLVvm9njBggWkpKSwadMmxo8f7zhuNBpJS0vzTQ2DkNlq44tt6niPGSPqLKeuKPD9fPV+9wnQSZIPIYQQwpVXyUddpaWlAHTs2NHt+MqVK0lJSSExMZEJEyYwb948UlJSPF7DZDJhMpkcj8vKygAwm82YzebWVK8e+/Vae91v9xRxpqKG5NgIxmQluF/vzCEMp3aj6IxYZrwDVqv64we+ii+YhXuMEl/oC/cYwz0+CP8Y2yo+b66nURRFacmLKIrC9OnTOXv2LD/88IPj+JIlS4iNjSUrK4vDhw/zzDPPYLFY2LRpE0ajsd51srOzmTt3br3jixYtIjo6ONfGWLBXy9YzWiam27i2m83tXPrZDZx/5FXORndndd/6cQkhhBDhqLKykpkzZ1JaWkp8fHyjZVucfNx333189dVXrFmzhi5dujRYrqCggKysLBYvXsyMGTPqnffU8pGZmUlxcXGTlfeW2WwmJyeHyZMnYzAYmn6CByWVZsa9uBKzVeGLe8fSPz3O7bz2+3no1v4F27BbsF7xsg9q3Xy+iC/YhXuMEl/oC/cYwz0+CP8Y2yq+srIykpOTm5V8tKjb5YEHHuCLL75g9erVjSYeAOnp6WRlZbF//36P541Go8cWEYPB0GZvemuuvXz3CcxWhX5pcQzp6t7dRHUpbPsAAG2XUWgD9I+2LX93wSLcY5T4Ql+4xxju8UH4x+jr+Ly5llfJh6IoPPDAA3z66aesXLmS7t27N/mc06dPk5+fT3q6h+moIeiTzeosl5+N9JB07fwMKoqgYw91F1shhBBC1OPVVNv77ruP999/n0WLFhEXF0dhYSGFhYVUVVUBcO7cOR5++GH+97//ceTIEVauXMlVV11FcnIy1157bZsE4E+HiyvYfLQErQau9rSw2M5P1dvht4Ihyr+VE0IIIUKEVy0fr7/+OgATJ050O75gwQJmz56NTqcjNzeX9957j5KSEtLT05k0aRJLliwhLi7OwxVDi73VY3yfTqTE1VlO3VIDR9ep9/tO9XPNhBBCiNDhdbdLY6Kioli+fHmrKhSsrBYL5za8Tz9NBjNGDK9f4MRmsFRBdBJ06uf/CgohhBAholXrfLQnp/71C35v+YKdxp70HHCX+8nyk/DOZer9rHGg0fi/gkIIIUSIkOSjOawW0vK+AGAgB8Ggcz+/4inn/awL/FgxIYQQIvTIrrbNcObAOsd9m77OQNKC7ZD7ofNxj4n+qZQQQggRoiT5aIaKZX9w3NdaqsDmsqrp6j8579/4b9lITgghhGiCJB9NUEqPkXl2nfvBmnPO+8c3q7e3fgr9pvmvYkIIIUSIkuSjMVYLyivDANim9ELR1g6RsScf5Seh7BiggS7nBaSKQgghRKiR5KMxRbvQ2tRd+vZm3oAmIlY9bipXb/d+pd6mDwFj6K9jIoQQQviDJB+NqFz3NgDrbP0ZMPVuMNZulGNPPnZ/qd4OrL9hnhBCCCE8k+SjIWcOEb3tXQBOxA5mUOcEZ+uGqRyObYKD36mPe10amDoKIYQQIUiSjwZYDqx03I+/sHZRMaNLt8tbFzsLywwXIYQQotkk+fDEXE31qpcBeFv7M8afP1I9bm/5OLXHWXbQz0BbZ9ExIYQQQjRIkg8PlLV/I7YiD4uiJWrI1UToa39NkYnq7Z7/qred+sF1bwWkjkIIIUSokuSjLqsZy//U3Xvn2WYx+ZLLnefi0tTbgm3qbZ/LZR8XIYQQwkuSfNT148sYqk9TrMRjHTGLTnFG57n4DPeyQ27wb92EEEKIMCDJh6vKMyjfPw/AEusk7hzf1/28veUDIG0IpA7wY+WEEEKI8CDJh52iwOb30ChWTikJ7Bvwa7omRbuXiUt33h96o3/rJ4QQQoQJfaArEDRWPA3/exWAr6yjuXtin/plEjLVW41OneUihBBCCK9J8mG392sAziqx7Oh5F7Mz4uuXScyEK16C6I4Ql+rnCgohhBDhQZKP6jLY8j6cOQjApTX/x+JpYxouf94dfqqYEEIIEZ7ad/KhKPDedDixGYA8WwqTRgygd6psEieEEEK0lfadfBz63pF4fGkdw+eai3l2soexHkIIIYTwmfaTfFjN6BbfyJhTRegWvwdWExz5AYBVjOQB8695+or+ZCRGBbiiQgghRHhrP8mHoqA9+A2pAGXOw6XaDvyt6goGpMcze1y3AFVOCCGEaD/aT/Kh1WG58m9s376dIUOGoNfp+GJfJQ9tSUGnj+DzG4ai18myJ0IIIURbaz+ftlodytCbyE+6CNuQG3nr3Fh+vSUDC3rmXj2QfmkeptYKIYQQwufaT8sHcM5k4WAZ/HrJdpbtPAnAAxf34sbzuwa4ZkIIIUT70W6Sj8LSasY8/x1qyCfRaODJqf2586Luga6aEEII0a60m+QjNd5IfKQejc3MBX3SuP/iPgzwtIqpEEIIIdpUu0k+NBoNK387nh++W8G0aUMxGAyBrpIQQgjRLrWfAadAXGS7ybWEEEKIoNWukg8hhBBCBJ4kH0IIIYTwK6+Sj+eff57zzjuPuLg4UlJSuOaaa9i7d69bGUVRyM7OJiMjg6ioKCZOnMjOnTt9WmkhhBBChC6vko9Vq1Zx3333sW7dOnJycrBYLEyZMoWKigpHmRdffJGXXnqJV199lY0bN5KWlsbkyZMpLy/3eeWFEEIIEXq8GoG5bNkyt8cLFiwgJSWFTZs2MX78eBRF4eWXX+app55ixowZACxcuJDU1FQWLVrE3XffXe+aJpMJk8nkeFxWpm68YjabMZvNXgfUGPv1fH3dYBHu8UH4xyjxhb5wjzHc44Pwj7Gt4vPmehpFUZSWvtCBAwfo3bs3ubm5DBo0iEOHDtGzZ082b97M8OHDHeWmT59OYmIiCxcurHeN7Oxs5s6dW+/4okWLiI6ObmnVhBBCCOFHlZWVzJw5k9LSUuLjG19Hq8XJh6IoTJ8+nbNnz/LDD+rW9GvXruWCCy7g+PHjZGRkOMredddd5OXlsXz58nrX8dTykZmZSXFxcZOV95bZbCYnJ4fJkyeH5Tof4R4fhH+MEl/oC/cYwz0+CP8Y2yq+srIykpOTm5V8tHjhi/vvv5/t27ezZs2aeuc0Go3bY0VR6h2zMxqNGI3GescNBkObveltee1gEO7xQfjHKPGFvnCPMdzjg/CP0dfxeXOtFk21feCBB/jiiy/4/vvv6dKli+N4WloaAIWFhW7li4qKSE1NbclLCSGEECLMeJV8KIrC/fffzyeffMJ3331H9+7um7J1796dtLQ0cnJyHMdqampYtWoV48aN802NhRBCCBHSvOp2ue+++1i0aBGff/45cXFxjhaOhIQEoqKi0Gg0zJkzh/nz59O7d2969+7N/PnziY6OZubMmW0SgBBCCCFCi1fJx+uvvw7AxIkT3Y4vWLCA2bNnA/Doo49SVVXFvffey9mzZxk9ejQrVqwgLi7OJxUWQgghRGjzKvlozsQYjUZDdnY22dnZLa2TEEIIIcJY0G3zak9w7IuN+ZLZbKayspKysrKwHMEc7vFB+Mco8YW+cI8x3OOD8I+xreKzf243p6Ei6JIP+zLsmZmZAa6JEEIIIbxVXl5OQkJCo2VatcJpW7DZbJw4cYK4uLgG1wZpKfsCZvn5+T5fwCwYhHt8EP4xSnyhL9xjDPf4IPxjbKv4FEWhvLycjIwMtNrGJ9MGXcuHVqt1WzukLcTHx4flPyi7cI8Pwj9GiS/0hXuM4R4fhH+MbRFfUy0edi1aZEwIIYQQoqUk+RBCCCGEX7Wr5MNoNPL73//e414y4SDc44Pwj1HiC33hHmO4xwfhH2MwxBd0A06FEEIIEd7aVcuHEEIIIQJPkg8hhBBC+JUkH0IIIYTwK0k+hBBCCOFX7Sb5eO211+jevTuRkZGMHDmSH374IdBVarbVq1dz1VVXkZGRgUaj4bPPPnM7rygK2dnZZGRkEBUVxcSJE9m5c6dbGZPJxAMPPEBycjIxMTFcffXVHDt2zI9RePb8889z3nnnERcXR0pKCtdccw179+51KxPK8YG6G/SQIUMcC/qMHTuWr7/+2nE+1OOr6/nnn0ej0TBnzhzHsVCPMTs7G41G4/aTlpbmOB/q8QEcP36cW265haSkJKKjoxk2bBibNm1ynA/lGLt161bv/dNoNNx3331AaMdmZ7FYePrpp+nevTtRUVH06NGDZ599FpvN5igTVHEq7cDixYsVg8GgvPnmm8quXbuUBx98UImJiVHy8vICXbVmWbp0qfLUU08pH3/8sQIon376qdv5F154QYmLi1M+/vhjJTc3V7nhhhuU9PR0payszFHmnnvuUTp37qzk5OQomzdvViZNmqQMHTpUsVgsfo7G3WWXXaYsWLBA2bFjh7J161bliiuuULp27aqcO3fOUSaU41MURfniiy+Ur776Stm7d6+yd+9e5cknn1QMBoOyY8cORVFCPz5XGzZsULp166YMGTJEefDBBx3HQz3G3//+98rAgQOVgoICx09RUZHjfKjHd+bMGSUrK0uZPXu2sn79euXw4cPKN998oxw4cMBRJpRjLCoqcnvvcnJyFED5/vvvFUUJ7djsnnvuOSUpKUn573//qxw+fFj58MMPldjYWOXll192lAmmONtF8nH++ecr99xzj9uxfv36KY8//niAatRydZMPm82mpKWlKS+88ILjWHV1tZKQkKD84x//UBRFUUpKShSDwaAsXrzYUeb48eOKVqtVli1b5re6N0dRUZECKKtWrVIUJfzis+vQoYPy1ltvhVV85eXlSu/evZWcnBxlwoQJjuQjHGL8/e9/rwwdOtTjuXCI77HHHlMuvPDCBs+HQ4yuHnzwQaVnz56KzWYLm9iuuOIK5fbbb3c7NmPGDOWWW25RFCX43sOw73apqalh06ZNTJkyxe34lClTWLt2bYBq5TuHDx+msLDQLT6j0ciECRMc8W3atAmz2exWJiMjg0GDBgXd76C0tBSAjh07AuEXn9VqZfHixVRUVDB27Niwiu++++7jiiuu4NJLL3U7Hi4x7t+/n4yMDLp3786NN97IoUOHgPCI74svvmDUqFFcf/31pKSkMHz4cN58803H+XCI0a6mpob333+f22+/HY1GEzaxXXjhhXz77bfs27cPgG3btrFmzRqmTZsGBN97GHQby/lacXExVquV1NRUt+OpqakUFhYGqFa+Y4/BU3x5eXmOMhEREXTo0KFemWD6HSiKwkMPPcSFF17IoEGDgPCJLzc3l7Fjx1JdXU1sbCyffvopAwYMcPyHDvX4Fi9ezObNm9m4cWO9c+HwHo4ePZr33nuPPn36cPLkSZ577jnGjRvHzp07wyK+Q4cO8frrr/PQQw/x5JNPsmHDBn79619jNBq57bbbwiJGu88++4ySkhJmz54NhMe/T4DHHnuM0tJS+vXrh06nw2q1Mm/ePG666SYg+OIM++TDTqPRuD1WFKXesVDWkviC7Xdw//33s337dtasWVPvXKjH17dvX7Zu3UpJSQkff/wxs2bNYtWqVY7zoRxffn4+Dz74ICtWrCAyMrLBcqEc49SpUx33Bw8ezNixY+nZsycLFy5kzJgxQGjHZ7PZGDVqFPPnzwdg+PDh7Ny5k9dff53bbrvNUS6UY7R7++23mTp1KhkZGW7HQz22JUuW8P7777No0SIGDhzI1q1bmTNnDhkZGcyaNctRLljiDPtul+TkZHQ6Xb2sraioqF4GGIrsI+4biy8tLY2amhrOnj3bYJlAe+CBB/jiiy/4/vvv6dKli+N4uMQXERFBr169GDVqFM8//zxDhw7llVdeCYv4Nm3aRFFRESNHjkSv16PX61m1ahV//etf0ev1jjqGcox1xcTEMHjwYPbv3x8W72F6ejoDBgxwO9a/f3+OHj0KhM//w7y8PL755hvuvPNOx7Fwie2RRx7h8ccf58Ybb2Tw4MHceuut/OY3v+H5558Hgi/OsE8+IiIiGDlyJDk5OW7Hc3JyGDduXIBq5Tvdu3cnLS3NLb6amhpWrVrliG/kyJEYDAa3MgUFBezYsSPgvwNFUbj//vv55JNP+O677+jevbvb+VCPryGKomAymcIivksuuYTc3Fy2bt3q+Bk1ahQ333wzW7dupUePHiEfY10mk4ndu3eTnp4eFu/hBRdcUG+K+759+8jKygLC5//hggULSElJ4YorrnAcC5fYKisr0WrdP9J1Op1jqm3QxenT4atByj7V9u2331Z27dqlzJkzR4mJiVGOHDkS6Ko1S3l5ubJlyxZly5YtCqC89NJLypYtWxxThV944QUlISFB+eSTT5Tc3Fzlpptu8jh9qkuXLso333yjbN68Wbn44ouDYprYr371KyUhIUFZuXKl21S4yspKR5lQjk9RFOWJJ55QVq9erRw+fFjZvn278uSTTyparVZZsWKFoiihH58nrrNdFCX0Y/ztb3+rrFy5Ujl06JCybt065corr1Ti4uIcf0NCPb4NGzYoer1emTdvnrJ//37lgw8+UKKjo5X333/fUSbUY7RarUrXrl2Vxx57rN65UI9NURRl1qxZSufOnR1TbT/55BMlOTlZefTRRx1lginOdpF8KIqi/P3vf1eysrKUiIgIZcSIEY6pnKHg+++/V4B6P7NmzVIURZ1C9fvf/15JS0tTjEajMn78eCU3N9ftGlVVVcr999+vdOzYUYmKilKuvPJK5ejRowGIxp2nuABlwYIFjjKhHJ+iKMrtt9/u+LfXqVMn5ZJLLnEkHooS+vF5Ujf5CPUY7eshGAwGJSMjQ5kxY4ayc+dOx/lQj09RFOXLL79UBg0apBiNRqVfv37KG2+84XY+1GNcvny5Aih79+6tdy7UY1MURSkrK1MefPBBpWvXrkpkZKTSo0cP5amnnlJMJpOjTDDFqVEURfFtW4oQQgghRMPCfsyHEEIIIYKLJB9CCCGE8CtJPoQQQgjhV5J8CCGEEMKvJPkQQgghhF9J8iGEEEIIv5LkQwghhBB+JcmHEEIIIfxKkg8hhE9lZ2czbNiwQFdDCBHEZIVTIUSzNbWt9qxZs3j11VcxmUwkJSX5qVZCiFAjyYcQotlct+NesmQJv/vd79x2Q42KiiIhISEQVRNChBDpdhFCNFtaWprjJyEhAY1GU+9Y3W6X2bNnc8011zB//nxSU1NJTExk7ty5WCwWHnnkETp27EiXLl1455133F7r+PHj3HDDDXTo0IGkpCSmT5/OkSNH/BuwEKJNSPIhhGhz3333HSdOnGD16tW89NJLZGdnc+WVV9KhQwfWr1/PPffcwz333EN+fj4AlZWVTJo0idjYWFavXs2aNWuIjY3l8ssvp6amJsDRCCFaS5IPIUSb69ixI3/961/p27cvt99+O3379qWyspInn3yS3r1788QTTxAREcGPP/4IwOLFi9Fqtbz11lsMHjyY/v37s2DBAo4ePcrKlSsDG4wQotX0ga6AECL8DRw4EK3W+V0nNTWVQYMGOR7rdDqSkpIoKioCYNOmTRw4cIC4uDi361RXV3Pw4EH/VFoI0WYk+RBCtDmDweD2WKPReDxms9kAsNlsjBw5kg8++KDetTp16tR2FRVC+IUkH0KIoDNixAiWLFlCSkoK8fHxga6OEMLHZMyHECLo3HzzzSQnJzN9+nR++OEHDh8+zKpVq3jwwQc5duxYoKsnhGglST6EEEEnOjqa1atX07VrV2bMmEH//v25/fbbqaqqkpYQIcKALDImhBBCCL+Slg8hhBBC+JUkH0IIIYTwK0k+hBBCCOFXknwIIYQQwq8k+RBCCCGEX0nyIYQQQgi/kuRDCCGEEH4lyYcQQggh/EqSDyGEEEL4lSQfQgghhPArST6EEEII4Vf/D7o3eLndlYv/AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Try your hand at trial and error data fitting\n", "\n", "# adjustable parameters\n", "CpH = 5 # joules/deg C\n", "CpS = 1 # joules/deg C\n", "Ua = 0.04 # watts/deg C\n", "Ub = 0.04 # watts/deg C\n", "\n", "A = np.array([[-(Ua + Ub)/CpH, Ub/CpH], [Ub/CpS, -Ub/CpS]])\n", "B = np.array([[alpha*P1/CpH], [0]])\n", "C = np.array([[0, 1]])\n", "\n", "pred = tclab_ss(A, B, C)\n", "ax = pred[\"T1\"].plot()\n", "data[\"T1\"].plot(ax=ax, grid=True)\n" ] }, { "cell_type": "code", "execution_count": 191, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 191, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9dvjw4bjzzjsxYMAAXHbZZfjPf/6D7t2749VXX9V8zNy5c1FSUiJ9FBQUBPsUiIjIjXwJsJn2EvJVX/LKt64/gD/Zkq/yWM/j1bIprGExlt81LHrU1NTg5ptvRl5eHr777juv2RU1VqsVF198sdcMi81mg81mC3SoRETkB/daEbNQZFgEAYAymtKTHbFY6s/JofIAM51vUxT0DIsYrOTm5mLNmjVo1aqV388hCAJycnKQnp4e7OEREVET5C07It5jlaWMahxOzePIGH5nWMrLy3Ho0CHp67y8POTk5CAlJQUZGRm48cYbsWPHDnzxxRdwOBwoKioCAKSkpCA2NhYAMG3aNLRr1w5ZWVkAgGeeeQbDhw9Ht27dUFpaildeeQU5OTl47bXXgnGOREQUJPKLtrmmhGSfq9zvrWBWvCvKYoGj7tF3vLPZr+eg0PM7YNm2bRvGjRsnfT1nzhwAwPTp0zFv3jysWLECADBw4EDF49auXYuxY8cCAPLz82G11id3zp8/j3vvvRdFRUVITk7GoEGDkJ2djWHDhvk7PCIiCqFwrePwNiUk1uVYrQAcrtt2HyvxPC48Tz1i+B2wjB071ntqTcdPdN26dYqv//Wvf+Ff//qXv0MhIiIC4F7D4nm/3gyLN8ywGIt7CRERkW6+AgOj+Ppj2dvd4n1Wq/eAxUSn2yQxYCEiIt3MFKRoUdt9WW3Vj/vxUT4CFkYsxmLAQkREDRIOwYsoGFNCZCwGLEREpJta9sIMfPWH0RNc+Z4SMue5NxUMWIiISD+TXrN9BRN6CmZ9ZVjCKaMUiRiwEBFRg5hpibOvoeiZEvI1I2Ses22aGLAQEZFu4XrR1tOHhRUs5saAhYiIdPPVUdYovmpY9GVYfE0JmemMmx4GLERE1CBmun4HUsOi9zRMdLpNEgMWIiLSzawrZZSZH88xOj33MpQ9tm5KyFcNizlPvclgwEJERLr5CgzMYOrrP2JH/jnFbXoyLGzDYm4MWIiIKOzJw5H9RWW44Y0fFffrqmFh2a2pMWAhIiLdzLqXkDv3sXlbJSSelZ4MCwtvjcOAhYiIdJNfsE116fYxGD2Bhp78CuMV4zBgISKisOd7lZCXx/oRhDBeMQ4DFiIi0s1XvxOjBNTptu5fX31YyFgMWIiIKOLpK7r1jTUsxmHAQkREDWSei7evkejpw6InYjHPGTc9DFiIiEg3804JBd7plkW35saAhYiIdDNrszifGZYg7CVExmLAQkREDWLO0EWdt8yIP7s1mzVgawoYsBARkW5mnRIJZJUQpAxL4K9DocOAhYiIdFN2ug2fq7f3TrcubM1vbgxYiIioQcwUrgRUw+LP65jppJsYBixERKSbabMqXsbldAo4X1Hj86GsuTU3BixERKSbWTc/1BqKIAi46f82+nis/hNh0a1xGLAQEVGDmDbbImOvdWL70XNej/FnWXMYnHLEYsBCRES6mfWCrTWuWh3Vtn41jtM9Igo2BixEROQHQeUz42lN1TgcOgKWumiHNSzmxoCFiIjCnlaGxaEjJVS/W7Oe1zFTmNa0MGAhIiLdFNdrE127azUyKbXedj0USXsf6qhh8WdQFFQMWIiISDeTxiuocagHJnriFRE73ZobAxYiIgp71RoBi1qGxX1ah0uVwwMDFiIi0k1+rTdTPYc/GRb3YUvLmvW8kHlOuclhwEJERLqZNRtRXas/w+Lepl/wo+rWrOffFPgdsGRnZ2PKlCnIyMiAxWLB8uXLFfcLgoB58+YhIyMD8fHxGDt2LPbt2+fzeZcuXYrevXvDZrOhd+/e+Oyzz/wdGhERNSIzXbprNIpuxeAkylofjLgf6VcfFjOddBPjd8By4cIFDBgwAAsWLFC9/+9//zteeuklLFiwAFu3bkVaWhquvPJKlJWVaT7nxo0bccstt+Cuu+7Crl27cNddd+Hmm2/G5s2b/R0eERGFkHJKyLhxuNOuYXENMloWsHhmWOr7sFx6UasQjZAC5XfAMnHiRDz33HOYOnWqx32CIGD+/Pl48sknMXXqVPTt2xfvv/8+Kioq8PHHH2s+5/z583HllVdi7ty56NmzJ+bOnYvx48dj/vz5/g6PiIhCyExBikgQBM0aFkddwBIbZZUd7/b4un8tAN7/9TBsnHu59msFMlAKSFBrWPLy8lBUVIQJEyZIt9lsNowZMwY//vij5uM2btyoeAwAXHXVVV4fY7fbUVpaqvggIqLGY5Z6jlqnoN04TsywRHnLsLj+tVgsiI6yIj05XvO1zFRo3NQENWApKioCALRt21Zxe9u2baX7tB7n72OysrKQnJwsfWRmZgYwciIi0sMsQYqcVnYFkAcs2hkWMW/CvYTMLSSrhNx3vBQEwecumP4+Zu7cuSgpKZE+CgoKGj5gIiLSxYw1LDW12gMRA5YYLzUsIjaOM7foYD5ZWloaAFfGJD09Xbq9uLjYI4Pi/jj3bIqvx9hsNthstgBHTEREDWWWa7fd4dC8Ty3D4r6BM4OQ8BDUDEvnzp2RlpaG1atXS7dVV1dj/fr1GDlypObjRowYoXgMAKxatcrrY4iIiADtJc2Aeg2Le6RVX3TLPixm5neGpby8HIcOHZK+zsvLQ05ODlJSUtChQwc8/PDDeP7559GtWzd069YNzz//PBISEnD77bdLj5k2bRratWuHrKwsAMBDDz2E0aNH429/+xuuvfZafP7551izZg02bNgQhFMkIqJgMePmhzUaTeOA+mXNsYoMi1bjOB0vZpJzbor8Dli2bduGcePGSV/PmTMHADB9+nQsWrQIjz76KCorK3Hffffh3LlzuOSSS7Bq1SokJiZKj8nPz4fVWv/LM3LkSCxevBh/+tOf8NRTT6Fr165YsmQJLrnkkkDOjYiImgCtHiwA4BB0rBJi0W1Y8DtgGTt2rNdlXRaLBfPmzcO8efM0j1m3bp3HbTfeeCNuvPFGf4dDRESNSD4lYpbpEa22/ADgcIidbmWrhNyOqV/WHOyRUTBxLyEiItLNlKuEdGRYoiyAuFDIM8PioquGxSTn3BQxYCEiorDmNcMitea3wlqXQvHcrbm+Nb8vZskqNUUMWIiISDcT1tzqWiUUZbVIAQn7sIQnBixERKSbvIbRLG3q9XS6dQUs6hkWkZ4pITIOAxYiIgprdh1TQlFWi3YNix9xlzlCtKaJAQsREelmzikhnRkWaNSwwI8aFpNklZoiBixERKSbGa/XtU4dq4RkGRbPolv9r2XG828qGLAQEVGDmOXi7SVekTrdRlks0iohrSkhX5v0krEYsBARkR9MEqXIeBuRUwxYoixSK1vtPixkZgxYiIhIN7NkVeS81ZWoZ1jUH89lzebGgIWIiBrMDEWoejIs0bIaFvdH+Lf3ofHn21QxYCEiIt1Mebn2Migxw2K1amdY4EcNiwnisyaLAQsREekWyAqbUPGW9XDUVeRG6+l0G/SRUTAxYCEiogYzQbziNWgSW7RYvXS69Weaxwzn21QxYCEiIt3MULPizmOKR0aeYfHV6ZaN48yNAQsREenmUf5hggu41ymhuvFZLd463Yp01LA0YHwUHAxYiIgorHmLmWpVVglp1eGwb5y5MWAhIiLdtLMTxtHVOE5Ww+LZOK6uD4ue1zLDCTdRDFiIiEg39+kXU1zA9TSOs1pgrbviBVLDYo4QrWliwEJERGFNb+M4sYbFo9Nt3b8WPTUsjFcMw4CFiIj0C2BJcKjoqWGxeul0Cx+t+ff/5Wq0TIhReyQ1IgYsRESkmxkv2N5WKtXUNWKJibJqd7qtoxWwxMVEcSdnE2DAQkREDWaGKRJvQ7hgdwAAmtui63drdroX3fomhitmON+migELERHpZsYLtrcxldlrAbgCFjHD4tlLxvWvtxoWMcFihimwpooBCxER6WbGC7a3EZVX1QAAmsdFS9NDr687rHx8fcQi+ffdw5AcH4PX7xjsdmzAw6UGijZ6AEREFL7McAH3VsNSXpdhSbRF4+iZCgBA9sFTysfX/SvPr1zWrQ1y/nylrHaFNSxGY4aFiIh0C2TjQCOUV9VNCcVp/31e34dFGZTIv7ZodMmlxsOAhYiIdDPj9VpvDYvm4+v+9ZZDkYpuTfkdaBoYsBARUYOZIeOgFUQIgiBNCblnWByylUKCjz4s8vvMcL5NFQMWIiLSzQy7M7vTGlJFtUO6L9EWo7ivqsbhcTyrVMyNAQsREenmsSTYkFEoaY1BzK5EWS2Ii1Fe7irVAhYvKRY9bfsptBiwEBGRfh5d7Y0PWbSGUFZVX7/iHoxUVtcHLHpOgVNCxmPAQkREYU2rhqXcreD2qcm9pfvkU0Li41l0a24MWIiISDf3C7YZLt9aWY/yKmXAcveozmjXIh6AckpI0LNMyMdrUegxYCEiIt3MeMHWmpYqt9d3uRWJtSwV8imhun+9t+ZnDYvRGLAQEVGDmSGA0VPDIoqPjQKgnmHRE5OY4HSbrKAHLJ06dYLFYvH4uP/++1WPX7dunerx+/fvD/bQiIgoQB7BgQmu4FpDOFVuB6DMsMTHuAKWqmo/a1ikolsTnHATFfS9hLZu3QqHo/4XYe/evbjyyitx0003eX3cgQMHkJSUJH3dpk2bYA+NiIgCZMbLtVYM8fevDwBw7SMkiothhiVcBT1gcQ80XnjhBXTt2hVjxozx+rjU1FS0aNFC9+vY7XbY7Xbp69LSUr/GSUREgTPDqhlfY5BPCSWoTAmJvNewNHBwFDQhrWGprq7Ghx9+iJkzZ/osWBo0aBDS09Mxfvx4rF271udzZ2VlITk5WfrIzMwM1rCJiEiDGadEfA1JPiVki66bEqpxehzntTV/XTBjwtNvMkIasCxfvhznz5/HjBkzNI9JT0/HW2+9haVLl2LZsmXo0aMHxo8fj+zsbK/PPXfuXJSUlEgfBQUFQR49ERG58yhhMcEF3NcQ5BmWKKsr8HCq7CXkTX0wY4ITbqKCPiUk9+6772LixInIyMjQPKZHjx7o0aOH9PWIESNQUFCAF198EaNHj9Z8nM1mg81mC+p4iShyVFTX4va3N2Ncj1Q8dEU3o4cTsUxx+fYjahIDD6cgD1iU9wXppSjIQpZhOXr0KNasWYN77rnH78cOHz4cubm5IRgVETUVS7YWIKfgPP615qDRQ4koZrxgextSenIcruqTJn0dVReVyBIsssd720uIjBayDMvChQuRmpqKa665xu/H7ty5E+np6SEYFRE1FdW1njUKFAxunW5NEMFoDeHGIe3x4k0DFLdZpYDFvwyLWIdp/Nk2XSEJWJxOJxYuXIjp06cjOlr5EnPnzsXx48fxwQcfAADmz5+PTp06oU+fPlKR7tKlS7F06dJQDI2IiCKM1iohq0oAYlWrYfFnLyFGLIYJScCyZs0a5OfnY+bMmR73FRYWIj8/X/q6uroajzzyCI4fP474+Hj06dMHX375JSZNmhSKoRFRE8HrSmi4X7DN8H3WCiKsKikTMYhxNLiGxQxn3DSFJGCZMGGC5g910aJFiq8fffRRPProo6EYBhERBVk4rRJSa6chrRJSqWHx1odFvMsEp9tkcS8hIopILJJsOrQzLGq3eU4JiU/gvQ8LGY0BCxER6eY5JWR8zkG7hsUzzFBb1izd5+U1pKJb40+3yWLAQkQRideV0PAIDszwjfYjw+J9WbM2qejWFCfcNDFgISKisOZPDYu0Ski16Ja7H5oZAxYiikisOQgNM64SUtSjyKivEtJe1uwNNz80HgMWIopIZriQRiIzfl+1xqRedOv6199lzdLmhw0YHwUHAxYiImowMxShaq4SUolYxGXNgkoNi7dlzWIwY4bzbaoYsBARkW7uPbbMUISqNQa1jIlYp+Jw+pdh8fVaFHoMWIiIKKw1pNOtouhWR2t+Mh4DFiIiajAzT5HoXdYMPTUs7MNiOAYsRESkmxkv2FpbwahmWFQ2PxR5W9Zc34eFjMKAhYiIdHOv4TDDBdyvPiwWlT4s/ryWGSO2JoIBCxERNZgZLuD+7SXk+le5rNl3DYu0SqgB46PgYMBCRES6mSA+8eDPXkKqy5rr1zVrYuM44zFgISIi3Tw63ZoggPEnw6K6rFm8z1sfFjDFYjQGLEREFNb8q2Fx/au+l5Ce12LEYhQGLEREpJsZL9f+9GFR73TrRw2LGb8BTQQDFiIi0s2j060pLuBaNSyetzW00y1LWIzHgIWIIpI5LqTUGPzKsKgsaxZ5q2EBG8cZjgELERHp5n69NkNNh1YQoZYxUath8Xa8x2v5MS4KLgYsRBSRuAw1REx4xfZnWbPU6VaxrNn3SUmdbpliMQwDFiIiajAzXL/9axznbVmzNgbAxmPAQkQRyQwX0khkxtb8KtsCAajPpihu87Ks2VtUwr2EjMeAhYiIdDNjIKg1JaTWh0VtWbMYvKhlZNyfy4zn31QwYCGiiCS/VrHuIHRM8b0NUqdbtZoX3S9GIceAhYgikupeMRQwM34rtcakd1mzoCfDIh3bkBFSMDBgIaKIx2tM8HjsJWTMMBS0sjzedmuWByxOp+tftSkkEYtujceAhYgikvwCo9Zzg4LDDN9av/YSUlvWLLbm95phsXh9LQo9BixEFJE4JRQaZmgU586fTrdWlSkhMXjRU8PC3yXjMGAhoohnxotsuPK8YBv/vdUaQZTKFU6aEnLKAxbfmx+Kd/J3yTgMWIgo4vGv4tAxw/dWu4ZF35QQdGRYWMJiPAYsRBSRlMuajRnDoeIyFJytMObFQ8QE8YkHv2pYVJY1SxkW33sfmiJAa6qijR4AEVEoCCpFlY2ppKIGV7yUDQD45YVrGv31Q8btim2K67cffVjUljWLsYu3VUI+XooaATMsRBTxjPiruLC0Uvq8xuFs/AE0IX5tfqjWmt/tPjXSKiGmWAzDgIWIIp4Rl5hYWcVnZY3DgBGEhvv30gzXb782P1SpYdFTdMs+LMYLesAyb948WCwWxUdaWprXx6xfvx5DhgxBXFwcunTpgjfffDPYwyKiJsyIPizRVlnAUh1BAYtH4zjjIxbtH6++Zc1Sp1svKRYGLMYLSQ1Lnz59sGbNGunrqKgozWPz8vIwadIk/OY3v8GHH36IH374Affddx/atGmDG264IRTDI6ImxogsgPyCWBFBAYsZaW9+6Hmb2rJmwZ8aFuPjsyYrJAFLdHS0z6yK6M0330SHDh0wf/58AECvXr2wbds2vPjii14DFrvdDrvdLn1dWloa0JiJKIIZcJFxyK5skZVhcSu6NcEFXGsMauGHmEX55UwFPt1WgJuGZuqbEpI63ZrghJuokNSw5ObmIiMjA507d8att96KI0eOaB67ceNGTJgwQXHbVVddhW3btqGmpkbzcVlZWUhOTpY+MjMzgzZ+IoosRlxk5H/BV9bUNvrrh4oZL9cNWdYMAH/8724UlVTp6nTLZc3GC3rAcskll+CDDz7AN998g7fffhtFRUUYOXIkzpw5o3p8UVER2rZtq7itbdu2qK2txenTpzVfZ+7cuSgpKZE+CgoKgnoeRBQ5nIZnWCJ3lZAZLuD+ZFii3IKS6lqn9Hhvq4TIeEGfEpo4caL0eb9+/TBixAh07doV77//PubMmaP6GPcoWJCa+Gj/9thsNthstiCMmIginRFLUeWNySqqIyjDYsqiW/01LO63CRBk1xzt1xCvR2YI0JqqkC9rbtasGfr164fc3FzV+9PS0lBUVKS4rbi4GNHR0WjVqlWoh0dETYAR1xj5hS2SlzWbgfaUkOdtUW5pFKcg73TLxnFmFvKAxW634+eff0Z6errq/SNGjMDq1asVt61atQpDhw5FTExMqIdHRBFK/pe/EX8VyzMsldWOiG04ZobT0syweFnWLHIKgqxxnO+9hCL15xgOgh6wPPLII1i/fj3y8vKwefNm3HjjjSgtLcX06dMBuGpPpk2bJh0/a9YsHD16FHPmzMHPP/+M9957D++++y4eeeSRYA+NiJoQRWt+I6aEZK8597M9GP2PtSip1F5IEC7MeMH2ow2LR52KIAj1rfm9vAb7sBgv6AHLsWPHcNttt6FHjx6YOnUqYmNjsWnTJnTs2BEAUFhYiPz8fOn4zp07Y+XKlVi3bh0GDhyIv/zlL3jllVfYg4WIAiK/sAp1X/94+DROldm1HxRE7n0+Cs5WYun2Y43y2k2NPzGUe3M4pyBvHKf9OCnD4ufYKHiCXnS7ePFir/cvWrTI47YxY8Zgx44dwR4KETVhygwLsPZAMWYu2obYKCsO/nWi9gODRG1lUkx05O2GYoaEi2YNi8ptqlNCOpY1+3wxCrnI+99DRARlwCBAwPoDpwAA1Y20EaFDJWKJj9Hu+h0uzBCguNNeJeQZgLgva3Y69W3dIK0SYsRiGAYsRBSR5BcWI/qwqF0EIyJgcbtgm/kCrpYvcY9h9GZYWMJiPAYsRBSRDC+6VYmS4mL4lhsKmo3jdCxrFmTLmtnp1tz4v4eIIpKi6NbgTrciXTUSJufROM4EF3DNzQ9V8iLeMiwsYTE3BixEFJGMvrCoZXX01EqYnfsZmOGM/MmwVNUoa5hcfVjEDIu3V2GnW6MxYCGiiCS/sBgRKKjV9qpNE1Hg/NlLqHXzWMXXrk63dcfrmRIyRYjWNDFgIaKIZKZOt6JIiFc8p4SMPynNIEIl/kiMi8H6P46V6olcjeMErcO9PRU1MgYsRBSRlMuajXj9SJ0Scl8lZDztDIt6mNGxVTNktIgHIDaOc92up8YoAn6EYYsBCxFFJKNXCakFJ5E4JeQ0wTn5s/mhSAxOXEW3OjrdSlNCZBQGLEQUkYzuw6I+JRT+lzv3U6hxmOCc/KhhEYkFtk7FXkLe+rBwXbPRGLAQUdgpKqlC9sFTXjMnyruMy7D0yUjyuC2S1DRS52BvNJc1e0mxiBkWQah/vLeMTASsSA97DFiIKOwMz/oW097bgrUHijWPMbwPS911vFVzG0Z3bwPA1QY+0tSa4KT8WdZcf1/9lJB4Ct4CHOm1/B0cBQ0DFiIKW9kHT2vep6hhaYSxuPv255MAgChL/fSDWjO5cOOe1aquNf6c/Nn8UFQ/JSTvdKt9PDvdGo8BCxGFLW9TLPISksaeitl05Ay+2lsEwNUKPkqafvBvHEfPXMB/tx8zVbGu+ymYIcOi9fPVW3Trfpvqc6FhP0MKnmijB0BE1FC1Xi7kRvZh2Zp3VvrcarFAEDMsflzbC85WYMw/1gEAKmscuGt4xyCOMHhMUcOi+fP1VsMiPlZfHxY2YjEeMyxEFLYcXlaoKJc166tPCBZ7bf1F3GqxKFak6LF853Fc9ve10tc/5GpPfTU29zMwwyohrRHYorUvcVINi1Nnp1sfr0WhxwwLEYUtvTUhAoRGTeVXy7IOUVaLdJHTG7C8tPqg4mszTLuIPJc1m2BsKt/Xyf3TFSu03MmDSEFHDYuXl6JGwgwLEYUtb7UdTgNXCVXLMyxWi+yveX0DaZkQo/jaDFkMkfsS4loTjE1tBAtuH6xrWbO80633vYQsmq9FjYMBCxGFLa81LAZNCTmdAlbtK5K+jrJAKrrVe21PTlBu0CfPsBScrUBltSPwgQaJGTIsDQlIrbJCaF2rhBoyMAoqBixEFLa8ZSwURbeNOCX0+a7jOFFSJX1ttcpqWALMsPxcWIrL/r4WV83PDs5gG8CMnW4bsoOyRbasWZBu07FbM+eEDMOAhYjClph5OF1u97iQON0yLI1lzc+ezeysVs8ltN5Euf2pX1uXxfi6bql0/tmKQIYYEM+i2/DOsDjlq4TCKI1SUlGDN9cfRmFJpdFDaTQMWIgobDmcAlbuKcTQ59bg6RX7FPfJL2JOQWi0KaHkeGV2xOkUZFNC9YMqq6rB3uMlqs9hr1EGAeLUl3sgYwa14Rqw1F395J1uvfdhafhrhcIj/92FF77ajzve3mz0UBoNAxYiClsOp4AXvtoPAPhg41G3ewXFZ/IMTCh3GPYIWATlvjWiXy34AZNf3YDsg6c8nqOyRlmjIha2miJgce90a4opIf+p/Uy8d7oVi26NP18AWFPXSfnI6QsGj6TxMGAhw9Q4nPh6byHOlNuNHgqFqVqnoDnNIl8J7H5IY3a+dQiCNCUkX9WUV3ehWbHrhMdjqtwCFnGZtLcMQGNx/86ZI8PSkBoWlSkhr7s1m4tZMj2NiQELGeb9H3/BrA934IY3fjR6KBSmHE5B841b+ZewckoolJ3u3VfwOByC18Zxakuz3TMsF+y1AIAo2Tu2WYo/zVDD0hDS/k5O/2pYTPJtb5IYsJBh1h1wpcJ/OWNcASGFN1fAon4FUdawuE0JhfCqIwYXIocgSFM54lTUv2SN4dSWZrsHPYUlVfh0W4EiwyLvptuYPFYJmWCfo8CWNdc/3msGS1wl5P9LUZAwYCHDpCfHGT0ECnOuv47V71PkVxpxSqjCLTsiCIKiSRkAvPxtbv1YVE5ALRj54393Kzrouk8bNRb3Go4agwInuYbUlcizXvWt+bWPr9/80O+XoiBhwEKGSW8RL31u1JsvNY5ahxN7jpUEfddhrzUsik63yimhUO5+7DEl5KwPWNS2ElBru6/VGK5I1t+lqsb4QAHw3ryvsTQkiLAogkixcZzvPixkHAYsZJhEW/1WVsfPN51eAk1R1lf7MWXBBvzjmwNBfV75X8ceBOWnyimhoA6j/nmdgseUUK1TUDSOs9d6BjTuqmrVAxZ5/xXDMix1wxWnuapNUMPSsFVCrn/lv0O69hLipJBhGLCQYeT/8U+XcaVQJHt3Qx4A4M31h4P6vLUOLzUsss/dszChKFj9z7YC9H9mFTbnnVXc7pTXsAgCLtjdlizrqGERyQMW98LcxiKONibKdU7hukpIrTW/jhIWTgkZiAELGUb+Pm2GtDKFXmxU4G858poPh84pIbjtJRSKKaFH/7sb5W7ZFcC1vLp+WbNKUa7bWFxZGFcQMKZ7G8V9BSbIsIhi6n6W5mjN7z//Nz9swIuEyKHicqOHYAgGLGQY+QUlXJdGkn9auO2R0xDy3xuHoJ2gd4tXFI9rzPjYISiXNZdVuU0ZuV3wT9f1JbJagLenDVXcJw8OjKphEb+NsVLAYvz/3YbVsLj+VfZh8XK8STqxFJytwBUvrTd6GIZgwEKGkb/JmOGvNAq9YAQs8sJVh1PQ7FrrvkrIvQi3sThkrfmdgoAL1e41LsoLfsE5VxYlPTkesdHab9FadS6hJoaI4tjMEbA0fEpInmHRU3RrdP+bHfnngv6cb6w7jF8v3IJqE6z48oYBCxlGfqExwzw4hV6LhNiAn0N+fc87fQGlVZ7TMIB7RkVZnKu2WicQZVU1iq9fvGmA4rXlXVXdp43cMyUFZ10F6O1bxsObY+eMLVQXp4TcM0RGCKToVhDq66D0dBI2uobF/fWjg7Bdw9++3o+1B05h5Z7CgJ8rlBiwkGHkFxAzNJ+i0JDXbLQM8pSQV+5TQk55ABPwMBTky423/+kK3Dikff1rOeuLbh1OoNwtwHKvaRHrVDJTEry+5lPL9+KHQ6cDGrc3eacvYPGWfM8MVt2XYtGtOTIs/j9GuVuz6zavRbcmaRznPgkazP2ljCrk1ivoAUtWVhYuvvhiJCYmIjU1Fddddx0OHPC+lHHdunWwWCweH/v37w/28MhEFDUsJk9FUsMdOVW/OVtsdFTAz6c3OyJ/Y5evBAGCv/mhmCVJT45Dq+Y2xX3yGhZB8Fz2XOb29cmyKum5fFHbODFYfvXqBjy+bA8W/viL4vb6VUJmKrr1fwzyPiz6WvObo3Gc++sHo5A9XAT9TNevX4/7778fmzZtwurVq1FbW4sJEybgwgXfO0oeOHAAhYWF0ke3bt2CPTwyEflcsFrzLIoMm/POSJ8HI1DQ+xyKoltBmVUJdqdbsRdJjMrFo9ah3PzQfUqopKJG8X+hom5JczNZnyItoWzPLwZSn+ccBwC88m0urp6fjeN1U1HmqmHx/zHyQmhBus38q4Q8poSigjcwk5yiJt//I/z09ddfK75euHAhUlNTsX37dowePdrrY1NTU9GiRYtgD4lMSn4BMcMW9RQau4+VSJ8HIzDVG/MoimwhhHRKqEYKWDzf8gUBUtGtQxBwyq3nULXDicoaBxJiXW/H9rpsTXyMdjYqLSkORaVVjbK0WdxV+qW6/Y/2F5UBkNWwmGA6N/C9hPRkWOpey+BJIfdXj7IGlncIdrYxlEKeSyopcb1ZpaSk+Dx20KBBSE9Px/jx47F27Vqvx9rtdpSWlio+KLzILygsuo1cJZX1BanB6H+i9zk8MyzK1UXBJK6uUJvyio22Ki6OR057ZpvPV9R/j8Q6Am8BS2JcXXDTCFOpZVW1qitjxKkIs68s0SJe551OeadbLxmWun+NnhJyzw4GOiPkq1OxvdaBjYfPmOLnHNKARRAEzJkzB6NGjULfvn01j0tPT8dbb72FpUuXYtmyZejRowfGjx+P7OxszcdkZWUhOTlZ+sjMzAzFKVAIyWsRzJBWpuDbfOQM1svqLILx17je6RzPZc3yr4N71RF/f2NlGZZ/3TIAHVsl4MWbBiimhPJ8BSx1U0Jxsb4DllBmWOTZojMXqj3vjxYzLMb/323Iz9OiWNaso9OtSYpu3QOHQINvXwHLX7/8Gbe9vQkL1h4K6HWCIehTQnKzZ8/G7t27sWHDBq/H9ejRAz169JC+HjFiBAoKCvDiiy9qTiPNnTsXc+bMkb4uLS1l0BJm2Icl8t3y1ibF18HIbOgOWNyWNTsUXwc8DIUalRqW6we1x/WDXKuFfjzsWs1T63Qi/0yFx+PPV9YHBHoyLM3jXKutQplhSU2Mk/b42vaLZ++PWGmVkPH/dwNZ1qxYJeSlisMsjePcA5ZA/wjwteDhg41HAbhqmOZc2T2g1wpUyDIsDzzwAFasWIG1a9eiffv2vh/gZvjw4cjNzdW832azISkpSfFB4UXZh8X4Nz0KvWD8nBs0JQRlABP0KSGHspmaO3HpaVlVrfQX7cDMFtL9Px46gx/rlihX+TElFMoMizxzsuGQ52qkmDDvdCtf1lx/W4heLIjcg9RA/0/JMyz/2VageF92z1zJp3eNEPSARRAEzJ49G8uWLcN3332Hzp07N+h5du7cifT09CCPzlzWHijGrW9tVOwP0pQo+rCY4E2PQi8oGRadvyoeU0KyxwV9lVCt9iohoH76QVzSHGW14LP7RuKKXqkAgAVrD+H2dzZj7/GS+gxLrJcut3XTRiENWGQXwg835Xvcf3XfNADm+L/rXgirp3hWDFjkv5O6Ot36PzyfBEHA/3adwIisb/HGOu8bhLrv9h3olJw8Y7Mj/zy6PLESe+oK5YvdCsT/8sVPAb1WoIIesNx///348MMP8fHHHyMxMRFFRUUoKipCZWV9V8a5c+di2rRp0tfz58/H8uXLkZubi3379mHu3LlYunQpZs+eHezhmcqvF27FpiNn8ZsPthk9FEMo+rCYYB6cQi84q4RcvzfNbdEY2rGlz+MA10VV3hI/2H8kq00JyUVJAUt99sRisaBNorJny+c5x+trWOoyLJde1Mrj+QbXnXcop4S81TbYoq0Y3sU1LjNkR91/nno61oqHyAMWo3Zr/nJPIR74ZCcKS6rwt6+99x/zmBIKNMOi8js0ZcEGjP/nOlzy/LeK2/+7/VhArxWooNewvPHGGwCAsWPHKm5fuHAhZsyYAQAoLCxEfn59xF5dXY1HHnkEx48fR3x8PPr06YMvv/wSkyZNCvbwDHey1NUUqm1SfVOo/UVl+GpPIS7unIJWzWIVO4Y6nQKe+d8+JCfEGj5/GGzydGNNrfFvehR6QVklJLVRB+K9FKbKLywPfLJT9TmCRSq6jVa/4olxjNiDRQxGurZprjjuwMlyjxqWt+4aih3557Al7yxyCs7j4Su6SxeZUGZYvGVOEmKjpJbwtU5Xa3tvOx2HmvtPU8/UjhjU1CoCFm8ZltCdX94pZSG2IAjIP1uBDikJHq/rMSUU4PdfK+g9fMqzOLy5jt5AoRT0V9dTrb1o0SLF148++igeffTRYA/FdOy1Dlw9PxsllTXY98zViLJapDfw3320A4DrL5cVs0ehR1oi7LUOXP7ieqnw7Xdjunp9gw438muXGVYaUOgFY5WQtO+L1SJd+FWP8/IcoZoS0uo6Kk0J1WV5xOme7m0TFcedvWCvr2Gp+7/ezBaNy7q1wWXd2kjH7azbAC+UGRb3v9wTbdFSM7n4mChplRDgKrzVCtYag/uPU8/F26qSYdET6ISiD4s8m2W1AG9lH0HWV/vx+yu646ErlA1U1TIiTgFoaP84X6uE5JLjA99aIxBNp6evgZ5f+TOufGk9Ptmcj3MVNXAKwKa8M6pvmvZaJ25840esP3gK3/1cLAUrADwaTmlZu79YdSWC2bin7CmyqGVTgtOHxfVvlMVHwOIlKAl2syxvnW4B+ZRQ/QUfAHqkKQOW4lK7tOrGW9GteN7uGycGi9MpeASXrWXTV/GxUYixygMWo///uvUm0RWweNaweAt0xGXeofiei9OAgCv4yPrKNS30rzUHPY51r2EBAvv+6+mvklRX5H1WZXl7Y2LA0gjeyj6C3OJyzPtffcHSrxdu1ZwLLbPXYvp7W/DFbuXOmeIeI95syD2NXy/aitH/8N54zwyURbecEoo0atMVwciwiBcYq9WC+BjlW5hyhYP2cwR9WXPdlGaMxioh8douBSN1XW3bJsWhXYv6XZnlRY7egjFb3euoXbyCQa2m7IK9Fol1UwLjeqQq+rQYXcfiWcPi+zEWlSkhb49r39K1GWUoFklU+fFzVMuqif8nSqtqMH/NQRwqLtf9fO4BS+fWzTyOaVd37pU1DkVw1dgYsDQCraWOANAsNgpHnlev1fnSbavv4lLXm9mqfUUYkfUtNh854/GYrb+cDWCkjUuxl5Dhf6FRsKkFLMHsw2K1eLYll9emeEvdB3tKqL5xnEbA4vaXuzzQ+uKBUZg97iKPx9i8vG+IwYw9RBkWtQCkuMyOz2dfiscn9sQfJvRQ7BLsz7RCKHjWsOifEnLqXCXUoZXrop0fioBF4+coZjbk1DIiL3+bC4dTwDvZRzB/TS6ueGm97td2z87ccrFnP7PWzWOl3+2zFcZlWRiwNAJv6cl7R3eF1WrB3aO0l3+P7Oqqxi8uq4IgCLj339tRWFKFV77z7FMT7A6eoaScEgqfcZM+VbI31ikDMgAEd5VQlMWC4V2UW3449GZYgpxiqS+61Ruw1GdPWjaLxR8mKAvq42KsXqcnxGCm2uEMek8ZQHkRmzq4HQDgpiHt0aVNc8yqq6WzWCzSRczoGjT3i7g/y5r1Zv06tXJlHo6eqQj6+6xW8XRrt1VkgHqG5a3sI1j04y84LOuirPePQPfvnVqdSkJsFFKaxQIAzpYzYIlYgiBIVf/3je0KQPmmJhZUPTW5N/b/5WqPx3dslSDNcxeWVGHj4fqsSnpyvMfxjbGP1doDxfjKLfvTEOzD0jgqqmsx9fUf8Mq32o0YQ+G+D7cDcGUdfnOZKyB3BLFxnNVqwbUD22HX0xM87gO8Z1GC/f/ELvVh0Vol5BawuBXPuwcn3qaD3O+vDMFKITFjYrEAf72uH16+dSCemtLb4zhxp2AjV/kJgqBYsg5A2grBm/qiW3nBq/bj2rd0vd9W1jiCXsuhFbA0i9WXYQFcPVKqZNM17/2Qp+u13bNjarVTUVYLemckYUD7ZF3PGSoMWEJMHg3/bmxX7H3mKqx8cBSa26Lx4Hhl9XdcTBRGd2+juO3uUZ3RO93VxXfdgWJ8KlsHr5a5CXaq253DKeDXC7fidx/t0F0ErEX+Vy4DltD5dNsx7Mg/L+222xgEQcCuuuZT1Q6ndMEOzl5Crn/Fi4v8DbZWdw1LaDIsWkW37hdCtYDkhsH1HcHlXXDVyKeL/hWCn6s4JRQTZUV8bBSuHdgOSXGef3lL3W4NzLBUVDsa2IdF3EFb/jjt42OirIirm8oLdpAoTgnJ65kA1x8b7rzVLX27v1j6/PmV+5F90LNDsefzKX92ar/D1bUC3ptxMT6fPQr9DAxajF1U3QTII+e4mCjERFlxUWoi9j5zlerx/3fnEHy3vxgjurZCZY0D7VrEo6SyBk9+thcHT5bj4Mn6Yiq1/zShzrDI/5IpqazxaHzlD8VuzWG0xbkRNh1x7ZbqHtDqEcpeHVrEfiOi6Lpak2DWsIhBULTsKqMouvXyHKHqw6IdsCi/TlBpT/DiTf0xvEsKPt6Sj+eu094sFgCiZa/z7oY83D/uIillHwy+anJEMdJ+QsYFLOJ7ktXiGcx6U79KqH7svpZD26KjUFXjDPpycvH/aPuW8YqVoWoFrv689tIdx3y+Z7hnbNSmNY2e8hMxwxJiYlARbbVovpnJxcdG4Zr+6UhpFitF28nxMbhrREePY9UuRKHoESBXYa9/zUAvPvKHm2Hr8lB47ouf8NcvA2tn7XQKuPWtTZj23hacLg8sq9VYzrjNcwczwyJNCdVdW+Tpf2WGRfu1glWDcKrMjtfXHcIPh1xTtVqFsh5TQioZFovFgpuGZuKz+y6VVqR4s2bOGOnzBz7ZIX3ucAr4POc4Zv17O/7wn104IbsA6iUGINE+mnuI72lGrhISuwfLp0/0NY5z/Ssfu6/HSauzglzsLK4Scq8fuaASsOh5r5zc37Wtjfh76Y3786lNa5olA86AJcTEVJ+3ngp6PDKhB1o3V/4FpZZhCXXNrTzDopau9EckZFiOnavAlFc3YKlKy+rSqhq8syEPb3+fh+JS30vStcjnmItK/H8eIxqQugdWYhYkuKuE6k9MfH7575T3otvAxiAIApbvPI4r/7Uef//6gPRXsdYfJYlu0ymBvh8AQNc29ctPfzh0Bk6ngK/2FGLiy9l4aHEOvt5XhKU7jvnc/8XhFLD72HnsKjgv3VYjmxLyRgxojFwlJPa2aWaTByw6MiwqvzM+MywxoVlOLmZSWjVXZqzVp4Rc3+v5twyUakpmjOykOOaiVFcH5XK7780K3a8jalk1syyK4JRQiEn7ggTYoTY+Ngoju7bGil0npNvUMizBXv3gTp5hCXQ9vvyCYpYI3l9Pf74Pe46X4A+f7sINQ9rjQFEZZn+8Aw+O74ahner3uTl+vhKpsu0Y/CEP5i7YAwsSG8tpzQxLEFYJiY3jZH8OW+vmA2obYUqoqKQKT362R1EvINK6wA/p2BJ/u6EfsnNPI/dkGS7v1bbBry+yWCx4f+YwTH9vCwDgqvnZyFXpv/HV3iKU22sVbdVLKmrw9b5CrP6pGJvzzqCsyvV7tWL2pejfvoUfU0KNn2HZkHsaF6prcVUf1+aL4v+JBFv9e6y+Piyuf8XfGT2BvS26bjl50KeEXM933cAM/HL6Arq3bY73Nx5FjUNAda1TMU0jZkQ6t26G92cOQ1lVLQ4Vl2PRj79Ix7Sqmx6sqnH6bNsv34F5ZNdWqr2EzPL+zIAlxMRUX1xM4MmsOVd2x7c/n4QtJgpnL1SrZ1gCfhXv5LUJaulKfygyLCaJ4P3x6bYCxUUr/0wFnvhsD3KLy/HAJzsVKfuCc5UY1EG5Ud/5imocPFmOYZ2VS3Pd1cjeHCsaUI9iQf2bVWPt+XLmQn2GpWVCjPSXeHD3ElJmWKqhDNi9/RXckCkhQRDwn20FeO6Ln1Fmr0VslBUPXdEN5fZaaYddrWXNUVYLbrm4A265uIPfr+vNmO5tcFFqcxwqLkducTmaxUbh7lGdcfdlXXCqzC7149hdcB4jurbCjvxzeG/DL1j900nVrMi6A6cUAYvPKSGrsgj18Kly7Mw/j6mD2ulaqeMvh1PAne9udo31kbHo1LqZlPWVB2T6Vgkpfyf1ZGXqG/YF9wIu/q4mxcfgk3uHo7rWifc3HgXg+sNQ/nslHmuLsaJFQixaJMTinFtvFHmmxl7r9LrqrKTCFbDcfkkHPPurPth3otTjmDENqJ0LBQYsISYuMwtGCrhT62bY8uQVyCk4jzve2azabCjUq4QqQjQlFIpeEqH2x//uVnzt3l1Y/v1R64757Bc/YdmO47htWAfcO7qLaodJQLkCo7wqsO95rVPQXHobTGINi9UCrJg9KsirhMRlzfW3Rbn11NhfVIq9xz3feEX+/sFYcLYCc5ftwYZDpwG4VvH848b+6NY2Ed/nnpIClmYG7PV17YAMvPX9Edx+SQf8dnRXqfg2OT4Gk/qlYeWeItz+zmb0TEvE/qIy6XE92iZiyoB0jO7eBjvzz+PpFfuw6cgZPDi+m+4poZi6/YOmv7cFH8wchml12Z7EuGgpAxJM8uXEn+08jsyUBOn3WVnD4v9eQnr+V4gBS7AL2d1LB2KjrYiJsqDGIaCiphbJqJ9SFOtn5Nmv1m5TSa1kBdj2Gh8BS12GpVdaIqKjrB4/87/d0A/XDWrXkNMKOgYsIVafYQnOG1kzW7Q0V6s2JRP6Gpb616yoduDznON4cdUBvHb7YPRv38Kv55Jfu4K9aiMUTpyvxHNf/oSbh2ZibI9Un8dfkE2fqRU+LttxHADwyZZ8fLIlHz89exUSVPouyOePH/hkJ06V2TFzVGfsO1GC6lqnR+bGnfy9u8bh1FX8HajzdX+1/WZ0F2SmJEgXGkFwZUEC+etbzKLIl/VHuWVw3vneew+K4+cr8HNhKd5cfxjXDWyHcT3Vf54Op4APNx3F37/ejwvVDtiirXhkQg/MHNVZCsJGXdQaL986EIeLyzGmR+P/JfrA+G6YfflFqpmzgZktsHJPEQDXrvCx0VZcP7Adpo3siD4Z9ctTxQvlj4fPYN2BYuncfNawyKLGJ5fvkT7fe7wkJAGLvJXCy3V9hcQl4M38nBJybxynL8MSqikhz+tEc1s0zlXUoLSyFumylcT2umjbJjs2o0U8po3oiA/qsjJJ8THS5rpVtQ5FwONODFiS6gp+5ZtYJsRGBT0rGAgGLCFWWe365QpWwALUv7nIo/xdBefx2NLdIV9tUyGbEvpkSz521/Xa+L/sI3jt9sF+PZcQZhmWxVsLsHJPEVbuKcLmJ8b7PP6krNBW7eeS0ixW8RfjmfJqJKR4/pd071j57Bc/IT05Dr/7aAcsFmDrk1d4/IWlpaZWAIK3+lWT+CYornqIclvJExtAwCJvHCeKckvv+9r87vmV+wG4Npj7POcEfnnhGo9j9h4vwROf7ZF+x4d1SsHfbuzvkQmzWFwN7IykNc135/COKCypwsGTZRjRpRVuG9bBo7ATqC/SBIAZC7dKewb5ysbJX7bgrPpqJKdTwA+HT2PDodOornVi+9Fz+PWlndCldXPYYqzomebqM1VRXQurjw0t1VbJ5dQVC/tddOv2O6OrhkUsug1ihqXG4ZSCJnnpQOvmNpyrqMHpcjt6wNU8VBAE6b3EfUXaE5N6SQGL1WJBXLQVF6odPrNB7v9X5UFqdAim9QLBgCXE1CLnQIkBi7yG5b6PdijW74eKvIZFfCMHgIxk/wtK5TGKWdb5e7P3eP357pGdu+iNOwbjdx/VLy+Vb0CmVrTm/lagNV2iVqEvzjMLgivQ8RawyKfe7A4H4OWvrWBxfxOUv/EFazm8/KIkBkSvrzuEKKsFO46ea/DzX7DX4qXVB7Hwhzw4Bdf0xqNX98QdwzqEpC4jlBJio/H0lD4+j7NYLLj14kws3loAwLUBK+B9PyMA6J2ehJ355z1uLyqpQnFpFT7dfgyLt+Z7BDO/X7JL+vzvN/THVX3SMP6l9WjfMh6f3TdSMwDz1qxS/n9AX2t+17/+Fd0Gv4ZFXkgvD7pSk2zILS5HsWzTW3ndkXu9VFxMFO4a3hGFJZXoltoccTFRdQGL+liPnrmA/UVl+KnQ9V6SLGVY6p/X2z54RmDAEmJiUOG+q2wgxCi8qm7nzJv/b6NqsBJo6t3dmp9O4rkvf1a9T/4fTS9FDUsYFN0ekM3/b89XXhCfnNQLF7sVzx47V1+3UqPjIq1Via92u7yg9JVvczHj0k64uJN68a484Gms5YmldQFLi3hXOkeZYXECaHgAL99LSCTucvx5zgnFsa2b23T1rqmorkVCbDRW7SvC0yv2obBu+fjk/un48+TeDV7hFU7m/aoPahwClu44hsS4aHRslYC7R3Xx+pinJvfGsXOVWO/WUfWrvUVYtvO4FJw2t0UjMS5a+r7KPbp0N7YfPYfT5XacLrej4GyltNEg4MoqlFTWoOBsJTbnufqKJMZFSyubAFe28rdjuuDdDa6pQH+WNYuN4/Q8Rtp0MogBi/hHoKtupf460aYuAJMHafLXVQsm/yJrOBinkokX/VxYiokvf6+4TT3DwoClSRF/wWKjg5dhEZdIOwVX4dme455/7QOuuhCrrlIyfe75YJvmfQ35qzmcalhqHE5FULgh97Ti/vjYKLRqFotLOqdgc55rx+wi2ZRQjY43OK3UrdoKKvkU05d7CvHlnkLVaQ1x7GqPC5WCsxXYUrdreLAyLLUOJ77dX6woZJa/l3Zt0wyHT7k2fhveJQX2WieS4mJgtQBrD/huT771l3P4cNNRrP7pJAAgMyUef7m2r65apUgRFxOFf9zYHw9f0Q2ZKb4b14mPmTupp0fAIl6Eh3RsiduGdcA1/dKl/ZMWb8nHwh9+wYGT9X8ALNlWIH3+2NLd6NsuCflnK1BwthIFZyukjI/oruEd8dvRXTF5wfcoqajBG3cMRmpiHCb2TcNXe4swa0xXn2MXszhicbZ/q4Rc/1cFQcCO/HPo2y5Zqm/xV0VdXWBztz/6xC7iioBFli3xteTcFqNdIPzF7hMet4nF2o1R49ZQDFhCrFZq2R28wEG+4uikl4ZkDqeAYM1Eubdad9eQ1R/hVMNS4Vbg7B4kxse4dq9dfO9w3PHOZvx4+AyKS+vfaPR8f7T62qgtP/XnLzx5wNIY/RRufWuT9LlWDYu7M+V2rD94CkM6tkTHVsoakS92n8CcJbuk78OgDi0AKC8wz/yqL3YdO4+Zl3ZWbCz423/XB9mDO7TA/FsG4eqXsz1+nmIvk2irBfeO7oIHLu/msUFhU2C1WnQHK6I0Wfbp+kHtkFxX8HnLxZno3jbR4/hbh3XArcM6IKfgPO5XmcreeOQMNh7x7NDaJtGGDikJ6NqmGe4c3hHJCTHI/uM4CEJ9tmTB7YNRcLYCnTRW3CnO1e0t2dcSbkBWdFsXOLyVfQRZX+3HvaO74IlJvXw+Xo343uq+XUNqouv7WiwLWMT/A7HR3nfzBoC4urFWqbxXuK9a/cu1fdAiwRWw+AqEjMSAJcT0NmDyh/yv1dIq7U6GwQwCflJZmx/oa8kfY/ZOt/K/7C0Wz9VY4puNxWKRLtJ5Z+q3etcTKGhtqKa2Tbw/mRL5NFAwMyxqPV0KSyoVFyDxe2GxWKRVC89/+TP+cdMAKYg5eLIM09/bgsKSKsTHRGHZfSPRq27Dz0U/5OGZL35SfL/Fmgl5EDSqW2uM6tbaY4yT+2fg8KkLuHtUZ9x6cSYsFgu+fPAyvJV9BJ9syVccO6RjSzx/fT9pd3TSp0VCLB6Z0B2HT13AnCu76w54Bma2wA+PX47sg6ew9kAx+rVLRsHZSvxUWILMlgnITElAZko8OqQkoH3LBNU6QIvFoqg9ibJadAUrADCiSyukJ8dJ01Sju/le4SUta651wOEUkPWVq3D7rewjeOzqnh5bMMg5na6NU9yPEWtY9GVYHIpxeBPnJcMiLxUY1ikFd43oJH0tr1sJ9VYv/mLAEmLixUJP9K6XxWKR1uh7K0IL5jSL+/bt1/RPx5e7C6WvG9L4LZxqWMS/yJPiorFx7nj0efobxf3yTsbiG4/8268WKLifsdaUkFrdiT8ZFvlrB6uF+g+HTmPOf3JwZe+2ePZXfWG1WnDuQjWmvbtFcZx8b5T05DgcO1eJZTuP4+q+aZjQJw1bfzmLuxdtRWldPUJljQNvrj+M+bcMxD++OYDX6/qb3DasA+4e1QlXvJQtPZ+eFP6UARmYMiBDcVvn1s2QNbUfZozshPyzFTh8qhypiTZcNzA0zc6agtmXd/N9kIbR3ds0aFPPQHVp0xwb547H13uLsHhrPuZO6unzMfWrhJzIO63sKrwl7yxW7DqOlGax+MOVPVBZ40BOwXlsOnIG5ytqsPqnk6iorsXcSb0wuX+6tF2DtBeSjoBF/P+rL2DRrmGRd7d1D0q8BV1GY8ASYr52cW2oaKsVNQ4Hjp3TXhkUzDb98oDkiUk9ke/WCM3RgFU+ylVCJg9Y6t5UEmJdfXA+vPsS/P2b/dJKKfnFs3mcytJklfNzz0ppVfPXqHxv1bq4anWxVUwJ+Zlhqapx4Pvc0xjdvbWUDj9UXI5ZH25HWVUtPtyUj4GZLXF13zTMWLQVucXlaJtkQ6dWzZCZkoDkhPqA5cWbBkjTRd/tL4YA4MFPdsJe68TgDi1w39iLcM8H27Dmp5P4/ZIcLK8roH1kQnfcP87VZ2RY5xRsqasRCnR34h5pieiRlogrEXibfApfV/dNw9V99fWMkfdhce8Ie9vb9VOhr609rPkcc5ftwdvfH8Ga34+B1Wqp31rAbUpICljKPWtY9NTLeA1YKuoDFm8BitlKCxmwhJh4oQp6wBJlAWq8b4YXzCkhcVpiaMeWuHd0Vzy+VNnlNeAaFrP9z3AjTgmJ+5WM6tYaI7peiq5PrASgPJdElRVTalNC7lM92lNCnt8btZqiaodT9Y1MUXTrJcPy3+3H8OI3BzB3Uk+pr8j9H+3At/uL8dTk3ph5aSccO1eJe97fqlihMW/FPrz87UEUnK1Ei4QYfHj3JeimUrswvEsr/PvuYbjr3S1YsesE/rOtAE4BuKJXW7x62yDERlulVT3Lc04gympB1vX9cPPFmdJzPD6xJ/78+V4M7tAS9429SPNciEJBzGys3FOIlXtcGebubZvj4EnPPZzctU2y4WRdXduRUxfw1Od78dfr+6luLQAAqXUBy/mKGthrHbBFRylqWHwRp4S+21+MymoHcuu2bzhUXK7o//TkpN6az+He8t9oDFhCTEzHB7sduhgAeSuGDWbAIi7LFae23AOUgFcJmT3DUi1mWOoDAvlfJvIaJfmbyQtT++HxZXtUp3XclzprFd2qBTtlKi36q6q1Ahb5smbtgOU/WwtQVFqFhxbnYFK/dGw+clbaK+nfG3/BwaIyaTVHuxbxWHzvcPz239vxU2Epyu21SIiNwqJfD1MNVkTDOqegWWyU1DH5tmGZ+Mu1fRFd9/27/ZIOeOXbXFgswFt3DcF4t00CB3doiS8euEzz+YlCKa2u35Q4pRJltWDuxF7o3LoZnv3iJ3xX9/9l2oiOWLy1AH0zkvDyrYPwec5xXDuwHcb/c70UdHy0OR8nzldicF2navcpoeT4GGnq/3R5Ndq1iJeyJXqmhEorXe8R3+w7iW/2nVQ95p83DUC/9smq9wHm2aVZxIAlxMSGaMGfEnJdLL3t5xPMrEWt29RWn4wk/He77P4GBSzKVUKNtTFfQ9QHLMr/MrPGdEXuyTJc0qWVx7EApH4SYqCw5qeTSIyLxrDOKR7Bg1aGRW/AUlmj3oK7WrGsWfvnVFFT/5yvrT2E+Wtypa8TYqMVS0/fmT4UmSkJ+PuN/TFlwQbEWK14666hUpt0LbboKEzun4El2wrw4Phu+P0V3RQ/81ljusBqcWVd+rbTfiMlMsKkful1wYIFGS3ikNkyAS3rpibfm3ExKqsd0uqyJyb1QmyUFVarRarxWfzb4Zj6+o/S8609cAo/F7qWd7tnWCwWC9o0t+FESRWunp+N6lqnrE2G7+vJRanNpb2vruzdFt1Sm6N720Qs3XEM39e1ZUjXaPgpLg9np9smpqY2NFNC4vN5ixOCOyVUl2Gp+wW+c3hHVFQ7kHuyDMtzTgScYQFc4w1mcXIwiWlb983tHp/oWagnz3qJmZdahxNFJVVSL5tDf53oMT/sT9FtmcrqMM2Ax0vRbXWtE5/tPIaE2GicLa9P/4rBSuvmsThdXi11wwSANXNG46JUVxalb7tkfHzPcCTGResOMJ67vi8evrIb0pPjPe5LiI3Gw1d01/U8RI0tJsqKq/uma94vXwqvtqppcIeW+P7Rcbjs7/UbpYr9muR7IYn6t2+BEyVFHn+gXK6x95Xc3aM6IykuGncM74i2sqXnFgvwfe5pdG/bHEM6qe9D9rcb+6NFQgymDm7v83UaEwOWEKtxhmZKSM+FPZjd7sXzEFP3MVFW3D/uIiz8IQ/Lc04EXMMCuLI0QeyvF1SVGhkWNTcPzcQHG49iZNdWUmBZ4xAUjeQqVIIL7cZxnj/IUrUMi44pJfkeKIIg4I//3eXRHVY0tkcbvHrbIPSbt0q67fGJPaVgRTSiayv3h3oVE2VVDVaImoLMlATsnjcBsz/eieyDp2CLtqJnehJ+NcBzP6pXbhuEA0VlsMVYkRAbhYTYaCTERuna6iUzJQFzJvTwuH1K/wy0SIjF4A4tNIt3k+JikDW1v/8nF2IMWEJMWtYc5BbHelJ1wZ0SEjNFyteNdmtv7Q+n2/jcvzYTMcPiXsmvpm+7ZGyaOx6tmsfiYF03zxqHU5GFKq30I0OiY4URoJ51cb12/bF//O9uDOucgo6tmuGDjUc1g5UOKQl4+ZZBSIyLwd2jOuPdDXm4pl867r3Me6t2IvItKS4GH8wchlqHU+pRpCY22uq1xqQhrFYLxhiwjDwYGLCEmFT7EeRNpPRMMTUkiNCitTw7yipOeTRgSshteGZe2lypUnTrjVicFytlWJyKTIdaDYrYj8Gd3qXIt7y1SbU9v/s00JvrD+PGIe3xly9+Un2e31zWGXdc0lFakvzU5N6YMbIT2reMN22NEVE4ijZxV1kzYsASYtKFPsjFS3qmhILZhV0MJtwzRfUZlsCKbgFzN48Tg4kEPzd5jImqD+jkBdJqGZYSldsA/3ayvmCvxbFzlThzwY6RXV2dX92nij7POYHv9hej1ilIe7z8d/sxAMDIrq3w5DWeyxz9bddORBRsDO9CrNoRmqJbPVNMoejD4j4lJKYyG1bD4vYaZs6w1K2gSfBzcyYxsKx2OFEuy6Co1aCIAcve4yU4VFy/MZw/SwunvbcFV83Pxu1vb8b6g6ewck+htO/R0t+NgNXiWsV0stSOi1Kb42839kffjCTp8f+++xK/zo+IqLEwwxJi4oU+2Ktf9BTxBrMmRGuLAfHrBu0lFE41LA3MsMinhCrsvjMsJZU1mPzqBgDA4ecnIafgHP7xzQHdr7f96Dnp8+U7j2NN3e7Ds8Z0xZCOKfjDhB7456oDSE2Mw5t3DkFzWzTuHN4RlTVOjO3RxtRtuYmoaWPAEmKh2PwQaPwMi3ge7q9bn2EJvOjWzBkWtcZxekTLlp/L61bUCmTPV9TghGzjwL3HS3DDGxu9Pv/Evmk4V1GNTUfOSre1axGP4+cr8dnO4wBc3Yn/MMG1VPj+cRdhxshOsEVbpbFFR1nxu7Fd/TovIqLGximhEKsJ1ZSQRoblvRlDpc+DukrI6WuVUOBTQmauYanwY5WQnPz7Ja9RUZsSOl1uV6zaufa1HzyOad9SuRz4xZsG4JPfDMf0ER0BAGO6t8Ffrusj3d8yIQav3DZI8fvXzBbNYj8iCjvMsIRYTYimhLSWNXdLTUSnVgn45UxFaDIsWquEglB025AsTWPR6nTrizxQOF9Z35hNbUoIcK3g0fK7sV3x2NU90fOpr6SNEuNiomCxWDBnQg/0aZeMSf3S4XAIaN08FvZaJ165bRAyWrDnCRGFPwYsISYu9w36lJDG88VGu1pBA6HpdOu+2imoq4RMPSWk3unWF0XAItshVW1ZsxqxRTYAtGnu2gztN5d1wavfHcLciT2lKbnk+BjcPLR+k8DNT1wBh1PQ1cKbiCgchOzd7PXXX0fnzp0RFxeHIUOG4Pvvv/d6/Pr16zFkyBDExcWhS5cuePPNN0M1tEallZkIlFbRbUyUVQoinMEMWJxaGZa6GpYg9GEx847NUobFz6LbKKsFYusS+ZTQ7rqVO970b5+MB8d3k76e1M/VEvzB8d3w7R/G4LdjtOtOoqwWBitEFFFC8o62ZMkSPPzww3jyySexc+dOXHbZZZg4cSLy8/NVj8/Ly8OkSZNw2WWXYefOnXjiiSfw4IMPYunSpaEYXqMKWWt+jaLbmCgLrHVXyGAGAJqrhAKqYXGbEjJ1DUvDim6B+izLpiNnpNt+lu3NI5o2oiO6tGkmff3qbYPQMy0RvxvbFc/8qo/UjC4myoqubZr7PQ4ionAWkimhl156CXfffTfuueceAMD8+fPxzTff4I033kBWVpbH8W+++SY6dOiA+fPnAwB69eqFbdu24cUXX8QNN9wQiiE2mlBtfqhVExMTZZWyHiHpwxLUVULKr800JVRUUoWPNh/FbcM64MipCzh7wVV/0pCApbquU623fioxURY8e21fnCqzY/3BU5jcP13aL+Sxqz03WCQiamqCnmGprq7G9u3bMWHCBMXtEyZMwI8//qj6mI0bN3ocf9VVV2Hbtm2oqVEvTrTb7SgtLVV8mFGtU72lfaDkgYMt2op2LeJxUWpz2KLrA5a5y/ag4GxFUF5P3M8mmH1YzLasubZuv59ahxNXzc/Gq98dwvWv/4A7390sHeNv0a03s8ddJH0u7qbaJtGGG4e017W5GRFRUxL0DMvp06fhcDjQtm1bxe1t27ZFUVGR6mOKiopUj6+trcXp06eRnu65nXdWVhaeeeaZ4A08RMS/roO+Skj2fHExUVj3x7GwALBY6qeECkuqcO+/t+Orhy4L+PVqfawS8qcbq8gMGRanU8CF6lo0t0Vj5vvbsPPoOUwekCHVm5wstSuOb0iG5XdjuyL74ClMGZCBTq2a4Q//yUHWDf0xpX86RnVrjX+uOoC/XNc3KOdDRBSpQrZKyH2TNEEQvG6cpna82u2iuXPnYs6cOdLXpaWlyMzMVD02VKpqHLBa6osbBUHA0TMVsFhcfzHHxURJWYNgrxKSZ2xioqyKr+XdStVqJRqifrVT6GpYjAhYnvnfPny8JR/3j7sI2QdPAQA+2aJeawW4sln+euzqnoppnav6XCX9Xg/v0gqfzhrp93MSETU1QQ9YWrdujaioKI9sSnFxsUcWRZSWlqZ6fHR0NFq1aqX6GJvNBpvNFpxBN0Ctw4lrF/yAo2cvoHvbRIzv2RbJ8dGY9z/1HXBD2YfFPYgIRXt1aUpIs4al4VNCMVEW1DiERgtYahxObDh0Gr3Tk/D+xqMAgPlrcj2Ou3ZgBj7POYEubZrhyKkLALQDaH9wx2MiIv8FPWCJjY3FkCFDsHr1alx//fXS7atXr8a1116r+pgRI0bgf//7n+K2VatWYejQoYiJiQn2EAMmCAK2/nIOB066NqjbfawEu495X6bazM/lsL7Ip2Y8pmlCcEHU2hOpPsPS8KLbaKsVNQ5HozWOe3zpHizdccxrtqRTqwS8fOsgPHZ1T7RNisO3P59Eq+bGBchERE1dSKaE5syZg7vuugtDhw7FiBEj8NZbbyE/Px+zZs0C4JrOOX78OD744AMAwKxZs7BgwQLMmTMHv/nNb7Bx40a8++67+OSTT0IxvIDkn6nA1Dd+xOlyu++DZZLight4yZdJa+2gHEy1GlsMBJRhkbX7r6wJ7ZRQda0T246eRWyUFUt3HAMA2Gs9A6SbhrTH5zkn8NItAwFA6hI7oU9ayMZGRES+hSRgueWWW3DmzBk8++yzKCwsRN++fbFy5Up07Oja76SwsFDRk6Vz585YuXIlfv/73+O1115DRkYGXnnlFdMtaS6pqMHof6z1+3EvTO0X9LHIp2bcgwhrSKaExM0P3TMsrtcOZJWQWAOk9zmcTgEWC7Dh0GnMX5OLF28agM6tm3kcV1ZVg2nvbUGM1YoL1bXYd0K9nudP1/TC8yt/xpt3DsG4nql4YlIvtGwW6/f5EBFR6ISs6Pa+++7Dfffdp3rfokWLPG4bM2YMduzYEarhBMU/Vx/QvO/Byy/C7Mu7Ydex83jysz1wOAV8cu9wOJ1A26TgTyVEKzIs7lNCymNPnK/Ezf+3EcfOVWLaiI64/ZIO6JmWBACYsyQHPxWW4tlr+6JV81h0bdMcgiDg7IVq/HKmAkM6tsTLa3KxM/+8+mvVvVhFtQO1DqdfHX3F+ER8zvyzFRAEAVU1TpwutyMzJUFx/KYjZ/DhpqPIPVmOMxfsOF3u6o0y7sV1mDIgA1MHtcOyncfx29FdsCXvLM5XVEvjdnftwAys2HUCM0Z2wj2XdcGvL+0sZYsYrBARmQ/3EtIpp+A8PtqsXD3SuXUzJMXH4OErumFcj1QAwMWdUrDq92NCPh75NJB7C3b3PMXIF76TPv9g41F8UFdo2rVNMxyuKya9+f82AgDG90zF6XI7dtXV5FzdJw1f76sviNaqYQGABWsPYVyPVBScq8CkvuleMz2nyuyorHF1jy0sqQIAPPflz/jnqoOorHHAagH6tUvG6O5t0L5lPFb/VIw1P5/UfL7/7TqB/+06IX3uTVpSHP550wA8OakXUuqCk1BMoxERUfAwYNGhqKQKDy/eCYdTwJQBGbhnVGes2HUCD17eDckJxhQFd2ld35q9V3qi4r62iXG6nkMMVuS+3V+s+FoerABAc7fiYfmFfv6aXGm1TVzMLgztmIKLUpsjp+A8uqU2x/e5pzF1cDsIAD7adFR1TGIQ4xSAXcdKpMApGF6/YzDstQ70Tk9GdJQVqUn6vk9ERGQ8Biw+3P72Jmw6cgZOAchIjsNfru2DFgmxGJDZwtBxjerWWvp8TPdUxX2zL78Iy3Yea1AzN196pScpvtZakVRV41o6vOHQaQCuDBUAvL7usMexj17dA3//Wnu6rSHSkuJwutyOK3q1RZm9BrUOARN6tw36JpRERNQ4GLD4EB1lhVMABma2wMu3DkSLBHPUN8TFROH9mcNwoKgUV/RSBiyZKQn44fHLcexcJXYVnMeSrQXYX1SmOGbJvcNxSZdW2HOsBLe/vQll9lrpvhkjO2HRj79ovq5ccnwM0pLiUFRa1aDzuG1YJu4be5HPgOXPk3ujuMyOt7IPe3TIBYBbL87E3hMlePW2wdiQewrXD26PymoHkuNjuGsxEVEEsAju7UbDVGlpKZKTk1FSUoKkpCTfD9DpUHE5mtui0TbJFtYNvwRBQEW1A1/tLcKVvdsiOV45lfXl7kLc//EOXNI5BUt+OwKnyuxIjo/BkdPlqK514pMt+bhxSCaGdGzp8dxOp4AuT6z0e0wzRnbC4xN7Ii4mCot+yFM03fvonkswuENL/G/3CRSXVuH+cRfBYrEg7/QFVFTX4ovdhRjfMxUV1Q5ER1kwsmtrL69ERERmpff6zYCFJO5bDfhj+9FzOFNux+COLTH0uTUAgOFdUnDD4PZIio/BpRe1Rt+nv5GOH9qxJT6dNUIKAp1OAecra5B/tgLHz1Ximv6e+0cREVHkYcBChjlQVIb4mCh0aKVclvzs/37CvhMlyJraD6lJcR4FvERE1PTovX7zikFB1yMtUfX2P0/p3cgjISKiSMFqRCIiIjI9BixERERkegxYiIiIyPQYsBAREZHpMWAhIiIi02PAQkRERKbHgIWIiIhMjwELERERmR4DFiIiIjI9BixERERkegxYiIiIyPQYsBAREZHpMWAhIiIi02PAQkRERKYXbfQAgkUQBABAaWmpwSMhIiIivcTrtngd1xIxAUtZWRkAIDMz0+CREBERkb/KysqQnJyseb9F8BXShAmn04kTJ04gMTERFoslaM9bWlqKzMxMFBQUICkpKWjPayaRfo48v/AX6efI8wt/kX6OoTw/QRBQVlaGjIwMWK3alSoRk2GxWq1o3759yJ4/KSkpIn8J5SL9HHl+4S/Sz5HnF/4i/RxDdX7eMisiFt0SERGR6TFgISIiItNjwOKDzWbD008/DZvNZvRQQibSz5HnF/4i/Rx5fuEv0s/RDOcXMUW3REREFLmYYSEiIiLTY8BCREREpseAhYiIiEyPAQsRERGZHgMWH15//XV07twZcXFxGDJkCL7//nujh6RLdnY2pkyZgoyMDFgsFixfvlxxvyAImDdvHjIyMhAfH4+xY8di3759imPsdjseeOABtG7dGs2aNcOvfvUrHDt2rBHPQltWVhYuvvhiJCYmIjU1Fddddx0OHDigOCacz/GNN95A//79pSZNI0aMwFdffSXdH87npiYrKwsWiwUPP/ywdFu4n+O8efNgsVgUH2lpadL94X5+AHD8+HHceeedaNWqFRISEjBw4EBs375duj/cz7FTp04eP0OLxYL7778fQPifX21tLf70pz+hc+fOiI+PR5cuXfDss8/C6XRKx5jqHAXStHjxYiEmJkZ4++23hZ9++kl46KGHhGbNmglHjx41emg+rVy5UnjyySeFpUuXCgCEzz77THH/Cy+8ICQmJgpLly4V9uzZI9xyyy1Cenq6UFpaKh0za9YsoV27dsLq1auFHTt2COPGjRMGDBgg1NbWNvLZeLrqqquEhQsXCnv37hVycnKEa665RujQoYNQXl4uHRPO57hixQrhyy+/FA4cOCAcOHBAeOKJJ4SYmBhh7969giCE97m527Jli9CpUyehf//+wkMPPSTdHu7n+PTTTwt9+vQRCgsLpY/i4mLp/nA/v7NnzwodO3YUZsyYIWzevFnIy8sT1qxZIxw6dEg6JtzPsbi4WPHzW716tQBAWLt2rSAI4X9+zz33nNCqVSvhiy++EPLy8oRPP/1UaN68uTB//nzpGDOdIwMWL4YNGybMmjVLcVvPnj2Fxx9/3KARNYx7wOJ0OoW0tDThhRdekG6rqqoSkpOThTfffFMQBEE4f/68EBMTIyxevFg65vjx44LVahW+/vrrRhu7XsXFxQIAYf369YIgROY5tmzZUnjnnXci6tzKysqEbt26CatXrxbGjBkjBSyRcI5PP/20MGDAANX7IuH8HnvsMWHUqFGa90fCObp76KGHhK5duwpOpzMizu+aa64RZs6cqbht6tSpwp133ikIgvl+hpwS0lBdXY3t27djwoQJitsnTJiAH3/80aBRBUdeXh6KiooU52az2TBmzBjp3LZv346amhrFMRkZGejbt68pz7+kpAQAkJKSAiCyztHhcGDx4sW4cOECRowYEVHndv/99+Oaa67BFVdcobg9Us4xNzcXGRkZ6Ny5M2699VYcOXIEQGSc34oVKzB06FDcdNNNSE1NxaBBg/D2229L90fCOcpVV1fjww8/xMyZM2GxWCLi/EaNGoVvv/0WBw8eBADs2rULGzZswKRJkwCY72cYMZsfBtvp06fhcDjQtm1bxe1t27ZFUVGRQaMKDnH8aud29OhR6ZjY2Fi0bNnS4xiznb8gCJgzZw5GjRqFvn37AoiMc9yzZw9GjBiBqqoqNG/eHJ999hl69+4tvQmE87kBwOLFi7Fjxw5s3brV475I+Pldcskl+OCDD9C9e3ecPHkSzz33HEaOHIl9+/ZFxPkdOXIEb7zxBubMmYMnnngCW7ZswYMPPgibzYZp06ZFxDnKLV++HOfPn8eMGTMARMbv6GOPPYaSkhL07NkTUVFRcDgc+Otf/4rbbrsNgPnOkQGLDxaLRfG1IAget4WrhpybGc9/9uzZ2L17NzZs2OBxXzifY48ePZCTk4Pz589j6dKlmD59OtavXy/dH87nVlBQgIceegirVq1CXFyc5nHhfI4TJ06UPu/Xrx9GjBiBrl274v3338fw4cMBhPf5OZ1ODB06FM8//zwAYNCgQdi3bx/eeOMNTJs2TTounM9R7t1338XEiRORkZGhuD2cz2/JkiX48MMP8fHHH6NPnz7IycnBww8/jIyMDEyfPl06ziznyCkhDa1bt0ZUVJRHhFhcXOwRbYYbcaWCt3NLS0tDdXU1zp07p3mMGTzwwANYsWIF1q5di/bt20u3R8I5xsbG4qKLLsLQoUORlZWFAQMG4OWXX46Ic9u+fTuKi4sxZMgQREdHIzo6GuvXr8crr7yC6OhoaYzhfI7umjVrhn79+iE3Nzcifobp6eno3bu34rZevXohPz8fQGT8HxQdPXoUa9aswT333CPdFgnn98c//hGPP/44br31VvTr1w933XUXfv/73yMrKwuA+c6RAYuG2NhYDBkyBKtXr1bcvnr1aowcOdKgUQVH586dkZaWpji36upqrF+/Xjq3IUOGICYmRnFMYWEh9u7da4rzFwQBs2fPxrJly/Ddd9+hc+fOivsj4RzdCYIAu90eEec2fvx47NmzBzk5OdLH0KFDcccddyAnJwddunQJ+3N0Z7fb8fPPPyM9PT0ifoaXXnqpRyuBgwcPomPHjgAi6//gwoULkZqaimuuuUa6LRLOr6KiAlarMgyIioqSljWb7hyDWsIbYcRlze+++67w008/CQ8//LDQrFkz4ZdffjF6aD6VlZUJO3fuFHbu3CkAEF566SVh586d0pLsF154QUhOThaWLVsm7NmzR7jttttUl6q1b99eWLNmjbBjxw7h8ssvN81yvN/97ndCcnKysG7dOsWyw4qKCumYcD7HuXPnCtnZ2UJeXp6we/du4YknnhCsVquwatUqQRDC+9y0yFcJCUL4n+Mf/vAHYd26dcKRI0eETZs2CZMnTxYSExOl949wP78tW7YI0dHRwl//+lchNzdX+Oijj4SEhAThww8/lI4J93MUBEFwOBxChw4dhMcee8zjvnA/v+nTpwvt2rWTljUvW7ZMaN26tfDoo49Kx5jpHBmw+PDaa68JHTt2FGJjY4XBgwdLy2bNbu3atQIAj4/p06cLguBarvb0008LaWlpgs1mE0aPHi3s2bNH8RyVlZXC7NmzhZSUFCE+Pl6YPHmykJ+fb8DZeFI7NwDCwoULpWPC+Rxnzpwp/d61adNGGD9+vBSsCEJ4n5sW94Al3M9R7FcRExMjZGRkCFOnThX27dsn3R/u5ycIgvC///1P6Nu3r2Cz2YSePXsKb731luL+SDjHb775RgAgHDhwwOO+cD+/0tJS4aGHHhI6dOggxMXFCV26dBGefPJJwW63S8eY6RwtgiAIwc3ZEBEREQUXa1iIiIjI9BiwEBERkekxYCEiIiLTY8BCREREpseAhYiIiEyPAQsRERGZHgMWIiIiMj0GLERERGR6DFiIyBTmzZuHgQMHGj0MIjIpdrolopDztc389OnTsWDBAtjtdrRq1aqRRkVE4YQBCxGFnHx7+iVLluDPf/6zYqff+Ph4JCcnGzE0IgoTnBIiopBLS0uTPpKTk2GxWDxuc58SmjFjBq677jo8//zzaNu2LVq0aIFnnnkGtbW1+OMf/4iUlBS0b98e7733nuK1jh8/jltuuQUtW7ZEq1atcO211+KXX35p3BMmoqBjwEJEpvXdd9/hxIkTyM7OxksvvYR58+Zh8uTJaNmyJTZv3oxZs2Zh1qxZKCgoAABUVFRg3LhxaN68ObKzs7FhwwY0b94cV199Naqrqw0+GyIKBAMWIjKtlJQUvPLKK+jRowdmzpyJHj16oKKiAk888QS6deuGuXPnIjY2Fj/88AMAYPHixbBarXjnnXfQr18/9OrVCwsXLkR+fj7WrVtn7MkQUUCijR4AEZGWPn36wGqt/7uqbdu26Nu3r/R1VFQUWrVqheLiYgDA9u3bcejQISQmJiqep6qqCocPH26cQRNRSDBgISLTiomJUXxtsVhUb3M6nQAAp9OJIUOG4KOPPvJ4rjZt2oRuoEQUcgxYiChiDB48GEuWLEFqaiqSkpKMHg4RBRFrWIgoYtxxxx1o3bo1rr32Wnz//ffIy8vD+vXr8dBDD+HYsWNGD4+IAsCAhYgiRkJCArKzs9GhQwdMnToVvXr1wsyZM1FZWcmMC1GYY+M4IiIiMj1mWIiIiMj0GLAQERGR6TFgISIiItNjwEJERESmx4CFiIiITI8BCxEREZkeAxYiIiIyPQYsREREZHoMWIiIiMj0GLAQERGR6TFgISIiItP7fx1rvPBMX0N/AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def pred_err(p):\n", " \n", " CpH, CpS, Ua, Ub = p\n", " \n", " # array parameters\n", " A = np.array([[-(Ua + Ub)/CpH, Ub/CpH], [Ub/CpS, -Ub/CpS]])\n", " B = np.array([[alpha*P1/CpH], [0]])\n", " C = np.array([[0, 1]])\n", " \n", " pred = tclab_ss(A, B, C)\n", " return pred[\"T1\"] - data[\"T1\"]\n", "\n", " \n", "pred_err([5.8, 1, 0.04, 0.045]).plot()" ] }, { "cell_type": "code", "execution_count": 194, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CpH = 5.228060928587527, CpS = 1.9896637181582368, Ua = 0.041571036467889934, Ub = 0.21309424723032316\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 194, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.optimize import least_squares\n", "\n", "results = least_squares(pred_err, [8, 1, 0.05, 0.05], loss=\"cauchy\")\n", "\n", "CpH, CpS, Ua, Ub = results.x\n", "print(f\"CpH = {CpH}, CpS = {CpS}, Ua = {Ua}, Ub = {Ub}\")\n", "\n", "pred_err([CpH, CpS, Ua, Ub]).plot()" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = np.array([[-(Ua + Ub)/CpH, Ub/CpH], [Ub/CpS, -Ub/CpS]])\n", "B = np.array([[alpha*P1/CpH], [0]])\n", "C = np.array([[0, 1]])\n", "\n", "pred = tclab_ss(A, B, C)\n", "ax = pred[\"T1\"].plot()\n", "data[\"T1\"].plot(ax=ax, grid=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ":::{admonition} Choosing a Loss Function\n", "\n", "Consult the documentation page [`scipy.optimize.least_squares`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html). Modify the regression to use alternative loss functions including `soft_l1`, `huber`, `cauchy` and `arctan`. \n", "\n", "1. Which gives the best result? \n", "2. From the documentation, why is the fit better? \n", "3. How much of difference does it make it estimated model parameters?\n", "\n", ":::" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 4 }