From 3af583f1ddc9cee4f2a3b292871228e4351d7a1e Mon Sep 17 00:00:00 2001 From: Gustavo Simas da Silva Date: Mon, 14 Aug 2017 19:04:12 -0300 Subject: [PATCH] Aula 5 parte 2 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit análise de malhas com fontes de corrente e exercicios --- ...An\303\241lise de Malhas-checkpoint.ipynb" | 462 +++++++++++++++++- "Aula 5 - An\303\241lise de Malhas.ipynb" | 462 +++++++++++++++++- Imagens/circuito-malhas.png | Bin 0 -> 8901 bytes Imagens/supermalha.png | Bin 0 -> 27240 bytes 4 files changed, 922 insertions(+), 2 deletions(-) create mode 100644 Imagens/circuito-malhas.png create mode 100644 Imagens/supermalha.png diff --git "a/.ipynb_checkpoints/Aula 5 - An\303\241lise de Malhas-checkpoint.ipynb" "b/.ipynb_checkpoints/Aula 5 - An\303\241lise de Malhas-checkpoint.ipynb" index c340bc4..587c268 100644 --- "a/.ipynb_checkpoints/Aula 5 - An\303\241lise de Malhas-checkpoint.ipynb" +++ "b/.ipynb_checkpoints/Aula 5 - An\303\241lise de Malhas-checkpoint.ipynb" @@ -23,7 +23,467 @@ "![](http://i.imgur.com/3Gu3UOb.png)\n", "![](http://i.imgur.com/V5yAmq0.png)\n", "\n", - "**Malha é um laço que não contém nenhum outro laço em seu interior.**" + "**Malha é um laço que não contém nenhum outro laço em seu interior.**\n", + "\n", + "![](http://i.imgur.com/eihmMJc.png)\n", + "\n", + "O sentido da corrente de malha\n", + "é arbitrário (sentido horário ou\n", + "anti-horário) e não afeta a validade\n", + "da solução.\n", + "\n", + "Etapas na determinação de correntes de malha:\n", + "\n", + "1. Atribua correntes de malha i1, i2, ..., in a n malhas.\n", + "2. Aplique a LKT a cada uma das n malhas. Use a lei de Ohm para expressar as tensões em termos de correntes de malha.\n", + "3. Resolva as n equações simultâneas resultantes para obter as correntes de malha.\n", + "\n", + "Resolução para a figura 3.17. \n", + "\n", + "Malha 1:\n", + "\n", + "\\begin{align}\n", + "-V_1 + R_1i_1 + R_3(i_1 - i_2) = 0\n", + "\\\\\n", + "\\\\(R_1 + R_3)i_1 - R_3i_2 = V_1\n", + "\\end{align}\n", + "\n", + "Malha 2:\n", + "\n", + "\\begin{align}\n", + "R_2i_2 + V_2 + R_3(i_2 - i_1) = 0\n", + "\\\\\n", + "\\\\-R_3i_1 + (R_2 + R_3)i_2 = -V_2\n", + "\\end{align}\n", + "\n", + "Reorganizando as equações, temos:\n", + "\n", + "\\begin{align}\n", + "\\begin{bmatrix}\n", + "R_1 + R_3 & -R_3 \\\\\n", + "-R_3 & R_2 + R_3\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "i_1 \\\\\n", + "i_2\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "V_1 \\\\\n", + "-V_2\n", + "\\end{bmatrix}\n", + "\\end{align}\n", + "\n", + "Note que **as correntes de ramo são diferentes das de malha, a menos que a\n", + "malha esteja isolada**. Para distinguir entre os dois tipos de correntes, usaremos\n", + "i para indicar correntes de malha e I para indicar correntes de ramo. Os elementos\n", + "de corrente I1, I2 e I3 são somas algébricas das correntes de malha. Fica\n", + "evidente da Figura 3.17 que:\n", + "\n", + "\\begin{align}\n", + "I_1 = i_1\n", + "\\\\\n", + "I_2 = i_2\n", + "\\\\\n", + "I_3 = i_1 - i_2\n", + "\\end{align}" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exemplo 3.5**\n", + "\n", + "Para o circuito da Figura 3.18, determine as correntes de ramo I1, I2 e I3 usando a análise\n", + "de malhas.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exemplo 3.5\n", + "Corrente I1: [[ 1.]] A\n", + "Corrente I2: [[ 1.]] A\n", + "Corrente I3: [[ -2.22044605e-16]] A\n" + ] + } + ], + "source": [ + "print(\"Exemplo 3.5\")\n", + "import numpy as np\n", + "\n", + "V1 = 15\n", + "V2 = 10\n", + "\n", + "#Malha 1:\n", + "#-V1 + 5i1 + 10(i1 - i2) + V2 = 0\n", + " #15i1 - 10i2 = 5\n", + " #3i1 - 2i2 = 1\n", + " \n", + "#Malha 2:\n", + "#-V2 + 10(i2 - i1) + 6i2 + 4i2 = 0\n", + " #20i2 - 10i1 = 10\n", + " #2i2 - i1 = 1\n", + " \n", + "coef = np.matrix('3 -2;2 -1')\n", + "res = np.matrix('1;1')\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente I1:\",I[0],\"A\")\n", + "print(\"Corrente I2:\",I[1],\"A\")\n", + "print(\"Corrente I3:\",I[0]-I[1],\"A\") #aproximadamente = 0" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Problema Prático 3.5**\n", + "\n", + "Calcule as correntes de malha i1 e i2 no circuito da Figura 3.19.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Problema Prático 3.5\n", + "Corrente i1: [[ 2.5]] A\n", + "Corrente i2: [[ 0.]] A\n" + ] + } + ], + "source": [ + "print(\"Problema Prático 3.5\")\n", + "V1 = 45\n", + "V2 = 30\n", + "\n", + "#Malha 1:\n", + "#2i1 + 12(i1 - i2) + 4i1 = V1\n", + " #18i1 - 12i2 = 45\n", + " #6i1 - 4i2 = 15\n", + "\n", + "#Malha 2:\n", + "#3i2 + 12(i2 - i1) + 9i2 = -V2\n", + " #-12i1 + 24i2 = 30\n", + " #-2i1 + 4i2 = -5\n", + "\n", + "coef = np.matrix(\"6 -4;-2 4\")\n", + "res = np.matrix(\"15;-5\")\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente i1:\",I[0],\"A\")\n", + "print(\"Corrente i2:\",I[1],\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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atWsZVB/Jt5MJSx4RvlcZAbJLubR2Fv/oV5zexztx0hft27dDs6a2ev/F0P7erzTEHN+Jy+2n4GNbzUaZ//77r4i/mVnuS+Eqd4iCjNRHnTp1EP8MsY/km8SEJY8I32uEgKEuk9NpEXRme9FDGmL8dsKn6hBMa1cLRsJTXDkcCcsB7VBbjYGWNNpTe5uFCg2Q+oimwjdv3RK3Mjg7O8Hezs5gbFlMWCp0NGdRHYGaNWvi3R7d0dm1E0Kvh+HoseNiYbq3sGisdytRLVq0AHm6KVpIR9y5VZg8cQNuZXyDn0RhddF//T54qkFWVIz2hdFeKF0GWn2kv3Zt2+D2nXDs238ANKWnDbxEavocmLD0uXfkdUt/gtC/tmGlV0XM9J0FZ5neE5JuYv9yT/wt2MIOkbhm1BPz5g2GnYny44KFpDs4/tsWbPnjFsy6dIS9aSJu+l1CjM1gTP94HHrbVpNxpyWvTMH3NBVxdGiBaqamOHjoL5w9dx5pr9Pg0KJFwQWLOZX2PdFeLDolQfMpYgXUdp2Lw5Fzi6Q96UBH3EyYML5IclQtTIsjsn2Ukq+P0hB7eQe+n7cSR+4nA2YdMcVzBWZ3q6/gVFcBqTe3YNyAa3A/vxKD6so8nHIKFem5E0pRGD58ZClqTd6mZD4PEfZ5/yIs+7/WgpXTSiHwjUx65mPhxNz3BLflF4WXmYIgZD4TLi8fLLSb+7fwhO4VhMzn54UVfVsIzcZuEW4kpufmyEwQbvwyUWjWZIjw7dlYQUnx3PwKrhITE4Vz5y4Ia9auF/btOyDcuROuIJd+RKWkpOiHIoIgBARcFfr3HyjcuHFD5zpRH/n+cyqnj+7ffyBXZ6aQcmOzMH6yl/DXuSvC5VN/CMvHdhSsmnwgrLv2Qi6vIGS+vCJ4DWghWDWeIfjEyD6cebMW9blDXnGGfVeaCSurZxKFwJV95AgrU0i7tk54r/FQYd21xOwOVBQn27fPhHNL3hOsGg8WPAPzP3xCWoiwzs1GsHJZIpx+LkNmsiIUXD9+HCMcOXJMWPHDSvHL8OzZMwW5OEoZAitW/CCMHTtOWbJW4omY6EeEfkyIsIi4FIdnwrkVPwknnuSST+bD3cL4JlZCl7XXhDxPReYT4dy384RvFo8qhLCK/twpH7fJDeP4Vl8RSMODoAuIrGgLm4ZVs5U0QqWGNmhZcR1OBkVjqmNT0Q1WTgtehuL4H+GA6US0aabA6XslS7i4WQIb/sbRq1PRrWednKLyF/K7plu2dNTrne3y+uvLPRn+pRNPta2TfB/R2weF7mwXjPD2u8PQunYuRRiZW6FltXKIqZQbB6Qjzncr/mo+EdOxBtsKUl4Lz51szQVVxWl6i0ASou8+Akxa421Z9+ymb6OeSTKO341BEpqimqz+yQn4j7Yemb2FqpUUWYXLoUIlsn2lIOGV8iNi6ItAZ0lFP46BVRPLwr8EsjrwNbZv3wE7OzvR2E2epWnFknwXajNo3EdGZmjmnHdrhRAfi/tJDhjYrlHW+5MQkP7oKFaedcDMRZYw+qsQzbXw3DFhFYKx/ien4kWs8gPkkmMTQNyUh7Cq1UZDGlilv0LKawGoIE9amUh/nQHAFO/UUL5bmwzr7u4fiO+90TL5qtXrYGjL5CXVv7S1gFzYUyBfhdLoSnPDv+KWyPYRvVQt9VErp5agFV3VwxvEnj+JwKFT8JVD9h6zN3exe+Ud9PpyNswrAIU6K9PCc8enNajeY3qasxKMzaSpYH4VjevWQNbrtDJpxg7o96ETkBiIgNsKyC4lAhdORAEWAzDApfCHmpbIaSsDvfJRvXp1cZl8584/xAPiZGrlSxkEduzYkXO3f/8B1K9fT83z5HOKq3RBfdS3b2+xj6pUroKdu/7E/v0+KveREHcaq/9ohB/nv5u1r0xIQOiv2xE32gNdZaaNBSqjheeOCatAhA0hsRosmlsCSU/wLJFGRdkh8RkeJxnDytoc+fdcV0OrSd9gUa+n2LBwPfxi0qRSQHo0/H78DhsSemLR+kloY6L6I0LL5LTz/eOPponTHNr5vnbdBlwNDDKYA+JygdDdlWSvkq0hOvqxOEWUjdPFNfUR7XyfPGki6MBA6qPNW7wL7qM3d7F/7R308pyOdpJX7Yx7OLVpO9YMc4aNhSWsLWzgOuswgMP4rL0NrD18FIy4iv7cqf406gI9lqkFBCqjsXNHWL25h/uxufamjNj7CH3TDD2d6+c1uCMDccd24HiKPcau241dH5rinzkjMetoDBB/GosGfYV/ao7BriMrMdZeQMDanbguw4OqKkwbEGm6+F5PN1y6dFncVU2vhnAAyF6lKNAUsbhcfdFUUeoj2tR7+vQZxX1EP2Bee5D8/lh0Nc8+Kic1BvefNces4CjcvS/9ReCc1wAAA/DTpQjc/XUw6uZppHaeO7Zh5QHVEG+MUMlhIGYN2oeVx29itF1rVMVLXDt+DM8HTcQQyd6Q0zQBGWnXsWXFI9ypl2WfMjM3xVOyWaW9QFyV2rB5fR/+u9bD//W/OH+kIb6YmlNY5Qvp9Q86yoTtWrmwKRpdUSoZ3N3dR+l0WpirRdYV9RHZtW7cvCX2UT67FpHV9wvxZ113TEqNRLB4cnMaYnz9kTpqNizkBRZ4r53njgmrQJD1KDH9KSIun8HRc4+BpGvw/ycApq0dYVOrMmDUAL2/W4Pk5Z74ZIG00/3/sO273jCXt6eLTUpB8J7dCM5pnhl6dMq6yQjci/WBOQmA2UyZm4IvaUXq/v0H4jTjeXy8+BK0IR9lUnBrNUv18lqdryB5y5k0yaNYHMlKfURvHlBQug1FeIrLK2diyuYgZOA0TspoXXHgOvg30ORAxqI/d0a0aUxGF4O+HDHifezZ86dBt8EQlafD+65du47gkBDx8D6yjej7O2klgTPZi5Ys+SanahpVzZs3F/b29jlxurooLX3EIyxdPSFlQC79Wvv6nhKnFPXrmcN91PtqLpWXAZBkmkj7rqQwcuQIjBgxvAjvL0qSCv4kojpxwheR96LEvXKGdMCiopax0V0RKhynEgJkuO3SxRUdO7QHTQH9/PxVXiZXqYJSlIlGV+T/kBzGrl7theLyxUirgu+95ybaqOjEUSIvOiXWUANPCQ215/RMb0W2EToJgEitrAc6hWHKlKnFblSXx536SNZBiL4e+SOvt+w9E5YsGnytFQRo9enixUs557zTuUv0S19WQ0JCgth0XRzKpymmsmfx0znvLVs6GEQfMWFp2uNcrlAEyH5CjlQlTzr66Ei10EaU8gySJx1D6SO2YZXyB7Ikm0eOVMlJJwVypKrvTjpLEquSqvvp02c5ffTOO+/ofR/xKmFJPSmltF55O4lKR5mUUiz0tVnUR3R89bVroaKKZMsq9LgZPWkME5aedIShqyE7tWhiaYnS7UjVMHtL6iN2pGqY/cdaawEBeSedhr7PRwuQ6J0Iyb0XbT0xdEeqbMPSu8fLcBSiqcXLxETEJySgatWqopNO3sagX/0n9RGRFXnGMXRHqrxKqF/Pl8FqIz/SoiNMOOgXArIjLXJ2S0cBGVpgG5ah9Zie6kvvDtIf2UmWLf9BPHNJT1Uts2pJfUT75H78caVBEhZPCcvs46ubhtOxu1H37ulGOEvVCgJ0+ujDhw+0Iqu4hTBhFTfiXB8jwAhojAATlsbQcUFGgBEobgSYsIobca6PEWAENEaACUtj6LggI8AIFDcCTFjFjTjXxwgwAhojwISlMXRckBFgBIobAd6HVdyIc336jUDqdfwydjoC3Hdh0+AGSnUVku7g+G9bsOWPWzDr0hH2pom46XcJMTaDMf3jcehtWw0K/X8olcgJqiDAhKUKSsWQh9w/0XEsz549zVPb22/Xwttv14SlpWWeeL7RAQJCPIJ+/hY/XnmFru7K5QvxF/Dj6CnYUutT7Dv6P9iblM/KPPcFbm7+DMP6jEfQtg340vUdJi3lMGqUwoSlEWxFL0TH5gYEBIhORv39z6oksF+/PnBxaSN67K1SJcunoEoFOZMKCGQg/oI3dry0hgsKcvj6HBfWLMHGG9b4eP+wXLKiGoyqw37sDMz4cwRWzt6ITie+QjfJU7IKGnCWwhFgwiocI63moONyDx/+C+TllwI5JZgwYTyaNWsKM7OaoF3IskEaed26dUv093fkyLEcp5tdu3bVudcVWV1K87UQdwqrDlth9keWWLrlmPKmvgzF8T/CAdOJaNPMNH++SpZwcbMENvyNo1enolvPOvnzcIzGCDBhaQyd+gXJDfnOnbvw/Hk8yM2Tq2unQqd6NBWkPxeX1qKnlZs3b+LIkaNYu3a9KMvDYyI6d+6svjJcIheB9Cgc+ikQ7T6ZjYZGBZAVlUhOwH/JAMzeQtVKiqxU5VChEk0RU5Dw6nVuHXylFQQMlrBopBIaeh3Xr1/H7du3RY/DhMiAAYPQsWNH1KtnjubNm+vF9Immf2vWrAVN/cjL7+jRo/ONpFTtTXK6SX/Dhw/D1q3eWLHiR3FaOWPGxzzaUhXEPPlScG/3VoT0no5F5pWB2DyJ+W+q1UZDGlilv0LKawGoIE9amUh/nQHAFO/U4Gl7fgCLFmNwhEVTpN279yIsLEwcodjZ2aFDh45o1KiRiERaWhr+++8/xMTE4OzZc6KnXfpyDxo0sFhcgct3B70ZP3/+fHFUNXfu51obDdGo65tvloBGbTTaSkxMxJdffsGkJd8BBd5nICl0J9bGDcCSUXVVM5AbO6Dfh07YtioQAbcT0cm5Wt4aUiJw4UQUYDEZA1xq5k3juyIjYDDnYdEo5a+/juDgwUMYNGgQOnTogMqVKxcKwIsXL+DrexLnzp3HpEke4gin0EJayiCRFYnTpUtyyQV6q1ZOekFaI0a8jz17/tQSiroUk4Qgz5EYueqWkkoG4KdLKzGobt7fdSHpOrZ/Nh3f/dsPG3+djW40MqOQHg2/72dgio85vtr+P4yxr64aCSqpXZfRhtNHeVEwCMIisvr22+/E0cOoUe6oXr163laocPfw4UNs3rwZbdu2wbhxY1UoUbQspPP//vc9Hjx4gGXLlmk8BVRVC30iLUP9MohYx/pgcvtvAK9DCvZhZSDu2C5cdRmFPmZPEHRwPw4cOIFE95/h1eE2Fo3eBqHvIAwZ1hfOdVNwZe1RVJ3mDofsXQ+q9mVx5DPUPtL7ne4SWTVs2BBTp05TQlaZSI44hT98I0D2UEWBpoxffvml6CNv27bfFGXRapy3tzeCg0MwY8YMnZMVKU5G+cWLF4l17tmzV6ttYWESAgIy0q5jy4oV8FrzB/wfvoaZuSnSyGaV9gJxVWrD7PV9+O9aD6/lS/HD7id4I0hl+VMbCOQd62pDopZl0MiKyGrYsOEFSBaQHB2Mv6+Wg5ubDYyV5KQpJBHImjVrsG/ffgwbNlRJzqJFZ63kHRO3KxCRFFegumj1kbZMqLICWVx6la56UhC8ZzeCcxplhh6dsm4yAvdifWBOAmA2U+aGL7WBgF4T1vHjfyM9PQP9+w/QRltFGURakyZNwtdffw1n51aFbitQt2IaEW7c+Iu4v6pv3z7qFi9y/hEjhsPX1xdeXquxapVnkeWVOQF1B2PT/cFKml0BdQevxt3BqxWkNyignILsHKURAno7JaRtC7//vhNjx45VybiuTuvJBvbBBx9g8+Yt6hRTKS/tXr937564Z0q93eiZSDz/Hdq3/hQHH6WpVJeiTFQnjSJJB7JrcWAEShMCygkrPQaXf5mFHlaWsLawhsvIn+AXo+SLRC+MjuyMyT7/5sNGeBqKQ55T0NaC5PTG3F+O4/rT9Ox86Xga+hfWz+gJ69YTsGJfCJ5mz/kvXbokTmvq1FGyUzjjFnZOnYAJE+jPA3O2hQF3tmGOeE9xc7HzljKLFtCuXTvExyeApm/aDHv37hdHV+pPBY1QpZ4Derk2g7lJ0Qa+VDftoD906JA2m8ayGIESR0DJNyMJN7d+j62v3LB09yi8iRhjeW8AACAASURBVPSD9/INmDLFGHv+nArHqjKb5Qp5YdSoliMGzvoKwp1gfHa8Jmxcu8ChllRtBdRydEPP1ntxsNkszBrWEpWyIfn9912YPXu2coDK28H9563Iekc1A0/9vDDnUmv8ML8baikvlSelb9++OH3aT9yImSdBwxvaxkAjG9pvpX4wQkXLgViySv2Sikr07dtb3J9FI9UaNWooysJxjIDBIaB4hJV4DUeiB2DpJwPRqXU7dBs5G0vn9wRCT+BcRIpMI2VfGJWJlr80aoAeYwahFq5i9/FbkJWAzH8RcMIY4/o2yyEr+uJXq1YtZzOovDht3Tdr1kzcJa4teRcvXhRFOTg4qCkyA0mPrsDHczqGeQVCyThWLZk0gqRAbwJwYARKCwIKCUvIqAO3cR1RO2cgVQnmVrYwRSVUrJgTiZwXRie0wVsFIlIOpm0HY6JjRUSt/wN+cdKUUMDrsBPYUe09dLfI3QR6924EHB3V/dIXqIDCRLJl0R8RpDZCZGQkaPOm2iMa4Tmizh/GL6tuwN6pMXKR0Fwr0oGmhZcuXdZcCJdkBPQMAYWEZVTDBq0sZSkoHfGxj/HKpivaW2W/H5XzwmgvNKyoQqsq2qL/hz1R8c1JbD95H5likRcIOXYWtgPbom4uDyIxMQl0DlRxhHfeeQepqXnGfBpXS+8KOjk5qV/eqDaat7ZCJVjBrrGCEwDUlyiWsLNrKr7CpGFxLsYI6B0CCgkrn5bCY1w4dBeD5g5BC/ENdemF0fHoLb2WkK+QfERF1O06CCNqJ+HK5iMISREgPA/AvsMtMKJz3ve44uLixCNU5CUovy+PWt0+w1Y17FeSrDp1aiM8PFy61fiTtjNQeOstZbvAChKdhocB/rhu2wGtGmljfJVVF71vSCdDcMiLwPWwMLx+rfwkBRpxFzbqJhkFhcLqKKgspylHQAXCSkecrzf+bDIH89zMYYTcF0Y/7ZqXaJRXk5ViZNYGI8a3BCL34s9z/yLG/xiuDesNZ9O8aiQlvUJKShYBFCazqOnGxpoQTP5a6WVrCra2tvkTC415gYjgOzBxtUdj8TWODCRFncG2BePxiYKV10LFyWWQyFQuuszenjlzNud0D0Ug3Lx1CxcvXlKUJMaFh0fg+PGTSkmPyLCwOpQK54QCEcjLFPmyCngTdRjrQlzx06cdYCZO21IQ/s8+HPIciVaWtFXBEtbtZ+MU4nFqVmdYW8zEwVjJRiUv0AQtho5Bz4r/wueX1Vi/5wkGvtsUVeWyWVpaICVFO9M0OdH5bu/ff6AhyeQTpXlEcgQuHX+Dri6NISQkIv3NM8SWM4Pxo8i8CxRq1iCRp0SmahYvldmJbCicPXdeYfuSkpIQFBSCxzExoGtFISzsBqpWrYI7Skbm9ExR4H1witArWlwBhCUgPeY0vLamYuS0rjAXz/0RkBr9HPVnHMHd+1G5f5c80QNm6OF1Fnfvr873drusikZ1O+L9D6yRcWUv9mT0RZ8WJrLJ4rWpqUm+s83zZdJSRGysdgzuRVEnMzoCQYk2aFE1GFsO3sObinVg3bgmKlUsoHtUqPDff7P2xZmZmamQu2xkIaJ6r6eb2FhF077bd8Lh7OwEO7tmuHwlIB8oz58/F8mMZFy5cjVfOkVIdTyPjy90aqlQAEcqRUDJN4LI6hSWzTqEGt2tkRp+DUFBQQi6fBhrNgbhdXkZC7lS0UoSjGqj44ghsEJt9PjAFRYKNGjQoIF4OJ8SCVqLpqNn6BQHsvUUNVSpkjVOlEhCLXkVKqFq+VD4HAcGuDvmG3GqJUsmc3Jy1sZZtVctZWSUpkuJoGxtbdCypaP4orh8+65dC4W9nR3atW0jvigvb+sKDrmGVk5OIBkUHjx4mEeEbB3t27cDTS85aA8BaQdnHolC/EV4esyC940k4PJBmbS66L9+HxoUga8AI1Ry6INJPR7jrU71FJ4XRATy8uVLPHnyBEp3ustopeklnVTau3cvTYvnKSedxS6RRJ7EQm7KWbpjZ2QBbloKKa8s+cmTOGVJZTKeTs8goqLg6NACq06vQ5curjAxyRrlS9NFqS/rmZuLti6JnIi8aLo4beokUUbbti4IDAxC48ZZh0dSJNm+pDqaNbXFhp9/EclPqkMsyP80RkAhYRmZdcScI9cxR1WxBb4wqkCIkSWGb/lWQUJu1ODBg3D2rL+SUxricG7lYmy+rszOZQTTvvPhOcIWBR1FdPToUfFEhdxai3ZF+57o2OZevbRDgkXTBoiIiCjWAwtl9aXzlvQtNG1mh0ULvxTVqlSpkjj1u3btOjp16iDGkW2qs2v20QuAeLw2Te8kwiKbVXN7uxyCa2prKxrXydZFhESfZPvq37+vKI/iaHpJ00yX1s5i3M6df8D/7Fk8e5rXnZuYyP8KRUAhYRVaqhgyvPtuD4wZMw5ubj0VnIFVG66frodrEfQIDb2GcuWMxHOkiiAmT1F6h4+OdpkzR5NXc/KIKvINrQzSiII88pREMIQTR1s5tcTOXX+KhCXZpiSyIcyIqIiwaJpHoy6yWbm92yMHTiI9ydb1bo/uos2L7ileCjS93Lf/gEhYJIfsWj9vWCcll9inPv6gqAKGAguSKsV0n4fsLh99NA27du3UemV07js5cJg2bapWZQ8Y0B/bt28rukwhCf8GBSA0OhExd0Jw/d8kqHsOHI0WKJD7MA6KEahZsyZqmpmBpoKSbUqWbKiUZOuSbFWy0z9Kl2xdNLq6deu2eC9bGxGdVAfZs8iuxUFzBPSWsKhJ3bp1A40U9u3T3gmaRFZ0gJ+b27tae+lZgp9IVisGbiMTNHAegoXHgnB4Xn84NDBRaOuT6lX0efr0afHVHPKww0E5AjQqpu0HZJtq2TL/62Bk67px8xbOn78AslnJB5r2ka3r0KG/xE9FtirZOsiuxUFzBPSasOhsp88//0x0IKEN0iKyWr16NSpUKF8s57pr3i1FK0meheg1ITqxgUPBCNC0j6ZpsrYp2RKSrYvykM1KUWjd2hnRj2NAn4pCYXUoKsNxihHQa8IilWnEsmLFctAU57fffgORjiaBVhxpZEXTgAULvtJEhF6XIXdf0pL63r37xFebyDM0h8IRoGkavbSuLJCtS942JZuXpolWTSzzrBbKptM1bYUoqA75/HyvGAG9JyxSm+wAP/ywXDx5dP78eSCDuaqBCM7Pzw/z5s1Dt25dMG/enFLnu4+IinwTkv9DOrSPRlfu7qNKXTtV7XN189G0T9rKoKgs/cjJrh4qyvPee1mbURWlUVybNq0LrENZOY7Pi4DerhLmVRPil4+M8N27dxVdtJPR/L33esLKyhqNGzfOc4wybQh98OC+uKxPvgxdXV2xadPGUvvA7NixQ4SLXnT+9dct4uqWvmytkO9HfbyXN7Qr0rGwPIpsV7JyCisvm5evlSNgMIQlNYGMyN9+u1Sc/ly4cAH+/mdEg6iUTp9mZjVEgzq5rH///ZHaMYTLVqBH15K9SlJJEARx1YsMyWTs5cAIlCYEDI6wJPBpCC/vpstQnUNKbdLkk+xVisKSJd9g+fLvtb4SqqgujmMEigsBg7BhFRcYhlaP/OhKVn/aMEo77zkwAqUJAYMdYZWmTtC0LeR7UD7QShSRlTZe6JaXzfeMQEkjwIRV0j2gYf1koyIPPVKoWdNMXBlkY7uECH+WRgSYsAy0V7dvz1oZJPW7dOmMSZM8SvXigoF2E6utZQSYsLQMaHGIk0ZXNKoiL8+8GlgcqHMd+oAAE5Y+9IIaOtC7lbRjf+TIERgxYjhvDlUDO85q+AgwYRlYH5Ld6uuvF7NR3cD6jdXVDgJMWNrBsdik8OkLxQY1V6SHCPA+LD3sFFaJEWAEFCPAhKUYF45lBBgBPUSACUsPO4VVYgQYAcUIMGEpxoVjGQFGQA8RYMLSw05hlRgBRkAxAkxYinHhWEaAEdBDBJiw9LBTWCVGgBFQjADvw1KMC8eWMQTomOm7dyNET8+xsbFi6+moaTqip0GD+uK9o6MDGjZsKMaRgxRDDnTQoyEGJixD7DXWWSsIJCQk4PLlyzh69HjOyRf0fmaLFi1E+XRMz5Mn/yExMQmJiYniuflSxf369RE9fBviMT70Lir5Orh69SpcXPK7LpPaqI+fRoKhUq0CNMviiaMKYCjxKHLHTiMQcnsl73i0xJUDRF+XR48eE53pkj50hljPnm5wcHAo8MQLeo+TXo0KDAyCr68v6Ax9Qzt/jMiKTqMdN24cDh48iE8+oZfnDYe0mLD04RtUynR4/fo17oSHi67dqWnkgJR8+umDI4abN29i+fIVItnQsTzDhw/T6L1MIq8zZ86IDlGIuGjENX78eL1+GV0iq9mzZ8HRsSXI9d33339vUKTFhFXKyELfmkNu4E+c9BXV6tq1Mxyyp1sloef+/QfEURXZpWbNmqkRUcnrTcQljdZILrmhK8hlmHz54rqXJyupXkMjLSYsqef4U6sIJCUl4dq16wgOCRFduLdo0Vx0P6bVStQQRgce7t69R2cjIWnkRiotW7ZMr0hLGVlJ8BkSaTFhSb3Gn1pB4MGDh6KN53FMjOgtuV3bNijMZ59WKi5AiERWdIbYmDGjC8hZtCRaaSRnthT0hbQKIyupxYZCWkxYUo/xp8YI6LPN6uzZs1ix4kfxwENdkpUEnkRaNWqYiW7WSnL7g6pkJeluCKTFG0el3uJPtREgovrn1Gls+mUzroeGwe3dHpj44XjRTqUPBnYiDyIrWskrDrIiAMl+NW/eXHE10dvbW21MtVWgQLJKjoDvH6cQkZyZp7o6dergiy++wKpVa8QtD3kS9eSGCUtPOsIQ1SBSsrezE6d+0Y9jcDcyUvTIrS9t2bBhA2hf1aefzi5WleiQRdrDdeTIMZDvyOIOBZIVKZMcjat/ByM6Of/mUX0nLSas4n6aSll9NKJ4t0d3TJs6CdWrV8fRY8dB+7BodZBGYCUV6EsbHBwiuj6rUaOGGmo8x/lveqPtNB88yjsAUUMG0LdvH5EsFfmOVEuQmpkLJSsV5OkzaTFhqdCBnKVwBMiw7tLaWZwSkhefsLAb4lTx/PmLoBXD4g5kaKdtBur7aayKeo6d0cnBHCZGmmtNtisPj4ni1JBWEIsjaIOsJD31lbTY6C71EH9qHYHnz58jOOQagoJC0NzeTrQlFcceJbJdTZ48BXPnfo7OnTtrvV2qCqQ9WlOmTEWHDu0xdepUVYtplK9gskrGrZ1fY8XJOKWyK/eci3Xudigvl0PfDPE8wpLrIL7VHgJpaa+RlpomCqxcpTIqV66kPeEFSLp48aKY2qZNmwJyKUgSkvDo8gF4TfHAqqBEBRnUi6JRlpubm2jLIvLSVSiYrKhWY9i5r8DWrVuz/n4Yh6ZogXE//JoT97MCsqKSRR5ppV7HLyM7Y7LPvzLNT8fT0MPw8ugMawtrtPXwxKHQOOS3qMkUyb5kwsqPif7GpD9BqM8PGN/NC0HpsmoKSI+9iF9m9EJTC0tYW7TF+ytOIya94EdASLqDY+vnYUSXgZi8YBm8ln+FyX3exYCZa3As/KVKD5CsFnRNdiuyX23e4i3as+q8UwefzPxItHPVrFlTPrtO7s+c8Re9Yau7pUB4dhcXDntj7dn6aGn9llZ0o/cpKdA7iLoIhZNV0WvVmLSEeAT9/C1+vPJKTokKqOXYE/1cGwOwh/t0Dwx0rA1VZuB8WoMclPp6K8Rfw4FDAYg4+SfOvfg/zJRVNDUMW+fvQvKIhdg1Og2Rfjvww/qZmPrWb/jjo1aoKps3+1qIv4AfR0/BllqfYt/R/8HeJHsyMPcFbm7+DMP6jEfQtg340vUdlR4k+Z3tnV07lcjOdhrJEDn07dtbQasLjjKq1QzO1qaAQ1NYmGrnt1xyy3b79h1I1wVroXpqcZCVpI1EWqq/e5iB+Ave2PHSGi6IkMTkfgpxuHnxNmDcD05q/Dhop1dy1eArHSFgZNYSQ8d9gJ6t68jVkInEwDN4/H9fYGY/Vzi3excj5i7C3G4VcWPXBdzNkMsu3j7HhTVLsPGGNaZ8MiyXrCjNqDrsx87AjCZh2Dp7I87EKxSQI5R2ttPxLN7btiM1LRXuo97H0KGDS4SsSKmYmBhRN1tb2xwdVb4QohFw7Cas3ZzQUJWfexUF0z6wyMhIFXOrlq04yUrSSCItVfZpCXGnsOqwFWZPaAOFY9XESFw9+wwV3dqhuRo/DkxYUm8Y7KeAzJpdMa5z3dyRkFFtNGlZFzCuBIVD6JehOP5HOGDaGm2ameZveSVLuLhZAnF/4+jVZ/nTs2No+vfvv9G4FxUlvi/YsEEDFNe0T5lSKSkpypIKj0+4h5AgM3SyN88yPqdH49yqTzH+w2HoZjMU356ORp6ZeOESxRympqbieVoqZi80W5HJqlY3zN/6GbrVkjexF1q1ajat9Cgc+ikQ7T7phYYVFckUkHwrAKeSTeDUvilqqfHjwISlCE+DiiuP6nYOsKgi0+vCS/wXlQirQW1hpeiZTE7Af8kAKryFqpVkyuW0uxwqVKKCKUh4pXwvFW0c7dSpAz7+aBro5Wb6Iq1dtwFXA4NKZCsDqf/o0SOxFeofrCcg+eZlnMh0gottBbx4kYL486dx320xtm7Zjf3r7bB7oQ9uFTzgzEFQ9sLKykrcEyYbp+l1kclK04plyhU80krBvd1bEdJ7PHqbV5YpJXuZigehV/Ef7NGjVb3cH1rZLEqumbCUAGPI0ULsFRwK7IbPRzaHwnW5arXRkAZW6a+Q8lqRYT4T6a/pm2mKd2qodhSwra0N3N0/wLChQ/DixQts+PkX8bUd2mJgGCEN0RG3kdTCClWDduPggzcw6zoao5tXz/5CVYDNqI6wVvQDUEgD33rLuJAcqif7+BxE27ZtxfOsVC+l/ZxEWoMGDcLq1WvEAxGzashAUuhOrI0bgE+7yoz45asXHiPY9yZQvwNaN1Ht+ZJEMGFJSJSWTyEGvquOo8nKT+BWW+GEEDB2QL8PnYDEQATcVrB8nxKBCyeiAIsBGOCi3sqe/M73ffsP5Ox8L06I1d9GYIQKlaqgfNhxHE/vjlGO1UR1haQonN/5P0ybH4ZW9nWgcIZTSMOePIkTd70Xkk2l5AULvkRaWir27durUn5dZQoNvSaeWLp8+XKZQwtTEP7PPhzyHIlWlrRabQnr9rNxCvE4NYu2MMzEwdh0CLHX4X81CcbdnWBdWdEIX7nWTFjKsTHAlBRE7d+OkF4LMbtdrQKG2tXQatI3WNTrKTYsXA+/mKy9UmKD06Ph9+N32JDQE4vWT0IbE80eEWnn+3s93UDvGdIhftfDwnSOqWRsl4zvqldYGZbuv+JO5CEs69ckh5iMTCzQ7r33MfMzG5ya7IWTcepbsciphXROvOr6KM5JWzUWLPhKnPqWFGkRWW3d6o0VK5bLnftlAufZR3H3flTu3yVP9IAZenidxd37qzGobjkk3gnGhYy66NHRFgosqIobnh2r2dNYoEhOLBkE0hBz+ld4J/fBtG71s43tyYiOipMzFGcg7tgOHE+xx9h1u7HrQ1P8M2ckZh2NAeJPY9Ggr/BPzTHYdWQlxtoLCFi7E9fVtNvQFgeyY4n2rKuBGDSwv2jnKo7TRqtUydrE8ezZcy11gxEq1LJFp1GT4OF8F3ceqb8BlBYmTE1NtKQPxBFNSZGWcrJStXkvcftyAJJhh7Z2b8v8qGYgKfwwfljkhZ3712HuhxsRlJj/wWPCUhVnvc5HZOWFT/+sjO72bxAeHISgoEBcObIJm4KS5F63EJCRdh1bVqyA15o/4P/wNczMTZFGNqu0F4irUhtmr+/Df9d6eC1fih92P8EbRWYuBXiQvYq2OJD9iuxYZM8iuxbZt4orSK/+PHz4ULtVpqfilXEXdLRVzx5FnnloX5j6iwAFq18SI60ik5UQh9B9G7F+dziAxwjxPY3rT2nEKiD90WEs+PwmOs6eAfehg9Cp3EEcCIzPB4ISI0e+fBxR0gikP0XE5TM4eu4xkHQN/v8EwLS1I2xqVUD85XWY7PGzuIIVcFxG0YrDseZCQ5lfMSktBcF7diNYuqUhe6esm4zAvVgfmJMAmOXZoiqTkHVJWxvu33+As+fOixEtWzrCza1HiTqcIOcSRQ9piNr5EfpuqojJk3rCslw6Gn4xUe0p8t27WfuvyOmDtoNEWt9++51o0xo2bLi2q8iRpzFZ1R2MTfcH58hxHDYP3sPm5dyLF8ITnNu0CQ+GeqKDWXkg8xUS4t7kzZN9xy8/K4SFI1VBgMhq7979oo2qfj1zDB8+tESJShWdizvPDz/8iLCwMGzbprvD/GiBgUiLnLzqgrQ0JitVwX7ph4XtN6DRPm9MsqsK4dEefDjyFsYd/QrdiMBkAo+wZMDgS/UQoH1YNOWjqSCdPbVq9To4OzuhlVPLEt9Aql5LdJObpoPkPZoO89NlKHykFYdzKxdj83Vlm2qNYNp3PjxH2MqZDwCdkxUBk/EGaW/eQR2zioDwHAG7jqL6vEVwlSMrysojLF0+SWVMtvz7hPrqSFWX3UKjHSIQCpLzi+3btxXooFVb+mh7pFUsZEWNF57iyqrF+F3oBNe3YvG4bj9MHNBU4XlkTFjaelpYTg4CNFXUV0eqOUrq4IJGVIsXL8GUKZNQtWpVzJw5q9icX0jN0RZpFRtZSYqr+MmEpSJQnE0zBPTJkapmLVC9lDSiohKWlhbiSunGjT/njLhUl1S0nEUlLX0lK0KFtzUU7dng0koQoOkhedShDaP1zM0xoH+/EvX6rERNrUXT6IoctUohKuq+eDyzND2U4ovjU7Jp0XuV6m4u1WeyIuyYsIrjCSpDddBxM/v3+4jHzVCzx48bIx4307hxo1KNwuHDf+Vr365df4D8IpZE0IS09J2sCEeeEpbE01TK6iSbVej1MFy7Fiq2jA7vs7BoXGa2OEhnyCvqVnIzVpJeoFWdHhoCWRG+vK1B0VPGcSohQERFG0bJyQTtw+rbp7fcu2UqiTH4TDt27FDYBtrAOmmSR7GsECpUALmv8RS0udRQyIrayFNCZT3N8YUiQPuwaM8V7b2iF5xpL5bhHCdTaPNUykCOUmmvlWygUdXy5d9jzpzPS5SsJJ0Kmh4aEllRe5iwpF7lT40QoBNGyZEqOZoghxPkSJUcUJSVsHfvvjxNpU2itDKo7fPb81SiwY0i0jI0sqJmsw1Lg87nIgUjMGHCRGzdurngTKUglUZXtNeKAp3bTmSl7ZectQ2TZNOqXLkKwsPDFRwRo+0atSuPbVjaxZOlASV2PHJxg09u6Gn65+4+SgMP08WtbVZ90khr8uSpBkdW1AImrJJ5brhWA0eAzlZv0KA+lixZrBd2KnXgJNIiZx3SUTzqlC3pvExYJd0DXL9BIlC/fn3RqG6Qyhuw0mx0N+DOY9VLDgFDHJ2UHFraq5kJS3tYsiRGgBHQMQJMWDoGmMUzAoyA9hBgwtIeliyJEWAEdIwAE5aOAWbxjAAjoD0EmLC0hyVLYgQYAR0jwISlY4BZPCPACGgPASYs7WHJkhgBRkDHCDBh6RhgFs8IMALaQ4AJS3tYsiRGgBHQMQJMWDoGmMUzAoyA9hBgwtIeliyJEWAEdIwAE5aOAWbxjAAjoD0EmLC0hyVLYgQYAR0jwISlY4BZPCPACGgPASYs7WHJkhgBRkDHCDBh6RhgFs8IMALaQ4AJS3tYsiRGgBHQMQJMWDoGmMUzAoyA9hBgwtIeliyJEWAEdIwAE5aOAWbxjAAjoD0EmLC0hyVLYgQYAR0jUOrcfI0Y8b6OIWPxqiDA/aAKSpxHXQRKlat6dRvP+RkBRsCwEOApoWH1F2vLCJRpBJiwynT3c+MZAcNCgAnLsPqLtWUEyjQCTFhluvu58YyAYSHAhGVY/cXaMgJlGgEmrDLd/dx4RsCwEGDCMqz+Ym0ZgTKNABNWme5+bjwjYFgIMGEZVn+xtoxAmUaACatMdz83nhEwLASYsAyrv1hbRqBMI8CEVaa7nxvPCBgWAkxYhtVfrC0jUKYRYMIq093PjWcEDAsBJizD6i/WlhEo0wgwYZXp7ufGMwKGhQATlmH1F2vLCJRpBJiwynT3c+MZAcNCgAnLsPqLtWUEyjQCRXBCkYnUhKdISBVQweRt1DIpgqgy3QXceEaAEVAVAaUskx7kifZDVyMhnyQz9PA6hE2Da+Dm1vEYuSo2+75Bvpx6HSHE49bxv3AqIBTXrl3BmRDAsXc39Og1FMP7OqJ2BSPl6gvxiPA/BT//SwgIuYIzga9g7dYX/Yd+gA/es4NZnrIC0uOC4bPVG9t2HcWtlw3QcdRojJ34Pt61NEUBtSivX2FKKiK8PdDn6/MKU6VI49Fbce7bbqgmRfAnI2BACCglrJw2VHTG0KmuqJczeayAOo2Mc5IN9sLoFcL3ecIzsC46trZBO9sQXDjyG4KP7MfR0LXY8lVX1FbKJi9xbctSLD9TAU1dndCldQT8fbfjJ99D8PtqO7ZNckCVbGCE+IvwHD8FG29URasRE/GRyT0c/u07TD0WhmV7v8dwy6pagrAKbMbvwN2xd7BtyFD85LBOjpgykXRnJ+bu1FJ1LIYRKAkEBCXhTeBKoXVjC8HKaaUQ+EZJJoOOThHiHv0nJL7JzGpF5ivh8aUNwjhrC8Gq8f8J3uEpBbTuuXDrXJDwMFECJlV4fGKJ0J3warFUOPcqW6aQKtz7faJg29hGcFt+UXgpRqcID3fPEJo1thLaLTkrvCygFo2SMm4L3gPtBYevTgsv8gmIE84cuKQgPl9GjmAE9BKBnHGT+mSZhCDPvrC2cMZkn39zi6fH4Mq2bzC2S3NYW3XD2CU7cCX2Lg56OMPaYiYOxqYDSEesz0xYW1jCxTMIFJMVFMVL9QzB+sAIXP51Lga0ss4pJzwNwf51i/HJ6L5wsbBE0y4j8fE3VGeaJFTJZxXUalAHESgJAgAAFAlJREFUJtL0zcgY5u36Y0hXMwCv8ColU0k5ijZDs06t0DDHblcZ5t37YyAVTXyCpy8zssoK/+LiwcvIQFuMHuIEU3HEVgUNadppnIGne/wQmiwUUI8WkzIj8NfheLgObsfTQS3CyqKKF4EiEJYCRYV4BK2dhTGLt+JCYnMMnTwALZIO4ePJP+Lk0zcKCqgT9QTB3t9hxrd7cCveBC0avI3yADIe+mH1qWRYuo3HQq+lmGoXj5NbFmLMJ38g4o0aZJD+EvdP/4kdp+NRvm1/dLNVb6omxETi2ksAtg6wrZ09006JReTNJMDYCo3fqZTbWBNzWNsYA4n38OC/17nxOrzKjL2N4ARZEs5EUoQPFvZpDmv7SfDyOQ//gFugJkghMzYAOxYMEn9YKM+aywE49c06+L1MRoT36Kx4i9HYFpEK4Cn8FnTNzrsYfi+luqiek/Dy6JAjx+ufCCSJlbxEhN8eeHkMwkK/x4gN+BmT7S1hbTEIX/s9RmZmLIK2L0A/C0tY20/Dtjsy2smmUXqfxTgYIZMuNSL7MzM2CH95L0C/QVsQdCe73RbN0W/BTgTF5vZBnjaL6T6ISMpuS1IE/PZ7YnKrxTh15zzWeHSAo8cO3EnKRIHl5HTJuSV5pBPpb2EJR481OFVAG3LKleULZeO+nCkhTXPy/PURPAMTBUFIFAJX9hGsGrcSJh14JIrJfHJE+EScUg0UVlx6JogzoMx44dq6/xNsRRkzBJ8Ymka9EWIOzBDltl4ZKEgTK8XxUj0WgpX1BGH9pX+FlMxMIf1Nuig/MzFBeCFN60iL1zcF75EtBavGg4V1114pa152fK4eWW1sLQxcsFe48fx1IeXkkjMfCyfm9hCsGrcUPth6U8gpHXNAmETtzjetfiT4TGwlWDWWsJSTV5Tb7Clh3j6jPrQXBm+9LWRIsinf0M8Fn+i0rJiMB8Lh3y7kTBczog8I0+wGCotPR2eVSQwTvCe2F6zsFgmnX5CUDOHF6UWCQ57pc4oQvvX/8uRJDNwkLFh1QYgRK84QEm9vFybZdREWnP4vuzzp1l6YtPKAEBhDusQLgSuHClZ2HoLnvjNCeGKGIGREC6cXDRSsBm4VwkU5WfU4TD0gRNO9pFtOutTI7E9ZTNymCqvPZLUpI8ZXWNzbXsiRI+brIkw78EDIECRdJdzihNNfdcn6Lth5CKuvRAsvAlcLfXuvFgJf3BS8ByorJ6eLdJvxQPCZ2keYtDVMoG+TkHhb8PlqoGBlN1Xwvp1/Mi8VK+ufhY+wyOg+YyY+/kT6G4LmZops9ZlIvHEZp2gg1XIIBrepmbUCZlQDDgMHoUORfxXK4x2PKRjXrj6qGBmhfIXyonwjk+qoVj4NL2KjcCsoCEHXn6Nio+oAHiDk3vNCajVC1UauWW2b9j46NkrBjZ2bsHFfCJ6qPDhLxaODK/HVn/dQ3nEi5gyzRcVCai2OZFoNDLofhbviXyRC/v4KLWlImh0yIy/C51YCoq6EIZYGEOUaof+YDtnTxafwX78ODyYtwOfd6kF8SEys0NHVSiqu4udzXN2/A7tWusO1CY0irODUayFOJT/EQd+bQLclCDm5GA6ohHdaucK5Lo1Cq8G6VQsYJ6fAzKEtbEzKAeVqor6lKRARhWhptEMavF0DlIzCdCvXFOMOnsGvoxsBxu3Q2zWrTeXqdsen84YDx/biZCSNEilUwts1jFEO5WBi0wadbCpnx9dCt2/3ZclAPTg0rYtqzjNw5NgMOItKKCuXXTzPRyZe+m/GwjNt4D7UDiaUZtIUg+YvwMeN/fHT9qA8I908Rcv4jSLmyQuJiSs++GQ2nPPlzBrU52bORHJCPJIponYNmMpQodFbNVCHvsWFzgoFpL/JHZ7nyqaramjetD7yrk+mIfbyHqxbsRq7AuPyZgcZlAoL5VHdeSRmOWflE6YPxo+Dx2Ljt8vQtO02THcUH6UChKQh5rQXpn+2F8/fHoBvfpwAZ1MZVjCugXdI4bQEvEzOBKplg5L5CglxZGOrCTPTfMAWUJ+mSVlfPpfw3PLlrHpgfNeN+GzWMGz5ayaWjO6Pnt1ssr48L8Pwz/7HqDS3mhzeueVVuhLlNMTCk39jnI20bpq3pDRxzBtb2F3WimgoXiM26Dj+ObMPi1edB1q6FVZQLr0cTOpbwgp+uBudBNgQsZ0EaLp5+E/4H/TC2mtpcBgiV0z+ViREdco9R5CvH5JtJqC+SHbZAk0s4dS6FpL3n0bQ3C7oJj0v8vWV4XsZWikqCuVgXMMs6wF/GIf4bLszSRUS4vBICVllvn6D3KwvcPfaLZUVEeL+wbLRC7Hrvgvm/3kGIXfv4e7969j9iZ3KMmQzGpmYw7IBMUwUQu7l34EmmxcgsvLEZI+NuAVnTFm/CKNs5QhOslUlR+a1VSXF4G5Ecn7bVt4KtHtXzgb9B9hkjZZIcrlGGLTuAHavWYhB0b9izvj30HGaDx5nApn/3UdYci20sHg7N7/G2gTD5/wDaEZMyivNjL2INR6DsejMC1Ts+iX2fN1JeWaVU15n2dFaL4T/m+ro8s1GLGwpjbAKEqJhOfkRY0FVcJqIgFYJy9SqBVrTACP8L/x19TnEWZWQgOvHjiIoD+DlYWbeQJx+vDzhj6vxxGYZSLpxGN5/PsyTs6CbjEd3cI6KWrvCrW0jccVPSAzDP3/dLaiYmCa8eIInqTJfIyERUce2Y9u5FwBs0Kbp29ky0pH09D/Exj7BCym/kIxHJ1dmkVW1jpiyeTVmt6uVfxNoOQt0eb8DyuMKdhwIQaIISCoe/b0fe5PLo9YHPdG6uH9Fk27ALyh7qlyuLpwHfIilx4Jxbs88tD/jiQ3+T1HOqgMGt0xEUHBUtnG8UDgVZ6jWAu8OrYXrX8/F4u0BWVNPMWcCrvmFaj7tybyD7VM+wilXT/w8+330dzbXkFgzkRQdhUjjbnjXuSYyI3Zi2ohz6LR7DWYN7Q3nuqqQFTQoVxPObt1gnByGkLv5FwqMh3aHc3E/F4p7UO9itUhYgFEDN8yY0RblEYqN7u9jypLlWDpzHDz+TkGLPHM5I1Ru3gUfWFQEItdjXI9BGDt6ALr124O677tlTUtUgKqCTRsMql0euOyFOXO/h9fKxZgyeDkiLJoUUlrA69ve6N28O0ZMnITJHh4Y27c7ek7fjFsZJrCb/gmGN5NWCWPxz/w+cG0/HltvihNeZFzfitGTNuFWRnnUbG6BCsG7sdbTE17i3xrslAgBlWHR50N4NK+MqPUz8eHc7+G5ZAbGzT+MN2/3x+djWsO0EE21mSyOSub8BVjXAF5exkH/p9niK6FO/bqogIawrm8ClLNEzwld8WjVt1jucyebtFKRGJ8io440nYrE5RtPkClOz07hwt1EIPk3eDiOxbYIY7gMHY6mCMWuhSOz7Vhky5qI09Uaab69QhyhpuF1/EvRBJEZex2Xqd6IKDy6cxH+9yR7lIy60mXEeRwPjBVHfJmxl7FtRwBc/zcRXaohi7yQgvhEKv8asSGBuPs6DZF3o3DH/yLuyfy+SeKAbNJTq1w5VHMZic/cHmPtV57Zq5u0sfc4dh5xxtLpHTXHJlexUnmlVcKCkRmcP/bC9iUT0cM2Hqd8LuBpwwnY/OscdJb/sTJpg+mbfsKUXvaoEf8Ez6p0xMzff8aCIfZQ2apj2gGzf1+DGQPNEbVnB3yCysP1f6uwcIBtIZ0l4E3VRujftyGSg07jlO8/uPyqCXqP+RzLfj+EXXM6wkzpLndASH+NV2INGXh+bifWrVqNtTl/W+H3MIvYKIuRWQfM3vwrvpnWHqm+m7Hutwg0GDUPa3Z9g2Fa2+VONdGrOaNh3aQ3ll5LRvKOCXDOXi6nJXP6s23vjl/ebpf9622C6i+u4mD2srrtxKvouONHjBFtTZVQb+A8eC91QNCs3nCibQ/7L+ERZLZm0KzSZiiWfe2Ec7O6wrbPd7hs6oKO1jXRdPRCeO0nWcYwcZ6Czfu/wyi77F8sYzd8vHkZPJyriPra9lyC63iIXeO7Yoh3CO54j4Xz+N+QjPNY2rMXFvrdgt+CXlmvHIlE2B0Lg2zx0Xp3YNVIUbfVN6qhh5sTjJNDcPpOTTg3UWwvE7vMpikaXF8CJ8KjxxZkjFqFFYMbiUb2al2mYPW4dKwd2gqOHhtx07Q93iWbUuBFhL9TDmeHdIXHjodAsh9+eH9K9naOciiwnHlzNFH0LTNpjnFev2HTe4+xsGdLWFs44P3t6XDfvQSD6uXFWdSb/4kIGNEyqa6xEGJ8MM11NnxNpmHnlTloW7kANtC1MixfQwSy31VcYYVfLy02QIMw7RMbBo/rE3DswHjYKCIRDZHhYsWHgJa7TUDq0yd4kS7DgenROPPrbzidUR61hnWEHZNV8fUu18QIlDIEVJ59qdbuDCSc+xZdV77AiH4tUatSGh6fO4D9tOXg7UHFbrNRTWfOxQgwAoaCgJanhJlIunUI67f44IzvOdyJz0D5Ru0xoF9/DBg5EF20epyKoUBcGvTMnk6R/UYMnbDw5K9K91bpXYtf+mFh+wnYJZkWjcca6LRW75AtdoW0TFjFrj9XyAgwAmUIAS3bsMoQctxURoARKHYEmLCKHXKukBFgBDRFgAlLU+S4HCPACBQ7AmWAsOg8Jn8c8JwElwV+mr8OUuxdwxUyAoyAPAIKCSszwhtD5HZJS7ulcz7tZQ9pkxerR/cv/bF80DjMWeULZedAqKdt9ouu4kFzzdFvgcwBbyoJyjphgAjUkQ5tYxJVCTXOxAgQAgoJq5zNeBy4fwvH6A14WgIOjcw+Vyn7fKWwv7Cwa56XA/UXzWrdsDTsOBa21Ia+mUgK+Ru+GIyfb0Yh/NKv6B27HMOW+as2csuMxdXVH+G90fvwoPEY7AuLRCh7sNHfZ4c10zsEFBJWoVqa2GHIKAfFbFdoYQPOkPkAQS9bwb1NXbHt5eq2w7jR7wF0flHOkcDK2peAoFUf4cPQ1thyah1mDe2SdTidsuwczwgwAvkQ0GCneyoiDp8F+vVFF83oLp8SBhNRzhJdushq+xr/3X+IhpOmw6XA40AykRS0HQt/aYSlvh/CRTxZU1YOXzMCjIAqCKhPOZlPcDNYOno4Ey/9Fou2mCzbFjkk+DfXGYFFVyz0k44w0YEzAvFkyC1Y2GcCtgWF4KDkMKHPAuwIyjpCRDkIpI8ftkllLDpgsufJXIcDygtmpYgOBL7HD1GjsfmTNgUfiZMZgX1LtgJDHZD550dZeNEJCDnOGAqrjNMZAUZARED5ofbZDgVE5xFyjijyHPafe1h/30W+QkxG9v3ARYJPuHSYfoagfWcEsvq5CZNWnclydCA5LLCbJeNgIb+vPtHJgpN04H+GkBh+QFhADgkmbhduk+MDpUFyvpCNSW/ZdioulBG+VRjceKCw4Lcr2c4YXgi3t04VHBoPFTwD4xUX4lhGgBHIhwDyxeREyHtAyU4gDyWL/sj2XiJlJkJaLfRtbC/0/WqZsPir3+W+9DIeR+QIUHL4mfWlJm8qcdlCJWKQdWoqr5OiPIIgvDgtLLCTvJ2Qgxd5wsrSR6o7q0KpDbI6SO1T9JkmxAT+LpKclSw55suarWOOt5nsDJInlzzkn68wRzACjIAMAupPCclDiUtNufFpuayD2rzdgR0+eOLimtegnOOM4Fbe1cb7UbpZJRPPUgci78YoPuJX1OcprKzNZaZy5WBi7QBnY/LoEqbCql8l1HV2x5LVc+CQHISr4fmPus0CiexckVnOOWRRK9cYHYe0yu8JRjYPXzMCjEAeBNQnLFSBzYCeCg5AS8bj4KdwHN0M5778HttlnV6KVerGGUGe1qh1k6yc0NSQk3X+eUEnRFbCOxZWMJZ3RCHVYWOZ13OKFM+fjAAjkA8BDQhLkiHrSOA1Yv224pDlbHz3zXdYPeIxls5aAz/Jo66unBFIqsh/imd+18IgtxaKz8YW9WmE5MDruCvr506U00h5Ofl66J7qetgCLrbVFKWKW92qOXfHIGPp7HMpWxKi7/4HhyEdYFWEXpCk8ScjUBYQ0OyrIm6A/A4HUA/V6LB+vx8wzbcVPqWzscvVQ7fFK7Cw0k7MXLAFV0XSqqkbZwQ5PRSJ88eCs7yykG7ev+NY19mY1qVWTo68FzXhMmYSejz4GQuXHcpeGXyJO/v/LLBc5mMfTLcfhIWSB5jMx/D76Vf894kH3s05h/s1HvvMhmOfNQiSyLBaR0z7X3uZkSftlt+LndcHYuHwbNdbmQ9xcFpX9PMMUDyNzdsAvmMEyiYCMvasnMssA7jcyqCcsVxyWZ6bVzJWyxvYJaO5jJGaZJErct9wIVGQXe2jOslYHizcJpfnOXWS7Ju5rsLFeIqT3J1/IHju2yBMsqPy5Pb8RJaLc2qRaICXaUuOkZtWBk8InuR+XZQ3UFiw9XRuuRw0ZC4kl+jZejlMXCn4BMbkun8Xs6YJ0QdmCQ7kwjzPauMLIdx3dbaOtDjxe7Zr9mz5ouvyLkLflVeyXJfLVMuXjAAjkIWAgR/gR/vAlsB1fCQ+M6QTMMvmbyO3mhEoMgKaTQmLXC0LYAQYAUZAfQSYsNTHjEswAoxACSFgwFNCeccIjTDKex+WdlNmaC8hhLlaRoAR0BoCBkxYWsOABTECjICBIMBTQgPpKFaTEWAElBzgx8AwAowAI6CPCPAISx97hXViBBgBhQgwYSmEhSMZAUZAHxFgwtLHXmGdGAFGQCECTFgKYeFIRoAR0EcEmLD0sVdYJ0aAEVCIABOWQlg4khFgBPQRASYsfewV1okRYAQUIsCEpRAWjmQEGAF9RIAJSx97hXViBBgBhQgwYSmEhSMZAUZAHxH4f6P/Fna/GCkhAAAAAElFTkSuQmCC" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exemplo 3.6**\n", + "\n", + "Use a análise de malhas para encontrar a corrente Io no circuito da Figura 3.20.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exemplo 3.6\n", + "Corrente i0: [[ 1.5]] A\n" + ] + } + ], + "source": [ + "print(\"Exemplo 3.6\")\n", + "V1 = 24\n", + "CCVS = 4#io\n", + "\n", + "#Malha 1:\n", + "#10(i1 - i2) + 12(i1 - i3) = V1\n", + " #22i1 - 10i2 - 12i3 = 24\n", + " #11i1 - 5i2 - 6i3 = 12\n", + "\n", + "#Malha 2:\n", + "#24i2 + 4(i2 - i3) + 10(i2 - i1) = 0\n", + " #-10i1 + 38i2 - 4i3 = 0\n", + " #-5i1 + 19i2 - 2i3 = 0\n", + "\n", + "#Malha 3:\n", + "#12(i3 - i1) + 4(i3 - i2) + 4i0 = 0\n", + " #i0 = i1 - i2\n", + " #-12i1 - 4i2 + 16i3 + 4(i1 - i2) = 0\n", + " #-8i1 - 8i2 + 16i3 = 0\n", + " #-i1 - i2 + 2i3 = 0\n", + "\n", + "coef = np.matrix(\"11 -5 -6;-5 19 -2;-1 -1 2\")\n", + "res = np.matrix(\"12;0;0\")\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente i0:\",I[0]-I[1],\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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BR+HnEYpa6NTEAazPFQiYWUageZLS9ul0bkTlynZo3ry5WWLBlS48AsWo0SUi+lIYMsu0QJuGlQpfA05psgiQBjd//tfiVJKOHTuIa5onTpyg9S4qJgsQV0xjBIqP6FJu4sLxOMCnCdzl584JLxB7YAO23KwKb6tIHLQYCP/xTWGrm80vNAaGIxY/Art27RYLQdOFaBCiUSMv8YDr4i8Zl6CkIVAsXVfhSRh2r/gJu+IzgX8v4+jhCDwRtytLw/193+Lz8KaYMmUI+vZvDcuV+xGSVNRNuEtas3B5SZuTX+WSkZGJ169f53RjGSFGQBsEikWjs6jqjf5fbET/LxSLKiScxS/fPkK/rc1hZwFkJSXisWIUE7tLxrVfPkbf830RvK4PauRTOyE5God/3YANv0fBrkMbeNgm4dqJc4h37YMJE4ehq1tFrafn5JNdsQeRPU7ZRUVdx9ix47Bw4UI9nykrICP+FH7+bhvu1nJBjbRYXIhvhI/nfoR29uqtyebWRsrtY8z3xUJ0qgHJQlL4CQTatcP2erTbRTriwi7gv/4D0Ni2WBRP1cXUmW8mkkI24suFJ5HZOf/jA4WEM/hhyFhsqPopdv/5f/CwkQ1RT3+Oa+s/Q/9uwxG6aQ2+alfdJMiOBiDUrW5p3boVypeX7Yais7ZQEvT6On6b8g3ujvoVC98iTFMQ9cso9PvOASeXdUc1FWYUc2sjJcSM/taIGERA5ut0vK5bDXalACEpFL9vscX0Ma1F7c7okdSygPRirNjyBD4t3ygg5TOcWTEfa6+6YOwn/XNJjlJZvAGPoZMwqd4VbJy6FsEJprEVyObNW/JgQufJLlr0HcaNGwc6JEev7mk0Tp/PgI21lezDYQW7alXxOvQ2Hqm0ophfG+kVfz0INyKiK4VKzfwwLiMYv+/4HevWhKLB9zPRu46ev956ALVAkUI8ji0NRsNPh8DbuoAmeBGBw7/HALZN0byBin16rZzQzNcJePwX/rz0tMCsjT0CaXPKO9KMGDFcJDndTFzWAIHKLmje+D9sWbYF5x+/AjLu4dShKLSf8DYaqJrvaWZtpAGCRhfFiLqugIVdK3wS0MroQNJtgWjAZT1OtRyK2XUscbAg4SmJ+Jd2JbKrgPJWKvpMsERpK3r7UpH4Mr0gaUYdTvPl5LU5WmM7fvx4PdvjVEBi5Y73v/sCIR/Ow9ABoejpUgpl3lmGFe+6qt5txYzaSAVaJcLLqIiuRCBWpEIKeH1rH/zD2uDLuXVRGg8KllaxGuqQIpfxEqnpAlBameyykJFOXVZbVK9UsrXf4OBgUZujScGDB79fjFNJSsHGYxDmzr6E4Cn7sO9ONTR1+xdJme6wyYM/ADNqo4IfWOOMUUC/yTgLXVJLJSSHYd2KBAz5rKNKg7bKell7ocdH3kBSCC5eT8obJTUWZ47cBhx7oVezynnDS4gPaXNbt25Dhw7tsWzZ0mIkOQIsA49P+WNCYGPsOnsQS0a64ObqyRi38hKSVJ3aaCZtVEIeJdXFFEzA9ezZW6A/bdy77w7UJrpO4r4OWSI0dXAUnFX+NRFG772vMp+spAhh05h2glv374Sgh2m5cV4/EIK+7iu4+UwQNl1NFLJyQ0rc1dWrVwX6MwqXdknwb9NRmBX0OLs4WQlC+KoPBLd644Sd916pLKKptVFxvB8qgdWRJ2t0qvlfL76lfabi0p3buJHz9w9+9LUDfP1x6k4ofu5TWynfTDw+tAWHUz0wdNUObPvIFsenDcSUP+OBhCDM8ZuJ45U/xLaDSzDUQ8DFlVsRWUIHXmmgwWCDDUoo57lNuI9rcdaoUlFmCrCoBK/efmideRcPHivbQc2njfLgVII82EZn1I0lIPNVJDYsvo/omtkvnZ29LZ6QTe7VczwuVw2u6XdwcttqnEx/gNMH6+DLcUZdoZJRuDc90anVE2w7ewPjfLxRDgJeP3uMeMcumJBn/zxuo5LQqEx0Rt9Kqbi8cwcu55TTDl3aZt9khuzCavlD0Owm58TiiyIgYOmMgf4/InHe1xg2rTla27/C7ejSGLNmkpr987iNioC2QZJaUBfYIDnpMZPC7DA8YMAg7Ny5XY+lYtGMQMlFwNTeD5PQ6HgL9ZL7QnHJGQFDIMCDEYZAmfNgBBiBYkWAia5Y4efMGQFGwBAIMNEZAmXOgxFgBIoVASa6YoWfM2cEGAFDIMBEZwCU09OVJ5kqZlpQeHJysmICFXcFyVCRhL1kCBSEXVHDKZuCZHBj6BcBJjr94ou7d+8hIvKK2lzoBaCzSvNzJ0+eQn5kV1Ae+ck29zDC9Y8//swXBgrPj6iiY2IQExOrVoYmeahNzAE6QYCJTicwqhcSEhKKc+fOq41w585dxD2MR3z8I5Vx6CW5ei0K5y9cVBlOngXloTYhB+B6dAxu3rqt9kPy7NkzMTy/j9WFC5dA++ipcwXloS4d++sOASY63WGZRxKR1MP4eFS2s1P7xf/n1GnUqmmvdutwekmc6zmBzktQpVVokkeegrFHDgL0ESL81X1ILoeFi/iHh0fkpJG/IG2a3LOEBLUfq4LykJfH1/pBgIlOP7iKUunlcXdvgGbNmqr84kta3Lvv9hO1NiItZUcvCZ2TUNPeHtRFUnYF5aEcn+9zEaDuJn2EevfuqfJDQh+W0NAwvP22r5hIVfeUtOkWLZqhVauWuBYVlStcdlVQHnkSsIdeEGCi0wus2cZn0sJatmgONzdXlV98OgCmceNGsLKygo+PN8LDIxVKI70k9vY10LSpD6iLJO/oRVTOg7pa7DRDgLqb9BGysbFR+SGh7mpDD3cxvH27trhy5aqCYEmbru/mhgb13URSVNa6lfMgUwU7wyNgEkvACgsbrefTl6tZqxY6duggviSUh/TFJ9IiRy8J2d58fbuI9028G2Prtu1o3rypSHzkKb0kdO3gUFeMR1qgJINeRNL06EUl18TbG9TV+l+XzuI95TF16mdITEwU7/lfLgJ0wE5jb2/xI0S+9CE5dvxveHl65kSi7mr3bl3Fe0dHBxw5egz0IalcOXuDU0mbpg8V/REpUps0a+ojpqG2oi4tfejIeXo2BJkqpHvyo4/ZzJmzxHD+pz8EzJro9Lmonx7ysmWtclqOvvhrfvpF1PCImEh7Iy2OXhBy9PIQadEXn14E5ZeE4pD2R1qgvX32yyf/ImaHe4l5kPZBcimP995/L4f4xIwM9M/YF4XTR+Dp01ztV/qQkM2NrqVuqvRRITzlPySSNj182Ic5iNIZF38eOpxDdNRW9IGTHLUrEZ30saI86F6fz6GUt7a/+lQCtC2LLuJz11UXKKqQQS+I9OWnYCI3IjYaXCB3OSwMpMXJO/riS6N3ZO+Rf0koXiMvzxxbnvKLSOGUh6RV0IuoKg/5/Mz5mrCSyE3CgWxtZHMjR91U+mDIu8aNvXJseWQvldemKZ5EitQ2ksZObSbvpI8V+anKQz4uX+sOASY63WFZoCQPd3dxqgm9CGQElydCSkxffOrqUDgZwUkLlHekVUi2PHUvCWkVpOmRZkgvonIe8vL4WhEBsrXRKDlpXPRL3VV5R+RImBLJkb2UurvKTrLlKWvsUjzpY0Wao6o8pHj8q1sEmOh0i2e+0kQtz84O+/b/IRrBVUUmLY5sQURo9GIpO9ICSVNT95JIWgXlQRoiO80RoA8JjZJv+W2b2E2le2VH5Hb48FHRW1kjJE8iR2obddq09LHasXO32jyU8+T7oiPARFd0DLWSQKN85cuXUzBIywsgLS41NQ2k/alyki2P7EWqXkRKQ1oFHRkob/RWJYv98iIgmROom6rKEbkRttTNVeWoTaht8tOmC8pDlVz2KxoCZj0YUTToCpeavvgdO7ZXm5i0uK5d38qx96iKSFpFlSrqjzakPF6lv1KVlP0KQIA+JJ07d1SpTUtJ6UOi3K2VwuiXSPLp01ryXgrXlAe1sSqNXSEi3+gMASY6nUGpmSD64stPYVCVqqBwVV0meTma5CEfn68VEZCmhyj65t4VpCkTgRVEYgW1cW5ufKULBLjrqgsUWQYjwAgYNQJMdEbdPFw4RoAR0AUCTHS6QJFlMAKMgFEjwERn1M3DhWMEGAFdIMBEpwsUWQYjwAgYNQJMdEbdPFw4RoAR0AUCTHS6QJFlMAKMgFEjwERn1M3DhWMEGAFdIMBEpwsUWQYjYGIICIKgdmv4klhVJrqS2GoloMz1G7iLu7Ao77hbAopu9kWk3VtKlSqF6dO/MBmyY6Iz+8daPwAM/fADcb+1n39Zj9Onz6o9ZUs/ubPUwiJAJEcEN3bsGIwYMdxkyM5CIB3VDJ2x74BrKk1CW4/T9u60vx5tCtqqVQveI89IG1ciOSK4Ro2yN4WNiAjHxo0BWLx4Ub4bTRhplXKKZXYaXVpaGm7fvo2srCzxl89TyHkW9HLx5MlT/PvoX3Frqjerv6l2aym9ZM5CNUZAFclRYiI8U9DszEKju3btGi5epEOGL4k773p6eoIUWVtbW1y/fl08PKZr13fQsmULUFi5cuU0fkA4Yl4EaBtx2jKejmqknZRpD76CdvzIK4V9DIWAOpKTz7+ka3YmTXREcGvWrBW1t+7du8PJyQlvvvmmfPuJ18+fP8fdu3dw5swZREfH4IMP3kfXrtkH0OSJzB5qEaAXhs66oG4q7ZBMm4dKOx6rTcQBxYqAJiQnFbAkk51JEh11T9ev34hz585ixIgROfYGqcHy+7137x7+/PMgUlNTMXHiRH5R8wML2efX0vkUdKhPalqaeFIZ7ZJc0H5sBYjlYAMgoA3JScUpqWRncjY6IrlvvvkWr169wsKFi7QiOWrMunXrYty48WjSxMdkRpykh1Rfv48fPxEP9bGrVAkVbW2Z5PQFtA7lFobkKPuSarMzKY1OIrk6deqgf/931T8WKbE4tv8+HHp3gqu1eq4vqV8v9RXXXwjNlyPNjs4pJUfH+tGJV+rOtdBfSVhyQQgUluTk5Za0d8OkiG7Rou9RpkwZDB06VL5N8l4/OYGF00LQ6vsp6FS1VN5wOR+pQX/5ZS0PUsjhkt8lvUh0ePPVa1GirY4Og+FjF/NDzHBhuiA5qbTSu1ESpp6oV2ek2pSQXxpRJfvaoEGDdFpiUtWbNGki2vx0KtiEhdEARPfuXTF+3Gi88cYb2LptO7Zu/V1cKWHC1Tb6qumS5KiyJakbqxuiy/gPEYHfY3inpQjNUNPeQhLuBG/CgrEf4ZOFG3Eg4jFyZypn4EnEASwd1R4ujk5w6TQNvxyKwBMpgvAYkftX4pMODdFi2CLsVkibnd+mTb9i5MiRKFu2rJoCFN6byPPcuXPivLvCSzG/lDQgQd1XOqs27mG82K2lg5vZGR4BXZOcVIOSQnZF7roKCeHYu/8iYo/+hF+ufoAdF6fCR+FsMQEZjy8hYNYMbC07FD/Mfg8+1VSTkRAfiAkdpuKo+0wc2D0S7mUsJDyBrGhs6jsPLxf8ggmNFA92Jm1u1649+Pzzz3PjK1ylIGrrPCw++ljBV/6m7FvTsWqwO9R1ZE+cOIGXL5MxbFgB3WJ5oWZ8rbwiokkTb81GsDPicX7jIny5cB/uZZZCpRbj8cOyiehkr/qZIYiF5Ggc/nUDNvweBbsObeBhm4RrJ84h3rUPJkwchq5uFSH3JJldq2hEcgmnsOSz9YiUlAtllCy8MfLHiWhnp/oN0a4bS5wQgYMbl2JZmUk4MtUHuZSRieSoQCxeeBRCY2fgWgwsuk3F9H4esMlpxGc4/fVgTI0fh92r+qCOJuoaLQEruksSQpZ0E5y9lwghrxWlZSWFCqsHNBYaDP1ViE7NUgzMc/dUODX/bcHZoY/gH/JcITTz1m/C4Pd/E25lKniLNytWrBSOH/9bePz4qWZ/UbuFz3p+JeyM+k+z+I+fCjdu3BJ69uwtpKam5i0A++QgEB0dI/z22zZhxcrVwqlTZ4SkpKScsIIvkoSrP08SxvrvE05dOicEbV8oDABVkQ8AACAASURBVPNxFtx6rRbCU1Q/O1nPTguLu3sKDYZuEK4mZeRmkZUoXP1lpNCgXl/hm38eCapT50Y31auHD+OFIUOGavd+aPoeKcWjd5DyojzVuwzhWfh+YdPGb4QPXRyFpktCBHnKyPrvL+GLZn2Exeeeim2W9eKssLjL28IXRx7KtWGKcGvvN8KUVeeEZxo2rCZcqMztWty/QOSmxVh6wQOfzugPt3I5lKxGhh1aDBiAhgjD2oBTeJzzdUnG1T+PoOLAdnBUUeK//jqC+vUbqJGpG2+yNTVs2BC3bt3SjUATkkIrIS6FhGLlqjXifDpaCTHx4/Fo27a1dlNNksJxMK4XFnzSG22btkSngVOxYMZbQMQRnIpNVYHYM5xZMR9rr7pg7Cf94WEjp21YvAGPoZMwqd4VbJy6FsEJmSrSm7aXRpqcDiHQrBtbCnaNemHokG7wUeyYAUjGlR1rsavSW+jaxE7Uwi1sPdG1nw12Ld6LK+kSIZSHU5+Z8J/QEnYFUYqsfipoQ4c1fxGKnavOIbNMIi78MgPjhnRHM8cWGLTgAGKTVT14FijT4G181LUaXh/cg6N3ZKfNp1zFoW1vonfbmnm6ILRu1dOzoV5sc8pINGzoIQ54KPvr615al/vXX39B+e+ff/4RbYYUpzgdTSvZvmMXgoKCUc/JCe++26/Qy72EzDfhO6wNquU8vFawd3aDLaxQRt6MIVX4RQQO/x4D2DZF8wa2km/ur5UTmvk6AY//wp+Xnub6m8GVoUlOglQzspNiK/1mxSH0yHWU8XZFbSvpISiP2m5uKBN7BqF3X5GdAvfP78XSsaOwLDRJSYD629yusfo4hQ7JjIvFxZQycJowB0umtYKtRSaSI9ZhZN+vML2GE7aP9oSVsnSLWujwXk9UPbwFGwOvoO9Ub6SePoCDb/fG+Gqqi2ttXUFZil7uy5e3RlLSS73IloTSJgORkZE4evSYOEVD8s/vl+xfb73lCy8vL1SqVCm/qDoPo3lyIz8aDhpkCAkJBW3L5O7eAC1bNNdOmwNgUckVTRSKn4GERw/x0rUjWjmrWH+ckoh/UwDYVUD5nBdDvoqWKG1FWl4qEl+myweY9HVxkZwEqjzZaTX1JDkeN2JTUKFTFeR+tkrBtsqbqIAzuBGXDMHuAc4cCMDKf7yx7nvN33vVzCGVuIi/QmoynsAGPm61YSsSdCnYeHXHYN9f8Nkfl3B3pCdc8+iUpWDXxg9DXbdgyS97cGpoZaTsvoO+YxrJVb6IBavaCTM2dtJaSL169XD06FGt02mSgAjuwIE/sGPHTjE6kRftGkG/dnZ2eQiM4j98+BDXr0cjOPgkFi/+QUw3cOAA9OrVM098TcpQlDgODnVBf9SNDQ+PRMCmzahpby9q24Ve0C88xJn9N+A3/VN4qiKyitVQh96IjJdIpW5NaUkLkGqShYx06jnYonolFUQpRTOh3+ImOQnKQpGd9OGShCj8JuHfxDRYVG0AHxdbwKs+HG3zkIdCCvkbvRJdKbvqcEUW0l9nilNJxMfQwg51GrwJXEhAUhYAVWW18kDfj7tjxZSDWLfkNcrcaoMvPHM5Xr4ChrxOTEzQWkvRpHzULV25crUYlYjK19e3wBFK0tzoz8PDA/369RV3gj127JhIlESWEydOwDvvvKNJ9jqNQ1NKyDbXvHnTnJUStFpC+5USGXh8LADb603DKl/7PCYLsdDWXujxkTc2LQvBxetJaOtTUbEuqbE4c+Q24DgGvZpVVgzjO+NDoGwFVCqjrliyj5UQh4uHrsHF9yvUUf6uqUsKyI3q5hOpsEEWdb3RxS0Fq6IeIBUOsBYFZX9ly/h6wkktzZZBjY5+GFDtD2z97Qha/N8uNFT1RZcVzEKLChe2LpTu2bMEODk5FkWEQlrSypYs8Re7qB06tMfo0aMKrYnRJN0PPxwikuSWLVtE4jx9+gy++urLYlnRQV1a0uToLyYmFvv2/yHa8fx699TAhifg9e0DWBXWDj9+2jofg3NFNBn9NeZcn4BvZ6+G97qpudNQMuJw4odvsSbxLczZPBrNbVR9URWaQyc3ZDONj4/HgwcPkJJC/epcR0sT7ewqF/gRy02h/RU9B9RdpF2C5TfQ1F5S0VJoN91EltcbddHQwxoHHj4FWd/sRO9MJD39Dy9RBy61bIDEywgLtUPbyfZqp4KpKrlaqlEVWWu/Um7oM20Q1s8IxNERTeFXpxzw+j7CT1vjgy+8oWCOURJuYdccA4Y3xtaldTCos4NKxY+SULeOtlYyhKOVF6Sp6MJRF2PGjBkieU6f/jnat2+vC7HiSzRt2ufiJF3qzo4dOw4LFy7U68ulruBEcFeuXMXD+HhxKZhmdjsBGfFBWLoxDQOn94a92B0VkBZ3H8+r10H1nO5pJh4f2oZLzd7H0FU74LlvD/ZOG4jAwT9haevrmDNkE4TuH2Lbwe7wqZGKCyu3ovz4wfCSG5hVV25t/aktz549K5oQNBmVr1zZTvwgNW3qI2rk2uZXUPziJrtCkRxVyrIWfN5ugNf77uBRJpA9ZS8dj+7cwmvXjvBxsELKxfM4kuWN79xK4/nzdLzxRh4rv0p4ik50GU8Qez4Yf556CCSH4+Txi7Bt2giuVWmCZ2lU8/0cG7/yx7xxnyD8f67A7fsoNWohprSppro7klNMG3j2fg+dYiqgTQ21+qyoAVWq9Ab+++8/lXvN5YjTwcXly5fx/vvvFVmSRHIkaPnypeI+eUUWqiSAiLN27dqYN2++SKiGIjsahY2IvILw8AixRO3btUXPnt01XNxPJPc3Fk45gOrjPkBaTDhCScrrBzh+MAvvza8rV0sBma8isWHxfUTXzLa/2dnb4gnZ5F49x+Ny1eCafgcnt63GyfQHOH2wDr4cJ5dcB5c04r9r126cPPmPKI3sqWQycHNzU2lXpfik6V29ehWSmYHsvrRcTtdmhiKR3YswbN34BO0m+aKulopwoUlORNAGnv0+Qq8N6/FX+CC4kyki9Rr++v0Jen3WG55W6bgRex3Jnm1QPnQH9tkPwFCvNMQe2IAtN6vC2yoSBy0Gwn98U9mYQG4jF3llRK6o4rui5V+Wlpbo1q273goRExODbdu2YcWKZUXKg7o2X3zxJcjeZwjykUjVwcFBr93YQq+EkENTSDiDH4aMxdqryXK+dFkDPVfvhn93+elFGXgU+CnaTTkgF9cOXZbux8+tLmFMq6n4Wy4EdpNVrNqRj6D5NbVhQEAADh48BNLO/Pz80KVLZ63NDrSH3+bNW8S5mUR4U6ZM1vlHj9pf624sbXox6yH8Vg2GuxYasGYkJyDjSSwunNoJ/8/W4UrrT7B0cg809XFBVVFbz29lxCvc3voxus7+D32XL8WCHjXxKHAuJkb2RMCs9rD7NxBjulzG4HNz0amiIkObBNFJjUnEoXqt62OcWjIX6yNVTTqlB9wCtt1nwH+Am9p+/5o1a8Rua1F3Hv7++x9EDWDRou/00m1R9brSCzV//tfo0aMbxo3TrVpDo6xHjhzDzVu3xcNvOnRop5cBG1X1Kg4/6cNB9loaOBow4N0i20CpfVasWCGaMciuRoNLunTS+6Gxza4QRKcZyemyVoCQEIS5bwfAeetaDHMth6zYAPT3u41PVBBd0buuui17oaSRmk5nPfz993E1Wl01tPt0NdoVSjrEScKk0U2b9lkhJWQnoweaujnUvaHRUkM5WqlADzmd5tShQwed5k2jrJ06dcAbld5AVNR1sUo0sZqmmpiakz4YpMXp0uRA7bN27U+ilkht9PLlS3FgSVf4Fakbq0EhioPkgCwkhZ9AoF07bK9Hpot0xIVdwH/9B6CximknJqHRUVvQCOakSZ9g6tSp4i7BGrSPRlFop+L/+7//w6BBA0Ejo4V11N2hgYFKleywbJm/FmKykHT6O7w1+Sm+DPwOfnXUL27PT6jUZaY42uWfn1TFMLLPRcfE4MKFS2IA2eccHR00tM8pyjK2O4nkyA736adTte6malof6srS9CDSFmkUXZdOvWZX+B5P8ZAcoZKJhKOz0GZ7SwSt64PqSefww5C9cFs5P3vQUwm4UvPmzZun5Fcib+nkrrp162Dp0mXw8fFBhQqaz5pWV2EiueXLl8PbuzH8/Hqri6aRP43KHTv2NyZPnoSaNWtqlEaKZJlJk4PLweftZqhVXtH2IMUp6Ld06dKoVq0aAgMDRWO5tmUoSD6F0+nu1d98Ez5NvGFToYI44noi+CRev84QbVkldbdhIojPP58mTt6m6Tr6PA+D5htmZmaKZEe/dK8rZ2trg9atW4PMJzVr2qN69Roy0RVQt3UP9OnTJ/uvXSVcP/kmRq6djVF9yc8P3RpWyTPzofhIjoptiXKVbZB56CCupCfiyrFbcJw8Eb3qVVA5yGkyGp30MOzevUd8mb/88qsijcJKJFemTGnMmjWzyHaYTz6ZKhZRX9qUVP+Cfg1dDl0MUhRUJ32GS5o45bFs2VK9aXLKdZA0O33YctVrdrJSaGCjK16SU0ar4PvCqQcFyy22GP3798Po0aPx3Xff4fz584UqB82Xo+4q2Zl0QXL0YNH8Klrwrp3LRPL9Cwj0n4D+S0Mg2+JAOxFKsakMVBYqkyGc8gHWpFWUJLdz5y5xkGDevLkGIznChwY5aCR20aLFILLVpZNsdmQPJMLS1pU0kqP6mRzRUaXIlvb11/Nw+PAh/PTTGtBAgiaO5uLt3r0L/v7+ok1uwoTxRdbkKF/qtpKjRfdaOeEZbp8+gF+WXYWHtwMKZ51TzFEqQ2EecEVJ6u9oJPb06bPitk00YVjatqlZUx+9dvvUl6hwITTvTbKX0ZnAmjnaFLIrWowPxH1a4lhIR6YYmm5Co7tEtrp2hSW7kkhyhJ1JjLqqegjowVyxYjlo9+FNmzaLh1g3auSF2rXrwN7ePicJfS1v3ryBq1evIS4uTrRH0Fw5Xe4CcvPmTdG+o7VMi2po2NQZVoiDu4Nu1vpSGUhTiIiI1PkkVdIS5Q/FGfz+oBJ9KA5NBqYRVtKuNHflUbNRe7Stai+3I67mqeVj0jNMgxJEtvrYqEEiuzzz7GjTi5/kS5J9XVJJjkpvcja6vM2T7UMvYXh4OG7evIWkpBfiDPVatWqLE40bN/YSR2r1NeWjVy+/Qo6ivcKdrePhG9AaBw6N1mrypjocyJ/sPzQzf9OmgPyiaRRmqscc0ij+hx8OE6fl6Hpem0bAyiIZohz0buQhO6VClmSSo6qYrEan1E7iWk/6gkluwIBBWLlyhXSrt1/JvvLmm9UKkcdzxF6Ohk27kXAQZ6hnIvn2KexevxGhzb7Bsj61CyEToLJQl0hXjg6wTk1NFbdlogOsS+roqjwef/8dJN7SigeNHW0KeeEodm84CIux/vjEp+haOGngNKWFtuLSF+Gq1exkFS/pJEfVMEkbncYPpgEi0k4W5GjnCq1dSizOHX6Njs0cICQmIeP1UzyytIP1/ZtQt8ZDkzyqVKkqRtPFgASRGm3LRFun007PNN9M3FI9RFylqklxjDJOWFiY1uYG4ekN2aaQtdDYpejTmyRgaFNVfQ8gSWSnPEBhCiRHODLRSU+Tnn/Lly+vdQ5ZcbEITXKFZ/nL2LDvFl6XeRMuDpVhVaZozValSvbebGlpRaHLvNWhLZkGD34P/fv1RcDGTXkjlBAf0sLJ1ujt7a1ViQu7KWRBmUgDSDduxBYUtUjhymRnKiRHoBTtjSkSrJy4QARKW6F8qQgEHgZ6DW4E7alSdQ5Pnz5THaAjX3ph/v3XMNNXdFRkBTGSFt6gQX0F/wJvcjaF9NZqU8iC5FL3lQZF7ty5W1DUIodLZLd27c/ikkGttkIvcu76E8BEpz9sRcm0Xx45Tae4yBfH0mkwtt6MxMFFveCo6nAY+chaXD99+kSMrfmUCS2Em0BU6UNAm2Rq5RJvZW8K6SHbFFJ4jNB1U9DF2Qkuzu9gytYrSJYOstJKMMS13I8eGebjQWRHqzJMheQIaiY6LR84baNLU0pevlTcbVZbObqMb0xl0WW9dCVL+hDQC6+5E5ByLXtTyGbippBpSDqzG4cdPseRm9dxdn0nXJ29FPulk+00F1wsMS0sLIpls1Z9VZaJTl/IysmlUTOaS2csjgztRdmgwFjqYVzleIU4cVNI5+xNIe+m4FVVX4zxrY3SKItq7d5Bj4pJeJlWhFnExlXhElUaJjoDNBcZtaVdaIuUnZCMB6EXERGXhPjoMEQ+SBYPHdJGpmRod3Z21iYZxy0QAQuUtiqHUlcO43BGZ7zfqDKq1ndBVdl5JkL8TUTU745OLuZxGlmBcBk4gtnMozMwrgrZ0VwsreZjKaSWu7GwQW2fvph9qPAbM9KSLHJaG9rlimHql9bW2cc40WRdyfRQcJ3LwmnwOkQPVhFTeIaLe2Lg+/UncNWhrVVFTuylBgHW6NQAo0tvelk0f2F0mXNeWUFBQeISMH2tAsmbY8nzobM2yCUk6GJS9SvEH96K863G4n23wm9o8OBBHErahgjG1PJMdMbUGnouCy1Spy40HcbCTj0CRRkpV5T6CvEntiKwfF+Mb1kVFsITXNh/Ho+1HHklcwNNGOZRckV0tbljotMGrRIYlw7HllZASIvUO3bsWAJrYrgik/ZNGx/Qh6HwLgOPTy3DmJFf48fh7dDA0QkuTr2wtXSdHLudprIlcwOdLsaucAiwja5wuJWIVPSirly5WpxsSrtfSOdV0BZA7PJHYMaML2Bnl9/Jw/mnF4/6bDcdB25OLyhigeFRUVFiG7JGVyBUaiOwRqcWmpIfQBocOVrAT1tVOTk56nxrppKPkuoa0Bw6Y/ggULeVtmny9fVVXVD21QgBJjqNYCp5kSR7nHzJb9++Iy66l/fja+NGIDg4WCxgu3ZtjbugRl46Jjojb6DCFk/S5pTT0/mu165dU/bmeyNBgDQ42i+Qfml6y9at28TJ3dxtLVoDsY2uaPgZZWpV2pxUUDrflQzt7IwTAdLgqKsaGxubs2/gu+/2N87ClqBSMdGVoMbStKhLly7PE5WWoY0fP96k1i/mqWQJ9yAtjjQ4crRNFLlBgwbxtBIRiaL9Y6IrGn5Gl5o2vqQ5V5Kj7X1GjRqJ9u0Lf/i2JIt/9YsAaXPKOz8fOfIX/ve/LvyBKiL0bKMrIoDGlpzsO5Lr0aObeBYpk5yEiPH+ymtz8qVMSEjEjBkzRHudvD9fa4cAa3Ta4WXUsSVtjmxwY8eOBi/zMurmUiicdH6sgicgzp8jjdxYlhAql6+k3DPRlZSWKqCcpBGsWLFCPLWqe/duRjEHrIAic7AMARpdpQEIZUca+fDhw7ktlYEpxD0TXSFAM8Yk1MWh0+R5GoIxtk7+ZTpw4A+FCKSR0+HV3JYKsBTphomuSPAZT2LtdsM1nnKbe0mUtTma/sMaue6fCiY63WPKEhkBjRH4/fffxbg8/UdjyAoVkYmuULBxIkag6AjQxO6zZ89h+vTPefpP0eHMVwITXb7wcCAjoD8E6LSxZcuW8oiq/iDOkcxElwMFXzAChkWgWbOmhs3QjHPjCcNm3PhcdUbAXBBgojOXluZ6MgJmjAATnRk3PledETAXBJjozKWluZ6MgBkjwERnxo3PVWcEzAUBJjpzaWmuJyNgxggw0Zlx43PVGQFzQcCs59ENGDDIXNq5WOrJ+BYL7JypCgQsBEHQ8txwFVLYixFgBBgBI0aAu65G3DhcNEaAEdANAkx0usGRpTACjIARI8BEZ8SNw0VjBBgB3SDARKcbHFkKI8AIGDECTHRG3DhcNEaAEdANAkx0usGRpTACjIARI8BEZ8SNw0VjBBgB3SDARKcbHFkKI8AIGDECTHRG3DhcNEaAEdANAkx0usGRpTACjIARI8BEZ8SNw0VjBBgB3SDARKcbHFkKI8AIGDECTHRG3DhcNEaAEdANAkx0usGRpTACjIARI8BEZ8SNw0VjBBgB3SDARKcbHFkKI8AIGDECTHRG3DhcNEaAEdANAkx0usGRpTACjIARI2CAMyOykJb4BIlpAkrbVEFVGwNkacSAc9EYAUbA8AgUkXWSEeo/EAOXRakoeS/8eG4J/Gqk4drG4Ri47BG6LN2Pn/vUVhHXeL2ExGs4HHgcl65GIOL8GUSgId7q2BlvD+iP7o3eRL4ACgmIPfk3Tpw8h4thFxAc8hIuvt3Rs997eO9td9iVtlCqeBbS7gdj7axZWBGcqie80hAbMArd5p1Wylvx1nrIRpz6phMqKnrzHSNQIhHI9z3VpkZlmr6L0e1qIrcvXAt1yim/yNpINI64Fmkx2DtvGULdW8LHzRsuIedxePNFHN56FJGb1uCrdtWhvpYvEL5hARYFl0b9dt7o0DQWJ49txo/H9uPEzM3YNNoL5aRqCkm4fWw95s9YiVNPMwHYSSE6/i0H1+FbcGNoNDb17YcfvVYpEVoWkqO3YvpWHWfL4hiBYkRAZ0RXod37mDzVR4WGYwOfqX/ixtRirGVRsq7UHnPOhaFGDRuxbkJaHC5smI3hi4Ow8ftDGNhmOFxz2V0xJ4uK8ByzEUGrvFBH7LK/QvzRRfhg9EaELN+HkA880daaaDIFsdum4/2vDiPJsTO6NriCw6czFGUZ7M4SNvW74r0mNw2WI2fECOgbAXWvqA7zpe5td7g4+mBM4INcuRnxuLDpawzt0BAuzp0wdP4WXHh0A/tG+cDFcTL2PaIXPQOPAifDxdEJzfxDkfvqq/KX8umL1SGxOL9uOno1cZGly8CTiECsnj0ZQ7s1g4tjQ3Tq/zEWbDqPRxkFnPZYrgpqy0iOCm9RrhZa9uuN9nTz9CXS8k1uhwZtm8hIjhKUhX3nnuhNylrSf3jygjQ3cuXh1Lk3evh9iV9//x4fNasq8y+Gn6xY/HEgAe36tORuazHAz1nqBwEDEJ2KggsJCF05BR/O3YgzSQ3Rb0wveCbvx8QxP+Dok9cqEmjj9R8uB3yLSd/sRFSCDTxrV0EppOHe8W0ISnPE/z6ahR++HYEGT09g09yxmLrlOjTPUUBG8i2c+HU7gvEGmg7rANdS2pQNEOJvIvwFADcvuFWTFGoLlLbvhvnLxqBljbLaCdRx7KxH13E5MUtOahaSYwMxu1tDuHiMxtLA0zh5MQpUhWyXjkehW7PDHZ3QaNRPuBD6Jxb4n8QLkD1wiPihcnEcgk2xaQCe4MSsjtl+HnNx4oWUF+VzFEtHtZaFjcbS47FIFjN5gdgTO7F0lB9mn3iIRxd/whgPJ7g4+mHeiYfIynqE0M2z0MPRCS4e47EpOrd0kA+j8G5zsS9WLlyqhuw361Eo/giYhR5+GxAaLau3Y0P0mLUVoY/Sc2JnPbqILbP8ZHWj8EDEJsvqkhyLE3v8MabJXPwdfRorRrVGo1FbEJ2chXzT5UhXuiB5VCYqv4jxCvydTx2UUvMtIUAHWBfeJQkhS7oJzg6Oef+8lwghr0myFKeJMHrvfTGrrP8OCp+4UJrewuJzT4Us8s1KEMJXfSC4ibImCYHxlPi1EL93kii76ZIQQRQnSlDlL+XjKDi7jBBWn3sgpGZlCRmvM4QsIUNISkiSS58lpEcHCO/VcxSc264UIjJEofn8uy8EjmySW0fvfsLsHRHCs9diyfNJpxSU9VA4Mr2L4OzQWHhv4zUhXSk4+1aqRy5eKqMV1TPzuhDQ2yO3Tjlt6CH02XhdyJTkU7x+nwuBca+yfTLvCgd+PSM8F+9eCXF7pwheXb8RguIpPFNIur5ZGO3uKHjNDJLFyRSeB80RvBw+EAJiUmVSU4WYjR8Izu5zhKDnlFOmkBTyszBr2RkhXsxYktNBmBX0ryw9PS+thNFL9gohYl4JQsiSfoKz+yjBf3ewEJOUKQiZcULQnN6Cc++NQowoJzsfr3F7hTi6T7oiBIxsJRcuVVL2K4+J7zhheXCciENm/DFhblcPIUeOGK+DMH7vXSEzp84Sbo+FoJkdsnF1HyUsvxAnPA9ZLnTvulwIeX5NCOitLp1SWaTbzLtC4LhuwuiNV4Qk8ku6LgTO7C04u48TAq5nt4IUlX/VI6AzjY4GIyZ8MhkTpb+PPFFZpZU+C0lXz+NvUqMa90Wf5pWzjfkWleDV2w+ti/z9KYXqo8ZiWMtaKGdhgVKlS8ECpWBTyQal0hLx6HYULodeRuTzMqhjDeBBNG49zu0Uq87eGnW6jMDETyZhzAcdUPtFKLavWo/d4U+Qb89VQVga7u9bgpnbb6FUo5GY1t8NZRTCi+eGRldD79zGDfHvJsL+monGclpq1s2zCIxKxO0LV/CIFBbLuuj5Yevsbu2LM1jz1T189O3H6FTDigJh49ocbV0JWG3cM1zaswXblgxGu3qktTjD+53Z+DvlHvYduwZ0mo+wo3PhBStUb9IOPmJeFeHSxBPWKamw82oBVxtLwLIyajnZArG3ESdpV1SMKpVAwbBxRpt2zuoLZlkfw/YFY92QuoB1S3SVDa5Z1uiMT794Fzi0C0dvklZKzgpVKlnDMqfOkiZeFZ2+2Z0tAzXhVb8GKvpMwsFDk+AjFkJdOplYhZ8svDi5HrODm2NwP3fYUJhNffjNmIWJDifx4+ZQOc1aISHfKCEg9Z2UvLW/VT8YoSwrCymJCUgh72qVYCtHtRYVKuFNevsL7EsKyHid241QzKEiGtavBYVXjeyBv63G90u34XKCZBdTTJX/XWX4DJ4EHzFSJsb3Xop+g1Zi4Qw3tDw4Hl5WKhldTuQrxActxYTPduFZlV74+ocR8LGVYxO5mMV7mU1UzWJyS2Hp3AXDO67FZ1P6Y8MfkzF/SE+81ckVNsjCi9Ag7Espj89sc8aOcxNqc/XiCo7vqYPZR//CMFfVsqQOrjZigewR5ghQ9/owjgfvxtxlp4HGvtqJITKr5QRnnMCNuGTAlQjxKMRu8YHtOLlvKVaGv4JX3wLEikSqTbpnCD12AimuiQCzHQAADyFJREFUI1BLJEmZfBsneDetipQ9QQid3gGdKsq9RAUUwVyDiwEhS1hXsssmonuPIc87QuJj3FdDclnpr5FLUc9xI1zV3D1VzZiBx0eWYNjcbbjb4kv89k84rpP2cmM3JhZqBkcp2NSqi1qUVex13HqWWypVuQNEcv4YM2otouCDsavn4H038dusOnpx+1q6omcv19xpQpZ14bdqL3asmA2/uHWYNvxttBkfiIdZ6fj3zk2kWDvDoTppc0V1lxF4+i4KR2jq8856dBYrRvXBnODnKNPxK+yc11Z9ZI1D0rPthE1n4+TrN9Dh67WY3VjS6PITUsh0yhpqfllwmEoEioXobJ090ZQUmpg/8MelZ9ndPyERkYf+RKhCMUvBzr622E16ceQkLiUQC2Yi+eoBBGy/pxBT/U0a7kdfxWuUh3PHTmhRpyJKIxNJIUE4mKA+VXZIBp7/+0RhZFVIvoHDG7bhLEVQGFDIQPKTf/Ho0X94niZ7XYUU3D+6JJvkKrbB2PXLMbVl1Xzm3RVUHgOGJ1/FidBn2Rla1oBPr4+w4NBlnNr5BVoF+2PNyWQ4t/WFV8oVhN1Qb9zXqMQVPfG/flUROW865m6+mN1FFhMmIvxEROG7Z1nR2Dz2Y/zdzh8/TR2Enj72uQSuUcGkSFlIjruNm9ad8D+fysiK3YrxA06h7Y4VmNKvK3w0HEDSPl1l+Ph2grUajK37dYYPa3NSI+X7WwxEB1jU9sWkSS1QChFYO3gQxs5fhAWTh2HUX6nwVOhzWqBsww54z7EMcHM1hnXxw9AhvdCpx07UGOSbbbPIt3oUaA3XFm1RFcm4+P2X+GLREvjPH4d+316BYwOFzFRISkF0wAdo3LE/Ro8ajTGjPkDP9l0xacNlZJbywdgFfdEgpwf6CMdndEO7VsOx8ZrYMUdm5EYMGf0zojJLoXJDR5S+vAMr/f2xVPxbga0SkajIuTi9RC1o2h+ASyXgxXnsO/lEVhwrvFmrBkqjDlxq2UDs1nZ7iJUz/XNHMlNeIEHBqiB1+27i/NX/kCV2I//GmRtJQMqvGNVoKDbFWqNZv3dRHxHYNnugzE5HtrqRCKpYt/DTXJLjcSP2FdITXoimkqxHkThP+cbexv3oszh5S7K3qUA79jQOhzwSNcysR+exactFtPu/kehQEdmkh1QkJFH6dDwKC8GN9Fe4eeM2ok+exS2VaqmMLLVKZ4mKzQbiM195jGlC92FsPeiDBRPaFB4bFVU2Za9iITpY2MFn4lJsnj8SXdwS8HfgGTypMwLr101De+UegE1zTPj5R4x9xwOVEv7D03JtMPm3nzCrr4eKycmqmsoStm0mYfPqT9Gz5i3s+Xk/LqMjvv15JnrWVs5MOX0Wytdph651U3H52DH8fSwML+u9jcHTfsCmYwH4vADtTMhIx0tRZCaendqKVcuWY2XO30acuJdNiMq56vdeNuWjXlcsCE9BypYR8JFNW6CpC/Tn1mowfqnSUqYt2OCN55ewTza9wW3kJbTZ8gM+JFuaZV30mrsc85qG4bO3GqPRKH/sPX+f7PQKztK1HxbO88apKR3h1u1bnLdthjYulVF/yGws3UOyrGHjMxbr93yL991lHx9rX0xcvxCjfMqJU1Tc3pqPSNzDtuEd0TcgDNEBQ+Ez/Fek4DQWvPUOZp+IwolZ72QvbRMJtDNmh7rh49WDgWUD4e0xGsuvVkQXX29Yp4QhKLoyfOqptgeKhXetj9qR8+FNeHTZgMz3l2Fxn7ri4EPFDmOxfFgGVvZrgkaj1uKabSv8j2xmIWcRU90S//TtiFFb7gEpJ/D9oLGyaTWWyDedfUPUU/U22jTEsKW/4ue3H2L2W43h4uiFQZszMHjHfPjVVAJaAXW+kUfAggZk5T2K81qID8T4dlNxzGY8tl6YhhZlCzLyF2dpOW+VCGSpW1qmMrYRetI8v/4YFTkCh/bms+rFCEvORVKPgKpviPrYOgsRkPbkPzyXX5WQEYfgdb8iKLMUqvZvA3cmOZ2hzYIYAXNHQGfTS7QDMhOJp75BxyXPMaBHY1S1eoWHp/ZiT8hjoIofPv+wKWy1E8ixGQFGgBFQi0AxdV2zkBy1H6s3BCL42ClEJ2SiVN1W6NWjJ3oN7I0OTrYlY2RSLaxmGvDiBGa3GoFtkumx8dyS1f1TLr/1UKw7N5fnqZnA41xMRGcCyHEVGAFGoMQgUEw2uhKDDxeUEWAETAABJjoTaESuAiPACOSPABNd/vhwKCPACJgAAkx0JtCIXAVGgBHIHwHjJzraOPHABszuNkI2w1xVhWjTxpPY6z8azWadKPzaSFWiS6pf1j3sG98RPfwvyjavLKkV4XIzAkVHoAhEJ797bPbSIWkJkbgT7Z6TuTuuFrqcaYj99XMMnLQA26LUbGtCsl+cxCK/YZi27BgUllkWOl8jTUjTHzwaosfc43IL342grFmPcGn5aDQSl5D5YXZgtHbkKn7Mtst2F+6I2SektbVGUDcugmkgoH5PTg1DxN1Wm8jtSvtciNk7R+ju4Ch4jdwsXKedX4vkZLvRKuxQq0KgbHfY3J1tVcQp0V60U+/XQp85x2S78MpX5pUQF3xGuFlUqOVFanydIITt3S1cFHf9fSXEX1gjjHannYEfayQhM/6MsHxkK8Fr5BJhT1BM9i66GqXkSIyA5ggUQaNTR/QV4drnSyyd1xYpx37BlkuyrX7URWd/DRF4hrA7DbFwWmfUUG615HDs2HZTbr8+DUXqIFrWrSg8b9ETzcRdf61Qo/m7GNwP2HfsSsEmhOSLWD5iBiIbLcGRn6eir7ihpw4KxSIYASUElF8ZpeDC3lqhuqMzrPEEV+481flmioUtVclOVxUdhvdDffmdZsUKJSL0l4VY+bCg7eD1U3vLeq3RQX4XjaynuBtZEx/18y5gC6Hscm9wnIp5E1vnJW/9FJelmikCeiI62e6zqApPxyqwhNwpTscjsu05Oac10UDCCWzKOVGpNcb4H1Vp38uKu5B78lIBpzllt2cJOllKq5OjpBOpEhHqPxIDl4UC4fPRrZ4TGomDMeoGZ/LiseJi9p5ruXhp1hZ53xdZO85ZhdtTf8Rkn0p5o8j5ZMUGYsGyDPi1TMGOMdknfzUaxadbyUHEl7pEQPNerpqYkm0sxx4n2WkcBWc6+SjpteIpTnTS0/MLgn/X9wT/kAQhM26vMN5bOtEoU0iK2SvMohOXcuRJNrrewqxfL2Tbp3JOQpoidzpV9qlWuTa6knSyVMEnR0mnQIl4uUsnTlGbyPDJOflKEITnQcIs9+yT2RTxoNOopBO7ZCd4ydk+C24LNc+AIFd+Bw+h+8y92adyqYsulbnrTGFzSHz2iWPSCV3iM1Msxka1peWAko+AzjS6lGOz0cPTGS6O9dFuwCZgtD92bBwLH5vSqNhpLk4FDIU1neLUyBU1KjbHlEPbMMUnAydX++NUj0HoW7+i7BSp3vji23Gok8e+ZwuXVl7ZXRw6CWn6VLyPIwg4cltN17gknSxlU+DJUdUdq4s7KlvWcEdLV+DmjXj1I5sVO2HBlcOY3Vh+B2XC4wR8vhgrO7HLCjVaDcRo3zKynXKfaNEWyp9aOvkqGDduncWOBX2BLVPRf9p+PFS50y6lTUbcjfuwbuqL3j41src3t2mID78YC6+on7BgV6yaNlXOl+8ZAc0Q0NE2TWXhNW8Pdg+vr92e/OLpT0/gPN1eblt0S9i4eMHHeolo0J7WqZXqmtjYw8UV2Ce+8PXz2oNK3MlSqqsJhZOj9iDy/CZxZ2BrLzXx1XnLsIbcAViWNVpj0jrZAZMvTuD4noLaolNenOXzo7MlPpyFpZl30G3xZcQk90ZNVWcaiHa8J4BSHSydW6NPY+BHdW0qnxdfMwJaIKAzjU6LPJWipuSvnSjF1u62JJ0spa5m8idHWcNrwgIlTU1dOlX+TxB6+bZ6TRC6aIty2YfmqMpe8rOsAgevqkiJvIN/82h9ZeHsIv/hkxLxLyNQeASKl+jE05/qIiUkEjfkDxwW61MXfr6e6jUI8eCTBupH90rYyVLqmlD7k6PUSJJpwNHLvsEihQm9spO2itIWCllmHwJzv2MTuOUZIZYiyk63ig3HtUdyU7zFNvVAn7YO2vUMJLH8ywioQaDoRCc79Uk6aUlNPmq8K6PZh6PR5e5PmL1wv2yk9QWi92zHoY5TMb5DVfFE9OypKkm4cS4ye0VAcjT2LV6B0AET8J63utG9yiXoZCl1zaDu5CiCMxPJYacR+kKmEolnfz5D+IHTqm1jlq7oP3dc9klbU7qKh75kr2SRTtrSpC2UmzEdDwOnolG3WdgSKp2YFYQl/gmYNKULauZUS4q3AqHiB40OihmJBR3PYfacHYgmP1pdEbAdV0Z/gv6yQ6yzHgZigkd/LA1NVM6Y7xkB7RAo/HiKNBqaPbrn7EC/HwgBMalKIuXjeQhvd+0mvLvxevZImxiTRlqPCP4jWwnZMnoLszYGKY3avRLiQ/bmxnEfJfgfk5tFLzfKKMrIGYGkdL+Jo7iif046+TJRuWkU87JwfeMHsjKQH83uvyYEzeyg5BcnxAd9I678cBblXRfiguYIXg69hVl7r6uZ2S8blez9vbBn/TjBi7DKKYsgCLKR6+z6dxC6dx2Vi2NmnBA0p7dYBq+Ry4XjMXeFkCX9BGd3aaRaEDLjjwlzu3oIztKIqqZ4dJ0pBCisRtCkLeSbN1NIur5ZGC0b4XV2aCWMXrJXCBFXScjHk43wKo+oJsUIx5eMysaD8JNG1WVJs0eY+4mj8/LS+JoR0BYB3mFYu+9CIWPzyVKFBI6TMQI6QSCnc6ETaSyEEWAEGAEjRICJzggbhYvECDACukWAu666xTOvND5ZKi8m7MMIGBgBJjoDA87ZMQKMgOER4K6r4THnHBkBRsDACDDRGRhwzo4RYAQMjwATneEx5xwZAUbAwAgw0RkYcM6OEWAEDI8AE53hMeccGQFGwMAIMNEZGHDOjhFgBAyPABOd4THnHBkBRsDACDDRGRhwzo4RYAQMjwATneEx5xwZAUbAwAgw0RkYcM6OEWAEDI8AE53hMeccGQFGwMAIMNEZGHDOjhFgBAyPABOd4THnHBkBRsDACDDRGRhwzo4RYAQMjwATneEx5xwZAUbAwAgw0RkYcM6OEWAEDI/A/wONDYc9pgxJVwAAAABJRU5ErkJggg==" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Problema Prático 3.6**\n", + "\n", + "Usando a análise de malhas, determine Io no circuito da Figura 3.21.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Problema Prático 3.6\n", + "Corrente i0: [[-4.]] A\n" + ] + } + ], + "source": [ + "print(\"Problema Prático 3.6\")\n", + "V1 = 16\n", + "CCVS = 10#io\n", + "\n", + "#Malha 1:\n", + "#-V1 + 4(i1 - i3) + 2(i1 - i2) = 0\n", + " #6i1 - 2i2 - 4i3 = 16\n", + " #3i1 - i2 - 2i3 = 8\n", + "\n", + "#Malha 2:\n", + "#2(i2 - i1) + 8(i2 - i3) - CCVS = 0\n", + " #-2i1 + 10i2 - 8i3 = 10i0\n", + " #i0 = i3\n", + " #-i1 + 5i2 - 9i3 = 0\n", + "\n", + "#Malha 3:\n", + "#6i3 + 8(i3 - i2) + 4(i3 - i1) = 0\n", + " #-4i1 - 8i2 + 18i3 = 0\n", + " #-2i1 - 4i2 + 9i3 = 0\n", + "\n", + "coef = np.matrix(\"3 -1 -2;-1 5 -9;-2 -4 9\")\n", + "res = np.matrix(\"8;0;0\")\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente i0:\",I[2],\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Análise de malhas com fontes de corrente\n", + "\n", + "**Caso 1**: Quando existe uma fonte de corrente apenas em uma malha:\n", + "considere, por exemplo, o circuito da Figura 3.22. Fazemos i2 = –5 A e escrevemos\n", + "uma equação de malha para a outra malha da maneira usual, isto é:\n", + "\n", + "\\begin{align}\n", + "-10 + 4i_1 + 6(i_1 - i_2) = 0\n", + "\\\\\n", + "\\\\i_1 = -2 A\n", + "\\end{align}\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "**Caso 2**: Quando uma fonte de corrente existe entre duas malhas: considere\n", + "o circuito da Figura 3.23a, por exemplo. Criamos uma supermalha, excluindo\n", + "a fonte de corrente e quaisquer elementos a ela associados em série,\n", + "como mostrado na Figura 3.23b. Logo:\n", + "\n", + "**Uma supermalha é resultante quando duas malhas possuem uma fonte de\n", + "corrente (dependente ou independente) em comum.**\n", + "\n", + "![](http://i.imgur.com/zLuuvRX.png)\n", + "\n", + "uma supermalha deve realizar a LKT como qualquer outra malha. Assim, aplicando\n", + "a LKT à supermalha da Figura 3.23b, temos:\n", + "\n", + "\\begin{align}\n", + "-20 + 6i_1 + 10i_2 + 4i+2 = 0\n", + "\\\\\n", + "6i_1 + 14i_2 = 20\n", + "\\\\\n", + "\\\\Assim:\n", + "\\\\i_1 = -3,2 A\n", + "\\\\i_2 = 2,8 A\n", + "\\end{align}" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exemplo 3.7**\n", + "\n", + "Para o circuito da Figura 3.24, determine i1 a i4 usando a análise de malhas.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exemplo 3.7\n", + "Corrente i1: [[-7.5]] A\n", + "Corrente i4: [[ 2.14285714]] A\n" + ] + } + ], + "source": [ + "print(\"Exemplo 3.7\")\n", + "V1 = 10\n", + "C1 = 5\n", + "CCCS = 3#io\n", + "\n", + "#Supermalha:\n", + "#2i1 + 4i3 + 8(i3 - i4) + 6i2 = 0\n", + " #2i1 + 6i2 + 12i3 - 8i4 = 0\n", + " #i4 = -i0\n", + " #i1 + 3i2 + 6i3 + 4i0 = 0\n", + " #i2 - i3 = 3i0 => i3 = i2 - 3i0\n", + " #i2 - i1 = 5 => i1 = i2 - 5\n", + " #i2 - 5 + 3i2 + 6(i2 - 3i0) + 4i0 = 0\n", + " #10i2 - 14i0 = 5\n", + "\n", + "#Malha 4:\n", + "#V1 + 8(i4 - i3) + 2i4 = 0\n", + " #-8i3 + 10i4 = -10\n", + " #-4i3 - 5i0 = -5\n", + " #-4(i2 - 3i0) - 5i0 = -5\n", + " #-4i2 + 7i0 = -5\n", + "\n", + "coef = np.matrix(\"10 -14; -4 7\")\n", + "res = np.matrix(\"5;-5\")\n", + "I = np.linalg.inv(coef)*res\n", + "i1 = I[0] - 5\n", + "i4 = -I[1]\n", + "print(\"Corrente i1:\",i1,\"A\")\n", + "print(\"Corrente i4:\",i4,\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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6YmgU61bXW0/SCST5JDkJINdO5LeOdAT1PfH2U99niOnLgYD05I38e0llavrs2ysH8Tq62bfvH5GRvXnzBuHh4aIvtS5dOuuo9ZzNyPqtI5nalq3bCt1vXU6K8r7j7WfeGHEJPUeAViuywYzVVgrV83EpIo9WaZ999nmORxMnjkfbtm1z5BXUDa2KZYMZF6bCs7pj4pWaukhxOb1FgLal9GncqKEYwo3kbpUr2aJ9+48Vu8XR25HkTRit0uTTiRMn4eXlVaDOIaV9ShWeya06RZna989+nDhxSq+CGbNMTTpb/N+gEaDVGsWkJMVbijTVunUro2NotEoj+Zl8ItOl+fN/Ep01yj8riHtarVGkKfIyXKpUKbRs2Vy0ES2IvrRpk1dq2qDGdfQGAXlFUINzRaQBkhRfVFGi08l+/foW+EpN6khA6oqIgxkrmg3OYwS0QEAzRVAtOtDDKmQGRfFF5dOQIYPRsaOGcRLkG8njXnogQ8GMyQyNgxnnARg/ZgTURYBWCufPX8zblbS6DRpQub//3pmD2nr1PEAMrSAN2C8HhxS6m/Qcg9TyhrefWgLH1QofAVLnqFqtCmJiY0UfX+T+h/KkQVcKn6LC6VF+lUaWA5oFT9aOzsqVKuHVq1einPLho0ewtLRUz9WQdt3prBYzNZ1ByQ0VNAKyJ290MEAC8kOHjojKuKS3ZqyJQt9RInfdw4cP07mSrTLcZE+VwyOy/dbpu3UBn34qm1HO12sE6Asn9e21ZvUavaY1P8RR1PX79+9j1qyZmDLl60JjaLI0SxWeh34xGFdCrui9uRSv1GRnj68NDgH6wmnmqNGwhpicnIQ1a1YX+Mmmuqg8faq7wC7q9qlpOWZqmiLG5RmBQkSgefPmhdibcXTF20/jmEceBSPACGQiwEyNXwVGgBEwKgSYqRnVdPJgGAFGgJkavwOMACNgVAgwUzOq6eTBMAKMADM1fgcYAUbAqBBgpmZU08mDYQQYAWZq/A4wAoyAUSHATM2oppMHwwgwAszU+B1gBBgBo0KAmZpRTScPpqgQyCtMX17Pie68yuT1vKjGrm/9MlPTtxlhegwSgX/+OaCSKd27d18M6adscOTNNzDwmLLHYn5efais/B49ZKb2Hk02D7VgECCGdOduNMKuXVfawanTZ0BuhJQliql54+YtUFuKkjp9KKr3PuYxU3sfZ53HrFMEKIoVheSjqPGKEjm0pPQyLg7Sa/lyV0JDxTbIGaOiRH3Y17RT2oeiOu9rHjO193Xmedw6QYDkXBRdqWtXSYR0ClIin8hDr7u7G5o0aSwGXZZ/TnUq2UrilJ4/f0H+sbitpT4+/thHfEbxNjkpR4CZmnJs+AkjkCcCFK2cGBI5q2zu7YXr12/kqEPbRtpWurnWRe1aTqK/f3mBP21L69atI8YpLWNtnUv2JtsHRUQPDg7J0Qff5ESAmVpOPPiOEdAIgYsXL6N+ZnyEGjWqg8LIUdQraSJZGQVXpvgKxPjoWlb2RttR2pY6OTmKVRo0qJ9L9ibbRy0nJ7EPWdkbtSHPKKX9v4//2fOtHs06vZwpKck5KLK1tdUbV845CNOzG1/fvkVC0cxZM1C9ejWxb2JcFBfzSuhVtG3TWmQ0JCsb0D+bNhdnZxw4eAjSQDE3b90St6VS4om5HT4SKMreKA4DbU1LmZnl6MPZubYYjV7ax85duxF8+bLSQwZp2+/Lf2ZqRTjTN2/eRHh4BEJDQ8XISMpIoQjcTZs2QYMGDcVtipmZmbKi723+jh3b9GLs7u6uCNi4SdyKkhoHbU3LlCmTRRsxKkqiHK2Srbgdpajyskkqe6OytJ2l1ZtsatyoYa4+xvqvly1SYNdF9eOhyYCYqWmClg7KpqSk4MSJEzhw4BDu3r0rtkihzyiWY9my5VC2bPYXIDk5GQ8fPgTFfTx37jz27z8olu/TxxddunQukshCOoDAqJugLWZNOzuQHOxa2PVcDIkGL5W9vU5IELejVEc2kext1eq1cLC3F7eanTt3lH0sbmOJWVIftDWl9jhlI8BMLRuLAr8igfDy5cvx8mUcKMI2hT0jAbGqlZeLi4tI16hRo0Tmdvr0GWzfvkP8EHPz9e2tsn6BD4o7yIVAnTou2PfPfpQqVSpLViZbiGRvtMUk+Vuvnj1kH4nXUtkbtUHbWUXBmkmOp6qPXI2+RxnM1Aphsml1tnz5Cpw8eQo1a9bE7NmzYGdnp3HPVIc+tErbt+8fkbEFBgZq3Z7GBHAFtRAgGRsxNFLjUJSksjeK5yndjsqXI9lbSAipgrjKPxLv8+pDYaX3JJNPPwt4okn4/+2334kMjbaYS5f6acXQZMksXbo0PvtsIJYtWyJmjx8/MdeJmWx5vi58BGhLSNtIZYmYlZdXM2WPRWbXvn07lYGDqQ9SFeGUEwGjYGq0EiK506lTp5CWloZ///1XvKY8elZUiRja1KlTER8fh4ULf8Inn3yiU1Jo1UaBbmkrO2fOXGZsOkU3f43RKaa8rEy2RXomPTWVzZe9dq2rmmFRH4q2prJtvI/XJoIgCIY68MuXL2PPnr2i6UidOnVgZ1dDFLbTeF68eI7o6Hu4ceOGuA3o3r0bGjRoUGhDJWY6cuQosb8FCxYo3WbogiDqa/78n8QTVJLTyZ+W6aIPfW6DTuT05fRTn3HSBW2GgLVBytSIUa1evQYffmiBjz9uh9Gjx+CDDz5QOGdv375FREQ4Dh36Fxs3/oFRo0aCGGBBJ5Kh0YEAbRGVyU10RQMdNHz//XciY6MV2++/rynwPnVFO7fDCOgaAYNiarQi2bZtO0g4TozMyUm5zEIKFDE7Nzd38RMZGYkFCxbCx8cHffv2KbBTQ9r+0qEAydC0ORCQ0q7Jf2JskydPwoQJE7Fq1SrMnTtHk+pclhEwGgQMRqZGDO2HH37EzZu3RMakDkOTnyWqQ0ztwYOHYlvUpq5TfHw8tmzZCtI907UMLS9a6QBh2LCh4jaUGCsnRuB9RMBgmNrSpctQpkxZTJkyRelWE0hAVOBuBEYlKJ1LWrmNHj0aVatWFRmb0oJaPiBVC9p29u7dS7MWEk5jXsOWGLPnPjI0q5mjdPPmzUWGSoy1IJh2js74hhHQQwQMgqkdOnQIcXHx6Ns324ZOMZZJeHw5CJcfJyl+LJPbuXMXpKWlY+fOXTK5+bskJkKKsZ06ddB822lmC7cOzeBq+yFM8keGyFCJsV66dCmfLXF1RsDwENB7pkbbud9+W4VBgwapWKFpDjyt2IYPH46AgI1KHfdp2qrU7YxW284S9ug29yeMblwu30yN5Hik5HvkSKCmQ+DyOkdAQMrN9ehrPx57Y9NUti4kRuDgym/h26IrRkxfgCULp2FEh7boMn45Dka+hsGqKagcte4f6j1T+/PPrfj8889RoUIFnY/+o48+EtvetWu3Ttq+fPmSyEw0PRwQEh/g4h4/jOq5HCFvdfPqtmzZQpSt0Y8Cp6JDQEi4jDVTlyA4XTUNQtxZ/NK3NyZfqI05B3bj9x+mYuK3P+L3A7uw0O0qJncYjPmnnzJjUw2j+DQfTO0tYk6vxsSR32KR3y+YO3IgRv92CjFpcl9K4Rmu/c8PI+o7wKGGE9pM+R0Hw55lTY7wPAz7fpuAVjW8MHjhLoQ9z/41oy8kbT2bNm2qdCjpt7Zg1JAhGCJ+pmJjxGtEbJyaeT8EQ0ZtwS0VLxS1TX3o4stPBuea64il4cXd89i3Zh3OurjC4YP8bj4lUEkxu337jlLs+EEBIyA8w9llO/HaU7GpU3bvL3F2+RysueGAkRN6wcWiWPYjk4/gMmgcxtW8Dv9Ja3AiTsXLnF3rvb7SUqVDwLvIvzB59EN8cWI+2pUpBry7gbW9xmCh3Vb4dayUvYUyKQ/XrmMxJ+M+Tk08AksnL/i4lc96blLODZ0+rocNe2rhq0k94Foy+0sdFnYNrVu3VrntLOY8AKv9B2RO4lMELZiP802+x9RWFdWaWNqGdu7cCdQXnVhqm8h6gZKzs7OGTRRHubrucChZCnVcqsJSw9rKikt14x48eKAFo1XWqv7k049QXFwcHj16JFqRkBsnsrfUH/9zaXgW6I9/6gzFGCzHRlXQvQ7Dob8iAcuhaFhbwRtQ0g4NfOyAVf/iwOVRaNVO97sWVeQZ2jMtmVo6XtwMxiVUwFizzMVeiY9QocIbbI5+jgxUgsxvDYASsG3bGwPK/4ONfwXi2kAXeJaSMq+3uH/pIsyHTEYdGYZGQF67dg0eHu4FjqmjoyPOnTuXL6ZGboIoyboOUpdw4X4wDl21R5sFMj8G6lZWUY6Y9J07xrNSI7Ozw4cPIzDwqDhqUtGpUKE8Pv30U+zcuRtv3rzJsiD5+OOP0ahRwwLTRVQBOwABaQ8PYPEpV4yfaQeTf1SXRlI8ntLZlvWHKCX3HZDUNEXxkvSNSkb8m9Q8GuPHWjK1Yijj5AbXpBVY9nsbOI1tCusnF3DwQgOM/N5RjqFlgmzpid4jGmHjj3/hj+O+qCddzaWG4+AfZujjXx3ye+Hw8HC0bt2mwGfJxsZW/MXPT0fk94wSrRQ0S+mIv30NoZauGFtd4vxRSLyLk3/7Y0VwQyxf3hUSt4KatWpMpWlVtmbNWly/fl20IPnuu+9yyVhbtWolDllqQXLy5EmsXbsOn346AO3b69bmNk9s393G9sUR+OT7SbAtDkhiSamoZVUeVWmBlvYGyakCUFz6gy+tk4G0VNp2WqJiaXYQKkVF2X95PqKsnFy+CUo6++LHmV6IXjIcfUdOwJgZV+GzfSH61ywlV1Z6a47anfugXYlYHPwjCPdEZSwBSVcOY5uTD5rZlJAWzPpPnkML4oAgq4PMC+qD+tJFUuUbTXH7r3Hz3EVktPKEk/Aar9KS8TQWqGD+DFeS86OxBlhaWuDRo8eKuzWQXLLvHTduAipVsgXZ0Hbo0FHlOyG1IBk1ajQmTZqEoKATmD59RuHp7AnxCFu3Cc8GDkPL8mquGcxd0ekLDyAhGJfCFehYJkfh7OFooEYXdGmQ7UTUQKaw0MnUkqkBEAWY32Ja+w/x4Og+HAu7g+iniVAlxjSxaYa+/RyQfn4H9oa+BoT/cGZnCHz6NkF5+R8nraCoiFZTl6otT9OqC11XyvgPt4Pj4OJqipD1B3H/nRlsHKrBumTJfPeUkJCIjz6yync7RdUA2esuXbpcZE7EzIhhySfJAdEQ+Wzxvlq1avj6669FResRI0bqTHVHYWfSzPS7OPb7Jizv5QnHGnZwqOEI74n7AOzDV00c4TBsj4KVmxXqDZ+LmZ88x6oZKxEU81baGpD2GEG//IhV8e0wc+VwNLTQ/iub3ahxX2mPkPAUp3/8HnsarMGpw8sw2DEKa4ZOxm/BcVknm7mgMymPZr49YI9QbPjrAl7EnMOu0Cbo5Gmdq6ihZmiuxV8MJUpl4Obus0jr0g1uWbJG3SBgaalA8Kybpgu0FVqh/fnnFtBWk5hTflKvXr3h5eWFb7/9tuBXbMU9MfFKNG7fk36icHpJFwBd8Ov5KNxe111OnJCOZwc341CyCwb9th1bv7DE0Sl9MPFADBB3HDO7TcPRMp9h6/7FGOQi4NKKLbimauWQH6CMpK6a62P50Qp4e2Urvttij3nn3WFrVQ/TNlRB2S+GYMnyQPT090VVhSsvE5R07Ywx7QPw1c518CtRAtHdpqCuki+ytXVp/Pfffyq3G/KUaXNPfVBf+UlSW9SYmBjNrAlMHTDgr1BIz2/zQ4N83YSEBBgiU6MDgTlz5mHhwoU6m3tibJTI3O7bb7+Rh6oI7wWkv72GDYseIqKSRF5mbWuJ5yRDe/sKz8zKwzH1Hk5uXYmTqY9wZn9VfCfxaFWENOt311oytXTEPbiLmA/sYGUuWeyZWNRFF98m+HX+IzxLB6oqa9mkMlr064xyh/zx119tMTewNpRttMhFUGxsjM5ebGVTQX3k1x2RmZlElkgqBpoq3yqjK7/5FBmcPHJCLk0AACAASURBVIUYWiLfcBSTQdfyVDKNmz9/PmgVWJi+9fLGPxlXdmzHlayC1miTGUslPfhvrAzOegBYj5e54UtFCChjPYrKyuQVRwX3Jmj0ei/O30yApxttcd4i7r84VOvXFE4qWy0G62bdMMhxM5bbd0brGrnlJNKOSIH01q1botsgaV5B/I+KikKTJk3y1TTphVEoOzpwIKPyok5SvTmKUGVIiRhORkYGGjdurHOySSY3dOhQLFnihz/+UKk5psO+i8Om+zLc7q6sSenzZQoKVMHv95RWVFCeswgBrWVqpna98OvGVgj7biS+WbgYfnOm47enffDblw2RM+CXAqBLOqPLiG5o37URbBRuUyV13NxcQdGT6Ji+oBK1TX0oC5KhSb/jxo2Dd77DlaUj8VEYLoQ9BGIicCXsERLljDTUoYlWaZQoWlX+k/r2i2JfwgPsHT0BW6I1nzfyZNyrV8/8k6ykBZLPVapUmV2fK8HHGLJVrqlUD/AD2HqPxur9o1UXU/i0JKr6/gw/hc+yM8k/GH0pSTFWoof0DKcXz8L6azmjmGfXMIFlx6nw83VSrCuXXTDritqmkGbUV36T5iZSinosBosqnug2cze6KXqsZt7evXtFZWLNVUxyd5Btv9haLdlfxr3T2Hb4IJ45DUKPSfWhTMlHvifSR7t//0GBr8zJW/KFCxeM0tJCHtP38T4fTK1w4KLYljNnzka9evXw0Ufl4T15Jbx11PWrV69AX/65c2frqEX9aIbii5LrITIxy3eStV8MU6e11wjdsxeRVkD8lv24MNgDraxz2pcoa4UsSGieCzpVr14Dfn5L8OWXhidvLGhsjKF9rbefhTV4Erp369YVa9eu1XmXW7duEdvWF8F+fgZIjEyaNm3aLHoLyf/KMdt+cbCHmrK5hDDsP9EIP87sCfNn/2DbicfKVXykBGf+j439T231jaCgINBHmqT3YWFXpVlK/5N3FlqZ0ykrJ+NDQO+ZGkFOBufFixfDzp1/62wGqC3SKaO2DT2RMTcFXCFmRm687969K8YFzd+4ZOwXO9sht72HotbT8OzUP7jSqT3afNIDA21f4siGwwh/p55QkOgmP3DqpOPHj2HjxmxhP13Th1ao6qRatWohJUWZGEOdFriMviJgEEyN5ELTp08D2VcSM8rPwQHVpTaoLWpTFzKnop5csoukRF53V6xYKcrS8r1Kk9ovjmsn2i+qNcaMeziyOQUD2juihHkddBjoDoTtwr6QV2pV16SQm5vi6OfqMkUDjgypCUzvZVmDYGo0M1LGFh//StQ1Ipc6miaqQ3pK1IaxMDTadtIKRzalpqbmT3NeG/tFCEi9fhiby32MllVI89ACdTr2QqNit+D/51k8U2+xJjsMldfkWUU+0bZSXesDExWn7vLt8r1hIaD3BwWycBJj+/bbKWL4OT8/PzFEXtu2bfMMlUeh8Y4ePQr6P3z4sHy5GJKlRx+uacspn86fvyDGAKVYoFqtRDPtF1cs3ITlco1/1WQfvvLxw+lc5j6vEHowCCYvrTBtuNSTcBreVTbHu/27cGRSWwywU66TSN3Y2FQEWWSow5hI2C+fPD095bOU3sfGPlX6jB8YNgIGxdSkUJOfMPKVRR4Ytm7dKnqtJTMleQeNpLhLjIyEwhQMZcqUr7T7kks71rP/p06dyrVKk5JIXi20Tpn2ixOzGkhD7J7J8J4I/Hp+MbrZ5H5thGdnseV4Kyz432gZR5/piAv6ER0Gb4b/nut5qndUrFgR9+/fV0vxllZlLi4uIHmiNJGcTJ1EIgjqxxgOiNQZ7/tWJvfbaSAI0AqE/GTRh/Sbnjx5IsbzPHDgoJhnamqKDh3aY9y4L3Wig6ZvsNAhx7p163ORRTKlkSOHi1/4XA8LLCMRt/b8jQf9vpVz9FkM1o07oZ/9ZqxQQ73D3d0dFGJQaqeZF7mkwyjL1NRlUhER4fDyapZX8/zcQBEwWKYmizetxOhDv9zr129Ax44dZB8b5fWJEydynfQNGTJYHLtWW05tURKeIezvNfhx0WnEd/fG2egq8Lb7UNIaxacICsYT8irxbAd+nl8JGNMfraTP5fokUzNTUxOQ7FOdLai9vUNWC9WqVVXbVjQ09CqaNWOmlgWekV0YBVMzsjnJczi0SqNgxdJUr56HGKBZGpdAmq+7/1L7RAUtmpSHm+90bPOdnvshxafoMAKL6JP7qcKcTp06Yv/+/eJ4FBaQyaxevXrWnbLT0KwCmRekcH3lyhWMGcOuLuSxMZZ7gzn9NBbAdTEO6SqNDOi/+eZrzJ07BwXH0HRBsfptkDlcVFSkuFrLqxYZqDdq1Egspug0VFH9LVu24NNP+xuVbFXRON/nPGZqBjb7JD8kXTQ6+Fi6dIleeATRJYS0dSZ/Z35+i9XSR5QeDik6DZWni+w9//vvaaYdsfxTvjcWBJipGdhMHjt2HAsXSvyNkRzRGBP5tvPx8cHy5cvzZGwkR6UPnYaqSmQ+9ddff+H777/nVZoqoIzgGTM1A5vEnj17FPLJZtEA9Pnng+DsXDtPxkaOJBs2bKiSSGJoZMA+YcJ4o9mmqxxwAT6sVLkyLgeHgBS89TWZCEZmL+Lr2xc7dmzTV7yZLg0R2LjxDzHO5+jRo/NUspZvmvTRtm3bJh4MLFq0kBmaPEBa3JMTAPLVdzc6WvzRadyoISws8vSgqEVP2ldhpqY9dlyzkBC4ceMGVq9eA1LObdMmbwsS6QknuZUij8ZDhw7hLaeO5yoxMRFXr17DldBQVLK1Rf36nqhePX8BcnRFIqt06ApJbqfAECAZ288/LxKDGe/evQerVj0U/a7J67IlJyfhxo2bYpT23r17iX7y1FXILTDijbRh0b74bYo4ukLVi1QDT16pqQESF9EvBOgE+PbtO2KkMaLs7793gpgYWZHUquXE5k8FOF2RkVG4fv0GnsTEoJ6HB9zdXfVu+8krtQJ8AbjpgkGATn1lXSv5+wcYlBUJBcWhqGNJSUm5ACIbZltbW73aLtOqLOzadVy9KnF93NzbC507d0RJHQTczgWADjKYqekARG6CEVCFAFmA0Orm8uVL2L//oKqiWc/ISsTDwwNt2rQuMtvlly9f4kroVYSEhKKOizM6dmhvEIctzNSyXiO+YAR0iwAxM7L+IJM28shLzgbIPrd27Vqwti6Ti0FQeXK9RJ5lzpw5C1qB0oe80tD2urDlg3ej74khH8lyxcHBHmXLltEtQAXUGjO1AgKWm32/ESDvIQsXLhKZGTElsmklJWFViQTuxLjo88knEu8z5LUkMDBQ9CFY2A4LGtT3BH2kcrTDRwL1Vo4miysfFMiiwdcGiYA+6SbSamvHjr9F1+q0Mps4cXy+V1h0MELWELR1pTanTv021yqvMCZOfjtKW2R9tDlmplYYbwP3UaAI6AtTI4Y2f/5PonIqhXb87LOBOh23dPVHjc6ePSvfzFJb4uQPDho1aoBaTk56c3DAZlLazizXYwRkEJBlaLNmzdQ5Q6OuaPu6YMECsdfx4ycWWYg/OvWkbalP2zZITk7GiROncOlSdohGGViK5JJlakUCO3dqbAgsX75CXKERQ5NVN9H1OGm7R4xt6tSp4oeuC3MLSKu0iMhIXLx4WRxay5bNFa/S0h7j9Jol2Hy/DGrbpCD8Qjzcxn2DEd6VoYzpCIkROPTHBmz46xasWzSDi2UCbgadR4xjd4wZ+znaO1lBrXg5ZPtpTKl37z7GNBweixoIFPWcHzp0SOjcuatA/wsrPXkSIwwa9LkwY8bMQukyISFBCDx6TFi+YqWwc+du4d69+yr6fSNE+g8W3KccFl5kULEMIfXmWqGrw9fCgf/eKayX8fKMsKhjXaH2oA3CjYS07DIZ8cKNtUOF2jV7CD+cihXE5rKfKrzi7aeuf0q5vfcKATLwlsZapRPLwkq0Ohs2bKi4OqQA1gWV6ORz1649CNi4Sexi8OefoWfP7nnYeb7EzdNXAQtzmIlLKxOUsC6Hiu9uIzpGkXePlzi7fA7W3HDAyAm94GJRLHs4Jh/BZdA4jKt5Hf6T1uBEHPmGV52YqanGh58yAioR2Lx5M0iPi0IvFnZq3ry5qMNGTJVOSHWdDhw4hL3/+0eMITugf1+0bdNaTZMoazg2dkbyxpVYe+Ep0pCCh6eO4WKrPmjvXCo3ma/DcOivSMCyPhrWtsz9vKQdGvjYAc/+xYHLL3I/l8thpiYHCN8yAuoiQOZOJ0+ewoAB/TXT+k84jXkNW2LMnvvIULczJeWkzJT02XSdOnZsj4Gf9kdFm4pYv2Ejjh47rubhxIdw7j8V03weYPmAgRg9eQJmXG6OrSv6oGYJBVKxpHg8JYux4h+iVEkFz2GK4iVp9ZaM+DeKVno5R85MLScefMcIqI0AbftoldayZUu164gFzWzh1qEZXG0/VE/wraJ1soMl1+6koEsnsLpOtM2lFdroUcNF78I7d+3Gli1/iQq5dGigLJlYuOKz2V+hneltHN91FNejH+BpQpri4lblUZUWaGlvkJwqKCiTgbRU2nZaomJpMwXPc2YxU8uJB98xAmohQAyElGHJ7bjGrndK2KPb3J8wunG5fDM1IrZFixai5QLZlxZUIkeQpMYx9svR4uku9fX72vU4c+YcyLeafBKencD8Uf+i/p4TOLBsCOyjVmHkyN8RkqBAJmbuik5feAAJwbgUniDfFJAchbOHo4EaXdClQd6mWszUckPIOYxAnghIGQg5R9QkCYkPcHGPH0b1XI6Qt4pWJZq0JilL+mu0YiSD+cJITk6O4mFBr549EB4RgVWr14rMLbvvBFzZ/Cu2ufZFnzrV4NR1KtZvnAKPG/5YfugBco/aCvWGz8XMT55j1YyVCIp5m91U2mME/fIjVsW3w8yVw9HQIm+WlXeJ7Ob5ihHQSwQqVrQpdLoo4DKlvOw5cxKWhhd3z2PfmnU46+IKhw8UyY9y1lD3rmnTJjh37ry6xfNVjlZmtEKjrah16dLo1rUzvLyayrT5Cg9vPELJslYwF3OLwcK1PXy9M3DtURxyrtXS8ezgZhxKdsGg37Zj6xeWODqlDyYeiAHijmNmt2k4WuYzbN2/GINcBFxasQXXcjYg06/kUpkeXK6CnMEI6CMC9AWr51kP6zcEwN3dDW6udQvFXOfOnTviyaNmmBRHubrucChZCnVcqkLBOZ9mzcmUJiN42g7TKWhBRRm7f/+B6FlYGp+ATkTLlFG0HSwPtzaeSPjzAm6NrgdX0ut4F4//ntihzxg7OeVbAelvr2HDooeIqCSRl1nbWuI5ydDevsIzs/JwTL2Hk1tX4mTqI5zZXxXf5RGHmpmazIvBl4aHAMl6hn4xWDyVo4AgS4//Bk9PD9TzcFfyhdPNGK9fvy7K0zRtTbgfjENX7dFmQSWdyNOk/ZNzSUpxcXE6ZWryFgRk5+nj0yaPH44PYNdnDtbHzcf3g75G86a2SLkbjfRRP2JKI2spyTL/k3Flx3ZcycqxRhsvyU168N9YKWuBZT0+q5SyC2ZqypDhfINCgE7pypZtgw/MPhCdGt67dx89unctMMZG/tEqVCivIUbpiL99DaGWrhhbPfMUT3iGkPU/4uuf9uIBnNB53q/4oX9dWOhuZ6ohjdnFSYXj1q1wlCpVSrTz1CiwSvHK8P7yN3h/md2e4qvisOm+DLe7L1PwuAp+v9ddQb7qLJapqcaHnxoAAuQSh76AS5f9hrcpb0XdKlq9Kd4aFeWAXuPmuYvIaOUJJ+E1XqWlI+HsThyq/jUO3wnHufWtcGPGEvzvnoygvAjJpfB3FIeAjNaDg0NENY4iJEftrnmlpjZUXFDfEJA6L5QGASFdKn2LQZkDs4z/cDs4Di6dTBGy/iBsh/dCpXI+GOFURZQzlff+BJ2sFuJNSn5VcnP0qvUNYUkHAPQhrC9fDgY5imzSpHGhyS61IZ6ZmjaocZ0iQ4AOBsIjIsUgIKXMzESdqaIKAvLmTe7AKaqBKYYSpTJwc/dZpK38Dm6lSgC1HLKqCDF3EFarI75zyFvBNKtSIV2QGgd9pMGMC0t2qc3wmKlpgxrXKRIE6Au1+c+tYt+tW7cUlUGLhBBR4bU56ARUo2TqgAF/hWKAokrCS1zaFQmfuRPgqMiUSFEdmTyKTkXJzEyBbaVMufxekuzS1rY9WrTwFoMZb9m6TQxmXLduHZHp5bd9XdRnmZouUOQ2CgUB+kJNGP8liKFRuDZS46BtkSpznYIizMbGRgyurJv23yLm0BZcaDIS/Z0stGqSDkYoEUaFkQjzlLcpSE5OES0qLC11qaCSvxHwSi1/+HHtQkZA6nVVPiCIs3NtkGC7sGRqzs7OYhwCWj3mj5G8RUzQFuwp1UNiNiU8x8V9d2DXpTHKa3ACSvIuCvBS0MkQ5Jgco6Cg3wJuv8ARIDnbhYuXRPWDSra2INMljdQPtKCQbD/pkz9F1zQ8O70YX3y+CreytORt0HnlTvh1VF+PjRjriBEj8c03X4PcEek6SeWY589fQBlra1GOWaNG9Tx01XRNhfrtMVNTHysuqecI0JaIfOWfPXdetIUsSD01fYJi06bN4qpx06aN+WSyOUdFzPLmrVui3h8pNLs4O+dzVZqz/YK64+1nQSFr9O0KSHsWhv3+S7C0xDgcnuQpZ/6SEwCd+Z/P2WzWHZnwkC4VqXfQF7Awt6JZRBTBBa0Wye0QuR/K36oxN/GPnzzJCmZctUoVDmacGyLOMR4E0hEXdgD7QsIQuDYIr8eMUzk0Ie4sfhk4EhvKTcbOA/Oz3TV/8wo313+FXh0GI2TjKnzvXVEj0yFFJjxFpd6hEgAdPzx16hRKlTIXt4EUY5SsGwrClTjJLRXJLpt7e+nt1pOg5pWajl+496O5YrB264JBLpXxcuk63FQ56Gz/82N3KfE/v80XiyetgdfhaWhlLeOfXkm78kF1O3ZobxDbIiXD0SibVmbr1q0XGdnIkcPFbSet0sigvaCSVEeNZGs/zl8IYmr6nJip6fPsGANtWf7nh6r2P7+K/M+PQqt2FZSOmmQ85F7nzt1oNGvaRPTGWlinnUqJKuQHJ06cEBkadbtmzVqYm5tj8ODBhUIFYX07KlKvV2kEBOupFcrr8B53okP/86Q6QUqelSvZ4kpoqKj8SauH9yXRKm3LFonysXTMSUlJoC0op2wEeKWWjQVfFQQC8v7ni8srX2nmf166FZJuQcnrah0XZ9Sr52H0W1Cp/Ex+mrZv34EPP/wQPXv2kH/0Xt7zSu29nPZCHLSO/c9LKScPHBQQhCwMKlSsgAMHDxWphYGUroL6T84fiXkpSiRTa9OmtaJH72Uer9Tey2kvzEFn+p8PH4MfZ6yEx7pJaGX7gYQAWf/zm9TzPy9PuTILA3KZ4+7uWmgWBvJ06fpeUQi8mjVrgg4LNHMprmvK9K89Xqnp35wYEUW69z+vDByp/WdcfLzo1JCcRRLDM4akaJU2ZMhgLFz4EzM0BRPMKzUFoHCWrhDQvf95ecrkTaR82rYpcBMpeRoK+n7t2nVZXZDscPTo0UYvP8wasBYXzNS0AI2rCEh7HoWLpw/izGvgTfBJHL1oifqeDiiX6yBAt/7npdjLWhCQMfvgzz8zmq2mdIz0XxoFnkLgDRs2tEBsO2X7M4Zrtv00hll8T8agyIKglpOT0WwzFU3jzz//AktLC/Tr10/nZlCK+ssrz9e3L3bs2JZXsSJ9ziu1IoWfO9cEAdpq/vffM1H5lOw7y5UtZ9QMjWRpnTp1ZLmZJi8Jm0lpiBYXL1IEpGocZKxOLr0pmK7UFQ7prxlbIgN1XRupGxtGisbDKzVFqHCeXiNA5jqyxtanTp8BfQozmLFeA/SeE8dM7T1/AQx9+FILA7ILLcxgxoaOmzHTz0zNmGf3PRob2YUWZjDj9whagxsqMzWDmzImWB4BeQ+tAz/tz3pc8iC9R/fM1N6jyTa2oUoD7L6MixMD7Op9MGNjmwA9HQ8zNT2dGCZLMQKk1kEnn7JBQIzx5FPx6DlXHQSYqamDEpfRCwRom0lqHBRrkpxEenk11Qu6mAj9QoCZmn7NB1OjAgE6DBgxfCgiIiNx8eJlhEdEoFGjBjB2qwIVkPAjBQgwU1MACmfpLwLkecO1bl3xI7X/JCsD8q3GiREgBJip8XtgsAhQwGL6kD0iMzWDnUadE87+1HQOKTfICDACRYkAM7WiRJ/7ZgQYAZ0jwExN55Byg4wAI1CUCDBTK0r0uW9GgBHQOQLM1HQOKTfICDACRYkAM7WiRJ/7ZgQYAZ0jwExN55Byg4wAI1CUCDBTK0r0uW9GgBHQOQLM1HQOKTfICDACRYkAM7WiRJ/7ZgQYAZ0jwExN55Byg4wAI1CUCDBTK0r0uW9GgBHQOQLM1HQOKTfICDACRYkAM7WiRJ/7ZgQYAZ0jwExN55Byg4wAI1CUCDBTK0r0uW9GgBHQOQLM1HQOKTfICDACRYkAM7WiRJ/7ZgQYAZ0jYJTuvMm9M6f3CwGe8/drvlWN1kQQBEFVAX7GCDACjIAhIcDbT0OaLaaVEWAE8kSAmVqeEHEBRoARMCQEmKkZ0mwxrYwAI5AnAszU8oSICzACjIAhIcBMzZBmi2llBBiBPBFgppYnRFyAEWAEDAkBZmqGNFtMKyPACOSJADO1PCHiAowAI2BICDBTM6TZYloZAUYgTwSYqeUJERdgBBgBQ0KAmZohzRbTyggwAnkiwEwtT4i4ACPACBgSAszUDGm2mFZGgBHIEwFmanlCxAUYAUbAkBBgpmZIs8W0MgKMQJ4IMFPLEyIuwAgwAoaEADM1Q5otppURYATyRICZWp4QcQFGgBEwJASYqRnSbDGtjAAjkCcCBRp4RUiJx3/xKRCKW6BcOQsUaGd5DpULMAKMwPuAgPZ8Ji0ESxr2woo4BTD5+OH0uu4od9MfnXouQ3zmvY2CovqblY5XtwKx5+gl3Ai9govHwwGPlmjRtgN6+34Mt/IfqCA9Da+izuLI8VO4eDEEF49fRaJTa3Ts0hP9+vvAxbpEdt3YPRjRZBKOZedkX+kat4wIbOzRE/OuJmX3keuqGvoH7MS8VuVyPeEMRsAQENCeqWWNzhr1fPvCq1LJrBxUrIZS2XcGeiUgOWI/5v1yFrW8PeDUtDpCTh/EluCD2LZ/NNYHTIZ3eWXwCUgI3YKp8wNR2rkxPFu5IzIoEFsWBWJb0HTs/uMLuJiZ5MSlhCd6jvJGJVmBgK5xNK2Fz/fewGdRAejVzh91czGv14gImI+tOSnjO0bAoBBQ9q3UYBA28Or/JSZ6WuSu4zkJl+9Nyp1vEDnFUNp7Kk5frwAbC4IpAykx5+E/dTx+PbERv+7vhmaDa0GWB2UPyxSWdb/A9lOL4FbVCsUhIC3mCOb2H4stF7dgZ3BPuHhZZxenKwtv9JswCZ46mJGcDWtyZ4VaPXugXqgmdbgsI6BfCCj+TuqIxrQQPzSoYQeHYXsQm9XmW8Re2Iy5A1uhVo06aDVwLv648AAP94yHQw1PjNjzKLPkI+wd5gmHGh2xJCQxqzagIJ+2wvXs4PaVPw6t+wZd6jmggV8I0qiW8AxhO3/DzHED0ameAxzsW8L3yx/wx4UYyXOZlnNemsCsXKVMhkZPTGFm2wg9ejQD8BYv37yF8oCpxfCRcyN4igyN6pqguG0zdO/mACAOD5+9ydmVntxlRB3BP0/d0a0Fbz31ZEqYDC0QKFCmlpuedCQE/46RA2bgj9NJcPMdiO6ur7BvzAT8cuR+7uIa5Vigyr3dmPnDDtyKs0DdKmVRjOqnP8SxpSeQUtMHQ2YtwtwvXfDi0HrMHfA9/oxUJVuS7zwNidEnsGnTSaCYFwa2rilpX76YsnvhGe5eJdbuiIa1yuYuZfMcwZtXYsmStdiy/ySuxSapYJq5q+c/JxWxN8IRn6Oh14jaMwudatjBbZgf9l46h8uhL7NLZMQiZNN08blDjaYYsSwIIUeXY0nQc2REBaAH/aDVqIMeARHIQAZeB82Cm5jXEjOCnme3kxiFY37DM581xQi/I4hKzBBXx4lRJ7HbbzgaTA/Cq9hzWD6sqdhmp1lHEZuRitiQLZjRoQ7E/gNuIPvnT/YZ0dENM/ZEyDzP7l68orHs24AZHYZgY0go9k7vBgeitcN0bA6JBVGTVS5rzPR8FvZGvc58+BpRQTuwZFg3zDgahsvLhsPNZTQ2RtBzDekRW6T2AjLHZwcHl+FYcjRK+RgyqXjv/1GEdq3Su2DBz6OGYF8996f+4mDhnSAI74IXC/Xp+dDdQgx1kvFYODCuiWBf3VHwWXhOeJ1BmWlCwtXVQp+a1E49Yfjuh5nkPBT2DK0n2FfvIPgFJ8iQqCBfSkvNHsK8w/eE5IwMIe1dmiA2n/FGiH+VKlP/jRDpP1hwqm4vtFhxVUiTeaLwMma3MDxrjPZC/S4zhR3XX4jjU1heYeY74b/D04XG1WsITn0ChMhUkTJJyRzty2DpMUBYdDpWMgaFbWqfmR7pL3TPGpNMn9U/FQIik7MapnK9R+0WHqdLstIfHxY2nXiWeXNf2DOqhdBxZqAQIz5/JYT7jxJcq7cQph/PLPPquDDd2UXo7h8uZDYhSPqWKZNwUVg27XfhUsxbSbsJ14WAoU0E12nHhVdifQl9rkMXC3uCY4R0IV1ICF4mdKzeRBi+eLtwPPKVIAhvhZjjPwgdZegX+3GeKOx5TO1Kacs5vqyBCslCpP+nme+yjzB86QnJmNIfC8dndhXss9qRlHOVYpJJq31XfyEyPV14dXym4Cri2kQYvvSsEPPqouDXvp/gFxwnGXdWO3nRQ5S9FR7vnijUH7pJCE8g9F4JkbtnSsbtf12Q/UZkj4OvCAEdrNTooGAUxk4Yn/UZXNcacmJwyY9HQiTOBtJqpREG9vCApVioGCxc28PX+6P8/8BYNUfH1tVhZmKCYsWLSWgwMcdHVsWQEh+LBD04hgAAE1hJREFUe7dCERISjviS5VAK6Xh85S6e5dWrWTW0Esc2Ev28qyAh7G+sXL0XYc/FzW1etWn/i7SH/+DHqVvxvFgjjPmmKxxKyKBTujlmngnB9eho3L53B9cvH8C6KZ+gTNxZrPn6D1xKUr7JVaNzFUXolPMSbt+jfulzFftne8isPlNw50wgIt5F41KoZKViWqkdBopb0wy8PrkeM+71xrwprWEjvkVWcPRqDHsVPeZ+lIHXl//B2s3z0a9JLcnKqG5nzAuMRdKu4whBC8y7fggz3M0Bm3po7WkDU5jCwsEVnuav8czaDS0crQCURIXKlVESD3H7cfZaDbDCR6I8NC/azOA4+A+EBAyCOSrCq0MjyZhMK6HVV5PQH4cRcDg6e7VWtjQsaMwW9mjmLR2xKaxazcJpsY2SqOjmCBurhph4cCsmepbOHLq69AB4fRarvg9Bh4HtUUvszAqO3Sdh3oRKOLZoOy6/zlo75ob1Pc/RgVha+UFBrq99Ujyeiju+MihtKdO1SSl8VOFDAMl5T4eQjnfvlExo2hskpwpAcSnTEJAWexFbVizGss0X5bZWeXcllijtiQGTPCWFhRHo+vMQDFj5E76r7Yl9X7pD5sxXQYN0QHAMC0bNwD8vbOEzfzZG1pdj+GZlUaWytKopzMo5o9WIcRj+7yksDDuLy7eT0cjNXFqgAP/TF98dUVk9mMH+497wXjQJXwVux/4JkzGg8ydoJTKRlwgJDEJSySGwNM/P7yK1cxb2sw9hp7JDFyVTnUWmkgtTx8HYfRPIiA3BP4En8L/py3ANXuiupLzSbAtbODgCe2/HIBG14Dh4M8LEreQhHD2xE7OWngHcfZRWlz7QjJ4MvA45jr1JVfFVZdkDOCs41KsL86QgHA0Zh1asdiOFN8f//LyRORpS68a8NCqK38+n+C/uXXYVIQHPHkjlEtnZkqt0pMoysYRoXL30Sr6Q5D7hPzx/nZ79TIjBkfkTMXfzEzSY/ieOX48SVyXhu8ZD+tuZXViNKxNLVLKzBfAOd65EQ0a6pKByJkMbNhEBNwDnMQvxU39nmCkomSuruBk+LFW4U0M0mDq2Q2fHbApNK3XHimM7sWR2Wzxe+g2GtfsEY/Y8QEbGC9y/9hzmrjVQMd9kpuLa7nO4oyXzyoWdNCMjVpRpNZp+Au9KtMTs3bPgKn2Wj/8ZolyvO2aeeIUSLb/Hjtle6rWmFT3yK0/1unrfS+X7ldQIQMvqcG9EqgxXsH3fVSSIO6t0JF4LxN7LstsGatUKto7lAUTjSFAY4tIEQHiFm9s342915fvpsYg4JRHOt2hbH1VpKyJIVhk5BeIKRiG8xtOnssL6dCRGH4F/wBkAJeDQ2AlEnbi9THyB2NhYPCXrCTEvAykPj2CByNBKof6YZfh9clNYSxeQWd0JSHvxGI8TZda0aXGI2rsR6y4kArbN0MChsDX+MpAYegYhmdsbUxtPdB78A/bfPYe/JtfF6e/X42RiVTTrUQ9JwddwWxToZw1Iw4sy8PRpBfOrP2PizC0IiU3NrJ+TBg0bBZCCqD++Rr+jXtj6+yT06OKZuUXWvCUkxuB2VDl086kLq4wIbBr5JY55+2H1pL7o7GmrRKVHvh9N6TGFlWdrdDN/jpAr0bkPBsxboa1nGflO+D4TAZk9YCFgYlINn4wbgk2nFuPGyqHoFtkbnas9x/G90TBzLwuEyP5cW8ClVTtUW/UbolcNRrugRnBBJM4me6F/pyrYul8NeovXQMMeTsCGk1j89fd45G2LlBvHEYzycAIQqaqJ1FvY+PEXOODQCE7WxYGUxwg5fUvcwharMw5zetfKlD+l43ngHHhP3IfSE3bi/CRPFE+/jg39xyDgUTpQ1h1OxUOxbbmM8lfFlhgywBMfkdTv/nZ06/knKnp7oLJZOuIiL+LKgySgWD0M+XkQGprn4oSqqM7ns1TEXtqAuf/UxoI5wOuTBxDq0R4trEwB0zKoVM0CcLRDZQtzcWv68aJpmLGgKpZM7QpHCyApIQFStiQSIt26XbiF2EG1YPNfCA6cuY1UPMDWwS1xffYu7OzdGV84/40Vm6ehz+ZpmfSbo9aEAGzzMCX1QC1SIh7ffgikJiAhKQMw/w+h56nfh7j94CZOxljDu4WdEoZ0B2cOXsEn9k1hg1hcDvgTB1tOwv9Ilph4Hbej3iI17jXod9U89hou3E4AoqLxMOIcYj5wh4dCarWgx8oTA79pgb2zf8BCu0X4tnstWCTewu7Nl+A9f7VkThT2xZmFu1JDMVjWH4E1W+bhc58aeB24H8ef1cRQ/1WY0ryC3GyYwqLRCKxZ9iV8nEsjPvYVzJpOxB+bp6GHg6VcWWW3ZdBs8jIsn9gZtnf3Yv3u60DzmVgzqzuqKKsizX9XClW6tkW1pGs4FhiIY+fewK7TIEz+eTP+3TYBja1FhRFp6Zz/hTSkvsncBr84g63LlmHFUpnPsQdZ0kPTCm7o51sP5g/O4VhgEMLghu6jf8C6Q+vxrXdFxQcuOXtT/47MpLrVgVO7ObgmMpaGEuG8qGZBag+14O27FWVb1wWJ32FljteX/oeNonpDPQy/3BABawbAkXhcpY6YuXkaPIOnoUNdL4zw24mLD97mlDGaOqLXou/Q5MQktKjZDbPOf4gWXg4o6fwpZizfhFWDasHUoiHG+wdg9kC3zHHYoM2EJVgyvD7MSS2kZnvRrCtp8xB4dgtAREQAergNwdakJFyb3R4e04/iUdAseMiMyW36dXiMnYmBWI0+RNvSa7Bs2xqetPI5/gC2ntWVMDQioQZcqlzFzLp2cKjZA7+n98HWn7tKLD2smuHLlQOApX3g4TIcy25YoY2PB8yTQnE8ohQsTo6A5+A/kITnuLhwEHxFVRZqsxxaaEyPFWoNXoid633w9Pv28KA58t0KDFyKRd2rqaA/E8b3+J8JHYEW+fiFh9g7qge++rcsRmzbgW8ai1+pIieLCdAMAdJNU2x+pVk7RVOa9OjmwHvwHXx1ZB0+l5EtFg093Ku2CBTySo3EHS8RGy9zSIC3iAn6E+sCXwDlW8DLRfa0R9thcT1GgBF4XxEoXJkaoRx/EjO9liClX3t4liuJ1CfnsX3HJcSjCtp90xeNLAufz76vk8/jZgSMEYHC334m3sSe3/yxJ+g4Tt96ARSrhvrdO6Nb117o2qImLApTLm6MM1okY5Ju3UieRMkcrnQIoEz3rEhoVNXpcwRN74Vhmx9kFmL3S6rQ0vdnhc/U9B0Rpo8RYAQMGgHe6xn09DHxjAAjII8AMzV5RPieEWAEDBoBZmoGPX1MPCPACMgjoMdMjfxPHcDG6b0y/XHJk555nxiFoF1+GFFvFoLYc4Hot+vJnklw67AcIfkyYVKCN2czAnqOgHZMLVMzXXSil6WNThrpEmeCu4Py78guI2oLRvf8EvM2h6uA8DmCFgzDsMnLcOytimIG/0jqYLEbZgc90c5yqIAwkBh4k+NGeYeJyjqUjkXyvuR8hwZiY1SKsoqczwiohYB2TC0zgEfkEfJ84IUZR25JfHJdP4R5NkGYMngQJufwQqoWLTkKkauWnWL7ObLlbsqh1Q//4qC6nhLkahvOLRnhP0DPgFWY2apSThOZjEc4eVLG1xdKolJ3P4QdHAdP0Q9XAY4yMQz7jpjC9/dzuE0G7x2eYEa3X/NYMWe6LVJElrsPmtlnewlRVITzGIG8ENCOqSlr1aIWus1dhBnur9mRnTKMtMl/HYX7tb7G1/IMDeTNYi/+upvDjFybHrSok4K7Iclo+GnjTIeKNmgw+FN0A/n6UuGU6fVNhJacidN3pc4pJc4xQwK+QL0eTWGv2zdSi3FxFUNHQPevkGlZVHctByTdwf2nRfFlM/QpUUC/VVN8/lkd5DIgSwzGumnrEaOgSsFnmaFmi8Y5QvplPL2H69V7o0cD5W5xMpKqoOtkqbfcTCozorDb7y46e6kyNC/4EXEPxoGA7plapgNBmNujesXiyA6ccQgRl1ZjhEtTjJBuTUnIHyAN3EHyuOU4lhXEQgbgjEcyAT7yCKCRVe01oo4uxwgXqaxPpm3Zw4X4J5IAGaJM6EcExaYiI/YSNmcG3nAbthkRMgJ32WcUVKTT9D2ZQUKyOpa5kD3suICIzCAmYhCQTZcQK7rVyVCBkYJgHdJ6iZewxHcwVtyKE71VONXIDGYiOzbZgxP54CbLzmX2n0muunMhM7rsS0mAkFkLn2KC/0iV215Tm5qoKbctzrhzDv9U6oZ2vPXMhpSvtEcgP6EaJEE0mgjDpYEg0mOES0uHCa7VXYSOiy8KCTkCZ6wSLsU8FYIX95M8S6fAHR2y6yaEC3umUZCLUUJAOAXTEDKDdLgIHaf9KQSLgTmyg0+M3n0/M5hHZtAM55nC8VfS8B5xQvDSucKyixSog1JmoAuxzFPh+LQWkiAbzsMEv93BkiAbCRQkw0WgAB+7jkeKgS3SYwKFWe3rZQcOSQ8XArq2ECR9pwsJ4ZuE4XKBRcTuMv9I8KHAIS7Cx0NXCCfEMUiDhDSRtKMCo1cUICULD0kgDleZ4CKCSI8MfcIzmbHJ4CGOracw6/hjEY/0x7uF0bJ0qzEXsuPKcS1Dv331rsL03eEaBgWh+RuXHawlR+N8wwhojoAOVmqxODa7s8TfU82m6Lca+GLJJqyf0BAWVq0w77w/+pMLb5vacLKpAM9JW7F/Un1kUOCOEw0xoKezZFtF8rip0zG2+kn8uikEss69SzrUh4cNRQOg4BPjMGVgSRz2P6bcBfTrUOxevQFLfZvCSTyddUen2YeQJPp2N5U5XKgEjzYeEpmQhR086pdD0jNr1G3hKNJkWqEK7Eq+xR3RP730h6MkypY2lwQAcWwIL8cPpA9y/Rf90odJxm/u7QNvcQwlYdNqZPYYLJRh1DBzu1kB1W1p41kSNnXcYZ8ruIhst4oOTiTBTTbXH4fJmTI5U5sm+GJUC0B0dpgZREXNuZDtTbymOb4Zjcjz2zF7ILB14mB8Qy6/cxVUkpFxH2f3lWdPrkrg4WzNEdCBlw46/dTU/1TmCZjjEFSW3YpIGQtFEvqmBVooHI8FKjtUBXZF43FiBsQ4IDnKZQatcJyFg7sHiw4NczwWb7RUGxBPfY9QNA+E7NuGk3uXYMXVt3DtkbsH1TlyY1BSOEewjmOhuLDmV1xDOdRVUl5xtgTrVLTOfmxqgwbjV2G3mPMcQRREJY+5aEXeb1UkU5uGGDh3EdKv9cSvl+8isXs1iaNJFXXokbj1dG6O9Xm0n0cz/JgRyEJA9ZuaVayALqIkjKlAWr8aiLN3tGReSgkid9erMaL+DJx89xFazF2DGe7KV2pKm1H3gWywjmIeGL1kitbBQ/KMJ6CLuTCtLsYuUHd4FEvgzpkQ1Cb//+pX4pKMgEoEioipZQbcSLqO0NuyG00JreY9W8NT6S83+Xt/ilrDO6OBwjLSoBVnMG/8DzmjayfeQJAqdQOVUAGiQrDvaXhtX46JPdvD00ZbhibxWa96nJoG61BGfOaq8NZqzFjwP5lDDWlwk9KS4CdazYV8nzSuBHg3qJn7pFa+KN3z1lMRKpyXTwTywdQyMgNtJCMuQdMVkSmsGvTBVz5PsGKaH/aKJ54ZSIw4hC37PTFvTDPxl9u0Yg3UNQdSbwcjVIw09BpRe5bj5+BWmNLfXfkXx8oDPYZ7Arf+xOyeUrka+Xg/BisnrYLj0TcQiY+jcQfS8aYiNjQYt1NJ5haNiJPncFepICkJd04fz4yWRKu9v3OMU/EcygXryIjNDB5CpeNwNSgsU+6YKfNLDMM/QY8UyLLM4Nh7AsY6AxGbJ6FDXfvMuASu6Hu8JJysiqs1F7lozHiAvaNbotN0aRSoVMQGrcHSWF9M8KmSpSCc8WQPxrj0wpKQ3PG7pFvP3D9gqWBTr1yIc4a6CGh+tkDHknQK6CI5QaxOp3s1BPuu/kKk9PAxs9Hs078agr1PB6FjT7kyCZHC0cV0Wio5Iew4zV84Hik5+ZTSlR4TLOzJKtNEGL74sBCZIO1I5rRPbONTISAyWVI1PUYI/mOa0DGTPtehy4Sj1HYu2j8VAsKv5BwPnZI+DBSmO2eOjdqgvLiHwvGZXcXxStq7IzltbD9T2CNHt5R+QTwddBG6L/5T2DC0iUxd2RPezH7kMJKcvhLOmeOOOZ95QrtJCBcxkJ6kuggdZwYKMenK8UiPuShsotNlEY+uwnT/4zI4CoKgxlxkjUm8yDxRzsTXXvYkWaag5KS1p+AXHCeTS5d06jlNQT49yzzpbb9MCM6aa7nqfMsIKEGAnUSqy/21Lfc6CDOafInr3xiSJ1htB8v1GIGiRyAf28+iJ54pYAQYAUZAHgFmavKI8D0jwAgYNAK8/Syw6ZMPRgKYD/TH6R9asfpCgWHODTMCADM1fgsYAUbAqBDg7adRTScPhhFgBJip8TvACDACRoUAMzWjmk4eDCPACDBT43eAEWAEjAoBZmpGNZ08GEaAEWCmxu8AI8AIGBUCzNSMajp5MIwAI8BMjd8BRoARMCoEmKkZ1XTyYBgBRoCZGr8DjAAjYFQIMFMzqunkwTACjAAzNX4HGAFGwKgQYKZmVNPJg2EEGIH/A3UTSddOHLo8AAAAAElFTkSuQmCC" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Problema Prático 3.7**\n", + "\n", + "Use a análise de malhas para determinar i1, i2 e i3 na Figura 3.25.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Problema Prático 3.7\n", + "Corrente i1: [[ 4.63157895]] A\n", + "Corrente i2: [[ 0.63157895]] A\n", + "Corrente i3: [[ 1.47368421]] A\n" + ] + } + ], + "source": [ + "print(\"Problema Prático 3.7\")\n", + "V1 = 8\n", + "C1 = 4\n", + "\n", + "#Supermalha (Malha 1 e Malha 2):\n", + "#2(i1 - i3) + 4(i2 - i3) + 8i2 = 8\n", + " #2i1 + 12i2 - 6i3 = 8\n", + " #i1 + 6i2 - 3i3 = 4\n", + " #i1 - i2 = 4 => i2 = i1 - 4\n", + " #i1 + 6(i1 - 4) - 3i3 = 4\n", + " #7i1 - 3i3 = 28\n", + "\n", + "\n", + "#2i3 + 4(i3 - i2) + 2(i3 - i1) = 0\n", + " #-2i1 - 4i2 + 8i3 = 0\n", + " #-i1 - 2i2 + 4i3 = 0\n", + " #-i1 - 2(i1 - 4) + 4i3 = 0\n", + " #-3i1 + 4i3 = -8\n", + "\n", + "coef = np.matrix(\"7 -3;-3 4\")\n", + "res = np.matrix(\"28;-8\")\n", + "I = np.linalg.inv(coef)*res\n", + "i2 = I[0] - 4\n", + "print(\"Corrente i1:\",I[0],\"A\")\n", + "print(\"Corrente i2:\",i2,\"A\")\n", + "print(\"Corrente i3:\",I[1],\"A\")" ] } ], diff --git "a/Aula 5 - An\303\241lise de Malhas.ipynb" "b/Aula 5 - An\303\241lise de Malhas.ipynb" index c340bc4..587c268 100644 --- "a/Aula 5 - An\303\241lise de Malhas.ipynb" +++ "b/Aula 5 - An\303\241lise de Malhas.ipynb" @@ -23,7 +23,467 @@ "![](http://i.imgur.com/3Gu3UOb.png)\n", "![](http://i.imgur.com/V5yAmq0.png)\n", "\n", - "**Malha é um laço que não contém nenhum outro laço em seu interior.**" + "**Malha é um laço que não contém nenhum outro laço em seu interior.**\n", + "\n", + "![](http://i.imgur.com/eihmMJc.png)\n", + "\n", + "O sentido da corrente de malha\n", + "é arbitrário (sentido horário ou\n", + "anti-horário) e não afeta a validade\n", + "da solução.\n", + "\n", + "Etapas na determinação de correntes de malha:\n", + "\n", + "1. Atribua correntes de malha i1, i2, ..., in a n malhas.\n", + "2. Aplique a LKT a cada uma das n malhas. Use a lei de Ohm para expressar as tensões em termos de correntes de malha.\n", + "3. Resolva as n equações simultâneas resultantes para obter as correntes de malha.\n", + "\n", + "Resolução para a figura 3.17. \n", + "\n", + "Malha 1:\n", + "\n", + "\\begin{align}\n", + "-V_1 + R_1i_1 + R_3(i_1 - i_2) = 0\n", + "\\\\\n", + "\\\\(R_1 + R_3)i_1 - R_3i_2 = V_1\n", + "\\end{align}\n", + "\n", + "Malha 2:\n", + "\n", + "\\begin{align}\n", + "R_2i_2 + V_2 + R_3(i_2 - i_1) = 0\n", + "\\\\\n", + "\\\\-R_3i_1 + (R_2 + R_3)i_2 = -V_2\n", + "\\end{align}\n", + "\n", + "Reorganizando as equações, temos:\n", + "\n", + "\\begin{align}\n", + "\\begin{bmatrix}\n", + "R_1 + R_3 & -R_3 \\\\\n", + "-R_3 & R_2 + R_3\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "i_1 \\\\\n", + "i_2\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "V_1 \\\\\n", + "-V_2\n", + "\\end{bmatrix}\n", + "\\end{align}\n", + "\n", + "Note que **as correntes de ramo são diferentes das de malha, a menos que a\n", + "malha esteja isolada**. Para distinguir entre os dois tipos de correntes, usaremos\n", + "i para indicar correntes de malha e I para indicar correntes de ramo. Os elementos\n", + "de corrente I1, I2 e I3 são somas algébricas das correntes de malha. Fica\n", + "evidente da Figura 3.17 que:\n", + "\n", + "\\begin{align}\n", + "I_1 = i_1\n", + "\\\\\n", + "I_2 = i_2\n", + "\\\\\n", + "I_3 = i_1 - i_2\n", + "\\end{align}" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exemplo 3.5**\n", + "\n", + "Para o circuito da Figura 3.18, determine as correntes de ramo I1, I2 e I3 usando a análise\n", + "de malhas.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exemplo 3.5\n", + "Corrente I1: [[ 1.]] A\n", + "Corrente I2: [[ 1.]] A\n", + "Corrente I3: [[ -2.22044605e-16]] A\n" + ] + } + ], + "source": [ + "print(\"Exemplo 3.5\")\n", + "import numpy as np\n", + "\n", + "V1 = 15\n", + "V2 = 10\n", + "\n", + "#Malha 1:\n", + "#-V1 + 5i1 + 10(i1 - i2) + V2 = 0\n", + " #15i1 - 10i2 = 5\n", + " #3i1 - 2i2 = 1\n", + " \n", + "#Malha 2:\n", + "#-V2 + 10(i2 - i1) + 6i2 + 4i2 = 0\n", + " #20i2 - 10i1 = 10\n", + " #2i2 - i1 = 1\n", + " \n", + "coef = np.matrix('3 -2;2 -1')\n", + "res = np.matrix('1;1')\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente I1:\",I[0],\"A\")\n", + "print(\"Corrente I2:\",I[1],\"A\")\n", + "print(\"Corrente I3:\",I[0]-I[1],\"A\") #aproximadamente = 0" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Problema Prático 3.5**\n", + "\n", + "Calcule as correntes de malha i1 e i2 no circuito da Figura 3.19.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Problema Prático 3.5\n", + "Corrente i1: [[ 2.5]] A\n", + "Corrente i2: [[ 0.]] A\n" + ] + } + ], + "source": [ + "print(\"Problema Prático 3.5\")\n", + "V1 = 45\n", + "V2 = 30\n", + "\n", + "#Malha 1:\n", + "#2i1 + 12(i1 - i2) + 4i1 = V1\n", + " #18i1 - 12i2 = 45\n", + " #6i1 - 4i2 = 15\n", + "\n", + "#Malha 2:\n", + "#3i2 + 12(i2 - i1) + 9i2 = -V2\n", + " #-12i1 + 24i2 = 30\n", + " #-2i1 + 4i2 = -5\n", + "\n", + "coef = np.matrix(\"6 -4;-2 4\")\n", + "res = np.matrix(\"15;-5\")\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente i1:\",I[0],\"A\")\n", + "print(\"Corrente i2:\",I[1],\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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atWsZVB/Jt5MJSx4RvlcZAbJLubR2Fv/oV5zexztx0hft27dDs6a2ev/F0P7erzTEHN+Jy+2n4GNbzUaZ//77r4i/mVnuS+Eqd4iCjNRHnTp1EP8MsY/km8SEJY8I32uEgKEuk9NpEXRme9FDGmL8dsKn6hBMa1cLRsJTXDkcCcsB7VBbjYGWNNpTe5uFCg2Q+oimwjdv3RK3Mjg7O8Hezs5gbFlMWCp0NGdRHYGaNWvi3R7d0dm1E0Kvh+HoseNiYbq3sGisdytRLVq0AHm6KVpIR9y5VZg8cQNuZXyDn0RhddF//T54qkFWVIz2hdFeKF0GWn2kv3Zt2+D2nXDs238ANKWnDbxEavocmLD0uXfkdUt/gtC/tmGlV0XM9J0FZ5neE5JuYv9yT/wt2MIOkbhm1BPz5g2GnYny44KFpDs4/tsWbPnjFsy6dIS9aSJu+l1CjM1gTP94HHrbVpNxpyWvTMH3NBVxdGiBaqamOHjoL5w9dx5pr9Pg0KJFwQWLOZX2PdFeLDolQfMpYgXUdp2Lw5Fzi6Q96UBH3EyYML5IclQtTIsjsn2Ukq+P0hB7eQe+n7cSR+4nA2YdMcVzBWZ3q6/gVFcBqTe3YNyAa3A/vxKD6so8nHIKFem5E0pRGD58ZClqTd6mZD4PEfZ5/yIs+7/WgpXTSiHwjUx65mPhxNz3BLflF4WXmYIgZD4TLi8fLLSb+7fwhO4VhMzn54UVfVsIzcZuEW4kpufmyEwQbvwyUWjWZIjw7dlYQUnx3PwKrhITE4Vz5y4Ia9auF/btOyDcuROuIJd+RKWkpOiHIoIgBARcFfr3HyjcuHFD5zpRH/n+cyqnj+7ffyBXZ6aQcmOzMH6yl/DXuSvC5VN/CMvHdhSsmnwgrLv2Qi6vIGS+vCJ4DWghWDWeIfjEyD6cebMW9blDXnGGfVeaCSurZxKFwJV95AgrU0i7tk54r/FQYd21xOwOVBQn27fPhHNL3hOsGg8WPAPzP3xCWoiwzs1GsHJZIpx+LkNmsiIUXD9+HCMcOXJMWPHDSvHL8OzZMwW5OEoZAitW/CCMHTtOWbJW4omY6EeEfkyIsIi4FIdnwrkVPwknnuSST+bD3cL4JlZCl7XXhDxPReYT4dy384RvFo8qhLCK/twpH7fJDeP4Vl8RSMODoAuIrGgLm4ZVs5U0QqWGNmhZcR1OBkVjqmNT0Q1WTgtehuL4H+GA6US0aabA6XslS7i4WQIb/sbRq1PRrWednKLyF/K7plu2dNTrne3y+uvLPRn+pRNPta2TfB/R2weF7mwXjPD2u8PQunYuRRiZW6FltXKIqZQbB6Qjzncr/mo+EdOxBtsKUl4Lz51szQVVxWl6i0ASou8+Akxa421Z9+ymb6OeSTKO341BEpqimqz+yQn4j7Yemb2FqpUUWYXLoUIlsn2lIOGV8iNi6ItAZ0lFP46BVRPLwr8EsjrwNbZv3wE7OzvR2E2epWnFknwXajNo3EdGZmjmnHdrhRAfi/tJDhjYrlHW+5MQkP7oKFaedcDMRZYw+qsQzbXw3DFhFYKx/ien4kWs8gPkkmMTQNyUh7Cq1UZDGlilv0LKawGoIE9amUh/nQHAFO/UUL5bmwzr7u4fiO+90TL5qtXrYGjL5CXVv7S1gFzYUyBfhdLoSnPDv+KWyPYRvVQt9VErp5agFV3VwxvEnj+JwKFT8JVD9h6zN3exe+Ud9PpyNswrAIU6K9PCc8enNajeY3qasxKMzaSpYH4VjevWQNbrtDJpxg7o96ETkBiIgNsKyC4lAhdORAEWAzDApfCHmpbIaSsDvfJRvXp1cZl8584/xAPiZGrlSxkEduzYkXO3f/8B1K9fT83z5HOKq3RBfdS3b2+xj6pUroKdu/7E/v0+KveREHcaq/9ohB/nv5u1r0xIQOiv2xE32gNdZaaNBSqjheeOCatAhA0hsRosmlsCSU/wLJFGRdkh8RkeJxnDytoc+fdcV0OrSd9gUa+n2LBwPfxi0qRSQHo0/H78DhsSemLR+kloY6L6I0LL5LTz/eOPponTHNr5vnbdBlwNDDKYA+JygdDdlWSvkq0hOvqxOEWUjdPFNfUR7XyfPGki6MBA6qPNW7wL7qM3d7F/7R308pyOdpJX7Yx7OLVpO9YMc4aNhSWsLWzgOuswgMP4rL0NrD18FIy4iv7cqf406gI9lqkFBCqjsXNHWL25h/uxufamjNj7CH3TDD2d6+c1uCMDccd24HiKPcau241dH5rinzkjMetoDBB/GosGfYV/ao7BriMrMdZeQMDanbguw4OqKkwbEGm6+F5PN1y6dFncVU2vhnAAyF6lKNAUsbhcfdFUUeoj2tR7+vQZxX1EP2Bee5D8/lh0Nc8+Kic1BvefNces4CjcvS/9ReCc1wAAA/DTpQjc/XUw6uZppHaeO7Zh5QHVEG+MUMlhIGYN2oeVx29itF1rVMVLXDt+DM8HTcQQyd6Q0zQBGWnXsWXFI9ypl2WfMjM3xVOyWaW9QFyV2rB5fR/+u9bD//W/OH+kIb6YmlNY5Qvp9Q86yoTtWrmwKRpdUSoZ3N3dR+l0WpirRdYV9RHZtW7cvCX2UT67FpHV9wvxZ113TEqNRLB4cnMaYnz9kTpqNizkBRZ4r53njgmrQJD1KDH9KSIun8HRc4+BpGvw/ycApq0dYVOrMmDUAL2/W4Pk5Z74ZIG00/3/sO273jCXt6eLTUpB8J7dCM5pnhl6dMq6yQjci/WBOQmA2UyZm4IvaUXq/v0H4jTjeXy8+BK0IR9lUnBrNUv18lqdryB5y5k0yaNYHMlKfURvHlBQug1FeIrLK2diyuYgZOA0TspoXXHgOvg30ORAxqI/d0a0aUxGF4O+HDHifezZ86dBt8EQlafD+65du47gkBDx8D6yjej7O2klgTPZi5Ys+SanahpVzZs3F/b29jlxurooLX3EIyxdPSFlQC79Wvv6nhKnFPXrmcN91PtqLpWXAZBkmkj7rqQwcuQIjBgxvAjvL0qSCv4kojpxwheR96LEvXKGdMCiopax0V0RKhynEgJkuO3SxRUdO7QHTQH9/PxVXiZXqYJSlIlGV+T/kBzGrl7theLyxUirgu+95ybaqOjEUSIvOiXWUANPCQ215/RMb0W2EToJgEitrAc6hWHKlKnFblSXx536SNZBiL4e+SOvt+w9E5YsGnytFQRo9enixUs557zTuUv0S19WQ0JCgth0XRzKpymmsmfx0znvLVs6GEQfMWFp2uNcrlAEyH5CjlQlTzr66Ei10EaU8gySJx1D6SO2YZXyB7Ikm0eOVMlJJwVypKrvTjpLEquSqvvp02c5ffTOO+/ofR/xKmFJPSmltF55O4lKR5mUUiz0tVnUR3R89bVroaKKZMsq9LgZPWkME5aedIShqyE7tWhiaYnS7UjVMHtL6iN2pGqY/cdaawEBeSedhr7PRwuQ6J0Iyb0XbT0xdEeqbMPSu8fLcBSiqcXLxETEJySgatWqopNO3sagX/0n9RGRFXnGMXRHqrxKqF/Pl8FqIz/SoiNMOOgXArIjLXJ2S0cBGVpgG5ah9Zie6kvvDtIf2UmWLf9BPHNJT1Uts2pJfUT75H78caVBEhZPCcvs46ubhtOxu1H37ulGOEvVCgJ0+ujDhw+0Iqu4hTBhFTfiXB8jwAhojAATlsbQcUFGgBEobgSYsIobca6PEWAENEaACUtj6LggI8AIFDcCTFjFjTjXxwgwAhojwISlMXRckBFgBIobAd6HVdyIc336jUDqdfwydjoC3Hdh0+AGSnUVku7g+G9bsOWPWzDr0hH2pom46XcJMTaDMf3jcehtWw0K/X8olcgJqiDAhKUKSsWQh9w/0XEsz549zVPb22/Xwttv14SlpWWeeL7RAQJCPIJ+/hY/XnmFru7K5QvxF/Dj6CnYUutT7Dv6P9iblM/KPPcFbm7+DMP6jEfQtg340vUdJi3lMGqUwoSlEWxFL0TH5gYEBIhORv39z6oksF+/PnBxaSN67K1SJcunoEoFOZMKCGQg/oI3dry0hgsKcvj6HBfWLMHGG9b4eP+wXLKiGoyqw37sDMz4cwRWzt6ITie+QjfJU7IKGnCWwhFgwiocI63moONyDx/+C+TllwI5JZgwYTyaNWsKM7OaoF3IskEaed26dUv093fkyLEcp5tdu3bVudcVWV1K87UQdwqrDlth9keWWLrlmPKmvgzF8T/CAdOJaNPMNH++SpZwcbMENvyNo1enolvPOvnzcIzGCDBhaQyd+gXJDfnOnbvw/Hk8yM2Tq2unQqd6NBWkPxeX1qKnlZs3b+LIkaNYu3a9KMvDYyI6d+6svjJcIheB9Cgc+ikQ7T6ZjYZGBZAVlUhOwH/JAMzeQtVKiqxU5VChEk0RU5Dw6nVuHXylFQQMlrBopBIaeh3Xr1/H7du3RY/DhMiAAYPQsWNH1KtnjubNm+vF9Immf2vWrAVN/cjL7+jRo/ONpFTtTXK6SX/Dhw/D1q3eWLHiR3FaOWPGxzzaUhXEPPlScG/3VoT0no5F5pWB2DyJ+W+q1UZDGlilv0LKawGoIE9amUh/nQHAFO/U4Gl7fgCLFmNwhEVTpN279yIsLEwcodjZ2aFDh45o1KiRiERaWhr+++8/xMTE4OzZc6KnXfpyDxo0sFhcgct3B70ZP3/+fHFUNXfu51obDdGo65tvloBGbTTaSkxMxJdffsGkJd8BBd5nICl0J9bGDcCSUXVVM5AbO6Dfh07YtioQAbcT0cm5Wt4aUiJw4UQUYDEZA1xq5k3juyIjYDDnYdEo5a+/juDgwUMYNGgQOnTogMqVKxcKwIsXL+DrexLnzp3HpEke4gin0EJayiCRFYnTpUtyyQV6q1ZOekFaI0a8jz17/tQSiroUk4Qgz5EYueqWkkoG4KdLKzGobt7fdSHpOrZ/Nh3f/dsPG3+djW40MqOQHg2/72dgio85vtr+P4yxr64aCSqpXZfRhtNHeVEwCMIisvr22+/E0cOoUe6oXr163laocPfw4UNs3rwZbdu2wbhxY1UoUbQspPP//vc9Hjx4gGXLlmk8BVRVC30iLUP9MohYx/pgcvtvAK9DCvZhZSDu2C5cdRmFPmZPEHRwPw4cOIFE95/h1eE2Fo3eBqHvIAwZ1hfOdVNwZe1RVJ3mDofsXQ+q9mVx5DPUPtL7ne4SWTVs2BBTp05TQlaZSI44hT98I0D2UEWBpoxffvml6CNv27bfFGXRapy3tzeCg0MwY8YMnZMVKU5G+cWLF4l17tmzV6ttYWESAgIy0q5jy4oV8FrzB/wfvoaZuSnSyGaV9gJxVWrD7PV9+O9aD6/lS/HD7id4I0hl+VMbCOQd62pDopZl0MiKyGrYsOEFSBaQHB2Mv6+Wg5ubDYyV5KQpJBHImjVrsG/ffgwbNlRJzqJFZ63kHRO3KxCRFFegumj1kbZMqLICWVx6la56UhC8ZzeCcxplhh6dsm4yAvdifWBOAmA2U+aGL7WBgF4T1vHjfyM9PQP9+w/QRltFGURakyZNwtdffw1n51aFbitQt2IaEW7c+Iu4v6pv3z7qFi9y/hEjhsPX1xdeXquxapVnkeWVOQF1B2PT/cFKml0BdQevxt3BqxWkNyignILsHKURAno7JaRtC7//vhNjx45VybiuTuvJBvbBBx9g8+Yt6hRTKS/tXr937564Z0q93eiZSDz/Hdq3/hQHH6WpVJeiTFQnjSJJB7JrcWAEShMCygkrPQaXf5mFHlaWsLawhsvIn+AXo+SLRC+MjuyMyT7/5sNGeBqKQ55T0NaC5PTG3F+O4/rT9Ox86Xga+hfWz+gJ69YTsGJfCJ5mz/kvXbokTmvq1FGyUzjjFnZOnYAJE+jPA3O2hQF3tmGOeE9xc7HzljKLFtCuXTvExyeApm/aDHv37hdHV+pPBY1QpZ4Derk2g7lJ0Qa+VDftoD906JA2m8ayGIESR0DJNyMJN7d+j62v3LB09yi8iRhjeW8AACAASURBVPSD9/INmDLFGHv+nArHqjKb5Qp5YdSoliMGzvoKwp1gfHa8Jmxcu8ChllRtBdRydEPP1ntxsNkszBrWEpWyIfn9912YPXu2coDK28H9563Iekc1A0/9vDDnUmv8ML8baikvlSelb9++OH3aT9yImSdBwxvaxkAjG9pvpX4wQkXLgViySv2Sikr07dtb3J9FI9UaNWooysJxjIDBIaB4hJV4DUeiB2DpJwPRqXU7dBs5G0vn9wRCT+BcRIpMI2VfGJWJlr80aoAeYwahFq5i9/FbkJWAzH8RcMIY4/o2yyEr+uJXq1YtZzOovDht3Tdr1kzcJa4teRcvXhRFOTg4qCkyA0mPrsDHczqGeQVCyThWLZk0gqRAbwJwYARKCwIKCUvIqAO3cR1RO2cgVQnmVrYwRSVUrJgTiZwXRie0wVsFIlIOpm0HY6JjRUSt/wN+cdKUUMDrsBPYUe09dLfI3QR6924EHB3V/dIXqIDCRLJl0R8RpDZCZGQkaPOm2iMa4Tmizh/GL6tuwN6pMXKR0Fwr0oGmhZcuXdZcCJdkBPQMAYWEZVTDBq0sZSkoHfGxj/HKpivaW2W/H5XzwmgvNKyoQqsq2qL/hz1R8c1JbD95H5likRcIOXYWtgPbom4uDyIxMQl0DlRxhHfeeQepqXnGfBpXS+8KOjk5qV/eqDaat7ZCJVjBrrGCEwDUlyiWsLNrKr7CpGFxLsYI6B0CCgkrn5bCY1w4dBeD5g5BC/ENdemF0fHoLb2WkK+QfERF1O06CCNqJ+HK5iMISREgPA/AvsMtMKJz3ve44uLixCNU5CUovy+PWt0+w1Y17FeSrDp1aiM8PFy61fiTtjNQeOstZbvAChKdhocB/rhu2wGtGmljfJVVF71vSCdDcMiLwPWwMLx+rfwkBRpxFzbqJhkFhcLqKKgspylHQAXCSkecrzf+bDIH89zMYYTcF0Y/7ZqXaJRXk5ViZNYGI8a3BCL34s9z/yLG/xiuDesNZ9O8aiQlvUJKShYBFCazqOnGxpoQTP5a6WVrCra2tvkTC415gYjgOzBxtUdj8TWODCRFncG2BePxiYKV10LFyWWQyFQuuszenjlzNud0D0Ug3Lx1CxcvXlKUJMaFh0fg+PGTSkmPyLCwOpQK54QCEcjLFPmyCngTdRjrQlzx06cdYCZO21IQ/s8+HPIciVaWtFXBEtbtZ+MU4nFqVmdYW8zEwVjJRiUv0AQtho5Bz4r/wueX1Vi/5wkGvtsUVeWyWVpaICVFO9M0OdH5bu/ff6AhyeQTpXlEcgQuHX+Dri6NISQkIv3NM8SWM4Pxo8i8CxRq1iCRp0SmahYvldmJbCicPXdeYfuSkpIQFBSCxzExoGtFISzsBqpWrYI7Skbm9ExR4H1witArWlwBhCUgPeY0vLamYuS0rjAXz/0RkBr9HPVnHMHd+1G5f5c80QNm6OF1Fnfvr873drusikZ1O+L9D6yRcWUv9mT0RZ8WJrLJ4rWpqUm+s83zZdJSRGysdgzuRVEnMzoCQYk2aFE1GFsO3sObinVg3bgmKlUsoHtUqPDff7P2xZmZmamQu2xkIaJ6r6eb2FhF077bd8Lh7OwEO7tmuHwlIB8oz58/F8mMZFy5cjVfOkVIdTyPjy90aqlQAEcqRUDJN4LI6hSWzTqEGt2tkRp+DUFBQQi6fBhrNgbhdXkZC7lS0UoSjGqj44ghsEJt9PjAFRYKNGjQoIF4OJ8SCVqLpqNn6BQHsvUUNVSpkjVOlEhCLXkVKqFq+VD4HAcGuDvmG3GqJUsmc3Jy1sZZtVctZWSUpkuJoGxtbdCypaP4orh8+65dC4W9nR3atW0jvigvb+sKDrmGVk5OIBkUHjx4mEeEbB3t27cDTS85aA8BaQdnHolC/EV4esyC940k4PJBmbS66L9+HxoUga8AI1Ry6INJPR7jrU71FJ4XRATy8uVLPHnyBEp3ustopeklnVTau3cvTYvnKSedxS6RRJ7EQm7KWbpjZ2QBbloKKa8s+cmTOGVJZTKeTs8goqLg6NACq06vQ5curjAxyRrlS9NFqS/rmZuLti6JnIi8aLo4beokUUbbti4IDAxC48ZZh0dSJNm+pDqaNbXFhp9/EclPqkMsyP80RkAhYRmZdcScI9cxR1WxBb4wqkCIkSWGb/lWQUJu1ODBg3D2rL+SUxricG7lYmy+rszOZQTTvvPhOcIWBR1FdPToUfFEhdxai3ZF+57o2OZevbRDgkXTBoiIiCjWAwtl9aXzlvQtNG1mh0ULvxTVqlSpkjj1u3btOjp16iDGkW2qs2v20QuAeLw2Te8kwiKbVXN7uxyCa2prKxrXydZFhESfZPvq37+vKI/iaHpJ00yX1s5i3M6df8D/7Fk8e5rXnZuYyP8KRUAhYRVaqhgyvPtuD4wZMw5ubj0VnIFVG66frodrEfQIDb2GcuWMxHOkiiAmT1F6h4+OdpkzR5NXc/KIKvINrQzSiII88pREMIQTR1s5tcTOXX+KhCXZpiSyIcyIqIiwaJpHoy6yWbm92yMHTiI9ydb1bo/uos2L7ileCjS93Lf/gEhYJIfsWj9vWCcll9inPv6gqAKGAguSKsV0n4fsLh99NA27du3UemV07js5cJg2bapWZQ8Y0B/bt28rukwhCf8GBSA0OhExd0Jw/d8kqHsOHI0WKJD7MA6KEahZsyZqmpmBpoKSbUqWbKiUZOuSbFWy0z9Kl2xdNLq6deu2eC9bGxGdVAfZs8iuxUFzBPSWsKhJ3bp1A40U9u3T3gmaRFZ0gJ+b27tae+lZgp9IVisGbiMTNHAegoXHgnB4Xn84NDBRaOuT6lX0efr0afHVHPKww0E5AjQqpu0HZJtq2TL/62Bk67px8xbOn78AslnJB5r2ka3r0KG/xE9FtirZOsiuxUFzBPSasOhsp88//0x0IKEN0iKyWr16NSpUKF8s57pr3i1FK0meheg1ITqxgUPBCNC0j6ZpsrYp2RKSrYvykM1KUWjd2hnRj2NAn4pCYXUoKsNxihHQa8IilWnEsmLFctAU57fffgORjiaBVhxpZEXTgAULvtJEhF6XIXdf0pL63r37xFebyDM0h8IRoGkavbSuLJCtS942JZuXpolWTSzzrBbKptM1bYUoqA75/HyvGAG9JyxSm+wAP/ywXDx5dP78eSCDuaqBCM7Pzw/z5s1Dt25dMG/enFLnu4+IinwTkv9DOrSPRlfu7qNKXTtV7XN189G0T9rKoKgs/cjJrh4qyvPee1mbURWlUVybNq0LrENZOY7Pi4DerhLmVRPil4+M8N27dxVdtJPR/L33esLKyhqNGzfOc4wybQh98OC+uKxPvgxdXV2xadPGUvvA7NixQ4SLXnT+9dct4uqWvmytkO9HfbyXN7Qr0rGwPIpsV7JyCisvm5evlSNgMIQlNYGMyN9+u1Sc/ly4cAH+/mdEg6iUTp9mZjVEgzq5rH///ZHaMYTLVqBH15K9SlJJEARx1YsMyWTs5cAIlCYEDI6wJPBpCC/vpstQnUNKbdLkk+xVisKSJd9g+fLvtb4SqqgujmMEigsBg7BhFRcYhlaP/OhKVn/aMEo77zkwAqUJAYMdYZWmTtC0LeR7UD7QShSRlTZe6JaXzfeMQEkjwIRV0j2gYf1koyIPPVKoWdNMXBlkY7uECH+WRgSYsAy0V7dvz1oZJPW7dOmMSZM8SvXigoF2E6utZQSYsLQMaHGIk0ZXNKoiL8+8GlgcqHMd+oAAE5Y+9IIaOtC7lbRjf+TIERgxYjhvDlUDO85q+AgwYRlYH5Ld6uuvF7NR3cD6jdXVDgJMWNrBsdik8OkLxQY1V6SHCPA+LD3sFFaJEWAEFCPAhKUYF45lBBgBPUSACUsPO4VVYgQYAcUIMGEpxoVjGQFGQA8RYMLSw05hlRgBRkAxAkxYinHhWEaAEdBDBJiw9LBTWCVGgBFQjADvw1KMC8eWMQTomOm7dyNET8+xsbFi6+moaTqip0GD+uK9o6MDGjZsKMaRgxRDDnTQoyEGJixD7DXWWSsIJCQk4PLlyzh69HjOyRf0fmaLFi1E+XRMz5Mn/yExMQmJiYniuflSxf369RE9fBviMT70Lir5Orh69SpcXPK7LpPaqI+fRoKhUq0CNMviiaMKYCjxKHLHTiMQcnsl73i0xJUDRF+XR48eE53pkj50hljPnm5wcHAo8MQLeo+TXo0KDAyCr68v6Ax9Qzt/jMiKTqMdN24cDh48iE8+oZfnDYe0mLD04RtUynR4/fo17oSHi67dqWnkgJR8+umDI4abN29i+fIVItnQsTzDhw/T6L1MIq8zZ86IDlGIuGjENX78eL1+GV0iq9mzZ8HRsSXI9d33339vUKTFhFXKyELfmkNu4E+c9BXV6tq1Mxyyp1sloef+/QfEURXZpWbNmqkRUcnrTcQljdZILrmhK8hlmHz54rqXJyupXkMjLSYsqef4U6sIJCUl4dq16wgOCRFduLdo0Vx0P6bVStQQRgce7t69R2cjIWnkRiotW7ZMr0hLGVlJ8BkSaTFhSb3Gn1pB4MGDh6KN53FMjOgtuV3bNijMZ59WKi5AiERWdIbYmDGjC8hZtCRaaSRnthT0hbQKIyupxYZCWkxYUo/xp8YI6LPN6uzZs1ix4kfxwENdkpUEnkRaNWqYiW7WSnL7g6pkJeluCKTFG0el3uJPtREgovrn1Gls+mUzroeGwe3dHpj44XjRTqUPBnYiDyIrWskrDrIiAMl+NW/eXHE10dvbW21MtVWgQLJKjoDvH6cQkZyZp7o6dergiy++wKpVa8QtD3kS9eSGCUtPOsIQ1SBSsrezE6d+0Y9jcDcyUvTIrS9t2bBhA2hf1aefzi5WleiQRdrDdeTIMZDvyOIOBZIVKZMcjat/ByM6Of/mUX0nLSas4n6aSll9NKJ4t0d3TJs6CdWrV8fRY8dB+7BodZBGYCUV6EsbHBwiuj6rUaOGGmo8x/lveqPtNB88yjsAUUMG0LdvH5EsFfmOVEuQmpkLJSsV5OkzaTFhqdCBnKVwBMiw7tLaWZwSkhefsLAb4lTx/PmLoBXD4g5kaKdtBur7aayKeo6d0cnBHCZGmmtNtisPj4ni1JBWEIsjaIOsJD31lbTY6C71EH9qHYHnz58jOOQagoJC0NzeTrQlFcceJbJdTZ48BXPnfo7OnTtrvV2qCqQ9WlOmTEWHDu0xdepUVYtplK9gskrGrZ1fY8XJOKWyK/eci3Xudigvl0PfDPE8wpLrIL7VHgJpaa+RlpomCqxcpTIqV66kPeEFSLp48aKY2qZNmwJyKUgSkvDo8gF4TfHAqqBEBRnUi6JRlpubm2jLIvLSVSiYrKhWY9i5r8DWrVuz/n4Yh6ZogXE//JoT97MCsqKSRR5ppV7HLyM7Y7LPvzLNT8fT0MPw8ugMawtrtPXwxKHQOOS3qMkUyb5kwsqPif7GpD9BqM8PGN/NC0HpsmoKSI+9iF9m9EJTC0tYW7TF+ytOIya94EdASLqDY+vnYUSXgZi8YBm8ln+FyX3exYCZa3As/KVKD5CsFnRNdiuyX23e4i3as+q8UwefzPxItHPVrFlTPrtO7s+c8Re9Yau7pUB4dhcXDntj7dn6aGn9llZ0o/cpKdA7iLoIhZNV0WvVmLSEeAT9/C1+vPJKTokKqOXYE/1cGwOwh/t0Dwx0rA1VZuB8WoMclPp6K8Rfw4FDAYg4+SfOvfg/zJRVNDUMW+fvQvKIhdg1Og2Rfjvww/qZmPrWb/jjo1aoKps3+1qIv4AfR0/BllqfYt/R/8HeJHsyMPcFbm7+DMP6jEfQtg340vUdlR4k+Z3tnV07lcjOdhrJEDn07dtbQasLjjKq1QzO1qaAQ1NYmGrnt1xyy3b79h1I1wVroXpqcZCVpI1EWqq/e5iB+Ave2PHSGi6IkMTkfgpxuHnxNmDcD05q/Dhop1dy1eArHSFgZNYSQ8d9gJ6t68jVkInEwDN4/H9fYGY/Vzi3excj5i7C3G4VcWPXBdzNkMsu3j7HhTVLsPGGNaZ8MiyXrCjNqDrsx87AjCZh2Dp7I87EKxSQI5R2ttPxLN7btiM1LRXuo97H0KGDS4SsSKmYmBhRN1tb2xwdVb4QohFw7Cas3ZzQUJWfexUF0z6wyMhIFXOrlq04yUrSSCItVfZpCXGnsOqwFWZPaAOFY9XESFw9+wwV3dqhuRo/DkxYUm8Y7KeAzJpdMa5z3dyRkFFtNGlZFzCuBIVD6JehOP5HOGDaGm2ameZveSVLuLhZAnF/4+jVZ/nTs2No+vfvv9G4FxUlvi/YsEEDFNe0T5lSKSkpypIKj0+4h5AgM3SyN88yPqdH49yqTzH+w2HoZjMU356ORp6ZeOESxRympqbieVoqZi80W5HJqlY3zN/6GbrVkjexF1q1ajat9Cgc+ikQ7T7phYYVFckUkHwrAKeSTeDUvilqqfHjwISlCE+DiiuP6nYOsKgi0+vCS/wXlQirQW1hpeiZTE7Af8kAKryFqpVkyuW0uxwqVKKCKUh4pXwvFW0c7dSpAz7+aBro5Wb6Iq1dtwFXA4NKZCsDqf/o0SOxFeofrCcg+eZlnMh0gottBbx4kYL486dx320xtm7Zjf3r7bB7oQ9uFTzgzEFQ9sLKykrcEyYbp+l1kclK04plyhU80krBvd1bEdJ7PHqbV5YpJXuZigehV/Ef7NGjVb3cH1rZLEqumbCUAGPI0ULsFRwK7IbPRzaHwnW5arXRkAZW6a+Q8lqRYT4T6a/pm2mKd2qodhSwra0N3N0/wLChQ/DixQts+PkX8bUd2mJgGCEN0RG3kdTCClWDduPggzcw6zoao5tXz/5CVYDNqI6wVvQDUEgD33rLuJAcqif7+BxE27ZtxfOsVC+l/ZxEWoMGDcLq1WvEAxGzashAUuhOrI0bgE+7yoz45asXHiPY9yZQvwNaN1Ht+ZJEMGFJSJSWTyEGvquOo8nKT+BWW+GEEDB2QL8PnYDEQATcVrB8nxKBCyeiAIsBGOCi3sqe/M73ffsP5Ox8L06I1d9GYIQKlaqgfNhxHE/vjlGO1UR1haQonN/5P0ybH4ZW9nWgcIZTSMOePIkTd70Xkk2l5AULvkRaWir27durUn5dZQoNvSaeWLp8+XKZQwtTEP7PPhzyHIlWlrRabQnr9rNxCvE4NYu2MMzEwdh0CLHX4X81CcbdnWBdWdEIX7nWTFjKsTHAlBRE7d+OkF4LMbtdrQKG2tXQatI3WNTrKTYsXA+/mKy9UmKD06Ph9+N32JDQE4vWT0IbE80eEWnn+3s93UDvGdIhftfDwnSOqWRsl4zvqldYGZbuv+JO5CEs69ckh5iMTCzQ7r33MfMzG5ya7IWTcepbsciphXROvOr6KM5JWzUWLPhKnPqWFGkRWW3d6o0VK5bLnftlAufZR3H3flTu3yVP9IAZenidxd37qzGobjkk3gnGhYy66NHRFgosqIobnh2r2dNYoEhOLBkE0hBz+ld4J/fBtG71s43tyYiOipMzFGcg7tgOHE+xx9h1u7HrQ1P8M2ckZh2NAeJPY9Ggr/BPzTHYdWQlxtoLCFi7E9fVtNvQFgeyY4n2rKuBGDSwv2jnKo7TRqtUydrE8ezZcy11gxEq1LJFp1GT4OF8F3ceqb8BlBYmTE1NtKQPxBFNSZGWcrJStXkvcftyAJJhh7Z2b8v8qGYgKfwwfljkhZ3712HuhxsRlJj/wWPCUhVnvc5HZOWFT/+sjO72bxAeHISgoEBcObIJm4KS5F63EJCRdh1bVqyA15o/4P/wNczMTZFGNqu0F4irUhtmr+/Df9d6eC1fih92P8EbRWYuBXiQvYq2OJD9iuxYZM8iuxbZt4orSK/+PHz4ULtVpqfilXEXdLRVzx5FnnloX5j6iwAFq18SI60ik5UQh9B9G7F+dziAxwjxPY3rT2nEKiD90WEs+PwmOs6eAfehg9Cp3EEcCIzPB4ISI0e+fBxR0gikP0XE5TM4eu4xkHQN/v8EwLS1I2xqVUD85XWY7PGzuIIVcFxG0YrDseZCQ5lfMSktBcF7diNYuqUhe6esm4zAvVgfmJMAmOXZoiqTkHVJWxvu33+As+fOixEtWzrCza1HiTqcIOcSRQ9piNr5EfpuqojJk3rCslw6Gn4xUe0p8t27WfuvyOmDtoNEWt9++51o0xo2bLi2q8iRpzFZ1R2MTfcH58hxHDYP3sPm5dyLF8ITnNu0CQ+GeqKDWXkg8xUS4t7kzZN9xy8/K4SFI1VBgMhq7979oo2qfj1zDB8+tESJShWdizvPDz/8iLCwMGzbprvD/GiBgUiLnLzqgrQ0JitVwX7ph4XtN6DRPm9MsqsK4dEefDjyFsYd/QrdiMBkAo+wZMDgS/UQoH1YNOWjqSCdPbVq9To4OzuhlVPLEt9Aql5LdJObpoPkPZoO89NlKHykFYdzKxdj83Vlm2qNYNp3PjxH2MqZDwCdkxUBk/EGaW/eQR2zioDwHAG7jqL6vEVwlSMrysojLF0+SWVMtvz7hPrqSFWX3UKjHSIQCpLzi+3btxXooFVb+mh7pFUsZEWNF57iyqrF+F3oBNe3YvG4bj9MHNBU4XlkTFjaelpYTg4CNFXUV0eqOUrq4IJGVIsXL8GUKZNQtWpVzJw5q9icX0jN0RZpFRtZSYqr+MmEpSJQnE0zBPTJkapmLVC9lDSiohKWlhbiSunGjT/njLhUl1S0nEUlLX0lK0KFtzUU7dng0koQoOkhedShDaP1zM0xoH+/EvX6rERNrUXT6IoctUohKuq+eDyzND2U4ovjU7Jp0XuV6m4u1WeyIuyYsIrjCSpDddBxM/v3+4jHzVCzx48bIx4307hxo1KNwuHDf+Vr365df4D8IpZE0IS09J2sCEeeEpbE01TK6iSbVej1MFy7Fiq2jA7vs7BoXGa2OEhnyCvqVnIzVpJeoFWdHhoCWRG+vK1B0VPGcSohQERFG0bJyQTtw+rbp7fcu2UqiTH4TDt27FDYBtrAOmmSR7GsECpUALmv8RS0udRQyIrayFNCZT3N8YUiQPuwaM8V7b2iF5xpL5bhHCdTaPNUykCOUmmvlWygUdXy5d9jzpzPS5SsJJ0Kmh4aEllRe5iwpF7lT40QoBNGyZEqOZoghxPkSJUcUJSVsHfvvjxNpU2itDKo7fPb81SiwY0i0jI0sqJmsw1Lg87nIgUjMGHCRGzdurngTKUglUZXtNeKAp3bTmSl7ZectQ2TZNOqXLkKwsPDFRwRo+0atSuPbVjaxZOlASV2PHJxg09u6Gn65+4+SgMP08WtbVZ90khr8uSpBkdW1AImrJJ5brhWA0eAzlZv0KA+lixZrBd2KnXgJNIiZx3SUTzqlC3pvExYJd0DXL9BIlC/fn3RqG6Qyhuw0mx0N+DOY9VLDgFDHJ2UHFraq5kJS3tYsiRGgBHQMQJMWDoGmMUzAoyA9hBgwtIeliyJEWAEdIwAE5aOAWbxjAAjoD0EmLC0hyVLYgQYAR0jwISlY4BZPCPACGgPASYs7WHJkhgBRkDHCDBh6RhgFs8IMALaQ4AJS3tYsiRGgBHQMQJMWDoGmMUzAoyA9hBgwtIeliyJEWAEdIwAE5aOAWbxjAAjoD0EmLC0hyVLYgQYAR0jwISlY4BZPCPACGgPASYs7WHJkhgBRkDHCDBh6RhgFs8IMALaQ4AJS3tYsiRGgBHQMQJMWDoGmMUzAoyA9hBgwtIeliyJEWAEdIwAE5aOAWbxjAAjoD0EmLC0hyVLYgQYAR0jUOrcfI0Y8b6OIWPxqiDA/aAKSpxHXQRKlat6dRvP+RkBRsCwEOApoWH1F2vLCJRpBJiwynT3c+MZAcNCgAnLsPqLtWUEyjQCTFhluvu58YyAYSHAhGVY/cXaMgJlGgEmrDLd/dx4RsCwEGDCMqz+Ym0ZgTKNABNWme5+bjwjYFgIMGEZVn+xtoxAmUaACatMdz83nhEwLASYsAyrv1hbRqBMI8CEVaa7nxvPCBgWAkxYhtVfrC0jUKYRYMIq093PjWcEDAsBJizD6i/WlhEo0wgwYZXp7ufGMwKGhQATlmH1F2vLCJRpBJiwynT3c+MZAcNCgAnLsPqLtWUEyjQCRXBCkYnUhKdISBVQweRt1DIpgqgy3QXceEaAEVAVAaUskx7kifZDVyMhnyQz9PA6hE2Da+Dm1vEYuSo2+75Bvpx6HSHE49bxv3AqIBTXrl3BmRDAsXc39Og1FMP7OqJ2BSPl6gvxiPA/BT//SwgIuYIzga9g7dYX/Yd+gA/es4NZnrIC0uOC4bPVG9t2HcWtlw3QcdRojJ34Pt61NEUBtSivX2FKKiK8PdDn6/MKU6VI49Fbce7bbqgmRfAnI2BACCglrJw2VHTG0KmuqJczeayAOo2Mc5IN9sLoFcL3ecIzsC46trZBO9sQXDjyG4KP7MfR0LXY8lVX1FbKJi9xbctSLD9TAU1dndCldQT8fbfjJ99D8PtqO7ZNckCVbGCE+IvwHD8FG29URasRE/GRyT0c/u07TD0WhmV7v8dwy6pagrAKbMbvwN2xd7BtyFD85LBOjpgykXRnJ+bu1FJ1LIYRKAkEBCXhTeBKoXVjC8HKaaUQ+EZJJoOOThHiHv0nJL7JzGpF5ivh8aUNwjhrC8Gq8f8J3uEpBbTuuXDrXJDwMFECJlV4fGKJ0J3warFUOPcqW6aQKtz7faJg29hGcFt+UXgpRqcID3fPEJo1thLaLTkrvCygFo2SMm4L3gPtBYevTgsv8gmIE84cuKQgPl9GjmAE9BKBnHGT+mSZhCDPvrC2cMZkn39zi6fH4Mq2bzC2S3NYW3XD2CU7cCX2Lg56OMPaYiYOxqYDSEesz0xYW1jCxTMIFJMVFMVL9QzB+sAIXP51Lga0ss4pJzwNwf51i/HJ6L5wsbBE0y4j8fE3VGeaJFTJZxXUalAHESgJAgAAFAlJREFUJtL0zcgY5u36Y0hXMwCv8ColU0k5ijZDs06t0DDHblcZ5t37YyAVTXyCpy8zssoK/+LiwcvIQFuMHuIEU3HEVgUNadppnIGne/wQmiwUUI8WkzIj8NfheLgObsfTQS3CyqKKF4EiEJYCRYV4BK2dhTGLt+JCYnMMnTwALZIO4ePJP+Lk0zcKCqgT9QTB3t9hxrd7cCveBC0avI3yADIe+mH1qWRYuo3HQq+lmGoXj5NbFmLMJ38g4o0aZJD+EvdP/4kdp+NRvm1/dLNVb6omxETi2ksAtg6wrZ09006JReTNJMDYCo3fqZTbWBNzWNsYA4n38OC/17nxOrzKjL2N4ARZEs5EUoQPFvZpDmv7SfDyOQ//gFugJkghMzYAOxYMEn9YKM+aywE49c06+L1MRoT36Kx4i9HYFpEK4Cn8FnTNzrsYfi+luqiek/Dy6JAjx+ufCCSJlbxEhN8eeHkMwkK/x4gN+BmT7S1hbTEIX/s9RmZmLIK2L0A/C0tY20/Dtjsy2smmUXqfxTgYIZMuNSL7MzM2CH95L0C/QVsQdCe73RbN0W/BTgTF5vZBnjaL6T6ISMpuS1IE/PZ7YnKrxTh15zzWeHSAo8cO3EnKRIHl5HTJuSV5pBPpb2EJR481OFVAG3LKleULZeO+nCkhTXPy/PURPAMTBUFIFAJX9hGsGrcSJh14JIrJfHJE+EScUg0UVlx6JogzoMx44dq6/xNsRRkzBJ8Ymka9EWIOzBDltl4ZKEgTK8XxUj0WgpX1BGH9pX+FlMxMIf1Nuig/MzFBeCFN60iL1zcF75EtBavGg4V1114pa152fK4eWW1sLQxcsFe48fx1IeXkkjMfCyfm9hCsGrcUPth6U8gpHXNAmETtzjetfiT4TGwlWDWWsJSTV5Tb7Clh3j6jPrQXBm+9LWRIsinf0M8Fn+i0rJiMB8Lh3y7kTBczog8I0+wGCotPR2eVSQwTvCe2F6zsFgmnX5CUDOHF6UWCQ57pc4oQvvX/8uRJDNwkLFh1QYgRK84QEm9vFybZdREWnP4vuzzp1l6YtPKAEBhDusQLgSuHClZ2HoLnvjNCeGKGIGREC6cXDRSsBm4VwkU5WfU4TD0gRNO9pFtOutTI7E9ZTNymCqvPZLUpI8ZXWNzbXsiRI+brIkw78EDIECRdJdzihNNfdcn6Lth5CKuvRAsvAlcLfXuvFgJf3BS8ByorJ6eLdJvxQPCZ2keYtDVMoG+TkHhb8PlqoGBlN1Xwvp1/Mi8VK+ufhY+wyOg+YyY+/kT6G4LmZops9ZlIvHEZp2gg1XIIBrepmbUCZlQDDgMHoUORfxXK4x2PKRjXrj6qGBmhfIXyonwjk+qoVj4NL2KjcCsoCEHXn6Nio+oAHiDk3vNCajVC1UauWW2b9j46NkrBjZ2bsHFfCJ6qPDhLxaODK/HVn/dQ3nEi5gyzRcVCai2OZFoNDLofhbviXyRC/v4KLWlImh0yIy/C51YCoq6EIZYGEOUaof+YDtnTxafwX78ODyYtwOfd6kF8SEys0NHVSiqu4udzXN2/A7tWusO1CY0irODUayFOJT/EQd+bQLclCDm5GA6ohHdaucK5Lo1Cq8G6VQsYJ6fAzKEtbEzKAeVqor6lKRARhWhptEMavF0DlIzCdCvXFOMOnsGvoxsBxu3Q2zWrTeXqdsen84YDx/biZCSNEilUwts1jFEO5WBi0wadbCpnx9dCt2/3ZclAPTg0rYtqzjNw5NgMOItKKCuXXTzPRyZe+m/GwjNt4D7UDiaUZtIUg+YvwMeN/fHT9qA8I908Rcv4jSLmyQuJiSs++GQ2nPPlzBrU52bORHJCPJIponYNmMpQodFbNVCHvsWFzgoFpL/JHZ7nyqaramjetD7yrk+mIfbyHqxbsRq7AuPyZgcZlAoL5VHdeSRmOWflE6YPxo+Dx2Ljt8vQtO02THcUH6UChKQh5rQXpn+2F8/fHoBvfpwAZ1MZVjCugXdI4bQEvEzOBKplg5L5CglxZGOrCTPTfMAWUJ+mSVlfPpfw3PLlrHpgfNeN+GzWMGz5ayaWjO6Pnt1ssr48L8Pwz/7HqDS3mhzeueVVuhLlNMTCk39jnI20bpq3pDRxzBtb2F3WimgoXiM26Dj+ObMPi1edB1q6FVZQLr0cTOpbwgp+uBudBNgQsZ0EaLp5+E/4H/TC2mtpcBgiV0z+ViREdco9R5CvH5JtJqC+SHbZAk0s4dS6FpL3n0bQ3C7oJj0v8vWV4XsZWikqCuVgXMMs6wF/GIf4bLszSRUS4vBICVllvn6D3KwvcPfaLZUVEeL+wbLRC7Hrvgvm/3kGIXfv4e7969j9iZ3KMmQzGpmYw7IBMUwUQu7l34EmmxcgsvLEZI+NuAVnTFm/CKNs5QhOslUlR+a1VSXF4G5Ecn7bVt4KtHtXzgb9B9hkjZZIcrlGGLTuAHavWYhB0b9izvj30HGaDx5nApn/3UdYci20sHg7N7/G2gTD5/wDaEZMyivNjL2INR6DsejMC1Ts+iX2fN1JeWaVU15n2dFaL4T/m+ro8s1GLGwpjbAKEqJhOfkRY0FVcJqIgFYJy9SqBVrTACP8L/x19TnEWZWQgOvHjiIoD+DlYWbeQJx+vDzhj6vxxGYZSLpxGN5/PsyTs6CbjEd3cI6KWrvCrW0jccVPSAzDP3/dLaiYmCa8eIInqTJfIyERUce2Y9u5FwBs0Kbp29ky0pH09D/Exj7BCym/kIxHJ1dmkVW1jpiyeTVmt6uVfxNoOQt0eb8DyuMKdhwIQaIISCoe/b0fe5PLo9YHPdG6uH9Fk27ALyh7qlyuLpwHfIilx4Jxbs88tD/jiQ3+T1HOqgMGt0xEUHBUtnG8UDgVZ6jWAu8OrYXrX8/F4u0BWVNPMWcCrvmFaj7tybyD7VM+wilXT/w8+330dzbXkFgzkRQdhUjjbnjXuSYyI3Zi2ohz6LR7DWYN7Q3nuqqQFTQoVxPObt1gnByGkLv5FwqMh3aHc3E/F4p7UO9itUhYgFEDN8yY0RblEYqN7u9jypLlWDpzHDz+TkGLPHM5I1Ru3gUfWFQEItdjXI9BGDt6ALr124O677tlTUtUgKqCTRsMql0euOyFOXO/h9fKxZgyeDkiLJoUUlrA69ve6N28O0ZMnITJHh4Y27c7ek7fjFsZJrCb/gmGN5NWCWPxz/w+cG0/HltvihNeZFzfitGTNuFWRnnUbG6BCsG7sdbTE17i3xrslAgBlWHR50N4NK+MqPUz8eHc7+G5ZAbGzT+MN2/3x+djWsO0EE21mSyOSub8BVjXAF5exkH/p9niK6FO/bqogIawrm8ClLNEzwld8WjVt1jucyebtFKRGJ8io440nYrE5RtPkClOz07hwt1EIPk3eDiOxbYIY7gMHY6mCMWuhSOz7Vhky5qI09Uaab69QhyhpuF1/EvRBJEZex2Xqd6IKDy6cxH+9yR7lIy60mXEeRwPjBVHfJmxl7FtRwBc/zcRXaohi7yQgvhEKv8asSGBuPs6DZF3o3DH/yLuyfy+SeKAbNJTq1w5VHMZic/cHmPtV57Zq5u0sfc4dh5xxtLpHTXHJlexUnmlVcKCkRmcP/bC9iUT0cM2Hqd8LuBpwwnY/OscdJb/sTJpg+mbfsKUXvaoEf8Ez6p0xMzff8aCIfZQ2apj2gGzf1+DGQPNEbVnB3yCysP1f6uwcIBtIZ0l4E3VRujftyGSg07jlO8/uPyqCXqP+RzLfj+EXXM6wkzpLndASH+NV2INGXh+bifWrVqNtTl/W+H3MIvYKIuRWQfM3vwrvpnWHqm+m7Hutwg0GDUPa3Z9g2Fa2+VONdGrOaNh3aQ3ll5LRvKOCXDOXi6nJXP6s23vjl/ebpf9622C6i+u4mD2srrtxKvouONHjBFtTZVQb+A8eC91QNCs3nCibQ/7L+ERZLZm0KzSZiiWfe2Ec7O6wrbPd7hs6oKO1jXRdPRCeO0nWcYwcZ6Czfu/wyi77F8sYzd8vHkZPJyriPra9lyC63iIXeO7Yoh3CO54j4Xz+N+QjPNY2rMXFvrdgt+CXlmvHIlE2B0Lg2zx0Xp3YNVIUbfVN6qhh5sTjJNDcPpOTTg3UWwvE7vMpikaXF8CJ8KjxxZkjFqFFYMbiUb2al2mYPW4dKwd2gqOHhtx07Q93iWbUuBFhL9TDmeHdIXHjodAsh9+eH9K9naOciiwnHlzNFH0LTNpjnFev2HTe4+xsGdLWFs44P3t6XDfvQSD6uXFWdSb/4kIGNEyqa6xEGJ8MM11NnxNpmHnlTloW7kANtC1MixfQwSy31VcYYVfLy02QIMw7RMbBo/rE3DswHjYKCIRDZHhYsWHgJa7TUDq0yd4kS7DgenROPPrbzidUR61hnWEHZNV8fUu18QIlDIEVJ59qdbuDCSc+xZdV77AiH4tUatSGh6fO4D9tOXg7UHFbrNRTWfOxQgwAoaCgJanhJlIunUI67f44IzvOdyJz0D5Ru0xoF9/DBg5EF20epyKoUBcGvTMnk6R/UYMnbDw5K9K91bpXYtf+mFh+wnYJZkWjcca6LRW75AtdoW0TFjFrj9XyAgwAmUIAS3bsMoQctxURoARKHYEmLCKHXKukBFgBDRFgAlLU+S4HCPACBQ7AmWAsOg8Jn8c8JwElwV+mr8OUuxdwxUyAoyAPAIKCSszwhtD5HZJS7ulcz7tZQ9pkxerR/cv/bF80DjMWeULZedAqKdt9ouu4kFzzdFvgcwBbyoJyjphgAjUkQ5tYxJVCTXOxAgQAgoJq5zNeBy4fwvH6A14WgIOjcw+Vyn7fKWwv7Cwa56XA/UXzWrdsDTsOBa21Ia+mUgK+Ru+GIyfb0Yh/NKv6B27HMOW+as2csuMxdXVH+G90fvwoPEY7AuLRCh7sNHfZ4c10zsEFBJWoVqa2GHIKAfFbFdoYQPOkPkAQS9bwb1NXbHt5eq2w7jR7wF0flHOkcDK2peAoFUf4cPQ1thyah1mDe2SdTidsuwczwgwAvkQ0GCneyoiDp8F+vVFF83oLp8SBhNRzhJdushq+xr/3X+IhpOmw6XA40AykRS0HQt/aYSlvh/CRTxZU1YOXzMCjIAqCKhPOZlPcDNYOno4Ey/9Fou2mCzbFjkk+DfXGYFFVyz0k44w0YEzAvFkyC1Y2GcCtgWF4KDkMKHPAuwIyjpCRDkIpI8ftkllLDpgsufJXIcDygtmpYgOBL7HD1GjsfmTNgUfiZMZgX1LtgJDHZD550dZeNEJCDnOGAqrjNMZAUZARED5ofbZDgVE5xFyjijyHPafe1h/30W+QkxG9v3ARYJPuHSYfoagfWcEsvq5CZNWnclydCA5LLCbJeNgIb+vPtHJgpN04H+GkBh+QFhADgkmbhduk+MDpUFyvpCNSW/ZdioulBG+VRjceKCw4Lcr2c4YXgi3t04VHBoPFTwD4xUX4lhGgBHIhwDyxeREyHtAyU4gDyWL/sj2XiJlJkJaLfRtbC/0/WqZsPir3+W+9DIeR+QIUHL4mfWlJm8qcdlCJWKQdWoqr5OiPIIgvDgtLLCTvJ2Qgxd5wsrSR6o7q0KpDbI6SO1T9JkmxAT+LpKclSw55suarWOOt5nsDJInlzzkn68wRzACjIAMAupPCclDiUtNufFpuayD2rzdgR0+eOLimtegnOOM4Fbe1cb7UbpZJRPPUgci78YoPuJX1OcprKzNZaZy5WBi7QBnY/LoEqbCql8l1HV2x5LVc+CQHISr4fmPus0CiexckVnOOWRRK9cYHYe0yu8JRjYPXzMCjEAeBNQnLFSBzYCeCg5AS8bj4KdwHN0M5778HttlnV6KVerGGUGe1qh1k6yc0NSQk3X+eUEnRFbCOxZWMJZ3RCHVYWOZ13OKFM+fjAAjkA8BDQhLkiHrSOA1Yv224pDlbHz3zXdYPeIxls5aAz/Jo66unBFIqsh/imd+18IgtxaKz8YW9WmE5MDruCvr506U00h5Ofl66J7qetgCLrbVFKWKW92qOXfHIGPp7HMpWxKi7/4HhyEdYFWEXpCk8ScjUBYQ0OyrIm6A/A4HUA/V6LB+vx8wzbcVPqWzscvVQ7fFK7Cw0k7MXLAFV0XSqqkbZwQ5PRSJ88eCs7yykG7ev+NY19mY1qVWTo68FzXhMmYSejz4GQuXHcpeGXyJO/v/LLBc5mMfTLcfhIWSB5jMx/D76Vf894kH3s05h/s1HvvMhmOfNQiSyLBaR0z7X3uZkSftlt+LndcHYuHwbNdbmQ9xcFpX9PMMUDyNzdsAvmMEyiYCMvasnMssA7jcyqCcsVxyWZ6bVzJWyxvYJaO5jJGaZJErct9wIVGQXe2jOslYHizcJpfnOXWS7Ju5rsLFeIqT3J1/IHju2yBMsqPy5Pb8RJaLc2qRaICXaUuOkZtWBk8InuR+XZQ3UFiw9XRuuRw0ZC4kl+jZejlMXCn4BMbkun8Xs6YJ0QdmCQ7kwjzPauMLIdx3dbaOtDjxe7Zr9mz5ouvyLkLflVeyXJfLVMuXjAAjkIWAgR/gR/vAlsB1fCQ+M6QTMMvmbyO3mhEoMgKaTQmLXC0LYAQYAUZAfQSYsNTHjEswAoxACSFgwFNCeccIjTDKex+WdlNmaC8hhLlaRoAR0BoCBkxYWsOABTECjICBIMBTQgPpKFaTEWAElBzgx8AwAowAI6CPCPAISx97hXViBBgBhQgwYSmEhSMZAUZAHxFgwtLHXmGdGAFGQCECTFgKYeFIRoAR0EcEmLD0sVdYJ0aAEVCIABOWQlg4khFgBPQRASYsfewV1okRYAQUIsCEpRAWjmQEGAF9RIAJSx97hXViBBgBhQgwYSmEhSMZAUZAHxH4f6P/Fna/GCkhAAAAAElFTkSuQmCC" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exemplo 3.6**\n", + "\n", + "Use a análise de malhas para encontrar a corrente Io no circuito da Figura 3.20.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exemplo 3.6\n", + "Corrente i0: [[ 1.5]] A\n" + ] + } + ], + "source": [ + "print(\"Exemplo 3.6\")\n", + "V1 = 24\n", + "CCVS = 4#io\n", + "\n", + "#Malha 1:\n", + "#10(i1 - i2) + 12(i1 - i3) = V1\n", + " #22i1 - 10i2 - 12i3 = 24\n", + " #11i1 - 5i2 - 6i3 = 12\n", + "\n", + "#Malha 2:\n", + "#24i2 + 4(i2 - i3) + 10(i2 - i1) = 0\n", + " #-10i1 + 38i2 - 4i3 = 0\n", + " #-5i1 + 19i2 - 2i3 = 0\n", + "\n", + "#Malha 3:\n", + "#12(i3 - i1) + 4(i3 - i2) + 4i0 = 0\n", + " #i0 = i1 - i2\n", + " #-12i1 - 4i2 + 16i3 + 4(i1 - i2) = 0\n", + " #-8i1 - 8i2 + 16i3 = 0\n", + " #-i1 - i2 + 2i3 = 0\n", + "\n", + "coef = np.matrix(\"11 -5 -6;-5 19 -2;-1 -1 2\")\n", + "res = np.matrix(\"12;0;0\")\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente i0:\",I[0]-I[1],\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Problema Prático 3.6**\n", + "\n", + "Usando a análise de malhas, determine Io no circuito da Figura 3.21.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Problema Prático 3.6\n", + "Corrente i0: [[-4.]] A\n" + ] + } + ], + "source": [ + "print(\"Problema Prático 3.6\")\n", + "V1 = 16\n", + "CCVS = 10#io\n", + "\n", + "#Malha 1:\n", + "#-V1 + 4(i1 - i3) + 2(i1 - i2) = 0\n", + " #6i1 - 2i2 - 4i3 = 16\n", + " #3i1 - i2 - 2i3 = 8\n", + "\n", + "#Malha 2:\n", + "#2(i2 - i1) + 8(i2 - i3) - CCVS = 0\n", + " #-2i1 + 10i2 - 8i3 = 10i0\n", + " #i0 = i3\n", + " #-i1 + 5i2 - 9i3 = 0\n", + "\n", + "#Malha 3:\n", + "#6i3 + 8(i3 - i2) + 4(i3 - i1) = 0\n", + " #-4i1 - 8i2 + 18i3 = 0\n", + " #-2i1 - 4i2 + 9i3 = 0\n", + "\n", + "coef = np.matrix(\"3 -1 -2;-1 5 -9;-2 -4 9\")\n", + "res = np.matrix(\"8;0;0\")\n", + "I = np.linalg.inv(coef)*res\n", + "print(\"Corrente i0:\",I[2],\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Análise de malhas com fontes de corrente\n", + "\n", + "**Caso 1**: Quando existe uma fonte de corrente apenas em uma malha:\n", + "considere, por exemplo, o circuito da Figura 3.22. Fazemos i2 = –5 A e escrevemos\n", + "uma equação de malha para a outra malha da maneira usual, isto é:\n", + "\n", + "\\begin{align}\n", + "-10 + 4i_1 + 6(i_1 - i_2) = 0\n", + "\\\\\n", + "\\\\i_1 = -2 A\n", + "\\end{align}\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "**Caso 2**: Quando uma fonte de corrente existe entre duas malhas: considere\n", + "o circuito da Figura 3.23a, por exemplo. Criamos uma supermalha, excluindo\n", + "a fonte de corrente e quaisquer elementos a ela associados em série,\n", + "como mostrado na Figura 3.23b. Logo:\n", + "\n", + "**Uma supermalha é resultante quando duas malhas possuem uma fonte de\n", + "corrente (dependente ou independente) em comum.**\n", + "\n", + "![](http://i.imgur.com/zLuuvRX.png)\n", + "\n", + "uma supermalha deve realizar a LKT como qualquer outra malha. Assim, aplicando\n", + "a LKT à supermalha da Figura 3.23b, temos:\n", + "\n", + "\\begin{align}\n", + "-20 + 6i_1 + 10i_2 + 4i+2 = 0\n", + "\\\\\n", + "6i_1 + 14i_2 = 20\n", + "\\\\\n", + "\\\\Assim:\n", + "\\\\i_1 = -3,2 A\n", + "\\\\i_2 = 2,8 A\n", + "\\end{align}" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exemplo 3.7**\n", + "\n", + "Para o circuito da Figura 3.24, determine i1 a i4 usando a análise de malhas.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exemplo 3.7\n", + "Corrente i1: [[-7.5]] A\n", + "Corrente i4: [[ 2.14285714]] A\n" + ] + } + ], + "source": [ + "print(\"Exemplo 3.7\")\n", + "V1 = 10\n", + "C1 = 5\n", + "CCCS = 3#io\n", + "\n", + "#Supermalha:\n", + "#2i1 + 4i3 + 8(i3 - i4) + 6i2 = 0\n", + " #2i1 + 6i2 + 12i3 - 8i4 = 0\n", + " #i4 = -i0\n", + " #i1 + 3i2 + 6i3 + 4i0 = 0\n", + " #i2 - i3 = 3i0 => i3 = i2 - 3i0\n", + " #i2 - i1 = 5 => i1 = i2 - 5\n", + " #i2 - 5 + 3i2 + 6(i2 - 3i0) + 4i0 = 0\n", + " #10i2 - 14i0 = 5\n", + "\n", + "#Malha 4:\n", + "#V1 + 8(i4 - i3) + 2i4 = 0\n", + " #-8i3 + 10i4 = -10\n", + " #-4i3 - 5i0 = -5\n", + " #-4(i2 - 3i0) - 5i0 = -5\n", + " #-4i2 + 7i0 = -5\n", + "\n", + "coef = np.matrix(\"10 -14; -4 7\")\n", + "res = np.matrix(\"5;-5\")\n", + "I = np.linalg.inv(coef)*res\n", + "i1 = I[0] - 5\n", + "i4 = -I[1]\n", + "print(\"Corrente i1:\",i1,\"A\")\n", + "print(\"Corrente i4:\",i4,\"A\")" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Problema Prático 3.7**\n", + "\n", + "Use a análise de malhas para determinar i1, i2 e i3 na Figura 3.25.\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Problema Prático 3.7\n", + "Corrente i1: [[ 4.63157895]] A\n", + "Corrente i2: [[ 0.63157895]] A\n", + "Corrente i3: [[ 1.47368421]] A\n" + ] + } + ], + "source": [ + "print(\"Problema Prático 3.7\")\n", + "V1 = 8\n", + "C1 = 4\n", + "\n", + "#Supermalha (Malha 1 e Malha 2):\n", + "#2(i1 - i3) + 4(i2 - i3) + 8i2 = 8\n", + " #2i1 + 12i2 - 6i3 = 8\n", + " #i1 + 6i2 - 3i3 = 4\n", + " #i1 - i2 = 4 => i2 = i1 - 4\n", + " #i1 + 6(i1 - 4) - 3i3 = 4\n", + " #7i1 - 3i3 = 28\n", + "\n", + "\n", + "#2i3 + 4(i3 - i2) + 2(i3 - i1) = 0\n", + " #-2i1 - 4i2 + 8i3 = 0\n", + " #-i1 - 2i2 + 4i3 = 0\n", + " #-i1 - 2(i1 - 4) + 4i3 = 0\n", + " #-3i1 + 4i3 = -8\n", + "\n", + "coef = np.matrix(\"7 -3;-3 4\")\n", + "res = np.matrix(\"28;-8\")\n", + "I = np.linalg.inv(coef)*res\n", + "i2 = I[0] - 4\n", + "print(\"Corrente i1:\",I[0],\"A\")\n", + "print(\"Corrente i2:\",i2,\"A\")\n", + "print(\"Corrente i3:\",I[1],\"A\")" ] } ], diff --git a/Imagens/circuito-malhas.png b/Imagens/circuito-malhas.png new file mode 100644 index 0000000000000000000000000000000000000000..09c45aa3f155e3a7563c17c1d7f550dbc1b4f565 GIT binary patch literal 8901 zcmeHtWmFu^yC*J#1_t*5f_n(T8FY}~PJlpg2!Y@pAP^YbA-D$!?(PyixD6WI-C-y1 z|GoE|`(e-7-Ou}Bx~6NYx}SQgdVW$Js;Vr910V+=ARyq#L!{La5D>%R-&-+|;72Y1 zEE`@RI;qP^B9x6%?!r${EWvNV2ndx?SPv$s@N-NDh@KMy0&e%;4`TnPA7%&$Abojh zu%^4wVS1DXP^Yec#V>#{lu=uk-$rz3#D>wFAbTq52Bac|WcK3KCFqpVs%lM+_>@R| zX_ypMEj&ssi4p9`tF>O3whjY)~uE?mhbW&vA7bIJ@X zjDR#q#6VwCzqTw79pk~7WX%C;1dbeYMGgtzs7#_Ugl9oyUgVbEXX;l@&IS6kPGHv& zi_|kuT1gGbA_0qbOp2?|dXvopUBYKxt^Q>ztZ)x@R0Q~SGT 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