{
 "metadata": {
  "name": "",
  "signature": "sha256:dea1ade2fa255da141fefac67f897fcfb05b4b88eed6e155adae3acfd2ba4e44"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Blade Element Force/ Moment Derivation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy\n",
      "import sympy.physics.mechanics as mech\n",
      "import scipy.integrate\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import collections\n",
      "import os\n",
      "import sympy_utils\n",
      "from sympy.printing.theanocode import theano_function\n",
      "sympy.init_printing()\n",
      "sympy.physics.vector.init_vprinting()\n",
      "%matplotlib inline\n",
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "plt.rcParams['lines.markersize']= 10\n",
      "plt.rcParams['font.size']= 12"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The autoreload extension is already loaded. To reload it, use:\n",
        "  %reload_ext autoreload\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Variables"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phi, theta, psi, P, Q, R, V, alpha, beta = \\\n",
      "    sympy.symbols('phi, theta, psi, P, Q, R, V, alpha, beta')\n",
      "    \n",
      "eta, eta_dot, alpha_l, alpha, beta_l, beta, s, t = \\\n",
      "    sympy.symbols('eta, eta_dot, alpha_l, alpha, beta_l, '\n",
      "                  'beta, s, t')\n",
      "    \n",
      "states_sub = {phi(t): phi, theta(t): theta,\n",
      "             P(t): P, Q(t): Q, R(t): R,\n",
      "             V(t): V, alpha(t): alpha, beta(t): beta,\n",
      "             s(t): s,\n",
      "             eta(t).diff(t): eta_dot, eta(t): eta}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Reference Frames"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "frame_i = mech.ReferenceFrame('i')\n",
      "frame_b = frame_i.orientnew('b', 'Body', (psi(t), theta(t), phi(t)), '321')\n",
      "frame_b.set_ang_vel(frame_i, P(t)*frame_b.x + Q(t)*frame_b.y + R(t)*frame_b.z)\n",
      "frame_w = frame_b.orientnew('w', 'Body', (beta(t), -alpha(t), 0), '321')\n",
      "frame_f = frame_b.orientnew('f', 'Axis', (eta(t), frame_b.x))\n",
      "frame_l = frame_f.orientnew('l', 'Body', (-beta_l(t), -alpha_l(t), 0), '321')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Reference Points"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "point_cm = mech.Point('cm')\n",
      "point_cm.set_vel(frame_i, V*frame_w.x)\n",
      "point_cm.set_vel(frame_b, 0)\n",
      "\n",
      "point_p = point_cm.locatenew('p', -frame_f.y*s)\n",
      "point_p.set_vel(frame_f, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Local Angle of Attack of Flapping Wing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vel_p = point_p.v1pt_theory(point_cm, frame_i, frame_f)\n",
      "vel_p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$V\\mathbf{\\hat{w}_x} + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)\\mathbf{\\hat{f}_x} -  s \\left(P + \\dot{\\eta}\\right)\\mathbf{\\hat{f}_z}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAbkAAAAbBAMAAAAT2exKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nEKtDDO7PtCvJM/ETVhAQK/8CAk7r0KjdnjIAAAAASUVORK5CYII=\n",
       "prompt_number": 5,
       "text": [
        "V w_x + s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7)) f_x - s\u22c5(P + \u03b7\u0307) f_z"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha_l_expr = sympy.atan(vel_p.dot(frame_f.z)/ vel_p.dot(frame_f.x)).subs(states_sub)\n",
      "alpha_l_expr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\operatorname{atan}\\left(\\frac{V \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) - s \\left(P + \\eta_{dot}\\right)}{V \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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AAElFTkSuQmCC\n",
       "prompt_number": 6,
       "text": [
        "    \u239bV\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) - s\u22c5(P + \u03b7_dot)\u239e\n",
        "atan\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n",
        "    \u239d       V\u22c5cos(\u03b1)\u22c5cos(\u03b2) + s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))       \u23a0"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta_l_expr = sympy.atan(vel_p.dot(frame_f.y)/ vel_p.dot(frame_f.x)).subs(states_sub)\n",
      "beta_l_expr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\operatorname{atan}\\left(\\frac{V \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{sin}\\left(\\eta\\right) + \\operatorname{sin}\\left(\\beta\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right)\\right)}{V \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdUAAAAyBAMAAAD4oVxKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaJVN0imavvMkQQ\nzbsZbzSbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAALbElEQVRoBd1ab4xcVRU/szPzdnf+7QJJW2p0\nH11QaawdqKE12OwEwod+0N0otqkaeUWElA/dCY2iEtOhJtJU466FtFKQTEmbtILZMeiH8sGd0ERa\nk7YbhQjI0qEmICa0K2j/Ytffuf/fn5nha/ck791zz+/ec89597773pvfEHWQdKMDeDVBR7sHuzq5\nyb6YOTeoTEtjEBs0nIw6XYTnTYsoVXeMjqpH7oIzHGqSn3GcJKrpmjXfNP8K0YGLVVi8ljAf8kUh\nTlu02lfXWhJsUd0K12GX1YXnnsqJOu20RkdTI8PSBWc41OSTjpdEdV3Tmgv/g56p4UTFJp9pqiwK\ncXrTqOYCJsIGNe0p96HVheellG9R0RodTY0MSxec4VCTkhOs49CohaeMCuVJHH3CMOyahd5jPcVB\nIgtrtBDEfLCBYW+QMmNOF7eh7u66TMR5RDsqmhSecNvF9VLVtZ1CZbkw7HbNQu8PjOmY0axiYY1m\nfIs6GnvuwSWtUWHSMRvVjtwFZzjcZJ1xkqiMNl3zREAerhZRfkyaH6zLEuc/GI2KFaUnwhp1cvV+\nYzoLz8j1cECE3SEmemQGuuAMh5pkRewxl9qwQSuiHGlQr1DSVaJn71jhna3lXv/Rsu1sE/v16s80\noDKaAOfX3M9NBYoGKtfcjctmtlyg3+559rO+7vviAyu+AV24fHnVF6hw63CDHWo8/dAjUNviL/z0\nXvbF3YULbsuSOSfL5HMqjA75JB8ZpUEqtChLpRoVT9N4gN5v4/huo7Dbq1BqBqsnDqdLoimjLCrX\nE0Rj9E+it3yPB4NnIv/I6r0oeOP0nqBDwYGATguHEve+SceC+9rj5TPCF3cP770bYGkr2VYImq7K\nJUzZCuWfpjTnWpqkAY7vbhyPE73b0+R9JQneD2/jdYGyV5Xr4SaVOdf3iP4NKzwTDMRzeBeO4gyN\n1r+GHf85Hk/i/WUqVT/XFs9Vvk3eJQmzCytDTavHtKlGyHSyJXdh6of9ntOByHWGBny0wobd+xHR\njxFQbg71ONw82SDc/wJFA5Vr9sqniXN9n+gDWNkz+UTTKKZwnKzC33+IBsrsUOLbmtQ7U26LFwqX\nKYNQuDsfVk76Vo9pPwxbBsY+IQ0c0ZFT50WuLZNrf4voi19SucZhGsWlUGh6dvbVX8/OIpHC2vkq\n53rG5pqvE12PgTjQaR9X5TJybbFDmeszuOkfb7bHM3O4Fkm5YpG0l1+Foew5BMeCleYFNNTgNaxy\nxRo+WSYaqchdOgHmRLHK9U6q5vV+Sl12cuU1zGt1Bw7e2s28fp/HEyMX8OaRxlS3wzlRLHMBO08H\ndOgJbz+wWMnxHeRI6UpT1rCDZMrUN+jkir2J79sRNODdJwFGoh5mKLI33Un0qJMr70142/F2ww9v\nLDwVlT2Y39/zeHJvQlTpuQ44Eh1vyO7sworHd0kbiV6HXoQqJF2jzNNUCjCpel7X4H6tUWpbDjdT\nFbnGYSSaQoiMsqh5Xdekd3gBqzUMz7wXH0Cs9DAO75eUDg7V6a/CIZIE/gOixXPPt8eR6JDqzi4c\nwepvJ6XJMJKqqTrWYf6WG27PTVz488SF/Wd5qfNqWXXNYO+tmAsEmgCjU19LouxG5frCtdc1Ds7/\n/OD8zq9crMkV/uJ1w7jrif7Op6MP3Ube1jUNdogq3wHpW66hrX57HKH8Ak25u3CBUsl7WomX/a24\nTVrWx4BsYEybjWYVCff7RBpVudomUoPnstS8yJU2uOrSCd+FFYHu0SYjgeqbV6UteGNIlsUxc8q2\nxdTGRMJ4vJJG84OxRmyA57IE0r4sw2c7cgecH68MR5vw7ibkZVXagjf8ZCkFMfs72lKY0ZpbCvhm\nPGMSUduyFBR8WTtujY5mR+6A90wSMRxtMuUrT/aKadejFa1FS68VtdAWbSkFWnNLAW/FxpOI2pZe\nK1+XNXPxLAjNjtwB7y0Tdjx5uL31Qs2cd61CX1mPmbRhk1ZM6Q0qdZExuYqGk1GnpfacChyjo35M\nnLvHXAzUiK4d9mnJf3dUhKI/OYi2of2CkoEWZdbzM2sDngNCUZ8cCzDX/hnK7KXppshVKHgKyRem\nieaCmlW8TY/hfXwYyxXzKpX35Ws40YRIdWB+IYhIJTtJhbeCqTrnKpUz4VwX0Nwi1+IYTT3f3EC+\nVEyu+FBcWJId44+x0efqr1FZKiZX80q1UDLG/drfopF9ze9RWSom1w7P16sze+zD3mPLXvoL9f0k\nEIr+5CDxcdwlqX0KD1EnTh+Bd2BnDM/j9ImrehT5y14cT7KoPhyYCQ7P13Yy2hCIw+NEW3otbdmp\nlVAp8A7sDNlXS+7nrV71qO5/yNeafS/sqxubUpbM79jxdtTIdRMZB6aD0++ICR3Uu7/D40QbFZva\nUtRKqBR4B3aG6E23/do69c0ow1TZIHYUDRqIrhCNt2zVaKYPB6aDm/INHlX0ZXgSQF8UFPVhYw1R\nJ8bKON6EMw478ycDshLqdryFx96eEC4qdhStGSe5DxAavuBioluKEfQoo5VYO23ArSzkFM7LtTFU\n7ja1wqRRHYXxnjA7c4cD400mcKqvsi5fYBwrkR3lmLIbJz3IM3su1FpWTB8OTAfX4cFSmpP9JgLF\n40R98i8iWl7RilMKHLkeDiy1YsIU7dwf+tKX2TRSFwA9qEr7yyPsxYoEjRP+mWi0Ko3u2YmMA1PB\nJVxH3annI6kZHqewdVWFjiy7nZiFASa4mS7sCrnsDProMNPLlqK2Wo4gzuPskrY1omQQjxIhg7QT\nGqhR5qvolRRZnNfp8Nsa/+DOMqR5nM2V3O7ceir5J5iFkb9gdmNXXHaGnekw36B3UXP30JFBxs/W\no2RQCfYIGaSd0NT2z4vvlKTIYrxOp99MiX8ghBgeZ5Yyl7Jlyl063BS/CmUruOM6syvi56MVcHIX\ne4KoML05ws+eggYSZpzuCVi7iEkMc0U8SoQMMrmubNL13C0hsjivE/0NGP2sbJOq5nEK51GfqhB9\nKFgYyTjgpbkTuxJiZ9idCrNw8RGuPYXj+NdZ3qB5NmSwsUbIoP4GUYQMMrni+3OgiiWcEFmc1ymN\n8QhtZBqjQDSPk+c4+AXjimBhZK64BzqyK/m6ZWdo7ezsxtnZv7HTP863cOZctWxkBa/nUa6Ic3XJ\nIMcJXcDjtYaVkBRZjNcZ8OGonWSrAtE8jrl65wUL8/HYlTRc7MChd1w1JffRS/youFsMIE9il1xZ\nxxM5zBXxGo6QQXpemYUZRZBJkWG58Q3m8DpDTThqJym5ERseZxZrrL9K+ct3Mgsj9yaMlp6D3o59\nwTuLYWd4HBXm60Tcy92bphvfWZ7bC2OEDOK9KUIG6Vz58TriF/h+jUeGRMcbLq/zGvy0lz0CMjzO\n5kG6DdEUy+uYhUGSte7sCiI17Ax7U2H+i3p81NawSUnPt6rpJQEqETKIR4mQQTrXIq7XkL8fbEJC\nZEh0CN4eVgflk945ACoZbbKSqvEZUnhsOKAHVv2MmIVBnZ/Y3diVEDuDPirMe2+4ERWzslmng/+4\nqUF1uA1zRTwKjr6WJYOUk95TFwap97SfHFmU1wn/qQfjhaVYDdejtfXGEKVOJAC8LDWD6ymR5mwg\nS3UuVcz3l2OXo/T7lgwKO3GaGlX22YUVMSkPIizGTsLESCdZbMC0b1RHAa5yNfjvHBhLJnwxS7Uv\nh2BZkaOM1y0ZFHaS0IV5IeSI8HlgMXj4f2kJffQbQALEplKggeNaCZXd2JkoDdE7n3Rx5Sg3Y6XO\nhLx3qog+PZhTDkwE12UJC/64k0fzRSy2qnjLbuxM5FudchsrcSfqu/tjkEFOXxFZLxYV76F80Kcc\nNFndnmzW1k1KSQXaEi674fx12120l0Xdm5oWqg8HJoLLd18TvQ3T++pWjjY5/v8DsqZ6Q0UgmIwA\nAAAASUVORK5CYII=\n",
       "prompt_number": 7,
       "text": [
        "    \u239b V\u22c5(sin(\u03b1)\u22c5sin(\u03b7) + sin(\u03b2)\u22c5cos(\u03b1)\u22c5cos(\u03b7)) \u239e\n",
        "atan\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n",
        "    \u239dV\u22c5cos(\u03b1)\u22c5cos(\u03b2) + s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u23a0"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C_L_alpha = sympy.Symbol('C_L_alpha')\n",
      "C_D_0 = sympy.Symbol('C_D_0')\n",
      "C_L_DM = sympy.Symbol('C_L_DM')\n",
      "C_L_0 = sympy.Symbol('C_L_0')\n",
      "c_bar = sympy.Symbol('c_bar')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C_L = C_L_alpha*alpha_l(t) + C_L_0\n",
      "C_L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$C_{L 0} + C_{L \\alpha} \\alpha_{l}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHQAAAARBAMAAAD+jZX9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nxI7c1zV4+me7HpqbM9bj2NwJ/wHUD3LYd1jnIAAAAABJRU5ErkJggg==\n",
       "prompt_number": 9,
       "text": [
        "C_L_0 + C_L_\u03b1\u22c5\u03b1_l"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k_CD_CL, rho, S = sympy.symbols('k_CD_CL, rho, S')\n",
      "C_D = k_CD_CL*(C_L - C_L_DM)**2 + C_D_0\n",
      "C_D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$C_{D 0} + k_{CD CL} \\left(C_{L 0} - C_{L DM} + C_{L \\alpha} \\alpha_{l}\\right)^{2}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWMAAAAbBAMAAABb6vPKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHa7q2Yiie9Umd3N\nRDIfxLosAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAE0ElEQVRYCdVXW2hcVRRdd5KZO+8ZG9AqYkYq\nrfTHIPGBfnTQ+BP9GKhVKaLzoShYyCQUtbU0QbAK0vZi/agiZmoCKT5IGrEKEjM//SlpO/0Q8iMM\nYkFEycRHpJGkrn0emUdyJ0KLMBtyztl7r732vvuce+YGaCtxx061Vb0s9lU80W4ln8VCvs1qPoqB\ncpuVDIym267k6bar2C3ekJKv3BCWTUmeE8ReBXO29T0WKvhFdL3r57H2UA9XrUmwpbcv95INaDn7\nIzsrQKKQ4Ii7c4iczvnynPf1GEdcXojWJIG3gA/5t7m0QpaAXz84wWxdZ0g0mW9mu9kartqF37yD\nDh8SE+I8zDzRJT8C2m22lkgmOn7tGtGXpEnz6+jeM5bE4jpXk+EIdR8Sg4wLR2LEaBtNNltL5FYT\nGVVd/GUdjyVxS+tcjYbEFDvoQ2KQkx4XyWJjXINms7VExoWGMsCMwB0yNIgliReCpysNniZFrh0/\nEg0N/SOzU9HahqPJtiHy4M6yjrEX3HBG64ld/eP3IzBUMJS25O7Lg/MM2d0/uB0aAwR7J7bk8dEf\nCtuRAyxJ5NIDqOMwVO7vZqEiDEliVwZw/yS1iMnWiNSuV8rOkZDXxbMVLGnLbEXPeAb4Of803jeq\nLXn0RzHsy6FrBBqD0Dk4D5KhqqAxD1gjeZ6mGofyA7FVs9ARKhFwIgv8VDIek60JqZxvAw8F0nL8\nIvwTOa7GNPAo0Jn9DikuRWzJkxeoJFdYYY/BYKHMrhNNAyVMrZ4EhuP2b0UuCqIqOMdGqETAgRLw\nZEE8FJOtCSmeKNv7uQs5FEnFwwaJPVIBprmlZ5YQ9qgfmpv7Zm5O3cjTL5SYlNTJjMZMgc8N9j5M\nA0VKXiN5k6UZDuVUQ0yl+thGSKIpfvpWEdnqCaCWrQkpznAP8Pog4rlayepGjjITd889togYfSLm\nuZ1V52oI96QJSGvMSIDPjZuA7rICxjxzrQsJdyNZ41B+eyMXTYRKNAIUFnFrN3mVmGz67i4apLuj\n6KC7wFfFQyrPa3JKgwdowiD1KjfuItNltN2QBKvOiosvtU1hSrEerY3qSV4/SxIhiZSc0S4zhv7m\nwk3zw1EMmgSJ8gxyJw3CNqgROYNHXKRIP8zXjEj7+kX+4m8p6eT+DR/mpmY0jSmZB3bVxbK2KUwh\nVdTaIWPM8mDVkSRrHBrAUvlJcIqKitAkCKTvS+T3W4TJ1oCM9uDZHxDNIjiZTG8jMlo08Nt6+8tc\ndhSAk9y0lCgUQ8Ie7s3gaxpeNBjEiAzlgPPAb7Sr7TIk8SKSl2scwiPijPV9IbOKUInYIhwM4pxY\nRWzJ9ciwh/ki8NqeXHQI9xIUN6VJgEjKg3MUM+tuDOUc48g2aQyfHtE0wF+8rHjPyqCFgM46Dmu2\ns4rQJCx5dw729lsruR7J47vANFqOVYCXrWJmevd52Ll2L39f7+c7eQtjNAZfwTnMM7uEQBYU/Qkr\nK/lf8q46DmWrDTrCkFzBgpesWmdDNsPNpg47FlDNAENW0bM7++k4++hOcNhA9k/cSafGwO0f4tO/\nsTw+WxZoR56DEgIeX/Hl0BE20TteFz5bJs9GorhDn+yJHrDeiTKcklWue1af+NfNsjlBR35zzH9F\n8MX8P+Qpk+Rfpd9ubTDyCJAAAAAASUVORK5CYII=\n",
       "prompt_number": 10,
       "text": [
        "                                            2\n",
        "C_D_0 + k_CD_CL\u22c5(C_L_0 - C_L_DM + C_L_\u03b1\u22c5\u03b1_l) "
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Force"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q = rho*vel_p.dot(vel_p)/2\n",
      "q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\rho}{2} \\left(V^{2} + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) - V s \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) \\left(P + \\dot{\\eta}\\right) + V \\left(s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) - s \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) \\left(P + \\dot{\\eta}\\right)\\right) + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2} + s^{2} \\left(P + \\dot{\\eta}\\right)^{2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 11,
       "text": [
        "  \u239b 2                                                                         \n",
        "\u03c1\u22c5\u239dV  + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) - V\u22c5s\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                                                              \n",
        "\u22c5sin(\u03b7)\u22c5cos(\u03b1))\u22c5(P + \u03b7\u0307) + V\u22c5(s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) - s\u22c5(sin(\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                           2                                  \n",
        "\n",
        "                                               2                       2    2 \n",
        "\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1))\u22c5(P + \u03b7\u0307)) + s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))  + s \u22c5\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "        2\u239e\n",
        "(P + \u03b7\u0307) \u23a0\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "          "
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = -C_L*q*c_bar*frame_l.z\n",
      "L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{c_{bar} \\rho}{2} \\left(- C_{L 0} - C_{L \\alpha} \\alpha_{l}\\right) \\left(V^{2} + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) - V s \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) \\left(P + \\dot{\\eta}\\right) + V \\left(s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) - s \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) \\left(P + \\dot{\\eta}\\right)\\right) + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2} + s^{2} \\left(P + \\dot{\\eta}\\right)^{2}\\right)\\mathbf{\\hat{l}_z}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 12,
       "text": [
        "                             \u239b 2                                              \n",
        "c_bar\u22c5\u03c1\u22c5(-C_L_0 - C_L_\u03b1\u22c5\u03b1_l)\u22c5\u239dV  + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) - \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                                                              \n",
        "V\u22c5s\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1))\u22c5(P + \u03b7\u0307) + V\u22c5(s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                         2                    \n",
        "\n",
        "                                                                          2   \n",
        "\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) - s\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1))\u22c5(P + \u03b7\u0307)) + s \u22c5(-\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                    2    2         2\u239e\n",
        "Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))  + s \u22c5(P + \u03b7\u0307) \u23a0\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                      l_z"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D = -C_D*q*c_bar*frame_l.x\n",
      "D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{c_{bar} \\rho}{2} \\left(- C_{D 0} - k_{CD CL} \\left(C_{L 0} - C_{L DM} + C_{L \\alpha} \\alpha_{l}\\right)^{2}\\right) \\left(V^{2} + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) - V s \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) \\left(P + \\dot{\\eta}\\right) + V \\left(s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) - s \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) \\left(P + \\dot{\\eta}\\right)\\right) + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2} + s^{2} \\left(P + \\dot{\\eta}\\right)^{2}\\right)\\mathbf{\\hat{l}_x}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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C93TMt3kAvxQPzghaq9bHl1BFHWD3Y/jiPzx6iM7GyDhuUqVPEwGbBh6VZNbuHkwv1vmx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\ndLxIFGlMwh+qB5+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       "prompt_number": 13,
       "text": [
        "        \u239b                                             2\u239e \u239b 2                  \n",
        "c_bar\u22c5\u03c1\u22c5\u239d-C_D_0 - k_CD_CL\u22c5(C_L_0 - C_L_DM + C_L_\u03b1\u22c5\u03b1_l) \u23a0\u22c5\u239dV  + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                                                              \n",
        "+ R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) - V\u22c5s\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1))\u22c5(P + \u03b7\u0307\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                       2      \n",
        "\n",
        "                                                                              \n",
        ") + V\u22c5(s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) - s\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                        2                       2    2         2\u239e\n",
        "\u03b7)\u22c5cos(\u03b1))\u22c5(P + \u03b7\u0307)) + s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))  + s \u22c5(P + \u03b7\u0307) \u23a0\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                  l_x"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "F_A = (L + D).subs(states_sub)\n",
      "F_A_b = F_A.to_matrix(frame_b).subs({alpha_l(t): alpha_l_expr, beta_l(t): beta_l_expr})\n",
      "F_A"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{c_{bar} \\rho}{2} \\left(- C_{D 0} - k_{CD CL} \\left(C_{L 0} - C_{L DM} + C_{L \\alpha} \\alpha_{l}\\right)^{2}\\right) \\left(V^{2} - V s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + V \\left(- s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right)\\right) + s^{2} \\left(P + \\eta_{dot}\\right)^{2} + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2}\\right)\\mathbf{\\hat{l}_x} + \\frac{c_{bar} \\rho}{2} \\left(- C_{L 0} - C_{L \\alpha} \\alpha_{l}\\right) \\left(V^{2} - V s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + V \\left(- s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right)\\right) + s^{2} \\left(P + \\eta_{dot}\\right)^{2} + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2}\\right)\\mathbf{\\hat{l}_z}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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Kd2oL3frNZ7ehcu78RW//DNLpQ9vTWFLmYXJN3UGiBNK8iyQQy0G0fKIDs0//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\nQmCC\n",
       "prompt_number": 14,
       "text": [
        "        \u239b                                             2\u239e \u239b 2                  \n",
        "c_bar\u22c5\u03c1\u22c5\u239d-C_D_0 - k_CD_CL\u22c5(C_L_0 - C_L_DM + C_L_\u03b1\u22c5\u03b1_l) \u23a0\u22c5\u239dV  - V\u22c5s\u22c5(P + \u03b7_dot)\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                                                              \n",
        "\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5co\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                            2 \n",
        "\n",
        "                                                                              \n",
        "s(\u03b2) + V\u22c5(-s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + s\u22c5(-Q\u22c5sin(\u03b7)\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                               2            2    2                       2\u239e\n",
        " + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2)) + s \u22c5(P + \u03b7_dot)  + s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7)) \u23a0\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                            l_x +                              \u239b 2                                              \n",
        "c_bar\u22c5\u03c1\u22c5(-C_L_0 - C_L_\u03b1\u22c5\u03b1_l)\u22c5\u239dV  - V\u22c5s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                                                              \n",
        "(\u03b7)\u22c5cos(\u03b1)) + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) + V\u22c5(-s\u22c5(P + \u03b7_dot)\u22c5(si\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                              2               \n",
        "\n",
        "                                                                              \n",
        "n(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2)) \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "   2            2    2                       2\u239e\n",
        "+ s \u22c5(P + \u03b7_dot)  + s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7)) \u23a0\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                l_z"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Moment"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_ac = sympy.Symbol('x_ac')\n",
      "M_A = (-x_ac*frame_b.x + s*frame_f.y).cross(F_A).subs(states_sub)\n",
      "M_A_b = M_A.to_matrix(frame_b).subs({alpha_l(t): alpha_l_expr, beta_l(t): beta_l_expr})\n",
      "M_A"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{c_{bar} \\rho}{2} \\left(- C_{L 0} - C_{L \\alpha} \\alpha_{l}\\right) \\left(s \\operatorname{cos}\\left(\\beta_{l}\\right) - x_{ac} \\operatorname{sin}\\left(\\beta_{l}\\right)\\right) \\left(V^{2} - V s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + V \\left(- s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right)\\right) + s^{2} \\left(P + \\eta_{dot}\\right)^{2} + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2}\\right)\\mathbf{\\hat{l}_x} + (\\frac{c_{bar} \\rho}{2} \\left(- C_{D 0} - k_{CD CL} \\left(C_{L 0} - C_{L DM} + C_{L \\alpha} \\alpha_{l}\\right)^{2}\\right) \\left(s \\operatorname{sin}\\left(\\alpha_{l}\\right) \\operatorname{sin}\\left(\\beta_{l}\\right) + x_{ac} \\operatorname{sin}\\left(\\alpha_{l}\\right) \\operatorname{cos}\\left(\\beta_{l}\\right)\\right) \\left(V^{2} - V s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + V \\left(- s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right)\\right) + s^{2} \\left(P + \\eta_{dot}\\right)^{2} + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2}\\right) - \\frac{c_{bar} \\rho}{2} \\left(- C_{L 0} - C_{L \\alpha} \\alpha_{l}\\right) \\left(- s \\operatorname{sin}\\left(\\beta_{l}\\right) \\operatorname{cos}\\left(\\alpha_{l}\\right) - x_{ac} \\operatorname{cos}\\left(\\alpha_{l}\\right) \\operatorname{cos}\\left(\\beta_{l}\\right)\\right) \\left(V^{2} - V s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + V \\left(- s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right)\\right) + s^{2} \\left(P + \\eta_{dot}\\right)^{2} + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2}\\right))\\mathbf{\\hat{l}_y} -  \\frac{c_{bar} \\rho}{2} \\left(- C_{D 0} - k_{CD CL} \\left(C_{L 0} - C_{L DM} + C_{L \\alpha} \\alpha_{l}\\right)^{2}\\right) \\left(s \\operatorname{cos}\\left(\\beta_{l}\\right) - x_{ac} \\operatorname{sin}\\left(\\beta_{l}\\right)\\right) \\left(V^{2} - V s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + V s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right) + V \\left(- s \\left(P + \\eta_{dot}\\right) \\left(\\operatorname{sin}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\eta\\right) - \\operatorname{sin}\\left(\\beta\\right) \\operatorname{sin}\\left(\\eta\\right) \\operatorname{cos}\\left(\\alpha\\right)\\right) + s \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right) \\operatorname{cos}\\left(\\alpha\\right) \\operatorname{cos}\\left(\\beta\\right)\\right) + s^{2} \\left(P + \\eta_{dot}\\right)^{2} + s^{2} \\left(- Q \\operatorname{sin}\\left(\\eta\\right) + R \\operatorname{cos}\\left(\\eta\\right)\\right)^{2}\\right)\\mathbf{\\hat{l}_z}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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PyYDfm2ure33KXd4Rfs1Cmgp0KrCJM3c87gWUoatGyDkSTihZHFTogCAMxF15qYov0xol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\nOnqHQIdAh8A4IvC/AV3vpaFUD8BgAAAAAElFTkSuQmCC\n",
       "prompt_number": 15,
       "text": [
        "                                                          \u239b 2                 \n",
        "c_bar\u22c5\u03c1\u22c5(-C_L_0 - C_L_\u03b1\u22c5\u03b1_l)\u22c5(s\u22c5cos(\u03b2_l) - x_ac\u22c5sin(\u03b2_l))\u22c5\u239dV  - V\u22c5s\u22c5(P + \u03b7_dot\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                                                              \n",
        ")\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5c\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                            2 \n",
        "\n",
        "                                                                              \n",
        "os(\u03b2) + V\u22c5(-s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + s\u22c5(-Q\u22c5sin(\u03b7\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                2            2    2                       2\u239e\n",
        ") + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2)) + s \u22c5(P + \u03b7_dot)  + s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7)) \u23a0\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                             l_x + \u239b        \u239b                                             2\u239e                                                \u239b 2                                                                                                                                                                                                             2            2    2                       2\u239e                                                                                \u239b 2                                                                                                                                                                                                             2            2    2                       2\u239e\u239e\n",
        "\u239cc_bar\u22c5\u03c1\u22c5\u239d-C_D_0 - k_CD_CL\u22c5(C_L_0 - C_L_DM + C_L_\u03b1\u22c5\u03b1_l) \u23a0\u22c5(s\u22c5sin(\u03b1_l)\u22c5sin(\u03b2_l) + x_ac\u22c5sin(\u03b1_l)\u22c5cos(\u03b2_l))\u22c5\u239dV  - V\u22c5s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) + V\u22c5(-s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2)) + s \u22c5(P + \u03b7_dot)  + s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7)) \u23a0   c_bar\u22c5\u03c1\u22c5(-C_L_0 - C_L_\u03b1\u22c5\u03b1_l)\u22c5(-s\u22c5sin(\u03b2_l)\u22c5cos(\u03b1_l) - x_ac\u22c5cos(\u03b1_l)\u22c5cos(\u03b2_l))\u22c5\u239dV  - V\u22c5s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + V\u22c5s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) + V\u22c5(-s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2)) + s \u22c5(P + \u03b7_dot)  + s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7)) \u23a0\u239f\n",
        "\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n",
        "\u239d                                                                                                                                                                                 2                                                                                                                                                                                                                                                                                                                                                         2                                                                                                                                                                    \u23a0 l_y +          \u239b                                             2\u239e                     \n",
        "-c_bar\u22c5\u03c1\u22c5\u239d-C_D_0 - k_CD_CL\u22c5(C_L_0 - C_L_DM + C_L_\u03b1\u22c5\u03b1_l) \u23a0\u22c5(s\u22c5cos(\u03b2_l) - x_ac\u22c5s\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "         \u239b 2                                                                  \n",
        "in(\u03b2_l))\u22c5\u239dV  - V\u22c5s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + V\u22c5s\u22c5(-\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        "                                                                              \n",
        "Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2) + V\u22c5(-s\u22c5(P + \u03b7_dot)\u22c5(sin(\u03b1)\u22c5cos(\u03b7) - sin(\u03b2)\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "             2                                                                \n",
        "\n",
        "                                                             2            2   \n",
        "\u22c5sin(\u03b7)\u22c5cos(\u03b1)) + s\u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7))\u22c5cos(\u03b1)\u22c5cos(\u03b2)) + s \u22c5(P + \u03b7_dot)  + \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                              \n",
        "\n",
        " 2                       2\u239e \n",
        "s \u22c5(-Q\u22c5sin(\u03b7) + R\u22c5cos(\u03b7)) \u23a0 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                             l_z"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Generate Numerical Routines"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def gen_aero_force_moment_funcs(F_A_b, M_A_b, const):\n",
      "    # generate a fast function to find the aero force\n",
      "    f_aero = theano_function(\n",
      "        sympy.symbols('P Q R V alpha beta eta eta_dot s'),\n",
      "        [sympy.Matrix([F_A_b, M_A_b]).subs(states_sub).subs(const)],\n",
      "        on_unused_input='warn', allow_input_downcast=True)\n",
      "    return f_aero"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compute_aero(f_aero, P, Q, R, V, alpha, beta, eta_l, eta_dot_l, eta_r, eta_dot_r, const):\n",
      "    \"\"\"\n",
      "    Given state of aircraft, computes instantaenous aerodynamic force.\n",
      "    \"\"\"\n",
      "    if abs(V) < 1e-3:\n",
      "        return np.zeros(3), np.zeros(3)\n",
      "    span = const['span']\n",
      "    \n",
      "    ode_left = scipy.integrate.ode(lambda s: f_aero(P, Q, R, V, alpha, beta, eta_l, eta_dot_l, s))\n",
      "    #ode_left.set_integrator('dopri5')\n",
      "    ode_left.set_initial_value([0,0,0,0,0,0], 0)\n",
      "    ode_left.integrate(span/2.0)\n",
      "    FM_left = ode_left.y\n",
      "    \n",
      "    ode_right = scipy.integrate.ode(lambda s: f_aero(P, Q, R, V, alpha, beta, -eta_r, -eta_dot_r, -s))\n",
      "    #ode_right.set_integrator('dopri5')\n",
      "    ode_right.set_initial_value([0,0,0,0,0,0], 0)\n",
      "    ode_right.integrate(span/2.0)\n",
      "    FM_right = ode_right.y\n",
      "    \n",
      "    FM = FM_left + FM_right\n",
      "    F = FM[:3]\n",
      "    M = FM[3:]\n",
      "    return F, M"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def calc_aero_forces(f_aero, t, eta_l, eta_r, P, Q, R, V, alpha, beta, const):\n",
      "    \"\"\"\n",
      "    Computes force history due to flapping motion of wing.\n",
      "    \"\"\"\n",
      "    \n",
      "    # do simulation\n",
      "    n = len(t)\n",
      "    F_b_vect = np.zeros((n,3))\n",
      "    M_b_vect = np.zeros((n,3))\n",
      "    \n",
      "    dt = np.diff(t)\n",
      "    eta_dot_l = np.diff(eta_l)/dt\n",
      "    eta_dot_l = np.hstack([eta_dot_l[0], eta_dot_l])\n",
      "    eta_dot_r = np.diff(eta_r)/dt\n",
      "    eta_dot_r = np.hstack([eta_dot_r[0], eta_dot_r])\n",
      "    \n",
      "    for i in range(n):\n",
      "        F_b, M_b = compute_aero(\n",
      "            f_aero=f_aero, P=P, Q=Q, R=R,\n",
      "            V=V, alpha=alpha, beta=beta,\n",
      "            eta_l=eta_l[i], eta_dot_l=eta_dot_l[i],\n",
      "            eta_r=eta_r[i], eta_dot_r=eta_dot_r[i],\n",
      "            const=const)\n",
      "        F_b_vect[i,:] = F_b\n",
      "        M_b_vect[i,:] = M_b\n",
      "    \n",
      "    return F_b_vect, M_b_vect"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Flapping Simulation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_aero_force_moment(t, eta_l, eta_r, F_b, M_b):\n",
      "    \"\"\"\n",
      "    Plots aerodynamic force history.\n",
      "    \"\"\"\n",
      "    plt.figure(figsize=(10,10))\n",
      "    plt.subplot(311)\n",
      "    plt.plot(t, eta_l,'b-')\n",
      "    plt.plot(t, eta_r,'r--')\n",
      "    #plt.xlabel('t, sec')\n",
      "    plt.legend(['left','right'], loc='best')\n",
      "    plt.ylabel(r'$\\eta$')\n",
      "    plt.title('wing movement')\n",
      "    plt.grid()\n",
      "    \n",
      "    lift = -F_b[:,2]\n",
      "    side = -F_b[:,1]\n",
      "    thrust = F_b[:,0]\n",
      "    \n",
      "    plt.subplot(312)\n",
      "    newton_to_grams = 1.0e3/9.8\n",
      "    plt.plot(t, lift*newton_to_grams)\n",
      "    plt.plot(t, thrust*newton_to_grams)\n",
      "    plt.plot(t, side*newton_to_grams)\n",
      "    plt.legend(['lift', 'thrust', 'side'], loc='best')\n",
      "    #plt.xlabel('t, sec')\n",
      "    plt.ylabel('gm')\n",
      "    plt.title('aerodynamic forces')\n",
      "    plt.grid()\n",
      "    \n",
      "    plt.subplot(313)\n",
      "    newton_m_to_gram_cm = 1.0e4/9.8\n",
      "    plt.plot(t, M_b*newton_m_to_gram_cm)\n",
      "    plt.legend(['roll', 'pitch', 'yaw'], loc='best')\n",
      "    plt.xlabel('t, sec')\n",
      "    plt.ylabel('gm-cm')\n",
      "    plt.title('aerodynamic moments')\n",
      "    plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def show_mean_force_moment(F_b, M_b, alpha):\n",
      "    newtons_to_gm = 1000/9.8\n",
      "    newton_m_to_gm_cm = 1.0e4/9.8\n",
      "    F_b_mean = F_b.mean(0)*newtons_to_gm\n",
      "    M_b_avg_gm_cm = M_b.mean(0)*newton_m_to_gm_cm\n",
      "    lift_avg_gm = -F_b_mean[2]\n",
      "    side_avg_gm = F_b_mean[1]\n",
      "    thrust_avg_gm = F_b_mean[0]\n",
      "    print 'lift:\\t{:10.2f} gm\\nside:\\t{:10.2f} gm\\nthrust:\\t{:10.2f} gm'.format(\n",
      "        lift_avg_gm, side_avg_gm, thrust_avg_gm)\n",
      "    print 'roll:\\t{:10.2f} gm-cm\\npitch:\\t{:10.2f} gm-cm\\nyaw:\\t{:10.2f} gm-cm'.format(\n",
      "        M_b_avg_gm_cm[0], M_b_avg_gm_cm[1], M_b_avg_gm_cm[2])\n",
      "    F_fwd = -lift_avg_gm*np.sin(alpha) + thrust_avg_gm*np.cos(alpha)\n",
      "    F_up = lift_avg_gm*np.cos(alpha) + thrust_avg_gm*np.sin(alpha)\n",
      "    print 'fwd: {:f} gm, up: {:f} gm'.format(F_fwd, F_up)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Load Aero Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s1_aero_fit = sympy_utils.load_repr(os.path.join('save', 's1_aero_fit.repr'))\n",
      "\n",
      "const = dict(s1_aero_fit['glide'])\n",
      "const.update({'span': 0.6, 'x_ac': 0.1,\n",
      "              'c_bar': 0.1, 'S': 1, 'rho': 1.225})\n",
      "\n",
      "# generate a fast function to find the aero force/moment\n",
      "f_aero = gen_aero_force_moment_funcs(F_A_b, M_A_b, const)\n",
      "\n",
      "pi = np.pi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Simulate"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sim_flap(V, alpha, freq, center, delta, flap_mag, f_aero):\n",
      "    pi = np.pi\n",
      "    beta = 0\n",
      "\n",
      "    t = np.linspace(0, 1.0/freq, 100)\n",
      "    \n",
      "    eta_l = flap_mag*np.sin(2*pi*freq*t) + center + delta\n",
      "    eta_r = flap_mag*np.sin(2*pi*freq*t) + center - delta\n",
      "\n",
      "    F_b, M_b = calc_aero_forces(\n",
      "        f_aero=f_aero,\n",
      "        t=t, eta_l=eta_l, eta_r=eta_r,\n",
      "        P=0, Q=0, R=0, V=V, alpha=alpha, beta=beta, const=const)\n",
      "\n",
      "    plot_aero_force_moment(t, eta_l, eta_r, F_b, M_b)\n",
      "    show_mean_force_moment(F_b, M_b, alpha)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Normal"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim_flap(V=1, alpha=20*pi/180, freq=5, center=6.5*pi/180, delta=0*pi/180, flap_mag = 100*pi/180, f_aero=f_aero)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lift:\t     64.99 gm\n",
        "side:\t      0.00 gm\n",
        "thrust:\t    392.79 gm\n",
        "roll:\t      0.00 gm-cm\n",
        "pitch:\t      0.71 gm-cm\n",
        "yaw:\t      0.00 gm-cm\n",
        "fwd: 346.872658 gm, up: 195.415610 gm\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KyluUEPo55//axL+ULGlmChg8GLp2hWnTin5N1RcpKNUVsYovJ4UAjwOlgYPA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kwKTXWdQrNw8PZBKs2qRMlsJdnbY2+aJoQA+bLk468Of/F93e9psawF/7fj/4iIjkjTa4rkBQUF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x65c6850>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Wings Up"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim_flap(V=1, alpha=20*pi/180, freq=5, center=50*pi/180, delta=0*pi/180, flap_mag = 100*pi/180, f_aero=f_aero)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lift:\t     90.97 gm\n",
        "side:\t      0.00 gm\n",
        "thrust:\t    391.75 gm\n",
        "roll:\t      0.00 gm-cm\n",
        "pitch:\t    366.03 gm-cm\n",
        "yaw:\t      0.00 gm-cm\n",
        "fwd: 337.011189 gm, up: 219.474190 gm\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R7H9/EpFPR2U/MhHxqJ1/bSa5azcWNB1Iz1l9yJ/f6ohERK5NYwq93MmTMD+i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\nV/MpCsu2/8p+ys8uT92CdVnVepVVJIQ3b0LPnrBggeUkhML8HO0dWd1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51OK9jNKxPbWw\nxKSwDKrp2B64CuRG1Rq2AIKAakARYJaJ7pccVVHN3PG7q3cH2gE14h0zaVK4cKGaV23fPsvutyaU\naw+uceDqAc7dPse5O+c4c+sc/9w8x93I26R96o4hKiMxjzIRFZ4Ru+hMuDikx8nRHgdHcHQw4OgI\njo4GHByfYnB6gObwkBj7h0QZHvAk9gH/RVwlvWN6CmYuSMEsBSmYuSCFsxamcp7K5HPNp/e3rxtN\ng3HjYPp0NaF7mTJ6RySEacVqsYTcCWHfvwf488QBTvx3hhuPrnI35irRhkfYReQk9l5u0sSmx8Hg\nhKNdWtLaO+HkkJa0Dg6kcYghjUMM9g5PsXeIwS5NDDFpHvDEcIuHsWHciw7jYdQDsjpnpUjWIni5\ne+GVzevZ12wu2fT+EQgzscSkENSydhWAXMB/wB4g2oTXf1eJ1RQORiWsL9QUdgLyG3dcUR0hfYz7\ngcavsi/7cY8tJR7Zt+z9uMeWEo/sW+5+3DFLiUf2LWs/7nGo8fEC9cXikkJLl1ifwkWo0dJfxHue\nyWoK+/ZVKzHMmGGSywkL87b9fjQNbt6EM2fUdvq0+nryJNy7p5Zwq1BBbR9+CJkzmy92S3Hjhhrg\n8957MH8+ODvrHZH5SJ9CkVTJLSuPHsF//8H58+q95ezZ51/v3IGyZXnWX7pCBcgmlYepgqXWFFqD\nJag5FLuhmrzXAxWBf+I9xyRJYVAQNGwIp05BlizvfDmRyt24Afv3q24Ge/fCoUOQPz/Urq22atXA\nxeWNl7EqwcHQpIla4efrr8HOTu+IhEi97t6FAwfU+8vever9JmtW8PVVf4c1a779KGlhGSQpTL7M\nqAExcfMUDgOWJnjOOyeFsbHq01jPntClyztdStiop0/VB4vNm9UWFATly6sEsUEDKFnSeqc2iolR\nfQf/9z/V37ZNG70jEsL2xMaqSou//oLff4ejR1Vi2KSJqtCQWkTrIUmheb1zUhgQAAsWwN9/S+1H\napaSzYEPHqg5+zZtgvXrVWLVqBE0bgw1aljPRLlBQeDvr1aTmTEjdU058ybSfCySSo+ycvs2bNyo\nEsTNm9WsGT16QL16MkjS0pkyKZSUxcRu3YIRI9Q/PEkIhalkyKCSwMmTISREvXnnyQPffqs+0bdo\nAfPmqT6Llig8XM092LCh+rp9u20lhEJYuqxZ1RrxK1bAlSuqxnD0aChQQNXqX72qd4QiJUhN4cve\nqaawa1c1f90PP5gwIiFeIywMNmyAdetgyxYoVkzVIDZuDF5e+jYzR0XB8uUwbBjUr6+mncmaVb94\nhBBv58gR1fq1bBnUqqX6/5YooXdUIj5pPjavZCeF+/erkZSnTydvYmMh3lVkpGpmXrdObbGxUKeO\n6otYqxa4uaVMHBcuwKxZqvayWDFV01ClSsrcWwhheg8fwsyZ8P33qml55Ej1ty30J83HFig2VjWL\njR0rCaGtCAwM1DuEl6RNq5LAKVPg4kXVB7FkSVi8WK0hXLasWlP499/V1BWmFBkJa9aoPkgffqhq\nCXfsUMvVSUJomeVFWCZLLCvp08OgQar7ygcfqL7Mn3yiprwRqYcsdmgiixaprx066BuHEHEMBnj/\nfbX166eStH37VBPz9Olw8KBa17lcObWVLKnmC8yVS63N+ro+sTEx8M8/6hoHD6qpLk6dUiuR+PvD\nb7/J9BZCpEYuLjB0KPTqpT58Vq0KrVvDmDGQKZPe0Yl3Jc3HL3vr5uMHD9Q/3tWrVQ2JENZA01Rt\n4qFDKrE7eRKuXVMdyu/fh+zZVYKYJg08fqy2R4/U1wcPVAJZvvzzpLJ06dQ9+bQQ4mV37qg+wxs3\nqr70LVta73RZ1kr6FJrXWyeFw4apprgFC8wUkRApLDISrl9XCWJMjKr1c3Z+/jV9+tQ3mbYQIvl2\n7VJz8+bNC9OmqVHLImVIn0ILcv48zJ6tRlUK22KJ/X5MJW1ayJcPKlVSzUNly6pO5QUKqBpESQjf\nXmouL8K0rLGsVKkChw+r94ty5WDCBPWBUlgXa0kKHYE5qPWfw4EjQL0Ez6kFnAYigG1A3gTnx6NW\nMQkDTJbCDRwIgwdDzpymuqIQQghhfRwd1UC2AwdUc3KdOqYf0CbMy1qSwjTAZaAakBEYASwH8hnP\nuwGrgC9RS9kdApbFe70/0BQoadwaG4+9k7/+Up3rBwx41ysJaySrU4i3IeVFJJW1lxUPD9i6VdUa\nlimjZkEQ1sGa+xQeA0YBvwE9gI5A3MQXzqgaQW/gLLAHtebxbOP5LsbXVEzkuknqUxgdDaVKqWbj\nJk2S/00IIYQQqdX27WpWjo4d1XylaWTOE5OTPoWQHSgMnDTue6GSxDiPgPPG4wDFEpwPjncuWaZN\nU6MvGzd+l6sIa2aN/X6EfqS8iKRKTWWlRg3V1/DwYTXp9b//6h2ReB1rTAodgF+A+ahaQAAXVF/D\n+MKBDMbH6YH7Cc6lT24At26pOZl+/FGG3gshhBCvky2b6mPYuDFUqKD6HArLZCkVuYGo/oKJ2RXv\nnB2wCHgC9I33nIeovobxZQIevOJ8JuOxRHXu3Jn8+fMD4Orqire397M+HoGBgUycCJ984kOxYs8/\n0cU/L/u2se/j42NR8ci+Ze9LeZF9W963s4MKFQKJjYWGDX2YMQPc3CwnPmvaj3scGhqKqVlTPZcB\n1S8wL9AAiIx3rjvQied9Cl2AWzzvU7gbmMfzPoVdjVulRO7z2j6Fhw9DgwZqfWNX12R/L0IIIYRN\nOnJE9cXv21etjiItbu/GVvsUzgDeB5rwYkIIarBJcaAF4ASMBI7yvHl5ITAQyAXkNj6e/7YBaJpa\nLuybbyQhFC9+ahPiTaS8iKRK7WWldGm15OayZdC9u1qCU1gGa0kK86FGC5cCrqOahR8AbY3nw4CP\ngDHAHaAs0Cbe62cC64DjqEEm64CAtw1i6VK1zJefX/K+CSGEEEJA7tywcyfcvAn166ulNYX+pNL2\nZYk2H0dEqPWNlyxRM7cLIYQQ4t3ExED//rB3r5r7181N74isj602H+tq7Fg1EackhEIIIYRp2NvD\nlClQty74+MgKKHqTpDAJLlyAGTPUWo5CxEnt/X6EaUl5EUlla2XFYIDvvoN27aBaNbh0Se+IbJel\nTElj0QYPVmscv/ee3pEIIYQQqdMXX4CLi0oMt2wBT0+9I7I90qfwZS/0Kdy8Gfz91RrHTk46RiWE\nEELYgDlz4OuvVR/D4sX1jsbymbJPodQUvsaTJ9CnD/z0kySEQgghREro2hWcncHXV9UYSmKYcqRP\n4Wt8/z0UKybrG4vE2Vq/H/FupLyIpJKyAm3bwg8/QJ068M8/ekdjO6Sm8BVCQlQN4eHDekcihBBC\n2J62bSE6GmrXhm3boHBhvSNK/aRP4cu02FiNBg2gRg21BI8QQggh9DFnDoweDdu3Q8GCekdjeWx9\nnkJP4AmwKMHxWsBpIALYhlojOb7xqJVPwoBxr7vBqlXw778wYIBJ4hVCCCFEMnXtqkYm16ol09WY\nmzUmhdOAA0D8ZUfcgFXAl0Bm4BCwLN55f6ApUNK4NTYeS9SAAWpeQgcH0wYuUhfp9yPehpQXkVRS\nVl7Ws6eaGq5mTbhyRe9oUi9rSwrbAHeBrbxYVdoCOIFKDKOAUah1kuN6IHQCJgLXjNtEoPOrbuLr\nq1YvEUIIIYRl6NcPevVS/6Nv3tQ7mtTJmvoUZgQOAjWAHkBBoIPx3E+oQTN94j0/GBgJ/AbcA2ob\nXw/wAbDdeM2EtJs3NdzdTR2+EEIIId7VyJGwdq3qY5g5s97R6M9W+xR+A8xG1fRpCc65AOEJjoUD\nGYyP0wP3E5xL/6obSUIohBBCWKZRo9Q6yQ0bwsOHekejn5gY6N3btNe0lClpAoFqrzi3C+iHGkhS\n2ngsYUb8kJdr/TIBD15xPpPxWKI6d+5M/vz5AXB1dcXb2xsfHx8VqLGvh+zLfvx+P5YQj+xb9r6U\nF9lP6n7cMUuJxxL3J02CRo0CqV4ddu/2wcnJsuIz537c4/XrQ03ev9Jamo/7A2N4nuSlB+yBU0BZ\noDuq32AV43kX4BbgDZwFdgPzUDWNAF2NW6VE7vXCMndCvEpgYOCzP1Yh3kTKi0gqKStJExOj5jKM\nioIVK2xrcOjJk+DjAwcOgIeH6ZqPrSUpTMfzpmADMBjID/QEbqNGH58H/ICNwP9QCWJc0uePSix9\nja/fhOqHGJDIvSQpFEIIIaxAVBQ0awZZssDChWBnp3dE5hcdDRUqqBHZ3bvbZp/Cx8BN43YD1fT7\nGJUQgpp78CNUbeIdVO1hm3ivnwmsA46jBqCsI/GEUAghhBBWwtFRzS185YoamWwLdTpjxkD27NCt\nm+mvbS01hSlJagpFkkgTj3gbUl5EUklZeXsPHqjl8CpWhEmTwJBKs5ugIGjQAI4cgVy51DFbrCkU\nQgghhEhUhgzwxx8QGAhffaV3NObx5Al07Ag//vg8ITS1VJpLvxOpKRRCCCGs0K1bUL06tG+vlsZL\nTQYPhsuXYdmyF2tCTVlTaClT0gghhBBCvBN3d9i6FapVA2dn+OwzvSMyjb//hl9/heBg8zaNS/Ox\nEMkUf84oId5EyotIKikr7yZnTtiyRTWzzpypdzTv7to1NfXO7Nng5mbee0lNoRBCCCFSlXz5VGJY\ns6Z5Vv5IKU+eQIsWKv4GDcx/P+lT+DLpUyiEEEKkAhcuQK1a0K8fDBigdzRvR9OgSxd49OjlfoTx\nSZ9CIYQQQog38PCAHTtUjWFkJAwbpndESTd5spp6Zs+elJtiR/oUCpFM0u9HvA0pLyKppKyYVt68\nKjGcPx9Gj7aOCa63bIGxY2HtWnBxSbn7Sk2hEEIIIVK13LlVYujrq2oMx4yx3AmuQ0JqCqcKAAAg\nAElEQVTgk09Uk3H+/Cl7bwv9kbxSG2AkkAe4DnQGdhnP1QKmGc/tN567HO+144GuxsezgVdVIkuf\nQiGEECIVCguDOnWgXDmYOhUcHPSO6EX370PlymrJvj59kvYaW13RpDYwDugEpAeqAheM59yAVcCX\nQGbgELAs3mv9gaZASePW2HhMCCGEEDbCzU2tenL1KtSrB3fu6B3Rc7duQY0aqjZTr9HS1pQUjjZu\nB4z7/wHXjI9bACdQiWEUMAooBRQ2nu8ETDQ+/5rxcecUiFmkYtLvR7wNKS8iqaSsmFfGjKqvXunS\n8OGHcPq03hHBlStqwu0GDeCHH/Rr2raWpNAe+ADIBpwD/gWmAE7G817AsXjPfwScNx4HKJbgfHC8\nc0IIIYSwIfb2MHEiDB+ukrHNm/WL5fx5qFoV/Pzg22/17etoLUlhdsAB+AioAngDpYERxvMuQHiC\n14QDGYyP0wP3E5xLb65ghW3w8fHROwRhRaS8iKSSspJy/Pxg5Uro0AGmTEn5kcnHj6u1mocPhyFD\nUvbeibGU0ceBQLVXnNsFNDE+ngLcMD6ehEoKRwAPgYwJXpcJeGB8nPB8JuOxRHXu3Jn8xiE/rq6u\neHt7P/sjjavWl33Zl33Zl33Zl/3Usb9nD9SpE8iCBbB8uQ8eHua///TpgXz5JcyY4UObNkl/fdzj\n0NBQTM2aRh9fRg0kWWTcb4FKCMsA3VH9BqsYz7kAt1A1imeB3cA81KhjUKOQuwKVErmPjD4WSRIY\nGPjsj1WIN5HyIpJKyoo+oqNVf74JE2DoUBg4ENKYoers8WP47juYMUPNndio0btdz1ZHH88DPgXc\nUSOMBwDrjOfWAMVRiaITatqao6iEEGAhMBDIBeQ2Pp6fQnELIYQQwsI5OKhkcP9+NXl0uXJw6JBp\n77FhA3h5wblzcOzYuyeEpmZNNYVpgJ+AdsAT1JQzQ1GjjUHNUzgVyAfsI/F5CrsZH89C5ikUQggh\nRCI0DX75BQYPhoYNoXt3NVI5uYNALl+Gzz5TfQinTVNzJZqKKWsKrSkpTCmSFAohhBCCsDCYNUs1\n8xoM0LmzGpSSO/ebX3v/PmzfrkY2L1sG/fqpmkgnpze/9m1IUmhekhSKJJF+P+JtSHkRSSVlxfJo\nGuzbp5LDFSugbFnw9oYsWSBz5udfQS2nt2ULnDgBFSuqyahbtYICBcwTmymTQksZfSyEEEIIYZEM\nBpXgVawIP/6o+gaGhKgVUS5cUF/v3oWoKKhSRc03WLmy6WsFzU1qCl8mNYVCCCGEsAq2OvpYCCGE\nEEKYiSSFQiRT/IlEhXgTKS8iqaSsCL1IUiiEEEIIIaRPYSKkT6EQQgghrIL0KRRCCCGEECZlTUnh\ne6hl7W4D/wFTAPt452sBp4EIYBuQN8HrxwNhxm2cuYMVqZ/0+xFvQ8qLSCopK0Iv1pQUTkYldDkB\nb6A60Nt4zg1YBXyJWhf5EGoZvDj+QFOgpHFrbDwmRLIdPXpU7xCEFZHyIpJKyorQizUlhV6oRC8K\nuAH8CRQznmsBnEAlhlHAKKAUUNh4vhMwEbhm3Cai1kYWItnu3bundwjCikh5EUklZUXoxZqSwr+A\ndkA6IDdQH5UYgkoYj8V77iPgvPE4qOQx/vngeOeEEEIIIWyeNSWFo4DiQDjwL3AQWGs852I8Hl84\nkMH4OD1wP8G59OYKVNiG0NBQvUMQVkTKi0gqKSvC1gUCsa/YdhqfcxAYDjgAWYA1qMEjAD8C0xJc\n8zjQ3Pj4HlA23rmyvJxExjkPaLLJJptssskmm2xWsJ3HxrijEsQM8Y41QyV+AN2BXfHOuaCakOP6\nFO4GusU73xXYY5ZIhRBCCCGE2RiAq8BQ1DQ0rsBvwGLjeXdUbWALwAmYwItJnz9wCsiF6o94EuiR\nEoELIYQQQgjT+hD4G7gL3AKWopLBOLWAf1A1hK+ap/C2cZN5CoUQQgghhBBCCCGEsDVZUE3ND4FQ\noO1rnjsAtVrKfWAO4JjM6wjrZaryEgg8Bh4Yt39MH6rQWVLLSnHUlFq3UH2jk3sdYd1MVV4CkfeW\n1C6pZaUTarGO+6hZWcbz4kpv8t6SiCXGzRmojOp7WCyR59UFrgNFUX0WtwNjk3EdYd1MVV62A35m\njfT/2bvvuKrq/4HjLzaCiuAeGc5cKc4cpIiae+80w4FWWl+zoeXPNC1HZWaZ5sg90hy5U1MxcY8c\nOSpNcqU5QUSQcX9/fA56uYJe8F7OHe/n43Ee3rPfwMfDm8/5DKE3c8tKWaA30Ib0f8nLs8U5WKq8\nyLPF8ZlbVl7T9ruj+kwcBIZm4TpOwxdIAEobbZtH2l/eqRYDnxitN0TVAmX2OsJ+Waq8gHpw97V0\ngMJmZOWZUJpHf8nLs8U5WKq8gDxbHN3TPBPeBtY8zXXsafDqrCgLJJF2DJ+jpD+bSXqznhREzaWc\nmesI+2Wp8pJqHOoVUCRqrm7hOCz1TJBni3Ow9M9Zni2O62nKSgPUlL9Zvo6jJ4U5eXSQ6jukHe/Q\n+FjTWU/Qjs3MdYT9slR5AVWFXwJVpT8DWAuUtFikQm+WeibIs8U5WPLnLM8Wx5bVstIHqAZ88TTX\ncfSkMBbIbbLND/WNedKxftq/dzJ5HWG/LFVeAPYDd4FEYD5qAPUWFotU6M1SzwR5tjgHS/6c5dni\n2LJSVtoBY4HmwM2nuI7DJ4V/ohpgGr9Tr8LD6lVjJ4Agk+OuosZFzMx1hP2yVHkRjs9SzwR5tjgH\n+TkLc2W2rDRD1Ri3Qv1eyup1nMYSVKcAHyAY1fumfDrHNUV1FCiPahcWgcq8M3sdYd8sUV78tP3e\nqP+UPVB/tZV+5CrCnmXmmeCNaoeaAnhpS1auI+yXJcqLPFucg7llJRQ1IUfwU17HqfiTdpyebtr2\n4qhq1GJGx76NGmYkddw5DzOuIxyLJcpLPtQrnhhUzeFu1Iw7wrGYW1YCUb/cU4Bk7d+/zbiOcCyW\nKC/5kWeLMzC3rGwD7vNwzMo7wHozriOEEEIIIYQQQgghhBBCCCGEEEIIIYSjmQts0TuITAhDDSEi\nhBA2y9GHpBFCOC6D3gFkwg+owYbFo3qS/nRuQohs5q53AEIIp+XB09WeuVgqkGwQry1CCGGzpKZQ\nCPEkTVDjMN5AjXMVAdQ0OSYnMBm4iJpt4TDQ3mh/IKo26GVgA2qIhE+1fe+ihtxIQM3T+T+TawcA\nS7VzrgBjSJsQhqGG58hhct5HPBzKI0S7f2PgVy3GE8BLJud8CpzU9p8HppF2VoAwVCIbAhwH4lDD\nQhQCGgJHtDi3kLZmMPU8Y9WBn1FDGt0B9gG1yFgUMFqL6Tbqe/E6asy6b1EzGVwEBpqcVxhVU3lL\ni3e7du9UIajvTXNgj3bMAdR4ZpVRM2bc1eIzHeOsOrBZi/8/YAVq2IxUo4C/gDbAadT3ZhsPp2UL\nQc3KAQ+HYZmtrQdr947RliM8+vMSQgghRDZqB3REDZBbHpiJShADtP0uqERjG1AXlQCGo5K8UO2Y\nQNQv/AuoxDBQWwaikpB+QClgAHAPNY9nqlWo0flDUAP6LkAlUpu1/d6ohKiX0TmuqCTqA209RLt/\namJRGpiHSpT8jM77EKiHSmxCgVOo9oupwlBjx21DJcZVtdh2AjtQSV2Qdt4PJucZJ4UVUYnWItR8\npSWBzkBtMhalxTtYO364FsvPRtuGadtSkzcXVDJ3GPWzqaTFdRPIa/K9OaR9Lo8a/+4oEIlKdstp\nX+Neo3gqoJLBkUBZ7WtaBvzBw8GWR6ESwQ3a96qyFkuEtt8DeEO7fwFtyYV6i3UTNY9rKW1pS8aD\n9AohhBBCB66oX9gva+shqETOdJ7N2aiEDh4mhcNNjrkAjDfZ9iVwVvtcWjvPeIBeD1SN2GajbZNR\nSUuqpqhBXQsaxZiCSnBTFdS2NSFj7Un72jdMO6ey0bZ3tW1VjbYNBq6ZnGecFC4AfnvMfdMTBaw0\nWndBJcerTbbdRCVaoL5vKaikLpUncBkYoa2HaMe0MTqmk7bNuLa3nbbNR1ufi5oxwZgXKtltq62P\nQn3deY2O6YpKXD219fTaFPpr2xoghMg28vpYCPEkJVBJzF+oJCQaVbuW+pqwJuoX/CXSjqzfg0en\n39pv9Dk3UBT1OtfYr6gkMnWqL1A1V6kSUa83jU1H1fA9p62HA+tQ81EbO2L0+SoqOSlotK2Ddv/U\nr2UhKgktZHSMAfXq2Pg6AMdMtuUl43aP1YGtGezLiAFVe2e8fs3kvgbUa9wC2npFVK3uaaNj7qNq\nDyuaXN/42hl9TRhduyYqaTT+mV9HJYbGP/fLWgzG6y5G10nPLWAWsAlVyzgUVRsphLAi6WgihHiS\ndahE4w1UzV4i6rViak2PKypRrJHOufdN1u9aKCbTZOukFlN/YALQmoe1VY+LBx7+cfwC6vXnWOAd\nVGJSB/Wa2dPo+BTS9nxO/ZyczjYX0u8lbUjnazCHabtEQwbbnvQHf3pxGV/H8Jhtqdd2QbUHNK3p\nBVVbmcr0e256nYz0R9UAv4SqzR0DDAJmPOE8IUQWSVIohHicvKg2ZkN4OC5gMdLW8hwE8qA6epzI\nxLVjUK+BG6Bqg1I1QHUQiUcle6BqAX/RPnuiaqlM7zUd+AqVzP2LamuXGcGomq6PjLZ1yeQ1zHUI\n9Wo3o6TRUk7w8Gd4StvmhUqApzzltQ8CVUg7j3NWpCaN6X0vTmjLJFQHm/5IUiiE1cjrYyHE49xC\nvaLsD5RB1ZwtQbUhTLUVlbCtRLU7K4l6PfomqgPJ44wzOq4MqqPJa6jaOlC9kdegeteGoF4nz0L1\ndja1XPv3/4Dvzfvy0jgN5Ed1cimJ6rjyehauY47PUF/vItT3qhRP7miSXs3ik7ZtRb2yX8zDjibz\nUYn1tExHndZYVLK5EJWkl0B1SvlK+2yuc9q/bVHff1/U92MC6o+BZ1Hl7kUy90eHECKTJCkUQjxO\nCipZKYVqXzYbVWvzr8lxbVBJ4ZeoGql1qCFOzhgdk16N2DRUzdyHqF/476Haj80xOqYPqi3gOlSv\n1Qs87MBiLAGVoLiSflL4pBq59aghacaivtYuWjym52X0OvhJ24zXf0cluflRvZZ/A94Gkh4TX1bv\n2w6V8K5HJYgFUK9jbz7mHHO2nUYlmjlRbf9OoGrxvFF/TKQe/6TrHEC9Jv4ONczON6hmBqVRPaX/\nQCX8u1Cvj4UQTsIT9TCPQr1a+g1oZrS/EepBdBc1JERxk/MnoF7/XOfRdi6BqGEz7qJ+aTVCCOFo\nlpG2N64QQgg75YMa8yo12WuJSg6LA/lQjdk7opLHz1ADraYagEoYi2jLCW1bqj2oMa+8UD0Mb2nX\nFELYP39Uh4T7QH2dYxFCCGElR1FJXH9U78JUPqhBb1OHKdhN2vZLvXmYNJZFNVr3Ndq/g7RJoxDC\nfkWh/oAco3McQghht2y993FBVEL3O2rmA+NxtOJQ7ZUqomYUqGCy/xgPx+GqiOohZzwcxlEeHadL\nCGGfAvUOQAgh7J0tdzTxQPXMm4tK+nxRNQHGYlBTIoFq7Bxtsi9nBvtMzxVCCCGEcGq2WlPoippB\nIZ6Hvc1ieXQaLT/UKPrp7ffTtmV0bh4eTTIpUqSI4fLly1kOXAghhBAiG53l0dmjssQWk0IXVA/k\n/EALHs4ScAJ41ei41LGsThjtD0INqApqUNXfjfaVRNUYxhrtX2B688uXL2MwWHMsWeEoRo0axahR\no/QOQ9gJKS/CXFJWRGa4uLiUstS1bPH18TTU5O1tUOOOpVqFGni1A2ocrJGoscv+1PbPR826UAQ1\nn+oQ1KtntGOOaOd4a9eoBKyw3pchhBBCCGE/bK2m8FlUL+N41CCmqfqjZlHoiJqaaSGwF+hmdMx0\nVG1g6kT1M0k7HVI3VJJ4E/hHu5bxJO1CZEpUVJTeIQg7IuVFmEvKitCLrSWF//D42sutqGmVMjJU\nWzK6dsMsxiXEI4KCgvQOQdgRKS/CXFJWhF7SmzfT2RmkTaEQQggh7IGLiwtYKJ+zxTaFQgghhBAi\nm0lSKEQWRURE6B2CsCNSXoS57LmsBAQE4OLiIosFl4CAgGz7+dlam0IhhBBC2Klbt27JsG4Wpr0e\nzp57Zdud7Ie0KRRCCCGywMXFRZJCC3vS91TaFAohhBBCCIuSpFCILLLndj8i+0l5EeaSsiL0Ikmh\nEEIIIYSQpFCIrAoJCdE7BGFHpLwIc0lZsQ9z587Fw8PjwXpERASurq5cvnxZx6iejiSFQgghhBBC\nkkIhskra/YjMkPIizCVlRX/379/XOwRdSFL4BCmGFJJSkvQOQwghhBBWEhISQr9+/RgxYgSFCxfm\nmWeeYd++fdSvXx8fHx8CAgLo0aMH165d0ztUq5LBq9MRPDuYG/ducD3uOrfu3cLL3YvaxWrTMLAh\nDQMbUrNoTTzdPPUOU+hM2v2IzJDyIswlZUUfy5Yto2fPnmzfvp3r16/TpEkT2rRpw7Rp07h9+zZv\nvPEGnTp1YseOHXqHCsCBSwf4/rfvLXpNSQrTMbbRWPL55CNvjrwE5AggLjGOned3sv3cdt7c+CZn\nbp6hzjN1CK8WTsfyHbN1tHEhhBBCWF6RIkWYOnUqACNGjCBPnjzMnTsXd3eVKi1YsICgoCAiIyMJ\nDg7WJcZ7ifdYemIp3x74lutx13m9xusWvb68Pk5H/WfrUyF/BQrmLIiHmwd+3n60KtuKiU0ncnjA\nYaIGR9Gvaj8++fUTgucEs/fiXr1DFjqQdj8iM6S8CHM5Q1lxcbHO8jSqV6/+4POJEyeoXbv2g4QQ\noHLlyvj5+XHixImnu1EWXIy5yHub36P4V8VZdmIZoxqM4sybZ3i/3vsWvY8khVkQkCOAzhU7c6j/\nIcKrhdNpWSe6Le/GuVvn9A5NCCGEsHkGg3WWrHJxccHX1zfNui1N11d9RnVSDCns7buXDT020LJs\nS9xc3Sx+H0kKn4KbqxthQWH8MegPKuavSI2ZNRi6ZSgJSQl6hyaygbT7EZkh5UWYS8qK/ipWrMje\nvXtJTEx8sO3o0aNER0dTqVKlbI9nTbc1TGw6kVIBpax6H1tLCgcBB4F4YI7R9kAgBbhjtAw3OXcC\ncF1bxpvsCwS2A3eBU0AjSwbt6+nLiAYjOPHGCf66+Reh80O5GnvVkrcQQgghhJUYDIY0NYODBg0i\nJiaGsLAwTpw4QWRkJK+88gr169enXr162R7fC8VeyJb72FpSeAkYA8zOYH9uIJe2fGq0fQDQFqis\nLa21bamWAIeAAFQyuRzIZ8nAAQrlLMTyLstpUrIJtWbV4rd/f7P0LYQNcYZ2P8JypLwIc0lZyX4u\nLi5pOo0WKFCAzZs3c/HiRWrWrEnr1q2pXLkyy5cvf+S8x63bG1uNfgxQDOitrQcCfwMeQHI6x+9G\nJZKztPXeQH+gDlAWOAbkRdUUAuwAFgPT07mWwRLtCJafXM7r619naoupdK7Y+amvJ2xPRESEvOYR\nZpPyIsxlz2XF1triOYInfU+1RNQi+ZytDkmT0Rf3D2AAtgDvATe07RWAo0bHHQMqap8rohLKu0b7\njxrtt4pOFTpROqA0bX9oy/H/jjMqZBSuLrZWMSuehr0+tIU+pLwIc0lZEXqx1SzFNCW+BtQAigPV\nUa+PFxntzwlEG63HaNvS25e6P5elgs1IUKEg9vfbz7Zz2+ixsofMjCKEEEIIm2UvNYV3gcPa5/9Q\nHVL+BXy1fbGo9oap/LRtpLMPIA8qMUxXWFgYgYGB6sA8eQgKCnrwl1tqWw9z108dPMVHz37EF5e/\noO+avrzq9yquLq5Zvp6s2866cbsfW4hH1m17XcqLrJu7nrrNVuLJSvzC8oy/vxEREURFRVn8HvbS\nptBUQVRS6IfqibwL1Vs5tU1hX22pi2pTeBTIz8NEcSewAJiRzrUt0qbQVFxiHM0XNad8vvJMaznN\n7hujCvtu9yOyn5QXYS57LivSptDysrNNoa1lJm6oziQjgaJAOKpjSTXUK+C/AH9gKqr3cOrQMgOA\n/wGNUV/TZmAyD5O+PUAkMAJoAXwPlOZhm0RjVkkKAe4k3KHJgibULlabSU0nSWIohBDCoUhSaHnZ\nmRTaWpvCEUAcMBToCdwDPgRKAhtRr3yPa9u7G503HVir7TumfTauBeyGapN4EzWUTUfSTwitKpdX\nLn7u+TO//vMrw7cNl/84QgghhLAZUlX1KKvVFKa6HnedkLkhdKvUjf+r/39WvZewHnt+xSOyn5QX\nYS57LitSU2h5zlxT6BTy+eTjl16/MP/ofL47+J3e4QghhBBCSE1hOqxeU5jqzM0zBM8OZnHHxYSW\nCM2WewohhBDWIjWFlic1hU6idEBplnRcQvcV3Tlz84ze4QghhBAiHWFhYTRp0uSprhEVFYWrqyu7\nd++2UFSWJ0mhzhqWaMjHIR/Teklrbsff1jsckQkyJpfIDCkvwlxSVmzPN998k2be4379+tGwYUMd\nI7IOSQptwGs1XqNxicZ0W95NZj0RQgghbEyuXLnw8/PTOwyrk6TQRkxqNolkQzLvbX5P71CEmey1\nd6DQh5QXYS4pK9kvJCSEvn37MmzYMPLnz4+fnx/h4eHEx8cDaV8fjxo1itmzZ7Njxw5cXV1xdXVl\n/vz5AMTGxjJ48GCKFy+Ot7c3JUqUYNy4cWnudenSJVq1aoWvry+lSpVi4cKF2fvFPoYkhTbC3dWd\nZZ2WseHMBmYemql3OEIIIYRTWb58Obdu3SIyMpJFixaxZs0ahg4d+mB/6oQT7733Hi+//DJ169bl\nypUrXLlyhS5dumAwGGjVqhXr1q1jypQpnD59moULF1KwYME09xk2bBhhYWEcP36cLl260Lt3b86c\nsY1+BZIU2hD/HP6s7b6W4duGs+/iPr3DEU8g7X5EZkh5EeaSsqKPvHnz8t133/Hcc8/RqlUrPvnk\nE6ZPn05cXBzAgx7Avr6+eHt74+HhQYECBShQoADe3t5s27aNX3/9lWXLltGmTRsCAwOpV68effr0\nSXOfN998k06dOlGyZEk++eQTvL292b59e7Z/velx1zsAkVbZvGWZ3mo6XZd35fCAwwTkCNA7JCHs\nxpXYK2z8ayN/3/qb+8n3SUhOICEpgYTkBFIMKVQvXJ1GJRtRPl95mWZSCB25fGyd/3+GkVkfDqdW\nrVppngt169bl/v37nD171qzzDx06hL+/P9WqVXvscUFBQQ8+u7m5UbBgQa5evZq1oC1MkkIb1L58\ne3ae30mvVb1Y030Nri5SoWuLpN2P/lIMKRy8fJD1f65n/V/rOXvrLC+VeomK+SuS0zMnXu5eeLp5\n4uXmhQEDey/u5cu9XxKfFE9oiVBCA0NpVroZRXMXtXqsUl6EuZyhrDxN8mYt2TW+oqenZ5p1FxcX\nUlJSsuXeTyJJoY2a0HgCDeY24PNdnzM0eOiTTxDCicQlxvH1vq/5au9XBOQIoGWZlkx8aSJ1n6mL\nh5tHhuf1q9YPgHO3zrHt3Da2ntvK+7+8T1iVMIbXHy4180I4sQMHDpCSkoKrq6qI2b17N15eXpQq\nVeqRYz09PUlOTk6zrUaNGty6dYtDhw5RvXr1bInZ0qQKykZ5uHmwtNNSJu2dxK///Kp3OCId0u4n\n+yUmJzLj0AzKflOWQ/8eYtur2zg58CSfv/Q5DQIbPDYhNFbCvwR9q/VlccfFnHjjBLH3Yyk3pRxf\n7vmShKQEq8Qu5UWYS8qKPm7cuMHAgQM5ffo069ev56OPPiI8PBwfH59Hji1ZsiSnT5/m5MmTXL9+\nnfv37xMaGsqLL75I165dWbNmDefOnWPXrl18//33j72vLc0AI0mhDXvG7xnmtpvLyyte5mqsbbQ3\nEEIPBoOB5SeXU2laJZaeWMqqrqv4sfOPVMhf4amvXShnIaa3nk5EWATbo7ZT/tvyLP19qU09qIUQ\n1uXi4kLnzp3JlSsXwcHBdO/enZYtW/LZZ5892G/c3rBv377UrFmTunXrUqBAAX744QcA1q9fT4sW\nLXjttdcoV64cr7zyCjdu3Ehzn/TubStsJxLbkW1zH5trxLYR7L64m809N+Pm6qZ3OEJkq79v/U3P\nlT1JSE5gfKPxNC7Z2KoP0e3ntjNk8xBK5CnBgvYL8PX0tdq9hHA09jr3ccOGDSlTpgwzZszQO5RH\nyNzHIo1RIaMwGAyM3jFa71CEyFbLTiyj9qzadK3YlQPhB2hSqonV/6puWKIhe/vuJbdXburPrc+l\nmEtWvZ8QQn8Gg8Euk1lLk6TQDri5urG442JmHJ7BjqgdeocjNNLux3ruJd7jtXWv8eHWD9nQYwP/\nq/2/bO2F7+XuxZy2c+hcoTO1v6/N4X8PP/U1pbwIc0lZyX6mr4edlfQ+thOFchZidpvZvLLqFX4b\n8Bt5ffLqHZIQVnH6+mm6/NiFCvkrcHjAYXJ75dYlDhcXF4YFD6NMQBmaLmzKzNYzaVeunS6xCCGs\ny1YGj9abrdUUDgIOAvHAHJN9jYDTwF1gG1DcZP8E4Lq2jDfZFwhs1849pV3L7jQv05zOFTrTd01f\nqea2Ac4wllh2W3ZiGS/OeZE3a73Jko5LdEsIjXWs0JGNPTYyaMMgPtv1WZavI+VFmEvKitCLrSWF\nl4AxwGyT7fmAFcBwwB+VOC412j8AaAtU1pbW2rZUS4BDQIB2jeXaNe3OuMbjuBhzkWkHp+kdihAW\n9fW+rxmyaQhbXtlCePVwm3qVU6NIDfb228vcI3P5cs+XeocjhBBWYWtJ4SpgNXDDZHsH4HdUYngf\nGAVUAcpq+18FvgAua8sXQJi2ryxQFRgJJAArgWNAR+t8Cdbl6ebJko5LGBkxkmNXj+kdjlOTdj+W\nYTAY+OCXD/j2wLdE9okkqFDQk0/SQbHcxfi5589M2juJH37/IdPnS3kR5pKyIvRia0lhKtMqgorA\nUaP1OOCMth2ggsn+Y0b7KgJ/o14dpzpqtN/ulMlbhokvTaTb8m7EJcbpHY4QWdCgUS8AACAASURB\nVJaUkkTfNX3ZFrWNXX12EZgnUO+QHqu4X3HWv7yetza+xfZz0gZJCOFYbDUpNG0w5wvEmGyLAXJp\nn3MC0Sb7cmawz/Rcu9SrSi+qF6nO2z+/rXcoTkva/TyduMQ42i9tz5XYK2zrtY18PvbRoqNywcos\n7bSUrsu7cvzqcbPPk/IizCVlRejFVnsfm9YUxgKmLc79gDsZ7PfTtmV0bh4eTTIfCAsLIzAwUB2Y\nJw9BQUEP/pOmVuvbwvrUFlMp9245Pr7xMSPDRuoej6zLurnrQbWDaLGoBbn+zcV7dd57MEC0rcT3\npPWGIQ35uvnXhI4OZUrzKXRt1dWm4pN1WddzXViH8fc3IiKCqKgoi9/DdlpypzUGKAb01tbDUe0G\ng7V1X+AaEAT8CexC9Vaepe3vqy11UW0KjwL5eZgo7gQWAOkNXW5zM5o8zoFLB2i1pBUHwg9Q3M+0\nQ7awpoiIiAcPQ2G+mIQYmi5sSs0iNZncbLJNdSjJrEl7JjHrt1lE9o7EP4f/Y4+V8iLMZc9lxV5n\nNLFlzjyjiRvgjarBdAO8tH9XAZVQHU68UZ1GjqASQoD5wBCgCFBU+zxX2/enduxI7dwO2rVWWPuL\nyQ41i9ZkSO0h9FzZk+SUZL3DEeKxYu/H0mJRC6oWqmr3CSHA23XepmmppnRZ3oUUQ4re4QghxFOx\ntSfyKOCjdLaNRo0tOAV4FtiL6l183ui4CUA/7fNMYJjRvmdRSeILwD/AQNRYh+mxq5pCgBRDCk0W\nNKHBsw34qIHpt08I2xCXGEeLRS0oE1CG6a2nZ+sMJdaUlJJE6LxQWpVtxfv13tc7HCF0JTWFlufM\nNYWjUDEZL6O1fVuB8oAPEErahBBgKJBXW4aZ7PsHaKidW56ME0K75OriyoL2C5h6YCq7zu/SOxwh\nHnEv8R5tf2hLYJ5Ah0oIAdxd3VnYYSET90xk/6X9eocjhMiCuXPn4u/vz71799JsHz16NCVLlgQg\nPDyc0qVL4+PjQ6lSpRg+fDj3798H4N69e3h5efHLL788OLdBgwZ4eXk9uGZ8fDze3t5s3Lgxm76q\nzHOcJ7OTK5KrCDNbz6THyh7cjr+tdzhOQRpVmyc+KZ4OyzpQwLcA37f53qESwlTF/YoztcVUuq/o\nTkxC+n3YpLwIc0lZyX7dunXDxcWFH3/88cG2lJQUZs+eTXh4OAaDgUKFCrFkyRJOnz7NV199xZw5\ncxg7diwAOXLkoE6dOmzbpuqc7t27x969e/H392fnzp0A7Nq1i5SUFOrXr5/9X6CZHO/p7MRaP9ea\nVmVbMWDdAKm+FzYhKSWJrsu7ktMzJ/PazcPN1U3vkKymY4WONCnZhNfXvy7//4SwM97e3rzyyivM\nnDnzwbYtW7Zw+fJl+vTpg4uLC2PGjKFmzZoUL16c1q1b895777F48eIHx4eGhrJ161YAIiMjeeaZ\nZ+jYseODbdu2baNmzZr4+vpm7xeXCbbWptAW2F2bQmP3Eu9Ra1Yt3q79Nn2q9tE7HOHEDAYDvVf3\n5urdq6zuthpPN0+9Q7K6uMQ4as6sydB6Q+lVpZfe4QiR7cxuU2itTmZP8fv75MmTVKpUiVOnTvHc\nc8/RqVMnUlJSWLlyJQAzZ85k1qxZ/PPPP9y9e5ekpCQMBgPx8fEA7Ny5k9DQUG7cuMG4ceO4desW\njRs3ZsKECRw4cIA6derQuHFjxowZk6m4nLlNoXhKOTxy8EPHH3h/y/ucunZK73CEExv6y1D+uPEH\nyzsvd4qEEMDHw4cfOv7AO5vf4c8bfz75BCGclcFgneUpVKhQgeDgYGbMmMF///3H2rVr6d+/PwA/\n/vgjgwYNonv37mzcuJEjR47w0UcfPWhTCFC7dm28vLyIiIhg+/bthIaG0rBhQ44cOcKFCxc4dOgQ\noaGhTxWjtZmbFAahOmfcAhKNlvuPO0noo2KBioxrNI4uy7twL/Hek08QWSLtfjL2+a7PWf/Xeta/\nvP7BwNTO4vmCz/NxyMd0X9Gd+8kPH5FSXoS5pKzoZ8CAAcyfP58ZM2ZQuHBhmjVrBsCvv/5K1apV\nGTx4MFWrVqVUqVKcO3cuzbBaHh4eBAcHs3LlSg4fPkxoaCh58+alYsWKfPzxx7i5uVGvXj29vjSz\nmJsULkENEF0f1Xs3dalgpbjEU+pXrR+VClTi7U0yDZ7IXnOPzGXKgSls6rmJgBwBeoeji9drvE7R\nXEUZu3Os3qEIITKhU6dOAHzyySf07dv3wfZy5cpx/Phx1qxZw9mzZ5k8eTKrVq165LVuaGgoixYt\nonz58uTLl+/Btnnz5lG3bl08PR3jrcktnKf9ocFRRMdHG0pNLmVY+vtSvUMRTmLN6TWGgp8XNJy6\ndkrvUHR3IfqCId9n+Qynr53WOxQhso0j/A4dPHiwwcPDw3Dp0qUH2xITEw0DBgwwBAQEGHLnzm3o\n0aOHYcqUKQZXV9c05x44cMDg4uJiGDx48INta9euNbi6uho++eSTLMXzpO8pYLGOEOYmepOBA8BC\nS93YhmnfY8dw6PIhmi9qzp6+eygVUErvcIQD23V+F+2WtmP9y+upVbSW3uHYhK/3fc2q06vY1mub\n3c/eIoQ5HGHw6i5dupCQkMDq1av1DgWwzY4m44BPgBPAdqPFoQaBdkTVi1Rn+IvD6baiW5r2TeLp\nSbufh05eO0mHZR1Y2H6hJIRGBtYcyJ2EO8w7Ok/KizCblBV93Lp1i82bN/PTTz/xzjvv6B2OLtzN\nPO5H4CxqDuJ4o+32/eeAk3jrhbfYFrWNYb8M48umX+odjnAwl2Iu0XxRcz5v8jlNSzfVOxyb4ubq\nxozWM2i+qDkzKs3QOxwhxGNUrVqVmzdvMnToUJseYNqazK1uvAPkAxKsGIutcKjXx6lu3rtJ1elV\n+ab5N7R5ro3e4QgHER0fzYtzXuTl519mWLDp7JIi1ZBNQ7h57yZz283VOxQhrMoRXh/bGlt8fbwT\n6Wls1wJyBLC001L6renHmZtn9A5HOICEpATaLW1Hg2cbMLTeUL3DsWmjG45me9R2tp/brncoQgiR\nIXOTwihgMzAdGGO0jLZOWMIaaherzaiQUXRY2oG4xDi9w7F7ztzuJ8WQQq+fepHPJx9fNftKOlE8\nQU7PnAwIGMCAdQOIT4p/8gnCqTnzs0Xoy9yk0AdYD3gCxbTlGW0RduT1Gq8TVChI5kcWWWYwGHhn\n0ztcib3CgvYLHHo+Y0uqW7wuzxd8nnE7x+kdihBCpEv+vH+UQ7YpNBaXGEfd7+sSXi2cgbUG6h2O\nsDOf7fqM+Ufns7P3Tvxz+Osdjl25FHOJyt9V5kD4AUr6l9Q7HCEsTtoUWp4ttinsBVQx2VYFeMUS\nQYjs5ePhw4ouKxj962h2X9itdzjCjsw9MpepB6ayqecmSQizoGjuorxd+22G/SKdcoQQtsfcpPAT\n4ILJtovAp5YNR2SXUgGlmN1mNl2Xd+Vq7FW9w7FLztbuZ/2f6xn2yzB+7vkzRXMX1Tscu5NaXobU\nGcLei3uJPB+pb0DCZtnzs8Xf3x8XFxdZLLj4+2ffH+DmJoW5gGiTbdGAn2XDEdmpZdmW9AnqQ9fl\nXUlMTtQ7HGHDdl/YTdjqMFZ3W025fOX0Dseu+Xj4MK7ROIZsGkKKIUXvcISwqJs3b2IwGOxqGb51\nOB2WdtA9joyWmzdvZtvPz9yk8BTQyWRbe217dooA7qHGTbxjcv9GwGngLmqmleIm504ArmvLeGsH\nai9Ghowkl1cuBm4YKO1AMikkJETvELLFyWsnab+0PQvaL+CFYi/oHY7dMi4v3Z/vDsDi44t1ikbY\nMmd5ttiCI1eOMOPQDKY0n6J3KDbB3KTwfWAmsAL4HFgJfA+8a6W4MmIABqJqLnMB5bXt+bTYhgP+\nwEFgqdF5A4C2QGVtaa1tc3quLq4s7rCYfZf28eUeme1EpHUh+gLNFjZj4ksTaVa6md7hOAxXF1cm\nNZ3EB1s/kOGhhNBJUkoSfdf0ZULjCRTOVVjvcGyCuUlhJPA8KtnyAfYDFbXt2S29HjYdgN9RieF9\nYBSqI0xZbf+rwBfAZW35Agizcpx2I5dXLtZ1X8ekvZNYfdo2JgC3B/bc7sccV2Ov0mRBEwbXHkzP\nyj31DsfumZaXesXrUadYHSbunqhPQMJmOfqzxVZM3D2RgBwBhAWF6R2KzTA3KQT4BxiHevU6nkc7\nnmSXccA1VELaQNtWEThqdEwccEbbDmo2FuP9x4z2CeAZv2f4qdtPhK8N5/C/h/UOR+js5r2bvLTw\nJbpW7MqQOkP0DsdhjW88nq/2fcXlO5f1DkUIp/LnjT/5fPfnzGg1QwbfN5KV70QMkNvSgZipFnAC\nVRvYHZgCBAEfohLFD4yOjQRmAPOBJFRi+Ke2rwzwB+knxQ4/TuHjrDq1ird+fos9ffdQLHcxvcMR\nOohJiKHx/MbUf7Y+nzf5XB6YVjZ0y1Cux13n+7bf6x2KEE4hxZBCyNwQOpbvyP9q/0/vcJ6aJccp\ndM/K/S1x4yzab/R5PioxbAHE8mii6ofqjEI6+/20bekKCwsjMDAQgDx58hAUFPSg4W9qtb6jrvtf\n9aeFewtaL2nNzt47Obj7oE3FJ+vWXd+4ZSNDfxlKvRfr8XmTz9mxY4dNxeeI6y8aXqTfX/347d/f\niP4jWvd4ZF3WHX39pO9JElMSqRRXiYiICN3jyex66ueoqCgsLSsJXiyQ09KBZNFG1PR7Cah2g8Ha\ndl9UzWEQqnZwFzAHmKXt76stddO5plPXFIKaxix8bTj/xv7LT11/wsPNQ++QbJLxw8QRJCQl0HpJ\nawrlLMTcdnNxdXHVOySH8rjyMvXAVFadXsWWV7Zkb1DCJjnas8WWnLx2kvpz6rOz907K5y//5BPs\ngB4zmhjTKyH0A5oC3qgazh7Ai8DPwCqgEqrDiTcwEjjCw9fF84EhQBGgqPZ5bvaFbl9cXFyY1nIa\n7q7u9FzVk+SUZL1DElaWmJxI1+Vd8fP2Y3bb2ZIQZrPwauGcu3WObee26R2KEA4rPime7iu6M67R\nOIdJCC0tM5nls6iaN1+T7YstF85j5QM2AOWAZNQYhSOArdr+Rqg2hs8Ce1G9i88bnT8B6Kd9nglk\nNM+U09cUpopPiqf1ktYUy12M79t8L4mCg0pISqDbim4kJieysutKPN089Q7JKS05voSv9n3F3r57\npR2nEFbw1sa3uHznMj92/tGh/o9ZsqbQ3IsMAz4CTqIGjzb2oiUCsSGSFBq5e/8uTRc2pWqhqnzd\n/GuH+o8k4F7iPTos64CPhw9LOi6RhFBHKYYUqk2vxqiQUbQr107vcIRwKOv+XMfADQM5MuCIw83b\nrsfr4/eAGtryoskiHJivpy/rX17Pnot7+GDrBzLriRHjRr/2KPZ+LC0XtyQgRwBLOy2VhNDKnlRe\nXF1c+TT0U4ZvGy5NNpycvT9bbM3lO5fpt6YfizoscriE0NLMTQpvoMYpFE7Iz9uPTT03sf6v9Yzd\nOVbvcIQFRMdH89KClyjpX5L57ebj7pqVgQiEpbUo04KAHAEsPLZQ71CEcAgphhR6rerF6zVeJ7h4\n8JNPcHLmVje2QHXs+Aq4arLv/KOH2zV5fZyBK7FXqD+nPmFBYXwQ/IG8SrZTN+Ju0HRhU+oUq8Pk\n5pOlraiNiTwfSc+VPflj0B94uXvpHY4Qdm1C5ATW/bWO7a9ud9g/fvV4feyJ6vm7D4gyWs5ZIghh\nHwrlLEREWARLTyxl8M+DSTGk6B2SyKQL0RcImRdCoxKN+Lr515IQ2qDg4sFUKlCJ6Yem6x2KEHZt\n1/ldTNwzkUUdFjlsQmhp5v5GmIrqbOKHShBTF/kz1skUyVWEHWE7OHL1CD1W9uB+8n29Q9KNvbX7\nOXj5IHW+r8OrVV5lfOPxUtObzTJTXj4N/ZSxO8dyJ+HOkw8WDsfeni226Nytc3T6sRNz282luF9x\nvcOxG+Ymhe6owZ/voKaMM16Ek8njnYdNPTeRkJRAy8Ut5ReXHfjp9E80X9Scb5p/w7t135WE0MZV\nKVSFRiUb8dXer/QORQi7Ex0fTaslrfgw+ENalGmhdzh2xdzfDO+hagU/BRy9wZ20KTRTckoyr69/\nnd+u/Mb6l9dTwLeA3iEJEwaDgYl7JjJp7yRWd1tNjSI19A5JmOnszbO8MOsFTg86TT6ffHqHI4Rd\nSEpJouXilpQJKMOUFlP0Didb6DFO4UWgIJCI6omcygA4Wr2sJIWZYDAYGBkxkiW/L2FV11VUKlBJ\n75CEJjE5kUEbBrH30l7WdV/HM37P6B2SyKTX171Obq/cTGgyQe9QhLB5BoOBgRsGcu72OdZ2X+s0\n7Qj16GjSE2gMNNc+9wRe0RbhxFxcXBjdcDQj6o+g4byGzDsyT++Qso0tt/u5GHORxgsacyHmApG9\nIyUhtAFZKS/D6w9n1m+zuBJ7xfIBCZtly88WW/b1vq/ZeX4nSzstdZqE0NLMTQobGS2NtX9DUYNX\nv4qqRRROrFeVXmx/dTvjd42n7+q+xCXG6R2S01rzxxpqzKhB01JNWdt9Lbm8cukdksiiYrmL0aty\nL8ZHjtc7FCFs2ro/1zFh1wTWdV9Hbq/ceodjt8ytblwKtAP2AxdQr4xrAuuAYkAloBOw0QoxZjd5\nffwUYu/H0n9tf37/73eWd1lO2bxl9Q7JacQnxfP+lvdZ88caFndcTN1n6uodkrCAq7FXqTC1AkcG\nHJEaXyHSsfXvrXRb0Y213ddSu1htvcPJdnq8PnYBuqFqBl8GgoEuQDLwAvAGMM4SAQn7ltMzJ4s6\nLGJgzYHUm12PBUcXyNR42eD09dPUnlWby3cu89uA3yQhdCAFcxakf7X+fLrzU71DEcLmrPtzHd1W\ndGN55+VOmRBamrmZZQzgj0oCU7kDt4BcJp/tndQUWsjhfw/TZ3Uf8vrk5dsW31IuXzm9Q7KoiIgI\nQkJCdI0hMTmRyfsmM2HXBD4N/ZTwauEy3IyNepryciPuBs9NeY794fsp6V/SsoEJm2MLzxZ78OOJ\nHxm0cRBruq3hhWIv6B2ObvSoKTyLqg009hpwRvucD7hriYCE46hWuBoH+x+kTdk2BM8OZvjW4dLW\n0IK2/r2VKt9VYdu5bezus5v+1ftLQuig8vrkZVCtQYzeMVrvUISwCfOOzON/P/+PzT03O3VCaGnm\n/gapBqwC3IBLQFFUrWEH4BBQH3gOmGmFGLOb1BRaweU7lxmyaQj7Lu3jm+bf0KpsK71DslsXoi/w\nzuZ3OHD5AF81/Yo2z7WRZNAJRMdHU/qb0uzsvdPhat2FyIypB6YyLnIcW17ZIv8X0GecQlDT2tUG\nigD/ArtR4xY6GkkKrWjL2S0M2jiIQjkLMazeMJqVbiYJjZmi46OZsn8Kk/ZOYmDNgQwLHkYOjxx6\nhyWy0fjI8Ry5coQfOv2gdyhCZLvklGTG/DqG+Ufn80uvX6QphUavpNBZSFJoZUkpSSw7sYzxkWr+\n3WH1htG5Yme7G1cqu9r9XIq5xOR9k/n+t+9pVroZo0NGUyqglNXvKyzLEuXl7v27lPq6FJtf2Uzl\ngpUtE5iwOdKm8FEXYy7Sc2VPXF1cWdhhIUVyFdE7JJuhR5tCRxGAeg0eC0QB3XWNxkm5u7rz8vMv\nc/S1o4xrNI5pB6dR9puyTNk/hetx1/UOz2acvHaSPqv78Py057mffJ/D/Q+zqMMiSQidmK+nL8OC\nh/HR9o/0DkWIbPPT6Z+oPqM6L5V6iS2vbJGE0IqcraZwifZvX6AqsB6oC5w0OkZqCnWw6/wuvt7/\nNT+f+Zm6z9Sla8WutCvXjjzeefQOLVtdvnOZVadWsfzUck5eO8mbtd7k9Rqvk9cnr96hCRsRnxRP\nmW/KsKLLCmoVraV3OEJYzb3Ee7y7+V02ntnI4o6LZciZDMjr46zxBW4CFXnYa3oecBn4wOg4SQp1\nFHs/lnV/rmPpiaVsO7eNBs82oO1zbalXvB7P5X3OIdsf/nP7H1aeWsmKUys4ee0krcq2omP5jjQt\n3RRvd2+9wxM2aMahGSw/uZzNr2zWOxQhLM5gMLA9ajv/+/l/VCpQie9afoeft5/eYdksSQqzpioQ\niUoOUw0BQoA2RtskKbQR0fHRrP5jNZvPbibyfCSx92Op+0xd6j1Tj3rF61Exf0X8c/jrFl9m2/0Y\nDAYu37nM4X8Pq+WK+jc+KZ42ZdvQqUInGpVshKebp/WCFrqxZDuxxOREyn9bnlltZhESaJlrCtvh\nzG0Kd0Tt4KOIj7h85zJjGo6ha8WuDlkZYEmSFGbNi8AyoLDRtnDUDC0NjbZJUmijLsVcYteFXew6\nv4s9F/dw+vppPNw8KOVfitIBpSkdUJrAPIHk88lHQI6AB4u/tz9e7l6Zvp/BYCAhOYGEpAQSkhOI\nT4onPimee4n3iE+KZ0/kHsrVKJdmW3xSPPeS7nEn4Q7/3f2Pq3ev8t/d/x58dnd1p3rh6lQrXI1q\nhatRvXB1AvMEykPPCVj6F/3CYwuZdnAakb0jpfw4iKSUJG7H32bTL5soW70st+Nvcyv+FncS7pCU\nkkSyIZnklOQH/7q7uuPt7v3IktcnL/l98pPfNz8+Hj56f1lm2fnPTkZGjOR89HlG1B9Bj8o97K7z\noV4kKcya9GoK30WNsZimpvBVIFBbyQMEoaoTASK0f2Vd1mVd1mVd1mVd1rN7PfVzlPZ5nvpHksJM\nSq9N4QLgAvCh0XFSU+hgDAYDiSmJJCYnkpiSyP3k+w8+u7q44uriipuLG26ubri5uOHu6o6Xuxee\nbp64urjqHb4QGVp1ahWjfx3Nof6HpKzagYsxF1n6+1IW/76YP67/wfMFn6dqoaoEFQoiqFAQzxd4\n3qJjjxoMBmLvx3It7hqX71zmn9v/8E/0P0TdjnqwnI8+T37f/JQJKPPgjUvpgNKUyFOCwDyBFm2i\nYzAYOHLlCKv/WM3qP1ZzIfoCLcu2pO1zbWldtjUebh4Wu5czkZrCrFsCGIB+qFla1gF1gFNGx0hS\nKMzizO1+ROZZo7wYDAZqzarFe3Xfo0vFLha9trCMG3E3WH5yOUt+X8Kxq8doX649Lz//Mg0CG2T4\nejQ7ny3JKclciLnAmZtn+OvGX5y5eYYzt85w7tY5zt0+h5uLG4F5AinhX4JiuYqRzydfmiWvT17c\nXd1JTklO84o7LjGOc7fPqeveVNc9e/MshXMVpk3ZNrQt15a6z9SVV8QWYMmk0Nl+Gm8As4H/gOuo\n+ZtPPfYMIYSwUS4uLnwa+ilvbXyLDuU7yC9YG3Ip5hKf7vyUxccX07R0U96u/TbNSjfLUvtma3Jz\nVUlfYJ5AGpdsnGafwWDg5r2bRN2O4tztc1yKucSNezc4ce0E1+Ouc+PeDa7HXScpJQl3V/c0b1y8\n3b0p4V+CMgFl6FqxK6UDSlPKv5T0IrZxzlZTaA6pKRRC2A2DwUDIvBDCqoTRu2pvvcNxeldirzA+\ncjwLji2gb9W+vF/vffL55NM7LOHAZEYTIYQQwMPawo93fExCUoLe4Tit63HXGbplKBW+rYDBYODE\nGyf4rMlnkhAKuyJJoRBZFBERoXcIwo5Ys7wEFw+mQv4KzDg0w2r3EOkzGAwsOraIilMrEp0QzbHX\njzG5+WQK5SyU5WvKs0XoRRqgCCGEAxjXaBwvLXyJXlV6SbutbPLvnX95bf1r/H3rbza8vIHqRarr\nHZIQT0XaFD5K2hQKIexS2E9hFMlVhLGNxuodikMzGAwsPLaQdza/w2s1XmP4i8NtrgOJcB4yJI11\nSVIohLBLF2MuUuW7Khx97SjFchfTOxyHdCX2CuFrwzkffZ45bedQrXA1vUMSTk46mghhA6Tdj8iM\n7CgvxXIXY0D1AYzYPsLq93JGuy/spsaMGgQVDOJA+AGrJYTybBF6kaRQCCEcyNB6Q9n410aOXjmq\ndygOw2AwMO3ANNovbc+M1jMYEzoGTzdPvcMSwuLk9fGj5PWxEMKuTdk/hbV/rmVTz016h2L34pPi\neWP9Gxy4fIBVXVdROqC03iEJkYa8PhZCCJGh/tX78/etv9l8drPeodi189HneXHOi9xNvMuevnsk\nIRQOT5JCIbJI2v2IzMjO8uLp5sn4RuN5f8v7JKckZ9t9Hcm+i/t4YdYLdK3YlR86/kBOz5zZdm95\ntgi9SFIohBAOqEP5Dvh6+rLw2EK9Q7E76/5cR+slrZnVehbv1n039fWcEA5PSvqjpE2hEMIh7L6w\nm67Lu/LHoD/w8fDROxy7MPPQTD6K+IjV3VZTq2gtvcMR4olknELrkqRQCOEwuq/oTsk8Jfm00ad6\nh2LTDAYDoyJGsej4Ijb22EiZvGX0DkkIs0hHEyFsgLT7EZmhV3mZ+NJEph+azh/X/9Dl/vYgKSWJ\n8LXhbDizgV19dumeEMqzRehFkkIhhHBgRXIV4f/q/x8DNwxE3oI8Kj4png5LO3DpziW2v7qdgjkL\n6h2SELqR18ePktfHQgiHkpSSRPUZ1fkg+AO6Veqmdzg2I/Z+LG1/aEsB3wLMbzcfDzcPvUMSItPk\n9bEQQgizubu6M63lNN7Z/A4xCTF6h2MTbsff5qUFL1EiTwkWtl8oCaEQ2FdSGAHcA+5oyymT/Y2A\n08BdYBtQ3GT/BOC6toy3ZqDCOUi7H5EZepeXus/UpVmpZozcPlLXOGzBtbvXCJ0XSs0iNZnRegZu\nrm56h5SG3mVFOC97SgoNwEAgl7aUN9qXD1gBDAf8gYPAUqP9A4C2QGVtaa1tE0IIpzGhyQQWHV/E\nkStH9A5FN5fvXKbB3Aa0KNOCr5p9hauLPf0aFMK67KlN4XZgIfB9Ovv6A72AYG3dB1UjGAT8CewG\nZgOztP29tXPqpHMtaVMohHBYMw/NZM6ROUT2iXS6hCjqdhSN5zcmvFo4Q4OH6h2OEBbhzG0KxwHX\ngEiggdH2isBRo/U44Iy2HaCCyf5jRvuEEMJp9K3WlxRDCnN+m6N3KNnq3t5CCQAADF1JREFUrxt/\n0WBuAwbXHiwJoRAZsKekcChQAigCzADWausAvoBp6+kY1GtmgJxAtMm+7JvIUjgkafcjMsNWyour\niyvftfqOD7Z+wPno83qHky1OXjtJw3kNGVF/BINqDdI7nCeylbIinI+73gFoIoD6GeyL1PbtN9o2\nH+gOtASmALFAbpPz/FAdUkhnv5+2LV1hYWEEBgYCkCdPHoKCgggJCVGBav9ZZV3WZV3W7Xn9nTrv\n0GpsKyY1nUSj0Ea6x2Ot9TM3zzDi3Ag+b/I5xW4WIyIiwqbiS289la3EI+u2tZ76OSoqCkuzpzaF\npjYC61FJYTjwKg/bFPqiXjOntincBczhYZvCvtpSN53rSptCIYTDSzGk0Hh+YxqXbMyHL36odzhW\nceDSAVotacW3Lb6lU4VOeocjhFU4Y5tCP6Ap4I2q3ewBvAj8rO1fBVQCOmjHjASOoBJCUDWLQ1Cv\nnotqn+dmT+hCCGF7XF1cmd9+PpP3TWb/pf1PPsHO7Dq/i5aLWzKr9SxJCIUwk70khR7AGOA/VA3g\nQNQQM2e0/deBjsCnwE2gBmA8bP90VBvE46hOJmtR7RKFyDLTVz1CPI4tlpdiuYsxtcVUeqzsQez9\nDFvU2J0tZ7fQbmk7FrRfQOvnWusdTqbZYlkRzsFeksLrQC1Uu0B/1GvfrSbHbEWNXegDhALnTfYP\nBfJqyzBrBiuEEPaiY4WO1C9en7c2vqV3KBax/ORyeq7qyaquq2hauqne4QhhV+y5TaG1SJtCIYRT\nib0fS9XpVRkbOpbOFTvrHU6WzTw0k5ERI9nYYyNVClXROxwhsoUl2xRKUvgoSQqFEE4ntVPGgfAD\nFPcznSXU9k2InMB3h75jyytbKB1QWu9whMg2ztjRRAibI+1+RGbYenmpWbQmQ+sNpeXilty6d0vv\ncMxmMBh4f8v7zD82n8jekQ6RENp6WRGOS5JCIYQQALxd+20alWhE2x/aci/xnt7hPFFCUgK9V/dm\nxz87+DXsV4rmLqp3SELYNXl9/Ch5fSyEcFophhR6rOxBQlICP3b+ETdXN71DStd/d/+jw9IOFPAt\nwIL2C/D19NU7JCF0Ia+PhRBCWIWriytz284lJiGGQRsGYYt/JB+7eowXZr1Aw8CGLO+yXBJCISxE\nkkIhskja/YjMsKfy4uXuxcquK9l3aR9jfh2jdzhprD69mkbzGzE2dCxjQsfg6uJ4v8bsqawIx2Ir\ncx8LIYSwIbm9crOhxwbqza5HoZyF6F+9v67xGAwGPtv1Gd/s/4b1L6+nVtFausYjhCOSNoWPkjaF\nQgihOXPzDCFzQxhQfQDD6w/XpWbuUswlwteGcy3uGqu6rqJY7mLZHoMQtkraFAohhMgWpQNKcyD8\nAJvObqLtD225HX872+5tMBhYcHQBVadXpXax2uzus1sSQiGsSJJCIbJI2v2IzLDn8lI4V2G2v7qd\nknlKUmNGDY5dPWb1e16NvUr7pe35bPdn/NzzZz5q8BEebh5Wv68tsOeyIuybJIVCCCGeyMPNg8nN\nJzO64WgazW/EwmMLrXKf5JRkFh9fTJXvqlAhfwUOhh+kWuFqVrmXECItaVP4KGlTKIQQj3H86nE6\nLOtA7WK1GVpvKJUKVHrqayYkJTD/6Hy+2PMFfl5+fNP8G14o9oIFohXCscncx9YlSaEQQjxBdHw0\n3+z/hqkHplKxQEWG1B5C09JNM90RJTo+mu8OfsfkfZMJKhTE+/Xep8GzDVJ/0QkhnkCSQuuSpFCY\nJSIigpCQEL3DEHbCUctLQlICS08sZdLeScQnxTP4hcHUf7Y+xXIXI5dXrkeOj0mI4bd/f+Pwv4c5\n9O8hNp7ZSPPSzXm/3vtULlhZh6/A9jhqWRHWYcmkUMYpFEIIkWVe7l70qtKLVyq/wo5/djBl/xQm\n7Z3EhZgLuLu6Uyx3MZUgeubi+H/HuRhzkcoFK1O9cHUalWjE2EZjKe5XXO8vQwiB1BSmR2oKhRDi\nKRkMBqITorkYc5GLMRe5HX+bSgUqUS5fOdxdpT5CCEuR18fWJUmhEEIIIeyCow5ePQg4CMQDc9LZ\n3wg4DdwFtgGm7xsmANe1ZbzJvkBgu3buKe1aQjwVGUtMZIaUF2EuKStCL7aUFF4CxgCz09mXD1gB\nDAf8UcnjUqP9A4C2QGVtaa1tS7UEOAQEaNdYrl1TiCw7cuSI3iEIOyLlRZhLyorQiy0lhauA1cCN\ndPZ1AH5HJYb3gVFAFaCstv9V4AvgsrZ8AYRp+8oCVYGRQAKwEjgGdLT8lyCcye3b2Tfdl7B/Ul6E\nuaSsCL3YUlKYKr334hWBo0brccAZbTtABZP9x4z2VQT+Rr06TnXUaL8QQgghhNOzxaQwvV4evkCM\nybYYIHUQrJxAtMm+nBnsMz1XiCyJiorSOwRhR6S8CHNJWRF6ya5xASKA+hnsizTZl15NYSyQ22Sb\nH3Ang/1+2raMzs3Do0lmqrMuLi6lMtgnRBrz5s3TOwRhR6S8CHNJWRGZcNZSF8qupDAkE8emV1N4\nAtVuMJUvUErbnro/CNUBBVR7w9+N9pVE1RjGGu1fkMH9S2ciViGEEEIIYWFugDcwDpgPeGnbQPUU\nvo3qcOINfAbsNjp3AHASKAIURSWC/Y327wE+187tANwC8lrp6xBCCCGEEE9hFJBisnxktL8RaozB\nODIep/CGtpiOU/gsapzCOO0aoZYNXQghhBBCCCGEEEIIYfMCUGMgxgJRQPfHHPs28C+qt/L3gGcW\nryPsl6XKSwRwD9UZ6g6qhlo4FnPLSiVgE3AN9QYkq9cR9s1S5SUCebY4OnPLyquovhTRwAXUG1M3\no/3ybEnHEm3xAeqh2iZWSOe4psAVoDyqd/J2VPvGzF5H2DdLlZftQB+rRir0Zm5ZKQv0BtqQ/i95\nebY4B0uVF3m2OD5zy8pr2n53VJ+Kg8DQLFzHafiiZjEx7lE8j7S/vFMtBj4xWm+IqgXK7HWE/bJU\neQH14O5r6QCFzcjKM6E0j/6Sl2eLc7BUeQF5tji6p3kmvA2seZrr2OLg1ZZUFkhCzX6SKqPZTNKb\nFaUgaq7lzFxH2C9LlZdU41CvgCKBBhaNVOjNUs8EebY4B0v/nOXZ4riepqw04OFwfFm6jqMnhTl5\ndJDqO6Q/m0l6s6KgHZuZ6wj7ZanyAqoKvwSqSn8GsBY1XqZwDJZ6JsizxTlY8ucszxbHltWy0geo\nBnzxNNdx9KTwSTOhPO5YP+3fO5m8jrBfliovAPtR820nosbd3AW0sFikQm+WeibIs8U5WPLnLM8W\nx5aVstIOGAs0B24+xXUcPin8E9UA0/iduvFsJ8ZSZ0UxPu4qaqDrzFxH2C9LlRfh+Cz1TJBni3OQ\nn7MwV2bLSjNUjXErHs7ylpXrOI0lqE4BPkAwqvdN+XSOa4rqKFAe1S4sApV5Z/Y6wr5Zorz4afu9\nUf8pe6D+apMpFB1LZp4J3qh2qCmo2Zq8sngdYb8sUV7k2eIczC0roagJO4Kf8jpOxZ+04/R007YX\nR1WjFjM69m3UMCOp4855mHEd4VgsUV7yoV7xxKBqDnejZuQRjsXcshLIw1makrV//zbjOsKxWKK8\n5EeeLc7A3LKyDbjPwzEr7wDrzbiOEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQ\nQgghhBBCCCGEEEIIIYQQQgghhBBCCCEsKQo1tZQQQjgcV70DEEIIO2IAXPQOQgghhBBC6GcBai7a\nONQco++acU4t4CBqfuwrwESjfbVRc9feAo4ADYz2BQBzgEvATdT8pUIIIYQQwkacI3Ovj/cAPbTP\nPsAL2ueiwHWgmbbeWFvPq62vB5YAfoA78GLWQxZCCCGEEJaW2aRwBzAKyGeyfSgw32Tbz0AvoDCq\nRtIvayEKIUTWSJtCIYSwnr5AWeAUsB9oqW1/FuiMenWcutQDCgHPoF4ZR2d3sEIIIYQQwjx/k/Xe\nxx2Be6jXyMOAGRkcJzWFQghdSE2hEEKY7ypQymRbFOq1b3p6Avm1z9Go3svJwEKgNfAS4AZ4AyGo\ntob/AhuBqUAewAOob6H4hRBCCCGEBbQB/kG97h0CeAIxqFfE6VmASiTvAMe18/+/fTumgRAKgCj4\nLGCGBrM0dHRn4PSQgAYKgoOf0Mwo2K03+5qrf3VWR/XrmY6rpmrteSxf1T6uAgAAoy3V9nUIAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAY6gbts4sZZi508AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa17b550>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Wings Down"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim_flap(V=1, alpha=20*pi/180, freq=5, center=-50*pi/180, delta=0*pi/180, flap_mag = 100*pi/180, f_aero=f_aero)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lift:\t     68.32 gm\n",
        "side:\t      0.00 gm\n",
        "thrust:\t    390.28 gm\n",
        "roll:\t      0.00 gm-cm\n",
        "pitch:\t   -526.90 gm-cm\n",
        "yaw:\t      0.00 gm-cm\n",
        "fwd: 343.380317 gm, up: 197.683540 gm\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YHZGISEaqKYTTwHfAaKAE0A64DZMYunITUNHxfT1MTeFsdwZ06JC5Q8LWrWa5\nGSWE/s/5rzbxP5Urw++/m68tWsDWlekrVnJG/UWyS31FrOKrSSHAE0Bx4BAwDXgM2OI4Vg1TY1jF\nsd0ZcyFKImbpmpnA6+4K5K9Vdpo3N2sQ/vADlC3rrjOLiJWKFIGPP4b/PJVASOt6LHt+ptUhiYh4\njIazMsrR9PGShydxcNp8Ar+cTo8eHoxKRCy1ecpflH6oJ7Et+tLe9gpBRTy+gIGISJa0TqFnZSsp\nTEpMYlnrgVTb9hsp386i9u0N8iE0EbHSkS2H2dumN8mFi1NnxXRCamhaQESspZpCix3eeJAtV3eh\n2OG9hMauVEJYQKnup+ApX78CDffP48zVddldvxsbN2R/VkH9RbJLfUWsoqQwh9bO3sWFyGYca9KF\n5vtmU6aaLkkUKUgKlyhMx7/fZfvYOXTqHMBMlRmKiJ/Q9HFGmU4ff/45DHshmRnPLqX98I75HJaI\neJvVq+HOO6FvX3jlFQhSmaGI5DPVFHpWhqTwwgUYNAjmzYPZs6F+fYsiExGvc/gw9O4NxYvDF19A\nSIjVEYlIQaKawnx06BBcfz3s2gUrVyohlEtU9yNgFreeNw/q1IEx10wkds5ml+3UXyS71FfEKkoK\nr2Dz9DXceN0h2rc3dynRHQ1ExJXCheG99+Dm2wtRpnsUK15y69r4IiL5QtPHGdntdjtLn5jONeOf\nY/PIr+kQ09nqmETER2z6fCVlH+nJ9nb96fDbSAIL6W9vEfEc1RR6lv33poOouW4257+eTZ07G1kd\nj4j4mEPrD3Cg3V2cLVmO+qumUrpKaatDEhE/pZpCDysVt4FSW1cpIZQrUt2PZCbs2krUi1/IibC6\n9Oh0nO3b1V8k+9RXJLtSU917PiWFLjTe9xNla4VaHYaI+LAiwUW4Yd1Yeg+pRrt2sHy51RGJiD/Z\nPnMDr1cb59Zz+nJS+BTwF3AO+Dwb7QcC/wIngM+AIpk1LFSskDviEz8XFRVldQjiAx59FGbNgg8+\niOLNNyEHt1aXAkqfLZKVPwd/S2ivznS6w71XwPpyTWEPIBXoBhQHHrxC227AZKATJjGcBSwHXnLR\nNlv3PhYRyYl9+8xC1zWqpzLx43OUrFDC6pBExMekpMCPt4yj6W9jODX5O+r3vU41hQ6zgO+BhGy0\nfQD4FNgCHAdGA9Eei0wKBNX9SE7ExtpYvBjaJPzAvmqt2bNol9UhiZfSZ4u4cvw43H47TD9+C8XW\nr6R+3+uR52zaAAAgAElEQVTc/hqeTAq/APYAMzGjeBU99DrZyY4bAOucttdj4inrkYhERFwoVgye\n+e12/r3lYYp1bs3qtxZYHZKI+IAtW6BFC6hVC6b/UY3yDcI88jqenD6+E5gNtABuBLoChTAjfG+6\n8XVeAapw5enjWOAJYJ5juzBwHgjHJK7ONH0sIh739zs2Kg+5hy23Pk/HWQMJCPTlah4R8ZTvv4eH\nH4YxY+ChhzIed+f0sSevqLiAqflb7njEAKFAq2w81wZ0yOTYknTHsvNGJALOC4WlVWaectU4Ojqa\n8PBwAEJCQoiMjLxY+Js2rK9tbWtb23nZbjIwim8KvcOZISP45rpz3LZsGCtWeE982ta2tq3dXrhg\nIYtHL+Kzf2L48ccAzp614WiCzWYjLi4Od/Pkn6avAQ2BacAC4KiHXic7I4XTgV3AcMd2F0dcV7lo\nq5FCyRabzXbxP69IVjLrL2eOnGHQo6dZuasCs2ZB9er5H5t4F322yMl9J9nS/D6Kn06g4uqfqFgn\n8wXwfeVCk/3A/wGRwE/AfDefPwgohhntDAKKOr66MgXoD9TH1BGOIHvL2IiIeFSJ8iUY920F+vWD\nVq3g99+tjkhErLTz520crtWS86GVqRe/8IoJobt5cqSwCeZijl8c28WBs248fwww0sW+0UA1YBMm\nCdznODYQGOqI41vgMcwUd3oaKRQRSyxYAH37wosvwrPPQoDKDEUKlJUjfqDGa/3Zet/rtJ/8cLae\no3sfe5aSQhGxTFwc9OyewqCg97hz/uMUDy1udUgi4mGpqfDKqFRavHUXVT94gYYPZ+fyC8NXpo9F\n/FpaUbBIdmS3v4SHwx8LLxCesJq4Ku3Yt3S3R+MS76PPloLlxAno3h1+WxhIk13f5SghdDclhSIi\nXqZEaDHa7JzGwRv6UaRDS9aM1XqGIv5o82az/mC1aqZ8pFIla+PR9HFGmj4WEa/x939/p/Lz97Ll\nxkF0/GGI1jMU8ROzvk1hwONBjB0L0dG5P4+mj0VECogmgzqR8udKDvy1l3t6p5CYaHVEIpIXKUkp\n/N5mGKcffJKffspbQuhuSgpFckl1P5ITeekvlVtWpfvu9ylZphCtWsGOHe6LS7yPPlv8V8K2I6y9\n6ibKbF3BjStfoXlzqyO6nJJCEREfUKwYfPopPP00tG0Lc+ZYHZGI5MSWaas5G9GMU7UjuTb+V8rX\nr2B1SBmoOCUj1RSKiFdbsQJ69YKHe53g5TeCCSqS2br9IuIN5r78Jy3fuIPYQeNo9fZdbj231in0\nLCWFIuL1Dh2C31oM45pTqwhf+gXl6nnfqINIQXfuHDz3HCz9PYlZ7+6m9k113P4autBExAuo7kdy\nwt39JSwMem8dzam6zTjbsBmbPl/p1vOLdfTZ4h/i4qB9e0hIgKWringkIXQ3JYUiIj6qULFCRC17\ng/3Pv0dY/1tZfO947Kma6RCx2i+/mHuZ9+0LM2ZA6fy7fXGe+PL08VNANNAQ+BJ48Apto4HPgDNO\n+24BFrtoq+ljEfE5u37dzoXud/Fr8+E89HNvSpa0OiKRgiclKYXfbn2XwRsfZPyMUNq18/xravrY\n2A+8AkzMZvulQCmnh6uEUETEJ9XoVpcqe5fzd/idtGwJW7daHZFIwZKw7Qh/V76FiivnsPDXC/mS\nELqbLyeFs4DvgYRstvflUVHxQqr7kZzIj/5SonwJPptciIEDTS3TV195/CXFA/TZ4ns2fPIn5yKu\nI7FWYxoeWEBYo4pWh5QrvpwUpslOsmcHmgCHgW3AcEBrOIiI3wkIgP79Yd48GD7crGt4/rzVUYn4\nJ7sdbLf9H5Ue78H+YR8TtWIMhYoVsjqsXPOHpDA7BYCLgQigAtATuAd43pNBif+LioqyOgTxIfnd\nX5o0gb/+ghO7jrKi4m3sse3M19eX3NNni284dgx69IBVG4py/o+VtBh9q9Uh5Zm3prM2oEMmx5ak\nO5adkcJdTt9vBEZjksI3XTWOjo4mPDwcgJCQECIjIy/+J00b1te2trWtbW/fXrvWxoOD7NiLdqV4\n51Z81OtJIh7v6DXxaVvbvrr9119w22022raFZ7c/RZEi+ff6ad/HxcXhbv5QZ/cKUIUrX32c3t3A\nC0BTF8d09bFki81mu/ifVSQrVveXzZNXEfzw3eyqfwutlrxN0dJFLYtFrszqviKZs9vhvffg9dfh\n44/hLvfenCRXdPWxEQQUw4x2BgFFybxO8CYgreqzHqamcLanAxQR8RYNHmhOmdg1FE2IJ/aq9vyz\nJcnqkER8ytEdCTzdaSNffAHLl3tHQuhuvjxSGAOMdLFvNFAN2ATUB/YBY4H7gGDgIDAVM8KY4uK8\nGikUEb9lT7Xz7ZDlPDG1Ne+/D/fcY3VEIt5v/cdLKPfMvfzd5ilu+O0FihSxOqJLdO9jz1JSKCJ+\n7++/oU8faNMGPvgAgoOtjkjE+6QkpfDHLW/SYOEH7B7xGc1jbrE6pAw0fSziBZyLfkWy4m39pUkT\nWL3aLGHTtKlJEsU7eFtfKaj+XbWP9RW7ErJqHinL//LKhNDdlBSKiBRQwcEwcSLExEBMlI1FPd7V\nvZNFgO++gxe7ruZEsy40OrSQq5pXsTqkfKHp44w0fSwiBc4e205O3noPZ4uHUn3B54RdW8nqkETy\n3enTMHAgLFgA06dDq1ZWR5Q1TR+LiIhbVYuqyTWHlnC6XjNoEsmKYd9bHZJIvlqzxpRSnDtnyil8\nISF0NyWFIrmkuh/JCV/oL4VLFCbqj1c4+NFMrho7kJ8iXyIx0eqoCh5f6Cv+JCUphSmPL6NbNxg5\nEqZMgdKlrY7KGkoKRUTkMo0ea0vIrrWsrNaLJk1gxQqrIxLxjN0L/2FT+Q7UmzGK1atSufdeqyOy\nlmoKM1JNoYiIw7ffwpNPwqOPwvDheNX6bCK5ZU+180f0pzSYNoyNtw+jw7fPEljIN8fJtE6hZykp\nFBFx8u+/MGAA7NsHkyfDtddaHZFI7h3acJC46x+m1Kn9FP5yKrXviLA6pDzRhSYiXkB1P5ITvtxf\nrroK5syBZ56B71qPxdbtDZLPJVsdlt/y5b7izex2+PJLuLHTeRKvaUqtQ8t9PiF0t0JWByAiIt4v\nIAAefBD2X9Obg7f1Z2v52ZSYMZmaN9ezOjSRLB04AI8/Djt2wOc/V6N58xirQ/JKmj7OSNPHIiJX\nYE9JZXHf8TScMZINXQfTdtYQCpcobHVYIhnY7fDFFzBoEDzyCIwYAUWLWh2Ve2n6GIoAnwFxwEng\nb+DGLJ4zEPgXOOF4rsqlRURyISAokI5fPcHZxX8RvNrGN+HP6zZ54nUOrInny/qjefMNOz/9BK++\n6n8Jobv5alJYCNgDdABKA8OBGUD1TNp3A4YCnR1tagKjPB+m+DPV/UhO+GN/qdIunKaHfsH+yqt0\n6wbDhpmFfyVv/LGv5KfU5FQW3zOOQs0aUzksmb9WpNC0qdVR+QZfTQrPYJK6PY7tucAu4LpM2j8A\nfApsAY4Do4Foz4YoIuL/AgID6PtoMOvXw/bt0LgxLF5sdVRSUMV+v4mNoe0JmTuN47NsRC0eTdGS\nunwiu/ylprAiZiq5MbDdxfG1wGvAN47tcsBhx9dj6dqqplBEJJe++w6efRZ6td7HsNHFKF+vvNUh\nSQFw7hxMf3Qxd0ztyea7R9Nu6qM+u+5gTqmm8HKFgenAJFwnhADBmFrCNCcdX0t5LiwRkYLnzjth\n82ZoefxX7A0i+CP6M1KTU60OS/zY/PlmhPrXk625sGodHb58vMAkhO7mrWOqNky9oCtLnI4FAlOB\nc8BTVzhfIqb2ME0Zx9dTrhpHR0cTHh4OQEhICJGRkURFRZnAHLUe2ta2c92PN8Sjbe/eLmj95e55\n/ZkyIpWUt9+mzHefU3zyePaXPeI18Xnzdto+b4nHW7dnzLDx0Uewd28U770HpUotZdspuIrKXhGf\nJ/uHzWYjLi4Od/Pl6eMAYCJQDbgZOH+FttMxNYfDHdtdgGnAVS7aavpYssVms138zyqSlYLaX1KS\nUlga/T/qfzWSdU3702z+G4SEWB2VdyuofSW7khKTmDpyB0OnRPDUUzB0KBQvbnVU1tFt7ozxmBrC\n64HTWbTthple7gwcAGYBfwLDXLRVUigi4mZHthzmq4EreHXtrYweDf37Q1CQ1VGJr1n9xjzKxjxD\nbFhbatk+o1YtqyOynpJCs6zMLsy0cYrT/gHAl5jRw01AfWCf49hAzLI0xYFvgceACy7OraRQRMRD\n/v7b3C7v9Gl4/31o187qiMQX/PPjFo4+NISwY9s48Pz/0eLV2wkI9NUUxr10oQnsxsReAnOxSNrj\nS8fxPY7tfU7PeQeohKkn7I/rhFAk25zrO0Syov5iNGlilqx5/nm45x7oc7ed3Uv3Zf3EAkR95ZKE\nBJjV7v8oc3sHTrfsTKWETbR8/Q4lhB7iq0mhiIj4qIAAkxBu3QrtKu+kVPvGLLpuIEd3JFgdmniJ\n8+fhnXegXj3YVPVGArZsIeqHwRQtrVuSeJJS7Yw0fSwiko8ObzzI5ntGE7FpBhu7DaHl9GcoHlqA\nrxwowFJSYNo0iImBiAh46y1o0MDqqLybpo9FRMRvVGhYkY4bPuLk3CUUW7+So2HXMHPURi6oyKfA\nsKfaWf7ibNpGHOfTT2HqVPjxRyWE+U1JoUguqe5HckL9JWs1b7qGVvtncnTcDCYurs0118CkSZCc\nbHVk+asg9RV7qp01YxewqXQryr4Xw1vPxbN4sS5AsoqSQhER8SqNHmnF3AXFmDTJJIX165spxZSU\nrJ4pvsKeauevV35mQ0g7yr78BCcffI46p9bQ4bEGBKiwzTJ66zNSTaGIiBf5/XcYMQIa7ZrDvTcc\nocX7/ShaqojVYUku2O3www/w5UvrGfVPX44MeJmWb/ciqIgWrcwtrVPoWUoKRUS8jN0Oqz9aDjEx\nXH1sI9tuHkjTTwZQqrJuYe8LkpPh22/hjTcgMBCGD4ce3e0EBikNyStdaCLiBQpS3Y/knfpL3gQE\nQLOnWtHsyC8cn/oDRdat4nyVmtjaj+DQnnNWh+dW/tRXTuw5wcejj1CrFowbB6++CmvWQM+eKCH0\nQkoKRUTEp9S/twlt9nzF6fnLOHPaTr1ri3DffbBypdWRSZq9S3ZjazqIlPCaBP48l5kzYdEiuO02\nVDPoxfRPk5Gmj0VEfMjRozBxInz0EYSFwdNPQ69eUFTrHOerlKQU1rzxK6njP6HOwSWsb9afuh88\nTeWWVa0Oza+pphCKAOOALkAo8A/wEvBLJu2jgc+AM077bgEWu2irpFBExAelpMDcufDBB3DdinHc\nVG8XVUc+SK1b61sdml/791/47DOYO24PE0705vhdj3DdW30oGVbS6tAKBNUUQiHM/Y07AKWB4cAM\noPoVnrOUy++T7CohFMk2f6r7Ec9Tf/G8oCC4/XaYPx8endEFAgMpeUcXNpRqzeJ+Ezix54TVIWaL\nL/SVc+dg5kzo0cMsML13L3z0QzUaJS6n/aT+Sgh9lK8mhWeAUZjEEGAusAu47grP8dVRURERyaGa\nN9YlavmblD+9h3ODh1PYNg+qV+fJ7vv5/nuT1EjOpCansvZdG39c8zB3hC3j449NjeCePfDJJ3Dd\nlX4Di0/wl0SpIhAHNAa2uzj+APARcBY4CkwF3gBcLYWq6WMRET+UsOMoX88P5ZtvYO1auPVW6N0b\nbrhB9YeZST6XzMZPlnJi8mzqrP+WU4XLcaBLX+q8cj+Vm1S0OjxBNYXpFQZ+BnYAj2fSpgaQCuwG\nGgJfYxLDN120VVIoIuLnDhww058zZsCFtZt4u8wrpN54M9c8eyMVIsKsDs9SZ86YKfjZsyH0m094\nOPUTDrbqztVP30mdHg2tDk/SKQhJoQ1TL+jKEqdjgcAXQDBwB65H/ly5G3geaObimP2BBx4gPDwc\ngJCQECIjI4mKijKBOWo9tK1t57ofb4hH2969rf7ivdv1wq5lx1uzWD93CtWPrKZmifocanoTse3D\nCe9Uk+uvz9940vbl1+u1b9OeTb/s5cMf41i9GnbsiKJ5c4iIsNGmjZ0+fTrl68+v7Stvp30fFxcH\nwOTJk8HPk8LsCAAmAtWAm4HzOXju3cALQFMXxzRSKNlis9ku/mcVyYr6i29ISkxi86d/cvyLn1gU\nX4e3TzxCy5bQvr15tGoFJUp4NgZP95WkxCRiv13LkbkrKPKnjbr/2ogt3ohp/W1cfz107Ahlynjs\n5cXNCsJIYXaMx9QQXg+czqLtTcAa4CBQD/gGc7XyKy7aKikUEREAjh2DpUth8WL44w9Yvx5eD32b\nJsE7sEc2odz1Tah5RyNKlPdwpphLSUkQGwvr1sGKFbB6WRI/rqzAwWLVOVi9JQFRHag9oAuVrqts\ndaiSS0oKzdIzu4BzXD5lPAD4EjN6uAmoD+wDxgL3YaaZD2LqCV9BF5qIiEgOnD4N279Zx8m5fxC4\n7m/K71tL9bNb+LdIOP9rM5HU5q2oXZuLjypVzL1+PSklKYVD6/7lyJo9nNq4m6T1Wyn6z2YGlRjP\n33vKUa0aNGwILVuaR7OIswRXKO7ZoCTfKCn0LCWFki2aDpScUH/xX0mJScT9spXNp6qy9WBZYmO5\n+Dh8GL4P7EF4wG5OlazI+TIVSS5XEULLEtvmAbjqKkqUMFPSxYuD3Q6xsz6gefnq2JNTsCenkHr2\nPCkJx1ldqzfxFypw7BgcP24ultmzB37YG0nFwEMcKV6VUyHVOF+jHkUiG1Dq3tuo0ySYYsWsfofE\nk9yZFBZyx0lEREQKqiLBRah717XUdXHs/Hk4sv4jTmyJh50Hse8+CPEHIeEou3emEB9nrvY9e9Z8\nDQiA9utsBNiTIDAIAoMIKFQEgkNIKn8bFapD3boQEgIVK0LVqnB1pdUUKR5Epfz+wcXvaKQwI40U\nioiIiE/Qbe5ERERExK2UFIrkkvOaUSJZUX+R7FJfEasoKRQRERER1RS6oJpCERER8QmqKRQRERER\nt1JSKJJLqvuRnFB/kexSXxGrKCkUEREREdUUuqCaQhEREfEJqikUEREREbfy5aRwGvAvcBLYCbyc\nRfuBjvYngM+AIh6NTvye6n4kJ9RfJLvUV8QqvpwUvgHUAEoDNwFPAzdm0rYbMBToDFQHagKj8iFG\n8WNr1661OgTxIeovkl3qK2IVX04KNwHnnLaTgUOZtH0A+BTYAhwHRgPRngxO/N/x48etDkF8iPqL\nZJf6iljFl5NCgI+B05gE8VVgTSbtGgDrnLbXAxWBsh6NTkRERMRH+HpS+AQQDFyPSQpbZNIuGFNL\nmOak42spz4Um/i4uLs7qEMSHqL9IdqmviFW8dUkaG9Ahk2NLMjk2DjOdPNDFsbWYpPFbx3Z5zFRz\nOeBYuraxQK2chSsiIiJiiX+A2u44USF3nMQDonLxnMJAQibHNgGRXEoKGwMHyZgQgpveWBERERHx\nvApAH6AkEIS5uvgE0DyT9t0wy9HUx9QR2oDXPR6liIiIiHhUeUxidwxzNfFK4Han49WAU0AVp30D\ngQNcWqewcH4EKiIiIiIiIiIiIl4iFJgFJAJxwD1XaHulu57k5Dziu9zVX2zAWcyI9SnMGpniX7Lb\nVxoCvwKHgdQ8nEd8m7v6iw19tvi77PaVB4C/ML+D9gJjMCV1OT1PgfKl41ECaIuZbm7gol03zPRy\nfSAE+B1z15Scnkd8m7v6y+/AQx6NVKyW3b5SF3gQU+Li6pe8PlsKBnf1F322+L/s9pXHHMcLAZUx\nCeLQXJynwCgJnOfyK4onc/kv7zRfYJatSdMJMwqU0/OI73JXfwHzwd3f3QGK18jNZ0JtMv6S12dL\nweCu/gL6bPF3eflMGAjMyct5fH3x6qzUxdz+LtZp3zogwkXbK931JCfnEd/lrv6S5g3MFNASoKNb\nIxWrueszQZ8tBYO7/5312eK/8tJXOgIb83Ief08Kg7l095I0p3B9J5Mr3fUkJ+cR3+Wu/gJmCL8G\nZkh/AvADUNNtkYrV3PWZoM+WgsGd/876bPFvue0rDwHXAW/n5Tz+nhQmAqXT7SuDeWOyalvG8fVU\nDs8jvstd/QXMMkmngQvAFGApcLPbIhWrueszQZ8tBYM7/5312eLfctNXumPWXr4JOJqH8/h9Urgd\nU4DpPKfemEvDq87S7nri3C7tric5OY/4Lnf1F/F/7vpM0GdLwaB/Z8munPaVGzEjxrdifi/l9jwF\nxpeYiwJKAO0wV9/Ud9Euq7ueZPc84tvc0V/KOI4Xw/yn7Iv5q023UPQvOflMKIapQ00FijoeuTmP\n+C539Bd9thQM2e0rnTG3922Xx/MUKGW5fJ2ePo79Ob3rSWbnEf/ijv5SHjPFcxIzcvgn0MXDcUv+\ny25fCcf8ck8FUhxfd2bjPOJf3NFfKqDPloIgu31lIZDEpTUrTwFzs3EeERERERERERERERERERER\nEZGCbhIw3+ogciAas+RIXhQCJgJHMHVpHfJ4PhERERGfNwmYZ3UQOVAMc1FBXtwNnAVaAWFcfuGc\niEgGhawOQEQkmwqTt9GzAHcFkg/OOR55UQfYDyzP43mKYK5wFBEREcmRrph1GxMw62LZgObp2gQD\n7wH7MHdnWAP0cDoejpnyvBf4CbOkwluOY0MwS3Scx9zX89l05w4FvnY85wDwCuZG8GnTx9GY5TyK\np3veSC4t/RHleP3rgcWOGDcBN6R7zmvAZsfxPcA4Lr+LQDQmkY0CNgBnMMtIVAI6AWsdcc7H3LYs\n/fOcNQV+wSyBdApYAbTANRuXljVxXtKkMPAm5n0/7/iZ7kn33FTgacz6Zscx7yWY9+IPx8+a9u/q\nfHu1Po6f5yywC/g/zPpoadph7r5x0vFYS8b3U0RERPxId6AnZkHd+sD/MAliqON4APA7Jjlqg0kA\nH8EkKZ0dbcIxycleTGIY7ng8iUmsHgZqAY9ikpCHnF5/FmY1/yjMAsBTMYlU2vRxMcytoO53ek4g\nZh2vlxzbUY7XT0tcamMSy2NcuqUhwDCgLWb9sM7AFsxUdZpozFpzCzGJcRNHbH8AizBJXaTjeV+l\ne55zUhiBScamY+5vWhPohZkadqUsMBaTDIYB5Rz7x2JqDNP+fV5yxNfZ6bmpjjZPYu6xWxuTECYD\n/wUaAXWBBxxf0+I9illMORxoD6zD3IYNzKzUUcx9WWs5HneQ+aK7IiIi4ocCMQnBvY7tKEwil/6+\nnBMxCR1cSgpfTtdmL2aky9l/gX8c39d2PM95Qd/CmJEx55rC9zCJWZpumCnSik4xpmIS3DQVHfu6\nkrkeXD7tG+14zrVO+4Y49jVx2vcccDjd85yTwqnA31d4XVdigB1O2yUcsT2Wrt13wAKn7VRMIu/s\nD2DOFV4rDhiQbl8Hx7nKYJLUVKBj1mGLiFX8/d7HIpL/amCSmB2YEboTmMSgmuN4c0yd2n4uX4m/\nLxlv17XS6fvSwNWY6VxnizFJZNqtwcDc6SHNBWBVuud8ghnhu8ax/QjwI+b+1c7WOn1/EDOqVtFp\n352O10/7WaZhktBKTm3smKlj5/MArE+3rxyZ1z025fLELTdqY953V+9fRLp9K9NtX0fmF+pUwPzb\nvsPl/54/YX722pgR1k+BXx37h3JplFFEvIQuNBERd/sROAQ8gRnZuwAswSQkYP4YPQE0c/Hc9Bc0\nnHZTTOmTrc2OmAYAY4DbMNOZWcUDl/6YbgnMwNzzejAm8WmNmWYu4tQ+FZMcpUn7PsXFvoB0bZ2P\n5+eFMjl539Pej2cwZQHp7Xd8HYAZob0BM9r6CvAUMCGXMYqIm2mkUETcqRymjvBNzMUTWzG1gmFO\nbf4CQjAXeuxM99h3hXOfdBxPPwXZ0fHcc5hkD8woYJoiZLzQBcxo4f2YZOVfzEUcOdEOU3s3EjMS\nGQtUzeE5sms1Zko8L4lhLObfwtX7tyFj8wyv3y2TYwcxyX89Mv57pl0QlGYTZkTxZsz9wtNPOYuI\niIifCMQkCTMxS6K0xtSjJWKSpzTzgG2Ymr2amOnRpzEXkMClmsI26c7/OJcuNKnDpQtNHnRqM9tx\n7ijMdPIULr/QJE1RTB3fOWBEumNRjtevnG7/BS5doHILZrTvIcfPcD8mOUrl0lR5NBmvIu7naOOs\nj2Nf2h/q6Z/XEDN69wXmvarFlS80gYw1hWBGRY8Ad2Gmb4c5foZOTm3Srvp21hVzock7mPrIaxwx\npk0B98Mkfy87Yr0G82873nG8tuO12wLVMf1iI2ZUVURERPxUBy4tTbIFU3e3g8uTwmLAG1waSfoX\nU2sW5TgejklW0ieFcGlJmiTM6Ncz6Y47L0lzCLNszCRc18S94zhP+uQvyvH6V0oKAUZjlr1JxEyb\n93E8zzkpTD8F3Y/Lp45xep5zUpj+ec0xo6+JmFHTP3E9BZ/mP5grnZ0VwrzvaUvSbHS8tjNXSSGY\nad8/MUn5cUyNY7jT8Tscx09jkvC/geGOY5UwfyjsxSTh+zEjtaWuEL+IFHBPYaaWzgGfpzvWBTMV\ndRqzvEO1dMfT/gI+QsarE8MxtS6nMb+kuiAiYmoCv7c6CBERyagH5q/Nj7k8KSyP+cu0J6Y+6C1g\nmdPxRzEJY2XHY5NjX5plmPWximJGLY45zikiBVNZzMhXEronsIiIV3uFy5PCAZgrBdOUwExhpNWz\n/MmlWiQw9UVpSWNdzMhjSafji7g8aRSRgiUOMwX7isVxiIh4DW9dkib9FXYRmNXx05zB1BJFYGpm\nGqQ7vp5L625FYOqPnJdYWEfGdblEpOAItzoAERFv461L0qRfp6sk5q96Zye5VKQcjClsdj4WnMmx\n9M8VERERKfB8ZaQwkYy3xCqDWTXf1fEyjn2ZPTeEjEkmAJUrV7bHx8fnNF4RERERK/xDxrtB5Yq3\nJoXpRwo3YW6+nqYkZp2uTU7HIzFXLgM0xiy1kHasJmbEMNHp+FRXLxwfH4/d7uqGAiKXi4mJISYm\nxuPDVp0AACAASURBVOowxEeov0h2qa9ITgQEBNRy17m8bfo4CLN+WSHH90UdX2dhFkS903H8P5h1\n0NLW4JoCDMJceXy14/tJjmPbHW3/43junY5zzfT0DyMiIiLiK7wtKRyBuYhkKGaB17OYFfKPYJaj\neQ04ilmw1XnB1U+AHzC3alrv+N75fpp9HM856jhHTyDBgz+HFABxcXFWhyA+RP1Fskt9RazibdPH\nMY6HKwsw91TNzFDHw5XdXH4bJ5E8i4yMtDoE8SHqL5Jd6itilbzcXN1f2VVTKCIiIr4gICAA3JTP\nedv0sYiIiIhYQElhDoSGhhIQEKBHPj9CQ0Ot/qd3yWazWR2C+BD1F8ku9RWxirfVFHq1Y8eOabka\nCziGxkVERMSD9Ns2o0xrCgMCApQUWkDvu4iIiGuqKRQRERERt9L0sUgu2Ww2oqKirA5DLJSSmsK+\nk/s4ePogKakppNhTSE5NJiU1hVR7KqHFQ6lSugoVSlZg8aLF6i+SLfpsEasoKRQRyYLdbmfLkS0s\nilvE9oTtxB6LJfZoLLuO7aJ8ifJUCq5EocBCFAosRFBgEEEBQQQGBJJwNoF9J/dx8vxJyh4oS51d\ndahepjrNKzenddXWRFaKpEhQEat/PBERwPdqCqsA44A2QBLwLfAckAJ0AT4CqgIrgGhgj9NzxwD9\nHd9/CryYyWv4XU1hdHQ0+/fvZ/78+cTExDB9+nR27Nhx8fg333zDiy++yO7du7n//vuZOHGihdFm\n5Kvvu/i2w6cP89vO35i3cx7z/5lPUGAQXWp0IaJCBLVDa1M7tDY1ytagROESWZ7rXPI54k/Fs+/k\nPmKPxrJy/0qW7VvG/7N33/E1X/8Dx183IRIJCWKv2LtCa6/YqzWitkqISLVGaZV+O9CWlvpVzVKj\nRilq1qyV2DVrVwli772zzu+Pc0PESrg3n3tz38/H4/Nwz+dz7/28cx3XO2eGXwvHN5svlXJVona+\n2tTOX1uSRCFEklhyTKG9JYULgJtACJABWA1MBH4HjgGd0VvcfQtUAyqZXxcC9AZqmcurgVHo7fES\nSpFJ4blz51i1ahV3797l4cOHj5Z5iYmJwcvLi549e9K9e3fc3d3p06cPx44dIzQ01ODINXv93IX9\nuRd1jzkH5jBx90QOXj6In48f9fLXo26BuhTKWMjiM+FvP7z9KEFcGb6SQ5cP0bhwY1oUa0H9AvVx\nS+1m0fsJIVIeR55oUgKYg24lvAisNJ/zR+97PN98bSBQGihsfl0AMBw4Zz6Go1sSHUZcUuXu7v7E\nun/nzp3j7t27NGzYkOzZs5M+fXqjQrQ7spZYynHg0gF6LO9B7hG5mffvPPpX7c+VvldY3GYxH5b/\nkMKZCr92Qvis+pIuTTpq56/NF9W/YFPnTRz44AAVc1Zk1LZRZP+/7LSe15pVx1YRq2Jf697Cvsh3\nizCKvSWFfwHtADcgJ9AQWAEUB/bGe949IBydMPKM6/viXXMIcf+hDRw4kEKFCgEwdepU8ubNC0D1\n6tVxcnKiZs2aTJkyhfXr1+Pk5ISTkxPTp083LG4hrEUpxdIjS6k6pSr1ZtQjdawX3+fbTcm9y/i/\nrk14o2RqChUCHx/ImROyZoXs2aFePfjiC/jzT7hwwbIx5UiXgw/Lf8i6gHUc7XGUmj41+XT1pxQb\nW4xR20Zx88FNy95QCCHisbfu44zAGqAU4AxMRXcZTwIuA5/Fe+4m4BdgOhCNTgyPmK8VAv7j2Ulx\niu4+HjhwILNmzeLIkSM8ePCAAwcOUL58ef7880/Kly+Pm5sb3bp1IyIiggULFgCQPn16XF1dDYvf\nXj93Ybs2nNxA/zWfcfbKTXwiBnJmTVOuXUlNhQpQuTJUqqQTwdSpIVUq/Wfq1BAVBXv3wvbtjw93\nd6hbF3r3hpIlLR+rUootp7cwZscYVoavpE2JNnQv350SWRzq91ohxHNYsvvYnmYfm9AthX8AFYB0\nwBT0BJI7QMJ+T0/gtvlxwuue5nPPFBgYiI+PDwBeXl74+vqmqOUB4hIsV1dXvL29Ab2FX5YsWR6d\nT5069aOyLYnrVon7+5CylJNSnjh/ImP/nshJj8uYwr4m++UcvFnPmZ8Xp6ZoUdiw4eXv5+4Ogwbp\ncmhoGGfPwqlTftStC7lzh9GmDfTu7YfJZNn4q+Spwvzl81l6ZCl1/qtD1TxVaZSqEfky5LOZz1fK\nUpay9ctxjyMiInBkmYFYdDIYpxl6LGEwumUwjju6CzluTOFmoEu860HAlufcRz3Pi649+TzLH68j\nICBA1a1bVyml1IABA1TBggUfXTtx4oQymUxq8+bNj84FBQUpPz+/17upBSX2c09uoaGhRocgEuns\nzXOq5pi2Ks3n2ZRbjdEq5IOHau9ey97j/n2lJk1SqlgxpcqUUWrmTKWioh5ft2R9ufPwjvph8w8q\nyw9ZVOs/WqtDlw5Z7L2F8eS7RSQFYLGuNHsaU3gFOA90Q3cde6EnkOwFFgIl0RNOXIEBwB4edxdP\nB/oAOdBjEfugu56twhppoRAi6ZRSDFg8BZ+hpdm3Ph8/5Arn4pLujB/rwhtvWPZerq4QFAQHDsA3\n38DYsVCjBhw/btn7ALi7uPNJ5U841vMYZbKVocbUGrRf0J7wa+GWv5kQwmHYU1Ko0EnfO+gE8Sjw\nEL3UzBWgBTAYuAa8BbSJ99oJ6KVq9qMnmSxBjzcUz+Di4kJMTIzRYdi8uCZ9YZu2/HucnJ/VY8jq\nsXySdRUXZg2mx/vupEv38te+DicnaNwYNm6Ed9+FChVgyhSoUcPP4vfycPGgX9V+HOt5jOLexak4\nqSL9Vvfj9sPbL3+xsFny3SKMYk9JIehFqauh1yjMjE78LpuvrQWKAWnR6xGeSvDafkAm8/G8hatT\nLJWE5sb8+fNz+PBhDh06xJUrV4iMjLRiZEJY1q3bMdQfOIKq08pTJFU9LnyzjSE9fUmVzCOonZz0\n5JPQUBg5Evz94fLll7/uVaRLk47Pq3/O/m77uXj3IkXHFmXanmmylI0QIknsLSkUr8BkMj1akib+\n4/jX4wsKCqJcuXJUrlyZLFmyMHv27GSL1Z7EH/QrbMP81WfI0q8m/9xbxNp2Wwn9ti+ZMhg7n65k\nST1LOU2aMHx9YcUK690re7rsTG02lQWtFjBu5zgqTa7EtjPbrHdDYRXy3SKMYm9L0iQH9eaEN4mO\njX50ODs5453Wmw2dNsjSKAaw1SVpwmTTepvx8CF0GLiSBbGBtCvQk2nB/XEy2dbvvGFhYZhMfrRv\nD19+CSEh1r1frIrlt32/8dnaz2hWpBnf1fmO9GlkcXp7IN8tIqGr964Sfi2cM7fOcPb2Wc7cOvPo\n2Nh5IzjoNnfJQW0/s/3R5vapnFIRHRvN1ftXqZmvpk0mJymdrSaFwjbs+ieaBsO+4k7+6cxpNYsm\npasbHdILHTum1zXs2hX6J8NAlhsPbvDJqk9YfXw1Pzf+mUaFGln/pkKIV3bhzgV2n9/NrnO72H1h\nN7vP7+bGgxsUzlSYXOlzkStdLnKmz0mu9LnImS4ntfLXAkkKrUY9LwGR5MQY8rmLZ4mJgS+GnWV4\nRBuKFkjLmg9mkNXD9tbWfJazZ/XOKO+8A999BxbeUvmZ1h5fS/CSYKrkqcKI+iPwTutt/ZsKIV7q\nbuRdwiLCWHVsFX8d+4vL9y7zZvY3KZu97KMjf4b8z+39sOTi1ZIUPk2SQhtjq5+7dPEY59o1aPB+\nGHsLtqVXpR58/7btdRcnlLC+XL0KDRtC2bJ6+RpnZ+vHcDfyLl+s+4LZB2czqsEoWpZoaf2biiST\n75aU78ytM8w5MIfl4cvZfnY7b2Z/k/oF6lO/YH18s/km6fvMUXc0EUII9u6FOp9O4l7Fz1nSYRb1\nCtU2OqRXkikTrF0LTZtC+/YwfTq4uFj3nu4u7oxoMILWJVsTsCiAJUeWMKbRGBlrKEQyuH7/OvMO\nzWPm/pnsu7iP5kWb06tCL2r61CRdGiuvlZVI0lL4NGkptDHyuYs4v82MIXheX7zKLWV9yFIKZyr8\n8hfZuAcPoFUrnRDOmZM8LYagWw37/NWH1cdXM6P5DKrkqZI8NxbCgcTExrDs6DKm/DOF0IhQ6hWo\nR7uS7WhUqBFpUqWxyD2k+9i6JCm0MfK5i6go6PXpLabdaUvJMg9Y2WkeGdwyGB2WxTx8CPXr667k\nH39M3nsvPryYkKUhdH2zK19W/5LUzqmTNwAhUqBr968xefdkxu0cR1b3rIS8GYJ/MX88XT0tfi9L\nJoW2PQjn2doA/wJ3gHCgqvl8beAwcBdYB+RJ8Lqh6J1PrgDfJ0ukIkWTtcSSx/XrUL3pCWa4VKZV\ng9xsCllplwnhi+pLmjSwcCGsXKkXuk5OTYs2Zc/7e9h+djtVf63KsWvHkjcA8RT5brFfey/spcuf\nXSgwqgD7L+1n7rtz+bvL33Qq08kqCaGl2VtSWBed0AUAHujdTY4D3sAC4HP0bic7gTnxXhcCNAXe\nMB/vmM8JIWxYRASUfXsX+8tV4ZtmXZni/3OKbcnKkAGWL4dhw3SCmJyyeWRjRfsVtCvZjkqTK7Hg\n3wXJG4AQdm7r6a00mtmIRrMa4ePlw3/d/2N68+mUy1nO6NCSxN66j7cAE4FfE5zvCnTkcathWnSL\noC9wxPy6KcAk8/VO5tdUesY9pPvYxsjn7ph27oQGH6zh4dvtmNHqF5oVbWZ0SMli1y5o0ACWLIGK\nFZP//jvO7qDVvFY0K9KMoXWH4uJs5dkvQtixjSc38vWGrzl69Sj9q/ank28ni40VTCxH7T52Bt4E\nsgBHgdPAaMAVKAHsjffce+iu5RLmcvEE1/fFu+aQIiIicHJyYsuWLUaHIsRTli6FWj1nE920PcsC\n5jlMQgjw5pswdSo0bw7h4cl//3I5y7Gr6y6OXT9G9V+rc+pmwm3khRDrI9ZTc1pNAhcH0qZEG470\nOML7b72f7AmhpdlTUpgVSA20QLcI+gJlgC8Ad+BWguffAuLmeHsANxNc87BmsLamTp06dOrUyegw\nHvntt99wcrKn6vc0GfdjHePGQftRo3Br2peNXdZQPa9t71CSWEmpL40bw8CBeh3Dq1etFtJzZXTL\nyOI2i2lRrAXlJpZj2ZFlyR+EA5PvFtt16PIh3p71Np0WdyKwdCD/df+PoLJBKaZF3Z7WKbxv/nM0\ncNH8+Ed0UrgBSLjQlidw2/z4ToLrnuZzzxQYGIiPjw8AXl5e+Pr6ykKiZpGRkbhYezG1F4j7soz7\n+5ByyikrBe07hLL07CQyN93Fuk6bOLHnBGH/htlEfMldDgmB1avDaNwYtmzxw8kpee9vMpkoF1WO\nL3J/QcjSELqU7UJ1VR0nk5NNfD4puRzHVuKRsh8X7lwgeFQwG09tZEDAAOa3ms/WTVvZtGGTIfUj\nLCyMiIgIHN0p4L14ZX9gNxAMbIp33h3dhRy3iNlmoEu860HocYbPop7nRddsWUBAgDKZTE8cU6dO\nVSaTSc2dO1c1btxYpU2bVuXPn1/NmDHjideaTCY1atQo1bZtW+Xp6alatWqlIiIilMlkUps3b37i\nuQUKFFADBw58VJ44caIqWrSocnV1VRkzZlTVq1dXZ86cUaGhoU/F06lTp+fGb6+fu0i86GilgkOi\nlXenYFV2XHl1+e5lo0OyCZGRSlWqpNSQIcbGcf72eVVlchX1zqx31I37N4wNRohkdOfhHTUwdKDK\nODSj+uSvT9S1e9eMDukpgMMOuh8EbAcyo2cZbzSf8wZuoJNEV2AYTyZ9IcAhIAeQEziInmjyLC/8\n4O3RzZs3VfXq1VWbNm3UxYsX1cWLF9WRI0eUyWRS+fPnV3/88Yc6duyY6t+/v0qVKpU6evToo9ea\nTCaVKVMmNWbMGHX8+HF19OhRdeLEiWcmhQULFlSDBg1SSim1c+dOlSpVKjVjxgx16tQptX//fjV5\n8mR15swZFRkZqcaOHatMJtOjeG7duvXc+O31cxeJ8/ChUi1bR6os3dqqGpNrqdsPbxsdkk05dUqp\nrFmVCg01No6H0Q9Vt6XdVJHRRdS/l/81NhghrCw2NlYtOLRA5RmRR7WZ10Ydv3bc6JCeCwdOClMB\nY4HrwHngJyCuL7M2ev3Cezx/ncKr5uNF6xS+8IO3V3Xq1HmiNS4usRsxYsSjc9HR0crDw0NNmDDh\n0TmTyaS6dOnyxHslJilcsGCB8vT0fG6yN2PGDGUymRIVu61+7qFG/y+dAty9q1S9RvdVto+aqIYz\nGqv7UfeNDslqXqe+rFypVI4cSp0/b7l4XtWkXZOU9zBvtfDfhUaHkmLJd4uxwq+Gq4a/NVTFxxZX\noSdCjQ7npbBgUmhPYwoBooEPzUdCa4FiL3htP/NhdaZBll/pRw2wzi8Cvr6+jx47OzuTNWtWLl26\n9MRzypcvn+T3rVevHvnz5ydfvnzUrVuXWrVq4e/vT6ZMmV47ZpEy3LgBjZre5UTFZlR9MwMzW/yW\nYgZrW1r9+hAUBG3bwurVkMrAb+6gskGUylqKFnNb8M/5fxjgNwAnk31PGhMC4EH0A77f9D1jto+h\nX5V+9KrYy+G+k+wtKbQL1krgrCHhpBGTyURsbOwT59zd3Z8ox80aVgnWDoyKinriNTt37mTz5s2s\nWbOG8ePH8+mnn7J27VrKli1ryR/BMHGDf0XSXb4MtRvd5Er9xtR/qxCTm0zC2SmZNv01yOvWlwED\ndHI4YAAMHmyZmF5V+Zzl2RG8A/85/hy8fJBpzabh7uL+8heKRJHvluQXeiKU4CXB+Gbz5Z+Qf8jt\nmdvokAwhv945CBcXF6Kjoy3yXpkzZwbg7Nmzj85dunTpiTLo5LFatWoMGjSIXbt2kT17dn7//fdH\n8cDTiaVI+c6fhyp1r3K5cS38K5dhStPJKT4htARnZ5g5E6ZN0zufGC2bRzZCA0Jxd3Gn2q/VOH3z\ntNEhCZFkNx/cJGRJCB0XdWRkg5HMazXPYRNCkKTQYeTLl49du3Zx/Phxrly58kSrXnyJSdLc3Nyo\nUqUKw4YNY9++fezatYuOHTuSJs3jRTsXL17MTz/9xK5duzh16hQLFy7k9OnTFC9e/FE8cc+7fPky\nd+/etcBPmbwSLh8hXu70aahS7xK3mtekY5U6jG44ymG6Hi1RX7Jmhd9/h86ddXJttDSp0jC16VTa\nlmxLxckV2XZmm9EhpQjy3ZI8lh1ZRsmfSwJwoNsBGhdubHBExnOMb2PBxx9/jLe3N6VLlyZr1qxs\n2bIlbmucJzzr3LNMmTIFDw8PKleuTLt27QgJCSF79uyPrmfMmJElS5bQsGFDihQpQv/+/fnyyy8f\nLaBdrlw5evXqxfvvv0+2bNno0aOHZX5QYbNOnIAqDc5zt6UfIdWb832d7xNd38Rj1apBcLAeY2gL\nDe0mk4m+VfoyvvF43v79bWbum2l0SEK80NV7V3lv4Xv0WNGDac2mMeGdCXi6ehodlk2Qb+Snqee1\nlskevMaQz93+HT0KNd45S0yHWvSo/h5fVP/C6JDsWlQUVK4MnTrBBx8YHc1jBy4doMnvTWhXqh1f\n1/zaYVqBhf1YfnQ5wUuCebfYuwypPSRFjIW15N7HkhQ+TZJCGyOfu307dAhq+Z8ktkNt+tYMoW+V\nvkaHlCL89x9UrQqbNkGRIkZH89ilu5doNrsZuT1zM7XpVNxSuxkdkhDcibzDJ6s+YWX4SqY2m4qf\nj5/RIVmMJZNC+TVOiFck435ebv9+qNHsODHv+fF5nR4OnRBaur4UKQJffw0dOuiWQ1uRxT0L6wLW\n4Wxypua0mly8c/HlLxJPkO8Wy/r7zN+UmVCG+9H32fv+3hSVEFqaJIVCCKvYswdqtTyKCvBjUL2+\n9KrYy+iQUpz334csWXRyaEtcU7ky038mDQs2pMKkChy4dMDokIQDioqJ4st1X9J0dlO+r/0905pN\nk7GDL2Gv3ceFgP3AHzzeC7k2ereT3MA2IBC9V3Kcoeg9jwEmAf2f897SfWxj5HO3P7t2Qf32h1Hv\n1WFow4F0Kdvl5S8Sr+TCBfD1hQUL9DhDWzNr/yw+WvkR05tPp0HBBkaHIxzEsWvHaLegHZncMjG5\nyWSyp8v+8hfZKek+1snfdh5v7eINzAc+R++JvBOYE+/5IUBT4A3z8Y75nBDCwrZvh3rtD6Leq82P\njQdLQmhl2bLB+PHw3ntw+7bR0TytXal2LGqziE6LO/Hzjp+NDkc4gJn7ZlJxckXalWzHsnbLUnRC\naGn2mBS2Qe99vJbHmbE/cACdGEYCA4HSQGHz9QBgOHDOfAxHtyQK8cpk3M/Ttm6FBgF7Ue/VYXST\nHwjwDTA6JJthzfrSrBn4+cHHH1vtFq+lcu7KbOq0iZHbRvLxXx8TExtjdEg2Tb5bXs3th7fpuLAj\n32z4htXvraZXxV6y7FUS2VtSmB4YBPTmyabSEsDeeOV7QLj5PEDxBNf3xbsmhLCATZugUdBueK8+\nE5qNol2pdkaH5FBGjIBVq+Cvv4yO5NkKZCzA1qCt7L6wmxZzW3A30v4WrBe2a+e5nZT9pSxpnNOw\nq+sufLP5Gh2SXbK3pPAb9HjAc+iu47juY3fgVoLn3gLSmR97ADcTXPOwXpjCEcj+pI+FhsLbITug\nQ0MmN/+ZliVaGh2SzbF2fUmfHiZN0gtb37hh1Vu9sgxuGfirw194uXpRY2oNzt+2gW1ZbJB8tySe\nUooRW0fQaGYjhtQawsQmE1PE2oNGSWV0AEngi55MUsZcNvG4tfAOuhUxPk/g9nOue5rPPVNgYCA+\nPj4AeHl54evrK/9IbURct0rc34eUjS9v3w5DZjpjat+Cvrk+IsPFDFAMm4nPkcqpUoVRpgz06ePH\nlCnGx/O88q9Nf2XwxsH4fubLkFpDCPIPsqn4pGwf5T//+pPvN31PdJ5otnXZxsm9JwkLC7OZ+KxV\njnscERGBI+uFTuTOm4/b6G7iXUAwsCnec93N1+LGFG4G4o92DwK2POc+6nledE1Yj61+7qGhoUaH\nYLglS5TyLLNaeQ32VqvCVxkdjk1Lrvpy+7ZS+fIptXRpstzutczcN1N5D/NWK46uMDoUmyLfLS+3\n+dRmlWdEHtV7ZW/1MPqh0eEYise9pq/NnrqPfwHyoyeQ+ALjgWVAPWAhUBI94cQVGADsAY6YXzsd\n6APkAHKaH09NvtBtm5OTE7NmzXrhc/z8/AgODk6miIQ9WLAAOny9DKeW7Vjcfj51C9Q1OiQBeHjA\nlCkQEgLXrxsdzYu1K9WORa0XEbgokHE7xhkdjrADsSqWYZuH0XxOc0Y3HM2P9X/ExdnF6LBSDHue\nljMAKAB0NJdrA2OAvMDfPHudwrjWwonIOoWPXLp0CU9PT9KkSfPc59SsWZNChQrxyy+/JGNkWkr9\n3O3Z7Nnw/qh5OL/zIcvf+5MKuSoYHZJIoGdPPbZw+nSjI3m5Y9eO0XhWYxoWbMjwesNxdnI2OiRh\ng67cu0LAogCu37/O7Hdnk8czj9Eh2QTZ+9i6HC4pTAxJCkWcKVOgz7TfSN2wL6sDV8gsPxt19y6U\nLg3/93/QtKnR0bzc9fvXaTG3BenSpGOm/0w8XGQuoHhs86nNtJ3fljYl2zC41mBSO6c2OiSbIYtX\niyTbtGkTVapUIX369KRPnx5fX19WrVoFPN19fPLkSRo0aEDatGnJkycPo0ePfur9oqKiGDhwIPnz\n58fNzY2SJUsakjAaKf6gX0fx00/wyZxxuDbuz/qgtZIQJkFy1xd3d/j1V+jWDa5cSdZbv5IMbhlY\n2WElmdwyUf3X6py9ddbokAzjiN8tzxOrYvlh8w/4z/VnXONxDKs77JkJ4b17cPOmPm7d0sft27a1\nL7g9sKfZx+IVRUdH06RJEzp37sx0c1/S/v37cXd/etq+UormzZuTOnVq1q9fj4uLC3379mX37t0U\nKlTo0fOCg4PZs2cPv/zyC4UKFWLbtm2EhISQKlUqOnfunGw/m0geSsGgrxWj935L+vrTWNdpA/kz\n5Dc6LPES1apBmzbQvbvu8rd1Ls4uTG4ymWGbh1FhUgUWtl5IuZzljA5LGOTa/WsELArg8t3LbO+y\nnbxeeVEKzp6Ff/7R+6vHHefOgYuL/q6Cx3/GxOgW80qV9DaQlSpBzpzG/UzC/rxwhk8ipwJZ/ngN\n165dUyaTSYWFhT3zuslkUjNnzlRKKbV69WplMpnU0aNHH12/fPmycnNzU8HBwUoppY4fP66cnJzU\nf//998T7DBo0SPn6+r5WrM+S6M9dWEVsrFIf9Y5R3h16qeKj31Dnb583OiSRBPfuKVWkiFJz5xod\nSdIs/Heh8h7mreYcmGN0KMIAW09vVXlH5FV9VvZRD6Ieqj17lOrfX8+sz5JFqfr1lerXT6nff1fq\n8GGloqOf/T537igVGqrUkCFKvf22UpkyKZU7t1J9+yp19myy/khWgwVnH0tLoTXY2Pi3DBky0KVL\nF+rXr0+tWrWoUaMGzZo1o0iRIk8999ChQ3h7e1OwYMFH57y9vZ947s6dO1FK8eabbz7x2ujoaFKl\nkiqVksTEQJeuUSx1DqJAteOseC+MDG4ZjA5LJIGbG0ybpscVVq8OWbMaHVHiNCvaDB8vH5r83oR/\nL//LVzW+ki3LHIBSih+3/sjQzUP5qswvXNnUDN+P4MED3eq9YIFu+UtsVXB311tAxi01rBQcPqz3\nCy9ZEt59F/r2hXgdYQ5NxhQ6iF9++YVdu3ZRt25d1q9fT6lSpZI0BlDFS3RjY2MB2Lp1K3v37n10\nHDx4kH379lk8dluV0sf9PHgALdveZ6l7C8pWvcK6TqskIXwNRtaXChWgUyd4/32b+531hXyz+bI9\neDsrwlfQdn5b7kfdNzqkZJHSv1ue5+q9qzT5vQkTt8ylYOh2hnRsxs2bMHUqHD8O330Hvr6JTwif\nxWSCYsVg5Eg4cgSyZ9fdyq1awe7dFvtR7JYkhQ6kRIkS9O7dm+XLlxMUFPTMpLB48eJcuXKFnJre\nJAAAIABJREFU8PDwR+euXLnCf//996gc10J48uRJ8ufP/8SRL18+6/8gwuquX4eaja6xMV89alZ1\nZ0n7RaRNndbosMRrGDgQwsNh5kyjI0mabB7ZCA0IxcnkRI2pNThz64zRIQkr2HhiK0VGlOXv5YVJ\nNWMj3dr6cPKk3tO7QoXXSwSfx9sbBg2CEyf0WMPGjaF/f8eenCJJoQM4duwY/fr1Y/PmzZw8eZKt\nW7eyYcMGSpQo8dRz69SpQ+nSpenQoQM7duxgz549tG/fHhcXl0ethQULFqRz584EBwczY8YMwsPD\n2bt3L1OmTGHYsGHJ/eMZJm7roZTm1CkoX/84/1WtTEDtisxuOVMWh7UAo+tLmjS6G7lPHz1Q3564\npXZjpv9M/Iv5U35ieTaf2mx0SFZldF1JTvfux9J06A/4TWhGjj2jmdHh/9i/x4X33oPUybTqjIcH\n9O4N+/bB/v1QtapumRQCUuA2d+fPn1f+/v4qV65cKk2aNCpHjhyqa9eu6tatW0qpJyeaKKVURESE\nqlevnnJ1dVW5c+dWo0aNUn5+fo8mmiilVExMjBo2bJgqWrSocnFxUd7e3srPz0/NmzfP4vHb6+du\nj/bsUSpLmW0q/aDsasy2MUaHI6xgwAClGjbUE4js0fIjy1XmYZnV+B3jjQ5FvIboaKVGTbmgXLvU\nVxk+qaj+XB9hdEhKKf3vYsQIpTJn1pNY7AEWnGgio3afZv6MnyaLKBvDVj/3+BuvpwRr14L//xaj\n3unCby0n06RIE6NDSlFspb5ERenuuA8/hKAgo6N5NUevHqXp7KZUy1ONUQ1HkSbV83djske2Ules\nQSlYuRI+/HE1Z94KpE2RQCa/N9DmFqPevRvatoUqVWD0aD1hxVY56uLVLsBkIAK4BfwDNIh3vTZw\nGLgLrAMS7n8zFLhiPr63cqxC2JWpU6HZkDGkbtaNtZ2WS0KYgqVOrbe+698fjh0zOppXUyhTIbZ1\n2cale5eoNb0W52+fNzokkQi7doFf7Sg6TO3PrZqdWN5lOtMDbXN3krJldbyxsbo72R4WgLcEe2op\nTAv0BX5F72ncGPgdKAncA44BnYElwLdANaCS+bUhQG+glrm8GhgFTHjGfaSl0MbI52490dHw8adR\nTDvfh0zl1rCm03LyZZDJQo7gp59gzhzYuBHsdSWpWBXLtxu+ZfzO8cz0n0nNfDWNDkk8w6VL8L//\nweINx0kX2I6ieTIxrflUMrtnNjq0l1JKx758OaxZA5ltMGTZ+/ixvcAgwBvoCFQ1n0+LbhH0BY4A\nW4ApwCTz9U5AVx4njfFJUmhj5HO3juvXwb/DZfYUaUn50h7MbT0TT1dPo8MSySQ2Fho00MtxDBxo\ndDSvZ/Wx1XRc1JHu5brzWbXPcDLZUydYyhUVBWPHwreDFW8GTWVXxk/5vNr/6FWxl139HSkFX34J\nixfrYTZZshgd0ZMctfs4oaxAYeAAUAKdIMa5B4SbzwMUT3B9X7xrQrwSe15L7PBhKN1gN7veKke3\nRlVZ0fFPSQitzNbqi5OTHjYwfjxs3Wp0NK+nboG67AzeycpjK2k0sxFX7tl3X5+t1ZVXsXq1XmR6\n8erLlPmuBRd8fiI0YB29K/W2q4QQ9HI433wD/v5QsyZcvGh0RNZjX38zj6UGZgJT0S2B7uhxhvHd\nAtKZH3sANxNc87BuiELYphUroHyXmVx/uz5TWg9nSJ1v7e5LWlhGjhzw88/QoQPcSvgNamdyps9J\naEAovtl8KTuhLFtObzE6JId08qROnt5/H979bDlHavtSJm9BtnfZTqmspYwO75WZTHpNw1at9O4o\n51PoMFZ77D52Amahk7qmQAzwEzpR/DDe8/YDXwELgRtAHWCn+dpb6Mko6Z/x/iogIAAfHx8AvLy8\n8PX1xc/PT7oxDRL/c4/7DTpuZp6UE1+OjoaOgWtYeHIiGd/ZycqARVz996rNxCdl48ozZ/oRFQWB\ngbYRz+uW7+S4Q9CfQbyd+m3alWpH7Vq1bSq+lFh+8AA+/DCMefOgx8dvcal0X/5cvZD+VfvzUZuP\nDI/PkuVNm/yYMQO++y6MjBmT//5xjyMiIgCYNm0a2OCYwrzoMXwJJ27PsuA9TOixgXmARsBD8/lg\nIIDHYwrdgcs8HlO4GT1BJW5MYZD5qPyMe8iYQhsjn/vrO3UKmnc+zjHftrxZPBNz28wgU9pMRocl\nbMSdO3q25eDB0LKl0dFYxplbZwhcFMi9qHvMaD6DAhkLGB1SirV8OfTsCaVKgX/f1Xy1oys18tZg\nZIORKXZYypdfwrp1+khj8IpIlhxTaCn90eP4dgIbExyWNB7YytOJpze6NdAfcAWGoSeXxAkBDgE5\ngJzAQfREk2d57gKRGTJkiFskUo5kPDJkyGC1RT9fR2hoqNEhJMrChUqlrzxLuQ/0Vj9uGaFi7XXV\nYjtn6/Vl2za9YO+pU0ZHYjkxsTFqxNYRynuYt5q8e7Ld1H1brytxwsOVatJEqUKFlJq75JrqtKiT\nyjsir1p5dKXRoVldTIxSzZsrFRRk/ELwWHDxaksNJOqL7pJ9C70UTPzDUvKiE7nSwAXgtvloi55p\n3AIYDFwzx9Em3msnoJeq2Y+eZLIEeHrj35e4du0aSik5LHjExsYyfsd4Mg3NxOANg3kY/fCp51y7\ndu3Va40De/AAQnrc4b15nfBqNpANXf+id6WP4n6rFOIJ5cvrLfBatYLISKOjsQwnkxMfVfyI0IBQ\nRm4bif9cfy7fvWx0WHbv9m347DO9CHrlyjB4/iI+OlKStKnTsr/bfuoXrG90iFbn5KS3jdy2DcaN\nMzoay7HU/w5HgDLohaPtnTnxFsnp5I2TdFvWjRM3TjCm4Rhq569tdEh2betWaN93J5ert6NpmaqM\nbzoKDxeZWyVeLDYWmjUDHx8YNcroaCzrYfRDvgz9kul7pzO83nDal2ovvyAlUWws/PabTgjr1IHu\nn59i6J4+7L+0n0nvTKJaXku2A9mH48ehUiW95qdRm9DY4jqFjYD26AkfCSdrn7LQPZKLJIUGUUrx\n539/8tFfH1E+Z3n+r97/kSt9LqPDsiu3b8Onn99l+ukBpH5zBj83HUnbUm1e/kIhzG7cgLfe0ktw\ntG1rdDSWt/3sdrou6Upm98z83PhnCmYsaHRIduHvv+Gjj3Ri+MOIB2yMGc5Pf/9E9/Ld6VelH26p\n3YwO0TBr10L79vozMs9RTVa2uE6hC1Af2Ibehi7uOGGh9xcOwGQy0bRoUw5+cJAimYrgO96XYZuH\nERljm31Z8WeC2YLly6FAvVX8lr4UjVpf4GjvA5IQ2hBbqy/P4+UF8+bpiQMHDxodjeWVz1menV13\nUr9AfSpOqsiQjUNs7jvGlurKf/9BixZ6AlJIiOLz6UvovKsEu8/vZmfXnQz0G+jQCSFA7dq69bRp\nUz1py55ZKikch55s4olOEOOOlLVLuUgWaVOn5euaX/N3l79Zf3I9xccWZ9b+WcSqWKNDs0nnzkGL\n967QavZ7ODcN4Y/AcfzR5je72EJK2CZfXxg+XK83Z+/rFz5LKqdUfFL5E3Z23cmmU5soO6EsoSdC\njQ7Lppw/r9carFpVjx38c+u/zEvzNv3W9OXnxj+zoPUCfLx8jA7TZvTsqWfwd+qkd0CxV5bqPr4E\nZEevGWjvpPvYxqw7sY7P1n7Gw+iHDK41mEaFGslYIODmTfhuWCSjt0zEVOMbOr/Vnu/qfY27S8LJ\n+UK8mpAQuHoV/vhDL96bEimlmP/vfPqt6UeRTEX4vs73vJH1DaPDMsy1azBihJ480akTtPvwOCP3\nDmLF0RX0q9KPHhV64OLsYnSYNunBA6hYUSeInTsn331tcUxhX3Sr4GAsODXaIJIU2iClFIv/W8zn\n6z4ng2sGhtQeQvW81Y0OyxAPH8LYcbEMmjcXVfMLyvoU5Ke3v8c3m6/RoYkU5sEDqFYN2rSBjz82\nOhrrioyJZPzO8QzeOJiGBRvydc2vyeOZx+iwks3Fi/DjjzBpku4GDfnkLFOPf8sfh/6ge/nu9K7Y\nO8WuOWhJBw7orfC2bYP8+ZPnnrY4prAXMAA9+/h0vMPeJpkIG2UymWhWtBn73t9H1ze7ErAogGq/\nVmPR4UXExBrTQJ3c436iomDGDPCptZpB598iT+sfWRT0C2FdVkpCaAdsaZxYYrm66vGFw4fDsmVG\nR2NdLs4u9KzQk6M9jpIrfS7KTChD31V9OX87+fczS866cuoU9OgBxYrB3buwZMMpvFr3oeGSUqRL\nk47D3Q8z0G+gJISJVLKkHl/YsSPE2GHfqaWSwg7obeQamh93AN4zH0JYjLOTMx1Ld+Roj6N0L9ed\nIRuHUHRsUcZuH8vdyJSwItLTrl6FwUNiyVZjKT131SJV0w+ZHPg/9vXYRq18tYwOT6RwefPCokW6\nK3H7dqOjsb70adLzba1v2d9tP/ej71N8XHE6Le7EgUsHjA7NYpTSM2UDA6FMGXB1U/y6dhMXa7Tk\nnWVlADj4wUGG1R2Gd1pvY4O1Qx99BKlT61+m7I2luo+/4XG3sSne40h0i+FKnl6qxlZJ97EdUUqx\n5fQWfvz7R9ZHrKdzmc4ElA6gRJYSRof22g4dgh9G3WLOf7+SqspocmfOQH+/nrQp2YbUzqmNDk84\nmKVLITgYNmyAQoWMjib5XL13lfE7xzNmxxjeyPoGH1f6mLr569rluOZbt2DmTBg/Hu7dg87BD/Gq\nMpfJB0dy8+FNepbvSaBvIOnSpDM6VLt38qRe2mn1aj1xy5pscUzhHKAZsB2dBOYBygFLgVxASeBd\nYIWF7veqMgKTgbroXVA+A35P8BxJCu3UsWvHmLBrArP2z8I7rTcd3uhA25JtyZk+p9GhJdq5czBv\nnuLXFfv4L+1k1Bu/0aBgfT6t3pOKuSra5X9EIuWYOBG+/x62bIGsWY2OJnk9jH7I7wd+5/+2/h9R\nMVG0LdmWtqXaUjhTYaNDe6HoaNi0SSeD8+ZB7ToxVGi9niMus1l4eAFlspehV4VeNCrUCCeTpToP\nBejhPkOHws6deiiGtdhiUjgXnVwtjHeuKXpB61ZAANAbMHrgU1wCGITegWUZUBm9L3IcSQrtXExs\nDBtObmDm/pks+Fd/6fkX9adO/joUzlTYYolVWFgYfhZYwv7cOfhjXixT/trOf04LcCm9gLTusQS+\n1Y4eFbrZVVIrns9S9cVoAwfqVsOwMPBwwE1ylFJsO7uN3/f/ztxDc8mRLgdtS7aldYnW5PbMbZF7\nvG5duXdPt1AtWqT/rvLkjaFc87+JKjKbZRF/kDN9TtqUaEOrEq3I65XXIjGLpymlt43Mm9e6Xcm2\nmBTeAjLw5JI0qYDrQLoEj43ijt4XuQQQbj43DTiHbjGMI0lhCvIg+gFLjyxl2dFlrDm+BoDa+WpT\nJ38dauWrRY50OV75vV/li1spOHoUNm1SrNx2gs0R27nivhHnEovw9vCifVl/WpdqQemspaVVMIVJ\nKUmhUtC1K5w+DUuW6LFTjiomNoawiDBmH5jNgsMLyJEuB9XzVKd63upUy1vtlb9fklpX7tzRrVHb\ntulW3NANURSusZtclTdwO9N6dl/ZTK70uWhdojWtS7SmUCYH6v832NWr8MYbuqXWWv/8bTEp/AeY\nAoyOd647j1vksgF7zH8apQywCZ0cxukD+AFN4p2TpDCFUkpx9NpR1h5fy5oTawiLCCOVUypKZilJ\nicwlHv1ZOFNhMrplxNnJ+ZXvdf8+nDgBR4/FsO/YRQ6eOsvRS6c5fGMvsdm2E5t9B2ldXCmbtTx1\ni1WkWbEmFPUuasGfVgjriY7WeySnSwfTpzt2YhgnOjaaf87/w8ZTG9lwcgObTm3Cy9WLyrkrUzhT\nYQpkKECBjAUokKEAGd0yJvmXPqX0GoKnTj0+9uyLYtPBCE7ePkK2EkfxzHeUmIyHORm1g3wZfKiR\ntwY1fGpQLU81sno4WH+/DVm6FHr3hn37wM0Km7/YYlJYFt117AycBXKiWw39gV1AdaAIMNFC93sV\n1dDd3NnjnQsG2gE1452TpNBBKKU4e/ssBy8d5MClAxy8fJCDlw8Sfi2cmw9u4pnGC8/UmXE3eeMa\n640pOi2x0amIiXI2H6mIinLiQVQkD6IfEBnzkMjYB0TFPiTG5QbOXmeJcb2EKxnJlCon2T1yUt6n\nFHWLladcznKv1UophNHu39ddY7GxenHrtGmNjsi2xKpY/r38L3+f+Zvwa+Ecu35MH9eOAZAlbXZc\nTelIrTxwivbAFJWO2AfuREU6ExmpiIyEyCj958PIaO5E3cLkdgsXj1s4pb2JcrnFQ+crZHHLQfFs\nhSjiXYhCGQtROFNhKuSqQEa3jAZ/AiK+li2haFG9p7il2WJSCHpbu4pADuA8sAWIsuD7v65ntRR+\ngk5Yn2gpDAB8zAUv9EBIP3M5zPynlKUc99hW4pGybZfjHttKPFK23XLcOVuJR8q2VY57HGF+PE3/\nYXNJoa171pjCGejZ0v+L9zxpKUyB7t+HPXtgxw691tqOHXD2LBQsqJfXiH/kywdZsry8SyyljBET\nySOl1pfYWL3bybp1sHIlZM/+8tekVDduPB7Xt2WL/q7JkgVKlNCtRHFHkSKQIcPz3yel1hVHN2YM\nzJ0LYWHg5GS597XVlkJ78Dt6DcUu6C7vpUAl4N94z5GkMAWIjdUDr1es0P9R7d2rV+wvVw7Kl9d/\nFisGqVIZHakQ9k8pGDIEpkzRs16Ta3svo0VF6eQv7nsmPFyvTVe5sj4qVgRvWftZmMXEQKVK8P77\nlt0bWZLCV5cBPSEmbp3C/sDsBM+RpNBO3bqlB/QuXw6rVkHmzNCwITRoAFWqWGeArxDisfHj9Zip\n+fN1QpQSXbigv2dWrIC1a3VvQ9z3TPnyMulGvNg//+i6cuCA/j/KEiQptC5JCu1ITAyEhsLUqfqL\nulo1ePtt/Y8ur5WX35IuHpEUjlJf/vxTL1nTrRt8/nnKaI0/eRIWLNDHgQNQvz40aqT/tMYi3o5S\nVxzVxx/DlSswbZpl3s+SSWEK+OcqHNHRozoRnD5dj9kJCIARIyz3m5cQ4tU0aaK7UDt10r+k/fYb\nFChgdFRJFx6uZ1XPn6+TwiZN4LPPoHZtSJPG6OiEPRs0SI8zXbcOatUyOponSUvh06Sl0Ibt2AHf\nfae3berYUSeDpUoZHZUQIqHYWD2w/ptvYNgwCAwEW1+P/cQJnQjOmQNnzkCLFvDuu1C9espo8RS2\n488/4ZNP9NqFr7sFnnQfW5ckhTZGKf0b1XffwZEj+h9SUBC4u7/8tUIIYx04AO3b61n9Q4ZA8eJG\nR/Sk48d1t/Aff+ik0N9fr79YowY4v/r69UK8VLNmehzq//738ue+iCWTQgtOihbC8v76Sw9Y//BD\n6NBBd+n07GkbCWFYWJjRIQg74qj1pWRJvUxLhQpQs6ZexHfvXuPiUQoOHdItmGXK6NmgR4/q8rlz\nerJMrVrGJoSOWlcczY8/6uP0aaMjeUySQmGTwsP1GJ4PP4S+feHgQd395OJidGRCiKRyddXj8Y4f\n17/kNWwITZvqZaOSw717+hfMjz/WS1E1aKD3pB05UieCEyZAvXrSRSySV/788MEH8OmnRkfymHQf\nP026jw10+zYMHgyTJulk8KOPZFC3ECnN/fsweTIMHQq5cukkrUEDPUHFEi10Dx/C/v16yZjVq3VL\nZZkyOvGrX1/fx9bHNwrHcO+eXtD8t9/02NVXIWMKrUuSQgMopf9R9O8Pdero8YM5ZGtgIVK0yEjY\nsEG34q1cqVvt6tTRyVuRIpAtm17yxcPj6SROKf1L5PXrcOyY7pLes0cfR47oGc81a+r38vODdOkM\n+RGFeKm5c3VjyK5dr9ZaLUmhdUlSmMwuXNATR86fh3Hj7GfRW1lLTCSF1JeXO3NGLzy/Zo1eBubC\nBX2AThDTp9eL1N+4ATdv6gXpvbz0mqRlyoCvL5QurZf7sOfF6qWuOBal9DjWli11d3JSOeI6hS7A\nz0BtICNwDPgMWBnvObWBsUBuYBsQCJyKd30oEGR+PAm9m4kw2KJFesuf4GD46ivZDUAIR5Yrl97+\nK/4WYErBnTtw8aJOBD09dSLo5SVjAEXKYDLBqFF6DcxWrYzdGtFeWgrTAn2BX9GJXmP0PsalgJOA\nNxCOTvqWAN8C1dD7GgOEAL2BuGUiVwOjgAnPuJe0FCaD27f1eMGwMJgxQ+8TKoQQQjiqnj31fto/\n/5y01znikjT3gEE8bvlbBpwAyprL/sABYD4QCQwESgOFzdcDgOHAOfMxHN2SKAywdavu5nFy0uN/\nJCEUQgjh6AYNgoUL9f7IRrGXpDChrOiE76C5XAKIv/LVPXTLYQlzuXiC6/viXRPJaPx4vWDnjz/C\nxIn2Pfhb1hITSSH1RSSW1BXHlCGDXi+zZ089bMII9pgUpgZmAlOBI+Zz7sCtBM+7BcSlHB7AzQTX\nPKwXokgoMhK6ddPjJjZv1muUCSGEEOKxzp3h7l291aIRbGWYbhjwvBV6NsW75gTMAB4A3eM95w6Q\nPsHrPIHbz7nuaT73TIGBgfj4+ADg5eWFr6/vo5lgcb/BSTnx5evX4aef/PD0hB9+COPMGShY0Hbi\ne9Wyn5+fTcUjZdsuS32RspSlnJjyyJF+tG8Pnp5huLk9fT3ucUREBJZmLxNNQMc6BcgDNAIexrsW\njB43WNVcdgcuA77o1sTN6Ekqk8zXg8zHs0azyUQTC9qzR3cXd+gAX3+txxEKIYQQ4vnatoXChfU4\nw5dxxIkmoJekKQo04cmEEGAhUBI94cQVGADs4XH38nSgD5ADyGl+PNXqETu4xYuhbl0YNgy+/Tbl\nJYTxf2sT4mWkvojEkroihg6FMWP0ep3JyV7+m84LdEXPKL6A7ha+DbQ1X78CtAAGA9eAt4A28V4/\nAb1UzX70JJMlwC/JEbij+vVXvf7gihV63SUhhBBCJE6ePHrCSd++yXtfe+o+Ti7Sffyahg/Xv+H8\n9ZfeqkoIIYQQSXPvHhQrBtOnQ40az3+eo3YfCxunlN67eMoU2LRJEkIhhBDiVaVNCz/8AL16QUxM\n8txTkkJhEdHRequ60FDYuFFvV5XSybgfkRRSX0RiSV0RcVq21Fs7Tpr08udagiSF4rVFRkLr1nDq\nFKxdC5kyGR2REEIIYf9MJhg5Er76Cq5fT4b7Wf8WdkfGFCZBZOTjiSRz5kCaNMbGI4QQQqQ0ISH6\n/9dRo56+ZskxhZIUPk2SwkSKitIthDEx8Mcf4OJidERCCCFEynPlChQvDqtXQ+nST16TiSbCcFFR\nenHNqCiYO9cxE0IZ9yOSQuqLSCypKyIhb2+9L/KHH1p3X2RJCkWSRUdD+/Zw/z7MmyddxkIIIYS1\ndekCDx7AjBnWu4d0Hz9Nuo9fIDpab1l38yYsXAiurkZHJIQQQjiGbdv01rGHD+tZySDdx4WAB0DC\nXLk2cBi4C6xD75Ec31D0zidXgO+tHGOKFBsLgYF6BpQkhEIIIUTyqlAB3n4bBgywzvvbY1I4FtgO\nxG/O8wbmA58DGYCdwJx410OApsAb5uMd8zmRSEpB9+5w+jQsWiQJIci4H5E0Ul9EYkldES/y3Xcw\naxbs22f597a3pLANcB1Yy5NNpf7AAXRiGAkMRO+TXNh8PQAYDpwzH8OBwOQIOKX4/HPYvh2WLAE3\nN6OjEUIIIRyTtzd8/bV1Jp3YU1KYHhgE9ObpvvMSwN545XtAuPk8QPEE1/fFuyZeYuhQ3Tq4ciWk\nT290NLbDz8/P6BCEHZH6IhJL6op4meBgvTfyzJmWfd9Uln07q/oGmIRu6UuYG7sDlxOcuwWkMz/2\nAG4muOZhhRhTnAkTYPx4vZext7fR0QghhBDC2RnGjgV/f8u+r60khWFA9edc2wT0RE8kKWM+l7Cl\n8A66JTE+T+D2c657ms89U2BgID4+PgB4eXnh6+v76De3uLEejlCePRs+/zyMkSMhZ07j47G1cvxx\nP7YQj5Rtuyz1RcqJLceds5V4pGxb5bjHERERFC0K589jMfayJE0vYDCPkzwPwBk4BLwFBKPHDVY1\nX49rOfQFjgCbgV/RLY0AQeaj8jPupVavVtSpY/kfwp4sXw6dOsGaNVCqlNHR2KawsLBH/1iFeBmp\nLyKxpK6IpHDEbe7ceNwVbAI+AXyA94Gr6NnH4UBnYDnwNTpBjEv6QtCJZR3z61cBI4FfnnEv5eOj\n2L8fPBy0g3nTJmjeXE8qqVjR6GiEEEII8TyOuE7hfeCS+biI7vq9j04IQa892ALdmngN3XrYJt7r\nJwBLgP3oSSZLeHZCCEC1anq2rSPauxdatNCDVyUhFEIIIRyHvbQUJid19aqiZEn44w+oUsXocJLP\nsWNQvTqMGAGtWhkdje2TLh6RFFJfRGJJXRFJ4YgthckqY0YYPRqCgvQ+g47g/HmoVw+++koSQiGE\nEMIRSUvh0x7tffzuu1CokF49PCW7fl23ELZtC//7n9HRCCGEECKxHHGiSXJ6lBReuAClS8OKFVC2\nrMFRWcmdO1C/vh4/OHw4mKRGCCGEEHZDuo+TSbZsOlHq2FGvHJ7S3L8PTZtC0aLwww+SECZV/DWj\nhHgZqS8isaSuCKNIUvgSHTroVsIPPzQ6EsuKjISWLSFLFvjlF3CSmiCEEEI4NGkbetqj7uM4d+9C\n+fLw8cfQubNBUVlQdLQePxgVpWdYp05tdERCCCGEeBUyptC6nkoKAQ4dgho1YO1aeOMNA6KykNhY\nCAyEixfhzz8hTRqjIxJCCCHEq5IxhQYoXlyv3/fuu3DrltHRvBqldDd4RAQsXCgJ4euScT8iKaS+\niMSSuiKMIklhEnToAH5+EBysEyx7EhsLvXrB7t2wdCmkTWt0REIIIYSwJfbWfdwGGADkBi4AgcAm\n87XawFjztW3ma6fivXYoEGR+PAno/5x7PLP7OM6DB1CpEnTpYj+TT2JioGtX+PdfWLZ1Crq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0m4TkL8H+r3XYh6rwrx6o4m8dUsvmrbJtQj+0U862gyH5VYT0l01LGNRiWbP6KS9AKoTikT9dcJ\n9a/+823U+++Jej/Gor4M5EeVuxok7kuHECKRJCkUQryMGZWsFEK1L5uNqrX5L85xTVFJ4QRUjdRa\n1BAn/1gcE1+N2BRUzdwXqD/4n6Haj82xOKYrqi3gWlSv1Qs868Bi6TEqQXEh/qTwVTVy61BD0oxG\n/a6t9Xjinveix8Gv2ma5fhSV5GZH9Vo+AHwMRL0kvqTetxkq4V2HShBzoB7H3nzJOQnZdhKVaGZA\ntf07hqrFS4f6MhFz/Kuusxf1mHgqapidSahmBoVRPaX/RiX8O1CPj4UQTuID1COJR8T+owDqUctJ\n1IdFCLHHwgL1rfKGvsRt4+KLGjIjAvUHqzZCCEe0lNi9cYUQQtipd1CPECYTOynMhhqstQXqscf/\noQZZjdETlTDm0pdj+rYYf6LGu3JH9S68pV9TCOEYvFEdEiKBNw2ORQghhBWNIHZS2APVszCGB2rA\n25ghCnYSu+1SF54ljUVRNY+eFvu3EDtpFELYtzBUx5URBschhBB2y1Z7H8dtPO1H7DG0HqDaKvmh\nZhMoGWf/YZ6NweWH6h1nORTGIZ4fo0sIYb98jQ5ACCHsna12NInbMNkTVQtg6S5qOiRQDZ3vxNmX\n4QX74p4rhBBCCOH07KWm8D7PT6HlhRpBP779Xvq2F52bmeeTTABy5cqlXb58ObHxCiGEEEIY4QzP\nzx6VJLaaFMY3gGlni/WYcayOWez3R/VcBjWg6lGLfQVRNYb3LfYviO/Gly9fRtNScixZ4SiGDRvG\nsGHDjA5D2AkpLyKhpKyIxDCZTIWsdS1be3ycBjXGlav+2l3/uQo16Gpzff9Q1Lhlp/Tz5qNmXMiF\nmku1H2qydvRjDurnpNOvUQpYkdK/jBBCCCGEvbC1pHAwqhPJ50AH1KwJg1BjD7ZADSx7EzXHaluL\n86YBa1CT1B/WX1tOhdRWP+emfo0WxJ6gXYhECwsLMzoEYUekvIiEkrIijGJrj4+H6Ut8NqGmVHqR\nz/UlPudQ0y8JYTX+/v5GhyDsiJQXkVBSVoRR4ps309lp0qZQCCGEEPbAZDKBlfI5W3t8LIQQQggh\nDCBJoRBJFBoaanQIwo5IeREJJWVFGEWSQiGEEEIIIW0K4yFtCoUQQghhF6RNoRBCCCGEsCpJCoVI\nImn3IxJDyotIKCkrwii2Nk6hsDKzZuav//7i939+548zf3Du9jmemJ/wJPoJUeYonpifAFAiWwkq\n5q5IhVwVqJi7IsWzFSeNSxqDoxdCCCFEapE2hc+z+zaFj6Iesfz4cn7/53fWn1lPNo9sNCjcgAaF\nG1AsazHSpkmLq4sraV3SkjZNWqLN0Ry9dpS9l/ey9/Je9lzaw9X7V6mWrxpd/LvwdrG3cXd1N/rX\nEkIIIUQc1mxTKEnh8+w2KdQ0jeXHl9N/Y3+KZi1KixItqF+oPvkz50/0tW49vMVv//zGrAOzOHL1\nCB1Ld6RbuW6UyP6ySWWEEEIIkZokKUxZdpkU7ru8j4//+Jh7j+/xbf1vqVXAerP6nbl5htkHZjPn\n4BwKehfkkyqf0Kx4s5iC6LRCQ0MJCAgwOgxhJ6S8iISSsiISQ3ofi6cu37tM0M9BNFnchM5lOrO/\nx36rJoQAhbIUYlTtUZz/+DyfVPmE4VuHU3lWZUL+DbHqfYQQQghhHOeu6omf3dQUbgnbQuvlrenq\n35WBNQaSyT1TqtzXrJlZemwpX4Z8SQHvAowOHE2F3BVS5d5CCCGEeMaZawpDgYfAPX05YbGvNnAS\niABCgHxxzh0L3NCXr1M60JS28PBCWi9vzaLmixhTZ0yqJYQALiYX2pZqy4neJ2hRogXNljSj5dKW\nnLt9LtViEEIIIYR12VtSqAG9gYz6EtPrIRuwAhgEeAP7gCUW5/UE3gZK60sTfZvd0TSNkVtHMihk\nECGdQqhdsLZhsaRNk5Ze5Xtxus9pSvuUptz0cozbMY4n0U8Miyk1yVhiIjGkvIiEkrIijGJvSSHE\nX0XaHDiKSgwjgWFAGaCovr8zMB64rC/jgaAUjtPqnkQ/IXh1MD+f/Jld3Xbhl8PP6JAA8EjrwZCa\nQ9gVvIv1Z9dTfkZ5dl3cZXRYQgghhEgEe2tTuBnwQ8X9N6pmcAvwHWog7t4Wxx4GhgKrgNtAXWCv\nvu8N/VrxPXO1yTaFdx7doeWylqR3Tc/iFovxdPM0OqR4aZrGT0d/4pP1n/B2sbcZXXs03um9jQ5L\nCCGEcEjO3Kbwc6AAkAuYDqwBCgKewN04x95FPWIGyADcibMvQ4pGakWPox7TZHETCnsXZlWbVTab\nEIIqnO1eb8fx3scBKDWlFGv+XmNwVEIIIYR4FXub5m6Pxev5QDugIXCf52v9vFCdUYhnv5e+LV5B\nQUH4+voCkDlzZvz9/Z+OGRXT1iO11jdv3syobaPwKeHD/xr9j61btqbq/ZOzPqXxFIr9VIwek3pQ\nr049JtafyKHdh2wmvuSuW7b7sYV4ZN2216W8yHpC12O22Uo8sm5b6zGvw8LCsDZ7e3wc12/AOuAx\nqt1gdX27J3Ad8AdOATuAOcBMfX+wvlSN55o29fh4cMhgNv67kZBOIaRPm97ocJLkfuR9BmwcwM8n\nf2Za42k0KtrI6JCsIjQ09Ol/ViFeRcqLSCgpKyIxnHVGEy+gMqoNYRTQBpiGSvxuA/8AXYFfgeGo\nBDEm6esJ9AXqoH7n9ah2iNPjuY/NJIVzDsxh5LaR/Bn8Jzk8cxgdTrJt/nczwauDqelbk2/rf0vm\ndJmNDkkIIYSwa87apjAtMAK4hqoF7I0aZuYf1NiDLYBRwE2gPNDW4txpqPaHR1AdUNYQf0JoMzad\n3cSATQNY9+46h0gIAWoVqMXh9w6T3jU9paeUZv2Z9UaHJIQQQgidPdUUphbDawqPXz9OwNwAlrVa\nRk3fmobGklI2nNlA8OpgGhVpxLh648jgZjf9fp6SRzwiMaS8iISSsiISw1lrCp1C+INwGi1qxIT6\nExw2IQSoW6guR947wuPox5SZWoat57YaHZIQQgjh1KSm8HmG1RRqmkbLZS3Jlykf3zb41pAYjLDm\n7zX0XNuTNn5tGFV7FB5pPYwOSQghhLALUlPooOYdmsep8FOMqTPG6FBSVZNiTTjy3hGuRlyl9JTS\nbAnbYnRIQgghhNORpNBGnL11ls82fMbC5gtJ55rO6HBSXVaPrCxqsYgJ9SfQfmV73l/3Pvce33v1\niQayHDNKiFeR8iISSsqKMIokhTYgyhxFp1WdGFh9IKV9ShsdjqGaFmvK0fePEhkdSakppfjjnz+M\nDkkIIYRwCtKm8Hmp3qZw1NZRhISFsKHjBlxMkqfH2HBmAz3W9qBGvhqMqzsOnww+RockhBBC2BRp\nU+hA9l7ay3e7v2Nes3mSEMYR00P5tQyvUWpKKSbtnkSUOcrosIQQQgiHJFmIgSIiI+iwqgM/NPyB\nPJnyGB2OTcrgloGxdceyJWgLK0+upMKMCuy8sNPosABp9yMSR8qLSCgpK8IokhQaqP+G/lTKXYnW\nfq2NDsXmlcxekpBOIfSv2p9Wy1rR9Zeu/HfvP6PDEkIIIRyGtCl8Xqq0Kdx1cRfNlzTneO/jMgdw\nIt19fJcRW0Yw++Bser7Rk/7V+st7KIQQwilJm0I7F22O5v117zOu7jhJZpIgk3smxtUbx8GeB7kW\ncY0ik4owdvtYHjx5YHRoQgghhN2SpNAAU/ZNwSudF+++/q7Rodi1vF55mdl0Jtu6bGPff/soMqkI\nk/dOTrXkUNr9iMSQ8iISSsqKMIokhansyv0rfLXlKyY3nBxT5SuSqXi24ixrtYxf2v7CH2f+IP/E\n/Hyx6Qsu3b1kdGhCCCGE3XC2rCQLMAuoC9wABgKL4xyTom0KO6zsQN5MeZ1uKrvU9M/Nf/h+9/f8\nePhH3iryFh9V+ogKuSsYHZYQQghhddZsU+hsSWFMAhgMlAXWAVWB4xbHpFhSuPnfzXT5pQvH3j+G\np5tnitxDPHP70W1m/TWLSXsm4Z3emzZ+bWjt15qC3gWNDk0IIYSwCkkKk8YTuAn4Af/o2+YBl1E1\nhjFSJCmMjI6kzNQyfF37a94u/rbVry9eLNoczbbz21hydAkrTqwgf+b8tC7ZmlZ+rfDN7Jvk64aG\nhhIQEGC1OJPqSfQTrkZc5caDG4Q/COfGgxvq9cNwIiIjiDJH8cT8hChzFFHmKKLN0Xil8yJr+qxk\n9chKlvRZyJo+K3ky5aFwlsKkcUlj9K/kkGylvAjbJ2VFJIY1k0JXa1zEThQFoniWEAIcAgJS4+YT\n/pxA4SyFaVqsaWrcTlhI45KGAN8AAnwDmNRwElvCtrD02FIqzqhIBrcMVM1b9enyeo7XbSopevDk\nAZfuXuLC3QtcvHvx6XLp3iUu3b3EpXuXCH8QTjaPbGT3zE7W9FnJ5pEtVsLn6uL6dEmbJi0mTNx5\nfIebD29y/r/zhD8MJ/xhOOdun+P6g+v45/TnjdfeUEuuNyierbjMtiOEEE7AmWoKawBLgdcstnUH\n3gVqWWyzek3hudvneGP6G+ztvpcC3gWsem2RdGbNzKnwU+y8sJOdF3ay48IOLt29hH9Of3wz+5LP\nKx/5vfKrn5nzkyV9FjzSepDeNX2SEkdN03gY9ZDbj27HWm4+vMnV+1e5cv8KVyKuqJ/3r3D53mUi\nIiPInSk3eTLlIW+mvOTOqF7nyZSH3Jlykztjbnwy+ODqYp3vd7ce3uKv//5i/3/72f/ffvZe2ku0\nFs27pd6lfen2lMpRyir3EcJZaJqGWTM/XTTUugkTaVzS4OriKl+6RLLI4+OkKQtsRz1GjvEp8CZg\nWX1n9aSw3Yp2FM9anKEBQ616XWF94Q/COXz1MOfunOPc7XOcv3Nevb5zjtuPbvPgyQMePnmIWxo3\n0qdN/zRBNGHCxeSCi8kFk8mEpmlERkcSGR3J4+jHT1+7p3HHK50XmdNlJnO6zHi5e+Gd3pucnjnJ\nmSH28lrG18jukd3wXuqHrx7mx8M/sujIIrJ6ZKXD6x1o93o7mZpROB2zZibsdhhnbp7hyv0r/Hf/\nv1g/7z6+S0RkBBFPInjw5AERkRE8jn787LNB/5yI+YyI1qKJMkfFShDd0rjhnsYdd1d30rmmwz2N\nO55unvh4+jz3GVE4S2FKZi9ptS+Fwj5JUpg08bUpXABcAL6wOE7rDPjqK5kBf549Yw7Vf8q6rMe8\ntpV4ZN2212Ne20o8sm676zHbbCUeWbet9ZjXYfrreeqHJIVJsBjQgG5AOWAtUAU4YXGM1WoKNU2j\nxpwaBJcNpkvZLla5prAdztwY/ObDm4zeNpo5B+fwQYUP+LTqp2R0z2h0WDbNmcuLPXgS/YS9l/ey\n4cwGNv67kYNXDlI+V3n8ffzxy+GHX3Y/SmYviVc6rxSPJTFl5e7juxz47wD7/9vPvsv72HVxF9Fa\nNM2LN6dFyRZUyVPFptpJC+uTmsKk8wZm82ycwgHAT3GOsVpSuPLESr7a8hV/9fhL/lMKhxR2O4zB\nmwez8exGhrw5hG7lupE2TVqjwxIiQaLN0Ww8u5FZB2ax/sx6CngXoG7ButQpWIfq+arjkdbD6BAT\nTdM0jl0/xorjK1h5ciVX71+lWfFmtC3Vlpr5axreHEVYnySFKcsqSWFkdCR+k/2Y3HAydQvVtUJY\nQtiuA/8doP/G/lyPuM7SVkspmrWo0SEJ8ULn75xnzoE5zD44m+we2elWrhvNSzQnh2cOo0Ozun9u\n/sPKEyuZe3Au7q7u9Kvcjzal2uCWxs3o0ISVWDMpdLHGRcTzpu6bSpEsRSQhdGAyP+kzZV8ry/oO\n6+lVvhfVZldj6bGlRodkc6S8GG9L2BbeWvgWZaeV5fqD6/zc5mf29dhHr/K9bCohtGZZKZylMP2r\n9efo+0cZFTiKeYfmUfC7gozdPpZbD29Z7T7CMUiXpRRw+9FtRm0bxaZOm4wORYhUYzKZ6FW+FxVz\nV6TVslZsO7eN8fXG4+7qbnRowskdunKIgZsGcvLGSQa/OZiVrVeSPm16o8NKVR7gRGkAACAASURB\nVC4mFxoWaUjDIg05eOUgE/6cQKHvC/F+hfcZUH0AGdwyGB2isAHy+Ph5yX58/Nn6z7jz+A7Tm0y3\nUkhC2Jfbj27T9ZeuXLh7gaUtl8r4nMIQMW1eN5zZwKAag+hZvqc8NrVw4c4FBm4aSGhYKF/X+Zp3\nX39Xxky0Q9KmMGUlKyn899a/lJ9RnqPvHeW1jK+9+gQhHJSmaXy3+ztGbxvN0lZLCfANMDok4SQi\nIiMYvHkw8w7No0/FPnxS5RPpHf8SOy/spO/vfXF1ceW7Bt9RMXdFo0MSiSBtCm3YFyFf0LdSX0kI\nnYC0EXs5k8nER5U/YknLJbRa1opNZ527OYWUl9Sx7/I+yk0vx7WIaxx//zjDAobZXUKY2mWlat6q\n7O62m55v9KTZT83o8ksXaW/opCQptKJ9l/ex9dxWPqnyidGhCGEzahWoxYrWK2i7oi3rz6w3Ohzh\noKLN0YzaOoqGCxvyVcBX/Nj8R3wy+Bgdlt1wMbkQ5B/EyQ9OkiFtBvyn+bMlbIvRYYlUJo+Pn5fk\nx8f1FtSjeYnm9Crfy8ohCWH/tp/fTvMlzZn/znwaFG5gdDjCgfx76186ruqIWxo35jWbR16vvEaH\nZPd+Pf0r3VZ3o3OZznxV6ytpi2nD5PGxDQr5N4Szt84SXDbY6FCEsEnV81Xn57Y/02lVJ349/avR\n4QgHsezYMirOrEiz4s3Y2GmjJIRW0rBIQw72OsjR60epOqsqf9/42+iQRCqQpNAKNE1j4KaBjKg1\nQmZzcCLSRizxquatyup2qwn6OYg1f68xOpxUJeXFujRN45ud39BvfT/Wd1jPp1U/dZies7ZSVnJ4\n5mB129UElw2m2uxqzDkwx+iQRApzjP9BBvv55M88jnpMm1JtjA5FCJtXOU9l1r67lq6ru7Lr4i6j\nwxF2yKyZ+fiPj5lzcA47u+6k7GtljQ7JYZlMJt6r8B5bu2xlzPYxfPLHJ0Sbo40OS6QQaVP4vES1\nKYw2R/P6lNf5pt43vFXkrRQMSwjHsubvNfRa14s93faQO1Nuo8MRduJR1CM6rerEtYhrrGqzCu/0\n3kaH5DRuPrxJq2WtSO+ankUtFpHJPZPRIQmkTaFNWXB4Adk8sknDeSESqUmxJvSu0Jt3lrzDwycP\njQ5H2IFbD29R/8f6mEwm/ujwhySEqSxL+iz83v538mTKQ7XZ1Qi7HWZ0SMLKEpoU+gMhwC3gicUS\nmUJx2YVHUY8YGjqUMbXHxGTqwonYSrsfezaw+kAKehek+5ruJHcmIVsn5SV5/rv3H9XnVOeN195g\ncYvFDj19oi2XlbRp0jKl0RS6le1GlVlV2HF+h9EhCStKaFK4GNgBvAmUsFhKplBcdmHqvqmU8SlD\ntXzVjA5FCLtkMpmY/fZsTtw4wfid440OR9iomw9vUu/HerT1a8uE+hMcpkOJvTKZTPSt3JfZTWfz\nzpJ3WH58udEhCStJaPXWLSALYORX+VCgEhClr19EJaYxagP/A/ICu4Eg4LzF/rFAzHgxM4EBL7hP\ngtoU3nt8jyKTirCh4wZe93k9Yb+BECJeF+5coNLMSsxsOpOGRRoaHY6wIRGREdRdUJcqeaowvt54\neSpjYw5dOUSDhQ0YW2csncp0Mjocp2REm8L5QHtr3DAZNKA3kFFfLBPCbMAKYBDgDewDlljs7wm8\nDZTWlyb6tiSb8OcE6haqKwmhEFaQ1ysvy1otI+jnIE7eOGl0OMJGPI56TPOlzSmWrZgkhDaqTM4y\nhHQKYVDIIKbum2p0OCKZEpoUjgFGAseAzRZLSArF9SIv+kRoDhxFJYaRwDCgDFBU398ZGA9c1pfx\nqJrEJLkecZ3v93zPVwFfJfUSwgHYcrsfe1QtXzVGBo6kzfI2PI56bHQ4ViflJXGizdF0XNURj7Qe\nzGgyw6kSQnsrKyWylyC0cyhjd4xlwp8TjA5HJENCk8JlwBlgCrAwzpKaxgDXge1ATYvtfsAhi/UH\nwD/6dlBtHy33H7bYl/ggto+hXal2FPQumNRLCCHi0b1cd3wz+zI0dKjRoQgDaZrGe+veI/xhOItb\nLMbVxdXokMQrFMpSiK1BW5m6byrDtwx3+I5jjiqhX73uoR7RGvn1vSKqpjISaAf8gKoN/BfVRvA6\nMNDi+O3AdNSj7yhUYnhK31cE+Jv4k+KXtik8f+c8ZaeV5dj7x8iZIWdyfh8hRDyuRVyjzNQyLGu1\njOr5qhsdjjDAoE2D2HB2A5s6bSKje0ajwxGJcOX+FeouqEvDwg35us7XTlXDaxRrtilM6Nevbaik\n6oA1bhqPUFTP5vhs1/ftsdg2H5UYNkIlh/eBuKNoeqGSWeLZ76Vvi1dQUBC+vr4AZM6cGX9/fwIC\nAgDoNakXDdI3eJoQxlTzx+yXdVmX9eSvT200lc4/d2ZS8Ul4uHkYHo+sp976prObWHxvMXu672H/\nn/sNj0fWE78e2jmU2vNrc/XYVYL8gwyPx9HWY16HhYVhbQnNLCcDrYCVwDWL7RowxNpBJdBvwDpU\nUtgd1W4wplrBE1Vz6I+qHdwBzEHVKILqhRwMVI3nui+sKTx54yQ15tTgdJ/TZE6X2Uq/hrBXoaGh\nT/+zCuvr+ktXXF1cmd5kutGhWIWUl1c7fPUwtefXZmPHjZTJWcbocAzjCGXl6v2rvDn3TXq+0ZN+\nVfoZHY5DM6L3sQcqAXMD8uhLXn1JDV5AfSAdqnazPVAD+F3fvwoohepwkg4YChzk2ePi+UA/IBeQ\nW389N7FBfBnyJZ9W+VQSQiFSwcQGE9lwdgNrT601OhSRCm49vEXzJc2ZWH+iUyeEjsIngw8bO27k\n+93fM/Ovma8+QdgEe3nYnw34FSgORAMngMHAJotjaqNqDfMDu4h/nMJu+usZJHKcwn2X9/H2T29z\nus9pPNJ6JPkXEUIk3NZzW2m7vC2Heh0iu2d2o8MRKcSsmWm8qDFFsxZlYoOJRocjrOh0+GkC5gUw\nod4E2pRqY3Q4DsmaNYUJvUgnVO9dyx68ZVBj/i2wRiA2JN6ksN6CejQv0Zxe5XsZEJIQzuuz9Z9x\n9vZZlrdaLo3WHdTQzUPZcm4LGzpuIG2atEaHI6zsyNUj1FlQh9lNZ9OoaCOjw3E4Rjw+HglciLPt\nIjDKGkHYupB/Qzh76yzBZYNffbBwGpaNfkXKGRE4gr9v/M2y48uMDiVZpLzEb/Xfq5lzcA5LWi6R\nhFDnaGXldZ/XWd12NV1+6UJoWKjR4YiXSGhSmBG4E2fbHVRbP4emaRoDNw1keK3h8oElhAHSuaZj\nauOp9PujH/ce33v1CcJunAo/RbfV3VjWahk+GXyMDkekoEp5KrGk5RLaLG/D0WtHjQ5HvEBCk8IT\nQMs4297Rtzu0VSdX8SjqEW1LtTU6FGFj7L13oD2pnq86dQvV5ast9juLkJSX2CKjI3l3xbt8FfAV\nlfJUMjocm+KoZaVWgVp8W/9bGi1qxOV7l40OR8Qjoc+gq6M6emwAzgKFgDpAQ9Q4go7kaZvCJ9FP\n8Jvsx6S3JlG/cH2DwxLCuV2LuEapyaXY1GmTzDnuAAaHDObAlQOsabdG2oo6ma+3f81PR39ia5et\nZHKPO8SwSCwj2hRuB14H9qGGp9mDmibO0RLCWKbtn4ZvZl9JCEW8HK3dj63L4ZmD4bWG8/6v79vl\nFFpSXp7ZeWEnMw/MZGbTmZIQxsPRy8rn1T6ncp7KtFzakifRT4wOR1hIaFIIcA419/DX+hK344lD\nufPoDiO2jmBc3XFGhyKE0HUv151HUY+Yf2i+0aGIJLofeZ9OqzoxpdEUmSrUSZlMJn5o+ANuadzo\nubanXX7Jc1RJ+Yp2l+enlHMkmqZpfLHpCy7fu8zcZnONjkcIYWHf5X00XtSYE71P4J3e2+hwRCJ1\nX90ds2Zm1tuzjA5FGOx+5H0C5gbQpGgThgYMNTocu2XEOIWW7qF6Izsq7fzt8/hP8+dQr0PkyZTH\n6HiEEHH0XtcbDY3JjSYbHYpIhNV/r+aj3z/iUK9DZHR35D8jIqGu3L9ClVlVGB4wnI5lOhodjl0y\nok1hrPtb48a2bPDmwfR8o6ckhOKlHL3djy0bGTiSVSdXsffSXqNDSTBnLy9X71+l59qeLHhngSSE\nr+BMZSVnhpysbbeWT9Z/wvbzDt1NwS4kJSnMYPUobMzv//zO59U+NzoMIcQLeKf3Zmydsbz/6/uY\nNbPR4YhX0DSN7mu608W/C9XyVTM6HGFj/HL4Mf+d+bRa1oqzt84aHY5TS0ytX37AH/CMs32R9cKx\nCdqk3ZP4oOIHRschhHgJTdOoPKsyH1b8kPal2xsdjniJHw//yPid49nTfQ9uadyMDkfYqB/2/MCU\nfVPY2XUnXukcfm4MqzGiTeEAYAhwHHgYZ18NawRiQ7TIqEiZvUQIO7D9/Hbar2zPyd4nSZ82vdHh\niHjceHCDUpNLsabdGirkrmB0OMLGffDrB/xz8x/WvrsWVxdXo8OxC0a0KfwMKK8vNeIsDkcSQpEQ\nztTux1ZVz1ed8rnK893u74wO5ZWctbx8sv4T2pVqJwlhIjhrWQGY2GAiGhof//6x0aHYvChzFG2X\nW3e2tYQmheGocQpT0geowbEfAXPi2V8bOAlEACFAvjj7xwI39OXrOPt8gc36uSf0awkhHMDXtb9m\n/M7xXI+4bnQoIo6NZzeyJWwLIwJHGB2KsBOuLq4sbbmUkLAQ/rfnf0aHY9Om7J3C1YirVr1mQqsb\nGwLtgYlA3AjOWymWdwAzUB9ID3Sx2JcN+AcIBtYAI1G1lFX0/T2Bj4FAfX0D8D0wTV//E9gBDAIa\nAbOAIqgEMi7tRQNpZsmShVu3biX+NxMv5O3tzc2bN40OQ9i5vr/1Jcocxf8ayR8RW/HgyQNen/I6\nk96aRMMiDY0OR9iZs7fOUm12NeY1m0e9QvWMDsfmXL1/lVJTShHaOZRSPqUgldsUNgNmAlnibNeA\nNNYIxMIIIA+xk8IeQCfUHMygptq7ger4cgrYCczWY0Q/twcqaSwKHAayomoKAbagOsjEJI2WXpgU\nmkwmGXndyuQ9FdYQ/iCc4v8rzrYu2yierbjR4QhgwMYBhN0O46eWPxkdirBT285to8XSFmwJ2kKJ\n7CWMDsemdP65Mzk8cjCu3jhD2hRORnU28QLcLBZ3awQRR3y/mB9wyGL9Aarm0E9fLxln/2GLfX7A\nWZ4lhOjH+iFEMjhzux9bk9UjK59X+5z+G/obHcoLOVN5OXTlELMPzOa7Brbf1tMWOVNZeZka+Wsw\nru44mixuQviDcKPDsRnbz29n09lNDKk5xOrXTmhS6Ipq53cPiIqzWFt81UaeqOn1LN3l2cwqGYA7\ncfZleMG+uOcKIRxAn4p9OHrtKJv/3Wx0KE4t2hxN9zXdGVN7DD4ZfIwOR9i5zv6daVmyJc2XNicy\nOtLocAwXZY6i96+9+abeNykyCHxC+3uPAwYCo4g/aXuVUODNF+zbHmdffDWF93l+vmUvVJIa334v\nfduLzs3M80nmU0FBQfj6+qoDM2fG39+fgICAFx0ukik0NPTp+xvzDdke1gMCAmwqHmdfd3d1p0Om\nDvT8oScnx5/ExeRiU/E5S3lZfnw5Hh4edC3b1SbikXX7Xx9dezTNlzSn2ZhmfFbtM2rVqmVT8aXm\n+orjK0hzIQ3H/ztO0PggrC2hz6AvAj7AE1RP5Bgaz/cCTq742hR2BzrzrE2hJ3CdZ20Kd6BqMmPa\nFAbrS1VUm8JDQHaeJYrbgAXA9HjuL20KU5G8p8KaNE2jyqwq9K7QW+ZRNcDle5cpPaU0O7ruoFi2\nYkaHIxzI/cj7VJ9dnQ6lO/Bp1U+NDscQV+5f4fUpr7M1aGusNpZGtCnsANQB3tJfdwA66ou1pAHS\noWov06DaK8Z0YlkFlAKa68cMBQ6iEkKA+UA/IBeQW389V993Sj92qH5uc/1aK6wYu8OZO3cuadM+\nG68xNDQUFxcXLl++bGBUtiXmW5ywHSaTiXF1xzEkdAiPox4bHU4szlBe+m/oT/dy3SUhTCZnKCuJ\nlcEtA2vareHbXd/yy8lfjA7HEP039Kerf9cU7XST0MfHtXn22Nhk8ToSNQbg7zw/VE1iDUbNmhKj\nAzAMGI7qadwC+AH4EdgFWI7YOA0oCBzR12cQuxawLSpJvIkab7EFsWs8hRAOokb+GpTIVoLp+6fT\np1Ifo8NxGlvPbWXrua2c6H3C6FCEg8rrlZef2/xMw0UNyZUxl1MNiL7t3DY2h21O8f9fCa1uXIIa\nlmYPcAH1yLgCsBb1qLcU0BL4LQViTG0O//g4MjISNze3lx4zd+5cunfvzpMnTwD1zTUwMJCLFy+S\nK1cuq8XiKO+psC0HrxzkrYVvcbrPaTK4ZXj1CSJZosxRlJtWjsFvDqaVXyujwxEO7peTv/DeuvfY\nGbwT38y+RoeT4iIiI/Cf5s/YOmNpXqL5c/uNeHxsQtW21QDeRbXtaw1EA5WA94Ex1ghIWF9AQADd\nunVj8ODBvPbaa+TNm5fdu3fz5ptv4uHhQZYsWWjfvj3Xr8uMEMIx+Of0p5ZvLSbummh0KE7hf3v+\nRw7PHLQs2dLoUIQTeLv42wyoPoCGCxty66HjTyjx2YbPqJKnSrwJobUlNClsAKyOs20dqo0hwEKg\nkLWCEta3dOlSwsPD2bx5MytWrKBu3brky5ePvXv3smbNGo4ePUrLlvKBnhjS7se2Da81nIm7JtrM\n+GaOWl6u3r/KyG0jmfTWpJgaC5FMjlpWrOnDSh9Sv1B9mi9tbnPth63pt9O/se70Oia9NSlV7pfQ\npPAMqjbQUi/UANKgpqGLQABgMll/Sa5cuXIxefJkihcvzh9//EHmzJmZO3cufn5+VKtWjQULFrBt\n2za2b9+e/JsJYQMKZylMq5Kt+Hp73KnQhTV9vvFzgsoEyYwTItWNrzeezOky021NN4dshhT+IJxu\na7ox9+25eKXzSpV7JjQpDAY+RQ1Ns1v/+RnQTd9fFNVRRACaZv0lud54442nr48dO0blypVxdX3W\nz6h06dJ4eXlx7Nix5N/MScSMHSVs1+Cag5l9cDYX7140OhSHLC87L+xk49mNKTKzgjNzxLKSEtK4\npGFh84WcCj/F0NChRodjVZqm0WtdL9r4taFWgVqpdt+EJoV/AUVQ7Qm/BdoDhYH9+v6tqB6/wgaZ\nTCY8PT1jrTvityoh4sqVMRfdy3Vn+JbhRoficKLN0fT+tTfj6o5LkZkVhEgIj7QerGm3hoVHFvLD\nnh+MDsdqFh5ZyPHrxxlde3Sq3jehSSGo4We2Aj8BW1ADWQs75Ofnx65du572LAY4dOgQd+7coVSp\nUgZGZl+k3Y99+Lza56w6uYpT4adefXAKcrTyMn3/dLzcvWhbqu2rDxaJ4mhlJaXl8MzBxo4bGbtj\nLPMOzjM6nGQ7f+c8H//xMT++8yPpXNOl6r0TkxQKO6VpWqyawQ8++IC7d+8SFBTEsWPH2L59Ox07\nduTNN9+kWrVqBkYqhPV5p/emX+V+DN4sLVys5ebDmwwNHcr3b30vnUuETSjgXYANHTcwYNMAlh9f\nbnQ4SWbWzAT9HES/yv0o+1rZVL+/JIVOwGQyxfrgzpEjB+vXr+fixYtUqFCBJk2aULp0aZYvX/7c\neS9bd3bS7sd+fFjpQ7ad28b+y/tffXAKcaTyMmTzEFqVbEVpn9JGh+KQHKmspKbi2YrzW/vf6P1r\nb349/avR4STJoE2DiDJH0b9af0PuL3/ln+fwg1fbEnlPRWqZvHcyq/9eze8dfjc6FLt25OoRas+v\nzYneJ8jqkdXocIR4zq6Lu2i6uClLWy0lwDfA6HASbPaB2YzeNpo/g/8ku2f2BJ9nxODVQog4pN2P\nfelWrhunwk+xJWyLIfd3hPKiaRp9f+/L0JpDJSFMQY5QVoxUOU9lfmr5E62XtWb3xd1Gh5Mgm85u\nYuCmgax7d12iEkJrk6RQCOEU3NK4MbzWcAZuGii100m08sRKrj+4Ts/yPY0ORYiXCiwQyJy359Bk\ncRNC/g0xOpyXOn79OO1WtGNJyyUUy1bM0Fjk8fHz5PFxKpL3VKSmaHM0ZaaWYUztMTQp1sTocOzK\nwycPKTm5JLOaziKwQKDR4QiRIKFhobRe1pofGv5Aa7/WRofznGsR16g8szJDaw6ls3/nJF1DHh8L\nIUQSpHFJw6jAUQwKGYRZMxsdjl0Zv3M85V4rJwmhsCsBvgFs6LiBfn/0s7lxDB8+ecjbP71N+9fb\nJzkhtDZJCoVIImn3Y5+aFmuKp5sni48sTtX72nN5uXDnAhN3T2R83fFGh+IU7Lms2KIyOcuwrcs2\nvt/9PYM2DbKJp1OPox7TYVUHCmQuwPBatjO4vi0lhR8A+4BHwJw4+3wBM3DPYhkU55ixwA19iTvZ\nqS+wGTU/8wmgtvXCFkLYE5PJxOjA0QwJHUJkdKTR4diF/hv783759yngXcDoUIRIkgLeBdjRdQcb\nzm6g2+puRJmjDIvlxoMb1FlQBxMmZr8926aGe7OdSOAdVOJXH0gPdLHY5wucBdIA8aX4PYGPgZjn\nGhuA74Fp+vqfwA5UItkImIWatu9GPNeSNoWpSN5TYZR6C+rRvERzepXvZXQoNm3buW28u/JdTvY+\niaeb56tPEMKG3Y+8T5vlbbj96DYL3llAQe+CqXr/U+GnaLSoES1KtGB07dG4mJJfN+eobQpXAb8A\n4S855kXxdgbGA5f1ZTwQpO8rCpQFhgKPgZXAYaBFsiMWQtit0bVHM2LrCB48eWB0KDYr2hxNn9/6\nML7ueEkIhUPI4JaBNe3W0LJESyrNrMSsv2alWsXElrAt1JhTg8+rfc7Xdb62SkJobbYX0cuz3XPA\nBWA2YDlIVkngkMX6YcBPf+2HqmWMsNh/yGK/EEki7X7sW/lc5amSp0qqNT63x/Iyff90MqfLbJO9\nNh2ZPZYVe+JicuHjKh+zufNmJu2ZxDtL3uFaxLUUvee8g/Novbw1i5ovolu5bil6r+SwxaQwvpT9\nOlAeyAe8AWQEFlrszwDcsVi/q2+Lb1/M/ozWCNYRBAUFUbdu3WRdIywsDBcXF3bu3GmlqIRIeSMD\nRzJu5zhuPrxpdCg2J/xBuMxvLBxaqRyl2N1tN8WzFafM1DL8cvIXq9canr9znuBfghm+dTihnUOp\nXdC2uzS4ptJ9QoE3X7Bve5x98X36RAB/6a+voTql/Ad46vvuA5ksjvfStxHPPoDMqMQwXkFBQfj6\n+qoDM2fG39/foeeinDRpEmbzs+E5unXrxpkzZ9i8eXOq3D80NPTp+xvzDdke1gMCAmwqHllP/PqV\no1eoElWFUVtH8U39b6S8WKx/GfIl1aKrcfPETfDB8HhkXdZTav3rOl/TqEgj3p3wLv3T9mdIpyG0\n9mvNjm07knz9K/ev0Pt/vdlwdgMftP6Afd33cWj3Ia5yNdnxxrwOCwvD2mzx698IIA+xO5rE5YNK\nCr1QPZF3oHosz9T3B+tLVVSbwkNAdp4lituABcD0eK7t9B1NkpIUhoWFUbBgQbZv307VqlUTfJ6z\nvKfCdl25fwW/yX7s675PetfqDvx3gAYLG3Ci9wmypM9idDhCpIpoczTrTq/j213fcjr8NB9U/IAe\nb/RI1P+B8AfhjNs5jhl/zaBT6U4MrDGQHJ45UjBqx+1okgZIh6q9TAO46z8BKgLFUPFmRfUs3oxK\nCAHmA/2AXEBu/fVcfd8p4CCqo0k6oDlQCliRkr+MLQkICCA4OJgBAwaQPXt2vLy86N69O48ePQJi\nPz4eNmwYs2fPZsuWLbi4uODi4sL8+fMBuH//Ph999BH58uUjXbp0FChQgDFjxsS616VLl2jcuDGe\nnp4UKlSIH3/8MXV/2VRk+a1N2K+cGXLyYcUPGRQSd5Qr67KX8qJpGh/+/iEjao2QhNAg9lJWHE0a\nlzQ0LdaUzZ03s/bdtZy8cZLC3xem9bLWDA4ZzPxD8/nzwp/ceHADTdN48OQBey/tZdZfs+j7W19q\nzatF4UmFufXwFgd7HuTbBt+meEJoban1+DghBgNDLNY7AMOA4UBBYDSQA/XYdz3QzuLYafoxR/T1\nGcSuBWyLShJvojqrtODlvZwdzvLly2nbti3bt2/n9OnTBAcH4+HhwXfffQc8/abBZ599xj///ENY\nWBgrV64EIFOmTGiaRuPGjbl48SI//PADpUuX5tKlS/z999+x7jNgwADGjh3L999/z4wZM+jSpQuV\nK1emcOHCqfsLC5EIn1T9hKKTirLv8j7K5ypvdDiGWnx0MQ+ePCC4bLDRoQhhGP+c/sxtNpcr96+w\n8exGToef5vd/fmfSzUmcCj8FQGR0JMWyFqO0T2lK+5SmcdHG+Of0J7tndoOjF9akvcjL9tmymjVr\nagUKFNDMZvPTbdOnT9fc3d21iIgIrXPnzlqdOnWe7gsODtYCAgJiXWPjxo2ayWTS9u/fH+89/v33\nX81kMmnffvvt021RUVFahgwZtOnTp78wNnt9T4XjmbZvmhYwNyDW/xNnc+/xPS33N7m1Hed3GB2K\nEDbLbDZr1yOua5FRkUaHomma+jtqrQTIlmoKHYbpK+s31dSGJu/fvGLFirF6EFatWpXIyEjOnDmT\noPP379+Pt7c35cqVe+lx/v7+T1+nSZMGHx8frl69mrSghUhFXct2ZeKuifx6+lcaFW1kdDiGGLl1\nJIEFAqmaN+HtgoVwNiaTiWwe2YwOI0VIUpgCkpvApQQtlTpzuLm5xVo3mUyxejY7klCLXtPC/rm6\nuDK2zlj6b+xP/cL1cXWx7sejrZeXo9eOMuvALI68d+TVB4sUZetlRTguW+poIlLQ3r17YyVnO3fu\nxN3dnUKFCj13rJubG9HR0bG2lS9fnlu3brF///4Uj1UIozQu2phsHtmYe3Cu0aGkKrNmpufanoyo\nNYKcGXIaHY4QwiCSFDqJ8PBwevfuzcmTJ1m3bh1Dhgyhe/fueHh4PHdshM3c0AAAEiNJREFUwYIF\nOXnyJMePH+fGjRtERkYSGBhIjRo1aNOmDatXr+bff/9lx44dzJo166X3Ta0aSiPIN3nHYzKZGFd3\nHENDhxIRGfHqExLBlsvLrL9mYdbM9Hijh9GhCGy7rAjHJkmhEzCZTLRq1YqMGTNSvXp12rVrR6NG\njfi///u/p/st2xsGBwdToUIFqlatSo4cOfjpp58AWLduHQ0bNqRXr14UL16cjh07Eh4eHus+8d1b\nCHtSMXdF3sz/Jl9v/9roUFLF1ftXGRQyiGmNp9nkXKxCiNQjf7Gfp72odsteB1quVasWRYoUYfr0\n+MbqNpa9vqcg7X4c2cW7F/Gf6s+fwX9SJGsRq1zTVstLh5UdyJUxF/9X9/+MDkXobLWsCNvkqINX\nixSiaZrdJl5CGCFPpjwMqD6APr/1cej/OxvObGDHhR0MrTnU6FCEEDZAkkInEPfxsLAO+Sbv2PpW\n6suFuxdYdXKVVa5na+Xl4ZOHvP/r+/zw1g94unkaHY6wYGtlRTgPyRSe53CPj22ZvKfCloWGhdL5\n584cf/+4wyVOg0MGc+LGCZa3Xm50KEKIZJDHx0LYAJmf1PEF+AZQI18NRm4dmexr2VJ5OX79OFP3\nT+W7Bt8ZHYqIhy2VFeFcJCkUQoiXGFd3HDMPzOTkjZNGh2IVkdGRdFzVkVGBo8idKbfR4QghbIg8\nPn6ePD5ORfKeCnvw3a7vWHNqDRs6brD79rlfhnzJwSsHWdNujd3/LkIIeXwshBCpqnfF3lx/cJ2l\nx5YaHUqy7Lywk5l/zWRm05mSEAohnmMrSaEbMAsIA+4CB4AGcY6pDZwEIoAQIF+c/WOBG/oSd9RZ\nX2Czfu4J/VpCJIu0+3Eeri6uTG44mU/Wf8Kth7eSdA2jy8u9x/fouKojUxpNkansbJzRZUU4L1tJ\nCl2B88CbQCbgS2ApkF/fnw1YAQwCvIF9wBKL83sCbwOl9aWJvi3GYmA/kEW/xnL9mkIIkSDV8lWj\nRYkW9FrXyy6bPPT7ox8189fknRLvGB2KEMJG2fLzg0PAMGAV0APoBFTX93mgagT9gVPATmA2MFPf\n30U/pwpQFDgMZEXVFAJsARYB0+K5r7QpTEXyngp78ijqERVmVODTKp/S2b+z0eEk2Oq/V/PR7x9x\nqNchMrpnNDocIYQVOUObQh9UMndMX/dDJYkxHgD/6NsBSsbZf9hinx9wlmcJIfqxfgghRCKkc03H\nouaL+HTDp5y5ecbocBLkWsQ1eq7tyfx35ktCKIR4KVtMCtMCC4G5qFpAAE9UW0NLd4GYT7gMwJ04\n+zK8YF/cc4VIEmn345xe93mdwW8Opv3K9jyJfpLg84woL2bNTLfV3QgqE0T1fNVffYKwCfLZIoyS\nWklhKGB+wbI1TjwLgEfABxbb76PaGlryAu69YL+Xvu1F52bm+STzqaCgIIYNG8awYcOYOHGi3f8H\nnTt3Lt7e3jx8+DDW9uHDh1OwYEEAunfvTuHChfHw8KBQoUIMGjSIyMhIAB4+fIi7uzsbN258em7N\nmjVxd3d/es1Hjx6RLl06fvvtt0THZ/n+hoaGyrqs2/x6n4p98E7vTfD3wTYRz4vWu0zswpm/zjAs\nYJhNxCPrsi7ryV8PDQ1l2LBhBAUFERQUhKMyAXOATYB7nH3dge0W656oR8hF9fUdQDeL/cGodobo\nxzzkWc0hwDZUm8P4aC/ysn227OHDh5q3t7c2b968p9uio6O1/Pnza6NHj9bMZrP25Zdfanv27NHO\nnTunrV69Wnvttde0oUOHPj2+Zs2a2sCBAzVN07QHDx5obm5umo+Pj/bHH39omqZpGzdu1NKmTavd\nv38/UbHZ63sqxH/3/tNyjs+pbTu3zehQ4rXo8CIt/7f5tSv3rhgdihAiBQFWa5hvS4+PpwDFgabA\n4zj7VgGlgOZAOmAocJBnj5fnA/2AXEBu/fVcfd8p/dih+rnN9WutSJlfw/akS5eOjh07MmPGjKfb\nNmzYwOXLl+natSsmk4kRI0ZQoUIF8uXLR5MmTfjss89YtGjR0+MDAwPZtGkTANu3bydv3ry0aNHi\n6baQkBAqVKiAp6djzQ8rxIvkzJCTGU1m0HFVR+48ittCxVi7L+7mw98/ZHW71fhk8DE6HCGEnbCV\npDA/quauDHAF9Vj4HtBO338DaAGMAm4C5YG2FudPA9YAR1CdTNYA0y32t9XPualfowUQnjK/CmAy\nWX9Jpp49e7Jjxw7+/vtvAGbMmEHjxo3x8fF5ul6pUiVy5sxJxowZ+eKLLzh//vzT82vVqsVff/3F\n3bt3CQkJoU6dOtSqVYuQkBBAJYWBgYHJjtOeWFbrC+fUuGhjGhZuSJdfuhBtjn7psalVXi7cuUDz\npc2Z3XQ2pX1Kp8o9hXXJZ4swiq0khedQsXigOoDELIstjtkElNCPCUSNa2jpc9SwM1mBAfFcv5Z+\nbgnU4NcpR9OsvyRTyZIlqV69OtOnT+fatWusWbOGHj3UE/Rly5bxwQcf0K5dO3777TcOHjzIkCFD\nnrYpBKhcuTLu7u6EhoayefNmAgMDqVWrFgcPHuTChQvs37/f6ZJCIQAm1J/A3cd3eW/de4YPrxQR\nGUHTn5ryceWPaVKsiaGxCCHsjy2PU2gU7UUf7PY+pt7ChQv56KOP6Nu3LzNnziQsLAyAPn36sHfv\nXnbt2vX02B49ejBr1iyio5/VfjRo0ICcOXOyaNEiLl++TLZs2fD396d8+fIsXLiQO3fu4ObmlqiY\n7P09FQLUbCG159emdoHajKkzxpAYzJqZlktbkjldZmY1nSXT2AnhJJxhnEKRAlq2bAnAyJEjCQ4O\nfrq9ePHiHDlyhNWrV3PmzBm+++47Vq1a9VyyFhgYyMKFCylRogTZsmV7um3evHlUrVo10QmhEI4i\no3tGfmv/G7/8/Qvjd45P9fubNTN9f+vLjQc3mNJoiiSEQogkkaTQibi7u9OhQwfMZnOspLBnz550\n7NiRLl26UK5cOfbu3cuwYcOe+8MSGBhIdHR0rMfEgYGBmM1mp3x0LO1+hKWsHllZ33E9P+z5gdkH\nZj+3P6XKy6OoR7Rb0Y5DVw/xS9tfcHeNO3iDsDfy2SKM4mp0ACJ1Xbp0ibfeeotcuXI93ebq6srU\nqVOZOnVqrGN79+4da718+fKYzeZY2xo3bhzrEbMQzixPpjys77iegLkBeKfzTvF5hm89vEWzJc3w\n8fRhfcf1pHNNl6L3E0I4NnnG8DyHbFN469Yt9u7dS+PGjdm4cSNvvvmm0SEB9v2eCvEif/33Fw1+\nbMCE+hNo/3r7FHmce+HOBd5a+BZ1C9blm/rf4GKSBz9COCNrtimUpPB5DpkU+vr6cvPmTfr27cuI\nESOMDucpe35PhXiZg1cO8u6KdymTswyTG07GO7231a59+OphGi1qxMeVP6ZflX5Wu64Qwv5IRxOR\naGFhYdy9e9emEkJ7J+1+xMv45/Rnf4/9ZPfITpmpZfh28bfJvubjqMf8sOcH6syvw/i64yUhdFDy\n2SKMIm0KhRAihaRPm57v3/qeRkUa0WFCBy5nvczIwJGJ7gwSZY7ix8M/Mix0GKVylGJDxw2UyVkm\nhaIWQjgreXz8PId8fGyr5D0VzuLGgxv0WNOD49eP065UOxoVbUS518q9tC2gWTOz8sRKBm8eTA7P\nHIwOHE21fNVSMWohhK2TNoUpS5LCVCTvqXAmmqax9dxW1pxaw7rT67j18BYNizSkUZFG5M+cn3O3\nzxF2O4xzd85x7s45jl8/Tib3TIwOHE29QvVk/EEhxHMkKUxZkhSmInt+T0NDQwkICDA6DGEn4isv\nZ2+dZd2pdaw9vZbrEdfJnzk/+b3y45vZl/xe+SngXYAyPmUkGXQy8tkiEsOaSaG0KRRCCIMU9C5I\nn0p96FOpj9GhCCGE1BTG44U1hVmyZOHWrVupHI5j8/b25ubNm0aHIYQQQtgleXycsl6YFAohhBBC\n2BJHHKfQDZgFhAF3gQP/396dh0pVxQEc/5YLYstzK9u1hRdmtGOBlW2U7RtBUbQZ1X9hBAUFFbRJ\n9l9E9EfZYlJEQSLVH9WLFiEMbBWi9Fm0l/m0jBatP3538L5pxDszR+/M3O8HLm/mnjuHM29+78x5\n59xzDjA7lz4V2ASszx231+UxD/g5Ox6oS5sKvAn8DqwATk1YdlWUa4mpGcaLijJWVJZOaRSOBL4C\nTgR2Be4Angem1F23K7BLdtybO38DcD5wWHacm52rWQR8AEwgGpMvAJNSvwlVy/Lly8sugrqI8aKi\njBWVpVMahRuAu4mGIcASYBVwVN11WyrvVcB84NvsmA9cnaX1A0cCdwJ/Ai8CHwEXpym6qmrt2rVl\nF0FdxHhRUcaKytIpjcJ6k4nG3Kd151cDXwOPAxNz5w8BPsw9/wiYnj2eDqwkho5rPsylS5IkVV4n\nNgpHAQuBBcDn2bmfgGOA/YCjieHjhbnX7AwM5Z6vy841Squl75Ky0KqewcHBsougLmK8qChjRWXZ\nXrOPB4j7BRt5J5e2I/As0ZA7H9i4hddMBr4jGna/A2uB04BlWfoxwBvEPYgXAvcwvGfw4Szvmxrk\n/QVw4FbejyRJUif4Ejio7EKktgPwBPA6sLXd4icTs5FrvX3vAtfl0ucA72WP+4E/2NxzCPA2cH2b\n5ZUkSdI28CiwFNipQdoM4GCiJ3Ei8BzReKy5AfgM2AvYm7gXMd/oWwo8CIwBLgJ+Zfg9iZIkSeoA\nU4ievw0MX4vwsiz9UmKyyG/E7OIFwO51ecwDfsmO+nUKpxDrFG4g1ik8JfUbkCRJkiRJktThJgAv\nEb2Mg2zufWxkLjGBZYjYYWV0i/moe6WKlwHiXtZar/eK9EVVyYrGyqHAa8QqCpvayEfdLVW8DGDd\n0uuKxspVxATbIWK5vnnAiBbyqZRF2TEWmEnMVD6kwXVnAN8D04BxxHDz/S3ko+6WKl7eBK7dpiVV\n2YrGSj9wDXAejb/krVuqIVW8WLf0vqKxcmOWPpKYU7EMuLWFfCpjJ2IXk/xU7ScZ/uVd8yyxdE3N\nyUQvULP5qHuliheIintO6gKqY7RSJxzE/7/krVuqIVW8gHVLr2unTpgLvNxOPp24eHVK/cA/xNqD\nNVvazaTRriiTgfFN5qPulSpeau4nhoDeAWYlLanKlqpOsG6phtSfs3VL72onVmYBn7STT683Cncm\ndi/JW0/j3Uwa7YpCdm0z+ah7pYoXiC78/Yku/ceAxcAByUqqsqWqE6xbqiHl52zd0ttajZVrgaOA\n+e3k0+uNwt+IXU3y+ohfzNau7ct+rm8yH3WvVPEC8D6x287fwFPEAutnJSupypaqTrBuqYaUn7N1\nS29rJVYuAO4DzgTWtJFPzzcKPyduwMyPqR/O5u7VvE+BI+qu+4FY6LqZfNS9UsWLel+qOsG6pRr8\nnFVUs7Eym+gxPof4Xmo1n8pYREwKGAscT8y+mdbgujOIiQLTiPvCBoiWd7P5qLuliJe+LH0M8Ud5\nOfFfW8/tTVlxzdQJY4j7UDcR23jmt/K0bqmGFPFi3VINRWPlFGLDjuPbzKdSxjN8nZ5Ls/P7Ed2o\n++SunUssM1Jbd25UgXzUW1LEyyRiiGcd0XP4HnDqNi63tr+isTKV+HLfBGzMfq4skI96S4p42Q3r\nliooGitvAH8xfCe4JQXykSRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJKQ0SW0tJ\nUs/ZsewCSFIX+RfYoexCSJIkqTxPE3vRbiD2GL2lwGtmAMuI/bG/Bx7KpR1H7F37K7AcmJVLmwA8\nAXwDrCH2L5UkSVKHWEVzw8dLgcuzx2OBY7PHewM/A7Oz56dlzydmz5cAi4A+YCRwQutFliRJUmrN\nNgrfAu4CJtWdvxV4qu7cq8CVwJ5Ej2Rfa0WUpNZ4T6EkbTtzgH5gBfA+cHZ2fgpwCTF0XDtmAnsA\n+xJDxkPbu7CSJEkqZiWtzz6+GPiDGEa+DXhsC9fZUyipFPYUSlJxPwAH1p0bJIZ9G7kC2C17PETM\nXt4IPAOcC5wOjADGACcR9xp+B7wCPAKMA0YBJyYqvyRJkhI4D1hNDPfeDIwG1hFDxI08TTQk1wMf\nZ6+vmQEMAL8APwKLiaFjgPHAAmLG8hrghXRvQZIkSanNBBaWXQhJkiRJkiRJkiRJkiRJkiRJkiRJ\nkiRJkiRJkiRJkiRJkiRJkpL6D6m/FOdAqo+5AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x714ce10>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Roll Left"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim_flap(V=1, alpha=20*pi/180, freq=5, center=6.5*pi/180, delta=-30*pi/180, flap_mag = 100*pi/180, f_aero=f_aero)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lift:\t     71.46 gm\n",
        "side:\t     14.96 gm\n",
        "thrust:\t    392.07 gm\n",
        "roll:\t     -2.29 gm-cm\n",
        "pitch:\t    -14.02 gm-cm\n",
        "yaw:\t    -48.45 gm-cm\n",
        "fwd: 343.990741 gm, up: 201.243569 gm\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3v/xiDWtvvWXpvSZMgIwMZ8tW7PqigDBi6L0lAjRo4JeA0N8UFAaBGTOgSxf4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\ns3sdCWzeaC9F3efzY/5R9sb8r01bKAaX7NwT8mPmobowuzVdl8PrSODyR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       "text": [
        "<matplotlib.figure.Figure at 0x6c62b50>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Roll Right"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim_flap(V=1, alpha=20*pi/180, freq=5, center=6.5*pi/180, delta=30*pi/180, flap_mag = 100*pi/180, f_aero=f_aero)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lift:\t     71.46 gm\n",
        "side:\t    -14.96 gm\n",
        "thrust:\t    392.07 gm\n",
        "roll:\t      2.29 gm-cm\n",
        "pitch:\t    -14.02 gm-cm\n",
        "yaw:\t     48.45 gm-cm\n",
        "fwd: 343.990741 gm, up: 201.243569 gm\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bJJSXXoLWrZ0ulYjklfh4ePZZ+OUXu737bkvYcD7KUyiW72LTJsuurYDQERr3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\nP6PQXhMlrtnmAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7560550>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Testing Aerodynamics Calculation Speed"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f_aero(*np.ones(9).astype(float))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([[ 0.00781278],\n",
        "       [ 1.04269888],\n",
        "       [ 0.28860479],\n",
        "       [-0.72146702],\n",
        "       [ 0.0354347 ],\n",
        "       [-0.10849115]])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f_aero(*np.ones(9).astype(float))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([[ 0.00781278],\n",
        "       [ 1.04269888],\n",
        "       [ 0.28860479],\n",
        "       [-0.72146702],\n",
        "       [ 0.0354347 ],\n",
        "       [-0.10849115]])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "f_aero(*np.ones(9).astype(float))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 119 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "compute_aero(f_aero=f_aero,\n",
      "             P=0, Q=0, R=0,\n",
      "             alpha=0.1, beta=0, V=1,\n",
      "             eta_l=0, eta_dot_l=0,\n",
      "             eta_r=0, eta_dot_r=0, const=const)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "(array([-0.00119207,  0.        , -0.01030249]),\n",
        " array([ 0.        , -0.00103025,  0.        ]))"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "compute_aero(f_aero=f_aero,\n",
      "             P=0, Q=0, R=0,\n",
      "             alpha=0.1, beta=0, V=1,\n",
      "             eta_l=0, eta_dot_l=0,\n",
      "             eta_r=0, eta_dot_r=0, const=const)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 loops, best of 3: 2.9 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 32
    }
   ],
   "metadata": {}
  }
 ]
}