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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Initial Value Problems - Project\n",
"\n",
"![Initial condition of firework with FBD and sum of momentum](../images/firework.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to end this module with a __bang__ by looking at the flight path of a firework. Shown above is the initial condition of a firework, the _Freedom Flyer_ in (a), its final height where it detonates in (b), the applied forces in the __Free Body Diagram (FBD)__ in (c), and the __momentum__ of the firework $m\\mathbf{v}$ and the propellent $dm \\mathbf{u}$ in (d). \n",
"\n",
"The resulting equation of motion is that the acceleration is proportional to the speed of the propellent and the mass rate change $\\frac{dm}{dt}$ as such\n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt} -mg - cv^2.~~~~~~~~(1)\n",
"\\end{equation}$$\n",
"\n",
"If we assume that the acceleration and the propellent momentum are much greater than the forces of gravity and drag, then the equation is simplified to the conservation of momentum. A further simplification is that the speed of the propellant is constant, $u=constant$, then the equation can be integrated to obtain an analytical rocket equation solution of [Tsiolkovsky](https://www.math24.net/rocket-motion/) [1,2], \n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt}~~~~~(2.a)\n",
"\\end{equation}$$\n",
"\n",
"$$\\begin{equation}\n",
"\\frac{m_{f}}{m_{0}}=e^{-\\Delta v / u},~~~~~(2.b) \n",
"\\end{equation}$$\n",
"\n",
"where $m_f$ and $m_0$ are the mass at beginning and end of flight, $u$ is the speed of the propellent, and $\\Delta v=v_{final}-v_{initial}$ is the change in speed of the rocket from beginning to end of flight. Equation 2.b only relates the final velocity to the change in mass and propellent speed. When you integrate Eqn 2.a, you will have to compare the velocity as a function of mass loss. \n",
"\n",
"Your first objective is to integrate a numerical model that converges to equation (2.b), the Tsiolkovsky equation. Next, you will add drag and gravity and compare the results _between equations (1) and (2)_. Finally, you will vary the mass change rate to achieve the desired detonation height. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Create a `simplerocket` function that returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (2.a). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt} \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `simplerocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s. \n",
"\n",
"_Hint: your integrated solution will have a current mass that you can use to create $\\frac{m_{f}}{m_{0}}$ by dividing state[2]/(initial mass), then your plot of velocity(t) vs mass(t)/mass(0) should match Tsiolkovsky's_"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" \n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" x = -dmdt\n",
" y = state[1]\n",
" z = u/state[2]*dmdt\n",
" derivs = np.array([y,z,x])\n",
" return derivs\n",
"\n",
"def eulerstep(state,rhs,dt):\n",
" next_state = state + rhs(state) *dt\n",
" return next_state\n",
"\n",
"def rk2_step(state, rhs, dt):\n",
" mid_state = state + rhs(state) * dt * 0.5\n",
" next_state = state + rhs(mid_state) * dt\n",
" return next_state\n",
"\n",
"def heun_step(state,rhs,dt,error=.00001,iterations=1000):\n",
" next_state = state + rhs(state) * dt\n",
" eps = np.finfo('float64').eps\n",
" for i in range(0,iterations):\n",
" next_state_1 = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e = np.sum(np.abs(next_state-next_state_1)/np.abs(next_state+eps))\n",
" if e<error:\n",
" break\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
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JTdXH0iuVVykpKfj6+no6DKWKFD8/P5KTkws8TqFIKkSkGfAcMNcYMysXXYLt1/M5tImzX0Pc0C8DEelj34K67sSJEzkGmhf921yPn4/1I9l04Aw/bD7strGVupboJQ+l8sZd/2Y8nlSISCAwCYjFuisjV93s17z+KZ/ffhkYYz4zxkQZY6LCw8MLMlQGkaHFeOzWtBMk7y3YwcUknbmulFKqaPB4UgEMxVoj4gVjzJFc9jlnvwbn0MZRdy5dWX77XTH9WlejVJAfAKFBfhyP1UmbSimliobCcEvpvUAq0EtEemWqq2W/9hWRu4HdxpjHgWi7vFIO41a0X6PTleW33xUTEuDLG51uICnFcN9NFfDy0tO4SimliobCcKYCrDhaudjK2PVV7f0oe3+j/VrHvnziSuNMbQvS74rqUr8sXRtFakKhlHIbEcnz1rt373wdKyoqChFh3bp1BY47Li4OESE4OOsJ5tKlSyMinDx5qbn9hdvWrVsREerWrevpUArM42cqjDGVs6sTkclAL+BlY8zwdH0OiMgGoCHwADA1U79WQCTWqpmrC9rvijEG/lkKKclQ8/Yrfnil1NWrV6/MJ4Lh6NGjLFq0iKCgILp27Zql/tZbb70SoamriMeTigIYhrWA1XsissoYsxtARCKAMXabd12sipnffpdf9K/8SgI1IqOcp2gAUlINS7Ydo2OdMjqrXSmVL5MnT85Stnz5chYtWkTp0qVd1ufX119/TXx8PJUrV3bbmKpoKCyXP/LMGDMHGIu1+uUWEflBRL4BdmEt8z0X6wFhbul3uR2OO8yze7+m32+vMWLdCGf5uugYOo9ayVPT1vPj5tzOY1VKKc+pVKkStWrVIiAgwNOhqCusyCYVAMaYfsC/gA1Ycy46AruxHgh2vzHG5f2Y+e13OR2KO8TPB34GYEH0AtYcWQPAwq1H+etwLADD5m/nQmLBFydRSqm8mjJlCq1atSI0NBRfX1/Cw8Np0KABzzzzDPv378/QNqc5FQkJCYwcOZKoqChCQkIoVqwYdevW5fXXX3fLio5gLYDWr18/RIT69etz8ODBDPV//vknPXr0oEKFCvj5+REREUGnTp34+eefs4xVr149RISlS5dme7ynnnoKEWHw4MHOsvPnzzNkyBAaNGhAUFAQ/v7+lC9fnubNm/Pmm2/meqGpU6dO0axZM0SE7t27k5CQwCuvvIKI8NJLL2Xbb8aMGYgIbdu2zdVx3MYYo1sBtkaNGhl3eWXFK6bu5Lqm7uS6pvO3nU1i7BFzfsuPptGQxabSqz+aSq/+aEYs2uG24yl1Ndq2bZunQygyli1bZgBTqVKlHNu9+OKLBjB+fn6mTZs2pnv37ub22283NWrUMID54YcfMrRv1KiRAczatWszlJ87d840bdrUACYkJMR07tzZdO3a1YSHhxvAXH/99ebAgQNZ+gAmKCgoS1ylSpUygDlx4oSz7Pz586ZTp04GMO3atTNnz57N0GfmzJnG19fXAKZBgwame/fuplmzZkZEDGDefffdDO0/+OADA5iePXu6/N5cvHjRlCxZ0oiI2bNnjzHGmKSkJOfXGRYWZu666y7TvXt306ZNG1OuXDkDmHPnzjnH2LJliwFMnTp1Moy9e/duU716dQOYl19+2aSmphpjjImOjjbe3t4mLCzMxMfHu4yrefPmBjBz5sxxWe9KXv7tAOuMi89Ej38oF/XNnUnFsfPHTJPpTZyJxcRPqhkzpIz5YfnvzqSi+qD5Zv+p8247plJXG00qci83ScWZM2eMj4+PCQsLM3v37s1Sv23bNrN///4MZdklFX379nV+mB89etRZfu7cOXPHHXcYwLRv3z5Dn7wkFceOHTONGzd2JgGJiYkZ2u/du9cEBgYawIwbNy5D3fz5842fn58REfPLL784y48ePWp8fHxMsWLFTGxsbJYYZs2aZQDTunVrZ9m8efMMYJo3b57lQz8lJcUsX748Q2yukoo1a9aY8PBw4+XlZUaNGpXluPfcc48BzKRJk7LUbdq0yQCmQoUKJikpKUt9dtyRVBTliZpXnYhiEfRt0Jfh66wbXcYG+3PHmRjuOjqazyL7sPngWRKTU3ln3nbG/V8jD0erVNH14ZKdfLx0V67adr+5IsPuq5+h7N/fbGbmHwdy1f/ZdtV5/rYaGcoem7yWpTuO56r/0Hvr0aPJdblqeznExMSQnJxM7dq1XU68rF27dq7GOXPmDBMnTgRg7NixlCmTNh09ODiYzz77jOuvv56ffvqJTZs20aBBgzzFuXPnTu644w727NnDwIEDeeedd7K0GTt2LPHx8XTo0IEnn3wyQ90dd9zB448/zpgxYxg5ciQtWrQAoEyZMtx+++38+OOPzJ49m0cffTRDP8cE1/S33x47dgyA1q1bZ5lX4uXlRatWrXL8Wr7//nu6d++OMYZvvvmGLl26ZGkzYMAA5s6dy5gxY7Lc+jt69GgA+vTpU+BHmedVkZ5TcTXqUbsH15e8HoB4Ly9GlI1EGj7Mm53qONss/Osov+x03zNHlFIqO5UqVaJMmTKsWrWKQYMGsXv37nyN8/vvv5OQkECNGjW45ZZbstRHRkZy2223AdZdKXnx22+/0axZM/bt28f48eNdJhQAK1asAMh2/Q1HwpD5+I72me+QOXr0KIsXLyY4ODjDLbmOOSWjR4/m888/z9M6GmPGjOHee+8lKCiIZcuWuUwoANq2bUudOnVYu3ZthrkrsbGxTJ8+HV9fX5544olcH9ddNKkoZHy9fBnYZKBzf6Gf4ffgYBpVCuW+myo4y9/8/i8SkvW5IEqpy8vLy4svv/yS0NBQhg4dSvXq1Slbtiz33nsv48ePJy4u7tKDAIcOHQKgSpXsHwBdrVq1DG1zq2vXrpw6dYpPPvmEPn365DsGx/HPnDnDhQsXnOWdOnWiVKlSrFy5kj179jjLp02bRkpKCl27diUoKMhZXq9ePYYNG0ZcXBxPPPEE4eHhVK9end69e/Pdd9+Rmup6xYK///6b/v37OyeGNmnSJMeve8CAAYCViDhMmTKF8+fPc99991GuXLkc+18Wrq6J6OaZORXppZ+02enbTiYhOcEci403dd9c6Jxf8clPOy/LsZUqynRORe7ldqKmMdbchhkzZpgnn3zS1K1b1zmxsWzZslm+567mVEyYMMEA5vbbb8/2GM8884xzUmL643KJORWPPvqocw7Bjh3ZT2avUKGCAczvv//usv706dMG64GT5vz5jHPXBgwYYADzxhtvOMvq1q1rALN8+XKX4x08eNCMGjXKdOvWzURGRjrHbtq0qblw4YKznWNORdWqVU2rVq2cczTST+Z0JS4uzpQsWdIEBgaamJgYY4wxtWvXNoBZsWJFjn1dccecCj1TUUi9GPUiQb5W5rv37F4mbZ1EREgAL3Wo6WwzatluDsRcyG4IpZRym+DgYLp37864cePYsmUL+/fvp0uXLhw9epRnn332kv0jIyMBMvyln9nevXsBqFChQrZtXHnvvfd44403OHToEC1btmTLli35isFRXrJkSYoVK5ahznEJZOrUqRhjWL9+PVu3bqVKlSq0bNnS5XgVKlSgf//+zJw5kwMHDrB27Vpq1KjB77//zocffpilfWBgIAsWLKBjx44sX76cDh065HibbVBQEI8++ijx8fFMmjSJn3/+me3bt1O3bt1sY7rcNKkopCKKRfD0jU879z/b/Bn79y7j/85PoU65EHy8hEeaV6FUsJ8Ho1RKXasiIyOd6zJs2rTpku2bNm2Kv78/O3fuZM2aNVnqDx8+zJIlSwBrgmNeDR48mHfffZfjx4/Tpk0b1q9fn6WNY4Lk1KlTs9QBTJo0KdvjN2zYkPr16xMdHc2KFSuYMmUKYC1/ntuVjqOioujXrx+Q/fcsMDCQ77//nnvuuYfVq1fTtm1bTp06le2Y/fv3x8vLi3HjxjknaPbv3z9X8VwOmlQUYt1rdad2mDWzOjE1kSGLnkR+G8n4qEMsfK4Fr91Ri2J+egOPUury2blzJ1OmTHE5d+KHH34ArMmcl1KyZEkeeeQRAPr168eJE2mTzc+fP8+TTz7JxYsXad++fZ7v/HB49dVX+fTTT4mJiaFdu3asXp3xEU59+/YlMDCQhQsX8sUXX2SoW7x4MRMmTEBEeOGFF1yO7zhbMWHCBGbOnImI8PDDD2dpt3DhQpYsWUJKSsZ5b0lJSSxcuBDI+Xvm5+fH7Nmz6datGxs2bKBNmzbOO0oyq1q1KnfeeSe7du3im2++oXjx4vTs2TPbsS87V9dEdPP8nAqHrSe3mvpT6jvnV/z4flljPqxnTEryZT2uUkWVzqnIvdzMqfj1118NYPz9/U3Tpk1Nt27dTNeuXU2tWrWc5T/99FOGPrld/KpLly6ma9euJiIiwm2LXxljzOeff268vLxMcHCwWbZsWYa6GTNmGB8fHwOYG2+80fTo0cM0b97cOUdk2LBh2X4vjh8/7lw4i0xrU6Q3ZMgQA5jQ0FDTrl0706NHD9OlSxdTpkwZA5iKFSuaw4cPO9tnt/hVSkqKeeSRRwxgatasaQ4ePOjyeIsXL3bG9PTTT2cb/6Xo4leFYLvcSYUxxgxbM8yZVLScVN+cObTush9TqaJKk4rcy01SERMTY4YPH246depkqlataoKCgkxISIipXbu26d+/v/n777+z9MkuqTDGmPj4eDN8+HDTsGFDExQUZAICAkzt2rXNoEGDzOnTp7O0z09SYUxa8hAYGGgWLlyYoW7Dhg2mW7dupmzZssbHx8eUKlXK3H333VmSI1e6dOni/ACfPHmyyzbbt283//nPf0yrVq1MZGSk8ff3N6VLlzYNGzY0Q4cONadOncrQPrukwhhjUlNTTf/+/Z0TOV0tQHbx4kXj7+9vgAL9/rsjqRCrTuVXVFSUcbW+vTvFJcbR5bsuHL9gLZbTtUZX3rzlTWf9oTPxDP7+L56/rQa1yxW/rLEoVdht37491wsyKXU1mD59Oj179qRt27Y5PqPkUvLyb0dE1htjojKX65yKIiDYL5h/3/xv5/6cnXNYf8yahLRgyxFuG7mCxduO8e9vtpCSqkmiUkpdKxISEhg6dChAtnNBriRNKoqIdte1o3Vka+f+f1f9l4SUBKpHBJGcYiUSfx44w/Q1+zwUoVJKqStl3Lhx9O7dm/r167Nt2zbatGnDXXfd5emwNKkoKkSEQU0HOdeuiI6NZvzy17h+dnv+3cTX2e79hX9z9OxFT4WplFLqCvjpp5+YMmUKp06d4l//+hdfffWVp0MCNKkoUsoGleX5hs879yceWMKO2D30OvURVUtbC7XEJSTz3+//8lSISimlroA5c+ZgjOHkyZNMmzaN0qVLezokQJOKIueBmg/QMKIhACkivFG6FKnH/2LEbSWcbRb+dZRFfx31VIhKKaWuUZpUFDFe4sXgZoPx87JW0tzu78eX7V/gpgYNeTAq0tnu9blbORuf5KkwlVJKXYM0qSiCKpeoTN8b+zr3R2+fwr7YfQy8szalg/0BOH4ugaHztnsqRKWUUtcgTSqKqF51elErrBYACSkJvPHbGxQP9OHte+o428xad4CVu056KkSllFLXGE0qiihfL1/eavYWPmI9+2PD8Q1M3z6d2yum8mAtf2e71Xs0qVBKKXVlaFJRhNUuVZvH6z/u3P9k3Uj2jW/GW76TqFO+OFMevZmXO9byYIRKKaWuJZpUFHF96vWhRmgNAC6aZF4v4Yfvrh/5se0JWtUI93B0SimlriWaVBRxvt6+vN38bedlkI0BAUwvWxkpUdHDkSmllLrWaFJxFchyGSTYl+jiGc9SnL2QxHd/HrrSoSmllLqGaFJxlehTrw81Q2sC1t0gA1cOJDk1GYBlO47T4aMVPDfrT9bsOeXJMJVSSl3FNKm4Svh6+/LOre/g42VdBtlycgufb/kcYwxTV0dzLDYBY+DlOZu5kJjs2WCVUh5TuXJlRITly5fn2K5169aICJMnT74icamrgyYVV5GaYTXpf2N/5/74TePZtvM7RoX+j5AAbwD2x1zg3QU7PBWiUkqpq5gmFVeZR+o8wo3hNwKQbJIZ+MtreG+ayNR6W51tpq7ex6rdun6FUkop99Kk4nlYdzwAACAASURBVCrj7eXNO7e+Q6BPIAB7/Hz5JLQEN/4zljtrFne2e2n2Jn02iFJKKbfSpOIqdF3x63gp6iXn/pclivNHl+H8t2tjQov5AnD47EV9RLpSKl/WrFlDt27diIyMxM/Pj/DwcDp37szKlSuztI2OjkZEqFy5crbjiQgikmP5rFmzuOWWWwgODiYkJIR27dq5PJ7yLE0qrlIP1HiAWyvc6twfuHkU/n4JDLuvnrPs242H+HHzYU+Ep5QqokaMGMEtt9zCV199RdmyZenSpQvXX3898+bNo1WrVkyYMMHtx3zjjTfo0aMHfn5+3HXXXURGRvLzzz/Trl07Vq9e7fbjqfzTpOIqJSK81ewtQv1DATh+4TiDVw+mY52y3N8w7RHpg77dytGzFz0VplKqCFm4cCEvvfQS5cqVY/Xq1axbt47Zs2ezevVqfvnlF4KDg+nfvz87d+5063FHjx7NH3/8wYoVK5g1axZ//fUXTzzxBImJibzxxhtuPZYqGE0qrmLhxcIZ3Gywc3/JviXM3T2X/95WluolrLKz8UnMXnfAQxEq5SHLhsF/S1jbsmFZ6xcNSqtf9WnW+u+fSatfNylr/ZzH0uo3z85aP+OhtPq/F2Stn3RXWv3eX/P+9eVCmzZtnJcXXG0rVqzI0ufNN98E4PPPP6dJkyYZ6po3b87rr79OUlIS48ePd2usgwcPplGjRs59Ly8v3n77bQB+/fVXkpJ0flhh4ePpANTl1ea6NjxY40G+2vkVAMN+f5uGJ+OYEdmcthcf4vW7b+CBqMhLjKKUutp07NiRsmXLZlu/cOFCjh075tw/efIka9eupXjx4nTo0MFln1atWgG4/ZLE3XffnaUsIiKC0NBQTp8+zalTp3L8WtSVo0nFNeClxi+x9tha9p7dS3xqIq8FGab+8zVrunSgWEN9RohS16LXXnuN1q1bZ1vfunXrDEnF3r17McYQGxuLj0/OHx0nTpxwV5gAXHfddS7LixcvzunTp7l4US/hFhaaVFwDAn0Cea/Fe/SY34Pk1GS2+vszOqI8z5WI8HRoSnlGm39bW3Y6vmNt2en8ibVlp+sX1padHrNyju+ReTnXe0BKSgoAJUqU4J577smxbenSpXM9bmpq6iXbeHnplfqiQpOKa0TtUrV59qZnGbF+BAATg3y5OTCAZunaXExKYen249xVv5xnglRKFVoVK1pnNX19ffO0dLefnx8AcXFxLuv37dtX4NhU4aHp3zXk4ToPc0u5WwAwGAb+OpCT8dbKmtuPxNJ51Er6z9jAzzuO5TSMUuoaVKFCBerVq8fJkycv+dyQ9MLDw/Hz8+PUqVMuL4vMnz/fjVEqT9Ok4hriJV4MbTGUUgGlADh18RSDVg4i1aQyatludh6z/pJ4afZmjp/Ta5RKqYyGDBkCQM+ePVm8eHGW+sTERL7//vsMEzV9fX1p0aIFYK03YYxx1q1cuVJvCb3KaFJxjSkdWJqhLYY691cdXsXktSP5MOVdagZbiUTM+URe/GoTqakmu2GUUtegLl26MGLECI4ePUrHjh2pWbMmnTt3pmvXrjRp0oSIiAi6dOnCpk2bMvR766238PPzY9y4cdSpU4cHHniAm2++mVatWtGvXz8PfTXqctCk4hrUrHwzHqv7mHP/022T2X5wGf8Ln4SXWJOmft11krEr/vFUiEqpQuqFF15g/fr1PPbYY6SkpLBkyRIWLVrE6dOnnStqPvjggxn6NGvWjKVLl9KuXTsOHDjgvOQxdepU59kPdXWQ9KeiVN5FRUWZdevWeTqMPEtKTaL3wt5sPrEZgHLJycw+cpLvao3jjXUBAHh7CbP6NCWqcpgnQ1UqT7Zv307t2rU9HYZSRU5e/u2IyHpjTFTmcj1TcY3y9fLl/ZbvE+IXAsARHx8G3dSRbvd0oVEla2nvlFTDMzM3cuZCoidDVUopVURoUnENqxBcgbebv+3cX3FyE9N2TOWT7jdRIjDtaaYvz9mMntFSSil1KZpUXOPaXteWXjf0cu5/suETjiVs54Ou9Z1lS7YdY/KqaA9Ep5RSqijRpELxbKNnaRDeAIAUk8LLK14mKjKRd29IW5Rm+d8n9GyFUkqpHGlSofD18mV4q+GU9C8JwPH447w6pxNd9w7i/yL2MqDt9Uzs3RgR8XCkSimlCjNNKhQAZYPKMvTWtPUrfvdJZUzJEN5K/pAXW5TB20sTCqWUUjnTpEI5tYhsQZ/6fZz7E0qWYHnTXhBY0oNRKaWUKio0qVAZ9GvQj2bl0x4zNujgQvbH7nfup6QaRi7Zyap/TnoiPKWUUoWYJhUqA28vb95r8R7lgqwnlZ5LOsfzy58nPjmek3EJPDxxDZ8s3cUzM//k6Fl9PohSSqk0mlSoLEoGlOTD1h/i62WtVbHz9E4Grx5McnIyp45Yd4ScjEug3/T1JCanejJUpZRShYgmFcqlOqXrMLDJQOf+vD3zWPJDZ74t9jYl5DwAG/af4Z152zwVolJKqUJGkwqVrfur38991e9z7o9IOcaWpGN8X34KgnWGYsrqfXy78aCnQlRKKVWIaFKhsiUiDGoyiPqlrdU1U0R4KaI0PtffwJ11yzjb/fubLWw7HOupMJVSShUSmlSoHPl5+zGy9UhKB5YG4LS3N88n72PwvbW5PiIYgItJqTw5bZ0+eEwppa5xhSapEJEBIvKViGwXkVMikiQiJ0TkJxHpKTks5ygiPUTkVxE5KyJxIrJORPqLSI5fX377XWvKBJVhZOuR+IgPANtjtvPB+rcZ+6+GBPl5A3AgJp4BMzeSnKITN5UqzCpXroyIXHJbvnx5gY/lGEtdO3w8HUA6rwIRwFZgFXAeqAS0BdoBXUXkPmNMhk8tERkN9AMuAkuBJLv9KKCdiDxgjEnJfLD89rtW3RRxE6/d/Bpvr7Geajp/73xqhNZgxIN38fS0NSTjw6+7TvLhTzt5uWMtD0erlLqUjh07UrZs2Wzrc6pTKjuFKanoBmw0xpxPXygidbA+9LsAvYBJ6erux0oMjgItjTG77PIywDLgXuBp4ONMY+ar37XuwZoPsj1mO1/v+hqAjzd8zCehq/mp7H7aHX2aKhEl6NqoooejVErlxmuvvUbr1q09HYa6yhSa0/zGmJWZEwq7/C9gtL17W6bqf9uvrzoSA7vPMaCvvfuai8sZ+e13TXNM3GwY0RAAg+HVU6tJPr+Bb65fyNz+zalSOsjDUSqllPKUovKhmWy/OpdwFJFIoBGQCMzO3MEYswI4BJQFmha0n7L4evsysvVI54qbF7y8GFCmNJWCThFcmM57KaXcYvny5YhItmc1oqOjEREqV66cp3GTkpIYN24cLVq0IDQ0lICAAKpXr84LL7zAiRMnsrSfPHkyIkLv3r05deoUzzzzDFWqVMHPz4977rknH1+ZuhwKfVIhIlWAp+zdH9JV3WS//mWMic+m+9pMbQvST9lKBZbi07afEugTCMBBX19eDA0iSUyGdlsPnSUhWaelKKUyio2NpW3btvTt25ctW7bQsGFD7rrrLpKTk/nwww+JiooiOjraZd+TJ0/SuHFjpk+fToMGDejSpYvO/yhECl1SISKPiMhkEZkuIiuAnUAkMMwY8226plXs1305DOd4ElaVdGX57afSqRlWk2G3DnPu/3FsLe/8/g7GWInFnPUHuW/MKv79zRZnmVJKAfTp04eVK1fStWtX9u7dy9KlS/n666/ZvXs3r7zyCvv376d3794u+86bN4/q1asTHR3N3LlzmT17NuPGjbuyX4DKVmE8Yd0ca0KmQzLwOjAyU7tg+zXLPIx04uzXEDf0U5m0q9SOATcN4NONnwLw9a6vqVKiCrWLdeKl2X8CwjcbDlGrbAh9WlbzbLBK2epNqefpEPJtS68tbhurTZs22daVKFGCM2fOuO1Y6W3bto1Zs2ZRqVIlpk6dSmBgoLPO29ubYcOGsXDhQlasWMGWLVuoVy/jz8vX15fx48cTEqL/PRdGhS6pMMY8DjwuIoFYZwoeAf4LPCgidxpjDttNHTc/5/XP4Pz2SxtApA/QB+C6667L7zBXhSfqPcHes3v5cc+PAIxYN4KPK+/lx/B1dDnRhxS8GbZgB9XCg2lXu8wlRlNKXSk53VJarFixy3bcBQsWAHD33XdnSCgcvLy8uPXWW9m8eTOrV6/OklQ0bNgwz/M31JVT6JIKB3u+wzbgZRE5CgzHWkPC8TCKc/ZrsIvuZKo7l64sv/3Sx/YZ8BlAVFTUNX1uX0QY3Gwwh+IOsfH4RuuOkD2zmZpwjFFhJekb0x1j4JmZG/m6XzNqlS3u6ZCVUnjultI9e/YAMHr0aEaPHp1jW1cTNitVqnRZ4lLuUWiTikwmYSUVnUTE1xiTBETbdTn9hjkWTYhOV5bffiobft5+fNTmI3rM68GhuEPEe3nxdJlwpibs4voU2H0Wziem8NjkdXzbvxkRIQGeDlldw9x5CUFBamreVtFNSbEmbzdq1Ii6devm2LZOnTpZylyd3VCFR1FJKs5gza3wAcKAY8BGu66OiARmcydHY/t1Y7qy/PZTOQgLCGN0u9H0nN+TuKQ4jvn48GzpCnzQuSH/N2EzcQnJHDoTzxNT1zOrT1MCfL09HbJSKhf8/PwAiIuLc1m/b19Oc96zqljR+putTZs2fPDBBwULThU6he7uj2y0xEoozgAnAYwxB4ANgB/wQOYOItIK666Ro8BqR3l++6lLq1ayGiNaj8BHrIRhx5ldTNgxhI+618fLnsmy6cAZXvxqE6mp1/RVI6WKjAoVKgDwzz//kJSUlKV+/vz5eRrvjjvuAGDu3LkkJydforUqagpFUiEiLUTkXyLi76KuOfCFvftFpudxOO5pfE9Erk/XJwIYY+++m/l5IQXopy6hWflmvH7LG879Xw/9yurTn/NmpxtwzI2dt+UII5b87aEIlVJ5UalSJapVq8aZM2cYPnx4hrq5c+fyySef5Gm8hg0bcs8997B7924efPBBDh48mKXNkSNH+OijjzTpKIIKy+WPaljzJkaJyAasswQhdvkNdpt5WLeWOhlj5ojIWKyltbeIyE+kPRisODAXa3In7uincue+6vdx8NxBJmyZAMBXO7/ihWqpLCu9nM4n+3HBK4hyJfS6qFKe9O677zJ58uRs63v06EGHDh0AGDZsGA899BADBw5kzpw5VK1alV27drF582YGDhzIO++8k6djT5kyhc6dO/Ptt9+yYMECGjRoQKVKlYiNjeXAgQNs376d1NRUnnrqKXx8CsvHlMqNwvLTWgEMAVoANYBmWLd+HgW+BqYZY+a66miM6SciK4H+QCvAG9gBTATGZne2Ib/9VO4MuGkAh+IOMX+vdWp05D9zKGtOMidsDMc6TaNl7QoejlCpa9uiRYtyrL/xxhudScUDDzyAv78/w4YNY9OmTezatYuGDRuyYMECatasmeekonjx4ixdupQZM2Ywbdo0NmzYwPr16wkNDaV8+fI89dRTdOnShYAAndRd1IiudlgwUVFRZt26dZ4Oo1BKTEmkz5I+rD+2HgAfYxh/JpGbe86H0tdfordS+bN9+3Zq167t6TCUKnLy8m9HRNYbY6IylxeKORXq6uTn7cfHbT6maomqACSL8Gx4KDu9M54EiktI5ljsRVdDKKWUKkI0qVCXVQn/EoxrP46IwAgA4pIv0HdJX47EHQHgWOxFHhy3ml4T/yD2YtaZ5UoppYoOTSrUZVcuuBxj2o8h2NdaqPR4/HH6/tSX4+djeGjcb2w7EsuOo+d4cup6faqpUkoVYZpUqCuiZlhNPmrzET5e1tzgf87+w4s/P8X/fAdys2wHYPWeU7qGhVJKFWGaVKgrpkm5JrzTPG2W+J8x2xkScIpJxT6kplhPm/9x8xHenrddH5eulFJFkCYV6oq6s+qdvNr4Vef+L8UCeScsgF610i57TPxtLxN+3eOJ8JRSShWAJhXqiut5Q0+eqPeEc/+H4GIcuuEid9RNewzz0Pk7+HZj1pX2lFJKFV6aVCiPGHDTAO6vfr9zf+q2KdxYbyM3Vwlzlr08ezPLdhz3RHiqiNPLZ0rljbv+zWhSoTxCRPhP0//QtmJbZ9moPz/mrmbR1CkTiD+JJKca+k5fz6YDZzwYqSpqvL29XT74SimVvcTERLcsia5JhfIYHy8f3m/1Po3LNnaWjdgwjD5hw5hQbAzepNDwulCqRQR7MEpV1ISEhBAbG+vpMJQqMowxnDp1ihIlShR4LE0qlEf5e/vzadtPqVOqDgAGw3/NEfDfzOxy05jUuxHB/oXlETWqKAgLC+P06dOcPHmSxMREvRSilAvGGFJSUjh37hwHDx4kISGBsLCwS3e8BP3fWnlckG8QY9uP5ZGFj/DP2X9IFuGFiNKMLVsef31Cocojf39/rrvuOmJiYoiOjiYlRRdUU8oVLy8vAgMDCQoKIjQ0FC+vgp9n0AeKFZA+UMx9jp0/Rq+FD3Mo7jAAxXyKMaHDBOqH13e2mbvxEK1qhBMa5OepMJVS6pqnDxRThV6ZoDJMuO1zwgPDAbiQfIGnfnqKHTE7MMYwetlunpv1J70n/UFcQrKHo1VKKZWZJhWqUKlYvCITOkwg1D8UgHOJ5+izuA9Ldm1iyZJ5AGw6eJbHp6zlYpKe1lZKqcJEkwpV6FQrWY3xt40nxC8EgNMJp3l3zRN8WuwtunsvBeD3PTH0nbaexOTUnIZSSil1BWlSoQql2qVqM7b9WIr5FAPgROpFHisXQf/AKbT02gTAsr9P8MzMjSSnaGKhlFKFgSYVqtBqEN6AUe1G4e9tTco84uPD4xUrUb3ZLc42C/86youzN5GiTzZVSimP06RCFWqNyzbmkzaf4udlJRaHSGJ14gd0vyVtkZbv/jzMoG+36CPTlVLKwzSpUIVeswrN+LDNh/h6+QJw4NwBtqS+y/2NQ5xt/rf2AP/94S9d6EgppTxIkwpVJLSMbMnI1iPxEWsxrH2x+9jlNZwXqv9FW68NgJVY7D4e58kwlVLqmqZJhSoyWldszQetPsBbvAHYG7uXn8xE3i72Kbf5bmJir8ZULxNyiVGUUkpdLrlOKkTkcREJvJzBKHUp7Su15/2W76clFr6+PFUmjDfDv+HWqiU9HJ1SSl3b8nKm4jPgoIiMEJHqlysgpS6lQ+UOdmJh/fru9fOlb4VwTiScztDu7IUknWOhlFJXUF6Sih+B4sDzwHYRWSginURELk9oSmXPSiw+cCYW0XEHeXTRoxw7fwyAQ2fiuevTX/lg0d+aWCil1BWS66TCGNMZqAq8C5wEOgBzgb0i8pqIhF+eEJVyLS2xsC6FRMdG88iiR9hyNJqHx6/g4Ol4xiz/h/c1sVBKqSsiTxM1jTEHjDEDgYrA/wG/A9cB7wD7ReRLEbklpzGUcqcOlTswvNVw510hB84d4KVfHuXjlGfo6PUHAGOX/8O7C3doYqGUUpdZvu7+MMYkGWOmG2OaAzcBXwDJQA9gpYisF5FHRcTfjbEq5VL7Su0zrGNxOP4Ez5fx5rVio7nbazUA41fsYej87ZpYKKXUZVTgW0qNMZuAwcAkQOztJmACEC0ijxX0GEpdSuuKrfm4zcf42YnFUR8fHisfQfEqaXeETPh1L4N/2KaJhVJKXSYFSipEpL2IfAPsBfoDF4GJQHdgPhABfCYizxQ0UKUupUVkC0a1G02At3WC7IS3NytDvufWGxKcbSavimbQ3K26pLdSSl0GeU4qRKSEiDwnIjuARcA9wGFgIBBpjHncGDPLGNMJaAacBzSpUFfELeVvYUy6p5ueTjjNHt/htKh7wdlmxpr9vPr1Zn0ImVJKuVleFr9qKCKfA4eAEUANYAVwP1DVGPOeMSYmfR9jzBpgHtZkTqWuiMZlGzOhwwRC/KzVNc8lnmOnDOe2usd5yHsZYJi9/iDTft/n2UCVUuoqk5czFeuAR+33nwP1jTFtjTHfGmNSc+h3HvDJb4BK5Uf98PpM7DiRUP9QAC4kX2Bj8kjuKv4lr/n8j/a1wul+s+a6SinlTnlJKqKBl7EucTxpjNmay35PAL55DUypgqoVVovJt08mPNBaQiVB4Nky4VQqsZQxLZPw89FH3yillDvl5X/VasaYEcaYM3k5gLGk5DEupdyiasmqTLl9ChWCygOQLMKrEaX5LvlwhnbGGC4m6a+pUkoVRF6SikUi8sKlGonI8yKyuAAxKeVWFYtXZModU6lWoioABnhr9Vt8seULZ5vhi//mwfGriTmf6KEolVKq6MtLUtEeqJuLdjcA7fIXjlKXR5mgMky+fQp1StVxln204SNGrBvB6KU7mLxsK5sPnuWh8as5evaiByNVSqmi63JcVPYDcpq4qZRHlAwoyecdPqdx2cbOssl/Tebv/X2Z4fcWpTjLruNxdB23iuiT5z0YqVJKFU1uTSrsJ5Y2wnrgmFKFTrBfMGPajaF1xdbOsmVeJ/m87HmmBwwmjFgOno6n67jVbD8S67lAlVKqCMrxVk8XcyM65DBfwgeoDpQH5rghNqUuiwCfAD5s/SGDVw9m7u65ACwPKsapykHE7/WFBDgZl8BD41czsXdjoiqHeThipZQqGiSn5yCISPrLGAbruR6XshnoYoy5JlYWioqKMuvWrfN0GCofjDF8uOFDJm2d5CyrEFSFQ9t7cu58EAD+Pl6M+VdD2tUu46kwlVKq0BGR9caYqCzll0gqHBMuBViMtSz38GyaJwKHjDF7ChhrkaJJRdE3eetkRqwf4dwvFRBB7N5HiTljPYzM20t47/76dG0U6akQlVKqUMkuqcjx8ocxZmm6AX4DVqQvU+pq0Ltub0oFluKN394g2SRz6uJxgq8bw0PeN+B9JoQZKe0Y8uM22teOoGQxP0+Hq5RShVaul882xrS4nIEo5UmdqnUiLCCM55c/T3xyPHFJsSwtvYr3zSkqxJ2mycPDNaFQSqlL0HWKlbI1r9CcSR0nERZgPS8kwcuL5yJKE1ThL6IigzwcnVJKFX7ZnqkQkYH227HGmNPp9nPFGDO0QJEp5QF1Stfhyzum8dSSPhyIO4QRYURAPDGbxvBco+fwEisP//voOcqXDCAkQB9ro5RSDtlO1LTv/DBAbWPMznT7lxwT65Ef3u4Ls/DSiZpXp5iLMTz9U3+2nEp7bt4dle/g7Vvf5vDpJO4fu4qI4gFMfqQxZYoHeDBSpZS68vIzUXMoVhJxMtO+Ule9sIAwvrh9Iq/88grLDywHYEH0Ao6eP0bQlrqEXSjO9vOR3Dv6NyY/ejM1yoR4NmCllCoEcrylVF2anqm4uqWkpjDsj2HM+nuWs+y6pBQ+OHKWIfHPsjq1DiEBPoz/v0Y0q1bag5EqpdSVk92ZCp2oqVQOvL28GdRkEC82etFZtt/Xm6cqlKBX8Bf4kMy5i8n0mvgHczce8mCkSinleZpUKHUJIkLvur0Z0WoE/l7WxMzT3t4MjCxG8YidACSlGJ6b9Sejft6Fnv1TSl2rcp1UiEhfEUkUkbtyaHO33eZx94SnVOHRoXIHvrh9EmF+JQBIMskklZpKuUq/4phuNHzxTl6es5nEZH1Qr1Lq2pOXMxX3ATHAghzaLLDbdC1IUEoVVg3CGzDt7plULl7ZWRZXbB6RNb6jotchwohlzvqD9Jr4BwnJKZ4LVCmlPCAvSUUtYIsxJts/wYwxKcAW4IaCBqZUYVUxpCLT7pxGk7JNnGVnvX+nYuVPmBLwOtXlILXKheDvc03cVa2UUk55SSrCgWO5aHcciMhfOEoVDSX8SzD2trHcX/1+Z9kWf+HlSF/eL/E+/+lQxYPRKaWUZ+QlqTgLVMxFuwpAXP7CUaro8PXy5c1b3uSlqJcQBIBDvj70rRDKbycy3mackqqTN5VSV7+8JBUbgaYiUi27BnZdM+DPggamVFEgIvSq04uP23xMMW9rZc3zqQk8vfRpJm+djDGGlFTDU9PWM2Lx36RqcqGUuorlJamYDPgCc0WkeuZKEbkemAt4221zTUR8RaSdiIwQkd9F5Ih9F8khEZkjIq0v0b+HiPwqImdFJE5E1olIfxHJ8evLbz+lMmtzXRum3jmN8kHlATAYRqwfwX9++w8jf1jJum27+PTn3QyYuZH4RJ3AqZS6OuV6RU0REeAH4E4gGVgJ7LCrawItsJb9XmiMuTNPQYi0B5bYu0eB9cB5rAmfde3yIcaYN1z0HQ30Ay4CS4EkoB0QAnwLPGBPIHVLv8x0RU2V3qn4Uzy//Hk2Ht/oLKue6M0bh+N4+eLL7DKR1K1QnAkPR1GuRKAHI1VKqfwr8Iqaxso+7gPG2kWtgafsrY1dNha4Nx/xpQJfAy2NMeWMMXcbYx4yxtQDugEpwOsi0iZ9JxG5HysxOArUt/vdC1QHttuxPJ35YPntp9SllAosxecdPqdLtS7Osl1+KbwY6cvbIUMoxVm2Hoql86jf2Lj/tAcjVUop98vXsz9EpCzWX/WV7KJ9wFJjzFE3xpb+eJ8DjwETjTGPpStfBzQCehljpmbq0wpYjpU4VEh/K2x++7miZyqUK8YYpm2fxvC1H5BqL4zlixfnjzxAwpmbAPDz8eK9++tx702RngxVKaXyLLszFUXigWIi0h8YBSw2xnS0yyKBA0AiUNIYE++i30Gsu1GaG2NWFaRfdjSpUDlZdWgVLy1/gXPJ551lEtuS2EMdsaYfQZ+WVXn19lp4e4mHolRKqbwp6g8Uc0wMPZKu7Cb79S9XiYFtbaa2BemnVJ41q9CMmZ1mUbVEVWeZKf4Lpa6fgo/3Wcpzks9+2cMjk9dyNj7Jg5EqpVTB5TmpEJGaIjJaRP4SkTP29peIjBKRWu4O0L7U0tve/TpdlWN1oX05dN+fqW1B+imVL5WKV2L6ndNpW7GtsyzRdyflq43go5DXudVrCwdPX0D0RIVSqojLU1IhIr2x1qB4CqgNFLe32lgTH/8UkV7uCk5EfIBpNu9aRwAAIABJREFUQAmsORs/pKsOtl/PZ+mYxrEIV4gb+imVb8F+wXzY5kP63djPWXbaO5F+5UN4MPQTpnb0pniArwcjVEqpgsvLU0obAxMAP6xbLu/GSiZuAO7COovgC0yw27rDOKwJoQeAnplDsl/zOikkv/3SBhDpY69pse7EiRP5HUZdY7zEi74N+vJJm08IshfKSvDyYlBEKb48v5Kk1IyXP4rCfCellEovL2cqXrbb9zTGdDXGzDfG/G2M2WGMWWCMeQDrg98HeKmggYnIx1h3fBwF2rm4s+Sc/RpM9hx159KV5befkzHmM2NMlDEmKjw8PIdhlMqqzXVtmNnpK6qGXOcsm7FjBo8vepwTF6wk9ZsNB3l8yjpiL+o8C6VU0ZGXpOJWYL0xZmZ2Dey6tUDLggQlIiOAZ4ATWAnFLhfNou3XSi7qHBzPKolOV5bffkq5TZUSVZjR6Stuq3Sbs2zD8Q08+OODzNmygmnffMfSHcfpMuo3/j7qMrdVSqlCJy9JRSlgZy7a7QLC8hcOiMj7wAvAKeA2Y8y2bJo6liysIyLZLU3YOFPbgvRTyq2CfIMY0WoEzzV8Di97ZfiT8ScZsmEA94QN42Wfmew/Gcs9o3/jh02HPRytUkpdWl6SitNAtg8TS6eq3TbPRORdrMssp7ESik3ZtTXGHAA2YM3xeMDFWK2ASKzLJ6sL2k+py0FEeKzeY4xrP45Q/1AAUjF8UCqUf8qvpqfPj8QnpTBg5kaG/LiNpJQc12JTSimPyktSsQq4WUS6ZNdARDoBTYHf8hqIiAwBXgXOYCUUuTlLMMx+fc9+oJljrIj/b+++w6uq0vaPf59UCL1DpNehOjQRUEEBGyJgwYZjG+dVsY1OeZ2fZXQcRJ1xnNdRhBEEAVFQAcWCDQtFBQsqgvQiSm+BkHrW7499EtJJ2SfnJLk/13WuTdYueQ77ysmdvddeC3gm+OWEAkbFLO1+IiHRP7E/c0bMoXv9ztlt79VI4PU2G4iK97oTTVmymaue+5zdSSnhKlNEpEglmVDsNOBjvHk4ZgLTgc14T1G0BX6D11EzGhjknCt2sDCzC4EFwS9XAqsL2XStc25Cnn2fAW7GmxjsfY5PDFYbb9bUSwqZUKxU++WlETXFT2mZaTy+4jFe+vHl7LYo4jj680gyDvUGoFGteJ6+shentCn1XUYRkTLxZZhuM7sNeIKCr3AYXuD4vXPuPyUs7lrg+WJs+rFzbnAB+18JjAO644WatcBUYGJRVxtKu19OChUSCgs3LeSh5Q9xLOP4oK/pB/vQf3dLVmZ2IzmqBg+N7MpV/YrqbywiEhq+zf1hZj2BO/Ge8EjECxM78K5i/LuYty0qDYUKCZWNBzdy10d3senQpuy2Dqlp3L0LHjl2O3+54TIGtGsYxgpFpKqq0BOKRTKFCgml5PRkHlz+IG9tfiu7LSEQ4LbkuowdV+KuSyIivqjoE4qJVEkJsQlMOH0C9516H3HmzWqaHBXFozUP8+DyB0nJON5pc+ehFI3CKSJhpVAhEuHMjDGdxjBz+GxaJjTLbn9l3Stc9dZVbDq0iZ2HUhj+f5/y+5e/4WhqRhirFZGqrNDbH2Y2uQzHdc65/ynD/hWGbn9IeTqSdoQHlz/IO1veyW6rFl2NXx/uS9Md0czIPIe2jWry9JW96NysdhgrFZHKrMR9KsysLGM0OOdcdBn2rzAUKqS8OeeYu24uj37xKGmBtOz2C44c5ZRdbXgg7X9IjanFAyO6csUpLTDNqS4iPissVMQUsc+NIaxHREop63bIyY1O5o+f/JHNhzYDsLBmDb6O2wk7fiY1pQN/mfcdyzftY/zobtTStOoiUg709EcZ6UqFhFNyejLjP/sbCzYtPN7ooknZfS7p+wcCUbRqkMBTV/SkR/O6YatTRCoXPf0hUgklxCbw8OmPMP608SREV/MaLZNqTd6keotpWHQSO/Yd5uKJy3ju000EAvojQkRCp1ShwsxqmtlgM7vUzPr5XZSIlMyIdiOYe+GrdG3QNbstpuY66rT9F/+o+wcGuZU8/OYaPtu8L4xVikhlV6JQYWa1gk+F7AU+AF4C/ifH+pvNbJuZneJvmSJyIi1rt2TGeTO4rtt12W2ZMcnc16waHZpO4f9aL9YInCISUsUOFWaWAHwE/BY4DLyHN0R3Tu/iTRs+2qf6RKQEYqNjuav3XUwaNomG8cf7UMysU5vnG/3A+gPrw1idiFR2JblScTfQE5gNtHHOnZt3A+fcRmA9cJY/5YlIaQxIHMCroxYwqFn/7LYNR7Zz+cLLmbVmFgEXICklnVtmfcnmvUfDWKmIVCYlmfr8O6A+0M45lxJsCwDTnHPX59juXaCLc655COqNOHr6QyKZc445P77M4yv/QWpmanb7gMQBJO44hTfXxnMkriEPjOjCmD4a00JEisePpz/aAV9kBYoi7AV041YkApgZl/3qcl6+4GU61euU3b7s52UsCvyLv9S7lzMylvPnV7/j5plfceBoWhFHExEpWklCRToQX4ztmgNHSleOiIRCu7rteHH4i1zX9Tos2BUqKdq4r2ktaiW+SK2ovbyzeifn/vsTlqzfG+ZqRaSiKkmoWAf0NLNCg4WZ1QVOBr4va2Ei4q+46Dju6nMXU86ZQtP4etnt79SqRqDtc0QnbGTX4VTGTvmch974gZT0zDBWKyIVUUlCxatAE2B8Eds8DNQE5palKBEJnb5N+/LqRQsZ3nJYdltU7EESWj5HfOOFYOlMXbqZC/+zhB9+PhzGSkWkoilJqHgK+BG408w+NrPbg+2tzOzGYAfNm4HVwHM+1ykiPqodV5sJZz7B44Mep058Ha/RHHENllC7zZM8WvOvxOz+npFPK1iISPGVaO4PM2uBd8WiD+DwxqnIOoAB3wAjnXPbfa4zYunpD6nodifv5v5l97N0x9LsthjnuOFAEgnRY7nutof1VIiI5OLL3B/Oue3OuVOAC4FJeINdfQhMBy4D+lSlQCFSGTROaMzEIRO579T7qB7tdZnKMGNS/dq82ewrNh7cGOYKRaSiKDRUmNkrZnaeFfAninNuoXPuFufcuc65Yc65651zc51zgdCWKyKhkDWd+qsXzqNX/c7Z7euSf2LMwjFM+W4KGYEMUjMy+evrq9l1+ERPlotIVVTo7Y/gwFYO+AXvSsQ055zG+M1Dtz+ksskMZDJz9XT+75unSQscH7eiR8Me9Dh2Dm99mc7Bai14aGRXLjw5UbdGRKqgwm5/FBUqnsa7pVGf4/0mlgBTgbnOueQQ1VqhKFRIZbXx4EbuXXIv3+87/oR4bABuOnCYHftG8ELmOZzbLZGHR3WjQc3iDGEjIpVFiftUOOfGAYl4weJdIACcjhcqdprZf81sQIjqFZEwa1e3HTPOn8HtPW8nJioGgPQoeKpBbX5s+R7N4tfy9vc7Oftfn/D2d7+EuVoRiQQlmfsjEbgG+A2QNd6vwxsUayowwzm3MxRFRjJdqZCqYN2Bddy7+G7WJG3JbnOBaNL2DiVt3xlANBf0aMZDI7tRv0Zc2OoUkfJR4tsfJzhYf+B64FKgNl64yATexgsYC51zVWI4PoUKqSrSA+k8/+1/mbhqEhkc75OdeewkUn65mKjUxtSpkcDDo7pxXvdmYaxURELN11CR46DVgUuAa4HBOVbtcc41LfWBKxCFCqlq1h9Yz31L72P1vtXHG10UYw6kEbXvNKZmjODpsX05t5uChUhl5cs4FXk5544552Y454YA5+LNUGpAo7IcV0QiV4d6HZh5/kzu7HUncVHBWx0WYE79GFa0+oS/N/gHQzs3CW+RIhIWZQoVZlbTzG4ws0+BdzgeJjQAlkglFhMVww3db+CVC1+hZ6OTs9s3xsUxvvEB/vnl4ySn6wExkaqmVKHCzM40sxeAncBkYCCQhjeR2HlAG98qFJGI1aZOG6ad9wL39P0z1c17QsQBM9fMZNSCUSzZsYRAwPHb6St4ecU2ynK7VUQiX0me/miD9/THNUBLvNsc4M338Tww0zl3IBRFRjL1qRDx7Diyg78tf4ilPy/L1d4j4RT6f3+QZ1Mv5+T2LXhkdA9aNkgIU5Ui4odSddQ0swS8JzyuxRujwoKvA8CLwBTn3DehKLiiUKgQOc45x8JNC3lsxWMcTD2Y3V4nM5Mb96XzzoEb+Cb619x9dkeuHdCamOgy3YEVkTApzYiaU/ACRQ28IBEAPsB7ZHSecy6twB2rGIUKkfz2HdvHYyse463Nb+Vqr340kT2/XIlLb0iP5nWYcFEPuiTWDlOVIlJapQkVWQ+ibwamAc87534KWYUVlEKFSOE+/ekTHv70L/ycdii7zQViSNt7Fmn7ziA6KpbfndGWO4Z0oFpsdBgrFZGSKE2omAFMdc4tDnVxFZlChUjRktOTeWblE8xYP5dAjomMM1Mb02xnf6KPNSe1fif+Pqo7p3VoGMZKRaS4SjP3x9UKFCJSVgmxCfyh/73MHj6bLg26ZLdHx+9md6sF9Et8jJFJk/n4h61hrFJE/KBeUiJSLro06MKs82fx575/JiHm+NMf82vXYF7rb+nQ4ms9cipSwSlUiEi5iYmKYWyXsSwYtYCzmvTNbj8YHcXfvvs31y+6no0HNwKwOymFDbuPhKtUESmFMs39IepTIVIWH279gEeW3s/O9MPZbTFRMfymy2848G0iczYkcOOgjow7s706copEkJBMKCYKFSJllZyezLOrnmXGDzPIcBnZ7Y3TA/xmXxTzD17H/vo9eWhkNwZ11LRCIpEgJBOKiYiUVUJsAnf1uYs5I+bQq3Gv7PbdsVH8oynUa/lffjm8mWumfsG4WV+x81BKGKsVkaLoSkUZ6UqFiH8CLsDrG1/nieV/50DgeHhwgRjS9g0ibd9gasRW4/fDNCKnSDjpSoWIRLwoi2JU+1G8MeZ9xrQ+P3uCIYvKIL7RB9Ro+wQpcd8x8c3lXPDUElZs2R/WekUkN4UKEYk4deLrcN+gR3lx+Gy6Nuia3R4Vd4CEFi/Qp9WDjDg0gd89u4g1vxwu4kgiUp4UKkQkYnVr2I1Z58/i/v73Uye+Tnb7soR4prTaxvAWT9KqYUwYKxSRnBQqRCSiRUdFc2nHS1k4aiGXth+dfUsk3YwFNZMZMX8Eb216K3vgrMMp6eErVqSKU0fNMlJHTZHytXrfah756M+sOpJ7WO9ejXtxR88/cs/UjXRp14p7zvsVjWtXC1OVIpWbxqkIEYUKkfIXcAEWblrIEyufYF/KvlzrRh9OJmb36cyzi7hpSFeuG9iGuBhdlBXxk0JFiChUiITPkbQjTPp2EjPXzCQjcHzgrFqZAXrvb8Ybe2+nbaPaPDCiqwbOEvGRQkWIKFSIhN/mQ5t5dNlDLN2d+2cxM7URqbsuIPNoJ4Z2bsy9w7vQumGNMFUpUnkoVISIQoVIZHDO8cm2xTy29H62pR/KtS7jSCdSd51Hw8xaXHRaD249qz014/XUiEhpKVSEiEKFSGRJz0xn1ppZTPp2EkfSj89yas64+HAyaXuG8HW9y1h455lERVkRRxKRwmhETRGpEmKjY7m227W8MfoNLu5wMRZ8CNWZ45U61fmozacMbPw8mTkmLxMRfyhUiEil1LB6Q/464K/MGTGHvvWPj8p5ODqalzK/YfTro/lw24fZ41scTE4LV6kilYZuf5SRbn+IRD7nHB9ueZd/Ln+I7em5h/Xu06QPoxKv4fG5vzDytJ7cPFj9LURORH0qQkShQqTiSMtMY/ba2UxaNYmk9KTjKxycf+QYCXv6817s5dx2Tncu6d2CaPW5ECmQQkWIKFSIVDwHUg7w7KpnefnHl8l0mdnt8YEATQ905Pu9Y+ncpDH3Du/MwPYNw1ipSGSK+I6aZtbJzO4ws5lmttbMAmbmzOySYux7pZl9amaHzOyIma00s3FmVuT7K+1+IlKx1atWj3v63cO8kfMY3KhXdntqVBRbG2ygRrvH2ZCyiKueW8YN01awYfeRIo4mIlki5kqFmT0J3FHAqkudc68Usd/TwC1ACvABkA4MAWoB84L7Z/q1X166UiFS8a3Y8Rn/WHIvP6TsytUeSG1I9T0DaZh8En36nsadQzvSsGZ8mKoUiRwRf6UC+B54HLgMaA98fKIdzOxivGCwE+jhnLvAOTca6ACsAUYDt/q1n4hUTn1POpXZY95lwukTaFajWXZ7VPxeUpsvoEHLf1H3+z/wj1cWh7FKkcgXMaHCOfecc+5Pzrk5zrmNxdztnuDyz8659TmOtQu4Ofjl/xZwO6O0+4lIJRVlUQxvO5w3Rr/B3b3vplZcrex131aLZ3qLn9lbZzobDxb340mk6qmwvzTNrDnQG0gD5uZd75z7GNgBNAVOLet+IlI1xEfHc223a3lr9Ftc3WYEOR8u/fzw91z0+kU8sOwBdh7dSUp6Jp+s20Ok3EYWCbcKGyqAnsHlaufcsUK2WZFn27LsJyJVSN1qdfnTGeN546K3Gd6ob3Z7wAV4bf1rXDDvAu58dRxzXniEq59bxnc/HSriaCJVQ0UOFW2Cy61FbLMtz7Zl2U9EqqDmtZoz4fypzLlgDgMSB2S3p2amsjR1KV+1XUTXpJv40zNTufXFr9i672gYqxUJr4ocKmoGl0X9BGc9B1YrR1tp98tmZr8LPn66cs+ePScsVEQqvs4NOjNp2CQmD5tMlwZdstuToqN4sQHsaPsyi7bNZ8g/P+SBBd+zJyk1jNWKhEdFDhVZQ92V9GZmaffL5pyb7Jzr45zr06hRo9IeRkQqoP6J/Zk9fDaP93+IljE1s9td7FGqNZtHfJt/Mmv1AgY9/gFPvPsjSSnpYaxWpHxV5FCRNcZuzSK2yVqXYzzeUu8nIgJ4T4qc23E086/4hPt+fQeNqjU4vi5uH9VPeok6J/2dtC9v4srHZvPyim1FHE2k8qjIoWJLcNmqiG1a5Nm2LPuJiOQSGxXLmJN/y5sXv82dve7M9RjqkWqHmZW4l9pNHmbvlulhrFKk/FTkUPF1cNnVzKoXsk3fPNuWZT8RkQJVj6nODd1v4J2L3+HG7jdSLSo2e9231eJ5NnkON757I6v2rMpu12OoUhlV2FDhnNsOfAXEAZfmXW9mg4DmeKNmLi/rfiIiJ1I7rja397qdty95l6uaDyE2R2747JfPGPvWWG794Fbe/H4JVzz1Lh9rjAupZCpsqAh6JLh81MzaZzWaWWPgmeCXE5xzAZ/2ExE5oYbVG/K/Q57kzYsXMbrdKKItOnvdxz99zP9+eTONom9j0ew7+c3ExXyxeX8YqxXxTyRNKNaL47/QAbrgPdK5Hsj+iXPOnZpnv2fwhtZOAd7n+MRgtYH5wCWFTChWqv3y0oRiInIiWw5tYeKqiby9+W1cjgfPzDkaJ53Exj1XcEbrLtx9dkd6NK8bxkpFiqewCcUiKVQMBk44W49zzvK2mdmVwDigOxANrAWmAhOLutpQ2v1yUqgQkeJaf2A9T382ng925/7McM7IONST1L1nMaxDV34/rCOdm9UOU5UiJxbxoaKiUqgQkZJavXsVzyy5n0+SNuVqdy6KuEOdGXSgDoH213Hb2V1p37jAMfhEwqoiTH0uIlIldG18Mk9ftICZ58+kf7P+2e1mAdLrruaj1kuJO3Ats1/9vzBWKVJyChUiImFycqOTmXz2ZKafO51+Tftlt2eY8U7tWF5NmMNfl/2Vn5J+CmOVIsWn2x9lpNsfIuKXlT8t5ZllD7Hi2M+52mMshgvbX8jVna/nxU8Pct1pHWhRPyFMVYqoT0XIKFSIiN9WbP+Eid8+y4q93+VqjyKKIUlpuH1nkNDlRm4a0kXhQsJCoSJEFCpEJFRW7FzBxFUTWbFzRa72KOfolFSXr/feyEXdezLuzPa0bKBwIeVHoSJEFCpEJNRW7FzBpK+e4vM9uWcOcM7IONydjP1DGN21N7ee1Z5WDWqEqUqpShQqQkShQkTKy1c7lvLssr+xPHlHvnUZh7sw5GBNana4gd8N6UHbRkVNxCxSNgoVIaJQISLlbdWeVUxaNYlPd3yab12/5DQaHO7P3+6eSlyMHvCT0NA4FSIilcTJjU7mmaHP8NLwlzizxZm51n2eEMdbTb/kpg9+y/Kfl2vCMilXulJRRrpSISLh9uPeH3huyf0sOrgWZ7lnMujesDu/7f5bNmxowikdTuLXLTS3iJSdbn+EiEKFiESKzfs3MOXLJ1j4yzIy88yH2Dotk+77EzlW9yYuH3Ym/do2CFOVUhkoVISIQoWIRJodR3bw/PfPM2/9PNICabnWNUl3bN07ih51h3HbmZ0Z1LERZvnmaRQpkkJFiChUiEik2pO8hxd+eIGXV7/AMXJPvBzIqEn6/tNoX20Ytw3uzjldmxIVpXAhxaNQESIKFSIS6Q6lHOTFzx5l5ta3OUzu2yIuM57OhxrTPKM/AwZfw8iezfXUiJyQQkWIKFSISEWRnJ7MK+te4fnvp7M3ZXeudXEBxxlJxrmDn+WcHgPDVKFUFAoVIaJQISIVTXpmOgs3LeS/305h+5GtudYZxtBWQ7m+2/V0a9gtTBVKpFOoCBGFChGpqAIuwOK1c/nvl0+xOvNQvvV9m/alW+BUMo915aqzepFYt3oYqpRIpFARIgoVIlLROedYufVDpqyfy9Kfl+Zb3y4tnY4HWlI98W7GDhtAhya1wlClRBKFihBRqBCRyuTH/T8y9fupLNqyKN9YF1HpNUjefwYDGg9n3KDu9G1dT4+jVlEKFSGiUCEildHPR37mhc8f57Xt73MsT25wmfGkHzyFjtXOYdzpfRjWNZFoPY5apShUhIhChYhUZodSDjLnswlM3/EphzIO51pnzjjtSCa1UwYzYPDdXNinbZiqlPKmUBEiChUiUhWkZqby5qY3+e+qqfx0dGu+9R1dfW4f8hCnNz+dKNM4F5WdQkWIKFSISFUScAGW7FjC5C+fYdXB1fnWt67dmqu7XM2IdiNISjYa164Whiol1BQqQkShQkSqqtU7Puf55eN57+hmAuT+XVIrtha9dkGjhDGcN+xq+rapr06dlYhCRYgoVIhIVbfz6E5mrZnFq+teJSk9Kde6GOfonlSdXdG/Z9zAwZzXrSmx0bo9UtEpVISIQoWIiOdo+lHmb5jPjB9msOPIjnzrM462oWbqmdzQazhXnNKGOtVjw1Cl+EGhIkQUKkREcssMZLJ49Sye/2YS3wYO51sfSKtHt8PNOPWki7ho2AW0alAjDFVKWShUhIhChYhI4Vbv+ob/rp7Fh9vfw+WZIbV6IMApSfFcdu4kTu/YN0wVSmkoVISIQoWIyIntOrqLWWtm89LauRzLzH/1YuBJAxnbeSwDEgfokdQKQKEiRBQqRESKLyUjhYVf/ofpa15ii6XmW9+6dmt+Hd2H5q43o88aSuNaeiQ1EilUhIhChYhIyTnn+HzDG8zauoiPd3yKy/NIao1AgD6HE6hb90YuG3IZ3ZvXCVOlUhCFihBRqBARKZtth7cxe+1s5m+Yz5H0I/nWZxzpSMuYsxl36nDO65aoR1IjgEJFiChUiIj442j6UeZ9PZkXV89ge1R6vvWBtPpUTx7ITW36Meqsc2lYMz4MVQooVISMQoWIiL8CLsBnP77G5DXz+PLwd5Dn1ki1QIDeR+L5Vf3LufOqP4WnyCpOoSJEFCpEREJne9J2nv92Fgs2zifNHc23vmfjnlzW6TKGtRpGXHRcGCqsmhQqQkShQkQk9I5lHOP1H+fz4hf/ZFNU/qdG6lerz8UdLqbeoQ4M7TmIZnUTwlBl1aFQESIKFSIi5cc5xzebFjHtm6l8kryejEBGrvVRztEz2WgTdTpDzrqXgR2aaSKzEFCoCBGFChGR8Nh7bC+vrX+NOT/OYVfyrnzrA2n1qZ1+Br/pfglj+3ahVjXNNeIXhYoQUagQEQmvjEAGH//0Mc9/Mp5VmbvzrXeBaNzRHgxtOISbThtO5+YNw1Bl5aJQESIKFSIikWPLrlVM+3Q8rx/dQjrJ+da3Scukc2p7Rg16gP7de4ehwspBoSJEFCpERCLPsYxjzF+3kKnfzmZn6vp86+Mtjgvaj+DSjpfStWHXMFRYsSlUhIhChYhIZFu9dzWTlzzJsgPLSYnK32mzc/3OXNBmNI2PtmVon77EaMTOE1KoCBGFChGRiiHp2H7mLnmU1/auZGta/r4X1QMBeh6tQddGlzHm3HE0raPJzAqjUBEiChUiIhWLc45Ve1Yxd91cFm1ZRGpm/nEvAimJtKs2lJv6XMI5nVsTXcAVjqpMoSJEFCpERCquQ6mHmLduPnNWPMn26Ix8610glriUXlzWbADXDBpD03o1w1Bl5FGoCBGFChGRis85xxdr5zP9q6ksSd+Bs/wTmrVOy6RbRid+O+oJ2jVrE4YqI4dCRYgoVIiIVC6HUg8x7dvXmPvjXA5lbs+3Pi4qjqGthnJxh4vp07QPUVb1OnYqVISIQoWISOXknGPlzm94/qPxrEhZU+CTIy1qtaB/nYH0iu/JOf3PrTJPjihUhIhChYhI5Xfk2H5mL36Ed1LWsS5pU771Uc7R41gMHeqOZOzQu2nbqHYYqiw/ChUholAhIlK1rN2/ltfWv8bCTQtJSkvKtz6QUZPGNoCrul7K2F59qRYbHYYqQ0uhIkQUKkREqqaUjBTmfTuH1796iu9jUwreKLUVF8Y245IBd9KzU+UZuVOhIkQUKkREZNPPXzLp82m8d+gb0u1gvvXVAgFOTqnNjRc+Sd/EvhW+c6dCRYgoVIiISJaMQAZvrv+IKateZnPyCrDMfNucVPMkRrYfych2I0msmRiGKstOoSJEFCpERKQge5P3Mf3dv7J47ydsjQ3kW28Y7ewkTqUllwy5h3YntS7/IktJoSJEFCpERKQozjm++OEN3ju0ire2vl1g584agQBNMrpyVucb+N0pQ6geFxOGSotPoSJEFCpERKS4UjNA/fjfAAAQbElEQVRTWbxtMfM3zmfZjmU4CvgdnN6ATjXP5Mael3J2x86YRd68IwoVIaJQISIipbFt1xpmfPh3lhxdxU+xBW/TOSWKXjX6cflZ99A6MXKGBleoKISZXQncDPQAooG1wPPAROdc/ptgeShUiIhIWTjn+HDDEiatms/apE9xUcfybRMfgGHtL2BEuxH0a9qP6Kjwjn2hUFEAM3sauAVIAT4A0oEhQC1gHnCpcy5/190cFCpERMQvx9KPMfXrN3l13Xz2ZqzCFXDno3H1xgxvO5yBDU7nlFa9sajyfzxVoSIPM7sYeAXYCZzhnFsfbG8CLAY6A3c65/5d1HEUKkREJBS2/bKaGYsfZVnyKrYV8PQIQJs06BXXjYvP+Avd23Qvt9oUKvIws5VAb+Aa59wLedYNAj7CCxwnFXUbRKFCRERCyTnH2v1reX3j67y1+S32p+wvYCOjRqALw1qez22njqJxzdDOPaJQkYOZNQe2A2lAXedcvhtYZvYTcBIw0Dm3rLBjKVSIiEh5SQ+ks/zn5Uxd8hTfHVtDWgEzp7pAHInRvbi6UQfGnHUb8fHVfa+jsFBRsccJLb2eweXqggJF0Io824qIiIRVbFQsZzQ/g2mXz+WdkW9zXfUzaJLZLNc2FpXGL+4zHts9g3Nm9uGuFy5izb41lMdFhKoaKrKey9laxDbb8mwrIiISMRrVb8FdY57m/evf5cVzXqd/vbHEZDbJtc2+mCjec+u54s0rOJB6IOQ1VdVQUTO4PFrENkeCy1p5V5jZ78xspZmt3LNnj+/FiYiIlET3pm2YfOGf+eq695jQ7zmGZCRSL+N4d8BTE0+lfrX6Ia8jsscBDZ2sm1CluhbknJsMTAavT4VfRYmIiJSFmTH8V/0Y/qtFpKYdY/6yKXwTvYMzW5xZLt+/qoaKrIHXaxaxTda6/IO0i4iIRLj4uOpcNvhWLivH71lVb39sCS5bFbFNizzbioiISBGqaqj4OrjsamaFPWvTN8+2IiIiUoQqGSqcc9uBr4A44NK864ODXzXHG/xqeflWJyIiUjFVyVAR9Ehw+aiZtc9qNLPGwDPBLycUZ1IxERERqbodNXHOvWJmE/FmKP3OzN7n+IRitYH5wH/CWKKIiEiFUmVDBYBz7hYzWwKMAwZxfOrzqRRz6nMRERHxVOlQAeCcexF4Mdx1iIiIVHRVuU+FiIiI+EihQkRERHyhUCEiIiK+UKgQERERXyhUiIiIiC/MOU2yWRZmtgfY6uMhGwJ7fTye+EPnJfLonEQmnZfIE4pz0so51yhvo0JFhDGzlc65PuGuQ3LTeYk8OieRSecl8pTnOdHtDxEREfGFQoWIiIj4QqEi8kwOdwFSIJ2XyKNzEpl0XiJPuZ0T9akQERERX+hKhYiIiPhCoSKEzOxKM/vUzA6Z2REzW2lm48ys2P/vZhZrZkPM7J9m9pmZ/WJmaWa2w8xeMbPBIXwLlZIf56WIY483Mxd8/cGPeqsCv8+JmVU3sz+Z2QozO2hmyWa22czmmtlAv+uvrPw8L2bW3MyeMrMfzeyYmaWY2Xoze9bM2oai/srEzDqZ2R1mNtPM1ppZIPg5c0kZj+vv56FzTq8QvICnAQccAxYC84DDwbbXgOhiHmdocB8H/BI81svAdznaHwr3+60oL7/OSyHH7gtkAIHg8f4Q7vdbEV5+nxOgDbA+uP8uYAEwB/gCSAPuDfd7rggvP88L0BM4ENx3OzA/+Pop2JYEDAj3e47kF/Bkjs/8nK9LIuEcZx8z3P9RlfEFXJwjBHTI0d4E+CG47o5iHuss4BXg9ALWXRb8JeaAM8P9viP95ed5KeDY8cBqYEfwB1OhIgznBKgBbMgK20BsnvUNgI7hft+R/grBeVkW3GdyznMCxAJTgutWhft9R/IL+C3wGDAGaAd8VJZQEarPw7D/R1XGF7AyeEJ+U8C6QTlOZJQP3+u54PGmhPt9R/orlOcFeDS4/whgmkJFeM4J8Ehwn+nhfm8V+eXneQGqcfyv6qYFrE/MsT4h3O+9orx8CBUh+TxUnwqfmVlzoDfeZda5edc75z7G+2u2KXCqD9/y6+CyuQ/HqrRCeV7MrB9wN/Cic+6NsldbNfh9TswsDrgx+OUE/yqtWkLws5KJd0UVwApYn/UI4lG8y/ASYqH8PFSo8F/P4HK1c66wH5AVebYtiw7B5S8+HKsyC8l5MbNqwHRgP3BH6curkvw+J73xbm9sd86tMbMBwY6zk8zsQTPrX9aCqwhfz4tzLh34IPjlg2YWm7Uu+O+Hg19OccE/kyXkQvZ7KqbUJUlh2gSXRU0yti3PtqViZk2Ba4NfvlqWY1UBoTovfwc6AZc75zSJUsn4fU66B5frzWwacE2e9feb2avA1UV8kEpoflZuAd7Bu5J0npmtDLb3BeoB/wb+WMI6pfRC9ntKocJ/NYPLo0VscyS4rFXab2JmMcBMoA7wgS67n5Dv58XMBgB3AvOdcy+Xobaqyu9zUj+4PAOIBv4BPAvsC7Y9g9c57TBwfUmLrUJ8/1lxzm0K/ry8AJxH7tu1K4FPglc0pHyE7PeUbn/4L+ueYagv4z0LDMF7PGtsiL9XZeDreTGz6sDzeL+gbvHjmFWQ3z8rWZ9nMXiX0v/onNvonDvonHsdGBX8XtdoXIQi+f4ZFgwU3wPtgZF4U3E3wjsn9YBXzex+v76fnFDIfk8pVPgvKbisWcQ2WeuSitimUGb2b+AGYCcwxDm3szTHqWL8Pi/jgY7AXc459WcpHb/PSc5t/pt3pXNuJfAl3ufe4GIcr6ry9byYWV28MSlqAec65153zu1zzu11zi0AzsXroHmfmXUo6ljim5D9nlKo8N+W4LJVEdu0yLNtsZnZP4HbgT14gWJ9SY9RRW0JLv06L6PxBrm6xsw+yvnC+5AEuDnY9lwp6q0KtgSXfp2TnNtsLmSbrPamxTheVbUluPTrvAzHuyrxmXNuU96VzrkNwOd4V5gGF7dIKZMtwaXvv6fUp8J/WY94djWz6oV0COubZ9tiMbPHgLvw7hEPc879UPoyq5xQnJcovOe5C9M2+KpbzONVNX6fk69y/LsBXvDOq2FweaSAdeLx+7y0DC4PFbHNweCyfhHbiH9C9ntKVyp85pzbjvfhFgdcmne9mQ3C66S0E1he3OOa2QS83tEH8ALFKl8KriL8Pi/OudbOOSvohfeIKcAfg22/9u+dVB4hOCc78P7iBa+/Ud7j1QN6Bb9cmXe9eELwGfZzcNk75+OkOY4Xi/c4MBR+hUl8FKrfU1kH18v/kc4u4fhoZO1ztDfGG8o53/CneCMBrgUeKeB4fwvucwDoHe73V1Fffp+XIr7PNDSiZljOCd6Ipg5vzo9f52ivBrwUXLcSsHC/90h++XlegvscDe7zHyA+x7p4YGJw3X6gTrjfe0V5UYwRNU/ws1Lic1ycl25/hIBz7hUzmwjcDHxnZu8D6Xh/PdXG67T0nzy7NcMb76BZzkYzuxC4N/jlBuA2s4IGpWOtc06jCBbBz/Mi/vD7nDjn3jCzfwB/AD43s8/xbheegjcc9A7gChf89JSC+XlenHO7zewWvDk+xgGjzexLvCcQege3TwWud84VdYukSjOzXniPRWfpElyOzzkjsnMu5wiYRf2slOYcn5BCRYg4524xsyV4P0SD8J6bXwtMBSY65wLFPFTOe4x9gq+CfIyGJj4hH8+L+MTvc+Kc+6OZLQNuwxsNMAFvIJ8ngAnOuYL6Wkgefp4X59x0M/sOb1yX04Gzg6t24IWNJ5z6iJ1IbaBfAe2lfmImFJ+HpsAuIiIiflBHTREREfGFQoWIiIj4QqFCREREfKFQISIiIr5QqBARERFfKFSIiIiILxQqRERExBcKFSIiIuILhQqRSsbMtpiZO8FrVHDbocGv3w9zzQ8H67i3iG1izeyAma3L0fZTcL/TyquOIvadGdx3rE+1ZL235n4cT6Q8aJhukcprEd4sgwXZVp6F+OQsvGnkJ5f3NzazocB7wAfOuaHl/f1FKgqFCpHKa4Jz7qMTbLMM6Iw3i2Skuyi4fC2E3+NJYCZQmvlB/gg8zPGpvkWqHIUKkSrMOZeMN4FQRDOzKGAk3gRUX4Tq+zjn9gJ7S7nvL3jTSItUWepTIVKFFdanwszaB9s3mOdWM1tlZseC/Rrmm1mXQo55tpk9E9x+n5mlmtlWM5tmZr8qZakDgSbA/OJMW56zf4OZdTSz2Wa2O1jLGjP7QzCo5N0vX5+K4CyO7wW/HJKnb8r7BX3PPMesbWb/Y2YLzGyjmSWbWZKZfWVm95hZtVL+n4hEHF2pEJGiGDADuAT4BFgP9MW7ajDIzH7tnNuaZ5/JQFNgNfAx3h8v3YBrgEvMbJhzbnkJ6xgdXJb01kdvYCJe35IP8YLJacDjwEnA74txjLfwbg+djXcl4t0c61YXY/9ewLPALmAdsAJogDeN9XhghJmd6ZxLLcaxRCKaQoWIFKUt4IDOzrnNAMG/rOcD5wD/C9ycZ587gcXOuUNZDWZmwe2eBiYBPUpYx2hgP16wKYk7gfuAv2dd4TCzs4D3gdvM7HHnXJF9IJxz483sC7xQ8YNz7toS1rAJr5Ppx865QFajmdUDXgaGAbcC/yzhcUUijm5/iFReiwt5nHRaCY9za1agAHDOpQAPBb8ckndj59z8nIEi2Oacc8/g9YfobmadivvNzawX0Bp43TmXUcLaPyNHoAjW8iFeqIgGBpfweCXmnNvmnFucM1AE2w8AdwS/vCTUdYiUB12pEKm8CnukdEkJjpHG8f4EOWV17kwsaCczawmcD3QCauP9AgdoFFx2BH4sZg1ZT33MK+b2Ob1ZSB+MtXhXCAqs32/BKzWnAacDzYHqeLeWsv6w61gedYiEmkKFSOVVnEdKT2SHcy6zgPbDwWW+ToZm9jDebZHovOtyqF2CGi4CjpC7L0NxFTYeR6H1+83MmuEFon5FbFaS/w+RiKXbHyJSlMCJNznOzC4D/h9ex8Yb8PpkVHfOmXPOgLlZmxbzeJ3wxtF4O3jbpaRKVH+ITMULFJ/i3S5qDMQF/z9qBLcp1v+HSKTTlQoR8dOlweWfnXNTC1jfvoTHK8utj7Azs9p4HVozgOHOuaQ8m5T0/0MkoulKhYj4qX5wuT3vCjPrRsmf+rgIr1/Hm2Wsq6zSgsuS/iFWF+8qxMECAgXAVWWqSiTCKFSIiJ+yOnDeaGaxWY1m1gSYRtH9LHIxsxZAH7z5Ng6faPsQ2xFcdjCzYr8HvHEtDgMNzWxMzhVmNpzjT3+IVAoKFSLip3/h/RIdCWwwszlmthDYCMQDr5fgWOUx10exOOc2At/iPS3yrZm9YGbPmdldJ9gvHW+AK4CXzWypmb0YHPdiIRqbQioZhQoR8Y1zbj3eCJJz8D5fLgR+hTeq5UCgoFsAhbkIr6PlAp/LLK1RwCtAQ7zbFjfgPTZbJOfco8AY4HO8kUWH491OuRJ4IFTFioSDFWMYfRGRcmVmjfBuHSx1zg0Kdz0iUjx6+kNEIlEDvGnESzost4iEka5UiIiIiC/Up0JERER8oVAhIiIivlCoEBEREV8oVIiIiIgvFCpERETEFwoVIiIi4guFChEREfHF/wd77KFhfgai0QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y_0 = 0\n",
"v_0 = 0\n",
"m_0 = 0.25\n",
"dmdt = 0.05\n",
"u = 250\n",
"m_1 = 0.05\n",
"N = 100\n",
"\n",
"T = (m_0-m_1)/dmdt\n",
"t_heun = np.linspace(0, T, N)\n",
"t_eul = np.linspace(0, T, N)\n",
"num_heun = np.zeros([N,3])\n",
"num_eul = np.zeros([N,3])\n",
"dt_heun = T/N\n",
"dt_eul = T/N\n",
"\n",
"num_heun[0,0] = y_0\n",
"num_heun[0,1] = v_0\n",
"num_heun[0,2] = m_0\n",
"num_eul[0,0] = y_0\n",
"num_eul[0,1] = v_0\n",
"num_eul[0,2] = m_0\n",
"\n",
"for i in range(N-1):\n",
" num_heun[i+1] = heun_step(num_heun[i], simplerocket, dt_heun)\n",
" num_eul[i+1] = eulerstep(num_eul[i], simplerocket, dt_eul)\n",
"\n",
"dt_ts = T/N\n",
"t = np.linspace(0,T,N)\n",
"m_teq = m_0-dmdt*t\n",
"m_3 = m_teq/m_0\n",
"v_teq = np.log(m_3)*(-u)\n",
"\n",
"fig = plt.figure(figsize=(8,6))\n",
"plt.plot(m_3,v_teq,'--',label='Tsiolkovsky')\n",
"plt.plot(m_3, num_heun[:, 1],':', label='Heun')\n",
"plt.plot(m_3,num_eul[:,1],'-',label='Euler')\n",
"plt.legend()\n",
"plt.xlabel('Final/Initial')\n",
"plt.ylabel('Velocity')\n",
"plt.title('Velocity vs MR');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. You should have a converged solution for integrating `simplerocket`. Now, create a more relastic function, `rocket` that incorporates gravity and drag and returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (1). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \n",
"\\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt}-g-\\frac{c}{m}v^2 \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `rocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s, . \n",
"\n",
"Compare solutions between the `simplerocket` and `rocket` integration, what is the height reached when the mass reaches $m_{f} = 0.05~kg?$\n"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state,dmdt=0.05, u=250,c=0.18e-3):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" x = -dmdt\n",
" y = state[1]\n",
" z = u/state[2]*dmdt-g-c/state[2]*state[1]**2\n",
" derivs = np.array([y,z,x])\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"g = 9.81\n",
"N = 100\n",
"\n",
"t_heun_2 = np.linspace(0, T, N)\n",
"t_eul_2 = np.linspace(0, T, N)\n",
"num_heun_2 = np.zeros([N,3])\n",
"num_eul_2 = np.zeros([N,3])\n",
"dt_heun_2 = T/N\n",
"dt_eul_2 = T/N\n",
"\n",
"num_heun_2[0,0] = y_0\n",
"num_heun_2[0,1] = v_0\n",
"num_heun_2[0,2] = m_0\n",
"num_eul_2[0,0] = y_0\n",
"num_eul_2[0,1] = v_0\n",
"num_eul_2[0,2] = m_0\n",
"\n",
"for i in range(N-1):\n",
" num_heun_2[i+1] = heun_step(num_heun_2[i], rocket, dt_heun_2)\n",
" num_eul_2[i+1] = eulerstep(num_eul_2[i], rocket, dt_eul_2)\n",
"\n",
"fig = plt.figure(figsize=(8,6))\n",
"plt.plot(m_3,v_teq,'--',label='Tsiolkovsky')\n",
"plt.plot(m_3, num_heun_2[:, 1],':', label='Heun')\n",
"plt.plot(m_3,num_eul_2[:,1],'-',label='Euler')\n",
"plt.legend()\n",
"plt.xlabel('Final/Initial')\n",
"plt.ylabel('Velocity')\n",
"plt.title('Velocity vs MR');"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(8,6))\n",
"plt.plot(m_3,num_eul_2[:,0],label='Euler with Drag')\n",
"plt.plot(m_3, num_heun_2[:, 0], linestyle='--', label='Heun with Drag')\n",
"plt.plot(m_3,num_eul[:,0],label='Euler NO Drag')\n",
"plt.plot(m_3, num_heun[:, 0], linestyle='--', label='Heun NO Drag')\n",
"plt.legend()\n",
"plt.xlabel('Final/Initial')\n",
"plt.ylabel('Height (m)')\n",
"plt.title('Height vs MR');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. Solve for the mass change rate that results in detonation at a height of 300 meters. Create a function `f_dm` that returns the final height of the firework when it reaches $m_{f}=0.05~kg$. The inputs should be \n",
"\n",
"$f_{m}= f_{m}(\\frac{dm}{dt},~parameters)$\n",
"\n",
"where $\\frac{dm}{dt}$ is the variable we are using to find a root and $parameters$ are the known values, `m0=0.25, c=0.18e-3, u=250`. When $f_{m}(\\frac{dm}{dt}) = 0$, we have found the correct root. \n",
"\n",
"Plot the height as a function of time and use a star to denote detonation at the correct height with a `'*'`-marker\n",
"\n",
"Approach the solution in two steps, use the incremental search [`incsearch`](../notebooks/04_Getting_to_the_root.ipynb) with 5-10 sub-intervals _we want to limit the number of times we call the function_. Then, use the modified secant method to find the true root of the function.\n",
"\n",
"a. Use the incremental search to find the two closest mass change rates within the interval $\\frac{dm}{dt}=0.05-0.4~kg/s.$\n",
"\n",
"b. Use the modified secant method to find the root of the function $f_{m}$.\n",
"\n",
"c. Plot your solution for the height as a function of time and indicate the detonation with a `*`-marker."
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [],
"source": [
"def f_m(dmdt,m0=0.25, c=0.18e-3, u=250):\n",
" ''' define a function f_m(dmdt) that returns \n",
" height_desired-height_predicted[-1]\n",
" here, the time span is based upon the value of dmdt\n",
" \n",
" arguments:\n",
" ---------\n",
" dmdt: the unknown mass change rate\n",
" m0: the known initial mass\n",
" c: the known drag in kg/m\n",
" u: the known speed of the propellent\n",
" \n",
" returns:\n",
" --------\n",
" error: the difference between height_desired and height_predicted[-1]\n",
" when f_m(dmdt)= 0, the correct mass change rate was chosen\n",
" '''\n",
" N = 100\n",
" m_1 = 0.05\n",
" height = 300\n",
" T = (m_0-m_1)/dmdt\n",
" dt = T/N\n",
" y_0 = 0\n",
" v_0 = 0\n",
" t=np.linspace(0,T,N)\n",
" num_heun_3 = np.zeros([N,3])\n",
" num_heun_3[0,0] = y_0\n",
" num_heun_3[0,1] = v_0\n",
" num_heun_3[0,2] = m_0\n",
" \n",
" for i in range(N-1):\n",
" num_heun_3[i+1] = heun_step(num_heun_3[i], rocket, dt)\n",
" \n",
" height_2 = num_heun_3[N-1,0]\n",
" error = height_2 - height\n",
" return error\n",
"\n",
"def incsearch(func,xmin,xmax,ns=50):\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.zeros(ns)\n",
" for i in range(ns):\n",
" f[i]=func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb\n",
"\n",
"\n",
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n",
" iter = 0;\n",
" xr=x0\n",
" for iter in range(0,maxit):\n",
" xrold = xr;\n",
" dfunc=(func(xr+dx)-func(xr))/dx;\n",
" xr = xr - func(xr)/dfunc;\n",
" if xr != 0:\n",
" ea = abs((xr - xrold)/xr) * 100;\n",
" else:\n",
" ea = abs((xr - xrold)/1) * 100;\n",
" if ea <= es:\n",
" break\n",
" return xr,[func(xr),ea,iter]"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"[[0.06428571]\n",
" [0.05714286]]\n"
]
}
],
"source": [
"min = 0.05\n",
"max = 0.4\n",
"rate = incsearch(lambda dmdt:f_m(dmdt,0.25, c=0.18e-3, u=250),min,max)\n",
"print(rate)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.05817733476096621 is equal to optimal mass flow rate\n",
"-1.0201750910709961e-06 is the error\n"
]
}
],
"source": [
"actual,out = mod_secant(f_m,0.01,min,es=0.000001)\n",
"print(actual, 'is equal to optimal mass flow rate')\n",
"print(f_m(actual), 'is the error')"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"actual = 0.05817733405\n",
"T = (m_0-m_1)/actual\n",
"\n",
"t_heun_3 = np.linspace(0, T, N)\n",
"t_eul_3 = np.linspace(0, T, N)\n",
"num_heun_3 = np.zeros([N,3])\n",
"num_eul_3 = np.zeros([N,3])\n",
"dt_heun_3 = T/N\n",
"dt_eul_3 = T/N\n",
"\n",
"num_heun_3[0,0] = y_0\n",
"num_heun_3[0,1] = v_0\n",
"num_heun_3[0,2] = m_0\n",
"num_eul_3[0,0] = y_0\n",
"num_eul_3[0,1] = v_0\n",
"num_eul_3[0,2] = m_0\n",
"\n",
"for i in range(N-1):\n",
" num_heun_3[i+1] = heun_step(num_heun_3[i], rocket, dt_heun_3)\n",
" num_eul_3[i+1] = eulerstep(num_eul_3[i], rocket, dt_eul_3)\n",
"\n",
" \n",
"fig = plt.figure(figsize=(8,6))\n",
"plt.plot(t_heun_3,num_eul_3[:,0],'-',label='Euler with drag')\n",
"plt.plot(t_eul_3, num_heun_3[:, 0], linewidth=2, linestyle='--', label='Heun with drag')\n",
"plt.plot(t_heun_3[99],num_heun_3[99,0],'*', label='Heun Detonation')\n",
"plt.plot(t_eul_3[99],num_eul_3[99,0],'*', label='Euler Detonation')\n",
"plt.legend();\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Position (m)')\n",
"plt.title('Height vs Time');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Math 24 _Rocket Motion_. <https://www.math24.net/rocket-motion/\\>\n",
"\n",
"2. Kasdin and Paley. _Engineering Dynamics_. [ch 6-Linear Momentum of a Multiparticle System pp234-235](https://www.jstor.org/stable/j.ctvcm4ggj.9) Princeton University Press \n",
"\n",
"3. <https://en.wikipedia.org/wiki/Specific_impulse>\n",
"\n",
"4. <https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T>"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}