PS-F1-Solutions.ipynb

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   "metadata": {},
   "source": [
    "# Problem Set F1 Solutions\n",
    "\n",
    "_PHY 323 Spring 2024, Prof. Ian Beatty_"
   ]
  },
  {
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   "execution_count": 2,
   "id": "525d7849-08d2-49d9-bd50-38dcb78f4af6",
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   "source": [
    "# Setup…\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import norm\n",
    "from IPython.display import display, Math\n",
    "\n",
    "def print_math(s):\n",
    "    display(Math(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e50c094-80d1-4252-8ba2-0304ea6758ec",
   "metadata": {},
   "source": [
    "## Problem 1: Explorers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "015a50b0",
   "metadata": {},
   "source": [
    "Plan: Represent each team's journey as a succession (sum) of displacement vectors to get their final position. Then, take the differences of their positions to get a displacement vector from one team to the other, and take its magnitude to find the distance between them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f14be75b",
   "metadata": {},
   "source": [
    "Team A: $ \\vec{r}_A = \\vec{d}_{A1} + \\vec{d}_{A2} $\n",
    "\n",
    "- $ \\vec{d}_{A1} = \\left< 0, 5, 0 \\right> \\text{ km} $\n",
    "\n",
    "- $ \\vec{d}_{A2} = \\left< \\cos(15^\\circ), -\\sin(15^\\circ), 0 \\right> \\times 15 \\text{ km} $\n",
    "\n",
    "Team B: $ \\vec{r}_B = \\vec{d}_{B1} + \\vec{d}_{B2} $\n",
    "\n",
    "- $ \\vec{d}_{B1} = \\left< 6 \\cos(45^\\circ), -6 \\sin(45^\\circ), 2.5 \\right> \\text{ km} $\n",
    "\n",
    "- $ \\vec{d}_{B2} = \\left< 0, 4, 0 \\right> \\text{ km} $\n",
    "\n"
   ]
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  {
   "cell_type": "code",
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   "id": "752cd1f2",
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\vec{d}_{A1} = \\left<0.000, 5.000, 0.000\\right> \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\vec{d}_{A2} = \\left<-1.812, 6.761, 0.000\\right> \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\vec{r}_{A} = \\left<-1.812, 11.761, 0.000\\right> \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\vec{d}_{B1} = \\left<4.243, 4.243, 2.500\\right> \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\vec{d}_{B2} = \\left<0.000, 4.000, 0.000\\right> \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\vec{r}_{B} = \\left<4.243, 8.243, 2.500\\right> \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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   "source": [
    "# Calculate…\n",
    "d_A1 = np.array([ 0, 5, 0 ])\n",
    "print_math(rf\"\\vec{{d}}_{{A1}} = \\left<{d_A1[0]:.3f}, {d_A1[1]:.3f}, {d_A1[2]:.3f}\\right> \\text{{ km}}\")\n",
    "d_A2 = 7 * np.array([ -np.sin(np.radians(15)), np.cos(np.radians(15)), 0 ])\n",
    "print_math(rf\"\\vec{{d}}_{{A2}} = \\left<{d_A2[0]:.3f}, {d_A2[1]:.3f}, {d_A2[2]:.3f}\\right> \\text{{ km}}\")\n",
    "r_A = d_A1 + d_A2\n",
    "print_math(rf\"\\vec{{r}}_{{A}} = \\left<{r_A[0]:.3f}, {r_A[1]:.3f}, {r_A[2]:.3f}\\right> \\text{{ km}}\")\n",
    "\n",
    "d_B1 = np.array([ 6 * np.cos(np.radians(45)), 6 * np.sin(np.radians(45)), 2.5 ])\n",
    "print_math(rf\"\\vec{{d}}_{{B1}} = \\left<{d_B1[0]:.3f}, {d_B1[1]:.3f}, {d_B1[2]:.3f}\\right> \\text{{ km}}\")\n",
    "d_B2 = np.array([ 0, 4, 0 ])\n",
    "print_math(rf\"\\vec{{d}}_{{B2}} = \\left<{d_B2[0]:.3f}, {d_B2[1]:.3f}, {d_B2[2]:.3f}\\right> \\text{{ km}}\")\n",
    "r_B = d_B1 + d_B2\n",
    "print_math(rf\"\\vec{{r}}_{{B}} = \\left<{r_B[0]:.3f}, {r_B[1]:.3f}, {r_B[2]:.3f}\\right> \\text{{ km}}\")"
   ]
  },
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   "cell_type": "markdown",
   "id": "a9ab4866",
   "metadata": {},
   "source": [
    "The displacement vector from team A to team B is $ \\vec{d}_{AB} = \\vec{r}_B - \\vec{r}_A $, and the distance is its magnitude $ \\left| \\vec{d}_{AB} \\right| $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "095fadfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\vec{d}_{AB} = \\left<6.054, -3.519, 2.500\\right> \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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     "data": {
      "text/latex": [
       "$\\displaystyle \\left|\\vec{d}_{AB}\\right| = 7.436 \\text{ km}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate…\n",
    "d_AB = r_B - r_A\n",
    "print_math(rf\"\\vec{{d}}_{{AB}} = \\left<{d_AB[0]:.3f}, {d_AB[1]:.3f}, {d_AB[2]:.3f}\\right> \\text{{ km}}\")\n",
    "d_AB_mag = norm(d_AB)\n",
    "print_math(rf\"\\left|\\vec{{d}}_{{AB}}\\right| = {d_AB_mag:.3f} \\text{{ km}}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "130a4085",
   "metadata": {},
   "source": [
    "If the radios have a range of 7.25 km and the teams are 7/.436 km apart, then **no, they cannot communicate.**\n",
    "\n",
    "> Update 2024-02-08: In the version of this solution originally posted, I screwed up the calculation of $\\vec{d}_{A2}$ badly, and all the subsequent numbers and conclusion were flat-out wrong. (Hey, we all make stupid brain-flops sometimes.) Sorry for any confusion caused!\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "628bb487-d42e-4b74-9549-cb1ab030722c",
   "metadata": {},
   "source": [
    "## Problem 2: Emergency Avoidance Maneuvers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d9c80b0",
   "metadata": {},
   "source": [
    "Let's start by defining some symbols for our given values. I'll take my coordinate system to put the station at the origin, with my initial position out on the $-x$ axis and my velocity therefore in the $+x$ direction.\n",
    "\n",
    "$$ \\begin{split}\n",
    "    &R = 175 \\text{ m} \\\\\n",
    "    &x_0 = -750 \\text{ m} \\\\\n",
    "    &v_0 = 25 \\text{ m/s} \\\\\n",
    "    &m = 35 \\times 10^3 \\text{ kg} \\\\\n",
    "    &a_\\text{max} = 0.40 \\text{ m/s}^2\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1922ddb9",
   "metadata": {},
   "source": [
    "### a) Time to collision"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed928f5a",
   "metadata": {},
   "source": [
    "I'm moving towards the station at 25 m/s, so without action I'll cross the 750 meters between me and it in\n",
    "\n",
    "$$ t_\\text{deer in headlights} = \\left|\\frac{x_0}{v_0}\\right| = \\frac{750\\text{ m}}{25\\text{ m/s}} = \\boxed{30\\text{ seconds}} $$\n",
    "\n",
    "Better think fast!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97e72c36",
   "metadata": {},
   "source": [
    "### b) Maximum braking"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b62c2b30",
   "metadata": {},
   "source": [
    "If I turn my thrusters towards the station to get a maximum acceleration away from it (i.e., maximum deceleration), I've got a 1D constant acceleration kinematics problem, with $a_x = -a_\\text{max}$. (I'll omit the x-component subscripts for this section, since everything is in the x-direction.) Here's the model:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    x(t) &= x_0 + v_0 t + \\frac{1}{2} (-a_\\text{max})\\,t^2 \\\\\n",
    "    v(t) &= v_0 + (-a_\\text{max})\\,t\n",
    "\\end{split} $$\n",
    "\n",
    "Do I stop in time? First I'll find the time at which the velocity goes to zero:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    &v(t_\\text{stop}) = 0 \\quad \\Rightarrow \\quad 0 = v_0 - a_\\text{max}\\,t_\\text{stop} \\\\ \\quad \\\\\n",
    "    &\\Rightarrow \\quad t_\\text{stop} = \\frac{v_0}{a_\\text{max}} = \\frac{25\\text{ m/s}}{0.40\\text{ m/s}^2}\n",
    "\\end{split} $$"
   ]
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   "cell_type": "code",
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\boxed{t_\\text{stop} = 62.500 \\text{ s}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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   "source": [
    "# Calculating…\n",
    "v_0 = 25 # m/s\n",
    "a_max = 0.40 #m/s^2\n",
    "t_stop = v_0 / a_max\n",
    "print_math(rf\"\\boxed{{t_\\text{{stop}} = {t_stop:.3f} \\text{{ s}}}}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "604f6207",
   "metadata": {},
   "source": [
    "Now, let's figure out where I am at this time:\n",
    "\n",
    "$$ x(t_\\text{stop}) = x_0 + v_0 t_\\text{stop} - \\frac{1}{2} a_\\text{max}\\,t_\\text{stop}^2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9eaf2ad5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\boxed{x_\\text{stop} = 31.250 \\text{ m}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating…\n",
    "x_0 = -750 # m\n",
    "x_stop = x_0 + v_0 * t_stop - 0.5 * a_max * t_stop**2\n",
    "print_math(rf\"\\boxed{{x_\\text{{stop}} = {x_stop:.3f} \\text{{ m}}}}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48e52311",
   "metadata": {},
   "source": [
    "_Uh-oh…_ $x(t_\\text{stop}) \\gt 0$, which means I'm on the other side of the station, which means that I'd have slammed into it before coming to a stop.\n",
    "\n",
    "How fast will I be going when I hit? The easiest way to find this is with that derived constant-acceleration formula that relates positions to velocities, having eliminated time.\n",
    "\n",
    "$$ \\begin{split}\n",
    "    v^2 &= v_0^2 + 2\\,(-a_\\text{max}) (0 - x_0) \\\\\n",
    "    &= (-25\\text{ m/s})^2 + 2\\, (-0.40\\text{ m/s}^2) (0 + 750\\text{ m}) \\\\\n",
    "    &= 625\\text{ m}^2/\\text{s}^2 - 600\\text{ m}^2/\\text{s}^2 \\\\\n",
    "    &= 25\\text{ m}^2/\\text{s}^2\n",
    "\\end{split} $$\n",
    "\n",
    "So I hit at 5 m/s — not super-fast, but likely hard enough to be fatal in the vacuum of space. 😱 😵"
   ]
  },
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   "cell_type": "markdown",
   "id": "04529357",
   "metadata": {},
   "source": [
    "_When_ will I hit? (The assignment doesn't ask you for this, but I'll calculate it anyway.) I can find this by solving the $x(t)$ equation for the time at which $x = 0$:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    0 &= x_0 + v_0 t_c - \\frac{1}{2} a_\\text{max}\\,t_c^2 \\\\ \\quad \\\\\n",
    "    \\Rightarrow \\quad t_c &= \\frac{v_0 \\pm \\sqrt{v_0^2 + 2\\,a_\\text{max}\\,x_0}}{a_\\text{max}} \\\\\n",
    "    &= \\frac{v_0}{a_\\text{max}} \\left( 1 \\pm \\sqrt{ 1 + \\frac{2\\,a_\\text{max}\\,x_0}{v_0^2}}\\ \\right)\n",
    "    \n",
    "\\end{split} $$"
   ]
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   "cell_type": "code",
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   "id": "4606a4fd",
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t_c = 75.000 \\text{ s or } 50.000 \\text{ s}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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     "output_type": "display_data"
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   ],
   "source": [
    "# Calculating…\n",
    "t_c1 = v_0 / a_max * (1 + np.sqrt(1 + 2 * a_max * x_0 / v_0**2))\n",
    "t_c2 = v_0 / a_max * (1 - np.sqrt(1 + 2 * a_max * x_0 / v_0**2))\n",
    "print_math(rf\"t_c = {t_c1:.3f} \\text{{ s or }} {t_c2:.3f} \\text{{ s}}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96da65b3",
   "metadata": {},
   "source": [
    "Why two solutions? Because the math doesn't know about crashing into the station, so it's happily telling us the time at which we zoom through the origin from $+x$ to $-x$, and also the later time at which we've continued on, slowed to a stop, accelerated back in the $-x$ direction, and are passing through $x = 0$ again. The earlier time is the one relvant to us: ***We crash after 50 seconds.***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21d7c4c5",
   "metadata": {},
   "source": [
    "### c) Perpendicular acceleration"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76c3f91a",
   "metadata": {},
   "source": [
    "If I turn my thrusters 90 degrees to my direction of motion, I've got a 2D constant-acceleration kinematics problem with $\\vec{a} = a_\\text{max}\\, \\hat{y}$.\n",
    "\n",
    "In the x-direction, my velocity remains constant at $v_x = v_0 = 25\\text{ m/s}$. Therefore, I reach $x = 0$ and either hit or pass the station at the same time calculated in part (a), $t_\\text{deer in headlights} = 30\\text{ s}$.\n",
    "\n",
    "The key question here is: By that time, has the y-component of my position become large enough to exceed the station's radius (thus missing the station), or not (thus splatting)?\n",
    "\n",
    "$$ \\begin{split}\n",
    "    y(t) &= y(0) + v_y(0)\\,t + \\frac{1}{2} a_\\text{max}\\,t^2 \\\\\n",
    "    &= 0 + 0 + \\frac{1}{2} (0.40\\text{ m/s}^2) (30\\text{ s})^2 \\\\\n",
    "    &= 180\\text{ m}\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1930be03",
   "metadata": {},
   "source": [
    "**That's 5 m beyond the station's rim, so I survive…**\n",
    "\n",
    "…assuming that the \"point particle approximation\" is sufficient here! If I'm using the ship's center of mass as it's \"location\" and the ship is larger than 5 meters in radius, then I'll clip the station's edge, with predictably dire consequences."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee59009f",
   "metadata": {},
   "source": [
    "### d) The hard part"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ae54fdf",
   "metadata": {},
   "source": [
    "> Note the typo in the problem: The wording for part (d) should read \"200 m in **radius**\" instead of \"200 m in **diameter**\". Sorry if that confused you.\n",
    "\n",
    "Were the station's radius 200 m instead of 175 m, then clearly neither solution (b) nor (c) would suffice. What other options are there?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05a04681",
   "metadata": {},
   "source": [
    "#### Idea 1: Full brake for part of the time, then full-sideways for the rest"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fec3256",
   "metadata": {},
   "source": [
    "Here's one idea: Aim the thrusters directly at the station and slow down as much as possible for some time $t_1$, then turn the thrusters $90^\\circ$ and try to move far enough to the side to clear the station. My idea is that the time I invest in slowing down, before starting to accelerate sideways, will be more than repaid by the extra time I buy myself before colliding. Let's see how that works out!\n",
    "\n",
    "For $0 < t < t_1$, the kinematic model is the same as in part (b), so at time $t_1$, my position and velocity are:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    x(t_1) &= x_0 + v_0 t_1 + \\frac{1}{2}\\,a\\,t_1^2 \\\\\n",
    "    y(t_1) &= 0 \\\\\n",
    "    v_x(t_1) &= v_0 + a\\,t_1 \\\\\n",
    "    v_y(t_1) &= 0\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1f195ab",
   "metadata": {},
   "source": [
    "For $t > t_1$, the kinematic model is like that of part (c), but starting later with different \"initial\" conditions:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    x(t) &= x(t_1) + v_x(t_1)\\,(t - t_1) \\\\\n",
    "         &= x_0 + v_0 t_1 + \\frac{1}{2}\\,a\\,t_1^2 + \\left( v_0 + a\\,t_1 \\right)\\,(t - t_1) \\\\\n",
    "         &= x_0 + \\cancel{v_0} t_1 + \\frac{1}{2}\\,a\\,t_1^2 + v_0 t + a\\,t_1\\,t - \\cancel{v_0 t_1} - a\\,t_1^2 \\\\\n",
    "         &= x_0 - \\frac{1}{2}\\,a\\,t_1^2 + \\left( v_0 + a\\,t_1 \\right)\\,t \\\\\n",
    "    y(t) &= y(t_1) + v_y(t_1)\\,(t - t_1) + \\frac{1}{2}\\,a\\,(t - t_1)^2 \\\\\n",
    "         &= \\frac{1}{2}\\,a\\,(t - t_1)^2 \\\\\n",
    "    v_x(t) &= v_x(t_1) = v_0 + a\\,t_1 \\\\\n",
    "    v_y(t) &= v_y(t_1) + a\\,(t - t_1) = a\\,(t - t_1)\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efb7ceba",
   "metadata": {},
   "source": [
    "I'll reach the plane of the station at whatever time $t_2$ makes $x(t_2) = 0$:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    &x(t_2) = 0 \\\\\n",
    "    &\\Rightarrow 0 = x_0 - \\frac{1}{2}\\,a\\,t_1^2 + \\left( v_0 + a\\,t_1 \\right)\\,t_2 \\\\\n",
    "    &\\Rightarrow t_2 = \\frac{\\frac{1}{2}\\,a\\,t_1^2 - x_0}{v_0 + a\\,t_1}\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9745b957",
   "metadata": {},
   "source": [
    "At that moment, my distance from the station's center is $y(t_2)$:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    y_2 \\equiv y(t_2) &= \\frac{1}{2}\\,a\\,(t_2 - t_1)^2 \\\\\n",
    "        &= \\frac{1}{2}\\,a\\,\\left( \\frac{\\frac{1}{2}\\,a\\,t_1^2 - x_0}{v_0 + a\\,t_1} - t_1 \\right)^2 \\\\\n",
    "\\end{split} $$\n",
    "\n",
    "Let's plot this as a function of $t_1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f8a51c56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting…\n",
    "def y2(t1):\n",
    "    return 0.5 * a_max * ( (0.5 * a_max * t1**2 - x_0)/(v_0 + a_max * t1) - t1 )**2\n",
    "\n",
    "t_values = np.linspace(0.0, 30, 100)\n",
    "y2_values = np.array([y2(t) for t in t_values])\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "ax.plot([0, 30], [0, 0], \"k\", linewidth=0.5)\n",
    "ax.plot(t_values, y2_values, linewidth=3)\n",
    "ax.set_xlim(0, 30)\n",
    "# ax.set_xticks(np.arange(0, 21, 2))\n",
    "ax.set_xlabel(r'$t_1$ (s)')\n",
    "ax.set_ylabel(r'$y_2$ (m)')\n",
    "ax.set_title('Distance from station center at passing vs. time to turn')\n",
    "ax.grid(True, color='gray', linestyle=':', linewidth=0.5)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fbd5221",
   "metadata": {},
   "source": [
    "**Conclusion:** This idea will not work. The longer I \"brake\" before thrusting sideways, the less distance off-center I achieve.\n",
    "\n",
    "> Confession: It bothers me that this graph seems to hit zero **before** $t_\\text{deer in headlights} = 30\\text{ s}$, and then curve back upwards. I may have an error in my derivation or calculation, but y'all have awaited these solutions long enough so I'll worry about it later."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f575fda2",
   "metadata": {},
   "source": [
    "#### Idea 2: Turn thrusters towards station, but not fully"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0413a479",
   "metadata": {},
   "source": [
    "Plan B is to aim my thrusters at some angle in between \"towards the station\" and \"perpendicular to the station\", in order to both slow my approach and push me to the side. It's conceivable that the x-component of acceleration might buy me enough extra time to allow the y-component to get me past the station's rim… or perhaps not. We need to math that.\n",
    "\n",
    "Let's define $\\theta$ to be the angle between \"towards the station\" and \"the angle I point my thrusters\", which makes it also the angle between $-\\hat{x}$ and $\\vec{a}$. My acceleration vector is therefore $\\vec{a} = a_\\text{max} \\left[ -\\cos(\\theta)\\,\\hat{x} + \\sin(\\theta)\\,\\hat{y} \\right]$, and the constant-acceleration kinematic equations for position are:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    x(t) &= x_0 + v_0\\,t + \\frac{1}{2} \\left[-a_\\text{max}\\,\\cos(\\theta)\\right]\\,t^2 \\\\\n",
    "    y(t) &= 0 + 0 + \\frac{1}{2} \\left[a_\\text{max}\\,\\sin(\\theta)\\right]\\,t^2\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75ac5e34",
   "metadata": {},
   "source": [
    "(Remember that $x_0 \\lt 0$ and $v_0 \\gt 0$.)\n",
    "\n",
    "To find the y-coordinate at the moment I pass the station, I'll solve the x-position equation for the time at which $x = 0$, and then plug that into the y-position equation.\n",
    "\n",
    "$$ \\begin{split}\n",
    "    &x(t_c) = 0 \\\\\n",
    "    &\\Rightarrow 0 = x_0 + v_0\\,t_c - \\frac{1}{2} a_\\text{max}\\,\\cos(\\theta)\\,t_c^2 \\\\\n",
    "    &\\Rightarrow t_c = \\frac{v_0}{a_\\text{max}\\cos(\\theta)} \\left( 1 \\pm \\sqrt{ 1 + \\frac{2\\,a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2}}\\ \\right)\n",
    "\\end{split} $$\n",
    "\n",
    "via the quadratic formula. (This is precisely the same expression as in part (b), but with $a_\\text{max}\\cos(\\theta)$ in place of $a_\\text{max}$.) As in (b), the two solutions have physical meanings, with the smaller one indicating the first time the ship passes the plane of the station (either splatting or missing), and the second one indicating the hypothetical time at which the ship would pass again, heading back in the $-x$ direction. We're only interesed in the first, smaller one, so we'll ignore the positive part of the $\\pm$:\n",
    "\n",
    "$$ t_c = \\frac{v_0}{a_\\text{max}\\cos(\\theta)} \\left( 1 - \\sqrt{ 1 + \\frac{2\\,a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2}}\\ \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88e9e0ec",
   "metadata": {},
   "source": [
    "**Sanity check 1:** For $\\theta = 0^\\circ$, this should agree with the time we found in (a): $t_c = 50$ seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c23de670",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\text{For }\\theta = 0^\\circ, t_c = 50 \\text{ s}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating…\n",
    "def t(q):\n",
    "    a = a_max * np.cos(q)\n",
    "    return (1 - np.sqrt(1 + 2 * a * x_0 / v_0**2)) * v_0 / a\n",
    "\n",
    "print_math(rf\"\\text{{For }}\\theta = 0^\\circ, t_c = {t(np.radians(0)):.3g} \\text{{ s}}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7c4d4c1",
   "metadata": {},
   "source": [
    "**Sanity check 2:** For $\\theta = 90^\\circ$, this should agree with the time we found in (a): $t_c = 30$ seconds. Unfortunately, I can't plug $\\theta = 90^\\circ$ directly into this equation because I get a zero over zero undefined result. I can take the limit as $\\theta \\rightarrow 90^\\circ$, though.\n",
    "\n",
    "For $\\theta \\approx 90^\\circ$, $\\cos(\\theta) \\ll 1$, which lets me simplify the square root via the binomial approximation $ \\sqrt{1 + \\epsilon} \\approx 1 + \\frac{1}{2}\\epsilon\\ $ for $\\epsilon \\ll 1$:\n",
    "\n",
    "$$ \\begin{split}\n",
    "    t_c &= \\frac{v_0}{a_\\text{max}\\cos(\\theta)} \\left( 1 - \\sqrt{ 1 + \\frac{2\\,a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2}}\\ \\right)\n",
    "    \\\\ \\quad \\\\\n",
    "    &\\approx \\frac{v_0}{a_\\text{max}\\cos(\\theta)} \\left( 1 - \\left[ 1 + \\frac{a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2}\\right] \\right)\n",
    "    \\\\ \\quad \\\\\n",
    "    &= \\frac{v_0}{a_\\text{max}\\cos(\\theta)} \\left( \\frac{-a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2} \\right)\n",
    "    \\\\ \\quad \\\\\n",
    "    &= \\frac{-x_0}{v_0} = \\frac{-(-750\\text{ m})}{25\\text{ m/s}} = 30\\text{ s}\n",
    "\\end{split} $$\n",
    "\n",
    "exactly as found in part (a). 😁"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3169e34d",
   "metadata": {},
   "source": [
    "My distance from the x-axis at that point is:\n",
    "\n",
    "$$ \\begin{split}\n",
    "  y(t_c) &= \\frac{1}{2} \\left[a_\\text{max}\\,\\sin(\\theta)\\right]\\,t_c^2\n",
    "  \\\\ \\quad \\\\\n",
    "  &= \\frac{1}{2} \\left[a_\\text{max}\\,\\sin(\\theta)\\right] \\left\\{ \\frac{v_0}{a_\\text{max}\\cos(\\theta)} \\left( 1 - \\sqrt{ 1 + \\frac{2\\,a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2}}\\ \\right) \\right\\}^2\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "480935c2",
   "metadata": {},
   "source": [
    "My distance from the x-axis at that point is:\n",
    "\n",
    "$$ \\begin{split}\n",
    "  y(t_c) &= \\frac{1}{2} \\left[a_\\text{max}\\,\\sin(\\theta)\\right]\\,t_c^2\n",
    "  \\\\ \\quad \\\\\n",
    "  &= \\frac{1}{2} \\left[a_\\text{max}\\,\\sin(\\theta)\\right] \\left\\{ \\frac{v_0}{a_\\text{max}\\cos(\\theta)} \\left( 1 - \\sqrt{ 1 + \\frac{2\\,a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2}}\\ \\right) \\right\\}^2\n",
    "  \\\\ \\quad \\\\\n",
    "  &= \\frac{v_0^2\\,\\tan(\\theta)}{2\\,a_\\text{max}\\cos(\\theta)} \\left( 1 - \\sqrt{ 1 + \\frac{2\\,a_\\text{max}\\cos(\\theta)\\,x_0}{v_0^2}}\\ \\right)^2\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a551b756",
   "metadata": {},
   "source": [
    "_Disgusting!_ In principle, I could find the value of $\\theta$ that maximizes this expression, and then plug that in to find out whether I can get far enough from the station's center, but that's more algebra than I really want to do. Instead, I'll plot $y(t_c)$ vs. $\\theta$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b6d7d721",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ubm4ay5ycnDT+uLl58ya8vb3h7Ozc4HPeuHEDjDF06tQJbm5uGh+JiYnqCTX0YWFhgfbt22ssS0tLg7e3t1aO9acN1f/RUM/X11fj3w4ODgAAHx8fncvv9cfd5s2bcfnyZfj4+GDgwIF46623mtQs1Nu9ezd69eoFKysruLi4wM3NDX///bfW76ep0tLSIBQK0bFjR43lnp6ecHR0vGcegPbvXRce+0L79u217lnWlFrqnwsAZs+erfVc//vf/yCXy7Uy9ff3v+fjAnWN8bZt29CpUydIJBK4urrCzc0Nly5d0vv3dKdOnTpp/DswMBBCoVBj9r0zZ85g3LhxsLGxgaOjI9zc3PDGG28A+O+1PGrUKDz22GNYv349XF1d8eijj2LXrl2Qy+Xqx3nppZfQuXNnTJgwAe3bt8fcuXNx6NChJtXZlN9PWloaAgMDtba7e39syEMPPQQHBweN09z27t2L3r17o3PnzgDqmuFNmzbh4MGD8PDwwMiRI7F582bk5OQ06TmaqzmvkabuU7q09HivS1VVFdauXQsfHx+NfbekpETnvnv3z1o/02z9z1p//Lj79+ns7HzPWWn1eY0S0lbQNV+EtAGZmZkoLS1t9I8SqVSKsLAwnDhxAn///TcOHTqEvXv3YsyYMThy5Eij77AqlUo8+OCDKCoqwmuvvYauXbvCxsYGWVlZeO6557T+h67vu7V3U6lUEAgEOHjwoM7HrL/eSR93jkDoq6Gfs6HlrJFrgYC663VGjBiBAwcO4MiRI3j//fexadMm7N+/X30dTEO+//57PPfcc5gyZQpeeeUVuLu7QyQSITQ0FDdv3mzaD9SApt54Wd+fuymauy+0pJb6/fn9999H7969dW5z9/PdOSrQmI0bN2LNmjWYO3cu3nnnHTg7O0MoFGLZsmVc3qm/+3d38+ZNjB07Fl27dsXWrVvh4+MDsViMf/75B9u2bVPXIBAIsG/fPpw7dw5//vknDh8+jLlz52LLli04d+4cbG1t4e7ujri4OBw+fBgHDx7EwYMHsWvXLjz77LPYvXt3o3Xx3FfqSSQSTJkyBQcOHMDnn3+O3NxcnDlzBhs3btTYbtmyZZg0aRJ+++03HD58GGvWrEFoaCiOHz+OPn36GKweoHk/t659qqHXolKp1PpefY/3DVm8eDF27dqFZcuWYciQIXBwcIBAIMCTTz6pc9/lfTwAmvcaJaStoOaLkDbgu+++AwCEhIQ0up1QKMTYsWMxduxYbN26FRs3bsSbb76JEydOYNy4cQ3+jz0+Ph7Xr1/H7t278eyzz6qX63O6Ub3AwEAcPnwYRUVFDY54BAYGgjEGf39/9TvVPPn5+eHff/9FeXm5xujX1atX1et58/LywksvvYSXXnoJeXl56Nu3LzZs2KBuvhr6He3btw8BAQHYv3+/xjZ3n8rX1EYKqPt5VSoVbty4oTFpQG5uLkpKSgyWh7H2hYayCAwMBADY29tj3LhxBnmuevv27cPo0aPx9ddfaywvKSmBq6vrPWu7lxs3bmiMmCQlJUGlUqlPj/3zzz8hl8vxxx9/aIxMNHQK7+DBgzF48GBs2LABe/bswaxZs/DTTz9h/vz5AOpOF5w0aRImTZoElUqFl156CV988QXWrFnT5BGqhvj5+SEhIQGMMY08kpKSmvwYM2bMwO7du3Hs2DEkJiaCMaY+5fBOgYGBWLlyJVauXIkbN26gd+/e2LJlC77//vtm1azv762pnJycUFJSorX87lFoQP/jfUP27duH2bNnY8uWLepl1dXVOutpivrjR1JSksY+W1hYeM8Rap6vUUKMjU47JMTEHT9+HO+88w78/f0xa9asBrcrKirSWlb/jmH9qUT195G5+3+m9e9g3vmOJWMMH330kd51P/bYY2CMYf369Vrr6p9n2rRpEIlEWL9+vda7pYwxFBYW6v38ujz88MNQKpX49NNPNZZv27YNAoHgnqNPLaFUKrVOk3F3d4e3t7fGqV42NjY6T6fR9TuKjIxERESExnb1M5I15Q+mhx9+GAC0buq8detWAHUzyhmCsfaFhvb3fv36ITAwEB988AFkMpnW9+Xn5zf7ueqJRCKt+n/55RdkZWU1qbZ7+eyzzzT+/cknnwCAet/VtZ+UlpZi165dGt9XXFysVefdx4u7MxcKheqZM+/cZ/UVEhKCrKws/PHHH+pl1dXV+Oqrr5r8GOPGjYOzszP27t2LvXv3YuDAgRp/6FdWVmrNrBcYGAg7OzuNnyE7OxtXr15t8Pq3evr+3poqMDAQpaWluHTpkkZtd8882pLjfUN07buffPKJ1qhbU40dOxYWFhbYvn27xvK7j7+68HyNEmJsNPJFiAk5ePAgrl69CoVCgdzcXBw/fhxHjx6Fn58f/vjjj0ZvZvr2228jLCwMjzzyCPz8/JCXl4fPP/8c7du3x/DhwwHU/Y/d0dERO3bsgJ2dHWxsbDBo0CB07doVgYGBWLVqFbKysmBvb49ff/21RReojx49Gs888ww+/vhj3LhxAw899BBUKhVOnz6N0aNH4+WXX0ZgYCDeffddvP7660hNTcWUKVNgZ2eHlJQUHDhwAM8//zxWrVqldw13mzRpEkaPHo0333wTqampCA4OxpEjR/D7779j2bJl6ndbeSgvL0f79u0xffp0BAcHw9bWFv/++y+ioqI03mnu168f9u7dixUrVmDAgAGwtbXFpEmTMHHiROzfvx9Tp07FI488gpSUFOzYsQNBQUEaf5xIpVIEBQVh79696Ny5M5ydndGjRw/1tNt3Cg4OxuzZs/Hll1+ipKQEo0aNwvnz57F7925MmTIFo0ePNsjPbqx9oaH93d/fH//73/8wYcIEdO/eHXPmzEG7du2QlZWFEydOwN7eHn/++adeP+vEiRPx9ttvY86cORg6dCji4+Pxww8/ICAgoMm1NSYlJQWTJ0/GQw89hIiICHz//fd46qmnEBwcDAAYP368erTqhRdegEwmw1dffQV3d3dkZ2erH2f37t34/PPPMXXqVAQGBqK8vBxfffUV7O3t1U35/PnzUVRUhDFjxqB9+/ZIS0vDJ598gt69e2uMlOrrhRdewKeffoqZM2di6dKl8PLywg8//KA+zjVl5MbS0hLTpk3DTz/9hIqKCnzwwQca669fv46xY8fiiSeeQFBQECwsLHDgwAHk5ubiySefVG/3+uuvY/fu3UhJSWl0+vnevXtDJBJh06ZNKC0thUQiwZgxY+Du7q5fCHd58skn8dprr2Hq1KlYsmQJKisrsX37dnTu3Flj0ouWHO8b2scmTpyI7777Dg4ODggKCkJERAT+/fdfuLi46PWzeHh4YOnSpdiyZYt6n7148SIOHjwIV1fXRn+/QqGQ22uUEKNrlTkVCSGNuvvmnfU3An3wwQfZRx99pDGteb27px4+duwYe/TRR5m3tzcTi8XM29ubzZw5k12/fl3j+37//XcWFBTELCwsNKYhTkhIYOPGjWO2trbM1dWVLViwgF28eFFrquL6Gxjfqx7G6qZHf//991nXrl3VNxWeMGGC+qbC9X799Vc2fPhwZmNjw2xsbFjXrl3ZokWL2LVr1xrNrbGp5nXVyBhj5eXlbPny5czb25tZWlqyTp06NXqT5TvV38T47mmrG6rjTnK5nL3yyissODiY2dnZMRsbGxYcHKx181uZTMaeeuop5ujoyHDHTZZVKhXbuHEj8/PzYxKJhPXp04f99ddfOqemPnv2LOvXrx8Ti8Ua0843dJPl9evXM39/f2Zpacl8fHwavcny3UaNGqW+uXVjDLkv1N/E9266smhof2eMsdjYWDZt2jTm4uLCJBIJ8/PzY0888QQ7duyYepv6zBqb0vtO1dXVbOXKleqbyg4bNoxFRETozKmx2u5WX0dCQgKbPn06s7OzY05OTuzll1/WusnyH3/8wXr16qW+cfKmTZvYzp07NW6HcOHCBTZz5kzm6+vLJBIJc3d3ZxMnTmTR0dHqx9m3bx8bP348c3d3Z2KxmPn6+rIXXniBZWdnq7dp7CbLd9P1+0lOTmaPPPIIk0qlzM3Nja1cuZL9+uuvDAA7d+5c42HfdvToUQaACQQClpGRobGuoKCALVq0iHXt2pXZ2NgwBwcHNmjQIPbzzz9r1XZnPo356quvWEBAABOJRDpvsny3u3/397q1yJEjR1iPHj2YWCxmXbp0Yd9//73Bj/e6FBcXszlz5jBXV1dma2vLQkJC2NWrV7VuiNxQ/br2BYVCwdasWcM8PT2ZVCplY8aMYYmJiczFxYW9+OKLjX4vY017jRLS1ggY0//KyNraWuTk5KCyshJubm6NzmRFCCGEEP289dZbWL9+PfLz8zWuHTNHH374IZYvX47MzEy0a9fO2OUQAyspKYGTkxPeffddvPnmm8Yuh5BW1+xrvsrLy7F9+3aMGjUK9vb26NChA7p16wY3Nzf4+flhwYIFiIqK4lErIYQQQsxIVVWVxr+rq6vxxRdfoFOnTtR4mYG7f7/Af9eYPvDAA61bDCEmolnXfG3duhUbNmxAYGAgJk2ahDfeeAPe3t6QSqUoKirC5cuXcfr0aYwfPx6DBg3CJ598onVPEkIIIYQQoG6iFV9fX/Tu3RulpaX4/vvvcfXqVfzwww/GLo0YwN69e/HNN9/g4Ycfhq2tLcLDw/Hjjz9i/PjxGDZsmLHLI8QomtV8RUVFISwsDN27d9e5fuDAgZg7dy527NiBXbt24fTp09R8EUIIIUSnkJAQ/O9//8MPP/wApVKJoKAg/PTTTzqniydtT69evWBhYYHNmzejrKxMPQnHu+++a+zSCDGaFl3zRQghhBBCCCGkaeg+X4QQQgghhBDSClp0n6/q6mpcunQJeXl5UKlUGusmT57cosIIIYQQQgghxJzo3XwdOnQIzz77LAoKCrTWCQQCve+IbgpUKhVu3boFOzu7Jt3kkRBCCCGEEGKeGGMoLy+Ht7c3hMKWnTio9zVfnTp1wvjx47F27Vp4eHi0qAhTk5mZCR8fH2OXQQghhBBCCDERGRkZaN++fYseQ+/my97eHrGxsQgMDGxRAaaotLQUjo6OyMjIgL29vbHLMStXr15F165djV2G2aFc+aBc+aBc+aBc+aBc+aBc+aFsDa+srAw+Pj4oKSmBg4NDix5L79MOp0+fjpMnT5pl81V/qqG9vT01Xwbm4uJCmXJAufJBufJBufJBufJBufJBufJD2fJjiMuR9G6+Pv30Uzz++OM4ffo0evbsCUtLS431S5YsaXFxxPxIJBJjl2CWKFc+KFc+KFc+KFc+KFc+KFd+KFvTpnfz9eOPP+LIkSOwsrLCyZMnNTpBgUBAzRfRKT8/v8XnyhJtlCsflCsflCsflCsflCsflCs/lK1p0/uaL09PTyxZsgSrV69u8awfpqasrAwODg4oLS2lYVsDKy8vh52dnbHLMDuUKx+UKx+UKx+UKx+UKx+UKz+UreEZsjfQu2uqqanBjBkzzK7xInzFxsYauwSzRLnyQbnyQbnyQbnyQbnyQbnyQ9maNr1HvpYvXw43Nze88cYbhq7J6GjkixBCCCGEEAIYtjfQ+5ovpVKJzZs34/Dhw+jVq5fWhBtbt25tUWHEPIWFhWHkyJHGLsPsUK58UK58UK58hIWFYfjwEaiqVdZ91ChRfcfXVbVKyBWquo87vq5RqCBXKNVf1ypVqFUyKJS3v1bVf81Qq1RBqWL/fTAG1e3PShWgUjGoWN0HALDb/2Gou0mpehkAAequEa/7rPm1UCCAQCCASAiIhEKIBIBIKIBQIICFqO6zSCiApUgIS5EAFkKh+mtLkRAWIgHEorplYovbH7e/llhofrayEEFiKYKVpRBWliJYWYogrf+3hQjh4adpf+WAjgP8ULamTe+Rr9GjRzf8oAIBjh8/rndRxkYjX/wolUqIRCJjl2F2KFc+KFc+KFdNjDFU1ChRXl2L8moFyqtrUVatQFlV/b/rllXIFZDJlaisUUAmV6BCrkCFXImKmrqvK2vqGihiWGKRAFKxBazFIkjFIliLRbC2tIBUXNekWYtFsJaIYCOxgI3YAjYSC9hKRLAWW8BWUvdva7EIdlYWsLOyhK3EAmILumSDjgP8ULaGZxIjXydOnGjRE5P7U0REBIYPH27sMswO5coH5cqHOedao1ChuLIGhbKaus8VNSiuqEFJZS1KqmpQWlmLkqpalFTWoKSqVv1vpUqv90FJK6hRMtRU1aK0qtZgjymxEMLOqq45q2/I7KwsYC+1hL2VJeylFrc/W8L+juUO1pZwlFrCWiwyyP2GjMmcjwPGRtmatmY1X+np6fD19W3y9llZWWjXrl2ziyLmq3v37sYuwSxRrnxQrny0tVwr5AoUyOTIL6/7UH99+3NhRQ2Kbn+UVyuMXS5pA+QKFeSyGhTIavT6fguhAI7Wdc2Zo9QSjtZiOEgt4SC1hJO1GE42dcucrOv+7Xj7syk1bW3tONCWULamrVnN14ABAzBlyhTMnz8fAwYM0LlNaWkpfv75Z3z00Ud4/vnn6X5fRENGRgacnJyMXYbZoVz5oFz5MJVc5Qol8srkyC2rRk5ZNXLrvy6tRm5Z3UdeuRyVNUpjl9oiYgshpHdcxySxEKmveZJY1l0LJbEQqb+2tBDCUiiAhUioeU2VhQCWQiFEwrrrrYRCAUS3r8uqvwar/rqsumu2oL6Gq+4r3LFMAMYYVLcvCmMMUDGAqb+u+3zntWUa15qpGBQqBqVKhZrb16cpVAw1ChUUKhVqFQy1qrrr1GruuJ6tRqFCjbL+Ore6z9W1ddfGVStUbWYEUqFiKNCjeROLhHCyqWvEXGzFdZ9txHC2kcDZxvL2ZzFcbcVwsZXAUWoJoZBPs2YqxwFzRNmatmY1XwkJCdiwYQMefPBBWFlZoV+/fvD29oaVlRWKi4uRkJCAK1euoG/fvti8eTMefvhhXnWTNsrBwcHYJZglypUPypWP1shVpWIorKjBrZIq3CqpQlZJFW6VVONWSRWyS6uQVVKNApmcex36sBGLYGdlefsaobpTzupOTROprymyuX2Nka3EAtbiun+XFeUj0Ld93YQR4vpmSwQRpz+ezVGtUoWq282YvLauMUtOz4KDixuqapSorKm75q66tv7ruolMKm5fg1d/TV7d13XX4dVfn2cKfV2NUnX7TYam7ftCAeBsI7ndjInhYiOBi60YrrZ1y1xtJXCzk8DVtm65xKLp1xnR8ZUfyta0Nav5cnFxwdatW7Fhwwb8/fffCA8PR1paGqqqquDq6opZs2YhJCQEPXr04FUvIYQQAsYYSqtqkVFUhYziSmQUVd7+XPfvzOIq1Bhx8gmBAHCyFsPZRgzn26d91X3UnR7maF13ipijVKz+uv4aIAuRfpMxpFlUwM+DbqzaEpa3R/vsrf6bwVlcLYWfn0uLHpcxhqpaJWTVCpRV1zVmsmoFZPK6yVXqltdNsFJWVYuy6lqUVdUtu/Nr/aZI05+KAQUyeZPfqHCQWmo0Ze52VnC3l8DNVgJ3+7p/u9lJ4GRtee8HI8RM6TXhhlQqxfTp0zF9+nRD10PMXGlpqbFLMEuUKx+UKx9NzZUxhnyZHKkFlUgtrEBaYYX66/TCSpTLW/f6KqmlCG52dX9UutlK4GpXPwJQd6qWs039KVxiOFqLW33EifZXPgyRq0AggLW4bpTSXc+J0lQqhnK5AqWVdZN/lFTV1H2+/e/S2xO5FFf+97m4oqZVJ3Spr+NmfkWj21mKBHCQCNHeJRMe9hJ42FvBw94K7nYSeDrUfe1hZwV7qYXJXKPWltCxwLTpPdshIfrw8fExdglmiXLlg3Ll4+5cZXIFkvNluJkvw828CiQXyJBSUIm0wopWud5KYiFU/8HnaW8FTwfNPwLdbr+LbyMx7f9l0v7Kh6nkKhQK1JNqNAdjDGXVCo2GrH6CmKLKGhTJbs/KWVm3rFAmRxnniWNqlQwFlUoUVJY0ut2dr00vh7rXp8ft16jn7X+720n0Hi02V6ayzxLdTPv/JMTsXLlyhaY/5YBy5YNyNRzGGPLL5bieK8ORcxfB7DxwM1+G5PwK5JRVc3teC6EAng5W8HaQwtvRCt6OUng7StHOUQovRyt42UvN5t112l/5aOu5CgT/NW1NPXuy/pYJBTI5CmU1KKyo+1wgq2vO6k5FrFHP/qngNLImV6iQVliJtMLKBrcRCgB3u7pmzNvRCp72da91TwcreDlI4eVw/zVobX2fNXd632SZh9DQUOzfvx9Xr16FVCrF0KFDsWnTJnTp0kW9TXV1NVauXImffvoJcrkcISEh+Pzzz+Hh4aHeJj09HQsXLsSJEydga2uL2bNnIzQ0FBYWTes16SbL/NCN//igXPmgXPVTKKtrsm7kleNaTjlu5MpwLbfcoPdJqicUAF4OUvg4S+HjZA0fZ2v4OEvR3ska7Z2kcLezum8mnKD9lQ/KtXH111/eefuFAlkN8sqr1bdnyCuTI6+8GsWVhj8GNIVIKICHnUT95ouXo1XdGzC335Rp5yiFg9TSLN6EAWif5cEkbrLMw6lTp7Bo0SIMGDAACoUCb7zxBsaPH4+EhATY2NgAAJYvX46///4bv/zyCxwcHPDyyy9j2rRpOHPmDIC6He6RRx6Bp6cnzp49i+zsbDz77LOwtLTExo0bjfnjEQBnzpzByJEjjV2G2aFc+aBcG1ejUCEpT4bE7LK6j5wyXMsp1/veRQ0RWwjh52yNDq426OBiDT8XG3RwsYGvszW8HK1geR+9o90Y2l/5oFwbJxAI4Ghdd51jp3tM+FKjUKFAJkdeuRwnImLg6tsReWX1t3aQq2/vUFRh2GOIUsVwq7Qat0qrgbRindvYiEVo5/TfyHg7p7rP7Z2kaOdoDXc7Cbdp9w2N9lnTZrCRr8zMTHh5eRm0087Pz4e7uztOnTqFkSNHorS0FG5ubtizZ496so+rV6+iW7duiIiIwODBg3Hw4EFMnDgRt27dUo+G7dixA6+99hry8/MhFovv+bw08kUIIZpKKmtw5VYZEm7VNVoJ2WW4mS9DrdIwJ08IBYCPszUC3WwR6GaDDq428Hep++xpb9Vm/ughhLRc/T348sqrkVMqR3Zp1e378cmRW1qN7LIq5JbKUaNsvRlNxSIhvB2t0N7JWt2Utb9PR9nvRyY58vXwww/j9OnT6nsLFBcX48aNGxg4cKDej1k/W4uzszMAICYmBrW1tRg3bpx6m65du8LX11fdfEVERKBnz54apyGGhIRg4cKFuHLlCvr06aP1PHK5HHL5f9OolpWV6V0zaVxYWBi9G8MB5crH/ZprcUUNLt8qRXxWKS5n1X3OKKoyyGNLLUXwkDL0CfRCoJtNXbPlbgs/F+tm3SOIaLtf91feKFc+GstVYiG6fQqxdYPfzxhDUUUNskvrboyeXVqF7NJqZJfW3c8vp6zua0PdcqJGqUJqYSVSG7j+zFIkQDtHKXycrdHeyVrzVGgnKZxtxK12WiPts6bNYM2XhYWFxk3dHBwcsHDhQsTExOj1eCqVCsuWLcOwYcPU9w3LycmBWCyGo6OjxrYeHh7IyclRb3Nn41W/vn6dLqGhoVi/fr3W8prHHkNRVRUcnZxQXFQEFxcXFBYWwsHBAbKKCkgkEqiUSqgYg1gsRmVFBewdHFBSXKze1tHREWXl5bCWSlFbW6vOqrq6GrZ2digtKVFv6+TkhJKSEtjY2kIul0MkEkEoEKCmpgbW1tYoKytTb+vs7IyioiLY29ujsqoKlpaWAGNQKJWwkkggk8l01y2TQWJl9V/dlpaorKzUrtvJCWVlZbCWSlFTWwuBQAALkaiubltblJaWatVta2uL6tt1CwQC1NbWwloqRVlZGZxdXFBUWIghDg4ofP11jboZY1DeWbejI4rvqKW+bisrKyiUSrD6uquqYG9vr113aSmsra1RU1sLoUAAoUgEua66nZ1RUlysrttCJALurvt2zvXfY29vj8rKSojFYqhu1y2RSFChq25HR8jKy+vqVtTNHGVZX7edHUru+N2r67axQU1NzX91y+WwtbHRXbedHaqrqmBhYYE+KhXKVCpIpVKUlZfD2clJs24HB1RWVNTVrVJBqVLV1V1RAUcHB911S6VQ1O+zlpaoqqqC3V37rKOTE0pLS2FjY4MauRxCoRBCoRA1NTWwuatuZ2dnFBUXw66+bsu6GbsUtbWwkkpRrqNuBwcHVNxRt0qlgvh23Q537bMOjo4oLy+H9K66q6uqdL/Wbtctl8shuqNuaxsblN2uu1t+PpirK4qKi2FvZ4eq+roZg0KhgJVUCll5eZs+RmSWypDp3QVnmS1uOPkg3soVt6wc0VJilQId5SXoUJaN7qwC3kUZ6IVKuJTnQwjA4oSFxmtNXF/37WMFHSOaf4wYevv4qusYAYEAitpaOkbocYzoVVmJCktLnceIO+s212MEr78juhUXA25uzf474s5jhEVVFQIsLeHfwDHC2cUFSWVVqHDxRrLSAgU2LsiytEG2pR1yrRxwy8IGBWJbMAM0RbVK1mhzZqOsgVd1CTooZPCsKEQHhQzt5CXwriyGP6qhKC812DGiV1UVKiwsmvV3BB0jGj9GqKysWryP1DPYaYeTJ0/GK6+8ghEjRqiX9ezZE/Hx8Xo93sKFC3Hw4EGEh4ejffv2AIA9e/Zgzpw5GqNUADBw4ECMHj0amzZtwvPPP4+0tDQcPnxYvb6yshI2Njb4559/MGHCBK3n0jXy5ePjQ6cdchAbG6tz9JG0DOXKh7nlqlCqcD1XhriMEsRlFCMuowQ38mQtvnFreycpunnZo5uXPYK87NDF0x6+ztYNnoJjbrmaCsqVD8qVD1PJtUahQk5pNTJLKnGrpBpZxVXIKqlEVkkVsoqrcKukulVOb/S0t4KvszV8XazhV//ZxQZ+ztZwtG7eZCCmkq05McnTDj/99FM8/PDDGDJkCAYOHIj4+Hj4+vrq9Vgvv/wy/vrrL4SFhakbLwDw9PRETU0NSkpKNEa/cnNz4enpqd7m/PnzGo+Xm5urXqeLRCKBRCLRq1bSPG5ubsYuwSxRrny09VyLK2oQk1aM6LRiXEgvRnxmKapq9b9vlthCiK6edujmaY9uXnbo5mWPrl72zb7vUFvP1VRRrnxQrnyYSq5iCyF8XeqaHV1UKoYCmRyZJVXILK5CZnElMovrGrP6r+UGOLUxp6waOWXVOJ9apLXOzsoCfi7W8HO2gZ+LNTq43P7sagN3O4lWY2Yq2RLdDNZ8+fr6IjY2FgcOHEB8fDw6d+7c7NkFGWNYvHgxDhw4gJMnT8Lf319jfb9+/WBpaYljx47hscceAwBcu3YN6enpGDJkCABgyJAh2LBhA/Ly8uDu7g4AOHr0KOzt7REUFGSAn5S0xN2jlsQwKFc+2lKujDGkFFQgOq0YManFiE4rws38Cr0fT2IhRDcve/RoZ4+e7RzQo50DOnvYGWRmwbaUa1tCufJBufLRVnIVCgVwt7eCu70V+vo6aa1njCFfJkdmcRUyiirVnzOKK5FRVIVbJVUtvg9aebUCl7PKcDlLe04CK0uhevbXDq51TZlEXoohti7wosmKTJLezVdGRobWHbQtLS3xxBNP4IknntDrMRctWoQ9e/bg999/h52dnfoaLQcHB0ilUjg4OGDevHlYsWIFnJ2dYW9vj8WLF2PIkCEYPHgwAGD8+PEICgrCM888g82bNyMnJwf/93//h0WLFtHolgloKwfbtoZy5cOUc1WqGBKzyxCZUoTI5ELEpBWjUM/pmS2EAnTzskdvH0f0bO+Anu0c0NHdltsU7qaca1tGufJBufJhLrkKBAK421nB3U53c6ZQqpBTVo30okpkFlUhvahS/ZFRVKn3cbteda0KV3PKcTWnXHPFPxmQWAjVI2X+rja3b9dR97WHvfaIGWkdel/zZWNjg5UrV2L16tWwtm54NppmFdPATrBr1y4899xzAP67yfKPP/6ocZPlO08pTEtLw8KFC3Hy5EnY2Nhg9uzZeO+99+gmyyYgPz+fhsM5oFz5MKVcFUoVErLLcC65EJHJRTifWoTyaoVej+XjLEVvHyf09nFEbx9HdPe2h5Vl6800aEq5mhPKlQ/KlQ/KtY5MrkBGfUNWWIm0ogqkFdb9O6u45aNmDbEWi+oaMTcbBNQ3Zbe/drS+922Z7jeG7A30br7Onj2L5cuXIzMzExs2bFA3R+aAmi9+zp07px6lJIZDufJhzFxVKoaE7DKcSSpARHIholOLIZM3v9myshQiuL0j+ndwQj8/JwS3d4SLrXHPAqD9lQ/KlQ/KlQ/K9d4UShVulVRrNGRphXVfpxZWoLqWz0QgTtaW8He1QYCbLfxdbRDoVve1r7N1q75RZ0pMovmq9+233+LNN9+Eu7s7PvzwQ43ZDtsqar74kcvldPonB5QrH62da3phJcKTCnAmqQBnbxaguLK22Y/hbie53Wg5o7+fE4K87bmdPqgv2l/5oFz5oFz5oFxbRqViyCuXI7WwAmmFFUgtrGvMUgrqPlfW6D+5UkOEAqCdkxQBrrYIuN2QBbrZoKObLdx0TPxhTkyq+QLqpnJ/7733sHXrVjz00EN4//33tSbLaEuo+eKHbvzHB+XKB+9ciytq1M1WeFIBMoubfyPjDi7WGOTvgkEBzhjQwRntnaQm/z9A2l/5oFz5oFz5oFz5OXXqFLr1GYSUggqk3m7IUm9/zWvEzFZioR4h+++zLTq4WkNi0fZHy0yy+bpw4QL27duHTz75BGKxGIsXL8batWtha2vb0odvddR8EUJ4UKoYLmaW4NS1fJy6no+LmSXNvsdWgJsNBvm7YHCAMwb5u8DTwXA3fiSEEGLeVCqG3PJqpORXILmgAqkFFUi5/ZFeVGnwa8yEAsDX2RqBbrbo6F7XkAW626Cjmx0crJt3mxJjMonma8eOHYiKikJUVBQSExMhFArRo0cPDB48GMHBwfjpp5+QlJSE/fv3o3///i0qsrVR88UPvdPFB+XKhyFyzSuvRtj1Apy6no/TN/JR0sxTCTu4WGNoR1cMCagb3XK3a/vNFu2vfFCufFCufFCu/Oibba1ShaziKiQXyJB8uzlLzpchpaACuWWGn53S1Vasbso6uduio7sdOrrbmuRMjCbRfPn4+GDQoEEYPHgwBg8ejH79+kEqlWpss3HjRuzZsweXL19uUZGtjZovfiorKw02Oyb5D+XKhz65qlQM8VmlOJaYi2NX83DllvZ9WRrjaivG0EBXDO/oiqEdXdDeyfx+r7S/8kG58kG58kG58sMjW5lccXu0rK4xu5lf36DJDH4ao53EAoHu/zVlnTxs0cndDu0cpUa7b5lJNF9NkZubC29vbyiVhr/ojydqvviJiorCgAEDjF2G2aFc+WhqrpU1CpxJKlQ3XPnlTX+HUGopwqAAZwzv6IrhnVzRxcPO5N7xMzTaX/mgXPmgXPmgXPlpzWxVKobssmrczJMhOV+Gm7cbs5v5MoOPlllZCm83ZHZ3NGZ28HW2hohzU2bI3kDvmyw3hbu7O44fP87zKUgbc/eNuYlhUK58NJZrblk1jibk4lhiLs7eLIRc0fR3/jp72GJUZzeM6uyO/h2c7rupe2l/5YNy5YNy5YNy5ac1sxUKBWjnKEU7RylGdta8b1t5dS2S8yuQlCdTN2RJeTKkFep3bVl1rQqXs8pwOUvzjBKxhRCBbnXNWGePuoask7st/FxsuDdl+uDafAkEAowaNYrnU5A2prS0VOOG2MQwKFc+7s41taACh6/k4NCVHMSmlzT5cewkFhjW0RWjurhhZGc3tHOU3vubzBjtr3xQrnxQrnxQrvyYSrZ2VpYI9nFEsI+jxvJapQpphZXqpiwpT6b+Wp8p8msUKiRmlyExu+GmrIunnfqzj5O10U5fBDg3X4TczdxPpzIWypWfxOyyuobrcg6u5pQ3+fsCXG0wtps7xnbzQD8/J5O715Yx0f7KB+XKB+XKB+XKj6lnaymqO32wo7vmjOj1pzDWN2NJeeVIypPheq4MpVXNv++lRlN28b/lVpZCdHK3QycPW3TxsENnDzt09rSDt4NVq2RHzRdpVXQNHR+Uq+EwVjdhxt+XsvH3xSxkliY16ftEQgEGdHDCuG4eGNPVHQFube82G62F9lc+KFc+KFc+KFd+2mq2d57COOqOUxgZYyiQ1eDG7WbsRq5M/XWBrKbZz1Ndq0J8Vinis0o1lttKLPDB48F4qAffUUNqvkiryszMNImhcHNDubYMYwwJ2WX461I2/r6UjfSiyiZ9n53EAqO7umNsN3c80Nm9Td2zxJhof+WDcuWDcuWDcuXH3LIVCARws5PAzU6CoYGuGuuKKmpwPbccN/JkuJFbXvd1rgyFFc1vymRyBdzsxIYqu0FcZjsUCoV44IEH8P7776Nfv36GfnjuaLZDfmhqWT4oV/1czy3HXxdv4a9L2UguqGjS97jaivFgkCdCuntgaKArxBZ0OmFz0f7KB+XKB+XKB+XKD2ULFMrkdzRkMly/3ZgV3+Nem5feGg97K+03Uk1+tsOdO3ciNTUVixYtwrlz53g8BWmjoqOj6aaKHFCuTZdeWInf47Lw56VbuJ4ra9L3tHOUIqS7Jx7q4Yl+fk4mOXtSW0L7Kx+UKx+UKx+UKz+ULeBiK4GLrQSDA1zUy+pPX6xvxO5sysqrFfB2sNLZeBka1/t8tVU08kWIeSmuqMFf8dn4LTYLMWnFTfoePxdrPNLTCw/39EJ3b3uTv4CZEEIIIc3HGENOWTUKymvQs72Dzm0M2Rvodb5MbW0txo4dixs3brToycn9JywszNglmCXKVVt1rRJ/X8rG/N3RGLjxX6z57fI9G692jlK8MCoAfy0ejpOrHsBg6zz0aOdAjZeB0f7KB+XKB+XKB+XKD2XbPAKBAF4O0gYbL4M/n74jX25ubjh79iw6depk6JqMjka++KmpqYFYzP9ixvsN5VqHMYbzKUX49UImDsbnoFyuuOf3eNpb4ZFeXpjYywu9fRw1Gi3KlQ/KlQ/KlQ/KlQ/KlR/K1vCMPvIFAE8//TS+/vrrFj05uf/ExMQYuwSzdL/nequkCp8ev4EHPjiJGV+ew8/RmY02Xk7WlnhmsB9+eXEIzq4egzUTg9DH10lrhOt+z5UXypUPypUPypUPypUfyta06T3hhkKhwM6dO/Hvv/+iX79+sLGx0Vi/devWFhdHzI85jpSagvsx1+paJY4m5OLn6AyEJxXgXmP4YgshHgzywNTe7TCys1uTZim8H3NtDZQrH5QrH5QrH5QrP5StadO7+bp8+TL69u0LALh+/brGOro+gjQkNzcXrq6u996QNMv9lGt8Zil+js7A73FZKKtu/LRCgQAYEuCCKX3a4aEens2exeh+yrU1Ua58UK58UK58UK78ULamTe/m68SJE4asg9wnrKysjF2CWTL3XGVyBf6Iu4U959NwOavsntsHutlgej8fTOnjDS8Hqd7Pa+65Ggvlygflygflygflyg9la9q43OeLkIZIJBJjl2CWzDXXy1ml2HM+Hb/HZqGiRtnotrYSC0wK9sbj/dujz10TZ+jLXHM1NsqVD8qVD8qVD8qVH8rWtOk94QYAnD59Gk8//TSGDBmCrKwsAMB3332H8PBwgxRHzE9+fr6xSzBL5pRrZY0Ce6PS8ein4Zj4STj2RKY32ngNCXDBthnBiHpzHEKn9URfHRNn6MuccjUllCsflCsflCsflCs/lK1p03vk69dff8UzzzyDWbNmITY2FnK5HABQWlqKjRs34p9//jFYkcR8BAYGGrsEs2QOuSblyfBdRCr2X8i65xTx3g5WeLy/D6b3aw8fZ2tuNZlDrqaIcuWDcuWDcuWDcuWHsjVteo98vfvuu9ixYwe++uorWFr+dxH7sGHDcOHCBYMUR8xPXFycsUswS201V6WK4d+EXDzzdSTGbT2F3RFpDTZeQgEwrps7dj7XH6dfG4PlD3bm2ngBbTdXU0e58kG58kG58kG58kPZmja9b7JsbW2NhIQEdOjQAXZ2drh48SICAgKQnJyMoKAgVFdXG7rWVkM3WSaEr5LKGvwcnYHvzqUho6iq0W29HKwwY4APZgzwadHkGYQQQggh+jCJmyx7enoiKSlJa3l4eDgCAgJaVBQxX2FhYcYuwSy1lVwTs8vw+v5LGBx6DBv/udpg4yUQAGO6uuN/z/bH6VdHY9m4zkZpvNpKrm0N5coH5coH5coH5coPZWva9B75Cg0Nxffff4+dO3fiwQcfxD///IO0tDQsX74ca9asweLFiw1da6uhkS9+VCoVhMIWzfNCdDDlXFUqhpPX8/BVWAoikgsb3dbJ2hJPDvTFrEG+aO/E95TCpjDlXNsyypUPypUPypUPypUfytbwTGLka/Xq1XjqqacwduxYyGQyjBw5EvPnz8cLL7zQphsvwtfZs2eNXYJZMsVcq2uV2BOZjge3ncLcb6Ibbbx6tLPH+9N7IeL1sXjtoa4m0XgBppmrOaBc+aBc+aBc+aBc+aFsTZveI1/p6elo3749FAoFkpKSIJPJEBQUBBsbG2RkZMDX19fQtbYaGvnip6SkBI6OjsYuw+yYUq4FMjm+jUjD9+fSUFRR0+B2FkIBHu7phdlDO6Cvr2Huy2VoppSrOaFc+aBc+aBc+aBc+aFsDc+QvYHeU837+/sjOzsb7u7uCAoKUi8vLCyEv78/lMrGb4hK7k/p6el0QODAFHK9kVuO/51OwYG4LNQoVA1u52orwaxBdacWuttbtWKFzWcKuZojypUPypUPypUPypUfyta06d18NTRgJpPJYGVl2n9QEeNxcHAwdglmyZi5XkgvxucnbuLfxNxGt+viYYf5I/wxubc3JBaiVqquZWh/5YNy5YNy5YNy5YNy5YeyNW3Nbr5WrFgBABAIBFi7di2srf+7NkOpVCIyMhK9e/c2WIHEvOh5liu5h9bOlTGG0zcK8PnJJJxLLmp02xGdXLFgRABGdHI1yVMLG0P7Kx+UKx+UKx+UKx+UKz+UrWlrdvMVGxsLoO4XGx8fD7FYrF4nFosRHByMVatWGa5CYlbKy8uNXYJZaq1clSqGQ5dzsP1UEi5nlTW4nVgkxKO9vTF/RAC6eNq1Sm080P7KB+XKB+XKB+XKB+XKD2Vr2prdfJ04cQIAMGfOHHz00Uc0IQVplnbt2hm7BLPEO1e5QonfYrPwxalkJBdUNLidg9QSzwz2w7ND/eBu1/ZPP6b9lQ/KlQ/KlQ/KlQ/KlR/K1rTpPdX8rl27qPEizZaYmGjsEswSr1zlCiW+i0jFA++fxGu/xjfYeHnYS/Dmw91wZvUYrArpYhaNF0D7Ky+UKx+UKx+UKx+UKz+UrWnTe6p5ADh27BiOHTuGvLw8qFSas5vt3LmzxcUZC001z49CoYCFhd7zvJAGGDrX6lol9kZlYPvJm8gpq25wuw4u1nhxVCCm9m3XZibRaA7aX/mgXPmgXPmgXPmgXPmhbA3PJG6yvH79eowfPx7Hjh1DQUEBiouLNT4I0YVu/MeHoXKtrlVi15kUjHr/BNb9caXBxqu7tz0+faoPjq18AE8O9DXLxgug/ZUXypUPypUPypUPypUfyta06T3y5eXlhc2bN+OZZ54xdE1GRyNf5H5TVaPEnvPp2HHqJvLL5Q1uN7CDMxaN6YiRbXDmQkIIIYQQfZjEyFdNTQ2GDh3aoie/W1hYGCZNmgRvb28IBAL89ttvGuufe+45CAQCjY+HHnpIY5uioiLMmjUL9vb2cHR0xLx58yCTyQxaJ9FfWFiYsUswS/rmKlfUjXSN2HwC7/yV0GDjNTjAGT8uGIyfXxyCUZ3d7pvGi/ZXPihXPihXPihXPihXfihb06b3CaHz58/Hnj17sGbNGoMVU1FRgeDgYMydOxfTpk3Tuc1DDz2EXbt2qf8tkUg01s+aNQvZ2dk4evQoamtrMWfOHDz//PPYs2ePweok+uvTp4+xSzBLzc1VoVTh1wuZ+OjfG7hV2vA1XUMDXbB0bCcMCnBpaYltEu2vfFCufFCufFCufFCu/FC2pk3v5qu6uhpffvkl/v33X/Tq1QuWlpYa67du3drsx5wwYQImTJjQ6DYSiQSenp461yUmJuLQoUOIiopC//79AQCffPIJHn74YXzwwQfw9vZudk3EsG7cuIG+ffsauwyz09RcVSqGv+Kzse3odaQ0MmX88I6uWDquEwZ0cDZkmW0O7a98UK58UK58UK58UK78ULamTe/m69KlS+jduzcA4PLlyxrreJ6SdPLkSbi7u8PJyQljxozBu+++CxeXunflIyIi4OjoqG68AGDcuHEQCoWIjIzE1KlTdT6mXC6HXP7f6VZlZQ3fPJa0jIeHh7FLMEv3ypUxhmOJefjgyDVczWn45osjOrli2bhO6Od3fzdd9Wh/5YNy5YNy5YNy5YNy5YeyNW16X/N14sSJBj+OHz9uyBrVHnroIXz77bc4duwYNm3ahFOnTmHChAlQKpUAgJycHLi7u2t8j4WFBZydnZGTk9Pg44aGhsLBwUH94ePjA6Du+rEzZ85AoVCoz58NCwtDeXk5Lly4gKysLCQlJSExMRH5+fmIjIyEXC7X2Laqqgrnz59Hbm4url27huvXryM7OxvR0dGoqKjQ2La2thZnz55FQUEBrly5guTkZGRkZCAuLg6lpaUa26pUKpw+fRolJSW4ePEi0tPTkZqaisuXL6OwsFBn3TKZDDExMRp15+XlITIyEtXV1RrbVldXq+u+evUqbty4gVu3biEmJgYymUxn3YWFhbh8+TJSUlKQnp6OixcvqutmjCEsLAyVlZUICwtDaWmpuu6UlBR13WfPnkVtba3Oum/duoUbN27g6tWryM3Nxfnz53XWHRkZiby8PCQmJiIpKQlZWVk661YoFDhz5oy67tTUVHXdJSUlOH36NFQqlcb3lJaWIi4uDhkZGUhOTsaVK1dQUFCgs+6KigpER0cjOzsb169fx7Vr19R1V1VVaWwrl8sRGRmJ/Px8jbovXLiA8vJynXUXFRUhPj4eqampSEtLw6VLl1BSUoLw8HCNunccOI7Jn5zG/G+jG2y8ujiL8MuLQ7Cgkxzd3KwQHR2NnJwcdd05OTmIiopS//7urPvcuXPIz89HQkICbt68iczMTMTGxmrVrVQqER4ejuLiYly6dAlpaWnquouLixEeHg6lUqn1WouNjUVmZiZu3ryJhIQE5Ofn49y5c1qvtcrKSkRFRSEnJ0f9WsvJyUF0dLRW3TU1NYiIiFC/1u6su6ysTL3t+fPnoVKpEB4ejpKSEnXdqampiI+Pp2MEh2NE/Wc6RjT/GFH/Pc09RoSFhaGsrEzjtVZfd0REBGpqarRea/fTMeLq1asNHiPqX2t0jGj+MeL8+fN0jOB0jLh27ZpB/46gY0TdMcJQWnSfL54EAgEOHDiAKVOmNLhNcnIyAgMD8e+//2Ls2LHYuHEjdu/ejWvXrmls5+7ujvXr12PhwoU6H0fXyJePjw/NdshBYmIiunXrZuwyzI6uXK/mlOG9g1dx8lp+g9/Xq70DVo3vghE0e6FOtL/yQbnyQbnyQbnyQbnyQ9kaniFnO2zRHdhOnz6NL774Ajdv3sS+ffvQrl07fPfdd/D398fw4cNbVFhTBAQEwNXVFUlJSRg7diw8PT2Rl5ensY1CoUBRUVGD14kBddeR3T1xB+HD1dXV2CWYpTtzzS6twtYj17HvQiYaemuls4ctVjzYBSHdPajpagTtr3xQrnxQrnxQrnxQrvxQtqZN79MOf/31V4SEhEAqlSI2NlY9clRaWoqNGzcarMDGZGZmorCwEF5eXgCAIUOGoKSkBDExMeptjh8/DpVKhUGDBrVKTaRxycnJxi7BLCUnJ6OsuhbvH76K0R+cxC8xuhsvX2drbJsRjINLR+KhHp7UeN0D7a98UK58UK58UK58UK78ULamTe/TDvv06YPly5fj2WefhZ2dHS5evIiAgADExsZiwoQJjV5j1RCZTIakpCT142/duhWjR4+Gs7MznJ2dsX79ejz22GPw9PTEzZs38eqrr6K8vBzx8fHqkasJEyYgNzcXO3bsUE81379//2ZNNU83WeZHLpfTKKOB1ShU+PbMTXweloqiihqd27jZSbB0bCfMGOADS5He77ncd2h/5YNy5YNy5YNy5YNy5YeyNTyTuMnytWvXMHLkSK3lDg4OKCkp0esxo6Oj0adPH/X9CVasWIE+ffpg7dq1EIlEuHTpEiZPnozOnTtj3rx56NevH06fPq2xg/3www/o2rUrxo4di4cffhjDhw/Hl19+qVc9xPAiIyONXYLZYIzhYHw2Htx2Cu8evK6z8bIWi7B8XGecXPUAnh7sR41XM9H+ygflygflygflygflyg9la9r0HvkKCAjAl19+iXHjxmmMfH377bd47733kJCQYOhaWw2NfBFTd+VWKd7+MwGRKUU614uEAswc6IMlYzvB3c6qlasjhBBCCDEfJjHytWDBAixduhSRkZEQCAS4desWfvjhB6xatarBWQUJqZ/Sk+gnv1yO1/dfwsRPwhtsvMYHeeDwspF4d0pParxaiPZXPihXPihXPihXPihXfihb06b3yBdjDBs3bkRoaKh67nuJRIJVq1bhnXfeMWiRrY1GvvipqqqCVCo1dhltjlyhxDdnUvHJ8STI5Aqd2/TxdcQbD3fDgA50g2RDof2VD8qVD8qVD8qVD8qVH8rW8Exi5EsgEODNN99EUVERLl++rL5BWltvvAhf8fHxxi6hTWGM4ciVHIzfFobQg1d1Nl7tHKVYNtAO+xcOpcbLwGh/5YNy5YNy5YNy5YNy5YeyNW163+crNDQUHh4emDt3LoKCgtTLd+7cifz8fLz22msGKZCYFz8/P2OX0GbcyC3H+j8TEJ5UoHO91FKElx4IxIKRASgtKqBp4zmg/ZUPypUPypUPypUPypUfyta06T3y9cUXX6Br165ay7t3744dO3a0qChivvSdCfN+IpMrEPpPIiZ8dLrBxmtan3Y4seoBLB7bCVaWIsqVE8qVD8qVD8qVD8qVD8qVH8rWtOk98pWTk6O+ufGd3NzckJ2d3aKiiPmi0ZmGMcbwd3w23v0rETll1Tq36ePriLUTg9DH10ljOeXKB+XKB+XKB+XKB+XKB+XKD2Vr2vRuvnx8fHDmzBn4+/trLD9z5gy8vb1bXBgxT3Z2dsYuwSQl5cmw7o/LOJNUqHO9l4MVVk/oisnB3joPqpQrH5QrH5QrH5QrH5QrH5QrP5StadO7+VqwYAGWLVuG2tpajBkzBgBw7NgxvPrqq1i5cqXBCiTmJSsrS+eI6f2qQq7AJ8eT8HV4MmqV2hOPWooEWDAiAC+P6QhrccMvV8qVD8qVD8qVD8qVD8qVD8qVH8rWtLVoqvnVq1fj448/Rk1NDQDAysoKr732GtauXWvQIlsbTTXPT0VFBWxsbIxdhtExxnDocg7e/isB2aW6TzEc0ckVb03ujkA323s+HuXKB+XKB+XKB+XKB+XKB+XKD2VreCYz1fymTZuQn5+Pc+fO4eLFiygqKmrzjRfhKyYmxtglGF1mcSXm7Y7Gwh8u6Gy8vB2ssH1WX3w7d2CTGi+AcuWFcuWDcuWDcuWDcuWDcuWHsjVteo98mTMa+SI8KJQqfHM2FVuPXkdljVJrfVNPMSSEEEIIIa3HJEa+CNFHWFiYsUswivjMUkz5/Aze/TtRZ+M1opMrDi0biVcf6qpX43W/5sob5coH5coH5coH5coH5coPZWvaaORLBxr54qe2thaWlpbGLqPVVMgV2HLkOr45mwKVjleam50EaycGYWIvrxZNDXu/5dpaKFc+KFc+KFc+KFc+KFd+KFvDo5Ev0mZFRUUZu4RW829CLh7cego7z+huvJ4a5It/V4zCpAamj2+O+ynX1kS58kG58kG58kG58kG58kPZmja6sIS0qs6dOxu7BO4KZHKs++MK/r6k+2bjndxtETqtJ/p3cDbYc94PuRoD5coH5coH5coH5coH5coPZWvaWtR8HTt2DMeOHUNeXh5UKpXGup07d7aoMGKecnNz4erqauwyuGCM4Y+Lt/DWH1dQXFmrtV5sIcSSMR3x/MhAiC0MO+hszrkaE+XKB+XKB+XKB+XKB+XKD2Vr2vRuvtavX4+3334b/fv3h5dXy65XIfcPqVRq7BK4yC2rxv/9dhlHE3J1rh/W0QUbpvREB1c+990w11yNjXLlg3Llg3Llg3Llg3Llh7I1bXo3Xzt27MA333yDZ555xpD1EDNnbheAMsawLyYT7/yVgLJqhdZ6R2tLrHkkCNP6tuP6BoW55WoqKFc+KFc+KFc+KFc+KFd+KFvTpve5TzU1NRg6dKghayH3gcLCQmOXYDBZJVWYvSsKr+y7pLPxerinJ44uH4XH+rXnPjJsTrmaEsqVD8qVD8qVD8qVD8qVH8rWtOndfM2fPx979uwxZC3kPuDv72/sElqMMYYfItMQsi0MYdfztda72orx+ay++HxWP7jZSVqlJnPI1RRRrnxQrnxQrnxQrnxQrvxQtqZN7+aruroaW7duxahRo7B48WKsWLFC44MQXS5evGjsEloku7QKz+48jzcPXIZMrj3aNaW3N44uH4WHe3q1al1tPVdTRbnyQbnyQbnyQbnyQbnyQ9maNr1vsjx69OiGH1QgwPHjx/UuytjoJsvkbowx/B53C2t/v6zzFEMPewk2TOmJcUEeRqiOEEIIIYTwYsjeQO8JN06cONGiJyb3p7CwMIwcOdLYZTRLUUUN3jwQj4OXc3Sun9HfB2880g0OUuNd4NoWc20LKFc+KFc+KFc+KFc+KFd+KFvTpvfIlzmjkS9+VCoVhELD3uOKp38TcrF6fzwKZHKtdR72EmyeHoxRnd2MUJmmtpZrW0G58kG58kG58kG58kG58kPZGp4he4MW/WZKSkqwZcsWzJ8/H/Pnz8fWrVtRWlraooKIeTtz5oyxS2iS8upavLrvIuZ/G62z8ZrS2xtHlo0yicYLaDu5tjWUKx+UKx+UKx+UKx+UKz+UrWnTe+QrOjoaISEhkEqlGDhwIAAgKioKVVVVOHLkCPr27WvQQlsTjXzxU1JSAkdHR2OX0ahzyYVY+fNFZJVUaa1zsrbEhqk9W31CjXtpC7m2RZQrH5QrH5QrH5QrH5QrP5St4ZnEyNfy5csxefJkpKamYv/+/di/fz9SUlIwceJELFu2rEVFEfOVlpZm7BIaVKtUYdOhq5j51TmdjdfYru44vHykyTVegGnn2pZRrnxQrnxQrnxQrnxQrvxQtqZN7wk3oqOj8dVXX8HC4r+HsLCwwKuvvor+/fsbpDhifpycnIxdgk4pBRVY+lMsLmVqnzZrIxZh3aTueLw//5sl68tUc23rKFc+KFc+KFc+KFc+KFd+KFvTpnfzZW9vj/T0dHTt2lVjeUZGBuzs7FpcGDFPKpXK2CVoYIzhl+hMvPXnFVTWKLXWD/J3xgePB8PH2doI1TWdqeVqLihXPihXPihXPihXPihXfihb06Z38zVjxgzMmzcPH3zwAYYOHQqg7gK/V155BTNnzjRYgcS8yGQyY5egVlJZgzcOxOOfeO0p5C1FAqwa3wULRgRAKDTN0a47mVKu5oRy5YNy5YNy5YNy5YNy5YeyNW16N18ffPABBAIBnn32WSgUdTedtbS0xMKFC/Hee+8ZrEBiXry8TON6qYibhVjxcxyyS6u11gW42eDjJ/ugRzsHI1SmH1PJ1dxQrnxQrnxQrnxQrnxQrvxQtqZN7wk3xGIxPvroIxQXFyMuLg5xcXEoKirCtm3bIJFIDFkjMSNXr1416vPXT6rx1P/O6Wy8Zg70xV+Lh7epxgswfq7minLlg3Llg3Llg3Llg3Llh7I1bXSTZR1oqnl+FAqFxiQtrSmjqBKLf4xFXEaJ1jpHa0u8N60XHurh2fqFGYAxczVnlCsflCsflCsflCsflCs/lK3hGbI3aNZvZsWKFXjnnXdgY2ODFStWNLrt1q1bW1QYMU9nz57FyJEjW/15D13Owav7LqKsWqG1blhHF2x9ojc87K1avS5DMVau5o5y5YNy5YNy5YNy5YNy5YeyNW3NGvkaPXo0Dhw4AEdHR4wePbrhBxUIcPz4cYMUaAw08mU+5AolQv+5im/OpmqtsxQJ8EpIF8wf3jYm1SCEEEIIIa3PaCNfJ06cUH+9e/dutG/fHkKh5mVjjDFkZGS0qChivsLCwlrt3ZjUggq8/OMFXM4q01rXwcUanz7Vt81d29WQ1sz1fkK58kG58kG58kG58kG58kPZmja9r/kSiUTIzs6Gu7u7xvLCwkK4u7tDqdS+Z1JbQSNf/MhkMtja2nJ/nj8v3sLr++Mhk2ufZjgp2Bsbp/aAnZUl9zpaS2vler+hXPmgXPmgXPmgXPmgXPmhbA3PkL2B3rMdNtSzyWQyWFm13WtnCF/Xrl3j+vjVtUq8vj8ei3+M1Wq8JBZCvDetJz5+srdZNV4A/1zvV5QrH5QrH5QrH5QrH5QrP5StaWv2VCj1E20IBAKsXbsW1tbW6nVKpRKRkZHo3bu3wQok5sXTk99sgikFFVj4fQyu5pRrrQt0s8Fns/qiq6d5jmTyzPV+RrnyQbnyQbnyQbnyQbnyQ9matmaPfMXGxiI2NhaMMcTHx6v/HRsbi6tXryI4OBjffPONXsWEhYVh0qRJ8Pb2hkAgwG+//aaxnjGGtWvXwsvLC1KpFOPGjcONGzc0tikqKsKsWbNgb28PR0dHzJs3j+70bUKqqqq4PO6hyzmY/Em4zsZrer/2+HPxcLNtvAB+ud7vKFc+KFc+KFc+KFc+KFd+KFvT1uyRr/pJN+bMmYOPPvrIoNdEVVRUIDg4GHPnzsW0adO01m/evBkff/wxdu/eDX9/f6xZswYhISFISEhQn+o4a9YsZGdn4+jRo6itrcWcOXPw/PPPY8+ePQark+ivtrbWoI+nUKqw+fA1fBmWrLVOainCu1N64LF+7Q36nKbI0LmSOpQrH5QrH5QrH5QrH5QrP5StaTPZmywLBAIcOHAAU6ZMAVA36uXt7Y2VK1di1apVAIDS0lJ4eHjgm2++wZNPPonExEQEBQUhKioK/fv3BwAcOnQIDz/8MDIzM+Ht7d2k56YJN/jJy8vTmqRF78cqq8bLP8bifEqR1rouHnb4bFZfdHS/Py44NWSu5D+UKx+UKx+UKx+UKx+UKz+UreGZxIQb9RISEnDo0CH88ccfGh+GlpKSgpycHIwbN069zMHBAYMGDUJERAQAICIiAo6OjurGCwDGjRsHoVCIyMjIBh9bLpejrKxM44PwkZKSYpDHiUwuxCOfhOtsvKb2aYcDi4beN40XYLhciSbKlQ/KlQ/KlQ/KlQ/KlR/K1rTp3XwlJycjODgYPXr0wCOPPIIpU6ZgypQpmDp1KqZOnWrIGgEAOTk5AAAPDw+N5R4eHup1OTk5Wp2+hYUFnJ2d1dvoEhoaCgcHB/WHj48PgLrrx86cOQOFQoGwsDAAddellZeX48KFC8jKykJSUhISExORn5+PyMhIyOVyjW2rqqpw/vx55Obm4tq1a7h+/Tqys7MRHR2NiooKjW1ra2tx9uxZFBQU4MqVK0hOTkZGRgbi4uJQWlqqsa1KpcLp06dRUlKCixcvIj09Hampqbh8+TIKCwt11i2TyRATE6NRd15eHiIjI1FdXa2xbXV1tbruq1ev4saNG7h16xZiYmIgk8l01l1YWIjLly8jJSUF6enpuHjxorpuxhjCwsLQq1cvhIWFobS0VF13SkqKuu6zZ8+itrZWZ923bt3C9evX8e6+c3jqq3PIL5dr/q6FwFuPdMEMv2rISoqQmJiIpKQkZGVl6axboVDgzJkz6rpTU1PVdZeUlOD06dNQqVQa31NaWoq4uDhkZGQgOTkZV65cQUFBgc66KyoqEB0djezsbFy/fh3Xrl1Dbm4uzp8/j6qqKo1t5XI5IiMjkZ+fr1H3hQsXUF5errPuoqIixMfHIzU1Fc7Ozrh06RJKSkoQHh6uVXdZWRliY2ORmZmJmzdvquuOiIhATU2NxraVlZWIjo5GTk6Ouu6cnBxERUWhsrJSq+5z584hPz8fCQkJuHnzJjIzMxEbG6tVt1KpRHh4OIqLi3Hp0iWkpaUhLS0Nly5dQnFxMcLDw6FUKrVea3fWnZCQgPz8fJw7d07rtVZZWYmoqCjk5OSoX2s5OTmIjo7WqrumpgYRERHq19qddZeVlam3raiogEqlQnh4OEpKStR1p6amIj4+no4Reh4jHB0dGzxG1H/W9xhx48YNXL16Vf1a01V3ZGQk8vLyzO4YERwc3OAxov61RseI5h8jJBJJg8eI+tcaHSOaf4yoqKho8BjR2N8RdIy49zHCysqq2X9H0DHi3scIQ9H7tMNJkyZBJBLhf//7H/z9/XH+/HkUFhZi5cqV+OCDDzBixIiWFXbXaYdnz57FsGHDcOvWLXh5eam3e+KJJyAQCLB3715s3LgRu3fv1ppi093dHevXr8fChQt1PpdcLodc/t8f8mVlZfDx8aHTDjkIC9P/xn9l1bV49ZdLOHRFu5Fu5yjF57P6ItjHsYUVtk0tyZU0jHLlg3Llg3Llg3Llg3Llh7I1PEOedtjsCTfqRURE4Pjx43B1dYVQKIRQKMTw4cMRGhqKJUuWIDY2tkWF3a1+2szc3FyN5is3N1c9tb2npyfy8vI0vk+hUKCoqKjRaTclEgkkEolB6yW66XswSMqT4fnvopGcX6G1blRnN3w4ozecbMQtLa/NooMsH5QrH5QrH5QrH5QrH5QrP5StadP7tEOlUgk7OzsAgKurK27dugUA8PPz43JzN39/f3h6euLYsWPqZWVlZYiMjMSQIUMAAEOGDEFJSQliYmLU2xw/fhwqlQqDBg0yeE2k+eqHd5vjyJUcTPnsjFbjJRAAy8d1xq7nBtzXjRegX67k3ihXPihXPihXPihXPihXfihb06b3yFePHj1w8eJF+Pv7Y9CgQdi8eTPEYjG+/PJLBAQE6PWYMpkMSUlJ6n+npKQgLi4Ozs7O8PX1xbJly/Duu++iU6dO6qnmvb291acmduvWDQ899BAWLFiAHTt2oLa2Fi+//DKefPLJJs90SPgaOHBgk7dVqRg+PHYDHx+7obXO0doSHz3ZB6M6uxmyvDarObmSpqNc+aBc+aBc+aBc+aBc+aFsTZveI1//93//B5VKBQB4++23kZKSghEjRuCff/7Bxx9/rNdjRkdHo0+fPujTpw8AYMWKFejTpw/Wrl0LAHj11VexePFiPP/88xgwYABkMhkOHTqkvscXAPzwww/o2rUrxo4di4cffhjDhw/Hl19+qe+PSQzs0qVLTdqurLoWz38XrbPx6tHOHn8tHk6N1x2amitpHsqVD8qVD8qVD8qVD8qVH8rWtOk94UZ6ejrat28PofC//q2oqAhOTk7IyMiAr6+vwYpsbXSfL35yc3O1Zqy8W2PXd03r0w4bp/WElaWIV4ltUlNyJc1HufJBufJBufJBufJBufJD2RqeSdzny9/fHwUFBRrLnJ2dUVRUBH9//xYVRcxXcXFxo+sbur5LJBRg7cQgbHkimBovHe6VK9EP5coH5coH5coH5coH5coPZWva9L7mq6EBM5lMpnEaICF3Eol0N04qFcNHx27gIx2nGTrbiPHpU30wNNCVd3ltVkO5kpahXPmgXPmgXPmgXPmgXPmhbE1bs5uvFStWAKi7D9fatWthbW2tXqdUKhEZGame+p2Qu9nY2Ggtq5ArsOLnOBy+kqu1rkc7e+x4uh/aO1lrrSP/0ZUraTnKlQ/KlQ/KlQ/KlQ/KlR/K1rQ1u/mqv38XYwzx8fEQi/+b4lssFiM4OBirVq0yXIXErGRnZ2vMPJlZXIkF38YgMbtMa9upfdohlK7vapK7cyWGQbnyQbnyQbnyQbnyQbnyQ9maNr0n3JgzZw4++ugjs5yQgibc4Ecmk8HW1hYAEJNWhBe+i0GBrEZjG5FQgDce7oa5wzpAIBAYo8w2585cieFQrnxQrnxQrnxQrnxQrvxQtoZnEhNufP7557Cw+G/gLC0tDR9++CGOHDnSooKIebtw4QIAYF9MJmZ+GanVeDlILfHt3IGYN9yfGq9mqM+VGBblygflygflygflygflyg9la9r0HvkaP348pk2bhhdffBElJSXo0qULxGIxCgoKsHXrVixcuNDQtbYaGvniR6li2HzoKr4IS9ZaF+Bmg69nD4C/K52rTAghhBBCTINJjHxduHABI0aMAADs27cPnp6eSEtLw7fffqv3TZaJeSuvrsW0bYd1Nl4jO7vhwEvDqPHSU1hYmLFLMEuUKx+UKx+UKx+UKx+UKz+UrWnTe+TL2toaV69eha+vL5544gl0794d69atQ0ZGBrp06YLKykpD19pqaOTL8NILKzFvdxRu5Mm01s0d5o83Hu4KC5He7wXc92pra2FpaWnsMswO5coH5coH5coH5coH5coPZWt4JjHy1bFjR/z222/IyMjA4cOHMX78eABAXl4eNSxEQ3RqEaZ8fkar8bIUCfDetJ5YOymIGq8WioqKMnYJZoly5YNy5YNy5YNy5YNy5YeyNW16/8W7du1arFq1Ch06dMCgQYMwZMgQAMCRI0fQp08fgxVI2rbf47Lw1FeRKKrQnFjD2UaM7+cNwpMDfY1UmXnp0qWLsUswS5QrH5QrH5QrH5QrH5QrP5StadO7+Zo+fTrS09MRHR2NQ4cOqZePHTsW27ZtM0hxpO1ijOHjYzew9Kc41ChVGuu6eNjh90XDMCjAxUjVmZ/s7Gxjl2CWKFc+KFc+KFc+KFc+KFd+KFvT1uybLN/J09MTnp6eGssGDhzYooJI2ydXKPH6/njsv5CltW6Qjy2+nj8UtpIW7XrkLnQ3ez4oVz4oVz4oVz4oVz4oV34oW9NGfwETgyquqMEL38fgfEqR1rrZQ/wwO9iOGi8ORCKRsUswS5QrH5QrH5QrH5QrH5QrP5StaaNZDojBpBRUYNr2s1qNl0AArJsUhPWP9kB5aYlxijNzxcXFxi7BLFGufFCufFCufFCufFCu/FC2po2GIIhBnE8pwvPfRaOkslZjubVYhI+f7INxQR4AgA4dOhihOvNHufJBufJBufJBufJBufJBufJD2Zo2GvkiLfZ7XBae/l+kVuPlYS/Bzy8MUTdeAHDx4sXWLu++QLnyQbnyQbnyQbnyQbnyQbnyQ9maNr1vsgwA1dXVuHTpEvLy8qBSac5oN3ny5BYXZyx0k+WmYYxhx6lkbDp0VWtdkJc9vn6uP7wcpFrfIxAIWqvE+wblygflygflygflygflygflyg9la3gmcZPlQ4cOwdfXF4MHD8bkyZMxZcoU9cfUqVNbVBQxfUoVw9rfr+hsvMZ2dccvLw7RarwA4PTp061R3n2HcuWDcuWDcuWDcuWDcuWDcuWHsjVteo98derUCePHj8fatWvh4eFx729oQ2jkq3FVNUos+SkWRxNytdY9N7QD1kwMgkio+x0XejeGD8qVD8qVD8qVD8qVD8qVD8qVH8rW8Exi5Cs3NxcrVqwwu8aLNK5QJsfMr87pbLz+75FuWDep4cYLoHdjeKFc+aBc+aBc+aBc+aBc+aBc+aFsTZvezdf06dNx8uRJA5ZCTF1qQQUe234WcRklGsvFIiE+mdkH80cE3POdluDgYI4V3r8oVz4oVz4oVz4oVz4oVz4oV34oW9Om91Tzn376KR5//HGcPn0aPXv2hKWlpcb6JUuWtLg4Yjpi04sxb3c0iipqNJbbW1ngq2f7Y1CAS5MeJzU1lQ4KHFCufFCufFCufFCufFCufFCu/FC2pk3v5uvHH3/EkSNHYGVlhZMnT2qMeAgEAmq+zMjRhFws/vECqms1Z7Rs5yjFN3MGoJOHXZMfy8nJydDlEVCuvFCufFCufFCufFCufFCu/FC2pk3v5uvNN9/E+vXrsXr1agiFdLswc/Xj+XS8eSAeqrumZQnysseuOQPgYW/VrMdTKpUGrI7Uo1z5oFz5oFz5oFz5oFz5oFz5oWxNm97NV01NDWbMmEGNl5lijOHT40nYcvS61roRnVyx/el+sJU0f/epqKgwRHnkLpQrH5QrH5QrH5QrH5QrH5QrP5StadO7c5o9ezb27t1ryFqIiVCqGNb9cUVn4zW9X3vsfG6AXo0XAHh5ebW0PKID5coH5coH5coH5coH5coH5coPZWva9G6+lEolNm/ejFGjRmHx4sVYsWKFxgdpm+QKJZb8GItvI9K01i0aHYj3p/eCpUj/0c5r1661pDzSAMqVD8qVD8qVD8qVD8qVD8qVH8rWtOl9k+XRo0c3/KACAY4fP653UcZ2v95kuby6Fi98F4OzNws1lgsEwLqJQXhumH+Ln6O2tlZrZkzScpQrH5QrH5QrH5QrH5QrH5QrP5St4ZnETZZPnDjR4EdbbrzuV/nlcjz55TmtxstSJMDHT/YxSOMFABEREQZ5HKKJcuWDcuWDcuWDcuWDcuWDcuWHsjVteo98mbP7beQrrbACz+48j7TCSo3lNmIRvnimP4Z3cjVSZYQQQgghhBiXSYx8AUBJSQm2bNmC+fPnY/78+di6dStKS0tbVBBpXZezSvHY9gitxsvVVoyfnh9i8MYrLCzMoI9H6lCufFCufFCufFCufFCufFCu/FC2pk3vka/o6GiEhIRAKpVi4MCBAICoqChUVVXhyJEj6Nu3r0ELbU33y8hXZHIh5u+ORrlcobHc19ka384diA6uNgZ/TplMBltbW4M/7v2OcuWDcuWDcuWDcuWDcuWDcuWHsjU8kxj5Wr58OSZPnozU1FTs378f+/fvR0pKCiZOnIhly5a1qCjC3/GruXh253mtxqublz32LRzCpfECaAYeXihXPihXPihXPihXPihXPihXfihb06b3TZajo6Px1VdfwcLiv4ewsLDAq6++iv79+xukOMLHb7FZWPXLRShUmoOegwOc8eWz/WFvxW+GHLr3BB+UKx+UKx+UKx+UKx+UKx+UKz+UrWnTe+TL3t4e6enpWsszMjJgZ2fXoqIIP99GpGLZ3jitxmt8kAe+mTOQa+MF0F3XeaFc+aBc+aBc+aBc+aBc+aBc+aFsTZvezdeMGTMwb9487N27FxkZGcjIyMBPP/2E+fPnY+bMmYaskRgAYwwfH7uBtb9f0Vo3vV97fD6rL6wsRdzrUCqV3J/jfkS58kG58kG58kG58kG58kG58kPZmja9Tzv84IMPIBAI8Oyzz0KhqLtuyNLSEgsXLsR7771nsAJJy6lUDO/+nYidZ1K01s0d5o//e6QbhEJBq9Ti5OTUKs9zv6Fc+aBc+aBc+aBc+aBc+aBc+aFsTZteI1+1tbWYMGECXn75ZRQXFyMuLg5xcXEoKirCtm3bIJFIDF0n0ZNCqcIr+y7pbLxWPtgZaya2XuMFAGlpaa32XPcTypUPypUPypUPypUPypUPypUfyta06dV8WVpa4tKlSwAAa2tr9OzZEz179oS1tbVBi7vbW2+9BYFAoPHRtWtX9frq6mosWrQILi4usLW1xWOPPYbc3FyuNZmy6lolFv5wAb9eyNRa9/aj3bF4bCcIBK3XeAFAr169WvX57heUKx+UKx+UKx+UKx+UKx+UKz+UrWnT+5qvp59+Gl9//bUha2mS7t27Izs7W/0RHh6uXrd8+XL8+eef+OWXX3Dq1CncunUL06ZNa/UaTUGFXIF5u6NwNEGz+bQQCvDRk73x7JAORqnr/PnzRnlec0e58kG58kG58kG58kG58kG58kPZmja9b7K8ePFifPvtt+jUqRP69esHGxvN+0Jt3brVIAXe6a233sJvv/2GuLg4rXWlpaVwc3PDnj17MH36dADA1atX0a1bN0RERGDw4MFNfp62fpPl0qpazP0mCjFpxRrLJRZCbH+6L8Z09TBSZYQQQgghhLQtJnGT5cuXL6Nv376ws7PD9evXERsbq/7Q1RwZyo0bN+Dt7Y2AgADMmjVLPd19TEwMamtrMW7cOPW2Xbt2ha+vLyIiIhp9TLlcjrKyMo2PtqpQJsdTX53TarzsJBb4du5AozdeYWFhRn1+c0W58kG58kG58kG58kG58kG58kPZmrZmNV+XLl2CSqUCAJw4caLBj+PHj3MpdtCgQfjmm29w6NAhbN++HSkpKRgxYgTKy8uRk5MDsVgMR0dHje/x8PBATk5Oo48bGhoKBwcH9YePjw8AoKioCGfOnIFCoVDvyGFhYSgvL8eFCxeQlZWFpKQkJCYmIj8/H5GRkZDL5RrbVlVV4fz588jNzcW1a9dw/fp1ZGdnIzo6GhUVFRrb1tbW4uzZsygoKMCVK1eQnJyMjIwMxMXFobS0VGNblUqF06dPo6SkBBcvXkR6ejqir9zAlE9O4cotzebRydoSq/qL0d1dgpiYGI268/LyEBkZierqao3Hr66uVtd99epV3LhxA7du3UJMTAxkMpnOugsLC3H58mWkpKQgPT0dFy9eVNfNGENYWBgGDBiAsLAwlJaWqutOSUnB5cuXUVhYiLNnz6K2tlbj8WUyGWJiYnDr1i3cuHEDV69eRW5uLs6fP6+z7sjISOTl5SExMRFJSUnIysrSWbdCocCZM2fUdaempqrrLikpwenTp6FSqTS+p7S0FHFxccjIyEBycjKuXLmCgoICnXVXVFQgOjoa2dnZuH79Oq5du6auu6qqSmNbuVyOyMhI5Ofna9R94cIFlJeX66y7qKgI8fHxSE1NhZeXFy5duoSSkhKEh4dr1V1WVobY2FhkZmbi5s2b6rojIiJQU1OjsW1lZSWio6ORk5OjrjsnJwdRUVGorKzUqvvcuXPIz89HQkICbt68iczMTMTGxmrVrVQqER4ejuLiYly6dAlpaWlIS0vDpUuXUFxcjPDwcCiVSq3X2p11JyQkID8/H+fOndN6rVVWViIqKgo5OTnq11pOTg6io6O16q6pqUFERIT6tXZn3WVlZeptFQoFVCoVwsPDUVJSoq47NTUV8fHxbe4YkZqaqn6t6aq7/rXG+xjh4eHR4DGi/jMdI5p/jBg4cGCDx4j61xodI5p/jLC3t2/wGFH/WqNjRPOPEfUzZTf37wg6Rtz7GOHg4NDsvyPoGHHvY4ShNOu0Q5FIhOzsbLi7uyMgIABRUVFwcXExWDHNVVJSAj8/P2zduhVSqRRz5syBXC7X2GbgwIEYPXo0Nm3a1ODjyOVyje8rKyuDj49PmzrtMKOoErP+F4n0Is2dw81Ogh/mD0JnD9O48XVkZCQGDRpk7DLMDuXKB+XKB+XKB+XKB+XKB+XKD2VreEY77dDR0REpKXVTlqempqpHwYzF0dERnTt3RlJSEjw9PVFTU4OSkhKNbXJzc+Hp6dno40gkEtjb22t8tCU382V44osIrcarnaMUv7wwxGQaLwDw9/c3dglmiXLlg3Llg3Llg3Llg3Llg3Llh7I1bc1qvh577DGMGjUK/v7+EAgE6N+/PwICAnR+tAaZTIabN2/Cy8sL/fr1g6WlJY4dO6Zef+3aNaSnp2PIkCGtUo8xJGaXYcYXEcgurdZYHuBqg19eHIIOrjYNfKdxFBYWGrsEs0S58kG58kG58kG58kG58kG58kPZmjaL5mz85ZdfYtq0aUhKSsKSJUuwYMEC2Nm13qjKqlWrMGnSJPj5+eHWrVtYt24dRCIRZs6cCQcHB8ybNw8rVqyAs7Mz7O3tsXjxYgwZMqRZMx22JbHpxZi98zzKqhUay7t62uG7eYPgZmd6N7u2tLQ0dglmiXLlg3Llg3Llg3Llg3Llg3Llh7I1bc1qvgDgoYceAlA3u+DSpUtbtfnKzMzEzJkzUVhYCDc3NwwfPhznzp2Dm5sbAGDbtm0QCoV47LHHIJfLERISgs8//7zV6mtN51OKMGfXeVTUKDWWB/s4YvecAXC0FhupssZJpVJjl2CWKFc+KFc+KFc+KFc+KFc+KFd+KFvT1uzmq96uXbsMWUeT/PTTT42ut7KywmeffYbPPvuslSoyjjNJBZi/OxpVtZqN1yB/Z3z93ADYSvT+tXKXk5ODdu3aGbsMs0O58kG58kG58kG58kG58kG58kPZmja9b7Jszkz5Jssnrubhhe9jUKPQnOzkgS5u2D6rH6RikZEqaxqZTAZbW1tjl2F2KFc+KFc+KFc+KFc+KFc+KFd+KFvDM4mbLJPWd/hKDp7/Llqr8Qrp7oEvn+lv8o0XAFy4cMHYJZglypUPypUPypUPypUPypUPypUfyta00ciXDqY48vXnxVtYtjcOSpXmr2tSsDe2PhEMSxH10YQQQgghhBgajXzdZ36NycTSn2K1Gq/H+rbHhzN6t6nGq/5O4sSwKFc+KFc+KFc+KFc+KFc+KFd+KFvT1qKRr9OnT+OLL77AzZs3sW/fPrRr1w7fffcd/P39MXz4cEPW2apMaeTrx/PpeONAPO7+Lc0c6IsNU3pAKBQYpzA9KRQKWFiY7oQgbRXlygflygflygflygflygflyg9la3gmMfL166+/IiQkBFKpFLGxsZDL5QCA0tJSbNy4sUVFkTq7z6bi9f3ajddzQztg49S213gBQGRkpLFLMEuUKx+UKx+UKx+UKx+UKx+UKz+UrWnTu/l69913sWPHDnz11VcaN3MbNmwYXehnAF+FJWPdH1e0lr8wMgDrJgVBIGh7jRcAdO3a1dglmCXKlQ/KlQ/KlQ/KlQ/KlQ/KlR/K1rTp3Xxdu3YNI0eO1Fru4OCAkpKSltR03/vsRBI2/JOotXzJ2E5YPaFrm228ACA7O9vYJZglypUPypUPypUPypUPypUPypUfyta06d18eXp6IikpSWt5eHg4AgICWlTU/ezjYzfw/uFrWstfCemCFQ92btONFwC67wQnlCsflCsflCsflCsflCsflCs/lK1p07v5WrBgAZYuXYrIyEgIBALcunULP/zwA1atWoWFCxcassb7AmMMW49ex9aj17XWvflwNywa3dEIVRmeUNh2ZmZsSyhXPihXPihXPihXPihXPihXfihb06b3b2f16tV46qmnMHbsWMhkMowcORLz58/HCy+8gMWLFxuyRrPHGMMHR67h42M3tNatmxSEBSPNZySxuLjY2CWYJcqVD8qVD8qVD8qVD8qVD8qVH8rWtLX4Jss1NTVISkqCTCZDUFCQWQx1tuZU84wxvHfwKr4IS9Za986j3fHMkA5cn7+1lZSUwNHR0dhlmB3KlQ/KlQ/KlQ/KlQ/KlQ/KlR/K1vBMYqr5emKxGEFBQRg4cKBZNF6tiTGGd/9O1Nl4bZza0+waLwCIj483dglmiXLlg3Llg3Llg3Llg3Llg3Llh7I1bXqPfIWGhsLDwwNz587VWL5z507k5+fjtddeM0iBxtAaI1+MMaz/MwHfnE3VWC4QAJum9cITA3y4PK+xqVQqOheZA8qVD8qVD8qVD8qVD8qVD8qVH8rW8Exi5OuLL77QeR+B7t27Y8eOHS0qytypVAxrfr+s1XgJBcAH04PNtvEC6mbDJIZHufJBufJBufJBufJBufJBufJD2Zo2vUe+rKyskJiYCH9/f43lycnJCAoKQnV1tUEKNAaeI18qFcObv13Gj+fTNZYLBcC2Gb3xaO92Bn0+QgghhBBCiP5MYuTLx8cHZ86c0Vp+5swZeHt7t6goc1XXeMVrNV4ioQAfz+xzXzReYWFhxi7BLFGufFCufFCufFCufFCufFCu/FC2ps1C329csGABli1bhtraWowZMwYAcOzYMbz66qtYuXKlwQo0FyoVwxsH4vFTVIbGcguhAJ/M7IMJPb2MVFnrCg4ONnYJZoly5YNy5YNy5YNy5YNy5YNy5YeyNW16j3y98sormDdvHl566SUEBAQgICAAixcvxpIlS/D6668bssY2T6ViWL3/ks7G69On+t43jRcApKSkGLsEs0S58kG58kG58kG58kG58kG58kPZmja9R74EAgE2bdqENWvWIDExEVKpFJ06dYJEIjFkfW2eSsXw2q+X8EtMpsZyS5EAnz3VF+O7exqpMuNwcXExdglmiXLlg3Llg3Llg3Llg3Llg3Llh7I1bXo3X/VsbW0xYMAAQ9RidpS3G699Ohqvz2f1w4NBHkaqzHhqa2uNXYJZolz5oFz5oFz5oFz5oFz5oFz5oWxNW4uar2PHjuHYsWPIy8uDSqXSWLdz584WFdbWKVUMr+y7iP0XsjSWW4oE2D6rH8bdh40XAFRVVRm7BLNEufJBufJBufJBufJBufJBufJD2Zo2vZuv9evX4+2330b//v3h5eUFgUBgyLraNKWK4ZVfLmJ/rGbjJRYJsf3pvhjb7f5svADAw+P+/dl5olz5oFz5oFz5oFz5oFz5oFz5oWxNm97N144dO/DNN9/gmWeeMWQ9bZ5SxbDql4s4oKPx2vFMX4zpen+/IK5fvw5XV1djl2F2KFc+KFc+KFc+KFc+KFc+KFd+KFvTpvdNll1cXHD+/HkEBgYauiaj0/dGao01Xl880w+ju7obutQ2p7a2FpaWlsYuw+xQrnxQrnxQrnxQrnxQrnxQrvxQtoZnEjdZnj9/Pvbs2dOiJzcn9acaajVeFkJ88Sw1XvUiIiKMXYJZolz5oFz5oFz5oFz5oFz5oFz5oWxNm94jX0uXLsW3336LXr16oVevXlod9tatWw1SoDE0t7tt8BovCyG+fKYfHuhCjRchhBBCCCFtkUmMfF26dAm9e/eGUCjE5cuXERsbq/6Ii4trUVFtiXpWQ2q8miQsLMzYJZglypUPypUPypUPypUPypUPypUfyta06T3yZc6a2t0qVQyv7ruEXy9o3sdLLBLiy2ep8dKloqICNjY2xi7D7FCufFCufFCufFCufFCufFCu/FC2hmcSI1/1EhIScOjQIfzxxx/qjz///LOlD2vyGmu8vqDGq0GJiYnGLsEsUa58UK58UK58UK58UK58UK78ULamTe+p5pOTkzF16lTEx8dDIBCgfgCt/n5fSqXSMBWaIKWK4bVfG268RlPj1aB27doZuwSzRLnyQbnyQbnyQbnyQbnyQbnyQ9maNr1HvpYuXQp/f3/k5eXB2toaV65cQVhYGPr374+TJ08asETTolIxrP71EvbF6Gi8nqHG617Ky8uNXYJZolz5oFz5oFz5oFz5oFz5oFz5oWxNm94jXxERETh+/DhcXV0hFAohFAoxfPhwhIaGYsmSJYiNjTVknSZBdXvE65eGGi+aTv6e6BJDPihXPihXPihXPihXPihXPihXfihb06b3yJdSqYSdnR0AwNXVFbdu3QIA+Pn54dq1a4apzoSoVAyr9+tuvHY805caryZydHQ0dglmiXLlg3Llg3Llg3Llg3Llg3Llh7I1bXo3Xz169MDFixcBAIMGDcLmzZtx5swZvP322wgICDBYgaZApWJ440A8fo7W3XiN6ephpMranrS0NGOXYJYoVz4oVz4oVz4oVz4oVz4oV34oW9Om91Tzhw8fRkVFBaZNm4akpCRMnDgR169fh4uLC/bu3YsxY8YYutZWc+d0kra2dnjzt3j8eD5DYxtLkQA7nu6Hsd2o8WqOqqoqSKVSY5dhdihXPihXPihXPihXPihXPihXfihbwzOJqeZDQkIwbdo0AEDHjh1x9epVFBQUIC8vr003XndSqRje/O2yzsZr+yxqvPQRFRVl7BLMEuXKB+XKB+XKB+XKB+XKB+XKD2Vr2vQe+UpPT4ePj496avm71/n6+ra4OGOp725Xfn8W++KLNNZZigT4fFY/PBhEjRchhBBCCCHmziRGvvz9/ZGfn6+1vLCwEP7+/i0qyhA+++wzdOjQAVZWVhg0aBDOnz/f7Me4+xovC6EAnz3VlxqvFggLCzN2CWaJcuWDcuWDcuWDcuWDcuWDcuWHsjVtejdfjDGdo14ymQxWVlYtKqql9u7dixUrVmDdunW4cOECgoODERISgry8PL0f00IowKdP9cX47p4GrPT+M2jQIGOXYJYoVz4oVz4oVz4oVz4oVz4oV34oW9PW7Pt8rVixAgAgEAiwZs0aWFtbq9cplUpERkaid+/eBitQH1u3bsWCBQswZ84cAMCOHTvw999/Y+fOnVi9enWzH6+u8eqDh3pQ49VScXFxdFDggHLlg3Llg3Llg3Llg3Llg3Llh7I1bc1uvupvnswYQ3x8PMRisXqdWCxGcHAwVq1aZbgKm6mmpgYxMTF4/fXX1cuEQiHGjRuHiIgInd8jl8shl8vV/y4rK1N/LRIK8MnMPniohxe/ou8j5nYbAlNBufJBufJBufJBufJBufJBufJD2Zq2ZjdfJ06cAADMmTMHH330UYsvOjO0goICKJVKeHhoXpfl4eGBq1ev6vye0NBQrF+/XnsFU8Hhyn58/sZ2vFtUBBcXFxQWFsLBwQEVFRWQSCRQKpVgjEEsFqOiogIODg4oLi5Wb+vo6Ijy8nJIpVLU1tYCACwsLFBdXQ07OzuUlJSot3VyckJJSQlsbW0hl8shEokgEAhQU1MDa2trlJWVqbd1dnZGUVER7O3tUVVVBUtLSzDGoFQqIZFIIJPJ4OTkhKK76q4/LbS+bktLS1RWVmrV7eTkhLKyMnXdAoEAIpEI1dXVsLW1RWlp6T3rrq2thVQq1ahbLBajpqam0bodHR01ammo7qqqKtjb22vVXVpaCmtr63vW7ezsjOLi4kbrrs+5/nvs7e1RWVkJsVh8z7rrf/dWVlZQKBQAoK5b1+++tLQUNjY2qKmpUdctl8thY2Ojs247OztUVVXBwsJCnaVUKkV5ebnO331FRQXEYjFUKhVUKhUkEkmT99mm1C2XyyEUCiEUClFTU3PPui0tLQFAnbcp1p2dnQ1PT0+tuhljUCgU96ybjhG6666vV9cx4s7XGh0jmneMkEgkkMvlOo8Rd9Ztiq81Uz5G1O8vzambjhH3Pkbk5+fDy8ur2X9H0DGi6ftsc/6OoGNE43Ub8pKqZjdf9T7//HPcOVFiWloaDhw4gKCgIIwfP94gxbWW119/XX06JVA38uXj44MPnuiNJ4bOMGJl5icpKQkdO3Y0dhlmh3Llg3Llg3Llg3Llg3Llg3Llh7I1vPrZDg1B7+br0UcfxbRp0/Diiy+ipKQEAwcOhFgsRkFBAbZu3YqFCxcapMDmcnV1hUgkQm5ursby3NxceHrqvmZLIpFAIpFoLadTDQ2PbvrHB+XKB+XKB+XKB+XKB+XKB+XKD2Vr2vSe7fDChQsYMWIEAGDfvn3w9PREWloavv32W3z88ccGK7C5xGIx+vXrh2PHjqmXqVQqHDt2DEOGDDFaXaTO3U0xMQzKlQ/KlQ/KlQ/KlQ/KlQ/KlR/K1rTpPfJVWVkJOzs7AMCRI0cwbdo0CIVCDB48GGlpaQYrUB8rVqzA7Nmz0b9/fwwcOBAffvghKioq1LMfEuPp1KmTsUswS5QrH5QrH5QrH5QrH5QrH5QrP5StadN75Ktjx4747bffkJGRgcOHD6uv88rLyzP6JBwzZszABx98gLVr16J3796Ii4vDoUOHtCbhIK2vfrZMYliUKx+UKx+UKx+UKx+UKx+UKz+UrWkTsDtnzWiGffv24amnnoJSqcTYsWNx5MgRAHUzB4aFheHgwYMGLbQ11V9UV1paavRGkhBCCCGEEGI8huwN9B75mj59OtLT0xEdHY1Dhw6pl48dOxbbtm1rUVHEfIWFhRm7BLNEufJBufJBufJBufJBufJBufJD2Zo2vUe+zBmNfPGjUChgYaH3pYakAZQrH5QrH5QrH5QrH5QrH5QrP5St4RmyN2jWb2bFihV45513YGNjo3FfLF22bt3aosKIeYqMjMSwYcOMXYbZoVz5oFz5oFz5oFz5oFz5oFz5oWxNW7Oar9jYWPUdn835Yr76wcCysjIjV2J+2rVrR7lyQLnyQbnyQbnyQbnyQbnyQbnyQ9kaXn2ehjhhkE471CE5ORmBgYHGLoMQQgghhBBiIm7evImAgIAWPUazTztsCoFAgC1btuhVkClwdnYGAKSnp8PBwcHI1ZiPsrIy+Pj4ICMjg66lMyDKlQ/KlQ/KlQ/KlQ/KlQ/KlR/Klo/S0lL4+vqqe4SWaPZph3e6cOECFAoFunTpAgC4fv06RCIR+vXr1+LCjEkorJsE0sHBgXZcDuzt7SlXDihXPihXPihXPihXPihXPihXfihbPup7hJZoVvN14sQJ9ddbt26FnZ0ddu/eDScnJwBAcXEx5syZgxEjRrS4MEIIIYQQQggxJ3q3b1u2bEFoaKi68QIAJycnvPvuu236lENCCCGEEEII4UHv5qusrAz5+flay/Pz81FeXt6iooxNIpFg3bp1kEgkxi7FrFCufFCufFCufFCufFCufFCufFCu/FC2fBgyV71nO3z22Wdx+vRpbNmyBQMHDgRQd1+BV155BSNGjMDu3btbXBwhhBBCCCGEmAu9m6/KykqsWrUKO3fuVN/7y8LCAvPmzcP7778PGxsbgxZKCCGEEEIIIW1Zi+/zVVFRgZs3bwIAAgMDqekihBBCCCGEEB3oJsuEEEIIIYQQ0gpaPlk9IYQQQgghhJB7oubrLp999hk6dOgAKysrDBo0COfPnzd2SW1OWFgYJk2aBG9vbwgEAvz2228a6xljWLt2Lby8vCCVSjFu3DjcuHHDOMW2EaGhoRgwYADs7Ozg7u6OKVOm4Nq1axrbVFdXY9GiRXBxcYGtrS0ee+wx5ObmGqnitmH79u3o1auX+maUQ4YMwcGDB9XrKVPDeO+99yAQCLBs2TL1MspWP2+99RYEAoHGR9euXdXrKVf9ZWVl4emnn4aLiwukUil69uyJ6Oho9Xr6f1fzdejQQWt/FQgEWLRoEQDaX/WlVCqxZs0a+Pv7QyqVIjAwEO+88w7uPJmN9lf9lJeXY9myZfDz84NUKsXQoUMRFRWlXm+IXKn5usPevXuxYsUKrFu3DhcuXEBwcDBCQkKQl5dn7NLalIqKCgQHB+Ozzz7TuX7z5s34+OOPsWPHDkRGRsLGxgYhISGorq5u5UrbjlOnTmHRokU4d+4cjh49itraWowfPx4VFRXqbZYvX44///wTv/zyC06dOoVbt25h2rRpRqza9LVv3x7vvfceYmJiEB0djTFjxuDRRx/FlStXAFCmhhAVFYUvvvgCvXr10lhO2eqve/fuyM7OVn+Eh4er11Gu+ikuLsawYcNgaWmJgwcPIiEhAVu2bNG4lyn9v6v5oqKiNPbVo0ePAgAef/xxALS/6mvTpk3Yvn07Pv30UyQmJmLTpk3YvHkzPvnkE/U2tL/qZ/78+Th69Ci+++47xMfHY/z48Rg3bhyysrIAGChXRtQGDhzIFi1apP63Uqlk3t7eLDQ01IhVtW0A2IEDB9T/VqlUzNPTk73//vvqZSUlJUwikbAff/zRCBW2TXl5eQwAO3XqFGOsLkNLS0v2yy+/qLdJTExkAFhERISxymyTnJyc2P/+9z/K1ADKy8tZp06d2NGjR9moUaPY0qVLGWO0v7bEunXrWHBwsM51lKv+XnvtNTZ8+PAG19P/uwxj6dKlLDAwkKlUKtpfW+CRRx5hc+fO1Vg2bdo0NmvWLMYY7a/6qqysZCKRiP31118ay/v27cvefPNNg+VKI1+31dTUICYmBuPGjVMvEwqFGDduHCIiIoxYmXlJSUlBTk6ORs4ODg4YNGgQ5dwMpaWlAABnZ2cAQExMDGprazVy7dq1K3x9fSnXJlIqlfjpp59QUVGBIUOGUKYGsGjRIjzyyCMaGQK0v7bUjRs34O3tjYCAAMyaNQvp6ekAKNeW+OOPP9C/f388/vjjcHd3R58+ffDVV1+p19P/u1qupqYG33//PebOnQuBQED7awsMHToUx44dw/Xr1wEAFy9eRHh4OCZMmACA9ld9KRQKKJVKWFlZaSyXSqUIDw83WK4WBqu4jSsoKIBSqYSHh4fGcg8PD1y9etVIVZmfnJwcANCZc/060jiVSoVly5Zh2LBh6NGjB4C6XMViMRwdHTW2pVzvLT4+HkOGDEF1dTVsbW1x4MABBAUFIS4ujjJtgZ9++gkXLlzQOFe+Hu2v+hs0aBC++eYbdOnSBdnZ2Vi/fj1GjBiBy5cvU64tkJycjO3bt2PFihV44403EBUVhSVLlkAsFmP27Nn0/y4D+O2331BSUoLnnnsOAB0HWmL16tUoKytD165dIRKJoFQqsWHDBsyaNQsA/a2lLzs7OwwZMgTvvPMOunXrBg8PD/z444+IiIhAx44dDZYrNV+EtDGLFi3C5cuXNa7zIPrr0qUL4uLiUFpain379mH27Nk4deqUsctq0zIyMrB06VIcPXpU6x1E0jL172wDQK9evTBo0CD4+fnh559/hlQqNWJlbZtKpUL//v2xceNGAECfPn1w+fJl7NixA7NnzzZydebh66+/xoQJE+Dt7W3sUtq8n3/+GT/88AP27NmD7t27Iy4uDsuWLYO3tzftry303XffYe7cuWjXrh1EIhH69u2LmTNnIiYmxmDPQacd3ubq6gqRSKQ1y05ubi48PT2NVJX5qc+SctbPyy+/jL/++gsnTpxA+/bt1cs9PT1RU1ODkpISje0p13sTi8Xo2LEj+vXrh9DQUAQHB+Ojjz6iTFsgJiYGeXl56Nu3LywsLGBhYYFTp07h448/hoWFBTw8PChbA3F0dETnzp2RlJRE+2wLeHl5ISgoSGNZt27d1Kd00v+7WiYtLQ3//vsv5s+fr15G+6v+XnnlFaxevRpPPvkkevbsiWeeeQbLly9HaGgoANpfWyIwMBCnTp2CTCZDRkYGzp8/j9raWgQEBBgsV2q+bhOLxejXrx+OHTumXqZSqXDs2DEMGTLEiJWZF39/f3h6emrkXFZWhsjISMq5EYwxvPzyyzhw4ACOHz8Of39/jfX9+vWDpaWlRq7Xrl1Deno65dpMKpUKcrmcMm2BsWPHIj4+HnFxceqP/v37Y9asWeqvKVvDkMlkuHnzJry8vGifbYFhw4Zp3b7j+vXr8PPzA0D/72qpXbt2wd3dHY888oh6Ge2v+qusrIRQqPknvEgkgkqlAkD7qyHY2NjAy8sLxcXFOHz4MB599FHD5WqoGULMwU8//cQkEgn75ptvWEJCAnv++eeZo6Mjy8nJMXZpbUp5eTmLjY1lsbGxDADbunUri42NZWlpaYwxxt577z3m6OjIfv/9d3bp0iX26KOPMn9/f1ZVVWXkyk3XwoULmYODAzt58iTLzs5Wf1RWVqq3efHFF5mvry87fvw4i46OZkOGDGFDhgwxYtWmb/Xq1ezUqVMsJSWFXbp0ia1evZoJBAJ25MgRxhhlakh3znbIGGWrr5UrV7KTJ0+ylJQUdubMGTZu3Djm6urK8vLyGGOUq77Onz/PLCws2IYNG9iNGzfYDz/8wKytrdn333+v3ob+36UfpVLJfH192Wuvvaa1jvZX/cyePZu1a9eO/fXXXywlJYXt37+fubq6sldffVW9De2v+jl06BA7ePAgS05OZkeOHGHBwcFs0KBBrKamhjFmmFyp+brLJ598wnx9fZlYLGYDBw5k586dM3ZJbc6JEycYAK2P2bNnM8bqpkBds2YN8/DwYBKJhI0dO5Zdu3bNuEWbOF15AmC7du1Sb1NVVcVeeukl5uTkxKytrdnUqVNZdna28YpuA+bOncv8/PyYWCxmbm5ubOzYserGizHK1JDubr4oW/3MmDGDeXl5MbFYzNq1a8dmzJjBkpKS1OspV/39+eefrEePHkwikbCuXbuyL7/8UmM9/b9LP4cPH2YAdGZF+6t+ysrK2NKlS5mvry+zsrJiAQEB7M0332RyuVy9De2v+tm7dy8LCAhgYrGYeXp6skWLFrGSkhL1ekPkKmDsjtthE0IIIYQQQgjhgq75IoQQQgghhJBWQM0XIYQQQgghhLQCar4IIYQQQgghpBVQ80UIIYQQQgghrYCaL0IIIYQQQghpBdR8EUIIIYQQQkgroOaLEEIIIYQQQloBNV+EEEIIIYQQ0gqo+SKEEEIIIYSQVkDNFyGEEEIIIYS0Amq+CCHkPvDAAw9g2bJlxi7D6AyVA2MMW7duhb+/P6ytrTFlyhSUlpY2+j2FhYVwd3dHampqq9RoCp588kls2bLF2GUQQojJoOaLEELMjCn98W5KtRjSK6+8gu3bt2P37t04ffo0YmJi8NZbbzX6PRs2bMCjjz6KDh06tEqNpuD//u//sGHDhns2poQQcr+g5osQQohONTU1xi7BJEVGRmLr1q3Yu3cvRo4ciX79+mHBggX4559/GvyeyspKfP3115g3b14rVtqw1vrd9ujRA4GBgfj+++9b5fkIIcTUUfNFCCFm5LnnnsOpU6fw0UcfQSAQQCAQqE9zU6lUePXVV+Hs7AxPT0+tkZoHHngAL7/8MpYtWwZXV1eEhISgQ4cO+PDDDzW26927t8b37tu3Dz179oRUKoWLiwvGjRuHioqKRmu526FDhzB8+HA4OjrCxcUFEydOxM2bN7XqW7JkSaM/Q3l5OWbNmgUbGxt4eXlh27ZtjY6+qVQqhIaGwt/fH1KpFMHBwdi3b1+jGX/wwQcYO3Ys+vbtq17m4eGBgoKCBr/nn3/+gUQiweDBgzWWV1RU4Nlnn4WtrS28vLy0TtFrSn1N+Zl1/W6b8tj32qah3/2dJk2ahJ9++qnRTAkh5H5BzRchhJiRjz76CEOGDMGCBQuQnZ2N7Oxs+Pj4AAB2794NGxsbREZGYvPmzXj77bdx9OhRje/fvXs3xGIxzpw5gx07dtzz+bKzszFz5kzMnTsXiYmJOHnyJKZNmwbGWKO13K2iogIrVqxAdHQ0jh07BqFQiKlTp0KlUmnV19jPsGLFCpw5cwZ//PEHjh49itOnT+PChQsN1h8aGopvv/0WO3bswJUrV7B8+XI8/fTTOHXqlM7t5XI5/v77b0ydOlVjeXV1NRwcHBp8ntOnT6Nfv35ay1955RWcOnUKv//+O44cOYKTJ09q1NuU+pr6M9/9u23KYze2TWO/+zsNHDgQ58+fh1wubzAfQgi5bzBCCCFmZdSoUWzp0qVay4YPH66xbMCAAey1117T2KZPnz4a2/j5+bFt27ZpLAsODmbr1q1jjDEWExPDALDU1NQm19IU+fn5DACLj49v8s9QVlbGLC0t2f+3d38hTb1hHMC/m78d/0ynzm1hBvZHMMcsNLALuwiljcrhRV3U1UCDuuoPusgMo0YUlBF5EdSNN0HYhUEIYXSTNTh1YYFEutRaRJDa2tIUJU8X4cGT+3POj5pjfj8w8Dzn3bvn2Xv1+J5zdv/+ffn8t2/fpJycHDmH5fnMzc1JOTk5kt/vV8zZ3NwsHT58OGpefr9fAiBlZWVJRqNRfgmCILlcrpj1NDY2Sk1NTYrY9+/fJUEQpJ6eHjk2NTUlZWdnSydOnFCVn5qal+pevrZq5k40JtHaL3n9+rWqcUREa8F/q9r5ERFR0mzbtk1xXFxcjC9fvihi0XZn4tm+fTvq6+tRWVkJl8sFp9OJgwcPorCwUNM8gUAAHR0dEEURk5OT8o5XMBiEw+FQVcPY2BgWFhZQU1Mjn8/Pz0d5eXnUz3z37h1+/PiBPXv2KOLz8/OoqqqK+p6RkREYjUa8evVKEd+/fz9qa2tj1jc7O4usrCxFbHR0FPPz89i5c6ccM5vNcr5q8tNS8/K1VTN3ojFq1z47OxvA7/veiIjWOjZfRERrhMFgUBzrdLoVl/UZjUbFsV6vX3EZ2cLCgvx3RkYGHj9+DL/fj/7+fnR1daG9vR2iKGLTpk2qc3O73SgtLcWdO3ewfv16LC4uwuFwrHgwhJoa1JqengYA9PX1oaSkRHEuMzMz6nsikQgsFgvKysrk2IcPHxAIBHDgwIGYn2WxWBAKhf55fvEsX1s1cycao3btv379CgCwWq2acyYiSje854uIKM0IgoCfP3/+lbmsVis+f/4sH0ciEYyPjyvG6HQ61NbW4sKFCxgcHIQgCOjt7VWdy9TUFIaHh3Hu3DnU19ejoqJCc6MCAJs3b4bBYMDLly/lWDgcxsjISNTxdrsdmZmZCAaDKCsrU7xi3ZtmsVgQDocVDemlS5ewb98+2O32mLlVVVXhzZs3itiWLVtgMBggiqIcC4VCcr5q8tNas5ba1YyJt/ZLhoaGsGHDBlgslrg5ERGtBdz5IiJKMxs3boQoinj//j1yc3NhNpv/91x1dXXo7u6G2+1GQUEBOjo6kJGRIZ8XRRFPnjyB0+mEzWaDKIqYmJhARUVFzFz0euX//QoLC1FUVITbt2+juLgYwWAQZ86c0ZxrXl4ePB4PvF4vzGYzbDYbzp8/D71eD51OF3V8a2srTp06hcXFRezatQvhcBjPnz+HyWSCx+OJ+n3Mzc3hypUrOHToEO7evYuHDx/ixYsXcXNzuVxoa2tDKBSSL8vLzc1Fc3MzvF4vioqKYLPZ0N7eLn8/avLTWrOW2hON2bp1a9y1XzIwMACn05lw/YiI1gI2X0REaaa1tRUejwd2ux2zs7Mrdqq0aGtrw/j4OBoaGpCfnw+fz6eYz2Qy4enTp7hx4wYikQhKS0vR2dmJvXv3xszlzx8Z1uv1uHfvHo4fPw6Hw4Hy8nLcvHkTu3fv1pzv9evXcezYMTQ0NMBkMuH06dP4+PHjivutlvh8PlitVly+fBljY2MoKChAdXU1zp49G3X8unXr0N3dDa/XC5/Ph7q6Ojx79izmTtmSyspKVFdXo6enB0ePHpXjV69exfT0NNxuN/Ly8tDS0qL4QWI1+WmtWcvc8cYkWnvg91MgHzx4gEePHsXNhYhordBJf17MT0RElCZmZmZQUlKCzs7OVf+B476+Pni9XgwNDa3Y/fubUqnmW7duobe3F/39/auaBxFRquDOFxERpY3BwUG8ffsWNTU1CIfDuHjxIgCgsbFxlTP7/UTEQCCAT58+Jdwp0yKVazYYDOjq6lrtNIiIUgabLyIiSivXrl3D8PAwBEHAjh07MDAwkDIPezh58uQ/mTdVaz5y5Mhqp0BElFJ42SEREREREVES8FHzREREREREScDmi4iIiIiIKAnYfBERERERESUBmy8iIiIiIqIkYPNFRERERESUBGy+iIiIiIiIkoDNFxERERERURKw+SIiIiIiIkoCNl9ERERERERJwOaLiIiIiIgoCX4BpfJyicC1AAIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting…\n",
    "def y_c(q):\n",
    "    a = a_max * np.cos(q)\n",
    "    t_c = t(q)\n",
    "    return a_max * np.sin(q) * t_c**2 / 2\n",
    "\n",
    "q_values = np.arange(0.0, 90, 1)\n",
    "y_values = np.array([y_c(np.radians(q)) for q in q_values])\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "ax.plot([0, 90], [0, 0], \"k\", linewidth=0.5)\n",
    "ax.plot([0, 90], [200, 200], \"r\", linewidth=0.5)\n",
    "ax.plot(q_values, y_values, linewidth=3)\n",
    "ax.set_xlim(0, 90)\n",
    "ax.set_xlabel(r'thrust angle $\\theta$ (degrees)')\n",
    "ax.set_ylabel(r'distance from station center, $y_c$ (m)')\n",
    "ax.set_title('Distance from station center at passing vs. thrust angle')\n",
    "ax.grid(True, color='gray', linestyle=':', linewidth=0.5)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50ae71d9",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "8a6812f4",
   "metadata": {},
   "source": [
    "**WOOOOOTT!!!** I can survive!! It looks like any thrust ange between about $38^\\circ$ and $75^\\circ$ will do the trick. I'll have the greatest margin of safety with $\\boxed{\\theta \\approx 55^\\circ}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ac38058",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e6537cf-7687-4639-8d83-279f485d3823",
   "metadata": {},
   "source": [
    "## Problem 3: Avalanche Patrol"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dbff458",
   "metadata": {},
   "source": [
    "### a) Kinematic model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6ce1cd0",
   "metadata": {},
   "source": [
    "I'll choose a coordinate system with the origin at the canon's location, with +y directly upwards away from Earth and +x horizontal, with the slope rising into the first quadrant and making an angle of $\\phi$ with the +x axis. In this coordinate system, the projectile's acceleration is a constant $\\vec{a} = -g\\,\\hat{y}$, so I can use the convenient constant-acceleration kinematic equations rather than resorting to integrals. Its initial velocity is $\\vec{v}_0 = v_0 \\cos(\\theta)\\,\\hat{x} + v_0 \\sin(\\theta)\\,\\hat{y}$, and its initial position is $\\vec{r}_0 = 0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5c3a973",
   "metadata": {},
   "source": [
    "$$ \\begin{split}\n",
    "    \\vec{v}(t) &= \\vec{v}_0 + \\vec{a}\\,t = v_0 \\cos(\\theta)\\, \\hat{x} + \\left[ v_0 \\cos(\\theta) - g\\,t \\right] \\hat{y} \\\\\n",
    "    \\vec{r}(t) &= \\vec{r}_0 + \\vec{v}_0\\,t + \\frac{1}{2}\\,\\vec{a}\\,t^2 = v_0 \\cos(\\theta)\\,t\\, \\hat{x} + \\left[ v_0 \\sin(\\theta)\\,t - \\frac{1}{2}\\,g\\,t^2 \\right] \\hat{y}\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8e3f400",
   "metadata": {},
   "source": [
    "### b) Distance up slope"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "409ee21a",
   "metadata": {},
   "source": [
    "The projectile hits the slope where the parabola of the charge's trajectory crosses the straight line of the slope.\n",
    "\n",
    "The line describing the slope contains all points $(x, y)$ such that $y / x = \\tan(\\phi)$.\n",
    "\n",
    "I can find the time at which the projectile hits the slope by solving the equation $\\tan(\\phi) = y(t_i) / x(t_i)$ for the impact time $t_i$:\n",
    "\n",
    "$$ \\tan(\\phi) = \\frac{y(t_i)}{x(t_i)} = \\frac{v_0 \\sin(\\theta)\\,t_i - \\frac{1}{2}\\,g\\,t_i^2}{v_0 \\cos(\\theta)\\,t_i} = \\tan(\\theta) - \\frac{g\\,t_i}{2\\,v_0\\,\\cos(\\theta)} $$\n",
    "\n",
    "$$ \\Rightarrow \\quad t_i = \\frac{2\\,v_0\\,\\cos(\\theta)}{g} \\left[ \\tan(\\theta) - \\tan(\\phi) \\right] $$\n",
    "\n",
    "(I have thrown away the $t_i = 0$ solution because it corresponds to the time at which the projectile initially leaves the plane of the slope — technically correct, but not what I'm looking for.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a17a65d4",
   "metadata": {},
   "source": [
    "The x-coordinate of the impact point is:\n",
    "\n",
    "$$ x(t_) = v_0\\,\\cos(\\theta)\\,t_i = \\frac{2\\,v_0^2\\,\\cos^2(\\theta)}{g} \\left[ \\tan(\\theta) - \\tan(\\phi) \\right] $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66d439fc",
   "metadata": {},
   "source": [
    "The distance $D$ along the slope that this happens is the hypotenuse of the right triangle with an angle of $\\phi$ and an adjacent side of length $x(t_i)$, so:\n",
    "\n",
    "$$ D = \\frac{x(t_i)}{\\cos(\\phi)} = \\frac{2\\,v_0^2\\,\\cos^2(\\theta)}{g\\,\\cos(\\phi)} \\left[ \\tan(\\theta) - \\tan(\\phi) \\right] $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6cf75bb",
   "metadata": {},
   "source": [
    "Remembering that $\\tan(\\theta) = \\sin(\\theta) / \\cos(\\theta)$, I can factor a $\\tan(\\theta)$ out of the expression and do a bit of cancelling to get:\n",
    "\n",
    "$$ D = \\frac{2\\,v_0^2\\,\\sin(\\theta)\\,\\cos(\\theta)}{g\\,\\cos(\\phi)} \\left[ 1 - \\frac{\\tan(\\phi)}{\\tan(\\theta)} \\right] $$\n",
    "\n",
    "An equilvalent form (reached via assorted trig identities) is:\n",
    "\n",
    "$$ D = \\frac{2\\,v_0^2\\,\\cos(\\theta)}{g\\,\\cos^2(\\phi)} \\sin(\\theta - \\phi) $$\n",
    "\n",
    "Neither of these is particularly pretty, but I don't think I can simplify it much more."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ca43d2",
   "metadata": {},
   "source": [
    "**Limits check:**\n",
    "\n",
    "1. If $\\theta \\to \\phi$, then $D \\to 0$, which is correct: The projectile is fired along the slope, striking it immediately (since we haven't built any \"launch height above the ground\" into the model). ✅\n",
    "\n",
    "2. If $\\phi \\to 0$, then $D \\to 2\\,v_0^2 \\cos(\\theta) \\sin(\\theta) / g$, a well-known result for the range of a projectile on level ground. ✅"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5102fa25",
   "metadata": {},
   "source": [
    "### c) Maximum distance up slope"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dc51009",
   "metadata": {},
   "source": [
    "This is straightforward, if algebraically tedious: Solve $dD/d\\theta = 0$ to find the value of $\\theta$ that maximizes $D$, and then plug this value back into the expression for $D$ to find the maximum possible distance up the slope.\n",
    "\n",
    "I'll start with my second-to-last expression for $D$ 'cuz I think it'll be slightly easier to differentiate. I'll also save some writing by rolling all the leading factors that don't depend on $\\theta$ into a constant I'll call $A$.\n",
    "\n",
    "$$ \\begin{split}\n",
    "    D &= A\\,\\cos^2(\\theta) \\left[ \\tan(\\theta) - \\tan(\\phi) \\right]\n",
    "    \\\\\\\\\n",
    "    \\Rightarrow \\frac{dD}{dt} &= -2\\,A\\,\\cos(\\theta)\\,\\sin(\\theta) \\left[ \\tan(\\theta) - \\tan(\\phi) \\right] + A\\,\\cos^2(\\theta) \\left[ \\sec^2(\\theta) \\right]\n",
    "    \\\\\\\\\n",
    "        &= -2\\,A\\,\\cos(\\theta)\\,\\sin(\\theta) \\left[ \\tan(\\theta) - \\tan(\\phi) \\right] + A\n",
    "    \\\\\\\\\n",
    "        &= A \\left\\{ 1 - 2\\,\\cos(\\theta)\\,\\sin(\\theta) \\left[ \\tan(\\theta) - \\tan(\\phi) \\right] \\right\\}\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc6cccd9",
   "metadata": {},
   "source": [
    "remembering that $\\sec(\\theta) \\equiv 1 / \\cos(\\theta)$.\n",
    "\n",
    "For maximum range, the derivative must be equal to zero, so:\n",
    "\n",
    "$$ 2\\,\\cos(\\theta)\\,\\sin(\\theta) \\left[ \\tan(\\theta) - \\tan(\\phi) \\right] = 1 $$\n",
    "\n",
    "This is a thoroughly disgusting equation to have to solve for $\\theta$, and if you got this far and quit I'd still high-five you.\n",
    "\n",
    "One way to proceed would be computationally: For each of many different possible values of $\\phi$, solve the equation with numerical methods to get the critical angle, and plug that into the expression for $D$. You could then have the computer make a plot of $D_max$ vs. $\\phi$.\n",
    "\n",
    "It turns out that there **is** a way forwards analytically. In case you'd like to beef up your arsenal of math tools, I'll plunge onwards and try not to get myself lost…"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24810fc3",
   "metadata": {},
   "source": [
    "For convenience I'll write $\\tan(\\phi)$ as $T$. Distributing the leading factor over the two terms in square brackets and using $\\cos(\\theta)\\,\\tan(\\theta) = \\sin(\\theta)$:\n",
    "\n",
    "$$ 2\\,\\sin^2(\\theta) - 2\\,T\\,\\sin(\\theta)\\,\\cos(\\theta) = 1 $$\n",
    "\n",
    "Rearranging:\n",
    "\n",
    "$$ 2\\,T\\,\\sin(\\theta)\\,\\cos(\\theta) = 2\\,\\sin^2(\\theta) - 1 $$\n",
    "\n",
    "Squaring both sides:\n",
    "\n",
    "$$ 4\\,T^2\\,\\sin^2(\\theta)\\,\\cos^2(\\theta) = 4\\,\\sin^4(\\theta) - 4\\,\\sin^2(\\theta) + 1 $$\n",
    "\n",
    "Aand, here's the key: Write $\\cos^2(\\theta) = 1 - \\sin^2(\\theta)$:\n",
    "\n",
    "$$ 4\\,T^2\\,\\sin^2(\\theta)\\,(1 - \\sin^2(\\theta)) = 4\\,\\sin^4(\\theta) - 4\\,\\sin^2(\\theta) + 1 $$\n",
    "\n",
    "Multiplying out and grouping terms by powers of $\\sin(\\theta)$:\n",
    "\n",
    "$$ 4\\,\\sin^4(\\theta) (1-T^2) - 4\\,\\sin^2(\\theta) (1 + T^2) + 1 = 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2efedc5d",
   "metadata": {},
   "source": [
    "Now I'll define $u \\equiv \\sin^2(\\theta)$, which reveals… a quadratic equation!\n",
    "\n",
    "$$ 4\\,u^2 (1-T^2) - 4\\,u (1 + T^2) + 1 = 0 $$\n",
    "\n",
    "The values of $u$ (related to the values of $\\theta$) that maximize the range can now be found via the quadratic formula:\n",
    "\n",
    "$$ \\begin{split}\n",
    "u &= \\frac{4\\,(1 + T^2) \\pm \\sqrt{16\\,(1 + T^2)^2 - 16\\,(1-T^2)}}{8\\,(1-T^2)}\n",
    "\\\\\\\\\n",
    "  & = \\frac{1 + T^2 \\pm T\\sqrt{T^2 + 3}}{2 \\left(1 - T^2\\right)}\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2838abb",
   "metadata": {},
   "source": [
    "Transforming back to my original variable $\\theta$:\n",
    "\n",
    "$$ \\begin{split}\n",
    "   \\theta &= \\arcsin\\left(\\sqrt{u}\\right) \n",
    "   \\\\\\\\\n",
    "   &= \\arcsin\\left( \\frac{1 + T^2 \\pm T\\sqrt{T^2 + 3}}{2 \\left(1 - T^2\\right)} \\right)\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64c90f48",
   "metadata": {},
   "source": [
    "Plugging this into the original expression for $D$ accomplishes nothing but a horrendous waste of paper. If you give me a value for $\\phi$, I can calculate the corresponding maximum-range angle $\\theta$ and from that the range $D$.\n",
    "\n",
    "As a sanity check, let's see if $\\phi \\to 0 \\Rightarrow T \\to 1$ gives us the expected angle of $45^\\circ$:\n",
    "\n",
    "Uh… Problem… the expression blows up. 😬\n",
    "\n",
    "> _That's it, I'm calling it quits for now. There's grading to be done!_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c252b3f0-6d33-4c65-9079-6bca9b5c9bb4",
   "metadata": {},
   "source": [
    "## Problem 4: Course Adjustment"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1722e4f1",
   "metadata": {},
   "source": [
    "This is a straightforward kinematics problem, albeit with many details to keep track of: Integrating the acceleration function to get velocity, and integrating the velocity function to get position.\n",
    "\n",
    "I'll work in units of kilometers and seconds."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea3b511f-bc5e-411a-b590-399ad08536db",
   "metadata": {},
   "source": [
    "### a) Acceleration graphs\n",
    "\n",
    "Let's plot the acceleration's magnitude $a(t)$ and components $a_x(t), a_y(t)$ vs. time to check this visually. In component form, the acceleration vector is:\n",
    "\n",
    "$$ \\vec{a}(t) \\equiv \\left< a_x(t), a_y(t), a_z(t) \\right> = \\left< a(t)\\,\\cos(\\theta), a(t)\\,\\sin(\\theta), 0 \\right> $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b11db7fe-b546-4fb5-ab98-e699d39bbfe2",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the plot…\n",
    "θ = np.radians(130) # degrees converted into radians\n",
    "a_max = 6.0e-4 # km/s**2\n",
    "t_1, t_2 = 2400, 9900 # s\n",
    "def a_(t):\n",
    "    if t < 0:\n",
    "        return 0.0\n",
    "    if t < t_1:\n",
    "        return a_max * t / t_1\n",
    "    if t < t_2:\n",
    "        return a_max * ( 1.0 - (t - t_1) / (t_2 - t_1) )\n",
    "    return 0.0\n",
    "a = np.vectorize(a_) # for calculational convenience\n",
    "t_min, t_max = -500, 10500\n",
    "t_values = np.linspace(t_min, t_max, 100)\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "ax.plot(t_values, a(t_values) * 1e4, linewidth=3, label=\"$a(t)$\")\n",
    "ax.plot(t_values, np.cos(θ) * a(t_values) * 1e4, label=\"$a_x(t)$\")\n",
    "ax.plot(t_values, np.sin(θ) * a(t_values) * 1e4, label=\"$a_y(t)$\")\n",
    "ax.plot(t_values, np.zeros_like(t_values), \"k\", label=\"$a_z(t)$\")\n",
    "ax.grid(color='gray', linestyle=':', linewidth=0.5)\n",
    "ax.set_xlim(t_min, t_max)\n",
    "ax.set_xlabel(\"time, t (s)\")\n",
    "ax.set_ylabel(r\"acceleration, a ($10^{-4}\\text{ km/s}^2)$\")\n",
    "ax.set_title(\"acceleration vs. time\")\n",
    "ax.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "215bbc72-47cf-4913-9dc2-86d2a2cd7881",
   "metadata": {},
   "source": [
    "### b) Velocity function\n",
    "\n",
    "Integrating an object's acceleration over time gives us the change in its velocity:\n",
    "\n",
    "$$ \\vec{v}(t) = \\vec{v}(0) + \\int_0^t \\vec{a}(t')\\,dt' $$\n",
    "\n",
    "Integrating the piecewise-linear acceleration function is tedious but not hard, leading to:\n",
    "\n",
    "$$\n",
    "\\vec{v}(t) = \\vec{v}(0) + \\left< \\cos(\\theta), \\sin(\\theta), 0 \\right> \\times \\begin{cases}\n",
    "   0 &\\text{if}\\quad t < 0 \\\\\n",
    "   \\frac{1}{2}\\,a_\\text{m}\\, t^2 / t_1 &\\text{if}\\quad 0 \\le t < t_1 \\\\\n",
    "   \\frac{1}{2}\\,a_\\text{m}\\, t_1 + a_\\text{m}\\,\\left(t - t_1\\right)\n",
    "       \\left[ 1 - \\frac{t - t_1}{2 (t_2 - t_1)} \\right]\n",
    "       &\\text{if}\\quad t_1 \\le t < t_2 \\\\\n",
    "   \\frac{1}{2}\\,a_\\text{m}\\, t_2 &\\text{if}\\quad t_2 \\le t\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "where the initial velocity $\\vec{v}(0)$ is $\\left< 1.626, 0, 0 \\right>\\ \\text{km/s}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5e4e06a-e518-41cb-b2df-ea27b816c009",
   "metadata": {},
   "source": [
    "### c) Velocity graphs\n",
    "\n",
    "Inserting the given constants into the abofe function for $\\vec{v}(t)$ and plotting numerically vs. time, we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c37bfe81-1bd9-4f45-a56f-0a008a78adc1",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GpPH88RuHyXza20oj5YEmTZrk7hKEF5G8CLUkM0ItyYxQ62zJjNFip6nLfHSx0NxlprnbQlOXmeYuC83dzq+tBgut3VYsdscAPrsDtBY0WrPra8/vLaCxOL9qrWg0R79qLaCxotFaj361Ob9qbKC1gsaGRmMFrQ2NZiDrPTvYjac/qieNlAc6cuQIERER7i5DeAnJi1BLMiPUkswItTw5M4qi0GawUt9poq7dREOnmcZvL13Or11mW/+fSGNDozOg0RpBZ0KjM6LRGtHoTGi0BjQ6E+iMR5sik7NJ0plc32t0pz8yMlA06NCiR6vRo0WPTqNHq9Gh1ejQneSrFg0ajRatRosGDdoTvtdoNEcf9/i41LF132YwGAgMDByS13kqVl8L+eSf1rbSSHmgsLAwd5cgvIjkRaglmRFqSWaEWu7KjM3uoKHTTG27idp2I3XtJmrbTdR1mGjocH6t7zBjsakZiVGcIz/6bjS6bmdzpO9yfj32b53x6PfGo/82OEeEBoKiRa/xR68JwEfjj58uAD9dAAH6QAL0AQTqAwj0cS7BvgEE+wQS4hdImH8gwb6BBOj98dX54qfz67H46nxdi4/WB71Wj1bjvisjVVRUkJKS4rbnP6ajo4P3+PdpbSuNlBBCCCGE8HiKotBhtFHVZqC61Uh1m5GaNiM1bSZq2o3Utplo6DRxeqcbOY42RJ3ORdft+qrVdx5tmrqONkzdzsPj+lW0Bh2B+GiC8NMGEaALJtAnmBCfUML9QgnzDyUqIJSIgFCiAkOJCQwjzD+EYJ9ggn2DCfIJwlfre9JRHOFe0kh5oPb2dneXILyI5EWoJZkRaklmhFr9yYyiKLQbrVS1GjnSYuBIq4EjLUaqWg1UtxmpbjXS/Z2z0tmdTZC+Ha2+w9kc+XSg0Xeg1XUdb5z0XerPD1L06JQQ/DQhBOhCCfYJI9wvnAj/CKIDI4gNjGRESCQjQ6MYERxJmH8YwT7Bbh3l8SbeuJ+RRsoDJSUlubsE4UUkL0ItyYxQSzIj1DpZZqx2B9WtRipaDFQ2d1PZYqCi2cCRViNVLQY6T3VOksaGxqcdrU+7s1E6+lXjc6xpOto4qZkZzh6MnlACtGEE6yMI84sg2j+SuOAYEkJiSAmPIzUiloSQaAJ9AmVkaBB5435GGikPdPDgwWE3ZajoP8mLUEsyI9SSzAg1zDY7n+3YT2TKeMqbuilr7qbiaNNU02bC3uexd4rzsDr/NrQ+rWh82tD6tKHRH/3q04ZWf3oXSlUULdhC0BNGoDaSMN8oIv2jiQuMISE0ltTwEYyOGsHoqHiCfP0G9sWLfvPG/YxckFcuyCu8nORFqCWZEWpJZsS32R0KVa0GShu7KW3qpqypi/ImA2VN3dS0G+n916WzUdL4tKL1aUHr23r0+xO+nsZ5SIpDj2ILQ69EEqSNJMIvltjAWJJCR5ASFs/Y6ETGxYwgJjhARo+8jKfsZ9T0BjIi5YG2bt3KggUL3F2G8BKSF6GWZEaoJZkZvjpMVkoauihp7Ka0seto4+RsmnpdM0ljczZFgc1ofVvQ+ji/anxanF+/YxY7RdGg2EJQbOH4EUWYTwyxASNIDBnJqIgExkUnMS4mjviwAHz1ct7R2cYb9zMyIuWBI1JCCCGEEENFURQaO80UN3RR3Njl/NrQRUljF/Ud37qWkcbibJJ8m9D4NKP1bUbr24TWt9l5jtIpzk861ig5rJHoHVGE+8QRGziClNBExkQmMTE2mbSoMEaE++Ojk0ZJuIeMSHm5rKwsr+vIhftIXoRakhmhlmTm7KAoCo1dZorquyis76Swvoui+k6KGrpoN544WmR3jiz5NeIT2Xi0UTq6+HSc+jkcvjgskTgsUfgTQ7T/SBJDEhkTmcLEmGTSY8JJiQwiLNBncF+s8DreuJ+RESkPHJHq7OwkJCTE3WUILyF5EWpJZoRakhnv0260UljfyeG6TgrqOiis66KwoZM2wwkNk9aA1q8RnW8DWr9GtL6NaI6NLp1ianDF7o/DEo3DEo2PI4bYgERSQpMYH5XK+NiRjIoJJsrPwYjoiCF4peJs4Sn7GRmR8nLFxcVMmzbN3WUILyF5EWpJZoRakhnPZbU7KGns4nBtJ/l1HRTUdVJQ10ltu+noFopzqnC/BrR+DfiFNqD1bXT++xSz4CkOn6PNUgxYYoj0TSA5NIlxUaOYEBvPqJhgRsUEERXU98Vi9+7dK42UUMUb9zPSSHmgmJgYd5cgvIjkRaglmRFqSWY8Q0u3hfzaDvJrOzhU28Hh2k6KG7qOTvpwrGGqR+tXj9+IBnR+9Wh9G9DozCd9TIc1DIc5FoclBp0tlhGByYyOTGNSTBJj4kJJjw0mNSpI9eQOkhmhljdmRhopD2Q2n3yHJ8S3SV6EWpIZoZZkZmgpisKRFiMHa9o5WONsmg7WtLsmftDoutH61TmXmHoC/erQ+tWftGFSFC0OS9TRhikWnS2OpOBUxkenMzE1hrFxwYyJDSEhPACtdmCmDJfMCLW8MTPSSHkgbwyScB/Ji1BLMiPUkswMHpvdQUljNweq2zlwtHHKr+mg02wDjQ2tbwNa/1p0/rUEhNWj9a9Dq+/s87GcDVM0DnMcDnMsGmscCUFpTIxOZ0JKBGPjQhgXF0JixMA1TCcjmRFqeWNmpJHyQN44tCncR/Ii1JLMCLUkMwPDandQWN/JweoO8o42Tvm1HZisDjS6TmfD5FeLNqqWQL9atH6NJ530wWGJxG6Ow2GOx2GOJ9o3mQnR6UxIjmBcfAjj4kMYFR3stustSWaEWt6YGWmkPFBJSYlXhkm4h+RFqCWZEWpJZtSz2R0UN3axv6qdvKp29lc7myaLzYbGpwWdfw1a/xp08bUE+decfJTJ7o/dNAKHeQQOczxa60hGh6czaUQME0aEOpf4UI+bTlwyI9TyxszI9OceOP252WzGz8/P3WUILyF5EWpJZoRakplTczgUypu72VfV5mqcDtZ0YLRanNOK+1ej8692Nk5+tX2ey6QoGhRLFHbzCBymEdjNIwjRJDEpLoWMkWFMHBnKxBGhpEUHofeCi9VKZoRanpIZr53+/JlnnuG9997j8OHDBAQEcM455/Dss88ybty4U97vnXfe4ZFHHqG8vJwxY8bw7LPPcsUVVwxR1QMvOzvb6y5IJtxH8iLUkswItSQzPTV0mth3pJ19R9rYV9XGviNtdJjMzinFjzZNupHVBPvXotFae91fcehxmOOPjjSNxG4aSbx/GhkjYpg0KoxJI0OZlBBKfKh/n1OLewPJjFDLGzPjUSNSixYt4sYbb2TWrFnYbDZ+/etfc+DAAQ4dOkRQUFCf99m2bRsLFizgmWee4corr+SNN97g2WefZc+ePWRkZHznc3riiJQQQgghPIPRYudATTt7K1vJPdJGbmUbNe0GNL7N6Pyr0AVUofOvQutfc5KmyRe7aSQOU4Lr68igZCYnRDJpZBiZCc7GKSrY/Z/ECyHU9QYe1Uh9W2NjI7GxsXzzzTcn7VBvuOEGuru7+eijj1zr5s6dy9SpU3n++ee/8zk8sZHKysryuo5cuI/kRaglmRFqDZfMKIpCebOBvZWt7K1sI/dIG/m1Hdi1begCjqD1P4Iu4Ag6/+q+D8+z+53QNCXiMI0kPjCJKYkRZCaGMTkhnMyEMI87n2kwDJfMiIHjKZnx2kP7vq29vR2AyMjIk26zfft27r///h7rFi5cyPr16/vc3mw295hesaOj48wLHWAzZ850dwnCi0hehFqSGaHW2ZqZbrONfVVt7K1sY3dFK3srW2k1dR0daXI2Tn6jjqD16f23guLQ4zCNxG5KxG5MwmFKIMI3gWlJEUweF05monO0KXqYjjSdrZkRg8cbM+OxZys6HA5+9rOfMX/+/FMeoldXV0dcXFyPdXFxcdTV1fW5/TPPPENYWJhrSUpKAqClpYWtW7dis9nIysoCnJ1xZ2cne/bsobq6muLiYvLz82lsbCQ7Oxuz2dxjW6PRyM6dO6mvr6egoIDCwkJqa2vJycmhu7u7x7ZWq5Vt27bR1NTEwYMHKS0t5ciRI+Tm5pKTk9NjW4fDwebNm2lra2Pfvn1UVlZSXl7OgQMHaG5u7rPurq4udu/e3aPuhoYGsrOzMZlMPbY1mUyuug8fPkxRURE1NTXs3r2brq6uPutubm7mwIEDlJWVUVlZyb59+2hvbycrKwtFUXp8bW9vd9VdVlbmqnvbtm1YrdY+666pqaGoqIjDhw9TX1/Pzp07+6w7OzubhoYG8vPzKS4uprq6us+6bTYbW7duddVdXl7uqrutrY3NmzfjcDh63Ke9vZ3c3FyOHDlCaWkpBw8epKmpqc+6u7u7ycnJoba2lsLCQgoKClx1G43GHtuazWays7NpbGzsUfeePXvo7Ozss+6Wlhby8vIoLy+noqKC/fv309bWxpYtW8jLy+txn46ODvbu3UtVVRUlJSWuurdv347FYumxrcFgICcnh7q6OlfddXV17Nq1C4PB0KvuHTt20NjYyKFDhygpKaGqqoq9e/f2qttut7NlyxZaW1vZv38/FRUVrrpbW1vZsmULdru91+/aiXUfOnSIxsZGduzY0et3zWAwsGvXLurq6ly/a3V1deTk5PSq22KxsH37dtfv2ol1d3R09Ppd27JlC21tba66y8vLycvL86h9xLHftf7uIz744APZRwyjfcS36+7PPmL79u1ev4+ora1l49c7eDu7lLv+8RmL/7KZjEc/Yfm/N/DHHa+zte2fmON+R/DYxwhM+Rd+sZ/iE3oQrU8HiqLBbhqBpXU2ptpldJf+BHvJE4y1PsiyEXfw8ymX8tGdi/jzBYE8f8s0pvrUcuG4WA7tyfbKfcRA/B2xbds22UcMo33EQPwd8cEHH3jM3xGny2MP7fvRj37EJ598wpYtW0hMTDzpdr6+vvz73//mpptucq37xz/+weOPP059fX2v7fsakUpKSvKoQ/vq6uqIj493dxnCS0hehFqSGaGWN2bGandwsKaDnPIWdle0klPRSmN3O7qAyh6LRmfqdV+HNRy7Mck50mRMQjEnMC4ummnJ4UxNDGdqcjjpMcHoBvmitt7MGzMj3MtTMuP1h/bde++9fPTRR2RlZZ2yiQKIj4/v1TDV19ef9D/Cz8/PI6ZWPJX29naPCJLwDpIXoZZkRqjlDZnpMFmdDVN5CznlreyrasVME7qACnSBFeiiywlOaECj6fn5seLwwW5MxG5MxmFMxm5MJjowmmlJ4UzLjGBasvO8piA/j/yTyWN5Q2aEZ/HGzHjUXkFRFO677z7ef/99vv76a9LS0r7zPvPmzeOLL77gZz/7mWvd559/zrx58wax0sHlrVOdCveQvAi1JDNCLU/MTH2HiZ1lLeSUt7CzvJXDda1o/GrQBZajCyhHl1pBsL6r1/0clijsRxsmuzEZrWUEE0dGMH1MBNNTIpiWFE5iRIBHvmZvIj8/oZY3ZsajGql77rmHN954gw8++ICQkBDXeU5hYWEEBAQAcOutt5KQkMAzzzwDwE9/+lPOP/98/u///o/Fixfz1ltvkZOTw4svvui213GmPOUQQ+EdJC9CLcmMUMvdmTk2m97Osmayy1rYVd7CkdY25+F5geXoAssJGlvZa/pxRdHhMCZgN6Y4F0MKEf5RTE+OYMbkCKYnhzM5MZwAX52bXtnZy92ZEd7HGzPjUY3UP//5TwAuuOCCHutfffVVbr/9dgAqKyvRao/PkXHOOefwxhtv8PDDD/PrX/+aMWPGsH79+tO6hpSnqqqq8rqhTeE+khehlmRGqDXUmXE4FAobOtlZ1kJ2WQs7y1po7G5FH1iGLrAMXWg5wbE1aDSOHvdTbIEnNE2p2E0JpEeHMzMlkhmpEcxMiSAtOsgrP/n2NrKfEWp5Y2Y8drKJoeKJ15EyGAwEBga6uwzhJSQvQi3JjFBrsDNjdyjk13awo/T4iFO7ucXZNB1b/HvPxuuwhjsbJkMadkMqensckxMjmJkaycyUCGakRBAR5DtodYuTk/2MUMtTMuP1k00Mdzk5OR5xQTLhHSQvQi3JjFBroDNjOzqjXnZZM9mlLewsb6HL2oouqBRdYCm6+FKC/Rp73c9ujj3aNDkbp2BdNLNSI5iVGcms1EgmJ4bh7yOH6XkC2c8ItbwxMzIi5YEjUkIIIcTZxO5QOFjTzvaSZnaUNrOrvJVuW5uzaTrWPPk19L6fKf5o0zQKuyGN6MAoZqdGMjvN2TiNiw+RKciFEANKRqS8XFZWltd15MJ9JC9CLcmMUEttZhwOhUNHD9XbXtLMzrIWOq2d6ANL0QWVoBtZQrB/z0uXKIoGhzkee/co7IZR2AxpJIZFMTstkjlpkcxOiyI1KlDOb/ISsp8RanljZmREygNHpCwWC76+cky3OD2SF6GWZEao9V2ZURSFooYuthU3sa3EeZ5Tu8ngnIY8qAR9UDFa/+pe13ByjjgdbZy6R5EWGcOctEjmjHI2TgnhAYP90sQgkf2MUMtTMiMjUl5u9+7dXn0dLDG0JC9CLcmMUOvbmVEUhYpmA9tLm9lW0sz2kiaaukxo/avQBxWjiykmOKACjdbe43Hs5hjs3enYDenYDWmkRcYxd1QUc9IimTsqirhQ/6F+aWKQyH5GqOWNmZFGygONGTPG3SUILyJ5EWpJZoRaY8aMob7DxNbiJrYWOxunmnYjGp9mZ+MUVkTwyBI0OlOP+zmsodi7R2MzpGPvHk1axEjmjYpyNk+jIokNkcbpbCX7GaGWN2ZGGikPVF9fT3R0tLvLEF5C8iLUksyI09FutLKjtJltxU18cbCGqg4raA3OximomKDoIrS+rT3uo9j9sXWnYzeMxtY9muSQZOaNimZeepSMOA0zsp8RanljZqSR8kD+/vJGI06f5EWoJZkRfTFZ7eypaGVLcRNbi5vIq27HodjRBlShDyokMKUIbcCRHuc5KYoOuyHZOerUPYY4v3Tmj45j3qgo5qVHMVLOcRq2ZD8j1PLGzEgj5YH8/PzcXYLwIpIXoZZkRsDxmfWONU47y1ow2xxo9G3ogwvxHVmIPqi41+F6dnMs9u4x2LrHEK4ZxzmjEjhnZhTnpEeRHCmz6gkn2c8ItbwxM9JIeaDGxkYSExPdXYbwEpIXoZZkZvg60mJgS3ETW4qb2FbcRKvBChobuoBy9JEFBAYVovv2tOT2AGzdo7F3jcXfOoFzUtKZPymK+aOjGRMbLI2T6JPsZ4Ra3pgZaaQ8UHp6urtLEF5E8iLUkswMH+1GK9tLmtlS3MiWoibKmw0AaHxa0AcV4h9ZgD6oBI3W4rqPomhwGJOwdY9FYxzP9PhMZo4O5aJJCWQmhKHXad31coQXkf2MUMsbMyONlAfKzc31uguSCfeRvAi1JDNnL6vdwb4jbWQVNbG5qJF9R9pwKAB2dIHl+MUWoAs+jM6vocf9HLZg7F1jsXePY2zoDBaMTuHc0dHMSInA30dHVlYW05Iz3PKahHeS/YxQyxszIxfk9cAL8gohhBCn49j1nDYXNZJV1MT2kma6zDYANLoudMEF6IMPow8q6nGuk6JosRuTsXeNI1Y/mQUpUzhvTCzz0qMID3T/BTGFEMJd5IK8Xi4rK8vrOnLhPpIXoZZkxrs5D9drco06HWkxHr1FQetXi29UPvqQw2j9q3rMsOewBWHvGoufdRJzR5zDhRNTmD86mqTIwO98TsmMUEsyI9Tyxsyc0YiU1Wqlrq4Og8FATEwMkZGRA1nbkPDEESmHw4FWK8egi9MjeRFqSWa8i83uYH91O1mFjWwuaiL3SBt2x9G3bo0VXWAp+pB89MH5aH3ae9zXbkxAMYxnXOgsLk2fxflj45g4IhStVt0EEZIZoZZkRqjlKZkZ1BGpzs5OXn/9dd566y127tyJxWJBURQ0Gg2JiYlcdtll/OAHP2DWrFn9fgHD3bZt2zj33HPdXYbwEpIXoZZkxvNVtxmPNk7OSSI6TDbXbRpdF/qwfGfzFFSERmt13aY4fLB1jyZGO43zE8/j0nnjmJ0aSYCv7ozqkcwItSQzQi1vzIyqEannnnuOp556ivT0dJYsWcLs2bMZOXIkAQEBtLS0cODAATZv3sz69euZM2cOf/3rXxkzZsxg1n/GPHFEqq2tjfDwcHeXIbyE5EWoJZnxPAaLjezSFr4pbCSrqJHSxu4et2t8G/EJPoQ+5BDagMqeh+xZQ9GbM5gcMY8l487jgrEJxIYM7IUtJTNCLcmMUMtTMjNoI1K7du0iKyuLSZMm9Xn77NmzufPOO3n++ed59dVX2bx5s8c3Up6osrLSI4IkvIPkRaglmXE/RVHIr+08OklEI7vKWrHYHSds4UAXUIkuOB99yCF0fo097u8wJTDSZyYXJJ3P9ybNZsKI0EG9npNkRqglmRFqeWNmVDVSb7755mlt5+fnxw9/+MN+FSQgLCzM3SUILyJ5EWpJZtyjpdvibJwKm8gqaqSx09xzA40NXWAx+pCjI0/6LtdNiqLDzzaGjPBz+N64hSwaPw5/nzM7XE8NyYxQSzIj1PLGzPR71j6j0YiiKAQGOmf7qaio4P3332fChAksXLhwwAocjob5jPRCJcmLUEsyMzRsdgd7j7SRVdjIN4WN5FW30+tHrzWjDzqMPuQg+uACNLoTmiuHP7H6aZw78nxunbKQ9OjoIa3/RJIZoZZkRqjljZnpdyO1dOlSli1bxg9/+EPa2tqYM2cOPj4+NDU18dxzz/GjH/1oIOscVjo7O91dgvAikhehlmRm8FS1GpwjToWNbC1uotNs67WNRteNPvgQ+tAD6AKL0Wjtrtv0Shhjg+eyZMxCrp10Pv56z7imk2RGqCWZEWp5Y2b63Ujt2bOHP/7xjwCsW7eOuLg49u7dy7vvvsvq1au9rpH62xdF+AcFu6+Ao8e2awCTycGX9UUAaDWg12nx0WnQazWu7310WvQ6Lb46LQG+OgJ8dAT66vA/+jXAR0eArw4/vXZQj5sX7peQkODuEoSXkcwMHJPVTnZZC98UNPJNYQMl35ok4hiNvsM56hSShy6wrMdkEUHaeGbFLOCmjCuYmzANrcb90/9+m2RGqCWZEWp5Y2b63UgZDAZCQkIA+Oyzz1i2bBlarZa5c+dSUVExYAUOFcvWv6H1c+8nfwoajr21dqFx/duGHhs6LOixKbrj36PDgg9GxRcj/hjxxaD4YcS5WNCj02oJ9dcTGuBDqL8PIf56Qv19CA1wfg0L8CEy2JeoIF8ig/yIDHJ+Hxbgo/o6I8I98vPzmT9/vrvLEF5EMtN/iqJQ3NB1dHa9JrJLmzHbHH1uq/FpQR9yEJ+QA71m2ov1G8WlKZdwzfhFjA4f7fEfeElmhFqSmaFht9uxWq3fvaEXOHz4MNOnTx+S5/L19R2Qa1b1+4K8kydPZsWKFXzve98jIyODTz/9lHnz5rF7924WL15MXV3dGRc3FFxTHP4qhFA/z34jU8umaDHgTweBdChBdBBIpxJ49N+BdBBEmxJEsxJKC6E0K86llRDsGj0Rgb7EhPgRG+pPXIgfcaH+xIUe/ffR72OC/dDrPO/T0+HEZrOh1/f7MxExDElm1Gk3WNla4jxcL6uwkZp200m31fg04xOa5xx5CqjucVtayESuGr2QhWmXkhSSNNhlDyjJjFBLMjO4FEWhrq6OtrY2d5cyYI5dl3YoaLVa0tLS8PXtPYgyqBfkPWb16tXcfPPNrFq1iosuuoh58+YBztGpadOm9fdh3eY923wCdT5uee5j41AazbHvj/4b0OJAjx0f7Ee/2pzfa5xffbHhj5lAjZkAnIuvxnm8vV7jIBQDoRhA06Sqpg4lkGZrCA0tEdQ3R1CvRFCnRLBTiaBOiaQe5zqb1o/4UH8SwgNIiAggITyAkSd8nxgRMKQzSw1H27ZtY8GCBe4uQ3gRycyp2R0K+6vaXLPr7a1sxXGKjxxP1jxp0DI5ehpXjLqMi5MvJi4obgiqHxySGaGWZGZwHWuiYmNjCQwM9PhR7dPR3d1NUFDQoD+Pw+GgpqaG2tpakpOTz+hnp3pEavXq1SxdupQZM2ZQV1dHbW0tU6ZMcQ2P7dy5k9DQUMaPH9/voobSsa5zxb++wTfQjedIKaAcbaAUBdfMTg5FweZQsNod2OwKNocDi13BdvTfZpsdo9WO0eL8arUr6LERgAV/zIRojIRgIFTjbKhCNd2EYiBEYyCMbiI0XUTSQZSmg0hNB5F0otOcfiSalFCqlGiqlBiqlBiqv/W9UeNPfKg/KVGBpEQGkRwVSGpUkPPfUYGE+LuneRVCiBPVtZucs+sVOSeJaDOc+lAZV/MUuh+df83x9WiZHT+Ly1KdzVNUQNRgly6EGGbsdjuFhYXExsYSFSX7mP5ob2+npqaG0aNH4+PT82/RQR2Rqqqq4vLLL8fX15clS5Zw1VVXMWnSJNfQ2OzZs9U+pEf4v+unfucPa6hkZWX1+1Mcq92B0WrHZLFjsNjpMtvoMFnpMNroNFnpMNnoMFppNlkpNVppN1hp7rbQcnTpNlsIo5soTQfRdBCjaSNO00Kcpo14TQtxmlbiaCVO00qAxkK0poNoTQdTKe2zngYlnDJjPOWV8ZRXxJOnxPOhEk+FEocJP2JD/BgVE0R6TLBziQ1mVHQQCeEBco7WaTqTvIjhSTLjnCRiZ1mL83C9okYK67u+8z4afSv60P34hOahC6hyrddpdMw6oXmK9I8czNLdQjIj1JLMDJ5j50QduwTR2aKzs9M1/8JgO9a32O32Xo2UGv06R8rhcLB161Y2bNjABx98QG1tLZdeeilLly7lyiuvJDLSe95E1HSdQ2Uog/RtJqudNoOV5m4zzV0WGjvN1HeaaOgwU99hOrqYaeg0EmjvIkHTRKKmkcSjX4//u5EwjeGUz1WtRFHsSKBISaBQSaTYkUCxkkAHQfj7aBkVHcy4+BDGxoUwLj6YsXEhJIQHnBXD1wPJnXkR3mk4ZkZRFIoauo42TqeeJOJEGn07+pA8fMP2ow2odK0/1jwtTF3IxckXE+EfMZjlu91wzIw4M5KZwWMymSgrKyMtLQ1/f393lzNg7HY7Ot3QnA5yqp+hmt6g35NNnCg/P9/VVO3evZvZs2dz1VVXcdNNN3n8VIae2Ejt2bNnyGYt6S9FUWjutlDTZqSmzUhVq5Hqo99XtxmpbjViN7SSqqknVVNHmqaOVO3Rr5o6wjV9TxEMUKdEUOhIpEhJ5JAjhUNKCsVKAlb0BPvpGRMXzLi4EMbFhzBxRCgTRoYSOowPEfSGvAjPMlwy09ptYUtxE5uLGtlc1ETtKSaJOJFG14U+5AAh0XlYfUo5ft6qhpnxM1mUuohLUi45K0eeTma4ZEYMHMnM4DlbG6mhOkcKBq6RGpDpVCZMmMCECRP4xS9+QWNjIx9++CEffvghAD//+c8H4imGlbg4zz8hWaPREB3sR3SwH5MTw/vcpstso6K5m8pmA+XNBna2dPNOs4GKZgOG9gZGUcMYbTVjNNWM0VQxWlvNSE0L8ZpW4nWtLCDP9VgWRUfx0cYqvzqZQ1UpfOxIpQPnL1xiRAATR4QycWSo6+twGb3yhrwIz3K2ZsZic7CnspUtRc7maX91O6f9UaHWREjkYSJiDtLGQRQcHDtLalrsNBamLuSylMuICYwZrPI92tmaGTF4JDNCrTM5xM5dBnxeypiYGO666y7uuusu1ffNysri97//Pbt376a2tpb333+fq6+++qTbf/3111x44YW91tfW1hIfH6/6+T2F0Wh0dwkDIthPz6SRYUwaGdbrNrPNTmWzgZLGLkoau1l/9GtDQwPxlgrGaKsYrznCRG0FEzQVhGkMTNRUMJEKOGHUt8wRx34lnf0do9jXNooXDqVixPnJQnigDxkjw8hMDCMzwbkkRpx9zdXZkhcxdM6WzCiKQkljN5uLGtlS1MT20mYMFvtp31+rtTIq+Qj+EfupNu/BplhoPXrbxKiJXJF2BQtTFxIf5L3vJwPlbMmMGDqSGaGWw/Hdh1t7mjNqpEwmE/v376ehoaHXi7/qqqtUP153dzdTpkzhzjvvZNmyZad9v4KCgh5Db7Gxsaqf25OcLRdWOxU/vY4xcSGMiet5/LSiKDR2milu7KK4oYsNdZ38X10H7fVlpFhKmKCpZKK2gomacpK1jaRp60mjnqW6bQDYFQ2FSiL7HensNY9md8lYthaPRME5q2R4oA+ZCWFkJIQxJTGMKUnhjAgLGPLXP5CGQ17EwPLmzDR1mdla3MSWoia2Fjed8ppOfRkR5sukUY3YAneT37GVels3HH2ItLA0Lk+7nMtTLyc1LHXgi/di3pwZ4R6SGaHWsbONmpubmTBhAjt37iQ1NfWk2994443MmjWLBx54YIgq7K3fjdSnn37KrbfeSlNT7+sTaTQa7PbT/1TwmMsvv5zLL79c9f1iY2MJDw9XfT9PFR0d7e4S3Eaj0RAb6k9sqD/npB//OSjKOdR3mCmo76SwrpPP6zqpqq4isHk/k5QSpmhLmawtIU7TxgTNESZoj3ADXwPQrgSy1zGGHMdYdpvGsrsonc1Fx3MbF+rHlMRwpiaHMzUxnMzEMK+aln0450X0jzdl5tjseluONk+HajtU3T/AR8ecURGMS+6gU7+T7fX/I9vY5GqeRgSNYFHaIq5Iu4JxEePOuhHrgeJNmRGeQTIj1Dp2AeennnqKpUuX9miiVq1aRUVFBe+9955r3cMPP8yCBQtYsWIFYWG9j34aCv1upO677z6uu+46Vq9e7fbjYKdOnYrZbCYjI4PHHnuM+fPnn3Rbs9mM2Wx2/bujQ92b8lAoLS0lJmZ4Hod/MhqNhvgwf+LD/Dl/7LGfzRQstsspbujiUG0HL9R0UFdVhk99LmNsBUzXFDFVW0KYxsAFun1coNsHOEet8pUUdjrGk+2YQHbHeD47ZOazQ/VHnwtGxwQzLTmc6ckRTE+JYHRMsMdOxy55EWp5cmbsDoW86na2FjtHnHIqWrGcxux6J8pICOW8MTGMT7JQZdnKp+V/542qctftYX5hLExZyOJRi5kaOxWtRjvAr+Ls48mZEZ5JMjM0HA6FVoPFrTVEBPoOyN9IZrMZq9XKyy+/zKZNm3rctnPnThYvXtxjXUZGBunp6bz++uvcc889Z/z8/dHvWftCQ0PZu3cv6enpA10T4PzD+bvOkSooKODrr79m5syZmM1mXnrpJV577TWys7NPOlPMY489xuOPP95rfVlZGdXV1cyZM8d1Ne6srCymTZtGUVERcXFxGI1GrFYr0dHRlJaWMnXqVLKzs13bzpo1i7y8PFJSUmhra0Oj0RASEkJ1dTUTJkxg9+7drm3nzZvHrl27GDt2LPX19QQEBODj40NzczMJCQnk5+e7tj333HPZunUrmZmZVFRUEBERgcPhoKurixEjRnD48OFedU+fPp2CggLi4+NddUdFRVFWVsaUKVPYuXOna9vZs2ezf/9+UlJSaG1tRafTERQURG1tLePGjWPPnj296h43bhy1tbUEBQWh0+lobW0lNTWVffv2cd5557F582bX1ylTplBeXk5ERAR2u53u7m5GjBhBQUEBs2bNYvv27b3qHjFiBN3d3djtdiIiIqioqGDy5Mm96t63bx9paWk0Nzfj4+NDQEAAtbW1hMansmHbPhwhcVTtzyLeWMQkez7TtUUkanqPouY7ktjhmEi2YwI7HeNpoecsLUG+WsZF+TIjNYpIpZ3rL5rFwdwcVy0zZswgPz+fhIQEOjs7URSF8PBwKioqyMzMZNeuXa5t58yZQ25uLqNGjaKpqclVd319PWPGjGHv3r2ubc855xyys7OZMGEC1dXVhISEoNFoaG9vJzk5mQMHDjBjxowejz916lRKSkqIiYnBbDZjMpmIi4ujqKiIGTNmsGPHDte2M2fO5NChQyQmJtLR0YGiKISFhXHkyBEmTZpETk5Oj7qP/c43Njbi5+eHn58fjY2NjB49ukfd8+fPZ/v27UyaNIkjR464Pilqb28nKSmJgwcPMm/ePLZu3drjd624uNhVt9lsJiYmhpKSEqZNm9bjd23mzJkcPHiQpKQk2tvb0Wg0hIaGUlVVxcSJE3vUPXfuXHbv3s2YMWOor6/H39/fVXd6ejq5ubk9fte2bdtGRkYGlZWVhIWFoSgKnZ2drt9LT9hHpKWlsW/fvn7vI7788ktmz57tEfuIrKwsQhPH8smeUg61ONhb3UW3RV3jFBPsw6QoHUtmpmNvOQip3fx3738pNR+/vp2PxofZkbO5JPESkqxJTJowqUfdx37Xxo8fT21tLcHBwWi1WlpbW0lJSSEvL4/58+ezZcsW132mTJlCWVkZUVFRWK1WjEYjcXFxFBYW9tq3uXMfcc455/Souz/7iNjYWEwmk+wjhsk+YiD+jvD19aWpqckr/46oq6vrVbcn7SOmTp1KaWkp6enpdJgdzP/DFlX7zIG2+f5ziI8Idh2NptPpsFgs+Pv7YzAYCAkJobOzk6CgIOLi4njyySe59dZb0Wg0aLVasrOzufTSS9m5cyeFhYX86Ec/oqGhga6uLnQ6HWFhYdhsNtfzzZ49m//9738EBwfz8MMPk5WVxccff0xgYCBmsxm9Xo/D4UBRFPR6PWazmcDAQLq7u121aLVaioqKiIqKwmAw9NhHJCYmMmLEiMGd/vzOO+9k/vz5/ZpU4nScTiPVl/PPP5/k5GRee+21Pm/va0Tq2I7WU6Y/l4vYDTxFUahqNXKgup2y0kLsFduJad7NdOUgY7XVvbYvcCSy1ZHBZkcm2Y4JGOg5NaZGA2Nig5mREsms1AhmpkSSFOmeiSwkL0Itd2fmSIuB7SXNbC9tZltJE/Ud5u++0wkCfXXMHRXFuaOjOW9MNMlRvmyu3syGkg1kVWdhczjfcLUaLXPi57B41GIuTr6YYN/gwXg5w4K7MyO8j2Rm8Jw4dXe3TcOMJ//n1np2P3wJUcF+p7XtxRdfzJQpU3juuedc6y666CIyMzN58sknefjhhyksLOSTTz4BnBNQ5OTkuD5giouLw9/f33VKz6effsrSpUvp6OjAz+/0agAPmP78b3/7G9dddx2bN28mMzOz15SFP/nJT/r70Gdk9uzZbNly8s782Cdknkx2PANPo9GQFBlIUmQgZI4AzsfhUCht6uaj4hK6CrMIqdvBaMM+xmmPME5bxThtFXfyKRZFx15lDFvsGWxxZLJfGYVd0VFY30VhfRdv7nRepDMmxI+ZKRHMSIlgZmokk0aG4qMb/EOGJC9CraHOTH2Hie0lzqZpe2kzR1rUzeal1cCUpHDOGx3NuWNimJoUjo9Ow77GfbxZ8hqbvtxEh+X4YdrjIsaxJH0Jl6ddTmygd08+5ClkPyPUksyIvmRkZHDo0CHXvzdt2kROTg5r164lJCSEiooKRo4c6bpdq9VSU1NDVFQUU6ZM6fV4I0eOxGKxUFdXR0pKypC8hhP1u5F68803+eyzz/D39+frr7/u8Um8RqNxWyOVm5vLiBEj3PLcA0U+xRkaWq2G0bHBjI6dAudMAe7DZLWzr7SMpgNf4FeZRVr7LhI09czRHGaO9jAPsI4OJZBtjkl85ZjK1/Yp1OO8KGdjp5lPDtTxyYE6wHmS+7TkcGamOketpiVHEOw34FcckLwI1QY7Mw0dJnaUtZBd6hx1Km08+QW4T2Z0bDDz06M4Z3Q0c0dFERbg/LCupquGVw/+iw2lG6joqHBtHxsQy+JRi7ky/UrGRowdsNcinGQ/I9SSzIi+ZGZm8v777wPOo4UeeughHnzwQaKjo+ns7MRoNPYaIdq7d2+fTRRAQIBz5mWDwTC4hZ9Ev/+q+81vfsPjjz/Or371K7TagfnUvauri+LiYte/y8rKyM3NJTIykuTkZB566CGqq6v5z3/+A8Cf/vQn0tLSmDRpEiaTiZdeeokvv/ySzz77bEDqcZdZs2a5u4Rhy99Hx5Rxo2HcaOBuABorDlOf+wm6sq9Jas8hlC4W6XaxSLcLfOCQI4WvHFP4yj6VvcoY7EcvdGW02tlW0sy2kmYAdFoNE0eEMjM1glmpkcxKjSQm5MxHRyUvQq2Bzkx9h4kdpc3sKHU2T6VN6hun+FB/5o+OZv7oKM5JjyY+7PgbqcFq4IPij/mw5EN21u10rQ/QB3BJ8iUsSV/C7PjZ6LS6vh5aDADZzwi1JDNDIyLQl90PX+L2Gk5XRkYGVVVVdHV1sWHDBmpra7n//vsBCAoKIjo6mtbW1h73yc3NPWkj1dLSAuC2iU363UhZLBZuuOGGAWuiAHJycnpcYPfYD/a2225jzZo11NbWUllZ2aOGBx54gOrqagIDA5k8eTL/+9//+rxIrzfJy8tj9uzZ7i5DHBWTMp6YlPHAKnDYsRzZTVPux+hKPiem46DzulbaCu7Rf0i7EkiWYzJf2qfxpWMa7Rw/J+PYbGR51e28urUcgLToIGYdbaxmp0WSHBmo+jwryYtQ60wyoygKlS0Gdpa1sKu8hV3lrZT1o3GKDPJl7qhI5qVHc056FKOig3pk36E42F2/m/XF6/m84nOMtuOHA86On81V6VdxacqlBPoE9ut1CHVkPyPUkswMDa1Wc9rnJ3mCjIwMAPbv388jjzzC6tWrCQoKApwXcZ42bRqvv/56j/vk5eVxzTXX9Pl4Bw4cIDEx0W3T7fd7solVq1YRExPDr3/964GuaUipOaFsqNTX17t9SnlxmrqbUIr/R/eBT/Ap/xI/6/HzNGyKlp2O8XzumMHnjplUKd/9aUlsiN/R0aoIZqVFMj4+FN13TCkqeRFqqcmMw6FwuK6TXeUt7CxvYVdZCw2d6iaHAAjx1zMnLYpz0qOYlx7FuLiQPqfLremq4YOSD/ig+AOqu45PBJMcksxV6VexJH0JI4NH9rqfGFyynxFqSWYGz6kmSvAGaWlpxMfH09zczKFDh1zXj7JarRw+fJjp06fT0NBAREQEAKmpqdxyyy3cc889BAUF9bhm1O23345Op+Pll19WVYPbJ5uw2+387ne/Y9OmTUyePLnXZBMnzsYh1Glra5Odj7cIikYz5UaCp9wIDjtU5UDRJmz5n6BvOsQ5OufyKK9xyJHC544ZfGafyUElBej9R2RDp5mNebVszKsFIMRPz/SUCGanRTIzJYIpSeH4+/Q8fEnyItQ6VWa6zTb2HWkjp6KV3RWt7KlspdNk63PbUwnx0zMrLZK5oyKZOyqKSSPDTvqhgNFm5IvKL1hfvJ6dtTtRcH6+F+QTxKLURVw9+mqmxEyRi+W6kexnhFqSGXEymZmZbNiwgbVr17qaKHD2FpmZmUyfPp21a9dy993OUyyefPJJfvnLX/L000/z85//nN///veAsxlav349n376qVteB5xBI5WXl8e0adMA57CaGDjyx4KX0uogeQ4kz0F/8WpoKYOCj+HwxyiV21yHAP5U/x5VSgwb7bP5xD6HXCWdvpoqgE6zjW8KG/mmsBEAX52WzMQw53lWKZHMSImQvAjVjmXm2GUB9lQ6m6bdFa3k13bg6MdxCs4Rp0jmpEUxd1QUE0eeejRVURTymvJ4v/h9Pi37lC5rl+u2OfFzWDp6KZekXEKAPkB9MWLAyX5GqCWZESfz4YcfnvL21atX8+CDD7Jy5Uq0Wi3Lly9n+fLlvbZ79dVXmT17NnPnzh2sUr9Tvxupr776aiDrECcICQlxdwliIESmwbx7YN49aLqboWgTHN4IJV+SaG3kbv1G7tZvpFkfyyf2ObxnmsFeZTQKJz/v0GJ3uP7gfQHnxUZTI/2Zm25iRorzXKuUKPXnWYnhod1oZX9VG5vzuyjdvovcI200dVn69VjRwb6uSVNmp0UyYcR3H4YK0GpqZUPJBt4vfp/ituOTCyUEJ7A0fSlXjb6KhOCEftUkBo+8Lwm1JDNCrWPzLixevJiioiKqq6tJSko66fY+Pj789a9/Hary+tTvc6TefPNNbrrppj5ve/DBB13Dbp7OE8+RysnJYebMme4uQwwWiwGK/weH1kPBp2A9fqK+wT+OnMDzeNMwi0/aEjnZSNWpRAf7MT05nOkpEUxPjmByYlivwwHF2c9ktXOotoMD1e3sO9JO7pFWSvoxDfkxSZEBzqYpNZJZaZG9Joc4FbvDzvba7bxX9B5fHfnKdcFcP50fl6ZcyvdGf4+Z8TPRagb/umuif+R9SaglmRk83n6O1Ml0d3e7Jp4YbAN1jlS/G6nw8HDefPNNLr/88h7rV61axVtvvUVtbW1/HnbIeWIjNZRBEm5mNULxF8ebKkun6yZbWDJl8ZfzmfY8NtaFk1/XQX9+W/VaDRNHhjI9OYJpyeFMT44gMSJARq3OIic2TXlVzpkhixq6sPfnGD2cmZmUEMaMZOcFpmekRPSYjvx01XTV8H7x+6wvXk9dd51r/cSoiSwbvYzLR11OqK9n7HfFqcn7klBLMjN4ztZGym63o9MNzQe/bm+kNm7cyC233MJHH33EueeeC8B9993He++9xxdffMH48eP787BDzhMbKbmI3TBlNUHJl3DwfechgCeMVBGXgWnCMvaGXsTWxkByKlrIPdKGyero11NFBfkyOTGMyYnhTE0KZ3JimFdNnzpcKYpCY6eZQ7Ud5Nd2kl/bQX5tB6VN3f1umgAiAn2YkRLB9JQIZiRHMDkxnADf/r2ZWR1Wvj7yNe8Wvsu2mm2uiSNCfUO5ctSVLBuzjHGR4/pdq3APeV8SaklmBs/Z2kh1dnYO2SGhbm+kAN544w3uvfdePv/8c15++WU++OADvvrqK8aO9Z6ryntiIyUElm4o/BTy1kHR5+CwHr8teR5MvgHrhKs52KIhp7yFnPJWcipaaepSPy31MQnhAUxNCiczMYxJI0OZNDKMyKDTv8ieGFidJivFDV0UNXRRVN/papyau/t3TtMxvjotE0eGMjUpnGnJzka6P9cv+7aKjgreLXqXD4o/oMXU4lo/J34Oy8Ys4+KUi/HTSbMuhBBn6mxtpIaS26c/B7j55ptpa2tj/vz5xMTE8M033zB69OgzeUiBfIojAN8gyLjGuRhaIP9DZ1NVvgUqt0Pldnw++SVTxy9Gp89kxc0/QdHqqGwxuKas3lPRxuG605+BrbrNSHWb0TX1OkB8qD8TR4YyaWQoE0c4m6ukSDkscKAoikJzt4Xypu7jTdPRxqm23XTGj6/RQHpMMJkJYUxJDGNqcgQTRoSQvW0rCxZMOuPHt9gt/K/if7xb9C4763a61kcHRHP16KtZNnoZSaEnP1FYeA95XxJqSWaEWkM5IjVQVI1I3X///X2uf+edd5g+fTrp6emudd5yHSlPHJGyWq29rsslBADt1XBgHeS+CY35x9cHx8Pk62HqzRA7wbW622xjX1Ubeyvb2FPRyt4jbbSc4YhGkK+O9NhgRscEkx4bzJjYYEbHBpMcGYheJ5MFfJuiKDR1Wahs6aa8yUB5czdlTd2UN3dT0WSg06z+Gk19ObFpykwIIzMxjIkjQgny6/152ZnuYyo6KlhXuI4Pij+g1dzqfH40zE+Yz7VjrmVB0gJ8tLIPO5vI+5JQSzIzeM7WESmHw+GauW+wueXQvgsvvPC0ttNoNHz55Zen+7Bu5YmN1LZt2zjnnHPcXYbwZIoCtbmQ+ybWvW/iY+04ftvIaTDt+5B5LfiHfetuCkdajOyramPfkTb2H52YwGi1n3FJvjotqdGBpEYFkRgRSGJEwNElkISIAMICzs43VKPFTmOnmdp254hedavRNbp37HuzrX/nsp1MoK+OcfEhTBgRyoQRoUwcEcL4+L6bpr70Zx9jtVv54sgXrCtYR3Zdtmt9XGAcy8Ys43ujv8eI4BGqHlN4D3lfEmpJZgbP2dpIdXV1ERwcPCTP5RHnSJ0NPLGRampqIjo62t1lCC/RVF9DdMtu5yhV0SY4OrU0PoEw6Xsw/TZImu0csuiDze6guLGL/Ufaya1q42BNB4drOwb8j/8Qfz2JEYHEhvgRHexHdLCv82vI0a/BfkQF+xLq74OfXuu2wwdNVjttBittRgttBivtRivtBistBguNnWYaOs00dJho7DLT2GEesBGlvui0GlKiAhkTG8zYuOONU0pkINrTuGbTyajZxxzpPMK6wnWsL17vOvdJg4bzEs/jurHXcW7Cuei1Z3SUuPAC8r4k1JLMDJ6ztZEaylFMjzhHSgyO+vp62fmI01bf1Er0pCUwYQl0N8H+t2H3v6GpAHL/61xixsP0W2HyjRAU1eP+ep2W8fGhjI8P5fpZzvNZbHYHZU3dHKrt4GBNB4dqOjhY006rwdpXCael02Q7Osvcd2+r12oI9tcT7OdcQvz1hPj7EOCrw0erwUenxUevdX2v12nx1WlAo8HhULArCg5FcX7vAIeiYHcomG12jFYHRosNo9WO0WLHYLFjstrpttjpMFoHvIE8Hb46rbNhigtmTGyI62tqdCB++oGfCva79jE2h42sqizWFqxla81W1/qYgBiWjVnGNWOukdGnYUbel4Rakhmhls1m87rDQaWR8kABAQHuLkF4kR55CYqGeffA3B/DkWzY8x848B40HoZNv4b/PQbjr4RZd0HK/JOOUul1WsbEhTAmLoSlUxMA52GBdR0mihu6XEtRQxclDV1nPJPct9kcinNU6AwaN0/jo9OQFBlIWlQQKVFBpEUHkhodRGpUECPDA9CdwQiTWifbxzQZm3i38F3WFa1zXfdJg4ZzRp7DdeOu4/zE82X0aZiS9yWhlmRGqDVU50cNJHlH9EDe1o0L9+ozLxoNJM91Louecc74t+ffULsPDr7nXGLGw6wVMPkG8P/uw1o1Gg0jwgIYERbAeWNietzW2m2huLGL0sYuqlqNHGkxUNVqpKrVSH2nqV8XEvY2AT46Rob7kxARSEK48/ywhPAAEo5+jQv1H9Jm6VROzIyiKOyq28XbBW/zZeWX2BTnoYoRfhFcPeZqrht7HUkhMvPecCfvS0ItyYxQ67sO6W9ubmbChAns3LmT1NTUk2534403MmvWLB544IEBrrA3aaQ8UHNzM0lJ8oeLOD3fmRf/MOcI1Ky7oCYXdr8K+9c6R6k+/jl8/ihMuQFm3gXxGf2qISLIl1lBkcxKjex1m9lmp7bNRFWrkZo2I41dZpq6zDR1WWg+4ftWg8XjGq5Qfz3hgb6EB/oQFuBDTLAfMaF+xAT7ERvqT2yIHzEhfsSG+BHsp/eaaeGbm5uJiIvgw5IPebvgbUrbS123TY2ZyvXjruey1Mvkuk/CRd6XhFqSGaGWzWbD1/fk16986qmnWLp0aY8matWqVVRUVPDee++51j388MMsWLCAFStWEBYW1scjDRxppDxQWlqau0sQXkRVXkZOhZF/hkufgH1vwa6XoKkQcl5xLklzYfZKmHAV6AfmYrx+ep3zELbooFNuZ7M7aDNa6TLZ6DLb6Dz6tcvsXNdptmG02LHaFWx2B1a7A8sJ31vtzi5Mo3FO0qDTaNBoNOi0zn9rNBr89FoCfXUE+OgI8NUT4KMj0FeH/9GvoQE+hAf4EB7oQ4i/j8eMIA2k4tZi3ut4j03vbMJgMwAQqA/kylFXcv246xkXOc7NFQpPJO9LQi3JjFDrVE2UwWDg5ZdfZtOmTT3W79y5k8WLF/dYl5GRQXp6Oq+//jr33HPPoNR6jKpGqrKykuTk5NPevrq6moSEBNVFDXf79u2Ti9iJ09avvPiHwZy7YfYPnBf53fUSHP4IjuxwLiEjnCNYM+5wnnc1BPQ6rWv2PjGwrA4rX1V+xVsFb7Grbpdr/aiwUdw4/kaWjFpCsO/QTDkrvJO8Lwm1JDOiL7GxsTz99NOsWLHCtW7Xrl2cd9557Nq1i8zMzD7v9/HHH+Pn58fcuXMBsFgsBAUFYbPZ2LZtG7/5zW+YM2cOO3bsAGDJkiW89dZbntVIzZo1i6uvvpoVK1Ywa9asPrdpb29n7dq1/PnPf+YHP/gBP/nJTwak0OFEdjxCjTPKi0YDaec5l84652x/OS9DZy18+SR883uYfB3M+VG/D/sT7tNkbGJd4TreKXiHBmMDADqNjguTLuTG8TcyO3621xyOKNxL3peEWpKZIaQoYDW457l9Ak86cVVfMjMzOXToUI91v/zlL7n77rtP2kQBbN68mRkzZrj+rdfr2bp1K3PmzCE3N5e4uLge05jPnj2bp556CrPZjJ/f4H1Aq6qROnToEE899RSXXnop/v7+zJgxg5EjR+Lv709rayuHDh3i4MGDTJ8+nd/97ndcccUVg1X3WS0rK0t2QOK0DVheQuLhgl/Cuavg4PuQ/U+o2Qt7X3cuqefBnB/CuMtBO/BTcouBk9eYxxuH32BT+SasDufMh1H+UVwz9hquG3sdhbsLmTNijpurFN5E3peEWpKZIWQ1wNMj3fPcv64B31Mfun+ijIyMHo3Upk2byMnJYe3atXR2dhISEtLn/SoqKhg58vhr1Gq11NTUEBUVxZQpU3ptP3LkSCwWC3V1daSkpKh4QeqoaqSioqJ47rnneOqpp9i4cSNbtmyhoqICo9FIdHQ0t9xyCwsXLiQjQz65PhPnnnuuu0sQXmTA86L3dU4+Mfl6OLLT2VAd+hDKNzuXiFTnCNW0W8Cv7x2eGHoWu4VN5Zt48/Cb5DXludZPjpnMzeNv5rKUy/DROWfRij031l1lCi8l70tCLcmM6EtmZibvv/8+4Jw19qGHHuLBBx8kOjoa5RQzThmNxl4Xzt27d2+fTRQcn37fYBjckbp+TTYREBDAtddey7XXXjvQ9Qhg69atnHfeee4uQ3iJQcuLRgPJc5xLe5XzPKrda6C1HD79JXz1NMy4FWbfDeEyM5O7NBoaWVu4lncK3qHZ1AyAj9aHRamLuHnCzWRE9/5gS/YxQi3JjFBLMjOEfAKdI0Puem4VMjIyqKqqoquriw0bNlBbW8v9998PQFdXF4sWLeK5555jzpw53HXXXWRkZLBq1Sqio6NpbW3t8Vi5ubknbaRaWloAiImJ6fP2gSKz9nmgUx0jKsS3DUlewhLhksdgwS9g35uw45/QXATb/grb/wETlzovBJw4c/BrEQAcaDrA6/mvs6l8EzaH89pPsQGxXD/ueq4dey1RAVEnva/sY4RakhmhlmRmCGk0qg6vc6djR63t37+fRx55hNWrVxMU5Kw9ICCARx55hP/3//4f5513HlqtllWrVgEwbdo0Xn/99R6PlZeXxzXXXNPn8xw4cIDExESiowd3wizvu4TwMFBRUeHuEoQXGdK8+AY6Z/O7ZyfcvBbSzgfF7rzA70sXw0uXOs+vstuGrqZhxOaw8Wn5p3z/4+9z08ab2Fi6EZvDxtSYqfz+/N/z6bWfcveUu0/ZRIHsY4R6khmhlmRG9CU4OJiUlBQeeOABtFotK1eudN1msVhYtGgRlZWVbNy4kX/84x+u2xYuXMjBgwd7jEo5HA4KCgqoqamhvb29x/Ns3ryZyy67bNBfjzRSHigiIsLdJQgv4pa8aLUwdiHc9iH8cAtMvQW0PlC1E965Hf4yFbb+GYyt3/VI4jS0mdp4Ke8lFr27iAe/eZDcxlz0Wj1XjrqStxa/xWtXvMai1EX4aH1O6/FkHyPUkswItSQz4mQyMzPZsWMHTz31FHr98YPjdDodu3btoqWlhbCwMHx8fHrcZ/r06axdu9a17sknn2TNmjUkJCTw5JNPutabTCbWr1/fo0kbLHJonwdyOBzuLkF4EbfnJT4Trv4HXPyo8zyqnJeh/Qh8vhq+/n8w9WbnbH/RY9xbpxcqbS/l9UOvs6FkAya7CYBI/0iuH3c914+9npjA/h377fbMCK8jmRFqSWbEyXz44Yd9rq+urmbFihV8+eWXXHPNNRw4cKDHBHarV6/mwQcfZOXKlWi1WpYvX87y5ct7Pc6rr77K7NmzXdecGkz9bqRWrFjB8uXLueCCCwawHAHOk+2EOF0ek5eQOLjoN3DeA3BgnfM8qvoDzuZq10sw5jKY+yMYdaGqa04MN4qisL12O68deo0t1Vtc6ydETuCWCbdwedrl+OpOfvX30+ExmRFeQzIj1JLMCDWMRiM333wzf/3rX0lLS+Ohhx7it7/9LW+//bZrm8WLF1NUVER1dTVJSSef5MrHx4e//vWvQ1E2GuVUcw2ewtKlS9m0aRMxMTHceOONLF++/KQzZ3iyjo4OwsLCaG9vJzQ01N3lANDc3ExU1KnPcRDiGI/Ni6I4p0vf8U8o+AQ4uquJHgdz7oYpN3rNybFDwWw383Hpx7yW/xpFrUUAaNBwQdIFfH/i95kZN3PALp7rsZkRHksyI9SSzAwek8lEWVkZaWlpvaYE92Y2m63HoX6D6VQ/QzW9Qb/Pkfrggw+ora3lkUceYdeuXUyfPp1Jkybx9NNPU15e3t+HFcDhw4fdXYLwIh6bF40G0hbATW/Cfbudh/f5BkNTAWy8H56bAJt+45xOfRhrNjbzz9x/ctm6y1i9bTVFrUUE6AO4efzNfPS9j/jLRX9hVvysAWuiwIMzIzyWZEaoJZkRaplMJneXoFq/R6S+raqqijfffJNXXnmFoqIibDbvmLXLE0ekhrIjF97Pq/Ji6oDcN2DnC9BSenSlBsZdAXN/CKnnDZvD/krbS/nPwf+woWQDFocFgPigeG4ZfwvLxi4j1Hfw9kdelRnhESQzQi3JzOA5W0ekFEUZ0A8NT8XtI1Inslqt5OTkkJ2dTXl5OXFxcQPxsMPWtm3b3F2C8CJelRf/UGfDdO9uuPkdSL8YUKBgI/x7CfzzHMh5BSzd7q50UCiKwq66Xdz7xb0sXb+Ud4vexeKwkBGVwe8X/J5Pln3C7Rm3D2oTBV6WGeERJDNCLcmMUMsbz6s7o0bqq6++YuXKlcTFxXH77bcTGhrKRx99RFVVVb8eLysriyVLljBy5Eg0Gg3r16//zvt8/fXXTJ8+HT8/P0aPHs2aNWv69dyeZMGCBe4uQXgRr8yLVgtjL4Pvvwf37IJZK8EnCBoOwUerjh/25xq18m5Wh5WNpRu54aMbuHPTnXxT9Q0aNFyYdCFrFq3hjcVvsChtEXrt0Hx665WZEW4lmRFqSWaEWiEhIe4uQbV+N1IJCQlcccUVNDU18eKLL1JfX88rr7zCxRdf3O9hue7ubqZMmcLf//7309q+rKyMxYsXc+GFF5Kbm8vPfvYzVqxYwaZNm/r1/J4iKyvL3SUIL+L1eYkZC4v/APcfgoXPQOQoMLXD9r/BX6bDf6+Hov+BF06l223t5j8H/8Pi9xbzq82/Ir8lH3+dPzeMu4EPr/6Qv1z0F2bEzRiyQxmO8frMiCEnmRFqSWaEWp2dne4uQbV+nyP1r3/9i+uuu47w8PABLslJo9Hw/vvvc/XVV590m1/+8pds3LiRAwcOuNbdeOONtLW18emnn57W83jiOVJdXV0EBwe7uwzhJc66vDgcUPIFZL8AxZ8fXx+ZDrNXwpSbICDcbeWdjiZjE//N/y9vF7xNp8X5xhDpH8lN42/ihnE3EOHv3gtVnnWZEYNOMiPUkswMnrP1HCm73Y5OpxuS53L7OVIrV64ctCbqdG3fvp1LLrmkx7qFCxeyffv2k97HbDbT0dHRY/E0BQUF7i5BeJGzLi9aLYy5FJavg/v2wNwfg18YtJTAp79yHva34adQl+fuSnspbS/l0W2Pctm6y3gp7yU6LZ2khqby6LxH+ezaz/jhlB+6vYmCszAzYtBJZoRakhmhljfO2jcgk024S11dXa+JLeLi4ujo6MBoNPZ5n2eeeYawsDDXcuyCXi0tLWzduhWbzeYajs7KyqKzs5M9e/ZQXV1NcXEx+fn5NDY2kp2djdls7rGt0Whk586d1NfXU1BQQGFhIbW1teTk5NDd3d1jW6vVyrZt22hqauLgwYOUlpZy5MgRcnNzCQ4O7rGtw+Fg8+bNtLW1sW/fPiorKykvL+fAgQM0Nzf3WXdXVxe7d+/uUXdDQwPZ2dmYTKYe25pMJlfdhw8fpqioiJqaGnbv3k1XV1efdTc3N3PgwAHKysqorKxk3759tLe3k5WVhaIoPb62t7e76i4rK3PVvW3bNqxWa59119TUUFRUxOHDh6mvr2fnzp191p2dnU1DQwP5+fkUFxdTXV3dZ902m42tW7e66i4vL3fV3dbWxubNm3E4HD3u097eTm5uLkeOHKG0tJSDBw/S1NTUZ93d3d3k5ORQW1tLYWEhBQUFrrqNRmOPbc1mM9nZ2TQ2Nvaoe8+ePXR2dvZZd0tLC3l5eZSXl1NRUcH+/ftpa2tjy5YtxMbG9rhPR0cHe/fupaqqipKSElfd27dvx2Kx9NjWYDCQk5NDXV2dq+66ujp27dqFwWDoVfeOHTtobGzk0KFDlJSUUFVVxd69e3vVbbfb2bJlC62trezfv5+KigpX3a2trWzZsgW73d7rd+3Eug8dOkSjI5Qd4Usx37uXonE/htiJYDXA7jXw/LlYnr+Qmk1/oTD/IHV1deTk5PSq22KxsH37dtfv2ol1d3R09Ppd27JlC21tba66y8vLycvLO+U+4q3Nb7Fy40qWrl/Ke0XvYXVYSQ9I5w/n/oEHIh/g2rHXkr01e8D2Ecd+1/q7j6itrZV9xDDaR3y77v7sI3x8fDxzH9HYyI4dO3q9HxsMBnbt2kVdXZ3rd82d+4ih/jviTPcRA/F3hF6vl33EIO0jLBYLZrMZq9WK0WjEZDJhsVjo7u7Gbre7DpHr7OxEURS6urqw2WwYDAbMZjNmsxmDwYDNZnNtc+J97HY7BoMBi8WCyWTCaDRitVrp6urC4XD02ra7uxur1YrJZMJkMmG1WvusxeFw0NXV1atug8GA3W7HarX2qLuzs3NQ6zabzTQ2Nva5jzhdAzb9+UA7nUP7xo4dyx133MFDDz3kWvfxxx+zePFiDAYDAQEBve5z7D/imI6ODpKSkjzq0L7i4mJGjx7t7jKElxhWeVEUqNgGu/4F+RvAcfQyC0ExMP02mHkHhCUOSSkOxUFWVRavHHiFvQ17AVwTSNyRcQdTY6cOSR39MawyIwaEZEaoJZkZPGfroX0mk2nIXs9AHdrn1RP8x8fHU19f32NdfX09oaGhfTZRAH5+fvj5+Q1Fef12rCMX4nQMq7xoNJA637l01MKefztHpzprYfMfYMtzMPZymHUnjLrIeZjgALParXxc9jGvHniVkvYSAHy0PlyVfhW3TbqNtLC0AX/OgTasMiMGhGRGqCWZEWp56NjOKXl1IzVv3jw+/vjjHus+//xz5s2b56aKBkZUVJS7SxBeZNjmJXQEXPArOO8BOLwRdr0E5Zud16Qq2AgRac4RqqnLIejMf0YGq4F3i97l3wf/Tb3B+QFOsE8w14+7nuUTlhMTGHPGzzFUhm1mRL9JZoRakhmh1nddwLm5uZkJEyawc+dOUlNTT7rdjTfeyKxZs3jggQcGuMLePOocqa6uLnJzc8nNzQWc05vn5uZSWVkJwEMPPcStt97q2v6HP/whpaWl/OIXv+Dw4cP84x//YO3ataxatcod5Q+YsrIyd5cgvMiwz4vOByZdDbd/BD/Ohtl3g18otJbB56udk1O89wOozHYeGqhSm6mNv+f+nUvXXcrvdv2OekM9Uf5R/Gz6z/js2s9YNWOVVzVRIJkR6klmhFqSGaHWiafe9OWpp55i6dKlPZqoVatWsWzZsh7bPfzwwzz11FO0t7cPRpk9DMo5UlqtlgsuuIDf//73zJgx47Tv9/XXX3PhhRf2Wn/bbbexZs0abr/9dsrLy/n666973GfVqlUcOnSIxMREHnnkEW6//fbTfk5PnP58KI8RFd5P8tIHSzfkrYOcl6F23/H1cRkw43aYfAP4n/r3va67jv8c+g/rCtdhtDknr0kOSeb2jNu5Kv0q/HSefYjwqUhmhFqSGaGWZGbwnK3nSDkcDrQnOSTfYDAwYsQINm3axNy5c13r58+fz+LFi/n1r3/dY/tZs2Zx++23c8899/T5eAN1jtSgNFJr1qyhvLycTz/9lB07dgz0ww8oT2yksrKy5Irg4rRJXk5BUaB6j7OhOvAu2I5OreoTBJnXOg/9Gzmtx10qOip45cArfFjyIbajk1lMiJzAXZl3cUnyJei0Q3ONi8EkmRFqSWaEWpKZwePNjVRsbCxPP/00K1ascK3btWsX5513Hrt27SIzM7PP+61bt44f//jHNDQ0AGCxWAgKCsJms7m2mTNnjqvveOKJJ/j888/ZvHlzn4/n0Y2UN/HERkoIMQiMrbDvLch5FZpOuL7JyGkw4w4OJ07mpcP/5fOKz3EoDgBmxM1gZeZKzhl5DhqNxk2FCyGEEMd9uwlQFMV15MRQC9AHqHp/vPjii5kyZQrPPfeca91FF11EZmYmf/7zn096v5/+9KcUFhbyySefAM7Rq5ycHObMmUNubi5xcXH4+/u7rnH76aefsnTpUjo6OvqcZM7ts/bddttt3HXXXfJpwyCQT3GEGpKX0xQQAXN/BHN+6JxCPecVyP+Q3OaDvLjzt2w+cHymz/MTz2dF5gqPnsL8TEhmhFqSGaGWZGboGG1G5rwxxy3PnX1zNoE+gae9fUZGBocOHXL9e9OmTeTk5LB27Vo6OzsJCQnp834VFRWMHDnS9W+tVktNTQ1RUVFMmTKl1/YjR47EYrFQV1dHSkqKilekTr8bqfb2di655BJSUlK44447uO2220hISBjI2oat2bNnu7sE4UUkLyppNCgp57DDV8u/Ai3saswFQKsoLOw2sKKtg7HmgxCeC2Hp4Nf3Tt2bSWaEWpIZoZZkRvQlMzOT999/H3BOd/7QQw/x4IMPEh0djcPhOOn9jEZjr5GjvXv39tlEAa7LIKm5uG5/9LuRWr9+PY2Njbz22mv8+9//5tFHH+WSSy7hrrvuYunSpfj4+AxkncPK/v37ZQckTpvk5fQpisI3Vd/w4v4XyWvKA0Cv1bN01FXcGTaJ5PyPofkjqNnjXDb9xnku1Yzbe51L5c0kM0ItyYxQSzIzdAL0AWTfnO2251YjIyODqqoqurq62LBhA7W1tdx///0A7Nixg8cff5xNmzYB8MEHH7Bx40ZefPFFoqOjaW1t7fFYubm5J22kWlpaAIiJGdxZdc/oOlIxMTHcf//93H///ezZs4dXX32V73//+wQHB7N8+XJ+/OMfM2bMmIGqddgYzCFIcfaRvHw3u8PO5xWf86+8f1HYWgiAn86Pa8dey+2Tbic+KN65Ycb10N0EuW84L/bbXOy84O/uNRA/GWbcBhnXQkC4u17KgJDMCLUkM0ItyczQ0Wg0qg6vc6eMjAzA2Wg/8sgjrF69mqCgIACmTZvmOuzPZrPxxBNP8NFHH7lue/3113s8Vl5eHtdcc02fz3PgwAESExOJjo4erJcCDNB1pGpra/n888/5/PPP0el0XHHFFeTl5TFx4kT++Mc/DsRTDCvf7riFOBXJy8nZHDY2lGzg6g+u5sGsBylsLSRQH8idGXfy6TWf8qvZvzreRB0TFA3zfwL35sDtGyHzetD5Qd1+2PgA/N94eP/oeVZeOlePZEaoJZkRaklmRF+Cg4NJSUnhgQceQKvVsnLlyh63JyUlUV5ezosvvsjixYsZMWIEAAsXLuTgwYM9cuVwOCgoKKCmpqbXNaM2b97MZZddNuivp9+NlNVq5d133+XKK68kJSWFd955h5/97GfU1NTw73//m//973+sXbuWJ554YiDrHRZ0Ou+fXlkMHclLb1aHlfeL3ueq9Vfx6y2/pryjnFDfUH485ceui+hGB3zHp1QaDaSeC9f8Cx44DAufgZgJYDPCvjfh1cvhbzNh65+hq2FoXtgAkcwItSQzQi3JjDiZzMxMduzYwVNPPYVef/zgOI1Gw+zZs/nqq6/45z//yYMPPtjjPtOnT2ft2rWudU8++SRr1qwhISGBJ5980rXeZDKxfv36Xk3aYOj3oX0jRozA4XBw0003sXPnTqZOndprmwsvvNA1DaE4fceGOIU4HZKX4yx2C+uL1/Ny3svUdNcAEOEXwa2TbuXGcTcS7BvcvwcOjIR5P3bO+le923nYX967zkP/Pl8NXzwB4y6Had+H9ItBd0ZHTQ86yYxQSzIj1JLMiJP58MMP+1yv1WqZPXs29913H0888USvGfxWr17Ngw8+yMqVK9FqtSxfvpzly5f3epxXX32V2bNn97hw72Dp97v9H//4R6677rpTXggsPDycsrKy/j7FsFVbW9tjikchTkXyAma7mXcL3+XlAy/TYHCODkX5R3FHxh1cN/a6gTt2XKOBxJnOZeHTcPB92P1vqM6B/A3OJWQETLkJpi2HqPSBed4BJpkRaklmhFqSGaGW1Wpl7NixREVFcffdd/e6ffHixRQVFVFdXU1SUtJJH8fHx4e//vWvg1mqS78vyFtZWUlSUlKvi3ApisKRI0dITk4ekAIHmydekLerq4vg4H5+ci6GneGcF5PNxLrCdbxy4BUajY0AxAbGcmfGnVwz5hr89UN0xff6g7D3decFf40tx9enzHc2VBOXgq/nfDo7nDMj+kcyI9SSzAyeU11M1pvZ7XZWrlzJ0qVLWbp06aA+10BdkLff50ilpaXR2NjYa31LSwtpaWn9fVgB7Nmzx90lCC8yHPNispl47dBrXP7e5Ty761kajY3EB8Xz8JyH+WTZJ9wy4Zaha6IA4ibBomfggQK4/j8w+lLQaKFiK6z/EfxhHHx4H1Rme8QEFcMxM+LMSGaEWpIZoUZJSQnjx48nKCho0JuogdTvESmtVkt9fX2v+dkrKiqYOHEi3d3dA1LgYPPEESkhRN+MNiPvFLzDqwdfpcnYBMCIoBGsnLySq9OvxkfnQdeva6+GfW84R6pay4+vjxoDU2+GKTdCqBz2IoQQQp2zdURqKA3UiJTqc6SOXTRLo9HwyCOPEBh4/NwDu91OdnZ2nxNPiNOXlZXFggUL3F2G8BLDIS9Gm5G1BWt59cCrNJuaAUgITmBF5gqWpi/1rAbqmLAEWPAgnPuAc2Qq979w6ANoLoIvHocvfwvpFzmbqnGLwWfo3gyHQ2bEwJLMCLUkM0Ktzs7OXhNMeDrVI1IXXnghAN988w3z5s3D19fXdZuvry+pqan8/Oc/95oL8XriiJTVasXHxwP/MBQe6WzOi8lm4p3Cd3g57+UeDdQPJv+AJelL8NF62es2d8LB9c6mqnL78fX+4ZBxjbOpSpjhnNRiEJ3NmRGDQzIj1JLMDJ6zdUTK4XCg1Q7IJW6/k9tGpL766isA7rjjDv785z97TPNxNtm1axfnnHOOu8sQXuJszIvZbmZd4TpeznvZNYlEQnACd0++myvTr/S+BuoYvxCY/n3n0lwCuW84r0nVUQ05LzuX6LHOw/4m3+gc1RoEZ2NmxOCSzAi1JDNCLYPB4HUTlPT7HKmzhSeOSDU3NxMVFeXuMoSXOJvyYrFbeLfoXV7Ke8k1jfmIoBHcPflurhp9lfc2UKfisEPZN5D7pnP6dJvx6A0aGHU+TLkZJlw5oLP+nU2ZEUNDMiPUkswMnrN1RMpms/W4QO9gcsuI1P33389vf/tbgoKCXOdKncxzzz2n5qHFCWpra2XnI07b2ZAXq93K+8Xv8+L+F6k31AMQHxTPysyVfG/09zzzHKiBotU5z5VKvwhMHc7zqPa96TyvqvRr57Ix2DmF+pQbIeVcOMNDH86GzIihJZkRaklmhFpWq3XIGqmBoqravXv3YrVaXd+LwSFXAxdqeHNebA4bG0o28ML+F6juqgac14FambmSZWOW4avz/Y5HOMv4hx4/9K+lDPa/7WyqWsud51Xl/hdCE2Hydc5D/2LH9+tpvDkzwj0kM0ItyYxQa6jOjxpIqhqpY+dHfft7MbB0Op27SxBexBvzYnfY+aT8E57f9zwVHRUARAdEsyJzBdeOvRY/nZ+bK/QAkWlwwa/g/F86J6bY95ZzooqOKtjyR+cyYqpzlCrjWgiO+a5HdPHGzAj3kswItSQzYjjo9/jZM888Q1xcHHfeeWeP9a+88gqNjY388pe/POPihqvW1laSk5PdXYbwEt6UF4fi4H8V/+Mfuf+gpL0EgAi/CO7MuJMbxt9AgD7AzRV6II0GUs5xLpf/Dgo/dTZVxZ9Dba5z2fQbGH0xTL4Bxl3+nedTeVNmhGeQzAi1JDNCLbvd7u4SVOt3I/XCCy/wxhtv9Fo/adIkbrzxRmmkzkBqaqq7SxBexBvyoigKWVVZ/HXvXyloLQAgxDeEOybdwc0TbibIRw4BOS0+/jDpaufS3QQH3oP9b0H1bij6zLn4BMGEJc7D/9IuAF3v3bw3ZEZ4FsmMUEsyI9Q68ZJK3qLfByPW1dUxYsSIXutjYmKora09o6KGu3379rm7BOFFPD0v2bXZLP9kOfd+eS8FrQUE+QTxwyk/5NNrPmXl5JXSRPVXUDTM+QGs/BLuzXEeAhiRCtZuZ3P1+jXw3AT45FdQvQdOmKDV0zMjPI9kRqglmRFqGY3G797Iw/R7RCopKYmtW7eSlpbWY/3WrVsZOXLkGRc2nJ133nnuLkF4EU/Ny/7G/fxl71/Irs0GwF/nz00TbuLOSXcS7h/u3uLONtFj4MJfwwUPQdUu2L8WDrwL3Q2Q/U/nEpkOmddB5nUemxnhuSQzQi3JjFDrVNeQam5uZsKECezcufOUo5033ngjs2bN4oEHHhiECnvr94jUypUr+dnPfsarr75KRUUFFRUVvPLKK6xatYqVK1cOZI3DzubNm91dgvAinpaXgpYC7vviPm75+Baya7PRa/XcNP4mPl72MffPuF+aqMGk0UDSbFj8B/h5Idz0NmRcA/oAaCmBb/4f/G0GXc/NhG1/g44ad1csvISn7WeE55PMCLW6urpOettTTz3F0qVLezVRq1atYtmyZa5/P/zwwzz11FO0t7cPVpk99PuCvIqi8Ktf/Yq//OUvWCwWAPz9/fnlL3/J6tWrB7TIweSJF+RVFAWNRuPuMoSX8JS8VHRU8Pe9f+fT8k9RUNBqtFyVfhU/nPJDEoIT3F3e8GbuhMMfQ947UPIlKMdO6NVA6rmQeS1MuAoCI91apvBcnrKfEd5DMjN4ztYL8p4sMwaDgREjRrBp0ybmzp3b47b58+ezePFifv3rX7vWzZo1i9tvv5177rnnpM81UBfk7feIlEaj4dlnn6WxsZEdO3awb98+WlpavKqJ8lTyKY5Qw915qe+u5/Htj7N0/VI+Kf8EBYVFqYtYv3Q9v53/W2miPIFfCEy5AZavg58XUjT2h5A0F1CgfDNs+Cn8YQz893rY97az8RLiBO7ezwjvI5kRfYmNjeWll17qsW7Xrl34+/tz4MCBPu/z8ccf4+fn16OJslgs+Pj4sG3bNn7zm9+g0Whcty9ZsoS33npr8F7ECc748sHBwcHMmjVrIGoRR02ZMsXdJQgv4q68tJnaeOXAK7xx+A3MdjMACxIXcN+0+xgf2b8LxYohEBRN7OJfQ1gYtFVC3jrn7H/1eVC0ybno/WHsQudhgWMuAx+Zln64k/cloZZkZugoioLBYHDLcwcGBqoaeczMzOTQoUM91v3yl7/k7rvvZsKECX3eZ/PmzcyYMaPHOr1ez9atW5kzZw65ubnExcW5RpZmz57NU089hdlsxs9vcK9LeUaNVFtbGy+//DL5+fkATJw4kbvuuouwsLABKW64Ki8vlx2QOG1DnReD1cBrh15jzcE1dFmdxzNPj53OT6f/lOlx04esDtF/rsyEJ8N59zuXxgJnQ3VgHTQXw6EPnItvMIy7AjKWQfpFoJeLJQ9H8r4k1JLMDB2DwXDKiRoGU1dXF0FBpz/7bkZGRo9GatOmTeTk5LB27VosFgt6fe/WpKKiotdEdlqtlpqaGqKionrlbOTIkVgsFurq6khJSVH5itTpdyOVk5PDwoULCQgIYPbs2QD88Y9/5Omnn+azzz5j+nT5g6q/IiIi3F2C8CJDlReL3cI7he/w4v4XaTG1ADA2Yiw/nf5Tzks4T46F9yJ9ZiZmHFz4EFzwK6jLc876d+A9aK+EvLXOxS8Mxi92NlVp54Pe+675IfpH3peEWpIZ0ZfMzEzef/99wDmS9tBDD/Hggw8SHR2N2Wzu8z5Go7HPc8H27t3bZ7MeEOA8imIoRun63UitWrWKq666in/961+u7tFms7FixQp+9rOfkZWV1e+i/v73v/P73/+euro6pkyZwl//+ldXs/Zta9as4Y477uixzs/PD5PJ1O/ndzdvvLKzcJ/BzovVYWVDyQae3/c8td3Oa8QlhSRx79R7WZS2CK2m36daCjc5ZWY0Ghgx2blc8phzOvWD7zuXzlrY94Zz8Q93Xvh30vcgbQHofIaqfOEG8r4k1JLMDJ3AwMBTzng32M+tRkZGBlVVVXR1dbFhwwZqa2u5//77Xbeff/75rhn38vLyyM7OJjo6mtbW1l6PlZub22cj1dLi/LA3JiZGVW39cUYjUic2UeA8XvEXv/gFM2fO7HdBb7/9Nvfffz/PP/88c+bM4U9/+hMLFy6koKCA2NjYPu8TGhpKQUGB69/e/sl4d3e3u0sQXmSw8mJ32Pmk/BP+mftPKjsrAYgNiOUHk3/AsrHL8NHKH87e6rQzc2w69aTZcNlTcGTH0aZqvfMaVXtfcy4BkTDhSpi41DlSJU3VWUfel4Rakpmho9FoVB1e504ZGRkA7N+/n0ceeYTVq1e7anc4HHzzzTcAPProo5x//vnMnDmTadOm8frrr/d6rLy8PK655ppe6w8cOEBiYiLR0dGD+Eqc+t1IhYaGUllZyfjxPU8qP3LkCCEhIf0u6LnnnmPlypWuUabnn3+ejRs38sorr/CrX/2qz/toNBri4+P7/ZyeZsSIEe4uQXiRgc6Loih8UfkFf8/9O8VtxQBE+kdyV8ZdXD/uevz1Z89Uq8NVvzKj1ULKOc5l0f+Dim1w8D049CEYmmDPf5xLQITz8L+J34NR0lSdLeR9SaglmRF9CQ4OJiUlhQceeACtVtvj2rM+Ps73iz/96U+Ul5ezZs0aABYuXMhDDz1Ea2trj0NGHQ4HBQUF1NTUEBQU5JqjYfPmzVx22WVD8nr6fUzODTfcwF133cXbb7/NkSNHOHLkCG+99RYrVqzgpptu6tdjWiwWdu/ezSWXXHK8QK2WSy65hO3bt5/0fl1dXaSkpJCUlMTSpUs5ePDgSbc1m810dHT0WDzNiaNrQnyXgcqLoihkVWVxw0c3sOrrVRS3FRPiG8JPpv2ET5Z9wq2TbpUm6ixxxpnR6iDtPLjyj/BAAdz6Icy8E4JiwNgKe1+H/14Dvx8N6++Bws/A1vex78I7yPuSUEsyI04mMzOTHTt28NRTT/U4ss1kMrFmzRqysrJ45ZVXXEeYZWZmMn36dNauXdvjcZ588knWrFlDQkICTz75pOsx1q9f36NBG0z9bqT+8Ic/sGzZMm699VZSU1NJTU3l9ttv59prr+XZZ5/t12M2NTVht9uJi4vrsT4uLo66uro+7zNu3DheeeUVPvjgA15//XUcDgfnnHMOVVVVfW7/zDPPEBYW5lqSkpIA5/GUW7duxWazuc7vysrKorOzkz179lBdXU1xcTH5+fk0NjaSnZ2N2Wzusa3RaGTnzp3U19dTUFBAYWEhtbW15OTk0N3d3WNbq9XKtm3baGpq4uDBg5SWlnLkyBFyc3MZN25cj20dDgebN2+mra2Nffv2UVlZSXl5OQcOHKC5ubnPuru6uti9e3ePuhsaGsjOzsZkMvXY1mQyueo+fPgwRUVF1NTUsHv3brq6uvqsu7m5mQMHDlBWVkZlZSX79u2jvb2drKws5x/kJ3xtb2931V1WVuaqe9u2bVit1j7rrqmpoaioiMOHD1NfX8/OnTv7rDs7O5uGhgby8/MpLi6murq6z7ptNhtbt2511V1eXu6qu62tjc2bN+NwOHrcp729ndzcXI4cOUJpaSkHDx6kqampz7q7u7vJycmhtraWwsJCCgoKXHUbjcYe25rNZrKzs2lsbOxR9549e+js7Oyz7paWFvLy8igvL6eiooL9+/fT1tbGli1bmDFjRo/7dHR0sHfvXqqqqigpKXHVvX37diwWS49tDQYDu3bt4v397/O9d7/HPV/cQ35LPn5aP+6YcAer41ezcvJKcrbnYDab2bFjB42NjRw6dIiSkhKqqqrYu3dvr7rtdjtbtmyhtbWV/fv3U1FR4aq7tbWVLVu2YLfbe/2unVj3oUOHXNep+/bv2rG66+rqXL9rdXV15OTkYDAYemxrsVjYvn2763ftxLo7Ojp6/a5t2bKFtrY2V93l5eXk5eV51D7i2O9af/cRZrN54PYRRhNZVRq48o9kzf4XtlvepzbpShyB0WBqg9zX4Y3rsP+/NCxv3c7Bd59FsRhkHzGE+4hv1612H5GTk0NycrKr7rq6Onbt2tXrd032EWfPPmIg/o5ITEyUvyMGaR9hsVgwm81YrVaMRiMmkwmLxUJ3dzd2u53OTue1ADs7O1EUha6uLmw2GwaDAbPZjNlsxmAwYLPZXNuceB+73Y7BYMBisWAymTAajVitVrq6unA4HL227e7uxmq1YjKZMJlMWK3WPmtxOBx0dXXx7rvvYjAYWLJkCRaLBYPBgN1u54MPPuCtt97ixRdfRKvV0tnZ6ar7oYce4k9/+pPrtXR2dnLLLbdw+PBhFEVh9erV2O12XnjhBWbOnMnUqVO/s26z2UxjY2Of+4jTpVEURTntrftgMBgoKSkBID09XfVJZyeqqakhISGBbdu2MW/ePNf6X/ziF3zzzTdkZ2d/52NYrVYmTJjATTfdxG9/+9tetx8L0DEdHR0kJSWd1tWLh0pWVhYLFixwdxnCS/Q3Lw7FwVeVX/HC/hfIb3FewiBAH8AN427gjow7iPSPHOhShYcYkn2Mww6V253nU+VvgK4TPgzzCYQxl8KEq5zXq/Lr/+HgYmjI+5JQSzIzeEwmE2VlZaSlpfU5m523ioiIICYmxtVLPPnkk1x55ZWu2//0pz9xzTXXuAZB+vLSSy9x3nnnMW7cuFM+16l+hh0dHYSFhZ1Wb3DGjdRAslgsBAYGsm7dOq6++mrX+ttuu422tjY++OCD03qc6667Dr1ez5tvvvmd26r5YQlxNnAoDj6v+JwX9r9AUWsRAIH6QG4afxO3TrpVGigx8BwO5+x/+R86z6lqrzx+m87PeX2qCVfC2MshKMp9dQohhBc4WxupoTRQjZSqySZOnJ7wuzz33HNqHhoAX19fZsyYwRdffOFqpBwOB1988QX33nvvaT2G3W4nLy+PK664QvXzewr5FEeocbp5sTlsbCrfxL/2/4uSducocpBPEDePv5lbJ95KuH/4IFcqPMWQ72O0Wkie41wuexJqc50NVf6Hzov/Fn7iXDQ652QWE5Y4J6wISxy6GsUpyfuSUEsyI9Tq7Ow8ownr3EFVI7V3797T2u5Mph+///77ue2225g5cyazZ8/mT3/6E93d3a5Z/G699VYSEhJ45plnAHjiiSeYO3cuo0ePpq2tjd///vdUVFSwYsWKftfgbnIxY6HGd+XFaDOyvng9/z74b6q7qgEI8Qlh+cTl3DLhFsL8woaiTOFB3LqP0Whg5DTncvFqaMiHwx85m6q6PCjf7Fw++QWMnO4cqRq/BGLGuq9mIe9LQjXJjFDrTE4PchdVjdRXX301WHW43HDDDTQ2NrJ69Wrq6uqYOnUqn376qWsCisrKSrTa43NktLa2snLlSurq6oiIiGDGjBls27aNiRMnDnqtg6WgoIAZM2a4uwzhJU6Wl3ZzO28dfos3Dr9Bi8l5cboIvwhumXALN0+4mRBf7/rURwwcj9nHaDQQN9G5nP8LaC2H/I+cjVXlDqjZ41y+eAKiRjtHqcZfCQkznaNcYsh4TGaE15DMCLVMJpPXXA/rmDM6R2rz5s288MILlJaW8s4775CQkMBrr71GWloa55577kDWOWg88RypmpoaRo4c6e4yhJf4dl7qu+t57dBrvFP4Dgabc+aZhOAEbpt0G1ePvpoAfYC7ShUewiv2MV0NcHijs6kqywK75fhtQbEw7nJnU5W2AHzkHIHB5hWZER5FMjN4ztZzpCwWC76+vkPyXG45R+pE7777Lt///ve55ZZb2LNnj2smvPb2dp5++mk+/vjj/j70sCdXAxdqHMtLQUsBrx16jY1lG7E5bACMiRjDXRl3sTB1IXptv3/dxVnGK/YxwbEw8w7nYuqA4v85G6uiz6C7Afb827n4BMHoi2DcYhhzmUxWMUi8IjPCo0hmBp8HzRc3IBwOx5A910D97Pr9l9WTTz7J888/z6233spbb73lWj9//nzXRbFE/9jtdneXILyEQ3Gws2knz5Y9S3bt8csDTI+dzl2Zd3FewnlndM6iODt53T7GPxQyljkXmwUqthwdrdoInbXO6dXzN4BGC0lznaNV466A6NHurvys4XWZEW4nmRk8Pj4+gPMSRAEBZ89RJkPZGFoszqMcdDrdGT1OvxupgoKCPmdjCQsLo62t7UxqGvYiIiLcXYLwcEabkQ0lG3jt0GuUd5QDoNVouST5Er4/8ftMjZ3q1vqEZ/PqfYze1zldevpFcPnvoW4fFHwCBR87J6uo3OZcPn8EosY4m6qxiyBpDuhkVLa/vDozwi0kM4NHp9MRHh5OQ0MD4Jyk4Wz40NRms2EymQb9eRwOB42NjQQGBqLXn9n7Qr/vHR8fT3FxMampqT3Wb9myhVGjRp1RUcNdRUWFa3INIU5U313P2wVvs7ZwLe3mdgACtAFcN/46bp5wMwnBCW6uUHiDs2Yfo9UenwHwwl9DWyUUbnI2VWWbobkIthXBtr+Af7jzIsBjF8HoiyFA/shT46zJjBgykpnBFR8fD+Bqps4GZrMZPz+/IXkurVZLcnLyGTeg/Z5s4plnnuH111/nlVde4dJLL+Xjjz+moqKCVatW8cgjj3DfffedUWFDxRMnmzCZTGfVyYPizCiKwq66XbxV8BZfVn6JXXEeLpEQnMDyCctZlLSI6JBoN1cpvMmw2MccO6+qcJPzvCpjy/HbNDpIngdjFzqX6LHOGQTFSQ2LzIgBJZkZGna7HavV6u4yBsRQNlK+vr49ZgE/kZreoN+NlKIoPP300zzzzDMYDM6Zwfz8/Pj5z3/Ob3/72/48pFt4YiMlF7ETAN3WbjaUbOCtw2+5LqALMCNuBssnLOfCpAvRaXWSF6HasMuMww5Vu6DwUyj4FBrze94ekeqcqGLMQkg9V2YB7MOwy4w4Y5IZoZanZGZIGqljLBYLxcXFdHV1MXHiRIKDg8/k4YacJzZSYngrbSvlzcNvsqF0A91W56xHAfoAloxawg3jb2BshFyYVIgz0loOhZ9B4SdQvqXn1Or6ABh1/tHG6jIIT3JbmUIIIYbekDRSK1asYPny5VxwwQX9ubvH8MRGylM6cjF0TDYTn1d8zrrCdexp2ONanxqayo3jb+Sq9KtOegFdyYtQSzJzAks3lH4DRZug6HPoqO55e8wEGHMJjL7UeTigfmiuceJpJDNCLcmMUMtTMjMkjdTSpUvZtGkTMTEx3HjjjSxfvpwpU6b0q2B38sRGSo4rHj4KWgpYV7iOjaUb6bR2As7Z9y5IvIAbx9/I3BFzv/NESMmLUEsycxKKAvUHjzdVR7JBOeG6Jr7BkHb+0cbqEghPdl+tQ0wyI9SSzAi1PCUzQ3ZoX2trK++88w5vvPEGmzdvZvz48dxyyy3cfPPNvWbz81Se2EhlZ2czZ84cd5chBkm3tZtPyj7h3cJ3OdB8wLU+ITiBZWOWsTR9KXFBpz/TkeRFqCWZOU2GFij9Cor+55y4ovtbs2NFj3M2VKMvgpT54HP2XM/l2yQzQi3JjFDLUzIzpOdIHVNVVcWbb77JK6+8QlFRETabbSAedtB5YiPV0NBAbGysu8sQA8ihONhVt4sPSz7k84rPMdqMAOi1ei5Kuohrxl7D3BFz0Wr6nkHmVCQvQi3JTD84HFC3H4o/dzZWVTt7jlbp/Z3N1OiLnc3VWTYToGRGqCWZEWp5SmbU9AYDcnVCq9VKTk4O2dnZlJeXy3UDzlBzc7NHBEmcubL2Mj4s+ZCPSj+irrvOtT41NJVrxlzDkvQlRAVEndFzSF6EWpKZftBqYeRU57LgQTC2QslXUPIFFH8JnTXO70u+gE2/htBE50hV+kXOwwEDI939Cs6IZEaoJZkRanljZs6okfrqq6944403ePfdd3E4HCxbtoyPPvqIiy66aKDqG5Z8fHzcXYI4A+3mdj4p+4QPSz4krynPtT7EN4RFqYu4Kv0qpsRMGbCrkEtehFqSmQEQEAEZy5yLokDjYefhf8VfQMU26KiCPf9xLmicFw1OP9pYJc7yukkrJDNCLcmMUMsbM9PvRiohIYGWlhYWLVrEiy++yJIlS4bsIlpnu4CAs/c4+7NVt7WbLyu/5NPyT9lWvQ2b4jy0VafRcW7CuSxJX8IFSRfgpxv43xHJi1BLMjPANBqIneBczrkPLAZnM1XyhXPUqjEfavY4l81/AJ8gSDsPRl0Ioy6AmHEefxigZEaoJZkRanljZvrdSD322GNcd911hIeHD2A5AqCuro6EhAR3lyG+g8lmYnP1Zj4p+4SsqizMdrPrtvGR41kyaglXjLqC6IDoQa1D8iLUkswMMt9A58x+Yy5x/rujBkq/hpIvnY2Vocl5ceDCT523B8c7G6pRFzivYRU60k2Fn5xkRqglmRFqeWNmBmyyCW/liZNNdHV1ed2FjYcLs93MjpodbCrfxJdHvnRdMBec5z1dnnY5i1IXMSp81JDVJHkRaklm3MjhgPoDzqaq9Guo3A42U89tosc6m6q08yH1XAgId0OhPUlmhFqSGaGWp2TGLbP2eStPbKQ85YJkwqnb2s3m6s18UfEFWVVZGGwG120jgkawKG0Rl6dezvjI8QN23pMakhehlmTGg1hNzutVlX7tXGpze84GqNHCiCmQtsC5JM8D36AhL1MyI9SSzAi1PCUz0kip4ImNlHC/NlMbXx35ii8rv2RbzTYsDovrttjAWC5JvoTL0y5ncszkfk1ZLoQQfTK2QvkW5yGAZVnQXNTzdq0PJM483lglzAQf91/AUgghzhbSSKngiY2Up3Tkw4miKJS1l/FN1TdkVWWxt2EvdsXuuj0lNIVLki/h4uSLmRQ9yaOaJ8mLUEsy40U6aqBss7OpKvsG2o/0vF3v75wFMPU85wQWCTNAP/CT2khmhFqSGaGWp2RGGikVPLGRstls6PUDcokvcQoWu4WcuhxX81TVVdXj9vGR47k4+WIuSb6E9PB0txy2dzokL0ItyYyXUhRoLXc2VGVZzgaru6HnNvoASJrtbKpSzoWE6QPSWElmhFqSGaGWp2RGGikVPLGR2rp1K/Pnz3d3GWelIx1H2F67na3VW9leux2jzei6zUfrw+wRs1mQsIAFiQtIDEl0Y6WnT/Ii1JLMnCUUBZqKoHzz0WUL/7+9ew+OsrrfAP7sPRty2SSb7CYhISDhfjEQCQFBOzKi0la8tNRSQetotVChKlZG0U47Cl7a8VqsnRacekllRqVF1OGHIIrIJYRLLgYQkkCu5LohuySb3fP740022SRAjiS775LnM3Nmd989u3teeGaTb877nhctZ/37dM5YjZgNpM1W7hvklxhmZkgWM0Oy1JIZFlIS1FhI1dXVIS4uLtjDuCI0tTZhX9U+7KnYg28qvkH5uXK/5+PN8Zg7XCmcZibORLghPEgj/eGYF5LFzFyhhADOFncVVqXf9C6sdEbl8L8Rs5SWkgWYIi/51swMyWJmSJZaMiNTGwR//ox6qaysVEWQQpHT7cThs4dxoPoAvq34Fvl1+fB2WwFLr9FjasJUZCdmY87wORgfO161h+z1F/NCspiZK5RGAySMU9qM+7tmrEq/Bkp2A6W7geZKZcn1sj3AV39RVgW0TwZSZwEjspXbiPheb83MkCxmhmSFYmZYSKmQGtbQDxUt7hbk1eThQNUBHKg+gILaArSLdr8+o6JHITspG9mJ2ci0Z2KYIfBLBw8m5oVkMTNDhEYDxI9RWuavO86xOtVVVJV+AzSWApWHlbZ3vfK6uNHKMuup2UDqTCB2FDND0pgZkhWKmWEhpUJarXpWhFObGmcNjpw9gsNnDyO3OheFdYV+q+sBgC3chkx7JrLsWchOyoZ9mD1Iow0M5oVkMTNDlEYDxI5S2rS7lW2OCqWgKtsDlO4BagqAuhNKy/u30mdYPBKsU4GxP1KKq8QpgM4QvP2gkMDvGZIViplhIaVCDQ0NSE1NDfYwgs7tcaOovshXOB0+exiVLZW9+iVHJGO6bToybZnItGdieMTwkD9cTwbzQrKYGfKJSgIm36k0AHDWKxcILtsDlO0FKg4CLWcR3vJ/QOn/KX30ZuU8q5QZyjlWw68BhoXW4Tg0+Pg9Q7JCMTNcbEKFi000NjbCYrEEexgB5fa48X3T9yiqK0JBXQGK6ovwXd13fhfCBQCtRovRltGYGj8VGQkZyLRlIjEiMUijVoehmBe6PMwM9Zv7PFB5CK7iHTCfPQyc/la5aHBPcaO7iqqULCB+HBCCf12mgcPvGZKllsxwsYkQd/ToUcyZMyfYwxg0Le4WfN/4Pb6r/w5F9UUoqivCsYZjcHvdvfpaTBZMiZ+CqfFTMTV+KiZZJ11x5zhdris9LzTwmBnqN0MYkDoTB0rdmPPL1YDXC9QeA87sU2auTu9THnceDnjoXeV1pijlGlbDr1FaciZnrYYYfs+QrFDMDGekVDgj5fV6Q/I40Z7aPG041XQKJxpP4HjDcZxoPIETjSd6LUHeKdIQifFx4zEhbgLGx47HROtEpEamDqnD9H6IKyUvFDjMDMm6aGac9cCZAx2F1V6g/CDgbundL3ZUt8JqOmCbBOiNgztwChp+z5AstWSG15GSoMZCateuXZg7d26wh9EvXuFFjbMGJY4SlDaVosRRgrLmMpQ6SnGm+UyvhSA6Wc1WpFvSfYXThNgJGB45tM5tGiihlBdSB2aGZEllxtMO1BQCZ/YrBdaZ/UDd8d79dCZl4Yrk6cqMVfI0pdjiz4ErAr9nSJZaMhPyhdQbb7yBF198EVVVVZg6dSpee+01zJgx44L9N23ahDVr1qCkpATp6el4/vnnccstt/Trs9RYSKmJEAKNrY2oOFeBipYK5bajlbeU47TjNM57zl/w9ZGGSIyOGY10SzpGx4zGaIvSYsJiArgXREQUVM56ZabqzH6llecC5xt79zPHKIVV0jQgKUMpriKv7JVXiUhdQrqQ+s9//oMlS5bgzTffRFZWFl5++WVs2rQJxcXFSEhI6NX/m2++wdy5c7F27Vr8+Mc/xnvvvYfnn38eBw8exKRJky75eWospAJRkQsh0OJuQd35Opx1nsVZ11mcdZ5FravWd/+s6ywqWyrhandd9L30Gj2GRw7HiKgRvpYWlYbUqFTYwm2cZRpkavkLDoUOZoZkDXhmhADqTyoFVWerPAJ4Wnv3jUzqKKoyugqs8NiBGwsNCn7PkCy1ZCakC6msrCxcc801eP311wEox0umpKTgd7/7HZ544ole/RctWoSWlhZs2bLFt23mzJm4+uqr8eabb17y8zr/sSoqKlRTSDU1NSE6OrrXdiEE2r3taPO2we1xw+11o9XTCqfbCVe7Cy3tLXC5XWhxt8DZ7oTL7UKzuxlNrU1Ka2uCo9Wh3Hc3wePt+7C7vljDrLBH2JEYngh7hB1Jw5JgH2ZHamQqEiMSoddy3ZJguVBeiC6EmSFZAclMe5tySGBFnnKB4IpDyiGBwtu7b3QqkDgZsE9RDg+0T2FxpTL8niFZasmMw+FAUlJS6K3a19bWhtzcXKxevdq3TavVYt68edizZ0+fr9mzZw8eeeQRv23z58/Hxx9/3Gf/1tZWtLZ2/cXL4XAAAJKSki5z9ERERBQYBR0tJ9gDIaIhLPhLY3RTW1sLj8cDm83mt91ms6GqqqrP11RVVUn1X7t2LaKjo30tJSVlYAZPRERERERDhqpmpAJh9erVfjNYDocDKSkp2FWwCxGREUEbV+d5RBpoUFFegeHDh/u2G7QGpekMXfe1Bui0uqCNl9Tj1KlTGDlyZLCHQSGEmSFZqs+MqxGozlfOs6o6AlTlK+dgoY+zF8KigISJgG0CYJuoLMNuHQPoTYEe9RVN9Zkh1VFLZjoP7esPVRVSVqsVOp0O1dXVfturq6tht/e9ao/dbpfqbzKZYDL1/rKcOnyqas6R0jfpMTF5YrCHQSFCo9Fg2DBepJj6j5khWarPzLBhgDUZmDi/a1vrOaC6QCmsKg8pRVZNEeBtBqq+VVonrR6wjgXsk5TCqrPAikjgcuw/kOozQ6qjlsx4PP1fQ0BVhZTRaMT06dOxfft2LFy4EICy2MT27duxfPnyPl+TnZ2N7du3Y+XKlb5t27ZtQ3Z2dgBGPDh6HqpIdDHMC8liZkhWSGbGFAGkZimtU3sbUFsMVB1VZq2qjigzWa4GoKZAafhPV/9wa1dRZZuotPixgMEc8N0JNSGZGQqqUMyMqgopAHjkkUewdOlSZGZmYsaMGXj55ZfR0tKCe++9FwCwZMkSJCcnY+3atQCAFStW4LrrrsNf/vIXLFiwADk5OThw4ADeeuutYO7GZTl27BisVmuwh0EhgnkhWcwMybpiMqM3AvbJSuskBOAo7yisjiqFVXUBUP894KwFTn2ptE4arXLh4ITxQMKErtvYqwCd6n6tCporJjMUMKGYGdUtfw4Ar7/+uu+CvFdffTVeffVVZGUpf1G6/vrrkZaWho0bN/r6b9q0CU899ZTvgrwvvPBCSF+Q1+12w2AwBHsYFCKYF5LFzJCsIZmZNidw9jtlSfbqAqXAqsoHXPV999cZlXOt4scBCeOU2/hxQMzIIVlgDcnM0GVRS2ZC+jpSgabGQkotFySj0MC8kCxmhmQxMx2EAM7VKMVVTVG32yLA3dL3a3RGIC69q7iyjlEOD4y9Spkhu0IxMyRLLZlhISVBjYUUERERhRCvF2gqUwqqs98BNd8pt2eLgXZX36/R6ICYNKWo6iyurGOAuNGA2RLI0RNRNyykJKixkFJLRU6hgXkhWcwMyWJmfiBfgdVZWH0H1B4Dzh4D2pov/LphCYA1XSmqrOnKjJY1HbCMCJnDBJkZkqWWzLCQkqDGQqqlpUUVyz9SaGBeSBYzQ7KYmQEmBNBc2VVU1RYrs1e1x4FzVRd+ndagzGLFXaUcGhjX2UYDkUmAVhuwXbgUZoZkqSUzMrVBaPxZY4gpKipCZmZmsIdBIYJ5IVnMDMliZgaYRgNEJSlt1PX+z513AHUnlFZ7XCm2Oh+3nwfqjiutJ70ZiB2prCgYk6bcxo5StkWnAFpdIPbMh5khWaGYGRZSKpScnBzsIVAIYV5IFjNDspiZAAqLApKnKa07r1dZpr3++47C6qRyW/890FCinItVU6i0nrQGIGaEUmDFjOy47WwjAFPkgO8GM0OyQjEzLKRUqLm5GYmJicEeBoUI5oVkMTMki5lRAa0WsKQorecslqcdaCwF6k8B9SeBho7b+pNKkeVp65rV6ku4VSmoLCMAS2rH/VTAkgZEDwcMYdLDZWZIVihmhoWUCg3x09ZIEvNCspgZksXMqJxO33W+VE9eD+Co6CqqejZXvXLhYWctUJ7b9/tH2DsKqxTlMMHo4crj6I7Cro8ZLWaGZIViZlhIqZDFYgn2ECiEMC8ki5khWcxMCNPqumaycF3v5883AQ2lSlHVWKbMbDWWKa2hVLk+1rkqpZ3Z1/dnhEUrRVVUMhCdDEQlw45IwFjjewy9aTD3kq4Aofg9w0JKhUpLS2Gz2YI9DAoRzAvJYmZIFjNzBQuLBhKnKK0nIQBnPdBYohRWTWeAxtNAU0drPA2cb1SKsfNNQHW+76XRPd8r3ApEJSpFVWSistBGZGK3bXYgzKIsxEFDUih+z3D5cxUuf+5yuWA2m4M9DAoRzAvJYmZIFjNDF9TarBRYnc1RDjSVw9NYBl1zpfK4/Xz/3ksfBkTYlAIr0t7VIuxApE15LsIGmGNVtdQ7DQy1fM9w+fMQt3//flVckIxCA/NCspgZksXM0AWZIoGE8UrrZnfnxVWFAFwNSkHl6CismiuV87YcFR33y5UZrfbzHYcWll78MzU6ICIBGBbfVVxFxCuPh8UDw6xd98PjAJ1hEP8BaKCE4vcMZ6RUOCNFRERENKS4XUBzFXCuWimumjtuOx+fq1HuO+vk39scoxxaGB6nFFnhscrjYR3bwuOUWa7wGKWvKZozXkMYZ6RC3K7Ov+IQ9QPzQrKYGZLFzJAs6cwYOi8oPPLi/TxuoKVWKao6i6tz1cq2lrP+zVkHCK8yI+Zq6PtCxn3RaJWCyhyjFFjmGMBsUc7hMluUx533wyzKeWZh0co1wIwRPM/rBwrF7xnOSKlwRqq1tRUmE1e3of5hXkgWM0OymBmSpYrMeD1KAXWuRimqeraW2q77rgZlYQ13y+V9pkYLmKK6CitTtwLLFNnRIpQ+psiO7RHKrXFYR+u4rw8bUkWZKjIDzkiFvEOHDiErKyvYw6AQwbyQLGaGZDEzJEsVmdHqOs6Xsvb/Ne2tSkHlqu+6dTUqqxNe6PZ8E3DeAXjdygzY+Y7tl0ujBQzDAGO4MmNnGNZxa1YKLYMZMIQrS8vrzcqtwawUYPow5ULKOhOgN/a4NQE6Y9etVq+cR6Y1KLfd7wewkFNFZiSxkFKhUaNGBXsIFEKYF5LFzJAsZoZkhWxm9KaOJdkT5V4nhHKeV6ujq7Bq7VgWvrW5o53ruHUot23nlH5up3K/rUVpbmfHe3qBtmalBYtGqxRaGp1yq9V1tI5tGm1H03S7320behRivQqzrsfTPe1ArgpKE1d7v7uqYLTUU21tLeLj44M9DAoRzAvJYmZIFjNDsoZcZjQaZebIGK4s2X45vJ6O4qpbYeV2ddx3dTx2dt1vb1Xut59Xmvt81/3280B7G+Bp7XbbCnjaOm7dykyaxw0IT++xCK/SNwBUU5S09v+sJ9WMmboYDFymk/qPeSFZzAzJYmZIFjNzGbS6rvOpAsnr7SqqvG7A0w5425UCy9uuFHhej/82ITqat6uh22NAed6n2/0eyzSUV1QgOSlp0HfzkppbgHU/6VdXFlIqpIaLkVHoYF5IFjNDspgZksXMhCCtFtB2nEMVDGHlQHJycD67O4ej3125SL4KVVdXB3sIFEKYF5LFzJAsZoZkMTMkKxQzw0JKhdLT04M9BAohzAvJYmZIFjNDspgZkhWKmWEhpUJ5eXnBHgKFEOaFZDEzJIuZIVnMDMkKxczwgrwqvCAvEREREREFnkxtwBkpFdq1a1ewh0AhhHkhWcwMyWJmSBYzQ7JCMTOckVLhjFR7ezv0ei6oSP3DvJAsZoZkMTMki5khWWrJDGekQtzevXuDPQQKIcwLyWJmSBYzQ7KYGZIVipkJftkXZJ0Tcg6JNeMHW3JysqrGQ+rGvJAsZoZkMTMki5khWWrJTOcY+nPQ3pAvpJqbmwEAKSkpQR4JERERERGpQXNzM6Kjoy/aZ8ifI+X1elFRUYHIyEhoNJpgDwcOhwMpKSk4ffq0as7ZIvViXkgWM0OymBmSxcyQLDVlRgiB5uZmJCUlQau9+FlQQ35GSqvVYvjw4cEeRi9RUVFBDxKFDuaFZDEzJIuZIVnMDMlSS2YuNRPViYtNEBERERERSWIhRUREREREJImFlMqYTCY888wzMJlMwR4KhQDmhWQxMySLmSFZzAzJCtXMDPnFJoiIiIiIiGRxRoqIiIiIiEgSCykiIiIiIiJJLKSIiIiIiIgksZAiIiIiIiKSxEJKRd544w2kpaUhLCwMWVlZ2LdvX7CHRAGwdu1aXHPNNYiMjERCQgIWLlyI4uJivz7nz5/HsmXLEBcXh4iICNxxxx2orq7261NWVoYFCxYgPDwcCQkJWLVqFdrb2/367Ny5E9OmTYPJZMLo0aOxcePGwd49CoB169ZBo9Fg5cqVvm3MDPVUXl6OX/3qV4iLi4PZbMbkyZNx4MAB3/NCCDz99NNITEyE2WzGvHnzcPz4cb/3qK+vx+LFixEVFQWLxYL77rsP586d8+tz5MgRzJkzB2FhYUhJScELL7wQkP2jgeXxeLBmzRqMHDkSZrMZV111Ff785z+j+xplzMzQtmvXLvzkJz9BUlISNBoNPv74Y7/nA5mPTZs2Ydy4cQgLC8PkyZOxdevWAd/fPglShZycHGE0GsW//vUvUVBQIO6//35hsVhEdXV1sIdGg2z+/Pliw4YNIj8/Xxw6dEjccsstIjU1VZw7d87X58EHHxQpKSli+/bt4sCBA2LmzJli1qxZvufb29vFpEmTxLx580ReXp7YunWrsFqtYvXq1b4+J0+eFOHh4eKRRx4RhYWF4rXXXhM6nU589tlnAd1fGlj79u0TaWlpYsqUKWLFihW+7cwMdVdfXy9GjBgh7rnnHrF3715x8uRJ8fnnn4sTJ074+qxbt05ER0eLjz/+WBw+fFj89Kc/FSNHjhQul8vX56abbhJTp04V3377rfjqq6/E6NGjxV133eV7vqmpSdhsNrF48WKRn58v3n//fWE2m8Xf//73gO4vXb5nn31WxMXFiS1btohTp06JTZs2iYiICPHKK6/4+jAzQ9vWrVvFk08+KT788EMBQHz00Ud+zwcqH7t37xY6nU688MILorCwUDz11FPCYDCIo0ePDvq/AQsplZgxY4ZYtmyZ77HH4xFJSUli7dq1QRwVBUNNTY0AIL788kshhBCNjY3CYDCITZs2+foUFRUJAGLPnj1CCOXLTKvViqqqKl+f9evXi6ioKNHa2iqEEOLxxx8XEydO9PusRYsWifnz5w/2LtEgaW5uFunp6WLbtm3iuuuu8xVSzAz19Ic//EFce+21F3ze6/UKu90uXnzxRd+2xsZGYTKZxPvvvy+EEKKwsFAAEPv37/f1+fTTT4VGoxHl5eVCCCH+9re/iZiYGF+GOj977NixA71LNMgWLFggfv3rX/ttu/3228XixYuFEMwM+etZSAUyHz//+c/FggUL/MaTlZUlfvOb3wzoPvaFh/apQFtbG3JzczFv3jzfNq1Wi3nz5mHPnj1BHBkFQ1NTEwAgNjYWAJCbmwu32+2Xj3HjxiE1NdWXjz179mDy5Mmw2Wy+PvPnz4fD4UBBQYGvT/f36OzDjIWuZcuWYcGCBb3+X5kZ6um///0vMjMz8bOf/QwJCQnIyMjAP/7xD9/zp06dQlVVld//d3R0NLKysvwyY7FYkJmZ6eszb948aLVa7N2719dn7ty5MBqNvj7z589HcXExGhoaBns3aQDNmjUL27dvx7FjxwAAhw8fxtdff42bb74ZADNDFxfIfATzZxULKRWora2Fx+Px+4UGAGw2G6qqqoI0KgoGr9eLlStXYvbs2Zg0aRIAoKqqCkajERaLxa9v93xUVVX1mZ/O5y7Wx+FwwOVyDcbu0CDKycnBwYMHsXbt2l7PMTPU08mTJ7F+/Xqkp6fj888/x0MPPYSHH34Yb7/9NoCu//OL/RyqqqpCQkKC3/N6vR6xsbFSuaLQ8MQTT+AXv/gFxo0bB4PBgIyMDKxcuRKLFy8GwMzQxQUyHxfqE4j86Af9E4io35YtW4b8/Hx8/fXXwR4Kqdjp06exYsUKbNu2DWFhYcEeDoUAr9eLzMxMPPfccwCAjIwM5Ofn480338TSpUuDPDpSow8++ADvvvsu3nvvPUycOBGHDh3CypUrkZSUxMwQdeCMlApYrVbodLpeK2pVV1fDbrcHaVQUaMuXL8eWLVuwY8cODB8+3Lfdbrejra0NjY2Nfv2758Nut/eZn87nLtYnKioKZrN5oHeHBlFubi5qamowbdo06PV66PV6fPnll3j11Veh1+ths9mYGfKTmJiICRMm+G0bP348ysrKAHT9n1/s55DdbkdNTY3f8+3t7aivr5fKFYWGVatW+WalJk+ejLvvvhu///3vfbPgzAxdTCDzcaE+gcgPCykVMBqNmD59OrZv3+7b5vV6sX37dmRnZwdxZBQIQggsX74cH330Eb744guMHDnS7/np06fDYDD45aO4uBhlZWW+fGRnZ+Po0aN+X0jbtm1DVFSU75en7Oxsv/fo7MOMhZ4bbrgBR48exaFDh3wtMzMTixcv9t1nZqi72bNn97qswrFjxzBixAgAwMiRI2G32/3+vx0OB/bu3euXmcbGRuTm5vr6fPHFF/B6vcjKyvL12bVrF9xut6/Ptm3bMHbsWMTExAza/tHAczqd0Gr9f03U6XTwer0AmBm6uEDmI6g/qwZ9OQvql5ycHGEymcTGjRtFYWGheOCBB4TFYvFbUYuuTA899JCIjo4WO3fuFJWVlb7mdDp9fR588EGRmpoqvvjiC3HgwAGRnZ0tsrOzfc93LmV94403ikOHDonPPvtMxMfH97mU9apVq0RRUZF44403uJT1FaT7qn1CMDPkb9++fUKv14tnn31WHD9+XLz77rsiPDxcvPPOO74+69atExaLRWzevFkcOXJE3HrrrX0uVZyRkSH27t0rvv76a5Genu63VHFjY6Ow2Wzi7rvvFvn5+SInJ0eEh4dzKesQtHTpUpGcnOxb/vzDDz8UVqtVPP74474+zMzQ1tzcLPLy8kReXp4AIP7617+KvLw8UVpaKoQIXD52794t9Hq9eOmll0RRUZF45plnuPz5UPTaa6+J1NRUYTQaxYwZM8S3334b7CFRAADos23YsMHXx+Vyid/+9rciJiZGhIeHi9tuu01UVlb6vU9JSYm4+eabhdlsFlarVTz66KPC7Xb79dmxY4e4+uqrhdFoFKNGjfL7DAptPQspZoZ6+t///icmTZokTCaTGDdunHjrrbf8nvd6vWLNmjXCZrMJk8kkbrjhBlFcXOzXp66uTtx1110iIiJCREVFiXvvvVc0Nzf79Tl8+LC49tprhclkEsnJyWLdunWDvm808BwOh1ixYoVITU0VYWFhYtSoUeLJJ5/0W4aamRnaduzY0efvL0uXLhVCBDYfH3zwgRgzZowwGo1i4sSJ4pNPPhm0/e5OI0S3S1QTERERERHRJfEcKSIiIiIiIkkspIiIiIiIiCSxkCIiIiIiIpLEQoqIiIiIiEgSCykiIiIiIiJJLKSIiIiIiIgksZAiIiIiIiKSxEKKiIiIiIhIEgspIiJSrZ07d0Kj0aCxsTHYQ5FSV1eHhIQElJSUXLJvbW0tEhIScObMmcEfGBERDRgWUkREpArXX389Vq5c6bdt1qxZqKysRHR0dHAG1c0999yDhQsX9qvvs88+i1tvvRVpaWmX7Gu1WrFkyRI888wzlzdAIiIKKBZSRESkWkajEXa7HRqNJthD6Ten04l//vOfuO+++/r9mnvvvRfvvvsu6uvrB3FkREQ0kFhIERFR0N1zzz348ssv8corr0Cj0UCj0aCkpKTXoX0bN26ExWLBli1bMHbsWISHh+POO++E0+nE22+/jbS0NMTExODhhx+Gx+PxvX9raysee+wxJCcnY9iwYcjKysLOnTv7Pb4//vGPePvtt7F582bf+C70+q1bt8JkMmHmzJm+bQ0NDVi8eDHi4+NhNpuRnp6ODRs2+J6fOHEikpKS8NFHH0n9uxERUfDogz0AIiKiV155BceOHcOkSZPwpz/9CQAQHx/f5zlGTqcTr776KnJyctDc3Izbb78dt912GywWC7Zu3YqTJ0/ijjvuwOzZs7Fo0SIAwPLly1FYWIicnBxfwXLTTTfh6NGjSE9Pv+T4HnvsMRQVFcHhcPgKoNjY2D77fvXVV5g+fbrftjVr1qCwsBCffvoprFYrTpw4AZfL5ddnxowZ+Oqrr6RmsoiIKHhYSBERUdBFR0fDaDQiPDwcdrv9on3dbjfWr1+Pq666CgBw55134t///jeqq6sRERGBCRMm4Ec/+hF27NiBRYsWoaysDBs2bEBZWRmSkpIAKIXRZ599hg0bNuC555675PgiIiJgNpvR2tp6yfGVlpb6PqdTWVkZMjIykJmZCQB9njuVlJSEvLy8S46FiIjUgYUUERGFlPDwcF8RBQA2mw1paWmIiIjw21ZTUwMAOHr0KDweD8aMGeP3Pq2trYiLixvw8blcLoSFhflte+ihh3DHHXfg4MGDuPHGG7Fw4ULMmjXLr4/ZbIbT6Rzw8RAR0eBgIUVERCHFYDD4PdZoNH1u83q9AIBz585Bp9MhNzcXOp3Or1/34mugWK1WNDQ0+G27+eabUVpaiq1bt2Lbtm244YYbsGzZMrz00ku+PvX19YiPjx/w8RAR0eDgYhNERKQKRqPRb4GIgZKRkQGPx4OamhqMHj3ar13qML0fMr6MjAwUFhb22h4fH4+lS5finXfewcsvv4y33nrL7/n8/HxkZGT0ezxERBRcLKSIiEgV0tLSsHfvXpSUlKC2ttY3o3S5xowZg8WLF2PJkiX48MMPcerUKezbtw9r167FJ598IjW+I0eOoLi4GLW1tXC73X32mz9/PgoKCvxmpZ5++mls3rwZJ06cQEFBAbZs2YLx48f7nnc6ncjNzcWNN974w3eUiIgCioUUERGpwmOPPQadTocJEyYgPj4eZWVlA/beGzZswJIlS/Doo49i7NixWLhwIfbv34/U1FRfH41Gg40bN17wPe6//36MHTsWmZmZiI+Px+7du/vsN3nyZEybNg0ffPCBb5vRaMTq1asxZcoUzJ07FzqdDjk5Ob7nN2/ejNTUVMyZM+fyd5aIiAJCI4QQwR4EERFRMJ06dQpjxoxBYWFhv5ZDv5RPPvkEq1atQn5+PrTaS//NcubMmXj44Yfxy1/+8rI/m4iIAoOLTRAR0ZC3detWPPDAAwNSRAHAggULcPz4cZSXlyMlJeWifWtra3H77bfjrrvuGpDPJiKiwOCMFBERERERkSSeI0VERERERCSJhRQREREREZEkFlJERERERESSWEgRERERERFJYiFFREREREQkiYUUERERERGRJBZSREREREREklhIERERERERSWIhRUREREREJOn/AVPyScxJob2NAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the plot…\n",
    "a_hat = np.array([np.cos(θ), np.sin(θ), 0])\n",
    "v_0 = np.array([1.626, 0, 0]) # km/s\n",
    "def v_vec(t):\n",
    "    if t < 0:\n",
    "        return v_0\n",
    "    if t < t_1:\n",
    "        return v_0 + a_hat * (a_max * t**2 / (2.0 * t_1))\n",
    "    if t < t_2:\n",
    "        return v_0 + a_hat * (a_max * t_1 / 2.0 + a_max * (t - t_1) * \n",
    "                        (1.0 - (t - t_1) / (2.0 * (t_2 - t_1) ) ) )\n",
    "    return v_0 + a_hat * (a_max * t_2 / 2.0)\n",
    "\n",
    "v_values = np.array([v_vec(t) for t in t_values])\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "ax.plot(t_values, np.linalg.norm(v_values, axis=1), linewidth=3, label=\"$v(t)$\")\n",
    "ax.plot(t_values, v_values[:,0], label=\"$v_x(t)$\")\n",
    "ax.plot(t_values, v_values[:,1], label=\"$v_y(t)$\")\n",
    "ax.plot(t_values, np.zeros_like(t_values), \"k\", label=\"$v_z(t)$\")\n",
    "ax.grid(color='gray', linestyle=':', linewidth=0.5)\n",
    "ax.set_xlim(t_min, t_max)\n",
    "ax.set_xlabel(\"time, t (s)\")\n",
    "ax.set_ylabel(r\"velocity, v ($\\text{ km/s})$\")\n",
    "ax.set_title(\"velocity vs. time\")\n",
    "ax.legend()\n",
    "pass"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c40e871e-6c95-408a-a777-cec10e46f254",
   "metadata": {},
   "source": [
    "### d) Change in speed\n",
    "\n",
    "The probe's initial speed is given as 1.626 km/s.\n",
    "\n",
    "The probe's final speed is reached when the acceleration falls to zero, at $t = 9900\\text{ s} \\equiv t_\\text{f}$. According to our expression in (b), that speed is:\n",
    "\n",
    "$$ \\vec{v}(t_\\text{f}) = \\vec{v}(0) + \\left< \\cos(\\theta), \\sin(\\theta), 0 \\right>\\ a_\\text{m}\\, t_2 / 2 $$\n",
    "\n",
    "Inserting the situation's given constants, we get a numerical value of:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f47730ee-a720-4a58-9473-10a552084567",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\qquad \\vec{v}(t_\\text{f}) = \\left< -0.283, 2.275, 0.000 \\right>\\text{ km/s}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Numerical calculations\n",
    "v_f = v_0 + a_hat * a_max * t_2 / 2\n",
    "from IPython.display import display, Math\n",
    "display(Math(rf\"\\qquad \\vec{{v}}(t_\\text{{f}}) = \\left< {v_f[0]:.3f}, {v_f[1]:.3f}, {v_f[2]:.3f} \\right>\\text{{ km/s}}\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fe4b9b8-0165-4a1e-8919-599750cd7434",
   "metadata": {},
   "source": [
    "with a corresponding speed of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "eada4660-a6f1-4272-a71c-4146f471fd08",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\qquad v(t_\\text{f}) \\equiv \\left| \\vec{v}(t_\\text{f}) \\right| = 2.293 \\text{ km/s}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Numerical calculations\n",
    "v_f_mag = np.linalg.norm(v_f)\n",
    "display(Math(rf\"\\qquad v(t_\\text{{f}}) \\equiv \\left| \\vec{{v}}(t_\\text{{f}}) \\right| = {v_f_mag:.3f} \\text{{ km/s}}\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "641cc060-c2bd-4ae4-addc-c381a692ac83",
   "metadata": {},
   "source": [
    "The probe's change in speed is therefore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a3c48762-f699-4bb3-b020-6df99d6bcc70",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\qquad \\Delta v = 0.667\\text{ km/s}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Numerical calculations\n",
    "Δv = v_f_mag - np.linalg.norm(v_0)\n",
    "display(Math(rf\"\\qquad \\Delta v = {Δv:.3f}\\text{{ km/s}}\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52bf8599-1e92-4c66-9419-6a93818fc959",
   "metadata": {},
   "source": [
    "This is positive, so **the probe's speed increases.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6612bfc6",
   "metadata": {},
   "source": [
    "### 3) Change in direction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08202601",
   "metadata": {},
   "source": [
    "To find the angle between the probe's initial velocity vector and its final velocity vector, I'll use the dot product trick:\n",
    "\n",
    "$$ \\vec{a} \\cdot \\vec{b} = a\\,b\\,\\cos(\\theta) \\quad \\Rightarrow \\quad \\theta = \\cos^{-1}\\left( \\frac{\\vec{a} \\cdot \\vec{b}}{a\\,b} \\right) $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "7daa2a11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\qquad \\boxed{\\theta_{i,f} = 97.092^\\circ}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculuation…\n",
    "q = np.degrees(np.arccos(np.dot(v_0, v_f) / (np.linalg.norm(v_0) * np.linalg.norm(v_f))))\n",
    "display(Math(rf\"\\qquad \\boxed{{\\theta_{{i,f}} = {q:.3f}^\\circ}}\"))\n"
   ]
  },
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   "cell_type": "markdown",
   "id": "b663224c-398f-4e2a-b81c-47bb124135fe",
   "metadata": {},
   "source": [
    "---"
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  }
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