{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1e64ea83",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# Analitična dinamika: prizma in valj\n",
    "\n",
    "Prevod Mathematica zvezka (J. Slavič, januar 2012) v Python.\n",
    "\n",
    "**Sistem:** prizma $A$ (masa $m_A$) prosto drsi po vodoravni podlagi brez\n",
    "trenja; njena vodoravna lega je $x(t)$. Po nagnjeni ploskvi prizme (kot\n",
    "$\\alpha$) se brez zdrsa kotali homogen valj $B$ (masa $m_B$, polmer $R$);\n",
    "njegova lega vzdolž ploskve, merjeno od vrha prizme, je $s(t)$. Sistem ima\n",
    "dve prostostni stopnji, $x(t)$ in $s(t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d2b67b73",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-09-25T06:43:29.307894Z"
    }
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   "outputs": [],
   "source": [
    "\n",
    "import sympy as sp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from matplotlib.patches import Polygon, Circle\n",
    "from IPython.display import HTML\n",
    "from ipywidgets import interact, FloatSlider\n",
    "\n",
    "sp.init_printing(use_unicode=True)\n",
    "from sympy import pprint"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5519020",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Kinetična energija\n",
    "\n",
    "Najprej definiramo manjkajoče lege in hitrosti, ki jih kinetična energija\n",
    "potrebuje: lego točke $A$ (prizma), lego in hitrost središča valja $B$,\n",
    "njegov masni vztrajnostni moment $J_B$ ter kot zasuka $\\varphi$, ki sledi\n",
    "iz pogoja kotaljenja brez zdrsa ($\\varphi = s/R$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "df4b389c",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-09-25T06:43:29.495309Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              2                                                  2             ↪\n",
      "    ⎛d       ⎞                                         ⎛d       ⎞        ⎛d    ↪\n",
      "m_A⋅⎜──(x(t))⎟                                   3⋅m_B⋅⎜──(s(t))⎟    m_B⋅⎜──(x ↪\n",
      "    ⎝dt      ⎠               d        d                ⎝dt      ⎠        ⎝dt   ↪\n",
      "─────────────── + m_B⋅cos(α)⋅──(s(t))⋅──(x(t)) + ───────────────── + ───────── ↪\n",
      "       2                     dt       dt                 4                  2  ↪\n",
      "\n",
      "↪      2\n",
      "↪     ⎞ \n",
      "↪ (t))⎟ \n",
      "↪     ⎠ \n",
      "↪ ──────\n",
      "↪       \n"
     ]
    }
   ],
   "source": [
    "\n",
    "t = sp.Symbol(\"t\", real=True, positive=True)\n",
    "m_A, m_B, g, R, a, b, h, alpha = sp.symbols(\n",
    "    \"m_A m_B g R a b h alpha\", real=True, positive=True\n",
    ")\n",
    "\n",
    "x = sp.Function(\"x\")\n",
    "s = sp.Function(\"s\")\n",
    "\n",
    "# Lega prizme A (masno središče je zamaknjeno za a)\n",
    "x_A = x(t) + a\n",
    "\n",
    "# Lega središča valja B na nagnjeni ploskvi prizme\n",
    "x_B = x(t) + R * sp.sin(alpha) + s(t) * sp.cos(alpha)\n",
    "y_B = h - s(t) * sp.sin(alpha)\n",
    "\n",
    "# Hitrost središča valja B\n",
    "v_B = sp.sqrt(sp.diff(x_B, t) ** 2 + sp.diff(y_B, t) ** 2)\n",
    "\n",
    "# Masni vztrajnostni moment homogenega valja\n",
    "J_B = sp.Rational(1, 2) * m_B * R**2\n",
    "\n",
    "# Kot zasuka valja pri kotaljenju brez zdrsa\n",
    "phi = s(t) / R\n",
    "\n",
    "Ek = (\n",
    "    sp.Rational(1, 2) * m_A * sp.diff(x_A, t) ** 2\n",
    "    + sp.Rational(1, 2) * m_B * v_B**2\n",
    "    + sp.Rational(1, 2) * J_B * sp.diff(phi, t) ** 2\n",
    ")\n",
    "Ek = sp.simplify(Ek)\n",
    "pprint(Ek)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ae0e16b",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Potencialna energija\n",
    "\n",
    "Višina masnega središča prizme ($b$, konstanta) in višina središča valja\n",
    "($h - s(t)\\sin\\alpha$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7e90a8ec",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:29.497207Z",
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     "shell.execute_reply": "2026-09-25T06:43:29.501197Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b⋅g⋅m_A + g⋅m_B⋅(h - s(t)⋅sin(α))\n"
     ]
    }
   ],
   "source": [
    "\n",
    "Ep = m_A * g * b + m_B * g * (h - s(t) * sp.sin(alpha))\n",
    "pprint(Ep)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d1a2d45",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Lagrangeva energijska funkcija\n",
    "\n",
    "V Mathematici je `L[t_]:=Ek[t]-Ep[t]` definiran pred `Ek` in `Ep` (odložena\n",
    "evalvacija); sympy odložene evalvacije ne pozna, zato Lagrangevo funkcijo\n",
    "sestavimo šele, ko sta `Ek` in `Ep` že definirana."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e1b1199a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:29.503276Z",
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     "shell.execute_reply": "2026-09-25T06:43:29.624934Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                                   2                           ↪\n",
      "                                         ⎛d       ⎞                            ↪\n",
      "                                     m_A⋅⎜──(x(t))⎟                            ↪\n",
      "                                         ⎝dt      ⎠               d        d   ↪\n",
      "-b⋅g⋅m_A - g⋅m_B⋅(h - s(t)⋅sin(α)) + ─────────────── + m_B⋅cos(α)⋅──(s(t))⋅──( ↪\n",
      "                                            2                     dt       dt  ↪\n",
      "\n",
      "↪                         2                 2\n",
      "↪               ⎛d       ⎞        ⎛d       ⎞ \n",
      "↪         3⋅m_B⋅⎜──(s(t))⎟    m_B⋅⎜──(x(t))⎟ \n",
      "↪               ⎝dt      ⎠        ⎝dt      ⎠ \n",
      "↪ x(t)) + ───────────────── + ───────────────\n",
      "↪                 4                  2       \n"
     ]
    }
   ],
   "source": [
    "\n",
    "L = sp.simplify(Ek - Ep)\n",
    "pprint(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a98f99b5",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Gibalne enačbe\n",
    "\n",
    "Eulerjevi-Lagrangevi enačbi za posplošeni koordinati $x(t)$ in $s(t)$:\n",
    "$\\frac{\\mathrm{d}}{\\mathrm{d}t}\\frac{\\partial L}{\\partial \\dot q} -\n",
    "\\frac{\\partial L}{\\partial q} = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9a5d2c3d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:29.626667Z",
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     "shell.execute_reply": "2026-09-25T06:43:29.662424Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     2                      2               2           \n",
      "    d                      d               d            \n",
      "m_A⋅───(x(t)) + m_B⋅cos(α)⋅───(s(t)) + m_B⋅───(x(t)) = 0\n",
      "      2                      2               2          \n",
      "    dt                     dt              dt           \n"
     ]
    }
   ],
   "source": [
    "\n",
    "dx = sp.diff(x(t), t)\n",
    "ds = sp.diff(s(t), t)\n",
    "\n",
    "ge1 = sp.Eq(sp.diff(sp.diff(L, dx), t) - sp.diff(L, x(t)), 0)\n",
    "ge1 = sp.Eq(sp.simplify(ge1.lhs), 0)\n",
    "pprint(ge1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "43928940",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:29.663856Z",
     "iopub.status.busy": "2026-09-25T06:43:29.663742Z",
     "iopub.status.idle": "2026-09-25T06:43:29.718184Z",
     "shell.execute_reply": "2026-09-25T06:43:29.717707Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    ⎛                        2             2       ⎞    \n",
      "    ⎜                       d             d        ⎟    \n",
      "m_B⋅⎜-2⋅g⋅sin(α) + 2⋅cos(α)⋅───(x(t)) + 3⋅───(s(t))⎟    \n",
      "    ⎜                         2             2      ⎟    \n",
      "    ⎝                       dt            dt       ⎠    \n",
      "──────────────────────────────────────────────────── = 0\n",
      "                         2                              \n"
     ]
    }
   ],
   "source": [
    "\n",
    "ge2 = sp.Eq(sp.diff(sp.diff(L, ds), t) - sp.diff(L, s(t)), 0)\n",
    "ge2 = sp.Eq(sp.simplify(ge2.lhs), 0)\n",
    "pprint(ge2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef893568",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Reševanje sistema diferencialnih enačb\n",
    "\n",
    "Gibalni enačbi sta linearni z nastavnimi koeficienti (pospeška $\\ddot x$ in\n",
    "$\\ddot s$ sta konstantna, sistem giblje enakomerno pospešeno), zato ju\n",
    "`sp.dsolve` reši v zaključeni obliki -- tako kot `DSolve` v izvirnem\n",
    "zvezku."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "51f8168f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:29.719450Z",
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     "iopub.status.idle": "2026-09-25T06:43:29.956420Z",
     "shell.execute_reply": "2026-09-25T06:43:29.956004Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x(t) =\n",
      "         2                 \n",
      " -g⋅m_B⋅t ⋅sin(α)⋅cos(α)   \n",
      "───────────────────────────\n",
      "            ⎛     2       ⎞\n",
      "3⋅m_A - m_B⋅⎝2⋅cos (α) - 3⎠\n",
      "s(t) =\n",
      "     2                     \n",
      "  g⋅t ⋅(m_A + m_B)⋅sin(α)  \n",
      "───────────────────────────\n",
      "            ⎛     2       ⎞\n",
      "3⋅m_A - m_B⋅⎝2⋅cos (α) - 3⎠\n"
     ]
    }
   ],
   "source": [
    "\n",
    "zac_pogoji = {\n",
    "    x(0): 0,\n",
    "    s(0): 0,\n",
    "    sp.diff(x(t), t).subs(t, 0): 0,\n",
    "    sp.diff(s(t), t).subs(t, 0): 0,\n",
    "}\n",
    "\n",
    "sol = sp.dsolve([ge1, ge2], [x(t), s(t)], ics=zac_pogoji)\n",
    "\n",
    "x_resitev = [enacba.rhs for enacba in sol if enacba.lhs == x(t)][0]\n",
    "s_resitev = [enacba.rhs for enacba in sol if enacba.lhs == s(t)][0]\n",
    "\n",
    "print(\"x(t) =\")\n",
    "pprint(x_resitev)\n",
    "print(\"s(t) =\")\n",
    "pprint(s_resitev)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c430db16",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Podatki\n",
    "\n",
    "Geometrijski podatki ($a$, $R$, odvisna $b$ in $h$) ter ostali podatki\n",
    "($m_A$, $m_B$, $\\alpha$, $g$) -- vrednosti so enake kot v izvirnem zvezku."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f8590c20",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-09-25T06:43:30.015511Z"
    },
    "lines_to_next_cell": 1
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x(t) = -0.545*sqrt(3)*t**2\n",
      "s(t) = 2.18*t**2\n",
      "koeficient pri x(t): -0.9439676901250382, koeficient pri s(t): 2.18  (ujema se)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "podatki = {\n",
    "    a: 0.1,\n",
    "    R: 0.05,\n",
    "    m_A: 1,\n",
    "    m_B: 1,\n",
    "    alpha: sp.Rational(30, 180) * sp.pi,\n",
    "    g: 9.81,\n",
    "}\n",
    "podatki[b] = podatki[a] * sp.tan(podatki[alpha])\n",
    "podatki[h] = 3 * podatki[b] + podatki[R] * sp.cos(podatki[alpha])\n",
    "\n",
    "x_num = sp.simplify(x_resitev.subs(podatki))\n",
    "s_num = sp.simplify(s_resitev.subs(podatki))\n",
    "\n",
    "print(\"x(t) =\", x_num)\n",
    "print(\"s(t) =\", s_num)\n",
    "\n",
    "# Kontrola: izvirni zvezek da x(t) = -0.943967690125038 t^2 in\n",
    "# s(t) = 2.1799999999999997 t^2.\n",
    "koef_x = float(x_num.coeff(t, 2))\n",
    "koef_s = float(s_num.coeff(t, 2))\n",
    "assert abs(koef_x - (-0.943967690125038)) < 1e-9\n",
    "assert abs(koef_s - 2.1799999999999997) < 1e-9\n",
    "print(f\"koeficient pri x(t): {koef_x}, koeficient pri s(t): {koef_s}  (ujema se)\")\n",
    "\n",
    "# Numerični funkciji za risanje\n",
    "x_func = sp.lambdify(t, x_num, \"numpy\")\n",
    "s_func = sp.lambdify(t, s_num, \"numpy\")\n",
    "\n",
    "a_val = float(podatki[a])\n",
    "b_val = float(podatki[b])\n",
    "R_val = float(podatki[R])\n",
    "alpha_val = float(podatki[alpha])\n",
    "h_val = float(podatki[h])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cabd4e48",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Prikaz teles\n",
    "\n",
    "Prizmo narišemo kot rdeč trikotnik, valj kot zelen krog s črto, ki\n",
    "prikazuje njegov zasuk (kot kotaljenja je $\\varphi = s/R$, zasuk je v\n",
    "smeri urinega kazalca, zato je kot na sliki $-s/R$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "51f5c906",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-09-25T06:43:30.021013Z"
    },
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   },
   "outputs": [],
   "source": [
    "\n",
    "def lege_teles(t_val):\n",
    "    \"\"\"Izračuna lege prizme in valja pri danem času.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    t_val : float\n",
    "        Čas [s].\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    x_val, s_val, x_B_val, y_B_val : float\n",
    "        Lega prizme, lega valja po ploskvi ter kartezični legi\n",
    "        središča valja.\n",
    "    \"\"\"\n",
    "    x_val = float(x_func(t_val))\n",
    "    s_val = float(s_func(t_val))\n",
    "    x_B_val = x_val + R_val * np.sin(alpha_val) + s_val * np.cos(alpha_val)\n",
    "    y_B_val = h_val - s_val * np.sin(alpha_val)\n",
    "    return x_val, s_val, x_B_val, y_B_val\n",
    "\n",
    "\n",
    "def narisi_sliko(t_val):\n",
    "    \"\"\"Ustvari sliko sistema (prizma + valj) pri danem času.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    t_val : float\n",
    "        Čas [s].\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    fig, ax : matplotlib objekta\n",
    "        Ustvarjena slika in osi.\n",
    "    \"\"\"\n",
    "    x_val, s_val, x_B_val, y_B_val = lege_teles(t_val)\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "    # Prizma (rdeč trikotnik)\n",
    "    prizma = Polygon(\n",
    "        [[x_val, 0], [x_val + 3 * a_val, 0], [x_val, 3 * b_val]],\n",
    "        facecolor=\"red\",\n",
    "        edgecolor=\"black\",\n",
    "    )\n",
    "    ax.add_patch(prizma)\n",
    "\n",
    "    # Valj (zelen krog)\n",
    "    valj = Circle((x_B_val, y_B_val), R_val, facecolor=\"green\", edgecolor=\"black\")\n",
    "    ax.add_patch(valj)\n",
    "\n",
    "    # Črta, ki prikazuje zasuk valja\n",
    "    kot = -s_val / R_val\n",
    "    konec_x = x_B_val + R_val * np.cos(kot)\n",
    "    konec_y = y_B_val + R_val * np.sin(kot)\n",
    "    ax.plot([x_B_val, konec_x], [y_B_val, konec_y], \"k-\", linewidth=2)\n",
    "\n",
    "    ax.set_xlim(-2 * a_val, 4 * a_val)\n",
    "    ax.set_ylim(-0.25 * a_val, 2.75 * a_val)\n",
    "    ax.set_aspect(\"equal\")\n",
    "    ax.grid(True)\n",
    "    ax.set_xlabel(\"x [m]\")\n",
    "    ax.set_ylabel(\"y [m]\")\n",
    "    ax.text(\n",
    "        0.5, 0.92, f\"t = {t_val:.2f} s\", transform=ax.transAxes, ha=\"center\", fontsize=12\n",
    "    )\n",
    "\n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20b1f338",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Ustvarjanje slike\n",
    "\n",
    "Enak posnetek kot v izvirnem zvezku, pri $t = 0.1$ s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bcf01574",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:30.022414Z",
     "iopub.status.busy": "2026-09-25T06:43:30.022301Z",
     "iopub.status.idle": "2026-09-25T06:43:30.156438Z",
     "shell.execute_reply": "2026-09-25T06:43:30.155876Z"
    },
    "lines_to_next_cell": 1
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "narisi_sliko(0.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91884d8e",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Interaktivni posnetek\n",
    "\n",
    "Ustreza `Manipulate[Slika[t], {t, 0, 0.4, 0.01}]` iz izvirnega zvezka:\n",
    "drsnik za čas $t$ med $0$ in $0.4$ s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5cbe4448",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:30.158307Z",
     "iopub.status.busy": "2026-09-25T06:43:30.158084Z",
     "iopub.status.idle": "2026-09-25T06:43:30.242981Z",
     "shell.execute_reply": "2026-09-25T06:43:30.242522Z"
    },
    "lines_to_next_cell": 1
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d5b37e828eba4a30bc043ddb20962ece",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.1, description='t', max=0.4, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.prikazi_pri_casu(t=0.1)>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "def prikazi_pri_casu(t=0.1):\n",
    "    narisi_sliko(t)\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "interact(prikazi_pri_casu, t=FloatSlider(min=0, max=0.4, step=0.01, value=0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6af7d75",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Animacija in izvoz v video datoteko\n",
    "\n",
    "Animacija se izriše z `FuncAnimation` in prikaže z `HTML(anim.to_jshtml())`.\n",
    "Izvoz v video (npr. `anim.save('posnetek.mp4', writer='ffmpeg', fps=25)`)\n",
    "je v izvirnem zvezku narejen z `Export[..., \"Posnetek.avi\"]`; ukaz je tu\n",
    "ohranjen v komentarju, saj zvezek ne shranjuje datotek."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "45cc8b3d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:43:30.244872Z",
     "iopub.status.busy": "2026-09-25T06:43:30.244773Z",
     "iopub.status.idle": "2026-09-25T06:43:32.117283Z",
     "shell.execute_reply": "2026-09-25T06:43:32.116740Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_imge3bf5e6a0289460596b7a69e751bb3a4\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slidere3bf5e6a0289460596b7a69e751bb3a4\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anime3bf5e6a0289460596b7a69e751bb3a4.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anime3bf5e6a0289460596b7a69e751bb3a4.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selecte3bf5e6a0289460596b7a69e751bb3a4\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_e3bf5e6a0289460596b7a69e751bb3a4\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_e3bf5e6a0289460596b7a69e751bb3a4\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_e3bf5e6a0289460596b7a69e751bb3a4\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_e3bf5e6a0289460596b7a69e751bb3a4\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_e3bf5e6a0289460596b7a69e751bb3a4\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_e3bf5e6a0289460596b7a69e751bb3a4\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imge3bf5e6a0289460596b7a69e751bb3a4\";\n",
       "    var slider_id = \"_anim_slidere3bf5e6a0289460596b7a69e751bb3a4\";\n",
       "    var loop_select_id = \"_anim_loop_selecte3bf5e6a0289460596b7a69e751bb3a4\";\n",
       "    var frames = new Array(40);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABLAAAAJYCAYAAABy5h8aAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anime3bf5e6a0289460596b7a69e751bb3a4 = new Animation(frames, img_id, slider_id, 10.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "\n",
    "def animiraj_sistem(trajanje=0.4, koraki_na_s=100):\n",
    "    \"\"\"Ustvari animacijo sistema.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    trajanje : float\n",
    "        Trajanje simulacije [s].\n",
    "    koraki_na_s : int\n",
    "        Število časovnih korakov animacije na sekundo (ujema se s korakom\n",
    "        0.01 s v izvirnem zvezku).\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    anim : matplotlib.animation.FuncAnimation\n",
    "        Ustvarjena animacija.\n",
    "    \"\"\"\n",
    "    fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "    ax.set_xlim(-2 * a_val, 4 * a_val)\n",
    "    ax.set_ylim(-0.25 * a_val, 2.75 * a_val)\n",
    "    ax.set_aspect(\"equal\")\n",
    "    ax.grid(True)\n",
    "    ax.set_xlabel(\"x [m]\")\n",
    "    ax.set_ylabel(\"y [m]\")\n",
    "\n",
    "    prizma = Polygon([[0, 0], [0, 0], [0, 0]], facecolor=\"red\", edgecolor=\"black\")\n",
    "    valj = Circle((0, 0), R_val, facecolor=\"green\", edgecolor=\"black\")\n",
    "    crta, = ax.plot([], [], \"k-\", linewidth=2)\n",
    "    cas_text = ax.text(0.5, 0.92, \"\", transform=ax.transAxes, ha=\"center\", fontsize=12)\n",
    "\n",
    "    ax.add_patch(prizma)\n",
    "    ax.add_patch(valj)\n",
    "\n",
    "    def init():\n",
    "        return prizma, valj, crta, cas_text\n",
    "\n",
    "    def update(frame):\n",
    "        t_val = frame / koraki_na_s\n",
    "        x_val, s_val, x_B_val, y_B_val = lege_teles(t_val)\n",
    "\n",
    "        prizma.set_xy([[x_val, 0], [x_val + 3 * a_val, 0], [x_val, 3 * b_val]])\n",
    "        valj.center = (x_B_val, y_B_val)\n",
    "\n",
    "        kot = -s_val / R_val\n",
    "        konec_x = x_B_val + R_val * np.cos(kot)\n",
    "        konec_y = y_B_val + R_val * np.sin(kot)\n",
    "        crta.set_data([x_B_val, konec_x], [y_B_val, konec_y])\n",
    "\n",
    "        cas_text.set_text(f\"t = {t_val:.2f} s\")\n",
    "\n",
    "        return prizma, valj, crta, cas_text\n",
    "\n",
    "    okvirji = int(trajanje * koraki_na_s)\n",
    "    anim = FuncAnimation(\n",
    "        fig,\n",
    "        update,\n",
    "        frames=okvirji,\n",
    "        init_func=init,\n",
    "        blit=True,\n",
    "        interval=1000 / koraki_na_s,\n",
    "        repeat=True,\n",
    "    )\n",
    "\n",
    "    plt.close()\n",
    "    return anim\n",
    "\n",
    "\n",
    "anim = animiraj_sistem()\n",
    "\n",
    "# Izvoz v video datoteko (privzeto onemogočeno):\n",
    "# anim.save(\"posnetek.mp4\", writer=\"ffmpeg\", fps=25, dpi=150)\n",
    "\n",
    "HTML(anim.to_jshtml())"
   ]
  }
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Xr1/O+nfddRc333wzo0ePpmbNmixbtoxly5axfv16ANavX891113Hxx9/zKJFi5g0aRInn3wyderUoWPHjqHsoyQVZsuXL+fU006le/furKm+hvglcWgERMJOlqRqQezCGJsbbeaKK67giCOP2OX7ukuSJO2M0It9165dGTp0KP3796dp06bMnTuXCRMmUKVKFQAWL17M0qVLc9Z/+OGHyczM5PTTT6datWo5j6FDhwLZt+T57LPPOOmkk6hXrx69evWiefPmfPDBB97LXpL+JAgCxo0b99+j9GdAcEYA+X/3tKKvJNAZj95LkqQCUSgmz+vTpw99+vTZ5mtTpkzZ6vmiRYv+dlulSpXirbfeyqNkklQ0bd68mYsvuZgnn3iSyIERguMt9Pni96P3sXdiXHHFFbz2+muMGzuO8uXLh51MkiQVIaEfsZckFaylS5dyRLsjeOo/T8EpHqXPd38cvT8bJn0wieYtm/PNN9+EnUqSJBUhFntJKkY++eQTDm5+MHO+mUPivAQ0CTtRMVIH4r3i/LD2B1q0asGbb74ZdiJJklREWOwlqZgYM2YMh7c9nJWpK4n1isE+YScqhipB/Pw4G6tupPMJnbnnnnsIgiDsVJIkKclZ7CWpGLj11ls566yzyGqQRbxHHMqGnagYS4dEtwTBoQHXXnstPXr0YPPmzWGnkiRJScxiL0lFWCwWA+C+YffBsRB0CSAt5FDK/u7bHjgVxowbQ6fjO7Fhw4awU0mSpCRlsZekIiozM5Pzep4HQHBSAIfivekLm8aQOCvBh1M/pH2H9qxduzbsRJIkKQlZ7CWpCNqyZQunnnYqr7/xevaCA8LNo79RE+Jnx/lk7iccfczRrF69OuxEkiQpyVjsJamIycrK4syuZ/LmW2+SODURdhztjBoQPyfO3K/mcmzHY1m3bl3YiSRJUhKx2EtSERKPxzn77LN59bVXSZyegNphJ9JOqw7xs+LM/nw2x3U+jo0bN4adSJIkJQmLvSQVEUEQcOGFF/Lc888RnBZA/bATKdf2gXj3ONNmTOPkLifnTH4oSZL0dyz2klREDBs2jNGjR2dPlNcw7DTaZftBomuCSe9O4pprrgk7jSRJSgIWe0kqAt566y2uufaa7Jnvm4adRrstA4JOAcOHD+exxx4LO40kSSrkLPaSlOTmz5/PGV3PIFInkn1vdBUNLYEWcPElF/PRRx+FnUaSJBViFntJSmJr1qzh+BOOZ1OJTdkz4PtVvWjpBIl9EpzU5SQWL14cdhpJklRI+SOgJCWpeDxO125dWfTzImJdY5AediLluVRInJFgbXwtJ5x4Ahs2bAg7kSRJKoQs9pKUpG699Vbefvtt4qfGoXLYaZRv9oBY1xhffvMlF198cdhpJElSIWSxl6QkNHPmTO648w6CIwKoE3Ya5buqkDguwdNPP83LL78cdhpJklTIWOwlKcls2bKFc849h0iVCLQNO40KTBNIqZ9Cr969+PXXX8NOI0mSChGLvSQlmYEDB/LNN98QPykO0bDTqMBEINE5weoNq7n88svDTiNJkgoRi70kJZGZM2cyaPAggrYBVA07jQpcWYh3jDNmzBhPyZckSTks9pKUJLZs2cLZPc72FPzirvF/T8lftWpV2GkkSVIhYLGXpCRx++23M3/+fE/BL+7+dEr+lVdeGXYaSZJUCFjsJSkJ/PTTT9w15C6CQz0FX2Sfkt8+zn/+8x8++eSTsNNIkqSQWewlKQkMGDCARIkEHBZ2EhUaTSG1Sir/uOEfYSeRJEkhs9hLUiE3b948Hn/iceKHxSE97DQqNFIgdlSMKe9OYeLEiWGnkSRJIbLYS1Ih1+/GfkTLRaFl2ElU6NSH6H5Rrrv+OhKJRNhpJElSSCz2klSIzZgxg/EvjSfWLgapYadRoROB+NFxPp3zKc8//3zYaSRJUkgs9pJUSAVBwHXXX0dq1VRoHHYaFVo1IaVeCtf3u56srKyw00iSpBBY7CWpkHrvvfd4f8r7xI6M+dVafytxdIJFCxfx1FNPhR1FkiSFwB8VJamQGj5iOKlVUqF+2ElU6FWFlLopDBs+jCAIwk4jSZIKmMVekgqhn376iZdffplY8xhEwk6jZJBokeDzTz9nxowZYUeRJEkFzGIvSYXQqFGjiKRFvLZeO68OpFZK5cGHHgw7iSRJKmAWe0kqZLKysnho5EPEG3nfeuVCCsQOjjF27FhWrlwZdhpJklSALPaSVMiMHz+elStWet965d7BEA/iPP7442EnkSRJBchiL0mFzIgHRxCtGYUqYSdR0tkDEg0TjHhwBIlEIuw0kiSpgFjsJakQWbBgAR+89wHx5vGwoyhZtYAff/iRd999N+wkkiSpgFjsJakQefnll0lJS/EWd9p1+0JqxVTGjx8fdhJJklRALPaSVIiMf3k8QUYAJcJOoqQVgVidGC++/KL3tJckqZiw2EtSIbFq1SqmTp1KUM8ypt1UH5b+tJTPPvss7CSSJKkAWOwlqZB44403CBIB1As7iZLe/hAtFeWVV14JO4kkSSoAFntJKiRefvllojWiUCbsJEp6qRDPiPPi+BfDTiJJkgqAxV6SCoEtW7bwxoQ3iNd1Nnzlkfowd/Zcfv7557CTSJKkfGaxl6RC4P3332fThk2ehq+8UwciKRFef/31sJNIkqR8ZrGXpEJg2rRppO6RClXCTqIiozREq0X5+OOPw04iSZLymcVekgqBmTNnkqiagEjYSVSUxKrE+PgTi70kSUWdxV6SCoHpM6eTqJYIO4aKmurwzdffsGnTprCTSJKkfGSxl6SQLV++nBVLV0C1sJOoyKkGiXjC+9lLklTEWewlKWSzZs3K/kv1cHOoCKoCkWjkv2NMkiQVSRZ7SQrZzJkziZaOQvmwk6jISYVo1SgzZ84MO4kkScpHFntJCtnMmTMJqgVOnKd84QR6kiQVfRZ7SQrZ5199TmIvJ85TPqkC337zLUEQhJ1EkiTlE4u9JIVs+bLlUDbsFCqyykBWVha//vpr2EkkSVI+sdhLUojWrVvHpg2boEzYSVRk/T62lixZEm4OSZKUbyz2khSipUuXZv/FYq/88vvYyhlrkiSpyLHYS1KIco6i7hluDhVhv48tj9hLklR0WewlKUQesVe+S4XUPVI9Yi9JUhFmsZekEC1ZsoRoehRKhp1ERVmkbMQj9pIkFWEWe0kK0bJly0gp45di5a9Y6ZhH7CVJKsL8aVKSQrRx40YoEXYKFXVBWpA91iRJUpFksZekEMViMb8S59b6sAMkoRTIimWFnUKSJOWT1LADSFJxFovFCFKCsGMkj0zgQaAKcDhQG4iEmig5pEBWlsVekqSiymIvSSGKxWIW09yYDWwCFv3+qAocBjQEoqGlKvw8Yi9JUpHmCaCSFKJoNAoesN95ZYCKf3q+DHgBGAHMAOyu2xZAaqq/y5ckqajyu7wkhSg1NZVIwkP2O+1A4ABgHvAh8Mcd3FYDbwBTgEOAlkCpgo9XaMUhLTUt7BSSJCmfWOwlKUSpqamQCDtFkkkh+9T7A4CFwEfAd7+/thF4l+zS35zskl8uhIyFTcJiL0lSUWaxl6QQpaenQyzsFEkqAmT8/lhKdsH/kuxLGzKBacB0oDHZ1+HvFU7MwiASi2SPNUmSVCQVimvsH3zwQWrWrEl6ejqtW7dmxowZ21131KhRtG3blgoVKlChQgXat2//l/WDIKB///5Uq1aNUqVK0b59exYsWJDfuyFJuValShUS6zxkv9uqAacDlwMt+O+vrRPAXLJn0n8G+DGMcOFL3ZhK1apVw44hSZLySejFfty4cfTt25cBAwYwe/ZsmjRpQseOHVmxYsU2158yZQrdu3dn8uTJTJs2jRo1anDsscfy888/56wzZMgQhg8fzsiRI5k+fTp77LEHHTt2ZPPmzQW1W5K0U6pVq0Z8Y9xJ3/JKReAE4CqgLfDng9TfAI8BjwPzKVaTFgbrA6pVqxZ2DEmSlE9CL/b33nsvvXv3pmfPnjRs2JCRI0dSunRpRo8evc31//Of/3DppZfStGlTGjRowKOPPkoikWDSpElA9tH6YcOG8c9//pOTTz6Zxo0b8+9//5slS5Ywfvz4AtwzSdqx6tWrZ/9lXbg5ipw9gWOAq4FjyZ5N/w8/AGOAh4FPgXiBpytYcYiti/13rEmSpCIn1GvsMzMzmTVrFv369ctZlpKSQvv27Zk2bdpObWPjxo1kZWVRsWL2/Y8WLlzIsmXLaN++fc465cqVo3Xr1kybNo1u3br9ZRtbtmxhy5YtOc/Xrl0LQFZWFllZHkZT/vhjbDnGircqVapQqlQp2Ey+/Kq1VEqprf4sdkoBh0NwSED8szixD2MEK38/VL8CeAkikyOkHppKtFmUSIkieIeCDUA6VK1aNd++3vj1TAXBcaaC4DhTQciP8RVqsV+5ciXxeJwqVapstbxKlSrMmzdvp7Zx/fXXU7169Zwiv2zZspxt/O82/3jtfw0aNIhbb731L8snT55M6dKldyqHtKsmTpwYdgSF7Jlnnsn3zxjdaNtnQRUrzSDRI8GMGTN48cUXmT9/PgDB6oCsN7JI/yCdzp07c/zxx1O2bNmQw+axwyAej/PGG2/k68f49UwFwXGmguA4U37auHFjnm8zqWfFHzx4MGPHjmXKlCm7Ndtvv3796Nu3b87ztWvXUqNGDY466igqVaqUF1Glv8jKymLixIl06NCBtDRvQ1VcBUHAXnvvRdYRWdn3Xs9jpVJKMbrRaM7/4nw2JTbl/Qcko9IQnBVQYlEJYh/GSCzInrxw3bp1jB07lrEvjCXaPErqoamklA/9irXdNx94AebPn/+XX3rnFb+eqSA4zlQQHGcqCKtWrcrzbYZa7CtXrkw0GmX58uVbLV++fPkOZ+8dOnQogwcP5p133qFx48Y5y/943/Lly7eaKGj58uU0bdp0m9sqWbIkJUuW/MvytLQ0/0Er3znOVLZcWX769ad8vZ/9psQmi/3/2v/3xzKyb5X3BdkT6mVB/OM48RlxOIjsW+XtHV7M3bYaUjJTqFatGtFoNF8/yq9nKgiOMxUEx5nyU36MrVAPRZQoUYLmzZvnTHwH5EyE16ZNm+2+b8iQIQwcOJAJEybQokWLrV6rVasWVatW3Wqba9euZfr06X+7TUkKS/169YmsKoLXdieLqsBpwBVAK7a+Vd6nwENkT7b3Qyjpdt8vsF/N/fK91EuSpPCEfip+3759Offcc2nRogWtWrVi2LBhbNiwgZ49ewLQo0cP9tlnHwYNGgTAXXfdRf/+/RkzZgw1a9bMuW5+zz33ZM899yQSiXDVVVdx++23U7duXWrVqsXNN99M9erV6dKlS1i7KUnb1bJFS9775D1ixMKOUrxVAI4H2gEzgOlkT2oI2aezzwdqAIcDdSkE95XZOdFlUQ5pc0jYMSRJUj4Kvdh37dqVX375hf79+7Ns2TKaNm3KhAkTcq4DXLx4MSkp//3p6eGHHyYzM5PTTz99q+0MGDCAW265BYB//OMfbNiwgQsvvJDVq1dz+OGHM2HChN26Dl+S8kuLFi2IrYll3/KuzA5XV37bAzgKOBSYDUwD1v7+2o/AM8BeZJ+ifxBQmA+EJyBYGvzl7DZJklS0hF7sAfr06UOfPn22+dqUKVO2er5o0aIdbi8SiXDbbbdx22235UE6ScpfzZs3z/7LUiz2hUlJoA3Zp+d/TvZ1+L/8/tovwHjg3d/Xafb7+oXNSkhkJv47xiRJUpGUJCcSSlLRtf/++1O2fFlYEnYSbVMUaApcAnQn+3T8P6wF3gKGAZPJvmd8YfL7mDr44IPDzSFJkvKVxV6SQhaJRGjZoiWRZU6gV6ilAPWBXkBPoN6fXtsEvAfcB7wB/Fbg6bZtKdSsXZNy5cqFnUSSJOUji70kFQItW7QkdVmhuDpKO2N/4P/IPorfmP9+N42RPfHecOAFsm+lF6LosiiHtHTiPEmSijqLvSQVAq1atSJrdVbhOdKrnVMFOJXsW+W1Bv64LW1A9nX5I4GngUW/LytImRAsCWjVqlUBf7AkSSpoHh6SpELgmGOOITUtldj8WHZBVHIpDxzH1rfK2/T7a9/+/tiX7Jn061Mwv1ZfCImsBMcff3wBfJgkSQqTR+wlqRAoW7YsRx55JCnz/bKc1EoDRwJXk130/3xp+0/AOOAhYA7Zp+3np28go04G9evXz+cPkiRJYfMnSEkqJLqc3IVgUQCbw06i3VaC7DMvrgBOAfb+02srgZeB+4GpwJZ8+PwEpH6byqldTs2HjUuSpMLGYi9JhcSJJ55IEA+yT9tW0RAFmpA9yd7/Afv96bV1wNtkz6Q/CVifh5+7BGJrY5x00kl5uFFJklRYWewlqZDYb7/9aNS4EcwPO4nyXITs2+OdT/bt8v58dvxm4ANgGPAa8GsefN43UK5COdq0aZMHG5MkSYWdxV6SCpFTTj6F6LdRiIedRPmmBtAduBRoyta3ypsJjACeB5bu+kekfpvKSSecRGqqc+RKklQcWOwlqRA5+eSTiW+Mw8Kwkyjf7Q10Aa4E2rD1rfK+AP4FPAV8T+5ulbcSYks9DV+SpOLEYi9JhUizZs044MADiMyKhB1FBaUc0JHsmfSPIntm/T98B/wbGAV8BSR2YnszoXzF8pxwwgl5nVSSJBVSFntJKkQikQhX9LkCvgHWhJ1GBao00I7sgn88UP5Pry0BngUeBGax/VvlZUL00ygX9b6I9PT0fAwrSZIKE4u9JBUyZ511FqVKl8oucCp+0oBWwOXAaUCVP722CniV7In2PuSvt0b8AhKbE1x00UUFEFSSJBUWFntJKmTKlClDz3N7kjo3dftHZlX0RYGDgIuBs4Gaf3ptPfAO2bfKe4fsW+cFEJ0ZpdNxnahVq1YBh5UkSWGy2EtSIXTJJZcQWxuDr8NOotBFgDrAecAFwAF/em0L2UfuhwHjIL4kTp/L+hR0QkmSFDKLvSQVQgceeCCHH3E40VnRsKOoMNkX6Ar0AQ7mv9/F48C87L9+9dVXYSSTJEkhsthLUiF1RZ8riC+Kw09hJ1GhUxk4GbgKOBQo8d+XjjjiiFAiSZKk8FjsJamQOvXUU6l/QH1S3k3J3X3MVXyUBY4F6kN6qXROPfVUWrVqFXYqSZJUwCz2klRIRaNRhgweQuL7RPb9zKVtWQGRLyMMHjSYF154Iew0kiQpBBZ7SSrETjzxRFof0prou1FIhJ1GhVFkcoR99t2Hiy++OOwokiQpJBZ7SSrEIpEIdw+5m/iSODgnmv7XjxB8HXDn7XdSsmTJsNNIkqSQWOwlqZBr27Ytxx1/HKlTUrNnP5cAAkh5N4UDDjyA//u//ws7jSRJCpHFXpKSwOBBg4mvisOssJOo0PgWEgsTDBk8hGjU2yJKklScWewlKQk0btyYc889l+jkKKwNO41CtwVSJ6TStl1bOnfuHHYaSZIUMou9JCWJe+65hwplKpDymre/K/begdSNqTz+2ONEIpGw00iSpJBZ7CUpSVSsWJHRj44mMT8Bn4adRqFZCHwCQ+4aQu3atcNOI0mSCgGLvSQlkRNPPJGzzz6b6Fuekl8sbYHU11I5/IjDueyyy8JOI0mSCgmLvSQlmeHDh1OxbEVPyS+Ofj8F/4nRT5CS4rdwSZKUzZ8KJCnJVKhQgcdGPeYp+cWNp+BLkqTtsNhLUhI68cQTOeecc4hOiMKKsNMo362D1Jc9BV+SJG2bxV6SktRDDz1E/Tr1SR2XChvDTqN8kwXRZ6NUKlWJZ8c+6yn4kiTpL/zpQJKS1J577snrr75OmaAMKc+nQDzsRMpzAfA6RFdEefXlV6lWrVrYiSRJUiFksZekJJCZmUkQ/HWmvJo1a/LSiy8RWRyBt0IIpvw1DZgLj49+nJYtW4adRpIkFVIWe0kq5BYvXkyd/fenw9FH88UXX/zl9Xbt2vHAiAdgBjCr4PMpnyyAyDsRrr/+ev7v//4v7DSSJKkQs9hLUiG3YsUKfly2jE/ff58mjRvTp08fVq1atdU6F198MRdffDGRNyKwKJycykMrIfpilE6dOnHHHXeEnUaSJBVyFntJShJvJBIMCQKeGjmSuhkZjBgxgqysrJzXhw8fTtu2bYmOi8KSEINq9/wGqU+nUnv/2jwz5hmi0WjYiSRJUiFnsZekJFECuAZYEI9z+tq1XHnFFTRt1IiJEycCkJaWxqsvv0rTA5sS/U8UloUaV7tiDaQ+lco+Ffbh3XfepVy5cmEnkiRJScBiL0lJZm/gEbIvp6/03Xcce+yxnHziiXz77beULVuWiW9PpGHthkSfjsIvIYfVzlubfaR+79J7897k99hnn33CTiRJkpKExV6SktTBwHvxOOOAuRMm0PCAA7j++uuJRqO8O+ld6u1fj+hYT+NOCqsh9clUKqdV5v0p77P//vuHnUiSJCURi70kJbEIcCYwLxbj5liMEUOHUi8jg1deeYX3Jr9Hw4yG2SsuDTOl/tav2aW+2p7VmPrhVGrXrh12IkmSlGQs9pJUBJQCbga+SSQ45tdf6dWrF8d16MAtA24ByD5yvyDMhNqmnyH6RJQaFWsw9cOp1KpVK+xEkiQpCVnsJakIqQH8Jwj4CIh88QWnnXYaAIe3PhzGAB8BQYgB9V+fQcoTKTRr0IypH05l3333DTuRJElKUhZ7SSqCDgWmx+M89Pvz6dOm0fbwtjARIi9FIOvv3q18lQAmAi/COWedw/vvvU/VqlXDTiVJkpKYxV6SiqgU4Kzf/35JZibTP/qISuXLE/06SvTfUVgbZrpiajOkjE0hMi3Cvffey+OjHyc9PT3sVJIkKclZ7CWpGLgF+CqRoO2aNcSyYqSsSCH6aBR+CjtZMbIKoqOjlF5WmjffeJOrr76aSCQSdipJklQEWOwlqZioDbwUBEwEamXFia+Lw2hgChAPNVrRFgAzIToqSs1yNZn1ySw6duwYdipJklSEWOwlqZhpD3yZSDAsgPQgAlMgMioCy8JOVgSthpSnU+A1OP+c85k9czb16tULO5UkSSpiLPaSVAylAlcCPwcBZwLB8gD+hUfv88ofR+lHRqmyuQpvv/02jzzyCGXLlg07mSRJKoIs9pJUjFUExgGzA6gVkF3sH8Gj97tj9dZH6ed9NY8OHTqEnUqSJBVhFntJEgcD3wFDgbRfyD56/wawPsxUSWYzMBmiD3uUXpIkFSyLvSQJgAhwDbAyAZ0C4BNgGPAu2aVV2xYDpkH0gSglPi5B3yv6epRekiQVqNSwA0iSCpeywJvA1wF0jcHnH5Bd8o8AWuJ3jj8kgM8g9b1U4mvinNfzPG655Rb23XffsJNJkqRixiP2kqRtOgD4DHgtgL03A29BZHgEZgNZ4WYLVRz4ElIfSYXxcMKRJ/DVl1/x6KOPWuolSVIoPO4iSfpbnYFlAdwL/HNdwOZXIPJ2hODgAFoAlUIOWFDWArMhdU4qsTUxDj3yUIaMH0Lr1q3DTiZJkoo5i70kaYf+uP7+kgBuAB7aHJCYESGYFpBSN4VE8wTUo+idBxYAiyAyMwLzoGTJkvQ4uweXXHIJTZs2DTmcJElSNou9JGmnlQaGA9cC18QDngfSl5Rk44JNpFZIJdY4Bg2AqmT/NiBZrQTmQernqcSWx6hTvw5XDLuCc845h3LlyoWdTpIkaSsWe0lSru0HPAd8AFy5OZM5wH4V9mPZrGVsfG8jqeVTidWJQX2gFoX/u00c+BH4BlK/TSX2S4yS6SU58YQTufTSSznyyCOJRJL5NxWSJKkoK+w/akmSCrG2wCfxOE8ANy5eTBCN0rNnT0qXLs3Lr77MTzN/IpoeJZ4RhzrAPkBlIBpmarJntP8VWAJ8C9HvosQ3xKm8d2VO6XIKJ510EkcffTSlS5cOOagkSdKOWewlSbslCvQCTo/FuD0W4/4nnqB69erce999NGjQgFdffZUXx7/I7FdnEwQBKSVSiFSNEK8ah2pAdfK37P9R4pcCSyBlWQqRZRHim+IAHHDgAZx61amcdNJJtGjRgpSUojZRgCRJKuos9pKkPFEOuBu4MAi4ZulSzjzzTI447DDuf+ABbrzxRtauXcucOXOYNWsWs2bN4uNPPmbhJwuzy35aCtEKURJ7JIjvEYcy/PexJ9kX90fJnpwvhezr9+Nkl/YEsAlYB6z//c91kLI+hejGKInVCeKbs0v8PvvtwyGtDqFF8xY0b96cZs2aUalScZnWX5IkFVUWe0lSnqoLvJJI8BZw9fTpNGvWjN4XXMDtd9xBu3btaNeuXc66a9euZe7cucyePZsff/yRJUuW8NPPP/HTkp9Y/tlyNm3YlKvPLplekr2r7M0+++xDjfo1qF69Ovvssw9Nmza1xEuSpCLLYi9JyhcdgU9jMUYC/UePZtwzz9D/1lvp06cPJUqUAKBs2bIcccQRHHHEEdvcxrp161i6dCmrVq0iFovlPBKJBGlpaaSlpRGNRqlQoQLVqlWjXLlyTnInSZKKHYu9JCnfpAGXA93jcQasX891117Lvx58kPtGjOD444/f4fvLlClDmTJl8j2nJElSMnOGIElSvqsMPAjMDQL2XbSIzp07c3ynTsybNy/saJIkSUnPYi9JKjAHAe8kErwEzJs0iYMaNeLqq69m9erVISeTJElKXqEX+wcffJCaNWuSnp5O69atmTFjxnbX/fLLLznttNOoWbMmkUiEYcOG/WWdW265hUgkstWjQYMG+bgHkqTciABdgK9iMQbG44waPpy6GRn861//Ih6Ph5xOkiQp+YRa7MeNG0ffvn0ZMGAAs2fPpkmTJnTs2JEVK1Zsc/2NGzeSkZHB4MGDqVq16na3e+CBB7J06dKcx4cffphfuyBJ2kXpwA3A/ESCzr/9xsUXX0zzJk2YMmVKyMkkSZKSS6jF/t5776V379707NmThg0bMnLkSEqXLs3o0aO3uX7Lli25++676datGyVLltzudlNTU6latWrOo3Llyvm1C5Kk3VQdeAKYDpSaN4+jjjqK0089lYULF4YbTJIkKUmENit+ZmYms2bNol+/fjnLUlJSaN++PdOmTdutbS9YsIDq1auTnp5OmzZtGDRoEPvtt99219+yZQtbtmzJeb527VoAsrKyyMrK2q0s0vb8MbYcY9qRRCJBqVKlSAC5HS1ZpUpt9WdhdjAwBXge6P/OOzRr2pTLr7ySvn37sscee4QbTn/Lr2cqCI4zFQTHmQpCfoyv0Ir9ypUricfjVKlSZavlVapU2a1Zklu3bs0TTzxB/fr1Wbp0Kbfeeitt27bliy++2O4tkwYNGsStt976l+WTJ0+mdOnSu5xF2hkTJ04MO4KSwDPPPMNiYPEuvn/ids6EKoz2BO790/P33nsvrCjKJb+eqSA4zlQQHGfKTxs3bszzbRa5+9gfd9xxOX9v3LgxrVu3Zv/99+fZZ5+lV69e23xPv3796Nu3b87ztWvXUqNGDY466igqVaqU75lVPGVlZTFx4kQ6dOhAWlpa2HFUiM2ZM4cjjzySj4BGuXxvVqlSTBw9mg7nn0/apk35ES9fLQZujkQYHwS0bNaMu4YOpXnz5mHH0v/w65kKguNMBcFxpoKwatWqPN9maMW+cuXKRKNRli9fvtXy5cuX/+3EeLlVvnx56tWrx7fffrvddUqWLLnNa/bT0tL8B6185zjTjqSkpLBp0yZSgF0dKWmbNiVlsa8NjAHeA678+GPatGlDj3POYdDgwVSvXj3kdPpffj1TQXCcqSA4zpSf8mNshTZ5XokSJWjevDmTJk3KWZZIJJg0aRJt2rTJs89Zv3493333HdWqVcuzbUqSClY7YFY8zr+AN8aMoV7t2gwaNIjNmzeHHU2SJCl0oc6K37dvX0aNGsWTTz7J119/zSWXXMKGDRvo2bMnAD169Nhqcr3MzEzmzp3L3LlzyczM5Oeff2bu3LlbHY2/9tpree+991i0aBFTp07llFNOIRqN0r179wLfP0lS3okCFwIL4nEu3LyZ/jfdRMN69XjppZcIgiDseJIkSaEJ9Rr7rl278ssvv9C/f3+WLVtG06ZNmTBhQs6EeosXLyYl5b+/e1iyZAkHH3xwzvOhQ4cydOhQ2rVrl3Pf459++onu3buzatUq9tprLw4//HA+/vhj9tprrwLdN0lS/ihP9uR6FwUBfX/+mVNPPZWjjjiCYSNG0Lhx45DTSZIkFbzQJ8/r06cPffr02eZrf5T1P9SsWXOHR2XGjh2bV9EkSYVYfeD1RII3gL5Tp3Jw06ZcdNFF3DZwIJUrVw47niRJUoEJ9VR8SZJ21/HA57EY9wQBY0aNom5GBvfff7/3IJYkScWGxV6SlPTSgKvIvv6+67p1XH3VVTRu2JC33nor5GSSJEn5z2IvSSoy9gJGArOBKt9/T6dOnTixc2fmz58fcjJJkqT8Y7GXJBU5TYHJiQTPA5+//TaNDjyQa6+9ljVr1oScTJIkKe9Z7CVJRVIEOA34OhZjQCzGw/fdR91atXj00UeJx+Nhx5MkScozFntJUpFWCrgJmJ9I0Gn1anr37k3Lgw/mgw8+CDuaJElSnrDYS5KKhX2AfwcB04C0r77iiCOOoOuZZ/LDDz+EHU2SJGm3WOwlScXKIcC0eJwngQ9eeokG9eoxYMAANmzYEHY0SZKkXWKxlyQVOylAD+CbWIyrMzMZfPvtNKhThzFjxhAEQdjxJEmScsViL0kqtsoAdwJfJxK0Wr6cs846i8PbtGHmzJlhR5MkSdppFntJUrGXAbwQBEwC1s2cSatWrTi/Z0+WLVsWdjRJkqQdsthLkvS7o4HZ8TgPBgGvPPUUdTMyGDJkCFu2bAk7miRJ0nZZ7CVJ+pNU4BJgQTxOr02buPGGGziwfn1efvllr7+XJEmFksVekqRtqAAMAz4LAmr/+CNdunTh2GOO4Ysvvgg5mSRJ0tYs9pIk/Y2GwIREgleBHz74gKZNmnD55Zfz66+/hh1NkiQJsNhLkrRDEeAE4ItYjLsSCf798MPUqVWLBx54gFgsFnY8SZJUzO1Usa9YsWKuHpUqVeKHH37I7+ySJBWoEsA1wPx4nNPWruWKyy+naaNGvPPOO2FHkyRJxVjqzqy0evVqhg0bRrly5Xa4bhAEXHrppcTj8d0OJ0lSYVQFGEX2JHtXfvstHTp04KQTTuCe++6jTp06IaeTJEnFzU4Ve4Bu3bqx995779S6l19++S4HkiQpWTQD3o/HeQ64dsIEGk6YwNV9+3LTTTdRtmzZsONJkqRiYqdOxU8kEjtd6gHWrVtHRkbGLoeSJClZRIAzgXmxGP+MxRgxdCj1MjJ4/PHHSSQSYceTJEnFgJPnSZKUB0oD/YFvEgmO+fVXzj//fFo1a8ZHH30UdjRJklTE7fSp+H+2ZMkSPvzwQ1asWPGXoxFXXHFFngSTJCkZ1QD+EwRcClz5xRccfvjhdO/WjbuGDKFGjRphx5MkSUVQrov9E088wUUXXUSJEiWoVKkSkUgk57VIJGKxlyQJOAyYEY/zJNDv+eep/9JL3HDjjVx77bWULl067HiSJKkIyfWp+DfffDP9+/dnzZo1LFq0iIULF+Y8vv/++/zIKElSUkoBegLzYzGu2LKFO269lQZ16jBu3DiCIAg7niRJKiJyXew3btxIt27dSEnx8nxJknZGWWAw8GUiQbNly+jWrRtHHHYYs2fPDjuaJEkqAnLdznv16sVzzz2XH1kkSSrS6gDjg4C3gV8/+YQWLVrQ+4ILWL58edjRJElSEsv1NfaDBg3ihBNOYMKECRx00EGkpaVt9fq9996bZ+EkSSqKOgCfxmKMBPo/8QTPjh3LzbfcwhVXXEGJEiXCjidJkpLMLhX7t956i/r16wP8ZfI8SZK0Y6lAH6B7PM4tGzZwwz/+wSMPPcS9w4fTuXNnv6dKkqSdlutif8899zB69GjOO++8fIgjSVLxUgkYAVwUBFz1ww+ceOKJdGzfnvuGD+eAAw4IO54kSUoCub7GvmTJkhx22GH5kUWSpGKrETAxkWA88O2UKRzUqBFXXXUVv/32W8jJJElSYZfrYn/llVcyYsSI/MgiSVKxFgFOBr6MxbgzkeCxBx6gbkYGDz/8MLFYLOx4kiSpkMr1qfgzZszg3Xff5bXXXuPAAw/8y+R5L774Yp6FkySpOCoJ/APoEY9z4+rVXHbppTw8YgTDHniAo48+Oux4kiSpkMn1Efvy5ctz6qmn0q5dOypXrky5cuW2ekiSpLxRFRgNzADKzJ/PMcccw6lduvD999+HnEySJBUmuT5i//jjj+dHDkmStB0tgA/jccYC/3j9dQ54/XWuue46+vXrR5kyZcKOJ0mSQpbrI/aSJKngRYDuwLxYjBtiMe676y7q167Nk08+SSKRCDueJEkK0U4V+2bNmuVqVt7DDz+cn3/+eZdDSZKkbdsDuBWYl0hwxMqVnHfeeRzSsiUff/xx2NEkSVJIdupU/Llz5/Lpp59SsWLFndro3Llz2bJly24FkyRJ27c/MDYIuAy48tNPadOmDWefdRaD77qLffbZJ+x4kiSpAO30NfbHHHMMQRDs1LqRSGSXA0mSpJ3XFvgkHudx4KZx43jxhRfod9NNXHPNNZQqVSrseJIkqQDsVLFfuHBhrje877775vo9kiQp96LABcAZsRi3x2Lc1r8/j44cydBhwzjttNP8hbskSUXcThX7/fffP79zSJKk3VQOuBvoHQRcs3QpZ5xxBu0OP5xhI0bQtGnTkNNJkqT84qz4kiQVMfWAVxMJ3gSWT5tG82bNuOjCC/nll1/CjiZJkvKBxV6SpCKqE/BZPM59QcCzo0dTNyOD++67j8zMzLCjSZKkPGSxlySpCEsDrgAWxOP83/r1XHvNNTRu2JA333wz7GiSJCmPWOwlSSoGKgMPAXOCgOoLF3L88cfT+bjj+Oabb8KOJkmSdlOui/25557L+++/nx9ZJElSPmsMTEokeAH4+p13aHTggfTt25fVq1eHnEySJO2qXBf7NWvW0L59e+rWrcudd97Jzz//nB+5JElSPokApwJfxWLcFo/zyP33Uzcjg0ceeYR4PB52PEmSlEu5Lvbjx4/n559/5pJLLmHcuHHUrFmT4447jueff56srKz8yChJkvJBOtAPmJ9IcPxvv3HRRRfRvEkT3nvvvbCjSZKkXNila+z32msv+vbty6effsr06dOpU6cO55xzDtWrV+fqq69mwYIFeZ1TkiTlk+rAk8B0IH3ePI488kjOOO00Fi1aFG4wSZK0U3Zr8rylS5cyceJEJk6cSDQa5fjjj+fzzz+nYcOG3HfffXmVUZIkFYBWwNR4nKeAqa+8QoN69bj55pvZsGFD2NEkSdLfyHWxz8rK4oUXXuCEE05g//3357nnnuOqq65iyZIlPPnkk7zzzjs8++yz3HbbbfmRV5Ik5aMU4Gzgm1iMa7OyuPvOO6lfuzZPP/00iUQi7HiSJGkbcl3sq1WrRu/evdl///2ZMWMGM2fO5OKLL6Zs2bI56xx11FGUL18+L3NKkqQCtCdwO/B1IkGbFSs455xzOOyQQ5gxY0bY0SRJ0v/IdbG/7777WLJkCQ8++CBNmzbd5jrly5dn4cKFu5tNkiSFrBbwXBAwGdg4ezatW7fmvHPPZenSpWFHkyRJv8t1sT/nnHNIT0/PjyySJKmQOhKYHY/zL+D1//yHerVrM2jQIDZv3hxyMkmStFuT50mSpOIjClwILIjH6b1pE/1vuomG9erx2muvhR1NkqRizWIvSZJypTxwL/B5ENDg558566yzAPjqq6/CjCVJUrFlsZckSbukAfBGIsFzvz8/7NBDufSSS1i5cmWYsSRJKnYs9pIkabcc+/uftwcBY0aNom5GBsOHDycrKyvUXJIkFRcWe0mSlCcuA+bH45y5bh1XXXklTQ48kLfeeivsWJIkFXkWe0mSlGf2Bv4FzAb2+u47OnXqxImdO7NgwYKQk0mSVHRZ7CVJUp5rCkz5/fr7z99+mwMbNuS6665jzZo1ISeTJKnosdhLkqR8EQFOB76Oxegfi/HQvfdSLyODxx57jHg8HnY8SZKKDIu9JEnKV6WAfwLfJBIc+9tvXHDBBbQ8+GA++OCDsKNJklQkWOwlSVKB2Bd4KgiYCqR+9RVHHHEE3bp2ZfHixWFHkyQpqVnsJUlSgWoDfByP8wTw3osvUr9uXW655RY2btwYcjJJkpKTxV6SJBW4FOBcYH4sxlWZmQwaOJD6tWvzzDPPEARB2PEkSUoqFntJkhSaMsAg4OtEgpbLl/N///d/tD30UGbNmhV2NEmSkkboxf7BBx+kZs2apKen07p1a2bMmLHddb/88ktOO+00atasSSQSYdiwYbu9TUmSFL4M4MUg4B1gzcyZtGzZkvN79mTZsmVhR5MkqdALtdiPGzeOvn37MmDAAGbPnk2TJk3o2LEjK1as2Ob6GzduJCMjg8GDB1O1atU82aYkSSo8jgHmxGI8GAS8/NRT1KtdmyFDhrBly5awo0mSVGiFWuzvvfdeevfuTc+ePWnYsCEjR46kdOnSjB49epvrt2zZkrvvvptu3bpRsmTJPNmmJEkqXFKBS4AF8Tg9N27kxhtu4MD69XnllVe8/l6SpG1IDeuDMzMzmTVrFv369ctZlpKSQvv27Zk2bVqBbnPLli1bHQlYu3YtAFlZWWRlZe1SFmlH/hhbjjHtSCKRoFSpUiSA3I6WrFKltvpTyg/5Nc7KAEOBC4B+K1fSrVs3jmrXjsFDhtCgQYM8/SwVfn7fVEFwnKkg5Mf4Cq3Yr1y5kng8TpUqVbZaXqVKFebNm1eg2xw0aBC33nrrX5ZPnjyZ0qVL71IWaWdNnDgx7AhKAs888wyLgV292/dEz1pSAcjPcdb79wfA999/z/fff59vn6XCze+bKgiOM+Wn/Li9a2jFvjDp168fffv2zXm+du1aatSowVFHHUWlSpVCTKaiLCsri4kTJ9KhQwfS0tLCjqNCbM6cORx55JF8BDTK5XuzSpVi4ujRdDj/fNI2bcqPeFKBjrNM4F/A4GiUtD324Kb+/enZsyepqf5IU9T5fVMFwXGmgrBq1ao832Zo3wUrV65MNBpl+fLlWy1fvnz5difGy69tlixZcpvX7KelpfkPWvnOcaYdSUlJYdOmTaQAuzpS0jZtstgr3xXEOEsD+gJnATetX0+fyy7joeHDGfbAA7Rv3z5fP1uFg983VRAcZ8pP+TG2Qps8r0SJEjRv3pxJkyblLEskEkyaNIk2bdoUmm1KkqTCpwrwKDATqPDtt3To0IEuJ53Ed999F3IySZIKXqiz4vft25dRo0bx5JNP8vXXX3PJJZewYcMGevbsCUCPHj22mggvMzOTuXPnMnfuXDIzM/n555+ZO3cu33777U5vU5IkFR3NgPfjccYCs998k4YNGnDDDTewbt26sKNJklRgQr0grWvXrvzyyy/079+fZcuW0bRpUyZMmJAz+d3ixYtJSfnv7x6WLFnCwQcfnPN86NChDB06lHbt2jFlypSd2qYkSSpaIkBX4MRYjLuBu+6+mycfe4xBd99Njx49tvpZQpKkoij0mWb69OlDnz59tvnaH2X9DzVr1typ+9f+3TYlSVLRVBoYAJyfSHD9qlX07NmTB4cP5/4HHuDQQw8NO54kSfnGX2FLkqQipQYwJgj4AEh89hmHHXYYZ/3f//HTTz+FHU2SpHxhsZckSUXS4cAn8TiPAZOee476desycOBANnmHCElSEWOxlyRJRVYKcD4wPxajz+bNDBwwgAZ16vDss8/u1OV9kiQlA4u9JEkq8soCdwFfBgFNly2ja9eutDv8cObMmRN2NEmSdpvFXpIkFRt1gZcTCd4GVs2YQfPmzel9wQWsWLEi7GiSJO0yi70kSSp2OgCfxmIMDwJeeOIJ6mZkcM8995CZmRl2NEmScs1iL0mSiqVUoA+wIB7nnA0buP6662jUoAGvv/66199LkpKKxV6SJBVrlYAHgLlBwH4//MAJJ5zA8R078vXXX4cdTZKknWKxlyRJAhoBExMJxgPzJ0/moEaNuOqqq/jtt99CTiZJ0t+z2EuSJP0uApwMfBWLcUciwWMPPEDdjAxGjhxJLBYLO54kSdtksZckSfofJYHrgfnxOCetXs0ll1xCs8aNmTx5ctjRJEn6C4u9JEnSdlQDRgMzgD3nz+foo4/mtFNO4fvvvw85mSRJ/2WxlyRJ2oGWwEfxOP8Bpr/2Gg0bNOCmm25i/fr1YUeTJMliL0mStDMiwP8B38Ri/CMri3sHD6ZeRgb//ve/SSQSYceTJBVjFntJkqRc2AO4DZiXSNB25UrOPfdc2rRqxccffxx2NElSMWWxlyRJ2gX7A+OCgPeAzLlzadOmDT3OOYeff/457GiSpGLGYi9JkrQbjgBmxuM8Akx45hnq1anDHXfcwaZNm8KOJkkqJiz2kiRJuykK9AYWxONcsnkzt9x8Mw3r1eOFF14gCIKw40mSijiLvSRJUh4pBwwFvggCDlyyhNNPP52j27Xj008/DTuaJKkIs9hLkiTlsfrAa4kEbwLLpk2j2cEHc/FFF/HLL7+EHU2SVARZ7CVJkvJJJ+CzWIx7g4Cxjz1G3YwMhg0bRlZWVtjRJElFiMVekiQpH6UBV5J9/X339eu5pm9fGjdsyJtvvhl2NElSEWGxlyRJKgB7AQ8Dc4KAqt9/z/HHH0/n447jm2++CTuaJCnJWewlSZIKUGPg3USCF4Cv3nmHRgceyDXXXMPq1atDTiZJSlYWe0mSpAIWAU4Fvo7FuDUe51/DhlEvI4NHHnmEeDwedjxJUpKx2EuSJIUkHbgRmJ9IcNzq1Vx00UU0b9KE9957L+xokqQkYrGXJEkKWXXgySDgYyB93jyOPPJIzjz9dBYtWhRyMklSMrDYS5IkFRKtganxOP8GPnz5ZQ6oX5+bb76ZDRs2hB1NklSIWewlSZIKkRTgHGB+LMY1mZncfeed1K9dm//85z8EQRB2PElSIWSxlyRJKoT2BG4Hvk4kOGTFCs4++2wOO+QQPvnkk7CjSZIKGYu9JElSIVYLeD4IeBfYMGsWrVq1oud557F06dKwo0mSCgmLvSRJUhI4CpgdjzMSePXpp6lXuzaDBw9m8+bNYUeTJIXMYi9JkpQkosBFwIJ4nAs2beLmG2/kwPr1GT9+vNffS1IxZrGXJElKMhWA+4DPgoC6P/3EKaecQoejj+aLL74IO5okKQQWe0mSpCR1APBmIsFrwI8ffkiTxo257LLLWLVqVdjRJEkFyGIvSZKUxCJAZ+DzWIy7g4Cn//Uv6mZkMGLECLKyssKOJ0kqABZ7SZKkIqAE0Jfs6+9PX7uWK6+4gqaNGvH222+HHU2SlM8s9pIkSUXI3sAjwCyg8nff0bFjR0464QQWLFgQcjJJUn6x2EuSJBVBBwNT4nGeBT596y0ObNiQf/zjH6xduzbsaJKkPGaxlyRJKqIiwBnAvFiMm2MxHrznHurWqsVjjz1GPB4PO54kKY9Y7CVJkoq4UsDNwDeJBB1++40LLriAVs2a8eGHH4YdTZKUByz2kiRJxcS+wNNBwEdAypdf0rZtW7p368bixYvDjiZJ2g0We0mSpGLmUGB6PM4TwJQXXqBBvXrccsstbNy4MeRkkqRdYbGXJEkqhlKAc4H5sRhXbtnCoIEDaVCnDmPHjiUIgrDjSZJywWIvSZJUjJUBBgFfJRI0X7aM7t270/bQQ5k1a1bY0SRJO8liL0mSJGoDLwUBE4HVn3xCy5Yt6XX++SxbtizsaJKkHbDYS5IkKUd7YG48zgNBwPh//5t6tWtz9913s2XLlrCjSZK2w2IvSZKkraQClwIL4nHO27iRftdfT6MGDXj11Ve9/l6SCiGLvSRJkrapIjAc+DQIqLV4MSeddBIdO3Tgyy+/DDuaJOlPLPaSJEn6WwcCbyUSvAIsfO89mjRuzBVXXMGvv/4adjRJEhZ7SZIk7YQIcCLwRSzGoESCJx56iLoZGTz00EPEYrGw40lSsWaxlyRJ0k4rCVwHzI/H6bJmDX0uu4yDDzqISZMmhR1Nkooti70kSZJyrSrwGPAJUG7BAtq3b88pJ5/Md999F3IySSp+LPaSJEnaZc2BD+JxngFmvvEGDRs04IYbbmDdunVhR5OkYsNiL0mSpN0SAboB38Ri3BiLMfzuu6mXkcETTzxBIpEIO54kFXkWe0mSJOWJ0sAAYF4iwZGrVtGzZ09at2jBtGnTwo4mSUWaxV6SJEl5aj/gmSDgfSDx2WcceuihnH3WWfz0009hR5OkIsliL0mSpHzRFpgRj/MYMHHcOOrXrcvAgQPZtGlT2NEkqUix2EuSJCnfRIHzgQXxOJdt3szAAQM4oG5dnnvuOYIgCDueJBUJFntJkiTlu7LAEODLIKDx0qWceeaZtDv8cObMmRN2NElKehZ7SZIkFZi6wCuJBG8BK2fMoHnz5lzYuzcrVqwIO5okJS2LvSRJkgrcscCnsRj3BwHPPf44dTMyuPfee8nMzAw7miQlHYu9JEmSQpEGXE729fdnb9jAdddey0EHHMAbb7wRdjRJSioWe0mSJIWqMvAgMDcI2HfRIjp37sxxHTvy9ddfhx1NkpKCxV6SJEmFwkHAO4kELwHz332XxgcdxNVXX81vv/0WdjRJKtQs9pIkSSo0IkAX4MtYjIHxOKOGD6duRgajR48OOZkkFV6Fotg/+OCD1KxZk/T0dFq3bs2MGTP+dv3nnnuOBg0akJ6ezkEHHfSX67DOO+88IpHIVo9OnTrl5y5IkiQpD6UDNwALEglOXL2aq6++GoAPPvgg1FySVBiFXuzHjRtH3759GTBgALNnz6ZJkyZ07Nhxu7c8mTp1Kt27d6dXr17MmTOHLl260KVLF7744out1uvUqRNLly7NeTzzzDMFsTuSJEnKQ9WAx4HJvz8/4YQTOP3UU1m4cGGIqSSpcAm92N9777307t2bnj170rBhQ0aOHEnp0qW3e7rV/fffT6dOnbjuuus44IADGDhwIM2aNeOBBx7Yar2SJUtStWrVnEeFChUKYnckSZKUD5r9/uco4ONXX+WA+vW56aabWL9+fZixJKlQSA3zwzMzM5k1axb9+vXLWZaSkkL79u2ZNm3aNt8zbdo0+vbtu9Wyjh07Mn78+K2WTZkyhb333psKFSpw9NFHc/vtt1OpUqVtbnPLli1s2bIl5/natWsByMrKIisra1d2TdqhP8aWY0w7kkgkKFWqFAkgt6Mlq1Sprf6U8oPjTAXhj/F1SqlSnADcBwy//36eeeopbr3jDs4880xSUkI/ZqUk589nKgj5Mb5CLfYrV64kHo9TpUqVrZZXqVKFefPmbfM9y5Yt2+b6y5Yty3neqVMnTj31VGrVqsV3333HjTfeyHHHHce0adOIRqN/2eagQYO49dZb/7J88uTJlC5deld2TdppEydODDuCksAzzzzDYmDxLr5/opNOqQA4zlQQ/hhnB5N9iv4fJkyYEEoeFU3+fKb8tHHjxjzfZqjFPr9069Yt5+8HHXQQjRs3pnbt2kyZMoVjjjnmL+v369dvq7MA1q5dS40aNTjqqKO2e5Rf2l1ZWVlMnDiRDh06kJaWFnYcFWJz5szhyCOP5COgUS7fm1WqFBNHj6bD+eeTtmlTfsSTHGcqEH83zj4Cro9G+Twep1vXrtx6221UrVo1nKBKav58poKwatWqPN9mqMW+cuXKRKNRli9fvtXy5cuXb/eLcdWqVXO1PkBGRgaVK1fm22+/3WaxL1myJCVLlvzL8rS0NP9BK985zrQjKSkpbNq0iRRgV0dK2qZNFi7lO8eZCsK2xtmRwFRgNHDjU0/x7Nix3HjzzfTt25f09PQQUirZ+fOZ8lN+jK1QL0QqUaIEzZs3Z9KkSTnLEokEkyZNok2bNtt8T5s2bbZaH7JPldne+gA//fQTq1atolq1ankTXJIkSYVKFOgNLIjHuWjzZgb8858cULcuL7zwAkEQhB1PkvJV6DOM9O3bl1GjRvHkk0/y9ddfc8kll7BhwwZ69uwJQI8ePbaaXO/KK69kwoQJ3HPPPcybN49bbrmFmTNn0qdPHwDWr1/Pddddx8cff8yiRYuYNGkSJ598MnXq1KFjx46h7KMkSZIKRnngHuCLIODAJUs4/fTTObpdOz777LOQk0lS/gm92Hft2pWhQ4fSv39/mjZtyty5c5kwYULOBHmLFy9m6dKlOesfeuihjBkzhkceeYQmTZrw/PPPM378eBo1yr7yNBqN8tlnn3HSSSdRr149evXqRfPmzfnggw+2ebq9JEmSip76wGuJBG8AS6dN4+CmTbnk4ov55Zdfwo4mSXmuUEye16dPn5wj7v9rypQpf1l2xhlncMYZZ2xz/VKlSvHWW2/lZTxJkiQlqeOA9rEYDwK3PPooY8eM4ZaBA7n00ku9hlpSkRH6EXtJkiQpP6UBV5F9/X3Xdevoe/XVNG7Y0FvkSSoyLPaSJEkqFvYCRgKzg4CqCxdy3HHHccLxxzN//vywo0nSbrHYS5IkqVhpArwbj/M88OXEiRzYsCHXXnsta9asCTuaJO0Si70kSZKKnQhwGvBVLMYt8TgP33cfdWvVYtSoUcTj8bDjSVKuWOwlSZJUbJUCbgLmJxJ0Wr2aCy+8kBZNm/L++++HHU2SdprFXpIkScXePsC/g4BpQImvv6Zdu3Z0PfNMfvjhh7CjSdIOWewlSZKk3x0CTIvHeRL44KWXaFCvHv3792fDhg1hR5Ok7bLYS5IkSX+SAvQA5sdi9M3MZMgdd1C/dm3GjBlDEARhx5Okv7DYS5IkSduwJ3AH8FUiQesVKzjrrLM4vE0bPvnkk7CjSdJWLPaSJEnS38gAXggC3gXWzZxJq1at6HneeSxdujTsaJIEWOwlSZKknXIUMDse52Hg1aefpl7t2tx1111s2bIl7GiSijmLvSRJkrSTUoGLgQXxOL02beKf/fpxYP36jB8/3uvvJYXGYi9JkiTlUgVgGPBZEFDnxx855ZRT6HD00XzxxRchJ5NUHFnsJUmSpF10APBmIsFrwOIPP6RJ48b06dOHVatWhR1NUjFisZckSZJ2QwToDHwRizEkCHhq5EjqZmQwYsQIsrKywo4nqRiw2EuSJEl5oARwDdnX35++di1XXnEFTRs1YuLEiWFHk1TEWewlSZKkPLQ38AgwC6j03Xcce+yxnHziiXz77bchJ5NUVFnsJUmSpHxwMPBePM44YO6ECTQ84ACuv/561q5dG3Y0SUWMxV6SJEnKJxHgTODrWIx/xmKMGDqUehkZjB49mkQiEXY8SUWExV6SJEnKZ6WB/sA3iQTH/PorvXr1olWzZnz00UdhR5NUBFjsJUmSpAJSA/hPEPAhwBdfcPjhh9O9WzcWL14ccjJJycxiL0mSJBWww4AZ8TijgckvvECDevW49dZb2bhxY9jRJCUhi70kSZIUghSgJzA/FuOKLVu487bbaFCnDuPGjSMIgrDjSUoiFntJkiQpRGWBwcCXiQTNli2jW7duHHHYYcyaNSvsaJKShMVekiRJKgTqAOODgInAbzNm0LJlSy7o1Yvly5eHHU1SIWexlyRJkgqR9sDceJwRQcCLTz5J3YwM7r77brZs2RJ2NEmFlMVekiRJKmRSgcuABfE4527cSL/rr6dRgwa8+uqrXn8v6S8s9pIkSVIhVQkYAXwaBNRcvJiTTjqJTscey1dffRV2NEmFiMVekiRJKuQOBN5OJHgZ+G7KFBofdBBXXnklv/76a9jRJBUCFntJkiQpCUSAk4AvYzEGJRI8/uCD1M3I4KGHHiIWi4UdT1KILPaSJElSEikJXAfMj8fpsmYNfS67jIMPOohJkyaFHU1SSCz2kiRJUhKqCjwGzADKLlhA+/btObVLF77//vuQk0kqaBZ7SZIkKYm1AD6MxxkDfPL66xxQvz79+vVj3bp1YUeTVEAs9pIkSVKSiwDdgXmxGP1iMYYNGUK9jAyefPJJEolE2PEk5TOLvSRJklRE7AHcAnyTSNBu1SrOO+88DmnZkmnTpoWcTFJ+sthLkiRJRcx+wNgg4H0g9umnHHrooZx91ln89NNPYUeTlA8s9pIkSVIR1Rb4JB7nUWDis89Sv25dbr/9djZt2hR2NEl5yGIvSZIkFWFRoBcwPxbj0s2bua1/fw6oW5fnn3+eIAjCjicpD1jsJUmSpGKgHHA38GUQ0HjpUs444wyObNuWuXPnhpxM0u6y2EuSJEnFSF3glUSCCcAv06fTrFkzLrrwQn755Zewo0naRRZ7SZIkqRjqCHwaizEsCHh29GjqZmRw7733kpmZGXY0SblksZckSZKKqTTgCmBBPM7/rV/Pdddey0EHHMAbb7wRdjRJuWCxlyRJkoq5ysBDwNwgYJ9Fi+jcuTPHd+rEvHnzwo4maSdY7CVJkiQBcBAwKZHgRWDepEkc1KgRV199NatXrw45maS/Y7GXJEmSlCMCnAJ8FYsxMB5n1PDh1M3I4F//+hfxeDzseJK2wWIvSZIk6S/SgRuA+YkEnX/7jYsvvpjmTZowZcqUkJNJ+l8We0mSJEnbVR14ApgOlJo3j6OOOorTTz2VhQsXhhtMUg6LvSRJkqQdagV8FI/zNDDt1Vc5oH59/vnPf7J+/fqwo0nFnsVekiRJ0k5JAc4CvonFuC4ri6GDBlG/dm2efvppEolE2PGkYstiL0mSJClX9gQGAvMSCQ795RfOOeccDjvkEGbMmBF2NKlYsthLkiRJ2iU1geeCgCnAptmzad26Nef26MGSJUvCDSYVMxZ7SZIkSbulHTArHudfwBtjxlCvdm0GDRrE5s2bw44mFQsWe0mSJEm7LQpcCCyIx7lw82b633QTDevV48UXXyQIgrDjSUWaxV6SJElSnikP3At8HgQc8PPPnHbaaRxz5JF89tlnISeTii6LvSRJkqQ81wB4PZHgdWDJ1Kkc3LQpl15yCStXrgw7mlTkWOwlSZIk5Zvjgc9iMYYGAWNGjaJuRgb3338/WVlZYUeTigyLvSRJkqR8VQK4muzr77uuW8fVV11F44YNeeutt8KOJhUJFntJkiRJBWIvYCQwG6jy/fd06tSJEzt3Zv78+SEnk5KbxV6SJElSgWoKTE4keA74/O23aXTggVx77bWsWbMm5GRScrLYS5IkSSpwEeB04OtYjAGxGA/fdx91a9Xi0UcfJR6Phx1PSioWe0mSJEmhKQXcBMxPJOi4ejW9e/em5cEH88EHH4QdTUoaFntJkiRJodsHeCoImAqkfvUVRxxxBF3PPJMffvgh7GhSoWexlyRJklRotAE+jsd5Enj/xRdpUK8eAwYMYMOGDWFHkwoti70kSZKkQiUF6AHMj8e5OjOTwbffToM6dRgzZgxBEIQdTyp0LPaSJEmSCqUywJ3A14kErZYv56yzzuLwNm2YOXNm2NGkQsViL0mSJKlQywBeCAImAWtnzqRVq1ac37Mny5YtCzuaVCgUimL/4IMPUrNmTdLT02ndujUzZsz42/Wfe+45GjRoQHp6OgcddBBvvPHGVq8HQUD//v2pVq0apUqVon379ixYsCA/d0GSJElSPjsamBOP82AQ8MpTT1E3I4MhQ4awZcuWsKNJoQq92I8bN46+ffsyYMAAZs+eTZMmTejYsSMrVqzY5vpTp06le/fu9OrVizlz5tClSxe6dOnCF198kbPOkCFDGD58OCNHjmT69OnssccedOzYkc2bNxfUbkmSJEnKB6nAJWRff3/+pk3ceMMNHFi/Pi+//LLX36vYCr3Y33vvvfTu3ZuePXvSsGFDRo4cSenSpRk9evQ217///vvp1KkT1113HQcccAADBw6kWbNmPPDAA0D20fphw4bxz3/+k5NPPpnGjRvz73//myVLljB+/PgC3DNJkiRJ+aUicD/wWRBQ+8cf6dKlC8cec8xWB/yk4iI1zA/PzMxk1qxZ9OvXL2dZSkoK7du3Z9q0adt8z7Rp0+jbt+9Wyzp27JhT2hcuXMiyZcto3759zuvlypWjdevWTJs2jW7duv1lm1u2bNnq9J21a9cCkJWVRVZW1i7vn/R3/hhbjjHtSCKRoFSpUjwBVM3le1NKlaIeMKxUKRJ5H00CHGcqGI4z/Z2jgEzgo48/ps0hh3Dtdddx44035no7/nymgpAf4yvUYr9y5Uri8ThVqlTZanmVKlWYN2/eNt+zbNmyba7/x8QZf/z5d+v8r0GDBnHrrbf+ZfnkyZMpXbr0zu2MtIsmTpwYdgQlgWeeeWa33l9vO2dBSXnJcaaC4DjT9hzwP8//dx6u3PDnM+WnjRs35vk2Qy32hUW/fv22Ogtg7dq11KhRg6OOOopKlSqFmExFWVZWFhMnTqRDhw6kpaWFHUdFlONMBcFxpoLgOFNBcJypIKxatSrPtxlqsa9cuTLRaJTly5dvtXz58uVUrbrtE06rVq36t+v/8efy5cupVq3aVus0bdp0m9ssWbIkJUuW/MvytLQ0/0Er3znOVBAcZyoIjjMVBMeZCoLjTPkpP8ZWqJPnlShRgubNmzNp0qScZYlEgkmTJtGmTZttvqdNmzZbrQ/Zp8r8sX6tWrWoWrXqVuusXbuW6dOnb3ebkiRJkiQlq9BPxe/bty/nnnsuLVq0oFWrVgwbNowNGzbQs2dPAHr06ME+++zDoEGDALjyyitp164d99xzD507d2bs2LHMnDmTRx55BIBIJMJVV13F7bffTt26dalVqxY333wz1atXp0uXLmHtpiRJkiRJ+SL0Yt+1a1d++eUX+vfvz7Jly2jatCkTJkzImfxu8eLFpKT898SCQw89lDFjxvDPf/6TG2+8kbp16zJ+/HgaNWqUs84//vEPNmzYwIUXXsjq1as5/PDDmTBhAunp6QW+f5IkSZIk5afQiz1Anz596NOnzzZfmzJlyl+WnXHGGZxxxhnb3V4kEuG2227jtttuy6uIkiRJkiQVSqFeYy9JkiRJknaPxV6SJEmSpCRmsZckSZIkKYlZ7CVJkiRJSmIWe0mSJEmSkpjFXpIkSZKkJGaxlyRJkiQpiVnsJUmSJElKYhZ7SZIkSZKSmMVekiRJkqQkZrGXJEmSJCmJWewlSZIkSUpiFntJkiRJkpKYxV6SJEmSpCRmsZckSZIkKYlZ7CVJkiRJSmIWe0mSJEmSkpjFXpIkSZKkJGaxlyRJkiQpiVnsJUmSJElKYhZ7SZIkSZKSmMVekiRJkqQkZrGXJEmSJCmJWewlSZIkSUpiFntJkiRJkpKYxV6SJEmSpCRmsZckSZIkKYlZ7CVJkiRJSmIWe0mSJEmSkpjFXpIkSZKkJGaxlyRJkiQpiaWGHaAwCoIAgHXr1pGWlhZyGhVVWVlZbNy4kbVr1zrOlG8cZyoIjjMVBMeZCoLjTAVh3bp1wH97Z16w2G/DqlWrAKhVq1bISSRJkiRJRdGqVasoV65cnmzLYr8NFStWBGDx4sV59h9a+l9r166lRo0a/Pjjj5QtWzbsOCqiHGcqCI4zFQTHmQqC40wFYc2aNey33345vTMvWOy3ISUle+qBcuXK+Q9a+a5s2bKOM+U7x5kKguNMBcFxpoLgOFNB+KN35sm28mxLkiRJkiSpwFnsJUmSJElKYhb7bShZsiQDBgygZMmSYUdREeY4U0FwnKkgOM5UEBxnKgiOMxWE/BhnkSAv59iXJEmSJEkFyiP2kiRJkiQlMYu9JEmSJElJzGIvSZIkSVISs9hLkiRJkpTELPa/+/XXXznrrLMoW7Ys5cuXp1evXqxfv/5v17/88supX78+pUqVYr/99uOKK65gzZo1BZhaySa34wzgkUce4cgjj6Rs2bJEIhFWr15dMGGVNB588EFq1qxJeno6rVu3ZsaMGX+7/nPPPUeDBg1IT0/noIMO4o033iigpEpmuRlnX375Jaeddho1a9YkEokwbNiwgguqpJabcTZq1Cjatm1LhQoVqFChAu3bt9/h1z8JcjfOXnzxRVq0aEH58uXZY489aNq0KU899VQBplWyyu3PZ38YO3YskUiELl265OrzLPa/O+uss/jyyy+ZOHEir732Gu+//z4XXnjhdtdfsmQJS5YsYejQoXzxxRc88cQTTJgwgV69ehVgaiWb3I4zgI0bN9KpUyduvPHGAkqpZDJu3Dj69u3LgAEDmD17Nk2aNKFjx46sWLFim+tPnTqV7t2706tXL+bMmUOXLl3o0qULX3zxRQEnVzLJ7TjbuHEjGRkZDB48mKpVqxZwWiWr3I6zKVOm0L17dyZPnsy0adOoUaMGxx57LD///HMBJ1cyye04q1ixIjfddBPTpk3js88+o2fPnvTs2ZO33nqrgJMrmeR2nP1h0aJFXHvttbRt2zb3Hxoo+OqrrwIg+OSTT3KWvfnmm0EkEgl+/vnnnd7Os88+G5QoUSLIysrKj5hKcrs7ziZPnhwAwW+//ZaPKZVsWrVqFVx22WU5z+PxeFC9evVg0KBB21z/zDPPDDp37rzVstatWwcXXXRRvuZUcsvtOPuz/fffP7jvvvvyMZ2Kit0ZZ0EQBLFYLChTpkzw5JNP5ldEFQG7O86CIAgOPvjg4J///Gd+xFMRsSvjLBaLBYceemjw6KOPBueee25w8skn5+ozPWIPTJs2jfLly9OiRYucZe3btyclJYXp06fv9HbWrFlD2bJlSU1NzY+YSnJ5Nc6kP2RmZjJr1izat2+fsywlJYX27dszbdq0bb5n2rRpW60P0LFjx+2uL+3KOJNyKy/G2caNG8nKyqJixYr5FVNJbnfHWRAETJo0iW+++YYjjjgiP6Mqie3qOLvtttvYe++9d/kMcBsosGzZMvbee++tlqWmplKxYkWWLVu2U9tYuXIlAwcO3OFp1Sq+8mKcSX+2cuVK4vE4VapU2Wp5lSpVmDdv3jbfs2zZsm2u7xjU9uzKOJNyKy/G2fXXX0/16tX/8stL6Q+7Os7WrFnDPvvsw5YtW4hGozz00EN06NAhv+MqSe3KOPvwww957LHHmDt37i5/bpE+Yn/DDTcQiUT+9pEXP5SsXbuWzp0707BhQ2655ZbdD66kUlDjTJIkbdvgwYMZO3YsL730Eunp6WHHURFTpkwZ5s6dyyeffMIdd9xB3759mTJlStixVESsW7eOc845h1GjRlG5cuVd3k6RPmJ/zTXXcN555/3tOhkZGVStWvUvExnEYjF+/fXXHU76s27dOjp16kSZMmV46aWXSEtL293YSjIFMc6kbalcuTLRaJTly5dvtXz58uXbHVNVq1bN1frSrowzKbd2Z5wNHTqUwYMH884779C4ceP8jKkkt6vjLCUlhTp16gDQtGlTvv76awYNGsSRRx6Zn3GVpHI7zr777jsWLVrEiSeemLMskUgA2Wf3fvPNN9SuXXuHn1ukj9jvtddeNGjQ4G8fJUqUoE2bNqxevZpZs2blvPfdd98lkUjQunXr7W5/7dq1HHvssZQoUYJXXnnF3xAXU/k9zqTtKVGiBM2bN2fSpEk5yxKJBJMmTaJNmzbbfE+bNm22Wh9g4sSJ211f2pVxJuXWro6zIUOGMHDgQCZMmLDVHDbStuTV17NEIsGWLVvyI6KKgNyOswYNGvD5558zd+7cnMdJJ53EUUcdxdy5c6lRo8bOffAuTvRX5HTq1Ck4+OCDg+nTpwcffvhhULdu3aB79+45r//0009B/fr1g+nTpwdBEARr1qwJWrduHRx00EHBt99+GyxdujTnEYvFwtoNFXK5HWdBEARLly4N5syZE4waNSoAgvfffz+YM2dOsGrVqjB2QYXM2LFjg5IlSwZPPPFE8NVXXwUXXnhhUL58+WDZsmVBEATBOeecE9xwww0563/00UdBampqMHTo0ODrr78OBgwYEKSlpQWff/55WLugJJDbcbZly5Zgzpw5wZw5c4Jq1aoF1157bTBnzpxgwYIFYe2CkkBux9ngwYODEiVKBM8///xWP4etW7curF1QEsjtOLvzzjuDt99+O/juu++Cr776Khg6dGiQmpoajBo1KqxdUBLI7Tj7X7syK77F/nerVq0KunfvHuy5555B2bJlg549e271jWHhwoUBEEyePDkIgv/eemxbj4ULF4azEyr0cjvOgiAIBgwYsM1x9vjjjxf8DqhQGjFiRLDffvsFJUqUCFq1ahV8/PHHOa+1a9cuOPfcc7da/9lnnw3q1asXlChRIjjwwAOD119/vYATKxnlZpz98bXsfx/t2rUr+OBKKrkZZ/vvv/82x9mAAQMKPriSSm7G2U033RTUqVMnSE9PDypUqBC0adMmGDt2bAiplWxy+/PZn+1KsY8EQRDk9vQCSZIkSZJUOBTpa+wlSZIkSSrqLPaSJEmSJCUxi70kSZIkSUnMYi9JkiRJUhKz2EuSJEmSlMQs9pIkSZIkJTGLvSRJkiRJScxiL0mSdtqiRYuIRCJEIhGaNm2629v7Y1vly5ff7W1JklRcWewlSVKuvfPOO0yaNGm3t7N06VKGDRu2+4EkSSrGLPaSJCnXKlWqRKVKlXZ7O1WrVqVcuXJ5kEiSpOLLYi9JUjH1yy+/ULVqVe68886cZVOnTqVEiRK5Php/3nnn0aVLF+68806qVKlC+fLlue2224jFYlx33XVUrFiRfffdl8cffzyvd0OSpGIvNewAkiQpHHvttRejR4+mS5cuHHvssdSvX59zzjmHPn36cMwxx+R6e++++y777rsv77//Ph999BG9evVi6tSpHHHEEUyfPp1x48Zx0UUX0aFDB/bdd9982CNJkoonj9hLklSMHX/88fTu3ZuzzjqLiy++mD322INBgwbt0rYqVqzI8OHDqV+/Pueffz7169dn48aN3HjjjdStW5d+/fpRokQJPvzwwzzeC0mSijeP2EuSVMwNHTqURo0a8dxzzzFr1ixKliy5S9s58MADSUn57zGDKlWq0KhRo5zn0WiUSpUqsWLFit3OLEmS/ssj9pIkFXPfffcdS5YsIZFIsGjRol3eTlpa2lbPI5HINpclEold/gxJkvRXHrGXJKkYy8zM5Oyzz6Zr167Ur1+fCy64gM8//5y999477GiSJGknecRekqRi7KabbmLNmjUMHz6c66+/nnr16nH++eeHHUuSJOWCxV6SpGJqypQpDBs2jKeeeoqyZcuSkpLCU089xQcffMDDDz8cdjxJkrSTPBVfkqRi6sgjjyQrK2urZTVr1mTNmjW53tYTTzzxl2VTpkz5y7LduYZfkiRtm8VekiTl2qGHHkrTpk2ZOnXqbm1nzz33JBaLkZ6enkfJJEkqfiz2kiRpp+27774sWLAAYJdvi/dnc+fOBbJvhSdJknZNJAiCIOwQkiRJkiRp1zh5niRJkiRJScxiL0mSJElSErPYS5IkSZKUxCz2kiRJkiQlMYu9JEmSJElJzGIvSZIkSVISs9hLkiRJkpTELPaSJEmSJCUxi70kSZIkSUns/wEQM04fRZUmggAAAABJRU5ErkJggg==",
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