{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Beispiel 18.4: Gas-Flüssig-Reaktion 1. Ordnung in einem Rührkesselreaktor\n",
    "Bearbeitet von Franz Braun\n",
    "\n",
    "Dieses Beispiel befindet sich im Lehrbuch auf den Seiten 284 - 287. Die Nummerierung\n",
    "der verwendeten Gleichungen entspricht der Nummerierung im Lehrbuch. Das hier angewendete\n",
    "Vorgehen entspricht dem im Lehrbuch vorgestellten Lösungsweg.\n",
    "\n",
    "Zunächst werden die benötigten Pakete importiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Import\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_bvp\n",
    "from tabulate import tabulate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Reaktionskinetik für die betrachtete Reaktion ($\\mathrm{A_1} \\rightarrow \\mathrm{A_3}$) ist geben als:\n",
    "\n",
    "\\begin{align*}\n",
    "r_\\mathrm{L} = k\\, c_{c_1,\\mathrm{L}}.\n",
    "\\end{align*}\n",
    "\n",
    "Für die Komponenten $\\mathrm{A_1}$ und $\\mathrm{A_3}$ ergeben sich die dimensionslosen Materialbilanzen für eine Reaktion 1. Ordnung im flüssigkeitsseitigen Grenzfilm (Mesoskala) aus Gleichung 18.15a zu:\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\mathrm{d} f_\\mathrm{1,L}^2}{\\mathrm{d}^2\\chi} &=  Ha^2 f_\\mathrm{1,L},\\\\\n",
    "\\frac{\\mathrm{d} f_\\mathrm{3,L}^2}{\\mathrm{d}^2\\chi} &= -Ha^2 f_\\mathrm{1,L}.\n",
    "\\end{align*}\n",
    "\n",
    "Die Materialbilanzen werden in folgender Funktion implementiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def material(X, y):\n",
    "    '''\n",
    "    Dimensionslose Materialbilanz (Mesoskala) für die Reaktion 2.Ordnung (Gleichung 18.15a)\n",
    "    y[0]       : Restanteil von A1\n",
    "    y[1]       : Restanteil von A3\n",
    "    y[2]       : erste Ableitung des Restanteils von A1 nach der dimensionslosen Ortskoordinate\n",
    "    y[3]       : erste Ableitung des Restanteils von A3 nach der dimensionslosen Ortskoordinate\n",
    "    dy2dX2     : zweite Ableitung der Restanteile von nach der dimensionslosen Ortskoordinate (Vektor der Größe 2)\n",
    "    X          : Ortskoordinate\n",
    "    '''\n",
    "    f = y[:2]  # Vektor für die Restanteile von A1 und A2 \n",
    "\n",
    "    dy2dX2 = np.empty_like(y[2:])\n",
    "    \n",
    "    dy2dX2[0] =   Ha**2 * f[0]\n",
    "    dy2dX2[1] = - Ha**2 * f[0]\n",
    "    \n",
    "\n",
    "    return np.vstack((y[2:],dy2dX2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die dazugehörigen Randbedingungen an der Grenzfläche zwischen flüssigkeitsseitigem Grenzfilm und Kernströmung, also für $\\chi = 1$,\n",
    "lauten unter der Annahme $D_\\mathrm{1,L} = D_\\mathrm{3,L}$ (s. Gleichung 18.17):\n",
    "\n",
    "\\begin{align*}\n",
    "f_\\mathrm{1,L}(\\chi = 1) & = f_\\mathrm{1,L,b},\\\\\n",
    "f_\\mathrm{3,L}(\\chi = 1) & = f_\\mathrm{3,L,b}.\n",
    "\\end{align*}\n",
    "\n",
    "An der Stelle $\\chi = 0$ (Phasengrenzfläche) werden gem. Gleichung 18.16 folgende Randbedingungen angesetzt (Erläuterung Lehrbuchtext zu Beispiel 18.4):\n",
    "\n",
    "\\begin{align*}\n",
    "f_\\mathrm{1,L}(\\chi = 0) & = f_\\mathrm{1,G,b},\\\\\n",
    "\\frac{\\mathrm{d} f_\\mathrm{3,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 0}\\normalsize & = 0.\n",
    "\\end{align*}\n",
    "\n",
    "Für die Berechnung der erforderlichen Restanteile von $A_1$ und $A_3$ in der Kernströmung der Flüssigkeit $f_{i,\\mathrm{L,b}}$ werden die Bilanzgleichungen auf der Reaktorskala (Mesoskala) auf Basis von Gleichung 18.38b formuliert. Es wird angenommen, dass $c_\\mathrm{1,L,e} = c_\\mathrm{3,L,e} = 0$. Es ergibt sich:\n",
    "\n",
    "\\begin{align*}\n",
    "0 &= - f_\\mathrm{1,L,b} - \\frac{Da_\\mathrm{I}}{Hi \\, Ha^2} \\frac{\\mathrm{d} f_\\mathrm{1,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 1} \\normalsize - Da_\\mathrm{I} \\frac{Hi - 1 }{Hi} f_\\mathrm{1,L,b},\\\\\n",
    "0 &= - f_\\mathrm{3,L,b} - \\frac{Da_\\mathrm{I}}{Hi \\, Ha^2} \\frac{\\mathrm{d} f_\\mathrm{3,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 1} \\normalsize + Da_\\mathrm{I} \\frac{Hi - 1 }{Hi} f_\\mathrm{1,L,b},\n",
    "\\end{align*}\n",
    "\n",
    "bzw. nach dem Restanteil in der Kernströmung $f_{i,\\mathrm{L,b}}$ umgestellt:\n",
    "\n",
    "\\begin{align*}\n",
    "f_\\mathrm{1,L,b}&=  - \\frac{Da_\\mathrm{I}}{Hi \\, Ha^2} \\frac{\\mathrm{d} f_\\mathrm{1,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 1} \\normalsize - Da_\\mathrm{I} \\frac{Hi - 1 }{Hi} f_\\mathrm{1,L,b},\\\\\n",
    "f_\\mathrm{3,L,b}&=  - \\frac{Da_\\mathrm{I}}{Hi \\, Ha^2} \\frac{\\mathrm{d} f_\\mathrm{3,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 1} \\normalsize + Da_\\mathrm{I} \\frac{Hi - 1 }{Hi} f_\\mathrm{1,L,b},\n",
    "\\end{align*}\n",
    "\n",
    "Die Randbedingungen werden in der Funktion _bc_material_ implementiert, die auch die Berechung der Restanteile in der Kernströmung enthält."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bc_material(y0, y1):\n",
    "    '''\n",
    "    Randbedingungen der Materialbilanz\n",
    "    y0    : Randbedingungen bei X = 0; \n",
    "                Vektor der Größe 4 : (Restanteil A1, Restanteil A3, Ableitung des Restanteils A1 nach der Ortskoordinate, Ableitung des Restanteils A3 nach der Ortskoordinate)\n",
    "    y1    : Randbedingungen bei X = 1;\n",
    "                Vektor der Größe 4 : (Restanteil A1, Restanteil A3, Ableitung des Restanteils A1 nach der Ortskoordinate, Ableitung des Restanteils A3 nach der Ortskoordinate)\n",
    "    f_L_b : Restanteil von A1 und A3 in der Kernströmung\n",
    "    f_G_b : Restanteil von A1 und A3 im Bulk des Gases\n",
    "    '''\n",
    "\n",
    "    # Berechnung der Restanteile in der Kernströmung der Flüssigkeit f_L_b (Bilanz Makroskala)\n",
    "    f_L_b    = np.zeros(2)\n",
    "    f_L_b[0] = - Da_I / (Hi * Ha**2) * y1[2] - Da_I * (Hi - 1) / Hi * y1[0]  # Restanteil von A1 in der Kernströmung\n",
    "    f_L_b[1] = - Da_I / (Hi * Ha**2) * y1[3] + Da_I * (Hi - 1) / Hi * y1[0]  # Restanteil von A3 in der Kernströmung\n",
    "\n",
    "\n",
    "    BC = np.empty(nu.size *2)  # 2 Randbedingungen (RB) pro Komponente\n",
    "    # A1\n",
    "    BC[0] = y0[0] - f_1_G_b    # RB an der Stelle X = 0 für Komponente A1 : 0 = f_1,L(X = 0) - f_1,G,b\n",
    "    BC[1] = y1[0] - f_L_b[0]   # RB an der Stelle X = 1 für Komponente A1 : 0 = f_1,L(X = 1) - f_1,L,b\n",
    "    # A3\n",
    "    BC[2] = y0[3]              # RB an der Stelle X = 0 für Komponente A3 : 0 = df_3dX(X = 0)\n",
    "    BC[3] = y1[1] - f_L_b[1]   # RB an der Stelle X = 1 für Komponente A3 : 0 = f_3,L(X = 1) - f_3,L,b\n",
    "    \n",
    "    return BC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Danach werden die stöchiometrischen Koeffizienten gemäß der Reaktionsgleichung, die Hatta-Zahl und der Restanteil von $A_1$ in der Kernströmung des Gases parametriert. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ha          = 0.3                 # Hatta-Zahl\n",
    "nu          = np.array((-1, 1))   # Stöchiometrische Koeffizienten für A1, A3 \n",
    "f_1_G_b     = np.array((1))       # Restanteil von A1 in der Kernströmung des Gases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da der Einfluss verschiedener  Dammköhler-Zahlen $(Da_I)$ und Hinterland-Verhältnisse $(Hi)$ betrachtet werden soll, erfolgt die Variation von $Da_I$ und $Hi$ jeweils in einer For-Schleife. Die Profile der Restanteile werden durch den Aufruf eines Solvers für Randwertprobleme (solve_bvp) auf Grundlage der Materialbilanzen und der Randbedingungen berechnet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Da_I_vec   = np.array((1, 3, 10))              # Vektor mit Dammköhler-Zahlen für Beispiel 18.4\n",
    "Hi_vec     = np.array((1, 10, 100, 1000))      # Vektor mit Hinterland-Verhältnissen für Beispiel 18.4\n",
    "\n",
    "Lösungen_Hi = []                               # Leere Liste zum Speichern der Lösungen für die verschiedenen Hinterland-Verhältnisse\n",
    "Lösungen_Da = []                               # Leere Liste zum Speichern der Lösungen für die verschiedenen Dammköhler-Zahlen\n",
    "N           = 101                              # Diskretisierung\n",
    "X           = np.linspace(0, 1, N)             # Diskretisierung der Ortskoordinate\n",
    "init_f      = np.ones((2, N))                  # Startwerte für Restanteile\n",
    "init_df     = np.ones((2, N))*1e-5             # Startwerte für die Ableitungen der Restanteile\n",
    "init        = np.vstack((init_f, init_df))     # Zusammengefügte Startwerte für die Iterationen des Solvers\n",
    "\n",
    "\n",
    "for HiHi in Hi_vec:\n",
    "    Da_I = Da_I_vec[1]\n",
    "    Hi   = HiHi\n",
    "    sol  = solve_bvp(material, bc_material, X, init , max_nodes = 1e10, tol = 1e-10)\n",
    "    if sol.success == False:\n",
    "        print(sol)\n",
    "    Lösungen_Hi.append(sol)\n",
    "\n",
    "\n",
    "for DaDa in Da_I_vec:\n",
    "    Hi   = Hi_vec[2]\n",
    "    Da_I = DaDa\n",
    "    sol  = solve_bvp(material, bc_material, X, init , max_nodes = 1e10, tol = 1e-10)\n",
    "    if sol.success == False:\n",
    "        print(sol)\n",
    "    Lösungen_Da.append(sol)\n",
    "\n",
    "Lösungen_Hi = np.array((Lösungen_Hi))\n",
    "Lösungen_Da = np.array((Lösungen_Da))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Abschließend werden die Ergebnisse grafisch veranschaulicht."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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jR9vbUmfNBUxKSoq9/cUXXzQ+Pj5m5MiR9rbY2FgTFBRkSpYsaaLTzZo7ceJEU7VqVfP222/b21JSUsxDDz1k6tevb86ePWtvnzdvnmnTpo35+OOPHWrr27ev6d27tzl16pS9bfPmzWbo0KFm9uzZDn0/+ugj89577zn03bdvn5k+fbrZsGGDQ9/w8HCzevVqc/78eXvb6dOnzfbt283By2as/ffff82xY8dMfHy8vS0pKckkJCQ47BuR/CD9LKnp/z3nFZrV/Nr3wTefrjTfUssYMGdsBc2Z8F25U6CIs1y8aMy//zrOym+MMevWGTN3rjHpfj4127cb83//Z8ynnzr2ffJJawb99DPlz51rjLu7NeN+enfdZc3iv359WtvSpVbbZT8bmrp1rfb0M+hv2GC1Vark2Ld1a2OKFDFmwYK0tn37jGnZ0ph+/Rz7LlpkzIcfGrN3b1pbbKwxO3YYc+CAkfwrPx2vb8mh5jNmzODee++1v/fx8WHevHkAuKa7n+jJJ5/kvvvuo0K6iU9cXV2ZPXu2fb1U7du3p0KFCtyZfuITYPr06RhjKJhuyE7z5s0pVqwYd9xxh0PfDz74gISEBIoVK2Zvq1+/PpMmTcrQd9SoUURHR1Mi3f1k9957L2+//Ta33367Q99BgwZx9uxZSqe7b6xy5cq8+uqrlLtsopVu3brx77//Uib1/iSgTJkyPPfccw5tAI888ggVK1Z0+NyiRYvSoUMHSl422UudOnXw9PR0aC9QoAANGjQgMP0wMKB8+fLUqlWLoukml3F3d6dSpUoUKlTIoW/BggUJDg7Gz8/P3maMoUCBAnin3gt1ScqlWWjT/xknX3ouq81mw5buXqm4uDhiY2MdRkAkJibanyPvku4s87///suePXs4kW6W1ZSUFL69NEtscrpnv/7+++8sXrzY4c8Y4IsvviA+Pp7XXnvN3rZt2zbefvttunTpQsd09/eNGDGCM2fO0Lx5c4pcOlu+YcMG+vTpQ9u2bWnQoIG9b/fu3Tl69Cjbtm2z/51ftWoVXbt2pXHjxqxdu9bet1GjRvz+++9s3LiR+peG2y1dupR27drxwAMP8P3339v7NmzYkF9//ZVvvvmG0NBQAL7//nueffZZqlSpwty5c+19hwwZwm+//cZrr73GQw89BFijKP73v/9RokQJxowZY++bOiqiffv29mcDnzx5krlz51KwYEGefPJJe9+tW7cSERFB9erV7X834+Li2LNnD15eXlRNHWYHnD9/nqSkJPz8/PBKPwxQRG56nZ5uzqeRsbi9+D/uN7s43agRkd9tIuCBqv+9ssjNyMvLcWK3VJeOxw5q1bJel/vyy4xtjz9uvVJn7U81f741iV2VKmltd91lXUm/fBK++vWtoeulSqW1GWNdtb/sZx9On7Ze6Z04AcuWOU46CNYM/qtXWxPeVa5ste3bZ21b8eLWcPxU3brBqlXwzjvw1FNW27//Qr9+Vr3pR3CuXWtdna9XL214fmKida++n1/mcy6IXK8cPw2Qh+gKwq0tJSXFJCUlmaR0zyBNTk42Z8+edbh6bIx1VfjPP/80p0+ftrclJSWZXbt2me3bt5vk5GR7+8GDB8369evNH3/84fC58+bNM7Nnz3Z4TuOOHTvMlClTzMaNGx2+7+233zZvvvmmw9/NDRs2mMGDBzuMEjDGujrepUsX8++//9rbli9fbpo1a2ZGjRrl0LdFixamZs2a5vfff7e3zZs3z5QsWdJ06dLFoW/VqlWNq6ur+e677+xtc+fONYCpX7++Q9/q1asbwKxZs8betmLFCgOYWrVqOfR94IEHDGAWLlxob9u4caMBTKXLzn43btzYAObLL7+0t23bts0AplSpUg5927RpYwAzefJke9vevXsNYAoXLuzQ98knnzSAeffdd+1tR44cMR4eHhn6vvbaa6ZixYoOnxsZGWkaNmxomjVr5vD3Z/bs2aZ3794Ooz4SExPNqFGjzFtvveXwZ79r1y4za9Yss3PnTofv+/77781PP/3kMNomKirKRERE5Mkzu/lFfjqDnl9ldR+8N3ym2UY1Y8BEuBQ1F7b9/t8riYjz/POPdcU93ag8c+yYMVOnGnPZzz5m7FhjHn/cmG+/TWvbvt2YEiWMqVnTsW+LFtYV9i++SGv7+WerLTDQsW+nTlb7hAlpbYcOWW3e3o59X3jBmDJljEn384GJjDSma1dj+vY1Jv3owK1bjZk92/EKfXKyMcePGxMd7dhXrio/Ha8VvEXkihISEszZs2cdbqswxhrOv2fPHhMVFWVvO336tAkPDzc//vijQ981a9aYmTNnmr///tve9vfff5tx48aZTy8b+vbxxx+bAQMGmG3bttnb9u/fbx5//HHTp08fh74vv/yyqVOnjlm8eLG97ffffzelSpUyd999t0PfJ554wgBm4sSJ9raDBw8awPj5+Tn07dmzpwHMmDFj7G3Hjx/P9JaEAQMGGMC8+uqr9rYLFy7Y+8bExNjb/+///s8AZuDAgfa2lJQUe9+TJ0/a2//3v/8ZwDz99NMOtd12223G39/fHD582N42c+ZMU61aNYcajDGme/fupkOHDubIkSP2ti1btpiXX345w8mcr7/+2nzxxRcOJ6COHz9uNm3aZPam/6HBGHPixAlz8uRJk5iYaG5m+elAnl9dzz4Y+fxks5OqxoA54RpoYnbv/++VRCR/+fdfK9Cnu3hiTp40ZsoUK9Sn9957xrRpY8zKlWltf/xhTOHCVqhP74knrEA+fnxa299/W22eno59n33Wak93y6I5d85qA2PS3dZn3n3XmFq1jEl/G2JSkjEvvmjMG29YtxakOnDAmE2bjEn3c4AxJl8H+fx0vFbwFpFbQnJyssPV6sTERHPkyBFz6NAhh34HDhwwmzdvdgi3MTExZtasWWbGjBkOfVevXm3efPNNEx4e7tD3mWeeMU899ZTD93366aemUaNGDvf3JyQkmPLly5syZco4/L/0xhtvZDpnhKurqwHMP//8Y2+70pwRAQEBBjD79u2zt02aNMkApn379g59g4ODDWB27Nhhb5s+fboBTNOmTR36VqhQwQBm06ZN9rbFixcbf39/07JlS4e+Xbp0Mffff7/DyZjdu3ebbt26mTfffNOh74wZM8y4ceMc5rg4deqUWbRokcN3GWONVvjzzz9v6ACc/kAeERHhcEIlPj7eREdHO4xYSF0nOjraYcRLQkKCiY6ONhfT/2CUxb4xMTEmOjra4e/LmTNnbvnj1fUes1986j3zC5WNAXPcrbi5uOfgf68kIvJf/v7bupKdbt4mc/asMePGWVfk03v3XWPq13e8cn/0qDE2mzEeHo59+/a1wni6+afM+fNpIT39MWPoUKtt0KC0tuRkY9zcjAkIMCb9CM5Zs6yTCp995vh9kycbM22adeU9/Xb8/bcxFy78937IZQreNykFbxG5WaTeGpHe4cOHzf79+x2uNh8+fNisWbPG/Pzzzw59P//8c/PBBx84TKz33XffmSFDhphp06Y59O3WrZtp3ry5w0mI+fPnm4oVK5revXs79E2drDF9mP76668NYBpdNiHPXXfdZQATFhZmb1uyZIkBTJ06dRz61qlTxwBmyZIl9rawsDADmLvuusuhb6NGjQxgvv76a3vb1q1bjaurq6lcubJD3wEDBph77rnHYWTEkSNHTIcOHewH8stHHIwePTrTEQc+Pj4GcNhP77//vgFM586dHfoWKVLEAGbPnj32tqlTpxrAtG7d2qFvmTJlDGB++umnDH1v5ePV9R6zU1JSTJ92o81vVDQGzL/uJUzcH4dypkgRkaxITnYMvMZYw9GXLTMm3W2BJirKuuJ9+RD2t94ypkIFY955J60tMjItpMfGprX/3/9ZbelG2pnkZCv8gzEnTqS1jxljtfXo4VhbzZrW6+jRtLaNG61h93PnOvYNDzfmu++MSTfaLzuuxOen4H1LTq4mIpLX2Ww2h4kAgQwTHKa2Zdbes2fPDG316tWjXr16GdpnzJiRoa19+/a0b98+Q/uBAwdITk52mIywVatW7N+/H4/0z8UFJk2axLlz57j77rvtbZUrV2bcuHEZJlV89NFHqVixosO2+Pr6Urdu3QwTRnp5eeHn5+cwgWJcXBzJycn2SRRT7d+/n507dxIZGWlvO3XqlMMEgJK/2Gw2Pp7/Ct2bXOTV9XOpmHiAf6s/TNHfvsP9Dk2UJCJO5OLi+Gg4sCaLS50wLlWBAtbkcJcbOtR6pefnB8eOWc+GTz+BbLt2UKZM2qRxYE0c99hjVl9//7T25OSMj+UzBnbvtn5N//PIjz/Ce+9B9+7WZHyp2raFyEhr0rvUyfGmTIHBg6FjR0j/s0aPHtZz5MeOtR6lB/DHH/D991C+vDVJX6p0kxcTE2M93i/1Z5CEBGub3NysRwCm7wfg7Z322L3ERKu/q6vjfspK39hYa394eaXtk3QTMf+nXDgRkGfoireISP4UHx9vjh496nBPuzHG7Ny506xcudIcTXe2/vjx42bs2LEaap7H3egxOykpyTxW9yVzgNuNAfOPd1mT9Pc//72iiMitKt0xyyQnW1ewV60yJt0EsCYszLoa/803juvee68xd9zheCX97betK+ndujn2LVjQak9/lX/KFKutTRuHrtGlSqVd8Qbrfv1Uo0db61w2Qs34+Fjt6W8nfP99q+2yEWqmSBGrPd0INTN1qtV22Qg1U6aM1Z5uhFpkFkao6Yq3iIjc9Dw8PDI8xhCwP5YuveLFizNgwACGDRsGWFfW01/B9/DwyHD1PrXf5dzd3XF3d7+hvukfTZnKzU2H5xvl6urKrE3/o+29iXzwy2Juv3iYf6rUJ3jft7iUyORRTCIit7p0j8vFxcV6zNrlGja0Xpfbti1jW79+1tXuy499778P589DcHBaW4kS8MgjULu2Y9/ExGsuP6+zGWOMs4vILVFRUQQEBBAZGYl/+uEVIiJyS4mJicHPzw+A6OjoTIOyM+l4lX374OLFi7Sq/jKfHVhKGY7wj38FSuzbjK144H+vLCIiTuVwvI6IwLdo0Tw11Dzq7FkCbrvtmo5VLlddKiIiInIT8/b2ZuGOMTxVuiVHKUnJqP0cq9wQc+q0s0sTEZGs8PVNC90AHh5WW/rQndrP19fxCr67u9WWPkhnta+Pj9We/p73LIxQU/AWERGRfK1AgQIs2DWKzoEt+ZcgSp7fa4Xv02ecXZqIiNwiFLxzybPPPkuXLl2cXYaIiMgtqXDhwszdNZx2BdtwgkBKnvmVY1VD4dw5Z5cmIiK3AAXvG1S/fv1MH9vz8ccf4+fnZ3+0zdixY5k6dWpulyciIiKXBAUFMXvXy7T2a89JilIyYjfHqja2HoEjIiKSgxS8b4Axhl27dlGrVq0My7Zv306NGjVwuXS/QOHChfPc5D0iIiK3mrJlyzJj2wAe9e7AKYpQ4t8d/FutKURFObs0ERHJxxS8b8CBAwe4cOHCFYN3avvhw4ex2WwcPnw4lysUERGRy1WqVImpPzxNC/fOnKEwwUe28m/N5hAd7ezSREQkn1LwvgE7duzA1dWV6tWrO7RfvHiRvXv3cs899wDw888/U7BgQcqWLZvp54wZMwY/P7+rvo4cOZLTmyMiInLLqFGjBhM2dKS5a3fOUZDgv37geK0WaY+WERERyUbXPv+5ZLBz506Sk5Px8fHJdHlq8N69ezfVqlW74uf06dOHDh06XPW7gtM/YF5ERERuWL16D/C/VbE0a+rKWjOVoP3fcuK+lhTfttx6bIyIiEg2UfC+ATt37qRt27a8/vrrDu2zZ8/mgw8+oEqVKoB1xbtGjRpX/JzChQtTuHDhnCxVREREMtG4cSjRC6Jp1s6VNXxM8b0biKjbmsAfl4K3t7PLExGRfEJDzW/Azp07adCgATVq1HB4nT17lmrVquF66eHqu3fvzjAcPT0NNRcREXGetm3b0HdGVZozgGh8CfxlPScfbAdxcc4uTURE8gld8b5Of/31F+fPn7cPJ09v586d1KlTB4CoqCgOHz581SveGmouIiLiXN26PcmFC1No0X8Iq3iPYjtXc6rBYxTdtAA8PZ1dnoiI3OQUvK/Tjh07cHFxyRCoExMT2bNnD3379gWsYeaurq7cddddV/wsDTUXERFxvn79+hAV9S6PvvIyK3iboltXcLpRR4qEzwUPD2eXJyIiNzENNb9OO3fu5M4778TPz8+hfe/evcTHxzvMaF6pUiU8dbZcREQkzxs27EXqDE2mFa9wES+KfL+EM02egMREZ5cmIiI3MZsxxji7iNwSFRVFQEAAkZGR+Pv7O7scERFxkpiYGPuJ0+joaHx9fZ1ckSMdr5y7D4wxPPfcEP6aUoyljMSTBM42epzCq2eBmwYLiojklvx0vNYVbxEREZF0bDYbkya9R5HOh2jLKOLxoHDYPM617ApJSc4uT0REbkIK3iIiIiKXcXFxYcaMj3Fv9SuPMZoE3Cm0ejbn2/WA5GRnlyciIjcZBW8RERGRTLi5uTFv3hdcbLSVjvyPRNwouOwrIh/vBSkpzi5PRERuIgreIiIiIlfg4eHB0qUzOXH/Rp5gLEm4ErBoBlFPPKPwLSIi10zBW0REROQqfHx8WLPmGw5WX0MX3iIZF/znfs6Frn0VvkVE5JooeIuIiIj8B39/f8LCZrO7wnK6Mo5kXCgwayoxPfrDrfOAGBERuU4K3iIiIiLX4LbbbmPjxm/4ocwievA2KdjwnTmZ2KefV/gWEZGrUvAWERERuUZBQUFs3PgV64ovoBfjAPD54iMu9hms8C0iIlek4C0iIiKSBWXLlmXjxuksLTyPp3kHAO+pE4kb8JLCt4hkUL9+fWw2GzabDTc3N4KCgmjXrh0//vijs0uTXKTgLSIiIpJFFStWJDx8KnMLzOXZS1e+vSa9R/yQYQrfImJnjGHXrl289dZbHD9+nIMHDzJr1ixcXFx46KGHWLdunbNLlFyi4J0Pbd68mZYtWxIcHIzNZmPx4sXOLklERCTfqV69OmvXfsCX3vPpx1sAeE54m4SXX1P4FhEADhw4wIULF3j44YcpXrw4ZcuWJSQkhHnz5lG3bl1effVVe98RI0Zw99134+vrS2BgIH379iUxMdGJ1Ut2UvDOh2JiYqhevTqTJk1ydikiIiL52v3338/y5WP51H0hzzMWAI93x5D46kjnFiYiecKOHTtwdXWlevXqDu02m43GjRuze/duwLoybozhk08+Ye/evUyfPp0FCxbw2WefXdP3jBkzBj8/v6u+jhw5kt2bJ1ng5uwCJPs1b96c5s2bO7sMERGRW0LDhg1ZuHA4bdqMwTV5DO/zCu5jR5Ho5or7qNedXZ6IONHOnTupWLEiPj4+GZZ5eHjg7u4OWEF81KhR9mVlypQhNDSUffv22duKFCnC6dOnM/2ePn360KFDh6vWEhwcfD2bINlEwTsLjDHExsbm+vf6+Phgs9ly/XtFRETk2jz66KN8/XUMnTp9iCujeZfXcH9zBElurri9/up/f4CI5Es7d+6kVq1amS7bt28flSpVAuDvv/9m3LhxbNq0iWPHjpGYmEhcXBxvvfXWNX1P4cKFKVy4cLbVLdlPwTsLYmNj8fPzy/XvjY6OxtfXN9e/V0RERK5dx44diY6O5umnv8SNN3iLEbiNeI1kNzdcXxnq7PJExAl27txJy5YtM7THxMSwdOlShgwZwqlTp6hduzYNGzZk/PjxlChRguTkZO69994MQ9SvZMyYMYwZM+aqffbu3Uvp0qWvazvkxil4i4iIiGSTXr16ER0dzaBBy3FlJP9jJK6v/h/Jbq64vvyis8sTkVz0119/cf78ee655x6H9uTkZPr06YO3tzf9+vVjwYIFJCcn880339hHuX700UckJiZSo0aNa/ouDTXP+xS8s8DHx4fo6GinfK+IiIjcHAYOHMiFCxcYPvwHXHmdUYzCdehLpLi64vLCYGeXJyK5ZMeOHQAEBQVx4sQJoqKi2LFjBxMnTuTo0aMsX76cgIAAbrvtNqKioli6dClVqlRh2bJljB07lhIlSlC0aNFr+i4NNc/7FLyzwGazaci3iIiI/KdXX32VqKihvPnOz7jxCq8zBpcXh5Di5orLwOedXZ6I5IKdO3cCUKFCBVxdXSlYsCAVK1akVatW9OnTxx6UW7ZsSa9evejatSve3t48+eSTdOjQgb///tuZ5Us2sxlz6zxoMioqioCAACIjI/H393d2OTkmOjqagwcPAlCzZk3Gjx9PSEgIhQsX1n0dIiJY99alztmRF+fRuFWOV1eTH/aBMYZ+/foxefJJRnMnr1561rf58CNs/fs5uToRudlcbVbz/Co/Ha/1HO98aPv27dSsWZOaNWsCMGTIEGrWrMnrr+uRJiIiIrnFZrPx0Ucf0bWrD6/xN2/xstU+oD9m8hQnVyciIrlJQ83zoQYNGnALDWQQERHJs1xcXPjiiy+IienIsIUnceElXuYdbM/1xbi4YHv2GWeXKCI3iVvtand+oyveIiIiIjnIzc2NWbNm0bTpcYYSyXisCdZsfZ6Fzz93cnUiIpIbFLxFREREcpinpycLFy7koYd+5wUSmcBAAEzv3jBtmpOrExGRnKbgLSIiIpILfHx8WL58Offe+yODceMDBmAzBtOrF8yY4ezyREQkByl4i4iIiOQSf39/Vq9eTdWqaxhIASbxnBW+e/SAr75ydnkiIpJDFLxFREREctFtt93GunXrKF9+LgMoyhSexWYMKd26w6xZzi5PRERygIK3iIiISC4rXrw4YWFhlCw1jecow6c8jYtJIeXJrjBnjrPLExGRbKbgLSIiIuIEpUuXJixsPUWLTeRZKvE5Pa3w3bkLzJvn7PJERCQbKXiLiIiIOMmdd95JWNh6ChYaQ29qMI2ncElJJqXTE7BggbPLExGRbKLgLSIiIuJEVatWZe3aNfj6vcbT3M8Mulnhu2MnWLjQ2eWJiEg2UPAWERERcbJ7772XlSuX4+E1hJ404EuexCU5iZQOHWHxYmeXJyIiNyhPBe+xY8dSu3ZtChQoQLFixWjTpg379u276jrTp0/HZrM5vLy8vHKp4rxp8+bNtGzZkuDgYGw2G4svO2AbY3j99dcJCgrC29ub0NBQDhw44JxiRUREBICHHnqIJUsW4er+HE/RlK/pbIXvxzvA0qXOLk9E8pn/ygySvfJU8N60aRP9+vXjxx9/ZN26dSQmJtKkSRNiYmKuup6/vz/Hjx+3v/7+++9cqjhviomJoXr16kyaNCnT5ePGjeODDz5gypQpbN26FV9fX5o2bUpcXFwuVyoiIiLpNWnShLlzvwGXXnSnFd/QCZekRFLaPwbLlzu7PBHJR/4rM0j2cnN2AemtXr3a4f306dMpVqwYO3bs4OGHH77iejabjeLFi+d0eTeN5s2b07x580yXGWOYMGECr732Gq1btwZg5syZBAYGsnjxYjp16pSbpYqIiMhl2rRpw5dfTqNLl2505RtcSKFj0lxS2rXHZfEiaNHC2SWKSD5wtcwg2S9PBe/LRUZGAlC4cOGr9ouOjqZMmTKkpKRwzz33MGbMGO66664r9o+KinJ47+npiaen53/WY4whMTHxGirPXu7u7thstmz5rEOHDnHixAlCQ0PtbQEBAdSpU4ctW7YoeIuIOEF8fDzx8fH295cfp+TW07lzZ2JiYnjmmSfownxcSOHxxPmktGmLy5LFoB+WRfIkYwyxsbFO+W4fH59sywyS/fJs8E5JSWHQoEHUq1ePqlWrXrFfxYoV+eKLL6hWrRqRkZG8++67PPDAA/z222+ULFky03VKlSrl8H7EiBGMHDnyP2tKTExk7NixWdqO7DBs2DA8PDyy5bNOnDgBQGBgoEN7YGCgfZmIiOSusWPH8sYbbzi7DMljevfuTXR0NEOGPE5nFuJCCu0TF1rhe+kSaNrU2SWKyGViY2Px8/NzyndHR0fj6+vrlO+W/5Zng3e/fv3Ys2cP33333VX71a1bl7p169rfP/DAA1SuXJlPPvmEN998M9N1jh49ir+/v/39tVztFhERySnDhg1jyJAh9vdRUVEZThLLrWnw4MFER0fz+uuP0YklzMHQLmERKa1a47JsKTRp4uwSRUTkGuTJ4N2/f3+WL1/O5s2br3jV+krc3d2pWbMmBw8evGIff39/h+Cdlc8eNmxYlte7Ue7u7tn2Wan3wkdERBAUFGRvj4iIoEaNGtn2PSIicu2u9ZYnuTW99tprREdHM25cWzqxlLmk0CZhiRW+ly+DdLePiYhz+fj4EB0d7bTvlrwrTwVvYwwDBgxg0aJFbNy4kXLlymX5M5KTk/n1119pkQMTj9hstmwb8u0s5cqVo3jx4oSFhdmDdlRUFFu3bqVv377OLU5EREQysNlsvPXWW0RHR/Pxx63pwErmk0Kr+GWkPNoSlxXLoVEjZ5cpIlj/XjXcWzKTp4J3v379mDVrFkuWLKFAgQL2e44DAgLw9vYGoFu3bpQoUcJ+r/WoUaO4//77KV++POfPn+edd97h77//5umnn3badjhbdHS0wxX/Q4cOsXv3bgoXLkzp0qUZNGgQo0eP5s4776RcuXIMHz6c4OBg2rRp47yiRURE5IpsNhsffvghMTExzJjRkg6sZB6GlvHLrfC9cgWEhDi7TBG5ifxXZpDslaeC9+TJkwFo0KCBQ/u0adN46qmnADhy5AguLmmPHz937hy9e/fmxIkTFCpUiFq1avHDDz9QpUqV3Co7z9m+fTsh6Q6+qfcNdu/enenTp/Pyyy9fmin1Gc6fP8+DDz7I6tWr8fLyclbJIiIi8h9cXFz47LPPiImJYf78R3mc1SwghUfiVpLS4hFcVq2Ey36GEhG5kv/KDJK9bMYY4+wicktUVBQBAQFERkZe1z3eIiKSP8TExNhnnc2Ls8DqeKV9cDUJCQm0bduWlSu34m1by3zzGi1YRYq3jxW+69d3dokiItkiPx2vXa66VERERETyFA8PD+bPn09ISDUummY8ZnuL1TTF5WIsKc1bwObNzi5RREQuo+AtIiIicpPx9vZm6dKl3H//HVw0TWnvMp41NEkL3//xOFYREcldCt4iIiIiNyE/Pz9WrlxJjRrFiU1pQnuXD1hHKC6xMaQ0aw7ff+/sEkVE5BIFbxEREbkukyZNomzZsnh5eVGnTh1++umnq/afMGECFStWxNvbm1KlSjF48GDi4uJyqdr8qVChQqxdu5bKlf2JSWlMe9ePWU8jXGKiSWnaDH74wdkliogICt4iIiJyHebMmcOQIUMYMWIEO3fupHr16jRt2pSTJ09m2n/WrFn83//9HyNGjOD333/n888/Z86cObzyyiu5XHn+U7RoUdatW8ftt7tzIbkJ7Vw/IYyGaeF7yxZnlygicstT8BYREZEsGz9+PL1796ZHjx5UqVKFKVOm4OPjwxdffJFp/x9++IF69erRuXNnypYtS5MmTXjiiSf+8yq5XJsSJUoQFhZGyZJJXEhuSju3zwknBJfoC6Q0aQo//ujsEkVEbmkK3iIiIpIlCQkJ7Nixg9DQUHubi4sLoaGhbLnC1dUHHniAHTt22IP2X3/9xcqVK2nRosVVvysqKsrhFR8fn30bks+ULVuW9evXU6zYBaKSmtLObTobaIBL9AVMk6awdauzSxQRuanFx8dnOC5dKwVvERERyZLTp0+TnJxMYGCgQ3tgYCAnTpzIdJ3OnTszatQoHnzwQdzd3bnjjjto0KDBfw41L1WqFAEBAfbX2LFjs2078qOKFSuyfv16ChU6RWRSM9q6fckmHsZ2IQrTpAlohIGIyHUbO3aswzGpVKlS17yugreIiIjkuI0bNzJmzBg+/vhjdu7cycKFC1mxYgVvvvnmVdc7evQokZGR9tewYcNyqeKb1913382aNWsoUOAfIpNa0MbtGzbzELaoS+F72zZnlygiclMaNmyYwzHp6NGj17yuWw7WJSIiIvlQkSJFcHV1JSIiwqE9IiKC4sWLZ7rO8OHD6dq1K08//TRghcOYmBieeeYZXn31VVxcMr8W4O/vj7+/f/ZuwC2gdu3arFixgqZNm3L+4iO0dlvFkqQOPBz5LaZxY2zr18O99zq7TBGRm4qnpyeenp7Xta6ueOdDmzdvpmXLlgQHB2Oz2Vi8eLHDcmMMr7/+OkFBQXh7exMaGsqBAwcc+pw9e5YuXbrg7+9PwYIF6dWrF9HR0bm4FSIikld5eHhQq1YtwsLC7G0pKSmEhYVRt27dTNeJjY3NEK5dXV0B67gk2e+hhx5iyZIleHjs5XxSS9q4zeM76mGLjMQ0bgw7dji7RBFxksmTJ1OtWjX7yc26deuyatUqZ5eVryl450MxMTFUr16dSZMmZbp83LhxfPDBB0yZMoWtW7fi6+tL06ZNHZ6l2qVLF3777TfWrVvH8uXL2bx5M88880xubYKIiORxQ4YM4dNPP2XGjBn8/vvv9O3bl5iYGHr06AFAt27dHIaFt2zZksmTJzN79mwOHTrEunXrGD58OC1btrQHcMl+jRs3Zt68ebi67uJcUmtauS20wvf585jQUIVvkVtUyZIleeutt9ixYwfbt2+nYcOGtG7dmt9++83ZpeVf5hYSGRlpABMZGensUnINYBYtWmR/n5KSYooXL27eeecde9v58+eNp6en+eabb4wxxuzdu9cAZtu2bfY+q1atMjabzRw7dizXahcRySnR0dEGMICJjo52djkZ3CzHqw8//NCULl3aeHh4mPvuu8/8+OOP9mX169c33bt3t79PTEw0I0eONHfccYfx8vIypUqVMs8995w5d+5cpp99s+yDm8U333xjbDabgQdMIbdT5jseMAZMSqFCxuzY4ezyRCQPKFSokPnss8+cXYaD/HS81j3eWWAMxMbm/vf6+IDNlj2fdejQIU6cOOHwCJiAgADq1KnDli1b6NSpE1u2bKFgwYLcm+7er9DQUFxcXNi6dStt27bNnmJEROSm1r9/f/r375/pso0bNzq8d3NzY8SIEYwYMSIXKpPLderUidjYWHr16sW5pPa0dF3CsuTW1Dv3AyY01Lrn+557nF2myE3PWXkBrj8zJCcnM2/ePGJiYq54u5DcOAXvLIiNBT+/3P/e6Gjw9c2ez0p9zMvVHgFz4sQJihUr5rDczc2NwoULX/ExMSIiIpK39ezZk9jYWAYMGMC55A60dF3K8uSWPHBuixW+w8KgZk1nlylyU3NWXoCsZ4Zff/2VunXrEhcXh5+fH4sWLaJKlSo5V+AtTvd4i4iIiNwi+vfvz1tvvQVs4FzyEzzquoIt3I/t3Dnrnu/du51doojkkooVK7J79262bt1K37596d69O3v37nV2WfmWrnhngY+PdSbJGd+bXVIf8xIREUFQUJC9PSIigho1atj7nDx50mG9pKQkzp49e8XHxIiIiMjNYejQocTExPDmm29yLrkLj7isYGVKC+4/uxXTqJF15fvSzwQikjXOygup350VHh4elC9fHoBatWqxbds2Jk6cyCeffJID1YmCdxbYbNk35NtZypUrR/HixQkLC7MH7aioKPuZLoC6dety/vx5duzYQa1atQAIDw8nJSWFOnXqOKt0ERERySZvvPEGMTExjB8/nnMpPWjhsopVKc2oc/YnK3yHh0P16s4uU+SmczPnhZSUFOLj451dRr6l4J0PRUdHc/DgQfv7Q4cOsXv3bgoXLkzp0qUZNGgQo0eP5s4776RcuXIMHz6c4OBg2rRpA0DlypVp1qwZvXv3ZsqUKSQmJtK/f386depEcHCwk7ZKREREsovNZuPdd98lJiaGTz75hEieobltFatNM+47uy3tyrfCt0i+NGzYMJo3b07p0qW5cOECs2bNYuPGjaxZs8bZpeVbCt750Pbt2wkJCbG/HzJkCADdu3dn+vTpvPzyy8TExPDMM89w/vx5HnzwQVavXo2Xl5d9na+//pr+/fvTqFEjXFxcaN++PR988EGub4uIiIjkDJvNxscff0xsbCxffvklUa7uNEtZw2rTlPvObEu78l2tmrNLFZFsdvLkSbp168bx48cJCAigWrVqrFmzhsaNGzu7tHzLZowxzi4it0RFRREQEEBkZCT+/v7OLkdERJwkJiYGv0vTzkZHR+Obx8YF6nilfZCbkpKS6NSpEwsWLMDdvTt+Se9b4ZttmNtuU/gWEafJT8drzWouIiIicgtzc3Nj1qxZtGjRgsTEGcR6DKUpa9jGvdjOnME0agS//ursMkVEbmoK3iIiIiK3OA8PD+bPn0/Dhg2Jj/+UeO/hNGGtFb5Pn8Y0bKjwLSJyAxS8RURERARvb2+WLFnCAw88wMWLk0j0HU0T1rKdWmnhe88eZ5cpInJTUvAWEREREQD8/PxYuXIl99xzDzEx40nxf4fGrLOHb0JCFL5FRK6DgreIiIiI2AUEBLB27VqqVq1KVNRYbIU+tIdvTp8GXfkWEckyBW8RERERcXDbbbexbt06KlSowLlzI3Ar8gmNWccO7oFTpxS+RUSySMFbRERERDIoXrw469evp0yZMpw+PQyPYtMJZb3Ct4jIdVDwFhEREZFMlSpVivDwcIKDgzl5cgjeQbMzXvn+7TdnlykikucpeIuIiIjIFd1+++2EhYVRtGhRjh9/Dt+Si2jMOnZS0wrfISEK3yIi/0HBW0RERESuqlKlSqxbt45ChQrxzz9P419mJaGsV/gWEblGCt750ObNm2nZsiXBwcHYbDYWL17ssNwYw+uvv05QUBDe3t6EhoZy4MABhz5nz56lS5cu+Pv7U7BgQXr16kV0dLRDn19++YWHHnoILy8vSpUqxbhx43J600RERMRJqlevzpo1ayhQoAB//92VguXCFL5FbmLZkRnk2il450MxMTFUr16dSZMmZbp83LhxfPDBB0yZMoWtW7fi6+tL06ZNiYuLs/fp0qULv/32G+vWrWP58uVs3ryZZ555xr48KiqKJk2aUKZMGXbs2ME777zDyJEjmTp1ao5vn4iIiDhH7dq1WbFiBd7e3hw61IHCd3znGL51z7fITSM7MoNkgbmFREZGGsBERkY6u5RcA5hFixbZ36ekpJjixYubd955x952/vx54+npab755htjjDF79+41gNm2bZu9z6pVq4zNZjPHjh0zxhjz8ccfm0KFCpn4+Hh7n6FDh5qKFSvm8BaJiNy46OhoAxjAREdHO7ucDG7F49XltA/ytnXr1hlPT08DmAoVVptCnDE7qGkMGFOsmDG//ebsEkUkC64nM+SG/HS81hXvrDAGYmJy/2VMtm3CoUOHOHHiBKGhofa2gIAA6tSpw5YtWwDYsmULBQsW5N5777X3CQ0NxcXFha1bt9r7PPzww3h4eNj7NG3alH379nHu3Llsq1dERETyntDQUObPn4+bmxv79zejeOWf0658nzxpDTvfu9fZZYrkPmflBSdkBskaN2cXcFOJjQU/v9z/3uho8PXNlo86ceIEAIGBgQ7tgYGB9mUnTpygWLFiDsvd3NwoXLiwQ59y5cpl+IzUZYUKFcqWekVERCRvevTRR5k1axadOnXi998bcddd3xH623rWE8o9J3dZ4XvDBqhSxdmliuQeZ+UFyPXMIFmjK94iIiIicl0ef/xxpk2bBhh+++1BSt79l658i4hkQle8s8LHxzqT5IzvzSbFixcHICIigqCgIHt7REQENWrUsPc5efKkw3pJSUmcPXvWvn7x4sWJiIhw6JP6PrWPiIiI5H/dunXj4sWL9OnTh19/rUONGrsI3b2eMEKpqSvfcqtxVl5I/e5sci2ZQbJGV7yzwmazhm/k9stmy7ZNKFeuHMWLFycsLMzeFhUVxdatW6lbty4AdevW5fz58+zYscPeJzw8nJSUFOrUqWPvs3nzZhITE+191q1bR8WKFTXMXERE5Bbz7LPPMn78eCCF3btrUu6eCBqxnl268i23GmflBSdkBskaBe98KDo6mt27d7N7927Amhxh9+7dHDlyBJvNxqBBgxg9ejRLly7l119/pVu3bgQHB9OmTRsAKleuTLNmzejduzc//fQT33//Pf3796dTp04EBwcD0LlzZzw8POjVqxe//fYbc+bMYeLEiQwZMsRJWy0iIiLONHjwYEaPHg2ksHPn3dxe64wVvm3pwrceNSaSZ9xoZpAsyoVZ1vOMW+XRJBs2bLBPu5/+1b17d2OM9XiA4cOHm8DAQOPp6WkaNWpk9u3b5/AZZ86cMU888YTx8/Mz/v7+pkePHubChQsOfX7++Wfz4IMPGk9PT1OiRAnz1ltv5dYmiojckPz0eJL8Svvg5jVs2LBL/75czb33HjKFOGN22tI9amzPHmeXKCImezJDTstPx2ubMdk473weFxUVRUBAAJGRkfj7+zu7HBERcZKYmBj8Ls06Gx0djW82zQKbXXS80j64mRljGDx4MBMnTsRm8+Dee//k4DYfwmyh1DS7oFgxCA+Hu+5ydqkiksflp+O1hpqLiIiISLax2Wy8//77PPPMMxiTwM6dFbjzvngamfXsTh123rChhp2LyC1FwVtEREREspXNZmPy5Ml07dqV5OSL7NpVgTvvS6Zh+vCte75F5Bai4C0iIiIi2c7FxYUvvviCxx57jMTEaH75pQLla0NDs55dLvfAqVMK3yJyy1DwFhEREZEc4ebmxtdff82jjz5KXNx59u6tyJ33udAoZZ1j+N6zx9mliojkKAVvEREREckxHh4ezJs3j9DQUGJiTvPHH5UpX9vNMXw3bKjwLSL5moK3iIiIiOQoLy8vFi9ezIMPPkhU1An+/LMqd9zrSaOUdexW+BaRW4CCt4iIiIjkOF9fX1asWEHt2rU5e/YoR45U4457vWmYso7drhp2LiL5m4K3iIiIiOQKf39/Vq9eTfXq1Tl58i+OH7+H22v5EJK83grfp09b4fvXX51dqohItlLwFhEREZFcU7hwYdauXUvlypU5duwPTp++j9vv8b0UvmtZ4bthQ4VvEclXFLxFREREJFcVK1aM9evXc8cdd/D3378SFfUAZWv4EZK8jl1u96aF719+cXapIiLZQsFbRERERHJdcHAwYWFhlC5dmoMHdxAfX58y1QsQkqTwLSL5j4K3iIiIiDhFmTJlCAsLIygoiN9/34IxjSlTze9S+K4NZ85Y4fvnn51dqojIDVHwFhERERGnKV++PGFhYRQtWpRfftmIh8ejlL67ACFJa9nlfil8N2qk8C0iNzUFbxERERFxqsqVK7Nu3ToKFSrE9u1rKFCgHSXv8ickcS073e/TlW8RuekpeIuIiIiI01WvXp01a9ZQoEABfvhhKcWKPUGJKlb43uV+H5w9a4Xv3budXaqISJYpeIuIiIhInlC7dm1WrlyJj48PGzbMpVSpHgRX8qdB4lp2etRJC9+7djm7VBGRLFHwFhEREZE848EHH2Tp0qV4enqyZs1MKlToQ1BFf0IS1rDLow6cO2fd871zp7NLFRG5ZnkqeI8dO5batWtToEABihUrRps2bdi3b99/rjdv3jwqVaqEl5cXd999NytXrsyFakVEREQkJzRq1IiFCxfi7u7O0qVTqVZtMIF3+tMgYQ07Pe+3wndoqMK3iNw08lTw3rRpE/369ePHH39k3bp1JCYm0qRJE2JiYq64zg8//MATTzxBr1692LVrF23atKFNmzbs2bMnFysXERERkezUokULZs+ejaurK/PmTaROnWEUK+9Pg/h04btRI9ixw9mlioj8J5sxxji7iCs5deoUxYoVY9OmTTz88MOZ9unYsSMxMTEsX77c3nb//fdTo0YNpkyZ4tA3KiqKgIAAIiMj8ff3z9HaRUQk74qJicHPzw+A6OhofH19nVyRIx2vtA8kzaxZs3jyyScxxtCr1wg2bBjBqb8usNGzGffEb4GCBWHdOrj3XmeXKiLZLD8dr/PUFe/LRUZGAlC4cOEr9tmyZQuhoaEObU2bNmXLli05WpuIiIiI5LzOnTvz+eefA/D552/QvPk7FCnnT/34NezwegDOn4fGjWHbNucWKiJyFXk2eKekpDBo0CDq1atH1apVr9jvxIkTBAYGOrQFBgZy4sSJK64TFRXl8IqPj8+2ukVERLIqPj4+w7FJRNL06NGDjz76CIBJk4bSrt2H3FamAA3iVrPDu15a+P7pJ+cWKiJyBXk2ePfr1489e/Ywe/bsbP/sUqVKERAQYH+NHTs2279DRETkWo0dO9bhuFSqVClnlySS5/Tr1493330XgPfee57OnT+lcOkCNLi4iu3eD0JkpMK3iORZeTJ49+/fn+XLl7NhwwZKlix51b7FixcnIiLCoS0iIoLixYtfcZ2jR48SGRlpfw0bNixb6hYREbkew4YNczguHT161NklieRJL7zwAm+++SYAY8c+Q69eX1GoVAFCLq5ku89DEBVlhe+tW51cqYiIozwVvI0x9O/fn0WLFhEeHk65cuX+c526desSFhbm0LZu3Trq1q17xXX8/f0dXp6enjdcu4iIyPXy9PTMcGwSkcy9+uqr9osmI0Z0pV+/+QSUKECD2JVs83nYCt9NmsCPPzq5UhGRNHkqePfr14+vvvqKWbNmUaBAAU6cOMGJEye4ePGivU+3bt0crlAPHDiQ1atX89577/HHH38wcuRItm/fTv/+/Z2xCSIiIiKSg2w2G//73/8YNGgQAMOGdWDIkGUEBPsREruC7b7pwrcm2xWRPCJPBe/JkycTGRlJgwYNCAoKsr/mzJlj73PkyBGOHz9uf//AAw8wa9Yspk6dSvXq1Zk/fz6LFy++6oRsIiIiInLzstlsjB8/nj59+mCM4eWX2zJs2DoKFPejfsxKtvk2gAsXoGlT+OEHZ5crIpK3n+Od3fRMUBERgfz1XND8SvtArkVKSgo9e/ZkxowZuLu78+GH6xgxoj4XImLY6NeS2tEbwM8PVq+GevWcXa6IZFF+Ol7nqSveIiIiIiLXysXFhc8//5yOHTuSmJjIwIFNGTNmC37FfKkfvZyfCjSE6Gho1gy++87Z5YrILUzBW0RERERuWq6urnz55Ze0adOG+Ph4BgwI5Z13duBX1IcGF5bxU4FGaeH722+dXa6I3KIUvEVERETkpubu7s7s2bNp1qwZsbGx9O8fwoQJv+JbxIf6F5ax1T8UYmKgeXPYvNnZ5YrILUjBW0RERERuep6enixcuJCGDRty4cIF+vV7mI8++h3f27xpELWUrf6NrfDdogVs2uTsckXkFqPgLSIiIiL5gre3N0uWLKFevXqcP3+efv0e4pNPDuJT2JsGUUv4MaBpWvjeuNHZ5YrILUTBW0RERETyDT8/P1auXEnt2rU5c+YM/fo9yOef/413IW8aRC5mS8FmEBtrhe8NG5xdrojcIhS8RURERCRf8ff3Z/Xq1VSvXp2IiAj696/HtGn/4F3Qi5Dzi9hSqDlcvAiPPALh4c4uV0RuAQreIiIiIpLvFC5cmHXr1lGlShWOHTvGoEEP8eWXJ/AK8KLBuUVsKdQiLXyvX+/sckUkn1PwFhEREZF8qWjRoqxfv54777yTw4cPM3jwQ8yadRovf08anFvIlsKPQFwctGwJa9c6u1wRyccUvEVEREQk3woKCiIsLIyyZcty8OBBXnqpPnPmnMOzgCcNzi7gh9taWuG7VStYs8bZ5YpIPqXgLSIiIiL5WqlSpQgPD6dEiRLs3buX//u/EObNi8LDz5MGZ+bzfZHWEB8PrVvD6tXOLldE8iEFbxERERHJ98qVK0d4eDiBgYH8/PPPDB8eyvz50Xj6eRByei7fFW2TFr5XrnR2uSKSzyh4i4iIiMgtoUKFCoSFhXHbbbexbds2Ro1qyoIFsXj4ehByai7fFWsLCQnQti0sX+7sckUkH1HwFhEREZFbxl133cW6desoWLAgP/zwA2PHPsKiRXF4+roTcnIO3wW2t8J3u3awbJmzyxWRfELBW0RERERuKTVr1mT16tUUKFCAjRs38t57bVi0KAEPH3dCIr7h2+KPQ2IitG8PS5Y4u1wRyQcUvEVERETkllOnTh1WrlyJj48Pa9as4aOPHmfJkiTcvd0JOTGLzUEdrfD92GOwaJGzyxWRm5yCt4iIiIjckh588EGWLVuGl5cXS5cuZerUzixZkoyHtxsNj3/FpuAnICkJOnSAhQudXa6I3MQUvEVEROS6TJo0ibJly+Ll5UWdOnX46aefrtr//Pnz9OvXj6CgIDw9PalQoQIrNXu0OFnDhg1ZtGgR7u7uzJs3j5kzn2Lx4mTcvdxo9O9MNpbokha+5893drkicpNS8BYREZEsmzNnDkOGDGHEiBHs3LmT6tWr07RpU06ePJlp/4SEBBo3bszhw4eZP38++/bt49NPP6VEiRK5XLlIRs2aNWPevHm4ubnx1VdfMW9eH5YsSbHC97EZbCjVFZKToVMnmDvX2eWKyE1IwVtERESybPz48fTu3ZsePXpQpUoVpkyZgo+PD1988UWm/b/44gvOnj3L4sWLqVevHmXLlqV+/fpUr149lysXyVzr1q35+uuvcXFx4bPPPmPZsoEsXmxw93Ql9Og0NpTqZoXvzp1h9mxnlysiNxkFbxEREcmShIQEduzYQWhoqL3NxcWF0NBQtmzZkuk6S5cupW7duvTr14/AwECqVq3KmDFjSE5Ozq2yRf5Thw4dmD59OjabjY8++oh1615i0aLU8P0F4WWessJ3ly4wa5azyxWRm4ibswsQERGRm8vp06dJTk4mMDDQoT0wMJA//vgj03X++usvwsPD6dKlCytXruTgwYM899xzJCYmMmLEiCt+V1RUlMN7T09PPD09b3wjRK6ga9euxMXF8cwzz/Dee+/h7e3NokVv0qaNK6F/f876si40PPwFdO0KKSnw5JPOLllEckl8fDzx8fH295cfo65GV7xFREQkx6WkpFCsWDGmTp1KrVq16NixI6+++ipTpky56nqlSpUiICDA/ho7dmwuVSy3st69e/PBBx8AMHr0aHbsGM2iReDu4ULo4U8JK/e0Fbq7dYOZM51crYjklrFjxzock0qVKnXN6yp4i4iISJYUKVIEV1dXIiIiHNojIiIoXrx4pusEBQVRoUIFXF1d7W2VK1fmxIkTJCQkXPG7jh49SmRkpP01bNiw7NkIkf8wYMAAxo0bB8Dw4cP5/ff3WLAA3NxdaHzoE9bd8SwYA089BdOmObdYEckVw4YNczgmHT169JrXVfAWERGRLPHw8KBWrVqEhYXZ21JSUggLC6Nu3bqZrlOvXj0OHjxISkqKvW3//v0EBQXh4eFxxe/y9/d3eGmYueSml156iVGjRgHw4osv8vffk+zhu+mfH7OufF8rfPfqBVeYWFBE8g9PT88Mx6VrpeAtIiIiWTZkyBA+/fRTZsyYwe+//07fvn2JiYmhR48eAHTr1s3h6nTfvn05e/YsAwcOZP/+/axYsYIxY8bQr18/Z22CyDV57bXXeOWVVwDo378/ERGfMX++Fb6bHJzE2jv7pYXvTz91crUikldpcjURERHJso4dO3Lq1Clef/11Tpw4QY0aNVi9erV9wrUjR47g4pJ2fr9UqVKsWbOGwYMHU61aNUqUKMHAgQMZOnSoszZB5JrYbDZGjx5NXFwc48eP55lnnmHGDE/mzevKY4/ZaHrgQ1ZXdKXpvg/gmWese7+ffdbZZYtIHmMzxhhnF5FboqKiCAgIIDIyMkvDAkREJH+JiYnBz88PgOjoaHx9fZ1ckSMdr7QPJO8xxtC/f38+/vhjXFxc+Oabb/Dw6MDjj0NSkmFVpSE0+2OC1XnSJHjuOafWK5If5KfjtYaai4iIiIj8B5vNxocffkjPnj1JSUmhc+fOwGLmzAE3NxvN/xjPyiovWJ379YOPPnJqvSKStyh4i4iIiIhcAxcXF6ZOnUqXLl1ITk6mQ4cOeHmtZPZscHW18cjed1h510tW5wED4NIjyUREFLxFRERERK6Rq6sr06dP57HHHiMxMZF27dpRsGBYWvj+7W1W3P1/VueBA2HCBKfWKyJ5g4K3iIiIiEgWuLm5MWvWLFq1akV8fDwtW7YkMPBbvvnGCt+P/jqG5dWsmdAZPBjee8+5BYuI0yl4i4iIiIhkkbu7O3PnzqVZs2ZcvHiRFi1aUKrUj3z9tRW+W/4ymqU1hludX3wRxo1zbsEi4lQK3iIiIiIi18HT05OFCxcSEhJCdHQ0zZo14847d/L11+DiYqP17lEsqTnS6jx0KIwd69R6RcR5FLxFRERERK6Tt7c3y5Yt48EHHyQyMpLGjRtTpcqvfPUVuLhAm10jWFxrlNX5lVdg9GjnFiwiTqHgLSIiIiJyA3x9fVmxYgX33XcfZ8+epVGjRtSo8TtffmmF77Y7hrO49v+szsOHw6hRzi1YRHKdgreIiIiIyA3y9/dn9erV1KxZk1OnTtGoUSPuu+8gM2deCt/bXmFhnbesziNGWC9jnFu0iOQaBW8RERERkWxQqFAh1q5dS9WqVTl+/DgNGzakXr3DzJgBNhu03zqUBfe/Y3UeNcq6+q3wLXJLUPAWEREREckmRYoUYf369VSsWJGjR48SEhJC/fpH7eH7sR9fZP4D463O//ufdd+3wrdIvqfgLSIiIiKSjQIDAwkLC+OOO+7g8OHDNGrUiNDQ40yfboXvx38YzLx6E6zOb71lzXiu8C2Sryl4i4iIiIhksxIlShAeHk6ZMmU4cOAAjRo1olmzk0ybZoXvDt8PZO5DH1qd33nHeta3wrdIvqXgLSIiIiKSA0qXLk14eDglSpTg999/p3Hjxjz66Bm++MIK3x2/7c+c+h9bncePh8GDFb5F8ikFbxERERGRHHL77bcTHh5O8eLF+eWXX2jSpAlt2pzns8+s8N1pU19mh3xidZ44EZ5/XuFbJB9S8BYRERERyUEVKlQgLCyMIkWKsHPnTpo3b87jj1/gs8+s5U9seIZvGn2Gsdngo4+gXz9ISXFu0SKSrRS8RURERERyWJUqVQgLC6Nw4cL8+OOPPPLII3TsGGMP353DevFN6BdW+J48Gfr2VfgWyUcUvEVEREREckG1atVYu3Yt/v7+fPvtt7Rq1YrOnS/y6afW8i7rnmJW4+lW+J46FZ59VuFbJJ9Q8BYRERERySW1atVi9erV+Pn5ER4eTrt27ejaNd4evp9c242vm36JcXGBzz6DXr0gOdm5RYvIDVPwFhERERHJRXXr1mXFihV4e3uzevVqOnToQPfuiUydai3vuroLXzX7GuPqCtOnQ48eCt8iN7lsD95Hjx6lZ8+e2f2xIiIiko10vBZxrocffphly5bh6enJ0qVL6dy5Mz16JPHJpQnOu63sxJfNv7HC95dfQrdukJTk3KJF5Lple/A+e/YsM2bMyO6PFRERkWyk47WI8zVq1IhFixbh4eHB/Pnz6d69O716JTNlirW8+/LH+fKRORg3N5g1C558UuFb5CblltUVli5detXlf/3113UXIyIiItlDx2uRm0Pz5s2ZN28e7du3Z9asWXh6evLZZ59hjAt9+0L3pe0xbebRbUUHbHPmWEPOZ80Cd3dnly4iWZDl4N2mTRtsNhvGmCv2sdlsN1SUiIiI3Bgdr0VuHq1ateKbb76hY8eOTJs2DU9PTz7++GPARt++8NTiNqS0XcBTKx7DNn++Fb5nzwYPD2eXLiLXKMtDzYOCgli4cCEpKSmZvnbu3JkTdYqIiEgW6HgtcnN57LHH+PLLL7HZbEyZMoVBgwbx7LOGjz+2lvdc1JJpLRdhPDxg0SJ4/HGIj3du0SJyzbIcvGvVqsWOHTuuuPy/zq6LiIhIztPxWuTm07lzZz7//HMAPvjgA4YOHUqfPoZJk6zlvRa0YFrrJRhPT1i6FNq3V/gWuUlkeaj5Sy+9RExMzBWXly9fng0bNtxQUSIiInJjdLwWuTn16NGD+Ph4+vbtyzvvvIOXlxejRo3CGOjfH3rNa4bpuIyeS1phW7EC2raFhQvBy8vZpYvIVWQ5eD/00ENXXe7r60v9+vWvuyARERG5cTpei9y8+vTpQ3x8PIMGDeLNN9/E09OTV199FbDC99NzGpPSaQVPL3kU26pV0Lo1LF4M3t7OLVxErijbHycmIiIiIiI3ZuDAgYwbNw6A1157jXfffZd+/eCjj6zlz8xuyGdtV2J8fGDtWmjZEmJjnVixiFyNgreIiIiISB700ksvMWrUKPvvP/zwQ8fwPasBn7ZbjfH1hbAwePRRuMotJiLiPFkO3q+//vpVJ2sRERER59PxWiR/GD58uH2Y+fPPP88nn3xCv37w4YfW8me/eoip7dZgChSADRugRQuIjnZixSKSmSwH73/++YfmzZtTsmRJ+vbty6pVq0hISMiJ2kREROQ66Xgtkn+8+eabvPjii4B1//f06dPp3x8++MBa3ufLenzSdg3G3x82b4ZmzeDCBSdWLCKXy3Lw/uKLLzhx4gTffPMNBQoUYNCgQRQpUoT27dszc+ZMzp49e93FbN68mZYtWxIcHIzNZmPx4sVX7b9x40ZsNluG14kTJ667BhERkfwgJ4/XIpK7bDYb48aN4/nnnwegZ8+ezJo1iwED0sJ335l1mdJuHSYgAL7/Hpo2hchIJ1YtIuld1z3eLi4uPPTQQ4wbN459+/axdetW6tSpwyeffEJwcDAPP/ww7777LseOHcvS58bExFC9enUmpT6s8Brt27eP48eP21/FihXL0voiIiL5UU4dr0Uk99lsNiZMmMCzzz6LMYZu3boxf/58BgyAiROtPs9Nv4+P24VhChWCLVugSRM4f96pdYuIJcuPE8tM5cqVqVy5Mi+//DKnTp1i6dKlLF26FMA+LOZaNG/enObNm2f5+4sVK0bBggWzvJ6IiMitJLuO1yLiHDabjY8//pj4+HimT5/OE088gbu7O88/3xqAgQOh/7Ra0CuM5xaFYvvpJ2jc2Jr1vFAhJ1cvcmvLluCdXtGiRenVqxe9evXK7o++oho1ahAfH0/VqlUZOXIk9erVu2r/pUuXctddd3HHHXcA1hWBDRs2APDII4/g4mINBNi7dy9//fUXd9xxB5UrVwYgJSWFVatWAdCkSRPc3d0BOHDgAAcOHKBMmTLcdddd9u9as2YNKSkphISE4OXlBcChQ4fYv38/JUqUoGrVqva+GzZsICkpiXr16uHj4wNY9+jt37+fYsWKOfTdsmULCQkJ1KpVCz8/PwAiIiLYv38/hQsXdqhh165dxMXFcdddd+Hv7w/A2bNnOXjwIP7+/lSqVMne948//uDixYvccccd9r5RUVH8/fffeHt7U758eXvfw4cPExcXR4kSJShQoAAAFy9e5NixY3h4eFC6dGl734iICOLj47ntttvw9fUFICEhgdOnT+Pm5uYwSiEqKorExER8fX3t+yw5OZmYmBhcXFzs2wuQmJhISkoKbm5uuLq6AmCMsS+32WyIiOR18fHxxMfH299HRUXl+Hc643gtIjfOxcWFzz77jISEBGbNmsXjjz/OkiVLeP755hgDgwZB/89rYp4Op9/iUGzbt0OjRrBuHdx2m7PLF7ll3dSPEwsKCmLKlCksWLCABQsWUKpUKRo0aMDOnTuvut5vv/3GkCFDCAgIICAggHfffZedO3eyc+dOh9D2zz//sGPHDv755x97mzGG7du3s337dpKTk+3tx44dY9u2bRw+fNjhu3766Sd++uknEhMT7W3//vsvP/74IwcPHnTou3XrVn744QcuXrzo0Pfbb7/l999/d+j7ww8/sHHjRqLTzVr577//Eh4ezs8//+zQ97vvvmPt2rVEprvP5/jx46xatYqtW7c69N24cSNLly7l1KlT9rYTJ06wcOFC+8mJVGFhYcyZM8dhiGJERARff/01y5cvd+i7du1apk2bxl9//WVvO3XqFJ9++imzZs1y6Lty5Uo++ugjfvvtN3vbmTNneP/995k8ebJD32XLlvHWW2+xbds2e1tkZCSjRo1i7NixDn1XrFjBmDFj+P777+1tsbGxvPfee4wfP97hz/7bb79l0qRJ/Pjjj/a2pKQkPv30Uz7//HOHP89du3bx1VdfsX37dofvmzdvHvPnzycuLs7eduDAAZYvX84vv/zi0HfDhg2EhYVl+LP//vvvOXDggEPfX375hV27djn0PXfuHL///nuG4aL//PMPR44ccfiBPi4ujlOnTjn8fUjdF7GxsQ5/r40xDvtFRHLG2LFj7cekgIAASpUq5eySRCQPc3V1ZcaMGTz22GMkJibStm1b1q9fz8CBMGGC1WfAZ9X5sO0GTNGisGuXFb5Pn3Zq3SK3smy/4p3enDlz6NixY459fsWKFalYsaL9/QMPPMCff/7J+++/z5dffnnF9erUqUPXrl0pWbIkYP3nlRqa0l8hveOOO/D09HT4Achms1G/fn0A3NzSdl+ZMmV4+OGHKVGihMN31atXD2MMHh4e9rYSJUpQr149goKCHPred999JCYm4u3tbW8LDAzkvvvuo3jx4g59q1evTlxcnP3KOMBtt91GjRo1CAwMdOhboUIFYmJiHPr6+/tTpUoVihYt6tC3dOnS+Pv7O/T18fGhXLly3HbZWdLAwEBsNptDve7u7hQvXpxClw1n8vf357bbbsPT09Pe5uLigr+/v8MV7NTP8PLycti/qf1TRyOkSg2F6f/cMmsDKzinXiFPlZKSYj95kb5/dHQ0p0+fJjY21t6WnJzMv//+y+XOnDnDn3/+6bAvjTHs3bsXgBYtWtjb//33X3bs2IExhmrVqtnbf/jhB5KSkrj33nvt+/Pvv/9m/fr13H333dx55532vqtXr+bixYuULFnS3vfPP/9kxYoVVKpUyeHf3Pz584mMjKR3794EBwcDsH//fhYtWsTtt99O165d7X2nTZvG6dOn6d69O2XLlgWsERBz586lVKlS9OzZ09535syZRERE0L59e26//XYAjhw5wrJlyyhatCgdOnSw9121ahUnT56kfv369s89ffo0GzZsoECBAjRr1szed9u2bZw+fZpq1arZ/y1duHCBnTt34u3tzX333Wfv++effxIZGUnp0qUpUqQIYI2iOHToEO7u7va6wDoxcfHiRQICAuwjLlL/7C8fRZGSkmKfqFEktwwbNowhQ4bY30dFReVq+M7p47WIZD83NzdmzZpFYmIiS5YsoVWrVqxatYqBA62fUwcNgoGfVsU8s5HnlzTE9vPP0LAhrF8Pmg9JJNflaPB+6aWXcv1Aft999/Hdd99dtU/Dhg3tw6hTpYbp9O644w77cPRULi4uNGjQIEPfcuXKUa5cuUy/63Jly5a1B5D/6lumTBnKlCmToT00NDRDW+nSpR2Gd6dq2rRphrZSpUpl+kNd+pCYqmTJknTr1i1D+6OPPpqhrUSJEjz77LMZ2lu3bp2hLSgoiMGDB2dob9++fYa2YsWKMXz48Aztbdu2pXXr1g6BPCAggJdeeinDldrGjRvz8MMP24evA3h7e9snKUmvTp06VK5cmYCAAHubm5sbTzzxBCkpKfZh7QB33XUXRYsWtYe/VM2aNctw0qVs2bI0aNAg05MuSUlJDicmihYtSvXq1e0niFKVL1+euLg4h75+fn6UKlUqw8mRggUL4urq6nASw8XFBW9vb4f9AGknLNLvy8zawLqlIDY21mG/xcfHc/r0afvtF6mOHz/O0aNHHUJzdHQ0e/fuzbDP9u3bx59//klwcLBD8N64cSP+/v4On7F9+3b++OMPHnnkEfvnREVFMXv2bLy9vXn55ZftfTdu3Mgvv/xC48aNeeCBB+yfO2HCBFxdXXnttdfsfVeuXMmOHTto0KCB/f+FixcvMmnSJFxcXBg0aJB9f2zZsoVff/2VGjVq2GtLTk5mzpw5uLi40L59e/v+2LdvHwcOHKBcuXIOt4Js2rQJFxcX6tSpY/+7cuLECU6cOMFtt93m8O/0r7/+wmazUbJkSfvnpo5U8PLycjiBkJCQgIuLC66urjqJcBPw9PR0+Ded25xxvBaRG+fu7s6cOXNo164dK1eu5JFHHmHNmjUMHGjddjloEAyaWgX6XArfv/5qhe+wMLjsQo2I5KwcDd7OGKK6e/fuDKFG8q/MroK7uLg4XLFP5ePjk6Hd1dU1w2gCgMKFC1O4cOEMfStUqJChb1BQUIa/czabjTp16mToe6UTKY0bN87QVr58eYd76lO1a9cuQ1ulSpUc7tVP9dRTT2Voq1q1qsN8Aan69++f4d9shQoVePHFFzPs4w4dOpCYmOhwYqJkyZJ0797d4UQDQEhICDExMQ6jQQoXLkzz5s0zBI2qVasSHBzsMGrD29ube+65J8OJguDgYFJSUhwmVnR1daVEiRIZPtfLywt/f3+HzzDG2INpeqkjItJvc+ocA+A4MuL8+fMcP37c4QRdcnJyhtsDIO3WFTc3N3vwNsawceNGAO655x77vtu/fz8bNmygZs2aDsH7m2++ISkpieeff94+quSXX35hzZo1VK1a1eGk1cSJE4mNjaVv3772ORR+/vlnVq9eTYUKFWjbtq2979dff010dDRt27a19z18+DBbtmwhKCjI4WTjpk2biI2N5b777rOf6Dlz5gx//PEHAQEBDn+3/vzzT+Lj4yldurT9pEBcXBynT5/G09PTYZRI6okcLy+vDH8mkvN0S4nIzcvT05MFCxbQsmVL1q9fT/PmzS8NO78PY2DwYBg0pRKm70YGLm2I7bffoEEDCA8H/cwskmtyNHhn9SpLdHS0w33Phw4dYvfu3RQuXJjSpUszbNgwjh07xsyZMwGYMGGC/epRXFwcn332GeHh4axduzZbt0PkVnH5v1k3N7cMQ/6BDLcSgBWQMxvJkdlIkMuvXqeqUaNGpt/VsmXLDO0PPfRQpn2ffvrpDO2ZPTGhYMGCDB8+PEPgaNasGY0aNXK4cu/t7U2fPn3sw9BT1a5dm/LlyzvsD1dXV1q1akVycrJDgLz99ttxdXV1GMFgjKFWrVqkpKQ4fF/hwoUpX758httGihUrRmJiokNfFxcXvLy8MpzwyOwEQkJCAnFxcQ5zFIA1N8OFCxcc7u+PjIxk//79Dm0Av/76K2fOnKFKlSr24B0REcH69espXbq0Q/Bev349J06coHPnzvbbJf755x++/vprihcv7jA6Zs6cORw5coTHH3+cKlWqANbtCzNnzqRo0aIOfZcuXco///xDo0aN7LcbnTlzhtWrV+Pn5+cwwmb79u2cPHmSqlWr2kcExcbGsmXLFof94uPjY/+zTU5OJjk5GRcXF4e//wkJCYB1hSk7+yYmJmKMwc3Nzf7nlf6WmNygUREiNzcvLy+WLFlCixYt2LRpE02bNiUsLIxBg+4BrPA9eHIFUp7bxOBlIdj++CMtfF92m6SI5IwbDt5FixbN9IBtjOF8Fp8buH37dkJCQuzvU+936969O9OnT+f48eMcOXLEvjwhIYEXXniBY8eO4ePjQ7Vq1Vi/fr3DZ4iIXM3l/395eHhkCLGurq4ZQjBAkSJFMgyXd3V1pWbNmhn6ZnY7iouLS6a3bFxpVELv3r0ztN13332ZnsR44YUXSE5Odgjpd999N+XKlctwO0D79u1JTEx0GOVRsmRJWrZsaX9iQaratWsTHR3tMNohICCA6tWrZxglEhQUhIeHh8NIE1dXVwoWLJjhdp/UEyDpT1akBtXLQ+j58+c5deqUPdyCdTvAwYMHMzxa8uDBg+zbt4/AwEB78I6OjnaYLPLdd9/llVdesd////3339tHHLRq1cqhX2JiIgMHDrR/z7Zt21izZg133323w2iUzEYc7N69m+XLl1OxYkU6depk7ztp0iQiIyN5+umn7SNDUueIyE7ZebwWkbzHx8eH5cuX07RpU3744QcaN27Mxo0bGTTobsAK3y98fAem3yaGLA/Btn8/1K8PGzaAJnQUyXE3HLzTz359oxo0aHDV4W7Tp093eP/yyy873McpIiKWzEYreHl5ZRiyD2R6+8Ntt92WYc4AINNbKEqUKJFhYknAIbSmKleuHAMHDszQ3rNnzwz//5cqVYpBgwZl6Nu0aVNiY2MdhqoXKlSINm3aZNjmu+66i8DAQIfbQTw9Pbn77rszfG5+l53HaxHJm/z8/Fi5ciWNGzdm27ZtNGrUiE2bNjFokPVY3MGD4cVJ5aD/RoasaIjtzz/TwncmxwIRyT42cwvd2BUVFUVAQACRkZEZrraIiMitIyYmxn7f+dmzZylYsGCeGmp+/vx5ChUqdEsfr3TMFrl+586do1GjRuzatYugoCA2bdrEnXfeyYQJVvgGGDfgKC+uDLHCd5kyVvjO5PYwEWdKf7yOjo62j07LK7JyrLqpn+MtIiJyozw8PByGYLu6uuLh4ZHh6nnqbQjZ3dfd3R0PDw+H+/Evn9BQRCQrChUqxNq1a7n77rs5fvw4DRs25NChQwwaBO+/b/V5+cNSvPPIJsydd8Lff1tXvv/806l1i+RnOXZkP378OPHx8Tn18SIiIpINdLwWyZ+KFCnC+vXrqVy5Mv/88w8hISEcOXLEIXwP/aAE41pswlSqBEePWuE7kydziMiNy7Hg3bVrVypVqsSLL76YU18hIiIiN0jHa5H8q1ixYoSFhXHnnXfy999/ExISwrFjxxzC9/9NDGJcsw2YKlXg2DErfP/xh1PrFsmPcuxxYuvXrwfgD/3DFRERybN0vBbJ34KCgggPD6d+/fr89ddfNGzY8NKEa8UB657v/5tQHDN4A0NdGmHbsyftUWOXHu8oIjcuS1e8X375ZeLi4hza3r90uuy3337L8LxXgEqVKt1AeSIiIpJVOl6LSHolS5YkPDyc0qVLs3//fho1asSpU6ccrnwPe78YbzXZgKleHSIirPC9Z48zyxbJV7IUvCdMmEBkZCQATz31FLGxsdSoUQOAV155hSpVqlCjRg26dOnCW2+9xfLly7O9YBEREbk6Ha9F5HJlypQhPDycEiVKsHfvXkJDQzlz5oxD+H5lfBHGhoZj7rkHTp2ywvfPPzuzbJF8I0vBOzg4mN27dwPw5ZdfEh0dTUhICABLlixh3759fPfddzz//PP2CR1EREQkd+l4LSKZueOOOwgLC6N48eL88ssvNGnShPPnzzuE71ffK8yYkPWY2rXhzBlo2BB27nRq3SL5QZbu8X7hhRdo2bIlderUAeDrr7+mXr163H333Xh7ewPg5+dHnTp17H1EREQkd+l4LSJXUrFiRcLCwmjQoAE7d+6kadOmrFu3jkGDrGcQDx4Mr71XCPPiOl51bYbtxx+hUSNYuxZq13Zy9SI3L5sxxmRlhV9++YVly5YxfPhwbr/9dg4fPozNZqN8+fJUr16dGjVqUKNGDZo1a5ZTNV+3rDzgXERE8q+YmBj8/PwAiI6OxtfX18kVOcqO49XNfLwGHbNFctovv/xCSEgIZ8+epV69eqxevRo/Pz8mTLDCN8CoF6N4bUsLbN9/D/7+sGYN3H+/U+uWW0t+Ol5nOXinuvPOO9myZQu+vr788ssv7N692/7as2cPFy5cuK7ic5IO4iIiAvnrQP5fbsbjNeiYLZIbdu7cSaNGjTh//jwNGjRgxYoV+Pj4OITvN16KZvjWR7Bt3gwFCsCqVVCvnlPrlltHfjpeX3fwvhpjDDabLbs/9obpIC4iIpC/DuQ3Iq8er0HHbJHc8tNPPxEaGsqFCxcIDQ1l2bJleHl5MXEiDBpk9Rn5Ugyvb2+JbcMG8PWFlSvh4YedWrfcGvLT8TpLk6tdq7x6EBcREZE0Ol6LyH333cfq1avx9fVl/fr1tGvXjvj4eAYOhAkTrD4j3/FlVO3lmNBQiImB5s1hwwan1i1ys8mR4C0iIiIiIjeHBx54gJUrV+Lt7c2qVavo0KEDCQkJjuF7nA8jay7FNG0KsbHwyCOwbp1T6xa5mSh4i4iIiIjc4h5++GH7MPOlS5fSuXNnkpKSHML3qHe8GVl9MeaRR+DiRWjZElavdmrdIjcLBW8REREREaFRo0YsWrQIDw8PFixYQNeuXUlOTmbgQJg40eozapwXI+5agGnVCuLjoXVrWL7cuYWL3AQUvEVEREREBIBmzZoxf/583NzcmD17Nj179iQlJYXnn08L32+O82RE5XmYdu0gIQHatYMlS5xbuEgep+AtIiIiIiJ2LVu2ZM6cObi6ujJz5kyeffbZjOH7bQ+Gl5+NefxxSEyExx6DBQucW7hIHqbgLSIiIiIiDtq1a8dXX32Fi4sLn332Gf3798cYw/PPwwcfWH3+N86d4bfPwnTuDElJ0LEjzJnj3MJF8igFbxERERERyaBTp05Mnz4dm83G5MmTGTx4MMYYBgyADz+0+vzvbTdeLTkT060bJCdD587w9dfOLVwkD1LwFhERERGRTHXt2pXPPvsMgIkTJzJ06FCMMfTvnxa+x45z5dXiX2B69ISUFOjaFWbMcGLVInmPgreIiIiIiFxRz549mTx5MgDvvPMOr7/+OgD9+8NHH1l9xo5z5ZWin2KeeRaMgR494FJgFxEFbxERERER+Q99+vRh4qWZ1UaPHs2bb74JQL9+aeH7rXEu/F/AZMxz/azw3bs3TJnirJJF8hQFbxERERER+U/PP/887777LgCvv/46b7/9NuAYvse9Y+P/fD/EDBxkNfTtm7ZQ5Bam4C0iIiIiItfkhRdeYMyYMQD83//9H++//z5ghe9Jk6w+496xMdR9PObFl6yGAQPgUj+RW5WCt4iIiIiIXLNhw4YxcuRIAIYMGcKkS4n7uefSwvc779p42byNGfYKlzrCuHFOqFYkb1DwFhERERGRLHn99dd55RUrVPfv35+pU6cCVvj++GOrz7vv2XgpfjRmuDUZG0OHwv/+54xyRZxOwVtERERERLLEZrMxevRoXnjhBQCeffZZpk2bBli3daeG7/fG23gx5g3MKGsyNl57Dd54wxkliziVgreIiIiIiGSZzWbjnXfeYcCAAQD06tWLr776CrDC96UnkDF+PLx4/jXM2LeshpEjYfhwa+ZzkVuEgreIiIiIiFwXm83GxIkT6dOnD8YYunfvzty5cwHo0yftaWLjx8MLJ4di3n3Pahg9GoYNU/iWW4aCt4iIiIiIXDebzcakSZPo2bMnKSkpdO7cmUWLFgHw7LPwySdWv/ffhyH/DMFMsJ4Hzttvw4svKnzLLUHBW0RERK7LpEmTKFu2LF5eXtSpU4effvrpmtabPXs2NpuNNm3a5GyBIpJrXFxcmDp1Kl27diU5OZmOHTuybNkyAJ55Ji18T5gAgw89j5l06Sbw8eNh4ECFb8n3FLxFREQky+bMmcOQIUMYMWIEO3fupHr16jRt2pSTJ09edb3Dhw/z4osv8tBDD+VSpSKSW1xdXZk2bRpPPPEEiYmJPPbYY6xevRqwwvelic+ZOBEG7++L+WQq2Gzw4YfWdOgpKU6sXiRnKXiLiIhIlo0fP57evXvTo0cPqlSpwpQpU/Dx8eGLL7644jrJycl06dKFN954g9tvvz0XqxWR3OLq6srMmTN57LHHSEhIoE2bNqxfvx6A3r0dw/eg33pjPv/CCt9Tpljj0hW+JZ9S8BYREZEsSUhIYMeOHYSGhtrbXFxcCA0NZcuWLVdcb9SoURQrVoxevXpd83dFRUU5vOLj42+odhHJeW5ubsyaNYvWrVsTHx9Pq1at2LhxI2CF708/tfp98AEM2v0UZsZMcHGBzz6Dnj0hOdl5xYtcRXx8fIbj0rVS8BYREZEsOX36NMnJyQQGBjq0BwYGcuLEiUzX+e677/j888/5NPUn7mtUqlQpAgIC7K+xY8ded90iknvc3d2ZM2cOLVq04OLFizz66KN89913ADz9tJWxbTYrfD//05OYr2eBqyvMmAHdukFSkpO3QCSjsWPHOhyTSpUqdc3rKniLiIhIjrpw4QJdu3bl008/pUiRIlla9+jRo0RGRtpfw4YNy6EqRSS7eXp6smDBAho3bkxMTAwtWrTgxx9/BKBXr7Tw/dFHMOC7jpjZc8DNDWbNgi5dIDHRyVsg4mjYsGEOx6SjR49e87puOViXiIiI5ENFihTB1dWViIgIh/aIiAiKFy+eof+ff/7J4cOHadmypb0t5dJ9nG5ubuzbt4877rgj0+/y9/fH398/G6sXkdzk5eXF4sWLefTRR9mwYQPNmjVj/fr13HvvvfTsaQXvXr1g0iQwpj0fzZuPrcPjMHeuddX7m2/Aw8PZmyECWCeTPD09r2tdXfEWERGRLPHw8KBWrVqEhYXZ21JSUggLC6Nu3boZ+leqVIlff/2V3bt321+tWrUiJCSE3bt3Z2monojcfHx8fFi2bBkPPfQQkZGRNGnShN27dwPQowd8cWl+tY8/hn5rW5OyYJEVthcuhMcfB83tIPmAgreIiIhk2ZAhQ/j000+ZMWMGv//+O3379iUmJoYePXoA0K1bN/uwcC8vL6pWrerwKliwIAUKFKBq1ap46GqWSL7n6+vLihUrqFu3LufOnSM0NJQ9e/YA8NRTMG2aFb4nT4Z+Kx8hZfFS8PKCpUuhXTuIi3PuBojcIAVvERERybKOHTvy7rvv8vrrr1OjRg12797N6tWr7ROuHTlyhOPHjzu5ShHJSwoUKMCqVauoXbs2Z86coVGjRvz+++8AdO+eFr6nTIHnljQlZely8PaGlSuhdWu4eNHJWyBy/WzGGOPsInJLVFQUAQEBREZG6n4xEZFbWExMDH5+fgBER0fj6+vr5Ioc6XilfSCSn507d45GjRqxa9cuihcvzqZNm6hQoQIAM2daV8CNgWeegckdN+LS6lGIiYGGDa0r4Hns/2zJOfnpeK0r3iIiIiIikmsKFSrEunXruPvuuzlx4gQNGzbkzz//BKwnic2YYV35njoV+sxuQMrK1eDnB+Hh0KIFXLjg5C0QyToFbxERERERyVW33XYb69evp0qVKhw7doyQkBAOHz4MQNeu1pVvFxf49FN49ssHSVmzDvz9YfNmaNYMoqKcuwEiWaTgLSIiIiIiua5YsWKEhYVRsWJFjh49SkhIiP25yE8+mRa+P/sMnvniflLWhUHBgvDDD9C4MZw/79T6RbJCwVtERERERJyiePHihIeHU758eQ4fPkxISAjHjh0DoEuXtPD9+efwzNR7SVkfDoULw08/QWgonD3r5C0QuTYK3iIiIiIi4jTBwcGEh4dTrlw5/vzzTxo2bMiJEycAK3x/+WVa+H56Uk1SwjZAkSKwY4c14drp007eApH/puAtIiIiIiJOVapUKcLDwyldujT79++nYcOGnDx5EoDOneGrr6zwPW0a9JpYjeSwjRAYCD//DCEhEBHh3A0Q+Q8K3iIiIiIi4nRly5Zlw4YNlCxZkt9//53Q0FBOX7qa/cQT8PXXVviePh16jb/LCt9BQbBnDzRoAMePO7N8katS8BYRERERkTzh9ttvJzw8nKCgIH799VcaN27M2Uv3cXfqBLNmgaur9cixnuMqkRy+CUqWhD/+gPr14Z9/nLwFIplT8BYRERERkTzjzjvvJDw8nGLFirF7926aNGnC+UszmHfsCN98Y4XvmTOhx5g7Sd6wGcqUgQMHrPB95IhzN0AkEwreIiIiIiKSp1SqVInw8HCKFCnCjh07aNasGVGXnt39+ONp4fvLL+GpN8pZV75vvx3++ssK34cOOXkLRBwpeIuIiIiISJ5z1113sX79egoXLszWrVtp0aIF0dHRgBW+Z8+2wvdXX0H318tY4fvOO+HwYSt8Hzzo3A0QSUfBW0RERERE8qTq1auzbt06ChYsyPfff8+jjz5KbGwsAI89BnPmgJubNfFat1dKkrR+I1SqBEePWuF73z7nboDIJQreIiIiIiKSZ91zzz2sXbsWf39/Nm3aRKtWrbh48SIA7dvD3LlW+J41C7oODbbC9113wb//WuF7717nboAICt4iIiIiIpLH1a5dm1WrVuHn50dYWBht27YlLi4OgLZtYd48K3zPng1dXwwkad0GqF7der53gwbw66/O3QC55Sl4i4iIiIhInvfAAw+wcuVKfHx8WLNmDY899hgJCQkAtGkD8+eDu7sVvrsMKkrS2nC45x44dQpCQmDXLudugNzSFLxFREREROSm8NBDD7F8+XK8vb1ZsWIFHTt2JDExEYDWrdPC99y50Ll/YRJXh8F998GZM9CwIWzb5uQtkFuVgreIiIiIiNw0QkJCWLJkCZ6enixevJjOnTuTlJQEQKtWsGCBFb7nzYPOzxUkccVaeOABOH8eQkNhyxbnboDckvJU8N68eTMtW7YkODgYm83G4sWL/3OdjRs3cs899+Dp6Un58uWZPn16jtcpIiIiIiLO07hxYxYtWoSHhwfz58+na9euJCcnA9CyJSxcCB4e1hXwJ/oEkLhsNTz8MERFQZMm8N13Tt4CudXkqeAdExND9erVmTRp0jX1P3ToEI888gghISHs3r2bQYMG8fTTT7NmzZocrlRERERERJypefPmzJ8/H3d3d2bPnk2PHj3s4fvRR2HRIit8L1gAHZ8uQMLildZw8+hoaNYMNm507gbILSVPBe/mzZszevRo2rZte039p0yZQrly5XjvvfeoXLky/fv357HHHuP999/P4UpFRERERMTZWrZsyZw5c3B1deXLL7+kd+/epKSkANCiBSxeDJ6eVgjv2NOXhIXLrSveMTFWh3XrnLsBcstwc3YBN2LLli2EhoY6tDVt2pRBgwZddb33nn2H4g8H4+fnh6+vLz4+PvZf0//e19cXLy8vbDZbDm6FiIiIiIhcr7Zt2zJr1iyeeOIJpk2bhru7O5MnT8bFxYXmza3w3aaN9WuH7t7MnbcEj86PwYoV1rj0RYugeXMnb4Xkdzd18D5x4gSBgYEObYGBgURFRXHx4kW8vb0zXe+F2aM5ML8mG0rdz9ZyCRy7uJdjx45x/Phx+6yIqWw2mz2QXymgX+/L29vb/ntXV9cc208iIpK3xcfHEx8fb38fFRXlxGpERG4+HTp0ICkpia5duzJ16lTc3Nz46KOPsNlsNGsGS5ZYs54vWQKPPenFvG8W4tmtY1oqnzfPmplNJIfc1MH7eiXhQq2kXdQ6tIv4Qx6s9wrlp8pNiW7tRYL5h2PHjnH06FGOHTtGREQEMTExxMTE5GhNHh4eGcL41d5f7dfU15Xeu7jkqTsMRERueWPHjuWNN95wdhkiIje11NnNn3rqKT7++GPc3d15//33sdlsNG0KS5da4XvZMnisswfzv5mLZ88uVuhu3956AHj79s7eDMmnburgXbx4cSIiIhzaIiIi8Pf3v+LVboCIjdvZM2E1xdd+Q4XYX3kkbiWP7FrJyV1FWV7gUVxq1Kd8gzh8/eJwdXWlUKFCBAQE4OPjg6enJ8YYLl68SExMDLGxsfZXTEwMFy9evOb3Fy9etNeUkJBAQkIC58+fz6ndZZc+5F/pldlyLy+vq65z+fLU9x4eHhquLyJyFcOGDWPIkCH291FRUZQqVcqJFYmI3Jy6detGUlISvXr1YuLEibi7uzNu3DhsNhtNmlihu2VLWL4c2ndyZ8GcWXi6u8OsWdCxI3z9tfWrSDa7qYN33bp1WblypUPbunXrqFu37lXXK1HzDiovGgYM40z4zxwZPZPS331NscQIel6YBt/CL9/ezeqij7Dv3vLEVD/J6dOn7et7enoSFBREiRIl7C9/f/8sh0tjDHFxcQ7hPX0wT/8+NbRfHtyv9D7196nvExIS7N+bmyEfrOH6Xl5eVwzm6Zdd/vsrLc/sfWYvNzc3hX4RyfM8PT3x9PR0dhkiIvlCz549SUxMpE+fPrz77rt4eHgwevRobDYboaFW6G7Z0rrFu10HNxbMnYmXmxvMnAmdO0NiIjz5pLM3Q/IZmzHGOLuIVNHR0Rw8eBCAmjVrMn78eEJCQihcuDClS5dm2LBhHDt2jJkzZwLW48SqVq1Kv3796NmzJ+Hh4Tz//POsWLGCpk2bZvj8qKgoAgICiIyMxN/f33FhUhInv1zD2QkzuP3XJXgYK6gm48I6WxN+uLMN5+uXoXDwz9hscRk+29fXlxIlShAcHExwcDAlSpTAx8cnm/fQ9UtOTiYuLu6KwTz9+6u9Uj/jWvrlhb9aLi4umQZyT0/Pq7anX57Z7zP79UrLPDw8NLxfJI+JiYnBz88PsI49vr6+Tq7I0VWPV7cI7QMRuVEfffQRAwYMAGDEiBGMHDnSviw83Hrk2MWL1pPFFi1IwWvgs/DZZ2CzWb/27OmkyiVVfjpe56ngvXHjRkJCQjK0d+/enenTp/PUU09x+PBhNqZ75t7GjRsZPHgwe/fupWTJkgwfPpynnnoq08+/5h1z7hwnPphD4mczKPXPj/bm8wSwyO1xDtZ7gmJtSlG6zD5OnrTuA89sNxYsWNAexFNft8oVDWMMiYmJVwzscXFxDm3x8fEO/TJbfvmyK72/fIK8vMDd3T1DOE//yqwt9eXh4XHFZZn1udLv07/XyQC51eWnA3l+pX0gItnh/ffft9/KM3r0aF599VX7sg0b4JFHrPDdtCksXpiC14v9YfJkq8Mnn8AzzzijbLkkPx2v81TwzmnXcxA3+/YT8e5MPOd+SaGoI/b2A5Rnnnc3ott0JaRHSe688zgREf/y77//cuzYMc6cOZPp5xUpUsThqnjx4sVxc7upR/znOSkpKfagHhcX5/D79CH+asszWz/15ED65Zn9mvr7vM7NzS1DGE//+/Rtly+71vb/erm7u191mbu7u04QSI7ITwfy/Er7QESyy7hx4xg6dCgAb7/9Ni+//LJ92caNVviOjbUe7714kcH7lcEwcaLV4aOPoF8/J1QtkL+O1wre1yolhZQNmzj93gwC1s/HMzFtlvON1GdJQHc8nmhP2+7+1KkD8fFxHD9+nGPHjvHvv1Ygj4yMzPCxLi4uFCtWzB7Eg4ODKVq0qB4vdpMzxpCQkGAP4pcH82tp/6/X5Z+f+v5K7XlxJMC1cHV1dQjp6cP65W2pYT2ztsuXXWn59bzc3Nwy/X3qy9XVVXMN5DH56UCeX2kfiEh2+t///sdrr70GwPjx4xk8eLB92ebN0KIFxMRA48awZLHBe8TL8O67XFoB0vWX3JOfjtcK3tcjJobkeQs5/8EMCu0KxwVrF8bizSLasiawOyW6NaJjZ1eqV7duEwHrL0tqCE+9Mh4bG5vh493c3ChevLjDEPUiRYroB3e5ISkpKSQmJjoE8vQh/fL3iYmJDm2Z/Zo+1F/P+9R60i/Pr/8lpQbyzEK6m5vbFX//X8svf12pPbOXq6vrf7Zn1sfV1dXefvmvmS13cXHJc/9/pT+QR0RE5MkDeXBw8C0dOhW8RSS7jRw50v7oxg8++MB+/zfAt99C8+ZW+G7UCJYuMfiMeQ3GjLE6vPUWXLpqLrlHwfsmlSMH8aNHSZrxFXFTZuB3bJ+9+RjBfMWTfFuuO7W7V6FTJ6hY0XFVYwxRUVEOV8X//fdf4uPjM3yNh4dHhvvFCxYsmOd+mBW5UUlJSQ5BPDWgZ/Zr6u9TX1fqe/nvM3t/pbbLX6n1XW2ZZJQaxtMH8st/f7XX5f1cXFz+c530fS7vn5yczOTUe/jysFs5dCp4i0h2M8bw2muvMeZSmJ48eTJ9+vSxL//uOyt8R0dDw4awbKnB591RkDop26hRMHy4Eyq/dSl436Ry9CBuDGzbRuIXM0n5+hs8o8/aF22nFjPpxp6qT9Csa1E6doQyZa70MYazZ886hPHjx4+TlJSUoa+3t7dDEC9RogQFChTI3u0SkSwxxpCcnOwQxC//NX1QT31lFuwvX375++Tk5EyXZ7bsWt+n1n619+l/TX0lJyc7e9fnS7dy6FTwFpGcYIxh6NChvPPOOwB8+umnPP300/bl339vzXIeHQ0hIdZzv30njoHUSdlee80K4Lr4lSsUvG9SuXYQj4+HlStJ/HwGrqtX4JJsheZE3FhJC2bSjdN1HqV9Z08efxyCgq7+cSkpKZw6dcrhqviJEydISUnJ0NfPzy/DlfG89hdURPKnlJQUewhPH8zTv0/9fWbvr3XZlV4pKSlXbEu/LCUlhYsXL/LupXv3NNQ8b1LwFpGcYoxhyJAhTJgw4f/bO+/wqKqnj3/TC6GkF6qIIFIF6b33XkILiCIqIHZFLCAgoCA/XgELSA2h997SlA4BpPde0gik9533j2H37s0GJYEkm5v5PM8+kLmzd++ebHbu95w5M7CwsMDixYsxbNgww/GDB1l8x8cDLVpwv+9iv80EPv+cHb74glPPRXznOSK8CykFEsSjooBVq5CxcCms/wkzmGPgjFUYAH8MhUPLBvAdYIE+fQA3t2c7bUZGBiIjIw17xe/fv4+oqKhs98eWLFlSJcS9vb3h4ODwot6hIAhCoUNLgVyryBgIgpCXEBHGjh2LuXPnwsLCAv7+/hg8eLDh+OHD3GIsLg5o3pzFt9OiX4APP2SHjz7iomsivvMULcVrEd75yblzgL8/Mpf6wyr8vsF8CZWxDEOx0nIIqrQvj4EDgR49gJIlc3b69PR0PHjwQLUy/rS2Zi4uLgYRrv+3qPQYFwRB0FIg1yoyBoIg5DVEhPfffx9//PEHLC0tsWLFCvj6+hqOHznCLcbi4oCmTYEdO4DiAb8D77/PDqNGAXPmANL6NM/QUrwW4V0QZGYCQUHAsmXQrd8Ay2SlsnkwWmIphmGbbR8071IcAwZwb8HcfsZSUlIQHh6Oe/fuGUT5o0ePsvU17jHu4+MDLy8v2NjY5O6FBUEQzBgtBXKtImMgCEJ+oNPpMHLkSCxcuBBWVlZYvXo1+vTpYzh+9CiL79hYoEkTYOdOoPjaRcCIEVzjacQI4I8/RHznEVqK1yK8C5r4eGDDBmDpUiA42GBOggM2oDeWYSgOObRB1x5WGDCA95s878J0UlKSoWibfmU8Li7OxM/CwgLu7u4qMe7p6Qlra+vnuwBBEIQCRkuBXKvIGAiCkF/odDoMHz4cy5Ytg7W1NdatW4cePXoYjh87xv29Y2OBxo1ZfJfY7A+8+Sag0wHDhgELFwJWVgX3JjSKluK1CG9z4tYtICAAtGwZLC6pW5MFYDCWYSjulqyOXr2AAQO4zcGLWpDO2mP8/v37SExMNPGztLSEh4eHSox7eHjASr5oBEEoRGgpkGsVGQNBEPKTzMxMDB06FCtWrICNjQ02btyILl26GI4fP87i+/FjoGFDYNcuoOTOVcCQIZzNOmgQL6TJAtULRUvxWoS3OULEeS3+/qCVK2ERo7QmO4HXeT84BkLn5ok+fViEN2v2YifZiAjx8fGqlmb3799HUlKSia+VlRU8PT1VYtzd3R2WknIjCIKZoqVArlVkDARByG8yMjIwePBgrFmzBra2ttiyZQs6dOhgOH7iBNC2LfDoEdCgAbB7N1By33q+Gc/IAPr1AwICXtzKmKCpeC3C29xJS+NKDkuXgrZvh0V6OgAgA1bYhY5YhqHYgu5w8bZH//6Ary/PwuVFgUUiQmxsrIkYT0lJMfG1traGl5eXoXibj48P3NzcRIwLgmAWaCmQaxUZA0EQCoL09HQMGDAAGzZsgL29PbZt24Y2bdoYjp88yeI7JgaoX5/Fd6m/tgB9+wLp6VwhefXq598bKgDQVrwW4V2YiI7mP+Rly3hF/AmxKInV6I9lGIoDaILy5S3Qvz9Pvr3+et52OSAiPHr0SLVf/MGDB0hNTTXxtbGxMRHjrq6uIsYFQch3tBTItYqMgSAIBUVaWhr69u2LrVu3wsHBATt27EDLli0Nx0+dAtq0YfH9xhvAnj2A8+GdQK9eQGoqV0Zetw6wty+w96AVtBSvRXgXVi5eBPz9+XHnjsF83aIilpEf/OGH63gZr7zCq+C+vkD16vlzaUSEmJgYlRB/8OAB0tLSTHxtbGzg7e1tIsYtpCeiIAh5iJYCuVaRMRAEoSBJTU1F7969sWPHDjg6OmLXrl1o1qyZ4fg//7D4fvgQqFsX2LsXcA7bB3TvDiQncyn0jRsBR8cCfBeFHy3FaxHehR2dDggN5WIO69cDCQmGQwctm2CJbijWoh8ewxnVqvEquK8v8Mor+XuZRISHDx+aiPH0J6nzxtja2pqIcRcXFxHjgiC8MLQUyLWKjIEgCAVNSkoKevTogT179sDJyQl79uxBo0aNDMdPn2bxHR0N1KnD4tvldAjQtSuQmAi0agVs3Zr7vsCCpuK1CG8tkZgIbN7Mqeh797IoB5BmaYet1A1LaCh2oSMyYIM6dViA9+8PVKhQMJer0+kQHR2t2i8eHh6OjIwME187Ozt4eXnBx8fHIMhFjAuCkFu0FMi1ioyBIAjmQHJyMrp164bAwEAUL14c+/btQ/369Q3Hz57lTkNRUUDt2sC+fYDrxQNAp07cNrhpU67XVLx4wb2JQoyW4rUIb61y/z6wYgWvhJ89azA/tnXHsvSBWEZ+CENdABZo2JBFeL9+QOnSBXfJAIvxqKgogxB/8ODBv4px/cq4iHFBEHKClgK5VpExEATBXEhKSkLnzp0RGhqKkiVLIjAwEHXr1jUcP3eOxXdkJFCrFotvt2tHgA4duPl3w4bc/LtUqYJ7E4UULcVrEd5ah4g3oSxbxkI8IsJw6KZjVfyRNBTLMRh3URYWFtyWzNeXCzN6eBTgdRuhF+PGaeoREREixgVByDVaCuRaRcZAEARzIiEhAZ06dcL+/fvh7OyMoKAg1K5d23D8/HkW3xERQM2aQGAg4HYrjJt/P3rEVdh27wZcXAruTRRCtBSvRXgXJTIyOAV92TJg0ybgSRswsrBAWIlWmBM7FBvQGwkoDktL/vLw9QV69za/74jMzExDmvqzinF9qrqIcUEQtBTItYp+DIBYEClj8NFHwP/9HzB+PPDDD2xLTARKluQuHo8eAU9+tZg4EfjpJ2D0aGDGDOXcpUqx7+XLgLs72/7v/4AffwQGD1b71qjBRYqDgoAyZdgWEADMnMmZpFOnKr49evDi1uLFwEsvsW33buDXX3nB66uvFN/PPuNr/eYbxffkST73q68CI0YovgsXcvVkX1+gXDm23b7N1+TlBXTsqPgePMjlXurUAdzc2BYfD9y4weNSsaLiGxvL8/PFiknbYUF4FuLj49G+fXscPnwYrq6uCA4ORo0aNQzHL1zgbd0REfzdERgIuN//h/uPRUdzLvrevcofp/CfaCleW+fTNQnmgLU13yV06sTRdv16YNkyWISG4o3YICxFEP60GYV9xXthdowf9u1ri337rPD++1yY0deXbypKlizoNwJYWVnB09MTnp6eeP311wGwGM+aph4REYHU1FTcvHkTN2/eNDxfv2dcCrgJgiBog8xM/tf4azwtjYsLG9fxJOIQmJX4eODBA9NjV6/yPLX+/ADfVJ86Bbz2mtp3/34WyMnJiu3mTWDLFiBr58w1a7gpyfvvK8L73Dng5595gcxYeP/8M9/Q16+vCO8TJ4Dhw4HGjdXC+8MPgePHge3bgc6d2XboEGe81qzJSXB6evTg+qyrV3PNF71v27ZAlSr8GnrefRc4cACYMgXo2ZNt16/zpIanJ7BkieL7559cdKp/f97eCvAkw+LFLP5HjlR8T5zgcX/tNWUc0tN53O3tFRvApWssLPK2Taog/BvFixfHrl270K5dOxw7dgxt2rRBSEgIXnvyZVC1KhASwuL7zBlexAoMrAWPkBCuwnbqFB/ct4//cIQihQjvokrJksBbb/Hj5k2eYl+2DDaXL6NTTAA6IQDxxb2xwX4Qfo4aih07amLHDsDOjnW7ry/QrZt5FWm0srKCl5cXvLy8nkmM37p1C7du3TI837iaul6QS2szQRCEguXqVfXPkyfzyrFxhx4HB+DePeX/ej7/nEVe1ppGly6xAHd2VmzvvMNxzdgGAMHBnDBmfI/cpw9QrRqvNhuzaBGvjutXxgGgeXNg/nygfHm17/jxwOPHat/XXuNrrlRJ7duzJ1Cvnvr13N05HletqvatXJmFq/EkuZUVX3/WRTb9hITxandqKpCUZEiKM3DjBk8MGDVPQUwMsGuXMhmgZ8cO7qJUrZoivMPDgU8/5Qw6Y+H9v/8By5dzBsGnnyq+r70G2Nry9egZNYrHcvJk4Ouv2fb4MU9I2NuziLd+cme7eDFPPvTpAwwcyLaMDGDCBPb9/HOlxfLp0/yZePVVXqXUc+4c+5Qvr5xXEEqWLIk9e/agTZs2OHHiBFq3bo2QkBC8+uqrAPhzpBffZ8/yv0FB1eAZEsJK/OxZoGVLTlnx9i7ItyLkM5JqLigQAceOcUG2Vas4oj4h3LMmluqGYnbUIISDvyQcHLhbgq8vz6ob3+yYM8Zp6vq2Zk8r4GZra6taGff29oarqysssy5dCIJQqNBS6ppWkTHIe3Q6Ft9WVoqwTEnhFWhLS/VkwZkzXLW5alVFK0RFsci2t+d7AT2rVrFo7d6dJwwAXt3/6iu+V1iwQPH97juuOfXpp9zyFOD1gLp1eUIgPFzxHT6cV9anTwe+/JJtDx4APj68Cp6ZqayGf/ABMHcup/JPnsy2+HhA/1FKSlLuW776is/50Uc8EaAfGysr/n9EhFL3Zto04PvveaJmzhzl2vQTDGvXKuOzdy8nFzZuDAwdqvguWcK3XL16KbW2IiKAu3d5QsV4IkOnM82WEMyDmJgYtG7dGv/88w+8vb0RGhqKV4z69V65wqL73j3+uwkKArwSrrL4vnOHe/sa72ERskVL8VqEt5A9aWkcCZctA7Zt458BkKUlrlRoh98T/PBHZE8kgT/8Tk6csubry2npdnYFefE5J2s19fDwcISHh2fbZ9zGxsZEjLu5uYkYF4RChJYCuVaRMRCykpDAD0dHRUCnpvKaQVoa6xk9+/fzSnbdukCDBmxLSmKRnZIC/PabImh//53rz/r6cuo8wD5ly/K/9+4pr/ftt5xuP2aMIryJeOJCp+OmMnrh/eOPwLhxwJtv8gq8nlKleEvDpUucoQAA8+bxOfv0AdatU3zLlOFK2UeP8vZggG/LJk8GWrTgGgZ6Jk4E4uJ40kGfon/zJm8RKFOG/fXcvMnv39Oz8N2zmRPR0dFo1aoVzp49i9KlSyM0NBQvv/yy4fjVqyy+797llfCgIMA75QZ/WG/e5F9UUFDB9fYtBGgpXovwFv6bmBjejObvz1VbnpDp6ISTL/XBz1FDsTqyJQgcwUqW5FlcX1/ezlJYC7bo+4xnbW2WnRi3trY2iHG9IHdzc4OVfrpcEASzQkuBXKvIGAjmSHw871d3cFAK8xFxyn1yMtCliyJkDxzg4lo1ayr74gFOfY+LYzGuX0lfuJDT4Lt352J8elxd+Tbs/HllW8EffwDvvcfn3LhR8S1fnovuHT2qZBqsWMEFA9u25RV4PdWrc1bCvn18rwbwesuwYbxCv2mT4vvZZ3zeceO4aB/AmnHtWhb0+lR+gDMj0tJ4u4R+u4NeaWh1515kZCRatWqF8+fPo1y5cggNDUUFIyF97RqL7zt3eKIlOBjwybjN4vvaNU5xCAoCjAS7oKCleC3CW8gZV6+yAPf35w1fT0j1KIO/yw7GlFt+CI2uZrC7unJVdF9f3s5S2HWoTqfDw4cPTcR42pOMAGP0BeCMV8Y9PDxEjAuCGaClQK5VZAwEgUV3YiLv79cvZNy+zUXy3NyARo0U35kzOf3/ww85/R4A9uzhKv116vAKvJ7XX+eCfSEhXHEf4C0CAwfq9yQrvjVrsqDes4cL/wG8f75rV84oOH5c8W3alCcc1q3j1XsA+Osv1pi1agFhYYrvZ5/xeceN49cEOLtgwQJ+v++9p/j+8w9PelSpokx46HT8rzkkHIaHh6Nly5a4dOkSKlSogNDQUJQz2jNw/Tq/x9u3OcM8OBgojXs863HpElC6NM/SVKlSgO/CPNFSvBbhLeQOIl79XraMV8MfPzYciq9cB7vd/TDx0kCci1aq0Xh4cH9wX1/+YjaHL8oXARGpxHh4eDgePHiAVOOKME+wsrKCh4eHqoibp6cnrKVqiyDkK1oK5FpFxkAQ8pe4OODWLS5qZ6z/1q/nvfQ9eyrbkcPCuAVfhQrApEmKb69eLMSXLlVS/3fu5FpAr7+urpTfvDnw9998G9mvH9sOHOB7xEqVeI+0ni5duJ7AwoVcFxjgrQS1avFKv1HjGnz3HVfnHzuWCyYCwMOHvDXA2ZknJvRcuMBp/y+9pBRQzO0K/f3799GyZUtcuXIFFStWRGhoKMoY7d++cYPF961b/P6Cg4Ey1uGcjnDuHF9AUJBpu4QijpbitQhv4flJSeENR/7+/K34pEgZWVnhYd0O2Ojkh4kne+D+I6X6mo8Pf8n6+vJMq9bSj4gIMTExhuJt+kdK1jKxACwtLeHu7q4S415eXrAprDn6glAI0FIg1yoyBoKgDdLSuIV1Zibvm9cTFMQr3M2bK4X8Ll8GZs/m6vdTpii+77zDq/M//8zp+ACL68aNuTf9tWuKb7dufFu6YIHSlu/sWa5Y7+7Oe+b1DB7M6fizZgEff8y227f5nK6uXPROz+zZfM3Dhimr+cnJXMTPyYlb7t2/fxctWrTA9etpKFeuBnbsWIhq1ZTK5Tdvsvi+eZMzy4ODgbL2UZxK8M8/fIH79nGagQBAW/FahLfwYomO5oag/v7AkSMGMxUvjnuN+mG5hR9+PNQcj+OU5e5y5bjXZ//+wBtvaE+E6yEiPH78WCXE79+/j2Tjhq9PsLCwgJubm0qMe3t7w9bWtgCuXBC0h5YCuVaRMRAE4d/IyOCEy9RUztTWc+AAry43bKi05rt9myvX29uzyNYzdiyL9EmTgCFD2Hb+PLfCc3HhlXI9Q4fy7a1x67u7d3kywdqaJxgsLIDbt2+jevVQxMf7wdV1Hs6d6wtPT0/ExbGgd3Bg/5s3+eexY4HLh2Mw5Wh7OF8PA1xcoNu9F8vO1oGTE0806G//YmO5E0GJEopN62gpXovwFvKOS5e4Oefy5aocICpbDlcbDMaCFD/8FlJV1RO0YkUW4L6+nD6kVRGuh4gQFxenSlO/f/8+EhMTs/V3dXU1EeP2+kakgiA8M1oK5FpFxkAQhIIgI4NXulNS1PXO9u8HLl7kvvH6BemICO4Jr9Px7a6eESNisXhxJnS6yXjttT0IDg5GeroHypThekf6Pd/Xr7OIjosDpnz2GF//3RE4cgRUqhQaPN6NY6iPxESu5A8A48dzS7uxYznVH+DU+Fq1gGLFeO+9iwvb9+3jFfomTThVX09wMIv/119XCgESme89t5bitQhvIe/R6Xj6cdkyLoEZG6scqvMGztT2w9zoAVixzwNJScrTKldWRHj16gVw3QVIfHy8ar/4/fv3ER8fn62vs7OzSZq6uX0pCYK5oaVArlVkDARBKMxcu3YNLVq0wL1791CjRg3s3h2EmBg3JCVx1fm7d7nw8LVrvPf899+B/h3jWCXv348kq+L4rNpOzDvVxCCKP/mEe81//bWSip+YyKnuABeg0///m2+AH37g9nK//MI249Z39+4pRfh++omr6r/9NqfO6/H1ZUE+ezYXvAN4b/3hw1xlv1kzxffmTRb0bm4vtpiyluK1CG8hf0lJAbZu5VydnTsN+8FhZYWMdh1xtLIf5tzqjk27HWC8Hfq11/iPv39/7oNYFElMTDTZM/7YqKidMSVKlDBZGS9evHj+XrAgmDFaCuRaRcZAEITCzpUrV9CiRQs8ePAAtWvXRmBgIFz0S9Jg8duqFReSK1+eV6Nfck/gjeohIcoytlET9sxMfuhTzdPTuXJ8wpOn6YsX79jBleibN+cOQwCn5devzyvsp08D+ltDfX/60aMV4U3ElfQzM3mSQJ/OP3Mmr/IPGcK383pcXLjVnnHru5Ur+bxdupj2nE9P59fTi/9793iPv4+PurhfQkIiihfneB0RkQB392KGiYi0ND6PtbW6H70+cdTBQRmP9HT2t7LiLQe58U1K4nGxt1cmF2Ji4uDqKsLbBAniZkZUFPeu8PcHjh1T7CVKIK1HX4SW9cPc082xa48ljLt11aypiHD93p2iSnJysiE9Xb86/tB4Q5IRxYoVMxHjJUuWhIW55hYJQh4iwtv8kTEQBEELXLx4ES1btkRERATq1q2Lffv2oVSpUobj9++z+L58meseBQcDFb2SuIz83r2sCLds4erneURCApdpcnBQqrvrdFydPj6ei9s5PKmRvH4937q3aqWuEK/vOX/njlL9/uefuW3c4MHqVHw3N94/f/Ys76cHgD//5Nfp1o3frp6KFRNx44aT/koRGVnM0FLuhx94ZX/ECC6mp6dYMRbJN25w5X2AV+0//hgYNAgICFB83d35vRtfy4IFwMiRQI8e6p72FSpwVfqjRzlrgX3jMHLks8Uq6WEkFBzu7pz/8sEHvGlm+XL+S759G7b+i9AOi9CuXDmkjB6MXe5+mP93VezdyzN0p09zmk2dOizC+/XjVhBFDQcHB7z00kt4yejNp6amGkS4/t+oqCgkJibi6tWruHr1qsHX3t7eRIy7uLiIGBcEQRAEQXgBvPrqqwgMDESrVq0QFhaGDh06YM+ePShZsiQAXuENCWEhe+kSp58HBzvi5S1buHz6jh3cNH3jRqBTpzy5RicnJUVdj6UlMHy4qW+fPkpVd2MePmSxbnwLOWAA7yV3dVX7jhnDIt1T6TqMYsU4wzXr/XxcXM7eizkjK96CeaHTcVNHf3/eD27811a3LhJ7+2GT/QAs3eWJoCBOf9FTv74iwo3bVQhAeno6IiIiVGnqkZGR0Ol0Jr62trbw8vIy7Bf39vaGu7s7LLXSeF0QICvehQEZA0EQtMSZM2fQqlUrPHz4EI0aNcLu3btV2wDDw7n3+YULnNYdEgJUKpvKN7ebN3Nu+dq1Sj+1IsL164l4+WVJNS90SBAvZCQnK/vBd+1S7QdHhw6I6+GHtandsWKTI0JCWLPradyYU9H79VP2jghqMjIyEBUVpaqoHhERgQz9OBthbW0NT09PgxD39vaGh4cHrK0laUYonIjwNn9kDARB0BqnTp1C69at8ejRIzRt2hQ7d+40xCKAq6S3bs37pH18OO288kvpnKu9di0rzJUrgb59C/Bd5C9aitcivIXCwdP2gxcvDvTpg5guflgV3hKr11ri7795NgrgdJemTXmysE8fpSKjkD06nQ7R0dGGVXF9qnqa8Sb7J1haWsLd3V21Mu7l5SW9xoVCgZYCuVaRMRAEQYuEhYWhTZs2iI2NRYsWLbB9+3ZVDIqMZPF97hzg7c0twV6tlAEMGwasWMELUMuW8WblIoCW4rUIb6Hw8ZT+4ChTBhg8GJEdh2LV6dewejVw8KBy2NKSi0L2788iXF+YQfh3iAgxMTEGEa5/JCcnZ+uv7zVuvDruoK/IIQhmgpYCuVaRMRAEQascPXoU7dq1Q1xcHFq3bo2tW7fCUd+sG7ze1KYNcOYMLxoFBQFVK2dyFbElS/imdtEiFuMaR0vxWoS3UHjR9wf39wfWrFH1B8frrwN+frjXfCBWh3phzRrgyBHlsJUVF7Ho359bLGQt+iD8O0SEuLg4k5Xxp/UaL1mypIkYd3JykiJuQoGhpUCuVWQMBEHQMocOHUL79u2RkJCAdu3aYcuWLbA32lAcHc3i+/RpLkIWFAS89qoOeP99YP58TuucP5/FuIbRUrwW4S1og5QU7nPo78/VH9PT2W5pCbRrB/j54dbrPbF6WzGsWQOEhSlPtbLiDg2+vty5wdm5QN6BJjDuNa4X448ePcrWV9/ezMvLyyDInZ2dRYwL+YKWArlWkTEQBEHr7N+/Hx07dkRiYiI6deqEjRs3ws6oStjDh3yPeuoU4OEBBAYC1asRMHas0nB77lxuiK1RtBSvRXgL2uPhQ2D1ak5FP3RIsTs58fL2kCG4Vr411qy3wurVwD//KC42NkD79rwS3qMH8KTTg/AcpKSkmLQ3i46ORnZfPXZ2dioh7u3tDTc3N6moLrxwtBTItYqMgSAIRYHQ0FB06tQJycnJ6Nq1K9avX6+qlxMTw+L75EneJhkYCNSoTtwge9Ysdpo1i5tUaxAtxWsR3oK2uXpV2Q9+7Zpi9/HhohRDhuCyQy2sWcNa/exZxcXWFujQgVfCu3UD5CPz4sja3iw8PByRkZHINO4P94SsFdW9vLzg6ekpFdWF50JLgVyryBgIglBUCAoKQpcuXZCSkoKePXtizZo1sLGxMRyPieGFobAwwM0N2LcPqFWTgPHjgenT2Wn6dODLLwvoHeQdWorXIryFogERcPgwp6KvXs3fYHpq1AD8/IBBg3AhrrRBhF+4oLjY2QGdOvFKeLduvHguvFgyMzMRFRWlWh0PDw/PtqK6hYWFqqK6/mG8N0oQ/g0tBXKtImMgCEJRYs+ePejevTtSU1PRt29frFy5UrXI8OgRi+/jx7k20b59QO1aBEyaBEycyE6TJgHfflswbyCP0FK8FuEtFD3S0oCdO1mEb93KPwNcpKJ1axbhvXvj7K3iWLuWRfilS8rT7e2BLl1YhHfpApjZ37+m0FdUN05TDw8PR1JSUrb+zs7OJvvGnWSWRMgGLQVyrSJjIAhCUWPnzp3o2bMn0tLSMGDAAPj7+6vE9+PHnI159Cjg4gLs3QvUqQNg6lTg66/Z6euvgcmT+b5WA2gpXovwFoo2jx4Ba9dyKvrffyt2BweutDZkCKhde5y5YI3Vq7l4+tWrareuXTkdvVMnwKgThJBHEBHi4+NNirjFxcVl6+/k5KQS4l5eXlLETdBUINcqMgaCIBRFtm7dij59+iA9PR2DBw/G0qVLYWVlZTgeGwt07MiJnM7OLL7r1gXw88+87xvgf3/6SRPiW0vxWoS3IOi5cQNYsYJXwo2XuD08gAEDAD8/UJ26OPWPBdasYRF+/briVqwYp6H3789fiNK6On9JSkoyKeL28OHDbH2zFnHz8vKCm5ubKrAJ2kZLgVyryBgIglBU2bRpE/r164eMjAwMHToUixYtUt2jxMXxveahQ0CpUsCePUC9euAK5x98wE5jxwKzZxd68a2leC3CWxCyQsTVK/z9gZUrgago5dirrwJDhgCDB4PKV8CJEzCI8Js3FTcnJ6B7dxbhHTpwerqQ/6SlpRmKuOn3jD+tiJuVlZWhiJtekHt4eKgqiwraQUuBvCCZN28eZsyYgfDwcNSqVQtz5sxB/fr1s/VdsGABli1bhrNPqljWrVsXU6dOfap/YRkDQRCEvGDdunUYMGAAMjMz8dZbb2HBggWqLi/x8ZxteeAAd+HZvRto0ADc2/vdd9npvfeAefO4vW4hRUvxWoS3IPwb6emcw+PvD2zaxP3C9TRrxiK8Xz9QKWccO6aI8Dt3FLfixbk1Wf/+XBTDqD2jUADktIibq6uryeq4o+wpKPRoKZAXFKtXr8bQoUPx+++/o0GDBpg9ezbWrl2LS5cuwcPDw8R/8ODBaNKkCRo3bgx7e3v8+OOP2LhxI86dO4fSpUub+BeGMRAEQchLVq9ejUGDBkGn02HkyJH47bffTMR3ly68W7JECRbfDRsCWLwYePttXkx66y0W44U0q09L8VqEtyA8K3FxwIYNLMKDg/nLDOC+Y127sgjv3Bk6GzscPcpF2dauBe7dU05RogRvHe/fH2jXjp8qFDxEhEePHqmE+IMHD5CYmJitf4kSJUyKuJUoUUL2jRcitBTIC4oGDRqgXr16mDt3LgBAp9OhbNmy+OCDDzBu3Lj/fH5mZiacnZ0xd+5cDB061OR4YRgDQRCEvCYgIAB+fn4gIowaNQpz585V3W8kJLD4/usvXuzZtQto3BhAQAAwdCig0/E96uLFQCFsxaqleC3CWxByw927vB98+XLgzBnF7uzMqtrPD2jcGDqywOHDvAq+di1w/77iWqqUIsLbtgWM2jUKZkJ8fLzJyvijR4+y9XVwcFC1NtPvG7csxOldWkZLgbwgSEtLg6OjI9atW4eePXsa7MOGDcPjx4+xefPm/zxHfHw8PDw8sHbtWnTt2tXkuLmPgSAIQn6xdOlSDB8+HESEsWPHYvbs2SrxnZjIdYaCg3m7465dQJMm4JvPQYOAjAygXz8W44XshlNL8VqEtyA8L6dP8yr4ihVqZf3SS4b94KhSBTod78NZswZYtw4ID1dcnZ2BXr1YhLduXei+E4sUKSkpJvvGo6KioNPpTHytra3h4eGhSlP39PSEjfyCCxwtBfKC4P79+yhdujQOHjyIRo0aGexffPEFQkNDceTIkf88x6hRo7B7926cO3cO9tkUwtCPwZ07d1RjYGdnBzvZsyMIQhFj0aJFePvttwEAn3zyCWbOnKkS30lJLL6Dgrjg786dvCsSmzez6E5P5xWfVasK1b5Hc4vXqampSE1NNfwcFxeHsmXLivDOirnfyAiFnMxMICSERfj69Zz7o6dePRbhAwYAHh7IzAT27+eJyHXrgIgIxdXFBejdm78jW7USEV4YyMjIQFRUlEqMR0REyL5xM8bcAnlWzD1ePa/wnj59On766SeEhISgZs2a2froxyArEyZMwMSJE5/r+gVBEAoj8+fPx7tPCqd98cUXmD59uon47tED2LePxff27UCLFgB27OCby9RUoHNnvk8tJJV/zS1eT5w4Ed9//72JXYR3Fsz9RkbQEElJPMO4fDlXutBX0bay4jLnQ4bwN6OjIzIzuSjGmjX8PRgZqZzG1ZW/J/v3B1q2LJRbc4osRISYmBiTVPV/2zeeNVW9VKlSsm88jzC3QJ4Vc49Xz5NqPnPmTEyZMgX79u3DG2+88VQ/WfEWBEEw5ddff8Xo0aMBAF9//TUmT56suldITuaF7T17AEdHYNs2XsjB3r1875mczIWGNm1iBzPH3OK1rHg/I+Z+IyNolMhIrrTm7w8cO6bYnZxYVfv58TeilRUyMrg4xurVXMctOlpxd3MD+vRhEd68uYjwwop+37hxEben7Rs37jeuXx2XfuMvBnML5FkpDPGqQYMGqF+/PubMmQOAi6uVK1cOY8aMeWpxtZ9++gk//PADdu/ejYYNG/7r+QvDGAiCIBQEv/zyCz788EMA2WcBpaTwFsZduwAHB2DrVqBNG3BmZteuvCm8ZUs+8CQWmitaitcivAUhP7l0iQtbLF8O3Lih2L29ufjFkCFArVqAhQUyMvj7ce1aXgl/+FBx9/BQVsKbNy+0HSKEJ6SmpqrEuL7feHb7xq2srODh4QFPT0/VvnFZAcwZWgrkBcXq1asxbNgw/PHHH6hfvz5mz56NNWvW4OLFi/D09MTQoUNRunRpTJs2DQDw448/4rvvvsOKFSvQpEkTw3mcnJwMvwtjCsMYCIIgFBSzZs3Cp59+CgCYPHkyvvnmG9XxlBSgb19ON7e3Z43dti244FCnTtyLrEkTTkM34+9YLcVrEd6CUBAQAQcPsgBfvRowXvGsXp0F+KBBQNmyALgYZXAwi/ANG9Qi3NNTEeHNmokI1wrG/caNH8bpTca4uLgYRLhekDs5OUmq+lPQUiAvSObOnYsZM2YgPDwctWvXxi+//IIGDRoAAFq2bIkKFSpgyZIlAIAKFSrg1q1bJud42p7twjIGgiAIBcVPP/2EL7/8EgAwbdo0k2yj1FQW39u2sfjevBlo3x7AkSO89TE2Fqhfn5fGnZ0L4B38N1qK1yK8BaGgSUvj0pP+/vzNqBdWFhZcEcPPj3PMnxQZSk/nipVr1wIbNwIxMcqpPD2VdPSmTUWEaw0iwuPHjw17xvXV1ePj47P1d3R0hLe3Nzw9PQ2p6i4uLtLiDNoK5FpFxkAQBOG/mTp1Kr7++msAXENDvwquJzWV7wu3bOFi5hs38oI3Tpzgvd4xMcDrr/MecFfXAngH/46W4rUIb0EwJx4/5jLn/v682VuPnR3QvTuvhHfsCNjaAlBE+OrVXCPDeOHcy4tnOfv140wiEeHaJTExEREREaqV8ejoaGT39W5tbW0Q4vpHUWxxpqVArlVkDARBEJ6NSZMmYcKECQCA2bNnG/Z/60lLA3x9+V7R1pazJ7t0AbfEbdsWiIoCatTgcugeHvn/Bv4FLcVrEd6CYK7cusW9wf39gQsXFLuLC397DhkCNGrEK+PgL9XAQGUl/PFj5Sne3moRLgue2ic9PR2RkZGGAm4RERGIiIhAenq6ia9xizNjUZ7dvlutoKVArlVkDARBEJ6d7777DpMnTwbA24D0lc/1pKcDAwdy3SAbG/63WzcA589z5bXwcKBqVb6Z9PYugHeQPVqK1yK8BcHcIQJOnuSibCtW8BejnooVgcGDWYRXrmwwp6XxpKVehMfGKk/x8VHS0Rs3FhFelNDpdIYWZ8aPp7U4c3JyMmlx5uLiool941oK5FpFxkAQBOHZISJ8/fXXhoKWv/32G9577z2VT3o63zauXcvie+1a7jCGy5eB1q2Be/eAV17hdMoyZQrgXZiipXgtwlsQChOZmfxluHw55wklJCjH6tXj/eC+vqo0obQ03razdi2nGGUV4fqVcBHhRRfjFmf6feMxxsUDjLCxsTFZGffw8Ch0qepaCuRaRcZAEAQhZxARvvjiC8ycORMAsGDBAowYMULlk5HB6zWrV3Nr2jVruPUYrl9n8X3rFi/sBAUB5csXwLtQo6V4bZbCe968eYYqqbVq1cKcOXNQv379bH2XLFmC4cOHq2x2dnZISUkx8ZUgLmiKxESulLF8ObB7N4tygDdzt2/P36o9egBGX1CpqbwSvno1V7aMi1NOV7q0shLeqJGI8KJOWlqaat+4PlU9IyPDxNfCwgJubm4mgtzcgqMxWgrkWkXGQBAEIecQET755BPMnj0bFhYWWLhwoYlWysgAhg3jREpra2DVKr4HxK1bLL6vXwfKlWPx/fLLBfNGnqCleG12wnv16tUYOnQofv/9dzRo0ACzZ8/G2rVrcenSJXhks9l/yZIl+PDDD3Hp0iWDzcLCAp6enia+EsQFzRIZyWp6+XLg6FHFXqwY9xobMoT37xhVWEtN5ZXwNWuyF+H6lXAR4YIenU6Hhw8fmqSqJyUlZetfvHhxEzFuLqnqWgrkWkXGQBAEIXcQEcaOHYu5c+fCwsICS5cuhZ+fn8onMxN4802+dbSyAlau5Ps+3LvH4vvyZU6NDAoCqlQpkPcBaCtem53wbtCgAerVq4e5c+cC4Bu9smXL4oMPPjDpTQew8P7oo4/w2LiS1FOQIC4UCS5f5m/RgACesdTj5cVVNYYM4bYRRuInNRXYs4fT0Z8mwvv3Bxo2FBEuqCEiJCQkqIR4REQEHho3mzfCxsbGpKp6QaSqaymQaxUZA0EQhNxDRBg9ejR+++03WFpaYvny5Rg4cKDKJzMTeOstYNkyFt8BAbxjEeHhvGBz/jz3qg0MBKpVK5D3oaV4bVbCOy0tDY6Ojli3bh169uxpsA8bNgyPHz/G5s2bTZ6zZMkSjBgxAqVLl4ZOp0OdOnUwdepUVMvmw6EfmDt37qgGxs7ODnZ2dnnyngShwCACDh9mEb56NWAshKpWZQE+aBBQoYLqaSkp6pVw4xbRpUvzbGi/fiLChX8np6nq+V1V3dwCeWpqKlJTUw0/x8XFoWzZskVadIrwFgRBeD50Oh3ee+89LFiwAJaWlli5ciX69++v8snMBEaMAJYs4fs6f3++PURUFPf5/ucfwM2N9yrWqpXv78Hc4nVWCq3wvn//PkqXLo2DBw+iUaNGBvsXX3yB0NBQHDlyxOQ5hw4dwpUrV1CzZk3ExsZi5syZ+Ouvv3Du3DmUyVKNTz8wWZkwYQImTpz4wt+PIJgNaWm8D3z5ct4XblwDoWlTFuH9+nGrMiNSUtQr4cYivEwZJR1dRLjwLBinqhuL8qdVVS9WrJiq17iXlxdcXV1h+QI+bOYWyCdOnIjvv//exF6URacIb0EQhOdHp9NhxIgRWLx4MaysrLBmzRr07t07iw8wciSwcCHfzy1dyreGiInhukFhYYCzM6/M1K2br9dvbvE6K0VKeGclPT0dVatWxcCBAw297PTIircggMuab9jA+URBQbwyDnBfiS5d+Ju2SxfA3l71NL0IX7OGtbuIcOFFkTVVPTw8/Kmp6tbW1vDw8FCJcU9Pzxx/h5tbIJcVb1NEeAuCILwYMjMzMXz4cPj7+8Pa2hrr1q1Djx49VD46HfDee8CCBbwbcfFiLsCGx4+BTp04i7JkSWDXLr7ZyyfMLV5npdAK79ykmmdHv379YG1tjZUrV6rsEsQFIQv37nE1jeXLOZVIT8mSrKSHDAGaNzdR0ikpvIC+du3TRXj//kCDBiLChdyRlpaGyMhI1ep4REQE0tPTs/V3dnY2WR0vUaLEUwu5aSmQaxUZA0EQhBdHZmYmhg4dihUrVsDGxgYbNmxA165dVT46HTB6NPD77yy+Fy4Ehg8H3+h16QL8/Tfg5ATs2AE0a5Yv162leG1Wwhvg4mr169fHnDlzAHB6RLly5TBmzJhsi6tlJTMzE9WqVUPnzp0xa9Ys1TEJ4oLwL5w5w6vgAQHA3buKvUwZ3uwzZAhQo4bJ02QlXMgvdDodYmJiTPaOxxt/6IxwcHBQ7Rn39PSEu7s7rKysNBXItYqMgSAIwoslIyMDgwcPxpo1a2Bra4vNmzejY8eOKh8iYMwY4NdfWXzPn897wJGYCHTvztmSjo7A1q1c/TyP0VK8NjvhvXr1agwbNgx//PEH6tevj9mzZ2PNmjW4ePEiPD09MXToUJQuXRrTpk0DAEyaNAkNGzZEpUqV8PjxY8yYMQObNm1CWFgYXnvtNdW5JYgLwjOg0/GM5vLlvKQdG6scq1kTGDyYhXiWGgrAs62EiwgXXjSJiYmqVfHw8HBERUUhu/BmaWkJDw8PlCxZ0lDdNSYmxiwDubu7e5GOVxKzBUEQXjzp6ekYOHAg1q9fDzs7O2zduhXt2rVT+RABH34IPFkHxR9/8B5wJCcDvXrxzZ69PbBpE9ChQ55erwjvPGbu3LmYMWMGwsPDUbt2bfzyyy9o0KABAKBly5aoUKEClixZAgD4+OOPsWHDBoSHh8PZ2Rl169bFlClT8Prrr5ucV4K4IOSQlBRg+3ZeBd+2DdCn+VpYAC1b8ip4nz6cmp7NU0WECwVFRkYGIiMjTQS5fh91Wloapk6dCgAYP348bG1tC/JyTUhJScH06dOLdLySmC0IgpA3pKeno3///ti0aRPs7e2xfft2tM6yek0EfPIJMHs2//zrr8D774Nv8Pr14/tCW1tg3TqgW7c8u1YR3oUUCeKC8BzExPCX6/LlvCKux86Ov3CHDOHiG9kIGElHF8wBIkJsbCzCw8Nx48YNdO7cGYAIb3NFYrYgCELekZaWhj59+mDbtm1wdHTEjh070KJFC5UPEfDZZ4B+9+6cOZyGjrQ0YOBALtZrbc1ta7NUSn9RiPAupEgQF4QXxK1bwIoVLMLPn1fszs5cVW3IEKBx42xV9L+J8NKlFRHeqJGIcCHvMA7kkmpunkjMFgRByFtSU1PRq1cv7Ny5E8WKFcOuXbvQtGlTlQ8R8OWXwIwZ/PP//R8wdiw4C3LoUGDVKsDKiu8JBwx44dcowruQIkFcEF4wRMCpU5yKvmIF8OCBcqxCBaUoW9Wq2T793/qEly7NWez9+j1VwwtCrtFSINcqMgaCIAh5T0pKCrp37469e/fCyckJe/bsUbV1Bvh2b/x4YPp0/nnWLODjjwFkZgJvvQUsW8Y3aosXsxh/gWgpXovwFgThxZCZCYSEAP7+nHpkrKJff50F+MCBgLd3tk83FuFbtgBxccoxHx9lJVxEuPAi0FIg1yoyBoIgCPlDcnIyunXrhsDAQBQvXhx79+411NfSQwR8+y3www/888yZwKefgovyvvsu8OefWcqgvxi0FK/l9lUQhBeDlRXQpg2wZAkQEcH7fbp1470/J0/yt3OZMkC7dsDSpWplDS6O2b076/bISBbffn5AiRLA/fvAL79wy8iyZTnF6e+/+bteEARBEARByD0ODg7YsmULWrZsifj4eHTo0AHHjx9X+VhYAJMnA999xz9/9hnw00/g1ZA//uAG4ETAO+8A8+bl/5soBIjwFgThxePgwHu9t2zh9PNff+Wlap0O2LcPePNNwNOT9wJt3cpFOozQ12tbtoxF+NatahE+Zw7QvDnr+A8+AP76ixfcBUEQBEEQhJzj6OiIrVu3olmzZoiNjUW7du1w4sQJlY+FBfD998DEifzzl18C06aBxfecOVwGHeAKbP/7X75ef2FAUs0FQcg/rl/n/eABAcClS4rd1VUpytaoEX+zZ0NqKrB3r7In3LjFuJeXsie8aVNegBeEp6Gl1DWtImMgCIKQ/8THx6Njx444ePAgnJ2dERQUhNq1a5v4TZnCqecAr4R/8w14xfvrr5+ocQBTpwJfffVc16OleC3CWxCE/IcIOHGCK2CuXMmp6XpeegkYPJgfr7761FOkpvLi+dq1wKZNIsKFnKGlQK5VZAwEQRAKhri4OLRv3x5HjhyBq6srgoODUaNGDRO/qVNZZwO8Cj5hAvgeb9IkZVl84kTOT3/Kosp/oaV4LcJbEISCJSMDCApiEb5hA5CYqByrW5dXwQcMYDX9FNLSWISvWcMr4Y8fK8e8vLi1ZL9+vEdcRLgAaCuQaxUZA0EQhIJDn25+7NgxuLu7Izg4GNWqVTPx+/FHYNw4/v9337HOtrAAl0DXr3Z/9RVXZcuF+NZSvBbhLQiC+ZCYyPvCAwKAXbuUjduWlkDbtrwK3qsXULz4U0+hF+H6lXBjEe7pqRbh1tZ5+m4EM0ZLgVyryBgIgiAULI8ePULbtm1x4sQJeHh4ICQkBFWzaRE7YwbwxRf8/2++4QVvCwvwPm/9vu+PPwZ+/jnH4ltL8VqEtyAI5klUFC9hBwQAhw4pdgcHoEcPFuEdOgA2Nk89RVoaEBioiPBHj5Rj7u6KCG/RQkR4UUNLgVyryBgIgiAUPDExMWjTpg1OnToFLy8vhISEoEqVKiZ+s2Y9aS+GLAvc8+ZxsTUAGDWKi7DloC+sluK1CG9BEMyfa9eAFSs4Hf3yZcXu5qYUZWvY8F9nUdPT1SI8JkY55u7OC+n9+gEtW4oILwpoKZBrFRkDQRAE8yA6OhqtW7fGmTNn4OPjg9DQUFSqVMnEb/ZsXtgGeAV8+vQnt2Z//gmMHMn7v0eM4PZjzyi+tRSvRXgLglB4IALCwliAr1qlLspWsaJSlC2bmVhj0tN5W7lehD98qBxzc1NEeKtWIsK1ipYCuVaRMRAEQTAfoqKi0KpVK5w7dw5lypRBaGgoKlasaOI3dy63egV4BXzGjCfie9kyYPhwbi3r5wcsWvRMN1laitcivAVBKJxkZPASdkBA9kXZBg/momze3v96mvR0ICSERfjGjUB0tHLM1VUtwv8lq10oZGgpkGsVGQNBEATzIiIiAi1btsTFixdRrlw5hIaGokKFCiZ+v/3GWeUA8NFHnIZuYQFeNBkyhGv4+PoC/v7/eXOlpXgtwlsQhMKPvijb8uXA7t3qomxt2rAI7937X4uyAazl9SJ8wwa1CHdxAXr2ZBHepo2I8MKOlgK5VpExEARBMD8ePHiAli1b4vLly6hQoQJCQ0NRrlw5E7/584F33+X/jx3LaegWFuAbrAEDeOWjVy8W47a2T309LcVrEd6CIGgLfVG25cuBw4cVu4MD0L07z7T+R1E2gEX4X38pIjwyUjnm7KwW4f8SLwQzRUuBXKvIGAiCIJgn9+7dQ8uWLXH16lVUrFgRoaGhKFOmjInfn38C77zD/x89muuqWVgA2LYN6NOHq+B26QKsWwfY22f7WlqK1yK8BUHQLvqibAEBwKVLit3VlYuyDR4MNG78n60tMjNZhK9bB6xfr95aXqoUi/C+fYF27USEFxa0FMi1ioyBIAiC+XL37l20aNEC169fR6VKlRAaGgofHx8Tv0WLuJ4aEfDee1zk3NISwJ493KUmJQVo3573+zk6mjxfS/FahLcgCNpHX5QtIIBTmsLDlWMVKihF2bLpTZmVzEzg7795JTyrCC9ZkmNIv34swu3sXvxbEV4MWgrkWkXGQBAEwby5ffs2WrRogZs3b6Jy5coICQmBdza1dZYu5bpqRLwC/vvvT8R3cDDQtSuQlMTFdLZsAZ7EZj1aitcivAVBKFpkZPAX/fLlnEOekKAce/11TkUfMADIZtY2K5mZwIEDigh/8EA5VqIEZ7b368cTuU/JoBIKCC0Fcq0iYyAIgmD+3Lx5Ey1atMDt27fx6quvIiQkBJ6eniZ+/v7Am29yUfO33+Y94JaWAPbvBzp3BuLjgSZNgB07+CbqCVqK1yK8BUEouiQl8exqQACwaxeLcoBTz1u3VoqylSz5n6fS6YCDB1mEr1sH3L+vHCteHOjWjUV4hw683VwoWLQUyLWKjIEgCELh4Pr162jRogXu3r2LatWqITg4GO7u7iZ+K1ZwJzGdjkX4n38CVlYAjhzhG6TYWKBBA74nK1UKgLbitQhvQRAEgEuYr13LIvzAAcVuZ8dL14MHA506PdMmbp0OOHSIBfi6dcDdu8oxJyfOqurXj08nIrxg0FIg1yoyBoIgCIWHq1evokWLFrh//z5q1KiBoKAguLm5mfitXs23VJmZLMIXL34ivk+c4H16MTFAnTq8B9zVVVPxWoS3IAhCVm7cUIqyXbig2J2dWTEPHgw0bfokR+rf0el4Ile/En7njnKsWDEW4X37cpZVNjVFhDxCS4Fcq8gYCIIgFC4uX76MFi1aIDw8HLVr10ZgYCBcXFxM/NauBQYOZPE9eDCwZAlgbQ3g9GmgbVvuUFOzJrB3LxKLFdNMvBbhLQiC8DSIgFOneD/4ypXqTdzlygGDBnHEqF79mU939Kgiwm/dUo45OnJHjX79WISbWVzRHCK8zR8ZA0EQhMLHxYsX0bJlS0RERKBOnTrYt28fnJ2dTfw2bAB8fXmX34ABvAfc2hq84NGmDd9zVa2KxK1b4VSpEoDCH69FeAuCIDwLmZlASAiL8PXruQiInpo1WYAPHAiULftMpyMCjh9nEb52LXDzpnLMwYHFd79+LMazFPgUXgAivM0fGQNBEITCyfnz59GyZUtERUWhXr162Lt3L0pmUy9n0ya+18nI4H8DAgAbGwBXrnCtnbt3kfjyy3C6dg1A4Y/XIrwFQRBySnIysG0bR4gdO4D0dLZbWAAtWrAI79vXUBjkv9B3O1u3jkX49evKMXt73gvety8XaCte/MW/naKICG/zR8ZAEASh8HLmzBm0atUKDx8+RMOGDbF79+5sv8u3bOF7nPR0oE8fTjC0sQFv+2vVCom3bkG//pAQEWGe8drH55li1X9vUNQgbm7A5MnKz48f882tvb1y/wwA48fzytP48YotLY1TQh0d+Xl6pk7lValPPjF9rZIl1Rmqc+YArq7A6NFq38qVAU9P9U330qVAmTLAu++qfRs1AipWBM6fV2wbNwJVqpj6du3KC3InTyq2ffuAN97gRvbGvPkmb109elSxHTnC2y3GjFH7fv4515w6fFixnTsH9O8PfPqp2nfGDO7fd+iQYrt5Exg1Cvj2W7XvkiXAF1/w6+qJigImTgRmzlT7bt8O/PwzixY98fHcH3DhQrXv4cOsk86eVWypqcDmzcDWrSx+9Fy5woubN24oNp2OVyhPnuTFTz3R0cDVq/yvMRERfN06nWLLyODPkPHzhUKIgwNPzW7axD3B//gDaNaMP0QhIdyk0tOTK6KvXw+kpPzr6Sws+O9x+nT+LIWFAePGAZUq8VM3bmQt7+4O9OzJi+6xsfnxRgVBEARBEHJOjRo1DHu8Dx8+jE6dOiHeOFvwCd27c9q5rS3fMvn68r0yXnoJ+Osv/lePpycLLnN6PEP7WT1FUninp5sKn9RUfmT1S0lROgzpSU7mhzFpaUBiouk5YmOBuDi1qEtO5oJ9iYlq34gIIDJSfW3x8cC9e+xvzK1bLArT0hTb48fA5cvqCsoAcPEicOaM+pofPuSb+4sX1b4nTnBBZ+Ob+qgoIDBQLcYBbru3dStft57ISF6x271b7bt7NwtqYyEbEQH89huLCGM2bmShfvq0+rzffw/89JPaNyAA+OwzvhY90dHA++8DY8eqff/8k1s0b96s2GJjWch07672nTsXaNWKn6MnORmoV48LLRrrqFmzgFdeAaZMUWxEgJcX4OHBY63nxx+5SHbWCQ9XV57MMd7zO38+4O1tOuHRuDHw2mss0PRs3sz2r75S+w4fzqukly8rtgMHeByyjuUPPwAffaQ+78WLPO5Llqh9V68G5s1TX++DB1yPLOvv/uhRLkxp/DmJj+dJDOOJI4A17K1b6r+NzExutf0f2rXgcHEBRo7k4HDzJjBtGlCtGv9xbtzI07heXty0MjhYPROTDRYW/BmbNo1/bydP8uRf5crKRJGfH3+2uncHli1TTwIKgtZYvHix6udDhw5hwYIFOHbsmMGWnp6ORYsWYfHixUg3mkE/efIk/P39cfz4cdU51qxZg7Vr1yLF6Ivl8uXL2Lp1K04bBx8AoaGhCAkJQbJREA0PD8fRo0dx3XimHMCVK1dw+fJlpBrdDCQlJSE8PByxWWbLUlNTkZGRgSKUeCgIQhGjVq1a2Lt3L0qVKoWDBw+ic+fOSEhIMPHr2pVvmezs+N/+/Z9onHLl+CZSK1ARIjY2lgDQuXOx9PixYs/MJLp9mx86nWKPiSG6dYv/1aPTEd24wY/MTLXvtWtEkZHq17x8mR/p6YotOprowgWie/fUvufOEZ0+TZSSotgiI4nCwvjcxoSFER0+TJSQoNjCw4n++ovozBm174EDRHv3Ej16pNju3yfavp3o0CG17759ROvW8bn03L1LFBBAtHOn2nfLFqIFC4hu3lRsd+4QzZnD/sasWkX044/8Ho19J04k+t//1L6LFxN99hm/Pz337hGNGkX0+edq33nziPz8iHbvVmwPHhD17k00YIDa9+efidq2JVqxQrFFRxM1akTUsKHa94cfiF57jWj2bMUWH09UtixR6dJEycmKfcIEouLFicaNU2wZGUQsv/k19EyaxLaRI9WvZ2fH9lu3FNvMmWwbMkTt6+zM9gsXFNtvv7GtVy+1b5kybD92TLEtW8a29u3VvlWqsD00VLGtX8+2Jk3UvnXqsH3HDsW2cyfbXn9d7dusGdvXrlVsf//NtldeUft27Mj2JUsUW1gY23x81L4DBhDZ2xPNn6/Yrl3j91yzptr3m2/4mv39FVtkJFG7dkTduql9Fy7kz9TGjYotMZHo44/5c5mRodj37SOaPp0oJESxZWQQ/blAR5snnaKMT79QfglPHmmepflEJ08S6XR05Ai/x7Q05RyPH2f/3XPkCNH48crvSv+wsSHq3Jn/doyfIzydhIQEAkAAKMH4i9RM0Mer2NjYgr6UAkM/BllvVT788EMCQOPHjzfYnvb7/OqrrwgAffjhhwabTqcz+EZERBjsU6ZMIQA0YsQI1es5ODgQALpx44bB9r///Y8A0MCBA1W+bm5uBIDOnj1rsP3xxx8EgLp3767yLV++PAGgI0eOGGxr1qyh4sWLU8+ePVW+7du3p0qVKtFho8AYGhpKjRo1onfffVfl+/nnn1OfPn3o+PHjBtuFCxdo9OjR9OOPP6p8ly9fTj/++CNdvHjRYIuMjCR/f3/atm2byvf06dO0f/9+1ZilpqbSrVu3VDZBEISsHDt2jEqWLEkAqEWLFk+Nu7t2KffEXbuyJlJ9v0dEsPgxo0fs/fvPHK+LpPAuyjcyQv6i06knc1JSeAIk6/fN7ds8mWM8QRMZSXTqlHpig4gnUoKCWAzquXGDhWLWiZTVq4n+/JMoKkqxnTvHot5YCBPxBMhXX/G59ISFEb33HtGMGWrfL78k6tePtaOeI0d4YiPLPSANH05UqxaLVD2HDvEkRvPmat/u3fkL13ji5uhR/gIuV07t27Mn2//4Q/3eACI3N7XvoEFsnzVLsd28yTYHB7XvO++wffJkxRYVpYhc4wm3jz9mm/GkS1KS4hsfT/yE4GA6VnsExaCUWjG/9hqNxw9UHjfowQPlHNOm8eG33lJfm5MT269dIzp7lid9vLzUp7S25gmMihV5YuPSJeX5W7fyRIiRXiEintTq358nCfUcO0Y0ZgxPbhnz++9EU6eqP5c3b/LnLMt9Ov39N0/OGN+Tx8YSHT9OZHSfT0Tsc/++elIrM5MnMoz/hl4UxoE8IiJB9Rqpqfw3ajwJys/hh/FnIC2NbcbXnVPfxES2G0/qPHwo8Uofszt37qyyL1iwgLp3707+RjNpycnJ1KVLF+rSpQslGw3wokWLqH379vTrr78abDqdjlq0aEHNmzenR0Yz0gsXLqT69evTDz/8oHq9unXrUtWqVeme0Wz5ggULqHz58jR27FiV78svv0wlS5ZUCdnff/+dAFCvLDOjZcqUIQAqgbxs2TICQB06dFD5VqlShQDQX3/9ZbCtX7+eAFDTpk1VvnXq1CEAtMNoZnTnzp0EgGrXrq3ybdasGQGgtUYB4e+//yYAVLlyZZVvx44dCQAtXrzYYDtx4gQBIJ8sM6P9+vUjW1tb+v333w22Gzdu0CuvvEINs8x0z5w5k7p160YbjWY7Hz16RGPHjqVxxl+uRBQSEkJ//PEHnThxwmBLS0ujwMBAOnDgAGUa/cHFxsZSVFSU6vMgCELBceTIESpRogQBoNatW1Oi8Y2sEXv38sIKwIsK0dHamSgX4S0IglmTmcliNj5ebY+KYsFn/OeclMSTBWFhat9//mEBeP26YouP5xXw5cvVvnv28MTEwYNq33HjeKHamBUriN58Uz2JkZTEs7QdO6qF27x5RI3qpNCmYRuI+vRRpnT1K+ENmhD9+itRdDRNn86H339f/Xr6QGScGfHzz2yrWZOoRg21CAeIGjfmzJSoKJ6kAHjSwphy5dh+9KhiW76cbe3aqX2rVmV7cLBi27BBeS1j3niD7du3K7bdu5XrNaZFC7avXq3YDhzIPjNiwAAiT0/OpNFz4QJR9eqmmRyTJhF16MCTDnoePCAaOFAJ5ECCKltpyhR+3SwLn+ToyHbjyan//Y9tgwapfd3c2G608Enz57OtRw+1b/nypuM/f77EK63FbGNRSMTv7+HDh5RuNOMaFxdHV65coTt37qh8T548Sfv376fHRul69+7do02bNlGIccoNEa1bt47mzZtHt4y+KC5dukTffvstzZ07V+U7bdo0GjZsmEr8//PPP9SuXTt68803Vb5vvfUWVapUiTZt2mSwHT16lOzs7KhixYoq3+7duxMAmm+UknT27FkCQO7u7irfgQMHEgD6n1H6240bNwgAOWSZGR0xYgQBoMlGM6NRUVGGv+UMo9mrjz/+mACoxHtycjK5uLiQj48PxRsFlQULFlCrVq1UEzRERGPGjKFPP/2U4uLiDLYTJ07QwoUL6aBxkCBe0fvnn38oNTXVYEtPTzf5vQtCUebgwYPk5OREAKhdu3aUlJSUrV9gIC+MAERt22pHeFu/oIx1QRCEPMHSkmuZZcXNjR/GODjw/uis1KzJD2OcnHive1bateNHVt9p00x9Bw7kR9Zr2LrV1HfUKGDUKDsAvfgRG8tVRAICgOBg2Bw5ABw5AIwdiy87dcKXSwfzBn04Gs6hrwFhXNn8rbfYrVgxru9x6RLXWVi6lPfrHzzIj/feAxo25LpvWWsaTJrEl1O+vGKrXp0LH1asqPbt25frSBjXEvH05Gt49VW1b9WqvKXduLi7jQ13XPP2VvtaWPDv2tooKum36lpZqX0fPuSaAcY1LhITuXBi1qJzJ09y3YFevRTbo0dcNVUQ8hNLS3VZneyq3xYvXhzFs2ldULt2bRObj48PevToYWLv06ePia1y5cqYNGmSiX3cuHEmtpo1a2JPNnsqF2atWAqgXr16qn3yepYsWYLExERV+6AKFSrg77//NvF999130bp1azRs2NBgK168OL766itYWFiofGvXro0ePXrgVaMvG51Oh2rVqiE9PR1WRl8WaU++IOzs7Ay2lJQUxDwpmmNra2uwX758GcHBwahjFEAyMjIwd+5cAMB4oyq7W7duxYQJEzBy5Eg0atTIYG/atClSU1Nx8+ZNlH/yZTpnzhx88sknGDp0KJYuXWrwbd68OZKTk7FmzRq89KRwVFBQEAICAtCgQQOMHDlSNZbp6eno1asX3J4EvaioKNy8eRNubm6G5+vHIuvnTBDMiUaNGmHnzp3o2LEj9u7di969e2Pjxo2wt7dX+bVuzU1junThgtB6stbHMgdydE35MBFgNmht9lwQBI1w9y7n89eurV6udnIiGjqUl4mN9yE8I5cvc1r466+rT2tpSdSqFa/CG6e4mwPGKd9paVwjwXirBBFnOpw+rd7PHhvL2xmyLP5RSAjR0qXq1PaoKKIpUyTV3NyRmC08LxkZGaqMgoyMDLpw4QKdPHmSdEZ/9P/88w+tWLGCwozSpdLS0ujbb7+lzz//nFKMvgyWL19OnTt3pnlG+3B0Oh1VqFCBPD09KdIofeaHH34gAPT222+rrqtYsWIEgK4ZFfD5v//7PwJAvr6+Kl9PT08CQP/884/BtmjRomy3YVSqVIlsbGzokNG+s71791LDhg3po48+UvlOnz6dPv/8c7py5YrBdufOHVq1ahWFGhd7Ic6uePDggWo1XxCeh9DQUHJ0dCQA1KVLF9XfmNqPyNFRnaGWNbOv4B+Sap4tEsQFQTB7zp3jTdgVKqi/2b28iD78kPORc7Hp+epVLgRXt676tBYWvNd+zhzeY11UkOJq5o+MgVDYSUlJoaioKFUtASKioKAg2rZtmyrN9tixYzR16lRav369yvett96ibt26qbYfLF++nMqWLUtvZSkEUrp0aQKg2gO/dOlSAkAdO3ZU+errBhiL7A0bNhAAapKlouobb7xBAFQF90JCQqh06dLULUuF0u+++46GDBlCR432zty7d4/mzJmjqiVARHTlyhU6d+6cKpVfKDoEBQUZild27979qRM7e/ZoR3hbEBE91/p6ISIuLg4lS5Z8pgbngiAIBQoR54gHBABr1qj70lWuDAwaxM29K1XK8alv3OAs97Vr1W0CLSyAJk24RXmfPkDp0i/gfZgpiYmJcHJyAgAkJCSgWLFiBXxFaiReyRgIQk6JiYlBYmIiPD09Dan0d+/eRVhYGFxcXNCsWTOD76xZs/DgwQOMGTPGkBofHByM77//HjVq1MCcOXMMvvXq1UNYWBgCAwPRqlUrAMDmzZvRs2dPNGzYEIcOHTL4NmzYEEeOHMHmzZvR/cm+pqCgILRp0wbVqlXD2bNnDb5t27ZFYGAgli9fjsGDBwMAwsLC0Lp1a1SuXFnVMnDy5Mk4deoURo0ahTZt2gAAoqOjsWTJEri6umL48OEG36tXryIxMRHlypWDs7PzixlcIU/Yt28funXrhpSUFPTq1QurV6+GjY2Nysc4XoeHJ8DJyfzitY/PM8aqFzt3Yd7I7LkgCIWStDSuDjZggFJtRP+oX5/o//5P3QMwB9y8yQXaGjXKvjDb//7HVfe1hqx4mz8yBoJgPuh0OlWhuMePH9Px48dVKfBERKtXr6YZM2ao0uhPnjxJ/fr1M0l379GjB7m4uNCWLVsMtuDgYAJAr776qsq3ffv2BICWLl1qsIWFhRFgWlW/b9++BEBVTPDKlStUrFgxqlSpksp31qxZ1Lt3b9U1xMfH06xZs2jBggUq39u3b9P58+dNMhiE52PXrl1ka2tLAKhv376UZtxflbQVr0V4C4IgFCbi4rgZe4cOvFlbr5KtrNi2bJlpCfhn5PZt7l3fpImpCG/YkKu9Z21vV1jRUiDXKjIGglD0SEpKosuXL6ta8hGxOPv111/pklGPzCtXrpCfnx+NGjVK5Tt8+HDy8PCgAKPepCdPniQA5O3trfLt378/AaBffvnFYLt27RoBICcnJ5Xv22+/TQBULQejoqLIxcWFypcvr5qYWLRoEQ0ZMoQ2bNhgsKWlpdH8+fNpxYoVqtoD0dHRdPfu3ae21yoKbN++3SC+fX19VeOjpXgtwlsQBKGwEh7Oq9316qlVsoMDr45v3cqr5bng7l2iX37hvt8WFurT16tH9OOP3E+8sKKlQK5VZAwEQXhRpKam0rVr1+jChQsqe2BgIP366690+vRpg+3u3bs0aNAgGjp0qMp31KhR5OLiolpJv379OgEgR0dHle8777xDgLr1XXR0tCHuGAvLTz/9lADQ559/rrrel19+mWrVqqXaA79582YaO3asqq0fEdHGjRtpz549qiJlKSkphaog3pYtW8jGxoYA0KBBgwztAbUUr0V4C4IgaIHLl4kmTuSm18Yq2dWVG4Lv35+romxEXHRt3jyili3Vi+wAUZ06XDn98uUX/H7yGC0Fcq0iYyAIgrmTmppK586do+PHj6vs+/bto5kzZ6oqzEdFRVH37t2pQ4cOKt+PPvqIrKys6PvvvzfYHj58aIhRxqnXn332GQGgTz/91GBLT083+EZHRxvskydPJgD03nvvqV6vVatW1L59e4qIiDDYDh48SFOnTqVdu3apfI8dO0ZnzpzJNwG/ceNGsra2JgDk5+dHGRkZmorXIrwFQRC0hE7Hlc8//JDI01OtkitU4Irp587l+vTh4US//UbUpo2pCK9Vi2jyZHXrLnNFS4Fcq8gYCIJQVNDpdIYVXiIW9AcOHKDdu3er/Hbu3Enjx4+nHTt2GGyJiYnUpEkTqlmzpkogf/HFFwSAPvnkE4MtIyPDEPuMW99NmTKFgKe3vrt69arB9ttvv5GbmxuNHj1a5Tty5EgaPnw43b1712C7ePEiLVu2jA4ePKjyjYiIoNjYWFV6vp5169aRlZUVAaDhw4dTXFycZuK1VDUXBEHQKhkZQFAQV0bfsAFISFCO1a7NVdEHDsx1+fKoKGDjRq6QHhgIZGYqx6pX5+roffsCr732fG8jL5Cq5uaPjIEgCELuycjIQHx8PKysrAzfoZmZmdiyZQsSEhIwYMAAQwXxrVu3YtOmTWjevDmGDRsGACAiVKpUCXFxcTh//jzc3d0BAFOnTsXXX3+Nt956CwsXLjS8XokSJRAfH48rV66g0pOOK3PnzsUHH3yAPn36YN26dQbfMmXK4N69ewgLC0OdOnUAAFu2bMH333+P1q1bo169ehg4cCB0Oh3q1q2LsLAwAEBERATc3d1hYWEBAEhLS0N6ejqsra1hZ2dnOH9iYiIAwMHBAZaWlgCA9PR0pKWlwcrKCvb29rnyTUpKAhHB3t4eVlZWALibgKur6zPFKst/PSoIgiAUXqytgfbtgaVLgYgIYNUqoFs3tp86BXz+OVC2LNC6NfDnn8Djxzk6vbs7MHIksHs3n37hQqBjRz792bPAhAlAtWr8mDCBbUVnqlcQBEEQCg5ra2s4OzurxKCVlRV69eoFPz8/Vduubt26YeHChQbRDQAWFha4du0aoqKiDKIbAN577z2cOXMG3377rer1pk2bhqlTp8LDw8Ng8/HxQdu2bVG7dm2Vb3JyMgCgePHiBtvdu3dx4sQJXL9+Hf3794e/vz8sLS0NohsAPD09ER0dbfh5xowZcHJywpgxY1Tn9/DwgJOTE27fvm2wzZs3D05OTnj77bdVvhUqVICTkxMuXLhgsC1ZsgROTk4YMGCAyve1116Dk5MTTpw4YbCtX78ez4r1M3sKgiAIhRdHR8DXlx8PH3IT74AAYP9+IDiYH6NHA1268Ep4ly6A0Szvf+HqCrz1Fj9iYoAtW/gl9u4Fzp8HJk3iR5Uqykp4zZrcO1wQBEEQhMKBi4sLXFxcTOyjR482sfXu3Ru9e/c2sUdHRyMlJUW1St2tWzdUqFABrq6uAIBBgwYhMzMTQ4cOVT03MTERjo6OAHjFG+DVff3KtTFJSUkG+9N89cnfxr6pqakAOEMgO9/k5GST8z4LkmouCIJQlLl5E1i5kkX4uXOKvWRJoE8fFuEtWgBPUqpyyuPHwNatwLp1wK5dgHF8qlSJBXjfvkCdOvkrwiXV3PyRMRAEQRD++OMPvPfeewV9Gf/Js8QqEd6CIAgC54CfPs0CfOVK4O5d5ZiPD+8FHzyY94bnUiHHxQHbtrEI37kTSElRjlWsqIjwN97IexEuwtv8kTEQBEEQjOO1OSPCOwsSxAVBEJ4BnQ746y8W4evWqfd+V60KDBrEj4oVc/0S8fHAjh2cjr5jB/BkuxcAoHx5FuD9+gH16+eNCBfhbf7IGAiCIAjG8ToiIsIs47WPj48I76xIEBcEQcghqam8PB0QwDnjT/Y9AQAaNeJV8P79udJaLklMZPG9bh2viCclKcfKllVWwhs2BCxfUElQEd7mj4yBIAiCoKV4LcJbEARBeDZiY7ktWUAAtynThw999fTBg4EePYDnCIpJSbwXfN061vnGHdB8fHjbed++QJMmud52DkBbgVyryBgIgiAIWorXIrwFQRCEnHP/PrcnCwgAjNpqoFgxoGdPFuHt2rEozyUpKdyqbN06rpIeF6cc8/ICevfmdPRmzXIuwrUUyLWKjIEgCIKgpXgtwlsQBEF4Pi5eZAG+YgVw/bpid3fn9mWDBwMNGjzXZu3UVGDPHmD9emDTJl581+PhwSK8b18uwP4sWl9LgVyryBgIgiAIWorXIrwFQRCEFwMRcOQIi/DVq4GoKOXYyy9zQbbBg7mZ93OQlgYEBnJhts2buW+4HldXoFcvXglv1Qqwscn+HFoK5FpFxkAQBEHQUrwW4S0IgiC8eNLTWR0HBAAbN3IFNT116rAAHzCAN24/58sEB3M6+oYNwMOHyjEXF85679sXaNMGsLVVjmkpkGsVGQNBEARBS/FahLcgCIKQtyQm8ibtgADetJ2RwXYLC16WHjyYq6aVLPlcL5ORAYSGKiI8MlI5VrIk133r14+3nmdkaCeQaxUZA0EQBEGEdyFFgrggCEIBEx0NrFnDIvzgQcVuZwd07coivHNn/vk5yMzkVuTr1/MjPFw5VqIE0LlzIlat0vcFNc9A7uNTtOOVxGxBEARBhHchRYK4IAiCGXHjBrByJYvw8+cVe6lSnB8+eDDQvPlzN+/OzGSNv3Yti/D79wEgEYDTE48EAOYVyIE4AEU7XknMFgRBELQkvJ/vbkYQBEEQcstLLwHjxwNnzwInTwKffQaULg08fgz8+SenoZcvD3z+OXDqlNI3PIdYWXHLsV9+Ae7cAQ4cAMaMeaHvRBAEQRAE4V8pmiveixejRL16QLVqfCAtjfvTALzKol9dOX0auHSJK/DWrMk2nY4LBQFAt25KtZ4LF7ilTsWKQK1ayotu3co3i+3aAQ4ObLt+nX3LlFHOCwBBQbxJsUkT7oULAHfvApcvc7+c6tUV36NH+bpr1waezAIhKorP7ewMVK6s+F64wL14XnlFOW9cHHDvHv9crpzie/cuVyvy8lKuNyUFePSI36urq+IbH89LScWKKaWDdTq+LktLdSUjQRCEZ0GfIx4QwJu1jfuGvfYar4IPGgRUqPBcL2M8gy6p5uaJrHgLgiAIWlrxBhUhYmNjCQDFAkQTJigHHj0iYnlMlJam2D/7jG2ff67YUlMV30ePFPuECWwbNUr9otbWbL93T7H9+CPbhg1T+5YowfbLlxXbnDls69tX7evtzfaTJxXbokVs69xZ7VupEtv371dsq1ezrUULtW/NmmzfvVuxbdvGtjfeUPs2asT2jRsVW3Aw26pWVfu2b09kaUkUEKDYjh8nKlaM6LXX1L7DhhF5ehL5+yu2y5eJXnqJqF49te8XXxDVqKH2vX+fqGFDotat1b6zZhG1a6e+hthYol69iPr0IdLpFHtAANGbbxKtW6fYUlOJxowh+vBDopQUxb5nD9E33xBt365+vR9/JJoxgygxUbGFhRH98QfRX3+pfdeu5d9JQoJiu3GDaNcuotOn1b7HjhEdOUKUlKTYHj0iuniR37sxUVFEkZFE6emKLSODP+eZmSQIZk1yMtH69fz3aWenfPcCRE2aEM2bx5/xXJCQkEAACAAlGP/dmQmGeBUbW9CXUmDIGAiCIAhaitdFM9W8aVP1aom1NdCiBT8sLBR7xYq8v/CllxSbhQXnLDZrxvmLesqWBRo35ucY06ABP4ybyXp5AW+8oT4vwKvftWqpiwq5uPAqT9myat+KFXkF29jXyYnTMj091b4eHvyaxr62tnzurDMzDg6AoyOPiTGWlur3Cyhpn8Zjprdl3ZOZmcmr4cZkZHC146Qktf3RIyAiglfa9aSm8n7QW7fUvrdvA2fOqHsIJScDhw9zP2Fjzp4F9u4Fbt5U+27cyBs/jd/HkSPAkiWc/qonLQ2YOxf4v//j96MnKAiYMoXPrUenA778klNkjd/fjh3Au+8C/v7qaxs6FPD1Vfc93rgR6NgRmD5d7duxI3+mbtxQbGvWAK++Crz/vtq3bl3+/Ru/j1Wr+PffsaOpb4kSwP79im33bs6I6NtX7TtoELeEMvY9dgxo3Rp47z2174QJQP/+/DvRc/Uq+02cqPZduhT45hv19UZGArNmAQsXqn1DQngcL19WbImJPMZBQWrfa9eA48f5c6UnI4MzRG7fVvsmJ/N50tMhFDD29kDv3rzyHR7On4E2bfhv9cABYPRowNubi7KtXKluWSYIgiAIgmBO5MNEgNkgs+cvmPR0XgU2XjlNTyd6/JhXko15+JBXY41XaZOTia5d45VdY27e5FXehw8VW2Ii0eHDvNprzJkzRHv3Et26pdgSEog2bSLaskXte+gQ0bJl6hXkxESi337jlTNj9u3jFevQUMWWksIr2+PHq1eQN28m+uADXpnTk5HBK/d+fkTx8Yp99WqiHj1MX69DB84+iIhQbP7+RLVr8+sZ8/rrROXLE129qtgWLSIqVYpo8GC1b5kyvDoYFqbYli5lW4cOat/KldluvBq/bh3bmjUzvQaAV+T17NjBttdfV/s2bcp24+yB0FC2ValiOg4A/570HD/OtjJl1L69e7P9t98U24ULbHN2Vvv6+bF9xgzFdvs222xt1b7vvsv2iRMVW0wMr7g6Oqp/95MmEZUtSzRtmmJLTeUxqFdP/btfupSoY0f19RIRDR3KnxXjDJrAQKJPPyVas0btO2sWvwdj33PniBYvNs2i2LOHaOdOorg4xRYZyX9D166pfe/dI7p7l69dT3o6f+YzMsjsuHeP6OefierUUa+CFyvGfwM7d6p/T9mgpRl0rSJjIAiCIGgpXovwFgStk5mpTqNPTWUhmfXv4PZtoitX1JMjMTEs1M6fV/seOsSi2zjN9949opUrWYAbs349b5kwnii4eZNF65w5at9ff+V0/qNHFdu1ayymxoxR+37/PW9h2LZN7Vu3LlGrVmrfsWNZIM+fr9hu3WKhllWkjxjBIm7KFMUWGamIO+Ox/PBDthlPjiQkKL7GAWL8eLZ9+KFi0+kUX+NJlx9+YNvbb6uvrVgxtl+/rthmz2bbwIFqX3d3tp85o9gWLGBbt25q35deYvvhw4ptxQq2Zd2y0aABT/IYC/19+4heeYVowAC17zvvEDVvTnTggGI7dYpTxz/7TO37v//x79h4kuj2bf49Z52o2r6df5eXLvFn85tviCpUUItwd3c+36pVRAcPEoWHK89PTaWE06eVQB4RYfo3kpCg3lJCxLaEBPVkY1oa25KTc++bmMh2o0mO2IcPi3y8kpgtCIIgiPDOY+bOnUvly5cnOzs7ql+/Ph05cuRf/desWUNVqlQhOzs7ql69Om3Putf2CZGRkQSAIiMj8+KyNUtKSgpNmDCBUrLehAr/ioxbzjGLMdOLI+NryMhgEWgseImI7tzhiYnbtxVbejqvuG7dql4tPnGCaMkS3p+vJzOTaOZMzq4wrgUQGMjCNOuK97vv8gq58YTHxo2U0bEj7WnTRj1ubdvyyrvxNS9fzhMQWQX9K69wPYrjxxXbsmUsYNu3V/tWqcJ242yQ9evZ1rSp2rduXbYbT8bs2sW22rXVvs2bs33tWsX2999sq1xZ7duxI9uXLFFsYWHKqrd+0sH40akTZ0QQEV26RAlPgjgASgB4ckXPlCn8nBEj1K/r6Mh24yyd//2PbYMGqX3d3Nh+9qximz+fbT16qH3Ll2e70YRT7Pz5hUJ05lW8JpKYnVvM4nu0kCFjljtk3HKHjFvOMBbeD42zYc2EQi28V61aRba2trRo0SI6d+4cvfPOO1SqVCmKMF4NMuLAgQNkZWVFP/30E50/f56++eYbsrGxoTPGqzxPuHPnDgGgO3fu5PXb0BSy6pA7ZNxyjoxZ7siTcUtLy37byM2bLGCNJwqio1kkGxd7JOIJhDVriB48UGy3bvEK9qpVat9Fi4i+/VYtVC9f5smGb79V+37/PYvX4GDFduECUePGvJqflsZif/BgpcCl/lGnDtEXX1CCo6NaeN+4oaxSf/cd+775pmJLSFCE97lzik1fLLN/f7Wvq6sipvU2fbHMrl3VvuXKKZMZT2yxc+ea/d9CXsZrIonZuUW+R3OOjFnukHHLHTJuOcNYeN/PWkTYDMjJ79Ps2ok1aNAA9erVw9y5cwEAOp0OZcuWxQcffIBx48aZ+Pv6+iIxMRHbtm0z2Bo2bIjatWvj999/V/nevXsXZcuWxZ07d1CmTJm8fSMaQlq65A4Zt5wjY5Y7ZNz+hcREYPNmbk+2e7ehMGIigCeNGJEAwLyakwBxAEoCZv07zct4DUjMzi3yfZBzZMxyh4xb7pBxyxnG7cTu378Pb2/vAr4iNTn5fZpVVfO0tDSEhYWhbdu2BpulpSXatm2LQ4cOZfucQ4cOqfwBoEOHDk/1FwRBEIoQxYpxFf7t24EHD4B587gDhfBcSLwWBEEQhJxh/d8u+Ud0dDQyMzPhmaUdlqenJy5evJjtc8LDw7P1Dw8PN/HVL+4/ePBAZbezs4OdcastQUVcXJzqX+HZkHHLOTJmuUPG7RmxswOGDAGGDEHihQtAw4YAgHsnT8IraxvGfCY1NRWpaWmGn+MTEoC6dWFmSWkG8jpeAxKzc4t8H+QcGbPcIeOWO2TcckaiUavQ+Ph4FCtWsDlqqampSE1NNfwcHx8PAM8Ur81KeOc16U/68tavX7+Ar6RwUjZrL3HhmZBxyzkyZrlDxi13VHn99YK+hKcSHx+PkiVLFvRlFAgSs58P+T7IOTJmuUPGLXfIuOWcKlWqFPQlPJVniddmJbzd3NxgZWWFiIgIlT0iIgJeXl7ZPsfLy+uZ/StUqIBr167BxsYGFhYWBrvMnguCIAgFSdYZdCJCeno6fHx8CvCqnk5ex2tAYrYgCIJgfjxPvDYr4W1ra4u6desiMDAQPXv2BMDFWgIDAzFmzJhsn9OoUSMEBgbio48+Mtj27t2LRo0amfhaWlqiYsWKeXHpgiAIglBkyOt4DUjMFgRBELSFWQlvAPjkk08wbNgwvPHGG6hfvz5mz56NxMREDB8+HAAwdOhQlC5dGtOmTQMAfPjhh2jRogV+/vlndOnSBatWrcLx48cxf/78gnwbgiAIgqBpJF4LgiAIwrNjdsLb19cXUVFR+O677xAeHo7atWtj165dhoIst2/fhqWlUoy9cePGWLFiBb755huMHz8er7zyCjZt2oTq1asX1FsQBEEQBM0j8VoQBEEQnh2zaiemZ8yYMbh16xZSU1Nx5MgRNGjQwHAsJCQES5YsUfn369cPly5dQmpqKt5//32MGjUK9vb2aNCgAY4ePfqvr7V27Vq8+uqrsLe3R40aNbBjx468eEtmz7x581ChQoVnGrcFCxagWbNmcHZ2hrOzM9q2bfuf46xVcjJuxqxatQoWFhaGFM2iRE7H7PHjxxg9ejS8vb1hZ2eHypUrF8m/05yO2+zZs1GlShU4ODigbNmy+Pjjj5GSkpJPV1vw/PXXX+jWrRt8fHxgYWGBTZs2/edzQkJCUKdOHdjZ2aFSpUomsUYw5Xni9dmzZ3Hjxo0cfa4lZjMSs3OOxOvcITE750i8zjlFJmaThli1ahXZ2trSokWL6Ny5c/TOO+9QqVKlKCIiIlv/AwcOkJWVFf300090/vx5+uabb8jGxobOnDmTz1desOR03AYNGkTz5s2jkydP0oULF+jNN9+kkiVL0t27d/P5yguWnI6bnhs3blDp0qWpWbNm1KNHj/y5WDMhp2OWmppKb7zxBnXu3Jn2799PN27coJCQEDp16lQ+X3nBktNxCwgIIDs7OwoICKAbN27Q7t27ydvbmz7++ON8vvKCY8eOHfT111/Thg0bCABt3LjxX/2vX79Ojo6O9Mknn9D58+dpzpw5ZGVlRbt27cqfCy6CSMzOHRKzc47E69whMTvnSLzOHUUlZmtKeNevX59Gjx5t+DkzM5N8fHxo2rRp2fr379+funTporI1aNCA3n333Ty9TnMjp+OWlYyMDCpevDgtXbo0ry7RLMnNuGVkZFDjxo3pzz//pGHDhhW5QJ7TMfvtt9+oYsWKlJaWll+XaJbkdNxGjx5NrVu3Vtk++eQTatKkSZ5ep7nyLEH8iy++oGrVqqlsvr6+1KFDhzy8sqKNxOzcITE750i8zh0Ss3OOxOvnR8sx2yxTzXNDWloawsLC0LZtW4PN0tISbdu2xaFDh7J9zqFDh1T+ANChQ4en+muR3IxbVpKSkpCeng4XF5e8ukyzI7fjNmnSJHh4eODtt9/Oj8s0K3IzZlu2bEGjRo0wevRoeHp6onr16pg6dSoyMzPz67ILnNyMW+PGjREWFmZIb7t+/Tp27NiBzp0758s1F0YkHuQvErNzh8TsnCPxOndIzM45Eq/zj8IaD8yuuFpuiY6ORmZmpqGoix5PT09cvHgx2+eEh4dn6x8eHp5n12lu5GbcsvLll1/Cx8fH5A9Ay+Rm3Pbv34+FCxfi1KlT+XCF5kduxuz69esICgrC4MGDsWPHDly9ehWjRo1Ceno6JkyYkB+XXeDkZtwGDRqE6OhoNG3aFESEjIwMvPfeexg/fnx+XHKh5GnxIC4uDsnJyXBwcCigK9MmErNzh8TsnCPxOndIzM45Eq/zj8IaszWz4i0UDNOnT8eqVauwceNG2NvbF/TlmC3x8fHw8/PDggUL4ObmVtCXU2jQ6XTw8PDA/PnzUbduXfj6+uLrr7/G77//XtCXZtaEhIRg6tSp+PXXX3HixAls2LAB27dvx+TJkwv60gRBKEAkZv83Eq9zj8TsnCPxumihmRVvNzc3WFlZISIiQmWPiIiAl5dXts/x8vLKkb8Wyc246Zk5cyamT5+Offv2oWbNmnl5mWZHTsft2rVruHnzJrp162aw6XQ6AIC1tTUuXbqEl19+OW8vuoDJzWfN29sbNjY2sLKyMtiqVq2K8PBwpKWlwdbWNk+v2RzIzbh9++238PPzw4gRIwAANWrUQGJiIkaOHImvv/5a1eJJYJ4WD0qUKGG2M+eFGYnZuUNids6ReJ07JGbnHInX+Udhjdma+W3a2tqibt26CAwMNNh0Oh0CAwPRqFGjbJ/TqFEjlT8A7N2796n+WiQ34wYAP/30EyZPnoxdu3bhjTfeyI9LNStyOm6vvvoqzpw5g1OnThke3bt3R6tWrXDq1CmULVs2Py+/QMjNZ61Jkya4evWq4aYHAC5fvgxvb2/NB3A9uRm3pKQkk2CtvxEiory72EKMxIP8RWJ27pCYnXMkXucOidk5R+J1/lFo40HB1nZ7saxatYrs7OxoyZIldP78eRo5ciSVKlWKwsPDiYjIz8+Pxo0bZ/A/cOAAWVtb08yZM+nChQs0YcKEItuaJCfjNn36dLK1taV169bRgwcPDI/4+PiCegsFQk7HLStFsUpqTsfs9u3bVLx4cRozZgxdunSJtm3bRh4eHjRlypSCegsFQk7HbcKECVS8eHFauXIlXb9+nfbs2UMvv/wy9e/fv6DeQr4THx9PJ0+epJMnTxIAmjVrFp08eZJu3bpFRETjxo0jPz8/g7++Ncnnn39OFy5coHnz5hWK1iSFGYnZuUNids6ReJ07JGbnHInXuaOoxGxNCW8iojlz5lC5cuXI1taW6tevT4cPHzYca9GiBQ0bNkzlv2bNGqpcuTLZ2tpStWrVaPv27fl8xeZBTsatfPnyBMDkMWHChPy/8AImp583Y4pqIM/pmB08eJAaNGhAdnZ2VLFiRfrhhx8oIyMjn6+64MnJuKWnp9PEiRPp5ZdfJnt7eypbtiyNGjWKHj16lP8XXkAEBwdn+z2lH6dhw4ZRixYtTJ5Tu3ZtsrW1pYoVK9LixYvz/bqLGhKzc4fE7Jwj8Tp3SMzOORKvc05RidkWRJLHIAiCIAiCIAiCIAh5hWb2eAuCIAiCIAiCIAiCOSLCWxAEQRAEQRAEQRDyEBHegiAIgiAIgiAIgpCHiPAWBEEQBEEQBEEQhDxEhLcgCIIgCIIgCIIg5CEivAVBEARBEARBEAQhDxHhLQiCIAiCIAiCIAh5iAhvQRAEQRAEQRAEQchDRHgLgiAIgiAIgiAIQh4iwlsQBEEQBEEQBEEQ8hAR3oIgvBCGDx+Ob775RmX766+/0K1bN/j4+MDCwgKbNm0qmIsTBEEQBMGAxGxByH9EeAuC8NxkZmZi27Zt6N69u8qemJiIWrVqYd68eQV0ZYIgCIIgGCMxWxAKBhHegiCY0K9fP7i7u2P+/PkG25EjR2Bra4s9e/aY+B88eBA2NjaoV6+eyt6pUydMmTIFvXr1yvNrFgRBEISiiMRsQSgciPAWBMGEX375BX369MGkSZMAAAkJCRgyZAjef/99tG/f3sR/y5Yt6NatGywsLPL7UgVBEAShSCMxWxAKByK8BUEwwdvbGx999BHu3buHhw8fYuzYsbCzs8OPP/6Yrf/mzZtNUtYEQRAEQch7JGYLQuHAuqAvQBAE86Ry5cpwdHTEd999h4CAABw9ehT29vYmfhcuXMD9+/fRpk2bArhKQRAEQRAkZguC+SPCWxCEbLG0tESNGjXw66+/4qeffkKtWrWy9duyZQvatWuXbYAXBEEQBCHvkZgtCOaPpJoLgpAtRAQAqFOnDj799NOn+m3evBk9evTIr8sSBEEQBCELErMFwfwR4S0IQrbMnj0bR44cgU6ng6Vl9l8VkZGROH78OLp27Zrt8YSEBJw6dQqnTp0CANy4cQOnTp3C7du38+qyBUEQBKHIITFbEMwfC9JPkQmCIDzhzJkzqFevHt5++238+eefSExMhLW16c6UhQsXYvHixdi/f3+25wkJCUGrVq1M7MOGDcOSJUte9GULgiAIQpFDYrYgFA5EeAuCoCIlJQX16tVDnTp1MHv2bLi4uODMmTOoXr26iW/37t3RtGlTfPHFFwVwpYIgCIJQtJGYLQiFB0k1FwRBxbhx45CYmIi5c+fC2dkZ5cuXx+zZs3H//n0T36ZNm2LgwIEFcJWCIAiCIEjMFoTCg6x4C4JgYM+ePejSpQtCQ0PRuHFjAMCff/6JcePGoVmzZti4cWMBX6EgCIIgCIDEbEEobIjwFgRBEARBEARBEIQ8RFLNBUEQBEEQBEEQBCEPEeEtCIIgCIIgCIIgCHmICG9BEARBEARBEARByENEeAuCIAiCIAiCIAhCHiLCWxAEQRAEQRAEQRDyEBHegiAIgiAIgiAIgpCHiPAWBEEQBEEQBEEQhDxEhLcgCIIgCIIgCIIg5CEivAVBEARBEARBEAQhDxHhLQiCIAiCIAiCIAh5iAhvQRAEQRAEQRAEQchD/h/bTRruL46mFAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors_Hi = ['black','gray','blue','red']\n",
    "colors_Da = ['black','blue','red']\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize = (10, 5))\n",
    "for Lösung, Hi, color in zip(Lösungen_Hi,Hi_vec,colors_Hi):\n",
    "    ax[0].plot(Lösung.x, Lösung.y[0], label = str(Hi), color = color)\n",
    "    ax[0].hlines(y=Lösung.y[0][-1], xmin=1, xmax=1.1, colors = color)\n",
    "    ax[0].plot(Lösung.x, Lösung.y[1], color = color, linestyle = ':')\n",
    "    ax[0].hlines(y=Lösung.y[1][-1], xmin=1, xmax=1.1, colors = color, linestyle = ':')\n",
    "\n",
    "for Lösung, Da, color in zip(Lösungen_Da,Da_I_vec,colors_Da):\n",
    "    ax[1].plot(Lösung.x, Lösung.y[0], label = str(Da), color = color)\n",
    "    ax[1].hlines(y=Lösung.y[0][-1], xmin=1, xmax=1.1, colors = color)\n",
    "    ax[1].plot(Lösung.x, Lösung.y[1], color = color, linestyle = ':')\n",
    "    ax[1].hlines(y=Lösung.y[1][-1], xmin=1, xmax=1.1, colors = color, linestyle = ':')\n",
    "\n",
    "ax[0].vlines(x=1, ymin=0, ymax=3, colors='black')\n",
    "ax[0].set_xlim(0,1.1)\n",
    "ax[0].set_ylim(0,3)\n",
    "ax[0].tick_params(axis=\"y\",direction=\"in\", right = True)\n",
    "ax[0].tick_params(axis=\"x\",direction=\"in\", top = True)\n",
    "ax[0].set_ylabel(r'$f_{i,\\mathrm{L}}\\,/\\,1$')\n",
    "ax[0].set_xlabel(r'$\\chi \\,/\\,1$')\n",
    "ax[0].legend(title = '$Hi$ =',frameon = False, alignment = 'left',ncol=1,loc=(0.025,0.7))\n",
    "\n",
    "ax[1].vlines(x=1, ymin=0, ymax=3, colors='black')\n",
    "ax[1].set_ylabel(r'$f_{i,\\mathrm{L}}\\,/\\,1$')\n",
    "ax[1].set_xlabel(r'$\\chi \\,/\\,1$')\n",
    "ax[1].set_xlim(0,1.1)\n",
    "ax[1].set_ylim(0,1)\n",
    "ax[1].tick_params(axis=\"y\",direction=\"in\", right = True)\n",
    "ax[1].tick_params(axis=\"x\",direction=\"in\", top = True)\n",
    "ax[1].legend(title = '$Da_\\mathrm{I}$ =',frameon = False, alignment = 'left',ncol=1,loc=(0.7,0.7))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für die Betrachtung des Einflusses von $Hi$ und $Da_\\mathrm{I}$ auf den Nutzungsgrad des Flüssigkeitsfilms $\\eta_\\mathrm{L,Film}$, den Nutzungsgrad der Kernströmung $\\eta_\\mathrm{L,b}$, den Nutzungsgradverlust $\\Delta\\eta_\\mathrm{L}$ und den Verstärkungsfaktor $E$ werden folgende Gleichungen ausgewertet (s. Beispiel im Lehrbuch):\n",
    "\n",
    "\\begin{align*}\n",
    "E &= \\frac{\\frac{\\mathrm{d} f_\\mathrm{1,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 0}}{f_{1,\\chi = 1}-f_{1,\\chi = 0}} \\\\\n",
    "\\eta_\\mathrm{L,Film} &= 1 - \\frac{\\dot{n}_{1,\\chi = 1}}{\\dot{n}_{1,\\chi = 0}} = 1 - \\frac{J_{1,\\chi = 1}}{J_{1,\\chi = 0}} = 1 - \\frac{\\frac{\\mathrm{d} f_\\mathrm{1,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 1}}{\\frac{\\mathrm{d} f_\\mathrm{1,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 0}}\\\\\n",
    "\\Delta\\eta_\\mathrm{L} &= \\frac{\\dot{n}_\\mathrm{1,L,a} - \\dot{n}_\\mathrm{1,L,e}}{\\dot{n}_{1,\\chi = 0}} = - \\frac{Hi\\,Ha^2}{Da_\\mathrm{I}} \\frac{f_\\mathrm{1,L,b}}{\\frac{\\mathrm{d} f_\\mathrm{1,L}}{\\mathrm{d}\\chi} \\Big \\vert_{\\chi = 0}}\\\\\n",
    "\\eta_\\mathrm{L,b} &= 1 - \\eta_\\mathrm{L,Film} - \\Delta\\eta_\\mathrm{L}\n",
    "\\end{align*}\n",
    "\n",
    "Diese Berechnungsvorschriften werden jeweils als Funktionen wie folgt implementiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cal_E(dfdx_0, f_0, f_1):\n",
    "    '''\n",
    "    Berechnung des Verstärkungsfaktors\n",
    "    dfdx_0 : Ableitung des Restanteils nach der Ortskoordinate an der Stelle X = 0\n",
    "    f_0    : Restanteil an der Stelle X = 0\n",
    "    f_1    : Restanteil an der Stelle X = 1\n",
    "    '''\n",
    "    return dfdx_0 / (f_1 - f_0)\n",
    "\n",
    "def cal_eta_L_Film(dfdx_1, dfdx_0):\n",
    "    '''\n",
    "    Berechnung des Nutzungsgrads des Flüssigkeitsfilms\n",
    "    dfdx_1 : Ableitung des Restanteils nach der Ortskoordinate an der Stelle X = 1\n",
    "    dfdx_0 : Ableitung des Restanteils nach der Ortskoordinate an der Stelle X = 0\n",
    "    '''\n",
    "    return 1 - dfdx_1 / dfdx_0\n",
    "\n",
    "\n",
    "def cal_Delta_eta_L(Hi, Ha, Da, f_1_L_b, dfdx_0):\n",
    "    '''\n",
    "    Berechnung des Nutzungsgradverlusts\n",
    "    dfdx_0  : Ableitung des Restanteils nach der Ortskoordinate an der Stelle X = 0\n",
    "    Hi      : Hinterland-Verhältnis\n",
    "    Da      : Dammköhler-Zahl\n",
    "    Ha      : Hatta-Zahl\n",
    "    f_1_L_b : Restanteil von A1 in der Kernströmung der Flüssigkeit\n",
    "    '''\n",
    "    return - Hi * Ha**2 / Da * f_1_L_b / dfdx_0\n",
    "\n",
    "def cal_eta_L_b(eta_L_Film, Delta_eta_L):\n",
    "    '''\n",
    "    Berechnung des NUtzungsgrads der Kernströmung\n",
    "    eta_L_Film  : Nutzungsgrads des Flüssigkeitsfilms\n",
    "    Delta_eta_L : Nutzungsgradverlust\n",
    "    '''\n",
    "    return 1 - eta_L_Film - Delta_eta_L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Berechnungen für verschiedene $Hi$ und $Da_\\mathrm{I}$ erfolgen jeweils in einer For-Schleife."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Berechnungen für Da_I = 3\n",
    "Res_Hi_var = [] # leere Liste zum Speichern der Ergebnisse für verschiedene Hi\n",
    "\n",
    "for Lösung, Hi in zip(Lösungen_Hi, Hi_vec):\n",
    "    Da     = 3\n",
    "    Res    = np.empty(4) # Array der Größe 4 zum Speichern von E, eta_L_Film, Delta_eta_L, eta_L_b\n",
    "    Res[0] = cal_E(Lösung.y[2,0], Lösung.y[0,0], Lösung.y[0,-1])\n",
    "    Res[1] = cal_eta_L_Film(Lösung.y[2,-1], Lösung.y[2,0])\n",
    "    Res[2] = cal_Delta_eta_L(Hi, Ha, Da, Lösung.y[0,-1], Lösung.y[2,0])\n",
    "    Res[3] = cal_eta_L_b(Res[1],Res[2])\n",
    "    Res_Hi_var.append(Res)\n",
    "\n",
    "Res_Hi_var = np.array((Res_Hi_var))\n",
    "\n",
    "\n",
    "\n",
    "# Berechnungen für Hi = 100\n",
    "Res_Da_var = [] # leere Liste zum Speichern der Ergebnisse für verschiedene Da\n",
    "\n",
    "for Lösung, Da in zip(Lösungen_Da,Da_I_vec):\n",
    "    Hi     = 100\n",
    "    Res    = np.empty(4) # Array der Größe 4 zum Speichern von E, eta_L_Film, Delta_eta_L, eta_L_b\n",
    "    Res[0] = cal_E(Lösung.y[2,0], Lösung.y[0,0], Lösung.y[0,-1])\n",
    "    Res[1] = cal_eta_L_Film(Lösung.y[2,-1], Lösung.y[2,0])\n",
    "    Res[2] = cal_Delta_eta_L(Hi, Ha, Da, Lösung.y[0,-1], Lösung.y[2,0])\n",
    "    Res[3] = cal_eta_L_b(Res[1], Res[2])\n",
    "    Res_Da_var.append(Res)\n",
    "\n",
    "Res_Da_var      = np.array((Res_Da_var))\n",
    "\n",
    "comb_Res        = np.hstack((Res_Hi_var.T, Res_Da_var.T)) # Kombinierter Vektor der Ergebnisse\n",
    "comb_Res[[2,3]] = comb_Res[[3,2]]                        # Tauschen der letzten mit der vorletzten Reihe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Ergebnisse werden in einer Tabelle ausgegeben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------  ----  -----  ------  -------  ------  ------  ------\n",
      "Hi / 1           1     10     100     1000     100     100     100\n",
      "Da_I / 1         3      3       3        3       1       3      10\n",
      "E / 1            1.62   1.07    1.03     1.03    1.03    1.03    1.03\n",
      "eta_L_Film / 1   0.76   0.11    0.05     0.04    0.05    0.05    0.05\n",
      "eta_L_b / 1      0      0.65    0.71     0.72    0.47    0.71    0.86\n",
      "Delta_eta_L / 1  0.24   0.24    0.24     0.24    0.48    0.24    0.09\n",
      "---------------  ----  -----  ------  -------  ------  ------  ------\n"
     ]
    }
   ],
   "source": [
    "# Ausgabe der Ergebnisse als Tabelle\n",
    "\n",
    "names_y  = np.array((['Hi / 1'], ['Da_I / 1'], ['E / 1'], ['eta_L_Film / 1'], ['eta_L_b / 1'], ['Delta_eta_L / 1']))\n",
    "Hi_table = np.array((1, 10, 100, 1000, 100, 100, 100))  \n",
    "Da_table = np.array((3, 3, 3, 3, 1, 3, 10))\n",
    "\n",
    "# Array for table\n",
    "table = np.hstack((names_y,np.vstack((Hi_table, Da_table, abs(np.round(comb_Res, 2))))))\n",
    "\n",
    "print(tabulate(table))"
   ]
  }
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