{
"cells": [
{
"cell_type": "markdown",
"id": "34986a52",
"metadata": {},
"source": [
"# M1.D6: Vibrational levels of diatomic molecules\n",
"\n",
"## Learning Objectives\n",
"\n",
"* Introducing the Schrodinger equation for nuclear motion and proposing a harmonic approximation for its solution.\n",
"* Plotting the solution of the harmonic oscillation and graphically investigate how the energy levels are affected by the harmonic constant or frequency of vibration.\n",
"* Graphically investigate how the vibrational levels are affected by the bond strength and atomic mass.\n",
"* Plot the wavefunction for the quantum oscillator. Assess with plots how mass and bond strength affects the \"quantumness\" of the system.\n",
"* Use the pyscf package to calculate the frequency of vibration of heterodiatomic molecules. Compare these frequencies with experimental Infrared spectra.\n",
"* Discuss the harmonic approximation and when it is important to introduce anharmanocity\n",
"\n",
"# The Schrodinger Equation of Nuclear Motion\n",
"\n",
"In our previous sessions we have studied the electronic levels of atoms and molecules.\n",
"The electronic energy is the energy considering the kinetic and potential energy of electrons when nuclei are fixed at a given position. Using this approach (Born-Oppenheimer approximation) we have a Potential Energy Surface (defined as $U(r)$ where r are the nuclear coordinates) that is the potential where the nuclei move.\n",
"\n",
"U(r) = Electronic energy + Repulsion between nuclei\n",
"\n",
"Assuming that we have calculated $U(r)$ we can build the Hamiltonian and solve the whole Schrodinger equation with now considering the nuclear motion.\n",
"\n",
"$$\n",
"\\hat{H}_{nuclear} = \\sum_{k=nuclei}-\\frac{1}{2m_k}\\nabla_{k} + U(r) \n",
"$$\n",
"\n",
"So we have a new differential equation to solve that depends on the nuclear coordinates \"r\" for any molecular system. \n",
"\n",
"$$\n",
"\\sum_{k=nuclei}-\\frac{1}{2m_k}\\nabla_{k}\\Psi(r) + U(r)\\Psi(r) = E\\Psi(r)\n",
"$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "4a06c3b7",
"metadata": {},
"source": [
"# The harmonic approximation to nuclear motion\n",
"\n",
"To simplify things, let's start with the simplest system, a diatomic molecule. Remember what we did for the hydrogen atom, when treating systems of two particles we can always reduce it as one particle of reduced mass $\\mu$. In that case the Schrodinger equation of the nuclear motion is (in atomic units)\n",
"\n",
"$$\n",
"-\\frac{1}{2\\mu}\\frac{\\delta^2\\Psi(r)}{\\delta r^2} + U(r)\\Psi(r) = E\\Psi(r)\n",
"$$\n",
"\n",
"Remember that the potential U(r) comes from solving the electronic states for each nuclear position. This is a hard task and it makes the differential equation not to have an analytical solution.\n",
"\n",
"Here comes the approximation. Let's assume that around the bond distance the potential is a parabola, or in physics terms, an harmonic potential\n",
"\n",
"\n",
"\n",
"Remember from physics that the potential energy of an harmonic spring is\n",
"\n",
"$$\n",
"E_{harmonic} = \\frac{1}{2}kr^2\n",
"$$\n",
"\n",
"We do this approximation because then the Schrodinger equation for the nuclear motion is solvable.\n",
"\n",
"$$\n",
"-\\frac{1}{2\\mu}\\frac{\\delta^2\\Psi(r)}{\\delta r^2} + \\frac{1}{2}kr^2\\Psi(r) = E\\Psi(r)\n",
"$$\n",
"\n",
"\n",
"A note here: We automagically simplified the nuclear coordinates \"r\" into just the distance between the atoms. Of course if we are using polar coordinates, besides \"r\" there will also be the other two angular coordinates ($\\theta$ and $\\phi$) that will be addressed later when considering molecular rotations. A molecule with 3N degrees of freedom (N being the number of nuclei) has 3 translational normal modes (along the x,y, and z axes), 3 rotational normal modes (around each of the three axes), and 3N-6 (the remaining number) different vibrational normal modes of motion.\n",
"\n",
"The solutions are famously known as the [quantum harmonic oscillator](https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator). The wavefunction (the eigenfunctions of the Schrodinger equation) is what is known as the Hermite polynomials and the energy (the eigenvalues of the Schrodinger equation) of the Quantum harmonic oscillator depends again on quantum number, the vibrational quantum number\n",
"\n",
"$$\n",
"E = \\hbar\\sqrt{\\frac{k}{\\mu}} (v + \\frac{1}{2}) \\textrm{ where } v = 0,1,2,3...\n",
"$$\n",
"\n",
"the frequency of vibration is\n",
"\n",
"$$\n",
"\\omega = \\sqrt{\\frac{k}{\\mu}}\n",
"$$\n",
"\n",
"so the eigenstates can also be expressed as\n",
"\n",
"$$\n",
"E = \\hbar \\omega (v + \\frac{1}{2}) \\textrm{ where } v = 0,1,2,3...\n",
"$$\n",
"\n",
"We will use the [classical harmonic oscillator](https://en.wikipedia.org/wiki/Harmonic_oscillator) to compare the quantum behavior with the classical one."
]
},
{
"cell_type": "markdown",
"id": "69af875e",
"metadata": {},
"source": [
"## The energy levels of the harmonic oscillator\n",
"\n",
"* A molecule with 3N degrees of freedom (N being the number of nuclei) has 3 translational normal modes (along the x,y, and z axes), 3 rotational normal modes (around each of the three axes), and 3N-6 (the remaining number) different vibrational normal modes of motion. How many translational, rotational, and vibrational modes does a diatomic molecule have?\n",
"* Your turn. Plot the energy of the different vibrational levels. Use atomic units so that $\\hbar=1$ and start with simple numbers of $k = 1,2,3$ or $\\mu=1,2,3..$\n",
"* Investigate the role of the spring constant k and the mass of the system. You may use the plots below to overlap the energy levels."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "fae2c149",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt \n",
"import numpy as np\n",
"fig = plt.figure(figsize=(7,5))\n",
"ax1 = plt.subplot(121) #121 means: the subplots will be 1 row 2 columns and this one is subplot number 1\n",
"ax2 = plt.subplot(122, sharey = ax1) #share-y means that it will share the y-axis with the ax1 plot\n",
"\n",
"k1 =1\n",
"k2 =2\n",
"x1 = np.linspace(-2,2.0,40)\n",
"x2 = np.linspace(-2,2.0,40)\n",
"ax1.plot(x1,0.5*k1*x1**2)\n",
"ax1.set_title(\"Energy levels for k=\"+str(k1))\n",
"ax2.plot(x2,0.5*k2*x2**2)\n",
"ax2.set_title(\"Energy levels for k=\"+str(k2));"
]
},
{
"cell_type": "markdown",
"id": "6b721074",
"metadata": {},
"source": [
"## The harmonic oscillator wavefunctions\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "723bfed0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt \n",
"import numpy as np\n",
"import numpy.polynomial.hermite as Herm\n",
"import math\n",
"\n",
"#Choose simple units\n",
"m=1.\n",
"w=1.\n",
"hbar=1.\n",
"#Discretized space\n",
"dx = 0.05\n",
"x_lim = 12\n",
"x = np.arange(-x_lim,x_lim,dx)\n",
"\n",
"def hermite(x, n):\n",
" xi = np.sqrt(m*w/hbar)*x\n",
" herm_coeffs = np.zeros(n+1)\n",
" herm_coeffs[n] = 1\n",
" return Herm.hermval(xi, herm_coeffs)\n",
" \n",
"def stationary_state(x,n):\n",
" xi = np.sqrt(m*w/hbar)*x\n",
" prefactor = 1./math.sqrt(2.**n * math.factorial(n)) * (m*w/(np.pi*hbar))**(0.25)\n",
" psi = prefactor * np.exp(- xi**2 / 2) * hermite(x,n)\n",
" return psi\n",
"\n",
"v=2\n",
"plt.figure()\n",
"plt.plot(x, stationary_state(x,v))\n",
"plt.xlabel(\"r\")\n",
"plt.ylabel(r\"$\\psi(r)$\")\n",
"plt.title(r\"Vibrational function $\\psi(r)$ for quantum number \"+str(v))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "48892701",
"metadata": {},
"source": [
"* Your turn: plot the first three wavefunctions of the quantum oscillator.\n",
"* Plot the square of the wavefunctions as it indicates the probability"
]
},
{
"cell_type": "markdown",
"id": "17a44ebc",
"metadata": {},
"source": [
"## Using the classical harmonic oscillator to assess the \"quantumness\" of the system\n",
"\n",
"It can be shown that for the classical harmonic oscillator [the classical probability density](https://en.wikipedia.org/wiki/Classical_probability_density) is the probability depends on the maximum amplitude $A$ of the oscillator\n",
"\n",
"$$\n",
"P(r) = \\frac{1}{\\pi}\\frac{1}{\\sqrt{A^2 - r^2}}\n",
"$$\n",
"\n",
"The maximum amplitude is when the oscillator only has potential energy and zero kinetic energy. So if we solve for r in the potential energy we obtain the amplitude\n",
"\n",
"\n",
"$$\n",
"E_{pot} = \\frac{1}{2}kr^2\n",
"$$\n",
"\n",
"so\n",
"\n",
"$$\n",
"r_{max} = A = \\sqrt{\\frac{2E}{k}}\n",
"$$\n",
"\n",
"or in terms of frequency and mass, since $k = m\\omega^2$\n",
"\n",
"$$\n",
"r_{max} = A = \\sqrt{\\frac{2E}{m\\omega^2}}\n",
"$$\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "81b8cea6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#source: UCD_Chem_110A%3A_Physical_Chemistry_I_(Larsen)/Text/05%3A_The_Harmonic_Oscillator_and_the_Rigid_Rotor/5.I%3A_Interactive_Worksheets/5.I1%3A_Simple_Harmonic_Oscillator_-_Plotting_Eigenstates\n",
"import matplotlib.pyplot as plt \n",
"import numpy as np\n",
"\n",
"#Choose simple units\n",
"m=1.\n",
"w=1.\n",
"hbar=1.\n",
"#Discretized space\n",
"dx = 0.05\n",
"x_lim = 12\n",
"x = np.arange(-x_lim,x_lim,dx)\n",
"\n",
"def classical_P(x,n):\n",
" E = hbar*w*(n+0.5)\n",
" x_max = np.sqrt(2*E/(m*w**2))\n",
" classical_prob = np.zeros(x.shape[0])\n",
" x_inside = abs(x) < (x_max - 0.025)\n",
" classical_prob[x_inside] = 1./np.pi/np.sqrt(x_max**2-x[x_inside]*x[x_inside])\n",
" return classical_prob\n",
"\n",
"plt.figure()\n",
"plt.plot(x, classical_P(x,4))\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"$P_{classical}(x,4)$\")\n",
"plt.title(\"Classical Probability Density of a Harmonic Oscillator, $E=E_4$\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e9a1f0cf",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAzoAAAKTCAYAAADR1X0mAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQABAABJREFUeJzs3Xl8VOW9P/DP7JN9JZuEgIKAIoLBKiBaF+Kl1vZ2uVK9Fa3QSnEp0NYr1/u7IrWlrUrTVkEtIvXWUrrYWitVYxUBsSoRlAooe1gSsu/JrOf3x1nmnJkzk5kwez7v1yuGzJw588wknme+z/f7PI9BEAQBREREREREacSY6AYQERERERFFGwMdIiIiIiJKOwx0iIiIiIgo7TDQISIiIiKitMNAh4iIiIiI0g4DHSIiIiIiSjsMdIiIiIiIKO2YE92AcHi9Xpw+fRo5OTkwGAyJbg4R0YghCAJ6enpQUVEBo5FjY2rsm4iIEiPcviklAp3Tp0+jsrIy0c0gIhqxTpw4gdGjRye6GUmFfRMRUWIN1TelRKCTk5MDQHwxubm5CW4NEdHI0d3djcrKSuU6TD7sm4iIEiPcviklAh25JCA3N5edCRFRArA0KxD7JiKixBqqb2LBNRERERERpR0GOkRERERElHYY6BARERERUdpJiTk6RESR8Hg8cLlciW5GSrBYLDCZTIluBhFRWvN6vXA6nYluRsqIVt/EQIcoEs4+YPfzwMR5QH4Ml5U99DrgcYnPQ2ETBAFNTU3o7OxMdFNSSn5+PsrKyrjgAFGstXwKHNsOXHIbYOJHMACAIAC7fwOUXQRUTEt0a2LC6XTi6NGj8Hq9iW5KSolG3xTx/2Xbtm3DI488gvr6ejQ2NuLPf/4z/v3f/z3kY9566y0sX74cH3/8MSoqKnDfffdh8eLFw20zUeLUPQi8/ytg62rgv47G5jncTuA3XxH//V/HgIyC2DxPGpKDnJKSEmRmZvKD+xAEQUB/fz+am5sBAOXl5QluEVGae+JS8bvXA1z2rcS2JVkcfA34693iv1d2JbYtMSAIAhobG2EymVBZWcmNl8MQzb4p4kCnr68PF198Mb7xjW/gK1/5ypDHHz16FJ/73OfwzW9+E7/5zW/w9ttvY8mSJRg1alRYjydKKkfeFL8PtMfuOdyDvn87+xjohMnj8ShBTlFRUaKbkzIyMjIAAM3NzSgpKWEZG1E8nHiXgY6saW+iWxBTbrcb/f39qKioQGZmZqKbkzKi1TdFHOjMmzcP8+aFX07z5JNPYsyYMaitrQUATJ48Gbt27cKjjz7KQIdSjyEOHwIFT3yfL03Ic3LYkUROfs9cLhcDHaJ4EFjCpBCERLcgpjwesU+3Wq0JbknqiUbfFPP82TvvvIOamhrNbddffz127doVdLKww+FAd3e35osoKRjjEeioLvrxeL40w3K1yPE9I4ozBjo+I+S94HU2ctF4z2Ie6DQ1NaG0tFRzW2lpKdxuN1pbW3Ufs3r1auTl5SlflZUxnPRNFAlDHGprveqMDmt5iYjSjjpzP9LxvaAYisunKP+ITJBGrINFaitWrEBXV5fydeLEiZi3kSgs8Qg8eNEnIkpvaV6uFZERktGhxIj52oZlZWVoamrS3Nbc3Ayz2Rx0wrDNZoPNZot104giF49SMnVGh50hEVH68XJAS8H3gmIo5sPTM2fORF1dnea21157DTNmzIDFYon10xNFV9wzOgx0KDINDQ248cYbkZWVheLiYtx7773cpI4o2TCL4cP3Iu21tbXh3/7t31BRUQGbzYbKykrcfffdcZmDH/Gntt7eXuzZswd79uwBIC4fvWfPHjQ0NAAQy84WLFigHL948WIcP34cy5cvx/79+7FhwwY888wz+N73vhedV0AUT/FYBc3r9v2bGR2KgMfjwQ033IC+vj7s2LEDv/vd7/CnP/0J3/3udxPdNCJS44d7H74Xac9oNOKLX/wi/vrXv+LTTz/Fxo0b8frrr8dlT82IS9d27dqFq6++Wvl5+fLlAIDbbrsNGzduRGNjoxL0AMC4ceOwZcsWLFu2DE888QQqKirwi1/8gktLU2qKd+kaMzrDJggCBlyJKYnIsJjCXi3ms5/9LKZOnQq73Y7169fDarVi8eLFWLlyZcTP+9prr2Hfvn04ceIEKioqAACPPfYYbr/9dvzwhz9Ebm5uxOdMJWvXrsUjjzyCxsZGXHjhhaitrcWcOXOCHu9wOLBq1Sr85je/QVNTE0aPHo0HHngAd9xxRxxbTSMS52L6jLBAZyT2TQUFBfj2t7+t/FxVVYUlS5bgkUceifhckYo40PnsZz+rLCagZ+PGjQG3XXXVVfjggw8ifSqi5BPvVdeY0Rm2AZcHF/zvqwl57n2rrkemNfzL669//WssX74c7777Lt555x3cfvvtmD17NubOnYt58+Zh+/btIR/f29sLQFzOf8qUKUqQA4jL+TscDtTX12sGqdLN5s2bsXTpUqxduxazZ8/GU089hXnz5mHfvn0YM2aM7mNuuukmnDlzBs888wzGjx+P5uZmuN1u3WOJomqEfbgPaYS9FyOxb/J3+vRpvPDCC7jqqqsiav9wxHwxAqK0EpdAR/1Bi4HOSDB16lQ8+OCDAIAJEybg8ccfxz/+8Q/MnTsX69evx8DAQFjn0VvOv6CgAFarNWBRmHSzZs0aLFy4EIsWLQIA1NbW4tVXX8W6deuwevXqgONfeeUVvPXWWzhy5AgKCwsBAGPHjo1nk2kk4wR8H74XSStafZPs5ptvxosvvoiBgQHceOONWL9+fSyarcFAhygS8Q50mNEZtgyLCftWXZ+w547E1KlTNT+Xl5ejubkZAHDOOedEdC69sgRBENJ6szqn04n6+nrcf//9mttramqwc+dO3cf89a9/xYwZM/DTn/4U//d//4esrCx84QtfwA9+8ANkZGToPsbhcMDhcCg/czNrGjZe231GWEZnpPZNAPCzn/0MDz74ID755BP893//N5YvX461a9dGfJ5IMNAhikQ85uhw1bWoMBgMEaXoE8l/BUqDwQCvV+z8IykPKCsrw7vvvqu5r6OjAy6XKyDTk05aW1vh8Xh0N6cOlsk6cuQIduzYAbvdjj//+c9obW3FkiVL0N7ejg0bNug+ZvXq1XjooYei3n4agUbYh/uQRth7MRL7JllZWRnKysowadIkFBUVYc6cOfh//+//oby8PLoNV0mNd5ooWcR9js7I6gAoUCTlATNnzsQPf/hDNDY2Kh3Ha6+9BpvNhurq6lg2MynobU4dLJPl9XphMBjw/PPPIy8vD4BY/vbVr34VTzzxhG5WZ8WKFcoCPICY0amsrIziK6ARg9d2H74XKWk4pWtq8nx/dZY8FhjoEEWCpWsUZ5GUB9TU1OCCCy7ArbfeikceeQTt7e343ve+h29+85tpveJacXExTCaT7ubUwTJZ5eXlOOecc5QgBwAmT54MQRBw8uRJTJgwIeAx3MyaooYf7n34XqSkSPqmLVu24MyZM7j00kuRnZ2Nffv24b777sPs2bNjPjcyDp/aiNJIXPbRYekaDY/JZMLLL78Mu92O2bNn46abbsK///u/49FHH01002LKarWiuro6YHPquro6zJo1S/cxs2fPxunTpzWlFZ9++imMRiNGjx4d0/YScXlpFb4XaS8jIwO/+tWvcMUVV2Dy5MlYunQpPv/5z+Nvf/tbzJ+bGR2iSMRlHx1mdEaSrVu3Btz2l7/8ZdjnGzNmTFw6j2SzfPly3HrrrZgxYwZmzpyJp59+Gg0NDcqGdCtWrMCpU6fw3HPPAQBuueUW/OAHP8A3vvENPPTQQ2htbcX3v/993HHHHUEXIyCKGmYxfNjPJaVo9k1XX3110IVhYo2BDlEk4rFyFTM6RBGbP38+2trasGrVKjQ2NmLKlCnYsmULqqqqACBgM+vs7GzU1dXhnnvuwYwZM1BUVISbbroJDz/8cKJeAo0kDHR8+F5QDDHQIYpEPErXBG4YSjQcS5YswZIlS3Tv09vMetKkSQHlbkRx4eWHewX30aEY4hwdokjEu3SNiIjSD7MYPnwvKIYY6BBFgquuERHR2eIEfB++FxRDDHSIIsFV15KelyUhEeN7RhRnzGL4jJD3QuDAZcSi0Tdxjg5RJOJSusY5OsNhtVphNBpx+vRpjBo1ClarNehmkSQSBAFOpxMtLS0wGo2wWq2JbhLRyDBCPtyHJc3fC4vFAoPBgJaWFowaNYr9Uhii2Tcx0CGKhPoCJQixWYVNM0eHgU64jEYjxo0bh8bGRpw+fTrRzUkpmZmZGDNmDIxGJvmJ4oIT8H3SPKNsMpkwevRonDx5EseOHUt0c1JKNPomBjpEkVCXrgne2JSycdW1YbNarRgzZgzcbjc8Hn6QCIfJZILZbOYoI1E8pXkWIyIj4L3Izs7GhAkT4HK5Et2UlBGtvomBDlEk1KVrXndsStmY0TkrBoMBFosFFosl0U0hItI3Aj7ch22ELEZgMplgMsWh/J00WKdAFAn1qmuxWgaaq64REaU3Bjo+fC8ohhjoEEVCXaoWqxprTb0yAx0iorTDD/c+fC8ohhjoEEXCv3QtFpjRISJKb1yMwIfvBcUQAx2iSGhK12KV0eEcHSKitMYshg/fC4ohBjpEkVBnWGI1gZKrrhERpbcRMgE/LAx0KIaGFeisXbsW48aNg91uR3V1NbZv3x7y+Oeffx4XX3wxMjMzUV5ejm984xtoa2sbVoOJEksVeMSjdI0ZHSKi9MMP9z58LyiGIg50Nm/ejKVLl+KBBx7A7t27MWfOHMybNw8NDQ26x+/YsQMLFizAwoUL8fHHH+MPf/gD3n//fSxatOisG08Ud+oMSzwWI2BGh4go/fDa7sNAh2Io4kBnzZo1WLhwIRYtWoTJkyejtrYWlZWVWLdune7x//znPzF27Fjce++9GDduHK644grceeed2LVr11k3nij+mNEhIqKzxAn4PnwvKIYiCnScTifq6+tRU1Ojub2mpgY7d+7UfcysWbNw8uRJbNmyBYIg4MyZM/jjH/+IG264IejzOBwOdHd3a76IkkJcMjpcdY2IKK0xi+HD94JiKKJAp7W1FR6PB6WlpZrbS0tL0dTUpPuYWbNm4fnnn8f8+fNhtVpRVlaG/Px8/PKXvwz6PKtXr0ZeXp7yVVlZGUkziWIozosRMKNDRJR+uBiBD98LiqFhLUZgMBg0PwuCEHCbbN++fbj33nvxv//7v6ivr8crr7yCo0ePYvHixUHPv2LFCnR1dSlfJ06cGE4ziaJPiEfpmnrVtdg8BRERJRCzGD58LyiGzJEcXFxcDJPJFJC9aW5uDsjyyFavXo3Zs2fj+9//PgBg6tSpyMrKwpw5c/Dwww+jvLw84DE2mw02my2SphHFCefoEBHRWeKHex/Ntg0CEGTgnGg4IsroWK1WVFdXo66uTnN7XV0dZs2apfuY/v5+GI3apzGZxN3lBc4/oFSjyejEqKPych8dIqK0xkDHh30exVDEpWvLly/H+vXrsWHDBuzfvx/Lli1DQ0ODUoq2YsUKLFiwQDn+xhtvxAsvvIB169bhyJEjePvtt3HvvffiM5/5DCoqKqL3SojiQd05xSOjw86QiIjSmbqfY59HURZR6RoAzJ8/H21tbVi1ahUaGxsxZcoUbNmyBVVVVQCAxsZGzZ46t99+O3p6evD444/ju9/9LvLz83HNNdfgJz/5SfReBVHcsHSNiIgoajTBDfs8iq6IAx0AWLJkCZYsWaJ738aNGwNuu+eee3DPPfcM56mIkosQj1XXuGEoERGNEOzzKIaGteoa0cjFjA4REVHUMKNDMcRAhygS3DCUiIgoegQuRkCxw0CHKCLxCHS4YSgREY0QmuCGfR5FFwMdokior8FxWXWNF30iIkpjXF6aYoiBDlFEVBdhjzM2T8E5OkRENFJwjg7FEAMdokioR5vcjtg8h2tA//mIiIjSDVddoxhioEMUEXWgMxibp9AEULzoExFRGhM4L5Vih4EOUSTikdFRB1Ac3SIionTGjA7FEAMdooioA52B4IedDU2miBd9IqK0FKuVO1ONx6X6gX0eRRcDHaJIMKNDRETREKs+JNWo3wf2eRRlDHSIIqK6CLtilNFxMaNDRJSeDL5/xmqeZ6rxMqNDscNAhygScc/oxOYpiIgoAQyqj13M6AAev/3omNGhKGOgQxQRrrpGRETDFYc+JJXwPaAYY6BDFAkhxp2UIGgXOeDoFhFR+oh1H5Jq/N8D9nkUZQx0iCIS407K4wz+fERElOIY6GgEvAfs8yi6GOgQRUI92uSKQSflv8ABR7eIiNIT5+gEvgfs8yjKGOgQRSTGo3EBHR8v+kREacH/QzwzOszoUMwx0CGKRKxXXWO9MtGwrV27FuPGjYPdbkd1dTW2b98e1uPefvttmM1mTJs2LbYNpJEtINBhRod9HsUaAx2iiKgDnRjso8PRLaJh2bx5M5YuXYoHHngAu3fvxpw5czBv3jw0NDSEfFxXVxcWLFiAa6+9Nk4tpZGLGZ0ArGKgGGOgQxQJZnSIktKaNWuwcOFCLFq0CJMnT0ZtbS0qKyuxbt26kI+78847ccstt2DmzJlxaimNWMzoBGKfRzHGQIdouPwXDojKOZnRIYqU0+lEfX09ampqNLfX1NRg586dQR/37LPP4vDhw3jwwQfDeh6Hw4Hu7m7NF1H4mNEJwIwOxdiwAp1I66AdDgceeOABVFVVwWaz4bzzzsOGDRuG1WCihGJGhyjptLa2wuPxoLS0VHN7aWkpmpqadB9z8OBB3H///Xj++edhNpvDep7Vq1cjLy9P+aqsrDzrttMIwoxOIPZ5FGMRBzrDqYO+6aab8I9//APPPPMMPvnkE2zatAmTJk06q4YTJQbn6BAlK4PBoPlZEISA2wDA4/HglltuwUMPPYTzzz8/7POvWLECXV1dyteJEyfOus00kjCjE4AZHYqx8IaxVNR10ABQW1uLV199FevWrcPq1asDjn/llVfw1ltv4ciRIygsLAQAjB079uxaTZQogtf377hkdLz6xxGRori4GCaTKSB709zcHJDlAYCenh7s2rULu3fvxt133w0A8Hq9EAQBZrMZr732Gq655pqAx9lsNthstti8CEp//tdzBjrs8yjmIsroDKcO+q9//StmzJiBn/70pzjnnHNw/vnn43vf+x4GBoKPhrMOmpKWZsPQgein2f3n6DCNTzQkq9WK6upq1NXVaW6vq6vDrFmzAo7Pzc3F3r17sWfPHuVr8eLFmDhxIvbs2YPLLrssXk2nkYSla4G4YSjFWEQZneHUQR85cgQ7duyA3W7Hn//8Z7S2tmLJkiVob28POk9n9erVeOihhyJpGlGcCNp/u/oBa1b0Tu/sCfF8RBTM8uXLceutt2LGjBmYOXMmnn76aTQ0NGDx4sUAxLKzU6dO4bnnnoPRaMSUKVM0jy8pKYHdbg+4nSh6WLoWgOXaFGMRl64B4ddBA2I5gMFgwPPPP4+8vDwAYvnbV7/6VTzxxBPIyMgIeMyKFSuwfPly5efu7m5O+qTk4D/aNNgd3UBn0C97ydEtorDMnz8fbW1tWLVqFRobGzFlyhRs2bIFVVVVAIDGxsYh99QhiilmdAIxo0MxFlGgE2kdNACUl5fjnHPOUYIcAJg8eTIEQcDJkycxYcKEgMewDpqSl99F2NEDoDx6p3f4Z3SIKFxLlizBkiVLdO/buHFjyMeuXLkSK1eujH6jiBTM6ARgRodiLKI5OpHWQQPA7Nmzcfr0afT29iq3ffrppzAajRg9evQwmkyUQP6jTY4ozx/zPx9Ht4iI0gMzOoGY0aEYi3h56eXLl2P9+vXYsGED9u/fj2XLlgXUQS9YsEA5/pZbbkFRURG+8Y1vYN++fdi2bRu+//3v44477tAtWyNKbrEOdDhHh4goPfldz519iWlGMuF7QDEW8RydSOugs7OzUVdXh3vuuQczZsxAUVERbrrpJjz88MPRexVE8RKQ0Qldana0tQ8rXvgIh1v6cOPUCvz35ybBbAoxvuB/Po5uERGlhwj7jxGBfR7F2LAWI4i0DnrSpEkB5W5EqUlnMYIgegZd+Pr6d3GqU1xKfcPbR+EVBKz8woXBTx9wPl70iYjSAwOdAKxioBiLuHSNaESLYETu8TcO4VTnAMYUZuK//m0SAODX7xzDvtMhyt04R4eIKD0xoxOIGR2KMQY6RBGRLsK2XPF7kDk63YMu/OafxwEAD954Ab792fNww0XlEATgV9uPBD+9fD6bvEohL/pERGnJ70O+1ytg6yfNONHen6AGxU5T1yD+sf8MXB6v9g5mdCjGGOgQRUIebbJLgUiQEbkX95xGn9OD8SXZuGZSCQDgW1eeCwD420en0dnv1D+/fD57rvb5iIgotQ2R0fnZ65/i9mffx7Vr3kL98Y44Niy2DjX34Lo1b2Hhr3fhf1/8WHsnqxgoxhjoEA3HEBmdl/acBgDcNGO0spnuxZX5mFSWA5dHwKsfN+k+Tun45PNzdIuIKE34Xc9dfYDXAwBo6XFg3dbDAACn24u1bx6Kd+Ni5lfbjqLX4QYAbHqvAYeaVQGes9fvaPZ5FF0MdIgi4Z/RGewKOKSlx4H3jrUDAD4/tUJz340Xiz9v2asT6LgGAI9Te36ObhERpQe967n0Qb9u3xm4vQJybOIaUW980oyuAVc8WxcTbo8Xf/tIHPjLsYuv7e/q/o9zdCjGGOgQRUS6CGcVi9/72gKO2Hm4FQBwQXkuKvK1e0VdO1ksY3v3aBscbo/2gX3i42C0+ErXOLpFRJQmVNdzk1X8Ln3Qr9snfvj/9tXnYWxRJgQB+KAh9cvX9jf2oM/pQY7djAc+NxkAULf/jHin2+Eb3DPZpEewz6PoYqBDFAl5tClrlPi9vzXgkO0HxdvmTCgOuG9iaQ6Ks20YdHnxwfFO7Z3yubJGATBon4+IiFKbcj03ALYc8Z+OHni9gjIn54rxxZgxthAAsEuqDEhlu46Lr2FGVQGuPF/sNz8+3Y1+p1ubzZHfD/Z5FGUMdIgiIl2Es8XMDPpatPcKAt4+JAYss8cHBjoGgwFXjC8CAOw4pH2sktHJKgKkeT0c3SIiShfS9dygDXSOtvWhe9ANm9mIyeW5uGRMAQDgo5OBpdGpRn4Nl4wpQHmeHaW5Nni8Avae7PLNcbVmA0aT9Aj2eRRdDHSIIiH4la71tyuTSQHgcEsfGrsGYTUb8ZlxhbqnuGKCOKq146BfNqiPGR0iorSlm9Hpxp6GTgDA1NF5sJiMOL80GwBwuNl/on7qOSS9hgmlOTAYDJheKQZxu090qhbfyQH7PIoVBjpEEZEuwpnFvp8HfHXU70jzc2ZUFcBuMUHPFVKm56NTXegeVE02lbNDmcXM6BARpR11RkeahznYhU/PiB/4LygXbxtfIgY6p7sG0SetVpaKvF4Bh1vEQEd+TRdUiK/x0zM9wKC8b1wO+zyKGQY6RJGQR5uMZiBDytioytd2SyNzco21nrI8O0YXZEAQgI9OqEoT5PPI83/Uz0dERKlNndHJlPqI/nYl6yEHA/mZVhRni4sVyIFCKmrsHkS/0wOz0YCqokwAvtd4uLkX6JcW88ksAjM6FCsMdIgiohqRU1Ze85Wg7TnRCQCYXpkf8izTpPv3nFCtqiNf9DlHh4goDan6j0xxrib623BICmbOk4IAADh3lPjvIy19cW1hNB2V2l5VlAmLSfy4qQQ6LX0Q5L4zk30exQ4DHaJIqEfk5MxLr7hUZle/C0daxQv7xWEHOp2+G6XzcI4OEVEa0mR0xIEyd28rGtr7AQATSnKUQ8cUihmQU50DcW1iNJ3sEF+X/FoAYGxRFkxGA3odbvR2SH0eMzoUQwx0iCKiGpHLPUf8d/cpAMCek50AgLFFmSjMsoY8y/Qx+eJjTnRCkC/sXeJ5kHuOanSLiIjSQ2BFQF97EwQByMuwKOVqAHCOtAebHCykopMdYpB2ToFvPzmr2aiUsXW3SxuHMqNDMcRAhygS6hG5vNHiP7tOAgB2S5u7TRsimwMAF1bkwWIyoLXXqXQGcsCEvEpwdIuIKM1oMjpi6ZqzR5ybOb4kGwbVAJccHCj9QwqSs1Hn5Gdqbh8vleUNdjWLN2QVw9fnxat1NFIw0CGKiGpEzi/Q+VAqQwsn0LFbTJgsrbCz50QnMKjaUyDvHI5uERGlHZ05On3i3Ez5w79stBTonErhQEfORo1WZXQA3zwdb69qMQIlxmOfR9HFQIcoEroZnRMAgP2N4hKhU87JC+tU8nH7GruVYAkZBYA1C8zoEBGlGZ2MjsXRDsD34V82Ot83R0dI0X7glE7pGuB7reZB8bWL85XY51FsMNAhioTgFb8bjJqMTme/E03dgwCA88tygjxYS87o7FcHOvI5DUbt8xERUWpT9x/SHJ0sTxcAAeeOytIcWpZnBwA43F509ruQajxeAWd6HACAcum1yOQV5bLc0qqjmYXs8yhmGOgQRUQuPYA0lwbAQAcONojza87Jz0Cu3RLWmeTN4fad7gY6jok35o2Rzs/SNSKitGQwAFklAAywwI1C9KCyUDuPxWo2Ij9T7Etaeh0JaOTZaetzwOMVYDAAo7JtmvsqCzJghBeFQqd4Q045+zyKGQY6RJFQrsEGwJ4LZJcBAJqP/gsAMCnMbI58rMEANPc4MNh4QLyxeILv/ADT+ERE6UJduma2wittUVBuaFdWWVOTA4SWntQLdJq7xTYXZ9tgNmk/ahZmWTHG2gOzwQvBYAKyxaAPAPs8ijoGOkQRUU0mBZTApO/0fgDApPLwA50smxlV0ijeYJNfoMPRLSKiNKOqCADgyBQHyiZkdCPLZg44uiQ3dQOdM1Ipd2muLeA+g8GAqTninnOOjBLAaGKfRzHDQIcoEuoROUAJTIxthwAAE8tyIzrdBRXi8eaOw9L5zteen6NbRETpwa//6LaUAAAmZXTpHi5ndJp7BmPetGg7I2V0SnPsuvdPyhRXGe2xlki3sM+j2BhWoLN27VqMGzcOdrsd1dXV2L59e1iPe/vtt2E2mzFt2rThPC1REvDP6IiBSX7fEQCRla4BwOSyXGSjH9kOaYfoovHa83N0i4goTWj7j1ajuCDBOGuQQCcn9TM6Jbn6gc65NvE1txrF8j32eRQrEQc6mzdvxtKlS/HAAw9g9+7dmDNnDubNm4eGhoaQj+vq6sKCBQtw7bXXDruxRAnnn9EpnQIAmISjsJqMGFecpf+4IC6oyMUFhuPiD7mjxdVn1Ofn6BYRUXrw6z9OewsAAOcY23UPL5GyIakY6DRLbS7JCSxdA4AK6TWf9uZLt7DPo9iIONBZs2YNFi5ciEWLFmHy5Mmora1FZWUl1q1bF/Jxd955J2655RbMnDlz2I0lSjy/jE75VADAaEMrphV7YTFF9r/U5PJcXGQ8CgDwlF/su4OjW0REaUbbfxx2iRmdEk+T7tFyRqc5BQOdtl55MQKr7v2l7kYAwCHpPWCfR7ES0acyp9OJ+vp61NTUaG6vqanBzp07gz7u2WefxeHDh/Hggw+G9TwOhwPd3d2aL6Kk4J/Rseeh0y4uM31N7umIT1eeZ8clFjGj05o9SXUPR7eIiNKKX//xrwExg58/cEL38FQuXWvvcwIACrP0Mzp50mveO1Ak3cI+j2IjokCntbUVHo8HpaWlmttLS0vR1KQ/InHw4EHcf//9eP7552E2B64qomf16tXIy8tTviorKyNpJlEM+WV0AHxqmQgAuNT4ScRnMxgM+IzpUwDAAfP5qjv8no+IiFKcr/8QBAHv94ila1ZHGzAYOKArl30Ndx8dr1eAcBaBgyAI8HqH9/j2fjnQ0cnoeL2w9YgDfB8NFKPP4WZGh2JmWIsRGFQf8gDxfwb/2wDA4/HglltuwUMPPYTzzz8/4P5gVqxYga6uLuXrxAn90Q6iuPPP6ADY7hQDnfP690R+vo7jGOU5A7dgxDvO8ao7OLpFRJRWVP1H14ALZxxWtAjSSp3thwMOlzM6nf0uONyeiJ6qZ9CFz/1iO65d8xZ6Bl0RN9Xp9uLf1+7ElY+8OaxV33wZHZ1Ap+c0DO5BuGDCKaEYJzsGwD6PYiWiQKe4uBgmkykge9Pc3ByQ5QGAnp4e7Nq1C3fffTfMZjPMZjNWrVqFDz/8EGazGW+88Ybu89hsNuTm5mq+iJKDNqMz6PJgS8+5AIC89g8BZ19kpzsmrli4VzgX/2pRdWQc3SIiSjO+/kP8cA+cMlSIt7UeCjg6L8MCqzTvs7XXGdEz/azuIA409eBISx+eeDMwiBrKc+8cw4cnOnGyYwAP/21/RI91e7zo7BeDK91AR9qOodlYCg9MONHezz6PYiaiQMdqtaK6uhp1dXWa2+vq6jBr1qyA43Nzc7F3717s2bNH+Vq8eDEmTpyIPXv24LLLLju71hPFm19G51BzLw57y3ASJTB4nMDhNyM73yd/BwBs9VyMA009qjvk0a2zay4RESUJVf9xor0fAHDGPk68qXlfwOEGg2HY83Te/KRZ+fdr+/SnFoTy2r4zyr+3ftIcUQlb54Avg1SQaQk84Iz4WpszxEHCEx39YEaHYiXi0rXly5dj/fr12LBhA/bv349ly5ahoaEBixcvBiCWnS1YsEA8udGIKVOmaL5KSkpgt9sxZcoUZGVFthQvUeJpMzpicGLAR5lSoH/gb+GfytkHHBazmq97L0Frr0NZqYajW0RE6SYwo9OVK5Y+48zHuo8ollde6w6/fKy114Gjrb7qgiMtfejqD798ze3xYu9J394+3YNuHGrpDfvxctlafqYFZr2VSKXX2pMnvvaTHQOcl0oxE3GgM3/+fNTW1mLVqlWYNm0atm3bhi1btqCqqgoA0NjYOOSeOkQpyy+j80mTOIG0afT14s37Xwq/fG3/3wBXP5BfhZ78C6TzyVkdjm4REaUVdUanQ8zouIul1TaDBDqjpOWZIyld293QCQA4vzQbYwozAQAfnuwM+/GfnOnBgMuDHJsZl40TV4arP94R9uPbpLYWZuovLY0z/wIAeEvEfk/MbrGKgWJjWIsRLFmyBMeOHYPD4UB9fT2uvPJK5b6NGzdi69atQR+7cuVK7NmzZzhPS5QE9DI6QMZ5s4GCcYCzF/hoc3inqt8ofp/2n5hYnqs5HzM6RETpJjCjY6mYCsAAdJ8Ees4EPEKe49LeF37p2qFmMftyQXkuLhqdBwA40BT+Nh3ygNsFFbmYco74+MPNkWd0dOfnuJ1Aszjnx36OuHfciY4B9nkUM8MKdIhGLL+MjhyYTCzPBS67U7xr+8/Ei3koJ3cBDTsBoxm45FZMKssBwIwOEVHaUvUfJ6WMTmlJCSBlNtDwTsBDirLF0rW2vvAzOseksrWxxVkYWyRmdBqkOUHhON4mHjuuOAtji8UpBsfawl9oJ+TS0k17AY8DyChEUaVcusY5OhQ7DHSIIuIbkWvrdSgTRCeW5gDVtwPZpUBXA7DnNyFOIQCvrxT/PXU+kFuBiVKgc+AMMzpEROlJvJ4LBuBEu5jRqSzMBKpminc3/DPgEUVSsNAWQemaHJSMLcpCVaEYqMjBSzjkoGhMUaYSKB2L4PHtUluLsnUCnVO7xO+jL8VoqW09g264la6OfR5FFwMdokgo12CDkn0ZU5iJLJsZsGQAVywT7657EGg/on+OD34tLittsgGfvR8AlIzOwTM90uo2HN0iIkor0uXcKxgw4BK3E6jItwNj5EBnZ8BDfKVrwwh0irPEQApQVnkLx3Hp8WMKMzG2SAxGGtr64Qlz5TW5zE43o3Nsh/h99KXIsJpQLGWsnB7p3OzzKMoY6BBFRM7o+MrW5CAFAHDpN4HKywFHN7B5AdDfrn344TeALd8X/33N/wD5YwCII29WsxH9To84SZUZHaKIrV27FuPGjYPdbkd1dTW2b98e9NgXXngBc+fOxahRo5Cbm4uZM2fi1VdfjWNraeQRr+duKWAozbXBZjb5Ap2mvcCgdi5NpKVrgy4PznSLgUZVYSaqpIzMyY4BuD3esM7RIGWbqgqzUJGfAYvJAKfHi6YwV36T21rgvxiBxwUc2Sr++7xrAACjCzIAAE4lpcM+j6KLgQ5RJFQ11vLkTk2gYzIDX30GyCwGzuwFnpwDvPs08OlrwJb7gN98FfA4gck3AjPvVh5mNhkxflQ2AHmeDjM6RJHYvHkzli5digceeAC7d+/GnDlzMG/evKCrgG7btg1z587Fli1bUF9fj6uvvho33ngjdu/eHeeW04ghyIGO+GNlgRiEIO8ccdBL8AIn3tU8xFe6Ft5iBE1dYjCSaTUhP9OCslw7zEYD3F4BLWGcY9DlQat03OiCDJiMBpTl2aVzD4TVho7+IKVrJ3eJg4AZhUDFNABQMk4OZnQoRhjoEEXEN0dHLl2bWJarPSRvNHD7y+IqbN0ngb9/H/jtfwDvPQUIHuDim4GvbACM2v/9NAsSMKNDFJE1a9Zg4cKFWLRoESZPnoza2lpUVlZi3bp1usfX1tbivvvuw6WXXooJEybgRz/6ESZMmICXXnopzi2nkUMb6MjZDADAuVeL3w+8rHmEHCy09zkhhBEENEqBTlmeHQaDAUajQSkPa+4eOtCRj7GZjciXNvssz83QnHsoyvLSWTbtHYdeF7+fdw1gNAEAKpWMjpxtYp9H0cVAhygSUkfjEYBPz4jLbU4qzwk8rmQS8O23get/BIy7Eii7CLjwS8DXXwC+9CRgDqxd1i5IwIwOUbicTifq6+tRU1Ojub2mpgY7dwbOe9Dj9XrR09ODwsLCoMc4HA50d3drvojCJmhL1+RsBgDggi+K3w/8DfB6lJvleS5ur4DuAfeQT9HULWZdyqUsDACU5IoBh7x4TujHi8FMaa4YKAFQZXTCC3Tk+URF/nN0DtWJ38dfq9w0uoAZHYotc6IbQJRaxItwU7cDAy4PbGajMlkzgDULmHmX+BWGieqMTiEzOkTham1thcfjQWlpqeb20tJSNDU1hXWOxx57DH19fbjpppuCHrN69Wo89NBDZ9VWGsnE67lLDnQKVIHOuCsBez7Q1yIuMz32CgCAzWxCts2MXocbbX0O5ElZlmCUjE6uL1s0Ss7ohBHonOmWH+8LlOSgKZyMjiAISulagTrQaT0INH4IGEzA+OuUmysLxXY6mNGhGGFGhygS0miTvNTmhNJsmIyGUI8I2ySpBO5oax/cAke3iCJlMGj/XxQEIeA2PZs2bcLKlSuxefNmlJSUBD1uxYoV6OrqUr5OnDhx1m2mEUS6nksLrmF0oap0zWQBJt0g/vvjP2sepi5fG4qcddHL6DT3DB2oyIFOqerxkWR0ehxuuKTsjCajs+d58fv464Bs3/9jcrA36GafR7HBQIcoIuJF+GirGOhM8p+fcxZKc23Iy7DA4xXQ2S+XKPCiTzSU4uJimEymgOxNc3NzQJbH3+bNm7Fw4UL8/ve/x3XXXRfyWJvNhtzcXM0XUfi0GZ0x6tI1AJjyFfH7R78HHD3KzXL5WmsYe+nIwYg6UBmVI/47rNI1JSPkm1/jy+gMvRiBvIdOptUEu0WchwOvB/jwd+K/p92iOb483w6DQSwHF7HPo+hioEMUCUFMrx9pFS/4mhXXzpLBYFDK19rlQEcIbzlQopHMarWiuroadXV1mtvr6uowa9asoI/btGkTbr/9dvz2t7/FDTfcEOtm0kgnXc+9ggFmowHleRna+8+9GiiaIK5MJgcG8GVGwsnoyCurleT4AhX532GVrknHlOaqAyWb5tyhyEtLa/bQ+eTvQE8jkFEATJynOd5mNqEs1w5BmZfKPo+ii4EOUSSktPrRtuhndMTzSYGO3KExjU8UluXLl2P9+vXYsGED9u/fj2XLlqGhoQGLFy8GIJadLViwQDl+06ZNWLBgAR577DFcfvnlaGpqQlNTE7q6uhL1EijdSddzAQZU5GcElj0bjcBnviX++90nlUUJiqTVy+SNOEORl4YuVi3tPCqCQKdNebwvUJL/3dozdKDV4R/oCAKw/VHx39W3A2ZbwGMqCzJVgQ77PIouBjpEEREvwqek9P7EKGZ01Odr63NF9bxE6W7+/Pmora3FqlWrMG3aNGzbtg1btmxBVVUVAKCxsVGzp85TTz0Ft9uNu+66C+Xl5crXd77znUS9BEp7gvLfysIM/UOm3QzY84C2Q0pWpzA7/NI1eWlndaAiZ3Rawwp0AvfAkc814PKgzxF65bd2/0Dn8BvA6d2AOUOzd5za6IIMCAIX4KHY4KprRJGQRpu8gjhiNioncHTqbEzyD3Q4ukUUtiVLlmDJkiW6923cuFHz89atW2PfICI1VUZHs+Kami0HmPNdoO5/gTd/CEz5ctila/1ON/qdYhZIE+jk+uboDLVAR5uyNLTv8Vk2MzIsJgxIm4lm2YJ/dNSUrnnc4usAgBl3AFnFuo8ZXZjpC2/Y51GUMaNDFBFfRzW5PPoTkc8vFQOdXqe8jwIv+kRE6UEV6PgvRKD2mTuB3NFA9yngrZ+GveqaXFpmtxiRaTUpt8tlbE6PF539wasFvF5BKY9Tl74BQHGOnFUKnRWSH1+UZQXeexo48y9xbs6c7wZ9TGVBhq90jSjKGOgQRUI12nRBRfQDnRy7BefkZ3B0i4go3Qi+0rXRBUFK1wDAYgfm/Vj899u1qBr8BMDQQUZrn29+jTprYzObkC/tvxNqQYHOARekBeG0e+DAlyFqGWKeTrtUjTDOcBp442HxxutWAllFQR8zuoAZHYodBjpEEfGNyF0Qg4wOIJav+Ua3eNEnIkoP8vXcELi0tL/JNwJTvgoIXkzZ+R3koyeMjI6UTckOLKlWVl7rDh7oyAsR5GVYYDFpPx4qCxKEkdGxwYnP7V8BuPqAsXOA6QtCPqay0JfR8XLVNYoyBjpEERBUNdYXxiCjA4gLEnAFGiKi9OJ0iyXJQ5auyT73CFAwFtaeE1hr+Tl6+3qVPkiPvFjBKL+yM0C98lrwTT+V+Tk6jw830OnsHcAvLI8jv+dTILMY+Mp6cTW5EMpy7UoGqntg6AUXiCLBQIcoAnInYzUbMa44OybPIQY6yjPG5DmIiCi+5M00YTAoCwyElFkI3Pw7CNZszDLtwy9Mteju6Qt6uN7S0LJR0m1tIVZuU1Zsy9J7fBhzdLwefLOzFtebdsFrsgLz/w/IKQt+vMRsMsJqFucUhbOENlEkGOgQRcDjFdPqY0flBO6BECWTynKVjE6o0TsiIkodLT3iRtMWkzHkymcaJZNhuHkTBgULrjPthnXTl4G+Nt1D5SBELyMjl7O1hggk2vqCP744Z4i9dBy9wB9uw+c8b8AtGNEy93GgKvhmvf5sFinQCWNTUqJIMNAhioAgzdQcPyo22RwAGFecBZNB/F+zd5BpfCKidNAilY1ZzKYhjvQz7kqsyPgfdAsZyGh8F1h/DXCqPuCwVp09dGRy8BIqoyM/vlAn2xSydK3lU+BX1wD7X4JTMOEu172wX/zloV+Xis0iLlndHsZeQUSRGFags3btWowbNw52ux3V1dXYvn170GNfeOEFzJ07F6NGjUJubi5mzpyJV199ddgNJkokeaLk+JLobhSqZjUbldG3No5uERGlhTPSRtPWSAMdAMdzL8WXnQ+hP2s00HEMWH8d8PpKwOkrZWsNUboml8qF6lPaeoMvZqAb6LgdwFuPAE/NAVo/gSerDDc7/wdvGC5Drj2ybRozrGbp/MHnEBENR8SBzubNm7F06VI88MAD2L17N+bMmYN58+ZpdpxW27ZtG+bOnYstW7agvr4eV199NW688Ubs3r37rBtPFG9yKdn40tgFOgBQkidu8MZ6ZSKi9HCmWyxdsw0j0CnMsuGQMBpbLt8EXPQfgOAFdvwM+MV04P31gGswdOmaNO8m1Mpt8n3+e+iob2vtdQIeF7D7N8ATlwFvPgy4B4Fzr8an//4y6oWJKMi0hl+aJ1ECnRCLJRANR8SBzpo1a7Bw4UIsWrQIkydPRm1tLSorK7Fu3Trd42tra3Hffffh0ksvxYQJE/CjH/0IEyZMwEsvvXTWjSeKp9Zeh7IK2rmjYhvolOaKeywwo0NElB7OdEsZHUvkgY6ckWl0Zogrmc1/HsivAnrPAC9/F1gzGf/ZswETDQ0YpVN6VqQOVIKQy9qKdBYjKM6xodJwBt/0/A5C7UXAi3cBHUeBrFHAl9cDt/4ZLUIeAP3St6Fk2sRAp6V3kHNTKaoiyi06nU7U19fj/vvv19xeU1ODnTt3hnUOr9eLnp4eFBYWBj3G4XDA4fB9wOvu7o6kmUQxsfdkF2ZKq6Bl2SJLy0eqVMrodPQ54PUKMMZo4QMiIoo9p9srZissvon3kVDm2MgZmcmfBybUAPUbgZ2/ALpO4A68iDtsL8Kz+VfApHniYgCVlwFZxUrpWVufA4Ig6GZcWv0XI+hvB059ABzfgZxPXsF2237x9h6IAc6se4FLFwLWLAC+jNBwAp0MaY6Ow+VBa69TWQ6b6GxF9GmttbUVHo8HpaWlmttLS0vR1NQU1jkee+wx9PX14aabbgp6zOrVq/HQQw9F0jSimNtzohO+NWRiG3gUZomBjtvjxZHW3pjOCSIiotg60dGvZCospuGUronBg6b0zGwFLvsWMOMOdOz5K97/y+O4yvgRbB2HgXceF78AIKccFYXn4UdmK1qEfDjfOQ5bZh5gMIpfghcY7MJXenYh39yKi954EvjrMaDTNyXBAMANI/7pmYzR1y7G2CvmA2ZtMNJ2FoGOSdprxwDgaGsfAx2KmmENS/uPBAQbHfC3adMmrFy5Ei+++CJKSkqCHrdixQosX75c+bm7uxuVlZXDaSpR1Hx4shPKvjYR1h9HSl662gDgo5NdDHSIiFLYkZY+GKT+I9L5K4A6o6NTzmwy41TZtfiWy4ax2V5s/aIDOLYdaPgn0HIA6GmEqacRt8if+F57Qfc57gLET4UnVTcWngeMngGMn4sFW7Ox87QX60tmYKw5MBDpkDccHUagI/epBgg40tKLz4wLXvVDFImIAp3i4mKYTKaA7E1zc3NAlsff5s2bsXDhQvzhD3/AddddF/JYm80Gm43RPCUPQRDw4YlOpaOKdUZHPr8BAj462YUvXzI6xs9HRESxcrS196z6D3neTLDloeWFCDJy8oGL5gAXfVW8Y6ATaDsEtH6KDS+9CaujDZ8/z4J8s0vM5AhewGDAoCkHL+zvRRvycNeX58JYOA4omSxuWiqxf/A+cLpZP9iCL6NTMJxAR9XnHW0NvikqUaQiCnSsViuqq6tRV1eHL33pS8rtdXV1+OIXvxj0cZs2bcIdd9yBTZs24YYbbhh+a4kS5ET7ADr6XTDI8XeMMzq+0S3go5OdsX0uIiKKKTGjIxlG/yGXg7UFWTXNt4eOX5CRkS9mZEbPwIs7xuDDk10ou2wGrrtAOzh95HQ3/nvvdhRn23DPJfqD0XKmJtiCBvIqoWeX0QEOtzDQoeiJuHRt+fLluPXWWzFjxgzMnDkTTz/9NBoaGrB48WIAYtnZqVOn8NxzzwEQg5wFCxbg5z//OS6//HIlG5SRkYG8vLwovhSi2NkjBRtGQ/wzOh+f7obL44XFxP19iYhS0ZGWPhScRUZHXkygo8+pO11AXqFzlM4eODJfsBSYkZFv01taWmlDTohNQwF09Lmk5xl+RY5cukYULRF/cpo/fz5qa2uxatUqTJs2Ddu2bcOWLVtQVVUFAGhsbNTsqfPUU0/B7XbjrrvuQnl5ufL1ne98J3qvgijG6o+1A8BZjchFRDq/zWyAw+3FvtNceZCIKBUJgoD9Td1n1X8UZFkAAG6vgO4Bd8D9ofbQkSkbUetkheSSuFALCQyV0ZGDpeEsRqCeo3OsrQ+DLk/k5yDSMazFCJYsWYIlS5bo3rdx40bNz1u3bh3OUxAllXePyoFOfDM6xVlWYBB4/1g7Lq7Mj/FzEhFRtJ3uGkTPoBu+fUIj7z9sZhNybGb0ONxo7XMgL9Oiud9XuhY8m6IsaKATqMjBT1GIx8srobX26Gd0zmZ5afk9ybaa4B0APj3Tg6mj84dxHiIt1sIQDaGr34VPzvQAUAU6ccroFOeIHYYcaBERUWrZL2Xky/OkIGKY/YccqLTrZGR8GZ0QgY5cuqZTeibfFmp+jbIggk7pm8vjRUe/WLo2rKWhpfekTHqP9jeyioGig4EO0RB2HW+HIADjirNUt8YxowNg17F2eL3cLZqIKNUcaBI/tI8usEu3DK//UObY6GRkmrvF4KMkRJDhC1SCl66FnqMTvHRNfrzJaEB+hiXg/qFJgU6uHOj0DOMcRIEY6BAN4T1pfs6lVfm+G+OU0cnPMMNuMaKj34XDnKBJRJRy5A/t5+RJgc4w+4/CEBmVFikjU5I7vNK18DJC0oII/U64PV7t8/f4FjMwGofx+qT3pDRXfI+Y0aFoYaBDNIR3j0iBzth81a3xyeiYDAIuGVMAAPjnkbYYPycREUXbfimjU5FvH+LI0ORsS7tfoOJ0e5VytpKc4M9RnB08UGruGTojVJhlhcEACALQ3q9tQ0vvIIBhlq0BUDI6OWI26EBTDwSBVQx09hjoEIXQ0edU9rG5YnyR746YZ3Sk/zUFAbPHFwMAth1sje1zEhFRVA04PTgmbYB5Tr48R2d4H72C7aUjZ2PMQ5SNqUvf/IMIOSMTKlAxGQ0ozNTPCimPD5ERCkl6T0ZlW2EyGtA14EJj1+DwzkWkwkCHKIQdh1rhFYDzS7NRnqsaKYtT6Rog4KrzRwEAdh5qhdPtDf4YIiJKKntPdcEriAFErk1a6HbYixHoz7FRBymhysbkQMd/iWqvV1CCpVAZIcCXFfLfSyecQCkk6T0xGw2YUJINAPjwROfwzkWkwkCHKIS3Pm0BADHY0IyAxad0DYKAC8pzUZRlRZ/Tg/rjHTF+XiIiihb5ml09pkDVawwz0MmSV13TBhnhlJ0BgN0iLlENaMvXOvqdcHsFGAyh9+EBgs/zOetAR9XnVVeJ5drs7ygaGOgQBSEIArYpgU4JAFWgE8eMjtFowJVSVmfbwZbYPi8REUVN/XFxjueMsQXAWW5PEGzVteae8OfHKIGKKiskB0qFmVZYTKE/FsoZnRa/vXTkxRCGX7rm6/PE9wrYxUCHooCBDlEQe091obnHgQyLSbzwJiijA0ApX6vbdybGz0tERNEgCIKSlbikSt2HnN0+OsFL14Ze7KBQZy+dSLIxctZIDq6G0wZ9qozOmEIAwMenuzDo8gzzfEQiBjpEQby8txEAcM3kEtgtJiQqowMAV08qgdVkxKHmXnx6hvsLEBEluyOtfejod8FqNmJKRR7ONqOjLO/c59TsqxZu6Rrgm+fT0huY0Qkn0CmTlsg+0x2bOTqAgMrCDIzKscHlEfDRya7hnY9IwkCHSIcgCHj5IzHQueGicvlG1RGxzugoDQEA5GVYcOX54uprf5PaRUREyav+mJjNuXh0Hqxm41lndAqyxBXV3F4B3YMu5XZ5s9BwgoxSaZ+dlm5fRiaijI60KE9TtzajI28iGo05OgaDAdXStgrvS/vYEQ0XAx0iHR+d7MLJjgFkWEy4emKJdGviMjoAcMNUMeB6+aPT3F+AiCjJbf20GQAw81x5a4Kzy+jYzCbk2OXFBHwZGWWz0HACnZzAQEUuQxtqxTXx8VLpmurx/U43eh3iKm7RyOgAwMzzxPdMXhCIaLgY6BDp+GP9SQDAtZNLkGE1iTcmcI4OAFw3uRRWsxGHW/qwm8tuEhElLafbi22finufXTu5VLzxLDM6gHrlNVWgIwUdJblhBCo6pWeRZHTUpWvygFtrj9iWDIsJWXJ/GTFtn3fNJHGAsf54Bzr9NicligQDHSI/vQ43XvhADHRu/swY1T2JyOj45Ngt+LyU1fnNP4/H9vmJiGjY3j3ahl6HG6NybLjonDzp1rPL6ACBiwkIguBb8Sys0jU5UFFndMLPCMlZnwGXB92DYhanpde36pthuK9NeZj4HlUWZmJiaQ48XgFbP2FWh4aPgQ6Rnz/vPoU+pwfnjsrCrPOKfHckOKMDAAtmjgUgztPp6OMoFxFRMvrHfrFs7ZqJJb5NPKOQ0ZEDlaYuMbho7XXC5RH3wAlnaecynTk2rRFkdDKsJuRninOFGrsGAACnOweltg13fg6g1+ddO1nM6ry+n6uN0vAx0CFScXu8eHbHUQDArZdX+Y1OJXaODiBOar3onDw43V489w6zOkREycbl8Sqrdl53QanqnrPP6IwuyAAAnOwYkL73AxADGKt56I90cjDS2e9Slm6OJKOjbsOJdrkN4vfKgsywHq9Lp8+T37s3DjRrFl8gigQDHSKVF3afwpHWPhRkWvDV6tHaO5Mgo2MwGHDnVecCANZvP8KsDhFRknnt4zNo6XGgONum7IEGICoZndFSMHFCCnBORBhk5GVYkCnNozndOYCufpeykEBpGHN81M91UmlDv9S2jLAer0/u83y3TK/Mx/iSbPQ7PfjL7lNncW4ayRjoEEkGnB78/PWDAIAlnx2PHLvF74jEZ3QA4HNTyjG5PBc9DjfWbj0U23YQEVFEnn9XzLZ/7dJKvyxL7DI64QYZBoMBYwrFQKWhvV8JUoqzbciymSNqg39GZ3SUMzoGgwH/eZk4T/b5fzZwtVEaFgY6RJJHXv0EpzoHUJ5nx60zqwIPSIKMDgAYjQbcd/1EAMCGt4/hQ67ARkSUFP51qgs7D7fBaABuvmyM9s4ofFCvLJSzKWJwIQcbowvDDzIqVYHO8TYx0BlTGH42Rn68HCQpwVYE5wik3+d9+ZLRyLCY8MmZHrz5SfNZnJ9GKgY6RAB2HGzFszvFuTmrv3wR7JYhlshMYEYHAK6eVIIbL66Axytg+e/3oIf1y0RECSUIAn60ZT8A4MaLK3BOvv8H/+hldLoGXGjvc+J4Wx8AoDKCsjElo9PWj4Z2MUipKsoK+/Fy6drxtj64PF6cbI/NHB1ALLVbMEsceHz4b/vhdHuH/xw0IjHQoRHv49NdWPybegiCWGrwWWWDUD9JktGRrfrChSjJseFwSx8W/6YeDrcnxm0iIqJgNr13AjsPt8FmNuK7cycGHhCFOTqZVrMSqBxo7Mb+xm4AwKSy3LDPUVUkBSrt/WholwKlCDJCE8tyAABHWvrwSVMPnB4vsm1mncAuEsH7vLuvHo/ibBuOtPbhl28cPIvnoJFoWIHO2rVrMW7cONjtdlRXV2P79u0hj3/rrbdQXV0Nu92Oc889F08++eSwGksUbVs/acbXnv4neh1uXDauECu/cGGIo5Njjo6sIMuKZ267FFlWE94+1Iavr38Xrb2OoMcTpTv2TZQor+87g5V//RgA8N2a8zGmKETgcJb9xyQp0HjrYAs6+l0wGoAJpdlhP378KPHYfae7se+0GCidNyr8jE55nh25djPcXgEvfXgagBj8KMtoD0eIPi/HbsH/+/xkAMAv3zik7HNHFI6IA53Nmzdj6dKleOCBB7B7927MmTMH8+bNQ0NDg+7xR48exec+9znMmTMHu3fvxn//93/j3nvvxZ/+9KezbjzRcB1r7cN3f/8hbn/2ffQMulFdVYCnF8wIXbImxDHQCSOjAwAXjc7DrxbMQI7NjPePdeC6NW/h1zuPod/pjnH7iJIL+yZKBJfHi3VbD2Pxb+rh9Hhxw9RyLLriXP2Do5DRAYBJ5WL25k/14kpk547KHrrcWuWi0XkwGIBTnQP48GQXAGB6ZUHYjzcYDJgst+EDsQ1y8DV8ofu8L047B3deKb6vy3//IX7yygH2cxSW8JbYUFmzZg0WLlyIRYsWAQBqa2vx6quvYt26dVi9enXA8U8++STGjBmD2tpaAMDkyZOxa9cuPProo/jKV75ydq0nGoLb40XngAsdfU4cae3DvtPd2Hm4FbuOdyjX069fPgb/7/MXwGYeqqOI44ovYWR0ZLPGF+PPd83G3b/9AAeaevDgXz/Go69+gtnjizHzvCJMKM3GmMJMFGRakWk1DX/naqIkxr6J4mHA6UFrrwP7G7tRf7wDL+45rWy++e/TKvDof1wcIrNx9nN0AGD6mHwAUDL40yvzI3p8jt2C8aOycbC5FwBQmGVFZYQLCUwfU4B3j7b72jAm/EBJVxh93n/92yQ43F5s3HkM67Yexh92ncDnp1bg8nOLMLEsB+V59ogCPhoZIgp0nE4n6uvrcf/992tur6mpwc6dO3Uf884776CmpkZz2/XXX49nnnkGLpcLFov/Er6Aw+GAw+Erwenu7o6kmRoNn+6B53cLhv14WVQ/4g5j5ZV4LqoY1nPFsEGBpx7mkwmAR/XQKulrHgBYgCybCcXZNmScNgFPh3E+jzzhPx6BgvQcDe8Ca2cOefR4AH+3COgsFoM6p0cADkL8AtArfRkAGI2AAQalXzEAgMEQl1dFiWNb8AdUjNWZN5AGUrFveu/Pv8Sovb8a9uOBKFyGk7QvGvI5YtAI/VNqbxUEwCvdNEb6+hIAs92AUTk25LZbYHgqxJP0t0n/OLur7RXji1GQaUFHv9gn3XhxRcTnmD2+WAl0Zp5XFPEA2I0Xl+PJtw4DACwmA2ouLB3iEUORnn/XBuDAy7pHGAGsBLC8xIWWHgdcTgHYBWAX4ABwDGK8ZDIE9m+qZ6Ak0mMtxtT734jpc0QU6LS2tsLj8aC0VPsHXVpaiqamJt3HNDU16R7vdrvR2tqK8vLygMesXr0aDz30UCRNC8rlGMR5Xu4gPyIZEPrK5gLQMYzzFugsPR1tBWPF764+oHlfWA8xACiQvsIqShWC/JvS0gnXYKKbEDOp2Dd5elsxjn1TagnVp/RIX+E4yz7EYjJi0Zxz8dhrn+Ci0fmYdV5RxOe4+5rx+NtHpzHg9CjbFUTigvJcfHbiKGz9pAULZo5FbsC+cxGS+7z+NlVAqC9X+grZz7F/SwmNg/0xf46IS9cABET+giCEHA3QO17vdtmKFSuwfPly5efu7m5UVlYOp6korZqIj699TqdRui3V/qRzjN7DwhkJ0X/c8Nqg+yi/43SfT/+RUXk+8UxhvA/hPC7s932I5wKQZTMj22aG6WwmSformxq9cwUz5jJgyT+B3jNROZ0gAA63BwMuD/ocHri9Xni9AjyC+P+jVwA8XgFxTtWl0ulT3nkVQeYNpJFU6pvGXnkLPh57iV+DAloY8LihrvVD9UfhXUsj6xeG1/+c3XOIZxjitQa0K3RDh3pvzEYDcjMssJtNw68+M9uB0ZcO88E+d109HndeeS5MRsOwypGLs234+3euhMcroCzPHvHjDQYDNn7jM3B5vLCYorCA72WLgcrPAM7eYT3c6wUG3B70O9zod3rg8QrwQoDXC3gFAV5BgOBlLxGJeLxbZmsGAoeUovwckRxcXFwMk8kUMELW3NwcMDImKysr0z3ebDajqEh/FMJms8Fms0XStKCycwtw4ZwvRuVcRHFVMln8igIDALv0dZaV1ERJJxX7pvKqiSivSs9SQooP81kGGKNyzv5vOSpBDiDWVI+eMfyHA8iSvojUIvoLtVqtqK6uRl1dneb2uro6zJo1S/cxM2fODDj+tddew4wZM3RroImIiCLBvomIiPREHIovX74c69evx4YNG7B//34sW7YMDQ0NWLx4MQAxtb9ggW/y/+LFi3H8+HEsX74c+/fvx4YNG/DMM8/ge9/7XvReBRERjWjsm4iIyF/Ec3Tmz5+PtrY2rFq1Co2NjZgyZQq2bNmCqipxcl1jY6Nm34Jx48Zhy5YtWLZsGZ544glUVFTgF7/4BZfvJCKiqGHfRERE/gyCMIz1JeOsu7sbeXl56OrqQm5ubqKbQ0Q0YvD6GxzfGyKixAj3+jusVdfiTY7FzmbPAiIiipx83U2BMbG4Y99ERJQY4fZNKRHo9PSIi9MPdxlPIiI6Oz09PcjLy0t0M5IK+yYiosQaqm9KidI1r9eL06dPIycnZ1jrxceTvK/CiRMnRnQpA98HH74XPnwvfFLlvRAEAT09PaioqIDRGKWlZNNEqvRNqfK3Fg98L3z4XvjwvfBJlfci3L4pJTI6RqMRo0ePTnQzIpKbm5vUfyDxwvfBh++FD98Ln1R4L5jJ0ZdqfVMq/K3FC98LH74XPnwvfFLhvQinb+LwHBERERERpR0GOkRERERElHYY6ESZzWbDgw8+CJvNluimJBTfBx++Fz58L3z4XlC88G/Nh++FD98LH74XPun2XqTEYgRERERERESRYEaHiIiIiIjSDgMdIiIiIiJKOwx0iIiIiIgo7TDQISIiIiKitMNAh4iIiIiI0g4DnSj54Q9/iFmzZiEzMxP5+fm6xzQ0NODGG29EVlYWiouLce+998LpdMa3oQkyduxYGAwGzdf999+f6GbFxdq1azFu3DjY7XZUV1dj+/btiW5S3K1cuTLg919WVpboZsXFtm3bcOONN6KiogIGgwF/+ctfNPcLgoCVK1eioqICGRkZ+OxnP4uPP/44MY2ltMO+KTj2SyO7XwJGbt80kvolBjpR4nQ68R//8R/49re/rXu/x+PBDTfcgL6+PuzYsQO/+93v8Kc//Qnf/e5349zSxFm1ahUaGxuVr//5n/9JdJNibvPmzVi6dCkeeOAB7N69G3PmzMG8efPQ0NCQ6KbF3YUXXqj5/e/duzfRTYqLvr4+XHzxxXj88cd17//pT3+KNWvW4PHHH8f777+PsrIyzJ07Fz09PXFuKaUj9k2hsV8a2f0SMDL7phHVLwkUVc8++6yQl5cXcPuWLVsEo9EonDp1Srlt06ZNgs1mE7q6uuLYwsSoqqoSfvaznyW6GXH3mc98Rli8eLHmtkmTJgn3339/glqUGA8++KBw8cUXJ7oZCQdA+POf/6z87PV6hbKyMuHHP/6xctvg4KCQl5cnPPnkkwloIaUr9k2B2C/5jMR+SRDYNwlC+vdLzOjEyTvvvIMpU6agoqJCue3666+Hw+FAfX19AlsWPz/5yU9QVFSEadOm4Yc//GHal0Y4nU7U19ejpqZGc3tNTQ127tyZoFYlzsGDB1FRUYFx48bha1/7Go4cOZLoJiXc0aNH0dTUpPkbsdlsuOqqq0bk3wjF30jvm9gviUZqvwSwb/KXbv2SOdENGCmamppQWlqqua2goABWqxVNTU0JalX8fOc738Ell1yCgoICvPfee1ixYgWOHj2K9evXJ7ppMdPa2gqPxxPwey8tLR0Rv3O1yy67DM899xzOP/98nDlzBg8//DBmzZqFjz/+GEVFRYluXsLIfwd6fyPHjx9PRJNohBnJfRP7JZ+R2C8B7Jv0pFu/xIxOCHqT1Py/du3aFfb5DAZDwG2CIOjengoieX+WLVuGq666ClOnTsWiRYvw5JNP4plnnkFbW1uCX0Xs+f9+U/l3Plzz5s3DV77yFVx00UW47rrr8PLLLwMAfv3rXye4ZcmBfyMUCfZNwbFfCg+vOSL2TcGly98IMzoh3H333fja174W8pixY8eGda6ysjK8++67mts6OjrgcrkCouZUcTbvz+WXXw4AOHToUNqOmhQXF8NkMgWMkjU3N6fs7zxasrKycNFFF+HgwYOJbkpCyav7NDU1oby8XLmdfyMUCvum4NgvhcZ+KTT2TenXLzHQCaG4uBjFxcVROdfMmTPxwx/+EI2NjcofzmuvvQabzYbq6uqoPEe8nc37s3v3bgDQ/E+UbqxWK6qrq1FXV4cvfelLyu11dXX44he/mMCWJZ7D4cD+/fsxZ86cRDclocaNG4eysjLU1dVh+vTpAMQa+rfeegs/+clPEtw6Slbsm4JjvxQa+6XQ2DelX7/EQCdKGhoa0N7ejoaGBng8HuzZswcAMH78eGRnZ6OmpgYXXHABbr31VjzyyCNob2/H9773PXzzm99Ebm5uYhsfY++88w7++c9/4uqrr0ZeXh7ef/99LFu2DF/4whcwZsyYRDcvppYvX45bb70VM2bMwMyZM/H000+joaEBixcvTnTT4up73/sebrzxRowZMwbNzc14+OGH0d3djdtuuy3RTYu53t5eHDp0SPn56NGj2LNnDwoLCzFmzBgsXboUP/rRjzBhwgRMmDABP/rRj5CZmYlbbrklga2mdMG+SR/7JfZLwMjtm0ZUv5TIJd/SyW233SYACPh68803lWOOHz8u3HDDDUJGRoZQWFgo3H333cLg4GDiGh0n9fX1wmWXXSbk5eUJdrtdmDhxovDggw8KfX19iW5aXDzxxBNCVVWVYLVahUsuuUR46623Et2kuJs/f75QXl4uWCwWoaKiQvjyl78sfPzxx4luVly8+eabuteG2267TRAEcSnPBx98UCgrKxNsNptw5ZVXCnv37k1soyltsG/Sx36J/ZIgjNy+aST1SwZBEIT4hlZERERERESxxVXXiIiIiIgo7TDQISIiIiKitMNAh4iIiIiI0g4DHSIiIiIiSjsMdIiIiIiIKO0w0CEiIiIiorTDQIeIiIiIiNIOAx0iIiIiIko7DHSIiIiIiCjtMNAhIiIiIqK0w0CHiIiIiIjSDgMdIiIiIiJKOwx0iIiIiIgo7ZgT3YBweL1enD59Gjk5OTAYDIluDhHRiCEIAnp6elBRUQGjkWNjauybiIgSI9y+KSUCndOnT6OysjLRzSAiGrFOnDiB0aNHJ7oZSYV9ExFRYg3VN6VEoJOTkwNAfDG5ubkJbg0R0cjR3d2NyspK5TpMPuybiIgSI9y+KSUCHbkkIDc3l50JEVECsDQrEPsmIqLEGqpvYsE1ERERERGlHQY6RERERESUdhjoEBERERFR2kmJOTo0QggC4HYAFnuiW0Lhcg0AloxEt0JDEAS43W54PJ5ENyUlmEwmmM1mzsGh9JKE1yZKUWH8LXk8Hrhcrjg1aGSIVt/EQIeSx2++DBx+A/j+YSCrONGtoaG8/wzw8nLgK88AF3010a0BADidTjQ2NqK/vz/RTUkpmZmZKC8vh9VqTXRTiM7ent8Cf/k28IXHgUtuTXRrKJV98gqwaT5w3UPAFUt1D+nt7cXJkychCEJ82zYCRKNvMggp8Jvp7u5GXl4eurq6uLJNOluZJ36/4THg0kWJbQsNTf59AcDKrsS1Q+L1enHw4EGYTCaMGjUKVquVWYohCIIAp9OJlpYWeDweTJgwIWDjNV5/g+N7k6SS7NpEKeyn5wL9beK/df6WPB4PDh48iMzMTIwaNYp9TpREs28aVkZn7dq1eOSRR9DY2IgLL7wQtbW1mDNnzpCPe/vtt3HVVVdhypQp2LNnz3CemkYCL0uOKHJOpxNerxeVlZXIzMxMdHNSRkZGBiwWC44fPw6n0wm7naWjREQAhvw84nK5IAgCRo0ahYwMlkpGU7T6pogXI9i8eTOWLl2KBx54ALt378acOXMwb948NDQ0hHxcV1cXFixYgGuvvXZYDaURhIFOikmuESz/UR8aGt8zIiIdYX4eYSYnNqLRN0V8hjVr1mDhwoVYtGgRJk+ejNraWlRWVmLdunUhH3fnnXfilltuwcyZM4fdWBohvO5Et4AiYTQlugVERETRJ3DgNdVFFOg4nU7U19ejpqZGc3tNTQ127twZ9HHPPvssDh8+jAcffDCs53E4HOju7tZ80QjCC0tqMXJNEyIiSkOsMEl5EQU6ra2t8Hg8KC0t1dxeWlqKpqYm3cccPHgQ999/P55//nmYzeF9IFq9ejXy8vKUr8rKykiaSamOGZ3UYmBGh4iI0hA/j6S8YRW/+dciCoKgW5/o8Xhwyy234KGHHsL5558f9vlXrFiBrq4u5evEiRPDaSalKo6gpBZmdJLK+++/j2uvvRb5+fkoKChATU0NF38hIhoOVpiE5Tvf+Q6qq6ths9kwbdq0gPuPHTsGg8EQ8PXKK6/EvG0RBTrFxcUwmUwB2Zvm5uaALA8A9PT0YNeuXbj77rthNpthNpuxatUqfPjhhzCbzXjjjTd0n8dmsyE3N1fzRSMIA53Uwjk6SaOnpwfXX389xowZg3fffRc7duxAbm4urr/+em5mRyOHgYtrEMWTIAi44447MH/+/JDHvf7662hsbFS+rrnmmpi3LaKhWKvViurqatTV1eFLX/qScntdXR2++MUvBhyfm5uLvXv3am5bu3Yt3njjDfzxj3/EuHHjhtlsSmtMFaeWJA10BEHAgCsxQXOGxRT2Kjyf/exnMXXqVNjtdqxfvx5WqxWLFy/GypUrI37eTz75BB0dHVi1apVS8vvggw9i6tSpaGhowHnnnRfxOYlSjtEMeJyJbgWNQCOx3wGAX/ziFwCAlpYWfPTRR0GPKyoqQllZ2bCeY7girjlZvnw5br31VsyYMQMzZ87E008/jYaGBixevBiAWHZ26tQpPPfcczAajZgyZYrm8SUlJbDb7QG3EymYKk4tSVq6NuDy4IL/fTUhz71v1fXItIb/vvz617/G8uXL8e677+Kdd97B7bffjtmzZ2Pu3LmYN28etm/fHvLxvb29AICJEyeiuLgYzzzzDP77v/8bHo8HzzzzDC688EJUVVWd1WsiShmcN0gJMhL7nUh84QtfwODgICZMmIBly5bhq1/9asTniFTEn1Dmz5+PtrY2rFq1Co2NjZgyZQq2bNmidKKNjY1D7qlDFBJL11ILP1SctalTpyqrUk6YMAGPP/44/vGPf2Du3LlYv349BgYGwjpPTk4Otm7dii9+8Yv4wQ9+AAA4//zz8eqrr4a9GAxRykvSLDNRMolWvxOO7OxsrFmzBrNnz4bRaMRf//pXzJ8/H7/+9a/x9a9/PWrPo2dYPd+SJUuwZMkS3fs2btwY8rErV64cdmqMRgiWrqWWJP1QkWExYd+q6xP23JGYOnWq5ufy8nI0NzcDAM4555ywzzMwMIA77rgDs2fPxqZNm+DxePDoo4/ic5/7HN5//33u3E0jQ5Jekyj9jcR+JxzFxcVYtmyZ8vOMGTPQ0dGBn/70p8kZ6BDFFDM6qSVJS9cMBkNEafxEslgsmp8NBgO8Xi8ARFRC8Nvf/hbHjh3DO++8o+wo/dvf/hYFBQV48cUX8bWvfS0GrSdKMswyU4KMxH5nuC6//HKsX7/+rM4RjtT4bdDIwoxOauHoaUxFUkLQ398Po9GomZAq/yx3YERpj9ckorMS7dI1Pbt370Z5eXlMnwNgoEPJiIsRpJYkzeiki0hKCObOnYvvf//7uOuuu3DPPffA6/Xixz/+McxmM66++uoYtpIoifCaRHRWIi1dO3ToEHp7e9HU1ISBgQFl77YLLrgAVqsVv/71r2GxWDB9+nQYjUa89NJL+MUvfoGf/OQnMWi9Fq8GlHxYupZaWCaSNCZNmoSXXnoJDz30EGbOnAmj0Yjp06fjlVdeicvIGVFS4DWJKK4WLVqEt956S/l5+vTpAICjR49i7NixAICHH34Yx48fh8lkwvnnn48NGzbEfH4OwECHkhFL11ILy0TOytatWwNu+8tf/jLs882dOxdz584dfoOIUp2RG4YShRLtfkfvfGq33XYbbrvttmGf/2zwakDJhxmd1MIyESJKJrwmEZGEgQ4lH2Z0UgszOkSUTFi6RkQSBjqUfLgYQWrh6CkRJRMOvhCRhIEOJR+WrqUWAy8jRJREOPhC0cZ+LmXxN0fJh6VrqSXJPlQIgpDoJqQcvmeUVvihlKJtiHJIXkNjIxrvK68GlHyY0UktSRLoyLs89/f3J7glqUd+z/x3yiZKSSxdo2gL8jdlMom3O53OeLZmxIhG35Qcn1CI1JjRSX7qUZYk+VBhMpmQn5+P5uZmAEBmZiYMBkOCW5XcBEFAf38/mpubkZ+fr3TaRCmNixFQtAX5mzKbzcjMzERLSwssFguMXNo8KqLZNzHQoeQjeBPdAhqK+neURB8qysrKAEAJdig8+fn5yntHlPKSZPCF0kiQvymDwYDy8nIcPXoUx48fj3Oj0l80+iYGOpR8WLqW/Dwu37+TaARL7nRKSkrgcrmGfgDBYrEwk0PpJYkGXyhNhJj3ZbVaMWHCBJavRVm0+iYGOpR8WLqW/NS/oySZo6NmMpn44X0EWrt2LR555BE0NjbiwgsvRG1tLebMmaN77I4dO/Bf//VfOHDgAPr7+1FVVYU777wTy5Yti3OrKeqY0aFoG6KfMxqNsNvtcWoMRSL5PqEQcR+d5OdVZ3R4GaHE27x5M5YuXYq1a9di9uzZeOqppzBv3jzs27cPY8aMCTg+KysLd999N6ZOnYqsrCzs2LEDd955J7KysvCtb30rAa+AokYd6Hi9SZV1phTF4Dll8f9+Sj7M6CQ/j+p3xDIRSgJr1qzBwoULsWjRIkyePBm1tbWorKzEunXrdI+fPn06br75Zlx44YUYO3Ysvv71r+P666/H9u3b49xyijr1NcnLElaKAvZzKYuBDiUH9SpeXi5GkPQ0wSj3D6DEcjqdqK+vR01Njeb2mpoa7Ny5M6xz7N69Gzt37sRVV10V9BiHw4Hu7m7NFyUhdZaZA2cUDaxcSFkMdCg5aAIddkxJTz1Kyo3SKMFaW1vh8XhQWlqqub20tBRNTU0hHzt69GjYbDbMmDEDd911FxYtWhT02NWrVyMvL0/5qqysjEr7Kco0pWvsTygKWP6YsviboyTBQCelMKNDSch/3yRBEIbcS2n79u3YtWsXnnzySdTW1mLTpk1Bj12xYgW6urqUrxMnTkSl3RRl6hWyPOxPKApYupaymIuj5KDOCnAxguSn/vDAjA4lWHFxMUwmU0D2prm5OSDL42/cuHEAgIsuughnzpzBypUrcfPNN+sea7PZYLPZotNoih11cMuBMxoudRk9S9dSFjM6lCSY0UkpzOhQErFaraiurkZdXZ3m9rq6OsyaNSvs8wiCAIfDEe3mUbyxFJqiQbONAjM6qYohKiUHLkaQWjhHh5LM8uXLceutt2LGjBmYOXMmnn76aTQ0NGDx4sUAxLKzU6dO4bnnngMAPPHEExgzZgwmTZoEQNxX59FHH8U999yTsNdAMcBV12i41H87LF1LWQx0KElwBC6leJjRoeQyf/58tLW1YdWqVWhsbMSUKVOwZcsWVFVVAQAaGxvR0NCgHO/1erFixQocPXoUZrMZ5513Hn784x/jzjvvTNRLoGjRDJyxFJqGiRmdtMBAh5IDSw1Si5dzdCj5LFmyBEuWLNG9b+PGjZqf77nnHmZv0hb7E4oCdZDMQCdlcY4OJQl1x8RSg6Tncap+YKBDRElEPfjiYX9Cw6T52wm9eiMlLwY6lBzUHZPbGfw4Sg5u1YRtZnSIKKkwo0NRwEV30gIDHUoS6hE4rnqU9NwDqh/YARBREmFGh6KBi+6kBQY6lBw0++hw1bWk5xr0/ZsdABElFQ6cURSoKxc4oJeyhhXorF27FuPGjYPdbkd1dTW2b98e9NgdO3Zg9uzZKCoqQkZGBiZNmoSf/exnw24wpSu/iwhH4ZKbJqNDRJRE1IMv6kEZoki4VP0cB/RSVsSrrm3evBlLly7F2rVrMXv2bDz11FOYN28e9u3bhzFjxgQcn5WVhbvvvhtTp05FVlYWduzYgTvvvBNZWVn41re+FZUXQWnA/yLiHgRMlsS0hYbGOTpElLTUcz4Z6NAwMaOTFiLO6KxZswYLFy7EokWLMHnyZNTW1qKyshLr1q3TPX769Om4+eabceGFF2Ls2LH4+te/juuvvz5kFohGIr+LCEfhkpuLc3SIKEkJDHQoCtzM6KSDiAIdp9OJ+vp61NTUaG6vqanBzp07wzrH7t27sXPnTlx11VVBj3E4HOju7tZ8UZoLyOiwNCqpuTlHh4iSFQMdigJmdNJCRIFOa2srPB4PSktLNbeXlpaiqakp5GNHjx4Nm82GGTNm4K677sKiRYuCHrt69Wrk5eUpX5WVlZE0k1ISMzophRkdIkpWmjk6HDSjYdLM0UlcM+jsDGsxAoNBu3GSIAgBt/nbvn07du3ahSeffBK1tbXYtGlT0GNXrFiBrq4u5evEiRPDaSalEr05OpS8OEeHiJKWOqMjXqsEQcCfd5/E7oaOBLWJkt2Bpm787r0GeLzS3w8zOmkhosUIiouLYTKZArI3zc3NAVkef+PGjQMAXHTRRThz5gxWrlyJm2++WfdYm80Gm80WSdMo3UiBjtcr4P4XPsJHJ7vw/KLLUJTNv4t427K3ET98eT9WfuFCzL1A+v+c++gQUbLSzNERr1Uv7jmNZZs/RK7djPceuA52iylBjaNk5PUK+OZzu3CifQDdgy5868rzOEcnTUSU0bFaraiurkZdXZ3m9rq6OsyaNSvs8wiCAIeDa9uTiv9FREoZ/37XCfx+10kcaOrBr3cei3+7RjiPV8B//fEjnOocwDef24X2Pqd4B/fRIaKkFbi89NqthwAA3YNuvPpx6FJ7Gnn+eaQNJ9rFzx2//MchCILgV0LPfi5VRVy6tnz5cqxfvx4bNmzA/v37sWzZMjQ0NGDx4sUAxLKzBQsWKMc/8cQTeOmll3Dw4EEcPHgQzz77LB599FF8/etfj96roDTgX7omBsKv729WbvrTB6fi2SAC8P6xdvQ43MrP7x1tE//hZgdAREnKb9W1AacHh5p7lZveOdyWgEZRMtup+pvocbjR1D3IRXfSRMT76MyfPx9tbW1YtWoVGhsbMWXKFGzZsgVVVVUAgMbGRjQ0NCjHe71erFixAkePHoXZbMZ5552HH//4x7jzzjuj9yoo9Qle7c/uAQiCgA9U9dSnOgfQNeBCXgb314mXA43aFQ/rj3fg36aU+3UAfr87IqJE8gt0Djb3wKu66Xhbf/zbREntWFuf5ucDjT0oZz+XFiIOdABgyZIlWLJkie59Gzdu1Px8zz334J577hnO09BIElC6Nojjbf1o73PCajYix2ZGW58Th5p7UF1VmJg2jkCfSqOg5Xl2NHYNov64FHhyx2giSlraQOdAYw8AwG4xYtDlRUM7Ax3Skv8m5L+R/U3duJqVC2lhWKuuEUVf4D46cqnB+FHZuKAiFwDw6Zle/wdSDB08I35A+OK0cwAAh1ukUS92AESUrATtHJ2DzeJ1bO4FZQCA010DcLg9iWgZJSk5y1cj/Y0cPNPLuahpgoEOJYeA5aUdSip5XHEWJpTkAAAONzPQiSc5sLlucgkAoGvAhY4+J2uXiSiJaTM6pzvF69W0ynxkWU0QBCgTz4k6+53oGnABAGadVwQAON05wAG9NMFAh5JE4Kpr8ghLVVEmzinIAAA0dnN/nXgZdHmUVdbGl2SjLNcOQKpl5mo0RJSs/ObonO4Sg5qKPLvSlzR1sS8hUaP0t1CYZcW5o7J9t3FALy0w0KHkoLNhqJzRGVuUhdJccf+cZgY6cdPSI658ZzUbkZdhQVVRJgApxc/9BYgoaWk3DG2UMjoV+RkoyhL7krY+bnFBInlArzjbiop8cUCvqWsQAgf00gIDHUoSgRmdE9LkwDFFmUo24Uw3O6d4aZKCyrJcOwwGgxLoBGZ0iIiSiGrwxesawJke8XpVnm9HYbYVANDW60xI0yj5tPaKnysKs6wozbXDYACcHi+cg6qV2Digl7IY6FByCFh1rV/JKJTm2lEqBTpN3YPiRl4Uc2ekQEfOplXkq0o+XKpVi/j7IKKk4rsmuR0DEATAYjKgOMuG4iwx0FE2P6YRT/5bKMq2wWIyoiRH7POcg+p5XOznUhUDHUoS2ouIe6AbfU5xVZyibCtKpA/bTrdXmTRIsSXXsMtBZnmenNIfABw9qiPZARBRElFndJzioExJjh1GowGFLF0jP3J2r0gKgsvyxEE9t5MDeumAgQ4lB7+LiKu/CwBgNYl76NjMJhRkihuFNnGeTlw0qzJqgO/i39nVCU1www6AiJKK75okSHt+jZJG6YtYukZ+2uSMjhQEy1k/r5MZnXTAQIeSRGBGBxA7JYPBAMDXUbGDio9WKdApzhbfdzmj09vV4XckOwAiSiKqwRejS5xnIV/H5FH7NpaukaRNnqMjBcGF0t+I/LcDgN1cCmOgQ8nBLysgDIqlUfLoGwDkZ4r/7uhnBxUP8vtcmCVm0uTMjuDo1h7IjA4RJRXfNcni7gMgYFSO2H8UZcsDZixdI5Gy6poU4MgBj9ml3reP/VyqYqBDScLvIuKUAh0plQwAhXKgw5G4uGjvF+dCFUjve67djEyrCVnwLx1kB0BESUSd0YEXdjiVjI5cAt3JuZ4kkQf18qS/jWLpc4fVw1XX0gEDHUoOfhcRk1McSVFndAqkzEJHPzuoeOiULv4F0iiXwWBASY4N2Qa/HcXZARBRUtFek3IwoAQ6uRliP9Iz6OYKngQA6B50AwDypL+NwiwrjPDCJnAfnXTAQIeSktmtrasGWLoWb3LmTB4BBcSyjxz4BTrsAIgomfgFMFkGVaBjF69nHq+AfmllTxrZegbFwVP5b6Mw2xpYucCgOGUx0KHk4HcRsXn7YYBXmTgKsHQtntwerzLKJZeuAeLO0Vn+gQ47ACJKKtprUjYGUCxVB9gtRlhM4gI33YOsDhjpHG4PBl1eAL5sX3GWDdkc0EsbDHQoSUgXEZMvg5MJhzJxFADyM1m6Fi/q+nU5nQ+IGR2ldM0kB0DsAIgoifhdkrINg8pKWgaDATnSyH33gDveLaMk0zPo+xvItpkBSBkdlminDQY6lBzki4glAzCKF5tsDGjn6LB0LW7k+Tm5djPMJt9lojjL6hvpsuWK39kBEFFSCczo5Ksy07l2sY9hRoe6pUG9HJsZJqOY6SvKsrJEO40w0KEkIV1EDAbAmg0AyDYMKKufAL5J8Qx0Yk/OmhWoSgcBoDjHhmyDVLtslwIddgBElEykwRcB4gdXMdDxZablEqVurrw24skZnVxV5YLdYkKxRVx+XP4b4oBe6mKgQ8lBuYgYINhyAAC56NdkdPIyWG4QL11SoJOvuvgD4nLfOegXf5B+T+wAiCi5iNckr1W8RhVZnLCoMtPypHNmdEj+G8iRsnyyUrv4OcMjDbxyQC91MdChJOHL6HjtBQCAPEOvUlcN+C5EvQ4uCxprPQ5pFRq/QKc424oCg7SJWmaRdCt/F0SURKT+wW0RAx15dF6WmyGVrnHQbMST/wb8+7oSm1g54jJzQC/VMdCh5KDK6Dis+QCAcssA7BaTcogc6Hi8AgZcXBY0lpSLv90vo5NtQz7EzVyRWSx+ZwdASWLt2rUYN24c7HY7qqursX379qDHvvDCC5g7dy5GjRqF3NxczJw5E6+++mocW0uxI16TXOYsAEChRVvunGOT99JhRmek61aWltZmdIot4u0OY6Z0C/u5VMVAh5KEL6MzYM4DAJxj69cckWExKZMF1SulUPQpEzT9Lv6jsm1KRsedUSDdyg6AEm/z5s1YunQpHnjgAezevRtz5szBvHnz0NDQoHv8tm3bMHfuXGzZsgX19fW4+uqrceONN2L37t1xbjlFnTT4MmCSStdM2r5Ezuh0cY7OiNejlK75DeqZxMUI+o1S6RoH9FIWAx1KDqqMTq9RnOReZtF2TgaDQVn+kYFObPU49NP5uRlmJdDpN+WLN/L6T0lgzZo1WLhwIRYtWoTJkyejtrYWlZWVWLdune7xtbW1uO+++3DppZdiwoQJ+NGPfoQJEybgpZdeinPLKfrEi1KfSRw0U8ptJdlSRqfXwcqAkU7+LOE/qFdkFP9muox50i3s6FIVAx1KEr6MThekumpjX8BR8sWIJQexJWd0/NP5BoMBhQaxdK2HHQAlCafTifr6etTU1Ghur6mpwc6dO8M6h9frRU9PDwoLC4Me43A40N3drfmiJCQNnHUZxEEzpdxWkmUTS6L7nRwwG+l6pUG9LJu2r5P/ZjoEztFJdQx0KDmoMjrtgpgqLjL2BBzGjE58dAdJ58M1ADvEevcOsAOg5NDa2gqPx4PS0lLN7aWlpWhqagrrHI899hj6+vpw0003BT1m9erVyMvLU74qKyvPqt0UK+I1Sb5GZXu1fUmmVexH+pjRGfH6pEAn2y/QyfaKgxitAlddS3UMdCg5CF7xu8GIFo94YckTAgMdeXK8PApDseHbW0B78Ud/OwDAJZjQ5raLt8m/O6IEMxgMmp8FQQi4Tc+mTZuwcuVKbN68GSUlJUGPW7FiBbq6upSvEydOnHWbKQaka1KrVwx0sjxdmruZ0SGZHOxmWU2a2zPd4t9Ms4dzdFKdeehDiOLBV7rW5BJXOfEfhQOAbJauxYWvdM0vozMgBjqdyEbXoDwayg6AEqu4uBgmkykge9Pc3ByQ5fG3efNmLFy4EH/4wx9w3XXXhTzWZrPBZrOFPIaSgPSh9Iz0IdXu8gt05IyOkxmdkS5Y6ZrN1QkAaHSJK/cx0EldzOhQclCVrp1yZgAAMt0dAYf55uhwJC6WfBM0/QKdvlYAQLuQg275d8AOgBLMarWiuroadXV1mtvr6uowa9asoI/btGkTbr/9dvz2t7/FDTfcEOtmUtyI16Qm6UOq2TMAuAaVezOljE4fKwNGvGClaxZHJwDglEMKdDigl7KY0aEk4cvoHBkUyw1sjjbA6wGMvpQy5+jER7DdotF7BgDQLOSjS/kdsAOgxFu+fDluvfVWzJgxAzNnzsTTTz+NhoYGLF68GIBYdnbq1Ck899xzAMQgZ8GCBfj5z3+Oyy+/XMkGZWRkIC8vL+jzUAqQMzoOK9yCEWaDV8xGWyoA+DI6/Qx0RjzdjI7bCaNLXHXtlDMTsIEDeimMGR1KDso1xIDDfXZ4BAMMghfoa9EclsM5OnERbMlN9DQCAJpRgK4BZnQoecyfPx+1tbVYtWoVpk2bhm3btmHLli2oqqoCADQ2Nmr21Hnqqafgdrtx1113oby8XPn6zne+k6iXQFEjrbo26EEnpDkW/W3KvfIcHZauUZ9TJ9CRSrS9ggFdYEYn1Q0r0OHu0xR94kVEMABtA160QhpRlT5Yy7i8dOy5PV443OJkXv90PnrEUe9mIR/dnKNDSWbJkiU4duwYHA4H6uvrceWVVyr3bdy4EVu3blV+3rp1KwRBCPjauHFj/BtO0SVdkgbdXrQJ4hLT6kEz+UMtFyMgeTECTV8n/a10GnLglT8mc0AvZUUc6HD3aYoJ6SLila4lzUKB+I+eM5rD5ECHGZ3YUS+5Ki/DqpACnTNCAefoEFGSkgbOYEAz5L7Et1CFfF1zeQQ43Vw1ciTzla6pVl2T/lbajYWq7o39XKqKONDh7tMUG+JFxCNdSzpM0qZ9QTM6DHRipVca5bSajLCa/S4RqoxO54CcVWMHQERJRPAFOp2mIvE2VV+SqVpKmAsSjFwuj1cJdDUZHelvpctcDAHS8vQc0EtZEQU63H2aYka6iHikwbUeS7H0D+1ysdk2cY5ONwOdmOnTG+GS9foyOg63dOFnB0BESUVQ/ttjkQMdX3WARTWI08fytRFLHeRq5uhIfyt9FlWgwwG9lBVRoMPdpyl2tBmdfpv0N9Z9UnOUUrrGOTox0xdkXwF4vUD3aQBAu6mIHQARJSdVRqffNkq8za86QN4gsp8LEoxYctma1WyExaT6OCz9rQzaS3y9Gwf0UtawFiPg7tMUdYI20BnIGi3+o1M794vLS8ee7uRMQMzmeJyAwQR3ZrnvdnYARJRUfPuyOTOkzxq92vme8kAOS9dGLjnIzbL6VS9IfyuurFIO6KWBiAKdaOw+/fvf/z6s3adzc3M1X5TutKVr7lz9QCc3wuWlewZdWLv1EJp7Boc+OI1t+7QFf/3wdFjHBtspWvld5I1GXk4GOwAiSk6Cr3TNk1Um3tbtn9GRV15jRmekkn/3gYvuSH8r6kCHA3opK6JAh7tPU8xIFxF5ARxDgbj3BbpOipuGSuTStX6nB27P0KvlPP7GIfz0lU9w05PvRLe9KeRkRz8WbHgP927ajaOtfUMeH7R0reO4+D1/DAqzbKoOIJqtJSI6W77SNSH3HPGm7lOAxzdAlinvpcOMzoglLy+e6Z/RkQb1hIJKVffGji5VRVy6tnz5cqxfvx4bNmzA/v37sWzZsoDdpxcsWKAcL+8+/dhjjym7Tzc1NaGrqyt6r4LSgLZ0LaPwHMBoAbxuZV4IAGSrNrBUL4McjJzFONbWjwNNI3NRi+feOa78+90jbSGOFCkbqAW5+CO/CkVZVnYARJScVHN0THkVgMkKCB6gx9eXyBmdoRYj6He68Yt/HMSWvY0hj6Pkse3TFjzy6gF09Yeey9vvkDM6qr7O2a/so2MprAKY0Ul5EQc63H2aYkLJ6IjfC7MzgPwx4n3tR5TDLCYj7Bbxz7Z7iAUJBl0etPU6lZ8PNPZEs8UpY3+jL8B772j7kMcHLV3rOCp+L6hCYZaVKX0iSlK+0rX8LBuQJy1o1OEb9JE/3A41YHbvpj1YU/cp/uuPH0HgtS4l/O+L/8ITbx7G1371z5DH9bvE332GOtCRB/RsecjOH8US7TRgHvqQQEuWLMGSJUt07/PfVVq9EzVRcNrStaJsGzBqEtB+GGg5AJx7lXJkts2CQZdjyAUJDrf0wqkqbzvZ0R/9ZqeAUx0Dyr/3NQ6d1ZJLOQIWI2g9KH4vGo9Cr5UdABElJ1VGpyDTChRUiX1J53EAcwD4rm/9Q2R0dh0XB4d6HG609DpQkmOPXbvprDndXhxrE/v6/Y3d8HgFmIz6i2UNKKVrqr5OqVwYg/xMC3u3NDCsVdeIos4vo1OcbQVKJon3Ne/THJorLzE9RG11c7dD8/OpzoEgR6YvQRA0r7u5xxHiaJE8wqnZR0cQgNZPxX8Xn68tXeMoJxElFV+gk59p8VUHqDM6tqEzOoMuDzpV5U8NbSNzsCyV+PfzoRYi8i1GoM7oSH8jBVUoyFQP6IF9XYpioENJQp6jI15UxIzOZPGu5gOaI8NdFvRMt/YCd7Jj5AU6Lb0OONy+rFZ7nxMOd+hSDd3Stb5WYLATgAEoOk9busYxLyJKJqpV1woyrUDRePH2toPKIb5V14L3I41d2j7kGAOdpHe8TbvgzqkQ/b5uoNN2WPxeMFYKdFQY6KQkBjqUHFQdk81sFCfCl8iBzn7NBUbONAyV0TkjZXTGFmUCCH3BS1fyay7Psys7gbcMkdWRO35N6VrrJ+L3/ErAkoGibCs4SZOIkpEAv9K1Uaq+RCKXK/WGyOic9ssONLQNvWolJVZDuzYYDVXJ0a9Xuib3daMmIsNqgtWsXpSHfV0qYqBDScK3wVtxtk3cgLZ4AmAwAY4uza7W2eFmdKSU9bTKfACBo3MjgZzVKs+zozTXprktGLnjz1Jf/Jv+JX4vuRAAUJRl46prRJScVIMv+ZkW36BZ2yHALQ70yANmoTI6/oNjpzpHXh+Sak77/Y5CBzo6ixHIc1GLzwcA5GVYffdxUC8lMdCh5KCaPCpmCwCYbUDReeK/VSNxcknV0HN0xAvepHJxw9kBlweDrpG1OVx7n1hfXphlRak0ifZMd+iMjm8fHdXF/8xe8XvZReL5sn2la1yJiIiSiXxNsppNsFtMQG4FYMsTtytoOwTAN4ofao6O/+BY10DolT4p8boGnJqfm0IMcA445UE9qa9z9gFdJ8R/S4FOrjrQ4aBeSmKgQ0nCV7pWlKW6sIySFyQIDHSGWhZU/kA/flS2supK5xDr6h9o6sYtv/ondhxsjaTxcbf67/vx3d9/CNcQm6Z29IsX/fxMK0pzxUAn1IUfCLJhaJM20MmxmZX31CsMvXErEVG8yIFOjl3qSwwG1eI2Yl8STkanU/rQLJc/+3+IpuQj9/Hy7yxUn9+nZHSkvq5Fmg+cWQxkFgIA8rOY0Ul1DHQoOQjyN4O4EIGsdIr4vXGPclO2ktEJHbTInVRhthX5GRYAvg/+erxeAf9Wux07D7fhB3/bF/S4ROvoc+Kpt47gTx+cxK+2Hwl5bKf0egsyLSiULtidId4DQGcxAtcgcEZ6P6RAx2AwKCNdgpcXfyJKHoI0+JIjXfcBaOd8Qr1haPABM3nDyaqiLPFnZnSSXqff76wzxO/Mt7y0lNHxG9AD/ErXmNFJSQx0KEkEyeiMuUz83uDb+CsrjEmkAJR9dnLtZrFOG6FHd46qJpoeS+JJpweafBufvvqvppDHdkivNz/T6nsPhuisA/bRafoI8LrEUa6CscpxuZni74kZHSJKJnJGJ1cT6FwgfpcCHXl56f4QJdByYFMVRnaAkkOn3+8sVHAasOqaXqCTyYxOqmOgQ8lBb44OAJwzQ1yQoOsE0CnWzmYp+x8E76AEQVACnRy7RVx5B6GzGeqJpw63VxnNSzYHmnybfg41OdaX0bEiL2PoYA9Q76MjBTon3xe/j75ULAGRyCNdnKNDRElFKV1TBTpyGfQZcWEVJaMToh+RPzSPKcxUfg52vXN5vPju7z9E7eufnlXTKbhn3z6Ku57/IOTvrNvvd9YVos/3BTpSX9f4kfg9WKDDjE5KYqBDSUIV6GSpStds2UD5VPHfJ94FEN6qa/1ODzxeubMzI1+6WHWE+JDvvzqLOqDQ8/S2w/jiE2+H3JAMEAMB9xBzaQDgxT2n8MXHd2Dvya6Qxx1o9GV0WnsdIRdYkF9vQaZFeQ9CZXScbi+cUluz5Yv/sbfF75WXao7NY+kaESUhZY6Ouuyo/GIABnFDyJ4zvgGzEKVr8kCRXAbldHsx6NK/lr/wwUn86YOTqH394JB7ldHwPPTSPry8txGPv3ko6DH+v7NQ/V2/unTN7QQaPxTvqLhEOYarrqU+BjqUHKTyp4CMDgCMmSl+P74TQHirrsnZHLPRgAyLCQWZQ8/R8d8zoSnEMsw7D7XiR1sO4MMTnXjt4zNBjwOAR179BBf876v416nQAcwjr36CD0924cbHd4QMjE53adsZatls9WIE8jylUCNc6uAxy2YCPC7g2HbxhnM/qzlWLl0DS9eIKIkYpGuSZsWsjHygVFweHw07lQnoA6Hm6AyI18OKfDvM0uIrwUqh/vaRbwuEE+0jb8+2WFNXY/x9b6PuMU63Vwlc5cUIugdc8AYZjNMsL930EeBxABmFvtVeAeRnqgZe2delJAY6lBxUpWvF6sUIgIBAR8nohFgtp2dQ7Ixy7GYYDAYUhDER3z+j09ob/Nj3jrUr/z7aGnw+jyAIWLv1MJweL37yyoGQx6kDllDBS3uftl2hNkKVy9QKsixhzdGR31Ob2QizyQicqgcc3UBGAVA+TXMsS9eIKBnJG4ZqPqQCvr6k4Z/ItIgZHafHqzuwJAiCssqado6jfr9wvM23UeWxEH0CDY+6n20Osum1HIQaDMDoAjHQ8QpAT5BB0QH1HB2pYsS/RFuz6hpL11ISAx1KCl4lo4PAjM7YKwCDEWjZD3QcD2t56W4l0BE7p3Dmp8gZHTn7094XfL8ZdfbnUHNv0OMOqu4LtVFne59TKbUDQm9y1iYFYPIqav6ZKJnYUYuvNy/DEtaCDAHzcw6/KX4fdxVgNGmOzZdKDBnoEFFSka5JeZkW7e1VvkEz9SaR/TrlvwMuD1weKWDKsCgLGwS7frb2+vqLZF7MJlWpA8l+p0d3WXA5MM21W5BhNcFuET/idgcZ3JMH9rKsZuDIVvHGqlmaY7gYQepjoENJQV7mUYBB+QCvyCz0jcR98nfV8tIhJiTKK65liMfm2IfOAsmZkollOQB8AYUe9e7Lh1uCBzq7GzqUfx9s7g06n+Zwi7ZjDBW8KO0sFdvZGiQgG3R5VfOULEoGpnvQpQmq1Hr9Nws9/Ib4/bxrAo711S4znU9EycMgjbznZfhndKQPsWf+BZunV9kLTK98TQ5ozEYDMq0mZdCsdzCwD+l3upUyKCB4oOPyeLHpvQZNUESinkEXnn/3eNC5t/7vaWtPYP/sW4BI7O9DDXB6vYIy3yrD6AaO7RDvGH+t5rh89ZxhZnRSEgMdSgpyqZnRaITNbAo8YOLnxO+fvBzWYgTKBc8mXujkx/TodFL+jxkrTWJs6wtvPs+pzoGgc2rkTUsBcTAoWAd3vC28QKfX4VYWCzh3lLS3Q5ARxh6HL42faTEpF31B8L3f/pTNQq1moLvRt+KaTqCjpPQ5ykVESSjff9AstxwoGAcIXhiOblfK1/p1Ah25KiA3wwKDwYAsq7x4QWAf4v+hO9gg2VNvHcaKF/Zi/lPvRPxa0t2S5z/AA3/+F1b/fb/u/f59Z4tOXyr/HuUV9eQ+T29e1YBq0DG7uR5w9QNZJUDJhZrjClQZHaebg3qpiIEOJYWeAXn0LMif5CQp0Dn2NrK94mpo/U5P0EmGcqpaHtkJJwskBzryai3+c2FkgiBoSssEIfi8lxa/WmL/n2X+iyQEWzZa7kAzrSaU59kBBC+lkEces61mGI0GWM1GZb+AYI/R7KHz8Z8BCEDlZUB+ZcCxSkqfgQ4RJRO5dC3DGnjf+f8mfv9ki1K+pjdo5r+fWKiS6ZZe7fU62IIFf5f2PTvc0hfWSpwjyfaDrQCAze+f0L1fXhhCpjdo6F+REKrfl4MigwGwHX9LvPG8qwG/zyC5dt/fUFc/M3GpiIEOJYWeQfEDvNkU5E+y8FxxpEXwIOfw35Sbg5WiqffQAYBsKeDRKzsAAI9XUC6G44rFSYxtQbIvHf0uOKSRHTlw6AgSFPlfjIMtcNDeJ3aM8oU5WEZHzjIVZllVS2brn1N+PfJrB3yBX7DMlq+jMAN7/yDeOOWruseqR7q4nCoRJYN+p1spXcvP1Al0Jt0gfv/k78iRpvAM6JQU9/rNV5QzOnpzQ1r8MjrBAp1M1bygvUOswjmSnGj3zb8JWIxI4v+e6gU68u9G/p1ly+WGuoGOeFuGxQTDwdfEG3UqF4yqwCfUYkaUvBjoUFKQS6mCBjoAMP0/xWM+/D9lqc9gCxL0KGUH0hwdW/ALHqANgMYWS6VrQYMSecKjGWW5ds1t/gIDnSDBk/T48SXZAIJfUOXnKcqyDrmKmpLRsakDHfExQ5WujTM0Aac/EBeBuPDfdY/Nlt5TAwR09CXn5qpENLK09zmVQEdeQlpjzExxFcmBdlQbxc099UrXfNdPMTgJta2BfF0vlhbSCRboHFNNqFdPrld7+aNGfO8PHwa9Rqcip9uLFS/sxeb3G3TvV8+/ae116Ga75PdUfo/15ujInwfkgDJH/p3pvJfy73yK5TTQ/DFgtAATagIbp1qBLdTWDJS8GOhQUuhVAh2d+TmyqV8DjBYYGveg2iqmt4MFLpFmdOR6bJvZiFHSiFKPw607aV9ZySzToixbHSyrIpeqyfNpgpWutUuPHycFWcE6Svl2cV8cqVMNOkcneEanO8j7IO9BcG3vX8UbzrsWyC7RPVYe6TJAQFuIFeqIiOKlo88F+aOpwaDzEcdkBs6fBwC42iNuWTCgk6Xpc2izA/J3vaBIHpiS53fqXb+7B12a67/e4Nj7x9px128/wB/rT6JuX+j92VLJP4+0YdN7DfivP+3FK/8K3ANH/V64PAJO6GyZIJejy32kXp/r/zvzbUUR+DuTf4+fN8iLEFwnLnwUQBXoBFlanJIbAx1KCj0DQ5SuAUBWETD58wCAW0x1AIIvSKBMJPWfo+N0687rUQdG6sBArzRO2Vshw6qUb7UHyWjIpWqTy3Oln0NndMYOsZuzHBBm281KRido6dowMjq9DjeyMIBLO7aIN1x2p+5xAJSRLgOCZ7SIiOKpvd8Jo0G6xqtG4zUuEstxrxx8EzY49TM6fnN0MkPM55HL3M4pyAAg9if+g2StfoNcetftXcd8q3Tq7aXm8njxq21H8Pq+M0GX9W/sGohJKbHb48XJDv0sFCBuor1u62Hd96dJ9VreV71GmX/pt14/KQeP8v44euXXfX6LEWSFWIRIXGlPQI1X2hD7Iv0SbWZ0Uh8DHUoK8gdvi96Ka2qfET94z/O8iVK0D5nRyZU+2MuZDEHQ3zNBXepmM5tglQIuvQukPJE/P9OCwqzgwcaA06O0b7K0ZPWQGZ1RvhFBvYBMPl+OzawpXdPr9JRjVYFb7hBzdPodbvyH6S3YvX1A0QQxoxOU3AEIDHSIKCloPzQHCXTOvRrIG4MsoRfzjO/pjvj7L0YQarXPXmmFy4r8DOU2/8Ek/yyPXp+h/oDfrLPv2t8+Oo0fbtmPRc/twtZPWwLuf/9YO2aufgOrXtoXcB8gzksJVi0gvg530EGwx988hCt+8iZekRZUUNt7sgu3rH8XP3nlAJ5/93jA/eo95PSCmA6/qgT/KgX1nnDn5MvBZGA7AzI6ciWHQ+dYpxszjftQ5m0GLFm+lV39GZjRSXUMdCgpyGlpS6iMDiBu+FY1G1a48S3zyyECHe2qazazUZnXo1e+5l/qlhOi1E0OdPIyVKVrOh/05aySyWhQRqGCdTLy48dJGR0hyG7OParOV55o63R7lf0A1PxHJNWvrztIZ+YY6MO3zVLZ2uXfDliBRkPJ6Agh9xwiIoqXdvUH6WAZHaMRuORWAMAt5n/olq71+k1sz7QGL4OS54YUZFqQIS1Z7X+tDwh0dKoA1EGAemsCWUObr6TrSEvgXj0/feUAAOD5dwPnwni9Aj738+245tGtuptX9wy6cP3PtuHqR7fq7itU+/pBAMB9f/ww4L4jrb695E60B5adNQ0Z6IRezKHP6VEyZKOlrFmoBQayAubo6Gd07jD9Xfxh2s2ANTPgGH/dDHRSEgMdSgphZ3QAYM5yAMDXTa9D6AgcPQKA7gFt4GIwGEKO7gSUuoU4Vpmjk2FRla7pbV7mW0lNCZx0Ls4er6CUqpXl2X0dpc7cGzkgy7abkWU1KcFbp84F2D94U7++YBmdzzT/EaWGTvRmVADTb9U9xoela0SUXDo0SwAHCXQAYPrX4YEJnzF+grzWDwLulj8c++bohCpd8x0bbO+WSDM6TTrBiHoZ66E2HfVfHa6934ljbf1o63NizWufBhy/fvtRnOocQGuvEw3t2hK1YGVySrtUlQp6VQvqoE1vEYGAjE6Q985iMqAkV5pDq1e6Ji9GEJDRCTzW1HEE1xp3iz9ctjjgfjVB+jvqYj+XkhjoUMIJgoBeaXlpa6jFCGTnXYsD9mmwGVyYtPdR3UP8MzpA6E1D/XdUlo/Vm7TvWxDAgvwQG5Kpz+mbG6PTSQ66la1o8jIsqpK0wIuqet6NJnjTO69Du2S1+vXplif0nMH1Hb8FAByYeBdg1lmaVU2d0eFiBESUBDr6wsjoAEBuBfYWi+VK1cc3BNzdpyoTBnzzPoYqcwsW6MhVC/JcH73BIXUQoFe61qwJGAKvuertCz4906u5Tz1P5kBTd8Bj/6Va7to/yDqpWhzA5RECAh/18+pt5KnOIOn1FXJFg/zeBAQ6qiqKUPNMfb8H7T46ev3u+YfWw2gQsC/rMqB4QsD9akqgE6Lsj5IXAx1KuF6HGy5pXxqLOYw/SYMBf6v4DjyCAWPPvAYcej3gEGWOToYvmxFq8zBljk5YpWu+xQhCBTA9qqAkVIDR4/Ct+GY1G0Pu5iy33b+demVuvX7Bm/jv4O3FqyuQJfRir3cs2sZ/KfD+ACxdo+Sydu1ajBs3Dna7HdXV1di+fXvQYxsbG3HLLbdg4sSJMBqNWLp0afwaSjETyV4nH4z5BjyCAeO7dgInd2nu899HJzOMjI72Wq89Tr6eKwvO6GTsNXN0ehwB8zSbVcGNf0bH6fZqlmk+1KwNdJp7fMFGu8571KYKvM74LYRwqMV3rgGXR9OOwHYHBmjqQKe9zxmwUEPHEKvWqd/fUP24vHiQXGYYNKPT8ikmnBZLtN8quz3gPAEMcqDDfi4VMdChhGvpcSgFBqZQc0JUevLOx3Meac37F+8BBjqV+zxeQfngn6OztHLoOTpyRif4vjudqtI1eZ8evTkv6qAk1MiS/6IBcqCj1xH2qkrX1O0MdV79jI7f8fv/BvzrT/DAiBWuRci262/apsFV1yiJbN68GUuXLsUDDzyA3bt3Y86cOZg3bx4aGvT37nA4HBg1ahQeeOABXHzxxXFuLcVK2BkdAM68sfizd474wyv3A6pMhW9iuzY70D9E6VpWkEULlEBH2pDaP9hwe7ya29xeIWDhnBZNoBM4r0WdaPEP+Jq6VEtb6wxMqUvp/Ofw+J/Lv+xOHei09DgCMj7q/tErBPYXyqqj0nvTHTBHx/f+htoiQS5dk39XOcGCojdWwQgv6jzVaC2YFnCeQAapXeznUhEDHUo4MdAZYjlQP1k2M37qno8222ig5zTw4l2AV8wKqS9quqVrOh1Vt1Lq5pcp0Qlg5A4rV5NGD54lyrablQyMw+2F0+31O04bkITK6PT4BS/hBG/Zuhkd1bm7TorvH4Dfmb6AfwnnanbwDk78XRkNgmY0kCgR1qxZg4ULF2LRokWYPHkyamtrUVlZiXXr1ukeP3bsWPz85z/HggULkJeXF+fWUqxoAp1Qc3Qglkr91DUfgwY7cPJ94MPfKffJH66z/RYj0M0k6GQcggU6ldLCNE63V7MMdKcqUJG7QfV1WhAEv0BHm1UZak6QOnjpc3ow6BdEqYMf/9I1//mi/j+rM/qDLq+mj3V7fIvlyK/LP9CRj68MsmiPejU1efNv//dPfF1yRkcKTu06v4tPXwX2vwQPTHjEfZOycEEoBoMc6LB0LRUx0KGEa+lVBTpDdEyybLsZA7Dj+Yr/AUxW4MDfgLd+AsDXOdjMRthUixtkSx/y9YKCbr+MTqgAQr4t164eXQo9R0cdbPh3lL4SM4vme6gSO/l8vhGr4BkldUYnYDECRw+w6WZgsBOomI41npsCHhOUKijVqycnihen04n6+nrU1Gh3Nq+pqcHOnTuj9jwOhwPd3d2aL0oumhUwhxg4y7Sa0YwC/DX3P8UbXrkf6BY3tPRfjEDJ6Dg9ARkL9dxJZdECv7k88of38jy7cpucgfA/hzz3U93/9DjccHp8g2RtvU5NO4LNCZIFZml89zvd2uDE/1j/7In/c/kHXer5Q+rXWJYrvnZ13yYIghKIyO+N//n75TJCq0nbl/q1q9+v3DCgkmKwG3j5uwCAbUX/gU+FSmXhgpCkv6OegcCyO0p+DHQo4dSla+FmdOQL2AHz+cDna8Ub3/oxsPePuquNqR+jH0BoHxMq+6MEEHbtamr+9dTqTI3JaFBGmfyzRMGyNHrZJPU+OnIb1M+le6xORqd70A14XMAfbgeaPgIyiyF89Vl0OQ2a84bm+131Od1Bl/omirXW1lZ4PB6UlpZqbi8tLUVTU+C+H8O1evVq5OXlKV+VlZVROzedPbH8K7KMDgD82f4loHyaOODz4l2A1xMwUCTP0XF7BU3A4fUKvo0qVaVr/tdD+cN7YbYNNmkuqjrT4Ct/832YVwcY/h/qnR6vJpjyH2wLDEa0WRT1ogD+pWgtOmVxav6Bj//jNQGclGWxmozKlgjq98bh9kLuOuV9iAKXl5YyNVJfmqX0pdp2+O+jI2d/HG4vnC4P8PJyoOsEkD8Gf8kTVxUNJ6Mj/x0JAveMS0XDCnQ44ZOiqaXHAYMhsoxOllJG4AGm/ydwuVh6hRe+BfO+FwD4sheyUEs89wRZXjrYKmmA2AHKJWmC4LsYK8c5tMFTsPkx/vNugmWTxNXp9I8N3U5fwCcfPzA4ALzwLXEhB3MGcMvv4cgZA7fU40Sa0TFA0N2bgSieDH4DJYIgBNx2NlasWIGuri7l68SJE1E7N529tj4noB5vGuJ3nyF/YHYD+NJTgNkOHP4H8OYPAzYMzbT4PhCrP8ir59GEKl1TDzzpDbppFjTQmSMqny8/0wJpVwHNc/hncPyDEf/2qPfx8f/w7n+s/7nVgYi6NK04WwxkelQVBn3qgUGd90b9Gkt0Mj6AmEUDgGxr8P5ZEATfXB7p9ypn1wDA9d4zwN4/AAYT8OX16HCLbZVLEkMxqFYY1VtsgZJbxIEOJ3xStA13jg6gumDWPAxM+zogeDB+xzL8h2krcjL0Mzp6QYF8IQ8oH/M71usVlBGqbLsZdosJVmmTU/+OxX+J62DzeZTjgqXbJQ63VwlEfJmnEHOEHNqgCBAXRrDDgccNjwAfvwAYLcB/PAuMrtZ0LllhXPzVQakBgSv1EMVLcXExTCZTQPamubk5IMtzNmw2G3JzczVflDw0fQmAITM6UvDS7/QAJZOAL/xSvGP7Y7javQOAr68xm4ywW3QyMdK112Q0wG4xBp3L06eUX5l15474BrEsutsGKBkfq36gJPdhchcaLCsi02R0hgh0uvzOrQ581Fmlkhy75rUCvr4py2ZSAg/165LLzTIspqCDkfLPmX4LQ6iPG3T5MkOZfr+zzxp3I/P1/xLvvOZ/gDGXBWR/QjMor19vnyBKbhEHOpzwSdGmXXc/stI15YJsNIqd1PRbYRC8eMTyNO4ceAbwegIeE7p0LfRqLX1O3543AUs8+5UO+Jc++AIY/eMCAiKHf0Ak/mww+DpoX8egPafD7VEWPVBnZ7IHTuKP1odwtelDCOYM4ObfARPnieeQOySrCUZjGL8H/4wOR7ooQaxWK6qrq1FXV6e5va6uDrNmzUpQqyjeAgKdMOboAL4P25h6EzDrXgDAY5Z1+Kxxt+b66dtLRy8AMYl7mwVZhlq9iluWTjCkLkvO0ekr1CuKKX2ZKmDwX+zAPwsjn1/Ouqjn6MgbdhZn2wLOC/jK4vQWC5Bfl8VkQGGWXJoWeH+WVb+sT71iXbB5UP2qc8jHqs8NaH8n6uzbZdZjeMLyCxgEL3DxLcAVy7TtsoVRuqb8HQkMdFJQRIEOJ3xSLAwvoyONDKk7E6MRuPEX2HPunQCAz/X+Cdj4eaDjOADVmvohFg7I9Z+jEyQoMRsNSp21vFdPYKbGP4DRz9T4r46WHSRwUhYisJqVQCTYOdUjakpHvf9vMP3qs5hiPIY2IQeNX/gtMOG6gNcW3vwcLbF0jR0AJc7y5cuxfv16bNiwAfv378eyZcvQ0NCAxYvFXc9XrFiBBQsWaB6zZ88e7NmzB729vWhpacGePXuwb9++RDSfokAz3xPAkBkdm5zRUV0/r1uJwQk3wmZw4ynLz2A/9g/lLt8HbN/11b/ELUv1YV1Nf2U2VeZDZy8e/YDApJsRUgKdQv15LnLwUqpTHiafpyxPCnScbr+FDtyac3frBDrqQKU3yPuTo9PufqfvdcnvnccrwKFanVQ9BwrQDzjlc2aqB+qOvY21noeQZXCgq3w2cOPPlc8Y8u8nnNI19Z5xehuiUnKLKNDhhE+KhWZN5zTMjI7MaMSO0d/EEue9cBgzgIadwLrZwLtPI1eqZPPP0rg8XgxIddbyvjjBNuJUz5GR63aVldcG/AMTbQeYG2Q1NV/mx2+z0mDH6e0NFKSdmVYTTP0twB++AWz+T2CwEx8bJuDzjh+htfAS3fOHl8qHX0YncKUeoniaP38+amtrsWrVKkybNg3btm3Dli1bUFVVBUCcL+pfYj19+nRMnz4d9fX1+O1vf4vp06fjc5/7XCKaT1HQ3DMYYUZHDHQG1EstG004ec0v8XfPpbAZ3DD87mZg17Oa4/t0goQsv0BHfU1WL1iQaVWtzKZbumbWXYxA/Tzyc6j7p245GJEzOn4DZf4rm+kFUaVS6ZkgaAO1bv9skerc6pK6LJ1Mk7qEOlQmK8tq1mRi9AIx+X3TDzi1wRD2vwT85svIwgB2ei7Anlm/BMxW5Xh1gDUk1Z5xzOiknmEtRsAJnxQtTrcXrb3Dn6MTrAxti/dyrL/w/4DKywFnD/D372POG1/CHONH6AkSkACqMrMgCwL4r5AGhMrUaOf9BMsSBVsyOuiiBepStCBzdHodbmRgEN8xvwD8Yro4H8dgAq5YhvtyfoxGFAU9f064gQ60pWvNzOhQgi1ZsgTHjh2Dw+FAfX09rrzySuW+jRs3YuvWrZrjBUEI+Dp27Fh8G01RE/kcHfFa5/IIcKlWUutzG3CP6x68arwS8LqBvy0FttyHfKt4jDoD5D8XUm8QbsBvwQK9/kub8QmcI6re10fvOXwZHTEYGXT59plRB1pKRkcniCrOtoVc6EA+t7Z0TV1SFzoQzNYZmFMWGrCJlQpyMNmvDmL8si96zyP/TrItBuCNh4HNXwfcg/jA9hl8w3UfOj2+Zb3V7Y5kPqq4GAH7uVQTUaDDCZ8UbWe6ByEIgEX5S4ws0HF5hIBNw+TRJk/+WOAbW4AbHgMyCpHVdRD/Z/0xHun5PnBgi7LBqBxoZFpNMEsLC+QGWTjAf88bwLeE5dBzb4IEMA65bE47RydYkKW7Car6ufvbkbPrF3jLthx3ejcDzl6gYjqw6HXgupWwZ2TqtrfPqe2wh+Q3R8d/kzkiongS92RTCXPVNUCbwehzuOGGGY9mfRe4+gHxxveewk86luM8w6mwStf0jjEaALvFOPSqazrly3pzWfQeL+9VA/j6EPXKcHKgo53fIgUb9sBskXoBnop8u9SuwABMXVKnG8AFWUTBf6EBvSDQN0fHJB2rP1dqrKERv3T+D7DtEfHGy76Npyt+AAesmt+HxysowWdYm2OrVl1jRif1RBTocMInRdupzgEAQIFUMhZ2Rkd1cVJfwAC/zT+NJuDSRcC9H6Bz6kI4BAsu8n4C/O5m4IlLgR21GGg/7TteIl+QB1weuFUjfT06WQ+53C1w1TX/QEd/kQH/TE2wpa3Vq/LIfEtRu4CTu4C/LQN+diEqP3gEJYZONBlLga9uABa9AZxzieYxcqmDf3vDWloaAAy+yweXlyaiRBMzOr7rtfoapcdqNsJikuds6JRT2S3AVfeJi7ZkFKLKdRhbrCsw4eNawNkPQDvZHvBlG4KVZxkMBt3J9Oq5mnolyeqAKtSk/hy7WVVi59E81mQ0oEhZAlon62I1BWSLBlweZQEeZVU1nbkxwfYQkufrZNv1M1H9qsfLbQh4Dr85OgHn8bhQ+q/1+Lt1Baa49wHWbHG58Hk/RqZdLtXzBY3qDFtYpdrS5xIjBM1mqJQaIp51vHz5ctx6662YMWMGZs6ciaeffjpgwuepU6fw3HPPKY/Zs2cPAGgmfFqtVlxwwQXReRWUshq7xEAnL8MMOBF2oCMvGzno8qLP4VZWewECFxYAAGQUYPDaH2Hue9VYaHkFd2a8CUPbIeD1BzHRsAr/Z5mM3cYrgO4LgNwKTVajz+FBXqbYYcoXS+08GXkTTt+F1OMVNCl59WMCStz8RgTlTs7pEUsPbGZtx6kEWV4vijo/xHfNv8cNzveA9aeVc3blTsRDrVejddzn8dyUOZrn02uv+vxhz9HRKV2LdhkrEVG4Il2MABCXNXZ53NqMjtMvez5xHrDkHex/6jZM7v0nph75FfDEq8C1/w+9g+K2GfL1XR3EyNfDfv/J9LoBgdS32MzIsOgES6plmpV2BgmEMq1m9Dt9m56qV4bTqxjQXVBAul+djZKDJL1sVZbVt1qcdllsl3JuJVs0qBPEWP3n34SYo2NVPc++vwKvr8Tk9sOAAfjYPh0X3vlroECcm6dXht6vek3yokKhsXQtlUUc6MyfPx9tbW1YtWoVGhsbMWXKlLAmfMrkSZ9VVVWshSac7hSzAPkZFqALCLd0DRAv6IMuZ8A8Hf/9a5Tj7Wa0IB8/dn0Nt933S2R8+iKw+/9gOPk+5pj+hTmD/wLWPAmUTYVl7BW4wZKBt13no3vQhbxMbSnbUHN01BfVwI1AgyxaIHeUqprhnkE3bNlSpzcwiEmGBlzXuwv40zrgyJso72vBPdLhgiUThsk3AtP+Ey+dqcILL36M6+0ZAe9b8JXaIpyj47cYgdPjRWe/CwWqoJOIKF6aexywRrAYASDO++gedGNAFej4ltpXXQtzyvC78Y+i8b0/4dHsTcjtagBe+CZuslfhgPEG5Fq/Jj5Gun66pZXD7BaTzj4wOosRqAIVu0Xvfl+wZJD6Sc2Hd3keizRXprXXl6XSzv8JDKJ85WeBWRlfIOJbTCBYu5QgRZPxkQf8VNkiveyZ/4pq6k1ZpeOVOTpW4N+M72HxwVXA3gMAgAFLAR7q/wp6xt+CJ6QgR37NgF8GS/WawhqYUx3T4xD/VjLCKXmjpBBxoAOIEz6XLFmie9/GjRsDblMvU0ikJmd08iMsXQPEC2NrrzPoLs7qeTSAvM+BuKJMj2BHRvVtQPVt+PvWHdhd9xv8R9aHmODcDzR9BDR9hCdMAEyAa8Mq4JyLgdIpKDtTiAsNXhRbCpXz6s3nkXeGtpqNSkYmd4iSNPk8JgiosvWi1HkChl0NQP8RoHk/Fp74AHfZ+oBGiF8ABFsOXu6/EK97LsFDS7+PvHyxXT0Nh3XfA/G2YIsnRDhHRxWUFmVa0N8PNHYNMtAhorjrc4hZGVsEixEAvuAj2Id3tSy7Ba95L8UvL7wRDxS8CbzzOIoGjuPn1rXo/dfvgdyFyJzmW8K8z+GG3WIKOo9HvQxzr2pSv03ZmFR/LpBR6ie1j5fvNwUEK9r5PZaA16teUMC/bE4v2+Nwe+H2eGE2GVXt8gUymkE/ncUINEFMwHujt6CBtCqqpwN4eyNu+uevsNDaAAwCMGcAs+7G/3k+j9/94xRu8uu/9FaC6/MLPIcmvt92swFwiZnDMUWZYT6WEm1YgQ5RtMgZnTw50Ikgo6O3VCUQODdG9v/ZO+84K6rz/3/m9rJ7txfK0kFBRBEsYLBFMESNpkliYvnG+lWTKDH5BU0i8WtJYoKYGCwxxhI1JMYUEyxYAUGEdVGkSGeXLWzf2/v8/pg5M2fK3d274F527/N+vRZ2587MPXfuzHnO5zzlSIu52RCIJhGIJVEpb2+2jcLjqYvRNO56PPyl0cCBtcCB93Dgw9cxLt0Ae7AR+LQR+HQVLgJwkRPAJwD2FAPFNfhiqhAldgHepkpgzQmAswjWkIhLLQfgdLiAnSIAEWMPd+Jiy06M9juA2t1AtAfpcBfuED9GkT2E6n/8Hgg2Av4mvCvEASeAd9T2uwAERRc6imdg7MnnAWPnQhg7F4vvegPxdBq3iy6wJXn5MAg9qjA7wtA1TpSOLHahIZzAoa4wpo2k4iEEQQwuLElck1zej4kzZkf0xQgA1fOi7Cv3jT0JG3DW7cBp1+OVJ3+O2Yf/hopEO/DuL2Fb82s845yOfyXmIBKYBRRUazwI0nlNPCNRNcRLETqaPBVVEAiK0JGOEUVRmyuj84rwpZfNPByKx8lhNXhteG8UbxtYSLdZkYRMIXXs3FohpK2opvcKpaIBnJ3agC/b12Hkk1uAdBKFALrEArxZeAm+9r93A95ydL+6U3Mehlm+U1j3ffSJfL1LvXagG2gLRknoDCFI6BA5pamby9EBsvLomM0OAWonWuQ2ejN8LrskdHjvC19JraASmP5VYPpX8b0D67D/UDOe+qIbs5yNQMvHOLjzQ3jCh1Ah+IFoN9DSjWoAX7YCCAB46x8AgBEAljsApAH8RXqfqQB+5wAQAfCytM0C4Ar2FHJV1FOwoFkshXf0dJSMnQFUTsWvttjw2E4XlsyejmvnTeA+k+TZ4jtyNU/JTOgcpdA1TpSOLnZhY1MCDV2Rfh5LEARx9GBVHysK7EBY3tgfodNL8QC9d1tJ8meiyOXDvwovx/fqz8IfT2vGWT3/Bg6+h7OEj3CW4yOk//AkMPEcjLKfgvFCBbyOCum8vYZ48R4dc88I+1jsmHgqjWRalNvIrdMTZ2JFnfgqNMtZ4UtX69aQ419jxRsSKRGheBJFHju3Ho3NdCFTs2pypmWhufybKnRi7IG/AQc2w7LvHTzqkPNi0gBGzcaOEV/CV9aNxqTyKnzNWy6fR5sTyzCr9MauS7YenTKvA+gGWnooT2coQUKHyCnNPbJHRzEo2eXoANpOk1/8U+/R4Y/RLGgmz6T53MYOMgAPDvlOxqyTLwIA/CJQi1c+acF9F47H5VNEoKcRu/fvx8o1H2GSN4pvnOAG4iG0dfuxo74VpU4R06ucgGBBJGVB3aEAYLVh7pSRgKsIAaEAT9Z2ISQU4I6vnwUUjQaKRmHRc/uxuSGIx+bOwgUnVAMAPt2yCSm0GnOP5BA+sxwhszA0tfqbuUdnIOWlR5W4AATQ0BnOvD9BEMRnRKM8yTKyyK0KnX6genTMk/M1+8p/h3WD5gRsaB93EXDKjUD7bjz52G8wL7YGk9EI7H4ds/A63nYCHY3VwL/OxzjXCZgsWBGKug3vWeCSBIW0ra/QtaRhP6/DakjoV0Px1NdYRVEp/Mzo8TEcy3lcusMJ5XV1PRr13GbeIj6Hh3/vYDSB0UIbjmt9Ffj3dvxo95v4pesQsFs6XgBwIF2F1eKpuPaWOyFUTUPPvg5E1r1vmuujFy9m4XRhnRepT+TrXV3oBAA0dpOdG0qQ0CFyRiiWVBYeUzwPWeboADD1ZADmYVtm6xOw6mM+XT6L2uGrRoSd3+X1AVWjgaoTEPP24Im3R6MaLnzjks8DANZvacT3927BnJoyvHDdGdKxgSguv/dNCElg7ze+CItFwKFmPx7cuBblBU7cMeN85X087hYAQZ0gY4ZO206zKjr+DPvy1yBTeel+u/M5UVpTIhlsEjoEQeSCQ7LQGeFzyjmM2S4+bZbvohM6JonyhpDf8sl4seBbuDtwEf725WKcmtiMhk3/QWV3HcoSLUDdnzERwGonEAx6gGdOh1h9IuYnE/hUqIHXEofTUQBA8tTEk2k4bFoxwsykPo/GZbfAZrUYws9UkWTXVm2Lp1Dk5sPPrIbJQLOKZ93hhGn+TyEnkljFOU3omjWBKUIDJgmNSL7+PmxtW7GicTMKnQGgTmpTGYCUKKDZOxWjz/gKGirPwzlPNaPQZcd1VdM034uZZ0hvv0zX9lH2zc6jU+2T8k8PUeTCkIKEDpEzWCGCQpcNLqXEYzYeHWPSIhMwXm7xT80xLuOMU6acHtXlrYoiddFO41o2fLlms3MyISWKUkdb6LIbFhVVzmmyEKh+BW59O/2axeXMK8/xbTcsGHokHp0iaa2Chi4SOgRBDD6H5L6HLWrZ7zXZzPJlYuaDZo8uJAwwroOm/i6g1T0ROP1zeNZ/AZ5dsx1LT+zEoqpGRPZvhHioFgVCGNj3NoR9b2OZbFLE3/0EKBmPp+wFaBArkFq3C6iciNHRZkRRiAKHAKugLSigF2Zqnot2HZ0CpxVOmxUOmwXxZBrBWBJFbvPws2BMe6xxDRv9uW3wOiyoQDeq0Yn4J/+CM3wYN8feQY29EcetXAJ7oAGvO+V1jjZK/xUCiItWxMqmofD4c7AqMAn/b5MX80+YjGVnnYzuQz0AWjTfhfmirOYFJApNii+EFe9PdrZOWmw1TkJniEFCh8gZDZ1SZzGq2A2wSjnZeHRYMQLO6DAvhVm1MX67eY5OhpkgkzA3fl92znCcc8ebiAanzQKbRUAyLSIUS0lCJ8MinWYJlJkKDJjt21sFtUxV19R1esyvnRFO6MiDi4bOCK2lQxDEoHNICV1zylv61weZTZhlCl1jfa954QJ+IK49ZzCWRAQuNFedDZw/BYFAFHPufR3HWxrwny+7EGn8BFs/XI/jhAYUIwR07sU5zNnwzhsAgJUA4ALER61IucvxH4cbXdES4J8voTThxPesPbAJRUDdYZwUDGKupQfFnSGgJQFnTz1qhMOoEgqBUDuqHHG0J5MI+bsRs0XhTgXhgYiCVA/K0IMR6IA3EAeaAV/bbpxp2YNTovXA1r34amozAtY21HzwKrA1jh917IHN0Y1pr0bh/MdhbHLJE2h/l/67UgBgBeCX/g7CjT3pERg3fQ6KJ5yKa95IYm13Bf5y6dk4ZUwJOt4/iMCmT1RvlEk+Db+oqN5zpPfSmNlx/do9fSPdS5WFDkhChyb0hhIkdIicsbctCACYWFEAZenlbKqumczEZVpDh9Frjk6G0DVNvHEv6+gAkkEr9jhMzykIAgpczO2fAOBSvDCZEijN8m76I8iYaDErRpBR6JgsSNcrnJipLnJCEKTY6/ZgHBWFzl4OJAiCOLockvMmRhRl59HxmFTvZN4BfV/LihGYFS7waoSO9pz6EsoFThtSsGJbehzCMy7A4XFRLHr/XRQ6rdj6g5OBtk/x82dfQVmiCVceDxSED6GjcTfKEIAFKdjChzHdAgAHgC11qAKw2A4gAeBff8QlAC5xANgl/dwC4BYngA+ln7WAVMbzSam9H8uXDL8Fvg7g6y5IxXEeAy4DcJlDeiscAK4HADuUHJrTAKmqTkj6Oy0KaEUxiqvHwVY8Gn/alsI+cQSWXn0pnNXHYeGKT9DQFcVLZ8zFKWNKUPfKasQR566NdI2ZmOSLIeivryhKNsfjsKniJVMxgngS6bQIi0UwrMvTJ8yjU+gEEMShLprQG0qQ0CFyxv52qWccX+7FQDw6ZqLFn0EMMHyK9yNhcoxO6Jh6dJiAUPe1Wy1w262IJFIIRCWhk8lTUyAncrLzZAxdUwoGSK+LotiPMDczQWZSeU6uRhdPpRFNpOCyW6XzM4MygHV0nFYLqn0uNPdE0dAVJqFDEMSgkUyl0SwvVTAia4+O0UuTqdS+UrjApF/WDMR1BQ70JZTddissApAWpfdSw67sQGE1UFiNN9wpNEQimDNvLsaVeXDqPW/AhiQ+XXIq4j3N+N9HX0GF0IN7z69EQ3ML3t++H2MLkvjcaAda29vQ1dmOckccZS4BoXAYSMXhtqRgEbUTXGbERBsSFicKvIXoiFvRFrWg2OdDdXkpPmwDdvbYMGPyeEyfNA4/f6MZjTEX7rzsLIwdNxlnrdiOQ/4kXr74c6j0OXHvR2/CahFw36R5gCDA6/wUQNSQA8REpF54qtdOnYBz29U18YKxpCR0YuYTdcxeiiIQTqRQ4LRx1zs7j05FgZSjE46n0BVOoJTWjBsSGJMYCGKQ0AidI/DoBDXFAlgFNfPwKzNPSSYvUKFuVo6v6KYXA+xYVlwhU+iYvtRlpupoBTqvSyyZRiIlas6hvrddc07+ONPKcw41mZXtF46nlK+g36FrvCgVRdSUSusKUEECgiAGk8OBGJJpETaLgHI2+MwyR8e0vHSGdXTCiRTSaRHRRBpyVWdNH663TfpBuCAImnXggiaDdF4ssYG53e6EtWgkXDWnYI04E39LnYPuWd/Fh1NuxZ3Ja/BE1U+Ab7+IdWc9hwviv8KtI/4M3L4LN41+CSfE/oSXLvoI+FkXLq/+N6ZGn8Qrl2zBp9ftweToMzjduhL4WSc2fHsPjos9g0sLXwBu/xT/N+E5fCH+S7x82p+Bq/+D58beizuS12HduFuAM7+P5xNn4/X0qbCMOQMoroHLJbmHArEEV+DGqng/+EICyVQasWRas11faCCshKSp19diEeCxs/BAredH76Vx2iywWuQqdYq9G5hHx2kTUClP4lH42tCBhA6RMxShUzEwj47ZCsqZvDMMJWzL9Bjd7J3OAPLvY/TAaIVJIIP3xaerkKbmxWTIu4lqhROQuaoMC4OLJVOIp9Ka13gsFgEFysJtCU07LIJUuadfaL4rETUlktCp7yADQBDE4KGUli52w6p0S/0VOlo7ol9802xfFjLFiyM28AaMeT9mFcH40Gu1EIzd9HW9h0kQBI19CunEgN52aYSbxQKXy4MIXPAnrQgmrUjABqfTCVisKHBJQlG1UdqQMP569S5UUqb5S3wVtBDnRWOiQ1mriInEDCFp+tB1fh0iHrZQuPSeCc05zSqzmiPfS6KI0XKF0UYqSDBkIKFD5IRwPKmsoTNhgB4ds0XX+szR0RUjiCZSiMsdtSF0Tef9UUpL2y2w6yq6MQ9SQBEmGXJv9IIog0dHH47Gh0dYLNprpF8ArjdRpD/G7PwDijsWRUyo8AJQc68IgiAGAza7Lg1Cs5s005dijiXVxTf1/TcLmQIku8MnwPP9snEdG6Nw0g74jR4k3itk9jofHaCKAavmtXAfldOCsZShWpl+0U+1IptV1y7V02R+7oSpYDQTaA6rRVk7SG/XM4Wk8Z6fVFpUoi08JgUG9LZcqbrW32IEyr0kYrQ8oUeV14YOJHSInMC8OaVeB4o9DgzMo2MMOWChY0V9hK7pPSWCYPSq6OvvZ1rHBjBWc1OLAfRe4CCQwQNlOF+GnB/NZ9KHwzltiss+U3uZFyjYhycsM6oBmFJVCADY2RLI8hwEQRADhw06R5e4s540y1SKGTBOFPEhZ+FYylTA8H/rF/Q0S6gP8efh3o/3CvVV8EAvKPRFE/TH8/mnfOlpaR/5WLmimd5bxIsoltdpJlSC3OfiJ/L4tXbMRIzBU5MhzMzLCSJ+sVf9dwEYK5Nm8hJlhnl0oHh0aCmFoQMJHSInaAsR4Mg8OlkIHZ/BoyJ7XhwmnhKnNsxMraSWuSP1R/vI0dF5XzKVjDaILLZfP6qoBXoRRZmOMYsR7xeC6tI/vloSOvvaQkjIoXMEQRCfNQdkezKm1INsJ830diTEJb/rbQLbDmhzazLlYipeCZMSyRohY9Jns4G9xnNkWKtHK1b0YkTvFWEig/e66EUQs3uiKOVu6l9XPj/XLo+ZJyqa1EQK6F8PcJ4oXsSwz5BIidJaPxnsGR/ixr4zq0WA02ayfp6ucBETRu5+e3TYL6J8jwEHKER7yEBCh8gJ+9t0QkcxTv0/BxMzbO0cAOgJ9+HRyeClMU3az2JfXwYPTOYCB9rcmEw5P3rh1NsCoHpRlCl8DzCG2vn7EIiZUT06o4rd8DqsiKfSysCDIAjis2aPHC47qbIg60kz/aRPppL/DKUgQdw8B4XfJxhLabwiZpXZzDwy/L6ZhBAvZvR5NGwhTDV0TReexnmDwsqaMtI2l90Cpu80r+tC1zSeJk6oFHKhb3oBpj++tzWI9O+RaUHvEBf65+GKHmj2zWDLzSYtzVEn9CZWFgAA9rZSiPZQgYQOkRN2HpbCmyZWSJ3GQDw6RR5pUB5JpBCV43OZR6c4w4BdHxKWKXQM0BqDVFrMOHsH8J4inUcnU01/QzhcJkEkhQ/05qVR44979yZpzq8z7t2K0MmyXCbn0bFYBEyWw9c+PUzhawRBfPaIoqgMOidVFiBbjw6b9AnKyfVM6GSa9FFCu3hviCGsSvXW8JXZMgqZmDGUSj1HynSwz4eIhXU5PKzYTDyVRiiWVIrTmOXo6L352uR9Y9gcH7oWNg3J4z1exs+lhq6lTHNqbVaL4pUJZhB5/Dl728d4rWQxGzFfOy8jXI7OJHnM0tgd0USTEMcuJHSInLCjSVom+YSRPnnLANbRcdiUmSfWcfU7RycmLR6mlqM2dpD8OQLRhNopm+boyB6YSFJT9SzT2jxGz495jo4oSvHEvX0uQxhaP/JtVI+RLHT68IRlRjUAAJTwtU8pT4cgiEGgxR9FKJ6CzSJgbFn2hW30Cz4rg+CM4c/qZFlfoWthztsAaCuzmXs2zIoRJE0nusxCxFSPjnqeFn/U0C41hNq8YIBZWBzbphEYJiHVLIeV91Tx11gJXYsmM07K8fk3gQzXmBeCZuvb8fAFe0RRVOxepu/YiDqhV+J1oEwuYb6fIheGBCR0iEEnFEtif4fUQUxjQofZpiw8OhaLoAzMu3VCJ1MHpjFq8aQye2cmChw2aSFQdt7eFiNVF/hU1w4AMq95w84ViJnPRLns2tr/vQod2bDEkmnEk2lOkPXm0dGGrnVH4gCAYk+WQofz6ABQChKQ0CEIYjBgxU/GlXu11TD7OWlmt1qUfI+eSEIJhc406aNOaiUyhq7xi17ya8mYVWYLckn9ZqFp4bi5oDILEWPva+eKAxyWq5t6HVbFpmgqtpkVQpDP3RGKKd4odo28LDcmnjS1iUysaQUYl5vEtdssh4c/XzCazDhx5+VymPx9VVvVVahLyR9qIB4dgHkOqfDOUIGEDjHobG/2QxSBykInygvYKtbZe3QAyBXbVI9EXx4dp80Cu1UVEL3lvvDn8Ucyz94BqkcoEE0qbSl0GauesfOxdmbK5REEgfPUJHrNoeHbE4gmMhoPHr0XiOU2ZQr5y4y5R2d7sz/L8xAEQWTPdjk6YNoINmmWfRg0G/D6I+qkUqb8DR83WcVEUcb8kXgqY9/NFyMw86qoYiml2AmfZp0dNUTMrKob+515dLReF7X/N6tAxn4/7I+p23Rr9IRiSdPQb0XIxM2rxRVw7c4UOm7qNcswachHW2ReKJxNRKoeO7tV6P+acdBO6LEJ2m1NPf08nsglJHSIQefDg10AgJljitWNAzBOgGo8usNxRBMpZfGyogyeCUlAqK717j4G+LwwCfTi/WFeFX80iZ5evCNsW084jmQqrdT+7zX3huuczYSO1SIo3pueSCLjYqWa9iqGXfbosOtwhB6dGTXFsAhSudemblpngCCIzxY22DSGQff/HGyiyh9NKN6BjKFrbPIrmsg4scZESCotoi0giQWDR6KPHBNeCAVMqnNqykvHjZ4T9jtbry6jGFHe27hGT4t8LF+Bjl8Q1KzdXgcnonTV3vjXeys0wBfjybQ2XpFbtXlMcGYSp17Oy6R8vy57/9eM03l0ThhZBADY1kQTekMBEjrEoFMrC51TxpRwWwfm0eGFCDM6FkFNxjSDT97vDDNRYp6E7+M6U3VWzSx0TT4n145ik8T+YpP28sdrz6nOavUVklfslbZ3heP9KkagL7Pd1/kzozUABU4bpo+SjMAH+zuzPBdBEER2bG1kQkfqdwZU2MatTvz0FRXAe8MzCh3O/jT3SBM++jzQ3hL++d+1nhNjUr+mvLSJoDjMPDomBQE0A3/uM7B9WwNM6PCeJkk0RBIpU++XtsiCiUeHq4CWqcgO8+j0RDJHKLDJzL4mIaXt6nv2FZpojnZCb/ooSVRvb/IrYXDEsQsJHWJQSadFVeiM5YTOAD06xVxnx7wSPrfddP0DBl84oFsWOqVec6FTxM3e9Vb5TJ3lS/bqHeE7586Q9N4+lw02q/FR5I1RX8a3VBZqXSE1zK23YgS8IQHUHKdMgi8jOo8OAJw+vhQAsHF/R3bnIgiCyIJWfxQNnREIAjCjRhY6A5g0U8PREn1W5PK5jKJIP0FksQiKIGiSvSKZFo8OaTwyJkIn3vt6NNI6O5nDz1oUj465N8jsM7D3YaFrZkUSpNeN5+aFjHnoGi90zEt5M1HYHoghkRIN7wFoJznV4gKZcnTUNfEU+5iN0NHn6FQUwOuwIhhLYhdVGD3mIaFDDCo7WwLoCMXhcVhx0uhi9QVRXmAy2xwdJXQtgfag1CmreT/mMFHTEYorYiNTyJZPE7qWuZoZn0/Tm3eEdc5pEajvDGva059zZhI6TKB0htXPVJbhvABQVsCugXTNephna6AeHVFdIPT08WUAgI37yKNDEMRnx2Z50uz4ap8qJJS+KAuhY+Jpz7joNDep1du+bHDf3B3RHKd/PVOOjRrilTL10rN9u8MJpcpngYnnpaUXMZJIiYrd1Ob/6EPX1GOdNgts8kQi81YVmhzLFzowL7KgeoT0Ioa1pbFbrRinL+GtETp9iFNefPWVg2WO1s7ZrBZlonbzAbJzxzokdIhBZd2eNgDSrL9Ds4LxQD066gCfddgVfQgdJgA6QzHF+9KXR6cnklBEQYnXTOiolc9a5ZhsM9HgtFmVSm6sNGUmL0oJJ8j69Oh4WVEGVehk+kwAUFEoXaOOYBzptMiF8A0wR4fj1PGlEARgX3sIrVxpU4IgiKPJxn2S13i2WXRAVh4d1cvfl3eg30VimNBRPDra85l6bDReF249GpNiBOz8jbKQEgTt8UxYsVxJMxEFqF4b/jOwz9ikCBl1f0EQlHM3mpy7kA9d66UsNgC0+ln+kt6jY2y7PkpDsc1hviJq38tK9JWDZYpJ5MLssVLkwvs0oXfMQ0KHGFRe33YYAHDWlArtC4pxyu6WZAP2Vn9MSfosL+xD6BSog/wueYBfkkFsaIWOtK+Zx4jvyA91SZ1zJtHAth+QS2yXZNhP8boE+xY67Jxd4QTag3HN8abn9kqfIZkWcagrgmhCmqmqLHRlPMYU9n1xBqDIbceJcp7OGztaszsfQRBEPxBFEW9/Kk2czZtczr8i/ZeFLVGXKYgr4czZhK6Ze3S0xQD0A2uNRyZp9MiwAjfxZFqZvDITDOy1IrddU+WThTMze8CLACsXWqd8Lrfx3GwiUG9LmM06bCJU2LFpEcqkHy9uzDxCBbq16Xw6odVbuHggphYAyiRO2fk0Ie79LS0NcPeSauc+J99za3e3IZlKmxxEHCuQ0CEGjZaeqBJq8IXp1bpXB1aMoMonDcxbA1GlQy/vZYAPqJ6O9mAcXaHeq40xr0xbQPX+mAkdvvJZgxySlkmUsO0H2qX9SjJ4Xphn6lBXuM9qckyodXLijYkZMxw2i9IOVrWo0GWDW2f8+kYbu8xg3++qrc1Zno8gCKJv9rYFUd8ZhsNqwZmTOKEzgHxPNjnWFogpg/NKn3n/yS+2zLwDZn0965NZiLJ+YM2EEL/uGr/QJ788gboAtTH8jFGqm6zT2xW9WMhUAMDsNf1EoD5agBdRHodVMeNJOVGfD6MWBEFpe6a16ZiIOdiR2Uayay6KQFO3sbIcD7PZPZGE4iWq6GNCVIvRo3NyTTFKPHb4o0llXEMcm5DQIQaNF2sbAACnjivBiCK39sUBFiOo8hk9On11YEwINXSFFQOSKcyLCamdLVIZSYuQOY+FddaHuqTO2azqGqB20Cx0LZM3ic2isTVp3HZrxkVAmSHY3xFSqsD0FroGqNeJlchknzUrFJ2jFToXnTgSAPDe3nZF+BEEQRwt/rWlCQBw5qQyjcdgIJNmzJNd3xlRhEdFBu8262vbuER5M6GjnxDTexv0Ics+l02z4KnFIhj6cLMcHfV82jboIwUMa/24tF4Wl91YXlo9l7Yd+rbrQ9v4463cwt4M/efSt10vCs0mL502q7IODguhy2Sbiz12OORr+4li77IQOoJxQs9qEXD+1CoA6r1IHJuQ0CEGhVgyhec21gMAvnnaGJM9BubRYQaqLRhTSmH2XYxAen1PaxCA5N1w2809GZXy4L+hM6Icm6miG5tN6it0jM0ess45kyBhHhkWCldd5MpY95/N5u2WK8AUumy6HCiTduiEVGVWM1wMc4/OmDIPPjepHKIIPPv+wQGclyAIwpxEKo2/1x4CAHz5lNHaFwcwaca8NzvkvtBps2RMVtfngNpMwsAA4+Bc720ocNo0x1WaTDTxnpAitx1Om9bjw6O3I/q/9WKDnzTTh9Xp99V7VPTeI70w4ScbS70Og83UX0N9yLS+PZnybvXtrC4yF6eCICht2qHYu2wm9oweHQD48sxRAID/fNyk5FkRxx4kdIhB4S8fNKC5J4oqnxNfPHGEcYcBenTKCxwQBGlhtk9bpEF+n8UIClgxAkmQjCp2ZxQQ+o6zt7A4/YzdqBK36X6jirXbM4XN6YVSb0JkRLHUzq5ewuv0sBnLT+R1KAbm0TE3AABwzefGAwCe3XCQihIQBHHU+M/HTWjqiaK8wIEF06p0rw7Eo6PtL6t8mSeVHDaLxg5UFDpN99VHFph5EPg+18xu8f24/niPw6YRK3ovi94Lo4+i4L1gfQmGUl0BnmLd3/owvypORJhV/+RFnVnItP77yBSlwW+3WoRe7Z6+jVlN7Clfr9bOnTGhDBPKvQhEk3hBnsgljj1I6BCfOU3dEfz69U8BALecO0njIlcZmEfHZrUonRuLra4pNRcYDL1BqSn19Hvf3jrSap0h0QuaTNsz7ad/70yzVQAwRvcZ+spTAoDRshDrKya9d8w9OgBwznEVmDmmGJFECj/91ycQTcQQQRBENoRiSTzwqmRP/ufM8UZ7MoBJM/1Auq9BMC9QakrM7YfeVowqNu7Hv69Z/8tPdplNRI3kbEdfHh29/eDDy/TeqxG6fQ05Otzf5QUOw3fAv5eZzeSvr9m1ZhN3vZ0D0F77igKnphhDb+8JZGvv2ISedqvFIuCGsycAAH731m6l8itxbDEgobNixQqMHz8eLpcLs2bNwtq1a3vd/91338WsWbPgcrkwYcIEPProowNqLDH0aA/GcM3TmxGIJnHS6CJcfvpY8x2PYBBcw3lO7FYBY8u8ve4/qtitxPYCwJhehJHDZtHMSPVmAMeXq+9b6LJlTIwcqRM2E8oLTPcr8TqU6jRA7x6XMq9DEwYxqbIw476MyZXa9x2dwWD3Si8eHUEQcM+l02GzCHht22Hc898dSNMq0sRnCNmm4U0ylcYP/voRmnqiGFXsxnfOHG+yV/aTZk6bVZPT0tcguJrri0dnsB/84NxuFUxtB9+nm73OF5Qx6/95QaAXI/pwM7144Sf49BNlRW67JpxbL5r4cxvybaG9fmYh3LzAM/tcTptV48EqLzSfuOM/Q1UvE4GANlRNEPoX9aA5AIDZhN7XZtVg2ggf/NEkbnn+Q0QTqf6flxgUshY6K1euxK233oo777wTdXV1mDdvHhYuXIj6enO33f79+/HFL34R8+bNQ11dHe644w5873vfw9///vcjbjxx7BKJp/DXTQ244ME12NHsR3mBAw9ffkovMy4D8+gAUEoZA5LY4BM6zbBYBEzmhIC+k9fDd8TTRvoy7jexQhU6mbw0+tccVkvGEDe71YIpVWo7exNZgiBoPsdxVebiiWeyTgzN4K5j/8lsAADghJFFuPuS6QCAP67bjyuf/AAf1neRd4c46pBtGt5saejGt57YiFe3tcBuFfDbb55sXiVygGHQ/ERPX5M+/KA60778YH5ksds0t5Pv083Cs7QeHePr/KSZPkRMn0fj1RUYOI6zLVOqtbZAELQFBPQiqkwjdIwCgxeCZtU/+/LoAFo7WVFgLmJGc7azug9xqt3X1ec4QUvmCT2rRcBD3zgZHocV7+/rxCUPv4f1e9vJxh1DZLM0LABg2bJluOaaa3DttdcCAJYvX47XXnsNjzzyCO6//37D/o8++ijGjBmD5cuXAwCmTp2KzZs349e//jW++tWvHlnr+0FXWzN2vfWsZlt/bj/9TdqvY8xP1I/36sd5+vVe+j+Ne/Xr0dOfpx8HiQAiiRRC0SS6I3E09USQTIlYCKCq2IVFp9Wgcu9BYG+GE7RslX/JXujMGF0MQEp41w/eMzGpsgBb5dyUvoTO7HElSsL+yTXFGffjPTq9hcPxwsZlt/Tqbp9Q4VXeexa/KJ4JY0o92CnnKekNlxkTK7Wer+NH9O/aaWDC9JOXgPoNprtcbgFOOL0HL314CKn9Il56DFjttKGqyIUSjwNOuwUOqxV2q6AMBvgrIgCGGHhBvxPRJ8fP/w6KSsr73nGIMtRs056P16NjxzoA5v0ys0GZul9R3dHkWJP9zI7l/uDtRV/2xcwmmB1t3o7e28sTS6bRE0mguSeK7nAckwFMc1hw2ewaTG1tAsyW6eqWqntmO2k2d1KZYhPmTizrdV8+ZKomw0QVbwNYPqgeXryYeTYmVqgTVmbJ8/w4Ze4kbZv7WirgOM5GHG9iL1q4vEr9xN3scaXK7x0mn43/LBMqjBEW/OuZIhVS3D0x3uQcgP576N2O8yXITxtf2sueJrB7afdrQI9x4mQygFVzwnj+g3qE25NY9eRLWOuyobrIjTJm47j1gyAIivli9i1fbZrVVYjZX/rfz/Q9shI68XgctbW1+PGPf6zZvmDBAqxfv970mA0bNmDBggWabRdccAH++Mc/IpFIwG43hvfEYjHEYmqso9/vz6aZGjpbDuL0HfcO+HhigFig+gujANb08zhb9gnxs8eVQBAkY/mVU0b1+5h/1DVifLkXZ0+p7HXfS2eOwjMbJCF1wsjMXo9JlQUodNkQTaRww1kTMu5X5Lbj6rnj8NT6AybrCWmZNbYE//lYWoumN5EFAFefOQ6vbz8Mp82CaSMye54YHocNC6dX45VPWnDquBJNRZ9+w76vtb/udbeTAJxkBcDeIg2gS/4hBoWGmRcMW6EzFG1T20evYc7e5QM+Pu/gv44P+7G/Lbucw7kTy/HYu/sASEnmvbHo1Br8s64Ru1sDmDnGfAKqwGnDDy84Dg+89imuOMM8ZPuiGSPx7q42lHmdOO94ox1aMK0KX581Gqu2NmOOifhaMK0aL3zQgBNG+kw9Sw8uOgm3rfwIX5s12vDaZM7rP6nCKHRuPHsiHn13L5YsPN7gjSpy23HucRV4+9M2fOPUGsOxs8aWoNhjx6njSnHZbOPr0vbRqO8M46smbQOAS04aiY8aunH13HEZIyROGOWDyy7l6V595jjTfRi8Tezr+zXA7NymJzLuMg7AHYB6n6YAdMo/REaaUQEcS0Knvb0dqVQKVVXaKidVVVVoaWkxPaalpcV0/2Qyifb2dowYYazAdf/99+PnP/95Nk3LiLuwBB8WnGXYfrSEs+E8/TixcJTefQBRXvL7D2Qn41H6LTaLAKfNAqfdCp/LBq/Tlt0ndRYCM7+dzREAgLFlXvzlujNQ4nVoQr1647LZNRhT6sEpY0r6nPk6ZUwJfvXVGSjy2Hvd1+OwYdX35sFmFUzjlnnuungavjZrtOlsF8+3Th+LQDSJz0+tzFgFiDF3Yjne+sHZiCRShgo8mXj48lOwZlfbwLw5AHDBfcAnL2aVY5USRfREEgjFUogkUkilReVHFM38kCqi4Reiv9R4BxKaODQYirbJVT0FH7ZwtknQ/NcnQsY/2Kb+nam3bsX0JZM37uudBMMvfbyHjNUiwGW3wuOwosSjzVns/Q0FYMY3+revzFmTy/GjLxyH8WXeDAVzVEq9Dvz3e59DVzjR67ptN587CQumVWXMGx1Z7MZz156R8XiLRcADXz8Jv/jqDFPP/znHVeD5607XhG/zfHnmaBxf7TONMPA4bFi+6GQEY0mMKTO+fuv5k3HRjBGYnuHcj3x7FjYf6DIVYFU+F2p/Mj9jtILDZsGvvnaS6WuMK+eMxZmTyjGllzDsykIX1v/48/A6rX1O1FksAp75zmnYfKATX88grjJy7h3A5ieBdP/yb1JpycYFYylEEkmk0iKSaRFpUQREo/kSlX/yj4SrFCZ1eI8qWYeuAcYwElEUex2Eme1vtp2xZMkSLF68WPnb7/ejpsY4K9AfRo47DiNvf3lAxxJDh9OznKGxWy2YN7mi3/tfZjJrZUZvIWs8giBkNCA8DpsF3/v85H6dEwAmVPSdm8NjtQg412Qmsd9M+5L0k817AiiVfwjiaDKUbNPM+d8C5n9rQMcSRx9BEHDTOZP6vb/NaulzcWoAmNzPybfeyCQYBEHA3Im9e2mn9uLdv3Rm5ggIl93aq41y2a343OTM791bSHZ/sFktmvC6TPS1MDbPWVMqcNaU/tt9hfFnST/9hGzcsUVWQqe8vBxWq9UwQ9ba2mqYGWNUV1eb7m+z2VBWZj44dTqdcDoHUuqWIAiCyDfINhEEQRBmZFV1zeFwYNasWVi9erVm++rVqzF37lzTY+bMmWPY//XXX8fs2bNNY6AJgiAIIhvINhEEQRBmZF1eevHixXjiiSfw5JNPYseOHbjttttQX1+PG2+8EYDk2r/yyiuV/W+88UYcPHgQixcvxo4dO/Dkk0/ij3/8I26//faj9ykIgiCIvIZsE0EQBKEn6xydRYsWoaOjA3fffTeam5sxffp0rFq1CmPHSlVFmpubNesWjB8/HqtWrcJtt92G3//+9xg5ciR++9vfDkr5ToIgCCI/INtEEARB6BHEIbCqkd/vR1FREXp6euDz9V02lyAIgjg6UP+bGbo2BEEQuaG//e+Aqq4NNkyLHcmaBQRBEET2sH53CMyJDTpkmwiCIHJDf23TkBA6gYC02vtAy3gSBEEQR0YgEEBR0fBdi2cgkG0iCILILX3ZpiERupZOp9HU1ITCwsI+F03MNWxdhYaGhrwOZaDroELXQoWuhcpQuRaiKCIQCGDkyJGwWLKuXzOsGSq2aajca4MBXQsVuhYqdC1Uhsq16K9tGhIeHYvFgtGjs1zJNsf4fL5j+gYZLOg6qNC1UKFroTIUrgV5cswZarZpKNxrgwVdCxW6Fip0LVSGwrXoj22i6TmCIAiCIAiCIIYdJHQIgiAIgiAIghh2kNA5yjidTtx1111wOp25bkpOoeugQtdCha6FCl0LYrCge02FroUKXQsVuhYqw+1aDIliBARBEARBEARBENlAHh2CIAiCIAiCIIYdJHQIgiAIgiAIghh2kNAhCIIgCIIgCGLYQUKHIAiCIAiCIIhhBwmdo8S9996LuXPnwuPxoLi42HSf+vp6XHzxxfB6vSgvL8f3vvc9xOPxwW1ojhg3bhwEQdD8/PjHP851swaFFStWYPz48XC5XJg1axbWrl2b6yYNOkuXLjV8/9XV1blu1qCwZs0aXHzxxRg5ciQEQcA///lPzeuiKGLp0qUYOXIk3G43zjnnHGzbti03jSWGHWSbMkN2Kb/tEpC/timf7BIJnaNEPB7H17/+dfzv//6v6eupVAoXXnghQqEQ1q1bh7/85S/4+9//jh/84AeD3NLccffdd6O5uVn5+clPfpLrJn3mrFy5ErfeeivuvPNO1NXVYd68eVi4cCHq6+tz3bRB54QTTtB8/1u3bs11kwaFUCiEk046CQ8//LDp67/61a+wbNkyPPzww9i0aROqq6sxf/58BAKBQW4pMRwh29Q7ZJfy2y4B+Wmb8souicRR5U9/+pNYVFRk2L5q1SrRYrGIjY2NyrYXXnhBdDqdYk9PzyC2MDeMHTtWfPDBB3PdjEHntNNOE2+88UbNtuOPP1788Y9/nKMW5Ya77rpLPOmkk3LdjJwDQPzHP/6h/J1Op8Xq6mrxF7/4hbItGo2KRUVF4qOPPpqDFhLDFbJNRsguqeSjXRJFsk2iOPztEnl0BokNGzZg+vTpGDlypLLtggsuQCwWQ21tbQ5bNnj88pe/RFlZGU4++WTce++9wz40Ih6Po7a2FgsWLNBsX7BgAdavX5+jVuWO3bt3Y+TIkRg/fjy+8Y1vYN++fbluUs7Zv38/WlpaNPeI0+nE2WefnZf3CDH45LttIrskka92CSDbpGe42SVbrhuQL7S0tKCqqkqzraSkBA6HAy0tLTlq1eDx/e9/H6eccgpKSkrwwQcfYMmSJdi/fz+eeOKJXDftM6O9vR2pVMrwvVdVVeXFd85z+umn45lnnsGUKVNw+PBh3HPPPZg7dy62bduGsrKyXDcvZ7D7wOweOXjwYC6aROQZ+WybyC6p5KNdAsg2mTHc7BJ5dHrBLElN/7N58+Z+n08QBMM2URRNtw8Fsrk+t912G84++2zMmDED1157LR599FH88Y9/REdHR44/xWeP/vsdyt/5QFm4cCG++tWv4sQTT8T555+P//73vwCAp59+OsctOzage4TIBrJNmSG71D+oz5Eg25SZ4XKPkEenF2655RZ84xvf6HWfcePG9etc1dXV2Lhxo2ZbV1cXEomEQTUPFY7k+pxxxhkAgD179gzbWZPy8nJYrVbDLFlra+uQ/c6PFl6vFyeeeCJ2796d66bkFFbdp6WlBSNGjFC20z1C9AbZpsyQXeodsku9Q7Zp+NklEjq9UF5ejvLy8qNyrjlz5uDee+9Fc3OzcuO8/vrrcDqdmDVr1lF5j8HmSK5PXV0dAGgeouGGw+HArFmzsHr1anz5y19Wtq9evRqXXHJJDluWe2KxGHbs2IF58+bluik5Zfz48aiursbq1asxc+ZMAFIM/bvvvotf/vKXOW4dcaxCtikzZJd6h+xS75BtGn52iYTOUaK+vh6dnZ2or69HKpXCli1bAACTJk1CQUEBFixYgGnTpuGKK67AAw88gM7OTtx+++247rrr4PP5ctv4z5gNGzbg/fffx7nnnouioiJs2rQJt912G770pS9hzJgxuW7eZ8rixYtxxRVXYPbs2ZgzZw4ef/xx1NfX48Ybb8x10waV22+/HRdffDHGjBmD1tZW3HPPPfD7/bjqqqty3bTPnGAwiD179ih/79+/H1u2bEFpaSnGjBmDW2+9Fffddx8mT56MyZMn47777oPH48Hll1+ew1YTwwWyTeaQXSK7BOSvbcoru5TLkm/DiauuukoEYPh5++23lX0OHjwoXnjhhaLb7RZLS0vFW265RYxGo7lr9CBRW1srnn766WJRUZHocrnE4447TrzrrrvEUCiU66YNCr///e/FsWPHig6HQzzllFPEd999N9dNGnQWLVokjhgxQrTb7eLIkSPFr3zlK+K2bdty3axB4e233zbtG6666ipRFKVSnnfddZdYXV0tOp1O8ayzzhK3bt2a20YTwwayTeaQXSK7JIr5a5vyyS4JoiiKgyutCIIgCIIgCIIgPluo6hpBEARBEARBEMMOEjoEQRAEQRAEQQw7SOgQBEEQBEEQBDHsIKFDEARBEARBEMSwg4QOQRAEQRAEQRDDDhI6BEEQBEEQBEEMO0joEARBEARBEAQx7CChQxAEQRAEQRDEsIOEDkEQBEEQBEEQww4SOgRBEARBEARBDDtI6BAEQRAEQRAEMewgoUMQBEEQBEEQxLCDhA5BEARBEARBEMMOW64b0B/S6TSamppQWFgIQRBy3RyCIIi8QRRFBAIBjBw5EhYLzY3xkG0iCILIDf21TUNC6DQ1NaGmpibXzSAIgshbGhoaMHr06Fw345iCbBNBEERu6cs2DQmhU1hYCED6MD6fL8etIQiCyB/8fj9qamqUfphQIdtEEASRG/prm4aE0GEhAT6fj4wJQRBEDqDQLCNkmwiCIHJLX7aJAq4JgiAIgiAIghh2kNAhCIIgCIIgCGLYQUKHIAiCIAiCIIhhx5DI0SGITKRSKSQSiVw3Y9hgt9thtVpz3QyCIIghSzqdRjwez3UzhhVkm4iBQkInX2j8EPjwaeC8nwLe8ly35ogRRREtLS3o7u7OdVOGHcXFxaiurh4eyed73gA+fRVYcA9gd+W6NQQxtDhUC9Q9M2zsxmAQj8exf/9+pNPpXDdl2DGsbNNnTTwMrP4pMPViYMI5uW5NTiGhky/84Vzp/1A78I3nctuWowATOZWVlfB4PNTxHQVEUUQ4HEZraysAYMSIETlu0VHgz1+V/i8aBXzutty2hSCGGk+cJ/0f6QYuezqnTRkKiKKI5uZmWK1W1NTU0AK7R4lhaZs+a9b+Btj0hPSztCfXrckpJHTyjdYduW7BEZNKpRSRU1ZWluvmDCvcbjcAoLW1FZWVlcMnVKCnMdctIIihS9unuW7BkCCZTCIcDmPkyJHweDy5bs6wYtjaps+Kzn25bsExw4CmG1asWIHx48fD5XJh1qxZWLt2bb+Oe++992Cz2XDyyScP5G2Jo4E49N3pLCeHDMlnA7uuwyr3SaCZVYIYMGIq1y0YEqRS0nVyOBw5bsnwZFjaps8KemYVsrb+K1euxK233oo777wTdXV1mDdvHhYuXIj6+vpej+vp6cGVV16Jz3/+8wNuLHEUGAZCh0Hhap8Nw/K6ktAhiIGTpkFTNgzLPvQYgK5rFtAzq5C19V+2bBmuueYaXHvttZg6dSqWL1+OmpoaPPLII70ed8MNN+Dyyy/HnDlzBtxY4iggirluAUEMPiR0CGLgDKMJMoLIC2isp5CV9Y/H46itrcWCBQs02xcsWID169dnPO5Pf/oT9u7di7vuuqtf7xOLxeD3+zU/xFGC3JlEPkIzgQQxcMhuEMTQgp5ZhayETnt7O1KpFKqqqjTbq6qq0NLSYnrM7t278eMf/xjPPfccbLb+1T64//77UVRUpPzU1NRk00yiN2hmbtjw0Ucf4Zvf/CZqamrgdrsxdepUPPTQQ5p9Dhw4AEEQDD+vvvpqjlqdIyyUuEoQA4Zmh4kB0NHRgdGjR0MQBMNSEFu3bsXZZ58Nt9uNUaNG4e6774ZI99nRg8Z6CgOquqaPkxRF0TR2MpVK4fLLL8fPf/5zTJkypd/nX7JkCRYvXqz87ff7SewcLejmHzbU1taioqICf/7zn1FTU4P169fj+uuvh9VqxS233KLZ94033sAJJ5yg/F1aWjrYzc0tFLpGEAOH4v2JAXDNNddgxowZaGzUVr30+/2YP38+zj33XGzatAm7du3C1VdfDa/Xix/84Ac5au0wg55ZhayETnl5OaxWq8F709raavDyAEAgEMDmzZtRV1enDLzS6TREUYTNZsPrr7+O8847z3Cc0+mE0+nMpmlEfyGhk1POOecczJgxAy6XC0888QQcDgduvPFGLF26NOtzfec739H8PWHCBGzYsAEvvfSSQeiUlZWhurr6SJo+xKHQNYIYMGQ3hjVH0y4xHnnkEXR3d+NnP/sZXnnlFc1rzz33HKLRKJ566ik4nU5Mnz4du3btwrJly7B48WIqOnA0oGdWISuh43A4MGvWLKxevRpf/vKXle2rV6/GJZdcYtjf5/Nh69atmm0rVqzAW2+9hRdffBHjx48fYLOJATMMb35RFBFJ5Gb2wm23Zt0pP/3001i8eDE2btyIDRs24Oqrr8aZZ56J+fPnY+HChX2Waw8Ggxlf6+npMfXWfOlLX0I0GsXkyZNx22234Wtf+1pWbR7ykEeHIAbOMLQbg8FQsk1H0y5t374dd999NzZu3Ih9+4zruWzYsAFnn322ZkL7ggsuwJIlS3DgwAEaGx4N6JlVyDp0bfHixbjiiiswe/ZszJkzB48//jjq6+tx4403ApDCzhobG/HMM8/AYrFg+vTpmuMrKyvhcrkM24lBYhje/JFECtN+9lpO3nv73RfA48juMZoxY4ZSmGPy5Ml4+OGH8eabb2L+/Pl44oknEIlEBtSWDRs24K9//Sv++9//KtsKCgqwbNkynHnmmbBYLPj3v/+NRYsW4emnn8a3v/3tAb3PkISEDkEMnGFoNwaDoWSbjpZdisVi+OY3v4kHHngAY8aMMRU6LS0tGDdunGYbiwpqaWkhoXM0oGdWIWuhs2jRInR0dODuu+9Gc3Mzpk+fjlWrVmHs2LEAgObm5j7X1CFyCN38OWfGjBmav0eMGIHW1lYAwKhRowZ0zm3btuGSSy7Bz372M8yfP1/ZXl5ejttuu035e/bs2ejq6sKvfvUrEjoEQfQPquA07DladmnJkiWYOnVqn/bFLNfbbDsxQGispzCgYgQ33XQTbrrpJtPXnnrqqV6PXbp06RHFfRJHyDCsauK2W7H97gty9t7ZYrfbNX8LgoB0WuqUBhK6tn37dpx33nm47rrr8JOf/KTP9z/jjDPwxBNPZNnqIQ5VXSOIgZOmQdNAGEq26WjZpbfeegtbt27Fiy++CEAVMOXl5bjzzjvx85//HNXV1aa53gBM872JAUDFCBQGJHSIIcwwVPmCIGQdPnaskm3o2rZt23Deeefhqquuwr333tuvY+rq6jBixIiBNnFoQrOEBDFwhqHdGAyGi23Kxi79/e9/1+y7adMmfOc738HatWsxceJEAMCcOXNwxx13IB6Pw+FwAABef/11jBw50hDSRgwQemYVhv4TSGQH3fzHNNmECGzbtg3nnnsuFixYgMWLFyszZFarFRUVFQCkBFO73Y6ZM2fCYrHg5Zdfxm9/+1v88pe//Ezaf8xCoWt5wYoVK/DAAw+gubkZJ5xwApYvX4558+aZ7rtu3Tr8v//3/7Bz506Ew2GMHTsWN9xwgybUk5Ch0LW8Jhu7xMQMo729HQAwdepUFBcXA4Cy7MjVV1+NO+64A7t378Z9992Hn/3sZxS6drSgZ1aBhE6+QUJn2PC3v/0NbW1teO655/Dcc88p28eOHYsDBw4of99zzz04ePAgrFYrpkyZgieffDK/8nMAEjp5wMqVK3HrrbdixYoVOPPMM/HYY49h4cKF2L59O8aMGWPY3+v14pZbbsGMGTPg9Xqxbt063HDDDfB6vbj++utz8AmOYchuEEeRoqIirF69GjfffDNmz56NkpISLF68WLN+InGE0DOrIIhDYClav9+PoqIi9PT0wOfz5bo5Q5OlRdL/Fjvws/bctuUIiUaj2L9/P8aPHw+Xy5Xr5gw7htX1Zff9/LuBM7+f27YMUYZK/3v66afjlFNOwSOPPKJsmzp1Ki699FLcf//9/TrHV77yFXi9Xjz77LP92n+oXJsBM4zsxmAwrPrOYxC6vlnw6Dyg5WPp96U9uW3LZ0R/+1+a5sw3SOUT+QI/hyNQMYLhTDweR21tLRYsWKDZvmDBAqxfv75f56irq8P69etx9tlnZ9wnFovB7/drfvICshsEMbQ49n0YgwYJnXyDDBaRL/BVZyh0bVjT3t6OVCplqNhUVVVlqO6kZ/To0XA6nZg9ezZuvvlmXHvttRn3vf/++1FUVKT81NTUHJX2H/NQvD9BDC3omVUg6593kMon8gSRhE6+YbY2R1/JzWvXrsXmzZvx6KOPYvny5XjhhRcy7rtkyRL09PQoPw0NDUel3QRBEEcVKi+tQMUICIIYnpBHJ28oLy+H1Wo1XZujr3U52CrsJ554Ig4fPoylS5fim9/8pum+TqcTTqfz6DSaIAjis4KidxTI+hNDliFQR2NIMmyuq8ajQyVLhzMOhwOzZs3C6tWrNdtXr16NuXPn9vs8oigiFosd7eYRecaw6UOPMei6ZgGFrimQR4cYcrAVnMPhMNxud45bM/wIh8MAjCtlDznSSfV3CxUjGO4sXrwYV1xxBWbPno05c+bg8ccfR319PW688UYAUthZY2MjnnnmGQDA73//e4wZMwbHH388AGldnV//+tf47ne/m7PPQAxtrFapn4nH42SbPgOGjW0aDMijo0BChxhyWK1WFBcXo7W1FQDg8XhokbGjgCiKCIfDaG1tRXFxsWK0hyxprqOn0LVhz6JFi9DR0YG7774bzc3NmD59OlatWoWxY8cCAJqbm1FfX6/sn06nsWTJEuzfvx82mw0TJ07EL37xC9xwww25+gjEEMdms8Hj8aCtrQ12ux0WC/U7R4NhZ5sGgzQJHQYJHWJIUl1dDQCK2CGOHsXFxcr1HdKQ6z7vuOmmm3DTTTeZvvbUU09p/v7ud79L3hviqCIIAkaMGIH9+/fj4MGDuW7OsGPY2KbBgDw6CiR0iCEJMyiVlZVIJBK5bs6wwW63D5/ZMr4YAcV2EwQxCDgcDkyePBnxeDzXTRlWDCvbNBjQRJ8CCR1iSGO1WqnzI8zRdPQkdAiCGBwsFgtcLleum0HkM+TRUaAAUoIghid8MQLy6BAEQRD5Aq2jo0BChyCI4UmaPDoEQRBEHkKhawokdAiCGJ7wrnvy6BAEQRD5AoWuKZDQIQhieEKue4IgCCIfofLSCiR0CIIYnohUdY0gCILIQ8ijo0BChyCI4QlfjIBydAiCIIh8gXJ0FEjoEAQxPKF1dAiCIIh8hDw6CiR0CIIYnmg6ehI6BEEQRJ5AOaoKJHQIghieaDw6NLtFEARB5Alk8xRI6BAEMTyhYgQEQRBEXkI2j0FChyCI4QktGEoQR4ZgzXULCIIgjggSOgRBDE/4qmvk0SGI7BFoiEAQxNCGejGCIIYnInl0COKIsJBHhyCIoQ0JnXyBZuaIfINfGZo8OgSRPWQ3CIIY4lAvli+QwSLyDfLoEMSRQTk6BEEMcQY0+l2xYgXGjx8Pl8uFWbNmYe3atRn3XbduHc4880yUlZXB7Xbj+OOPx4MPPjjgBhMDhIQOkW/QgqEEcWRYyG4QBDG0sWV7wMqVK3HrrbdixYoVOPPMM/HYY49h4cKF2L59O8aMGWPY3+v14pZbbsGMGTPg9Xqxbt063HDDDfB6vbj++uuPyocg+gEJHSLf4IsRkEeHILKHtxvpNAkfgiCGHFn3WsuWLcM111yDa6+9FlOnTsXy5ctRU1ODRx55xHT/mTNn4pvf/CZOOOEEjBs3Dt/+9rdxwQUX9OoFIj4DKASByDdoHR2CODJ4u6GZOCAIghgaZCV04vE4amtrsWDBAs32BQsWYP369f06R11dHdavX4+zzz474z6xWAx+v1/zQxwh5NEh8g2+GAF5dAgie3i7ocl5IwiCGBpkNfptb29HKpVCVVWVZntVVRVaWlp6PXb06NFwOp2YPXs2br75Zlx77bUZ973//vtRVFSk/NTU1GTTTMIMEjpEvqHx6OSuGQQxZLGQR4cgiKHNgEa/giBo/hZF0bBNz9q1a7F582Y8+uijWL58OV544YWM+y5ZsgQ9PT3KT0NDw0CaSfDw349mppsghilpqrpGEEeEJkeHhA5BEEOPrIoRlJeXw2q1Grw3ra2tBi+PnvHjxwMATjzxRBw+fBhLly7FN7/5TdN9nU4nnE5nNk0j+kJvsCyO3LWFIAYDfmBGOToEkT2aHB0KXSOIIQHZOw1ZeXQcDgdmzZqF1atXa7avXr0ac+fO7fd5RFFELBbL5q2JI4UPQaBYayIfoHV0COLokSSbTRBDglQi1y04psi6vPTixYtxxRVXYPbs2ZgzZw4ef/xx1NfX48YbbwQghZ01NjbimWeeAQD8/ve/x5gxY3D88ccDkNbV+fWvf43vfve7R/FjEH2i8eiQ0CHyAFpHhyCOEO65SUZz1wyCIPqP5lntPa0kH8ha6CxatAgdHR24++670dzcjOnTp2PVqlUYO3YsAKC5uRn19fXK/ul0GkuWLMH+/fths9kwceJE/OIXv8ANN9xw9D4F0TdUPYfIN0SqukYQR4RIQocghhz8s2q1564dxwhZCx0AuOmmm3DTTTeZvvbUU09p/v7ud79L3ptjAfLoEPkGeXQI4gghoUMQQw56VjVQzeF8gYQOkW9Qjg5BHBkajw7l6BDEkIB/VmmSj4RO3sDf7GlKVCPygFRc/Z06e4IYAOTRIYghh+ZZJdtHQidvIINF5BmaGWjq7Akia0w8Ot3hODqC5N0hiGOJnnAC7ey5JI+OBhI6+QKFIBD5Bi/oqbMniAGgnSDzRxNY+NBazH9wDfxRigwgiGOBZCqNC3+3FucvexeH/VHy6OggoZM3kEeHyDPIo0MQR4ZuguzJdfvR3BNFZyiO9/d25K5dBEEofHSoB4e6IugOJ/C7t3bTJJ8OEjr5Anl0iHyDOnuCOEK0E2Tv71PFzXoSOgRxTLB+T7vy+8Z9nTTJp4OETt5AQofIM5JcMQLq7Akie3QTZPvbQ8qfHx3qHvz2EARh4OPGHuX3gx1hpBMUtcNDQidfII8OkW+QR4cgjhD1uYlHwzjsV21Hq5/sCEEcCxz2q7Yunkqjyx/Q7pDn9o+ETr7ArxJPOTpEPqCpPJPOvB9BEOZwz41+8NQaiCKdzu8BFEEcC/BCBwA6uv3aHfLc/pHQyRvIo0PkGSToCeLI4GaCA8EgAOCk0UUAgERKRFc4bnoYQRCDQyotoi0gjelmjikGAHQHyKPDQ0InXxCp6hqRZ9BaAnnHihUrMH78eLhcLsyaNQtr167NuO9LL72E+fPno6KiAj6fD3PmzMFrr702iK0dCqjPTTQSBgCMLvWgzOsAAE0oG0EQg09HMIa0CFgE4ISRPgBANBzS7ZXf9o+ETt5AQofIM2gtgbxi5cqVuPXWW3HnnXeirq4O8+bNw8KFC1FfX2+6/5o1azB//nysWrUKtbW1OPfcc3HxxRejrq5ukFt+DMM9NvGYJHQqCpyo9LkAAIcDZEsIIpewyYbyAieq5ecyGg1rd8rziT4SOvkCFSMg8g3y6OQVy5YtwzXXXINrr70WU6dOxfLly1FTU4NHHnnEdP/ly5fjRz/6EU499VRMnjwZ9913HyZPnoyXX355kFt+LKM+N4lYBABQUehElc8JAGj1k9AhiFzC8nOqfC5UFErPZSIa0e2V3/aPhE7eQB4dIs8gj07eEI/HUVtbiwULFmi2L1iwAOvXr+/XOdLpNAKBAEpLSzPuE4vF4Pf7NT/DGm6CIBWXnqfKQifKvNKAqjOUyEmzCIKQ6JTz5Eq9DlQWSh4dNimhkOcTfSR08gX+PiePDpEPkEcnb2hvb0cqlUJVVZVme1VVFVpaWvp1jt/85jcIhUK47LLLMu5z//33o6ioSPmpqak5onYf+6jPjSivzVFR6ITPbQMA+KMkdAgil/gj0jNY5LYrHp1Ugjw6PCR08gby6BB5Bnl08g5BEDR/i6Jo2GbGCy+8gKVLl2LlypWorKzMuN+SJUvQ09Oj/DQ0NBxxm49puAkCMckJHZcdgDrIIggiN/ijSQCAz21ThI6oXzA0zyf6SOjkCyY5Oq9sbcYZ972J5W/sylGjCOLoEImn8MWH1uKyRzeguUeezSKPTt5QXl4Oq9Vq8N60trYavDx6Vq5ciWuuuQZ//etfcf755/e6r9PphM/n0/wMb9TnxpLiPTqS0OkhoUMQOYVNNvhcdpR5HRAEwAl92ff8tn8kdPIGrUcnmkjhf5/7EC3+KFa8sxcpWviNGMKs39uO7c1+fHCgEw+89qm0kTw6eYPD4cCsWbOwevVqzfbVq1dj7ty5GY974YUXcPXVV+P555/HhRde+Fk3c+jBTRB4ID1PxW4HimShw2aTCYLIDSx8tMhth81qgc9lhwe69IQ8n+iz5boBxCCh8+hsbexR/own0/iksQcn1RQPfrsI4iiwZleb8vumA53S/Z4ij04+sXjxYlxxxRWYPXs25syZg8cffxz19fW48cYbAUhhZ42NjXjmmWcASCLnyiuvxEMPPYQzzjhD8Qa53W4UFRXl7HMcW6jPTSEi8DqscNgs8LnkHB3y6BBETlE8OvLkQ7HHjoIA5ejwkEcnb+Bu9FQMHx7s0ry66UDnILeHII4emw6o93NDZwRt3bqVofO8o88HFi1ahOXLl+Puu+/GySefjDVr1mDVqlUYO3YsAKC5uVmzps5jjz2GZDKJm2++GSNGjFB+vv/97+fqIxx7cBMEXiGqeHJ8ikeHhA5B5BJ/RM7RkfPmit12FICqrvGQRydf6MWjAwCHuvQzAAQxdGjokhZIEwTpVt/e0Iqz+R3yvKPPF2666SbcdNNNpq899dRTmr/feeedz75BQx71uSlABEUeBwCooWvk0SGInMKHrgFAscdhFDp5PtFHHp28QZujU98pDQzPmlIBgIQOMXTpiSQQkHMF5k2W7ufm9m7dXvnd0RPEgOAmCAqEKIpd0pBB8ehEkhBpEoEgcoYauib5LYo9dngFqrrGQ0InX+Bv9EREETpzJpQBABq7SegQQ5NGWaSXeh04vroQAHC4U+uxzPeOniAGhva5qXKlAEDJ0Ymn0ogl04PeKoIgJJTy0lzoWiF5dDSQ0MkbuBWuo0F0h6VZgDMmSKuAH5JDfwhiqMFE+qhiN2pKPQCAzq4O3V753dETxIDQTRBUOqSytQVOGyzy8kQUvkYQuSGVFhGMSUKnUJ58KHUJcAq6ZzLPJ/pI6OQL3I2eikiz3WVeB6ZUSTPggWiSEkuJIUmjLNJHl7hRU+IGAAR6dMU18ryjJ4iBoX1uymWhIwgCPA5pYBWKpwa9VQRBAJGE+ux5ndLzWOHQr6FDkNDJG7gVruNBAMDoUg+8ThsK5QekLRAzPZIgjmXagtJ9W+VzKR6dkL9btxcJHYLIGnmCICFIRQhK7aqNcDusAIBwnNbSIYhcwJ49QQCcNmk4X26XhE4cDnXHPJ/oI6GTL3A3ui0hCZ0RPhcAoLRAeiC6QjQTQAw9OkOSJ7LU60C1fE/bkiHtTvndzxPEAJEenLDFCwAosao2wqsIHfLoEEQuiMjPnsduhSBIsaTFNmkyIiR4uD3z2wCS0Mkb1Bvdmo7DgQSqfE4AQIlcMrSDhA4xBOkMSR17idcBr9MGj8OKAoGSMQniaBGCNGgqtqjVnNxy6BoJHYLIDezZY88ioD6jQbjVHcmjQ+QFuhvdiwgq5dnvMi95dIihSxfz6MiCvaLQiQLoimvkeUdPEFnDPTNs0FTICR3m0YlQ6BpB5AQmdDzyswgARVZp4s+fdnF75rf9G5DQWbFiBcaPHw+Xy4VZs2Zh7dq1Gfd96aWXMH/+fFRUVMDn82HOnDl47bXXBtxgYqBob/QCIYIqWeiUeMmjQwxdOmSPTql8H1cUOFFIHh2CODI4odOdloUO1JBQlqMTipFHhyByQcRE6BSI0jPqT7shQi6NmOcTfVkLnZUrV+LWW2/FnXfeibq6OsybNw8LFy5EfX296f5r1qzB/PnzsWrVKtTW1uLcc8/FxRdfjLq6uiNuPDEABOkrL0BUCV0jjw4xlOkKqzk6AFBe4IQX8syzfL/ne0dPENmjPjNtqQIAgCflV7axwVU4QUKHIHIBq7rmsqtCx52Uqup2okCqUgAg3yf6shY6y5YtwzXXXINrr70WU6dOxfLly1FTU4NHHnnEdP/ly5fjRz/6EU499VRMnjwZ9913HyZPnoyXX375iBtP9BN+kOf0AQAKYPTodIZJ6BBDi1RaRLd835Z4pQXTpNA12aMj3+/53tETRNZwdqMtLS1D4E50K9u8LEcnRqFrBJELWNU13qNjiUhLK3SJhQB5dABkKXTi8Thqa2uxYMECzfYFCxZg/fr1/TpHOp1GIBBAaWlpxn1isRj8fr/mhzgCuJtcZEJHiKCiQPLosNyGTvLoEEOMnkgCafn2LuFydJTQNZcsdPK8oyeI7FGfmU5Reo7ssS5lm5uqrhFETjELXUNYWiy7E4Vq6FqeT/RlJXTa29uRSqVQVVWl2V5VVYWWlpZ+neM3v/kNQqEQLrvssoz73H///SgqKlJ+ampqsmkmYUC9yZMOaWauyBJBkVuaAS+h0DViiNIle3MKnTbYrVJ3pvXoFMl75ndHTxBZw00OdEKyG4I8iALUwVWEQtcIIieYVV1jQqdLLFRD1/J8om9AxQgEJe5PQhRFwzYzXnjhBSxduhQrV65EZWVlxv2WLFmCnp4e5aehoWEgzSQYYlr5NW6TYq0rHQlYLNJ35nNJD0kgSiEIxNDCH5Hyc3yyaAekYgReg0cnrT+UIIje4J6ZdlGeMIioHh2PPLgKUegaQeQENsng4XJ0IIeudYqcRyfP7Z+t711UysvLYbVaDd6b1tZWg5dHz8qVK3HNNdfgb3/7G84///xe93U6nXA6ndk0jegNTs1HrD54AVTZ1apUbJDoJ6FDDDHYPasROoVOeFh1KHeJ9H+ez2gRRPbwoWuSRwdmHh0KXSOInMBydNwmoWvdFLqmkJVHx+FwYNasWVi9erVm++rVqzF37tyMx73wwgu4+uqr8fzzz+PCCy8cWEuJI4BbD8FWDACotgWVbYWyR8cfTQxqqwjiSAnI9yy7hwFJ6JQKUl6f6CmXt+Z3R08QWWMSuoZwh7Ld46QFQwkil6iha7zQ4T06Mnk+0ZeVRwcAFi9ejCuuuAKzZ8/GnDlz8Pjjj6O+vh433ngjACnsrLGxEc888wwASeRceeWVeOihh3DGGWco3iC3242ioqKM70McRfj1ECBd83KrKnTYbHg8mUY0kdKUKiSIYxl/RPbouFSPTpnHCjuk+zvqLJWWOszzjp4gssdYjACpOBALAC6fEi4TogVDCSInRPWha6Ko5uiQR0cha6GzaNEidHR04O6770ZzczOmT5+OVatWYezYsQCA5uZmzZo6jz32GJLJJG6++WbcfPPNyvarrroKTz311JF/AqIfqDd5BySDVQK1kl2BwwZBkJ6RQDRJQocYMjAvpM+tdmXORAAQpHs+YPHJa7rnd0dPEFnDTQ6E4UTM4oYzHQGCrZLQodA1gsgpBo9OtAdISmvItYs+9RHO84m+rIUOANx000246aabTF/Ti5d33nlnIG9BHE349RBSUgiCL60KHYtFQIHThkA0CX80gYpCyo8ihgYsdI336CDcDgDoET3wxwVUAnnf0RNE9nDLEkBAyFkJZ+QgEGgCyidR6BpB5JiwUl5aHsoHmgEAcbsP0agTafLoABhg1TViqKHe5E1JqepaQapbswcbKFLlNWIooYauGctrdog+hJRBWH539ASRNbrJgYhLLjgUkMLPPco6OmQzCCIXGNbRkYVOzFMNAJSjI0NCJx/gbvLGmBcA4OJWuAa4ymsRKkhADB3U0DXOoxOSPDpdKEQwJgudPO/oCSJ7tB6dpFcaPMHfBABw22nBUILIJWySQUk38EtCJyU/q2mx72Vf8gESOnmBarD2Rz0AAFsyDCSiyvZCWkuHGIKw+7VQ49GRhE6nxqNDEERWiFqhIxYwj440mPJS6BpB5JSwwaMjTUIIvhEAyKPDIKGTD3A3eUPYhpgoDwpDrcp2FrpGJaaJoYSyYCifoxNsAyAlY5JHhyAGiqj5TSgaKf0he3T40DUxw/PVGoji2Q0HEEuSGCKIbEilRbzwQT0aOsMZ91Gqrjm0Hh2r/KyqHp38tn8kdPIC9SbviaZwWJQXUZQNFqDmOARI6BBDCObRKeA9OvKsVotYqgqdPO/oCSJrdB4de/Fo6Y+eQwDUwVVaBGJJ85XXb1u5BT/91zb89J+ffLZtJYhhxm/f3I0lL23FVX/6IOM+hqpr/kYAgLO0BgB5dBgkdPIBncFqQZn0h/xQAGoYgjowJIhjn2BMFjpOTuj0SPd1M0oRIo8OQRwxIgS4KidKf3QdAMBVekLm8LX39kiFQf66+dBn2j6CGG78+f2DAIB9baGM+0T0Vdc69wMA7OXj4bRZaB0dGRI6eYE2BKHTKq8Wz3l0FKFDOTrEEIItVqgROn7Oo0NV1whiYIhau+GpkoVOpBOI9sBqEeCwSUMIs8pr+nA2ihYgiP6RTovoCMWVv1mIGo8oigjzoWvpNNAtiSOUjEeR204eHRkSOvmAzqPjt1dIf/SoHp0Cp7zKdYyEDjF0YPerRyN0ZI+OWEY5OgQxYNRnxmW3wVVQDHhl2yF7dby9LBrayQ3UAKCpO2rYhyAII11h7bNTb5KnE0+lkUpLz6jLbgWCLdJioYIVKKqRhQ55dAASOnmHCAEhFysTygsd2aNDayIQQ4RYMoVESurAC5jrPh4Cot0AgGaxVJnxyveOniCyhpscKHI7pF9Kxkn/yyEyLGTGrLrh/nZtyE23bvBGEIQ53bplPva1BQ378JMLHodVeSZRXANYbVqhk+cTfSR08gFdCELcK1fP6WlQtrPQNfLoEEOFEJdP5pU9kixRWnQUIix4qKMniAGjPjPFHrmqYakcvtaxB0Dvi4Ye9sc0f3eFKXSNIPqDflKgNRAz7BORJ/HsVgF2q0V5JlE6AYD0zGpHfvkLCZ28QBu6ligaK/3RsU8ZABaQ0CGGGOxeddossFnlrqxzHwBAKB2PEo8DIpXXJIiBIduGtCioC/JWHCf937YTACd0TIrY9OhmpcmjQxD9oyukfXZ6TCYJlIprbLFQ+ZlExfEA2CLaNNEHkNDJDzQ3uQCUjJd+jfUA4U4A/a+6drAjhF2HA59FKwlCIZpIofZgV68JzKaFCDr2Sv+XTUSp10HJmAQxYETl32ImdCqnSv+3SoMqVtY2bJIsrV+TTR+OQxCEOfocHbP1DQ0V11p3SP/LQodydFRI6OQF2pu8yOcDfKOkPzqlgaEqdDIbo12HAzj7gXew4ME1+NeWxoz7EcSRcsOztfjqI+tx+R82ZtyHeXS8vNCR72eUTkBZgYM6eoIYKCITOoIauiYPotD+KZBKwisPsiImoWt6j45+8EYQhDndOg+O/lkCVI+Oslgo8+jIkxHFbproY5DQyQdYCII86Cv1OpU4TjYDroauZfbo1NV3cb93fwYNJQiJd3e1AQC2NvZkXFWdeR+9Zh6d0oko8zopR4cgBowqdIqYR6d4LOAoAFJxoG2n4tExsxt+eXBmt0rPYHeIPDoE0R/YpIDNIj07/ohxIoHlxbnsViDUDgSapRcUj46NJvpkSOjkBarBAoBSrwMonyy9JM8CsJXlg73k6PAlDhtMyh0SxNFAH498qCtiul9IWSzUqm5s+1T6v3yyNnQtzzt6gsgakQtd88hV1ywWYNQp0u+Nm5XZ5IhJ6BqbhR5T6gFAHh2C6C+scMeYMunZMfPoRHiPTlOdtLFsMuDyAQCKPFR1jUFCJx/gDBYAlBc4gKoTpD9atwNQy/PGk2kkUmnT09R3qgPOTINPgjhSGrq0ItpsDQFAFeVKjHKoQ1pLAAAqp2pD1/K8oyeI7FEnyJRiBAAw+lTp/4ZNSiK02YKGbHA2tswLwDxHJ5UW8dN/foJrn96EZAa7QxDDDVEUsfivW/D9v9SZRiz0RKRJgbGlmYWOUoyAFzojZyqva0LX8nyij4ROXiAbLJHz6FRNl146vA0AV54XmSuvaTw6XWHDytcEcTQ4pBM6mbyHqkeHJWNK9zJKxgHOQpR5HQC57gliYCj9u4ASDy90TpP+P7QJLqW8tFkxAun5rClxS3+bDNae2XAAz75/EG/saMWuw8a1QghiONIWiOGlDxvxry1NeOiN3YbXA+zZkYWOaTGCBOfRObRJ2sgJHR+to6NAQicf4Dw6giCHIbDqOf5GINwJm9UCp026HdhDpocfcIbjKcPK1wRxNGjo1HoL6zt6FzqKSG/5RPq/UvJWlnqdlIxJEANGtRslLHQNAEbPlv5v/xTFgvSsmoWuMWEzotidcZ8PuVzP9qBxrRCCGI60cff6loZuw+vMto0okp6d3kLXCuwADq6XNo47U3mdqq6pkNDJC9QQhBKPA1aLALiKpHhOAGj4AABXkMCkgk4ylTYImzYyTMRngP6+yjQAYquxK8UIGmul/+VZLW3VNYIgssKs6hoAeMuVYjZjI5IXNWri0WGDsxFFLgDmBQu6OJtCQofIF9qD6n1vNmHMPKTs2QlEk0ilRdN9JiV3A/Eg4C4Bqk5UXi/iwk3TaRI6xHCHC0GQwnlkxpwh/V8vzQZ4e1k0lJ9RGCsnyOlLIBLE0YAtLDiujCUxm99nhtC1xs3S/6NnAQDKvJSjk2+sWLEC48ePh8vlwqxZs7B27dqM+zY3N+Pyyy/HcccdB4vFgltvvXXwGjoEEEUpZ4ZNkGmoOR0AMKZHeubMQtfYGlhVPmmwZlaCupOEDpGHtAfUe92sSAd7ntizAxgLRYUT0t/Hh+X8nHHzpGIhMkVuu5KuEM7zheBJ6OQDssFKQ5Dycxhj50r/178PQB0wmi0aygabhS6bIpYyCZ2DHSFTdyxBAEAilcabOw6bJjAD6n01rlxOYs5QrSnIr6MTbAO6DgAQgFGS0Cn1OpSS6mmx94VwiaHPypUrceutt+LOO+9EXV0d5s2bh4ULF6K+vt50/1gshoqKCtx555046aSTBrm1xz4heU21tJnQmTwfADCmfQ0AY1iaVNRGmlyoKHQCkBYV1ed18s92W8AodFJpkXJBiSGNWZENPmqhK5ww3OOsdHSxxw6H1aLZxmChaxOD8gTf+LM0rztsFogCS0fI70kEEjp5gRqCUFZg4tFp/BBIRLi1dIzqnxmkEo9DKTXKKoPouei363Dp79/Dzhb/0foAxDDi7pe345qnN+PBN3aZvs6qM42TqzX15dHxOm3AAXnmvnKaFJYJKRdNECShQxWdhj/Lli3DNddcg2uvvRZTp07F8uXLUVNTg0ceecR0/3HjxuGhhx7ClVdeiaKiokFu7bFPQPHiC8p6OQoTPw9YbPAF92GMcNggdHgbwoSOKALRhPY57AzzHh1daHQghln3rMYtz9eR2CGGJD/71yeY8fPXsa9NW2iD9+jEk2mDR5T97XXY4HGytaqShn28iGBkYKu0YfzZhve3yPYv1MtC8PkACZ18gCtGoPHolIwHCqqBdAJo/FBJ6jZbS4cNNks8dhTLsZ9mCXLtwRgC8vGvftJyND8FMUx49v2DAIDH3t1n+jpLYh5fzoSOuaBmMf8FTiuwX5pZxgS1s7daBHhk8U5CZ3gTj8dRW1uLBQsWaLYvWLAA69evP2rvE4vF4Pf7NT/DFWUiSzDJc3MXA2PmAADOt3yozC4zWJ6n02ZRliPe5jcAAG63SURBVC7gtwPSjDQvfPShax/Wd6E7nMB/tzZj9fbDR/JRCGLQ+bC+C89sOIhwPIW1u9s1r+nvdT6EM50WNaWjvQ7zxdwjiRQ+b/kQNjEOlE5U10bkEOQFR0MZCkzlCyR08gLOo+N1qpsFARgrGSvse1vJ0QmaPBRssFnscaBITkw1C13b1RJQfv9gf+dRaT0xfGjpiSq/syp/evSha4Fo0lSoKOvo2K3AnjeljTr3fYFTuleTKQpdG860t7cjlUqhqqpKs72qqgotLUdvwuX+++9HUVGR8lNTU3PUzn2swXt0TDluIQDgAusmg0cnzBUKsVgEZWHRMDdY69RNYOg9OnxYW219V9btJ4hcUntAvWf1k8cdugIE/GQe/yx5nVZlAlrv0YnEU7jYukH6Y/pXTSckBDl0LUgeHWLYI2YIXQOAKZKxwo6X+xm6ZkexW87RMfHo7OSEzsEMZYGJ/GV/e0j5PZZMo8dELHfrFkuTthn3Y/dpVWgn0FMP2D0G932Biwkd8ujkA4LO2IuiaNh2JCxZsgQ9PT3KT0NDw1E797GGvzePDgBMuwQiBJxu2YnS6CHNS0Fd6XdF6CRU29KlG+zp7Q4vfPRr8HzU0I0rn/wA25uGr0eNGBo0dIZx1ZMfYJ3Oa8NHvHQEe7/XeY8OH8bmslmVBbFDOq+pEO3C2ZaPpD+mf9W0bRbZoxM0WYcnnyChk0eIACoKnNqNUy4ALHagbSfGpiVjFTSpjsNC14o9DqXUqNkgdS8Xi9oejJnGVm860IkXaw8ZthPDg65QHCve2WN6f3SEtC77PbrY5WhCDWcpK3DA55I6ebOCBEoJzqbV0obJ8wGHR7NPIQmdvKC8vBxWq9XgvWltbTV4eY4Ep9MJn8+n+RmusEUKMwrFotEI10ge1AsSb2heYp4bFnbjMQm/0UcE6JOt+cGhft9bV27Bml1tuPyJ9/v1WQjis+KWF+rw7q42XPnkRs12jdDR2T19Tg5/f7PnwOOwwmIRMk5Azw68A4eQQrBoClB5vGnbLMyjQ0KHGPZw5aXLC3VCx10MTDgHAHBiQEroNvfosBwdh1KfvdukGAE/MxEzSbITRRFff3QDbv/bR9iwt2MAH4Y41rn5+Q/xq1c/xQ/+9pHhNf2aAfpZXWYcrHIHXyLnlJkVJJBmjUWUHHxF2jD1S4Z9yKOTHzgcDsyaNQurV6/WbF+9ejXmzp2bo1YNbZhHpzePWGT6twAAF6XfBlKq3QhxgzX+fz6Xh3l9qnySTdLnIHRyg0N9Pmi9vHg1LXFA5JqP5Aqz+qVq+CgEvd1jzwcr1MGHtrExk0eZJLBqjgEAiCK+GPk3AKB18qKMbbPK5ab1HtF8g4ROXqAWIzB4dABg6sUAgGkdrwEQTRd2Yw9KkdvWa46OPnFc77Jt8as5Gh8f6u7vByCGEOtlAfvGDmMCsf5+0N8v7J7yuWwQBEER1fqOWhRFhGJJTBf2w9G9D7A6gMnaRHRAFTqpNOXoDHcWL16MJ554Ak8++SR27NiB2267DfX19bjxxhsBSGFnV155peaYLVu2YMuWLQgGg2hra8OWLVuwffv2XDT/mCPInrlehI44ZSHaRR+qhC6IW/+mbGez0izv02ywFtYN9iKJlGZRRD6PQW9r+LBWvix1MJbEfz5uMniHCOJIiSVTWLW1WTM5l2mJBEArzvX5Z0zws/FYKGZ8LtgzY7q+4d63MDbdgIDoRuD4yzK2gYWuBaLmBX3yBRI6eUA4Lj1wIgTFqGiYdglg96I0tBenCzsRMClGwMIYCl12JZzIrDqb3iDpXbY7mtWY6k+5fB5GKJbE8xvrTc9NHDt80tiDN0wqIcWSRg8ej35mS3+/sKRJnyxwCuV7TX9PxpJpJNMirrTKM/jTLgFcxjAiCl3LHxYtWoTly5fj7rvvxsknn4w1a9Zg1apVGDt2LABpgVD9mjozZ87EzJkzUVtbi+effx4zZ87EF7/4xVw0/5jDH+3bo+PxePBkUsrzFNcuA9LScxbUha6xwRrv0QnpBnuANhGbHxzqPTr8ALOhS80F/dO6/bjl+TpcsHyNZjX4dFrEtqYe6geIPmH3SkJ3r1z+h4246bkP8dCbu5VtrX51fOOwWTT2roebxOvQVVljk8lsPBYy9egwoWPVHANRBN5bDgB4MXUWXAUlGT+LVV6DJ0Aeneyh1aeHFuoMhKAYHA3uYmCGNCtwpe0109A1NtAsdNmUSla9VWdjtlE/sOWTR7eZJJLe/rePcMc/tuKOl7b2+pmI3HLR79bh2mc2K257xu7D2pybZq7KGmAUvnqPjn6AVCjfawFdjHEolkQxAviSVS4dfOp1pu0sdEmhbyka4OQFN910Ew4cOIBYLIba2lqcdZZahe+pp57CO++8o9lfFEXDz4EDBwa30ccozIvKKjeZ4bJb8WxqPvyiB5aOXcD2fwBQV2Jna4C47SYeHXmfEq8DVotxBfdMoWuiKGoWXOTt0NbGHgBAQ2cE27lJtT+s3YcLf7sOv1ltvnYXQTCe3nAAF/52HX75yk5lW3NPBLUHpSpq7+9TQ+4DXDWzeDINP3cv9uhC15gISqdFRdBXMqHDTwDEdEJHtoWKl3Lf28D+NYiLNjyR/KKynxksdE1vP/ONrIUOrT499OhiBqO36kOnSQPFCyybURAxFgpgHpYCly3jLLsoikouxaSKAgDGUKUmbuCrryUPAK/Ia+/8+6Mmw2uptEienkFEFEXFk8fDf28f6sq+tum+06buiOZvdj9MqpTuD4PQiar3GaB6dPy6ey0US+Fy65twCQmg+kSg5jTTz1DgZqFrJHQIIhtYArOlF7thtQiI2QrwR9mrg9VLgUREGbixRGo2wcaXlw7xiyI6jGu48fYlGEsqM+zd4QQSKdF0P95/zIe+3S8PWh95Z28vn5gggJ+/LIWuPrFuv7KNH8fwwkI/BmoLqOMbPkcnyYkb3mtZ6cscuubVPTvBWApIp4A3lgIAnk3NRyMq4LL3Q+hkWNw9X8ha6AzG6tP5tCjbYNAtC51ey6xWnYDuEfNgE9L4WuDPhpfZjIDPZVcGofFUWhOqFEmkEE9KxmiiLHTadTP4fK5FdyShcfWm9Nl8Om5+7kPMuf9N1FPZ6kHhT+8dwIylr+P1bdpKVrsOqyGHe1q1Hhx9dTR9EQHm4ZtYIS8GGjIPXWMDJBZ6pjcoYX87brD9R/pjznczinifi4QOQQwEFtfPFh3MhMdhxWOpi5AoGCmVeX/vIWXgxhKq3ay8NDdzzXt91Flr6XV+0UQGsx36yRR+tprvf3hbw8Kt9Wxr6sGPXvwIe1qNYdTE8KaxO4IfvfgRNh3oe70/v+YeU3/X26VWOV8snRYNeaVMxDOvpiAApd7eihHoSrPHk8CmJ4DmjyA6C/H75CWa181goWvBWMK0Am6+kJXQGazVp/NpUbbBoEsROr1/3R2n/wgAMD/5DtC6Q/MaH7rm5Va65sMG2KDWYbVgVIkbgDG2mp+ZT6VFzd/8GivSvtpjX93WgkA0iV+9tlOzPZlKY/HKLXj0XZqty5ZQLInrn9mMv23WrgciiiLu/o80s/Wb17XhHnx42idyqAhDL1z0wofdD2wx0Eyha6rQYd5D7Xl9Hz6CIiGM/cIY4MSvZfx8Po8UupZOi4b8IYIgMhPoR+gaIIWlReFE82l3ShvW/BpFPZL9KHCy8BtusCaj8ejoFkWMcs+qTRZabIZcHw7NDzb5QShvP8q5PCBW9t4fTeDC367DXzcfwrMbDiqvh+NJXPHHjbj/Fa0NJIYuj767F197ZL3m3nmp9hD+uvkQvv7oBjT3SJEHmXK4/BHuHovwQsd8Ii8YTypV2Byy2GAhacyr6bFbUejUCnzpd+0kAbOFzmAj8Obd0rnm/QSdkHJS3f3w6OjHWvlGVkJnsFafzqdF2QYDlqNj6WNmzjp6Fl5JnQoLROC/tyuJpcmUWia60GWH1SIohoufiWDvU+yxZwxv03cM/EC4NaDN59jfpgof3mht1Q2u1+1px0t1jfjFKztNB7OUgCoJF7Pr8Ni7e/H69sP44Ysfa7bz8e3lhdpFZvdxa98c9mtnV/ULexqLDUj3wxi5apLh9ajWbW96H7XvRvW2PwAA/lxwJWDJ3NGzfDIBoiZxlCCIzMSTaUTkAVdvoWuAOtBqGb0QOP4iIJ3A1w7eDTeicCsend4GdEaPDhsUCoIqUpgI0ldUC8SMk22AdpKNL16wt13qv3hvNB9S/af3DmDt7nY89u4+zft0huKGiZ13d7UZthGDx57WAF4ziTho9WvHEr94ZSc2H+zC//1HrajIewY/aZTsXVO3epzdKiheEL/Oa8gKXehD6dn9y+yYw2pBiVeyQer9Kwsdp40LS+vFo+O0wYYkrj18DxAPAjVnoGvqtwEALrul13EdW0dHgGiYIMgnBlSM4LNefTqfFmUbDLrC/fPoeJ023Jv8NsKiEzi4Dqh7BoD2IWQDzwKTASgzLMUeuzILoS9YoHfn9uYG5gfNjV1qrkd7QDtg5cuL7mrRhlKt3FSP6Utfw191Hov6jjCufPIDbNa5rdNpEZ809igheMcqrf4oDnUZQ/geemM3fvrPTzQVhwDgyic/wDm/fgcNndpj+AU7+SozfIffqfPS8IMJ/VpKeg8O/3qKC0cZXeIxPZ659dl9xqqvKYYmnQZe/j4s6QTeSZ2ET7xnojdYvyTAKKQJgjCnPRgDs+iCpQ+PDvPWJFLAxQ8B3kqMjB/AMvsjKHBIZ/GalJdmYsbrtBnKTyt5Cpy3Ry+CGGzyTBRF9ET40LWksp0f1DI7w9uiGNffr+aqSTI7sL89hDPuexMX/W4ddrZIg+LG7giuevIDXPS7dZr+9uWPmnDzcx9q7ObBjhAO+6n/6S8dwZgmnDAhR208v1GbC37+sjW44dla1Mm5oof9UXxh+Rqcdt+b2KIrlANAI4r4sQm7F/jiAomU6gXh75W0qIprQ0i1Tsy4HVaDmOEFvnpv91J1zW7BnbbnMCWxA3AWAV95DOGEKO9jHpKpILD/RE1xj3wjK6EzWKtPE0cXFk7Ul0enwGnDIbECv0nKoUCv3gG07VIeZpfdArvshjXLnQhoSlCbV8vSu0+7MsRUA9pBMy90QvGUxnNzoEP1/Hzc2K2eOxTH//v7VkQTaby4WVtg4ZqnN2HNrjZ843HtytorNzfgot+twz3/1a6lcbAjhG898T7W7GrTbBdFER/s7zziqib720MaTwnj3v9ux53/2KqJr02nRXzuV2/jc798WzPTFE2k8OAbu/Ds+wdRx3XysWQKa3e341BXBD98UbuIZws3k8mLIL9GZGrFkXamNK2ZLeXXwQG0oog3/COLXADMPH5yMQLZOPj0gvq9B4GD7yFpdeMnye+gUBZCGVGEjoiWnvzt6AkiG6TJI6nPEdA/j040kQK85cCiZ5GAHQutm3DKnt8DkGalAW15aY1HR1esgIkZt8bbk8GjE2W5DylNkQLWN/ZEtMUL2AA3U4UsvtgKm4j5Z10j4vJE0IF2qT9s6VFt0j4u7Pq7L9Thv1ubsXJTg3Lusx94B6ff92afeRKxZMowyVbfETbkrx6LE3H6NqXTIg52hDSfOZlK97r2DOOcX7+D85etUWzSu5+24aW6RtzB2UJ+PRsW9t7QGVZCxlg4Nh/JwHsU+e+c3Sv6vDA2iZppbKIPr2fhmKpQtyq2LBRLavbxOGzca5lD1ybtfQr/Y3tNevGSh4GScUpBg97C1iTUiT59Yah8IiuhQ6tPD026I/0oRgDZDSoAf0otRGzMPCARAv56JYJ+qZwiEzeAOhA1q5JT2EtlNiYIxpYZQ5f0IojvXJp6tNW7+OOY4QG0a/Pw6yvoP/puOWwhqTMg98iu7We4mG0A+NGLH+O9PR248skPNNuffO8ALntsg1KphdHcE8H/e/Fj1B7UeowefXcvHn5rt6bzjyVTOPfX7+C837yrxI8DUiz5H9bux3Mb6zWGtKknohiVHVyJbt7Dw69XxHdw+lCzXVy+DS8Y+Q7cH01qE3578cox4TpezsHpMRE6DpsFpV4pHC4c1y4SyPbxGooRJIB97wBv3QMAWD/lRzgkVpiXS9fAvniRZlQJop+0BWIQWA2zvkLX5JlnpZrUmDPwu4LvAQAm73ocWPsbeJTy0vyATs3RyTTr7XVYuWTs3j06XSHzfMA2XQRASJmN5/o4rk/TDIbDqlhS9pWP4/M2WPhaQDfxBGgnkBrlKpSJVBovf9SEt3YeVmxBNJHCeb9+F196eJ2y7bVtLTjrgbfxk39+opxj2epdmPHz17CtSXpPURTx/b/U4bsv1GlEwE3P1eLtna3KcXX1XVjy0lZNCNNfPqjHH9aoIXqReAo//ecnWLe7Xdm2+UAnbny2VmNf7vrXJ7j6Tx8ofXdjdwSn/N9q3PkPdVmIh97cjbMfeAd/5rwwV/9pE864/01NG9bvacc/6g4pIjgcTyrjBuaViXNipaFTuoafNKkhg6wdervF/6/ft0eTayOLEF0oGosCME7QJjTHMVQxzoWnObT3doS7t/WvAarY9zqtQN1zGFt7PwDgt9YrgWlf0ryPu5dCBAA0E30dFLrWf2j16aFHt5Kj0/vXLQgCCpw2pGFB8+d/BxRUA207MOqVa+BEXBEvgBpaFIwZO4sCp83U4xNPphFNSB0Wy9HgPTp6rwjfEenXY+GP4wfomWK0+dCF3mbD4hnyeT461G26ncX8vlireoxEUcTZD7yDlZsb8KtXP1XbE07gF6/sxK9f36Xp/A9znob396s1+us5A7mLE3B80Ya9XB4TMwAANG77Vs7Q89ctnkxrOlheMPJGHIBGJBhmt7hwESZ6zIoNsJnUQqdNCX3ktwOqoSnU5ehUhvcCK68AxDRw0uWoLbkQgCq4M8KFrpHQIYj+0RqIcX6c/nl0InG17/yPcBYeSMgrtr95N07aswKAqFknR5m5dloNxQr4WW9F6MS0s+XsfZmNMRS+iahFB3hY2BHfx/F9Gt8fsUmdgEmYEz9YZ3mjO5rVfprpQ/5YVsjlvx8347sv1OE7T23G+/ukybAN+zrQ2B3BzpaAMlD+hVwW+4UPVHvx2zd3I5pI44HXJNvSEYrjX1ua8PJHTUpf/+Abu7Bqawv+56lNynFfXrEeL3xQj3v/KxVZiCVT+PFLW3Hvqh2KGPvD2n149v2D+PYfNyrHfe3RDXh1WwuWyGvbJVNpPL3hIN75tE0JGXt6/QEEY0k8x9k1trDmTzmRtm5PO7rDCcXbsvtwAJc/sRG3rfwIz22UJhf53Cl2DfnvhAkcPleX2Rn+O2XjCX04NQuP9JsIXaOINoau8e/HR7vwx5t5K0Nm3koWusY9F6x9M5teAP51EwDgieRC/CF1kbJPRBfelhl1oo9ydLKAVp8eWoiiqDzolj5ydAB14Oi3lgDf+ivg9MF3eCMetv8OJU7jfnwHxAbNhS67abUs/neWo8ELE/3gWjOLpu9ouLwR/gHWHqOej5/Va9CFYrF2i6KoCXHgZ3eYQGP7AZnLYbcFY4qY2s112nyOCF+yuZnzVvEzaQc7VRHDFwc4wAkdvtQzP+PGvy//2bvDCcWVrx8Y8NdRPzjg99Uf122SszOujAkd3qMjl4522eC0WeGwyTX+Y8ZBBu/RmSocxEPxu4CYHxh7JnDRg4Z1OjKjzmiR0CGI/jEQj46molosid+nLkXLqf8PADBpx++xzP4IkrEwtw+/jo48GGSz+opn16qEvelFULUc/hrMkC/BZuGDusEr69f5Pq5HXuogmkhpJru6lZl7o6eAn8RhfSzL3wFUDxPfr7L+mu+r2e/buIG7mcDSw8wPX2SFteNAL0swbJXDu3m7wGb7eXuih4m0di5CgH0X+tBqM/iQNWafDnEh6ex3PsqAXbtO7lqzaAW+/SyP1K8Zb0jXTh+BYCaM2XEhXVik2b3Cb2drTVX7pHtRuUe5RT/ZWEhfTIP3ZIbiKeW6xWIx/MT2LE7d+YD02inX497ktxCKJZXrrOQA9RW6JlDoGjDAYgS0+vTQoTMURzIlPRTWPnJ0AGhDCEacBHzjeaQsDsy31uL/Aj8DolJnrAgiU6HDha5xYsHPzegXe4w5PKwzYbP53RnyOwC9J8g81lrf6bGOVl/pixkafYgD8xTpB/Zs1owfOFsEtYPnRZjTpj5ivFeJN368t4o3NLxHhw9F29/OCxo+VE81Gj0mRpjBOn5j6e/MZTP5xF523KhiqYR4t4lYZR47v0l4gFI62iz8kVuYFgBKOuvwF8f/oUzwQ6yeAXzjOcDuUhew7bdHRzSE7REEYU5bMKoKnT48OmxWmR/IMu9L9PTvA1/8NUTBiq9Y1+GX/h8B7XukfeKqmNHPbGs8OrqwN7ZPlbzYIutX9Lk7rO8Jx8wHr3wfl5QLpWSyM315dNh789vY4JsfpDNvhTa3Vfq9rr5b2cYmJ/mICUAbjWCX7flhbgKN2STe1OvzgpgO4ftDVqWM31UvWNg5Wzi7x2wLHxZvthA4oLU3u2U75zex/3vbjEKHD0tk9oZffJa93hM22jC9RydoInSUe0h/r8j3nN5Wsvdm90ulLHTY/hHu/mX3dkAROiyszaqxX+FECvA340eHf4Rrba9IG8/7KdLz74UIC9KiWjQjW48OFSMghjVN3VG1ek4/PDpevadm/Dy8cfJDCIouTIt9BDz5BaB9txKaps3RkWfsudCkYCypdJjMQPBCyKzyyWh5kGzWETGYAUqlRU0b+AG+vnPKlFjYLFcY69R1iGyGqUPXcTMBwg/w06K6OCovwjqCccXQ8DNh/LG80OHbzMd2t3HHNnar23lR1dTNCR3uPPpqY8x4ZAr1kH7Xz46yGS81p2aM8j1J5xNF9bsYUezSHAfAIE7M8rhC/D61T6No5ZdRJISxOT0F/kX/ANwlmnP1N0eHQtcIov+0+rnQtT7mx9jK7CxHRxRFZWbc47QCp12Hg198Dl1iAY5L7wUemwd88AdE4lLf4DHz6GhEkLlHh5Wd1m8vcmttE58XBJiHrgFSf6i3M2zgzHudWT/Je6vVkCVu8C3bgc6g0Sb5TYROOx+ZIJ+bjyRIpUVNX87yS/lSykyE8F9ZVzihiT5Ii8bjDsu2McktrNzFlVEGVDHD96Psd95boA8zBySBxts85kEyE3z8fp0mXrGQ8n2rx3aZFAcwO5+0PYFYMqW5trx942HCh3kF2b0V0nluKgqdmv1DpqFr2vvR67DBabPIAlJEevPTwIrTMS3xCQKiG9s/9zBw1u3wONXcaL1XqO+qa5SjA5DQGfY0dkf6HYIAqINQvhPZ5T0Vl8V/Br+tDGjdDjx2Nk7zvwpA1AgVvhgBq7omiuq52Os+t918Nl9+fbTJYqNqRTett0fvau4t3I0ZiUyejEwVwPTbWaUy/XnYdn72KZ5KKwa1PWDu0eGr9/Bt5iuiBTKIkExi0B9V3dx6jw4zSvrrk8kbxu/L9rFbBYyQQ0e6OaPMDOrIIuk7DHLu9iB3fwCq10Yf/uhDCJPeux14+XsQUnG8kZ6FK+I/hl/0aPbjz5ERgULXCCJb2oKxfnt0WPgMG+RHE2nFa6DMWI8/C1+M3Y/3xelAIgysuh1/tdyJU4Rd8mBQl6MTU2fE3bpiBGwfRejEtJ4eNuiM6PZnZApH6okkDMshsFBcbd8qCx2TwTdvzxRvRNi4n1lIN+9N6I4kDN6l7nBcIyKY54QPXWNeGl6EtfRENZN1STk8m+8PW00Ey2F/TJm84zls4tHhoxWaeyJIp0XNcKO5J6LxrKheNeNEaaiva8gEg2b9JLMcnQxCJ5Y0meQznhPgPTTae0t/L1awtZ7iWsHrcVhR4NAKHfY9exxWCIKAk51NeM5+H3yrFwPRHuy0TMSX4vcgMlnKQ7VaBOUZY89FRBZpfRYj4Cb69OOAfIKEzjCniRc6fU3Nga+mps5sBGJJbBfH4U8n/AkYJ1Vj+8Lun+NZ+/1w+/er+3GhSU6bBXaroNnu58QK7/FhsNdrSjJ7dJgXodNkRogdkzapwAKoHZ6+k1MFjXZ7sA8B1KNbA4YZIb1niBkB3qUfSaSUUA/eeHVnEC58m82umb79vKdL39Ezo6Bfw8ZvYswr5Y6dvcZmGovcdhTJ4YdKPLk86ykIQKUcViIJXa2bXw1d062RI4qYG1+P150/QtGuFwEIwHk/xRL7jxGBK7Pnp1dUoRMyCU0hCMJINjk6+tA19owJAuCysUUPrWhGGS6P/xjiF34J0VGIGZb9eMm5FIUvX4cR0X3yscbyvF5dMQLDLHoiJXuRmKfHoZxDFEVDgnkwwwSWP5LQeG4Ate8083Z3mgy+NWJFfp2fSWdtCegmd/hzsPfV26POkFboKCHUfOia/Do/qG3xRzQFadoCMYiiqHhxAFW88GFprYGoZrKtPSgdx29jx/HeoabuKLojCU0YXCCa1Ni2kBL6ZRI+xglTVeio+ynV9zjvC9tPH0GQSosGex+MJg3ePEVsZvDo6O8t/eKfqgAyelz0FQXZuarSrcBLN+BF/BBnWrchbXUB8/8PVwn3Y784Am67atu8ugloJrz6n6MjaiI+8g0SOsMcSejI9GNNV72bFVA7AcE3ErjyX8B5P0XK4sA86yf44b7/AV7/KRBq1xQjEATBUHmNncfnsisr1pvNlNWUSt4As/wOlhcSUESI9D8zhmkRCMaZEMkkUDIJnUweHV1HGTMXTEwE6IVFu4nQAXjBoe3EWRy2XtAwz0hA555nXhQz0ceO5enQxTOXyILFzJgz75reo+Nz27Wln6EOIAqcNrjtVtjkoG79wKJA79GJJYFDm5F+8gt42LoM1UIXUiUTge+8Cpx1OwrdDsPnZgOi/uboKPHlJmEVBEGoiKKoGRj3ZTiU0DXdLLfHblXWbmMhNmnRgtis69B69XqsTJ6DtCjAuuOfmP/ul/Go/UGMCWwBOHHicdrgZuvoJMxn0VNpEfFUWhmUMk8Py2lg+5fJJe1Zv6r3aIcTKUMfGolLIsrMTvlNB+7qQLnDJL8kbOrRMYbYdUfiBu9CRyiuCc3uCMaQSmtzD1sDUWmBVO77a/XHNCFvkUQKgVhS45lp8ccM33trIKbxFsWSafijSc252Tm0aw8lDPkgwVhSkz8TT6URT6YzCD6jgOGvoZkwZLZeb+uC0aTpuksRnaBhE3nsnG5dXljEEC6p3y6La50Y95iso1Pm347l9odxde2XgY//AgtE/Cd1Oj760ivAmd9DUF4MlHk5+d/1AiubHB1/NGm4p/IFEjrDnKaebD062gcKUDsBn8sGWKzAWbfj3fNfxjupk2BHAlj/W2D5DFzW/QQq0aWEJukrr7HBs89t73UdnpGKmDGKLfaavtJOeaFTqeLVYzILB6ix2YYZnpgxbprfP5MAMnOJAzCUcVSFjnY7y6/Rh0uw9vHvm0iJSkyxvj3seL23gp2HbWdr1zBjyYxDDSscYJIYOqpE+xovZn260DPlNadNKlWu+/5Vj44kkAodVsyxbMO8jf8LPPF5WBreR1S043fJSyHesBYYc4b8XsZcHvad9TdHR0ncpfA1gugVfzSJeDI9gKprWo8O/2zyM8+hWBIBWyn+X/J6XCY8AEy7FCIEfMG6Cfd0/RB4ZC5mNP8NhQjrPDragXB5oUM5ZySeMuTusDax/VnCuH6gzEoDh2MpQ18ciicRTaQ1660pRQ64wXJIN5PP3ocv3sK3XS+cJM+T1oOvrxbXEYxrxFBaDgvXludPSZNlXOW4YCypyeUEmFdDG+bNxAejKxQ3hIZ3h+MaO6OKRq23XV/hK2QSLsavl8NfE/491RLh6rawST4U83CY5Zbq826CsYTyHuy7D+oEBO+hEUVRFdfydvbdMvFdroSuMY8LWwtH8ugUIIzTu/4D/HEBbj9wPS61rodFTAETzsUPih7ELYnvo9MxSnNOPv/Gq89hYwuG9nMdHfb8Nffkp1eHhM4wp7E7mlWODjNOZlVm+AVDLWUTcHXiR1hacBcw4mQgEcKi2N+x3vldnLDuFmDfOyhwaKuN8KFr+mIEoigq78O8NsG4VMhAk+Qu54XovS2FLpuSKKj3ZPh0A24+z8TsXAxFoBm2Z/IMGWO3petnPoOoVPTRhUtk8sSYCSCz7exz6bfrrx17XRE6XGU1fb6UfsargKsYw/ZVPDp6oRvTvl5miwCbnsDtB2/AC457MabzPQACQlMX4ZzYMvxe+AZsLq/y+RTPUcw4YCjsZ46OHEGDxq787OgJor+wGfsCZUa5f6FrkYR2AMoLHatFUAVFPKUMHJucE4DLnsb2S1/FX5LnIAoH0LodlzYtw2bnjbh4x+2Y1PYa3Iga8iJ8LjscVuM5fW67MukVjqsz+iwMV5kVT+hn6ZOGyaJwPGWsQGkSYhWWPT+8WBF1HiXAmK/Kfo+ntGKqJ5wwrRan3xaOpbTtSCQN4oS/Nuq2pMZzEo4nNVXM2HH6sD/pXJzAi6WQSKU1wsrsOobiKUOodEh3bQMmgo99RxGdgJTeW7ufZLeMtlrvvQly29h3H0+mNeHe6r2SQiyp5pzx90o8peak6vPFQvEk3Ihiatc7mF37I3zgvBk3+h8CGjYiBQv+kToTb5/9InDlP9HknaZcj2girYT88d4avUcn26prpV7pWTQrFJEP9DUdSgxxmrojGJOFR8c8dI3N4usXDBXwtjgTS6+/Ddj1GmpfWIpZwg4UH3gFOPAKnrJW4u+202BpdgBTzleLEbiMHp1QPKV0JmxwzQoZCIKgvDZC5+1R2ua0I+pOoy0QM4RZjSrxwN/sN5SVHF3iwf72kOFcFkGaLcu0snJfIXBduhwdNcxOe56+8oz0xsIfTaDYY1eMisdhRTieQk8koemk2edinq2gInTc2NbkN3i2WE5UJCGFzSW4DlwfuqaUfzZZFJZ/TfrfDiAivR4PYWLH2/it/RVcuKEWSMcxEkBUtGNrxUU49Zs/xcFYBVrq1qKcqzIDZPDoRI2zxuYwj470F782EUEQRliYU4nbBkTQt0dHF7qmenS0gzCvw4ZoIq4ZLLM1cixV0/Dj5PV41PkdvLOgBY1vrMCoxAGMbXsHY9vewRanHdvaTgTevwylMS8OoEwpVBCPpDWDcq/DCo/DingyrfH0VCqz8VpBVlbgxKGuiBTSFVVzEHsiCUTiKc0SCdJxbJZfHUCn0iJiybTBexCKJXXCwDipFogmDIKiO2wsRhCKa8/F2sK/ZziWMgzsw/GUZpkDti3MlwPX/Q1I9sAokHTCyqRNwVjK9Dro7WUoltTY1kRKvoYx7efhvRzsPdnxDFGUimAYKuxFE8r+7Dv1R5OG7179LFrPTTiuFUpK0QHddS6X9y+JN0GsfRrXNLyAXzs3w/Wx/JkF4KAwGmM/fx2uq5uItxoteLzyRADaMRcvUnkvqEdf0IDl6PSz6lqpxw50qhVm8w0SOsOYWDKFtkAMYwXm0en/gqH8A6d6TezcfnIJz2gSEASkJ1+Ar8VSmIwG/PO0nfDs+Bsq4q240fYf4J3/AFvGYD5ORpNlIkpto1WPjpww6Oe8LEVuO+xWAYmU5FmwsFl5i6B0NKq3RRVhEV0yLPNQjCp2Y0ezXxUoYSZ03LLQ0eb7jChyo7E7YpJbZIM/mlTr88ttrih0oi0QM7SpyufEYX/McB5+uyiqlevKC5xoD8bQE5FCBtjMTrXPhRZ/VA5nUL+XkcVu7GkNwh/VbmefS/XoME+Z1qPDOk3m6WH7MiFltwqoLGRlovUeHXVRWH3VukKXHRBFTLS14STrezj+rceAtvdxfSoGWAGkAVSegPW+C3DzJ1NwbuVUnFo2EcH9ncp3yaMXOrGkGprRd46OdM+z0LWDvSykRxCE6tEp8TCh07vdMC72aQy9AaSCBB0h7YCShaWx0JzWhBM4/Qb8YMuJ6DrwEX43Yz9qml6BO1CPUxIfAq9+iJcA1DsqULrmHCyyluNNYQIiMTX/wOOU1t7pRkIamLPcHaUaWxJJLkyr3MuKF6gD9IpCJ3oiUtgT+zyFThsCsSSX+2MczOtzIPQeECkEWSsEgmbHJVImosYoIMJx7YA7pPPUSPskFQ+X2taUxjvEXyf+84R1/avRE2QUQ6FYUuOBUc5lsnCrPlRQCjVTt8VTaTlMTNv2dFo0CLMQJ0rYd8VfR/ad8vdficeuTGzyYpkJnVA8pbTHYbMotkjygCUxWmjD6dZdqHzrv1jreB01ljbgZWAmAAhAyDMa0UkLcd2mUaj3nIDNn1uAxk1rAASU54NPF2Dtd3P5bdI+eqGjivpekZ/dUjkPtylPQ9dI6AxjWOK10yY/MFmUl9ZUXTPx6BToBp+S6xjYhRpYLroOuPA+PPXM4yg/uAoX2D+CvbseZ6IeZzqA9LrfAftn4ce2CtSlJyPceRICySIAkrdHEAQUOG3oCidkoQPl/fWDXl6E8UKHD4VjXglFACkDf3Pv0KhiSejoq66NLHbD3xJQq8hx528LxJTz8x4USdDoQ8ik7cFYQhP/XVPqRnswppnNs1kEVPqcaPFHpapAUXWAwIoI8ALIYbMobnR/VPL0MOM4QlfIgR1TJJf7DsgzbGwA4HPZlXBAVt5aLThg1RYTSKdh6diNRda38dWu/cCDO/CwvxGwA2iRvr8WSzX+E5+JE75wLeac+Xns21iPrk8+Uc7JOnH9TDAT2MpaB9y92XdHz0Sy9Ce/CCtBEEbYDHd5gQPoAPqKBDCsE5KhIqLHzgaJ6oCSDfY8TjXPRxrEpvGpOAYNJ38F4TOX4PZH/opLvdtw8+j9SOx/D2MsbcDOv+EOAHc4gcSf78cNwmRMs43A5PZWjLd50ASvLA7kWXoWXqQTGmrYUZIraODAnlZJFLHjywocinfHbE0S6XNpB+6RhNHDos8TDERNws1iZmF0xsR6vRfAXHik4LSZnUvradKLqAh37fhzRTiBEdMVFACYcNOLGqNwC8VShrDtQNToIdLn+8RTaXmSULMZEe6zs+8qzL0v+05DvEfRYYXHYUNQ9rzpwxzDivgQUWP3Y3T7WtxqewVz2+tR9dg+rHNKk3P4GKixAAnRCoyehb91TcYzXSfih5d9GVOqffjwg7fhUqrFMUHOKhKy50e93nobyELU9BVM+xvRUCLb8XwtxkNCZxjTKJcTrChwSjNzAwxd83PufAYTHPFUGrGkmsRpswiSm1zw4EDlfCzdMxm3zhmJWye24JV/PY/jgh9ggqUFOLQRN7K77+EHMbagBg/bR6LVOhHYGccURwAfhL1y0rnU7gI+t0dXKKDQZUM4rr4WS6pxw/pKbWq+j7nQGVlsngc0qtiNnS0BpXP2cwKorr5bzVWJqefZ0iCdJ50WlWpwbHuQ8w4JguS5Ycfzn4vPPeKFHVuryM9vd9o0YpU3lob8Jm5A4nPbJaETUT06PrcdPrfWaxOMJeFAAuNT+zHqwAe4y/YqToocBH5xCF+JB/EVOwBp0WukYMWW9ASIkxZg9gXfxpXPtWJXawjPV58MCILxu8wwQFI8R7q1Dtx2K2zWvryUqjcQII8OQfQFsxuVLKm/jwky/Wwzv1gij4ebuQ7rBnT6FeIV74xcnnePOBpPpMfjO5efh1N/9k/MsuzCH89NYufG1zA58SlcsU7MxEbMtAHY/E+cAaDH6UH61em4KlCGadZyTAsHMVqIoFEsU0o/WwSgWJ4w4r0vfHUtxUvgknJ/4sm0Zk20Mq8DHaG4MlgGoEQk9HD9KYOvksbeQy8WzESTac6MzvNj5vWJJJIIxU1C1zgRE0umTQsxeGPavjiSMHqf9NVEw/GkRgyxcxlEU9zo0ekIxjWLm/Lnt1oE5bW2oLwwqgCUeBzoDMXRGYprcmkOdIQ1go59pxGN0JHCH4PyPRmMJlGBLkyPfYSrrGswM9SMES91o865HSViEHgXONEGICn9JEQrdlvGYdqcC3HdWi/eS0zGa19diCef2oQ9YhAep10ZU0UTaSRTabVQgeLRUaNo9BMADMOiuRlspQH52S2Rc3SaSOgQw41DnUzoOPoVaw0YjVYilVaqffEeHS/3IPID9gKXTVlBmZ2rK2EHjluIhxxe7Ix/A3+9rBqnCTvx93//A9NSO3G85RBcwQZcZG0A4huBvzyPlQCCThfS/56CSME43GazIYFxKOlwogw96Ij7kEylNWFloZjq7WHeFosAVOkG+IbCBjFtiJe+6pu+GpxSZYyFuvm04V18CBzbHuRC0RSBxcUoSzkvavszC5pMAkjdzi/EaebpUctBq98ZH4YWT6ZhRxKT7O0ob9uIb1nfwKRYM8Q/P4ZbDm7DT53NsH4sfZj/YbdBHEhYnPgwOR7xUWdg3vmX4p4tXvxpUxu+N2IyZldNQTDWrLwfayt/fTN13j5dGWvFq9XnbBYUbc88Oj2RBHrCCWUNIIIgtDCPTkUBq2rWl0dHEiv6JHGDR4crWqAf0LEV4tMiP4sunZuv6haKpRCCG2vFk2D9/Bfxf3vno+5AK57+ggN1G99BWWAnLqpsg6vzUxQJYaDtAywEsNAOYP2zWOeU8gLFZyfgCbsHrZYq1LQeh3oLUNITQiBZDkDUCB02KHZzuT8dcvlkj0PybHeE4ugKxRXvfEWBE026hToLnJLngIUGuuwWxba26xZzjCRMwtRiKUQSulCvSEJTKS2VFjULc0rfRwoOq9Gjoz9/R8gowMy8MPpt+oUoQzGjSOPDsvht7FzsWvDn8jqsCMVTitApctsRlAs3sLLXXocNXqcVnSFt+8vke5fPM5K+UxGIdMHbdRjzLbX4fPf7mCPuRbG9CRNW/gxrk/Vwu+LARuAcO4AUgMMABCAFC5LFE/CfjhHYa5+CL15wIb76Dz9GVZTgrQXnoO6D1QgnpLBzflFQ3jvDh8J5dGGbQe4a6ScJ1GIE2vLV/bKBUD06zXm6lg4JnWHM/g4p8XpEkRNoA/rn0ZErpekG+YDWcFktgtIRBWNJZTbeWLDAeC5HxUSgZhYeWj0S9Z1h/OOa6Qjt24h317yNs4paMc93GImWnSgQokDHx/B1fIzv2wCEATy/DLUuICQ6ITw8GlfGfJhp92Ji42Q0pUrgt4go7IgidDgGLyKwOQu5qmvanJgRBs+NVtDoB9Z6AaQIJm5/8wpxqhBxWC1KJ8wLEX5toSAngApdNm7GJ6URND63GtLFCyPVo6P19BS6bLAiBVukHTi8DVMjdTjB0o6xu3bi5sQ2CPZDmL4qClekGZ8622DpEoG/A/cyTbAHKAcAAYjbCmAdMQNP7S/CJ+lxuO/mb+O+jQk8+0ETbp04GfMmToFr904Abeo6OroBEAtJ04f8ZfLo6MuP9llxDXJjIZWXZDlQ9Z1hnOgp6sexBJF/NHZJXs/yAvnB76dHJ5aUZqxDcfNZaTWhOmXw6AiCAK9DCp8NcV4Jj8OmDATjybTiWWZr9LgdViRgQ1PhiVgpuFCfPAtTLp2LFW9sR9PuLfjZaQJ2bK1FVaIe55X3wNK5Fy4hAXR/ivPZWPLAq5jnALBb+nOp04HY9kpc6PCgLV2MyR9Ows3WJMriNaixuLBT8CDcWgEPovDYC5XPxa9BUyYLnTY57MpmEVDssSMYSyoD91KPAy3+KNKiuqg0KzDD5/swL1I4YfTo6JcsMNsWMSlGEOBClBl6wZKpWpt+G3s/5nHhPVus7byoYZ8xEJUiLwCpbz7UFVGujdsuCchQPKVcQ7fdClEUEQ+nlWvtcVjhsVnhRQThw/txorAPFbYQzo5ux1jrXpz8ycv4SfgAih0dmLI9hCXOVjgPJ4DDwJUOAI3yh7AC6IEkaEQByaIxWNNVjj0YjXlz5+FHa+LwjDweyy6fgx888DY8ghWnFp+IGDYpokS6D+LS/Z1QhbrTZuVyjhOKuFWEDgvb5MIQjUJHOwGtLtXQv9Bt5rWk0DVi2LG/jQkdOdk8G4+ObmEzj8MYJsQ6IskDwR48PryNDcS1uTFsgMreyy96cNB3Gv6Q8qJxVDXmfWsWbnnqfez99CPcdYYNheEGbN+2BTMLujDV2YF09yF4hRjQtRdTAEyxAji4DicD+KIDwCfSzzYXEIcN+FcZXnE4EOkpRvqvE7DUEkTA4sG03VtwtbUFkbgb4rYwpob2wSMImCwUYyTaEYk7kIoGEI5EAIiGkDY2MB8pX99gVFpzgbnPeWHEl8HmK85ptnOeGL2HRkAa0VAAMWcYI9CBSdYYJqS7cIqwG5WHm1CYEPBN63ZMTwg4sUGA13YQUw+KqOoRsdJxCJXpEMb8OYTdzi5Y4iLwCPAwADgAvA9cDEidfZf85QlAQrDDVjIG77QVYq84Apd94Tz8bgvwz0Me3HHZ2bh05mjcd+crSKVF/LhwEvzxHZrvVS0/rRWABS7j64AqhPSzVJkWJtXHMZui3PMixpZ50B6M4WBnCCeOJqFDEHpEUeRCnvvn0eEFDT+brx+EKevhcN4E/liP0yoJHV1om4c7D/N8sLwGxUukKXBgg9PpxnZxHHZWTsOy9EQEEkm8dfnZuOyRdfBEmrD0TCfe2FCLaZ5unFkeRkfjXky0d6Ao1Qm3EIc7eginMnN34AP80A45XwmAE8BbwEUuIJ6yIdRTiFaHF753KvC43QK/UAhXrBw7rBbU7KrF160BpOwFcFuKsEMQIbYAo9CGSkc5wg4B3TFVZFQUOnGwI6zJN6kslERAOKZNou8KJxRhYLMIsFoExJKqV8Rtt8qeIbUYgdNmkfbhPE1MjLBtvDgJydeZeVw6QwnFvjEPFWtDZaETzT1RzffH2h7iPg/7jKydFqQxxpNEqqsD6cPbcYqwCyPtSZRb4ghZuzHm0034nrUBNekkHEIINnsPTn43jVcch1GRDKHI74fdlQTeBi5iSyg1QsoPZULGAiAK5VYOWYuwN1EKV+VEbAuXYFOPDwvnnYE73w2iSSzD+msvwHX3vQkAqKo6CdvFj3C6w6PJJVOKbti19yJfqpvd316nDd3hhEZM8q8BUqh5JMMkgbqOTlJTgru/OTrFcgh6QB5z8IWl8gESOsOY/e2y0PGxpz/7HB2zQgSMAqcNhyFVDwua7McvGMqXS2ahSPzAnoWasde8bhf2iKOxvfh4CCXAfR+dii+PH4UHF52Mz/3fKjjDTXjqq6Px77WbEWpvwKLjbRD9Teg5XI9xDj98Yg+sqRgcSALhw5hqAZBuAHZsxbdZEz94GUvZ8/63x/AgIBmxV4D1rBDZL4A3AaSdAsSXnTjHaUEcdqQf9OHfSCLusGPsO0X4pyMEIW6B7U/F+JvDDxEWTF1XhOftATh6bBjxbx+etvvhFQWMqXXiOIcfJfUWVHTa8W+HH4VBAb4tVlzsCKNouwWeT9P4wBlCQUsCjuY4fupKAJulJl3iAtAs/VzpBLBP+jnVDsAv/cywQcqVCQCnWwCIUDr6tChA8JZhV9CFDtGHWdOmYEObA+8eduL0mSeh21aFB94PYv7sE/CLr52E2+5+Hd3hBM6ZchY2ffQx2tCNApdDKRrBcof094CyoKg8m8dC9wplMaxfh0cJQ3RrO2GfzqMT1HmGeke+50URY0s9qD3YRXk6BJGB1kAM0UQaVougLDDc1wSZw2aBw2pBPJXW5hnonk9WCpev8KVZK8RhAxBDTySBREqUX7fBYbUo3gI2GGeiSR/Wxs6pbOdyWLxOG5wOB+rDVdjqmoLnU8WYWuCD97TxuG3lR5g3thzBUBgdzfvxmy9U4cnXNqJC6MYFY4BDDQcxozgCR6QdBckOlFlCsIkJOJCEI92FEksX0HMII9jHCQIX2QHsk0OgACAEyb58DFztgtQ/C0DMaUf6fSe+7bQBURf8DitiogOeXV5cZBfhTHnQahfgO1yAzrgFnTYLCmxutNtSmLynGLfZQrDZ7EgLVgRFYNqBUvyP1Y9Clwvt6TRKQm44Ew5UWCIocTvQFYpjbMM2fNnSCYtFQKHTCn86gbENn+Arlk5ln/KwEz7RihHWACpcFvjTUUw9UIjrrR2wIYVyhxXBVAQn7PFiia0bIwQbumxh2NMpTDhow1n2HlSlRETtYVQeEpGOR2BzxOCLJGFxRlG4MYnvOaNwCClJRLoAfAT8jxNSZc4oJLGyHzjbDoA5qqwAuoFRzK7JJAQH2tIFCFl8sBWWo67LhepR47D6kICWdCn+5wtzsPiVw7AVVuHkCdX455Ym/OSkqXh3VxvWdrZjjPt41Is7YRGAEq+6GG07523jQ/ZZqJxb8cxIr/F5WXx4Wnc4oRSisAjqYqVm5aUN+W2sGEEspVlzqU+hIz+7LpsFpV4pl6m+M4wTRubXRB8JnWFKKi1qQ9eA/nl05EGlVNM+ZRAgPHzoEVupvtBpJnS0OSpseyE3o+/XDZL5qm6s2ew1p9uD/aEROFx2Gv4reLAzFcDc009DfWcYP/nnJ1gwqQpfPHEEfrxyIxaMs+Gn51XhtqfeRrklgJ+eW4Vn365DqTWGK04pw38374IXEZw5xoW9Dc3wIoLR3jSS4R44BNVFbxFEIBVFEbuEPT2YyGb8OoCT2e/NUGcCDwNzWTnlJuBs9ns7UGmB1HF3AiUWKMmNZWw7gAJB3l9HXLQibXUBdhfaIhaknYWwe4qxrVNASWk5Kisq8K+dQfiKSnHS5DF44oMOVI8YjR9+5UzM/d1WdKEQ7y0+Hxfc/xYAYOfXvoB3XtmJp5oOwF0wEcm0iA7sg8/jUL777nACPZGkQWQUumzK2gR6rx7/HbLj+IUD2T0VS0qlXjOJav16PVkJHc6jM6ZMWi/oYAetpUMQZuyTowBqStywW1jn07+Q53g4rQm50g/CvJwoCZokXbPZcu2stxWCIMDjsCIQTaoeHTYbzuc3JFRBwwaG3eGEksDO50uwQarXYYWbqwbnTwioF6uQHH0G3rRIno1gySi8tL8RV00ei50tAWzc34kvzRiB1R/vx7xRFozzxrF1z0EsGGfH7oMNGOeJYlJBAofb2jCpGAj0dKHcHkeRNQrEgiixxeFIhaQQOgBOIQGkE3ALAFJAFbMfUWCCFZI9sEIuKARp1BaX/28HPs8uoQhJGBwGvmQHkJD/jsk/DnmbA0ATcDkby6d029g+cfmHP9dh4BI2FEjo2hCFOqIMyG2Oc/8DkmclDemWYv/LxEUrYlYvupJOJOwFiFm8aI7aUVhUgt3dAnxFpfDDhV3dFkwYOwarDyQxauRIwFOGf+2KYcFJ4/Hvj5owqbIAXzppJJat3oWvlI7CSwckt871487AIXE9ipNWQ94VoN53XocNdqtFLTwhh855HDa47BYIgrRuTxsXPsf/327itWG2ihWiKHCqucy8pzMSN8+94XOntVVH++fRgShifLkXnaE49rWFSOgQw4ODHSHEk2m47GoSer8Mli4MQS9AeNSqWWoOSoHGo8PlnMiCyWGzwCUvhMVX3VKLCtgNr+nfz+x9+dLTUo5LAlE4kSiohmvMDKxLtwNp4NsT52D56omo9rhw5SWfxx11r8EfTeJfXzgTl/z+PQDAzp9+AZ/75VvoDEbxjxtm44rH1sCJJN669Qx885E1SMUj+OWlx+H//rkFXmsCT1wxE9c9vQkWpHHb+ZPwuzd2ocxjww8vmIyf/mMrbBYRV5xegz9vOICJlT7Mnz4Cy9/aj8oiD86cXInnNzfhtAkVOHlsOX779j4cP6IYk0cU47naVnzh5HEYV12Opa/sw5zjRmFkeQn+8F49rj9rAmaPLcH1z9ZiZnUx5k4sw+/f3ourJ47DgmlV+M0nGzHFVgDbiHH4T/oTLCiqgnPUiQhYDyGdSqNJXjiMVcnj832S8mwq86Twldf0icZKGF7UmKfFBE+A+341HTwXksLfI3pRzXsGgSwqzgDgO/pJlQUAgF2Hg/04jiDyj33t0rMxvtwLyT2M/pgNeOXlAILcrLS+9Dsf2qNMjJkUuGELljpsFtjlcGkmdBSPjlKaVx5cBrXiSMmb4Uo5SxW2pO2sZDE/0OWT771OK7xy4YF2ZV9VQHWE44jAhbC7HF2FLmxIFwAow4bUFEwt8OGk0UX4S3MDZntLsLm9CydU+FBT4sGr21pwYkURtjb24PzjyuDv7sKhw62YMcKFgy0duHR6Gd7eVg8nEhhfbEVntx9nTSzEln0tGF0gIBwOwSbGMLXSg32tPagqsKE7GEGp2wIb0ghFoijzWBGMRDHKZ0e7PwynJQ2XFYgnEigtcKAzGIfXaUMoloTdZoXDZkEwmoTXaUMwlkJZgQMdwTisFgEOmwX+OFBa6EVzIAGv24mOiAibzQ6Py4WmQALFBW60BFOYXF2MbS1hJEQLCrxeNIWAk8ZX4919ART7fKgPpBERHThveg3+sbUTY6vL8FFzDIWFBThlUg3+UteKE0dJ1+bUkSVwO2xYs6tNuYbnV1YilkxjbUc75qAMG9IdOK+gEoUuG6Jo0hSIUEQHl6+klhFXS2Tz94riuXEyL4z0/fOChuWS8UUl9KK7jQsnZCGD7H5lHh3edqmha6qIceufnf/f3pmHV1Wd+/975vmcTGSChIQZARmCVaiIU+NDrVrlZ7W2ltpqS3utgrXPA9perFe0drDeXrX8WtEOt6321qu9/VVvpX0s1eKACFURKygShgQIJCQk5GQ4+/fH3mvvd629TkhQcsjJ+3keHnLW2Wuftdfee73rHda7yDpdIf/CAdPT2S/E0FdbEsOmXS12pM9IghWdPOWfTWaO30llCfg81ss+AI+Oz+uxFwu2KemMVaRJ7nFC10RqYDqJpRZ/+/uIUHScibfHkrSijIY86Rfhy5PmWNBvW2FEekUn81cAbV292GfFpQd85sQ/EQ6g+Wg39h4F2hCHxwPESsfhUPh9NKa7sN0/GRuNLhQGA/BPrsdLPgPHevpQn5iBP2VSmBSLI3D6R/H/nogDGWB6wVQ8mdmG+qIyLJwyEc/8+QWU94VRkKjCXzPbMbq4GlOryvBSJowOpGAECvCWEcX5BRPgLUzgMJrR3B1AottUQhIhJxlBf1nXVAU0YWUIaiL94PF47Axubcd60Ztx0kvTe0azvonzJYm3RUxe3FnVSD0ywPt9XvtZO9rVa6/hUkPXxHk6uvvQ25dxMtUNJBkBGeinlCcAAO/sb0cmY0gbsjEM46zrHDcqDhiWojMATcexOMupeyl0v5Cjabe8EBM+x7LuDmtTJ5fxoGwp93nF+C2UJifDmc/rQdQystHF//I6H3kC3NLZQ7xIZFLc3m2XiXYLBS1GQufEfjuxoN/lsQqFgsiEU9iHDIzOMBqNOM4vGY/XvEl092bwRjqIw5lu1FZPxH9u345yI4ymHvM3vlBbi0f27UR5Joym3i7MSKbg9Xrwj/ZWlCGE/T1pXDOhGr9+ucEMxYoGcainG1dPqMJjG3ejNBzCgZ40xqViKImH8Mr7h+0ycYzHAxQHQmjuSePTE6rxm1caUBYxzz0mHsGE0jj+2nLQbsPnq2vwRPMetHf1IpH2o72vFzePnYjf79iO4p4gDvWZffHRsknY9vo7aO0MoxFdCIdiCIUjUt9EqVLZ4SiaPm+f1Ne6exIJOP0v7l3I77Wf0W4iQyIBv3OsrUSLNTfm/beVk7CzFudoutd+tsSzZivd5NkQxBSPDvXYiHbR5A+qkYBuKnqiodvjRsUAYEQqOsfbhIIZpmyzFJ0p5Qk4O2sNbGJXkGUCrWInE8iajIAoMiQNtFOfZhkTk1zFa9MlewPod21ko8xk2C9ZRo5Yik4qGoDX67EFYpO1M7B6LrEAN2FtWCrKhQIUD/rN81j1GsV5lFC7xiOOxSYW9NmbnQoPSiIcsI/tSMuKCN2A085Q5kpe4E4vraadthXBtLN2SvWUifYLK5S4L20apVT832LtFQE4eypRZcZeo6Px9oj7oSoxzjPkXENSedaokn003WunTy2IBHF8nIG+pjiGoN+Lzu4+7G7hdToMo7LjIPXoWHJjAAYyMak7SkLXsqeX1hvG1BAiqihFFAu9vf9OWEwgnYmvaXU3vz9AwpFoPXtSG/Q72eDInjmRoHsCTNf+NGsUpQMkUYIaxhQJ+uz+oOuMIso107C7w9YEv9RaY0u9ViWJoKsdMaWPhAcjYwAt1pg5KiGfK6K5JnGMYQCHO9JKPUdxiymeEHqNQn6JttMNVkusc9GkCVGlb+Ihv0tZiQZ8xOtH75/7nqhto/cOgJ32m/bbwSzPivgtcW2O0iJ7Z1SPDn1+40odqujQd6eTPH8Uca7O7uyhoVqIoW9ciano7Dgw8iIaWNHJU7Y1mta4yeVJOAJrYHULrLUZLZ3dRCD1v0ZHzahGv+/NGPYgktBsOkqTEegWqqtCUShI+9vSdgYY6tGRPESKd8FROAZWLvaUSEZURUEMckp5qzOQicX65vmP2cfZCkA3VQADWa9ZDckT15skXhjJs6U93vFg0esVv5kkSpOqdIr/6WZjurVUalY16u2xFc+IPDjTkLm2LN5DM9zRa5+rtdM8rmAge+GQgd7v82JSmRm+9ta+tux1GGaEIuTG1IrBGci0C6pdu7sTj47GMKZOYt2JCtxKkONNkSejcWsMEaFroi260DVR50ins4g8RsoPkN8Uk2IxcY+GHAObY+xzvAxOJkmnzFkz5CgLYnF5POS3vU6CUZbCIo4J+rwotGR0L1l/pJ7fyZoHaSNN+pmuWxJlRbGgPWyKMqHo2G0POQqe3YaAT7pntO2CoN9rywVnQb3PvmZpPZXSh9GQz9XXsZD+nkQU5TMe9iPkd0K9xD488bATzuhec2Pdf1WhscPQFA+Q4rGjz7+q6NB5Ulzz7qgenRh9d8Qzddz1OQA19E2tSAIA/rm/Hb19msW/eQwrOnmIYRjYsrsVADCrKkUykwxM0ymMmQNRa6d70kuhIVJi8ikGYACSR0N4TJKaF5x6KtRwqfZ0j72hp+qV2Gd5JfzWAnfhZWjv6nGFQYm2Nh2RBy2dIgI4Cper3GqDUHSE98JWII7ojxflSaK4GIbTHjnttLovTsDuZ51Hp7vPiSOOh/x22w2DDOguD1an1T+yUtKmyYAn/t9jeUGiQZ8dOy/O19yRtjMlOZMN8/9jPX1osYRQSvHo2N7DTseTpCpDtB/bunps6yR91rLjDPQAMGN0AQBgy57WAdRlmJFD89E09rel4fGoBrLBbUsg1hmoHh0xeTvWrV/7KSaGTdZkkHp/XeFF1mcx/qqTVBHqI35HTArFhFoYXuhGzd1k8hcJ+lxRDKZXQPU2+12TUqoQ0TI13Tb1BtHj1Gx1QskQUC+/046AyxOejARc7SgXW02QeroNmtVJtNgUW6rn8ry721WitD0W9LkU4IjmmmMhv+s4Gv7nHOdzGcZ0Clc8ZEZqiPsv7nUy7NyXFmsOE1MUmrYu2YOirukR/aDzItHrAYhHh/Sv+C5jwJaT7v4Q3tA+bRh4Voihr6owinjIj+7eDN4bYeFrrOjkIXtbj+Fgexp+r8fKrjFwgQU4IUGtnd2uJAGUBFFUWu3Jp3OczqMhrdEhbu7+Q9dkoaiGlSWsdSZCMHb1OBuKpZQ1P3bIlqKgiPKEkjHMrbgoHh0lg5zwAKWsPnS3NYBwwGcvUhQKIBW4XT0ZW3FMhP3SzuN2GJ8lYIWFai/pC7pI0b4uRUlU22knHDjmZMCzlc5IQKpD76Hdf62Ot0cM4nQgFt4g9TkS3sPDx3vW7HDFE/foAMDs6gIAwOaG1uPXZZgRhPDm1BTHzHd3EB4d8c4e6XTCiV2TeBpSm5bDkQFn3Giyxwo6GZSt5RHFo+Mcpy8XbVEXeScj7gm73+tB0OfVKjqq4pAgHh2BOZa71xm6N1B1T/rjIfckvUxRMuIhv6vNNPSZ/iYtC/g8KIkH3ceE5LaqipTf63EpLImQX8qwatYLuPpCbbup8LkVYPcGmT6XHEhG/HYIunOc+7qpd4teJ+D2MsZDAdfvqAqNc6xQaPTrZ/oLvaRh/vQ3ADN0T2B7iVz9QWSpmEtpDIJuHEOf1+sxPbUAtu47MoC6+QMrOnnIpl3mro+nVSbNDGeDXaNjTSBbOnvsOGGd9dwJW+pBK1kTQ3FCpdwvJ62vrguhIVHqxNY9WbfKQ357Xrv7cKd8PkURKVBC0fa2CiuiotCQtTX0f7F7uOopEV6PlOKZErHN4riUrTx02uelAoB6wITyle7N2FanpLWWSEwGnPMHpOQC4npp8gVd39kTlWM9ThihHYIm950u4UQjWfskFvkH/V57R261XwTinu5rPWaHSajreABzF3HADKdsPWat0TkBj87sqgIAwOt7WpHu7ctSh2FGHkL5n1aZtEoGbiAriDme625rt3tVZogx99DRtL07vM6jI9Yp0HEgqoR4pRRPvXOc8OjoFSC3J8RMJSxCYwFTGaJGOtoGXep7nVKlHpfUeE6iQZ3y43dN+guiAal98ZBfs47RrUDEQ/JvJsIBlwJGDWz0XFJoVdh9TDZlTu2LgkhAmshHNEqNriymvcaA29Oh6+tIwLWZdCKL8mJeq6LoZHmGxGe1DUJRFM+rHZKn8eg4dZzvvF5nTZmQ+6oRLxzw2c+ASCYwIPmnGPqmjzbTSm8ZYYY+VnTykBe2NwMAzhpXbJUM0qMTdSa9B+2FjRpFh8TLtmYJJ1KVEjqoiMGn+WjadiWrIV+tZM2IeLHFwGIrLVa51+tM8IVHR1VcRByv2BAsHnbaQH9X/C+OVz06wjJTqChfInwrmyAWn4XQF8cnwn74fV6yt5ATw04H7cMdeoVJIMrFPVTbb8ej22tm5EE63etsRmaHrlnfid+mExDRXnXNj9MeoRjKipVA9F/DYTnrnYqILW8+mkZrR49Ut1+UgX78qDhK4kF09WTw2q7W49dnmBHCxvcPAwA+UltkFgzCQCYMEe9aWduCfq92wg44YzMgjxfq2EHHCtXCbY+vromvXqER5er44xjC3GOa6ulIRQLaZCq6SbrWozOA0DVzgu/U9XpMiz89X1wzOU9k+U1J3mYJeXMpOiG5LJsypPMg0fskMrjSSX4q4lb4YhqFLxbUX487/M99Tcmw20ujZgIFTNEQDfpcnhFhrNXdG7Ntbu+TuDapbdKzrXiBVAXdJZfd8y3xjom9rgYk/xRD3xk15rv9yvstA6ibP7Cik2cYhoEXdpiKztkTSkSh9e0A1+gQ67nIeKK6rgF50q9bo0OPabA8LNRSIQaU3dYk1+txBJKo15cx7OarXhinveScEbdwMuvoPQnqgFgcE5tkyr8hdglX3fVCyVLPr2YlE4jjsiooMXe53+fVHC8rIa7zqOUi6YDSHp03DHCElFlHnRzIVkLAsURl89i8f8jy6ETV783+a7A28RSeKhWRZajpSJe9OPVEPDper8d+L57ffnAA9Rkm/+npy+A1KxJATIYGYyArVCZhxbGg6z1W39dIwAe/z5mCqJNdOu6odcW44vKSKOsDnXJrMuqKOHBPgJ0xXR3rA9pxWxeKpfPoqOteololyacoeH7Jcw9YoWsahUWneKje9+N5b5wyOTxZpzjoFCSq1IiQcjrJT0UC2hA+3Z5LOtnpUog0Cl4qEnB5RHSGQbGnm2tuYCkZqhfGDn9TvUKWQqzKXDovyRZiSduSra6gyDI2i72uhLG2XxRD39yaQgDA201tOGLN2UYCrOjkGa/vOYLGI12IBHyOZW6QHh0xGLR09tibcJXE3IpOsVW261CH7QVwDzDmZxGOUEKysJQoGVkS4YAd9qQKBTHhB9xCjCpX2Sx2LqFlDWZFymAhBo9ixYMlrCmqoCzMInDVMDt6Hbp2isFSVRSFIkPb6fN67EHV7SEJas+jeqrUdtLU2YCpzIiJiqpMSR4d5fqEQmJ/tvpR9SCpv7/dSnmp9rtAPGsiNabH4z6XFmWgB4BzJ5cCAP60tQmGYWgqMczI4pWdh9HR3YfiWBCTysw4/sEYyMR7LDzjulDnRMgPunWVOnaok11qaVfHaTH+uSaQ1jnc5Vk8OhqDVLaxOxnRKTr6ybdu02PdxNkdNuWXZKhQ0CSPjsbDog9nC7g8ZmJPuf7aoK73SYTMjGUBn1NRr2zJZTrFoEDj0YmH/FpPmd6jo/a1T5uEIRLwKe21lBHyXDrJdvTGv6weHU1CBPXcgDNnoHXp9enOIdAZ8cQ7JcLUTyQZT2kijImlcRgG8Nd3Dgygfn7Aik6e8Yd/7AMAXDC11FyfAwzaoyOEyu7DnXYstTqBBYAyK0e+UGLCAa/zmxbqgEzTTarCiwo2nzLxLpQGKL1XBcguyNQ6QkEpVtog2qQqYcKaopYLxUi9zmyeJNGObJZFei2RgGPpon1VFAvaCqGUGCDkt/tfHSh1lkvaTvVcVPCorn1dMgKB2j/qZ3UCIO6reIZKE/LiVfs8lkdRKESpSOD4u0IDcAZ6p+SCqaUI+r1492AH3mrkNNMM8+zWJgDmu+G8V4Pw6GQZRyk0tBjIHr4joGOFen47m6Zm3QvgNpSpIcMCNaQXcMYkWub1QNqkmdbXrQdSx0xTIZJlY0ks5JI/sZBf9ugIT7zSbzqFRadAyB4deU+5bPUSYVlpEptKq0rM8dboqOtjxXWEA15J4S1JhFzPS1SjzCXD+jBB9TlKRsQm2M45xbmop8RZX6s3vunWMwGaJAVZjJf0mc0WSilwezPlz4DGKHsCodsAcOFpZQCAZ9/af/z6eQIrOnnEse4+/NemPQCAT84aTb4ZnEenssDcpVgseosE3FlMAKA4HpIGLN0Gji6LP5n4Bnxe6WUtS6gpLInwiVFlJvsLTwcbc/8Vc2BUJ9BCEVBD8oQVpljxYAmBpKb6FOdRPRGDCV3zeZ2McfRaRiVCtleFDnJUOFIBSK+FWgU9Hqffs4XYqX/rLF/ONTjXJJRduw3HU3SypJcWlGpCJAGgxLpm8UxWpiLa41xoBvpEOIALp5penf98qWFg52GYPKWrpw+/twxki6ZXOF8MwkCmWpezhdXQcUV999V1oHSsUCd1YnzzeT3SYndaTifFZda4ohqAdB5/YYSiE+hUJOBS1EQ91QioSzyQjLgViuJ4EMXK+KgLXVPbl7ASvlCFRc2UJjJy6jbwptcVV9bjBH1ehPzKmiCNQqBb2xNXFB1dprNUJGBt6OocVxwLuibx8ZBPo1S610iNioeyyrQCjVJDn7lsxj9xjCqL7HMoz2K28sJ+PDrqvENtFw3p1J1P97lfSOTCounlAIB1b+2301nnO6zo5BG/fOl9HDnWg+qiKM6bUup8MUiPzuhCeRKp8+YApjAp7sdDAwAVqf7PRetXFMjHlpLUlFTQVRYoSoukBDnHUYWgLKUqOuZx6oZmjudGP6iox4t2qdepZjMT6ELXypNh24pKBy+qVFE3OFUeqOWQtpn2V3EsZKezdnvR9J6b0aSPVeFSQfpSTR+qKnyqYjhaucdF6vHJLIqOep7CASo6AiVE7fPzawEAT7y2x84IxzAjkSc370VrZw8qU2GcM2kU+WYwa3TkMaIoi7W5QBrH5XdYHUMlj45rjQ6xlpOJKh2b6ORSyJJsayOpQlCoseiLemp9MxmB7H2oKAjD75OTMegm6UWxoDRmx4I+hPw+pKQJsnudpJrpExAJBNyedto3OqVOt47HPJ+mrJ91QmaGTXmtjfg9eh/E/afjfnE8hHDAJ3t+dEkSwn6Xgas0GUI04JMeUd290kVMiL6h2z0Ajryjio7XAzvrGW2DSBYhzkMT6cgeHdkTVanMR+i7kE2ByRZm3y8aQ9+M0SlMq0yiuzeDX7286/jnyANOSNF56KGHUFtbi3A4jLq6Ojz//PP9Hr9+/XrU1dUhHA5j3LhxWLNmzQk1lsnOrkMd+NFfdgAAbjx/ghLWMziPTlLZfEz1tFDoYFBTEnV9X1Ukl6meEjrQVygvfzWpS1/+aNAvvfRUyFJBSuur5y7M4okRCoU6qIjj1Im7OI86AAurIJ2QF8WCtmeMWnBo22j7pTC/OFV09IodVYCosKTnry6W70e20DWqkNCNXwFgDOnXcMAnKZRuj47zXdDvdVnJqpXnI1vomvoMjhmooqMZ6AHgjJpCnDWuCN29GXzzqTeRyfBanXyAZdPgaO3sxv1/fgcA8IWza2W5MQgDWX9hOxQ67qnGisJoQJlw6tfo+Eg6XkAeC6iyVJ6kBhnh0XGviQGUNToRd+iaGE/VjJBiskyVGiELVO+GqgyGAz7J0KdTxkT71FAy85zyRF5NCe2qp0mxrYagiXpxzbmk9T7K7wUtD4R8zZayRbw34trouC9kBJ2eVBVFXXvmRALuDGkhvw9er8fewBpwFBX6rOm8LuqaVIE4hhrxypNhO7qCbro6pjAqJd2g966/NTrqxq1U3mbbH059pwa0j5yyRgcw9ze8YcE4AMD/Xf+evTVEPjNoRefxxx/HsmXLcPvtt2Pz5s1YsGABFi1ahIYGfQjIzp078fGPfxwLFizA5s2bcdttt+Gmm27CE0888YEbz5jsbO7A5x/diKPpXswdW4j/M2eMfMAgPTqA+QILplYksx5HJ67jSuKu76uIEEpFZEEGyBNjVRmpUpQECvXq0AGlpjim/VsdWMTGcdGgvEBWKBQ01bP5+2Y7Y0p2MntQTClubmuQnjDK6ZMaomTQQbQiizWHKlVUmaDCkSonxVk8OtJvJbMrDNTiSC1MHo9HsoSpykkFuReqx4ve3zEFEXttkSAa9EvWLTUUjrZTnty4lWo97oEeMK/p25dOR9DvxV//eRAr/vt1dHb3DvCczKkIy6bB0d7Vg3/59WvY35ZGbUkMnz1rrHLEwA1kfp9XGheyhZbS8U317qrrQOiYTev5vB5pcknlDh2LJpY55cKAoq4hFeORHLbr9ggIBUfNJBfym+ezdkcA4MgWNfGCLpukvNeKtb6S/O740rhdX+Ds5+LUVRUP4WXQJQeQt3iQPSdC0dVtA0HLktY6IRWqIAnlb3ypI4ftSAoq2ywZIbZUAMz7pMoKj8ej7UMAUlKZuEZ5dULDSegkkZFBoigJWVdKZBGVh/TZVqNL6DNTSDKoZksOpDt/tiQ7NMoiEfJrE0S5yNJfl86sxMyqArSne/GlX2zCoaNp7XH5gvtJPQ733XcfvvjFL+L6668HANx///3405/+hB//+Me45557XMevWbMG1dXVuP/++wEAU6dOxauvvorvf//7WLx48Qdr/SARL4N4Jwzdd1KZOE6uB80xuuP6O790LuV3dOegL3J3XwYH2tJ4/1AH1v/zIP7w+j709BkYXRDBf1wz2zVADNajA5gTS7FQ+7TK7IoOfUHHjYq5vtdZbijUgu9SdEjdurGF0ndiUzoAmFaZsv+eZW0IKa5BQJUWtR3UmJ9Q3PGw3n86+NB7JwSJEHiAqZSIe0D7hx4z107hCkSJ8KUeFz/JGlMsufr163WoUnH66ALnPOR5UJ8NKvhnVhXgd9YaLzWsZGxx1N5HR52gUFyhauQeqPtI2HWSYeyzdkNXw1douyeVJ+xNDftrg0QWjw4ATC5P4LuLT8fy327Bb1/dgxe2N2Nx3RjMqipAdVEUyUgAIWudl18jdKXP2X42y/HMh89wlE1UJhnWZwOy7LH/VsoMyHLFMMw/pDrKOdu6erCv9Rg27jyM3766B01tXYgGffiPT892KQGDNZBNq0za2wjMUcZrwcyqAvz35r0A9MrQYbJmgMqGCFEIwoqxTJqQknNSA486LgHymL5w8ij8+1+2A4BtjBtX4sizN/e6d5Kn9TOayUFNcQz729J2WJc4N5VddFzQZYabP97cC496LOZZZVWFUXs8TEUC8JJzCSVxQqmj7Ik+qCmOYj3MyX1xPIhIwIeCaACtnT0YbxnmqAFzopWFj/ZzWTIMr9eDwmgALZ09mD7anCPMqXLuuxgy548vcV0jlbNqtj3KmMII9rQcw9ji/g1bp48psDdKFzJOrOcEnHkBVX4WTnLC+8cURm0ZFCNGUIEU+RChbVfW9xDliRpnXe+WAlWYZpM5DGUW6dsxRVHNPE+H3tDn9Xrwo6tn4fKHNuCNvUdwwX3rcdXcKswbX4wxhVEURgMIBXzweTzweEwFWPw9HGXZoBSd7u5ubNq0CStWrJDK6+vrsWHDBm2dF198EfX19VLZRRddhLVr16KnpweBgFt7TafTSKcdDbOt7cQzI737xksY/8RFAJzhevjdJjcVAGYCuAzAfQEAAQBdAH7YX62BX/kFU0vtrByn9ePRuWLOGPzqZdNiWlviVnToy37pzNGu76+cOwaP/H0nAKC6SK5PJ/FnTyyRvpMW0ZPBZRzxoITIbtL05bxsltyORdPL8cybTbjlY5Ok486bUorfbdqDL58zTgrpmD++GBvePYTrz67VvvRUKaP1qLCmgtdHFJqFE50Yeaq0LZg4ClPKE3i7qV1SYs6bUmqX0/tEFabCmN5CpIZS1J9Whm899SYAOewDAOZUF9pCVR20z6wtxpt72xAL+lzPymSRqhZub4+AxvPPyjLIA7JgP6NGP5FyY/VtTydwR8r17ScBfFI0Kw1AP4zlBbs/8zdUTZyZ62acFIajbHrxl6sw7937AQydTBoFYDyABQBuAQDxmv+0n0oDnNjQ0JpxGlkAAPXTyrDqf7YCcHvZAdML0Nnd51qfAQALJpZgc0Mr1ny2TiqnsiCiSUAAyGPWlXVj8Nw/D+DXN5xll82uKkAi5Ed7uhczrN3jvV4PVi6agnueeRvLLpxoH7vswon4wz/24eElZ9hlQc3i8R98aib+980myahVUxzFO/uPuo4FHMWMGrLEnkaXzqrEX94+gM+eNdb2Zn/zE1Nx7uRRmDu2yFaEXr7tAvzvm004d7IpR+bWFOHJr87HG3uP4OMzzEQTt108FWeOKza95JbC8fiX5uGd/e0431rbO398Me6+fAZqSqK2onLzBRMxsTSOC6aU2R6JZ24+B3/f0Ywzx5ntTEUD+Nl1Z+Ch5961PYQ0IkQYsqhRTshQn9eDvowhecLWLjkDz28/KK851vDjz8zB5x/dKMmFz82rwdf/6x/44tm19v2vIc+l6CMAuP/qWbhyzYuYVBbXynTqKaTfq8kt/vUT07Dk0VdQlgxLSTIAU8n/x+5WbfupQbB+Wrn2GDqX0r0fWkRbn/mG+Y8wFsBrgDkGZAC8Yv0bYhoxChV37DipvzEoRae5uRl9fX0oKyuTysvKytDU1KSt09TUpD2+t7cXzc3NqKiocNW555578O1vf3swTWMGwth5Az70yroqbNl9BIc70pjWj0enbmwhvnrueOxuOWYLCIrH48G/XTYNbzW24csLx7m+n1qRxK9vOBPvHuxweY7OmTQK88cXY2ZVgWtR/12fnIFv/f5NrFg0RSr3eT24/uxarNu2H4uVEL41n52D9e8cxK31k6XyH141CysXpV3rV+5dfDpWLJriWndy9+Uz8FpDi0th+sGVM/HYxgbc9cnpUvnXzp+Anz7/nut3//3qWfjZhvdx8wWOEPV6PXj5tgvwl20HbMEEmILhjzctQEtnt9SecMCHP3ztbOxpOeZSNJ/6l4/ip8+/h+Ufm+T63W//4S08vGSuVF6WDOPmCyai4XAnpiv38mvnT8Dre1q1AudL54xDUSyIT82t0oYbPHPzAvzg2XfwjYsmu+oCwNfrJ+NouhffuGhKvymjv3TOOLzXfBQ3XzDJla0oK4kKoLAWaNk5sOOZYQnLppNI9cDkxtJzxuOPrzfiU3PHZLU2V6QiuPG8CdjbekxrQFu75Azc88w2fOeK013f/ey6jyDd2+fKAPqpuVV45IWd0sQVABbXmUY44RURfO/Kmejty0iZrTweD/76jXPR1NYlGcu+vHA86qeVS2HUyy6chGUXymPqDz41E1/42UZ86xOn2WVjCqO4foEs8+6/aja++qtN0ph828en4OcbdtnjYyIcwG9uOAuhgNdWRCpSEfz2y/J9KE2EcYUi48qSYSyZXyOVza4uxOxqRwEI+X2SbAFM7/bkcsco5fd5cc2Z1a5zX/fRWqmsPBXG4jq5DedOLrX3KgNMmfz0TQuwv63LlrHXzhuLJzfvlSb1a5fMxar/2Yp7rpiRtV0A8NBn5mDZ41vwgysdo01pMoynb14gHXf57NGYVV0gKd0l8RDWLT8HiXBA8pJVFkSw/hvnuuTP8gsn4Xev7cbXzp8olX/l3PH49csNkuwGgBljUtiw4nxXeCUAPPDp2bjpsc348jnuedCoeAhL5o1Fn2H0O99auWgK7v/zdvwrec76pXoesPXJgR2bx3iMQeyYt2/fPowePRobNmzAvHnOS7d69Wr88pe/xNtvv+2qM2nSJFx33XVYuXKlXfb3v/8dZ599NhobG1Fe7tZedVazqqoqHDlyBMlk9odAR293Gm0tzg7o4uGzvTvkWfSIUlqmFOm0fd05dEYw51weTZn7/GobPR/E7uf1AdGi4x/HnBS6ezOu9UnMENHXCxxrGXQ1AwZ6MwbSPX3oI/GN6oipDqDqkHqqpDlIFZXCHxhESlKLtrY2pFKpExp/h4rhKJuOdbTj2NEjkkzyeGQ5ZH5W5ILHLWfUMlrHdd7BMEzkRiZjDDCU5+TR05eRJs/MyeNU6OtT4ZkbEMdagb6eQVXpzWTQmzGQMQxkMgYyGTM8Uxei+UHxen0oGOU2Kg2EgcqmQXl0SkpK4PP5XBayAwcOuCxjgvLycu3xfr8fxcXF2jqhUAih0AAttsfBHwyhqGzM8Q9kmJMIKzk5xOcH4qOOf5yCB2ZE6EBy2zC5ZTjKpkgsgUgscfwDmeNyKkw4cz3xHkmcCn19KjxzAyJSMOgqfpzAAv5TmEE9LcFgEHV1dVi3bp1Uvm7dOsyfP19bZ968ea7jn332WcydO1cbA80wDMMwg4FlE8MwDKNj0GrxLbfcgocffhiPPPIItm3bhuXLl6OhoQFLly4FAKxcuRKf+9zn7OOXLl2KXbt24ZZbbsG2bdvwyCOPYO3atbj11ls/vKtgGIZhRjQsmxiGYRiVQXunrrrqKhw6dAh33nknGhsbMX36dDz99NMYO9bMsNHY2CjtW1BbW4unn34ay5cvx4MPPojKykr86Ec/GvLU0gzDMEz+wrKJYRiGURlUMoJcMRwWwzIMw+QjPP5mh/uGYRgmN5yUZAS5QuhiH2TPAoZhGGbwiHF3GNjEhhyWTQzDMLlhoLJpWCg67e3tAICqqqoct4RhGGZk0t7ejlTKvVfWSIZlE8MwTG45nmwaFqFrmUwG+/btQyKR0O5jcyoh9lXYvXv3iA5l4H5w4L5w4L5wGC59YRgG2tvbUVlZCa8392ldTyWGi2waLs/aUMB94cB94cB94TBc+mKgsmlYeHS8Xi/GjBlee+Ekk8lT+gEZKrgfHLgvHLgvHIZDX7AnR89wk03D4VkbKrgvHLgvHLgvHIZDXwxENrF5jmEYhmEYhmGYvIMVHYZhGIZhGIZh8g5WdD5kQqEQVq1ahVAolOum5BTuBwfuCwfuCwfuC2ao4GfNgfvCgfvCgfvCId/6YlgkI2AYhmEYhmEYhhkM7NFhGIZhGIZhGCbvYEWHYRiGYRiGYZi8gxUdhmEYhmEYhmHyDlZ0GIZhGIZhGIbJO1jRYRiGYRiGYRgm72BF50Ni9erVmD9/PqLRKAoKCrTHNDQ04JJLLkEsFkNJSQluuukmdHd3D21Dc0RNTQ08Ho/0b8WKFblu1pDw0EMPoba2FuFwGHV1dXj++edz3aQh54477nDd//Ly8lw3a0j429/+hksuuQSVlZXweDx46qmnpO8Nw8Add9yByspKRCIRnHvuudi6dWtuGsvkHSybssNyaWTLJWDkyqaRJJdY0fmQ6O7uxpVXXomvfOUr2u/7+vpw8cUXo6OjAy+88AIee+wxPPHEE/j6178+xC3NHXfeeScaGxvtf9/85jdz3aSTzuOPP45ly5bh9ttvx+bNm7FgwQIsWrQIDQ0NuW7akDNt2jTp/r/xxhu5btKQ0NHRgZkzZ+KBBx7Qfv/d734X9913Hx544AFs3LgR5eXl+NjHPob29vYhbimTj7Bs6h+WSyNbLgEjUzaNKLlkMB8qjz76qJFKpVzlTz/9tOH1eo29e/faZb/5zW+MUChkHDlyZAhbmBvGjh1r/PCHP8x1M4acj3zkI8bSpUulsilTphgrVqzIUYtyw6pVq4yZM2fmuhk5B4Dx5JNP2p8zmYxRXl5ufOc737HLurq6jFQqZaxZsyYHLWTyFZZNblguOYxEuWQYLJsMI//lEnt0hogXX3wR06dPR2VlpV120UUXIZ1OY9OmTTls2dBx7733ori4GLNmzcLq1avzPjSiu7sbmzZtQn19vVReX1+PDRs25KhVuWP79u2orKxEbW0trr76arz33nu5blLO2blzJ5qamqRnJBQKYeHChSPyGWGGnpEum1gumYxUuQSwbFLJN7nkz3UDRgpNTU0oKyuTygoLCxEMBtHU1JSjVg0dN998M+bMmYPCwkK88sorWLlyJXbu3ImHH3441007aTQ3N6Ovr89138vKykbEPaeceeaZ+MUvfoFJkyZh//79uOuuuzB//nxs3boVxcXFuW5ezhDPge4Z2bVrVy6axIwwRrJsYrnkMBLlEsCySUe+ySX26PSDbpGa+u/VV18d8Pk8Ho+rzDAMbflwYDD9s3z5cixcuBCnn346rr/+eqxZswZr167FoUOHcnwVJx/1/g7ne36iLFq0CIsXL8aMGTNw4YUX4o9//CMA4Oc//3mOW3ZqwM8IMxhYNmWH5dLA4DHHhGVTdvLlGWGPTj/ceOONuPrqq/s9pqamZkDnKi8vx8svvyyVtbS0oKenx6U1Dxc+SP+cddZZAIAdO3bkrdWkpKQEPp/PZSU7cODAsL3nHxaxWAwzZszA9u3bc92UnCKy+zQ1NaGiosIu52eE6Q+WTdlhudQ/LJf6h2VT/sklVnT6oaSkBCUlJR/KuebNm4fVq1ejsbHRfnCeffZZhEIh1NXVfSi/MdR8kP7ZvHkzAEgvUb4RDAZRV1eHdevW4fLLL7fL161bh8suuyyHLcs96XQa27Ztw4IFC3LdlJxSW1uL8vJyrFu3DrNnzwZgxtCvX78e9957b45bx5yqsGzKDsul/mG51D8sm/JPLrGi8yHR0NCAw4cPo6GhAX19fdiyZQsAYMKECYjH46ivr8dpp52Ga6+9Ft/73vdw+PBh3HrrrbjhhhuQTCZz2/iTzIsvvoiXXnoJ5513HlKpFDZu3Ijly5fj0ksvRXV1da6bd1K55ZZbcO2112Lu3LmYN28efvKTn6ChoQFLly7NddOGlFtvvRWXXHIJqqurceDAAdx1111oa2vDkiVLct20k87Ro0exY8cO+/POnTuxZcsWFBUVobq6GsuWLcPdd9+NiRMnYuLEibj77rsRjUZxzTXX5LDVTL7AskkPyyWWS8DIlU0jSi7lMuVbPrFkyRIDgOvfc889Zx+za9cu4+KLLzYikYhRVFRk3HjjjUZXV1fuGj1EbNq0yTjzzDONVCplhMNhY/LkycaqVauMjo6OXDdtSHjwwQeNsWPHGsFg0JgzZ46xfv36XDdpyLnqqquMiooKIxAIGJWVlcYVV1xhbN26NdfNGhKee+457diwZMkSwzDMVJ6rVq0yysvLjVAoZJxzzjnGG2+8kdtGM3kDyyY9LJdYLhnGyJVNI0kueQzDMIZWtWIYhmEYhmEYhjm5cNY1hmEYhmEYhmHyDlZ0GIZhGIZhGIbJO1jRYRiGYRiGYRgm72BFh2EYhmEYhmGYvIMVHYZhGIZhGIZh8g5WdBiGYRiGYRiGyTtY0WEYhmEYhmEYJu9gRYdhGIZhGIZhmLyDFR2GYRiGYRiGYfIOVnQYhmEYhmEYhsk7WNFhGIZhGIZhGCbv+P89/g+XLQqnUQAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt \n",
"import numpy\n",
"import numpy.polynomial.hermite as Herm\n",
"import math\n",
"\n",
"#Choose simple units\n",
"m=1.\n",
"w=1.\n",
"hbar=1.\n",
"#Discretized space\n",
"dx = 0.05\n",
"x_lim = 12\n",
"x = numpy.arange(-x_lim,x_lim,dx)\n",
"\n",
"def hermite(x, n):\n",
" xi = numpy.sqrt(m*w/hbar)*x\n",
" herm_coeffs = numpy.zeros(n+1)\n",
" herm_coeffs[n] = 1\n",
" return Herm.hermval(xi, herm_coeffs)\n",
"def stationary_state(x,n):\n",
" xi = numpy.sqrt(m*w/hbar)*x\n",
" prefactor = 1./math.sqrt(2.**n * math.factorial(n)) * (m*w/(numpy.pi*hbar))**(0.25)\n",
" psi = prefactor * numpy.exp(- xi**2 / 2) * hermite(x,n)\n",
" return psi\n",
" \n",
"def classical_P(x,n):\n",
" E = hbar*w*(n+0.5)\n",
" x_max = numpy.sqrt(2*E/(m*w**2))\n",
" classical_prob = numpy.zeros(x.shape[0])\n",
" x_inside = abs(x) < (x_max - 0.025)\n",
" classical_prob[x_inside] = 1./numpy.pi/numpy.sqrt(x_max**2-x[x_inside]*x[x_inside])\n",
" return classical_prob\n",
"\n",
"plt.figure(figsize=(10, 8))\n",
"plt.subplot(3,2,1)\n",
"plt.plot(x, numpy.conjugate(stationary_state(x,0))*stationary_state(x,0), label=\"n=0\")\n",
"plt.plot(x, classical_P(x,0))\n",
"plt.legend()\n",
"plt.subplot(3,2,2)\n",
"plt.plot(x, numpy.conjugate(stationary_state(x,3))*stationary_state(x,3), label=\"n=3\")\n",
"plt.plot(x, classical_P(x,3))\n",
"plt.legend()\n",
"plt.subplot(3,2,3)\n",
"plt.plot(x, numpy.conjugate(stationary_state(x,8))*stationary_state(x,8), label=\"n=8\")\n",
"plt.plot(x, classical_P(x,8))\n",
"plt.legend()\n",
"plt.subplot(3,2,4)\n",
"plt.plot(x, numpy.conjugate(stationary_state(x,15))*stationary_state(x,15), label=\"n=15\")\n",
"plt.plot(x, classical_P(x,15))\n",
"plt.legend()\n",
"plt.subplot(3,2,5)\n",
"plt.plot(x, numpy.conjugate(stationary_state(x,25))*stationary_state(x,25), label=\"n=25\")\n",
"plt.plot(x, classical_P(x,25))\n",
"plt.legend()\n",
"plt.subplot(3,2,6)\n",
"plt.plot(x, numpy.conjugate(stationary_state(x,40))*stationary_state(x,40), label=\"n=40\")\n",
"plt.plot(x, classical_P(x,40))\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ef700729",
"metadata": {},
"source": [
"* What conclusions do you extract from the above computational comparisons? When does a quantum oscillator compare to a classical oscillator?"
]
},
{
"cell_type": "markdown",
"id": "839593d9",
"metadata": {},
"source": [
"# Infrared spectroscopy\n",
"\n",
"Remember that in our previous session we were able to calculate a frequency analysis of molecules (from the second derivative of the energy). These calculations can give us a good approximation to the peaks of absorbance in Infrared Spectroscopy.\n",
"\n",
"Let's run a frequency analysis of carbon monoxide. Notice that first we must optimize the structure so that the frequency analysis "
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "d5e5919d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"overwrite output file: m1d6_co_fq.out\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"geometric-optimize called with the following command line:\n",
"/Users/pratr001/miniconda3/envs/pchem/lib/python3.12/site-packages/ipykernel_launcher.py --f=/Users/pratr001/Library/Jupyter/runtime/kernel-v30bf7441fdfe734567d2f39bf552819b8eeaaf6cd.json\n",
"\n",
" \u001b[91m())))))))))))))))/\u001b[0m \n",
" \u001b[91m())))))))))))))))))))))))),\u001b[0m \n",
" \u001b[91m*)))))))))))))))))))))))))))))))))\u001b[0m \n",
" \u001b[94m#,\u001b[0m \u001b[91m()))))))))/\u001b[0m \u001b[91m.)))))))))),\u001b[0m \n",
" \u001b[94m#%%%%,\u001b[0m \u001b[91m())))))\u001b[0m \u001b[91m.))))))))*\u001b[0m \n",
" \u001b[94m*%%%%%%,\u001b[0m \u001b[91m))\u001b[0m \u001b[93m..\u001b[0m \u001b[91m,))))))).\u001b[0m \n",
" \u001b[94m*%%%%%%,\u001b[0m \u001b[93m***************/.\u001b[0m \u001b[91m.)))))))\u001b[0m \n",
" \u001b[94m#%%/\u001b[0m \u001b[94m(%%%%%%,\u001b[0m \u001b[93m/*********************.\u001b[0m \u001b[91m)))))))\u001b[0m \n",
" \u001b[94m.%%%%%%#\u001b[0m \u001b[94m*%%%%%%,\u001b[0m \u001b[93m*******/,\u001b[0m \u001b[93m**********,\u001b[0m \u001b[91m.))))))\u001b[0m \n",
" \u001b[94m.%%%%%%/\u001b[0m \u001b[94m*%%%%%%,\u001b[0m \u001b[93m**\u001b[0m \u001b[93m********\u001b[0m \u001b[91m.))))))\u001b[0m \n",
" \u001b[94m##\u001b[0m \u001b[94m.%%%%%%/\u001b[0m \u001b[94m(%%%%%%,\u001b[0m \u001b[93m,******\u001b[0m \u001b[91m/)))))\u001b[0m \n",
" \u001b[94m%%%%%%\u001b[0m \u001b[94m.%%%%%%#\u001b[0m \u001b[94m*%%%%%%,\u001b[0m \u001b[92m,/////.\u001b[0m \u001b[93m******\u001b[0m \u001b[91m))))))\u001b[0m \n",
" \u001b[94m#%\u001b[0m \u001b[94m%%\u001b[0m \u001b[94m.%%%%%%/\u001b[0m \u001b[94m*%%%%%%,\u001b[0m \u001b[92m////////,\u001b[0m \u001b[93m*****/\u001b[0m \u001b[91m,)))))\u001b[0m \n",
" \u001b[94m#%%\u001b[0m \u001b[94m%%%\u001b[0m \u001b[94m%%%#\u001b[0m \u001b[94m.%%%%%%/\u001b[0m \u001b[94m(%%%%%%,\u001b[0m \u001b[92m///////.\u001b[0m \u001b[93m/*****\u001b[0m \u001b[91m))))).\u001b[0m\n",
" \u001b[94m#%%%%.\u001b[0m \u001b[94m%%%%%#\u001b[0m \u001b[94m/%%%%%%*\u001b[0m \u001b[94m#%%%%%%\u001b[0m \u001b[92m/////)\u001b[0m \u001b[93m******\u001b[0m \u001b[91m))))),\u001b[0m\n",
" \u001b[94m#%%%%##%\u001b[0m \u001b[94m%%%#\u001b[0m \u001b[94m.%%%%%%/\u001b[0m \u001b[94m(%%%%%%,\u001b[0m \u001b[92m///////.\u001b[0m \u001b[93m/*****\u001b[0m \u001b[91m))))).\u001b[0m\n",
" \u001b[94m##\u001b[0m \u001b[94m%%%\u001b[0m \u001b[94m.%%%%%%/\u001b[0m \u001b[94m*%%%%%%,\u001b[0m \u001b[92m////////.\u001b[0m \u001b[93m*****/\u001b[0m \u001b[91m,)))))\u001b[0m \n",
" \u001b[94m#%%%%#\u001b[0m \u001b[94m/%%%%%%/\u001b[0m \u001b[94m(%%%%%%\u001b[0m \u001b[92m/)/)//\u001b[0m \u001b[93m******\u001b[0m \u001b[91m))))))\u001b[0m \n",
" \u001b[94m##\u001b[0m \u001b[94m.%%%%%%/\u001b[0m \u001b[94m(%%%%%%,\u001b[0m \u001b[93m*******\u001b[0m \u001b[91m))))))\u001b[0m \n",
" \u001b[94m.%%%%%%/\u001b[0m \u001b[94m*%%%%%%,\u001b[0m \u001b[93m**.\u001b[0m \u001b[93m/*******\u001b[0m \u001b[91m.))))))\u001b[0m \n",
" \u001b[94m*%%%%%%/\u001b[0m \u001b[94m(%%%%%%\u001b[0m \u001b[93m********/*..,*/*********\u001b[0m \u001b[91m*))))))\u001b[0m \n",
" \u001b[94m#%%/\u001b[0m \u001b[94m(%%%%%%,\u001b[0m \u001b[93m*********************/\u001b[0m \u001b[91m)))))))\u001b[0m \n",
" \u001b[94m*%%%%%%,\u001b[0m \u001b[93m,**************/\u001b[0m \u001b[91m,))))))/\u001b[0m \n",
" \u001b[94m(%%%%%%\u001b[0m \u001b[91m()\u001b[0m \u001b[91m))))))))\u001b[0m \n",
" \u001b[94m#%%%%,\u001b[0m \u001b[91m())))))\u001b[0m \u001b[91m,)))))))),\u001b[0m \n",
" \u001b[94m#,\u001b[0m \u001b[91m())))))))))\u001b[0m \u001b[91m,)))))))))).\u001b[0m \n",
" \u001b[91m()))))))))))))))))))))))))))))))/\u001b[0m \n",
" \u001b[91m())))))))))))))))))))))))).\u001b[0m \n",
" \u001b[91m())))))))))))))),\u001b[0m \n",
"\n",
"-=# \u001b[1;94m geomeTRIC started. Version: 1.1 \u001b[0m #=-\n",
"Current date and time: 2025-04-17 09:18:59\n",
"#========================================================#\n",
"#| \u001b[92m Arguments passed to driver run_optimizer(): \u001b[0m |#\n",
"#========================================================#\n",
"customengine \n",
"input /var/folders/1b/pw4sp5tj3_16kjl12vvf8vt40000gq/T/tmp9jxui42q/e755909d-da98-40d0-ba86-cc14bfe0450f \n",
"logIni /Users/pratr001/miniconda3/envs/pchem/lib/python3.12/site-packages/pyscf/geomopt/log.ini \n",
"----------------------------------------------------------\n",
"Custom engine selected.\n",
"Bonds will be generated from interatomic distances less than 1.20 times sum of covalent radii\n",
"6 internal coordinates being used (instead of 6 Cartesians)\n",
"Internal coordinate system (atoms numbered from 1):\n",
"Distance 1-2\n",
"Translation-X 1-2\n",
"Translation-Y 1-2\n",
"Translation-Z 1-2\n",
"Rotation-A 1-2\n",
"Rotation-B 1-2\n",
"Rotation-C 1-2\n",
" : 1\n",
" : 1\n",
" : 1\n",
" : 1\n",
" : 1\n",
" : 1\n",
" : 1\n",
"> ===== Optimization Info: ====\n",
"> Job type: Energy minimization\n",
"> Maximum number of optimization cycles: 300\n",
"> Initial / maximum trust radius (Angstrom): 0.100 / 0.300\n",
"> Convergence Criteria:\n",
"> Will converge when all 5 criteria are reached:\n",
"> |Delta-E| < 1.00e-06\n",
"> RMS-Grad < 3.00e-04\n",
"> Max-Grad < 4.50e-04\n",
"> RMS-Disp < 1.20e-03\n",
"> Max-Disp < 1.80e-03\n",
"> === End Optimization Info ===\n",
"Step 0 : Gradient = 2.498e-01/2.498e-01 (rms/max) Energy = -112.6189499615\n",
"Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 5.00000e-02 5.00000e-02 6.71931e-01\n",
"Step 1 : Displace = \u001b[0m9.837e-02\u001b[0m/\u001b[0m9.837e-02\u001b[0m (rms/max) Trust = 1.000e-01 (=) Grad = \u001b[0m7.714e-02\u001b[0m/\u001b[0m7.714e-02\u001b[0m (rms/max) E (change) = -112.6652860802 (\u001b[0m-4.634e-02\u001b[0m) Quality = \u001b[0m0.998\u001b[0m\n",
"Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 5.00000e-02 5.00000e-02 8.79414e-01\n",
"Step 2 : Displace = \u001b[0m2.321e-02\u001b[0m/\u001b[0m2.321e-02\u001b[0m (rms/max) Trust = 1.414e-01 (\u001b[92m+\u001b[0m) Grad = \u001b[0m4.568e-02\u001b[0m/\u001b[0m4.568e-02\u001b[0m (rms/max) E (change) = -112.6663834887 (\u001b[0m-1.097e-03\u001b[0m) Quality = \u001b[0m0.324\u001b[0m\n",
"Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 5.00000e-02 5.00000e-02 1.40021e+00\n",
"Step 3 : Displace = \u001b[0m8.632e-03\u001b[0m/\u001b[0m8.632e-03\u001b[0m (rms/max) Trust = 1.414e-01 (=) Grad = \u001b[0m4.454e-03\u001b[0m/\u001b[0m4.454e-03\u001b[0m (rms/max) E (change) = -112.6672145698 (\u001b[0m-8.311e-04\u001b[0m) Quality = \u001b[0m1.115\u001b[0m\n",
"Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 5.00000e-02 5.00000e-02 1.26368e+00\n",
"Step 4 : Displace = \u001b[92m9.326e-04\u001b[0m/\u001b[92m9.326e-04\u001b[0m (rms/max) Trust = 2.000e-01 (\u001b[92m+\u001b[0m) Grad = \u001b[0m3.002e-04\u001b[0m/\u001b[92m3.002e-04\u001b[0m (rms/max) E (change) = -112.6672219101 (\u001b[0m-7.340e-06\u001b[0m) Quality = \u001b[0m0.935\u001b[0m\n",
"Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 5.00000e-02 5.00000e-02 1.34887e+00\n",
"Step 5 : Displace = \u001b[92m5.889e-05\u001b[0m/\u001b[92m5.889e-05\u001b[0m (rms/max) Trust = 2.828e-01 (\u001b[92m+\u001b[0m) Grad = \u001b[92m3.235e-06\u001b[0m/\u001b[92m3.235e-06\u001b[0m (rms/max) E (change) = -112.6672219430 (\u001b[92m-3.293e-08\u001b[0m) Quality = \u001b[0m0.985\u001b[0m\n",
"Hessian Eigenvalues: 5.00000e-02 5.00000e-02 5.00000e-02 ... 5.00000e-02 5.00000e-02 1.34887e+00\n",
"Converged! =D\n",
"\n",
" #==========================================================================#\n",
" #| If this code has benefited your research, please support us by citing: |#\n",
" #| |#\n",
" #| Wang, L.-P.; Song, C.C. (2016) \"Geometry optimization made simple with |#\n",
" #| translation and rotation coordinates\", J. Chem, Phys. 144, 214108. |#\n",
" #| http://dx.doi.org/10.1063/1.4952956 |#\n",
" #==========================================================================#\n",
" Time elapsed since start of run_optimizer: 0.775 seconds\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimized CO structure:\n",
"[[0. 0. 0.08466366]\n",
" [0. 0. 1.21533634]]\n"
]
}
],
"source": [
"#pip install geometric\n",
"\n",
"from pyscf import gto, scf\n",
"from pyscf.geomopt.geometric_solver import optimize\n",
"from pyscf.hessian import thermo\n",
"from pyscf import lib\n",
"\n",
"# Convert from Bohr to Angstroms\n",
"bohr_to_angstrom = lib.parameters.BOHR \n",
"\n",
"molCO = gto.M(\n",
" atom = 'O 0 0 0; C 0 0 1.3', # in Angstrom\n",
" basis = '631g',\n",
" symmetry = True,\n",
" charge=0, \n",
" spin=0,\n",
" verbose=3,\n",
" output='m1d6_co_fq.out'\n",
")\n",
"# Perform the Hartree-Fock calculation\n",
"co_sp = molCO.RHF.run()\n",
"co_opt = optimize(co_sp).run()\n",
"print(\"Optimized CO structure:\")\n",
"print(co_opt.atom_coords()*bohr_to_angstrom)\n",
"hessian = co_sp.Hessian().kernel()\n",
"\n",
"# Frequency analysis\n",
"freq_info = thermo.harmonic_analysis(co_sp.mol, hessian)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "a8187bae",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'freq_error': 0, 'freq_au': array([0.23108101]), 'freq_wavenumber': array([1187.86897303]), 'norm_mode': array([[[ 0. , 0. , -0.1637143 ],\n",
" [ 0. , 0. , 0.21807219]]]), 'reduced_mass': array([13.44847911]), 'vib_temperature': array([1709.07897771]), 'force_const_au': array([0.05339843]), 'force_const_dyne': array([11.18048088])}\n"
]
}
],
"source": [
"print(freq_info)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c6840077",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimized CO structure:\n",
"[[0. 0. 0.15999114]\n",
" [0. 0. 2.29665282]]\n",
"\n",
"Vibrational frequencies (in cm⁻¹):\n",
"[[[ 6.20971779 6.20971926 5985.86892547]\n",
" [5985.86892548 6.20971022 6.20971021]]\n",
"\n",
" [[5985.86892548 6.20971022 6.20971021]\n",
" [ 6.20970714 6.20970733 5985.86892548]]]\n"
]
}
],
"source": [
"from pyscf.hessian.rhf import Hessian\n",
"# Compute the Hessian for frequency analysis\n",
"mf = scf.RHF(co_opt).run()\n",
"hessian_calculator = Hessian(mf)\n",
"hessian_matrix = hessian_calculator.kernel()\n",
"\n",
"import numpy as np\n",
"# Convert Hessian to vibrational frequencies (in cm⁻¹)\n",
"frequencies = np.linalg.eigvalsh(hessian_matrix)\n",
"frequencies = np.sqrt(np.abs(frequencies)) * 5140.48 # Conversion factor for atomic units to cm⁻¹\n",
"\n",
"# Print results\n",
"print(\"Optimized CO structure:\")\n",
"print(co_opt.atom_coords())\n",
"print(\"\\nVibrational frequencies (in cm⁻¹):\")\n",
"print(frequencies)"
]
},
{
"cell_type": "markdown",
"id": "4162a875",
"metadata": {},
"source": [
"* Look at the calculation above: find the force constant and the reduced mass of the CO molecule. Use the formula relating those to find the frequency of vibration. Notice that it's giving you the wavenumber in cm-1. How are those magnitudes related?\n",
"* Your turn: Choose 3 other diatomic molecules. Based on the information that the calculations are giving you, plot the energy levels of each. (Do not use symmetric molecules N2, O2... as only molecules with dipole will absorb in the IR spectrum)\n",
"* Find online the experimental frequency of absorption of your molecules and compare them with your results."
]
},
{
"cell_type": "markdown",
"id": "50190464",
"metadata": {},
"source": [
"# Anharmonic corrections\n",
"\n",
"\n",
"We can use the [Morse potential](https://en.wikipedia.org/wiki/Morse_potential)\n",
"\n",
"$$\n",
"E(r) = D(1-e^{a(r-r_{eq})})^2\n",
"$$\n",
"\n",
"Where D is the depth of the well (bond energy), $r_{eq}$ is the equilibrium bond distance, and \"a\" is related to the square root of the force constant\n",
"\n",
"$$\n",
"a = \\sqrt{\\frac{k}{2D}}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3ed6ce44",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt \n",
"import numpy as np\n",
"fig, ax = plt.subplots()\n",
"#the x axis is the atomic number\n",
"\n",
"distances = np.linspace(0.5,2.0,40)\n",
"\n",
"k = 10\n",
"req = 1\n",
"D = 10\n",
"a = np.sqrt(k/(2*D))\n",
"\n",
"harmEne = []\n",
"anharmEne = []\n",
"for r in distances:\n",
" harmEne.append( 1/2*k*(r - req)**2 )\n",
" anharmEne.append ( D*(1 - np.exp(-a*(r-req)))**2)\n",
"\n",
"ax.plot(distances,harmEne,'.r-')\n",
"ax.plot(distances,anharmEne,'.b-')\n",
"ax.set_xlabel(\"dist\")\n",
"ax.set_ylabel(\"Energy\")\n",
"ax.set_title(\"Harmonic vs Anharmonic potential\");"
]
},
{
"cell_type": "markdown",
"id": "93101b43",
"metadata": {},
"source": [
"* How do you think adding anharmonicity will affect the vibrational levels? Will they be equally distanced? Will they be further apart than in the harmonic potential?"
]
},
{
"cell_type": "markdown",
"id": "bd453b9b",
"metadata": {},
"source": [
"# Questions\n",
"\n",
"* Submit in a separate notebook the questions listed above"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "pchem",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.2"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": true,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 5
}