{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Advanced Tutorial 4 : build a Spectral Deferred Correction solver based on generic time-integrators\n", "\n", "📜 _Previous advanced tutorial on [SDC](./13_nonLinearSDC.ipynb) focused on its implementation for non-linear ODEs using_ $Q_\\Delta$_-coefficients._\n", "_But we can also define a SDC sweep **without**_ $Q_\\Delta$ _**coefficients**, and extend this idea to many other time-integration approaches._\n", "\n", "> ©️ Credits to [Martin Schreiber](https://www.martin-schreiber.info) for the [original idea](https://gitlab.inria.fr/sweet/sweet/-/blob/main/doc/time_integration/spectral_deferred_correction_methods/spectral_deferred_corrections_with_less_pain_ver_2024_01_19.pdf?ref_type=heads).\n", "\n", "\n", "$\\phi$**-based time-integrator** : \n", "\n", "Considering a sequence of nodes \n", "$\\{\\tau_1, ..., \\tau_M\\}$ discretizing one time-step \n", "$\\{t_0, t_0+\\Delta{t}\\}$ into\n", "$\\{t_1, \\dots, t_M\\} := \\{t_0+\\Delta{t}\\tau_1, \\dots, t_0 + \\Delta{t}\\tau_M\\}$.\n", "We can write one time-integrator computing the step solution through all node as a \n", "$\\phi$ function such that :\n", "\n", "$$\n", "u_{m} - \\phi(u_0, u_1, ..., u_{m}) = u_0\n", "$$\n", "\n", "This allows to represent any time-integrator, \n", "without writing it in a $Q$-coefficient framework.\n", "In particular, if we look at the Picard form of an ODE written \n", "at a given time node :\n", "\n", "$$\n", "u_m = u_0 + \\int_{t_0}^{t_m} f(u(s), s) ds\n", "$$\n", "\n", "the $\\phi$ function simply corresponds to a given discretization\n", "of the integral into the time nodes\n", "$\\{t_1, \\dots, t_m\\}$, with **no dependency to the next time nodes**.\n", "\n", "**Continuous Spectral Deferred Correction**\n", "\n", "To retrieve the original SDC formulation of SDC, we define the error\n", "$e^{k}(t) = u(t) - u^{k}(t)$\n", "and put it in the Picard equation above to get :\n", "\n", "$$\n", "\\begin{align}\n", "e^{k}(t) + u^{k}(t) \n", " &= e^{k}(t_0) + u^{k}(t_0) + \\int_{t_0}^t f\\left(e^{k}(s) - u^{k}(s), s\\right) ds \\\\\n", " &= u_0 + \\int_{t_0}^t f\\left(e^{k}(s) + u^{k}(s), s\\right) ds.\n", "\\end{align}\n", "$$\n", "\n", "Noting \n", "$u^{k+1}(t) := e^{k}(t) + u^{k}(t)$\n", "and adding the difference of the two same integral terms with $u^{k}$ we get :\n", "\n", "$$\n", "\\begin{align}\n", "u^{k+1}(t) \n", " =&~ u_0 + \\int_{t_0}^t f\\left(u^{k+1}(s), s\\right) ds \\\\\n", " &- \\int_{t_0}^t f\\left(u^{k}(s), s\\right) ds + \\int_{t_0}^t f\\left(u^{k}(s), s\\right) ds \\\\\n", " =&~ u_0 + \\int_{t_0}^t f\\left(u^{k+1}(s), s\\right) ds - \\int_{t_0}^t f\\left(u^{k}(s), s\\right) ds \\\\\n", " &+ \\int_{t_0}^t f\\left(u^{k}(s), s\\right) ds\n", "\\end{align}\n", "$$\n", "\n", "$\\phi$**-based Spectral Deferred Correction** : \n", "\n", "We write the continuous SDC equation at a given time node $t_{m+1}$,\n", "use a given $\\phi$ **time integrator** to replace the **first two integrals**, \n", "and write the **last integral using a quadrature rule on all time nodes** :\n", "\n", "$$\n", "u^{k+1}_{m+1} = u_0 + \\phi(u_0, u^{k+1}_1, ..., u^{k+1}_{m+1}) - \\phi(u_0, u^{k}_1, ..., u^{k}_{m+1})\n", " + \\Delta{t}\\sum_{j=0}^{M} \\omega_j f(u^k_j, t_j)\n", "$$\n", "\n", "or in final form :\n", "\n", "$$\n", "u^{k+1}_{m+1} - \\phi(u_0, u^{k+1}_1, ..., u^{k+1}_{m+1})\n", " = u_0 + \\Delta{t}\\sum_{j=0}^{M} \\omega_j f(u^k_j, t_j) - \\phi(u_0, u^{k}_1, ..., u^{k}_{m+1})\n", "$$\n", "\n", "✨ And there it is : no need of any $Q_\\Delta$ coefficient !\n", "We just need to use the definition of a time-integrator that allows to \n", "\n", "- evaluate $\\phi(u_0, u_1, ..., u_{m+1})$ for any sequences of node solutions up to the $(m+1)^{th}$ one,\n", "- solve $u - \\phi(u_0, u_1, ..., u_{m}, u) = rhs$ for any $rhs$ vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prerequisite\n", "\n", "We use the same as for the [previous tutorial](./12_nonLinearRK.ipynb) :" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.optimize import fsolve\n", "\n", "u0 = np.array([5, -5, 20])\n", "sigma, rho0, beta, epsilon = 10, 28, 8/3, 5\n", "\n", "\n", "def f(u, t):\n", " x, y, z = u\n", " rho = rho0 + epsilon*np.sin(t)\n", " return np.array([sigma*(y-x), x*(rho-z)-y, x*y-beta*z])\n", "\n", "\n", "def fSolve(a, t, rhs, uInit):\n", "\n", " def res(u):\n", " return u - a*f(u, t) - rhs\n", "\n", " return fsolve(res, uInit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition, we define our underlying collocation problem :" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from qmat.qcoeff.collocation import Collocation\n", "\n", "qGen = Collocation(nNodes=4, nodeType=\"LEGENDRE\", quadType=\"RADAU-RIGHT\")\n", "nodes, weights, Q = qGen.genCoeffs()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "Consider a Backward Euler step between each node, and let us write it in $\\phi$ formulation.\n", "Defining $\\Delta{\\tau}_m = t_{m}-t_{m-1}$, we have for each node\n", "\n", "$$\n", "\\begin{align}\n", "u_1 - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0 \\\\\n", "u_2 - \\Delta{\\tau}_2 f(u_2, t_2) &= u_1 \\\\\n", "\\dots& \\\\\n", "u_M - \\Delta{\\tau}_M f(u_M, t_M) &= u_{M-1}\n", "\\end{align}\n", "$$\n", "\n", "By substitution we can rearrange those into :\n", "\n", "$$\n", "\\begin{align}\n", "u_1 - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0 \\\\\n", "u_2 - \\Delta{\\tau}_2 f(u_2, t_2) - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0 \\\\\n", "\\dots& \\\\\n", "u_M - \\Delta{\\tau}_M f(u_M, t_M) - \\dots - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0\n", "\\end{align}\n", "$$\n", "\n", "so we can identify the $\\phi$ function for Backward Euler :\n", "\n", "$$\n", "\\phi(u_0, u_1, ..., u_{m+1}) = \\Delta{\\tau}_{m+1} f(u_{m+1}, t_{m+1}) + \\dots + \\Delta{\\tau}_1 f(u_1, t_1)\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def phi(uNodes, t0, dt):\n", " tau = [t0] + (t0 + dt*nodes).tolist()\n", " out = 0\n", " for i, u in enumerate(uNodes[1:]):\n", " dTau = tau[i+1] - tau[i]\n", " out = out + dTau*f(u, tau[i+1])\n", " return out" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we can define a function to solve $u - \\phi(u_0, u_1, ..., u_{m}, u) = rhs$ for any $rhs$ vector :" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import fsolve\n", "\n", "def phiSolve(uNodes, rhs, uInit, t0, dt):\n", " tau = [t0] + (t0 + dt*nodes).tolist()\n", "\n", " for i, u in enumerate(uNodes[1:]):\n", " dTau = tau[i+1] - tau[i]\n", " rhs = rhs + dTau*f(u, tau[i+1])\n", "\n", " m = len(uNodes) - 1\n", " dTau = tau[m+1] - tau[m]\n", " def res(u):\n", " return u - dTau*f(u, tau[m+1]) - rhs\n", "\n", " return fsolve(res, uInit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now, we just need to implement the $\\phi$-based SDC formula as defined before :" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "nSweeps = 4\n", "uNodes = np.zeros((nSweeps+1, nodes.size, u0.size))\n", "\n", "tEnd = 10\n", "nSteps = 1000\n", "\n", "uNum = np.zeros((nSteps+1, u0.size))\n", "times = np.linspace(0, tEnd, nSteps+1)\n", "\n", "\n", "uNum[0] = u0\n", "for i in range(nSteps):\n", " dt = times[i+1] - times[i]\n", " tNodes = times[i] + dt*nodes\n", " u0 = uNum[i]\n", "\n", " # Initialize k=0 with u0\n", " uNodes[0][:] = u0\n", "\n", " # Iteration loop\n", " for k in range(nSweeps):\n", "\n", " # Loop on nodes\n", " for m in range(len(nodes)):\n", " rhs = uNum[i].copy()\n", "\n", " # Quadrature terms\n", " for j in range(len(nodes)):\n", " rhs += dt*Q[m, j]*f(uNodes[k, j], tNodes[j])\n", "\n", " # Phi correction term\n", " rhs -= phi([u0, *uNodes[k, :m+1]], times[i], dt)\n", "\n", " # Phi solve\n", " uNodes[k+1, m] = phiSolve([u0, *uNodes[k+1, :m]], rhs, uNodes[k, m], times[i], dt)\n", "\n", " # Step update\n", " uNum[i+1] = u0\n", " for m in range(len(nodes)):\n", " uNum[i+1] += dt*weights[m]*f(uNodes[-1, m], tNodes[m])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And that's it 🥳 ! We solved our non-linear time-dependent ODE on the given time frame using 4 SDC sweeps, \n", "without using any $Q_\\Delta$ coefficients ...\n", "\n", "As before, we can plot the solution with respect to time : " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "plt.plot(times, uNum[:, 0], label=\"$x(t)$\")\n", "plt.plot(times, uNum[:, 1], label=\"$y(t)$\")\n", "plt.plot(times, uNum[:, 2], label=\"$z(t)$\")\n", "plt.legend(); plt.xlabel(\"time $t$\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> 💡 Note that we retrieve exactly the same solution as the first application example given in [previous tutorial](./13_nonLinearSDC.ipynb).\n", "\n", "And as before, we can implement a function to reuse it with different time resolution, blablabla ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the internal $\\phi$-SDC solver\n", "\n", "An optimized implementation of this $\\phi$-SDC approach is implemented in the `qmat.solvers.generic.PhiSolver`\n", "class, along with some classical time integrator written in $\\phi$ formulation.\n", "As for the `CoeffSolver` used in previous tutorials, they use a `DiffOp` class to evaluate $f(u,t)$.\n", "\n", "Looking at the non-perturbed Lorenz example problem (again), we can solve it with $\\phi$-SDC using those few lines :" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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u8riCwmAG1C4E5UFtYa+LgkKwUGUgBYUggVIKfAFIuEXQGgYQPvbYY6JsoYiKgoKCQvBQZEVBIUigfRMemmPHjgnvB7wwaBP+wQ9+oN5bBQUFBRugykAKCgoKCgoKEQ3VuqygoKCgoKAQ0VBkRUFBQUFBQSGiociKgoKCgoKCQkRjwBtsMUgLw9QQYOTE4DEFBQUFBQUF+4HkFAQbopvSX4DmgCcrICqjRo0K98tQUFBQUFBQsADMaSssLBzcZAWKCv+xiBtXUFBQUFBQiHxglhvEBl7HBzVZ4dIPiIoiKwoKCgoKCgMLZiwcymCroKCgoKCgENFQZEVBQUFBQUEhoqHIioKCgoKCgkJEQ5EVBQUFBQUFhYiGIisKCgoKCgoKEQ1FVhQUFBQUFBQiGoqsKCgoKCgoKEQ0FFlRUFBQUFBQiGgosqKgoKCgoKAQ0VBkRUFBQUFBQSGiociKgoKCgoKCQkRDkRUFBQUFBQWFiIYiKwoKCgpDDO3d7dTb2xvul6GgYBqKrCgoKCgMIeyt2UvLXlhGP//05+F+KQoKpqHIioKCgsIQwn3r76PmzmZ6/eDr1NLZEu6Xo6BgCoqsKCgoKAwh1LXV6fe3V20P62tRUDALRVYUFBQUhgjgUznefFz/97HGY2F9PQoKZqHIioKCgsIQQV17HbV2ter/LmkqCevrUVAwC0VWFBQUFIYIylvKXf5tVFkUFCIZiqwoKCgoDBHUt9e7/LuipSJsr0VBIRAosqKgoKAwRMlKbVtt2F6LgkIgUGRFQUFBYYigvkOSlYKUAnFb01YT5lekoGAOiqwoKCgoDDFlZWzGWP3fPb09YX5VCgr+ociKgoKCwhBBQ3uDuB2TPkbcdvd2U2NHY5hflYKCfyiyohCxeGnfS3TP2nvEHBMFBYXg0dAhyUpOYg6lxqWK+6oUpDAQEBvuF6Cg4AmQp+/+7G5xPysxi26ae5N6oxQUgkRTZ5O4TY1PFecV/g2T7biMceq9VYhoKGVFISLx2fHP9Pvry9aH9bUoKAwWYCYQkBKXIsgKoDqCFAYCFFlRiEgcbTjqMiVWmQAVFIIHDy5Mjk2m7IRscb+2XbUvK0Q+FFlRiEgYY8AhVZc3uyZvKigoBI6WrhZdWclMzBT3lbKiMBCgyIpCROJYk+uANRULrqBgXxkoOS5ZLwMpg63CQIAiKwoRicqWSnEbRVHi9niTmmGioGBnGSgrIUsfbqigEOlQZEUhIsF19Jm5M8WtIisKCvaVgaCsZCZkurQzKyhEMkJGVu677z6KioqiW265RX+st7eX7rrrLiooKKCkpCRavnw57dy5k4YCntjxBP3ms9+oDBEP6Orp0sOrpmRPEbeVrVJpUVBQsIbunm5q7WrVPSvpCeke5wUpKAxZsrJhwwb6xz/+QbNnz3Z5/P7776cHHniAHn74YfEzw4cPp7POOosaGxsHfafLA58/QC/ue5Ee3/F4uF9OxAEXz17qFfcnZEwQt9Wt1WF+VQqRgIN1B+n6FdfTR8c+CvdLGXBgosJloIz4DHFfkRWFgQDHyUpTUxNdffXV9Oijj1JWlqyRsqry4IMP0s9+9jO69NJLaebMmfTkk09SS0sLPfvsszSYsbp4tX5/TcmasL6WSATX0DMSMigvOU/cr25TZEWB6NYPb6W1pWvpB6t+QJ3dneotCQBt3W26DywhJkFXVlQZSGEgwHGycvPNN9P5559PZ555psvjhw8fprKyMjr77LP1xxISEmjZsmW0Zs3gXsAP1R/S7++o3qEuum7gVkrU1HOScsT9qtaqUH5EChFqDj1cf1gvFe6t3RvulzSgwGMrQFRQkjcqK9g8KigM2bj9559/njZt2iRKPO4AUQHy8/NdHse/jx7tCwRzR3t7u/hiNDQMPHMYX3D5olvcVEzjM8aH9TVFYiR4eny6mGECqDKQwr7afS5vwo6qHboBW8E8WYmPideVSx5miJZmRPArKAw5ZaW4uJh+8IMf0NNPP02JiYlefw4M3wgwfPfH3I26GRkZ+teoUaNooOFYo2uGSFFDUdheS6RnQeQm5epdDMaau8LQg5HkA/tr94fttQxEtHdJspIYI6/HibGJQmUB6juUyVZhiJKVzz//nCoqKmjBggUUGxsrvlavXk1//vOfxX1WVFhhYeD/cVdbjLjzzjupvr5e/wIpGmiOfPZfzM+b3y9aXsEwvyQ2RXQt8AVVqSuhx33r7qOr37xaqBjhRnmLa4qxCgoMTlkBlMlWgYY6WTnjjDNo+/bttGXLFv1r4cKFwmyL++PHjxfdPytXrtT/n46ODkFoli5d6vX3wteSnp7u8jXQ8kMgu8LkNit3lnisrNmVsA11MFmBLA2VTS8FKZNtyJWMZ/c8S9uqttEjWx+hSCErTPJV9k5g6OjuELdM/gHVvqxAQ92zkpaWJjp8jEhJSaGcnBz9cWSu3HvvvTRp0iTxhfvJycl01VVX0WAFG0URdT0idYTHHeNQh14Gik0WtzDZYhetlJXQ4pOST1ymYGNnblzoQg2eDzUvbx5tqtgkyIq/srGCH2VF862oMpDCkDbY+sMdd9xBra2tdNNNN1FtbS0tWbKEVqxYIYjOYI+RH5Y0jPKTZblLkRXvY+wB1REUvkwTRmdPp/j39JzpYSf6s4bNEsokWnEx14aPD4XAlRUuA3EIo4JCpCKkZOXDDz90+Td2REiwxddQAe9gMPGUM0TURGHvZSCAy0BqOmz4WuyBvTV7w0pWOLwMRB/nDkg+1BVFVgLLWUmITeivrKgUW4UIh5oNFGI0djTqbbmsrGDHCOOtgucyEE+H5XlBCqFBcaM0r88dNlfcHmk4EhFEH+fOyNSR4n5Jc0nIXwc2F9957zv027W/HVD5JB6VFUVWFAYIFFkJE1lJi08TO8LoqGhhuA3HmHaQpIqWCor0MhBPh61pDf17NFSBsg97hObnh9/QitfDxwUWWPZ7lTaVhvy1/GXzX+jTkk/phb0viDTdgRgKx1CeFYWBAkVWQgyuDWN3GBsdS7mJuWHxrUDSP/flc+mCVy5w8SZEVBkoLtVFWalpV2QlVABRwXym2KhYPXitpCn0KoY7yWeij1JQOJKNoaSsPtY3LmNV8SoayAZbXIcAVQZSiHQoshJiNHb2KStAfkp4TLYv7n1R1LARtPbM7mcoktDc1RcKB2QnZotb5VkJHfh4zE3OpcLUwrCTFSb5ILCC5GthgaEmK3hfeHYVsLliMw0UqDKQwkCGIithLAMBvEMMdTlmfdl6/T4k7UhCc4dnZUWRldChqkWSgLykPCpILRD3UaoMV4ow+1W4bMGm2lC3sx+oOyBuk2KT9H9jZMaAMth6KAOpYYYKkQ5FVkIMviiw/DoseVjIL7pYcIxmSWSYhMMz409ZYc+Krqy01w4oQ+NABqsH6FrDgpYWlxY2j4ixTMHnTbiUlSP18rxZWrBULPogKuF6T+xsXVZlIIVIhyIrYZKzWVkJRzorzyLCIjQ2fay4v6d6D0UCQEaMs4GMygoWBi6jDWa0dbXRpvJN+uISViVDW8xYXQlXKUgn+QkaWdG8XqFONS5tlsQE3Uij00dHRJeULaFwavKyQoRDkZUwti6HK/CML64gKpOyJrnI2+FGR0+HLqtzGQg7QW5jHgqloDs+uoOufedauvXDW8P2GninzYuZ3n2jLdZhez0aeWJlBQpQZ3dnyF4Hj8YYnjJcJ/oDhaz48qzgvOMykYJCJEKRlRCDlQF3OTuUZSBuQcXucEz6GJdMjXCDVRWjsjKUfCsYaskdJh8d+4h2Ve+KCLLC3qrKVpnAHG5lBbcw2oZaXWHjMcgKnzsDZRCpp9ZlbALQ8QWoFFuFSIYiKyEucbgbbMNRe2czLy64o9JGifvFTZFFVmBgRAYNg30rkeStcQIbyja4/Dtc5mcmBzpZ0bxVPC4iXOVTVlZwbPAxEUqiz+cOAh2ZrLCPZSCSFaSI68MMtdKfgkIkQpGVEC/EPb09XslKqMyjvDtEZLlOVhoig6xwtwmXfRhDpX15e9V2lxLY5xWfR0TZJVKUFSZP4SL6fPxB6RudNjrsLd3BkhVApdgqDAQoshJCsKoSHx1PibGJLp4VJHSGqn2QZxENT+5TVlAaioQWTJhLAX5/GEMlcv9w/WFxe9HEi8Tt/pr9EVEG4jlW4VZWmOSHg6yASLOvA6nKUCaZ/PMmZKAZbAE1zFBhIECRlRCCyYjxgotdDv87VHI2X9wR+IVFCOSpq7dLNw9GAlnhHAt3shLqXI1Qg0sKZ4w+Q9xWtFaEJQPDPdeEiUG4lJWWrhaXdvZwkBUmcPDK4HWgNIbpz9hoDATFz5PBFlCR+woDAYqshHHmDSPU7cucoYHdIWr/hWmFEWOy9RRcBWQn9GWtOA2Qg39u/2fI00mhvPHfNyNnhj7o8lCd6/TjcJSBWFmBZygcCpyn8iCfN6EiK3oJKCFLeD3iouN0wlTWEn6i7w+qDKQwkKHISjguuIYul1DvEHHB4l0qAr+MbamRpKx4LQOFYAf7o9U/ogc3PUjfXvltOtZ4jEIFbgvGThfHyITMCWFpK8cOnI/VjMQMF2KLckc4TM4tnS39FDe9ky5EJJ+JJJ83ABNKLq1GMtq7PHtW1HwghYEARVYiwDwaSrJS1yZVlZioGD2VFN6VSNkdsrKSGBMesoI21DXH1+if13/3/5dCnuGhfR5MVkI9aJLLTiAnbPSNiY7Rg9jCUQpigm0k+qEuA/G5w1PAAfatRALRt+xZ4WA41Q2kEMFQZCUMF1x3P0ZIyQrHqCdkCinbZZhiBOwOvSkroWpdXle6zuXfHx77kEIFXvBGpEila1zGuLCEjhmj7Y3t4/A4hctkq5MVYxkoxPOBdGUlwaCshGkQqSOeFe1zV1CIRCiyEkK0drZ6JCuhTLE1khVGRCkrJspATrZ4b6vcJm6/MuUr4nZ/7f6QmSdZseAFEKF9QKhnz3gygoe7fZnPnbAqK+z10o5Fl3NnICgrPV5alzVfkgqFG9iob68P+aysUEKRlTBL2aFOsfVYd48kZcVbGUiT3hELzu+jE2AVY9HwRXqceqhSZGtaa1xUpMLUQn3QZCgHOHozgocrGA7dNvjcvXlWcDywp8VJMGkd8MpKrOoGGmw42nCUzn/lfDrzP2fSO0feocEIRVbC4FkJaxnIU91d2x1GBFnxoqyA4DGBcbIUxNHpICpTsqeI+3tr91IowH8XkxX4IdAai+MmlKZWfZCkm7cqXMoKnzfurwn3+ZgIhcnWo7IyQDwrILt8bqky0ODDo9seFcpKd283/X797yMiM8tuKLISQvDuz5vBNhQXXF/KCuYWGWfzRJKyEgqTLYgcL0gIy5ucNVnc31e7j8JBVmCEZDWD5zmF8jiNFGWFS0DIN4mLidMfh+cqlL4VJvouyorWDYQY/kgOhsPi1Uu9PkPhlGdlYKKrp4veL3pf/zc2vetL19NggyIrEaCscF4EFqvunu6QKytYlLgzKNzqir77c5OqQ0FWuASE3TKUnClZmrJSEx5lxVgKKmkuCX8ZKEzKijdjeqhVSX2YojaEFDAGw0Xy3CruBPLYuqzNBsL7HMoJ1oMVUGcx4ytUpdt9tfuoqbNJXMMvmiCTr9eWraXBBkVWIsCzgkUYFzzszJwOPWPlwDhjxaiuhNtkyxfVpJj+C5PTHUFcAuIBdaysIFWW6/2hJisFqQXitqQxcshKVUtV2DuB+gUqhkBZwYLgbjw2BsNFsm/FSFaQWG0E/h5cfwDVvhwcPi//nC5+7WL6xrvfoH9s+weFAtsr5Tyx2cNm04L8BeL+1oqtNNigyEoEKCuQt0MVJ++pGyiSTLb8Hrl7VlyGGTpE6Ioai8QtD6iDwoIFG6MInE73xY6Wd+6eyEooy0DNXc0eSTWXgaraqhxXAP11AvVTVtqcJ1BNHU0eSRyn+1Y0y4nMkd62zJEFDLSns7qiOoKCw8ObH9b9Io9ufzQknYSHG+Q8sUlZk2he3jxxf0fVjpBssEIJRVbCnMIZajmbhykapexIal/2ZgI0lq64a8ZusBeDTZO4qDNxYdXFKTABQ1gfLxzG9uVQloG8eVZAokKlAEZaGQiSPjxdnlq6dbLSErlkhb1g7n6Vfr6VQRQMh88MoypQogsFcAxCWeHNINSslUdXhmye2Nj0sUIVxnmK7rlQdTGGCoqsRECCbTjISmq8TCaNNGVFLwN5WJicnryMoYHGcgcwOl2SFaeVFS4B4SJnDGJjshJSZYXLQLEp/RRANrSG0mTrswwUIoMtLv68Y+ZU336R+xFcBvIWCMfgsjB72gYDUbl99e100WsX0RVvXKGrYk5iY9lGYWKelj2NrptxnXjso2MfhWxS+7iMcWKDhbliofTahQqKrERAGSiUHUGe6u6RqKz4KgM55VnhBZh3ykColBU9YyWprwTkXgYKlWFPb132UHYJh8nWVxkoVGSFST6UJffXMRCyVrwNMQzVRiDUwMiMFUdX6AbUx3c87vhzbqncIm5RilkyYom4j2GoTnaJtXa16jPFxmaM1ctBwP66/TSYoMhKCOHNYBvKFFveYXjdHYbbs9Ld6r0M5HA3EJMV9mYYzbbsZ3EKTFJ5ujSDs1aw2IRqYJ+3MpCRVEeKshIqRdJoOjYqXwOlDORtLlCoJlhvqdgi/BxcsnAarx983eWzeXn/y463liPtGpieM52mZk8Vm1L40Jyc7VXUUCTUHJT1uUw+MXOiy+sZLFBkJUKUlVCMu0ftlmvX/ZQVzacR7t0hT4b1WQZygKxAJuddZV5SXr8yEC4KToLNtcb8G+42YfIUquAxb91Axot/SJUVE+cNiJyTypM3c+1AIStcBvKUX+S0QgWz59ff+Tr9fdvf6eq3rg6Jv+iTkk/E/d+d8jvxmUGN3Vm109HnZVKCAaQomaI7B9hUvsmx5yzWytPwq7BxmrsYoayEMvnaaSiyEgGhcKGK3DfWbd0vunowXEdjSKLLrRhsWXVwQqrmCyjIgbGtm8tAIArG9k+7wV0Y7sZn42DDUPlWWMmIGGWl078iic+GS5yhLJ8OFoOtkfTZDbTwoqOOSfk/t/+TnARUUDwPWrTn5s2lpQVLxeMflTjnH4HXh987HkCqd+ZU73B+UnuK3GxyOQhGfVzLw735tBOKrIQIYLj6DjEuPF0NTFawQwXzNwILE5eGwnmAcxnIk2eFlRW8j8YIdjvACw0WHmNrJ3wyeF8gtR5rPEahDBxjFKRI3wrXpoecZ8WHMR3HMh+3oTh3PBE4LqGC0IQ7Adqqwdap6w82H/CPALfMv0Uv0TjZobO9SuaOTM2ZKjYfp4w8Rfz705JPHXvOQ/WH9I0FHyMcKulkAna5dq3mzSZ/xkjgNppvBwMUWQnhzobjrsPVgqm3Xmppte6IhK4GX2UgXARw8XGiFMSLr7ETCABx4RPfSZOtt0nHwPDU4SElK7pnxa0byCVrJYTTXX21LofKZMvKinsXXSQR/aA8Kw69h0hyxXNj548OGfgqcKzDw+IUuNwzK3eWPpQU2F2z2zF19GC9LAGNzxyvP8blGJSHnJrVU655DPnazeAhrE43BoQSiqyECEYlwFPdmMkKTmSnwnx0c62HC24ktC8jaIyn63raAYI4OOVb4cWXPwcj2GTrZPuyXgYyZKz0U1aaSkOiAHoLhTOSuVCWPHyVgVz8Xg4Gw+lkxc2YPlBKQf6UFafKQJ8el2rGySNPppjoGDpp5Eni3+wpcQI7qyVZ4RZetP9DIQVh2F2925HnLG6Q14Zx6bIEBBSmFQqCDYLklEG/rKV/Gch4zVJkRcHyBRdEBSetOyD/c2nGqdZcVla8khWNnYdrgqxx1+OpDORk+zKTH+NEXQYrK46SlQ7/npVQKCtQALlrwlPJg5UV7MBDNbjPVxko1H6vgUpW/LUus7ICn4Od6gNHwS8ZvkQnLU6TFS7JsLKBTQ6bXbdVbgsZaUDXGLcRO1UKKveirIzJUGRFIdgLrpfdIU4op0tBfMH1WgYKc14EmwB9XVSditxn8uOJrGCHBITLszIiNXRkxei58Nh9oy1qMEzy6IYhVQYapGTFZbNkU0I0lFJepNHKC5ww4gRxi8f5mLfb6MrTo7mTD5idO9vFz2I3jJ43I/TJ7TX2k5Xunm79ed2VFVUGUnCk/ZKRm+gwWfFRd48Ez4qxE8g9y4LBZMLuyH1WVoxzedyVlWNNISArCd6VFZADpzu1jB1rnj4DeIb4PQpVR5C/MlBIzOlmz50w5xRZ9axgs2R3Keho41GxAcE1j88hEEvusHNC5TBOTjdea5F9Auyp2UOhVDj0NmIHMk9q2mrEpgHnqXv5mstAJU0lg2aStvKshAj+doehCIbTo/bjIvOC6yu9tt98oHZ7yQqrBPz7jShMLdRPfKcG+Hmb2cSmW1bDnC7R+cpY6de+HKKOIH9EP5SddJ4M0JFA9INVVpy4/nDcOxZsY+l7zrA54nZr5VbHyAov1u6kAd4RuzsJ4fPyp6zsrbU/+r5Ce05sct27O+Etw/nS3dvt6CYrlFBkJdSR4V7q7kDIykDxkV0G8hZc5aTkr8/mcQtl4wsQFAUY9Jx4b7Dz4QuoJ7ISyo4gM2SFfSshU1Z8JD87nRHirqx4e18GusHWCe8PqxjcwstA9gngREcQG0q5DGL826AIwmdld6IsNjrcGOBOVjhNFuet3W3tVdwUkJzrUSkbbCZbR8nKI488QrNnz6b09HTxdeKJJ9Lbb7/twkjvuusuKigooKSkJFq+fDnt3OlsyuBQVlb81d15d4iTj1WOSFNW9JwPmxdKX2Ug7Ap5oKATvhXjpFtvnw13BB1vPh5WYmD8DELVvuxrWnnIlRUvfq+8lMgmK6aUFZtJHxvSje28xpZidO3YnbDKC7O7soLFW1c5bB7wx585rh3uZTYETPLxaXfmSbX2OfHn5g5FVgJAYWEh/e53v6ONGzeKr9NPP50uuuginZDcf//99MADD9DDDz9MGzZsoOHDh9NZZ51FjY1SEh9M8BUIx+CD2rFuIC8TlxnY1fOCEI6Lrk5WfCgrTsS9Y7flqwwEjEwb6VhHkJ6xEpfmsVPMaKBzun3ZlLIS4vZlX7OBjCQfPianOpR0ZSU+xSfRxwLiVKaGHflFoSwDMbHnMqpRbUDZAtcju5VClGoB3lwY4VRIG6ut7qoKY0LGBHFrt6JTpX1O/Lm5Q5GVAHDhhRfSeeedR5MnTxZf99xzD6WmptLatWsFo37wwQfpZz/7GV166aU0c+ZMevLJJ6mlpYWeffZZGmzwtzsMSRnIR2Q47z7CWXvXy0A+lBW+INj5+nDRRG3XWzcQMCrVOZOtr4wV9+nLISsDeQiEC0cwHEpkvPj7KwM52aGknztelBXsqmOjYgVZCmVgnl0GW7uvP7i+M7HnbjpGXEycvoAjqM1OsKeLzxcjJmc74x/RU2TdzLUMVpY4OM4uVGvlOk/ZUIOxIyhknpXu7m56/vnnqbm5WZSDDh8+TGVlZXT22WfrP5OQkEDLli2jNWtkPPNggr+siFB6VryVGsKdtRKIsgKCYZdRjktAUBO8Xcz5guuksuLNrxLKrBVfUfvhiNxnVcUX0cfix+U7p9QeX3H7ADoymMRFosnWjGfFzo0AjmkmeJ6IA7cy29mdg+sHq9J8vnhUVmr22Vp+8mauZTAxO1Qn819sV1YSfSsrbDoe6HCcrGzfvl2oKSAi3/nOd+iVV16h6dOnC6IC5Oe7slH8m7/nCe3t7dTQ0ODyNVg8K063Lutx+16UlXCbbM0oKyBa/B7a5VvhzBZvJSCX9mUHPCu+OoH6kRWHy0B61L6ZbqAQGGyZkMLgzKMWfJFsJ8gK1BImcd5KqJFusjWjrPAxVtYU/EaFzxPuSnHHtJxp4nZPtX1khTdYeD5P59L4jPFC/cJ10M7rm7e25X7Kis1loOo238oKkxUcj+EcTjtgyMqUKVNoy5YtovRz44030rXXXku7du3Sv28cGgeA8bo/ZsR9991HGRkZ+teoUXIRGeihcMbaI37WiYOruaPZtLISjvZlXxOXGTg27C4F8W7Mk7m2XzCcE2UgH3OB3BcS/M1OtU+b9awYfUNOj6A3Y/h1WhHEuchzvXydOwOBrPjaCLAvCp9rsIMGi5s8l4DcVY49tfaRFVYdca54WkOgwGEisd2+Fb/KSuYE3U9jZ9t0tVYG8uZZgbk3MyHT8fTtQUNW4uPjaeLEibRw4UJBNObMmUMPPfSQMNMC7ipKRUVFP7XFiDvvvJPq6+v1r+Li4kETCocLMn/fCXXFX9y+8YIVqcqKEx1BSL301rbMYJMg0jHtTt4041nB7gm7QnhrnCy/+JoLZHz/oyhKLGhOmcHdW/59nTdOeZkYXM6AKdQXkY7krBUz3UAg61CvQMyCJVzezLXuZSCQSz7/ggUTVU8lIMakzEm2h7R5mnzs/r5CtcX7amdHUDWTFS9loMFWCgp5zgp2YijljBs3ThCWlStX6t/r6Oig1atX09KlS73+/ygncSs0fw0Wg62TvhWYFJkweTMJRopnxezCZNcO1kwZCIs3XxTsLgWZ8aygS4gvhk76VnTPig9vFXaofJzyTJRwdQIx+L1xQtUwer18qb4DvQwE3w1vVoI9/3Wy4kVZwYaJS6t2mWz5NbtHzxvBs3r21zlAVryUgYzqil2loPbudn3z6U1ZMZKVogZnBikOGrLy05/+lD7++GM6cuSI8K6g8+fDDz+kq6++Wpz0t9xyC917773Cx7Jjxw667rrrKDk5ma666ioaigZbl2AmmwOujIFE3tovI8Wz4mv357IotFaErAzkpMnWDFkx7hiPNx0Pq2cF0Bc1G/wNdpw3TpYv/eUT9VN3mgemwdalRT5IQuyPrDhhsjWWgbyBQ9oO1B6w7Xxhz5m3MpCRrPCQxWBRo40bgRLm67oxmJQV14xem1FeXk5f+9rXqLS0VPhLEBD3zjvviCwV4I477qDW1la66aabqLa2lpYsWUIrVqygtDTvO/+BCt1g6yNnxUnzIp9Q6LQxY1TEAo4LnK+dWDhC4RxRVrRuIF9lIAA7QUSE266stJsjK6KrotxZZYWPUzNkBUPhHFdW/MwFCoWq4a/lPxQm31AoKy4m22CVlSbfZSAmKyuPrrSfrGiDP30pKyANKGP6uhaaAX/WINO+yCzMvXYqK1WGjBVfah8PcxwMyoqjZOWf//ynz+/jTUaCLb4GO8zuEJ2qvfsbxMaAISs+Ol7ER+NE9LUzClcZyO64dzNlICdNtr6GGIY6GM6Mwdb4WpwuF5rponNaEfQXte/pPUEHkbdhnOFUVnzFAtj1uYIEMHEwo6zYZXY141kB4cc1GMcVFnBWPOww1/oiDXYrK9V+0msHY9ZK5JxNgxxmPStO5Wn4G2LoEgwXplKQ2TKQ3UZGVla8BcIxeJdodxmIPxt/O3eO3HdUWTFMXfaFUOW+BFoGArGwewaL7lnxQ/Rx3oCggOg7bTy2em75U1bsKAOhNAiyhvPYW1stwPH3MJ2y8hOMF5Jfsy/PCj4fLgXZ4VvxZ651Jyu4dgT7t7rMBfLx/gI84RobMjQHDGQoshJBrcsu3Tg21739DTGMBJOtlTKQHfHq3I3gj6w4lbUSqGclFAbbiFFWTJaB8HqZiNtNsvWMFT9EHyUF7lTj2PeB5lmxowzEbcuIvPelLuE6AyUXHW4H6oLzkGAxBglAl5ovo6uLydaGjiAz5lpWQHB+43p1pP6I423LDJw3eUl5g6IUpMhKiGBWzrbL4GbVJBjKaHcrCbZMVnARhNxsx4RYLgNlJ5gz2OJCHmwOhSWyktpnsHUq38Q0WUmOrDKQk74Vs6qky7njcHhfoJ2APE7Cr8FW+1yDOffNmGtZxeW8lWCHC/LrhdLgTz2ylaz4CYQz/q12dgRVmywDGX0rA91kq8hKiGBWzuadDS64dg5E8zfE0NMFN9S7QzPBVbyD5YUp2CnEIEj82fgz2GLXjIs9Lvx2dcHgM2aCYNazggXc7qwXALs+syFsTJyQ+eLk4D6z5VMnO4LMpNf269hyeDq2FVXFlMFW+1xxveBrhhPmWsaUbHvICp+Pvvwq7lkrwao5ZgLhPJpsbZgRVOVniKHH9uVGpawoBDCMzUzOCsKnsCDambVitqPB6I1wskXWE5g0+FNWXPwbQe5gefAdAtfM+Hns9q0YFwR/nw2OHW6vdkLRMKZr+lNWxOC+aDm4z8nYfbPlUydVSSvKSqjPHV8weiT8KSv43PkYs7q4mVVWjGQl2I4gM34VxsSsifrrDDYp3GwZyMVka8OMoGqTZSAXk239wDbZKmUlBDAOY/OnrKC84YRnxMwQQwaPVw/1Bddsgq2d6o+xbdmXm9+pjiBWSHBcmGmj5IuxE58NKwg4Bv0RRpfj1MH25UDKQE4RBbOelVAaj62QFRxfZjqUgg0SY7LCHi9f0IcL1gY3XNBMxgoDZAzlEyTKBluS0ZWVFP/Kil4GskFZqdEM3IGUgY42KrKiYHJ3iJ0o0j/DsUM0E7Xv6aJvh4HVLNq72k0rK3YtCnrbsh9zrVMmW85YMaN4Od0RpPtVYlNMEbdQDFc0253kJMm2eu4MpKh9Tx0klslKAGUgMVwwOlYov8FsPMxkrHjyrQRTCoJvjdVvU8qKNn0Z7yvU9lB0A7m3Lzs9y8tJKGUlBDAbGe7k7kzvBvIRte+pBdMOA6sTyopdC5PeCeQnY8WpFFtWVjB0zAycKnUE0nnj/lqcVFYCKQM55bUyMwDU/TXg84mUhcFsIFy/IDELZSC0x3LZbGSaPEd9AZs3biXeW7vX0ah9T2QlmIwXXBuhzoBs+Uu/Zl8LjiGU+IPJPWnvbtfL+mbKQLhm4XqOzYjdyeihhCIrIYDZYWx2p0h62h2a2cFDLuadQihNtoF4VngHZZeywtNJTSsrNpeB/HUCuZM0Jz4Xs51AoWxfDoTo83uD12PnZGqzgYrGcxfvpRMmaCfblvuVDSwsqHxeYMdv9npnR0dQIGUgl4GGQWStsF8Fxnsz5TWoleMzgzfZVmsbSFynzWw+QVL5fRnI4XCKrIQAZjssHC0DBdANFA7fCnaheoKtn5EExnIIFu1gdrBmA+EYRoOtHTtns1H7/TwzNme9WCErofBnBNINhEUDRumu3i5bJ1MH0vZvNEFHim8l0DLQmLQxltVDf9OWnegIwt/HZZFAlZVg2pfNti17KgUF45WpMhm178mHpMiKgi1ty06aKAMpA4WjfRklJ0iqgSoreG+DSWbkbiCzZIWlbSzs/P+GImrfXdmxiywZ0dzVbI1UO+hZCaQMhMnU/JrsPG753AmUxEWKb4W9YIEqKzBxBtq+HEgnkHvsvtUyEJMGXDfMlnPhlUGAHP5Gq6XuQNqWGXZkrVRrrzc30b9fhaHIioLtu0PjiR6samAlMjwU5QZPYFUFSIj1f1E1RnkHk2mhdwOZLAPhefniZIdvxWoZCLt9O8iSx4nLseYWZd4923mcBtMN5IQiCBMle6lMm6DDFKpol7ICUsZdJoGabHVzbQBkhWP3cRxZKZ3x+Y8NjFmlAeSXX6NVk63ZqH1PWSvBzAiq5kA4E34VhiIrCrbvDvmCC9aP3Tt7KmzzrASorIRqd+jSMWVyEiq/xmBKInp6rQmDnPsibUcphlUhswZbmI/tJEvBlIH4/QdxcmLuCAgQ+70CfU12kWw21wZy/kacstITmME2mMXNShkIxz6/Z/tqAje8srLHpWGz0H0rFktBgWSsuCsrSJO1moJdFUAgHEORFQVHdofG3bsdCyIC6ZgMBOxZCVESJ78+s++RscUymEU7UGXFvRQTamXF7uf3RFbMLsqCOGlzR+yeRM2lQfhPAimh2k2y2a+C4zJQEh0pZCVQgy0wLmOcJdXBShnIxWRroRQUSCCcne3LVjwreI04lnBNtnr+VnMgnImMFU8+pFDGUdgJZbCNQM+K3UZK4xRas2Ql1Fkrurk2JnCyEkyMdKCeFbt3KZFIVsyqGE4bfo3pouEqAzFZCeg9YeXNAQIXijKQiwE1gG4ZLMBMHAJRVoI12fJz8jXLLII12VrxrKBriE22VpNsqy2UgVAig2qNYyHUA2rtgiIrIUCg+RWAnbHuvCAGsjvEbiEmKkZIlU7GqVvJWOmXB2ExvAplBs5ZCURZGZsxVh9tb1s3kEmDrZNkhRVAS2TFgYXZqEjCPBuOMlAgyc+MUemj9OMyErJWAjXYWi2RiJbx3m6Kj46nYcly+nTAZMWKstIUWNuyp/blQDdk+FyZrATiWQH09mWLJtvqAKL2GSAqrK4E45cJJxRZidASh515HlYuuDi4WVYNxQ4xmDKQVbICHw+XGQJRVjgREnXnYBejYJQVu9UMS8qKjf4db68nkGPC7qyVQNqWje8JPGcgWxyLPpBC4YyqA0if2fk5fB6iY85M7ogRU7NkR9CB2gMBezkCzVgxbnZArHDtCVSJgyKLMiW3zAeCYDuCqtsC7waygySFG4qsRGCCrd1JqYGEWtlJBiwFwllQVipaKywNJGNVBZ9LILtOPC8WI7yvwSZCBppgGxLPSpjKlcFE7TuVtWLl3AEp4N223Z9RqDwrIO/cbWfW0wHybiTzgQAEByQZBOBIvfw9ZgBFxGoZCBsyXsADLQVxKQW+kUBIoEvWSn3olBWXQYpKWVGwq3XZ7t0zZyWY7QRyJwOhuOCyZyUQsoIFnhd5K68x0LlADFz0eQcfTCkIO0gmCFaUFSzGxknJtrUuR0oZyMLrQbmIM3hsIfoWVEm7zN/hVFaslILYw8Vl0kAAJYbzVnZU7TD9/0G5wnmE/z/Q0hPAUf+BJtnq7dIBqjkAEySQMvh8Ar1ONgUQtW93IF04oZSVCGxdNi4CqIsaR7yHUlnhRTEUqYdWDLYA12GtmGz19FqTQVJ2+1aMgVtmMzwAEDQmN3YqGsGUgbC7tdqKaVfysxOKYLDnTiSRlUA2AlZMtjpZsaCsALNyZwVMVrh8A5OrWT+ex46g2gOWlBWzgxONQIs1AuygIgXqrarWlFyUrwLdfBrLT5HgpQoUiqxEaBkICyh+HqmuwZoFdWUlgAXR2PUSEmVFM9gGoj65mxktty0nmjfXevKtBGuuBTmAJB3uxdAKWUGpAEoT5PiyprKwnzd2d2tZVVZ4sxFMp1q4lRUOazPbocPnAr//VsnK9qrtAZOVQDNWgp0RxM9rRVmB+set4YGqHNWGEpDZADwGPhc0TYCAszl4IEGRlQgcZAjgQLSrFKTPBbIoZYditLgVz0qwyoretmxBWeGLTSD1dTvMtU6WGawoGThO9c61pvDmvtgxiM+O1uVILQMF4lkBZuTMELe7qnf5NSvjOXgBt0pWZg+brU9CNlve5Pc30FwXd2UF53EgCrZVU697KShQ/0gVB8IFkLHCAFnlNSWYQYrhgiIrIYBVOdsuk60+FyhAZQWmN+5qcHq0uFWyEkw5JhhlRScrDeEhK2MyxtjWPh2MsuKkydaKwda4WNqhajBZCfTccapjK1QGWz7G8d7j/Pe3uBU3FAsVGKUJKwspxyVAqUP78+7q3ab+H/6MmRxaeU6kV8OQvadmT0jKQMH4R6o0spKbnGvteW2YTRQuKLISoaFwdraFWmm/5Isb7xyc3iFaMdgaZ21YqcPq4UoWLq5cBkKJjhcDq2WgQDqB3J/fLrICox/vLM3OBnKarFhVVnSy0lAUdKAhx+0HSuCYrMAAypuFgVYGQrliZu5McX975XbTJaBAyxMM/H+BloK4/MvvdzDPacUrE6yyEihpKNNIUiCpud6ulwMNiqxEYNy+++45mN27SxkoQJOg0RPitMlWN9gG+B5BWUEnAFSKQNUffZeitWgGAvw/WMCwGFo1cgajrLCiFOyx4X6MBrMw232MMMkP9PVgAYEHCAbGYNM6eaZWoOcOfp7nTYW7FMRk2sw0c3eYJQ86WdGuWVbBpaBtldtM/TwTZC79WQETMrNkBeSPrzVWvTLchYTNRiCEulybRxToaAH35x2I7cuKrERogi0wLn2cLbtnq1J2KLNW9FC4ALuBoP7odVirkqoFsoIdGX8+Vk98Hv4XSHotg58bO3crk2q9HaPoqIiLibP0WuwiTsEabEFU+JgI9jWxuhOoKml3VpId5vVAlRVg1jBJVrZV+SYP3N7MO3erCETlwDGLjKVglBUrZIUJMDZWVlRRANEH6OjBZ1PSWOJoxL+nMhCycwZaR5AiKw4D7Zzc0hmoasC+CEiOrDwE5VkJsNUtlB1BVuL2g5U2gyErdtR/g1FWQHz5ghWMyTdYv4pR5YF/INDcCDOvKVCS72K8DpJkWzWn2zW7KpyeFWB27mz9GDfOGHMHdwxxVopVwNQLpRQ5Jjwo0Bs42wfnj1XSAMzMmakTWzPE3zg40WrJC4Sarx97avc4OunZ/VxFaCKOa/5dAwWKrDgMo6s90B0iZGSciDCuBSOx8wloqQwUoqwVK3H7wSQzYlFlg22g4UrBDHsLdoiiE8pbsGQFF22UGPCe2jlp2KrB1s72Zat+L+NrsINM2rERsEJWELSGawBKFRvLNno9dw83HLaFrOAaxb9jY7nn52PwIEArIXRGwGDP/sCdVTtNzyKyWgJiTM+ZHrBXpoLnEVkkKzgGxmXK60YghuJIgCIrIWpbBpMOVF4XpQZNXeGLQajLQMbOCidlQ6vdQFaVFRAVkEDs4qy0Lhvrv1ZHzPPcGKvPb6dvJRgVA+8hewbsLAVZ7aKzq30ZC7TVjCLAjnPXzkGGVs4t4MQRJ4rbNcfXePw+AtXwXmFzFeicHE9YlL9I3G4o2+Dz5/i846yUUJWfWNGx2gnkXn4yQ5BYIefz1GoZyDiHSZEVBVvMtf0ueBZ3zyAY7I3IiA9cKsWuCosRThI7Zq3YbbC16qznEhAusGYn+nojKyg1WEkZtjLx2e6sl37R9gF2AjnVnWSXshJMCQbHPJsfrZQZjOduOP0BwSgrwIkFkqx8VvqZx+/vrpFtxlBErJZFjFg0fJEpZYXJCp+HdhAHf94cO5J63Z9zZ/VOUybbCk1VAXG2QuD7Tbg2GfYXKVDKisOwahK0i6xAsWDPjJULLkx5LJE66SDXW5djrCkrIFSY9cMkxGm/Cu9uUKZDLoSlnBeLs4mcIAjNXdbLQE50JxnPHSuvickKukWsjgHg8imMkFZUCdHGS1FCnXE6p8hU3L6FcwtYPGKxOL9wnHnqrtpUsclFnQgW8/LniecDKfDlW2GywmVgO7qQtlZs9UssmaxYDb9j4HWDQEL5NqMAlmpeGaslIAaX2ZSyohB0eq3HTguLu2e+4KLLw+pr4DIL14gdjduPClzlwN/FFw6zJ6CeBGnRrwJgF6kPQgtwaqvLbCKrZMVgbPWXMOpke7vL+AEb/RnBlKZwQQfJAZG03Fqu5eBY6dayc+ClXWWghFhrygoIOZtQPyn5xOV7WNjZy7Jw+MKgXys/Hy+o68vWe93csOmfvWPBGntB5rCB8KXQ4u+1i6zgmhzI8MYSbewKbx6tYkrWFL2cZZxPFulQyorDCKbu7p6UaiXgik2cUFWsSrRsyHJSWWnVFqbE564mapWLuJN1WC5p5SZaV1ZcBqEF6FvBbpePDatkBXkiWBChHARrbA3Gm2FXoq+dZSAc65wSatVTFEy3ll3KaLDA4hpsGQhYNmqZuH33yLsuj2PBQ1cJPHlzhs0hu7C0YKm4/ejYRx6/v7d2r7gewu9lNTHXCPgJ5+TN8Vt+QikGajVm7FiN+PdWCjKbKVMY5PPCUMw5LRhtMFCgyEqEptcaI+9xIcDv8dfK5wnB+FXclRUnL7itWnt1YnMF0faXAv7/p+ZMDagOy3K21XClYE227FdBG6GVlnIAUjkrGsHO+giWrPDrgGJlR2IrFiIr08qdaC0Ppi023GTF6KWyWgYCzh13rq50GEutrLSgBGRVufWE5aOW67+/s7t/GY9D41C+scMnAyzMX+jX2MtkHITBypRnb/OXzJhsj2nGXlbrgsFANNkqsuIweHdo9UTGCcF5DVYueDpZSYhcsiJ2f70ynyOpp5eoeJ3jJ5/tZCXAEfPsV8EuJ5iL7cSs4DqS+pEVi8QJ5SP2/9ihrkDmR7dWMETfGIAVVGifHcpKQ/jJitUyEBvtQQxAIl/a17eZePPQm+L2zNFnkp0A+YFiAj+HJ6Vja+VWcWunmsNkBc/nzbfCxDdYc627sgKTsidS5oSyMlBNtoqsOAw9p8GiF8BIFqxcdOs7rKekul9wUTpxosaJWHS+NCThIlF90PLJh3oyE0Qnp6a6l4EQYhWIoqAPUbTYCcQIxjNjV3u7E4ZfLpHBoGqV6PN7E47QPic6toIxrqNsEawScPXUq8XtM7ufEecY/iaQBih8rLzYBfxOVldWFa/yqqzYSVZAxlAqQ6SAt2utsfPJDsD3gmsASKW/UtAxO5UV7fXz3zMQoMiKwwgmVMqO8DHeHQazKGIBy0vKc8y30qoNiwMSQFZqDkJuCeh3wCiL14jduJk6LJfUglVWoFixOx919FCZaxmcMRGsssILczBkxUo4n5kRFVaVJ349MNj627U6YbB1T6E2BkSGWlkJxq/COHvs2UJhgQ/uV2t+RfdvuF88fvLIk0V4nN04ffTpuk/G+PmBDGOzgRLqjFxZRrED6HzktunVx1Z7/BmeBj0tZ5ptpGxB/gK/Xpn69np9o2gHWWFFB5uccByXVqDIisPgqa3BKCuTsyZbNkPZ4VlxMdk60BHU1iB3DHG9vRQrHqgnam+07Fvxt0OBAsID6oIlK8YL167qXYGXgYJVVrQyEC7gVlt07fCsBFMS89kJZLEEBIBEYpPQ1dtlqTRlh7ICAygILUi00/O17B5j4Q545+5eerdYYN858g59XPKxUGu+P+/75ARgskXIHJQOI3l4v+h9vaXaaqu9N5w26jRx+2Hxhx6JH6t007Nl+qwdYLLyefnnXn/mqNaBhFJrMBkrxnMD7y265QK5bg1asnLffffRokWLKC0tjfLy8ujiiy+mvXtdd5+oDd51111UUFBASUlJtHz5ctq501yi31BRVrjVDItAoLNX7PCsOO1baa2VC0kSxBS++DQHHkDHOQ9cz/bnV8HCbMfFjmOzAznp7ch54TIWFnQQleKG4uDnR9lAVqyOH7ArY4UBRcZKYKCdBlvxGizOrrK1bdkGZQWA8vDbk34rFjvs8P+47I96CdZugBxdNPEicf/JnU/qPpL3j0qycsboM2x/zlMLT9XLTNWtrtk4UCFAfLHBsGOT4+6V2Vyx2ev1/aB27NgRgMfHJWfLbK/0PVF7SJCV1atX080330xr166llStXUldXF5199tnU3Nwn+99///30wAMP0MMPP0wbNmyg4cOH01lnnUWNjQOn/9sMWQnmoouOINTt4e0IdHdmbF0OBnrWigNloDZtkU1ExkrqMMtkhevX/sbLl7WU2eJXYfAuiyViM6hsqQw6NhvALtcOkhCswRbg14E8CF9D78yA//9gO0yCGYlgh8HWbhIXKOxoW3bHhRMupPe+9B69c9k7eqnGKVw59Urx2rdUbqEPij6gLRVbaEf1DlECcuK5QUKw+YAS5t42va50ne0dSKyc47zDMe/N8LpfO3bsIivGzZ2Z1N5BT1beeecduu6662jGjBk0Z84ceuKJJ6ioqIg+/1zKXWDKDz74IP3sZz+jSy+9lGbOnElPPvkktbS00LPPPkuDAXYoK1iQ2LcSaCnILmUl2M4KX2jVykBJ0fFEKdbJCk4+GDKxWPpKsuWR7LaRFU1ZQceHGXOvncqKHR1BOA+DDYXjziaeDROsisBkJbWlluh/PyDSwhUDBWetBKOsBEtWdM9ZkCbooNJrbSgDhQMg81dPk8ben37yU/rhhz8U9y+YcIEt544nsGLz+sHXXR7/7PhnLhkwdgHjPrgU5Gv+kl0BeAxWVvxt7oakZ6W+Xi6c2dnZ4vbw4cNUVlYm1BZGQkICLVu2jNas8fyhtbe3U0NDg8uXE/i05FO6ffXt9K8d/wrq97C8HswiEIxvxS5lhZ8fRMCOHA0j2pqk0pGEC2qKpjQ0yTkYgQDvMZMqXycg+xeCTaBkwFyIRRptnWY/n4pW+fexcdkWk61FrwgMdpC37ViY7SK1utJTfYjo838RffJgUEQuGHN6sOdOsAMvI6kMFA7cPPdmUSpBaRDnDdSPH8z/gWPP98UJXxQbRBheuYsLmxAeK3BSwUm2P+cphaeI2w+P9ffK2D0HyZjxgr8ToX6exigMWbKC3dttt91GJ598slBQABAVID/fddYB/s3f8+SDycjI0L9GjRrlyOuF2xwudG9xzwHvEINQVoIhKzyTJNiUR1ywuWRh90W3tUl25iRA8k/RXmeLtVkqZkpBTFaCHS3vyWRrJokSqGrRlJXk8CsrrP6hvdWuskuwKoLendSjpTYf6t++GkiLJgyKgZJsnood7LljJPrBlscsG2yDCIQLN9Cl87cz/0Y/WfwT+t6879Fz5z/nmKoCgAyhwwn4545/6qZe+MLQDWXXJseIZYXLdP+IuyqMf1e2VgrV2I45SAwYddkP6cvci5C8363/Ha0qsnYODjiy8t3vfpe2bdtGzz33XL/vudf/QGy81QTvvPNOodDwV3GxdVOhL3DwDve2h7MMBPBBFQhZwcnFu8NgZuDY0ZXkCy2akS0F5k5uE9XaRq2SFTPOeruCnYylIDO+FbRhcjeQHcqKPv25schSG6KxBBRsLd7q+AGvhl8mK8e3EFloP8ZUbSut5dhJ83sZbHu5IPra5xzqUpDeuhxEIFwkACQa5aAbZt/gKFFhfHv2t/VSEIyvj+94XPz7ogkX2epXYeSn5OtemY+PfezyPb6WTc6abHv30+Lhi/2m9sKrg2wdb+3cg4qsfO9736PXX3+dVq1aRYWFfel7MNMC7ipKRUVFP7XFWCZKT093+XIC3MsOf4OVmTzurcvBHmS8CEDx4V2nP9S01ug75mBbZJ0kK7wwpYCoJGqSe5s1soJ2RmB71XaPAXYd3R36QDA7ycq0bK19ucZ/RxDvnND2GWyJAcDFG1+BlKHsNtfaXfLQXxMSjQEsug3yc7OqegVigGYyiYnLdiwQwWQl2REKN5DLQOEA/BxfGPsFcU5d8/Y14njGuXrF1Csce04OwePWbHeyskDztdgJzpXxRVbY78VNFoOSrEAhgaLy3//+lz744AMaN05mdTDwbxAWdAoxOjo6RBfR0qX2mpisSIFY5NGB48us6Qs40O1IsOWW0oKUAnF/T/WegEpA2BmiNhmRZKW3l5q7tEwNEKoEbcG0kLPCJBPjCZAf4OkERGQ1Phe0+9q5Q+OQJZzY/qR+HqIIn4tduzR97LvJY8PuQDgGy9Q4Zzj4zgoatRKMUFZStY1LXVFw3VoBpHXya89OyrblM7Izg8aSwXYAl4HChV+e+EudIEAZv//U+23ZXHjDOWPP0echYWAig8PiFjhAVubnzxdrA1RZb74Vnjtmp18m4sgK2paffvpp0dmDrBUoKPhqbZXyKi4Ct9xyC9177730yiuv0I4dO0T3UHJyMl111VUUTmDXy730PJMhUEBG5vkmwZaBAE5rROueGXBOgB1TSd27GrzNzggY7Q3UQlK5Sk3KDroMBJxYcKKLe9+IfXX79F2CnXIu/DwgkyBC/tz13LZsh1/FXdmxEp/NJuxgyx0AVAhWJYMhtY3ae5QGD03+zKDIipVocfarINTNDoRNWbExFG6oAeT9iXOeoDcueUO0atvdBeQOXJPm580XG63/7v+veAwqMK630VHRtHC4zGOx+2/ka4enzR2UaI7LsNMvE3Fk5ZFHHhG+EgS9jRgxQv964YUX9J+54447BGG56aabaOHChVRSUkIrVqwQ5CbcCNa3wuUNZALYIcNyX/yOqh2BGQRt8KsA49LHiaAmqEU8WydoNFdRs6b6JGPXkshkxXrOzokjJFlZW7q23/c4AMnOmG7G3Ly54haZEL7AZSi7WqetBtPZPaeIwRe/YCa6NmolzDSYujM1E339saDKQEhf5rKIWaIPZSViif4Q6QYKJ7ChgaHWbq+IN3x5ypfF7VM7nxKT2V898Kr498L8hcJ/5QROGHGCuHX3ynAzAsgTNtvBZkJFfBnI0xfUE+PBgATb0tJSamtrEyUg7hYKNwpTC11yOQIFlwNS4lNs2cVzqQF+jFB2AjHiYuL0uqVtpSCQlWj53ogLApeBLHpWgEUjFokSHk409wFyTPSY+DlCVirMkRU+vuwAqwfYuQc6B8dOZcWuIWm6ZyWtIKh2dgAGW1zocdE166Vhz0p2gj0LBM4b7I7xXnMZMBQY6DkrQw3wyaCZAuNAfrDqB4K0GEmMEzhttBwx8FHJR0JJ8eRXgarihLE4EKjZQCaUFasj73n+jB0lIGNfPGqLXEowtTu0kZHb7ltprqSW6GgDWQm+DISsEN4tYIYJA1HWrDw4QVbm5c3T4/67e7q9/hwrdXaMemeg9AJJF38j15jDpqxYMLS6o0nrxEnLGE2Ummc5KBDARZYJlFnlic3pdp07IAtM9INRnCIhwVbBOSAg7ucn/Fwo2Mh1QbYMSkNnjTnLsefEtRD+OWyu3aM6eOPFamk4ociKifRLqxHzeiCcTWQFffF8wTNTCtKVFZSBID13BzZXyFcLtW0X3OZKatYYuytZabTFrPbO4Xd02R2LJy7e+DzszFgxhrPhb8BJ72sHzx4oO8kKFmQrsf8At7fb5c/QE33rzSf6uqOxV+7wUjFAMyU3KLLi0q1llqxoJVS7ykBAoITJzjKQMtgOHEChfezsxwRBuWrqVfSXM/5iS4OEN+B38wBHjDQwgs29TvhlAoUiKz7AhiJcdH3tlJ1OwLRaCtKNnNgxP3YG0b0FRLv/F/IJwz7RXEVNmrIipokaPSucsWEBZ4w5Q1ygoTLwboFzAmDAdeLkx66IS0E8R8QdMOByGciOUe92fDZc8sjgtnGbWqlhLreiwCEfCNZ0ID0LZCU4ZcXKHBS7DbZ2eXksKysDPGdlqAGdPw8sf4DuXHJn0KnSgYwYWHF0he7rwvrFuUBOdCIFCkVWfACLCeRT1H2PNx0P+M2t77CfrARismUT7IjKg0Qln8usitW/t2VBxIILA5g9ZSAPnhUsVkHE+uME54mtj25/VJRH3jj0hvg37yKcAJt7Pyvt34nELb04nuCpsXNyq8vO3UTWixH8OTqxMFvxrRiTZlMwNZnnRTVZJytz8uborcOe8nfcgQhywE5ToR3lsUDBC49SVhR8YcmIJaKbEQTl7cNv69cwbDiQRxWKID5/UGTFz055XIbMhgnUB2DnXB5Pygral32F1eF73DdfcMxg+CzbHtRFHyQAkdNWFkWvZSD2rMSmEMEIGB0XtG8FuHb6taIFHSrH1W9dLQgWfBlO1n/ZK4MgJ3ezGsBtgCAqeG12go8NZK0EYrJlZcUuz0qwC3OjNisquaeHYjNGEiVl9h0PFtU2XGxx3OLiyx1hZsiKnYSSyeTx5uP2EH0TgOdBVy0VFHysdWzifWz7Y2JD9dqB11xUl3BDkRU/YI+IlUTOBm2xzYi3j6ygBRLR09gd+npN2MFDTscOPq9Y1h11lPruVnGyTdanZyU+BeaLoIPhGKPSR9FtC25zea3fn/99RzsjYEBG9xUydjx1BXHkuxMBSwjDA+FAkKHZUgNIre5ZsakbKNiSR0P90b70WhwL7GOC2hYEgZ07TJboNldu9vlz8Nmw+mInWYEBGp9RsJ1SgYBHBgQ780lh8OMrU74ijLYIiLthxQ0inA7l8ksmXUKRAEVWTPpWkNEQCZ4V7Mb5ousrIpnLVnlJuRTbqGWiTD63T12JELLSa+wGgrICsG8liPZlBuaJ/OrEX4ndwV0n3kWXT7qcnASMrhxK52nc+96avS67bLufWx/7btKbgUUZLb1OKStopeb2WbOorZPdd1lRsZK8xiVKxQ1ok+eUk63lrEhi/IDd+Rp2tHUHAjY4I7FZQcEXkLIOjwzAE6a/NPlLjgxutAJFVkx2BAVTBrJzETDOc/A1rE/3q8RqKgVaQEfIuj3VHo4YstLRXEVdxm4gwIb2ZeMCfvnky+nB0x6kyyZfFpKsAJ7Yihkf7gFgrDQ4QVaA2bmSrGyt2BrQMYr3HtNt7QLq32j7hVco0FJQbYPslsqKNphC9ZlR1smKcSK3L8M8kxUMl7Mbofat6MpKnFJWFPwDJXJcK08fdTrdPPdm+vHiH1OkQJGVAJQVXHitGGzTdRnbXrKysWyj1zRMnaxExcgH8qYRZWuzmWqt5ca4S/zwgLB6ZAk93dRsmB/DdfWi5lhxu/eotTC+cOPUwlOFAoZ8Hg5VAlCW49KdU2SFjaTIejEDnntldzqmUHk04uRv/IA7ajWykGVUNWwgKyi9oW0dPg5fJVT2qzhBVri9PFTty7pnRSkrCiYBFfqh0x+i78z5ju2+umCgyIofjE4fLU50tACihTncnhUOh4O7H8ZI42LoqQxU0KGZPPOmEmVp2SI1wZEVlLU4fTWoi25LDTVrRyBq6qiPbimuo311koC9tn5fSKPJ7fQm8ByRtw6/pT++r2afICwoL9jdtmzsFouiKGHiNBMcyAPTnIjSDrQkxajVwgyzjOeNDWQFJkJ+Tb5USVZWhifb261lVCXhCwiK6JuE8qwoDBYosuLvDYqK1qXbndU7I6IMhNh7rr978kUATGLGNmsXxLzpROlyajOh2yJIEqAPVTQ5p8hvJ5C2i357eym1kpT/W5sbaH+F9fblcOKCCReI21cOvCIIirGdGQFLTpWj8D5OzJpoWtFwkqwYyy6BgLuTsowzrWwgK0ZV0tPcKEZZi0ZWbG4tBzITM3UPgNmxGVaBjjBWg5XBVmGgQ5EVk0oGsLPKPFlBl0VDh6asODBW/JSRp4jbj4591O97UCNY5p7YoO2usyf0hWuhpTbIi77ujTBZbvCIlr5AOE75hbLS0ivNlEnUQZuL+spEAwlnjDpDdAWhzIIUXWDl0ZUunhanwCTBzGejlzyS7S95gNCC7KMkaRx57w81XXKmVpaxDGMTWWHzM8zpTCLdwfOkuHPHbugBdQGSOKslIECVgRQGOhRZCcRQGkCuCLosOAfFbs8KsHzUcl3Odg+5Qsw+VB0sFOPrtU6gzNGyq4KJk8WhcO7eCFxwLZdqmiupXiMreI/we3aXNlArSaNnUlQ77TwevMk2HID6ddW0q8T9Bzc9SGtK1oiSGSZwnznmTEefm2cU+Sp1hEJZESqP1qIdyMJcp3UPZaX2TaXu1lI8O1vqgvZbQenE5HBPqiCOQTbTj0cgnQOwWh6zWgLCnBkcjwoKAxmKrASgrKDt1NtuzJtfBfKrE0PE4KVBYF1Xbxd9WvKpy/c4Inl08ghKRIgW2j55GJw+FK4i6Is+zFeQ7FF/t4TmampgshKfTsfr26ihrYvao6SykkzttLcsuKyVcOKa6dcIbwoIwbff+7Z47MIJFzo26p2xKH+RXrY0psGGmqxYLQXVkixdZBlaJlcekkmsb2/cSz3IX7EIEHgO7vNUQkXMPrwk8P0gudMJsCqJcDonPVnKXKswmKDIikligDIF8iLM5q3wEEE7I8zdsbxQqisfFH/gkaxMTNJiyjMKZV6Fkaw0SfnfKtDmyoqT5VJQS5VOVlAq262pKEkpst06idqppE7uDgciED73h1P/oB8DUBk4pM5JjEgdIQzQyE/hvAR/ZMWJMpBRRTB9jLQ3UY12rGZnSWUDatuWSrmotzfW0Ef7rScwA2x+/vjYx/2+x0NLQTKdCg9EcCA2MCgTH22QAXhOoLVTBcIpDB4osmLmTYqK1tUVsxfdylZtiGCyczMVMKwPWFW0ymUHza9xagxnrMh4fFeyEtwF38UbYTLTw2MZKKZPWdlbLlWU9LR0vQxUWt9GXd3WBxqGG7OGzaJ3LnuHXrzgRXrxwheFwTJUsz6A9aWuI9+NwK7eaWUF4+3ZTMpzanyhs6GEGrVjIitNdkyt2FlODSQN2OlRLfTh3uCO3VMKTxHnNJSn4sZil+/xZsSpEhCAkgy3/ztZClJR+wqDCYqsmMS8fOkD2FzhO6qbwW2jeUnOLAIsJ0OqRlv1O0ekiRM+GX2sd29Cn1+FkWKPshKokdMjmvuUFZCV4hppCExPl76alKgO6u7pFYRlIAP5MegoC2VmAXe98MRpb+ofypooeSBm2wlgHg+IEJ7HzHFSXyvJQlQvfEzyOFh3uJoae2WoWTq10LrDciKyVWBOEJfKVhxZ4XEcAodBOgXdt+KgyVa1LQ9StNQQvf8borX/F3RX50CCIisBmhbNkhUO23JyWiXaXy+ddKm4/9Sup0QqJy5+qLujbDWrTSuhZHpSVoLzrBjJCiLVmztlB4dVsoIyEJd8UtOkIpQVJ/1Bx2oHbikoXFg8fLGemIvjwRO4BDEiZYRjBkwco/xafBEnRnmt7GIbRtEiFwVkdWtxnUFZaab95Y3U3uU9gdYMzhl3jrh998i7Lo8zoYIi5iT43PEX/R8MlGdlkOK/1xN9/Eeid35MtOUZGipQZCWAiwukY6S2cmiUmTLQsGRndqwMzG6AKoHAutcPvk4v7n1R7xaKrz/WF7XPSJXehO7G4JUVJHxioYOaY6kUZPCsCIOtRlbS02WpJD2GyUpfC6aCOeC4Q0oupgy7G7DdW3THZjhjJPWUuOwPZQ2yLDM8WvpFoLY1d3RTW7QkK5nRLdTV00sHgszfOXP0mWLIJ2b08Lym2rZa3e/F87ecwvx8WR7bV7vPsXA45VkZhCjdRnTgvb5/Q10ZIlBkJYA2TI5IN6Ou6GTFIXndOHzqW7O+Je7/cs0v6X+H/ifuXzX1KqK6on5loJVF0v+x/9AhqmgIvryyMH+huOXSU0BortI9K0h9PV4nX09WhiQrqdEyfVcpK9Zj/4HVx1b7VFac6npxJyvwZ3BpwhvKmmXycn6cVNeYlGRnyw6qtCjZ1ny0OjgCiwnTiBUHntz5pLjFlFmQOxhgnd5kQHHF+47nc0pdUZ4Vh4ESTNUBoi4tJTwU2PmKvB17ClFUNFH5dqL6gTmWJFAosmLBLGgmv6KqxfkyEONr07+mdwZxy+wsdOo0lLiUgWqbO+jxz+UuLqm7kf66yvt8lEAXIl8ToD2iu4uotUZXVmJ6U6i1U5v+mym9CsnawqTIijUsK1wmbqGseGq5P9xwOCTKCjqTkAaLNFV/RL9MK5/mJ8r0Wk4wzh8myUMytdpCVoCvz/y6PhIBgY8v7XtJV11CgQX5C0xfT6xAeVYcJiqvf4/o4QVEf55H1KDlWTmN/TJYkuZf2zeY9qhn5XSwQZEVCyrCutJ1EVMG4tAnDJ567OzH6Klzn6LbF95O1FhGhKjt6FiiNBmu9cGeCqrokvJ6ZlQTvbGtVHgCggGi44Ed1Tv0cfSm0Cp9FBwK19Img+ByUxMoIUmm2Sb0SrJS2SRvFQLDzNyZItMFAWibyjd5LwM5rKwYfSv+SG25NvyTo+73V8gOsZF58jyK7e2keOqkohoLHikP78/ZY84WLd5ffeuros0bJuhLJl1CISUrFc6QFT4fVXqtAwBB2PxveR9Twj/+EzmOtnqici3IcNwpRIXynKLSIFLEBxAUWQkAi0YsEnVuTNMtbfLOpLGLZVNjKJQVAH4atKvCCCzmznAJKH0kUbScvLx6XyXV90oikEatVNPcJjIs7No1B9QV1FxJKEg1amSluUWSlZGZiUTanKC4HlkWqmxUZMXqMXHaqNPE/TcPvenyPWQGHWuUniaECzoNDmLz5p9hlHVL5WR4+iiXMtDoEX1ddSnUSkVa51iw+MUJvxAdSwhXBL4/7/uOzATyRVZ2Ve0KjOibxJBRVhB8ufNVoh0vS8U2FNjwT3mbpZ07O15y/rmPodTeS5Q5hihtuBxOC1TuoaEARVYCAEyg2I0Zh9J5QnmzNK9il+Z0WqlX1Be7+FWgoHy8v5Lqta6K6KheSqMW2l4SnLkPxIgVp4BKQc1V1BwVRT1aAFhdU6y4LchMIoqTF9cY7WKryIp1IDEXWHF0hYtfBF1CWKBxfDoVCGfESSNPEi3SMLT6mhNURrJcNTxzvIy+18jKhOGZRNqimxLVZksZCEDuzQsXvED3nHwPPX7O43TdzOsoVChILRAGdXwOTuStsGeFh4QOWnzwG6L/XEv00jeI3r3T+efraifaJ6Mi6NJ/ECVlE7XWEpU4o5DpKNYU/dGS+NMwmdVDFYqsKPhIv/zsuHeywvHzhWmFYncbFtQddSErByubqLalk+LjE6hXu3hlRjXTtmP19nV7BGKybamiOs1cmxiTSBWNPX1kJV4jVD0dFEPdVNPcHnS5aqgCShvSWNFa/kFRX9IxmzoxVM+pCdBGgBTxAD9PybFAZ2cLVUbL1zI8ZypVN3eITiC8vFHZyUQJUhVMpTbROdbRZU9YIMzdX5zwRf04DiVYXQnY82UCPDMMf19IvRyVe4MeOGkazVVEnz3c9+/1jxLVuQb92Y7i9RhSJTsrCxf1kYfjvtOig8Yx7RgZpZV/WFlBGarNwRlqZduJNj5OdNy5NnszUMqKxamtGDGPXBNPKGqQZGVMWt9sk5CDT1gtvXaHpqBML0inqCTZbZNBzbS9JLjBcAAHbCGl1LSc3VxF1TGyPJWTlKNnrBiVFSAlqp3AU6qbVSnICkCWsRADL+x9QZ9Fw2Q7lAs0kmN9dScVl2+jrqgoSurpoWHZk/VSz/D0REqIjSGKl2QlO7ZNHBNlAzwsEGAvD64ndoOnvoeMrKAcA4Xjr4uJHppDVG5+8KtlbHpSTpEvmC87ZFAm2f4fZ5/zsDbpftypcoxJgczgohKHyUr5Tnk7XDPWJmURpWolSxBEpwAV6Y1bidaFt01akZUAgd0hAsww1dhbZwO3hGKmUNjgVgbaUSIvXDMKMuRBDrIS1Ux7SoMP2IKCBO8KfCtmgr8EmquoUiMr8PVwxorwrIiZLHKHPSJZ/rgqBVnH5ZMvp/joeHG8ritbJ/JEcAucMlISiFC2UmNh9kRqD2hZPRO7YbOK1RONhaoCJMhFtzBZHq/ljW2DZvODCdBMLgassrLtBaJdr8n7KIu8dbvzz7n1BXm76FtEMy5x7ZhxCodX95EVgMnKcXOBoZYVpCYtGytPK/8Aw6bI22qZD+QI0J4N5MgJ6uGCIisWOm+4Tfj9ovd9loHGGKbGhhx6xopUVnYel8rKjIJ0Im0+zfC4VhGwxYuCVaCMAE8CZ1WYQnMlVWlkBVk0x43KCnYrWiloZIpUAhRZsQ7E3X9pypfE/bvW3EX3b7hfEEvMp3FyBo478HwoScE789ExbXdqwEGOutembvNxOdqNrIxIkmRlMCgrMPOiGwvBinaXgnheWMjIytq/ydtF18suRHTMVOx29hpXtVfmjUw9j2jCaX3lEvhKnAB+LysoY092JSsgDE6Vv8p39hl6tXIo0JhUIG5LixwkK0yEcidROKHIigWcOUbmMLxX9J7HEe9cBgqbsoLXpKfXjhKvcZc20XjmSCgrkqyMS5VmxkOVwbeBnjzy5L5gLTPzKlqqqBLSvphMnUMVWsePICuAVgoakSx9CYqsBIcb59woiAISmN849IZ47Nuzv02hBEjteePOE/ffPOzanQTs1xTJifFS+StyJytaGSg/QYZwldsQahhJ6oovH1xQyooWsOco4Gso20YUE0902k+JJmpZNbted+45OckVLbxQi7GQ4xaZQhUOlaDwe/H7+fmAlFw9HoKq9jtLVvLlQF0m8//aJa+Pn2z4nNYeqnYu+A7IUWRlQF5c0A6I2H3It0Z0dHfQsaZj4fWsNFcSYcItdhzpI8UgwMb2LoqJjqIJw1J1sjIqSV70D1c121J7h+qExZCVJd+vsVr3rCRGZ4pzIj42mnJSZAszxckFKj9R7qJV1kpwQOnyr2f8VUwPx/0fzP+BPrU7lGCyAlLrHjN/sFXK3BO17qQiL8rKsPjBRVa4rdtO3wo2DExWkHLtOLbLQD2a/AWi5GyiKefKfx/xbKa2BQdXyduJ2nFs9I84VZLh34vnMRjT27X2/5pih5Skiv5k5YGV++hQh+w2LaAquufN3eY2ioGuJeI8jSLKdj7iwBeUsmIBCTEJeinotYNajVYDhvpBYseCEKq8Bq8lILD92HjRCQSMyUkWhIDLQAXxsvRypLrZlsnCC/IWmC8FNVfqnpWoHrkIjcxM6utM0cpAwxKVsmIXJmROoOcveJ4+ueITfURDqDExa6KIs8c5wgoPAOJyuFOSlynpsjRVXCOPz1HZmtqmyd/ZsZKslDUMDtM1TM7Ib4LX7XiTHDcQLDCJnbNjELngOJiUTD1f3o4+sS8bpLt/erJ9uSO4sMkStEAoyYqGPWUN9HqxPEZffGcV7S2TJNFJZaWupYPe3F5Kx3plWOKo6EoRQ7FTU9BtAytFsBMYGh/CAUVWLOKyyZeJW1xwjWbBHZVSaZmePT0kLaE+yUqGa7DWRKgqgKas5Ma22lYGAti38nHJxwF5Vro7JFkpgLmWoZ0YOfHyQlfdFML5GwqOD98Ent39rPBqcOQ89oRjOzopN3OMaEs+Xs9kxVVZyYyRJKV8EHhW2FMye9jswDxffsCqCkiQ46FwaJvltlb2caBkgFIJsn0wfM9uYB5O43GiqBiigr6hk6XJsp23dM9asaA7RlZGyOeEknH367toX5dUAwt6jtMvX3NV24MGuk4rNMUmT5KV17YcF+dIcp5Mny6IqqFo6qGVu4IfUOvRrxLmEhCgyEoQZQ8YaJFfgdkiDO6GmZffx7xDDrcBhqysTMhjspKlR+4Dh2woAxm7PdaXrtfNfR7R2UbUVkdVWs5Ka5tcjAoyDBdVrQyUFSfLQKp1efAArdRYoFEu5HOHM2CWtraJdkwYrqFoJ8ZF07DUBPk/akbRtOi2QdMNZHboZKAwloAc3zQVrSXq7ZYejoxC+Vh0NPVqcfAdR9Y4lzmSP11XYWG4/s5KeUxkNB+lbzyxjrq67cni0a9bTBo0ZWXtoRr67FA1FUdLo+v4qDJad7iG9pfbqK7UHJZlfZBOrRTz8X45Q+vkeTOFmTmWuiiPaum93eXOKCthNtcCiqxYBC4Al0+6XJ/aioh9+FXYJMd16EggK/2UFa0MlNLTpJtX27QhgsFgfMZ40dmA98JTt4eOpnLCs9VoykpDU7KruRbQLkAZmuRf1aiUlcEClAy/PkMOEfx/n/8/OlR/iN498q7499nNMmyL/SqjspL7FlutDJRCbfriZHuNPsxkBXPH/E2mjjhzLZeAWFXBud3cQc+WyBLFu++toI1H5PgR21CilYAQyqbh/nf30I6WTOqkWDEEtaz4EL28SWs0sKsUg3lrybk6KePfP3mazD6ZEAOy0Esv2fq8mlKDluXoGOrp6aWNR+X7uWhCPlG6JEqF0VWiDGRrM0J1ZLQtA4qsBJlfgWROzAp6ZtcztPLoSmrsbBStonOGacE94UyvzZIG3wMVUjmZqCsrkqzEdtRTSrwkDBzKFgywqJw15iy9U8orGsuoPDaGuqOihCm3uoHnAhmVFXk/PUYrA6lQuEGFa2ZcI2byIHr/olcvEh6LGe0dNL+9nSh9RH9zraEMlNgjj+f2rh6qb3XIDxFiTMqcRAUpBWJmk5lBqRGVsXJEK12JUDaJH7+8jT6sk/OcxvccpRuf2UQNbZ32+1U0sgLi+vqW49SNzOtMWRqZEH2cnvpMuxbaAU6o1cy12OC9u6NMPHTKYryOKErqbaFsaqQ3t5XaR6R1v8p0XSmva+mkpLgYGUWRLonTvAx5zmwqqiXboJSVwQFIrDfPvVncf+DzB+hXa36l1+TDFrMP1PZF7de3dFKVNrXYvQwU1VpHhVlyMThWGzxZAbjDBLV3rzvEpjI6GitnASFMrrTOrW0Z0EYCpEZ36Ds1Fbk/uEzqD532EOUlyQUtOyGTfl1ZTVE4b1KHU3GtWyAcoHW1xHQ2U1ZynLhfPkhMtiD6rK58WPzhwCEr8KuUsl9FetY2F9UK78R+ksrupOgSqmlsoefWmegSNAMYdtk7MlLOJXtufZHIjFo8NpsSh0vfyuSYUqE0wABrC9iXo5WAUP5Bl+WIjERaMH64jN8HwY6pFtdTu+ZX6W3Y+XIu3YYjkozMG51JcSilZ4yU/86UJH7TUZvISlcHUa2czE65WvhcGKGUlSABYnLZpMuol3rFrgidDtdMv4bCBkRe62WgMXRA86sgsjw1IdalDATfSGGWJAjHtMUhWMBYzMFfa0q81Koby6g4Lk7PoukLhOtvsE2mdtEhiHj1WicMcwphw6SsSfTGpW/Qv8/9N715wn00ubNTdrDFxNIxvROov7JC7Q2Uny6PlbJB0r4MLB8lOwxRQmXjccSTFeFX6XHxq/ztw4PidtHcuWLTEU9dNC6qVKgctmw4oDTAw5GYIcoTUDDe2Ca7qK5cMoood7K4f0pWrW5GtQVMykZI1XztQZlrcsqkXIrGTCstgPOUYfLY/fiA9JXYVgbKl+ZaLqktHKsNydXKQBMTG+xVVmoOSS8SjiFMeQ4zFFmxYUf0yxN/SQ+f/jD95qTfiAsvavJhQ3MFUXe7zFjJKNTNtXoJyKCsUEcTjc6Ms1VZwftxxmiprrx95G3PP9RYSkfjJHEakTRKDKvr71mR72F0VytlJcsykeoIGnxAp8rcvLmU2qIFWqXLXWKfZyXJA1lp0snKYMla4Rbm5NhkqmytFHO2ggHK0UBqXGpI/SrwS3ywR07VvmHZRL10sSDxuCg1f2rHAs7mWqgq0dG0t7yRDlY2i1iGM6fl62RlRrw0m364t9Jmc+1cXVkBTpyQIx/XyNribKlwfKqZYINCe2OfupEnycp6jawsGpvlcs4URMvHMZzWFmMx0oHZXBuuztZQkZWPPvqILrzwQiooKBCL2KuvvuryfTDiu+66S3w/KSmJli9fTjt3avW5AQSUfJaNWkYXT7w4vETFWAJCHTMmjg5WeCAr2JFo4BTbEpvICnD+eJm1sKpoVb/gL4HGcirSykApMZKxIwwuMU76ZwR4rH1nix4Ux+UshUEItKIadom+ykAg2VAKB1P7MhAfE0/LCpeJ+yuOrAjqd2H+E5CVqC1oIfKrvL71uFBP5o7KpEn5afocm7OHyYGp7+6UHg97/CqyBLRipyQlp04aRmmJcUQ5E8S/s9uPiTV2d2lD8KQWoWxQGZJzBDmAV4qHw544PtclKmJSgvxbPy+qDd63UrFH3qYOJ0rJodL6VrGxhJAzb3SWyzmT0lZByfExwstlS4dn1T7X+UODmaw0NzfTnDlz6OGHDSO8Dbj//vvpgQceEN/fsGEDDR8+nM466yxqbHQgVGeooJ+51q1tGYiOIUqQhGVMcoetZSCeAYNyWEdPB71z+J3+P9BYSkVaGSi+J6+/qgJwAFFnC+VqrauKrAxiNGhkJaOQGts6hYGwfxlIO4bbGykvXR4TPKZhsOCcseeIW5j1g1noqtvkrj8nUdv1O+5XkcoKl2MunT/SxeswO0GSlHd3lgdfCnLrBPpon1ROTp8qryWULUMFYxpLaGFBosvPWAZnxaAEFBVF6w/XiNL0+NwUGp6R6NJ9OaynkmKjo4TKFHTjQr8SUK0+kFYv62tkJarhOE0bIQMAQdAGk7nWcbJy7rnn0m9/+1u69NJL+30PJ+KDDz5IP/vZz8T3Z86cSU8++SS1tLTQs88+6+TLGtzQzbUaWeGMlWGaUsFIkmRlZGK7rWUgACraRRMuEvdfOfBKv+93NJVRkVYG6u3M7e9XMZSBhLKSysqK8qwMerKSPlJPrs1Oie+7IAMJWhJrVxvlp8YOujIQByuiFFTaXBpUKaimVZYEspM0X4MTKPpM+lVADjJGUnVTO20plqrC2dOHu+zKc9qOUFpCrNhwsCJhCS01fe20IxeIDqPN2nPCOyIA9UM7Vs4ZKa9vIBdBoXSri1/lM82vcgKXgAzKSkxDMU1Hl44wG8vXFry5drqbX8WgmGllIDQuzBwur5s8Cy4oVHIZSJbVhqxn5fDhw1RWVkZnn322/lhCQgItW7aM1qzxHiLU3t5ODQ0NLl8KBtRp9c2sMaK1jifXupSBDCbbvNg2fYfa3hV81oqxFBQXHUc7q3fSlgpt96Vhb1sFdUVFUVZcGjU2pXlRVjRy1dGnrOBiqDDIy0AZIz37VQDDjJuCJBklXz7IlJXE2ERRUgY4eyZilRU3vwq8IRCDpo9I71MbtIUuuvognTReXnM+Cca3UvK5vM2eIGYQrTlQLZQaKBy6CofajxaetjhdKhEbg+2QYbIyXCYNrzko/4YTxxvJihaIV1dM80Zl2kNW9LblmeJmvaasLGJzLZAyTE657u2hedlyQ7crWGVFDDBkZWUIlIF8AUQFyM+X7V4M/Ju/5wn33XcfZWRk6F+jRkk2q9BfWcGAQkiV6YmxfSmgDC1rJY2aRL8+cLzOvl1qTlIOXTjhQnH/iR1P9H2jq522kjyhpudMo+Oa58AlvbZfGUh5VoaOslKolyRdSkBAbLyc6ismL8syUeUgU1aAc8bIUtCKoyssdwVVt2pkJSknZH6VD/ZWuJZjWG2Aj6+nk84ZKRWzoEy2bvkqH++X5Z1TJ8sAOh0gM/CPxFYK7oJroeWwNLRKM2kYMUfEKOzR5v+cYCQrWjcQtdbQwgJ5vd1cXBscYTCUgRraOvU27IVjslzL+mmyFDQjpVFXVoLyy+B87GyWJCjMAwwjphvIPQoab7CveOg777yT6uvr9a/i4uIQvMoBBEPGCvtVYHTr955qykpUW73t7cuMa6dfK25XFa+iQ3WH5IONZbQuUZ7IiwuW6s/Jr8E9wZY6milHV1ZUGWhQortL+JgE0gt0NbAfWTF0BOUldOiKIBI9BxNOLjxZJM9iqvuGMq3zJQCA4NS2y0USoZWOoK2+T20Yc5LoPmFfyGlGshIdrXseTkyr0n0XrVoHoOVOoMKFYq34SCMregmIoflWkpqO0hQYfQ0lFEvlEHRYorSUNY7WaV1Ak/NTaVhagmvjguYFnK9lnuwsabCuWDccl+8z5h/lThb5KeAfGEibpxnMdWi+lTHxdcJ8W93cEZyfi821eB9jpL9wyJIVmGkBdxWloqKin9piBEpF6enpLl8KGjpbieo18pYzsX/MvgdlhUQwXJLtHUHA+MzxdPqo00UGzf0b75dj6+sO05ok+XwnjTzZMFnXbWHiriplsB38aCqX3gfs4lLzXKL2+0ErBWXFdogdM4LAagZZ/g4C874w7gvi/usHXw/4/69rr9MVGce6gThfRfOrfH60lhrbukRYHzqBXKCVEfLbj1JBRiJ1dPfQBivEARlShk4ghK7h+hEXE+WqcBjICrJC2N/BYWpBlYCio/talt2f06CuFFCleC/wt+4utdgwwmoOSmmxCbq51qUE5EZW4pvLaIJ2vQ/Kt6KXgCLDrxJWsjJu3DhBWFauXKk/1tHRQatXr6alS5eG62UNbGDgFWbXguGn5Orm2n5+FbdguJG6smIvWQFuW3ibiNT/tORTem7Pc/TCwdeoIzqKJvTG0ujUCXqHT39lRVuoOpTBdsiUgCBlR8dQsXYcukTtuykrsZ1Nekt7xSBJsXUf9shdQcap7oGYazMTMoVvzBEc/shjCWjZ5GEUg629EcPkghdVtY9OmphrvRSE3T6iELCRyZ+lqyoLxmRRitGIbSQr1Yf0xZ3n6QRrrl1z0C1fxQjNtxJVX0xzNNK2VTMAB9sJtME9X8UDWYEaw+beoHwrurk2MjqBHCcrTU1NtGXLFvHFplrcLyoqEmWJW265he6991565ZVXaMeOHXTddddRcnIyXXXVVU6+rMELfZz3RGEy85ix4lFZSXakDARgMvX3531f3L9v/X30UImcGfSNhNF6Wx+6BDKS3C6qes5Ks+63wXygwTK4TsEADr3KHC0+374ykBuBdQuGy0tLHHTTlxmYLYZzB0nQ8K5YMdc6VgICDmvTocfJEQGrtCA4lxIQgw2aVXt1ssLqREAo1mYmjVwgUo4/2icJzymT3PwqgJa1AqV5UaG8liB6v7ldGrOtkpWKxjahWEPVWzLOE1nRfCt1xTSnMEiyYugEau/q1jut9ORaI7gjqKFEGJyDVlY4AG/Y1IgpszpKVjZu3Ejz5s0TX8Btt90m7v/yl78U/77jjjsEYbnpppto4cKFVFJSQitWrKC0tBAM3xqM0CdkThI15EOVbgMMjfAYuW+/sgJcN+M63b8CXNbYRBfmztVLQIXZhsm6PpSVts4ePe1WYbApglhdxwoTJEKtsDnv1yHmFgyXr2WtVA5CZQXnA6srr+zv3/4fVnNtczVRmdZWPe5UscnZV94kPjMoK/3AoWJV++nE8XKhRfsy5pYFhOL18nbUYurs7qHPtI4cj8+JDhlxrPRSQW+FGJKKrqGAu3N6uvv+1hGzae0hqW5MG55OWZqy5wI22dYX6+Wwrcfqgst2yZ9JO4T3pUe086PzyVFlRRh7+7qQMFl68T3v0R/f1dSWwUhWkEiLnZL717/+9S/9hESCbWlpKbW1tYkSEPJWFCyiqm+cN6R01EsT46Jdpxl7UFbYG8CpoXYDn/Pti26n9y5/j96Km0R3VdVQVOYo7+Zao2elp5OSY3r1jiXVvjwIUauRlaxxevIm1D4xpM0dxmA4VlYGYUcQgKyimKgY2lSxifbVaoZHEyhvkYmuw5I8LOJ2qiqIf0/N01UVlGMytdEY/Uoy8COBYFK1yHzCZn3d4QDVlWMaWSlcLDwy2LigFMhKggsM7cvwrXDphKPqA1IY0BUD4pM7Wc9X8VgCMior9cdodqE022IUQMATp9ub+kyuI+b25auMyfLcgMJt04ZguCPVzdRkRUmC7xHlNpQQcyeL+H67oy0GZDeQggPKSm6fuXZ8bqocsuVDWWFzKybYIpvFKeSn5NOoenlho4zRujfBs5HSsHuAyTZNtS8PWmBgGpA9XlcDx7uHGHqcD5QwaMtAfL6cPvp0cf/5Pc+b/v+KG6XJflSaQ7EOh7Sp0OPl4MUPfJWAAHSTsIekci8tnZDr4v0wHQbHi3fhIn3eD1qWPV7fXEy2B/XSyYZAw+H0OUTzhZ+K1RyP5lpDii2GyaKLkUuZ248FGIRXBlWlV/q40vJ1c/DicV5KewZlJTc5VpwbEEj2Wpk4XbajTxGLjadtmjI0WytrhQuKrAxSz4reCeSpBOSmrMC1nhIvlYug46H9oZ4nQvtRVpCngZY9LgWlcOT+4Or8UDCWgcbR4ao+ku0RPEW4o5GGae2bg9Fgy7hy6pXi9o1Db+iTlP3hWOMxcVuYpu227QRWQANZQQsykw6XfBVvpSBBVuRCzyqFKXAXUM4kMSNntdYmvXyKD/VIy1oBGeZFHrknKCEF/LyFi8RcniPVLaLctVgrZ3klK2jF7+rQfSvsNzGN41qQZsE84RnZqJmDPfpVgNR8eb3E/KKmiuB8K3oJaAZ1dPV1M7FSFC4osjJYgJ1Hq9aalz2B9pfLA2ySN7JiUFYgK7K6wm2jjs0SQW4AkFHovW0ZgNTJ6opqXx68gNyNSeFcBtKUlXFelZW+MlC+lnEx2FJsjViYv5AmZk4URttXD7gOgvWGY00aWUl1gKygLIL5YzEJRGOW0meHqoSXAi3JnGfiEQaTLbcZY1qy6aA2NteOWizKfph9g0uER3Oth/ZlxDdkJscJ31tAcf96rssi+vSAJFezRmZQOgYmegK8MrGJsq27oaTPtxIwWdksbwvm0v6KJjErC6XwGZofpR9EMNxwe3wrehfSTBFCBzsB3juP3XkhhCIrgwXcaoZpy/HJ+kHK9ct+SNLa3zqaREKj3hHkJFnhDBgQpYQ0w2RdD8qK0bfS0ayn2KpguEHaCYQZNkmZumdlgicTYb8yECsrg7MMBGAjwerKU7ueok6kqfpAV08XlTaVOqes7HlT3k44TRDHlbukP+b0aXk+wzz7lJV9wpjKO3/TXUFHtREso5bQaq0EhLIEDKdmyApKRQvHaKUgs76V1jpBrgRGLtTTcn0SJLwHhlLQHKsmWx4QWTCP1mrv0cKxWZ59XP1KQSVi0KF1ZaWvZZpJFgiaz883BFBkZbDAcIDBCMVlIGbY/YAsFkZbvc6a2UfitNyPEes8WZeJUj8YhhmqycuD3a8yTsjzrOx5VVYM3UA8eRm780hpr3QCF028iHKTckWi7ZuHNbLgBfiZrt4uka+Sl+yjLGMVe96Qt1MvEO/5e7srXAcXegOHi2mLf18pyETeSkdzn8Ix7tS+EpCnLiBP7ct1RaIks3icZrI9XBvYdOessdSTnEuf7K/ynJbrDp2sHBVKCMpG8AOWaaNF/KK9sS+UbcRc3Yh8gjefjKeOII0MYiwAOkNNA89dfVDez5+pz1SCeTrcUGRlsIDb64bPpP3lTSLZE9LdCB4o5kk21KKhRUeQpm5wxoXzRkpJpmAEc5ms60VZ4fZlpawM3k4gEBW0lybHx9Bw9zjxfspKoyCwgzXF1j3R9prp14j7/9z+T+pGO60fc+3I1JEUHWXz5b2uWO748XunnEtbjtUJooicJL8LKYeLtVSL1uelE3PMm2wx3bmnU5jyO9JG62Fwy3z5VdjHgWsISjJ1RbrfA/4PU+T2yKfydtQJQqlGhD28ffNG+1m4DcpKcnwsTdbKY6bVFUHMesXf25uSq7dLL/FmrvWQtYLNJ14rSnSYixSYVwYD5QqFsZdTc1mVCicUWRksMNQZuQQEdu1TuktislKrd+Q46lmp0Rh79gTRzgdwNLRHGCL3eT4QJ94qDD5lRfer5KZ4P24NZAWSOBuvB2v7MuPLU75MafFpdKThCL1z5B2vP8ctzhMyNVXBTmz/j7wdvVQkZHMJCKQhPtbPUgL/WYa2iFftFamySLqVkfkt5tJyx51KnxysErH+eWkJNNdfd4poX+4rBc0syBBRDlB0D2qbJVODGsedQh9rqgpalv3+rQayAgTsW8EoA2DMicKvgsGJiXHR/rtxDGQFZS+2AATkW2E1aeR8YShGwwWUobmjw9sJBCiyMhiAnVa5lnY4fJZep/TqV/HRvhwqZYUvFj7JiiEYTk1eHqTQY72n6McEyIpXGMpAABYtIKihbQMAKXEperDinzf9mdoxWM8D9tbI93NKtuYRsbMLaPPT8v5cmTC+Yqec63bWdO+z3Lx1BKUlxtECTaF4f7ckPWbIylvb5XOeO3O495ZlIwxZKyAZ80bJ51znr4UZxu/jm+T9safor7HfdGdPyBzjQlbYt2K6I4j9OaNPoDXaWIIFY7L8kyRDGchoAQjMUNw3e4lVFawjXtXvEEKRlcEA1Bi7WolikwQRMCorPuFhmGFDW5fwkzjrWRmvjwJAQJRXGCL32bMCKVZhkAALIMd6502lPdpxO3W4j64SQzcQwFkrg9lky7hmxjXCh3K8+Tg9u/tZjz+zrUqmns7IkfNkbMOhVVIZBVmcfpHwxEEdjY2OouVTTHpj9CRbqf6cPUOSnBWaQuMRzVV6G2/HqJN0gnTerBHmnlNvXz7oEubGE6K9ongtUU+XUEkqYvLp86Ja88TMjayw32NTUa3/YDUYqJkwjF5KqzhPZpIJkmRQVgBWYgJK7S35XN6OXCiC9ziILhKgyMpgQLnmV8mfTj0ULdr6AlVWMAiM1QtH1JXONpHqKJCDMpCWp2FaWZGLEiTcgHISFCIXjWXi2BMeiJxJ/jvY3LqBgL4U28GtrABJsUn6nK1Htz1KlS2uC25FSwUdbThKURRFc/Pm2vvkH/1J3s77miCMr20p0c2m/eZ6+TPZVu5xWfihctR58xztx1ykXqEYf1QWJzZTw9ISvOeNuMNQBgJO04jVJweqfBMHLgGNPUWQKfBqlHNGZHjpXPRUBoLC0dUh4iNwbUXb9BZ/xAER+9h4JmVRS8Z4vVvqdF8ZNv2UlVIxoXq+VrrZVlIv8lL8Aq8X+TDIaymYa+hCCr9fBVBkZVCZa2cJEoCaLnryJ+f7IAJuygrg5EBDGVgnJ0J3JmTp3pgJ3nJg3DwrmUlx+jRX1HAVBgEqNVUlezy1UZzuY/LawWYMhUMEek93n7IySFNs3XHhhAuFatLY2Ui/WvMrl8GeHxbLsDZ8Pz3ez0bFE5oqpF+iy4347f4f0dFPZPz60u+J53xtiyw1XDxP282bgaF9GRiTkyJUNJiq39e6ivph79vydvK59Ox6qVRcPLeg/2Rnk2QF3TkgOy0d3bTeVynowPvydtyp9K6m5nxhpp+OJ0ZKrlS5cb2rLxb+KzYg+23VPsqm3iX02aFaQTIwLmWir+skQ+SsREkzckuVKKci8BO/w5RvhTuu8qZTRVuM6CSC7YeHT4YbiqwMBrBsOGKuLt3NGZVBsb568t2UFcDRYLiKPfqJgPbozm4572eEt64PwBAKh/o0ZyqYDpJSiGzwMTFsqigrdGsdbF47gYxlIL19Wf5sWf3QOCbQ4fPbk35L8dHx9HHJx/TvXf/Wv/f6wdfF7Rljzgj8Fx/+mOjB2USPn0P0lwVE2/4jy3RooX3jVvkzS79HlDGSNhfXiWsEurZM+1WMykrDMV0ZO2eGJACvakqNC0CaDn4g7paPOI1W7ZWE5srFmnIRCFlBSaa7U1xHTtO6iHhMQD/Ul2hx91FUmX+y3rHEr9UvsMJnjXUpfZseMXCQSdIy/fVBVYkyk3GCsQbogAIaSsT/w51Lm7R1wSdYTRp9An2kGYphSvaZZRNCKLIy0NHdRVSiGcFGLdHJiqm+eDdlZbTWvoxIadvB486HTdV30Jj/4tMkp7cuy9eDoWWA8q0MMkUwf0ZfCWi4nw42pINiKB7Q3kQFmZKsHHd6TEQEYWLWRLp1gSQQf9z4R3py55P08r6XaWvlVpGvcvHEiwP7hSAlb94myw8c3vjfbxE9NIfo/04haq4UXYa07A7x7dc2S2Jx9vR80ZprGsnZMuHV4Fu5bH6hXpbpp+iCQMFInZpPTx3NFC/zpIk5vkvH7kgbIVUO+E+0UEouqaCbyahM6dj/rrwtXEQv7m4TJBq+DZ/Gb3fkTnSZ18a5MpuLasWIAq95Mpq5tmv86fTuzr7APdNwM9lyKQh+Gb9gI/P4Zbqn59TJkaGqAIqsDHSABEAST0gXRIAPSlNkxU1Z4c4cNr/aCq1OTXnTdCOl11EA/ULhJLnRTbaqfXlwgFM6R8w138EmxjD0mWwdLV1GMK6edjVdNfUq6qVeQVju+uwu8fh1M64TAXIBAfI/yANKbLcfIDrt53KBR6w+CMyoJURfe5UoLkn4PP63TSbkXhRICYgxbKoLWRmdkywWcnCGf6896vqzO14SN+0Tz6OnPpNE42snaIqFWURH93UEaWFnyybniQySY7WteuiZC/ZJstIz+Qv0/AZZeroiEDUHyGGyIsPdxuQki3IOFGUQM6+5Lt0dosX7k9osEdMAVePkQMowGSP71CFYjDRlBZtYj8SM0ViuXaOjqGf0SfprNGXsDREUWRno4JkZIxdQbWuXrlpwi14gygrXRU1lEFhVVvKm0U5tYeJIaL/dQJqyotqXBxHwmTKBLZhrMIX76ARyN9l2NIkFAIDxsqHNoS62CATUp58s/gn9fMnPKS8pT5hvvzrtq3TT3JsC/2U8mHDiGUSpw4iW/Yjoh7uJrn6Z6JvvEX3jXfk4Eb2zo0x4xlCqO8WKlyFvmrwt3ao/9I2TJJl4+rOjfUZbqAy7ZFnr+fYTqbG9S/hboOYEDPbKaFlUSfEx9IWZspvov5s00z8D5alDq8XdjfGLxfyytMRYOt9s9xEDAxcBLYkWnxeXzNgD47UENPF0elXzBF04e4TviH0/HUHzR2dRfEw0lda3+Q6HO/KxvB0+iz6vlL5AhP3Nj5BOIECRlYEOlu7GLNVLQCivYP6GVWUFk41r7TSxYoBhrbZryptOO0tl37/XoVwe4vYBDoZTKbaDAFg4kCyakkddyfm0XcuCmGVmsqshGA5dbDARAiVOjoqIQGAB/MrUr9D7X36f1l+9nn68+McUyyUyKxuesSe7zg6bdCbRqEVSzdLwzFpWGkb598R5AlQaY5YIPDbT8oSi1tzRTb9/R8vd2fOWUFTb00bTr7fK69IdX5hiLlvFHSPmuE4yJqIvLZTlp1c2l7ga9jH7qKuVerPH032fy+f6ysJRguAEBE7s1cpARs/Le7vL+3c0QvXQFJ3W0cv1ElBABmYPZSC8blbZvSo6RsI67lT631b5/549Y3hgRMlhRM4riTDsLWukJz49rPf1R2wYHDPi8afpg7ZO9Bd97UVZwYWfd6oH7FRXhFlNRjjXR2fo05Z9dn24xe0by0CVqgw08ME+q4K5tKe8SXRnYCc3Kc+EsmIoAwF9paChRVZsA2fdDJ/t95q4/kiN6MS5YlGAZRHG6BP7rgna5wfSddeF08X959YX0UufHyPaLI3DT7ecQFjXz5s1nE6fakFVAUbM7afmILoew/nQTozrvI5tL4ibA8PPo83F9ZQQG003LNNMulbKQFA4NDPxorFZ4hqG+IV+3U94bRg9EZtEL9ROptbObqF0c/pt4MqKJBzAKZrvxGu2TE+P1iJO1D1uOb21XZb5LpwToJrkMBRZ8QIMj7r7f7vov5s8uNQjBTjhW2ulX6Vgnu7gNpWyaJy8jN+hgVuJeRCirQvTyHm6NwGkKDPZj/pj6AYC0HIIVAyBTI1BD8x7AUYtFqZDAJHeplpSDWUggAl2yRDzrdgCbFS0kgGC+XzhmXVSHT1rWj4N9zZzzIynArH7UNWK1+sPLxmfQzecKknBYy/9j+jwaurujaLHm08SwZH3XeqbSJlSVkAGtI0ZCNJNy2Vg3D8+OkRHq5tl6zbC74joJ/vle3H9KeP1LJ+AIMzEeS5kEErU5QsKdVLmgp3/FTfdk86mR9dKVeWbJ48LfNJx+kiXQDpg+WT5OjAyoLm9y3MQXFO5WEc+65kulHV4ZSKlZZmhyIoX8Pj50khOxty3Qg8uKqrrEDVJJEqy89wvknP7DKyaL2TiMAfIyvHN8rZgnm4ANrVjcOsGKtAukMfr1Q56QAOSN5OV0X3lS9TXTUFPsZXHKKcvK2UliEGSWFiNk9jdgEWON25fPUFLaLWKcafKW203z/jJF6YKwvLNWJmt8nbPYho5dgo9e/0J5oPnvBEHTpXl2Tdabgq6izDs7/qnNlLD2icFidoXO5k+b8ym8bkp9N3TNYXECkZoBKusT9G5YtEoUVXD5Oidx+v7zoedr4i7q2JOEvN4sDG7xIqBOUd7veh80q6b8IHB4Iu/02O7Nk/SnnQWPfu5rCTAoxNJJSAgsl5NBIGzHsrNjvUOB/b8T95OPY9WayUgGKIwd8MUsEONkWoFQoSMJlt7yYqmrIyYq/f7mzJu6cqKLAMVaDvo0ro23852hchfILGTi4mn3pHz9aAsDLczBQ6Ga9dUOo2s4CKvYGGSsjF11QsQAtfU3kVjte6doDDtgr6wOZQgNMCP8tOlKXR5nCSyky/+Cb3w7RP0jWNQYD8Oe/w0deX+y+eIYMFD5XXU9PHfxOOPti6n9MRY+sc1CykxLkCvihFcVkMqLb+M3BS6YLb0lcCfI65j8AzVFVFPbBLduV2WXn541mRrz52SqynmvbpfBn8nG4Q5edgF8OkgEmbUWbpXJmhC6gAUWfECljnhj+iKxHj32iMypwJR5ZPP1QdtLTNbAgJA8Tn3AFkKTpAV1E7xWqOiqXfkAn3GhqnW6jgt2lrbIfBngnou6r4KAxS8YBTMp4O13SIqH0PaFo41q6y4loGUZyUIaNkjlDnK5489u16WgK5eMsaaydWI8adJ3xHKT2zuZbz/a4rq6RBq8eQFpwdeBvH6nMtdjaQaUEKEcnNj/i4qiKqhyt50OjLiPHrl5pPMpcaaKT8Jz14fbj1zkujQgYcEJSja8E/x+Mrok6myPUZko3xpoe/PwyvwfuW6zmACLp0vVRooKy7jVOCVQXt1TDw9XDxOZMqAjE7xNZ8rTFBkxQtghEL9HB8eangRByRMAmNPphpKo080v4rpSGgjE+eBYRBptNZR7FJt6QhCdgCPAmiMESQDpjW/Qxbd4vYB7DS4fVntogcw9q+UtxPPoE+1DgWYD03vJN3KQOxZGWpZK7aA53VlSC+FJ2w/Vk87ShrEAnuZ5rkICnGJRDO04LpPH+x7fO87RNtxXYsiOvs3ZCu49ASVQ7vWMSbkJNNtSVJdSDjhevrPd0/zPQ0+0DJQObKw+hR6hNr95Fzpifn72+upc7v0qzzcuEwEXz50xTzz4wQ8YRjPYNI6q8QmNE3ktfT0Ev3zE4OhePMz4qZx7Dn01CY5fuCWM7X/P8KgyIoX4GDh8fNlkeZbgXS6hce1Xy3c2109vaIVOOCTzE1ZSU+ME1IvwO2kQQEzRYAxJ+uECjtov+PO3Q22WtlHLwVFcnlOwTu6OvQcC5CVD7UI9YDMfO7dQFrycm1LpyhVKAQAXrg5pt0DntOC0c6ZOdy+6PWTbpWq8L53JEk5+hnRf2+Q3zvxZuFvsxWYmyN+Z69GiAzY8RJFQaWOT6P0U2+27zmzxhGlDifqbu+nIH39pLGi1HNl7AcUR120tWc8NefOoudvOEEfe2IZuays9JEVgA3MT689SgcqGuU4g+0visf+X9UisYYg3XfxuMgYXOgORVZ8gGulZZG2MB54T5ZWULuf9kV6XeuLv2iu1mNvhazACa9hljZaPGiyAoLBC9PYk4UbHTjFbCoiKytAp/QjjGCTrfInDExgUFtHozB3N+XMok8PVOsdJqbhVgYCweZF9Iiv4CuF/mjRZtUk53g11nK8/pWLLZYmvMXRL/ymvP/cV4ie+AJRe71sbT79F858UnOvlrebntI3P9RcTfTuT+X9k39AlBKkH8e9JMPlp8Or3b4VRd87KZ9uS5UqY9yJN9K7t5xKk/JtKL/kT+/Xqs1doiAjICXfeXoT1W9+RXSC1sbm0r/Kx4vogN9ePJMiFYqs+AAvjOWRpKzgJPvkAXl/wbV0sL5HTA/FecHGrWDKQMCskbJEsyNYsoL0RpgpY+KpY9RJupESY+UDJita1gorK4qsDFBoLZo09Xz6cF8VdXT3iJkrAfkDDKFwDLS3Opa+PJihGeu9kZU3t5eKsDaorabzm8zinHuI5lyl/SOKaM6VRFe9KMtETmDW5fKagjTtTU9KL9x/rpWq8rBpREu/b/9zMlnRBjK6YP3fKaatVqTdTj/nm/Z134xcIN9PbGibXLNV7r1klmgegbJy5H/3i8eeajuVoqNj6C9XzdOvr5EIRVbMtC9HkrKCkelo+4yJF3Lpvz49Ih4+Y2qetQPNrQwEzNaUFb/zJPwBEi8w9mT6tLhdBH+hJQ/D6kzP9XDv/GCyEkmfiYL5EhA6QICZl9HrWqT42TPyAzNSupWBgPG5PCpCKSsBoaXGNcbADRwQdun8QvvMrozYBKJLHiG64zDRHYeILvk/okST1wYrQJfMaT+T99/6kRzUiFBNXGMue1S+Hrsx4XSiqBgZ38BTxtkr9MlD8v7ynxBFB9F15A60oPOIAcx9MgBNCs9cv4SuziuiOdEHqa03jlakfJGe/MZiWj4lgIGJYYAiKz4QNuMekmm9XVjelpNPQVTqY4fJtEfDfA07yAoyUGCmq2hsD24CMy9Mk87RL3rnzhweWDeB2y56RIZSVgYskOeAAMLU4VSdu0jPfLh0XoCmTbcyEI+YAA4pZcViGai/T6G+tVM3QCNB1jHguT08vyM44Uai6RfJgYHNFTJE7eoXRQOAI0jLJ5pyrry/UXb9UHcX0Ws3y3Jo4WKiGZfa/7yFC+Xtsb7gPcaE3BT6bY7cSLbMuIJe//HFERcA5wmKrPgAeuKBI0g3DAVg8np4MdFvcokeO5No6wtE3VqLLi7yz18tWw2zxhKd+iN6/NPDoo0XA75OtJp9kNqfrKArg0Pb1mmlm4BRc0ieKFHR1Db5AlqxS7ZWnxfoQDDeaWnKSkGmpnYpz8rAw8bH5e38a+iVrWWido7I84DbJN26gbjDAjiklBXzQBlE67TzVAZatadCTAlGiQ7dJIMCUDC+9KQc0HjlC0Tf3SDmqjmKRZo3Z+MTMtPklRtkCzVKUl/8i1SQ7cboE/v8je7Yv4Ki4KGJiafss24PrvMohLAw9WrogLtijla1iHKI7TKoEWhte+7KvtwDyHf4ev9uOdsCpZ/WGimBX/EsVbbH0mMfHxI/+v0zJll/bXCrA41S+WAsGZ8t5oDAZxLweHRgm3SZ07hl9G5RlNilwQNkOvjLi7LCahc6tDAMLNJSFhW8oHiDlNyjYqhr3jX0xN/lNNqrllg4tuK9e1YOVTWJuIGBcgEOK3A9AaLj+s4zAzBhmdXQQQVcKzGgMVRArsyU84n2vkn0vObRQWnokr/7HXFgGZPPlc+BDXD1QaIcOVpAdAC9q5XClnxHbnwHCNSV3gfQQobjGuPJq+2cQuwJaCEDUUkrIPrOJ0Rn/FJGYCM4CQc5LizZE4i+8Q5R/gx66P19wvg2pzAjuIsJ5ytADtbC1wD05AMf7q0MPBQP3gTsIoC5V9Oz62Tr41cWjQp8EcHcI57crOXfIKcFeQFDbcrugAV8Tx/eK+/PuZJePxwlcnLQwWMpUtxYBtJKpmNyUigxLloMphNzXhQC6wRy2+zgnOcS0FnTLQ4QVJDAe3vpP4jmflX6ZrD5vPZ1oulfdO4dSsnpy5bZ/lLf4+/dLUPgUP4/9fYB9QkpZcUHUA4pyEgSF1ZcAHnqryPYoXVJLP6WrJ/i64SbpYscZqzscZKhx8QK4+szGgH4ybnTglN8YMbCThX1UxAjbbT5wrHZYjHB+HQoLEsnBFDTxJyLpjKh2mxJO5XWHd4oZhZ92Uoqo66sSLICvwu6R/aUNYpZSFyqU4hwrwqO4+g4al96K/3pcZms+a1TxlmLFOcBnMjMaKsXfgeQ4KnD02lLcR3tKm3Qy0IK1tqWdxxvEJs0zOSZUeB9ZpBCAKXLi/9KRPgKEeZeJQczrnuEaN5XZSfeWu35UX7yMQsqEqGUFT/AACjgcJWDJltIc0fXyPtTL+x7HC18U88jWnKDGDIFotLR1UN3/neb2KxeNr/QuleFAaLD6ophUicu/mdOk+7wt7dLOdgUYB5b/Xt5f/G36KEPZUz3xfNGWutWcvOsACArAMiKQpgA9ax8p0spxiMay4jeuE3eP+n79NhOmT6MoZSWTeGx8UQJGf1a7qcXyGOFJ3srmO0E6l+aXXNQvq8njJdEUGEAYsalctMLv+P/m0G04ufy8VPv6DP9DiAosuIHvDA6mt9wfItMOUT7oKZseMMjHx6kfeVNIpb55+dPs+f5maxw9LaGC+fI3JZXt5RQS0eXeRNlzUGxW/s4+zJatbdSqCo8jj1guJWBAFZTFFkJExDj/Zf5RI8sJfrDJElGGlw9TwK4SD77Fdl1kTed9k7+Nj30nvSq3H7OlOCGxPEC22IgK9oIBygrCsEpK+sOSSJje7aKQugQE0v05X8TDYMvppcoNono7HuITtNC8AYYVBnID6aNCMFurXy7vB05v1/t2Ig9ZQ308Cp5sf/lhdMpy67oay9k5aQJuUJZOlrdQq9uPu7fDAllBoZgXAeX/oh+/D85g+K6pWOty/JMVgw7eKWshHnUw0vflP4qGPi6WmVL5pZniU74DtGSG4mSMokOvE/07p0ymCo5h5ov+Rd97/k9IgQOmUCWvCruYYYIHDQoKxg3AWw7Vu+8IX4woLVO3uLzMgDv3dZjdeanoytELrLHEd24RnZnYqSCkzk2DkMpK37AF8CdTpIVuLWBXO8DpGB4+9F/tolWQhjevqipHraAJ666kRX4Q76mjQr/66oD1NbpJf9FvMB2ov9+W5gee0edSD84MF8Et4FY3HJWEIOx3DwrwHhNWVGZGmEAvCcg1yCRP9xLdO3/ZFYESMsn/4/oT5OJfptH9PyVkqhkjqbOr71ON75dLxRB+L5+d9ns4IkEh5ixOqCVgTBzCj4rpbqZAHxqxpA9DUU1LWLgKLKW4ANSGATt2rmTBjRRARRZ8QOcrCjZVjW1U4VTsftMVri9zAMe/fiwmNUDw9s9F8+0d9eYoZGVOukvMeKrJ4wR8czwGfxt1QHvu+3/3UJUtIZ6E9LonribaeWeKnGx+8uV8yg1IQgBT/esGNtU5cUVZKixTcuhUQhtXD6i0ZHRg46Db64guvJ51+Fz6DY46QfU9s3VdOOKNvpoXyUlxcXQ49ctFCnGQYNnuBjKQAmxMTRXS1/eeKQ2+OcY7OCcGre2ZZiUgWka+VNQiASoI9EPkuJj9BKGY+pKtUYCciZ6/HZFYxv95QNZ/vnFBdMpTxsDYBvYJ1Oxu2/Alwb4Cn5+gfTGPLzqgJ69oEOkMd5EtPVZ6o2KoXtTfkyP7YoWPpU/XzmPZo4M0nHOF1KDZwXlLxAoYG+ZH4Ongn3AscEhU1PP73scxBmGvRs+JLqzhOhHh4hu309Np/6Svv7cPnpvd7loN3/kq/P1UQ5Bg5UVDKIzABO9gQ1HNPNoKHHkU6K/nUj0h4kyobRRBiFGLDgB2E1ZQRkNmFs4sLpFFAY3FFkxgdnagrupyIHdGhJqWdFAjooH/Pn9/WKuzpxRmXTZ/CBr/Z4AAxbGtSPLpan/BRYDEjFxFdkmNz+7iX739h45SLChlHr+dQHR1ueoh2Lo9q4b6dHj4yklPob+dvV8+oIdYVIePCvA1BGSxOxWZsrQAccpjg+EiI1a4r1FMyWH6tu66KuPrROhglDWbJ89ktxfWQEWaePt1xysDm6uVaCoKyZ65ktySB7SoDc/TfS3JUS7XqOIhTYcVE8ENnjjjN1VCgqRgIggK3/7299o3LhxlJiYSAsWLKCPP/6YIglIcwXWWo2e92dK7emS0ctp/aPoMZfoufUy1fbOc6c6YxqMS+ojSuU7PP7Iby6aSV9eWCjSQf9v9UH6xf1/oKo/LaHo4s+osTeJru+4hV7uXEqLx2bTG98/hc6eYVPqpU5WGjwan3crZSV0KNkkb9EO6WMybl1LhyAqKCdkJcfRs9cvoRPs7ipJ6e9ZAU4YlyNUHJQt4ZEJGT7+E1Fns/TvXP0y0fDZshvqxWuI/vcDl8DFiAFvANyUFX7fJucPkoh9hUGBsJOVF154gW655Rb62c9+Rps3b6ZTTjmFzj33XCoq6sv8CDeWjJMXWlx8Wzt8mEytACZEALHHHmZEPPXZUUEQlk7Isf+Cb0T+DHlbvsvjt2Njoun+y+fQP6+YQo9nPkH/jP8T5UbV0+6e0XQl3UeJMy8Qu+cXvn2C3q1jCzzkrISsS0vBFVWyFIk2ZG+ACfvaJzYIfxXa65+74QT7Sj8ey0BV/cq2nD3EgxJDkjnDKaFn/IJo0plE139AdPKtqJERff4von8sJ9q/sl+ZNSLKQAbPCohmZWO7uD9JkRWFCELYycoDDzxA3/zmN+lb3/oWTZs2jR588EEaNWoUPfLIIxQpQPsuPBLoxNl41OZaOA8QRFuZhwv/8+slabMcoBUoWSnb5v1njnxKZ6y6hE5vW0m9FEWNC26k7Fs+pv/ddR399ar5tGzyMPuVH2POimEa9UwOACttoPYumwmkgh9vledyJcouv3xtB20trqPM5DhBVBzrJmGDrRtZAdAaDfCkb8dxfLPsrEFpaszJ8rGYOKIz7yL62ivy3K7aS/TM5XJAKUZReHjdYTPYxvdtLvZXNOkzuIIyxisoDCay0tHRQZ9//jmdffbZLo/j32vWaImubmhvb6eGhgaXL6eBBfjUyXInt1KbHmwb2CPigaxg6mlDW5dI+zxduwA7hkJtsNeRT/rv/vDvdX8nevJCovoioswxFPX1tyjtwt9Rfnams3kWerpmb18uhJa1gnEASPR1tK08kgDCtukpoq3PuxiOQwaE/fkwgr+7s4xe3HhMdM+hC8zRMgJmaAEY68CTyTVgsjcM3lB39peHwIB99BN5i+m97urohNOIblpLdOJ3iWISiEo2Er1xC9EfJlD7n0+g0ue/Tzvf+zet37lXkDyY6XtgDguTwXaf9n5NylfjChQiC2ElK1VVVdTd3U35+a4LNf5dVuY54v2+++6jjIwM/QsqTChwjubBWLGz3F7jXpMmVaMN1A2vbTkubi+cWyAyTxzF6BOIYhPl9OXSra75Ka99l+jtO4h6u4lmfZnoxk+dH6vOwA6VZ1gYzJQgSPNHy86PTUeHQJsqul4ePY3o9e8RvfJtoj/P9Tz+3SngmPehrKA8evf/ZAnxpuUT6ZRJ/Y9nWwFyHxNP1NtD1CDPE0ZOaoJu5n1xozbF3OkuIIBVFU+E+5x7qOv7W2nnzB/RkTj5/iXU7KYRe56kGZ98lxb/ZzElPbqUVvz+Kvrmr35Pl/31I/rNG7tEy3fAg0QDNtj2kcpDlfKxiWq2kkKEIexlIMB9Z+4rffLOO++k+vp6/au4OAQXI6S5TswVXS5lDW1ikKD9ZCW/Xwlo1V75PVsD4HyZbCefI+9j984dDk+cR7TladkthKhmTA/1ME7eUSCzw1gy07BAS9ccEpka7/1SkgUcJ1njpLEUUfa73wjN8+P5MDQQyB7f79vPrS+i0vo2UT747umelRdbAQVDT17ufw1A9xrw/PpiZ7N4QOKglgBjTvT6Y0eqmunipw7Q+Rvn0fLG39D8tv+jW3tvo1fjzqPD0TJ4cXJ0CX019n16IuY+erjiWqLPHqbrH/+ETrjvAzGmoMHOvwOv24OygrRq8aeoAaEKEYawFiVzc3MpJiamn4pSUVHRT21hJCQkiK9QA3kj584aQS99foye31AsphLbWgZKcS3zoPOovatHlIB45onjWHS9bLWEIRAqys5XidrqiBIzib70BNGE0yksgJkSC7VbnX+x1qaK9ljsPmECHpQAoUXpB8CsjxFzZI7HjpeI/nMd0VdfIhq/3NnXgLhuIL1QElsDOrt76NGP5fdvOm1CcDN/AkHmaPm6DAM4GadNyaMJw1LoYGWzMKnffNpEh0lclNcEapSivvKPtSJZNz0xlr5+0jj64twCkcSsb8owVPDoGuqGWrbjFRrRXkO/iHuGrot7j25r/jb9v/fa6d9rj9C9l8yyp9Ous0WqUm6ty0U1UlkZnS0HuCooRArCenWPj48XrcorV650eRz/Xro0RGWGAMC7tTe3ldq3y9GVFVeysnqfVBGWTXHAtOoN404hmv0VSVRAWEBUkEr67dXhIyoubaquZGVOYYZI9K1v7aStWpDVoAQIJNrbRy4gGr1Etg1f8neiGZcQ9XTK9tgqL+nCdqGhRN6ymmHA6r2VQlVB98/lC/p/3zHoycv9lRWUTVnhwfBP7nCxHVwaw2txI3EAjs1vPrlREJWZI9Np5W3L6NazJosUZpfzGqWiaRdQzIUPUsyP9hFd+Gei9JE0isrpxYTf0k2Zn1FVUwfd8O/PhcoSdCmazbVQTBGboCnaiNoHxiiyohBhCPtW9LbbbqPHHnuMHn/8cdq9ezfdeuutom35O9/5DkUa4JGYlJdKrZ3dup8kaGAirQey8sl+uTCf6nTt3x0X/Y3o/D8Rzb+W6NJHib65UrZVhxMcAOaWVgol5eRJksis1kpmg3YeDzDti64TVS/+P2mMxs7+ua/IXA+nwGmsaf0VT/aFYDghIu9DhkxZPhGmbw+4aM5IQWib2rvoD+/ucZas5HpWbv747l5BAAqzkuipbyyhfDPp07EJRAuuJbrpM+ERi6IeuqPtL/S3yZvFt//fe/vojyv2Bve6jSUgjTSB0LV19giDdEFmf+KloDCkycpXvvIV0a7861//mubOnUsfffQRvfXWWzRmjHYhiiBgJ8STh59ccyT43Q26GDjUyuBZqW/p1FsIudQRMmARXPQtoi/+mWj2l6XBNdzwoqwAp2tGyje3lzqfWAr14j9fJ0Jq76Z/u7RSOwb8Tcc2yPvupmYoLFc8K0szWDRfudG5HA903QCpriUI+EHYW3X5whCqKsYBnB7KQKyuYDo5gC4lfp2OZM946JBC+efpdTKd+g+XzxHdawEBxnJ4xE76gfjnecV/or8vld06f111kF7drKldNgXCsaoCoqJmAilEGsJOVoCbbrqJjhw5ItqS0cp86qmnUqQCMjfyBw5UNNHHmvphGWwYjYohSuojJZuKa/X2XHQ2DHl4CQADzp6RLxJL4U1wtIW5oZToiS/IQX5HPiZ6/btEL31dBoI5CYQG4jhBxD1SUd0BRe7KZ6kXnTH73qbjK//iezq2zeVKKIDIH8KxGvIJvWz0ZcLgAQvGZOsZRXe8tI1qmztCNtfr/1YfEtzxnBn5elBdwIDqcebdRHOuEh6Tc/bfTT88RX4GP391h0i4DqoTyJCxwmRF+VUUIhERQVYGEtIS4+hL2g7yiU8PB/fLWFVBvdqQz7BZ6zaaN9qB5M+BCFZW3LqB+PM4c7pUpYLaafrDh/fK58+bQbT8p5I8wEvy7p3kKI5pnSYjZnuNuH+vdjg9FP01cT/n01/Tl3/zuJjfZCtpadSUlTRXZeW93ZLEOJ4D5Al5csCmaLd3KxEacccXpgizLcocWOBtVeBqDnvskKpuaqfXtsjj8cblQZp7QVjO/6MkRI3H6ebol0QnHMpb9761O8j02j5lpaS2Vdyio0tBIdKgyIoFXLd0rLh+rNpbSQcrg5g/wq2g6LYxYLM2op1zRIY89KF1nhekS+bK4Y6vbT0uOlNsB8yIHKeORWP5j4m+rLV3b3iMaNt/nPuISrfI25ELPX77PxuL6VtPbaQHG0+n1b3zKCGqk35B/6C/r95Pl/xtDVU1tdscXthHVrDof7y/MnxkBS30aOM2vk8egO6k//eVuRQTHSXKha9vtclvxkQJSHcdMPrGtlLq6uml2YUZNHeUDZsOKCDn/VHcjd7wGP3h9FThLXlre5m1KAUPZaDShjZxO0KRFYUIhCIrFjAmJ4XOmCp38//6VJvtYwWcyJrkejHbXSovJLO0ac9DHuzn4d29G06dPIyGpSWInbMjEet735KtnlgYR2tZGlPPIzr1R/L+W7cTNfVXfWxBtZYamzup37d2lNTTT1/ZLu5fvWQMLfn+k9Qbl0KLovfR15M/FROpMVCwub3LRmUl36VsUNHYTnExUXrmTcjB05+Pek68ZmA+0fe07qBfvraTyurlwhwUEJiISeUeFKdXNJXvYo1I2wKk4U48U3SGjd//hN55hW6ngIHj2a0MxO/JiAwTJmAFhRBDkRWL+MbJskMGuSswxFoCWoPdlBUsuNgNQ7lRU0/JtV0WCwPX2g2AGfDaE6UhG3kfthtt92jBa7O+pHdOCCz7iZxAjM9x5S/I2Yh719RY/I13vb5T+EXOmp4vpmIn5oyhqNNkWeqnif+lwlSiPWWN9DON0NhtBF9/uEYn1SHLVvHUbg/se8f1cRwnIDCHP9YVTGStQOlAO/Gd/90W/HHCBA4x+kl9ZA2R+Rh6Clwwp/8k9aAghiNCfn2Gblwsn/O93eWBK7ydGllDarUGtJ8DiqwoRCIUWbGIE8fn0NThaaKN+YWNRcEpKxwnj3WxTJpEx+WkiAmyCtr7E6+l5tZ79qVctWQMJcZF046SBhESZxuwoBWvl/fdg9fQOXXBgzIQbOtzRMc+t/fjQrcRT+XOdiUrH+6rpI1HaykpLoZ+fdGMvnEMi79NlDGaYlvK6bl5u0Tp49Utx+n93UHMtBJeoV5pBGezsyE5eFGoO9aMmHKe9A+V7yAqWiuNwO/dTfSnaURPnEv05AXy/ur7KS6K6IEvz6H4mGhRwv1wb6V9Ph4Dif14X5VO4vLSbFYpxpwkjdbd7TSu9G29/IZNU0Do0siKIRumrF56VkZkKM+KQuRBkZUg2pi5y+DJNUetze9gz4qhDLRHKwFNC1Vq7UAAFgJuU/WSqYG20C8tGGVdFvcGRLnDlxAdKwPy3FG4kJqmXC7uHnnpp7SpqNbe5+7ukDNw3MLYuPx45eLRrotLbDzRMlmeGrXr7/SdpXJn/+s3dln383AXFrxDBiM4qwcLx4SRrMCcPucKef+pi4gemEb0yQNE7fXSX4O27s5molX3EL36HTHz5usnSVX0t28G8Z4Y/SppIzwHOk4e5sy5MO+r8v7mp/VS0CubSqg7kAGIXa7KCszYtZpCPFyVgRQiEIqsBNK6+uHviD78vb6jQmR2VnIcldS10pqD1baUgSDbA1OGh3j+TqSDjZTVWuy7B9xw6nihJKClfNuxvgnNQYFVFZR74vtHkD+99ihduP0k6uyNobF1a+neRx6nH764ldq7uu3zq+Bvj+5T2YprWsSCiHXr2qUe8ojmXCkTVZsr6fv5Oyg3NV7MfAl4983gsDl9ArZc3A5opQcks4YVZ/2aKH+WXIBF0u9Coq88Q3TbbqJbdxBd/Igkm9teIPr0Qbr59IkibRft7q8HE+7ooUMKpaU1ByW5O0ULLLQdMy+Xf0/ZNjozv1GkOGNm2YYjmn/GDDpbXcgK+1WS42PESAAFhUiDIitmUHuU6B/LiD68T7aw/t8pIuIbdfrzZ8td1RvbjttSBjpUJReAiXlqRLsLhmlzVyq9J5GOyk6mi+bKoY9/XWVT/PxxmRoqkmLd8M6OMtEKe7gnjz5KOVs8dkPsm/TypmN06wtbqCeQna6veTxubbF4XmDx2Gxh9u4HBPkt/Lq4m7DlX3rr7D8+OmTtNTFZMfgy9pY1ip08FK3hZlJZnQRI1A0fyrTl728muv59EV0vVCAwurlX6Z00tOpeSm88TN86Rb6nf//ooPXPyYOyUlzTKmLxYTqeY0cXkCek5MhyEPxaB1bQGVopKKBSn14Gkp/dca0EBFUlZOM9FBQCgCIrZvDWj2TrZs4k+YWIfMxj6emhC2YX6AtIwLtpD2Wgw1XSQIqQLQUDhk31S1aAm5ZPEOvTuzvLRYJo0KjUYs3zZBIqA6ZqNq6ilf306+4S98+K2UTjY6pES+m/1gTRKQY0aATYrQT01g65SDJR9oh510gvR8lGumpUDaUlxopja7XWahwQuOPFQFY4gG9GQXpkLG7wD41a7HEitMCC64gmniXLau/fTVefMFqEO+4rb7KebOtBWfm8SL5XMwocNh3DqwPsfUvPGXpfy7wJTFmRJUSenZRvt8dGQcEmKLLiD6XbiPa/Kwd+Xfk80VdfJkpIJzq+iWjXK7RobDblpydQQ1sXfaQZ66yWgZCuWafVjcd62jEPZXB66/EtRN3eW3En5qXROdOH2+ddqdonb90m6j6x5jBVN3cIBezO86ZSVN5UMewxinrp4UkyyO337+yh43XaohBUhkcfKUGn2OYiedx8wdf03dRhRNMuFHeTdr9MX14o/TzPrSsKQlnpKwPtKpVEe3rBAPFWgVCdc480Q+95g9Jrd+mjM1DKC2oEgYGsbDoaooykKV+Qt0Vr6ZQxiULJOVTVTEXVLebbrg3KCpOV3DSVmK0QmVBkxR82PCpvMeEWw8qyxhCd+F352Oo/UEwU0bkz5WIScMeFW84KLjbcOqg6gTwoKyCJMEuW+27FRYsqh8SZvnh7233y3BkDWWnp6KInNIPrrWdO7hvet0QO35xW8SadODad2rt66IGVGtkJRllJk+od8JnmjUInWp6/8svMy+Tt7v/RlzUjJjpg6lo6LJKVPgVwf7ksV07JH0DeqmFTiGZeKu+v+wddsUgSuI/2V4l2Y+sJ1H3eFPZKOZ4+jeGiGaPFhPS0ik0iRwZYe9ikd67L1bMC4g3Ay6OgEIlQZMVf6+iet+T9+df0PX7Cd6R8WrmbqGQTLZ8iXf8wdgaU3aAn2ErPiioB+TpSo4nGaTOjdv+v7/M5uIpo7f8R7X1bn9MzqzBDBMXBUwFPQnAG1175+XDkPxGt2FkusjpGZSfRF2Ya1I0JZxCl5FFUSzXdM0tK8v/ddEwYYoMqMxiUFTZynzTRhHlzwulEccmig2pK70HRYdbR3UNva56XYDwrfKyOHzbAvFUaoaQdL9P41E5BKnCcWDLatrDxWL4v8L6grBQyxWnsyfL2yCe0RGsfX3eoxlLOSpWmrCBcUUEhEqHIir9OEEz6xWKlGdoE8G9NYqctz9CScTkiuwFdQayOWCkDHdH+37HKr+JbKdjwT9mZ9fBCon9fTPTOj4meu0KaoLUOmpuXy1yS/wQT2mcsARl8Gf/V0kkvnVcouo9cfBPaaxxf+pboBoF307J3RTdwGpUVWWpcamYwHrqXJp0l7+96nS7UAspW7CyzqABm6ZOWkVw7IL1VMErnz5TKws5X6NL5UnF6eVNJEMpKjp7oi9wlhBSGpIw7VrsmHf2UloyXr2FdoMqKlrOilBWFSIciK75wYKW8nXSO7LAwgrMddv+PkmKjaNG4LH0KremdDTvyNXmdJ6iqqadeMP0i6V0ByUNnFrplQPQmnysX0opdRE9fKobaLR6XLUolHV099Ko2UM5yN45hoi5KKJ9oJtVL5nmIUkfKLbD3Lbp+iezSeHFjceBDBTGPqL3BRVmpae6gI1pZa+FYk9km076ovZ636cxp0oj56cFqUcqyqqwcqZKvAS3RaJsdUADp5M9o56t04ewRYsYORhMENMG4o6Vvwde8PBw7MCkv1ZXEOoVRJ8jb0q20oDBV/GnHalvNlbTYs8JlIG2GVK6a8q4QoVBkxReQiGmM9DZi7ClyCBg6g8q20skTZSnoIy0QyvQgMUBLZ4UyA6ipp96O1hhpcEZnx+QvEF3w/4hu20V01fNEN62TdXwkvq74uehQYU/Cc+uLrEWr12u5JMgs0QB/A9QSECGPCtjI+fJ1dLbQydE7qCAjkRrbukQkuiVVBccGBvYR0VbNDzF+WIp5koBSEEyllbtpUnKzKF2BwKFkaZWscHv9+NwBVgJizLhY3h75mDJ76vW5Rqv2VATeIYWOK+3z2Vce4owkdD7Bx9XVRqkNB2iCVpLDzKhAc1bQbg3kpCrPikJkQpEVb4D/oeRz1x2MEUgK5fj1/SvpZM1DsP5Ijbnchg6NrMSl6Kmgx+vkjqhATT31jtQ8ogsfIrrqBaKF3+gbxIYBe5f9U4u+f1ZE3188b6SQ5LHj3W7mAu4pQRbg9FwYVLUFbZnmU+oHMdRJdmpEH1hJl8wfqSeMWisB9XlitmqJsQFN8UUGyQjZSRV1+CM6bYpUez49EARZqRzg7fUgkyPmEPX2CPX0NC2n5INAyEpLTd/7q5UIkT0DgMiGBLhu4O8Ajm+m2drg023H6gPKWQGR5+ncSllRiFQosuINZdvkCQ2J18PEWwH2Axz8gKaNSBOzabCLNuVb4YF8CXI3hLh+pFAChVlqNoclFC7sK8998gBlJseLIX/Am9tKg1BWpK8BF3UoK8DyyXKB83lc7F9JF82RfpOPD1QFVnrBjBs3srLFClkBmFQf+lD3unBXkZUEWz6+ofAMWCBzBTjwvj5fB+bl1o5uS34V41yvkA4g5REQx7cIYzmw3QxZMeSsNLV3ic41QJEVhUiFIiv+SkCjT3CdtGvEGM2NX7KJYns7xeAy46Li15MAoJREROWN7aIrAXkJw1TdOPiptHveFJ6T82eN0IPUAioF4WfrNGUFLaLaIo0dKNSa+WN8EAYcF+gWazxOk+ioXnox7Wfyshju0oLYZmrHmWmgZAkUrRVmcBzO+yuazHkbsKjxLlwzgh/WykADVlkBJp4pbw9+QFOGJYvSKxZs0wZV/nw0vwo8Sewnmjo8hNkzrKyUbRMTpQFTKqIhZ6VaKwGlxMeoyASFiIUiK74uZmfeLaO6vSFngsxY6G4XO5t5WhDUZjPD7DqaXJSVktq+iaf6BF0Fa1kawqfRS7T1edFWDsULMeicumpaTUCmC5AhSzkbtdkrUDb0bBVPQNCW1mYdtX8lnTHVQsKoG1lBYCB34AS8c4fiBNQcpCxq1BfTDYdrzbfXIxQxIU0QvsOVA7Rt2b0rCH6P1hqKqthJJ2qKk+n5Om5qE9rTsdlIS4gVIZEhAycrV+6lydqIDhwnfjvgDDkrXALKUZskhQiGIivegETSk2/pa1H2BGxRobwAxWt1ed6cstLoYq7lpFNlrrUBczSCufU5So6L0Us2PFMnoBIQyKjW3rleW9wXjc0yX3op+kzvwnl/T4X5OTRGT4TBvIkSIWLiAwK8JrlT5P1jG2i+FljGhl1TxylMpFFRImG5WSuVDOhyJcfzA0Vr9c90w5FaS2QSXThAYXZyaMcPYMMUFSM6x9I6q4ShG9hX0Wg6Z4XNtejuUlCIVCiyEiz4gndsg55aCUOn39o3KyuaQZQ7gZS51gZMPV+W15A+e3wznTNTkoWAZsC4+VWAzcVyIVs4xkTb8JgT5W3ROlo8NlMQDOxgd5U2WFoM9U4Tq36IUdogxuJ1+oA9Nuz6RJv2eqFCGAbeYWFzdPZNKMAbjaLP9FZwvCco2QVKJrntOeQELjZBEhagYjdN0o4PPl48oqdHqsFAXJJSVhQGBBRZCRYj5srb0m2ihAMJGHIwz07x61nRykC8Mxs5kHerkQKEoYlSkMwX4bZylIFY8jY/l6egz5OgGUsxvM8v8mfJTq/2eoqv2au3x5ovM/DwQLkY7tUWn8lWO01GLpC3pVt0BRDeBhyrPtHuSlZKtY41TOcd8BitEcqjn9H4nGQxQRq+lR3H6wPukNKVlXCcvyh9cikoP9VlHIJHMFEBYvs8K8pcqxDJUGQlWAyfJW/rjoqkT/YD7C3zcbFwUVZSXcpAhapt2T51RXwQb4kI8ekj0gNr2eVuHLRKo2mkoknkq2Qlx5mLJBdlBk3NKPpMhNQB6w/XWFNWtOPJsrIyXDNilm6jCbkpwkzZ0tEt/i5zZEU+b6nWsQZiPuABAocSSlMZRTUe1wkle5PMjcrIdCMryRRyDJsmbyv3mFNWuBPIzbOiykAKkQxFVoIFZGCtW4TKtusZCz4vFu5eAFUGcq41tXwHUVMlnTJZ5uCYnoyNsD8gNd/l84S51bQngXfuogunj6yY6koyzJ3Bz+vKilWykj9dLswtVRTTXKZ3FPktBfFxmsjKilauHAzKCrxIGJAJlG6jhRpZ+fxobQCjMjLCWwYyJizXHNKD4VgF9Aju7oqOFaS6ulkz2KohhgoRDEVW7IAWuoX2QV5MOHPBb86KpqyU1Ws71sxBsAhEAlJy5AwY4OgndOokHjZZaY4ssLKSIv+/vVbSSUctkbdF60QGRkJstJjBclDrpjGrrIjujtZOEQtvOdsECzNPji7dppeC/Jps3Uh1qXacDh8Myorbucs5Jaa6xtyGkIa1DISQO6D2CI3NkcrO8fo27yMeDBkrAEzT4tcosqIQwVBkxQ7kz5C3Fbv0xQxplj4XRUPrMsLCEMwE5Kmpp45MpYXEj3wULPych2GuDJTvkk4akLLBgV31RZTQUa8bsP2WgoxzZ5Jz9MRYzIwKytTKJcuy7TRDU1Z4no1/gy2TFTaCDxJSjVlTQOk2mjGij3j4bf01kBWcvzwIMCxloOxx8rb+GGUnyPZpwOu0b0PGClCr/a0IUVRQiFQosmIHeMdauY8m5smBYrgAcEug71C4FKpokBePpLiYwNtSFbyDJ2Uf+UQs8hxHbsqT0FTuWgYqs6CsYEBl5hh5v2y77onwW3oxzp2JT6Wj1ZKsjAl2km+e5m2o2qd7X/b5I9XuBltWAAehspKRHKcrIzv9GeQNZIUzktITY8Mz2BHqH8zc1EtR9cU0JlcSJq+k3JCxAtS3yOsU/FgKCpEKRVbsdONX7aVEw3h43o37nA0Un6aHfeWlJ4Q2o2GokJXKPcK3wu2pG/1laWDx1pWVYdTQ1ilkdWByXpr1MsNIqaxs85cwajTXRkXpiw5L/EGT6qq9In02NjqKGtu7dALij6yA1PSRlcGirMzqmwPVUqN3enFasNe5YZ0aEUjMCK+5FsA1g9WV2iM6qWWS6ytjxUVZSVLKikLkQpEV2wxuUXK31VShtw+yz8Ff6zLHnqsSkAO+FU74RJYGd3sc9VeGaerbfabk0X7tcxyenih231a7cDgOHb/Pq5/AQ4aHbcqKTlb2U3x0n//F93HaZ7Ctae4QGSRYG/PTBwlZgeeEPR+lW2lGgQnfChM47f8Pq7mWwX9DzWGd1B7xRlb42I5LFMdhq3YsZqYoZUUhcqHIih2AeTFLk/urkHUgd98HfKVIGlqXuQyUN1gWgEgCR80f36yXYWBwxcLrFayqQFpPSNXb0AMqAXlQVqBGoD20q6eXdvsKh3NrWz7Kyoom71sGdt/oAIEq0HhcP065xOXPs8KqCvI44P8ZNGB1pWKXrqzs9JW1wiUglMaiY6g43MqKm8l2TDYrK348K7FJwrgNxERH6V4XBYVIxCC64oQZHGdetU8f8HakqsWksqKRFWWudXAq7WbR7QBPkd/2VLeMFT091gpZYQNn1T6K6mzVW4Z9DpszzJ1B6cU2ZSUmjih7fD/fiillxUBWBk0JqN+5u19XVpA/41X9iqS2ZQYnLTeU6CnYXst7ejdQAtVqfpXMpDhVglaIaCiyYhd4Eag9qi8qXmVYF2UlzVAGGmSLQISRFXhReC7ONl8tu27mWm5Dt5RxkjZczhfq7RFx6Gzy3Xas3tREX5i0MYsHpRdbFkODGdxUgJjBs8KdQIOPrEySt1X7RQI1jLIIAPR6/rbWRU7bMiN9pIGsJOqZOB7N05yzEpekty0HXN5UUAgxFFmxC1wGqj2iKyvY2XicEYQLiKF1WS8DKWXFfsCzEhMvd8O1R2hWYaZ/smAw14pANu4EskJWwDK4C6dyj/78O3wpK4YyEKsqBRlJvic9B7ww79OVIkSze43dNygrx+sGWSeQ+3tSvV+oC0zivEbWe81YCWMZSJsMTvUl+ucDktvQKiMRPCsriVSndwIpc61CZEORFbtrxnVHRQsgdmdAkaesA1wssNPm1mVWVkI5Wn6oAIPeOAendItB2ajz3rJrSK+FsoFuCXAOLiEF0y02bYRcCA9WNlFnd49fg61tfhUP5cpRWUkUFxMl5uGwauLdYJtBZYNVWcmZ1KeotdXTJO1z3l/hn6w0t3fp/qewzvVK18pATWWUFNMr5hwZB6R6zlnpU1ZQBlJQiGQosmIXOE+j9ojYnY3V1JXDnmKvWVUB4kBWWFkZZItABJaCpo5IEws0CAjviL2WgVLy9BLJmOxkSoqPCY4gVO6jkZlJwsjY2d2rh72ZUVaC9qv0UxEOUmxMNI3KTvbur8J0XqOyoqcsDzJlBaMEUofL+1UHdFLq1SBvzFipC3PGijFrBbk82AQ1lfWVgjyR0C6jZ0UFwikMDCiyYncZCBey1lo9a8Vj1gEvAPGp1N7Tq+9uVBnI+cnYKKVw+cOrybWpUt6m5vWVgKxOOwaGccvwPkFkeXKy15EMhonLtmWsuJNqTJXuaqdx2nF6uNobqe41GGwH0VwgH+WxQMpAbK5l0hc2REcTpY/oVwriAamec1aSqK5VM9gqz4pChEORFbsQn6LPkYHJlpUVjyY9Q9typaaqxMdEqwuG4+MQdosbPZzNm2/FYLDVO4GsDhA0Kiu1hwVBMI5k8F0G6lNWRmvtqEEjJZcoDgtrr4hn149TTwogm2uj46gnOoHK6+WxOnxQkpU+QsllIKiiHkt1LmQlAsy17qWghmNCwQNYDfNssE2kumZtLpAiKwoRDkVW7ATvWuuO0jjNY+CxDOShbXlYmkqvdQzsGWkqE0SAw9m2l9T5bV3Wpx0Ho6ygIwiZHJDoqw/qk7n9k5VsOlpjs2cF5htDydI3WekrAVW3dFJH9yALhPOirMCTkxIfI/JwPCqjHslKmJUVIL1A3jYc131FHpUVJisw2GrKSoYy2CoMZbJyzz330NKlSyk5OZkyM+Vu1h1FRUV04YUXUkpKCuXm5tL3v/996ujwEdgVyTAGM3H7sicvgIdAOJAVBYeAIXyZo+V9tA9rZAXKSj+TLf6tGWx7kof1zQQKRlnBCm+Iuuff5XGIIMzXnXKBrItK00uEGGJoG/i9AKn2VQbiQLjEvrZllCrjYgbhHid7govnbKKvUpCHMlBEKCsgxUBTuZ614rsMlKh7VpSyohDpcPSqA9LxpS99iW688UaP3+/u7qbzzz+fmpub6ZNPPqHnn3+eXn75ZfrhD39IA7t9+ajuWSlv9DCq3eBZqVRR+6EBx+5X7BJ5KUhgbWzr6j/sDS3O3ZIsl3SlifZPGHJZgQha3ancR1OHy5RUmDMb2zo9qyrRsXS0URp6kf2RHB/rzHGqKTaY0NvlXvLwEAg3fLC1LffbaBwVhHXisFS9a8tXKFxEKStaLhCUQTbYcru557h9dANxKJxqXVYYwmTl7rvvpltvvZVmzdLirN2wYsUK2rVrFz399NM0b948OvPMM+lPf/oTPfroo9TQ4COOfAAoK9ipYIIyNur9uk46mvuVgQaltB5J4KyTil1CGZg+It2zyZbNtQkZtK9aEokJw1KDVxP0LpwDIoALc4Y8BrIZzbVaCci2TqB+5coikd8C4obupH4LmzEQrm4Qm2uNahMGjLbW0oS8FH00g3dlJTOyPCs6WelTVsoa2vpn6BiUFb11WXlWFCIcYdVzP/vsM5o5cyYVFGi1ViI655xzqL29nT7//HOP/w++ByJj/IoYGCKvISVzhwB2rd7KQOUNaohhaJUVabLVfSvuSba6udbgVwmmBMTI4qm4h8UNm2z7lYJc2pY1smJ3pwkrK3VHKTo6Sv/9/UpBOlkxRu1HwKLsBOIS+9qXa48Igsqx+97ISmtMamRkrDC08RDUWC5iEKKjSBCV6iYtV8XNs9Ibm6DIisKAQVjJSllZGeXna7sBDVlZWRQfHy++5wn33XcfZWRk6F+jRo2iiIEeeV0qbkZnJ3kOhvOgrKhAuNCVgSB3zfIWe28gK7pfJRhzrfs4hhpJVryabD0GwjmkrKDkYfj9/Uy2ehkoffDOBfKSQj3BUAbq52vSyEppuyydIF8lPTEuopQVDCbMSZU+OL7GuJOVjqgEYZoGVIKtwqAjK3fddZdQDXx9bdy40fTvw8+7AxcHT48Dd955J9XX1+tfxcXFFDFI03IO2utFxw+bIvuRFYNnpS9qfxAvApEAlGGiouVC01hGsw2x9z1GmbzZkLGimSuDMtcaJx4DLVXi8/evrGQbAuEcUlbEa2nSx0P061zzYLAdoXkhBns3H97z2OgoaunoFqUUlxKKttgXt8RHTgnISFZQSuzq0HObOCHbPW6/qTtWj01Ithp4qKAQIgTs2vvud79LV1xxhc+fGTtW8274wfDhw2ndunUuj9XW1lJnZ2c/xYWRkJAgviI2CTM+Tda9G0tptB4M50VZEVH7qhsoZLH7UDeqD4iOnAljTqWkuBhhoD1U1dwXpa8pKz0peXRQKwHYoqygIwkDDUEQag7T5PwxurLiQs71ics5dGS/RlbsylhhYKZNYqY0itYV0dicVM+ZQENhLpAXky08SiAs8KwcrGju+7vZr0JRdKRJLvCjIsFcCyRlCWM29XQJ0g2yshNkRdsQ6dDIVqNGVuCh8rY5VFAYsGQF7cX4sgMnnniiaG8uLS2lESNG6KZbkJEFCxbQgARSJKsaRdbB6OzpPj0r3XEpVN2sykAhw7CpkqxU7qXY8ctpRkE6bTxaK/JW+siKVFZqozKFRI4dJwds2aKuCLJyiCZOniGk+vrWTipvaO8LWtOUlba4TDGXCBg3zGayAmSMkmSl4TiNzZ3rswzUE5+me6uGRBmoTpbHUAoSZKWyiU6elOtmrk2nYxqBixhlBSm2KXlEjcdFphCrtf3KQJqy0tAJstWt2paDQE9Pz8CN2ggB4uLiKCbGHtXOxn5IzxkqNTU14hZtylu2bBGPT5w4kVJTU+nss8+m6dOn09e+9jX6wx/+IH729ttvp+uvv57S02W3xoADSkFV+yRZKVyol4Fcds+astLcmyi6hWCEy0mJULVoMIGzTir3iJtZhRmCrMC3csm8Qhdl5VinVFMQvQ4Tqi2AyfbYBmGyTYyLERH6WAwRu+9OVqp7JHnC7hhdZY6Q6vLtwgw+dsJJ4iF0tqB9GTODjAbbZkoSAWl4Gwb1SAg3L88EENhd5a4m20hNrzWabEFWYLJNl9kxTDTdBxnWd+K46lZtyxYBknL48GFBWBS8AxlrqKIEq945SlZ++ctf0pNPPqn/G+3JwKpVq2j58uWCcb355pt000030UknnURJSUl01VVX0R//+EcasGCTbeNxsSPH59Pa2S12yXrwm7ZjreuWNe/c1ASxy1YIgbICVO516wgymGy1QLj9zXIBmq5NSbYF7FvRTbbpgqygFLR8Sp6LwbasUz7/eCdUFWPaaWOpaKNG+3JHV48o94xmj4xGVmq6E/X2ep3IDGplpYiop9vFZBvxGSvuHUEtVZSXNt2LwVa+7lqhrKi2ZSvA5hMVAaxhaPKIhqql0O89amlpoYoKeU3l6klEkpV//etf4ssXRo8eTW+88QYNGvAwsYbjYgFAjgXCv4pqmvvIiqas1HTGD95ZK5EIPZhtr8uMoJ3HG/oUBS1qf3u9/EymF0hCYws8tC+/ub3UtSNIU1aKWiVZGZerlacc61wr0duX91c0Cd9KH1mRr6uqM2FoHKd4T4Tno1OQuAkaUXQlK4aMlQotvVbr+osIJOfI25ZqGpbprQwklZbaDrnAqoyVwNHV1SUWYsRuIKFdwTMgQAAgLHl5eUGVhBQddGw+h2xfHuWpfVkjK5Udst1RBcKFCBzMBt9IcxWNz00RM2CgfInwL8i5GlnZUCU/Gw6PswV6+/IRceOxI0gLhTvQLAkCXqOjnWsNx12C51xm4WhkpbxNvhcg3oMa0TF9JK6uWJaBRBmlvS9pWFNWuuLT9ah62zxNNpMVjkOoNJaBUHfWlJXqdnn5V23LgQO2BgAxGwq+wWQOjTPBQJEVu5HGZKXEpZOjqLq1n8G2ok0KW5xmqhCCydicVFq5VygKM7W8la3FdZIo9MqL0P6mRFHCm+ZEGajhmGgt5ayVA5VNfVH3WhloT31caMpAGlnhwZsu4we01mXOExnU5loGHx/1xSI7hT06hzjJtlWSlaaoFF2VSIuEjBVGcra8banRX3tlU3tfVow2SgKoapOl50w1xNAyVBdV6N4jRVYc9AIALKm7KiuSrBxv7Zv9ohBq34o02S4YkyVu1x2u0T+z9oQc6qRYoWrYOpMnZRhRXIqcvlxXJFpe0W0Er4hoG4bxUTs2dtTKY4MzUJwrA/lXVoqa5WsZEUkKglPQhzwWiZt+SbZaGaiuN8WZdGE7y0AaWcEoBVaBuBMIqGyTl//slAgiWwoKXqDIilNkBeWE7k7Pkfvt8sJ3rFm+/aoMFAbfCjq20D4/QV7cPztYRb1a6a42Ru5OF4/Tdql2ATsM3WR7SCg76DbSS0GaX6U3OpbKOxNFKBkfP455q1DW6GjWB2/qykpPtz79+ZA2UDGiyh1OAS3dRrKizwhyJStVnVJl4iylSCQrCbExeluyHgynZawgILGqRap5SllRGAhQZMVuIPgrGheIXpGUyim2R2u0HWtXhzTwCbLCysoQkNcjBblTXJSVhWOyxVTl4/VtVF0mW1aLO2VpaMk47cLvSPDYYZduI5h84aMBOuKh9kSJYyfoAYrekIAAQ82821Cqp+QWVbfIwXc8FwiqQl1U5LXoOoVMjazUy2Tsfh1BetR+QoQqK1oejEZ89awVDoZjZSU2UVdblGdFYSBAkRXb39FolxkdTFZg0mvr7O4bYohdrLYeDPouiwhuX06Kj6H5o2Up6Mjhg+L2YJskEEvG26ysAKys1EqT7Rwt9n9LUZ00/qKCGCPJ0vQCB7OGoPLovpUSMaUXpA1BeCJeXisB9cYkUGlzz9BRVryUgfTpy5rB9lib9PHonVMRqKwAbLLVO4K0jBVXsqLKQAquqK6uFt07R47I65Q3XH755fTAAw9QKKDIihNI08hKY5m4EHCo17HaFp2sYBGobpOmN6WshBDDtGA4+FO0XfKFc+SiXVYiT8zy3ixhbHUkWl5XVuRzzR0tycq2Y3XU0yTJSlWPJEs8bNExcEdQY6nI+eGS01Ek2erptXKxRtfUkGhx5TJQ/THROcPJxvDydMIErR0zR5pjI1RZ0cgKXmd3p+5b6SsDSWWlNy6JGrQOJ1UGUvA0MPjCCy90GZ1zyy230MUXX9wvSw0p9A0NfUqsU1BkxQnwqPmmMuGEdhloqPlVemC0RFxDXDSlJzoad6PgPheHO7YqpW/lgtkjxDC3hNYKnaxcOFv7GafIihYMNykvTRABzCiqLJcdZCUdKaEhK4asFcDFt6KRlY4Y+djILAQcDoHgQvGeRElvR3Ol6NSDCRomVXH+amTlcFOcMxOxg0USyG/fnKn+ZSBJWnpiEkQXMzAkSKiCabS2ttI///lP+ta3vuXy+IYNG2jx4sUuj82ePVsQmmeeeYachiIrjiorMrpdJytYBLSMla5Y+RguhkNiEYhEdUXzrWBnedmCQsqLkkME62Jy6KsnaGmmdkMPhjsidu5QNOaMkupKeakkDcXt8tiY4ThZcW1fZt+K6EzS2pZbo1OGTgkIiI3ve1/qioQJmtvHxWBLrXW5tkdm9AxLTYi8rBgMNOSsFW5f1stAUlnpipaPpyXGOueLGmpprR1dYfnqZdZpEs899xwlJiZSSYm83gAgJiAe9fX19Pbbb1NsbKyY3cf5KMiTWbNmDf3sZz8T69WSJUv0//eLX/yi+J1OQ23pHVZWjHXto9iZDZc71vZo+VieMteGx7dy6EOdrAA/PW8qde9qIOoi+uZ5S/vShp0oM0RFy0UDc4jShtPyKcNozcFqqqqQF4/a3jSRnpqRFBeytGVjAJ1o0x0lyUoTJenKypABPiOoTfCtFC4UvpUdJQ20v7yRztaUlYbeZJo6It2+uVF2l4KQGSSC4ca7lYEkaemMkp4bZa61BwiWnP7Ldykc2PXrcwKKWLjiiivod7/7nSj1PPzww3T33XfTu+++S2vXrqWMjAz66KOPaOFCOdcOQOrsJ598IggK5vvl5+cLssOA2oLf1d7eLoYQOwVFqUOgrLi0L2vKSmuU/LBVIFz425eBtNgeyuySpsQFM2c4u3PPKHTxrZw1XZLbzkY58bma0unUycPIcbhlrUzW2qhF/L9WBqrpSnQxmg4JGILhAEznBvYUlemhgQ2UbG+6sUMmW/bDweBv7AbqiJKLijLXDj1ERUUJn8ljjz1G9957Lz300EP0zjvv0MiR8noAUy3GCDAw9+j48eOUk5NDc+bMEUMJMZyQgf8PRKWsTG7OnYJSVkKhrBg9KxpZaeyRF5ER2vwOhfC1L/d1f/TK0DaEtzkJ+FbwfPCtjD5BBL9NyU+jrFptcGBvGn3TKc+MjzIQx/9jllVbcy3hyKzskDtwNpoOCXD7stYRxMGBB4uOidsuiqVWSqBpkU5WmqsoP5/JSpuc/K7lrLST/FyVudYeJMXFCIUjXM8dKC644AKaPn26UFVWrFhBM2bMcPGsGJUTYPPmzYKo+Jr/g1lJTkKRlVB6VmpaqLe9UdjfeOIymxoVwtC+jMUI5BEx/JrhVRAJpz1EeI7DH+nKCvC9MyZSzkuSrAwfUUjztS4hR8FGY0ya7uoQCxfSlLELr62poRGGqH0YgYcM9GA4qaxgJAMM2N3wqyRIVQUmVltHMTgVua+1Lrd39VBDaxdlaMpKW68sMWanqNk2dqkVtqZdO4x3332X9uzZI2YcoaxjRG5uLtXWSv8eA+Ufb2SlpkaOCBk2zNlNnioDOdkSikWgp1uYE1HabuvsoeZGLQFT27GyqVEhhEjJ6QvP4lIQEwfOQXESbtOXgQtmF9CoRLkzue3ipaExXWMHHqMtVtqogSnDpVrQUC8vQI29iaL1fkiNhHArAyEJdlZhBqWT/HzqepIpITY68pWVlmpKjOtrORf5OZpnpVUjK6oTaOhh06ZN9KUvfYn+/ve/0znnnEO/+MUvXL4/b9482rVrl8tj27dvFwZcT9ixYwcVFhYKkuMkFFlxAigjwESJGTDNlRQfG61ndjTUS8Za2S5ZuFJWwh0Ox2TFoKw4DbesFYHOVorvkEQ2NVfztIQiwNCQtQJM00pBTRpZaepNFiWgIdWxZgyG0zotTp00jDKiZAkXygpGMYAIRCRSXFNs89P6SkHcDdTcI8mKMtgOLRw5coTOP/98+slPfkJf+9rX6Ne//jW9/PLL9Pnnn+s/AwKzc+dOF3Wlp6eHtm3bJrwr6Bgy4uOPP6azzz7b8deuyIoj72pMn++h0dW30twkP+im3gRBYpTBNtzty7vlLZeBQqGsuKXYGn0jFJdMlBiCEhDDkGILzNPSfFsbZYtuIyXp06GHDNgAjQDHVnnBvnheAeVEN+rdWpfO18zJkYikbFeyoiVkC2VFy1lp6pabJWWwHTqoqamhc889V7Qa//SnPxWPLViwQIS/oSWZMWvWLNEN9OKLL+qP/fa3v6UXXnhBmGlBcBhtbW30yiuv0PXXX+/46x84RbaBBkTuozUVXxpZ+exQNbU1aS2hvUmipTkiWx+HAvI1Q9nxzfK25lDolRUcG+yZYbIC8hBKFUMnK6UuZlIxGygGZaAkOmWsA2MHIhlxSUQpebKMi1JQcraYSn3x5ESiQ0Tx6XmibBex4JwVjWjlc4qtQVlhsqIMtkMH2dnZtHu3tjkz4LXXXuv3GEpDt99+uyAh6Ab66le/Kr7cgfA4tDSfcMIJ5DSUsuIU0oa7KCuTtd1pa7NUVloogcYqv0r4MHqpvC1aJ1NJq/fLf+c52LZsXEyQpGtUdIxkJZRw6whCvszcUZl6yaMpKplOmujAQMcB1hEEnJgvZyQtnT01soPU2GCrkRWePSbalzXPSn2nLGEpg62CJ5x33nn07W9/2yU4zhPi4uLoL3/5C4UCEXzGDXAYhhkao9M7WvrCtqYXOJxQquDbswIjInaam56S/iLspplkOo3cya4GX60Mo2efhArcEcTPT0RXLR5NWVFyLMSYwlHOzEgaYB1BAtpU7Cj2hAwQZYWDJ2UZSCorNR2SrHDCrYKCO37wgx/QqFHaeeAFN9xwA02ZokVBOAxFVkKkrMwcmS6m2sZ1y46Clt5EmlOoyErYAHPpmJPk/ffulreFi0JXguFgOm36c9iVFc1gC4jRAzHyOP3OuX1JlkMKbh1BAs0ytM/xHB67yAoUw55u3Rcny0DSs1LfKS/9KkFbYaBAkZUQKSvowV84Jltvf2yJTqFF44aYFyDSMOVcedsjp8/SpLPC0I20J8xkxTXFFojp6aT4Hnmc5uVFsDcjVB1BjJaqgUFWdIN2ryAs3HZuVFZaKVENUVUYUFBkxSnoLaF9EcSXLyikdM0LMHF0IaUnqmmnYcX0i/vkfuSuzLw0dM89bJqbshKmMhDPB4Ky0tPjUj4Q03vZWzNky0BF/cpAIqcnkoGRDvFaB1drra6sYJhhb4ckoa29CABUQ1QVBg4UWXG6DKQpK8DF80ZSbozc2XzrrHmOPbWCScQnE13zGtHynxJ9c0VoF2YuA1UfIOru7OtGynRo2rMvBRCZQD1dfWUODMEDkjJlG/5QhHsZCHkrA6UM5OZbyUlNENO9e3qJOts1skIJev6KgsJAgCIroSgDacFSMb3dlKDJ6/l5rhHHCmFCzgSi5T+Wt6HO8khIlyUoTIBGqzBIQ6hfR0xc37HK6k4Lk5UhXKbkbiCoTBjqiK/uDvkYpx9HMkA0gdZaQVSGpcpSUFebVHbbKE6P4ldQGAhQZMUp8AKACxzL6liQGENVXleQgJH3/7d3J1BR1e0fwB9ZBgRZFAQUlcCXNzUWUVNcCsut5OjRXvWYYRqlx0pFzV4XzIVcSpNOudsp6uSGJ7dM+actB+VPJSkGopmW2yt6UPN1AQGVec/zu3NnmBFQdObOvTPfzznTzFyGmetlmvvM83t+vye0g3SbZyPJy/C72eEEYrGKrTGzIk+BdUYePqbaD54RJGdVuNElZ+TUrlp/oOptPe5UyMGKBwUhswIagmDFluPG8jdT+SRQ/l/TBx5/owXn1rKLdH3sa+laDl6UZrHWCjIrNRTZGoeAVF6vUsv05YimUsNUvVxgK2pWkFkB7UCwouD0ZTGVsHqKFpxbpEU/jTDDQnVKM84IMgwDyZlAZ86sWNatXPuPdNtXob5N1g5WAhuJ6waGqctcsyIvFgegBQhWFJy+TNxinmEICFjzDkTB0dKx0DWSZifZgzwjyLDkvqnAFsGKMbMiF9rKtSyaCVakv2V4oJRZcbsrBSvlpEMTVajVlStXKCgoSDQ+rMuQIUMoPT2dlIBgxR6ZFSUb1YG6F6Yb+jlR1/FEwzfYL5NhmVmRC2y9DCc8Z2WcvnzGtJKtvE3t5EDTkFkJF8NAevLQGzIrep1hG8C9Fi1aJBocPvaYqVfapEmTaNAg8y9Us2fPpgULFtD169XqMW0EwYqSmRVjsILiWjAI/AdRvwVEEQn27zIsryli6NYr2hE4s8BI6brkd6Krp8yHhjQ2DMSNVL1c7pJrA2lmYqNGPljnCWp069Yt0aDwtddeM9uel5dHnTt3NtsWExMjApr169eTrSFYUXJhOLnAFsEKqEkTw3RpHurgRndyoa38/nVWITHSNTe5/M9B6XZQO9JisMKNFzuGmno8PfGYQj2wQHVatGhBK1euNNuWm5tLXl5edObMGcrKyiI3Nzfq2rWr+Nnt27dJp9OJx6SmplKDBg1Ep2XZwIEDaePGjTbfb6lPONiGTy2ZFRTYgpo0CpJqZipvEl09bZq95uzBCv//y40ebxQTVRj+3w0ytEnQSrAiD+kR0bOtfYguEd3Wu9JTjzv539baeC2t29IaWopz96pXT7P4+HiRJZHp9XoxxMOXsLAw+vDDD6lTJ1NPMFdXV8rJyREByuHDhyk4OJg8PU3F2Zxt4WGjiooK8vCw3QwzBCu21Ki2mhUMA4GK8AcdL0Z34TepV9HNEvv0KVKjiJ5Ev22QbgdHSeuvaIFc/2RsnUA0Ii6Q6Geiu64e9K8OGpnVpBUcqCy00/8vM4uJdN71ClY+//xz4/0vv/ySzp49SzNmzBD3uai2eXPTv8XFxYWKi4spICCAYmNj73m+0NBQEahcvHhRBDu2gmEgpTIrHHkbZwOhwBZUOhR0+v+lBngu7tpYqdXWYoebbkf9izTDovMy89BXiGvPho3IzRUf/c4qPj6ejh07Rjdv3qSysjKaOXMmzZ8/n3x8fIw1K9UzJyw/P7/GQIU1bCgNL/Jz2RIyK0pkVjjq5uW6Sw3fWL1xEgCVCfiHdP3H/0nXTcKl2UrOjgufBy6TTvpdxpFmWHReFpkWwxor5G6qXQErDsVwhsNer10PPMTDQzuHDh2i7777TmRMkpOTjT8PDAykq1dNGTnGwz+1BSt//y0NNTZtatueWQhWbImX5eb+L7zMPmdX5PQ61wgAqEngP03TdKvfB6IOL2vvKIjOy4Y6JB4K4mBFrqmo58kNHnAotR5DMfbk6ekpAo+tW7fS2rVraefOnWKoRxYXF0fr1q0z+53CwkIaPHhwjc935MgRUbTLQY4t4auTYmutXKgWrKCJIahMC1NBnVlXaNAui7VWyLDUPrlj5VpnFx8fTx9//DH17t2bevXqZfazfv36UVFRkVl2paqqigoKCkTtyrVrhtpLg/3791PfvharcWspWOEinVdffZXCw8PFmFbr1q1pzpw5VFlp6FxqwIU9vPiMt7e3iMwmTpx4z2M0TV5E6vIJ08qgCFZAbRo/Zr6UfLgd130Bq3deFpBZAYP27duL6clLliwhS9HR0WKoaPPmzcZtXNOSmZkpimnT0tKM28vLy2nbtm00ZswY0myw8vvvv4tobM2aNSJK4+lQq1evFsU8srt371JiYiKVlpaKqVGbNm2iLVu20FtvvUUOo0mEdH32Z+maCxdRYAtqTGN3T5Fuh0QTtZLWWAANs5y+fBs1KyDhRdzeeOMNevzxmjOo77zzDn300UfiHM6SkpLo/PnzYprz0qVLjY/jxeN4SjNnamzNZjUrzz33nLjIIiIi6Pjx47Rq1Sr64IMPxLY9e/bQ0aNH6dy5c8apUnwgRo8eLZbw9fX1Jc3jQkX25/emFTBRuAhq1GUsUfhTRI3DpZoH0DbL6cvGzAoKbJ1RVVUVXbp0SQQYfC7mjEht+vfvTydOnBABSsuWtbeYcHd3p2XLlpESFC2w5bGuJk1M/U9++uknioqKMpvTzeNlPGf74MGD9Mwzz5DmBT5uvoS5HLwAqFFQW3vvAdhoFVtTzQoKbJ3Rvn376Nlnn6U2bdqI4lo/v7rX+0pJMWRa6zB27FhSimLByp9//ikisOopJF5EhlfDq65x48ZiaV/+WU04kOGLTIkGSo+EU+rV8bdWAAB7BStuKLB1Rj179jQO62hRvWtW5s6dK3oD1HX59ddfzX6HK4h5SGjo0KH3NEfix1vicbGatjNe1pcjQvlSV4pKNQvDyV1tWWhHe+4NADhdsGKoWbkjZ1YwDATaU+/Myvjx42n48GqrOtageltpDlR4OIebIvGc7upCQkLol19+MdvG06W4cZJlxkXGSwJPmTLFLLOi+oAl6gWiXMO4Xutn7b03AOCMU5crbkrXvP4KgKMHKzy9+EEXf+HiHA5UOnbsSBkZGWYLzzAOYLiQ9sKFC9SsWTNj0S03Q+LfqQn/zJbNkmzi6X8TuXsTtXjStAQ/AICSw0C8ijbTSn8jACVqVjijwmNkrVq1ErN/uAq5ekaF8UIy7dq1o5EjR4r53rxs79SpU8WcbYeYCSTz9CV6RmoSBQBgl6nLlXKwgswKaI/NghXOkJw8eVJceCley5oUxv0Jdu3aJeZ7d+/eXSweN2LECOPUZgAAsHJmRYfMCmiPzYIVXiuFL/fDmZdvvvnGVrsBAODc66zInZflmhVkVkCD0BsIAMARWXZe5qaGDDUroEEIVgAAHJHceVkeCjIOA6FmBbQHwQoAgDPUrRiHgVCzAtqDYAUAwOFnBF2pNhsIwQpoD4IVAABHD1aunibSV5kvFgdQgytXrlBQUBCdPn2a6jJkyBBKT08npSBYAQBwVF4B0vWl46Z6FXTUhjpwS5sBAwaYrUQ/adIkGjRokNnjZs+eLRZ1Vao/H4IVAABH5SOtDE4lx6RrZFWgDrdu3aJPP/30nh5+eXl51LlzZ7NtMTExIqBZv349KQHBCgCAo/KRVgunkqPStZdhWAic1sKFC2tsQMxDOllZWeTm5iZa4TDu06fT6Sg3N5dSU1PF47p06WJ8roEDB9LGjRu1vSgcAACoJLNS/l/pGpkVm+BV2W/JXa0V1tCtoQgiHtSECRMoOTnZeD8tLY12795Nw4YNE6vHd+rUyfgzXmU+JydHBCiHDx8WDYY9PT2NP+dsCw8bVVRU2LxnH4IVAABHz6xY1rCAVXGg0mWDKeOgpF9G/EJe7l4P/HgfHx9xYfPmzROBSnZ2tmiLw0W1zZs3Nz6Wmw9zn7+AgACKjY2957lCQ0NFoHLx4kUKCwsjW8IwEACAo2psKpIU/Fvaa09AZebNm0cZGRkiUJEDDa5ZqZ45Yfn5+TUGKoz7+bGysjKb7y8yKwAAjso3lMjNk+hOuXTf37bffp0VD8VwhsNer22NQIUFBgbS1auGxpcGPPxTW7Dy999SR++mTZuSrSFYAQBwVC4uRE1aE5UUSfcbI1ixBa4Zqc9QjD3NqyVQYXFxcbRu3TqzbYWFhTR48OAan+vIkSNi+IiDHFvDMBAAgCNrHme63ay9PfcE7Gz+/Pm0fPlyyszMFAWxXGvCF647Yf369aOioiKz7EpVVRUVFBSI2pVr166ZPd/+/fupb9++iuw7ghUAAEeW8DZR4ONEvecSeWH1WmeesbRkyRK6fPkyxcfHU7NmzYwXHuph0dHRYjbQ5s2bzQIcDm64mJZnDsnKy8tp27ZtNGbMGEX2v4Ge/wUaxqvn+fn5iYjP19fX3rsDAAAOjk/Up06dovDw8HsKUrVu9+7dNHXqVDHEw7OBarNixQrasWMH7dmz56GPVX3O36hZAQAAAKF///504sQJOn/+PLVsWfvsMXd3d1q2bBkpBcEKAAAAGKWkpND9jB07lpSEmhUAAABQNQQrAAAAoGoIVgAAAEDVEKwAAAA8BI1PptXUMUKwAgAAUA/cjZhVVlbiuN2H3DeIZw89CswGAgAAqM+J082NvLy86NKlS+IkXNd6JM6cUSkrK6OSkhLy9/c3BngPC8EKAABAPXsB8cqvvNjZmTNncOzqwIFKSEgIPSoEKwAAAPWk0+koMjISQ0F14KzTo2ZUZAhWAAAAHgIP/zjacvtqhYE2AAAAUDUEKwAAAKBqCFYAAABA1dwcZcEZbjUNAAAA2iCftx9k4TjNBys3btwQ13W1sgYAAAD1nsf9/PzqfEwDvcbXC66qqqLi4mLy8fERc9+tHfVxEHTu3Dny9fW16nMDjrPS8H7GcXYkeD9r/1hz+MGBSvPmze+7sJ7mMyv8D2zRooVNX4P/OAhWbA/HWRk4zjjOjgTvZ20f6/tlVGQosAUAAABVQ7ACAAAAqoZgpQ4eHh40Z84ccQ22g+OsDBxnHGdHgvezcx1rzRfYAgAAgGNDZgUAAABUDcEKAAAAqBqCFQAAAFA1BCsAAACgaghWarFy5UoKDw8nT09P6tixI+3fv1/Zv4yDW7RoET355JNi5eGgoCAaNGgQHT9+3N675RTHnVd6njRpkr13xSGdP3+ekpKSKCAggLy8vKh9+/Z08OBBe++WQ7lz5w7NmjVLfD43bNiQIiIiKC0tTaxmDg9v3759NGDAALGaLH9GbN++3eznPBdn7ty54ud83Hv27ElFRUWkFAQrNcjMzBQf5qmpqZSfn09PPfUUPf/883T27FnF/jCOLjs7m9588036+eefae/eveIDqG/fvlRaWmrvXXNYeXl5tHbtWoqJibH3rjikq1evUvfu3cnd3Z2ysrLo6NGjtHTpUvL397f3rjmU999/n1avXk3Lly+nY8eO0eLFi2nJkiW0bNkye++appWWllJsbKw4rjXh45yeni5+zp8lISEh1KdPH2N/PpvjqctgrnPnzvpx48aZbWvTpo1++vTpOFQ2UlJSwlPo9dnZ2TjGNnDjxg19ZGSkfu/evfqEhAR9SkoKjrOVTZs2Td+jRw8cVxtLTEzUJycnm2174YUX9ElJSTj2VsKfxdu2bTPer6qq0oeEhOjfe+8947by8nK9n5+ffvXq1XolILNiobKyUqRt+Vt+dXw/NzdXmQjSCV27dk1cN2nSxN674pA4i5WYmEi9e/e29644rK+//po6depEQ4cOFUObcXFx9Mknn9h7txxOjx496Pvvv6c//vhD3P/tt98oJyeH+vfvb+9dc1inTp2iixcvmp0XeYG4hIQExc6Lmm9kaG2XL1+mu3fvUnBwsNl2vs9/LLA+DuSnTJkiPoSioqJwiK1s06ZNdOjQIZG6Bdv566+/aNWqVeK9PHPmTDpw4ABNnDhRfKi//PLLOPRWMm3aNPHlpk2bNuTq6io+rxcsWEAvvvgijrGNyOe+ms6LZ86cISUgWKkFFxhZnlAtt4F1jB8/ngoKCsS3I7AubumekpJCe/bsEcXiYDtc4MmZlYULF4r7nFnhAkQOYBCsWLemcN26dbRhwwZ64okn6PDhw6LGkAs/R40aZcVXAjWdFxGsWAgMDBTRumUWpaSk5J6oEh7dhAkTRPqcK9FbtGiBQ2plPKTJ712e0Sbjb6J8vLlQrqKiQrzf4dE1a9aM2rVrZ7atbdu2tGXLFhxeK3r77bdp+vTpNHz4cHE/OjpafLvnmW4IVmyDi2kZnxf5fW6P8yJqVizodDrxwc4zVKrj+926dVPkj+IMOCLnjMrWrVvphx9+ENMQwfp69epFhYWF4tunfOFv/y+99JK4jUDFengmkOX0e66rCAsLs+KrQFlZGbm4mJ+6+H2Mqcu2w5/PHLBUPy9yfSfP6lTqvIjMSg14zHnkyJHiQ71r165iuidPWx43bpwifxRnKfjkNO6OHTvEWityJsvPz0/M4Qfr4GNrWQfk7e0t1gFBfZB1TZ48WXxw8zDQsGHDRM0Kf3bwBayH1wLhGpVWrVqJYSBeXoKn1CYnJ+MwP4KbN2/SyZMnzYpq+QsNT3rgY81DbfzejoyMFBe+zWsJjRgxghShyJwjDVqxYoU+LCxMr9Pp9B06dMCUWivjt15Nl4yMDGu/FFjA1GXb2blzpz4qKkrv4eEhljtYu3Yt3n9Wdv36dTH1vlWrVnpPT099RESEPjU1VV9RUYFj/Qh+/PHHGj+TR40aZZy+PGfOHDGFmd/fTz/9tL6wsFCvlAb8H2XCIgAAAID6Q80KAAAAqBqCFQAAAFA1BCsAAACgaghWAAAAQNUQrAAAAICqIVgBAAAAVUOwAgAAAKqGYAUAAABUDcEKACimZ8+eYtluAID6QG8gALCK+7WK54643LjS3d3dLkecg6TTp0/T9u3b7fL6APDwEKwAgFVcuHDBeDszM5Nmz55t1oWYG1Ryo0p7ycvLo8TERLu9PgA8PAwDAYBVcAt5+cJBCWdaLLdZDgPx/QkTJohtjRs3puDgYNGluLS0lF555RXRNbp169aUlZVl/B1uZ7Z48WKKiIgQAVBsbCx99dVXte7X7du3SafTUW5uLqWmpor96tKlC/7qABqCYAUA7OqLL76gwMBAOnDggAhcXn/9dRo6dCh169aNDh06RP369aORI0dSWVmZePysWbMoIyODVq1aRUVFRTR58mRKSkqi7OzsGp/f1dWVcnJyxG1uec8ZoG+//VbRfyMAPBoEKwBgV5wZ4QAkMjKSZsyYIbIlHLyMGTNGbOPhpCtXrlBBQYHIuKSnp9Nnn30mghjOrowePVoEK2vWrKnx+V1cXKi4uJgCAgLEa3GWx9/fX/F/JwA8PNSsAIBdxcTEmGVBOKiIjo42buOhIVZSUkJHjx6l8vJy6tOnj9lzVFZWUlxcXK2vkZ+fLwIVANAmBCsAYFeWs4O4pqT6NnmWUVVVlbiwXbt2UWhoqNnveXh41PoaPPyDYAVAuxCsAIBmtGvXTgQlZ8+epYSEhAf+vcLCQho8eLBN9w0AbAfBCgBoBs8Omjp1qiiq5SxLjx496Pr162KmT6NGjcRaLjXhx3LNC9eueHt723UKNQDUHwpsAUBT3n33XVF0u2jRImrbtq0otN25cyeFh4fX+jvz588Xa7/w0FFaWpqi+wsAj66BnhctAAAAAFApZFYAAABA1RCsAAAAgKohWAEAAABVQ7ACAAAAqoZgBQAAAFQNwQoAAACoGoIVAAAAUDUEKwAAAKBqCFYAAABA1RCsAAAAgKohWAEAAABVQ7ACAAAApGb/Azl3thpAmaS5AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qmat.qcoeff.collocation import Collocation\n", "from qmat.solvers.generic.integrators import BackwardEuler\n", "from qmat.solvers.generic.diffops import Lorenz\n", "\n", "scheme = \"BE\"\n", "nSteps = 1000\n", "nSweeps = 4\n", "\n", "qGen = Collocation(nNodes=4, nodeType=\"LEGENDRE\", quadType=\"RADAU-RIGHT\")\n", "nodes, weights, Q = qGen.genCoeffs()\n", "\n", "solver = BackwardEuler(Lorenz(), nodes, tEnd=10, nSteps=nSteps)\n", "uNum = solver.solveSDC(nSweeps, Q, weights)\n", "\n", "plt.plot(solver.times, uNum[:, 0], label=\"$x(t)$\")\n", "plt.plot(solver.times, uNum[:, 1], label=\"$y(t)$\")\n", "plt.plot(solver.times, uNum[:, 2], label=\"$z(t)$\")\n", "plt.legend(); plt.xlabel(\"Time $t$\"); plt.title(f\"Using {scheme} and {nSteps} time-steps\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "📣 Additional $\\phi$ integrators can be implemented, using the following template :" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "from qmat.solvers.generic import PhiSolver\n", "\n", "class Phidlidoo(PhiSolver):\n", "\n", " def evalPhi(self, uVals, fEvals, out, t0=0):\n", " \"\"\"\n", " Parameters\n", " ----------\n", " uVals : list[np.ndarray] of size :math:`m+2`\n", " The :math:`m+1` time-node solutions + the initial solution :math:`u_0`.\n", " fEvals : list[np.ndarray] of size :math:`m+1` or :math:`m+1`\n", " The :math:`f(u,t)` evaluations at each time nodes (+ initial solution),\n", " up to time-node :math:`m`.\n", " It can eventually contain a pre-computed :math:`f_{m+1}`\n", " to spare one :math:`f(u,t)` evaluation.\n", " out : np.ndarray\n", " Array used to store the evaluation.\n", " t0 : float, optional\n", " Initial step time. The default is 0.\n", " \"\"\"\n", " out[:] = ... # your implementation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For more details, see the [short developer guide](../devdoc/addPhiIntegrator.md) on this aspect.\n", "This can allow to develop SDC algorithm based on any kind of time-integrator \n", "(exponential, etc ...)\n", "\n", "> 💡 Per default, a specialized `PhiSolver` class can take any kind of `DiffOp` class to define the ODE problem.\n", "> But some specific time-integrators, like a Semi-Lagrangian method for advective problems, \n", "> may be restricted to some specific problem classes.\n", "> In that case, you can still use the base `PhiSolver` class, but you'll have to overload its constructor to provide a specific `DiffOp` instance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fun fact\n", "\n", "Back to the $\\phi$-SDC formula\n", "\n", "$$\n", "u^{k+1}_{m+1} - \\phi(u_0, u^{k+1}_1, ..., u^{k+1}_{m+1})\n", " = u_0 + \\Delta{t}\\sum_{j=0}^{M} \\omega_j f(u^k_j, t_j) - \\phi(u_0, u^{k}_1, ..., u^{k}_{m+1})\n", "$$\n", "\n", "we can rearrange it into :\n", "\n", "$$\n", "u^{k+1}_{m+1}\n", " = u_0 + \\Delta{t}\\sum_{j=0}^{M} \\omega_j f(u^k_j, t_j) + u_0 + \\phi(u_0, u^{k+1}_1, ..., u^{k+1}_{m+1}) - u_0 - \\phi(u_0, u^{k}_1, ..., u^{k}_{m+1}).\n", "$$\n", "\n", "Now, looking back at the definition of those $\\phi$ integrators,\n", "we can actually write each part on the right hand side as a dedicated time-integrator.\n", "So if we note :\n", "\n", "- $G[t_0 \\rightarrow t_{m+1}](u^{k+1}) := u_0 + \\phi(u_0, u^{k+1}_1, ..., u^{k+1}_{m+1})$,\n", "- $G[t_0 \\rightarrow t_{m+1}](u^{k}) := u_0 + \\phi(u_0, u^{k}_1, ..., u^{k+1}_{m})$,\n", "- $F[t_0 \\rightarrow t_{m+1}](u^{k}) := u_0 + \\Delta{t}\\sum_{j=0}^{M} \\omega_j f(u^k_j, t_j)$,\n", "\n", "it produces the following formula :\n", "\n", "$$\n", "u^{k+1}_{m+1} = F[t_0 \\rightarrow t_{m+1}](u^{k}) + G[t_0 \\rightarrow t_{m+1}](u^{k+1}) - G[t_0 \\rightarrow t_{m+1}](u^{k}).\n", "$$\n", "\n", "... which resemble furiously to a [Parareal](https://en.wikipedia.org/wiki/Parareal) formula (what a chock 😮).\n", "\n", "> 🔍 There is still one main difference between $\\phi$-SDC and Parareal : here the $F$ integrator **depends on nodes forward in time**, which is not the case for Parareal." ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 2 }