{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The HFM library - A fast marching solver with adaptive stencils\n", "\n", "## Part : Isotropic and anisotropic metrics\n", "## Chapter : Asymmetric quadratic metrics\n", "\n", "In this notebook, we demonstrate anisotropic fast marching with *asymmetric quadratic metrics*, in two and three dimensions. The metrics considered in the notebook are a generalization of Riemannian metrics, featuring an additional non-symmetric term. \n", "They are also a special case of non-symmetric Finslerian metrics.\n", "An *asymmetric quadratic metric* measures vectors according to the formula:\n", "$$\n", " F_x(v) := \\sqrt{ \\|v\\|^2_{M(x)} + \\max\\{0,<\\omega(x), v>\\}^2}\n", "$$\n", "where $M$ is a field of symmetric positive definite tensors, and $\\omega$ is a vector field. As evidenced by the above formula, the role of the vector field $\\omega$ is to further penalize motion in its direction.\n", "\n", "The HFM software computes the distance associated to a given *asymmetric quadratic metric*, and the corresponding minimal paths, by solving a variant of the eikonal PDE. Namely for all $x$ within a domain $\\Omega$\n", "$$\n", " \\sqrt{\\|\\nabla u(x)\\|^2_{D(x)} + \\max\\{0,<\\eta(x),\\nabla u(x)>\\}^2} = 1,\n", "$$\n", "where $(D,\\eta)$ is the dual metric.\n", "Some algebraic formulas allow to express the dual metric in terms of $(M,\\omega)$, the primal metric.\n", "\n", "**Technical note** The two and three dimensional implementations use different discretization schemes: semi-Lagrangian, vs Eulerian. The latter one in addition involves a relaxation parameter. As a result two dimensional implementation can reach high levels of accuracy (including second/third order), whereas the three dimensional one is best used in contexts where speed and qualitative behavior are most important.\n", "\n", "**References** The experiments presented in this notebook, or related variants, are presented in the following publications.\n", "\n", "Mirebeau, J.-M. (2014). Efficient fast marching with Finsler metrics. Numerische Mathematik, 126(3), 515–557.\n", "[link](https://hal.archives-ouvertes.fr/hal-00736431)\n", "\n", "Duits, R., Meesters, S. P., Mirebeau, J.-M., & Portegies, J. M. (2018). Optimal paths for variants of the 2D and 3D Reeds-Shepp car with applications in image analysis. Journal of Mathematical Imaging and Vision, 1–33. http://doi.org/ https://doi.org/10.1007/s10851-018-0795-z" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[**Summary**](Summary.ipynb) of volume Fast Marching Methods, this series of notebooks.\n", "\n", "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n", "\tbook of notebooks, including the other volumes.\n", "\n", "# Table of contents\n", " * [1. Case of a constant metric](#1.-Case-of-a-constant-metric)\n", " * [2. Application to vessel segmentation](#2.-Application-to-vessel-segmentation)\n", " * [2.1 Preparation of a synthetic example](#2.1-Preparation-of-a-synthetic-example)\n", " * [2.2 Extraction of a tubular structure](#2.2-Extraction-of-a-tubular-structure)\n", " * [3. Asymmetric Rander metrics](#3.-Asymmetric-Rander-metrics)\n", "\n", "\n", "\n", "This Python® notebook is intended as documentation and testing for the [HamiltonFastMarching (HFM) library](https://github.com/mirebeau/HamiltonFastMarching), which also has interfaces to the Matlab® and Mathematica® languages. \n", "More information on the HFM library in the manuscript:\n", "* Jean-Marie Mirebeau, Jorg Portegies, \"Hamiltonian Fast Marching: A numerical solver for anisotropic and non-holonomic eikonal PDEs\", 2019 [(link)](https://hal.archives-ouvertes.fr/hal-01778322)\n", "\n", "Copyright Jean-Marie Mirebeau, University Paris-Sud, CNRS, University Paris-Saclay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Importing the required libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:25.813113Z", "iopub.status.busy": "2024-04-30T08:56:25.812762Z", "iopub.status.idle": "2024-04-30T08:56:25.822094Z", "shell.execute_reply": "2024-04-30T08:56:25.821505Z" } }, "outputs": [], "source": [ "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n", "#from Miscellaneous import TocTools; print(TocTools.displayTOC('AsymmetricQuadratic','FMM'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:25.825062Z", "iopub.status.busy": "2024-04-30T08:56:25.824687Z", "iopub.status.idle": "2024-04-30T08:56:26.144208Z", "shell.execute_reply": "2024-04-30T08:56:26.143857Z" } }, "outputs": [], "source": [ "from agd import Eikonal\n", "from agd.Metrics import AsymQuad,Riemann\n", "from agd.Plotting import savefig; #savefig.dirName = 'Figures/AsymmetricQuadratic'\n", "from agd import FiniteDifferences as fd\n", "from agd import AutomaticDifferentiation as ad" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.145981Z", "iopub.status.busy": "2024-04-30T08:56:26.145829Z", "iopub.status.idle": "2024-04-30T08:56:26.147896Z", "shell.execute_reply": "2024-04-30T08:56:26.147605Z" } }, "outputs": [], "source": [ "import numpy as np; xp = np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0.1 Additional configuration\n", "\n", "Uncomment the following line to use the GPU accelerated eikonal solver." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.149291Z", "iopub.status.busy": "2024-04-30T08:56:26.149184Z", "iopub.status.idle": "2024-04-30T08:56:26.150718Z", "shell.execute_reply": "2024-04-30T08:56:26.150494Z" }, "tags": [ "EikonalGPU_config" ] }, "outputs": [], "source": [ "#xp,Eikonal,plt = map(ad.cupy_friendly,(xp,Eikonal,plt))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Case of a constant metric\n", "\n", "In order to illustrate the concept of asymmetric quadratic metric, we compute the distance map with respect to a metric independent of the position $x$ within the domain. It is defined by \n", "$$\n", " F(v)^2 = \\|v\\|_D^2 + \\max\\{0,<\\omega,v>\\}^2,\n", "$$\n", "where $D$ is the identity tensor, and $\\omega = (1,1)$.\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.152050Z", "iopub.status.busy": "2024-04-30T08:56:26.151942Z", "iopub.status.idle": "2024-04-30T08:56:26.154526Z", "shell.execute_reply": "2024-04-30T08:56:26.154282Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'AsymmetricQuadratic2',\n", " 'exportValues':1,\n", " 'seed':[0,0],\n", "})\n", "\n", "# Define the domain\n", "n=201\n", "hfmIn.SetRect(sides=[[-1,1],[-1,1]],dimx=n)\n", "X,Y = hfmIn.Grid()\n", "hfmIn.SetUniformTips((6,6))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.155932Z", "iopub.status.busy": "2024-04-30T08:56:26.155821Z", "iopub.status.idle": "2024-04-30T08:56:26.157651Z", "shell.execute_reply": "2024-04-30T08:56:26.157416Z" } }, "outputs": [], "source": [ "hfmIn['metric']= AsymQuad(xp.eye(2),[1,1]) # Inputs are : D, w" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.158969Z", "iopub.status.busy": "2024-04-30T08:56:26.158891Z", "iopub.status.idle": "2024-04-30T08:56:26.209222Z", "shell.execute_reply": "2024-04-30T08:56:26.208836Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.014873 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the metric is constant, the distance map from the origin is simply $u(x) = F(x)$.\n", "\n", "The additional cost of motion in the direction $\\omega = (1,1)$ is clearly visible.\n", "Each level line of $u$ is built of two half ellipses, defined by the tensors $D$ and $D+\\omega \\omega^T$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.210864Z", "iopub.status.busy": "2024-04-30T08:56:26.210746Z", "iopub.status.idle": "2024-04-30T08:56:26.317495Z", "shell.execute_reply": "2024-04-30T08:56:26.317229Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[5,4]); plt.title('Distance map, asymmetric quadratic norm'); plt.axis('equal'); \n", "plt.contourf(X,Y,hfmOut['values']);\n", "plt.colorbar();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the metric is constant, minimal geodesics are straight lines toward the origin." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.319032Z", "iopub.status.busy": "2024-04-30T08:56:26.318920Z", "iopub.status.idle": "2024-04-30T08:56:26.382729Z", "shell.execute_reply": "2024-04-30T08:56:26.382442Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[4,4]); plt.title('Minimal geodesics, for a constant metric'); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(*geo) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Application to vessel segmentation\n", "\n", "Non-symmetric metrics are well fit to extract structures possessing a preferred orientation. For instance, the contours of two dimensional objects are naturally oriented, by rotating the outward normal clockwise. See the notebook [VI - Rander metrics](http://nbviewer.jupyter.org/urls/rawgithub.com/Mirebeau/HFM_Python_Notebooks/master/A6_Rander.ipynb)\n", " for a discussion on image sub-domain segmentation.\n", "\n", "In the following experiment, we illustrate a different use of non-symmetric metrics, to avoid the shortcut's problem in tubular structure segmentation. A similar effect can be achieved with the use of non-holonomic metrics penalizing curvature, such as Euler-Mumford elasticae, see [IV - Curvature penalized planar paths](http://nbviewer.jupyter.org/urls/rawgithub.com/Mirebeau/HFM_Python_Notebooks/master/A4_Curvature.ipynb). \n", "Curvature penalization models can be simpler to use, but are much more computationally expensive." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Preparation of a synthetic example" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.384250Z", "iopub.status.busy": "2024-04-30T08:56:26.384164Z", "iopub.status.idle": "2024-04-30T08:56:26.409448Z", "shell.execute_reply": "2024-04-30T08:56:26.409171Z" } }, "outputs": [], "source": [ "def gamma(t):\n", " return ad.array((xp.cos(t),0.5*xp.sin(2*t)))\n", "def gamma_tgt(t):\n", " tX,tY = -xp.sin(t),xp.cos(2*t)\n", " tN = xp.sqrt(tX**2+tY**2)\n", " return ad.array((tX/tN,tY/tN)) \n", "def gamma_normal(t):\n", " tX,tY = gamma_tgt(t)\n", " return ad.array((tY,-tX))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.410889Z", "iopub.status.busy": "2024-04-30T08:56:26.410804Z", "iopub.status.idle": "2024-04-30T08:56:26.467997Z", "shell.execute_reply": "2024-04-30T08:56:26.467689Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T=xp.linspace(0,2*np.pi,100)\n", "plt.axis('equal')\n", "plt.plot(*gamma(T));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The construction of our example involves running a first fast marching." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.469528Z", "iopub.status.busy": "2024-04-30T08:56:26.469421Z", "iopub.status.idle": "2024-04-30T08:56:26.471852Z", "shell.execute_reply": "2024-04-30T08:56:26.471611Z" } }, "outputs": [], "source": [ "isoIn = Eikonal.dictIn({\n", " 'model':'Isotropic2',\n", " 'exportValues':1,\n", " 'seeds':gamma(T).T, # Second T is transposition\n", " 'speed':1,\n", " 'seedValueVariation':gamma_tgt(T) # Interpolates data defined at the seeds\n", "})\n", "\n", "# Define the domain\n", "n=201\n", "isoIn.SetRect(sides=[[-1.1,1.1],[-0.6,0.6]],dimx=n)\n", "X,Y = isoIn.Grid()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.473255Z", "iopub.status.busy": "2024-04-30T08:56:26.473158Z", "iopub.status.idle": "2024-04-30T08:56:26.489609Z", "shell.execute_reply": "2024-04-30T08:56:26.489295Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.003778 s.\n" ] } ], "source": [ "isoOut = isoIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We computed the distance to the curve, and an extension of its tangents." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.491196Z", "iopub.status.busy": "2024-04-30T08:56:26.491085Z", "iopub.status.idle": "2024-04-30T08:56:26.559782Z", "shell.execute_reply": "2024-04-30T08:56:26.559403Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAGfCAYAAACX9jKsAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAABTPElEQVR4nO2dfXgV1Z3Hv4GQhFJyLcQEEAjUrRBerBIKBF9rbYAt9aXtAosbqLW02KUqtG6hPFVw20atutRa0IpoV1HZVmltZWPpU1TagBaEapeAFikJQkAs3MRWwkvO/oH3em/uzc19Ob8z58x8P89znwcmM3Nn7sz5zWd+5y1PKaVACCGEEOII3bw+AEIIIYSQTKC8EEIIIcQpKC+EEEIIcQrKCyGEEEKcgvJCCCGEEKegvBBCCCHEKSgvhBBCCHEKygshhBBCnILyQgghhBCnoLwQQgghxCnyTXzJ8uXL8YMf/AAHDhzAyJEjsWzZMlx00UWdrr969WrceeedeOONNxAKhTB58mTcdddd6Nu3b5ff1d7ejv3796N3797Iy8vTeRqEEEIIEUIphdbWVgwYMADdunWRW1HCPPnkk6pHjx7qwQcfVDt27FA33nij6tWrl9q7d2/S9Tdu3Ki6deumfvjDH6o333xTbdy4UY0cOVJdddVVaX1fU1OTAsAPP/zwww8//Dj4aWpq6vJZn6eU7MSM48ePx5gxY7BixYrosoqKClx11VWora1NWP+uu+7CihUrsHv37uiyH/3oR7jzzjvR1NTU5feFw2GcccYZaGpqQnFxsZ6TIIQQQogoLS0tGDRoEI4ePYpQKJRyXdFqo+PHj2Pr1q1YuHBh3PLq6mrU19cn3WbixIlYvHgx1q1bhylTpuDQoUP4+c9/js985jNJ129ra0NbW1v0/62trQCA4uJiygshhBDiGOk0+RBtsHv48GGcOnUKZWVlccvLysrQ3NycdJuJEydi9erVmD59OgoKCtCvXz+cccYZ+NGPfpR0/draWoRCoehn0KBB2s+DEEIIIfZgpLdRR4tSSnVqVjt27MANN9yAW265BVu3bkVdXR327NmDuXPnJl1/0aJFCIfD0U86VUuEEEIIcRfRaqOSkhJ07949Icty6NChhGxMhNraWlxwwQW4+eabAQDnnnsuevXqhYsuugjf/e530b9//7j1CwsLUVhYKHMChBBCCLEO0cxLQUEBKisrsX79+rjl69evx8SJE5Nu849//COhi1T37t0BnM7YEEIIISTYiFcbLViwACtXrsSqVavQ0NCA+fPno7GxMVoNtGjRIsyaNSu6/mc/+1k8/fTTWLFiBd5880384Q9/wA033IBx48ZhwIAB0odLCCGEEMsRH6Ru+vTpeOedd3DbbbfhwIEDGDVqFNatW4fy8nIAwIEDB9DY2Bhd/4tf/CJaW1tx33334Rvf+AbOOOMMXHbZZbjjjjukD5UQQgghDiA+zotpWlpaEAqFEA6H2VWaEEIIcYRMnt+c24gQQgghTkF5IYQQQohTUF4IIYQQ4hSUF0IIIYQ4BeWFEEIIIU5BeSGEEEKIU1BeCCGEEOIUlBdCCCGEOAXlhRBCCCFOQXkhhBBCiFNQXgghhBDiFJQXQgghhDgF5YUQQgghTkF5IYQQQohTUF4IIYQQ4hSUF0IIIYQ4BeWFEEIIIU5BeSGEEEKIU1BeCCGEEOIUlBdCCCGEOAXlhRBCCCFOQXkhhBBCiFNQXgghhBDiFJQXQgghhDgF5YUQQgghTkF5IYQQQohTUF4IIYQQ4hSUF0IIIYQ4BeWFEEIIIU5BeSGEEEKIU1BeCCGEEOIUlBdCCCGEOAXlhRBCCCFOQXkhhBBCiFMYkZfly5dj6NChKCoqQmVlJTZu3Jhy/ba2NixevBjl5eUoLCzE2WefjVWrVpk4VEIIIYRYTr70F6xZswY33XQTli9fjgsuuAAPPPAApkyZgh07dmDw4MFJt5k2bRoOHjyIhx56CP/0T/+EQ4cO4eTJk9KHSgghhBAHyFNKKckvGD9+PMaMGYMVK1ZEl1VUVOCqq65CbW1twvp1dXWYMWMG3nzzTfTp0yfj72tpaUEoFEI4HEZxcXFOx04IIYQQM2Ty/BatNjp+/Di2bt2K6urquOXV1dWor69Pus0zzzyDsWPH4s4778RZZ52Fc845B9/85jfx3nvvSR4qIYQQQhxBtNro8OHDOHXqFMrKyuKWl5WVobm5Oek2b775Jn7/+9+jqKgIa9euxeHDh/G1r30Nf/vb35K2e2lra0NbW1v0/y0tLXpPghBCCCFWId7mBQDy8vLi/q+USlgWob29HXl5eVi9ejVCoRAA4J577sEXvvAF/PjHP0bPnj3j1q+trcXSpUsT9jPq8f9Ct55FGR9rYWNBxtt0Re+9ojVzUUK727peyQeEzy40+n2t5cnvVd20DT4uuv/BAw+L7XtSvwbt+7y6eFvW265tOV/jkZzmueYK7fts3FeifZ+ATBzrDFPxLV1cjoOmY1sE3TEu21jW/t6xtNcVrTYqKSlB9+7dE7Ishw4dSsjGROjfvz/OOuusqLgAp9vIKKWwb9++hPUXLVqEcDgc/TQ1Nek9iRyhuOjH9LmauobSDxypB6UU2QoIxcWMuPTeqzwTl9Dutk4/LuPVuei+jibuQVF5KSgoQGVlJdavXx+3fP369Zg4cWLSbS644ALs378f7777bnTZ66+/jm7dumHgwIEJ6xcWFqK4uDjuky26f3ATBdsPBTYbvCjcJq5nYWOBaMFv3Fci8tB8rrlC5AGfqYhQXOQfGl5Ji18EJRNMnrNrAiM+zsuCBQuwcuVKrFq1Cg0NDZg/fz4aGxsxd+5cAKczJ7NmzYquP3PmTPTt2xfXXnstduzYgRdffBE333wzvvSlLyVUGenENXEJWiHuDD9LjCRSD08vBYbiInvPeC0tQcfE76D7Gkvek+JtXqZPn4533nkHt912Gw4cOIBRo0Zh3bp1KC8vBwAcOHAAjY2N0fU//OEPY/369fj617+OsWPHom/fvpg2bRq++93vih2jS+LCQpyc2N/FRL1x771KvC1M5L6UagvTuK9EpB3Mc80V2tvArG05P2UbGN3iIiEtgIy4mJAWL2CsS07kd5GMczrjW2FjgUgMEx/nxTSRfuKDVixJq8GuzoJvIttC0sdU4zcTDXpdbMxrqhGvC+LiYraF0uIGknFOZ2xLJ4a1v3cMTdcvSWucFyO9jWzFFXFhYc6O0O42Y1kYQFZiXMzCSGVgJKG4eNt7iLEucyQzMTZnYAI7MaML4sK63twx+Ru63hbGpYa8ElBcvM22MNblhtTvZ1tX+AiBlBdXxIXow2SLfenCLtkjSbI3ks24Ii5S156Ncf2B1O+p697Qee8GTl5sFxcWZllMZmFMSIwUQRIYl8RFAkqL/wiCwAS6zUsuSImLVxTsTBwA8PjwxHF1dK/nBSZa60eQ7pUk2RbGlXYw2eKKtAD+Exeb8UOMA2TinK54pqP9S6B6G+kKAEEQl1iODx/Y5TqZrmcTfumVJNWY15WeSJkQdHGhtCSiK8bZFt8A/TFOVyzrGLMy6W0UGHmxVVxMFehIgYsUrHQKqiSdFfCOx2kKCkxqpOZF8kJiXBEXv2RbbJKW2LhnIhZ2/A4vxcZGgaG8xJBMXoIsLl5LSq5QYrLDJYkxKTAUl2DOtWZbHPSLxOgWmEzkxfcNdoMqLgU791lXYLPB9Hm4Oo9IRyR7I+nGVENeiouZKUtsEhdb42DkuLw4Np3XR8c9le39zga7aaCz0JuQFj9iOu1qYoA76cHtpIbldrEhr25xYfuWD/BCVjqLc7HxwZVYmM656EZnfNPRiDebWOXrzIuOQEBxsQuTbyt+yMJIjQviUgbGBXGRHL9FCq+yLKnKv5cZDd1In4dNGbJs8K28FDQFR1z8UlgzwW8SIz0uTFAFxhVxkcBvI38HMc4Bsuet6zp6UX3kW3nJFRfEJaiFORbTEiONiwKj+4GuSziCKi6SIuzV23rQ4xwgF+tsEphMkg6UF2EkxYV8gCmJcT0L40o1Uq7iEWRxkcDLhriMdfH4XWDShfKSBF0XQKKwM9uSGr9JjBSuCEymEiIxESTFxd4BNIOKRJxzTWAoLx2wXVxIevilKkk6C6MbL9vBSEiL7vNxrWGul9kWxruusVVgTEB5icFWcWFBzg6/NeiVwC8CE9RsC+CfCWL91FPIJLp/Mx3X3UT2hfKiGQlxIdljeoA7SaSyMK435A2quEjdD15JC8mNoAkM5eV9dPzQFBc7MflG52oWxsWGvGzfoh+T4kJp0Y9tAiMJ5QX2iQsLtRwmJUaSIFcjSUgLQHExLS5EBpt+W8nsS+DlxUZxIfKYkBhWI32A1HD6ugiyuJhs38IXMzPo+o1trj7i3EYWwUJtnoKd+8TnEAFkZ6vWMbdIRyTmRZKYE0kHEj2KdONitoXxzFt0xTYT87xlQ6AzLzZlXVjQvcMvWRjdBCEDQ3HRC3sM2YUtGRiJeziw8kJxIR0xITCSEuNKQ15bBCao4iJ1HzKO2Ykt10X3vRxYeckVios/cb1HkivtYLwWmCCLi26YabEfHdfHtvYvgZSXXH9Aiou/8UOPJFcExguJobjogzHMHWwRGF0ETl5MThyVChZ6+zHVFkYyC6Mb19vB6PwuiSo1lwaeYwxzDxuuma77O3Dykis6goANNxBJHxONECkw8gKjW1x041rDXOImuV47W6qPAtVV2obqItcKfceudp0df7rrRdZ17XeIINm1WqpbtVRXagBau1NLdaVmNRHJlUziWxCwoft0YOTFhuoiW2/42ILZ1cM53Qd3ZL3O9hf7d9cwMTaMhMAAsH48GN0CQ3HRj4tlNh0yKdOpYqYLv490DEuHXF+qWG2UJn58izk+fGDCDaz7hu5qf14XoGxhNdIH2NoTieKiF7/2KkoWBzPdXuf+TOF69VEgMi+sLkrEpsLFLExyXKtGsikDE0RxYbYlnmTlMvY8pGOgy3EtXbysPgqEvOSC38TFJmnpiGupV1NIVSP5VWBsFxfXsi0u0lmc8yL+pfpOr39fHS9fucanbGOR76uNvG7r4vXNGYvN4tIRV1KvgLmB7XTjxyokioseXK0iciluAHbEZBevMxAAeckFv7Rzca1Ax+LKsVNgPsArgaG46MG1h1kkRrgQJ5Lh8rFH8GLuIyPysnz5cgwdOhRFRUWorKzExo0b09ruD3/4A/Lz83Heeedl9b25BAu/VBe5XigiuHAerg5qJzEwmmmBobjowYaYlS5+eOjH4uW52DD6bqZlRFxe1qxZg5tuugmLFy/Gtm3bcNFFF2HKlClobGxMuV04HMasWbPwqU99SvoQRfA6CPitYAPunFPsoHZS94ELWRgTAiMxxQDFxW5ciQPZ4OW5uXL9I4jLyz333IPrrrsOX/7yl1FRUYFly5Zh0KBBWLFiRcrtvvrVr2LmzJmoqqrK6nt7N3mbdfESvxbsCK6liaUkJugCIzEqr87j5VD/+nGlzOeKq+eZc/Ylg+e2qLwcP34cW7duRXV1ddzy6upq1NfXd7rdww8/jN27d+PWW2/t8jva2trQ0tIS9/EarwKBSw90Xbh0zkEWGJ1SIDWho25xkYDiEhy8OF8bqo/SRVReDh8+jFOnTqGsrCxueVlZGZqbm5Nu88Ybb2DhwoVYvXo18vO77sldW1uLUCgU/QwaNCinY871h/dSXIKMK+cvJTBBbAejE9vFRWoCT4qL3bgqMCYw0mA3Ly++D7dSKmEZAJw6dQozZ87E0qVLcc4556S170WLFiEcDkc/TU1NWo45Gygu3uLK78BqJLtwQVwkcOEh5VJmVQoXz99E9kV0kLqSkhJ07949Icty6NChhGwMALS2tmLLli3Ytm0b5s2bBwBob2+HUgr5+fn4zW9+g8suuyxum8LCQhQW6hnAK5cfnOJiBy5N+igxOq8LA9rpHswuF4IoLi6UD8Y1b7Fh8LquEJWXgoICVFZWYv369bj66qujy9evX48rr7wyYf3i4mK89tprccuWL1+O3/3ud/j5z3+OoUOHSh6uc5go4LE3X6pAmu56JgjCsNypoMCk9/06cUFcbCwPLkmKlzHOi5cyGyZvTIX49AALFixATU0Nxo4di6qqKvzkJz9BY2Mj5s6dC+B0tc9bb72F//7v/0a3bt0watSouO1LS0tRVFSUsFw3rmVdJG+qzh586T4Qu1rPVMF3QWKkAgQFJvX36sSFOYpsLAM2Pxi7Kjsd/24iprkoMJLZF3F5mT59Ot555x3cdtttOHDgAEaNGoV169ahvLwcAHDgwIEux3wh8UgVelMTbEW+hxJzGgqMOYEJmrjYeM/bKC25lhNTMuOiwEiRp5TydvIfzbS0tCAUCuG8mu+he0FRWtu4lHWRuIm8mhU0ghfVTDYGdcCd66tTYEzJC8XFe2x6CJqKe364rrlet3R/61PHj2H7o4sRDodRXFyccl3OKu0QrjzYsj0GkxJja8PeIDbiNZF9sVlcglBN5JW0+DG+MftymsBPzOh141IvsaFgxxI+u9DoMdlWGCNIdKWWGgtGF5JdqIMmLrbhRTkzHUvSQecxuTb+i8R9Hnh5yQWT9qvzZrWxYMdi8vhsFRhATmJ0YrPA6B7ZF3BDXGzJung1RovNsQ3Qd3w2xy4TBFpeXHnr0S0urmBKYmwfCIsC491+YqG4pA+zLalx5Tg7YlP2JdDykgu2BIlMcLXAmJQYW7G9GskmgQmquNiC6XLkkrTEouOYbY5Z0lBessDF6iIXC3dHgp6FsX1KARsEJsjiYsMLlRfi4jJBExid939g5cWFtx+KSyKmq5JiPzZAgdG3fjpQXNLHZBlxNduSDNcExoZ7DQiwvGSLqQtHcUmNF+dFgUkP0wIj0TAXsF9cIg26bXiYmCobfpIW3dgSn0xBefExfi/kDGR6cVFgpKTFZnGxRVgiSD80I+Xcz2XdtXOzoeFuIOXFhSqjXHGtMORCELtWSz28bBaYjqJie7YF8Mfoqp0hXZ3qd2HpiGvVR14TSHnJFleqjEwX+NbyvISPF1Bg9GCrwAAfSEzQxCUo2Rabsywm4ptLAuN19oXTA/gMW+ax6biN7gdDZ5iaasCW6QVcmNRR92SOEtguLrbgxWz2XtDV/Rr7d1OxzUa8nDYgcJmXXIKKiYtky1s9AK1vGaazMibe3my5VlJv5TZnYHRCcUkP6WyLl+SSOdYd11zKvnhJ4OQlF2wKJMnQGQAkJcNPEmNbN2qbR+O1TWB0N8wFKC6Z4pW0SFRz69yX1zKXCdnep7mWlUDJi+0NdW14CJoUC5NVCUHJwgD6JcaPAiNxHBSXzPCybZ709+gg19/HppgkQaDkJRdsCibJ0BEIvGiXwCyMHBQYc99v+4tRtkjcz6aribzoRGB7Gy8/EBh5ySW4mBAXrx96Xhc20xIjidfXMhYKjPz3+rU7tJS4mMTLuKbju5l96ZzAyIvNeN012mtxicWUxAQpC0OBkfs+ikv6+D3b0tlx5IpL7V9MQnnpAluCSWf49cb2U1WSDQRZYCQa5gL+FBcp6TYVp2yRlli8Ph7pGMSu0oLYXB/t9cPN64KVCr9UJXl9jSMEUWCk9u1XcZHAhLjYKC068etLai4EQl6yxYaAkgo/VRelwg9VSRSY1EhIBsUlPSSzLdIPXVekxetjtCX+6ITyQpzB9SyMLQEkCAIjVU3kF3GJCIur2RZXpCWWXI/X1uyLV9MEUF46weu3oa4IStalIyazMBLYIjA6sU1gXGnf4qW4SCL5kHVRWmzBb7GH8tIJfrvQsfih8JsIYlJpbxvuLT+OxCs1Yq5fsi2A/NxEUuLiF2lh9kUflBeSE22Djyd8TOJqFsaGrtR+EhgXsi2A/RndbKG0pI/fzidXsi1nlBcPyfbhlUug0FVwUomKaZExlYWRwGuJ8YPAUFzSw7X2LV4+5JO9lHnxcqYT6fvP9P1NeSEZk0kB9pPESPdG8kpivGx/0RVdVQVRXNKD4tI16QqKjnjG7Evu+F5ebB3jxYsHVa4FJhcRMS0xkvh1TBhdD1iJMpdMUigu6eFSN2jT1UTZZlRczsBIYvJe97282EguwcTWBlvp4qcsjBQUmOREsjCujJhrAy6NluuFtOS6DxKPydhFeekEr9+WbENnQfVLFoYCkxqXZEDqWP3Ws8h1cbGp3Qqrjj4gm/Lna3lxKXhKk0tBkSrspgKJZBbGxCiiXqBTYGwvhxSXrnG9mkgq1nghQtleB697N+rG1/KSLbZmXfz4kAT8IzG68TrY2DoSry4kxcpv4iKBy9JCvIfyEgBszLp4+V0UmPTxq8BISovXQ/7rxFVxMSktLsmR1/EkFZmWSd/KS/Ge7IKTrVmXoGAyCyMBBSY1NgiMVI8iP2VbADfFxbVMS7a/RS7Xxut4ogsj8rJ8+XIMHToURUVFqKysxMaNGztd9+mnn8anP/1pnHnmmSguLkZVVRWee+45E4dJOuBlEDARhKSqkSTaB/gl4ADeCYzUUP9ev/CwfYv30uKSMEmSa1nIJOkgLi9r1qzBTTfdhMWLF2Pbtm246KKLMGXKFDQ2NiZd/8UXX8SnP/1prFu3Dlu3bsUnP/lJfPazn8W2bdukD9UYXgc7l2AW5gP80AMpgmmB8eP4LQDbtwAUh2yQjCWmykWeUkr/gAkxjB8/HmPGjMGKFSuiyyoqKnDVVVehtrY2rX2MHDkS06dPxy233NLlui0tLQiFQrj4wluQn1+U8fGa+OFNTwuQbeCwLSgUNhaI7l9i7BDAPw9Ol6omYvHTxIod0XlNXBMXv8SnXOJOrve25L2czb158uQxvPj72xAOh1FcXJxyXdHMy/Hjx7F161ZUV1fHLa+urkZ9fX1a+2hvb0drayv69OmT9O9tbW1oaWmJ++R0zD5Kz/sN6dSwS92pvbhPJQKddAaG4pIeFJfcyfaYvBzvxeXnnai8HD58GKdOnUJZWVnc8rKyMjQ3N6e1j7vvvht///vfMW3atKR/r62tRSgUin4GDRqU83FLYvpm8UvWJRZpgWE1klkkBMaF8WVywXZxkSpHXrdtsQ2bh8+QFn0jDXbz8uJvYqVUwrJkPPHEE1iyZAnWrFmD0tLSpOssWrQI4XA4+mlqatJyzLZh803qBS5nYXRiWmCkGqjqlA0/jt0SiwviIoGfpSWX3yyozwZReSkpKUH37t0TsiyHDh1KyMZ0ZM2aNbjuuuvwP//zP7j88ss7Xa+wsBDFxcVxH1vxy5tyOgweeNjI91BgvKtCsrEaieKSPhQX/bhynBGk72vJ/YvKS0FBASorK7F+/fq45evXr8fEiRM73e6JJ57AF7/4RTz++OP4zGc+I3mICUj92EEUl8EDDxuRGMksjGR3ap14dX9JSEy2AuLnaiIgmOJispooEq9MvXiR3BCvNlqwYAFWrlyJVatWoaGhAfPnz0djYyPmzp0L4HS1z6xZs6LrP/HEE5g1axbuvvtuTJgwAc3NzWhubkY4HJY+VGtxqZdRsoLPLExy/CIwgExX6kxkRFJcbMi62Cwuku1bTJBMWLwQGL9O1ChVfsTlZfr06Vi2bBluu+02nHfeeXjxxRexbt06lJeXAwAOHDgQN+bLAw88gJMnT+Lf//3f0b9//+jnxhtvlD5UK4KUy6Qq8H7JwujGT/XVNlYj5YoNMcF2cZHAhLhIxSTXqo6kkXqpEh/nxTTZjvMiHaRyuYCuZF4yCQSN+0qy+o5MkBoXRmI8GJ0Paa8fuKbHg/HLODodsX0AOlfFxUScMj3mS7ZlwLZxzawZ54V8gA3B0CZczsJIpMl1Pli8bl9lMgOjW/psGe4/iOIi3b7FhfYspuc68jpW5ALlhWghm6BgsipJAgpM50h3p9Y9jovXwgLISAvgjrhI4YW0sOpIHsoL7AhctuBFoTMRXCgw5pEqVxLZFq+RulY67ycXG+bmGldsz9TowOs4kS2UF7h78VLhYst1CsxpdE4nIPU2ny42iEFn2HJsroiLBFJl0oUqIt3kcr1dfAZSXohVSAedILeDcTFASUFxSR/X2rfYIi0uznUkgbNdpclpTM8k7TomJEYC2wOPXyZ0zAXbjkc3LoiLBFIxwxYZIvFQXt6Hb6XZI1m4gy4wEvLqRRbGlrYlNhxDBNsb57omLsTel12Jckd5MYArYmRrC3nJLIxkNZIupAKSn+ZEcg2Kiz78KC62Z3BtgPIijEuD09mOa1kYFwTGK7yQGFukKWjiIvWCYLJRbrbfY+sLoRfoLn+UF+IU0lkY3dguMF5nBU1JjF/FRWfPNEBGXCTwY7bFS2wpH5lAeXkfiYvnRdYlKFBg/IWLwTMTgjhqLsWFSEJ58Rmmq4y8DCQutYOxWWC8zr5EkBIYr8XI9moiwA1xCeLYLaawJQZkAuUF3gc3G3C1btalaiTdAuOn0Xgj+KksSmVbgiouXmPDMbiM7rIQeHnxU7AMMkEUGMCf1Ug6y6Tp8h0RFheyLQDFxQSuvBja8gKTLoGXF0koRmahwOSGTcEr17LjRW8myd+P4hI8TM8wLYlE2Qi0vFAu/IdUNRIFxg28GkeG4qK3fLB9izdI3MdSZSPQ8kJyw+bgQoHJHlsEJlMJ8ePLSFDFRYpJ/RowqV+D2P79gC3lvysoL8L4MaDqQjqQSAmMzmBNgckdr0ftdWFyxQhBFZegSYstVUeScYTyIoxLDwFTdAwkkoHFhWokmwXG6/u3Kynx+uUgqOIiMZyApLgEjdDutqy3daXBfKDlxevAbAu2tIZ3MQujC1sFBrBDYpLhR3GR6gqtW1x0I1E+g5ZtsRWpchpoeSH2IZ2F0U1QBAbwTmKSBT+/iotuXKgmkhIXkjlel6tMCLy8SAbjbPfNCRnlgg8FJne8kJhIuxav27cAFBddsJooNb33qqy2y6XKSAqJMht4eZHCxjS7DWQSWCgwepBqvBfEe5ziogdWE9mH1y8FmUJ5QTCDsCtIBSSJdLXNAiNFkMqOK0P9B1VcbKWwscDrQ7AC3XJEeXkfnYEpCLNJmx7jxZUsjG6B0fUgcuW+shEXZoQGZISX4hIMXMu6AJSXKC5evKARRIEB9D2UWH2UGUGeowiguBC7obwIkIsI2djYKhmN+0o8+V7JaiSdUGDcRVJaKC56YPsWvbhYfikvkMm6MJMjCwUme6Qeoi4GQFNISWNQxcUlbBlHy2t0x4fAy4uNkuFK9iUbnmuu0LYvCkxuUGAScaWaCKC4EL24VnYDLy+SmBajbMcFcBkKTG5QYGSRqiaiuPifbK+xjY3zJWJCoOXFxqwLyRyJ+m/dXaltFxiJ0XhdI8g9iiguxDUCLS/kNH4Zh8D2LIztdd9+mU7ABlwSF91QXIgJKC/CMLtjliAJjMTDzC/TCWSKzuMLqrjozlayRxFJBeVFGNuDth+hwOSGZHdqG8sDxSV3mG3RD+c2So0ReVm+fDmGDh2KoqIiVFZWYuPGjSnXf+GFF1BZWYmioiJ89KMfxf333y9yXDYGUi+wvTojG6TawejCBYEJwpgwNosLG+YSk7hWSyAuL2vWrMFNN92ExYsXY9u2bbjoooswZcoUNDY2Jl1/z549+Od//mdcdNFF2LZtG7797W/jhhtuwFNPPSV9qNqxKUgHFQpMbtjYc0EXusqn1BxFumHDXG/wS5vCXHFubqN77rkH1113Hb785S+joqICy5Ytw6BBg7BixYqk699///0YPHgwli1bhoqKCnz5y1/Gl770Jdx1110ix2ejYGQbCF2YzM+L4BQkgXGlGsnrcqdTXHTjQrYFoLj4CdeyLoCwvBw/fhxbt25FdXV13PLq6mrU19cn3WbTpk0J60+aNAlbtmzBiRMnEtZva2tDS0tL3IcQl/BjtR0hxDw2tneRQlReDh8+jFOnTqGsrCxueVlZGZqbm5Nu09zcnHT9kydP4vDhRNOvra1FKBSKfgYNGqTvBAghhBBiHUYa7OblxadBlVIJy7paP9lyAFi0aBHC4XD009TUpOGICSGEELfwcxu1juRL7rykpATdu3dPyLIcOnQoIbsSoV+/fknXz8/PR9++fRPWLywsRGFhcC4Y8R9BbNDnYh07IcQeRDMvBQUFqKysxPr16+OWr1+/HhMnTky6TVVVVcL6v/nNbzB27Fj06NFD/zEKBtFs951tvaULcxvpnJjRq+9s3FeibV86xaX3XiVyD/ixHl1XuZf4bSSuoYQg6ywHgDexgZzG6wb02SBebbRgwQKsXLkSq1atQkNDA+bPn4/GxkbMnTsXwOlqn1mzZkXXnzt3Lvbu3YsFCxagoaEBq1atwkMPPYRvfvOb0odKfMZzzRWBEhcJJB7OtmRddAqM7t9JSmB0SwwFpmvYIP80ugVJXF6mT5+OZcuW4bbbbsN5552HF198EevWrUN5eTkA4MCBA3FjvgwdOhTr1q3D888/j/POOw//+Z//iXvvvRef//zntR+bLUHUa/xYbSERBIMkLhIPZBvRGQMkBMaFLAwFRgbTQ1+4ln3JU5HWsD6hpaUFoVAIF194C/Lzi1Kua0pesrkpTI/1ks3bQbbjPEiP50BxyQ0pabH5ZcHmkXYBjv2im2xjRLZxINsyb3qKAKkymm75OnnyGF78/W0Ih8MoLi5OuS7nNhLGNZt1HYpLbkhVE9ksLoDdGRiA7WAI6QjlhfimTlaifQvFJXtckBYpKDD6oMCQZARaXpgV8Qe2N8wF7G5XJNG+xUVp0X3MUgKjW2LYkJe4SKDlRRrTcuTC3Ea6sb2aCNAvLjofXsy2yCLVfsiFLAwFJjdMt3eRRCImBF5ebMy++HmURJ0N8CguucFsSyIS50CB0UfQBMYkrpXfwMsLICMwNkqRn6C4ZE9QukHbBAVGHxLVxJLYXGVsEt1yRHkRIBdxcSXrortLZLpIBa4giYsErr21pUKq6ktKGoMoMACzMDpxsfxSXt6HmRL7kQpWFJfccDHwpYOkxOiGAkOCBuXlfXQGqVz25Uo6XyIQpSKI4qKzZ4kr95WNSEiMSz2RdEKBsRMXX94pL/Dvm6MfkKwmsl1cdCEpLkEqOxIC40IWxhWBsVVi/DKOVq44N7dRUAlSUM+ETAKMK9kWwF5xkSSI93hQq5FcEBiAWZhccC37Enh5kQzA2e4722DmykOvKyTfooImLn4Z7v/48IFxHy+hwOiBApOabMftsrHTh0SZDby8ELuQDDwUl9zwagC6ZIGPApMeto/GK1F9C/hHYEzjdbnKhEDLSxDT3smwYRwC6WwLxSV7bB011+tA60p36iA35KXEeI9UOQ20vJjAxqDvNR2DimvZFiAY4mKDtHQV+PwoMIA7WRidsBpJH7lUHeksU5Llk/IijNfB1Wak34yksi1BERdX8LodDAVGH5ICEySJsWVoBMk4QnkhWWN6rJdMsL2aCKC4dEWmQuLHFwUKjF6CJjHZYEv574pAy4sfg13QcaF9C0Bx6Ypsy6ZXWRjJ3y2oAmPzy5FfkbiPpcpGoOVFGsqRWVxo3wJQXEzghcRIthEKosAAdmd3pcn2+thSZRSLRLkIvLxQMPxBEMXFr7NDu9JgsDOCPCcSBSYRG3pzpoNrLy+BlxeAAgNkX8C8DiyS6WXbxUUntgQuP5VFqTmRJLpS68SvAmPDMbiM7rJAeXkfvwRNv4yymw6S0kJxMY9UGfS6bLswsaMrAkOBkMGWGJAJlBdBgjC7tFe4km0B7BYXG/C6q7MpKDB6oMAQgPJCHMOlaiLAfnHx+o3LlLTYIke2VyNRYIKJLeUjEygvwniRffFr1ZFL1USA/eLiJV5kW2wJ0LY35rV9PqQIJquRsv0eVxrrmkB3+aO8GMDrt9t0sbWguZZtAdwQF68mWbRFIrwkaAIDMAuTCX59AdUJ5eV9XBEMG5EMHpL7Dqq4eDFnkS3SYsMxRKDA6MOPApMNtmZoJcod5cUQ2QYqW29GaaRTwkEUF68mWrRJGAD7jkc3QRYYiZhBMcoNzipNAoEJaZFq32K7uJAPsEVgXBiRV0pg/J6Fyfb8WGWUHpQX+DOwu1gApIOOC9kWQO+Dx6tsSwRbJCEZthybKwLDLIzd5HK9XXwGUl5gTxCzAS9G2jURaIIqLl4iVa7CZxdq25ctbXFcEBjArWokIPcXoiAIkNdxIlvyvT4AElxMBAbJwEhx6RwJIYiVlsi/df1mkeP18neLfLfu3y60u02r8PXeq9Banqdtf8Dpcto2+LjWfUaIxJnBAw+L7D8Ztvbc9BPMvBjChrc7m3BZXCRS6BSX1HT28NX5UAbsyMQEcToBQLYdDOBGVZLpmaS9jhW5QHl5H68DVlAwFUBcqSYCKC5d0ZWg6BYYwJ8S44LAAPJZi3RjkO2iE3QoLzF4HaxcJ1VhNyktQRUXr/FCXDJdL1NsiAkUGBlSxaRcYhWrjOKReqESlZcjR46gpqYGoVAIoVAINTU1OHr0aKfrnzhxAt/61rcwevRo9OrVCwMGDMCsWbOwf/9+ycM0gkvTBORS+JIVelNvMC5VEwH+6g6t+yEfPrtQTEgyhQKTGsmeSF5LjElc7CGaDk6O8zJz5kxs374ddXV1qKurw/bt21FTU9Pp+v/4xz/wyiuv4Dvf+Q5eeeUVPP3003j99ddxxRVXSB5mHDYEKteJBANmWzrHL+IiUb2SrbTYIjtS2CwwgNtZGABGYxbJnTyllMgd19DQgBEjRmDz5s0YP348AGDz5s2oqqrCzp07MWzYsLT288c//hHjxo3D3r17MXjw4C7Xb2lpQSgUwsUX3oL8/KKsjl3yQZBtoM82MGfbK0Cq5b9uXOpNFMEP4mJzN2g/zQWVDJ2/vYTw6e6JFMGFmJRLPDLdWDeCTc+7kyeP4cXf34ZwOIzi4uKU64plXjZt2oRQKBQVFwCYMGECQqEQ6uvr095POBxGXl4ezjjjjKR/b2trQ0tLS9zHj/ipbYQOpFPKFJfkSDVk1VlN5Of2LwAzMH7Er1VGkojJS3NzM0pLSxOWl5aWorm5Oa19HDt2DAsXLsTMmTM7tbDa2tpom5pQKIRBgwbldNzSDwPTDxsv2r1IYkJaKC5mkZANqTYzFJj0cL0djCvY/FIrXVYylpclS5YgLy8v5WfLli0AgLy8xPShUirp8o6cOHECM2bMQHt7O5YvX97peosWLUI4HI5+mpqaMj0l4gjSQUtSWvwgLl72JrJp/xSY9AlSFsbFuYxcfgHKeITdefPmYcaMGSnXGTJkCF599VUcPHgw4W9vv/02ysrKUm5/4sQJTJs2DXv27MHvfve7lHVfhYWFKCx0q6Fewc591gRAFzARqJhtMY+pBrbhswu1X4fjwwf66loA+kfijSAxIi/wQVxwoS2MBH5q65INGctLSUkJSkq6bo1dVVWFcDiMl19+GePGjQMAvPTSSwiHw5g4cWKn20XE5Y033sCGDRvQt2/fTA/Reigu6WHq7Yri0jW29CjK9ft0XhMbBEb3i5BrAgNQYrLBdXEBBNu8VFRUYPLkyZgzZw42b96MzZs3Y86cOZg6dWpcT6Phw4dj7dq1AICTJ0/iC1/4ArZs2YLVq1fj1KlTaG5uRnNzM44f541pGi9Ts6ayLVLjt/hJXHTjZZdmv04noBOJ+xeQbU8G+D9euUCuZaFlaPrlU3Scl9WrV2P06NGorq5GdXU1zj33XDz66KNx6+zatQvhcBgAsG/fPjzzzDPYt28fzjvvPPTv3z/6yaSHEpDZjxCL14Eo6JhqkOdKtgXwXlxs75prwzF4LTES94hr7WAA9xr0etE92ut4ogvRWaX79OmDxx57LOU6scPMDBkyBELDzgSaXFK2krO9dvweE0gGTopLamwQlwgS7WAAb2enlpiV2sVqJMBsVZJLsuR1PElF+OxC4PixtNfn3EZJsDX7YnO3uFxwXVyk0uxeBxq/iksEySkI/JSFcbUaCXAvE0PSx9fykktgslVgsiWXICFV+E1WEblUTWQDuu5/m+Yo6gwKTHq4WI0UQSrWeCFG2V4Hr1+GdONreSH60FlITb4NuVZNFMEPPYtsl5ZYKDDp4bLAAHZlYjiq7gdkU/4oLx7gxQzTtmBSWigumWOzuLSW58V9dOOSbKWLlMC4NK1AMnRIjC0SZBMmY5fv5cXWgOTFAyrX4JBLgfdTtoXikhpTk/25IjBeV0FL3VOutoOJJRKXMo1NFJfkmLzXfS8vRD+ZFFzT0uJytsUrcfG6m28qusqyUGDSwyWBAbypUokVmVQxS0c8Y5VR7lBePCTbgJJLwNBVaFIV8GzfZrLFxNuaVJD2UloAu0fOTVdMKDDpQYHJjI4yY1N7mWyQvv9M39+i47wQ/+N1YTYR4PzYDRrwh7h0XF/n/eDXKQUkkBwPBpARVK/wWspsI9v7hpmXTrA9wNiQffESU9kWikt6eCkuurbtDIkpBbxC8t6TbA9mui2MFLmeg60dNry4pykvneB1ilcaVwOBqSAmWU3kN2wRF5376Iif5kSSvgclH7B+kRgv8FvsobwQZzAVtPwuLraOnKtTOqQExi9ZmEhbK9fawURwUWKYdUkkl/JEeUmB7dmXXG9mVwq/yWwLxSV9bBUXyX0C/qpGAuQajUsPKwC4IzFeH6Mt8UcngZAXW8d6Aby/qbwuVKkwGZj8OnZLLEESF+l9+01gAPd6I8XiisRkC2eRTiQQ8pILNgSVVNiaSswVk9JCcckMV8Ql9jtcaQfjNZJZGBPYKDG2HY9uvIpxlBcLyPXi+6n6yA9VRID347fEEmRxkf4+PwoM4Na8SMmwRWJ0HINfX1BzJTDyYvsM014/6Lwu6H6pIgK8v5axUFzkv5cCkz6mH8RexjUbxMWmWKSbwMhLrtgSUDpDR1DwoqCblpagZFsAiovJ77e5XV0uuNqQNxYvsjBevwwGgUDJi+0BxoYHn6mC7idpAey4dhF0jyHiJ3GJYLvA2PSy5HJD3lgiMUc67ujaP7MuqQmUvOSKTQElGTqDgWQBN/lWYkJabAkSEgOf+VFcIkg05KXAZIZX7TliRUaX0OgUI5fauWR7n+ZaVgInL7n8YCYeUl433o1FZ2E09dYTIUjZFqnRWv0sLrFQYNJDUmBseFhnG6N0xzUdv4UtsUkSTsxIuiSdgtnxAeBVna+pIGhLcJB6uAVFXCK0ludpn9RR171o02SOkeOQuO+kJnfMhmT3Qux9zDYtp/FSrgOXeckFUxfKpuxLuuhOwWYDxUUPNotL2+Dj0Y9ubM/ABCkLY0MmpiMm4ptLWRevpgWIEEh5scXuJbGx8EthMthRXNJHpwwkExYpgdF53H7tRg3It/eyWWQkcElcbCCQ8hIU/F7ogxTYTGCzuGTzt1ywXWBsysSYeGD6vay7dm5eZ10AykvGuFJ1FMG1QpEuXpyXLW81QWqcm46cuFCNJJXttUViTJUNP0qMrvOxJT6ZIrDy4kLVEQUmEVPBK5ISj/3YAMVF3/rp4ILAAHZUJ5ksI36UmFww+dvbcK8BAZaXXDB58SgwpzEtLTZCcZHbLhUUmPQxXXb8ENdyxdZ4lQyd93+g5cX2+Y5042pBD1pj3GRIDD7nN3HRtX0yXBEYG/BCYFyMbUETF90EWl5cQecN6lIhZ7blNDaPmgvYJS669xOLCwJjy0uVF+XJJYlx5Tg7YkND3QiUlxxwsfoIsL+QB7HrczJsH+4fsFNcYvene58UmPTx6qXA5tgGsIGuLgIvL35P4abCtkJuWqpsLfxS0hIkcZHct26B8XsMYhbmNDqPyYvf1KasC8DpAZyiYOc+7Q81G4bkNh1kbJUWwP5GuRFcEZfY7yhsLNC2P5unEwDsmlIAkJ1WIBWpflNTcU93fHNNXKQIfOYFcKvhrsSN69VbiheZFpsCeiwuTK4YwTVxkfoum6cTAOwZAyYWm8qf5Ai+QRsdOBVSksjMi4NIZGCAD94QpN9ImGmJx4Wh/iO4Ki6x3xmkDAzALEw6dPzNMy07fm6jZ9N1ikU083LkyBHU1NQgFAohFAqhpqYGR48eTXv7r371q8jLy8OyZcvEjjGCS9kXQPYmjn1riC2UHZd39naRaj1mWuKhuJjHhQyMn+dEimBz2cw0xpnARXGRfBEWzbzMnDkT+/btQ11dHQDgK1/5CmpqavCrX/2qy21/8Ytf4KWXXsKAAQMkD9FppDIwHUmncNqUHrU5KMZCcfGOyDHoysLozsAAMu1gALvKR2fHYqNseRnjXBQXacQyLw0NDairq8PKlStRVVWFqqoqPPjgg/j1r3+NXbt2pdz2rbfewrx587B69Wr06NFD6hATcC37AtgViGzAld+D4mIHOo9HdwYGkLmeNraF6YgLWVM/o+P+kG5+ICYvmzZtQigUwvjx46PLJkyYgFAohPr6+k63a29vR01NDW6++WaMHDmyy+9pa2tDS0tL3McrKDDe4srv4Iq4tJbn+VpcIrggMFISYzuUGHfiWiwmenKJyUtzczNKS0sTlpeWlqK5ubnT7e644w7k5+fjhhtuSOt7amtro21qQqEQBg0alPUxA7n/6F4KjIs3uS5cOXepHkU2j+EC2CsuEWwXGEAuC+MCrpRv3bC6qHMylpclS5YgLy8v5WfLli0AgLy8xEKslEq6HAC2bt2KH/7wh3jkkUc6XacjixYtQjgcjn6ampoyPSXteHnxg1bIXZG2oHaFBvSLy+CBhzF44GGt+wQoMLbjQjnXiaviYmr8nIwb7M6bNw8zZsxIuc6QIUPw6quv4uDBgwl/e/vtt1FWVpZ0u40bN+LQoUMYPHhwdNmpU6fwjW98A8uWLcNf//rXhG0KCwtRWJj4Y7UOysMZiV+fFhLdFU1iqiGvV7gUxCSvQ1DFpeO/G/eVaNu/zq7Ukd/S9oa8gH3dqTvD77EtggvXIhm5xqTWQenHn4zlpaSkBCUlXQeLqqoqhMNhvPzyyxg3bhwA4KWXXkI4HMbEiROTblNTU4PLL788btmkSZNQU1ODa6+9NtNDzYlcA4TXwcDGsRRyxYUCber3Drq4dFxuq8AAbvREAryPWenix9gWwcvf37XfU6zNS0VFBSZPnow5c+Zg8+bN2Lx5M+bMmYOpU6di2LBh0fWGDx+OtWvXAgD69u2LUaNGxX169OiBfv36xW2TLlKp23Sx4WZwIRilgwvnYeJ6S7VvcVVc0v17ptg+FgwQ7CokwJ0q43RxXVxyzrpkWEZEB6lbvXo1Ro8ejerqalRXV+Pcc8/Fo48+GrfOrl27EA6HJQ8ja7ye80cXLhdyV47dlLjoRuKhalpcMl0vXSgwbhCJES7EiWS4fOwRTIsLAOQppfTmMz2mpaUFoVAIZ3/7++heVAQgtzpnHalZm25MVwKTTb9ZV1BcPsArcYlFZxUSoG8guwi6q5AAuQHUXCqHsTDOpY8No+hGYtGpY8ew+/vfRjgcRnFxccptOLdRF+ioW7apLtnm+mJbfqNMoLh8gA3iEtnO9jYwgF6JidwjEu1gAPfKZrKGvR3PwVQMtPm3s+E5kG0sCsSs0rkGah0PDxtuklhsKlCupk2lr6nU4GR+Fhdd23dEYpwaV6qRAPviVzrEVicliy/SccfVuJYJXjatCIS86MAv7V9iSVa40i1sutZztXCbEBcJgiAuuvcTgQJj/7QC2ZBKbtLdPp392YZN1UXZEIg2LxFyTdP6rf1LOnSVes10PT/gori4IC2AfuGIoLMaSXcbGMCtdjCAv8t3MvwW32ztXcQ2L52Q63gLfmv/kg66MzEu46K0ABSXyL51CYzuNjCA3FgwgF0zvrtKEOJbJthQE8FqowzxY/sXkhoT6XKKi5y4SHyHVBWSK9VIjGHu4np1UYTAyYvXA9dFYOG3H1PSEmRxkZqnKNX36aJt8PFAt4NhDHMPG66Zrvs7cPIC2NH7CLDjRiKJmGqYKJl6dUVcvIANefXh10a8fsSGdi46CaS86IAC409cHeI/gtRQ/34RF6nvD7LAAIxjtmOLuOi8pwMrLzp+RAqMv3C5ighwI9sCeC8uEYIsMMzCBAdbronuezmw8gJQYMhpXG6QG4Hikh1BFRiA48EEAV3XwYu5i7oiUF2lbce1btR+wHVpASguuSIxnQCgdzwYiSkFAD3DP3RGZ2WLMc4MtoiLFIHOvAB2ZV8AZmBM4ZdsC8VFDxLH50oWRro6syOMcfLYJC5SmcPAywtgp8CwgOsn8ru63pMIkAsILojLpH4NmNSvQes+gWALDGD2DZvxTY4giAtAeYlim8AALOC6MCmDJt5ipbItLozhEistEhJDgTErMIxxegnS70l50QwFxi5M/n6sJvoACQnoTFSCLDAudafuDEpM7uj+DW3PugCUlzh0/dgSAsPCnTnMtnSN6+KS7t8zxRWBAfzRDgYwW63rJ3T/Xi6IC0B5ScBWgQEoMeliuppIEqm3a8A/4hK7nk6Jkaj2cmlKAcC7niaMdekRVHEBKC9JsVlgAFYlpYLZlvRwQVyylZGgZmH8JjAAY11nSMidrV2iO4Py0gkUGLcw2YvI9WyLK+Li5fYdcUlg/FKNFIGxLh6J30PXtTU58THlxQAcyVIOP0kL4Ga2xTZx0b2fCK4IDOC/LEzQ4xwgF+tsEpfjg9IvD76Vl0x+hM7QGQAkC30QJcZP7VoA2WwL4EY1EaBfOCgw+vEqCxPEOAfInrdN4pJpOfCtvAB6goIrAgME4+3Eb2O2APLZlqCKi9R+2ZD3NDZKjJ96LEmfh2ttXDrCuY3SoLU8T9ucIpEbRno+Eb/NH2I6GLkuLYDcG71L4hK7/+eaK7TuU/ecSMDpa6ZzTiRAbl6kCNIxrTO6igkuzBXnlWTpjG9eZF0An2deAH0BXPeDxkQWhm8fmeOHbAtAcTH1PaxG+oBI2bHpjd7WOOjlcflBXICAZF50vc3ozMAAsjO6RuiYibElM9PVjLN+zLQAlJZYTElLx+8MagYG0B/DOiO2PJnOyCSjszgYu8z095pGd4zzUlwAIE8pJX8nG6SlpQWhUAiDVixBt55FcX/TFQwkCr+XBbyrwpuu8KSbprXpTcjkWyLF5QO8EJdYdAsMAO0CE0FCYkwITEdskJhU6IyDtmGjuACJMav9vWNoun4JwuEwiouLU27r+2qjWGytQgK8HwgqWYHruLyrRnKp9tXV37zAZLaF4vIBXouL1DFI/FaAW+PBpMK2KqWOdBW7ulrPtvgWwRVxyZRAZV4AvW8xUm8vtr+huA6zLenhV3HpiCtZGIkMDOBNFgZgnJNGIs5JiwszLynQGez9NhBUEGC2pWskugIDdooL4E4WRrIhr+ksDMA4J4mL4pIpgZMXwB2BYeHWh8leRCakxaVqIsBecYngksC42hspGYxzepH6PW0TFyCg8gK4ITAA305yxWRwNBH8Xawmsl1cIrgiMIA/szCMdbkh9ft5cT+kQyC6SneGzu6Ikl0QvRoEymX81K4FkJUWwJ32LVcXb0tYtrblfG37d6UrNSDXnRow16W6IyaGj/AbkrFOZ2zTHcMCm3mJoDsDwyyMt5jOtLguLi61b0kmLqmWZ4tUBsaldjAAszC2I/072SwugLC8HDlyBDU1NQiFQgiFQqipqcHRo0e73K6hoQFXXHEFQqEQevfujQkTJqCxsVHsOHX/sH6cT8R2TP8upqTFtWoiwKy4pPv3TJGq7nKtHQxAibENE7+L7eICCMvLzJkzsX37dtTV1aGurg7bt29HTU1Nym12796NCy+8EMOHD8fzzz+PP/3pT/jOd76DoqLEbs86cUlgABbsCF5Ii+vZFsBf4pLpepngisAA8vcMJcZbTEmLC+ICCI7z0tDQgBEjRmDz5s0YP348AGDz5s2oqqrCzp07MWzYsKTbzZgxAz169MCjjz6a1fd2Nc5LV+iuQzZVbxy0emLTwcxU0Ka0xJONkOhsAxPBlbFgALnxYDri1fgwEfwe81yPcdnEMivGedm0aRNCoVBUXABgwoQJCIVCqK+vT7pNe3s7nn32WZxzzjmYNGkSSktLMX78ePziF7/o9Hva2trQ0tIS97EJUw+9IL2ZuF6oO8NVcZEi20wKMzCy91EErzIxEWIngrRxUshs8Oo8bBCXTBHrbdTc3IzS0tKE5aWlpWhubk66zaFDh/Duu+/i9ttvx3e/+13ccccdqKurw+c+9zls2LABl1xyScI2tbW1WLp0acLyP8+c36W5EUL8yQiBfS4eKbBTQkiUlpYWhK5fkta6GWdelixZgry8vJSfLVu2AADy8hJtTimVdDlwOvMCAFdeeSXmz5+P8847DwsXLsTUqVNx//33J91m0aJFCIfD0U9TU1Omp0QIIYQQh8g48zJv3jzMmDEj5TpDhgzBq6++ioMHDyb87e2330ZZWVnS7UpKSpCfn48RI+LfmyoqKvD73/8+6TaFhYUoLHQ7VUgIIYSQ9MlYXkpKSlBS0nVDs6qqKoTDYbz88ssYN24cAOCll15COBzGxIkTk25TUFCAT3ziE9i1a1fc8tdffx3l5eWZHiohhBBCfIhYg92KigpMnjwZc+bMwebNm7F582bMmTMHU6dOjetpNHz4cKxduzb6/5tvvhlr1qzBgw8+iL/85S+477778Ktf/Qpf+9rXpA6VEEIIIQ4hOs7L6tWrMXr0aFRXV6O6uhrnnntuQhfoXbt2IRwOR/9/9dVX4/7778edd96J0aNHY+XKlXjqqadw4YUXSh4qIYQQQhxBbJwXr4iM85JOP3FCCCGE2EEmz+/Az21ECCGEELegvBBCCCHEKSgvhBBCCHEKygshhBBCnILyQgghhBCnoLwQQgghxCkoL4QQQghxCsoLIYQQQpyC8kIIIYQQp6C8EEIIIcQpKC+EEEIIcQrKCyGEEEKcgvJCCCGEEKegvBBCCCHEKSgvhBBCCHEKygshhBBCnILyQgghhBCnoLwQQgghxCkoL4QQQghxCsoLIYQQQpyC8kIIIYQQp6C8EEIIIcQpKC+EEEIIcQrKCyGEEEKcgvJCCCGEEKegvBBCCCHEKSgvhBBCCHEKygshhBBCnILyQgghhBCnoLwQQgghxCkoL4QQQghxCsoLIYQQQpyC8kIIIYQQp6C8EEIIIcQpKC+EEEIIcQpReTly5AhqamoQCoUQCoVQU1ODo0ePptzm3Xffxbx58zBw4ED07NkTFRUVWLFiheRhEkIIIcQhROVl5syZ2L59O+rq6lBXV4ft27ejpqYm5Tbz589HXV0dHnvsMTQ0NGD+/Pn4+te/jl/+8peSh0oIIYQQRxCTl4aGBtTV1WHlypWoqqpCVVUVHnzwQfz617/Grl27Ot1u06ZNmD17Ni699FIMGTIEX/nKV/Dxj38cW7ZskTpUQgghhDiEmLxs2rQJoVAI48ePjy6bMGECQqEQ6uvrO93uwgsvxDPPPIO33noLSils2LABr7/+OiZNmpR0/ba2NrS0tMR9CCGEEOJfxOSlubkZpaWlCctLS0vR3Nzc6Xb33nsvRowYgYEDB6KgoACTJ0/G8uXLceGFFyZdv7a2NtqmJhQKYdCgQdrOgRBCCCH2kbG8LFmyBHl5eSk/kSqevLy8hO2VUkmXR7j33nuxefNmPPPMM9i6dSvuvvtufO1rX8Nvf/vbpOsvWrQI4XA4+mlqasr0lAghhBDiEPmZbjBv3jzMmDEj5TpDhgzBq6++ioMHDyb87e2330ZZWVnS7d577z18+9vfxtq1a/GZz3wGAHDuuedi+/btuOuuu3D55ZcnbFNYWIjCwsLo/5VSAMDqI0IIIcQhIs/tyHM8FRnLS0lJCUpKSrpcr6qqCuFwGC+//DLGjRsHAHjppZcQDocxceLEpNucOHECJ06cQLdu8Qmh7t27o729Pa3ja21tBQBWHxFCCCEO0trailAolHKdPJWO4mTJlClTsH//fjzwwAMAgK985SsoLy/Hr371q+g6w4cPR21tLa6++moAwKWXXorDhw/jvvvuQ3l5OV544QVcf/31uOeee3D99dd3+Z3t7e3Yv38/evfunbJ6KlNaWlowaNAgNDU1obi4WNt+bcLv5+j38wP8f45+Pz+A5+gH/H5+gMw5KqXQ2tqKAQMGJCQxOpJx5iUTVq9ejRtuuAHV1dUAgCuuuAL33Xdf3Dq7du1COByO/v/JJ5/EokWLcM011+Bvf/sbysvL8b3vfQ9z585N6zu7deuGgQMH6juJDhQXF/v2Zozg93P0+/kB/j9Hv58fwHP0A34/P0D/OXaVcYkgKi99+vTBY489lnKdjomffv364eGHH5Y8LEIIIYQ4DOc2IoQQQohTUF7SpLCwELfeemtczya/4fdz9Pv5Af4/R7+fH8Bz9AN+Pz/A+3MUbbBLCCGEEKIbZl4IIYQQ4hSUF0IIIYQ4BeWFEEIIIU5BeSGEEEKIU1Be3ud73/seJk6ciA996EM444wz0tpGKYUlS5ZgwIAB6NmzJy699FL83//9X9w6bW1t+PrXv46SkhL06tULV1xxBfbt2ydwBl1z5MgR1NTURGfgrqmpwdGjR1Nu09nkmz/4wQ+i61x66aUJf+9q/isJsjm/L37xiwnHPmHChLh1XL6GJ06cwLe+9S2MHj0avXr1woABAzBr1izs378/bj0vr+Hy5csxdOhQFBUVobKyEhs3bky5/gsvvIDKykoUFRXhox/9KO6///6EdZ566imMGDEChYWFGDFiBNauXSt1+F2Syfk9/fTT+PSnP40zzzwTxcXFqKqqwnPPPRe3ziOPPJK0TB47dkz6VDolk3N8/vnnkx7/zp0749az6RoCmZ1jsriSl5eHkSNHRtex6Tq++OKL+OxnP4sBAwYgLy8Pv/jFL7rcxvNyqIhSSqlbbrlF3XPPPWrBggUqFAqltc3tt9+uevfurZ566in12muvqenTp6v+/furlpaW6Dpz585VZ511llq/fr165ZVX1Cc/+Un18Y9/XJ08eVLoTDpn8uTJatSoUaq+vl7V19erUaNGqalTp6bc5sCBA3GfVatWqby8PLV79+7oOpdccomaM2dO3HpHjx6VPp0Esjm/2bNnq8mTJ8cd+zvvvBO3jsvX8OjRo+ryyy9Xa9asUTt37lSbNm1S48ePV5WVlXHreXUNn3zySdWjRw/14IMPqh07dqgbb7xR9erVS+3duzfp+m+++ab60Ic+pG688Ua1Y8cO9eCDD6oePXqon//859F16uvrVffu3dX3v/991dDQoL7//e+r/Px8tXnzZvHz6Uim53fjjTeqO+64Q7388svq9ddfV4sWLVI9evRQr7zySnSdhx9+WBUXFyeUTa/I9Bw3bNigAKhdu3bFHX9sebLpGiqV+TkePXo07tyamppUnz591K233hpdx6bruG7dOrV48WL11FNPKQBq7dq1Kde3oRxSXjrw8MMPpyUv7e3tql+/fur222+PLjt27JgKhULq/vvvV0qdvoF79Oihnnzyyeg6b731lurWrZuqq6vTfuyp2LFjhwIQd+Ns2rRJAVA7d+5Mez9XXnmluuyyy+KWXXLJJerGG2/UdahZke35zZ49W1155ZWd/t2P1/Dll19WAOICr1fXcNy4cWru3Llxy4YPH64WLlyYdP3/+I//UMOHD49b9tWvflVNmDAh+v9p06apyZMnx60zadIkNWPGDE1HnT6Znl8yRowYoZYuXRr9f7oxyhSZnmNEXo4cOdLpPm26hkrlfh3Xrl2r8vLy1F//+tfoMtuuY4R05MWGcshqoyzZs2cPmpubo/M2AacH7bnkkktQX18PANi6dStOnDgRt86AAQMwatSo6Dqm2LRpE0KhEMaPHx9dNmHCBIRCobSP5eDBg3j22Wdx3XXXJfxt9erVKCkpwciRI/HNb34zOru3KXI5v+effx6lpaU455xzMGfOHBw6dCj6N79dQwAIh8PIy8tLqB41fQ2PHz+OrVu3xv22AFBdXd3p+WzatClh/UmTJmHLli04ceJEynVMX69szq8j7e3taG1tRZ8+feKWv/vuuygvL8fAgQMxdepUbNu2TdtxZ0Iu53j++eejf//++NSnPoUNGzbE/c2WawjouY4PPfQQLr/8cpSXl8ctt+U6ZooN5VB0biM/09zcDAAoKyuLW15WVoa9e/dG1ykoKMBHPvKRhHUi25uiubkZpaWlCctLS0vTPpaf/vSn6N27Nz73uc/FLb/mmmswdOhQ9OvXD3/+85+xaNEi/OlPf8L69eu1HHs6ZHt+U6ZMwb/8y7+gvLwce/bswXe+8x1cdtll2Lp1KwoLC313DY8dO4aFCxdi5syZcZOpeXENDx8+jFOnTiUtQ52dT3Nzc9L1T548icOHD6N///6drmP6emVzfh25++678fe//x3Tpk2LLhs+fDgeeeQRjB49Gi0tLfjhD3+ICy64AH/605/wsY99TOs5dEU259i/f3/85Cc/QWVlJdra2vDoo4/iU5/6FJ5//nlcfPHFADq/zqavIZD7dTxw4AD+93//F48//njccpuuY6bYUA59LS9LlizB0qVLU67zxz/+EWPHjs36O/Ly8uL+r5RKWNaRdNZJl3TPEUg81kyPZdWqVbjmmmtQVFQUt3zOnDnRf48aNQof+9jHMHbsWLzyyisYM2ZMWvvuDOnzmz59evTfo0aNwtixY1FeXo5nn302QdIy2W8mmLqGJ06cwIwZM9De3o7ly5fH/U3yGnZFpmUo2fodl2dTLqXI9lieeOIJLFmyBL/85S/jpHXChAlxjcovuOACjBkzBj/60Y9w77336jvwDMjkHIcNG4Zhw4ZF/19VVYWmpibcddddUXnJdJ8myPZ4HnnkEZxxxhm46qqr4pbbeB0zwety6Gt5mTdvXpc9JoYMGZLVvvv16wfgtIH2798/uvzQoUNR2+zXrx+OHz+OI0eOxL25Hzp0CBMnTszqezuS7jm++uqrOHjwYMLf3n777QQ7TsbGjRuxa9curFmzpst1x4wZgx49euCNN97I+cFn6vwi9O/fH+Xl5XjjjTcA+OcanjhxAtOmTcOePXvwu9/9rssp7HVew84oKSlB9+7dE97EYstQR/r165d0/fz8fPTt2zflOpncBzrI5vwirFmzBtdddx1+9rOf4fLLL0+5brdu3fCJT3wies+aJJdzjGXChAl47LHHov+35RoCuZ2jUgqrVq1CTU0NCgoKUq7r5XXMFCvKoZaWMz4i0wa7d9xxR3RZW1tb0ga7a9asia6zf/9+Txt7vvTSS9FlmzdvTrux5+zZsxN6qHTGa6+9pgCoF154IevjzZRczy/C4cOHVWFhofrpT3+qlPLHNTx+/Li66qqr1MiRI9WhQ4fS+i5T13DcuHHq+uuvj1tWUVGRssFuRUVF3LK5c+cmNBScMmVK3DqTJ0/2rMFuJuenlFKPP/64Kioq6rLRZIT29nY1duxYde211+ZyqFmTzTl25POf/7z65Cc/Gf2/TddQqezPMdI4+bXXXuvyO7y+jhGQZoNdr8sh5eV99u7dq7Zt26aWLl2qPvzhD6tt27apbdu2qdbW1ug6w4YNU08//XT0/7fffrsKhULq6aefVq+99pr613/916RdpQcOHKh++9vfqldeeUVddtllnnazPffcc9WmTZvUpk2b1OjRoxO62XY8R6WUCofD6kMf+pBasWJFwj7/8pe/qKVLl6o//vGPas+ePerZZ59Vw4cPV+eff77xc8z0/FpbW9U3vvENVV9fr/bs2aM2bNigqqqq1FlnneWba3jixAl1xRVXqIEDB6rt27fHdclsa2tTSnl7DSNdUB966CG1Y8cOddNNN6levXpFe2UsXLhQ1dTURNePdNGcP3++2rFjh3rooYcSumj+4Q9/UN27d1e33367amhoULfffrvnXaXTPb/HH39c5efnqx//+MeddltfsmSJqqurU7t371bbtm1T1157rcrPz4+TWpNkeo7/9V//pdauXatef/119ec//1ktXLhQAVBPPfVUdB2brqFSmZ9jhH/7t39T48ePT7pPm65ja2tr9JkHQN1zzz1q27Zt0R6JNpZDysv7zJ49WwFI+GzYsCG6DgD18MMPR//f3t6ubr31VtWvXz9VWFioLr744gTDfu+999S8efNUnz59VM+ePdXUqVNVY2OjobOK55133lHXXHON6t27t+rdu7e65pprErordjxHpZR64IEHVM+ePZOO+9HY2Kguvvhi1adPH1VQUKDOPvtsdcMNNySMlWKCTM/vH//4h6qurlZnnnmm6tGjhxo8eLCaPXt2wvVx+Rru2bMn6X0de297fQ1//OMfq/LyclVQUKDGjBkTl+2ZPXu2uuSSS+LWf/7559X555+vCgoK1JAhQ5JK9c9+9jM1bNgw1aNHDzV8+PC4B6NpMjm/Sy65JOm1mj17dnSdm266SQ0ePFgVFBSoM888U1VXV6v6+nqDZ5RIJud4xx13qLPPPlsVFRWpj3zkI+rCCy9Uzz77bMI+bbqGSmV+nx49elT17NlT/eQnP0m6P5uuYyRD1Nl9Z2M5zFPq/VY2hBBCCCEOwHFeCCGEEOIUlBdCCCGEOAXlhRBCCCFOQXkhhBBCiFNQXgghhBDiFJQXQgghhDgF5YUQQgghTkF5IYQQQohTUF4IIYQQ4hSUF0IIIYQ4BeWFEEIIIU5BeSGEEEKIU/w/xf3uaohsSPkAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Y,ad.remove_ad(isoOut['values'])); plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.561489Z", "iopub.status.busy": "2024-04-30T08:56:26.561364Z", "iopub.status.idle": "2024-04-30T08:56:26.628635Z", "shell.execute_reply": "2024-04-30T08:56:26.628341Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var = isoOut['values'].gradient()\n", "plt.quiver(X[::5,::5],Y[::5,::5],var[0,::5,::5],var[1,::5,::5]); plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.630484Z", "iopub.status.busy": "2024-04-30T08:56:26.630370Z", "iopub.status.idle": "2024-04-30T08:56:26.632955Z", "shell.execute_reply": "2024-04-30T08:56:26.632711Z" } }, "outputs": [], "source": [ "distGamma = ad.remove_ad(isoOut['values'])\n", "baseSpeed = np.exp(-(distGamma/0.1)**2)+0.1\n", "baseCost = 1/baseSpeed\n", "\n", "tgtGammaX,tgtGammaY = var\n", "tgtGammaN = np.sqrt(tgtGammaX**2+tgtGammaY**2)\n", "tgtGammaX,tgtGammaY = tgtGammaX/tgtGammaN,tgtGammaY/tgtGammaN" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.634402Z", "iopub.status.busy": "2024-04-30T08:56:26.634291Z", "iopub.status.idle": "2024-04-30T08:56:26.698483Z", "shell.execute_reply": "2024-04-30T08:56:26.698213Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAGfCAYAAACX9jKsAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAABVzUlEQVR4nO3dfXhU1YE/8G8gJEEkgxgTQCBQV3m3llAgqMWqjbC1FtsuUN1AuxZLu1SBtltSf63g2kasWmotoCjaIirbKlYrm0pXVGpAC0LVgmiRmghEjIVJqBJecn5/0BkzmZf7ds6959z7/TzPPA9M7rzcufec+c55u3lCCAEiIiIiQ3QJ+g0QEREROcHwQkREREZheCEiIiKjMLwQERGRURheiIiIyCgML0RERGQUhhciIiIyCsMLERERGYXhhYiIiIzC8EJERERGyffjRZYuXYqf/OQn2L9/P0aMGIElS5bgwgsvzLr96tWrceutt+LNN99ELBbDpEmTcNttt+H000+3fK329nbs27cPPXv2RF5enszdICIiIkWEEGhtbUW/fv3QpYtF24pQ7JFHHhHdunUTK1asEDt27BDXX3+96NGjh3j77bczbr9x40bRpUsX8bOf/Uy89dZbYuPGjWLEiBFiypQptl6vsbFRAOCNN95444033gy8NTY2Wn7X5wmh9sKM48aNw+jRo7Fs2bLkfcOGDcOUKVNQW1ubtv1tt92GZcuWYffu3cn7fv7zn+PWW29FY2Oj5evF43H06tULjY2NKC4ulrMTREREpFRLSwsGDBiAQ4cOIRaL5dxWabfR0aNHsXXrVixYsCDl/qqqKtTX12d8zIQJE3DDDTdg3bp1mDx5Mg4cOIDf/OY3+OxnP5tx+7a2NrS1tSX/39raCgAoLi5meCEiIjKMnSEfSgfsNjc348SJEygrK0u5v6ysDE1NTRkfM2HCBKxevRrTpk1DQUEB+vTpg169euHnP/95xu1ra2sRi8WStwEDBkjfDyIiItKHL7ONOqcoIUTWZLVjxw5cd911+OEPf4itW7eirq4Oe/bswezZszNuX1NTg3g8nrzZ6VoiIiIicyntNiopKUHXrl3TWlkOHDiQ1hqTUFtbi/PPPx/f/e53AQDnnnsuevTogQsvvBA333wz+vbtm7J9YWEhCgsL1ewAERERaUdpy0tBQQEqKiqwfv36lPvXr1+PCRMmZHzMBx98kDZFqmvXrgBOttgQERFRtCnvNpo/fz7uvfderFy5Ejt37sS8efPQ0NCQ7AaqqanBjBkzktt/7nOfw2OPPYZly5bhrbfewgsvvIDrrrsOY8eORb9+/VS/XSIiItKc8kXqpk2bhvfffx833XQT9u/fj5EjR2LdunUoLy8HAOzfvx8NDQ3J7b/yla+gtbUVd911F7797W+jV69euPjii7F48WLVb5WIiIgMoHydF7+1tLQgFoshHo9zqjQREZEhnHx/89pGREREZBSGFyIiIjIKwwsREREZheGFiIiIjMLwQkREREZheCEiIiKjMLwQERGRURheiIiIyCgML0RERGQUhhciIiIyCsMLERERGYXhhYiIiIzC8EJERERGYXghIiIiozC8EBERkVEYXoiIiMgoDC9ERERkFIYXIiIiMgrDCxERERmF4YWIiIiMwvBCRERERmF4ISIiIqMwvBAREZFRGF6IiIjIKAwvREREZBSGFyIiIjIKwwsREREZheGFiIiIjMLwQkREREZheCEiIiKjMLwQERGRURheiIiIyCgML0RERGQUhhciIiIyii/hZenSpRg8eDCKiopQUVGBjRs35ty+ra0NN9xwA8rLy1FYWIizzjoLK1eu9OOtEhERkebyVb/AmjVrMHfuXCxduhTnn38+7r77bkyePBk7duzAwIEDMz5m6tSpePfdd3HffffhX/7lX3DgwAEcP35c9VslIiIiA+QJIYTKFxg3bhxGjx6NZcuWJe8bNmwYpkyZgtra2rTt6+rqMH36dLz11lvo3bu349draWlBLBZDPB5HcXGxp/dORERE/nDy/a202+jo0aPYunUrqqqqUu6vqqpCfX19xsc88cQTGDNmDG699VaceeaZOOecc/Cd73wHH374ocq3SkRERIZQ2m3U3NyMEydOoKysLOX+srIyNDU1ZXzMW2+9hT/+8Y8oKirC2rVr0dzcjG9+85v4+9//nnHcS1tbG9ra2pL/b2lpkbsTREREpBXlY14AIC8vL+X/Qoi0+xLa29uRl5eH1atXIxaLAQDuuOMOfOlLX8IvfvELdO/ePWX72tpaLFq0KO15Xm0chlN7qmtYWnVwgq3tnm4YkvVvh/fEcj62525n7/+0XUcdbW+qg0MKHD+m9az2nH8/dXDc8jmqBu5y9JrVp2VuXSTSid26rKNc9VpnVvUc4Lyuy8X0etBN/ZbgtZ6zW8epqtsOt+Z+/x0p7TYqKSlB165d01pZDhw4kNYak9C3b1+ceeaZyeACnBwjI4TAO++8k7Z9TU0N4vF48tbY2Ch3JzLQLbictuuo8QXWCTf7a/V5Ht4TszwmTips4OR54uaLgcgvpgaXRB2Q6WY6L/tip57LxWkdFySl4aWgoAAVFRVYv359yv3r16/HhAmZC83555+Pffv24fDhw8n73njjDXTp0gX9+/dP276wsBDFxcUpN5XsFPanG4b4GlyiymkB77m7i5TC7SbEEOnETbB2cu7b+TFgpzx2FKaAYpebfbb6XK2OjZ1jrEOdpny20Zo1a1BdXY3ly5ejsrIS99xzD1asWIG//OUvKC8vR01NDfbu3Ytf/epXAIDDhw9j2LBhGD9+PBYtWoTm5mZ87Wtfw8SJE7FixQrL10uMVv7ja/2kdxvZDS655DppGFq8cdLcatW8CrAricLJTWixy05LC8C6zgun3Uq56rpcdZyduk12fXa4tR0XjNxna7aR8jEv06ZNw/vvv4+bbroJ+/fvx8iRI7Fu3TqUl5cDAPbv34+Ghobk9qeeeirWr1+Pb33rWxgzZgxOP/10TJ06FTfffLPqt5qT1+Aiq7WFBTm7xGdjp3AnPu9cBTtxzHIV8KcbhjgKMKsOTmCAocA4CS5OWlnsYmjxzkk9B5z8zLPVc4f3xLLWb3bqtiDrM+UtL35T0fKiMrgwtKgjsyWGrTBkMoaW8LJbz7mt4/xsgXHS8sLwYiFqwaX7a3sBAB+OPNPX7VSSVbgB+SGGAYZUkx1cohBaTKrfEmTUc0EHGIYXSeHFS3CR0U3kV2FOFMBsEgVTxnZBFXK/x8OwFYZ0IGNmZIKq0ALoEVxk14NBsVPX6RpgGF4khBdVwUWn1harQqhSGEIMW2FIVzJbW1QMwk0wIbS4pXtrs6qBvF7qMYYXj+HFquCr7CaSXZiDDCgyqKgAdJ+VxBBDXshqbQlbaNGpLvQr2HgJMUG0wDC8eAgvYQkuOhVUGcIQYhhgSDW/govbFXH9Di2614N+hBiTAgzDi8vwoiK4MLTIpXuIYSsMBUW3lb87UxFccg2YNbkulF3PmRJgGF5chBcVY1z8DC4mF1Q3ggwxbIUhnUSttYV1nXtWdZzsAMPw4oCb8MLgYq4gfqEksBWGgqZra4vKVpaoklXX6RxgGF4chJcgggtDi3wmhxgGGHJDt+CicjwL67qPyKjrdA0wTsKL0gszhgGDixm6v7ZX6mfi5GJofl7JlVeqJkB9cHFy0USVF0uUXa7DQMbnYXW8sh37bOeMVR2mos6KdMuL2wG6QQYXFmR7/Own7oitMKSSH+NbdFmLinWdNa/1nG4tMGx5sYHBJdyCbIWxuhx9Lk83DLHdEsNWmGiR1doiY0kH1V1ErOvs8fo5yW6B8VMkw4tpwYWF2R3Zn5mT42gVYGR3JVG46dBNpDq0APyB5obX7weZAcbP7qPIhRcTgwu5Z/pYGCetMBROfgQXK360tLCu8yaIAJOJXwEmcuHFjSCCCwuzXCpaYewcXzvdSLJaYdiNFC52j6dVyNU1uLCOk09lgMkkyAG8kQovXlbQ7Ux1cCH5VFSWTkJMLmyFoY5Uj28JupuIdZw6Xuq5XMdbt/EvkQkvMruLGFzMpqKZWsdWGDJTmLuJ2Nrin6ADjOrWl0iEF9njXHJxW+hZqIMRxHgYv9aFYTeSecIWXDr+UGD95j8/A0wmKgNMJMKLG27GuXgJLhQcE1th2I0UPmEZ38Kwohe/Aozb8S9uhT68uGl1YXCJJr8DDOBvKwzpycnA3Gx0GN/CwKIvv46Lm94Kt3VTqMOLXwN0GVzCQ2YF7NeMJAYYc4Whm4ihxQxujpHO419CHV5ykTVAl8ElnIJqhXG7Oi8DjHnCElzIHH4FmExkdx+FNrw8cmic48f4NeWLBd4MQbTCANar82ZjdxwMB/IGL+jgIqubiMzjR4Dxo/sotOEllyDHubDAm0d2iLGD3Ujh5XVgrtfrE/E6ayQ7wGTipvvISaND5MJLkONcWODNJivEyBwLkw0DjJ5kDMzNxu7AXK9Yj4WDzOMYRPdR5MJLJn6Mc2GBD48gQkw2DDBmkDWjKBsOzCU/+NF9ZFekwouT7iKZWODDyc+uJLfdSE7GwZAaQY9vATgwlzLTtfvIjsiEl6CnRVM4+TmgV3U3EgfyyqcyuPi5fguFl6ndR5EJL5mwu4hkCGJ13mzYjaQPr8HFauE5KxzfQnY5Pc46dB9FIrzI6C5icKFcGGCoIxkzirLh+BbSQdDdR5EIL3Y5afKywoIfPX5f5JEBRj9hGZhL0WNa91How4vdVheOc8nuw5FnSt0uzPy+yGOucQ9WA3ntYICxL+iBuV7Ht7C1xVrY6ziTuo9CH168inJ30Ycjz0wW1sS/MxVeJ9tFhd8L27lpheFMJHl0CC5ehKXOUqFznZatfouqoLqP8oQQwvGjNNbS0oJYLIY5f7wSz/19ZNrfVbe6mFgJBFkQTfy83JDxGR8cUmC5TetZ7Vn/durgeNa/VQ3cZes9VJ9Wb2u7KPHaTQQwuOhAZj1o+mfq9LPIVTdlqpOy1UUTe7+Guy5Yi3g8juLi4pyvGdqWl2feOdvzc4Q9uOjwC0KH9+AHGS0xHAejHxnjW7xOhfbCtDpLtlwtxTKe11QmdB/5El6WLl2KwYMHo6ioCBUVFdi4caOtx73wwgvIz8/HeeedJ+V9OGl1Cfs4F90KlumF3S5ZISYXq3Ew2TDAOMOBuXrrGEyy3fx8D2Eno/vISaOD8vCyZs0azJ07FzfccAO2bduGCy+8EJMnT0ZDQ0POx8XjccyYMQOXXHKJsvcWxdlFuhck3d+fLKoDDJD9/GaA8S7I4MKF53LTtQ4JIjx5EdTsI7uUj3kZN24cRo8ejWXLliXvGzZsGKZMmYLa2tqsj5s+fTrOPvtsdO3aFY8//ji2b99u6/USY16GP/Jf6HpKYfJ+la0uplQEuheWTEz5bN3yekyCHgcTxTEwQQcXr8Japkys3wD9j4ef419OfNCGHdNvDX7My9GjR7F161ZUVVWl3F9VVYX6+uyV3v3334/du3fjxhtvtHyNtrY2tLS0pNzskJUEdT/xEkwt2Cb8QvHC9HEwUWuBMTm4hHUqtOl1hMnvPRO/hlwoDS/Nzc04ceIEysrKUu4vKytDU1NTxse8+eabWLBgAVavXo38/HzL16itrUUsFkveBgwYkLaNk8FBYRvrYnrBTgjLfmQi6wrVufCaSN55CS4cmCtfmOoEnfdF5sUbZQ7e9WXAbl5eXsr/hRBp9wHAiRMncNVVV2HRokU455xzbD13TU0N4vF48tbY2Gj5mKi0uuhaGLzQuZB7YXqAAcLdCuM1uGSjemBumFtbwkjX/dLxHFIaXkpKStC1a9e0VpYDBw6ktcYAQGtrK7Zs2YI5c+YgPz8f+fn5uOmmm/DnP/8Z+fn5eOaZZ9IeU1hYiOLi4pRbR6paXXQ8mAlh/YLvKIz76NdMpGwYYDIzObiEUdjKfWe67p+s6dOyWl+UhpeCggJUVFRg/fr1KfevX78eEyakVwjFxcV49dVXsX379uRt9uzZGDJkCLZv345x48apfLuhoOLEPzikwNbAULvbyaRrQfci6KnUXJH3Iwwu+gj6B4uf9VsY6zXZrAeVeDR//nxUV1djzJgxqKysxD333IOGhgbMnj0bwMlun7179+JXv/oVunTpgpEjU1fFLS0tRVFRUdr9dkRtXReZJ3ymQmq34ObaTsXnnNjvMFXY3V/b6+l4nrbrqOXx6rm7S9aZSIf3xLLORHq6YYjlTKRVBycYPxNJRXDh+i3uBPFlnq38ZLpfVb2m27F0Wi9lq4cy1T2H98TQveyA7edWHl6mTZuG999/HzfddBP279+PkSNHYt26dSgvLwcA7N+/33LNF93odkIB/i0/L/M1ZBd4HQu7F4l9cXtsGWDcY3AJnt+BxUv91/mxYfgxnI3XH1ayhPbaRuWLb0aXoqKUv4V1XRdTgks2sgu6bsdHBi/HmGvB2Of1AosMLt74+aXoR50X1nV5ZK390rneaT9yBG9/7//ZWudFectL2Oh2IvmxyJlqifcgK8SEtRsJcHe8E59rrmOd+HLNFGKi0gITVHAJ6xecXSoDS9D1m4yWZh1blHVofQnthRk7C+NYlzAEl45kD4gLeoCfCl4qsSAvKaD7IF4GF/+pLp861m9R5WTmkV2RCS8y6FRJeO1GcFKQWs9qT96s/p5rO1Xvz0rYQgwDjFwMLv5THVpkBwVZ9Zvb96Zj/RX0uReJMS9hHOvi9mS2W3C8BpBs3CRtjonJTHXLW7ZzIExjYFQt98/gkpkJLS1u6z6ndZubc0C3Yy577IuTMS9sebFJp5NGZXCR0XIi+/ll/4rS8VeMG0EtaBeWFhhTg4upq+bqHFxktKo4fY4wtMAEeR4yvBhGdXDxi9OKgl1JakQ1wJgcXEyjsqy5qRdkd3Pneg0rYQgwTsgc+xL68CKjy0iXCkNVcFHd2iLztVWEGJMFeU0kEwOM3YtI6hZc2NqSykk9oDqoWL122AV1XnKqdMi5HdeQkGt8g112rluReB92E/jBIQWcWv1PMqYtWi1ol20xO6/TqP3kdWAuEFxwMZGqS5XYJSM4WNV/Muo2N3WZjtOn7bKzeKYdoW958UqXE8RNRaBDcEk8T+JmxWmfMbuSTjK1Bcav1hcTg4uprS2A/ODiZoakGx3rKjv1ldO6LRvTu49knKdOu45CHV7CuLaLXV6Ci93C6IaqECOTqSEmyKtS6xxgTA0uppJVdhKBxc2yDnY5DSt2nsvq/WVjeoDxW6jDS1jImo6W4HYpeJlk/FrpSMXaDlENMWEKMHbHtzC4yCHrUiVuB+FakRlWrF7DDZMXsnNy3mYrG6e+ZT+ShHbMy6lvdQEK0++PQqtLLm7W7rCj89gGOwM2O75uri8+J+NhZF9qADC3f9nLWJggxsDIvIyAytYWgMGls6Cur2Y3sMiQOHed1G2ZzqHWs9o9rSzbman1k1ehXaRuxNd/jK6FRWl/N22WkcxWF7fBRcagS7sF3s4AOCcFX2aI0eF8cEvlTLVMvCxk5zXAmBpcADPPsSAuU2K3RdZtcHFS51nVbW5a7kxewM7u+ZDpuJ9oO4K/3P19LlIXNbKDS9XAXdJmi9h9Lq/9xp1xWvVJbis207qQGFz8I6NbVXX3kBOJOsppnWf1mGzvQ/b4F9N4/WEZqfBiWpeRrC9LVcu8u+EkxOQS1KwkBph0bgKMFTcBhsHFP353E8kOLR2DiqwfaUEHGJPrJjciFV6cMK0ycXqiBxFcOr+G1evYbYXxe1aSqQN5AX0CjOxF7LwOzD28J8bgYpNfwcXJwnJOQ4sqbgJM2Ph1PkcmvIR9rEs2Ttc78HtRMZkhxg62woQrwKhcMRc4uU8MLh+R0U0k81IluoSWzq/lRNhaX/x6D5EJLyaRPTW6s2yFPcjVUO2GmFyC6ErSobJww7QAkymgBN1NBDC4OCHzwrA6hpbOr5sJx7/IE5nZRnYrGR0qFNmXGe9IRnCxOxvE7cBLO19oOs5K0uHccUqXWUhOzz8GF3/5FVys2O16kRlYMtV3Xs+/TOeezNlHQZ5fTs6VzueFk9lGkQgvJnUZqQwuQObCb6eg+zV9tSMZIYYBJjcvX0pBBhg7VCw8l8DgYp/Xy5QA/oUWp/Wcly5LlQGG4cVAXsKLDpWK360ufgSXjlSEGLbCeBPGAOPkCyOBrS2pdGht8SO0+PHDLNP56DRAm9L64ld44ZgXg8noLrIiM7gkns/pc5o4K8mksTA6XUrAaql+K1YzirJhcEkVdHBRPaYlUQ/JqN/sPEem9+i0TjZl7IuMywTYwfASYapXOrV6bifPH8SsJK8YYE5SsZCd08cwuNjj18JzXq+v5jW0yOb2OTPtq9srYndmUv3jBsOLRrw0tyXIanVRGVy8vI6fs5KiGGBUzULKRlaAUbnwXBSCi6y1i1QHF91CS+fXyEVGl2gYW1/cYniJqCCnRXcWZFeSFRlTqk0KMICaadS5QoLXAKPjirmAWcHFKzvlJNePBqvyqnNo6fx6udjtPpLV+mICt+WM4SVEZA3S9bOwd35dv7uS/GqFYYDJveCbmwBjNT4myOBiClNaW5zyO7SQ/0IfXkyphGR0GcmgQ4EPqivJiowAY1KI0WUhOyA9qFiFllwzOfwILia0uugeXNy0tugQWmS1vphOdRkIfXihVDp1F+USRFeSnVaYqHUjqaqA3F7MUWVrC8Dg4oSXbiJA7vXVdAgtHenwXkw4D71geNGALgN1dShwnanqSsqFrTCp3FSCdga65gowbq5IHeTA3AQTvjD8uD6Rl2nQTldb1rHeksHruBdT6hfA3Y8GhhcyguyuJDutMFZkzUYyoZLxuwsJsLf4oJ1t/eomikpwseJHN5EJoSXX+zOlBVxnoQ4vpiynrILTgbq6VwSAuq6kbPwKMIAZv5J0DDBBj28xJbQA+gcXu0yoq1QyZbq0aqEOL2Hj9DpGYSW7K0mHcTCAGQHGLRUBJuiF50wJLYD3S0DoML7FhNYWL1QM2g1zncLwgvC1ujhlaoUgsxVGp24knQWxEi+Q3sISdHAxicprVwH+jG+JSh0VZU7LZGjDS6+/mjFF2i9h7WP1uxXGCgNMbl4CDGA9mJfBJVXQwSUbp+Nboirb5+ukngmyPlFZXnwJL0uXLsXgwYNRVFSEiooKbNy4Meu2jz32GD7zmc/gjDPOQHFxMSorK/H73//ej7dJBnMTYrLRIcCEmZ0A4+Qq4B0fZ/W6UQkuXgeC6zC+JezdRGH9QemFk0YH5eFlzZo1mDt3Lm644QZs27YNF154ISZPnoyGhoaM2z///PP4zGc+g3Xr1mHr1q349Kc/jc997nPYtm2bkvdnUoVkVxgXPLJLZoDJ9jn6MQ4mzK0vgL3WD7sBxq+BuaYIy/iWsHCyL6rq7jC2vuQJIYSSZ/6ncePGYfTo0Vi2bFnyvmHDhmHKlCmora219RwjRozAtGnT8MMf/tBy25aWFsRiMZx/yULk5xfZev6gKya7J5bdAbtOZhqFqZLobNXBCba31XXhs6DPTStBz2DxY+E53Y9BR7q2tgDRDC4J2eqiTPVOpvom23nu9NwO8ly2c24eP34EL/zfQsTjcRQXF+fcVmnLy9GjR7F161ZUVVWl3F9VVYX6ensnaHt7O1pbW9G7d++Mf29ra0NLS0vKzSS6/8I2WRi6kXQ/P7zOuvGymJ0fC88xuHxE9fiWsHcTZRKVSwWooDS8NDc348SJEygrK0u5v6ysDE1NTbae4/bbb8c//vEPTJ06NePfa2trEYvFkrcBAwZ4ft8mido0aaecVIi6Tqc2YSE71d1InbuGeH2iVDoHFzuiFlqckjFwFwhX95EvA3bz8vJS/i+ESLsvk4cffhgLFy7EmjVrUFpamnGbmpoaxOPx5K2xsVHKe9aNl1/vHBhmv3LUeTq1CQFG5UwkgBdWlM3L+JaoT4N2Igr76Del4aWkpARdu3ZNa2U5cOBAWmtMZ2vWrME111yD//mf/8Gll16adbvCwkIUFxen3Eyh4svISZNj1AqUkwDDbiT3VAcYlY8HzAsubs8Jr9cnyobToJ2x23Ukq/UlLJSGl4KCAlRUVGD9+vUp969fvx4TJmQfTPnwww/jK1/5Ch566CF89rOfVfkWjauoyBu/upGsMMBk5zaAMLjYpzK42BHF8S1R299MZJYv5d1G8+fPx7333ouVK1di586dmDdvHhoaGjB79mwAJ7t9ZsyYkdz+4YcfxowZM3D77bdj/PjxaGpqQlNTE+LxcA1iUnUlabJHl3EwbkUhwDgJI1G6RlGCycGFUvnVtW/aOZ6L8vAybdo0LFmyBDfddBPOO+88PP/881i3bh3Ky8sBAPv3709Z8+Xuu+/G8ePH8Z//+Z/o27dv8nb99ddLf29hOpDZcLxLdjqMg2GAyc1OKInSNYoSGFzCj9c6yk35Oi9+c7LOi+5z3hNUrO8CsCLpyO6aMKrWgwnzWjCA2vVg3H52JnxumegUXHg1aOdUrPnipAwEfd7nOn+1WedFZ0EfwKCxIkkV9DgYtsDklq0byU1wMbW1BfA/uORqWeT4Frm8tJJHcdBuZMMLUWcmBxgTyAgMibDidgE6k0NLEMElG3YT+YNdR9kxvATE1Eo07GRMp7a6LlIuXhayM4HMABPEawdB5QJ0DC7+4+ciB8NLQLx+2diZacTBuu6onk7NAON/iDAxuKi+MjSDi5lkrPdiSl2RC8MLURYMMOqYPO5ENRmXgwgquHB8izf8wWlfZMOLKZV82MdB6M7UAGPK+e1HiDEpJMk4bkEGF5IvbBdqlFUeIxtegsTLApjFxAADmBPQAXUBg8ElFYOLHrx+XrxUAMOLkbiyrv/sNofrGGBMCTEmBQ3ZGFwoIQpdRzLKOsOLz2QsTmdHFApAEOwGmFwzkTJRPY3apAAjK8SYEoYYXIicY3ghcshrNxIDjDWvwcOU4OLVwSEFDC6UJOPipKaIbHgJonKT8eWRqSLieBf/McCo57aMmhRcVE6FBhhcdKbiM+SYFwpclE5CUzHA6IfB5SMMLuERthlHMkQyvJhUwbnB8S7+YYBRy0lZNaVce13qn8GFZDClDsgmkuElTJjIg+d1JpKXABOFFjqrUGLSgnd+tLYwuESDybNOZQSnyIUXUyo5FVj5qBVEgAHCvxovkL3cmlKeVS/1D+Q+VxhczMIrTFuLXHgJkikVLbmnKsBE/XICQGr5iUprC8DgQieF5QrTsl6T4YVIMhUBBlA/DsYEpoUWP65R5Ca45FqLqCMGF7V0+HxN+gHTUaTCiymVHmB/vv7hPTHF74TcMCnAmFp56SzIheeAk+dQruBihw5frJSbyeNevIpUeDGpkrb7JcQBu/pigIkmHYJLNrwydLj03O39K9ykH/UdRSq8EPmNASZawhBcyD+rDk6wvW1YWtl5VWkD8cshmkwLMDxP3ZExvoXBhbxycokAU1tdgAiGF5MrZjv9m1ygTk8mBRjA7HIShCBnFOUa3wIwuJjo6YYhltvI6DIyWbT33kd+XU2a9OU1wHhZC8YNtsLYE+SMIqvQwuBC2QTZ6iLjtSMZXsJSIfOCjObxEmAAd4vZybiUQFjKjGxeF54LspsIYL1A5opkePGbqqtJk5lMDDBAeEK/LCavmAswuJjE7mBdJ+NdTMfwQhQABhizMbiQn+y2skdpyAHDiw9k9O9FfXBWGDHAmEfXaxQ5Gd/C4EJhEMlvRJOnh3XkZN6/k/UEyD8MMOYIemAuV8wlmUwvw5EML0FwEpii1G9J3gNMNlYBRsZA3iiQ0drCgbkkm8njIGXUHZELLya3utjpOrKzPgDpx7R1YBLCHmBMvyI0wOBiIq7XZS1y4SVIJgcnUo8BRi8MLkT6Yngh0kiQAcZLiAlrgHFL1fgWgBdXJAIiFl7Y8kEmCCrAAN5aYcIUYFTOKPLS2sIVc4lOilR4CVPlSuFmcoAxvZzpGlzsYHAJB45dtOZLeFm6dCkGDx6MoqIiVFRUYOPGjTm3f+6551BRUYGioiJ87GMfw/Lly/14m0RaCfJaSBwH4xyDC/nJ5LW/jLi20Zo1azB37lzccMMN2LZtGy688EJMnjwZDQ0NGbffs2cP/vVf/xUXXnghtm3bhu9///u47rrr8Oijj6p+q8p5rdBNnhpH7qhcB8aPgbymhRi375fBhUxj+jAK5eHljjvuwDXXXIOvfe1rGDZsGJYsWYIBAwZg2bJlGbdfvnw5Bg4ciCVLlmDYsGH42te+hv/4j//AbbfdJuX9mFaZOsUpduGjKsAA6gfyAuaUOTfvU9UaLlwxlyg3peHl6NGj2Lp1K6qqqlLur6qqQn195gK3adOmtO0vu+wybNmyBceOHUvbvq2tDS0tLSk300Xp+hREUeXkqvAUbWG8MKPXlh+l4aW5uRknTpxAWVlZyv1lZWVoamrK+JimpqaM2x8/fhzNzc1p29fW1iIWiyVvAwYMkLcDRERECvCSLd74MuInLy8v5f9CiLT7rLbPdD8A1NTUIB6PJ2+NjY0S3jEREZE67O7zRml4KSkpQdeuXdNaWQ4cOJDWupLQp0+fjNvn5+fj9NNPT9u+sLAQxcXFKTfTmdT0R+HH8zE7L59Nrq4ATpWljux2MZo05MDrWDil4aWgoAAVFRVYv359yv3r16/HhAmZm8wqKyvTtn/66acxZswYdOvWzfN7Mn2EtRVWeuFjp3k513HP9SVpNd3Sa3Dp/tpeY8qc2/dp9Rnl+oy9BphVByew+4EiSXm30fz583Hvvfdi5cqV2LlzJ+bNm4eGhgbMnj0bwMlunxkzZiS3nz17Nt5++23Mnz8fO3fuxMqVK3HffffhO9/5juq3qpzXStzkef3kjpfgcnhPLOuXY8/dXXwJLqYxMcAAHD9BzpkyCzAb5d+G06ZNw5IlS3DTTTfhvPPOw/PPP49169ahvLwcALB///6UNV8GDx6MdevW4dlnn8V5552H//7v/8add96JL37xi6rfKpFWvAaXbOyEYC/BxaTWFpkYYMhPJq/7JSM45YnEaNiQaGlpQSwWw/mXLER+flHK33SoUJ0ctEz9l51P2Ex9odnWh+AAMXOYHFzCgJcIID/kKuedy3emcp2pPDspv0GV12zl6/jxI3jh/xYiHo9bjl+NVD+ESc1kJg28IrkYXILnZV+8tsBkO4ZPNwyxPQ6GKOwiFV6IdBdUcDlt11EGF4nsBBgO5CVyj+HFRya1/JD/VAQXDsx1z+t+2flcOQ6GyJ3IhReTA4SdAVq8tpGZVAUXKwwuuTHAUBC45IW1yIWXoHgdqEvhpaqrKBev3URA+INLgtfZU3Y+awYYcsrkpTNk1B3m7r0HJre+dOTkwm6cgaAnrwvQZZOrYpOxYm5UgktHqlthcnXxcSAvyWZ6GY5kePGbjLBk8px+ykzVyrkMLurIaIWxwoG8RNYYXogCwOBiNpMDDMBWGNPY7R6O0nXIGF58IKPCN7l/k1IxuIQDAwz5JYwXZvQqkt+IYamEnQzWZEWlBxODS1SX+7fDj4G8ucbBZMMAQ2EXyfASBCeVXJSa/qJE5UUWs+E1itQLcjq1VYDhQF7KJsiJKzJeO3LhxeTK2E7XEdcH0FOQS/67YXI5CULQAUbGQF7Sh531uqI+iSNy4SVI/EKIpiCX/HeKrS3uyQgwQa4HwwATDk7GvZi8bAjDC5FCpgUX8kbGZxh0gGGI8Y+T9becrOulM1mBKVLhxaTK2e6Xj9sVVkk9BpdoMj3AAGyFMYWMriNTW18iFV5MOkh2m/7CksbDhsEl2nQIMFyRN/xkjHkztfxHKrwQ+cHUq0Ob4MORZxrzI0TG+CEvU6kBjoPRnZPPl63sqRhefGRKpUvumXZ1aJN+dXUsP6aFGC+CXtCOASa8gij/sl4zcuHFlApPBVZCagURXLxcHdrU4GLnft2E4ZpI5B8vS15EoQUWiGB4CRs2JQbP7gwNFcElCqwCSlRaYewGGFUr8jLA6MXkS8bI+OFk7t57YEpF5xYXqvOP3Qpdt+BiSquLk7JqSrn20gpjt6WNAYasmFIHZBPJ8GKCqPyqNhmDi35MCTBAcBd2ZIDRg4rBulH63ohseAmiklN1dWleoNF/DC7quS2jUQowbqdTM8CQ6SIbXojcsju+hcHFPa8BxKQA4xUDDCU4uTSA6RhefCbj6tK8QGNwvAzMBRhcrMgcfGtKgAlyQTsGGDIVwwuRDV5nFAHBBBeTLrRoSthQgQGGEqIwTVpGWWd4CYCKLxOOe1HH6/gWILjgYgKVU51NCkQMMNHh9fMyeZq0LJH9BEyp2E1J0mFlYnBha4v/ryELAwx1Fra1vHhVaSLFTA0uJjBpYTm/+XVNpExkBBiGGPc4VtE+hpeAeK2cOGhXHSfjWxhcnAsitJgYlFRfUkBVgAHYCqNStuPmpN4wpa7IheElICZWplEgq7WFwSUzGee92+mgppY5Bphw4eciB8ML0T+p7CYCeK0imcHl4JACVyHG5ADj5ZICueQKMNnOZwYYf6gY72LKDx0rkQ0vplZisrBS+YiTfnodg4sJlZHX8pYtrLgNMKaWf78DDJD9vHYSYFjfWIvCFGmZIhtewihso9L94CS0MLi4IyO4ePl7NgwwqdwGGLbC2Mcp0vJE+pMwtfJygoN2s1M9vgVgcFEdXLwytRVGpwADsBtJBXYZ5aY0vBw8eBDV1dWIxWKIxWKorq7GoUOHsm5/7NgxfO9738OoUaPQo0cP9OvXDzNmzMC+fftUvs1A+HWZAMrMj24iBhf3ocDpmBavIcfEEMMAEx5+/cg07RzPRem331VXXYXt27ejrq4OdXV12L59O6qrq7Nu/8EHH+Dll1/GD37wA7z88st47LHH8MYbb+CKK65Q9h7DdDDJmg7jWwAGl1zcBhEZrTSm1Qc6BhiuB5NZ1PY3E5nlK08IIaQ9Wwc7d+7E8OHDsXnzZowbNw4AsHnzZlRWVuL111/HkCH2kuaf/vQnjB07Fm+//TYGDhxouX1LSwtisRjOv2Qh8vOLbL1GkF8Gdg9mtoq59az2tPtOHRxP+X/VwF1Zn7f6tHpbrx8GMkILwOBiJYjg0pGMwYsmfM4duf3MrT7vTPVLQud6prNc9U5HUamDstU/meqbTHWMjPVdAL2/744fP4IX/m8h4vE4iouLc26rrOVl06ZNiMViyeACAOPHj0csFkN9vf2TNR6PIy8vD7169cr497a2NrS0tKTcwshLhcxxL3qMbwHCHVy8dr3YCS6tZ7Unb16ex4ppLTBu2WmBcTOVGmA3UkdR2Ee/KQsvTU1NKC0tTbu/tLQUTU1Ntp7jyJEjWLBgAa666qqsKay2tjY5piYWi2HAgAGe3rdpOO4lN7+6ieyMbwnztYpUD8zNFFgYYD6iciE7gONg/BTVVhenHH/zLVy4EHl5eTlvW7ZsAQDk5eWlPV4IkfH+zo4dO4bp06ejvb0dS5cuzbpdTU0N4vF48tbY2Oh0lwKl+5eSyXSYBg2wtSUXOwNzc4UUqwAjYyCvKXQOMBwHkxlbxd3Ld/qAOXPmYPr06Tm3GTRoEF555RW8++67aX977733UFZWlvPxx44dw9SpU7Fnzx4888wzOfu+CgsLUVhYaO/NZ6D7l4Nqqw5OCF2fs5MKkONb3PNjGnSucNJxm1zH4uCQAk/H4cORZ2p/LBK6v7bX9XFJfEa5jkvP3V2yHpNEWck2FubphiG2xsGEsU7ygq0umTkOLyUlJSgpKbHcrrKyEvF4HC+99BLGjh0LAHjxxRcRj8cxYUL2L5dEcHnzzTexYcMGnH766U7foiMmVUx2Hd4TsxxMF1aygkuQoQVgcAHsBZeO2zLAnOQlwAAnz12rAANkPz656p8oBhgndZKqhUbDFlwAhWNehg0bhkmTJmHWrFnYvHkzNm/ejFmzZuHyyy9PmWk0dOhQrF27FgBw/PhxfOlLX8KWLVuwevVqnDhxAk1NTWhqasLRo9Fb/pjsczq2hcElOG7Gt9hh9Riv3UimdSHp3I1kR9i7kdhllO7Qv9gvn0pHe65evRqjRo1CVVUVqqqqcO6552LVqlUp2+zatQvx+MmU/s477+CJJ57AO++8g/POOw99+/ZN3pzMUAKcfQhRENaC4rSC07mbyBQqZxRZBZBTB8dztiraCT1RCTCA+eNggGgP5pXRZRTGVhfARbeRE71798aDDz6Yc5uOy8wMGjQIipadycmkJmEVTG2idVqpuW1tAfwLLrqfh0EFl86B5dTB8azHzKoLKfFe3B6vxGeg+7FK8DoOxuq4cRxMdlEOXk4dHFIAtB2xvT3n2RqElwk4yU1ri67ToDsy5cvQDRWLoeVqhVHdAgOY1QrjtQXGy3owALuR7OC1jJwJ9beek8rJpIrIjkwFIVclYUKl4KbyMqWbyIRKRsdVXHNtY2fsTJSuieT1HNNhHAxgRl2lUhS6pu0IdXih8HATWnReLTfBhAXoAHfBxesaLk5mzHkZByNrPRgTQozuASZMrTC53l9YxyD6ieFFA6quMB2G1hfZXUSAHuNbTAktgPvgYiVbqLAalJtNkAN5E6ISYHS4rABgRohxy+twAFPqF8Bd2WN4IS2p6iLSYXyLSZWKqi/jXMEll6qBu3IO8GSAsUfGOahLNxKgX4jR4b2YcB56EfrwIqMy8oOq1hendCh0sruIALa2uOH3GJdcwaNzaLEKMEGOgwHM+OIwIcCYGGKsXt/uVaRNp7oMhD68RJ3TriMguACjqovIa2sLEL2F51QEl1zBwSq4ZLtfVSuMKT96vNI9wADuxofoEGJILYaXiNJpwFgQXUSA/daWKAUXLwNPrYJLNm6Ci91tggwwJrS+AHJaBP0YB2NCiJHV6hKl5S/clrPofEIG8HPgrhW/CnxQXURcdC6dqgXoVAYXO9sGORPJlAADmNMKo2uIcRNcnDJlmrQf5z3DS4QF2X0URBcRYP8XDYOLfW6/3GUFFzuP4SUF7JHVCmPFS4AB9AsxboOLylYXk+ofNxheDKa69QWQH2CC7CLyK7hEZWAuIH9wrtU4Fiu5Hh/kirwmBRhAj/Vg/AgxMuo3t8/htE4OY6uLlzKVJ4K4mJBCLS0tiMViGPH1H6NrYREAcy5iBTiv5LIdfCdfGna+LLxeV8RNAbdTKclqaQGi19oC6BdcZNL1yuFROkcAb2v+JNhd90fGOeSkrrNTr8lqdTHle8xLeDnRdgR/ufv7iMfjKC4uzvnYSIQXwP6B16FiURlgZHxx2C3cbn+RyAgtgL9dRIAe545TukyHdnr+2T23GGDk0CHAAP6GmIRM9Z3X809lcAEYXozkNbwAwVcsssILoC7AqOJ1MC7A1ha7TAsunb9EGGD8pUuAAYIJMU45CS5AOFpdAP/CC8e8aMjpyee0As1WeIKcPu3nLCKAV4I2KbhUn1af8dev3RZADuSVw69xMHbKsOoxMV4FFVyiJDLhxbQrTMv6UnQ6ct3vgh7ELKIodxMB5gUXq7/bCTFeAozK9WB0qGuc8GM9GMDsEOP0dcLSXeT3e4hMeHHKtEpFVusL4E+AkRlaghjbokMl4UaYgovTbd3ORALULmhnWl3j13owgLoQo6qOc9tFmYmpLS5+nc+RCi+mLfmtuvUliABjt+LQsYsI0OOXjVthDS5OH6PjirwmBhg/upESZIcYIDXIyKjv3AQXmSvpmlw3uRGp8BJ2uSoDtwFGVohxElp0m/6cYHLloEtwscPLtHwGGH/5GWAANSEmwW2Ysdqe41wy89qYEJnZRgkm9iGqnn0EePuyAVK/DNwEHh1nEXWkw3nghk7ruADWrS5e1xNKCHomktvzz9TzDPBnNlJnMqdXW0mcu07qN7+Ciy7njdcF6jhVOhZD+eKbEdt7SsZtTJp2BsgNL4D7a82ooHtoAfQ4B9yIanDpyMsiYglum/wZYNxRFWIAf+u3qAUXwN/wwm4jA8ieOu31uiIy2G3WDWJcS4KpA3O9XBkaCE9wsfu8VpckcHtJAbfN4iZ2HyXIGsyrujvJTbeSXSqfW2cyLgtw+GP2QigQ8vCSrXIxbeCuG14DTNAFO4hZRAlRDS1AuIKL0+dngJFDVtlJhBgVA3sTZIYZr+P1TG918Vuow4sMulQibk5SLwEGkNcK46RyCGoWEWBuaAH8aa43Mbg4fR3dAowu9Y9TssuRmxDjhtMw47Ruy8b04CLjPLXb9ZeQ7/kVSWun7Tqas/LsubtLzpPGr+ZPp5UNZxF9xNTg4je710SqGrgr6ziYUwfHM5aJ1rPac57DB4cUuD5nPxx5ppHnaPfX9koPX4nP0E4gTBwPp1+KHcmo/1SMjTLxfEiQ1fMR+pYXGV1Huvz6cXvC2mmBkbnegBNOX1tFa4vJTA4ufrW6dH5NVSvyqp5GrUs95ISq8uWkHkjUMUHUc0HVq34K6rwM/ycbMqoCDOBvQdMhtDC4RCu4OH193QIMYGaIUVnWvAzuVRlo7D4vW11OctM6xvBik04VhuoAozLEBB1aALMLv0xRDS4JMi4pkInqAAPoVR/ZpbLcea0jZAQZp88RhuAS5HkYiTEv2fqjvfRDm8pqDExCx8+rY2Wc6XPMVFnLCEAMLdmpnAoNhD+4JHgdBxPEGJgEE8fCJN6vii89J+NhcrFTx3mt38IQXJyS2eoCsOXFEZ1+7Xg5kd1OP8xWYGU3w7KLKDcGF7m8zkRiC4xzqlthZP/wkVW/uX1vOtZfQZ97kQkvYVzzxe/riqjG0JKb6sXngOgFlwQGGP+pLp8qQowXOr0Xv8ludQEi0m0kk25NtV6nI8pqavWC3UPWggotQPiDS0LifVp1I6noQgK8lQPd6iUnOr5vld1JnflR58mo23Q8rjoE5tC2vPQob0m7L4ytL4C8Jbn9xsG49jC4+MvLTCS3LTCAnJlIpku0xvjRatpxBV/Z9ZCs5wxDfeak1SXT93Y2bHlxQcdfOTIWhOpY2FQFOlUhSbfjIYMfV+llcMnMzkBeNy0wQO7Bnl4H8upYN3mhcoBvZ50/d7t1YNTqNF1CstKWl4MHD6K6uhqxWAyxWAzV1dU4dOiQ7cd//etfR15eHpYsWeLq9TNVvmFtfQHknuyZfpF0/qWS7ZeLnW1k0rWQe+HHNYoYXHJT0QID2BsH43VBu7AJoozbrd+ixOm55aTVxekVv5WGl6uuugrbt29HXV0d6urqsH37dlRXV9t67OOPP44XX3wR/fr1U/kWXdO1glBRyO0W0iAKc9iCS5AXVwROViDZKhGrqy8nhCG4JAQVYADvK/KGTdAD8P2s38JWr6mgLLzs3LkTdXV1uPfee1FZWYnKykqsWLECv/vd77BrV+4KcO/evZgzZw5Wr16Nbt26eXofUWt9AYIv5H4I4z4GuWIuIOc6RWEKLgkMMHoJW7nvTNf906nVBVAYXjZt2oRYLIZx48Yl7xs/fjxisRjq67NXBu3t7aiursZ3v/tdjBgxwvJ12tra0NLSknLzi+6Vg66FwIswhhbA/OBi95pBpjI5wOheT7kR1npA132SFVxkUhZempqaUFpamnZ/aWkpmpqasj5u8eLFyM/Px3XXXWfrdWpra5NjamKxGAYMGJC2jZNUF5bWl4SwFPKw7EcmYQguUeA1wOSaieTHNZHCKCx1gs71m8xzR1arC+AivCxcuBB5eXk5b1u2bAEA5OXlpT1eCJHxfgDYunUrfvazn+GBBx7Iuk1nNTU1iMfjyVtjY6Otx3lZHKcjUyoFXQuGFZ0LtQwyxrd4uUYRg4szqi7oCPCijm6ZXkeY/N4z8asBIE8IIZw8oLm5Gc3NzTm3GTRoEB566CHMnz8/bXZRr1698NOf/hRf/epX0x63ZMkSzJ8/H126fJSpTpw4gS5dumDAgAH429/+Zvn+WlpaEIvFMPyR/0LXUwpT/pZp+mK2aYtOB2aZdAKaUIGZ9Hm6FeRUaI5v8cbO9ZAyTaNOyFQXJai6GnFHYS5fJtRvgBnHQGZ3kZ1WlxMftGHH9FsRj8dRXFyc87Ucr/NSUlKCkpISy+0qKysRj8fx0ksvYezYsQCAF198EfF4HBMmZC741dXVuPTSS1Puu+yyy1BdXZ0x7OjEpPUVZKwJo4opn6FXQc8oyobBxR4v68AA2deCAaxX5AW4HkwuVmvDBFX/mfZ5q+4u8spxy4sTkydPxr59+3D33XcDAK699lqUl5fjySefTG4zdOhQ1NbW4sorr8z4HIMGDcLcuXMxd+5cW6+Zq+UFYOtLZ7qEGBM/OzdMH98CMLh05LUFBvDWCsMWGO9U1oGmfr5uPhOvrS4AMLH3a7jrgrW2Wl6UrvOyevVqjBo1ClVVVaiqqsK5556LVatWpWyza9cuxOPuBuzkcnH/Nz0/h9O+O12CgBNBFy7T+6vtkrV+C4OLXuyOgdF5HEzUya6D/Lq8gU5kBBenlLa8BCHR8jLnj1ei8NRuGX/1qGx9AYIPBLLkanZ1s10Uyfpy4FL/erPTAgOoGwfDFhh1ola/yWx1cTLmrmrgLrQdPma75YXXNrLgpm85LP3JdvchDPsqm8xftKqCC1tb5LEzBgZQNw6GY2DU4eeSm9PWv2zBxanQXlU6IdOH4mTVXSB8a7+QOrKno3q5RpHVUv92MLjYZ/ezUtmFxAXtyAu/Zxd5Efrw4oTMEdGsBKJHdmjh+Bbz2F1pWFWAATgOhtwJanaRm1YXICLhxW7rSy5uKgRWAtFhQjcRwODiF68Dea1W5LXCBe1ItaC6ixIiEV6y8aP7iBVA+IUpuIT9GkV+UtmN5MclBQDWX1FhUndRQmTCi5OEx/EvZJfM2USqxrcAnFEUFNPHwQAMMGFnWndRQmTCCyCn+8gNFv5wMmUaNINLsIIOMAC7kSgz2YvRZSK7uyghUuElG3YfkROyKnK7v4o5vsV8YRjIC7AeC5OgVtGVJXLhJcjuIxZ8swURWhhcwkV1gOE4GFLFaXDJRkarCxDB8AI46z5igCG/Qwtg3drC4GIulTORAI6DIWt+jHNx0100vdeLtl83tOHFyYeQ4Mf4F4AF3xQy+/mdhBY/xrcwuAQrLONgyDxBjXOx4rROCm14sZLrV01nKmYfseDrze/pz4D1Fw5bW8KFAYb8FuQ4F1ndRQmhDi9WlUPQ06dZ8PUju7VF1tgWBpdwCkuAYV2mPz+CSzZWdZSbuinU4QVwF2D8Gv8CMMDoxLTWFoDBJQxkzUTyuqAdQ0x4+XVc/OguSgh9eAHcfTgMMNHh98UUATmtLQwu4eJ1IC8QfCsM8FF5YpjRg9tjoGt3UUIkwosVJ+NfrHgJMCzo/lIRWryu2wLIbW1hcDFLGLqROmOQCY5fwSUbFd1FCZEJL27HvzgdwAt4K/ws4OqpqEjZ2kKy+BFg/FgPJhOGGP/4GVzcTIv2WkdFJrwA/g3gBRhgdKQqtOjU2gIwuISBrAAT9How2bCOU8dLPScruFiRUUfle36GCDh1cByH98TS7m89qx09d2fPfweHFOC0XUddvWbi5Ov+2l5Xj6dUQbS0AN5DC8BBuVGVOJ6rDk7IuV3i/Hi6YUjGv2ervwDrOgzwVo/l0rFMsp6Tw0s95yao+j3OpaNItbwAcruPALUtMAB/oXgV1LgWQE5rC4MLhXEcTGfsTvJOZXDRZZxLR3lCCCHlmTTR0tKCWCyGP77WD6f2zJ7NrH7NZPsVk+0XjNWvFxm/XPjrxBlTW1uc/mphcIkGqzorIVvdBWSvvxKs6jFATl2WC+s5Z7zWc26Di4pxLodb23HByH2Ix+MoLi7OuW3kWl4STGuBAdgK44TJrS12cTZRtOgwDgZQOxYGYCuMEzoFF79FtuUlwcQWGIC/TrJhawtFgepWGDstMAkqW2JYz2Um60KxuTgNLjK6i9jyIpGOLTAAW2E6M31si11sbSFAj+nUCapnJbGuSxXW4OJU5FteAHu/YmS3wABshZEhqJYWgK0tFDwZLTCAvFaYBBWtMVGu5wB5dZ3OwcVJywvDyz+ZHmCA6BRuFb/EZIYWgOu2kH/sBhhA/WDeTGQHmajUcwl+Xrok6BYXhhcX4QVQE2AA/8bBAOEv2LoHF5nrtgAMLmSfH7ORAH1CDPBRfZepXjC5LgxqBfBMvKzlwvDigJfwArgfwAt4b3pliMlO99ACsLWFgudHNxLgPsAA6qdad6R7PejHeB5TggvA8OIpvADBtcAAbGLtLGqhBWBwIW/8CjAJuoyJsaJTXejXIGQvi8/5HVwAhhfP4QUINsAA/hTuIAtzUDMI2EVEUSBrHAwQvhDTmap6MMhZUl6vtxZEcAEYXqSEF0BdgAH0WMkyIVfhtXv9ETfb+YmtLRRFslphAPshBnAeZHQIMYDZdVyCqcEFYHiRFl4AbwEGMKcVJiHXADi325lQmAE5oQVgawvpRWYrDKAuxOgSYAD59aAfZNRzQQYXgOFFangBohdgwkLn0AIwuJB/ZAcYIBohxgSqF9P0K7gADC/SwwugNsAADDEysYuIKDOGmPCQVc/lqt/8DC6ARpcHOHjwIKqrqxGLxRCLxVBdXY1Dhw5ZPm7nzp244oorEIvF0LNnT4wfPx4NDQ0q36olOwdI9QXRAPUXRTOZ0yX97fwSYXChMHFy/lUN3GXr/E6UEzutk7pcdsBkTj8XU4KLU0pbXiZPnox33nkH99xzDwDg2muvxaBBg/Dkk09mfczu3bsxduxYXHPNNfjyl7+MWCyGnTt34pOf/CRKS0stX1NVy0uC1xYYQO4aCvx14n9LC8DQQmZz0gKTYLclBlCz2F3U6zqnQc7LbMmggosW3UY7d+7E8OHDsXnzZowbNw4AsHnzZlRWVuL111/HkCGZC8L06dPRrVs3rFq1ytXrqg4vgD8rWbJg5+bmF5nfU58TGFxIVyaGGCA69V0Q9VyQLS5adBtt2rQJsVgsGVwAYPz48YjFYqivz7zj7e3teOqpp3DOOefgsssuQ2lpKcaNG4fHH3886+u0tbWhpaUl5aaa6iu6Ava7kRKi1LxqSnDhFaBJd27OTyflwG5XklOJrpNMN9N52Re/LxYbpHxVT9zU1JSxm6e0tBRNTU0ZH3PgwAEcPnwYt9xyC26++WYsXrwYdXV1+MIXvoANGzZg4sSJaY+pra3FokWL0u4fNWCnZXLz4uMD7W6o7C0QEXlmuy5LeZD0t0H0z8YHewPAHbe8LFy4EHl5eTlvW7ZsAQDk5eWlPV4IkfF+4GTLCwB8/vOfx7x583DeeedhwYIFuPzyy7F8+fKMj6mpqUE8Hk/eGhsbne4SERERGcRxy8ucOXMwffr0nNsMGjQIr7zyCt599920v7333nsoKyvL+LiSkhLk5+dj+PDhKfcPGzYMf/zjHzM+prCwEIWFhTbfPREREZnOcXgpKSlBSUmJ5XaVlZWIx+N46aWXMHbsWADAiy++iHg8jgkTMg8SKygowCc/+Uns2pXa7/bGG2+gvLzc6VslIiKiEFI2YHfYsGGYNGkSZs2ahc2bN2Pz5s2YNWsWLr/88pSZRkOHDsXatWuT///ud7+LNWvWYMWKFfjrX/+Ku+66C08++SS++c1vqnqrREREZBCli9StXr0ao0aNQlVVFaqqqnDuueemTYHetWsX4vGPRkBfeeWVWL58OW699VaMGjUK9957Lx599FFccMEFKt8qERERGSK0lwewM0+ciIiI9ODk+1tpywsRERGRbAwvREREZBSGFyIiIjIKwwsREREZheGFiIiIjMLwQkREREZheCEiIiKjMLwQERGRURheiIiIyCgML0RERGQUhhciIiIyCsMLERERGYXhhYiIiIzC8EJERERGYXghIiIiozC8EBERkVEYXoiIiMgoDC9ERERkFIYXIiIiMgrDCxERERmF4YWIiIiMwvBCRERERmF4ISIiIqMwvBAREZFRGF6IiIjIKAwvREREZBSGFyIiIjIKwwsREREZheGFiIiIjMLwQkREREZheCEiIiKjMLwQERGRURheiIiIyCgML0RERGQUhhciIiIyitLwcvDgQVRXVyMWiyEWi6G6uhqHDh3K+ZjDhw9jzpw56N+/P7p3745hw4Zh2bJlKt8mERERGURpeLnqqquwfft21NXVoa6uDtu3b0d1dXXOx8ybNw91dXV48MEHsXPnTsybNw/f+ta38Nvf/lblWyUiIiJDKAsvO3fuRF1dHe69915UVlaisrISK1aswO9+9zvs2rUr6+M2bdqEmTNn4qKLLsKgQYNw7bXX4uMf/zi2bNmi6q0SERGRQZSFl02bNiEWi2HcuHHJ+8aPH49YLIb6+vqsj7vgggvwxBNPYO/evRBCYMOGDXjjjTdw2WWXZdy+ra0NLS0tKTciIiIKL2XhpampCaWlpWn3l5aWoqmpKevj7rzzTgwfPhz9+/dHQUEBJk2ahKVLl+KCCy7IuH1tbW1yTE0sFsOAAQOk7QMRERHpx3F4WbhwIfLy8nLeEl08eXl5aY8XQmS8P+HOO+/E5s2b8cQTT2Dr1q24/fbb8c1vfhN/+MMfMm5fU1ODeDyevDU2NjrdJSIiIjJIvtMHzJkzB9OnT8+5zaBBg/DKK6/g3XffTfvbe++9h7KysoyP+/DDD/H9738fa9euxWc/+1kAwLnnnovt27fjtttuw6WXXpr2mMLCQhQWFib/L4QAAHYfERERGSTxvZ34Hs/FcXgpKSlBSUmJ5XaVlZWIx+N46aWXMHbsWADAiy++iHg8jgkTJmR8zLFjx3Ds2DF06ZLaINS1a1e0t7fben+tra0AwO4jIiIiA7W2tiIWi+XcJk/YiTguTZ48Gfv27cPdd98NALj22mtRXl6OJ598MrnN0KFDUVtbiyuvvBIAcNFFF6G5uRl33XUXysvL8dxzz+Eb3/gG7rjjDnzjG9+wfM329nbs27cPPXv2zNk95VRLSwsGDBiAxsZGFBcXS3tenYR9H8O+f0D49zHs+wdwH8Mg7PsHqNlHIQRaW1vRr1+/tEaMzhy3vDixevVqXHfddaiqqgIAXHHFFbjrrrtSttm1axfi8Xjy/4888ghqampw9dVX4+9//zvKy8vxox/9CLNnz7b1ml26dEH//v3l7UQnxcXFoT0ZE8K+j2HfPyD8+xj2/QO4j2EQ9v0D5O+jVYtLgtLw0rt3bzz44IM5t+nc8NOnTx/cf//9Kt8WERERGYzXNiIiIiKjMLzYVFhYiBtvvDFlZlPYhH0fw75/QPj3Mez7B3AfwyDs+wcEv49KB+wSERERycaWFyIiIjIKwwsREREZheGFiIiIjMLwQkREREZhePmnH/3oR5gwYQJOOeUU9OrVy9ZjhBBYuHAh+vXrh+7du+Oiiy7CX/7yl5Rt2tra8K1vfQslJSXo0aMHrrjiCrzzzjsK9sDawYMHUV1dnbwCd3V1NQ4dOpTzMdkuvvmTn/wkuc1FF12U9ner61+p4Gb/vvKVr6S99/Hjx6dsY/IxPHbsGL73ve9h1KhR6NGjB/r164cZM2Zg3759KdsFeQyXLl2KwYMHo6ioCBUVFdi4cWPO7Z977jlUVFSgqKgIH/vYx7B8+fK0bR599FEMHz4chYWFGD58ONauXavq7Vtysn+PPfYYPvOZz+CMM85AcXExKisr8fvf/z5lmwceeCBjmTxy5IjqXcnKyT4+++yzGd//66+/nrKdTscQcLaPmeqVvLw8jBgxIrmNTsfx+eefx+c+9zn069cPeXl5ePzxxy0fE3g5FCSEEOKHP/yhuOOOO8T8+fNFLBaz9ZhbbrlF9OzZUzz66KPi1VdfFdOmTRN9+/YVLS0tyW1mz54tzjzzTLF+/Xrx8ssvi09/+tPi4x//uDh+/LiiPclu0qRJYuTIkaK+vl7U19eLkSNHissvvzznY/bv359yW7lypcjLyxO7d+9ObjNx4kQxa9aslO0OHTqkenfSuNm/mTNnikmTJqW89/fffz9lG5OP4aFDh8Sll14q1qxZI15//XWxadMmMW7cOFFRUZGyXVDH8JFHHhHdunUTK1asEDt27BDXX3+96NGjh3j77bczbv/WW2+JU045RVx//fVix44dYsWKFaJbt27iN7/5TXKb+vp60bVrV/HjH/9Y7Ny5U/z4xz8W+fn5YvPmzcr3pzOn+3f99deLxYsXi5deekm88cYboqamRnTr1k28/PLLyW3uv/9+UVxcnFY2g+J0Hzds2CAAiF27dqW8/47lSadjKITzfTx06FDKvjU2NorevXuLG2+8MbmNTsdx3bp14oYbbhCPPvqoACDWrl2bc3sdyiHDSyf333+/rfDS3t4u+vTpI2655ZbkfUeOHBGxWEwsX75cCHHyBO7WrZt45JFHktvs3btXdOnSRdTV1Ul/77ns2LFDAEg5cTZt2iQAiNdff93283z+858XF198ccp9EydOFNdff72st+qK2/2bOXOm+PznP5/172E8hi+99JIAkFLxBnUMx44dK2bPnp1y39ChQ8WCBQsybv9f//VfYujQoSn3ff3rXxfjx49P/n/q1Kli0qRJKdtcdtllYvr06ZLetX1O9y+T4cOHi0WLFiX/b7eO8ovTfUyEl4MHD2Z9Tp2OoRDej+PatWtFXl6e+Nvf/pa8T7fjmGAnvOhQDtlt5NKePXvQ1NSUvG4TcHLRnokTJ6K+vh4AsHXrVhw7dixlm379+mHkyJHJbfyyadMmxGIxjBs3Lnnf+PHjEYvFbL+Xd999F0899RSuueaatL+tXr0aJSUlGDFiBL7zne8kr+7tFy/79+yzz6K0tBTnnHMOZs2ahQMHDiT/FrZjCADxeBx5eXlp3aN+H8OjR49i69atKZ8tAFRVVWXdn02bNqVtf9lll2HLli04duxYzm38Pl5u9q+z9vZ2tLa2onfv3in3Hz58GOXl5ejfvz8uv/xybNu2Tdr7dsLLPn7iE59A3759cckll2DDhg0pf9PlGAJyjuN9992HSy+9FOXl5Sn363IcndKhHCq9tlGYNTU1AQDKyspS7i8rK8Pbb7+d3KagoACnnXZa2jaJx/ulqakJpaWlafeXlpbafi+//OUv0bNnT3zhC19Iuf/qq6/G4MGD0adPH7z22muoqanBn//8Z6xfv17Ke7fD7f5NnjwZ//Zv/4by8nLs2bMHP/jBD3DxxRdj69atKCwsDN0xPHLkCBYsWICrrroq5WJqQRzD5uZmnDhxImMZyrY/TU1NGbc/fvw4mpub0bdv36zb+H283OxfZ7fffjv+8Y9/YOrUqcn7hg4digceeACjRo1CS0sLfvazn+H888/Hn//8Z5x99tlS98GKm33s27cv7rnnHlRUVKCtrQ2rVq3CJZdcgmeffRaf+tSnAGQ/zn4fQ8D7cdy/fz/+93//Fw899FDK/TodR6d0KIehDi8LFy7EokWLcm7zpz/9CWPGjHH9Gnl5eSn/F0Kk3deZnW3ssruPQPp7dfpeVq5ciauvvhpFRUUp98+aNSv575EjR+Lss8/GmDFj8PLLL2P06NG2njsb1fs3bdq05L9HjhyJMWPGoLy8HE899VRaSHPyvE74dQyPHTuG6dOno729HUuXLk35m8pjaMVpGcq0fef73ZRLVdy+l4cffhgLFy7Eb3/725TQOn78+JRB5eeffz5Gjx6Nn//857jzzjvlvXEHnOzjkCFDMGTIkOT/Kysr0djYiNtuuy0ZXpw+px/cvp8HHngAvXr1wpQpU1Lu1/E4OhF0OQx1eJkzZ47ljIlBgwa5eu4+ffoAOJlA+/btm7z/wIEDybTZp08fHD16FAcPHkz55X7gwAFMmDDB1et2ZncfX3nlFbz77rtpf3vvvffS0nEmGzduxK5du7BmzRrLbUePHo1u3brhzTff9PzF59f+JfTt2xfl5eV48803AYTnGB47dgxTp07Fnj178Mwzz1hewl7mMcympKQEXbt2Tfsl1rEMddanT5+M2+fn5+P000/PuY2T80AGN/uXsGbNGlxzzTX49a9/jUsvvTTntl26dMEnP/nJ5DnrJy/72NH48ePx4IMPJv+vyzEEvO2jEAIrV65EdXU1CgoKcm4b5HF0SotyKGXkTIg4HbC7ePHi5H1tbW0ZB+yuWbMmuc2+ffsCHez54osvJu/bvHmz7cGeM2fOTJuhks2rr74qAIjnnnvO9ft1yuv+JTQ3N4vCwkLxy1/+UggRjmN49OhRMWXKFDFixAhx4MABW6/l1zEcO3as+MY3vpFy37Bhw3IO2B02bFjKfbNnz04bKDh58uSUbSZNmhTYgF0n+yeEEA899JAoKiqyHDSZ0N7eLsaMGSO++tWvenmrrrnZx86++MUvik9/+tPJ/+t0DIVwv4+Jwcmvvvqq5WsEfRwTYHPAbtDlkOHln95++22xbds2sWjRInHqqaeKbdu2iW3btonW1tbkNkOGDBGPPfZY8v+33HKLiMVi4rHHHhOvvvqq+PKXv5xxqnT//v3FH/7wB/Hyyy+Liy++ONBptueee67YtGmT2LRpkxg1alTaNNvO+yiEEPF4XJxyyili2bJlac/517/+VSxatEj86U9/Env27BFPPfWUGDp0qPjEJz7h+z463b/W1lbx7W9/W9TX14s9e/aIDRs2iMrKSnHmmWeG5hgeO3ZMXHHFFaJ///5i+/btKVMy29rahBDBHsPEFNT77rtP7NixQ8ydO1f06NEjOStjwYIForq6Orl9YormvHnzxI4dO8R9992XNkXzhRdeEF27dhW33HKL2Llzp7jlllsCnyptd/8eeughkZ+fL37xi19knba+cOFCUVdXJ3bv3i22bdsmvvrVr4r8/PyUUOsnp/v405/+VKxdu1a88cYb4rXXXhMLFiwQAMSjjz6a3EanYyiE831M+Pd//3cxbty4jM+p03FsbW1NfucBEHfccYfYtm1bckaijuWQ4eWfZs6cKQCk3TZs2JDcBoC4//77k/9vb28XN954o+jTp48oLCwUn/rUp9IS9ocffijmzJkjevfuLbp37y4uv/xy0dDQ4NNepXr//ffF1VdfLXr27Cl69uwprr766rTpip33UQgh7r77btG9e/eM6340NDSIT33qU6J3796ioKBAnHXWWeK6665LWyvFD07374MPPhBVVVXijDPOEN26dRMDBw4UM2fOTDs+Jh/DPXv2ZDyvO57bQR/DX/ziF6K8vFwUFBSI0aNHp7T2zJw5U0ycODFl+2effVZ84hOfEAUFBWLQoEEZQ/Wvf/1rMWTIENGtWzcxdOjQlC9GvznZv4kTJ2Y8VjNnzkxuM3fuXDFw4EBRUFAgzjjjDFFVVSXq6+t93KN0TvZx8eLF4qyzzhJFRUXitNNOExdccIF46qmn0p5Tp2MohPPz9NChQ6J79+7innvuyfh8Oh3HRAtRtvNOx3KYJ8Q/R9kQERERGYDrvBAREZFRGF6IiIjIKAwvREREZBSGFyIiIjIKwwsREREZheGFiIiIjMLwQkREREZheCEiIiKjMLwQERGRURheiIiIyCgML0RERGQUhhciIiIyyv8HOZbwHcnf8NsAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Y,baseCost); plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Extraction of a tubular structure" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.700111Z", "iopub.status.busy": "2024-04-30T08:56:26.700003Z", "iopub.status.idle": "2024-04-30T08:56:26.702429Z", "shell.execute_reply": "2024-04-30T08:56:26.702195Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'AsymmetricQuadratic2',\n", " 'exportValues':1,\n", " 'seed':[0.75,-0.5],\n", " 'tip':[-0.75,-0.5]\n", "})\n", "\n", "# Define the domain\n", "n=201\n", "hfmIn.SetRect(sides=[[-1.1,1.1],[-0.6,0.6]],dimx=n)\n", "X,Y = hfmIn.Grid()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.703891Z", "iopub.status.busy": "2024-04-30T08:56:26.703784Z", "iopub.status.idle": "2024-04-30T08:56:26.705881Z", "shell.execute_reply": "2024-04-30T08:56:26.705641Z" } }, "outputs": [], "source": [ "tubularMetric = AsymQuad(baseCost*fd.as_field(xp.eye(2),baseCost.shape), # D=baseCost*Id\n", " [5*tgtGammaX,5*tgtGammaY]) # w\n", "hfmIn['metric'] = tubularMetric" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.707292Z", "iopub.status.busy": "2024-04-30T08:56:26.707192Z", "iopub.status.idle": "2024-04-30T08:56:26.755256Z", "shell.execute_reply": "2024-04-30T08:56:26.754828Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.013042 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The front propagates along the tubular structure. This propagation is asymmetric, since the direction proportional to the tangent is strongly penalized." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.756918Z", "iopub.status.busy": "2024-04-30T08:56:26.756790Z", "iopub.status.idle": "2024-04-30T08:56:26.822088Z", "shell.execute_reply": "2024-04-30T08:56:26.821783Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Y,hfmOut['values']); plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.823659Z", "iopub.status.busy": "2024-04-30T08:56:26.823549Z", "iopub.status.idle": "2024-04-30T08:56:26.890345Z", "shell.execute_reply": "2024-04-30T08:56:26.890056Z" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Y,ad.remove_ad(isoOut['values'])); plt.axis('equal')\n", "plt.plot(*hfmOut['geodesic'],color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exchanging the role of the seeds and tips yields the other half of the tubular structure, thanks to the metric asymmetry." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.891993Z", "iopub.status.busy": "2024-04-30T08:56:26.891885Z", "iopub.status.idle": "2024-04-30T08:56:26.893683Z", "shell.execute_reply": "2024-04-30T08:56:26.893449Z" } }, "outputs": [], "source": [ "hfmIn['seed'],hfmIn['tip'] = hfmIn['tip'],hfmIn['seed'] " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.894994Z", "iopub.status.busy": "2024-04-30T08:56:26.894893Z", "iopub.status.idle": "2024-04-30T08:56:26.942625Z", "shell.execute_reply": "2024-04-30T08:56:26.942158Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.013061 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:26.944233Z", "iopub.status.busy": "2024-04-30T08:56:26.944138Z", "iopub.status.idle": "2024-04-30T08:56:27.012523Z", "shell.execute_reply": "2024-04-30T08:56:27.012255Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Y,ad.remove_ad(isoOut['values'])); plt.axis('equal')\n", "plt.plot(*hfmOut['geodesic'],color='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In contrast, a symmetric metric cannot recover such a structure, due to the shortcuts problem." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.014090Z", "iopub.status.busy": "2024-04-30T08:56:27.013982Z", "iopub.status.idle": "2024-04-30T08:56:27.015836Z", "shell.execute_reply": "2024-04-30T08:56:27.015589Z" } }, "outputs": [], "source": [ "hfmIn['metric'] = AsymQuad(hfmIn['metric'].m,[0,0])" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.017237Z", "iopub.status.busy": "2024-04-30T08:56:27.017137Z", "iopub.status.idle": "2024-04-30T08:56:27.054994Z", "shell.execute_reply": "2024-04-30T08:56:27.054695Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.008746 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.056539Z", "iopub.status.busy": "2024-04-30T08:56:27.056417Z", "iopub.status.idle": "2024-04-30T08:56:27.125366Z", "shell.execute_reply": "2024-04-30T08:56:27.125055Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Y,ad.remove_ad(isoOut['values'])); plt.axis('equal')\n", "plt.plot(*hfmOut['geodesic'],color='red');" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.126951Z", "iopub.status.busy": "2024-04-30T08:56:27.126837Z", "iopub.status.idle": "2024-04-30T08:56:27.128567Z", "shell.execute_reply": "2024-04-30T08:56:27.128342Z" } }, "outputs": [], "source": [ "# Save for future use\n", "hfmIn['metric']=tubularMetric\n", "tubularIn = hfmIn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Asymmetric Rander metrics\n", "\n", "In this section, we present a highly tunable class of metrics, strongly asymmetric and anisotropic, referred to as *asymmetric Rander* metrics. They generalize both Rander metrics and asymmetric quadratic metrics, and take the following form\n", "$$\n", " F_x(\\dot x) := \\sqrt{ \\|\\dot x\\|^2_{M(x)} + \\max\\{0,\\}^2+\\max\\{0,\\}^2}+,\n", "$$\n", "where $M$ is a field of positive definite matrices, and $u,v,w$ are vector fields, with $w$ small enough.\n", "\n", "Clearly, asymmetric Rander metrics reduce to:\n", "* Riemannian metrics if $u=v=w=0$. (Or $u+v=0$ and $w=0$, why ?)\n", "* Asymmetric quadratic metrics if $v=w=0$.\n", "* Rander metrics if $u=v=0$.\n", "\n", "Using several non-zero vector fields among $u,v,w$ one can achieve anisotropies that are not realizable with the simpler metric classes, and whose uses cases are yet to be determined.\n", "\n", "**Limitations.** Fast marching with Asymmetric Rander metrics is currently only available in two dimensions, and is not GPU accelerated." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.129948Z", "iopub.status.busy": "2024-04-30T08:56:27.129857Z", "iopub.status.idle": "2024-04-30T08:56:27.131759Z", "shell.execute_reply": "2024-04-30T08:56:27.131502Z" } }, "outputs": [], "source": [ "if xp is not np: raise ad.DeliberateNotebookError(\"Sorry, asymmetric Rander metrics are not supported by the GPU Eikonal solver\")" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.133247Z", "iopub.status.busy": "2024-04-30T08:56:27.133147Z", "iopub.status.idle": "2024-04-30T08:56:27.137774Z", "shell.execute_reply": "2024-04-30T08:56:27.137522Z" } }, "outputs": [], "source": [ "from agd.Metrics.asym_rander import AsymRander" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.139387Z", "iopub.status.busy": "2024-04-30T08:56:27.139290Z", "iopub.status.idle": "2024-04-30T08:56:27.141662Z", "shell.execute_reply": "2024-04-30T08:56:27.141408Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'AsymRander2',\n", " 'seed':(0,0),\n", " 'exportValues':1,\n", " 'factoringRadius':-1, \n", " 'exportGeodesicFlow':1,\n", "})\n", "hfmIn.SetRect([[-1,1],[-1,1]],dimx=101)\n", "X = hfmIn.Grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since we use a large factoring radius, constant metrics are reproduced up to numerical precision." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.143053Z", "iopub.status.busy": "2024-04-30T08:56:27.142945Z", "iopub.status.idle": "2024-04-30T08:56:27.145190Z", "shell.execute_reply": "2024-04-30T08:56:27.144977Z" } }, "outputs": [], "source": [ "def check(constant_metric):\n", " # Run\n", " hfmIn['metric'] = constant_metric\n", " hfmOut = hfmIn.Run()\n", " \n", " # Display\n", " plt.axis('equal')\n", " plt.contourf(*X,hfmOut['values'])\n", " plt.scatter(0,0,color='red') # Seed position\n", " \n", " # Check : \n", " assert np.allclose(hfmOut['values'],constant_metric.norm(X))\n", " assert np.all(np.isfinite(hfmOut['flow']))\n", " assert np.sum((constant_metric.norm(hfmOut['flow']) - 1)>1e-8)<12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Choosing $u$ and $v$ as large vectors, while $w=0$, yields a metric that almost forbids motion except in the cone defined as \n", "$$\n", " \\leq 0 \\text{ and } \\leq 0\n", "$$\n", "\n", "**Constructor of `AsymRander`.** Input arguments are $m,u,v,w$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.146539Z", "iopub.status.busy": "2024-04-30T08:56:27.146431Z", "iopub.status.idle": "2024-04-30T08:56:27.280851Z", "shell.execute_reply": "2024-04-30T08:56:27.280518Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.00835 s.\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "check( AsymRander( np.eye(2), [4.,0], [0.,4.], None ) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we choose $u=0$, while $v$ and $w$ are non-zero." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.282557Z", "iopub.status.busy": "2024-04-30T08:56:27.282429Z", "iopub.status.idle": "2024-04-30T08:56:27.374600Z", "shell.execute_reply": "2024-04-30T08:56:27.374296Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.008991 s.\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "check( AsymRander( np.eye(2), None, [0.,4.], [0.5,0.] ) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously, all three of $u,v,w$ may be zero, producing even stranger anisotropy shapes. \n", "\n", "Alternatively, as discussed above, we may reproduce an asymmetric quadratic metric by choosing $v=w=0$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.376234Z", "iopub.status.busy": "2024-04-30T08:56:27.376112Z", "iopub.status.idle": "2024-04-30T08:56:27.423797Z", "shell.execute_reply": "2024-04-30T08:56:27.423406Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.012941 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "asymQuadOut = tubularIn.Run()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.425417Z", "iopub.status.busy": "2024-04-30T08:56:27.425302Z", "iopub.status.idle": "2024-04-30T08:56:27.481336Z", "shell.execute_reply": "2024-04-30T08:56:27.480987Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.015474 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "tubularIn2 = tubularIn.copy()\n", "tubularIn2.update({\n", " 'model':'AsymRander2',\n", " 'metric':AsymRander(tubularMetric.m,tubularMetric.w,None,None),\n", "})\n", "asymRanderOut = tubularIn2.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Most values (95%) are reproduced up to machine precision. " ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.482925Z", "iopub.status.busy": "2024-04-30T08:56:27.482808Z", "iopub.status.idle": "2024-04-30T08:56:27.485178Z", "shell.execute_reply": "2024-04-30T08:56:27.484937Z" } }, "outputs": [], "source": [ "assert np.sum(np.abs(asymRanderOut['values']-asymQuadOut['values'])>1e-8)/tubularIn.size < 0.05" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference between the non-reproduced values is rather small, yet non-zero." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.486568Z", "iopub.status.busy": "2024-04-30T08:56:27.486470Z", "iopub.status.idle": "2024-04-30T08:56:27.488339Z", "shell.execute_reply": "2024-04-30T08:56:27.488105Z" } }, "outputs": [], "source": [ "valueDiff = np.abs(asymRanderOut['values']-asymQuadOut['values'])\n", "assert np.max(valueDiff) < 0.06\n", "assert np.mean(valueDiff) < 3e-4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The reason some values are not exactly reproduced is because the numerical scheme involves adaptive and anisotropic stencils, which depend discontinuously on the metric. Due to numerical discretization errors, the stencil may differ at one place, and this creates a discrepancy between the numerical solutions, which is propagated in a subdomain. This behavior may be avoided by using fixed stencils, but in that case the scheme becomes more numerically expensive and less accurate." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:56:27.489734Z", "iopub.status.busy": "2024-04-30T08:56:27.489628Z", "iopub.status.idle": "2024-04-30T08:56:27.558165Z", "shell.execute_reply": "2024-04-30T08:56:27.557852Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Places where the cost functions differ\")\n", "plt.contourf(valueDiff>1e-8);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3", "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": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 2 }