{ "cells": [ { "cell_type": "markdown", "id": "7258b087", "metadata": {}, "source": [ "# 13 · Outline Areas: the shoelace formula, its gradient, and its Hessian\n", "\n", "A **closed outline** (or *chamber*) is a loop of edges through 2D vertices. simkit measures the\n", "**signed area** each loop encloses with `outline_areas` and differentiates it with\n", "`outline_areas_gradient` and `outline_areas_hessian`. We check the area on shapes we can measure by\n", "hand, see why the loop's orientation sets its sign, follow the gradient to inflate a star, and verify\n", "both derivatives against finite differences." ] }, { "cell_type": "markdown", "id": "ade57f11", "metadata": {}, "source": [ "Imports, and every tunable parameter of this notebook." ] }, { "cell_type": "code", "execution_count": 1, "id": "815d0aef", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:37.630464Z", "iopub.status.busy": "2026-09-24T03:44:37.630320Z", "iopub.status.idle": "2026-09-24T03:44:38.186855Z", "shell.execute_reply": "2026-09-24T03:44:38.186296Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import os\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import simkit\n", "import utils\n", "\n", "NOTEBOOK = \"013_outline_areas\" # this file's name\n", "RESULTS_DIR = utils.notebook_results_path(NOTEBOOK) # results/013_outline_areas/\n", "MEDIA_DIR = \"media\" # tracked copies for the website\n", "# 1 · known areas and the shoelace fan\n", "N_GON = 8 # sides of the regular test polygon\n", "R_GON = 1.0 # its radius\n", "PENTAGON = np.array([[0.0, 0.0], [2.0, -0.3], [2.4, 1.1],\n", " [1.0, 2.0], [-0.5, 1.2]]) # irregular CCW pentagon (fan picture, derivative checks)\n", "FAN_SHIFT = np.array([0.8, 0.6]) # moves the pentagon off the origin so some fan triangles are negative\n", "N_SIDES_SWEEP = np.unique(np.round(np.logspace(np.log10(3), np.log10(2000), 40)).astype(int)) # n-gon sizes\n", "# 2 · orientation\n", "RECT_W, RECT_H = 1.6, 1.0 # rectangle for the winding test\n", "FLIP_HEIGHTS = np.linspace(-1.0, 1.0, 81) # top-edge heights swept through the degenerate A = 0 loop\n", "# 3 · gradient ascent on a star\n", "STAR_POINTS = 10 # star tips (the loop has 2 * STAR_POINTS vertices)\n", "STAR_R_OUT, STAR_R_IN = 1.0, 0.42 # tip and notch radii\n", "DT = 0.08 # gradient-ascent step size\n", "N_STEPS = 90 # gradient-ascent steps (video has N_STEPS + 1 frames)\n", "FPS = 20 # video frame rate\n", "# 4 · finite-difference checks\n", "FD_H_GRAD = 1e-6 # central-difference step for the gradient\n", "FD_H_HESS = 1e-3 # central-difference step for the Hessian\n", "SEED = 0 # random pose for the \"Hessian is constant\" check\n", "# plot colors\n", "POS_C, NEG_C, EDGE_C = \"#2a9d8f\", \"#e76f51\", \"#264653\"" ] }, { "cell_type": "markdown", "id": "df348f6c", "metadata": {}, "source": [ "## 1 · Known areas\n", "\n", "The signed area of a closed loop with edges $E$ is the shoelace (Gauss) formula below. We evaluate it\n", "with `simkit.outline_areas` (edges from `simkit.closed_polyline`) on a right triangle ($A=\\tfrac12$), a\n", "unit square ($A=1$) and a regular $n$-gon of radius $r$ ($A=\\tfrac12 n r^2\\sin(2\\pi/n)$); each panel's\n", "title compares the two, and they agree to every printed digit.\n", "\n", "$$A = \\tfrac{1}{2} \\sum_{(i,j)\\in E} \\big(x_i\\, y_j - x_j\\, y_i\\big)$$" ] }, { "cell_type": "code", "execution_count": 2, "id": "84ec53e1", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:38.188085Z", "iopub.status.busy": "2026-09-24T03:44:38.187956Z", "iopub.status.idle": "2026-09-24T03:44:38.361162Z", "shell.execute_reply": "2026-09-24T03:44:38.360843Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "shapes = [\n", " (\"right triangle\", np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]), 0.5),\n", " (\"unit square\", np.array([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]), 1.0),\n", " (f\"regular {N_GON}-gon (r = {R_GON:g})\",\n", " simkit.circle_outline(R_GON, N_GON + 1)[0][:-1], # drop the repeated closing vertex\n", " 0.5 * N_GON * R_GON ** 2 * np.sin(2 * np.pi / N_GON)),\n", "]\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(13, 4.2))\n", "for ax, (name, X, exact) in zip(axes, shapes):\n", " E = simkit.closed_polyline(X)\n", " A = simkit.outline_areas(X, [E])[0]\n", " utils.draw_closed_outline(ax, X, E, color=POS_C)\n", " utils.setup_axes(ax, title=f\"{name}\\nshoelace A = {A:.4f} (exact {exact:.4f})\")\n", "fig.suptitle(\"Signed area of closed outlines via simkit.outline_areas\", y=1.03)\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"known_areas.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"013_known_areas.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1e44bf3a", "metadata": {}, "source": [ "Each shoelace term $\\tfrac12(x_i y_j - x_j y_i)$ is the signed area of the triangle (origin, $p_i$,\n", "$p_j$). Below, the pentagon used in section 4 is shifted off the origin and each edge's triangle is\n", "coloured by its term: edges that walk counter-clockwise around the origin give positive triangles\n", "(left), edges facing the origin give negative ones (middle), and the overlap outside the pentagon\n", "cancels, leaving exactly its area (right). The printout lists the five terms and confirms that the\n", "shift does not change the area." ] }, { "cell_type": "code", "execution_count": 3, "id": "8fcaabc2", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:38.362404Z", "iopub.status.busy": "2026-09-24T03:44:38.362320Z", "iopub.status.idle": "2026-09-24T03:44:38.621376Z", "shell.execute_reply": "2026-09-24T03:44:38.620969Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "terms: [-0.72 1.9 2.63 1.23 -0.63] sum = 4.4100\n", "outline_areas: shifted 4.4100, unshifted 4.4100\n" ] }, { "data": { "image/png": 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XLlxY6XGKBUborC5RjLqiNAw0QkUd6GwyvXbFUcUHDx4URsXQfYTa0e3bt2PEiBHCdUqCr7jQiC6aukojy+qrIa9LI3BrO7NLI9cUaN/RiCsaqUqj2hRoG90XHx9f6bE0sio2NrbWstLIXSrjk0b/UtnoTDidPX/SdOP6oBHRFafb0mq7VB7ariCTyYRR3RU/2+POvFfc34qy0j6vuJ1uV0Sj+Ci/F53xf/HFF7F7925hdBuNIqcRa/VBeRtpFHHV9A+KdA806pdGEdJIBvoO6e+CphXTiAfGWN3MmjWr0m0avUt/WzTSkVDdT1Mm6W+s4t8+jbKltDiKtA00K4KeR3/vFXPz0t8vjQCuiOoixewMeu309HQhbQzVTw1pKxQLbtHIYZqdokCjMakeoTZE0S7QKB4aLUSzNyp+HkpHQaOzKqahqI/6vi6N3FXMoKmKRuhWHC2sqM+rpnei7TS1l/ZdxWMCqncrTh2uitqfuqQCotdLTEwURmypCo2erTjTRbEyPM2MobQNVbfXpb1SJxptd+DAAWF0Mo1+o7z09LuqiEY00whmmmJN3xGNrqbvdtmyZcL+Y4xpt4r9BurzUFtGaRioDmxom1SftoPaXWonK7YdgwYNEuqaEydOVHo81ZU1zdqs2s9RHPNX7Qso+j9V+zl1qevpteoz+pdGOStSM1EfhfqNlKqvah1aE6pTabbNky41pbOoitpf6k9WHU1dVzRymH4XVdMpMcaYMjgFhB6hTnNFlO6ApnYqppRQLiq6XXWlVOpwUyNN9xOahkMHAjTtn9I50FQlmm5L03VUtZgbrWLq5eUldKoVBxB0nVJH0HQiQtOBKSBMaQfoUhNKc1BfDXldRdqGqiinYNUDJuqs01SvqnkKaXvF4CxNpaWOHQUYKH3CkCFDhOBmbVORH4e+F5qCRcF8OjCi9BY0/ZU6/MrkjaIpY1U/A6F8Yo/7bLWhadw15X6m31dFdZkKRp+Vppf9888/wuetKzp4pKlrlLqjpgN1CpBUzOtJfzN0cEkBaJrqVXWfMMaqq/p3ogjWUj1B+QLpxBd1+qq2WwqKQKWiXarablEwuKbUNlS/UMeNcgpWPIFZWx1eF/T3Tx00mkpL+XOpbqI2QnGyktDnoRNXlOZCVW1VQ173cZ+zPvU5BXrpfSlnJX1OOilGQQBKH0HBVjoZR/VkQxZDpYVyqN6m1Ef0vVLKKTq+6NWrV71fqyGfjTyuvaIThHTyoCJq5ynwoSqUDkqBpodTEJhQHs7a0DEFpYCgHM/0G+TF4RjTbnRih9LR0Akfaj8qniCrOtBB1ajtoHQLtQV1lW07qP+jSPdXcTsFudVV11OAlwK9FPylVEgVT+xRu09p3Og9HocGdNBFWXSClNJbUL+tIYuyUd+c0udR/n86mcuYvuEUEOrDAWA9VjUA+aTtFe+n0U00spIWy6LOBo0+ocaVtqmqoaJOJeWApDPSNEKHRrtQLifFKC/FSCPq5FTNFazQkGBpQ163ttG/tXUIa9te8eCPcmRdv35dGFVFo5+pg00Bd8oXXPFse11R3mIakbZr1y7hO6PcmnTgSTkEO3bs+Njn1nbWvD6fry4jv+jMe8VOK+ViptvU6aWTAgpVR/bVRNGxr9pRfxwK4FKuSMpxVjUfJwWF6YCWToZU/XyK4AsFDTgAzNiTPakOpHqY2hrKvV7TYxvSztCCcrR4GJ1QokVJ6e+WXpvqQaprlWmrKG8ijaiiepZmHlBHl07aKdDnoferbTGa2jrhT1Lf131cDsKGtlf0mjRajEY70YwIGrlKJ2zpZC21XfUNjFKwk3IV0ywjei0aQUUjYSnnMJ14ftxxiiraqoqfrSaUj7Hqwn8UbGhoLv0nofaO9iV9x48LADe03WOMaQbNxKTgL7UbdNKH2g2q2+ikz+NmU6gCvT7NHKHj7prQ4BNl2o661K11qevrg/ozlL+YgsB0qYrq0CcFgCnwToH5J6HZRI9b8JPW16HPRnmQq+bupfUHaJtigc+a0D6gE8oVFyalnPCKgUq0jfobDTnJypgYSGUS4dLg5xc3/Lm6jgPAeoTO9lY8g0uLtNABgKLTQguI0G16nGK0iSIIRyNi6f6KaFQlXShISyu20pRbanBrC04+KbBcU6eaDgDogIBGrdLU4IoL6lDHlgLD1OGjKUsNUVOZVPG6qkIHF7SwD10oBQEFhWkhnoYEgBWjvmlkLF3oe6apyxS4p8CIoqNZdaVxGu1EB1SNoeqZd8VBD01nrrhycV0oppnVJ7BCixTSwWnV9A+EDrJof9FUNdoniqnkhBZoqu97McYeX1fR3yK1WVU7ohUp2iVqzyoG5Wj0DdUfFU/W0YlLWmCU0ktUrPtp9L4ybRWVkUYwUdCTZjHQ61OQueKMGPo8NNKJRjY1ZCGY2sqk7OuqCtWPNPKXLpSCgBYApUWHKCjckHaU0iTRMQBdqL6lEcV0rEGBdjoRV1NbVXFEuDrRyUiaAlyRuldgp4BEXUYENqTdY4xpBrVJNNCkYjoBWoCsprqtoR7XdlC/QtP9nCfV9fVBAV4KqtKo2aqoXabFzGkQzePaSlqMrqaZiFU9aSYiDSihWUY1jWam4DBdqDxVZzhWfD4d19AxS1W0aKli0IkiBRNjukYikwiXBj8fHACuDZ820iNVG0Ra4ZsoproPGzZM+L9qriLqzJHhw4eXNzhVR8dQYIwUFBQ8tpEndT2woSB0hw4dhE41XZydnctXjlWcXaZUFBQgjoqKqvZ8OkP6JFSmquVRxeuqQsVpUooRbzRFquI+poMLmsr8pAAtrfZbdVVbOvijQHfF16NtVfN+URqMuuTN0hQ6MVD1d0e/T0VO3or5Lmk/0P6iUeU1oRMZdEa9d+/eNd5PB6i0LyoeHNJ+pYNOCly7uLio6FMxpt+oE0h1MZ0ErNre0G1F/Ui5BikNAaV7UeSkJfQ3WXUav2JEUsXXo9XGg4ODKz1OMSKnPp1wqhtoBgyt9E31S8X0D4RyGVPdsWTJkmrPpXI/6b1qaz+VfV1VqGm0aU3HBNShpfq3vm0fnWyj+pW+N0XaDmqrKCBKU5gVqB2kDrW6UfCZgiYVL/UNVNS2P2pKBUInMmjqMv3WK+7zqu0y7RvKGUn7q+oIZcaY9qE2qWr7Rn0zVR5z19TPUbQd1PbRjMCq6PEV21N1qUtdT6iepPrySSfJKMhL6e0o/VDVC52cpZG3NJu0MXIA04Alao+qXhT9bbquyDlf02ekPkzV5yraeSoj3VYcFzDGWH3wCGA9QlMUR44cKUxLpUafRn1SriXF1Hr6n85EU8CPGn86u3n+/Hkh2EVnKBUdCrpNU3TGjBkjdMKoQaXON+VtVASRa0KjOAmNCqKGkabYU0qCxzVg1ImmaTDUuaJcwFWnulBnh0YYUSNKiwDRgQN1jGjxBBoV9aRpkFQmehwFuSl4RyO56LWUfV1VoPekUa9URhoJTIsd0WgBOohRoJxhFCin7+1xC8HFxMQII7PogI9el9Jo0MEDje6uOKqaRhbT4kwUAKepYREREcLBYdU8XtqEvhNKDUIXCpDTQSB9ttOnTwupHDp16lT+WPo90++YRvzRSOqKKNhPwQTKYVnbiImZM2cKqThoQUXapxQs3rBhgzDqjNKhMMZUg9oW6gDRKCAKgFEbRCesqB2jv2/626aFGKnDSH/LNJWWpslTHUePp/qQXqPi3zJ1DKmDSG0XndCk16LRQFQnKhZ5JDQ6iLbRiUcafUz1L+Vhp0tt6H2pPHShx1cdVUXtKdUflG4iPDxcmIZKbSDNxKDUEd9++22l3OK1tZ+UU5BOalHggOpuZV9XFShfPZ04pH1KI7IpiEnHCJTrvuLJNMo5TwuVPSkdEH0GGlFLI6do9s/Vq1excuVK4fUVC7bRZ6f8kfRd0j6hk3s//vij8H2pe/GkJ1GcfKRFXAm1EadOnRKuv/fee4/dH3TSm9pqCqBToJm+R1rkVBHcVaAgBr0Pfbd03ELHJHQCk9oxGn2t7hHJjDHlUZtE9QOlfqA2h/pm1Megk5qqQm0H1Y1UX9AxMo2QpbaS0iBRPUJloNRI9Ljc3FxcunRJ6GtQO6ruY/+61PWE+jlPGnFLn4X6o9TPrQnNWKWZEXRyuOoJWnXkAKZ1bOhSE6qzq478rfoZaxqIohjtSzmFqz6f9hv13RUzEqlPolgMlI6PFPntGdObFBA8ArhWHADWI9SZpWAqBbgoAEiBREowXxEFt2i6CXWeqZNNDTN1wCtOkVUEhindAwUQqVGh6a/UqD5ukQBqsOjsJXW4KdcTpZugDviTAsDUYaLOXU0NNh0wUFmoA0ode+p00oFT+/bthUXPnoQCvxRIoPegwCEFUinoq+zrqgJ1aumAhnIo0igq6ljTARwdtNUX5QWkACmNIqKDTfr+6cCEclVSsFeBgt30nVCHk74jWiGYznRTh1Rb0X6hctLvlfJj0UkCOpCi3xl9t3WlyKFJJ0VqQ4EhyjFGZ99ppB8dLFNHnfJeVhxpzBhTHrVVFNCj3OeKfIBUl1GnsWInj9oyCqLRiBwKwNLJTKo7qQ6tODKTOrlUR1BOPjqxRZ08OhFKgdKqHUtqC6nTRItq0bRUagMfFwCmYGfPnj2FE090Iq1qDnFCdRJ1sun9adE4xUJ1lOf8SYve0IhoKg+1u1Rm+ryKk3fKvK4q0HdBwQLF6GcKGtBxAn1nDel0UkCb6mNqnykwT/uWvsuKwVNqj6nOX7hwoVAf07EHBcEpYKrpADDl16+I9otCxc9Qk9mzZ5fnUaZgBgVr6PdO3ysFhxXouuL3S7OS6EQItUXUpo8bN04Nn4oxpmp0go5O5lF9R7PJqL6mALAqjyep30eDFL788kuhTqG6mQLANNOFTkDRCSNqAyklAQ3koTa3oXW3Our6uqLXofaeBq/UhPoGFFimx9HIY1UG2bUB5YevmAKJ+q50IXQswAFgJjYSqUS4NPj5pZwCojaS0rqszMREjUZHUWNOnQRtHsnJGGOMqQKdYKTRPhQ4pRkqjDHGGGOMMWh1akc6YfF3Bz+Y13MR4Ypyi4vxzKUIIV0Yndxij/AIYMYYY4yJFo2cogXXKqZ7oNFMNC2+votHMsYYY4wxxjRHIpMKlwY/HzzGtTYcAGaMMcaYaNHia5Sqgaa+07ROSgFAaWwoZQNPh2eMMcYYY0w8OAew+nAAmDHGGGOiRfluKTfwd999J4z6pUXYaIEtWjSLcqMyxhhjjDHGxIFm9SmVA7iEcwDXhnMAM8YYY4wxxhhjjDHGNJoD+HCXzjA3UCIHcFExBoaEcg7gGvAIYMYYY4wxxhhjjDHGmEZJZGVpIBr8fE4BXCsOADPGGGOMMcYYY4wxxjRKIpMIlwY/v5RTQIg6AFxSUoI7d+7A0tKy0irfjDHGdENpaSmys7Ph4uICqbThq76qE7dFjDGm+7g9YowxpmliaIuY+IgiAEzBX1rghTHGmG67ffs2XF1doY24LWKMMf3B7RFjjDFN0+a2SF0kUqlwUeb5TMQBYBr5q/jxW1lZabo4jDHG1JD0n070Kep7bcRtEWOM6T5ujxhjjGmaGNoidZFIJcJFmeczEQeAFWkfKPjLAWDGGNNd2pzmh9sixhjTH9weMcYY0zRtbovUhRaAU2YROCnnAK4Vj41mjDHGGGOMMcYYY4wxHSWKEcCMMcYYY4wxxhhjjDHdxSkg1IcDwIwxxhhjjDHGGGOMMY2SSJRcBE7CiQ5qw3uGMcYYY4wxxhhjjDHGdBSPAGaMMcYYY4wxxhhjjGkUp4BQHw4AM8YYY4wxxhhjjDHGNEoqkwiXBj+/pOHP1XWcAoIxxhhjjDHGGGOMMcZ0FI8AZowxxhhjjDHGGGOMaRSngFAfDgAzxhhjjDHGGGOMMcY0SiKVChdlns9qxgFgxhhjjDHGGGOM6Y1bmRnYEXsZSdlZaGZphefatEcLa1tNF4sxvccjgNWHA8CM6ZGUu/dxMykZLZs5w6mpvaaLwxhjTA9xW8QYY0yTdsZcxgen/wEtFVVKIwYB/HYpFJ/0HoQxbdrzl8MY00kcAGZMT2z56xA+/O5nlJaWQiqV4JN5szBuyEBNF4sxxpgeCTpwGB+sWI0SbosYY4xpaOTvB6f+QYkQ+q2MtndybIYWVjb83TCmITwCWH04OQZjOo4CvhT8/eDbn4TrpKSkVLhNo7AYY4yxxhB94xbeX/6jEPzltogxxlhjyy2U471Th2oM/uLfkcA7YqIavVyMsQp/h1KJ0pf6+PzzzxEQEABLS0s4ODhg9OjRiI6O1smvhAPAjOmws+FRGD/vHSHYW1VJSQmiYuI0Ui7GGGP6Iy8/H6v/2I7x896t1uWmtmjjnv3lJygZY4wxVZMXF2PTlXAMCVqLsNQ7tT6uuLQU4WnJ/AUwpkeOHz+O119/HWfPnsWhQ4dQWFiIwYMHIzc3F7qGU0AwpoOuxMXjm98CcSo0XLhtLAUKSqo/btE3P+D9/AKMHNAHEkn9zpQxxhhjj1NYVISg/YexKjAId9Mf1Pq4X7buEtqtj+fNhJuTI+9UxhhjKkEzTvZdv4bvw4KRlJNVp+eEpCRh0fEDeLtbP9iamPI3wVgjKxvF2/CxqvUdAXzgwIFKt9etWyeMBA4NDUXfvn2hSzgAzJgOuZWUjG/Xb8a+Y6eF2zIJMLa1PQxLS5Gz/xJ2t3ZBqUQCSWkprAoKkQngv19+h71HTuDjN2aimWNTTX8ExhhjIkejevefOIMV6zYjITlF2Obm7Ij5L08SRgNTPnp6jFQqxaCeATh+/iJOh0VixIyFmD91Il4cNQwymUzTH4MxxphI0aySE4k3sSLkNGIy7tX7+XuvX8OppFtY1K0fhnt48kAZxhoRBXClFMho6POLy56blVX5pI+xsbFweZLMTIqSAHZ2dtA1HABmTAek3c/AqsBt2PrXIRSXlA31HdrCBnP8HBH3IB/Xd0Wi0+10+KZl4Z6pMZo8LIClvAhHmzfFQXcHnAwJx/DX5mPhtBcwecQQ7ngzxhhrUIf7VGgElq3dhCtxN4RtTWxtMGfyWGHRUSNDQ2Fb3y4dcetOMlq4OMOpqT1uJiXj/RWrcT7yMj7/6Xf8efQ0Pl0wC14eLflbYIwxVi8XU+9gechphKYmVbvPwtAIYz19YGJggJ/Cz5cFdikDkaRstHBFGfkP8fbxA8II4vd7DoCLhRV/E4yJaBE4Nze3Sts//PBDfPTRR499Lg1QmD9/Pnr16gUfHx/oGkmpCJKuUeTe2tpaiMRbWXHFy5hCdm4u1mzdjXU7/0R+gVzY1svZEnP9neBpa4rMfDl+OXYDnbeF1LrT0syMsNXLFfE25sJtP682WLpgDtq0rFxhMqbv9bwYysiYpkRci8HXv24SgrjEwswMr44biZfHDIe56ZOn0NIB97YDh/Hlmg3Izs2DgUyG1yaMxuxJz8PYyKgRPgFj4qnrxVBGxhpbbMY9fBt6BkcT4qvdZyyTYUQrb4xq4w1zw7I2JTknG4dvxSEtLxcOZuYY2KI1suQFWHXxLG5nl40AVDAzMMT8Lr0wydsPUk6bxxqBPtbzis8cPmkwLI3KBg00RLa8EP5/HMTt27cr7TvjOowAnj17Nvbv349Tp07B1dUVuoYDwIyJUH5BATbtOYCfNu9AZk5ZcvIO9qZ4w98ZXRwtyh/37flEeK05DqMa8v9WRHefdbHD3tZOKDCQCR3vWZOew8wJz8FIicqXMV06yBFDGRlrbNcTErF8XSAOnT4v3KZRvjSTZMbEMbCzrv/fSer9dCz5YU3563m4NcOS+bPQxcdb5WVnTKx1vRjKyFhjuZOThZVhwdgTd7XaQqMyiQSDW7YRRv3WNZ9vYUkxdsZcwbboKBSVVu5E+Ts44+Neg9Da1l6Fn4Cx6vSxnld85ojJQ5QOAPttOlDvffef//wHu3fvxokTJ+Du7g5dVK/Myp9//jkCAgJgaWkpJEUePXo0oqOjH/scSqBMUysqXkxMTJQtN2N6qai4GEEHDmPwtLnCKCkK/npYGWNZ3xb4fXDrSsHfP+MzYHfk6hODv4qKoOeddLx9Lgbt72YJ77NyYxBGv/5/uHjl8X/jjGkCt0eMaVZy2j0sXv4jnp25UAjWUj7f5wY/hb9/+w6LZr7coOAvcbS3w8oP/ovv338LTe1sEH87CZPffB8fr/wFObl5Kv8cjCmD2yLGNCf9YR6+OHccw7b9jt01BH/7uLbE94NG4DW/gHot5mYolWG8Vwd889QweNo1qXRfeFoyxu4OFEYJy4uLVfRJGGM1pYBQ5lIfpaWlQvB3586dOHLkiM4Gf+udA/j48eN4/fXXhSBwUVER3n33XQwePBhXrlyBuXnZ9PGaUNS9YqBYyLXDGKtXpXTo9DksXxuI+MQ7wjZHM0PM8XXE8Ja2kFWp5O7k5CP20h34x6XVay/bFBRh2qVbiGhqhR2ezYSRXZMWLsbkEUOx4JUXYGHGK+Ey7cDtEWOakZGVjZ+37MTG3fshLywUtg3q2RULpk5C6xaqSx00uHd3dPPzwVdrNggnPgP3/o3DwRfw0dwZGNC9i8rehzFlcFvEWOPLLZTj96gwrIsKE65X1cnRBZO9/eBuo9wCTm5W1ljaZzAO3IjBxsvhyC8uKh8h/MPFs/j7Riw+6T0Ifg7OSr0PY0yzXn/9dQQGBgqjf2mwa0pK2QLGNBrZtA5pzHQ2AHzgwIFqo3tpJHBoaCj69u1b6/Mo4Ovk5NTwUjKmx86GR+Gb3zYiMjpOuG1tJMN0HweMa2MPY5m0xjyKgRGp6Lg3vEHvR6Fk/7tZaJORiz1tnHDB2Q4b9+zHP2fO45N5M9GvayelPxNjyuL2iLHGlZefj/U79+GXrbuRk1c2Ererbzu8OW0K/L3bquU9rS0t8OmC2Rj+VG98sOInJCSnYPaHX2BYv554b86rsLexVsv7MlZX3BYx1nhoxG1Q9CWsDj+H9PyH1e5va9sEL7b3R/smjip7T8r3O8zDEwFOrvgp4jzCUssG4pC4B/cx+c8tmNzOH2907lmeW5gxph2LwNXVjz/+KPzfv3//StvXrl2LqVOnQm8DwFVRTg1iZ/f4s2s5OTlo0aKFEJjq1KkTPvvsM7Rv316Zt2ZM512Ji8c3vwXiVGhZINdEJsGL3k3xoldTWBrJan1eUEw63PZH1i+/Sw3Mi4ox6WoSOqc8EBaJS7l3HzPe/wzPPtUbi2e9AjvueDMtwu0RY+pRWFSEoP2HsSowCHfTHwjbvDxa4s1pk9Gni3+jzOrq4d8Be1Z/g5Ubt2Lt9r346/gZnAmLxKKZUzF6UD+eWca0BrdFjKleSWkp9l2/hu/DgpGUk1XtfldLK0z29kdXZ1e1tQdNzcyxuHt/nEq6hV8jQ4TF4gilndh4JRyHb13Hh70GCmknGGPKkUilwkWZ59d3trW+aPAicBTMHTlyJB48eCCskFeb4OBgxMbGwtfXVzgo+vrrr4WkypcvX651Vb2CggLhUjEZtJubm14lwGb661ZSMr5dvxn7jp0WbsskwNjW9njNxwH2po9Phh6bkYcDB2Pgc6hsFXZVKZBKcMDDESfcmqBUIhFGZS2ePQ0jB/ThjjfT+EIH6mqPuC1i+oz+rvafOIMV6zYLI2+Jm7Mj5r88SRiBSzl/NeFybDwWL1+Fq9dvCrd7dfLFx/Nmws1JdSO+mH5raHvEfSPGVIvCFCcSb2JFyGnEZNyrdn8TUzNM8PJF/+bukEkar03KKsjH2kuhOJ5Y1g5VNKKVF97u1q9eOYcZq/F3pseLwF1+dYTSi8C1/3WvXu07tQeAZ8+ejf379wud7doCuTUpLCyEt7c3Jk2ahCVLltT4mI8++ggff/xxte38BTJdlnY/A6sCt2HrX4dQXFK2ctvQFjaY4+cIVwvjJz6/qKQEy07eROcNwUqP/q1NgqUptng3Q7JF2UENjf76+I2ZaObYVE3vyPSFMgc56mqPuC1i+ogOC0+FRmDZ2k24EndD2NbE1gZzJo/FuCEDYWTY8ANyVY5KppHAtFhpgVwOU2NjzJ86ES+OGgaZrPYZMoypsz3ivhFjqnMx9Q6Wh5xGaGpStfssDI0w1tMHQ9zbwkiDdT6lg6B0FPceVl6glIK/i7r1w3APTx4owxqMA8AcANaaADCtkEcJkmnkVENWyBs3bhwMDAzwxx9/1Hg/j7pi+iQ7Nxdrtu7Gup1/Ir+gbCGDXs6WmOvvBE/bup89XnspFda/nYRt9qPR8+pQLAGONm+Kg+4OKJJKhY73wmkvYPKIIdzxZo1+kKPO9ojbIqZvIq7F4OtfN+F8ZNksEgszM7w6biReHjMc5lq4CMbNpGS8v2J1eXk7tG2NTxfMElJUMNaY7RH3jRhTjdiMe/g29AyOJsRXu89YJsOIVt4Y1cZba/LtPiwqROCVCPwVHy2kg6ior2tLvN9zAFwseAQiqz99DgBfeW2U0iOA2/2yW6/2nVpyAFOseO7cudi5cyeOHTvWoM52cXExLl26hGHDhtX6GGNjY+HCmC7LLyjApj0H8NPmHcjMyRW2dbA3xRv+zujiaFGv1wpJzUZB6C21B3+JrBQYdOsufO9mCrmB422ApT+uxZ9HT2Hpgjlo01J1q8Azpsn2iNsipi+uJyRi+bpAHDp9XrhtaGiAKSOGYsbEMbCz1t4D55bNnPH7/z7EtgOH8eWaDbgUE4fn//M2XpswGrMnPQ9jI+0IEDDdxX0jxlTjTk4WVoYFY0/c1WqBVJlEgsEt2wijfrUttYKpgSFe9e2C3q4tseriWdzOLlsjiVD6ilE7NmB+l16Y5O0nLCjHGKsD+ltR5u+F/9ZUEwB+/fXXERgYKIy2srS0REpKWU44itKb/jsy5KWXXkKzZs3w+eefC7c/+eQTdO/eHa1btxbyM3711Ve4desWpk+fXp+3ZkxnFBUXY+ehY/h+wxak3ksXtrlbGWOunxP6u1rVe6pQflERjkSlIuBULBqTQ54cc8LicdbFDntbOyHiWixGz3kLsyY9h5kTnoOREmftGHsSbo8YU15y2j2s3BSEHQePCvlLKa8vLao298XxcHEQR2ofKvP4YU+jX7fOWPLDGiGI/WPgdvx98iyWzJ+FLj7emi4i02HcFjGmnPSHefg58gI2X41EYUlxtftpUbVJ3r5wMrfU6l3tadcEXz81FDtjrmBbdBSKSsvS+eUVFeKzs8eEEcIf9xqE1rb2mi4qY0yP1SsA/OOPPwr/9+/fv9L2tWvXYurUqcL1hISESguDZGRk4LXXXhOCxba2tujcuTPOnDmDdu3aqeYTMCaiUSKHTp/D8rWBiE+8I2xzNDPE7A6OeNbdFjJpw85yrY1MQ7vtF6AJ9Jfe80462t3Pwva2zXC5qZWQk3H/iWAsXTAbHdt5aqRcTPdxe8RYw2VkZePnLTuxcfd+yAsLhW2DenYVFngT6ywOR3s7rPzgvzh46iw++WEN4m8nYfKb7+OFEc/gzVcmw8LcTNNFZDqI2yLGGia3UI7fo8KwLipMuF5VJ0cXTPb2g7uNnWh2saFUhvFeHdDDpTlWhZ9FdPqjhevC05IxdncgZvgFYLpvgEZzFzOm7WhAnKSBsRHF85mKF4FrTPqY/4TplrPhUfjmt42IjI4TblsZyTC9vQPGt7WHsazhS7YdS8zE9V2R8AhPgKZRRRLR1Ao7PJshx8hAmHkxZeRQzJ/6AizMtGu6FtM+YqjnxVBGxh4nLz8f63fuwy9bdyMnr2zRmoAO7fDmtMk6dcIuMzsHX63ZgKADh4Xbjk3s8NHcGRjQvYumi8ZEQAx1vRjKyFhN5MXFCIq+JCyelp7/sNr9bW2b4MX2/mjfxFHUO7CktBQHbsRg4+Vw5BcXVbqvtY09Puk9CH4OzhorH9N++ljPKz7ztdnPw9JYiRzABYXw+nG7Xu07tYwAZozVz5W4eHzzWyBOhYYLt01kEkzxaoqXvJvC0ki5M7+Z+XKERKWgsxYEfwmdZ/O/m4U2GbnY08YJF5ztsGH3fmE67ifzZqJf106aLiJjjOmlwqIiBO0/jFWBQbib/kDYRgul0QKefbt01LmREtaWFvh0wWwMf6o3PljxExKSUzD7wy8wrF9PvDfnVdjbWGu6iIwxplcoILrv+jV8HxaMpJysave7Wlphsrc/ujq76kSbRPl+h3l4IsDJFT9FnEdYatnsTxL34D4m/7kFk9v5443OPbVmQTvGmO7jEcCMqcGtpGR8u34z9h07LdyWSYCxre0x3ccBTUxVkxv32/OJ8FpzHEZlKaa0ToytubBIXLpp2UHNs0/1xuJZr8COO95MpGe5xVBGxiqivL77T5zBinWbhSAocXN2xLyXJmJ4/16VUnbpqof5BVi5cSvWbt+L4pIS2FhaYNHMqUKuY10IMjD9rOvFUEbGCE02psXQVoScRkzGo5QICk1MzTDByxf9m7tDJpHq7D44lXQLv0aGIEteecFuZ3NLfNhroJDrmDF9r+cVnzn69bFKjwD2/GGbXu27uuIAMGMqlHY/A6sCt2HrX4eEjiYZ2sIGs30d4WZprLL3+TM+AxlbQ+AalwZtViCV4ICHI064NUGpRCKMylo8expGDujDHW8muoMcMZSRsfLOZmgElq3dhCtxN4RtNOr19cljMW7oIBgZ6t8inZdj47F4+SpcvX5TuN2rky8+njcTbk7inmbM9LOuF0MZGbuYegfLQ04jNDWp2s6wMDTCWE8fDHFvqzf5cLMK8rH2UiiOJ5a1QxWNaOWFt7v1g60Jp81j+lvPKz5zzNzxSgeA236/Va/2XV1xAJgxFcjOzcWarbuxbuefyC8oW8igl7Ml5vo7wdNWtQ35nZx8bDl8Hf57y9JKiEGCpSm2eDdDskXZvujTxR8fvzETzRzFsco8Uz8xHOSIoYyMRVyLwde/bsL5yMvCzjA3M8X0caPw8pjhMDfV744lpcKgkcC0WGmBXA5TY2PMnzoRL44aBpmeBCCYbtT1Yigj01+xGffwbegZHE2Ir3afsUyGEa28MaqNt96mPqB0EJQD+d7Dslz8ChT8XdStH4Z7ePJAGaaX9bziM8fOowBww+uH7AI52nzLAeCacACYMSXkFxRg054D+GnzDmTm5ArbOtib4g1/Z3RxtFDLdN5lwbfRce0piG2SVLEEONq8KQ66O6BIKhU63pR/cvKIIdzxZqI4yBFDGZn+up6QiOXrAoW868TQ0ABTRgzFjIljYGfNv9eKbiYl4/0Vq8uD5B3atsanC2YJeZEZE0NdL4YyMv1zJycLK8OCsSfuqrA4dEUyiQSDW7YRRv3yKFfgYVEhAq9E4K/46Gr7qq9rS7zfcwBcLPhvW5/pYz3PAWD14wAwYw1QVFyMnYeO4fsNW5B6L13Y5m5ljLl+TujvaqW2s7Zbrt0DNgbDIaX64glikWZmJOQGjrcxF277ebXB0gVz0Kalm6aLxjRIDAc5Yigj0z/JafewclMQdhw8KpwkpLy+lN927ovj4eLAsyxqQ/tq24HD+HLNBmTn5sFAJsNrE0Zj9qTnYWykn6PSmHjqejGUkemP9Id5+DnyAjZfjURhSXG1+ym/7SRvXziZW2qkfNosOv0eVl08i9vZmZW2mxkYYn6XXpjk7ScsKMf0jz7W84rPHLdggtIjgFsv36JX+66uOADMWD3zKh46fQ7L1wYiPrFsNVdHM0PM7uCIZ91tIZOqr4GOzcjDgYMx8DlUNmJJzCg78lkXO+xt7YQCA5nQ8Z416TnMnPAcjIz0LzclE8dBjhjKyPRHRlY2ft6yExt374e8sFDYNqhnV8x/eRKfUKuH1PvpWPLDmvKR0x5uzbBk/ix08fFWzxfHtJ4Y6noxlJHpvtxCOX6PCsO6qDDhelWdHF0w2dsP7jZ2GimfWFDQfGfMFWyLjkJRaeXVvf0dnPFxr0FobWuvsfIxzdDrAPCbk5QPAH/zh17tu7riADBjdXQ2PArf/LYRkdFxwm0rIxmmt3fA+Lb2MJapNyFDEaV+OHkTnTcEiy71w+M8MDbA9rbNcLlpWcXcqrkrli6YjY7tPDVdNNbIxHCQI4YyMt2Xl5+P9Tv34Zetu5GTV5Y/MKBDO7w5bTLXnUo4eOosPvlhDe6mPxBuvzDiGbz5ymRYmJup5otjoiGGul4MZWS6S15cjKDoS0Ie2/T8h9Xub2vbBC+290f7JrzIZn3czsrEqvCzwqjgigylMszwC8B03wC9WTCP6Wc9zwFg9eMAMGNPcCUuHt/8FohToWWLrpnIJJji1RQveTeFpVHjNMJrL6XC+reTsM0ugK6hvFcRDtbY0dYFOUYGoFlOU0YOxfypL8DCTL8XLNInYjjIEUMZmW4vYBa0/zBWBQaVBykpZy3lUu/bpSMvGKMCmdk5+GrNBgQdOCzcdmxih4/mzsCA7l1U8fJMJMRQ14uhjEz3lJSWYt/1a/g+LBhJOdXT0blaWmGytz+6Ortym6TEPv77Rgw2XA5HfnFRpfta29jjk96D4Ofg3NCXZyKij/W84jNff+sFpUcAt/o6UK/2XV0Z1PmRjOmZW0nJ+Hb9Zuw7dlq4LZMAY1vbY7qPA5qYNl6agpDUbBSE3tLJ4C+hpBn+aZlok56DPW2ccMHZDht27xem434ybyb6de2k6SIyxphGc9XuP3EGK9ZtRkJyirDNzdkR816aiOH9ewk5f5lqWFta4NMFszH8qd74YMVPwv6e/eEXGNavJ96b8yrsbax5VzPG9DIF3onEm1gRchoxGZVHp5ImpmaY4OWL/s3dIZNwm6QMyvc71MMTXZxc8VPEeYSllqUcJHEP7mPyn1swuZ0/3ujcE+aGnK+e6SaJVCpclHk+qxkHgBmrIu1+BlYFbsPWvw6huKQsD9PQFjaY7esIN0vjRt1f+UVFOBKVioBTsTr/PZkXFWPS1SR0TnkgLBKXcu8+Zrz/GZ59qjcWz3oFdtzxZozpWYf7VGgElq3dhCtxN4RtFIB8ffJYjBs6CEaGnC9dXXr4d8Ce1d9g5catWLt9L/46fgZnwiKxaOZUYYE9dS30yhhj2uZi6h0sDzmN0NSkavdZGBphrKcPhri35dQEKtbUzByLu/fHqaRb+DUyBFnygvKZkxuvhOPwrev4sNdAYYE9xnSNRCoRLso8X0wKCwuRkpKCvLw8NG3aFHZ26subzikgGPtXdm4u1mzdjXU7/0R+QdlCBr2cLTHX3wmetppJRfBj2B24rTkOc3nlBQF0XYFUggMejjjh1gSlEokwKmvx7GkYOaAPd7x1lBimOYmhjEw3RFyLwde/bsL5yLJFP83NTDF93Ci8PGY4zE05NU5juhwbj8XLV+Hq9ZvC7V6dfPHxvJlwc+LclrpKDHW9GMrIxC024x6+DT2Downx1e4zlskwopU3RrXx5lGojSCrIB9rL4XieGJZO1TRiFZeeLtbP9ia8LGBrtHHel7xmW8selHpFBDuX2zQ6n2XnZ2NjRs3YvPmzTh//jzkcrkw+IMGGbi6umLw4MGYMWMGAgICVPq+HABmei+/oACb9hzAT5t3IDMnV9gfHexN8Ya/M7o4Wmhs/xxLzMT1XZHwCE/Q2+8owdIUW7ybIdmi7KCmb0BHIR9jM8emmi4a08ODHDGUkYnb9YRELF8XKKTAIYaGBpgyYihmTBwDO2v+zWky/zKNBF65MQgFcjlMjY0xf+pEvDhqGGS8II/OEUNdL4YyMnG6k5OFlWHB2BN3VRhtWpFMIsHglm2EUb8ccGx8lA6CFt6797BsAVgF+i4WdeuH4R6ePFBGh+h1APidl2FpokQAOF8O989/19p9t2zZMixduhStWrXCiBEj0LVrV7i4uMDU1BTp6emIiorCyZMnsWvXLnTr1g3ff/892rRpo5L35gAw01tFxcXYeegYvt+wBan30oVt7lbGmOvnhP6uVhptQDPz5fjl2A103hYCfVcsAY42b4qD7g4okkqFjjctejR5xBDueOsQMRzkiKGMTJyS0+5h5aYg7Dh4VMj5S3l9KdXA3BfHw8WBT3hpi5tJyXh/xerykdkd2rbGpwtmCYvxMd0hhrpeDGVk4pL+MA8/R17A5quRKCwprnY/pRqY5O0LJ3NLjZSPlXlYVIjAKxH4Kz66WoC+r2tLvN9zAFwsuE7QBXodAF48FVZKBICzKAC8dJ3W7rtJkybhvffeQ/v27R/7uIKCAqxduxZGRkaYNm2aSt6bA8BM79DQ+kOnz2H52kDEJ5Yl1nc0M8TsDo541t0WMi3IGfPt+UR4rTkOI/3K/PBYaWZGQm7geBtz4bafVxssXTAHbVq6abpoTE8OcsRQRiYuGVnZ+HnLTmzcvR/ywkJh26CeXTH/5Ulct2kpCtBvO3AYX67ZgOzcPBjIZHhtwmjMnvQ8jI14QR5dIIa6XgxlZOKQWyjH71FhWBcVJlyvqpOjCyZ7+8HdRn05KVn9Raffw6qLZ3E7O7PSdjMDQ8zv0guTvP2EBeWYeOljPa8vAWBN4gAw0ytnw6PwzW8bERkdJ9y2MpJhensHjG9rD2OZdqwW+Wd8BjK2hsA1Lk3TRdE6FA8/62KHva2dUGAgEzresyY9h5kTnoORES+IJGZiOMgRQxmZOOTl52P9zn34Zetu5OSVTeUM6NAOb06bjI7tPDVdPFYHqffTseSHNeXpOjzcmmHJ/Fno4uPN+0/kxFDXi6GMTLvJi4sRFH1JSCmQnv+w2v1tbZvgxfb+aN+E851rKxqpvTPmCrZFR6GotPKoIX8HZ3zcaxBa29prrHxMOfpYzys+8833pikdAG756W96te/qyqDOj2RMxK7ExeOb3wJxKjRcuG0ik2CKV1O85N0UlkYyaIs7OfmIvXQH/hz8rRGF6HveSUe7+1nY3rYZLje1EnIy7j8RjKULZnPghDGm9blkg/YfxqrAINxNfyBso/QBlNamb5eOnLtPRBzt7bDyg//i4Kmz+OSHNYi/nYTJb76PF0Y8gzdfmQwLczNNF5ExxqopKS3FvuvX8H1YMJJysqrd72pphcne/ujq7MptkpYzlMow3qsDerg0x6rws8KoYIXwtGSM3R2IGX4BmO4bACPOV8/EhGZkKzMrWwtmdDfE8uXLsWDBAly+fBleXl5qSXfJAWCm024lJePb9Zux79hp4bZMAoxtbY/pPg5oYmqoddNKAyNS0XFvWZCa1c6moAjTLt1ChIM1drR1ERZOmrRwMaaMHIr5U1+AhRmvhMsY0676ff+JM1ixbjMSklOEbW7Ojpj30kQM799LyPnLxGlw7+7o5ueDr9ZsQNCBwwjc+zcOB18QFiwd0L2LpovHGGPlKfBOJN7EipDTiMl4FChUaGJqhglevujf3B0yCbdJYuJmZY2lfQbj7xsx2HA5HPnFReUjhH+4eBZ/34jFJ70Hwc/BWdNFZaxOJFKpcGkoZZ6rSf7+/sL/7777Lq5duyYsCkd5gjt06AAfHx88++yzSr8Hp4BgOintfgZWBW7D1r8OobikbErM0BY2mO3rCDdLY2ijLdfuARuD4ZBS/Ww8q12ugQx72jjhgnNZbjLnpvb4eN5M9AvoxLtNRMQwzUkMZWTa1+E+FRqBZWs34UrcDWGbvY01Xp88FuOGDoKRoXadiGTKCQ6/hA9W/FQe5B/Wryfem/Oq8J0z8RBDXS+GMjLtcTH1DpaHnEZoalK1+ywMjTDW0wdD3NvyKFEdcDcvFz9FnEdYatk6Nwo0HnJyO3+80bknzA05X70Y6GM9r/jMtz56TekUEC0++kUU++727dtwc6t5TaOcnBxhNPClS5cQFRWFFStWKP1+HABmOiU7Nxdrtu7Gup1/Ir+gbCGDXs6WmOvvBE9b7R0VGpuRhwMHY+BzqGxlcVZ/MbbmwiJx6aZljcWzT/XG4lmvwI473qIghoMcMZSRaY+IazH4+tdNOB9ZVq+bm5li+rhReHnMcJibam97xJTzML8AKzduxdrte4UT0DaWFlg0cypGD+rH06lFQgx1vRjKyDQvNuMevg09g6MJ8dXuM5bJMKKVN0a18eaAoC6efE66hV8jQ5AlL6h0n7O5JT7sNRB9XFtqrHysbvSxnld85oRPZigdAG7+wc+i2Hfm5uZ48803sWjRIpiZqT99GAeAmU7ILyjApj0H8NPmHcjMyRW2dbA3xRv+zujiaAFtVlRSgmUnb6LzhmAhxy1ruAKpBAc8HHHCrQlKJRJYW1pg8expGDmgD3e8tZwYDnLEUEameZSSZvm6wPLFwQwNDTBlxFDMmDgGdtb8u9EXl2PjsXj5Kly9flO43buzHz56YwbcnHhBJW0nhrpeDGVkmnMnJwsrw4KxJ+4qSqvcJ5NIMLhlG2HUr60Jn4zUZVkF+Vh7KRTHE8vaoYpGtPLC29368W9Ai+l1AHjJTFiZNHzWdlZ+AZq//5Mo9t2ZM2eEvL+JiYlYunQppk6dqtb34wAwE7Wi4mLsPHQM32/YgtR76cI2dytjzPVzQn9XK1EE/dZeSoX1bydhm135DC1ruARLU2zxboZki7ID274BHYV8jM0cm/Ju1VJiOMgRQxmZ5iSn3cPKTUHYcfCokPOX8vrSqM+5L46HiwPXPfq66B+NBKbFSgvkcpgaG2P+1Il4cdQwtSzswfSnrhdDGVnjS3+Yh58jL2Dz1Ugh/2tVNOpzkrcvnMwt+evRI5QOYnX4Odx7mFdpO50AWNStH4Z7eIqiz6xv9LGe18cAsML69euxePFiODg4CKke+vTpA3XgADAT7dSWQ6fPYfnaQMQnluU4cjQzxOwOjnjW3RYykaz8GJKajZD9V+F5KlbTRdE5xRLgaPOmOOjugCKpVOh4L5z2AiaPGMIdby0khoMcMZSRNb6MrGz8vGUnNu7eD3lhobBtUM+umP/yJLRpWXNOL6ZfbiYl4/0Vq8vTgXRo2xqfLpgFLw+egquNxFDXi6GMrPHkFsrxe1QY1kWFCder6uTogsnefnC3KVsvg+mfh0WFCLwSgb/io6uNCu/r2hLv9xwAFwuuS7SJPtbzis98e+kspQPAbotXi27f5eXl4YsvvsCyZcswZMgQfPXVV3B3d1fpe3AAmInO2fAofPPbRkRGxwm3rYxkmN7eAePb2sNYJp4kCvlFRfju+E0E/HFO00XRaWlmRkJu4Hgbc+G2n1cbLF0whwMzWkYMBzliKCNrPHn5+Vi/cx9+2bobOXllo2oCOrTDm9Mmo2M7T/4qWCU0KnzbgcP4cs0GZOfmwUAmw2sTRmP2pOdhbMQL8mgTMdT1YigjUz95cTGCoi8JozvT8x9Wu7+tbRO82N4f7Ztw6hlWJjr9HlZdPIvb2ZmVdomZgSHmd+mFSd5+kPJoYK2g1wHgz+coHwB+Z5UoA8BhYWHYtm0bvv/+exgZGWHu3Ln44IMPYGGhmrSmHABmonElLh7f/BaIU6Hhwm0TmQRTvJriJe+msDQS31TKH8PuwG3NcZjLSzRdFJ1He/isix32tnZCgYFM6HjPmvQcZk54DkZGhpouHhPJQY4YysgaZ1p/0P7DWBUYhLvpD4RtNJKTZhj07dKRp1Gyx0q9n44lP6wpzxHt4dYMS+bPQhcfb95zWkIMdb0YysjUp6S0FPuuX8P3YcFIysmqdr+rpRUme/ujq7Mrt0msGkoPsjPmCrZFR6GotHI/1N/BGR/3GoTWtva85zRMH+t5fQwAr169GhcuXBAuV69eFVLI+fj4oHv37vDz88PmzZsRFxeHHTt2oEuXLkq/HweAmda7lZSMb9dvxr5jp4XbMgkwtrU9pvs4oImpOIN3xxIzcX1XJDzCEzRdFL3ywNgA29s2w+WmZQ1Bq+auWLpgNo/W0wJiOMgRQxmZekdw7j9xBivWbUZCcoqwzc3ZEfNemojh/XsJB2yM1dXBU2fxyQ9ryk8ivDDiGbz5ymRYmKt/BWgm/rpeDGVk6kmBdyLxJlaEnEZMxr1q9zcxNcMEL1/0b+4OmYTbJPZ4t7MysSr8rDAquCJDqQwz/AIw3TcARpyvXmP0sZ5XfObEL15XOgDsuugHUew7Nzc3dOvWTQj40qVz584wNa28QOdnn32GwMBAREVFKf1+HABmWivtfgZWBW7D1r8Oobik7Ozk0BY2mO3rCDfLhlcImpaZL8cvx26g87YQTRdFL1HeqwgHa+xo64IcIwPQLKcpI4di/tQXYGHGqyFrihgOcsRQRqaeDvep0AgsW7sJV+JuCNvsbazx+uSxGDd0EIwMxXkikmleZnYOvlqzAUEHDgu3HZvYCQuWDuiu/AgPptt1vRjKyFTrYuodLA85jdDUpGr3WRgaYaynD4a4t+WAHav3aPK/b8Rgw+Vw5BcXVbqvtY09Puk9CH4OzrxXNUCvA8D/mwsrUyUCwA8L4Pr29zqz71JTU+Hi4oLi4uqLe9aXgUpKxJgKZefmYs3W3Vi380/kF5QtZNDL2RJz/Z3gaSv+AN26yDR02MHBX02h5QH90zLRJj0He9o44YKzHTbs3o9/zpzHx/Nmol9AJ42VjTGmXSKuxeDrXzeVL95lbmaK6eNG4eUxw2Fe5ew8Y/VlbWmBTxfMxvCneuODFT8JI8tnf/gFhvXriffmvCqcaGCM6bfYjHv4NvQMjibEV7vPWCbDiFbeGNXGG+aGnEuc1R/l+x3q4YkuTq74KeI8wlLLFlcncQ/uY/KfWzC5nT/e6NyTf2Os0UikEuGizPPF6PPPP8c777wj5AFu3749jI3LguCOjo44cuSISt6DA8BMa+QXFGDTngP4afMOZObkCts62JviDX9ndHFUTdJrTfszPgN2R67CiNP+apx5UTEmXU1C55QHwiJxyXfvY8Z7n+HZp3pj8axXYMcdb8b01vWERCxfF1iep9XQ0ABTRgzFjIljYGct/pEETLv08O+APau/wcqNW7F2+178dfwMzoRFYtHMqRg9qB/n8GRMD93JycLKsGDsibsqzF6rSCaRYHDLNsKoX1sTPhnJlNfUzByLu/fHqaRb+DUyBFnyAmE7/fY2XgnH4VvX8WGvgejj2pJ3N2Nq0r9/f+H/L774ApcvXxbSy1Eg2NfXV7jQSGAKBiuDU0AwjSsqLsbOQ8fw/YYtSL2XLmxztzLGXD8n9He10pmOz52cfGw5fB3+e8sWsWPao0AqwQEPR5xwa4JSiUQYlbV49jSMHNBHZ35/2k4M05zEUEamnOS0e1i5KQg7Dh4Vcv7SgRcF4Oa+OB4uDk159zK1uxwbj8XLV+Hq9ZvC7d6d/fDRGzPg5qTcAT/TrbpeDGVkDZP+MA8/R17A5quRwmJdVVEAbpK3L5zMLXkXM7XIKsjH2kuhOJ5Y1g5VNKKVF97u1o9PPDQCfaznFZ856ev5SqeAaPbWClHsu+zsbFha1lyfP3z4UMj7GxkZKVxOnTqFYcOGYcmSJQ1+Pw4AM43mVTx0+hyWrw1EfGLZdBNHM0PM7uCIZ91tIRPp0P2aUCBhWfBtdFx7Crwkg/ZKsDTFFu9mSLYoG03RN6CjkI+xmSMHftRNDAc5Yigja5iMrGz8vGUnNu7eD3lhobBtUM+umP/yJLRp6ca7lTWqwqIiYSTwyo1BKJDLYWpsjPlTJ+LFUcMg4wV51E4Mdb0YysjqJ7dQjt+jwrAuKky4XlUnRxdM9vaDu40d71rWKCgdxOrwc7j3MK/Sdhp1vqhbPwz38OSBMmqk1wHgZQuUDwAvXC6Kfefv748DBw7AycmpTo+nReJCQ0Mb/H4cAGYacTY8Ct/8thGR0XHCbSsjGaa3d8D4tvYwluleiHTLtXvAxmA4pGRpuijsCYolwNHmTXHQ3QFFUqnQ8V447QVMHjGEO956fpAjhjKy+snLz8f6nfvwy9bdyMkr6+AEdGiHN6dNRsd2nrw7mUbdTErG+ytWl+eg7tC2NT5dMAteHjwFV9/rejGUkdWNvLgYQdGXhEBbev7Dave3tW2CF9v7o30TngXAGt/DokIEXonAX/HR1VKR9HVtifd7DoCLBddB6qCP9bw+BoBfeeUVIb/v33//DS8vr/Lt4eHhePfdd/HXX39VenxhYSEMlViAmnMAs0Z1JS4e3/wWiFOhZWkQTGQSTPFqipe8m8LSSKaT30ZsRh7SIhLhw8FfUZCVAoNu3YXv3UwhN3C8DbD0x7X48+gpLF0wh0cDMqYjIyyD9h/GqsAg3E1/IGyjoBqd7OnbpSOPaGFaoWUzZ/z+vw+x7cBhfLlmAy7FxOH5/7yN1yaMxuxJz8PYiBd9YkysSkpLse/6NXwfFoyknOoDRFwtrTDZ2x9dnV25TWIaY2pgiFd9u6C3a0usungWt7Mzy+87kXgTo3ZswPwuvTDJ209YUI4xVZBIpMJFmeeLxdq1a/Hhhx+id+/e2LVrFxwcHPDee+9h+/btQrqHqpQJ/hIOALNGcSspGd+u34x9x04Lt2USYGxre0z3cUATU+V+xNqsqKQEOyNT0PlQ2egdJh4OeXLMCYvHWRc77G3thIhrsRg95y3MmvQcZk54DkZGuvu7ZUxXUTqe/SfOYMW6zUhIThG2uTk7Yt5LEzG8fy8h5y9j2oR+k+OHPY1+3TpjyQ9rhIUJfwzcjr9PnsWS+bPQxcdb00VkjNUzBR4FzlaEnEZMxr1q9zcxNcMEL1/0b+4OmYiCGEy3edo1wddPDcXOmCvYFh2FotKyFc3zigrx2dljwgjhj3sNQmtbe00XlekCSgWqTDpQkaUS/fjjj2FsbIynn34axcXFGDhwIIKDg9G1a1eVvxcHgJlapd3PwKrAbdj61yEUl5Q1FENb2GC2ryPcLBs+rF8sNly+i9a7wjjvr0jRYXfPO+lodz8L29s2w+WmVkJOxv0ngrF0wWyeIs6YiDrcp0IjsGztJlyJuyFss7exxuuTx2Lc0EEwUvJsOmPq5mhvh5Uf/BcHT53FJz+sQfztJEx+8328MOIZvPnKZFiYm/GXwJiWu5h6B8tDTiM0NanafRaGRhjr6YMh7m1hxLm+mRYylMow3qsDerg0x6rws4hOf3QCIzwtGWN3B2KGXwCm+wbwb5gpRSKVChdlni8Wqamp+Oyzz/DLL7+gXbt2uHbtGqZOnaqW4C/hADBTi+zcXKzZuhvrdv6J/IKyhQx6OVtirr8TPG3LFtjSdSGp2SgIvQXb7AJNF4UpyaagCNMu3UKEgzV2tHXB9YRETFq4GFNGDsX8qS/Awkw/ftOMiVHEtRh8/eum8jyq5mammD5uFF4eMxzmpvy3y8RlcO/u6Obng6/WbEDQgcMI3Ps3DgdfEBYsHdC9i6aLxxirQWzGPXwbegZHE+Kr3Wcsk2FEK2+MauMNc0NO68K0n5uVNZb2GYy/b8Rgw+Vw5BcXCdsLS4rxw8Wz+PtGLD7pPQh+Ds6aLipjWs/d3R2enp4ICgrC8OHDhQXhJkyYgISEBPzf//2fyt+PF4FjKpVfUIBNew7gp807kJmTK2zrYG+KN/yd0cXRQm/2dn5REb47fhMBf5zTdFGYiuUayLCnjRMuOJetwuzc1B4fz5uJfgGdeF/r+EIHYigje4RO1CxfFyhMmSeGhgaYMmIoZkwcAztr/v6Y+AWHX8IHK34qT2cyrF9PvDfnVWF0O9Ptul4MZWTAnZwsrAwLxp64q9UW0JJJJBjcso0w6tfWhE9GMnG6m5eLnyLOIyz1TqXtNAF/cjt/vNG5J5/YaCB9rOcVnzl55dtKLwLn/J//iWLfbd68GRMnTqy0LSwsDM8++yzGjBmDH374QaXvxwFgphJFxcXYeegYvt+wBan30oVt7lbGmOvnhP6uVnq3eMGPYXfgtuY4zOVlaS+Y7omxNRcWiUs3LRutMWJAH7w7cyrsuOOtswc5YigjA5LT7mHlpiDsOHhUyPlLOVRHD+qHuS+Oh4tDU95FTKc8zC/Ayo1bsXb7XiHVlo2lBRbNnCr85vXt2Euf6noxlFGfpT/Mw8+RF7D5aqQwKrKqPq4tMcnbF07mlhopH2MqT7OVdAu/RoYgS1555quzuSU+7DVQ+M2z+tHrAPCqRbAyNWn46zzMh/OcL0S9727evImhQ4fi6tWrKn1dDgAzpSv8Q6fPYfnaQMQnlp35czQzxOwOjnjW3RYykSXgVoVjiZm4visSHuEJmi4KU7MCqQQHPBxxwq0JSiUSWFtaYPHsaRg5oA93vHXwIEcMZdRnGVnZ+HnLTmzcvR/ywkJh26CeXTH/5Ulo09JN08VjTK0ux8Zj8fJVuHr9pnC7d2c/fPTGDLg5OfKe18G6Xgxl1Ee5hXL8HhWGdVFhwvWqOjm6YLK3H9xtymaRMaZLsgrysfZSKI4nlrVDFY1o5YW3u/Xj0e712Z96WM9zALiyjIwM2NraQpU4AMwa7Gx4FL75bSMio+OE21ZGMkxv74Dxbe1hLBNP4m1VysyX45djN9B5W4imi8IaUYKlKbZ4N0OyRdkUvr4BHYV8jM0cebShLh3kiKGM+igvPx/rd+7DL1t3IycvT9gW0KEd3pw2mRdqZHqlsKhIGAlMi5UWyOUwNTbG/KkT8eKoYZDxolI6VdeLoYz6RF5cjKDoS1gdfg7p+Q+r3d/WtglebO+P9k34hAzTfZQO4qfw87j7sCwdpAKlOlnUrR+Ge3jyQJk60OsA8I/vKD8CePbnerXv6ooDwKzersTF45vfAnEqNFy4bSKTYIpXU7zk3RSWRjK93qPfnk+E15rjMOLMD3qnWAIcbd4UB90dUCSVCh3vhdNewOQRQ7jjrSMHOWIoo74Fu4L2H8aqwCDcTX8gbPPyaCn83fXt0pE7F0xv3UxKxvsrVpcvfNihbWt8umCW8PfBdKOuF0MZ9UFJaSn2Xb+G78OCkZSTVe1+V0srTPb2R1dnV26TmF55WFSIwCsR+Cs+ulr+676uLfF+zwFwseC663H0sZ5XfOaUnxYrHQB2mrlUr/ZdXXEAmNXZraRkfLt+M/YdOy3clkmAsa3tMd3HAU1MDfV+T/4Zn4GMrSFwjUvT+32hz9LMjITcwPE25sJtP682WLpgDk9B14GDHDGUUR9QXt/9J85gxbrN5YtfuTk7Yt5LEzG8fy8h5y9j+o7+TrYdOIwv12xAdm4eDGQyvDZhNGZPeh7GRmW565l463oxlFHXU+CdSLyJFSGnEZNxr9r9TUzNMMHLF/2bu0Mm4TaJ6a/o9HtYdfEsbmdnVtpuZmCI+V16YZK3H6Scr75Geh0A/vl95QPAM5aIbt/FxMTAw8MDBgYGansPDgCzJ7qbnoEfNm3D1r8OCQuMkKEtbDDb1xFulg1fnVGX3MnJx5bD1+G/t2xUNNNv9Fdy1sUOe1s7ocBAJnS8Z016DjMnPAcjIz5ZItaDHDGUUecXGQmNwLK1m3Al7oawzd7GGq9PHotxQwfByJD/thirKvV+Opb8sAaHTp8Xbnu4NcOS+bPQxcebd5aI63oxlFFXXUy9g+UhpxGamlTtPgtDI4z19MEQ97Yw4rQrjAloIcSdMVewLToKRaWVp8n6Ozjj416D0NrWnvdWFfpYz+t7AFgmkwmLvrVt21Zt71GvU5Kff/45AgICYGlpCQcHB4wePRrR0dFPfF5QUBC8vLxgYmKCDh064K+//lKmzKyRZOfmYvm6PzBo6uv448+/heBvL2dLbB7aBp/1as7B3wqjbAIjUuHLwV9WoWLteScdb5+LQfu7WSgqLhZyMo5+/f9w8cqT60z2ZNwe6ZeIazF46b8fYfriT4Xgr7mZKea9PBGH1q3E5JFDOfjLWC0c7e2w8oP/4vv330JTOxvE307C5Dffx8crf0FOblnObNZw3Bbpj9iMe/jPP3swZd/WasFfY5kMY9v64MfBozCytTcHfxmrwFAqw3ivDvjmqWHwtGtSad+EpyVj7O5AYZQw5dJmTECjwqVKXEQ6qry0tGrCFA0HgI8fP47XX38dZ8+exaFDh1BYWIjBgwcjN7dygu+Kzpw5g0mTJuHVV1/FxYsXhaAxXaKiolRRfqYGtHDIb9v2YOBLc7D6j+3IL5Cjg70pfhnogZVPucPTtmyhK1YmKCYdbvsj6/fHxPSCTUERpl26hZeiEmAhL8L1hERMWrgYn676FTl51RcJYXXH7ZF+oL+Z/3zyJcbPe1fIZ2poaIBXnhuBf9b9gDkvjIW5KbdHjNXF4N7dse/nFRg3ZKBwO3Dv3xg2Yz6OnOVFa5XBbZHuu5OThXdP/I0xOzfiaEJ8pftkEgmGurfFqqdH4YV2fjA35PQqjNXGzcoaS/sMxmu+XWAiM6g0QviHi2cxbncgItKSeQcySCRSpS9MDSkg7t69K4wEpoOfvn371viYCRMmCAHiP//8s3xb9+7d4e/vj9WrV9fpffRx+Lsm0CjFXf8cw3frtyD1Xrqwzd3KGHP9nNDf1YoXL6hBbEYeDhyMgc+hsoVWGKtNroEMe9o44YKznXDbuak9Pp43E/0COvFOU0E93xjtEbdFjSc57R5WbgrCjoNHhVkWlNd39MB+mPvSeLg4NG3EkjCme4LDL+GDFT+V59Ae1q8n3pvzqpBShSlX13PfSHekP8zDz5EXsPlqpBCgqqqPa0tM8vaFk7mlRsrHmJjdzcvFTxHnEZZ6p9J2Grc5uZ0/3ujcU+9PqOhjv0PxmVPXfAQrMyVSQOTlw3H6R6Lbd1KpFNeuXVNrCgilsgvTDiV2dmUBjZoEBwdj4cKFlbY988wz2LVrlzJvzVSIzgH8c+Y8lq0NFKYGEkczQ8zu4Ijh7rYwoGH0rJqikhLsjExBZw7+sjowLyrGpKtJ6JzyQFgkLvnufcx47zOMGNAH786cCjvueCuF2yPdkJGVjZ+37MTG3fshLywUtg3sEYAFU1/ghRQZU5Ee/h2wZ/U3WLlxK9Zu34u/jp/BmbBILJo5FaMH9eMT/krgtkj8cgvl+D0qDOuiwoTrVXVydMFkbz+429Te/2WMPV5TM3Ms7t4fp5Ju4dfIEGTJC4TtNDJx45VwHL51HR/2GiicaGF6SJHKQZnnM9UGgGlEzvz589GrVy/4+PjU+riUlBQ4OjpW2ka3aXttCgoKhEvFMwFMPc5FROHrXzchMjpWuG1lJMP09g4Y39YexjIeOv84Gy7fRetdYZz6gdVL24xc/N+5GBzwcMQJtybYe+QkToZcxOLZ0zDiqT7c8dai9ojbosaTl5+P9Tv34Zetu5GTV5aXNKBDO7w5bTI6tvNsxJIwph9MTYzxf9NfxLB+vbB4+SpcvX4Ti75eiT+PnsRHb8yAm1PlupI9GfeNxI3yjwZFX8Lq8HNIz6+epqutbRO82N4f7Zvw3wZjqiCRSIQAr19TJ6y9FIrjiTfL70vOzcasg7swopUX3u7WD7YmnPJLr1AKB2XSOHAKCNUHgCkXMOXxPXXqFNSxoMLHH3+s8tdlj1yJi8c3vwXiVGi4cNtEJsEUr6Z4ybspLI1kvKueICQ1GwWht2Cb/ehEBWN1ZVxSilFxKeiYmokt3s1A2a7+73/fCcHgj+bOQDNHnuKuDe0Rt0XqV1hUhKD9h7EqMAh30x8I27w8WmLhtBfQt0tHPiHCmJq1b+OBoO++EEYC02Klp0IjMGLGQsyfOhEvjhomrEjN6ob7RuJUUlqKfdev4fuwYCTlVB905Gpphcne/ujq7MptEmNqYGVsgnldeqGPmzt+Cj+Puw8frS+19/o1YZTwom79MNzDk/8GGVNSg8Lq//nPf4QcikePHoWrq+tjH+vk5ITU1NRK2+g2ba/NO++8I0yhUlxu377dkGKyGtxKSsbCz5djzOv/FYK/Mgkwvo099o70wut+Thz8rYP8oiIciUqF56myUdOMNVTz7IdYeCEOQ6+nQFZSihMXLmL4a/Oxftc+FPNKuBpvj7gtUu9IuX3HTmHY9Pn4eOUvQvDX1ckBX789Dzt/+FLIjU0jQxhj6mdoYIAZE8YIaSG6+rbHw4ICfP7T75gwfzGuxT8akcVqx30jcabAO377Bp7ftQmLTvxdLfjbxNQMr3fsjuUDhqObixu3SYypGaVXWTFweFmgt8L2jPyHePv4Acw5tFtYlJHpAeoDKHthygeAqaGkA5ydO3fiyJEjcHd3f+JzevTogcOHD1fadujQIWF7bYyNjYVkzRUvTDl30zPw0fe/YOj0edh37LSwbUgLG+x81hPvBDRDE1ND3sV1tDYyDe22X+D9xVRCVgo8fesu3jofC48HuULHe+mPazFp4XuIvcknvzTZHnFbpJ7v7WRIOJ6f+zYWfr5CWISKFp56f86r2L/mWyEnNi2AwBhrfC2bOeP3/32IJfNmwtLcDJdi4vD8f97Git//QIG8ei5Uxn0jsbqYegcv/7VNCCjFZNyrdJ+FoRGm+nTCykEjMbBFK8h4KjFjjcbUwBCv+nbBZ32fgZtl5YVJTyTexKgdG7DpSrgwcp/pMOoLKHuppxMnTmDEiBFwcXERTvhpYs2yt99+G/b29tqTAoKmNgUGBmL37t2wtLQsz5tIK/WZmpblZXnppZfQrFkzYeosmTdvHvr164dvvvkGw4cPx+bNmxESEoKff/5ZHZ+HVZGdm4s1QXuwbsde5BeUHbz3dLbEG/5O8LTlXDr1dSwxE8ZnrsNcXsK/NaZSjnkFmBMWj7Mudtjb2gkR12Ixes5bmDXpOcyc8ByMjPgkTUXcHolPxLUYIef8+cjLwm1zM1O8OnYkpj73LMz/PYZgjGkWnYAZP+xp9OvWGUt+WINDp8/jx8Dt+PvkWSyZPwtdfLz5K6qA2yJxic24h29Dz+BoQny1+4xlMoxo5Y1RbbxhbmikkfIxxsp42jXB108Nxc6YK9gWHYWi0rK+d15RIT47ewx/xUfj416D0NpWvcEypj85gHNzc+Hn54dp06bhueeegyYoYqjqJCml4Th1fXAtQ6nXrl2LqVOnCtf79++Pli1bYt26deX3BwUF4b333sPNmzfRpk0bfPnllxg2bFidC0mLwFGQmdJB8GjguqGRGpv2HMDqP7YjM6csj46PvSnm+Tuji6NFnfc9eyQzX45fjt1A520hvFuYWj0wNsD2ts1wuWnZ7IdWzV2xdMFsnV4Mq771vCbaI26LGuZ6QiKWrwsUAknE0NAAk0cMwcyJz8HOmmf4MKbNDp46i09+WFOeo/uFEc/gzVcmw8LcDLqqPnU9943EgaaNrwwLxp64q6ja8ZVJJBjcsg3GevrwQlOMaaHbWZlYFX4W0emVR+sbSmWY4ReA6b4BMNLBfPX62O9QfObUDV/Aysyk4a+Tlw/HFxc1eN9JJBJhluno0aOha+oVANYUffzxN1RRcTF2/XMM363fgtR76cI2dytjzPVzQn9XK85fpYRvzyfCa81xGPHgX9YIqGKOcLDGjrYuyDEyEFIZTRk5FPOnvgALM90bLSmGel4MZdQmyWn3sHJTEHYcPCrk/KWRhaMH9sPcl8bDxYEXOmRMLDKzc/DVmg0IOlCWQsepiT0+mvsanureBbpIDHW9GMqoDdIf5uHnyAvYfDUShSXF1e7v49oSk7x94WRuqZHyMcbqhlI+/H0jBhsuhyO/uKjSfa1t7PFJ70Hwc3DWqd2p1wHgTf9TPgA8+W0OACubAoJpL4rj/3PmPJatDUT87SRhm6OZIWZ3cMRwd1sYSDkRtjL+jM+A3ZGrHPxljYb+Yv3TMtEmPQd72jjhgrMdNuzeL/ydfzxvprBIFmPaKCMrGz9v2YmNu/dDXlgobBvYIwALpr6ANi3dNF08xlg9WVta4NMFszH8qd74YMVPQu7uWR9+gWH9euK9Oa8KebwZ0ya5hXL8HhWGdVFhwvWaFpua7O0Hdxs7jZSPMVY/UokEQz080cXJFT9FnEdY6p3y++Ie3MfkP7dgcjt/vNG5J6dw0QXCQm7KpICQlAeUq67vYmxsDH3GAWAdcC4iSsirGBkdK9y2MpJhensHjG9rD2MZL6ajrDs5+Yi9dAf+cWkq+LYYqx/zomJMupqEzikPsNXLFcl372PGe58Ji2W9O3Mq7LjjzbREXn4+1u/ch1+27kZOXp6wLaBDO7w5bbJOpy9hTF/08O+APau/wcqNW7F2+178dfwMzoRFYtHMqRg9qB/PMmMaJy8uRlD0JawOP4f0/IfV7m9r2wQvtvdH+yaOGikfY0w5Tc3Msbh7f5xKuoVfI0OQJS8onzm58Uo4Dt+6jg97DRRG9zPm5lZ54MmHH36Ijz76SGt3DOUAfueddxAWFob27durJVjNAWARuxIXj29+C8Sp0HDhtolMgileTfGSd1NYGuleHhxNoGnLgRGp6Li3bB8zpiltM3Lxf+dicMDDESfcmmDvkZM4GXIRi2dPw4in+nDHm2lMYVERgvYfxqrAoPI8oV4eLbFw2gvo26Uj/zYZ0yGmJsb4v+kvYli/Xli8fBWuXr+JRV+vxJ9HT+KjN2bAzYkDa0wz08P3Xb+G78OCkZRTecQXcbW0wmRvf3R1duU2iTGRo/ysFOD1a+qEtZdCcTzxZvl9ybnZmHVwF0a08sLb3fpxXm9RjwBWYgb7v8+9fft2pfQZxlo++pfWryFffPEFLl++LKTPo0Cwr6+vcAkICICjo3LHWZwDWIRuJSXj2/Wbse/YaeG2TAI839oer/k4oImpoaaLp1O2XLsHbAyGQ0r1g0nGNCXB0hRbvJsh2aIsF3DfgI74aO4MNHMUb15VMeS5EkMZG/sE2f4TZ7Bi3WZhSjhxdXLA/JcnYXj/XsJBC2NMt0/+0EjglRuDhMWHTY2NMX/qRLw4ahhkIl6QRwx1vRjK2Fgp8E4k3sSKkNOIyai8QBRpYmqGCV6+6N/cHTJlphMzxrQWpYP4Kfw87j4sW/hewdbEFIu69cNwD09RnvjR6xzAW76BlRJr3mTlPYTjhDdFkQP49u3b1UYqKzx8+BBRUVGIjIwULqdOnRIWL1+yZEmD348DwCJyNz0DP2zahq1/HUJxSdlKZENa2GCOryPcLLX7bIYYxWbk4cDBGPgcuqzpojBWTbEEONK8KQ66O6JYKhE63jTicvKIIaLseIvhIEcMZWysDvep0AgsW7sJV+JuCNsoB+icF8Zi/LBBMDLkE5GM6ZObScl4f8VqnI8sO17q0LY1Pl0wS5gJIEZiqOvFUEZ1u5h6B8tDTiM0tWztk4osDI0w1tMHQ9zbwkiEx0SMsfp5WFSIwCsR+Cs+WkgHUVFf15Z4v+cAuFiIq67U6wDw1mXKB4DHL6zXvsvJyUFcXJxwvWPHjli2bBmeeuop2NnZoXnz5lAXc3NzvPnmm1i0aBHMzMye+PjOnTsjNDS0we/HAWARyM7NxZqgPVi3Yy/yC8oWMujpbIk3/J3gadvwPwxWu6KSEiw7eROdNwSDxwswbZZqZowgr2aItzEXbvt5tcHSBXNEt9iWGA5yxFBGdYu4FiPknFcEeszNTPHq2JGY+tyzMDfl9ogxfZ4RsO3AYXy5ZgOyc/NgIJPhtQmjMXvS8zA2MoKYiKGuF0MZ1SU24x6+DT2Downx1e4zlskwopU3RrXx5oWgGNND0en3sOriWdzOzqy03czAEPO79MIkbz9hQTkx0Md6XpMB4GPHjgkB36pefvllrFu3Dupy5swZLFiwAImJiVi6dCmmTp362McXFhbCUInBNhwA1mI0nW7TngNY/cd2ZOaUTWnwsTfFPH9ndHG00HTxdNpvl1Jh89tJ2GaXJZZnTJvRfICzLnbY29oJBQYyoeM9a9JzmDnhORgZiWM0phgOcsRQRnW5npCI5esCcej0eeG2oaGBMNp85sTnYGetX/uCMVa71PvpWPLDmvK6wsOtGZbMn4UuPt6i2W1iqOvFUEZVu5OThZVhwdgTd7XaCD+ZRILBLdsIo35p2jdjTH8VlhRjZ8wVbIuOQlFp2axpBX8HZ3zcaxBa29pD2+ljPV8eAA5aoXwAeNx8Ue279evXY/HixXBwcMCKFSvQp08ftbwPB4C1UFFxMXb9cwzfrd+C1HvpwjZ3K2PM9XNCf1crUeawEZOQ1GyE7L8Kz1Oxmi4KY/XywNgA29s2w+WmZQ1dq+auWLpgNjq289T6PSmGgxwxlFHVktPuYeWmIOw4eFQY4Ud5fUcP7Ie5L42Hi4N4c04zxtTr4Kmz+OSHNeULQ74w4hm8+cpkWJg/eXqjpomhrhdDGVUl/WEefo68gM1XI4XATlW0GNQkb184mVtqpHyMMe10OysTq8LPCqOCKzKUyjDDLwDTfQO0OkWMPtXz1QLA276DlbkSAeDch3Ac+4bo9l1eXp6wABylnxgyZAi++uoruLu7q/Q9OACsZXkV/zlzHsvWBiL+dlk+K0czQ8zu4Ijh7rYwkHLgV93yi4rw3fGbCPjjnNrfizF1oFExEQ7W2NHWBTlGBsIiqFNGDsX8qS/AQokzqeomhoMcMZRRVTKysvHzlp3YuHs/5IWFwraBPQKwYOoLoksvwhjTjMzsHHy1ZgOCDhwWbjs1scdHc1/DU927aPVXIoa6XgxlVFZuoRy/R4VhXVSYcL2qTo4umOztB3cbO42UjzGm/UpKS/H3jRhsuByO/OKiSve1trHHJ70Hwc/BGdpIH+r5qjgAnIewsDBs27YN33//PYyMjDB37lx88MEHsLBQTQYADgBriXMRUUJexcjoslGnVkYyTG/vgPFt7WEs4yy0jeXHsDtwW3Mc5vLK00UYE5tcAxn2tHHCBeeyjpFzU3t8PG8m+gV0gjYSw0GOGMqorLz8fKzfuQ+/bN2NnLw8YVtAh3Z4c9pkUYwkZ4xpn+DwS/hgxU9ISE4Rbg/r1xPvzXlVWDxSG4mhrhdDGRtKXlyMoOhLWB1+Dun5D6vd39a2CV5s74/2TRw1Uj7GmPjczcvFTxHnEZZ6p9J2Gl43uZ0/3ujcU+vyhutyPf/EAPD275UfAfz8XFHsu9WrV+PChQvC5erVq8JsSx8fH3Tv3h1+fn7YvHmzsDjdjh070KWL8ifQOQCsYVfi4vHNb4E4FRou3DaRSTDFqyle8m4KSyPtnZKgi44lZiJ+VyTcwxM0XRTGVCbG1hxbvVyRblp2UDNiQB+8O3Mq7LSs4y2GgxwxlLGhCouKELT/MFYFBpVP2fbyaImF015A3y4dOfUQY0wpD/MLsHLjVqzdvhfFJSWwsbTAoplTMXpQP62rX8RQ14uhjA0Zqbfv+jV8HxaMpJysave7Wlphsrc/ujq7at1vhjEmjtnWp5Ju4dfIEGTJK6/z42xuiQ97DRRSymgLXazn6xwA3vGD8gHg514Xxb5zc3NDt27dhIAvXTp37gzTKgtrf/bZZwgMDERUVJTS78cBYA25lZSMb9dvxr5jp4XbMgnwfGt7vObjgCam4li0SZdk5svxy7Eb6LwtRNNFYUzlCqQSHPBwxAm3JiiVSGBjZYHFs6dhxFN9tKYTJYaDHDGUsb4or+/+E2ewYt3m8tF5rk4OmP/yJAzv30s4C80YY6pyOTYei5evwtXrN4XbvTv74aM3ZsDNSXtGc4qhrhdDGR/nVmYGdsReRlJ2FlwsrOBmaY3AqxGIyaicq5M0MTXDBC9f9G/uDpmE2yTGmHKyCvKx9lIojieWtUMVjWjlhbe79dOKxSTFXs8rFQDeuUr5APCYOTqz71JTU+Hi4oLi4up58OuLA8CNIOXufdxMSkbLZs6QyaT4YdM2bP3rkDACggxpYYM5vo5wszRujOKwGnx7PhFea47DiDM/MB2WYGmKLd7NkGxR1qD2DeiIj+bOQDNHzS/mJYaDHDGUsa7tUQsXJ8QlJGLZ2k24EndDuI+mY895YSzGDxsEI0M+EckYU9+MAxoJvHJjEArkcpgaG2P+1Il4cdQwyLRgQR4x1PViKGNtdsZcxgen/xGmXtOoX1q7oCYWhkYY6+mDIe5ttXqhJsaYOFE6iJ/Cz+Puw9xK2yn4u6hbPwz38NToQBkx1/MNxQHg2kevnzhxAv369YOyOACsZrTwxQffrkZJSalwoCMzkKGoqCxy39PZEm/4O8HTVvNnmPTZn/EZyNgaAte4NE0XhTG1K5YAR5o3xUF3RxRLJULHm6b5Tx4xRKMdbzEc5IihjHVtjyoyNzPFq2NHYupzz8K8ypQjxhhTFzoZ9f6K1TgfeVm43aFta3y6YJaQfkaTxFDXi6GMtY38fXbHeiHwWxtjmQwjWnljVBtvrcvJyRjTLQ+LChF4JQJ/xUdXOxnV17Ul3u85QJiloAliredVEgDevVr5EcCjZolu3y1fvhwLFizA5cuX4eXlpZa+uYHKX5FVGmlVsbNN/1Lw19PGBG91dkEXR9Ws5Mca7k5OPmIv3YE/B3+ZnpCVAk/fugvfu1kI8mqGeBtg6Y9r8efRU1i6YA7atHTTdBGZutqjFaurdbrHDRmIhdMmw85aPAdHjDHdQDPjfv/fh9h24DC+XLMBl2Li8Px/3sZrE0Zj9qTnYWzEwT9dQ2kfHjeezsPaFot7PKUV068ZY7rP1MAQr/p2QW/Xllh18SxuZ2eW33ci8SZG7diA+V16YZK3H6RakjZPH1DKQroo83wx8vf3F/5/9913ce3aNSEXcPv27dGhQwdhYbhnn31W6ffgREpqHtlQdaQVebOTMwd/tST3ZWBEKnz3li3Ax5g+ccwrwJyweIy9lgTjomJEXIvF6Dlv4fsNWyCXF2q6eEwd7VENI65oUUAO/jLGNIXyjI8f9jT2/bICT/fqiqLiYvwYuB2j5/wfQqKu8hejYyjnbw1dIwF112mkHQd/GWONzdOuCb5+aigmevnCoEKu8byiQnx29hhe3LcVcRn3+YthKpednV1+/amnnhL+3717N6Kjo3Hq1Cm88cYbaNKkCf755x+VvB8HgNU8skEqrXz2gW42t+Jcv9ogKCYdbvsj+Y+A6S1qAHreScfb52LQ/m6W0PGmnIyjX/8/XLwSreniMXW3R1IpWrg4835mjGmco70dVn7wX3z//ltoameD+NtJmPzm+/h45S/Iyc3TdPGYijSztBL6QjWhXJsOZua8rxljGmEolWG8Vwd889QwISBcUXhaMsbuDhRGCctVsBAXewIawUuB+AZfxDMCuE+fPkhJKVuIuyoLCwt069YN06dPx4oVK1TyfhwAViOnpvb4ZN6sSp3ugW7WcDTjKW2aFpuRh7SIRDikZGm6KIxpnE1BEaZduoWXohJgIS/C9YRETFq4GJ+u+hU5eQ81XTymwvao4mIW78x8WdjOGGPaYnDv7tj38wohPQ0J3Ps3hs9YgKNnQzRdNKYCz7VpX+uib7TIzcAWrXk/M8Y0ys3KGkv7DMZrvl1gInuUMbWwpBg/XDyLcbsDEZGWrNEy6jylgr//XkSiY8eOQpCXUj5UFB4ejmHDhqn8/cSzZ0SKDmC/nDERL7Qt62RfS3/42IUPmPoVlZRgZ2QK2h0qW3SEMVY29dI/LRNvn41BQHI6qJrasHs/np0xH8cvhPEu0pH2aP4LU2Bv27Q8DQ5jjGkba0sLfLpgNtb970M0d3ZCyr37mPXhF1jw2TLcf/AoPyMTnxbWtvik9yBIa8gE/HrH7nC2sNRIuRhjrCLK9zvUwxPfDnwWnRxdKt0X9+A+Jv+5BZ+fPYbcQjnvOKaUtWvXYurUqejdu7eQ8iEmJgbjx49H586d1bIIHAeAG4F5iRz/8XeGhaEUt3PkCE7OaYy3ZbVYf/kuWu8K4x8/YzUwLyrGpKtJmHnxBuweypF89z5mvPcZ3vrft0jnjreo0egqY2MLPP3USOH2pr1/cxCYMaa1evh3wJ7V32D6uFGQSaX46/gZDJs+DzsPHRPqMyZOY9q0x59jX4a3vUOl7S2tbTVWJsYYq0lTM3Ms7t4fC7r0gpXRozSe1AJtvBIuLBJ3MvEm7zw1LQKnzEVMPv74YyxcuBBPP/20sNgb5QUODg7G3r17Vf5eHABuDLlZMDWQYqSHnXBza8y9RnlbVl1Iajbkobdgm13Au4exx/DMyMH/nYtBv4S7kJSWYu+Rkxj62jzsOXKCO94i9eDBA0hNrBDQsSdMjE2QcCcFZy5GarpYjDFWK1MTY/zf9BcR9N0X8G7VEg+yc7Do65WYvvhT3E5J5T0nUi2sbPBF32cqbTtwI0Zj5WGMsdpQ+rQ+ri3x3cBn0c+1ZaX7knOzMevgLiw6fgAZ+Zw2T2X0KAVEamoq5s2bh08//RTt2rWDoaGhMCK4a9euank/8ewZESvJK8szO75NWRqIk3eykZTD0wUaW35REY5EpcLzVGyjvzdjYmRcUopRcSmYF3IdzjkP8SArB//3v+8w4/3PkJR6V9PFY/V042YCrO3dYGxsgu5d+gnbNu05wPuRMab12rfxEILAb06bDGMjI5wKjcCIGQuxbsdeFPOCPKLU2tYeXZ1dy2+fSLyJHDkP0GCMaScrYxPM69IL7/V4Ck1NKy9Yuff6NYzYsR5/Xr/GA2VUtgickheRcHd3x4kTJxAUFITQ0FBs374dM2bMwFdffaWW9+MAsJoVFRVBml+W8qGFlTG6O1kIUwa2xd1X91uzKtZGpqHd9gu8Xxirp+bZD7HwQhyGXk+BrKQUJy5cxPDX5mP9rn3c8RaR5LR0mFnYCNf79Bgk/H/sXCgH8xljomBoYIAZE8YIaSG6+rbHw4ICfP7T75gwfzGuxfMUXDGa6OVXfl1eXIyjCTc0Wh7GGHsSygm8YuBwDPfwrJTNnEYAv338AOYc2o3zybexPOQU3jr6l/D/rcwM3rGsRr/99hsuXryI4cOHC7eHDBmCo0ePYvny5Xj99dehahwAVrOkpCQ4SgvLbytGAe+6no6CYl6Ap7EcS8yE8ZnrMJfzPmesIWSlwNO37uKt87HweJArdLyX/rgWkxa+h9ibt5Fy9z7OhkcJ/zPtVFBYNo2NODq4wLN1e2FR0i37Dmq6aIwxVmctmznj9/99iCXzZsLS3AyXYuLw/H/exorf/0CBXM7tkYgMaOEBBzPzSmkgeLFsxpi2MzUwxKu+XfBZ32fgZmld6T6azfDK/u34NTIEf9+MxdpLoXh2x3rsjOUF6OtMKlX+IhITJ06stq1Tp044c+YMjhw5ovL3E8+eEanE2GtoZmFUfrtPMys4mRniQUExDt7ilYwbQ2a+HCFRKXAPT2iU92NMlznmFWBOWDzGXkuCcVExIq7FYuSsheg/ZSZefvsjPPXSLAQdOKzpYrIaFBRWXjSpb8+nhf+37v8HcvmjE5WMMabtpFIpxg97Gvt+WYGne3VFUXExfgzcjgEvzUH/F2dxeyQShlIZxnl2qJRPM/JuikbLxBhjdeVp1wRfPzUUE718YVAl7ywdddMJreLSUuH/D079g1tZD3jn1oGuLwKXkPDkuFTLli2FILBiUKmqcABYzQoy02Eke7SbDaQSjP13FHBQLI+UawzrItPQYUdIo7wXY/qAarSed9Lx9rkYtL2fLRzUKEKLJSWl+ODbn3gksJYpLS1FvrxyANjHuxNsrG2RkZWN/SeDNVY2xhhrKEd7O6z84L/4/v23YGdjhXsZD8rzL3J7JA4UAK4YODkQz4vBMcbEdSJrvFcHfPPUMNiZmNb6OApJ7oiJatSyMe0UEBCAmTNn4sKF2tOTZmZmYtu2bfDx8RHyAqsKB4DVLbdsAbiKRnvYCoHgS/fzcCU9T+1F0Gd/xmfA7shVGHHmB8ZUzqagCE/dqr4YXElJCW7dSeY9rkUePHgAqYlVpW0ymQy9uw8Urgfu5cXgGGPiNbh3d3w6f3a17dweab+mZuYY1LJV+e2QlCTczcvVaJkYY6y+3Kys4W3vUCkvcEV0ajIpu3psiNWATgoqe9FiV65cgbm5OZ5++mk4OTkJ+X9fe+01zJ07F1OmTBFSQDg4OAj5gb/88ku88cYbKntv7d4zOqAkr/ofub2pIZ52K8sVszWGRwGry52cfMReugPXuDS1vQdj+uyqTzMk923z7yFN5am5LVycNVYuVt2Nmwmwtnertr1n1wGQSWUIvxqDK3HxvOsYY6LVrpV7tW3cHonDJO9Hi8GVoFTIm8kYY2LjaGZevt5GVbS1mWXlwRisZqUSqdIXbWZvb49ly5YhOTkZK1euRJs2bXDv3j3Expa1fZMnT0ZoaCiCg4MxbNgwlb63gUpfjVVSVFQEaX4OYCqrtmfGt7XH/lsPcODWAyzo6AxrY/4qVIlGfARGpKLj3nD+VTKmYvGtHHC3vQu6WRZhvEkhQvIluFP0qLP9ybyZcGpaluqGaYfktHSYOXpW225laQ1/364IDQ/Gpr1/Y+mC6iPoGGNMDDKzcyrd5vZIPDo7NkNrG3vEPSgbGPPPzThM8OwAQ1n1PhRjjGmrAS1aYWfslRrvo+Eyz7X1afQyiRIF0ZXJ46vlOYAVTE1NMXbsWOHSWLQ7NC5ylKzZUVrzwjp+TczQ1sYEBcWl2B2f0ehl03VBMelw2x/JP3DGVCjRxQZnn/WFYzcnTG9aiA4mpcgpBlL+Df5+s2g+jq7/EeOGlKUVYNqjoJCOhWo+GOrbo2wxuL1HTlQLoDDGmFicCLko/N/DvwPWf/kRt0ciQu3TJG/f8ttZ8gKcucOLNzPGxMXFwgpedk0rbZNJJJBKJPik9yC0sLLRWNmYOFCKPnXiALAaJcZeQzMLo1oPdCa0LRshty32vrCIElON2Iw8pEUkwiGFc+wwpgpptmYIHtoBxn1b4DXHYnQ3LS6/LzSfpmtK4OHmgmef6s0jf7VUQWHtbYxHy7ZwcXJDgbwQOw8dbdRyMcaYqpy4UBYAfrp3N3Tz8+H2SGRGtPaGueGjftOBG7wYHGNMXGgR0pS8R4Mpmpqa45UOnfHn8y9jTJv2Gi2bmJRCyRQQIg5zlqo5LijePSMCBZnpMJLVvouHtrSFhaEUt3PkCE7mUVeqUFRSgp2RKWh36LJKXo8xfZZpZojgwe3xcHBbTHcqwgDzf4f6VnAhr2xUad+AThooIavrgUS+vPaDCToh2bfnYOE6pYGgFDqMMSYm2bm5CLt8TbjeN6CjpovDGoCCvyNbe5ffjk6/h/gH6bwvGWOicTMzAxn5D8tvv+YXgAVdevPI34amgFDmIiLnzp0rv66Ysfnw4UMho0BVly8rF+fiALA65T5+BKqpgRQjPeyE61tj7qm1KPpi/eW7aL0rjH/YjCkhz0iKcwO8kfJse0xtVoJnLQqFXIpV0QnK8/8e4/Ttwh1ubfXgwQNITR6/6ERAx54wMTZBwp0UnLkY2WhlY4wxVTgdFonikhK4u7rAzcmRd6pITfR6lAaC8ChgxpiYhKXdqXS7t2tLjZWFice4ceMqDdzZvn27sDDc8OHD4evrWylA/OKLLyr1XrzymBqV5GUBpo9/zPg29giMvoeTd7KRlCOvNWUEe7KQ1GzIQ2/BNruAdxdjDSCXAhG9PGHiaIaJlvmwEHKY136e8LocyCiWwMTYCAEd2vE+11I3bibA2t7tsY8xNjZB9y79cOz039i05wB6d/ZvtPIxxpiq0j/w6F9xa21rj67OrjifnCjcPpF4Ey+17wgLI2NNF40xxp7oYuqjAHBzKxse+dtQwiheJcaqauEI4PHjx9e4nQK+6emVZ7ssWbIEoaGhcHR0FP5/+eWX8e677+KFF15QOkUEB4DVpKioCNL8HMD08UmcW1gZo7uTBc6m5GBb3H3M83dWV5F0Wn5REY5EpSLgVKymi8KY6NCE/4huHkAzK4y2LICdgbxOE0QUo397dPSFkZGh+gvKGiQ5LR1mjp5PfFyfHoOEAPCxc6FISr2LZo6VF7FgjDFtRJ2hkyHhwvV+nI5I9CZ6+ZUHgOXFxTiacAMjWntpuliMMfZYuXI5rqU/mtXdh0f/NlipRCJclHm+tvnnn3+wYcMGWFhYVDuGOXHiRLVYIgV/SefOnYX7x4wZg7i4uFoX9a4rTgGhJpSvw1EYPfdk4/9dDG7X9XQUFHPuxYZYG5mGdtsvNOi5jOkrqm2i/JsjdIw/BrQ1wUu2hbAzqHuzUJ7/l9M/aLWCwkf5pB7H0cEFnq3bC4uSbtl3sFHKxhhjyoqOv4W0++kwNTbm2Sg6YEALDziYmVdKA8GLZTPGtF3E3eRKdRUHgJVAo3+VvWiZ/v37w9LSEv369at0oe2U5qEiBwcHREY+SslnZ2eHQ4cO4erVq5W2N4T27RkdkRh7rc7pHPq4WMHJzBAPCopx8Fam2suma44lZsL4zHWYyzl4zlhdxXg6IWSUPzr5WGGaXSFcjep3NjGnGLjyb7YVnnKr3QoK6z5VqG/Pp4X/t+7/B3J53U5iMsaYJp0IKUv/0N3fh2ej6ABDqQzjPDuU307OzUbk3RSNlokxxp4krEL6B2OZDAFOrrzTWLkdO3agb9++qAkFdyuikcIUBK7IyMgIf/zxB44fPw5lcABYTQoy02Ekq9vuNZBKMLZN2SjgoNj76iqSTsrMlyMkKgXu4QmaLgpjonCzuT3OjfBHyy5N8WqTQngaNyyPUGg+jSCWwMPNBa5OlRsopj1oWlG+vO7fsY93J9hY2yIjKxv7TwartWyMMabK/L99AngxUl1BAWCDCiO4DsTHaLQ8jDH2pOPti2nJ5be7OrvBxICzrTZUKSRKX8SqpKQEzZo1g5OTU4339+rVS6nX5wCwuuRm1evhY1rZCYHgS/fzcCU9T23F0jXrItPQYUeIpovBmNZLaWqB4GG+sOndDNMdCtHZRLkR8+XpHzjfolZ78OABpCZWdX68TCZD7+4DheuBew+osWSMMaa87NxchF2+Jlzn2Si6o6mZOQa1bFV+OyQlCXfzcjVaJsYYq83NzAxk5P+7OAqnf1BaqUSq9IXVjPeMmpTk1S8AbGdigKfdrIXrW2N4FHBd/BmfAbsjV2HEmR8Yq9V9SxMEP9MBxQNbYbpjIfqYFiu9tyi9lWIBOM7/q91u3EyAtb1bvZ7Ts+sAyKQyhF+NwZW4eLWVjTHGlHU6LBLFJSVwd3WBm1PZgilMN0zy9iu/XoJS/H2TF3pmjGmnsLRH6R9Ib14AjmkpDgCrAa3aJ83PqffzFIvBHbj1AJkFRWoome64k5OP2Et34BqXpumiMKaVcowNcG5QOzwY6olpLkUYYl4EqVQ1Vf51OZBRLIGJsREvuKPlktPSYWZhU6/nWFlaw9+3q3B9096/1VQyxhhTXfoHHv2rezo7NkNrm7K+EfnnZhwKi5U/ic0YY6p2sUL+3+ZWNmhhVb9jb6b7i8BpC94zapCUlARHaf0Xz/FrYgZPWxMUFJdid3yGOoqmEygvSmBEKnz3hmu6KIxpnXwDKc7380TCSB9McSvFaMsiGKgo8KugGP3bo6MvL7ij5QoKAYmk/nmw+vYoWwxu75ETyMyu/wlNxhhrjJyLJ0PKjgX7cToinUNt1yTvRyujZ8kLcOYOr/nBGNMuuXI5rqXfK7/dh0f/Kq1UIlH6wmrGAWA1SIy9hmYWRg060Bn/72Jw22Lvo4TmWbNqgmLS4bY/kn+8jFVQJAVCe7ZG9Cg/jGspxQSrQpioOPBbLf9vF15wR9sVFDasHfFo2RYuTm4okBdi56GjKi8XY4wpKzr+FtLup8PU2Jhno+ioEa29YW74qE914AYvBscY0y4Rd5MrxW04AMy0GQeA1aAgMx1Gsobt2qEtbWFhKMXtHDmCk3nUVVWxGXlIi0iEQ0r9ciwzpqsoBXZE55aIGN0RQ9sYYoqNHFYG6qvac4qBKwVl13nKrfaPjsuXNywATCck+/YcXJ4GgmZeMMaYNjkRUpb+obu/D89G0VEU/B3Z2rv8dnT6PcQ/SNdomRhjrKKwCukfjGUyBDi58g5SEi8Cpz71jhKcOHECI0aMgIuLi9BB3LVr12Mff+zYMeFxVS8pKSnQWbkND06aGkgxysNOuL415tFUAgYUlZRgZ2QK2h26zLuDMQBXfZohZHRH9Gpngam2cjiqMfCrEJpPQWcJPNxc4OrkoLHvgduiJ3vw4AGkJlYN3scBHXvCxNgECXdScOZiZINfhzHG1Jn/t0+AZmejcHukXhO9HqWBIDwKmDGmTYMtLqYll9/u6uwGEwMDjZZJJ1AKB2UvrEb1jhbk5ubCz88PP/zwQ72eFx0djeTk5PKLg4PmAgfqVpKn3OjUcf+mgTh5JxtJOXIVlUr81l++i9a7wnjYOtN78a0ccG6kP7z9bPGqvRzuRo2XLqY8/YOG8y1yW/RkN24mwNrercH72NjYBN279BOub9pzoMGvwxhjqpadm4uwy9e0YjYKt0fq1drWHl2dH42oO5F4Eznyf6ciMcaYBt3MzEBG/r+Lo3D6B9WRSJUaBcyLwNWu3qcnhg4dKlzqiwK+Nja6vxpiUVERpPk5gKmswa/RwsoY3Z0scDYlB9vi7mOevzP0XUhqNuSht2CbzQd8TH8lutggsVNzdLACRpnWf6FJZVF6K8UCcJrO/8tt0ZMlp6XDzNFTqf3cp8cgHDv9N46dC0VS6l00c2yq1OsxxpgqnA6LRHFJCdxdXeDm5KjRncrtkfpN9PLD+eRE4bq8uBhHE25gRGuvRnhnxhirXVjao/QPpDcvAMca6MqVK0hISIBcXnkA6MiRIyHKHMD+/v5wdnbG008/jdOnTz/2sQUFBcjKyqp0EYukpCQ4SpUPzIxvWzYKeNf1dBQU63fuxfyiIhyJSoXnqVhNF4UxjUizNUPw0A4w7tsCrzkWo7tpsUbKcV0OZBRLYGJsJNoFd/SlLSIFhWW5fJXh6OACz9bthcUttuw7qLKyMcaYKtI/aHr0rzL0qT1S1oAWHnAwM6+UBoIXy2aMadrFCvl/m1vZoIWV7g94bAylkCh9EYv4+Hghw4KPjw+GDx+O0aNHC5cxY8YIF1VTewCYDmxWr16N7du3Cxc3Nzf0798fYWFhtT7n888/h7W1dfmFniMWibHX0Mzi0Wq1DdXHxQpOZoZ4UFCMg7cyoc/WRqah3fYLmi4GY40u08wQwYPb4+HgtpjuVIQB5kUa/RYUo397dPQV3YI7+tYWkYJC1aQG6dvzaeH/rfv/gVze+CPPGWOsas7FkyHhwvV+Gk5H1BD62B4py1AqwzjPDuW3k3OzEXlXh9eTYYxpvVy5HNfSH63Z1IdH/6qMPi0CN2/ePLi7uyMtLQ1mZma4fPmysLZAly5dhPXUVE3te8bT0xMzZ85E586d0bNnT/z222/C/8uXL6/1Oe+88w4yMzPLL7dv34ZYFGSmw0im/G41kEow9t9cwEGx96GvjiVmwvjMdZjL9XsUNNMveUZSnBvgjZRn22NqsxI8a1EIqVTzDVl5/l8Np39oCH1riyhAki9XTQDYx7sTbKxtkZGVjf0ng1Xymowx1lDR8beQdj8dpsbGopyNom/tkapQANigQqf+QHyMRsvDGNNvEXeTK81E4AAwa4jg4GB88sknaNKkidDfp0vv3r2FE79vvPEGVE0jEYWuXbsiLi6u1vuNjY1hZWVV6SIauaqbkjWmlZ0QCL50Pw9X0vOgbzLz5QiJSoF7eIKmi8JYo5BLgQt9PHF9pB8mtgDGWhbCSAsCvySnGLjybwpuMU+51Ze26MGDB5CaqKa8MpkMvbsPFK4H7uXF4BhjmnUipCz9Q3d/H9HNRtHH9khVmpqZY1DLVuW3Q1KScDcvV6NlYozpr7AK6R+MZTIEOD1arJIpicYcURq7Bl/E8w0UFxfD0tJSuE5B4Dt3yn5XLVq0QHR0tMrfTyORhfDwcGH6ky4qyVNdANjOxABPu1kL17fG6N8o4HWRaeiwI0TTxWBM7Wh8+8VuHrg82h+jPaR4wVoOCy0J/CqE5lM5JfBwc4GrkwN0gS63RTduJsDaXnVThHt2HQCZVIbwqzG4EhevstdljLGG5v/toyMnI3W9PVKlSd5+5ddLUIq/b/L6IIwxzcy0u5iWXH67q7MbTAwM+KtQ1f6FVOmLWPj4+CAiIkK43q1bN3z55ZfCugA0KtjDw0Pl71fvX2lOTk6lM9Q3btwQDlrs7OzQvHlzYYoSLYS2fv164f4VK1YIOS3at2+P/Px8rFmzBkeOHMHBg7q3mExRURGk+TmAqUxlr0mLwe2/9QAHbj3Ago7OsDbWj4rlz/gM2B25CiPO/MB0GP28r/g3x0N3Owy2kMPViPKrameDVZ7+QUvyLXJb9HjJaekwc/RU2f62srSGv29XhIYHY9Pev7F0wWyVvTZjjNVVdm4uwi5f06rZKNweNZ7Ojs3Q2sYecQ/KBsb8czMOEzw7wFCmur4XY4w9yc3MDGTk/7s4Cqd/ULlSiUS4KPN8sXjvvfeQm1s2m4WCvs8++yz69OkDe3t7bNmyReXvV+9oYkhICJ566qny2wsXLhT+f/nll7Fu3TokJycjIeHRlH25XI4333xTCApTUmNfX1/8888/lV5DV9BndJRSAEd1ByF+TczgaWuC6Ix87I7PwEveTaHr7uTkI/bSHfjHpWm6KIypTYynEx54OaG3ZRE8jane0N6GitJbKRaA05b8v9wWPV5BIWCk4oOfvj2eFgLAe4+cwH+nvwhrSwuVvj5jjD3J6bBIFJeUwN3VBW5Ojlqxw7g9ajwSiQSTvH2xJPiocDtLXoAzdxLQz829EUvBGNN3YWmP0j+Q3rwAHGugZ555pvx669atce3aNaSnp8PW1lZo8zQeAKZVamnIe20oCFzRf//7X+GiDxJjr6G9hZFKX5O+9PFt7LHkfBK2xd7HFK8mkIrojEZ9lZSUIDAiFR33lq3uzJiuudncHil+buhkVYzOJhT41X7X5UBGsQQmxkZas+AOt0WPV1BYirJsUqrj0bItXJzccCflNnYeOoqpz41Q8Tswxljd0j9oy+hfwu1R4xrR2hvLQk4jt1Au3D5wI4YDwIyxRnWxQv7f5lY2aGFlw9+ACpVKpMJFmeeLmZ2dndpeW9x7RssUZKbDSKb6XTq0pS0sDKW4nSNHcHIOdFlQTDrc9kfyD5PpnJSmFgge5gvr3s3wmkMhOpuIJ7+JYvRvj46+OrPgji6jk7T58tpP1CpzQrJvz8HCdUoDQSfsGGOsMeu2kyFlAwT6aUk6Itb4zA2NMLK1d/nt6PR7iH+Qzl8FY6xR5MrluJZ+r/x2Hx79q3KlkCh9EZOTJ09iypQp6NGjh5BVgGzYsAGnTp1S+XtxAFiVclW3AFxFpgZSjPIoOwuwNeZRZaNrYjPykBaRCIcU9exHxjThvqUJgp/pgOKBrTDdsRB9TYtF90WU5//VkvQP7PEePHgAqYl6VogP6NgTJsYmSLiTgjMXI/mrYIw1muj4W0i7nw5TY2OtmY3CNGOil2+l2zQKmDHGGkPE3WSUVJgRzwFgpozt27cLaSBMTU1x8eJFFBQUCNszMzPx2WefQdU4AKxCJXnqC1yOa2Mv/H/yTjaScsqmPOmSopIS7IpMRbtDlzVdFMZUIsfYAOcGtcODoZ6Y5lKEIeZFkErFV+XmFANXytohrZpyy2p342YCrO3d1LKLjI1N0L1LP+H6pj0H+GtgjDWaEyFl6R+6+/vwbBQ919rWHl2dXctvn0i8iRz5vwcrjDGmRmEV0j8Yy2QIcHpUFzHVpoBQ5iIWn376KVavXo1ffvkFhoaPZtr26tULYWFhKn8/8ewZLVdUVARpvvrSM7SwMkZ3JwvQuaZtcWUr3+qS9ZfvotWuUP5BMtHLN5DifD9PJIz0wRS3Uoy2LIKBCAO/CqH5QAkk8HBzgauTg6aLw+ogOS0dZhbqy0XWp8cg4f9j50KRlHqXvxPGWKPm/+3DJyOZMArYr3w/yIuLcTThBu8XxpjaUxFdTEsuv93V2Q0mBvVeVos9aT9LJEpfxCI6Ohp9+/attt3a2lqY1alq4o1KaBnK1eEoVe+CTuPblo0C3nU9HQXFupN7MSQ1G/LQW7DN5jP3TLyKpEBoz9aIHuWHcS2lmGBVCBMRB36rpX/gfIuiUVBYlq9XXRwdXODZur0w/W3LvoNqex/GGFPIzs1F2OVrwnWejcLIgBYecDAzr5QGouK0bMYYU7WbmRnIyP93cRRO/6A2+pQD2MnJCXFxcdW2U/5fDw8Plb+f+KMTWiIx9hqaWRip9T36uFjBycwQDwqKcfBWJnRBflERjkSlwvNUrKaLwliD0KmYiM4tETG6I4a2McQUGzmsDHSjaqV+1IV/j3E4/694FBSqvwPct+fTwv9b9/8DuVy9Jz8ZY+x0WCSKS0rg7uoCNydH3iEMhlIZxnl2KN8TybnZiLybwnuGMaY2YWmP0j+Q3rwAHFPSa6+9hnnz5uHcuXPCAJ47d+5g06ZNeOuttzB79myomm5EKbRAQWY6jGTq3Z0GUgnG/psLOChWN9JArI1MQ7vtFzRdDMYa5KpPM4SM7ohe7Sww1VYORx0J/CpclwPpxRKYGBvxgjsimpqWL1d/ANjHuxNsrG2RkZWN/SeD1f5+jDH9pkj/wKN/WUUUADaokOvxQDwvBscYU5+LFfL/NreyQQsr9aVc02f6lAN40aJFeOGFFzBw4EDk5OQI6SCmT5+OmTNnYu7cuSp/P/HsGW2Xq74F4Coa08pOCARfup+HK+l5ELNjiZkwPnMd5nLdSWfB9EN8KwecG+kPbz9bvGovh7uRbk45PP/v6N8eHX15wR2RoFxRUhMrtb+PTCZD7+4Dheub9uxX+/sxxvT7xNbJkHDhej9OR8QqaGpmjkEtW5XfDklJwt28XN5HjDGVy5XLcS39XvntPjz6V230KQWERCLB4sWLkZ6ejqioKJw9exZ3797FkiVL1PJ+HABWkZK8xgkA25kY4Gk3a+H61hjxjgLOzJcjJCoF7uEJmi4KY3WW6GKDs8/6wrGbE6Y3LUQHE90M/FbL/9ulo6aLwuroxs0EWNu7Ncr+6tl1AGRSGSKuxeJybHyjvCdjTP9Ex99C2v10mBob82wUVs0k70eLwZWgFH/f5LRyjDHVi7ibXCnPOAeAmbIKCwuFkb+xsbEwMjJCu3bt0LVrV1hYWEBdOACsAkVFRZDm56CxKBaDO3DrATILiiBG6yLT0GFHiKaLwVidpNmaIXhoBxj3bYHXHIvR3bRY5/dcTjFw5d91GXnKrXgkp6XDzKJxpqNZWVrD37ercD3wz78b5T0ZY/rnREhZ+ofu/j48G4VV09mxGVrblPWNyD8341BYrPvHaYyxxhVWIf2DsUyGACdX/grUpBRKpoAQSZjT0NAQkZGRjfqe4tgzWi4pKQmO0sZbBMeviRk8bU1QUFyK3fEZEJs/4zNgd+QqjDjzA9NymWaGCB7cHg8Ht8V0pyIMMBfnCZeGCM2nkTQSeLi5wNXJQdPFYXVUUFg2laix9O1Rthjc3iMnkJndeCdCGWP6l/+3TwDPRmHVUZs3ydu3/HaWvABn7vAMQ8aYalMRXUxLLr/d1dkNJgYGvIt1LAXEDz/8gJYtW8LExATdunXD+fPnoW5TpkzBr7/+isbCv1oVSIy9hvYWRmjMA53xbeyx5HwStsXexxSvJpA2YodfGXdy8hF76Q7849I0XRTGapVnJMWl3p6waWKMqeYFMBJO8OjX+bLy9A+cb1FUCgpLYdmI7+fRsi1cnNxwJ+U2dh46iqnPjWjEd2eM6brs3FyEXb4mXOfZKKw2I1p7Y1nIaeQWyoXbB27EoJ+bO+8wxphK3MzMQEb+v4ujcPoHnbRlyxYsXLgQq1evFoK/K1aswDPPPIPo6Gg4ODioNZvAb7/9hn/++QedO3eGubl5pfuXLVum0vfTr4iGmhRkpsNI1ri7cmhLW1gYSnE7R47gZHGMuiopKUFgRCp895Yt5MGYtpFLgQt9PHF9pB8mtgDGWhbCSKp/1SSlt7rw7zEO5/8V1+iEfHnj5qWmE5J9ew4Wrm/a+7dQzzPGmKqcDotEcUkJ3F1d4ObkyDuW1cjc0AgjW3uX345Ov4f4B+m8txhjKhGW9ij9A+nNC8CpValEolwKiAYMjly2bBlee+01vPLKK0IuXgoEm5mZCcFZdaKF3zp16gRLS0vExMTg4sWL5ZfwcNXHzXgEsCrkNs4CcBWZGkgxysMOm6LvYWvMPfRyacwxXw0TFJMOt/2RfNaBaR0KWUV08wCaWWG0ZQHsDGgEif4FfhWuy4H0YglMjI14wR0RefDgAaQmVo3+vgEde2LXvk1IuJMiBGv6dPFv9DIwxnQ7/QOP/mVPMtHLF39cjSi/TaOA53TszjuOMaa0ixXy/za3skELq8ZZb0NfKZPGQfF8kpVVOU5nbGwsXKqSy+UIDQ3FO++8U75NKpVi0KBBCA4OhjodPXoUjUl/IxwqVJLX+AFgMq5N2YIHJ+9kIymnbMqTtorNyENaRCIcUjSzrxirLfAb5d8coWP8MaCtCV6yLYSdAVeL5/8d/dujoy8vuCMiN24mwNrerdHf19jYBN279BOuB+490OjvzxjT3VkNJ0PKRr/043RE7Ala29qjq/OjRZlOJN5Ejvzf1WwZY6yBcuVyXEu/V367D4/+baQRwMpdiJubG6ytrcsvn3/+eY3vd+/ePRQXF8PRsfJMI7qdkpKi/g8M4MqVKzhw4AD27NlTftm7d6/K34dHAKsgZ4c0PwcwlaGxtbAyRncnC5xNycG2uPuY5+8MbVRUUoJdkanodOiypovCWLkYTyc88HJCb8sieBpTjl9x5NFu1Py/XXjBHTFJTkuHmaOnRt67T49BOHb6bxw7F4qk1Lto5thUI+VgjOmO6PhbSLufDlNjY56NwupkopcfzicnCtflxcU4mnADI1p78d5jjDVYxN1klFB+vH/1adaC96ZI3L59G1ZWj2ZHGtcw+lfT4uPjMWbMGFy6dElIrUcnv4liUW8KTKsSD3VTUlJSEhyFBaI0Y3zbslHAu66no6BYO3Mvrr98F612hfKPjWmFm83tcXaEP1p2aYpXmxTC07hxc6Zqu5xi4Mq/A2Z4yq24FBQ+OlhobI4OLvBs3V44QN6876BGysAY0y0nQsrSP3T39+HZKKxOBrTwgIOZeaU0EBUDN4wxVl9hFdI/GMtkCHBu/Nl2+qa0VKL0hVDwt+LFuJYAcJMmTSCTyZCamlppO912cnJS62edN28e3N3dkZaWJuQcvnz5Mk6cOIEuXbrg2LFjKn8/DgArKTH2GppZGEFT+rhYwcnMEA8KinHwVia0TUhqNuSht2CbzVOwmGalNLVA8DBfWPduhtccCtHZRDtPmGhaaD6lxpDAw80Frk7qW/GUqV5BoWY7uX17Pi38v3X/P5DLNXdilDGmW/l/+wTwbBRWN4ZSGcZ5dii/nZybjci7jTN9lzGme2g05sW05PLbXZ3dYGLAk+jVT4pSJS71DXMaGRmhc+fOOHz4cPk2Wtiabvfo0QPqRDmGP/nkEyEITXmH6dK7d28hXcUbb7yh8vfjALCSCjLTYSTT3G40kEow9t9cwEGx96FN8ouKcCQqFZ6nYjVdFKbH7luaIPiZDige2ArTHQvR11S10yh0Nv0D51sU3QFqvlyzAWAf706wsbbFg6xs7D+p3gUTGGO6LTs3F2GXrwnXeTYKqw8KABtIHvXNDsTH8A5kjDXIzcwMZOT/uzgK5//VaQsXLsQvv/yC33//HVevXsXs2bORm5uLV155Ra3vSykeLC0thesUBL5zp2zEeYsWLRAdHa3y9+MAsLJyNb+o2ZhWdkIg+NL9PFxJz4O2WBuZhnbbL2i6GExP5Rgb4Nygdngw1BPTXIowxLxIOKPGakezJC/8e4zD+X/F5cGDB5CaPMpxpQk0dap394HC9U179mu0LIwxcTsdFonikhK4u7rAzanyoiyMPU5TM3MMatmq/HZIShLu5uXyTmOM1VtY2qP0D6Q3LwDXKEohUfpSXxMmTMDXX3+NDz74AP7+/ggPDxcWZau6MJyq+fj4ICIiQrjerVs3fPnllzh9+rQwKtjDw0Pl78fRECWV5Gk+AGxnYoCn3ayF61tjtGMU8LHETBifuQ5zOU+zZ40r30CK8/08kTDSB1PcSjHasggGHPitk+tyIL1YAhNjI15wR2Ru3EyAtb3mc5L17DoAMqkMEddicTk2XtPFYYyJPP0Dj/5lDTHJ26/8eglK8fdNno3IGKu/ixXy/za3skELKxvejToaACb/+c9/cOvWLRQUFODcuXNCQFbd3nvvPSHdBKGg740bN9CnTx/89ddf+O6771T+fhwAVkJRURGk+TnQBorF4A7ceoDMgiKNliUzX46QqBS4hyf8f3t3Ah9Vfe+N/5OZycwkmckK2YdAiIQtkAAJa0DBaq1VsLdW9GprLT6t97aP1dpe++9TW2t7fW5btb29ttr2KrWP1l160QJuICioZCGByBYSiAlJJjDZw2yZ+b9+Z7JCwCSznXPm8/Z1zJlhJnNmy2/me37n8w3rdlBkcWuA8hV5OLp+IW6crsFN8S4YWfidkI8HZv8uL1rAhjsK02y1IdYU/g+l8eYEFC4okdafe31HuDeHiBQaabOn7IC0voZxRDQJi9OykJfo+24kvH2yFq4Ad1InInXrdTpxxHZm6HQpZ/+qvgAcDldffTW+9KUvSet5eXk4cuQIzpw5IzWFW7t2bcBvjwVgPzQ1NSFNI49GNwunxCI/yQhHvxd/r2sP67Zsrrai4NWysG4DRQ6xv6xq8XRUbSjCNZdF49ZEJ+J1/NPmV/7vEjbcURqHC4iKkseHndXLfc3gtr67G53d8thJSkTKcbTuFKxnbYgxGHg0Ck2KGA9vnrNg6HSX04G9pzkxhYjGr6qtGR6RjzegNCuHDx+FRHJyctC+17FK4ofG40eQZdJDDsQL5CsDzeBePn521B+rUHq9rh3J7x6GnskPFAKH52ehbEMRVs414fYkJ9JY+J20nn7gE4dvnYfcKo/DFd4GcCPlTp+FzHQLHE4XXntrZ7g3h4gUZneZL/5hWeF8Ho1Ck3Zd3hzERQ9/T9tez2ZwRDR+FSPiHwxaLYozwh+1FikiaQZwqLEA7AdHpw16rXwewmumJ8EUrcGnPU7saw79rKvTPXYcP3ga2bXWkN82RZa6man46PpCzFmYhG+kODFDL5/il1KV28Vs6ijkWjKRnZ4a7s2hCR4ubXfK5z0gdkiuXnGVtP7s1h1DuVZERBPJ/y0t5tEoNHmi+Ht93pyh00dtZ1DXYeNDSkTj+mxdaW0eOl2SYYFRp+MjFyJeb5TfC41NPtVLJeoNfwO4kWJ0GqzPTZbWXzw2nFcTCuIL/nNVrViw1ZfZRhQMjZmJ+PCLC5C2NB2bprpQYJRP0Us18Q/MW1Scjo4OaIzxkJPiohUwGoxoON2CDyqqw705RKQQ3b29qKg5Iq3zaBTy18bZwzEQAmcBE9F4nOxsR7t9oDkK839JRVgA9oOnT14FYOHGgRiIPae70dTjDNntvnTMBsu2ar6gKCisSbHYd00BDKtzcGdaP5bFsJFHIInEmP0Dn3GY/6s89ScbkJAir8PSDAYjli1ZI60/t3V7uDeHiBRC7DDq93gwIzsTlvS0cG8OKVxeUgpKMrKHTu9uPIke50DeFRHRRVRYh+MfhFVsABdSjIAIHhaAJ8ntdkNjl19zm5x4A5almyDmRb5cezYkt3m8vQ/WqkaktsivIE7K1hkbjX1XzcO5q2ZhU7oba+Pc4d4kVTrhBGz9UTAa9Gy4o0DNVhtiTYmQm9LlV0o/d31UjqbWtnBvDhEpwGD8w5qSReHeFFKJjbMXDq07+/uxs6E+rNtDRMrK/50Wn4icePl9zlazSCsA79mzB7feeiuWL1+OpqYm6by//vWveP/99wN+WywAT5J4YtI0LsjRV2b5ZgFvOWGDoz+42Ytujwdbqlsx962aoN4ORZY+vQYfrZ2Dli/Ow+1ZHnzR5IJGwz9XwfLxwOzf5UUL2HBHgRwuX+6u3KSlZiI/b57UlPT5N94M9+YQkQIyF/eU+aLEeDQKBcranFykxsaNioEIV7NsIpK/XqdTygwfVMrZvyEXSQXgV155BVdffTViYmJQWVkJh8N3lEpnZyf+/d//PeC3x4rKJDUeP4Is03BnWTkpzYxHemw0Ohz9ePNUZ1Bv65maNszcUs4XEgWEUwPsL83HiesXYmMO8GWzC3oWfkOX/7uEDXeUyOGS7xfZ1Ss+J/18cdvbcDrludOUiOThaN0pWM/aEGMw8GgUCphojRY35hcMnW7u7UZ1WwsfYSIaU1Vb86idRKVZOXykKGh+/vOf44knnsCf/vQnREdHD52/cuVKVFRUBPz2WACeJEenDXqtPB8+nSYKXx7IAn7pePBiIMpau+EsP4WkbmZpkX/EPPXKpbmo2VCIDbka3JLghImF35Do6Qc+GXgLs+GOMmfM2Z3yLQDPn7MIiQlJ6OjqxrY9+8K9OUQkY7vLfPEPywrn82gUCihRANZFDX9v2153jI8wEX1m/INBq0Vxhrz6bEQCaRav149FQTOAjx49itWrV19wfkJCgtToO9DkWcFUgl55593eMDNZKgQfPNuHT2x9Af/9drcbOw+1Iv/94wH/3RRZhd9DhdNQfkMh1s4y4qtJLiTr+GcplMrt4nmIQq4lE9npqSG9bfKf+GCgMcbL9qHUarVYtWydtP7s/2wL9+YQkQLyf0uLeTQKBdbU2DhcOX3m0Omylia09fXyYSaiCyZWVFqbh06XZFhg1On4KIWY+G7q76IU6enpqK2tveB8kf+bm5sb8NtjpWWSPH3yLgAnG3X4nCVBWn/xWOBnAT9dbcXcV/YH/PdS5DiWn4796wuxaH487kh2IVuvnD/Uqox/KGbDHSWqP9mAhBR5z0xYUbIWWo0WVUeOo+Z4Xbg3h4hkqLu3FxU1R6R1Ho1CwXDznOFmcB54seMkJ7EQ0WgnO9vRbh9ojsL8XwqBO++8E3fffTc++ugjqafL6dOn8eyzz+K+++7DXXfdFfDbYwF4EtxuNzT2HsjdYDO47ac60OlwB+z37mrshGHvCcQ6g9tgjtTp5LQUfHhdIaYvmYpNU1zIN8j38HW1E/FW+wc+4zD/V5marTbEmuTdmTjenIDCBSXS+nOv7wj35hCRDH1QUY1+jwczsjNhSU8L9+aQCi1Oy0Jeou+7kfD2yVq4+vvDuk1EJC8V1uH4B2EVG8CFRSQ1gbv//vtxyy23YN26dejp6ZHiIDZt2oRvfvOb+M53vhPw22MBeBKampqQppF/M5uFU2KRn2SEo9+Lv9e1B+R3dtqdKDvUghkHGgLy+yhytEw1Yd8XFiBhVRbuTHVhsZE7EMLthBOw9UfBaNCz4Y5COVyQ9hbL3erlvmZwW9/djc5u+e9AJaLwxD+sKeHRKBQcYqy8ec6CodNdTgf2nub3GSIaO/93WnwicuLlPclCrfzK/x1YlDQ2/ehHP4LNZsOhQ4fw4Ycfoq2tDQ899FBQbo8F4EloPH4EWSY9lPBi+spAM7iXj58d1c1ysjZXW1HwalkAto4ixVmzEfuuLkD/upnYlObC6hjOtpCLwdm/y4sWsOGOQjlcyphBnzt9FjLTLXA4XXjtrZ3h3hwiklnm4p6yA9I6j0ahYLoubw7iooe/w22vZzM4IvLpdTpx1HZm6OEo5exfCiG9Xo+5c+eipKQEJpMpaLfDROtJcHTaoNcqo3Z+zfQkPFbZjE97nNjX3IOVmeZJ/67X69qR/O5h6Dlxk8ahx6BDTeksTEmOxh1xTug04j2jjPdNpPh4MP93CRvuKLVoYncqowAsdkiuXnEVnn/1v/Hs1h346oZroZH+JhBRpDtadwrWszbEGAw8GoWCShR/r8+bg78drvK99mxnUNdhQ25iMh95oghX1dY8asJcaVZOWLcnkolnwZ8YB7l/O7r33nvHfdlHH300oLfNAvBk9Mq7AdxIMToN1ucm49mjZ/DisTOTLgCf7rHj+MHTKKy1BnwbSV3sOg2qV14GU2oMbjU5YNSI/GkWeuSmpx/4xOFbZ8MdZero6IDGGA+lKC5agS1vPIuG0y1S3mfpksJwbxIRycDuMl/8w7LC+TwahYJu4+wFQwXgwVnA/1K0jI88UYQbGf9g0GpRnCHvJstq5m+Mg9wjICorfZ97PkswYv5YAJ4ET18XEAPFuPGyFKkAvOd0N5p6nBOOr/B4PHiuqhVFW32H5xGNxa0BqpblQZdhxo0mO+J1IiebhV+5KreLLthRyLVkIjs9NdybQ5NQf7IBCSnK+XBqMBixbMka7PpgB57bup0FYCIalf9bWsyjUSj48pJSUJKRjY+bG32vv8aT+Oq8Ipj0Bj78RBF8VF2ltXnodEmGBUYdS2Vhez78bOQm9yZwO3eGLw6P1ZkJcrvd0NiV1cAmJ96AZekmaSr8y7VnJ3z9l47ZYNlWzRcLjUkkglQtno6qDUW45rJo3JroRLyOf1rkbv9g/EMxG+4oVbPVhliTsppTlC6/Uvq566NyNLW2hXtziCjMunt7UVFzRFrn0SgUKhtnLxxad/b3Y2dDPR98ogh2srMd7faB5ijM/yUV426NCWpqakKaRsxs1EJJvjIrBR+29GDLCRu+VZAGwzgzjI+398Fa1Yj5LcqJvaDQOTw/C915qVhrdmGG3sl9Sgoh4q0GG8Ax/1e5HC5AH4RDg4IpLTUT+XnzcLS2Bs+/8Sa+d8c/h3uTiCiMRBxMv8eDGdmZsKSn8bmgkFibk4vU2DhY+3qHYiCunZkPjcLGVCIKjArrcPyDsIoN4MJK7REQ48kDFvEPRqMReXl5WL9+PZKTA5NVzwLwBDUeP4J5E4xQkIPSzHikx0ajpc+FN0914rrcpM+8jtvjwZbqVix6qyYk20jKUTczFW3zMrHU7EaBURR+SUlOOAFbfxSMBj0b7iiYw+XF5Nt6hs/qFZ+TCsAvbnsb37n1K8z8JIpgg/EPa0p4NAqFTrRGixvzC/B45YfS6ebeblS3taAwNYNPA1GE5/9Oi09ETryyjrBTG+/AUcb+XF8pKisrUVFRgf7+fuTn50vnHTt2DFqtFrNnz8bvf/97fO9738P777+PuXPn+n17PE57ghydNujHOXtWTnSaKHz5shRp/aXj44uBeKamDTO3lPNFQkMaMxPx4RcXIG1pOjZNdaHAqKQ/rzRocPbv8qIFLL4pOKvM7lTm+2/+nEVITEhCR1c3tu3ZF+7NIaIw/h3bU+brL8GjUSjURAFYFzX8nW573TE+CUQRqNfpxFHbmaHTpZz9SyEkZvdeeeWVOH36NMrLy6WlsbERn/vc53DzzTdLCQSrV6/GPffcE5Dbm3Alc/fu3bjuuuuQmZkpTUvesmXLZ15n165dWLRoEQwGgzSFefPmzVCsXuVGIdwwM1kqBB8824dPbH2XvGxZazec5aeQ1O0I2faRfFmTYrHvmgIYVufgzrR+LIvpD/cmkR8+Hsz/XaLchjuRPhZ1dHRAY4yHEok92quWrZPWn/2fbeHeHCIKk6N1p2A9a0OMwaDoo1EifTxSqqmxcbhy+syh02UtTWgbiIQgoshR1dYMj8jHG1CalRPW7aHhCAh/FqX41a9+hYceegjx8cPf6xISEvDTn/4Uv/zlLxEbG4sHHnhAKgyHpQDc29uLhQsX4vHHHx/X5evr63HttdfiiiuuwIEDB/Dd734XmzZtwo4dO6BEnj7lFoCTjTp8zpIgrb947OKzgO1uN3YeakX++8dDuHUkR52x0dh31Tycu2oWNqW7sTbOHe5NIj/19AOfDOzXUXLDnUgfi+pPNiAhxQKlWlFyBbQaLaqOHEfN8bpwbw4RhcHuMl/8w7LC+Yo+GiXSxyMlu3nOcDM4D7zYcZLffYgiOf7BoNWiOEO5n6/Vwosovxel6OzshNVqveD8trY2dHX5ao+JiYlwOp3hyQC+5pprpGW8nnjiCcyYMQOPPPKIdHrOnDlSfsVjjz2Gq6++GkridruhsfcAMcpqAHd+M7htpzqw/VQH7inKQILhwpfA09VWzH1lf1i2j+ShT6/BwVX5SJxiwO1xDuilxofKiz6hC5XbxZecKORaMpGdnqrYhyiSxyKh2WpDbJovJ0qJ4s2JKCwoQXnVPjz3+g784p67wr1JRBSm/N9SBe+MFCJ9PFKyxWlZyEtMQW2Hb2LM2ydrcVN+AaK1yv2uR0QTiyKqtDYPnS7JsMCoY5uscIukJnDr16/HHXfcIX0mKC4uls7bv38/7rvvPmzYsEE6/fHHH2PWrFkBub2gV3T27dsnZVqMJD7ciPMvxuFwSNXukYsciPyNNKkQplwLp8QiP8kIR78Xf69rv+DfdzV2wrD3BGKd/sRuk1I5NcD+0nycuH4hNuYAXza7oNew8Ksm+wfjH4ojq+GOmsYiweHydYdVMtEMTtj67m50dveEe3OIKIS6e3tRUXNE8UejTIbaxiMlE+PozXMWDJ3ucjqw93RDWLeJiELnZGc72u0DzVGY/0th8OSTT2LdunXYuHEjcnJypEWsi/PEDmNBNIP785//HJDbC3plp6WlBWlpaaPOE6fFB5dz54bfbCM9/PDDUu7F4GKxyGMafuPxI8gy6aH0DzpfGWgG9/Lxs6PybjrtTpQdasGMA/zgE2lEub9yaS5qNhRiQ64GtyQ4YWLhV3XE232wAZyS838jfSwSHC5lNoAbKXf6LGSmW+BwuvDaWzvDvTlEFEIfVFSj3+PBjOxMWNJH/21WO7WNR0p3Xd4cxEUPf7/bXs9mcESRosI6HP8grGIDOFmIpAgIk8mEP/3pTzh79iwqKyulRaz/8Y9/RFxcnHSZwsJCaQkEWU7t++EPfyhlYQwun376KeTA0WmDXivLh2xCrpmeBFO0Bp/2OLGveXjW1eZqKwpeLQvrtlHoC7+HCqeh/IZCrJ1lxFeTXEjWKf81TmM74QRs/VEwGvSKbrgT6WOROFzN7lR+AVjskBycBfzs1h3weHjkCVGkxT+sKYmso1HUNh6pgSj+Xp83Z+j0UdsZ1HXYwrpNRBT6/N9p8YnIiU/kQy8DHq//i9KYTCYsWLBAWsR6sAQ94CQ9PR2tra2jzhOnRZe7mJiYMa8jOuKKRXZ61XG4VYxOg/W5yXj26Bm8eOwMVmaa8XpdO5LfPQw9v39HjGP56WifnY5Ssxv5BhFtopw9ZTQ5g7N/lxctUHTDnUgfizo6OqAxDneKVbLiopXY8sZzaDjdIs0ILF0SmL3bRCRfYifWnrIDEXk0itrGI7XYOHsB/na4atQs4H8pWhbWbSKi4Op1OqUdPoNKOfuXwuSdd96RFtEM7vwJMU899VRAbyvoU/2WL18u3ZmR3nrrLel8pfH0qaMALNw4EAOx53Q3Klq7cfzgaWTXXth9kNTn5LQUfHhdIaYvmYpNU1zINyhwFxlNyseD+b8R+IVbTWNR/ckGJKSo4/Bfg8GIZUvWSOvPbd0e7s0hohA4WncK1rM2xBgMEXk0iprGI7XIS0pBSUb20OndjSfR43SEdZuIKLiq2ppHxWGWZuXwIZeJSIqAePDBB3HVVVdJnwvOnDmD9vb2UUvYZwD39PSgtrZ26HR9fT0OHDiA5ORkTJs2TTpESTRLe+aZZ6R//9a3voX/+q//wg9+8AOpu927776LF198EW+88QaUxO12Q2PvAWLU0RU2J96AZekmfNjSg0f2n8YdW30zMUi9WqaaUF+ci9mJwHUxym5mSBPX0w98MvBdRg0NdyJ1LBKarTbEpuVDLVYtvxK7PtiBXR+Vo6m1DVlpU8O9SUQURLvLfPEPywrnq+JolEgej9Rk4+yF+Li5UVp39vdjZ0M9rsubHe7NIqIQxD8YtFoUZ6hjcoUaeL1R0uLP9ZXiiSeewObNm3HbbbeF5PYmPAO4rKwMRUVF0iLce++90voDDzwgnW5ubkZDw3ATsRkzZkgfaMSe7YULF+KRRx6ROtiJbrdKIj64pWnUVTT7yizfLOB6Wx/6Ncp5k9DEnDUbse/qAvSvm4lNaS6sjunnQxiByu0i8zkKuZZMZKenQukidSwSHC5ffq5apKdmIj9vnjQL4/k33gz35hBRiPJ/S1WwMzLSxyM1WZuTi9RYX8OdwRiIkbMDiUhdUUSV1uah0yUZFhh1QU9HpXESf3r9XZTC6XRixYoVIbu9Cb/KL7/8cukNczGiej3WdUQ3OyVrPH4E80zDHWLVICNGhzh40avT4kBqAopbOsK9SRRAPQYdakpnYUpyNO6Ic0KnEft72OAtUu0fjH8oVkfDnUgdiwSHywsz1EU0gztaW4MXt72N79z6FVXMCiSiC3X19KKi5ohqjkaJ9PFITaI1WtyYX4DHKz+UTjf3dqO6rQWFqRnh3jQiCrCTne1otw80R2H+L4XRpk2b8Nxzz+HHP/5xSG6PuznGydFpg16rnuKZ2+PB1kNWrD7Rim0z0/FBVgoLwCph12lQvfIymFJjcKvJAaPGzcJvhBPfSwcbwEVi/q+aiCKD3amg3drjNH/OIiQmJKGjsx3b9uzD+nWrw71JRBQEeyur0e/xYEZ2JizpaXyMSVZEAfjJAx/D7fU14dled4wFYCIVqrAOxz8Iq9gATlbEUati8ef6SmG32/HHP/4Rb7/9NhYsWIDo6NGTYB599NGA3h4LwOPVq54GcMIzNW2YuaUcOrsbb85IRUNCLD41G2Hptod702iS3BqgalkedBlm3GiyI14nIkvUs9OCJu+EE7D1R8Fo0Edkwx016ejogMYYD7XRarVYtWwdXt/xMp79n20sABOpPP5hTYk6jkYhdZkaG4crp8/E9vrj0umylia09fVK5xOROvN/p8UnIic+MazbQ5GbAVxdXY3CwkJp/dChQ6P+LRiRfywAj5OnrwuIgSqUtXbDWX4KSd2+jlALrZ2oSE+SZgFvPNIU7s2jCRJzFA4ung53ThKuMduRpnOy8EujDM7+XV60gIfWK1z9yQYkpKizScWKkiuw7a3XUHXkOGqO12HeZbnh3iQiCvARDHvKfE2HeTQKydXNcxYOFYA98GLHyeO4da7vyzkRKV+v04mjtjNDp0s5+5fCaOfOnSG9PRaAx8HtdkNj7wFitFA6u9uNnYdaseR93wcbYWWjTSoAV6Ql4rraFsS52SRMKQ7Pz0J33lSsNbsxQ8/CL43t48H8X8Y/KF6z1YbYtHyoUbw5EYUFJSiv2ofnXt+BX9xzV7g3iYgC6GjdKVjP2hBjMPBoFJKtxWlZyEtMQW3HWen02ydrcVN+AaK1yv8eSERAVVvzqAaPpVk5fFhkxt9GbkpqAjfok08+kRrGiqZwI2cAX3fddQgkFoDHoampCWkacTi98gf+p6utmPvK/lHnTe/qQ1b3OTSZY7A/IwmXfzq8R4zkqW5mKtrmZWKp2Y0Co3htEo2tpx/4xDfZXzUNdyKZwwXog3A4kJyawYkC8NZ3d+MHm25DgtkU7k0iogDZXeaLf1hWOJ9Ho5BsiS/cN89ZgIf2+WZldTkd2Hu6AWssM8K9aUQU4PgHg1aL4gx1HlmnZF5ESYs/11eKuro63HDDDTh48KA0/gw2lR2Mf+jvD+zkTAaEjkNT7RFkmfRQul2NnTDsPYFYp6+xwSDx0lrZ6NvL/UFWshQpQPLUmJmID7+4AGlL07FpqgsFRgXu3qKQKrf7gvBzLZnITk/lo69wDpe63/O502chM90Ch9OFV98M7SFRRBSa/N9S7owkmbsubw7iooe/+22vPxbW7SGiwBDFtUpr89DpkgwLjDrOiaTwufvuuzFjxgxYrVbExsaipqYGu3fvxpIlS7Br166A3x4LwONg77BBr1X2Q9Vpd6LsUAtmHGgY89+LWjtgdPXjbKwBR5M540purEmx2HdNAQyrc3BnWj+WxTCmg8Zn/2D8QzEb7qjhQ6vdqe4CsNjbLWYBCyIGwuPhLkkiNejq6UVFzRFpnUejkNyJ4u/1eXOGTou80LoOW1i3iYj8d7KzHe32geYozP+VLY/X/0Up9u3bh5/97GeYMmUKNBqNtKxatQoPP/ww/vf//t8Bvz1lVzVDpbcLSre52oqCV8su+u8Gjxclze3S+gfZKSHcMrqUztho7LtqHs5dNQub0t1YG+fmA0bjJo4gGWwAx/xf5evo6IDGGA+1Ky5aCaPBiIbTLfigojrcm0NEAbC3shr9Hg9mZGfCkp7Gx5Rkb+PsBaNOcxYwkfJVWIfjH4RVbAAnT14RhTD5RVxfKfr7+2E2m6V1UQQ+fdr3Gs3JycHRo0cDfnssAI+Dp0/ZBeDX69qR/O5h6D9jItWKJl8MxOEUM84ao0OzcTSmPr0GH62dg5YvzsPtWR580eSS9gYRTcQJJ2Drj4LRoGfDHRWoP9mAhBT155QZDEYsW7JGWn926/Zwbw4RBTD+YU0Jj0YhZchLSkFJRvbQ6d2NJ9HjHGiqQESKz/+dFp+InPjEsG4PXboJnD+LUsyfPx9VVVXS+tKlS/HLX/4SH3zwgTQrODc3N+C3x4rSZ3C73dDYe6FUp3vsOH7wNLJrrZ952dRzTsyydcMbFYV9Wckh2T4azakB9pfm48T1C7ExB/iy2QU9C780SYOzf5cXLWDDHRVottoQa4qMD6qrll8p/dz1UTkaWz57/CIiecfX7Ck7IK3zaBRSko2zFw6tO/v7sbOhPqzbQ0ST1+t0SnEug0o5+5dk4P/8n/8zFHknir719fUoLS3FP/7xD/znf/5nwG+PBeDP0NTUhDSNE0okXkjPVbViwVbfh+7xWDXQDO6jjGS4NMqZOq904i1fuTQXhzYUYkOuBrckOGFi4ZcClf+7pIiPpQo4XMMdYdUuPTUT+XnzpMLRC/94K9ybQ0R+OFp3CtazNsQYDDwahRRlbU4uUmPjRsVAeJQ0tYyIhlS1NY96/5Zm5fDRkSnRwNzfRSmuvvpqfOlLX5LW8/LycOTIEZw5c0ZqCrd27dqA3x4LwJ+hqfYIskzDXWCV5KVjNli2VU/oSZ57phtJdid69TocSE0I4tbRYOH3UOE0lG8oxNpZRnwtyYVkHd+W5L+efqBm4EhFNtxRB4crsr50DjaDe3Hb23A4lbkjloiA3WW++IdlhfN5NAopSrRGixvzC4ZON/d2o7qtJazbRET+xz8YtFoUZ6g/Vk2pIikCYizJyclBm/SjC8pvVRF7hw16rfIKcsfb+2CtasT8lonlF4t7urzJhn/MTMcHWSkobukI2jZGumP56WifnY5Ssxv5BhegoD1VJH/ldt/e01xLJrLTU8O9OeQnMRPW7lT4p5kJmj9nERITktDR2Y7tez7E+nWrw71JRORH/m9pMY9GIeURBeAnD3wMt9d3iO72umMoTM0I92YR0QQ/R1dam4dOl2RYYNSxFEbhce+99+Khhx5CXFyctH4pjz76aEBvm6/6z9KrvAZwbo8HW6pbseitmkldf+lpG3bMSEVDQiw+NRth6bYHfBsj2clpKWhZaMGi+H78k1EUfomCGP9QzIY7atDR0QGNMR6RRKvVYtWydXh9x8t49n+2sQBMpEBdPb2oqDkirfNoFFKiqbFxuHL6TGyvPy6dLmtpQltfr3Q+ESnDyc52tNsHmqMw/1f2vN4oafHn+nJWWVkJl8s1tH4xwZgFzALwZ/D0dQExUJRnatowc0v5pPM9zK5+LLR2oiI9SZoFvPFIU4C3MDK1TDWhvjgXsxOB62JY+KXgEYe9DDaAY/6vOtSfbEBCSuQdqrai5Apse+s1VB05jprjdZh3WeC74RJR8OytrEa/x4MZ2ZmwpKfxoSZFunnOwqECsAde7Dh5HLfOLQz3ZhHROFVYh+MfhFVsACdrHq9v8ef6crZz584x10NBedkGIeR2u6Gx90JJylq74Sw/haTugfDPSVrZaJN+VqQlolenDdDWRaazZiP2XV2A/nUzsSnNhdUx/eHeJFK5E07A1h8Fo0HPhjsq0Wy1IdaUiEgTb05EYUGJtP7c6zvCvTlENMn4hzUlPBqFlGtxWhbyElOGTr99shaufn6eJ1Ji/u+0+ETkxEfeZ2oliZQMYJfLhXXr1uH4cd8OxlBgAfgSmpqakKZRTuMZu9uNnYdakf++/y+g6V19yOo+B7dWg/0ZSQHZvkjTY9DhoyvnouOafNyR6cbn49zQaPiWo+AbnP27vGgBG+6ohMMVnMOAlNQMbuu7u9HZ3RPuzSGiCWQu7ik7IK3zaBRSMjH+3jxnwdDpLqcDe083hHWbiGh8ep1OHLWdGTpdytm/JBPR0dGorq4O6W2yGnUJTbVHkGXSQymerrZi7iv7A/K7RJlhZeNZaf2DrGT42h7QeNh1Gny8Jh8N18/HrRYvNpjd0LHwS+HI/13Chjtq4XApZFd2EOROn4XMdAscThdefTO0h0kR0eQdrTsF61kbYgwGHo1Cindd3hzERQ9/L9xefyys20NE41PV1gzPiCmhpVk5fOhkzosovxeluPXWW/Hf//3fIbs9ZgBfgr3DBr1WGTXyXY2dMOw9gVhn4Eq1Ra0d+J+8DJyNNeBosglzbJx5dSluDVC1LA+6DDNuNNkRrxM5v8p4/ZB69PQDNQMJMGy4o55ZdHanN6JnXolZwM+/+pQUA/G1G67l0RRECrC7zBf/sKxwPo9GIcUTxd/r8+bgb4erpNNiRmFdhw25icnh3jQiGmf8g0GrRXFG5PXUUBpR0fIrAxjKip196qmn8Pbbb2Px4sWIixvdYPTRRx8N6O2xOnUpvV1Qgk67E2WHWjDjQGAPRTJ4vChpbpfWP8gezr2iC//AVC2ejqoNRfh8XjRuTXQiXse3FoVHuV28JqOQa8lEdnoqnwYV6OjogMYYj0hWXLQSRoMRDadb8EFFaA+VIiL/8n9Li3k0CqnDxtnDMRACZwETyX8SRaW1eeh0SYYFRh3nQJJ8HDp0CIsWLYLZbMaxY8dQWVk5tBw44IvRCiS++i/B09cFxED2NldbUfBqWVB+94qms9g9bQoOp5hx1hiNFLuY1UqDDs/PQnfeVKw1uzFDL/KiWfglmcQ/FLPhjlrUn2xAQkpkz1YwGIxYtmQNdn2wA89u3Y7SJey+TiRnXT29qKg5Iq3zaBRSi7ykFJRkZOPj5kbp9O7Gk/jqvCKY9IZwbxoRjeFkZzva7QPNUZj/qxj+NnJTShM44S9/+Quys7MvOLpR7Lz49NNPEWisVl1iKrbG3gu5e72uHcnvHoY+SPPcU885McvWDW9UFPZl8RCnQXUzU/HR9YWYszAJ30hxYYZeQX9lSLXEYDfYAG4NC8Cq0Wy1IdbEbsWrll8pPR67PipHY4s13E8LEV3C3spq9Hs8yLVkwZKexseKVGPj7IVD687+fuxsqA/r9hDRxZWPiH8QVrEBnKIKwP4sSjFjxgycOTPcpHCQzWaT/i3QWAC+iKamJqRpxIxO+TrdY8fxg6eRXRvcL8KrBprBfZSRDJdGOYHawdCYmYgPv7gAaUvTsWmqCwVGBf11IdU74QRs/VFSw50l8+eEe3MoQBwuXw5upEtPzUR+3jxpj/gL/3gr3JtDROOIf+DsX1KbtTm5SI2NGxUDMbLBFBHJR6V1uAA8LT4ROfGcUKEEHm+U34tSeC8yfvT09MBoNAb89hgBcRFNtUcw1zTc6VVuPB4PnqtqRdHWwOeCnG/umW4k2Z1oN+pxIDUBxS0diDTWpFicWDYTeQka3BnnDvfmEI1pcPbvsqICNtxREYfLC3O4N0ImRDO4o7U1eHHb2/j2rTfCoJfvOE0UqcSXmT1lvs+nq5cw/5fUJVqjxY35BXi88kPpdHNvN6rbWlCYmhHuTSOiEXqdTqlZ46BSzv4lGbn33nuln2KSzwMPPIDY2Nihf+vv78dHH32EwsLAR96xAHwR9g4b9Fr5TpB+6ZgNlm3VIZnCLW5jeZMN/5iZjg+yUiKqANwZG41PVs1CZlI0NsU62HmelJH/yy/cqiqk2J2cWTRo/pxFSExIQkdnO7bv+RDr160O6/NDRBc6WncK1rM26WiU4oK5fIhIdUQB+MkDH8Pt9WXwba87xgIwkcxUtTWPmp1fmpUT1u2h8YuEDODKysqh73oHDx6EfsSkFrG+cOFC3HfffQG/XRaAL6a3C3J1vL0P1qpGzG8J3TYuPW3DjhmpaEiIxadmIyzddqhZn16Dg6vykTjFgNvjHNBrRPM7+e4QIOrpB2ocvseBh9yqR0dHBzTG+HBvhmxotVqsWrYOr+94Gc/+zzYWgIlkaHeZ70vNssL5PBqFVGlqbByunD4T2+uPS6fLWprQ1tcrnU9E8lAxIv/XoNWiOCOyGyoridwLwL/4xS/wxhtv4MCBA1KxVnxfm6idO3dKP7/+9a/jt7/9LeLjQ/N9jxWti/D0ybMA7PZ4sKW6FXPfqgnp7Zpd/Vho7ZTWxSxgtXJqgP2l+ai9fiE25gBfNrugP68jI5EcldsBD6KQa8lEdnpquDeHAqT+ZAMSUviBdaQVJVdAq9Gi6shx1Byv42uNSKb5v6XFjH8g9bp5znAzOA+82HHSVwwmovATsyorrc1Dp0syLDDqOPeRAsPpdOLGG2/EXXfd5ffvevrpp0NW/BVY2RqD2+2Gxt4LOXqmpg0zt5SH5Ylb2WiTflakJaJXp4WaiAO4Kpfm4tCGQqzP1eCfE5wwsfBLSox/KF4U7k2hAGq22hBrYsOKkeLNiSgsKJHWn3t9B19vRDLS1dOLipoj0jqPRiE1W5yWhbzE4Ukxb5+shau/P6zbREQ+Jzvb0W4faI7C/F/FETN4PX4swZ4B/OCDD+Kee+5BQUEBlIYF4DE0NTUhTeOE3JS1dsNZfgpJ3QPHeYfY9K4+ZHWfg1urwf6MJKil8HuocBrKNxRi7SwjvpbkQoqObwtSFjHIDTaAW8MCsKo4XL7mAHRhMzhh67u70dndw4eHSCb2Vlaj3+NBriULlvS0cG8OUdCIsfnmOQuGTnc5Hdh7uoGPOJEMlI+IfxBWsQGconi9UX4vQldX16jF4QhPHU1OWOkaQ1PtEWSZ5NVZ3O52Y+ehVuS/H77Di8TbaGXjWWn9g6xkqXiqZMfy07F/fSEWzY/HHSkuZOtZZCFlOuEEbP1RUsOdJfPnhHtzKIAcLgV0MQiD3OmzkJlugcPpwqtv+jK0iEg+8Q+c/UuR4Lq8OYiLHv7OuL3+WFi3h4h8Kq3DBeBp8YnIiefRdErMAPZnESwWCxISEoaWhx9+GJGOBeAx2Dts0Gvl9dA8XW3F3Ff2h3szUNTaAaOrH2djDTiabIISnZyWgg+vK8T0JVOxaYoL+QYWWEjZBmf/LisqYMMdleWX2Z38+3SxmVeDs4BFDITHo/RdkkTq+Ju1p+yAtL56CfN/Sf1E8ff6vOEd70dtZ1DX4YvMI6Lw6HU6pffioFLO/o1Yn376KTo7O4eWH/7whxe97P333y99v7jUcuSIL+JKyZiEPZZeeTWA29XYCcPeE4h1hv8LrsHjRUlzO3ZPm4IPslMwx6acQ29bpppQX5yL2YnAdTGucG8OUeDzf/mFW1VER1mNMXRNAZSmuGgltrzxHBpOt+CDimqULikM9yYRRbSjdadgPWuTjkYpLpgb7s0hComNsxfgb4erRs0C/peiZXz0icKkqq0ZnhEhsKVZOXwuFGYwy9ef6wuiudp4G6x973vfw+23337Jy+Tm5iIQ7r333nFf9tFHH0UgsQA8Bk9fFxADWei0O1F2qAWLD8gnU2pF01mpAHw4xYyzxmik2OVdTD1rNuLYisswLUmDTTFOaNjcjVSkpx+oGYgz4iG36lJ/sgEJKZZwb4ZsGQxGLFuyBrs+2IFnt25nAZgozHaX+eIflhXO59EoFDHyklJQkpGNj5sbpdNvnzqBytZmpMTEYOOcBShMzQz3JhJFlIoR+b8GrRbFGfwsrTQjYxwme/2Jmjp1qrSEQmWl7/PSoIqKCrjdbuTn50unjx07Bq1Wi8WLFwf8tuWVcyAD4oHX2HshF5urrSh4tQxyknrOiVm2bnijovDC7Cw0mI2Qox6DDh9dORcd1+Tjjkw3Ph/nZvGXVKfcLpoZRiHXkons9NRwbw4FULPVhlgTM8suZdXyK6WfOz8sw2Obn0P1kVq+BonCnP9bWsz4B4osG2cvHHX6rL0Px9rP4md7d+Lxin1h2y6iSIwiqrQ2D50uTs+GUcc5jxRYDQ0NOHDggPSzv79fWhdLT8/4jo7fuXPn0HLddddhzZo1aGxslArBYhHRFVdccQWuvfbagD91fDecp6mpCWkaJ4DwFzW3nrAh+d3D0Ic/+eECg5tUm2zGb5JMWNLcjluONEEO7DoNqldeBlNqDG41OWDUuLmvg9Qf/1C8KNybQgHmcAH6KDanvJT01EzEmxPQ1d2JJ/72qrRs+Nzl+I/7vs3XI1EIdfX0oqLGl43Ho1Eo0sREX/wr9TsNdViRmYOidM4EJgq2k53taLcPNEcR45FlBh90BQrHDOCJeOCBB/CXv/xl6HRRkW/HtyjoXn755RP6XY888gjefPNNJCUlDZ0n1n/+85/jqquukqIpAokF4PM01R7BXNNwN9dwaeq2o/ZQMwprrZAbMeO3NmlEA7ioKJRlJMGticLMzj5M7XNgap8TCQ5XSKeYuzVA1bI8aDPMuNFkR7xORFNwkjuplxjcBhvArWEBWHUcLi/M4d4ImTvZUCsVf0fa8tYuRGs1WLqwADMsmZiemQFTXGzYtpEoEuytrEa/x4NcSxYs6Wnh3hyikHqi8qNL/vtDH+5ElileWjJNZmRKP33rCQaj1FyIiPxXPiL+QVjFBnARnQEcLJs3b5aWQOjq6kJbW9sF54vzuru7EWgsAJ/H3mGDXhveoqHoZv636lYUbfV1UpabuoQ4qeg7SlQUDqQnScsgfb8HU6RisAOpfU5MPTe47kCMO3DTmsVvOrh4Otw5Sfi8yY70aDGDm4VfUr8TTsDWHyU13Fkyf7gLNanjEDa7M8ifXlTgxMmjY57/0vZ3pWXQ1OREzMjOxPSsTN/PbN9PEZsSzUMDiQIW/8DZvxSJrH2fHR/Y1NMlLeeL1UVLxeAskxkZA0VhUSgW6zx0nWhiKq3DBeBp8YnIiWeUGsnbDTfcgK9//evSTOCSkhLpvI8++gjf//738aUvfSngt8cC8Pl6LxyYQ+2lYzZYtlXLtoSZ29nrm3o4sgjs9aKopQNOnRbWWAPOxujh1Gpw2hwjLeczOd0DM4VHFIj7HJhyzgndBObsH56fhe68qVhrdmOGnoVfiiyDs3+XFRWw4Y7KdHR0QGMcX9faiNZz4R5zYe7sRThn70VbWzN6ervQZuuQlo+rPxl1Oa1Gg+yMNOQOFIenZ2cMFYhTk5M4K4tonDus9pT5Ji2sXsL8X4o8qbFxaO6d3EytPrcLtR1npeV8KTGxyIwbPWM4yxyPqTFx0vhFRMN6nU4ctZ0ZOl3K2b+KJfcIiEB64okncN999+GWW26ByyWOYAd0Oh2+8Y1v4Fe/+lVAb0v63QH/jQrn6esCLqxXhszx9j5YqxoxvyX8heiLmdZtlzJ/ReyDVAT2ei/IAO6PAmxGvVQMbos1wBqrl36KpcsQjR69TlrqE+NG/e4orxfJdlEMdg7NFh4rUqJuZira5mViqdmNAqPvjUIUsfm//MKtOvUnG5CQwq7FF+NyOvDBtj8jO3cxlixyoKxi99C/LVm0Gjff+C9Dp8+d60Xbmeahxdp2emjd5XLiVFOztADlo24j1mgcKAZnDM8eZqQE0QWO1p2C9axNOhqluGAuHyGKON8uWo4733ztov9+zYxZcHk8ONXVjlNdHXD294/r95491yctB8+0jjpfF6VBWpyJkRJEI1S1NcMzovJXmpXDx0ehPB7f4s/1lSI2Nha///3vpWLviRMnpPNmzpyJuLjRdbJAYQF4BLfbDY29F4gJzx5Vt8eDLdWtWPRWDeROFHtXNZ1FfUIcZnT2SkXhkbReYOo5EfvgBM6O3iNu12pwJkYPa5wBbTGiOCwKw74CsUOnxdkYMYPYgCMpo9MvRaREgssNQ5weM43AUqNLegH39AMmbUjuNpFsiNd9jcO3zkNu1afZakNsWn64N0OWWhtrcfDDrShaeztMCVMwfe5KrFx2FepPHcWMnHxMs+SNunxMTJx03vnni7ilru52XzF4oChsbfMVhm3tVvTZ7aiprZOW8zFSgmjY7jJf/MOywvk8GoUi0orsHHxp1jy8euzC73Di/IdWfW7otMjKbuntxsmuDqlhlbR0+X4293RjPBPX3F4PIyWIzlMxIv/XoNWiOIMTKZQqkmYADxIF3wULFiDYWAAeoampCWkaESNgRDg8U9OGmVvKZRv9cD5R9D2/8Dsexn4Psnvs0jKSeJ9263WjCsKDBeKzsb5IiTatHugHGnuB93qHH6lEjRdZ0YAlGsiK9ko/s6OBjGhAz74KpELldpF/HYVciy/HlNTF4RJ/u/jH63wH921Fd3c7Vq6/F5oRh7+OVeD9LOL6iQkp0nLZzPmj/s3tduGszXrejOHTE46UkGYMZ2UwUoIiIv+3tJjxDxS5RJH3C7n5+F35XikTWMRCfGfxCizPnHbBOJFlTpCWlefNULS73WgQhWExU7izHfWdvhnD4menY3zfuRgpQZEaRVRpFUdz+RSnZzNDmxRjz549ePLJJ6UZwC+//DKysrLw17/+FTNmzMCqVasCelssAI/QVHsEc016hENZazec5aeQ1D0wpS8CiVJHvNMtLXkdvmYKnbHR+GTVLKQlarFI70RTvwaNLqDRFTXwEzjbH4UOTxQ6HIMzIoeLJhp4kabzFYN9i3dofYoW0LC+QkqPfyheFO5NoSBwuLwYfQxEZBuMfMjIXYzFJRuCfns6XTTSUrOk5Xz+RkoMxkowUoLUoKunFxU1R6R1Ho1CkU4Ue88v+E6EaPo2K3mKtJyvw35OKgxLReFOX1GYkRJEPmIGfbt9oDmKGI8sM/jQKFgkzQB+5ZVXcNttt+Gf//mfUVlZCYfDVw/s7OzEv//7v+Mf//hHQG+PBeAR7B026LWhn38r9vbuPNSKJe8fD/lty1WfXoODq/KROMWA2+Mc0GvcUjl3+ECO4Xd1n8eLJhfwqQvST1EcHlzv80ah2Q1p8TXMGq74GqO8yBwoBkszh3XeoXVGSpCciUFtsAHcGhaAVTmLwe5U0CeXEEc+hBsjJYiG7a2slg5pz7VkwZKexoeGKEgSjTEoFEtq5qjzGSlBBJSPiH8QVrEBnKKJCF+PH1+FFBQBjJ///OdSI7ivfvWreP7554fOX7lypfRvgTapAvDjjz8uhRS3tLRg4cKF+N3vfoeSkpIxL7t582Z8/etfH3WewWCA3T7x6ICg6w1P47Wnq62Y+8r+sNy23Dg1QNXKfBjSYrHRbIdJIxq8XbooH6sBLjP4Fh/vUJHM1u+VZgn7CsRRaHT7Zg03uwC7Nwp1TkiLT9SoSInBmcKMlCC5OeEUr+0oqeHOkvlzEMnUOB51dHRAY4wP92bIOvJBjhgpQZEc/xDps3/VOBaRMjBSggiotA4XgKfFJyInPpEPCynC0aNHsXr16gvOT0hIkL4Thr0A/MILL+Dee++VqtRLly7Fb37zG1x99dXShqemjp1DGR8fL/37oCiZ5hp6+rqAmNDe5q7GThj2nkCsU0n7KQJP3PuqpbnwZsVjvdmBFJ2oyvr3ZV+8zFJ0vmWh9LwO70Zye4EWt684fKlIiUOMlCAZGpz9u6yoIKIb7qh1PKo/2YCElMhuXBHqyIdgY6QEqfVohT1lB6T11UsitwCs1rGIlI+REhQJep1OHLWdGTpdytm/qvh8IRZ/rq8U6enpqK2txfTp00ed//777yM3Nzf8BeBHH30Ud95559Cea/Fh54033sBTTz2F+++/f8zriA814o7JmdvthsbeC8SEboZRp92JskMtWHygAZFc+P2kcBrOTU/GVWYnsvWfPeM3EHRRw7nAPoyUIAXm/0bwF241j0fNVhti0/IRqeQW+RBsjJQgpTpadwrWszbpaJTigrmIVGodi0jdGClBalHV1gzPiIJf6XnNFUl5IikD+M4778Tdd98tfWYQnw1Onz6Nffv24b777sOPf/zj8BaAnU4nysvL8cMf/nDUIY9XXnmltJEX09PTg5ycHHg8HixatEgKM543b95FLy+CjwfDj4WuruBHMzQ1NSFNI2adGhEqm6utKHi1DJHqWH462meno9TsRr5BFH7lMfuBkRIkZz39g80OI/uQ21CMR+EYi6TbdQH6CJ0NpqTIh/BGSrhx1tY6qgndmYH1nt4utNk6pOXj6k8uOFQ4OyMNuaIRXVYmZljEzwxMz85EanISZyHShOwu88U/LCucH7FHo6j5uxFFJkZKkNJUjMj/NWi1KM6I7KPo1MDrATwe/66vFPfff7/0WWDdunXo6+uT4iBELJQoAH/nO98JbwH4zJkz6O/vR1ra6CYP4vSRI74OwOfLz8+XqtkLFiyQOtn9+te/xooVK1BTU4Ps7Owxr/Pwww/jwQcfRCg11R7BXJM+ZLe39YQNye8ehl5BL85AOTktBS0LLVgU349/MorCrzIwUoLkoNwuZs5HIdeSiez0sQ8tjQShGI/CMRYJDpcXZkQWtUU+BJtOp0Naapa0nO/cuV6pIDy4DBaIxeJyOXGqqVlagPJR14s1GjEjO1NapmdnjCgQZ8IUG+J8LFJU/m9pBO+MVPN3IyLZR0qY45GgN3DnZQQTh/pXWsVnGp/i9GzpdUqkFFFRUfjRj36E73//+1IUhNhBPHfuXJhMpqDcXtDfHcuXL5eWQeIDzpw5c/Dkk0/ioYceGvM6Yi+6yNIauZfbYgnunhx7hw16bWhmGzV121F7qBmFtVZEkpapJtQX52J2InBdjHIKv+PBSAkKefxD8SI+6EEej8IxFokPsnango5bCoBIi3wINkZKUCh09fSiosZX4Izko1HU/N2IKGiREmLpakdzT/eIEL6Lc3s9aOrpkpbzxeqipWJwlsmMDPHTHI/MON86C4HqJ15L7faB5ihiPLLMCOv2UGBEUgTEIL1eLxV+g21CBeApU6ZAq9WitXX0Xjlxerw5VtHR0SgqKpKq2xcjpjyLJaR6Q3MolZje/bfqVhRt9TXNiARnzUYcW3EZpiVpsCnGGXGH9TJSggJFDGaDDeDWRHgBOBTjUTjGItHtVWOMR6Rg5EPoMFKCAmlvZbVU2Mm1ZMGSPnr2ayRR9XcjogBgpAQFU/mI+AdhFRvAqYLH61v8ub6SvPPOO9JitVqleuFI4oihsBWARVV68eLF0sZt2OA7RFNsoDj97W9/e1y/QxwmdfDgQXzhC1+AnHj6uoAQHOH40jEbLNuqQ9DmLPx6DDocKp2FqcnRuCPOCZ1U+I2Eez4+jJSgiTrhBGz9UVLDnSXz50T0A6jW8aj+ZAMSUtQ/q4uRD/LCSAmabPxDpM/+VetYRBQKjJQgf1VahwvA0+ITkROfyAeVFOXBBx/Ez372MyxZsgQZGRlBj7SZcASEOPzoa1/7mrSBJSUl+M1vfoPe3t6hzrdf/epXkZWVJWVVCeLOLFu2DHl5edLMpl/96lc4deoUNm3aBLkQzVQ09l4gJrjFyePtfbBWNWJ+i7obN9h1GlSvvAym1BjcZnLAqHGz8DtBjJSgsQzO/l1WVBCxDXfUPh41W22ITcuHmjHyQVkYKUFjRdXsKfMdybZ6SWQXgNU6FhGFGyMl6LP0Op04ajszdLqUs39VI5IiIJ544gls3rwZt912W0hub8IF4JtuugltbW144IEH0NLSgsLCQmzfvn2o+UFDQ8OoQ/zb29tx5513SpdNSkqS9pLv3bs3JPkW49XU1IQ0jVPshwzabbg9HmypbsWit2qgVm4NULUsD9oMM2402RGvEzm/nPEbaIyUiFxD+b/8wq3a8cjhAvRB3vMbTox8UI9QRkrMyM7C1ORENvqRiaN1p2A9a5OORikukM/fz3BR41hEpPRIicGsYdGETjSk63TYx/X7+9wu1HaclZbzpcTESvnCQ03oTGYpc3hqTJy0XRRaVW3N8Iyo9JWe93og5fJ6vNLiz/WVwul0Sr0AQiXKK3bjy5xodJCQkCB1yo2PD3w24t53dmDuqX1BbQL31MFWJD61B0ndDqiNSCk5uHg63DlJ+LzJjvRoDoBy4/YCLW6g0TW4RA2tn+2/eLFJAy/SdEB29ODiHVqfogU06q1TyU5PP/BPDVHwIArv/OX3yE5PhZoE+++8Urbxb6+9iym5K6HmyIfpc9V3/2j8zp3rlQrCg8tggVgsLpfYGT+2WKMRM7IzpWV6tq8oLH6KQrEpNgQZXjTkjy+8hkeeehZXLF2MJ372Q9U9MhyPiNSnw35OKgSL4vCpTl9R+JRY7+qAs7/fr9+ti9IgLc6ErIGi8FCB2ByPBL2BOy+D5L8q9uHdhjpp3aDVYu8/36Wqxn9KGIuCdZ8ffKYdxtjJ32d7Xxd+8tUkRTx2//Zv/waTyYQf//jHIbk99bxD/GDvsAW1+FvW2g1n+SlVFn8Pz89Cd95UrDW7MUMvvrix+KvUSImRxeFPXZDO6/NGodkNafHFDwxXfI1RXmQO/E5LNJCl8w6tm7Qhv4uqV24XO1uikGvJVF3xl3zE/li7U/b7ZCeMkQ80EiMl1JP/Wxrh+b9EpKxIiSKxpGWOOl80s2zp7cZJMXN4YNawtHS1o7mne8Q3potzez1o6umSlvPF6qKlYnCWyYwM8dMcL80iFutqKlaG4zNzpbV56HRxejYfT1Iku92OP/7xj3j77bexYMECqTHsSI8++mhAb49/dYTe4GXyikNRdh5qxZL3j0NN6mamom1eJpaa3SgwiqgHUmOkRHu/d6gY/KmYNTwwi7jZBdi9UahzQlp8hovDiZrhmcJZ0V6pKCzWM6LF4e0hv4vqin8oXhTuTaEgEVmQGqO891JPFCMfaLwYKaEMXT29qKg5Iq1HegM4IlI+WURKSEVhRkpMhHgu2u0DzVHEeGSZMaHrk7xFUgZwdXW1FB0lHDp0KOi3xwKwiDDo6wKCdPTg09VWzH1lP9SiMTMRjYumoSAeWB/Dwq+aiRjSZJ1vWSi9P7znRUp4Lxop0eGJQocDOCRNeh+u+DJSYvKD2GADuDUsAKtW/ckGJKRYoLbIh8UlG8K9OaRwOp0OaalZ0jLRSIlTTc3SApSPul6s0SDFSDBSYmL2VlZLM+ZyLVmwpPsybomI1EjM0J2VPEVaghEpcfZcn7QcPNN6QaREusk0VBRmpMSFyltPjzq9ig3gVMXj8UqLP9dXip07d4b09iK+ACwalWjsvUBM4KMLdjV2wrD3BGKdIiVX2axJsTixbCbyEjS4M84d7s2hMGOkRGidcAK2/iip4c6S+XNCfOsUKs1WG2LT8hX/gDPygZQRKeFATW2dtJxPNJzz5Q1nSU3opg9kD4v4negIP2R3MP6Bs3+JKJIFO1KisbtLWs7HSAmfSutwAXhafCJy4hP9fk6JwuHee+8d8/yoqCgYjUbk5eVh/fr1SE5ODsjtRfanWABNTU1I04hj2I0B/b2ddifKDrVg8YEGKFlnbDQ+WTULGUnR2BTrGNXFmCgQkRJi/TQjJS5pcPbvsqIC6PWjc4FIPRwuEZGi7IwURj6QqiMltBpp1qs0azgrEzMs4qevIZ0oGosP62rPXNxTdkBaX72E8Q9EROdjpETw9TqdOGo7M3S6lLN/VSeSIiAqKytRUVGB/v5+5Of7JgIdO3YMWq0Ws2fPxu9//3t873vfw/vvv4+5c+f6fXssANcewVyTHoG2udqKglfLoFR9eg0OrspH4hQDbo9zQK8RcQ8s/tLkMVIiAPm//MKtag6XF2YoEyMfKFIiJU42NUtLJEZKHK07BetZm3Q0SnGB/19CiIgiCSMlAqOqrRmeERW+0vOym0n5IqkAvH5gdu/TTz+N+HhfL5jOzk5s2rQJq1atwp133olbbrkF99xzD3bs2OH37UV8AdjeYYNeG9jC5tYTNiS/exh6BSY/ODVA1cp8GNJisdFsh4mFXwoBRkpcXE8/UCNlKfOQW7XPrLM7FfRpZQRGPpCaMFLi4naX+eIflhXO59EoREQBxEiJ8asYkf9r0GpRnKGO/hkUmX71q1/hrbfeGir+CgkJCfjpT3+Kq666CnfffTceeOABaT0QIr4AjN4Ls3X80dRtR+2hZhTWWqEkolZdtTQX3qx4rDc7kKITsRic8UvhF+mREuV28f6MQq7Flz9J6tTR0QGNcXjgVwpGPlCkYKTEcP5vaTHjH4iIQoGREhdOmKi0iqNwfIrTs6WZ1aQuYob3yFnek7m+UnR2dsJqtV4Q79DW1oauLl+tMjExEU7nUFHDLxH/bvH0dQEBOjJPNBz5W3Urirb68tGUUvj9pHAazk1PxlVmJ7L1jHogZYiUSImh+IfiRaG/cQqZ+pMNSEhRzgwGRj4QRVakRFdPLypqjkjrbABHRBR+kRgpIRrqtdsHmqOI8cgyI2i3ReHj9fgWf66vpAiIO+64A4888giKi4ul8/bv34/77rsPGzZskE5//PHHmDVrVkBuL6ILwKIJiMbeC8QEZqbrS8dssGyrVsy82WP56WifnY5Ssxv5BlH4ldnUR6IIj5QQOy8HG8CtYQFY1ZqtNsSm+YL/5Y6RD0T+R0qIWUydXTZfMXioKNwiFYht7Vb02R2oqa2TlvOJhnOiMCwVhbMyMF1a9x0lEh2kmVB7K6ul7va5liypER4REcmXWiMlykfEPwir2ABOlbziPz9m8YrrK8WTTz4p5ftu3LhRqk8OTiz42te+hscee0w6LZrB/fnPfw7I7UV0AbipqQlpGjGV2uj37zre3gdrVSPmtwQ2UiIYTk5LQctCCxbF9+OfjKLwSxQ5lBQpccIJ2PqjpIY7S+bPmfwvItlzuMRrRf474Rj5QBQYYoZUYkKKtFw2c/6ofxNfAM7aWkfNGD4zsN7T24U2W4e0fFz9yajrabUaqTgrzRrOysQMi/jpmz0sisb+zMoajH/g7F8iIuVScqTE6Z4u7Kg/NnQ6I86MnPjEcW0XkVyZTCb86U9/koq9dXW+nf65ubnS+YMKCwsDdnuRXQCuPYK5Jr3fv8ft8WBLdSsWvVUDOWuZakJ9cS5mJwLXxbDwSyT3SIldvb6fhXPz2XBH5RwuL8yQL0Y+EEVupESz9Qze2bdfWl+9hPm/RERqJOdIiXdOncDvKz8cNa+zubcbrx2vwQ2XzfP7vpO8iAgHT4REQAwSBd8FCxYg2CK6AGzvsEGv9T+w4ZmaNszcUi7b6IezZiOOrbgM05I02BTjlBqZEJG8IyW2dQMvdPou/+GBg3hp+zu48fPr+LSpkDjEye6U76FKjHwgitxIiS1vv4cf/+aJoUMxP20e/cWdiIjUL5yRElNi4tDQ3THmdR94/20sSsviTGCVEZ85/IqAkHkTuHvvvRcPPfQQ4uLipPVLefTRRwN62xFdAEav/3ENZa3dcJafQlK3NPVPVnoMOhwqnYUpydG4I84JnVT4ZfGXSO6REvFRXnR5h88Tg9gDv30SpYsLkT41hU+gynR0dEBjjIccMfKBKHIjJTSaKHg8o79EPfj4n3H50sUci4iIaMKREmIRs4e7nI5xR0pcrPgrjX0AXj12CPcsWcVngxSjsrISLpdraP1igtFQMaILwJ6+LsCPRsrij9rOQ61Y8v5xyIldp0H1ystgSo3BbSYHjBoRJs3CL5FcIyUanMApVxSa3FHo7Ae6vBf+sfd4PDh1uplfulWo/mQDElIskBNGPhBFXqSEta0Zra0NsLY14aytDe5+XzOSkTgWERFRICMlfIXhjglHSgx+u2oaY+YwKZvY93ze/ucJX1/Odu7cOeZ6KERsAVjMhtDYe4GYyRdGn662Yu4rvkw0OXBrgKpledBmmHGjyY54ndirwMIvUbiImbvnvECnJwpdhjj0GWKhiTNBE2uCJs6MxLg4JMeZsSQ+EVOn5WBKWjr0BiMOHDmObz7w8KjDV0R0S05mBp9MFWq22hCblg+5YOQDkfp4+vtxrrcDfd1n4eqzQeN1IVoLROuAqTogKwOItmQiKSEfaanJmDplCuqaWnDTd/8/jkVERBS2SIn3Pq1HU8/YRV4xZUY0kiN18Xq80uLP9ZXi3Llz0ues2NhY6fSpU6fw2muvYe7cubjqqqsCfnsRWwBuampCmkYce22c1PV3NXbCsPcEYp3hT5gWW3Bw8XS4c5LweZMd6dHifrHwSxTU953Xi24P0AEduo1xcMfESUVdTWwcNLFmaOJ8p00pU5E6LQdzUlNhNpvHdSjHmpJFeOi735JiH8RsK1H8/dnd3+TsX5VyuAB9EA7xmQxGPhApj9vlQG+XDY7es3Cd64BO45UKu3odpCKvXgsY9VpYpiQhbVYKUlJmwmAYyi26qIWzzRyLiIgorJESt84txBdffUb67nU+cc6XZo2OPSLlE0+1PzG+Mo8AHmX9+vX40pe+hG9961tSLGBJSQn0ej3OnDkj5f/eddddCKTILQDXHsFck35S1+20O1F2qAWLDzQg3A7Pz0J33lSsNbsxQ8/CL1EguEQznX6gI9qIXkMsEGtC1MCsXa0o8MaZoDXFIykjE7nZ05CSkgKjcXI7ky5GNHwTmb8i9kHM/GX2r3o5XF6Yw7wNjHwgkh8xI8Rxrge9Xb5Zux5XD6J1Ub6Zu9rBAm8UEmP1yLekIHWqBYmJBdBqtQHbBo5FREQUTjkJSfjZqiulhm9iuoSo7Q3+FOfnxCfyCSLFqqiowGOPPSatv/zyy0hPT5dygV955RU88MADLAAHir3DBr12crNkN1dbUfBqGcKpbmYq2uZlYqnZjQKjL0CaiPyLZNAOzNrVD0QyWNLSkZSUJOUnhoMo+rLwq/7XpN0Z3t3UjHwgklckgzR7V1qPQlaCGWlzkpE6da7ULToYDUE+C8ciIiIKpxsum4dFaVlSwzeR+StiH8TMXxZ/1Uk0oD2/Ce1Er68UfX190lHCwptvvinNBhZH/y5btkyKgwi0iJ0BjN7JhYVvPWFD8ruHoQ9T8kNjZiIaF01DQTywPoaFX6JQRDIQBYs41EdjDF92GSMfiJQTyUBERBSpRLH3niWrwr0ZFKIJMiN74Uzm+kqRl5eHLVu24IYbbsCOHTtwzz33SOdbrVbExwf+O2LEFoA9fV1AzMSu09RtR+2hZhTWWhFq1qRY1C6bicsSNLgz7sKuzERqNt5IhuSMLORmW4ISyUAUDPUnG5CQYgn5g8vIByJlRjIQERERkTo88MADuOWWW6TC77p167B8+fKh2cBFRUUBv72ILAC73W5o7L1AzPgjIEQjpr9Vt6Jo6wGEUmdsND5ZNQsZSdG4M9YhTQcnishIBss0WNIzwhrJQBRozVYbYtPyQ/rAMvKBSNmRDERERERq5fX4Fn+urxRf/vKXsWrVKjQ3N2PhwoVD54tisJgVHGgRWUVpampCmkY0TBv/DMGXjtlg2VaNUJVf+/QaHFyVj8QpBtwe54BeI+IeWPwl5WAkA9Fnc7gAfQgLSIx8oEjESAYiIiIi5dQRxOLP9ZUkPT1dWkYqKSkJym1FZgG49gjmmvTjvvzx9j5Yqxoxv2VyucET4dQAVSvzYUiLxUazHSYWfknGkQyd0Ub0MJKBaNIcLi98sf/BxcgHUnMkQ1+3Dc7es4xkICIiIlK4SMoADrWILADbO2zQa8c3m9bt8WBLdSsWvVUT1G0Ss9SrlubCmxWP9WYHUnRihjJn/FJ4IxnOGWN9WbuMZCAKyvvN7gz+BxRGPpDqIxlmM5KBiIiIiOhSIrIAjN7xz+R9pqYNM7eUB60UKwq/nxROw7npybjK7ES2nlEPFKTXmteLbg/QAR26jXFwx/jydTWiiVqsGZqBvF1TylSkTsvBnNRUmM1m5hsSBUlHRwc0xsB3dx2JkQ8kR4xkICIiIqKxeDxeaZksf66rdhFZAPb0dQExn325stZuOMtPIanbEZTtOJafjvbZ6Sg1u5FvEIVfNhKhyWEkA5Hy1J9sQEKKJSi/2+m0Y++2/0ZG7mIsLtkQlNsgmnAkQ3QUojVAYqwe+ZYUpE61IDGxAFqtlg8mEREREUEkOPiT4sAEiIuLuAKw2+2Gxt4LxFx6Tq/d7cbOQ61Y8v7xgG/DyWkpaFlowaL4fvyTURR+icbGSAYi9Wq22hCblh/w38vIBwoGj6cf53oGIhnO2aDxjBXJoEFWgomRDEREREREMhNxBeCmpiakaUS+rvGSl3u62oq5r+wP6G23TDWhvjgXsxOB62JY+I10F0QyDEYxnBfJYJ6SiqmWaYxkIFIZhwvQRwX2yA9GPlCgIhn0YuauzuubuasFjHotLFOSkDYrBSkpM2EwGPhgExEREVHgm8D5EePAJnAXF3kF4NojmGvSX/Iyuxo7Ydh7ArFOkdDrv7NmI46tuAzTkjTYFOOERsPmbpEayaAdzNyNM0FrikdyRhZysy1ISUmB0XjpnRJEpC4OlxfmAP0uRj7QWBjJQERERERK+/wqJsv5c30aW8QVgO0dNui1Fy/AdtqdKDvUgsUHGvy+rR6DDodKZ2FKcjTuiHNCJxV+WfxVMvHHxO4FOjxR6DLE4ZwxVirsakRx1ySKuyapuKuPT5Rm7VrSM5CUlASdLuLeakT0WX9LnIH5cMLIh8jESAYiIiIiIhqvyKtK9XZd8p83V1tR8GqZXzdh12lQvfIymFJjcJvJAaPGzcKvSiIZxAxeEyMZiMhPHR0d0Bjj/X4cGfkQWZEMepG3KzVU8zKSgYiIiIhUR8Q/+BUB4cd11S7iCsCevi4gZux/23rChuR3D0M/yeQHtwaoWpYHbYYZN5rsiNeJnF/O+JVrJIOvqCtiGXwzeDUmMyMZiCgk6k82ICHFMunrM/JBvZEMem0UEmP0yLckI3WqBYmJBdBqteHedCIiIiKioGMBOHgiqgDsdruhsfcCMRcWZZu67ag91IzCWuuEf6+oFx9cPB3unCR83mRHerRoMsfCr5wiGQwJSZiSbWEkAxHJQrPVhti0/Eldl5EPColk8Lql5mk6rRfROl8jtWidBlkJJqTPScHUKXMRFxeHqAA3AiQiIiIiUioxgdefSbycAHxxEVUAbmpqQppGFGdHN9vyeDz4W3UrirYemPDvPDw/C915U7HW7MYMPQu/oYlkGJixy0gGIlIohwvQT6Lwx8gHeUUyDBV2GclAREREREQyFlkF4NojmGvSX3D+S8dssGyrntCc3bqZqWibl4mlZjcKjCLqgSaCkQxEFMkcLi/ME7g8Ix/CF8kgfibGGBjJQEREREQUZIyACJ6IKgDbO2zQa0eXeY+398Fa1Yj5LZduDjeoMTMRjYumoSAeWB/Dwu/5GMlARDSOv5PO8R/XxMiHyWEkAxERERGR8r4ricWf69PYIqoAjN7RRV63x4Mt1a1Y9FbNZ17VmhSL2mUzcVmCBnfGuRGpkQw9HqB9rEgG0Uxt4KdpSiqmWqZhTmoqzGYz8w2JiEbo6OiAxhg/rseEkQ9jYyQDERERERHR+EVUAdjT1wXEDJ9+pqYNM7eUXzL6oTM2Gp+smoWMpGjcGeuARqPO5m6MZCAiCo36kw1ISLFc8jKRGvkwViSDXqfxNVI7L5Jh9jTRSM2CxMQCaLXacG86ERERERH5yeMRi9ev61MEF4D37t2Le+65B7cum48Vi3Kk88pau+EsP4WkbseY1+nTa3BwVT4Spxhwe5wDeo2Ie9CoIpLB10TNDI1psJmaCYaEJEzJtsCSnoGkpCTodBHx0iAiCvl4dMcdm/DN+x/H/KIVERX5MBzJYIPr3FlovG5fAzWdL29XWnRRyEowIX2OKO7ORVxcHI8iISIKwlh077334tFHH8WKFWOPRUREROHACIjgiYgq3+9+9zt8/PHHmOLuwTcW5cDudmPnoVYsef/4BZd1aoCqlfkwpMVio9kOk4wLv4xkICJS3nh09Ohh/M8LT4xZAFZq5MNnRjLoAKNeC0tKItJmpSAlJRcGgyHcm01EFLFj0UcffYT/+q//YgGYiIhkRc5N4E6ePImHHnoI7777LlpaWpCZmYlbb70VP/rRj6DX6yF3qi8AnzlzBi+//LK0/uaBIzjT3YuXjndi7iv7R11OzBKvWpoLb1Y81psdSNE5w1r4vXgkQxy0cb7cXa3JjKSMLORmW5CSkgKj0Ri27SUiovGPR3veehWd//YoEpKmyDrygZEMRETqHYteeukl/Od//iemTFHP0SZERETBcuTIEXg8Hjz55JPIy8vDoUOHcOedd6K3txe//vWvZf/Aq74A/Je//EV6goR+rxcP/eMjLGyLRqzTd574/yeF03BuejKuMjuRrQ/ujN9xRTLEmmBI9EUyTMvIlCIZmG9IRKSe8Uj8fOv1Z/Hl2+4OW+TDhZEMLui1vlm7jGQgIoqMseiZZ56R4iCIiIjkQM4zgD//+c9Ly6Dc3FwcPXoUf/jDH9RbAH788cfxq1/9SpryvHDhQukwopKSkoteXuxd/vGPfyxNl77sssvwH//xH/jCF76AQGpqakJra+sF5//+97+Xiq4Srxev7C7HfHsyagE05KSga/oUFMW5cYWxC+n6ER3iJoGRDEREoaXU8cgLL7a+8ATi9EBvbxdmF1+HltMNwOkGJKWkISU1K6CRDMMF3dGRDNNSkpA6K5mRDEREkTgWeb3Stl9++eUXXC4tLQ1ZWf6NRURERBPlgVeqrflzfaGrq2vU+QaDISgRdJ2dnUhOToYSTLgA/MILL0h7iZ944gksXboUv/nNb3D11VdLVe/U1NQxmwzcfPPNePjhh/HFL34Rzz33HDZs2ICKigrMnz8/UPcDX/nKV6TbOl9UVNSIL9xAe28Pvose3z/WNQB1vtXFacl4dcOai/5+RjIQEcmLkscjsUOyubEejz38bwP/+ouhy81ZuAK/fOq9cUYy9A5l7Q4WeMXPxBgDZk8TjdQsSEws4FEkRERBouSxSPysq6vD4sWLL7jcypUr8f777wdse4iIiELJYrGMOv2Tn/wEP/3pTwN6G7W1tdJOXyXM/hWivEPfRsdHfLApLi6WmgYMHjokHtjvfOc7uP/++y+4/E033STlYbz++utD5y1btgyFhYXSB6XxEJX7hIQEqbIeHx8/5mX+/Oc/46677kJ/f//wF+xxiAKgjYrCD1YW4fIFcy+IZNDGmhA1IpJhKiMZiIgCbjx/58M9Ho13Gyc9HkVFQaPR4ra7foLlpZePGcmgj45CYrwJ6WmiuDsFcXFx0vWIiCg845HqvhtFRUk7DcW2fOMb3xj39YiIKLzfjdRynzf+4Bj0BvOkf4/T0Y3nfzkLn3766ajHznCJGcBivBZH41zK4cOHMXv27FFH2qxZs0Y6ikaMuaqbAex0OlFeXo4f/vCHQ+eJLuVXXnkl9u3bN+Z1xPnn50qJveJbtmy56O04HA5pGXT+1O2xbNq0Sdprfv3116O9vR1ut/szryO2Pd5swq9/8QtccfXnMSU1FWazmV+miYhkLhTj0WTGIr/Go/gE/PY/f4cr110hNfYMxiFKREQUOGr7biQKv2L8+fvf/y4VpYmIiEJN7LSc4DzVC64viOLveIvn3/ve93D77bdf8jIi73fQ6dOnccUVV2DFihX44x//CKXQTbRrrNiLLDKhRhKnRTe8sYgsrLEuL86/GHFI1IMPPoiJEh9UqqqqcMMNN2D//v1DDQ4utndbZHO99tprSE9Pn/BtERFR+IRiPJrsWCRwPCIiUj+1fTcSM5n53YiIiMJJNHHzhLgJ3NSpU6VlPMTMX1H8FfFJTz/9tLTjVylkuaViL7qY6j64iKnb45WRkYHdu3dj48aNl7ycyN567733WPwlIqKAj0Ucj4iIKFD43YiIiCj8mpqapMiHadOmSbm/bW1t0g7cS+3EVewM4ClTpkiHBp3fUVacvtgsWnH+RC4fiO58er1eOnxJp9ONebiTOF/cF3E5IiJSnlCMR4HoFMvxiIhIvfjdiIiIKLDEDN7JzOIdef1geeutt6TGb2LJzs4efbt+xFbIcgaw+CIrpjm/8847Q+eJQ4nE6eXLl495HXH+yMsPPmgXu3wgiG0SHXkvlnUlzn/++ecveRgUERHJF8cjIiIKN45FREREwckA9mcJlttvvz3ktxnWCAjRtOBPf/oT/vKXv0hd8ER3WdHJ9utf/7r071/96ldHNUK4++67sX37djzyyCNSFtZPf/pTlJWV4dvf/jaCZe/evbBardK6mCEmZvx+61vfkn6K04L4d3E5IiJSJo5HREQUbhyLiIiISJUF4JtuuknKunjggQdQWFiIAwcOSAXewWYGDQ0NaG5uHrq86Ir33HPPSZ3xFi5ciJdfflnqciu60gbLiy++OKqT7Z49e/CHP/xB+pmcnDxUBH7ppZeCtg1ERBRcHI+IiCjcOBYREREFjtfj8XuhsUV5FTBXuaurCwkJCVITnvj4+EteVsQ6iEZwYoav6Hx7fidbUZwWnXA/+ugjpKamSqeV1LWPiEiNJvJ3XinbyPGIiEh51DYecSwiIlIeJYxFwbrPN3z7IKIN5kn/HpejG6/9V0FEPXbjpbrK57lz53DZZZdJkQ/vvffeBc19RHF49+7d+OY3v4lZs2ZJlyciIuJ4REREasPvRkRERCTo1PYwxMXFSVEPUVFRl2zY8MQTT0hBzZe6HBEREccjIiJSKn43IiIiJfG3qZoCQg7CRnUFYGG8RV0Wf4mIKJg4HhERUbhxLCIiIqXwerzS4s/1KYIKwERERERERERERKQcLAAHj+oygImIiIiIiIiIiIjIhzOAiYiIiIiIiIiIKKw84j+vx6/r09hYACYiIiIiIiIiIqKwErVf/zKAA7o5qsIICCIiIiIiIiIiIiKVUsQMYK/XV/3v6uoK96YQEVEQDP59H/x7L0cci4iI1I/jERERhZsSxqJgYRO4CC8Ad3d3Sz8tFku4N5VYMWMAAAqYSURBVIWIiIL89z4hIUGWjzHHIiKiyMHxiIiIwk3OY1GwiKK3P4XvSCyaq6oAnJmZiU8//RRmsxlRUVGT2nsiisfid8THx0MteL+Uhc+XsvD5Ci0xUIsPOOLvvVrHIoGvK2Xh86UsfL6URa7PVySMR3J97P3F+6UsfL6URa3Pl1zvmxLGomDxeDzS4s/1ScEFYI1Gg+zsbL9/j3gzy+UNHUi8X8rC50tZ+HyFjtz3bgdqLBL4ulIWPl/KwudLWeT4fEXKeCTHxz4QeL+Uhc+Xsqj1+ZLjfZP7WETKo4gCMBEREREREREREakXM4CDhwVgIiIiIiIiIiIiCiuv1yMt/lyfxqZBBDAYDPjJT34i/VQT3i9l4fOlLHy+iK8rvl/4d0BZ+Hwpi1qfLyVQ62PP+6UsfL6URa3Pl9rvG9FIUV62yCMiIiIiIiIiIqIwNeMTucdX/vNeROtNk/49LmcP3n52BTo7O2WV6SwHjIAgIiIiIiIiIiKi8PJ4pRxgf65PY2MBmIiIiIiIiIiIiMLK4/VIiz/XpwjOACYiIiIiIiIiIiKKRJwBTERERERERERERGHl9TMCwq/4CJVTzQzgxx9/HNOnT4fRaMTSpUvx8ccfX/LyL730EmbPni1dvqCgAP/4xz+g9Pu1efNmREVFjVrE9eRm9+7duO6665CZmSlt45YtWz7zOrt27cKiRYukzpx5eXnSfVX6/RL36fznSywtLS2Qi4cffhjFxcUwm81ITU3Fhg0bcPTo0c+8ntzfX5O5X0p5f/3hD3/AggULpMB7sSxfvhzbtm1T9POlJGodi9Q4HnEsUs5YJHA8Utb7i2NR+Kl1PFLbWCRwPFLOeKTWsUjN3484HimP1+uB1+PHwggIdReAX3jhBdx77734yU9+goqKCixcuBBXX301rFbrmJffu3cvbr75ZnzjG99AZWWl9MdNLIcOHYKS75cgCj7Nzc1Dy6lTpyA3vb290n0RH+DGo76+Htdeey2uuOIKHDhwAN/97nexadMm7NixA0q+X4PEwDryORMDrly89957+Nd//Vd8+OGHeOutt+ByuXDVVVdJ9/VilPD+msz9Usr7Kzs7G//3//5flJeXo6ysDGvXrsX69etRU1Oj2OdLKdQ6Fql1POJYpJyxSOB4pKz3F8ei8FLreKTGsUjgeKSc8UitY5Gavx9xPCIawasCJSUl3n/9138dOt3f3+/NzMz0Pvzww2Ne/itf+Yr32muvHXXe0qVLvd/85je9Sr5fTz/9tDchIcGrJOIl+Nprr13yMj/4wQ+88+bNG3XeTTfd5L366qu9Sr5fO3fulC7X3t7uVQqr1Spt83vvvXfRyyjl/TXR+6XE99egpKQk75///GfVPF9ypdaxKBLGI45FyhqLBI5Hynl/DeJYFDpqHY/UPhYJHI+UNR6pdSxS+/cjjkfy1NnZKb3m1vzTTu+6jfsnvYjri98jfh+NpvgZwE6nU5rpduWVVw6dp9FopNP79u0b8zri/JGXF8Te44tdXin3S+jp6UFOTg4sFsslZ/0piRKeL38UFhYiIyMDn/vc5/DBBx9Azjo7O6WfycnJqnq+xnO/lPj+6u/vx/PPPy/tuRdREGp5vuRIrWORwPFIWc9XJIxFAscj5YxHHItCS63jEcciZT1fkTIeqXUsUuv3I45HCoqA8HOhsSm+AHzmzBnpjZyWljbqfHH6YnlB4vyJXF4p9ys/Px9PPfUU/v73v+P//b//B4/HgxUrVqCxsRFKdrHnq6urC+fOnYNSiQ82TzzxBF555RVpEYPm5ZdfLh3SJkfi9STiN1auXIn58+df9HJKeH9N5n4p6f118OBBmEwmKTP7W9/6Fl577TXMnTtXFc+XXKl1LBI4HvlwLJIPjkfKGI84FoWHWscjjkXDOB7Jg1rHIjV+P+J4ROSjG/hJKiBm+I2c5Sf++M6ZMwdPPvkkHnroobBuG409YIpl5PN14sQJPPbYY/jrX/8qu4dMZEKJrKr3338fajLe+6Wk95d4XYm8bLHn/uWXX8bXvvY1KdfrYkVgokBT0vsl0iltLBI4Hinj/cWxiMKNY5GyKG08UutYpMbvRxyPlMXjEYvXr+uTSgvAU6ZMgVarRWtr66jzxen09PQxryPOn8jllXK/zhcdHY2ioiLU1tZCyS72fInA+ZiYGKhJSUmJLD9EfPvb38brr78udSkWQfqXooT312Tul5LeX3q9Hnl5edL64sWLsX//fvz2t7+VPowp+fmSM7WORQLHIx+ORfLA8Ug54xHHovBQ63jEsWgYx6PwU+tYpNbvRxyPlMXr8UiLP9cnlUZAiDezKHC88847Q+eJQw/E6YtlXorzR15eEJ0uL3Z5pdyv84nDv8ThDiJqQMmU8HwFipi1KafnS/SiEB8CRITAu+++ixkzZqji+ZrM/VLy+0v87XA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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_p = PENTAGON + FAN_SHIFT\n", "E_p = simkit.closed_polyline(X_p)\n", "i, j = E_p[:, 0], E_p[:, 1]\n", "terms = 0.5 * (X_p[i, 0] * X_p[j, 1] - X_p[j, 0] * X_p[i, 1]) # one shoelace term per edge\n", "A_p = simkit.outline_areas(X_p, [E_p])[0]\n", "A_unshifted = simkit.outline_areas(PENTAGON, [E_p])[0]\n", "print(\"terms:\", np.round(terms, 3), f\" sum = {terms.sum():.4f}\")\n", "print(f\"outline_areas: shifted {A_p:.4f}, unshifted {A_unshifted:.4f}\")\n", "\n", "X_fan = np.vstack([[0.0, 0.0], X_p]) # vertex 0 is the origin\n", "T_fan = np.column_stack([np.zeros(len(E_p), dtype=int), E_p + 1]) # triangle (origin, p_i, p_j) per edge\n", "vmax = np.abs(terms).max()\n", "lims = utils.auto_limits([X_fan], pad=0.15)\n", "fig, axes = plt.subplots(1, 3, figsize=(14, 4.6), layout=\"constrained\")\n", "for ax, keep, title in zip(axes, [terms > 0, terms < 0],\n", " [\"positive terms\", \"negative terms\"]):\n", " m = utils.plot_scalar_field(ax, X_fan, T_fan[keep], terms[keep], cmap=\"coolwarm\",\n", " vmin=-vmax, vmax=vmax, lims=lims, colorbar=False,\n", " title=f\"{title}: sum {terms[keep].sum():+.2f}\")\n", " utils.draw_closed_outline(ax, X_p, E_p, color=EDGE_C, fill=False, lw=1.5, ms=3)\n", " ax.plot(0.0, 0.0, \"k*\", ms=12, zorder=6)\n", "utils.draw_closed_outline(axes[2], X_p, E_p, color=POS_C)\n", "axes[2].plot(0.0, 0.0, \"k*\", ms=12, zorder=6)\n", "utils.setup_axes(axes[2], *lims, title=f\"all terms: A = {A_p:.2f}\", grid=False)\n", "fig.colorbar(m, ax=axes.tolist(), shrink=0.8,\n", " label=r\"signed triangle area $\\frac{1}{2}(x_i y_j - x_j y_i)$\")\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"shoelace_fan.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"013_shoelace_fan.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e9e3e70f", "metadata": {}, "source": [ "A regular $n$-gon is a circle we have not finished drawing, so its shoelace area should approach\n", "$\\pi r^2$. Taylor-expanding $\\sin(2\\pi/n)$ predicts the gap $\\pi r^2 - A_n \\approx\n", "\\tfrac{2\\pi^3}{3}\\, r^2 / n^2$ (dashed); the measured error (dots) lies on it, second order in $1/n$." ] }, { "cell_type": "code", "execution_count": 4, "id": "f46d54fe", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:38.622459Z", "iopub.status.busy": "2026-09-24T03:44:38.622378Z", "iopub.status.idle": "2026-09-24T03:44:38.885279Z", "shell.execute_reply": "2026-09-24T03:44:38.884808Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "err = []\n", "for n in N_SIDES_SWEEP:\n", " X_n = simkit.circle_outline(R_GON, n + 1)[0][:-1] # n-gon: drop the repeated closing vertex\n", " A_n = simkit.outline_areas(X_n, [simkit.closed_polyline(X_n)])[0]\n", " err.append(abs(A_n - np.pi * R_GON ** 2))\n", "\n", "fig, ax = plt.subplots(figsize=(6.5, 4.4))\n", "ax.loglog(N_SIDES_SWEEP, err, \"o\", color=EDGE_C, ms=4, label=\"shoelace error\")\n", "ax.loglog(N_SIDES_SWEEP, 2 * np.pi ** 3 / 3 * R_GON ** 2 / N_SIDES_SWEEP ** 2, \"--\", color=NEG_C,\n", " lw=1.5, label=r\"$\\frac{2\\pi^3}{3}\\, r^2/n^2$ prediction\")\n", "ax.set_xlabel(\"number of polygon sides $n$\")\n", "ax.set_ylabel(r\"$|A_{\\mathrm{shoelace}} - \\pi r^2|$\")\n", "ax.set_title(\"Regular polygon area converges to the circle\")\n", "ax.grid(True, which=\"both\", color=\"0.92\")\n", "ax.legend()\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"circle_convergence.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"013_circle_convergence.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "83b7b49c", "metadata": {}, "source": [ "## 2 · Orientation is the sign of the area\n", "\n", "Walking the same loop clockwise instead of counter-clockwise negates every shoelace term, so $A$ flips\n", "sign (left two panels; the arrows show the walk). simkit keeps this sign rather than $|A|$ because the\n", "signed area is a polynomial in the vertex coordinates: its derivatives exist everywhere, including the\n", "degenerate $A = 0$ loop where $|A|$ has a kink. The right panel shows exactly that by sweeping the\n", "rectangle's top edge to height $h$ through zero: $A = W h$ (width $W$ = `RECT_W` = 1.6) passes\n", "straight through, $|A|$ has a corner." ] }, { "cell_type": "code", "execution_count": 5, "id": "0067167d", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:38.887132Z", "iopub.status.busy": "2026-09-24T03:44:38.887005Z", "iopub.status.idle": "2026-09-24T03:44:39.100039Z", "shell.execute_reply": "2026-09-24T03:44:39.099565Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "counter-clockwise A = +1.600, clockwise A = -1.600\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.array([[0.0, 0.0], [RECT_W, 0.0], [RECT_W, RECT_H], [0.0, RECT_H]])\n", "E_ccw = simkit.closed_polyline(X)\n", "E_cw = E_ccw[::-1, ::-1] # same loop, walked the other way\n", "A_ccw = simkit.outline_areas(X, [E_ccw])[0]\n", "A_cw = simkit.outline_areas(X, [E_cw])[0]\n", "print(f\"counter-clockwise A = {A_ccw:+.3f}, clockwise A = {A_cw:+.3f}\")\n", "\n", "A_flip = [simkit.outline_areas(np.array([[0.0, 0.0], [RECT_W, 0.0], [RECT_W, h], [0.0, h]]),\n", " [E_ccw])[0] for h in FLIP_HEIGHTS]\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(15, 4.4))\n", "for ax, (E, A, c, label) in zip(axes, [(E_ccw, A_ccw, POS_C, \"counter-clockwise\"),\n", " (E_cw, A_cw, NEG_C, \"clockwise\")]):\n", " utils.draw_closed_outline(ax, X, E, color=c, arrows=True)\n", " utils.setup_axes(ax, title=f\"{label}\\nA = {A:+.3f}\")\n", "ax = axes[2]\n", "ax.plot(FLIP_HEIGHTS, A_flip, color=POS_C, lw=2.5, label=\"signed $A$\")\n", "ax.plot(FLIP_HEIGHTS, np.abs(A_flip), \"--\", color=NEG_C, lw=2, label=\"$|A|$\")\n", "ax.axhline(0.0, color=\"0.6\", lw=0.8)\n", "ax.set_xlabel(\"top-edge height $h$\")\n", "ax.set_ylabel(\"area\")\n", "ax.set_title(\"signed area is smooth through $A = 0$\")\n", "ax.grid(True, color=\"0.92\")\n", "ax.legend()\n", "fig.suptitle(\"Same four vertices, opposite winding: the sign flips\", y=1.03)\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"orientation_sign.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"013_orientation_sign.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "68ec907e", "metadata": {}, "source": [ "## 3 · The gradient inflates the shape\n", "\n", "`area_system` wraps the three simkit calls in the energy / gradient / Hessian triple used throughout\n", "these tutorials, with the area $A(x)$ playing the energy, as a function of the stacked vertex positions\n", "$x = [x_0, y_0, x_1, y_1, \\dots]$ (tutorial 15 builds its pneumatic chamber energy\n", "$\\tfrac12 k\\,(A(x)-A^\\star)^2$ on this triple). simkit returns derivatives over each loop's own\n", "vertices in `np.unique(E)` order; our loops visit every vertex, so that order is the global one." ] }, { "cell_type": "code", "execution_count": 6, "id": "9b607a70", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.101301Z", "iopub.status.busy": "2026-09-24T03:44:39.101209Z", "iopub.status.idle": "2026-09-24T03:44:39.103488Z", "shell.execute_reply": "2026-09-24T03:44:39.103049Z" } }, "outputs": [], "source": [ "def area_system(E_loop):\n", " \"\"\"Signed area A(x) of the closed loop E_loop, with its gradient and Hessian, in stacked x of shape (2n, 1).\"\"\"\n", "\n", " def energy_func(x):\n", " A = simkit.outline_areas(x.reshape(-1, 2), [E_loop])[0]\n", " return A\n", "\n", " def gradient_func(x):\n", " g_A = simkit.outline_areas_gradient(x.reshape(-1, 2), [E_loop])[0].reshape(-1, 1)\n", " return g_A\n", "\n", " def hessian_func(x):\n", " H_A = simkit.outline_areas_hessian(x.reshape(-1, 2), [E_loop])[0]\n", " return H_A\n", "\n", " return energy_func, gradient_func, hessian_func" ] }, { "cell_type": "markdown", "id": "830c2c68", "metadata": {}, "source": [ "Differentiating the shoelace formula gives, for vertex $i$ with neighbours $i-1$ and $i+1$, the\n", "expression below: $\\nabla_i A$ is the neighbour chord $p_{i+1} - p_{i-1}$ rotated clockwise by\n", "$90^\\circ$, so it points along the outward normal with half the chord's length. The figure draws this\n", "field on a 10-point star, coloured by that length: the notches, whose neighbours are two far-apart\n", "tips, get the long arrows. The printout checks the chord formula against `gradient_func`.\n", "\n", "$$\\frac{\\partial A}{\\partial x_i} = \\tfrac12 (y_{i+1} - y_{i-1}), \\qquad\n", " \\frac{\\partial A}{\\partial y_i} = -\\tfrac12 (x_{i+1} - x_{i-1})$$" ] }, { "cell_type": "code", "execution_count": 7, "id": "16197e03", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.104405Z", "iopub.status.busy": "2026-09-24T03:44:39.104323Z", "iopub.status.idle": "2026-09-24T03:44:39.201774Z", "shell.execute_reply": "2026-09-24T03:44:39.201485Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |grad_i A - rot(chord_i)/2| = 0.0e+00\n", "|grad_i A| at tips 0.130, at notches 0.309\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_star = 2 * STAR_POINTS\n", "radii0 = np.where(np.arange(n_star) % 2 == 0, STAR_R_OUT, STAR_R_IN)[:, None] # tip, notch, tip, ...\n", "X0 = simkit.circle_outline(1.0, n_star + 1)[0][:-1] * radii0 # drop the repeated closing vertex\n", "E_star = simkit.closed_polyline(X0)\n", "energy_func, gradient_func, hessian_func = area_system(E_star)\n", "x0 = X0.reshape(-1, 1)\n", "\n", "g0 = gradient_func(x0).reshape(-1, 2) # per-vertex dA/dp_i\n", "g_len = np.linalg.norm(g0, axis=1)\n", "chord = np.roll(X0, -1, axis=0) - np.roll(X0, 1, axis=0) # p_{i+1} - p_{i-1}\n", "print(f\"max |grad_i A - rot(chord_i)/2| = {np.abs(g0 - 0.5 * chord[:, ::-1] * [1, -1]).max():.1e}\")\n", "print(f\"|grad_i A| at tips {g_len[0]:.3f}, at notches {g_len[1]:.3f}\")\n", "\n", "fig, ax = plt.subplots(figsize=(6.6, 5.6))\n", "utils.draw_closed_outline(ax, X0, E_star, color=EDGE_C, lw=2)\n", "q = ax.quiver(X0[:, 0], X0[:, 1], g0[:, 0], g0[:, 1], g_len, cmap=\"plasma\",\n", " angles=\"xy\", scale_units=\"xy\", scale=1.0, width=0.012, zorder=5)\n", "fig.colorbar(q, ax=ax, shrink=0.8, label=r\"$\\|\\nabla_i A\\|$ = half the neighbour chord\")\n", "lims = utils.auto_limits([X0, X0 + g0], pad=0.25) # star plus arrow tips\n", "utils.setup_axes(ax, *lims, title=r\"area gradient $\\nabla A$ (points outward)\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"gradient_field.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"013_gradient_field.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4338cab0", "metadata": {}, "source": [ "Gradient ascent $x \\leftarrow x + \\Delta t\\,\\nabla A(x)$ moves every vertex uphill on $A$, so with a\n", "small step the area grows every step. Because $A$ is quadratic, $\\nabla A = Hx$ with the constant\n", "Hessian of section 4, and each step multiplies $x$ by $I + \\Delta t\\,H$. The star mixes just two\n", "eigenvectors of $H$: the regular 20-gon, with eigenvalue $\\lambda = \\sin(2\\pi/20)$, which grows, and the\n", "alternating spikes, with $-\\lambda$, which shrink. So the loop rounds out and the area's per-step growth\n", "approaches $(1 + \\Delta t\\,\\lambda)^2$. The cell measures $\\lambda$ from `gradient_func`, compares the\n", "growth rates, and reports how round the final loop is (spread of its vertex radii)." ] }, { "cell_type": "code", "execution_count": 8, "id": "11813ce6", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.203250Z", "iopub.status.busy": "2026-09-24T03:44:39.203150Z", "iopub.status.idle": "2026-09-24T03:44:39.208419Z", "shell.execute_reply": "2026-09-24T03:44:39.208070Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "area grew from 1.298 to 126.337 (grows every step: True)\n", "lambda = 0.3090 (sin(2 pi/20) = 0.3090), eigenvector residual 1.1e-16\n", "per-step area growth: first 1.0699, last 1.05006, predicted 1.05005\n", "final radius spread (std / mean) = 0.48%\n" ] } ], "source": [ "states = [X0]\n", "areas = [energy_func(x0)]\n", "x = x0.copy()\n", "for _ in range(N_STEPS):\n", " x = x + DT * gradient_func(x) # one step straight uphill on A\n", " states.append(x.reshape(-1, 2))\n", " areas.append(energy_func(x))\n", "areas = np.array(areas)\n", "print(f\"area grew from {areas[0]:.3f} to {areas[-1]:.3f} (grows every step: {np.all(np.diff(areas) > 0)})\")\n", "\n", "x_reg = simkit.circle_outline(1.0, n_star + 1)[0][:-1].reshape(-1, 1) # regular 20-gon, closing vertex dropped\n", "g_reg = gradient_func(x_reg) # H x_reg = lam x_reg\n", "lam = (x_reg.T @ g_reg).item() / (x_reg.T @ x_reg).item()\n", "print(f\"lambda = {lam:.4f} (sin(2 pi/{n_star}) = {np.sin(2 * np.pi / n_star):.4f}), \"\n", " f\"eigenvector residual {np.abs(g_reg - lam * x_reg).max():.1e}\")\n", "rate = (1 + DT * lam) ** 2\n", "radii = np.linalg.norm(states[-1], axis=1)\n", "print(f\"per-step area growth: first {areas[1] / areas[0]:.4f}, last {areas[-1] / areas[-2]:.5f}, \"\n", " f\"predicted {rate:.5f}\")\n", "print(f\"final radius spread (std / mean) = {radii.std() / radii.mean():.2%}\")" ] }, { "cell_type": "markdown", "id": "b274da95", "metadata": {}, "source": [ "The printout confirms the analysis: $\\lambda$ equals $\\sin(2\\pi/20)$, the last step's growth matches the\n", "prediction to $10^{-5}$, and the final radii vary by under 0.5%. The video plays the ascent: the star\n", "(dashed ghost) rounds into a regular 20-gon while, on a log axis, its area climbs every step and merges\n", "onto the predicted rate $(1 + \\Delta t\\,\\lambda)^{2k}$ (dashed, anchored at the last step)." ] }, { "cell_type": "code", "execution_count": 9, "id": "d395a04e", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.209414Z", "iopub.status.busy": "2026-09-24T03:44:39.209348Z", "iopub.status.idle": "2026-09-24T03:44:44.070691Z", "shell.execute_reply": "2026-09-24T03:44:44.070232Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "steps = np.arange(N_STEPS + 1)\n", "A_pred = areas[-1] * rate ** (steps - N_STEPS)\n", "pred_label = r\"$(1 + \\Delta t\\,\\lambda)^{2k}$ prediction\"\n", "fig, anim = utils.animate_outline_trace(\n", " states, steps, {\"area $A$\": areas, pred_label: A_pred}, E=E_star, rest=X0, color=POS_C,\n", " colors={\"area $A$\": POS_C, pred_label: NEG_C}, dashed=[pred_label], logy=True, fps=FPS,\n", " xlabel=\"gradient-ascent step\", ylabel=\"enclosed area $A$\", title=\"area climbs every step\",\n", " scene_title=\"inflating the star\")\n", "fig.suptitle(r\"Following $\\nabla A$ inflates the loop and grows its area\")\n", "fig.tight_layout()\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"inflate.mp4\"), fps=FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"013_inflate.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "c772551e", "metadata": {}, "source": [ "## 4 · Checking the gradient and Hessian against finite differences\n", "\n", "We compare `area_system`'s analytic gradient and Hessian on the irregular pentagon against central\n", "finite differences of its area (`simkit.gradient_cfd`, `simkit.hessian_cfd`). The signed area is\n", "bilinear in the coordinates, so the Hessian is a constant matrix of $\\pm\\tfrac12$ entries that only\n", "couple the $x$ of one endpoint to the $y$ of the other; the printout also confirms that it is identical\n", "at a random pose and that $\\nabla A = Hx$ exactly." ] }, { "cell_type": "code", "execution_count": 10, "id": "d01efd85", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:44.072309Z", "iopub.status.busy": "2026-09-24T03:44:44.072211Z", "iopub.status.idle": "2026-09-24T03:44:44.529471Z", "shell.execute_reply": "2026-09-24T03:44:44.529021Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |grad - fd| = 6.78e-10\n", "max |Hess - fd| = 5.14e-10\n", "max |H(z) - H(rand)| = 0.00e+00\n", "max |grad - H z| = 0.00e+00\n" ] }, { "data": { "image/png": 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cSDc0u0Za+/zzz13hSRd6BQcVLEaPHu0KVeEosCuAqAag1weiLt6q3afmCQocutA/8sgjLkioQKLCiHz11Vd2wgknuM/WDcFff/3lCldKJkajTpPVpMC7adBnvPXWWzZw4EDbsmWLv3PlwGShkopjx461RYsW2eOPP+6CuW4E5IwzzrBly5bZc8895/qHUTMKibTfKtTpM6dNm+b6Q9Frj24snnrqKTvuuOP2KKwqCKtgqvWI+mHRcQCATBJrHPBcdtllLhGmGKBl1RG+ru26xnpUgNK1VklK/asmZCps6Jp/1113hd0OxYh//vOfLvn1+++/B/Wv+9prr7n36u8HHnigi3X6vAsuuMAVWkQDFkSieKNtOumkk1zTPsWwDz/80D799NOY+sHasGFDTMdSMeXUU091D+u0bV7cUKxS3FKhWVQQPuWUU+yQQw5x+6IClR68BXYRoiZ6l19+uSsgXnHFFS4B++WXX9q8efPcg8RI4jn2GzdudPcRiquKk+rfUg/dlKTVsQKARNHDJD3wULlE1zollaKVK3Rt/c9//uMemFWpUsUeeOABO/PMM23lypUuORaOYpTilq6H//rXv9w8bz2q3KAEqCpJaHvUBZPiobpc+u2336IO9PLHH3/Y8ccf79avfdBDn6efftpddwuj2KDllKhU3B0+fLib365dOzdfTcf/9re/Wd++fS0Wig/h4lS4/ooVf4444gh37NW0Xcm/F154wSVQX3rpJfdAUVTeU1lMMbNjx44uhqhcpLKZtk107PV5Or4qR6nGppKTOh6RBn7T56hsd+6557qWZ1u3brUnnnjCunfvbvPnz9+jKxU9cNMy+n50n6B7BMWsH3/8MataOiAD+IA01rNnT1+lSpV8q1ev9s/7/vvvfWXKlFFm0T9v1KhR7vW55567x2fs2LFjj3lz5851yz/11FP+eb169fJVqFDB9/PPP/vnffvtt768vLygdcnkyZPdvBUrVrjXAwcO9NWvX9+3YcOGoOXOOeccX7Vq1fzb4G3ngAEDgpY7/fTTfbVq1Qqad9dddwWtI5qPP/7YLT9p0qSg+TNmzHDzp06dGjT/r7/+8rVs2dI3bNgw/7z+/fv7atSoEdP6ACBdxBoHvGt7t27dfAUFBf75V155pYsFmzZtKvQzL7zwQhez/vzzT/+8fv36+Ro1auR/vXTpUreORx55JOi9p556qq9x48b+9X722WduOW1TqNDPfO+999yyl19++R7LBu5HOPosvbew6dJLL/Uv//TTT/tyc3N9H374YdDnTJgwwS2rWCT33Xefe71+/fqI6z7ttNNcHCpMaLyN59gfc8wxe3zHO3fu9NWrV8935plnFrpeACgJ77//vrsOvfjii0HzvTJBIL0uV66c74cffvDP++KLL9z8Bx98sNDroq6luuaFGjNmjG+vvfbyLVu2LGj+iBEjXFxbuXJlods/btw4t64XXnjBP2/79u2+Aw44wM3X/kWKTaLXPXr02ONzQ2NLYaLFKE2KmZ7jjz/e17p166B4oFjYpUsXX7Nmzfzz2rRpE3bbPBs3bnSfrTJZYXTcA4+9yliKNaGftffeeweVAfX96fNVBvz999/981999VU3/7XXXovp+ACpgmbXSFuq5fjuu++6p1R6yuZRU4FItRUuuuiiPeapiV1g9XqN5qzPUDMwPdny1qUR17QuPREMfGqnp1SFUUzUU7SePXu6/9ZTOW/Sezdv3uxfT6TtVK0WbZeelBWVasQ0b97c3yzPM3nyZFeDx3vK53nyySfdUzs9+QzcX9US0dNRAMgUscSBQKrRF9gMTNdoxQk13w73maqxoGu+llMtEzX3ikS1Gjt16mTPPvusf55qQaq2fJ8+fYrU/EwxSO8L7dBfYvk8NTdTTY5wU6gXX3zRxQrFm8B4p9r14jUr8/ryUhPpSE37tIya88XbvCyeY6+aQKpNGtg3l2q4qEYJAKSabt26uea3HtUer1q1apGvWbpm6/qoskDgNVvrUVybM2dOoe9/8803XQs01VD3qLWA4mRpUlPncDHK66YqMJ6qVqZqunvxQZPivspl33//vb+coxikWo2aFynWKGaoCbnKR7FSf5xeP5CKf9omtUZQK4Rw9xxnn322+348XmsH4hTSDc2ukbZUrV1V/VVADBVunqgpcyh9hqrUKwmnYOM1xxYlBkV9eWk5NdkOpT6qFHgj0XvVl4r66tAUaV8CBSY4xQs4Cmy6wSgq9Umi5gUKVk2bNnWfpyZwao6nwmVg0wUVUtUEUduuSbx1qwmdmioAQCaIJQ7Eeo32qMCi0UpVyAl9cBTuMwOpmZmacSuZ2ahRI1c4VFJUzdCKOpqqHtIFNuOOhwpKKojGQoW07777LmI3IF68U2FKzc7UnE1xSc321IxMBVhv4DM1f9ZDRiUDFdfV9YmaW6u5XGHiOfZq7heagNX3qebdAJBqQuOPd82KJ/kVes3W9S7aNVvlmcB+c/XgRpPilK7PoddRlY9Kk67l4eKUHmAFUvceivE33HCDmyLts8o56hJESU09FFQfm+qiQ3FYCV9RdyHqEktNxtWMXV1sqTsRxfB69eoVur2q5HHPPfe4B2KK74WVVWO55wDSAclHZJXA2hAe9dGhAqf6XdRI0Or4VwFUibdYO1oujPcZqlnRr1+/sMt4QcwTaYS6wAJxUSgYqq8X1X5UQFVfjuoQWsnHQBqUQMFa/W1pCqVBZxSAASATxBsHol2j9cBGfWjpgY2utaqlogc8qtGghFq02KL1qh8s1X7UACzPPPOMqxFR2oW5otC+qb/Ee++9N+zfNaCBF49Vo0Y1ITXYgAZMUJ+ZqiH5zjvvuGOsGpQaKO311193f1cNzocfftj136h+nsOJ99gnKt4CQCKU9DVL10T1X6hBwcJR4k3UH2Vg7X5VUlCfiOnGiwFXXXVVxNZrXiWWo48+2j28Uw19xSU9MFP/xRMmTHAPzkT3DWrdpsocaiWnhKYeZurhl/qvDEcxXYPvqEWdamaqX399r3qf1heKOIVMQfIRaUsXahUo9AQrVLh5kahzeSUF9fQpsOafV9tP9DRQBaVw1e5VMCqM3qsOofW0MNaaI7EoStM7PYU7+eST3dM2FdyUhGzTpo0deuih/mX0FO322293zSW8zpQD6Vgx4jWATBJLHIiHmmCpCZcGBVDhxaNRPWOhGooarVnJRzW11iAsoZ3+xxMDlIBToSh0EJtE0Lq++OILV5Mx2jaqhqOW06RkpQZd0AMyJSS9eKmBAFRLUpNGCFXtyFtvvdV1CRJYY7+kjj0AZKJI12NdszUoS7QyiuKRWgl41IJKVDtf5QIlPwPXEa18lCzedmuglljKZYqZajmmScdJcUVJVy/56B1D1X7UpLKiBozR/YSSjJHuObQdilOBxyxc1yhAJqHPR6QtrxmYnjT9+uuvQYlH9Y0Vz+eEPi188MEHg5oWaBk9HdO61A+iR03LVKCL9vkaCU01NsIl7dSMoShUIJN4C8eq5ah90D6qH63QWo8q/Gnf1YxAzd9CJwVLRrwGkEliiQPxfp4EfqYSZ6q1Fys17dJI26oVoc9TbciixgDFIG1LuNqCJV3DT/1oqel6uFrzKrhu377d/bcSoaG8ET5VI1+URAykPrJatGjhtjmwmVpJH3sAyDSKGeHiha7Zc+fODVue0fLqi1DU3YXKXd7kJfFUqUHlMCXUPOpfN1JXU6lQeeXYY4+1Rx991I3mXVi5LDQGqZm5akV6MUr7qQeVgZSIVKUTb5lY49S8efPc9wBkMmo+Iq3pyZOqwSsgXnzxxa6g+NBDD7l+ORYvXhzTZ6hvjqeffto1s1OhRhd+9TFVq1atoOVUaFOzL3Xye8kll7hgrMJpy5Yto/YNpZqEqsmhQQQGDx7s1qOCl5qBaV3hCmHRtG/f3v2rWiIqlOoJnqr9ewXSSHSToBqQKtCqrxLVqvGsWrXKHT/1NeYNBhBKQVXHXM0WvH65ACCdxRoH4hngS30yqTbl5Zdf7mo26PPjSfSp5qPWr/4eNYiaCkyh12Jdp9X8SwUdXfsVY8L1F9W1a1eXzHzggQdcrQx1m6Fr+Icffuj+pmt+SdF6XnjhBTdwmuKe4rNis/q10nwVcNWEXE2i1exa+6maM+pjSwlC9dt15JFHus9SH4+KV/oM9aelB36KUXqP9jlRxx4AMo3KDY888ojdcsstLoGmmKJuLlQemD59uouDagqs5fSQSBUNlFD86aefrHbt2hE/V+UaXZfVtdPChQvd4DO65mrQmVQ1fvx4F2fURYi2X4nUtWvXutivbqdUe190P6BEpY6JakAuWLDAHRMvZi5btszV3FcCV8uWKVPGXn75ZfdZoQ8MA+lYq9ajBvtUPFPNfMVyfYZqVwKZiuQj0pqCgWo5qt8O9bGhvqRUoFEBpbDRREP7N9QTKDUn0NMrFXJU6AztB0T9MqrQNGzYMNfflApISkjqqVm05KMKTfPnz3fbpmCjApYKlUpcqoZhUajvlTFjxrhgpaSoCpIKXtGSjwqMukG48847XbAMbIKn/dLnqK+xSFTgVe0V9UkSbgAeAEg3scaBWOn6rn4K1QRLA58oGaZ+f1VIifUzVctPTY0VL8INNKMHTupCQ82PlejTAzH1Wxku+Sj6m+LYE0884QqbSrQqCahkXUnSQym1ElC/WE899ZQriKkQqsLdFVdc4e8/7NRTT3WF2kmTJrmRRlW4VV+NiqvaNrnwwgvdd6Im2SqQKe4qoahjmshjDwCZRvf46rNR9/8a5VnXWyUfdX3+4IMPXMsnPezSdVt95upaHXg9jkTvnzVrlus7WZUy9FoVG/TQLFX7h1eST4lErwsq1XBUMlZ9NOo4eRRvlJhVpQvVZNSDMiVvvRG0Ve4899xz3f4r4aoyVvPmzd2DNrU4iERJ3jVr1rjalypbanvURFvHX12HAJkqx8ejYGQgdeCr0S7D9dEIAEA60IMgJQtVSEnlWiQAAABAYWgzibQX2PmxKOH45ptvumryAACkI9XAVE0I1Z4g8QgAAIB0RrNrpD015VL1df2r5gTqz0TN1a655ppkbxoAAHFR34dq8q1+pdQUTE2VAQAAgHRG8hFpT/2JPPfcc65ZmgZQ6dy5s+u3hP4IAQDpRiNcq78s9T+lAWK8EaABAACAdEWfjwAAAAAAAAASgj4fAQAAAAAAACRExjW7LigosF9//dWqVKliOTk5yd4cAEhrPp/Ptm7dag0aNLDcXJ5XpRtiIoBEIT4gXsQkAIlCTEp9GZd8VOKxYcOGyd4MAMgoq1atsn333TfZm4E4ERMBJBrxAbEiJgFINGJS6sq45KNqPHonXdWqVZO9OQCQ1rZs2eIe6HjXVqQX73v76MM5Vrly5WRvTkZY2r53qa7voIUvlur6kP4uGPFbqawn/68dtnBWb+ID4o5JH374ETGphCxrf2ZGxyRfEnqJy7GCUl9nJiMmIWOTj15TayUeST4CQMleW5Ge35sSjySQS0alnDwrTXxviFeZsltK9aARHxDvuUJMKjmZHpNIPqY/YhI8dOAFAAAAAAAAIP2Sj3PmzLGePXu6gQr0pOuVV14pdPnZs2e75UKnNWvWJHIzAQAAAAAAAKRbs+vt27dbmzZtbMCAAXbGGWfE/L6lS5cGNZmuW7duiW1Tfn6+7d69u8Q+D8HKli1reXmlW/0fAAAAAAAAWZh8POmkk9wULyUbq1evXuLbs23bNvvll1/cMOxIDNVU1Yi4DGwAAAAAAACAlBxwpm3btrZz505r1aqV3XTTTXbEEUdEXFbLaQocmTVSjUclHitVqmR16tShc+wEUFJ3/fr17jg3a9aMGpAAAAAAAABZLqWSj/Xr17cJEyZYhw4dXELx8ccft2OPPdbmzZtnhx56aNj3jB071m6++eaon62m1kqOKfFYsWLFBGw9RMf3p59+cseb5tcAAAAAAADZLaWSjwcddJCbPF26dLHly5fbfffdZ08//XTY94wcOdKGDRsWVPOxYcOGhTYLRuJwfAEAAAAAAJCSycdwOnbsaB999FHEv5cvX95NRdFy0jhLlG8GDE3YZwMAssf48ePtrrvusjVr1rhB3B588EEXGwEAIC4BANJBrqW4xYsXu+bYiE7NnWMZqEfH9Pnnn9+jn82tW7dymAEghUybNs3V7h81apQtWrTIJR+7d+9u69atS/amAQCyEHEJAJByyUeNLq1ElyZZsWKF+++VK1f6m0z37dvXv/y4cePs1VdftR9++MG+/vprGzp0qL333nt26aWXJnIzs0645KPmValSJWnbBADY07333muDBw+2/v37W4sWLVy/yBo4bdKkSRwuAECpIy4BAFKu2fWCBQusa9eu/tde34z9+vWzKVOm2G+//eZPRMquXbts+PDhtnr1ale4OuSQQ+zdd98N+oxM06dPH1u6dKnbd/VV+cQTT9iff/7paiJeccUV9vrrr9vmzZvtgQcesJNPPjnie+rVqxf0uXfffbctW7bMJk6c6F5v2rTJDjjgAPv222/txhtvdJ+pdRx++OGuMKu+Gjdu3OhqTn733Xcu8avvRy655BK76KKLknB0kC2K0gXCR/k74lq+xuDr4l4HkEy6xi9cuNA9qPPk5uZat27dbO7cuWHfo8HaNAX2gwwAQDLiEjEJAFAqNR81UrVGmA6dlHgU/Tt79mz/8tdcc42r9fjHH3/Yf//7X3v//fczOvHo1fZUkvbLL7+0o446ym666SY3X8lBJV8V4B966CG78soro74n0KBBg+yVV15xSUeZPHmynXbaaVa3bl0bPXq0O66q7ajEY6C//vrLLXf++ee7z9f097//PeHHAQAQbMOGDZafn29777130Hy9Vv+P4YwdO9aqVavmnwobgA0AgETGJWISACBt+nzMdFOnTrUOHTpYq1at7PHHH/c3Ua9QoYKdccYZ7r87d+7sRv2O9p5AqsGopKGa5inh+8gjj9iQIUOibo9qVKrm5bnnnuufV7t27RLaWwBAIqk2ih5eedOqVas44ACApCAmAQDSZrTrTKZRvNWcWs0UVCNx+vTprkm0aARvNYWWvLw895Qx2ntCXX755XbqqafawQcfbHXq1LF27dqV4t4BAIpDD350/V+7dm3QfL0O7WrDo9ihCQCAZMclYhIAwEPNxyRSH4sa5KVWrVquD5VHH320RN/TvHlza9q0qV1wwQVBtR6rVq3qasSEc9BBB7n+Np977rmgJhYAgNJVrlw5a9++vc2aNcs/r6CgwL1WjXgAAIhLAIB0kNU1H78ZMDSp6z/xxBPtmWeecQk/JRPVWbMG2ynJ92iUVCUeA/ttPP74492ANOpTskuXLkH9PpYpU8aNOH7ZZZfZbbfd5jqR1oAzF154YQntNQAgVhqoTYO0qauNjh07uj5/t2/f7ka/BgCgtBGXAABFkdXJx2QrW7asTZs2LWjerbfe6v71BoqRypUru34bo72ncePGQe8TDdqj5KHe59EgBJ988knQct7nixKb77zzTgnsIQCgOM4++2xbv369615Dnfm3bdvWZsyYsUdn/wAAlAbiEgCgKEg+Zqhff/3VjjvuOKtZs6a9/fbbyd4cAEARqfZ6LAOGAQBQGohLAIB4kXzMUA0aNLAlS5YkezMAAAAAAACQxRhwBgAAAAAAAEBCkHwEAAAAAAAAkBAkHwEAAAAAAAAkBMlHAAAAAAAAAAmR1QPObHzstoR9do3B10Vd5tVXX7URI0ZY+fLl7emnn7bzzjvPPvzwQ6tSpUqh7xs0aJD16dPHunbtaq+88orVq1fPDj/88GJvc4cOHezuu++2Y489Nmgdv//+u/Xs2dO2b99uvXv3tosvvjjo9b/+9a9irxsAAAAAAACZJ6uTj8k2YcIEu/HGG+3cc891rxcvXhzT+x5//HH/fyv52LZt2xJJPkZax8yZM61y5cr28ccfu9fTpk0Leg0AQLKcN3R1qa7v6aVvlOr6kP6+PahHRp6jW7dutbZvF/9z/vzzT9u1a1dMy5YrV84qVKhQ/JUCCdJ36KpSPbbEJKR6THpq6VulFpPalXJMEuJS7Gh2nSSXX365q+V43XXXWZcuXdy8nJwc27Rpk/vvxo0bu8Rk586drUmTJnbLLbf436uaiUo6vvnmmzZ9+nS76667XALSSxiqFmWnTp3s0EMPtaOPPtq++OKLsNvwySefuPe1atXK+vfvb3/99dce63j33Xft6quvtk8//dQtG+41AAAAUJRCXoOKla1atWoxTbon1nsAAEh2TCIuxYeaj0nywAMP2JdffmlDhw61Xr16hV1Gici5c+fahg0bbP/993cJwn322cf/95NPPtlOPfVUlwTU54hqIz733HM2Z84c15xbCc5//OMf9s033wR9trL5Z599tk2ePNm6detm77zzjk2ZMmWPbdDfRo8e7RKRmiT0NQAAABAv3Y9utHx7skJTqxSlTsQOK7B+a35076H2IwAgmTGJuBQ/ko8pTElDqV27tjVt2tRWrFgRlHyM1I+kajqq5qNHfTb+8ccfVrFiRf+8JUuWWJkyZVxyUU444QS3DgAAAKA07VUmz/bKySt0mRxffqltDwAge8USk4S4FB+Sjyks8KluXl5eULPoSHw+n/Xr189uuy3+wXTU7BsAAAAoTTllcy0np/BaJjk+X6ltDwAge8USk9xyxKW40Odjmqtatapt3rzZ/1rNsJ955hlbuXKle11QUGALFizY433Nmzd3ycz333/fvVbfjcuXLy/FLQcAAADMcvNyLLdMlCmPh+QAgBSJScSluFHzMc2dd955dv7557v+Fy+99FIbNGiQ3XnnnXb66ae75KL6LejRo4d16NBhj1GZNGr1JZdcYvn5+XbYYYdZmzZtkrYfAAAAyE45ZXMsJ7fw5GJOAclHAEBqxCS3HHEpLlmdfKwx+Lqkrn/27Nl7NJn2/PTTT0F/C6y9GPg+JQ1DB5M555xz3BSNRtlevHhx1G1TclNTpNcAAABAUeVVzLW83MIbZOUV0OwaAJAaMcktR1yKS1YnHwEAAACkQBO3KM2qc/Op+QgASI2Y5JYjLsWF5CMAAACApMnJy3FTocsYyUcAQGrEJLcccSkuJB8BAAAApHbNRwp5AIBUqvlIXIpL1iUfA/tVBMcXAAAAyaWO/aMOOOOj5iMAIDVikluOuBSXrEk+li1b1nJycmz9+vVWp04d998o+cSujq+OrY43AAAAEE1OXq6bCl3GqEAAAEiNmOSWIy7FJWuSj3l5ebbvvvvaL7/8ssdI0ig5SjzqOOt4AwAAANHQ7BoAkCpodp0YWZN8lMqVK1uzZs1s9+7dyd6UjKUaj+maeGw5aVzc7/kof0dcy9cYfF3c6wAAAMhkuWVyLK9M4bVMcnMKSm17AADZK5aY5JYjLsUlq5KPosRYuibHAAAAgKwc7Zq+tQAAqTTaNXEpLlmXfAQAAACQOnJyc90UbRkAAFIhJnnLIXYkHwEAAACk9mjXMYw8CgBAqY12TVyKC8lHAAAAAKk94AzN2wAAqTTgDHEpLiQfAQAAACQNNR8BAKmCmo+JQSN1AAAAAEmTk/O//rUKnXKKVmwZP368NW7c2CpUqGCdOnWy+fPnx/S+559/3nJycqxXr15FWi8AIINjUhHj0vgsjkkkHwEAAAAkTV7Z3JimeE2bNs2GDRtmo0aNskWLFlmbNm2se/futm7dukLf99NPP9lVV11lRx11VDH2CgCQyTEp3rg0LctjEslHAAAAAElv4hZtite9995rgwcPtv79+1uLFi1swoQJVqlSJZs0aVLE9+Tn51ufPn3s5ptvtqZNmxZzzwAAmRqT4o1L92Z5TCL5CAAAACBpYmrelvu/YsuWLVuCpp07d4b9zF27dtnChQutW7du/nm5ubnu9dy5cyNuy+jRo61u3bo2cODABOwpACBTYlI8cWkXMYnkIwAAAIDkiaeGScOGDa1atWr+aezYsWE/c8OGDa7GyN577x00X6/XrFkT9j0fffSRPfHEE/bYY48lYC8BAJlY8zGWuLSBmJTY5OOcOXOsZ8+e1qBBA9c55iuvvBL1PbNnz7ZDDz3UypcvbwcccIBNmTIlkZsIAAAAIIniKeStWrXKNm/e7J9GjhxZItuwdetWO++881zisXbt2iXymQCAzE8+JiIubc3AmFQmkR++fft214nmgAED7Iwzzoi6/IoVK6xHjx520UUX2bPPPmuzZs2yQYMGWf369V1HnAAAAAAySyx9Z3l/r1q1qpuiUWEtLy/P1q5dGzRfr+vVq7fH8suXL3ed+qvihKegoMD9W6ZMGVu6dKntv//+Me8TACA9xdqfYzxxqTYxKbHJx5NOOslNsVKHm02aNLF77rnHvT744INd84f77rsvYvJR7ekD29SrjT0AAACAdCroFd4gK96O/cuVK2ft27d3lRl69erlTybq9ZAhQ/ZYvnnz5vbVV18Fzbv++utd7ZP777/fNasDAGS+WGKSt1ysyhGTEpt8jJc6fw7sFFqUdBw6dGjE96g9vUb+AQAAyXfe0NWlur6nx+1TquvLdN8e1KPU19li6RuWyTJ9/0pCbplcyytbeEEv1xd/b1HDhg2zfv36WYcOHaxjx442btw41zJLI41K3759bZ999nHliQoVKlirVq2C3l+9enX3b+h8pI++Q1eV6vqISSXru4Nir8hUUjL9ml3a++ezzIxJRYlLw7I8JqVU8lGdP4frFFq1Gf/44w+rWLHiHu9Re3p9iR4ty5NJAAAAID0Ejhpa2DLxOvvss239+vV24403unJG27ZtbcaMGf7yxsqVK90I2AAAxBOTihKXzs7ymJRSycei0MA0mgAAAABkdp+P8VIT63DNrL2BLgvDwJcAkH3i7fMxHkOyOCalVPJRnT+H6xRanXeGq/UIAAAAIL0lMvkIAECqJB+zWUolHzt37mxvvvlm0LyZM2e6+QAAAAAyT6KaXQMAkCrNrrNdQo/Wtm3bbPHixW6SFStWuP9WW3avv0Z1qum56KKL7Mcff7RrrrnGlixZYg8//LC98MILduWVVyZyMwEAAAAkuZZJtAkAgFSJScSlFKr5uGDBAuvatav/tTcwjEb4UXv13377zZ+IlCZNmtgbb7zhko3333+/7bvvvvb444+7Ea8BAAAAZB5qPgIAUgU1H9Mw+Xjssceaz+eLq8NMvefzzz9P5GYBAAAASKWCXh7NrgEA6RGTvOWQpn0+AgAAAMgu1HwEAKQKaj4mBslHAAAAAEnDaNcAgFTBaNeJQfIRAAAAQNJQ8xEAkCqo+ZgYNFIHACBFjR071g477DCrUqWK1a1b13r16mVLly5N9mYBQInKyY1ldFEOerIRkwBkg9hiEnEpXoRxAABS1AcffGCXXnqpffrppzZz5kzbvXu3nXDCCbZ9+/ZkbxoAlJjYCnk5HPEkIyYByAaxxiTiUnxodg0AQIqaMWNG0OspU6a4GpALFy60o48+OmnbBQAlSiOGRhs1lFFFk46YBCArxBKTvOUQM5KPAACkic2bN7t/a9asGfbvO3fudJNny5YtpbZtAFBUuXl5boq2DFILMQlAtsYkbznEjlQtAABpoKCgwIYOHWpHHHGEtWrVKmJ/XNWqVfNPDRs2LPXtBIB40bwt/RCTAGQqml0nBslHAADSgPp+/Prrr+3555+PuMzIkSNdTRRvWrVqValuIwAUuXf/3CgTI86kFGISgKyOScSluNHsGgCAFDdkyBB7/fXXbc6cObbvvvtGXK58+fJuAoC0EkvH/Qw4kzKISQAyWqyDyRCX4kLyEQCAFOXz+eyyyy6zl19+2WbPnm1NmjRJ9iYBQInLycl1U7RlkFzEJADZIJaY5C2H2JF8BAAghZu1TZ061V599VWrUqWKrVmzxs1Xf44VK1ZM9uYBQMlQ7RFqPqY8YhKArBBLTPKWQ8xI1QIAkKIeeeQR13fjsccea/Xr1/dP06ZNS/amAUCJycnNjWlCchGTAGSDWGMScSk+1HwEACCFm7gBQKbLycu1nLy8qMsguYhJALJBLDHJWw6xI/kIAAAAIGlyYujcP6bO/wEAKIWY5C2H2JF8BAAAAJA8alIdrVk1za4BAKkSk7zlEDOSjwAAAACSJicnx03RlgEAIBVikrccYkfyEQAAAEDy5MRQy0TLAACQCjHJWw4xI/kIAAAAIGno8xEAkCro8zExSD4CAAAASB7VHolWg4QaJgCAVIlJ3nKIGclHAAAy3NL2va1STl6prOvppW+UynqyxXlDV5fq+vj+kAw5eXluirYMMsOy9mcSk9IUMQnxyrGCtFtPLDHJWw6xI/kIAAAAIHlyc/43RVsGAIBUiEnecogZyUcAAAAASZOTm+umaMsAAJAKMclbDrEj+QgAAAAgeXJy/jdFWwYAgFSISd5yiBnJRwAAAABJbuIWpQYJzdsAAKkSk7zlEDOSjwAAAACSh5qPAIBUQc3HhCD5CAAAACBp6PMRAJAq6PMxMUg+AgAAAEie3DyzvLzoywAAkAoxyVsOMSP5CAAAACBpcnJy3RRtGQAAUiEmecshdhwtAAAAAEnu3D+GqQjGjx9vjRs3tgoVKlinTp1s/vz5EZd97LHH7KijjrIaNWq4qVu3boUuDwDI4phUhLg0PotjEslHAAAAAMmj2iOxTHGaNm2aDRs2zEaNGmWLFi2yNm3aWPfu3W3dunVhl589e7ade+659v7779vcuXOtYcOGdsIJJ9jq1atLYCcBABkVk+KMS9OyPCaRfAQAAACQ/JFFo01xuvfee23w4MHWv39/a9GihU2YMMEqVapkkyZNCrv8s88+a5dccom1bdvWmjdvbo8//rgVFBTYrFmzSmAnAQAZFZPijEv3ZnlMIvkIAAAAIHlyc2ObzGzLli1B086dO8N+5K5du2zhwoWumdr/X02ue60aJLHYsWOH7d6922rWrFlCOwoAyJiYFEdc2kVMIvkIAAAAIIniaN6mZmfVqlXzT2PHjg37kRs2bLD8/Hzbe++9g+br9Zo1a2LarGuvvdYaNGgQlMAEAGS4OJtdxxKXNhCTGO0aAAAAQBLl5Zrl5UVfxsxWrVplVatW9c8uX758Qjbp9ttvt+eff971uaWBAQAAWSKWmFTKcen2DIhJZZK9AUgtLSeNi/s9H+XviGv5GoOvi3sdAAAAyFCx9J31f39XAS+wkBdJ7dq1LS8vz9auXRs0X6/r1atX6HvvvvtuV9B799137ZBDDollDwAAmSLW/hzjiEu1iUml0+w6nuHEp0yZYjk5OUFTumZ2AQAAAEQRR99asSpXrpy1b98+qGN+r6P+zp07R3zfnXfeaWPGjLEZM2ZYhw4d+OoAINvE2edjLMoRkxJf89EbTlwj+SjxOG7cODec+NKlS61u3bph36Ossf7uUQISAAAAQHbXfIyHyiD9+vVzScSOHTu6csj27dvdSKPSt29f22efffz9c91xxx1244032tSpU13FCa9vyMqVK7sJAJAF4qz5GKthWR6TEp58DBxOXJSEfOONN9xw4iNGjAj7HiUbozWHAAAAAJABAjruL3SZOJ199tm2fv16V3hToa1t27auRqM3CM3KlSvdCNieRx55xI1I+ve//z3oc0aNGmU33XRT3OsHAGRoTPKWi8PZWR6TEpp89IYTHzlypH+eDqZGjJs7d27E923bts0aNWrkmkYceuihdtttt1nLli3DLqthzAOHMtfQ5gAAAADSRE4MzdeKkHyUIUOGuCkcddwf6KeffirSOgAAWRaTvOXiNCSLY1JCk4+FDSe+ZMmSsO856KCDXK1Ide68efNm1+Fzly5d7JtvvrF99913j+VVJfXmm29O2D4AqTrYT7wD/QiD/aQeBnkCAGS9BDW7BgAgVZpdZ7tSGXAmHuoAWm3dVQX1mGOOsf/85z9Wp04de/TRR8Mur1qVSlJ6k4Y5BwAAAJAmcvNimwAASJWYRFxKnZqPxRlO3FO2bFlr166d/fDDD2H/Xr58eTcBAAAASEOxjBoa52jXAAAUSawjWROX4pLQKF7U4cQDqdn2V199ZfXr10/glgIAAABIBl9OTkwTAACpEpOISyk22nW8w4mPHj3aDj/8cDvggANs06ZNdtddd9nPP/9sgwYNSvSmAgAAAEhK/1rRBpwh+QgASJGY5C2H1Ek+xjuc+MaNG23w4MFu2Ro1ariak5988om1aNEi0ZsKAAAAoLSpkBc1+UizawBAisQkbzmkTvIx3uHE77vvPjcBAAAAyHyxNF+jeRsAoDTE2qSauJSCyUcAAAAACIuajwCAVEHNx4Qg+QgAQIY7aOGLVqVKlWRvRkY4b+jqUl3f0+P2KdX1ZYNvD+pRqutrsfSNUl1fWsrL+98UbRlkBGJSySEmpT9iUprGJG85xIzkIwAAAICkodk1ACBV0Ow6MUg+AgAAAEgeml0DAFIFza4TguQjAAAAgKTx5eS6KdoyAACkQkzylkPsSD4CAAAASB6NKhptZNEYRh4FAKBUYpK3HGJG8hEAAABA0vgshpqPRg0TAEBqxCRvOcSO5CMAAACA5KHmIwAgVVDzMSFIPgIAAABIGl9urvly86IuAwBAKsQkbznEjuQjAAAAgORhtGsAQKpgtOuEIPkIAAAAIGl8luOmaMsAAJAKMclbDrEj+QgAAAAgadSxf9QBZ2Lo/B8AgNKISd5yiB3JRwAAAADJQ7NrAECqoNl1QpCqBQAgDdx+++2Wk5NjQ4cOTfamAECJ8uXkxDQhdRCTAGR7TCIuxYeajwAApLjPPvvMHn30UTvkkEOSvSkAUOJodp1eiEkAMhnNrhODmo8AAKSwbdu2WZ8+feyxxx6zGjVqFLrszp07bcuWLUETAKS83DzzRZm0DJKPmAQg48UQk4hL8SP5CABACrv00kutR48e1q1bt6jLjh071qpVq+afGjZsWCrbCAAlMbJotAnJR0wCkOlijUnEpfiQfAQAIEU9//zztmjRIpdUjMXIkSNt8+bN/mnVqlUJ30YAKKkmbtEmJBcxCUA2iDUmEZfiQ5+PAACkICUOr7jiCps5c6ZVqFAhpveUL1/eTQCQVlSpMdqAMlR8TCpiEoCsEUtM8pZDzEg+AgCQghYuXGjr1q2zQw891D8vPz/f5syZYw899JDr3zEvjz7QAKQ/n+W6KdoySB5iEoBsEUtM8pZD7Eg+AgCQgo4//nj76quvgub179/fmjdvbtdeey2JRwAZw5eT46ZoyyB5iEkAskUsMclbDrEj+QgAQAqqUqWKtWrVKmjeXnvtZbVq1dpjPgCks1j6zqJvreQiJgHIFrH250hcig/JRwAAAABJU5CT56ZoywAAkAoxyVsOsSP5CABAmpg9e3ayNwEAShzNrtMTMQlAJqLZdWKQfAQAAACQND7LcVO0ZQAASIWY5C2H2JF8BAAAAJA09PkIAEgV9PmYGCQfAQAAACQNNR8BAKmCmo+JEX0IHwAAAABIEJ/9b2TRQqciFlvGjx9vjRs3tgoVKlinTp1s/vz5hS7/4osvWvPmzd3yrVu3tjfffLOIewUAyNiYVMS4ND6LYxLJRwAAAABJr2USbYrXtGnTbNiwYTZq1ChbtGiRtWnTxrp3727r1q0Lu/wnn3xi5557rg0cONA+//xz69Wrl5u+/vrrEthLAEAmxaR449K0LI9JNLsGAABp69uDepTq+p5e+kapri8bnDd0damuj+8w9RTk5FpBTl7UZWTLli1B88uXL++mcO69914bPHiw9e/f372eMGGCvfHGGzZp0iQbMWLEHsvff//9duKJJ9rVV1/tXo8ZM8ZmzpxpDz30kHsvSrBWUYbWgfnuoJNKdX1cz0pepsekTP3tleR+xRKTvOXiiUv3ZnlMyswzDwAAAEBa8OXkxDRJw4YNrVq1av5p7NixYT9z165dtnDhQuvWrZt/Xm5urns9d+7csO/R/MDlRbVSIi0PAMjemBRPXNpFTKLmIwAAAIDk8fly3BRtGVm1apVVrVrVPz9SrccNGzZYfn6+7b333kHz9XrJkiVh37NmzZqwy2s+ACA7xBKTvOVijUsbiEkkHwEAAAAkUyzNcP/3dxXwAgt5AACUfkz633JCXIoNfT4CAAAASJpYOu6Pt2P/2rVrW15enq1duzZovl7Xq1cv7Hs0P57lAQCZJ9bBZOKJS7WJSfT5CAAAACB5EjGqaLly5ax9+/Y2a9Ys/7yCggL3unPnzmHfo/mBy4s694+0PAAg8yRitOtyxCRqPgIwazlpXNyH4aP8HXG/p8bg6zjcAAAg4TUfZdiwYdavXz/r0KGDdezY0caNG2fbt2/3jzTat29f22efffyDA1xxxRV2zDHH2D333GM9evSw559/3hYsWGATJ07kGwOALJGImo+S7TGpVEa7Hj9+vDVu3NgqVKhgnTp1svnz5xe6/IsvvmjNmzd3y7du3drefPPN0thMAAAAAKWswJcb0xSvs88+2+6++2678cYbrW3btrZ48WKbMWOGf1CZlStX2m+//eZfvkuXLjZ16lRXsGvTpo39+9//tldeecVatWpVovsLAEj/mBRvXDo7y2NSwvt8nDZtmsvwTpgwwSUeld3t3r27LV261OrWrbvH8p988omde+65Ltt7yimnuIPdq1cvW7RoUdoeZAAAAAClW/NRhgwZ4qZwZs+evce83r17uwkAkJ0SVfMx22NSwms+3nvvvTZ48GBXlbRFixYuCVmpUiWbNGlS2OXvv/9+O/HEE+3qq6+2gw8+2MaMGWOHHnqoPfTQQ4neVAAAAAAZ0OcjAACJjEnEpRRKPu7atcsWLlxo3bp1+/8rzM11r+fOnRv2PZofuLyopmSk5Xfu3GlbtmwJmgAAAACkBwp5AIBUQfIxDZtdb9iwwfLz8/1t2D16vWTJkrDvWbNmTdjlNT8cNc+++eabkzr4RkkOvJHsgT++GTDUkimZxz7Z+57M9Wfzvmf7bw4AgJQo6PkS0+waAICSjkneckixAWcSaeTIkbZ582b/tGrVqmRvEgAAAIAYFVhOTBMAAKkSk4hLKVTzsXbt2paXl2dr164Nmq/X9erVC/sezY9n+fLly7sJAAAAQPpJ5IAzAACkyoAz2SyhNR/LlStn7du3t1mzZvnnFRQUuNedO3cO+x7ND1xeZs6cGXF5AAAAAOlLzdtimQAASJWYRFxKoZqPMmzYMOvXr5916NDBOnbsaOPGjbPt27e70a+lb9++ts8++7i+G+WKK66wY445xu655x7r0aOHPf/887ZgwQKbOHFiojcVAAAAQCkr8OVYgS836jIAAKRCTPKWQwolH88++2xbv3693XjjjW7QmLZt29qMGTP8g8qsXLnSjYDt6dKli02dOtWuv/56u+6666xZs2b2yiuvWKtWrRK9qQAAAABKGc2uAQCpgmbXaZp8lCFDhrgpnNmzZ+8xr3fv3m4CAAAAkNliab5G8zYAQGmItUk1cSkFk48AAAAAEI7PjS4afRkAAFIhJnnLIXYkHwEAAAAkDTUfAQCpgpqPiUHyEQAAAEDS0OcjACBV0OdjYpB8BAAAAJA01HwEAKQKaj4mBslHAAAAAEmT78txU7RlAABIhZjkLYfYkXwEAAAAkDQ0uwYApAqaXScGyUcAAAAASUOzawBAqqDZdWKQfAQAAACQND7f/6ZoywAAkAoxyVsOsSP5CAAAACBpCizHTdGWAQAgFWKStxxiR/IRAAAAQNLQ7BoAkCpodp0YJB8BAAAAJA3NrgEAqYJm14lB8hEAAKStFkvfSPYmZJTzhq4u9XU+PW6fUl9nJvv2oB6lsp4dvvwS+6x8X46boi2DzPC/Bo0FlomISekfk54a17CU11i6v4XS/u1lakzylkPsSD4CAAAASB5fjmvmFm0ZAABSIib933KIHclHAAAAAElDs2sAQKqg2XVikHwEAAAAkDSMdg0ASBWMdp0YJB8BAAAAJA01HwEAqYKaj4lB8hEAAABA0vhi6F8rpv63AAAohZjkLYfYkXwEAAAAkDQFvv9N0ZYBACAVYpK3HGJH8hEAAABA0hT4ctwUbRkAAFIhJnnLIXYkHwEAAAAkTUEMNUi0DAAAqRCTvOUQO5KPAAAAAJKGAWcAAKmCAWcSg+QjAAAAgKQh+QgASBUkHxMjN0GfCwAAimn16tX2z3/+02rVqmUVK1a01q1b24IFCziuADKyf61oE5KPuAQg08Uak4hL8aHmIwAAKWjjxo12xBFHWNeuXe2tt96yOnXq2Pfff281atRI9qYBQImi5mN6IC4ByAbUfEwMaj4CAJCC7rjjDmvYsKFNnjzZOnbsaE2aNLETTjjB9t9//4jv2blzp23ZsiVoAoB0KehFmxLp999/tz59+ljVqlWtevXqNnDgQNu2bVuhy1922WV20EEHuZrp++23n11++eW2efNmy1TxxiViEoBMjkmJjEu/Z2BMIvkIAEAKmj59unXo0MF69+5tdevWtXbt2tljjz1W6HvGjh1r1apV808qJAJAqisoyLH8KJOWSSQV8r755hubOXOmvf766zZnzhy74IILIi7/66+/uunuu++2r7/+2qZMmWIzZsxwBcRMFW9cIiYByNSYlOi41CcDYxLJRwAAUtCPP/5ojzzyiDVr1szefvttu/jii90TzCeffDLie0aOHOmecHrTqlWrSnWbAaAokl3D5LvvvnOFtMcff9w6depkRx55pD344IP2/PPPu8JcOK1atbKXXnrJevbs6Wr+HXfccXbrrbfaa6+9Zn/99ZdlonjjEjEJQDpKds3H7zI0JtHnIwAAKaigoMDVMLntttvca9Uw0ZPMCRMmWL9+/cK+p3z58m4CgHRS4PvfFG0ZCe1OoiSue3PnznXN2nTN9XTr1s1yc3Nt3rx5dvrpp8f0OXrooyZyZcpkZhEr3rhETAKQqTHJWy4RcWluhsYkaj4CAJCC6tevby1atAiad/DBB9vKlSuTtk0AkAjx1DBRdxKB3UuoaW9xrVmzxjUjDqTCWs2aNd3fYrFhwwYbM2ZMoc3i0h1xCUA2iLfmY0nHpTUZGpNSIwUKAACCaKTrpUuXBs1btmyZNWrUiCMFIGtHu1Z3EqrJ4SmsdsmIESPcICnRmrcVl2q99OjRwz0wuummmyxTEZcAZIN4R7uONS6NyPKYRPIRAIAUdOWVV1qXLl1c87azzjrL5s+fbxMnTnQTAGRrs2sV8AILeYUZPny4nX/++YUu07RpU6tXr56tW7cuaL76yNLoofpbYbZu3WonnniiValSxV5++WUrW7asZSriEoBsEG+z61jj0vAsj0kkHwEASEGHHXaYu2lQh/2jR4+2Jk2a2Lhx49zodwCQrTUf41GnTh03RdO5c2fbtGmTLVy40Nq3b+/mvffee66PQ3X2X1jtku7du7taLhoJukKFCpbJiEsAskG8NR9jVSfLYxLJRwAAUtQpp5ziJgDIZPn5/5uiLZMo6k9XNUUGDx7sBk/ZvXu3DRkyxM455xxr0KCBW2b16tV2/PHH21NPPWUdO3Z0hbwTTjjBduzYYc8884x77Q06oMJlXl6eZSLiEoBMF0tM8pZLhIMzNCaRfAQAAACQcTUf4/Hss8+6wp0KcxpR9Mwzz7QHHnjA/3cV/tQPrwp2smjRIjfqqBxwwAFBn7VixQpr3LhxYjcYAJBWNR+zPSaRfAQAAACQNAUBfWcVtkwiaRTRqVOnRvy7Cm6+gJLmscceG/QaAJA9MclbLlFqZmBMIvkIAAAAIGlUYIpWaEr1QhUAIHtikrccYpdrCaTReNQxvkb+qV69ug0cONC2bdtW6HuUsc3JyQmaLrrookRuJgAAAIAkN3GLNgEAkCoxibiUQjUflXj87bffbObMma5Nev/+/e2CCy4otPqoqGNNjezpqVSpUiI3EwAAAECS+ArMCgqiLwMAQCrEJG85pEDy8bvvvrMZM2bYZ599Zh06dHDzHnzwQTv55JPt7rvv9o/SE46SjfXq1UvUpgEAAABIEakw4AwAAKky4EwmSljyce7cua6ptZd4lG7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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "E_pent = simkit.closed_polyline(PENTAGON)\n", "energy_p, gradient_p, hessian_p = area_system(E_pent)\n", "z = PENTAGON.reshape(-1, 1)\n", "\n", "g = gradient_p(z).ravel()\n", "g_fd = simkit.gradient_cfd(energy_p, z, FD_H_GRAD)\n", "H = hessian_p(z)\n", "H_fd = simkit.hessian_cfd(energy_p, z, FD_H_HESS)\n", "H_rand = hessian_p(np.random.default_rng(SEED).standard_normal(z.shape))\n", "g_Hz = g - H @ z.ravel()\n", "print(f\"max |grad - fd| = {np.max(np.abs(g - g_fd)):.2e}\")\n", "print(f\"max |Hess - fd| = {np.max(np.abs(H - H_fd)):.2e}\")\n", "print(f\"max |H(z) - H(rand)| = {np.max(np.abs(H - H_rand)):.2e}\")\n", "print(f\"max |grad - H z| = {np.max(np.abs(g_Hz)):.2e}\")\n", "\n", "fig, axes = plt.subplots(2, 3, figsize=(13, 7.5), layout=\"constrained\")\n", "idx = np.arange(len(g))\n", "ax = axes[0, 0]\n", "ax.bar(idx - 0.2, g, width=0.4, color=POS_C, label=\"analytic\")\n", "ax.bar(idx + 0.2, g_fd, width=0.4, color=NEG_C, alpha=0.7, label=\"finite diff\")\n", "ax.set_title(r\"gradient $\\nabla A$\")\n", "ax.set_xlabel(\"local dof [x0, y0, x1, y1, ...]\")\n", "ax.legend(fontsize=8)\n", "ax = axes[1, 0]\n", "ax.bar(idx, g - g_fd, color=EDGE_C)\n", "ax.set_title(f\"gradient - finite diff (max {np.max(np.abs(g - g_fd)):.1e})\", pad=14)\n", "ax.set_xlabel(\"local dof\")\n", "ax = axes[1, 1]\n", "ax.bar(idx - 0.2, g, width=0.4, color=POS_C, label=r\"$\\nabla A$\")\n", "ax.bar(idx + 0.2, H @ z.ravel(), width=0.4, color=EDGE_C, alpha=0.7, label=\"$Hx$\")\n", "ax.set_title(f\"$\\\\nabla A$ vs $Hx$ (max diff {np.max(np.abs(g_Hz)):.1e})\", pad=14)\n", "ax.set_xlabel(\"local dof\")\n", "ax.legend(fontsize=8)\n", "vH = np.max(np.abs(H))\n", "for ax, M, title in [(axes[0, 1], H, \"analytic Hessian\"), (axes[0, 2], H_fd, \"finite-diff Hessian\")]:\n", " im = ax.imshow(M, cmap=\"coolwarm\", vmin=-vH, vmax=vH)\n", " ax.set_title(title)\n", " fig.colorbar(im, ax=ax, shrink=0.8)\n", "R = H - H_fd\n", "vR = np.max(np.abs(R))\n", "im = axes[1, 2].imshow(R, cmap=\"coolwarm\", vmin=-vR, vmax=vR)\n", "axes[1, 2].set_title(f\"Hessian - finite diff (max {vR:.1e})\", pad=14)\n", "fig.colorbar(im, ax=axes[1, 2], shrink=0.8)\n", "fig.suptitle(\"simkit.outline_areas derivatives match finite differences\")\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"derivative_checks.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"013_derivative_checks.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "bc46d6e1", "metadata": {}, "source": [ "All residuals are at the $10^{-10}$ level of finite-difference roundoff, and $\\nabla A - Hx$ vanishes to\n", "machine precision: the analytic gradient and constant Hessian are exact." ] } ], "metadata": { "kernelspec": { "display_name": "simkit", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }