{ "cells": [ { "cell_type": "markdown", "id": "2d369eab", "metadata": {}, "source": [ "# iLQR compared with gradient descent\n", "\n", "A finite-horizon control problem can also be solved by treating the input sequence $u_{0:T-1}$ as free parameters and minimising the rolled-out cost $J(u)$ with a first-order optimiser such as Adam. This is the *shooting* or *backpropagation-through-time* approach.\n", "\n", "This notebook compares that approach with iLQR on the same pendulum swing-up as the [previous example](simple_pendulum.ipynb). iLQR uses the problem's temporal structure: its Riccati backward pass is a Newton-like step computed in $O(T)$. It typically needs far fewer iterations than gradient descent and reaches a better optimum." ] }, { "cell_type": "code", "execution_count": 1, "id": "b97af309", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:40:59.183069Z", "iopub.status.busy": "2026-10-14T22:40:59.182766Z", "iopub.status.idle": "2026-10-14T22:40:59.888546Z", "shell.execute_reply": "2026-10-14T22:40:59.887808Z" } }, "outputs": [], "source": [ "import time as timer\n", "\n", "import jax\n", "import jax.numpy as jnp\n", "import jax.random as jr\n", "import matplotlib.pyplot as plt\n", "import optax\n", "\n", "from diffilqrax.ilqr import ilqr_solver, ilqr_simulate\n", "from diffilqrax.typs import System, ModelDims, iLQRParams, PendulumParams\n", "\n", "jax.config.update(\"jax_enable_x64\", True)" ] }, { "cell_type": "markdown", "id": "cf077ba3", "metadata": {}, "source": [ "## The problem\n", "\n", "The pendulum swing-up from the previous notebook:" ] }, { "cell_type": "code", "execution_count": 2, "id": "e4e00a2b", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:40:59.892407Z", "iopub.status.busy": "2026-10-14T22:40:59.892076Z", "iopub.status.idle": "2026-10-14T22:41:00.231868Z", "shell.execute_reply": "2026-10-14T22:41:00.231274Z" } }, "outputs": [], "source": [ "DT, DAMPING, U_MAX, HORIZON = 0.05, 0.1, 3.0, 100\n", "dims = ModelDims(n=2, m=1, horizon=HORIZON, dt=DT)\n", "\n", "\n", "def dynamics(t, x, u, theta):\n", " \"\"\"Euler step; x = [angle, angular velocity], angle 0 is hanging down\"\"\"\n", " acc = -theta.g / theta.l * jnp.sin(x[0]) - DAMPING * x[1] + u[0] / (theta.m * theta.l**2)\n", " return x + DT * jnp.stack([x[1], acc])\n", "\n", "\n", "def cost(t, x, u, theta):\n", " \"\"\"Small running cost on angle, velocity and torque, plus a smooth barrier at |u| = U_MAX\"\"\"\n", " barrier = jax.nn.softplus(5.0 * (u - U_MAX)) ** 2 + jax.nn.softplus(5.0 * (-u - U_MAX)) ** 2\n", " return 0.1 * (1.0 + jnp.cos(x[0])) + 0.01 * x[1] ** 2 + 0.01 * jnp.sum(u**2) + jnp.sum(barrier)\n", "\n", "\n", "def costf(x, theta):\n", " \"\"\"Be upright (angle ±pi) and still at the final time\"\"\"\n", " return 50.0 * (1.0 + jnp.cos(x[0])) + 5.0 * x[1] ** 2\n", "\n", "\n", "model = System(cost, costf, dynamics, dims)\n", "params = iLQRParams(x0=jnp.array([0.1, 0.0]), theta=PendulumParams(m=1.0, l=1.0, g=9.8))\n", "Us_init = 0.5 * jr.normal(jr.PRNGKey(0), (HORIZON, 1))\n", "time = jnp.arange(HORIZON + 1) * DT" ] }, { "cell_type": "markdown", "id": "e689ea07", "metadata": {}, "source": [ "## iLQR\n", "\n", "We compile the solver once with `jax.jit` and then time a second call." ] }, { "cell_type": "code", "execution_count": 3, "id": "87bd8e8d", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:00.235116Z", "iopub.status.busy": "2026-10-14T22:41:00.234882Z", "iopub.status.idle": "2026-10-14T22:41:01.849255Z", "shell.execute_reply": "2026-10-14T22:41:01.848365Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iLQR: J = 17.8970 in 184 iterations, 169 ms\n" ] } ], "source": [ "solve = jax.jit(lambda p, u: ilqr_solver(model, p, u, max_iter=300))\n", "jax.block_until_ready(solve(params, Us_init)) # compile\n", "\n", "start = timer.perf_counter()\n", "(Xs_ilqr, Us_ilqr, _), J_ilqr, cost_log = jax.block_until_ready(solve(params, Us_init))\n", "t_ilqr = timer.perf_counter() - start\n", "iters_ilqr = int(jnp.sum(jnp.diff(cost_log) != 0)) + 1\n", "print(f\"iLQR: J = {float(J_ilqr):.4f} in {iters_ilqr} iterations, {t_ilqr*1e3:.0f} ms\")" ] }, { "cell_type": "markdown", "id": "3ed85d7e", "metadata": {}, "source": [ "## Gradient descent (Adam)\n", "\n", "`ilqr_simulate` rolls out the dynamics and returns the total cost. It is differentiable with respect to `Us`, so `jax.value_and_grad` gives $\\nabla_u J$ by backpropagation through time." ] }, { "cell_type": "code", "execution_count": 4, "id": "ad07486a", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:01.852840Z", "iopub.status.busy": "2026-10-14T22:41:01.852557Z", "iopub.status.idle": "2026-10-14T22:41:06.387807Z", "shell.execute_reply": "2026-10-14T22:41:06.386600Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Adam: J = 20.4651 after 5000 steps, 1943 ms\n" ] } ], "source": [ "def loss(Us):\n", " return ilqr_simulate(model, Us, params)[1]\n", "\n", "\n", "optimiser = optax.adam(learning_rate=0.05)\n", "\n", "\n", "@jax.jit\n", "def adam_step(carry, _):\n", " Us, state = carry\n", " J, g = jax.value_and_grad(loss)(Us)\n", " updates, state = optimiser.update(g, state)\n", " return (optax.apply_updates(Us, updates), state), J\n", "\n", "\n", "n_steps = 5000\n", "run = jax.jit(lambda u: jax.lax.scan(adam_step, (u, optimiser.init(u)), None, length=n_steps))\n", "jax.block_until_ready(run(Us_init)) # compile\n", "\n", "start = timer.perf_counter()\n", "(Us_gd, _), gd_log = jax.block_until_ready(run(Us_init))\n", "t_gd = timer.perf_counter() - start\n", "(Xs_gd, _), J_gd = ilqr_simulate(model, Us_gd, params)\n", "print(f\"Adam: J = {float(J_gd):.4f} after {n_steps} steps, {t_gd*1e3:.0f} ms\")" ] }, { "cell_type": "markdown", "id": "9177fad4", "metadata": {}, "source": [ "## Comparison" ] }, { "cell_type": "code", "execution_count": 5, "id": "248d085e", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:06.391111Z", "iopub.status.busy": "2026-10-14T22:41:06.390846Z", "iopub.status.idle": "2026-10-14T22:41:08.702524Z", "shell.execute_reply": "2026-10-14T22:41:08.701989Z" }, "tags": [ "thumbnail" ] }, "outputs": [ { "data": { "image/png": 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z5YOX0ad5uCtCFw2Mpye7+vXrx6233sqTTz6JxWIhNjaWb775hoEDB9K3b1+6du3K7NmznftfdtlllJeXn7eN0WazERISwhdffMG//vUvwJHseumll3jttdcA2LhxI3369GH+/Pncd999AHz11Vfce++9zpXMzsUbkl0mk4mTJ09SUFDAt99+y8cff8xff/1Fu/N8yThXZVdCQoJHPFchhFCSJ703XIraPk+71cqRa4ZiTkkBwK9LF0LvuIOga4ejUntfdVFBqZmr3v2LzCIjD13RjBeGt1U6JKclO1MZ98UO1Cr46qE+9GoapnRIQngtaWMUilOpVPg0b45P8+ZEPPQglqwsilatomjFCko3bMR88iQ5H88nZ8EnBA4eTNjdY4jp3p1pN3asMtz+2aGtmf77/ioJMBXQOFyquoTrqPz8aL19m2Lnrq4DBw6wefNmfvjhBwC0Wi2jRo1i/vz5DBw4kH379vHII49UeUyfPn1YtWqV8+eMjAxeeuklVq9eTWZmJlarldLSUk5WLE5RqVOnTs7/H13RktyxY8cq28rLyyksLPTqLyV6vZ4WLVoA0L17d7Zs2cJ7773Hhx9+eM79fXx88PHxqc8QhRBCNARqNXHT3yTv8y8oXLaMsqQkypKSKPjhB+Kmv4n2H2MLPN2UJXvILDLSLDKACVe1UjqcKv7VKY7VB7L4dlsKTy1OYumTl7tslUbj4cPkf/udY3zMyZNYMjLQhIeja9QIXXwjAgcOxDBgACqdrBIpGjZJdol6o42MJPTWWwm99VZsJSUUr11H/jffULJ+PUXLllG0bBm+7dsz9O4xXD5hICcKzc55XiH+OmcCDMAOLN2VzgOXN1P2SQmvpVKpUNWgukop8+fPx2KxVBlIb7fb8fHx4YMPPqjWMe6++25ycnJ47733aNy4MT4+PvTp0weTyVRlP90ZH5oqW5DPtc1ms9X6+Xgim81WpXJLCCGEqA8qlQr/7t3x796d6Kws8r7+mpx5H1Pyv/9x9IaRxE2fjqF/P6XDrBMr9mXw/fZTqFXw9s2d63VGV3W9OqI9W47nciKnlJd/3M37t3et0+NbCwrI+mA2eV98AVZrlftspaWYkx1zzAq+/Q5NeDjBI0YQdvcYdDExdRqHEJ5Ckl1CEeqAAIKGXkPQ0GswHjpE7qL/UvDTT5Tv2UPqs8+hjYyk9UMPEXr7bUDVgfbrD2fxwaojvP7rPvRaNS2iDLJCo2iQLBYLn332Ge+88w5XX311lftuuOEGvvzyS9q2bcumTZsYM2aM876NGzdW2Xf9+vX85z//cc6dSk5OJju76rw94TBp0iSGDRtGYmIiRUVFfPHFF6xevZo//vhD6dCEEEI0YNrISCLHjiVo6FBOPTUB48GDJD/wADGv/R+ht9yidHiX7MO/jgJwf/+mdG8cqnA052bw0TJzVBdumvM/fv47lYnXtCYhrG4unBavWUPqs89hzc93nGvQIAxXXIG+cSLa6BisuTmYU1Mp37efgiW/YM3KJveTT8j/+muiJk4k5NZbvLK1VYgLkWSXUJxPy5bE/t8UIp8aT/7ir8n7/HMsWVlkvPEG+d98Q/RLLxLQqxexwX7EBvtxWbMwio1WFv7vOJN/2gPICo2iYVqyZAl5eXncf//9BAcHV7nvpptuYv78+TzzzDPcc8899OjRg379+vH555+zZ88emjU7XRXZsmVLFi1aRI8ePSgsLGTixIn41aCVsiHJzMxkzJgxpKWlERwcTKdOnfjjjz+46qqrlA5NCCGEwKd5c5p8vZiMN6aS/803pL86BW1EBIFXXql0aLVmtdnZnepYrX1UzwSFo7mwromhdIoPISk5ny3Hc+sk2VV+4AAp45/CXlqKT8uWRL8wiYB/rgLdrCkAwSNGEDXhKYrXriPnww8p+/tv0l99lcKlS4mdOhV9fKNLjkcITyHpXeE2tKGhRDzyMC1WLCfm1VfQBAdjPHiQk2Pu5tSECZjT0wFHyfYDlzet8libHV74fjdpBecfjC2Et5k/fz5Dhgw5K9EFjmTX1q1badu2LS+//DLPPvss3bt358SJEzz66KNnHScvL49u3bpx11138cQTTxAVFVVfT8OjzJ8/n+PHj2M0GsnMzGT58uWS6BJCCOFW1L6+xPzfFIJHjgSrlVMTnqZs506lw6q1Y9kllJqs+Ok0NI0wKB3ORVUOp99yPO+Sj2XJySHl0cewl5YS0LcPTb//7uxE1z+odDoCB11J4y8+J3rS86j8/CjdvJkTY+7CnJFxyTEJ4SlkNUYXaigryLiKNT+frPffJ++rxWCzofLzI+LRRwm/7142nMhn9LxNZz1GVmgUtXG+FQJF3fOG1RgvVUN6rkIIcSkayuulq56n3Wwm+bGxlKxdiyY0lCZfL0af4N6VUefyU9Ipnvwqie6NQ/nu0b5Kh3NRf+5J56FF22gRZWD5hAG1Po7dZOLEffdRtnUbusaJNF28GE1ISI2PY0pOJvnBhzAdP45Py5Y0/u8iNOe4UCqEp6jua6ZUdgm3pQkJIWbyZJp+9y1+3btjLysja8YMTt53P/GUo1b9Y3+ViiYR7j9QXAghhBBCCFdT6XTEz3wX3/btseblkTHtTaVDqpXdpxwtjB3iPCPh2aOJo7LrcGYxuSWmi+x9fpnvzqRs6zbUBgMJc+bUKtEFoE9IIOHjj9FGRmI8dIjkx8ZiKy+vdVxCeApJdgm359u2LY3/u4jYN6eh9vendPNmysfcxqudA6jMd6mAqTd2kCH1QgghhBBCVFAHBBD39tug0VC8ciWl27crHVKN7T5VCED7OM+oRgoL0NMiytFuufV4bq2OYUo5Re5//wtA3FvT8Wl2aSvQ6+MbkfDxPNSBgZRt20b6K69c0vGE8ASS7LqA5ORkBg4cSLt27ejUqRPffPON0iE1WCqVipAbbqDJt9/i07o11pwcek55jKeDHSvGtY0NkuH0QgghhBBC/INPs6aE3HgjAJn/fgdPmmJjt9vZUzGcvn0jz6jsAuhZUd219UTt5nZlf/ABmM0E9O1D4KBBdRKTb+vWxM/+ANRqCn76mdItW+rkuEK4K0l2XYBWq2XmzJns3buXP//8k/Hjx1NSUqJ0WA2aT7OmNFn8FSG33AJ2O+2++QiAQxlFlJutCkcnhBBCCCGE+4kYNxaVry9l27dTvGq10uFUW0peGYXlFvQaNS2jApUOp9p6NgkFYPOxmld2GQ8fpuDnnwGIHD++LsMioFcvx/coIH3qNOxW+f4kvJckuy4gNjaWLl26ABATE0NERAS5ubUrRRV1R+3rS+xr/0fc228RSzkh5UWYbXZ2HjildGhCCCGEEEK4HV10NGF33QVA1rszPCbJUTmvq1WMAb3Wc766VlZ27T5VQKnJUqPHZr33PthsBF41BL9Oneo8tsgnn0AdFIRx3z7yv/2uzo8vhLvwnFeMWlizZg3XXXcdcXFxqFQqfvzxx7P2mT17Nk2aNMHX15fevXuzefPmcx5r27ZtWK1WEjxwBRNvFXzddTT5dCFti1MBWDl9DubUVIWjEkIIIYQQDcm0adPo2bMngYGBREVFccMNN3DgwAGlwzpL+IMPoA4OxnjoMAW//KJ0ONWyO7VyOL1nzOuqFB/qR0yQLxabnaTk/Go/rmzXLoqWLQO1msgnn3RJbNqwMCLHjQUga+ZMrAUFLjmPEErz6mRXSUkJnTt3Zvbs2ee8f/HixUyYMIFXXnmF7du307lzZ6655hoyMzOr7Jebm8uYMWP46KOP6iNsUQN+HTvSd3h/AHYTyPHbR2M8fFjhqIQQQgghREPx119/MXbsWDZu3MiyZcswm81cffXVbjf+RBMURPj99wOQ99/PFY6mevakVgynb+RZyS6VSkXPpo7qri3Hqj+3K/sDx/fW4BEj8GnRwiWxAYTefjv6Fs2x5uWR/Z//uOw8QijJq5Ndw4YN4/XXX2fkyJHnvH/GjBk8+OCD3HvvvbRr1465c+fi7+/PggULnPsYjUZuuOEGnn/+efr27XvB8xmNRgoLC6vchOv17NIcgP1RzbFkZHDijjspP3hQ4aiEEEIIIURD8Pvvv3PPPffQvn17OnfuzMKFCzl58iTbtm1TOrSzhNxyMyqdjvLduynbs0fpcC7Ibrc72xg7xHnOcPpKlXO7tp6o3hgcU3IyxWvWABDxyMMuiwtApdMR/dxzAOR/8y220lKXnk8IJXh1sutCTCYT27ZtY8iQIc5tarWaIUOGsGHDBsDxAnvPPfcwaNAg7qrocb+QadOmERwc7LxJy2P96BQfjEatIltnoKhzL6wFBSTf/wCm5GSlQxNCCCGEEA1MQUVbWFhY2DnvV/ICuTY0lMCrrgIg/2v3Xmk+s8hIdrEJtQraxHhissvx+99+Ig+L1XbR/fMXLwa7nYD+/dE3aeLi6CCgf390CQnYSkspWrHC5ecTor412GRXdnY2VquV6OjoKtujo6NJT08HYP369SxevJgff/yRLl260KVLF3bt2nXeY06aNImCggLnLVmSLfXCX6+lTYxjdZaMp17Gp2VLLFlZnLzvfswZmRd5tBCebeDAgYyv45V6hBBCCFE7NpuN8ePH069fPzp06HDOfZS+QB4yahQAhb/8grXYvVotz1RZ1dUiyoCfXqNwNDXXOjqQAL2GEpOV4zkXrpyymUzkf/c9AKG331Yf4aFSqQgeMQKAgh9/qpdzClGfGmyyqzr69++PzWYjKSnJeevYseN59/fx8SEoKKjKTdSPbomOMuGkbBMJ8z9Gl5CAOTmZ5Afux5JX/T55ITzN999/z2uvvQZUL/G1ZMkSBgwYQGBgIP7+/vTs2ZOFCxdW2ef48eOoVCrnLSwsjAEDBrB27VoXPQshhBDCO4wdO5bdu3fz1VdfnXcfpS+Q+/fqib5JE2ylpRQu/bVez10TlfO6PG04fSW1WkWjUD8A0grKLrhv0R9/YM3LQxsTg2HAgPoID4Dg6x3JrpING6RIQHidBpvsioiIQKPRkJGRUWV7RkYGMTExCkUlaqtb4xAAdpzMQxcVReInC9BGRWE8dJiURx/DZjQqG6BoUNIKyvjfkeyLfrCpC2FhYQQGBlZr31mzZnH99dfTr18/Nm3axM6dO7ntttt45JFHeOaZZ87af/ny5aSlpbFmzRri4uL417/+ddZrphBCCCEcxo0bx5IlS1i1ahXx8fHn3U/pC+QqlYqQW28FIH/x1/V67pqorOzytOH0Z4oNrkh25ZdfcL+8L74EIHTUrai0WpfHVUmfmIhf165gs1G4ZEm9nVeI+tBgk116vZ7u3buz4oz+ZJvNxooVK+jTp4+CkYna6JrgqOzafaoQo8WKPj6exAXzUQcHU5aURNpLL2O32xWOUngSu91OqclS49uiDcfp9+ZKRs/bRL83V7Jow/EaH6Mmf6vVbWNMTk7m6aefZvz48UydOpV27drRokULnn76ad5++23eeecdNm3aVOUx4eHhxMTE0KFDB1544QUKCwvP2kcIIYRo6Ox2O+PGjeOHH35g5cqVNG3aVOmQLip45A2OQfV79lC22z0H1R/NdrRYto6u3kU9dxQb7AtA6gUugJYfOEDZjh2g1RJy8831FZpT8PXXA1Dw88/1fm4hXKn+0sYKKC4u5vDhw86fjx07RlJSEmFhYSQmJjJhwgTuvvtuevToQa9evZg5cyYlJSXce++9CkYtaqNxuD9hAXpyS0zsSS2kW2IoPi1aEP/eTE4+8CCFv/yCT/PmLl/ZRHiPMrOVdpP/uKRj2Ozw8k97ePmnmn2I3Pt/1+Cvr9uX52+//Raz2XzOCq6HH36YF154gS+//JLevXufdX9ZWRmfffYZ4LhQIIQQQojTxo4dyxdffMFPP/1EYGCgc/5vcHAwfn5+Ckd3btrQUAKvvprCX3+l4Mcf8evQXumQzpJV5OjMiA7yUTiS2qus7EovOH9lV96XjqquwCFD0EZG1ktcZwoaNpSMN97AeOAA5fv349umTb3HIIQreHVl19atW+natStdu3YFYMKECXTt2pXJkycDMGrUKP79738zefJkunTpQlJSEr///vtZQ+uF+1OpVHRLDAEcK55UCrjsMmJeegmArJkzKfzzTyXCE0JxBw8eJDg4mNjY2LPu0+v1NGvWjIMHD1bZ3rdvXwwGAwEBAfz73/+me/fuDB48uL5CFkIIITzCnDlzKCgoYODAgcTGxjpvixcvVjq0CwoaNhSAknXrFI7kbOVmKwVlZgCiAn0Vjqb2YkMqK7vOneyyGY0U/roUgNDbRtVbXGfSBAdjuPJKAAp+kuou4T28urJr4MCBF20HGjduHOPGjauniIQrdU0MZfm+TJbty+DaTrHOKymht43CeOQIeYsWkfrsc+gbN8G3dSuFoxXuzk+nYe//XVOjx6QXlDNkxl/YznjZUatg+YQBxARX/4Oan06ZFYf+WbW1ePFi2rRpw+7du3n22WdZuHAhOp1OkdiEEEIId+WpozL8e/cGjQbT8eOYU1PRxcUpHZJTZVWXXqsmyM9zv7LGOWd2nbuNsfivv7AVFaGNicG/V6/6DK2K4OtHUPTnnxT+9htRz05EpVIpFosQdcWrK7tEw5JfagJg09Fc+r25ksVbTjrvi37uWQL69cNeXs6p8ePdepll4R5UKhX+em2Nbs0iDUy7sSOaig8IGpWKaTd2pFmkoUbHccUHjJYtW1JQUEBqaupZ95lMJo4cOUKrVlWTwAkJCbRs2ZKRI0cydepURo4ciVEWexBCCCG8giYwEL+KleZL/vc/haOpKrMi2RUV6OPRiZfKi53na2MsXOJYDTPo2uGo1Mp9NQ/o1w+VXo8lPR3TsWOKxSFEXZJkl/AKaQVlzF93+oXZZocXvt/tXA1PpdUS9++30cbEYDp2jPTJkz32Kpxwb6N6JrLu+Sv58sHLWPf8lYzqmah0SADcfPPNaLVa3nnnnbPumzt3LqWlpYwZM+aij//Pf/7jyjCFEEIIUY8C+joW5nK3ZFdWkSM5FBXoufO6AOIq2hiLjBaKys1V7rMWFVG8ejUAwdddV9+hVaH29cW/R3cASta719+CELUlyS7hFY5ll1RpHQOw2u0czy51/qwNDaXRjBmg1VK4dCn5X31Vz1GKhiI22I8+zcOdrbT1KSsri6SkpCq3jIwMEhMTeeutt5g5cyYvvvgi+/fv58iRI8yYMYNnn32W119/nQ4dOpz3uCqViieeeII333yT0tLS8+4nhBBCCM8R0LcvACUbNmK32RSO5rTKyq5ID092+eu1BPs5RkCk/aO6q+jPP7GbTPi0bIFP69ZKhFeFf5+KxOeGDQpHIkTdkGSX8ApNIwJQ/6PCWaNS0STCv8o2/25diXr6aQAypk5z26WWhaitL774wrkwR+Vt3rx5ADz11FN8//33rF27lh49etCiRQuefvppFi5cyAsvvHDRY999992YzWY++OADVz8NIYQQQtQDv86dUfv7Y83Lw7h/v9LhOGU52xg9dzh9pdiKVsbUf8ztKvhlCQBB/7rOLVo1KxOfpZs2YTebL7K3EO5Pkl3CK8QG+zHtxo5Uvk2ogKk3djhnZU3YPXdjGDwYu9nsmN9VWFivsQpRl1avXs3MmTOd/99ut591e6liRVKA66+/njVr1lBcXExOTg5dunRhzpw5Vaq1mjRpgt1up0uXLlXO5e/vT25uLs8++2x9PDUhhBBCuJhKp3MORnenVsbMwtMzuzxd7DnmdpkzMijdtAmAoGuvVSSuf/Jt2xZNcDC2khLKdu1WOhwhLpkku1xg9uzZtGvXjp49eyodSoMyqmciE652DNju3zLivLOSVCoVcVPfQBcfjzklhdQXXpD5XaJBCgsLY/ny5QwePJgNUrIuhBBCNEjOVkZ3SnZVzuwK8oJkV4jj4nvqGcmuwqW/gd2OX7du6OMbKRVaFSq1+nQroxv9LQhRW5LscoGxY8eyd+9etmzZonQoDU6XhBDg7J74f9IEB9Po3XdR6XQUL19B7qef1kN0Qrif8PBwJk+ezODBg5UORQghhBAKCOhX0b62dRu28gt/hq4vmV7UxhhXUdmVdkYbY+ESRwtj8HX/UiSm83EuWCAXQYUXkGSX8CpNIwIAOJFTgvWfE+v/wa9jB6ImPQ9A5r/foWzXLpfHJ4QQQgghhDvRN2uGNioKu8lE6bZtSocDeM+AeoCYirEq6YWORKL51CnK9+wBtZrAa65RMrSzVFb5lf39N9biEoWjEeLSSLJLeJW4YD/0WjVmq51TeWUX3T/09tsJHDoULBZSn5mIrURe1IUQQgghRMOhUqncqpXRarOTU+w9M7vi/jGgvmjFCgD8u3VDGxamWFznoo+PR5eYCBYLpVs2Kx2OEJdEkl3Cq6jVKpqGO6q7jmYXX3R/lUpF7JRX0cbEYDpxgvRp01wdonBjNjdacttbyb+xEEII4X78e/cGoCzpb4UjgZwSIzY7qFUQbvD8ZFflzK60gnLsdjtFy5YDEHjVECXDOq+APtLKKLyDVukAhKhrTSMCOJBRxLHsEga2vvj+muBg4qZP5+Q991Dw7XcYLr+CoGuudn2gwm3o9XrUajWpqalERkai1+vdYglob2K32zGZTGRlZaFWq9Hr9UqHVCvTpk3j+++/Z//+/fj5+dG3b1+mT59O69bVeLERQggh3JRf504AlO/Zg91iQaVV7mti5UqM4QYfNGrP/zwWE+So7Co1WclNy3K2igYOcdNkV9++5C9e7BZVfkJcCkl2Ca/TNNJR2XUsu/otiQG9exH+wAPkzJtH2uTJ+HXuhC4mxlUhCjejVqtp2rQpaWlppKamKh2OV/P39ycxMRG12jMLi//66y/Gjh1Lz549sVgsvPDCC1x99dXs3buXgIAApcMTQgghakXfpAlqgwFbcTHGw4fxbdNGsViyirynhRHAT68h1F9HXqmZo8vXYrDZ8G3XDl0j91iF8Z/8e/UEwHT4CNaiIjSBgQpHJETtSLJLeJ3KIfVHs2o2fyvy8XGU/O9/lO/ZQ+rzk0hcMB+Vh34hFzWn1+tJTEzEYrFgtVqVDscraTQatFqtR1fN/f7771V+XrhwIVFRUWzbto0rrrhCoaiEEEKIS6NSq/Ht2IHSDRsp27lT0WRXZpFjkLs3DKevFBvsR16pmWOb/qYj7tvCCKANDUXXqFHFIP29BFzWW+mQhKgVSXYJr9MsouaVXQAqvZ64f7/NsRtvonTjRnI/+YTw++93RYjCTalUKnQ6HTqdTulQhIcoKCgAIOwCA2aNRiNGo9H5c2FhocvjEkIIIWrKr0NHSjdspHzXLrj1VsXiqGxj9JbKLoDYYF/2phWSfDzVkexy0xbGSr7t2ztXjZRkl/BUUrYivE5lZdep/DLKzTWr0PFp2pToFyYBkDnzPcr376/z+IQQ3sFmszF+/Hj69etHhw4dzrvftGnTCA4Odt4SEhLqMUohhBCienw7dQSgbOcuRePIcq7E6KtoHHUpNsTxXLL1BvSNG6Nv0ULhiC7Mt+JzTfme3QpHIkTtSbJLeJ2wAD1Bvo6ixeM5NavuAgi5+WYMQwaD2UzqCy9gN5vrOkQhhBcYO3Ysu3fv5quvvrrgfpMmTaKgoMB5S05OrqcIhRBCiOrz6+QYUm88fBhbaalicTgru4K8qbLLsSJjll8IgVcNcfuRDn4d2gNQtnuPwpEIUXuS7BJeR6VS0TTSAMCxGs7tqnx87CuvoA4Oxrh3HznzF9R1iEIIDzdu3DiWLFnCqlWriI+Pv+C+Pj4+BAUFVbkJIYQQ7kYXHY02KgqsVsr37VMsjsqZXV7VxmhwjMjI8gtx+xZGAN927QAwnzyJtWJkgxCeRpJdwitVzu06WsO5XZW0kZHEVLQzZs+ejfHQoTqLTQjhuex2O+PGjeOHH35g5cqVNG3aVOmQhBBCiDrjDq2MmRWrMXrTgPrQTEdVd3ZAGL4VFXTuTBMSgq5i7EL53r0KRyNE7UiyS3ilprUcUn+moBEjMAwYgN1sJvXFl7DLCn1CNHhjx47lv//9L1988QWBgYGkp6eTnp5OWVmZ0qEJIYQQl8yvoyMRU75rpyLnt9vtzmSXN83sCt69DYBsvxBw8xbGSr7OVkaZ2yU8kyS7hFeqi2SXSqUi5v+moDYYKN+5k9yFn9ZVeEIIDzVnzhwKCgoYOHAgsbGxztvixYuVDk0IIYS4ZH4dHYPJlarsKiy3YLLYAO+q7PL/318AGFUa8ks9Yx6wX3tHsqt8j1R2Cc8kyS4XmD17Nu3ataNnz55Kh9Jg1UWyCxyzC6Kffw6ArPffx3js2CXHJoTwXHa7/Zy3e+65R+nQhBBCiEtWuQqfOSUFS25uvZ8/q2JeV5CvFl+dpt7P7wrm9HTsB/YRbCwGILXAM6rBnSsySmWX8FCS7HKBsWPHsnfvXrZs2aJ0KA1WZbIrt8REfqnpko4VfNNNBPTrh91oJP3VKdjt9roIUQghhBBCCLeiCQpCXzGPUokkx+mVGL2nhbF47VoAonA8t8rn6O6cQ+pTUrDm5ysbjBC1IMku4ZUCfLREVyxXfKnVXSqVipgpU1D5+FC6aRNFfy6rixCFEEIIIYRwO34KDql3Dqc3eE8LY8maNQBEB/sBkF5YrmQ41aYJCkLXOBGAsj17FI5GiJqTZJfwWnXVygigj29E+AMPAJAx/U1sMoxaCCGEEEJ4Id8OjmSXIpVdFW2MUUHekeyym0yU/G8DAHHxUQCkF3hGsgvAr31lK6Mku4TnkWSX8FpNIwwArD2URVod9MaHP3A/2rhYLKlp5MxfcMnHE0IIIYQQwt34tGwJgPHY0Xo/t7ON0UuG05fuSMJWUoImLIxGjWMAyPCQyi4AX+eQekl2Cc8jyS7htQrLHCud/LAjlX5vrmTxlpOXdDy1nx/Rzz4LQM6CBVhyci45RiGEEEIIIdyJvpljZpc5OQWb6dJm39ZUVnFlsss7ZnaVrHW0MBou709MiGe1McLpIfVlu5VZnVOISyHJLuGV0grKWLo7zfmzzQ4vfL/7kiu8Aq+5Bt8OHbCXlpL94YeXGqYQQgghhBBuRRsZidpgAJsN84kT9Xru0wPqvaOyq/gvR7Ir4PIriK4Yuu9JbYy+7doCYElNw1pYqHA0QtSMJLuEVzqWXcI/F0202u0czy69pOOqVCoinxoPQP6XX2E+deqSjieEEEIIIYQ7UalUzhUZjUeP1eu5K2d2ecOAekt2NsZDhwAI6NfXmeyqHMLvCTSBgWhjHO2XxsNHFI5GiJqRZJfwSk0jAlCrqm7TqFQ0ifC/5GMH9O2Lf+/e2M1msudKdZcQQgghhPAuPhWtjKZj9Zvsyi52tE1GesHMrtLNmwHwadMGbWgoMRXJrtwSE0aLVcnQasSnRQsAjIcPKRyJEDUjyS7hlWKD/Zh8XTvnz2oVTL2xA7EVS/5eCpVKReSTTwCQ/+OPmDMyLvmYQgghhBBCuAt902YAmOpxSL3RYqWgYuauNyS7SjY5kl0BvXsBEOKvQ691fP2ubNf0BKeTXYcVjkSImpFkl/Bad/dpgqaiuuuHx/oyqmdinR3bv1s3/Hp0B7OZ3E8W1tlxhRBCCCGEUFrlkPr6bGPMqajq0mlUBPvp6u28rlJZ2eXfuzfguGBeWd3lSUPqfVo6kl0mSXYJDyPJLuG1VCoVoQF6APRaTZ0fP+KhhwDI+/prLHl5dX58IYQQQgghlODTrKKy6+hR7P8chOsiWRWzrCIMPqhUqovs7d7MGZmOFlCVCv/u3Z3bYzxwSL2zsuuQJLuEZ5Fkl/BqlVeF8krrftnkgMsvx6dtW+ylpeQvXlznxxdCCCGEEEIJusREUKuxlZRgycyql3NmF59Odnm6yqou37Zt0QQHO7dXrjKZ4UGVXfrmzQGwZGVhLShQOBohqk+SXcKrhfo7KrvyS811fmyVSkX4PXcDkPfVYuwWS52fQwghhBBCiPqm1uvRJcQD9Tek/nRll75ezudKpZs3AadbGCtVVnZ5UrJLYzCgjY0FZG6X8CyS7BJeLcTfUdnlimQXQOCwYWjCw7Gkp1O0fIVLziGEEEIIIUR986nnIfWVlV1eMZzeOa+rV5XtMcGVM7s8Z0A9nDmk/ojCkQhRfVqlAxDClUIqKrtc0cYIjqteIbfeQs6cueT9978EDb3GJecRQgghlGa3WjEdPUrZnj0Y9+3Dbreji45GGxWNX+dO6BPrbiEYIYTy9M2awerV9Tak/syZXZ7MnJ6O+cRJUKurzOsCiK6s7PKgmV3gSHaVrF0rlV3Co0iyS3i10IrKrspljF1yjlGjyPloHqVbt2I8dAifli1ddi4hhBCivlmLS8j78gtyF36KNSfnvPsFXHE5YXfdRUC/fqjU0jwghKfzqViR0XS0viq7HBenPb2yq3STo4XRt317NIGBVe47XdnleckuAOPhQwpHIkT1SbLLBWbPns3s2bOxWq1Kh9LgOSu7SlxT2QWgi4khcNCVFC1bTv633xE96XmXnUsIIYSoL3azmZz5C8j55BNsFUOJVf7++LZti2/7dqh9fDCnZ2BOSaEsKYmSNWspWbMW33btaDTjHfRNmij7BIQQl0Tf1JHsMtZTG2OWlwyoL9nkaGEM+EcLI0B04Olkl91u95hVJ31aVia7pLJLeA5JdrnA2LFjGTt2LIWFhQSfsfqGqH/OmV0urOwCCL7pJoqWLafg55+JenoCKr3nD9YUQgjhOuVmK9tP5LHhaA47UwrQadQE+WoJ9tcxoFUkl7eMRKNW7kuQOT2dU09NoGzHDsDxpTfikYcJuvZaVNqzPz6aTp4k7/MvyP/uO8r37uXYTTcTO3UqQddcXd+hC1Hv1qxZw9tvv822bdtIS0vjhx9+4IYbblA6rEumb+aY2WVJTcNWVobaz8+l58v2kjbGUue8rt5n3Ve5GqPJYiO/1ExogGd8Z/CpWJHRmpWNNT8fTUiIsgEJUQ2S7BJeLcSvcjVG11V2ARj690cbGYklK4uilatkdpcQQohzyisx8cGqw/x34wmMFts59/lk/XEahfhxS4947u7TpN6/DBWvW0/qxIlY8/JQGwzEvPwSQf/6FyqN5ryP0ScmEj3pecLuu5dTE56mbNs2Tj35JGX33UfUxGc8pnpBiNooKSmhc+fO3Hfffdx4441Kh1NntKGhaEJCsObnYzp+HN+2bV16viwvGFBvycnBnJICKhV+Xbuddb+vTkOov468UjMZReUek+xSBwSgi4vDnJqK8fBh/Hv0UDokIS5Kkl3Cq1XO7Mpz0WqMlVRaLcEjR5Lz0Ufkf/+dJLuEEEJUYbRYWbDuOP9ZfZiicgsAUYE+9GkeTo8mYWhUKorKzZzMLWXJzjRO5Zcxc/khvtqczKzRXenZJKxe4iz45RdSn3sebDZ82rUlfubMGg2e10VH0/jThWTNnEnOx/PJXbAAlU5H1FPjXRe0EAobNmwYw4YNq/b+RqMRo/H0anyFhYWuCKtO6Js1o2z7doxHj7o02VVutjpfGyM9uLKrfP9+APSNG6MxBJxzn+ggX/JKzaQXlNMmJqg+w7sk+pYtJNklPIoku4RXC65sY3Rxsgsg5EZHsqtk/f+w5OaiDaufLyZCCCHcW2ZhOQ//dxs7TuYD0DY2iOeHteGKlhHnrHh6+V/t+H13Ou+vOMTR7BJu+2gjT1/dikeuaI7aha2NBUt+dSa6gkeOJObVV1D71PxLp0qrJeqZZ9AlJpI++RVyPvwQbXgYYWPGuCBqITzPtGnTmDJlitJhVIu+WVPKtm/H5OIVGbMrqrr0GjVBfp77FdVYkezyadvmvPvEBPuyP72IDE8bUt+8BSV/rcF4SOZ2Cc8gS+UIrxbqf7qN0W63u/Rc+iZN8G3fHqxWiv74w6XnEkII4RmSkvO57oN17DiZT5Cvlndu6cyvj/dnQKvI87b2+eo03NC1Eb883p+RXRthtdl56/cDPP3N39hsrnkvK/ztN1KffRZsNkJuuZnYN16vVaLrTKG33krk+PEAZEydRsEvS+ogUiE836RJkygoKHDekpOTlQ7pvHwqhtSbXDykPss5r0vv0W3P5fscyS7fNuevgnMOqS8wnncfd3R6RUZJdgnPIMku4dUqk10Wm50Sk+tXxwwaPhyAwl+XuvxcQggh3Nvvu9O59cMNZBQaaRll4Odx/bmpe3y1q7MCfLTMuLUz02/qiFat4ocdp5j22746j7NkwwZOPTPRUdF1443ETJmCSl03HxHDH36I0LvuAiDthRcoP3CgTo4rhCfz8fEhKCioys1dOVdkPH7cpefJLnbM1/XkeV0A5fsdr9G+F6jsig4+vSKjJ5EVGYWnkWSX8Gq+OjV6rePPPK/EtUPqAYKGO+Y1lG7bhjk93eXnE0II4Z5WHcjk8S+3Y7LYGNI2mu8f60uTiHPPb7kQlUrFqJ6JvHVzJwDmrT3GvDV1V2FhSjnFqacmgNVK0LXXEvva/9VZogsc8UdPeh7DwIHYzWZSJz6LzeT692MhRN2onNlnPpns0i6JyjZGT16J0VZe7mz39Gl9gTbGIEeyy+PaGCtW57Tm5GDNz1c2GCGqQZJdwqupVCrnkPqCMtfP7dLFxuLXozvY7RT+9rvLzyeEEML9bDyawyOLtmG22vlXp1g+vKs7gb66Szrmjd3ieX6Y48vTG0v38cvfqZccp62sjJRx47Dm5+Pbvj2xb7x+wRUXa0ulVhP7+mtowsIwHjxI9vvv1/k5hBCuoUtIAJUKW3Ex1rw8l53ndBuj5ya7jIcOgc2GJiwMbVTkefeLCXY8R09LdqkDAtBGRQFgcuPWWyEqSbJLeL0QP0crY15p/VxJPt3K+Gu9nE8IIYT72JmSz/0Lt2C02BjcJop3R3VBU0dD5R++ohn39msCwAvf7+JUflmtj2W320l76WWM+/ejCQsj/oNZqH196yTOc9FGRBD72v8BkDN/AaVbtrjsXELUt+LiYpKSkkhKSgLg2LFjJCUlcfLkSWUDqwNqHx+0MTEAmE6ccNl5Kiu7PLmNsXxfRQtjmzYXnDsW7aGVXXC60s90wvP/toX3k2SX8Hoh9bgiI0DQ0KGg0VC+e7dLPxQIIYRwL1lFRh76bBslJit9m4cz+45u6DR12xL40rXt6JoYQpHRwnPf7qz1wPr8b75xXJTRaol/bya62Ng6i/N8AgcPJvimG8FuJ/X5SdjKap+sE8KdbN26la5du9K1a1cAJkyYQNeuXZk8ebLCkdUNfUICAGYXJu/OHFDvqaqzEiOcTnZlF5swWWwuj6su6RpXJLtOyncc4f4k2SW83pkrMtYHbVgYAX36AFC4VAbVC+Ft1qxZw3XXXUdcXBwqlYoff/xR6ZCEGzBbbYz9fDvpheU0jwzgw7u646ur+5ZAjVrFO7d0xlenZt3hbD7fVPMvHKbkZDLenA5A1FNP4d+zZ12HeV7Rk15AGxuL+dQpchcurLfzCuFKAwcOxG63n3Vb6CV/43pngsN1rWunK7tcV2HqatVZiREgzF+PTuOo/Mos8qzqLn1iYwDMUtklPIAku4TXq6zsyqunyi44o5VRkl1CeJ2SkhI6d+7M7NmzlQ5FuJE3ft3H5uO5GHy0fDSmxyXP6LqQZpEGnh/qqByYunQ/x7NLqv1Yu9VK6vOTsJeW4t+zJ2H33uOiKM9NYwgg6umnAcie9zHmzMx6Pb8QouZ0la1rUtl1Xnabzbna7IVWYgRQq1VEBXpmK+PpxKcku4T7k2SX8Hohzsqu+kt2BQ4ZDDodxkOHMR47Vm/nFUK43rBhw3j99dcZOXKk0qEIN/FT0ikW/u84AO+O6kLzSIPLzzmmTxP6NAunzGzlxR93VXuVtNyFCynbtg21vz+x06bV6cqL1RV07XB8O3fCXlpK9qxZ9X5+IUTNVFbzuLJ1LbvY0YER4aEzu8wnT2IvLUXl44O+SZOL7h8TXJnsMro4srqlr4fEpxB1RZJdNTBy5EhCQ0O5+eablQ5F1MDpmV31t9S5JiiIgF69AChesaLeziuEcD9Go5HCwsIqN+E9UvJKeemH3QA8MagFV7WLrpfzqtUq3rq5E3qNmvWHc/jrYNZFH2M8fJisme8BEP3iC+jjG7k6zHNSqVREP/c8APnffkd5xZwbIYR70idWzuxyTRtjmclKsdECeO6A+srXMZ9WrVBptRfdPzrIM1dkrKzys+bkYC0uVjgaIS5Mkl018OSTT/LZZ58pHYaoodDKZFdZ/VV2QUV1F1C0bHm9nlcI4V6mTZtGcHCw85ZQMehXeD6bzc7TX/9NkdFC98ahPDG4Zb2ePyHMn7v7Oioupi3dj/UCw+rtdjvpU/4Pu9mMYcAAgm+8sb7CPCf/bl0JHDYU7HYypk+vdmWaEKL+6RIqEhx5eVhdcMGmcl6XXqsm0OfiiSJ3dHpe14VbGCudbmP0rMoujcGAJjwccO3qnELUBUl21cDAgQMJDAxUOgxRQ8F+jjbGvHqs7AIwDHIku8r+/ltmkgjRgE2aNImCggLnLTnZdQN+Rf2av+4Ym47l4q/XMOPWzmjrcOXF6hp3ZUuC/XQcyCjiu+0p592v8OefKd2yBZWfHzGTX0alUtVjlOcW9fTTqHQ6SjdspGzrVqXDEUKch8YQgCYiAnDNkPqsyuH0Bh+3eG2qjfL9+4CLr8RYqbKNMdPDKrvgdCujK1fnFKIuuEWy69SpU9x5552Eh4fj5+dHx44d2VqHH3qqu3LW7NmzadKkCb6+vvTu3ZvNmzfXWQxCOZWVXQX1OLMLQBcdhW/nTgAUr1xZr+cWwpvt27ePV155hUGDBtG8eXNiY2Pp1KkTd999N1988QVGo3tdJfXx8SEoKKjKTXi+/emFvP2HYxjxy/9qR+PwAEXiCPbXMe7KFgDM+PMgZSbrWftYCwrImP4WABGPPYqukTLti/+kj493VphlfzRP4WiEEBfiTHAk132Cwzmc3kNbGAGM1VyJsZKzjdHDVmOEM+Z2yYqMws0pnuzKy8ujX79+6HQ6fvvtN/bu3cs777xDaGjoOfdfv349ZvPZSYu9e/eSkZFxzsdUZ+WsxYsXM2HCBF555RW2b99O586dueaaa8iUihyPFxqgTGUXQOCQIQAULZe5XUJcqu3btzNkyBC6du3KunXr6N27N+PHj+e1117jzjvvxG638+KLLxIXF8f06dPdLuklvIfVZufZb3distoY3CaK23oq25p6V5/GNArxI72wnAXrz14UJXPmTKy5uehbNCf87rsViPD8wh+4H9RqStaupXzvXqXDEUKch76iBd8VCY5sZ2WXZ67EaC0owFLxndGnVatqPSa6oo0xvcDzkl06WZFReAjFm6KnT59OQkICn3zyiXNb06ZNz7mvzWZj7NixtGzZkq+++gqNRgPAgQMHGDRoEBMmTODZZ58963HDhg1j2LBhF4xjxowZPPjgg9x7770AzJ07l19//ZUFCxbw/PPP1/bpCTcQ4ldR2VVmxmazo1bXX3l04OAhZL0zg5JNm7AWFaGRNlghau2mm25i4sSJfPvtt4SEhJx3vw0bNvDee+/xzjvv8MILL9R5HMXFxRw+fNj587Fjx0hKSiIsLIzEiqudwrt9tuE4O1MKCPTVMu3Gjoq33fjqNEy8pjXjFycxb+1R7u3XBH+94yNe2e495H+1GICYyZNR6d3ry6Q+IYGg4cMpXLKE7HnziH/3XaVDEkKcgysTHJWVXZ46nN6clgaAJjQUjaF6Vb5RQZVtjJ53Ya4+VucUoi4oXtn1888/06NHD2655RaioqLo2rUr8+adu5RdrVazdOlSduzYwZgxY7DZbBw5coRBgwZxww03nDPRVR0mk4lt27YxpKIKp/JcQ4YMYcOGDTU+3uzZs2nXrh09e/asVTyibgVXtDHa7FBUbqnXc/s0a4q+WTMwmyn+a029nlsIb3Pw4EEee+yxCya6APr06cNXX33FxIkTXRLH1q1b6dq1K127dgVgwoQJdO3alcmTJ7vkfMK9pOaX8e+K9sXnhrZxfmFR2nWd42gc7k9+qZnFWxwzdex2O5lvvgl2O0HXXedcJdjdhD/4IABFv/+B8djZlWlCCOW5MsFRWdkVYfDsZJcuNrbaj6lsYywyWigx1u/3k0ulr0h8mqWNUbg5xZNdR48eZc6cObRs2ZI//viDRx99lCeeeIJPP/30nPvHxcWxcuVK1q1bx+jRoxk0aBBDhgxhzpw5tY4hOzsbq9VKdHTV5cKjo6NJT093/jxkyBBuueUWli5dSnx8/HkTYWPHjmXv3r1s2bKl1jGJuuOj1eCvd1QBKtvKKKsyCnEpdDqdS/evroEDB2K328+6LVy40CXnE+7llZ/3UGKy0r1xKKN7uU8ln0at4sHLmwHw8dpjmK02ipYvp3TrVlS+vkRNeErhCM/Pt3UrDAMHgt1Ozvz5SocjhDgHZ4LDFQPqvaSyS1uDZFegr46Aiu8nmUWeVd1VObPLkpWFrbRU4WiEOD/F2xhtNhs9evRg6tSpAHTt2pXdu3czd+5c7j7PXInExEQWLVrEgAEDaNasGfPnz6+XFoLlkqzwWKH+ekpNZeSX1e+QeoDAwYPI+egjStatw242o3LRF3AhvN37779f7X2feOIJF0YiGqo/9qSzbG8GWrWKqSM71mtbfHXc3D2emcsPciq/jCXbk+n49r8BCLv3nhpVHCgh/KGHKF69moKffibyiSfQRUUpHZIQ4gyVM7ssmZnYSktR+/vX2bGzix0Xoz21sstSi8ougOggX45ml5BRWE7TCGUWOakNTXAwmuBgrAUFmJKT8W3dWumQhDgnxZNdsbGxtGvXrsq2tm3b8t133533MRkZGTz00ENcd911bNmyhaeeeopZs2bVOoaIiAg0Gs1ZA+4zMjKIiYmp9XGF+wjx13Eqv0yRyi7fjh3RhIVhzc2ldNt2Ai7rXe8xCOEN3v3HLJ+srCxKS0udbY35+fn4+/sTFRUlyS5R58pMVv7vF8cA9YeuaEbrGPebweir03BP3yb8+8+D/GdJEu+dPIk2MoKIBx5QOrSL8u/WFb+uXSnbsYOC774j4tFHlQ5JCHEGTUgI6uBgbAUFmJJT8G1dvUHs1eH5lV2OTqCaJruignycyS5Po2vcGOvOnZhOnJBkl3Bbircx9uvXjwMHDlTZdvDgQRo3bnzO/bOzsxk8eDBt27bl+++/Z8WKFSxevJhnnnmm1jHo9Xq6d+/OihWnV8yz2WysWLGCPn361Pq4wn2EVMztKiit/8oulVqN4fLLAShevbrezy+Etzh27Jjz9sYbb9ClSxf27dtHbm4uubm57Nu3j27duvHaa68pHarwQh+uOcKp/DLign15fFBLpcM5rzsva4y/Ts0ho5atUW2IevJJ1AGeUTEQevttAOR9/Q12i2fNsBGiIahsXzMn1+2sJu+Z2VWzIonoipmPnpjscv4tyIqMwo0pnux66qmn2LhxI1OnTuXw4cN88cUXfPTRR4wdO/asfW02G8OGDaNx48YsXrwYrVZLu3btWLZsGZ988slZV/0rFRcXk5SURFJSEnB65ayTZ/zHOWHCBObNm8enn37Kvn37ePTRRykpKXGuzig8W4i/Y/UpJSq7AAxXDgSg+K+/FDm/EN7m5ZdfZtasWbQ+42pi69ateffdd3nppZcUjEx4o5S8UuasPgLAC9e2xa9izoo7CvHXc706C4AfOg8jeORIhSOqvsBrrkETGoolLU3eL4VwQ5WtjKY6HExearJQarICEGFwr9Viq8tSi5ldADHOZJdnzeyC08muuvxbEKKuKZ7s6tmzJz/88ANffvklHTp04LXXXmPmzJnccccdZ+2rVquZOnUq3333Hfozls7u3Lkzy5cv55ZbbjnnOaqzctaoUaP497//zeTJk+nSpQtJSUn8/vvvZw2tF54pxM9R2ZWnQGUXQEC/fqDVYjp2DNMJWaZXiEuVlpaG5RyVH1ar9ayWdCEu1dSl+zBabPRuGsa1Hd179pU5I4Ohvy9AZbexI6ARR3PLlA6p2tQ+PoTcdCMAeV9+pXA0Qoh/0lUMqTfVYTVPdpHjQrSPVo3BR/EJOzVmt1oxV3zuqHkbowdXdrngb0GIuqZ4sgvgX//6F7t27aK8vJx9+/bxYMUS1Ody1VVX4et79jLfXbt2JT4+/pyPqe7KWePGjePEiRMYjUY2bdpE794yW8lbhFZUdhUoVNmlCQzEv1s3QKq7hKgLgwcP5uGHH2b79u3Obdu2bePRRx9lSMUKqELUhf8dyWbprnTUKnh1RPt6WRDnUmTP/g9RBRn0LndUGny5ybO+iISMGgUqFSXr1snFISHcjD7RMWbGdLLu/tvMOqOF0d1fX8/FkpUFVitoNGgjI2v02OggR9tmpgdWdukSJdkl3J9bJLuEcLXKmV1KVXYBjmXVgeLVkuwS4lItWLCAmJgYevTogY+PDz4+PvTq1Yvo6Gg+/vhjpcMTXsJqszuH0t/RuzFtY4MUjujCjMeOkV+xwM+YqzoA8O32FMrNViXDqhF9QgIBl/cHIG/x1wpHI4Q4kz6+EQDm1NQ6O+bpeV2e2cJYOa9LGx2FSlOzFvfKmV3pHlnZ5Uh8WtLSsJV7XvyiYZBkl2gQKmd25ZcpmewaAEDpli3YSkoUi0MIbxAZGcnSpUvZv38/33zzDd988w379u1j6dKlREVFKR2e8BLfbU9hf3oRgb5anrqq7lYec5XsWbPAasUwYADXDO9DXLAv+aVmftudpnRoNRJ62+0AFHz3HTaj51U8COGtKmdSWdIzsNvtdXLMnGJH14WnDqe3OIfTx9X4sTFntDHW1b9nfdGEhjoXP6nL5KcQdUmSXaJBCK2o7MpXqI0RQN+0KbqEBOxmMyUbNigWhxDepFWrVowYMYIRI0bQqpX7JyOE5yg1Wfj3H47Voh8f1IKwAPeuOijft4/Cpb+BSkXkhKfQqFXc3svRZvL5Rs9qMzEMuAJtbCzWggKKV61SOhwhRAVtxcUku9GINT+/To7p+SsxpgM1n9cFEBnoeM5Gi43CMs9agValUqFrVFHpd+qUwtEIcW6eNwVQiFoIcSa7lKvsUqlUGAYOJG/RIopWryZQ5goJcUlSUlL4+eefOXnyJCZT1UT2jBkzFIpKeIuP1hwls8hIQpgfd/dtonQ4F5X1/iwAgoYPx7dildJRPROYueIQW0/ksT+9kDYx7t2GWUml0RA8YgQ5H35IwQ8/EjR0qNIhCSEAtV6PJjwca04OlvR0tKGhl3xMZ7Ir0L0vKJyP2VnZFVPjx/rqNIT468gvNZNRVE5wxfcVT6GLi8N48CDmU1LZJWrObrGg0ro2HSWVXaJBqGxjzFOwsgvAMMDRyljy1xqPK1cWwp2sWLGC1q1bM2fOHN555x1WrVrFJ598woIFC0hKSlI6POHhMgrL+fCvowA8N7QNPtqazWGpb2U7dzoqoNRqIsaNdW6PCvLl6naOVaW/8LBB9cHXXw9A8bp1WLKzFY5GCFFJV7FSvTk9vU6O5/GVXekVM7tqUdkFEB3ouSsySmWXqK3ygwc5MnQYxWvXufQ8kuwSDUKIn+NKSVG5heRc5eZl+ffqicrfH0tWFuV79yoWhxCebtKkSTzzzDPs2rULX19fvvvuO5KTkxkwYAC33HKL0uEJDzfjz4OUma10TQzh2o61+wJTnyqruoKvvx6fpk2r3De6t6OV8ccdpzBaPGdQvU+zpvh27gRWK4W//qp0OEKICtoYRwWTJSOjTo6XXeThM7tSKyq7YmqZ7AquGFJf4IHJrjjHnDJJdomasJlMpE58FnNKCnn//a9LC0Ak2SUahD/2nL76NODt1SzeoswVbrVeT0DfPgAUr16tSAxCeIN9+/YxZswYALRaLWVlZRgMBv7v//6P6dOnKxyd8GQHM4r4ZlsyAC9d2xaVSqVwRBdWun07JevWgVZLxGOPnnV/3+YRxAT5UlhuYeW+TAUirL3K6q78H39SOBLhSRYtWkS/fv2Ii4vjxIkTAMycOZOffpK/o7qgq0h2SWWXg7ONMa62lV2O551Z5HmLcTgru2RAvaiBrJnvYTxwAE1YGLFvvO7Sz1mS7BJeL62gjJd+3O382WaHF77fTVpBmSLxOFsZXVy2KYQ3CwgIcM7pio2N5ciRI877sqXlSVyC6b/tx2aHoe1j6N44TOlwLirrvfcBCBk5En1Cwln3a9Qqbujq+ELy/Q7PuvoeNGwY6HQY9+2j/MABpcMRHmDOnDlMmDCB4cOHk5+fj9XqqGYMCQlh5syZygbnJZyVXel1U9mVVZHsivTAmV228nKseXlA7QbUA0QHSRujaDhKNm4k95NPAIh9/TW0EREuPZ8ku4TXO5Zdgu0f1ZFWu53j2aWKxGPo3x9wzFixFhQoEoMQnu6yyy5j3TpHwnj48OE8/fTTvPHGG9x3331cdtllCkcnPNWGIzms2J+JRq3i2aGtlQ7noko2baZ00yZUOh0Rjz5y3v1u7Ob4QrJqfya5JcrOrqwJbWgogQMHAlAg1V2iGmbNmsW8efN48cUX0WhOz9rr0aMHu3btUjAy76GLqZjZlXHplV3lZitF5Y5VCD2xsquyqkvl7486qHYLgEQHOZ63Zya7HG2MlqwsbEbPq0wT9ctaUEDq85PAbifk1lsJHDTI5ees9vj7rl27XrTETKvVEhMTw1VXXcXDDz+MXu95GXrhfZpGBKBWUSXhpVGpaBLhr0g8uthY9M2bYzpyhJING2SVKSFqYcaMGRQXFwMwZcoUiouLWbx4MS1btpSVGEWt2O123vxtHwCjeyXSLNKgcEQXZrfbyZpVUdV1y83O2Snn0io6kA6Ngth9qpAlO1MZ06dJPUV56YJvuJ6iZcsoWPILUU9PcPnKTcKzHTt2jK5du5613cfHh5IS5Wa2ehNtdEVlV9qlJ7tyKpLvOo2KYD/PWokQwFLRyqmLja11K9bpyi7PSxZpQkNR+flhLyvDkpaGvkkTpUMSbspus5H6/CQs6enoGzcm+vnn6uW81f7EcMMNN1x0H5vNRmZmJq+//jr79u3jP//5z6XEJkSdiA32Y9qNHXn+u13YARUw9cYOxAb7KRaToX9/co8coXjdOkl2CVFDVquVlJQUOnXqBDhaGufOnatwVMLT/borjb9TCgjQa3hicEulw7mo0o0bKdu6DZVeT/jDD190/5Fd49l9ai/fbT/lUckuw+WXowkNxZqVTcmmTRj69VM6JOHGmjZtSlJSEo0bN66y/ffff6dt27YKReVdTld2ZWC32y9p3k52xZyq8AAft5+PeC5m53D6mFofw5PbGFUqFbpGcZgOH8F06pQku8R5ZX8wm+JVq1Dp9cS98w5q//opOql2suuVV16p9kFvv/12br31Vkl2Cbcxqmcif6cU8MWmk4zqmcConomKxhPQvz+5n35Kybr1l/xBQYiGRqPRcPXVV7Nv3z5CQkKUDkd4AZPFxlu/O2ZCPXhFMyID3budxm63O1dgDBk1Cl109EUfM6JzHFOX7uPv5HyOZBXT3M0r1yqp9HoCr76a/MWLKfztN0l2iQuaMGECY8eOpby8HLvdzubNm/nyyy+ZNm0aH3/8sdLheQVtxeuNvawMW2EhmuDgWh/LOZzeA+d1waUPp4fTya7MIiM2mx212rO+E+jiHMkumdslzqdw2TKyK/JCMf83Bb8O7evt3C6Z2dWtWzdGjx7tikMLUWuVH+yLjBaFIwH/nj1Q+fhgSU/HdPiw0uEI4XE6dOjA0aNHlQ5DeInPN53gZG4pkYE+PHh5M6XDuaiS9f+jbMcOVD4+hD/4QLUeExnow4BWkQD8sN2zvpQEDXNUQBctW47dbFY4GuHOHnjgAaZPn85LL71EaWkpo0ePZs6cObz33nvcdtttSofnFdS+vmgqLjSZL3FIvcevxJjuSHZpazmcHiDCoEelAqvN7mzr9CSyIqO4EOOhQ6Q99zwAYXePIaQa3YJ1ySXJLoPBIDNThNuJDXZcOUkvUL5MWO3ri3+PHgAUr1uvcDRCeJ7XX3+dZ555hiVLlpCWlkZhYWGVmxDVVVhu5v0VhwB4akgrAnzceybUmbO6Qm+7DV1UVLUfO7JiVcYfk05ht9svsrf78O/ZE01EBLaCAko2bFA6HOHm7rjjDg4dOkRxcTHp6emkpKRw//33Kx2WV6lM7lgucUh9drEjueOpyS6Ls42x9skurUbtfP6e2Mqod67IKMkuUZU5PZ2TDz6ErbQU/8suI2rixHqPQVZjFA1GZZmwOyS7AAIud6zKWFKxopwQovqGDx/O33//zYgRI4iPjyc0NJTQ0FBCQkIIDQ1VOjzhQT786wh5pWaaRwZwa494pcO5qJI1ayj/eycqX99qV3VVGtI2Gn+9hpS8Mv5O8ZzVgFUaDUFXXw1A4dLfFI5GeAp/f3+iapAMFtVX2TptvsQh9Z5f2VUxoP4S2hgBYjx4blfl4ijSxijOZM3P5+QDDzgG0jdtSqN3ZyiywIx7X770ULNnz2b27NlYrValQxFniAmu7Ikvd4ueeEP//mQyndKtW7GVl6P29VU0HiE8yapVq5QOoUGylZZiSknBmpuLtbAQW1ERdqsVlV6PWq9HExqKLiEBXUyMR6yal1ZQxsdrjwHw3NA2aDXufQ3wzFldoaNHo42IqNHj/fQaBreN5pe/U/l1ZypdEkJcEKVrBA0fRt4XX1C0YgU2kwm1rPgtzqFp06YXnIMq7e91Q1sxpL7uKrs8779nu91+embXJQyoB4iqmBOZWeR5KzJKG6P4J1tZGcmPjcV0+Aja6GgS53+MVqEL0TX+JPrZZ58xatQofHyqZuBNJhNfffUVY8aMqbPgPNXYsWMZO3YshYWFBF/C0EZRt6ICfVCpwGy1k1tqUvwqkr55c7QxMVjS0yndsgXD5ZcrGo8QnmTAgAFKh+DVbKWllO/fj/HAAcoPHMB46DCmEyewZmdX7wBaLT7Nm+Pfqxf+vXoS0KvXJQ0xdpUZfx7EaLHRs0koV7W7+JB3pRWvWEH5nj2o/P0Jf6B2bVnXdoytSHalMWlYW8Uv/FSXX7duaKOisGRmUrJuHYGDBikdknBD48ePr/Kz2Wxmx44d/P7770xUoIXGW1Umdy55ZldFcsfdFwU5F2t+PvayMgC0l5rs8uTKropklyUjA7vJhEouRDRoNqORlCeepGz7dtRBQSTM+8hZ/aeEGie77r33XoYOHXpWWXBRURH33nuvJLuE29JV9MRnFRlJLyhXPNmlUqkwXN6f/G++pWTdOkl2CXERJ0+eJDGx+iupnjp1ikYVH8LE+dlNJsoPHKR89y7Kdu6ifPdujEeOgM12zv3VQUFoIyPRBAWhDgpEpdFiN5mwG41YcnIwJydjN5sxHjiA8cAB8hYtQqXTYRg4kOAbrsdw+eVu8WF4T2oB325PAWDS8LZuvyqu3WZzVnWF3XUX2rCwWh1nYOtIDD5aUgvK2ZGcR/fGtTtOfVOp1QQOvYa8zxZR+NvvkuwS5/Tkk0+ec/vs2bPZunVrPUfjvbTRjuSOJb3htjFWPndNWNgld2dEB1XO7PK8yi5NeDgqHx/sRiPm9HT0NficJryLzWgkZew4StatQ+XnR8Kc/+DbqpWiMdU42WW328/5gTAlJUWqmITbiwnydSa7OjRS/u81oJ8j2VW8bj3uX1MghLJ69uzJDTfcwAMPPEDPnj3PuU9BQQFff/017733Hg899BBPPPFEPUfp3mxGI8ZDhzEe2E/Z7t2U796Dcf/+c65wp42MxKddW3xbtcKnVSv0TZuhT4i/aIWW3WrFkpFB2c6dlG7eTMnGTZiOHqVo2TKKli1DExlB+L33ETrqVtQBAa56qheO0W5n6tJ92O3wr06xdEt0/zlvRb//jvHgQdQGA+H33lPr4/jqNFzVLpofdpzil7/TPCbZBRA0bBh5ny2ieMUKaf8XNTJs2DAmTZrEJ598onQoXkFX0cZozmi4qzFWtu3VRdVK5VzhrCLPq+xSqVTo4uIwHTuGOTVVkl0NlK283JHoWr/ekej6cC7+3bsrHVb1k11du3ZFpVKhUqkYPHgw2jNmcVitVo4dO8bQoUNdEqQQdSU6yJddpwpId5My4YA+l4FajenIEcypqYqWeQrh7vbu3csbb7zBVVddha+vL927dycuLg5fX1/y8vLYu3cve/bsoVu3brz11lsMHz5c6ZAVUZlsMqemYkpJwXT8OKYjRzEePYrp+HE4xzxJTXAwvp064dexI74dOuDbvj266NoNdlZpNOji4tDFxRFU8bmg/MABCn76mYJffsaalU3mW2+R89FHhN17L2H33I3ap36/6Kw6kMn6wznoNWqeG9qmXs9dG3arlawPZgMQdu89aEJCLul413aM5Ycdp1i6K43J/2rnOa2MXbqgjY3FkpZGyfr1BA4erHRIwkN8++23hNWyGlKcrbJtz5KWdt5CiIsxW23klToutHjizC5z5UqMsZc2nB5Oz+zyxMoucLQymo4dkyH1DZS1uJiUseMo3bQJlb8/iR/Oxf88F6XrW7WTXTfccAMASUlJXHPNNRgMBud9er2eJk2acNNNN9V5gELUpZhg91raVxMcjF/nzpTt2EHxunWE3nqr0iEJ4bbCw8OZMWMGb7zxBr/++ivr1q3jxIkTlJWVERERwR133ME111xDhw4dlA7VJdb9uZHPV+ytsi3IWk6EqYiIsnwSc1NolHYUe37+eVsQATShofi0aY1v23b4deyAb4cO6OLjXdrG59u6Nb7PTiRq/JMU/LKE7I8+xHziJFnvvkv+t98SPWkSgYOudNn5z2S22njj130A3Nu/CQlh/vVy3ktR8MsvmI4eRRMcTNjdd1/y8S5vFUGgr5bMIiNbjufSu1l4HUTpeiqVisCrhpD32SKK/lwmyS5xlsqL85Xsdjvp6elkZWXxn//8R8HIvEvlaoy20lJsxcVoAgNrfIzcEsdwerUKQv09MNlVOZz+EldihNOVXe7y/aSmZEXGhsuSk0Pygw9Rvncv6oAAR0VXjx4XfZzVZudYdjE+Wo1LP4dVO9n1yiuvANCkSRNuu+22swbUC+EJYoP9AEgvcJ83k4D+/SjbsYOSdesl2SVENfj5+XHzzTdz8803KxbD7Nmzefvtt0lPT6dz587MmjWLXr16ufScx09m8pvqHw3P2oqbPxAO/k3KaJWXTNecIwywZdI0PAB948b4NG+GvmkzfFq1RBsVpdh8KpVeT8hNNxJ8/QgKly4l850ZmJOTSXnsMQwDBxIzZUqtK8qq66vNJzmSVUJYgJ6xV7Zw6bnqgs1kIrtyVtcD96M542JjbfloNVzTPoZvt6WwZGeaxyS7AIKuusqR7Fq9GrvZjEqnUzok4UYqL85XUqvVREZGMnDgQNq0cX0VpxLvDUpQ+/ujDg7GVlCAJT29VsmurIrh9GEBPh5TXXomc1rdtTFGVczsyi42YrXZ0XjYv4dzRcZTsiJjQ2JKOUXy/fdjOnECTVgYCfM+wq99+7P2Kyg1czCziIMZRRxIL2L3qQL2pRVRZrby8BXNmDS8rctirPHMrkGDBpGVlUV8fDwAmzdv5osvvqBdu3Y89NBDdR6gEHWp8sqJu7QxAhj69yd71geUbNiA3WJBpa3xf5ZCiHq0ePFiJkyYwNy5c+nduzczZ87kmmuu4cCBA2ct3lKXunRqxpP5u50/2+2Qp9KRZdORbtFwoARK8SMpqhVJUa34BGgTE8j1XRoxqmcChgD3uXKu0moJHjGCwMGDyZ77ITkLF1K8ejXHRowgZsoUgoZe45Lz5peamLHsIADjh7QkyNf9EyX5X32FOTUVbVQUYXfeWWfHvbZTLN9uS+G33em8OqK9x3y58uvWDU1YGNbcXEq3bCGgb1+lQxJupPLivBKUem9Qii46GmNBAeb0DHxatqzx40/P63Kf96aasFS0MWrroI0xPMAHjVqF1WYnp9joXJ3RU5xOdkllV0NRtms3yY8+ijU7G11cHOFzP+JEUCQn9qRzIqeEY9mlHM0q5khWifO/9X/y12swWc/fiVAXavytevTo0Tz00EPcddddpKenM2TIEDp06MDnn39Oeno6kydPdkWcQtSJmMpklxtVdvl26IAmOBhrQQFlO3fi362b0iEJIS5gxowZPPjgg9x7770AzJ07l19//ZUFCxbw/PPPu+y8HXp1oEOv87doWqw2DmQUse1EHsv2ZrDhSA7704vY//t+3l1+kOs6xXF//6a0iwtyWYw1pQ4IIOrpCQTfcD2pE5+lfO9eTo0fT/H1I4iZPLnOB9i/8+dB8krNtI4OZHQv9x+iay0uIXvOXAAixo5F7edXZ8fu19zRyphdbGTHyTx6NPGMeUYqjYbAwYPJ/+YbCpctk2SXqKKwsLDa+wYF1e1rYU3eG4xGI0bj6S+ANYnbXWhjojEePIglo3YrMmYXO9oYIwM9s1vI2cYYe+mVXRq1igiDnoxCIxmFHpjsqqhuM6VKsstblZmsnMov41R+GUc2bOfAryvIaHw1md0akRHRiJwF+4H95318XLAvrWICaR0dSLu4IDo0CqZJeIDLL7TVONm1e/duZznu119/TceOHVm/fj1//vknjzzyiCS7hFurnNnlTpVdKo2GgH59KVz6GyXr1kmySwg3ZjKZ2LZtG5MmTXJuU6vVDBkyhA0bNpzzMfX1pUarUdM+Lpj2ccGM6dOE/FITf+xJZ9HGE+w+Vch321P4bnsKwzvG8NSQVrSMrnnbiav4NG9Ok6++JGvOHHI+/IiCn36mfO9e4mfNQt+kSZ2cY29qIZ9vOgHAqyPao9Wo6+S4rpS7cCHWvDz0jRsTcuPIOj22XqtmSFvHqoy/7073mGQXQODVV5H/zTcULV9OzMsvo1K7/+9S1I+QkJCLtmlXDlS3nmOxjtqq6XvDtGnTmDJlSp2dXwm6aMeQenN67VZk9OSVGO0mE5asLKBuZnaBo/vEkewqpyPKrxhfE5WVXZb0DGkv91DlZispeWUk55WSkldGSm7F/+aXcSqv1Jmcdmo24PT/L7UAEOyno0m4P43DA2gc7k+zyACaRxpoGhFAoEKV9DVOdpnNZue8ruXLlzNixAgA2rRpQ1pFhlsId1XZxlhUbqHEaCHAxz1aBgP69adw6W8Ur1tP5BNPKB2OEOI8srOzsVqtREdXnZ0VHR3N/v3nvqKl1JeaEH89o3omcmuPBHYk5zN/3TF+3ZnG0l3p/LY7nZu6xfPc0DZuc1VdpdcT9eSTGPr3J2X8eIyHDnPs5luIm/7mJQ8it9vtvPrzHmx2R/ten+buP6PKkpND7oIFAEQ+Nd4lXx6uaR/DDztO8dvudF68tq1is9xqKqB3b9QGA9asbMqS/sa/W1elQxJu4pNPPuH555/nnnvuoU+fPgBs2LCBTz/9lGnTptGkjpLn/1TT94ZJkyYxYcIE58+FhYUkJCS4JDZX0cZWJrtq9/0vu8hz2xjNGRlgt6PS69HU0SqfUYG+QAEZRe5zQb66tJERqHQ67GYz5owM9BXjjoR7MVlsnMwt4XBmCceySyraDUs4mVtKemE5dvuFH++PlaiCTKLK8kiMC6fV1VeQEB5AQpg/CWH+BPu5X5Kzxt/027dvz9y5c7n22mtZtmwZr732GgCpqamEh7v/h0fRsAX66jD4aCk2WkgvLKd55KUP+q0LAf37AVC+axeWvDy0oaEKRySEqCtKf6lRqVR0Swyl2+hQHh9UyLvLDvLHngy+3ZbCH7vTGX9VK8b0aYzOTSqd/Lt3p+l333HqqQmUbdtGythxRD49gfAHHqh1Mubnv1PZfDwXP52GF104CLUuZc+eja20FN/27Qm8+mqXnGNAq0j8dBpO5ZexJ7WQDo08o5pApddjGDiQwiVLKFq2TJJdwumzzz5jxowZ3H777c5tI0aMoGPHjnz00UesXr1aueDO4OPj4/GLfVVWdllqWdmVU7EaoydWdplTK1sYY+vsIkHlkPrMwnPPN3JnKrUaXVwcphMnMJ9KlWSXwmw2OydyS9mbWsiB9EIOZhRzMKOIE7mlWG3nz2gF6B0rI8aH+pMQ5kejED/iQ/2J1ZpRT52CZvN6VGo1URMnEnbP3R5xgazGya7p06czcuRI3n77be6++246d+4MwM8//+yVq40I7xMd5ENxloWMAvdJdumio/Fp1QrjwYOUrP8fwf+6VumQhHB7ixYtYu7cuRw7dowNGzbQuHFjZs6cSdOmTbn++utdcs6IiAg0Gg0ZGVU/3GdkZBATE3POx7jTl5o2MUF8eFcPdpzM45Wf97AzpYDXluzlm63J/PuWzm6T7NBFRdF44SdkvDmdvM8/J+udGZhOnCD2lVdqXOFUUGrmtSX7ABh7ZXPiQupu7pWrGA8fJm/x1wBETZzosjY9P72Gga0j+W13Or/vTneb3391BF51lSPZtXw5Uc9O9IgP3cL1NmzYwNy5c8/a3qNHDx544AGXnbc27w2eThvjqGKrdWWXB7cxOldibHTp87oqRQc6uk8yPbCyCxytjKYTJzCnpEBvyQnUp1P5ZSSdzCcpOY+/kwvYm1ZIsdFyzn0D9BqaRzlaC5uEB9A0IoDEcH8ah/kTFqA/6720/OBBUh4bizklBXVAAI1mvINhwIBzHtsd1TjZNXDgQLKzsyksLCT0jOqThx56CH9//zoNTghXiAn25UhWiVvN7QIwXHG5I9m1do0ku4S4iDlz5jB58mTGjx/PG2+84Zy9EhISwsyZM12W7NLr9XTv3p0VK1Y4l7i32WysWLGCcePGueScrtA1MZQfH+vH11uTmf77fvanF3H97PU8NrA54wa1wEerUTpEVDodMS+/hL5pUzKmTqXg2+8wnzpF/KxZaAzVv1Ax7bd9ZBcbaR4ZwINXNHNhxHUnY/pbYLViGDKYgMt6u/RcQzvEOJJde9J55prWLj1XXTJc3h+Vjw/m5GSMBw7g26aN0iEJN5CQkMC8efN46623qmz/+OOPXVpR6y3vDTWhq1hh0pqVXavHZ1W2MbpJK31NWNLqbiXGStEVlV0ZHljZBbIiY31Kzi1l3eFsNh/LZfOxXE7ll521j16rpk1MIG1iAmkdE0Tr6EBaRBmIDvKp9sWhopUrSX1mIrbSUnTx8STM+U+tVl5VUq0GFmk0GiwWC+vWrQOgdevWLuuBF6KuVc7tcrdkV8DlV5Dz8XyK167DbrPJwF0hLmDWrFnMmzePG264gTfffNO5vUePHjzzzDMuPfeECRO4++676dGjB7169WLmzJmUlJQ4V+DyFGq1itt6JTKkXTSv/LSHX3elMWvlYZbtzeC927rSOsY9BtiH3XkHuvhGnJrwNKUbNnJizBgSP/oIbUTERR+78WgOX21JBuDNmzq5RRLvYorXrKFk7VrQ6YieONHl57uyTRQ6jYrDmcUcziyiRZR7/N4vRu3vT0C/fhSvXEnRihWS7BIAvPvuu9x000389ttv9O7tSBRv3ryZQ4cO8d1337n03N7y3lBdmorXYGtBATaTCbW+ZrO3Kgdee+TMrtS6W4mxUuX3kww3+35SXbqK1kVJdtU9o8XKhiM5rNiXydpDWRzPKa1yv0atom1sIF0SQugcH0Kn+BCaRwbUeiEeu91OzkfzyJo5E+x2/Hv1otF7Mz1yzE6Nk10lJSU8/vjjfPbZZ9hsNsCR/BozZgyzZs2S6i7h9mKDK5JdBe71ZuLfrSvqgACsubmU79mLX8cOSockhNs6duwYXbuePafHx8eHkpISl5571KhRZGVlMXnyZNLT0+nSpQu///77WYOJPUWEwYfZd3Tj2l1pvPzjbvanFzHig3W8MLwtY/o0dov2sMCBA2m86DOSH3oY4959HB99B4kfz0OfmHjex5Sbrbzw/S4ARvdOpKcHrDZoN5sdVV1A2J13om/c2OXnDPLV0a9FBKsPZPHHngyPSXYBBA4eRPHKlRSvWEnk2LFKhyPcwPDhwzl06BBz5sxh3z5H+/J1113HI4884vJZid723nAxmuBg0GrBYsGak4O6BlVOVpud3BJHBVOkR7Yxnp7ZVVcqF4uRyi4Bjs8wqw9k8svONP46kFWlLVGrVtE1MYQ+zcLp1TScrokhdbboms1oJO2llyn85RcAQm6/jZgXXvDYFTZr/K8yYcIE/vrrL3755Rf69XMM1V63bh1PPPEETz/9NHPmzKnzIIWoSzFB7pnsUul0BPTtQ9Gy5RSv+UuSXUJcQNOmTUlKSqLxP5IBv//+O23bun4A+bhx47yuNWV4x1h6Nglj4rd/s/pAFq/8vIc1B7P49y2dCQ1Q/sq7X/v2NPnic04+8CDmkycdCa/5H+Pb+tytd7NWHuJodglRgT48P8wzqn7yvvwK05EjaEJDiXj0kXo779D2Maw+kMVvu9MYe2WLejvvpTIMHAgqFeV792JOS6vTL57C85jNZoYOHcrcuXN54403FInBG98bzkelVqMND8eSkYElO6dG//3llZqw2UGlgjA3eH+pKXNqxcyuuLpsY3R8P8kpMWKx2mpdlaOUyvllJkl21ZrdbmfriTy+3pLM77vTKTojwRUV6MOQdtFc2TqKy5qFEehb98knS1YWKeMep+zvv0GjIfrFFwgbPbrOz1Ofavxf0Xfffcf8+fMZNmwYQUFBBAUFMXz4cObNm8e3337rihiFqFPuXCYccPnlAJSsWatwJEK4twkTJjB27FgWL16M3W5n8+bNvPHGG0yaNIlnn31W6fA8VmSgD5/c05MpI9qj16pZsT+T4e+vZduJXKVDA0DfuDFNvvgcnzZtsGZnc+KuMZQlJZ2139bjucxZfQSA/7u+PUEu+FBY18wZGWS99x4AkePHowkKqrdzX9UuGrUKdp8qJPUcsz/clTY8HL+KCs+ilSsVjkYoTafTsXPnTqXDaFAq28kt2Vk1elzlcPpQf73HJXXsdrtLKrvCA/Ro1Crs9tMtnp6kcgVGS0YGdpPnxa+kwnIzC9Yd4+p313DL3A18sy2FIqOFuGBfHr6iGT+O7cfGSYOZOrIjV7WLdkmiq/zAQY7dOoqyv/9GHRxM4sfzPD7RBbVIdpWWlp6zHDcqKorS0tJzPEII9xIT7J4zuwAMV1wBQNnOnVjy8hSORgj39cADDzB9+nReeuklSktLGT16NHPmzOG9997jtttuUzo8j6ZSqbi7bxN+fKwfzSICSCso59YPNzL3ryPY7edfsrq+aCMjafzZp/h17YqtsJAT991PycaNzvuLys2MX5yEzQ43dm3E0A6eUe2T8cZUbCUl+HXpQsgtN9frucMNPvRo7GjzXLY34yJ7u5fAwYMAKF4hyS4Bd955J/Pnz1c6jAbjdLKrZkPqs4s8d16XNT8fe5njokBdDqhXq1VEOVsZ3e87ysVoIiJQ+fiAzYY5w7PeR5SSVlDG1KX76DttJf+3ZC+HMovx02m4tUc8Xz/ch3XPDWLS8LZ0SQhBrXbdSInides5MXo0lrQ09E2a0HTxVwT06eOy89WnGie7+vTpwyuvvEJ5+en/CMvKypgyZQp9vOQfRXi3ymRXZqGR5FzXzvapKV1MDD6tWoHdTsn6/ykdjhBu7Y477uDQoUMUFxeTnp5OSkoK999/v9JheY12cUH8/Hh/RnSOw2qz8+Zv+3nws20UlJmVDg1NUBCJ8z8moG9f7KWlJD/0MEUrVwHwyk97SMkrIyHMjynXt1c40uopWr2aoj//BI2GmCmvKrJAydXtHRcy/9iTXu/nvhSGQY5kV8mWLViLihSORijNYrEwZ84cevTowcMPP8yECROq3ETd0kRWDKmvabKrorIrPMDz5nVVrsSoiYhA7VO38XtyskulUqGLc7QyytyuC0srKGPS97u4fPoqPlpzlGKjhRZRBl67vj2bXhzMWzd3plfTMJcmuCrlffMNyQ8/jK2kBP+ePWny1ZfovWjhwRrP7Hrvvfe45ppriI+Pp3PnzgD8/fff+Pr68scff9R5gELUtRX7MgGwAwPeXs20Gzsyquf5hxzXN8MVl2M8eJDiNX8R/K9rlQ5HCLfn7+8vi6O4iMFHy3u3deGyZuG8+sselu/L4F+z1jLnju50aBSsaGxqf3/i587h1IQJFC9fQcoTT/D3M2/y/X5Qq2DmqC4uKfWva7bSUjL+7zUAwu65+7wzyFztqnbRvP7rPjYdyyW/1ESIv2dUXPg0bYq+WTNMR49SvGYNwdfK+2ZDtnv3brp16wbAwYMHq9znDotteBtnZVdW7ZJdEYGel+xyRQtjpaggX6CAzCLPHVJvOnYMc0qK0qG4pbwSE7NXHeazjScwWRwL/fVqGsYjA5oxsFVUvSS3KtntdrLnzCH7/VkABI24jtjXX6/xqqrursbJrg4dOnDo0CE+//xz9u/fD8Dtt9/OHXfcgZ+fX50HKERdSiso48Ufdjl/ttnhhe93c0WrSGKD3ePvN+DyK8j5eD4l69Zjt9kUucIvhDvq2rVrtb+sbN++3cXRNBwqlYrRvRPp2CiYRz/fRnJuGTfO+R+vXtee23slKPoFUq3XEz9zJqmTXuDvv7bw6m4jaH14fFBLujd2/9UXATLfnYk5NRVdXJyiKwo2Dg+gTUwg+9OLWLk/kxu7xSsWS00FDh5EztGjFK9YKcmuBm7VqlVKh9CgaCMigVq0MRZ7bhujOdV1ya7oIEfyL9MDK7sAdPGOFRllSH1VVpudr7ac5O0/DpBf6qiO79UkjGeuaU2vpvX/WcVus5Hx+hvkffEFAOGPPEzkk0965QWBWq1R6e/vz4MPPljXsQjhcseyS7D9Y+SM1W7neHap2yS7/Lt1RR0QgDU3l/I9e/Dr2FHpkIRwCzfccIPSITRoHeOD+fXxy3n6mySW78vkhR92sfV4Lq+P7IC/vm6WvK4NlVaL7+T/4/U3fqUcHzpnHeKOU9lAK8Viqq7idevJW7QIgJgpr6JWuELx6nbR7E8v4s89GR6V7DIMGkTOvI8pXrMGu8mEysuuTIvaSamoLomP95y/ZU+jjQgHwJKTU6PHOSu7DFLZdaaowMpFtDy3sgukjfFMu1IKeOGHXew6VQBAm5hAJg1vyxUtIxRJLtnNZlKfe57CpUtBpSL6xRcJu/OOeo+jvtT40+m0adOIjo7mvvvuq7J9wYIFZGVl8dxzz9VZcO5m5MiRrF69msGDB8vKkx6qaUQAahVVEl4alYomEe7TAqXS6Qjo25eiZcsoXrNGkl1CVHjllVeUDqHBC/bX8dFdPfhwzVHe/mM/3+84xe7UAmaP7kbL6EBFYjJbbYz9cgep+NJIbeKFzYvIWV+KqqiIiHFj3fZKpSUvj7RJkwAIHT0aQ8VqvEq6un0M7688zF8Hsyg3W/HVaZQOqVr8OndGExGBNTubki1bMPTrp3RIQiE2m43XX3+dd955h+LiYgACAwN5+umnefHFF1FLtXydutTVGCM9MdmVmgqALs51lV0ZRZ5Z2aV3JrtSFY5EeWarjVkrDzN71WGsNjuBPlqevroVd17WWLEVSO0mEykVox/Q6Wg0/U2Chg9XJJb6UuN/6Q8//JA2bdqctb19+/bMnTu3ToJyV08++SSfffaZ0mGISxAb7Me0GztS+dVHBUy9sYPbVHVVCrjC8aWneM0ahSMRQoiq1GoVjw5szhcPXkZkoA8HM4q57oN1fL01ud5Xa7Tb7Uz+aTcbj+YSoNew4InBNH/sAQCyZ88mY+o07DZbvcZUHXa7nfRXp2DJykLfrBlRE59ROiQA2scFERfsS5nZyrpDNWtLUpJKrSbwyoEAFK+UNraG7MUXX+SDDz7gzTffZMeOHezYsYOpU6cya9YsXn75ZaXD8zqVyS5rrWd2eV4VpjnNkcipy5UYKzlmdjkW0fJEuooqyoY+s+twZhEj/7Oe91ccwmqzc22nWFY+M5B7+jVVLNFlM5lIeeJJipevQKXXkzD7A69PdEEtkl3p6enEnuM/7sjISNIqyjq91cCBAwkMVObKtag7o3om8sbIDgC0jQ1yq+H0lSqv8Jfv3IUlL0/haIRwP6GhoYSFhZ11Cw8Pp1GjRgwYMIBPPvlE6TC92mXNwln6xOVc3jKCcrONZ7/dyVOLkygsr5/VGu12O6/8vIcvNyejUsHM27rSOiaIiEcfJfqllwDIW7SI1InPYjeZ6iWm6sr/9luK/vgDtFri3n4LtZvMPFWpVFzdPgaAP/d62KqMVzpWZSxatbLek67CfXz66ad8/PHHPProo3Tq1IlOnTrx2GOPMW/ePBYuXKh0eF5HUzGzy1Zaiq2k+iucZxdVzuzyvMouS+XMrrhGdX7s6Io2xkwPreyqbGO0ZGZic7P33fryy9+pjPhgPbtPFRLir2PW7V2ZPbobkQouxmAzmUgZO47i1atR+fgQ/5//YLjiCsXiqU81TnYlJCSwfv36s7avX7+euIrlRmvrzTffRKVSMX78+Es6zj+tWbOG6667jri4OFQqFT/++OM595s9ezZNmjTB19eX3r17s3nz5jqNQ7iPbo1DAUjJK3XLD8W6mBh8WrcGu50Sqe4S4iyTJ09GrVZz7bXXMmXKFKZMmcK1116LWq1m7NixtGrVikcffZR58+YpHapXiwz04dN7ezHxmtZo1Cp+TEpl2My1bDxas/ktNWW325nyy14+23AClQqm39SJq9pFO+8Pu/MO4t6aDlothb/+ysmHH8Za0dKktNLt20mvWH0x8okn8GvfXuGIqqr8d1y+LxPrP4dcurGAPpeh8vXFkpqGsWIBJdHw5ObmnrMDpU2bNuTm5ioQkXdTB/ijqkjWV3dul91uJ6fEUbkU7mHJLpvJhCXL0bLpijbGqIo2xuxiE2ar+1UlX4wmLMzx92C3Y/HyIph/MlttvLZkL49/uYNSk5W+zcP5c/wVXNf50vIjl8pusZD69NOUrF2Lys+PhA/nYujfcFr9a5zsevDBBxk/fjyffPIJJ06c4MSJEyxYsICnnnrqkobWb9myhQ8//JBOnTpdcL/169djNp991Xjv3r1kZGSc8zElJSV07tyZ2bNnn/e4ixcvZsKECbzyyits376dzp07c80115CZmVmzJyI8QpPwAFQqKCy3kFvinlceDFcOBKBIWjKEOMu6det4/fXXWbRoEY8//jiPP/44ixYt4vXXX2fbtm3MmzePt99+m/fff1/pUL2eWq1i7JUt+Prhy0gM8+dUfhm3z9vI60v2Umqy1Pn5TBYbL/24m4X/O+5IdN3YiVt7JJy1X/CIESTMnYvK35/SDRs5cdcYzOnKViuZ09JIefwJMJsJvPpqwh+4X9F4zqVX0zCCfLXklpjYdsJzKovVfn4EVMzqKlq5UuFohFI6d+7MBx98cNb2Dz74gM6dOysQkXdTqVRnzO2qXitjYZkFs9WRSA8P8Kw2RkvFe4jKxwdNaGidHz/MX49W7Ri2klXkea2MKpUKXSNHcqchDakvLDdz94LNzF93DIBHBzbns/t6OdtSlWK32Uh7eTJFy5aj0ulI+M9sAi67TNGY6luNk10TJ07k/vvv57HHHqNZs2Y0a9aMxx9/nCeeeIJJFYNWa6q4uJg77riDefPmEXqBFw6bzcbYsWMZPXo0VqvVuf3AgQMMGjSITz/99JyPGzZsGK+//jojR44877FnzJjBgw8+yL333ku7du2YO3cu/v7+LFiwoMbPZ/bs2bRr146ePXvW+LGifvjqNMRVzOk6ml39suv6FDjI0ZJRsm5dgy0FFuJ8/vjjD4YMGXLW9sGDB/PHH38AMHz4cI4ePVrfoTVY3RuH8duTl3N7rwTsdvh43TGumrGGP/fUXYIpvaCc2+dt5PNNJwF488aO3Nrz7ERXJUP/fjT+7DM04eEY9+3j+C23UrZzZ53FUxO2sjJSxo7DmpODT5s2xL05DZUbDsvWadQMbuuo7qrL3119CBx0JSBzuxqyt956iwULFtCuXTvuv/9+7r//ftq1a8fChQt5++23lQ7PK9U02ZVVMa8r0FfrMYtgVDKdTAZAlxDvksVP1GoVURXtbpkemOyC062MpgYytyujsJxb527gf0dyCNBrmHtnd54b2kax2VyV7HY7mdOnU/DDD6DR0OjdGQT06aNoTEqo8W9BpVIxffp0srKy2LhxI3///Te5ublMnjy51kGMHTuWa6+99pxfXKoEq1azdOlSduzYwZgxY7DZbBw5coRBgwZxww038Oyzz9bq/CaTiW3btlU5v1qtZsiQIWzYsKHGxxs7dix79+5ly5YttYpH1I9mkQEAHMtyz2SXb4cOaCIjsJWUULpZ/paEOFNYWBi//PLLWdt/+eUXwsLCAEdVr8xZrF8BPlqm3diJT+7pSXyoH6fyy3ho0Tbu/WQzu1IKLunYaw5m8a9Za9l2Io9AXy3zxvSo1sxFvw7tabL4K3xatsSSlcWJu8ZQsOTXS4qlpmxGIylPPEn53r1oQkNJmP0Ban/3WQX4n66uaGVcti/DLVv9z8cwYACoVJTv2aN4FZ9QRtOmTTl48CAjR44kPz+f/Px8brzxRg4cOEDjxo2VDs8raSPCgeonuzx5JUbTieMA6BNd97dUWQ2UXuCZc7sa0oqMhzOLuPE//2N/ehERBh8WP9yHoR1ilA4LgLzPPiP3U8fCerFvvE7gRfIs3kpb2wcaDIY6qVz66quv2L59e7UTQ3FxcaxcuZLLL7+c0aNHs2HDBoYMGcKcOXNqHUN2djZWq5Xo6Ogq26Ojo9l/xtyHIUOG8Pfff1NSUkJ8fDzffPMNfRpghtRbNIsIYO2hbI5ku8ccl39SqdUEDryS/G++oXjlygbVXy3Exbz88ss8+uijrFq1il69egGOdvilS5c6VwZetmwZAwYMUDLMBuvKNlEsazaAWSsPMW/tUVYdyGLVgSwGt4nisSub0y0xtNpXxfekFjD99wOsOeiYk9ImJpC5d3anSURAtePRx8fT+MsvSZ04keJVq0h95hnKkpKIenYiar1r22hsRiMp4x53zsuI/2CW88q3u7qiVSR6rZoTOaUczCimdYxnJI21ERH4de5MWVISxatWEXr77UqHJOpZ06ZNSUtL44033qiyPScnh4SEhCqdIaJuaCpXZKxhsssTh9ObTpwAQO/CxGllZVeWxw6pr1iR0cvbGA9lFHHbRxvJKTHRNCKAz+7rRUKYe1zEKlq1iow3pwMQNXEiITfcoGxACqp1sqsuJCcn8+STT7Js2TJ8favf05qYmMiiRYsYMGAAzZo1Y/78+S4pJf2n5cuXu/wcov40jXDvyi4AwyBHsqto1SqiX36pXv7OhfAEDz74IO3ateODDz7g+++/B6B169b89ddf9O3bF4Cnn35ayRAbPD+9hmeHtuHm7vHMWnmYn5JOsWJ/Jiv2Z5IY5s91nWMZ1CaaltEGgnx1VR57Kr+MlfszWbkvg1UHHEkurVrFnZc15rmhbfDT17z1RWMIIP6DWWTNfI+cefPI++9/Kd2+jfgZM9A3aVIXT/ks/0x0Jcydi3/37i45V10K8NHSv0UEK/dn8ueedI9JdgEYBg+iLCmJopWS7GqIzleJWFxcXKPvGqL6nG2MWdVMdlW050UEeta8LqinZFeQd7Qxmr24jfFIVjG3z9tETomJ9nFBLLq/N2FuMn+ufP9+Tj39DNjthNxyC2H33at0SIpSNNm1bds2MjMz6datm3Ob1WplzZo1fPDBBxiNRjSasz/QZmRk8NBDD3HdddexZcsWnnrqKWbNmlXrOCIiItBoNGcNuM/IyCAmxj1KEUXdaxZpANx3ZhdAQJ8+jtWl0hyrS/m2bat0SEK4jX79+tGvn1Q8urtmkQbeHdWFxwe1YPaqIyzdlcbJ3FJmrzrC7FVHAIgO8iHUX0+x0UJRuYWCsqoL0VzXOY6nr2pVo2quc1FpNEQ9PQG/7t1Ie34Sxr37OHbjTUROmEDo7behOsdnjtoynzpFyvinKN+1y5noCujdq86O72pXt4tm5f5Mlu3L4PHBLZUOp9oCBw0i650ZlG7ciLW4BI3h0v5mhGeYMGEC4Bi3MnnyZPzPaBO2Wq1s2rSJLl26KBSdd9NGRAI1aWN0zKEND/C8yi7zCce8SH0T1yW7ogMdSdnMQg9PdnlpZdfx7BJGz9tIdrGRtrFB/Pf+3oS6SaLLkpND8qOPYS8txf+yy4iZ/HKDL5RQNNk1ePBgdu3aVWXbvffeS5s2bXjuuefOmejKzs5m8ODBtG3blm+++YaDBw8ycOBAfHx8+Pe//12rOPR6Pd27d2fFihXcUFHmZ7PZWLFiBePGjavVMYX7q6zsOpFTgtVmR6N2vxcDta8vAX37UrxyJUWrVkmyS4gz2Gw2Dh8+TGZmJjZb1SW6r7jiCoWiEufTLNLAO7d25rUb2rNiXyZLdqay42Q+mUVGMgodt0pqFXRLDOXKNlFc0z6aFlF1W1kUOHAgvj/9SOozEyndsoWM11+n4KefiP2/KXXyOlu8Zg2pE5/FWlCAOjiY+FnvE9DLcxJdAIPbRqNS7WJnSgGp+WXEhfgpHVK16Js1Q9c4EfOJk5SsW0vQ0KFKhyTqwY4dOwBHZdeuXbvQn9GerNfr6dy5M88884xS4Xk1bWTNBtTnlHhmG6PdYnEOXa+Pyq4MT21jjHckuyxZWdiMRtQ+nvV7vpCsIiN3zt9ERqGRVtEG/nt/L7dJdNmtVlInTsSSloa+SRPi35uJSqe7+AO9nKLJrsDAQDp06FBlW0BAAOHh4WdtB8cXm2HDhtG4cWMWL16MVqulXbt2LFu2jEGDBtGoUSOeeuqpsx5XXFzM4cOHnT8fO3aMpKQkwsLCSEx0DLedMGECd999Nz169KBXr17MnDmTkpIS7r23YZf+ebNGIX7otWpMFhun8spIDHePPut/Chx0JcUrV1K8chWRjz2mdDhCuIWNGzcyevRoTpw4cVbbikqlkrksbsxfr+W6znFc19mxPHlhuZkjmcUUlVsI9NUS6KslMtCXYD/XfkjTRUeTuPAT8r/+mswZ71K+axfHbrqZoOHDiXj4IXxa1ryayZyRQfYHH5D/7Xdgt+PboQPx7810+xld5xIZ6EO3xFC2nchj+b4MxvRponRI1aJSqQgcNJjcTz6haMVKSXY1EKtWOVbgvPfee3nvvfcICgpSOKKGo8arMRY5Krs8rY3RnJoKFgsqHx+0/5jzXJeiPLyySxMSgtrfH1tpKeZTqfg0a6p0SHWi3Gzlwc+2kpJXRpNwfz5/4DLC3Shhmz13LiX/2+CcDaoJDlY6JLegaLKrptRqNVOnTuXyyy+vcsWmc+fOLF++nMjIyHM+buvWrVx55ZXOnytLne+++24WLlwIwKhRo8jKymLy5Mmkp6fTpUsXfv/997OG1gvvoVaraBoewIGMIo5kF7ttssswcKBjdanduzFnZKCTv0kheOSRR+jRowe//vorsbGxDb5M25MF+eromhiqyLlVGg2ht9+OYfBgMt98k8Klv1G4ZAmFS5ZgGDKY4Ouvx9C/P2q/C1c1mZKTyV+8mNxF/8VudHxBCbn9NqInTXL5AHxXurpdNNtO5PHnHs9JdgEEDnEku4r/+gu72SxXtxuQTz75ROkQGhztGQPq7Xb7Rd+PPXVAvXNeV2ICKrXaZec5PbPLMyu7VCoVuiaNMe7dh+noEa9IdtlsdiZ8nURScj4h/jo+ubcXkYHu8/dbsmED2R/MBiD21VfwadFC4Yjch9slu1avXn3B+6+66qpzbu/atet5HzNw4MBqLZ09btw4aVtsYJpFOpJdx7JKuLK10tGcmzYiAr9OnSj7+2+KV60m9LZRSockhOIOHTrEt99+Swt5Qxd1QBcVRaMZMwi7/35yPvyIoj//pHj5CoqXr0BV0U7u07Il+sQEtFFR2EpKsOYXYEo+SfFff2E6fMR5LL/u3Yl6egL+Z8wj9VRXt49h2m/72Xg0h4JSM8H+npE08uvSBU1YGNbcXEq3bSPgssuUDkkIr6UJDwfAbjZjKyy8aEWJxya7jjuSXToXtjDC6cqunBITFqsNrcZ1iTVX8W3ZCuPefZQfPEjgkCFKh3PJ/v3nAZbuSuf/27vv+Cbr7YHjn8yudLd0D/amIAKiooDIUEFQUa8ogtsLXhVQwYX6u4rXcREV170KLgS9AiqiyF6yoWwQCrSF7pbulSb5/ZE2tHRD2ydJz/v1ykv75Emek9DmSU7OOV+dRsWn9/a1jcKxB2Xp6Zyb8Uz5QPo78L71VqVDsit2l+wSoiVVvFidyshXOJK6GYYOpWj/fvLWr5NklxDAgAEDOHnypCS7RJNy696d8PfnUXLyJNk//I+81asxJiWVt5Kvq/2GGg3uffvi98BkDNdf7zSVhm0DPOgUZOCv1HzWHkvltivClQ6pQVQaDYbBg8lZupS8NWsl2SVEM1K7uKD28sKcm0tZRkadyS6LxWJLdgU6WrIroXw4fTMnu/w99GjUKkxmCxn5pQR7O94qoi6dOgFQ8tcJhSO5fH8cTuGjDdYvtN68rRcD2vkrHNEFFouF5FdexZSZiUvnzgS98ILSIdkdSXaJVq1iRcZ9Cdkk5xQR4m2fA3gNQwaTPncuhdu2Yy4sRO1uny2XQrSUJ554gunTp5OSkkLPnj3RXdSm1KtXL4UiE87ApUMHgmbNpM3M5yg5epSC7TsoTUzAmHiWsvR01J4GND4+aP38cR/QH8OgQWicdEbQyO7B/JV6klWHUxwm2QXWVsacpUvJW7eWoBeed5oEpBD2SBsQQGluLmXpGbi0b1/rfgWlJoqN1gVlHG1mV2n8GaD5k11qtYpAgwspucWk5hY7eLLrL4UjuTxnzxcy44f9ADx4bVtu72tf58DcX34hf+1a0OkIfest1K6O97vS3CTZJVq1uHRrRdfhpFyueXMdc27ryV39IhWOqjqXjh3RhYdjPHuWgj//dIqSYCEux+233w7AAw88YNumUqls80JkQL1oCiqVCtdu3XDt1k3pUBQzvHsw7687yca/0ikqNeGmr75Stj3yGDgQlasrZUnJlBw7JqsZC9GMtAEBlJ46Ve+Q+ow8a1WXm06Du96xPoZemNnVvMkusM7tSsktJi3PMYfUVyS7SuPjHXZFRqPJzBPf7SO3uIyYCB+eG9lF6ZCqMKamkfLP1wEInDIF186dFI7IPjleE7AQTSQ5p4hPN16Ys2K2wPNLD5GcU6RgVDVTqVQYhloXWchbs1bhaIRQ3unTp6tdTp06ZfuvEKJpdA/1IszHjWKjmY1/pSsdToOp3dzwuOYaQM6bQjS3Cysy1v0akVlQPq/Lwaq6LEYjxrPnANBHt0Cyq2JFRgcdUq9tE2htZzWZKI2Lq/8GdujtVcfZl5CNl6uWD//WB73WftImFouFlNmzMefm4tqjB/4PPah0SHbLfv7VhGhhpzMKMF+0boHJYuFMRqEyAdWjoporb/16LEajwtEIoayoqKg6L0KIpqFSqRjZIxiwzi5xJJ5DhwKQV9e8NSHEZdMGlq/ImJlZ537peaWA4w2nN547ByYTKldXtG3aNPvxKlZkTM11zMoulUplq+4qdsBWxh2nMvlsk/WL07fHxxDhZ1/jY3J/XUn+hg2odDpC57yBSutYVZItSZ4Z0Wq1DfBAraJKwkujUhEdYF8vaBXc+/a1rS5VsHMnhvJvrIVozY4cOUJCQgKlpaVVto8ZM0ahiIRwPiO6B/P5ltOsOZqK0WRG5yCrgxmGDAa1mpKjRzGeO4cuLEzpkIRwSpqKyq70etoYHXUlxorh9JGRqNTN//rXxtP6/KQ7aGUXWFsZC3ftcrgh9UWlJp778QAAd/eLYET3YIUjqspcUEDaW28BEPD3x3Hp2FHhiOybJLtEqxXi7cac23ry3I8HAVCp4I3betjtkHqVRoPnDTeQ/cMP5P2xWpJdolU7deoU48aN4+DBg7ZZXYBtCLXM7BKi6fSN8iXAoCcjv5TtpzIZ1DFQ6ZAaROvnh/sVV1C4ezd5a9bgd//9SockhFPS+le0MTppsutM+byuFqocD/Iqb2N00MoucNwh9XPX/MWZzEKCvVx5/mb7m/WY8cknlKWloYuIwK/S3FpRM8f4ak6IZnJXv0jG9g4FYPLV0XY5nL4yz+HDAchbswaLfJgXrdiTTz5J27ZtSUtLw93dncOHD7Np0yauvPJKNmzYoHR4QjgVjVrFjd2CAFjlaK2Mw28EIHf1aoUjEcJ5VbQxNjTZFWhwrJldtuH0US3zOaGisivVoSu7rBVHjpTsik3M5r+bre2Lb9zWAy9XXT23aFklp0+TufBLAIJmzXLIwf8tTZJdotVrH2gAoKDE/pNHHgP6o/bywpSZSdG+fUqHI4Ritm3bxmuvvUZAQABqtRq1Ws21117LnDlz+Mc//tFsx3399de5+uqrcXd3x8fHp9mOI4S9qWjlWHU4FfPFAy/tWMW8y6I9e+v9IC6EuDS2AfVpaXXul1E+s8vf0Sq7ypNduhaq7LINqHfkyq6O1squsrQ0TNnZygbTAEaTmWf/tx+zBcb1CWNolyClQ6rCYrGQ+sYcMBrxuG6QtU1f1EuSXaLVC/a2nlCSc+3/2xOVXo/nEOuqjLl//KFwNEIox2Qy4enpCUBAQABJSUmAdXD98ePHm+24paWljB8/nscff7zZjiGEPbq6fQCerlrS80rYHX9e6XAaTBcaimvPnmCxyKqMQjQTXai1S8KUlYW5sPaFnmyrMTposqvl2hitz09GfgkmB/pyoTKNwcM2J9ERhtR/vS2ev1Lz8ffQ8/It3ZQOp5r8jRsp2LwZlU5H8PPP28Z2iLpJsku0ehUzulJyihSOpGE8R5S3Mv6xGovZrHA0QiijR48e7N+/H4ABAwbw1ltvsXXrVl577TXatWvXbMd99dVXefrpp+nZs2eDb1NSUkJubm6VixCORq9V21oZVx5MVjiaxvG80drKmCetjEI0C423N2ovL6B85cJaZORXrMboOG2MltJS22PSR0W3yDH9DS62RbQy8x24uqtibtdx+052ZRWU8t4aa4wzRnTG18O+fj8tZjPp894HwHfifeijo5UNyIFIsku0erbKrhz7r+wC8LjmGtQGA2UpKRTu2q10OEIo4sUXX8Rcnux97bXXOH36NIMGDWLlypW8//77CkdX1Zw5c/D29rZdIiIilA5JiEtyc88QAH47lOxYrYw3WlsZC3bswJSTo3A0QjgnXbi1iqc08Wyt+2TklVd2eTpOZVfpuXNgNqNyc0PbpmUW59CoVbZWz7Q8J0h22Xll19zVf5FbXEbXEC/uvNL+3qPl/bGakqNHUXt44P/QQ0qH41Ak2SVavYpkV15xGfklZQpHUz+1iwteo0YCkLN8ubLBCKGQESNGcNtttwHQoUMHjh07RkZGBmlpaQwdOlTh6KqaNWsWOTk5tktiYqLSIQlxSa7tGICni5bU3BL2JDhOK6NL27bW5dnLyshbv17pcIRwSvpwa5LAeLbmZFex0URe+ftsR2pjLD19GgB9dHSLto5VtDKmOsCYldo4wpD64yl5fLvD2qb68i3d0Kjtqz3QYjKR/sEHAPhNmoTW11fhiByLJLtEq2dw0eLpqgUcp5XRe+xYAPJWrapzNoIQrYmfn98lvRGdOXMmKpWqzsuxY8cuOS4XFxe8vLyqXIRwRC5aja2V8dcDjtrKuEbhSIRwTrqIcABKz9b8hU7FSox6jRqv8vfdjqDkxEkAXDp0aNHj2obUO3Bll2tFZdeJE3Y5esVisfDPX49gtsDI7sEMbO+vdEjV5P76K6Vxcai9vfGbdL/S4TgcSXYJAYQ4WCuj2xVXoIuIwFxYSN4aeeMuxOWYPn06R48erfPSnHPAhHAkNzlqK+Nwa7KrYMsWzAUFCkcjhPPRh1uTXcazNc/sqjyvy5GGa5fElSe72rdv0eNWVHY58oqM+uho0OkwFxZiLF9IyJ5sPZnJ5hMZ6DVqnr+pq9LhVGMxGkn/cD4A/g8+iKZ8YSbRcJLsEgIILh9S7yjJLpVKhfettwLSyijE5QoMDKRLly51XvR6+xpWKoRSBnW60Mq415FaGTt3RhcZiaWkhPyNG5UORwino6toY6ylVd8R53UBlJ6MA8ClY8tWdgWWV3al5jnGZ5OaqHQ6W5Kw+OhRhaOpymKx2IbS3zMgkkh/d4Ujqi7n518wJiSg8ffH794JSofjkCTZJQQQ4mU9oaQ4SLILwPvWMQAUbNtul9+WCOGMEhISiI2NJSEhAZPJRGxsLLGxseTn5ysdmhAtwkWrYVhFK6MDrcqoUqnwGjECgNzfflM4GiGcj21A/blzWCzVqz7Ty9sYHWlel8VspuTUKaDlK7vaeDp+ZReAa4/uABQfPqxwJFVtOZnB7vjzuGjVPD64Zf9tG8JiNpP5xRcA+D8wGbW7/SXjHIEku4TA8VZkBNBHRODevz9YLJxf8r3S4QjRKrz88sv06dOH2bNnk5+fT58+fejTpw+7d8vKqKL1sLUyHkxxqFZGr5tGAZC/cRMmSVCLJvL6669z9dVX4+7ujo+Pj9LhKEYXFgYqFZbCQkxZWdWut1V2GRynUtp47hyW4mJUej26Fl5JOaj8i/h0B67sAnDr0QOA4kP2k+yyVnWdAKxVXRXPtT0p2LzZOqvLwwOfO+9UOhyHJckuIbgws8tRBtRX8C0vac1esgRzsWOfDIVwBAsXLsRisVS7DB48WOnQhGgx13UKwNNVS0puMTtOV/9Qa69cunRB37YtltJS8tetUzoc4SRKS0sZP348jz/+uNKhKEqt16MNslZ91tTKWDGgPtCB2hhLTlrndenbtUOl0bTosSsqu1IdvbKre0Wy61CNFX9K2Hwigz0VVV3X219VF0DmgoUA+IwfL7O6LoMku4QAQnwca2ZXBc+hQ9GFhmLKzib311+VDkcIIUQr4KLVMKpHMAA/7695GLU9UqlUeI2yVnfl/rpS4WiEs3j11Vd5+umn6dmzZ4NvU1JSQm5ubpWLM6gYUl9aw5D6CwPqHS/Z1dItjABtygfUp+eXOFQF7cVcOncCnQ5TdjbGc8qPXak8q2vCgCja2GFVV/GRIxRu3w4aDX4T71M6HIcmyS4hqFTZletYyS6VVovvhHsAyPr6G7v5xkQIIYRzG9vbOp/n1wPJlJSZFI6m4WytjH/+iSknR+FoRGs1Z84cvL29bZeIFm6Ray4624qM1Su7HHFml204fYeWT3YFGFxQqcBktpBZUNrix28qar0e106dAGt1l9K2ncpkb0I2Llo1j11vnyttV1R1eY0ciS40VNlgHJwku4Tgwsyu7EIjRaWO86YdwOeOO1C5uVFy7BiFO3YqHY4QQohWYEA7f9p4upBbXMbG4+lKh9NgLh064NKxIxiN5K1Zo3Q4opWaNWsWOTk5tktiLSsYOhpdREVl19lq12U4YLKrJM6a7NJ3aNmVGAF0GjX+Htb5ZmkOPrfLtWJu12Hlk11fbDkNwPgrw+2yqsuYkmJbRMVv8mSFo3F8kuxqhHHjxuHr68sdd9yhdCiiiXm6aPHQW3vxHa26S+Ptjc+4sQBkfPyxssEIIYRoFTRqFWNirN84/xSrfGtKY3jdfBMAuStlVUZRs5kzZ6JSqeq8HDt27JLv38XFBS8vryoXZ1DRxmhMrCHZlVcxs8sxBtRbzGZbssulfcsnuwACPa3JmLQ8B5/bVb4iY5HClV2nMwpYeywNgMnXtFU0ltqcX/QdlJXh3r8/buXPm7h0kuxqhCeffJKvvvpK6TBEM1CpVJVWZHSsIfUA/g89BDodhTt2UCirwgkhhGgBt5a3Mq45mkpesVHhaBquYm5XwfbtlNWwapwQ06dP5+jRo3Ve2rWzzxYoJVWsWGi8qLKr2Ggit7gMcJzKLmNSMpaiIlQ6HfpIZdpMg8rndqU52BfxF6u8IqOSI1cWbj2NxQJDOgfSPtCgWBy1sRiNZC9dClxYhExcHkl2NcLgwYPxlNUQnFaIt3VIfYqDDakH0IWG4nPbbQCk/XuuzO4SQgjR7HqEedEu0IOSMjOrDqcqHU6D6aOicO3eHUwmW7uIEJUFBgbSpUuXOi96vWNUKLUk28yu5GQsxgsJ8IqZUzqNCm83nSKxNVbJyRMA6Nu2RaXVKhJDxYqMaQ6+IqNLhw6o9HrMeXkYExIUiSGnyMgPe6xJ2Aevtc9Edd6GDZgyMtAEBOA5ZIjS4TgFxZNdH3/8Mb169bKV8A4cOJDfmviNx6ZNmxg9ejShoaGoVCqWL19e437z588nOjoaV1dXBgwYwM6dMv+oNamo7NpxKsshq7sCHn8MlZsbRXv3yipTQgghmp1KpeLWGGt110+xjrMqI4D3mNEA5Pz0s8KRCEeXkJBAbGwsCQkJmEwmYmNjiY2NJT8/X+nQWpw2MBCViwuYzRhTUmzbK1oY/T1cUKlUSoXXKKVxyg2nr9DGSdoYVTodLl27AMq1Mi7ZlUBhqYnOQZ5c08FfkRjqk/3DDwD4jBuLSucYSWF7p3iyKzw8nDfffJM9e/awe/duhg4dyq233srhw4dr3H/r1q0YjdVL5Y8cOUJqas3fKhYUFBATE8P8+fNrjWPJkiVMmzaN2bNns3fvXmJiYhgxYgRpaWmX9sCEw8kq/9Zpye5ErnlzHUt2KfPNw6XSBQcT8MjDAKS9/TbmwkKFIxJCCOHsbu1tndu19WSGQ1VGe918M2g0FB84QMmpU0qHIxzYyy+/TJ8+fZg9ezb5+fn06dOHPn36sLsVjpVQqVQXqrsqDd2vGE4f6OkYLYwAJSeVG05foU1FG6ODD6gHcOt+oZWxpZWZzHz5ZzwAD1wbbZcJV2NSEgWbtwDWxcdE01A82TV69GhuuukmOnbsSKdOnXj99dcxGAxs37692r5ms5kpU6Zwzz33YDJdWDHv+PHjDB06lC+//LLGY4waNYp//vOfjBs3rtY4/v3vf/Pwww8zefJkunXrxieffIK7uztffPHF5T9IYfeSc4pYf+xCYtNsgeeXHnK4Ci+/Bx5AFx5OWWqqDKsXQgjR7KIDPOgX7YvZAj/urT6U2l5pAwIwXHstINVd4vIsXLgQi8VS7TJ48GClQ1OELtxa7VlaaUj9hZUYHaf1s+TkSUC54fRQqY3RwSu7oNKKjAcPtvix1x5L41x2Ef4eetusSXuT/eNSsFhwHzAAfVSU0uE4DcWTXZWZTCYWL15MQUEBAwcOrHa9Wq1m5cqV7Nu3j4kTJ2I2m4mLi2Po0KGMHTuWZ5999pKOW1payp49exg2bFiVYw0bNoxt27Y1+v7mz59Pt27d6Nev3yXFI1re6YwCLp5yZbJYOJPhWNVRahcXgp6fBUDm519QdOCAwhEJIYRwduOvtA5v/mF3okPNjPQuX8k45+efsZjNygYjhJPQh1cfUp+Rb+2ecJTh9BaL5cJKjB2VS3bZVmN08JldAG49y5NdR45gqVS00hKW7LJWGd5xZTiuOk2LHrshLCYT2T/+CIDP+PEKR+Nc7CLZdfDgQQwGAy4uLjz22GMsW7aMbt261bhvaGgo69atY8uWLdxzzz0MHTqUYcOG8fFlVLFkZGRgMpkICgqqsj0oKIiUSv3mw4YNY/z48axcuZLw8PBaE2FTpkzhyJEj7Nq165JjEi2rbYAH6osqWjUqFdEB7soEdBk8hw7Fa/RoMJtJmjkLc4njnyCFEELYr5t7huCh13Ams5BdZ84rHU6DGYYMQe3pSVlyMoU75T2bEE2hoo2x9OyFNsb08sqkAAdpYyxLTsZSWAg6HfoIZVZihAuVXel5JQ71RUJN9O3aoXJzw1xYSOmZMy123JScYjYct3bv3Hmlcv+WdcnfvJmylBQ03t543jis/huIBrOLZFfnzp2JjY1lx44dPP7449x///0cOXKk1v0jIyP5+uuvWbJkCVqtls8//7xFem/XrFlDeno6hYWFnD17tsbqM+GYQrzdeGNcT9vPahW8cVsP2wqNjib4hefRBAZQeuoU6fPeVzocIYQQTszDRcstvayzu77fnVjP3vZD7eKC16hRAOTUsniREKJx9BHlM7vOXli04kIbo2Mku4qPHQfAJTpa0UHhFTO7Sk1msgurz6x2JCqNBtfyYpaiFmxl/HHvWcwW6BftS/tAQ4sdtzFyli0HwHvsrahdHONvxFHYRbJLr9fToUMH+vbty5w5c4iJiWHevHm17p+amsojjzzC6NGjKSws5Omnn76s4wcEBKDRaKoNuE9NTSU4OPiy7ls4jrv7R9I7wgeAF27qyl39IpUN6DJofHwIefU1ALIWLCB/61aFIxJCCOHM7uxn/YD764Fk8kvKFI6m4bzH3gpA7h9/yMIuQjQB24D6hARbNZKtsstBZnYVxcYC4NqrZ907NjMXrQYfd2uyzRnmdrn1tD6fxQdbZkVGs9li+wLGXqu6TPn55K9fD4D3rbcqHI3zsYtk18XMZjMltbReZWRkcMMNN9C1a1eWLl3K2rVrWbJkCTNmzLjk4+n1evr27cvatWurxLB27Vqp3mplKpJdKbmOv+qJ59Ah+Nx5J1gsJD3zLMZUWVlUWBUfP05pvHVVmtzff+fksBspqmUFXCGEaIgrIn1pF+hBkdHErweSlA6nwdz69EEXGYmlsJDcVX8oHY4QDk/fti0qvR5TTg7G8vcattUYHaSyq2jfPgDc+/RROJLKQ+od/7OJW3nysKUqu3acziI+sxCDi5abe4W0yDEbK2/1GiylpejbtcOla1elw3E6iie7Zs2axaZNmzhz5gwHDx5k1qxZbNiwgQkTJlTb12w2M2rUKKKiomwtjN26dWP16tUsWLCAuXPn1niM/Px8YmNjiS3P0p8+fZrY2FgSEhJs+0ybNo3//Oc/fPnllxw9epTHH3+cgoICJk+e3CyPW9inzsGeABxLyVM4kqYR9PwsXDp3xpSVRdKMGVjKHOfbdtE8ys6f5/StY4kbMRKAc089jfHsWc498Q+FIxNCODKVSmX75rxiGLAjUKlU+Nx2GwDZS5YoHI0Qjk/t4oJbr14AFOzcCVQaUO8AM7ssRiNFh6yVR252kexyniH1ruWVXSVHj2IuLW324y3ZZf2sPzomFHe9ttmPdylyf/kFAK9bbm6RsUytjeLJrrS0NCZOnEjnzp254YYb2LVrF6tWreLGG2+stq9areaNN97gxx9/RK+/UAYbExPDmjVrGF/L6gW7d++mT58+9Cl/wZo2bRp9+vTh5Zdftu1z11138c477/Dyyy/Tu3dvYmNj+f3336sNrRfOrYuTJbvUrq6EzZ2L2t2dwl27SP/gQ6VDEgoznqu54sJsbP43HUII53bbFWFo1Sr2JmRzNDlX6XAazOf220CrpSg2luLjx5UORwiH596/PwCFO3dRWmYmp8g6b8oRZnYVH/8LS1ERam9v9G3bKh1Opcoux0926cLD0fj4YDEaKWnm19qcIiO/HbIuNHdXP/tsYSxLT6dg+3YAvG+5ReFonJPiya7PP/+cM2fOUFJSQlpaGmvWrKkx0VXhxhtvxNXVtdr2Pn36EF7eI36xwYMHY7FYql0WLlxYZb+pU6cSHx9PSUkJO3bsYMCAAZf12ITj6RTkiUplnS2Qme/4JxUAl3ZtCX7NOr8r89NPyfn5Z4UjEkII4YzaeLoyood11ulX2+IVjqbhtIGBeN5wAyDVXUI0hQvJrp1k5Fvb77RqFT5uyg17b6iKFka33jGo1Ip/VCbQy3naGFUqlW0OWtGBA816rN8OJlNSZqZzkCcx4d7NeqxLlfvbb2A24xrTC32k486KtmfK/wULYUc8XLRE+rkDcNxJqrsAvG+5Gf+HHwIg6YUXZWB9a1bL0tUqpHRaCHH57h8YDcDyfefIcaDVw3zvuhOAnJ9/kUH1Qlwmt94xqHQ6ytLSSDlhTXz7G/So1fb/XsM2r6t3b2UDKWdrY3SCyi4At57WFtfiA807t+uX8tmRt/YJtdv2wJwVvwLgfctohSNxXpLsEuIiFa2MR50o2QUQ+PTTeI4cCUYjZ/8+hYJt25QOSdgRCzUnwYQQojH6RfvSJdiTIqOJH/Y4zuwu96uuQhcViTk/n9yVK5UORwiHpnZ1xS0mBoCz+48AjtHCCFAYW17ZZQfzuuBCG2O6E8zsgpYZUp+eV8K2uEwAbukZ2mzHuRylZ85QfOAAaDR4jRqpdDhOS5JdQlykS7AXAMccaN5IQ6jUasLe+heGIUOwlJSQ+PjfyVu3XumwRAsoiYvj3PQZlMTFQT3fbllMphaKSgjhjFQqFfdfHQ3A19vjMZsdI5GuUqvxvdNa3XV+sbQyCnG53Pv3AyD5L2tllyMku4ypqZQlJYNajVv5MHWlOdNqjHBhSH3pqVOY8pqnsOD3Q8mYLRAT7k2kv3uzHONy5fxqreryGDgQbUCAwtE4L0l2CXGRisquPfHnSc4pUjiapqXS6wmb9x6G66/HUlzM2SlTyPxiAZZaWtuEc4i/byK5v/5K/MT762xjzPrqK45f2a/FloQWQjinW3uH4uWqJT6zkI0n0pUOp8G8x41DpdNRfOgQRYcOKx2OEA6tYm5XamIq4BjJrqJ9sQC4dOmM2sND2WDKBXldaGN0hvfrWj8/dOVztovLV71sar/sTwbgll72WdUFkPf7KgC8br5Z4UicmyS7hLhIXEYBAKcyCrjmzXW2ZWudhVqvJ/zDD/C5+y6wWEh76y3OTn2CsvPnlQ5NNBNTVpb1v5mZde6X+sYcLEVFJL/4UkuEJYRwUu56LXdeaV396ss/zygbTCNo/fys7f5A1ldfKhyNEI7NLcY6tyuzzPpzgKde2YAa4MK8LvtoYQRoUz6gvrDURH5JmcLRNA1bK2MzzO1KySlmV7z1fe/NvUKa/P6bQsmpU5ScOAE6HZ5DhygdjlOTZJcQlSTnFPHvPy4shWu2wPNLDzlfhZdOR/Ds2QS9+CIqnY78tWs5fetYCv78U+nQRCM4wzd8QgjndN/AKFQq2HA8nROpjjMD0+/++wHIXfkbxpQUhaMRwnGp3dxwjelFtou1YyLQASq7Lszr6q1sIJW467UYXLSA8wypdy0fUl90sOlXZPz1YDIWC1wZ5Uuoj1uT339TyPvjDwA8Bl6Fxts+V4p0FpLsEqKS0xkFXDxexGSxcCbD+VZmUqlU+N07gegli9G3a0dZWhoJDzxI8uxXMOXnKx2eqEfSiy9yesytmEtLlQ5FCCGqifL3YES3YAA+3hincDQN59ajO+79+kFZGee/+UbpcIRwaB79+9uSXfbexmguLqb4yFHAfobTV7DN7XKyIfXNsSLjL/utqzDeYqdVXQC5q6zJLq8RIxSOxPlJskuIStoGeHDxqsgalYroAPscbtgUXLt1o+3/fsDnb3cDkL1kCaduGU3+pk0KRybqkvO/Hyk5cYL88kUGjElJpH/0ka0dNeeXFWR8+pmSIQohWrnHB7cH4OfYJM6ed5wvjfwmTwbg/JLvMeUXKByNEI7LvX9/zrsYAAgw2HcbY/Hhw2A0ogkMQBcWpnQ4VQQ625D6rl1Bo6EsLQ1jamqT3W9iViGxidmoVXCTnSa7SuPjKTl6FDQaDEOHKh2O05NklxCVhHi7Mee2nlUSXjNv6kKIt32WwTYVtbs7IbNnE/nll+giIylLSSHxkUc59+yzTXoSEs3BWop45t57yXj/A5KefQ6ApGeeIX3uXIqPHGnY3VRapdFSVkbGJ59QdLB5BocKIVqHmAgfrungT5nZwn83n1Y6nAYzDL4efXQ05rw8cpb+qHQ4Qjgst969yXa1VnZ5pScpHE3dCnbsAMD9ir6o6lm5uqW1KR9Sn+4kbYxqd3dcOnYEoOhA07UyrjpsbT3v39aPNp6uTXa/TamiqstjwAC0vr4KR+P8JNklxEXu6hfJ1plDaR9oXYXFTadROKKW4zGgP+1+Wo7fpEmgUpH78y/EjRhJ+gcfYi50nG/lWxfrG7KyJOvKM4Xbt1e51pST0+h7LI2LI/29eZwZP976c2Iiya++SmmCcy3WIIRofo9f3wGAxbsSyMx3jA9qKrUav0nW2V1ZX36Fpcw5hkIL0dJMOj25euv7aZft9t0xULjN+v7JY+BVCkdSna2N0UmSXQBuPStaGZsu2bXmqPUL+uHlLfT2KG+VdRVGT2lhbBGS7BKiBiHebtzR17qS1JJdCU43oL4uajc3gmY+R/T33+N2xRVYiovJmD+fkzcOJ/O//5WWDoUoNYw+fvJk4m4cTvZ3i4mfNEmRGOzFmTNnePDBB2nbti1ubm60b9+e2bNnUypz04So1TUd/OkV7k2x0cxCB1qZ0fvWW9H4+GA8d47c8g8nQojGyShPcGvMJtRr7ffvyFxURFFsLAAeV9lxsivXOdoYAdx6xwBQtL9pkl05hUZ2nbGO8hjWNahJ7rOplZ49a22XVavxHHaD0uG0CpLsEqIWpvLkwsFzuVzz5jqW7GpdVS1uPXsQ9e03hL33HrqICEyZmaS98y5xN9xA+kcfYcrOVjrEWhlTU21vWpxB8bFjnBh4NVmLFrX4sSu+6QRr9djZJ/6Budh53mw1xrFjxzCbzXz66accPnyYuXPn8sknn/D8888rHZoQdkulUvH49dbZXV/+eYacIqPCETWM2s0N3/vuBSDjo4+xmEwKRySE40nOsb5f8CvJoywujpI4+1ysonDPXixGI9qQEHRRUUqHU00bLyes7OpVviLjoUNN8vq64a80TGYLnYIMRPrb56zlvPIWRvd+/dD6+yscTesgyS4hapCcU8S//zhu+9lsgeeXHmpVFV5g/ZDiNXIE7Vf+SsicOeijojDl5JDx/gecGDyE5Jdepvj4X0qHWc3J6wdz5u6/NXxelZ1Lev55TNnZpL72f/XvfPGciSaeO5G3ejXnv1vcpPfpKEaOHMmCBQsYPnw47dq1Y8yYMcyYMYOlS5cqHZoQdm1E92A6BRnILS7js032+WG3Jn4TJ6L28qI0Lo7c335XOhwhHE5qebKrjdYMQN4ffygZTq0Kt28DrFVd9javCyCofP6UMyW79O3bozYYsBQWUnLy5GXf3+oj1hZGe63qAsj9o7yFcfiNCkfSekiyS4ganM4owHxR15jJYuFMRuucW6XS6fAZN5Z2K38l9J13cOnSBUtxMdk//MDpW28l/v5J5K76A4udtXMVOkB1V/ay5WR9+23dO9XVwajAm7K0f/2LU6NHc/bpp7GYzYq1WNqDnJwc/Pz86tynpKSE3NzcKhchWhO1WsX04Z0B+GLLGYdZUUzj6Wmb3ZXx0UdS3SVEI6WUt92FtPEGIPeP1UqGU6sCO57XBRcqu1KdqI1RpVbj2rMHAEWx+y/rvkrLzGz8Kx2AG+w02WVMTqZ4/wFQqfC8UZJdLUWSXULUoG2AR5UVGcE6BjyzoKTVVXdVptJo8L7lZtouW0rUN19bhytqNBTu2MG5J5/kxPWDSXnjDYqPHVM6VMB6IrVnFrOZ5FmzSP2/f2JMTbNtL9i5k/SGfrBqqlxXI5NmJSdOkvfb7/w14CqO9+5Dzi+/NFEgjuPkyZN88MEHPProo3XuN2fOHLy9vW2XiIiIFopQCPsxvFsQvSN8KDKa+HDd5X+L31L8Jk5E7e1N6alT5K5cqXQ4QjiUlPLKrvB24aDRUHL0KKWJiQpHVZUpO9vWCeA+wD6TXYHllV15xWUUG50n6e7Wq3xu14HLS3btOpNFXnEZAQY9vSN8miCyppe32prodbviCnRt2igcTeth358EhVBIiLcbc27riaZSAsACTF20r1XO77qYSqXC/corCZ/3Hh1W/4H/I4+gDQzEdP4857/6mtNjx3Fq3G1kfflllSROywfa+Jc4UwOqbs5/9x3pH310KRFVZTZf+N/CC4P/EybeT8b7H5Dz8yUkkKolrWpPYlWpyLrE6ixzXh6WkhKSnnmWjE8/u6T7UNrMmTNRqVR1Xo5dlMA9d+4cI0eOZPz48Tz88MN13v+sWbPIycmxXRLt7I2+EC1BpVLx7EhrddeiHQkkZDpGpbTGYMB/8iQAMuZ/JCszCtEIFZVdoUHeuPfrB9hfK2PBzp1gsaBv3x5dkH0mIbxctbhore9p03Kdp5XRLaZiSP3lJbsqVmEc0rkNmourFexEbvnvvdeI4QpH0rpIskuIWtzVL5ItM4fw1h29qmxvrfO7aqMLDaXNtKfpsH4dEZ9+Yq320ukoOXqU1DlvcnLwYOLvm8j5xYspy8pq0dhUmsa9xOX89BN/9R9Axief1LlfyquvkfH+B5TGx1e7zmI2k710GSWnTtd/wHoSTKUJ1e//8jVfy2H63Lmc/+GHZrv/5jJ9+nSOHj1a56Vdu3a2/ZOSkhgyZAhXX301n31Wf4LPxcUFLy+vKhchWqOr2wcwqGMAZWYL/159vP4b2Anfe+9F4+1N6Zkz5Pz0s9LhCOEwKiq7grxcbXOKcu0t2bXtwrwue6VSqSoNqXeeVka3GOtnrNK4U5jy8y/pPiwWiy3ZNaybfbYwlqWnU7RnL4C0MLYwSXYJUYcQbzfCfd2qbTdZLOwpX95WWKm0WgzXX0/4vPfouGkjQS++iFufPmCxULhrFymvvMqJQdeR8NDDZC9d1qAKqssPqnEvcUkvvgRA+nvzat3HUrkaq6h6wjP3l19Ifv55Tt10U7Xrspcvp3Dfvgv3VV81VUvOwmqi2V8pL73cJPfTkgIDA+nSpUudF71eD1grugYPHkzfvn1ZsGABajtvlRXC3jw7ogsAP+1PIjYxW9lgGkhjMOD/iLWCM/299zAXFNRzCyEEXKjsCvZyxXPYMFCpKN5/gNIE++mQKLTzeV0V2jjhkHqtvz+68HCwWCg+ePCS7uNEWj6JWUXotWoGdQxo4gibRt6aNWCx4BrTC11IiNLhtCryLl2IetQ0vwvgH4v3tfp2xtpofX3xu3cC0d8tosO6tbR55hlcu3cHk4mCLVtIfv55/rrmWhIeeYTzP/zQbBVf5sJGtslUSmTVqvIcrRoSRLUNxS/ct4/kmbOI/9s9NR7vklf/qe92dV3figfLX4qKRFdkZCTvvPMO6enppKSkkJKSonRoQjiMnuHe3NYnDIsFXv7pEKaLV4OxU7733YcuIoKy9HQy/vtfpcMRwu5ZLBZbZVewtyu6Nm3wuOYaALJ/+J+SodkYU1IoPXMG1Grc+/dXOpw6tfF0viH1AG69rNVdl9rKuO6YdVzK1e39cddrmyyupmRrYRwuLYwtTZJdQtSjYn7XxSkDaWdsGF1oKP4PPkDbH/9H+99/I/DJf+DSsSMYjRRs2kzKSy9z4tpBxN83kayvvsaYnNxkx059/fXG3aAByR9LlYRY9USSqpZqMmNN32JWvq9LTXZd/EGxnvupXI1mPHv20o7ZSq1evZqTJ0+ydu1awsPDCQkJsV2EEA0386YueLpoOXA2h8UO8qWRWq+nzTMzAMj6YgHGc+cUjkgI+5ZTZKSkzPo+J8jLWpXkc+d4ALKXLrWLFbwLtm4FwLV7dzR2PmIg1MfaaZKU7VyfOypaGYv2H7ik2288bl2FcUhn+5y3Vnb+PIU7dwHgKcmuFifJLiEa4K5+kXxwT59q26WdsXH00dEEPP447X75mXa/riDwqaesFV9mM4W7dpH6xhucHDKU0+PvJOOz/1ByugFzry5iaUh1Vm0aWdmlaswQzJra3eobEF+RuKojCZe74qIh9hfvW1eIlfYtS02tY0cBMGnSJCwWS40XIUTDtfF0ZdrwTgC8veo4WQXKf+htCM8bb8S9Xz8sJSWkvftvpcMRwq4ll1d1+brrcNVpAPAcMgRNQACmzEzy1m9QMDqr3N9XAeA5dIjCkdQvonysSkKWYyzu0VCVh9Q39v1UQUkZu+Ot3SHXdQps8tiaQv7atWAy4dKtK3pZjbvFSbJLiAbqG+Ur7YxNyKV9ewIee5S2P/6PDmvXEDRrJm5X9rXOczh4kPR//5tTo24i7pZbSJs3j6JDhxt2EmzmlbIsldsYa5zX1PATdZXHU0NFVkNaG0viTlW9z5KqsxxMGRm136ckaYQQCrnvqii6BHuSXWjk7VXH6r+BHVCpVATNmgkqFbkrV1K4Z4/SIQlhtyrmdVVUdQGodDp8brsNgOzvv1ckrgqm7GzbcHrPESMVjaUhIv3dAUjIcq7KLpeuXUGnw5SV1eiK2W1xmRhNFiL93Ikuf37sTe5vvwPgNXyEwpG0TpLsEqKB6mpnnPXjQWlnvAy6sDD87r+f6G++oePmTQS/+ioegwaBTkfpyTgyP/6EM3fcwcmhN5Dyz9cp2L691uXfqySjAGNqWtMGW8/MrlrVlFhqYBtjnbPH6qkuq/jWUggh7IlWo+a1W3sA8N3ORLbFZSocUcO4duuGzx13AJD80suYS5xnWLQQTSm1vLIrxNu1ynaf8da/n4KtWylVcJxC3tq1UFaGS+fOuLRrq1gcDRXpZ03mnM0qdKqKcrWLC65duwJQFNu4uV0b/7K2MF7XKeDSZ982o7L0dFtC1eumUQpH0zpJskuIRqitndEMvL7iqCS8moA2IADfu+4k8j+f0WnrFkLf+heew4ejcnOjLDmZ8998Q8KkyZy45lqSnptJ3po1VeZQXZwEy5g/v0njq9wmWdNqQrW9AamxvbKBya4a533ZbnbpA+qd6c2SEMLx9G/rx9/6W9s6Zvywn/yS5q3MbSptpk9DExBA6alTZHzyidLhCGGXbCsxXpTs0kdE2MWg+oovA71GOkbFTbivNdmVV1JGdqFR4Wialq2VsZZFnmqz6YQ12XV9J/uc15Xz669gNuPWuzf6yEilw2mVJNklRCP1jfKtcQzSioPJXPPmOmlpbEIaLy+8x4wh/P15dNr2J+EffYT37beh8fXFlJNDzk8/cXbqE/w18GoSp0wle9lyytKrtu1dapl8rbO/KlV2ZS9eUu1qY1JSw49RKdmUv3lzDXs0wbdUdSW0JNclhFDYCzd3I9zXjXPZRfxzxRGlw2kQjY8PwS+9BEDmf/5L8THHaMMUoiVVrMRYuY2xgs+ddwKQvfRHRQbVO1oLI4CrTmNbkTHxvHPN7XK/wlpIULR3b4NvcyajgPjMQrRqFQPb+zdXaJcl92frXF2vMaMVjqT1kmSXEI0U4u3Gw4NqLneuaGncnyhD65ua2tUVz6FDCH39dTpu2UzU11/hd//96MLCsBQXk792LcmzZnHqppuq3fZol66NPl7pmfgat1dOguVv2FDtenN2To37Vp4lZqwYBl8pEVXy11+NjhGg5MTJS7pdeQCXcVshhLh8Bhct74yPQaWCxbsSWXfMMRbL8BoxHM8bb4SyMpJfeLHW1nohWitbZVcNyS7PoUPQBAZgSs8g55dfql3f3GwtjF26OEQLY4UIv4q5Xc6V7HLrY012FR8/jrmgoEG3qajqujLaF4OLttliu1QlJ09SfOQIaLV4jZIWRqVIskuISzD52ra1jkoyA7fO/5NPN8a1aEytiUqjwb1fP4JmzaT9mtW0Xb6MgClTcOnSpdbbHO3SleRXXiF/y9YGnUjPf/ddzVfU84GmSoKrUhWYxXRhu20GV+V9a8o7aS7tJbqu9kRLfStACiFEC7uqnT8PXGP9wPncjwdJz3OMOVjBL7+E2suL4sOHyfjsM6XDEcKuVFR2XdzGCNZB9f6TJgOQ8elnLZ4stg0Nd5AWxgoVc7sSnWxIvS44GG1oCJhMFB082KDbbDxeMa/LPldhzPllBQCGQYPQ+voqHE3rJckuIS5BxbD6uv6A5vx2jOeXHZA5Xs1MpVLh2qULgU9Mpd3yZbRfs5rgV2bXuG/24iUkPvQQx/sP4Mxdd5P27rvkb9qEKS+v2r7nv/66xvuotb3RtsOFBFJpYuKF7eZKg+0t1e/LUlxc7a4Kd+2u+1gNiKHuNkZJdgkh7MMzIzrTsY2B9LwSnvhuL2Wmel5r7YA2MJDgF18AIOPD+RTu2qVwRELYj9pmdlXwvfsuND4+GBMSyP3ttxaLq+z8+UotjI6V7IrwdQOcr7ILwL3PFQAUNqCVsaTMxLZT1kVNrrfDZJfFbCbnl58B8JYWRkVJskuIS3RXv0i2zhrKI4Pa1TpZadGORK6es06qvFqQPjwc37vvpuuxo7ZLu5W/4nHNNXiNHo0uNNT6zdH+/WT+578kPvIofw24itO33V7tvvJqaFNszLePxYcOXbhdpQ9uhTu2l2+8kGzK+emnarcv3L69wceqovIssI0bL7qu5v2EEEJJrjoNH9/bFw+9hu2nsnh71XGlQ2oQ7zFj8B47Fsxmzk2fQVlWltIhCaG4YqPJNkS9pjZGALWHB36TJgGQ8cmn9X+Z2ERyfvoJTCZcunbFpa3jtDDChTbGs042swsutDIW7Yutd989Z85TWGoiwOBC12CvZo6s8Yr27KEsKRm1wYBhyBClw2nVJNklxGUI8Xbj+Zu7snzK1bXuY0GqvJTm0q4dkZ//l7C336LDurV0WLuGkDfn4H37beiiIsFstvbVX+TsY49z+rbbSf9wPnkbNlCWno6lEcvMJz0388IPld7ElZwsT362QLKp2uDXSseU1RiFEPakQxsDb4+3rsr16aZT/H4oWeGIGib4pRfRt2tHWVoaSTNnttiHdmEfzpw5w4MPPkjbtm1xc3Ojffv2zJ49m1IFBq/bi9Tyqi5XnRpvN12t+/neOwG1lxelcXHk/fFHs8dVlpFBxvyPrMe+++5mP15Tc9aZXVBpSH1sbL2voWuOpgFwXacA1LXNlVFQzs/Wqi7PEcNRu9ac7BUtQ5JdQjSBmAhfZo2qfV4USJWXPdGFheEzdiyhr79Oh1Wr6LBxA6HvvoPP3XdV27f4yBEyPvyQs489zolB13F67Lgq1x/t0pXSs2cvJI6qzOGqlFiqNL/LXFxUfd9GqDdJVWfrYj1zwoQQQkE39QyxLQIz44cDHEnKVTii+qk9PAib+29Uej0FmzaT8cknSockWtCxY8cwm818+umnHD58mLlz5/LJJ5/w/PPPKx2aYpJzLgynV6lqT0ZoDAb87r0XgIyPP2n2RHHaO+9izsvDtXt3fO6oXtFv7ypmdp07X4TJ7Fxv4lw6dULl7o45L4+Sk7UvvmSxWFh1OAWAEd2DWyq8Bis7f942r8v71lsVjkZIskuIJvLo9e2ZdVOXWlsa4UKV19urZJlye6ILCsL75psJeeUVW+tjp927CX33HYJeeAGvMaPRd2gP6ppfMuOG3chf/Qdw5u6/VasQM2VnA1SpCMv5cal12yW8UbGYzfVXhNU1oL7SG8nSU5J4FULYn+dGdmFgO3/yS8qYvHAn57LtvyratXNngl56EYCM9z9o0RlEQlkjR45kwYIFDB8+nHbt2jFmzBhmzJjB0qVLa71NSUkJubm5VS7OpKKyK6iWFsbK/Cbeh9rDg5Ljx8lZtrzZYircu5ec5db7D375JVQaTbMdq7kEebmi06goM1ucrltEpdXiFtMLgKK9+2rd78DZHM5lF+Gu19jlvK7z332HpbgYl25dce/XT+lwWj1JdgnRhB69rj1/zhrKPf0j69xv/vo4aWu0cxqDB94334zfffcS9tZbtF+xgs67dxG1aJHtA42NToc5L4+i2Nhq9/PXVQM5eeNw0t97r8r24uN/YS5s2PLKlVlKSuqtCKuz8qtSgq3gzz8bfXwhhGhuWo2aT+7rS6cgA6m5JUz6Yic55fN/7Jnv+PH43T8RgKSZsyjav1/hiIRScnJy8PPzq/X6OXPm4O3tbbtERES0YHTNr66VGC+m8fEh4O+PA5D29tuUnT/f5PFYyspIee3/APAZfwduMTFNfoyWoFGrCPd14lbG8iH1RftqH1L/2yFrVdeQzm1w1dlXwtJcXMz5b74FwP+BB+usahQtQ5JdQjSxEG833ritZ71VXtLW6HjU7u64X9EHvwkTqgzA77JnN21/+omwf79LwJQp1W5nrLwqY7nTt97K6TFVy5sT/z7F1udfm+wfl9Zf5l+pZbK6Sq2VZXXtJ4QQyvF207Fwcn+CvVw5kZbPw1/tpqjU/l+z2jz7LIbBg7GUlJD49ymUnj2ndEiihZ08eZIPPviARx99tNZ9Zs2aRU5Oju2SWMP7BEdW30qMF/ObOBGXTp0wZWeT9vY7TR5P5oIFlBw7htrbm8Bp05r8/ltSePmKjGeznO8L84oh9YW1DKm3WCz8Vj7LcWQP+2thzPnpZ0xZWWhDQ/AaMVzpcASS7BKi2TSkyquirfHJxfukysuBqfR6XDt3wuummwh8YuqFJNjRI3TcuoWor78i9O236r2f/HXrSHr2uSrbjnbpWuXn1H/+k+L6qgXqSoZVus6Y7BjDn4UQrVOojxsLH+iHp4uWnWeymLxwJ4WlDV8RVwkqjYawd9/BpUsXTJmZJEyahDElRemwxCWYOXMmKpWqzsuxY1XHUpw7d46RI0cyfvx4Hn744Vrv28XFBS8vryoXZ5JSaWZXQ6h0OoJffQWAnKVLKdy1q8liKdy1i/T35gEQ9MwMtL6+TXbfSoh04iH1br1jQKXCmJBAWUZGteuPJucRn1mIi1bNkC5tFIiwdhazmawFCwDwv/9+VLraF2YQLUeSXUI0o4oqrylD2te530+xSQyUKi+no1Kp0Pr7496vH96jR1etBjt6hI5bNhO16Fvb/j7j72hQf3/8fROr/Hz6rqqD9bO+/qbW21ZucSzcvr2hD0UIIRTRJdiLhQ/0w+CiZfupLCZ9sYv8EvtOeKk9PIj49BN0kZEYz54l4f5JGNPSlA5LNNL06dM5evRonZd27drZ9k9KSmLIkCFcffXVfPbZZwpGrjxbZVcDk10A7n364HPnnQAkv/Iq5kasfl2bsvR0zk6bBiYTXmNG43274w2lv1hFsivxvPMluzSenrh07AhYZ6xdrGKF3us6BWJw0bZobPXJX7+e0jNnUHt64n37HUqHI8rZ12+JEE7qmRFd8HLT8ebKY3UugDfnt2McSc5l5qguhHi7tVh8ouWpVCq0AQFoAwLoeuxotestFgulp89gTEyg5NRp0v71L9t12sBAytLTbT8X7z9Q5bYXzwerLPmlly4/eCGEaEF9o/z4+sH+TPx8JzvPZHH/Fzv54v5+eLvb7zfnuqAgohYuIP6+iZTGx5MwaTJRXy5EG2h/A5VFzQIDAwls4L/XuXPnGDJkCH379mXBggWoa1nQprVIbcTMrsraTJ9G3tq1lMbFkfTsc9ZVTi/xubSUlXFuxjOY0jNw6diBkFdecYoZShFOXNkF4H5lX0r++ouCbdvwGl61FbBiXtcoO2thtJhMZHxsXYXX9+670Bg8FI5IVGjdr8SNNG7cOHx9fbnjDsnWisZr6PB6qfISYE2GubRri+H66/GfPKlKVVjHzZvocmA/7Vb+Svj8Dwl99x0Cp1eaQVHHG0NTevWycCGEsHd9In355qEBeLlq2RN/nnEfbyUh074/7OlCQ4n8ciHa4GBKT53izD0TKD1zRumwRBM7d+4cgwcPJjIyknfeeYf09HRSUlJIaaXtqyazhdQ8a1VWY5NdGm9vwt59F5VOR96qVaS++Wbdi+7UwlJWRvLs2RTu2IHK3Z2wefNQu7s3+n7ska2yywlndgEYBg8GIH/d+ir/9ifT8jiRlo9Oo+KGrkEKRVez898uovjQIdQeHvjed5/S4YhKJNnVCE8++SRfffWV0mEIB9bQtkaQWV6ibiq9Hpd27fC84Qa8b76ZgIcfvpAQO3KYLkcO03l/LG2XLSX8k49tt/O+/bZmj81cXNzsxxBCtD4xET58/9hAQrxdOZVewLiPtrI3oelXbmtK+vBwor5ciC4iAmNiImf+dg9FBw7Uf0PhMFavXs3JkydZu3Yt4eHhhISE2C6tUUpuMSazBbUKAg0ujb69x1UDCHlzDgDnv/qarAULG3V7c2kp556eRs6PS0GtJvSNN3Cp1G7q6CLKV2PMyC+x+xmGl8J9wABU7u6UpaZSfOiwbfuPe62LfVzdPgBvN/up6jUmJZFW3lHRZsZ0dG3sa5ZYayfJrkYYPHgwnp6eSochnMAzI7ow66Yu9e5XUeX1/NIDkvQSjaJSq1G7uODatSuegwfbEmGhr79eZW5Ypx3bCf/oI8I/mo9/HcN0GyPln/9skvsRQoiLdQn2YvmUa+gR5kVmQSl3f7adb3fEX1L1R0vRR0UR/d0iXLt3x3T+PPH3TyL3jz+UDks0kUmTJmGxWGq8tEZrj6YC0DPcB63m0j5qet98M22efRaAtLfeIuX//om5qP73wab8fBIffZS81atR6XSEzXsPr5EjLikGe+XtrsPL1TqJ6Ox55/tsoHZxwXDttQDkr18HQGpuMQu2ngbgngF1d8i0JIvFQvKrr2IpLMTtiivwuWiGrlCe4smuOXPm0K9fPzw9PWnTpg1jx47l+PHjTXqMTZs2MXr0aEJDQ1GpVCxfvrzG/ebPn090dDSurq4MGDCAnTt3NmkcQlT26HXt2TZrKGN7h9a776KdiZL0Ek1OpVKh8fbGc+gQPIcOpc30aVXaJSsunWP3Ef39EsI//ACNn1+99+vRv38LRC+EaK2CvFz5/tGB3NgtiNIyMy8sO8QT3+0jr9iodGi10gYEEPXVl3gMGoSlqIhz/3iS1LfexlLmfJUZonVbsd86RHx0r8urbPObPAn/Rx4B4Py333J67DgK9+6rcV9LaSlZ33xL3PARFG7bjsrdnYjPPsXrxhsvKwZ7ZZvbZeet3JfK84ahAOSttSa75q7+i2Kjmb5RvgzvZj8tjLm/rqRg4yZUOh0h//faJc+XE81H8QH1GzduZMqUKfTr14+ysjKef/55hg8fzpEjR/DwqD7cbevWrfTv3x/dRct5HjlyBH9/f4KCqv8BFBQUEBMTwwMPPMBtt9XcwrNkyRKmTZvGJ598woABA3jvvfcYMWIEx48fp42UI4pmEuLtxnt396FrqBdzVh6rd/9FOxNZtDORKYPb88zI+ivDhGgKaldX3Hr1AsBz2LAa97FYLJjz88ld+Rteo0e3ZHhCiFbIXa/l03v78t8tp/jX78dZcSCZQ+dyeHt8DP2i60/KK0Ht4UHER/NJm/seWV98QdYXX1B84ACh776Drob3r0I4mpScYnbFZwFwU8/LS3apVCraTHsa9379SH7xRUrj44m/5x70bdvicfXVuPbogSkzA2NSEvmbt2BMTARAFxVJ2Ntv2963OKNIP3cOJ+U67ZB6j+uuA42GkuPHOXLgJN/vtv7bPn9TF7tZZKD4yBFSXnkFAP/HH8Olff0jakTLUzz9+PvvvzNp0iS6d+9OTEwMCxcuJCEhgT179lTb12w2M2XKFO655x5MJpNt+/Hjxxk6dChffvlljccYNWoU//znPxk3blytcfz73//m4YcfZvLkyXTr1o1PPvkEd3d3vvjii8t/kELUozFVXgDzN8QxeaFUHgr7oVKp0Hh64nvXnXbzRkQI4dzUahWPXNee7x+9ilBvV85kFnLnp9uY/dMhCkrss2JKpdMR9Owz1oHZHh4U7t7NqdFjyF6+vNW2vQnn8duhZCwW6BvlS6hP06wqbhh0Le1++RnvceNArab09GnOf/stybNmkfbOu5xf9B3GxEQ0AQEEvzKb9itWOHWiC6BriBcAKw8mKxxJ89D6+uJ+xRUAvPnzQcwWGNE9iL5R9vFFRumZMyQ8/Ajm/Hzcr7ySgIceUjokUQvFk10Xy8nJAcCvhlYZtVrNypUr2bdvHxMnTsRsNhMXF8fQoUMZO3Ysz5b3djdWaWkpe/bsYViligW1Ws2wYcPYtm1bo+9v/vz5dOvWjX79+l1SPKJ1qqjyasgsL4D1x9J59Kvd0tYohBCiVesb5cdvT17HnVeGY7HAl9viGT53E78eSLbbBJLXiOFE/+8HXHv0wJybS/LMWZx9/O8YW+kKfsI5rDhgTb7cfJlVXRfTeHkROucNOm3fRtgH7+N7z99wHzAAr9Gj8X/sUULmzKHDqt/xvftuVDr7GV7eXO7qF4FOo2J3/Hn22fkiHZfKMHQoBwLasylfj0at4lk76WgxpqaS8MCDmDIzcenWlfCPP0Kl1ysdlqiFymJH7wLMZjNjxowhOzubLVu21LpfQkICgwYNYuDAgWzbto3BgwezcOHCBlUTqFQqli1bxtixY23bkpKSCAsL488//2TgwIG27c8++ywbN25kx44dAAwbNoz9+/dTUFCAn58fP/zwQ5X9L5abm4u3tzc5OTl4eXk14BkQwio5p4gP1p5k0c6EBu0/a1QXHr1eymeF42pNr5et6bEK0dI2n0hn5o8HOZdt/SLoyihfXrqlGzERPsoGVgtLWRmZn39B+ocfgtGIys0N/4cfwv+BB1C7uiodnuJay+ulMzzOpOwirn5zHSoVbJt5A8He8vvbnKZ/v58f957l5p4hzJ9whdLhNLnjB05w54K95LgYuKdPMG/c1VfpkCg+/hdn//EExvgE9FFRRC36Fq2/v9JhtUoNfc20q8quKVOmcOjQIRYvXlznfpGRkXz99dcsWbIErVbL559/3iJtM2vWrCE9PZ3CwkLOnj1bZ6JLiMsR4u3GG7f1ZNusodzTv/5VR+b8doy3V9U/80sIIYRwZoM6BrJ62nU8Nawjrjo1u+PPc+v8rTz05W4Ons1ROrxqVFotAY8+Qtsf/4fbFVdgKSoi4/0POHXTzeT89JMMsBcOo6Klrl+UnyS6WsBDg9oC1tbRRCeb3ZWaW8wDKxPJcTHQ8XwiU1TxSodE9vLlnLnrLozxCWhDQ4j4/HNJdDkAu0l2TZ06lRUrVrB+/XrCw8Pr3Dc1NZVHHnmE0aNHU1hYyNNPP31Zxw4ICECj0ZCamlrtOMHBwZd130JcjspJr971fCs9f30cs3861DKBCSGEEHbKXa/lqWGdWD9jMLf1CUOlgjVHUxn94RYmL9jJlhMZdtfe6NqpE1HffkPoO++gDQ7GmJRE0nMzOXXLaHJ+/lmSXsLu2VoYL3MVRtEwXUO8GNQxALMFvth6WulwmkxOoZGJn+/kXHYRkVojr237nPx336I0XpmEV1lmJkmznid55iwsxcV4XHstbX/8EX14mCLxiMZRPNllsViYOnUqy5YtY926dbRt27bO/TMyMrjhhhvo2rUrS5cuZe3atSxZsoQZM2Zccgx6vZ6+ffuydu1a2zaz2czatWulekvYhRBvN5ZPuYZJA6Pq3O/LbfEyuF4IIYTAeu789129Wf309YzrE4ZaBeuPp3Pv5zsYPncTX2+PJ6fIqHSYNiqVCu9bbqb9yl8JfPppNN7elJ45Q9Kzz3Fy+HAyP/8CU479VacJsfVkBrGJ2ahUMKqHFAq0lIcHtQPg+12JdvVadqkOJ+Uw9qOtHE/No42nC18/MYSQru0x5+SQ+PcpmPLzWywWc0kJGf/5D3HDR5CzbBmoVARMnUrEp5+g9fVtsTjE5VE82TVlyhS++eYbFi1ahKenJykpKaSkpFBUVH3ottlsZtSoUURFRdlaGLt168bq1atZsGABc+fOrfEY+fn5xMbGEhsbC8Dp06eJjY0lIeHCPKRp06bxn//8hy+//JKjR4/y+OOPU1BQwOTJk5vlcQtxKV65tQdThtQ9m2v9sXRekQovIZrFmDFjiIyMxNXVlZCQEO677z6SkpKUDksIUYcObQzMvas3a6cPZuLAKDz0Gk6k5fPS8kP0e30NUxftZf2xNErLzEqHCoDa3Z2ARx+h/dq11qSXjw9lScmkvf02JwYPIemFFyjcvdvuqtNE63TwbA6PfLUbgHF9wmjjJS2MLWVQxwC6BHtSUGrinVXHHfY1wWKx8O2OeMZ99CenMwoI9Xblqwf7ExXkTdgH76MNCqI0Lo6kGc9gMZmaNZayzEwyPv6YuBuHk/7uvzEXFODavTtR33xN4NQpqDSaZj2+aFqKD6ivbdbWggULmDRpUrXtq1evZtCgQbheNLRz3759BAYG1tgCuWHDBoYMGVJt+/3338/ChQttP3/44Ye8/fbbpKSk0Lt3b95//30GDBjQuAdUiTMMmxT26dNNccxZWfeMrilD2vPMCPtYuUSI+jjK6+XcuXMZOHAgISEhnDt3zlZV/Oeffzb4PhzlsQrhrHKLjfyw+yxLdiXwV+qFSgEvVy3DugYxokcw13QIwOCiVTDKC8zFxeSuWEHWV19T8tdftu26yEi8bhqF1/DhuHTt2iLza1taa3m9dNTHeTqjgDs+/pPMglKubu/Pgsn9cNFKMqAl/X4ohce+2QPAA9e05aVbHOu14GRaPq//eoT1x9MBGNqlDe+Oj8HX48IKh0UHDxI/4V4spaW4xcTg98ADeA67ockST6b8Agq2bCbvjz/IW70Gi9FaJacNCiLw6afwHjMGlVrxGiFRSUNfMxVPdjkzRz1xCceQnFPEKz8dZtWR1Fr3kYSXcBSO+nr5888/M3bsWEpKStA1cLlzR32sQjgbi8XCoXO5/Lj3LCsOJJORX2K7TqdRcWWUH9d1CuSqdn70CPNGp1H2w47FYqFo716yly0jb+VvmAsvDKXWRURgGDIYw6BBuPfr5zQrObaW10tHfJy7zmTx1OJYzmUX0SPMi+8evgpP14adB0XT+nZHPC8ss3Z1TL4mmpdv6Wb3Ca+sglI+WHeCr7fFU2a2oFWrmDGiM48MaodaXT323JUrSXpupi0RpYuIwHP4jXj0749b375oDIYGH9uUm0vRwYMUxcZStHcfhbt2YSkttV3vFhOD770T8BwxArVeX8c9CaVIsssOOOKJSzieyQt3sv5Yeq3XS8JLOAJHfL3Mysri8ccf59y5c2zZsqXW/UpKSigpufAhOjc3l4iICId6rEI4O5PZwt6E8/x2MIU1R1NJuGh1MzedhiuifOgd4UNMuA8xET608XRR7AOlubCQvLXryPvjD/I3b8ZSXGy7TuXiglufPrj3uxL3K/vh1qsnajc3ReK8XI54brgUjvQ4swpKefO3o3y/+ywA0f7u/PDY1QR6uigcWev23c4EZi09CMCwrkG8emt3wnzs7+/+TEYBn285zQ97Eik2WlvHh3Vtw6ybutI+sO6EVVl6OlmLFpG96Luq8wvVanTBwejCw9GFhaH2NKB2cUGl02MuKcacl48pL5eypGRKExIwnT9f7b51UZF4DhuG16ibcOvRvUkfs2h6kuyyA4504hKO7dGvdkuFl3BojvR6+dxzz/Hhhx9SWFjIVVddxYoVK/CvY/npV155hVdffbXadkd4rEK0VmcyCtj4VzpbTmaw60wW2YXVhz/7e+jpGuJF1xBPOrbxpH0bDzoEeuLt3rLVLebCQvK3bKFg8xbyN2+mLCWl6g4aDS4dO+LWqxeu3bri0rkzrp06ofbwaNE4L4UjnRsux+U8zk82xnEsOZc7+kYwsL0/mhqqYprCybQ8vtuZyP/2nLUNQ7+7XwTPjexSpeVMKOf7XYk8v+wgZWYLbjoN/7ihIw9cG614a2mx0cTqI6n8uPcsG/9KpyL70CPMi+dGdmFQx8BG3Z812b+Wgh07KNy1C2N8Qv03uoguLAy33r1x690b9wH9cenY0e6r4cQFkuyyA63lBC2Ul5xTxMA56+rc58ooX166pSsxEbKCiLA/Sr5ezpw5k3/961917nP06FG6dLEmjDMyMsjKyiI+Pp5XX30Vb29vVqxYUeubJKnsEsKxmc0WTqTlszs+iwOJOew/m81fqXmYa3kH7eOuI8rPnUh/D8J83AjzdSPcx40gL1eCvFzw89A324cqi8VC6alTFO7aReHOXRTu3k1ZWlr1HVUqdGFh6Nu3w6Vde/RRUegjI9BFRqILDkaltY95Za3lvfSlPk6z2cL176wnMcu6sFeItyu39g7j2g4B9In0weMy5s4ZTWYOnM1m68lMNhxPY29Ctu26zkGevD6uB1dG+13y/YvmcTwlj5eWH2LnmSwAAgx67uoXwT0Dolq00iuv2MjmExmsOZrK6sOp5JWU2a4b2qUNDw1qy8B2/k3yWliWkUFpQiLGc2cxnkvCXFiIpbQUS2kJKhdX1J4GNAYD2qBg9FGR6MIj0BjsP9kvaifJLjvQWk7Qwj4s2ZXAcz8erHe/MB9X+kT4VNlWZDRRUFKGwUWLBSgoKUOrVlFQal3xxEOvoaDUZFupymgyU1pmQq/TgAVKy0yo1CqMZWbKanj3bzJbym+rQqNWYTJb/z/Q04VHr2/H+CsjL/PRC0en5Otleno6mZmZde7Trl079DXMbTh79iwRERH8+eefDBw4sEHHk3ODEI6vqNTEX6l5HE3O5VhKHnHp+cSl5ZOUU1zvbfUaNf4GPQEGFwIMevw8XPA36PF11+PjrsPbTYePmw5PVx1eblo8XXUYXLTotY2fGWaxWChLTaXowAGKDx6i+Ngxio8dxZSeUfuN1Gq0QUHoQkLQBQehDWyDtk0btIEBaHz90Pr7ofH1RePtjcrNrVmrIVrL6+WlPk6LxUJsYjY/7j3Lz7FJ5BZfSCho1Cq6hnjSPtBAlL8HEb5u+Ljr8XLV2pJgJrOFMrOZ8wVGMgtKSM8r4VR6ASfS8jmRlmdrM6u4vyGd2/C3/hEM7tym2SrIxOWzWCws23eOf/1+jNRc65dtahX0b+vH0C5tGNqlDe0DDU36t5tfUkZsQjY7T2ey43QWexPOYzRd+EwQ5uPGbVeEMa5PGO3qaVcUoj6S7LIDreUELezH/sTz3Dq/4avC2YtIPzc2PTtU6TCEghz19TIhIYGoqCjWr1/P4MGDG3SbisealJREcHCw7c1maWkpRqMRrVaLi8uF2ScFBQUAuLm5oS5fDchoNFJaWopGo6myOnFj9i0sLMRiseDq6oqmfEWjsrIySkpKUKvVuFWa8dOYfYuKijCbzbi4uKAtrw4xmUwUFxc3al+VSoW7u7tt3+LiYkwmE3q93rYYQGP2NZvNFBVZqx88KrVvlZSUUFZWhk6nsyU0G7OvxWKhsHxQuLu7e7V/z8bs25B/+6b4Panp37Mpfk8q/j0v9/fk4n/Py/09qe3f83J/Tyr/e1bsW1haxsnk85xKzSM5r5TUAhNnzxdx7nwhKVnZZOYbUekuzPqymIxYTCZUag0q7YX2R3OpNWlWeV+dyoS7Fjxc9Xi6u+Om1+Cu16A1l+Kq1eDh4Yabiw5XrQadyoTGYsbVRYeHuxt6rRoXjRqTsQidWo2b2YQqPQ1SUzCeS6QsKQlVeiq69HQ0xlLUFjPGslJUZgtuKtBhQWMxYzabMZnL0GDBXaVCo9Wg9fCg1M0VjZsbbgYDejdX1G5umLUajCoVap0edzc3gl99BZVK1ajXiNTUVIKDgx3u3NBYTXEOLDaaWHs0jdVHUth15jznsosuOy5fdx0D2/szsH0Aw7sFEeTlHAsftBZGk5nVR1L5els8205V/VLP30NPjzBveoZ5076NB2E+7oT5uuHvocdFq66WCDObLeQVl3G+sJSU3GISswpJzCrkRFo+R5NzOZNZdc4hQLsAD27o2oZhXYPoF+1X4+B5IS5FQ18zZQ1NIZxITIQvs0Y53myuhKwiftjd+H57IVrSjh07+PDDD4mNjSU+Pp5169bxt7/9jfbt2ze4qquy0NBQMjIuVFe8/fbbGAwGpk6dWmW/Nm3aYDAYSEi48Dcyf/58DAYDDz74YJV9o6OjMRgMHD161LZt4cKFGAwG7r777ir7duvWDYPBwN69e23blixZgsFgYMyYMVX27devHwaDgc2bN9u2rVixAoPBwLBhw6rse91112EwGFi1apVt27p16zAYDNWep1GjRmEwGFi2bJlt2/bt2zEYDMTExFTZ9/bbb8dgMPDtt9/ath08eBCDwUDHjh2r7HvfffdhMBj47LPPbNvi4uIwGAyEhYVV2ffRRx/FYDAwb94827bk5GQMBgM+Pj5V9p02bRoGg4E33njDti0nJweDwYDBYKCs7EJVxQsvvIDBYOCFF16wbSsrK7Ptm1NpuO4bb7yBwWBg2rRpVY7n4+ODwWAgOTnZtm3evHkYDAYeffTRKvuGhYVhMBiIi4uzbfvss88wGAzcd999Vfbt2LEjBoOBgwcvVAN/++23GAwGbr/99ir7xsTEYDAY2L59u23bsmXLMBgMjBo1qsq+AwcOxGAwsG7dhbb6VatWYTAYuO6666rsO2zYMAwGAytWrLBt27x5MwaDgX79+lXZd8yYMRgMBpYsWWLbtnfvXgwGA926dauy7913343BYGDhwoW2bUePHsVgMBAdHV1l3wcffBCDwcD8+fNt2xISEjAYDLRp06bKvlOnTsVgMPD222/btmVkZNj+PSu467V8Mfd1xg1oz9l1X/PKmO789/4r+d/DfYn9v1tJnHsHq58YwPIp1/DfiVdyRcYaEufeQdiJH7ntijCGdW1Dv2hfEufeQeLcO3Apy79wvK3/48A/b+Xg93M5nppHbGI2f8Zl8s0Tw/nPQ9fyw8ZYFu1I4Iutp3l77gc8N6Y3s57+O/+34ggvLT/Esz8e4N5h/Rg/sCMPf76Wv2/L5e+n3Hlgx2nu+O+73HvkJE8MeoK/D53OYzc8w7hTcYw+sJ17Y+5k4siXmDBqNuOiBzPkyH6GF6i5/ZbXGTvyNW4Z9BxXxR6n94qfuU7Vg8FtbuM6z1H0T/Sk07x5dP/uFwYVX2H78NyY14iLfx9F7Vx1Gm7uFcJ7d/dh68yhbJ05lE/uvYJZo7rwt/6RDOoYQEy4N+0CPGjj6UKQlwthPm5E+rnTK9ybIZ0DuaNvOM+M6Myn9/Vl7fTr2fPijXw0oS/3XRUliS4HpNOoualnCN89chUbnxnM7NHdGNQxAL1GTWZBKRv/SufD9Sd5esl+7vx0G9e8uY4uL/1Ohxd+o9crq+jz2h/0emUVPWavosMLK4l57Q8Gv7OBuz/bzjP/O8D7607y26EUW6Ir1NuVsb1DmXNbT9ZNv551Mwbzws3dGNDOXxJdQhH20ZAvhGgyj17fHlQwZ+UxpUNplD8Op0o7o7Br7u7uLF26lNmzZ1NQUEBISAgjR47kxRdfrFJhI4QQdQnzdbdVgq0P9WY50L+tP/++s7dtH9Xj1v9unXkDvn7+FJSYeOONXby1GW7sFsT0hwZQUFJGkdHEXfPUlBjh8evb4xEQQrHRzMYMP34HIn3dGRYTSmmZdRTBdxo1JUDXEE/cg7wxmszEe7mSBbjp1AR7uWKyWDCZLSSpwIS17VKrVmG65GYQFWa1sgOyW6MwHze7XI1PKCPK34PJ17Rl8jVtKTaaOJqcy6FzORw6l0tCViHnsotIzinCaLL+/Vduia3MQ68h0NOFCD93wn3daRfgQbdQL7qGeOEnCxUIOyNtjM3IUdtyhHNIziniqcWx7DidpXQoDfL2HT0l2dWKtabXS2ljlDbG2vaVNkbHb2NsyL6N+be/1N+T5nqNMBqNFBYVg0qNi6srZosFswXyCwowmcy4uLii1mgwWywYjWUUlxSjVqlxdXOzVQZJG2N1rekcKOyX2WyhsHyOb15xGWaLBY1ahUalwt1Fg7ebTvGVHYUAmdllF+TEJezB/sTzTP9+PyfTC5QOpVYys0u0ptfL1vRYhRDicrSW18vW8jiFEKIpNPQ1U9oYhXByMRG+rJk+mP2J5/lpXxLp+dVXiioqNZFfal2NEQvkl15YjVEFuJevxmistBpjSZnJ9u1OSZkJtUpFaR2rMRrLV2NUq1WYK1Zj9HLhketkNUYhhBBCCCGEEE1Hkl1CtBIxEb7ERPgqHYYQQgghhBBCCNGsZDVGIYQQQgghhBBCCOE0JNklhBBCCCGEEEIIIZyGJLuEEEIIIYQQQgghhNOQZJcQQgghhBBCCCGEcBqS7BJCCCGEEEIIIYQQTkOSXUIIIYQQQgghhBDCaWiVDsCZWSwWAHJzcxWORAgh7FvF62TF66Yzk3ODEEI0TGs5N8h5QQghGq6h5wZJdjWjvLw8ACIiIhSORAghHENeXh7e3t5Kh9Gs5NwghBCN4+znBjkvCCFE49V3blBZnP2rEgWZzWaSkpLw9PSkf//+7Nq1q8r1/fr1q7Kt8s+5ublERESQmJiIl5dXs8V4cQxNfbv69qvr+pqua8i2ln4eL/U5bMxtL/V5bMx2R30eG3O75n4elX4O64q1qW7XXH/TFouFvLw8QkNDUaudu8O+8rlBpVI16rYt9XtkL1rb44XW95jl8Tq/y3nMreXcIOeFxpHHLI/ZmbXGx93Yx9zQc4NUdjUjtVpNeHg4ABqNpto/3MXbatrHy8urWX/JazpmU96uvv3qur4hz1lN21r6ebzU57Axt73U57Ex2x31eWzM7Zr7eVT6Oawr1qa6XXP+TTvzt/aVVT43XKrm/j2yN63t8ULre8zyeJ3fpT7m1nBukPPCpZHH3Dq0xscMrfNxN+YxN+Tc4LxfkdiZKVOm1Lutpn2a26Ues6G3q2+/uq5vyHNW07aWfh4v53jN/Tw2ZrujPo+NuV1zP49KP4eXc0x7+psWQgghhBBCiMshbYx2Kjc3F29vb3JyclpdRrcpyfPYNOR5vHzyHIqm0Np+j1rb44XW95jl8Tq/1viYW1JrfH7lMctjdmat8XE312OWyi475eLiwuzZs3FxcVE6FIcmz2PTkOfx8slzKJpCa/s9am2PF1rfY5bH6/xa42NuSa3x+ZXH3Dq0xscMrfNxN9djlsouIYQQQgghhBBCCOE0pLJLCCGEEEIIIYQQQjgNSXYJIYQQQgghhBBCCKchyS4hhBBCCCGEEEII4TQk2SWEEEIIIYQQQgghnIYku4QQQgghhBBCCCGE05BklwNasWIFnTt3pmPHjvz3v/9VOhyHNW7cOHx9fbnjjjuUDsVhJSYmMnjwYLp160avXr344YcflA7JIWVnZ3PllVfSu3dvevTowX/+8x+lQxJ2aP78+URHR+Pq6sqAAQPYuXOn0iE1m02bNjF69GhCQ0NRqVQsX75c6ZCa1Zw5c+jXrx+enp60adOGsWPHcvz4caXDalYff/wxvXr1wsvLCy8vLwYOHMhvv/2mdFgt5s0330SlUvHUU08pHUqzeeWVV1CpVFUuXbp0UTospyPnBucm54fWd34AOUc0FUl2OZiysjKmTZvGunXr2LdvH2+//TaZmZlKh+WQnnzySb766iulw3BoWq2W9957jyNHjvDHH3/w1FNPUVBQoHRYDsfT05NNmzYRGxvLjh07eOONN+TvWlSxZMkSpk2bxuzZs9m7dy8xMTGMGDGCtLQ0pUNrFgUFBcTExDB//nylQ2kRGzduZMqUKWzfvp3Vq1djNBoZPny4U7+ehoeH8+abb7Jnzx52797N0KFDufXWWzl8+LDSoTW7Xbt28emnn9KrVy+lQ2l23bt3Jzk52XbZsmWL0iE5FTk3OD85P7Su8wPIOaJJWYRD2bp1q2Xs2LG2n5988knLokWLFIzIsa1fv95y++23Kx2G0+jVq5clISFB6TAcWmZmpiUqKsqSnp6udCjCjvTv398yZcoU288mk8kSGhpqmTNnjoJRtQzAsmzZMqXDaFFpaWkWwLJx40alQ2lRvr6+lv/+979Kh9Gs8vLyLB07drSsXr3acv3111uefPJJpUNqNrNnz7bExMQoHYZTk3PDMqXDaHFyfnBuco5oWlLZ1cIaUn5bVzlyUlISYWFhtp/DwsI4d+5cS4RuVy73eRRWTfk87tmzB5PJRERERDNHbX+a4nnMzs4mJiaG8PBwnnnmGQICAlooemHvSktL2bNnD8OGDbNtU6vVDBs2jG3btikYmWguOTk5APj5+SkcScswmUwsXryYgoICBg4cqHQ4zWrKlCncfPPNVf6endmJEycIDQ2lXbt2TJgwgYSEBKVDchpybmid5Pzg3OQc0bTnCEl2tbD6ym9bWznypZLnsWk01fOYlZXFxIkT+eyzz1oibLvTFM+jj48P+/fv5/Tp0yxatIjU1NSWCl/YuYyMDEwmE0FBQVW2BwUFkZKSolBUormYzWaeeuoprrnmGnr06KF0OM3q4MGDGAwGXFxceOyxx1i2bBndunVTOqxms3jxYvbu3cucOXOUDqVFDBgwgIULF/L777/z8ccfc/r0aQYNGkReXp7SoTkFOTe0PnJ+cN7zA8g5olnOEc1aNybqRA3lt/WVI9fUxvjtt9+2SLz26lKexwrSxnjBpT6PxcXFlkGDBlm++uqrlgrVrl3O72OFxx9/3PLDDz80Z5jCgZw7d84CWP78888q25955hlL//79FYqq5dT0N+XMHnvsMUtUVJQlMTFR6VCaXUlJieXEiROW3bt3W2bOnGkJCAiwHD58WOmwmkVCQoKlTZs2lv3799u2OXuLysXOnz9v8fLyahWtSC1Bzg2t69xgscj5wVnPDxaLnCMsluY5R0hllx1pSDly//79OXToEOfOnSM/P5/ffvuNESNGKBWyXZKy7qbRkOfRYrEwadIkhg4dyn333adUqHatIc9jamqq7VuMnJwcNm3aROfOnRWJV9ifgIAANBpNtWq/1NRUgoODFYpKNIepU6eyYsUK1q9fT3h4uNLhNDu9Xk+HDh3o27cvc+bMISYmhnnz5ikdVrPYs2cPaWlpXHHFFWi1WrRaLRs3buT9999Hq9ViMpmUDrHZ+fj40KlTJ06ePKl0KE5Bzg2ti5wfnPf8AHKOgOY5R0iyy440pBxZq9Xy7rvvMmTIEHr37s306dPx9/dXIly71dCy7mHDhjF+/HhWrlxJeHi4JMIu0pDncevWrSxZsoTly5fTu3dvevfuzcGDB5UI12415HmMj49n0KBBxMTEMGjQIJ544gl69uypRLjCDun1evr27cvatWtt28xmM2vXrm0V8ytaA4vFwtSpU1m2bBnr1q2jbdu2SoekCLPZTElJidJhNIsbbriBgwcPEhsba7tceeWVTJgwgdjYWDQajdIhNrv8/Hzi4uIICQlROhSnIOeG1kHOD1bOfH4AOUdA85wjtE12T6LFjBkzhjFjxigdhsNbs2aN0iE4vGuvvRaz2ax0GA6vf//+xMbGKh2GsGPTpk3j/vvv58orr6R///689957FBQUMHnyZKVDaxb5+flVvtk7ffo0sbGx+Pn5ERkZqWBkzWPKlCksWrSIn376CU9PT1si3NvbGzc3N4Wjax6zZs1i1KhRREZGkpeXx6JFi9iwYQOrVq1SOrRm4enpWW3GjoeHB/7+/k47e2fGjBmMHj2aqKgokpKSmD17NhqNhr/97W9Kh+Y05Nzg3OcGkPNDazg/gJwjmuscIckuOyLlyE1DnsemIc9j05DnUTSFu+66i/T0dF5++WVSUlLo3bs3v//+e7WKQWexe/duhgwZYvt52rRpANx///0sXLhQoaiaz8cffwzA4MGDq2xfsGABkyZNavmAWkBaWhoTJ04kOTkZb29vevXqxapVq7jxxhuVDk00kbNnz/K3v/2NzMxMAgMDufbaa9m+fTuBgYFKh+Y05Nzg3OcGkPODnB+cV0ucI1QWi8XSZPcmGkWlUrFs2TLGjh1r2zZgwAD69+/PBx98AFhLNiMjI5k6dSozZ85UKFL7Js9j05DnsWnI8yiEEEIIIYQQypLKrhZWX/ltaytHvlTyPDYNeR6bhjyPQgghhBBCCGE/pLKrhW3YsKFK+W2FyuW3H374IW+//batHPn9999nwIABLRypfZPnsWnI89g05HkUQgghhBBCCPshyS4hhBBCCCGEEEII4TTUSgcghBBCCCGEEEIIIURTkWSXEEIIIYQQQgghhHAakuwSQgghhBBCCCGEEE5Dkl1CCCGEEEIIIYQQwmlIsksIIYQQQgghhBBCOA1JdgkhhBBCOJgNGzagUqnIzs5W5Phr166la9eumEymevf9/fff6d27N2azuQUiE0KI1kvODUJcIMkuIYQQQgg7NnjwYJ566qkq266++mqSk5Px9vZWJKZnn32WF198EY1GU+++I0eORKfT8e2337ZAZEII0TrIuUGIukmySwghhBDCwej1eoKDg1GpVC1+7C1bthAXF8ftt9/e4NtMmjSJ999/vxmjEkIIIecGIS6QZJcQQgghhJ2aNGkSGzduZN68eahUKlQqFWfOnKnWqrJw4UJ8fHxYsWIFnTt3xt3dnTvuuIPCwkK+/PJLoqOj8fX15R//+EeV9pKSkhJmzJhBWFgYHh4eDBgwgA0bNtQZ0+LFi7nxxhtxdXW1bdu/fz9DhgzB09MTLy8v+vbty+7du23Xjx49mt27dxMXF9ekz48QQrRGcm4Qon6S7BLCDtRUhqw0lUrF8uXLlQ5DCCFatXnz5jFw4EAefvhhkpOTSU5OJiIiosZ9CwsLef/991m8eDG///47GzZsYNy4caxcuZKVK1fy9ddf8+mnn/K///3PdpupU6eybds2Fi9ezIEDBxg/fjwjR47kxIkTtca0efNmrrzyyirbJkyYQHh4OLt27WLPnj3MnDkTnU5nuz4yMpKgoCA2b958mc+IEEIIOTcIUT+t0gEIIWDp0qW2F/7o6GieeuqpFkt+vfLKKyxfvpzY2Ngq25OTk/H19W2RGIQQQtTM29sbvV6Pu7s7wcHBde5rNBr5+OOPad++PQB33HEHX3/9NampqRgMBrp168aQIUNYv349d911FwkJCSxYsICEhARCQ0MBmDFjBr///jsLFizgjTfeqPE48fHxtv0rJCQk8Mwzz9ClSxcAOnbsWO12oaGhxMfHN/o5EEIIUZWcG4SonyS7hLADfn5+TX6fpaWl6PX6S759fSdOIYQQ9sXd3d32YQYgKCiI6OhoDAZDlW1paWkAHDx4EJPJRKdOnarcT0lJCf7+/rUep6ioqEqbCsC0adN46KGH+Prrrxk2bBjjx4+vEguAm5sbhYWFl/z4hBBCNJ6cG0RrJW2MQtiBijbGwYMHEx8fz9NPP23rv6+wZcsWBg0ahJubGxEREfzjH/+goKDAdn10dDT/93//x8SJE/Hy8uKRRx4B4LnnnqNTp064u7vTrl07XnrpJYxGI2Dt43/11VfZv3+/7XgLFy4EqrcxHjx4kKFDh+Lm5oa/vz+PPPII+fn5tusnTZrE2LFjeeeddwgJCcHf358pU6bYjiWEEKJ5VW4NAevreE3bKpZ5z8/PR6PRsGfPHmJjY22Xo0ePMm/evFqPExAQwPnz56tse+WVVzh8+DA333wz69ato1u3bixbtqzKPllZWQQGBl7OQxRCCNFIcm4QrZUku4SwI0uXLiU8PJzXXnvN1n8PEBcXx8iRI7n99ts5cOAAS5YsYcuWLUydOrXK7d955x1iYmLYt28fL730EgCenp4sXLiQI0eOMG/ePP7zn/8wd+5cAO666y6mT59O9+7dbce76667qsVVUFDAiBEj8PX1ZdeuXfzwww+sWbOm2vHXr19PXFwc69ev58svv2ThwoW25JkQQohLo9frqwwObip9+vTBZDKRlpZGhw4dqlzqqu7t06cPR44cqba9U6dOPP300/zxxx/cdtttLFiwwHZdcXExcXFx9OnTp8kfhxBCtEZybhCibpLsEsKO+Pn5odFo8PT0JDg42HZCmTNnDhMmTOCpp56iY8eOXH311bz//vt89dVXFBcX224/dOhQpk+fTvv27W0lwi+++CJXX3010dHRjB49mhkzZvD9998D1rJhg8GAVqu1Hc/Nza1aXIsWLaK4uJivvvqKHj16MHToUD788ENbv38FX19fPvzwQ7p06cItt9zCzTffzNq1a5vzKRNCCKcXHR3Njh07OHPmDBkZGbZv3y9Xp06dmDBhAhMnTmTp0qWcPn2anTt3MmfOHH799ddabzdixAi2bNli+7moqIipU6eyYcMG4uPj2bp1K7t27aJr1662fbZv346LiwsDBw5sktiFEKK1k3ODEHWTZJcQDmD//v0sXLgQg8Fgu4wYMQKz2czp06dt+128AgrAkiVLuOaaawgODsZgMPDiiy+SkJDQqOMfPXqUmJgYPDw8bNuuueYazGYzx48ft23r3r07Go3G9nNISIit/18IIcSlmTFjBhqNhm7duhEYGNjo1/C6LFiwgIkTJzJ9+nQ6d+7M2LFj2bVrF5GRkbXeZsKECRw+fNj2+q/RaMjMzGTixIl06tSJO++8k1GjRvHqq6/abvPdd98xYcIE3N3dmyx2IYRozeTcIETdVBaLxaJ0EEK0doMHD6Z379689957Na7G2LVrV2688Ub+8Y9/VLttZGQker2+xttt27aNQYMG8eqrrzJixAi8vb1ZvHgx7777LtnZ2UDtqzG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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(12, 3.2), layout=\"constrained\")\n", "axes[0].loglog(jnp.arange(1, n_steps + 1), gd_log, c=\"C3\", label=\"Adam\")\n", "axes[0].loglog(jnp.arange(1, iters_ilqr + 1), cost_log[:iters_ilqr], \"o-\", c=\"C0\", ms=3, label=\"iLQR\")\n", "axes[0].set(xlabel=\"iteration\", ylabel=\"cost J\")\n", "axes[0].legend()\n", "axes[1].plot(time, Xs_gd[:, 0], c=\"C3\", label=\"Adam\")\n", "axes[1].plot(time, Xs_ilqr[:, 0], c=\"C0\", label=\"iLQR\")\n", "for s in (-1, 1):\n", " axes[1].axhline(s * jnp.pi, ls=\":\", c=\"k\")\n", "axes[1].set(xlabel=\"time (s)\", ylabel=\"angle (rad)\")\n", "axes[2].plot(time[:-1], Us_gd[:, 0], c=\"C3\")\n", "axes[2].plot(time[:-1], Us_ilqr[:, 0], c=\"C0\")\n", "axes[2].set(xlabel=\"time (s)\", ylabel=\"torque\");" ] }, { "cell_type": "code", "execution_count": 6, "id": "98877a97", "metadata": { "execution": { "iopub.execute_input": "2026-10-14T22:41:08.705695Z", "iopub.status.busy": "2026-10-14T22:41:08.705250Z", "iopub.status.idle": "2026-10-14T22:41:08.709324Z", "shell.execute_reply": "2026-10-14T22:41:08.708708Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " final cost iterations time (ms)\n", "iLQR 17.8970 184 169\n", "Adam 20.4651 5000 1943\n" ] } ], "source": [ "print(f\"{'':6s}{'final cost':>12s}{'iterations':>12s}{'time (ms)':>12s}\")\n", "print(f\"{'iLQR':6s}{float(J_ilqr):12.4f}{iters_ilqr:12d}{t_ilqr*1e3:12.0f}\")\n", "print(f\"{'Adam':6s}{float(J_gd):12.4f}{n_steps:12d}{t_gd*1e3:12.0f}\")" ] }, { "cell_type": "markdown", "id": "170b0558", "metadata": {}, "source": [ "In this run, Adam also finds a swing-up, but it is a different and more expensive one. It stalls at a higher cost and oscillates with the fixed learning rate. iLQR reaches a lower cost in far fewer iterations and less wall time. Each iLQR iteration costs more than an Adam step, because it needs a backward pass, a rollout and a line search, but each step uses curvature, whereas Adam sees only the poorly conditioned gradient of a long rollout.\n", "\n", "## How to adapt\n", "\n", "- **Your own problem:** both methods take the same `System`, so swap in your dynamics and cost to compare them on your task.\n", "- **Tuning the baseline:** the Adam learning rate and step count are the key knobs. Too large a learning rate diverges on long horizons.\n", "- **When gradient descent is preferable:** with non-smooth costs, or when $u$ comes from a policy network rather than a free sequence. Even then, iLQR solutions make good targets or warm starts." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.11" } }, "nbformat": 4, "nbformat_minor": 5 }