{ "cells": [ { "cell_type": "markdown", "id": "c2a5205f", "metadata": {}, "source": [ "# Which bootstrap should I use?\n", "\n", "There is no universally best bootstrap. The right method depends on what you are willing to assume about the process that generated your data. The way to see that is to take series whose dependence structure we set ourselves, then watch each method succeed or fail against it.\n", "\n", "The workhorse here is a stationary AR(1) process, `x[t] = phi * x[t-1] + e[t]` with `phi = 0.5` and unit-variance noise. Its theoretical autocorrelation is `rho_k = phi**k` and the long-run variance of the sample mean is `sigma_eps**2 / (1 - phi)**2 / n`, so we always have a true value to compare the bootstrap against.\n", "\n", "The recipes:\n", "\n", "1. IID resampling destroys autocorrelation.\n", "2. Block methods bias the AR coefficient downward, and tapering recenters it.\n", "3. Block length is a bias-variance knob.\n", "4. Model-based bootstraps win when correctly specified and fail when misspecified.\n", "5. `diagnose()` as a closing advisor." ] }, { "cell_type": "code", "execution_count": 1, "id": "ef458962", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:43.077923Z", "iopub.status.busy": "2026-06-22T16:15:43.077378Z", "iopub.status.idle": "2026-06-22T16:15:43.887351Z", "shell.execute_reply": "2026-06-22T16:15:43.886346Z" } }, "outputs": [], "source": [ "# On Colab or Binder, install tsbootstrap first (skipped if already present):\n", "try:\n", " import tsbootstrap # noqa: F401\n", "except ImportError:\n", " %pip install -q \"tsbootstrap[examples]\"" ] }, { "cell_type": "markdown", "id": "ea345211", "metadata": {}, "source": [ "## Helpers: DGPs, an OLS lag-1 estimator, and a coverage Monte-Carlo\n", "\n", "The pieces every recipe below leans on, all defined inline." ] }, { "cell_type": "code", "execution_count": 2, "id": "26b8bd97", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:43.893073Z", "iopub.status.busy": "2026-06-22T16:15:43.892773Z", "iopub.status.idle": "2026-06-22T16:15:44.186806Z", "shell.execute_reply": "2026-06-22T16:15:44.185451Z" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from tsbootstrap import (\n", " AR,\n", " IID,\n", " CircularBlock,\n", " MovingBlock,\n", " ResidualBootstrap,\n", " SieveAR,\n", " StationaryBlock,\n", " TaperedBlock,\n", " bootstrap,\n", " diagnose,\n", ")\n", "from tsbootstrap.block.pwsd import optimal_block_length\n", "\n", "PHI = 0.5\n", "\n", "\n", "def ar1(n, phi=PHI, rng=None):\n", " \"\"\"Stationary AR(1) with unit-variance Gaussian noise, started at 0.\"\"\"\n", " rng = np.random.default_rng() if rng is None else rng\n", " x = np.zeros(n)\n", " e = rng.standard_normal(n)\n", " for t in range(1, n):\n", " x[t] = phi * x[t - 1] + e[t]\n", " return x\n", "\n", "\n", "def ar1_coef(series):\n", " \"\"\"OLS lag-1 autoregression coefficient (the estimated phi).\"\"\"\n", " s = np.asarray(series, dtype=float)\n", " a, b = s[:-1], s[1:]\n", " return float(np.dot(a, b) / np.dot(a, a))\n", "\n", "\n", "def sample_acf(series, max_lag):\n", " \"\"\"Sample autocorrelation rho_k for k = 0..max_lag.\"\"\"\n", " s = np.asarray(series, dtype=float)\n", " s = s - s.mean()\n", " denom = np.dot(s, s)\n", " return np.array([1.0 if k == 0 else np.dot(s[:-k], s[k:]) / denom for k in range(max_lag + 1)])" ] }, { "cell_type": "markdown", "id": "277274e7", "metadata": {}, "source": [ "## Recipe 1: IID resampling destroys autocorrelation\n", "\n", "Plain i.i.d. resampling shuffles observations independently, so any ordering information, and therefore all serial dependence, is gone. We can see this directly: for an AR(1) the true autocorrelation decays as `phi**k`, the sample ACF tracks it, but the ACF averaged over `IID()` replicates collapses to roughly zero at every positive lag. IID manufactures white noise." ] }, { "cell_type": "code", "execution_count": 3, "id": "6136d222", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:44.191967Z", "iopub.status.busy": "2026-06-22T16:15:44.191647Z", "iopub.status.idle": "2026-06-22T16:15:44.584031Z", "shell.execute_reply": "2026-06-22T16:15:44.582488Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "original lag-1 ACF: 0.503 (truth 0.500)\n", "IID mean lag-1 ACF: 0.000 (collapsed toward 0)\n" ] } ], "source": [ "rng = np.random.default_rng(0)\n", "n = 1000\n", "x = ar1(n, PHI, rng)\n", "MAX_LAG = 12\n", "\n", "lags = np.arange(MAX_LAG + 1)\n", "theoretical_acf = PHI**lags\n", "original_acf = sample_acf(x, MAX_LAG)\n", "\n", "iid_res = bootstrap(x, method=IID(), n_bootstraps=300, random_state=1)\n", "iid_acf = np.mean([sample_acf(v, MAX_LAG) for v in iid_res.values()], axis=0)\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.stem(\n", " lags - 0.12,\n", " theoretical_acf,\n", " linefmt=\"black\",\n", " markerfmt=\"ko\",\n", " basefmt=\" \",\n", " label=\"theoretical phi**k\",\n", ")\n", "ax.stem(\n", " lags, original_acf, linefmt=\"tab:blue\", markerfmt=\"bs\", basefmt=\" \", label=\"original sample ACF\"\n", ")\n", "ax.stem(\n", " lags + 0.12,\n", " iid_acf,\n", " linefmt=\"tab:red\",\n", " markerfmt=\"rx\",\n", " basefmt=\" \",\n", " label=\"mean ACF over IID() replicates\",\n", ")\n", "ax.axhline(0, color=\"gray\", lw=0.8)\n", "ax.set_xlabel(\"lag k\")\n", "ax.set_ylabel(\"autocorrelation\")\n", "ax.set_title(\"IID resampling collapses the autocorrelation to zero\")\n", "ax.legend()\n", "plt.show()\n", "\n", "print(f\"original lag-1 ACF: {original_acf[1]:.3f} (truth {PHI:.3f})\")\n", "print(f\"IID mean lag-1 ACF: {iid_acf[1]:.3f} (collapsed toward 0)\")" ] }, { "cell_type": "markdown", "id": "b500a296", "metadata": {}, "source": [ "The red marks sit on the zero line: the IID bootstrap throws away exactly the structure a time-series bootstrap is supposed to preserve. Use it only when you have already decided the data are independent." ] }, { "cell_type": "markdown", "id": "0a19a985", "metadata": {}, "source": [ "## Recipe 2: block edge effects and the downward AR-coefficient bias\n", "\n", "Block bootstraps resample contiguous blocks to keep local dependence. But the joins between blocks break dependence at the seams, which biases the estimated AR coefficient downward. We estimate the lag-1 coefficient on every replicate for four block methods and compare the distributions to the original-sample estimate. The tapered block down-weights block edges, so it recenters closer to the truth." ] }, { "cell_type": "code", "execution_count": 4, "id": "430b3b55", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:44.588132Z", "iopub.status.busy": "2026-06-22T16:15:44.587893Z", "iopub.status.idle": "2026-06-22T16:15:45.079200Z", "shell.execute_reply": "2026-06-22T16:15:45.077814Z" }, "nbsphinx-thumbnail": { "output-index": 0 } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CircularBlock mean coef = 0.4709 (original 0.5067)\n", "MovingBlock mean coef = 0.4713 (original 0.5067)\n", "StationaryBlock mean coef = 0.4634 (original 0.5067)\n", "TaperedBlock mean coef = 0.4882 (original 0.5067)\n" ] } ], "source": [ "orig_coef = ar1_coef(x)\n", "B = 400\n", "\n", "block_specs = {\n", " \"CircularBlock\": CircularBlock(block_length=\"auto\"),\n", " \"MovingBlock\": MovingBlock(block_length=\"auto\"),\n", " \"StationaryBlock\": StationaryBlock(avg_block_length=\"auto\"),\n", " \"TaperedBlock\": TaperedBlock(block_length=\"auto\"),\n", "}\n", "\n", "coef_draws = {}\n", "for name, spec in block_specs.items():\n", " res = bootstrap(x, method=spec, n_bootstraps=B, random_state=2)\n", " coef_draws[name] = np.array([ar1_coef(v) for v in res.values()])\n", "\n", "fig, axes = plt.subplots(2, 2, figsize=(9, 6), sharex=True, sharey=True)\n", "for ax, (name, draws) in zip(axes.ravel(), coef_draws.items()):\n", " ax.hist(draws, bins=30, color=\"tab:blue\", alpha=0.7)\n", " ax.axvline(orig_coef, color=\"black\", lw=2, label=f\"original {orig_coef:.3f}\")\n", " ax.axvline(draws.mean(), color=\"tab:red\", lw=2, ls=\"--\", label=f\"mean {draws.mean():.3f}\")\n", " ax.set_title(name)\n", " ax.legend(fontsize=9)\n", "fig.suptitle(\"Block bootstraps bias the AR(1) coefficient downward; tapering recenters\")\n", "fig.supxlabel(\"estimated lag-1 coefficient\")\n", "fig.supylabel(\"frequency\")\n", "fig.tight_layout()\n", "plt.show()\n", "\n", "for name, draws in coef_draws.items():\n", " print(f\"{name:16s} mean coef = {draws.mean():.4f} (original {orig_coef:.4f})\")" ] }, { "cell_type": "markdown", "id": "a1331257", "metadata": {}, "source": [ "Every block method sits to the left of the original estimate: the seams cost dependence. The tapered block is closest to the truth because its window weights down the very edges that cause the bias.\n", "\n", "The bias has a second source: where in the series each method samples. The in-bag counts (how often each original index appears across replicates) reveal it. The moving block, whose blocks must start in `[0, n - L]`, under-samples the two ends; the circular block wraps around, so its coverage is flat." ] }, { "cell_type": "code", "execution_count": 5, "id": "1d53f4cf", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:45.082667Z", "iopub.status.busy": "2026-06-22T16:15:45.082515Z", "iopub.status.idle": "2026-06-22T16:15:45.323557Z", "shell.execute_reply": "2026-06-22T16:15:45.322247Z" } }, "outputs": [ { "data": { "image/png": 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7TXx8vOTi4mIzWbasa20IAfbYtGmTBEi7du1Stvn7+0sGg0GKiYmxqqckCSFAr9dLzZs3l5o3by41atRIcnZ2lho0aCDt2bPH5vzl6xETEyPpdDrp0UcftSp38uRJSavVSk899ZQkSZJDbSLXdcKECVJpaan0zDPPSAaDwWEhr3zdvv76awmQsrKyrMqVlpZaLQrb44EHHpD8/f1tttsTAuxh7z44emxVqOZAVVDembBr164AVk5Vq1evpnnz5nTu3Nmq7Pjx423O9/vvvxMcHMxtt91mtb1Tp06EhYWxZs0aZdt7773HwIEDGT9+PE899RT33HMPTz755GVfk4yHhwfe3t78/PPP7Nq1y0o1ZmnvLEkS8+fP584776RDhw60aNGCli1bkpKSwsmTJwGh9tq5cyd333231bF6vd5GTZWbm8uff/7J8OHD8ff3t9o3cuRICgsL2bRpU4X1Tk9PR6fT4eHhYXe/JEk26s+7774bFxeXStXUWVlZbNu2jbvuugt3d3dlu0aj4cEHHyQpKYm9e/eSk5PD33//zejRo+3adZZ39vn222+5/fbbeeSRR1i6dKnVuR2lum0mSRJjx461Kte1a1fy8/MVc7bq3DNHcOQ3HeWHH35gxowZDBs2jIcffthq36BBg1i2bBl33XUXnTp1YuzYsWzfvh1/f38mTJhgV8Xr4+NDQUGBVYQOvV5PREQEoaGh1arbXXfdhZOTE3PnziUvL49Fixbx4IMP2i3raJ8CeOSRR0hISODPP/9Uyv3666+UlpbatIE9ruQ9nzp1Kn/88QfLly9n1apVvPDCC7zxxht8//33ldbpenmmHB3rKsORcdCy7L333mt1veDYPXb0Wa+Na6rsWqvqS5czjl+J8SwrK4vt27czevRoK5McJycnRo8ebXVsbbadbOJyuW0O9vvNypUrKSwstPvur43flElLS2Py5MkMHDiQ1q1bExERofTJ8v27e/fuNGzY0KqeMkFBQUr0mxUrVrB06VLq1avHqFGjbM5Tnr/++guj0WgznjZv3pyePXsq7+/qtElOTg7Dhg3jt99+46+//uKRRx6pujHsIDvhvvPOO1Ym1TqdDq229qbS1bkPtYHqGFwFYWFhVt9l27bU1FRlW0JCgo09s71jAS5cuEB2djatW7cGxEMv/yUnJ5OYmKiU1Wq1TJ06la5du+Lk5MTXX39dG5ekoNfrWbx4MU8//TQ9evTAz8+Pvn37MmbMGMaMGaM82BMnTuTLL79k8uTJvPTSS/j6+qLVahk9ejQFBQWAsMuVJMmut3r5bfHx8ZSWlrJy5Upat26tDMCSJCkDqmU7lMfDwwOj0UhRURHOzs42+7VaLXXq1LHZVrdu3UpthhMTE5EkifDwcJt99evXV+oeFBSE0Wi0GgQrori4mBdeeIFWrVoxderUGg8W1W0zg8FASEiI1Tks+27jxo2rdc8cwZHfdIR58+bx1FNP0b9/fxYuXGjjTGUvooKXlxcjR47kq6++Ijo6mmbNmlntz8vLQ6/X4+rqWp1LsouHhwd33XUXv/zyCz4+PhQVFdkV+MHxPgVw2223ERISws8//8ywYcMAmDVrFn379qVp06ZV1utK3nNLx2CAXr16ce7cOZ5//nmGDx9u87zJXC/PlKNjXWU4Mg7KyONNeRy5x44+67VxTRXhSF+6nHH8Soxncl+z994tv6022y4oKAitVlvjUJSW2Os3Fy9eBHDo2agpubm5dOvWDb1ez6RJk4iIiMDd3Z0LFy4wdOhQm/5t73mWKe8Y3KpVK3r06EG9evV44YUXrBY6yyOPhRWNF7t37waq1ybLly+nqKiIDz74gIEDB1ZZviKGDx/OG2+8wddff80XX3xBs2bNGDRoEE8++aQyn7tcqnsfagNVCKgCnU5nd7vlyoGHh4fdXAD2tnl6etKgQQMWL15s97yWK1rFxcU89dRTBAUFkZGRwRtvvGHlXFQR7u7udjuLPYeZwYMHc/LkSaKjo9m2bRt//PEH99xzD3v27GH69OkUFxfzzTff8Oijj/Lmm29aHZuWlqZE55FX5e0575Tf5unpCcCoUaN49tln7V5DcHBwhdcnD5LJycl2B/yysjKysrLw9fW12p6enl5pEhy5XvauQY5x7OnpqVyzpSBYEU5OTvzxxx+MGjWKYcOGsWzZMtzc3Ko8rqK6OdpmlU2M5L5bnXvmCI78ZlUsWbKE+++/n969e7Nq1apqTdrlNqqo74eGhtZadIYHH3yQAQMG8O6773LbbbcRGBhYaZ2q6lMgJiYPPPAAn332GUlJSZw5c4aTJ0/yxhtvOFSnq33PO3fuzKJFizhw4ECFQsD19ExVNdZVhqPjoIzBYLD77nDkHlfnWb+ca6oMR/rS5YzjV3I8c/RdXFtt5+7uTteuXdm9ezcFBQWXtdBgr99YPhv23ncgngm9Xl/h2BcUFFTp765YsYKzZ8+yfft2evbsqWyvSLCpbuhMX19fGjduzM6dOystZzlelF+USEtLU/Y70iYy9957L05OTkyaNAlfX98aW1NoNBqmTJnC5MmT2bNnD1u2bGHWrFnMmDGD7du3K1Yil0N170NtoJoD1QI9e/bkxIkTpKSkWG3fuHGjTdmBAwdy5swZvLy87CY7suzQzz//PAcPHmTJkiV89NFHREZGMmfOnCrrU79+fZKTk8nJybHaXpmJTdOmTXnooYdYvnw5/fr1Y9myZYB4+RUVFdmYTOzZs8cqyUXdunUJDw9n8+bNNufesmWL1ffQ0FAiIiI4ePAgzZs3t9sO5Sfwlsix4Q8ePFhhmfLXevjwYTIyMqwerPLUqVOH+vXr2yScAhED2mAw0KVLF0JCQmjRooWiuqyKoUOHsnbtWvbs2cNNN91EZmZmlceU53LbzB7VuWdgHvhLS0urXX9HWLVqFffccw89e/Zk9erV1Tab2rx5M66urnZXzffv30+vXr1qq6r069ePhg0bcv78+QpNgcDxPiUzYcIESktLmT17NjNnzsTb27vmUR/sUN17Xhnyi0l+MdvjenymKhrroOI+7ug46AhV3eOaPOuVXZM9auNZvpwx6UqOZ/bec/bexTLVbTt7TJw4kezs7EqFh7lz51b7vICyel0+IpklWq2WsLAwzpw5Y7U9NjbWJuqTPeS5Qvn+XZO2sIdkyi9S2VgBKO/n8uNFbm4uu3fvVsZwR9pERqvV8sMPP/Dqq6/y1FNPMWXKlJpcgoLBYKBXr168/vrr/PPPP4pGqzaozn1wcXGplXexKgTUAs8//zwajYZHH31UCeO0a9cuu4PRxIkTCQkJsbGPy8jI4Msvv1Q69bx58/j+++/5+OOP6d27Ny+88AKjRo3iiSee4MSJE5XWZ8yYMRiNRt5//31ArIxPnz7d5uV6+vRpXnvtNS5cuKBsi42NJSYmhpYtWwJidaVTp07MmTNHUc/GxMTwyiuv0Lx5c6vzvf7662zatIlvv/1WMXH64Ycf7CZP+vzzz9m7dy/PPPMMWVlZyvbo6GieffZZu9kFZbp164aPjw9bt261u9/JyYkFCxYQHR0NiJWQxx9/nNDQ0Cptq99++23279/Pe++9p7TX/PnzmTNnDk8//bRir/zJJ59w8uRJHn/8ceXBLSgoYPr06crvWtKrVy82bdrE2bNn6devH0lJSZXWwx6X02YVUZ17JpvzyAlvapMNGzZw11130a1bN/78888K/T0A3nrrLXbu3KmEz83Pz+ell15i27ZtvP766zarwidPniQ5OZlbbrnFantNQoTKaDQatm3bRlRUFLfffnulZR3tUyAmJH379iUyMpJFixZxzz331IoJkyXVuecVsXPnTn7++WciIiIqFazh+nimHBnroOI+Xp1xsCocuceOPOuOXpM9autZvpwx6UqMZ2+88QZbtmzhyy+/VPr2V199ZRMe2tG2c3SMuPPOO5k4cSKTJk1i0qRJVpqHM2fOMHbsWOV9XF06duzIuHHjmDZtGgsXLlQ0H+fOnePdd99Vyt1zzz2sXr2aPXv2AGLl/NVXX6VJkyZV/kbv3r3R6XR8/vnnGI1GJEliwYIFHD9+vEZ1tqS0tJR33nmHlJSUKnME9O7dm4EDBzJlyhR27NgBiPH90UcfJScnR9HCOdomlkydOpWPP/6Yt956i5dffrna1/HTTz8xe/ZsK78yeY5X1fPmKNW5D40bN+b48eMOh12tkMt2Lf4XUFl0oHXr1lmVLSkpkQCr0J2SJEkbN26UGjduLBkMBikkJEQaPHiwdOzYMbth9C5evCiNHTtWcnV1lQICAqTg4GApICBAeuGFF6SEhATp+PHjkru7uzRq1Cir47KysqSmTZtKLVq0sBsZx5LPP/9ccnNzk/z8/KSgoCBp2rRpNtGB8vPzpY8++khq1KiR5OPjI4WHh0uurq7SvffeKyUmJirnOnHihNShQwfJyclJqlu3rtS8eXNp586ddqMOTJs2TfL09JS8vb2loKAg6Y033lBCepYPYbVx40ape/fukl6vl8LCwiRPT08pIiJC+vrrr62iJtjjueeek+rWrWvjlS9HD4mJiZE6deok1alTR9JqtVLHjh2lo0ePWpW1F6FBkkQEpzp16kju7u6Sn5+f5O3tLU2aNMkqoockiegkbdu2lbRarVSvXj3J29tbeumll6S8vDyrulhy+vRpJdyZZajW8lRUN0fazN7vSpIkLVu2TAKknTt3Wm139J4VFhZKAwYMkJycnKTGjRtLzZs3VyJEVPc3y9OsWTOrKDTl/yxZt26dNGjQIMnd3V0KDw+X9Hq91KhRowojZ02aNEny9fWV8vPzrbbXNERoZdiLDiRJjvcpSZKkX3/9VQLsRhyTpMrDC5bncu95+ehAzZs3lwIDAyUXFxfpoYcesgnLeb0+U46OdZX1cUfHwYruhSVV3WNJqvpZd/Sa7FGbz/LljONXYjz76KOPlL4dGBgovfrqq0pUPjk6kKNtd+bMGQmQnnzyyUqvw7JOPXv2lJycnKTw8HApJCREcnNzk26//Xbp77//VspV5xmWJDHveOuttyQ/Pz/Jzc1NCg4Olpo0aSItWbJEKZOdnS3ddtttkkajkerWrSs1a9ZM2rNnj8PRgX766SfJ29tb8vX1lfz9/aW7775bOnLkiARI33//vVKufNhNS8pHB2rSpInk5uYm1atXT/riiy9s3tf26pGVlSU9+OCDkrOzsxQcHCw5OTlJLVu2lNauXVvtNrFX1xkzZkg6nU6JGlQR5et26tQp6aGHHpI8PT2levXqSQEBAVKdOnWkTz/9tMJzyFQnOpCj92HHjh1ScHCw5OPjIzVv3txmvugoqhAgiZBSUVFRVuHM8vLypKioKOXlY0lUVJTdMHaSJGIfy+eRY8TKMWHt/e758+dtzpWUlCRFRUXZTFokSZLS0tKkqKioCuPSWlJQUCDFxMQo55HjXNsLgZaRkSHFxcVVOminpKRI8fHxSjiwCxcuSBcuXLApV1hYKMXExCht99Zbb0kajaZCwSU7O1s6e/as3bauiJiYGMnJyUlavny51fakpCTp1KlTyvf4+PgKQ0CmpKRIUVFRFf5GXFycdP78+UoHCkmSpNTUVOnChQs2A1z5ushkZmZKUVFRUkJCQoXnrKpulbVZRb+bk5MjRUVFSQUFBTb7qnPP0tLSpFOnTlnFFq/Jb1py9uxZq5jl5f/sUVxcLMXExFT4LEqSCA8YHh4uvfXWWzb7qhMiND09XYqKilLCWVZEbGysdObMmQr3O9Kn5PHo5MmTdvfb6xtX6p7L1235ZzkGOFI3S67lMyXjyFhnr4/LVDUOVlRHS6q6x5Y4Mj46ck32qM1nuSbjuCPH1qQ+RUVFUkxMjBI6Vu4f1X33zZ49W9LpdA7dJ0vy8vKkc+fOSUlJSXb3V+cZtsRoNEqxsbGVjnmpqalSbGxspe/ps2fP2s2rYTQapQsXLihhMOV+mpGRoZSJjo6u8Dk7f/681Vhx6tQpm5CajtRDksT85ezZsxW2oWWdK2qTiuoqx+K3N8eqqm5lZWVSXFycTWjbyoiPj7cKvSxz5swZu+8fR+6DXC42NlY6efJkjfMEaCSpBunxVFSqQc+ePcnJybGbYfhymDhxIuvXr+fAgQPXZTruG5krdc+uNt999x0ffPABp0+frtTESOXfc89VVGqLBx98EL1ez08//XStq6KickVQfQJUao2CggLef/99srOzARE/efLkyezcubNGNnhV8f777zN//nyHHAlV7HO179nV5o477uDAgQOqAGDBv/2eq6jUFu+++y5ffPHFta6GisoVQw0RqlJrODs7U1paSqNGjXB1dSUpKQk/Pz++/vprHnjggVr/PRcXF6t4xCrV52rfs6tNTfId/Nv5t99zFZXaQs5loaLyb0U1B1K5IiQkJFBWVkadOnVUU50bBPWe/fdQ77mKiorKf5drag6Ul5fHTz/9ROfOnfHw8Kgw5KMl+/bt45577qF+/fo0btyYBx54gNjY2KtQW5XqEBoaSt26ddWJxQ2Ees/+e6j3XEVFReW/yzUVAt5//3127tzJW2+9RV5eXpW23UajkSeffJIRI0awdetWVq9eTWJiIoMGDSIvL+8q1VpFRUVFRUVFRUXlxua6MAe6ePEiYWFhbNy4kf79+1fr2HPnztGoUSM2bNigZJGrirKyMuLj4/H09FRXwFRUVFRUVFRUVP4VSJJETk4OderUQautfK3/hncMliNclM8SWhnx8fGEhYVdqSqpqKioqKioqKioXDPi4uKqDI5xQwsBZWVlTJw4kVatWtG5c+cKyxUVFVFUVKR8l5UfcXFxeHl5XfF6qqioqKioqKioqFxpsrOzCQsLw9PTs8qyN7QQ8PTTT7N//362bduGXl/xpUydOpV3333XZruXl5cqBKioqKioqKioqPyrcMTc/YZNFvb888+zYMEC1q9fT4sWLSot+/rrr5OVlaX8xcXFXaVaqqioqKioqKioqFx/3JCagBdffJHZs2ezfv16OnToUGV5Z2dnnJ2dr0LNVFRUVFRUVFRUVK5/rntNwNNPP03Xrl2V7xMnTuSXX35h/fr1dOzY8RrWTEVFRUVFRUVFReXG5JoKAXPnzsXDw4PmzZsDcMstt+Dh4cGHH36olCksLCQ/Px+AtLQ0Pv30U3Jycujbty8eHh7K36+//npNrkFFRUVFRUVFRUXlRuOa5gkoLS2lsLDQZruTkxNOTk6AiOxTVlaGq6srALm5uXbP5eLiUqlzsCXZ2dl4e3uTlZWlOgarqKioqKioqKj8K6jOHPea+gTo9Xo8PDwqLVPelr+q8ioqKioqKioqKioqlXPd+wSoqKioqKioqKioqNQuqhCgoqKioqKioqKi8h9DFQJUVFRUVFRUVFRU/mOoQoCKioqKioqKiorKfwxVCFD5d5ObDEd+h7Kya10TFRUVFRUVFZXrhhsyY7CKisMsfhjOb4XEozD4XdCqcq+KioqKioqKijojUvn3cnajEAAAdnwF2z67tvVRUVFRUVFRUblOUIUAlX8vv42w/n52IyQcVk2DVFSqQ0khzB4O27+81jVRUVFRUalFVCFA5d9JSYH5c0hb8f/CdvixL2z99NrUSUXlRiRmI8RsgnVvX+uaqKioqKjUIqoQoPLvJDNO/A9pCw+utt63ccrVr4+Kyo1EegxMbwmHF0Beqnl7Ue61q5OKioqKSq2iCgEq/07Szoj/vvXBxQvJyZNknY5SeX9RDqx8Ds5vv1Y1VFG5fvn7Lci+BMsehxVPm7ennrp2dVJRUVFRqVVUIeA6QZIk/oz5k9SC1KoLq1ROZhwsuEd89qoLwMdezgwKr8uE0CAkEKYN+3+BX269VrVUUbl+Kc6xvz1FFQJUVFRU/i2oQsB1wrIzy3h166s8uf7Ja12VG59tn5s/B0YAsMnTB4ADLi5sdXWBtLPmMqqjsIoKJB6D2SOEKVBpsf0yGeevZo1UVFRUVK4gqhBwnbD1oghlGZUehSRJ17g2NzgxG8X/Pi9Du7FkFWVxEfOkZpurK3uyotng5io2pMdcg0qqqFxnLH5IPDvz74W8FOt9QS3F/8zYy/uNxKNwYPblnUNFRUVFpVZQhYDrhJisGLufVaqJsQQyLoDehayezzB+3aP0XtAbAFe9mPTP9/Zkgree54MDyddoICXqWtZYReX6oCBT/E+JgswL1vuGfCj+WwoBZWUQf6h6mrQfesOKZ+D4HzBzCOyZcRkVVnGIsjK4dECMjSoqV5Ntn8PPQ6Ewy3ZfaZEIPbxVzd9zLVGFgOsASZKIzTG/XHcl7KJMUk1UakRmLEhG8GvEojOLOZxyWNn1VPunbIqn6nSQm3Q1a/jfRdVwXd94BJs/l5Va7wtpI/5nXIBdPwhtwWfNILIfbP7IsfNbmhitfBbidsGfL19enVWqZsnDMGMA7P3pWtdE5b9ESSGsnwyxO2Hxw7DzO+t3wKUDIvTwhvdUk9xriCoEXAcUlBZQavHSnbZnGkOXDCXH5JxXJpWx4cIGtlzccq2qeOMgm/b4NaKg1JwroEtIFx5o9YBNcSEEmEwfsi7Bl+1gw/tXo6b/LXKT4bMIddXnesbieQEgtD20HQN3/wpu/mBwg+yL8NercGo1h0uz6Bdelyknfqbfgr6cTD9Z8bnz02FPpPm75cpg4tFavYz/NJcOQHaC+XtuChxfJj6f2XBt6qTy3yRmk/nzmfXw9+sQf8C8rTDT/Hn753BytSoMXANUIeA6ILMoEwAfZx9lW0JeAqfSRSSOpdFLeX7T8zy14Sn2J+2/BjW8gZAdF/0akpyfrGz2dvIG4Nl2/0NjsRiRptOaNQFr3xLHq8nEap99syA3Uaz6qFyf5CRaf+/6KNwZCa1GgEYDQS2sdk8O8CNdp2OBhwvpRRl8e/BbscOeU/Hat2Dtm/Z/94feYCy1v0/FcZKjxIr/D73N2/LTzJ9TKhHSVP7dlBbD9q9g41THnjVJuvwJecJh220nVpg/51gIqxvegwX3wpl1l/ebKtVGFQKuA7KKxKpYI+9GfNz3YwJcAwBIyk+ixFhC5BHzCtqO+B3XpI43DLJDo0cwsdlmE6tAt0AAHm3/JEcePMqD9QYDkKjXs/D0IlZGLUCK3WVxHjVUa61SfpVZ5fri0n4oLpcIrPEg6++h7cyfH/4bfTnrLg+tQaxETwkREw5LDs21/u7XGFy8zd9z4mtWbxUzcbvF//xUyEuDI79DQYZ5f1ac2K7iOGln4ejia12LyyP5JHwQCOsmweZp8McT1oJAdgJs/xLOmSwNCjLhk8aw8hk4skiE3D7yu9DmycQfhAtVzEXsBdzY/gVc2Ck+l190AEg6Vp0rU6kF9Ne6AiqQVSyEAG9nb25peAvns8/z3aHvSMxLZPnZ5STkmSXmfYd/Bbcm0PyWa1Xd649zW8UgNmiSefLu5s/FSxcBaB/YnifbWYdeDQhpDxfXs8DLg1iDAfZMoVFRKq3kAvGHoOngq3UF/15Ki8RLpbToWtdEpTKWP2P93dkbvEKttzUeCPt+JtWvPm+d+oWTzk5Wu3PTTsPpv4RPzrpJzPVw40hWNO+XeqCU7P6kiNrl7AEX95nzdGTGUupVh3d2vEO7wHaMbj76ilzmvxZJEgKYzA+9hWDVdox1ubRocPe/unW7kfm6o/jvEQQN+17butSUzdOsvx9dBK6+cOsn4vvGKXDwN/H5hRNiIp6fBgfniD+ZxoPgvqVCgIjsL7a9kQBObvZ/VxYChn8rMo+fFxEQmTUUXj1vXwgwHVNiLOGt7W/Ro04PRjQZUd0rVqkGqibgOkDWBHg7i5WxELcQAL448AWf7xcx778Y8AV6tByTCimZPxZO/XVtKns98uvtQo34Y1/YNxMAo4sPaQVpOOucmX3LbHxcfKwO8XPxAxACgImTTubP6opELVCQKV4WX7a1tvs+sfxa1UjFHqVFkHpafH5iG4z+Df5nJ5N2xO0w+jc+bz2I7fG2+5NyLoFFQINph77kz3N/Mv/Qj+ZCQ6eKSajeGRr0gs4Pi+2ZsRxJOcKKsyt4f5fqk+MwUSvF38nVcOBX83ZZs2Kp3QTr/CgqjpN4g74Pyoxweq34fPsX8Lhptf/YEnMZy7F5TyQYK8gRcnaD0BYkHjFvqyhvSPJJuLhHfG45HB5cBf5NzftP/mkWAoZ8CIMni89pQghYe2Etf577k0nbJ1V4acYyI78e/5XzWRXUQcUhVCHgOkAWAmSfgGB3c5SO7OJsWvm3YmDYQJoavCjWaohxMthK9/81CjIrfaFlGpwxSkYCXAPQaDQ2+4Pdgm22nXEygElYOJt40MqxWKUGHF8KySegtNC8CgTw+/3wUUPIVk1AakRRTu1O5pJPQFkJ1OkoogC1vAN8wqyKbL24lYGLBvH4pdVcLDKbBXgYPNh6t8jLEaUtZeSFxSzydOe4hUD9j7trxb/tEy7+Z8aSlG+O0rXw5ELuWnEXl3Iv1cIF/kuRJFg4XvzF7rRfJtvUfnoX8b+KnCgxmTH/zXEv/VzlJqAVTYyvNzLj4Md+cGyp+J4aDSV5Is9H54eESZ/BTZiJlZWJP3kBACBqReVZwX8dBidXmb+nVzAOrXtb/Hf1BWdP8fnOH0FjmnKe22zui82GQqcHxee0M5xKO8lrW19TTtV3QV8WnFxg8xMb4zby6b5PGfbHMDWa4mWgCgHXAeU1AXXc61jt71mnJxqNhpZaoXY74eQkItn8l1n2BHzXHZKO292daurZsn9FeVoHtEan0Vlti3Fyht4vsM3VhRF5B/h478e1WuX/HJZRSspTkA5bVAfsGjHnLmGmUEHft8KRsKwJppU9S5v/csw+MZuUghR2xO/gQLLZ7KSuR1183ALw1AqDnzNaI+8F+DO2rtmU6KLeZHV6m53IULIQkH7Oyofng90fcCrjFN8d+q7q+v9XsYyuYmkKZIkcda5uJ/E//WyFySg3XNjA8OXDmb5veu3V8UYg/Zx4l8weIYTrFc+KkJYrnzOXyb9BfMRWPQ8Jh0TiPxCfQUT6knH1Exq7wkwhAJTkg5vpPZkeA/9YaOKCWkG9Lta/YYrwdsLJwPTT8ykpn39CksxRgO5ZaN5etxNMWC8+XzogTNPc/MGvkRAWfMIhL5n5h763Ol1GUQZTdk9hWfQy0+klfjr6E4tOL1LKqAFTao4qBFxj3t35Ll8dFE50Xk5eADTwbsD4FuOVMq38haV68zIxaT3jZBAOsNdzRI2cRJjeCiZ7w4JxtXvuMqNQSxqL4Z8P7BZJRbRNRUKAm8GNVgGtrLbtcHXm7vStfOXrA8Di0ze4Q9i1pqoX576ZN77T3bUgzmTiITvyVcTRxfBxQ+HfUhmySj+gmd3dUWlR7EncY3ffS51fAqBFQOsKT5+i01H80ino8ojtTjkTceJRq1wpMtlF2RXX+1oSu9vaUfJaYOnkG2ty0mw5wn7ZOh0ASMg4S//f+zP7uG3W5un7xeR/wSnbVdd/Ndu/FNrKpKPCpPTAr8JcZv8v5jLXo9bSWAKn/4bodeJZLy2C89usy8gLBaFtzdvchCksBRnCWRig6U1Wh210c6Vfkwj23fkle277kLKH1kCLO5T9pcCYuqHMyjzK2gsmc6PMODi/XbRbXgp4h0N4N+v6eNcV/9Oixf8GvUXkMVDOr60gK/nbO96mpKyE7dHL+fLAl1ZBUi5kl0tumHJKDT3sIJclBKSlpbF3797aqst/jqyiLKuJpuWE9dWuryqfW/iL0Hx1SoRKMkmnAyTIM4fAvO6IWiliioNQH9aGY6gkiYEv7YxQcQKc+tO836ue8jHVpNKuSAgAGNt8LAGuAYxoMkLRwpzMOE2UhcNjnvw7KtXHjno9Tq/jlZa92N/uTrFhyQTIuniVK3aV2DNDTDCqojrCvJzVF6p+ppZMEC/61S9WXi4rTvyXV+XLMW3PNMqkMivNWWv/1qwYsYIedXoAEOxRt8LTSxoNiZIYu0rLSvl478esjlktdgY0A4Mbhakn2X5pm82xmy5u4kBSBavc14q4vfDzzWLCeC2xJ2Tf9B48sAoeKZcTwCRs/WZMJb0wnU/2CafQ0rJSJUeNLIQFugZeuTpfD8hmMDKWplTlI2TJXI+a9yUTYN5omHuX+PzHk0KYAdDqYd/PsMMUpcvSHl8WArIuitwRWr3oN27md+XLgQGkG/N56O+HmbB2AtMSN8GY36C+CD+7x8VFKZtaYOqH3/cUjv6rngcgvU5r3tj6BjGZFiZo7oHi92TCups/Nx4ozpdXcfLOuOw4klY9Z7Pd0pSQrIvCMX7GoH/vu6UWqZEQkJmZyYgRIwgICKBr167K9hEjRrBzZwW2iSpW5JXk0XtBb6ttdcu9SGffMptP+31KHQ9hHhRcKCakic4mb/ycSswtKiMnUSSQuZIZXMuvkl3uSkrWRfi2K0yrDyuft96nd4WXTsP9ZofT1EKxSlaZEDCs8TA2jt7I+73etzENkqk0AZJK5chCgGzvOXQa9zdoypqCOD7W5SjFpJRT/HX+L+Jzr8PVtpogSXBgtsiGu+5tKK5EkDz7D3wQ5JhGZMfX8FF983d58l4VVa1YyytvdoQASZKIzhCrdrOGzlK2tw5oTUPvhsr3B1o9gAYND2Zms/hiAi/llfFiegadCsSkZNbxWaTkp7Do9CJ+O/GbYvNbIpWxJLQxXerXJa0wnSY+Tfhh8A/c3/J+5dyzjpt/97og2bS66mj7XynkcMgyGh1414OGfYTphbeFX4dPGDh7USxPEoH8knyGLBnC0/88bZWs0klnHfXpX0VhFnzaVITJBPOiUnlME1KFXDuRbOwQnxvPirMrKjS5qjUKs20DLByzGEPKSmHVC+bvfuZnFTdTdKhzW0Qkr7qdRPSjB1crRXRY13/+yfkUGYsUk8FzTuaJvDJul9PavevlwsqYlTyx/gnzRq0OPC2ijpk0VICiiUwpsRbEOgZ15NaGIorYmcxoErS2bZuYZ7o/WZfg81bCSsBYBLt/sCmrYk2NhIBXXnmFoqIiTp2ydiB58sknef99NbKDI9ibXMqTfZkOQR0Y0mCI8j2kQEycDhs0LPVwh5yKJeZKmTMKFj0ozDGulEq7vMPQ5QoB2z432S/mmVXfbgEUajTkdLwPPIPBvzH7W9/OuIiOfHHgC6ByIcCSigbtE2knLq/e/2Xklcq+E+GlU5R2fZRUYz4AJzJO8XWrgTwTFMDnp+YycfNE3t7+9jWsbC1y4g9YYRFyM6mSPvTbSPEi/uu1isvIrH3L+vven4RvTJmx8uMss/PKlJWZfTYqEQIyizLJKckh2C2YDkEdCHUXL/BOIZ2syjX3a87mkat5NiOT5iUlPNhiHA9l5dDCXSxsLD69mGf/eZa159cqx5SWlfLCpheYrDPX7/Wur9Orbi8mdpnIqpHCAfG6ewYtVzIr83u50pTXtHmGiEkWCBOLsfOgfi9oPIi5eTG8GORPgUWMhONpx0nOT2b7pe2sObdG2S4nr/xXkhwlxqUjC4WWLO2smDD7NzGXuW069Hre+jhLDVwljP9zPG9ue5O/zl/h6H25lVgBWK76y/hYLB7IQsBZk7ZI9hcIioChIuCIs533YUxmDHgEcdjZiWn+fsr2A0n7MBaLcX2nizP9wuvSq3kr/kneB2AV4hywFgJC2pg/e9UFvSspCB+DGTfPoFfdXkzrM43GPo0BOJN0iC1utoEGkmTtQflkY1WZQqrUTAhYtWoVP/74I82aWduQdunShc2bN9dKxf7tnM209ar3dPKs9BjvfHPil3cC/c12ddVFDn+5+iX4tNmVeZHJnv+ypJ99mepUU4i283o9Cz09xDrFnZGMj+hEz5S/yCnOIfLoDB7MO8KRIvPL0VEh4MM+H9rdft1NQG4klJwNAeAZQm45VXtk/hk2ubsxK1WYFO5O3H21a3hl2Pmt9feZg+3bp1pO4rzq2O53hMPzzc5/5TGZuFmt0B1ZBBf3i6zY0yNMofoSwNkLXH1sTiGbiIR7CQFh4e0L+bD3h9xc/2absr5eYRgmrIPHNkHvF2D4d7Trbl6NPJZ2jIu5ZvV8XE4cmy+a3xejirV0DTVrlut71SfINYjk/GSzycH1gKVQVVHbXw3KmwP5NrT+HtoWHvoT7lvKtP2fsU5vZK27Oab7zniz1n7ZmWXK57ySPIpvlGg41aUk3/w5eh1cEhNV6nSA1neJCWqrkbYCcWGWImyfzzrP3Ki5GO0I3ykFQjtzxR1VZVNgv0Ywdj6MXyKe9y6PQJu7bMvrLARXV9MEPv6g+B9mfuboeD85Q6aQqRPC5PeDv2dU01EAnM44De3vZVJQkNWpT2acZuYhMeZ94edDuk5HdnGOVRlJkriYc5Gfjv5Edn2Tn0DDfiJfiIxWS1lAY9J0Opy1TnQL6cYPg38g1COUdoFCA/H9yTlW5rpTek8BTOZAealmZ+4hU8X/KqJhqdRQCMjIyMDX1xfAKvxibm4uWq3qa+wIMVmiczb2buzYAaXFaMrbK+6OFCsZ33aDnQ5E0YheD992t95WVmIeDGoTk7NhQlhHdri6UJR5ofLylbH+XcUZcnzDJnwQ4MdCTw/KwrpxqlAMhtP2TOPrg1/bHOqofWvvur05cr85/nGjYrEaoQoBNaTMKFbanDzBIOxHc8q9GOyRkHsNV1ZrA0myH7Vn/6/W3zPOi6ycMoVZYnUv+aT9mOSlRebweoPesd5nWsmXJImT6SfNph2SaZJSVgolhXB4ISx9BH4aKBIEASy4R/wPjLB7OXLEnnBPMSnydfFlWONhaDUVjPNhXcWEyuAKHcbRuV4vq93J+eYVzDv+uMNqn39eBpRaTz5bBghb9iMpR7husFwVTo6quvzGD+G3O4XpSW1SXhPg38huMcvwiYUW7+cZR2con/cmWvv2/Wu1AYUWAnHyCbPA3vxWGPUTvHBc2Mx7WZjmeoQAkiL8PbH+CabtmcacqDlcyL7A61tfp8+CPvx63PyMX/Ewq7ImIKwbRNwKTQbDK2fh1k+tIwG1uRtGl3MC97CYxOucKWrUjzMZJpMoJ3fONRG+Lh2DOtK7bm+a+grNwqmMU+ARhNaOpmHe2eWk6rSccHYGzHl4ZHot6MXTG57mywNfck/OQcpeOgX3LbM5z3nfMEo1GkIMnlZzy64GfyKM5r7rbTRyMN+LWxregk6jIz43ntL9FmaDrUaIjOTZl6DYQvBTsaFGM/ZOnTqxbJm4gZY36qOPPqJnz561U7N/MRmFGYr69dmOzxLsFmyT0dYGU/r3RwrN7S1lXxRmMikn4e/XIeV0RUcL5o6CFDsvraKqJ2fVwlgCeSmUOXkyNn07j4cE8WWCgxqiQ/OEcCMjSbDNHLIuq1Q80DtCGpNmNA+0K86usHs6f1fHs2Na9mU/jQ7nsjJis85TUlbLL++rxZkN8M+UK+v7URG5yYAEHmYhLLvEfqQXL6N5Re3mJTc7JCxct+QkitVG3wZiNVzGWExKfgof7/2YjEv74Mty4TgzzsM3neG7bvBDL9j8MWx4z2zqs2maCOsX0gb6vGhts2xa7dpycQt3r7ybKbunQEmBtZPjnkhY9ljF9a7T3u5meQXeMndJdQhwDWBwuDnzdkXxvOuWaRidk2tjZ985uDMA+5L21ej3rwiWoTlTqvAZKsyCzR8J04uqyjqC5bNcXlh0s6/1TCtIs7sdzGGpy/OvFQIstWLntwtBwLOOiKqk0ZjNqfRO8ORueOaAedJckIEkSUruih8O/8Dty25nVcwqMosyrYSqK95+sj+Iu8Uil84grsEy1O+dM0SyLktMK/8SQJNBTD4wnZErRrL9kkgAKC98RfiJhYHmvs0BkyYAc5/x1Drx+yWxaJNWnMUcL2HJMLTBUDaP2cyC2xfQwk8ENckpzuFslrB+iM2JZX3aEXNbm8gpzuG+YmHd0MfZerzRnN9KuzyzBm5aShr6pGMYCnNo7NOYQmMh59JN859ODwnNqp9JKK4ooZkKUEMhYOrUqTz11FM88sgjSJLEpEmT6Nq1KzNnzlR9Ahxg7fm1pBem08q/Ff3q9WPdXev4X/v/VX5QvhjIn9MFKavbeRoNHPndXKaC0FpA5f4DuTX0LajwfGKVIt0rmHTTpP3Pwji76lMrUqPhj//BmoliEiRJ1s5vbUYrHy95BlaYSEi2W4bqCQEA90bcC8CYjHTCSksppYyEzPPVOsc1p8wIs26DOXfClo8h7hqY2cjmXxYravLkvoFXA2XbqBID22Mv4asxq6st4z/fcMjqZ79G1qvaB37l+dX38duJ33h/3VPm7fcsNNsjW5qZbJwi4nFHr4WMC2ZBWF7lu3MGeJhelKYsm7JJx+LTiymbEmJdrwpC6SpY2gxbkF0sJk1y+OKa8PmAz21WBi0Z3Ww0f7m0JthohIxzVvs6h5iEgMRrLASUGYX5SGmRtSagqol9tIWNcmXJqBwhbq8I+brtc6HZubgHLJ14LU0rLChvk+0mwUOtHmRjtylsGfGnEoLakozCDJttNzR5qXBhp7UmQM5oW7cj2LNgCIoA/8Yihj3AieUkp5i1fLnlHFjlfD+AVc6LK4KsCfAIst3nFQrDvoIxc8zhNy0JasUpJwND69XhY09nVsUI35sn1j/BOzveUUJ+tvQXWjhZE3A6/TSSJJFRJPrG0s6TaFFcwp05oh1meYsxokuIyCvQyr8VD7Z60G7118eut/qeU5zDS5teIrtMjJm3Gcs5pxdmUb/E7LxeJ8ykYfyqPS1NgsbxXNMCQkuThlHWbsr3GTicctiuUJycn8zQJUN5Y+sbZq3If4QaCQF9+vRh69atFBQU0LRpUxYsWEDDhg3ZuXOnVbQgFfvIk9fhTYaj0+rsZrS1Id9sX+1jymqbodMKD3iZylZQy00ES/q/hvEWUzKs2g41akoHnuRhfvGnUVZ5pJ38dHOCExCToAvbhWAA4BPO/OZm04LTGaf5+/zfNqdx1btaDTwGrcGmTGVM7DKRZXcsY2hAB8JNg86FcxuqOOo6IycBLliEW6wo7N2VpBIhoHVAa3rV7UWwWzBDe0wE4K1is63y4eTDV6+etYkkiSRDIISAAGu1+ZF80SZ7pDxz7I36PSHi9orPmRqtJOchvCfc8pH47B4gbIFBCB6lxRgls5B93KncS9RynJDp9yrc8Y2IDtLuHrs/L9+zyxECANILzQEI+tazDq35UOuHhOYEbFbtmvs2R6/Vczbz7LXNCnpkoQjFuPC+cpqA05Vr2ix9QS53seXMeqERXj9ZZAk2FkPdzjD8OwjvAZ0n2D2svBAwMieHF7PyCVhwH9q/Xmd8y/E2x0SlOWDmdCOx+iWYNRT2/Gi7rwItmIIsBGx4l1OzBtnu1rta5fUB6/5+RZD7kkcFGrpOD0CLYdaHFOfy+tbX2Zm4m3vr1SXeoOe3NGvfhaXRSxXTsNam3B/ezt6EuoeSUZTBzGMzlWvzDRPhgVsViYl7mWkeIwvuAAPCB9A+sL3yvWuImB9aRoLLKc5h/J/j2ZkgfFReSsugdWa5aEyFmdQvMWvk63QwjbOFWbR2F6HBfylJFC7FsuNx81sAkI4to8hYxP6k/Yz/czwP//2wTXMtPr2YS7mXWBmzkpErRl5fPkhXmBoJAZMnT6Z9+/bMnTuXU6dOER0dzcKFC2nfvj2TJ0+u5Sr++5CFgPIhQSvFpAnAzR9fZzEoZZVTp1FUyWTPwoHtvHcIt6asZ8T5BSLnQG5KxcfVBFM4tURXa0fn5MxKnHSWPS5emIEtzNviDyrOzyVNb+bD/dYZR+dEzbE5zabRm6rXruXQa/U08W0Cd3xNfUm0b+ylG8xhtXzoQAcjW9QaF/eLELRg5fAqTyi9nb35YfAPrL97Pd2biBfVzWnxrB4pQtTZSxp1Q5B2xhxKMKwbdHxA2OgOnkyWxUpjllbDx34+cOdP4OIFg96GO74WDrUDykUAil4Lh+aKFd+7ZoKTu3mfjwgBWRa7g+VfN2dT3CZl115XYZtLsP0kXhlaLaukHIzt74VH/wF3+xozWRNQVdCC6jCp+yQ6BXfC19mXnffspJ5nvQqFAL1WTz2PehSXFZsjgFwL5Hwk0X9br/6XFtg+b5ZYamcvVwiQ866AiIKi0cLgydBhHDz8l13HbrAIn2iia0GhcAwHODSHWxrcQv+w/gDKZHZv0r8s/8+JP8R/e9ryRgMqPXSnXuKsQWgqzxtsF5V237ubV7u+ShMfc4ShvJK8KxsmVI625xlSeTkL1pxfw6qYVTy27jGKqxCoRzUdpUTkARTH3HlR88gqysLd4I6zRzDc/QstW45RyrnqXKw0va56V3679Te6hnTF29mbN7u/CVgLAXNOzFF8JOu6hzI+OwfK+xAWZBJcal7kcGlxOzQVwQlud29IHfc6nNUaOeTibG6TJjeB1sC7ucfoPKezknFY/i1Lym+bGzW30vb5N1EjIeDdd9+t0T4VgfwA1HGvRkQQRQjwU2zyLtRrZ1umIpVzglhdndHnUYb5OZGYn8z5wlQGh9dlXk4VvgTVxZS/IMngYrU5I9mOwyMI4eXsPyLe/0N/wkiTT8B5syYgwatim+TXu77OQ60e4tE2j+JmcKNn3Z4MCh/EpO6Tan4N/o1p0Easju7JtojklJcKvw6DU1cwBFx++uUlVysv1FU2SaltJEk4nspCgLetJsBqQunsIVZuCtKpU1qGXqPnYs7Fa7vqW1PkF1dQS+GQp9VC10eh9wtcjBhqVXSOtxe0vVt80eqg4/3CobbfRBGesEEf4vQ6Hi08yQJ3F+5u1JS3jnxnPbFwC+CQixvtGobzlp+1Kcjnfr6ceHyDiHQiY3CHYSJ52fsBfrwet4pvDn1j91KyirI4lX5Kydh7uULAt4O+pX9Yf7aO2UqIewjfD/6e1XeuxsPJVO8KhACAME8h7FxT4dBygUWeSMrReCozw7QSAirWuH554Eve3/l+5RPH8r/TeKBtRlY7WGoCnq93MwPyLZxW9a7o9v3MV9ll/DNqPf9r/z90Gh17EvZU6ktww2FpOw8w4gd4bDM8fxTqdbZ/DCIT7WM5BxlRT7yrYw16mzKyJv+HwT8oWi6jZKTQWGhTttawNDt0kBILx3R/F/tC/5I7lrBx9EYm95xstV2OnidHP5IXImk1kuY3f6SUC/EItRs04NtB37J65GoaeTfC08mTlIIUioxFSJLEwlMLAZg1ZBaLhi1Gr3cV71nLhG6FmTQtKWF0cA9e7/q61bW7XzpA/3r9AIh1cgWTpQRObhDckiUeQsu8/Gy5vAoyksTRcgkJ/4z588rnerhOqNVQPidOnCAgwLGQjP9l4vNMQoBHdYQAk3rRzR9XvYiT+5qURNGdP3Km19PM9fJAWv8OfNIETq2xPT41GiPw1UVbE5qp1ILqK+WUyJAqScoqRZJedC9/rRAG0pOP2x4nSbD8KRHBJLybiMwQZLLlO70GdopJygUXd6vDLFf7OwV34sXOL/Jsx2cBYQL0xYAvGN18NJfD4AZD8DSW8Y8xg4s5plW4TVNFkpX5Yyo/uKbkJMFnzWHeZZy/vHnX5doiV4eccmpcO+ZAnoZyE8omwnFUf2o1dTzqUGgsvDETh8mTtEYDbGxxU0wJ/hoUm1/EWUVZrD2/1iYyy5YWg/il4whuDavLLldXpgT4cbI0h+Vnl1urqbVaPvezNtOZnGKeuC0+/6e1zXDDvkI4AdaZQkXOOiYiahjLjMw/OZ9DyYcoKC1g1IpR3LXyLrbHC2fByxUC+tbry9cDv1ZMGV31rtbnrEQIkMOTfrbvM5t9V43yCaU8Q6GesH22WrU8+SccXkhhaSE/Hf2J8xYhUW2eDQt+OvoTv5/+vXKH0kyTzXO7ewGNCAfpAHLErR8H/8iE/tPQuFvakUvw58toDs0hMC8NLycRcaXQWMjvp363f8IbDUmyzZXhESTMgCrIki1jaRYlYRYCQtzFarOPs4+yP9g9mG8HfatE0rpi2eaNpaLP6V2EU7ODyONvK/9WbLh7g9Xz19q/NW0D29LUp6ndsNoGrYH6Xma/IT9Xs6mvQWfWjpQPAy3jondRFi/ld3dCbgIxWTGkFabRwKsBnUM64+nsJYJJSEYosDCpKshEC0xq9Qj3trjXVAmTpmLzNMJTxPN5wd3Leuy1jJRkgaVAZPzjKZJMUcumebSmvld94vPiRTSk/wDVEgJCQkIICQmx+iz/BQUF0bZtW8aMuUKTo38JiXmJpBem4+/ij5vBreoDZCzMgSzVjpfqd2Vk/Aqm+fux38UZkGDNq9bHShLkJpFoqDgTpPFyw2j98T+RIfX8NiVEYpxGSNItTWrF9Azb3AjEbDKrauWIJwHNSNTpSNWZu2dsOcunXnXM/gENvBtcXt0rwCuwBT0LxKrZLUtvIWrmAJGg6UqSeETY+sZsFNqG6t6X7ARF66MkjSkfT/xKYpkkzreBmHjKVavItERerd43i2YmJ7SvDnx1JWt5Zagk6VaykzDP6VNQQK9S8ZL67tB3vLT5JSsb1RJjCU9teIrPDn5p9ycOJh9kZ/xO5SUmWWhM/om9yKjcPH6PF6t1exP3Wq8UNugtzIlGfE8dnRh7jJKRkrISPtz9IR/u/pAPdn3A4tOLRdxtCy7XJ6BK5DbLuGBjYy9HJ4lKj+J81vkrWw97FOeLqEUGd2HiFXG7iMvub5qEZJyHS/vZt/sL7t7yAjGrnuSvPV/w5YEvGebnRLpsClaBOVChRRbfuJwKshCXGUXWdJ0zDP8W3kxQbJ4ro7C0UMm/EeIRIiLIjJkDHe4DrQEsflv2HbqrmYgzL9ton8s659iENjPu6i44OEphphhTLXGxHxWpPJZ+bGk6LbF6MeH9btB3DG88nF+H/mpzjKzdGv/neH46egXeF1mxYtHMt6F9h+YKkMffUc1GodPqGNt8LACPtnmU+bfPZ84tcyr1Twx2M2vj72pqnYvgvpb3ATi08CYLAe/seIcRy0cAZmdiAGQh1VJzJvvhyKv8YJVoLPyEMCWN8ysX4MAyGZkFymJK2llSjy3AqNEQXlLCbWkJdAoWiRBXn16C0ZEQwDc41RICPv30Uz799FOrz/Lf119/zfbt2/nmG/vqZRXBugsiWkR557gqsRACxkaMRYN4WP8484dSJNWU4IOSAhG/ev27wqykMBNKC4n1tFaJPtHOnM477eKu6tXHkowLcMnkYLTrOzgtTGWiisRkpEcDYbuXkZ8sXhKHF8DSx4S5z3bTZKfFMOj6OMXGYj47/B03hddlYFg9ZCvAOIvwki46F6v2c9Y517zuleHiQ7hFQKN3jXaiEdW2ytAyhN38MbCuGll0jSUQ2U+EgwQIFtEdruqLWVZT+zYUNu4WNuxyjHibiE2NBkBQK0iL5sWA7jjrnPn7wt9mc4TkKBEus7bjrNc2coheO0JAqullHWg00qG1sLued3Kesl9OznQ++3ylP/HS5pd4bN1jPLL2EUqMJeSazvtFUgqBRiEQRHg3wM/Fj/PZ50kPbgFdHwf3QKSI2/ju0He8lXuCeKNZuEzJT1EynJ7KOMU/sf/Y/G5t+gTYxWBa1SzKFk64Ftze2Ow4XV44uSrIgm1QBNzxFYydC8GtzNqLDe/BjIG8eDySk85OPBcUyKl93yuHrwkyTUwqEAIso8pcyK4gn0p+usjp4hkiJn4G26yp9s5798q7lQl8iJvJVjq8Gwz/RgiFlpjGiTYBbXDWOXM09SgbLmzgjj/uYMquKZX/WGGWCG07584q63XVsefz5oAQIEkSJzPMQsAjdepwyaAnoAya+DThg94f0MjH1hzHwyCEgEu5l/jygB1hPmYzbP+q5u8OxRSoYeXlylF+Eebxdo8TeVMkT3d4GqDKACVK/hFgZNORVvte7PQiPw7+kUfaVK2dau4nhPoDyWYTnH4mcx7ArL2Un5ek4+ZcRpb3Lbw7NOovPpqCeMQ6W88FJAuNhSUvb36ZQ8mHIDueJL2YN4WUGiE7XjE//OXUAmbNvVkI3/9iqiUEjB8/nvHjx7NmzRrls/w3ZswYunWr2j7xv876CyI01s0NbDNuVoqSfVWYAw1vImL/7k4wO61myqsCxXnwXXcRVnDXd0p40Fg369W8p9o/RVe9sO1Luhwh4ISFrZ3JgS5Lq+FiXgI+zj60DBK+CxlajbAVX/mceNH/cqtY8Ta4Cz8Agwszj87kl+O/ACBp4ICLMzTsS4LJua2JTxN+u/U3+tbry0udXiLypkiuGBoN4RZmiTqLMbsE2HJ+HflfdxCmO5+3EWFNqyLhSOVxi/PK2eGm29GepEbbT0gVs9l6ohEkQv8lZscxZPGQK7MqVZ40U327PmaOqmFCnuBYqpUBMalpKkyCwvKzGRg2kDKpjI1xG8X+77qLCDk7r9MFhsIsIcyeEqtRBLWwKZIs4lYQWGrkpmYjbfafyzrH/9b/jztX2J9EyeYHMgeSD7AhbgNJzkLI6t32QWWfJjCCRt5icjJ61RjGcYmSF05wQsrn+8Pf29jGnkg7oUwQQGQ7NWgNVg5+bvpqaC1rihxNafNHVpsNWoOStfSaRO2QI5QFNLPe3vxWuzbZ550MnLNwIF0b3EB8yE0Sds6/3A6/36/szyo2CwEVagIKzOagjrIqZpWVUGmjeZaFGBnTQpOTzok2AW0oLSvl+U3PA7AyZmXlPxa7SzwHCYfh9N/X18TJXvS7SsyAJEnioz0f0f/3/hxJNiepO2sybx2cl09l02V3g7XpalH5yFyz74B1k4RZaU3IMi1GVWHKVB7Zv0fW6jnrnOlRp0fFif/KIftp6TW2fhF6rZ6edXui19ruK0/5kLQt/FrQp14f8wbZf0P2ZVvxrHmfpfO7RgPtxYJKiFEIAeUjYRU6mYXlANcAbmkotGdHUo9w35r7SEg/TaJp8TRY0kBuMvXdzSasX/r5CFPnfzE18gkYOnRo1YWqQVlZGbm5uRgtkgY5QknJdb4yaIfPB3zO5B6T6RZaTYFJ1gS4C3s9OVeAZUbbDNl8xlJ1mxmnRCw56Gx+QD/qI160chKgxIwzwtawJsjmPBYc7yrCfbb0b6nECE/X6eDAr9YqaIDmQ4UTD7A/2Tpk2R9d7oHRs5UVwE/7fUqEXwQajYYHWz9Ijzo9alZnB6nTZqzy2c+if87x9uSpzS/ylj5HaD6yYkVY08pWdwoy4Mc+IlGUJMHemUJbY3mMbLrT8X7zMZaUGWHmTfB9T/PLID0GljwClhkTAdrfAy7ezCqMJT4vni8PfElJiWkFuKzM2vGqNigpMK9S+Te22lUmlXEx5yI6jc6+L4zsO5B5QQkxdzaznABUmQPmtWTWbWaNTfvxdlfoUk0TgUCjkUa+Tbmj8R30qdtHsb/9/MDnbLtkDusqr0YBLB+xnIdbm02G5Odp+ZnlZEsl+Bo8cR5ooTFqOUJ5rpPykziScoQ/YpZXGGtfjhMuIyHRJqCNlbbNoTDGl8tok2lFZpzNWCRf81VxVk0/B0seNU9kZSHAv4l1ORcv6DtR+RoimW0Wt7uZJx9Hci6Q7+YrJsnxB+H8VrFwYnI2ttQEVCgEWGiCq8JYZiQxL5Ed8TuUbY+2edS2oI0QYBaw5NjwMlVqgs5vNX+eNxo+byXaEcS48Ocrtlmza4IkVX8F3Z4vhr5i7fHhlMPMiZpDemE6OSW2YbfvysoSC20VIGsCZBR/svKU9zNxFDvhlx06zCToezs5ZgpVnje7v0kz32bMvmV21YUrQc4/AELAn3HzDGtBxKOcOZDluF/+vpmizzlL4Kd3I6c4h/wSs5Yz1+SvoAP+GP4HHYM6Wh1+IO0YSXqTn4fOHZAI15gFeB+jUZhe/YupsWPw/v37eeONNxg/fjxjx461+nOUxMREPvjgAxo2bIinpydbt26t+iDg/fffx9/fHxcXF1q0aMH69eurPug6wc/Fj1HNRlU7fr3ZMVi8DAPdAm2KpOl0NtsozoV9P5Os0/FXWTYuOhc2jt7IrY1uBSDYZJ+XeHYtfBAIlw7YnqMyZFMgS5Oc0HbsCxIToQ5BHQh2C8ZJoyfayUBcqklo6fMyjJoJvZ4TYe4Q/hKWQg3A6kubSSorVoQAS7vEq0FEn9eUzznhXUV9gX/chNAiO1gqlA9tZollRuf0GFj9otDWnLZw1pZXP2R7/vJCQOJR87bdP4j/c0bB0UVw0jSZa3ITPLUHfMKROj7AHlfzvRkwtxvFRTnCGfuz5rYOczXlxHL4sC5EmTI3l1sh3Ri7kUJjIXU86tjv+/ILbec3BF88BJgiUVi+8B1YZbrqFOVCkkUseDuRRjILM9mbEYUGqH+nmAhN6T2F7wZ/p6jB5WydMm91fwudRkcr/1Y08m5k1e8n95iMXqNXhIYgjzpCiL77VxgzF1qNsHlOtl/abqU1dNW7KjG7N8Ta5sFoG9iWh1o/hJPWydpe90ri6gsBzYXZS7b1xEk2IZt1fJZiOnXF+ONJOPo7zL9HmFOeNbVPubwPAETcJmyYw3tSEmAtJDQoLqFbYHtKpVI2e/uzwsOdkmOLzQVSxQqjpRBQoZBjER2uKp5Y/wQ3Lb6JLRfFSvOm0ZuUoAlWlBdW882/bel3BpBfkl95xK7z22y3HV4g/q94RsTnX2mnDtVl01T4IFi8d6pCkuDwQttAGeVW6stTPqQqwPMdn+flzi+zIM+J5iUllY6b5TUBVonDLKNMXbYQUI3AIpg1TjX174nwi2DJHUtoE2jfzt5RLB2P3Q3utlmrZQ2HHIpX1igPs2NaZRF9Lthk7mZpMphjmhM1L9Ph7ezNiCYjrBZYYnPjOeIsfCXDteI9WX/2XWLyD+RqtZRczeh614AaCQG///47ffr04fTp08ydOxe9Xs+hQ4dYuHBhtVbnf/rpJwoKCpg3b17VhU18++23fPLJJyxZsoTc3Fzuvfdehg0bxtmzdswm/k3kp4FGB6YHRgnRZUGGVkuaVovVHTiyEE4s56xBjxGJbqHdrB7CeqYVn1iDHqQy2Pdz9eolawHaWTiES2VKxJMuIV1wM7gxqv7NlGo0rPTwAIMbtBsLbe6Cm95THvppe6YpEQxkjJKRf+L+Ia0gDXeDuzmk4FXCy8mLpXcsBWB/2jGe0CRzqWEPKtRZ2XsZyqRaCAFfW6xIbJ5mnuzKZl/yhCMzjrTsOHO4MsvzyyZB8uq7zG2fQaCwu9zkYuCMReKoLA0s3/QmHJ4n1OTVFfoq4twWEdFBxiID7YXsC4pZgWXsaSssXmgBu4WJ15mMMxRbClWVhFi8ZsTutP5usTr3xf4v+GDXB2yI3UB+aT6D699ESDNrZ87yk/XvBn3HX6P+omednmwbu41fhv4CiCQ7ver0YlL3SQwIH6A4rwEMa2xKCtRqBLS43e55z2WdY1fCLgxaAxtHb+TvUX8rqnEQk75bGpi/t/RvSYBrABvHbOSHwT9Uq0kuC1l43B0pzGZMTu7ymJVakMrsE5e3ElklsgCSeERo2OJ2i/vasJ9tWRdveHovjF+iJFHqGNiBpzMyWRCfSKc6PQF4xaWYNwP9ef+CEJJTtVrKksUkJyvObIqZUZAi+nl+ulhBl7GIDlcZxcZi9ibuRafR0di7Mfe3vL/irOk2mgBzNJaG3mYBwaA1YJSMFUcuks2AypNwCFLPwFELwae0mLySPCvBp1ps/kgkvjvggFYhei0sewxkweuWj6HxIHhkXaWHlV/993PxY0KbCTzQ6gFaOZneu5a+W1VwJtNisi/H9wfrRHLVQT5HdTUBsjmQ8xV28neA0c2EA/FN9W+y3RkunhkumBZGZHOutnYWmOXEYECwKYqYpRD3zjGRHM7TpPV20buwaNgi3u0pQtlHFyaz2c0VHRr6BotFERdJ4q+4eMJKSijVaEioIvvzsuhlPLL2kRs2y3aNhIAPPviA3377jcWLxcM1Z84cTpw4wbPPPoubm+O2o2+99RZTpkyhfn37Kevt8cUXXzBhwgT69++Pq6srkyZNIigoiB9+uIovqqtNcb5ISuPmp0QDaB/U3qbYaScn+tevxwOhtqvlSaY45eVtixuGiPOcl+MfV2eSXVosXtYAbUaLVUitHmOv54hKj0Kv0dMmQKwa9KwvbL6jnQzQ+WEIaMrG2I3suCRU1jFZMWyIFWHLHmr9EK56V2WA+HD3h0hIZse2q4zlysH2S9sZyiWOuphX163WxyoTAkyJz2yIP2ieTJpyLOAZAgY31rk6MWDprby0+SWxEmcZrSA73lYA0OisXg6bC8X5/peRxaA8oSbdbLnyW1sT6/IrY3oheGQVZXH7MjEx9XH24dUur5Y/UuBdT/kYZFqFOZt1lkm73jOXsXyBXi+U9+8wrUyVSWXMPDaThacWciFHCDJyBk5LZCc5mS4hXZToGR5OHrjoXZTPP9z0gxJ9456Ie9BqtDza5lHub3k/5QlyC7L6HpMVQ0lZCb3q9CLANQBfF18i/CKU/T3r9BTRY0zIKnsvJy+cdBVHFat1ZDOyXd8KE5Mf+0FZmWIOBHA0pYaTJ0exjEAStUKsHD+4qsJkXLj6UGZwIasoC2edM7/c8iuPj1qK+yP/iMSDFixz0bLZ1YUB9evxxam5fLl8PDPPLlX2p2degE+bwscNYcG95gMd1AScyzqHUTIS4RfBHyP+YGKXiRUXDmgmFmDkrLMWAQRa+bciyC2IIQ2G0MJP+LhUqKW4uFcsIHmUG59P/wW7vwdzfmxKsuIYt3ocw/8YTn5+Omz7wmzWWBWW5otO7nBoPsRVktTs2FLr701vhvuWCqfuSigf5tIyDKjimFqJJqC8SZeViaulhivpeNWmTaf+grMbrbfJ7eXtuBBQUFpAZlEmGjQ25krXgte6vcbUPlN5sdOLtjv9G4s+mR4j3ncFGeDsJYIHlEfvDBPWwWObrUwgQdzHQ+nCskBjYdLjbnBXxreNJakUaLW08myAn0WiRndJIlDWBuTb1wQk5SXxv/X/4+0db7M7YbeVOee2S9t4b+d7HE+z47t3nVEjIeD06dPceqswJzEYDOTn56PVannrrbf4888/a7WClqSlpXHmzBn69rWOrNOvXz927boMx9brHTv2oCHuIRy47wAvdXqJ+1uI8FznnYSZxVEXZ9DoeLNOGB/4i5WLxIY9leMsaeAvBnjFkS3bwQEZ4OIeMajV6cC8wjj6Hv6YdwY+yZCTP1JkLCLcK1yZQDT2FxOO9e5uzNYVklWUxbMbn+Xx9SIi0N/nhEnM8MbDeaHjC+wZt8cqDChcuVCgVeGid1FyM9gj2dIMq1JNgGlFyORg+JmvDy+GhAghIvmEiJZ0ca+YyHuHIZXk85WvD5JGRJXa/0Nns7kNQEoUOV93JMYqgY0EOvE9qyiL1cniJTkoL59JGeLldkJr8TLNqiU7e0thor75vlm+EOfcOkdkh7WHm1k75Wc01+/PZIuXfHX6ZnXJSzXHYa+MohyzjTjYmn+ZNBqWq6ZyLH578bf71etntV2e9FfFoPqD2H3vbp7t+Kxde33ZnMNJ62TlrNcx2KyBah3QWik3MHwgIxqPoG+9vjzQ8gEl1vlVx8afQoL0GCtB3NE2qjHlhc3gVlUmZcouysYoGfFz8RP3I6wL1O1otx1fCBamnLOK4vgp8zBxFrrbDKnYPGU++w/MvVtExXLQJ0DOfFqhxs0Sg6tIlnXfH+K7hTmQm8GNdXet4+O+Hysx4X888iOjV462XfHMNi1cNBti+xvlQir/dWY5Z7POklaYxpYd02D9O/Bl26rrCiJMq8y5LfDHEzBzsLVwkBkrns8LO6zHSicPK+1kRZzJOGNjDlRdIaBfmNAY9arbC61Gy8Gkg+bIOpZjTEE6TG8B+2bZOQti8W/+GPhthPAFA3GtWXEiW3R5oasSlkYvpchYRPfQ7ui0dsyGrzIGrYHbG91uX7Ov0Sj5TFhrmpiXT/ZmSVhXqNNemdvI9y+3xCzMnSl3yfJ4IosG4V7hwheh5QiljGuZeBILLPMVWDDv5Dyrib+lU/KKMytYdHoRx1P/pUJAUVERrq5iUlSnTh1OnhRqzcLCQoqKLiPTaRUkJQkJLzDQukMEBgaSnFzximZRURHZ2dlWf4DVMSkpKWRliQe7tLSUhIQE5Vpyc3NJTDQPDKmpqWRmZgJgNBpJSEigsFA4u+bl5ZGQYO4MaWlpZGSIQbOsrIyEhAQKTLHn8/PzSUhIUEw90tPTSU8XHU6SJBISEsjPz4f8VApwJkEfRplpwMvIyCA7I5sHWz/Is52ew6fIByejmHDry/RE3fILK520LPTy5MzAqfy6V6hPg92CSUxMJDdXPCBuuFG32J8UrRP5Gg1ZGWmkpJgl36SkJHJyhHq0uLiYhIQExeQrOzmOZPwhuDXzTs7DmGNkzam/ScpPQlumpYGmAcXFwn7XS/LCu1gMoJ9cWsvWU1txLRV9aMKaCWw5sQV9mZ4hDYaQl5dHYmIidT1NK6IlHtQ31OeFTi9cVnsXFBRYtXdGRobS3oC5vS3Kyu1dR1sHjxLzgOVd5I2zUWgDThjcSHBugtE9lOMFSXy15WOSks12iUlJSeTm5EDqaYoxkNDqCUrR8YuPF9sM3hzUB4mX15EFJONPTudnwD2AVI0TmVIgujIxgu0qyCe5yGxPn4If7/iFMbxeHeYHNSSBIIpDhUozNzeX1/58jUKTQ6p3iQf6Li8SXFpKqs7ACW0wRThBZqzS3tXpszLp6emibF4KEpAw8GsKbv9RacMLFy+ABDfXvxkvoxdpaeaJRkJCAnl5wsGusLiYhDFrMYb3Rge4lbgp7Z2l1ZJIILk52WAspaioiEvxlygqFteWlZXleJ/NzrZ67pOTk8V48GM/Sr5oT8K500qfzcnJUcYcMI0RSyfCN50pPb1ejBFp4qWeixuJBCiryGcvncWtVGhFNZIGnyIfvLWi/1v2WZ1Wx6ddPqWRUyPua3lftcYIZ51zhX22gXcDvu/1PYsGLVKCCPgU+RBqEOrzwsJCEhISmHnTTGbePJPGzo3xKvXi20Hf8nKXl0WfNY0RRUVFJCQkUFpaWnvtjQjskJCQYN3eGrMWMwU/svCEhEMEOAfwUtOX0JfpSSlIuWJjckFWKgn5WiST5iEDb9INZpMDe+2dnp/Oa1tfw63EjWDM9U9MTMRPK86jL9PjU+SDRtJQotHgWuqKZ7HZ2da72BvnUmdKNBrSNU7EE0QpOoheS/bZ3aSkmyadrn4kJycr7S23odze0YnReBV7KdGhUlJSlPaW32tye+fm5or+bQo2kZpTqLwDjUYjSYlJlBSXEOAagLPRmV2ndhGVHsW2S9us2zA/gwSCKHAR156PCwn9pivXlo4PGS5iAn409Tg+RT4YjAY2ph+jABcSyvwoixH+gBkZGRWPEfFRJBCEES3EbCITL1LxFYtRQGLcOXK/GwzfdKZo1nASSjwobT0WntpL1thVpFic116fPZ16mpErRrLs2DK8is0mM/6l/uY+6+Qtxtlcce02Y0RSIkPj4olsOIbP+3xOM10ziouLySjMIDcnh8Q9y5SyqfiSmZMLq57HaLqPVn02WoTFPOjsxDcbPyItPQ2y4igrKSDBqwMFJUIwcGQecejSIQDubHCn1Xut0vY2jRFywJbMzExSU83aIst5RK2PES3GifY+s0m0t1uo/fa2mLcFOgfiU+RDUrbYn5yZjHeRGHPDS0pITYpXxggXrQt1jHUwGMX7NMS9iRgjBr0N7kGk4YN7qfDtyC/ItDuPiMsWY797iTvuJe5KgsvzcefZfmE7Wo2WXkG9Km3vxMREpb3lNpTbOysry6q9LcdkuQ3l9s7OzrZqb8vPVXHZGYNHjBjBAw88wAcffMCdd97JwIEDL/eUVVJWLqpJWVlZpdErpk6dire3t/IXFiakwN9/N2dEXLx4MTt2CNOU7OxsIiMjlRfH4cOH+fVXsw3i8uXL2bJFOF3l5+cTGRlJbKxYUT1+/DgzZ85Uyq5evZp//hFxt0tKSoiMjCQmRqzWnD59msjISOXh/fvvv/n7b7EiLkkSkZGRnD59GvLTiCGcyMQ2yoPzzz//sHq1CEnorHNmYMIAwvLEdQUUBvD7moPKJHXmiTi6pArnvhD3EH799VcOHxY2nImJifSIH4Cr0ZU76oXyfq6fYuYFMHfuXPbvF+rMlJQUIiMjlQFmz8k4FjCcZFdPLmRfoEdyD5pki5VFj1IP/A75KQ/s4UOHGZAyQDnvgQ0HaJ4lTCFOJ54mIjqCesZ6tA1sy9GjR5k1axbNfMWKec+Mnjzi9gj1vepTWFhIZGQkFy6IFdioqChmzJihnHfNmjWKo3hpaSmRkZGcOSNW4KOjo4mMjFQesrVr1/LXX38px0ZGRioC7fnz54mMjFQEwRYZLeiUarbDHpBobu+junpEFt9Bnl8rxtYNYf/e4/y60NxfZs+M5OCX90BaNIm6ukRuuUhC15cAaJrdlPVlt4oQkwdmM48R7JWECdUZfQCDEwbjWSImCzFlrZnHCHHSgGYs4naSSsUq2vfOXkRqxrOh8Qh2xu9k977d+B4TWqC2Ri0ruYUteY1oVVSMi9GFRdI44giFzFj2HtrLjJ9mcCZDtNPKlSvZuFGooIuKioiMjOT8+fMAnDx5kshIc1jWv/76i7Vr10JuMkZ0RG48R3SCeEGeOXOGfcv3oZN0+Lr4sn79etasMTvpzZgxg6goYd504cIFIn//i8IuTwHQK705nVOFk+0Zg4FZjOao1BTykjl9/jQ/zfiJofOHciLtBNu2bWPpUrPqf86cORw8KF6gSUlJREZGKhOWXbt2mZ/7S/tZMO839uzaDtkXSceHyNnzSTkt+vv+3duZG/kFLHoILh1g8YK57DglJp7Zaz4QY0SqeAEdDnuQX50eVLJVblu7jRaZQsvmbHRmcMJgjOmi35UfI45vPc59hvt4pcsrNR8jgJiYGCIjI5UxIulwEtvWb1OCCAxIGIAxQdQhNjaWyMhIDEYDXUO7smXLFpYvN4cOtRwjEhISiIyMVCZCO3bscHyM2LOHBQsWKGV///13RWubkZFBZGSkMkYcPHiQORvN5m5LdcPZRhe4dIDc3FwurLuAX5EfyfnJyhghs2LFCjatWwOft6Fw2/c1HyOO7iNSMx6jadV4LX35K9Xsr2JvjJi8dTLb47fTKrMVDS+aNRk///wzMafEffQv8mdwwmBcjEKL0SKzhTImA/RN7EvbbKE1iNKFMEMznv8FNOSgsxM7d+1h0TmTwOAeyLx589i7V2jIUlNTiYyMVCYLGdEZ9ErqpZiDLVq0iJ07halhZmYmkZGRivB08OBBZs+erTheLsvtoLzX8vLyiIyMJC4ujnDPcMLywhiQKMbvzKJM6zEiN5NIzXjO57vBA6s42fJlIrdcFAnJgL/oz1qDCImdF7OJwQmDCS0I5VRRGiudmhCpGU/pti+hpID1y+awRrYmyEmyHiNiLxCpGU8h4r22iR6s4GY4JwSIWb/N42ixWDi6RAiRmvFsbTiAdM8AtkXFVzlG7I4RjvNNspvQI9kcdc4ryos9e4SgkS55E6kZT0qqmMjt37+fuXPnKmUXz/6RXdu30uOfTyjY+zutz7TGt8iX3JJcDu/Zwq9JLYSpS5+XWM4QttAdgPyzO2znEUuF2eb9dUI4se8i85f/BiknKcFAZHa/ao0R+fFCcNVl6KzGCMt5BMDMmTM5flysXstjhCz0XtUx4uRFcPYiA9HeSQahQT548CBz5sxRyi5dupRt28RqvI/Gh8EJg8lIEmP96ROn6Z/YH4APU9JYsWIlmzZtAoSA0zOuJwFFQgB2y3AXY4R/Y5gYzZrGH+CB8JHKK8yxO4+QEzaOKBtB+/T2XMoVmupff/4Vv2w/OgZ1JDsx22oesXHjRlauNIfb/fnnnzl27BgAcXFxREZGKkLBli1bWLbMLDTOnj1b6bOJiYlERkYqQs3OnTtZtGiRUtbyc1VoJKn6GSs2bdpE//79ASEVvf322+zcuZOIiAg+/PBDgoKCKj9BOS5evEhYWBgbN25UzmuPzMxMfH19WbRoEXfdZc5YN27cOOLj45VBqTxFRUVWGors7GzCwsKIjo6mSRMxaU1JScHJyQlvb29KS0tJSUnBz88PZ2dncnNzyc3NVbIlp6amotfr8fHxwWg0kpycjK+vLy4uLuTl5ZGdnU1oqJBc09LS0Gq1+Pr6UlZWRlJSEj4+Pri6upKfn09WVhYhISFoNBrlofDz80OSJBITE/H29sbtzCoKlj5NZov7CL77E7RaLRkZGZSVleHvL9TD980dzYmisxTritGX6RkeOpyliUuRNBKeRk+kMolcQy5/j/obba4WDw8PPDw8KCoq4v0N77MyaSVl2jJcS11Z0Pd7GjUVE96kpCTc3Nzw9PSkuLiYtLQ0AgICMEglZK94g8JjKzjYaxQvx/+FV7EXJdoSCvQFaMu0zOg1g/YN2uPk5CQk+MwkRv4zEp1GRwf3DhzPPC7KSlq8ir3o2KAjX978pVV7x+fGU5RdhK+b72W3d0FBAZmZmUp7Z2RkIEkSfn5itS4hIUG0t5ubUjY4OBitVsuiw4uYvnc6uQYhiXsXeVOoL6RIV0R379Y80Ox/rD78IauKL+Fa6sq4puN4ru9zIEkkfdQZ98J4PMin2L0uaeM3kOeUx8hVI3EtdeXmnGJKDdncn5VNQLEXri8ewtPLi41ftuJtVz9alSaz3d2JkBJX5l5MJYg0aDGMlKjtjKvjR4JzMdoyLcNDhrMicQVGrZH23u05l3KOLKcstg1fRUlGDga/MFbMbMUnfn6MzQ/gjowo5gQHUxw2kD0X9lDmUcaOe3c41Gfl9k5PT0dTZsT3m6ZIBncSH96nlM3OzWbOgTl8H/M9T7Z/krH1x1r12YSEBLy8vHB3d6ewsJCMjAyC/HzQLbqPuLN7+NzXn3XepfTNL+Ctwnp4Zp3CY8IKtpQW8Oa6N8l2yuaVbq9we53bKS4uVjSEFfZZg4Hs7GwKCwsJ8nKGaeEk44/Lvb/hNe9WStCTih/+Xe7G6bYPydn8HfkbPyMYMcFKwQ8nivEml1KXQFLGb8Rvdj+ci9PIffY0ucWSMkbM3z+fLw59Qb4+H42kwbvYmwWjF1DXp+6VGSPs9Fl5jJh6bCp/n/8bnyIflo9Zjp+3n7m9g4LQ6XRkZmZSWlpKQIB4KSYmJlqNEenp6QQGBqLX68nKyqp+e5veCcnJybi4uODl5UVJSQmpqan4+/srY0R+bg7BPwrhKaXnuzjt+BRvvyBK/7ebhORERqwbgc6gY8MdG8jLy7Mek4/Mx2fLWxjRkvzoUXz9AxwfI9ydcfXyo+DoajKXPE9IRHc0HceTse4zpNum49egtc0YkZuXS0ZmBsPXD6eEEtxK3LivxX083etppQ09PT357cxv7L+0nyFBQ3jv2HtIGgnXUlf0ZXo0ukyydTq8i71pVZLDDvcyxmYW8JdrKNmGbLQaI8vd++F66RjzNedw6/k8w8LHKe0tt6Hc3hPXTmTHhR1MvWUqfev1JSUlBWdnZ7y8vJT3mtzeubm55OXlERwcDNPqk1qowfDMHrz9g5Rx1s/Pj90pu3lx7Yu4lLqQ5ZzFAy0f4KFGD5nbcNVLJO1bgc+tb+Pa9T7zGJF3HOaMIh0fNCN/xHfZGJ4NDOCgoQ55+jxKdCUYjAaaFjjzS24KrmGdST69A93g9/Hv/QBEDiAh/iJeY37AvcUgCjd+Tsbm7wgiFR1lZOJFKToC2g2F26aTuHMhHhvfwIN8inDisyY3s7D0GEMbDeWNdm9U2WfXp67n4wMf41rqiqHMQLaTmNBOaTeF/o36iz67eTqpG7/Hv9+jOPV5npyCIvLz80UblhlJ+aQrTgWJYoyo152n/RqyO2s3vw37jQaxJ8ld8SohLXtDn5dI/fEO9JTiQw7Grk+R3OEZ6/falh8I2P0eHRuG41Hiwdigzjzn34Syde+Q1OFFfG6e6PAYMWHzBOKK4lg7fC0UYDNGVDomX6sx4vdRlFw8IMbkHuNxGvKOGCPk9i43bzuffp77Ft9HcGAwi0cuZn30eiZvnEx3XT6fxp0ltcur6Hs9qcwjnp93D9tLzlCiK+HbPt/S1LWp1Rjx3d5P+D1pNR8UutD1jhU284jXDr7GgZQDfNz5Y97d+S55hjzuaHwHvsW+zD8/n/va3cfjLR+3OybL7S2PEe7u7kobyu2dlZVFSUmJ0t5JSUm4u7vj4eGhtKHc3tnZ2RQVFSntffbsWZo0aUJWVhZeXpU7gtco5p7lRN3V1ZVPPvmkJqdxiKKiIsrKynB1dcXHx4dWrVqxYcMGRQgoKyvjn3/+4ZFHKs5U5+zsjHO5THKAlbBiaWKk1+uVzgAoHV1GvikAOp3Oqqy7uzvu7uYQYfLNBtBqtVZl3dzcrByp5ckoiLjcStn8NFwpwjXAR3EM9vW1jg7kHRJE8UWxYlKqLWVJ0hLkjCY5uhzQwZPtnhQx2i3M8JydnWkQ1oCyFKFdKdAXUPb7EHhkCwS3VB42ACcnJ1Gnggz4qgNeBRl4AWckoSa7s8OdbL24lfi8eNbcucYqKoWnpyeenp7Uca9DfF48+3L3oTPoWDdqHSOWjyBTk0n/hv1t2rt8fS+nvV1dXRUzNnttWFnZu9rehcZVw8qzKzmQfIAs5yxc9a64SC7syjrGrr1PKWUL9AUka03qzaRjBBeao0OUOjuxK3eXEqatQF/Acl8Ad1Z7uLOow2tEeHkhSRK/NGpNZvoJGgd14FhBLInk4KlJF352re8iIGolKU7ugIYybRnLkpcpur1DWYfACfrU7YO3T33wEdu7FBYiaSTmu6cw3z0AMELiOnAGSiCvJK/6ffbsRkBC4xGolC0pK2H036PF6ogGfF18K21vFxcX8/fxiwlb8SwvHZnDTs9Qtri5UhpYH4+sg5B9iSRDCZnOmQBkFGbg7W0dYs5unzXh5eUlBkVTZI4g0iDvPAAGSgklGZLEaotnUTyemNWxgZhNx/RFaYQWnITiNKjXFQ+/YMtuSo4hh3y9WEGTNBKZzpkEe4l6XZExgor798OtH2bbpW2E+oXi5+1n296Aj4+PVRvKk2sQY4Rl2Rq1twnLMddgMFiVlccIwnvApQME9psAJ36G9LPo008TVrcVPm4+JBckIzlLhHia6xgQEAAeYpVdRxmhC2+GF4VTYJXtnbINfnoS+r6Cq6sPriSDbzg0G4JvOTt3ub7GMiP3b7if7KJsSkw2/fmGfJrUNTsCy234RLsnoJ3IuJrpLJwzO5ZqOLFxEqOzc1k5bhatA1qzfNHd7AAW+LgCmQCUoSEx6zDN8k4zo14wnJiFl1c9RgcLB3GdXsfBgoP0MPbA1+BLJplkO2UrYRcdfq+5+RNQeBYMQlOkjLPJUTTOTqVIV0SRTiykJeYnWrdhYaZ4brzENqXPGgPAPRA/twBoNxS0M8nd/rry7AKU6Eo44VHC3twc0uK38F4DP746+xt9ej8A8QcIBTi5GOq1xrDnK/Z4FNG9QEOwEXwMRijJhsPz4chCQup1BfJhyFScezzJ/F/bgEY4aW6vt52epkhNYL/PZiUKrV6BvoACCpjQegLtAtsxINyswTa4+4hrPbEEtn6E57Av8ewgElYRt5vAgjMiSWP2RfQXd+FUL4zSnFJyS3LxSD+OB6lQpwOEtCEgtL6IoATojs4jtOf/wEX0YXdXF9zj/ybK5OeXa8jlp4xNNIlezm1IhDZuDaZnvaoxIig4iITiBJx1zoR4h6DxMVtNODwmcw3GiMDmGC7uEe0dJHxclDHChGX/DvUOJdM5k7JCMZcp1hWT5ZyFh0bUOyBmCdz2BiD6t48unZIy8ew2C25m5S/p7++Pu48nJEGhscDuOJu9RwiJrcNa4xnlSV5eHivOmvxQdCK4QlVzjtpsQ0vKm8xXRo3MgcrKyhQVnSVRUVE2pjqVUVpaSm5urpWNZW5urmKzCPDUU0/RpYtZbfraa68xa9YsFi5cSGxsLM8++ywFBQX873//q8ml3Bg44BRW3uHXHo+1fczu9vLOayk6rQghWRFxe6zi158tEQ9Dx6COLBq2iL9G/VVhWDrL7U18mhDiHsLqkatZMWIFI5qMqPIarhUajYa7mt3FVwO/on9Yfz7t9ymbx2y2H38bWHF2BQeSDsDxP8SG1qOgyU1Mj+jJ2zveVkJmlue50yL84V/n/+KAKbJBcNNbqeMh1KEJep0Ii9biDnI7jKe0iiRO5eN9Nx0xE9dKHvuUCiIhVMrGKeJ/a3O22wtZFxT1KAghoFr4NaJuqVGJaLRRb+S0wUBZ1kXF9hKoOGxhVVg66J0xhQzs/hRoDRC7A6JWWed1KI9UJpK9AbQYRm5xrlWSmqS8JJtDHMmmeSVo6d+StXet5ddbaiFZ09XgvmUw8Qw4e0ITEVWMOGGOIZu53L3ibpLykqz7q2U87+xLSqb0SpEkWPoIGIvh4Gyz82kVTqQHkw8SnRFtFZMcoKmPnVwCJvRaPY+0eYQJbSbQoe39jGs8EsOtn3Jn0ztp5tuMp4oN+Jeaw+x2DBCZ1p/VZfCWn/klvyN+B0XGIrKKsvj20Le8uvVVHl/3OGDOOVDthFAmvwBL52AAvutO6O8PWW2y6duFmeJ/+ehJOgM8exAeNUUja3oTuaZFrHaF1r6DT4UE8XagP6UaDU+SxJLDZvMtDs+Dz5rxu76YtwL9eaxRc2jQB+6yCGctlYEcajXQOrNzdnE2r259lfv/so2iJROdEc2PR3602jay6UgrAQAwOwannBRJpCyzxMshmxsPUMJZepryGeQW55pDgoa2E2aDD/0Jr8WJPl6QARveM4eFjdkEcbs55e5j9fMf+3oIkbN+TyqipKzEKrN2emE6pVIpwW7BVyfpX20RbpEItArHfBBm0b7OvmQXZ5Nfkq84Bns2MyW3tczRcGI5WZnnlK/25k+uJofwgvLJTU0oyddcvFl6x1Lm3TpPiaQF9qPBXY/USAj45JNPrGzkZX755Rc+++wzh8+zcOFCQkJC6NixI+7u7tx9992EhITw6aefKmVcXFyspNzx48fz1Vdf8e6779KhQweOHTvG+vXrqVOneokzbijk0G2VCAFVJdEaFD6owqgAHYM74mkwS9cper2YBFVE/EGrr2cKxKp3E58mGHQGq3B+5fF3MV+D/JD4u/rT0LvhDTFAeTt78/XArxnSYAiuelcGhlfsAzPr6ExzjOoeT8P4xaxNP1bp+ePz4ikxlvBnjDnKlo+LjxI28pu2Q8m//w9mnfiVQ53sJ+azjL1slY4d0LUcjlslE/KUgmoKAYXZIlmcwQ36mROrnc2yztthkxCmKkyDfhfTZOGTrMOMqhfKzxfXWgkXNRcCLKIiHTfZXXZ+WElcx96f4OIelnq4M8vbk3UWGWAVTgv/htKAJvT/vT93rTSbKJYPEzjvVsdzoVwJvJy8Ko1wdV1hcBXZeAHqtBf/TSumsn9DfF48gxcP5uYlN3Ms1fRM5ZabnJqOqRTLZHw5SZBm6rc+4fbLm7BMsOasc+aL/l/w4+AfHYvKAyKC1/BvoKs5k69bm9H0LRQLYDqNjjuajgQgT6tls0X/O5F2gifXP0nvBb2JPCL8c6LSxaKcIgRU93mT3y0WWYPlvAFaYEHPaXwz8BtAaAKsKMgU/y1Dq8o4e4pwngAu3uRoxRj/Zpk3Lxc5M0Gyn4l48qGvOG6R3wRgq6kNYkpzRcjW5kPtX4tPfQrtTNzOZZ3jeOpxqwzZxcZiZh6dyfMbn7cpbzdLcvkoNZbRbeS+498Yej8POifcTRHhcktyId203xQdDid366zTR3+H2cPF5yTRpxPDhFluR5PDcLpOx9nAxiKEdAV8vOdjblp0k5J4U45aUz5s8HVPxK3mz36OPVdyyOVVMauUnEMergEimlJBBuz4Bs6sh9/v56GsbLSSxJSe79k9l6sp6VtBWZE5OpMFOcU5SshVTydP2gS2YeaQmbzR7Q2+HPClsGK4AajR0tS3336rONFa8vTTT9OvXz8mTqwkNrEF48aNY9y4cZWW+eabb2y2PfbYYzz2mP1V7X8lDmgCwr3ML61uId1oG9iWB1o9wMd7P+aeiHto5V9xbOQA1wC2jN3CjCMz+O7wdyQ7u0PaOZEa3cldZLT95wNo0FuoXi1enIUaDbH5ibjoXBzq9JaagM4httlVbzTqetSlgVcDzmefV7b9nZLPkEA3tsdvJzfzAh4hbYQKGBT1oz0MGj0lUimXci+xP0k4UfUP689N9W9SYqOvSz/CjnUPkleSRz0P23Cb3s7evNntTdZdWIeLzsUmTTqIl1taof2Y39XWBMTuEqtw4T2U3AAAZzOthQB7da0UUyzvQXn5/BTagPOlYkA/nH6SDFfzokCmvApZXSyFAICQNhDQBDzuh3VvQ8xGjjk58Y6FunbzHcvx2/wZxGy0Clcap9VQZCwiLieOwtJCXPQuxOaI83cL7cYTbZ+47Cyb/1lC24v/8YcA24lMaVkp3xz6RiQ0yzX13fCeQpuz8UNxL2/9FBoKYfh81nme3/g8z3Z8Vgjwlv3AWGTOuu1buSZgd6JwIp01ZBYt/FvYZImtEf1e4ZkO91J46CseavVQhYsiCXkJVuEIZfJL8mueFVZ+tyQchkb9xWeLJF+tXIIoq9cJrUZrTvSVlwpHfodL+8T3ivIoWJDr5ApSKY3aP0iLbk+QVpjBzEXWq+035+ax1sOdPa7OtDJZBZQA213thIYd8T2knILjS8330quOskpbnrGrxcJJXY+6tPRvyXs73zObcJTDrhBQfkU6PUaE7Yz+25QTwVTGqw60vxePGLHAkJd6WmQ51rtYJbgCzNnhQSSmAzAlkkt0Etd8d0hvwuI2sdzTg79DG9Nckuz2jyJjEQtOCSfb3078xtQ+UzmXJVa863s5no/pusDVF27/HPLSwLPyRU6Z+1rex66EXaw5t0bJpeTh5CE0OAUZsPZNpWyHomIOtHgGnUnYtvl506JJgUYrksO5mhfPSowlFJQW4OXkhVZjXkv3dPLknoh7qnul15QaaQJSU1MxyHHlLTAYDFah2FRqCSVbZMUr7I29zZLyhDYTeLbjs3g7ezOl9xRaB7SucpVdr9UrL9iLsgpSTms+b7TInrnrO7MA4OoHT2wneuyvGCUjzf2aOxR/uGtIV+Vz5+AbXwgA+G7wd8y9dS4rR6xkeXIudXJT6RDYjhLJSJxBDx0fUKLGlFokLQH4oNcHyuc+9UT+i0Mph8gpySHUPZSvB36Nq97VSi2dVyKiB1zMFYlnLLNHB7sF4+/qz+Jhi1k6fKndezKl9xT8Xfx5Md02w2G1NQFyptCwrlab5SyZk7pPYt6t8yrOD1AR/o1h0Dt4uPoxp+c03u7xNgCxOi3ns8wJ0mqsCSif5KvHM4BIE/9RWBNOGwycdbIe407kx8OIb21W4WKMZjOghLwEio3FXMq9hKvelRk3zfhXCLvXjMAIkTcj5RSUldldzVSSh8mZRTveJ1b+Eg4Js41fbxeJDYEl0Us4m3WW5zY+J6J7lBcGZQKsk7gtOr1IWf3PKMwgOiMab2dvOgZ3rB0BwESgVz0+7vsxLfxbEOEXwePOYVUfZOJk+knySvLwdPKsfiz4Br3F/63TTXkJ0mGNxWJeYRZajRYvJy8KSgsoKsoRWc//ft1cxp4mwAJJkshFwkmjx7nb/0Crw98tgO+DByllQl0CGFIm/PeOuolJ+D9urnRsGE6ZxTtsT8Ievj/8PaVtR8NN74K3aKdsrYZPDn/H6YxKTPmA46nHmbxjspUA0MKvBXXcxUJWS/+WGLS2cxw8yy10lRaIXDlyPHswr1oHtcLdZB6du+trkVHdr5Hi1yeTgpGP/Hx4z9+XLa4uIj9AihACkjRiBTq425M0MeX4+CnnJO/tek8kjyzH3kRzXhV5IUnWyjqspbqe6Pww9HNsURnMSQ4T8hIUTYCnk6fZjEumTgd46RS6bo9XeC5XgxAC8rUam7wQNRa2r0NqJAR06dKFb7/91mb7119/TefO6guv1nFAE2Ap5df0pSQPEst1RSzydKcg+YRtobqdhGnLQ38S5+7N0vRDgPnhq4pbG93K5B6Tea3raw75MdwIhHmG0TawLQ28G9DIpA3x0YoXWZZWK5KQIJwJi8vM/i6+zr7c0fgO3unxDh/1+UhJhrb1ogh5Z+mr0bNOT17u/LLd328baE62I6+4N/drbpVgqXz5TWM2cXubCcq2JqYVt2QLe3uHML2sCGphtVlWRfeu27vmq+B9XoSJZ/Fu2JeRTUaiR0OMk4EsY4HSxzOKapiqPfGI9ffWowCIPBLJHF0BD9QJ5my5hY4fD/+IZTC1vS7OJOt0nCk0C07xufG8sOkFQNy/G8HE7bpG7yQSiJkmWxrM7emkdcJJ60R2cTZ52fGQZBqvmtwE7e61Ps/s4ZBwWJkYACw7s8wsBPSdCMGmfurkaTVRyyzM5L2d7/H8xucpk8qULKAdAjtYrQJeCZ6ufxsPZtpf1W7g1cDqu7ziW21/AIC2Y4QfRGGm0HKllptEmzRucuKsrIO/2ibMMlRublZoLKRUMuLh7GXVvr17mrOIN/JrTssHhY/OOhc9i4PCeSPQ+r3nqnPh8XWP892h75hzQoSLjNZpiHIy8KOPN7NPzOZ/6yv3EdwWv83KLOiuZnfxy9Bf+GnITzzU+iF+HPyj/QO1du53arTIaCtjShiIuz8epoRTeXI/KadJSC1I5fY/hjHH24tFXp48FRIksscnHAa9K4kmu/YQtxAadjf7ny0+vZiZR2danSu/JJ/Zx2cr3xPyEkgtSFW0sjekEFBN/Fz80Gv1XMq9xIHkAwAiQ7KlEPDCcXh0Y6UmVWCpCbAVAtILxcKsl/N/VAj44IMP+Oijjxg4cCCTJ0/mnXfeYcCAAXz66ad8+OGHtV1HFVkIkJ237GDQmScsNRUC2gW2o39Yf0qReC/An2lnFsJBEQO5xPRH/9fJ6v8Keb7hjFoxisWnhcrYUSEAYFSzUYxrUbkZ2A2L6QXgY3q0MnU6RY2YUpBitXrTOaSz4nB8a6NblbwIay+sBaxNvADaBNifTI9qOkr5XN4HoDJ8LGz4exUIm9PYxIPWGTirQhYCAs1CQFZRFpdyL+Hj7EOoe2gFBzqIaRKt1+qp52q2x23n1RidRkdmYSbVjnKcl2Z2AA1qBeOXKlmWZQ1GrlYrbG+BzkZxLw+lHGJH/A5KbpvOeb2eh0ODGRRel23x25VTX8q9xMFk4TNzayMLm1aVmiObS6RGWwm2a0atoamv2Je4+xsoyRNmXe4BEN7N+hyxO+DHvsQlmf2Zfj/1u1nb6RMOo2aI/jBmttWhyQXmREax2bFcyBbOng29y2c3vgKEtqduqVl72CGog/I52C2YjaM3Kj5Av54Qfnr2MlNXiUZjtlXPjLPVkJgmQfKkJ2tPuUny88eUZ7U8Wy5u4c1tbyoTJxszG69QHm/7OB2COjC552TqetSlW4i4f1M9DeSVm3jrtQZKJdEmS6KXUFhayAPSRUbXDeUvdzccYfsl8zN7Z9M7eafHO7gZ3AjzDOPFTi/iU5lWQ66/PLFMOwPFJqfTCetB1sK4BZg1ASZfCFoMszrVVwe+Ir8032qbtPUzkIzsazOMM6ZV/CD3ILqEdKFjUEd61REZ2decX2N13Cf7PmFnwk6rbSfSTihaEUtrgX8rWo1W6f/RGSKze5hnmPBZk/GqW2FftUQWAlZ4epCaLZ6HEmMJRcYilpxeAkBr/xvD+bcyaiQE9OnThx07dhAYGMjcuXOZP38+QUFB7Nixgz59HJ+EqDhIYaaIWmKofID77ZbfeLvH2zWW+DUaDd1Duyvfl+aeheVPAjC6bghD64ezy9WVvgv70n1edwpKC5Sy8sD0n8c0YfEuESvr2VqtMJ3C2lnUWefMsx2sIwuVN48qH7WpQ1AHJnaeyP/amVe5Gnk3YkD4AHrW6Ym7wZ3B4YMdrqrBYuWuf764l5syozg1/86KDrHGWCJWDLUGsVpr4lDyIUAIhrW5Et422Ozf0DjtAmGeYRSXFdu8+KokwTQRbHozPLkDmgyyW2x3WTY6jY6Px65XTK6eWP8E/TY/ydbuDyrlDqUcUj6vObeGnOIcgtyCeLj1w9Wrl4p9AkwRruIPcvO5/UzMyGZp8BCC3IIUITPBtApOj6fFCz7YwgdqoNlU44JFRJBzWecoizX5ttXtLLRZT+6AxtbO/pZ+MifSThBrmhCEeTluqlNjQtvSqsisPbQcI/xc/QhwDVDGe1kTcH+riqPgVIrsDL3lE2G/DuZ3TqF11KGsclGRkgxO/HXuL7sC+VMbnmLF2RXKqr2HwcOmzNMdnmb2LbMJcRex7n8a8hOdgztTbPKh6hzcmaMPHMVV70pOiVmbcz77vHACRUy2k/XVc3N8ruNzvNvz3WodwxNb4LbP4CaTQ2nqaXMkqtB25nLuAXgqQoCWuGGfssrTQ2kjSZLsjl05psAb8zTiOp20TjjrnHEzuPHrLb/y3eDv8HLyIjojmoxCsyZUXpADlPfA6pjVJOYlEuoeeuM5BtcQxWfFRGOfxtaRgRx8J1kGUvgxZgV7E/fScU5HOs/pzLyTItBDjZ+164ga6zI7derEwoULiY6O5vTp0yxcuJBOnTpVfaBK9TCWiPB1Tu5Vdt72Qe25u9ndl/Vz5UNKApQBZ5ycSNbC1oSdNraI9TzqKVE7/vMERQDgnSdWvbK0WkUTcDFH2PCPajqKDXdvUMx/ZILdg61U/D3q9LDar9FouL/V/TzZ/knaB7YHUDQqXw38irV3ra18BcsOT7d/mpE5uXS0CNl3d8kZJEe0AfGHRN8MaSPCAZqYfUKspPar169adamKV7q/xc11etO6qJhhl05yX7AQPBeeXOj4SXJTIGaz+Fyvi81uy1W5ImMRwxoPI9AtkLe6myeSOcU5fHxprc2xHgYP9iUJJ8nyApzKZSCvUP/zPtotH3N/ZiZNd4kQkrJJYYJplVlR8Yd2EL44Qz8Spj4vn6HQPYgkrYSn3o36XvUpLismKf0M04NCmHZ+eflfVUjON2sCjqYeVZy+r8o9dvakTY8XedunA73q9LLSoOo0YsVZNtGRtw0IG1D+LI7hYxJqzm2G7V+IzyEm7aMsBEjiHZSl1SomMLnuAQxePJiJWyZyOOVwhaf/85yIeCZrPKvCUqspCzr2BIh3d1Y8ibdsG3vU6B76NYIuj5j7ZcxmKMoS5roWwRFwD8TLNI6u8XDn1mNf8frW1zmSKkwRL+ZeJDEvkTrudfikrznXUirFpGq1pBmFdjbyZnOGdhCr3R1NCyKy1hGsJ60PtHoAMLd5l5Au/xnTRMvFyfaB7YXJXnnTNQew9AkpKS3goz0fWe130bn8K8b5K2vQqHL5FAsnUCXM2hXGUougkyTKgHyLwUMJx2fi2Q7P8vOQn1ExESiEAK9Lwh4xSyeEgMLSQt7bJVaOGno3rDCE31vd38LLyYs7m96phDuzx6f9PmV6/+mK0Oesc66Rk9Lj7R7nvU4T0Wq0ymAgaTRcTDxY6XEAnBe+C4pTIVBYWsjexL246l0Z1WxUBQfWDG9nbz676Xvmt3mWFsUl3BR7CIB9SfvsOsnZkHQCPm8JO76yqbdMQq45sIFeq+fFTi8CVdvTdgvtRuRNkZWWUakhltFTLDGWmjUBplwlstYNrRbu+Aq6PyG+ewQS1+o2AMIK85WX9x+e7sxyd2LuyXlM3z/dagIhYxlzfXfibsW84qpNAAa8zt3DZ/PDTT/g7+qPi05EjJEnKZbPfYh7SM3zUXhYRGCRzVuCTeYOhVkgSXhHrwdMGs7OD8M9CxhVv4FymGX4XsBKMyCbA93c4GaHqtMl2CykywElPCxCclr6h/g4+9hddGgVUHFUPLA1uawWwa2FSVCaMDuxifrj6kfzYttocLImaV+iWDDoHNKZoQ2H0tujAQCf+fkyoH49DmQLUyB7vl2yaajse7Xuwjql7/52y2+0D2rPzfVFO2vQWIWN/rfzXs/30Gv1jG8xnun9p4uNshCgs00aWxGNvM3+G0vSD3Mq4xR6jfnZMkrGf4Vg5bAQEBAQoGTKlT9X9KdSi8gJiKowBaotAlwDeK7jcwAYNRqSdDpyO5uTxRxNPap89nPx49G2jxLqcZl23/8mAsXE3ccoojpkabVgcGVj3EYlMlBlkXK6hXZj05hNTO4xudKfCXYP5qb6N9XOINT9f/BOBt8O/l7ZtPP8Wk6ln6rc3v6iKRJFfbMp2Lmsc0hINPFpgnM1Btxq0VLE0vZNiaapb1Oyi7PZEW8bstiG7V8IzQWIUH11rTWX6YXpVjHQP+j1gZLkrKLJQu+6vekR2oNH2zxKm8A23NZITDQdneioOEBABUJA0lFCssUqfaKcwKqS4AmxLYWPRv3CPMILhKnFd74+yv5Zx2bx3D/P2RxnqQmIzogmOT+Z5r7Nr1lgg8V3LOb2RrfzdIenAeucAJcVm7zlCGhezo9FTkpVmAW7f8C7WLyP9rk4g084xU0GEW/hM1HeFMOe4769sMX2aBXQinEtxvFa19eUSaylY/esobOU/DivdHmFdoFmU5wZN8/g9ka383b3t5Vtsq24LETBZQpyLl5wszm6G151rffr9LjZGT/lBHOy1rBLiBB2/E3XsqVcThJ7iRZlHzxZCPhsn8jP1CO0hxIa85N+n7Dh7g1sHbuV/mH9q3FhNzYjm45k//j9vNr1VbOFQjtTTh2LvBxV4eHkwaf1rcOHLhy2kECTb5qL3k7I2hsQh5cMLOP124vdr3KFMA26OF0dIQDgkTaPsPfoXHaUpJKo1+ER1glSxQqQHOf+vZ7vWaVhVzHh4g0N++KdIOI9/+HpwXOFaVZZbi1fVvawG5ruSmISJHrX7c0HHq15K/cY70fPg+h5TOszTZnY2pBsyhoeYnaOuirh6DxDhR9CZhy39n2CLzOimbJrCmtGran8uASLiEB+jUFvLaRsiN1AmVRGt9BuPNX+KSsnTIPWwPT+0/lg1wdMaD2BT/YJ9f3rXV+3EhA+6PUBwxoNswqFq3KZVDSxn3kzoTqgbojIpA2VhlGONa1Sh5WU0vTkeuYG2S5Y2bPRlkPxhrqHkpCXgAYNz3V87pqtAtb3qs/UPlOV71ZCgPtlCAFObnDPfJhW35wF2BR6k/w0OP4HfkahcVvh6cHTej0a2QzLRPlJf/nswgGuAbg5uKCl1Wh5retrVttkrUwTnyZ0Cu7EnFvnkFWURXO/5vwT+49SrlNQJ8W/beWIlWg0GlILUnl+4/NM6T2FRt6NyC/Nd7guFdJ0iMVnO6vt7e7h/dQDfO3twa2NbuOX47+QmJdITFYM6y6IKEiyn4e/Vxgk77Y63MfZx+77QBYCjqcdR5IkJS/Ce73Mia+0Gu1/xg+gPDZRu256V9yfhn2rdR5vb3PUxRZ+LWjm24zp/afz/MbnrZ7BGxmHhYCxY8fa/axyhTHFhKcWY1E7QkBYd4hZRXKf5yHEVqU6MHxg9bNS/lcY9TPeP5odrH859gtGSWgG3u7xds2id1wlOod0gTNmk6/fT/1uXwgozhex9p08rVbA5HB09nxLag2tDrzrQsZ5Hm54G7NO/MLF3ItsittU8YpXWZk5YydYOTLLyDG2RzUdZSUAyNxU/yYGhw9Go9HQwLsB57LO2WgI9Fo9veqqTvK1ikYDYd0hbhc8c0Aksdr0IRiLCUVM/hNMDqGS3oUn1j2Oh8GDz/qL1dGC0gIOJB1QIsLULy1lcF4+dUtKuWSwfQXKCd9A5OTYk7AHvVbP/Nvms/DUQiL8IqoVhetKYxkStLyfUY245WNY9hj0fx18TedLOwvFOdxcnM8HAULQOuXiSlA5ISC9wPz9QNIBJZKSzOWaUI1uNprfT//OC51EGN4Q9xBFI2N57ZbR8uTt9b3qs2XMltoV3jyDhTNwwmFo8f/27jwuivr/A/hrWe5bQAEFPJBDVLzNgxTNKxQ1r8wjlbS0Ms9+eVSoHabfzMpKs0wtLW9FzUotb0UFxRMPFBFRLrnvY+f3x7ojK4fLsrAL+3o+HjyWnfnMzHt2Vpz3fK7Bpde/sgZDBQFDJRKEPgrFhmsbkJCdgB23diC3KBf9GvcTa4ad7Er/zbQ3LTsBtjO1Q2PrxojJiMGdtDvILMiEuaF5nRl2W+OMzMpO0p7DyraJ+Lsi8WrboC2OvnpUQ4Fpn5qNB6nGaKEmAAAaPPljkmzfBGYlqmAB+WgFdWGSjGpjWR/N3rkAy609kAUZDkQfENumNjDT7SczjTpMRsMb6/DQUP4kpdxE7/FtAIK8+VOJ/1QVSUDJ9pTVwtYNSL0Hg5RotLBrgbPxZzH9v+nYNmgbWti3KF0+K+FpUyDnNkD/0kMZK9rqVpTAKG4gerj0QA+Xyj1VoioYs1X+dLpeE7HJHQDY1W8BI2QhwVCKYgCPsuLEpmHFsmJkFmRi6bmlYgdJCyMLdH5pLgxD3sMLeXnY9aSjaUv7luL4/6l5qWITx9CHoSiQFeDFRi/C3sweb7d9u8ZOWVV2Zk9rP15pXvbsp5XS5lX56Er1vQADQ/nABhlPJia0ccPkFuPxc+RvuC/Lg9GT0WnMDM2QW5Qr1gScjDtZ5lj9BYp/g2qa22kuxvuMLzPZaWLdBC82erHCdv7VUnszbre8D0V5s9o+Oaai6VJCToL4pHqYx9OR2NqXMXmmvVn5zds6OnZETEYMjsQeAfD8TtBUeVb1nj4sUly/uqbSfQJU+SENEmsCajYJULR7S8xJLDWture9d53oEFOdjE1tcPr1CHjV80JSbhKOxh4FADiY6/i/D1Nr9JPaim+PxB5BfHZ86XIpT4ZatFe+Ya6RmgDg6XCGGwJgmfG0M++pEmP2K1GMe960J/DWcaBeY6XVgiA8HfqxnEnWSIvMbJ8+lS4xMZ2B+0twMrZGkUSCRKlUbCMNyCcD67G1h5gAAMAbrd6Ak1cgYGoLD/OnTWe2DNqCDo7yPiIp+U+fZl99LK8V0+VZn62NrfFlzy/xS/9fKrxprBSnVvIRvyQS5VlyG3jD7cncDGsurRHbtyvGoFd0/v0rWrlpXkBTeV+DV71frVJYZoZm5dZ2GEgM8EOfH0o1Iap2Fval/p6UxdnCGUYGRohKixI7l5fsw6GY86KkigaHUPQlOHxf3lSXNfOaZ1WiP4aTkVUFJWsvtfoEUA0SawJqtjmQokPNL1efjvzzus/rGOw+uGojKugRiUSC2R1m463DT6cm1/WaAACYatEc1x6fxnkzeZOIaYenYdfgXcqJX/aTsdNLPP3KK8pDbGZszVRLN+oIXJSPO94x9hL+tZf/sS45ZJ4SRRJgq/zdLSwuxOyjs3E77TYyCzPhaO5YZzp81VklZ13t/BZaXcxBbMw/6OfWCO0jN4ur/or+CwKUO2Z2ce4i7zcwIwLDAUSc+wwvucnnibAzlT9RH71/NFytXLHSfyWuJctrByozGaI29G/S//mF1NXED0iUfw7o+AbcrOX/N2QWZiL4dDAAeR+gq4+vIj47Hun56eJwyApLui/B+53eL7d5iz4wNTRF94bdcfTBUaV+JgoGEgMsfGEhLj06h/ldPsSj3KQKH6Yo+hIoEt+6MHutrik5GpWjYc3eg9UUtfoEUA0q1FISUGJ2VgUrY6sKn0xQaSU7yBpIDMQbDV1mYdUQ664lwrep/IY5Ki0K4Qnhyk9Ds56MCGLxNKm5l3EPAgS427pXf02R9yBg/0wAwOiMTBRbOuFLk3zxCVspiv4AzyQBl5Mv4+iDo+J7Jri1gNQIeOMQAAlg0wj9m76Mv2L+AQBcSLwgFiv5OyBvoiY2FTOrBzPIh9pVKPlvMzYzFuuurBObCLWwK6OJmb7o+X9Aw3ZAy6GAkRm8FMOHlqC4WY3LioPfFuWhdxtaNISJ1AQmZtU0Wlgt0tutt/j3xsHModQDh9HeozHaW36vZW1W8f8VjhaOYr8AgM2BqkPJTtkNDOrm97dK8wScOHECa9euxdq1a3Hy5ElNxUQlFWinOVBZw1g+O/wbPV/J9roNzBtAqphSXpdZ1IcEwEf2L4iLSo2akvVk1A/Lp0lAVFoUgBroDwAAlvXlHRghf5Lx+sPbMDM0Q2JOojiClZKbT5onuHVRWvxs0qDpCc6omrh2BlzlzSF6uPTAcI/hSkM/AhCH5O3l2gvf9voWu4fsrnAM/axC5Zvbv+79hYyCDPjY++h3UwsLB6Dta/LOlZA/HQ0fFw5fB1+xiLOlszir9rOm+Ko+LGNd19n56ahhmphnouQM0iU7iJPmOUlqeNS+GqJWEhATE4NOnTqhZ8+eCA4ORnBwMHr06IHOnTvj/v37mo5Rv9XwZGEKDmYO2DJwi9IwoKxurLySTxIcTHW8P4DCkxv7URJbrO+/HsDTiW1EiuZAFk9rjO6m3QVQA/0BFF54C3hZPlSnBEAjU3vIBJl8WMKS43OnxQKPIuSxNlYeuedmyk3x9xZ2LTDKa1QNBE6aZCQ1wqJui3Bu7Dms778er/u8Lq4zNjDG172+Ri+3XqWHDXyG4t+nnamd0qy7ikmX6CljqTEaWz9tB9/Upmmp/ggfd/0Yv/T/BSM8R9R0eDqrkeXTkdSGNh9a5f2VrJ3V60S1Gv1p3gZb4h7BsqiMh0t1gFqjA02ePBl2dna4d+8e3Nzk2ez9+/cxZcoUTJkyBf/8849Gg9RrNTxZWEktHVrix74/IjYjFjtv78SklpOevxGVy8SwllQnKmYOPf8TfFuPgKGBIa4mX0WRrOjpk1RFc6AyagKqdY6AZ73wJvDgHHBlOxpKLRAF4OVdLyMsPgsmg76SNxs69JG8rHtv+fCiJdxOlc/2uXXQVp1v900Vk0gk6OjUEbfTbovLWti3eO7Nv8K0ttNgIDHAmBZjYG1sjTWX1yC7IJuJYTlKdqBvYt2k1MSCvVx76fRwyNryY98fcS35Gga7lzGkaCW94PS0tpZNGauHm1kDoKAQyM/QdijVQq0k4OTJk7h9+zZcXJ42GXFzc8O6devg4VHO7I6kHrEmoOaTAAVXa1fM7DBTa8evK55trqCzSoz7b3zzAJpYN0FUWhTisuKePv3LLt0nQCtJACCf+AtAfok/0pGyLLTdPhEI+BK4tlu+sIlyW+ViWTFup92GgcSg5mOmatOtYTd41PNAj0Y9MKHlBJW3szCywOyOs8X3szvMrqA0lWxaZSw1FudCUWACULZuDbtpbKLN+ub1ETI0BKl5qWhbv61G9knPMH3SAiKvbiYBajUHatSoEWQyWanlMplMKTEgDRBrAupmz3R94mhRS8YZbtDi6cQ3jy6LN8iKm3wUFwIZjwCpsThDa0ZBBmIzY2FtbK004kWNcGoNAHglI01c9Ju1Fc6ZmgBHv3hazr230mYPsh4gtygXTaybwERaS2pp6LkaWzfGrsG7MLPDTNQzLbudOlWdYkQixRNtxYhygLxmjWpGM5tm6ODYoXb0N6uNFM2g62ifSLWSgClTpiAoKAh3794Vl929exeTJk3ClCnsBKRR4igsfKpSW/3Y50d0ce6C6e2mazsU1UgkwOBV8t8fRcDdQp7Y34k9DWwYBIT9AsgKAQdPsXlN5ONIAPKhFGt8DgnPAYBdMwTE3cTcLHln0IOWFnjbsT6KcpLlZV75EbBRfkCh6A/gVY8jXhFVlpu1G06OPolF3RYBAD7q8hFecHoBmwM2s2kd1R11vCZAreZAP/zwA+7fvw93d3fY2dlBEASkpspnCoyKisIPP/wglr13755GAtVbGXHy1xJNNKh26daoG7o10kz1b40xswVsGwNpMfA88j+ggR2uPDgB3DsL3DshL1PfWyx+I+UGAC2Npy41BHr8HyR7pmJASgJ+MHdGjoEB8g0MkCo1QP1iGeD6QqnNFDPLKmZzJqLKKdkZtalNU/zc/2ctRkNUDRTfcfYJeOqjjz7SdBxUnoyH8lfrhhWXI9K0Bi2AtBh0yM0BYIfwvAQUAxArnUskAYrJgZpYN6nhIJ9oPRKIPQvHxEgcyc/CWDtzROXG47FUKk8CbFzxdfjXiE6Pxlf+X2Hn7Z3YeXsnAKBP4z7aiZmIiHQbawJKmzx5sqbjoLIUFwKZ8fL+AKYc/otqWH0v4NbfsJXJ4JlfgFsmxrhtbATvgidDpTXuKhZNyJHPG6C1fg9SQyDwawCAOYAmR2Yh6n48kqVSwKkFiiTAuqvrAMj7Auy4tQMA0LZ+W6Vh+4iIiESmtvLXPPYJKOXx48c4f/68pmKhZ2XGAxDktQA13c6aqP7TWVJ98/MBANeMjeULXDorjbmvSAKczJ1qLr4KKMYsn+bUAG818UC739qJ6+Iy43A77TYMDQyxfsB6bYVIRES6zuzJ4AK5qdqNo5qolQSkpaVh6NChcHBwQOfOT2fAGzp0KM6cOVPBllQpmY/kr9Y1PNoKESAfTae+N2DfHD5SSwBApIkxMGYbMH6XUmIanx0PQHdGQLI3fTpx0ekE5QcVJ+JOoEhWBB87nwpnkCUiIj0nJgEp2o2jmqiVBPzf//0f8vPzcfPmTaXlb7/9Nj755BONBEZ42gZNUR1FVJOsHIF3zgLTw+HTWD685hFzM6Q7+gAmVmKxguICpOSlwMrIChY6MpStsdS43HUn404CALzsOCoQERFVwMxW/lpHawLUegy2f/9+hIaGirMFK3Tq1AnHjh3TSGCEp73RFePUEmmJt2M7tIj7B5EmxpgTuhiQAJ90+wRrr6zVuVoAoOwOypNaTcL6q+txL+MeADyd+IyIiKgsUiPA2EreJ0BWXGrW+dpOrZqA1NRU1KsnryIpOSZ4VlYWDAyq1M2ASirIkr+WeOpKpA1SGxfMSZE/CTkbfxZnH53FR6c+wo5bO8Qn6y5WujNRYG+33ljeYzma2TQTl3V17qpUxs3K7dnNiIiIlJkrmgSlaTWM6qDWHXuHDh2we/duAMpJwLJly9CtWy0bD12X5SuSAEvtxkHUoAXaPukcrHA2/qzS+8ZWuvNkXSKR4OWmL2OM9xgAwMBmA+Fjr9wHgDUBRET0XHW4c7BazYGWLl2KgIAAHD9+HIIg4KOPPsI///yDK1eusDmQJuVnyl9ZE0DaZuMCk6DDGBa1BbvuHyyziJu17j1ZH+k1Eq7Wrujo2BHGUmN0ce6ikzUXRESko+pwEqBWTcCLL76IEydOIDc3Fx4eHtiyZQuaNm2KM2fOKI0WRFVU8CQJMGZNAOkA105Y3GsFIsZHoH2D9qVWl5w9VFcYSAzQrWE3saPwzPYzMdh9MIK7BlfYeZiIiAhAnR4hSK2agDVr1mDq1KnYvHmzpuOhksSaAHYMJt0hNZCitUNrXEi8AAAY7zMeN1Nu4sVGL2o5sufzsvPCZ36faTsMIiKqLRSTtdbBCcPUqgl47733UFxcrOlY6FnsE0A66uVmL8NAYoBXvV7F/3X6P6zrvw7mRubaDouIiEizFA9iFSM21iFq1QT4+PggPDycTX+qG/sEkI5qad8S/478F/VM6mk7FCIioupj+iQJyGMSAAAICgrC6NGj8fHHH8PHxwfGxspta9u2bauJ2EgxRCj7BJAOcjBz0HYIRERE1UusCcjUbhzVQK0kYMaMGQCASZMmlbleEAT1I6KnxMnCWBNAREREVOPYHEhZUlKSpuOgsuRzsjAiIiIirVHcg7E5kJyDA5sB1AixJoCjAxERERHVONO62xxIrdGBqAYIgnw4KqkJYGSq7WiIiIiI9I+iJqAONgdiEqCrCnMAWdHT8WmJiIiIqGbV4T4BOpEEZGdn48GDB5WaeyAnJwdxcXEoKiqqxsi0SDEphSmbAhERERFphThZGJMAAPIZgzWhuLgY77zzDuzs7ODr6wsnJyds2bKlwm3u3r0Lf39/2Nvbo3PnzrC2tsY777xT95IBxZeNNQFERERE2sHmQMo0NWPw8uXLsW3bNkRERCAlJQWfffYZxo0bh6tXr5a7zZtvvoni4mIkJiYiLi4OZ86cwcaNGzWWmOgMsSaASQARERGRVhiayPtn5mfK+2vWIWolAYoZg6tq9erVmDx5Mlq0aAFAfoPfrFkzrF27ttxtoqOj0bt3b1hZyTOzNm3awN3dHdHR0VWOR6cwCSAiIiLSPhMreT/NwlxtR6JRWpsxOCEhAbGxsejatavS8u7duyMsLKzc7ebMmYNly5ahc+fOaNy4MQ4ePIj4+HhMnjxZnVPRXRwelIiIiEj7TK2BnGR5bYCxubaj0RitzRicnJwMALC3t1da7uDggFOnTpW73fjx43H8+HEMGzYM9vb2SE1NxZdffinWJpQlPz8f+fn54vuMjFrQrisvTf7KmgAiIiIi7Sk5QpCVo3Zj0SCtzRhsYCBviVRYWKi0vKCgAFKptNztBg8eDAMDAyQmJsLGxgaXL19Gz549IZPJMH369DK3Wbp0KRYvXlzlmGsUmwMRERERaV8dnTVYrT4BDg4OFf6owsXFBQAQHx+vtDw+Pl5c96xHjx7h6NGjmDVrFmxs5DfHvr6+GD58ODZv3lzusebPn4/09HTxJzY2VqUYtYpJABEREZH2Ke7F6tgIQWrPE5CcnIx169Zh4cKF4rLQ0FCVRw2ysrJChw4d8M8//4jLCgoKcPjwYfj7+4vLkpKSxJt2KysrSCQSpKamKu0rJSVFTArKYmJiAmtra6UfncchQomIiIi0r44OE6pWc6CIiAj07dsX9evXR2RkJD777DMAwIYNG3D9+nUEBQWptJ/g4GAMGzYMbdu2RdeuXfHVV1/B2NgYU6dOFcvMnz8foaGhuHr1KiwtLTFy5EgsXLgQVlZWaNasGQ4ePIiQkJAKawJqJdYEEBEREWmf2CcgU7txaJhaNQFz5szB7Nmzcf36daXlU6dOxcqVK1XeT2BgILZv346QkBCxk/Hx48eVOgs3aNAAbm5u4vsNGzZg2rRp+PrrrzF27FgcPXoUu3btwujRo9U5Fd2lSAI4OhARERGR9pg+uRerY30CJIIqQ/k8w8bGBg8ePICVlRUMDAwgk8kAANnZ2bCzs1MaiUcXZWRkwMbGBunp6brbNOjnPsCD88C0M4Cjj7ajISIiItJPp74BDn0M+M8H/OdpO5oKVeYeV62aAKlUiszM0lUiN27cgJ2dnTq7pGexORARERGR9rE50FMBAQFYtGgRZDIZJBIJACAmJgbTpk1DYGCgRgPUW2ISoKM1FURERET6QGwOlKbVMDRNrSRgxYoVOHPmDJydnSGTydC6dWs0b94ceXl5WLp0qaZj1E956YDEADC21HYkRERERPrL1Fb+mpumzSg0Tq3RgRwdHREeHo6QkBCEhYVBJpNhwYIFGD58OIyNjTUdo/4pygeK8gCzesCTmhYiIiIi0gIzW/mropVGHaFWEgAAxsbGGDlyJEaOHKnJeAjgHAFEREREuoI1Acru3r2L77//HpGRkQAAHx8fvPvuu2jSpImmYtNfHB6UiIiISDeY1ZO/sk8AsG/fPnh7e+PYsWNo3LgxGjdujKNHj8LLywsHDhzQdIz6J58jAxERERHpBMX9GGsC5JOFLV68GPPnz1davnTpUsyaNQsBAQEaCU5vcXhQIiIiIt1gIJW3zsjPAIqLAKnaDWl0ilo1AXFxcXj77bdLLZ82bRri4uKqHJTeYxJAREREpDsU/QLqUOdgtZIAHx8fXLp0qdTyS5cuwceHs9tWGZMAIiIiIt1h9uSerA71C1CrPmPs2LEYOXIkPvjgA3Tq1AmCICAsLAzLli3DwoULERERIZZt27athkLVIxwdiIiIiEh31MERgtRKAmbNmgVA3jfgWTNmzFB6LwiCOofQbxwdiIiIiEh3KB7M5ted5kBqJQFJSUmajoNKYnMgIiIiIt2heDCbn6ndODRIrSTAwcFB03FQSflsDkRERESkM0ys5K91KAlQq2MwVTOxJoDNgYiIiIi0jkkA1Qg2ByIiIiLSHUwCqEZwdCAiIiIi3aFonaFosl0HMAnQRRwdiIiIiEh3KO7J8upOEqByx+DDhw+rvNM+ffqoFQw9wSSAiIiISHfUweZAKicBAwYMUHpfXFxcZjmpVIqioqKqRaXPZMVAQSZgbAVI1Rq8iYiIiIg0qQ4mASo3ByoqKhJ/fvzxR/j6+uLIkSPIyspCVlYWjhw5Al9fX6xdu7Y64637ODwoERERkW7R5ySgpC+//BJbt26Fv78/LCwsYGFhAX9/f2zduhVffvmlpmPULxwelIiIiEi3MAmQu3fvHuzt7Ustt7OzQ3R0dJWD0mscHpSIiIhItyjuy/LStBqGJqmVBLRp0wZz585Fdna2uCwrKwvvv/8+2rVrp7Hg9BKHByUiIiLSLSY2gMQAyEnRdiQao1bP07Vr1yIwMBDOzs5o0aIFBEHAjRs3YGdnh/3792s6Rv3CkYGIiIiIdIuBAWBmB+QkAwU5gLG5tiOqMrWSAF9fX9y6dQu7du3C9evXAQCzZs3C8OHDYWxsrNEA9Q6bAxERERHpHnN7eRKQm6K/SQAAmJiY4LXXXtNkLAQABVnyVxNL7cZBRERERE+Z28lfcx4DNi7ajUUD1J4xODk5GevWrcPChQvFZaGhoeXOH0AqKnjSz8LIQrtxEBEREdFT5k8Gxakj/QLUSgIiIiLQokULrFixAp9//rm4fMOGDdi4caPGgtNLhbny1zpQzURERERUZ5SsCagD1EoC5syZg9mzZ4v9ARSmTp2KlStXaiQwvVWYI381YhJAREREpDPMniQBuanajUND1OoTEBYWhj179gAAJBKJuNzDwwO3bt3SSGB6S2wOxCSAiIiISGewJgCQSqXIzCw9Y5pimFCqAjYHIiIiItI9iuHb68iswWolAQEBAVi0aBFkMplYExATE4Np06YhMDBQowHqnULWBBARERHpHBMr+as+JwErVqzAmTNn4OzsDJlMhtatW6N58+bIy8vD0qVLNR2jflHUBDAJICIiItIdiiRAMZx7LadWnwBHR0eEh4cjJCQEYWFhkMlkWLBgAScL04SCJx2D2RyIiIiISHfUsZoAtScLMzY2xsiRIzFy5EhNxkOFnCeAiIiISOfoaxJw8uRJlXfq5+enVjCEEs2BzLQbBxERERE9ZWwpf83Xs+ZAL774oso7FQRBrWAIbA5EREREpIvE0YEytBuHhqicBOTm5lZnHKQgThbG5kBEREREOsNEUROgZ82BTE1Nqy2I2NhYJCQkwNPTE9bW1iptU1xcjMjISJibm6NZs2bVFluNK8wBJFJAaqTtSIiIiIhIwdAEkBrXmdGB1BoiFADu3r2LOXPmICAgAAEBAZg7dy7u3btXqX3k5eVh+PDh8PLywvjx4+Hk5IRVq1Y9d7tdu3bBxcUFQ4YMwZAhQ9C3b18kJyereSY6RFYMFOUBxhZAiZmYiYiIiEgHmFgBxQVAUb62I6kytZKAffv2wdvbG8eOHUPjxo3RuHFjHD16FF5eXjhw4IDK+1m8eDHOnTuHO3fuIDIyEr///jvee+89nD17ttxtjh8/jpEjR+Kzzz7DnTt3cOXKFSxcuBAJCQnqnIpuKeBEYUREREQ6y7juNAmSCGr04vX09MSkSZMwf/58peVLly7Fhg0bcPPmTZX24+TkhGnTpiE4OFhc1rp1a3Tv3h1r1qwpc5vevXvDyMgI//zzT2XDFmVkZMDGxgbp6ekqNz+qEekPgJUtAQcv4N1z2o6GiIiIiEpa7QckXAHeiwDsmmo7mlIqc4+rVk1AXFwc3n777VLLp02bhri4OJX28fDhQyQkJKBDhw5Kyzt37oyLFy+WuU1+fj5OnjyJwMBAZGZmIjw8HI8ePXrusfLz85GRkaH0o5PynsRlqkOJCRERERHJ1aHOwWolAT4+Prh06VKp5ZcuXYKPj49K+0hJSQEA2NvbKy23t7cX1z0rOTkZhYWFuHz5Mry8vDBlyhR4eXmhf//+ePz4cbnHWrp0KWxsbMQfV1dXlWKscYohp0yYBBARERHpHMWEYXWgc7BaScDYsWMxcuRIfPXVVzhx4gSOHz+Or776CqNGjcK4ceMQEREh/pTHyEg++k1eXp7S8tzcXBgbG1e4zaFDhxAREYELFy4gOjoa0dHRmDt3brnHmj9/PtLT08Wf2NjYSp5xDclLl7+yJoCIiIhI99ShWYNVHiK0pFmzZgEA5syZU2rdjBkzlN6X1+XA1dUVBgYGpZoPxcXFwc3NrcxtHBwcYGFhgWHDhqFBgwYA5DUHI0eOxNatW8uN18TEBCYmJuWfkK4QmwPZaDcOIiIiIiqtDnUMVisJSEpKqvKBzc3N0a1bN+zduxfjxo0DAGRnZ+Pw4cNYtGiRWC4qKgqZmZlo164dDAwM0Ldv31KJw4MHD1C/fv0qx6R1+U9qAtgciIiIiEj36HtNgIODg0YO/umnn6Jv376YP38+unbtilWrVqFBgwZ48803xTJffPEFQkNDcfXqVQDAkiVL0L17dwQHB6N79+44e/Ysfv/9d2zbtk0jMWkVmwMRERER6S59TwIUsrOzkZqaWmq5i4uLStv37NkTR44cwffff49z586hdevW+O2332BpaSmW8fDwQEFBgfi+devWOH36NFauXInly5fDzc0Nx44dQ7du3apyKrpBbA5kq9UwiIiIiKgM+p4EREREYNKkSeV2/K3M1APdu3dH9+7dy13/wQcflFrWqlUrrFu3TuVj1BocHYiIiIhId9Wh0YHUSgKCgoLQqlUrrF69Gra2thoOSY+xORARERGR7hI7BuvonFOVoFYScP36dRw7dgxWVlaajke/cXQgIiIiIt2laK1RB5oDqTVPgIeHB+7fv6/pWIjNgYiIiIh0lzhjsJ42B1q2bBkmTpyI4OBguLu7QyKRKK339vbWSHB6h82BiIiIiHSXvncMLi4uRmRkJAIDA8tcX5mOwVQCmwMRERER6S597xg8c+ZMjB07FtOnT2fHYE3KzwAgAYzZ14KIiIhI5+j7jMHx8fFYsWKF0nj+VEXFRfKs0sQaMFCrqwYRERERVSexOVDtHx1IrbtNb29vREVFaToW/cZOwURERES6TWoEGJrKOwbX8ubvatUEDB8+HK+99hqWLFmC5s2bl+oY3LZtW03Epl/y2R+AiIiISOeZWAHZSUBhLmBsru1o1KZWErBw4UIAwKhRo8pcz47BauDIQERERES6T5EE5GfqXxKQlJSk6Tgoj82BiIiIiHSeonNwQRYAR62GUhVqJQEODg6ajoPYHIiIiIhI94mzBtfuzsEchkZXsDkQERERke4zqRvDhKqVBOTl5SE4OBg+Pj6wtLSEqamp0g+pgc2BiIiIiHSfOExo7Z4wTK0k4OOPP8auXbuwYMECZGdnY9OmTXjvvfdgYGCA999/X9Mx6gc2ByIiIiLSfWISULtrAtTqE7B161bs27cPvr6+GD9+PIYPH44RI0agQ4cO+O677zQdo35gcyAiIiIi3Sd2DK7dSYBaNQGxsbFo2bIlAMDCwgLp6fIb2IEDByIsLExz0ekTRRLA5kBEREREukvsGKyHSYAgCJBKpQCA5s2b49ChQwCA8PBwWFvzJlYtYk2ArVbDICIiIqIK6HPHYBubp+3WZ82ahddffx0dO3bEyy+/jDfffFNjwekVsU8AkygiIiIinVVHOgar1ScgLS1N/H3ChAlwd3dHaGgovL29MWjQIE3Fpl84OhARERGR7tPnjsHP6tq1K0xNTeHi4qKJ3ekndgwmIiIi0n2KjsH6OFnY8ePHMXnyZPH9kCFD0KlTJzRp0gQHDx7UWHB6hUOEEhEREek+RauNgtrdHEitJGDevHli2//w8HCEhoYiKioKX375JYKDgzUaoN7IzwIgAYzMtR0JEREREZVHnzsGX7p0Cb6+vgCAw4cPY9iwYXB3d0dQUBCuXr2q0QD1giAARbnyBEAi0XY0RERERFSeOtInQK0kwM7ODpGRkQCAkJAQ9O7dGwCQlJQEOzs7zUWnL4ry5K9GptqNg4iIiIgqps+jA40fPx4DBgxAs2bNEB0djYEDBwIA9u/fjyFDhmg0QL1QmCt/ZVMgIiIiIt1mXDeaA6mVBHz22Wdo2bIlYmJiMGrUKFhZyTOi1NRUfPjhhxoNUC8oagIMWRNAREREpNMMpICRhbxjsEwGGKjVsEbr1EoCJBIJxo4dW2o5EwA1iTUBZtqNg4iIiIiez8QSKMyW/yiaB9UytTN1qWuYBBARERHVHsYW8teCbO3GUQVMAnQBkwAiIiKi2kPRL4BJAFVJ0ZMkwJBJABEREZHOqwOdgzWSBBQXFyMsLAzx8fGa2J3+YU0AERERUe1hoqc1AcePH8fkyZPF90OGDEGnTp3QpEkTHDx4UGPB6Q0mAURERES1h772CZg3bx7efPNNAEB4eDhCQ0MRFRWFL7/8EsHBwRoNUC+Ik4UxCSAiIiLSeWISoGfNgS5dugRfX18AwOHDhzFs2DC4u7sjKCgIV69e1WiAeqEwR/7KeQKIiIiIdJ/xk2FB9a0mwM7ODpGRkQCAkJAQ9O7dGwCQlJQEOzs7zUWnLwoVNQGcMZiIiIhI59WB5kBqTRY2fvx4DBgwAM2aNUN0dDQGDhwIANi/fz+GDBmi0QD1gqImwIg1AUREREQ6T5EE5GdpN44qUCsJ+Oyzz9CyZUvExMRg1KhRsLKSV4mkpqZy1mB1FLEmgIiIiKjWUMwSXKBnSYBEIsHYsWNLLWcCoCbF6EDsE0BERESk++pAcyC15wlITk7GunXrsHDhQnFZaGgoiouLK72vixcv4u+//0ZsbGyltktMTMSePXtw5cqVSh9Tp4hDhLImgIiIiEjniTMG196aALWSgIiICLRo0QIrVqzA559/Li7fsGEDNm7cqPJ+MjMz0bNnT/Tv3x+fffYZvLy8sGjRIpW2LS4uxsiRIzFq1CisW7eusqegWxRZpCKrJCIiIiLdJdYE6FkSMGfOHMyePRvXr19XWj516lSsXLlS5f18+OGHiIuLw82bN3HixAns378fixcvxtGjR5+77ZIlS+Do6AgfH5/Khq97FF8gJgFEREREuk9RE1CLOwarlQSEhYXh3XffBSDvH6Dg4eGBW7duqbQPQRCwadMmvPHGG6hXrx4AoHfv3ujQoQN+++23Crc9fvw4Nm7ciB9//FGd8HWPIglQdDIhIiIiIt1lomgOVHv7BKjVMVgqlSIzM1McFUjhxo0bKs8T8ODBA6SkpKBNmzZKy9u2bYtLly6Vu93jx48xbtw4bNiwQUwenic/Px/5+fni+4yMDJW2qzFsDkRERERUe+hrx+CAgAAsWrQIMplMrAmIiYnBtGnTEBgYqNI+0tPTAaDUjby9vT3S0tLK3W7SpEkYPXq0OEGZKpYuXQobGxvxx9XVVeVtawSTACIiIqLaQ+wYnKndOKpArSRgxYoVOHPmDJydnSGTydC6dWs0b94ceXl5WLp0qUr7MDY2BgDk5OQoLc/KyoKJiUmZ22zbtg3Hjx9Hx44dsWfPHuzZswfp6em4c+cO9uzZA0EQytxu/vz5SE9PF38qOwpRtRP7BFhqNw4iIiIiej5jPW0O5OjoiPDwcISEhCAsLAwymQwLFizA8OHDxZv753Fzc4NUKi11Qx4bG4umTZuWuY2lpSX8/f3x+++/i8tSUlJw/fp1bNiwAYMHD1bqo6BgYmJSbmKhE1gTQERERFR7GJoAEmmtTgIkQnmPz2tA3759YWpqin379gGQzzjs4uKC//3vf3j77bcByIcjTUlJKbf5T9u2beHv74+vv/5a5eNmZGTAxsYG6enpsLa2rvJ5VNmnjoCsCPgoGSgjiSEiIiIiHbPUDchPBz56DEjVeq6ucZW5x61SxNnZ2UhNTS213MXFRaXtly5dihdffBFTpkxB165d8eOPP8Ld3R1BQUFime+++w6hoaG4evVqVULVXcVFQFEeYGrDBICIiIiotjCxlCcBBVmAma22o6k0tScLa9euHSwtLeHq6lrqR1UdO3ZEWFgYzMzM8M8//yAwMBAnT56EqampWKZdu3Z46aWXyt1Hr1690Lp1a3VOQzewPwARERFR7VPLRwhSqyYgKCgIrVq1wurVq2Fra1ulAFq2bIlvv/223PXvvPNOhdtXZnIyncT+AERERES1j9g5uHZOGKZWEnD9+nUcO3as1DwBpAYxCWBNABEREVGtIdYE1M4kQK3mQB4eHrh//76mY9FPYnMg1gQQERER1Rq1fJhQtWoCli1bhokTJyI4OBju7u6lhuX09vbWSHB6If/J7MUmOjBKERERERGpxuRJEpBfO2sC1EoCiouLERkZWe7swFocdbT2yXuSBJgyCSAiIiKqNfSxY/DMmTMxduxYTJ8+vcodg/UeawKIiIiIah997BgcHx+PFStWwNKSnVmrjDUBRERERLVPLU8C1OoY7O3tjaioKE3Hop9YE0BERERU++hjc6Dhw4fjtddew5IlS9C8efNSHYPbtm2ridj0A2sCiIiIiGofk9pdE6BWErBw4UIAwKhRo8pcz47BlZCfLn9lTQARERFR7WGsh6MDJSUlaToO/cWaACIiIqLaRx+bAzk4OGg6Dv0l9gmw0W4cRERERKQ6fZks7OTJkwAAPz8/8ffy+Pn5VS0qfcKaACIiIqLaR0wCMrUbh5pUTgJefPFFAPL2/orfy8M+AZXA0YGIiIiIah99aQ6Um5tb5u9URawJICIiIqp9TGp3cyCV5wkwNTWFqakpAKBLly7i+2d/unTpUm3B1kl56YBEChiZazsSIiIiIlKVoiaglo4OpNZkYZcuXSpzeXFxMa5du1algPRKUT5QnC+vBXhmrgUiIiIi0mH60icAAEJDQ8v8HQBkMhnOnDkDNzc3zUSmD/LYH4CIiIioVpIayVty5GcCglDrHuhWKgno2rVrmb8rODk54Ztvvql6VPoin/0BiIiIiGotUxsgM0c+a7CJlbajqZRKJQGZmfLqDgcHByQnJyutMzIygomJieYi0wd5itmCOUcAERERUa1jagNkPpLf09XlJMDSUt72KS8vr1qC0TusCSAiIiKqvUyfPMjNSwdsXLQbSyWp1TGYNIR9AoiIiIhqr5JJQC1TqZoA0jDWBBDVOEEQUFRUhOLiYm2HQlRtpFIpDA0NIallHRWJah3Fg1wmAVQprAkgqlEFBQV49OgRcnJytB0KUbUzNzeHs7MzjI2NtR0KUd3FmgBSC2sCiGqMTCZDdHQ0pFIpGjZsCGNjYz4lpTpJEAQUFBQgKSkJ0dHR8PDwgIEBW/8SVQt9TAKSkpJw8eJFpKSklFo3evToKgWlN1gTQFRjCgoKIJPJ4OrqCnNzztBNdZuZmRmMjIwQExODgoICmJqaajskorpJ35KAnTt34vXXX0dhYSGsrUvfwDIJUFH+ky8MawKIagyfiJK+4HedqAbU4iRArb8Q8+bNQ3BwMHJzc5GcnFzqh1Qk1gRwngAiIiKiWkdMAtK0GoY61EoC4uPj8c4770AqlWo6Hv0i9glgEkBEuiM2NhZOTk64d+9enTn+zZs34eTkhKSkJI3tk4hI72oCWrVqhZs3b2o6Fv2Tx47BRFSxjIwMODk5wcnJCTdu3FBaV1BQAG9vbzg5OeHIkSMaO2ZxcTESEhJQVFSksX0Cyufi5OQEV1dXvPDCC/jyyy8hk8mq9fiFhYVISEjg0LBEpFmmtvLXWpgEqNUnYOzYsRgzZgw++eQTNG/evNQIG23bttVEbHVfPjsGE1HFZDIZEhIS4OTkhF9++QXLly8X14WEhCA9PR0JCQnIz8/X2DFdXV3x6NEj1K9fX2P7BJ6ey/r16zFgwAAUFhbi/PnzmDBhAgoLCzF//nyNHo+IqNrpW03A9OnTcfPmTYwaNQrt27dHu3btlH5IRawJICIVvf766/j111+Vno7//PPPmDBhQqmyd+/exejRo9G0aVO0bNkSH374oVKS0K1bN6xatUppm5SUFLi4uODYsWN4+PAh2rZti9jYWABPm9L8+eefGDhwIJo3b46+ffvi4sWLSvu4fPky+vXrh2bNmqF///7Yu3cvnJycStUc29raijUBw4YNw0svvYRTp05VeP7POycAePz4Md577z34+PigVatWWLRoEQoLC8vcn0wmw7vvvouuXbsiPj6+wmMTEZVL35KApKSkCn9IRfkZgEQKGHG4QiKqmL+/PywsLPDnn38CAO7fv49jx45h/PjxSuVyc3PRq1cvFBUVYe/evfj222+xefNmTJ8+XSzTu3dv/PLLL0rbbdu2DQUFBejevXup5jiKpjRz587F7Nmz8ddff6FRo0YYOnQoCgoKAABZWVno27cvnJycsG/fPsycORPTpk1DQkJCuTfiABAdHY3z58+jU6dO5ZZR5Zyys7Px4osvIiIiAmvXrsXWrVshkUiwdevWUvsrKCjAmDFjcOzYMezcuRNOTk7lHpuIqEKmejZjsIODg6bj0D9FBUBRHmBWD+CERUTa83kjoLig5o4nNQYWxFV6M4lEgqCgIKxbtw5DhgzBL7/8goCAADg6OiqV27BhA7KysvDrr7+K8yH88MMPGDRoEIKDg9GoUSOMGzcOn332Ga5fvw4fHx8AwObNmzF69GgYGpb/38I333yDl156CQDw+eefo1GjRrh9+zZatmyJDRs2QCKR4Oeff4axsTFatmyJzz//HBMnTiy1n0mTJmHq1KkoLCxEamoqhg8fjg8//LDc46pyTr/++isePnyIU6dOoV69egCAli1bQhAEpX1lZ2djwoQJyMzMxPHjx8WyRERqMTQBDM3kSYAg1Kp7Og4irC3sD0BElTRx4kQcPHgQcXFxWL9+PYKCgkqVuXz5Mjp27Kg0IVrPnj0hk8lw7do1AIC3tzfat2+PzZs3AwBiYmJw6tQpjBs3rsLjt2zZUvy9QYMGACAOC3316lV07NgRxsbGYplu3bqVuZ+VK1ciIiICly9fxsGDB3Hx4kXMnj273OOqck5nz55Fx44dS93UP9tnLTAwEAUFBTh8+DATACLSDFMbQJABBVnajqRS1KoJyMvLw9KlS7F9+3bcv3+/1AgOeXl5GgmuTsvPlL+aWGk3DiJ9p8ZTeW1p1KgRevfujQkTJqCoqAgvv/wyUlNTlcoUFBQo3YgDgKGhISQSidh0BwDGjRuHb7/9Fp9++il+//13NG/eHJ07d67w+GUNC6140l5QUAAjIyOldc/GoaDoE6A4p4ULF2Ly5MlYvHgxbG1tS5VX5ZyKiopgYmJSYfyAPJE5ffo04uLi4OHh8dzyRETPZWoDZMXLawNq0X2dWjUBH3/8MXbt2oUFCxYgOzsbmzZtwnvvvQcDAwO8//77mo6xbirMkb+yPwARVcIbb7yBf//9FxMmTCjzptzLywuXL19WGnIzIiICgiDA09NTXPbaa68hNjYWp0+fxubNm59bC/A8Hh4euHLlilLzm8uXL6u0rZmZGWQyGbKzs8tcr8o5tWzZEhEREUqJTlm+/fZbBAYGolevXoiKilIpPiKiCik6B+emaTWMylIrCdi6davSfxrDhw/H8uXLsX79ehw9elST8dVdhbnyV2MmAUSkuldeeQWPHj1CcHBwmesnTZqEtLQ0LFmyBEVFRUhOTsbs2bMxYMAApSTAyckJvXv3xrx583Dt2jWMHTu2SnFNnDgRcXFx+PLLL1FcXIxHjx7h448/fu52SUlJ+O6779CyZUs0atRI7XMKCgpCXl4e3n33XWRmZqK4uBh79+7F/v37lfYlkUiwevVqDBw4EP7+/kwEiKjqzGzlr7Vs1mC1koDY2FixbaiFhQXS0+U9ogcOHIiwsDDNRVeXFTx54sWaACKqBAMDAzg5OZXb9KV+/frYvXs3tmzZAisrKzRs2BA2NjZYv359qbJjx47FyZMn0bVrV7i7u1cpLmdnZ/z+++9YsWIFrKys0K5dOwQGBgIo3Sxo0qRJcHJyQv369eHq6gpra2uEhISUu29VzsnR0RH//vsvrl69inr16sHOzg7r168vs4mTRCLBmjVrEBAQwESAiKrO7En/otzUisvpGInw7NAJqmwkkYhVvm3btsXChQsxcuRIHDt2DKNGjUJCQoLGA9WkjIwM2NjYID09HdbWWuqYe/Mv4I/RQKsRwIh12omBSI/k5eUhOjoaTZs2hampqbbDUZkgCEhISICdnV2ZbewrWp+eng4TE5Nyz1fxVN3CwgJWVk/bsRYXFyMpKQn169eHVCoVyzVo0AAGBk+fHcXHx5c6rkwmQ2ZmJmxsbPDvv/+iX79+SE9Ph6WlpRirglQqhb29vdI+yzp+Zc4JkI8AZGhoqJQolXUOiniePf+6orZ+54lqnb/mAWdXA4HfAh1Kz91Skypzj6tWx2AbGxvx91mzZuH111/HsmXLcP36dcyZM6dS+yooKMC///6LhIQEtG7dGh06dHjuNvfv38fZs2dhaGiIzp07l1uFrNMUfQLYHIiIKiCRSCocx76i9SX/VpfF0NCwzG2lUqnS8vLKPbvsq6++wiuvvIKmTZsiJiYG8+bNw6BBg2BpaanSuZR3/MqcEyCvoX5WWeegajxERBUyt5O/5qZoN45KUisJSEtLE3+fMGEC3N3dERoaCm9vbwwaNEjl/SQlJaF3794oKCiAr68vZs2ahVdffRVr1qwps7wgCBgzZow4FFxOTg7Gjh2Lzz//HDNnzlTnVLSngB2Diahu8fHxQf/+/REfH4/i4mIMHjwY3333nbbDIiKqXrW0OZBaScCz/Pz84OfnV+nt5s+fDwC4ePEizM3NER4ejk6dOiEwMBADBw4sVV4QBAwZMgSbN28Wq3N/++03TJw4EYGBgVVu01qjFB2DmQQQUR0xYMAA3Lp1C1lZWbCwsCg1Rj8RUZ2kSAJyaldNgNqThSUnJ2PdunVYuHChuCw0NBTFxcUqbS+TybBt2zZMmjRJnACmQ4cO6NatG7Zs2VJ2sAYGGD16tFL70f79+0Mmk+HmzZvqnop2FLJjMBHVTZaWlkwAiEh/iM2B9KAmICIiAn379kX9+vURGRmJzz77DIB8avfr16+XOYvls2JjY5GZmSlOWa/g4+NTqRGG9u/fD6lUCl9f33LL5OfnIz8/X3yfkZGh8v6rTQH7BBARERHVerW0OZBaNQFz5szB7Nmzcf36daXlU6dOxcqVK1Xah+JG/NnZIevVq6fyTXpkZCRmz56N2bNnw8XFpdxyS5cuhY2Njfjj6uqq0v6rFScLIyIiIqr9zJ7UBOhDc6CwsDC8++67AKBU5evh4YFbt26ptA8zMzMAQGZmptLyjIwMsXlQRe7evYt+/fohICAAX3zxRYVl58+fj/T0dPEnNjZWpRirFZMAIiIiotpPn0YHkkqlyMzMLDWu8o0bN2BnZ6fSPho3bgxjY2NER0crLY+Ojkbz5s0r3DY6Ohr+/v7o1q0bfvvtt1JjTD/LxMSk3Il1tIbNgYiIiIhqP2NLwMBQ3hxIEIBa0idKrZqAgIAALFq0CDKZTKwJiImJwbRp08QZIp/HyMgIAwYMwJYtW8SJxx4+fIgjR45g8ODBYrljx45h27Zt4vt79+7B398fXbt2xebNm0tNJFNriDUBZtqNg4iIiIjUJ5HImwQVFwAF2dqORmVqJQErVqzAmTNn4OzsDJlMhtatW6N58+bIy8vD0qVLVd7PsmXLEBERgSFDhuDzzz9H79698cILL2DcuHFimd9++w1LliwBIJ/9sFevXsjLy0OPHj3w888/Y82aNVizZg1u3Lihzqloj5gElJ7UhoiospKTkzFx4kQkJiZW+7EOHjyIDz/8sNqPU93H3LdvHz755BON7pOI9FQtbBKkVnMgR0dHhIeHIyQkBGFhYZDJZFiwYAGGDx9e5rT25fH29sbly5fx66+/IiEhAXPnzsXrr78OQ8OnYfn7+6Nx48YA5FPJ9+/fHwBw5coVpX21bt1anVPRHkWmyOZARKSCgoIC7N69G+fOnUNubi7c3d0REBCAFi1aAACysrKwceNGfPjhh2jQoEG1xnL9+nXs2bMHn376aZX3dfLkSfz888/iewsLC3h4eGD8+PGwt7evlmMqXLp0CX/++Sc++ugjje2TiPSUWYlhQm3dtBuLitSeLMzY2BgjR47EyJEjqxSAi4sLFixYUO76krUCFhYW5c4mXOvkPRkBydRGu3EQkc67fv06AgMDYWFhgVdffRX29va4e/cuRo8ejYkTJ2LWrFlwcHDA+vXr4ejoqO1wKyUqKgobN27E+vXrAciTmT/++AP/+9//cOHChVp3PkSkp2rhhGFVmjE4Ozsbqamlx0StaLhOeiIvXf7KJICIKpCXl4eBAweiRYsW2Lt3r1JN6bJly8TBFfLy8nD06FEEBATAysoKcXFxWLhwIT755BP8/vvviIqKwrRp09C+fXtkZ2fjt99+w6VLl+Di4oKgoCA4OzsDAH7//XckJiZi5syZ4nGOHDmCv//+G8uWLSszxrNnz2L16tUA5A9rfHx8lCaCBORNbyIiIvDKK69g06ZNSExMxC+//CKunzhxovj7hAkTYGtri7///hsTJkwo97NJSEjAunXrcO/ePbi4uGDSpEmlhoCu6FyfJZPJxJqGDz/88LmDThARicwVcwXUniRArb9wERERaNeuHSwtLeHq6lrqh1SgSAJMrLUbBxHptG3btuHevXtYuXKlUgIAyIdobtasGYCnzYEU86ykpqZi48aN8PPzQ0JCArp27QoHBwckJCSgXbt2+Omnn+Du7o68vDz069dPHK753LlzOHz4sNJxbt68iZ07d5YbY4MGDeDv7w9/f394e3tj+/bt6NSpEwoKCsQyly5dwldffYXhw4fDzs4OPXr0KHd/SUlJkMlkcHBwKLdMbGwsfH19cfz4cbRq1Qrh4eHw9fVVmj3+eedaUkFBAUaPHo0dO3ZgypQpTACIqHLMat+swWrVBAQFBaFVq1ZYvXp1qcm+SAXFRUBBpjwBMKiloxsRUY04e/Ys7Ozs4OXlpdb2s2fPxowZM8T3b7zxBoyNjREaGgojIyMAwMyZM6s0jHLTpk3RtGlT8f3UqVPh5eWF7du3Y+zYseLyrKwshIWFwd3dvdQ+FDUBWVlZOHPmDBYuXIiAgIByjxkcHIymTZviwIEDMDAwwHvvvYc+ffpgwYIFYsKyYMEClc41KysLw4YNQ3Z2No4dO4Z69eqp/VkQkZ4SmwPV8STg+vXrOHbsWKl5AkhF+ewPQKQrXtj8AgplhTV2PCMDI5wde1bl8hkZGahfv77ax1MMpqDw119/YebMmeJNMQClDrjqOnv2LPbv349Hjx6hqKgIBQUFpUZtc3d3LzMBAOSDQABATk4OZDIZtm/fjqCgILGm41nHjh3DO++8o/TEfvTo0Zg3b574XpVzTU9Px0svvQQ7OzscOnRIpckqiYhKqYWjA6lV3+nh4YH79+9rOhb9wf4ARKQiR0fHKs1y/mxtbWpqqsZHD1q9ejX69u2L7OxstG/fHv7+/rCzsyvV7KaimuOJEydi4sSJePvtt7Fr1y7Uq1cP8+fPL7d8UlJSqRt6BwcHpKSkoKioCIBq55qamorr16/D39+fCQARqU9fmgMtW7YMEydORHBwMNzd3cUJwxS8vb01ElydxSSASGdU5qm8NvTt2xcrVqzAoUOH0Ldv3yrvz8XFBVFRUeWuNzExUWrLD6DMASBKWrNmDRYvXoxZs2aJy7788ssqxenp6YnLly+Xu97NzQ337t1TWhYdHY1GjRqJfSeed64A0KRJE/zvf/9DQEAAjIyMMHv27CrFTUR6qhaODqRWTUBxcTEiIyMRGBgIHx8ftGjRQumHnoNJABGpqF+/fujVqxemT59eqgb2wYMHOHjwYKX2N27cOKxduxYxMTHispMnTyI7Wz53iYeHByIiIsT3OTk5+OOPPyrcp0QiUUoU9uzZg2vXrlUqrpJycnJw8uRJtGrVqtwyI0eOxPr165GSIv8PNyMjAz/++CNGjBghlnneuSq8+OKL+PPPP/Hxxx9j5cqVasdNRHqsFjYHUqsmYObMmRg7diymT5/OjsHqYBJARCqSSCTYvXs3pk2bBm9vb/j5+cHOzg7R0dFITU3FV199Van9zZ8/H9euXYOvry969OiBjIwMSCQS/P333wCAMWPG4JtvvkGbNm3Qrl07REREoGHDhsjJySl3n/PmzcPEiRMRFhaG4uJiXLp0CR4eHpWKS9ExODc3F6dOnUK9evXKHZIUAObOnYsjR46gVatW6Nq1K86fPw8nJyd8/PHHKp9rST169MCBAwcQEBAAiUSiNEQqEdFz6UtzoPj4eKxYsQKWlpaajkc/cHhQIqoEGxsb/P7773j48CHOnz+P/Px8NGvWDG3atBE7vT47WZiLiwvWr18PGxvlhw3GxsbYtm0brl69iqtXr8LNzQ1dunQRO9iam5sjLCwMx44dQ15eHr755htkZmYqPdnv16+f0mhAo0ePRufOnREWFgYLCwu8+OKLOH/+vNLgEYMHD0a7du1KnZufn584URgAmJqaYvbs2ejcubNSU9Nnj2lhYYEjR47gzJkzuHfvHmbMmAE/Pz+ljsLPO9dnY+rRowdOnDiBy5cvIysri//HEZHqamFzIIkgCEJlN+rQoQPWrVuHtm3bVkNI1S8jIwM2NjZIT0+HtbUWbsRD1wB/fwC8OAd46ePnlyeiKsvLy0N0dDSaNm0KU1NTbYdDVO34nSeqYZ85A0V5wEePAS3NNVKZe1y1agKGDx+O1157DUuWLEHz5s1LdQyurclBjSl80h7V2EK7cRARERGRZpjZARkPgPz0pzUDOkytJGDhwoUAgFGjRpW5Xo3KBf1S8CQJMGISQERERFQnmNeTJwE5KXU3CUhKStJ0HPqlgDUBRERERHWK4sY/N02rYahKrSTAwcFB03HoFzEJ4MQ0RERERHWCmATUjhGCtNNrQd+JSQBHniAiIiKqE5gE0HMVPhlvm82BiIiIiOoGs9o1YRiTAG0QOwazORARERFRncCaAHouNgciIiIiqluYBNBzsWMwEdWw7OxsbNmyBVlZWUrLb9y4gV27duHff//VUmR1z6FDhxAXF1etxzh27Biio6Or9RhEVEm1bNZgJgHawCFCiaiGJSUl4bXXXkN8fLy4bNWqVejWrRs2b96MEydOaDG6p+7evYt9+/ZpO4xSQkNDcfbs2eeWu3jxIiZMmABbW1ul5dHR0di6dStu376t8jEvX76M3bt3IyIiotS6e/fuYdy4cSrvi4hqgFgTwCSAylPIycKIqGZZWFjg1VdfhZWVlbhs7dq1WLx4MXbu3IlFixZpL7gS/vvvP0yfPl3bYZTy3XffYfXq1c8tN3/+fEyfPh0WFvK/71evXkVAQABeeukljB8/Hv/8889z91FcXIzRo0ejZ8+eWLNmDV566SUMGzYMhYWFYpnx48fj/v37OpkwEektM1v5a166VsNQFZMAbSjIBgyMAENjbUdCRDouMTERW7ZsUZqJPS8vD1u2bEF6uvw/mvT0dGzZsgV5eXm4ffs29u/fj6tXryrtx9zcHEOHDoWFhQVyc3OxZcsWxMbG4ubNm9iyZYvSE+oHDx4gJCQEhw4dQk5OjtJ+Sh7r0qVL2LlzJ+Li4nD79m0cOHAAhYWFCA8Px969e/Hw4UMAQGFhIY4dO4YDBw4gJaX8J2RxcXE4f/682HRpy5YtiIyMRHx8vPg+JCQEN27cKLVtyeOfOHEC27ZtE2+ac3Jy8Pfff+Po0aNIT0/HhQsXcOrUqVL7uHjxIvbs2YOLFy9CJpMpLY+JiUF0dLQYx+PHj8uM4dChQ5gwYYLS5/Xuu+8iKioK5uaqNQH96aef8NdffyEsLAz//PMPwsPDceTIEfzwww9iGQMDA4wZMwbff/+9SvskohpgYi1/zcvQbhwqUmuyMKqC4kKguAAwtdF2JERUC1y/fh2vvfYaRowYAUND+Z/stLQ0vPbaa7hy5QpsbGwQGxuL1157DYMHD0Z0dDRcXV1x9OhRzJgxA59//jmAp82Bbt++DTs7O+zZswf5+fkIDw9HcnIy7Ozs4OHhgWXLlmHx4sXo2rUrkpKSkJCQgJCQEHTp0gUAxGMNHDgQ9+7dg4+PDxo3bozQ0FB8+umncHBwgKOjI7KysnD58mV89913+Oqrr9CwYUOkpqbi/v37OHXqFDw8PEqd66NHj3Dx4kXk5ORgz549AOTJS+PGjcX32dnZOHXqFF5++WVs2rQJEokEAPDPP//g008/hZubG0xNTdGwYUMMGjQIMTEx6NWrF0xNTeHu7o7IyEg4OjrCzc0N3bt3BwCkpqZi2LBhiI6ORps2bXDt2jU4Ojpi7969sLe3x5UrVxAbGwuJRCLG0bFjR9jb2yvF/+eff8LT0xMNGzYUlymOURmbNm3CkCFD4O7uDgBo0qQJhg0bhk2bNmHGjBliud69e+Prr79GTk6OygkGEVUj0ydJQH7tSAIg6KH09HQBgJCenl7zB89MFIRga0H42rfmj02kx3Jzc4Xr168Lubm52g6lUo4cOSIAEAoLC8Vljx49EgAIV65cEQRBEK5cuSIAEKZPny6W2b9/vyCVSoXExERBEAQhOjpaACDcvn1bLOPo6Cj89ttv4vvLly8LBgYGwv79+8VlkyZNElq0aCEeX3GsiRMnCjKZTCy3atUqAYCwe/ducdmgQYMEAMJff/0lLvP39xemTZtW7vn+9NNPQuPGjSv8TJKSkgRnZ2dhx44dpY6/fv16pbKDBw8W+vTpIxQUFAiCIAhhYWGCgYGBMHz4cLHMmDFjhBEjRojnWFhYKAwYMEB46623xDJjx44VJkyYUGFc48ePF4YNG1buehsbG2HVqlUV7kMQBMHa2lpYtmyZ0rKVK1cKJiYmSsvi4uIEAMLp06fL3E9t/c4T1VrFxYIQbCMInzprLYTK3OOyOVBNU3QWUXQeISKty8zMREJCgvg+KSlJbGpTVFSER48eIT8/HwCQlZWl1Lk2OTkZaWlpAORtuR89eoS8vDwA8qfWjx49Ess+fvwYmZmZ1XYeU6dOFX/39/dHcXEx7ty5o/L227ZtQ6tWrTBw4EBx2cKFCxEZGYnLly8rlZ0+fbr4FF6hQYMGGDp0qPi+S5cucHNzw4ABA5SW3bp1S+WYFAoLCxEaGopdu3bh8OHDcHV1xblz55TKWFtbKzXFyc/Px/79+zFz5kwYGRkBADp06IDevXuLZbKzs7Ft2zZ4e3tjz5492L59O3bt2gU3NzccOXKkUjEmJyejXr2q/W0XBAEZGRmws7NTWm5vb4/8/HzxuwVAPFZycnKVjklEGmJgAJhYyft+FhdpO5rnYhJQ0xRjx5rZVVyOiGpMeHg4Nm/eLL7fsWMHTp8+DQDIyMjA2rVrxZv5S5cuYePGjWLZkJAQHD9+HIC87fnatWtx//59AMC1a9ewbt06seyff/6J8PDwajuPkjeOJiYmAKB00/g8MTExaNasmdKypk2bwsDAADExMUrLnZ2dS23/7A2wiYlJmcsqExMAXLlyBc2aNcPrr7+O9evXY8+ePUhISEBiYqJSOScnJ6XEJC4uDjKZDE2aNFEqV/J9XFwcioqKEB4ejh07dmDnzp3YtWsX0tPT4efnV6k4LS0tkZ2dXaltniWRSGBsbFxqKNesrCxxnYLiWCU7exORlpnUniZB7BNQ08QkgDUBRLqiQ4cOaNGihfh+xIgR4s2WtbU13nzzTfEGu02bNmJbbQAYMmSI2Fbf3Nwcb775pnjj27JlS7i6uoplBw4cqHQTpwoDA/mzmpIdVSt7E60qBweHUjf7aWlpkMlkcHBwUFr+bC1AdVq4cCF69+6tlHwNGDBAqbN0WTEp2uwramoUUlOfTuRjbS3/D/vdd99FQEBAleL09PTE4cOHq7QPAHB3dxcTSYWYmBg0adJE/D4AEOcJ8PT0rPIxiUhDTK2BDMiTAHPdfuDLmoCaxiSASOdYWVnB0dFRfF+/fn3Y2Mg77xsaGsLZ2Vl8sm5paQknJyexrIODgzgmvFQqhbOzM0xNTQHIh+Us+cTc3t6+0k9tGzVqBACIiooSl1W2mYqq/Pz8EBoaKo7qAwDbt2+HtbU1fH19q+WYz7K0tCyV5MTHx8PLy0vpfVmj+zzLxsYGPj4+CAkJEZdlZWXhv//+E987OTmhTZs2WLNmTantS074VVZcz3rppZfEjs2VcevWLWzZskV8HxAQgJCQEBQUFACQN4XavXu3UjMtADh16hR8fHyUOiITkZbVohGCWBNQ0xSzyOl4dkhEusHd3R3du3fH66+/jqlTpyImJkap6ZImDRs2DH5+fujduzfeffddJCUlYfny5Vi+fLmYFFW39u3bIykpCZ9++imaN2+ONm3aYOjQoVixYgVMTU1haGiIVatWibUvz7N06VIMHz4chYWF8PLywvr162FgYKBUa7B27Vr0798f/fv3xyuvvIKsrCwcPHgQHTp0wNKlSwHIRwOaP38+fvzxR9jY2KBv376lRgfy9/dH48aNsWvXLnEir9TUVHFugMLCQly4cAFbtmyBq6urOHLQgQMHMGvWLIwePRoA8H//93/Ytm0bBg4ciGHDhiEkJASZmZmYP3++0vG2bt2KyZMnq/EpE1G1qUUjBDEJqGmsCSCiSjpw4ABWrVqFM2fOwMvLC0eOHMEHH3wg1kDY2tri1VdfhZmZmbiNgYEBXn31VTRo0ABA2ZOFDR06tFR7+QMHDmD9+vU4e/YszM3NsXfvXvTt21dcX9axAHmTlGefVHt7eyt1CgaAVq1aVXiunp6eOHDgAPbu3Ytr167B3Nwc8+bNg4uLC44dOwYTExN88803iI6OVmoaU9bxAWDw4ME4dOgQ/vjjD0RGRuLjjz/Gpk2blOLv3Lkzrl+/jg0bNuDMmTNwdHTEvHnzlDoQT5w4ETKZDOfOnUNWVlaZQ4RKJBJ8+OGH+Pbbb5WSAMWwooGBgeLwp126dBGTAC8vL7z66qvifho0aICwsDCsXr0aZ86cwQsvvIANGzYo1UCdP38e9+7dYxJApGtqUU2ARHi2UaUeyMjIgI2NDdLT08X2oDVm/2wgbB3wyo9Am9E1e2wiPZaXl4fo6Gg0bdpUbK5DdV9GRgYsLCwglUoByDtve3h4YMGCBXjnnXc0fjxBEDBjxgy8++671dpW//vvv4eLiwuGDBlSbhl+54m0YP8sIOwXrd3nVeYelzUBNY01AURENSYmJgbTpk3DiBEjIJVKsWHDBlhbW2P8+PHVcjyJRIJvv/22WvZdUnUkMESkAbZuQP0WgKHuJ95MAmqa7yiggQ9Q31vbkRAR1XmtW7fG119/je3btyMtLQ0TJ07E5MmTSzVnIiLSCL9Z8p9agElATfN6Wf5DREQ1omPHjujYsaO2wyAi0ikcIpSIiIiISM8wCSAiIiIi0jNMAohIr+jhgGikp/hdJ6KKMAkgIr1gZGQEAJWezZWotlJ81xXffSKiktgxmIj0glQqha2tLRITEwEA5ubmSrPGEtUVgiAgJycHiYmJsLW1FedIICIqSetJQHp6Onbt2oWEhAS0bt0aAQEBz/2PWZ1tiIgUM64qEgGiuszW1lZplmEiopK0mgTcv38ffn5+aNSoETp27IhVq1ahc+fO2LVrV7k39epsQ0QEyCdycnZ2RoMGDVBYWKjtcIiqjZGREWsAiKhCEkGLPYdee+013L17F6dOnYKhoSFu3boFHx8f/PHHHxg5cqTGtnlWZaZUJiIiIiKqDSpzj6u1jsHFxcUICQnB+PHjYWgor5Dw9PREjx49sGPHDo1tQ0REREREyrTWHOj+/fvIzc2Fh4eH0nIPDw+cPXtWY9sAQH5+PvLz88X3GRkZVYiciIiIiKh201oSkJWVBQCwsbFRWm5rayuu08Q2ALB06VIsXry41HImA0RERERUVyjubVVp7a+1JMDS0hKAfKSfktLS0sR1mtgGAObPn4/Zs2eL7+Pi4uDj4wNXV1e1YiciIiIi0lWZmZmlHpo/S2tJgKurK8zMzHD79m30799fXH779m14eXlpbBsAMDExgYmJifje0tISsbGxsLKyqvERhTIyMuDq6orY2Fh2StYzvPb6i9def/Ha6y9ee/2lzWsvCAIyMzPRsGHD55bVWhJgaGiIIUOG4LfffsPUqVPFkX6OHz+O33//XSy3d+9ePHjwAG+//bbK2zyPgYEBXFxcquO0VGZtbc0/CnqK115/8drrL157/cVrr7+0de2fVwOgoLXRgQBg2bJlePjwIXr06IH33nsPvXv3RmBgoNJQn3v37sUPP/xQqW2IiIiIiKh8Wp0szM3NDVevXsXOnTuRkJCANWvWYODAgUpNdAYPHoz27dtXahsiIiIiIiqfVpMAQF5lERQUVO76wYMHV3obXWZiYoLg4GClPgqkH3jt9Revvf7itddfvPb6q7Zce63OGExERERERDVPq30CiIiIiIio5jEJICIiIiLSM0wCiIiIiIj0DJOAGhYdHY3w8HBkZ2drOxTSkIKCAly5cgXR0dGQyWTllouKikJ4eDhyc3OrVIZ0z8OHD3Hy5EkkJiaWuf7mzZu4cOEC8vPzy92HKmVIt2RnZ+PChQtISkoqt0xkZCQuXryIwsLCKpUh3ZGXl4dr167h8uXL5f5fLggCrl27hkuXLqG4uFjtMqRdaWlpOHXqFOLj48stk5iYiPPnz5f791+TZTROoBqRnp4u9OnTR7C0tBQ8PT0FS0tL4ddff9V2WFQFOTk5wty5cwU7OzuhdevWgrOzs+Dl5SWcOXNGqdzjx48FPz8/wdraWvDw8BBsbGyE7du3V7oM6abMzEzB29tbACCsX79ead3Dhw+FDh06CPXq1ROaNWsm2NvbCwcOHKh0GdI9ixcvFiwsLARfX1+hSZMmwjvvvKO0/t69e4Kvr6/g4OAgNGnSRHB0dBSOHDlS6TKkW9atWyfUq1dP8PLyElq2bClYWFgIy5cvVyoTGRkpeHp6Co6OjoKLi4vg4uIinD17ttJlSHvu3LkjvPHGG4Kzs7NgYGAgrF69usxyM2fOFExMTAQfHx/BxMREmDlzZrWVqQ5MAmrI5MmTBS8vLyElJUUQBEH46aefBENDQ+HmzZtajozUFRcXJ/zvf/8TsrKyBEEQhKKiIiEoKEho0KCBUFBQIJYbPXq00KZNGyEzM1MQBEFYuXKlYGJiIsTExFSqDOmm8ePHCx988EGZScCAAQOEbt26Cbm5uYIgCEJwcLBgbW0tJCUlVaoM6ZYvvvhCsLa2Fs6dOycuW716tVBUVCS+9/PzE1566SXxb8GcOXMEe3t7IT09vVJlSHckJSUJBgYGwsqVK8VlmzZtEgAI169fFwRBEGQymeDr6ysMHTpUKC4uFgRBEN544w3B1dVVyMvLU7kMadeBAweEtWvXCllZWYKFhUWZScCGDRsEc3NzISIiQhAEQbhw4YJgZmYmbNy4UeNlqguTgBqQl5cnmJubC9999524TCaTCQ0bNhQWLlyoxchI00JDQwUAwrVr1wRBkNcAGRkZCRs2bBDLFBYWCnZ2dsLSpUtVLkO66ddffxXat28vFBQUlEoC4uLiBIlEIuzZs0dclpWVJZiZmYn/oahShnRLTk6OYGNjIyxZsqTcMrdu3RIACIcPHxaXJScnC4aGhsJvv/2mchnSLTdv3hQACKGhoeKy6OhoAYBw/PhxQRAE4dy5cwIAISwsTCxz7949AYCwb98+lcuQ7igvCejRo4cwevRopWUjRowQevbsqfEy1YV9AmrAzZs3kZOTgw4dOojLJBIJOnbsiIsXL2oxMtK08+fPw8jICG5ubgCAq1evorCwUOnaGxoaom3btuK1V6UM6Z7bt29j7ty52Lx5M4yMjEqtj4iIgCAIStfVwsICLVq0EK+rKmVIt4SFhSE9PR2BgYGIj4/HhQsXkJaWplRGce1KXld7e3s0a9ZMXKdKGdItnp6eCAoKwsyZMxESEoI///wTkydPxtChQ9G9e3cA8utqYGCAdu3aids1btwYDRo0ULr2zytDuu/ixYtK/34BoHPnzkrXUFNlqguTgBqQkpICQP4HviR7e3txHdV+t2/fxkcffYRZs2bB0tISgGrXnt+P2qegoACjR4/G4sWL4e3tXWYZXvu66eHDhwCAjRs3ol27dggKCoKzszOmT58O4cncmykpKZBKpbCxsVHa9tlr/7wypHveeOMNpKen4/3338f//d//ISoqCtOmTYOBgfx2KiUlBba2tuJ7hWev/fPKkG4rKipCZmZmmX+7MzIyUFxcrLEy1YlJQA1QPCXMy8tTWp6bmwtjY2NthEQa9uDBA/Tv3x89e/bEZ599Ji5X5drz+1H7fPHFF8jLy0OrVq1w8uRJnDx5EoA8EVQ8veG1r5sU1+zOnTuIiYlBREQETp8+jZ9++gm//PKLWKa4uLjUaD/PXvvnlSHdcvfuXfTu3Rvvvfcebt26hWvXrmHlypUICAhAeHg4APl1ffbfM1D62j+vDOk2qVQKAwODMv92GxgYQCqVaqxMdWISUAMaN24MAIiLi1NaHhcXJzYbodrrwYMH8Pf3R6tWrbBt2zYYGhqK61S59vx+1D4mJiaoV68e5s2bJ/4AwPbt27Fy5UoAvPZ1VZMmTQAAkyZNEm/Y2rVrhxdeeAEnTpwA8PS6KmoNFB4+fFjq2ldUhnTLoUOHIJPJMGXKFHHZK6+8AkdHR/z5558A5Nc1JydHqYlYUVEREhMTla7988qQbpNIJHB1da3wb7emylQnJgE1wMXFBd7e3ti7d6+4LDExEWfOnEHfvn21GBlVVVxcHHr16oUWLVpgx44dpZ7ieHl5wdXVVenaK54eKq69KmVIt3zwwQdiDUDJmoAFCxbg119/BSBv621nZ6d0XRXzSSiuqyplSLe0adMGTk5OSv9pC4KAhw8fon79+gCArl27wsLCQum6njlzBomJieJ1VaUM6Zb69eujsLBQaRz3rKwspKamitfe398fRkZGStf10KFDyMnJQZ8+fVQuQ7qvb9++2L9/v9gMUBAE7Nu3T+nfr6bKVJtq73pMgiAIwu7duwWpVCp88sknwu7du4WuXbsKbdq0URpKkmqXlJQUwdPTU/D09BT+/fdf4cSJE+JPWlqaWG7Tpk2CoaGhsHz5cmHnzp1C+/bthS5duohDw6lahnQbyhgi9PvvvxdMTU2Fb775Rti2bZvQokULoV+/fpUuQ7pl48aNgr29vbB69Wrh77//FsaPHy9YW1sLd+7cEcssW7ZMHFVky5Ytgru7u/DKK68o7UeVMqQ7srKyBE9PT6Fz587Czp07hb179wovvfSS4OTkJCQmJorl5s+fL9SrV09Yt26dsGnTJqFRo0ZCUFCQ0r5UKUPak5GRIf5/bmZmJsydO1c4ceKEcOPGDbHMnTt3BFtbW+H1118X9u7dK4wfP16wtbVV+jugqTLVRSIIT1IPqnaHDh3CTz/9hJSUFHTs2BEffPAB6tWrp+2wSE03b97EG2+8Uea6r7/+Gh07dhTf79+/H+vXr0d6ejq6du2K999/H9bW1krbqFKGdJefnx8WLlyIl19+WWn59u3bsXnzZuTk5KBHjx6YPXs2zM3NK12GdMuBAwewfv16ZGRkwNvbG7NmzRKbCils3rwZW7duRX5+Pnr37o2ZM2fCxMSk0mVId6SkpODbb7/FhQsXUFxcjNatW2PGjBlwdnYWywiCgHXr1mHPnj0oKirCgAED8O677yo1FVWlDGnP9evX8eabb5Za3qdPHyxatEh8f+PGDXz55Ze4e/cumjVrhrlz55YaLEJTZaoDkwAiIiIiIj3DPgFERERERHqGSQARERERkZ5hEkBEREREpGeYBBARERER6RkmAUREREREeoZJABERERGRnmESQERERESkZ5gEEBFV0okTJ3Dx4sVq36am9vvff//hypUrGopIN1TX511dxzlz5gzCwsI0EBERkWo4NR0RUSUtW7YMzZs3R7t27ap1m5ra75IlS+Dn54fWrVtrMLKac+zYMdjY2KBt27bisur6vJ+lqeN88803sLW1VZppnIioOjEJICKqpB49esDJyanatyHVLF26FK1atVJKAmrq8+Z1JaLaikkAEemtgoICnD59GmlpaWjdujXc3d2V1v/333+oX78+GjZsiLNnz8Lc3Bz+/v7o2rUrLC0tlcpmZGTgxIkTsLa2Rrt27XDlyhUYGRmJT3af3Uaxbzc3N1y8eBEymQxdunSBubm5WOb8+fO4c+cOAMDBwQFt2rRB/fr1NX6eCikpKWIsPXr0gImJidL6mzdv4tatW2jUqBHatm0LA4OnLUoFQUBYWBgePnyIZs2alapVKOuztLOzQ0JCAvr27atUNiIiAomJiejXr99zP4PQ0FDEx8fDyMgIW7ZsAQAMGjSozGuk6vWu6Jo8S53rCgCZmZk4fvy4+H0pS0Wf6fXr13Ht2jUMHz5cvA5paWn4+++/0aNHDzRs2LDcmImIACYBRKSnbt68iQEDBsDIyAhNmzbFqVOnMGXKFKxcuVIss2TJEhQVFSEuLg4tW7ZE165d4e/vX6oJyMWLF9GvXz80aNAADRs2xN27d2FpaYmuXbuKScCz2yxZsgTFxcV49OgRvL29cevWLRQXFyM0NFS8yb148SL+++8/AEB8fDzCw8OxevVqjBs3TqPnCQBHjx7Fxo0b0apVK0RGRsLMzAxHjhwRn3K/9dZb2LFjB7p3746EhAQYGRkhJCQE9vb2ePToEQYPHoz09HS0aNECERER8Pb2xu7du8Wb37I+y7Zt22L48OGIj4+Hra2tGMtbb72F7t27o1+/fs/9DMLDw5GQkIC8vDzs2bMHANCrV69Sn7eq1/t51+RZ6lzXq1evok+fPrC3ty/1fVF43mdqZ2eHd955B1FRUZg/f774ud25cwfDhw9X+ftBRHpMICLSQ/7+/sKgQYOEwsJCQRAE4ezZs4JUKhX+/vtvsUzPnj0FW1tbITY2VmnbgQMHCjNmzBDfd+vWTRg5cqRQXFwsCIIgHDp0SAAgvPXWW+Vu07NnT8HJyUmIj48XBEEQ8vPzBU9PT2HJkiXlxhwSEiJYW1sLGRkZ5e5X3fM0MTERIiMjBUEQhJycHKFTp05CUFCQIAiCcO/ePQGAcOvWLXGbc+fOiZ9Lv379hClTpojnn5eXJ7zwwgvCwoULlY7x7GdZWFgo1K9fX/j555/FZbdv3xYACOHh4Sp/Bv379xfmzJmjVO7Zz0XVz6Gy10Sd69qjRw+l78tff/1V6vuiyme6b98+wcjISDh37pzwyy+/CObm5sKNGzfKjZWIqCTWBBCR3klISMDRo0dx/PhxGBrK/wx27twZffv2xdatW9G/f3+x7CuvvAIXF5dy9/Xo0SOcPn0aoaGhYrOMPn36KLVPL88rr7wCR0dHAICxsTG6deuGmzdvKpVJTk7G5cuXkZycjKKiImRlZeHGjRvo1KmTRs8zMDAQ3t7eAAAzMzNMnz4db7/9NtatWwdjY2MYGBjg8uXL8PDwAADx+A8fPsTBgwexfPly7Nq1C4IgQBAENGvWDEeOHCl1viU/S0NDQ4waNQqbN2/GG2+8AQDYvHkzWrRogfbt22vkM6js56DKNXmeivYRHx+P48ePK31fBgwYAF9fX3F7VT/TQYMGYcqUKXj11VeRlJSElStXwsvLq1KxEpH+YhJARHonJiYGANCsWTOl5e7u7oiMjFRa5uzsXOG+YmNjAQBNmjRRWv7s+7LY2dkpvTcxMUFmZqb4ftWqVZg/fz58fX3h7OwMIyMjAEBiYuJz9w1U7jyfjbdp06bIyspCSkoKnJ2dsWbNGkyfPh0zZsxAr169MGHCBPTp0wf37t0DAJw6dQrh4eFK+3j2Jr2sz3Ls2LHw8/NDXFwcGjVqhN9//x0TJkzQ2GdQ2c/heddEFRXt4/79+wDK/rwVKvOZBgcHY+3atfD09MSbb75ZqTiJSL8xCSAivePg4ABA3hG2UaNG4vKUlBRxnYJEIqlwX4obvrS0NPHpLwCkpqYqva+snJwczJo1C7t370ZgYCAAICsrC1u3boUgCCrtozLnmZqaWuq9kZERbGxsAABTpkzB5MmTcfXqVezduxcDBw7EH3/8AU9PTwDAggUL0Llz5wrjKeuz7Nq1K5o2bYo//vgDPXv2xO3btzF27FiNfQaV/Ryqm729PYDS34/U1FSx/4W1tTUA1T7TDz74AE2aNEFUVBR27NiBESNGVFPkRFTXcLIwItI7jRs3hqurK3bt2iUuy8zMxD///AM/P79K7atJkyZo2LAhQkJCxGUJCQk4e/ZslWJMTk5GcXGxUvOOHTt2VGoflTnPv/76C/n5+eL7Xbt24YUXXoBUKkVqaipycnIgkUjQunVrLFy4EF26dEFoaCh8fHzg6uqKNWvWlDp+XFycSnGOGTMGmzdvxubNm+Hn54fGjRtX6jOwtLREXl6eRj6H6takSRO4uLiInZgBefOf0NBQ8b2qn+mOHTvwxx9/YNeuXfj000/x1ltvqfyZExGxJoCI9I5UKsVXX32FMWPGIDMzE82bN8fPP/+MRo0a4a233qrUvgwNDfHpp59i6tSpSEtLg4uLC9asWQNzc/Pn1iJUxNXVFe3bt8eECRMwefJkREVFYd26dUrDcj5PZc6zoKAAffr0wbhx43DhwgVs3rwZ//77LwB5k6cRI0ZgxIgR8PT0RGRkJM6dO4fPP/8cBgYG+OWXXzBkyBCkpqbi5ZdfRmpqKvbv348hQ4Zg7ty5z41z3Lhx+OSTTxAVFYUVK1ZU+jPo2LEjfvjhB7Rr1w4WFhYYNGiQ2p9DdZNKpfj888/xxhtvID09HS4uLvjhhx+UhhlV5TN98OAB3nzzTXzxxRdo3bo1WrVqhb///hsTJkzAoUOHqvTdIyL9wJoAItJLI0aMwPHjx1FYWIgzZ85gzJgxOHXqFIyNjcUyvXv3VuqwqdCjRw+ljquTJk3C7t27kZiYiKioKHz99ddo3749rKysyt2mrH136tRJfDItkUhw6NAhvPzyyzh27BgA4PTp0xg7dqxSk5Zn96vueX7//feYMWMGrl69CqlUipMnT+LFF18EAPj6+uLo0aOwsrLC8ePHIZVKcf78eXTv3h2AvCP0tWvX0K5dO5w6dQrp6elYvny5UgJQ3mcJAJ6enpg5cyYGDRqEkSNHistV/QxmzZqFuXPn4tSpU9izZw+ys7NLfS7qXu+S16Qslb2uADB+/Hjs27cPSUlJuHPnDlatWoXg4GCl9v7P+0z37duHiRMnYsaMGeJn9euvv6JBgwY4d+5cufESESlIhMo0rCQiolJSU1Nha2srPn19/Pgx3N3d8eOPP+LVV1/VcnRERESlMQkgIqqi48ePY9GiRRg2bBiKiorw448/wtLSEidPniw16y4REZEuYBJARKQBJ06cwJ49e5CTk4O2bdsiKChIHM6SiIhI1zAJICIiIiLSM+wYTERERESkZ5gEEBERERHpGSYBRERERER6hkkAEREREZGeYRJARERERKRnmAQQEREREekZJgFERERERHqGSQARERERkZ5hEkBEREREpGf+H2FWj/lYCP9UAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "MovingBlock edge mean usage 0.574 vs middle 1.076\n", "CircularBlock edge mean usage 1.030 vs middle 1.074\n" ] } ], "source": [ "L = 25\n", "mb = bootstrap(x, method=MovingBlock(block_length=L), n_bootstraps=B, random_state=3)\n", "cb = bootstrap(x, method=CircularBlock(block_length=L), n_bootstraps=B, random_state=3)\n", "\n", "mb_usage = mb.inbag_counts().mean(axis=0)\n", "cb_usage = cb.inbag_counts().mean(axis=0)\n", "\n", "fig, ax = plt.subplots(figsize=(9, 4))\n", "ax.plot(mb_usage, color=\"tab:orange\", lw=1.4, label=\"MovingBlock\")\n", "ax.plot(cb_usage, color=\"tab:green\", lw=1.4, label=\"CircularBlock\")\n", "ax.axhline(1.0, color=\"gray\", ls=\":\", lw=1, label=\"uniform target (1.0)\")\n", "ax.set_xlabel(\"original observation index\")\n", "ax.set_ylabel(\"mean times sampled per replicate\")\n", "ax.set_title(f\"Index usage (block length {L}): MovingBlock starves the ends, CircularBlock is flat\")\n", "ax.legend()\n", "plt.show()\n", "\n", "edge = list(range(L)) + list(range(n - L, n))\n", "mid = list(range(n // 2 - L, n // 2 + L))\n", "print(\n", " f\"MovingBlock edge mean usage {mb_usage[edge].mean():.3f} vs middle {mb_usage[mid].mean():.3f}\"\n", ")\n", "print(\n", " f\"CircularBlock edge mean usage {cb_usage[edge].mean():.3f} vs middle {cb_usage[mid].mean():.3f}\"\n", ")" ] }, { "cell_type": "markdown", "id": "e18e5d24", "metadata": {}, "source": [ "The moving block visibly droops at both ends: the first and last observations can only appear in a few blocks, so they are under-represented. The circular block's wrap-around fixes this, at the cost of joining the end of the series back to its start." ] }, { "cell_type": "markdown", "id": "907dcfc9", "metadata": {}, "source": [ "## Recipe 3: block length is a bias-variance knob\n", "\n", "The block length controls how much dependence the bootstrap preserves. Too short and the replicates look i.i.d., so the variance of the sample mean is underestimated. Too long and there are too few independent blocks, so the estimate is noisy. We sweep the block length and compare the bootstrap estimate of `Var(mean)` to the known long-run value." ] }, { "cell_type": "code", "execution_count": 6, "id": "fc89d199", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:45.327407Z", "iopub.status.busy": "2026-06-22T16:15:45.327241Z", "iopub.status.idle": "2026-06-22T16:15:45.747366Z", "shell.execute_reply": "2026-06-22T16:15:45.745212Z" } }, "outputs": [ { "data": { "image/png": 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Rb1y7do3IyEjdbTMzM1xcXChdunSGfRMvX76MmZkZ1apVS3dfVFQUd+7cwcbGhipVqmR6pjo5OZmbN29ibm5O5cqV9bqCXLhwQdf+WdevX+fJkydUrVo109nZXpRNq9Vy69Yt4uPjqVChgt7X/S/a7927dwkPD6devXrpthkYGEh4eDiVK1fGzs6OBg0aYG5uztGjR/XWS0lJ4caNG8TGxmJpaak7O2rMPp+X3W0/lZCQwO3bt7G3t6d8+fJotVpOnjxJmTJlKFWqlN66QUFBhIWF6Y7z5s2bxMXFUatWrXTbzepxhrTf/61bt7CwsKBMmTJYW1tneZzPHk9cXBy3bt3C2dk5w7P8mT0PDD1mY/IFBATw8OHDTLsQZPXayOr3lZng4GDu3buHk5MTnp6eGa5jyHG/aP85eTyNeY6/6P3hKUOeZ0LkB1I4CyFEBsLDwylXrhxDhgxh7ty5po4jhBAiH5A+zkKIQu/EiRPs27dPdzs2NpZhw4aRmpqqm2ZZCCGEkMJZCFHolSlThtmzZ1O8eHG8vb0pUaIEZ86cYcOGDUaN9yuEEKJgkq4aQgjxn+joaO7cuYODgwOVKlUydRwhhBD5jBTOQgghhBBCGEC6agghhBBCCGEAKZyFEEIIIYQwgEy5nce0Wi0PHz7EwcEBlUpl6jhCCCGEEOI5iqIQExODu7v7C2fXlcI5jz18+JAyZcqYOoYQQgghhMjCgwcPMpyI6SkpnPOYg4MDkPaLKFKkiInTCCGEEEKI50VHR1OmTBld3ZYZKZzz2NPuGUWKFJHCWQghhBAiH8uqW61cHCiEEEIIIYQB5IyzEEIInaQ7d0GTCmpzrCpWMHUcIYTIV6RwFkIIoRMwaBCpISGYu7riceigSTIoikJqaioajcYk+xdCFEwWFhao1eocbUMKZyGEEPlGcnIyjx49Ij4+3tRRhBAFjEqlonTp0tjb2xu9DSmchRBC5AtarZa7d++iVqtxd3fH0tJSxr8XQuQKRVF4/PgxgYGBeHh4GH3mWQpnIYQQ+UJycjJarZYyZcpga2tr6jhCiAKmRIkS3Lt3j5SUFKMLZxlVQwghRL7yolm7hBDCWLnxDZbJzzgnJSWxe/duQkJC8PHxoUGDBrnSJjvbvX37Njt27KBWrVo0adIkx/mEEEIUXE/7YFeqVCnD+0NCQoiOjsbDwyPP95XT9UX23b59m2LFiuHk5GTqKBkKDAzE3NyckiVLmjpKgWTSj/WhoaHUrl2b8ePHs2/fPjp06MDgwYNz3CY7201KSqJnz56MHz+etWvX5jifEEKIgm3p0qWMHj060/tXrlzJxx9//FL2ldP1RfZERETQrFkzUlJSTB0lU7du3aJLly4oimLqKAWSSc84T5gwAQsLC06cOIGNjQ3nz5+nbt26dO3alS5duhjdJjvbHTVqFI0aNcq1fEIIIUxHo1U4eTeC0JhEXBysqV+hGGozucAwtwQHBxMbG0vlypXzZP3cEBQURHR0NNWqVUt3X0xMDNevX6d27dpG9XGdO3cuXbt2xcXFJTei5okWLVqgKAqbN2+ma9eupo5T4JjsjLNWq2Xt2rUMHDgQGxsbAGrVqkWjRo1Ys2aN0W2ys90NGzawf/9+5syZkyv5hBBCmM5O/0c0+XY/by0+waerz/PW4hM0+XY/O/0fmTpagbFixQpGjhyZZ+vnhkuXLlG7dm0iIiLS3ff9998zaNAgo4pmjUbDsmXL6N+/f27EzFNvvfUWixcvNnWMAslkZ5wfPHhATExMuk+E1apV4/Tp00a3MXS7Dx48YMSIEWzfvj3Dq7eNyQdpXT+SkpJ0t6OjowGoWrVqlhe81KlTh82bN+ste+ONNzh79uwL20HamfNRo0bpbmeUPTObNm2ibt26uttbt25l+PDhWbazt7fn2rVresvGjh3LX3/9lWXbTp06sXDhQr1l9erVIzg4OMu2s2fPpl+/frrb169fp3Xr1lm2Azh16hRubm6624sWLWLatGlZtqtSpQr79+/XW9a/f38OHTqUZdshQ4YwZcoUvWWlS5c2KO+qVato0aKF7vbBgwcZMGCAQW0DAwP1bk+dOtWgN9LmzZvzxx9/6C1r1aoVN27cyLLtl19+ydChQ3W3Hz16xGuvvWZQ3n379uHp6am7/eeffzJu3Lgs25UsWTLda3LYsGFs27Yty7ZvvfUW3333nd6yqlWrEhsbm2XbBQsW0LlzZ93tM2fOGHx25+rVqzg4OOhu//DDD/zwww9ZtnsZ7xF/2tpRwsyMR48e0fK/5+nLeo8oVaoU06dPJykpCScnJ8qVK6d3/5UrVzL9ivz4gwRm+YWnWx4clciIVWcZ38SZ18vYZJm5WrVqWFpa6m4/fvyYhw8f6m8zOJioqCguXLjAo0ePsLKywt3dXe/5C3Dnzh1iYmJ0t6Ojo4mIiKBUqVJYWFjolpcoUQJ3d3cSExO5f/8+FSpU4OrVq+n29dS1a9dwcnLC1dWVihUr6j2XkpKS0mUrVqxYuuOMjo7GxcWFihUr6rI8fPiQx48fZ5o1OjqaCxcuEBISonvN1axZEwsLCy5cuMCdO3coXrw4RYoU0Vv/4cOH/Pnnn0Da2VCVSqXrh33//n38/f2xt7cnKCgIgKJFi+Lm5qb3N/Px48e4u7vj5eVFQEAA1tbWqNXqdO9zAK6urjg7O/PNN98wYMAALCws8PLyQqvVsmzZMsaNG8fFixfx9/cHwNHREXd3d739hYeHExsbS+3atbGwsCA2NpbIyEiePHmCnZ2d7vfxdL1y5coREhJCSkqK7v29ePHiREZGUr58eezs7IiLi+PWrVt6v6uHDx9SsmRJ3Qm6p4+bpaUlarWaYsWKUb58eUJDQwkJCUm3z9DQUFJTU3Fzc0OlUmFra4uHhwctW7Zk8uTJJCUlERAQYNC46K6urnr9ojUaje4xykrlypWxs7PT3Y6MjOT+/ftZtlOr1Xh7e+ste/DgQYYfep5XtGjRbL1HwP8PSXf58mV69eqlW379+nVatmyZ5T7BhIXz0zeTokWL6i13cnLSFZvGtDFkHY1GQ79+/fjss8+oU6dOruUD+Oabb5g6dWq65Y8eZX3Go0yZMumWPX78WPdm8iLPZ1IUxaB2kDYE1LMSEhIMavvsm/VTT548MahtRi+K4OBgg9o+/waQmppq8LE+PxNZbGysQW0dHR3TLQsLCzOobVRUVLplhuZ99kPY09uGts0ohyFtw8LC0i0LCQkxqO3zBadGozE4b2pqqt7t+Ph4o481IiLCoLZPnjxJt+zhw4d6xU5mEhIS9G4nJycbnPf5vofR0dEGtX0Z7xGaipXAzEzvd/ey3iPMzc3RaDSkpqaSmpqKoigkpPz/azYmIYmUlNR07bSKwqLT6X+XAE8f6UVnnuDlbIbZC66qt8rgJKRGo0n3h1ij0RAaGkqfPn2Ij4/n8ePHNGvWjM2bN2NlZaVbLzU1lZSUFOLj4/n66685duwYzs7OREREMHr0aF2Xv8TERD7++GOWLl1KmTJliIyMZPz48TRr1gyNRoOiKKSkpJCamsrMmTO5f/8+33//PSkpKWi1Wv3jVZR02Zo0acLUqVOxtLTUy+Lu7k5oaCg//fQTAwcORKPREBUVlWlWf39/9u/fT0JCgu6D0/bt29m1axcffvghzs7OREVF0axZMyZMmKBbPz4+nunTpwNQo0YNNm7cyJYtW1AUhaioKBo2bEitWrV0H+zDw8OxsLDg22+/1X0YWbduHadOnUKr1RITE8PDhw9p06YN48eP1/ug81TXrl1Zt24dffr00S3bvn07YWFhDBgwgI0bNzJ79mzg/98HZs2aRfXq1YG0D4u7du3Czs6O2NhYOnbsSNWqVfH09ESr1eoe902bNrFjxw7MzMxITEwkNDSUBg0a0LJlSxYuXIi9vT3BwcFs3ryZunXrkpKSgkajYf78+WzYsAFXV1dCQkJ46623dI/phQsXWLFiBYDug8yvv/6q6x7yNJutrS3h4eE8efKEKlWq8PPPP+seCx8fH5KSkvD398fW1tagPtnPP5cAg/tyP/+eptVqDWqb0eygGb3mMvL83wxIy5tVW41Gk+79OzU11aA6DUxYOD/9dPX8H6jo6OhMx+80pI0h6/zxxx9cunSJ3r178/PPPwNpxcKFCxf4+eef+fDDD43KBzBx4kS9szrR0dGUKVMm3afnjJQoUSLDZaVKlXphO0D3Cf8plUplUDsg3ZuOjY2NQW0zmnnHycnJoLYZnQEx9Arg5x9/c3Nzg4/1+a/n7O3tDWrr6uqablnx4sUNaptR0W1o3mf/CD+9bWjbjHIY0rZ48eLplrm6umb4AeB5zz8n1Gq1wXnNzfXfjmxtbQ1qm9HzplixYga1zeiqeHd3d4POOD97hgjSXkeGHuvzQyIVKVLEoLYv4z3i6Wvk2d/dy3qPcHV1Ra1WY25ujrm5OQkpGry+3JXlfgwRkaDlnU2PX7jOmt7u6Zap1Wq9s8NPl125coWff/6ZJk2aEBERwaBBg/jpp5/0viUxNzfHwsKC5cuXc//+fXbs2IGjoyNHjhzhs88+o0aNGlSuXJkFCxawc+dOrl27RtmyZYmKimL+/Pm66YFVKhWJiYmMGTMGBwcHFi9erHtveP7vikqlSpft3Xff5e+//2bQoEF6WZo1a8b27dvp2rUrr732Gk5OTi/M2qhRI/r27culS5f0voGbNm0an3/+Ob6+vkBaYZeamqpb/9y5c8yfPx/4//fSM2fOcPDgQerXr687u96qVSvdNpctW8bs2bP5/fffdY/5mTNn2L59Ox06dODx48c0aNBAd1zP69GjB4sXL+by5cu6b70WLVpEnz59KFq0KC1btqR27dq69VeuXMmsWbNYvXq1bn83btzgjz/+4K233gLg66+/plixYlhaWuoKPrVazb1791i2bBk+Pj48ePCA7t27Ex8fz6lTp3B3d+fLL7/kiy++YMeOHVhYWLB69WqOHz/Oli1bcHZ2JjQ0lAEDBlC7dm2aNGlC06ZNGTFihO61OHfuXMaPH8+qVat0+7x9+zZLliyhVq1axMTE0KNHDw4fPkz37t2BtKmlHRwcePz4MZUqVUr3HM5IRjWKIe0g/XuamZmZQW0z6jKT0WsuI8//zYCs8yqKglqtTvf+bW5ujpubm0HFs0ox0WWXKSkp2NvbM3/+fL2vdn19fbG3t2fdunVGtTFkncOHD/P333/rbXvNmjWUKlWKJk2aMG/ePDQaTbbzZSQ6OhpHR0eioqLS/eESQoj85mbzFqSGhGDu6orHoYMvdd+JiYncvXuXChUqYG1tTXxyaq4Vzoa4Ms0XW8uszydNnz6djRs36nUR+u6779iyZQuHDx9mzpw57N27l507dwLg5eXFyJEj9f6W1K9fn969ezN27Fh8fHz44IMPGDFiRIb72rJlC3FxcbRv357vvvvuhWPRZpUtqyxZ3T9r1iz8/PzYunWr7v7OnTtTokQJJk+enO4iwIzWnz59Ojt37sTPz09vXY1Go/uaPiwsjA4dOpCYmIiFhUWWx5WRnj174uDgwIoVKwgKCqJcuXL4+fnRsGFDIO2s6IMHDwgPDycmJoYWLVoQGxuLnZ0dc+bMYfXq1Xr7mz17Nlu2bOHIkSO6ZXPmzGHjxo16x1K+fHmmT5+u61a3d+9e3n77bV1R1qBBA5o1a6Z3NnzOnDm4urry008/GZTt+X1269aN1157jcmTJ+uWWVtbs2PHDoO7IBQGz7/HPMvQes1kZ5wtLCzo0KEDf/75J0OGDEGlUhEYGMjBgwdZtGiRbr0DBw4QHBzMW2+9ZVAbQ9Zp1qwZzZo108vj5+dHixYt+PHHH4G0T0uG5BNCCJE3bCzUXJnmm+V6J+9GMHD5qSzXWzHoNepXSP9t17P7M5Szs7Pe7eLFixMenr6PNaR1PXj+24Jn13/8+HGG32o9FRkZyePHj6lbt65BEzi8KFtWWbK6PyN///03y5cvZ8KECVy/fp02bdowe/bsF579e/6brd27d/Pee+8Bad+iqFQqtFqtrm9zVseVkaFDh9K9e3d++uknli1bhpeXl65oPnjwIO+88w4ajYYSJUrozl6GhIRQsWLFDDOWK1cuXX93SP/Nirm5ud4yc3Nzve4DISEhbNiwgQMHDui1K1++vMHZMtrns/sIDw8nKSkpXR9gkXMmHcf522+/5dKlS3Tu3Jlp06bRqlUrGjVqpHfF6h9//MGMGTOy1caQdXIrnxBCiLyhUqmwtTTP8l9TjxK4OVqTWUmpAtwcrWnqUeKF28nOrGL+/v56hcqZM2eoUqVKhutWqVKFM2fO6G6npKRw8eJF3fpeXl4cPXpUr82z1zdUq1aN3bt38+mnnxp0ge+LsmWVJav7zc3N0/WFNTMz48MPP2Tt2rWcOXOGHTt26LoVZLR+RiZMmMDo0aMJDAzk3LlzrFy5EtDvd5udxxygXbt2lCxZkpUrV7J06VKGDRumu2/SpEmMGDGCoKAgzp8/rzcyV2aaNGnC3bt3M7w2Iju8vLwYMGAAp0+f1vv31VdfGZ3teU8vhH9aaIvcY9JxnD09PfH392flypWEhIQwadIk+vfvr9dvpVWrVnq/eEPaGLLO8/r27ZtulidjtiOEEOLlUpupmNLFixGrzqLi/y8IBHTF9JQuXrk6nnNYWBjvvPMOQ4YM4eLFiyxbtowdO3ZkuO7YsWPp168fJUuWxMvLi4ULF2Jubk7fvn3Tsk2ZQocOHShSpAjNmzfnwoUL3Lhxg//973+6bdSrV48DBw7Qtm1bYmNj+eyzz4zKllWWrO6vXLkyc+fOZf/+/RQpUoSaNWvSoEEDBg8eTK1atbh37x4PHz7UnSXOaP2MODs7c/DgQerWrUt4eDgzZ87M0WMOaR+8hgwZwuTJk0lNTdUbkcjZ2ZkjR47QqFEjIiMjmTVrVqbbeeppd84tW7bwzjvvZLl+Zp6eiLO0tKRx48Y8fvyYv/76i549e9KvXz+jsj1vy5Ytur7ZIneZvAJ0c3N74ZBTzw47ZmgbQ9d51oQJE3JlO0IIIV6+9t5u/DqgDlO3XOFRVKJueUlHa6Z08aK9t9sLWmePu7s7H3/8MZUqVWLOnDlYWlqyceNGmjdvnrbPkiX1zoS+8cYbbNiwgSVLlrB27Vpq1KjBv//+q7vQuXnz5vj5+TFv3jwOHDhA3bp1+eabb3T7etpvuHr16hw+fJj333+fChUq0K1bt2xnyypLVvd36dKF06dPM23aNGJjY9m+fTvbtm1jzpw5rF27lmLFirFs2TLdhYIZrf/sMT21dOlSvvrqKyZOnIibmxuzZs1KN2JGhw4daNasWYbHlZn33nuP9evX07ZtW70LtRcuXMiUKVOYNGkSrq6uzJw5k7Fjx+r6vT7/O3zq008/Zd68ebrCOaP1fHx89C48dnBwoFatWrrb9erV49SpU8ydO5c9e/bg4uLCO++8oxvO0phslSpV0n1YiY+PZ/369en6kIvcYbKLAwsLuThQCPEqCZn9HZroKNRFHHEdN/al7vtFF+4YSmYOLJimT5/O6dOn2bhxo6mj8Oabb/L111+nG7c7v9iwYQPnz5/PcGjcwu6VvjhQCCFE/vOyi+XcpjZT8Xol56xXFMJIz4/Kld90795dNyydyH0mvThQCCGEECIrGXXvEMIU5IyzEEIIIfK1p0PVCWFqcsZZCCGEEEIIA8gZZyGEEDq3O3QkNTQUcxcXKu3Ybuo4QgiRr8gZZyGEEDra+Hi0cXFo4+NNHUUIIfIdOeMshBBCx7J8ecwc7DF3Lp71ykIIUchI4SyEEEKn3G8rTB1BCCHyLemqIYQQQmTD7NmzX9npjOfNmydj/OZAamoqNWvW5Nq1a6aOkqnVq1fTv39/U8cosKRwFkIIIbIhOTmZhIQEU8cwyqucPT9YtmwZ5cuXp2rVqqaOkqlevXrh5+fH2bNnTR2lQJLCWQghhBAFxh9//EHZsmVJTk5Od9+SJUuoXLkyGo3GqG3/8ssvDBw4MIcJ85a5uTl9+/bll19+ybN9HDhwgPr16+Ps7EzDhg05fPhwjtY3dHu///479vb2TJ48OUd5ckIKZyGEEDpBY8YS8P5ggsa82lNvi8Kre/fuREdHs3HjxnT3LViwgDfffBO1Wp3t7d66dQt/f3/atWuXCynzVseOHVm/fj2KouT6tu/cuUOnTp3o06cPFy5coHv37nTo0IGAgACj1jd0e4GBgUydOpWKFSuSlJRkdJ6cksJZCCGETvypU8QdPUr8qVOmjvLK+O233/Dw8OD8+fNAWh/onj17Mm7cODw8PKhYsSIzZ87Ura8oCr/88gu1atXCzc2N9u3bc/HiRQCSkpIoXrw4V69eBeDKlSvY29vz008/6dpXr16dXbt2GbSvrLwoi6HHMmPGDCpXroynpyeff/45rVu3ZunSpZnuc/bs2fTo0YPRo0fj6enJ22+/zfjx4xk5cqTeeq1ateK3337L9nHa2toyYMAAFi1apLf83LlznD17liFDhrBu3Trs7e2xt7enbNmyvP322zx+/Fi37rx58+jcuTMTJkygatWq9O7dm2PHjuHh4YGdnZ3eeh07duSTTz7Bw8ODsmXL8tNPP3Hx4kVatmxJiRIlaN26Nffv39fLsnXrVpo0aULJkiV5/fXX2b17t+4+Q7NNnjyZKlWqUKFCBb766iu97detW5cnT57kSV/spUuXUq1aNUaPHk3p0qUZP348lSpVYtmyZUatb+j23n//faZOnYqLi0uO8uSUFM5CCCGEkaZMmcLMmTPZuXMntWrVAtL6Ea9fvx43NzeOHDnC4sWLmTZtGseOHQNg8eLFTJkyhdmzZ3P69Gnq1KlDixYtCAsLw8rKiho1arBnzx4A9uzZQ/Hixdm5cycAt2/f5saNGzRq1MigfWXlRVkM2f6vv/7KggULWLFiBfv27SMqKor9+/eTkpKS6T6Tk5PZsGEDzs7OHDp0iMWLF5OUlERiYqLeevHx8brtZPc4hw0bxv79+7lz545u2cKFC2nbti0VKlSga9euBAcHExwczKFDh0hNTWXIkCF6Gbdt24a1tTUHDhxg5cqVBAUF4erqmu5YduzYQbly5Thy5Ajfffcdn332GYMGDWLGjBlcvHiRokWLMmrUKF2bHTt28PbbbzN27FguXrzIuHHj6NWrF1euXAEwOFuRIkU4dOgQK1as4LvvvmP//v26dezt7bGxsSEoKCjDx+fgwYO64jyjf9WrV8/093fu3DkaNmyot6xhw4acO3fOqPUN2d6vv/6KhYUFAwYMyHGenJLCWQghRL72ww8/ULp06Sz/vfHGG+navvHGGwa1/eGHH7KVKTk5mbfffpt9+/Zx7NgxKlWqpHd//fr1+eyzzyhZsiStW7emUaNGnD59GoBFixYxZswY2rVrR6lSpZgxYwbOzs6sWbMGgDZt2rB3714A9u7dy5QpUzh27BjJycns3buX+vXr4+DgYNC+spJVlqy2v3TpUiZMmECTJk10j6Ozs3OW+/X29mbSpEmULFkSa2trg7Jm5zh9fHxo0KABS5YsASAuLo4///yTYcOGAWn9gJ8WiRUqVGDevHls2bJFr+D38PDgq6++ws3NDWtraxRFQaVSpdtXzZo1GT16NCVLlqRPnz64ubkxZMgQGjVqhJubG4MHD9bLOWfOHMaOHUvXrl1xcXGhe/fuvPnmm/z+++8GZ6tRowbjx4/Hzc2N5s2b07x583SPhZmZGVqtNsPHp2nTprriPKN/p17wjVNUVBRFixbVW+bk5ERUVJRR62d1/507d5gxYwYLFy7MlTw5JeM4CyGEyNeio6MzPXP2rDJlyqRb9vjxY4PaRkdHZyvTv//+S1RUFP/++2+GhaKbm5vebVtbW+L/m40xICAAT09P3X0qlQpPT0/d1/lt2rTh22+/JTExET8/P37//XcWLVrE0aNH2bt3L23atDF4X1nJKoshx1K5cmXdfRYWFpQvXx5I63by7GPzv//9j3fffReAihUrGpTvWdk9zmHDhjFx4kSmTZvGX3/9hZ2dne7DVWBgIBMmTODo0aOEh4ej1WrRarU8fPiQcuXKAVChQgW97ZUsWVKvy8Szy59lY2Ojt8zGxoa4uDjd7Vu3bnH06FG9ribJycn06NHD4GxZPRYJCQnExcWlW+8ptVqNvb19Jo/ci9nb26d7vURFRWW6vazWz+r+gQMHMnXqVEqVKpUreXJKCmchhBD5WpEiRTL9o/msEiVKZLjMkLZFihTJVqamTZvSsWNHOnTowI4dO6hbt67Bbd3d3dP1eb137x5t27YFoF69eqjVaubPn0+VKlVwcnKibdu27N69mwMHDvDJJ59kK2tOshjS/tmLsLRaLYGBgQBYWVkRHBysu+/ZM8vPn7m1trZOd4YwPDzcsIPIRJ8+ffjss8/YsmULixYt4r333sPcPK3sGT58OEWLFmX37t2UKFGC6OhoypUrp3dW9/mMDRo04MaNGyQlJWFlZWV0rtKlS/Ppp58ydOhQveXZyZaVc+fOYW9vj5eXV4b3Hzx4kM6dO2favly5cly+fDnD+2rUqMHx48fT7a9169ZGrZ/V/UeOHOHs2bN8+umnACQmJnL48GE2bNjA7du3s50np6SrhhBCiHxt1KhRBAYGZvlv8+bN6dpu3rzZoLbP9kE11NChQ/nxxx/x9fXFz8/P4HYDBgzghx9+wN/fn5SUFH766Sfu3r2rO+NoZmZGixYtmDVrlu7scps2bVi0aBFJSUnp+nPmRFZZstK3b1/mzJnDrVu3SE5OZvr06YSEhOjuf7bf7NPCMCM+Pj7s2bOHgIAAUlJSmD9/Prdu3crRsdnY2DBgwAAmTpzImTNn9PoJh4eH4+bmpjvz/fzFdRmpXr065cuX5+DBgznK9cEHHzB37lwuXryIra0tiYmJLF++nG3bthmd7Xl79uyhS5cumY4ekpOuGgMHDuTkyZP88ccfJCcn8/vvv3Pu3DndtwlHjhzB3t6e0NBQg9bP6v6YmBi9bE2bNmXEiBFcunTJoPa5TQpnIYQQwkj9+vVj6dKlvPHGG3ojI7zIyJEjefvtt2ndujX29vYsXbqULVu26HU1adOmDREREbrC+fXXXycpKYlmzZphYWGRa/kNyfIio0ePpk2bNtSpU4eSJUty//59vL29sbS0zFaOPn360LJlSzw9PXF3d+f69eu6iy1zYtiwYVy/fp127drpupBA2igdGzduxNramkqVKqXro56Z4cOH6/oiG6t///5MmzaN9957D1tbW7y9vblz547uDKmx2Z5SFIU///yTESNGZLrO064amf2ztbXNtG316tX5448/mDBhAjY2NnzxxResWbNG1+VHo9EQFxen61+d1fpZ3f98NrVajYWFhS5jVu1zm0rJi0H+hE50dDSOjo5ERUVl+6tAIYR42W42b0FqSAjmrq54HDr4UvedmJjI3bt3qVChgsEXjJlCSkoKGo1GL2NiYiKKomBjY5Pp/U//4D9Lo9FkeFZQo9GQkJCAnZ2drstAfHw85ubmekVpdvaV2fovymLo9p+WEqmpqZQsWZLVq1dn2t3jRRm0Wi1mZmnn9BISErCwsMDc3Dzbx/msuLg4LCwsMizmU1JSdO1jY2N1j3dmGRMTE6lWrRr79u2jYsWKGa4XHx+PlZWV7rHUaDQkJibqDWP3VGa//+xmS0xMxMzMDEtLS9auXcvSpUvZsWPHCx+X3JCcnJzucc3oufui9bNzP+gfa3bbv+g9xtB6TQrnPCaFsxDiVSKFs8iOx48fs2TJEj744APMzMz44osvWL16Nffu3Suwv8OkpCTUavULu56YUlJSEmZmZrn6zURBkRuFc/78rQshhBAi33N2diY+Pp4qVaoQHR1N7dq12b17d4EtmoEcXRj4MuT3fK86KZyFEEIIYRQzMzO+/vprvv76a71uFkIUVPIMF0IIIUSOSdEsCgN5lgshhBBCCGEAKZyFEEIIIYQwgBTOQgghhBBCGEAKZyGEEEIIIQwghbMQQgjxEg0aNIiLFy+aOsYLbdmyhSlTppg6hgB27drFpEmTTJpBng//TwpnIYQQOhW3baPK6VNU3LbN1FEKrB07dhAaGqq7bUgh/bKL7du3b3P06NFM788PxdyrJCeP1927dzl8+HAuJ8qerJ4PhYkUzkIIIXTU9nao7e1R26efHlik2bt3L926daNbt2707t2bMWPGcOXKFaO316dPH9zc3HS333nnHfz9/V+4jqGePHlCt27duHPnjm5ZSkoKvXr14pdfftFbd+HChUyfPt2g7Xp6etKhQwfd7e3bt/P5559nO19uyg8ZMsvx/OOVn5n6cbx9+7bu9dWtWzcOHTqUbp0rV64wfvx4BgwYwPTp0/U+iOY1KZyFEEKIbLh37x5+fn4MHDiQN998k4iICGrVqsW5c+eM2l779u0pUaKE7vb27dsJCwt74TqGcnJy4vz58+zcuVO37OTJk+zbt49ff/1Vb90FCxagUqkM2m758uVp2rSp7vadO3fw8/PLdr7clB8yZJbj+ccrPzP14+js7MzAgQMZOHAg+/fv58GDB3r37927l/fffx8XFxfat2/P8ePHqVevHhERES8ln8wcKIQQQmSTtbU13bp1A6B3795cunSJRYsW8euvv6LValm2bBlHjx7F3t6eHj160LJly0y3NWjQID777DNq1KjB+PHjiYmJ4fPPP6d48eI0bdqU0aNH660DcOzYMf744w9iYmJo0qQJgwcPznQCktatW7Nv3z4++OADAPbt28egQYP4/fffCQkJwdXVlbCwMC5cuMCCBQv02h44cIC1a9eSlJREv379aNWqFZDW9eDQoUPMnDmTc+fOsXjxYoKCgnSPyf/+9z9KlSpFSEgICxYs4ObNm5QvX56PPvqIkiVLZpjz+PHjfPvtt0Bawd+sWTMGDhyoK+b//PNPQkNDGTlypK7NlClTqFevHqVLl840w/Xr11m6dCmPHj2ievXqfPTRR9jb2wNpfXdPnz7Na6+9xrZt20hMTGT48OF4e3szb948Ll68iLe3N2PGjNFNZf2inJk9Fv7+/rrH66mQkBAWLlzIzZs38fb25tNPPzV4qvIXPa5Pj6lFixYZ/u4g7cPTb7/9hkajoWvXrpw6dYqaNWtStmzZDPNn9XzITUWLFtXt29LSMt39devW5dixY7rnRd++fSlatCgHDhygZ8+euZ7neXLGWQghhE748hU8nv8z4ctXmDrKK6VChQo8fvwYSPtD/sMPP9CkSRNKlSpF165dWbFiRaZtn+3z3KlTJ6ysrGjfvj0DBw6kefPm6da5fPkybdu2xc3Njfbt23PhwgUmTJiQ6fbbtGnDgQMH0Gq1QFrh3Lp1a5o3b86+ffuAtIKoSJEi1KtXT9fu1KlTfPfddzRs2JBSpUrh6+ur60LybL/bUqVK0aBBA0qWLKk7U+jo6MitW7eoXr06oaGhdOzYkaioKGrVqpXubPpT5cqV07Vv1KgR33//PWPHjtXdf+XKFU6fPq3X5ujRo9y+fTvTDGfOnKFu3bokJyfTtm1b9u/fT/369UlMTATSugX88MMPLFiwgMaNG2NtbU2rVq3o2LEjycnJdOrUidWrVzNmzBiDcmaW4/l+yjdv3qRq1arcunWLdu3aERkZqftgk5WsHtfbt2/z448/Zvq7O378OK1atcLR0ZHXX3+dWbNm8f3333Pz5s1M82f1fHiev7+/XneL5/8NHjzYoGPNiJOTk943I4GBgSQlJVGuXDmjt5kdcsZZCCGETsSKFaSGhGDu6orzoIGmjgOkFfMRLyg8DeU+ezZ2Derrbsf9e5KH48YBUGzgQKOP98mTJxw5coThw4dz4cIF1q9fz82bN6lQoQIARYoUYdKkSQwcmPX2mzVrhqWlJU2aNKFFixYZrnPjxg3Kli2r64far18/njx5kuk2W7duTWRkJOfOnaNatWqcPn2aZs2acffuXfbt20e/fv3Yt28fLVq0QK1W69rZ29uzceNG3Vm/w4cPs2fPHry9vfW27+LiQo0aNbhx44buTCHAl19+SY8ePXRnLPv160dgYCC//vorX3zxRbqc7u7ueu1btGiBj48P3377rV6ujGSWYfr06fTp04cff/wRSPtQU6lSJX7//XeGDh0KgKOjIxs2bMDCwoL+/fuzdu1amjdvrhtFws7OjjFjxjB//vwsc2aW43mff/45HTp04Pfff9cti4yMfOExPmXI4/qi392sWbMYPHiw7ux3jx49KFOmzAsfx6y2+bynhXdmbGxsDDrWF+nWrRvx8fG6b3ue/dCXl6RwFkIIka9pY2NJDQnJ8XaU5OR0t59uVxsbm61thYeH061bN1JSUjh16hSVKlXis88+Y8uWLZQpU0ZXNENaMfzo0SMiIiIoVqxYjo+jQ4cO/Pbbb9SvX5+2bdvSsmVLWrduDcA///zDH3/8AaQVfH/88QcuLi54e3uzf/9+wsPDqVGjBg4ODrRq1Yo5c+YAsH//fj7++GO9/VStWlXvq3JXV9ds9SM9e/Ystra2egXY1atXMy2aUlNT+fPPP/Hz8yMsLAytVktSUhIPHz7UFXbZ5e/vr3ehm6WlJQ0aNNA7U+rp6YmFhQUAKpUKZ2dnfHx8dPeXKFFC77hzI+f58+eZOHGi3rKiRYsa1NaQx/VFv7srV67Qv39/3X0ODg56x5uZ7Dwfihcv/sIPDrlh4MCBxMfHs3v3bqZMmULTpk2pXLlynu4TpHAWQgjxDPfZs1GSk1Fl0LfQVMzs7TF3dc3xdp4/JpWlpW67Zv/1eTWUnZ0dAwcOxMLCgrJly+Lt7Y1KpcLBwYHY54rw2NhYzMzMsLPLnZFKrK2t2bhxIxEREZw4cYI5c+bwyy+/sH79emrWrKkrAp/+D2ndNfbt20dYWJiuX6qXlxdJSUkcPHiQmzdv0qZNG739ZHShoKIoBue0s7OjQYMGtGvXTm95ZqODjBkzhgMHDjBs2DBcXFzQarVs2rSJuLg4ANRqNRqNRq9NQkLCCzNk9vtwcHDQ3c7oOJ9f9uxxZ5XTEA4ODkRFRRm8/rMMeVxf9Luzs7NLl/X5xygj2Xk+PP+B5XnFixdnyZIlWe7zRZ4W5v369aNp06YsWLBA90EwL0nhLIQQQufZrgz5hfMg47tRvIhdg/p4HDpoVNtnLw58VoMGDUhISODvv//mzTffRFEUfv75Z5o0aaK7uCwrRYoUITo6OtP7/fz8KF68OFWrVqVjx46oVCrefPNNAKpUqUKVKlXStWndujULFy7k4cOHzJ07V7e8RYsWTJo0CXd3d6pVq2ZQPkMzd+nShT179jBnzhxsbW2BtP7ZmRWMx44dY8iQIbq+vs/3Cy9btix///03qampmJubc/XqVc6ePUvv3r0zzdC6dWuWL1/OoEGDsLW1xd/fnwMHDjDuvy46xsgqZ1a/P0jry75gwQIGDBiAs7MzGo2GHTt20Llz5yz3n93H9XmtWrVixYoV9O/fH0tLS44fP86FCxd0Z6ENyZ+VvOyqsXnzZlq0aEGRIkUACAsL4969ey/lwkCQwlkIIYTINa6urixcuJAhQ4Ywf/58wsPDSUlJYfPmzQZvo3v37gwfPpwlS5bQvHlzRo8erXe/g4MDffv2Ra1W4+zszMmTJ7MsBJs3b05KSgo3btygcePGuuUtW7Zk2LBhvP3229k70Oe0atWKTz75hObNm+Pk5MT//vc/Jk2axJ07dyhbtiy1a9fm8ePHqFQqVq5cmeE2Bg0axOjRo9m4cSPR0dF6Z4UB3nzzTebMmYOXlxdly5YlIiJC74KwjDJMnjyZ06dPU6VKFTw9PTl16hSjRo3K0WgQWeXMKMfzJk6cyJUrV/Dw8KBOnTrcuXNH7wLEF8nu45pR+/bt2+Pp6UmFChUIDg7Gw8ND14/ckPxZyUlXDa1WS48ePQCIiYnhxx9/ZO3atQwaNIiuXbui0WioW7cu7u7umJmZcebMGdq1a8fw4cON2l92qZTsfO8isi06OhpHR0eioqJ0n46EEEKkl5iYyN27d6lQoYLBw3KZwv3797l27Rq+vr6ZrvPkyRMuXryInZ0dPj4+emebd+7cSd26dXXjMj9/G+DChQs8ePCAkiVLUq9evXTraDQaLl68SHh4ONWrVzdocpS9e/diZmamVzRGRERw+PBhqlevjoeHh2757du3CQkJoVGjRrplp0+fxs7OjmrVqnHv3j0ePHigNzbxkydPOHv2LDExMbRp00Y35FtQUBDXrl2jRIkSeHt7ZzpsHqSNkX316lVcXFyoU6cOmzZt0ttWUlISJ0+exMrKipo1a3LmzBlcXV2pVKlSphkUReHKlSs8evSIqlWrUrp06Rce5759+6hWrRru7u66x+j48eN06tTJ4JzP5wgLC0v3eEHa6CS3b9/Gy8tLt7+MHpOM2mb2uGb1u4O0SXDOnj2LoijUrFmTevXqMXHiRAYMGJBh/pCQkCy3mVsURWHTpk3plnt7e+v6MCckJHD27FlSUlLw8PCgVKlSBm37Re8xhtZrUjjnMSmchRCvkrh/T+r6OL/sbhuvSuEsxKssKSmJ48eP60Zt2blzJ507d9adxS7IcqNwlq4aQgghdB6OG6cbjs7Y/r9CiPxLrVYzY8YM3aQu58+fZ968eQW+aM4tUjgLIUQ+pdEqnLwbQWhMIi4O1tSvUAy1mWFTIgshREbMzc3ZvXs3/v7+hIWF4e3tbdR07oWVFM5CCJEP7fR/xNQtV3gUlahb5uZozZQuXrT3zro/qxBCZEalUhk0drNIT6bcFkKIfGan/yNGrDqrVzQDBEclMmLVWXb6PzJRMiGEKNykcBZCiHxEo1WYuuUKGV21/XTZ1C1X0GgL7nXdWq3W1BGEEAVQboyHYfKuGrGxsWzZsoWQkBB8fHx004bmtI0h6wQGBnLgwAFiY2OpXr06zZo107t/165dnDt3Tm9ZiRIleP/997N5lEIIYZiTdyPSnWl+lgI8ikrk5N0IXq/k/PKCvQSWlpaYmZnx8OFDSpQogaWlZYazlQkhRHYpiqIb8/rZWTWzy6jCOTY2lhMnThAYGAhAmTJlaNiwYbanEw0KCqJp06Y4OTlRp04dZs2aRYsWLfjrr78yfbM0pI0h68yYMYOVK1fSuHFjzM3NmTZtGl5eXmzbtk03RMmGDRs4ePCg3iDeMkSSECIvhcZkXjQbs96rxMzMjAoVKvDo0SMePnxo6jhCiAJGpVJRunRp3WQvxshW4ezn58cPP/zA1q1bSUlJ0U2ZmJCQgIWFBW+88QYjR46kSZMmBm1vwoQJODk5cfz4cSwtLbly5Qo1atTgzTff1M0aY0wbQ9Zp2bIlEydO1A0Y/vnnn1OuXDm2bNmim74T0gbcnjVrVnYeJiGEMIqiKFx5aNhUty4OBfNDvKWlJWXLliU1NRWNRmPqOEKIAsTCwiJHRTNko3Du3bs3hw8fpn///uzcuZPXXntNN81kTEwMJ0+eZOvWrfTs2ZPmzZvz999/v3B7Go2GDRs2MHPmTCwtLQHw8vKiSZMm/PPPPxkWzoa0MXS7z85+A2nzppuZmaU7fR8UFMS8efNwdHTk9ddfp0qVKoY+ZEIIYbA7j2OZvMGf43fCs1zXTAURsUkvIZVpPP0qNSdfpwohRF4w+OLA+vXrc+/ePX744QdatWqlNze7g4MDrVu3Zu7cudy7d4/XXnsty+0FBAQQFxeHp6en3nJPT0+uXr1qdJvsbPfu3bvMmjWLSZMm0aZNGz788EPeeOMNvXViYmK4du0a69evx8fHh+nTp7/wuJKSkoiOjtb7J4QQmUlO1TJv303a/3SE43fCsbYwo0ftUqiAzHr3ahX48K9zDF95htDogtdlQwgh8iuDzziPHTvWoPVsbGwMWjc2NhYAR0dHveVFixbV3WdMm+xsNyUlhcjISMLCwggLCyMuLo6UlBSsrKwA+PDDD/n11191/aLXrVtH7969adWqVboz1k998803TJ069cUHL4QQwKl7EUxcf4lboWnvTc2rlGB6N2/KFLOlXXXXDMdxntSxKjdDYvnl4G12Xg7m2O0wvujsRa+6peVCOiGEyGMmG1Xj6YWEz5+RjYqKyvQiQ0PaZGe7VapU0fVfDg4OxsvLi2rVqjF69GiAdIOD9+zZE1dXV/bv359p4Txx4kRGjRqlux0dHU2ZMmUyXFcIUThFJaQwa8c1/joZAEBxe0u+6OzFGzXddcVve2832nqVzHTmwPbeboxfd5FLQVGMXXuRzRceMrO7D2WK2ZrsuIQQoqAzqnCOjIxkxowZHD16lIiIiHT3X7t2LcttlC1bFmtra27dukW7du10y2/dupVpP2JD2hizXYCSJUtSo0YNzp8//8LcarU60zPiAFZWVroz1kII8SxFUdh6MW1GwLD/+ij3qVeGiR2rUtTWMt36ajNVpkPOebkXYcMHjVjqd5cf9tzgyM0wfH88zFhfT955vbxMzS2EEHnAqMJ5yJAhXLhwgbfffhsnJyfjdmxuTufOnVm1ahXDhg1DrVZz584dDh06xO+//65bb8eOHTx8+JD333/foDaGrJOSksLt27epWrWqbj+hoaFcvHiRtm3bAmkXIl67do3q1avr1tm1axdBQUE0b97cqGMWQhRegU/i+WKjPweuPwagYgk7vunuQ4OKxo/FbK42Y1jzSrT1cmXC+kucvBvB1C1X2HrxEd/29KGyi0PWGxFCCGEwlWLENCqOjo6cOXOGypUr52jnd+/epVGjRnh6elK/fn3+/vtvvLy82Lp1q26YuMGDB3PixAn8/f0NbpPVOsnJyTRq1Ijy5cvj5eVFZGQk//zzDx4eHmzbtg0HBwdSU1Np2LAhZcuWpXr16gQEBLBmzRoGDx7Mzz//bPAxRkdH4+joSFRUFEWKFMnR4yWEePWkarSsOHaP73ffICFFg6XajA9aVmJEi0pYmedsWKRnabUKf54MYNaOa8QmpWKpNuOT1pUZ1rwSFmrDJ4m92bwFqSEhmLu64nHoYK7lE0KI/MzQes2owrls2bJcvHiRokWL5iQjAOHh4axZs0Y3w1+PHj10BTDA+vXrCQgIYOTIkQa3MWQdrVbLzp07OXfuHHZ2dtSuXTvdmeRn13FycqJJkybUqFEjW8cnhbMQhdelwCgmbriIf1DaNRf1KxRjZncfKrvY59k+H0YmMHnDJd2Z7WpuRZjdswY+pR2zaJlGCmchRGGUp4XzqFGjcHJy4osvvshRyMJACmchCp+4pFS+332DFcfuolXA0caCSR2r0rtuGcxeQt9jRVHYdP4hU7dc5kl8CmozFUOaVmRkGw+sLV58llsKZyFEYZSnhbOvry+7d+/Gy8uLypUrpxsCaePGjdkOXFBJ4SxE4bLvaghfbrpMUGQCAG/UdOeLzl6UcHj5Fw2HxSYxdcsVtlxIm766QnE7ZvV4cb/q8OUr0MbGYmZvj/OggS8pqRBCmFaeFs4fffTRC+/PTh/ggk4KZyEKh9DoRKZuucK2S48AKO1kw/Ru3rTwdDFxMthzJYTPN14iJDptJI+3G5ZjXHtPHKxlZj4hhIA8LpyF4aRwFqJge3pR3rc7rxGTmIraTMXgJhX4tI0HtpYmGyo/nejEFL7ZfpW/Tj4AwN3RmhndfWhZ1fSFvRBCmJoUzvmEFM5CFFw3QmKYuP4SZ+4/AaBmaUdm9vChurthF+KZwrFbYUxYf4mAiHgAutcuxRedvShml34caSGEKCzyvHAODw9n3759BAQEkJqaqnffhAkTjNlkgSSFsxAFT2KKhp/332Lh4dukaBTsLNWMeYUmHklI1vD97ussO5p28aKznSVTu1ank48b2rh4QAFUqO0znsVVCCEKmjwtnI8fP06nTp0oVqwYt2/fpnr16ty6dYukpCRq1qyZ5ex7hYkUzkIULMduhTFpwyXuhaedsW3r5crUN6rjXtTGxMmy71zAE8avu8iNkLTZUNt6uTJ6yWiU0FAZVUMIUagYWq8ZPir+M8aOHcvEiRO5desWAP7+/gQFBdGhQwd8fX2NSyyEEPlYRFwyo/++QL8l/3IvPB7XIlYsGFCXxe/UeyWLZoDaZZ3Y+nFTRrbxwEKtYs+VEMJikkwdSwgh8i2jzjg7ODgQGBiIo6MjarWa+Ph4rKysuHfvHo0bNyYoKCgvsr6S5IyzEK82RVHYcC6Ir7de4Ul8CipV2qgUY3w9KVKARqW4HhzDuHUX8d3wP4okx2FZrBgNl/6Pss62po4mhBB5Lk+7aqhUKp42c3Nz49ChQ1SpUoUnT57g7u5OQkKC8ckLGCmchXh13QuLY/LGSxy9FQ6Ap6sD3/T0oU5ZJxMnyxsarcLyo3eZs/s6iSlarC3MGNPOk0GNK7wSfbeFEMJYL61w7t+/PzExMQwdOpQ//viD+/fvc+zYMeOTFzBSOAvx6klO1bL4yB3m7btJUqoWK3MzPm3jwZCmFbFQG9XD7ZVyPzyOCesucfxO2geGWmWKMrtXDaq4Opg4mRBC5I087eM8d+5c3c+zZ88mISGBvn37cvPmTRYuXGjMJoUQIl84c/8JXeb78d2u6ySlamnqUZzdnzXjgxaVC0XRDFDO2Y4/hzRgVg8fHKzMOf8gkk7zjvDT3pskp2pNHU8IIUxGxnHOY3LGWYhXQ3RiCrN3XuOPfwNQFChmZ8kXnavRrVYpVKrC200hOCqRzzdeYu/VUCCtu8rsXjWoWaaoaYMJIUQuemkToKSkpGBhUXAukMltUjgLkb8pisJO/2CmbL5M6H8jSvSuW5pJHavhVAgnBbn/7kBSw8Mwdy5Oud9WAGmP0daLj/hq82XC45IxU8H7TSowqq0nNpZq0wYWQohckKddNVJSUvjqq68oU6YMlpb//4flgw8+0A1RJ4QQ+d3DyASG/H6aEX+cJTQmiQrF07oofNe7ZqEsmgGS790j+dZtku/d0y1TqVR0qenOnlHN6VbLHa0Ci4/cpf1Phzl+O9x0YYUQ4iUzqnD+5ptv+Oeff/j+++/1ljdr1oxp06blSjAhhMgrGq3CMr+7tPnhEHuvhmKhVvFJq8rs+LQpjSoVN3W8fKuYnSU/9q3NsoH1cHO05n54PG8tPsHE9ZeITkwxdTwhhMhzRnXVqFixIhs3bqRGjRp6I2wEBwfj5eVFRERErgd9VUlXDSHyF/+gKCZtuMTFwCgA6pVz4psePnjIiBEA3GzegtSQkCxnDoxJTOHbnddYdSIAANciVszo5kMbL9eXlFQIIXKPofWauTEbDwoKwsPDA0Dvohlzc3MZw1kIkS/FJ6cyd88Nlh29h0ar4GBtzsQO1ej7WhnMZIzibHOwtmB6Nx8613BnwrqL3AuPZ/Dvp3mjpjtTunjhbG9l6ohCCJHrjOqqUaVKFY4ePQroF86rVq2iRo0auZNMCCFyyYHrobT94TCLj9xFo1XoVMONfaOa069BWSmac6hhRWd2jmzGsOYVMVPB5gsPafPDITadD0IGbRJCFDRGnXGeOHEiAwYM4PPPPwdg3bp17Ny5k+XLl/PPP//kakAhhDBWaEwi07ZcYevFRwCUKmrD192q06qqdCfITdYWaiZ2qEYnHzfGrb3IteAYPl19nk3nHzK9mzfuRW1MHVEIIXKFUYVzv379UKlUTJ8+Ha1WS69evahSpQorV66ke/fuuZ1RCCGyRatVWHP6Ad9sv0p0YipmKnivcQU+a1sFOyuj3vaEAWqULsqWj5uw4OBt5u+/xf5robSbe5iJHavy1mtydl8I8erL8TjOCQkJaLVa7OzscitTgSIXBwrxct0KjWHi+kucuvcEAJ9SjnzTwwfvUo4mTvZqMPTiwCy3ExLDuHUXORcQCUCDCsWY1bMGFYrL3wohRP6Tp+M4P8vGxkaKZiGEySWmaPhhzw06/HSEU/eeYGup5vNO1djwQSMpmk3Aw9WBtcMbMaWLFzYWav69G0H7Hw+z8NBtUjUybbcQ4tVk1HeWiqKwefNm/Pz8ePLkSbr7lyxZkuNgQghhqOO3w5m84RJ3wuIAaF3Vhaldq1PaydbEyQo3tZmKQY0r0KaaKxPXX8LvVhjf7LjGtkuP+LZnDaq5ybdwQohXi1GF89ixY/nll19o1qwZRYsWzeVIQghhmMj4ZGZuv8rfpwMBKOFgxdQ3qtPBu6TeiD/CtMoUs2Xl+/X550wg07de4WJgFF3m+/FBi0p82KoyVuYybbcQ4tVgVOG8fPlyDhw4QIMGDXI7jxBCZElRFDZfeMi0LVcIj0sGoH+DsoxrXxVHGwsTpxMZUalUvFmvDC2qlOCLTf7suhzCvP232OEfzLe9alCnrJOpIwohRJaMKpy1Wi3VqlXL7SxCCJGlgPB4Jm+8xJGbYQB4uNjzTQ8f6pUvZuJkwhAuRaxZMKAuO/yD+XKTPzdDY+n56zEGNarAGN8q2FrKqCdCiPzLqIsDe/ToIf2YhRAvVYpGy68Hb9Pux0McuRmGpbkZY9pVYdsnTaVofsWoVCo6+rixd1RzetYpjaLAsqN3aTf3MH7/fSASQoj8yKjh6IKDg/Hy8qJixYpUqlQpXV/C1atX51rAV50MRydEzp1/EMmEdWkTawC8XtGZmT18ZGizPJBbw9Flx6Ebj5m0/hJBkQkAvFmvNJM7eUm3GyHES2NovWbUd2IjR45Eo9FQvnx5HBwcjA4phBAvEpOYwpxd1/n9xH0UBZxsLZjcyYuedUrJxX8FSPMqJdj1WTO+23mN347f5+/TgRy8/pivu3njW72kqeMJIYSOUWec7ezs8PPzo3bt2nmRqUCRM85CGGfX5WCmbLpMcHQiAD1ql2Jyp2o421uZOFnBdrtDR1JDQzF3caHSju0vff+n7kUwft1F7jxOG1qwk48bX71RnRIO8nsXQuQdQ+s1owrnUqVKceXKFRwdZVKBrEjhLET2PIpKYMqmy+y+EgJAOWdbZnTzoYlHcRMnEy9LYoqGeftusvDwHTRaBUcbC77s7EUP+aZBCJFH8rRwfu+996hUqRKTJ0/OUcjCQApnIdLTaBVO3o0gNCYRFwdr6ldIu7hv1Yn7fLfrOrFJqZibqRjWvCIft/LA2kLG+S2M/IOiGLf2IlceRQNpXTpm9vChVFEbEycTQhQ0eVo4t2nThn379uHl5UXlypXTnQHYuHFjtgMXVFI4C6Fvp/8jpm65wqOoRN2y4vaW2FuZcy88HoA6ZYsys4cPVUvKa6awS9FoWXT4Dj/tu0lyqhY7SzXjO1RlQINymJmpMvwQpjaTs9JCiOzJ04sDq1atStWqVY0OJ4QonHb6P2LEqrM8/2k9LDaZsNhkrM3NmNzZi/71y2ImxY8ALNRmfNiyMr7VSzJh3UVO33/Cl5sus+XCQzrVcGPhoTt6H8LcHK2Z0sWL9t5uJkwthCiojDrjLAwnZ5yFSKPRKjT5dr9ekfM81yJWHJvQWs4YmlDI7O/QREehLuKI67ixpo6jR6tVWPXvfb7dcY24ZE2G6zx95vw6oI4Uz0IIgxlarxk1AYoQQmTXybsRLyyaAUKikzh5N+IlJRIZid62jai164jets3UUdIxM1Pxzuvl2f5pUyzNM/7z9fRM0NQtV9Bo5byQECJ3ydymQoiXIjTmxUVzdtcThdfDyESSU7WZ3q8Aj6IS6bvoOBWK2+FgbUERawuK2Jj/97M5RWzSljn897ODlbl0DxJCZEkKZyHES+HiYJ2r64m8UXb5ctCkgjr//nkw9MPVqXtPOHXviUHrqlRgb/lfEa0rrM3/K7j/W/Zf8Z1WcD/7c1pBntlZcCFEwZF/3xmFEAVK/QrFcHGwIjQmKcP7VUBJx/8fmk6YhlXFCqaOkCVDP1y917g8zvZWRCemEJ2QSkxiCtGJqUQnpOj9nJSqRVEgJimVmKRUo3PZWKj1i24bC70z3A7PFOJF/iu2HZ8pxK0tzF7ZcapldBNRWOS4cE5JScHCwiI3sgghCjAzFZQsknHh/PTP65QuXvLHVmSpfoViuDlaExyVmG6EFvj/D2GTOxn2fEpK1RDzXxEdnfhfgZ2Q+l/BnZJ2X7qf0/6PSUwl9r9iOyFFQ0KKJtMPh1mxUKsyPMPtYKV/dvtpN5Pnz47bWZqmu0lGQ0zK6CaioDKqcE5JSWHGjBksXbqUwMBAng7M8cEHHzBq1CgqV66cqyGFEK++7ZeCuRgUjdoMnGwtCYtN1t1XUv7IimxQm6mY0sWLEavOogK94tmYD2FW5mqs7NUUN3I691SNltikVGISU4lKSMnkDHcGxfcz62kVSNEohMclEx6XnPVOM6BSgYNV+v7b+j9n3g3Fwdocc3X2uptkNsRkcFQiI1adldFNRIFj1HB006ZNY82aNUyZMoU+ffroCufVq1ezfft2fv/991wP+qqS4eiEgKj4FFr/cIiw2CQ+ae3Bp6095GvdfCpqy1a0iQmYWdvg2KWzqeO8UEE506koCnHJmnQF9tMz2lmfCU8lWZP5xZLZYWepTtd/+//PcJvrXWhpZ2nOmH8uZFroPz3z7ze+lby+Rb6XpzMHVqxYkY0bN1KjRg1UKpWucA4ODsbLy4uICBlO6ikpnIWA8Wsvsub0AyqVsGP7p02xMpcptPOrm81bkBoSgrmrKx6HDpo6Tpakb22axBRNhme69Ytv/UL82eI7PpNxsXPDX0Ma8nol5zzbvhC5IU9nDgwKCsLDwwNA70IGc3NzEhISjNmkEKKAOnY7jDWnHwAwq2cNKZpFrlKbqaQoA6wt1FhbqHFxMK59ikZLbLr+28+c4X6m+H5anD94ksDDyKz/5ssQk6IgMapwrlKlCkePHqVNmzZ6hfOqVauoUaNGroUTQrzaElM0TFp/CYD+DcryWnkZMUOI/MhCbYaTnSVOdpYGtzl+O5y3Fp/Icj0ZYlIUJEYVzhMnTmTAgAF8/vnnAKxbt46dO3eyfPly/vnnn1wNKIR4dc3bd5N74fG4FrFifIeqpo4jhMhFWY1uAml9zmWISVGQGFU49+vXD5VKxfTp09FqtfTq1YsqVaqwcuVKunfvntsZhRCvoCsPo1l0+A4A07p6U8Rahq0UoiB50egmT33S2qNQ9jkXBZfR4zi/9dZbvPXWWyQkJKDVarGzszNqO1FRUaxfv56QkBB8fHzo2LFjlgPAG9LGkHXu3LnDvn37iI2NpXr16rRt29ao7Qgh9Gm0ChPXXyRVq9C+ekl8q5c0dSQhRB5o7+3GrwPqpBvdxNxMRapW4e/TD+hZp7TMqigKjBw/k21sbIwumgMCAvDx8WHRokUEBQUxdOhQevTowYsG+jCkjSHrfPXVV3Tt2pXz589z7949Bg8eTNOmTYmPj89RPiEErDh2jwuBUThYmzO1a3VTxxFC5KH23m74jW/FX0Ma8lPfWvw1pCG7P2tGEWtzzgVE8vXWK6aOKESuMXg4ujZt2hi80b179xq03ltvvcWdO3c4evQo5ubm3LhxAy8vL/766y969+5tdBtD1jl9+jR169bVnT1++PAhZcqU4c8//6RPnz5G53ueDEcnCpsHEfH4/niY+GQNM7v70K9BWVNHEtnwqg1HJ/KvA9dDeW/FKRQFvutVg971ypg6khCZMrReM/iMc7169Qz+ZwiNRsOmTZt4++23MTdP6zFSpUoVmjVrxtq1a41uY+h269Wrp9flQq1OGyLLxsbG6HxCFHaKovD5Rn/ikzXUL1+Mvq/JH0ohCquWni6MbF0FgMkb/fEPijJxIiFyzuA+zrNmzcrVHQcEBJCQkKAbD/opDw8P/v33X6PbZGe7t27dYtWqVURHR7N3717GjBlDly5djM4HkJSURFJSku52dHR0pusKUdBsvvCQQzceY6k245uePpjJRUFCFGoft6rMxcBI9l0LZdjKM2z5uAnFsjHknRD5TY76OD958oSTJ09y8uRJnjx5kq22sbGxADg6OuotL1q0qO4+Y9oYs93k5GQiIyMJCgoiMTHR6O0AfPPNNzg6Our+lSkjZ9xE4RARl8zULWl9GT9uVZlKJexNnEgIYWpmZip+6FOL8s62BEUm8Mlf59Bo5Toh8eoyqnCOjY1l8ODBuLi40KBBAxo0aICLiwtDhw4lLi7OoG3Y26f9UY2K0v/qJjIyUnefMW2ys93KlSvz1Vdf8fPPP3PmzBl27tzJ/Pnzjc4HaWNcR0VF6f49ePAg03WFKEimb7tCRFwynq4ODGteydRxhBD5hKONBQvfroeNhRq/W2HM2X3d1JGEMJpRhfOIESM4evQoGzZsIDg4mODgYDZs2MDhw4f54IMPDNpGmTJlsLGx4ebNm3rLb968iaenp9FtjNkuQIkSJfD29ubSpUs52o6VlRVFihTR+ydEQXfk5mPWnw1CpYJvevrI0FNCCD2eJR2Y3SttZuFfD95mp/8jEycSwjhG/XXbsGED//zzD507d8bV1RVXV1c6d+7MP//8w7p16wzahrm5OV27dmXlypWkpqYCcOPGDQ4fPkzPnj11623evJlffvnF4DaGrJOSksKFCxf08jx8+JDz589TvXr1bOUTorCLT05l0oa0D5zvvl6eOmWdTJxICJEfdanpzpCmFQAY/fcFboVm3u1RiPzK4OHonlW6dGnOnz9P8eLF9ZaHhYVRu3Ztg7snBAQE0LhxY8qUKUO9evVYv349r732GuvXr9eNeDF48GBOnDiBv7+/wW2yWic5OZnmzZvj7OyMl5cXkZGRrF+/njp16rBhwwbduNSG7CsrMhydKOhmbr/KosN3cHe0Zveo5thbGT2vksgHZDg6kZdSNVoGLP2XE3ciqFTCjo0fNsZBZhUV+YCh9ZpRhfOHH36IVqvlxx9/xMrKCkgbTeLTTz/F3Nycn3/+2eBtRUVFsW7dOt3MfJ06ddIrSjdv3kxgYKBeF5Cs2hiyjqIoHDhwgHPnzmFnZ0ft2rVp0KBBtvNlRQpnUZD5B0Xxxs9+aBVY+m49WldzNXUkkUNSOIu8FhabRJf5fjyKSsS3uisLBtSVGXmFyeVp4ezr68vu3bspXrw4NWrUQFEULl26RFhYGO3atdONhQywceNGow6goJDCWRRUqRotXf93lMsPo+lcw42f+9UxdSSRC6RwFi/DuYAn9Fl4gmSNlnHtPfmgRWVTRxKFnKH1mlHfqXp4eKQb39jLy8uYTQkhXlFL/e5y+WE0jjYWTOki02oXFC5jxqBNTMDM2ibrlYUwUu2yTkztWp2J6y8xZ9d1vN0daValhKljCZElo844C8PJGWdREN0Pj6Pd3MMkpWqZ3asGb8pUukIII0xYd5HVpx5Q1NaCLR81oUwxW1NHEoVUrk+5LYQQkHZ9wKQNl0hK1dKokjO965Y2dSQhxCvqqzeqU7O0I5HxKQxfdYbEFI2pIwnxQkZ11VAUhc2bN+Pn55fhjIFLlizJcTAhRP607mwQR2+FY2VuxszuPnJRjxDCaNYWan4dUJcu8/24/DCayRv8mdO7hryviHzLqDPOY8eO5a233uLSpUvExsam+yeEKJjCYpOYvi1tWu2RbapQvridiROJ3JZ05y5JN2+SdOeuqaOIQsK9qA3z+9XGTAXrzgay6t8AU0cSIlNGnXFevnw5Bw4cyHD4NiFEwTVtyxUi41PwcivC4P8mMhAFS8CgQTKqhnjpGlUqzoQOVZm5/RrTtlzGy82BuuWKmTqWEOkYdcZZq9VSrVq13M4ihMjHDlwLZfOFh5ip4NueNbBQyyUSQojcM6RpRTr5uJGiURix6iyhMYmmjiREOkb95evRo4f0YxaiEIlLSuXzjWmzd77XuAI+pR1NnEjklSKdOuHYqydFOnUydRRRyKhUKmb3qoGHiz2hMUl8+MdZUjRaU8cSQo9Rw9EFBwfj5eVFxYoVqVSpUrpO/KtXr861gK86GY5OFARTt1xm+dF7lHayYfdnzbC1lGm1hRB5487jWLr+fJSYpFQGNirPV2/IOPEi7+XpcHQjR45Eo9FQvnx5HBwcsLe31/snhCg4zgU8YcWxewDM7O4jRbMQIk9VLGHPD31qAbDi2D02ngsybSAhnmHUX8AtW7bg5+dH7dq1czuPECIfSdFombj+EooCPWqXkpm9hBAvRVsvVz5pVZl5+28xYf1Fqrg64OUu39oK0zPqjHPRokWpWLFibmcRQuQziw7f4VpwDMXsLPm8s5ep4wghCpFP21ShhWcJElO0DFt1msj4ZFNHEsK4wtnX15eff/45t7MIIfKRO49j+WnfTQC+6FyNYnaWJk4kXobbHTpyvW49bnfoaOooopBTm6n4sU8tyhSz4UFEAp+uPo9Gm+3LsoTIVUZ11QgICGD58uX8+eefVK5cOd3FgRs3bsyNbEIIE9FqFSauv0RyqpZmVUrQrVYpU0cSL4k2Ph5tXBza+HhTRxGCoraWLBxQjx6/HuXQjcf8tPcGo9p5mjqWKMSMKpyrVq1K1apVczuLECKfWHP6Af/ejcDGQs2Mbt4y/a0QwmS83IvwTQ8fPltzgXn7b+FTuihtvVxNHUsUUkYVztJNQ4iCKzQ6kZnbrwIwul0VyhSzNXEiIURh1712aS48iGLFsXuMWnOeTR81pmIJGcVLvHwy9ZcQQs9XWy4Tk5hKjdKODGxU3tRxhBACgMmdqlG/fDFiklIZvuoMcUmppo4kCiGjB2QNDw9n3759BAQEkJqq/+SdMGFCjoMJIV6+3ZeD2X4pGLWZilk9amAu02oLIfIJC7UZP/evTed5ftwIiWXcuov8/FZt6UomXiqjCufjx4/TqVMnihUrxu3bt6levTq3bt0iKSmJmjVrSuEsxCsoOjGFLzalTas9tFlFGTNVCJHvuDhY8+uAuvRddJxtFx9Rq3RRhjST4XHFy2PU6aSxY8cyceJEbt26BYC/vz9BQUF06NABX1/fXA0ohHg5Zu+8Rkh0EuWdbfm0tYep4wghRIbqlnPiy//Glf9mx1WO3QozcSJRmBhVOF+4cIGhQ4embcDMjKSkJJydnfnll19YtWpVrgYUQuS90/ciWHUiAEibVtvaQm3iREIIkbkBDcvRs05ptAp89Nc5HkYmmDqSKCSMKpxjY2NxdHQEwMXFhfv37wPg6OhIRERE7qUTQuS5pFQNE9ZfAuDNeqVpVLm4iRMJIcSLqVQqZnT3prp7ESLikhmx6gyJKRpTxxKFQI6v/GnVqhVjxoxh69atfPDBB9SuXTs3cgkhXpJfDtzmVmgsxe0tmdSxmqnjCCGEQawt1CwYUJeithZcCIziq82XTR1JFAJGFc5z587V/Tx79mwSEhLo27cvN2/eZOHChbkWTgiRt26GxPDLwbRrFb56ozpFbWVabSHEq6NMMVvmv1UbMxWsPvWAv04GmDqSKOCMGlVj5MiRup9LlSrFnj17ciuPEOIl0WoVJqy/RIpGoXVVFzr5uJk6khBCZFtTjxKM8fVk9s7rTNl0mWpuRahVpqipY4kCyqgzzvHx8WzcuFF3e/fu3XTu3JlPP/2U+Pj43MomhMhDf/x7nzP3n2BnqeZrmVZbCPEKG9G8Er7VXUnWaBmx6gxhsUmmjiQKKKMK588//5yAgLSvQyIjI+nduzdOTk4cOnSIcePG5WpAIUTuexSVwLc7rwMwrn1V3IvamDiREEIYT6VSMad3TSqVsONRVCIf/XmWVI3W1LFEAWRU4fzPP//Qp08fAHbt2kXNmjVZuXIla9euZcOGDbkaUAiRuxRF4YuNl4lNSqV22aIMaFjO1JGEECLHHKwtWPh2Xews1Zy4E8G3O6+ZOpIogIwqnJ88eYK1tTUA+/fvp3379gC4ubkRFRWVe+mEELluh38we6+GYKFOm1ZbbSZdNIQQBUNlFwe+f7MmAIuP3GXLhYcmTiQKGqMK5zp16jB16lR2797NmjVr6NixI5A2MUqtWrVyM58QIhdFxacw5b8hm0Y0r4RnSQcTJxL5jWX58lhWroRl+fKmjiKEUdp7uzGiRSUAxq29yPXgGBMnEgWJSlEUJbuNzpw5Q9++fQkICODjjz9mzpw5AHTr1o1BgwbRtWvXXA/6qoqOjsbR0ZGoqCiKFCli6jiikJuw7iKrTz2gYgk7tn/SVGYIFEIUSBqtwrvLTuJ3K4wKxe3Y+GFjHG0sTB1L5GOG1mtGFc5PKYqidyV+eHg4zs7Oxm6uQJLCWeQXJ+6E03fRCQD+HvY69SsUM3EiIYTIOxFxyXSZ70dQZAJtqrmw6O16mEnXNJEJQ+s1g7tqHD16NN2y54evelo0+/n5GbpZIcRLkJiiYeJ/02r3a1BWimYhRIFXzM6ShW/XxcrcjL1XQ/n5wC1TRxIFgMGF88CBA+nQoQObNm0iMTEx3f3x8fGsXbsWX19fBg4cmJsZhRA5NH//Te6GxeHiYMWEDlVNHUcIIV4K71KOTO/mDcDcvTc4cC3UxInEq87gmQP9/f2ZN28eH374IaGhoVSvXh1XV1cURSE4OJgrV65QsmRJPvnkEzZv3pyXmYUQ2XD1UTQLD90BYFpXb4pYSz8/kbmgMWPRPHmC2smJUnO+M3UcIXKsd70yXAiMZNWJAD5dfY4tHzehnLOdqWOJV1S2+zinpqZy+PBhjh49yoMHD1CpVJQuXZomTZrQtGlTzM2NmsW7wJI+zsKUNFqFHr8c5UJgFL7VXVn4dj1TRxL53M3mLUgNCcHc1RWPQwdNHUeIXJGcqqXPouOcC4ikakkH1n/QCFtLqVfE/zO0Xsv2s8bc3JxWrVrRqlWrHAUUQuS9347d40JgFA5W5kzr6m3qOEIIYRKW5mb82r8unef7cS04honrL/Fjn1rprtUSIitGjePs5uaW2zmEELks8Ek8c3anTas9oWNVXItYmziReBVU3LaNKqdPUXHbNlNHESJXlXS05pf+dTA3U7Hp/ENWHLtn6kjiFWRU4ZycnMyTJ09yO4sQIpcoisLnG/2JT9ZQv3wx3nqtrKkjiVeE2t4Otb09anvpAyoKnvoVijG5UzUAZmy7yr93wk2cSLxqjCqc+/Xrx3fffUcOhoAWQuShzRcecvD6YyzVZszs4SNjlwohxH8GNipP11rupGoVPvzzHMFR6UcKEyIzRvWMv3HjBrt372b16tVUrVoVS0tLvfs3btyYG9mEEEZ4EpfMtC1XAPioVWUqu9ibOJEQQuQfKpWKb3r4cD04hmvBMYz44wyrhzbEylxmUhVZM6pw9vDwwMPDI7ezCCFywfRtVwmPS6aKqz3Dm1cydRzxiglfvgJtbCxm9vY4Dxpo6jhC5AlbS3MWvl2XLvP9OBcQyddbrzC9m4+pY4lXQI6m3BZZk+HoxMvkdzOMAUv/RaWCtcMbUbeck6kjiVeMDEcnCpMD10N5b8UpFAVm96rBm/XKmDqSMJFcn3JbCJG/JSRrmLQhbVrtdxqWk6JZCCGy0NLThc/aVAHg843+XAqMMnEikd8ZPfp3eHg4+/btIyAggNTUVL37JkyYkONgQojs+XHvDQIi4nFztGZse5lWWwghDPFRy8pcDIxk79VQhq86w5aPm1DMzjLrhqJQMqpwPn78OJ06daJYsWLcvn2b6tWrc+vWLZKSkqhZs6YUzkK8ZP5BUSzxuwvA9G7e2FvJjFhCCGEIMzMVP/SpRdefj3I3LI5P/jrHb+/VRy2jEYkMGNVVY+zYsUycOJFbt24B4O/vT1BQEB06dMDX1zdXAwohXixVo2X8uototAqdarjRupqrqSMJIcQrpYi1BQsG1MXGQo3frTDd5FFCPM+o01IXLlxg23+zSpmZmZGUlISzszO//PILjRs35ttvvzV4W48fP2b16tWEhITg4+NDr169UKtfPCSMIW0MWefQoUMcO3YMc3NzmjRpwuuvv653/7p16zh+/LjeMjc3N0aPHm3w8QmR15Ydvcvlh9E42ljwVZfqpo4jhBCvJM+SDszuVYOP/zrHrwdvU6OUIx18ZKZkoc+oM86xsbE4OjoC4OLiwv379wFwdHQkIiLC4O3cvn0bHx8fNm7ciEajYeLEiXTs2BGNRpOjNlmto9VqqV+/Pl999RUxMTEEBQXh6+vLJ598orevPXv2sHv3bkqWLKn75+zsbPDxCZHXAsLj+WHPDQAmd6xGCQcrEycSQohXV5ea7gxpWgGAMf9c4FZojIkTifzGqOHoVCqVbtbA/v37ExMTw9ChQ/njjz+4f/8+x44dM2g7vXr1Ijg4mMOHD2NmZsa9e/eoUqUKy5cvp3///ka3yWodRVE4c+YM9erV0213x44ddOzYkUuXLuHt7Q3A8OHDCQsLY+3atdl9iHRkODqRVxRF4e2lJ/G7FUajSs78MbgBKpX0yRM5I8PRicIuVaNlwNJ/OXEngool7Nj0YWMcrC1MHUvksTwdjm7u3Lm6n2fPnk1CQgJ9+/bl5s2bLFy40KBtpKamsm3bNvr374+ZWVqM8uXL07x580xnHjSkjSHrqFQqvaIZoHbt2gAEBgbqLb9z5w5ffvkl33//PSdPnjTo2IR4GdafDcLvVhhW5mbM7O4jRbMQQuQCc7UZP/erg5ujNXcexzHmnwvIlBfiqWwVzl9++SX37t1j5MiRumWlSpViz549xMbGcvr0aXx8DJt55/79+yQmJlKpkv7MZpUqVeLGjRtGtzFmuwC///471tbWegW1SqXCwcEBgCtXrtCsWTO9Y89IUlIS0dHRev+EyG1hsUl8vS1tWu1P23hQvridiRMJIUTBUdzeil8H1MVSbcauyyH8eui2qSOJfCJbhfOiRYuoWLEi7dq1Y82aNSQnJxu94/j4eIB0p8MdHR2Ji4szuo0x2z18+DBffPEF3377LcWLF9ctHzduHIcOHWLatGksXbqUrVu38tNPP7F///5Mj+ubb77B0dFR969MGZmFSOS+r7deITI+hWpuRRjStKKp4wghRIFTq0xRpnVNu+B6zq7rHL7x2MSJRH6QrcI5MDCQ9evXY2VlRf/+/XF3d+ezzz7D398/2zu2t7cHIDIyUm95ZGSk7iyvMW2yu91///2XLl26MHr06HQXB1aoUEHvdps2bShdujRHjhzJ9LgmTpxIVFSU7t+DBw8yXVcIYxy4Hsqm8w8xU8G3PX2wUMsEoEIIkRf61i9L39fKoFXgk9XneBARb+pIwsSy9RfX3Nycbt26sWXLFgICAhg9ejTbtm3Dx8eHhg0bsnjxYmJiDLsCtWzZstjZ2XH9uv5YideuXaNatWpGt8nOdk+ePImvry/Dhw9n5syZBuVOTU0lKSkp0/utrKwoUqSI3j8hcktcUiqfb0j7oDqocQVqlC5q2kBCCFHAffVGdWqWdiQyPoXhq86QmJL5yF+i4DP6VJW7uzsTJ07kxo0bHDp0CE9PT0aOHImbm2FjHqrVanr06MFvv/2mK0T9/f3x8/Ojd+/euvX++ecfvv/+e4PbGLrdU6dO0a5dO4YPH57huNOpqan4+fnpLfv7778JDg6mbdu2hj5MQuSq73ffICgygdJONoxuV8XUcYQQosCztlDz64C6ONtZcvlhNJM2XJKLBQsxo4aje5ZWq2Xv3r0sXbqUTZs2YWtra/BYzo8ePaJp06bY29tTp04dtm7dSrt27Vi1apVuncGDB3PixAlddxBD2mS1TlxcHGXKlMHCwoK3335bL9Obb75J/fr10Wg0tGvXjpSUFKpXr05AQAD79u1jwoQJfPXVVwY/PjIcncgt5x9E0v2XoygK/PZefZpXKWHqSKIAkuHohMjYsdthDFjyL1oFvu5anbdfL2/qSCIXGVqvGV043717l+XLl7NixQoCAwNp2bIl77//Pj179sTKyvBJGOLj49m6datuhr8WLVro3b97924ePnzIwIEDDW6T1ToJCQn873//yzCPr6+v3sggJ0+e5Ny5czg5OdGgQQPKlStn8LGBFM4id6RotHSZ78e14Bi61y7F3D61TB1JFFBSOAuRucWH7zBj+1Us1CpWD21I3XLFTB1J5JI8KZwTEhJYv349y5Yt48CBA7i7u/Puu+/y/vvvU7GiXNmfESmcRW7434FbfLfrOk62Fuwd1Rxne5khUOQNKZyFyJyiKHz01zm2XXyEi4MVWz9pgouDtaljiVxgaL1mnp2Nurm5ERcXR+fOndm8eTMdOnRArVbnOKwQInN3Hsfy076bAHzR2UuKZpGn3GfPRklORmVpaeooQuQ7KpWK2T1rcDMkhhshsXz4x1n+HNJQRjcqRLL1m540aRKBgYFs2LCBzp07S9EsRB7TahUmrr9EcqqWph7F6V67lKkjiQLOrkF97Js2wa5BfVNHESJfsrMyZ+Hb9XCwMufUvSfM2HbV1JHES5StwnncuHG4urrmVRYhxHP+Pv2Af+9GYGOhlmm1hRAin6hQ3I4f/rvWZMWxe2w4F2jaQOKlke8WhMinQmMSmbk97UzG6HZVKFPM1sSJhBBCPNXWy5VPWlUGYOL6S1x+GGXiROJlkMJZiHxq6uYrRCem4lPKkYGNyps6jigk4v49SewRP+L+PWnqKELke5+2qUILzxIkpmgZvuoMkfHJpo4k8pgUzkLkQ3uuhLDt0iPUZipm9fTBXC48ES/Jw3HjeDBkCA/HjTN1FCHyPbWZih/71KJsMVseRCTw6erzaLQyOUpBJn+NhchnYhJT+GJj2oQ/Q5pWpLq7o4kTCSGEyExRW0sWDKiLtYUZh2485qe9N0wdSeQhg4ejq1q1qsEbvXbtmlFhhBDw3a7rBEcnUs7ZlpFtPEwdRxQyxQYORBsbi5m9vamjCPHK8HIvwqweNRi55jzz9t/Cp3RR2nrJYAoFkcGF88iRI3U/3717l++//55u3brx2muvAXDq1Ck2btzI6NGjcz2kEIXFmfsRrDxxH4CZ3X2wtpAhH8XL5TxooKkjCPFK6la7FOcfRLLi2D1GrTnPpo8aU7GEfAAtaAwunIcPH677uX379ixZskRvGmyAFStWsGbNmlwLJ0RhkpSqYfy6SygK9K5bmsaVi5s6khBCiGyY3KkaVx5Gc/JeBMNWnmHjh42xs8rWXHMinzOqj/O///5Ljx490i3v0aMHJ06cyHEoIQqjXw/e5lZoLMXtLZncqZqp4wghhMgmC7UZP/evjYuDFTdDYxm39iKKIhcLFiRGFc5WVlbs378/3fL9+/djbS1ztguRXbdCY/jlwG0ApnSpTlFbme5YmIYmNg5NbCya2DhTRxHileTiYM2vA+pioVax7dIjFh+5Y+pIIhcZ9f3BqFGj6N+/P++//z6vvfYaiqJw+vRpli5dyrRp03I7oxAFmlarMGHdJZI1WlpVdaFzDTdTRxKF2J1OnUgNCcHc1RWPQwdNHUeIV1Ldck582aU6X2z0Z9aOa3i7O9JIut8VCEYVzuPGjaNixYrMnTuXlStXAuDl5cXvv/9Oz549czWgEAXdHycDOH3/CXaWar7u5i3TagshRAEwoEFZLjyIZO2ZQD766xxbP26Ce1EbU8cSOWR0j/VevXrRq1ev3MwiRKETHJXItzvShm8c6+tJKXlTFUKIAkGlUjG9mzfXgqPxD4pmxKoz/DmkIRcDowiNScTFwZr6FYqhNpOTJa+SHF3qqSgKwcHBuLnJV8tCZJeiKHyxyZ/YpFRqlSnK26+XN3UkIYQQucjaQs2v/evS5Wc/LgRGUW/6XhJSNLr73RytmdLFi/beUke9Koy6ODAhIYGPPvoIe3t73N3ddcvfffdd/P39cy2cEAXZTv9g9lwJwdxMxbc9a8hZByGEKIDKFLPlndfLAegVzZD2reOIVWfZ6f/IFNGEEYwqnKdMmcLJkyfZsmWL3vLu3bszderUXAkmREEWlZDCl5svAzCiRSU8SzqYOJEQQoi8oNEq/HM6MMP7ng5UN3XLFTRaGbbuVWBU4bx69WpWrlxJq1at9JY3btyY3bt350owIQqyWTuu8jgmiYol7PiwZWVTxxFCCJFHTt6N4FFUYqb3K8CjqERO3o14eaGE0YwqnENCQihdujSA3ggAqamppKSk5E4yIQqoE3fC+evkAwC+kWm1hRCiQAuNybxoNmY9YVpGFc7e3t66CVCeLZwXL15M3bp1cyeZEAVQYoqGSesvAfBW/bI0qOhs4kRCCCHykouDYRPDGbqeMC2jRtX46quveOedd/j0008BWLhwITt37mTz5s3s3LkzVwMKUZD8vP8Wd8LicHGwYkKHqqaOI4QQIo/Vr1AMN0drgqMSyawXs5tj2tB0Iv8z6oxzly5dWL16NQcOHMDa2pqRI0cSGhrK9u3badu2bW5nFKJAuBYczYJDadNqT+taHUcbCxMnEkIIkdfUZiqmdPECILOxk8o72yEDK70ajCqclyxZgq+vL4cOHSIuLo6EhASOHj2Kr68vS5Ysye2MQrzyNFqF8esukapVaOflKmN2CiFEIdLe241fB9ShpKN+d4xithaYqeD4nXC+333DROlEdqgURcn2+CcqlYrMmr3ovsIoOjoaR0dHoqKiKFKkiKnjCBNZfvQuU7dcwcHKnD2jmqd78xQiv7jZvAWpISGYu7riceigqeMIUaBotAon70bozRy49swDxq9Lu/bl667VZTIsEzG0XsvRzIHPCwoKwsnJKTc3KcQrLygyge92XQdgfIeqUjQLIUQhpTZT8Xol/YvC+7xWlpDoJH7Yc4MvN1+mhIOVfCuZj2WrcK5Xr16GPwNotVru3r1L+/btcyeZEAWAoih8vuES8ckaXivvRL/6ZU0dSQghRD7zcavKBEcn8ue/AXyy+jyr3reSiwXzqWwVzr169QLgzJkzup+fsrCwoHz58rzxxhu5l06IV9yWi484cP0xlmozvunhg5lc/SGEEOI5KpWKr7t6ExaTxO4rIQz+7RRrRzSiiqvMKpvfZKtwnjBhAgDFixdn8ODBeRJIiILiSVwyU/+bVvvDlpWp7CJvgEIIITKmNlMx763aDFjyL6fvP+HdZSdZN6IR7kVtTB1NPMOoUTWkaBYiazO2XyU8LpkqrvaMaFHJ1HGEMIjta69h17gxtq+9ZuooQhQ61hZqlrxbj8ou9jyKSmTg8pNExcuMzPmJUaNqAAQEBLB161YCAgJITU3Vu2/OnDm5Eq4gkFE1Cie/m2EMWPovKhWsHd6IuuXkolkhhBCGCYpMoMcvRwmJTqJ++WL8/n59rC3Upo5VoOXpqBp79+6la9eu+Pj48O+//9K8eXP8/f0JDw+nWbNmRocWoiBISNYwaUPa0EJvNywnRbMQQohsKVXUht/eq0/vBcc5eS+CkavP87/+dVDLdTImZ1RXjUmTJjF37lxOnDgBwMGDBwkICKBv3754e3vnakAhXjU/7rtBQEQ8bo7WjPX1NHUcIYQQr6CqJYuw6O16WKrN2Hk5mKlbLss8GfmAUYXz5cuX6devHwBqtZrExERsbW2ZM2cOa9euzdWAQrxK/IOiWHLkLgBfd/XGwVqm1RZCCGGc1ys5M7dPLVQq+P34fX45eNvUkQo9owrn+Ph47O3tAShZsiR37twBwNLSkpiYmNxLJ8QrJFWjZcL6i2i0Cp183Gjj5WrqSEJk2/13B3K7c2fuvzvQ1FGEEECnGm5M6ewFwHe7rvPP6QcmTlS45XjmQF9fXz744AMGDhzImjVraNiwYW7kEuKVs/zoPfyDoilibc6UN7xMHUcIoyTfu0dqSAjamFhTRxFC/Gdg4woERyex4NBtJqy/RHEHK1p6upg6VqFk1BnnlStX6n6ePXs2bm5ufPXVVyiKwuLFi3MtnBCvioDweL7fkzat9uRO1XBxkGm1xavJzNYWMzs7zGxtTR1FCPGM8e096VGnFBqtwgerznL+QaSpIxVKRg9HJwwjw9EVfIqi8M6ykxy5GcbrFZ35c0gDVCq58lkIIUTuStFoef+30xy+8ZhidpasG9GICsXtTB2rQDC0XjPqjLMQ4v9tOBfEkZthWJqbMbOHjxTNQggh8oSF2oxf+9fBp5QjEXHJvLPsX0JjEk0dq1Axqo9zSkoKv//+O35+fjx58iTd/Rs3bsxpLiFeCeGxSXy99QoAn7b2kE/+Qggh8pSdlTnLBr5GrwXHuB8ez3srTrF66OvYW+X4sjVhAKPOOH/00UeMGzeOlJQUSpcune6fEIXF11uv8CQ+haolHRjarKKp4wghhCgESjhY8ft79XG2s8Q/KJoRq86QnKo1daxCwag+zkWLFuXIkSP4+PjkRaYCRfo4F1wHr4cycPkpzFSw4YPG1CxT1NSRhMixkNnfoYmOQl3EEddxY00dRwjxAhcDI+m76ATxyRq61XLnhzdrYSazCxolT/s4m5ubU6ZMGaPDCfGqi0tKZfIGfwAGNa4gRbMoMKK3bSNq7Tqit20zdRQhRBZqlC7KL/3rYG6mYuP5h3y785qpIxV4RhXO/fr14/vvv5epH0Wh9cOeGwRFJlCqqA2j2lYxdRwhhBCFVAtPF77tWQOAhYfvsNTvrokTFWxG9SSfOHEi1atXZ9WqVVSsWDHdKAJ79+7NlXBC5EcXHkSy/GjaG9OM7t7YyQUZQgghTKhn3dKExCQye+d1vt56BRcHK7rUdDd1rALJqL/4Q4cOxdraGl9fX4oWLZrLkYTIv1I0Wsavu4hWgW613GkhMzcJIYTIB0Y0r0RodBIrjt1j9N8XcLa3pFGl4qaOVeAYVTjv3buXc+fOUbVq1dzOI0S+tvjIHa4Fx+Bka8EXnWVabSGEEPmDSqXii85ehMYksv1SMMN+P8OaYa/j5S4DE+QmowrnEiVK4OrqmisBHj16xKpVqwgJCcHHx4d+/fphYWGR4zZZraMoCrt37+bYsWOYm5vTpEkTWrZsmSv5RMF0NyyOH/feBODzTl4421uZOJEQQgjx/9RmKn54sxbhsSf5924EA5efZN2IRpQpZmvqaAWGURcHdu3alRkzZqDV5mzMwBs3buDj48OBAwdwcHBgxowZtGvXDo1Gk6M2Wa2j1WqpXbs2P/74I2q1mri4OHr06MHQoUNznE8UTIqiMGn9JZJTtTT1KE6POqVMHUkIIYRIx9pCzaJ36uHp6kBoTBLvLj/Jk7hkU8cqMIwax7l+/fqcOnUKNzc3KlSokO7iQD8/P4O20717d548ecKBAwdQqVQEBgZSqVIlFi9ezDvvvGN0m6zWURQFf39/vXGo9+7dS9u2bTl//jw1a9Y0Ot/zZBznguHvUw8Yt+4i1hZm7B7ZnLLO8uldFEw3m7cgNSQEc1dXPA4dNHUcIYSRgqMS6fHLUR5GJVKnbFH+GNwQG0u1qWPlW3k6jnPHjh2ZMmUKQ4cOpW3btrRp00bvnyFSUlLYsWMH/fr10xXepUuXpkWLFmzatMnoNoaso1Kp0k3eUr16dQCCg4ONzicKptCYRKZvS5tWe3RbTymahRBC5HslHa357b36ONpYcDYgko//OkuqRmYXzCmj+jh/9dVXOd5xQEAASUlJVKhQQW95xYoVOXr0qNFtjNkuwLJly7C1taVevXo52k5SUhJJSUm629HR0ZmuK14NU7dcIToxFZ9SjgxqXN7UcYQQQgiDeLg6sPTdevRf8i97r4byxSZ/Znb3SddTQBjOqDPOuSEhIQEABwcHveVFihQhPj7e6DbGbHfv3r189dVXfP/99zg7Oxu9HYBvvvkGR0dH3T+ZYfHVtvdKCNsuPkJtpuKbHj6Yq032khFCCCGyrV75Ysx7qzZmKvjr5AN+2nfT1JFeaQafca5VqxYA58+f1/2cmfPnz2e5PXt7ewAiIyP1lj958iTTviWGtMnudo8cOUK3bt344osvGD58eI7yQdrkMKNGjdLdjo6OluL5FRWTmMIXm9Km1R7ctALepRxNnEgIIYTIPt/qJZnW1ZvPN/rz496buDhY069BWVPHeiUZXDgPGDAgw5+NVbZsWezt7bl69Srt27fXLb969SpeXhmPj2tIm+xs9+jRo3Ts2JHRo0fz5Zdf5jgfgJWVFVZWMkxZQTBn13UeRSVStpgtI1vLtNpCCCFeXQMaliM0OpF5+2/x+cZLlHCwoq1X7gwtXKgoRli8eLFR9z1v0KBBSo0aNZT4+HhFURTl3LlzipmZmbJ582bdOn/88YcyY8aMbLUxZJ2jR48q9vb2ypdffpmjfFmJiopSACUqKsrgNsL0Tt+LUMpP2KqUG79V8bv52NRxhHhpbjRrrlzxrKrcaNbc1FGEELlMq9Uq4/65oJQbv1WpMnm7cvpeuKkj5RuG1mtGDUenUqnIrNmL7nteaGgoLVq0ANK6guzcuZPu3buzdOlS3TqDBw/mxIkT+Pv7G9wmq3ViY2MpVaoU1tbW9O7dWy9T//79ef311w3eV1ZkOLpXT3Kqlk7zjnAzNJZedUszp3dNU0cS4qWR4eiEKNhSNVqGrjzD/muhFLW1YO3wRlR2sTd1LJMztF7L1cI5KCgIHx8fIiIiDN5WUlISu3bt0s3M17BhQ737Dxw4QHBwMG+99ZbBbbJaJzExkSVLlmSYp1WrVnpdMQzZ14tI4fzq+WnvTebuvYGznSV7RzXHyc7S1JGEeGmkcBai4ItPTqXf4n85/yCSUkVtWP9BI1yLWJs6lknlSeH8dKi2M2fOULduXb37tFotd+/epX379vz1119Gxi54pHB+tdwKjaHjT34ka7TMe6s2b9R0N3UkIV4qKZyFKBwi4pLp9esx7oTFUbWkA38Pf50i1hamjmUyhtZr2RrHuVevXkBa4fz056csLCwoX748b7zxhhFxhTA9rVZh4vpLJGu0tPQsQZcabqaOJMRLV3b5ctCkgtqoYf6FEK+IYnaW/PZefXr8eoxrwTEM/f00v71XHytzmV3wRYzqqrFkyRIGDx6cF3kKHDnj/OpYdeI+n2/0x9ZSzZ5RzSlV1MbUkYQQQog85R8URd9FJ4hNSqVTDTfm962NmVnhmyAlT6fc7tWrF7/99pvu9t9//03Dhg3p378/T548MWaTQphUcFQi3+64BsBYX08pmoUQQhQK3qUcWfh2XSzUKrZdfMTX264YPMhDYWRU4TxhwgRSUlIACAsLY9CgQbz++us8ePCA0aNH52pAIV6GKZv9iUlKpVaZorzzenlTxxFCCCFemsaVi+tGkFp+9B6LDt8xcaL8y6hObJs2bWLGjBkA7Nixg8aNGzN37lwCAgJo0KBBrgYUIq/t9H/ErsshmJupmNXTB3Uh/IpKiKeitmxFm5iAmbUNjl06mzqOEOIl6VqrFI9jkpi+7Srf7LiGSxErutcubepY+Y5RhXN8fLzu5/3799O2bVsAnJyciIuLy51kQrwEUQkpfLnpMgDDm1eiaknphy4Kt9A5c3SjakjhLEThMrhpRYKjElnid5ex/1zE2c6KZlVKmDpWvmJU4Vy/fn3Gjh1LmzZt+Oeffzh16hSQNtrG0yHrhMivNFqFk3cjCI1JZNP5h4TGJFGxuB0ftaps6mhCCCGESU3qWI3QmCQ2X3jIiFVnWDPsdbxLOZo6Vr5hVOE8f/58Bg0axM6dO5k8eTLVqlUDYObMmUycODFXAwqRm3b6P2Lqlis8ikrUW96tdimsLWQIHiFcxozRddUQQhQ+ZmYqvutdg/C4JI7eCmfg8pOsH9GYss62po6WLxg1HJ0wnAxHl3/s9H/EiFVnyegJrwJ+HVCH9t4ydrMQQggRk5hCn4UnuPIomvLOtqwd0Yji9lamjpVn8nQ4uqcUReHRo0c52YQQL4VGqzB1y5UMi+anpm65gkYrnyOFEEIIB2sLVgx6jdJONtwLj+f9FaeIS0o1dSyTM6pwTkhI4KOPPsLe3h539/+fkvjdd9/F398/18IJkVtO3o1I1z3jWQrwKCqRk3cjXl4oIYQQIh9zKWLNb+/Vx8nWgguBUXz451lSNFpTxzIpowrnKVOmcPLkSbZs2aK3vHv37kydOjVXggmRm0JjMi+ajVlPiIIq6c5dkm7eJOnOXVNHEULkA5VK2LNs4GtYW5hx8PpjJq6/VKgnSDGqcF69ejUrV66kVatWessbN27M7t27cyWYELnJxcGwflkuDtZ5nESI/C1g0CDudHmDgEGDTB1FCJFP1C7rxP/61UFtpmLtmUDm7L5u6kgmY1ThHBISQunSaYNi/197dx4VxZXvAfzbzdbK0gIKKiAIgoqoCGpcEnUiOrjhFiU6aDRxX+KSeTMuSZAkx5yME18yxjFER9xGEY1rxpgYByMim0bcEDdWB9lEaARZurveHz56bFlsWqBo+H7O4Ry7+tatb1dR8qO4dUsi+e/DIpRKpeaJgkTNRVmlCvvjMupsIwHQSS7DwK42TROKiIjIgIzsaY+Nk70AAFsj72NPTJq4gUSiV+Hs5eWFf//73wC0C+ft27fD19e3YZIRNYAcRRkCQ2Nw8tpDVD0Q8MXnAla9Dp7gyacGEhER1SJwQBesHuUBAAg+cRM/Xm99E0ToNY/zhg0bMHv2bKxYsQIAEBoaitOnT+PEiRM4ffp0gwYk0tfVzEIs2HsJOYpytGtrgm1/8EXR04pq8zh3lMsQPMGTU9ERERG9xPI3uyFbUYb9cRlYcTARthZmreqvtXoVzhMmTEB4eDg2btwImUyGlStXwsfHB6dOndI8fptITMcT/4M/Hb6GcqUaHvYW2DF7gGby9lGeHTVPDrSzfDY8g1eaiYiIXk4ikeDTiV7ILy7Hz0k5mLc7AYcWDUH3jpZiR2sSfABKI+MDUJqWWi3gyzO3sTXyPgBgZA87fPW2NyxlJiInIzIMd4ePgDInB8b29nD/9ZzYcYiomSqrVCFoRxwupT9GRysZjiwZgs7tDPeJo03yABSi5uRJuRIL913WFM2Lhrvhu9n9WTQTERE1MJmJEXa80x/d7CyQrSjDOzvjUVTa8ieIYOFMLUJmQSne2nYRZ5JyYGosxf8G9sWaMT04BIOIiKiRtGtrit3vDoS9lRnu5j7B/D2XUFapEjtWo2LhTAYvPrUAE7dGIzm7GO0tzBC+YBAm93MUOxYREVGL59CuDXa/OxCWMmPEpxVgRfgVqNQtdxQwC2cyaAcTMvCHHbEoKKmAl4MVTiwbCp8u1mLHIiIiajV6dLTCd7P6w9RIip9u5mDDiZst9umCLJzJIClVaoScvIk/f38dlSoB4/p0wqGFhn1jAhERkaEa7GaL/w30hkQC7I1Nx9/P3Rc7UqNg4UwGp+hpJebuSkBYdBoAYPUoD3wzox/amBqJG4yIiKgVG9enE4LHewIANv10GxGXMkVO1PD0mseZSCwpeU8wb/clpOSXoI2JETZP74sxvfngEiIiouZgztCuyCkux7Zz97H2yHV0sDDD73rYiR2rwfCKMxmMqLt5mLQ1Gin5Jegsl+Hw4sEsmomIiJqZP/2+O6b4OEClFrDkn78hMbNQ7EgNhoUzNXuCICAsOhVzwhKgKFPC19kax5e9jl6d5WJHIyIiohdIJBJ8MbUPhnl0wNNKFd7dlYCUvCdix2oQLJypWatQqrHu6HWEnEyCSi3gLV9H7J//GjpYmokdjYiIiGphYiTFtj/4oI+jHAUlFXgnLB65xWVix3plLJyp2Xr0pBxB/4jDgfhMSCXA+rE9semtPjAz5k2AREREzZ25mTF2zhkAZ9u2yCx4irlhCXhSrhQ71ith4UzNUnK2AhO3RiM+tQCWZsb4x5wBmD/MFRIJnwRI1Jisxo2D/K2psBo3TuwoRNQCtLcww553B8LW3BQ3sxRYtPcyKpRqsWPpTSK01BmqmwmFQgG5XI6ioiJYWVmJHccg/HwzG6sOJqKkQgVn27b4xzv90c3OUuxYREREpKdrDwrx9nexKK1QYZJ3Z2ye7g2ptPlcDNO1XuMVZ2o2BEHA1sh7WLjvMkoqVBjazRbHlw5l0UxERGTg+ji2w7YgXxhLJTiWmIUvTieLHUkvLJypWSirVGHlwURs+uk2BAGYPdgZu+YORLu2pmJHIyIiogYw3KMDvpjaBwAQej4F/7iQKnKi+uMDUEh0OYoyLNhzCVcfFMFYKsGGgF4IGuQsdiwiIiJqYFN9HZFbXI4vTifj0x+SYGdphgl9O4sdS2csnElU1x4UYv6eS8hRlKNdWxP8/Q8+GOLWXuxYRK3W/TFjoczNhbGdHdx+PCV2HCJqgRYNd0WOogy7Lqbhg4irsDU3xZBuhvGzn0M1SDQnrmZh2rcxyFGUw93OAseXDmXRTCQydWkp1CUlUJeWih2FiFooiUSCj8Z7YmzvjqhQqbFg72UkZSnEjqUTFs7U5NRqAX/96TbeP3AF5Uo1Rvaww5ElQ+Bsay52NKJWz9TFBabd3GDq4iJ2FCJqwYykEmye7o3XutrgSbkSc8LikVnQ/H9h53R0jYzT0WkrKVdi1cFE/JyUAwBYONwVf/p9Dxg1oylpiIiIqGkUPa1EYGgMkrOL4drBHBELBuNu7hPkFpfBzlKGgV1tmqRG0LVeY+HcyFg4/9eDx6WYt/sSkrOLYWokxedTemOqr6PYsYiIiEhE2UVlmPL3aGQVlcHESIJK1X9L005yGYIneMLfq1OjZuA8ztSsJKQVYOI30UjOLkZ7CzMcWDCIRTMRERGho1yGeW+4AoBW0Qw8K6oX7/sNp288FCNaNSycqdEdTMjAzO2xeFRSgV6drXBi2VD4OluLHYuIiIiaAZVawPaolBrfqyqjQ04mQaUWf5AEp6OjRqNUqbHxVDJ2Rj+b4Hxc707YNK0P2pry246oufrPH/8HqsePYWRtDYe/bhI7DhG1AvGpBXhYVFbr+wKAh0VliE8twGA326YLVgNWMNQoip5WYvmBKzh/Jw8AsMrPA++P7AaJhDcBEjVnpQkJUObkwNjeXuwoRNRK5BbXXjTr064xsXCmBpeS9wTz9lxCSl4JZCZSbJ7ujbG9G3dQPxERERkmO0tZg7ZrTCycqUFF3c3D0n/+BkWZEp3lMnw3uz+8HORixyIiIqJmamBXG3SSy5BdVIaaRjFL8OwGwoFdbZo6WjW8OZAahCAI2BWdijlhCVCUKeHTpR2OLRvKopmIiIjqZCSVIHiCJ4BnRfLzql4HT/BsFs98YOFMr6xCqca6o9ex4f/veJ3q44gDCwY1iz+pEBERUfPn79UJ24J80FGuXTt0lMuwLcin0edx1pXoQzXS0tIQFhaGnJwc9O7dG++99x5ksroLLl3W0aVNTk4OwsLCkJycjDVr1qBHjx5a7+/evRuRkZFayxwdHfHZZ5+9widuWQpKKrBo32XEpxZAIgHWjemJeW905U2AREREVC/+Xp0wyrMj4lMLmvzJgboS9YrzjRs30LdvXyQlJcHd3R3ffvstRowYgcrKyldaR5c2W7Zsga+vL1JSUrB7925kZ2dX21ZMTAxu3ryJESNGaL4GDBjQsDvBgCVnKxDwzQXEpxbA0swYO98ZgPnDXFk0ExERkV6MpBIMdrPFRG8HDHazbVZFMyDyI7fHjRuHiooKnDlzBsCzK8DOzs7YunUr3nvvPb3X0aXNnTt34OLigtzcXDg5OSEyMhIjRozQ2taiRYuQn5+Pw4cP6/0ZW+ojt88k5WBl+BWUVKjgbNsWO2b3h7u9pdixiOgV3R0+QjMdnfuv58SOQ0TUJJr9I7erCtvAwEDNMnt7e7z55ps4efKk3uvo2q+HhwdMTU1fmjM5ORlLlizB2rVrcerUqXp/zpZGEAT8/dw9LNh7CSUVKgx2tcWxJUNZNBMREVGLJ1rhnJGRgcrKSri4uGgtd3Fxwf379/VeR59+ayOVStG9e3f06NEDarUaM2bMQFBQUJ3rlJeXQ6FQaH21FGWVKqw6mIi/nL4NQQBmDXLGnvcGwtr85b+AEBERERk60W4OfPr0KQDA3Nxca7mlpaXmPX3W0aff2mzYsAF2dnaa11OmTMHgwYMxc+ZMjB07tsZ1Pv/8c4SEhNRrO4YgV1GG+Xsv42pmIYykEmwI6IVZg5zFjkVERETUZES74lw1fqSwsFBreUFBAeTymuf+1WUdffqtzfNFMwC89tprcHJyQmxsbK3rrF27FkVFRZqvzMzMem2zObr2oBAB30TjamYh2rU1wd73BrJoJiIiolZHtMLZyckJcrkcN2/e1Fp+48YNeHl56b2OPv3WR2lpKeq6n9LMzAxWVlZaX4bs5NUsTPs2BtmKMnSzs8DxpUMxxK292LGIiIiImpxohbNUKkVgYCB27tyJJ0+eAADi4uIQFxeHmTNnatqFhYXhww8/1HkdXft9GaVSiePHj2st27ZtG/Lz82sdptGSqNUCvvz5NpYfuIJypRq/694BR5YMgbOt+ctXJiIiImqBRJ2OrqCgAH5+fnj8+DF69+6Nc+fOYe7cufj66681bebNm4fY2FjcuHFD53V0aXPhwgXs2LEDpaWlOHToEH7/+9+jY8eOmDRpEiZNmgSVSoW3334bSUlJ8PT0REZGBm7duoWNGzdi2bJlOn9GQ5yOrqRcidURifjpZg4AYMEwV/zZv0ezm0uRiBoep6MjotZI13pN1MIZeHZl9/z585on/L04nOLixYvIy8vDxIkTdV5Hlzb37t3DhQsXqq3n7e0Nb29vzev79+8jMTER1tbW8Pb2ho2NTb0+n6EVzg8el2Le7ktIzi6GqZEUG6f0xlu+jmLHIqImwsKZiFojgymcWzpDKpwvpRVg4d7LeFRSgfYWZgid5QtfZ2uxYxFRE2LhTEStka71mmjT0VHzEpGQifXHrqNSJaBXZytsn90fndu1ETsWETUx13/9C4AAgEOziIhexMK5lVOq1Pj8x2T840IqAGCMV0d8Ob0v2pryW4OoNTKy4A3ARES1YXXUihU9rcTyA1dw/k4eAGDFSHesGOkOKW8CJCIiIqqGhXMrlZpfgvd2JyAlrwQyEym+nOaNcX06iR2LiIiIqNli4dwKXbibj6X7f0PR00p0ksuwfXZ/eDnU76mKRNQyPQrbBfWTJ5BaWMB27hyx4xARNSssnFsRQRCwJyYdn/yQBJVaQL8u7RA6yxd2ljKxoxFRM1Gwa5dmVg0WzkRE2lg4txIVSjWCT9zEgfgMAMAUHwdsnNwbMhMjkZMRERERGQYWzq1AQUkFFu+7jLjUAkgkwNoxPTD/DVdIJLwJkIi0df7LXyBUVEBiaip2FCKiZoeFcwuiUguITy1AbnEZ7CxlGNjVBvdyn2DengRkFjyFhZkxvn7bGyN72osdlYiaKfPXBoodgYio2WLh3EKcvvEQISeT8LCoTLPMuq0JSitUKFeq0cWmLXa80x8e9pYipiQiIiIyXCycW4DTNx5i8b7f8OKz0x+XVgIAPOwtcHDBYFib80+vRERERPpi4WzgVGoBISeTqhXNzysuU8KqjUmTZSIiw1USF68Z48xhG0RE2lg4G7j41AKt4Rk1eVhUhvjUAgx2s22iVERkqLL+9CfNdHTuv54TOw4RUbMiFTsAvZrc4rqL5vq2IyIiIqKasXA2cLo+vIQPOSEiIiJ6NSycDdzArjboJJehthmZJQA6yZ9NTUdERERE+mPhbOCMpBIET/AEgGrFc9Xr4AmeMJLyYSdEREREr4KFcwvg79UJ24J80FGuPRyjo1yGbUE+8PfqJFIyIiIiopaDs2q0EP5enTDKs2O1JwfySjMRERFRw2Dh3IIYSSWcco6IiIiokXCoBhERERGRDlg4ExERERHpgIUzEREREZEOWDgTEREREemAhTMRERERkQ5YOBMRERER6YCFMxERERGRDlg4ExERERHpgA9AaWSCIAAAFAqFyEmIiF7uiVIJpUoFY6WS/28RUatR9f9dVd1WGxbOjay4uBgA4OTkJHISIqJ6uHcXkMvFTkFE1KSKi4shr+P/PonwstKaXolarUZWVhYsLS0hkUgAAAMGDEBCQkK9+tF1HYVCAScnJ2RmZsLKykqvzK2FPsdBLGJlbeztNmT/DdGXvn3wnBafIZ3PAM/ppuqrqc7p+rTnOa2bpj5HBEFAcXExOnfuDKm09pHMvOLcyKRSKRwdHbWWGRkZ1ftkqe86VlZWPCFfQp/jIBaxsjb2dhuy/4boS98+eE6Lz5DOZ4DndFP11VTntD7b4TldNzHOkbquNFfhzYEiWLp0aZOsQ3UzpH0qVtbG3m5D9t8QfenbB89p8Rna/uQ53TR9NdU5bWjff4ague5TDtVoYRQKBeRyOYqKivibLFELwHOaqGXhOW3YeMW5hTEzM0NwcDDMzMzEjkJEDYDnNFHLwnPasPGKMxERERGRDnjFmYiIiIhIByyciYiIiIh0wOnoiIgMVEZGBioqKmBiYgJnZ2ex4xARtXi84tyKxMXFoVevXrC0tMQ777yD8vJysSMR0SuYO3cuRo0aheHDh4sdhYhekVKpREhICOzs7GBra4s1a9aIHYlqwMK5lRAEAbNmzUJISAiysrLw6NEjfPfdd2LHIqJXcPbsWcTExIgdg4gawLVr1yCRSJCUlISEhATs378fUVFRYseiF7BwNiBPnz7FL7/8gqtXr9baJisrC5GRkbh7967W8rS0NCiVSrz11luwtLTEsmXL8NNPPzV2ZCKqQ3p6OrZv345ff/21xvcFQUBUVBTCwsIQGRkJtVrdxAmJqD6Ki4vx888/Izk5udY2aWlpiIyMRHp6utZyHx8ffPzxx2jfvj1cXV1hb28PGxubxo5M9cTC2QAUFxdj9erVcHNzw7Rp0/D555/X2G7dunVwc3PDmjVr4OvriylTpqCiogIAkJ+fjw4dOmja2tnZIT8/v0nyE5G2hw8fIiAgACNGjMCHH36IvXv3VmtTWVmJgIAATJ8+HadPn8bs2bMxcuRIPH36VITERFSX3NxcLF68GB4eHpg6dSq+/fbbam3UajXeffdd9OrVC2vWrEHPnj2xaNEi1DQrcEhICPz8/NCrV6+miE/1wMLZADx+/BgODg64ceMGhg4dWmObkydPYtOmTYiMjERcXBxu3ryJCxcuYNOmTQCADh06ICcnR9M+JydHq5AmoqZTWVmJefPm4d69e+jZs2eNbUJDQxEVFYX4+HgcPHgQly5dQlJSEjZv3tzEaYnoZXJyctCnTx/cuXMH3bt3r7FNaGgovv/+e1y5cgVxcXGIi4vDnj17sGfPHk0btVqNFStWQKlU1nqRjMTFwtkAdOnSBR988EGdf7LZvXs3hg8fjkGDBgEAnJycEBQUhF27dgEAnJ2dIZPJsG/fPuTl5eGrr76Cv79/U8Qnohd06dIFAQEBMDIyqrVNeHg4AgIC4OTkBACwt7fHtGnTEB4ermnz8OFDzTCse/fu4fHjx42enYiq6927NxYvXgxLS8ta2+zevRuTJ0+Gh4eHZp3x48drfk6XlZVh2rRpcHR0RHBwMJRKZY1Xo0lcLJxbiMTERPTr109rWb9+/XDv3j2UlJRAIpFg3759+PLLL9GzZ0906dIF8+fPFyktEb3MzZs34enpqbXM09MTycnJmrHO69evR1BQEGQyGfz9/XHgwAExohKRDq5evVrjz+mq+5YuXryI48ePY+3atZDJZJDJZDynmyHO49xCFBYWVrsibWtrq3nP3Nwc/fv3x5UrV8SIR0T1pFAo0K5dO61l1tbWUCqVKC0thYWFBXbu3ClOOCKql7KyMpSVldX4c7qwsBCCIODNN9+EUqkUKSHpilecWwhTU9NqNw2VlpZq3iMiw9KmTRsUFxdrLVMoFJBIJJDJZCKlIiJ9mJiYAECNP6dNTEwgkUjEiEV6YOHcQri4uCAzM1Nr2YMHD2BhYYH27duLlIqI9OXu7o7U1FStZampqXBxcYGxMf9YSGRIjIyM4OTkVOPPaRcXF3FCkV5YOLcQ/v7+OH36tNbTAI8cOYLRo0fzN1kiAxQQEIATJ06gpKQEAFBeXo7Dhw8jICBA5GREpA9/f3+cOHFCc4+CUqnE8ePHeaO+gZEIvGXTIJw5cwYqlQrBwcFo06YN1qxZAzMzM/zud78D8GzKun79+qF79+6YM2cOzpw5g4iICMTGxsLLy0vk9ET0PEEQEBoaCgDYvHkz7OzsEBQUBLlcjhkzZgAAioqKMGjQIFhZWWHSpEn48ccfkZGRgfj4eNjZ2YkZn4heoFQq8csvvwAA3n//ffTq1QsLFy6ElZUVhgwZAuDZg098fX3h5+eHSZMmISIiAhcvXsRvv/0GBwcHMeNTPbBwNhABAQGah5lUsbGxwf79+zWvc3JysHnzZiQnJ8PBwQHLli2rdlc+EYlPrVZjyZIl1Zbb2dnhk08+0bwuLi5GWFgY7t+/D2dnZ8ydOxfW1tZNGZWIdFBSUoKpU6dWW+7m5oatW7dqXqekpODrr79Gamoq3NzcsGrVKnTp0qUpo9IrYuFMRERERKQDjnEmIiIiItIBC2ciIiIiIh2wcCYiIiIi0gELZyIiIiIiHbBwJiIiIiLSAQtnIiIiIiIdsHAmIiIiItIBC2cialVKSkoQHh6OJ0+e1NqmoqIC4eHhKCwsbNLtNnaGV1Hf/M/Ly8vDv/71LwDN73PpS5/PUVRUhKNHjzZeKCJqdCyciahVycvLw4wZM5CdnV1rG4VCgRkzZiAtLa1Jt9vYGXRVVlaG8PBwFBUVaZbVN//zVq9ejYSEBADifq6GpM/nsLKywoYNG3DkyJHGC0ZEjYqFMxERaSksLMSMGTOQmZn5yn1dv34dR44cwapVqxogmWGTSCT485//jHXr1oEP7SUyTMZiByAiEsudO3dw+/ZtuLi4oHfv3i9tn52djfj4eJiZmWHIkCGwtLSs1qa4uBixsbEQBAGDBw+usU2VrKwsnD9/Hm+88QYcHBx0yqxQKBATEwMA8Pb2hr29vea9kpISnDx5EuPHj0dubi5u3boFR0dH9O3bt1o/t2/fRnJyMtzc3NCzZ08cOnQIo0aNgo2NDY4fPw4AOH36NG7cuIEOHTrAzc1Ns25KSkqdfT9v69atmDRpEuRyeZ3tdNm3tWW2tbWtsc/KykrExsZCoVCgb9++cHR01Hq/rmMVEREBtVoNIyMjODs7o1+/fjAxManzMwB1Hx8AmDx5MhYuXIizZ8/Cz8/vpf0RUTMjEBG1IqmpqQIAYcyYMUK3bt2E0aNHC23bthVWrFihaZOXlycAEK5cuaJZtmXLFqFNmzbCiBEjhH79+gk2NjZCZGSkVt+HDh0S5HK54O3tLYwePVpwd3cXYmNjtbZ79+5dQRAE4fbt24Kzs7OwdOlSQa1WV8tZU4bDhw8L1tbWwrBhwwR/f39BLpcL33zzTbXPNmHCBMHT01MYN26cYGFhISxfvlyr708++UQwMzMTRo4cKXh5eQljxowRAAgxMTGCSqUSJk6cKAAQ/P39hcDAQCE4OFjnvl/k6Ogo7Nix45X3bV2Za5KZmSm4uroKXl5eQkBAgODq6iqEhITodKwEQRBmzpwpBAYGClOnThXc3d0FT09PISMj45WOTxU/Pz+t7zciMhwsnImoVakqAP38/ISKigpBEAQhLi5OkEqlwvnz5wVBqF4U3b17VzAxMRHCw8M1/SxfvlxwcXERysrKNG1MTU2Fr776StMmOztbU9g9XzhfvnxZsLOzEz7++ONac76YISUlRTA3NxfOnTunaZOQkCDIZDLh1q1bWtt49913NcX4uXPnBIlEIqSnpwuCIAi3bt0SpFKpcPLkSUEQBEGtVgtBQUFaRejDhw8FAML169er7be6+n5RTk6OAEC4ePFirZ9Ll32rS+YXbdiwQRgyZIjmtUqlEo4dO6bZZl3H6kUqlUqYOnWqMGfOnFo/hy7Hp8qqVau0shGR4eAYZyJqlVauXKn50/vAgQMxYsQIRERE1Nj2+++/h5OTEwIDAzXL1q9fj7S0NMTFxQEADhw4gI4dO+L999/XtLG3t8egQYO0+jp37hzefPNNfPjhhwgJCdE574EDB2Bra4u8vDwcOnQIERERSElJgY2NDaKiorTaLly4EBKJBADw+uuvQyqV4s6dOwCAo0ePwsPDA+PHjwfwbNztH//4R51z1NX3i/Lz8wEA1tbWtfany77VJ3ObNm3w6NEj/Oc//wEASKVSTJw4EYDuxyopKQk//PADIiIi0KFDB8THx9e6vfocH2tra82+ISLDwjHORNQqubi4aL3u2rUr0tPTa2ybnp4OV1dXrWX29vYwNzfXrJORkYFu3bppisravP/++xg5ciSWL19er7xpaWmoqKjA4cOHtZa/8cYbaN++vdYyGxsbzb+NjIxgbGyMsrIyAEBmZma1z/7i67rU1feLLCwsADwbe10bXfatPpkXL16MxMREuLu7w9PTE6NGjcKyZcvg4ODw0mP19OlTTJgwAVeuXMGAAQMgl8uRmZmJ3NzcWrdXn+NTUlJS59h3Imq+WDgTUav0+PHjaq9fLHCqtG/fXnP1s0p5eTlKS0s167Rr1w6PHj166Xb37NmDhQsXYt26ddi4caPOea2srGBtbY3w8HCd16mJjY0Nrly5orXsxX3RUDp37gwLCwukpqbC19e3xja67Ft9MltaWmL//v0oKSlBdHQ0tmzZgv79++PevXsvPVZ79+7F3bt3kZ6erin+v/nmG2zYsKHWdepzfFJTU9G9e/eXtiOi5odDNYioVTp27Jjm30VFRTh79iyGDh1aY9vXX38dV69exf379zXLDh8+DJlMBh8fHwDA6NGjce3aNSQmJmqtm5eXp/Xa29sbZ8+eRWhoKNavX69zXn9/f9y6dQu//vqr1vLi4mIUFxfr3M/QoUNx+fJlPHjwQLOsahaNKlXFYm1XknVlbGyMYcOGITo6utY2uuxbXTK/qGqIhrm5OUaPHo2//e1vyM7ORnp6+kuPVXZ2NhwcHDT7AXg2pKQu9Tk+Fy9e5IwaRAaKV5yJqFXau3cvlEolevToge3bt8PJyQmzZ8+use3o0aMxduxYjBo1CitXrkRRURG++OILfPTRR5rpxkaNGoVZs2Zh5MiRWLFiBezs7HDs2DHMnj0bM2fO1OrP29sbv/zyC/z8/CCRSPDZZ5+9NK+fnx8WLFiA8ePHY/ny5XBzc8Pt27dx9OhR/Pzzzzr/6X/MmDEYMmSIZuhCTk4Odu7cCQCaoQsWFhbo3r07vvjiC0yePBn29vZa09HVx/z587Fs2TL89a9/hZGRUbX3ddm3umR+0bZt2xATE4OxY8eiXbt2+Oc//4k+ffrAw8MDnp6edR6r8ePH49NPP8XKlSvh5eWFo0ePIjExscb8VXQ9PtHR0VAoFJg2bZpe+5OIxMUrzkTUqpibmyMwMBDnz59H586dER8fj4kTJyIqKkpzs6CZmRkCAwO1bmr7/vvvsX79eiQmJiIrKwsHDx7E2rVrtfretWsXduzYgaysLNy4cQMffPCBpmiu2m5VAdWvXz+cOXMG9+/f18z7+7yaMoSGhuLw4cN48uQJLl68CHt7e8TExKBr1641bqPK9OnTteaJPnXqFObOnYtLly7B1NRUc/X9+fV++OEHuLq64tSpU4iKitK57xcFBASgQ4cOmrG/+u5bXTI/77PPPsNHH32Ehw8fIjY2FpMnT0ZUVBSMjZ9dL6rrWPn4+CAqKgpKpRLR0dEYN24cjhw5gilTpmj61+f4AMCWLVuwcuVKravZRGQ4JILAxxcREbUmBQUFWjf57dixA6tXr0Z+fj5MTU0bfHuxsbE4deoUPvnkE737aOrMjeHx48dYtWoVtm3bhjZt2ogdh4j0wMKZiKiVWbJkCSQSCXx8fJCcnIytW7fi008/xQcffCB2tFoZYmYianlYOBMRtTIVFRXYtWsXLl26BGtra4wbNw7Dhg0TO1adDDEzEbU8LJyJiIiIiHTAmwOJiIiIiHTAwpmIiIiISAcsnImIiIiIdMDCmYiIiIhIByyciYiIiIh0wMKZiIiIiEgHLJyJiIiIiHTAwpmIiIiISAcsnImIiIiIdPB/U+MIFyM+/E4AAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "block length 1: Var(mean) = 0.00133 (truth 0.00400)\n", "block length 2: Var(mean) = 0.00185 (truth 0.00400)\n", "block length 5: Var(mean) = 0.00314 (truth 0.00400)\n", "block length 10: Var(mean) = 0.00353 (truth 0.00400)\n", "block length 20: Var(mean) = 0.00313 (truth 0.00400)\n", "block length 50: Var(mean) = 0.00308 (truth 0.00400)\n", "block length 100: Var(mean) = 0.00228 (truth 0.00400)\n", "block length 200: Var(mean) = 0.00159 (truth 0.00400)\n" ] } ], "source": [ "sigma_eps2 = 1.0\n", "true_var_mean = sigma_eps2 / (1 - PHI) ** 2 / n\n", "\n", "grid = [1, 2, 5, 10, 20, 50, 100, 200]\n", "var_estimates = []\n", "for bl in grid:\n", " res = bootstrap(x, method=MovingBlock(block_length=bl), n_bootstraps=B, random_state=4)\n", " var_estimates.append(float(res.values().mean(axis=1).var()))\n", "\n", "auto_len = optimal_block_length(x.reshape(-1, 1), kind=\"circular\")\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4.5))\n", "ax.plot(grid, var_estimates, \"o-\", color=\"tab:blue\", label=\"block bootstrap Var(mean)\")\n", "ax.axhline(\n", " true_var_mean,\n", " color=\"black\",\n", " lw=2,\n", " ls=\"--\",\n", " label=f\"known long-run Var(mean) = {true_var_mean:.4f}\",\n", ")\n", "ax.axvline(\n", " auto_len, color=\"tab:red\", lw=2, ls=\"-.\", label=f\"Politis-White automatic length = {auto_len}\"\n", ")\n", "ax.set_xscale(\"log\")\n", "ax.set_xlabel(\"block length (log scale)\")\n", "ax.set_ylabel(\"estimated Var(sample mean)\")\n", "ax.set_title(\"Block length trades bias for variance\")\n", "ax.legend(fontsize=9)\n", "plt.show()\n", "\n", "for bl, v in zip(grid, var_estimates):\n", " print(f\"block length {bl:4d}: Var(mean) = {v:.5f} (truth {true_var_mean:.5f})\")" ] }, { "cell_type": "markdown", "id": "8f313711", "metadata": {}, "source": [ "Short blocks sit well below the dashed truth line: they behave almost like IID and miss the positive dependence that inflates the variance of the mean. As the block grows the estimate climbs toward the truth, then becomes erratic once the blocks are so long that only a handful fit in the series. The Politis-White automatic length lands in the useful middle region.\n", "\n", "One caveat: that automatic length is optimal for the variance-of-the-mean target. It is not guaranteed optimal for every statistic you might bootstrap; a different functional can prefer a different block length." ] }, { "cell_type": "markdown", "id": "06893440", "metadata": {}, "source": [ "## Recipe 4: model-based bootstraps under misspecification\n", "\n", "Model-based bootstraps (`ResidualBootstrap`, `SieveAR`) fit a parametric model, then resample its innovations. When the model is correct this is efficient: tight intervals at near-nominal coverage. When the model is wrong, the bootstrap inherits the model's error.\n", "\n", "We run a small coverage Monte-Carlo for a 95% interval on the sample mean. The correct process is the AR(1) we have used throughout. The misspecified process is an AR(3) with real dependence at lags 2 and 3; we deliberately fit a fixed-order AR(1) residual bootstrap to it. `SieveAR` selects its order from the data, and `MovingBlock` assumes no model at all, so both should stay closer to nominal." ] }, { "cell_type": "code", "execution_count": 7, "id": "e5888323", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:45.751554Z", "iopub.status.busy": "2026-06-22T16:15:45.750979Z", "iopub.status.idle": "2026-06-22T16:15:45.759702Z", "shell.execute_reply": "2026-06-22T16:15:45.758018Z" } }, "outputs": [], "source": [ "def coverage_mc(dgp, method, true_mean, M=150, B_inner=99, n_obs=600, alpha=0.05, seed=0):\n", " \"\"\"Fraction of (1-alpha) percentile intervals for the mean that cover true_mean, and mean width.\"\"\"\n", " rng = np.random.default_rng(seed)\n", " covered, widths = 0, []\n", " for _ in range(M):\n", " series = dgp(n_obs, rng)\n", " res = bootstrap(\n", " series,\n", " method=method,\n", " n_bootstraps=B_inner,\n", " random_state=int(rng.integers(1_000_000_000)),\n", " )\n", " if len(res) == 0: # preparation failed (e.g. non-stationary fit)\n", " continue\n", " means = res.values().mean(axis=1)\n", " lo, hi = np.quantile(means, [alpha / 2, 1 - alpha / 2])\n", " widths.append(hi - lo)\n", " covered += int(lo <= true_mean <= hi)\n", " return covered / M, float(np.mean(widths))\n", "\n", "\n", "def dgp_correct(n_obs, rng):\n", " \"\"\"AR(1), phi=0.5, true mean 0. Matches ResidualBootstrap(AR(1)).\"\"\"\n", " return ar1(n_obs, PHI, rng)\n", "\n", "\n", "def dgp_misspecified(n_obs, rng):\n", " \"\"\"AR(3) with real lag-2 and lag-3 dependence, true mean 0. An AR(1) fit cannot see it.\"\"\"\n", " phi = (0.3, 0.2, 0.35)\n", " burn = 100\n", " z = np.zeros(n_obs + burn)\n", " e = rng.standard_normal(n_obs + burn)\n", " for t in range(3, n_obs + burn):\n", " z[t] = phi[0] * z[t - 1] + phi[1] * z[t - 2] + phi[2] * z[t - 3] + e[t]\n", " return z[burn:]" ] }, { "cell_type": "code", "execution_count": 8, "id": "a5164f6e", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:45.763058Z", "iopub.status.busy": "2026-06-22T16:15:45.762850Z", "iopub.status.idle": "2026-06-22T16:15:51.114342Z", "shell.execute_reply": "2026-06-22T16:15:51.112106Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "method cov(correct) width cov(misspec) width\n", "------------------------------------------------------------------------\n", "ResidualBootstrap(AR(1)) 0.91 0.305 0.52 0.479\n", "SieveAR (order from data) 0.91 0.305 0.87 0.947\n", "MovingBlock (no model) 0.86 0.282 0.83 0.804\n", "\n", "nominal coverage = 0.95\n" ] } ], "source": [ "methods = {\n", " \"ResidualBootstrap(AR(1))\": ResidualBootstrap(model=AR(order=1)),\n", " \"SieveAR (order from data)\": SieveAR(),\n", " \"MovingBlock (no model)\": MovingBlock(block_length=\"auto\"),\n", "}\n", "\n", "rows = []\n", "for name, spec in methods.items():\n", " c_ok, w_ok = coverage_mc(dgp_correct, spec, true_mean=0.0, seed=10)\n", " c_bad, w_bad = coverage_mc(dgp_misspecified, spec, true_mean=0.0, seed=20)\n", " rows.append((name, c_ok, w_ok, c_bad, w_bad))\n", "\n", "header = f\"{'method':26s} {'cov(correct)':>13s} {'width':>8s} {'cov(misspec)':>13s} {'width':>8s}\"\n", "print(header)\n", "print(\"-\" * len(header))\n", "for name, c_ok, w_ok, c_bad, w_bad in rows:\n", " print(f\"{name:26s} {c_ok:13.2f} {w_ok:8.3f} {c_bad:13.2f} {w_bad:8.3f}\")\n", "print(\"\\nnominal coverage = 0.95\")" ] }, { "cell_type": "markdown", "id": "cfeb059e", "metadata": {}, "source": [ "On the correct AR(1) process all three methods land near nominal, and the model-based pair give the tightest intervals: when the model is right, modelling pays off.\n", "\n", "On the misspecified AR(3) the fixed-order `ResidualBootstrap(AR(1))` collapses well below nominal. It imposes an AR(1) structure that cannot represent the lag-2 and lag-3 dependence, so its intervals are too narrow for the true variability of the mean. `SieveAR` recovers most of the coverage because it selects the AR order from the data, and the assumption-free `MovingBlock` stays robust. The failure here is the fixed, wrong model, not model-based bootstraps in general; a block method is the more robust choice when you are unsure of the structure." ] }, { "cell_type": "markdown", "id": "cf3b6ee8", "metadata": {}, "source": [ "## Capstone: `diagnose()` as an advisor\n", "\n", "Choosing by hand requires knowing the truth, which in practice you do not. `diagnose()` reads the data and recommends method specifications from what it measures. We run it on four series with very different structure." ] }, { "cell_type": "code", "execution_count": 9, "id": "d56160d9", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:51.118810Z", "iopub.status.busy": "2026-06-22T16:15:51.118547Z", "iopub.status.idle": "2026-06-22T16:15:51.345400Z", "shell.execute_reply": "2026-06-22T16:15:51.343674Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "AR(1) stationary -> ('StationaryBlock', 'MovingBlock', 'SieveAR')\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "random walk -> ('ResidualBootstrap(model=ARIMA(...))', 'SieveAR')\n", "near-i.i.d. -> ('IID', 'MovingBlock')\n", "bivariate (VAR-like) -> ('ResidualBootstrap(model=VAR(...))', 'StationaryBlock', 'MovingBlock', 'SieveAR')\n" ] } ], "source": [ "rng = np.random.default_rng(7)\n", "series_ar1 = ar1(600, PHI, rng)\n", "series_rw = np.cumsum(rng.standard_normal(600)) # random walk (unit root)\n", "series_iid = rng.standard_normal(600) # near-i.i.d.\n", "series_var = np.column_stack([ar1(600, 0.6, rng), ar1(600, 0.6, rng)]) # bivariate\n", "\n", "examples = {\n", " \"AR(1) stationary\": series_ar1,\n", " \"random walk\": series_rw,\n", " \"near-i.i.d.\": series_iid,\n", " \"bivariate (VAR-like)\": series_var,\n", "}\n", "for name, s in examples.items():\n", " d = diagnose(s)\n", " print(f\"{name:22s} -> {d.recommended_methods}\")" ] }, { "cell_type": "markdown", "id": "f170b3cc", "metadata": {}, "source": [ "Read these carefully. `diagnose()` inspects two things: serial dependence (lag-1 autocorrelation) and stationarity (an augmented Dickey-Fuller test). It recommends specs from those signals: block methods and the sieve for stationary dependence, an integrated model or the sieve for a unit root, IID when dependence is weak, and a VAR for multivariate input. It does **not** detect volatility clustering, regime shifts, or seasonality, and it is deliberately extensible rather than exhaustive. Treat it as a fast, transparent starting point, not an oracle.\n", "\n", "No peer bootstrap or uncertainty library (MAPIE, darts, arch) ships a from-the-data programmatic recommender; tsbootstrap provides `diagnose()` for this.\n", "\n", "### The thesis\n", "\n", "There is no universally best bootstrap. IID is fine only without dependence. Block methods are robust but bias the dependence and need a length. Model-based methods are efficient when correct and fail when misspecified. The right choice depends on what you are willing to assume about the data-generating process, and `diagnose()` is there to help you make that assumption explicit." ] } ], "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": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }