{ "cells": [ { "cell_type": "markdown", "id": "cc462662", "metadata": {}, "source": [ "# Forward forecast intervals\n", "\n", "A bootstrap usually answers a question about the *past*: how uncertain is a\n", "statistic computed on the data you already have. `forecast_intervals` answers a\n", "question about the *future*: given a fitted model, what is a plausible range for\n", "the next few values of the series.\n", "\n", "The idea is simulation. Fit an autoregressive model once, then run it `horizon`\n", "steps past the end of the data many times, each run driven by a fresh sequence of\n", "innovations resampled from the model residuals. That gives many possible future\n", "paths. The interval at each step is the empirical quantiles of those paths.\n", "\n", "Below we build a forecast fan, check its coverage against fresh future paths, and\n", "trace how the interval width grows with the horizon. One limitation worth stating up\n", "front: `forecast_intervals` supports AR models only and refuses ARIMA or VAR." ] }, { "cell_type": "code", "execution_count": 1, "id": "44df4694", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:53.914956Z", "iopub.status.busy": "2026-06-22T16:14:53.914697Z", "iopub.status.idle": "2026-06-22T16:14:54.730056Z", "shell.execute_reply": "2026-06-22T16:14:54.729210Z" } }, "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": "5d72894b", "metadata": {}, "source": [ "## How a forward interval is built\n", "\n", "`forecast_intervals(X, model=AR(order=p), horizon=H, alpha=...)` does five things:\n", "\n", "1. Fit an AR(p) to `X` and keep its coefficients and residuals.\n", "2. Center the residuals (subtract their mean) to form an innovation pool.\n", "3. For each of `n_bootstraps` replicates, draw `H` innovations from that pool and\n", " run the fitted recursion `H` steps forward, starting from the last `p`\n", " observations of `X`.\n", "4. Stack the replicate paths into an `(n_bootstraps, H)` array.\n", "5. Read the per-step quantiles: `alpha/2` for the lower band, `1 - alpha/2` for the\n", " upper band, and `0.5` for the median.\n", "\n", "The return value is a tuple `(lower, upper, median)`, each a 1-D array of length\n", "`horizon`. Coverage here rests on large-sample behaviour of the fitted model under serial\n", "dependence; it is not the exact, finite-sample kind you get from exchangeable data,\n", "which is exactly why the empirical checks below matter." ] }, { "cell_type": "markdown", "id": "07225042", "metadata": {}, "source": [ "## Data and helpers\n", "\n", "A small AR(2) data-generating process, the bundled lynx series from sktime, and a\n", "coverage Monte-Carlo." ] }, { "cell_type": "code", "execution_count": 2, "id": "d388cf05", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:54.734140Z", "iopub.status.busy": "2026-06-22T16:14:54.733855Z", "iopub.status.idle": "2026-06-22T16:14:55.055650Z", "shell.execute_reply": "2026-06-22T16:14:55.054891Z" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from tsbootstrap import AR, ARIMA, VAR, forecast_intervals\n", "from tsbootstrap.errors import MethodConfigError\n", "\n", "PHI = (0.5, -0.3) # stationary AR(2) coefficients we will reuse as ground truth\n", "P = len(PHI)\n", "\n", "\n", "def ar2(n, rng, phi=PHI, burn=100):\n", " \"\"\"Stationary AR(2) with unit-variance Gaussian noise, true mean 0.\"\"\"\n", " z = np.zeros(n + burn)\n", " e = rng.standard_normal(n + burn)\n", " for t in range(len(phi), n + burn):\n", " z[t] = phi[0] * z[t - 1] + phi[1] * z[t - 2] + e[t]\n", " return z[burn:]" ] }, { "cell_type": "markdown", "id": "4042365c", "metadata": {}, "source": [ "## An AR forecast fan on the lynx series\n", "\n", "The Canadian lynx series is a classic short, cyclical record of annual pelt\n", "counts. Counts are strictly positive and the cycles are sharp, so we model the\n", "series on the log scale, where an AR fit behaves better, then exponentiate the\n", "bands back to the original count scale for plotting.\n", "\n", "We hold out the last few years so the fan can be compared against what actually\n", "happened." ] }, { "cell_type": "code", "execution_count": 3, "id": "750a534c", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:55.058609Z", "iopub.status.busy": "2026-06-22T16:14:55.058356Z", "iopub.status.idle": "2026-06-22T16:14:55.582289Z", "shell.execute_reply": "2026-06-22T16:14:55.581274Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "forecast horizon: 8\n", "lower/upper/median shapes: (8,) (8,) (8,)\n", "90% band, year ahead +1: [601, 3563] pelts\n" ] } ], "source": [ "from sktime.datasets import load_lynx\n", "\n", "lynx = np.asarray(load_lynx(), dtype=float)\n", "log_lynx = np.log(lynx)\n", "\n", "HOLDOUT = 8\n", "train = log_lynx[:-HOLDOUT]\n", "actual = lynx[-HOLDOUT:] # the held-out years, on the original count scale\n", "\n", "lo_log, up_log, med_log = forecast_intervals(\n", " train, model=AR(order=4), horizon=HOLDOUT, alpha=0.1, random_state=0\n", ")\n", "lo, up, med = np.exp(lo_log), np.exp(up_log), np.exp(med_log)\n", "print(\"forecast horizon:\", HOLDOUT)\n", "print(\"lower/upper/median shapes:\", lo.shape, up.shape, med.shape)\n", "print(f\"90% band, year ahead +1: [{lo[0]:.0f}, {up[0]:.0f}] pelts\")" ] }, { "cell_type": "markdown", "id": "81d5f080", "metadata": {}, "source": [ "The fan below shows the tail of the training series, the 90 percent forecast band\n", "fanning out over the holdout, the forecast median, and the values that actually\n", "occurred. Read the band rather than the median: lynx cycles are hard, and an AR\n", "model captures only the linear part of the dynamics, so the median can miss a turn\n", "while the band still covers the outcome." ] }, { "cell_type": "code", "execution_count": 4, "id": "82d65096", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:55.586669Z", "iopub.status.busy": "2026-06-22T16:14:55.586508Z", "iopub.status.idle": "2026-06-22T16:14:55.796633Z", "shell.execute_reply": "2026-06-22T16:14:55.795867Z" }, "nbsphinx-thumbnail": { "output-index": 0 } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tail = 30\n", "years = np.arange(len(lynx))\n", "train_years = years[:-HOLDOUT]\n", "fut_years = years[-HOLDOUT:]\n", "\n", "# Anchor the forecast at the last observed training point so the fan, the median,\n", "# and the actuals all start from the data rather than floating one step to the right.\n", "anchor_year = train_years[-1]\n", "anchor_val = lynx[:-HOLDOUT][-1]\n", "band_years = np.concatenate(([anchor_year], fut_years))\n", "lo_p = np.concatenate(([anchor_val], lo))\n", "up_p = np.concatenate(([anchor_val], up))\n", "med_p = np.concatenate(([anchor_val], med))\n", "act_p = np.concatenate(([anchor_val], actual))\n", "\n", "# Okabe-Ito colorblind-safe palette.\n", "C_TRAIN = \"#000000\"\n", "C_FCST = \"#0072B2\" # blue\n", "C_ACTUAL = \"#D55E00\" # vermillion\n", "\n", "fig, ax = plt.subplots(figsize=(9, 4.8), layout=\"constrained\")\n", "ax.plot(\n", " train_years[-tail:],\n", " lynx[:-HOLDOUT][-tail:],\n", " color=C_TRAIN,\n", " lw=1.6,\n", " label=\"training series (observed)\",\n", ")\n", "ax.fill_between(band_years, lo_p, up_p, color=C_FCST, alpha=0.22, label=\"90% forecast band\")\n", "ax.plot(band_years, med_p, color=C_FCST, lw=2.0, ls=\"--\", marker=\"s\", ms=4, label=\"forecast median\")\n", "ax.plot(band_years, act_p, color=C_ACTUAL, lw=2.0, marker=\"o\", ms=5, label=\"actual (held out)\")\n", "ax.axvline(anchor_year, color=\"0.5\", ls=\":\", lw=1.2)\n", "ax.annotate(\n", " \"forecast start\",\n", " xy=(anchor_year, ax.get_ylim()[1]),\n", " xytext=(4, -10),\n", " textcoords=\"offset points\",\n", " color=\"0.4\",\n", " fontsize=9,\n", " ha=\"left\",\n", " va=\"top\",\n", ")\n", "ax.set_xlabel(\"year index (annual observation)\")\n", "ax.set_ylabel(\"lynx pelts (count)\")\n", "ax.set_title(\"AR(4) 90% band covers the held-out lynx counts; the median misses the peak\")\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(fontsize=9, loc=\"upper left\", framealpha=0.9)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fd83cd27", "metadata": {}, "source": [ "The band widens as it reaches further ahead, and it stays wide throughout. A\n", "short, sharply cyclical series carries a lot of forward uncertainty, and the\n", "simulation passes that uncertainty straight into the band rather than collapsing\n", "it onto a tight point forecast." ] }, { "cell_type": "markdown", "id": "ba401cdf", "metadata": {}, "source": [ "## Does the band cover at the nominal rate?\n", "\n", "A 90 percent band should contain the truth about 90 percent of the time. On a\n", "synthetic AR(2) we can measure that directly, because we know the process that\n", "generates the future.\n", "\n", "The recipe: fit one band from a single realisation, then draw many *fresh* future\n", "paths from the same true AR(2), continuing from the same last `P` observations, and\n", "count how often each future value lands inside the band. With nominal `1 - alpha`,\n", "the per-step hit rate should sit near `1 - alpha`. The Monte-Carlo below uses a\n", "modest number of paths so it stays fast in CI." ] }, { "cell_type": "code", "execution_count": 5, "id": "2c11798e", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:55.800830Z", "iopub.status.busy": "2026-06-22T16:14:55.800688Z", "iopub.status.idle": "2026-06-22T16:14:55.846932Z", "shell.execute_reply": "2026-06-22T16:14:55.845753Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "per-step coverage: [0.78 0.815 0.762 0.774 0.799 0.794 0.783 0.784]\n", "mean coverage: 0.786 (nominal 0.80)\n" ] } ], "source": [ "rng = np.random.default_rng(0)\n", "n, H, alpha = 400, 8, 0.2 # 80% nominal coverage\n", "x = ar2(n, rng)\n", "\n", "lo_c, up_c, med_c = forecast_intervals(\n", " x, model=AR(order=2), horizon=H, alpha=alpha, n_bootstraps=999, random_state=0\n", ")\n", "\n", "M = 2000 # fresh future paths\n", "last = x[-P:]\n", "hits = np.zeros(H)\n", "for _ in range(M):\n", " path = np.empty(H + P)\n", " path[:P] = last\n", " e = rng.standard_normal(H)\n", " for h in range(H):\n", " path[P + h] = PHI[0] * path[P + h - 1] + PHI[1] * path[P + h - 2] + e[h]\n", " future = path[P:]\n", " hits += ((future >= lo_c) & (future <= up_c)).astype(float)\n", "\n", "coverage = hits / M\n", "print(\"per-step coverage:\", np.round(coverage, 3))\n", "print(f\"mean coverage: {coverage.mean():.3f} (nominal {1 - alpha:.2f})\")" ] }, { "cell_type": "markdown", "id": "245cd0e2", "metadata": {}, "source": [ "The mean coverage lands close to the nominal 0.80. It will not match exactly: the\n", "band is read from a single fitted realisation, so it inherits that realisation's\n", "sampling noise, and bootstrap forecast coverage is asymptotic rather than exact.\n", "A result this close to nominal is what calibrated bands look like." ] }, { "cell_type": "markdown", "id": "81e0e73a", "metadata": {}, "source": [ "## Uncertainty grows with the horizon\n", "\n", "Each step forward compounds the innovation drawn at that step on top of all the\n", "uncertainty already accumulated, so the interval should widen monotonically (up to\n", "simulation noise) as the horizon grows. We read the band width straight off a\n", "single longer forecast." ] }, { "cell_type": "code", "execution_count": 6, "id": "6304bec5", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:55.850452Z", "iopub.status.busy": "2026-06-22T16:14:55.850304Z", "iopub.status.idle": "2026-06-22T16:14:56.013547Z", "shell.execute_reply": "2026-06-22T16:14:56.012084Z" } }, "outputs": [ { "data": { "image/png": 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SSy9RrVq1bO3xtMI+fn7p0iYrV67Ezs6Ot956S7PN2to62zwzUXAyZ0Xky5PzNQDNB/bTFWW0OX/+PHXq1GHRokWa4QyKoqAoCpaWlgQFBWXbv379+jmO0bt3b5ydnfHx8dHM8/Dx8cHKyoqxY8dq9vP396dv376oVCp69OhB5cqVMTc3R1EUvaoC9ejRA4Ddu3czevRoDh8+zE8//YSiKEyZMoXk5GTNXISsfbUJCAjghRdeyLE9r7G1eSno+5JbO+dmzpw5zJgxA1dXV/r06UPnzp3p3bt3tophur7HuhzLkHRpo/yenwVtd10Y+jx+WmG8Zn3f28J+rXkpjPPjaT4+PtSoUSPbcBVFUbCysmLFihUsXbo0x2OyhgomJSURERGBnZ0dAwcOzDFnIiue3IZ0PSkuLo4+ffpw8+ZN/vrrL62/+7oeL8vTn13m5ubUrVs31yTs6ee8evUqAI0aNcqxb6NGjdi2bRu3b9/m4sWLADRv3lxrHFnDea5du6Z5n7Jey+XLl1Gr1Vy7do0OHTrQpUsXJk2axI8//kj37t3p1q0bXbp00bStLvscPHiQefPmZXvd7733Hi4uLvTs2ZNVq1bx4YcfYmZmxsaNG4mJicl2US0qKorevXtz7do1evfujYuLC5aWlqjVatRqNVFRUdm+MOv6WZ3f4z59/js6OmJhYZHt/L948SLu7u55Jkjnz5/Hzs5OUzQiq/0VRcHCwiLP35HCPn5+6dImAQEB1KpVSzP8XNtjRcFIsiLy5ckrj4DmCnxuZTRzk56ejrm5ueaK1ZP+7//+L8dkytw+tMzNzZkwYQKLFi3i9u3bODk58dtvvzFo0CDN1UCAN998E0tLSy5cuICtra1m+8WLF4mIiNAp3ifVq1cPZ2dndu/ejaurK4mJifTo0QNFUUhMTOTYsWPs2bMHZ2dn6tatm+exFEXJ9UuArl8MnlbQ90WXq7EAb7zxBj179mTz5s0cPXqUN954g9TUVJYtW8arr74K6P4e63IsQ9KljfJ7fha03XVh6PP4aYXxmvV9bwv7tealMM6PJx09epSAgABmz56dbQ4GwNChQ/n1119ZuHAh1tbW2e57shqYoiiMHj2akSNHcvz48WwT2KtUqQJkzOnQJiEhgX79+nH+/HnWrl3LwIEDte6bdRxdLx5o+zzLShSe9PTnTdY+T09+f3Lbk0lHXp+TWXOR1Gp1jvfJ3d1dU47d0tKSffv2sWfPHnbt2sW+fftYvHgx7u7u/Pvvv3h6euq0T8eOHbPNTXmyV3ry5MkMHz6cPXv28Nxzz+Hj44Onp2e2CdcLFy7k0qVLXL16NdsE8Q8++IBdu3Y9s+20ye9xnz7/s17Lk+e/tr9bT0pPT8fS0jLX35Fx48blWQGxsI+fXwVpk9zOZaE/SVaEweX1S9qgQQPMzc0LXCpw4sSJLFiwgNWrV+Pl5UVkZGSOIWD+/v707Nkz25eetLS0Ai3+1KNHD3bs2IGrqysNGzbUfEFo2LAhu3fvZu/evfTp0+eZx/Hy8sr1iuPly5dzbDO1Dz0vLy9mzZrFrFmzSExMpG/fvrz11ltMnjwZCwuLfL3HzzqWrgzVRoY6Pw1J1/M4rzYoit/Jp+nz3hritebGFM6Pn3/+maZNm2qGCT0pKiqKypUrs2nTJs1Qk9yoVCq+++47du7cyeuvv87x48c192X1SgQEBNCuXbscj01KSmLgwIH4+vqyZs0ahg0blme8V69epXr16jonK1euXMnWM6JWqwkICNCpt9jLywv4r2ftSZcuXcLW1hZnZ2dNKfVz587lKM+cJev5WrZsyZtvvpnn85qZmfHcc8/x3HPPaZ6rRYsWLFy4UDOc6Fn7dO7cmc6dO+d6/IEDB+Lk5MTKlSupU6cOhw8fZtGiRdn28ff3x8PDI0elLH3XOSvM4zZs2JDff/+dR48e4eDgkOs+DRo04MqVK3zwwQf5rrpZ2McvDF5eXmzfvp2UlJRs8WT1FgrDMK1vQaJEyPoCnzWG+klvv/02Z8+eZfXq1TnuCwoK0nn4TK1atejatSsrV67Ex8eHmjVr5hh6Vbt2bfz8/LJV/fn6669JTEzMz8vJpmfPnty/f5///e9/9OrVS7O9V69erFixgnv37j1zvgpkjO8+efJktvUNoqOjWbduXY5982rPopSens7hw4ezbStbtiy1a9cGMr6cgG7vsa7HAli8eHG2Kmy5MVQbGer8NCRdz+O82qAofiez5Oe9fZohXmtujH1+xMTEsHHjRnr37p3r/ZUqVaJVq1asWLHimTE4OjryzjvvcOLECbZs2aLZ3qBBA5ycnHKd25OSksKQIUM4dOgQf/zxByNGjHjm85w4cSJbha1n+eWXX7LNg1i1ahURERFMnDjxmY9t0qQJzZo14/vvv+fBgwea7adPn2bbtm1MmDBBM6ysR48efP3111y7di3bMbK+hNevX59evXrx+eef5+iNUxSFQ4cOARAYGMjt27ez3e/h4UGZMmU056gu++TFysqKcePGsXnzZr744gvMzc1zVJOqXbs2N27cICoqSrNt7969nD59+pnHz0thHPe1115DrVbzf//3f9lef0pKiqYi5rRp00hJSWH27Nk5etXu37+vdW5WURy/MEyYMIGYmBi+//57zba0tDR8fHyKNI6STnpWhMF16NABZ2dnpk2bxvPPP4+VlZVmTYNx48YRERHBK6+8wurVq2nRogVJSUlcvnyZu3fvZvvj+yyTJ09mzJgxhISEaMYEP2n+/Pn069dPM+446wrd888/n6/neVKPHj1QqVRERUVlS0p69uzJkiVLNGPtn2XGjBkcPnyY/v37M2rUKCpUqMDRo0eZOnUqr7zySrZ982rPoqQoCh988AExMTG0atWKypUrc/nyZbZv387SpUs1V5V0eY91PRbAJ598Qt26dfP80mOoNjLk+Wkoup7HebVBUf1Ogu7nSWG91twY+/z4448/SExM1JqsAPTp04ePPvqI0NDQbBPDc/PWW2/x7bffMnfuXAYMGICZmRkqlYqxY8eyZs0afvjhh2y9V++88w47duygTZs2BAcH5+gZmjp1arYhtCdOnOD27duMHz9el2YBMtqmc+fOdOrUiYiICDZs2MCrr77K8OHDdXr82rVr6dOnD02bNmXIkCEkJCSwbt06unbtmq034o8//mDw4ME0adKEwYMHU716dS5cuEBsbCzHjh0DYM2aNYwaNQpvb28GDx5MzZo1uX37NidOnKBly5Z07tyZyMhI+vbti7e3N/Xq1UOlUvHvv/9ib2/Pe++9B6DTPs8yefJkli5dyk8//cTzzz9P1apVs93/f//3f/z111+0adOGIUOGEBERwfXr13n77bd1fo7cFMZxmzdvzurVq3nllVc4c+YMXbp0ITExkUOHDjFv3jwaNGhAs2bNWLduHZMnT2b//v107twZKysrAgMDuXTpEj///LPW+RyFffzC0LNnT2bNmsU777zDkSNHqFOnDseOHWPGjBmsXbvW5EZGFFeSrIgcateuzdy5czXVNyDjQ2Tu3Lk5umYdHR2ZO3cujRs31mwrV64cZ8+eZfPmzdy+fTvHmgZz5sxhwoQJ7Nq1i/DwcFxdXRk6dCidOnXSjP3U9nxPGjJkCO+//z6KouSojAPQtWtXrl69yvbt24mJiWHGjBn06NGDLVu2UKdOHc1+9evX14xjfpYqVaqwePFiHj16RMeOHTXbO3XqpIn36ePkdnxLS0v++ecfdu3apVkU8r333uPx48fMnTs327oIebVnft6X3OTVzk/HbWFhwcGDB7l06RLHjx8nMjKSAQMG8MMPP+T4A6zLe6zLsSIiIkhISGDQoEF5vg5DtlFBzk9d293Ozo65c+fmWDCucePGzJ07N9sCg7qex3m1QWH+Tj79mvNznjzNEK81N0V9fjzN1taW999/P9c1ULKMGTOGlJQU7t+/T61atXL9HH7yeKtWreL48eOaGCDjyvQ333zDjh07GDBggGb/1q1ba9Z9enq+DJDjCnXW8FpdLrxkad++PR07dmTTpk1UqlSJadOmaSp0Zcnr88bT05MrV66wfft2rly5QvXq1dm2bRtdunTJtl/lypU5evQohw8f5uTJk6hUKt5+++1ssVaqVIk9e/Zw+vRpfH19iYuLo2vXrsybN0+TCHbo0IHAwED27t2Lv78/KpWKhQsX0rt372wT7J+1z7PUrVuXJUuWEB0dnevnmKurKwEBAfz999/cuXOHQYMG8fzzz3P+/Hnmzp2LnZ0dADVq1GDu3LmaIXNPyjpXs4bJGeq4c+bMybEw6pgxY+jVqxfbt2/n5s2b1K9fn/fee4+aNWtq9hk6dCi9evVix44dBAUFUbZsWbp06ULPnj2fOXTLUMfPrU103ZbfNlm0aBFDhw5l3759WFlZ8euvv2rmLj1Z9U3oT6XkNvtNCCFMwC+//MKsWbMIDQ3NdbKjECK7qVOncu7cOU6ePKnX42/dukWdOnVYt24dzz///DP3//HHH5k6dSrXr1/Hzc1Nr+cUoqTZvn07/fv3Z8+ePflK+kXupH9KCGGynJyc+OWXXyRREUJHn3zyCT179tR5fZSnhYaG8umnn+qUqAgh0MynyZKYmMiCBQtwdnbWWnxB5I8MAxNCmKx+/foZOwQhihUnJ6cCVXbr2LFjtiGuQoi8rVmzht27d9OhQwfS0tLYuXMnUVFRbNmyRefhgiJvMgxMCCGEEHo5ffo0W7ZsYebMmXnOMRSiJPPz8+P48eM8ePAANzc3BgwYIL8PBiTJihBCCCGEEMIkyZwVIYQQQgghhEmSZEUIIYQQQghhkkrlBHu1Ws3t27cpX7681rr4QgghhBBCiMKhKApxcXFUr149zwU0S2Wycvv2bVxcXIwdhhBCCCGEEKVaeHg4NWrU0Hp/qUxWslYUDQ8P16ziWtTUajWRkZE4OTnlmU2WRtI22knbaCdto520Te6kXbSTttFO2kY7aRvtpG1yio2NxcXFRfO9XJtSmaxkDf2ys7MzarKSlJSEnZ2dnLRPkbbRTtpGO2kb7aRtciftop20jXbSNtpJ22gnbaPds6ZkSGsJIYQQQgghTJIkK0IIIYQQQgiTJMmKEEIIIYQQwiRJsiKEEEIIIYQwSZKsCCGEEEIIIUySJCtCCCGEEEIIkyTJihBCCCGEEMIkSbIihBBCCCGEMEmSrAghhBBCCCFMkiQrQgghhBBCCJMkyYoQQgghhBDCJEmyIoQQQgghhDBJkqwIIYQQQgghTJIkK0IIIYQQQgiTJMmKEEIIIYQQwiRJsiKEEEIIIYQwSZKsCCGEEEIIIUySJCtCCCGEEEIIkyTJihBCCCGEEMIkSbIihBBCCCGEMEmSrAghhBBCCCFMkiQrQgghhBBCCJMkyYoQQgghhBDCJEmyIoQQQgghhDBJkqwIIYQQQgghTJIkK0IIIYQQQgiTJMmKEEIIIYQQwiRJsiKEEEIIIYQwSZKsCCGEEEIIIUySJCtCCCGEEEIIkyTJihBCCCGEEMIkSbIihBBCCCGEMEmSrAghhBBCCCFMkoWxAxBCCCGKWnBMJD5BpwiMuoNXpWpM8myFh72TscMSQgjxFElWhBBClCqrgk8x+dgGVKhQFAXV3SC+uHwQn/YjmODR0tjhCSGEeIIMAxNCCFFqBMdEMvnYBtSKQrqiRk3m/4rCpGPrCYl9YOwQhRBCPEGSFSGEEKXGyuDTqFDlep8K8Ak6VbQBCSGEyJMkK0IIIUqNsPhoFJRc70tXFLZHXCEuNamIoxJCCKGNJCtCCCFKDTfbilp7VgAuPbxLrQ0LWeJ/kMdpqUUYmRBCiNxIsiKEEKLUmOjRErWSe89KlgfJCcw8vY3aGxfy/dVjJKenFVF0QgghnibJihBCiFLDw94JLztHzc9mqDBXmWGmUuHTfgTru4zD274yAHcex/LGiU14/rUIn6CTpKrTjRW2EEKUWkYvXRwcHMzevXuJj4+nfv369O7dGzOzvHOokJAQdu/ezcOHD6lZsyaDBw/G1ta2iCIWQghRXJ15EE5AbCQALSrVoIaVLV6VqjHZqzV1MpOYIa4NWRN6no/8dhMaF8XNhEdMPraBRRcP8FHTXoxyb4L5M/5OCSGEMAyjftrOmzePYcOGERAQwN27d3nttddo164dCQkJWh/z66+/Ur9+fY4dO0ZiYiI//PADderUITQ0tAgjF0IIURx9cekgABYqMzZ0GcfyJv1Z0LyPJlEBMDczY1yd5gQM+T/+124YNcraAxAS94Cxh9fQaMsS/gq7iFpRG+EVCCFE6WLUZGXIkCFcuHCBr7/+miVLlnDixAlOnz7N1q1btT5m0aJFTJ48mT/++IPPPvuMw4cPY21tzYoVK4owciGEEMVNaFwUG29cBGB0rabUtK2Q5/6WZua87NWG4KGz+ab1IKqUKQ/AlUf3GHbgV5r/8xXbwq+gPGMOjBBCCP0ZNVlp2rRprtvzGtLl4OCAWv3f1SxFUVCr1VSokPcfHSGEEKXbUv9Dmsn1Mxt01vlxNhaWTKvXgdBhc/iiRX8qWZcFwC/6NgP2rqTt9m/ZeztIkhYhhCgEJjFnZfXq1cTGxnLgwAFmz55Nv379tO6/YsUKpkyZwvDhw3F1dcXX15fevXvzxhtvaH1McnIyycnJmp9jY2MBUKvV2RKfoqRWqzWJlshO2kY7aRvtpG20k7aBB0kJrAw+DcBzzl40cKia73axMbPg7fqdeNmzFd9cOcaSy4eISU3iZORNeu76H52r1OLjps/RsYp7Yb6UIiHnjHbSNtpJ22gnbZOTrm1h9GTF3NwcGxsb4uPjiYuL49q1ayQlJVGmTJlc97937x63bt2ievXqWFlZkZ6eTlhYGPHx8Vofs3DhQj7++OMc2yMjI0lKMs7iX2q1mpiYGBRFeWZBgdJG2kY7aRvtpG20k7aBJcG+PE7PWDdlsnNj7t+/X6B2eblaQ4Y7evDj9TP8HHaWxPRUDt0LpcvO5XRxdGOWR3uaOFQrjJdSJOSc0U7aRjtpG+2kbXKKi4vTaT+VYkL91lFRUXh7ezNz5kxmzZqV4/7U1FScnZ2ZOnWqJvlQq9W0aNGCJk2asHLlylyPm1vPiouLCw8fPsTOzq5wXswzqNVqIiMjcXJykpP2KdI22knbaCdto11pb5vEtBTcNi4gKjmR5pWcOdlvOiqVymDtEpkUz+JLB/kh0JekJ9ZkGeBSj0+aPEejisUvaSnt50xepG20k7bRTtomp9jYWCpUqEBMTEye38eN3rPypEqVKlG/fn0uXbqU6/13794lMjKS9u3ba7aZmZnRunVrTp06pfW41tbWWFtb59huZmZm1BNGpVIZPQZTJW2jnbSNdtI22pXmtvn12lmikhMBeLdBV8zNzTX3GaJdqpS1Y0nrgbzTsDMLLuzjf5lrsmwNv8LW8CuMdG/CR0164e1QucCvpSiV5nPmWaRttJO20U7aJjtd28ForZWSksK5c+eybbt16xZ+fn40atRIs23z5s18++23AFSvXp3y5ctz6NAhzf1paWn4+vri7e1dNIELIYQoNtLVapZcPgyAu21Fhro1LLTnql7Wnu/aDiF46CwmebTCXJXxJ/bP637U3/wF4w+vJTQuqtCeXwghSiKj9ayoVCqmT5+Ora0t9erV49GjR2zevJl27dplmyy/bds2Tpw4wbRp0zA3N+e7777jlVde4fLly9SqVYv9+/fz4MEDPv30U2O9FCGEECbq7xuXNAnCOw06Y2Fm/oxHFJyrbUVWdBjB7Ebd+NhvN39cO49aUfj12lnWhJ5nokcr3m/cAxdbh0KPRQghijujJSuWlpYcPXqUw4cPc/78eerVq8frr79O8+bNs+03ePBgWrVqpfn5xRdfpHPnzhw4cICoqCjef/99+vXrp3VyvRBCiNJJURQW+x8AoJJ1WV7yaFmkz1/HzpHfOo1hdsNufOS3m41hF0lT1Pwv6AS/hJzmVa+2zGnUjapl7QiOiWRl8GnC4qNxs63IRI+WeNg7FWm8Qghhiow+Z6VTp0506tRJ6/25lTF2dXVlwoQJhRiVEEKI4u7Q3WuceRABwBt121PWwsoocdSvUJUNXV/kfNQtPji/k23hV0lRp/PN1aP8HHSSLlVrsetWECqVCgUFFSoW+x/Ap/0IJhRxgiWEEKZGZvgIIYQokRZfOgiAjbkFr9dtn+e+RaFpJWe29pjE8X7T6FHdA4DH6ansuBWIGoV0RY1a+e//ScfWExL7wMhRCyGEcUmyIoQQosS5FH2HHbcCAJjo0QonG1sjR/SfNpVd2fPcFA72mUqNsvZa91OhwidIe6VLIYQoDYw+DEwIIUoSmXtgGr70PwiAmUrF2/W1DzU2ps5Va9Ohijt/Xr+AQs4lzxQUwuKjjRCZEEKYDklWhBDCQFYFn2LysQ2okLkHxhQe/4g1oecBGOrakNp2jkaOSDs324qYqVSk57I+swoVbrYVjRCVEEKYDhkGJoQQBhAcE8nkYxuyzTmQuQfG8fWVI6QpagDebdDFuME8w0SPlrn2qkBGNbNJnq1yvU8IIUqLfCcrN2/eZOnSpQwaNIgWLVrQokULBg8ezLJly4iIiCiMGIUQwuStDD6NClWu98ncg6LzKPkxPwWeAKBL1dq0dKpp5Ijy5mHvhE/7EZipVJirzLKdQb2cPaljwr1CQghRFHROVsLCwhg1ahS1a9dmxYoV2Nvb061bN7p164adnR3/+9//cHd3Z/To0dy4caMwYxZCCJOiKAonIm+Qnnk1P8f9MvegyPwUeJz4tGQA/q9hF+MGo6MJHi0JHDKLdxt0YYRbY6qVsQNg9+0gTtyXv6dCiNJN5zkrrVq1YtKkSQQEBFC7du1c9wkJCcHHx4eWLVty//59gwUphBCmSFEU9t4O5iO/3fjeD9O6n8w9KBrJ6Wl8deUIAA0cqtLb2dvIEemujp0jC1v0BeDKo7s03bKMFHU6Lx39k/MD38LGwtLIEQohhHHo3LNy+fJlFi5cqDVRAahTpw4LFy7k8uXLBglOCCFMkaIo7LkVRId/v6fX7v/lmahARs+KzD0ofL9fO8vdx3EAvNuwCypV7sPyTF09h6p81LQXAAEx9/nYb4+RIxJCCOPROVlxcsq79GZYWBiJiYk67SuEEMWRtiTF1sKaOY268U3rQZlzD/77kqwCfNqPkLkHhUytqPnS/xAANcraM8q9iXEDKqB3G3SheaUaAHzhf5AzD8KNHJEQQhiHXtXAzp49y7Rp0zQ/jx07Fnd3d6pWrYqvr6/BghNCCFOQMdwriI5PJSnlLKyY06gb14e/x4LmfZlWr0Pm3IOuVLIuC0D1snaMr9PCiNGXDtvCrxIQkzH8+M36HbEyL96V+S3MzFnVYSSWZuakK2peOvInyelpxg5LCCGKnF7JysyZMxk5ciQA/v7+bN26lRMnTvDuu+8yZ84cgwYohBDG8mSS0nPX/zj2RJIyu2E3wobPZUHzvjjalNM8JmvuwQdNegJwKzGW03JVvNB9kbkIpL2VDS97tjFuMAbSsGI13m/cHQD/R3f57MJeI0ckhBBFT69k5cyZMzRv3hyA3bt3M3jwYFq3bs1bb72Fn5+fIeMTQogip0uSsrBF9iTlacPcGmlKGa+77lcEUZdex++HcfTedQBe9WqLnZWNkSMynDmNutOkYnUAFl7cz/moW0aOSAghipZeyYqtrS1hYWEAbNu2jW7dugEQExODra2twYITQoiipCgK+24H02nHD3onKVmql7Wnc9VaAKy/fgG1lrLGouC+uHQQACszc6bX62DUWAzNMnM4mIXKjDRFzUtH/yRFhoMJIUoRvZKVYcOG0a9fPwYOHIifnx8DBgwAYNeuXfTp08egAQohRGF7MknpsesnzVX6chZWzGrYlevD39M5SXnSSPfGANxKjOHYvTBDhy2AoJhINt/MqEA5tnZzqpe1N3JEhtekkjNzGmVcFLwQfZtFl/YbOSIhhCg6eiUrS5cuZcaMGdSpU4d9+/ZRoUIFAAICAvjwww8NGqAQQhQWXZKURS364WSjX4/xULdGmKsyPmZlKFjhWOJ/CAUFgJkNOhs5msLzfuMeNHCoCsD8C/u4FH3HyBEJIUTR0KtcSp8+fdi7N+dEv8WLF9OjR49c7xNCFExwTCQ+QacIjLqDV6VqTPJshYe9lAnXh6IoHLgTwkd+uzmSmaBARpLyRt32vNOgs94JypOcbGzpUd2DXbcC2Rh2ka9bP4+FmXmBjysy3E2MZfW1MwAMdKlPXYcqRo6o8FiZW7Cq40jabPuW1MzFIk/0nybnkxCixNMrWdm3b1+u29VqNQcOHChQQEKInFYFn2LysQ2oUKEoCqq7QXxx+SA+7UcwwaOlscMrNrQlKWUtLHnDuz0zG3YxSJLypJHujdl1K5D7SfEcvHuNHtU9DXr80uzbq8c05XzfbdjFuMEUgRaOLvxfwy4svLifs1ERfOF/kDmNuhs7LCGEKFT5SlZCQkJyvQ0ZiYqvry/Ozs6GiUwIAWT0qEw+tgG1okDmcBeUjP8nHVtPhyrusuDgMxgjSckyuGZDppj9Rao6nXWhfpKsGEh8ajI/BGSs69XWyZX2ld2MG1AR+aBxTzbf8OdqzH0+Or+bgS71qV+hqrHDEkKIQpOvZMXDwyPX21lsbGz49ttvCx6VEEJjZfDpzBK4So77VKjwCTrFwhZ9iz6wYkBRFA7evcZH53dz+F6oZntRJClZHKzL0MfZm3/CL/P3jUv80HZIsV+w0BSsCDrJo5THQEavikqlMnJERcPGwpJVHUfSbvt3pKjTmXj0T471e0OGgwkhSqx8/cW8fj3jiqS7u7vmdhZLS0uqVKmChYX8ERbCkMLiozUTiJ+mKAph8dFFHJHpeXo+z0TPltxKjM01SXnduz0zG3SmcpnyRRbfSPfG/BN+mYcpj9lzO4h+LvWK7LlLolR1OssuHwbA086JgS71jRxR0Wrt5Mrb9Tvxpf8hTj0IZ9nlw7zbsKuxwxJCiEKRr8zCzc0NgLi4OFlPRYgi4mZbUWvPihqFiw/vEJWUQKV8ltUtKZ6ez8PdQD73zz53zlhJSpaBNetTxtySx+mprLvuJ8lKAa2/foGbCY8AeKdBZ8zN9CpsWax90rQ3/9y8QlBsJPPO72Jgzfp42Vc2dlhCCGFwOn/CBwQEEBAQAEBERITm59z+CSEMZ6JHy4wv4VpceXSP+pu/ZMsN/yKMyjQ8OZ8nXVGjRsmc25PBxtyCdxt04fqw91jcsr9REhUAW0tr+rvUBWDLzcs8Tks1ShwlgaIofOF/EIDKNra8WLu5cQMykjIWlqzsMAIVKpLT05h4dD3pall4VAhR8uicrNStW5e6detmu63tnxDCcDzsnRjq1lDzsxkqzFVmmKGiccVqANx7HMeg/b/wwqE/iEpKMFaoRS5jPk/uVMDLnq2NmqQ8aaR7EwDiUpPZESEXdfS153YQF6JvAzCjXkdsLCyNHJHxtK/izox6HQDwvR/GN1ePGjkiIYQwPJ2HgYWHh+d6WwhR+CIzExAHKxu6VHLDq1I1Jnu1pnb5Svx+7RzTT27mUcpj1oSeZ9+dEH5sO5RBrg2MHHXhuhEfzbrr50nX0uukUqk07WYK+taoi62FNfFpyay7fp4hTySgQneLLx0EMtbEmerd1qixmILPmvdha/gVrsVFMffsDga41JPqgEKIEkXnZKVGjRq53hZCFK641CTNyupjazVnrntbKleujFnmOP1xdZrTo7oHU3w3sjX8CvcexzF4/y+MqdWUb1oPKnFzWR4mJ7Lw4n6+uXpUs8ZGblSocLOtWISR5a2MhSXP16zPH6Hn2BZ+lfjUZGwtrY0dVrFy7kEE++4EAxm9ZhWsyxo5IuMra2GFT4cRdNmxnMfpqUw6up4DfV7FTFX65vEIIUomvUt3JSYmEhAQQHR0zkpEPXr0KFBQQoj/7L8dQpqSMRb9Oefc1+ioVtaOLd1fKtG9LElpqXwfcIzPLuzjYWbJ2rwoKEzybFUEkeluVK0m/BF6jsfpqWwNv8LoWk2NHVKxkjVXxVxlxpv1Oxo3GBPSuWptXvdux/cBvhy+F8oPV315I3N4WEkQHBPJyuDThMVH42ZbkYkeLfGwdzJ2WEKIIqJXsrJ7927GjBlDVFRUrvfnNRlYCJE/O25lzG+wNregS9XaxEc/ynU/lUqltZdldK2mfFtMe1nUipq1oX7MPbeDG/EPNdvbV3bji5b9CYyJZNKx9ZpqYCqVCgUFn/YjTG44TK/qnjhYleFRymPWhfpJspIP1+Oi2BB2EYBR7k1wNaFeM1OwqEU/tkdcJSz+IbPP/ktfl7rUKl/J2GEVWLZqfyioULHY/wA+7UcwwaOlscMTQhQBvfqJ33zzTSZPnkx0dDSKouT4J4QwDEVR2HkrEIDOVWpR1sLqmY/J6mX5rdNoKliVAWBt6HnqbfqCTTcuFWq8hrb3dhAt/vmasYfXaBIVL3snNnebwJG+r9O2shsTPFoSOGQWM+t3ZmA1L2bW70zgkFkm+UXGytyCIa4Zc1V23grgUfKze4hEhmWXj5Ce2cP4bsMuxg3GBNlaWuPTfgQACWkpTD66HrVSvKuD5aj298T/k46tJyT2gbFDFEIUAb2SlRs3bjBv3jwqVKhg6HiEEE8IiLmv+ZLeu4a3zo9TqVSMrd2cy4PfZUDmmh73k+IZsn81Yw79wQMTmniemwvRt+m9+2d67vof56NvAVClTHl+bDsU/0Ezed61QbYVy+vYObKgeR+WN+nPguZ9TK5H5UmjMquCpajT2Xyz9JWb1kdUUgI+wSeBjN6pxhWrGzki09StugdTvNoAcODuNf4XeMLIERVMRrW/3Ov9qVDhE3SqiCMSQhiDXsmKt7c3YWFhBg5FCPG0rF4VgD7OuicrWTRzWTqNydbLUt9Ee1luxj9k/OG1NN2yjF2Zr72chRUfN+1FyNDZTPFui4WZuZGjLJiu1WrjlDkc78/rfsYNppj4IcCXxMy1af5PVmrP0+IW/XEp5wDAu6e3cyM+57zS4uLKo7ua3rSnKSiEFePXJoTQnV7JytSpUxk/fjwHDhwgPDyciIiIbP+EEIaRtR6Hq20FvPScUKpSqXihdjMuD36XgS71gf96WUYf/N0kelkeJT9m1ulteP79Ob9eO4uCgrnKjKnebbk2bA4fNOlVYipnWZiZM8ytEQB7bgebRPubssdpqXybuX5I04rOdKtWx8gRmTY7Kxt+bj8cgPi0ZF4+trFYDs/ecP0Cu24Fab1fBSZV7U8IUXj0SlZefvllzp49S7du3ahZsyYuLi7Z/gkhCi4hNZlDd68BGb0qTw570ke1snZs7j4hWy/Luut+1N/0BX+HGaeXJTk9jaX+h6j910IW+x/UlCIe4tqQy4Nn8kPboVQxgQUdDS1rKFi6ouavzEnjInerQ05r1sv5v4ZdCvx7UBo85+zFRI+MSnh7bgexMrj4DJeKT01m4tE/GXHwN5LV2kuTpysKQ0pAlUMhxLPpVQ3s6tWrho5DCPGUQ3dDSVGnA9Db2csgx8zqZelWrQ6v+v7FP+GXuZ8Uz9ADqxnl3oRv2wzGsQgqhqkVNesyK3yFPVHhq11lN75o0Z92VdwKPQZj6lDFnepl7bidGMuf1/2YIosb5ipdreZL/0MAuNlW0PRIiWdb0nIAu24FcisxhrdPbeU5Zy9qZA4PM1WnI28y5tAaQuIyJs5XtC7LmFpN+SHAV1MNTP1EL9H4I+vY1esVXGwdjBSxEKIo6JWseHvnf+y8ECJ/skoWW5qZ0626YYe+ZPWyrAk9z7QTm3iY8ph11/3YfyeE5W2HFurq6vtuB/N/Z7ZxLuqWZpunnROft+jH8zXrl4or52YqM0a4NearK0c4eDeUO4mxVCtrZ+ywTM7mm/5ci8sokf92/c7Ffr5SUXKwLsP/2g2j314fYlOTeOXYRrb3nGSSv1/pajWL/Q/wwbldmjWlulWrw68dR+Nczp4Z9TriE3SKsPhoXMo5cOXRPbZHXOVqzH3abf+W3c+9Ql2HKkZ+FUKIwqJXsuLn55fn/U2aNNHnsEKIJ+yMyJhg3qGyG+UtbQx+/Kxelu7V6vDq8b/YcvO/XpaR7k34zsC9LBejbzPrzPZsRQOqlCnPR016MsmzNZal7IvoqFpN+OrKERQUNoRdYHo9WeTwSYqisPjSASDjCvtEEyxFber6utTlxdrN+fXaWXbcCuDXkDOMN7F2DI9/xLgjazh0NxTIuDjzWbPevNOgM2aqjJHqdewcWdiir+YxakXNmyf/4durR4lIjKHDv9+zvcck2lR2NcprEEIULr2SlaZN817IrDhO5hPClITEPtAMhchPyWJ9VC1rx6ZuE1gbep5pJzcTnZzIn9f92H8nmOVthzK0gENvwuMf8cH5nawOyZg4DxkVvt5t0IV3GnQuMRPn86uVY03cbCsQFv+QP69LsvK0I/dCOfUgHIDXvdtRrpSeJwW1rPXz7L4dxN3Hcbx56h96OntSvay9scMCYGPYBV45tpGHKRnrDXnaObGm8ws0d6yR5+PMVGZ83fp5qpYpz9xzO4hOTqT7rh/Z2PVF+tSoWxShCyGKkF4T7CMjI7P9u3fvHkePHqV58+asWrXK0DEKUerszKwCBvqVLM4vlUrFmNrNuDxoJs/XzKgYFpmUwLADvzLywG9EJsXn+5iPkh8z+8x2PP9exC8hZzQVvl71akvI0Nl82LTkVPjSh0qlYmTmRHvf+2HFusRsYVh86SAANuYWvFG3vVFjKc4qWpflx7ZDAXiU8phXff8y+gXF+NRkJh1dz/ADv2kSlZc9W3Nu4JvPTFSyqFQq3mvcnZ/bD8dMpSIxLZWBe1fxx7VzhRm6EMII9OpZcXTMueBa5cqVWb16NePGjWPChAk6H8vf3589e/YQHx9P/fr1GThwIBYW2sOaO3cuycnJOba3bt2a4cOH6/y8QpiyrPkqzmXtaVChapE9b1Yvy7rrfrxxYhPRyYmsD7vAgbshOveyJKen8UOAL/Mv7CU6OVGzfXDNBixs0Rcv+8qF+RKKlVHuTfg8c6jT+usXeFfWEAHg8sO7bI/IKOQyoU5LKpfAinBF6XnXBoyu1ZS1oefZGn6FNaHneaF2M6PE8vQk+gpWZVjRfoTe8+Qme7bG0bocow79TnJ6GmMPr+F+Ujxv1e9kyLCFEEakV8+KNjVr1iQoSHtd9KfNmjWLl156ibt375KUlMSsWbNo1aoVcXFxWh9TpUoVqlatqvmnUqlYsmQJ9+7dM8RLEMLoktJSOXAno2Rxb2evIp8Qq1KpGF2rKZcHzWRQzYzSoE/3sgTHRDLnzL+MPvg7c878S3BMJGpFzdrQ83j//Tlvn/pHk6i0dXLlaN/X+bv7BElUntK4YnU87TLWz/nz+gUjR2M6vvQ/CGSsUv5Og87GDaaE+Kb1ICrb2AIw/eRm7ibGFunzp6vVLLq4n3bbv9MkKl2r1ubioHcKXNBjkGsDdvV6GbvMuX1vn/qH2We2G70HSQhhGHr1rCQlJeXY9vDhQxYtWkTt2rV1Ps64ceP4/PPPNT+/+eabVK1alW3btjF69OhcHzN9+vRsPy9atIgyZcowduxYnZ9XCFN25N51HqdnrNbdu4ZhShbro2pZO/7uNj5HL8uOiKvEp6VgpjJDQUGFisWXDuBSzoEbCf+VIfa0c2JRi74MqtnAJCsQmQKVSsWoWk34xG8PZ6MiCI6JxEPPxT9LilsJMfwReh6AIa4NqGOXsydf5J+jTTl+aDuEYQd+JTo5kddPbGJj1xeL5HczIuER4w6v5WDmulEWKjPmN+vNzAZdMDczzDXTzlVrc7jva/Te/TN3H8fx+aUD3E+K53/thkkVOSGKOb0+JcqUKZPjX/Xq1Vm/fj3ffvutzsdp0CD7gk7JyckoioKDg4POx1i5ciXDhg3L12OEMGVZQ8DMVWb0qOZp1Fhy62WJS0tBIWNBQ7WiZPyPoklUKtvYsrztEPwHz2Swa0NJVJ5hpHtjzW3pXYGvrxwhNXN9oXcbdjFuMCXMULdGDM8cyvn3jUtsCCv88+2vsIs02rxEk6h42DlyvP80ZjXqZrBEJUvjitU51u8N6pTPSHBXBZ9myP7VJKalGPR5hBBFS6+elSNHjuTYVqFCBerUqYO1df4mzAYGBvLzzz8TGxvLkSNH+Pjjj+nTp49Ojz18+DDBwcH4+PjkuV9ycnK2eS6xsRnd32q1GrVana94DUWtVqMoitGe35SV9rbJmlzf1qkmdpbW2drBWG1T2caWjV3GMXj/L2yN0L4obPvKbmzvMVFTarko4yyu5423XWUaVqjKpYd3+fO6H+816mbw5ygubROT8pgfA48D0KmKOy0ruRRqzMWlXQzpm1aDOHDnGg+SE3j9+CY6V6mFU+bwsCcVtG3iU5N56/Q/rAw+rdk20aMly1oOxPapzzVDcitXgcN9ptJvrw/no2+zNfwKvXb9jy3dJlDBuqxBnqM0nje6krbRTtomJ13bQq9kpUOHDvo8LFfW1tZUrVoVCwsLUlJSOHv2LAkJCZQr9+z1HXx8fPD29qZjx7xLfi5cuJCPP/44x/bIyMhch7QVBbVaTUxMDIqiYGbgq0vFXWlum/DHMVyNuQ9Ae/sa3L9/P9v9xm4b83QFM1SoyTkW3AwVTuY2PH4Yy2OKdjw8GL9tCqKfUx0uPbyL/6O7HLl2Ba/yhh36VFza5ofQU8SlZlxYerlGkxznv6EVl3YxtE+9uzL1wjYeJCcw5fCf/NhkQI59CtI2fjF3ed1vO6GJGb2tDpY2fNGgF/2repL4MIbEZzy+oFTAn82GMvH8Fo5G3eTY/TA6bPuONS2HUs2m4MUaSut5owtpG+2kbXLKa476k/RKVgzJzc2NmTNnAjB79mw8PT35+uuvee+99/J8XGxsLBs3buTTTz995nPMmTOHt99+O9tjXVxccHJyws7OOKtGq9VqVCoVTk5OctI+pTS3zabAUM3tYV7NqFwp+4R0Y7eNV6VqqO4GQS4TV1UqFV6VqlG5snEm0Ru7bQpiok17FgUdBWBvbDgda9cz6PGLQ9skp6fhc9APgPoOVRhVv7VmUcDCUhzapTC87OTErodhbL7pz5Y7gYz1asUQ1+yT3PVpG7Wi5kv/Q8w7/99K9F2q1uKXDqNwKedg6JeRp8rA7qqvMu7IWv66cYmA+AcMPrWeHT0nFbjQR2k9b3QhbaOdtE1ONja6LXht9GTlSQ4ODtStW5crV648c9+1a9eSlpbGiy+++Mx9ra2tcx2eZmZmZtQTRqVSGT0GU1Va22bX7YzV3Svb2NLMsUauX9aM2TaTPFvxxeWDud6noDDZq7X8TunBw8GJFo41OPMggj/DLvBJs94Gn+tj6m2z7poftx9n9MjNbNAFC/Oi+fNk6u1SWJa3HcLhe6GayfZdq9Whkk32EQ35aZuIhEe8eHgtB56YRP9ps968a8BJ9PlVxsyKP7uMY9rJTSwPOM6NhId02rGcf3tOoqVTzQIdu7SeN7qQttFO2iY7XdvBaK2VkpLCiRMnsm27ceMG58+fp2nTppptGzZsYMmSJTke7+Pjw+DBg3Nd80WI4iglPY19t0MAeM7Zq9CvKuvDw94Jn/YjMFOpMFeZZfvfp/0IqdxUAKMyF4gMjn3A+ahbxg2miGVdkQeoXtaOMbWaPuMRoqCqlrXj69bPA3A/KZ4ZJ7fofay/wy7RaPMSTaLiYeeIb783mF0Ik+jzy9zMjO/bDOGjJr0AeJCcQNedP7Lnlu7LLAghjMtgnyJhYWEkJuo+ElWlUvHee+/RpUsXXnvtNcaMGUOjRo3o0aMHr7/+uma/Xbt2sWrVqmyPvXTpEqdPn+bll182VPhCGJ3v/TDi0zLG6/epUfir1utrgkdLAofM4t0GXRjh1ph3G3QhcMgsJni0NHZoxdoItyaa239e9zNaHMbwb0QAVx5lrJX1Zr2OWBVRr0pp90KtZvR3qQvAH6Hn2Hrzcr4en5CazMvHNjD0wGrNSvQTPVpxbuBbBe65MCSVSsWHTXuxvO0QVKhISEuh314f1mWWyBZCmDa9kpWzZ88ybdo0zc9jx47F3d2dqlWr4uvrq9MxLC0t2b9/P4sXL6Zx48b07dsXX19f/v7772xj2EaMGKGZ05IlKSmJZcuW0a2b4avmCGEsOzKrgKlQ0bO6cUsWP0sdO0cWtujL2i5jWdiir/SoGICLrQPtK7sBsO66X6la0O6LSwcBsLO04RWvNkaNpTRRqVT82HYY9lYZf3On+P7Fw2TdLjqefRBBs3++YkXQSQAcrMqwoes4fDqMwNYyf1VBi8qr3u1Y33UsVmbmpKrTGXNoDd9eOWrssIQQz6DX5auZM2dqJrb7+/uzdetWTpw4we7du5kzZw6HDh3S+VitWrWiVatWWu/v1atXjm0tW7akZUu5iitKlp23MuartHJywdHm2dXwRMkzyr0Jx+6HcTPhEScib9A2M3kpyU5G3uDwvYzCElO82mBvVcbIEZUuzuXs+arV87x09E/uPI7lrVP/8EvHUVr3zxqy9/65nZr1cDpXrcVvHcfgYutQRFHrb5hbYypalWXQ/l+IS01m+snN3E+K55Omz8maUEKYKL16Vs6cOUPz5s0B2L17N4MHD6Z169a89dZb+Pn5GTI+IUqFWwkxXHx4B4DezsZbtV4Y1zC3RphlfmEqLQtEZvWqWJqZM6Ne3mXoReEYX6cFfZwzhp6uDjnDDi1rKd1KiKHnrv8x68x2UtXpWKjMWNC8D/uee7VYJCpZulX34GDvqVTOXF9m/oW9TPHdSFpm8iWEMC16JSu2traEhYUBsG3bNs1wrJiYGGxtcy4uJYTI267MXhUw7fkqonBVLWtHl6q1AVh//QLpJXzxsOCYSP6+4Q/A2NrNcC5nb+SISieVSsVP7YZRPnP41svHNhKTOQcly6Ybl2i0ZQn772QUAalTPmMS/ZxG3Y0+iV4fzRxrcKzfG7jbVgTg56CTDD/wG0lpqUaOTAjxNL0+YYYNG0a/fv0YOHAgfn5+DBiQsaDUrl27dF59Xgjxn523MuarVLQuS4tKLkaORhhTVlWwO49jOXIvNO+di7kllw+hZC4wOrNBZyNHU7q52DqwpGXG3/JbiTF02fkjU/228e7pbYw88BtD9q8mOnM+y0seLTn/vGlNotdHHTtHjvV7g8YVqwOw+aY/vff8nCNRE0IYl17JytKlS5kxYwZ16tRh3759VKhQAYCAgAA+/PBDgwYoREmXpk5nz+1gAHpV9yyWVymF4QxxbYhFZtnqkjwU7N7jOH4JOQNAf5e61HOoauSIxGTP1tRzyFgw8eLDO2y5E8DSK4dZH5ZxHjpYlWF9l3Gs7DDSZCfR51e1snYc6jOVTlVqAXDobiiddyznTmKskSMTQmTR61uRpaUlM2bMYOnSpdnWRFm8eDEuLnJVWIj8OBl5k0eZV/JkCJioZFNOUw1uY9hFzSTmkua7q8dITk8D4N0GXYwbjAAgJPYBAY8iNT8/XY9uS/cJDHdvXLRBFQF7qzLs6vUyg2s2AOBC9G3ab/+OkNgHRo5MCAEFWGclISGBLVu2sGzZMs22oKCgUlVuUwhDyCpZDBmLQQoxqlYTIGMBu6w5AiVJfGoy3189BkBrp5p0zLyqLYxrZfBprRWxzFVm7IgIzPW+ksDGwpINXV/kZc/WAFyPj6b99u849yDCyJEJIfRKVoKCgqhfvz5Tpkzh7bff1mz/9NNP+fPPPw0WnBClQVbJ4maVnKlSpryRoxGm4Pma9bEyMwdK5gKRK4NPaRYRfLdBFykZayLC4qM1c4iepqAQFh9dxBEVLXMzM35qN4z3G/cA4H5SPF12Lmd/5jBdIYRx6JWsvPnmm4wYMYI7d+5k2z5jxgy+/PJLgwQmRGlw73EcZ6Myrtz1dpYhYCKDvVUZ+tbIWFn87xuXNMOlirvgmEhmnd7GnLP/AlCzXAUGZQ69EcbnZlsRFbknjipUuGVWzirJVCoVnzbrzTetB6FCRVxqMn32rGBjWMmdPyZKl+CYSOac+ZfRB39nzpl/CY6JfPaDjEyvZOX48eO89957Oa6GeXt7c+nSJYMEJkRpsPtWkOa2zFcRT8qqChaTksTuW8V/+M2q4FN4b1rMl/6HSMwsDxue8JDfrp01cmQiy0SPlnn2rEzy1L6Ac0kzrV4H1nQeg6WZOSnqdEYc+J3lAb7GDkuIAsn6HP7C/yDrwy7whf9BvDct5pfg08YOLU96JStqtZqUlBSAbAlLWFgY9vZSJ18IXWWVLLa3sqFNMS8DKgyrv0tdylpYArCumA8FC46JZPKxDagVBfUTX4YVYNKx9TKR2UR42Dvh034EZioV5iozzMj8X6XCp/0I6tg5GjvEIjWqVlO295hEOQsrFBReO/430078zZyz/zLVbxvvnd1RLK5KCwHZP4fTFXW2/039c1ivZKVnz56a4V5ZycqDBw+YPn06vXv3Nlx0QpRg6Wq1ZjHIHtU8sMicoyAEQDlLawa41Adgy83LJKalGDki/a0MPp3n8CKfoFNFHJHQZoJHSwKHzGJm/c4MrObFzPqdCRwyiwkeLY0dmlH0dPbkQO9XcbQuB8B3V335wv8g/9wJ5MvLh4rFVWkhIOtzOHem/jmsV7KyZMkSNmzYQN26dVEUha5du+Lu7k5YWBiLFi0ydIxClEhnoyKIylxkTYaAidyMzCwTm5CWwr8RV40cjf7C4qO1VoosDRO3i5s6do4saN6H5U36s6B5n1LXo/K0lk41+b3zaM3PCqCm+FyVFgLg1IObpBfTz2G9khVXV1cuXrzI9OnTeemll3Bzc2PBggX4+flRvXp1Q8coRIkkJYvFs/Rx9qZ85uJ760L9jBtMAdQs55Bt+NeTSsvEbVG8HbwTirmWqnWmflValG6KovDlpYMcyKMMvql/Dlvo+8Dy5cszdepUQ8YiRKmSVbK4YYVq1CjnYNxghEmysbBkcM0G/HrtLNsjrhKXmkR5Sxtjh5Vv8XkMYSttE7dF8ZRR1jl3pn5VWpReMSmPmXh0PX/fyLv4lal/DuucrAQEZFwF9vb21tzWxttbhrQIkZeopARORt4EoLf0qog8jHRvwq/XzpKUnsY/N6/wQu1mxg4pXw7dvcaPgcc1P5urzFBQUKFCQSmVE7dF8fNfWeecKYupX5UWpdPF6NsM3f8rIXEZQxTdbSvyYp3mfHphr+bzt7h8DuucrNStm1HzX1EUzW1tZBV7IfK253aQpkSozFcReelR3YOK1mWJTk5k3fXzxSpZiU5OZOyhNagVBRtzC/7q+iJH7oURFh+Nm21FJnm2Muk/kEJkmejRksX+B3K9z9SvSovS57eQs0zx3cjj9Iwy8f1q1OW3TqOpYF2WsbWb4xN0qlh9DuucrISHh+d6WwiRf1lDwMpZWNG+sptxgxEmzcrcgqGuDfk56CS7bgXxMDmRCtZljR3WMymKwuSj64lIjAFgaauB9HWpR1+XekaOTIj8yyrrPOnYelSoSFfUmvuWtx1q8l/2ROmQnJ7Gmye3aHqzzVQqPm3am9mNumKmypimXsfOkYUt+hozzHzTOVmpUaOG5vaJEycYNmxYoQQkREmnVtSaZKV7NQ+szPWeOiZKiZHuTfg56CSp6nQ23fBnYjG4ivtT4HE23fQHYFDNBrzq1dbIEQlRMBM8WtKhijsrAk+yPyKQ049uA2AtZeeFCQiLi2b4wV858yACAEfrcqzt8gI9qnsaObKC06sa2OjRo1Gr1c/eUQiRw4XoO9x7HAdAnxoyX0U8W5eqtalSpjxQPBaIvPzwLm+d+gcA57L2rGg/PNsCwkIUV1llnf9qPZKqmb+Ty5+YkyVMQ3BMJHPO/Mvog78z58y/JX7xzp0RATTf+pUmUWnr5Mr5598qEYkK6JmseHh44O/vb+hYhCgVnixZ3NtZ5quIZzM3M2O4WyMA9t0J5n5msmuKHqelMurg7ySlp6FCxR+dx1DJppyxwxLCoCzNzJnkkdHDeTLyJucyvyQK41sVfArvTYv5wv8g68Mu8IX/wRK7eGe6Ws1H53fRd48P0Znrtk2v24GDfaaWqCqjeiUrb775Ji+88ALbtm0jNDSUiIiIbP+EENrtvJVZWc++Mm7lpYKM0M1I9yYAqBWFv55RhtKY3j29Ff9HdwGY27g7navWNnJEQhSOlz1bY5bZYyi9K6YhOCaSycc2oFb+W7SzpC7e+SApgb57VvCx3x4UFMpZWLG28wt83WZQiRterleyMmXKFPz9/RkwYAC1a9fGxcUl2z8hRO4eJT/G9/4NQEoWi/xpV9mVGmXtAdNdIHLLDX++D/AFMoYhfNikp5EjEqLwuJRzYEBmwYg1oed4lPzYyBGJlcGnM0tM56SCErN456nImzT7Zxm7bwcBGRc/Tw2YzqhaTY0cWeHQK/W6evWqoeMQolTYdydYU0Wmt5QsFvlgpjJjpHsTllw+xJF717mVEINzOXtjh6VxKyGGicfWA2BvZcOazi9gIROPRQk31bsdW25eJjEtlV+vnWF6vY7GDqlUC4uPRq3kPqc6XVFYd92PF2o3pUGFakUcmWEoisLyAF/ePPUPqep0ILMAS/thxXLBYF3plazIoo9C6CerClgZc0s6V6ll5GhEcTPSvTFLLh9CQWFD2AXerN/J2CEBGeOmxx5eoxkz/VPbYTLEUZQKPat7ULt8Ja7FRfFjwHGm1e0gxSSMRK2oCY2LymXZzv+ExUfTcPMS+jh7827DLnSpWrvYvF8JqclM8f2LP0LPAWChMmNJqwGl4pzTaxgYQEJCAlu2bGHZsmWabUFBQbIgpBBaKIqimVzfpWptbCwsjRyRKG5aOLpQq3wlwLSqgn1+6QAH714DYKJHK0bWamLcgIQoImYqM01Z7qsx9zmU+XsgilaqOp3xR9Zx6oFu6wDuuBVAt50/0mrb16y/7kdaZi+FqQqMuU/rbd9oEhXnsvYc6vMa0+t1LPGJCuiZrAQFBVG/fn2mTJnC22+/rdn+6aef8ueffxosOCFKksuP7nIrc4E8WbVe6EOlUjHSvTGQUYHoelyUkSOC4/fD+OD8LgC87J34pvXzRo5IiKL1kkdLrDMnNP+QOWdLFJ341GQG7F3J79cyvshXsSmPGSrMVWaYqf77f1WHkQQPnc1U77bYZL5fZx5EMPLg73j+9TnfXTlKQmqyMV9Krv4Ku0jLrV9z+dE9ALpVq8O5gW/SroqbcQMrQnpXAxsxYgR37tzJtn3GjBl8+eWXBglMiJIme8limVwv9DMqsyoYwPrrF4wXCBCT8pgxh/4gXVFjZWbO2s5jKWdpbdSYhChqlWzKMdIt4yLCphv+3EmMNXJEpUdkUjzddv7Irswh1q0cXfAfPJPAobN4t0EXRrg15t0GXQgcMosJHi2pY+fID22HcnPE+3zYpCeVrMsCcD0+mmknN1Nzw2d8cG6nSZSHT1WnM/PUVoYd+JW4zCTqvUbd2d3rFSpnrvFTWuiVrBw/fpz33nsvR9eTt7c3ly6ZbklNIYwpa75K7fKV8LB3MnI0orhqWKEade0rA8YdCqYoCq/6/kVY/EMAPm/Rj6aVnI0WjxDGNNW7HQBpipoVQSeNHE3pEBYXTfvt33E6c+hXb2cv9vd+FUebctSxc2Rhi76s7TKWhS36UsfOMdtjnWxs+ajpc9wc8T7ftxmsGV4bnZzIpxf24rrhM1713Wi0xSRvJ8bQbeePLLl8CMgoWvJP95f4rHkfzM30nsFRbOn1itVqNSkpKQDZEpawsDDs7U2nOo0QpiIuNYkj964D0qsiCiZjKFgTAPyibxMYc98ocawOOaNJlvo4ezNDqiCJUqy1U02aVsxI1v8XeMLk50AUdxejb9Nu+3cEZ66bMq52c/7pMTHfPbtlLax4rW57gobMYn2XcbR0zFh+Iyk9jZ8CT+D192KG7PuF4/fDDP0StDp09xrN/vmKo5nfGZpWdObcwLcYULN+kcVgavRKVnr27KkZ7pWVrDx48IDp06fTu3dvw0UnRAlx4M41TZlBKVksCmrkE0PB/jRC70pQTCRvnNgEQJUy5fml48hSMclTCG1UKhVTvTMm2kckxrA9XJZ4KCyH7l6j478/cOdxxnC7dxt04ZeOI7EsQKl0czMzhrs35mT/6RzsM5V+NeoCoKCw6aY/7bZ/R4ft37Hlhr/W0sgFpSgKiy8doPvOn7iXOQxtkkcrjvV7Q9PzU1rplawsWbKEDRs2ULduXRRFoWvXrri7uxMWFsaiRYsMHaMQxV7WqvVWZuZ0lRW9RQF5O1SmScXqQMYCkUVZhTE5PY1RB38nIS2jd/3XjqNK3fhpIXIzplZT7DLXupCJ9oXj77BLPLf7Z2JTkwBY0nIAi1v2x0xlmKFRKpWKzlVrs63nJC4PnslLHi01SdCx+2EM2v8L9TZ9wc+BJ0hKSzXIc0LG/L8h+1cz68x20hU11uYWrGg/nBUdRlBGKofql6y4urpy8eJFpk+fzksvvYSbmxsLFizAz8+P6tWrGzpGIYq1J0sWd6paSyYgC4PI6l25GnMf/4d3i+x53zv7L+ejbwEZVzR7ybBGIQAoZ2nN+DotANh9O4iQzCFKwjB+DPBl2IFfSU5Pw0Jlxu+dxvB2g86F9nz1HKqyssNIwoa/x6yGXbG3ykhEA2MiecV3I24bF/DZhb2a9aX0dSH6Ni3++ZrNN/0BqFW+Esf7TWOSZ+sCv4aSQu9UtHz58kydOhUfHx9WrVrFgAEDsLDQa41JIUq0oNhIzSTkPs4yBEwYRlYJYyi6ifY7IwJYevkwAC0cazC/mQz7FeJJr3q30dz+KfC4ESMpORRF4cPzu5h6/G8UFMpZWLGt5yReqN2sSJ6/ell7FrXox83h77Ok5QBqlM2Ym33vcRzvn9tJzfXzmXFiM2Fx0fk+9urg07TZ9g0hcRmJ7QCXepwZMEOKlTxFr2Tl7NmzTJs2TfPz2LFjcXd3p2rVqvj6StenEE/KVrK4hlyFFobhXr4SrZ1qAhnJSmEPBbv3OI7xR9YBYGthzZpOL2BlLheohHhSPYeqdK5aC4CVwad5bMChQqVRmjqdV33/4hO/PQA4WpfjQO9Xec4IPbp2Vja83aAzocPf47dOo2lUoRoACWkpfHP1KHX+WsSYQ39wPurWM4+VlJbKlGMbmXD0T5LS0zBTqVjQvA+bu0+gQmY5ZfEfvf7SzJw5k08//RQAf39/tm7dyokTJ9i9ezdz5szh0KFDBg1SiOIsq2RxzXIO1LWvYuRoREky0r0JJyNvEhoXxdmoCFpkVrIxNLWiZvyRddxPigfg+7aDpfy2EFq85t2OQ3dDiU5OZEPYBV7MHBom8udxWipjDv2hGR7lZluBXb1ewdPInz2WZuaMrd2cF2o1Y8/tIL7wP8je28GkK2rWhp5nbeh5ulfz4N2GXehV3ROVSkVwTCQ+QacIjLpDlfIOHLl/nSuZizw62ZRjXeexdKvuYdTXZcr0SlbOnDlD8+bNAdi9ezeDBw+mdevW1K9fXxaFFOIJiWkpHLx7DYDezt5SMUkY1Ai3xrxzaisKCutC/QotWVl2+bBm0bUXajVjXO3mhfI8QpQEg2o2oEqZ8tx7HMcPAb6SrOjhUfJjBu5bqSn537hidXb0nEy1snZGjuw/KpWKXs5e9HL24nzULb7wP8j66xdIV9TsuxPMvjvBNKpQjVaONVkZcgoVKtSKGuWJ9dTbOrmyoeuLOJeTZT/yotcwMFtbW8LCwgDYtm0b3bp1AyAmJgZbW1uDBSdEcXfo7jWS09MAGQImDM+5nD0dqrgBGSWMC6Ok5tkHEcw5uwPImPj5Q9shknQLkQcrcwsme7QC4GTkTZ2GBYn/3EqIoeO/32sSlS5Va3Ooz1STSlSe1rSSM2s6v0DI0NnMqNeRchZWAFx8eIcVwSdRKwrpiponB+uqgBXth0uiogO9kpVhw4bRr18/Bg4ciJ+fHwMGDABg165d9OnTx6ABClGc7YzIuBptoTKjezXp4hWGNyqzKlhEYgzH798w6LHjU5MZfeh3UtXpWKjMWNN5DHaZFXGEENq94tUGs8ykfrmUMdZZwKP7tNv+Lf6PMiocDnNrxI6ek7G3KmPkyHTjVr4iX7V+npsj3uezZn0om5m05MZMZcZv184VYXTFl17JytKlS5kxYwZ16tRh3759VKhQAYCAgAA+/PDDfB3r7NmzLFy4kLlz57JmzRpSUlJ0etz+/ft5//33WbBggaaXRwhTsyNzfZX2VdzkS54oFMPcGmm+FBm6Kti0E5s0K0R/2qw3rZ1cDXp8IUqqmrYV6F+jHgB/hJ4jJuWxkSMyfScjb9Dh3++4mfAIyJj7s67zWGyK4TojFa3L8l7j7vSr4Y22fmgFhbD4/FcQK430SlYsLS2ZMWMGS5cupWnTpprtixcvxsVF9zHTb731FjNmzCApKQkbGxvmz59P8+bNiYmJ0fqY9PR0Ro8ezZgxY1AUBUVRGDx4MFeuXNHnpQhRaK7FPtB80ZOSxaKwVC5Tnm7V6gCwIewi6WrDDAVbG3qeX0LOANC9mgf/17CLQY4rRGnxWt12ACSmpfJryFkjR2PadkRcpdvOH4nKXLPkk6bP8V2bwZibGWaxR2OpXd5R64KVKlS42VYs4oiKJ53PgtGjRxMcHPzM/YKCghg9erROx3zttdc4evQoH3/8MfPmzePo0aNcvXqV7du3a33MN998w7Zt2zh+/DifffYZc+fO5ejRozg5SWUaYVqyqoAB9K4hyYooPFlDwe49juNQZkGHggiNi+JV37+AjFKhv3YaZbAVooUoLXpW96B2+UpAxlCwwi4vXlz9GnKGAXtXkZiWiplKxf/aDWNek54lYm7cRI+WKOT+visoTPJsVcQRFU86//Vp0qQJLVq0oGfPnnzzzTccO3aMkJAQgoODOXLkCEuXLqVLly60aNGCxo0bP/uAgIdH9jH8cXFxqNVqKlWqpPUxP/zwAy+88ALu7u6abeXKlZNkRZicnZlDwKqVsdPUYxeiMAx2bYilmTlQ8KFgqep0xhz6g9jUJABWdRxJ9bIyAVSI/DJTmTHFK2ORyKsx9w1yIaEkURSFLy4dYPyRdaQramzMLfir63he9mrz7AcXEx72Tvi0H4GZSoW5ygwzMv9XqfBpP4I6do7GDrFY0Ll08axZs3jppZf48ccf+fHHH7l69Wq2++vVq8fo0aPZsGFDvhKHq1ev8v333xMbG8uJEyf4/PPPee6553LdNzY2lpCQED744APWrVvH2bNnqV69OsOHD6dGjRpanyM5OZnk5ORsxwFQq9WoDTRkIr/UajWKohjt+U1ZSWibpPRU9t8JAeA5Z0/NkMWCKgltU1hKc9s4WNrQs7oH/0YE8NeNS3zbepAmeYH8tc2H53ZxMvImANPqtqevs3eJbdPSfM48i7SNdvlpm/G1WzDv3C6S1Wn8EOBLpyq1iiBC49G1bdSKmnfPbOerK0cAcLAqw+ZuE+hYxb3EnXMv1m5OOydXzTorXpWqMcmzFXXsHEvca80vXV+/StHzG1R0dDQRERGoVCqcnZ2pWFG/cXc3b97kn3/+4cGDB6xbtw43Nzc2bNhA+fLlc+wbERGBi4sLdevWxcPDg/bt23Py5El27tzJ7t27ad++fa7P8dFHH/Hxxx/n2B4UFJTr8xQFtVpNTEwM9vb2mBXzMZmGVhLa5vCDG4w8vQGAn5r0Z2A1wwwDKwltU1hKe9tsvHWFaRf/BeD3FkPo7vTflyJd2+Zo1E1GnFqPAtQv78S2ti9gU4JXqS/t50xepG20y2/bTLvwLxtvX8FCZcbZrlOobF2uCKI0Dl3aJkWdzpsXd7DpTsbog6rWtqxtORTv8iV7hIz8TuUUFxeHp6cnMTEx2NlpL02td7JSGGJjY/H09OT1119n3rx5Oe6PiYnBwcGBHj16sGfPHs32/v37k5CQwIEDB3I9bm49Ky4uLjx8+DDPxilMarWayMhInJyc5KR9Sklom3dPb2PplcOYqVTcH/khFazLGuS4JaFtCktpb5vYlCSqrf+EpPQ0xtVuzi8dRmru06VtHiQl0PSfZdx+HEsZc0tO959OXYcqRRW+UZT2cyYv0jba5bdtjt+/QYcd3wPwSZPnmNu4e2GHaDTPapu41CSGHfiNvXcy5kB72Tmxo+dkXG0rFHWoRU5+p3KKjY2lQoUKz0xWTOqSmZ2dHV5eXgQFBeV6v729PTVq1MhWgQygadOm/P7771qPa21tjbW1dY7tZmZmRj1hVCqV0WMwVcW9bXbezphc38bJlUplDLtQanFvm8JUmtvGwaYsfWvU5e8bl9hy8zIp6vRsJT/zahtFUZjsu4HbjzOGyH7d+nnqVywd86xK8znzLNI22uWnbdpVcaNJxer4Rd/m5+CTzGncDYsnhmmWNNra5v7jOPru8eFsVASQ8fdxW4+JVLIpuT1NT5Pfqex0bQejtVZKSgqHDh3Kti0kJIRz587RvHlzzbY1a9awYMECzc9jxoxh//79pKVlrAqenp7Ovn37ciQwQhjLzfiHXHl0D5CSxaJoZVUFi01NylaN7ll+CPBla3hG+fdhbo2Y7Nm6MMITolRSqVRM9c4oYxye8Ijt4Vef8YiSJzQuivbbv9ckKv1q1GXvc6+UqkRF6M9oyYpKpWLRokW0adOGiRMnMmTIEJo0acKAAQOYOnWqZr/9+/ezZs0azc/vv/8+1tbWNG7cmIkTJ9K0aVMiIyNZunSpMV6GEDlkL1nsZcRIRGnTz6Uu5TJXTNa1KtjF6Nu8c3orADXLOfC/dsNKRMlQIUzJmFpNKW+ZMcJjeeBxI0dTtPyibtFu+3eExGWsOza+Tgs2dZ9AOcucI16EyI3RhoFZWlqyY8cOLl68yPnz5ylXrhyLFy+mTp062fZ74YUX6N79v/Gd5cuX5/Dhw+zfv58bN24watQounTpgpWVVVG/BCFytTMiY9Kgk005mlVyNnI0ojQpa2HFwJr1WRt6nq3hl0lITc7zC0FiWgqjD/1BcnoaZioVf3R+wWDzq4QQ/7G1tGZ8nRZ8d/UYu24Fci32AbVLQdnaA3dCeH7fKuJSM+YNz27YjQXN+8gFEZEveicriYmJBAQEEB0dneO+Hj166HycRo0a0ahRI633d+3aNcc2c3NzevbsqfNzCFFUUtLTNBMHn3P2koX0RJEb5d6EtaHnSUxLZVv4VUbWaqJ137dP/aMZsvhB4550qOKudV8hRMG86tWW764eA+DHwON80XKAkSMqXBuuX2Ds4TWkqNMBWNZqIG/W72TkqERxpFeysnv3bsaMGUNUVFSu95tQgTEhitTxyBuaK0i9Zb6KMILnnL2wt7IhJiWJddf9tCYrf4dd4qfAEwB0rOJeoisUCWEK6leoSueqtTh0N5RVwaf5tGnvbEUwirvgmEjNWiIJpLMn88KdpZk5qzuOYnQtmVss9KPXZd8333yTyZMnEx0drVns7sl/QpRWOyMy5quoUNHL2dPI0YjSyNrcgsE1GwCw41YAMSmPc+wTHv+IycfWAxmLsf3eaUyJrk4khKmY6pUx0T4qOZENYReNHI3hrAo+hfemxXx5+RBb7gRoEhVrMwu295gkiYooEL2SlRs3bjBv3jwqVCj5dbGFyI8dtzLmq7RwrIGTjWFLFguhq1GZXwyS09PYcvNytvvS1WpeOPwHDzOTmBXth1OzFKxxIIQpGOzagCplMhaj/iHA18jRGEZwTCSTj21ArSikK2qevGSdqk7Hvbx+i4YLkUWvZMXb25uwsDADhyJE8XY7MYYL0bcB6FNDhoAJ4+lWrQ6VMifK//lUVbDPLu7lyL3rALzi2YahbtrnDAohDMvK3ILJHq0AOBF5g/NRt4wcUcGtDD6NitwnzKtUKnyCThVxRKKk0TlZiYiI0PybOnUq48eP58CBA4SHh2e7LyIiojDjFcJk7XqyZLGzlCwWxmNpZs6wzCRk960gopISADh2P4yP/fYAUNe+MstaDzRajEKUVq94tcEssxrW8hLQuxIWH41aUed6n4JCWHzOQkxC5IfOE+xdXFxybOvWrVuu+8q8FVEaZc1XqWBVhlaONY0cjSjtRrk34afAE6Qpav6+6U/nctUYe3wNakXB2tyCdV3GUtZCSr4LUdRq2lagX426bA2/wh+h5/iiZX/srcoYOyy9lbWwRNu3PhUq3GxlGJgoGJ2TlatXS9+Kq0LoKk2dzu7bQQD0cvbC3ExKFgvj6lilFlXLlOfu4zgWXtzHJ+np3E6KA+DLFv1pVLG6kSMUovR6zbsdW8OvkJiWym8hZ3mjXgdjh6SXh8mJ7LkdrPV+BYVJnq2KMCJREumcrHh7/zcGv0ePHuzduzfX/fK6T4iS6lRkOI8yJyzLEDBhCszNzGjgUJW7j+O4kfAo233lpEdFCKPq5exJrfKVCI2L4ocAX16v277YLZSoVtSMPbyG8MzPFxVgpjJDURRUKhUKCj7tR1CnFCx+KQqXXpd/9+3bl+t2tVrNgQMHChSQEMXRzswqYJCxzoUQxhYcE8n+OyG53jfZdwMhsQ+KOCIhRBYzlRlTvNoAcDXmPofvhRo5ovz72G8P/0Zk/O0bXLMBgUNmMbN+ZwZW82Jm/c4EDpnFBI+WRo5SlAT5WhQyJCQk19uQkaj4+vri7OxsmMiEKEayShY3qVidamXtjByNEJkVelQqyGUOoYqMCj0LW/Q1QmRCCICJHq344PwuktPTWB5wnM5Vaxs7JJ39c/Myn2QW6/C2r8wvHUdhZ2XDguZ9uH//PpUrV8ZMhkMLA8lXsuLh4ZHr7Sw2NjZ8++23BY9KiGLk/uM4zjzIqIInJYuFqQiLj0bRMu1VKvQIYXyONuUY7taI36+d46+wi9xNjKVqMbjYFRQTybjDawEob2nNpm4TsLOyMXJUoiTLV7Jy/XpGbX53d3fN7SyWlpZUqVIFC4t8HVKIYi9rYj3IfBVhOtxsK2aufZB7z4pU6BHC+KZ6teP3a+dIU9T4BJ9ibuMexg4pT3GpSQze/wuxqUkArO44Cm+HykaOSpR0+eqjc3Nzw83Njbi4OM3trH/Ozs6SqIhSKatksZ2lDW0ruxk3GCEyTfRomWfPilToEcL42lZ2pXFmZb6fAk+Qrs59vRJToCgKE4+u58qjewC816g7g10bGjkqURronF34+fnpfNAmTZroEYoQxY9aUWsWg+xR3QNLM3MjRyREBg97J3zaj2DSsfWoUEmFHiFMkEqlYqpXW149/hfhCY/YHnGVgTXrGzusXH3hf5CNYReBjEIynzR9zsgRidJC52SladOmOh9UFoUUpcXZBxE8SM5YHVyGgAlTM8GjJR2quLMi8CSBUXfwqlSNyV6tJVERwoS8ULsZ757ZRlxqMssDfE0yWdl7O4g5Z/8FwN22Ims6vyDriYkio/OZ9vDhQ82/n3/+mdq1a7NhwwbCwsIICwtjw4YN1K5dmxUrVhRmvEKYlJ2ZvSoAvZ1lcr0wPXXsHFnQvA/Lm/RnQfM+kqgIYWJsLa15sXZzIONvyjUTKyseFhfNqIO/o1YUyphbsqn7BCpalzV2WKIU0TlZcXBw0Pz7+uuv2bhxI8OGDcPV1RVXV1eGDRvGxo0b+frrrwszXiFMyo7MGvP1HargYutg3GCEEEIUS1O922lu/xR4woiRZPc4LZWhB1YTlZwIwM/th2vm2AhRVPTqwwsJCcHFxSXHdhcXlxzrrwhRUkUnJ3LywU1AelWEEELor36FqnSqUguAlcGnSEpLNXJEGUP6px7/i3NRtwCYUa8jL9RuZuSoRGmkV7Li7e3NJ598QlpammZbWloan3zyCd7e8qVNlA57bgWhzpyfJeurCCGEKIip3m0BiEpOZEPmRHZjWh7gy+qQMwB0qlKLL1r2N3JEorTSq9bwDz/8QP/+/dm4cSNNmjRBURT8/PxISUlh+/btho5RCJO0M3PV+nIWVnSo4m7kaIQQQhRnQ1wbUtnGlvtJ8SwP8GVcneZGi+XYvevMOLkFgOpl7VjfdZxUuxRGo1fPStu2bQkNDWX27NnUrFkTV1dX5syZQ2hoKK1btzZ0jEKYHLWi1kyu71atDtbmssaQEEII/VmZWzDZM+M71PHIG/hlDr8qancSYxl24FfSFDWWZub81XU8VcqUN0osQoCePSsA9vb2TJs2zZCxCFFsXIy+w93HcYCULBZCCGEYr3i1ZuHF/SgoLA84zk/thxXp86ekpzHswK+av2/ftRlMm8quRRqDEE/TOVkJCMgY8uLt7a25rY3MWxElXbaSxTJfRQghhAG42lakn4s328Kv8kfoOb5o2R87K5sie/63T/2D7/0wACZ5tOJlTxktI4xP52Slbt26QEZ1iKzb2siikKKkyypZ7GnnRK3ylYwcjRBCiJLiNe92bAu/SkJaCr9dO8vrddsXyfOuDj7N9wG+ALR0dOG7NoNRqVRF8txC5EXnZCU8PDzX20KUNjEpjzVXnmQImBBCCEN6ztkLd9uKXI+P5ocAX17zblfoScO5BxFMOf4XAE425fir63hsLCwL9TmF0JXOyUqNGjU0t8+ePUunTp2oUKFCoQQlhCnbdzuENEUNSMliIYQQhmWmMmOKVxtmn/2XK4/uceReKJ2q1i6053uQlMDg/b+QnJ6GucqMP7uMk0WOhUnRqxrYSy+9hKOjI02bNuWtt95iy5YtPHz40NCxCWGSskoW25hb0LkQ/4AIIYQonSZ6tsIqs1TwDwHHC+150tTpjDr4OzcTHgGwuEU/ularU2jPJ4Q+9EpWHjx4wJkzZ3jxxRcJDQ3NkbwIUVIpiqKZr9Klam3KSDe5EEIIA3OysWW4W2MA/r5xiXuZ1bkMbe7ZHey7EwzAKPcmvFW/U6E8jxAFoVeyYmZmpklMNm/ezP79+xk3bhyXLl3iq6++MnCIQpiOK4/uEZEYA0BvZxkCJoQQonC85t0OgFR1Oj5Bpwx+/A3XL7DY/yAADStUY0X74TKhXpgkvZIVf39/vvvuO4YOHYqTkxM9e/YkLi6OZcuWcfHiRUPHKITJyBoCBjJfRQghROFpW9mVRhWqAfBT4HHS1WqDHfvyw7u8dPRPABysyrCp23jKWVob7PhCGJJei0I2bNgQR0dH3nzzTT766CMaNGgg2bgoFXZEZKyv4m5bEQ87RyNHI4QQoqRSqVRM9W7L1ON/czPhEf9GXGVAzfoFPm5MymMG7/+FhLQUVKj4o9MYasvfM2HC9OpZmTFjBtWrV+fjjz9m0qRJzJ49mx07dhAXVzhjKoUwBfGpyRy5FwpA7xpekqALIYQoVC/Ubkb5zB6P5QaYaK9W1Iw7vJbg2AcAfNS0J31d8l47Twhj0ytZ+eqrr7hw4QJ3795lzpw5JCUlMXv2bBwdHWnbtq2hYxTCJBy4E0KKOh2APjJfRQghRCErb2nDuNrNAdh5K5DQuKgCHe+zC/vYGn4FgAEu9Xi/cY8CxyhEYdMrWclibm6OhYUF5ubmmJmZkZaWxpUrVwwVmxAmZeetjCFgVmbmUtpRCCFEkZjqnXERWEHhpwL0rvwbfpUPz+8GwMPOkd86jcZMVaCvgUIUCb3O0pkzZ9KiRQsqVqzI2LFjCQwMZMyYMZw4cYLo6GhDxyiE0T1ZsrhjlVrYykREIYQQRaBBhWp0rOIOgE/wKZLSUvN9jJDYB7xweA0KCuUsrNjUbQL2VmUMHaoQhUKvCfYBAQGMHDmS5cuX06xZM8zNzQ0dlxAmJTj2AdfjMxLx3s5eRo5GCCFEaTLVux1H7l0nKjmRjTcuMjZzaJguElKTGbJ/NY9SHgOwqsNI6leoWlihCmFweiUr27ZtM3QcQpi0J0sW964hyYoQQoiiM8S1IU425YhMSmB5wHGdkxVFUZh8bAOXHt4B4P8adGG4e+PCDFUIg5PBikLoIGsIWI2y9tR3kCtSQgghio61uQWTPVsD4Hs/jAvRt3V63FdXjrDuuh8A3at58FnzPoUVohCFRq+eFUPy9fVl165dxMfHU79+fUaPHk2ZMtrHUf7+++8cPHgw2zZnZ2c+/vjjQo5UlFaP01I5ePcaAL1reEvJYiGEEEXuFc82LLp4AAWF5QG+/NhuWJ77H7gTwrunM0bC1CznwLouY7Ewk2H7ovgxas/KG2+8wQcffICNjQ1Vq1blm2++oWnTpjx8+FDrY44ePYqfnx9t2rTR/GvcWLo0ReE5dPcaSelpgJQsFkIIYRxu5SvSzyXjb9Dv184Rm5Kkdd/w+EeMPPgb6Yoaa3ML/u42AUebckUVqhAGZdSelZkzZ+Lm5qb5+eWXX8bR0ZF///2XF154Qevj3NzcmDx5chFEKMR/JYstVGZ0ry4li4UQQhjHVK92bAu/SkJaCr9dO8vrddvn2CcpLZWhB1YTmZQAwE9th9LcsUZRhyqEweicrAQEBDx7p0ze3rpdfX4yUQGIiooiPT2dKlWq5Pm4wMBApk+fjr29PR07dqRXr146xyaEroJjIlkZfJqVQacAaFrRWUo9CiGEMJrnnL1ws61AWPxDlgf48pp3uxxDk6ed3MzpB+EAvObdjvEeLY0RqhAGo3OyUrduXZ0PqiiKzvtevnyZZcuWERsby5kzZ/jmm2/o0UP7iqoqlYpatWrh5ubGrVu3GDp0KEOHDuWXX37R+pjk5GSSk5M1P8fGxgKgVqtRq9U6x2pIarUaRVGM9vymzBTaZlXwaV45vhEVkJ55Pp+JCmdl0Ckm1GlhtLhMoW1MlbSNdtI2uZN20U7aRjtjto0KmOLZhjnndnD50T0O3w3VrMEC8L+gE6wIOglAOydXlrToX6RxynmjnbRNTrq2hc7JSnh4uN7B5MXe3p42bdrw4MEDrl69yl9//cWLL76Ivb19rvt/8MEHVKtWTfPz0KFD6dChA6NGjaJ37965PmbhwoW5TsCPjIwkKUn7mM/CpFariYmJQVEUzMykKNuTjN02oQkPecV3I2qyJ90K8PKxDdQ1L497uQpFHhcYv21MmbSNdtI2uZN20U7aRjtjt01/B3c+VJmToqTz1YUDeDXJmIty9uFtpp/cDEBl63J836APj6KKdqFuY7eNKZO2ySkuLk6n/VRKfrpBCll8fDyenp688sorfPTRRzo/ztXVlfHjx/PJJ5/ken9uPSsuLi48fPgQOzu7goatF7VaTWRkJE5OTnLSPsXYbfPe2R18efkQ6UrOjN9cZcbM+p1ZYKTyj8ZuG1MmbaOdtE3upF20k7bRzhTaZuzhNay97oelmTk3hr0HQMtt33ArMQYLlRn7e79K+8puRR6XKbSNqZK2ySk2NpYKFSoQExOT5/dxo5cufpKtrS0eHh6EhITk63GPHz/Oc+iZtbU11tbWObabmZkZ9YRRqVRGj8FUGbNtbiQ8RK3lfFJQuJHwUM4bEyVto520Te6kXbSTttHO2G3zet32rL3uR6o6nV67fyYmJYlbiTEAfNX6eTpWrWWUuMD4bWPKpG2y07Ud9GqttLQ0vv32Wzp16oSbmxs1atTI9k8XycnJ7Nq1K9u2q1evcvbsWdq0aaPZtnr1aj788EPN827fvj3bY37++WciIyPp00cWOhIFl65WczPhEQq5JysqVLjZViziqIQQQoj/BMZEam77P7pLeOIjANpXduM173ZGikqIwqFXsvLZZ5+xbNkyhgwZwo0bN3j//ffp1asXd+/eZdSoUTodw9zcnB9//JEmTZowZswY+vbtS4sWLRgxYgRTpkzR7HfkyBH++usvICMj9fHxoXHjxowePZr27dvz1ltvsWzZMtq1k19OUTDRyYn02+uD7/0wrfsoKEzybFV0QQkhhBBPCI6J5GXfDbned/z+Da7FRRVxREIULr2Gga1evZo///yTli1b8tZbbzFlyhReffVV2rdvz9q1a3V7YgsLNm3aRFBQEOfPn6dcuXL8+OOP1KxZM9t+EyZMoG/fvkBGgvP3338TGBiIn58fFSpUoFmzZjg6OurzMoTQOB91iyH7fyEsPmNB0mplynPvcTwqlQoFBRUZ//u0H0EdOznfhBBCGMfK4NOoUEEuIwBUKhU+QadY2KJv0QcmRCHRK1m5efMmTZs2BaBMmTLExcVhZ2fHiBEjmD59er6O5enpiaenp9b7O3TokGObl5cXXl5e+QtaCC1+DTnDFN+NmlXqh7k1YmWHEdx7HI9P0CnC4qNxs63IJM9WkqgIIYQwqrD4aK1DlRUUwuKLtgKYEIVNr2QlPT0dC4uMh7q7u3P06FH69u1LYGAgZcrIonmieEhJT+OtU//wQ4AvAGYqFZ8378c7DTqjUqkob2kjV6eEEEKYFDfbitp7VmRepSiBClwN7NVXX2X06NG0bduWU6dOMXbsWEPEJUShupUQw/ADv3I88gYAjtbl+LPLWLpV9zByZEIIIYR2Ez1astj/QK73ybxKURLplaykpqZqbk+bNo2aNWty/PhxRo0axYsvvmiw4IQoDIfvXmP4gd+4nxQPQCtHFzZ2HY+LrYNxAxNCCCGewcPeCZ/2I5h0bL1mPqXMqxQlmV7JyoEDB+jevbumPvLzzz/P888/b9DAhDA0RVH4+soRZp7eplnw8RXPNnzTZhDW5ia15JAQQgih1QSPlnSo4i7zKkWpoNc3tL59++Lk5MTo0aMZO3asZrK9EKYqITWZycc2sO66HwDW5hZ832YwkzxbGzcwIYQQQg917BxlXqUoFfRaZ+XWrVvMmTOHY8eO0axZM+rXr8/ChQu5efOmoeMTosCCYyJps+1bTaJSs5wDR/u+LomKEEIIIYSJ0ytZqVy5MtOmTePEiROEhIQwcuRIfvnlF9zc3OjcubOhYxRCb1tvXqbltq/xf3QXgB7VPTg78C1aOLoYOTIhhBBCCPEsBR6oX7t2bd577z1atWrF7NmzOXz4sCHiEqJA0tVqPvLbzfwLezXbZjfsxvxmvTE30ytHF0IIIYQQRaxAycrJkyf5448/+PPPP4mJiaFv37588MEHhopNCL1EJyfywqE/2HkrEABbC2tWdxzFELeGRo5MCCGEEELkh17Jyocffsgff/xBaGgonTp1Yv78+QwfPhwHBwcDhydE/vhF3WLI/tVcz1zB19u+Mpu6TcDbobKRIxNCCCGEEPmlV7KyadMmXn75ZcaMGYOLi4z9F6bh15AzTPHdSFJ6GgBDXRuyquNIylvaGDkyIYQQQgihD72SlQ8++IBhw4YZOhZhJMExkawMPq2p1T7RoyUe9k7GDktnKelpvH3qH74P8AXATKViUfO+zGzQBZVKZeTohBBCCCGEvvRKVkaPHs2QIUM0i0KK4mtV8CkmH9uQbRXcxf4H8Gk/ggkeLY0d3jPdToxh+IHf8L0fBoCjdTnWdRlL9+oexg1MCCGEEEIUmF7ZhoeHB/7+/oaORRSx4JhIJh/bgFpRSFfU2f6fdGw9IbEPjB1ing7fvUazf77SJCotHV04O/BNSVSEEEIIIUoIvZKVN998kxdeeIFt27YRGhpKREREtn+ieFgZfBoV2odJ/RRwvAij0Z2iKHx1+TDddv7EvcdxALzs2ZrDfV6jpm0FI0cnhBBCCCEMRa9hYFOmTAFgwIABud6vKIr+EYkiExYfjULu75VaUVhy+RAH7l6jlZMLrR1r0sqpJl72TpipjDf8LyE1mZd9N7I29DwAVmbmfN92CJNlNXohhBBCiBJHr2Tl6tWrho5DGIGbbcU8+lVAAc5GRXA2KoLlZPSy2Fna0NLRhdZONWntVJNWji5ULWtXJPGGxD5gyP7VXHp4BwCXcg781fVFWjrVLJLnF0IIIYQQRUuvZMXb29vQcQgjmOjRkkWX9ud6nwp4qU4rguMiORsVQWJaKgCxqUnsuxPMvjvBmn1rlnOglVPNzN4XF5pXqkE5S2uDxrot/ApjD68hJiUJgO7VPFjb5QWcbGwN+jxCCCGEEMJ06L2CfUJCAnv37iU0NJS33noLgKCgIDw8PKRcbDFhb2WDuUpFuqKgAlQqlaYq2JPVwNLU6Vx+dI+TkTc5FXmTk5E3ufzonmYI2c2ER9xMeMTGsIsAmKvMaFChKq0ye2BaOdaknkMVzPWoHqdW1Hzst4dP/PZots1q2JX5zXpjYWZe8EYQQgghhBAmS69kJSgoiF69epGUlMS9e/c0ycqnn35Kv379GDVqlEGDFIVjRdAp0jPnF42p1ZR0RcHNtiKTPFtRx85Rs5+FmTmNK1anccXqvOLVBoC41CTOPojISGAehHMy8ia3EmMASFfUXIi+zYXo2/wcdBIAWwtrWjjWyExgXGnl5EKNcg45YgqOicQn6BSBUXeo6eCIX/RtDt8L1Rzjl44jGerWqDCbRQghhBBCmAi9kpU333yTESNG8Pnnn2dba2XGjBm8+uqrkqwUA2nqdH4MzJiH0rBCNX7rNCZfPWLlLW3oUq0OXarV0Wy7lRDDqQc3NT0wpx9EEJ+WDEB8WjIH717j4N1rmv2rl7WjlWNNzfyXgJh7vHFic0bvjqKgvhOg2dfbvjJ/dxtPXYcqBX3pQgghhBCimNArWTl+/Dhr1qzJ8eXW29ubS5cuGSQwUbi2hV8lPOERAK97tzPI0D3ncvYMLteQwa4NAUhXqwmIuc/JzKFjpx7c5NLDu6QragBuJ8ay+aY/m28+vWZPzgpla7u8IImKEEIIIUQpo1eyolarSUlJAcj2JTcsLAx7e3vDRCYK1fcBx4CM6l4v1G5WKM9hbmZG/QpVqV+hKhM9WwEZpYfPR9/mZOQNTkWGc/LBTW7EP8z7OCoz/gy9QJOKzoUSpxBCCCGEME16JSs9e/bkyy+/ZPHixZpk5cGDB0yfPp3evXsbNEBheIEx99l7O6Oa1/g6LbA1cOWuvJSztKZDFXc6VHHXbLv3OI7hB37l6L3rua76oqAQFh9dZDEKIYQQQgjToNfqfkuWLGHDhg3UrVsXRVHo2rUr7u7uhIWFsWjRIkPHKAzsh6u+mtuvebczYiQZqpQpT/vK7loXm1Shws22YhFHJYQQQgghjE2vnhVXV1cuXrzI77//zpkzZ1Cr1QwZMoTx48djZ1c0CwQK/SSkJvNLyBkgY60Sb4fKRo4ow0SPliz2P5DrfQoKkzKHkQkhhBBCiNJDr2SlR48e7N27l6lTp2q9T5imP0LPE5uasbDi63WN36uSxcPeCZ/2I5h0bL2mGphK9d+aL0+WUhZCCCGEEKWDXsnKvn37ct2uVqs5cCD3q+PC+BRF4furGRPrXco5MMClnpEjym6CR0s6VHFnReBJAqPu4FWpGpO9WkuiIoQQQghRSuUrWQkJCcn1NmQkKr6+vjg7S8UmU3XsfhgXH94BYIpXG5NcAb6OnSMLmvfh/v37VK5cOds6PkIIIYQQonTJV7Li4eGR6+0sNjY2fPvttwWPShSKrF4VSzNzJnu2NnI0QgghhBBC5C1fycr169cBcHd319zOYmlpSZUqVbCw0GtkmShkdxNj+etGxoKdw90aUaVMeSNHJIQQQgghRN7ylVm4ubkBEBcXh62tbWHEIwrJz0EnSVWnA/C6d3sjRyOEEEIIIcSz6dUNYmtrS2JiIgEBAURH51ysr0ePHgUOTBhOmjqdnwJPANC4YnXaVnY1ckRCCCGEEEI8m17Jyu7duxkzZgxRUVG53q8oua1DLoxly83L3EqMAeB173aoVCojRySEEEIIIcSz6VVq6c0332Ty5MlER0ejKEqOf8K0/BCQsWK9vZUNY2o1NXI0QgghhBBC6EavnpUbN24wb948ypUrZ+h4hIFdfXSP/Xcyyky/VKcl5SytjRyREEIIIYQQutGrZ8Xb25uwsDADhyIKQ1avCsBr3qazYr0QQgghhBDPolfPytSpUxk/fjxffPEFderUyTEHokaNGgYJThRMXGoSq0POANCruice9k5GjkgIIYQQQgjd6ZWsvPzyywB069Yt1/vzM29l//797Nq1i/j4eOrXr8+4ceMoX163NUD279/PypUr6d27N2PHjtX5OUuL36+dIy41GYDX60q5YiGEEEIIUbzolaxcvXrVIE/+yiuvcPv2bbp3746FhQWrVq1iyZIlnDp1ikqVKuX52Lt37/LSSy+RmJiIo6OjJCtPURRFs2J9zXIO9KtR18gRCSGEEEIIkT96JSve3t4GefIPP/wQZ2dnzc/jx4+nYsWK/Pvvv4wbN07r49RqNePGjePtt99m1apVBomlpDl8L5TLj+4B8Kp3W8zN9JqeJIQQQgghhNHonKwEBAQAGYlK1m1tdE1mnkxUAO7cuUN6ejouLi55Pm7RokWYm5szffp0SVa0yOpVsTIzZ7JnayNHI4QQQgghRP7pnKzUrZsxjEhRFM1tbfIzZ+XixYssXryY2NhY/Pz8+Omnn+jSpYvW/Y8fP863337LuXPndF7cMDk5meTkZM3PsbGxQEYPjVqt1jlWQ1Kr1SiKUijPfzsxhk03/AEY7taYSlZljfY69VGYbVPcSdtoJ22jnbRN7qRdtJO20U7aRjtpG+2kbXLStS10TlbCw8NzvV1QTk5O9O7dmwcPHnDr1i1WrlzJsGHDqFixYo59Hz16xJgxY1i+fDnVqlXT+TkWLlzIxx9/nGN7ZGQkSUlJBYpfX2q1mpiYGBRFwczAQ7S+DvYlTck4AUZX9ub+/fsGPX5hK8y2Ke6kbbSTttFO2iZ30i7aSdtoJ22jnbSNdtI2OcXFxem0n0oxoSXnExMT8fT05KWXXuLTTz/Ncf/y5cuZM2cO/fv312z7999/qVKlCs2bN+fXX3/N9QTIrWfFxcWFhw8fYmdnVzgv5hnUajWRkZE4OTkZ9KRNVafjvnEBdx7H0ayiM6f6T9e5B8pUFFbblATSNtpJ22gnbZM7aRftpG20k7bRTtpGO2mbnGJjY6lQoQIxMTF5fh/Xa4J9YSlbtiy1atXSuuBk9+7d+e6777JtO3LkCK6urvTu3Vvrl3Jra2usrXOu3G5mZmbUE0alUhk8hn9uXOLO44xM9fW67TE3NzfYsYtSYbRNSSFto520jXbSNrmTdtFO2kY7aRvtpG20k7bJTtd2MFqykpyczM6dO3n++ec12y5evMiZM2cYPXq0ZpuPjw8hISEsXLgQT09PPD09sx3nyy+/xNvbW0oXZ/o+IGNifQWrMoyq1cS4wQghhBBCCFEARkvtzM3NWbt2LXXr1mXIkCF069aNNm3aMGHCBM2ik5AxoX7r1q3GCrNY8X94h0N3QwGY6NGKshZWRo5ICCGEEEII/RmkZyUhIQGAcuXK6f7EFhasW7eOGzdu4OfnR7ly5WjQoAFVq1bNtt/kyZMZNGiQ1uMsWLCAKlWq6BV3SfNDgK/m9lTvtkaMRAghhBBCiIIrULJy4cIFJk6cyLlz5wBo2rQpq1atonHjxjofw9XVFVdXV633t2nTJs/H9+3bV+fnKsliU5L4LSTjfejt7EVtO0cjRySEEEIIIUTBFGgY2Lhx4xg7diwJCQkkJCQwbtw4XnzxRUPFJvLh15AzxKdlVDx7vW57I0cjhBBCCCFEweUrWRkzZgyRkZGan8PDwxk9ejRly5albNmyjB49mps3bxo8SJE3RVE0Q8DcbCvQx9nbyBEJIYQQQghRcPkaBtaiRQtatGjBp59+yosvvsiECRPo3LmzZk7Jpk2bGD9+fGHEKfJw8O41rsZkLPw41bsd5lISTwghhBBClAD5+lb79ttvc+jQIf744w969erFG2+8weLFi0lPTyc9PZ3FixezbNmywopVaPH91YxyxdbmFkz0aGXkaIQQQgghhDCMfE+wd3NzY9euXfz2229069aN6dOn8/nnnxfbxQeLu4iER2y+eRmAUe5NcLTRvSKbEEIIIYQQpkyv8ULp6emMGTOGs2fPcv78eVq3bo2fn5+BQxO6+F/gCdIVNQCve7czcjRCCCGEEEIYTr6SlStXrtCxY0dsbGywsbFhyJAhvP/++8yfP5/hw4cza9YsHj9+XFixiqekpKfxv6CTALR0dKGlU00jRySEEEIIIYTh5CtZGTt2LM899xy3bt3i1q1b9OrVi7Fjx9K7d2/8/PxISUmhSZMmhRSqeNrfNy5x73EcIL0qQgghhBCi5MlXshIaGsqUKVOoXLkylStXZsqUKYSEhAAZq9cvW7aM33//vVACFTl9n1mu+P/bu/O4qOr9f+CvYRVRQBAUBMUNQcs0F9xIVFJ/7jeXa66Zdr1a1xaX6pZfKyu75L2mpeaCpterXdOxNHfQDFBwwRVBQFBBFmdYhn1Y5vP7g8t5MDIDgyEzwuv5ePSoOfM55/Oe95w5nTfnfD7H0bo5pnXsZdxgiIiIiIjqWZ0G2E+fPh0BAQGYMmUKAOCnn37Cq6++qtWmX79+9Rcd6XUjKxVhGUkAgPld+8PGwtLIERERERER1a86FSsbN27Evn37EBYWBgBYsWJFtWKFGkblQyBlkGGR90AjR0NEREREVP/qVKyYm5tj1qxZmDVr1tOKhwygKinCnrtRAIAx7t7o2NLJyBEREREREdW/Oj9nBQAiIyNx/vx5ZGRkQAiBtm3bYtCgQfD19a3v+EiHXQmXUVBWAgB404cD64mIiIiocapTsaJQKDB58mSEhoaiRYsWaN26NWQyGRQKBfLz8+Hn54eDBw/C2dn5acXb5AkhpFvAOrd0wqh23YwcERERERHR01Gn2cDeeustlJaWIjIyEnl5eUhKSkJiYiLy8vIQERGB0tJSvPXWW08rVgIQkhaPOyoFAGCR90CYyZ7ouZ5ERERERCavTldWjh07hps3b8LT07Pae76+vti3bx969uxZX7GRDhtjKq6qNDO3wLyu/Y0cDRERERHR01OnP8ubmZmhtLRU7/ulpaUwM+Nf+p+WB/nZOJwcDQB4tVNvOFo3N3JERERERERPT50qi4kTJ2LatGkICQlBWVmZtLysrAxnzpzB1KlTMXHixHoPkipsvRMBjRAAgDe9Bxs5GiIiIiKip6tOxcqGDRvQrl07BAQEwMrKCk5OTnBycoKVlRVGjBgBDw8PrF+//mnF2qSpy8uwLS4SAODr3B59WrsbOSIiIiIioqerTmNWHBwc8OuvvyI2Nhbnz59Heno6AKBt27YYPHgwunXjzFRPy8F7N/CoOB8Ar6oQERERUdPwRM9Z8fb2hre3d33HQjXY+L/piltb22KqJycxICIiIqLG74mKlfj4eISHhyM9PR0ymQydO3dGQEAAHBwc6jk8AoBrmQ9x/tE9AMACL180s7A0bkBERERERA2gTsVKfn4+XnvtNRw8eBAAIJPJYG9vj5ycHNja2iIwMBCLFy9+KoE2ZZVXVcxkMvzVe4CRoyEiIiIiahh1GmC/dOlSZGVlISIiApGRkfD398fXX3+Nhw8f4tNPP8WKFSuwd+/epxVrk5StLsR/7kYBAMa5d0eHFo5GjoiIiIiIqGHU6crKgQMHEBUVhQ4dOgAAduzYAT8/PyxYsABLly6Fu7s7vvrqK8yYMeOpBNsU/ZBwGUXlFc+2edNnkJGjISIiIiJqOHW6slJaWqo1LqVVq1bIycmRXk+YMAGxsbH1FVuTpxEabPrfE+u7tGyNALeuRo6IiIiIiKjh1KlY6dWrF/7xj39ACAEhBL766is899xz0vsPHjyAj49PvQfZVAWnxiMhTwkAWOwzCGayOn1dRERERETPtDrdBvbFF19g9OjR2Lp1K4QQKCwsxNGjR6X3AwMDERgYWO9BNlUb/3dVxcbcEq916WvkaIiIiIiIGladihU/Pz9cu3YNv/zyC4QQGD9+vNbzVoKCguo9wKbqfn4Wfk25DQCY2flFtLJubuSIiIiIiIgaVp2fs9K1a1csW7bsacRCVXwfGwGNEACAN705sJ6IiIiImh4OgjBBxWWl2B4XCQAY5OKJXk7tjBwREREREVHDY7Fign66dwNKdQEAXlUhIiIioqaLxYoJ2hgbDgBwadYCkz17GjkaIiIiIiLjYLFiYq4oUxCpeAAAeMPLF9bmdR5WRERERETUKLBYMTGbYiumKzaTyfCXbgOMHA0RERERkfGwWDEhWepC7E2MAgBM8OiB9i1aGTkiIiIiIiLjYbFiQnbGX0RxeRkA4E0fDqwnIiIioqaNxYqJ0AgNNsdeAAB0s3fGCNeuRo6IiIiIiMi4jD56+9SpUzh58iTy8/PRo0cPzJ07F/b29vW+jqk7+fAO7uZlAgAWew+CTCYzckRERERERMZl1CsrCxYswKZNm+Dp6YlevXph79696N27N5RKZb2u8yzYGFMxsN7Wwgpzu/Q1cjRERERERMZn1Csrq1evhqurq/R69uzZcHBwwPHjxzF79ux6W8fUJeVl4lhKLABgVucXYW9lY+SIiIiIiIiMz6hXVqoWHQCQnJyM8vJytG/fvl7XMXWbYy9AQACouAWMiIiIiIhMYMzK9evXsWbNGuTm5uLGjRsICgrC0KFD63UdtVoNtVotvc7NzQUAaDQaaDSa+vkgdaTRaCCEQEGJGkHxFwEAQ1w88ZxDW6PFZCoqc9PU86ALc6Mfc6Mfc6Mb86Ifc6Mfc6Mfc6Mfc1OdobkwerHSpk0bTJo0CUqlEkqlEps3b8bEiRPh5ORUb+usWbMGn376abXlCoUCxcXF9fZZ6kKj0UClUuG/KbeQpS4EAMx0fQ6PHj0ySjympDI3QgiYmXHCuqqYG/2YG/2YG92YF/2YG/2YG/2YG/2Ym+ry8vIMaicTQoinHIvBioqK4OXlhblz5+Lzzz+vt3V0XVnx8PBAdnY27Ozs6iX2utJoNFAoFJhw6b+4nJmCNs1a4N6Uv8PK3Oj1o9FV5sbZ2Zk/6McwN/oxN/oxN7oxL/oxN/oxN/oxN/oxN9Xl5uaiVatWUKlUNZ6Pm9SZsY2NDTp27Ij79+/X6zrW1tawtrauttzMzMyoO8x1VTouZ6YAAP7SbQCaWVoZLRZTI5PJjP79mCrmRj/mRj/mRjfmRT/mRj/mRj/mRj/mRpuheTBattRqNQ4ePKi17OrVq7h8+TKGDBkiLdu6dSuWL19ep3VMXbxKgb9fOY6/XDsCADCDDAu7DTRyVEREREREpsVoxYq5uTkOHToELy8vTJgwAS+99BIGDx6MBQsWYMGCBVK7ixcv4vjx43Vax5TtjL8I70OBWBv9G5KL/jfQHwKnU+OMHBkRERERkWkx2m1gFhYW2LNnD1JSUnD9+nXY2tqiR48ecHZ21mq3cOFCTJkypU7rmKp4lQILwn+CRscwofnh+zGkTUd0sWtthMiIiIiIiEyP0W+ac3d3x9ixY+Hv76+z6OjXrx9Gjx5dp3UMlZWVJf13dnY28vPzAQBlZWVQKpUoKSkBABQWFiIzM1Nqm5OTI81goNFotNoWFRVBqVRKbVUqlTRV8o64i2ivaYbmoiLttsIMHsIaEIAMMuy6eV5qK4SAUqmUZitTq9VQKpXSNG+5ublQqVRSP0qlEkVFRQCAkpISrbZ5eXnIycmR2mZmZqKwsFCrbVlZGQAgPz8f2dnZWjmqbFtaWqrVtqCgQCuHWVlZ1XJYWlqqM4dV811eXl4t31U/m658V06YUFO+K9tW5rC4uBhKpRKVc0roymFN+a6aQ135Li8vl3KoL9+P51BXvgsKCrRyqC/fuvZZffnOycnRm+/Hc5iTk1Mth5X5rsyhrnw/vs9WtjVkn30834/vs0qlsto+WzXfVXNYW74f32cfz3fVHDb0MUJfvqvus096jFCpVI3qGPH4Pvukx4icnBweI6D7GFHZlseIpnGMqK/ziKKiokZ1jKiv84i8vDwpXn35ftaOEfVxHmEIoxcrxnT69Gnpv0NCQnD9+nUAFV+mXC6XkhkfH49ff/1Vavvbb78hKioKQEXS5XI50tPTAQCJiYn4+eefpbZhYWG4dOkSACA5NwsflnnAWzQHAPQULfBxWQeYARAQsLmnwPnz5wFUHGTkcrk0ccDDhw8hl8ulHe7SpUsICwuT+vn555+RmJgIAEhPT4dcLpd+MFFRUfjtt9+ktr/++ivi4+MBVPxY5HK5tGNfv34dISEhUtvjx4/j9u3bACp2arlcLv0wo6OjcerUKa183rp1C0DFD1gul0s/itjYWBw7dkxqe+bMGVy7dg1AxQ9CLpdL0zbfvXsX4eHhUttz587hypUrACp+/HK5HGlpaQCApKQkHDp0SGobHh6OyMhIABU/JrlcjpSUikkMkpOTIZfLpQNHRESElG8AkMvluHfvHgAgNTUVcrlc+iFevnwZoaGhUtvDhw/j7t27AICMjAzI5XLpoBMVFYWzZ89KbY8ePYo7d+4AqDjgyOVy6Qd/8+ZNBAcHS21PnDgh5TsnJwdyuVw6YN2+fVsr38HBwbh58yaAioOVXC6XDix37tzB0aNHpbZnz56V9tmioiLI5XJkZGRI+T58+LDUNjQ0FJcvXwZQcQCVy+VITU0FANy7dw9yuVxqe/78eURERACoOCDJ5XIkJycDAFJSUiCXy6WDb2RkpNb3eujQISQlJQEA0tLSIJfLpYPZlStXcO7cOantkSNHkJCQAAB49OgR5HK5dOC+du0azpw5o5XD2NhYABUHbblcLh00b926pfW7P3XqFKKjowFU/A9KLpdLB/3bt29Lt6ACDXOMKCsrg1wux8OHDwEA9+/fh1wul/7HeP78+Sc+RoSGhkr5ftaPEQkJCThy5IjU9o8cI37//Xcp343hGHHixAmp7R85Rvz888/Sb6GxHSOOHTv2h44RlfmOiYlpVMeI+jqPSEhI0Mr3s36MqM/ziMr9A3j2jxH1dR5hENEEqVQqAUAkJSVJy7KyskReXp4QQojS0lKhUCiEWq0WQghRUFAglEql1DY7O1vk5uYKIYQoLy/XaltYWCgUCoXUNicnR6hUKiGEEB9c/FV4Bn0smgctF9ixVNgGLRceQX8XCFoqzHcuFx+H/SK11Wg0QqFQiKKiIiGEEMXFxUKhUIjy8nLpM+Tk5Ej9KBQKUVhYKIQQQq1Wa7XNzc0V2dnZUlulUikKCgq02paWlgohhMjLyxNZWVlS28zMTKltSUmJVtv8/HyRmZmp1fbxHJaUlOjMYdV8l5WVaeUwLy9PxMbGSvHryndxcXGt+a5sW5nDoqIioVAohEaj0ZvDmvJdNYe68l1WVibFry/fj+dQV77z8/O1clg13wqFQqSlpYny8nKd+6y+fGdnZ+vN9+M5zM7OrpbDynxX5lBXvh/fZyvbGrLPPp7vx/dZhUJRbZ+tmu+srCxRXl4u0tLSxKNHj2rM9+P77OP5rprDqm0b4hihL99V99knOUaUl5eL2NhY6bM+68eIgoKCavvskxwjSktLRUxMjBR/YzhG1LbPGnqMyMjIEA8ePBDl5eWN5hhhaL5rO0YUFxeLtLS0am2f5WPE4/l+0mNEeXm5SExM1Pqsz/Ixoj7PI3JyckR8fLz0+lk/RtTHeUTl+XhlW31M6jkrDSU3Nxf29va1zutc3+JVCngfCtQ5ZsVMJsOdV97nmBVU/PXt0aNHcHFx4fR+j2Fu9GNu9GNudGNe9GNu9GNu9GNu9GNuqjP0fJzZakBd7Z0RNHgazGQymMvMYIb//VsmQ9DgaSxUiIiIiIiqMKmHQjYFr3XthyFtOmL7nUjcyUxDNydXLOjmy0KFiIiIiOgxLFaMoItda3zZ5//xciARERERUQ14lkxERERERCaJxQoREREREZkkFitERERERGSSOGaFiIiIqBEQQqCsrEx68GND02g0KC0tRVFREcfjPqap5sbKygrm5uZ/aBssVoiIiIiecWq1GikpKdKT5I1BCAEhBLKysiCTyYwWhylqqrmRyWTw9PREy5Ytn3gbLFaIiIiInmEajQbx8fEwNzdH+/btYWVlZZQTYiEENBoNzMzMmtQJuSGaYm4qH4R57949dO/e/YmvsLBYISIiInqGqdVqaDQadOzYEba2tkaLoymekBuqqebGxcUFeXl5KCkpgY2NzRNto+ncNEdERETUiDWlsRD0bKiPfZJ7NRERERGRiUpPT0dkZGSD9Xfz5k0kJibqfT81NRWXLl1qsHhYrBARERFRo9fQJ/31JTg4GAsXLqyXbRmSg08//RS7d+/W+/6xY8fwt7/9rV7iMQSLFSIiIiJqMA8ePEBYWBgyMjJ0vp+eno7Q0FAkJydXey8jIwMXL15EcXGx1nKNRoOzZ89CCKG33+joaOzcudPgONPS0nDx4kWD2z8LnsUcsFghIiIiauLiVQp8ePkYXv1tDz68fAzxKkW996FWq/HKK6+gd+/eWLZsGbp06YLPPvtMq82XX36Jzp07491334WPjw+WLFkivXfixAn06NEDixYtwgsvvIDc3FzpvfXr1+PQoUM1Dl4fMWIEvv/+e4PjPXnyJBYvXlyHT2j6nsUcsFghIiIiasJ2xl+E96FAfH3rN+y/dx1f3/oN3ocC8UN8/Y5LWLt2La5du4aEhAREREQgMjISa9aswe+//w4AuHz5MlauXImQkBBcvnwZUVFR2LFjBw4fPgwA+Mc//oGtW7fiypUr6NmzJ3788UcAQEJCAoKCgrBmzZoa+3/8FqjKsRcajQZ37txBVFQUSkpKAAAqlQq3b99GXl4egoODERwcjLy8PGndrKwsREREICUlRauPqtuMj49HeHg4goODpe1WiouLw40bNwAAmZmZUh+XL1+u87NyQkJCtNY5c+YM7t+/L72+fv067t27pzMHQMVMZZXxlJaWSstry4GuvD0NLFaIiIiImqh4lQILwn+CRgiUC43Wv+eH70dCrrLe+goPD8fYsWPRqlUrAED37t3Rp08fqej46aefMHDgQAwYMAAA4OXlhXHjxmH//v0AgOzsbHTo0AEA4OnpiezsbAghsGDBAmzYsKHWaZsfH/tx7NgxzJgxA35+fpg9ezYmTZqE3r17Izc3F8nJyTh69CjS0tLw1Vdf4auvvkJaWho0Gg3efvttdOrUCe+++y569+6NefPmQaPRaG1z0KBBmDFjBn766SfMmzcPv/zyi1Ys06dPR0hICAAgKSlJ6uMvf/kLPDw8cPz4cYPz+vbbb+PIkSMAgJiYGIwYMQKrVq2S3n/llVdw/fp1nTkoLCzEmDFjMHjwYCxYsAC9evVCUlISAOjNAVBRYOnK29PA56wQERERNTLvRP6Ca1kPa22XmJcFjZ5xHhohMPzE9+jU0rHGbfRybIdvfCfW2peTk5PWlQiNRoPU1FQ0a9YMABAfHw8vLy+tdbp27YrTp08DAPz8/PD5559j5syZ2LdvH3766Sds3LgRPj4+8Pf3x9WrV2Fvb49OnTrVGkulpKQk7N69GwMHDkRpaSl69eqFf//733jzzTexfPlyfPfddwgODpbab9q0CSdOnEBCQgJat26NvLw8DBo0CLt27cK8efMAVFzp2bx5MwICAgAAtra2+OGHHzB58mQAFVc6bt26hVmzZgEA+vbtq9XHwYMHsXDhQty7d8+gqX8DAgIQHByM6dOnIzg4WHoNAPfu3cP9+/fh7++vc91vvvkGycnJuHv3Luzs7HD+/Hn4+flh/PjxeO6553Tm4Pfff68xb/WNxQoRERFRI3Mt6yHOpeufftZQyQU5SC7I+eMBAfjrX/8Kf39/fPzxx+jXrx9++ukn5OTkSLcQlZSUSIVLpWbNmkGtVgMA1qxZg9WrV2Pv3r0IDAyEq6srNm/ejAsXLmDcuHFITExETk4O3n//fbz77rsGxdS9e3cMHDgQAGBpaYn+/ftLVxZ0kcvlGDx4MK5duyYt6927N0JCQqRixcvLSypUAGDevHkIDAxEamoq3N3dsXPnTowfPx7Ozs5Sm9LSUsTGxkKpVMLOzg6pqal4+PAhPDw8av0MAQEBeOuttwBUXDn5y1/+gvfffx8xMTEICwtDv379YG9vr3PdkydPYv78+bCzswMADBo0SLqyVZO65u2PYLFCRERE1Mj0cmxnULvEvKwaixEPWweDrqwYYvDgwQgPD8e2bduwfft2jBw5EuXl5TA3NwcAODs7Q6HQHtivUCikk/oWLVrgH//4B4CKcRYvv/wy1q1bh5iYGCQmJiI6OhopKSno2bOnwcVK8+bNtV6bm5ujrKxMb/vMzEykpqbiwYMHWsv79Okj/XflbW6VunTpgoEDB2LPnj1YunQp9u7dqzUj17lz5/DnP/8ZDg4OaNOmDSwtLQEAjx49MqhY8ff3x8OHD3Hnzh2EhoZix44dePnll3H69GmEh4drFU6PU6lU1QoZfYVNVXXN2x/BYoWIiIiokTHktiygYsyK96FAnbeCmclkODP6r+hi17peYiouLkafPn3Qv39/ABWD1FeuXInt27cDqChmPvzwQ5SUlMDKygpCCJw+fRrTpk2rtq2tW7fC09MTI0eOxIkTJ+Dh4QFzc3O4u7ujuLhY2sYfYWlpifLycq1lPXv2hI2NTbUZtVQqVY3beu211xAYGIhu3brBwsICo0ePlt5bs2YNFi5ciE8//RRAxXTBbm5uNU7DXFWLFi3g6+uLL7/8Ep06dYKTkxMCAgLwww8/4NKlSzXO5uXt7Y3IyEi8/vrrACqubl27dk36jnTloKGxWCEiIiJqorraOyNo8DTMD98PGWQQENK/gwZPq7dCBah4Rsr8+fMxf/58FBUV4Z///CeGDx8ujeWYOXMmAgMDMWXKFMydOxe//PILlEolFi1apLWd5ORkrF+/HhcuXABQcVXj6tWr2LFjB2JiYtCvX78/XKgAFSfycXFx+PHHH9G6dWv4+vrik08+Qd++fWFtbY1hw4YhOzsbBw4cwJ/+9CcsWLBA77amTp2KJUuWYMWKFZgzZ450NQkA3N3dceLECfTq1QuFhYX49ttvDRqrUlVAQABWr16N5cuXA6iYonjGjBmwsrKSbtfSZdmyZXjppZfg6uqKF154ATt37tQaKK8rBw2NxQoRERFRE/Za134Y0qYjguIu4l5+FjxbOGK+V/96LVQAoEOHDli9ejU2btwItVqNpUuXYu7cudKzUWxsbBAaGorAwEAEBQXB09MTFy5cgIuLi9Z29u3bh3Xr1km3Kzk7O+PQoUP47rvvYG9vL80u9jhXV1et8Rjt2rWTriBU6t69O2xsbABUFEH/+te/sH//fuTm5mLTpk3w8vLC7du38e2332L37t1wdHTEkiVLMGrUKL3bBCqufixbtgxhYWGYP3++1nv//Oc/pc/s5OSEf/3rX1izZo00juTxuHWZMGECwsLCMGnSJACAo6Mj5s6dC3t7e63C7fFt9e3bF2fOnMH333+PuLg4vPrqq+jbty88PT315qC2vNU3mTD0GlMjkpubC3t7e6hUKmlHaGgajQaPHj2Ci4tLnavnxo650Y+50Y+50Y+50Y150Y+50c8Uc1NUVIT4+Hh07dr1qZ0wGkIIAY1GAzMzsxofztgUNdXc1LRvGno+bhq/MiIiIiIiosewWCEiIiIiIpPEYoWIiIiIiEwSixUiIiIiIjJJLFaIiIiIGgGNRmPsEIi01Mc8XixWiIiIiJ5hlVPTFhQUGDkSIm0lJSUAAAuLJ39aCp+zQkRERPQMMzc3h6OjI9LT0wEAtra2RplWualOz2uIppgbjUaDtLQ02NraslghIiIiasratWsHAFLBYgxCCAghIJPJmswJuaGaam7MzMzg7u7+hz4zixUiIiKiZ5xMJoO7uztcXV2lW28amkajQVZWFhwdHU3mgZmmoqnmxtra+g9/XhYrRERERI2Eubm50Z5ir9FoYGlpCRsbmyZ1Qm4I5ubJMVtERERERGSSWKwQEREREZFJapK3gVXO+Zybm2u0GDQaDfLy8tCsWTNeDnwMc6Mfc6Mfc6Mfc6Mb86Ifc6Mfc6Mfc6Mfc1Nd5Xl4bc9iaZLFSl5eHgDAw8PDyJEQERERETVdeXl5sLe31/u+TNTHoyWfMRqNBqmpqWjZsqXRpo/Lzc2Fh4cHkpOTYWdnZ5QYTBVzox9zox9zox9zoxvzoh9zox9zox9zox9zU50QAnl5eXBzc6vxalOTvLJSOeezKbCzs+NOqwdzox9zox9zox9zoxvzoh9zox9zox9zox9zo62mKyqVeNMcERERERGZJBYrRERERERkklisGIm1tTVWrVoFa2trY4dicpgb/Zgb/Zgb/Zgb3ZgX/Zgb/Zgb/Zgb/ZibJ9ckB9gTEREREZHp45UVIiIiIiIySSxWiIiIiIjIJLFYISIiIiIik9Qkn7NibOHh4di2bRtSUlLw448/onXr1sYOySRkZ2djy5YtuHTpEmxsbDB06FDMmTOnyQ9Gy87OxtSpU6stX7VqFfz8/IwQken46quvEBwcXG25g4MDDhw4YISITMvx48dx4MABPHr0CM899xzee+89ODs7GzusBpefn4+9e/fi559/xosvvojPP//8ido0RhkZGdixYwfOnDmDmTNn4rXXXqvW5vz589i7dy8ePHiA9u3bY968eejTp0/DB9vAEhISsGXLFly9ehUff/wx/P39td7fvXs3du/erbXM3t4eBw8ebMAojePixYvYunUr7t27h507d8LDw0N6r7i4GOPGjdO53uzZszF37tyGCrPBCSFw8uRJ7Ny5Ezk5OTh58mS1Nvn5+fjuu+9w+fJlmJmZYeLEiZg5c6YRon12sFhpYHPnzkV8fDz69++PXbt2obi42NghmYTi4mIMGjQIU6dOxZw5c5CRkYEvvvgCR44cweHDh40dnlGp1WqEhIRg27Zt8PT0lJZ369bNeEGZiPHjx6Nv375ay1599VUMHz7cSBGZjsDAQKxevRqrVq3C+PHjsX//fvj6+iIqKgoODg7GDq/BpKen48UXX8SYMWOgUqlw7dq1J2rTGJ07dw6zZs3CzJkzERsbi4SEhGpttm7dioMHD+JPf/oTRo4cibNnz8LX1xe//vorRo8ebYSoG8aWLVuwdu1avP766wgJCcGCBQuqtUlMTERGRgbWrVsnLbOysmrIMI1i8eLFuHTpEvz9/REUFISCggKt9y0tLfHBBx9oLYuIiMDKlSvx0UcfNWSoDW7YsGGwtrZGu3btdBatRUVFGDBgAFq0aIGlS5ciPz8fH3/8MaKjo/Hll18aIeJnhKAGlZGRIYQQ4uzZswKASE5ONnJEpqGsrEzk5eVpLTtw4IAAILKzs40TlIlIS0sTAMTNmzeNHYrJCw8PFwDE6dOnjR2KUWk0GmFnZyfWrFmjtczb21t88sknRoys4RUXFwuVSiWEEOLPf/6zGDt27BO1aYyys7OFWq0WQgjRrVs38dFHH1Vrk5OTU22Zv7+/mDlz5lOPz5gUCoXQaDSitLRUABD79u2r1mbVqlVi8ODBRojOuCrPYy5duiQAiJiYmFrXmT17tujSpYvQaDRPOzyjqszNzp07hbm5ebX39+zZI8zNzYVSqZSWnT17Vpibm4uUlJQGi/NZwzErDczFxcXYIZgkc3NztGjRQmvZlStX4O7ujpYtWxopKtPywQcfYMKECXjvvfdw584dY4djkrZv345OnTphxIgRxg7FqAoLC5Gbm6t1JU4mk6FDhw44fvy48QIzAmtra9jZ2f3hNo2Rg4NDrVcC7O3ttV7n5OQgMTERPj4+TzM0o2vdujVkMlmt7e7evYtJkyZhxowZWL9+PdRqdQNEZ1x1PY9RqVQ4cOAAFixYYFBOn2W15SYjIwMtWrSAk5OTtMzT0xPl5eU4ffr00w7vmcVihUzK+vXrMWLECHh5eeHEiRM4c+YMzM3NjR2W0fXq1Qvjxo3DnDlzoFAo0LNnT51jNZqy/Px87N+/H/Pnz2/0/0Osja2tLXr16oU9e/agtLQUABAXF4fw8HAkJSUZOTp61mg0GgQEBMDPzw8dO3bEzJkzq93m0xSZm5tj3LhxmDlzJvz9/bFx40YMGDCgSRQsdbF3716UlpbqHA/V1AwaNAgqlQpyuVxatmPHDgDgsbkGHLNCJmXUqFHw8fFBQkICAgMD8emnn2LPnj3GDsuonJycEBkZKf0FdMqUKSgrK8M777yDW7duGTk60/Hjjz9CrVZj3rx5xg7FJPzwww+YNm0aPD090b59ezx8+BABAQE4d+6csUOjZ4xMJsMHH3yAgoIChISE4Ntvv8Xw4cMREBBg7NCM6r333oOtra30ety4cfDy8sK2bdvw1ltvGTEy0xIUFIQJEyagTZs2xg7F6AYMGICvvvoKs2bNgo+PDwoKCtClSxe4urpKf1ii6liskEnx9vaGt7c3Ro4cCV9fX/Tt2xeLFy/GoEGDjB2a0VhaWlZbNmbMGOzfvx/FxcVo1qyZEaIyPUFBQRg7dixcXV2NHYpJeOGFFxAdHY34+HhkZWWhV69eWLZsGdq2bWvs0OgZI5PJpMJk4sSJyMvLw4oVKxAVFWXkyIyraqECAG5ubnjhhReafF6qunHjBq5cudJkZtczxPvvv4+FCxfizp07sLW1hZeXF1q2bMljcw1YrJDJ6tChA4CKmXpIm1KphIWFBSws+BMGgNu3byMiIgJHjx41digmxcLCQhpboNFocPLkSYwdO9bIUdGzrkOHDjqnZKWKY/MLL7xg7DBMxvbt29GhQweMHDnS2KGYFAcHB/j6+gKomGK+pKSkyY+1rAnHrJBJuHDhAiIiIqTX5eXl+Prrr2FjY9Okr6oAwOHDhxEfHy+9TkpKwrp16zBx4kQWK/8TFBQEd3d3jBo1ytihmIzffvsN9+/fB1Ax9/8nn3wCpVKJZcuWGTkyepYEBQUhNzdXev3w4UPs2bOnyd8CBgDffvstSkpKpNffffcd4uLiMHnyZCNGZTrUajX+85//YP78+TAz4+lmpX//+9/QaDQAKgbcL1++HNOmTUOPHj2MHJnp4plOA/vhhx+wZ88eZGdnA6h4JoS1tTU+/PDDJl1Vt23bFgsXLkRcXBzc3d1x9+5d2NnZQS6XN/lLoy4uLpg2bRqKiorQsmVL3Lp1C5MmTcKmTZuMHZpJKC0txb///W8sXryYkzFU4ejoiDFjxsDW1hYKhQJmZmY4ceKEdMWyKZk8eTJUKhVu3bqF8vJyBAQEwMbGBkeOHKlTm8ZGqVRi+vTpAIDk5GT85z//QUREBJ5//nnp2SEWFhbo2bMnHB0dYWZmhtu3b2PixIlYv369MUN/6i5fvowPPvgAQggAwBdffIHt27dj/PjxePvttwFUzIzWoUMHtG/fHgqFArm5udi+fXuj/3/5jz/+iO3btyMvLw8A8Prrr6N58+Z45513tB4GeejQIahUqiY1jrDyQcVpaWnSxBQA8M033+C5554DAKSmpqJ9+/bo0KEDrl+/jgkTJmD79u3GDNvkyUTlL5EaxN27d3XO+PDcc881+ZNyoOJHnJSUBFdXV3h6evKvMf8jhMDdu3eRmZmJLl26aE172NTl5+cjIiICffr0QatWrYwdjkkpKyvD9evXYWlpieeff77JzpL2+++/a/0FHKg4Ca/6RHJD2jQ2arUaoaGh1ZY7ODhoPWy1tLQUMTExKCkpQadOneDo6NiQYRpFZmYmrl69Wm25u7s7vL29pdeFhYWIjo6Gra0tOnfuDGtr64YM0yju37+vdbW/ko+PD9q1aye9jo2NRXZ2NgYOHNiQ4RlVdHQ00tLSqi3v16+f1jTgmZmZiI2NRadOnTjO0gAsVoiIiIiIyCTxz9ZERERERGSSWKwQEREREZFJYrFCREREREQmicUKERERERGZJBYrRERERERkklisEBERERGRSWKxQkREREREJonFChHRY86cOYORI0eie/fu+O6774wdToOYM2fOU30q+aJFi7BmzZqntn1D5ebmYsCAATof3PYse9rfX22WLl2KTz75RHr9zjvvYOfOnUaLh4gaDxYrRERVqNVqTJ48GQEBATh48CCmT59u7JD+sDfeeAOBgYE1tnnw4AEUCsVTiyE5ORkZGRlPbfuG+uyzz9C9e3eDnhptSN5MxdP+/mrz8OFDpKenS6/nzJmDFStWQKVSGS0mImocLIwdABGRKXnw4AFycnIwa9YsuLm5GTucepGcnAx7e3ujxvD999/DysrKqDGoVCps2bIFZ8+eNai9KeTtWfXiiy/C09MTO3fuxDvvvGPscIjoGcYrK0RE/3Po0CGMGjUKADB06FB4e3sjKSkJABAZGYk//elP6NmzJ0aPHo0jR45orbt7925MmDABBw4cwPDhw9G9e3cUFhYCAI4cOYKxY8eid+/emDx5MsLCwqr1/euvv2L8+PHo3bs3XnvtNTx48EB6b+XKlfD29oa3tzeGDBmC5cuXV/uL9Y0bNzBjxgz06dMHEyZMwNGjRwEAK1asQFhYGHbu3Clto+q2qyopKcHq1avh7++Pl156CVu2bKnWZuvWrfD390evXr0wZ84cJCQkaL0/Z84cBAYG4v/+7//Qv39/vP766wCAL774AkFBQQCAixcvSrFU/aeyraH9fP3117XGW9XBgwfh5OSEvn37/qG81fZ9VuZg5cqV8PPzw+DBg7Fr1y6tNvr61cWQ7x8w7PurLXZD+hJC4Ouvv0a/fv0wYsQIfPPNNxBCVOtr8uTJ2L17t97PRURkEEFEREIIIXJycsThw4cFABEaGipiYmKEWq0Wt27dEtbW1mLZsmUiIiJCrF27VlhaWorDhw9L665bt05YWFgIPz8/cebMGRETEyM0Go3Ytm2bcHNzE7t37xZRUVFi06ZNonnz5iI0NFRad9OmTcLGxkYEBgaKixcvil27dolXXnlFej8tLU3ExMSImJgYcfbsWREQECCGDRsmvV9YWChat24t3nvvPXHlyhVx7NgxMWHCBHHr1i2RmpoqhgwZIubNmydto6SkpNpnHzp0qLCwsBAffvihuHTpkti5c6ewtLQUR44ckdoEBgYKe3t7sWvXLnH+/Hkxffp04ezsLLKysqptZ+nSpeLSpUviwYMHQgghxo4dK95++20hhBAFBQVSLDExMeL3338X9vb2YsmSJXXup6Z4Hzd79mwxderUP5Q3Q77PytjeeOMNERERITZu3CiaNWsm/vvf/9bary61ff+G5sOQ2A3p6/PPPxetW7cW+/btE2FhYWLs2LHCwsJCLFy4UKvd2bNnhUwmE5mZmXq/EyKi2rBYISKq4ubNmwKASEtLk5b9+c9/FiNHjtRqt3jxYtGrVy/pdWWxUnW9kpIS4ejoKH7++Wetdd99910xadIkIYQQxcXFwt7eXgQGBmq1KS0t1RtjZmamACDi4+OFEELExMQIAEKpVOrcxqhRo8TSpUtr/NxDhw4Vo0eP1lo2fvx4sXjxYilOOzs7sWnTJq3td+jQQXzyySda2xkyZEi17VctVqoqKSkRfn5+YuDAgaK4uLhO/dQUry5+fn7inXfekV7XNW+GfJ+VsXXv3l2rzfvvvy969OhhUL+1efz7r+yzpnwYGnttfVV+Pzt27JDa5OXlCQcHh2rFSlxcnAAgoqKiDPpcRES6cMwKEVEtrl69qnWLEgC8/PLL2Lp1K8rKymBhUXEobd++Pdq2bSu1iY6ORlZWFlasWIGPPvoIouIPRMjKyoKTk5PURqVSYezYsVrbr9wmAKSnp2Pt2rW4ePEilEolNBoNZDIZkpKS0KVLF3Tu3Bk+Pj4YN24c5s+fj2HDhqFz585a2zDECy+8oPXazc0Njx49AgAkJiYiNzcXw4cP14rR398fV69e1Vqvf//+Bvf5t7/9DUlJSbh06RKsra0RExNjcD81xatLSUkJLC0tpdd1zZsh32eloUOHar329/fH119/DbVaXed+a/v+DcmHobHX1tfdu3eRm5ur9flatGiBPn36VIu7coxSSUmJzs9FRGQIFitERLUoKiqCjY2N1jIbGxuUlZVBrVZLJ5mPtykqKgIAfPfdd/Dw8NB6r/JETq1WAwCaN2+ut/9Ro0bBw8MDH3/8MVxdXWFhYYHnn39eWtfS0hKRkZHYs2cPjh8/juXLl6NHjx44ePAg2rRpY/Dn1HWyLP43FqHys+jKQ2pqarVlhti8eTN27dqF0NBQqcirSz81xatL27ZttWbMqmveDPk+KzVr1kzrdfPmzaHRaFBcXAx7e/s69Vvb929IPgyNvba+Krej6/M9rjLXhsy8RkSkDwfYExHVokuXLrh586bWshs3bsDNzQ22trZ61+vatSvMzMyQnp5ebTB5p06dAABeXl4wMzNDVFSUzm0kJyfjxo0b2LBhA0aOHInnn38eMpkM5eXlWu1atmyJRYsW4eDBg0hJSYFCoZCeEWNubl7jSbwhOnfuDJlMpjMPXbt2rfP2fv/9d7z99tsICgrSGvBe3/1U5evrWy3PdcmbId9npejoaK3Xt27dgrOzszS7WE39VmXo918bQ2I3pK9OnTpBJpNpfT4hRLXPCwBRUVFwc3ND+/bt6xQrEVFVLFaIiGqxaNEi7N27FxcuXAAAJCQk4JtvvsGiRYtqXK9169aYPXs2PvroI1y/fh0AoNFoEBISIs2M5eTkhBkzZuDvf/+7NONVdnY21q5dCwBo1aoVLC0tce7cOQBAXl4elixZotXP1atXsX79emn2sZKSEpSWlkonxq6urtKsZk/K3t4er776Kj755BNkZWUBAPbt24eIiAgsXLiwTtt68OABpkyZgvfeew8zZsx4av087pVXXkF0dLR0haaueTPk+6x0+vRpaYav5ORkrF27Fm+88YZB/VZlyPdvCENiN6SvVq1aYcqUKVi1apU0S9iGDRuQmJhYrc9Tp05h8uTJdY6ViKgqFitERLWYOnUqli1bhhEjRsDNzQ09evTA6NGjsXz58lrX3bx5M8aPH48BAwbAzc0NDg4OCAwMhK+vr9Tm+++/x4ABA9C9e3e0a9cO3t7e0jNeWrRogY0bN+LNN9+Eh4cH2rZtiy5dumjdutO5c2ckJSXB1dUVnp6ecHd3h6+vL958800AwMKFCxEeHg4PD48apy6uzYYNG+Ds7AxXV1e0adMGb731FrZt24aePXvWaTvHjh2DQqGAXC7XOXVxffXzuG7dumHkyJHSk9WfJG+GfJ8AMGnSJHzwwQdwdXVFp06d8Pzzz+Pvf/+7Qf1WZcj3b6jaYje0rw0bNkAIgTZt2sDFxQVyuRwvvfSSVhulUonjx4/r/ExERHUhE3/03gAiokakpKQEiYmJ6Nq1K8zNzbXeKy4uRmpqKpydndGyZUut97Kzs5GTk4OOHTvq3K5arUZqairatm2rd0xHQUEBlEol2rdvD5lMVm39hw8fok2bNrC1tUVcXBzatWundRtaeXk5Hj58CGdn52p9lJWVITU1FYWFhejcubPWQHOg4mpH8+bN0bp1a2lZRkYGysvLqz0cMysrCyqVCh4eHtXGSejaDgCkpKTAysoKLi4uyMnJ0XraeSVbW1ut8RR17UdfvFVFR0djxIgRiIuLg52d3RPnrabv09/fH0OGDMHnn3+OzMxMlJeXw8XFpVosNfX7uNq+/7rko7Z90ZB9Daj4Tu3s7GBnZ4fU1FSYm5tLY26WL1+OgoICbNq0qcbPRURUGxYrRETUpNy7dw/Ozs41jjf6I6oWK01VUlJSjYU5EZGhOBsYERE1KZ6ensYOodHTd4WRiKiueGWFiIioHum7FY6IiOqOxQoREREREZkkzgZGREREREQmicUKERERERGZJBYrRERERERkklisEBERERGRSWKxQkREREREJonFCpEJWrduHYKDg/W+f+rUKaxfv74BIyIiIiJqeCxWiBrY2bNn8c9//tPYYRARERGZPBYr1OgFBwdj3bp1xg5DMmzYMCxdutTg9qYWPxEREVFDYbFCREREREQmiU+wp3onhEBISAjOnTsHlUoFNzc3TJkyBV26dAFQMd7i5s2bcHd3x5UrV1BeXo6BAwdiypQp0jYuXbqEEydOQKFQwMnJCRMnTkSvXr309nn//n3897//RXJyMuzt7TF8+HAMGzYMN2/exMaNG7Xarl69Gi4uLjX2URlj27Ztce3aNZiZmeGll17CmDFjIJPJtLZXXl6O9957D++++y48PT2Rnp6OVatWYcKECRg7diwAYOXKlXjllVfQu3dvnD17FlFRUdLVFY1Gg6NHjyI0NBRCCLz44otISUlB79694eLiojP+a9eu1ZpDIiIiomedhbEDoMYnLCwMx48fx8KFC+Hh4YHQ0FBs2LABn376KVq1agUAiIuLw4svvojPPvsMGRkZ+Ne//oXu3buje/fuiIqKwo8//ogFCxagc+fOSEhIwJYtW7Bs2TJ4eHjo7HPv3r3w8vLCkiVLUFhYiODgYKhUKvTs2RNTp07FzZs38e6770rtDekjLi4OXbt2xWeffYbU1FRs3rwZDg4OGDx4sFbf5ubm6Nq1K27fvg1PT0/ExMTAxcUFt2/fxtixY5GVlQWlUolu3brpzVdYWBgWLVqEtm3b4uTJk0hISEDv3r31xl9bDomIiIgaA94GRvXu/PnzGD58OLy8vGBjY4ORI0fC2dkZFy9elNp4eHhg2LBhaNasGTp06IAuXbrgwYMHACoGoI8cORI+Pj6wsrJC9+7d0b9/f631H2dhYQFra2tYWVnB0dER06ZNg4ODg972hvTh5OSE8ePHw8bGBp07d8bw4cNx/vx5ndvz8fFBbGwsACA2NhZjxoxBSkoKiouLcfv2bbRv3x7NmzfXm6+AgAB07NgRNjY2mDBhQo2xV6oph0RERESNAa+sUL3Lzs6Gi4uL1jIXFxdkZ2dLr1u2bKn1vpWVFUpLSwEASqUScrkccrlcq02fPn0AAAsXLpSWTZ8+HcOGDcPrr7+Oo0ePYs2aNbCzs0Pfvn0xcOBAvTHW1gdQUaxUveXL2dkZOTk5Orfn4+MDuVyO4uJixMfHY/bs2YiIiEBcXBxiY2Ph4+OjN5acnBw4OztLr83MzODk5KS3faWackhERETUGLBYoXrXqlUrKBQKrWWPHj2Cp6enQes7Ojri5ZdfxvDhw3W+v2XLlmrLnJycMGfOHACAQqHAunXrYGFhgX79+sHMrPoFxNr6AIDMzEwIIaSCRaFQ6L3i4ebmBltbW4SEhMDR0REtWrSAj48Pbt++jdjYWLzxxht6+3FwcIBSqZReazQaZGZmSq91xU9ERETUFPAsiOrdwIEDcebMGSQkJKCoqAinTp3Co0eP0K9fP4PWHz58OI4fP47bt29DrVZDqVTi+PHjuHTpkt51tmzZgoSEBJSUlECj0UAIAbVaDQCwt7eHUqlEYWFhnfrIzMzE0aNHUVRUhLt37+Ls2bM1Xq3x9vbGqVOnpKsoPj4+uHDhAoqLi9GpU6ca83X69Gncu3cPRUVFOHLkiNYVHF3xExERETUFvLJC9W7IkCFQq9X44YcfkJubCzc3NyxZsgSOjo4GrV95K9ahQ4eQkZGBli1bon///ujZs6fedfz9/fHzzz/j/v37aN68udZtYM8//zwuXLiADz74AGq1GqtXrzaoDy8vL6hUKqxcuRJmZmYYOnQoBg0apDcGHx8fREZGSsWKh4cHzM3N0alTJ1haWupdz8/PDyqVCps2bZJmA6ucOU1f/ERERERNAacuJtLh1KlTiImJwdtvv23sUIiIiIiaLN4GRkREREREJonFChERERERmSTeBkZERERERCaJV1aIiIiIiMgksVghIiIiIiKTxGKFiIiIiIhMEosVIiIiIiIySSxWiIiIiIjIJLFYISIiIiIik8RihYiIiIiITBKLFSIiIiIiMkksVoiIiIiIyCT9fxgtqnXhODrHAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "width at step 1: 3.29\n", "width at step 20: 3.67\n" ] } ], "source": [ "rng = np.random.default_rng(1)\n", "x_long = ar2(600, rng)\n", "H_long = 20\n", "lo_w, up_w, _ = forecast_intervals(\n", " x_long, model=AR(order=2), horizon=H_long, alpha=0.1, n_bootstraps=999, random_state=1\n", ")\n", "width = up_w - lo_w\n", "steps = np.arange(1, H_long + 1)\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4.4), layout=\"constrained\")\n", "ax.plot(\n", " steps,\n", " width,\n", " \"o-\",\n", " color=\"#009E73\",\n", " lw=1.8,\n", " ms=5, # Okabe-Ito green\n", " label=\"90% interval width\",\n", ")\n", "# Mark the one-step width and the long-horizon plateau so the rise is legible.\n", "ax.axhline(width[0], color=\"0.6\", ls=\":\", lw=1.0)\n", "ax.annotate(\n", " \"one-step width\",\n", " xy=(1, width[0]),\n", " xytext=(2.5, width[0] - 0.18),\n", " color=\"0.4\",\n", " fontsize=9,\n", " va=\"top\",\n", ")\n", "ax.set_xlabel(\"forecast horizon (steps ahead)\")\n", "ax.set_ylabel(\"90% interval width (series units)\")\n", "ax.set_title(\"Interval width rises, then flattens at the AR(2) process-variance ceiling\")\n", "ax.set_xticks(steps[::2])\n", "ax.margins(y=0.15)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(fontsize=9, loc=\"lower right\", framealpha=0.9)\n", "plt.show()\n", "\n", "print(f\"width at step 1: {width[0]:.2f}\")\n", "print(f\"width at step {H_long}: {width[-1]:.2f}\")" ] }, { "cell_type": "markdown", "id": "34e1b6ef", "metadata": {}, "source": [ "The width climbs from the one-step value and flattens out. The flattening is\n", "expected for a stationary AR: the forecast variance converges to the process\n", "variance as the horizon grows, so the band approaches a finite ceiling rather than\n", "widening without bound. A non-stationary process (a random walk, say) would not\n", "level off, but `forecast_intervals` rejects unstable fits before it gets that far." ] }, { "cell_type": "markdown", "id": "68448524", "metadata": {}, "source": [ "## Supported models: AR only\n", "\n", "`forecast_intervals` currently supports AR models and nothing else. Passing an\n", "ARIMA or VAR specification raises `MethodConfigError` right away instead of\n", "returning an approximate result. The cell below calls it with each unsupported\n", "model inside a `try/except` and prints the error it raises." ] }, { "cell_type": "code", "execution_count": 7, "id": "55e267ee", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:56.016154Z", "iopub.status.busy": "2026-06-22T16:14:56.015982Z", "iopub.status.idle": "2026-06-22T16:14:56.021187Z", "shell.execute_reply": "2026-06-22T16:14:56.019938Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ARIMA -> [TSB_UNSUPPORTED_MODEL_FEATURE] forecast_intervals currently supports an AR model; got ARIMA\n", "VAR -> [TSB_UNSUPPORTED_MODEL_FEATURE] forecast_intervals currently supports an AR model; got VAR\n" ] } ], "source": [ "for model in (ARIMA(order=(1, 1, 1)), VAR(order=1)):\n", " try:\n", " forecast_intervals(x, model=model, horizon=5)\n", " except MethodConfigError as err:\n", " print(f\"{type(model).__name__:<6} ->\", err)" ] }, { "cell_type": "markdown", "id": "32bfa458", "metadata": {}, "source": [ "Both calls raise `MethodConfigError` with the code `TSB_UNSUPPORTED_MODEL_FEATURE`.\n", "Out-of-sample forecast intervals for ARIMA and VAR are planned for a later release.\n", "Until then the function raises rather than returning an unvalidated band.\n", "\n", "If you need a rough forward band for a non-AR model today, you can drive it\n", "yourself from bootstrap replicates: fit your model, simulate forward paths from\n", "resampled innovations, and take per-step quantiles, which is the recipe\n", "`forecast_intervals` automates for the AR case. That is a manual workaround, not a\n", "supported API, and it carries the same asymptotic-coverage caveats shown above, so\n", "treat its output as indicative rather than calibrated." ] }, { "cell_type": "markdown", "id": "856479e9", "metadata": {}, "source": [ "## The forecast fan in one paragraph\n", "\n", "A forward band is nothing more than many simulated futures read off at per-step\n", "quantiles: call `forecast_intervals(X, model=AR(order=p), horizon=H, alpha=...)` and\n", "you get back `(lower, upper, median)`, each of length `H`. On the synthetic AR(2) the\n", "bands cover close to nominal against fresh paths, and they fan out with the horizon\n", "until they hit the process-variance ceiling. For now the function is AR-only and\n", "raises `MethodConfigError` for ARIMA or VAR; wider model support is on the roadmap." ] } ], "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 }