{ "cells": [ { "cell_type": "markdown", "id": "2bf8d226", "metadata": { "id": "2bf8d226" }, "source": [ "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/MeiraDavidson/math_module2/blob/main/notebooks/ch1_sequences.ipynb)\n\n", "# Chapter 1 — Companion Notebook\n", "## Patterns That Go Somewhere\n", "*What does a list of numbers want to become?*\n", "\n", "Three live experiments on the central idea of the chapter — that a never-ending list can be *sneaking up on* a single number. You will play the $\\varepsilon$–$N$ game against a shrinking tolerance, watch a race between a base and an exponent decide a $1^\\infty$ limit, and climb a cobweb staircase to a fixed point you cannot write in closed form.\n", "\n", "> **How to use this notebook.** Run every cell from the top (Shift+Enter). Each widget below is live — drag the sliders and watch the picture respond. Requires `ipywidgets` and `matplotlib`." ] }, { "cell_type": "code", "execution_count": 1, "id": "c9a91ce6", "metadata": { "id": "c9a91ce6", "executionInfo": { "status": "ok", "timestamp": 1782334601155, "user_tz": 240, "elapsed": 17, "user": { "displayName": "Meira Davidson", "userId": "09448014842742744623" } } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import animation\n", "from ipywidgets import (interact, interactive, fixed, Dropdown, Checkbox,\n", " Button, Output, VBox, HBox,\n", " FloatSlider, IntSlider, FloatLogSlider)\n", "from IPython.display import HTML, display, Markdown\n", "\n", "# Book 2 palette — matches the printed figures in figures/png/\n", "BLUE=\"#1f4e79\"; RED=\"#c0392b\"; GREEN=\"#2e8b57\"; ORANGE=\"#e08e0b\"\n", "PURPLE=\"#6c3483\"; TEAL=\"#1b9e9e\"; GRAY=\"#7f8c8d\"; DARK=\"#2c3e50\"\n", "SHADE=\"#9fc5e8\"; SHADE2=\"#f4b6ad\"; SHADEG=\"#a9dfbf\"; LIGHT=\"#d6dbdf\"\n", "\n", "plt.rcParams.update({\n", " \"figure.figsize\": (7.2, 4.5), \"figure.dpi\": 96,\n", " \"font.family\": \"serif\", \"mathtext.fontset\": \"cm\", \"font.size\": 12,\n", " \"axes.spines.top\": False, \"axes.spines.right\": False,\n", " \"axes.grid\": True, \"grid.color\": LIGHT, \"grid.linewidth\": 0.7,\n", " \"lines.linewidth\": 2.2, \"lines.solid_capstyle\": \"round\",\n", "})\n", "\n", "def axes(ax=None, title=None):\n", " '''A clean axes with a light grid; returns the axes.'''\n", " if ax is None:\n", " _, ax = plt.subplots()\n", " if title:\n", " ax.set_title(title, color=DARK)\n", " return ax\n" ] }, { "cell_type": "markdown", "id": "634bff18", "metadata": { "id": "634bff18" }, "source": [ "## 1. Name your tolerance — the $\\varepsilon$–$N$ game\n", "\n", "Here is the definition turned into a game. A skeptic names a tolerance $\\varepsilon>0$ and bets your terms cannot get within $\\varepsilon$ of the limit $L$ *and stay there*. You answer with a **cutoff** $N$: a seat number past which **every** term is inside the window $L\\pm\\varepsilon$. If you can win for any $\\varepsilon$ the skeptic dares to name, then $a_n\\to L$.\n", "\n", "Pick a sequence and drag $\\varepsilon$. The shaded band is $L\\pm\\varepsilon$; terms still *outside* it are grey, terms from the cutoff $N$ onward are green. Watch what happens as you shrink $\\varepsilon$ toward zero: the band pinches, and the cutoff $N$ marches to the right. That trade-off *is* the limit." ] }, { "cell_type": "code", "execution_count": 2, "id": "82d940d0", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 503, "referenced_widgets": [ "ddbdca0b4496447783a318e03476cb1a", "2ea5882df49e4d18b48fca57fe94860e", "fcaf52e98909494bb2d173510569c45c", "7ed876d033b041889d0973a7cefe67ee", "ad296f2cd5e04e18a5d06c4f892cc2e2", "8f02ed1ede9641d49c110744b5bbbef2", "d565712c19a5432c99201633ac0d4f56", "5ae8237a837c4b6d906e6a19fddda25d", "ba0c1c011739424bbf0f63bce835e065", "c6ad5c62dfb947b0891e0a07a8f2e384" ] }, "id": "82d940d0", "executionInfo": { "status": "ok", "timestamp": 1782334609049, "user_tz": 240, "elapsed": 277, "user": { "displayName": "Meira Davidson", "userId": "09448014842742744623" } }, "outputId": "24b8bdd3-742b-4b24-e124-fb941c795979" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "interactive(children=(Dropdown(description='sequence', options=('a_n = 1/n -> 0', 'a_n = n/(n+1) -> 1', 'a…" ], "application/vnd.jupyter.widget-view+json": { "version_major": 2, "version_minor": 0, "model_id": "ddbdca0b4496447783a318e03476cb1a" } }, "metadata": {} } ], "source": [ "# The convergent sequences on offer, each with its true limit L.\n", "_SEQS = {\n", " 'a_n = 1/n -> 0': (lambda n: 1.0 / n, 0.0),\n", " 'a_n = n/(n+1) -> 1': (lambda n: n / (n + 1.0), 1.0),\n", " 'a_n = (-1)^n / n -> 0': (lambda n: (-1.0) ** n / n, 0.0),\n", " 'a_n = (1/2)^n -> 0': (lambda n: 0.5 ** n, 0.0),\n", "}\n", "_NTERMS = 40\n", "\n", "def _epsilon_N(seq='a_n = 1/n -> 0', eps=0.2):\n", " rule, L = _SEQS[seq]\n", " n = np.arange(1, _NTERMS + 1)\n", " a = rule(n)\n", " inside = np.abs(a - L) < eps # term is within the window\n", " # Cutoff N = smallest index past which ALL later terms stay inside.\n", " # Scan from the right: the last term that is still OUTSIDE fixes N.\n", " outside_idx = np.where(~inside)[0]\n", " N = int(n[outside_idx[-1]]) if outside_idx.size else 0\n", " past = n > N # the green tail\n", "\n", " fig, ax = plt.subplots()\n", " axes(ax, f'{seq} (tolerance \\u03b5 = {eps:.4g})')\n", " ax.axhline(L, color=DARK, lw=1.3, zorder=1)\n", " ax.axhspan(L - eps, L + eps, color=SHADE, alpha=0.45, zorder=0,\n", " label=f'window L \\u00b1 \\u03b5')\n", " ax.scatter(n[~past], a[~past], s=34, color=GRAY, zorder=3,\n", " label='before cutoff')\n", " ax.scatter(n[past], a[past], s=34, color=GREEN, zorder=3,\n", " label='from N onward (all inside)')\n", " ax.axvline(N + 0.5, color=RED, lw=1.6, ls='--', zorder=2)\n", " ax.annotate(f'N = {N}', xy=(N + 0.5, L), xytext=(N + 2.5, L + 1.4 * eps),\n", " color=RED, fontsize=13,\n", " arrowprops=dict(arrowstyle='->', color=RED))\n", " ax.set_xlabel('n (seat number)'); ax.set_ylabel('a_n')\n", " ax.set_xlim(0, _NTERMS + 1)\n", " pad = max(eps * 1.6, 0.05)\n", " lo = min(a.min(), L - eps) - pad\n", " hi = max(a.max(), L + eps) + pad\n", " ax.set_ylim(lo, hi)\n", " ax.legend(loc='upper right', framealpha=0.9, fontsize=9)\n", " plt.show()\n", "\n", "interact(_epsilon_N,\n", " seq=Dropdown(options=list(_SEQS), value='a_n = 1/n -> 0',\n", " description='sequence'),\n", " eps=FloatLogSlider(value=0.2, base=10, min=-3, max=0, step=0.05,\n", " description='\\u03b5', readout_format='.4g'));" ] }, { "cell_type": "markdown", "id": "bad98b62", "metadata": { "id": "bad98b62" }, "source": [ "## 2. A race for $1^\\infty$ — where does $\\left(1+\\tfrac{b}{n}\\right)^{pn}$ land?\n", "\n", "The form $1^\\infty$ is indeterminate because the answer hinges on a *race*: how fast the base $1+\\tfrac{b}{n}$ sinks toward $1$ against how fast the exponent $pn$ climbs. The gauge that settles it: look at $(\\text{exponent})\\times(\\text{base}-1)$. Here that is $pn\\cdot\\tfrac{b}{n}=b\\,p$, a constant — so the sequence lands on\n", "\n", "$$\\left(1+\\frac{b}{n}\\right)^{pn}\\longrightarrow e^{\\,b\\,p}.$$\n", "\n", "Drag the base-rate $b$ and the power $p$. The blue dots are the sequence; the red line is the predicted limit $e^{bp}$. Push the product $bp$ toward $0$ and the limit slides to $1$; crank it up and the limit shoots toward $\\infty$. Set $b=p=1$ to recover the birth of $e$ itself." ] }, { "cell_type": "code", "execution_count": 3, "id": "1521c18a", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 531, "referenced_widgets": [ "8c8a75b78f274dd49a4224fb9dc949e1", "b6d7fb0e187840b5aed4aeeedf6e12e4", "2c793e9786884199bb2f775dd76ba45f", "a9cdf3a3820343749fef6074e96ec88c", "39b7be29b29840888b0f637c6cb10c5f", "191d018e26624daa90adec4f344de1ff", "c72e3b9226924a80b5ff6014708f21e4", "bdba1375e4b7432c8e02743f830d3922", "a982d25ce8ec49a481abe4d2d180cb33", "d8f0cdb5a72d439a907ed0b2b3231db5" ] }, "id": "1521c18a", "executionInfo": { "status": "ok", "timestamp": 1782334662886, "user_tz": 240, "elapsed": 174, "user": { "displayName": "Meira Davidson", "userId": "09448014842742744623" } }, "outputId": "1cfc8596-770f-4739-b9df-5dfb0750a0cd" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "interactive(children=(FloatSlider(value=1.0, description='base-rate b', max=3.0, min=-2.0), FloatSlider(value=…" ], "application/vnd.jupyter.widget-view+json": { "version_major": 2, "version_minor": 0, "model_id": "8c8a75b78f274dd49a4224fb9dc949e1" } }, "metadata": {} } ], "source": [ "def _race(b=1.0, p=1.0):\n", " n = np.arange(1, 121)\n", " a = (1.0 + b / n) ** (p * n)\n", " k = b * p # the gauge: (exponent)x(base-1)\n", " limit = np.exp(k)\n", "\n", " fig, ax = plt.subplots()\n", " axes(ax, f'(1 + {b:.2g}/n)^({p:.2g}\\u00b7n) \\u2192 e^(b\\u00b7p) = e^{{{k:.3g}}}')\n", " ax.scatter(n, a, s=20, color=BLUE, zorder=3, label='the sequence')\n", " ax.axhline(limit, color=RED, lw=2.0, ls='--', zorder=2,\n", " label=f'limit e^(bp) = {limit:.5g}')\n", " ax.axhline(1.0, color=GRAY, lw=1.0, ls=':', zorder=1, label='y = 1')\n", " ax.set_xlabel('n'); ax.set_ylabel('a_n')\n", " lo = min(1.0, a.min(), limit); hi = max(a.max(), limit)\n", " span = hi - lo or 1.0\n", " ax.set_ylim(lo - 0.08 * span, hi + 0.12 * span)\n", " ax.legend(loc='best', framealpha=0.9, fontsize=9)\n", " # A one-line read-out of which way the race tipped.\n", " if abs(k) < 0.05:\n", " verdict = 'b\\u00b7p \\u2248 0: the base wins, limit swings toward 1.'\n", " elif k > 0:\n", " verdict = f'b\\u00b7p = {k:.3g} > 0: balanced, limit = e^{k:.3g} = {limit:.4g}.'\n", " else:\n", " verdict = f'b\\u00b7p = {k:.3g} < 0: limit = e^{k:.3g} = {limit:.4g} (below 1).'\n", " ax.text(0.5, -0.22, verdict, transform=ax.transAxes, ha='center',\n", " color=DARK, fontsize=10)\n", " plt.show()\n", "\n", "interact(_race,\n", " b=FloatSlider(value=1.0, min=-2.0, max=3.0, step=0.1,\n", " description='base-rate b'),\n", " p=FloatSlider(value=1.0, min=0.2, max=4.0, step=0.1,\n", " description='power p'));" ] }, { "cell_type": "markdown", "id": "4e1e4b5f", "metadata": { "id": "4e1e4b5f" }, "source": [ "## 3. Climbing to a fixed point — the cobweb for $a_{n+1}=\\sqrt{2+a_n}$\n", "\n", "Some sequences have no closed form, yet still settle on an exact limit. Take $a_1=\\sqrt{2}$ and $a_{n+1}=\\sqrt{2+a_n}$. It climbs: $\\sqrt2,\\ \\sqrt{2+\\sqrt2},\\ \\ldots$, bounded above by $2$. If it converges to $L$, then $L$ must satisfy its own rule, $L=\\sqrt{2+L}$, which gives $L=2$ — a **fixed point**, a value the process leaves unchanged.\n", "\n", "The **cobweb** makes this visible. The blue curve is $y=\\sqrt{2+x}$; the grey line is $y=x$. From a term on the diagonal, go *up* to the curve (that computes the next term), then *across* to the diagonal (that copies it back onto the input axis), and repeat. Drag the number of steps and watch the staircase spiral into the corner at $(2,2)$ where the two graphs cross. The dots on the right are the same terms, marching to $2$." ] }, { "cell_type": "code", "execution_count": null, "id": "1992699a", "metadata": { "id": "1992699a" }, "outputs": [], "source": [ "def _g(x):\n", " return np.sqrt(2.0 + x)\n", "\n", "def _cobweb(steps=6):\n", " # Build the orbit a_1 = sqrt(2), a_{n+1} = sqrt(2 + a_n).\n", " a = [np.sqrt(2.0)]\n", " for _ in range(steps):\n", " a.append(_g(a[-1]))\n", " a = np.array(a)\n", "\n", " fig, (axL, axR) = plt.subplots(1, 2, figsize=(10.4, 4.6))\n", "\n", " # --- left: the cobweb diagram ---\n", " axes(axL, 'cobweb: y = \\u221a(2 + x) vs y = x')\n", " xs = np.linspace(0, 2.6, 400)\n", " axL.plot(xs, _g(xs), color=BLUE, label='y = \\u221a(2 + x)')\n", " axL.plot(xs, xs, color=GRAY, lw=1.4, ls='--', label='y = x')\n", " axL.plot(2, 2, 'o', color=RED, ms=8, zorder=5)\n", " axL.annotate('fixed point (2, 2)', xy=(2, 2), xytext=(0.9, 2.35),\n", " color=RED, fontsize=10,\n", " arrowprops=dict(arrowstyle='->', color=RED))\n", " # staircase: (x, x) -> (x, g(x)) -> (g(x), g(x)) -> ...\n", " x = a[0]\n", " axL.plot([x, x], [0, _g(x)], color=GREEN, lw=1.4, zorder=4)\n", " for i in range(steps):\n", " y = _g(x)\n", " axL.plot([x, y], [y, y], color=GREEN, lw=1.4, zorder=4) # across to y=x\n", " axL.plot([y, y], [y, _g(y)], color=GREEN, lw=1.4, zorder=4) # up to curve\n", " x = y\n", " axL.set_xlabel('x = a_n'); axL.set_ylabel('a_{n+1}')\n", " axL.set_xlim(0, 2.6); axL.set_ylim(0, 2.6)\n", " axL.legend(loc='lower right', framealpha=0.9, fontsize=9)\n", "\n", " # --- right: the terms approaching 2 ---\n", " axes(axR, 'the terms a_n \\u2192 2')\n", " idx = np.arange(1, len(a) + 1)\n", " axR.axhline(2.0, color=RED, lw=1.6, ls='--', label='limit L = 2')\n", " axR.plot(idx, a, '-o', color=BLUE, ms=6, zorder=3)\n", " for xi, yi in zip(idx, a):\n", " axR.annotate(f'{yi:.4f}', xy=(xi, yi), xytext=(0, 7),\n", " textcoords='offset points', ha='center',\n", " fontsize=8, color=DARK)\n", " axR.set_xlabel('n'); axR.set_ylabel('a_n')\n", " axR.set_xlim(0.5, len(a) + 0.5); axR.set_ylim(1.3, 2.08)\n", " axR.legend(loc='lower right', framealpha=0.9, fontsize=9)\n", " fig.tight_layout()\n", " plt.show()\n", "\n", "interact(_cobweb,\n", " steps=IntSlider(value=6, min=1, max=12, step=1,\n", " description='iterations'));" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "name": "python", "pygments_lexer": "ipython3" }, "colab": { "provenance": [] }, "widgets": { "application/vnd.jupyter.widget-state+json": { "ddbdca0b4496447783a318e03476cb1a": { "model_module": "@jupyter-widgets/controls", "model_name": "VBoxModel", "model_module_version": "1.5.0", "state": { "_dom_classes": [ "widget-interact" ], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "1.5.0", "_model_name": "VBoxModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "1.5.0", "_view_name": "VBoxView", "box_style": "", "children": [ "IPY_MODEL_2ea5882df49e4d18b48fca57fe94860e", "IPY_MODEL_fcaf52e98909494bb2d173510569c45c", "IPY_MODEL_7ed876d033b041889d0973a7cefe67ee" ], "layout": "IPY_MODEL_ad296f2cd5e04e18a5d06c4f892cc2e2" } }, "2ea5882df49e4d18b48fca57fe94860e": { "model_module": "@jupyter-widgets/controls", "model_name": "DropdownModel", "model_module_version": "1.5.0", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "1.5.0", "_model_name": "DropdownModel", "_options_labels": [ "a_n = 1/n -> 0", "a_n = n/(n+1) -> 1", "a_n = (-1)^n / n -> 0", "a_n = (1/2)^n -> 0" ], "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "1.5.0", "_view_name": "DropdownView", "description": "sequence", "description_tooltip": null, "disabled": false, "index": 0, "layout": "IPY_MODEL_8f02ed1ede9641d49c110744b5bbbef2", "style": "IPY_MODEL_d565712c19a5432c99201633ac0d4f56" } }, "fcaf52e98909494bb2d173510569c45c": { "model_module": "@jupyter-widgets/controls", "model_name": "FloatLogSliderModel", "model_module_version": "1.5.0", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "1.5.0", "_model_name": "FloatLogSliderModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "1.5.0", "_view_name": "FloatLogSliderView", "base": 10, "continuous_update": true, "description": "ε", "description_tooltip": null, "disabled": false, "layout": "IPY_MODEL_5ae8237a837c4b6d906e6a19fddda25d", "max": 0, "min": -3, "orientation": "horizontal", "readout": true, "readout_format": ".4g", "step": 0.05, "style": "IPY_MODEL_ba0c1c011739424bbf0f63bce835e065", "value": 0.002818382931264455 } }, "7ed876d033b041889d0973a7cefe67ee": { "model_module": "@jupyter-widgets/output", "model_name": "OutputModel", "model_module_version": "1.0.0", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_c6ad5c62dfb947b0891e0a07a8f2e384", "msg_id": "", "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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QG+Dk5GgswJ/lXrqUWSHyrPy8N3P7Ooy/kRGzdxbnXqZUSZP9xF/PyFP/D8aYbavRaOHk5Gh2ZX1WuneMwOPkVIyf/j0+nzIPpUu5Yefvi/L1uytIbi7OePAoGeq0NLNe58zXulsuvq53c3n6/sjmBiGZy12fblcQ76cZPyzBydMXsOy7KfB42gP6rMUrN2DPgaP46J3+6BDRwri8d9d2uHLtBpas+QM1q1fBa23CX3B2WYu/cRNfz12IKhXLYdJnQ43DYwL9fTF13Mfo/e4ofDHtOyyaM8msrUyWsa1Gq83XsYlehIWtHfp+8Sos+PU39O7aDt+M+8j4xyxzXOLLkrzk2E5rGWOr0+mxZ/8RdI5sle02Umn2BcrLmPe1eTGRE5VKjZ37DmHzjr04eOwU9HoDAv19MWb4EES2aprlBO655VO5AgAgMSnrXui7SRnFTdWn2xUFJ6eMr3Et+c9SZnH6wVu9MaDna7lul9NrJr/vzby+DjXaF+cts/be9Ov3+f6nRavVYtjYqbh6LQE/TB+HenVrv3DowvMKa4xt1coV8eDRWSTee2AcwpHp7tOe7qrPXWCVlcz3R+b74FmpT1RQqdNQzsvTeNOFl30/zZ6/FNt2R+OXb78yzkDwvOjDJwAAofUDzNaF1AvAmo3/ICr6SL4L20PHYqHT6dAwqI7ZWP46tWrA2ckRh4/HQqVSm12MnPmedc5iCAhRQWBha4fW/PEPnBwdMGbYYIv3mmTFWsbYHj4Ri8fJqdkOQ7A0rVaL/w6fwJYd+xAVfRhp6Rr4VK6A997shQ6tm2c51U9+VCrvjQreZXEl/gY0Gq1JYZKersGVazdQsbxXkc6IkNnbmpsxkM+rWjmjWMlquEhaejoeJ6fC1cUZHmVK5Wo/2X3lGnvuIlxdSqBqpdwX/IX93vSpXAFXryXgbtJ9s7HXaenpePQ4BV6e7pBIJKhaqQLOX47DnbtJZoWtSqXGqbMXEejvixI5zKKyfc9BRB8+ga/GDENoFtNV5UZhjbFt1CAQx2PO4uzFK2Zj/89evAIACM3FzA8hT88rs43Jfi483c8zBebLvJ+mf7cYO/cdwtL/fW18f2u1Wly8cg11atUwbpd5e2kJzP/hkT79j+VlpgpUqdV4eoAsSaVSCCHwRG1e2GaOHc7qGxOigsAxtnZILpf/f3fMMxJuJ1ogGuu1c+9BeJQpbZW3gJw0az5adhuE4WOn4njsObzeORJrf56FTcu/x3tvvl5gRW2mXl0iodFosWPvQZPlO/YehEajRa/OkQV6vBepXqUS5HI5bmUxVybw/xfmZH4Vr9PpMWXeQtxOvIcmrwSjTOmS2H/kJJ6o1Cbtdu07DABo16r5C2eVaBPeFEqlAjv3HjQb6nH/4SMMHP4FrsSbT7eUk8J+b2b20O3cd8hs3Q+/rMZ7oyYbe6I7tsm4uGxbVLTZthu27MCYr+dCqci5b+Tu017JrMZCr/tzK/63aGWe4i9IXdu/CgelEv/s3GeyXKVSI2r/UdSsVgX1n7teQKVOMxteUqFcWTRv1AAnYs+Z/ZOzZec+SCQSs/dHXt9PQgh8PWcBdkcfwZJvvzZ5f99Nemj2DVfA0ynbspqHN3NZwDPTuuVVgL8vgIxZGZ6/icWFK/FIfaKCd1mPLC8Ou3M3CXK5HNWqVMz38YlywsLWDr3WJgxqdRpmfL/E+J/92YtX8NOytRaOzHoYDAbs+u8wXm0eWmDTZhWkf3dH49XmjbBo7iRsX7cQo4a+le044ILQv0dH1A/0x+z5S3HhchyAjD9gc35ahvoBtdGve4dCO3ZWnJ2d0CCwNs5fjsvy7lCVK5aHg1KJi1euAQCOnDyN9X9vh5OjAxwdHPDV6A+h0WoxadZ8412QLlyJx/8WrYRP5QoY/k7/F8ZQ1qMMxgwbgluJ9zD120XGHrAbt+7gky9n4JXgughv0jBP51XY781XWzRCp7bh+GtblPECOSEEtkXtx5qN/+CjZ867b/cOeCW4Lpb/9hd2Rx+GEOLp++IQvlu0CiM/GPjCeZNbNQuFk6MD/vfzCmMRZDAYEBV9BN/+vNKiF5R6l/XAqKFvYf+Rk1i29k8YDAaoVGpMnPkjtFotvhr9ocl7X6VOQ/u+76NV98GIPXfRZF/jPn4HJd1cMXbKt3jw6DGAjCEUf/6zCwN7dzGZGxjI2/tJCIFJM3/E2j+3IqReXfy5dRd+XLLG+LPi97/Mzu3dN19HmVJuWLj8d+zZfwR6vR5anQ5/b9+DtX9uRYVyXuifzUwvudEwqA4iwhrjwuV4zPj+F+Nr/0r8DXw59TtIpVKMGvpWlm3PX4pDg8DaeZ4vnSi3JCK39wwkm6HV6bBszZ/489/dSLybhJJurqhZrQpC6tXF7PnL4OTkCGcnR/yz+qdsp6R53mv9hyLpwSOkPlHBpYQzqlQsjzULZ2La/xZhy459ePg4GQ5KJVxcnLHk26+N48yK2oGjp/D5lHkAMq6sNxgMcH/6lfOHg/qgx2ttAADHY87izWHjsHD2RDRuGGSyj+8Xr8Lvf2/H/QePIJfLUdLNBfO+Gg0A+PjL6XicnAqdTgf3MqXQq3Mk3h/Yq8DP4/mvMItCWno6Fiz7Df/s3Ad1WhqcHB3R7tXmePfNnsbxg0Vp596D+PjL6Vg0d1KWX3P/tS0K85euRWqqCq4uJfDem6/jtbbhxvVnzl/GwuW/4+SZjLlAnRwdERHWCG/372n86v3w8Vh89tUcpKaqkK7RoHRJNwTV9cN334w17ufA0VNYsnojzl68AgelEq4uJdC+dXMM6NnJ+P75/a9t+P6X1cbevtKl3FDWvQzWLZptEnNe3puLV67P1+tQCIHf/tqWcYOGO/cgl8tQpVJ5DOnX3WwqMY1Gi2Vr/8TmHXuR9OAhnBwdUaViOQzs3QXNQs1ng8jKpavXsPy3v3Dk5GmkPlFBJpMZbwjRvnWLF94AobDt+u8Qflm1ETdu3gYABNbxw/Ah/cxuMKDVajFg6Fgk3ruPxfMmm/U43rmbhG8XrsCBY6dg0BtQ1rMM+nbrkO18rrl9P928fReRvd994XnE7tloFs+iFesRfeSE8XXn6V4aLRo3xJB+3VG6lOndF+Ou38RbH2XcwCTztVO6pBukMil6dIzAh4P7mmyv1+uxbtO/+HvbHlyJvwGpVAKFQoGgOn4Y2Kuz8a5ozzp66gzeGv4F5kz+LMs5qIkKAgtboizM+P4XbPp3N6I2LoVcbn3jkCnDe6Mm43FyClbOn26VPetElEEIgYHDxkGhkGPR3MmWDodsGP8SEGWhWpWK+Hz42yxqrdyM8Z8CAMZ8NbdYTidHZA8MBgPGT/8eT9RqzJo40tLhkI1jjy0RFWsajRY/LVuLls1CEFDb19LhENFzrsbfwPrNO/Dh4L65Ht5GlF8sbImIiIjIJnAeW8pWbidGn/fVaATXrVUEERERERFljz22RERERGQTePHYU0IIqNXqLOfEJCIiIiLrx8L2qbS0NDg7OyMtLc3SoVjUtYTblg7B4piDDMwDcwAwB5mYB+YAyDoH2uTH2NOkLvY0qQtt8mMLREXPYmFLJtI0WkuHYHHMQQbmgTkAmINMzANzADAHxQELWyIiIiKyCSxsiYiIiMgmsLAlIiIiIpvAeWyJiChbQgi7v6gWAAx6nd3ngTnIOgdCoUTIxh2QSiWQu7haKDLKxMKWiIiylJqaCnXKQ1y8yCu99QYDLl5MtXQYFsUcZJ8DqVSKqlWrwkHKL8ItjYUtERGZMRgMiI+PR0m3kihXzhsSicTSIVmUTqeDXG7ffzKZg6xzIIRAYmIi4uPj4e/vDymLW4uy71coERFlSaPRwGAwwNPTA05OTpYOx+JY1DEHQPaFrbubGx4lJSEtNQXObiUtFB0BVnbx2O3btxEZGWn3PQNERNaCn8dELyAERJoaBq0Geo3G0tHYPaspbDds2IDGjRvjypUr+Wo/b948+Pv7IzAwEPXr18cff/xRsAFmQQgBjVbL2/ASERERWQGr+U5h+vTp2L59O6ZMmYLLly/nqe20adMwa9YsHDp0CNWrV8f27dvRvn17bNq0Ce3atSvwWFVqNfYdOoxjsbHQaDRQKpVoEBCA5qEhcOZXdkRkw7R6A/SGwtu/TAooZFbT50JExYzVFLbR0dH5Grvz6NEjfPXVV/j0009RvXp1AEBERATatGmDkSNHFnhhq1KrsWjVajxKTobBkPHprtFocOjECVy4cgVD+vZhcUtENkmrN+DMLRXStIVX2ToqpKhT3rnAitupU6dCp9Phyy+/zFM7vV6PV199FXv27EFcXBwqVqxYIPG8yMyZM/HDDz/g4cOH6Ny5M3799dciOS6RrbCawja/A9K3bt0KlUqFli1bmixv1aoVRo4cifPnz6NWrVoFESIAYN+hwyZFbSaDwYBHycnYd+gw2oaHFdjxiIishd4ApGkNkEslkEsLfuytziCQps3oEVbICmafn3zySb6Gi8lkMkRFRRX5GONRo0bhyZMn2LFjB4taonwo9t/3xMTEAAB8fHxMlmc+z1z/PK1WC7VabfLzIkIIHIuNNStqMxkMBhyPjeWYWyKyaXKpBHJZIfwUQrHs4OAAR0fHAt+vteLFfmTvrKbHNr+SkpIAAK6upnf7cHNzAwDcv38/y3ZTpkzBpEmTzJZfjLuR7YegTqeD5gVXPKZrNDh7Ka7YToliMBhw4ep1S4dhUcxBBubBvnNg0OugNxggkPHZBwB6nQHCYIDBABgKoYAyGASEwQC9TgedJPt+l0GDBmH58uVo1qwZduzYgatXr6JVq1a4fv06bt26hddeew0ajQYTJ07ExIkT4eXlhZ07d+Lnn3/G9OnTERoaCjc3Nxw9ehTe3t747bffjJ/7S5cuxbx58+Dl5YXXX38deHr+AhkdInPmzMGGDRsgl8tRs2ZNzJ07FxKJBM2aNcP169cxYMAAfPvtt1i0aBF27dqFVatWYcuWLRg2bBgaNGiAdevW5SIPBgghjHnPq9y0u3TpEt566y3I5XKkpqaiTZs2+Oabb3Js8+xrwV5llYNnO7Ou37oDebJpR5lftcpFERo9VTyrrwIwbtw4jB492vhcrVbD3d0dvj6Vsp2zUQgBpVKZY3HroFTCv6ZPsf2v+cLV63b/JmQOMjAP9p2DtLQ0XLyYCgn+f6iYThggkUohlUohLYTeVakQkEgBmVwOuTz7wvbXX3/F7t27MWPGDDg4OODff//FvXv3EBMTgwYNGqB///549dVX0aBBA6SlpWHp0qWQy+V4//33kZiYiJ9//hmnT59GyZIlERgYiL/++gt9+vTBmTNnMHz4cJw5cwY+Pj6YP38+8PT8JQBWr1mDX3/9FUeOHIGzszOGDBmCkSNHYvHixfjjjz9Qv359zJ07F3K5HDt27MDOnTshkUjQqVMnrFu3zhjHC/MglUIikeRq25MnT+Ljjz82Wda6dWvj43nz5iE4ONis3YIFC9CpUyeMHTsWDx48QL9+/V54PM5jm/08tjLnEpAqHeBTtQqcn3askWUU+6EIHh4eAICUlBST5cnJyQAAd3f3LNspFAo4OTmZ/LyIRCJBg4CAbO8qIpVKUT8goNgWtURExUWHDh3w999/AwCOHDmCbt26YcuWLQCA48ePo379+tm2DQ0NRenSpSGVSlG3bl3ExcUBAH7//Xc0btzYOJStV69eJu1+/fVX9OrVC87OzgCAt956C8uXL4der0eNGjVQvnx57NmzBxqNBs7OznBycsL+/fuhUqmgVCoLpSgMDg5GVFSU8QeAyfOsiloAqFGjBq5fvw4hBMqUKYN//vmnwGOzFxKJBDJHR0gVCkiVSkuHY/eKfWEbGBgIAIiPjzdZnvlBlbm+oDQPDUEpNzez4lYqlaKUmxuah4YU6PGIiMhcZmH75MkTODs7o1OnTti8eTMePnyIUqVK5djB4PZMj5qjo6PxW7jbt28bO0sAoEyZMibtEhIS4OnpaXzu6ekJrVaLxMREk5j27NmD8PBwtG/fHps3b8aOHTvQqlWrAjnvgtK7d2+cOHEC/v7+2LRpk6XDISowxa6wvX//vslQgMjISDg7Oxv/U820e/du+Pv7F+iMCADg7OSEIX37ILRePTg8/c/MQalEaL16nOqLiKiIvPrqq7h06RKWLFmCiIgItGvXDsePH8fy5csRGRmZr32WK1cO9+7dMz5//hqNSpUqmay/d+8eFAoFvLy8AAAdO3bE5s2bsXXrVnTo0AEdOnTAli1b8M8//7z01JOxsbGIjY19qX0867XXXsM777yDc+fOoVOnTgW2X3skhIBBp4MwGCD0ekuHY/eKVWEbFxeHChUqoHPnzsZlpUqVwpdffokffvgBV69eBQDs2LED//77L2bNmlUocTg7OaFteBjGfDgUY4cPw5gPh6JteBiLWiKyCzqDgE5fCD+G3M8o4+zsjPDwcHz11Vdo27Yt3N3d8corr2Dq1KkmY0zzokePHjhw4IDxb8mqVatM1g8cOBDr1q0zzqKzbNkyDBgwADJZxtxkzZo1Q1JSEs6cOQMvLy9ERETg4sWLSEhIyHZYXG4dO3YMx44de+F2uZ2V5/LlyyhfvryxTb9+/cyG9FEuCQFd8mPo1Sro1CpLR2P3rGYU+KhRo7B9+3Zcv55xBXLmuKDDhw9D+bRn1MnJCWXKlDG+GTONGTMGjo6O6NixI+RyOWQyGX777bdCuevYsyQSCZQKRaEeg4jIWsikGTdQSNMa8lSE5oWjQorc3puhY8eOSEtLQ8mSJQFkDAXYs2cPXFxcAADbt2/HtGnTcOfOHQwbNgyNGzfG0qVLkZaWhvnz50Mmk2Hr1q1wdHSEr68v+vbtix9//BGvvfYavLy8jD2ZvXv3xqpVq9C3b1/cunULrVq1gkwmg6+vL7799ltjPAqFAm3atEHdunUBAC4uLmjRogWaNGmS6/P/6aefsG7dOty9exc9evQwLr927RqGDh1qtn1WF489K7uLxxYtWoTPP/8c33zzDdLT0+Hn52f8W0tUnEkEJ10FkDErgrOzM1QqVa4uJLNV9nwVeCbmIAPzYN85yJgV4SKqVatmLBQB+72lLmcEYA6AbGZFMBiQcuc2Ll+7hpo1a8LVwzOb1lQU7PsVSkREeaKQSQvsrmBERAXN+v4tJiIiIiLKBxa2RERERGQTWNgSERERkU1gYUtERET0EiQKBSQyGSRSDkC3NBa2RERERPkkkUqhcHWDzNEJ8qe3WybLYWFLRERERDaBhS0RERER2QQWtkREVKxMnjwZ3t7emDhxYr7a3759Gy1atEDTpk3RsGFDqFS2cxvUrM7tu+++Q1BQEIKCgvDTTz9ZOkSbIwwGaB89gl71BDrVE0uHY/dY2BIRUaEQQkCj1aKgb3A5fvx4REZG5rv9jz/+iFq1aiE6OhrDhg2DRCIpwOgKVtWqVREVFZXr7bM6t08++QT//PMPoqKiULp06cIL1o4Jgx5CCAhDId6Wj3KFdx4jIqICpVKrse/QYRyLjYVGo4FSqUSDgAA0Dw2BsxXcsjwhIQFVqlQBALz55psWjqZgPX9u165dg06nQ/ny5QEAvXr1smR4RIWOPbZERFRgVGo1Fq1ajUMnTkCj0QAANBoNDp04gUWrVkOlVhfYse7evYsePXogJCQEHTp0QFJSknHdv//+i8aNGyMsLAyvvfYabt26BSBjGMM///yDpUuXIjw8HBcuXIBWq8WoUaPQpEkTNGnSBCNHjoRWqwUAdOvWDY6Ojpg9ezY6deoET09PLF261KRNs2bNMGnSpGx7pnU6HcaMGYMmTZqgRYsWeP3113H16lXMmTPHZEjFhAkTUKpUKSxduhQA8NZbb+HOnTv4+OOPER4ejmPHjgEAfv31VzRq1AgtWrRAt27dkJiYmOW57dmzx1jIhoeH4/PPPy+w3BNZKxa2RERUYPYdOoxHyckwPPeVrMFgwKPkZOw7dLjAjrVr1y4sWbIEhw8fRoUKFTB8+HAAQFxcHHr06IGlS5diz549iIyMxBtvvAHg/4cxDBw4EFFRUfDz88O0adNw4sQJ7Nu3D/v27UNsbCymTZsGANiwYQO8vb1x7tw5bNq0Cb/99hs8PT0xY8YMHDt2DPv27cPu3bvx77//YuXKlVnG+ey2e/fuRdmyZbF371588sknJkMqJk2ahODgYOPzJUuWwNvbG/PmzUNUVBQaNGiAffv2YeTIkfjrr7+wd+9e1K9fH3379s3y3MLCwrBmzRoAQFRUFKZOnVpguSeyVixsiYioQAghcCw21qyozWQwGHA8NrbAxty2bdsWrq6uAIABAwbg999/h16vx6pVq9CwYUP4+fkBAPr27YudO3fi9u3bWe7n119/xRtvvAGZTAaZTIY33ngDS5YsMdmmU6dOADJ6Pjt06IClS5fizTffhEwmg0KhQM+ePbF8+fIs979kyRIMGDAAMlnG5P1jx45FWFhYvs75119/RceOHeHp6Qkgo1d3165duH79er72R2RrOMaWiIgKhFanMw4/yE66RgOtTgelQvHSx3v2Qih3d3dotVokJSUhISEBZ8+eRXh4uHF9lSpVkJiYiHLlypntJyEhwVgoAoCnpycSEhJMtilZsqRZmzlz5hgL4NTUVJQqVSrLOJ/ff+Z41/xISEhAYGCgSayZyytXrpzv/RLZCha2RERUIBRyOZRKZY7FrYNSCYW8YP70PHjwwPg4KSkJCoUCHh4eqFSpEho2bIjNmzcb1z98+BBubm5Z7qdSpUq4d++e8fm9e/dQsWLFHI9dqVIlfPHFF+jZsyeAp0MtHj3K1f7v37+PlJQUVK1aFUqlEunp6cZ12e0jp1gBvDBeInvBoQhERFQgJBIJGgQEQCrN+k+LVCpF/YCAAptea8uWLUhJSQGQ8RV9jx49IJPJ0KdPHxw6dAjXrl0DkHGRWXh4eLZDJAYOHIgVK1ZAr9fDYDBgxYoVeOutt3I89sCBA7Fq1Sro9XoAwLJlyzBlypRst12+fLlx2zFjxuDUqVMAAB8fH5w+fRoAcPnyZVy6dMmkraurK1QqFXbv3o1vv/0WAwcOxJYtW4wXyi1btgytWrVib60lSSRQlC4DmXMJyEu4WDoau8ceWyIiKjDNQ0Nw4coVswvIpFIpSrm5oXloyEsfY/Lkydi6dSs6dOiAfv364fbt2/D09MSvv/4KIKNYXLVqFfr27QuFQgGpVIoFCxZAoVAY2zo6OuLSpUtYuXIlRo0ahcePH6N58+YAgCZNmmDMmDEAgDfeeAN37tzBJ598gtGjRxsv1Bo1ahS+/PJLNG3aFE5OTqhYsSIWLFiQZbyjRo1CcnIymjVrBplMhrCwMHTu3BkAMGjQIGzatMk4y0HDhg0xbdo0eHp6okOHDnj33XcxcuRIuLm5YfHixahTpw5mzZqFjh07QqlUwsPDA6tWrTLJS+a5TZ06Fb179waQMTZ43LhxiIiIeOn8kymJRGLyQ5YlEQU9c3YxpVar4ezsDJVKBScrmGfRUi5cvQ6/avb9nz9zkIF5sO8cpKWl4eLFi6hWrRpcXPLWC5U5j+3x2FikazRwUCpR34rmsc0PnU4HeQENoSiumIPsc5D5fvH19YWjo6MFIqNM9v0KJSKiAufs5IS24WFoE9YCWp0OCrmcPVlks4QQ0KmewJCeDn16GsDC1qJY2BIRUaGQSCQFMvsBkVUTAoa0NBh0Whie3tiDLIcXjxERERGRTWBhS0REREQ2gYUtEREREdkEFrZEREREZBNY2BIRERGRTWBhS0REREQ2gYUtEREVO0+ePEGHDh3QpEkTBAcHG2+fW1QmTJiAqlWrwsfHB0+ePDEu37RpE4KDg1G1alVMmDChSGMqSIsXL0bVqlUxcODAHLe7detWrs6zW7ducHR0RFRUFDQaDcLDwyGRSBAfH5/l9qtWrcKQIUPyEbmp9u3bIyoqymy5Xq9/YQzPWrJkCQ4cOJD1SokEMhcXSB0cIXPgHLaWxnlsiYioUAghkKbTwFGuLPAbNKxZswZarRb79+/H33//Dam0aPtpJk2aBIlEgq+//hpjxozBd999BwDo1KkT3NzcEBUVhYkTJxZpTAVp8ODBuHHjRo5FX1paGrp27Wq8pW9ONmzYgKpVqwIAlEoloqKicnxN9OrVC506dcpr2GbWrFkDV1dXs+UymeyFMTyrT58+aN26NRYuXAh/f3+TdRKJBDKlA6RyOaSct9niWNgSEVGBeqxOxc8HN2JD7C480ahRQumEbgGt8HajrijplLfb82YnISEB5cuXBwB07NixQPaZHyNHjsTMmTPRq1cvNGvWzGJxWMJ3332H+vXro3r16gW+b5lMludbOWfFzc2tAKIBHB0dMWzYMIwcORJbtmwpkH1S4eBQBCIiKjCP1anov/ILrDqxFU80agDAE40aq05sRf+VX+CxOvWlj7Fw4UIsWbIEW7duRXh4OPbs2WP8WvmHH35Ahw4d4OrqiqioKKSkpGDw4MFo1qwZGjdujOnTp0MIYfJ1+A8//IDIyEjUrFkTe/fuxezZs9G0aVM0btwY9+7dyzGWyMhIDBo0CIMHD0ZaWlqu4k9MTET37t3RokULNGrUCMuWLQMAXL9+HY0aNYJEIsGyZcvQunVr+Pn5Yf/+/QCAL774AnK5HCEhIbh58yZSU1Ph6uqK5ORk6PV6hIaGomrVqoiNjcW+ffvQtm1btG7dGk2aNMEff/wBAGbn/Wyu7t27h/bt2yMkJAQ9e/Z84bmvW7cOLVq0MD6/efMmunfvjoiICDRt2jTfPdaxsbHG4RxAxvCOWrVqISwsDKNHj0ajRo3QtGlT3L17FwCgUqnw+uuvIywsDM2aNcOIESMAADNnzoS3t7dJHEuWLEHdunXRunVrLFq0yOzYM2fORKNGjdC8eXMMGzYMGo3GuC4sLAw7duzAgwcPTNoIIWDQaiH0ehh0vPOYpbGwJSKiAvPzwY24mXwPeoPeZLneoMfN5HtYdGjjSx/jnXfewcCBAxEZGYmoqCiEhYUZx1Hev38fmzdvxsKFC+Hm5oaPP/4Yer0e//33H3bt2oWVK1dixYoVxq/DASA9PR1bt27F0KFD0a9fPzRt2hTR0dHw9PTE4sWLXxjPnDlzkJaWhi+//DJX8ffr1w8BAQHYu3cv/v77b4wZMwb79u1D5cqVsWbNGgCAk5MTduzYgcGDB2PSpEkAgK+//hqNGjXCiBEjUKFCBezYsQNqtRrbt2+HTCbDp59+itmzZyMgIAApKSn44YcfsGPHDuO5PX782OS8n8/V0KFDUalSJRw+fBiLFy/G9u3bsz0HIQROnjyJatWqGZepVCoMGTIE27dvR3R0NPbs2YOdO3fmKifPCggIwLx584zPO3XqhDFjxuDo0aN47733cPDgQZQsWdL4u1m6dCnc3d2xZ88e7NmzB//99x8AYNSoUYiMjDTu58yZMxg6dCj++usv7NixA9rnbn+7cuVK/PLLL9i1axf27t2LxMREzJgxw7je29sbSqUSsbGxzycDupRk6NPU0OfynxsqPCxsiYioQAghsCF2l1lRm0lv0GN9zC4IIQoths6dOwPIGBMZHByMlStXYtCgQQAyisVevXphyZIlJm0iIiIAAHXr1oVKpUKjRo0AAIGBgbh69eoLj+nq6orFixdj3rx5OHz4cI7b3rx5Ezt37jTG5OHhgY4dO5rFlFmQBQYGIi4uzri8Y8eO+PvvvwEA27Ztw+DBg41fjW/btg1t2rQxnsuXX36Jpk2bolOnTrh//z4uXLiQba6CgoKwceNG9O/fH0DGV/jPFoXPu3//PnQ6ncn41UqVKmHnzp1o0qQJwsPDce7cORw7dizHfOSFn58ffHx8AJjmpUyZMti3bx8OHToEmUyGPXv2ZNn+999/R+PGjY376NWrl8n6pUuXonfv3nB2doZEIkGfPn2wfPlyk21cXV2RmJhYYOdEBY+FLRERFYg0ncY4/CA7TzRqpOk0OW7zMkqWLGl8fO/ePaSnp8PT09O4zNPTEwkJCSZtMoszuVxuUqjJ5XKTr6Jz0rp1awwZMgSDBg3KsU3msV8UU+bYUEdHR5P9dejQAVu3boVOp8OjR48wYMAA/PPPP9Dr9Xjy5Ikx/jfeeAMeHh6Ijo5GVFQUvL29oVKpTI7xfK50Oh08PDyMy8qUKZPteWT+c/LsxVfTpk3D3r17sXPnTkRFRSEyMtLsmC/j2fGyz+ald+/eGDNmDD766CPUrFnTOLTjebdv387x/BISErBq1SqEh4cjPDwc06dPN7soUSKRwGAwFNQpUSFgYUtERAXCUa5ECaVTjtuUUDrBUa4skng8PT3h4OBgMlb03r17qFixYqEcb+bMmVCpVJgyZUq221SqVMkYR35iCggIgIuLC3766ScEBwejcePGSE9Px/z58xEaGmrc7vDhw2jbtq3x+fNfuz/P09MTcrncJK779+9nu727uztkMhlSUlJMjtmiRQs4OTnl6pgFJSkpCb169cLBgwexbt06fPHFF9i9e7fZduXKlcvx/CpVqoQhQ4YgKioKUVFROHjwIPbt22eyTUpKCry8vArnRKhAsLAlIqICIZFI0C2gFWRSWZbrZVIZuge2KvCpv7IjlUrxxhtvGHvw1Go11q1bh7feeqtQjufi4oJffvnFrBh6Vvny5REREYGlS5cC+P9xrnmJqUOHDhg/fjw6duwImUyGyMhIjB8/Hh06dDBuU6NGDRw6dAgAEBMTg9u3b+e4T5lMhm7duhm/ek9OTsbmzZuz3V4qlaJOnTom8wfXqFEDR44cgcFgwJMnT4xjXQvb999/b4w1ICAAZcqUgV5vPhymR48eOHDggHF4yfPTlA0cOBC//fab8SLA3bt349133zWuv3//PtRqNerUqVNYp0IFQZAQQgiVSiUACJVKZelQLOr8lWuWDsHimIMMzIN950CtVotTp06JlJSUPLV7pEoRHX/+SNSb3VcEzuxl/Kk3u6/o+PNH4pEqb/vLyoIFC0SVKlWEl5eXaNWqlRBCiIiICAFAhIaGip07dxq3TUlJEYMHDxZNmzYVoaGhYtq0acJgMJi1OX/+vAgKChIODg7inXfeEX/++afxGLNnzxZardYkhvHjx4sqVaqIoKAg8eeff5qsGzZsmJgwYUK28ScmJoru3buL5s2bi9DQULF06VIhhBD3798XoaGhAoDo1KmTuHbtmjGmAQMGGNtv3rxZVKtWzfh85cqVwtfX1+QY//33n6hVq5YIDw8Xw4YNE97e3iIoKEicOXMm21zdvXtXtGvXTjRs2FB06tRJDB48WHh5eYlJkyYJIYRZDiZPniw++ugj4/Pbt2+L8PBwERQUJPr27SvCw8NFlSpVxMqVK0XXrl2Fg4ODCAoKEgcPHhRhYWHGGBISEkz2GxMTYzzvHj16iJ07dwo/Pz9RsmRJMX78eLPfzYEDB0SrVq1Ey5YtRYMGDcSYMWOEEELMmDFDeHl5iSpVqohFixYJIYT45ZdfhL+/v2jZsqWYO3euMYZr1zLe67NmzRIhISGiZcuWonPnziIxMdEY18aNG0V4eLjZ79Og14vHNxPEsf3RIvne3Wx/71Q0JEIU4ij+YkStVsPZ2Rkqlcr4NYo9unD1OvyqVbZ0GBbFHGRgHuw7B2lpabh48SKqVauW5/lEH6tTsejQRqyP+f95bLsHtsKQ0IKbx7ao6XQ6yOX2PfX78zlISUlBWFgYNm/ejHLlylkwssKn0+kQERGBmTNnomHDhibrhMGAlDu3cfnaNdSsWROuHp7Z7IWKgn2/S4mIqMCVdHLBp+ED8ElY/0K78xhZnqurK9auXYu5c+eaTItli5YuXYrPPvsMwcHB5islgMTBARKZHFI7/+fHGvA3QEREhUIikcBJ4WDpMKgQ1axZ0+aLWgAYMmQIgIye2+dJJFIoSrhA5ugImaP9fuNrLXjxGBERERHZBBa2RERERC+BlytZDxa2RERkJvMiodzeoIDIXgmDAU+S7kGXkgyhLrgbUlD+cIwtERGZkclkcHFxwZ07iXB0dDS7A5O94awIzAGQdQ70Oh0S792D9mwMZHXrWigyymTfr1AiIsqSRCJBxYoVcebsOVy+fNnS4Vic3mCAzM6Le+Yg6xwIIaC9dxfp61dB0qufhSKjTCxsiYgoS0qlEk6upeBT0dvuxxDG3bgFn0rlLR2GRTEHWedA9yQVx4YOAAwGC0VFz2JhS0RE2ZJIJHBw4JRdUpkcjo6Olg7DopiDrHOg1aSzqLUi9v2dAhERERHZDKspbO/evYt+/frBz88Pfn5+6NGjBxISEnLV9vbt2xgyZAhq1aqFwMBA1KlTB9988w20Wm0hR01ERERE1sIqhiJoNBpERETA19cXZ86cgUQiwaBBg9CyZUucOHEix/uUGwwGtG/fHlqtFtHR0XB3d8eJEyfQpEkTPHjwALNmzSrCMyEiIiJ7I3MuYekQ6Cmr6LFdtmwZYmJiMH36dMjlcshkMkyfPh1Xr17F/Pnzc2x7/vx5nDx5EoMHD4a7uzsAoF69emjTpg1WrlxZFOETERGRnVK4lUSzHYfQbMchKNxKWjocu2cVhe369etRuXJlVKtWzbjM29sb/v7+WL9+fY5tM+eTe/7+zTqdDnq9vuCDJSIiIiKrZBWFbUxMDHx8fMyW+/j4IDY2Nse2vr6+6Nu3LxYsWID4+HgAwK5du7B9+3YMGzYs23ZarRZqtdrkh4iIiIiKL4mwgskJlUol2rZti7/++stkef/+/bFy5UqoVCo4OTll216n0+GTTz7B/Pnz4enpidTUVEybNg0ffPBBtm0mTpyISZMmmS0/eeaCXU9nYjAY7P4OQ8xBBuaBOQCYg0zMA3MAZJ0DQ1oakn/5DgDgNmgYpM/VEH7VKhdZfGQlF4+9jLS0NERERECr1SI+Ph4VKlTA8ePH0blzZzx8+BDjxo3Lst24ceMwevRo43O1Wg13d3f4+lTKsYi2dReuXrf7NyFzkIF5YA4A5iAT88AcAFnnQJv8GPv37wYA1B//NcfZWphVFLYeHh5ISUkxW56cnAxnZ+ccC81ffvkF//33H/bu3YsKFSoAAOrXr4+RI0dixIgR6NChA4KDg83aKRQKKBSKAjsHIiIiIrIsq/hOITAw0Dg+9llxcXEICAjIsW3mGNyaNWuaLPf19YUQAkeOHCmwOImIiIjIellFYdutWzdcu3bNpLhNTEzEuXPn0L17d5NtExMTYXjm1nVly5YFAFy/ft1ku2vXrgGAcQowIiIiIrJtVlHYDhw4EAEBARg9ejR0Oh0MBgPGjBkDHx8fvP/++8btoqOjUb58eQwdOtSkraurK7744gvjcIbr169j1qxZqFatGtq1a1fk50NERERERc8qClulUont27dDJpPB398ftWvXRnJyMnbt2mVy1zEXFxeULFkS5cqVMy7z8fHB4cOHUaZMGbzyyisIDAxE27Zt0bZtW0RHR9v1hWBERERE9sQqLh4DAC8vL6xatSrHbYKCgvDgwQOz5bVq1cKaNWsKKzQiIiIiKgasprAlIiIiKm5kzs4I/O4X42OyLBa2RERERPkklStQukGIpcOgp6xijC0RERER0ctijy0RERFRPhm0WtzftwsA4N68FaS8+ZNFsbAlIiIiyie9WoWzX3wKAGiyNRpSBW+pa0kcikBERERENoGFLRERERHZBBa2RERERGQTWNgSERERkU1gYUtERERENoGFLRERERHZBE73RURERJRPUqUSFXoNMD4my2JhS0RERJRPMkcn1PhotKXDoKc4FIGIiIiIbAJ7bImIiIjySQgBodUCACQKBSQSiYUjsm/ssSUiIiLKJ11KMvaF18e+8PrQpSRbOhy7x8KWiIiIiGwCC1siIiIisgksbImIiIjIJrCwJSIiIiKbwMKWiIiIiGwCC1siIiIisgmcx5aIiIgonyRSKRzLVzQ+JstiYUtERESUT3IXV4T+vtXSYdBT/NeCiIiIiGwCC1siIiIisgksbImIiIjySffkCWJGvIuYEe9C9+SJpcOxexxjS0RERJRPQq/Dw0PRxsdkWeyxJSIiIiKbwMKWiIiIiGwCC1siIiIisgksbImIiIjIJrCwJSIiIiKbwMKWiIiIiGwCp/siIiIiyid5CRc0XL7R+Jgsi4UtERERUT5JZDKUqF7T0mHQUxyKQEREREQ2gT22RERERPlkSE/H7b8zhiKU69gVUgcHC0dk31jYEhEREeWTPj0Nl2d/DQAoG9GOha2FcSgCEREREdkEFrZEREREZBNY2BIRERGRTWBhS0REREQ2gYUtEREREdkEFrZEREREZBM43RcRERFRPkkdHFD1nWHGx2RZLGyJiIiI8knm4IgqA9+1dBj0lNUMRbh79y769esHPz8/+Pn5oUePHkhISMh1+1OnTqFz586oX78+atWqBT8/P3z22WeFGDERERERWROrKGw1Gg0iIiKg0Whw5swZnD17FiVKlEDLli2Rmpr6wvb79+9Hu3bt8Nlnn+H48eM4f/48hg8fjnXr1hVB9ERERGSvhMGA9HuJSL+XCGEwWDocu2cVQxGWLVuGmJgYbNy4EXJ5RkjTp09HhQoVMH/+fIwaNSrbtkIIDB48GCNGjEDTpk2Ny9955x1Uq1at0GMnIiIi+6VLTcHBzq8CAJpsjYbCraSFI7JvVtFju379elSuXNmkEPX29oa/vz/Wr1+fY9v//vsP58+fR8eOHU2WKxQKtGvXrlDiJSIiIiLrYxWFbUxMDHx8fMyW+/j4IDY2Nse2+/fvBwA8fvwYnTt3Rp06dRAYGIgvvvgCarU623ZarRZqtdrkh4iIiIiKL6sYipCUlIQGDRqYLXdzc4NKpYJarYaTk1OWbW/cuAEA6NOnD9auXYuQkBCcOnUKHTp0wOHDh7Ft27Ys202ZMgWTJk0yW34x7gYcHR1f4myKN4PBgAtXr1s6DItiDjIwD8wBwBxkYh6YAyDrHBiepBgfX76WAGmJxybr/apVLpLYKINVFLYvIy0tDQAwePBghISEAACCgoIwevRoDB8+HHv27EFYWJhZu3HjxmH06NHG52q1Gu7u7vD1qZRtEW0PLly9bvdvQuYgA/PAHADMQSbmgTkAss6BNvkx7j59XKNKRY6xtTCrGIrg4eGBlJQUs+XJyclwdnbOsdB0dXUFAAQHB5ssr1evHgDgyJEjWbZTKBRwcnIy+SEiIiKi4ssqCtvAwEDEx8ebLY+Li0NAQECObWvVqgUg4+uBZ8lksiyXExEREZFtsorCtlu3brh27ZpJcZuYmIhz586he/fuJtsmJiaaFKvt27eHTCZDTEyMyXanT58GALzyyiuFFzgRERHZNYlMBlf/ALj6B0DytFONLMcqCtuBAwciICAAo0ePhk6ng8FgwJgxY+Dj44P333/fuF10dDTKly+PoUOHGpdVqlQJw4cPxw8//IBLly4BAG7evIkZM2YgIiICLVu2LPLzISIiIvsgL+GC+otWo/6i1ZCXcLF0OHbPKi4eUyqV2L59O0aMGAF/f39IJBLUrVsXu3btgovL/79IXFxcULJkSZQrV86k/cyZM+Hh4WHsvdVqtejevXuWsx4QERERkW2yisIWALy8vLBq1aoctwkKCsKDBw/MlstkMowdOxZjx44trPCIiIiIyMpZxVAEIiIiouJI9yQVx956Hcfeeh26J6mWDsfuWU2PLREREVFxI/R6pF44a3xMlsUeWyIiIiKyCSxsiYiIiMgmsLAlIiIiIpvAwpaIiIiIbAILWyIiIiKyCSxsiYiIiMgmcLovIiIionySu7ii8V9RxsdkWSxsiYiIiPJJIpVC6e5h6TDoKQ5FICIiIiKbUGiF7YYNGwpr10RERERWQZ+ehvhf5iP+l/nQp6dZOhy799JDEXQ6HRITE6F/7jZy48ePR7du3V5290RERERWy5CejmuLfgAAVOjRFzIHRwtHZN/yXdieO3cOb7/9Ng4cOFCQ8RARERER5Uu+C9tBgwbBwcEBM2bMQJkyZSCV/v+oBiEEJkyYUCABEhERERHlRr4L2zt37uDKlSsmBe2zEhMT8x0UEREREVFe5fviMT8/v2yLWgDo2LFjfndNRERERJRn+S5sv/76a4wYMQKxsbFISzO/CnDAgAEvFZitEkJAo9VCCGHpUIiIiIhsSr6HIoSEhEAikeB///tfQcZjs1RqNfYdOoxjsbHQaDRQKpVoEBCA5qEhcHZysnR4RERERMVevgtbLy8vvPfee1muE0Jg4cKF+Q7K1qjUaixatRqPkpNhMBgAABqNBodOnMCFK1cwpG8fFrdERETFkMzRCTU/m2B8TJaV78K2fv36Oc58cPny5fzu2ubsO3TYpKjNZDAY8Cg5GfsOHUbb8DALRUdERET5JVUqUb5LT0uHQU/le4zt5s2bc1y/YsUKk+f22oMrhMCx2FizojaTwWDA8dhYjrklIiIiekmFdkvd5/30009FdSirotXpoNFoctwmXaOBVqcrooiIiIiooAidDqkXzyP14nkI/i23uJe+pW5u2WuPpEIuh1KpzLG4dVAqoZAX2a+CiIiICohO9QTHBvYAADTZGg2FW0kLR2TfiqzHViKRFNWhrIpEIkGDgIBs5/yVSqWoHxBgt/khIiIiKihFVtjas+ahISjl5mZW3EqlUpRyc0Pz0BALRUZERERkO1jYFgFnJycM6dsHofXqwUGpBJAx/CC0Xj1O9UVERERUQDiws4g4OzmhbXgY2oS1gFang0Iu5/ADIiIiogJUaD22uueuDLTXi8eeJ5FIoFQoWNQSERERFbBCK2xDQkzHjWZ3lzIiIiIiooLwUkMRjh8/jsWLF+Pq1atIT083Wff8ncfefffdlzkUERERkdWRyOQo07i58TFZVr5/A//88w969OiBwMBAnD59Gg0bNgQA3LlzBxcuXDA+JyIiIrJV8hIlEDB7vqXDoKfyXdhOnjwZO3fuRKNGjVCvXj3s3r3buO63337DwYMHCyRAIiIiIqLcyPcYW7VajUaNGgEwvzCsZ8+eOHHixMtFRkRERESUB/kubGUymfGxXC7H7du3jc8fPXqE8+fPv1xkRERERFZOl5qCg10jcLBrBHSpKZYOx+7lu7CtUKECxo8fj/T0dISFhaFNmzb49ttv8e233yI8PBz+/v4FGScRERGR1REGA9ITbyM98TaEwWDpcOxevsfYfvLJJ1i7di3u3buHcePG4cCBAxgxYgQAoFq1ali9enWBBUlERERE9CL5LmzDw8MRHh5ufB4dHY3Lly8jPT0dtWrVglzOKS+IiIiIqOgUWPUpkUhQs2bNgtodEREREVGeFNqdx4iIiIiIihILWyIiIiKyCSxsiYiIiMgm8AovIiIionySu7qhxb5TGU+k7C+0NBa2RERERPkkkUiAZ25aRZbFfy2IiIiIyCawx5aIiIgon/Rpalz9cS4AoNoHIyBzdLJwRPbN5npsv/jiC0gkEixdutTSoRAREZGNM2g0uPX7Ktz6fRUMGo2lw7F7VlPY3r17F/369YOfnx/8/PzQo0cPJCQk5GkfCQkJmDNnTiFFSERERETWzCoKW41Gg4iICGg0Gpw5cwZnz55FiRIl0LJlS6SmpuZ6P2PHjkWrVq0KMVIiIiIislZWUdguW7YMMTExmD59OuRyOWQyGaZPn46rV69i/vz5udrHsWPHEB0djWHDhhVytERERERkjayisF2/fj0qV66MatWqGZd5e3vD398f69evz9U+Pv30U0yZMgUODg6FFSYRERERWTGrKGxjYmLg4+NjttzHxwexsbEvbP/HH39ArVajV69euT6mVquFWq02+SEiIiKi4ssqpvtKSkpCgwYNzJa7ublBpVJBrVbDySnr6TO0Wi1Gjx6NxYsXZ0ySnEtTpkzBpEmTzJZfjLsBR0fH3AdvYwwGAy5cvW7pMCyKOcjAPDAHAHOQiXlgDoCsc2B4kmJ8fPlaAqQlHpus96tWuUhiowxWUdi+jPnz56NOnTpo1qxZntqNGzcOo0ePNj5Xq9Vwd3eHr0+lbItoe3Dh6nW7fxMyBxmYB+YAYA4yMQ/MAZB1DgxaLTy+yZjH1r2WL6QKhSVCo6esorD18PBASkqK2fLk5GQ4OztnW2g+evQIU6dOxd69e/N8TIVCAQVffERERPQSpAoFPMMjLB0GPWUVhW1gYCDOnz9vtjwuLg4BAQHZtjt48CDkcjl69uxpXJY5Pdj48eMxb948dOvWDePHjy/4oImIiIjIqlhFYdutWze8++67iI+PR9WqVQEAiYmJOHfuHKZOnWqybWJiIjw9PSGVShEZGYkbN26YrI+KikLLli0xefJkDBw4sIjOgIiIiOyRQafF4xNHAQAl6zWEVM5vgy3JKmZFGDhwIAICAjB69GjodDoYDAaMGTMGPj4+eP/9943bRUdHo3z58hg6dKgFoyUiIiLKoFepEPPR24j56G3oVSpLh2P3rKKwVSqV2L59O2QyGfz9/VG7dm0kJydj165dcHFxMW7n4uKCkiVLoly5cmb7uHv3LoKDgzFkyBAAGUMRgoODcfTo0SI7DyIiIiKyHKsYigAAXl5eWLVqVY7bBAUF4cGDB1muK1u2LE6ePFkIkRERERFRcWAVPbZERERERC+LhS0RERER2QQWtkRERERkE1jYEhEREZFNsJqLx4iIiIiKG6lCAa/2nY2PybJY2BIRERHlk8zJGbW+mGLpMOgpDkUgIiIiIpvAwrYYEEJAo9VCCGHpUIiIiIisFociWDGVWo19hw7jWGwsNBoNlEolGgQEoHloCJydnCwdHhERkd3TJj/Gwc6vAgAa/bkTCreSFo7IvrGwtVIqtRqLVq3Go+RkGAwGAIBGo8GhEydw4coVDOnbh8UtERGRFTCkp1k6BHqKQxGs1L5Dh02K2kwGgwGPkpOx79BhC0VGREREZJ1Y2FohIQSOxcaaFbWZDAYDjsfGcswtERER0TNY2FohrU4HjUaT4zbpGg20Ol0RRURERERk/VjYWiGFXA6lUpnjNg5KJRRyDpEmIiIiysTC1gpJJBI0CAiAVJr1r0cqlaJ+QAAkEkkRR0ZERERkvVjYWqnmoSEo5eZmVtxKpVKUcnND89AQC0VGREREmSQSCeSubpC7urHDyQrwu2wr5ezkhCF9+2DfocM4HhuLdI0GDkol6nMeWyIiIqshd3VD03/3WzoMeoqFrRVzdnJC2/AwtAlrAa1OB4Vczv8GiYiIiLLBwrYYkEgkUCoUlg6DiIiIyKpxjC0RERFRPulVKpwdPwpnx4+CXqWydDh2j4UtERERUT4ZdFrc2/EP7u34Bwad1tLh2D0WtkRERERkE1jYEhEREZFNYGFLRERERDaBhS0RERER2QQWtkRERERkE1jYEhEREZFN4A0aiIiIiPJJ5uyMoB+XGR+TZbGwJSIiIsonqVyBUsENLB0GPcWhCERERERkE9hjS0RERJRPBq0WSbu3AwA8WkZAqlBYOCL7xsKWiIiIKJ/0ahXOTfwMANCkUTSkipIWjsi+cSiCjRJCQKPVQghh6VCIiIiIigR7bG2MSq3GvkOHcSw2FhqNBkqlEg0CAtA8NATOTk6WDo+IiIio0LCwtSEqtRqLVq3Go+RkGAwGAIBGo8GhEydw4coVDOnbh8UtERER2SwORbAh+w4dNilqMxkMBjxKTsa+Q4ctFBkRERFR4WNhayOEEDgWG2tW1GYyGAw4HhvLMbdERERks1jY2gitTgeNRpPjNukaDbQ6XRFFRERERFS0OMbWRijkciiVyhyLWwelEgo5f+VEREQFRapUomKfN42PybJY5dgIiUSCBgEBOHTiRJbDEaRSKeoHBEAikVggOiIiItskc3RC9WGjLB0GPcWhCDakeWgISrm5QSo1/bVKpVKUcnND89AQC0VGREREVPhY2NoQZycnDOnbB6H16sHh6dchDkolQuvV41RfREREhUAIAX2aGvo0NS/QtgIcimBjnJ2c0DY8DG3CWkCr00Ehl3P4ARERUSHRpSRjf2RTAECTrdFQuPGWupbEwtZGSSQSKBUKS4dBREREVGQ4FIGIiIiIbAILWyIiIiKyCSxsiYiIiMgmsLAlIyEEdDodr+okIiKiYslqLh67e/cuRowYgaNHjwIAAgICMG/ePFSsWDHHdrdv38ZPP/2EjRs3wmAwQKfTwd/fH5MmTUJAQEBRhF7sqdRq7Dt0GMdiY6HRaKBUKtEgIADNQ0M4RRgREREVG1bRY6vRaBAREQGNRoMzZ87g7NmzKFGiBFq2bInU1NQc206aNAmrV6/G5s2bcfr0aZw8eRIymQyhoaGIjY0tojMovlRqNRatWo1DJ04Yb8er0Whw6MQJLFq1Giq12sIREhERWS+JVAqnSlXgVKkKJFKrKKvsmlX8BpYtW4aYmBhMnz4dcrkcMpkM06dPx9WrVzF//vwXtv/ss89QqVIlAICjoyOmTZsGtVqNhQsXFnboxd6+Q4fxKDnZ7Da8BoMBj5KTse/QYQtFRkREZP3kLq4IWbsZIWs3Q+7iaulw7J5VFLbr169H5cqVUa1aNeMyb29v+Pv7Y/369Tm2/f777zFo0CCTZeXLlwcAPHz4MNt2Wq0WarXa5MfeCCFwLDbWrKjNZDAYcDw2lmNuiYiIqFiwijG2MTEx8PX1NVvu4+ODnTt35thWLjc/hYsXLwIAwsPDs203ZcoUTJo0ybxt3A04Ojq+IGLboNPpjMMPspOu0eDspbgs82yrDAYDLly9bukwLI55YA4A5iAT88AcAPnLgV+1yoUUDWXFKqqVpKQkNGjQwGy5m5sbVCoV1Go1nPJwEdPChQtRp04dDBgwINttxo0bh9GjRxufq9VquLu7w9enUp6OVZwJIaBUKnMsbh2USvjX9LGr2/JeuHqdH0RgHgDmAGAOMjEPzAGQdQ50T57gzOcfAQDqTP0W8hIlLBEaPWUVhW1B2rlzJ9auXYu9e/fCwcEh2+0UCgUUdn7LWYlEggYBATh04kSWwxGkUinqBwTYVVFLRESUF0Kvw6OjB42PybKsYoyth4cHUlJSzJYnJyfD2dk51z2op06dwptvvolNmzbB39+/oMO0Sc1DQ1DKzQ3S567klEqlKOXmhuahIRaKjIiIiChvrKKwDQwMRHx8vNnyuLi4XM9FGxMTgy5dumDNmjVo0qRJAUdou5ydnDCkbx+E1qsHB6USQMbwg9B69TCkbx/OY0tERETFhlUUtt26dcO1a9dMitvExEScO3cO3bt3N9k2MTHR7GvzmJgYdO7cGcuXL0ezZs0AZNy44d133y302G2Bs5MT2oaHYcyHQ9HztS4Y8+FQtA0PY1FLRERExYpVFLYDBw5EQEAARo8eDZ1OB4PBgDFjxsDHxwfvv/++cbvo6GiUL18eQ4cONS6LjY3Fq6++irZt2yI+Ph4rVqzAihUrsHbtWly4cMESp1NsSSQSyOXyPI2pFUJAo9VySjAiIiKyOKu4eEypVGL79u0YMWIE/P39IZFIULduXezatQsuLi7G7VxcXFCyZEmUK1fOuGzChAlISkrCggULsGDBApP9hoWFFdk52BvehpeIiIisjVUUtgDg5eWFVatW5bhNUFAQHjx4YLJsw4YNhRkWZSHzNrzP3rEs8za8F65c4dhcIiIisgirKWyp+MjNbXjbhrO3nIiIbJ+8hAsarvrT+JgsyyrG2FLxwdvwEhER/T+JTIYSVaujRNXqkMhklg7H7rGwpTzR5vI2vFodJ6kmIiKiosWhCJQnCrk8V7fhVcj50iIiIttnSE/H7U2/AwDKdeoBaQ53PaXCxx5bypPM2/A+f6eyTLm5DS+nCCMiIluhT0/D5blTcXnuVOjT0ywdjt1jtxrlWfPQEFy4csXsArIX3YaXU4QRERFRYWKPLeVZfm7DmzlF2KETJ4zDGDKnCFu0ajVUanWRngMRERHZHvbYUr5k3oa3TVgLaHU6KF5wxzJOEUZERESFjT229FIkEgmUCsULx9RyijAiIiIqbCxsqdAVxBRhvOCMiIiIXoRDEajQvcwUYbzgjIiIiHKLhS0Vuswpwg6dOJHlcITspgjLvODs2bG5mRecXbhyJdsL1YiIiIqKzMERPu+PMD4my+JQBCoSzUNDUMrNzWz+25ymCMvNBWdERESWJHVwQOUBg1F5wGDenMEKsLClIpHXKcIK4oIzjsslIiKyLxyKQEUmL1OE5eWCM6VCYbKc43KJiKioCL0e6XcTAQAOZb0gkcksHJF9Y2FLRS5zirCc5PeCM47LJSKioqR7kopD3dsAAJpsjYbCraSFI7JvHIpAVinzgrPnx+Rmyu6CM47LJSIisl8sbMlq5fWCs4Ial6vT6Tgul4iIqBjiUASyWpkXnO07dBjHY2ORrtHAQalE/WzGy3JcLhERkX1jYUtWLS8XnFlqXK4Q4oWxERERUeFjYUvFQm4uOMvvjSByMy63bXiY2f7Yy0tERGRdOMaWbEpRjcvN7OU9dOKEsYc4s5d30arVUKnVBXhWRERElBssbMmm5PVGEHkZl/usgph9gTeQICIq/iQyGdzqBsGtbhDnsLUCHIpANqewx+Xmtpe3TViLLI/LIQxERLZDXsIF9RautHQY9BR7bMlmZY7LzemCrvzMl5vfXl7g5YcwsJeXiIgoe+yxJbvXPDQEF65cMRtakN243PzOvgBY5kI1ztpARET2goUt2b28zpeb39kX8juEIb/TkXHIAxFR4dM9ScXJD94EAAT/uAzyEi4Wjsi+sbAlgum43LOX4uBf0yfH3s289vIC+b+BRH56eQtibt7MO7Cxl5eIKHtCr8eTSxeMj8myWNgSPUMikUCei6/s89rLCxTthWoc8kBERPaIhS1RPuVl9gUgf0MY8tPLW5yGPLAYJiKigsTClugl5eauaJmK4kK14jDkgcUwEREVBha2REWoKC5Us/YhDyyGiYiosLCwJSpieR3CkNdeXmsf8lCciuG8XkDHApqIyLJY2BJZSG6HMOTnQjVrHfJgq8Uwe5OJiKwDC1uiYiCvvbzWOuTBFovh4jK0ggU0UeGQu7iiyZZ9xsdkWSxsiYqRvFyoZo1DHmyxGLb13mQOxyDKmUQqhaJUaUuHQU+xsCWycdY05MHWimH2Jr9cm2cVVS80C28i28bCloiM8noHNnsvhtmbnP82z7YtiiK6OPRcs+gunvTpabj+6yIAQOU3hkDm4GjhiOwbC1siMpPbO7ABhT/+F7DeYpi9yflvAxRdEW3tPdfFYbw1h6Vkz5CejutLfgIAVOw1gIVtNq78MBsJK5egyqD3UXXI0EI7DgtbIioQhTn+11qLYfYm57+ABoquiLbmnmtbLLqLS6FeFMV9YXgSdwXnJn4Gzf0kaB/cR83PJqB8l54m2+hSknHyw7egS34MvUoFB+9yqP7hSJR+pbFlYr56GTfXLs9xG+2jh7g6fx4enzwKqUIJiVKByv2HwLNVmzwdi4UtEVlMcS+G89PG1nqT83unu6Iqoq2959rWim4W6oWvhE91NFy2HvGLfsC1X+bj8txvUKJ6TZQMCDZuI3d1Q8Nl63Fn8x94dOIIan0xpcjjfNal2V/DvVk4kqJ2ZLlen6bGqQ8HQVGqNBos/Q0yJ2ck7duNM59/BL/0r+DdrnOujyUtqKCJiIpCZjGcl2ESYz4cirHDh2HMh0PRNjws2z9GmcVwaL16cFAqAWQUf6H16mX7Bzk/bZqHhqCUmxukUtOP4BcVw89v/2y77HqT89ImsxjOSXYFdF7aAHkriIu6TW6LYSFEkbcBclcMP8+a22QWw4dOnDD+rjKL4UWrVkOlVherNkXJvVlLSGRynB03Aun37lo0luwk/rMJ+tRUlO/WO9ttbq5biSdXL6H6R59B5uQMAPBo3hLuTVrgyrczoE/LfZ5Z2BKRzctvMdzztS4vLIafb1NYBXRei+H8tCmqAhoouiI6P21YdLNQf5k2RcnFtxb8xn0FTdI9nBk7Agat1qLxPE+XmoKrP85BjZHjIMnmMwIA7m7fDEXpMnCpWctkeenQptAlP8aDg//l+pgcikBElIW8XED3bBtrGlphrcMxgKIb02zNQz+sebiIrY3rLsw2LesF5XjOha3sq5F4cvkiri9biEuzvobf55PytZ9bG9fi1h/rcrVt1SEfwqN5yxduF7fgfyjTqBlKBtTDo+NZ/xNg0GjwJP4q3GrXNVvnVKEyACD14nl4hkfkKjYWtkREFlSYxXB+2hRVAQ0UXRFtrRcS2lrRba+Fuk6vz3GbolD1nWF4cvUy7vy1Hq5+tXP82j875bv2QvmuvQosppQLZ3Fv51Y0XPlnjttpkx8Dej1kJVzM1slKlMjY5tGDXB+XhS0RUTGTl2I4P23yOp/x823yUnQXRRFtzT3XtlR022uh7lDCBb5Pe0lljkV/MRmQkfvaE6bhxDv9cHneNJSo7ouSQfUtEgsACIMBl2Z9japDhkJZuky+95Of2SdY2BIRUZYKezgGUDS90Plpw6KbhXpu28gcHFDute5m67Ni0Gnx8NB+lAltCom8YEswmbMz6sz4DscH98aZcSPQYEnuhhUUhtub1kPodSjX5fUXbqtwKwnIZNA/STVbp0vNWKYolfvi2GoK27t372LEiBE4evQoACAgIADz5s1DxYoVX9hWq9Vi8uTJ+O233yCXy+Hm5oYZM2agWbNmhR02EREVgMLuhc5Pm6LsubaVotveC/WcJJ+JwcXpE6G6Ho+Q1X/DsVz5XLfNLafyFeH/9RzEfvwOznz+Mbw7ds1124IcY/vwcDT0qak49tb/z6+rV6kyjvPHOiTt2wW5qxuCv18CqVKJElWrQX3zhtl+1DevA8i4SC63JOL5yxMtQKPR4JVXXoGvry9Wr14NiUSCQYMGYf/+/Thx4gRcXMzHXTzrvffew65duxAdHQ1PT08sWrQIw4cPx/79+xEcHJyrGNRqNZydnaFSqeBkgXnprMWFq9fhV62ypcOwKOYgA/PAHADMQSZrzUNR3pwgt8V9fo6TOVdsXsZoW0sbodMh9fIFAIBLDT+znljdk1TELfgfbq1fjZL1GsL3swlwrlz1Bdl7sfhFPwBAlnfxurl+DS7P/hpKD0+UDmli8XlsAeDR8cM49eGgLO88dv3XnxH307dosHwDXKr7Gpef/mwYHsccR6M/duR6mIdV9NguW7YMMTEx2LhxI+RPXxDTp09HhQoVMH/+fIwaNSrbthcuXMDChQuxaNEieHp6AgCGDBmCuXPnYty4cdi8eXORnAMREVFRK8qebmuaJcRSbbIq7nWqJzg+KOOiqyZbozO+Wn8qac9OXJrzDQzpafAb+xW82neGRCKBQauF5n4SNPfvQZN0F+lJ//9Ycz8JmqR70KYkw//r2XDzD3hR+sxU6N4bT65cwO0/fstzW0uo8Hp/JP67GVfmTUfdGd9B5uSM+9FRuL9/D/zGfZWnsctWUdiuX78elStXRrVq1YzLvL294e/vj/Xr1+dY2G7cuBFCCLRsadol3qpVK/z0009ITU19YY/vs9K0BkjkWU/tYS/StPZ9/gBzkIl5YA4A5iAT81BUOZAhXScA5OUL5aJpI5fLzdrodP//OF0noNcaoL5xDVemfI4n507DuVoNlAisj7s7/kHCmmUZt8J99NB0v65uUHp4QunhCQd3T5SoVhMOXt4oUbW6WQzP3lIXAJL27UKt8VNNejoBoMYnY6G6Fpfrcyssj2NP4NKsr82GInh36IqKr/cHkHHRXfAPS3B1/jwce7MHpEoHSBQK+E+eCc9WbfN0PKsobGNiYuDr62u23MfHBzt37nxhW6lUisqVTb8i8vHxgU6nw9mzZxESYj4GRqvVQvfMpNfqp3cP6fzmMMhkVpEWi5g5fgTa9XnP0mFYFHOQgXlgDgDmIBPzwBwAWefA0aDDmKePew75BGlSOfrcPwu/9EcwANClJEP7+AEcypaDi19tOLh7QulRFkoPDyjdPaF094DMwTHXMWTeUvdFpHIFgn9YmvuTKyQlA+rlKl5FqdL5noP3WVYxxlapVKJt27b466+/TJb3798fK1euzHHca5s2bXDgwAGkpKSYLF+0aBHefvttbNmyBe3atTNrN3HiREyaZJ7AfYeOw9Ex9y8wW+Ps5AiVOs3SYVgUc5CBeWAOAOYgE/PAHABZ50A8SYXq07cy1s9eAkkJFwiDHvozJ6E7uAeGmKOQyOTwbNUG3h26omRwg3xNY0W5Y7ddk+PGjcPo0aONz9VqNdzd3aFzKQ+dheahswbC8BA6lwqWDsOimIMMzANzADAHmZgH5gDIOgdCkmx8rHMpB0kJt4wnjStD3rgTGrgbcHf7Ftz5eyNODR0Ip4qVUan/IJTr1KMoQ7cbVlHYenh4mPW4AkBycjKcnZ1znKXAw8MDKpUKer0eMpnMpC0AuLu7Z9lOoVBAkcWg9qCKLnY9K8K1G48QXCn3Y5JtEXOQgXlgDgDmIBPzwBwAWedAl2LAsaePAyq4QO5qul6hkKJCj76o0KMvUi+ex53NG5F8JoaFbSGxisI2MDAQ58+fN1seFxeHgICcrwYMDAzE6tWrcePGDVStWtWkrVwuh7+/f55icVRI4aiQ5qmNrbH38weYg0zMA3MAMAeZmAfmADDPgVb+/8MKHOQSKHLIkYtvLdTw/bzQYiPAKl6h3bp1w7Vr1xAfH29clpiYiHPnzqF7d9O7eSQmJppMkty1a1dIJBJERUWZbLd79260adMmTzMiEBEREeWFVK6Ae7OWcG/WElJ53qZRo4JnFYXtwIEDERAQgNGjR0On08FgMGDMmDHw8fHB+++/b9wuOjoa5cuXx9Ch/z+xr5+fH9555x1MnToVSUkZU18sWbIEV65cwZQplp+QmIiIiGyXzNkZdWd8lzH/qrOzpcOxe1ZR2CqVSmzfvh0ymQz+/v6oXbs2kpOTsWvXLpMeVxcXF5QsWRLlypUzaf/dd9+hZ8+eaNq0KerWrYuFCxdi27Ztub7rGBEREREVf1YxxhYAvLy8sGrVqhy3CQoKwoMHD8yWKxQKfP311/j6668LKzwiIiIisnJW0WNLREREVBzpUpJxoFMrHOjUCrqU5Bc3oEJlNT22RERERMWNEAKapLvGx2RZ7LElIiIiIpvAwpaIiIiIbAILWyIiIiKyCSxsiYiIiMgmsLAlIiIiIpvAWRGeyrySUa1WWzgSy0pLS2MOmAMAzAPAHADMQSbmgTkAss6BVq1Gut4AIKOG0CmUZu0cHR0hkUiKJEZ7JxGcmwIAkJiYCG9vb0uHQURERDZGpVLBycnJ0mHYBfbYPpV5696kpCQ42+m9ntVqNdzd3XH//n27fQMyBxmYB+YAYA4yMQ/MAfByOXB0dCykqOh5LGyfkkozhhs7Ozvb7Zs2k5OTE3PAHABgHgDmAGAOMjEPzAHAHFg7XjxGRERERDaBhS0RERER2QQWtk/J5XJMmDABcrn9js5gDpiDTMwDcwAwB5mYB+YAYA6KC86KQEREREQ2gT22RERERGQTWNgSERERkU1gYUtERERENoGFLdml27dvIzIy0q5vccgcEBHlrHnz5pBIJIiPj7d0KJRLdl/Y3r17F/369YOfnx/8/PzQo0cPJCQkWDqsIhMfHw8XFxcEBweb/Tx69MjS4RWKDRs2oHHjxrhy5UqO22m1Wnz55ZeoVasW6tatiyZNmuC///4roigLV25zULVq1SxfGzt27CiiSAvPyZMn8fbbb6N27doICAiAv78/hg8fjnv37plsl5qaig8//BB+fn7w9/dHmzZtcObMGQtFXbBymwOlUpnl6+Ds2bMWirxgXblyBSNHjkSDBg3QoEED+Pr6onnz5ti8ebPJdrb8mZDbHNjyZ8Lz1q9fn+3v15Y/F4o9YcfS09NFYGCg6NGjh9BqtUKn04k33nhD1KhRQ6SkpFg6vCIRFxcnwsLCLB1GkQoJCREXL14Ub775psjpLfDuu++KmjVrirt37wohhPj555+Fk5OTOHHiRBFFWnhym4MqVaoUXVBFzM/PT3Tr1k2kpqYKIYR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\n" 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