{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "The STFT depends on both the signal as well as the window function, although one is typically interested only in the signal's properties. The design of suitable window functions and their influence is a science by itself. Following Section 2.5 of [Müller, FMP, Springer 2015], we discuss some examples that illustrate how the window may affect the spectral estimate computed by the STFT.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Window Type\n", "\n", "The seemingly simplest way to obtain a local view on the signal to be analyzed is to leave it unaltered within the desired section and to set all values to zero outside the section. Such a localization is realized by a **rectangular window**. However, using the rectangular window has major drawbacks, since it generally leads to discontinuities at the section's boundaries. Such abrupt changes lead to artifacts due to interferences which are spread over the entire frequency spectrum. Rather than being part of the original signal, these frequency components come from the properties of the rectangular window.\n", "\n", "To attenuate the boundary effects, one often uses windows that are nonnegative within the desired section and continuously fall to zero towards the section's boundaries. One such example is the **triangular window**, which leads to much smaller ripple artifacts. A window often used in signal processing is the **Hann window** (named after the meteorologist Julius von Hann, 1839–1921). The Hann window is a raised cosine window, dropping smoothly to zero at the section boundaries. This softens the artifacts in the Fourier transform of the windowed signal. However, on the downside, the Hann window introduces some smearing of frequencies. As a result, the Fourier transform of a signal's windowed section may look smoother than the signal's properties suggest. In other words, the reduction of ripple artifacts introduced by the window is achieved at the expense of a poorer spectral localization. \n", "\n", "\n", "\n", "\n", "In the following code cells, we illustrate the effect of the window type using a chirp signal as example." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:58:43.404088Z", "iopub.status.busy": "2024-02-15T08:58:43.403796Z", "iopub.status.idle": "2024-02-15T08:58:45.567901Z", "shell.execute_reply": "2024-02-15T08:58:45.567285Z" } }, "outputs": [ { "data": { "image/png": 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RUbzwbY/HE1bnhYgcAN4EMBRARwDjiKijVO0MgMkAXq5A2yrlu+++wwMPPIChQ4fi5ZdfhtPpBACMHTsW33zzDXJzczFmzBjT92T79u3o3r07Dh8+jBUrVuCFF17AggUL0KtXr4C/tZycHNxyyy04cuQIJkyYgE6dOmHKlCkBwv7JJ59E27ZtUVpail69evk9oBcuXIiHH34Yjz76KMaPH4/evXsbf3tvv/02jh49in/+858YPHiw8T3i8Xgwffp0JCQkYP/+/caPv6effhpz585F//79/QTMmTNnMHjwYFx33XXGXEHr16/HggUL4HK5jDlKZs2ahZycHPz222+GczJjxgz88Y9/RJ8+fbBz507jnHv27MHYsWPh8Xjw5ptvwuPx4Pvvv8eZM2dw+eWX49tvvzVc7BMnTuDmm29Geno6OnfubMwdVVpaitmzZ2P48OE4fvw42rZt6zev1LRp03Dw4EHMnj0b119/PcrLy/HFF18Yx0+dOoUNGzZgyJAhALzzYiUnJwe4KW63GwsXLsTo0aNRr149ozwzMxMALN2X5cuXY+DAgUauphV8rijx/dUEEhHipbS0FJ9//jmuu+4649evTEZGBnbt2qVM7LTLkSNHUF5ebjgvzZo1Q2lpqS2bVhQvwUJBgD3nhVufdpyXJk2aKJ2XnJwcNGvWDECgQBFFgnzfRDEiCg/xGmbtRTGgEi8q50Vsw7cZY4ZQ4O2DiRfelpfJ+xyrnBerumb74kNMdlCAc6JArivui2KD913MeRGPiWGAsrIyw3kRQ0+iCxNu8QKgB4A9jLF9jDEXgPkA/IZdMMayGWPrAciKIGjbqqS0tBR33HEH0tPTMW/ePMM143Tu3BmzZ8/Gt99+iyeeeCKgfW5uLkaPHo2YmBj89NNPyMzMxBNPPIFly5Zh586deOSRR/zq/+Uvf0F2djYWLlyI1157DTNnzsSRI0f8Jrt85513sGfPHvz973/Hpk2bcMUVV2DChAnYv38/3G43nnnmGXTs2BE5OTn417/+hQMHDmDmzJkoKSnB66+/jqFDh+Ljjz/GTz/9hD59+uDo0aNYuXIldu7ciddffx0pKSmYM2cOdu/ejblz5+KGG25AaWkp+vfvj5kzZ+Kdd95B7969sW7dOvTp0wfTpk3DTz/9hCeffBKpqam44YYbMHv2bGRlZWH69Ono378/OnXqhGeffRb79u3Ds88+iyuvvBLl5eXo168fPvjgAyxevBijRo2Cw+HAc889h71792Lt2rX47LPPEBsbi9mzZ4MxhgULFqC8vBzjxo3D2bNnsWDBAtx88834+eefcezYMaxatQpnz57F/fffj0aNGmHkyJFYs2YN8vPzUVZWhlmzZmHEiBG48sor0bt3byQnJ/uFjr788kswxozJOqOjozFw4ECsXLnS74frjz/+iDNnzmDkyJF+798ll1yCFi1amIqX3bt3Y+/evRg6dKitz1/r1q2RkZERMLGnxh/zzKFqxFdffYXc3FzceOONpnW6du0Kxhi2bNlimc1tBc9v4c5L06ZNAXjzWerXr2/ZlouX1NRUpKSkWGarl5eX4+zZs2jYsCHKyspMxQu3mFu2bAlAndtRVFSEqKgopKamBszVwo83bNgQ+/fvtxQvZkmq/BwcUWSI7UUBoBIvZWVlKCsrQ0xMjF9dK1Eih2Lkeqq2JSUlSExMtBQvcgjFzHkRRQBwLhQl/9oWwzO8vlxHzGuRRYSYsCuLCr4vCyIxsdbsfHLYyI54OY9ho+YAxCEUWQB6VnVbIrobwN3Aub+bUJk1axb279+PVatW+f3CFrntttuwbt06vPLKK2jYsCEee+wxAN7PCBcVa9euNVxTwBtemDJlCqZNm4YRI0ZgxIgR+Omnn/D222/jwQcfREZGBgCgT58+GDduHKZNm4Zbb70VKSkpmDp1Kq688koMHz4cRIT58+ejU6dOmDRpEm6//Xbs3LkTCxYsQHJyMm688UYMGDAAzz//PMrLy5GdnY0///nP6N+/P5o3b45hw4bhqquuQkpKCpo3b47bb78d27Ztw5tvvonCwkLExcXhzTffRHZ2NgYNGoR7770XAJCSkoIvvvgCXbp0QadOnTBy5EhkZ2djxowZGDJkCBYtWoTBgwfj2LFj+OCDD4zv7KuuugpEhLlz56KkpASDBg3CHXfcAcAbTl21ahX69OmD6dOnY/bs2di4cSMGDBiA7t27G0OHjx8/jrVr1+Kf//wnunTpAiLCU089hWXLluGLL75AamoqBg0aBAC49tprMX36dHzxxRdwOBw4fvw4Jk2aBMArTIYMGYLly5fD4/EgKioKq1atQv369dG9e3fjvcrMzMSiRYuwY8cOdOzoNfn+/e9/G+2lzxyGDBliiCw5IXfFihUAYFu8AN7Zyv/3f/8XZ86cQUpKiu12tYmIcF4WLlyIpKQk48Opgv/hb9q0qcLX4fZkixYtAHjdDCBwAjcV2dnZaNCgAaKjo9GgQQPTUBBwztWoV6+eUVcVmuJuBu+HSrwUFhYiISEBdevWVYaNiouLUbduXcTGxgbkhnBBkJycHCBeSkpKjC9uM/FiZ1sUKvx6YhnfVomfqhA5KvHicrkCnBfx/vNj8v+ieyKicl7MxIt8zEqgWAkbs22xnujkMMYs26i2q5jAWbm8M/lWaVtWyQVg8/Ly8Nxzz2HAgAFB8xP+/ve/Y9y4cXj88cfx6KOPYtmyZRg3bhwWL16MadOmKX9EPffcc+jSpQvuuOMO9O3bF0OGDEHTpk3x3HPP+dV76aWXQETo0KEDGjVqhBMnThhlgFeY/d///R+++uor3HvvvejatStGjx4NwPsw/dvf/oZTp07hz3/+MzIyMnD11VcDAK688kqsXr0a2dnZ+PnnnzF58mTExMRg0qRJxoiY++67D40bN8Zll12GgwcPIisrCwcPHsShQ4fQr18/JCcn45133kF2djZatmyJe+65Bx06dMANN9yAHTt2ICMjAwMHDsT111+PLl26ICsrC1OnTkXLli3Rvn177NixA9u2bcPmzZtx8OBBDBw4EPHx8Rg/fjwWLFiAvXv3GnOhjB07Fj/88ANefPFF3H333cZI08suuwytWrXCRx99hM8++8xYLgbwir/69evj888/x5w5c9C0aVMMGzbMuLc8vLRlyxYwxrB69WoMGjTIz2HjAkV0Uz7//HPj9csMGTIEubm5xkSlIitWrED79u39ljQJxrBhw+DxeLB69WrbbWob1V68lJeXY+nSpRgxYoSRu6GiadOmaNy4caXEixj64ecEEDR/hbfl7Ro0aICioqKAX/QcLjKSkpKQlJSE8vJyZV0uKBo3bgxAPddJUVGRIV5U4qa4uBhOpxN16tQxdV5SU1MDzl1SUoIGDRr41QO8D8SoqCjExsaaOi9m5SoBIs5jIrdXiRxVuCfUsFFJSUnAvuycWP2vyp8JJl7MknKDOS/iMTORYXY+t9vtN+rJbvvzRBaANGG/BQDrIXlV0zYkXnnlFZw6dQp/+9vflLOgisTExBizfHM3ZdmyZXjkkUfw0EMPKdvExcXho48+QsuWLRETE4NRo0ZhyZIlSEpK8quXlpaGtWvXYtq0aZg2bRqWLVuGXr16+dW5++67cfXVV6O4uBjPP/+8X3+7d++OG2+8EYwxTJkyxe9Yr1698OWXX+Kuu+7CH/7wBwBAx44d0adPHzidTjz66KNG3fj4eDRv3hwtW7b0y9cYMmQI3nvvPXz66afG9/JTTz2F+Ph4PPvssyAiREVFYc6cOfjjH//ot7ZanTp10KlTJ1x++eVo3ry5UT5p0iQjHMrXSONDhzMyMvDqq68adYkI1157Lb7++muUlJTg1ltv9Xtfhg4disWLF2PFihWYMGGCnxuSmZkJIsKLL76IhQsX4ujRowFuSsuWLdGhQwesXLkSALBv3z789ttvAWu3cQYNGmS4OCLFxcX4+uuvjbwYu3Tv3h0NGjRQjozSeKn2YaNvvvkGp0+fxg033GBZj4jQsWNHv2SwUDl58iQcDocRIgrFeTl16pTxsOc235kzZ4x8ExEuMpKSkowHdV5enpEUyOFio379+oiNjTUVL3Xq1EFSUlKFxAsRISUlRXmMv37ZeYmLi1OKl5iYGJSVlfkJMVWYJ5goUYkXWUAAgWEd3j+xTCVexCRZfh2r84rOiHwuvm8mIORzqhwUM+fFypWRt8WcF5XgISJbYSP5tVUh6wG0I6J0AEcAjAVwywVoa5uTJ0/ilVdewU033eQXQrAiKioKb775Jq655ho4nU7079/f8kcWAFx66aW2Zu7u2bMnevY0j6xFRUXhk08+wTfffKN8OM6YMQNdu3ZVhtu7d+8e8Brfe+89vx9hweChH06XLl2Qm5vrN1O06jpmXHrppbj66qtRVlZmiJo2bdrgq6++QufOnREfH+9Xf+TIkXjjjTfQunXrAGE3cuRIY2FdeYRqo0aNcM8992DmzJlYsGABAASIF8Arct566y2sW7fOcFRGjBih7Hv9+vXRs2dPLF261BBvgPf5VVJSElLICPCG0zIzM7FixQojvKXxp9rfkUWLFiEhIcGWcr3kkkuwc+dOW6ODVGRnZyM1NdX4oCQnJyM+Pt6W85KTk2OIHi5izHJZuPNSt25dYw4Xs5AQ4P2lkpiYGNR5KSoqCphkrLi4GAkJCabixUzYlJSUGCJMTraNj4+H0+n0Ey881yQqKso0bKQKEdkNG6nEix1BIwsPfszKialq50WcY0XlvFgJm1DDRvL57DgsZiOvzOYGqQiMsXIADwBYBWAHgH8xxn4lonuI6B4AIKImRJQF4E8AnvKtUJ9k1rbKOufj9ddfR2FhIaZOnRpSOyLC9ddfj8zMzKDCpapp1KgRbrrpJqVL1Lx5czzxxBOWk6KJtG3b1m+V9YqgWuIiFD777DNjmDRnwIABSE1NDah71VVXoVmzZvj9738f8PozMzONxNs2bdoEtH3rrbdw9OhRvPXWW3j11VeNVAGRRx55BGlpaRg0aBDefPNNdOjQAW3btjXt+x133IFffvkFP/74o1G2YsUKxMfH46qrrgr62mWGDRtmjITSBFKtnRePx4MlS5YgMzPTb/lwMzp06IDc3FwcP37cCPmEgvyrg4jQuHFj5XTSMjk5ObjssssAnHNezPJexLARFwZ2xItVzktiYiIAb2hJjMkGc174MdldMhMv3HmRxQsXNaWlpQHiJSEhAUVFRcoQkUq8qJJz7YqXYMID8D64rfZdLpffSCezBF6xvpV4kR0Us9CQyl2xGzbigl2sJ4aNrBJ2zfKVqjr/hTG2HMByqWymsH0c3pCQrbZVSUFBAd544w2MGjUKl1xyyfm6jCYI/MecHWJjY7Fv3z7lCNTk5GQsXLgQF198sWn7Jk2aGMnIKlq0aIHvvvsOgwcPxvbt2zFlyhTTugBw66234rHHHsMbb7yB3r17G5MK9u/fP8BVt8OQIUOMSfV69OgRcvuaTrV2XtavX4+jR48GnZWQw790Kho64rPeigRLvuXk5uYaokEMG6ngIqSqnJc6deoY4k5eBVoUKKqEXafTifj4+ICcm+LiYsNBksVLfHw84uPjA8RLXFycspy/RjlEFBUVpSxTiZzKOi9yHVlAyOdVhVLEc4oOl2r4cyjuitkxcV91TDyHOBmYSvCIQka8L4D5SLHatFTAnDlzcPbsWWPUkCYyiIuLMw2pjBw50lK82KFp06b45ptv8Mgjj/jl7ahITEzEhAkT8Omnn+LYsWN46aWXsHv3biNvJ1QaNGiA3/3udwFOlMZLtRYvixcvRnR0tGmcUaZDhw4AKi5esrOzA5YesCNePB4PcnNzjdE5XMSYLaQnJ+ya1eXDFh0OB+rWrWsZNuLKXhQOjDEUFRXB6XQiISHB1HmRxUt5eTncbrdp2EjlvHBHRj5XaWmp8RplUZKUlBTgvIjDnO3mvFgl25qJl2DOi0okideTE4eDOS92EnaDJfOKx8R7YyZy7Do3F8p5qa64XC5Mnz4dV111FX73u9+FuzuaakZKSgpefvllpKWlBa173333oby8HBMnTsRf/vIXjB07FuPHj6/wtYcOHYqNGzcq162r7VRr8bJkyRJcffXVQedY4TRv3hyJiYm2VvhUoUpWS01NNV1rhFNQUACPx2OIF/6wVg1dFsuTkpIMV0JVt7Cw0MjwDxY24s6LKDTKysrg8XiCho1kwcG369atG5DDwp0Xp9MZIFLMymXnhf9ft27dAOdFJV7i4+NDcl7cbrfhGlQkbCSLD1UIykqsWO1bHbMabSQLG/EemwkgMyHD63Fqu/Myb948ZGVladdFU2natWuHzMxMrFy5EpdeeqmxJlZFGTJkCBhjfjMCa7xUW/GyY8cO7Nq1C9dff73tNkSEtm3bhrQgGKe0tBR5eXkVChvxGXi5eLESJMA5lyUxMTFo2EgUL1ZhI5XzwrdDDRvxbafTibi4uIAcFbOcl2DOi8plUQkacZ4SXiYLCIfDYSpMVOGRYHWsnBfZ4VGJG7NEW3lfJSLs5MPIwkZ2SIIJFnmotJ05emqDePF4PHjppZfQpUuXkIezajQqnnnmGfTu3RuLFi2ytRyAFRkZGWjQoEHQhR9rI9U2YXfx4sUAYExWZJeLLrqoQs4Lt+VUYaOcnBzlzIkcPhMuDxfFxcUhLi7OdBG2vLw81KlTxwgHAZUTL2bOCxcXCQkJpnktKvHC28XHxweIF9F5EUUdFy9ut9tozxhTho1cLhdiYmL8HBVRqPD3wkq81KlTx68sKioKHo8nqPDg28GcFlUCryiEgokhu86LVWjHauSQKByt8lzMzm1nduTaEDZasmQJdu7cifnz51fqF7JGw+nVqxe+//77KjmXw+HANddcg1WrVukh0xLV9k4sWbIEPXr08JvEyA4XXXQR9u/fH/IwT3mCOg5PWlUtj86RnRfAGxKycl64aOGjhMzECz8eLGwUzHlRiReeD2PmvHDxIjspKodFTOTl5XwUjCpsxAWenbCRSryI9Vwul3GfVMJEbGdWJ1jOi9vt9lseIJSwUbBZdCvivIjvs1l4SWwjJ+xq58Urrl944QW0bdvWcukRjSacZGZm4sSJE9i6dWu4u1KtqJbiZf/+/Vi/fr0x3XUopKeno6SkxNbcLCL8176ZeLEKHYUqXvLy8gw3IioqComJibZyXuScFZ6QG8x5cTqdAWEefpyLF3EorShe+PBnjkqkAGpBIibmAv4Ju2Z1VULFTLyID31+n8ySbV0ulzEHRahho2BrF1mNLuL7VvO1WCXVhprzYjdhVzsv3gX5Nm7ciEcffTRg8UWNprrAF4zUoSN/qqV4mT9/PgDvuhahwteP4Iss2oU7L3LYiE+OZJW0y8NDoYgXcT4Ds6n9CwoKjIcyz1kRHSX+oLGT88LFhjiBnyhexPPZyXkxc2TMBIm4z4WEqm5FnRd+n0Qhwmf8taoTFxfntx8bG6sMC4USJrISM6E4L3bDRqEKGbl9bUzYZYzh+eefR7NmzSo1GkSjOd80bdoUXbp0MZYq0HipluJl3rx56NOnD1q1ahVy2/T0dADetShCIVjYyI7zIk4OFyxsJK5lYiZeROeF/69aCdrMeeHbokARH8J89l1ZvNjJebETNpKdF7thI1XCrhz+kXNeVM6LeC4z8ZKQkOA3z0udOnX8jjudzqA5MXbCRqKDYhZSsnJerBJ25RCSnYRdefi7arsmOy/Lly/Ht99+iyeffPKCz4qr0YTKkCFD8P3335tOv1EbqXbiZdu2bdi+fTtuuaViS5e0atUKRFQh8RIbGxuwQNr5EC9i2AiA6RwuKvEi1uMPILs5L0DgQ8/KeTELD4UaNuLOS6hhIzPnxeFwBAyfVuW8yOKFCzwuIKKiohAfH+/XRhYvCQkJITsv8n5paanhmKmScs2EjVVIySxPRWwjCha7OS/i56emOi9utxuPPfYY2rVrh7vvvjvc3dFogpKZmYmysjKsWbMm3F2pNlQ78fLRRx/B4XDgpptuqlB7vgpqqGGjkydPomHDhgEjDuyKl4SEBL91PZKTky1HG4lhI7ORRCrxIua9cPEizrBrlfMilvHtYOJF5byICbs8DCUm8prlvNh1XjweD9xut6l4iY2NRWxsrNJVEV0R0Z0R82K4GImJiTFCS7JY4efmYiZYmMhqqLQ8MshuaMhu2McsedfKrbGzXVOdl/fffx+//vorXnjhBeXU8hpNdaNPnz6oW7euXmVaoFqJF5fLhffeew/Dhg0LyD0JhfT09Ao5L6rVVBMTExETE2M61T/gvzQAJ5SwUUXFixg24gJE9VBThYbcbjdcLleFcl648yIuOMjDRmIuTLCcl9jYWD9BExUVZYgwl8vllwfDBY3YNlTnRRYvsbGxhngRxYooRnjYqDI5MPLEgXadF6twk5l4sRJDZuGh2pTzUlBQgKeffho9e/YMulK9RlNdiI2NxTXXXIPly5dXeOHhmka1Ei9Lly7FiRMncM8991TqPK1atcKhQ4dCamMmXogIKSkpluIlJyfHL1kXOCdeVB80lfMixzK582DHeUlISDBCIGbOi5VACTXnhTssYhurUJDT6UR0dLQybCSXcfdKdlDEMi46RFdFFD1iO1H0iOKlrKzMVLyIgkJ2YuQcGB524vvR0dGWQkM1i67ZcGaXy2UabjJbudtqbpdQnZeaKF4efvhhHDt2DNOnT9fzumgiiuHDhyMrKwvbtm0Ld1eqBdVKvMycOROtWrXCkCFDKnWeli1bIisrK6QvXx42UhFsll0z8VJWVub3YAHOhRjk0Uay8yIuyij+bxY2AhAwHNpKvNgRNqp5W9xut1HO63o8HpSVlQXM/8JfOxclqrCRHA7iNr7ojvCESlG8yM5LfHw8HA5HQP6KeC6rsJGZOElISPATRLKY4cfFfS4a+KSGdsNG4r2Xt0NJ2A01ybe2JOwuXLgQ7777Lh5//HH07t073N3RaEJi6NChAKAXavRRbcTL5s2bsWbNGvzhD3+o9JwLaWlpcLvdIc31Yua8AAjqvIiLMnLM1jfiIoWHOfh2RcSLGDbi/9t1Xuy6MionRXZexHJen8+uK5arXBZZ0IjOC3dHZDdGlfMiujFi2AgwFy+i8yI6LbIYscqBEfeJyBh6LbpB4r0WrxUdHV2hXBb5mJywKzo5dtya2uC8HD58GJMmTUK3bt0wderUcHdHowmZpk2bomvXrlq8+Kg24uWFF15AUlIS7r333kqfi6/+efjwYVv1CwsLUVRUVGHxkpOTo8x5AUITL2KIKRTnhT8kZedFHCotJ+zadV5E8SI7MrxMXECRl4uukyxUREdFdE9UYaOYmBjTMrMkXjPnRR5tpHJeuFiRw0Zmo49EcRMdHe13Pn7PxfdBHOkkCh2OVS6LmRCpiPNiJ+elpjgvu3btwlVXXQWXy4V58+bpJF1NxDJ8+HD8+OOPQdfbqw1UC/Gyfft2LFy4EA888ECAg1ERQhUvZusacSqa8wIgYMSRmXjxeDzKOVxCES8q58XhcBjrCAH2nBd+zCyHJZjzYlaucln4zL6lpaWWLouqTBVyUuXKqJwXLl64+2HmrMhiReW88EnpRDFUXl4eIBidTqdfSCkmJsbY5w9U/v45HA7LsJGZ82I1QsmOYKlpzsuKFSvQu3dvFBQUYM2aNWjXrl24u6TRVJjhw4fD4/Fg9erV4e5K2Am7eGGMYfLkyahXrx7+9Kc/Vck5W7ZsCQC2k3bNJqjjWIkXxpil8yIn4qrEC89/EUNHVZXzwh+goYaNYmNjjSRgs1wYXqYSL6WlpQHOiyphl++rhIpV2EhM2BXdGHm0ET+/2+1Wihcz50XMgRFfu1UYST6fKmzExQUXTrJLU1xcbAgb3s7hcBhChC/MZiVeROdFFCC1zXn55ZdfMGzYMKSmpmLdunXo0aNHuLuk0VSKbt26oWHDhvj888/D3ZWwE3bx8uGHH2Lt2rV4/vnnjTlVKktycjISExNtOy92xEthYWFA8i1wbt2byoaNxGPAOZHCj1U054UfC1W88DI7zotK1Mjixcx5Ac6JErFMTKrlZbLIKSsrg9vthsfjsXReRCeJiCzFi9Pp9Jven98/UUyahY3k86nCRvye8bpczIjihQsbVa6M/F4RkbHNE5a5YKnto42SkpIwb948bNy40Vg2RKOJZBwOB0aOHIlly5Ypn0e1iSoRL0SUSUS7iGgPET1ut922bdtw3333oV+/fvjDH/5QFV3h/UFaWlqVho0A9crSPCwkixfupoQiXkSXRnZe4uLiEBUVFeC88LAQYO28hJLzwsUFvy5PwA3FeRHLVfkt4igiUZTw12InbCSKCKucFy4euGDgro4c5lHlociiUXZTrJwX+Z6LbaOjoxEdHW3cW3GeHu68iPebixx5Ph/xPRdnHY6KijJGgXHMREpNdV7S09Mxbtw4v781jSbSGT16NPLy8vDVV1+FuythpdLihYgcAN4EMBRARwDjiKhjsHY//PADBg4ciOTkZMybN6/KV3UNRbwEc16sZtk1Ey9V5bzwhycRoU6dOgHipU6dOsZ8FSrnpaJhI9F5AQITcK1yWwB12CiY8xJqzot4n6ycF15HFhdm++K94PdPfj/EkJ0ohsQRRKqwEd/n11IJG9l54eJFzKMRhY3ZNr/X/G+rpKTE2K4tOS8aTU1j4MCBSEpKwqJFi8LdlbBSFc5LDwB7GGP7GGMuAPMBXGfVYNeuXejTpw8SExOxZs0aNG/evAq64U/Lli1DEi8JCQnGg0mGOy+qvJdg4qWiOS98W+yTLF4KCwuNhx5Q+ZwXXsZn0ZXbmTkvdh0Z1TwvfD/UnBdexu+TmMQr57yI4oW7M8HEi5wMLecXiU5MqGEj0XmRhQ0PKcnHzJwXUbA4nU5jW7y3otCUxQ+vw9HiRaOp3sTFxWHEiBFYsmRJxLujlaEqxEtzAKJKyPKV+UFEdxPRBiLa4HK5MHXqVGzZsgUXX3xxFXQhkLS0NBw/ftxWXNBqgjqgYuLF6XTC4XBUmfPCt2XnRRQvsvNSVFRkS7xER0fD4XD4DYkWw0aAv5NSkYRdLl54KMOuyxITE2M6SZ14z1TrFMlCQ55RtzLiRdwPNWxUVFQU4LxYJezyY6WlpQHiQxSs4tIM4vsjujD8XpaXl/uJGk5NChtpNDWV0aNH4/Tp0/juu+/C3ZWwURXiRTXHdsCc+Iyx2YyxboyxbpdddhmeeeaZgBWcqxI+XPrIkSNB61pNUAfYEy/yayEi5fpGKkfFTs4L31aFjThWzktMTAyISJnzIrcVnRdRjIi/6s0Sc+VyIkJ0dLThivAcjGDOiziRnN2wkey8mOW8qMQGH77MzyuLFznnRTzOl3KQz2cVNjJzXsSwkSxEiouL/UQJnxRPFDLie8HrifeZtxfruFwuv9ASRzsvGk31JDMzE06ns1aHjqpCvGQBSBP2WwA4WgXnrRShzPVSGfHCxYnsvADecJBKvMTHxxtTxwPmzktsbKxfvWBhI6vRRkTkF1aQH5rykOjKOi+8nI/w4c6LnAcDmDsvKoeGl3GHRA4bqUYpWeW8iPO8qJwXs5wXvq9yTKyGSvN92XlRJeyqQkoqASSKFy7czNwWlXgR62vnRaOp/tSpUweZmZlYtGiRsf5ZbaMqxMt6AO2IKJ2IYgGMBfBZFZy3UvC5XuyIl2Bho7p168LhcIQUNgK8bowq50Ue/WA2z4ucg2MnbCQu7ic6L4C/QJEfmvKaRFY5L2aT1MkjiFSjlsxCTGajjVQz7NrJeRHr2HFeVOKFiwj+fvB7zI+L/RVDQRXJeVGNRFKJF1HkcPElCxarbVGwmG1ztPOi0VRfxowZg6NHj+Lrr78Od1fCQqXFC2OsHMADAFYB2AHgX4yxXyt73srSokULAMEnqmOMBXVerFaWNgsb8TKV8yKLl7i4ODgcjoCwkR3xIoeNeDkQXLzw4de8LX9YVsZ5kcNGZuKlIiOLVOElO+KlIqONRDEi3lMxFCUKK1m8lJeXGxP92XFeVMdUYSNRyHCRI76/HDNhEsx54fcSAO68805oNJrqyciRI5GUlIQPPvgg3F0JC1UyzwtjbDljrD1jrA1j7H+r4pyVJSEhAQ0aNAgqXvLy8uByuSzFC2C+snRubi4SExOVQ73tihciClic0Y54UYWNAP+5XGTxYnXMaqi0nPPCk3zthI34MTEfxc5oIztlYsKuLF5k1yRYzossRqycl8LCQqXY4U6I2+0OCP/I7opVwq7KeXG5XH5rR1mJFzsixY7A0Wg01ROn04mbb74ZCxYs8Hsu1BbCPsPu+cTOcOlgE9RxrJwXs8Rju+IFCFxZuiJho1CdF7NjsujgZbITwNtYjTbi+3yeF7s5L6LAqEjCrlnYyGqotChWzJwX8R7LAkl2U8zcFVHoWM2+K881I2/zc4jvYSjbZoLlfImXYJNZkpfXfMe3ElFX4dgBItpGRFuIaMN56aBGE2GMHz8ehYWFWLx4cbi7csGp9eLlxIkTAMwnqONYiRdVvgvgzWWxk/MCVI14EX/ZM8b8hkoDCEjYlY+JYSNVzos8koWLF9FNsRs2CsV5kYdKq5Jx5UnqzJwXcdST2Yy7/N7K11HluKjCRqJ4kSeb4/fezHlhjFk6KuJ7VhHnJdQQUlVhczLLoQDa+f7dDeBt6Xh/xtjljLFuVd5BjSYC6du3L9LT02tl6KjGi5dgYSM+u27jxo0t65mJl7y8PFPxEorzIgsdK/HCGFPWEX/Zl5WVwePx+Ikb0V2RhY1d5yUqKsp4YFo5L6qwUSg5LypBU1JSYsxPYpbzohpiLYeNRLESGxsLxpjfUGd+f+SwUbCcGL7P3RTeXs6XEUc68aRYWZTw8/L7rNq2qieez06SrvxZOA/YmczyOgAfMC/rANQjoqbnozMaTU2AiDB+/Hh8+eWXtqYFqUnUePGSm5trJNWqOJ/OS1JSEgoKCvxGbYTivMj1EhMTjTWGPB4PSkpKTJ0X+Rc9EDznReW8yGGg+Ph4YzkCWbzExsb6OS98sUV+Hu4G8X07M+yauSwVTdiVnRexjpmTIh432xfDPXLYiDtTVgLFKhxkJkSswkZ2QkJ2XJgqxM5kllZ1GIDVRLSRiO42u4g4GSYPCWs0NZnbb78djDG888474e7KBaVGixc7c71w58VOzkt+fr7fQndAcPECBE77b0e8qOqJc4zISaCAv/MiT7IGWOe8iCEllfPCh0rLDzwuXmJjY40J6aKiopTOC3BuIj7RPRFFCXd2REHjcDgQFRUVIFTEe2snYVd0Z4INjVY5K3LYSNznfYiJiTHmXbASIVbH5HCQ3I4nh0dYwq6dySyt6vRhjHWFN7R0PxH1U11EnAwz2N+0RlMTaNOmDYYNG4aZM2caP5RqAzVavPC5XqxCRydOnED9+vWNh6EZfHFGeWVpO+JFDAeFIl5UYSPA+zBWzcAbzHmxynnhQsTj8fiNapFzWOSHnyxSeLkqYRc4N6mf6Lzw+8Pr8OReLkJ4mVgvlIRd2XkpLS01EnTNnBa7YSPxcyMeBwLdFVFIynXtho3EY1YixywMZCZYRFF0nsSLncksTeswxvj/2QAWwxuG0mg0ACZPnozjx4/j008/DXdXLhi1XrxkZ2cHzXcBzs2yKw+XthptxCef4w9st9uN4uJi2zkvVs6Lylmx47yYjUTiCbvyhGfiEF6V8yKLFLNy/j+/F2ahH16Xixf+oDYTL6FOUhcbG+sX1pHDRlYJuaLT4na7g4qVYAKlsq5MRUYbie+TKLzE854n8WJnMsvPAIz3jTr6HYBcxtgxIqpDRHUBgIjqABgMYPv56KRGE4kMHjwYHTp0wGuvvRburlwwarR4adKkCaKjo4M6L8HyXQD1EgFlZWUoLi4O6rzwBzZ/0HJRIyI6L+Xl5SgtLQ1ZvARzXhISEoLO8yKvSiyLF/mhaOa8mIWN+L2Ij483Hp6y8xIXF2e8PtF5sQob8TK3242SkhLExp5bWkFO2JVn3OV1RLHi8Xj8jjPGAsSIHDYSr8nPL+5X1HkxEzZ2w0byBHR8YkI+V498zfOR82I2mSUR3UNE9/iqLQewD8AeAHMA3OcrbwzgP0T0C4CfASxjjK2s8k5qNBEKEeHBBx/Ezz//jHXr1oW7OxeEGi1eHA4HWrRoYZnzcuLEiZCcF1G8WK1rBJiLF7OwUWFhITwejzIkJO6LYaNQnBdx7SOzhF1xFl3xf5VIMRMv3HlRJf6KYSOe36JyXlShJJV4kYUJL+M5ODExMQFhI3mf3zNZNMj7qhwXq7CRvC+Hf+zmvIjvodgnq/NbjVDi53Y4HMoQlHz9qkI1mSVjbCZjbKZvmzHG7vcdv4wxtsFXvo8x1sX379LqMhGmRlOdGD9+PJKTk/HKK6+EuysXhBotXoDgw6WDLQ3AUYkXq3WNgNDFCx+NY1bPbs5LUVGRqfNSVFQExpgybFRWVuY3GggAoqKijFBLKM6LnCMjuyyiI6NyXsREXLlMFBFmbgzflp2W2NjYgH0AAQm8/Hhl9sV+8vtoVld2V+yEm+w6L2J7h8Ph195MvIjX12g01Z/ExEQ88MADWLBgAbZu3Rru7px3arx4SUtLMxUvpaWlyMnJqbDzEky88PAQfzjzB63sqIh1CwoKTOupxIsocMRJ0MycF75wo8p5EV+T/PALxXnhYSPVGkny+WVHhf9v13kJJl5UTgsfuh5MfKicF1GAmI02Uu0HO7fdyefMcl6IyK9vdia2MxMvcl81Gk1k8MgjjyA5ORnPPPNMuLty3qnx4qVly5bIyspSrpDL54Gw47wkJSUhKirKT7zwbS5sVG2Ac86L1SKOXIQUFBQohQkQ3HkhIjidTkvnhbcvKSlRihc+mkoWKaE4L3bDRvx/lfNiJV6sJqnjZWI7ceiy7H4E2w8mToKJGTNBECwp12yUkpnzYhWGsgob2TmXRqOJDOrXr48pU6Zg6dKlWL9+fbi7c16pFeKlvLwcx48fDzjGJ6iz47xERUUFTFQXTLzIo424eKlXr15AXVG82AkbmdXhSblWCb1nz54FY0w5O29OTg6AwF/uPB8mlIRdO+JF5byowkZWOS9EBIfD4TfBnRg24gQTHxURJ6E4L6IgsCtQAHNhY5W8azZvi5XzYuYSaTSayOGhhx5CgwYN8NRTT4W7K+eVWiFeAPVwabuz63JSUlL8hkoHEy8xMTFwOp0B4kUVZuIiJD8/P6SwkVzHjvPCHSd5GDVwTryowkPBJqnjxMXFGcnHqknqxCUGguW8mIWSHA4HiMgYBSSHTcR2nGBiRZWwK48eqox4seu8yHXFe27XebGT82KVsKvFi0YTmdStWxePP/44Vq9ejX//+9/h7s55o1aLl6NHvXNkNW8uz1Kuxsx5qV+/vmmbpKQk46FrNTpJzHkxCxs5nU4QkaV4kZ0XlXg5deqU3z4QKF5UzksoYSNVbgvgFXDy0F27OS9iG1GsqOrw/gRzWoI5L3zWYH7+YGLFbKh0sJFMZi6KSmCpjlm5NWbzueiEXY2mZjJ58mR07NgR999/v99ivjWJGi9erJYIyMrKAhGhaVN7a7+pxIvT6fR7UMjUrVs35JwXM+eFiJCQkGCEjaKiogImFJOdF/G4lXiRw0byon1mIqW8vBxFRUUBYSNZBIlhI7mu1TwvYtiIYyZaVG4FPxYdHR3gztgRM/L/8jXs5shYCRveTzPxYiWIzASH+L6biR8z50WHjTSayCY2NhazZs3CoUOH8Oyzz4a7O+eFGi9ekpOTkZSUpHResrKy0LhxY78HkBUq8cKXDTBDXFk6NzcXCQkJygeDnYRd4NzK0nxFab5IIkd0XuLj440JyfgxwNp54a9PFE5WCbtAoCCJj49XJuaq6sbGxqK8vNzYFuuq2ov17DgvsrAJ5pzwcBQAv4c5P6d4XDVJXUVHG5kl90ZFRZm2E9uIoTggMM9F3FZNTKedF42mZtG3b1/8/ve/x9///nds3rw53N2pcmq8eAG8oaODBw8GlB85csR2yAhQixezfBeOLF7MhlWrcl6sxIvZGkmi8yKKE8CeeOE5PbIrY+a88NelStgV6/DjxcXFQaerl10f8Zi4HUrYSOXgBHNagjk8oYSRuDBSHZP3RSEhhq3kY6okYI54j8XriuLLynmRRbFGo4k8XnrpJTRq1Ahjx471W36mJlArxEt6ejr27dsXUJ6VlYUWLVrYPk+DBg2Qm5trOAV2xQv/0FiJFzHnJT8/Hw6HQzlNu+y8yHDnRZ7HhR8DrMNGXLzII5GsnJeioiK/a6kEjtmCgKJ44OdQtbcSLyphIjsvKoEjLlEgXkt0WoLtW4WNRHEjCwLZ3ZAdH37MSryI24wx286LuG3mwmjxotFEPikpKZg/fz727NmDu+++G4zJC7lHLrVCvLRv3x579uwx5vvghCpeuFDh+RynT5+2JV54rouVeOE5DwUFBcjNzUW9evWUDxBRvFg5LypxU1HnhYeBPB6PqWsih5nkOiphIW+rXBY74sVO2Eh1nri4OMs8GVmsiPkzfN/uaCR53hTZNbE6ZidsJF/DSrzwLzC5XAyHafGi0dQM+vXrh+effx7z58/HW2+9Fe7uVBm1RryUlJQgKyvLKCssLEROTk6FxAt/wNsRL/Xr1zdCTVbihYiQmJiI/Px85OTkmNYTw0ZWzkteXl5AYrAsXlSCg782eekA3kY1o694biC482ImgFTOS1WFjVTiRXZe7DgtIvJDPljYSMQqryQU50UWNuJr48hhIy7i4+Li/NweXh4bG1ujfqFpNLWdxx57DCNGjMDkyZOxZMmScHenSqg14gUA/vvf/xplPIGXj0ayg7hEgNvtxsmTJ9GkSRPLNqmpqcjNzUVZWZmleAHOrSydk5OjnMgOsBc2KiwsRH5+fsDq1XbDRk6n0y/Rlw+J5tcXy+VzA+c/bCSLCt7OykWRQ0K8jmqEjjgHjdiGn0t8yItYOTGyULEa0SMPe65Izov4Psn3W+y/SrzExMRo8aLR1CCioqIwf/589OjRA2PHjsXatWvD3aVKUyvES7t27QD4i5e9e/cCANq2bWv7PKJ4OX36NNxud1Dx0rBhQwBewXDq1CnL0Ul169a1LV7y8vICxAlwLkE4Nzc3wHnhD3mrSery8/OVE9+J15fbmJ0L8F/gURYF8raVS6MSObxM5c7YcV7knBXehj+4+T53LsyOc4INlZbrymEjUTzI5xHvhyrnRZx8Tny9cj+txAt/Xdp50WhqHnXq1MGyZcvQtm1bjBw5EmvWrAl3lypFrRAvzZo1Q0JCAnbv3m2U7dmzB0Bo4oULj5MnTxrLDdgVL8ePH8fp06eNfRWhOC9nz55VTo5Xr149uFwuZGdnB4iX6OhoxMbGKvNaRCEkj1ISxUuoYSPVGjuqCdTi4+ONB6lV2Egc/m1HvFjlvJiFjcSwigivKz7kRUIRL/Hx8QFlfP0tp9PpN9pIDPvExcUpnRdZvIht5NcYTLxo50WjqZmkpKRg9erVaN26NTIzM/Hxxx+Hu0sVplaIFyJC+/btsWvXLqNsz549SE5ODpqzIsKHVR8+fBjHjh0DYF+87Nq1C4yxoOKF57xUVLzwshMnTiidGe6cxMTEBExkxgWIWaKvfExsb1Yu9oFvi2VcIJjNCCu7MapRTVbihf8fSsKu7KzI+2ZhI6fTGXA+LijkkV+ig8Lh4kUWNmJejZynoppwTkZ2uoKFjbTzotHUXJo1a4bvvvsOffr0wS233IJnnnnGGEEbSdQK8QIAnTt39puoZ/fu3Wjbtm1Ioyri4+PRuHFjHDp0yHBegs3Om5qaCgD47bffAFivo5SYmGiEfKwSdnNzc1FaWmrqvHBUM/lysaYazcSvKYsX8Zyh5ryITg0XLWIZf6ibuTv84czPL/aZ1+PHVH3gdcycFzm3Bwh0XmSxYhY2ksULESmHcfNryWKDf4GIwkZ+j2TxYTZJndyGI4eNRMEkOkryyDyNRlNzqFevHlauXIkJEybgueeew4ABA5Sz0Fdnao14ycjIwPHjx431jLZt24aOHTuGfJ5WrVrh4MGDxhsdTLxwp4WLFyvnpXHjxjh48CAKCgoM0SMjigcr5wWA0nkRxYsMFy/yMVFIhSpeVM6LKE74uUURIV6PP7x5W/6wFc/DhY9KFMniRawjiw+zsJEcJhLDKyKyeBHPIYsQlfMithHzWuRjYniJX08OG4lYhY34ucRyHTbSaGo+cXFx+Mc//oEPP/wQmzdvxqWXXopXX301YlyYWiNeunXrBgDYuHEjTpw4gWPHjuGKK64I+TxcvOzduxfNmjWzXNcI8ObJxMTEYNOmTQCsnZdmzZoZs/GaiSIxzBXMeVElB9sRL3IoTawrihFRvIiCwyxZlAsHUQDxc7tcLqNM5RipxAsvU4024ufg1+LiSOy//LA3c1543/i5ysrKAl4H74csXvhrFvvNryWvSyUmF3MxKIsIvkQBv57YZ9WkhuLr4NvifC6i28PPq8NGGk3t4bbbbsOWLVvQu3dvPPzww+jWrRuWL19e7b8Dao14ufzyy+FwOPDDDz9gw4YNAFAh8ZKeno4DBw5g586daNOmTdD6DocDrVu3xv79+wEArVu3Nq0rLlVgJl7EeWlU7owoNFRCiQsaK/EiiyJRmIiCSHz4mjk+ouPAH46hOC/yOcVfBVw8qASk7PLwfqiEkdxGrsvFjDwpoLyfkJAQIGisxIvcF35/4uPjla+XHxPFCz+Hy+VSOm1AoHgRQ2j8tYliSjsvGk3tok2bNlixYgUWLFiAvLw8DB8+HL169cLSpUsDvruqC7VGvCQkJODKK6/EsmXL8MUXXyA+Ph49e/YM+TxXXHEFXC4X1q1bh4svvthWGz6iqWHDhspZcTnNmjUzts0SgUXx0rJly4DjjRs3Vm5zuKtiJXxk8SIKHZXwEM9rdl3gnAgQH9r83HbFi+iWWAkS2Xnh7cwe8GIb3he+zx0R3pbvy++l0+kMuHf8+nbEiziUXOU08WNcvBCRUa+0tNQ0YddsyQJ5hJconrR40WhqF0SEG264Abt27cLs2bNx7NgxjBo1Cm3btsVLL72EI0eOhLuLftQa8QIA1113HbZt24ZXX30VAwcODBryUcHDTwBsix8+z0x6erplPdHJ4RPryYjiRTXBnvjgVy06yYWFKuTEf3nLro8oquSRL6rrmgkv/kAUxY1KqKjKuMgRr88f7Kqkay4s+INazOcwg4sJ/hCX97lQkPc5CQkJAYm5vG9yH+vVqxcgXrjLIh6TRYTD4fArk90iFeIx8d7WrVs3YMkDwF9IajSa2kVMTAwmTZqEvXv34tNPP0XLli3x+OOPIy0tDYMGDcJbb73lN1t9uKhV31J33XUX0tLS4HA48Nhjj1XoHG3atEGPHj2QkJCA4cOH22ozevRoAF7xZEWHDh3QuHFjdO/ePWCuFU5qaio6duyItm3bBuRMcHr37o2EhASlM9OjRw8AQJ8+fQKOXX311QC8yc0iSUlJSE9Px5AhQwLa9O3bF506dfKbV4S7OjfccINfXb4vzq3DtydOnGiUNWnSBFFRUbjpppuMMu5y3XzzzQH97dy5s1F27bXXon79+sYD+PLLLwcADBgwwK8vYsiwX79+AM4JHv5+tWrVCgBw4403AjgX8uN95UJy6NChAM6JmosuugjXXHONX7+vvfZaAN74MuB1qrhA+fOf/wwA+P3vfw/AK+74PXz66acB+L8nffv2BQB07drVqHfHHXcA8AoV3k9+fwBg0qRJiI2NRXJysvF6UlNTMWzYMABeISxu33///dBoNLWX6Oho3Hjjjfjmm2+we/duPPPMMzh8+DDuv/9+pKWloUuXLpgyZQqWL19urPd3QWGMVfgfgJsA/ArAA6Cb3XYZGRksXOTk5LADBw5U+hyHDh0Kqc2+ffuY2+0OWu/UqVMsNzfXss7p06ct65SWlrLTp0+bHt+/fz/zeDzKY0ePHlWWHz9+XHnNnJwcdurUKWX9goICvzK32832798fUPfw4cOsrKzMr+zEiRPM5XL5lR06dCigbO/evX77+fn5LDs7O+D84us9c+YMy8/PN/aLiorYiRMnjP2ysjK/z0h5eTk7cuSIse9yufyuIV/zzJkzrLCw0O+18OsXFxf7nevYsWOspKSEMeZ93w4fPmwcO3r0qHFf8vLy2MmTJxljjHk8Hnbw4EGj3pEjR4zP1smTJ437XlBQYHwOXC6X8T65XC7jOm632/gsl5eXG+d1u93s5MmTDMAGVonviHD+C+f3jEZTE/F4POy3335jL774Iuvfvz+LjY1lABgRsU6dOrGJEyeyt99+m61bty7g+9+KinzPEKtEbJuILvEJl1kApjDGNthp161bN8aTZjUaTfWFiDYyxroFr1n90N8zGs35paioCOvWrcP333+PH374AevXrzdmcCcipKen45JLLsEll1yCdu3aoW3btmjTpg2aN28u5y+G/D2jnhjCJoyxHbyTGo1Go9Foag8JCQkYMGCAEZZnjOHgwYP45ZdfsHXrVmzfvh07duzAl19+idLSUqNddHQ00tLSkJaWpkxvsEOlxItGo9FoNBoNcC7nrnXr1n45nm63G0eOHMHu3buxb98+HDhwAAcOHMDhw4fxn//8p0LXCipeiOhLAKrhI39hjC21eyEiuhvA3YB6iK9Go9FoNJqah8PhQMuWLdGyZUsMHDgw4HhFojdBRxsxxgYxxjop/tkWLr7zzGaMdWOMdbOaIl+j0dRMiCiTiHYR0R4ielxxnIjoNd/xrUTU1W5bjUZTu6hVQ6U1Gk14ICIHgDcBDAXQEcA4IpIXFxsKoJ3v390A3g6hrUajqUVUSrwQ0fVElAWgF4BlRLSqarql0WhqGD0A7GGM7WOMuQDMByBPfHQdgA98oyfXAahHRE1tttVoNLWIyo42WgxgcajtNm7cWEBEuypz7QgiFcCpcHfiAlFbXmtteZ0A0KqKztMcwGFhPwuAPEW1qk5zm20B+OfWASglou2V6HM4ieTPmO57eIjkvttba0cgXKONdkXq3BGhQkQb9GutWdSW11nFqDLy5EmmzOrYaestZGw2gNlAZL9Puu/hQfc9PBBRyBMy6aHSGo3mQpAFQFyMqwWAozbrxNpoq9FoahE6YVej0VwI1gNoR0TpRBQLYCyAz6Q6nwEY7xt19DsAuYyxYzbbajSaWkS4nJfZYbpuONCvteZRW15nlcEYKyeiBwCsAuAA8A/G2K9EdI/v+EwAywEMA7AHQBGACVZtbVw2kt8n3ffwoPseHkLue6XWNtJoNBqNRqO50OiwkUaj0Wg0mohCixeNRqPRaDQRxXkVL5WZDjySsPE6ryaiXCLa4vv3TDj6WRUQ0T+IKNts/owa9J4Ge5015j2taUTSUgKqzxkRpRDRF0S02/d//XD20QwiSiOitUS0g4h+JaKHfOXVvv9EFE9EPxPRL76+T/WVV/u+c4jIQUSbiejfvv2I6DsRHSCibb7vzQ2+spD7ft7ES2WmA48kQpi6/DvG2OW+f3+9oJ2sWt4DkGlxPOLfUx/vwfp1AjXnPa0xhPD3WF14D4Gfs8cBfMUYawfgK99+daQcwCOMsUsA/A7A/b57HQn9LwUwgDHWBcDlADJ9I9wioe+chwDsEPYjqe/9fd+bfF6akPt+Pp2XykwHHknUqqnLGWPfAjhjUaUmvKd2XqemehJRf48mn7PrALzv234fwKgL2Se7MMaOMcY2+bbz4X2QNkcE9N/3/VTg243x/WOIgL4DABG1ADAcwDtCcUT03YSQ+34+xYvZVN+h1qnu2H0NvXwW5QoiuvTCdC0s1IT31C615T2NJGrC56+xb34b+P5vFOb+BIWIWgO4AsBPiJD++8IuWwBkA/iCMRYxfQcwA8CjADxCWaT0nQFYTUQbybucB1CBvp/PeV4qMx14JGHnNWwC0IoxVkBEwwAsgTesUhOpCe+pHWrTexpJ1JbPX7WBiBIBLATwMGMsj0j1FlQ/GGNuAJcTUT0Ai4moU5i7ZAsiGgEgmzG2kYiuDnN3KkIfxthRImoE4Asi2lmRk5xP56Uy04FHEkFfA2Msj1uUjLHlAGKIKPXCdfGCUhPe06DUsvc0kqgJn78TPNTq+z87zP0xhYhi4BUuHzHGFvmKI6b/AMAYywHwNby5R5HQ9z4ARhLRAXjDogOIaC4io+9gjB31/Z8N78LOPVCBvp9P8VKZ6cAjiaCvk4iakO/nCBH1gPe+n77gPb0w1IT3NCi17D2NJGrCUgKfAbjDt30HgKVh7Ispvs//uwB2MMamC4eqff+JqKHPcQEROQEMArATEdB3xtgTjLEWjLHW8H6+1zDGbkME9J2I6hBRXb4NYDCA7ahA389b2Kgy04FHEjZf540A7iWicgDFAMayCJ3amIg+BnA1gFQiygLwP/Amu9WY9xSw9TprzHtak6jEUgJhweRz9jcA/yKiuwAcAnBT+HpoSR8AtwPY5ssdAYAnERn9bwrgfd/otCgA/2KM/ZuIfkT177sZkXDfG8MbogO8+mMeY2wlEa1HiH3XywNoNBqNRqOJKPQMuxqNRqPRaCIKLV40Go1Go9FEFFq8aDQajUajiSi0eNFoNBqNRhNRaPGi0Wg0Go0motDiJcIgogZ0biXj40R0xLddQERvnadrPkxE48/HuSuCb1VS0wnhiGg+EenZbjWaSkJEbuH7ZotvGYAaARFdQUTv+LbvJKI3pONfE1E3dWv9PRNuzufyAJrzAGPsNLyroIKIngVQwBh7+Xxdj4iiAUwE0PV8XeM88Da8635MCndHNJoIp5gxdrnqgG+SOmKMeVTHI4AnATxfifb6eyaMaOelhkBEVxPRv33bzxLR+0S02udSjCai/yOibUS00jelN4gog4i+Ie8CWatIvfrzAACbGGPlvjaTieg3ItpKRPN9ZXWI6B9EtJ6INhPRdb5yBxG97LvuViJ60Fc+0Fdvm69dnK/8ABFNJaJNvmMdfOUNfK9lMxHNgm/9Gt91l5F3ccTtRDTG1+fvAAzyCS+NRlNFEFFrItrhc3k3AUgjoj/7/va3EtFUoe5fiGgXEX1JRB8T0RRfueFoEFEqeae5598X04Rz/cFXfrWvzQIi2klEH/mEE4ioOxH94PsO+JmI6hLRd0R0udCP74mos/Q66gLozBj7xcZrHik4T7uIaL/vkP6eCSNavNRc2sC7ZPp1AOYCWMsYuwze2WCH+wTM6wBuZIxlAPgHgP9VnKcPgI3C/uMArmCMdQZwj6/sL/BOUd0dQH8A08g79fPdANKF+h8RUTyA9wCM8fUnGsC9wvlPMca6wvurZoqv7H8A/IcxdgW800i39JVnAjjKGOvCGOsEYCUA+H4J7gHQJZQbptFoAnAKD+7FvrKLAXzg+3u8GN4FSXvA6whnEFE/IsqAd+r6KwCMBtDdxrXugnc5ke6++pOIKN137AoADwPoCOAiAH3Iu/zDJwAeYox1gXeK/2IA7wC4EwCIqD2AOMbYVula3eCdll5kjBgi89UBY+wzxtjlPgfqFwAv+8r190wY0eKl5rKCMVYGYBu806Sv9JVvA9Aa3i+dTvCu6rkFwFPwLmIn0xTASWF/K7wi5DYA5b6ywQAe953nawDx8AqMQQBmcteGMXbGd939jLH/+tq+D6CfcH6+uNtGXz/hOz7Xd45lAM4Kr2UQEb1ERFcyxnKF82QDaKa8MxqNxi7F/MHNGLveV3aQMbbOtz3Y928zvE5MB3jFzJUAFjPGihhjebC3vtRgeNdF2wLgJwANcG6l9p8ZY1k+wbAF577DjjHG1gPGYqnlAD4FMML3A20ivD+WZOTvNQD4RHitlwPYIB4kokd99+NNoVh/z4QJbXfVXEoB768DIioT1t3xwPu+E4BfGWO9gpynGF4xwhkOr5gYCeBpIrrUd64bGGO7xIY+a1def4Ls9BuAG/6fz4B1LBhj//X9whsG4EUiWs0Y+6vvcLyv7xqNpmopFLYJwIuMsVliBSJ6GIq/WR/lOPfDWfxuIQAPMsZWSee6Gue+F4Bz3w2q7xcwxoqI6At4Xeeb4XNQJOTvNUuIaCC86+30kw7p75kwoZ2X2ssuAA2JqBfgXdreJ0RkdgBo66sTBSCNMbYW3kS1egAS4V0E70EhDn2Fr+1qAPfwmDARpcC7cmtrImrrq3M7gG+C9PVbALf6zjEUQH3fdjMARYyxufBauWJScXsA1XZBPo2mhrAKwEQiSgQAImpORI3g/Zu9noicvvySa4U2BwBk+LZvlM51L53LyWvvCz+bsRNAMyLq7qtfV8g/eQfAawDW+xxfGeN7LRhE1ArAWwBuZozJQkV/z4QJ7bzUUhhjLiK6EcBrRJQM72dhBgL/EFcA+NC37QAw11efAPydMZZDRM/52m71CZgDAEbA+wXS3ldeBmAOY+wNIpoA4FPfF816ADODdHcqgI+JaBO8QueQr/wyePNrPADK4MudIaLG8Nq7x0K8LRqNJgQYY6uJ6BIAP/p+uxQAuI0xtomIPoE3xHMQ3uRWzsvwriB8O4A1Qvk78IaDNvm+R04CGGVxbZcvSf91InLC64AMgncE5kYiygPwT5O2O4komYjqMsbyg7zMO+ENYfHVkI8yxobp75nwoleV1gTFl6j3KGNsd7j7Ygci+iOAPMbYu+Hui0ajuTDTOkjXawZv/l0Hs6Hcvu+JfMbYOxW8hv6eCSM6bKSxw+PwJrhFCjnwJgJrNJpaBnkn1PwJwF+CzEHzNvxzaUIlB/p7Jmxo50Wj0Wg0Gk1EoZ0XjUaj0Wg0EYUWLxqNRqPRaCIKLV40Go1Go9FEFFq8aDQajUajiSi0eNFoNBqNRhNR/D9pcGWYaV2cXAAAAABJRU5ErkJggg==\n", 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