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2JiUlMTLTb7UVFRVu2bBnoMuPGjbPZbOIysizb7fbS0tJ169aptlBMmaF2uVw2m23ixIkTJ07koGWAHrLLmHfQY15ZlocPHy6+U1ZWNmfOnFPuKqb8VFlZWWxs7E033SRJktPp7OjouPLKK1UY84oJ/szMTMa8gN6yy5h30Lw3Uo0YMeK0lx8xYsS0adPE17Gxsf78yNC9+uqrnZ2dSnYB6Cq7lDcyxcXFvfbaa+wCB+gzu5Q3aALIXOjKeOWVV955551PPPGE8p329nan06lMOwDQMLuUN2gqKioGFTWHw1FRURG62zN16tS4uLg333xT/DM9Pd1ut5eUlLS3t/NkAdpmV5IkqRc+eT9ES5YsEQ9aS0tLeXm5+Lq8vNz78gNdpra2Vny9ZMmSga5ooKfDx9Pk/VPeV9fS0qLcDD/vHQD/FRcXd3R0BPzjbNo+jbBbz6vPewcw2mW2wV9iAkGd4zaI4fBQqu0/5bgN5557Ls8y9M/j8dhsNpPJ5L1MPrBf5XA4bDbb6tWrDx06pFV2JdbzMu4Gwu6FcOjQod/+9rebN2/256dkWT5y5IhYzO50Op1Op9VqlWV548aNt99++2ADGpTsMuYFEH4mTZo0bdo0sVzHN7vdvnPnzvHjx4t/bt68ecGCBZIkGQyG8847b+/evZpkV+LcwwDC0Y9//OMPPvjAYrEMdAExvF2wYIH36bebmpqUf1oslnfffVeT7DLmBRCu4uLiTvl9t9tts9liY2OtVqt3diVJ8u5mampqbGysJtmlvADCVVdX1ym/L84be9pK1tfX+3lmgKBnl/ICCEuVlZUzZsw45f+yWCxWq7WmpsZut/dZAjF58mSPxyO+bm1tPeOMMzTJLuUFEH727Nlz8uRJUcNly5a9+uqr/c++k52dPW/evJ07d9rtduWbS5curayslCRJluWPPvpo9uzZmmRXYlVZWGBVGaKcWBmWn59fUFDw+eefv/fee7fddpvBYNi3b5/b7Z4/f77D4Rjo4Hwej+fw4cPKtjjRaLHxrc+ZD1XLLuWlvEAY6+rqKi0tfeCBB5xOp491DgEIaXaZbQAQxuLi4qZOnaocGSpcssuYlzEvALWzy5gXANTOLmNexrwA/pfD4UhJSVEhu5SX8gKQJElyOp0JCQnqZFditgEAVM4u5QVAdtXOLuUFQHbVzi7lBUB2TepfNeUFQHYpLwBEdHYpLwCyS3kBINKzS3kBkF3KCwCRnl3KC4DsUl4AiPTsUl4AZJfyQpIkSXI4HDFeJEkSX/g+bRSA/i8lyY8zwKuPww+GAY4SCQSc3YHOjMmYFwCiKLuUFwDZpbwAEOnZpbwAyC7lBYBIzy7lBUB2NWDgCQOgE1u3bv3www9jYmJSUlKWLFkSqdmVWM8bHk8S63kRHYPWlJQUsdfDnj17tm3bVlRUZDAY/PnB8MquxGwDAJ2oqKhQdjabNWvWww8/nJubG5HZpbwA9GL+/Pkio8K4ceOys7N37NgRedmlvAD0Yt68eT/72c88Ho/ynRtuuOHDDz8cYnY9Ho/L5Ro/frzL5Xr11Vc3bdoky3IAN0+W5ZKSEqfTuW7dukOHDlFeAJHAYDC89NJL1113nXd8Ozo6hjjaNRqNZrO5vb3dbDbfcMMN8+fPX7t2rY+au93uU/6vwsLCnJwci8Xy8MMPP/XUU943kvICCGMWi8Vms1133XV2u12WZYfDceWVVwZ3kmHSpElxcXEDdTMzM7O5udlms/W/wNtvv202m8U7xPz58w8fPkx5AYQ3kVpJkkwm02uvvSbGmImJifPnzw9idoXzzjtvoIGt+M1Wq7Wmpka5SYL3oSYtFsvHH388pAE+TzkAzbM7b948g8HgdDotFovBYMjOzs7Ozg7uaFcxbNiw014mOztbluWKioqkpKRTXl1cXBxjXgBhn92SkpKEhAQflwzWSoavv/7an4vV19dLkpSent7/fx0/fvyLL76gvEAYc7lcAf/fiMmuzWZbvHixj5NHBHEB2YEDB8SMrY/H3GazpaSkWK1WZVcO7wmKd99912KxUF4gXJWVlY0fP97HBfbt2zfQ9v1ImmTIyspSIbuyLG/atCknJ0eSpKNHj65evdrpdJaUlCgX8Hg8Npvt+PHjVqu1z+1Zt26duGRra+vf/vY33+0+LXZLDQPsPTwoVqtVvLRuvfXWl1566eDBg0uXLg34deJ2u/fu3dvZ2el2u9vb2++//34fgbBarVu3bk1ISDh69Kg/v7ypqendd99dunSp74stW7bs+eefj9Tn67RnqBxidt1u965du55//vlly5a1tbUtXbpUnM+wrKzstttuMxgMbrdbuXaXy+XjT8XlctXV1X355Zd33nmnP7s1+9IL3eNpGpSCggLvx62lpaWlpSXg31ZcXKx83d3dnZ+ff9ony//n6/777/fnYlVVVY2NjRH5ZHV3d3d0dPi4QG1tbW1tbSiuuqam5rnnnhN/IerfcWYbEGn6rAA1m81GozHg35acnKws7RwxYsTIkSP9HGft27fvtJfpM7wSe1splOudMWOGj125wprRaFRnbre/WbNmTZo0yWazaXJmYlaVIdL0f6EO5aWlrG3yeDy/+tWvTjszoBg/fvzVV19dWVk50MfSY8eOTZgwQflnUVHRF198MWnSpNdff/3qq6+WJCkjI0O8Z5hMpsjezqZ+dpX4anXvKC+iVExMTP9vdnd39x8gy7L8yCOPeDyeX//6134On0Xrb7755iNHjgw0b/jRRx9deOGFyj+vu+66pKQkSZI+/fRTq9Xa/4ZFzCO/Z8+e9vb2hQsX+pgqDd9D4fiJ2QZEPnHAlN/97nfeuySdcvatf1jdbndpaelDDz30+OOPD3bWwveK/ZMnT3755ZfKP0V2PR7PWWed1f/Cfs5yhIXLLrts2LBha9asefbZZ0958JqIzy7lRVQQB0y55ZZbHnnkEe8xb3/999bftWtXXl7eKRd1DlFGRsann37afyA8bdq0/oPuU+Y4vMiyvG/fPlmWjUajLMv333//uHHjfvnLX/7tb3+LtuxSXkSRcePGeTwepa0+xrxiUae42He/+90tW7bk5eXt2bNnz549GzZsCNbtGT9+fP+jrhw8eHDMmDF9vnnkyJGLLroo3LO7evVqWZZ/8YtfSJK0YMGC1157LTs7+7777psxY0a0ZZfyImKnF8Q0bp8J046ODn9mDIxGY0ZGhvj6qquuWrp06caNG7u7u48cOVJYWOjjB5Wrc7lcVqv1lltumThx4kAbxwwGQ3d3d1dXl/c3p0+f3n9eeNOmTVOmTAnr7K5cubKwsHDGjBknTpwQj/AXX3zhcDi872z0ZFdiT4rweJLYkyIYj+Hrr79uNBpnzpypqyStWbPm8ccf93GZkydPPvbYY/n5+eGbXY/H89577/3lL39JTk5WdhH2eDze74JRlV3GvIgKNpstKyvr008/1VV2pW+P9Op7xdgzzzzzwAMPhMtDLZYke2d3586dK1asmDVr1nXXXffZZ58pK/yiObuMeRnzQhejQh/rq3z/X/1oaGiw2WzXXnvt+++//9577z3wwANms3ndunUPP/yweI+RJGnPnj1vvfXW7bff7j3J4Ha7m5uboyq7Eut5AT2MfAP+vzrx5ptvTpkyRUybzJw5U5blZ555Jjs7WyyGE3fB4XBcdtllZ5xxRp/sHjt2LNqyy2wDgKFyOBwbN248cOCA97vFXXfdtWnTphkzZrz88svim62trUaj0Xslg8juEA+3yJgXQDSaOnXqn//859zcXMlrf1yDwXDOOeecf/75TU1Njz322GeffdZnnUk0Z1dinjc8niTmeaF7sizn5uYuXbpUiW9tbe33vve9Uy7ji/LsMtugqvXr1xcVFXl/x26322y2oqKi9evXn3I3ytNatWqVsv+V9y9fv369zWZ77LHHfve73/HIQ42PzwZDaWnpli1b9uzZI76zfft2ssuYV2N2u33ChAlTpkxRHnC32/3000+vXbtWkqQdO3YMGzbslKf88z3mdTgc/bdO2O32uLg48f2tW7cmJiZqeEwmRNvId+PGjZdffnlKSkp7e/vUqVPJLmNeLWVnZ8fGxnp/Z+/evddff7342mw2B/AW6PF4Ro0a5XK5WltbvYfMb7zxhnLavrlz5x46dIjHH6qNfH/5y1/u3r27paWF7FJePers7ExOThZfWyyWvXv3DvY3NDQ0bN68Wfr2MIbKpzzJaymSyWT67LPPeLShphtuuMF7DQPZPcVbFA+BhkaMGKF87X2cFIfD0WdvK3EUgj4n+Jo6daoy1ZCfn19QUCBmFbyP+ipJ0vDhw6Pz4XW73R6Pp6mpSZKktLS0pqamzs7OjIyM48ePO51O3z+blJSUmJio/Eh7e3tXV1daWpr4gMKfru9hb/+8kl3KqyPKYbP7HJwwMzPTe/JhoHneESNGeO/8/oMf/ED8s66uLi8vT3xTluVoKK/H43G73XV1deIot11dXXFxcYmJiSaTSZk99y6mnwlQfkR8IcvykSNHnE6n0+kUV9Ta2pqRkWEymYZywqFoeAsku5RXLywWS11dnXhJ19TUxMfHD/Y3VFRUSF7Hx2ppaRGnIMvIyFBOofr+++8nJCRE3qMny/KBAwfa2trEP9PS0kwmU/9TOQR9NCceVSUimZmZIvqVlZXiGZwwYUJycjIhJruUV7/l/e1vf5uRkTF69Gi73R7AwagWLFhQVlbm8XhGjBhhs9k6OzvF9O7y5ct/+tOf/vGPf/R4PIWFhcqhZiNgYNvQ0CAOqygCp4fXs9FoNBqNyujY+y0hLi5u6tSp0VxhsjsQVpWp9UB/e9avJUuWeKfQ5XJ99dVXycnJZ5xxho+f9fE0id9gNBrF51/l9X/kyJHPP/98ypQpYbHjvw9Op7Otra2zs9NisaSmpobR3fGu8IQJE8LrxpNdyku1o+5pkmW5vr6+tbU1KSkpMoaNHo+npqYmLi6uq6tr9uzZET8QJruUl/KGWXDF15H6Od37TSU9PT0iR8Fut3vv3r0D7RkEykt59TWlEFUTo94JjqTDJLrd7m3btimra0B5Ka9OP4N3dnZmZWUpZyuINh6Pp7KyUpKkBQsWhPu7DtmlvJRX11wuV1NTU1xcXKR+4g6Aw+FobW21WCxhOj1Kdikv5dV7XzIyMtgZbKB+7dq1K+ymIMgu5aW8eqRMa0bAZ2p1piBqamokSZo3b57+PxOQXcpLefXY3J07d0qSFA2rqUL00Om5v2SX8lJenc4tMM6N1P6SXcpLeWluhPe3oqJCV/O/ZJfyUl4dcblcdXV10bxQLHQ8Hk9ZWVlOTo7m2yfJLuWlvDrqQmVlZfiuiwqj97aqqqrly5dr9XmC7FJeyquj6YWuri72GVWN3W6XJEn9B5zsUl7KqwvipajhECxqybJcWlqq5uQD2aW8lFcXr/ydO3cqpzqGVpMPTU1NKqx8ILuUl/LqZaibm5vL7r86eQtMS0sL3eCX7FJeyqs9u93OUFdvxDniFi1aFPT3QrJLeSmvxsTCJmZ1dTv4raioCO6SPrJLeSmv9qOqtrY2FjDoXBDXmZBdykt5NWaz2TjGWLgIyiw82aW8lFfjz7CFhYX33nsvMwzRM/NAdikv5dXyaeIVGNbsdvuECRMGu1chTzrlpbxaPk0Oh0OSJNYwhLXBzs6T3VD7Dg8BfLDZbImJiWQ33FkslunTp5eUlJBdxrzQ9ZhXrMyfPn06xxuLGGJXY9/b3MguY15o+RItLCycN28e2Y0kBoMhNze3oqLC4/GQXcoLPWZ3zZo17BMckfG1Wq1lZWVut5vsMtsAvcw2uN3uvXv3sqNExCspKVm8eLHymYbsMuaFZsTLj+xGg7y8vG3btomRL9llzAvNxry8/KKQ0+kcPnz47t27ed4Z80Kz0S4vv2iTkJDwzDPPLF68mIeC8oLsQr3n/cknn1SmHUB5oRJZlnft2kV2o/B5V95uved8oQ7mecPhSQrZPK9YWk92ozC7O3fu7LMptaSkhGMuM+aFGi+/wsLC3NzcKHi+XmoAACAASURBVH8cPB6Py+UaaOeCKMmuGPnW1NTIssxLgzFvlHI4HDNnzuz//YSEhKNHjwbrWmw2WyhOG6O3yhw5cqS9vV2SpK6urri4uFGjRjmdzqSkpMTExIF+6vjx406n02KxtLW1ie/ExcUlJiaOHz8+3B+ugbLr/WbMTjSUF6GabYjUj5ayLB84cODLL7/s6uqSJGnChAkJCQlB2Qfa7XY3NzdLktTa2hofH5+WlhZ2IfadXeUyFRUVVquV1x3lpbxBfpocDkdKSkrEHJNB1FaMT+Pi4qZOnarCO4rH42loaFD6npqaqvMK+5Nd5a5VVlYSX8pLeYP5NLlcrvb29gg48KPH46mpqYmLi5MkSZ3anvaWdHV1zZ49W4efJPzPboT9kVBe6KK8EXBYBlmW6+vrxaRtenq6rkaa4ra1trYmJSXp57YNNrsR+cGI8kKz8ob7GjKXy1VXVxcfHz9v3jz9f7QXbw9paWnanjA0sOwKJSUlQzyBJigv5Q3jxQziHOaaVyywDxm7du3Sagg8lOwq8WW5N+WlvEOKV9h9eBTh6OzsXLBgQVgvwxATwZIkqTlaH3p2lVvO4esoL+UNcOQVXtO7ohoqpyqS7lRQsis4nc7Y2Niw+7RBeaFxecNuhabD4di/f3+kzjCq0N8gZleIhp1uKC+CXN4wetm4XK6qqqpoOHqAeDtMSkoK+sqtoGdXYMKX8lLeCPyo6PF4ysrKcnJyoupTrdj+lpWVFaz59xBlV+I0UcHGEXMifGDldDr13zK73V5TU5OXlxdtk4kmk8lqtTY3N9vt9qA83aWlpSGKo3hviJ7jCjHmReBjXv2vxxRDXe9TMUbte2RFRcVQBr/qHOzGZrOxVzHlpby+uFwuSZL0PIoUq3T5ADv0B0S1Y4yxyIzZBpzmpVhXV6fb7MqybLPZUlJSeA17y8zMnD17dklJyaA+1Kt5aEex5ZM5B8a8jHkH/FSo2/UMYrMSq5R8P30ZGRn+vHFqckRd1jlQXsp76rQ1Nzfr80BTTqezra2Noa4/Mw9iFKy37EqS5HK5jh8/brFYeJqYbcD/2bVrlz6zK2pCdv2ceUhJSSkpKdFbdiVJMpvNTqeT54jy4t/qlpWVpcMbVlJSkpKSwkDJfyaTKTc3d/369f3Pjab5aXsWLVoUlJVwlBeRQJbl1tZWva3QEtvTcnNzOdjrYBkMhjVr1pSWlnrHVw9nSxNXzekyA8Y8bzg8SX7P89rtdr0dYoaTKgaF3W6fPn26yWTS1ePJ8l7GvPjfAQjZjUjZ2dnbtm07evSorh7PpKQkVpgx5o32Ma/eVpKR3aA/ngsWLNi8efO4ceP0c6tYYcaYN6p5PJ6kpCSyG8HZLSwsrKysfOWVV3Q1u5qTkyP2lgTljUaVlZW6WklGdkP0NpaXl7dz5079xNdsNtfV1fEcUd7oHfDq5/bY7XayG7pPD/PmzSssLNRPfDMyMhj2Ul4GvBqz2WzTp08nuyHKrvTtUrOKigqGvZQXWr444+PjdXJjxH4crNsNXXaV+GZlZdlsNp3cVIvF4na7ecoobxTZuXPnvHnz9HBLxGuP7IY6u4LJZMrIyBA7ZOuhvLt27eJZo7xR9PqU9LGGV5blbdu26fN4EZGXXeVjvvKGpznW9lJeBrwaKCwsZF2nmtkVMjMzd+3apYetbZmZmTU1NTx9lDcqdHZ26mHAa7fb7733Xp4OlbMrLFq0SD9b2ziSg5/Yhy0cnqQB9mFzuVxGo1HzeVWO1qphdnX1FHg8noaGBmacGPNGuLq6Os2zK047RHY1zK4kSWazua2tTfPxptFo7Orq4qmkvGHwYnO5XIcOHQrg77XP3hMej6fPanaXy9XU1BTqu1BRUbFo0SKeSg2zK2RnZ+thziEtLY29Kiivrnk8nqVLl5pMpsTExIKCgh07dgzqx2tqapSPdW63e8OGDRMnTlRexuLYfSdPnlyxYkXohkIul8tisbDThObZFbKysjQ/VQR7VVBevXO73Tk5OUaj8YwzzrjnnnsOHz48qB/v7OxUXre7du0qKChQ/ldpaemDDz5oNpu///3v33333aHb4lxVVcU8g06yK0mSyWRyOp2azznoZ78ePWO0ohmTyVRfXy8Gp/v27Rs1apT/P/vmm2+ef/75Lperrq5u586dv/rVr8T3xU5NW7duPfvss8Xw5+uvv37nnXc+/fRT5WctFktsbGxTU1NnZ2dGRoYyVBns7bfb7cuXL+d51El2BbHOQdujlc+ePdvhcLCdjfLq1IgRI0aNGvXII4+MHDnyzTfffPbZZ085Lj527JgkSU6n0+l0WiwWp9N5wQUXzJ0799lnn505c2Z7e/u6deuUboqX3Oeff+792uvo6Oj/UlR+xOPxuN1uEXGLxdLW1jZhwgRxXQkJCQNtwRNr5o1GY7iH78iRI33eDlW7U6E4kKbBYEhKSnK73RpuejUaja2trZSX8upUXV3djBkzrrnmGkmSfv7zn69ZsyY/P//w4cNtbW1NTU3333+/94WnTJkiSVJCQsLRo0ftdvu4ceMWL17sdru7urr6/4l//vnn3v88ceKE79eJaI1osZg9sFgsokrNzc2SJIkNgBMmTEhOThYXrqysDLvTwIh3F7FZsrW1VYz9+7/Vud1ucTHlXqempgZ9Ljt0xy/OzMzU/CQ9SUlJsiyzAcAH1vNqpra29qKLLvJ4POKDf01NTV5enpK2f3uS/n09b3p6ekxMzDvvvGO329PS0sQ3xea17u5uo9FotVq3bNki/u7dbndNTc1NN90UrBFiU1NTWVlZWlra8uXLx48fr/NXl8fjUaa5xXnMAvgNDQ0NosKzZ88Oyog41IeNF6sLAphBCuL7Sn19PcNexrz6+oR74MCBtra2999///3337/xxhuzs7MlSWpoaPBna5XH42lra9u8ebMkSeIH+wxgJUm69dZblb/7xsbGMWPGBOuTrNlsPn78+BtvvLFs2TIxTx3SgeFQOByOrq6uuLi4IZ4S1Gg0KgVxOp1tbW1xcXHp6ekB/04VztZhNpu1PUkPo13GvHrhdrubm5u9h04ej+e+++678sor09LSnn/++ZycnFmzZp36SfIa85aVld1xxx1ibNvnMpIkKRdbv379BRdc8Mknn3zzzTcPPPBAEO9ISkrKmWee+d577/UfGLa2tsbHxwc2tAziG9vOnTs7OzsXLFgQohnbIV5FSUlJbm5uqNuk+e5kOjwNNuWNImLLWHx8fFpaWsCf/rzLe/XVV3/22WfvvPOO92ts5MiRkiQtWbIk1Ads3bNnzw033OD7QOxiOlWSJIvFouaaMxFESZJUe8E7HI7W1tZBnXVUzR5pO+xlT2LKq01w29rapEDnFgcqryzLw4cP37Bhw3333afJ/brggguGDx9+4MAB/197XV1dEyZMCHWCxTuc+qdeVnLff+ZH82Gg5gdz0HxDn671Ing6OjrKy8vLy8s7OjqC+GuVp6m2ttZkMgX3l/uvsbFRkqSXX355sD/Y3d1dW1tbXl7e0tIS9FvV09MT9Ac8gDtYXFzc3d3t4zLV1dU9PT0q37Dy8nINH5bq6mqaMBDGvMH5YFVTUyN2TAjFBmVlzLtmzZqXXnrp448/1uRu/uxnP9u9e3dTU1PAoza3271r1674+PhgLRIQny38GW+qM/kgSdIpP19rNemp7dHsdHIsPca8EaixsbG8vLy2tjakwxnlabrkkkvy8/O1Gtadc845RUVFQfltYgjc2Ng4xCHVEH9DKD70FBcX62G0y7BX5yhvgJ9wq6urVfuQK8rb2dkZGxtbW1uryV1+8sknJUny/YE6gJqXl5cHECY9zDD4uG0FBQXKPdI2u5rfAMpLeTWOxdDLu2PHjokTJ2r1Kpo2bdodd9wR0rcxP7PeJ216jq/m2VUeXspLecOV2HqmyZBTlPehhx666qqrNLnvYttaTU1NSK/Fn61w+s+ucjtvvfXWEydO6OHGaDjh0NHREYrNqpQ3KrS0tAx9UnLo5Z04caJWk7wPPvhgcnKymo/2QC/X4uJi/WdXjPVOnDihkzeJlpYWDWdmGPaeEsfnPc3GWbFvgtVq1fZAtLIsf/PNN1lZWZpc+7Zt226//XZ1rstsNotFoDabrc/ZDdTZ+2voxEqGM844Y82aNXo4T4TZbN67dy8vZ12hvAMuFCspKRHN1fDII4oDBw588cUXU6dOVf+qq6urDx8+vGLFCpVjofTX7XaLNVuLFy8Ol+yK22kwGLKyskK9YyEob4Q012azNTQ05OXl6aG5whtvvDF8+HBNjof78ssvz507V5NVmaK/zc3NN998s8fj0f/K0P7rdk0mk8Vi0fzUZNOnTxdvYOpLS0sTR3MG5R3wE73dbq+pqbFarXrb37yhoeG6667T5KorKyvnzp2r4X0/fPhwVVXVe++9Z7fbNT/VzaCyK1gslrq6Om1vuclk0mrCYfz48YM90xXljSJOp7OiomLevHk62SGq/6s6NTVV/et1uVxnn322ho/J0aNHV69efdttt91///3z5s2rqKgQu4qFS3aFRYsWlZaWansLlRP3qcxgMIhjmIDynmJ6ISEhwWq16nYa8Ztvvpk/f7761/unP/3p8OHDGm5dXLZs2b/+9a/i4mLxGrZarSkpKTabTVcfYG02m++dgw0GQ05OjrZzDhaLhU/9lFd30ws6n0M8++yzExIS1L/el19+eeHChRoOJB0Ox5///Oc+M6dWq7WmpkYnkw8lJSVZWVmnfc82m81VVVUa3s7U1NSGhgZNrjouLo7U9hXNq3TDZXGoVs9UT0+PJElPPPGEVjsjJCcnX3fddT4uEKLjn/mvuLjY/6Wy4pht2q4y1uR6tb3XrOfV0VDXZrMdP348Ly8vXI6Zn5KSov6VHjhwIDY2dsGCBZrc5aeeeurTTz996qmnfHyEV1aeaTL4LSkpWbx4sf+flsRJeaPwFZeYmKj56g5mGzTmcrlKS0sXLVqk7Z4Rg5WRkaH+lTqdzjPOOGPSpEmavDs+/vjjV1111WkX9pnNZrH9SuXX9mCzKyxYsEDDLYRpaWmarC0bP348qY3q8obdUFdx8cUXq3+l5eXlP/jBDzS5v6+99tp3vvOdDRs2+HNhg8GQl5d3/Phx1Qa/gWVX82Hv+PHjm5ub1b9eg8EgThCFqCuv2+0uKSkJu6GuYuzYsepf6bvvvjtv3jxN7m9BQcGll146qD1ZLBbLokWLKioqQj2sCzi7yscXrT56GwwGcQ5W9YXp647yDonD4Whubg7Hoa54z5Ak6YorrlD5ej0eT0dHx4gRIzS5y83NzQ8//HAAZRH7vNntdn1mV0yPNDU1RVtonE4ntY2i8oqNaSkpKeF7DlSt1mC63e6xY8dqcoyeF198ceTIkbNmzQrsxzMzM6dPn15SUhL0mYehZ1eIwlVWSUlJ1DZayut2uysqKhYtWhTWZ4ISwzf1t1HU1dX9z//8jyZHrti0adNtt902lN9gMplyc3NLS0uDOPMQrOxKkjR16lSttrNpFf3oXNQRjeV1OBx79+7V825pfvrud78rPkerfL0HDx78n//5H03eLw8dOnTttdcO8feIzW7Nzc1BaVwQsytpup1NqwVemizOobxqs9lsiYmJ+jwCw2CdddZZmlzvO++8M336dPWvd+/evePHj09PTw/Kb8vMzExMTBzicRqDm10hPj5ek6dVwwVe7LscyeUVE7tZWVn6OcDj0Meemlzv8OHDx4wZo/71Pvvss2PHjg3iGN9sNi9YsCDgad9QZFfSbmmthgu8tDpMJeVV4001AiZ2+/jb3/6myfVu37798ssvV/96m5ubg77XnNFozM3NDWDBWYiyK2l6nghNNnaxM0XEltftdpeVlUXAxG4fynEbVDZ27NhRo0ap/yR+/PHHoZgTFAvOtm3b5n98Q5fdKGQwGI4fP87jEGnldTqdYsUuz2iwPj2ceeaZ6q9+b29vHzFixJQpU0L0+8U2N3/WlqqQ3WhbZsCS3kgrr8Ph+PLLL8N3xa5vmoy5Dh8+7HK51N+N4p133jl58mRI73JmZuaXX37pe8GDOqNdrXYnY5mBLj4ERMBoNzExMWK2p/WnyRa22NhYSZKGDRum8vWOGjVq8uTJob6WzMxMt9ttt9tPufplsNl1OBytra3PP//8smXLZFn2f75LnKBMObeeLMtHjhxR+S9ZluX6+vrW1tYvv/zyzjvvVG2mzu1279q16+uvvz7vvPM0OeS/9sL6GJeDOjpqmNLkaWppaUlOTlb/0Lc33XTT3Llz1bmujo6O4uLiYP1Fiefogw8+WLdunZ8HfW5paVEe4e7u7urqanWe6MbGRuUAx8ohqjs7OxcuXNjd3R266y0vL1dugHIbbDbb7t27OT5vOImSDSAjR47U5Ho1Oc/xV199pdr6ZZPJtHjx4pKSkiD+RaWlpc2dO3f79u3+XNh7eHv48GHVlp8r861Hjhz56KOPxDg3Li7ummuuCenCL2WzwebNm5VvXn755ZocG4R5XrKrx3le8fpU/6q/+eYbNac4vOMbrL+ozMzMd955J+AqqclsNhcWFirTDnV1dSF9xsUUliRJhYWFyv195plnvv76ax8/ZbPZYmJixo0bZ7PZ9uzZ87vf/a7/umzlMna7fc+ePQUFBV1dXTabraGhYfXq1TpdR8wkg85NmDBB/afpv/7rvzT527jmmmt++MMfqnylHR0d11577RD/orwfrkcffVR8sWTJkv6vOO9T4/SZz1HnMVc+9Stefvnl3NzcgwcPhnoKq8+5kQ4ePPjII4+cOHHC/4e3pqZmoHMaKZdpbGwsKSlRruX1119ntoHRrr8bbWK+Jc6YLb4eN26cOjdAqyNLffPNN+ovIt62bdu6desWLlwYrGObffbZZ8pYrP9LTleLcNxud2lpaXJy8tNPP63yyUeMRuOkSZNWr169du1a/3/q/PPPP+3p62NjYy+99FLlWjSZN4u02YYomWTIzMw85Ra2o0ePqnYbvv/976u/o/13vvMd5TOpmn9R3/ve90pLSy+55JKhfzL1eDznnHOO+Npqtcb0o+HZgPqQZXnv3r25ubnf//73lRuvwvXabDZlrtlgMCQmJjLPq2s2m419ilTT09Oj/gTZd7/73ZMnT2ryRj558uQnnnjiggsuGOKhvJ544onFixf7M+bV6ggyysF6WltbR48ercycHj16NKQ7WSjHgz948GBqaqpS/y+++CLgd47BfkzRz1F7wqa8TqczKysrCrOr1UGtNNnjaM6cOX/961+1+vx09dVXP/jggxMnThzUsNTtdrtcLnH0xYKCgptuusnPNbn939jmzp2rwh1PS0sTX5x11lmXX375LbfcsnHjxtra2srKypCe4lqZJVizZk1FRYXT6Tx06NBvfvObu++++7Q/q0x/GY1G5ev6+vr6+vpTXubcc89Vvq987fF4ysrK9PLCDoutTLW1tcoCwGgjPgmqfKXiMD0ffvihyte7ceNGde6sj4204tDABQUFqq2r7e3tTUhIEK/HJUuWqLBYW5O/5P5b9vz8KfHIlJeXe3890GUaGxuVr1taWlR7VAe9SVb/6WlpafHeHBxtfvjDH0pa7EkhSdIHH3yg8vXu2LFDkqRQL1zxvTamp6dn2rRp4uXq5z4RgRloG70K45gwKi97UmjD7Xa3t7dH6jEZ/KHhMf0CnoAL2CWXXJKcnHzs2DE1Jxn6MBgMdrt99OjRW7duveqqq0I32R1tR8zRat6MLWyBzKBv27YtmrOrSf5EfcaPH6/+S9RsNg8fPjx0U8x+ro0xmUz79u2TJGn37t1TpkwJ0elzou2IOcr8MnRdXlmWCwsLOfCjVvtWqr+uVrBYLCE6Z/ugliSazWZxIIVjx44NdpubPzwej9hHRn2anJOCE1KETXkrKirWrFnDMxTwyc+H6Nxzz1U2XKhc3lCMeQNYkpidnZ2fny++njlz5vr164N4exoaGpSVVSrTZP6Kk7CFR3ntdntWVlaEnV0i4A/+mlzvxRdf/K9//Uv9673++uuDvpQ44CWJ69atU9758vPzs7KygrWfW1dXlybPrNvt1mrPhQg+lGuElNfpdE6YMIE9JgTfxxMJnZkzZ2qyKSY1NTUmJsbPw335+eeUkJAQ8J/Tm2++qaxy3b1792WXXRaUdwWtNq95PB5NTonW3t7Oa1nX5fV4PE6nU5NDN+nTZZddJmkxTWaxWEaMGKH+9RoMhpkzZwZrxfsQsytuT21t7ejRo8U/Gxsbp0yZMsT5EKfTOXXqVE3+nOrq6jQZa2u1OZHy+kWWZXEWS54YhRihqD9NlpCQ8M0334R0gddAli5d2tHRMfToDz27gslkEguNhWPHjr3yyitDvGFaHcZFqzGNVmN8yuuXioqK3NxcnpX+5VX2eVeNyWQ6cOCAJod3SU9PHzly5COPPKKH7AqZmZlbtmwRXycnJzscjoAnfGVZ1nBlqzj0HWNeyvtvL5WMjAy2qvX/tCt57fOupszMzP3792tyl6+88so333wz4LoFN7vCbbfdtmrVKovFcvjw4d27d1911VWB3bydO3fOmzcv2v6MGfPqtLwej6etrY2tnwPx/rSrmkWLFr333nua3N9169a53e6tW7fqJLvC448//sgjjzzzzDOSJAUc387OTq2GF263m90ZKO+/KSsrU+08VOFIkw+Jl112mcfj0WQlptFonD9//sqVK7u7u3WSXTEYv+aaa77++usXXnghsPg6HI4FCxZo9Ve0d+9eTQY3Gi5lo7y+2O325cuX82T48OGHH6p/pVOnTv3mm28OHz6syV3+f//v//X09Pzxj3/USXYVy5cvP/fcc6uqqs4+++zBxre1tVWfp0gI9SdaFonqrrxiE3YU/jkOyj//+U/1F3gZjcbY2FjvQ6CqKTU1ddmyZUVFRX4OutXJrnhY4uLiZsyYsWXLlkHF1263azjg1VBTUxMvcN2Vd9u2bcwz+EOTBV6XXXaZJlPMwqOPPhofH/+rX/1KP9kVMjMzd+3adfXVV/sfX/F/NQwQk7z6ou1BKqurq0N6CNTIIAaAmhzetLa2dvLkyd3d3Vrd902bNkmStH//ft+HGFf/XNQ9PT3iALti2kGSpLlz5/r4Yy4uLtb2T12rwwFreERgjs/ra56BZWT+uPTSS//7v/9b/etNT0+PiYmpqanR6o6vWLHiiiuu+OEPfzjQnIPKo12FwWCYMGGC2+32Z+TrdDpzcnK0/VPXZGGiwGJefc02MM/gv+Tk5EOHDql/vQaDYcqUKc8++6yG9/2VV14xmUw/+clP9JNdwWKxbNu2TZIk3/GVZdnpdGq7YlKWZU0OUSZJksvlYpZDR7MN1dXVGn6GDbvZhpdeekmrJ+vZZ58dPXq0tp+UxfEqn3jiiT6fYdWfZOiju7tb+RRfVVV1/vnn9592KC4u1vxPqLa2VqtnUMNZDmYb+hKfHNnc6T+x11OITo7g2+LFi7/44ovXXntNw7tvtVrz8/MLCwuVvZnFF5qvVRJ/w+Lv+eqrr37xxReTk5O9R74lJSX+rJhsamryHimH4olmWo8xry5GAeE15hX/1eocgpmZmenp6Zo/DvPnzz/nnHN2795dW1urq4023n/PNTU1ycnJYuS7f/9+f0blyhHoxbBUfB3E0+V2d3dr+HAx5j31i1r9q2xpadHqvNNhXd65c+fecMMNWr14JEnSfHbo+PHjs2bNGj9+/NNPP62rJ6jPn7QS32nTpvn5Gb+7u1u5Uz09PcENpYYriHp6erxPbg8tZxuqqqo4PkMAcnJyXn31Va3mOpKSkl588UVtH4GRI0f++te/HjVq1IoVK4J46PShM5vNVVVVyj9nzZr1H//xH+edd967777r504WRqPx2LFj4pL19fXp6enBXdWg1VTDgQMHxJsQNF7b4HA42FE4MJMnT5Ykqbm5WZMVDj/60Y/+8Ic/aPsIOByOYcOGvffee7fccsudd95ps9n08+wsX75cOXGnw+GYOnXq1q1b+8z5+nbZZZcp56YMYihdLpdWJxuWJKmtrY3NOdqXV5bl6NxvPShmz54tfbvIQX2rVq06evSoJofr9d6klpmZaTAYXnrppdtvv/2ee+558MEHg3VitKBsapNluaSkJCUlJTMzc9asWWVlZf7H90c/+pH3drZgnYqprq5Ow4+YGi4iZgubLuabImCeV2zpWrx4sVY3Y+LEiVpNNJ9yk9qTTz4ZHx+fnp6uh80G3d3dixYtmjlzZp+/cO8Nbqf948/Pz6+pqREX27hxY7hvW+vu7maSV/stbMrelgi4vOXl5ampqVpt6RJTq+ovofWxkqGxsVGc36GoqEjDN/Xi4uJp06alpqY+9thj/Z+d2tpaP+O7ffv2yspKZbXD0JeyaDvW0XARMeX9P+Xl5TwNQyxvR0fHxIkTtRrF9PT0mEymBx54QCfZVW7VtddeK0nSlClT1B/8trS0XHLJJWPGjLn22mtFc0+ZSz/j293dXVNTI74e+phX87GOVosgWdvwfzweT1JSEmu5h8hkMo0ZM0ZZ/qn+dra8vLzy8nLVjpWuzO36vlWVlZW1tbVffvmlxWJZuXKlOjfP5XLdddddWVlZX3311e9///vKykox1ZuUlNT/BojTuJ12ztdoNM6aNUt8ffLkSVmWhzKLrflphzQ83RzzvLz7nWZUsmHDhr///e++P5d5P00PPfTQqFGjlH92dHTU1ta2tLRs2LChs7PTeyxWW1v7wgsvfPDBB8GduZMk6cEHH9TDaLe/ysrKpKSkMWPGLFy48MMPPwzRDTt48OA111wjSdJ55523ZcuW/k/cQH/t1dXV/s/5Pv3000OZK9B8wKvJAeSYbej7cuUwcad06623fvLJJyKUBQUF/pT39ddflySpvr5e/JTy6hIRV7J7zz33iK9zc3OD+wLIz8+XQr9XxVD2UqupugEoGQAAIABJREFUqbn44otHjx596aWXFhcXB+vui0M0pKWljRkzZuLEiadsrnLjB3p8CgoK/I9v+M7wMtjSRXl5DgYaFDz33HPK1z5C0+ejyejRo1euXCleXd69fv3115WXt5KblpaWqqqq4L6PJicnr1q1Sp/ZVfz1r3+96aabxowZYzabp02b9uSTTwa2nb2lpaW8vDwnJ+e8886TJOnmm29+4403hvI3r0J89bA1m1e9bzG93+4nHroZ3oaGBt9TddGpurp68uTJH3744bBhw0aPHj1jxoyBLhkT829P08MPP1xRUaHsUiHL8pEjR55//vmkpCSxl4rValX2MpBl+Te/+c26deuCeMv/8Ic/5ObmHjx4cNKkSZrM7Q7qz++tt97asmVLfX39xx9/LCbKp0+fbrFYLrzwQovFcuLEiTPPPFNc+Ouvv/7Xv/7ldDpPnjxps9mOHz/e1NTU3d0dGxu7cOHCH/3oR9ddd52fq9HFzhQDXXj9+vVFRUWff/753LlzX3vttaBv/7Db7fPmzdNws4rL5TIajZx7Tct5XtbwDuTtt98uKCgQD85vf/tbZfx72jGv2J7uPSpsaWmpqanZvXv3KYcbQVkZ2mdIde65506ZMkWfo92BbvO+ffvKy8tXrFgxZ84cSZJGjhw5bty4tLQ0k8k0btw48XJISUmZOHHiRRdddO211/7kJz955JFHGhsbA/sD9j3qLCgo8OdMFmE6uceAV+PZBtbw+vDcc895f/79+c9/7j0Rccq3yYSEBHGByy+/fMWKFX1+4bp168T0Yp/DXCnzv8FN5AUXXBDcF5j6RyBraWnZt2+fON7NBx988I9//COIc+KnHXOEKL56qB6veo3Ly1JqH6qqqrxf5/n5+X6OeXt7e0tKSi688ML9+/d7H5/w7bffFgtaQzrPq7j++utHjx4drE1tejvwozrDjqDHt7GxUfM9+nxsYIQitOt5W1tbWcM7kIsvvvg///M/xddvvvlmQkKC/z+7bNmyjz76aP/+/eJgDsKf/vSn8ePHS5K0dOlScZYaSZJ+//vf+5hBHoqysjKDwZCbm6u3uV2dMBgMpz1qwdq1a1euXClOI7R06dIhXqMeTjskSVJXVxfHZjmtEG5h872RAZIkNTQ0bN68+cILLxw1apSPQ7j12cImzJw58+TJk2VlZU6nU/yqu+++W9nkZbfbOzs7P/nkkxkzZiiL84POZrPdc889b731lsViIbsBb15WNrgVFBSsXbt2KE/HokWLtB3rsEVd+y1szLIHbUroVE9TbW3thRdeqPli9YyMjPj4+IA/KUfeJENgM54FBQXnnnvu2Wef7WNZ92nnrPVweBq2qGs82+DxeIYyDsJppaenjxw5Upmv0Mpf/vKXhISEVatWMdo9JXFm+NNebO3atb/4xS8+//zzoqKi9evXBzDPUFdXp4dXnIZHYWfMy8ZNNca8vb29995771DGm8Hy6KOPnnfeeS+//DKj3SF++CsoKJAkKYCRr04OR8W2Nb1sYUNI/eQnP+ns7PzLX/6i7c144IEHMjMzf/Ob3/gzuIue0a4iPj7ezwPfrF27tqCgYLAjX4fDkZWVpYeRJuc90HjMy1ufOmPe3t7ehQsXZmZm6mEFVXx8/OWXX+7PyCt6RrvCYHdtGNTIVxwySSd3k+OgazzmZVmJalauXPnJJ59oeJIewWAw7Nmzx+Vy3XPPPYx2+zAajV1dXf5f3v+RryzLu3bt0smDWVlZyaYd/wW/vB6PJy4ujkdWHeJVd+edd2p+SywWy1133fXKK6/4WBcVhdkV4uLiBnXUYCW+Gzdu9BHf0tLSRYsW6eEOigNw83rUcraB/dbUnG3o7e2tqamRJEkP5yLr7e29+eabTSbTKT//Rtskw9C3OYtph+Tk5FNOOxQXF+tnTo8lpNrPNnR1dbGsRE0ZGRkTJ058+OGH9XBjXnzxxcmTJ8+fP1/s38FoVxHAWXjFyPfw4cMvvPBCn5Gvw+FYvHixTub0PB4Pp5/QeMzLLLv6Y97eb0+YePDgQT3c2p6enjlz5pxzzjnKMDzKR7tCwOdo6D/yra2t1dWrjL0nAhDkvYcdDgc7DgbdKfce7uOiiy7q6ek5fPiwHm6w2+3Oyclxu9319fXiOML8VUiSZLPZrFZrAD+4fv36/Pz85OTk22+//corr9TV4+nxeGpqarKzs3l+tdzCNqhtuAii5557btiwYZovchBMJlNVVVVXV9fFF1/c2dlJdodImXZ49tlny8rKdPV4VlZWkl2Ny+vxeCZMmMBjqonMzMyEhAQ9LHJQ4utwOIYNG7Z06VL/97CIbBaLJeCHYu3atatXr/7444/feuutAHYvDt2AlyUN2pe3pqaGBX0aev755//xj39UVVXpZMKhp6ensbFx9OjRc+bMOXr0KE+QxWJRzuE0WA6H49prrxUj3/Ly8uCe3mkoA14+0OhitgEamjRp0pIlS9auXevnvqohze6xY8csFovJZNqxY8exY8dmzpzZZ7VDdApsOk5ZGSKmHZqbm1988UXN4+tyuRhpaV9eWZbDZQeK9evX22w2m81mMplsNtvKlSuH8tt+/etfx3zL98dAl8sVExNjNpsD28zijz/+8Y/79+/X9tOokl3xz9TU1GPHjiUmJv7gBz/QyTS0huLi4gb7vuhwOEaNGqUMLZU5X83jW1VVRXkDF4XHalBWfYu73+esZaFeIR/Awz6oyxcVFY0dO1arHSs6OjpOueCpp6fn5ptvliTJx4k+o0FPT8+gFtgVFxefci2astTMx0mkQopjs+hlT4owOlZDnzfqnJycSHor/dnPfhYbG3vHHXdoPtr1ZjAYtm7dumrVqjvuuOPuu+/WfD5EKwaDwc8JB1mWS0pKli9ffspzp2s78pVlmWOz6GXMG44H5B363e/o6CgoKKiurt6+fXtubu7f//53P8e8jY2Nq1atUs7THtzb+fTTT0uSpPIOnQONdvuPlUaOHKmHs2noeTfijo4Ofw65q9XIVyeHAw7v3aOiedc1H0UTe4X10X9eoru72/tP0PvM7f7MNjz66KMheoeYPXt2YmKiap8H/cyucuFLL71UkqQXXnghCl9yLS0tvt91qqur/Z+RUD++OjntEOX934FMOL4Hehetu7t748aNTz755FBy8Oijj552KOdd3o0bN4aovC0tLZIkXXPNNXrLrjLdKQ6ydf3110fhdOFAw96enp6BJnZPG9/Ro0evXr1anQEv3dRLecP03D99iiaa+PTTTzc2Nvo55u3o6CguLlb+abPZTrtpS53y9vb2FhUVmc3mUA9PAsiu95/NqFGjRo8eHW1jqFO+XlpaWgI+AIJyMPVQx5dDNAQL63n7uvHGG+12u9Vq7f9g2Ww2cRmn0yl2RjrrrLPOPvtsZfvS/v37zWazfja1xcTEzJkzJ3Sbs3xsUvNHdnb2wYMHp0yZMmXKlNtvv31QR7CNJLIs2+128YAEdpw/5Xi+mzdvfuCBB0L3dIuNhFRCF1vYwnGSd8mSJeLuew9RxXe6u7tPO2Xmfdypjo6O6urqgwcPbtiwwfdwQMwASJKUkZGhXF1CQkKIxrziGk0m0/3336+30W6fj9gPPfSQJElmszlKPsl6T/XW1tYGa4NVqEe+3h/voP1sQ2NjY2R8ABEptNlsejuk4VDeIDds2CBJUn19vT6z6/0Lb7rppjFjxkyePPndd9+N+BdebW2tWMAQ3DUeoYsv6xl0V97IOMF7ULaw6bC8vb29s2bNuvjii4O4ISvo2VXs378/JSUlPj7++uuv18lZNkLxl/bQQw/l5OSE6A1efJ4LbnxZz6DH8nLQa52Xt6OjIzEx8YorrtB5doUTJ048//zzZ5999pgxYxYuXBhJ/e3u7r7vvvtiY2MnT5788MMPh+haenp65s6dK+K7atWqoPxC1jMw5o1k3d3dYnBRXl7e2NjY8i0xHy22fZeXl4uvB/vuOHr06C1btgw9u+pM9vX09GzZsiU5OdloNN5yyy3hPuBqaWlZunRpbGxsfHz8li1bBrsPccDxlSRp6PFlnkGP5e3o6IjUT4Xq9KW2tlasnBdJPeWcQP8xb0tLizjFTnl5eXV1tT9PgdifeN++ffrPrvfjU1JSIsa/KSkpYbekqaenZ/v27RdeeKHJZLrkkks2bdqk3P5Qv3CCFd/q6uqo3dtQ1+VlqiGwhFVXV4vg+pOS0842iF8oWjzQLzxx4kR6evpFF10U2AtJ/ez2+TMTa9eSk5NXrlyp/yFwY2NjQUHB+eefL0lSSkrKKZ+XUH9YHHp8Gxsbmd6lvJEwmSCGqINtn//zvGIQPdAZJzs6OkaPHp2enj7YkaO22VXU1NTcddddkiQlJiaec845BQUFOjnpp/dnkYKCgokTJ1544YWpqal5eXk+yqXCa2co8e3u7mYiUb/lZerdzxdkeXl5wK+0ALawKZXvE1lxkoi8vLywy26fd5eMjAxxrKy0tLT8/Hxth2aNjY3FxcUpKSljx46VJGnWrFn+TIyo07XA4iv2Y+aVy5g3XInNZUOc0Qt4bUNPT4/YKOddge3bt5955plFRUXhmF1v//znP6urq3/605+OHDkyNjZWHPDzueeea2lpUWE6WGzwvPXWWy+55JLU1NRLLrnkxhtv3Lx5s/+r91QbtQQQX7aqhdpQz/rOad59nIGirq4uIyNj6PsT+3PWd987p+7cuVOSpHnz5oldP3Nzc3fs2FFUVHTTTTf53lt027ZteXl5+n+0Gxoa7Ha73W53OBxms9nlct14441jxoy5/PLLr7jiCpPJNMSDyXo8HrfbXVdX989//vPVV1/t6OgQ3582bVpGRsaPf/zjAJ5lp9OZmpqqzs64sixfddVVu3fvliTpoosuWrNmzaJFi84444xTXlgcF5jD74bUkF7Sbrfb4/Ho50gF+tkNv7S0NCcnJ1iPzBDLq9yqior/3967xzV1pfv/C41HbUQQjBK5BagIOFHUqm3i3YIOMmqtDUK9lNdLO1EZe7RqX9qeVrD1eJuOCnbojK9yiiUOeDmFQqrkWE2bTcVbKWmxVTEbEcGkoyDZXppQfn+s3+xvJoGwd+6X5/1XCHtn77XWXp/9rGc961ll+E1gNBrnzp2rVqutbFrqRbJrVsw7d+6Ul5fX19erVKq2traQkBCSJBMTE8eMGdPe3p6YmDht2rTOzs7u7u6hQ4dGR0eHh4c/ePBg4MCBJEm2t7cjhG7cuBEcHPzVV18hhH766ac7d+6MHj36119/RQiNHDkyLi5uyZIlSUlJdravi7uP0WhMSUk5f/48Tmz2+uuv7969u8f3QVhYWI/p2AFPUV5XvrS9BbVarVarJRKJPdVCEMS0adMsvw8LC7NzE1+SJBsaGlJTUxFCc+bMaW1trampsexmXiq7vRX522+/ffLkSV1dnUaj6erqampqevz48a1bt4KDg2NiYjQajUAgqKuri4iI4PF4v/zyy8CBAzs6OqZMmfL06dMJEyaMHz9eIBDEx8c7XI9cPGRsbGycMGHC06dPBQJBVFSUQqGwvB+EEIxiPT1jDkyvWU5KOCNIEzlu65Dufy1J0mq1BoMhPDw8JCTELNbCk327TgKbwK7HxcEDjx8/jo6O5vP54eHhf/3rXy19+jBt4x1+XrVaDZuP0n7AoqIiqVTqjBGAQ7wNPVo38fHx06dPHzhwYG1tLfb6+ZK16xUjJBf3IIqi5HK5UChMSEgwG+Vcv34drF2X0c/O5wZqEI9ny8vLc3JyvMjxIhaL4+PjS0tLP//88/v378+dO9doNILsul55XXxFLpf7yiuvWMpuaWkpyK7X+HlJkoTpNRe4xpxh85qa6i+//LJQKBw7duzLL7+8YcMG6BWufGe7vQfB69b7bN6amhqQXeTNMxJcLlcqlf79738/f/781atXT5w44bf7sbsFt/cgkF2vVF4/d/LioaK3j9E4HM6aNWveeuut69evt7W1zZkzR6/XQ8dwDe7tQSC7Xqm8FEXhhUN+a+0GBgb6gGtMp9OdPHmyvLz85MmTCoVCp9NNnToV77gFOJvAwEB37T4Hsutmi8eelvPbWsNld4aHDq+Vamlp6ejoQAjhwH6EEEmSCKGWlhaEkAMDS027X3Z2dlFR0ddff52QkPD8889fuHABwuld8yy5frWYTqe7dOkSyK4bsX3qhiRJ+xdlemlXUSgUWVlZjvpBo9F47dq15ubm9vZ2nAjGTPJMZ9jwGq2amprg4GCE0OTJk23WR0urB4cWxcfHx8fH9+vXr6KiAua7nQp+0bp4kg2WS3i98vphYANeg+so2cV9oKOjY+bMmVbeYVZiG3B2iOjo6OTkZFZvwd4GmwRBhIeHc7ncjIyMc+fOnTlzBi94A5yEi/uRWq1++PAhyK77gQVsbEvtkBxOeDsJhnmt+mwmem8Lhpl/ra9Sw2U0GAy4fzpkLy/AE/qRw7c6BtyQJdIPlRfvjeZKzWW7ehj/uPV3Q5+Lg+ncrAaDIScnZ/DgwVKpFHIGerXy4iXjDtx/GnCb8vrb9mv278Cq1+vz8/NtePpZDU3wffa2AJ9hTgbTXb5LSkqGDx8+ffp06LfOwAX9SKvVQr5dUF4/9TPgFOk2NpJNe1Lk5+eb3TCrVDim5VWpVFFRUSEhIZBRxeuUF++HAvXsafQDTzfD+ajo6Gib0zLIZLLAwEAHhkP0CV6cVlhYSIeLso3flEgkOJ86nge/cOHCmDFj5s+fX1hYCM+DA+ns7HTej8vl8s7OTlc+eIDTZ9j8yua12WowGAy5ubl2DvTsaab8/HytVmtb4seqqipTDwN2+44YMWLp0qUwdPVwPy921oODCLwNXow9E2tMdkJ0qvJ2d3dXVlZu27bNUbpQVVUVFhYWGhrqb+4mL1Je8DD4srfBf9LlqNVq2yIuZTIZvfWZG/0kGo0mMzPTtjWH0dHRZstb09LS6uvrR40a9dxzz+3duxcy7HhavLlMJgMPg+cDft6+A91FIpENJxYUFKSkpLhddrFvVygUlpaW2iC+YrG4vLzc7Esej3fx4sWXX375rbfemjRpEl7ZDNiGA5Pm6HS6srIyiUQC+xWA8no9NTU1Nhi8BEFkZGS4N++B2ZRaTk5OaWmpDSZqcHCw5VmDBg36+OOP6+vrKYoSCoWHDh0C49c2HJV2Si6XX79+PSsrC/ZFBOX1eiiKio6OtkHyOjo6PEp2MVKptKysjO1Ppaam0kEOlvbaTz/9tG3btrfffnv06NFff/01PDNsaWhosH9YVlBQMHPmTFgT7BfKizO2+Dbl5eU2PM0KhSItLc3TZBchxOFwRCIRW+cAh8OhU6b1+N/t27crlcrg4OC0tLRly5a5K+2hl2KlbvuE9urm5OT4Ye4qP1XepKQk364anU7X1dWl0+nInuhtcC2XyxctWuTG2zYajVYSAAoEgsrKSra/mZKSYn3HsIkTJ3733Xd/+9vfzpw5w+fzZTIZOB+cDUEQ4NX1XsAl9P8cCzqdDuf9Qgg1NTVt27ZtypQp06dPR/+eihfnabxz505LS0tTU5NQKFSr1fislpaWIUOG2G994PSpCKHIyEi6mw0dOrS5udl6VjOj0VhdXW3d4s7OzpbL5aysch6Pp1Ao+uzhWVlZixYtysnJ+eMf//inP/3p448/Xrp0KTxaDockycrKyuzsbHAveDH+HM+r1+txiq+qqqr6+nrTsHOtVsvj8ZRKJasKQQht3LgR/6AN9aPX60tKSizPNW0mfMM9/rjBYKiqqnJSlDGr+NArV67g3JK/+93vIOzXgf0ILwqHKoWVFF4JTiBSUlJSX1/fmwDl5uYihFjJ05YtW/h8Pn2KVqutqqqykrzGDCypDFdSaDQa/LawQXbZHkwXx/RyDEsUGxs7YsSIV155BcTCzn6E38qQNwOUt9vrHgL87GLB7fPg8ePHZ2RksPrx0NDQoqKi3izrkpKS3vqYRqOxvtCzt6EJvVTJBiW1bTEx21MMBkNxcXFsbCxCaPny5Xfv3oUux7YfgeaC8to+/HS7WcHq2cWb7/Yoo1ZUic/nd3Z2sr0NlUrV541ZcQrp9fqDBw/aoIl6vZ6tDWvDVWj93bNnT0hICJ/PX7hwIdi/DPsRbStALYHyepnNi3Mzsu3q9fX1AoGA1VnJycnLli1jbnpjTysT2bWuvAaDoaKiwrbOyfYslUplTw4KnDh42LBhXC534cKF58+fh+7XWz/CDjGwc0F5e7bgPN/Ote0msZOX+fF3794dMmTI5cuXWcnQ4sWLt2/fzqiRerkZ2smAfco29HlWSmqDmdwjSqVSKBTy+fwxY8bs3bvXz/NpmT2ittkKgNfRz87oFs+MDysoKMBBTrZlurl79y4OJmPIuXPngoKCJk2axPyUL7/88uLFi5GRkQUFBbZVo2kAGV4vx3YJw9SpU2tra5kfz+Vym5ub7W+gGTNm1NfXV1RUzJkz5/333w8LC5NIJHgzUD+MD6MfWrlcLpfLY2NjbX5uAX+JKvPANzPD8bt1eDze5s2bmR8vkUhSU1NZGbwJCQnz58+na9Jy/wjrNm+PU2o2+BzYWsoOH//q9fri4uLRo0cjhEaOHPnWW285xKz2CrRa7YEDB44fPw6OBfA2eLHDAftP7R+6GgyGwMBAVioWERFRUFDA/Pji4mI+n2860Y99oL2Jjpny9hbJoNFo2O4sy1asbZ5k65PPPvsMr7sLDw8PDQ3Nzc31VQnGD+qzzz6LEBoxYsTNmzdBhkB5uz2kH7rF1KX1i8/nM3+p4AUUtbW1zC+RkpIyefLk3nzTlsavqfJaDyBjq6QajYbVu8rZphmedVy+fHlUVFRUVFRsbOyqVavsnNnzHH9uSUnJ5MmTIyIiEEIrVqxQqVQVFRWgQaC8tuid2wuArUW2tp4VCIKIi4tjrkf19fURERHMb0Cv1wcGBspkst6KYxnbSytvn3G7bBen6fV6VgMXG8xqm5v1/Pnza9euDQ4OxuHAM2bM+Oijj7zLQmxvb//kk0+WL18eHBwcGRmZmJi4efNm0xcJOBlAeb1SeXvcYddOSkpKIiIimB//wQcfsHKX/+1vf0MImWprSUkJj8czPQZvnmamvD3KLl6pXFJSIpVKKysrtVotVtL8/Pz8/Px9+/YdPnzYgQMX+vddbC3++c9/Hj9+/MiRIxFCcXFxL730kscGAODlhTk5OSEhIdh/HR8f/9577/XoPAHl9VvsypjT0dHh3lxirDbTZU5XVxfzgwUCATbKGPL48eOJEyfSWW9IkhQKhWa7ReTk5BAEcf36dTolSo+pcAiCiIyMxIlssrKy9u/fP2vWrEuXLrW0tMTGxuKDjx07plarrSS7oZPyMEyd4/okkAKBYNOmTZs2baIoqq6uTqFQVFRUvPvuu42NjaGhoePGjROJRElJSSKRKCIiwsV5welESzdv3rx169bFixfx9yNHjszOzp4wYUJqaqqVTM3u7UGAt+YqCwoKcqPstrW1OUN2nz592traykqmhwwZwvz406dPh4eH03paU1PT45ZZYrGYJElaNHft2rV9+3azY3D2MlpVsYIHBQWVlZXt2rULf/niiy/i+Nne7oftnghO3aW8z7A2sVgsFot37NhhNBrPnj3b3Nz85ZdffvTRR8OGDdPpdJ2dnXw+f8KECeHh4bNmzQoODk5KSurs7ExMTLRfkXEEGN5+sLKysq2tDb8vu7q6+vfvP2DAgKFDh65bt27mzJmxsbEM89Wxeu0BoLxufmNj2XVSWtKnT58uXLiQ+fFnz55lFX3522+/PXr0CH8uLCy08vIQCAQ6na6urg4htH37dkvtEAqFdCUUFRXduHFj3rx5WBrons/j8Rwbdm3dgnbdg8vhzJs3DyG0evVq/A5ramoqLS0dPHjw+fPnv//++4qKioEDB96+fRshFBER0dXV1draKhaLhwwZMnjw4F9//XXChAk4x/Tjx48fPHgwYMAA2jh9/PjxlStXtFptR0fH1atX79+/b2ptjBw5MiEhYdCgQX/84x9jY2OTkpJstrU9pDIBL1PepKQkiqJcnAwfZ6p13vM6dOhQVtsEcDgcWkmZ0L9/f2xmyuXy7Ozs3so4bdo0028GDBiAEAoLC7O0x0+cOHH+/PmNGzfiX4uOjjZVCvpcD7RhHSvEcXFxeFiwceNGekhx7dq1wMBAnEm5q6vru+++u3nz5m+//cbhcK5cuVJRUcHhcJqbm3/55Rd8SkRExOjRo7u6uvCWKzExMStXrrx///5vv/320ksvoX/P1GwnRqMRZBeU1xZ4PJ5Op3Ol8uLxnbOf159//pn5wXPmzPnrX//K/Phhw4b169ePJMlbt24lJSXRHl6SJOleLRaLu7u7jUYjdjIMGDBApVL1mAY7Ly/vzTffNE1A3tTUVFNTQ5vSFEVZV1623gYv2gWKw+HgR0UgEODaW7Fihefc3p07dxy1/SXgddi1epjL5dq/fx9zKIoqLS11dh7+p0+f3rt3j/nxzc3NKpWK+fGDBg1qbm4WCAQ5OTmCf2FpTNGySw9jLZ0GarV67dq19JsPb1wUHR0tEonozXtu3LgxZswYB9aPz+8C5TJaWlpglTAor424bJLNaDSWl5c7Y0rNjPDwcFbiEhoaGhISwvz4SZMm0WNbK4U1k12xWFxTU2MWVyCXyzUaTU5OTlFREUmS+/btwzZUdnb2f//3f1MU1dHRceDAgZkzZ1q5Fqt3J+yuBgCOwc6oNJctY3N43K6VeMzY2Fjm11KpVGPHjmV+vEajefbZZ+nozszMTNwQdHSqwWDIzc01/UG6mcwqgT4FJ7iqr6+n9zTC6diPHz/e542xWqTrmck6vBRIvAsrKTxdeauqqlyWS1Cj0YwdO5bV6mFWq427u7vj4+N3797d29otM9k1W8NmvbvasHqY7Ro2H1jI6yHAMgp/xl5vAw5vcPasWmRkpMuXILJLAAAgAElEQVTm8Xg83m+//cZ8xl8gEHC5XFZJDl955ZWysjLLkbulk8FyyiglJUUul/fmB8dbIDvP1VhTU+PipQq+itFoHDp0KNQD+Hlt16lbt2459QEtLS11ZfANl8v95z//iaNoGTJ8+HBWiW5Xr16t1+tPnTrFSnbpCke9pOJVKpVTp05lVdimpiZWx0MUlKO4c+cOq6WPACivuU45JFt2b5SVlUmlUhdXyvDhw6uqqpgf/8ILL1RWVjI/XiAQjB49eseOHbSAMpRdTFpaWlFRkaXBi41iViVlGyLm1Lb2KxoaGlwcCA/4lPIihFitO2AFSZIikcj1w9sXX3wRrwRjyPz58x8/fszK61JaWsrhcFasWGE0GlnJLiYjI8PM51BUVGSW1aFPdDrd5MmToQ8AgFcqr/NC6ysrK90S8Dh16tTm5mbmSjpnzpy2traPP/6Y1Vjhk08+USgUeXl5bGWX9jnQnuKCgoKMjAy2xVQoFFaSufT4IgSldhRuzHkC+IjyOmmSjSCI3hbXOpvo6Oi4uDjm6yM4HM7KlSvx5m/Mee6558rKyvbt23ft2jUbbjI1NbW6uhohpFarMzIyWGmoba/MhoYGG64CWEJRFEyvgfLaS0REBKv5KCbgBCjucoSJxeLGxsbPP/+c+Smvv/76w4cPz549y6qMly5dksvlFy5cWLBggVmiSCZyL5fLDx06FBgYaIMgEgRhfYWFldsmSTIgICAgIODixYuvvfYa8zsnSXLr1q1sLyeTyQiCaGxszMnJYVXDMplMLpfjix47dsxzel1dXV1iYiKoj1/jqHhbhwfwujdudMOGDUFBQaxOSUhIeO655xgebBq3+9VXX4WGhnK53CNHjvRYastm0mg0ixcvjoqKWrVqlc0rU1gdb5aXnX549Hq9VCpl0lh4oQfbR84sA/qWLVuYR8ua3vC2bds8J5bTc7bRArw1ntcZYPele+NG582b19HRwcoOPXLkyOXLl+mECdYLaOrbnT17dlNT0+zZs1evXh0bG7t///7erms0GgmCWLx4cVpa2q1btyorK9esWWODq4ckyfT0dFan1NbW9mgjc7nctLQ0JkF1pjktmSMSiUyHPs888wzDE+Pj402z3zJZ4a1SqSiKIknSSrCdSqXCVv9PP/1EjwBcmb0EAJv338wZB64xc7vBi025MWPG7Ny5k5VVmJCQsGTJEubWrqUlixNTjBo1KjExcdq0aStWrHjxxRcRQgsWLEhKSoqKinr22Wfnz59vWkU2LEK1/xTTh0ej0SiVSqaLJm195PR6/XvvvVdZWWnDosTly5dbv0O8jSlCCFesTCY7cOCA5Q2YHqNUKrds2YJXV165cmXjxo3MnxNYvQY4Rnkd+zB5yHr2uXPnzpo1i+160MjISCtjSSuya3qMUqk8dOjQSy+99Oqrry5YsAAhlJmZ+eqrr/7973+33ICS7YtKpVKxfU1abgFnqrz19fU//vijqX5ZebvboLwGg+Hw4cPr169vb2+3+flct24dq7eCpfJaHnP+/Pk+j3dI/QOgvE53XXnOc6lSqUaPHs0qoUx3d3dGRkZYWFiPRWAiuzbYiaxee31mfmDYKKaSWlJSwvwG2CovFn0bKs1gMJje88mTJ/vMUMFWeb/55hsblBecvIAj/byOWk/hxpAGM6ZOnTpw4MD8/HxWZ/3lL395+vTpkiVLrPt2HQiHw2G+CLiwsFAikTiwUSiKevjwYXJyMnYfB/SEPaWrqakRCAR0pTU2NjI8sbq62nSlH+w1CfhaVBk9E8I2LqrHbuw5mQE4HM7ChQtlMhmrKSw+n//FF180NDTIZDIXyC5m0aJFTGb2CILIyMhgew94JWFv/y0oKIiKisK6LBAIerMTrQR+Wa/efv36IYTWrl1bWFgok8l27txJn2i9yKmpqehfi6obGhquXLli26oco9GYl5fH6pS8vLzeEhnrdDpILQ84bIbNUcMoT5t5wJMq7733HtsT169fHxQU9N1339njZGA1Qu/Th6DVam1rILNfNhgMGo3mm2+++eabb27evEmSJMPfoTMRmxanqqrK0nNtdjl6Ekyj0dAOBIbFwWdduXKlz8PwjWVmZpq+Kuhrmc6wWR5DFw3fnpUSwdwa4GA/r0OU1wNdYP/1X/8VFBRkg27OmDEjIiLi7t27dsouQ+W17gzV6/VsA3jpE50qFjb/eH19vTdmCoZs6IDjldfOyTG9Xs92OstlZq9MJrNhhmfWrFkjRoxobm62t5EYKK+VeTbLyARQCrcA8WSA42fY8JSUUqm0+XSlUumB6V+5XO7bb7/97rvv2rBgQSwWx8fHz549m4kT1n6vdI+TSDqdrrCwkG0aM/pctqnWASvU1tayTaAMwAwbo87vkxmYtm3bdvPmTVbpe/CU2o4dO86dOxcWFiYSiSwz6roAtVp96dIlm7cNVSgUzt7p2d+AHT0AxysvLTq2neWxqo0zOh4/fvzKlSvMZRdHMnA4nHPnzqWnp7/55pvr1q1z6t69M2fONDWuCYJ4+PChbdZunyENgGv6BQCxDc71ZDl2/bEzPHSTJk0aPXp0n7M6vUUyFBcX83g8kUiEAx4c7uc1naLE82nWYwb6LIVtM3KAlVkQ2DwUcIqfF7GM6jelubnZkzdH4XA4J06cuHHjxp/+9CeG1q7Zv1asWKFUKu/fv5+SkiKRSFpbW51xn7du3ZLL5XV1dTk5Ofbk0nXLJky+TVNTE7gaAGfZvDZHOHjFnG9xcXFoaGhvARgM43bxj4SGhkqlUoY7rvfZTDjJC54N++WXX+wsZn19Paut4AEmETIQ1QA4K6rMbMzr7FPcQnp6ekxMTI8DeebpBbA3IDY2dvjw4dOnT8f5rmxTXo1G8/bbb2MX+ZIlS65cuWKnaNqW2AEAVwPgfuVl23W1Wq23GFkGgyEkJCQ5OdmsI9mQ1cVgMJw4cWL69OmjRo0KCwt74YUXPvzww8uXL1v+jqnyGgyGmzdvHjlyZPny5cOGDUMIDRs2LDc3l44atvMdZv+6D8D+HgH4PAHdVpfV24ZOp6MoivkyebVanZiY6C1eMJ1Ol5ycnJiYePr0aXzPcrk8NTXV5vunKKqsrOzLL7+sr69/+vRpZ2fnP//5zylTpgwfPhwh1NXVdebMmbS0tK6urrt37z58+BB70kePHr18+fI//OEPEyZMMP01uVxuczyDTCaTSCTgjnQsJEkihNyylyvguVNHzvhRHo+nUCiYP2oPHz70ot7O4/GKi4v/8Ic/LFiwoKqqqrq62h7ZxVFr2dnZOF6YJMnOzs7Lly//+OOPLS0tv/zyS2BgIEJo0KBBRqMxOzt75MiRIpEoMDAwNDS0x1+zOTiPIIiUlBSQXYdTU1OTlZUF9QA4XXkRQsHBwUajkWE39roMfnPnzt28efPOnTsnTpx48eJFB6oVfl2ZreULCAg4efKkU0tEEMTQoUNha2GHYzQa2e7xDPgDztqHLTU1lcneXHaaaW4kLy8vKyvr3r17aWlpT5488Zwbs+E1plar4+PjPXDptg+Ah0RQD4CLlJdVYK83Zq2Wy+WffvppZmZmXV3dokWLPGeFUlJSEqsUE2q1OiwsDKxdJ9He3g4OHMB1yosYp+tGjtvPwpWyi327Bw4c+Pzzz6urq3/3u9/ZnxjeUTC/E5lMBrLrPNRqdUpKCtQD4FLl5XK5DJXXuxxhZpEMM2bMqK+v7+rqSkhIuHr1qreUwmg0FhQULFq0CGTXqcoL1Qu4WnkRQkKhkIn95UX7o/QYQCYUCr/++uvw8PBFixYdOnTI83Oj6HS66upqqVTqySu2vR2dTgeuc8BtyqtQKHymsqzE7fL5/KtXr65ateqDDz6YO3cuDuF0C30aWXK5/NKlS2lpaeB/dCoKhQKUF3CP8iKEoqOjbcgp7l2yi+FwOO+///6ZM2du3rw5bty43bt322z8EgRhtncv/sDn8/s8d+DAgVassIKCgpkzZ9q81AJgCEVRkFQecKfyisXi8vJyn5ddmuTk5Kampg0bNhw6dCgsLMy2TTrEYnGPq4eZZDi7c+eO5ZdGo1Emk12/fj0nJwc8DC6gvLwcksoD7lReJmZvS0uLb8iuqfH7/fffC4XCBQsWvPDCCwRBuOvmjUajXC6vrq6WSCSgBS6rc1g9Abhfefs0e21L6euZskvD4/HOnTv3ww8/8Hi8JUuWxMbG/s///I8rJ98oipLJZDiSH7y6rqSsrAxWTwDuV17ktd5e7BW1R7MEAkFFRUVNTc3EiROzs7Pj4uLeeecd522ISVHUuXPntFotzo+elZUFmuti8HMOdQ70gSckyvPAzd67u7vt3FCnx7S8xcXF48aNCw8Pj42Nzc7OZphFvs9munv37pEjR3DSsrCwsLt370IWPkgICXgyrnszY7O3x+kdtVrtafE3BQUFGRkZjg2D53K5K1asWLFihVqt/t///d/PP/98/vz5fD7/mWeeEQqFmZmZMTExUVFRTGbASJJsaWk5ffr01atX5XI5/nLNmjX5+fn3799nEgIBOMnghZAGgAlOyc/bGzKZrMd0eQRBeNTkjzNkt0daW1uPHz/e2NhYU1Oj1Wr79evX2dlpNBo7OjpmzZrF5XK7u7s5HE5FRcXixYu1Wi1C6NGjRwaDISAggCTJ/v37p6amLl68WCQS0Tk5PfA15j/09oQDgBku9UYJhUKSJD08RbTLZBchxOfzN2zYQP/5888/Dxw4sKGhoaGhYciQIV9//fXTp0/79++PEBo8eHB4eHhoaOi0adMCAgJEIhGPx+vROm5ubgbldQs6nQ4MXsATbd7ejALPSdrvStll0UgBLJrJnj0pADB4AdfQz8XXS0lJsQxuFQgEnhDS65myywqKorwoCYYvoVarRSIR1APgocrL4/Gamposw1rdnqLXB2QXIVRXVxcREQGPtVuUF3ZaAzxXeRFCEomkurra7Ev3bkvhG7KLX2AQSep65HK5RCKBegA8WnmxNFgurHBXckWfkV3ALcDSCcA7lBchlJaWVlRUZPpNcnLytWvXQHbtlIDIyEh4pl1MeXk5TGkC3qG8CKGMjAzTRbRcLre5uRlk1x7q6uoSExPhmXYlMLEGeJny8ng8tVrtxu0bfM/JAE5eF2M0Gn1jYs16IhG1Wu05ewyC8joAiURSWFhI/zl58mTnpZLxedk1fYfpdDqSJEmSPHHiBP7gjDec2RX7PB7fiS91Hpx7ky6aaYU76Yq4ZRnm9lOpVAwPMxgMVg4QCoVbtmwBrfQd5eVwOOnp6bTaYisYZNc2amtrZ86ciT+XlpbiD6+88gpCqLi4uMd06Xby6aef0rtmSKVS6wcHBATExMTExMT4TIWTJJmUlIQHGdu3bzet8DVr1jjjinl5eW1tbQghpVK5Z88eK29TkiQDAgKmT5/O5GdLSkomTpxo/Zi9e/fu378f5NJHlBchJBAIXOxz8NVIho6ODnox8YQJEwQCAR4FCwSCuXPnOuOKfD6fTrx08uRJ6we7eKmkC0YYNTU1tJ9h+fLlphW+aNEiZwh9SEiIUCgUCAQrV64cNWqUZWimabdiWOEEQUyZMqXPw0aMGEFRlG9s6wXK24PPISUlxalmr6/KLkVRpgHRycnJpv9NTk52UpEJgpDL5SdOnGB1SnFxMZNtjTyZsrIy0wBeerSBSU9Pd/gVIyIi6KsYjcYffviBSQg8QRBqtXr//v29iebt27dnz55t6s2oqqpSqVRfffWVSqUy9VdMmzYNvL2OxBNSVWo0GpVK5ez0pg7Pt+sy+mym3irNhvbVaDSWD0lmZqZlruHc3Fw6O7BUKmVSCvp+1q9f772ZVevr6zUajaMqvKSkxLLC8/Pzezu+vb19+fLlFRUVTCocP/B6vf69997r8Zh9+/bRn69du/bee+/V19erVKrjx49rNBrTYqpUqqqqKsir6335ea37HBoaGnD2XitpfMHa7Q0H7vrFcKDK5XLfffdd2u3wwgsvdHR0uHchosuGF2q12oGZcbKyshj+mtFoPHz48MCBAwsLCxl2EPzAc7ncF198sccDBgwYQH9OSEjYsWMHQujEiRMzZ8406yzh4eF6vR5MVd/xNmDotRXO2KvYt2WXIAiz0a4ljY2Na9euJQjijTfeoCgKT4sVFhZ+9NFH+ICNGzfacF3684wZM06dOuUPHaaoqIiJUJ46dWr//v0EQchkMp1Oh/Mpv/baaxcvXsQaStc8c3bt2vXGG29IpVIH2iXt7e09+pQtO0tLSwvOEA34lPIihKRSqUwmwxacA+fcfH5xsOncWm8cPXo0Pz9fLBZLJBL6YKlUOmTIEPSvmDDsCsTT4mZYag1FUWVlZfSf5eXlzz33nM/3Frlcnp2dzeTICxcubN68WSwWR0dH42dPIBAcOXLkwYMHCKHa2tq7d+/ih1wmk1lWeEFBgdkPtra2xsbGXr16lbZ/jx49an+J4uPjGcbA3b59m2GwBOBlysvhcEQikVqtTk1NtTJvC7JrZp4wSQv56NEjHP9kuvdHcXExno5XKBTvv/8+jk/A3gYz8BsRSw/efIjL5c6bN48gCJIk9+/f/+DBA59Px06SZGRkJBN7U6fThYeH4890hZMk+cEHH4wbNw4h1NTUtHDhQqVSib0NlhWek5ODz8rLy8PK+OjRo2XLlt26dSs3N1elUv3nf/7nwoUL7S9UVFQUreY0PXoVrl+/DmnwHIkHbiCo1+tLSkoMBoPfTqkxn7fpbSqGnijDk2NbtmzB9Yk33DRrejxBt2PHjj7vxGAwmLaLwWDQaDT37t1jOL2GL5qZmYk/9zZP5YEYDAbrc7/0RBl+dOnKpCvc9Kfw4oUtW7Yw2TWVPsu0zq1vnGrW+tY7u+VttLe3m33z+PFjJo8HwKJTe+amv48fP7ZzItVnZNeK8jLcuri7u/vmzZtSqbSqqgqLnWk/1Gq1v//97xFCK1asYPhrfggdyMGQw4cPf/rppyqViq5w01bD9b927VpPKNrx48evXbtm/Zj169c/fvwYHgMfV15sX1RVVdksBL4ku1aU17YIPGyd0ediCxRfxTJ6DMCPkz0jMFzDtIGfmZmZmZmJzVIP2SLe+m1otVpf6k0egqv3YWOITqe7fv16U1OTDeE7vufb7XEfNrlcPnPmTIeH3wGWIRzx8fGQvhnw2Rk2U/CDHhoayjb5iJ+kOcdxCCC7LrAA6KcRAHxfefGkcFdX1+nTp5lHmPnP7hJFRUWQjdsFsltaWmoaDQIAvq+8CKG0tLRff/312LFjILtmfoaMjAx4dp2K0WhUKBR0dBcA+JHyIoQ2bNhw7dq1xsZGkF1TPwOMf53Nrl27YFNLwHl46AybmfWxevXqI0eO9Lbhgs/LrukMW15eHp0wAXDeqCI1NRU2+AD8WnkRQk+ePFm5cqXpclUatVodFhbmvbJLkmRXV1d4ePigQYP6VN6CggKpVGqmCEaj0VIj8CLg6OhoeMTZAntRA+Bt+P8ZNGjQwYMHLUd/Xi27Op0Or8RFCG3fvv2LL76wfjxBEBkZGWYiq9PpzNLlUBSFQ/Gqqqry8vLgEWeFTCYD2QVAef8ffD4/Ly9v06ZNPmPtKhSKyMhIgUAQFxe3c+fOlpYW66YxsnDv6nS6tra2mpoa0y///Oc/Hzx4UCAQrFu3LjIy0jSjGGAdtVqdkpICsguA8v4bCQkJc+fOxRtYeLvsIoQWLVpEb9L+6NEj68lPa2pqLMObeDyeZZ6ab775hq6WgQMHwiPOEIIgAgMDQXYBUN4eWLBgQWRk5K5du7xddhFCXC4Xuw5OnDjxl7/8ZenSpb05JRBCzNfymVZLSkoKww1oQXYRQj6wfzsAyutE8R0/fvyXX37pA7VPkuTWrVuTkpJ27dpl2u0JgqBTtY4YMQIhhD/z+fw+f9Nssyx/2CfCIbILKyYAUN6+xTc0NBTvXOLVstvS0rJ3716cYNd0qZ5YLMaZSnASSPSvjDlMNo40tXkvXbrk82lz7QTvuAqyC4DyMhXfyZMnm064eR0//vjj7du3Ozo68J9mCarVavWlS5dsWEOVnp5O799848YNOkU30KPshoWFgewCrseLY8UXLFgQFxf32muvWVlk4cnExMTEx8cfOHBAq9WGh4ffu3dvypQppuNf2zIzSCSSN998UyKRlJeXx8bGgu+yNyBuF3Aj3rGSwgqtra3btm07fPiwzyTuslSEHrNEIoRkMtmrr76KP2s0GhBZkF0AlNd1GI3GZcuWvfPOO8nJyV5dEJwcy3KVWm/KC9j2tFRXV0NqYwCU1zHdadeuXcHBwevWrfPS5fYEQXR0dPToYQDldexzsn37dsjJAIDyOoxDhw79x3/8h1gs9q4JfYqiioqKsrOze7PCQHkdNaS4dOkSpMIBQHmdYjnq9fobN25YETKPMsHKysqio6OtT6+D8toPSZI1NTU2bC4FAKC8jFCr1c3NzUFBQU1NTYsWLfJY/cXpcpiYYKC89r+PEQTtAqC8LhhXKhQKiURSXV3d3t7uUfprNBpra2tZvRVAee2p7cLCQghjAEB53dDlCIJoamoSiUTujbuiKEqpVDK0c0F5HVLhRUVFlrEiAADK6/QRfVBQEB5mYk9fdHR0cnKyK01g2siNjo6eOnWqDSoAymsDarVarVaDYxcA5XUPJElWVlaaGj60Izg+Pt55g1Cj0Xjt2jV8ITu1HpSXLTKZTCgUQs4KAJTXUzwPZqLc0NCAP0+ePNl+FabVFiFkv+CC8trsYfCKyBYAlNcvsLJUgVbhoKAgnMImMjIyMDAQIRQREdGjf0Cn0+FtgLEHgz4rNjbW4X0elNchTQwAoLzuAS/PZWgQURSFc912dnbS2b8wIpEIIcTlcl0zYw7Ky2S0UVZWBnv5AKC8ngsOpPUiywiU1zp4Mk0ikUAMAwDK6+nGr0Kh8OR1FqC8DE3dwsLC9PR0yNMGgPKC8QvKC80HAKC8vUNRVHl5uYf7B0F5exyygFcXAOX1bjzcUQjKa+peYJJjCABAeb2mS1dXV3vm6BWUF4NXgcNMGgDK64POh6KiIk+bsQHlxQsRYX0EAMrr4/28pqbG7Rl2QHk9sC0AAJTXFXaWJyQY9E/l9czxBwCA8roCT8gw6W/KiwNOYBoNAOUF/XWn/vqP8tKZPEFzAVBe4N90wfXpB/1BeXFgH/hzAVBewNpYODg42GW72Pqw8tJp42FZBADKCzCSDLzJmwskwyeV1/UvMAAA5fW1YbLNO/34m/LSRi7sGQGA8gIOsODq6uo6OjoiIyMdLii+obz0K8rF++ABACiv74OTuQQHBztkeyEfUF6dTnfp0iXkoP2WAACUF+hbcdrb2+0fVnuj8uJtRkFwAQCU120SfP36dbzru20DbW9RXuxyaWpqcqzJDwCgvIDtmO5MHBkZmZiYyHBGzpOV12y7ZedNMwIAKC/gGPOwo6MjKCgIIWTdFvY05aVvHjl0c3sAAOUFXGo23rlzp6GhAQsZQig+Pt50qO525dXpdG1tbc3Nze3t7cHBwawMdgAAQHm9A5IkGxoaIiMjcRjWtGnTNBoNj8dzgWmJXwOdnZ20V6S5uTkpKSkiIgKkFgBAeX0ZgiCmTZtm+X1ISMjRo0dpRQ4PD6+pqUEIiUQi+hgul2tlaoskSfpzQ0NDe3u7SCSizW2cFQghBMkTAACU1+8biYG3gaIonU5n9iU2nAMDA82+d435DAAAKK+PKy8AAF5EP6gCAAAAUF4AAABQXgAAAACUFwAAAJQXAAAAAOUFAAAA5QUAAABAeQEAAEB5AQAAQHkBAAAAUF4AAABQXgAAAACUFwAAAJQXAAAAAOUFAAAA5QUAAADlBQAAAEB5AQAAQHkBAAAAP1VeiqLMvjEajY2NjdCiXofRaDQajZZftra2+l5hKYoiSfLJkyeW33d0dPhey5IkaVku1zSuWSVbPmNMCPgXrM4iSbLPE71SeQsKClJTU02/IQhi165dCKGtW7eC/npX51y5cuXLL79s1r7V1dWtra2bNm2yrcN4ZkkLCgpu3bqFENq9e/epU6fo77Oysurq6s6ePbt161afaVmCIGpraxFCZ8+e3bRpk4sbVyaTDR48mBa+gICAAQMGFBQU2PZrpvvP5uTk9PZCpf8UCATd3d197Frb7W2oVCq9Xm9255mZmfiDwWDYuHFjt2/hjc3EkKqqqvr6etMCarXa/Px8+r/0Zx8oaUlJCf3nJ598otFo8PcqlYr+kv7s1Wi12tzcXPrP06dPu75xKyoqlEol/qzX622rWFORxA9qj51Ro9GYNi6Tnut9Nq9YLOZyuWa2vUgkwp85HM6oUaPAlvQW0tLSAgMDTb9RKBTp6en48+TJk2NiYnyjpKmpqfRTajQa1Wo1fow/++yzqVOn4u9nz559/fp1Hygsj8d76aWX6D/Pnj3r+sadM2dOQ0MD/qxUKulKthmhUNiHGesPfl4zQkJC6M/PP/+8qeUPeGO/pT80NTX5RqE4HI5AIEAINTU1ZWdnL168GBfz2LFjHA6HHqX6jN0gFAqxVbRp06aFCxe6vnG5XG5bWxueEGpvb6cr2SHQnlyZTCaTyWJiYl599VU+n+/dymvqn6ZhXirLyTfAe3n06JEvObUPHjyoVCqLiopmzJjhD80nEAg+/PDDH374ocde6ezGnTRp0ldffUVRVHR0tGN/ubOzU6vVdnd3Z2VlZWVlYW8Dq2nDfp7ZWpZuESul4nK59+/fp/+8cOECNi4ALwVPQyGEdDpdeHi4z8hudXX1G2+8sXLlSmx/4fmlDRs20KpEkqTpk+zVhZXL5fSf8+fPLy8vd33jzpkz58qVKw5xNZhy9uzZW7du0ca7/3obeDwe3a4+MxXut6SkpCiVSvol6kDPmnupqam5ffs27Xl88uQJdunOmzevrq4Of/ntt99GRUX5QGEfPHhw+fJl+s/bt28HBwe7vnk+/E0AAAdNSURBVHGxJ/3evXuOdTUMGjSotrbWTpemj/h5d+zYkZeX19jYuH379uXLl4N+efV7FCEkl8uvXr167tw5iUTiG+VqbGxcvXp1bW1tbm7umTNnpFJpfHw8QigtLe3w4cMEQZw6deq7774Ti8W+0Yhz584lCIIkyVOnTlVWVuIwUNc37rhx4+Li4hBCEokkICDg6NGjAQEBdoqmWCx+++239+zZQ9t5XC63vb0dIaRWqxn+SIDX2RRZWVnHjh1DCIWFhZm6IIxGY1NTE65lHyMgIMBnTD/LouEP+fn5ppGSRqNRp9OxmrLw/AE47WS4c+cOj8czDdGhKMpoNAYFBflS4+KSDhs2zKxcrmzcJ0+eDBo0CH/es2fP8OHDV61axdwExs+nae8TCARYuOvq6n799dcpU6bQPz5v3jyKokzfnVZ6rs92aVBeAABMkclkx44d+8c//mEWlspQedVq9bhx47CVkJ6ejkPiSkpKsrKybOi50KVBeQHA96EoSqfTRUREyGSylStX2mzzOqrnQsYcAAB8nzVr1sTExJSVla1atYqtn9fmvA0pKSm9HWOv8lqxtJ2HWy7qxuv6VWHddd033ngDKtmHu49MJsPht93d3cyjTs2WETOEjoutrq7uVc3tHMa6ZSDsrtG3X10XKhkK6xuF9Uw4UAUAAPgqFEXhYH+cNCMiIsKxsb22v4fA5oXrQmGhkn31oiRJWublCQsLmz17NpbjkJCQ4ODgpKQk7CUA5YXnFSoZKhkK6xTltc64cePGjh0rEonS09Odp8UBBoNhwIABMCoBAMCvyMzMRAglJCQ8++yzCCGhUBgYGMjlcu1MyAA2L1wXCguV7O+F1el0paWlpi4Fs9WD7gKUF64LhYVK9uXCeib2xvNii90twwT/ua5fFdavrguF9VvgLeQNjQTGAgCAzQsAAACA8gIAAIDyAgAAeBUCgQCnuXHe/rkymQxfgsfjebcDEWd+6+rq4nA4Dt/kznPwEz+vTqejKOrRo0fh4eE+liPcCg0NDTjaybfp6OhoaWl55plnPGf9rmUvQ3YkhGR7rX5e3VGVSmVERERcXNyxY8e++OILeG97L3K5vK2tTSAQxMfH79mzh96azOdLPXbsWJ8vplqt/uCDD2JjY3k8XmFhITzt3u1tUCgUkZGR+P25efPmn3/+GZrTezlz5kxsbCxCiMPh5OXl/d///Z/PF5kkycjISJ8vptFovHz58rp16wYNGvTo0aMbN27A0+7dyiuRSBITE/HnBw8eQFt6Ne+88w69sujBgwddXV0+r0eVlZVCodDnW/batWsIIYFA0NjYGBgYePDgQde81bBHVSaTEQTB1oGLT+fxeARBHD16dOvWrRRF9XjMkCFDCIKQyWQ5OTkURZEkKZPJtm7d2tjY2Mc1ur2f48eP7969W6PRdPsovtFMTDAYDPv27ZNKpXq93rdLWlJSYjAY/KFxP/nkk8rKyqqqqps3b27cuFGpVLrs0hs3btRoNAaDoaqqikkvM2sLhBB+DvV6/b59+3o7S6vV4mOkUin+3N3dvX79euvX8vT8vD3uw6HX67F9pFar5XL5smXLli5dCmajDzg9L168uHHjRp+fXlOr1SKRyDMnmhzOw4cPHz58iLf8+PDDD3Nzc2fMmOGaS+/cuXP9+vUCgeCdd96x7RewznC5XCtpxXCGHS6X279/f+bZdjy97a1MNep0uocPH7711lv08M1PHmVfld3JkyenpaX5Q2ti5aUHvyRJeuyMv/3weDycDAzz/PPPkyTpmky4XC5XIBA8efLEA+vWi/28Fy9ebG1tbWhowH9WVFSAfnkvjx49On78eEdHB/5TJpP5cGGzsrIE/wL7QH34NZOSkvKPf/zDaDTiF+pnn33msgTkBEGsX79+/Pjxx44dc+DP4rLYebwXK29CQsLSpUu///77/fv3nzlz5ocffgD98l4mTJjw+uuv5+bmnjp1qri4eMiQIVAnPmPzLl68ePXq1d9++21WVtbevXtdNrDAV8/MzPz5558dtT6Coqg333yT1Sm///3vLSfo/GXqBmbYAE9DpVLhPpifnw+14Vg0Gg2u25KSErqerU/Cm+ohfXpmZqZer6c/93gJ/H2PDlIr14IkWF4A5CoDABf0MgRr2AAAAFwJTj/gmrwNw4cPB2MKbF4AAFwN2LwAAACgvAAAAKC8AAAAACgvAAAAKC8AAAAAygsAAADKCwAAAIDyAgAAgPICAACA8gIAAACgvAAAAKC8AAAAACgvAAAAKC8AAAAAygsAAADKCwAAAMoLAAAAgPICAACA8gKugCCIABMQQvgDn8+HygEAHwA2+PKGRoJ92AAAbF4AAAAAlBcAAACUFwAAAADlBQAAAOUFAAAA5QUAAABAeQEAAEB5AQAAAFBeAAAAUF4AAAAAlBcAAACUFwAAAADlBQAAAOUFAAAA5QUAAABAeQEAAEB5AQAAAFBeAAAAUF7ATkpKSqASAMCX+P8AS9DvUCXyZjMAAAAASUVORK5CYII=)
528
2
D
22
D
tytx
2
tVTd
T
DR
T
)YVXV(2
VC
(79)
Realsolutionsexistif
(
VTd
2
VTdVTd
C)cosBsinA
(80)
Equation (76) can yield up to two own velocities
0V
,whichownvesselmustadopttoachievethe
required distance D at the required time TD (in
respect to the selected object) for various assumed
owncourses.
9.4 Graphicalinterpretation
A graphical interpretation of solutions given by
Equation (76) can be obtained in Cartesian
coordinates of own velocity
(Vx, Vy) substituting
Equations(5–7,24)toEquation(25)
2
D
2
VTdy
2
VTdx
T
D
)BV()AV(
(81)
Theaboveequationrevealsthatthelocusofpoints
forwhichDandT
Dareconstantsisacirclecentredat
(A
VTd,BVTd)andhavingradius DT
D
/ .
Figure 5 illustrates a family of circles (81) for
variousrequiredDandT
Dforanexemplaryobjectas
well as, for comparison, circles V(T
CPA=const.)
(Equation(47))andthelineV(D
CPA=0)(Equation(36)).
Figure5.CirclesD,TD=const.
=0.2h,X=Y=5n.m.,Vtx=‐10kt,Vty=10kt
It should be noted from Equations (73) and (74)
thattherecanexisttwotimesofapproachatdistance
D: shorter‐approach at the point A (Figure. 1) and
longer‐approach at the point B. If only the earlier
(thefirst)approachisinterestingforus,then,forthis
time condition
TCPA>TD for selected own motion
parameters V, should be fulfilled. This criterion
fulfilpointsofcircleV(D,T
D),whichlieinsideacircle
V(T
CPA=const.)forthesametime(markedinFigure5
bythethickerline).
Graphically solutions of Equation (76) are the
intersectionpointsofthecircleV=f(D,T
D)withaline
ofanassumedowncourse.
10 TIMETOMANOEUVRE
It has to be emphasized that the manoeuvres
calculatedinthepreviousSectionsarekinematicand
should be undertaken immediately. If we require to
have the time lapse t for calculations, for the
decisiontoinitiate
amanoeuvreandfortheexecution
of the calculated manoeuvre then (X, Y) in the
previous equations should be replaced by (X
t, Y
t)
respectively,givenbyequations
X
t=X+Vrxt (82)
Y
t=Y+Vryt (83)
11 CONCLUSIONS
Formulae for such approach parameters as the
predictedobjectCPAdistance,thedistanceoncourse,
the distance abeam, any distance and the times
intervals to their occurrences in a Cartesian
coordinatessystemhavebeenderived,analyzedand
graphically interpreted in the combined coordinate
systemforposition
andmotion.
More than 80 directly applicable formulae for
collision avoidance and quite reversed purposes‐
manoeuvring to required approach parameters,
intentionalapproachesandnavaltacticalmanoeuvres
havebeenprovided–almostallofthemarederived
fromonebasicequationofrelativemotion.
Theintroductionsuchauxiliaryparametersasthe
distance
on course and the distance abeam, apart
from the main approach parameter‐the distance to
CPA,makespossible:
aresignationfromassumption(Section2)thatthe
mass of each object was concentrated at a point
which can have significance when distances are
comparabletoobjects’dimensions,
more complete
analysis of the main parameters
(e.g.conclusionsinSections7.5,8.5and9.2).
Interpretationandplottingofderivedformulaein
the combined coordinate system of position and
motionenabletheirapplicationsaswellincomputer
controlled radar systems as in manual radar plots –
some of them are very simple in
manual plots as it
hasbeenshowninLenart(1983).