![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYUAAAJvCAIAAAAbdlpmAAAACXBIWXMAABYlAAAWJQFJUiTwAAAgAElEQVR42ux9d1wU1/r+tC2wNOm9CSqKHUXBHkVRYzfqNRpLbqIfu6YYS+yJsVyNiTeaaDSWGKNoNHaNvSN2VBBQeu91d9rvj/fr+c2lLn13Oc8ffGCZnTlz5sxz3v6SoigSVUEURZIk6+Qw3TwVHnxFh/E8L4rigAEDrl69qlQqBUHged7GxubEiRMdOnSgaZqiKEEQKIoiSRL+SxAESZI7duzw9fXt3bt3VFTUqlWrlixZ0qpVK1EU4Xj4Bf0URVEQBLguSZLwp0wmE0WR4ziGYURRpGkaLxu9Hrw2oAgMjErWB0WRJBkZGdmiRYv79+8nJiZGRkZ26NDhk08+KSwsBA4CBuF5nud5hmHgz8OHDz98+FCj0URFRR08ePDvv/+G9cpxHNANugT8Dv8FbgKag//KZDKWZbXZNTEMYb3hKcCoBCDvEATh6enZunVrS0tLV1fXadOmPXv2LCwsTKPRkCSZlpZ26dKlI0eOPHz4MD8/XxCEe/fu3b9///DhwxRFnThxgqbpP/74Izs7G06VlpZ25cqVkydPFhQUkCRJkmRERERsbGxcXNy1a9dIkrxz505iYuLbt29PnTr16NEjbSQjDMMAg6cAoxKQJElRFE3THMchiQl4BDSpyMjIvn37kiRpZmaWmppqbm5+5syZO3fu8Dz/4sWLxYsX37x5kyCIiIiIS5cujRgx4sqVKx999JEgCObm5jk5Obt27RoyZMiUKVMePHggk8lkMtnevXs/+OADiqIcHR0LCwtLSkq+/vrrL774Aj+LJgFRC4DCXyeH6eap8OArOkwQBI7jXF1dW7RocefOndDQ0Dt37gwZMiQgIKCgoEAQhJUrV3p7e8fFxbEse/bsWZlMNnHiRJZl/fz8Vq5cybLskSNHGIZZvXo1y7LR0dGWlpajRo3KysriOG7q1KkWFhapqamjR4+maXrIkCERERFnzpwhCKJ169a5ubk5OTlDhw51dXUtKirCy0bfB68NsHyEUcV2BSbn169fDxo0yNjYWBAEZ2fn33//XS6Xi6K4bNmymTNnPnv2LCkpKSIiAo4nSdLKysrMzIymaZVKxXFcYmIiRVHbtm3Lysry9PS8desWz/NeXl6FhYWnT5/med7a2nr//v2mpqZv3rwhSbJXr14qlYogCDs7OyAv/CywvoaB+UgUBEEQhGbNmt2+fdvd3V0ul3Mch/xiz58/nzZt2suXL93c3Ozs7AiC4DiOpmlwuoHbBWzVYLemKGr//v3Hjh0DZbB58+YuLi4EQcjlcpVKhUxFLMsiRxtFUQyDF2qTALZnY1S1RCiKpmk/Pz8PDw9wvcNPgiDUavWQIUNKSkpu3LgRHh6+ceNGnudRBADHceCAg4MpiuJ5niTJH3/88fXr15GRkc+fP1+6dKm/vz/P8yzLgk8NzgB+OqAkoEX8IDAfYTR1kCQJIUg8z8vlcvDEg0uepuns7OzExMRhw4Z16NBBEISbN2+CsgbSkEwm4zhOEAQwh4uiOG7cOKVSmZSUBMR07ty5jz/+ODk5GegG+fJAqgI6A1EL8xHW1zAw/s/dAbwgJSlQvqysrLp167Zz586MjAyO4w4ePEiS5OPHjxMSEuRy+S+//DJgwAAjIyOKom7evBkWFtatW7dly5atX7/+0aNHDMMcOXJk0qRJnp6eIE+Brgd0xjAMwzBgTQdtDj+LpgB65cqVWu6TdXWYbp4KD77cw8A+bW9vHxgY2KpVK+kxICUFBwcTBFFUVNSyZctt27b5+vpaWVn17dvX2dm5uLi4a9eu7du3t7e3VygUrVq1cnV1DQgIaN++fUpKCkEQixYtWrBgAchfQ4YM8fX1pWna2tqaoqi5c+eampqSJOnk5NSuXbvOnTujCEm8bPR38FWfBOeL4MFXchiIJ8AFiBFAfYM/WZZVKBQo6hqs3QRB0DQNp+J5Hpm3UVIIz/OQDsKyLMMwcDDLsqDigdKHtDYwZmvDR3jZ6PgVq+YjaeQ+BgYGRj1BK1kMy0d48HjwePA6Ih9h/xoGBoauAPMRBgYG5iMMDAwMzEcYGBiYjzAwMDAqQ4PGZ6NagqgYoJame/R7ndjwqzxhKZ9jtS4KAc2VXwX9WZFzs1REYpXHVHlraFRVXr0Sf2sNRgI/tXHiVPSvat1mlU+w3HnQZuRaLglY0rXJbqnx467NkqhkcVZ+L2UXqvT2a/C2NhwfQVwcRLtJ77PKQdcJB1XrhLW5IioCLT0JEDFkclX3QtUaTEUHo1Fpf3DlK1WbOUTRj3V7j7V5guXOQ0XflR6m5caJ3kmUi6dlWHndPu46mYpy56HyFxxSfCBwXzobushHKOkpJSWFZVmapoFKq9xMtBEWavzIK98ianDRUidHRTMIgpDL5ZAboc02W61jqry1cj+vK6IvdyQQjQ2UVJsNoFq3WeUTrK7gWdFcVXRRiCzXaDQQqq7N8tZyKmq8ULVZElXOVZVPBw6GaHuUg21lZaVSqXSXjwiCSE1N/fvvv62trY2MjEBeqEjINIDYMLhBnudTU1OjoqICAwNh3yCaQmAbRWVmZj5//jwwMLByGcFgQgpBJmIYJjY2Njk5uW3btkqlUi6XQy0nHR987U/Fcdzdu3dbtWoFGYjJyckmJiajR4/WXX0N1mWLFi169uyJKmxVyUeV7PM1m/RyT1jRFaurp0i/i+SjtLS0q1evDho0iHyHyg0NVRqYKpqKKmUiLU9erVFV9ARzc3NVKtWgQYMqL8ivjYWi1MxXuSQqeYI1E061WRLwuyAIcXFxr1696tWrF1Ro0V7WqHJJVDIP2izmaomH2iwP6cFqtbqgoOC9996zsbEhCCIhIeH58+fV3dsajo9QkiRN05BLqSWh6J39CN0X+skwjFKpRPUSG8V+VHa2ayyZEtqZqGH7qY9HXBv7UZU3WO6br80IkX2QYRiZTFaqpJwO2o8qn4pqOZ0IgoDaWEqlEr5bkepTBR9pOVl1eJhUqa6BN6eeRlWvV7SwsOjatWupf+nL4Gt2DEmSRkZGfn5+2hysa4Ov2WFov7GysmrXrh1U0UQ+ZR0ffO1PRdN0jx49jI2Npa95dZ3jTIOpo1LTF3pCFRk7DSy3kKIoBwcHeDzIvWjwWZ00TTs6OlZ5sMHYj1BVOaVSCeZRaeEUg7cfEQTh6OiI/KpS6KK+1pShveZiSKjBcjSAp4wedHU9/QZz+7W5cRyfjYGBoTOkhqcAAwMD8xEGBgYG5iMMDAzMRxgYGBiYjzAwMDAfYWBgYGA+wsDAwHyEgYGBgfkIAwNDz4HzaRvtinjwePAGOXhUOAXn09bvYbjRqPRRoooxFeUr4ZlvyoPH+bQYDQdpgacqhdymlkiMUWNg+xFGDQHFfWqpcWNgYPkIo4YEhH5yHJeSkpKfn48qOlUCKysrGxsbqIwDdf5BYW9qFTkwMB9h1DEfAa2o1erZs2eHhoZWLh+BphYUFPTjjz+iyoGImPCUYmA+wqghoGtTaGhoSUlJRETEvXv3UlNTXV1dEdFUxEf5+fmXLl0yMzMDyYhhmM6dO5uYmOApxcB8hFFD0DQdGxs7derU+Ph4nuc5jrOwsPjjjz+8vLwq/+LFixenT59eVFQEpMYwzMGDB4cPH47t3BiYjzC00ssIifuM5/mMjAyWZSMjI1NTU3meNzU1JUnS1dXV2dkZ+ttUIh/Z2NgYGxuD5Qj6XGVnZ8fHxyuVSpVKZWxsXLYENQbmIwyM0toZWJ3/+eefJUuWJCUlFRcXFxQUBAUFrV27liRJY2NjFxeXKk8VGBh44cKF4uJiuVzOcRzHcWvXrv3666+VSuWcOXPmzJlDEATLshRFlW0JhYH5CAODoChKo9Go1Wq5XP7kyZPw8HCgDFEU27Rp07FjRxSGWyV9KJVKHx8f4n8biCcnJ4uiePv27Y8++oimaSMjI0xDGJiPMMpHRkbG/v37nzx5olAobt26pVarmzdvPnz4cFNT0wEDBqBerNqoV+hgoDmWZefMmZOdnX337t0rV64sXLhQLpf37Nlz9OjRMpms8ma2GJiPMJoEoAU70AFFUWlpaT/88ENcXBzwCEmS/fv3X7dunUKhgEb10GqY5/kqGQSkKvgpiqJcLg8KCkpKSrp3715GRsaePXsIgnjz5k1QUJCFhQX0LCMIQpszYxgaH+F82sa6ok4NHv5F03R2dvbatWuLioqSk5OTk5PNzMzGjRvn6ekpCEL//v1BGkKUgVimyiui/BIUEtm3b99NmzYVFxe/fv364MGDDx48WLBggVKpdHd3X7RokUKhIEmS53kkf+F8Wn0ZfG3yaUktB1T79DyIPUlMTIyOju7duzfKxsT5tLpwRY7jNBoNSZKRkZH+/v4cxwEX+Pn5/f77725ubqilZS0brsIykHLTs2fPBg8enJSUBH/a2tqGhoY6ODiUIj6cT6svgwdKSUpKevr06aBBg3A+LUa1ERsbu2vXLo7jEhISNBqNKIoymczf33/atGmOjo7gpCckTrda2p5RV2VBEJycnGbNmhUbG5uXlxcSEpKZmbl8+fJ+/fpNnDhREASssmH7UbUByxQJ8OhznucFQZDJZDzPY+9JIwISX2maloonHMcJglBQUCAIwsmTJ7/77jtpHZhWrVpt2rTJ39+/lCWoliMp1VWZJMlmzZp9+eWXHMdlZ2c/e/bs1atXv/322+PHj/v27WtjYwOH4SAAzEc12e5KaX8URcE7gNdTo/MROLZA0kG6/ZkzZw4cOCCKYnh4OHxuZGS0dOlSY2NjJyentm3bNtgISZK0srL6+uuvb968+d///vfFixczZ84cNWrU5MmTgUnxQ8R8pC0ghLfsohEEAURumqZx9YlGBMw/IiMQOoqLi0+cOHHs2DHp/mFtbT1nzpwGTi6DsYmiOGrUqLZt2+7bty8vL+/MmTNyuRz4CO9nmI+qgbS0tBMnTuTn57do0WLYsGHo87///js1NZWiqKFDh9rZ2eHpblxwHHf37t379++DrTo/P//OnTvwqltaWgYHB4ui6OnpaWxs3MB11CBCErYuW1vbjz/++Nq1a/fv33/48OGhQ4dGjBhhZGSEH1+TgKgFQOEq+yHP8yUlJeHh4V5eXp06dfrkk08UCsXEiRNZloWcAKVSOWbMmH79+rVs2fLJkycajSY2NvbatWvo6+WeuaIr1uCYuj2sUU4FEwVzJUWpY9CR6HjpeSD9VRCEDz74AJRoiqJAXAKX2YABA0pKSuDBNfrM8zx//PhxYENfX98nT56g24cb0ZGHqMvLpnGvKAhCfHz8mTNntPw6Qq3kI57n1Wr11KlTGYa5fPmySqVyc3P7+uuvZ8yYUVRUtGLFik8//fS7775jWTYgIGDBggVnz56F2BO8DVTXtlLuRiL9HR0TGxsbFRVV6lsURcErHR4ejopeu7u7g5bEMEy3bt3kcrk03qdx90gPD49OnTpFR0cnJiaeOnXK2trawcGhyvK4GE1XX4Nl/fbt2/v373/22WeQpT1+/PjVq1evWbPG3d3d0dFx7dq1IPz36tXr559/joyMtLCwwLbJmvFRJe8hoh6NRrN169ZDhw6VMtiBq4Hn+aysLNi++vTps3nzZrATcRxnaWlZSWX+BiYjiqJ8fHyOHj36ww8/bNmy5ZtvvuE4btmyZXglYD6q7CUhSdLT0/PMmTPvvfceTdMkSV67do3juPnz5w8bNqxVq1YWFhagOLRs2ZKm6ZcvX3br1g3LR9UFy7IlJSWlksWk4WdIPkpMTHz48GFaWlpZqQpFn4J7wc/Pz8fHRy6XUxQFaSJVBls3JP8yDOPu7t6lSxeZTKZWqyE6iSAIhUKhVCrxksB8VP66MTY2HjRoEJBOSEjI7Nmz/f39e/bsifZk2HVBTUtLSxME4eHDhzk5OUqlsm3bthCG22QBTkkUE0SU15BDEIQzZ85s2bIlMzOzXPkF5hZOVVxcHB8fj6L10TEymczHx2ft2rVmZmbAPl5eXpCTQRAECnfUHWEQ7jQoKOj8+fMcx128eLFXr16CIHTs2HH16tWurq4oigr73XRnMVMUlZiYGB4eTtP0mzdvYG1XSx+qbf4aaAFXr1799ddfb9y4sXz58n//+98kSdra2iI+Ql0oPD09SZJ0cXHp2LGjUqk0Nzev/Mw1HlX9HVa3p5JODvEulyI0NDQmJkb6fu7bt+/69euVnBboBqIHPTw8IM1CKoeKoti/f/8hQ4aUIr5yT6g7M29hYQGpRcXFxTdu3Hj06FFCQoKHh8e0adOg7lLZkDecv9ZYVwTh2tLSskOHDhRFqVSq5ORk6QPSaueosR2e47iSkhJRFHfv3k1RVHBwcHR0NDho1Gr1vHnzmjVrlpCQwLIsz/Pvv/++i4tLRkZGfHz8zZs3gcXKuoGamqMEecTQL0VFRb169UKN9FAQcyWWHZIkLSwsbty4gc7MsizLsqWcceB8kHriynVU6dTMwwoBz2BUVJSvry/c8pYtW2AFlnXrYP9aI14RrSvwr50/f76iF7zu/WsghuXm5q5bt87Z2fn3338HkzbP83K5fMKECTt37vzwww9Pnz595syZy5cvf/rppxYWFgUFBfAaEE24TSBItoIgREREvHjxAtEKy7I5OTlv376Vbilt2rSxsLDQaDQVGXdEUbS2tnZzc0NmoLL6F0hecrkcFSEqK1nopiEfjdPa2nr06NEsy0ZERFy4cMHV1VUQBEtLS39//4oaCmA0JNDSkm4n1X3Hmdq8VARBvH37NjY2lqbpvn37qtVqkiQdHBz27dvXqVOnjRs3Ll68uF27dmlpaQEBAUuWLIEsTTTKphl0i8iosLBw27ZtBw8eRA8SbEAFBQXoYA8Pj507d7q4uEjfzHJFZXt7+0rqJSAuK9cirst8hJQyMzOz2bNnd+zY8ZNPPrl48eL169cpirKxsTl79qy3tzcO4G50lFpaNfPVMrW5vCiKvr6+586dy8rKgh2YJEl7e3s7OztRFP/9738PGTLk7t27Hh4ePj4+4FqG9Nqm/NhIkiwqKiosLMzIyHj+/Dl03ZCmaCkUCmSldnV1bdmypbm5OQQKVa53G3wghaWlpY+Pj5ubW15eHlgGiouLnz17ZmtrC7ZIDH1HbeOPoLBWKX8QaG00Tbu7u4MrRFqcCQSrJovU1NTly5dfvXqV5/nExETIswdl7aOPPpo9ezYhCTgyNze3srLSRpxBfV8Ne/bc3NwOHjyYm5ublpa2YMGC169fz58/v0uXLrt37zY3N8ciUtPlI5CPGIZBRU5BEQPjBQhBSN4uV18wSMBtlqIG2Mwhwz4rK+vBgwcxMTFSpRWmqH379h07dpROV6nK05Vc1OCjlmGWFAqFl5cXNMh1cXGJioqCureZmZlIRMK6W1PkI0Q3yHqKqvlJN3OkRKBXq4msFSQVFhUVbdmy5eXLl3Dv6enpL1++BHGmR48eI0aMAHFSJpMFBwcjJiqV7aHl69pEJpamaWNj4y+//LJ169a7d+9OSUlZsmTJunXrmjdvjjYD3MetyfERRkU0BBSTnZ0tCEJqaur27dtTU1NlMhnLssbGxtBFw9TUdNKkSVOmTEESkEwm4zhOp6ITdVYI5Xm+f//+7dq1u3v37tOnT0+ePNm1a9epU6daWlri4jaYjzBKq2xv3rxZvXo1iEWpqalgJ3J0dFy3bp2pqSm02QgMDGQYBvER2KSxuqHNDDMMIwiCra3t1q1bQ0JCtm3btn79+pycnFWrVpUb8YCB+agJvR7IDITix8LDw8+cOZOXlwfmajjSw8Nj8uTJxP96spFlDTLU8N5eJVBsBEEQfn5+FhYWu3fvzszMvH79enZ2tpWVFWpxQTThMDfMR01aICIIguf52NjYQ4cOFRcXP336FMiIIIigoCBXV1eCILp3715KCJL+RNHYeEqrBLJLQg84IP2IiIj169dPmzbNx8enqdkrMR9h/B+kW/Ht27fXrFmjVqvBug8Oxw0bNrRr1w41VsQzVrfEhHIAMzMzN2/ebG1t7eXlBWXntG+ii6ETfIT7Qdb+itCH/vz580VFRffu3WNZdvDgwd7e3hBVZGVl5ezsjMhIm3tvyMHr9cwTBCEIgrOz8+eff56dnQ0znJ6evn///gkTJiiVynKLqOCZr9cr1qYfJNNg7eWkOVlSgUJP+0GifiqQQ7hz584DBw7A0jc3N1+6dGn37t3LPWGdNzgkmnZXQpqmraysVq5cSbzrrzVx4sQjR44MHDjQwcEBgm+lket45hvmiqQEWF9rCGRnZ58/fz47O1sUxQcPHigUiq5du5qamnp4eHh4eGA3WaMozjRNjx071tzc/M8//wwICOjSpQuuR4rtR4YPjuPu3Lnz0UcfsSwLJgwPD499+/ahujx4ihoesAeMHDnSzs5uyJAh/v7+J06cMDIywvYjzEcGjtTU1GvXrhEEYWxs7OHhQZJkQEAALH2wWeCyvI3CR+BGgCK8hYWFeGPAfGSAohBE3xGS8nUHDhzYsmULz/O9e/fevHmzlZWVQqFo1qwZegHwntzwgDlHlIRi5Q2Mc8FjWOrupAmPmI8MecuFcCGomnry5MmioqKCgoKQkBCZTNa1a9fJkyf7+voa5NLXd9TAnqovtIvK+5Rte6UXlfYwH9Wcj+DpQonyGTNmFBYWwoddunTZtWuXt7c3IfFxYkrSnQcHUlK5ndwNQC0l/reMBGJevY7vx3yk1R4rimJeXt7Dhw+Lioqg8Cv0eoLqTrhPoa5BEASGYbKzs2NjY93d3Q2Jj1iWzcjIUKvVDMNIqVYURSsrK2NjY72O/8R8VDUfQTrCzp07N23axPN8YGDgpk2bSJK0s7ODvvLSnA+MRmci9CBevXo1bNiwqVOnzp8/X6lU6vWLCmWORVG8ePHimjVrMjMzoRoE0s4YhlmwYMG0adOwfGTgYj9sSo8fP4YOaO7u7p07dy63UBFGo28ehKR4M3QlefbsGfRc0WsPA9wax3FRUVFPnjyBWvXEuwLQkCaZlJSk76sR81HV+212dvaSJUtOnTplYmLy3Xff9e3bF8pZQNoU9qPp4HvboUOH3bt3Hz58+NixYydOnCgpKZk3bx60KdXffVGj0WzevPnnn38uKSlp3br1Z599BlXVOY47evTo2bNnCf0vy4f5qOr1nZyc/NdffxUWFrq7u3/wwQfm5uaIhlClcDxRuvO8RFE0NjYeMWKERqP566+/iouLT5w40blz58DAQP19XWmahnyAxMREmqZ79OgxZswYaPQExs2zZ89Cf71SHY/1jI9wPq30MJSVxvN8SEjI/fv3WZaNj4/Pzs5u167dggULVCoVStFElFT2/LhLaqNfkWGYnj17Ll269OzZsw8ePJBKT/oy89LGxXfu3Dl48OCzZ8/s7e3Hjh07btw4aHcoTQVFgSnau/xxPq2O5tNKu9kVFRU9f/587dq1L1++hK83a9Zs/vz5//rXv7QpzGxgiZH6OHgQWl1cXJYtWyaTycLCwkCG1T4mQxemSxCE9PT0jIwMEPRCQkIYhhk/fvyKFSuUSiVahyRJOjo62tvbQ7cIW1tb/c2nxbaP0uQtiuKOHTsmT54cEREBUbBWVlY//fTTyJEjKYrC9Rv1RbtBj0mj0eippY8kyWXLlg0bNmz8+PEcx509e/bChQuLFy82MTGhaRrdF0EQgwYNunDhQl5e3vz581NSUnA8pN4DdDR4zC9fvoyOjkbOmmbNmrVt21alUsEBOO5RL54m0lwYhqEoClpI0jSNGjrrJj0JggA2II7jSkpKnjx58ubNG4ZhGIZp27YtBL7B4KFvKFCPqampr68vNBMvLi7W38WJ5aP/vxcxDFNcXDxv3rwjR46gJTt9+vRffvlFWm+QwD5+PaEkKGXL87woirt37968eTPLstWyiTSOjMAwBEHs27evX79+z549k8vlCxcunDdvnlwuhwJP0uUn1YlQ1p7+PjXMR/+DkpKSW7duFRYWwpI1NTUdM2ZMr169CBx+rW9khGyUCoWCJMmMjIyrV68WFRUhuUln90WWZVmWvXXr1oMHDzQajUwmGzlyJJQYRTuioQLra6VVNvSnp6fn4MGDfX19YafFZZj1S9qFgGaGYXr37j1ixIjLly8/efLku++++/e//+3p6amzb7UgCLGxsRDs9uGHH7Isa29vDwVtUAcazEdavcxEGTO77kcwo96NIOiCqAw/Fy1aNH36dJlMhjPU9JGPELp377579+6ZM2cePnx4w4YN3t7eOstHsMBOnTq1cOHClStXbt68GfoRwCJsCoaCuuFayKORChfSKUZeAN1cAQhxcXEnT57My8uTy+Xt2rVr3rw5EBO2FukjQLUBmJiY+Pn52draEgRx586dZ8+eQYKF7shEYOQSBOHNmzd3796labqwsFAmkzEMAzbsJvLUmLp69hzHlRumDFZhEEB0diMF9/DixYtDQkJYlp0yZcqqVaucnZ0xGRmGGk6S5Jw5c0RR/OKLL3799dfnz5+fPn3a2tpapxahIAh5eXlr1649evQoQRAmJiZN8GHVDUegKHXkv0CfFxUV6XJGBayDoqKi33777e7duxzHde7ceezYsQ4ODpiJDEl9YxjmvffemzRpkqWlJdTr0LVNMSEh4ccff7xy5YqZmVm/fv26d++O+aiGmg7IPgcOHOjTp09hYSEobi9evBg7dqyHh0fv3r23bduGwreQ+tZYLzwKYxdFEQg0LS3t888/j4uLoyhq1apVgwYNYhgGdzc1kCVOUbA+27dvv2fPnk6dOikUCshElaY4wO+NUvUcXoobN26sXLkyMTGxe/fuR48e7du3r5aiADoJOpWOiKVE9U2utdLXUGw+RVEsy27duvXp06dJSUnNmzdPTEwcMmSITCZbtWqVRqNZvXp1Xl7ekiVLiHfljRvR7YpCziCkKDo6+ubNm/n5+Uqlsl27dmDshIGB/QjDMFgJfvHz8/cqUXEAACAASURBVCsuLn78+LGPj4+rqyvq09nA3nS0CAmC4DguKSnp9u3b4BDs3r27qamp9qmgEGMFJd7B+KA7anK1+ag2eXeIU3ie//nnn1+9eoVcVL/88ktJScnx48ehtvTt27c3btw4fvx4KGDWuPm08MxgCebk5EyfPv3Ro0ccx61YsWLy5Mlg9azozE0qJdUgB7948eKAgIDp06f36NFj7969MpkMdQEoJVnU6+BREAkUkPj4449v3LhBkuSSJUtmz55dNhm13FOh1G4Q50mS5DgOTOPVkmLqY+bLZvbWez4tzCbHcYcOHdq3b9+mTZvmzp3LsmxeXt4PP/zg6OjYrl07+G7Pnj2PHTsWGhrap08f5NqoxIVZ35l+MPLMzMwLFy68evWqqKioS5cuPXv2dHJyqmTimmajUUMaPMS4+vr6dunShSCIEydOGBsbOzg4tGzZ0sTERLog63vwwCMQqPn3338/fvyYoqj+/fv36dMHhKNyI61LnQqt5JSUlNu3b7948QLybLXMYq2nmQeRjeO4GqQN1lwfQYUTU1NTly5dum7dOmiXThAETdNqtRrNC4rZ12g0PM/HxMQYGRmpVCo3NzczM7OGV9lQUZFLly7NmjUrJyfH0tLy6NGj4FDDMGDAYnNzczt69OihQ4cmTpxIEISPj8+RI0e8vb0boDoSKjuL3tJz584tWrRIo9G89957x44dk8vl1X0HCYI4efLkrFmzRFH09/dvLPsRXDcjIyMxMZGiqOjo6Br0v6uVfw1IcfXq1V5eXpMnT05OTkYRH1AaCpmuwVhjYWEB3KRWq4uLizUaTSOuS1EUCwoKCgsLaZqWyWSgSGIYNqS6g6urq52dHc/zb9++vX//fkZGBlHPIa8oUVYQhPj4+BcvXrx69So1NdXW1tbOzq5jx47VNf2gkrXgxWYYplWrVlCkrVHmFkQQtVpdWFjIcVwNDMS1ko8EQYiMjNyzZ4+Li8tXX3116tQpURQ3b968evXqgQMHxsTEID9adHQ0RVEtW7ZkGKZdu3bdu3eH6Wss0yZsU6DAg+yGY6+bDiXBS+Ln57dhw4avvvoqMTHxq6++unfv3urVqy0sLOp7F2QYJiEhYe7cuREREQRBdO7ceceOHSYmJq6urjUzRYMVnCCIoUOHLlmyBAygjfJaQY8Ta2trQRBcXFyeP39eXUqqFSPQNO3g4LBr1y7oTaxQKKCar0Kh+OCDD6ZOnXr8+PHRo0ezLHvp0qWBAwe6ubllZGQAcQIXEI3RxxV5dgsKCoCbIOUSv6tNgYxQ00QjI6O+ffu6ubklJCSA/QU09/qmQqjIfvXq1ZycHJqmW7duHRQUBBG5NUtPQz7+tm3benp6Ni7RS0stEtWP6ak5H8HEWVpaTpkyBR4zx3FPnz5dtmyZSqUaMmSIn5/fggULnj59evXq1YiIiPXr1yNjW8M355Ca+kVRjI2N/eGHH06ePCkIwqeffjpo0KCmGQ7b1ICsyLAMLC0tV6xYERkZSZJkWlraV199VVxcTLwLSVGpVGvWrHFxcUG1JaVmIIZhWJaFOKZy9cGy/qaEhISvv/46MzMzNze3oKDAxsZm2rRpI0aMqHEdG+Rfg2tB3F9jlQyUMmmNLXFMXb3tBEEEBwc/ffrU3t6eYRgLC4uDBw/u2LHjp59+at269fHjx4cOHQosXm6aW8PIRChe4969e3v37s3Pz7ewsJgxY0b79u2xvtbUQJKkTCbr27dvnz59aJr+559/du3alZKSAv/iOI6iqKFDh1pbW0MdJaRMCYKgUCiAkqT6CCxv5HSGUiEoU4rjuFu3bv35558oNNzLy2vRokW1lMgMrDRg3fARxEO2bNly9+7dqH6dp6fnhg0bVq5cCdoQPFFIVm6s9UeSZFJS0qpVq06ePJmbm9uyZctvvvmmZcuWBM7db5K6G8QcAdF069bt8OHDBQUFsFR+/fXXI0eOfP7555s2bSq1PGia/vTTTz/66CPU0EEqE9E0/ccff2zfvh2sAUhHYxgmOTlZEIQFCxYEBQURBOHo6AimltoQSg1iDg2fj0DvRWmBSBMWRdHIyAimG8WbNYpbDdmw09PTL168mJaWRlGUm5tbt27dIH8a1zZqgvIR7JEgNRsbG3ft2hUx1OPHj//888+kpCTwGktrVJAkGR4eLggCeMpKFdjhef7Bgwd37txBJgK0Q8NVhg0bBp2XpIRSM0pCvXCIxrDD6rR8hERHFO1alrPgv40ycXB1nuehlAwyaUvVb4ymxkel6smglSmKYlBQUHp6erlrFbbbRYsWgdQj5Slw10JrxrZt2wYFBUl1Oo7jbG1tW7VqVarIbA32frSAExIStm3bxrLs4sWLhw0bBotcf9vMMU1n8cGDhEBNeJYQe9YUyu5hVGupEATh6+u7bt26cjcqQRBWrFjx888/QzXrUl8ElY2iqPHjx8+bN69sCS3I7ailpA8mLZIkIyIitm3bNmzYsEOHDoElRK9XclPhI5C3o6KiLl26lJGRQdO0t7d3t27dQJ3E8hFGWUG+kuaAbdu2bd++vVqtlslkKP8JVD8wZiuVyk6dOhkZGcFuVyfamVQ+4nleo9GEhoa+ePGic+fOnTt3RjSn10Upmkp/WoqikpOTZ8+effnyZVEUW7du/dtvv7Vv3x5ZHPU6u5XA+bR1d6oqlR2SJCdMmPDBBx+gxKOyB4Bdoiz7VPSV6t6jKIoxMTHDhg1r1arV6dOnzc3NS5XHwf1pdbo/LQRhFxUVQe/zDz/8sFWrVlJjFk5JxYMvpXZVovjQNA1euepesfIXRJtTIVstQRCQfaVSqaRG27rtwdvA/Wmbir5GUVRBQYEoitbW1osXL+7bt6/Bt47BMFR1EiSvoqIiw1vATcWIm5CQ8NVXXz169IiiKNDqsQEbQ093Vp7nb9y4sWzZsvz8fMxHegMIzQDJNiEh4dy5cyzLIvtiqW5rGBg6vpiJd5YjtVp95cqVK1euILVRR2rUYj4iKjcEgFKGnqKLi0twcLCbm5s0VAoDQ7/0NblcrtFoWJbt1KlT7969GYYxGOODIduPICAb5RMpFIrly5dPmDBBoVAYzH6C0USArNSgr/E8b2lp+eeffzo7OzMMo8stfDAf/X9NG6Tc169fP3/+HDK2IZkOh2Vj6Km+VlhY+PLlS5Iku3TpYm5uDqmjBtN4gjLIJ4dAkmReXt6UKVMWLlxIEASErlWS1IKBoeN8dP369YkTJ+bm5m7cuNHCwgKqFBhMTK8BvpClQsKysrKeP3/OsqxKpTIzM5Mehv39GPq1qlmWffv2bVpamrm5uZeXF/G/1QWwvqaLkNqGwsLCli5dWlhYaGlp+e233wYEBGAdDUNPwXHc1q1bo6KiNmzYEBgYCO0zDGxPNTQ+Aus1y7IFBQWCIJw6derChQsURdnb248bN06pVGKZCEMfoVar37x5c+HCBXd397Fjx5qZmXEcZ3j9Sg0tfw3aG2zcuPHXX3/leR5KFEMyLSraXZvsIZwCplODLysgGNjMI0vo7t27t23b9vnnnw8fPtzCwgL6AhA62bgU56/9z4c8zycnJ799+xZVgPPw8OjYsSOqK9LwHSjr9VRNc/Bo/ZT7tlRiHNSjmUf9FB89ehQXF2dra+vr62tlZVWl6RPnr+kiYKWamJjs27evdevW0GEN1SfF0Osn2xT0brjHvLy82bNnd+rUaf/+/S4uLoZ9y4xhP07YXtzd3Zs1awb6No6ENBhK0mg0hYWF5QZtKJVKpVJpAAtYo9GkpqZGR0f7+PjY29s3Vu8QzEe14iC0ZCGYFYRGqJ5neCbApklGgiB8++23165dg4fLsqxcLgdvhkwma9269YoVK0xMTBqxf0TNAPslKmf67bffXrhwITs72wDotanLRwCo7InfYQPbdViWPX/+/P379wlJSWn4CW2TFy9ebGRkhGo26hHVwpgh8Prq1at3796lKIrjuLJt4DAf6RmcnZ0/+eQTa2tr/A4bEi5cuHDw4MGIiAiSJMeMGePj4wOl9dVqNUmSv/32W0pKyty5c8eOHTtixAj9shiicmtXr149evTokydPaJoePnz4pEmTUCq/ARtADZyPfH19P/vsM6yjGRiOHDly4MABmqYZhpkzZ07Xrl1RuinHcdHR0YcOHTpy5EhGRsagQYOMjY31SxUFIejw4cM///wzRVEymWzmzJndu3dHShyWj3Rd5YbtkSCIrKys69evP3nyBBaoQqHQL/MBRkVAdkCwZFMUZWFh0aVLF0dHR4qiaJqGjrIymaxPnz43btxISkqKioq6fv16hw4dbGxsIGAHrDOgEzW84lOqyxYhqY1LEERubu6DBw9ANYM7gk6ldnZ27u7uIBNVFK2ia9o0IakU3hT9/dDliuf5Q4cOrV69OiMjAwUfYRgM4F0l3nktVq1aNXbsWChlj9Y9TdMTJkyws7P76KOPEhISxo0bN3Xq1A0bNkAjENT5ulG0HunLCZ4W4l0VCp7nQ0JCFi1ahFpUfv755//8848oijKZrOkYHAyBj6TFHvPy8oCMUGVIDIMhI1EUOY47f/78vXv3RFF0cnIyMzNDyjhqj6xSqfz9/QcPHpyRkWFkZMTz/P79+0EqEQRh8ODBjo6OjSg4EARRUlJy4cKFzMxMoFcgnZCQkPz8fEdHR29vb5VKBaJftZrfYD7SFT6C0msgh4OsKJPJGqUxN0a9yhcvX7787LPPYmJigH3kcjm4olCrH/hpY2Oze/dunudLSkr++9//zpgxA8oqchy3Y8eOqVOnNpbWA8wSGxs7b968xMREUELRLchksq+++mrKlClwawRBQNAcLG/MR9XT7VEzFlCUpLFb9f34UX01tEkKguDl5dW8eXP8GhsGYAnxPF9UVKRSqTw8PCwtLYl3Dilpx3b4EyQjpVLp7Ozs7e3NsmxGRkZ+fn54eHhYWJhSqWzWrBnYnipvbVRLU5F05Ws0mujoaLVaHRUVlZ6eLoqio6OjQqFANiMrK6vmzZsbGxujxYxaKOvXtoFeyeq++HWTTyv1biBLYUVJs/WaT4uy+Hx8fI4fP+7g4IDCUmp5j9ofQ+B82vq5IqpJNnHixG+//dbExKTcBYB+gdf4ww8/HDVqFGhtCxcu3LZt2/bt20VRHDRo0J9//imXyytSiGozeNTkVrraw8LChg8fnp+fD2paixYtDhw44ObmhiQ7mqaNjY2RE63OR9Uwz7rx82lJknz8+PGrV6+6devm7OyMPn/79u2zZ8+aN2/eqlWrUnp+3ebTSm8bPpfJZFBaWCrG1+YeCZxPqxuDJ0ny7du3t2/fDgwMNDU1lX4XHYaswuB4NTMzI0kyMDBw6NChaWlpGRkZMTExT58+PXbs2IgRI+RyeVknbC0HDxGbarX62rVrxcXFILNfvnw5JyfHxsYG0tB69+7dsmVL6Nhe6o0FOis3XVxflk3N8mkJaAQuCAIYgMsFqtdR9nOO41iWXb9+vUqlcnJyYhhm8eLFcKrvvvuOpmlra2sLC4vOnTtHRkZyHJeQkHD58mX+HSo5s1gVpMegkWzYsAE4qH379oWFhZXfV22uqDunaiKDB4SGhjo4OJAkaWZmduLEiVLfRX/CQy/16Hmez8jIyMzMPHPmDBCQg4PD2bNn4cywING3OI4TqgM0SPRdnuevXbtmZWWlVCrlcrmxsTFN00ql8o8//khNTU1PT8/Pz4dXQPr1Uregj8sGbio+Pv7MmTNavn0IDNj2a1DbCTReQRAOHz68atWqX375ZdSoUStWrNiwYcMXX3wRHh6+YsWKkSNH7tq1S6PR9OzZc/78+SdPnuR5nmGY+iinLwjC27dv4+Pj4cwQwYGrrxmYPRs91vz8fHjzy40vK7c+OhhoBEFwd3f39vZOTU01NjbOyMh4+/YtvEUKhcLU1BSqC2lpskHpZhqNJicnJy8vD9Qu8PDGxMRAiWRYh0ZGRlZWVl5eXlZWVgRBlA04kC5X/TVgI2UTaSfVsB+Bcwrid6r1ZQjlYFl2y5Ytjo6O48aNIwji66+/ViqVMpns7NmzlpaWW7duharVbdu2PXXq1OvXr01MTIA+63aZiqJ49+7dOXPmvHjxgngX3IH9/YYE8JlIDSssy9Yg2FUUxRYtWpw5cwZqUW/cuHHBggWQLCaXyydMmLBmzRoU0l3lG4FMk+Hh4TNnzoyJiSHepfvK5XJfX98//vgD2Id4F4fp4uJi2NskEjVA5KyWoMNkZ2dzHAf7Bhjzq3Xhly9fPnr0yMfHZ/PmzSdOnBg+fPjUqVNZlv35558dHBzs7e1Bcw4MDAwJCbl79+7AgQNZlq1bjwYwaVxc3KtXr2CjMzExad++PW4fYkiAR3z9+vWcnByoZu/k5FTd/Ank3HBzcxMEwdzc3MHBwdLSElkz09PT79+/b2JiotFotHyRYGM+f/7806dPBUFwcnIyMjICx46Hh4ePj49KpZK+qFJPtKHyEbz1NegKx4wZM+bRo0cTJkwYNmxYhw4dHBwc0FmkIe2VCGYkSUZHR4eHh3t7e69du/bYsWOXL1/Ozc21tbUFOQVFBomiWFRUFBcX9+TJE5VK5ejoaGpqWlf3L5fLaZqGjMpJkyZ988031aVXDF1GamrqjBkzrl69ynHc/PnzV65cWYPENJQCBtKWlZXVjh071Go1svvs27dv2LBhsIq0XHvwIoDpx8/Pb8eOHZ6enuBrVqlUsAhLGaoJQ0zTh9cwPz8/KSlJEIQ3b95kZWVV9yTM4MGDHz58uGfPnl9++cXc3Hz48OEjRozo1q2bpaUlzClBEJW82ED2/fr127lzp1wu79+//5QpU/bu3Yvc/2igHMeZmZnRNF1YWJiWlmZkZGRqampkZFT7ZFfkSUEKmqWlZZ0wHYbuQBCE9PR0MBXb2tqamprWTB9HaSXwJ1RuQ/44Dw+PZs2agRlIGiaijbkTejR6e3ubmJiU5Sx9twppqabl5OSkpqaSJJmdnV2DOj/MwoULhw4devTo0RcvXty7d2/fvn179uyxtrYODg4eOnTo+++/X1EhKBR4Jopiu3btQJOHbuJbtmzp27dvYmIiQRCQxJiRkUEQROvWrSmK6tKli7+/P/G/AZMYGNpQUj0tGLQUe/bsuWfPntzcXLCaI/qopGy+VPbx9vaWBhA1KYCQ6OTk5OjoSJKkm5tbeHh4TfJpvb29ly9fHhERsW7dusOHD/M8n5WVdfDgwT///DMgIGDfvn1OTk7lLg6SJD08PFq3bn3r1i14YKdPnxYE4bfffnv69OmXX375999/Dx06VKPRnDt3rnfv3p6enmlpaWA/AnMXUZ6XAQOjohVf38lctra2/fr1KzcxvcrrwleaZiI3su2USuuvLi8zycnJ33///e3bt0NDQ4EgvLy8goODFQrF/v37r169evXq1YkTJ1akihsZGS1evPjf//73mjVrfHx8Vq9ePXToUH9//1atWm3ZsmXBggUvX768f/8+qIQoCx/ZlepJi8ZufoNc8Wih10ewCOhrKOWoFB9ps883ZXkfpWQgAkK1OqtFScyXX375xx9/EATh6ek5YsSIgICAvn37WlhYCILAsuz333/Psmzl+9UHH3xgYWHxzTfffP/992vWrJk2bRpBEBYWFufOnVu8ePHKlSt9fHz27t07duxYCEmAb8Hjr9fZwTCMXRfZJlAMR0lJCSKOOrlQ2VKwZaONq9TXpEaMpklJiJWQzb7a8UcBAQHOzs79+vXr3r072AhB8OE4bsmSJZ07dx40aFBFlwcZRyaTBQcH9+/fPysry8nJCUgRCO63335bt26ds7OzUqlEnWNxWSIM7Zc4LKekpKR9+/aBRbJDhw5QLJFoMo2Pmg6YTz75RJqJi1iGYRgLC4t//etflSjPSEAFVrK3tweLI1pGMpnMw8MDHYbq8tV5Pi06v/SnNlep8RV16lSGOnhkkTl48ODq1asFQXB2dt66dWtgYKC0yiKeeZ26Yq3yactGuCIHPHLzV7ILSevdlT1MKrhKIy/qoz8tOlUpWRGnpOrv4NHWolarUWVIY2NjaW42nnndvGLN8mlxBDOGTutrHMeRJJmTkwOfmJiYQJ9hDMPU1/AUYOgsRFHMysr66aefjh8/LpPJhg0bNn78eHd3dzwzmI8wMBoaFEUlJSXt2bMnPj7e3Nx8woQJI0eOxDG0mI8wMBoOqFx0YmLiTz/9lJKSYmlpOXHixI4dO0r/i4H5CAOjIQB+3lu3bu3du5fjuMDAwOXLl1dUNgjDcCRiPAUYOqimgas4PT0dEvHt7e2hJA5W1jAfYWA0tHAEmQeoXQ0Ko63DmGwMrK/VI/DOaUjgOC43NxeK0kKZV6ymYT7CwGiEfUUUxdjY2Dlz5jx48ECpVM6aNWvmzJl4ZjAfYWA0Ah+RJBkVFXX+/Hm5XO7u7v7hhx96eHjgmcF8hIHR0CgqKjpw4MD58+dJkjQ3N58yZQrkRWJ9rUnwUSM2GiXqNJ8W5cThfFq9GzzkNkI7itevX3/55Zd5eXk0Tffr1+/LL7/UvsMwnnlduGLj96fV5jA0snrKpyUkmbQEzqfVt8FDOf3FixffunWroKDAwcHhiy++6NGjB/EuFkmbOut45nXnijXLp8X6Goau2IxycnL++uuvuLg4kiQdHR1nzpyJyqRhHz+2H+nTakZ1l5BMhN3/+kJDBEFQFJWZmXno0KHU1FSCILp37x4cHIwq4Ujr6mPo0cMlql8wz0DkI6h+C7G8IN4TuHigzgO6DEGg4+nTp5cvX15SUuLk5HTo0CE7OzssFukpalO6kzKM++d53tnZuWvXrtAjEM0IXhw6votACeMnT57cuXNHrVa7u7u3b9/e1NQUmr7iKWpqMAQ+An0tMDBwz549//rXv1ClSizk6/6DE0UxOTl52rRpO3fupGl648aNu3btMjc3x5IR5iM9Bjhf3N3dvby8WJa9efPm5cuXceMAXaYh+CU+Pn7Hjh0vX740MjIaOHBgnz59bG1tYTtBqhyGPj7fmnXKowxpFgRBABPSrVu3vv322+LiYrw4dA2IYkRRZFn25MmTW7du1Wg07du337Rpk7W1NQi2YDzCEq7+Qhp80xT56P/u510XuuzsbCzz6/LmwfN8UlLSvXv3WJZVKpUdO3a0sbFhWRY/taYMQ4s/4jgOglYYhsEZBjq7c4qiePHixRUrVrx48cLS0nLjxo0DBgwwMTHBAlETh4E8fqSyyuVyiEXieZ7jONTXVAd1llLatShBlZ+j3/WlRJn0FjiO43k+MTHx8ePHhYWFpqamffv2dXZ2Bncblo+wfGQImiqsdbVaTUjasRO6F90rzcaqKLun3M/LUhJYWHSfj4A0KYoSBOH48eO7du0SBCE8PJxlWR8fn/Xr1zs5ORG4yzmGYeTToshsURQtLCyUSmVJSQnLsjk5OQqFAlQAbRSBBstmBAtXQUGB1H9ULh9JyVQ6bzRNy+VyuVwOd62lL6OxcixFUSwuLoZOaiEhIZcuXYKQMaVSOWDAgIEDB2rDqjifVl8Gj/Np/0/oIEly1KhRFhYW//3vf0NDQ99///3Ro0cvWbJESzJqmGxGEBZu3rz59ddfQ89VLWUi6VzJZLKJEydOnToVnOKg6TTA4Gt2qmfPnn355ZfFxcUsy758+RKy+V1dXVetWtW3b1+ZTFalDIszmfVu8I2ZT1uKGtHn0JoGVT6uP30NORcdHByGDx9+69at27dvP378GOp4Qa/3BlPHiP/tySOKYkpKSkFBgUajgXEyDHP8+PEbN27UWNUiSVIQhICAAIhjBsu9qampvb09XBcIuuFVUXTvcKccx5WUlJw6derixYtwgFwuNzc3p2l69OjRo0ePVqlUWEnBqHs+koo8pV4b9IY0hQlFbyOipLy8vClTpsTExIDCAlORm5tLUVRtDO2hoaGQdAoCF03Tbdu23b17t5mZmTbiUj1tDFLLnSAIgiD89NNPW7duRTr1hAkT5syZwzCMjY2NkZER0jfxq4hB1KE9u9xQWlhqTaqBH7x1Go2GeBd8kJeX9+LFi8TERKkuhsTGGkOj0SQkJAAFEO+6kqWnp5uZmQHxofz4hpSP0A7EcZwgCMXFxU+ePMnOzob7pWm6devWnTt3ZlmWoijEXJiSMOqSjyiKioqKevr06eDBg6VRPykpKRcuXGjbtm2HDh2aCCVRFJWfn79s2bL79++DBKRWq4GMQBagaXratGn9+/fXUoeV2o9KEd+dO3e+//57oABBEBISEkaNGmVmZubl5bV06VIfH5/GmoHCwsLt27f//fffxcXFkZGRwJht2rRZsGDBwIEDRVGUyWQ8zyO/G+YjjNryEQqiSU9Pnzx58s2bNxmGsbOz2717d48ePXie/89//rNmzRojIyOCIFxcXI4fP25nZ1ffihvSGaF7F0gK9XFFoAAgX7DggO1ZEISsrKzz589HRUWVtdmTJGlmZjZkyJChQ4cSWnj9KnpR4cw2NjY7duwoKiqCw8BaTBDEy5cvP/jgA29vb0EQILMPmZPq+82HgRUXF1+5cuX27dtS12fXrl0nTZokl8vhSLRvNYqpC6NeVQR4EWqw0zC1uSroI8uXL79x48Zff/3l4+PTpk2bcePGRUZGPn/+fO3ataNGjdq+fbtGo+nZs+fHH3986tSp+n4fSJJUKpWDBg26f/9+WFgY7MP1EagtDSMCJ1dBQUFISEhubm5sbGxCQgL8y8fHp2XLlgzz/+Mq3NzcfH19a8mSMIdeXl5z58599eoVnD8+Pv7evXsymSw/P//gwYPR0dE8z7dt27ZPnz4KhQKFjNYrGYmimJ2dvW/fvtDQUBinvb19YGAgSZLBwcE4Yh5DqzVUOUCuLvuhIAhqtXrs2LG2trbp6eksy7Zp08bMzKyoqGjevHmOjo4ZGRkajYbjuPHjx9M0HR4eHhcXd+3aNZT7Wu6ZK7qi9qPSoVVuvAAAIABJREFUaDSXLl0iCGL48OEajYbn+ZqdrZJjBEEAEwnEf7Mse+nSJXt7eyQNgVU7JCREo9FoNBr2HUpKSuDeazMquDQ0blWr1SUlJRzHXblyBSzEhKSmop+fX3x8PJrqKm+zxjMPo+J5/p9//lGpVCCXkST5+eefq9Xq4uJiCAqr2ys27qnw4Cs6TBCEuLi4c+fOabPIpaiVvgYmyUGDBoWEhMydO7dHjx6vXr2aPHkyx3FHjhyxsrKysLCARRkQEPDHH388ePDgvffekwbd1BPDIkExISEhLCysU6dOSE2oW7s1SZIZGRlxcXF5eXk3b94Er5m3tzcIAkZGRh4eHihbHZlXaq83SUPSQTMVBMHJycnf3z89PT0nJyc1NZXneYVCkZKSEhYWZmFhAZXq6lVE4nn+zZs3t2/fLikpadasmZ2dnUKh8PX1ZRgGNEdcYg2jvvQ1VCJ2wIABNE2fOnXqn3/+oSiqf//+NE3n5uZaW1sj+wXHcfBachwXExNjbm6uUqmcnJxMTU3rnCbgFQWfd1hY2JgxY8LCwsB0VYcAy5QgCCdOnFi0aBEKtu7UqdPRo0fNzMzAaqtSqWCipCYkJD3VxmYsFYJEUWQYxtvb++TJkyUlJZGRkVOnTn39+rVGo0lMTJw6derFixc7deqE3PClzlMnNiNwX4wePfrVq1c8zy9atOjjjz+madrY2BgYU2ozwjA8QJhrVlZWamoqOLjy8/Oru8iZWr78JSUlc+fOtbGxuXbtmp2d3eTJk+fNmxcYGAgKBWyJFEUxDAOWHYIgCgsL09LSFAoFsFL92TJBUMrOzgbve92CoqicnJzr16//+eefubm59vb23t7exsbGQ4YMsbe3l8lkyKPfkM4jlUqlUqnat28/YcKE27dv0zQdHR0dHR39yy+/dOvWTS6X9+3b187Org6z3uDuNBpNaGjouXPnXr9+TdN0UFBQUFCQpaUlqmWOYfDgeV4mk7Esm5aWJghCbm6uRqOp9uIXaofQ0FCZTDZjxgye5zUazatXr2Qy2dChQ8eOHdu8efO8vDywccyZM8fExCQyMhLsR2A9EeoT//zzD0yEmZlZXFxcnZ8fdFKlUglXWbZsWWFhIcuy/DuAMUVocHAcx3Ecy7LFxcUajebo0aPm5uYgjtE0/euvv4IoV4dj02g0qampfn5+oJa2adMmNjYWzQAydWEYPKSPOy4u7vTp09JlppX9qMZ5LvBhs2bNLC0tHzx4kJuba2xsvH//foZh1q9fn56eHhwc/MUXX/znP/8JDQ3du3fvpEmTvLy83r59C7ISEvDKlY9qk1kjbXwEQoo2STTaXFGa+HL//v2dO3eq1WobG5shQ4YMGzYMfFhSvaySRgv1l4gk1QRpmg4ICJg2bdpPP/0ElQ+2b9/+5s2bWbNmWVlZlRvGXd2Zh06NoigWFBQgUzok+qJ4q9rfI85f0/3BS22jUKZVaqBoIP8az/OnTp3y9va2s7Pz8PAwMTHZs2cP7NIrV66Uy+X29vYKhaJVq1bx8fGCICQmJl65cqX+/Gvo88uXL8MNmpqaxsfH15WvgWVZQRDy8vLmzJkDVqpJkyaBGKi9D6thHCXg9RMEIS0trU2bNmDIA9358uXLlTzW6voZWZZNTk5u1aoV7DQdOnRISUnRfkvELioDGzyKzj1z5oyWX68z/xrHcYMHD+7fv/+JEyfCwsLGjRvXvn17GMRXX30VHBx86NAhPz+/MWPGQBo3GLb1V0mmKCojI+PGjRuPHj2SyWTNmzfv3LkzJIWi7C0dGSqqjqRSqfr06ZObm5uQkAAP7ty5cx4eHm5ubnVixYyNjb1x40Z2djbHcc2bN+/VqxcEwWJg1MQeWWP5COwUEF8j1SHRJ2q1GswZJSUlYFVJSEi4fv26/spHPM///PPPwK3t27d/+vQp3KP0XnRHPkID02g0W7duRSQlk8nmz59fXFxc+5kvKSmZOHEiwzAURVlbW1++fBlKHWH5CMtHDSofSd23yIUMJgMwKEBxCfgFcjtRPQo95W6O4yIjIx8+fAgx323btnVzc4MMe9RHQHekP2n1GcinRw+I47jk5OQ6cbHxPA+aOLhT7ezspMYjvN9jNJC/X2qmklYUQaExpcy6Nctn0SnExcVNmzbt+fPnoigGBQUtX74cNDXgZV0rjFuq4CQKmIKnAOakOoFMJkOPFXdMw2gcPmqCSE1NDQsLg52/S5cuzZs31xeGBREV59Bj6Lp9Fk9BtQQBSJ0Fw7x+vd49evTYvHmzi4sLfo4YmI8MAWDPRhKHvvQagtE6OjrOnTu3VatWyHZYGz5Ftw+JsqCrQnIMquWOFwwG1tfqk7wpChWZRf0m9UJKQk1WUOWT2vAFqliUkpIya9asBw8e0DQ9a9askSNHenp6ogBUTEkYWD6qX6C8PMiJA8WtqU0C4pq8vLy7d++yLMswTFBQUI8ePSBxD8tHGFg+agh9TS6Xm5qazpgxY+TIkboWANmQgIQA4GIQlyBPRVpdF1MSRrX5yAD6QVZ+idqfjXiXxaNWq1mW7dGjx9KlS6VO7rJf1NnGftpMizangiIqqOwksu6jtMFqaYW4paIhDR73gyzn87LV72t8Noip+f333zdt2iQIglKpRMajGk9XAydGVjTbtcynLdtft1TQE05JJXA/yOoYWLH9qGrQNF1SUnLlypWnT59SFFUf1ZQwMDCw/UhbKRTRkDYFNDAwMGoGLB9VNUHv0l/AU15WK2myHA2p1ESta+9iYGD5CKPmgDrFP/744/HjxzMyMuBDlmXxzGBgPsJoBBQWFh44cODZs2cEQQiCAGFHeFowMB9hNI7KBiFIgiBYWVl1797dw8MDTwsG5iOM6qlaxDtzGDT/gAyYGpQfgS+SJLl06dIZM2ag1gYYGDUGlrGbFlBEdWJi4sOHDwsLC6HvSI1jqUmSNDMzMzIyQoFaGBiYjzC0Ak3T4A67evXq+PHjjx07VssqBdK6w1g+wsB8hFE9+kCskZCQ8OrVKy37QVUiHwHqsMckRpMFth81LYAFGiUWGRkZ1VKoQYWQKmqlh4FRDT7C+bTaHFP2bJWfUJcTI6VHlk16rNngK3kQdTt4XTsVHnzZw3A+bTmf11U+LVFxrmBtpqux8mmJ/60EUjbpsWaDLzdzEqekNuXB43xaDAwM/QbmIwwMDMxHGBgYGJiPMDAwDIGPkHO3VFvucgNz0ec4bNcwwHGc1IeCAyAxGpmPUJVS5KmBeBa0QDmO43meZVloCgSfYEoykLVCUWq1ugZOXAwMLVG9eEiO41DDP+JdcJ3UVQyZUJCciY7BG6lhgCRJhUJBvEvuxwHZGI0sH0ElaY1GA3mYqFmrWq1OSUm5e/cutCqFz3meLywsvHXrVnp6Ol64BgBQ0nmez8rKOn36NFRiwzHZGI2przEMM3HixO7du2s0GtDXCgoKPv30Uy8vr5EjRwYEBERERIAMdfjwYVdX16CgIG9v7wEDBqSmpsKmimQlLDQ1ClB32YqaNVWir0ExgN9//33BggWJiYlStR1PLEapZVaDHnyUlqfmeV4UxSdPnvj7+4eEhERERGg0Gp7neZ7/6aefDh06tG7dusjISEEQBg8eXFJS8ujRo5kzZwYEBERFRT18+DAhIWHRokXQQVBqCMfruKH3H4pCJj/inV0Pnq82uxH8kpubW1BQIG15xHGc1NqNgclIEIQalI7Qlo9gEZ8/f16hUMhkMoVCAbW4cnNzt2/f7u/vP2fOHCMjo7lz5yYlJaWmpp47d06hUGzbts3BwcHLy6tDhw4nTpyIjo5mGAZeCcxEjbVQZDIZSsdHD6JaTVNQ6iycged5mqZrUNENw4AloxokixBa5tMim/Rnn302f/78rl27vnjxAmjlzZs3CQkJs2fPBjN2nz59NBpNnz59cnNznZyc3NzcYAvt1q3b8ePHQ0NDe/fuXVxcDB3fS5nDy96VNnde0ec4n7aihQKKtqWlZf/+/f39/aXphNqfCnYjmqYHDhzYsWNHohatbgmckmpwgxdFkWVZ6FosTZasmo+0JDC0H8rlcliLQDQcx1EUpVKpkLpIkmR8fDz1Dmj75Xleo9GwLBsWFpaammpsbNyhQwc3N7dy99UaZ/qB+iDt2ly2Y2qVGbylomzgRpCQWKXHUJfzaZGm1qtXrx07dpibm2t/KmlSLkVRgiCYmZn95z//admyZX3fI86n1f3Bg5gcExPz+PFjiqJSUlJkMhlRTTNxzWVsiqIYhpHL5YIg5OTkEBJDabt27V69eoVefrAskCTp7e1N07SPj0+XLl3kcrm5uXmda21SJ7QgCFJKQhxapW4COoh0bCicqpT9Re+ApsLY2FipVNb4PDADMplMLpdjDQUDvXrOzs5mZmYEQcTGxsbFxVXXRkzVckWamJgoFIrbt28DCzx58oRhmNOnT0+aNKmwsDA/P1+j0chksmfPnpmYmLi5uVEUZWlp6eDgYGlpKZfL69xbLCUjmqalhlv4lzaGkrIKMMdxSMFEtKu/fASCbW3Mz8g3h23YGNJVIZfLLS0tLS0t7ezsjIyMqk1qtaFDQRDc3NxmzJhx+/btO3fuFBQULFy4sE2bNra2tmPGjImLi/vmm29EUQwLCzt//vykSZOcnJykQ68nKQNs+6ampg4ODnK5nOO4mJiYjIwMlOai5czm5ubGxcUlJCTExsYmJCTQNG1iYmJjY+Pk5KS/8hFq/10bSkXTiGv4Y0hfGVgP8EvNFli19TWe501MTCwsLORyOZiTFi5ceOrUqcGDBzs4OGRkZGzfvp0giH79+n322WebN2++cOFCYmIiQRDTpk1DNiYQ7epjawWaoyiqbdu2V69e3b59+9atW99///2AgICQkBClUqlNJUMQH9atW3fo0CGIaVAoFFOnTg0NDSVJ0tbWFhRj/VoryKOP5D6oww9ti6Srp6J0EPT4oCkALIZqOeYwDJuPkNSMVkW1/Ws1uPC3335bUlKCkkKcnJxCQ0P37t17//791atXe3l5QejB2rVre/XqtXv37uDg4Hnz5llZWVWSfFu3eixBEEql0sPD47333jt79mxJSQnLsnfu3DE1Na3Eo1dKODp79mxKSopKpXJ0dGQYpkWLFs2bN9fTJAl01x07doyKioqOjo6KigoNDTU2NgY5187OzsXFpewCkj4syEZ8+fLl8+fPBUFwcHBo3759DWRyDIwKXz3t/cTEOy+v1A8lreUO/wVdANJowSUMPjh4kxMTE6Oiovr06YPiIeu2Xq2UbqAVT25uLsMwN2/enDRpkkajqbzKrVRAUKvVSqVy06ZNo0aNksvlZmZmKGyncllUBx0lyO1YWFiYlpY2cODAqKgokBZB2Bk3btzOnTvL3l0pJ258fPygQYNev35NEMSvv/46bNiwSpwS2EXVNAcPayYpKenp06eDBg2qR/8aRVEQOiS1+KIVj9oKSt3kKEcEWImo5zQRpAnC2BiGsba2FkXRzc3N2NgY8oErqo4iTWQBtdTBwaFDhw52dnbSkgbaPyTdAQhBBEEYGRm5urq6u7tnZGRAzD3HcUVFRZGRkYmJiXCbFfERTdPPnz9PTk4GN0qbNm1MTEzwlo5Rh6geH4H9XPqJ1Hwg3VqRhQUdIM1caxg9FnEHRVFubm6//PJLcXFxRcOQUgxFURA0CEFSIOUR/xuAo6fqPRiAvvnmm5iYGNhXMjMz169f//jx4xEjRiiVysoTR7KzswsKCrp3775u3bqWLVviOHuMxuQj/YWJicngwYMrj8AuN9HX8PzZJEl27tzZz88PjNnp6elnz549efLk48ePK8+BBCGLJMlu3br17NlTr+OwMDAfNfJLCIJSRfbsso6kWjZu1eV5QIY2URQtLS0/+eSTdu3aoWS0iqxjYCuUyWQDBgxAUdr4FcLAfFRDbaWUPb4S+ahUOKWB8VGpWxs4cGBwcDDP8wzDVOJ/BHlKWoNYqhdjYNQBHxlkf9pyD0PmLW1CkKRJatXNNSV0OzES3A6IRJCBr9Tn5epr5cpEtXyIBE5JNazB4/60DXQY9jrjwePBa3kY7k+LgYGh38B8hIGBgfkIAwMDA/MRBgYG5iMMDAwMzEcYGBiYjzAwMDAwH2FgYGA+wsDAwMB8hIGBoe9oQvlrdTV4HTwVHjwevO5cEeevNdBhOIsKDx4PXsvDcP4aBgaGfgPzEQYGBuYjDAwMDMxHGBgYmI8wMDAwMB9hYGBgPsLAwMDAfISBgYH5CAMDA6OmqF7/NVEUoT8X6t4F7d5RdCZ0E5T28OI4DjrqQDsdaU9tDAwMjJrzEbQM1Gg0FEWh3oGouxn6BX1IUZRMJoPvQndT3GQZAwOjQj6qVrIcSZIcx719+zY7O7tTp040TXMcR5Lky5cvb926RVFUs2bNBgwYYGZmRpJkfn7+tWvXUlJSrKys/Pz8nJ2dkWSE82nx4PHgDXXw9Z5PC6INRVE0TZ88eXLGjBnZ2dnJycnm5uY0Td+6dSs4OLhTp05ubm4nTpxo0aLF7du3aZqeOHHinTt3xo4dm5SUNHny5L/++gv6vpdq+toU8mlLPVFp81vdH3yNj9FyIRpkSmrZJ65Hg6/ZqUrdJiKjauXTaqWvQeN2juPWrFmzefNmtVqN1K6cnJxp06b5+PhcuHCBYZhDhw5NnTr12rVrmZmZ586d2759+/Tp0ymK8vf3nzVr1sOHDwlJ6/dS9GnAKNt3u4kA1km1ViSG/oLnefSsRVFEthrtoa1pmeM4iqL69++/YsUKMzMzMAzxPJ+Zmfn27dvp06fTNE2SZEBAgCiKq1atOnr0qKen5/Tp02GUffr0iYmJCQ8P5zhOLpfDoMEW3qReziZISRhNCkjIADdXdRe8VnRA07RcLqcoKjAw8LPPPnNxcSFJEvxlXl5eL168+Pjjj8GJdvz4cblcvnDhwtOnTysUCoqigHQcHR1FUYyMjKQoKj8/n+f5suqlAUMQBJ7nm5qkAHeNhaOmAxBKAGq1uqSkpLpPXyt9DfnpaZqG94rjOJZlGYbhed7LywviAL755pvVq1ePHDkyKCgImIh4ZwJHZMnzfFhYWE5OjrGxcZs2bTw8PMqlJAMw7EkVb5Zlk5KSXFxcgLW1J2K9toNqNJrMzExHR0edGnz9zQMyQWg0mpycHGtra4h90V4JqPKidTv4OrwiHBkVFZWWlpaVlUXTdHx8fHWLsWkrH0kVK/iFYRj4naZpQRCePHkyfPjw7777bvXq1b/++qsgCDKZjOM4giDUajUcLIqinZ0dRVFeXl5dunTp0qWL/f9r77zjoji7PT7bWdpSRTAoUkQkqKBEQQE1iiZC7Bg1JmrMTXjvqyIG0Bt9NxgSQIztzY3JjTGWaGzBGMQeo2JDEcVGUKwoTdoC0rbdP568s8PScYHd5ff9w8/MsE55ZuY355znPOfp2bP5gEtrgjKd+bM27Yp5MyoqKm7evMm0YLX85DWCTCa7evVqizvs5JPvuJYnfc1sNjs/P//OnTt1dXVktZW7as2br9mT1+ARyUf35s2b1tbWXl5eXl5eHh4elpaWbX1muK/ywBHb5+LFi9OnT3/58uXWrVtDQkLIn3x8fJ48eVJbWysUCqVSaVZWlpGRkZOTE0VRvXr1cnBwIP9X731pEtDlcDg1NTUaf+G1/NqJadAmA0HXvRXyhhMrmDaXusMdJw95bW2tlZWVSCQiLlRFRQXZ3hl6RLS/trZ29erVFEXdvXvXzs6OfCJYLFZoaOi0adPWrl27atWqJ0+eHDp0aNq0aU5OTnl5eYWFhYWFhUKhsB3ldXUOFosll8tzcnIkEklpaSmHw+HxeN0haqZUKl+8eJGfn19WViYQCLqDHsnlch6PR3zz/Pz80tJSU1PT7iPHFRUV5eXl+fn5HA6Hy+UWFhZWVla29dpZrXS5iWqQiKyXl1dubu6jR4/4fH5WVpaHhwefz583b56NjY1SqXRwcJg3b15tbe2sWbOSk5P9/f1v3LhRW1t74sSJN954o7Ky8uTJk3V1dVwul87wbt5waCqTpfkMpmZ+09Qla0QZGyaeKBSK2trakpISW1tbpVJJrlqzR6RvUDNtSH7D/AConWqLbdUwnbV5ampqSktLe/bs+eqXqRNWBh0nraqqevnypbm5OZfLpY2m1jyrLT7J9E3UYHM1nyrV+l3JZLL8/HwzMzOhUKhUKqVSad++fX19fdt049qmRxRFVVdX79+/39DQcMqUKcRpXLFiRUFBAfkOyOVyY2PjjRs3GhgYSKXSpKSk/fv3Ozg4fPjhhy4uLuSBlslkTeVnM1+VRl8b5rW1qGVN3cJX0aMWk98aNdGJALHZbDqERH7T1NejxSdY7YgtXkLrd6g2wLDR/6h2gU0dlPSicrnc5r8oajeo0UeilW9Fax6JRnfV4lm1NQRDBnKS4BFxGqhmZ9Np8ZFgfsOab6tWvj5U/UTqhjtvSo+aeR/lcjk9WJUIAulx61j7iB6JRgRIqVRyOBzyppEfE8OVRBBa/HS3u0Hb9NJqRI/ampestvOGf+q0TGiNtFVTetTMEVuTia43+dkN+9ra8T1r9x1s98lrxD5i3m61XWk+P5t5ADJenx7oTz4CCoWCNgHIdqJTRG5JbjedstRMiKvFr25T19ZpnTiv4jUwJ57roCNqZIetaeTW7KT5KfY6qOW1p2e2TQ9wVz2ozZuK7XsC6SecSEHb/ntbR9urfRCIucSMLHTz/DfSs/Dtt9/m5OQQq9Xc3DwyMpLNZldVVR04cODWrVssFmv69OnDhw9Xe291KFat5kccP368rKzs3XffJe4eSQHZs2cPRVFjxoyZMGEC+T4VFBRs3bq1vLycw+HMnz/fxcWFdg9167EhTgCbzf7ll1+CgoJMTEzIi3Dv3r2ffvqJuAUURQ0bNmzGjBkKheLgwYNXrlyRSqXDhw9/6623jI2Ndasnh7akKisr161bV1lZqVQqTUxM5s+f37t3b4VCkZWVtWPHDplMZm1t/f7771tZWZFcxYMHD6ampsrlch8fn5CQkJYvWdkKSPtq5GfauSsNHlGhUJw/f97W1vbQoUMPHz58/PjxvXv3ZDJZTU3NjBkzhELhxo0bT58+bWVllZaWRn5P0KHmksvlRF9kMllpaenGjRu5XK6Li0ttbW1dXZ1UKt2zZw+bzf7v//7vPXv28Pn8ZcuWVVdX5+bmOjs79+3b9/jx42vXrhUIBLt27SKJtcx8fe1vB/LJKS0t/eabb/h8/sGDB6VSKYmefPjhh/7+/ufOncvOzn7y5ElpaWldXd2uXbs4HM4//vGPlJQUR0fHwYMHV1dX69YzL5PJ6urqysvLR44c6eTkdOHChQsXLtja2pqbm+fm5kokkl69ek2fPj0lJSU4OLhHjx4vXryQyWSrV6/mcDgrV67MyMhwdnYuKSlp8XDQIw0fUS6X/9///Z9YLJbJZHK5vLa2lmS0p6am8vn8iIiIurq6urq6wMDAWbNmyWSyZsRIm1ueXF1NTc20adMEAgGHw+nbt69CoZBKpZWVlb6+vr6+voWFhTKZbPbs2ba2tuXl5UuXLmWz2SdOnJDL5dXV1U5OTv369autrSWNoFuPjVwunzRpEhnFuXv3bnITpVJpUFDQkSNH6urqSBMpFIq6urpJkyZNmzZNIpHI5fL9+/ezWKzk5OSG+9dyPZLL5TExMWw2+8CBA3V1dXK5/OTJk2w2e926db/99puLi0tBQYFcLk9JSWGz2TExMVlZWWZmZpMmTZJKpVKpNDY29tmzZy0eDqUaNQzpYUxJSbl9+3ZOTk5hYSG5ndu2bROJRGKxmAT+X3/99aNHj758+VIXC9TRJ8zlcn/++ecrV67w+XyBQECe3VOnTqWmpo4ZM8bS0pLD4UybNu3FixdLly7NzMwcP378mDFjSPp+SEjIw4cPs7KydM7BJ5e5Z8+eGzduGBkZsVgs8n4SF+zKlStPnz59+vRpeXk5UaXTp09/+OGHBgYGCoViyJAhHA5n8+bNuhiFMDExGTNmDKkapFAoTE1NKYrauXPnmjVrJk+ebG1trVAoBg8ebG5u/ttvvx07dqyiomLJkiVE1P75z3/K5fIWDwQ90jAsFqusrOzPP/+cMGHC+PHj3d3df/75Zy6Xm5+fz+Px+Hw+h8PhcDiOjo7kCSZhCN26RtKPS/41MDDo06cPm82WSqWkamhlZSX9cioUCpKNkpqaeuvWLTMzMzrpoV+/fiSipHO3mPTi8/n8119/3dLSksViCQQCklZWXFwcExMTFBTk7e09fPjwq1evkq4bW1tbLpdLQjAymayqqkrnLpnH44WGhh4/ftzIyEipVL58+XLfvn0CgWDPnj3Pnj0zNDQk0WsjIyNnZ+eqqioybN7a2po88IaGhq358ECPNAyHw+ndu3dkZOTt27dv3rw5a9ashQsX/vHHH6TIL4vFkkqlJGxHQidEjPQjY5uM6iYKS/f1MjObiNlP/ScVi7zVepOtzmKxvL29N2/efPfu3YyMjJcvX06ePPnu3bvV1dU8Ho80CMmQbNMQCi3RI1Krmjy9GRkZb7311vr16+fNm+fs7GxgYEB6z+n+d2ICc7lckiNKV9mHHnUBY8eOjY2NNTMz43A4q1atMjAwmDhx4sWLF8k7Sb6TEomEz+fTBav05p0kXhud20E/zU5OTj169GCxWCQ9ksViFRUVsdnsnj176s1wCjabvWbNmnnz5snlcgsLi6ioqLKyst27d7PZbBJRosdsCgQC3Rq8STx0mUwmkUgiIyMDAgKePXu2ZcuWTZs2kdgZyekhd7yoqIiuss/n8+VyOe3PQo+6gKNHj0okEhKfMzExUSgU48eP/+KLLyQSyY0bN4iBcO/ePU9PT9rK1ZtrVygUQ4cONTExyc/PJ11Ot2/ftrCw+OGHH/r06XP9+vWysjJiNP32229WVlakGol+tED4h4FEAAAgAElEQVRaWhqJ5pI0ZRsbG7lcHhAQ0KdPH1LnQKlUFhUVsVisOXPmkKIXugIdb37vvfe+/fbbuXPnXr58ee7cueTDExgYmJaWRuygBw8ePHjwwM/Pb8CAATKZ7NixYxRF8fn8y5cvt+rDg/41zR5RJpP1799/yZIlNTU1Uqk0KirKwMDg+vXrz54969mz5xtvvFFeXp6RkdG7d+9Lly7pR8tLJBJjY2NnZ2eyXaFQhIeHGxoaXrp0KTU11cjIaMqUKTU1Nb/++iuPxwsLC5PL5Tt27BAIBJ9//nlrOvu1sB1IB79UKnV2dt61a5dcLicDp4yMjPbu3VtTU1NZWenh4TFgwACJRLJ69WoLC4v09PSSkhJfX19bW9tGe761+ZknF7t3714ej7dq1SpyvSTIXVdXd/78eTMzs+PHj9fV1b3//vsCgeDRo0cVFRXDhg1zdXV98ODBs2fPBg0aRPp20N/fqUeUSqW//PILn88fMmSIr6+vmZnZN998Q0zWU6dO2draurm5OTg4BAYG1tTU6EHLy2Sy8vLyXr16ke8hudLs7GwfHx8nJycbGxtHR8fMzEzyBC9atIjD4QwaNEggEPj7+5eUlNCpTLqVf0S/om5ubpcvXyZd+9nZ2QEBAVZWVn5+fkOHDnVzc7t06RIptmNvb+/g4DBw4EBzc/Nt27Y1qsLa39+/ZMkSNpvt4uLi4+MzcuRIPz+/WbNmPXr0SCaT/eMf/7CxsRkyZIiRkVFcXBx5ES5fvtyrV6/evXs7OTlZWFjU1ta2eLg2j6d9xZ/p3EQRbf0NCeAdO3aMOCx+fn79+vWjfezbt2+np6crlcqgoCBzc/MWC55rf8sTf/PevXvV1dUDBw6k0xeqq6sPHTrEYrHeeustU1NT4sKwWKyLFy9mZ2cbGxsHBweTQY6tKaOuVe3A7BL9448//Pz8SLhaqVTW1tYeOnSooqLCzMxs3LhxhoaGJE1ZIpEQ88HX15dkXZGeVl155qVSKYvFysrKSktLI/l0xMsWiUSBgYFGRkYymWz//v2VlZXe3t4eHh708NXCwsLDhw9TFDV69GgXF5eW+wSgR5o9Ym1tLT1ZJv34klERJLLA4/HoQmUt9rNof8uTj2fDIipkI1V/bhWFQsGcRpQ52OjVx9x2vh7R7yq5KDIdIXO6Zjo4KJPJiGbRPybZErryzJMUUNIbQz4tdEpHXV0dCVqTx5tspEeqMqvctCZ+BD3CyePkcfKddMSW9QizVwMAOoFWlSWAfYSTx8nj5LXEPtKlJAigW9D1+ejPo1rxSQDUwMMBOlaMSJocPVAGAOgR6Bo9IgOGSUp6N5lYBUCPgNZB6hxUVFSQ8uo1NTUlJSUwkQD0CHQBCoViwoQJfn5+EolEoVAsWrTI2tr6u+++Q8sA6BHoAvto1KhR9+7dmz9/flxc3M8//9y3b9/p06ejZUBzjw36+3HyHbErhUKRk5MzaNCgiooKks67ffv2WbNmNUxJR8t3k5OHfQS60j7q1atXREQEGVAyc+bM2bNnI54NoEegyygtLSX9/c+fP6+qqtK5uogAegT0xD7KzMxct24dm822s7O7ePHixo0bYR+BFh4bjF8DHYFSqQwODk5NTd23b5+9vf2MGTOePHny448/TpkyBY3TbT9RLf8GnywAAPw1AACAHgEAoEcAAAA9AgBAjwAAAHoEAIAeAQAA9AgAAD0CAADoEQAAegQAANAjAAD0CAAAoEcAAOgRAABAjwAA0CMAAIAeAQAA9AgAAD0CAADoEQAAegQAANAjAAD0CAAAoEcAAOgRAABAjwAA0CMAAIAeAQCgRwAAAD0CAECPAAAAegQAgB4BAAD0CAAAPQIAgG6qRzKZjPUfcA8AAASWUqnsmgP/R4m66gQAANoGtwuVCAAAut5fAwAArdMjOGsAANhHAADoEQAAQI8AANAjAACAHgEAoEcAAAA9AgBAjwAAAHoEAIAeAQAA9AgAAD0CAADoEQAAegQAANAjAAD0CAAAoEcAAOgRmgAAoCVw0QSgTYjD4oXFVWUvyxv+SfSa3YpNEWgi0G66YL4j5vwiqJ+tWyyfunRbWlJTfxXxhP2senv5+EdviEJbAegR6CjCI6OvnziTWZLTmh+HeIzlutuuWyNGuwHoEdAw8aFxxy4db6UYEdws7P1HTYChBKBHoGN9NHtjyzf7+6r97HHR8zOP09Xct4UBMyO2rkQbAugR0ADRM1dsvrRfzfBxH+X7zYYvG/44bq7412vHciqLmRvDAuYs3xmNlgTQI/BKiMPiv0/8gbmlxcBQeGT0/bNXruZlMTcGuY7YcnI72hNAj0A7UQtgi3jCBYFzojYvb5+LB0kCrQH5kKBlMaIoar7v1FaKEUVRcYnrwwLmMLcczrqwcNwHaFgAPQJtpvz6Q6YYBbmOaGsMaPnO6CWTPxbxhExJipuLDAAAPQJtIT407nDWBXrVzcLe1NOxHftZsSli3sT3mZL008VEcVg8WhhAj0BrOZ+ewhQjz8BR7c5sJJJEr0qk1emXzqGFAfQItNY4YvaOTfAZ/4pp1is2RcwbGkyvXs3LQiAJNAX610A9godNpPXI29Y1KTVZI7sdPXi0WkAK3W0A9hFojri5YqZxNNLLT1N7DvR/Wy22DSsJwD4CTZKwIObrU9voVQ0aR4TYxQnbkndIpNX0FqRuA9hHoBHEYfFbzu6lV0U8oZePv2YP0bC7bcPZXbGLE9D4AHoE6vH8zl2m5TLfd2pHDM1X626jKOrEuSNofAA9AvVIeagamh/qM6Pj3KgVmyKYqduZJTnLpy5F+wMC4kegXuRIxBNmPbjV0Ud81z+EWZzk46kfoVISgH0EKIqizt25RC/7OXp1whHthrszA0lZ6ddwFwD0CKgnQLo4u3XCQdetEc/3nUqvnnmcHh8ah3sB4K91d5iZivbGllfvpnbaob0HDKOLt9kbW/oFvY2S27CPQPdl+dSlzLTpkOHBnXn06QFT6OWcymLZnTzcEdhHsI+6KWrlH0c5eO05t6+Tz0EtsL104sLWV1kCsI+A/vD8zl16WcQTCvr16PxzsBvubm9sSa8eOHswPBIZ29Aj0P1g5hx94DNl+5ZvOv8c1q0Rw2sD0KPuTsKCGDohW8QTes8f1lVnErV5eYjHWHp1361T6GuDHoHuRVbOfXrZz9Fr3JsTu/BkuO62zHSkY5eO4wZBj0A3ddZc7V269mTWrREvDJhJr2IQCfQIdF9nTRumkI3YunKUgyo1/GDGKVTahh6BbkHnDxBpDa5eQ2ivTSKtxiAS6BHQf7pkgEhriN4QNWWQKrCNQSTQI6D/3M/OpJe9bV21Kv8wLnG9m4U9vYp0JOgR0GfCI6OZkWx/dx9tO8MJPuPp5ZzKYn52Ge4a9AjoJ7I7edoWyVYjavPyINcR9Oq2tCQEtqFHQA+JD43bd+sUvTq+/wjtPE9TT0dmOhKmkIQeAT2EGTkS8YRcd1vtPM91a8SzhwbRq1fzsqJnrsDtgx4B/SE8Mvpw1gV6dWHATG0uNiTeG+tt60qv7k47jMA29AjoDz3yFPSyvbGlFkaO1PAdNopelkircy/fwU2EHgE94ddrx+hln76e2n/CKzZFzBuqqg935nE6vDboEdAH4uaK6cqwFEWZu/TVjdOun460O+0w+tqgR0DnufFEFckOch2hQ5MLBfq/zfTazp05hrsJPQI6THhkNLMmrJPb6zp08mpeG4b+Q4+AbqMWyV6xKULHnM36Xtu2tCSMa4MeAV3lwr00elknItkN8R81gZkheeDsQdxW6JHmYc41AjqCheM+YI7mt3Vy0sWriN4QxSzYllNZHDcXM7VBj4BOIQ6LZ+ZABrmO0DlnjSZi60rmuLafLiZGiWNwi6FHQGdgljQT8YS6FcluSC/3AfSyRFrNzniBWww90iSYD7LjUOtWWxA4R3eNI9prmz5YVY0k8dbpxUu+wI2GHgEdQK1bTT/mfWX37SniGdImUvm9R7jR0COgAzBzIHW0W60hmzaumjLoTXr12J1zqxZvwr2GHgGtRhwWz3TWdLRbrXEf38PS3kg1xfaNVEzWBj0C2s3zO3eZzpquR46YxEevnO6pMpGu5mUlLEApEugR0No3NjSO2c0/bcgEPbvAqN1fDWBkbG85ewDVkRpl+959C0YvXLr4c105YS7umZ4RHhmdcvYI0zhavlMP39U3R75z9/f/JcsSabXsTh5uvRozh06+9uJupVJh/JBNUdT6TTqgSrCP9A1+dhmztEjI8GC9vMzPvlk6xVNl9+27dQqD2tTE6Gzh7UqlgqKoSqUi6dBu+GugC4yjgxmqiv2jHLy0vw5kuxG6WjMHtW09sQteG+GjCf88W3ibuYUIE/QIdLZxxJzOyG64ux5f7Lo1YuagNom0+v7ZK3gGtu/dd+fBJR09eeiR3hpHUwaN1eaK/RohYuvKEA/VFNtX87K6eXWk7Xv3fb8y/mGtBHoEupgeeQqmcVTnbNYdrnpT8ndq1ZFiFydAjNR422kU9Ah0Ksw6R+P7j9B744hGrTrSiXNHIEZMjFlskcdr0CPQeehHnaP2Eb0hijl/ZGZJTjesjnQkYXdTbppPryE60dkPPdIT4kPjUh6qRofodJ2j9qE2fyRzcqfuwKL5YrUONSZWQ1115UKgR/rAgbMHmZEjXa9z1D68fPzp5W5VQPLjyZ/u/2MXveooEI17zZvprA0eMQB6BDoJtbnV5k18v7sZR7TXplZAsjsEtj+a8M8/rv/O3DJkZNDJZ1fp1UCfaR/MDIEegU6C6Zt0Q0+NiVoByW3JO/Rbkrbv3fdn5glmruOMN+fUlb5k2krf7onVoSuCHumVccR8IbuniRQWMIcpSYmnDujxlLZnv1OJkTGLPclrsoGd4FD6b/QPPNxH69YVQY90mNjFCT9dTGQaRzo08WwHsXxnNNNry6ksTr90Ti+vdK7vrCMPztCr/o7+3/+29ulxVYa6MYtt6m4BPQKdxLbkHXQYG8YRzZaT25mSdDUvK3rmCj27xplDJ196fo0pPQGfBEZ89hWzl83f0T/hy/+BHoHOIHjYRKYYhfrMgHHElCRm0vbutMP65LWR3n3aU7PhCIInzf5gZoiacRTwSSBFUafWbti4WmdCSNAjnSQ+NI6Z/RjkOkK8NxbNwiTQ/216WSKtvpaasmN3oh5c19LFnx89/Qu96igQ+Y+avn7T5w2No/73C28u/s70Yq3fHaGuSBL0SPcIj4w+n55Cr9obW245uR3NosaKTRHzhqpqP6U9/+vcT4d0/aK2792XejSJGcMeMjLo3z9FUxTFNI5M2NyPzJxY6S9rnkkoipJJa/3uCKFHoEO4fuIM0zjSv3K0miIucT3TazucdeG/xryn02KkNijEp9cQIkZqxtF/9fHjsOq92jJpLfQIaB7vAcMyS3KYxpFelqPVFG/6v8kcavt79uXP3lmko27a9yvjmaIT0OP1nRf/dtyykv6kt5txhSMtHHX0fkGPdOqDXz/byM3C3i/obTRLM6zctHLexPeZkvTjjaPxoTE6J0ZJh+pZRjYcwdsRs8nyzKGTr5Sp5sX80H64mnFEURTHw0QnrhT1/HUGcVj8EUYq9igHL7vh7t2nqEi7WbEpQqkw2H70B4m0imw5cDapIFKuK01HxIiZhG3MYmc8ukOWF80XX3uhmtvKQWjRqHH0wKhmCOwjoCniQ+O+T/yBaRy5eg2BGLWS//lm0YejZ9OrOZXFujIfScRnX6mJUUCP11etUdl3584coP9qxhV+0e9tYhwZWJkyjaOQyHD4a0Bjbtr65C3MLUjFbiuRW5aPcvCiV3VlPpIL+35VE6O9ab/R42M/nvxpgVwVqP63+zTimZb7Cpg7kfEUunKboEc6IEYbzu5ibgnxGGvq6YiWaSt2w92ZgaQDZw9q+XwkH034JzNmRMSIXt2+d9/ljKP06my7IeTqCkfwKYqqKSon27k8wWVFBfQIdIgYzRsazHW3hafWDtTmI8mpLL5+4ozWStJHE/6ZdFcVLnzDrK+aGH2/Mp5pHE228SBiFLRsqYWq3AjFtTFY8i+dGS6DeLaWEh4Zzc8u25aWxNwYFjAHvfuvQsTWlVnj7tOTiWeW5FAnzmz36vfBu7O05ySXLv789smTt14W0FscBSLX4Hoj9X/98gem6fQv5/EGHB4Ro42rY32kf9sZAmOj676igbpzg2AfaSMJC2JSDh+BGHUEpp6OzCTJzJKco98e1CoxSjq0mylGFEV5uI9mjoxdNF/M7OAfZGLnKXqNiBFFUaOyVV37Nf0orZJa2Ee6ZxblXr5z5nG62naIkQa9tnCKok6codNKzzxOT1gQow0T+ZJJrplbbDiC4YPe+v63tSrB+uRfx88coFcdhBaf93ureKQBEaNTazeYVqqcuGNKyTCdujsspVLZ2Ydksejlzj+6lptFW87uZY7apyjK3tgyZHiwHk973Xomjr/4hllSTkmulYnFS6OB/945/1V0/zpDkkQ8YdfW+V26+PPTSfuZ8SCKot4w6+saXM8yihLHXNl7OLOqiKyacYWr+71tOK4nEaMfY9d43uDTQ0M4HiZDov+hW7cY9pG2sHDcB3RcgybIdYSpp2PEGogRRVFUdvbH11RindR7wfN2y/S6NeLYGsPM374nq6S4LUVRXSJJi+aLj57+hdmvTzXoTaMoavueX0SpT2kxoigqxM6TFiOKooZmGtZK/y5Wy7Y0S7bz3HLmNkVRvc/lr/jXWNhHsI9aRXxo3LFLx5mj0ohZND1gStTm5WgfYhkV5ixlpoMSo2a+79RXcWOjZ67YfGk/c4edbCWRIbINfTT/UdPJQFmajatjza+XRV77ld4yy87LbOIg8arPyOqptRtML6rMq+TpPoV2quKQuiJJsI+6mMUTP9l365TaxhCPsVx326g1ECPac0nanFmstlEirWZOydsOxHtjc8bl0mZpJ1tJEZ99dWHfr2qTODY0i/4Wo4tFkXdV9VLMuAb88QNpMfoxdo3HVdWn/WE/O6YYURT11L8n/DXQ7MsQFn/uzDE1s0jEEy4InAOzSI2cklym5UgMJXtjy5Ge/q+45y0ntzM95c6RpI8nf3rrzp8Np5Md95o3PWSf9tH6PnkhSimMzKrX2TouYFp89Er6N96PTGqovxMgqwwFZyd46uiNhh51DQkLYvY0CF2TIbIwixpiZaL62tNeW05l8fnr56KoVx0306gklT59rnTvofH60x9P/vRyxlG1uDVFUY4CEV1ZjSlGnqfLygrKv3taL7AYMvSdTYxfep4uo7OxKYpKDvFteFyDct0IjECPusAsykq/ptajD7OoeYx6OjS63b1XP43sv6Ek7Ug/TKVTNxKT+w8fqyYTmlUiYxa7r6H1e58vUZu1kYhRTVH5judXH1eX0NsneU3elKjq/j+1doMFw8xKH+ZSaWpIUZT1/doKG36N6d+xWrOUe9Q7Htp/oxHP7jxiFyfkPXhw6dF1tbist62ri5/3urWfQ3eatyjVkiHmDQ2+9XJG8nFfTR2i0S5OiqJsOIKBtgN7jvZoh7kU8dlX+X/euvT8mlr3GW0WebiPZqYX0T6acbpCJq3dk5u+O1c1j0jwgAk/HPuGXt24OnbkHaH8Px38ufZWJyZ5K9lsq6S7lZxiauRIokfW92udjZ68P3sq9Ah69LdNlH7p3L2ip2oOGnmpon5cZW5uAcVpkbi54uO3zuVWFNmZWA1zHKxZMSJ8uTAuKSWRaY8w8TCyEfIMbexczYbYNaNNEZ99VXYt9/GT6y9lNQ2DRISAHq/3Hv+G2k6YSiSRVq+6d4R5Jh5GNiczLzDFyOeukKqrpcNG+xaMEVSy+Gdu1XEltBhR6O+HHjFR61SmQY++drL+X4l1Ny+evn8loyK3mZ85CkRGXING/6Q22qOtSkRR1N2K/OX1A9jGLHbwpNnrN/1tRH++/JuxT2X8GpUYXRg7sFYqqrh/Zf2a0Jjlvz+f4EhHjjwr7+uEcQQ96nAadQHsjS2DPMZghiKtJX71SbaNov/vKYcKbh0uvKORfRqz2EOsB7SoRI2KkQ1HMCZ4Bi1GMct/tzKXeaXeZ4aNSmtNezmXE90JPaNKaNIh4wh61NliFOQ6wt7CDkqk/cSuPpXrYzXij1t9sp5lVRZ+9/RCU05ci5Agke+sNxpGrNWUqFEx8jCyGTx1IlGxHbsTnxb2tKrNZ4rRbS+XHIlSnDCNPnM628j6fu3qj4boULNDjzqE8Mjo+2evMGclevVkYtDJfLXqaM6b9uZF5f7Hb1gUV9TIpRJZTU516aGCW827crQG8c2NDOwEDSNNh79e/1qhQd39crXtDcVoktdkOtq9Y3fiw8rXjJSlAcdv0D8otrc9bfoi4YtlZHXVsn1Fwapp062S7n7xdQj0qFvrUXxo3NYTu5ih6y4frgnaR1T47rpRHjWmrB65JT5/3rYobrzQooGVKWXAqu4hO6aU0DnTakR/8eUElkhYyFWWyWorXzb8QVrZ09XZx5sSo4hVXwt7jzJRFDHFSGZnldmr+MMVkbRgXTd2ocPYBuVK7tUTtFRBj7qjHsUuTtj4n1GaECM9YMfuxOfZpsQD6pFb4pl63y6nSLOHkEir//fJ2ctlOY2KUcSqry14g5769xRU1U7enWJY9bdzx+UJUtyr6dqPO3YnZr/s88JFQIsRdf78+jWhutXa0CNNIg6L/z7xB+YWNwt7/1ETUHtf1yHmCXnbjcurnDKfMSM47UZgbPS4Z8WyvdsqlXI1MTL1sGW/tBUZmZe72Zb3ZA+8mq12xKOeMqYtxgwbURTV69jDlXHv6Fw7Q4806aYdOHuQmesY4jF2U/J3eJn1xlBiGiAshcI6v8zt5hPHe7lt3RWXJ1D255/nSDL+fHDkwRnmnxwFosFeb9u7B9DiwlIo+t96OvxsvW4+uhokYdmn26qChtKrdhmVq5YM18VGhh5phoZdaaE+M9CPpmf8vO/g01sGOW/aN/xTj9ySEWk5Zo+fNfPf+S6mz3rUEB0hBfkL6yqYedveFo7ewYvy3uxbz8TOeKwmRmqF1tRi2DqUjQ096iQxgmWkxyz7dJuZff/cQcaN/tUuo7LyyUMZu44tLG4qlrxovvja+cPM1G2hoVGf8e+4TZlZz5urqu1/6wnTTePyBNlDFMzJHaMjfi3z60fHsCmKMjyc9vXaeTrattCjV6Vh+nWQ64gtJ7fjvdV7VbIyfa1wsA1TC9QQ5cqMbz5lbqmS5F9MT/wrL5u50dS+z9BPlorsHdTEaOquFIPqeuNv1WJGah1qFEWZ/n4zft1s3W1V6NErER8ax5w5Fl1p3ZBVy/ZJh/ST2LVcKuPByeSs3/fXSsqYG63dB/p+KmZzOKoXRKEYejH79fR60WsuT+C1N4y5pWGHmvHZTN3KNmoI6o20n/DI6OQTByBG3RwiAauW7WP1d6LVQQ2FXJ71+4G/Dv6itn3g3I/6jpnAFKOhF3Nev5nFqqtnFvFdTA8Zl3g1LUYURZml3BPruBjBPnolgodNZGZgLxs7D7OAwIkzZZnwrKzlBnwSYJLkPM5NS310+qiaWfTacL8BM94zsraxvl/Lq5Ky8golvPvvsoXyWxVqZpGyP19tmpCGFpnOjQuBHmkYtbrXCGADNT6ZFHnhr5MvqtVTug35gnfHLTEU9ZTLpZUGj0nM+8fYNd55pjXPJGpiVOJNjf20npsWFb67/J16M87qdIca/DUNEB8ad/wvVYeam4U9190WzQIITZWCpCjKUSAa9lbwV5v+i95ClMjjmbKGkjCVqNKL/aiPtdrssquW7dNjMYIetZPz6Sn08DQRT+g/akL0GmRgdzbisHh2Xllm3oOXtY0MBzMSGLnZOilszTohOT7is6+KLz7Myc+kKKqwpqxRJTJmsf0d/QM+CaRH+TeqRBQ9ECRqBXOuAjJqhJlnRFGU/R85r7lV640YwV9rp3HE7FNbOnEhaqp1GuGR0TYVgtKCgtSHN9SmZmkRe2PLQb36uzi7VQlYry5SEZ99VZNbS1FU4a0MtQnU1Ajo8bqls9u3e2LVbCI174zA8TA5zC1VG5QbHfFr/kRXtV/qetc+9EhjekSPC/G2dU1KTYZMdE6zn09Pya8ozql81eGsIp7QVGA4bcgElrFQweO0vkt0+959Ny7crXpaeTnj6EuFtNGS2GpKRBdgi/7iSzMl29ZA0P+ZYaNKZPCa6KptOT1Yn0ZtYJoeixH0qM3EzRXnlhRsSv4ubq7412vHUHC2c/yyJ1lZx+6c66D92xtb+vT1NBQIzW1sGt7NRfPFNXnF8tqalxVFzdtBTNeMlIJ8TcByNxTy5WyjKq5ax1lrlKhRMRLlynjX7n2h+1370KNXJWFBzNentlHIwO4sosQx7IwXP6U3aYGOcvBysOplbmPT8E+lBQWPi56rzSvVGm3qJRBRcqlUIauTK5oKBjXEhiMYPugtvrmRIUs5boCF1QsBu5RiTovWViVq2KmvHxmP0CONfaWPnEikh++jg7/DGzwkas+1Iw1nZHGzsLcxtXaw6iXo3bP1YaDwyGjRk5qcktyC8iJm1tirMMjETsQTvmZgNtDEboBJ2yakblSJln26zdLa8YWbecMxKDpaz6itdHH/GovF0hVJen7nLrOWiJ2FDSSj4/hiesT3Vw6qGy9Glu+NeHvJFnE7drhujZj5aREWV5W9LG+HAeUgtJjWc5ARh28vNLcRmLTtZeMJpB7cF0JpQZ30wxWfDKyvRGb2/auChlY19h+t79eSiUP0/r53sX2kQyaSq5MH/a2eNzQ4LnE9VKODWD516ba0emWkRTzh+15vfbZ/jcaPFR4ZbVvEKS4rLqooSXl4XSJVFwQzrnCgqZ23qDdFUYNNe4l4wjYJENfGoKxXHUVR9xU13L72zHyiHbsT76TVmPCNlbY9mqoWQFFU73P59MQhekV5hlQAAA0jSURBVA/yj1pFwoIYZsJRnbMZ2qTTxOiDYVOq7Uw/27iqIw7HtJsiVn1tVmNZaWYilFfaPS2yySulKKqtRhBFUXwX03IL6X1FDbevDS1AdDLRqmX7BDwDpW2Pkr4uNe+wmoowiXJlouyiEmnGCp0qgA37qDNgVjhCMLvjWDzxk+N/XWBK/7vB73VVtd/WD9zXIPrdfabt9pFOiJE4LJ5Zbs3V3gXC0RHEh8YxhwT+PX9v15UeJ6IQFb5bZPOa3IAvNeQ1NXxfw0o0e3C3fQbQv9Y248je2PLq3VRoh8aJXZywLXkH0zJaGDBT2+olRKz62rjGgcPhVQ7sXWvMaaYSWysxKFdaX32mkEpLZSW6W9RRf+wj7ae0tCTloaoLZtqQCWgTjRMeGX393BktFyOKopj1ZyNWfW1YbUmWDZWG/N69m4lJq9lBpjnlkoJndVzJ+jWh1DseeACgR61ly7Jvme8JJpjtCPjZZczBaOP7j9D+SlIJ3SnM3Gmw0QTNcy37Jr3s5+iFBtE4cXPFzA61INcRSDSFfQQaQRwWz8yXc3F2Q5tovIW/P7tL5cvwhKaejmgW6BFohNL7j+hle2NLDJ3VOOmX6o2SXRA4J2oNGhn+GmjAssjVzCKQQR5j0CaaZeG4D5hDycIC5kDxoUegcXjZpcxI9ozPZ6NNNEjcXDEzq8vb1hV9BQD+WuOIw+KZQdbJA8cOcEO/rCablxk2sje29PLxR7MA6FHjMOMaIp7wZR9DtIkGeX7nLrN5p46dvmID5q0D8NcaY1nkamZc4wOfKd9s+BLNokGYKabzfadiEk0APWoS0yeqGmBuFvZs+zq0iQb5Ys4qpJgC6FFrqZbW0Mtv9B38zvtz0CYa5Eq2yjia4DYSDQKgR20AkWwNEv/JWqYv7OCEYgkAetQsqQ9v0MvmxqZoEE2xY3fivpQD9KqPtcvSjeFoFgA9ahJxWDxzbGe1JXrWNMbdAynPK1Szp40aBmcNQI+ab5G8MnrZzcI+egMmwtaY0P92Q1VuLdjFd8m3n6FZAPSoOc5kXVZ9wF2Ho0E0xbM7d8pkqm41kyFOaBMAPWqDs6awRd1+zbBjd+L5h9fp1enDJjEL6QMAPYKz1nmUnM5i5hzJHBGVA9AjOGtdxO3Hf9HL/n0942P+B20CoEdw1rrGWUt5pHLWbHo6oE0A9Kiltsgvh7PWERScukvP+yriCWN+Xo02AdCjlpy1vy7CWesIsnLuM501NAiAHrVAxGdfMZ21EmsO2kRTMEfz9+vdDw0CoEctYPpcSi+7m9tv/CYGbaIREhbEMHvWtH8iIwA96nrKS1XjGIY7wqfoEGcNE0YB6FGr4HL49LKcpUSDaARxWDzTWXO1x2h+AD1qBUXlKvuIy0bwSDOkXzoHZw1Aj9rMuUeqz3gVT4AGeXUSFsQwSx3NHhqENgHNw1IqO9s3YbFY9HLnH72pN+frU9v+/ozzDbMYc2SDdjN68Gi6y9LNwv7PG3+iTQDso5apF3NFgowmUEt2D/R/G20CoEet4uwjxFw1/WDVH5mMGUQA9Ki1VNSpJhRBzFUjYGQygB4BbXTWMDIZQI9aS+ziBHq5t5ElGkTjzhpGJgPoUWvJe/CAXna07oMGgbMGoEddxqMilWcxuI8bGgTOGoAeaQWFtmgQOGsAetR13Ct6Si+jyPyrc+4vOGsAetQu1Kph4IF4dWftTimcNdBOuN38+nMKntHLWlINQxwWb1wuLS4rZm60NLPUicQo+bMX9HJ/SzhrAHrUFpjB7K7NzA6PjO6Rp7hwL405BpXJkcF/2JhaD+7jVmjL1lq/MqvgIb082tUXLxiAHrUThaALWiNurjg7/3FBedG9oqe059gomSU5mSU5Zx6ni3jC8usPnXs6LN8ZrW1tWFNXSy/3sLTCQwWgR7pB7OKEjBtXzzxOb+t/lEirD2ddoLIu/DrgWMjwYK3y4zgKVcGGwroq3GUAPdJ2wiOj+dllBzNONWUQ2Rtbvtlf5ewUVZQ8ePGUmdRDyKks/vrUtnPDLnn5+GtDpCZq5Vd/FatOskhWh3sNoEdaTcKCmOSzBxpVIiJDgt49G4pLeGT0hApBaUHBH39dzKmsF+q+mpd1L+mpsLiqy903q1xFmezv6zLlG/77p2jcbgA9aoOdwgweVwlYHX248usPUx6mq4nRKAcvT3cvBY/TTFEOZgA7dnHCg8zbh7MuMD24DWd33fDPdPUa0oWGEuZZA9Cj9mNTIWDaJh36JseHxiWfaMQsCvWZId4b26ZdEdmKD407n57C1NMzj9PPPE6v4Nd0Ve8bSveDV6Rb50OWFhTQyz4d+T2Pmyten7xFTYyCXEd8PPWjtooRTdTm5UmpyfOGBqtt371npzgsvkv8UJTuB7CPNIOhoKOSs6Nnrth8aT9zi5uFfaD/2xopmRiXuF602C7x1AFmUOnIiUTDUGXU5uVd5axhnjUA+0jrCI+M9h4wTE2M5g0N9gwcpcH6rSs2RVy9m8o0lHIqi49dOh4fGteZVwpnDcA+0l5iFyckJ6sHjMIC5nRQL1hc4npqKkXnEGSW5FSePVjzkVz8w2edcLH87DI4awD2kfaK0bbkHUwxsje27DgxoiWJ6SjlVBZvPv5TeGRndLofzDhFL2OeNQA90mox8rZ1nTp2eifkB205uT3IdQSzUEEnhLfVItmSPgZ4BgD0SCuImytWE6Mg1xFJqcmdNuHPlpPbpwway9xSev9Rhx5RLZKNGlIAeqQVLBz3wYazu9TEaMvJ7Z2tiYnrQzxUknT8rwsdGttGJBtAj7SOd/1DmDnTXSVGBK67Le21SaTVW0/s6iBJQtoRgB5pHfGhccyR+vbGliEeY7tKjCiKWrdGzIwrS6TV65O3JCyI6WhnDU8CgB51MbGLE7ae2MUUo+kBUzYlf9e1ZyXeGxsWMIe5Zd/lJM0eIjwymmkSwlkD0KOuFyNmAFvEE04PmNLJudFNsXxn9LKx8+jVnMri5VOXanD/agMA4awB6JEWiRHxWbREjAgRW1eOclC5UdvSkuLmdkj/F7NgEwDQo84mPjSuYdd+F8aMmsLTvV5YZ8PZXZqykpgDkgHQeT1isVg62nDv+oeoDdnXTjGiKCpq8/KPp37E3HIw45RG8raZadlCHtIgwauC8WvtYeG4D9TqXmutGBFIaac9ST8TAZVIq/nZZa+4T2ZPP4Wp1gD8tS4hbq6Y2akk4gm1XIxoSWLmbb96IInZ0x/kOgJTrQHokcYoqihpzc9iFyf8dDGRXrU3tlwQOEf7xYhQ52zGHNq24eyudkuSOCwePf1A3/RIqVR24dFFr9nRy2qp1U2JETOATfKMtKo3rXnWrREvCKyXkfTTxcTYxQnt2NXzO3eZooyefgD76FVZsSnC3tiSKTetFyOKonz6euqQGBGiNi9nJklKpNUXU8+8onGEnn4APdIMPU1Uc6iypfLWi1GQ64guz8BuH8t3RjMl6WpeljikbaEfdp4qFi7iCeucEckGmgH9ayoazaYhkxRpz0BZTUnShWFp9Nwke9OOUGEWrQ9IF1eW0stTBo2NQ4ERAPtII/gOG0WHeBtm5cQuTkg5fETPxIjgMGgovVwmq752+VzrnbVbz1WTLJnb2OAtApqC1fkRZWYOZNfGswneA4bRk3O4Wdh7Bo5at0YcHhl9/cSZhlNU64cYESImLdp5/Si9uvCNyTEH1rb4vxaO+4AWaG9b16TUZLxFAPaRxggZrpqZI7MkZ/eenT17O+/es1NNjEQ84bKx8/RGjCiKSjj0b29bV3p1//XjLSZtq0Wy+1rZ4/kB0CNNkmcld7No7r1ys7AP8Rg7cdp0/evVHuE3jlm27fqJM81Lklo3v45G9IHWgng2tW6NOJyiqMa8M6YHp5fXvnxtWNnDJ9vSkmjzkDpxJpyiGr3e8MjojOd/0avThkzAwwM0C+JHqpdN9KRmd9phZiWj+b5TC23Zel+gfvTg0UwtblSC1QJqIp4w68EtvD8AegQ0r8VqwXs1SWr4g46eSw7AXwPwWHOYjtviO3mGAmFVbfWt51lqalVoi8gjgH0EOtFKahT9DqiBrgVfOaCykjwDR7XY1QgxArCPQOdZSTYVgq0n6s1qSf2nmEGBSS3ECECPQGeTsCCmuOzvtPU6geG6X75EmwDoEQCgu4D4EQAAegQAANAjAAD0CAAAoEcAAOgRAABAjwAA0CMAAIAeAQCgRwAAAD0CAECPAAAAegQAgB4BAAD0CAAAPQIAAOgRAAB6BAAA0CMAAIAeAQCgRwAAAD0CAECPAAAAegQAgB4BAAD0CAAAPQIAAOgRAAB6BAAA0CMAAPQIAACgRwAA6BEAAECPAADQIwAAgB4BAKBHAAAAPQIAAOgRAAB6BAAA0CMAAPQIAACgRwAA6BEAAECPAADQIwAAgB4BAPQFLpqgQ2GxWPSyUqnsPtfbrS4W1wv7CACgd5LX+brOVFkAAIB9BACAfQQrCQDQBP8PtiNO5VsVHaQAAAAASUVORK5CYII=)
Drawing an elephant with four complex parameters
Jürgen Mayer
Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstr. 108, 01307 Dresden,
Germany
Khaled Khairy
European Molecular Biology Laboratory, Meyerhofstraße. 1, 69117 Heidelberg, Germany
Jonathon Howard
Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstr. 108, 01307 Dresden,
Germany
!Received 20 August 2008; accepted 5 October 2009"
We define four complex numbers representing the parameters needed to specify an elephantine
shape. The real and imaginary parts of these complex numbers are the coefficients of a Fourier
coordinate expansion, a powerful tool for reducing the data required to define shapes. ©
2010
American Association of Physics Teachers.
#DOI: 10.1119/1.3254017$
A turning point in Freeman Dyson’s life occurred during a
meeting in the Spring of 1953 when Enrico Fermi criticized
the complexity of Dyson’s model by quoting Johnny von
Neumann:
1
“With four parameters I can fit an elephant, and
with five I can make him wiggle his trunk.” Since then it has
become a well-known saying among physicists, but nobody
has successfully implemented it.
To parametrize an elephant, we note that its perimeter can
be described as a set of points !x!t",y!t"", where t is a pa-
rameter that can be interpreted as the elapsed time while
going along the path of the contour. If the speed is uniform,
t becomes the arc length. We expand x and y separately
2
as a
Fourier series
x!t" =
%
k=0
!
!A
k
x
cos!kt" + B
k
x
sin!kt"", !1"
y!t" =
%
k=0
!
!A
k
y
cos!kt" + B
k
y
sin!kt"", !2"
where A
k
x
, B
k
x
, A
k
y
, and B
k
y
are the expansion coefficients. The
lower indices k apply to the kth term in the expansion, and
the upper indices denote the x or y expansion, respectively.
Using this expansion of the x and y coordinates, we can
analyze shapes by tracing the boundary and calculating the
coefficients in the expansions !using standard methods from
Fourier analysis". By truncating the expansion, the shape is
smoothed. Truncation leads to a huge reduction in the infor-
mation necessary to express a certain shape compared to a
pixelated image, for example. Székely et al.
3
used this ap-
proach to segment magnetic resonance imaging data. A simi-
lar approach was used to analyze the shapes of red blood
cells,
4
with a spherical harmonics expansion serving as a 3D
generalization of the Fourier coordinate expansion.
The coefficients represent the best fit to the given shape in
the following sense. The k =0 component corresponds to the
center of mass of the perimeter. The k=1 component corre-
sponds to the best fit ellipse. The higher order components
trace out elliptical corrections analogous to Ptolemy’s
epicycles.
5
Visualization of the corresponding ellipses can be
found at Ref. 6.
We now use this tool to fit an elephant with four param-
eters. Wei
7
tried this task in 1975 using a least-squares Fou-
rier sine series but required about 30 terms. By analyzing the
picture in Fig. 1!a" and eliminating components with ampli-
tudes less than 10% of the maximum amplitude, we obtained
an approximate spectrum. The remaining amplitudes were
Fig. 1. !a" Outline of an elephant. !b" Three snapshots of the wiggling trunk.
648 648Am. J. Phys. 78 !6", June 2010 http://aapt.org/ajp © 2010 American Association of Physics Teachers
Downloaded 25 Sep 2013 to 131.211.208.19. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission