数据结构之二叉树(BinaryTree)

导读

  二叉树是一种很常见的数据结构,但要注意的是,二叉树并不是树的特殊情况,二叉树与树是两种不一样的数据结构。

目录

   一、 二叉树的定义

  二、二叉树为何不是特殊的树

  三、二叉树的五种基本形态

  四、二叉树相关术语

  五、二叉树的主要性质(6个)

  六、二叉树的存储结构(2种)

  七、二叉树的遍历算法(4种)

  八、二叉树的基本应用:二叉排序树、平衡二叉树、赫夫曼树及赫夫曼编码

一、二叉树的定义

  如果你知道树的定义(有限个结点组成的具有层次关系的集合),那么就很好理解二叉树了。定义:二叉树是n(n≥0)个结点的有限集,二叉树是每个结点最多有两个子树的树结构,它由一个根结点及左子树和右子树组成。(这里的左子树和右子树也是二叉树)。

  值得注意的是,二叉树和“度至多为2的有序树”几乎一样,但,二叉树不是树的特殊情形。具体分析如下

二、二叉树为何不是特殊的树

  1、二叉树与无序树不同

  二叉树的子树有左右之分,不能颠倒。无序树的子树无左右之分。

  2、二叉树与有序树也不同(关键)

  当有序树有两个子树时,确实可以看做一颗二叉树,但当只有一个子树时,就没有了左右之分,如图所示:

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" 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三、二叉树的五种基本状态

  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alt="" />

四、二叉树相关术语

  满二叉树:所有叶子结点全部集中在最后一层,这样的二叉树称为满二叉树。(注意:国内的定义是每一层的结点都达到最大值时才算是满二叉树;而国际定义为,不存在度为1的结点,即结点的度要么为2要么为0,这样的二叉树就称为满二叉树。这两种概念完全不同,既然在国内,我们就默认第一种定义就好)。

  完全二叉树:如果将一颗深度为K的二叉树按从上到下、从左到右的顺序进行编号,如果各结点的编号与深度为K的满二叉树相同位置的编号完全对应,那么这就是一颗完全二叉树。如图所示:

  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*s5la51OAKGodcrCwtK+qtwedisTsdyAGJLt26jp84AQmbw664PcgLaYvDaXe4kHA5nBq2eUQ4wr8qDDi2+OTlu9we0M8Fh8gfyIE0q9VOsZbIDddBEbmcHk11uOyo4+LFiytVqgQiUmGw0W5FgVQ3GXROSJH+JVb7/wGnAJLZSGeSKhjCW7CLtwCXLl2Kjo4+cuRIJpXAkb45ZMoqgGwA0A9sAvlEa4seAggAgt54zQZzFYfhP479YPKUx59ojgPQvdI8CvQYMS/tg4VxqlAqJNGRwAEin7sLeBeomKJ4tUw4G7VWrRrfffctro5qma0m/GJBVxCKxpoNI4OiimppToeoOYoNZWSF5B28ZB+gE8IKCIMpbSasBwRiMsIFkDHBAuvx5JNPDhs2DHsRs5rMVq6ow+n1zThX6j7S98ALZiP4CsouZJuYcD2iUL6k63GKCz1AMMiebkjbf2Tfz2t/Wb121W/rNx49fMKUZr7BKLGwpbTY4A1sSML3OFw0VCEyvg0ooL/IKjmZZs4BN3sHl1s5f/HC7LlzHm/2WMmYqNBcOQtH5C9XrkyhQoXC8oXHlCwdW77ivv0HqRjkcUXxoCGoi8trAZhOMud/cVPoHwMdOfWBwxSwDSQ2WxwoBxcF/g5Wxuk0Llu2sPfz3Rs+2qB0hbJVatUICs1dpEjRYUOGL/5igd1oJtXNuHPENb9n3ki+fwVxDMrPIwFumCSPWrFc2V9+/hG1MKTrWZFQJkQhomYa2p59P35FBpQVSxligf2VanwzEN+gXTNCB23fgf2FCkcggSiHMkQAbrPDFiOBBVvoD/TyqC6bFYVzO+xiy1+Nne9ye1DdqoPCUBGm2GwOi8Ums4KFlbli0RvTYY5xDhpr3LhxrVq1wilYnA6cgsJSxMNbAJbALeRwC0gFkPcTmWxyVfIY29nSdejQ4f3330dCcp2DZt8Q557xKoA7CApIBP9MJuKAUFLimMViEgntyJFjc+d8/kzPPnVqNyoXW7loqbK6nMFt2rUfMWL477+ucRrTYYkocFA9BgNCihuaZbUjQy/T7iZwCXCSwh3oGn4R6xw+fDA2tqxenybiNwp3qAtBWi0KZqMeDhaOdZBKTU2ndd8Fe9gIZDcg3AGQQFNC08Wom0IeCx1GxWm3USsnJyfXqFHj008/5bomJadyjW12r5UGYHJZozm3AACWEugNFwOHgjWL2bhi6ZKpkydobuexowcnTnivXv3aRYoWqla7ast2LVs91bpNqydrV6tTPDKmfu0GH06aeunCVRDWYvIaWJa/wWQ0mk2sNf8CoHhamncsQ3RUbsSpaMHNmzd36tI5tkL5vv1eWrd+7aWLZz0KmhisoCkTcJfLln9bsVKVyKJRjRo/8vvvm3GWzWKlQEd0+9nFSNuO/KULuC3cakRHFhfwvliFLok0OeOd23e0bv54mdLFe3TvNO+LuRu3/n7o2NEez/bu2vOZ7dt3zpwxa+jLA/PnzdP+qXb8GVuASXzrQOFOgbuDJEmfDgGuqzhdTrtj1c+/PNyosVFvYAnKmvrKEQnsldESgNP5eN88MwG7EeVwYKo3GmrWrrVqzWrQiFfNVgsS0Geni27zga8OrDhsKBNKIeT7v5bbg9cKuyg0pjqiZGaTHZ1j7kbbbVRZ5IpwHpY1OTXp+PHjcXFxqHWnTp26du3KMYeMMFB9JLj6/8UAJSYm8nihr1YA8kLYLgcU58yZ06RJE9+mlLxncKl88wkgu4CsWQax2ciAqyYTFNM9f/7nFStWjI2t0L/foMWLlh48cOzosdOxlau/+9741b+unzx5Yqtmj5UvHTN84MD4y5c5B5tdMZmpR4GuqogU7joluFftu3Cn4plnnhk/fjwfg/LQrWrNA32nVRQrw/6h44HuBxJ/IS8NRVHoxpXKLoDJlTrrA1X0LSkFpb5+/fqpU6dMJtO5c+eKFi3666+/si7jTy/iVIA7kyLptbR/l+2DCMiHBCW8CSXS4JtUj8t55MD+9k+2qVSx/MAB/Y8cOZRuSDNYjQqxjHyKy+q0Ge1H9h8e+PKgcmVi+/cfcO0azZqFbYfv4aywwG2hh88X+v8DLpETMM/4ZSPMtjolJaV///6VKlVa/PVXJos5TU+lJX/kxpEUAbNzwfmpafrK1Wv16vNCteo1O3XumpCQQI7A5TAavM4X5l26m3/nd24V6DDbUHQuPTQSV0exYEpatmxds2bNH75fmZQYj0OMRj1qcvzkiWJRxS9eusJnWQx6m9X8zZKlzZs379y5M39CnB+A4gzvNnAV9prQnNTUVE57L+3RXnzxxfPnz0PxNm7ciFDsq6++2rJlC7aw9KGTUtnYj/LoAk6XE5z/FogYePAGy+fzv6jXoD6vcoiTbtBv27F99Zp1P/+yesNvv584dZKOQ6HcLiwmcbMP4Rdt/KflNgGzm65PxiXgP5KSkmiTyIdiHcHRP//8c/iIV5o89mh4/rAcQbqqVatGRUWFh4cXKlSodOnSTz755LVr1+gswQdIgIXAW2T36/8PhJIAp5EPpI1fuSUTsBeBV/HixdEuuDrbROiA1ziKdpFpTgSQvUA3pASbmI2iX6H++eee2Niyzz77DLqD2IheIhhrsypvjHqnd9+XoMbQJtpus8ZfvTJlwoTIQhFvv/kO91ORC/oOsNoWm9nuvG1+/iuoUAQYG2ExqDJwzLASiHWSk5Nh935ZvWrFym/xu+/AfvQi+Bxpr1mZoFbM4Rv6la3o7GsKYORRcSTYVH799dc9evSAMcmXL1/JkiWLFStWsGDBXLlylS1bVqfTffLJJ2lpaWycWW6UhQBMruzbBMAAKeyKmPMAg26zq4p7zNvvVCxX9svPv6DeMsIacbsHsbRVBDHecBmEwq9HS09NmzTpQzTB1KlTOTeoEqKhlDQaVKPjbxMwutLuwlyDvZyG3UbvdNiwYWSivR1pHGCmjoDDyqM1bLHx51LUA0eOI9aJT0iaMHEyujc7dmwThSZFYHWQ9l96n9vC/56MDKr5Zr3km6XValSfPn26xWLiOS5Ou4MllJSUcvz4SXStUVvhuqigAPzrrFmzKleu/MMPP3BZmdZ3FZAL6568llSh5JS0devWd+rUBe0Np16vXr2uXbv2ee7ZRg3rV6wQW7ZMqSaPPIr4DDlA01ARWX2kZUP+E1A9OZwzcPAgmDakt2zb2u/l/jGlSuYrkL/xIw8/3alj+6c7NHmsadnYcrlzhTZ7/ImFC74Ug3Vy1E5k9LfLbUN0D8XUAV4XlaCMVq1ag+4y2mXKlCmbN/+enp6KY7iC+EV8s3DhwqCgoIjCkR2e7nTm7HmojC84Zv0X4LBGtoucwgXs27dv4sSJrVu3joiIgCnMkydPWFgYylC9evVBgwatWbOGzwVQQjQQ4EtO33QA2QOC1Q6HCwvWoKQffPBedHSxDRt+ZTZKD4qQ6OyZi9fjE1kPsIsnvLhsdpfDOaD/wIfq1Ltw4ZKk070Z0WF9kbzjbhJU48svv4RhKVGiRI0aNdDTQ7eqVatW2BJTvETJmOID+r+8f99esJe1ks8CEJ/xVAlWtWzHZ1RE6jX6lnAT6C+1a//04q+WwID4ajrqjt7L0KFDQ0NDSxSP+ujDSQY9fRYeQAjIUuV72ffAWWQj8J1QJOCXkxISWzRr3rfP8ylJyaC726XYrd67JawjIBJ8NP6gKXQPkVhFvUr4tbZt24KQ3P2WCw6ia9wmeCxHr/e6V7TXli1b0DsVd3J4npzqdNoRxFLxcQksqgcF4wgJP1YbujJafHIaftHY23ZsL1Ou9Lr1a+G2UE2pHcg5Q91uu5y3CnR8g3SIBr+ff/5ZjVrVt+/cQiUW4kYx3S7VahYzP7BBFB2ixH+zw2KwUuWZqadOnapWrRrcGB1xryBlJKOcRYu/LhdboWOnLl99vTQhIUHYGhoPsHAzaKo+PfW39RtatWiJCGD8+PHcpZDTR1JSUvDrK5lMoIqLGBkLeLN67ZqiUcUaNm40/ZMZ5y9ewF5inEqxjBAV8fXnH38CWUOCgseNGWu3kiRvNahzmzCZUHIVUR+CT7CEq3Px4uWHH360RYsWv//+O+8VdVdsdpoYwccAOP74yRNR0SVee31U4SJF3x091mAwcWsyH/4F4bghZGzO/Vps3LBhQ506dWJiYiDz9evXo2nQdjCUjRs3hsU8evQotnfr1g19wcmTJ1++fJnyygDKyRkGkP0gBhcBdJCgVt27d+/bt69RzF212+kD+7yLZ/A4nXSooOsNIEJC+ytO98oV31aILX/ixAkQhk0QOhveg+4muGzo5uEXhenb98XixWPA1Y0bN3rHUMVYhbeP53LEXbsyY/rHtWpWf/jhRj///KNQPa8e4QhpHLDwra7sAraNAIzqL7/8Avv5zDPPXLkah4pYrHa7CGRhW1jlofssEHgEdC+HDR1cNLLwzz/9wFMF+JMvADs2aZECQKCDBQlEjdWqVJ054xP2C6oi4h/mDdlnG42DEohdfMeA01hc9OiTddKkSfUa1DfB85lNYBrOSzfciET/n2APwIrJXWi0Xd26dXfu3AnyI1LhQAe8poUeHVChz95yqnCsJrPFgSMsDprMa0VYJvYcOnIwukTR4yePUO5kAbyK8O/uWwH/GOiAhZy7ZOSyZctiY8smJcehRh7oo+YBd0kTRaFdVqeQoUdMN1MR5Yiaka7C6EDPYcXgHeG3ZsyYIa5wd8EaAqDwLB14x+o1azRv3WbfoaPYZxNxqIB4QlVTjYZ0nm/LYyqHDx8dMGBQ6dKl+W2e8j6xzPlvwS2IJS7+evOWLerWe+jcuXMiIFAVBLFirkxG2//lLhioicsVLhy5a9cfPOJCkNnJ5fYhwzIO+1avXo2O5rKl3/CAHE80Vlw2G0WlaDGedExI1xux/6ef19Rt0Nhsd73Q/+WGjR5GlzotjfpeLDQ+8rYAXnFJOE66dOkS+hb169dHrINVNBZ/rfPChQtly5bFXm4+kAcnwoehc4yQCLXALmwHYAflSE8A2QtmE423M+Gfe+55RDns1XwbFARgEwTVcznBHEVMVaZnBsWYjlctTAbjxt/Ww2smJyUgQpLb7ypohk3GU6iLF39dpky5N99823fKv1Fvwq94dEOjboymWi0GtwJKK+s3rKnfoM7TT7dPSkowmPT8SDAWHAqdxJK9Ah32F2i4l156Ca6OP82hiCc85CA1EtJpiQEeMoMDB/QfN3b0wQP76j1UZ8CAAbyXjQy0nq1EAAwxTqmkpaU88sgjH3/8MbbYrS6iCz1YY+aEw+aNJCBq4XEgcFrcqkM8m0IjnVhS0pJHvfVm6yfbcNPwcrsQTw1TfO9d17TiJUrOX7CQFZbbV7AdB7ishlQKdGgbTvQWEj/MdjvUGaywmsWqevjEofD8eeAFkAv8BZsFJk9G5reBfwx0mF6Su7t370aEfvnyRcTrFmsaZCgKSYvC469YnMLw0EQ7ulNiEDNsSfI+xbp27VqZMmWQm3f9boI7BxygrFq1Kioqavm3K1AelA2/bERkzJHhtlV5J46HCbZt2xYbGztv3jxs4WEM/v0ncGi858+9FSpVnDHzE645DDTHthm3kCjEFs8j0O0gfsCSnrwgr38lMrLY9OmfiPMyROy73D64wBxbfPXVV+XKlaMXmqke8fAeFcZihsVBYRTBSNqC2AiNjqsZLFYIKDndiBWbS12ydEWp0hR88Kg7PZB1++DhMQ7y1qxZU6xYsQULFnA0wwNsnAAuXryYye1xlHn06NGKFStOmDBBznhg/AsFCCDLwd583Lj327d/GglWWKEyNMzOxCCWEo1BTrKYUB+rjTqCRhsiCM0O3RLHqE7bz99/W6FsKaRNJgvc6l0HrDwstEcb+eqoatVqXL+eIO7de9iOUz+b1ZYXoVysa4rbju6hxWqYN+/TmJjiFy9fMFmoX4HFKawDaidcQfYAay7aqGvXrv3794faesdu0aAWeoAZC7/CA5A9Ex5mYNsLe4guVp8+feTXrb3HwGhmxEYPPFQRDSsDB748bNgQrPP0NSwuh4glVc1qFv7LozktDghVODjiGw7hV43IQMdqp/tW7Tq0n/7JDKfiAm3FSxluEyA4h7ECr78+asjQ4byGVhPtq6DvDKZrHhTMpUFfWQlwoqrZHW6rk2y6TfFQKcWCVZemGKz6j6d/9MILL/i6AKbZnQx02KMgd/AMKF269KZNm0QBcSUQl9w5jqArYhtSVFh6QJqGp6hmGvxquls+XkDgEu/fv79EiRIoMYorSXw3qMyXA7777ruyZcuePHkShYVhZFHanSQyHmKheeAoNt2hpDajsWgxos7ihLutXbu2HIiSReUAQgod25HGyoaNv5UpV3bbju1IY8El0BFFziLwgzLDjpOUXDYkKNDhlnbCtgmriLjnkUebvv32u8iLZyEoTpf37YtYbhMcazNLEFUgyrwedxXXFTGKaCyx2M0G/MJPYBeP6KBpcDVuWI618Yv0L6vWoPkoiPTGiFRxZgsjwzP9I5AzH79o0aJSpUpBvLwK4UnZEucyenJyIxJyIw5+5ZVX6tevz+fyMfLIALILeIB97959MTGlaCDEZ6MYyEGCbvCjbZGgN4WQuXRQJACVgRN10y/2Cc2A8rqwvDps8Esv9sX67avLrcDsYlMLhWLFh81wOtS+z/fr2qWn9/WbZPq91t8p7kTTFhe91QK/Qu/IzvDbHLDAda39dU3BiELHThzHsbBLqDMWhDskBT+DVFX+lfrIFua5557jbwMzcACOQyV9Qxzxn8Dn8iE8lE6zSVQVsc7zzz/PxwAQO1/uQYM0pBAay4r9yO+b1leqVMHhsMEcWq00IMqOy2nzDpY4zPyOEpxBtxEyXm1AkY3dCd9NacQ0OMRqtyWlJFeqUvn02TPiQcXbBg9VYjGZTPA1kUWjzl+4IjYwWGdBfqitUF70XsTNH+rmo5PgJA1HpwCBDkI1bMMi+A+9cLrc9lq1au3YsQMZSY2TlLst3GqODnMX+Oijj/r16wfCCYsDPXfA+YrSgKZCoFhgBRBVmtLh0E0mg8XtMSEUYBuU4cCY5Xq9/p133nnzzTdliaV/YiNypwCdRM579+4tWbLk1atXkTlsD8osIgqUisdXRMCBAtoRSWREph7NCsGLSvLdR7ohWq3a0qVLuaicMxJcBfRdpKwOHTlcrnzs/oMHeGgnOTWFBWS3WTwq22SKKtxOyAaneONFu8vbK7XZFYvViT5QgwaN5s37wmw02SxWKpVYHLb/EUP8E2w2x7Vr16Kiog4dOoDC8Mg5lpSEONTd44JiKDQ0lxHtoYKQESyuyU49Zl4sML2alqI3LVm6rGHDhjhMDEp5AVGwNP6nVeKxpV9++QXRJ9+lYmLIHDKBM5Qk4Z4ijkQ+/MEjWAQUGOADAsheQFjzxBPNf/rpF7vdKbmTYQqIjWh8u8NsMqeT8VEtmgJVJfuTYCAmGVwU6+A8umnucXnsRos+5aG6tfftO0B6focAvvkSmxnLnBw75oM2relVv/A6dAjKi184E9FLoTdjoc+ErhS4zcrlUeVjvXLq8e49f5QsXepq3DWksYUfmfHPW1fSnjOQ5tVZs2Y1b94cCQiHdRyAVqI6nGahwVTy8Wwz0V0Uq2p6Kt2rYu/epEmT2bNn8178PphgcQHMPYBvCDRp2vjHH78XfQBCaoqY0MmswzbWGMidPBqN38CmM6nwi4XfdcLuCb+g4vRPZjz7XG/ee9sQp1G4o2lvvPHmG6PewgboHX6hwvRmAbg5j8NlTtFcxrT4ixVKlw7OGZJDF6zTBefLXzgsf2GdLqRIsRg4F7hcHI2MUAnx3kyUUJk/f37Xrl2ROXMGQpDp28L/uHUFLoJ58oOUIqKkBeITpaGF6oTui8OqWdPJBim2L7/8UpczdOA7E3jSBwrnaxeA8+fPlytXDsEHr/qGrpy4I0BuKD+8+9atW739MDfHZxAiaofCgAMwQDSk5nEi3gSRvBWyOmi3U4wLMs6ePVugQIHr168jT7CI5SOrBiBhs9lq13noh19WwaThRF6o3YmUNJZDQyZuRBUupwURoR1BFg7QW7zBBMIdHMdnpaXpS5QoefTwEawg3BFFxk666G0BWSliAgRsx7Rp05CDuGPFYQ0CbeoB04JYh576o0AH4QvVUcx58xYMkV9G15lL2KpVq09mUG58FcBXFLcA35g4efJkZGQkaMDGDoA8WaR/C1+GgEW4FsCr7dq1e/vtt3lvANkRq1ateuih+pzOGICk28aCD7Q4XfCaZHYc1lTNlKS5LfPmzNTlCJ408zO4wUQr+onETMFqcBiK7Fow77Mn27YjitwhSKIyJAO/Xfk9VF6vN/LrcAB+SQQV2mgQwQ10SkH3j6ZOUJeaXhMIJZILSk43iFVt3ufzGzRqiDAI+SIAQlb+GbuzGZfayonExMQ8efL4ftZQTg2kRkSVqNLcoAS2FbQ5YwFknnFxcUWLFuUXW/AMhAcQkMZNBFC3b9tSu1Y1HtrBuqKo9GZt6gPDrtOIjj4llXwZvTTcYU5PTk1P+3zRIl1Q8OtvvY280oz0YkBqCRGL8GKymKOKR1+8eJGvcXtA7C6e7YKHLVo06tz5y8jc5lIdYoBAFBLMN2i2NE01r/9pRZBOlzs0PDRXOOIbnS6Ul/cmfmRT6I4BAgucLkqFE5EDvbIhOjr6ypUrzA12BP9CL241GZmz/uyzz7p3757haYTeZoxDIEUXxArE6jRoitGRcOHwri0FCxbUheYbMWmOgbpgBC4Z8pS+sEePHgsWLGBjQTZDgHfdEXBuCAYnTZqEBIcmsFZiHI+mZXlNpzmNxtPIProQftAzb2gnp+ZUNYONXDsIgTLjXKg3LPJTTz0lnwjgS8gbWDhm/MQJfV94iZuKRwIp4X3HqyJGdFwWY6oYx3NoblhkxeIgs4ElPsWIE7FY0JvD5TVtx45d1atWk2ODTnp3iDAZtwMcbne40V1+/PHHsUr1oDeFQw0Ql8EiU5Tjthgp7lFdbrvZ7bCKW2x0IgqTZoIwxD0C0W9GOWl6vEofaq1UsXxqShJqzcApLGQkMnmFTICsGjVqxK+RRJoPZmEykJZZMWH4F0dK64ljuNeIw8qXL3/w4MGMMYAAshlatGjx/fc/clq0uTfcgWbxmKvdAQ1C4zoUe6rmNu769cfcsJc5gl9770M9zDS8rNnpAClBT0Q5DqPdkAz7G1Oy7PnL3ldA/XcwGwE5VgG+GQyG4iVKnjp9FqsgJEwEEdWjiTeakKm0m/TQL9VqImUXH6yATrFCoWKoZEJKOmu9UHGtU5fO02ZM5/wBaS39ChzoQEOhj6y8QLdu3b744gs2hvK5DdpNohBxHv7IsKguh/fBK3Q7U1LTUWs4RYebhrQtVjs/Z4fz5s2bx115SN7XODxQ4E6dd4Wgdu/W5euvvnQ46L1NWE9Jgf/yssdisjpo+F+xpiVrKvhmgZc5fOSYLjg3oop3xnyQqreAaYmpeuYbf4OIR3peHjjg/fff52vcBui6FOggsWnTpvr1GmMDmpLzB6jFFRAAhTG7DXEtH30oh04XHJKHopwcuXIEh+mC80aVjF316ybSc6EIUBss8ABQIyzY0LNnz/nz57McfKLn28M/BjrMZuQO175s2TKkU1PhoUXFRJ8DZeKS0X/I1JmsuVPt109BqISg8LdnLL1spZEAzof+iWw5vXnz5pYtW8pyg9kcDN1BHDp0CMEgElLx6Ial956RCzGG2w5Pb3OaYBZpUAexsdWKsJLqZXRq0EUYV6zK4VOUtkGDBlu3boWxk4YPgD3CFqhoTKmSScmpJhvdkOZFDD7jSDHh16OoDiIfLx47bUFIA2OWZnLgOCwIynFFnIgOIqL1bl26zv/8C/GGCRI7DcaQ8G4D/LaCylWqbd2+TRgRFfGWm17CDSE4FJvBmp5YrkRkLhFa5wvJmTckZ+5QxNpATl3OECjJ96s3mBQSRbqVOIHiWUXn9eX+L330IQWRgLR3bJpv3ZSLFy8GqeAnuPXluQzQI5Npk83HoQxEzSfK03///fd69eplyieAbAG9Xl+4cGFoP9KsUnKmDiB6riCdy2bX2xzQAnP8yb1FQ3TFCoQj0Hlj/MdGqCooIQ6iqF0xaw6oFdREffGlAXM+W8D5/HdIQvoGHxMmTBg0ZDCPwUA/sUWM3VLIRTeFqTvhcpnTVJtB2HoEaharC4XT0mzU6aEulyh5qsGMk+OuJ6AThag9IR7nyi+u+B1Y0SAQGHN2E6dPn46JifHtbWO7sJCquC1OcqBwx6OIh+aoUug/w8LkL1A4OHeY3kwvaM94eMhrb41GY9myZc+epSDyAVRt5ht7GTaJSKDPHFkkIj0tiUd0cAQW/JPfUSEh05wYkM2kOVLPHd8PCetyILDIM+HDmUw2i51aCIvZTrdHxWQd9dSZk+XLl+OmuQ3Q5d1i/pn21ltvjf9gMjakm8jnIwEO2G0mUkaEB470+LP7e3Vqk5CQwFf3Fka5ca8AC7aLKIenuZHuw0v8+OOPPXr0YKfwr4OEW83RYUeSN29e6LaXvt4HkkU1ICNRMooHPEbNGa9Zr1QpGlIsTBcSEqoLKTR80kJYJluG6FglAG5CsDkqKkq+ZwL5U/183Nt/BLLq16/ftGnTpGES2oLSuMzmFKspBUUDIdzWtIeql4ePD9bpCoTlDQvLRx4/R1iugjH7TiVAcWnwShSPc/jll18aN26MNOQu1Y/3vvvuuwMGDeSHQfh15mwBcay3W0OGD61uR4DlssIc2+bN/USXE5fLE1O20oWriUYbhUU43UyfwyIcOXS4TKnSyEGfjigThWdzehuw2ZVz5y9XrFSN35FAjxfSaJZY0MtUrOkJV2IiC3Cgg1/IIXdoEOLusPD8efMX0uUKP3ruKp9gUak1UTwUwWjUnzp2tHKlWPHE7I34lTlzC0BoVatW3b9/PxKSEr70ZZX2xddff42wa/Dgwd71DPBZaF9cun79+uKdQAFkM2zYsKFp06acvvFWBa+5IMK7VcQDUERQz5R4/WTDCsUKCKKiU/jG+OkG9FDdWpqYLA9yqbZUsqpguOJat/a3FmLqzB0Bk036crAUv6VKlbp8laZeQrnEYLuquMlmkKZjcdvS4i9XLF2sUN6cBXLr0AOkcfsCkbqc4dGxNc7FpUGnYJvg5HGCI2N6Emz6vM/mIiv6+B31KsVWfwI0LpOSjh07dsSIEUjI7Rm2EeWnUI/snmL3IMrxKE0efZhaT5czT97wJctXGqxOvcUBOZDDY8+S8XDDK6+88sDelWZJslGV1vXEiWNVKlfMCBZVm51eN2x3gI5seFWHVYTUHrM9/ZKmplWvUAIWPVd4lE4XPvq9qWa7996QwUxOCn84HS0knuRS8+bNLd5fdTvA+eh+23FF7cknn/zpx9VweMgZi0thJijkZdD3sCTuWLvi9aEv4Ay0tclOgT6inBQTNT0SFNSgMCAAakrZihu+5DTVw4cPV69eXToLwDf9/8StAh3g0KFD1apVY9oBPL2OZCOKhSKKC0LEek2NH/9Kj6lv9y8fFU6DAeExA95fkIBmECcCMhNuMzRkzZo19+zZ47vxX1Tgn4AQCmYIzc/X5XDHTh/iRlgGoqDMFrshfvFn0+Hgc+fQ5QkmMyQcfWjeiJKjxk1HtwIH2YXCSqqh2MWKFePbmTzKmnFTT0Pcdj0hHgdBbfGLlsavw+UU7zejB1+xzXunzGPr2r4ljHW+vCGw1wu/+UFvo3lY/HATigsKIlRCnm6X8lCdurt37UAOdGft9kd0cPjQYa+++dZoPs9oQvAJK4TMHW7q+9rmzfwIEggP0hUICYItpvrnypkvTDRijpDuz71kdlMjYmG7DB0RWVF5qlWtuPcPbwty28mw8p+AcOTRRx+VDS3epXHDPkLIMg2g+Xbs2IFWCQkJmT9/Pr9XHg3Ktw/i4+PFUTTS8+WXX7744osy9AwguwDdg/feew8J1iNSMrpZTPTg0RGXYrVYqcekN8Z9Mm3szHGvlgjVFQ7LrcuRa+yMz9FPShcLaGeDlVctqjmJxu3dzuSk9EJFaED3joCZyeRk9v7www+PPfYYPAQv4nMT8D3QLEURk4o8TvPP3y7hLgQvZGHQvc6Z//X3PiYD5BYdDqH1qDfZC03bt/fPhg/VpfvU9IQEuRB/AxTQ9zYx0rDkFy5c4E4OerBoygwthqtwaHaDaiG7d+3i2by5gkKCcxYqVOCbb5ajZlx3tB2y0zsoAbPJ58KSnD9/vnLlyg/mHB0WghQFfsHA779f2euZHm7FrtAkX9VssbGXyeAIIgPEMoh1jJon7eVnn3z3jUE5coaGFSqt0+Uf+dYEiBqLyUp6hYVZJ86lWaS1alfbs+c2X/tC55MjQKJWrVq7du7FBm/m3k6LothIKzVnWvc2j0AFdDlzoG//8BOtLyVSoM8LOjEc6PA5ItsbgU5CQkKhQoVk/PDvgoT/MRn5559/fuqpp5C4cbOGy0JFwT9swVVRVMuyhbOnj30l9eS2mDy64JxBulxF+437An4J1kvcvsk4z2eazjPPPLN06VJsQR3wC/D2O4K1a9e2aNGCPaIPYDfNFMCoNsWQDKr06dYOrj0kpy40WJcDxigsP/pcuqCwLftOIVqxUwt6wbqNQr722msfffQR0ix6bIGGIyJE1MmTnRE1czN7x7GRJAk4PPY0zW2+fu5onjyhuqCc+P3666+xI91KtEW3Bmm92fvOCYDctuqZ+tGU4UOHYZM3yrxN4IyWrdqsXrNOnMrtBVJhcZA/UOyj33ytW8f23qdCcEWPZk5P1hypz3Ztq8sdvmHfKbo7IAZyjCbvSyDFYxRUr4EvD5o3bx6HF778uwUXhw8fPnv2TJhC0eBUKMlgKis0TkzLQAlttvSkpCtFIwqEhobqcoS+9f4kHEcn4A+dEHEuXxqyMVtN4eF55U3GALILnn/+eQSpnOb4JiVJ3CKnG//oDpL9AFcNxqSVPyx9fUS/tNN/lMmjywNdDcrz0qgJKZqGIIje60UZOLwjOoqVHqa0uvLlj6DNdwhsAdidA506dfp2+QoYenqgkllJ+k6fMSflUkyq09C+XRuUNG9IDoQ7BXLlgKnRBYfr8kTsOHzSpAq7KYZz5EMP/BKv6CJRVy9c8UqAdNbvwHoHzYU0IJa8efMijY1eH3EDitucCqOnWRKO7vodtc8Vlj9nrgKXr1GPhd67IVQdvzYxBRCNzXKAAWGzUKRIEX5z4IMGNo9sSFna8JvTpk17beQIMdWJwPrC46B0s4WeLwHxjJojZcHsD+ZNezfu/JGY4ohywhFbv/fxFwYXPS8Nw4ngCMLlSfHiXcT0wu5ne/dYsnTRbfNNTGVBs5UuXfbMmXMoiveb/MiIHJaCLgBU8uLxPwuF6PLmRKAPDcivgyrkCA4NL7B+6w5UBgt0AQSgE/FHGeJEt8etstKBOWzwAamAt4X/MaKzePHiPn36SL8FF46LUJziSNdcaSRTxYIgfM+ew62f7o0iOs7sqpmfplPrQiOee3sG+ls4HoJEGb2/HhTfG4QOGTb0ww8/RGZQj79Tkv+EkSNHTpkyRQ63QG2IOBA++3hQJCnJeO102+aNk9LSUSNVsyqa1eyhuY0cn3kQEUHIolBSApAyB3+8hbURhZ81a9bAgQNRKWylmuKPZkfifMQTnIlFc8Rf272mAIQTFKYrXOaaxZNu96BXh1MciJZcdJcMiyizuENP88vMO7fvaNiQbpbR7Pp/AxqTTEvjp9wVC3q9dEEs9HRVemra6HfexYXoSyX0MXM0Dkpuc51eWzq3LvaRx05rWjwVHUW0a4rZ5aYo1eGkB/JRzy+/+ObZXvTGC5YDh7BMTW5NSIkJygcANWvX2PPnLuyHYRT9EqozxOV9jICEhhQumOa0X6xYNl9uUCkkty6kyOAJcw0KtRupAYJn8RpZRbgIiNDqMj/apNGWzYG7V9kMUKV169Zxx5QNJD2P7XFpNiMF4rTYXU7rnj/3NmvdFu1uOLatQi5dWBC6huEDx8+76NHAbOgsKR1skcfhtKBHqyIvaHypUmWSkpKYkJSzMAJI/GtTI+0JcihTpszl8+dAcYptvJEWAOtOCo0+S9L1MzUaNoJ3sdjd4LbbTKYAjIeRQcpBr06jN4iQ0tA0CzHMLNSq9zP9oFm4iNj4L4t698CeBpJkafz22/+xdx0AUhRZu3dnNufE7pJzEBHFgDmiYEIMiDnniGJAEVHMYlbARBYRxZzFgIKSUXJOm8Pk6enp6Z6e/r+vanZc4+963B13x6OZ7VBd4dUL36uurv7iiCOOwE5C2UFxfUdz6CMaPKu+6AzDl5ahpLX6bHkD7UnM9rkqwQDYZDSZ06ug9paeeBddzsxDzvPmzUuY3/8dAiclM2FUE/tjx44dOXKklF7+4BwkBzYQmsNPFYhJ39HwknmfXnjmiTG1rm7b2jYF+QjklfTC6x942iP8Gow8FCSGSNJk4Ap2h0OE1+ede9bMvwF0mp5s9OrVe+XK1fJM0yJSwAYQaQi7evetV2fIJ85JnPmZnqI4gXgA/JOUsU9N9lhUYUgFQRfbhXoJ8w5NEWAO98mcm7vdFtEfAh2ZF4DOhRdeiB3JXJzyUUtRlaAd2Gl7ttqGd91Pa44+4eyqIL82pq39rqsYpEXUcvuzrwPoQFNxV/NN9A7nQN162wi5iDVIgtZdSKeeeuqbb74p92HpZP0hDmG0IBaw3V47bE5+5pGHx9yJKqFFoWgoYpsuk3MbsbGNMEBgv+h33J6wcatXr+7atauUPJyUO5dffvmECRPQv1J0RCNxJyyCzmMO9Pi3/zT3gCIF+p5S1v2T9Q31JsUOhbBXJXMgfxzeEj4/alIco5bX7SkoKOLHX2ESmHXLKBDwFRTmhOA2RDliDgFaE195DzGB3xd/OwxSxZZwL/jZC8NbKcoNDz2+1bY3Cym0Tc023dAiaJURhi+BUtkfvPfVCcfD/cTlT+Ypu1KyJSGR8pKqqlk5mWKQ3xSzwtleloiLYtO5VCNwVDXQ5k3Xn/LYA9d2LshwKE4lrfV1j89ANSj25EwYQIdZ86VdvpZo2vpll144Yfzzog176D+GhgwZAj2lCEjxA0G0DJUDM9Gg6a+zY9qqFctPGHgiNEX1eaNbFnZOFhYzJf/y+1+qagLi9JfwmpxlT9lmmBuzszNzPB5Pwrb8ShpbRL8yUDDuWVlZMcidQZ2HVKJ6gmA5sAVt/6Z3Zzw/6qFHKLRQfj/1BWFWIEKTGIYB57QcMRWPn4lAC3QzwsfKlh595IFn77iVj/PQFqEYuxEJ3v7CDKH7zjvvPJqtptVl5Q6v0ck12IFNT95yfkESuizjhCvvhFNoBMfATrDPDDL0wr5YWQM8oodswlKgCy64YNKkSdKY/K+R5HNC8MAEuMvbb7+TrAU/RNSO31hE8AxnERtHjdVLvj938CB/7TbbClat/7HY6SzIzlecuTePmwigwwccuD2Ke4BydNUA6rENxPiWPfSMU2fPntZSeRMV4espRxx59DfffIszciJvwOOWwCsacttGsH2rLKCCzFQlNz8lKYn6i8NsYB9IRVLJpHcWIf6GDhDdsHURbFKncGLLli2lpaXIWcqYKLbF9IdAR+b4zjvvnHQSPZk8BFPgJwOmEfDW2FGXrVfaanWXzj3q/Dzv8wRDmxb3KxJAJyn7hkcnbzN+BjrwTnJHssaImpdefhmAlBwGkJ0aV49dQX369FmyZIncTzzAsmKaEYVhdHHEpNE99KQTUFUHR6Cy9trvMHfY9hi2lw/OgSgMX6M3Xl1BQEsJcJOcnCxPSriNnQEDBnz66acw1gAkbAkbibbA5IXphQ1k6b7rumEFilKUkXbQicMqxON52ZfesOHRkFG8NFFb3AuLAp5TiJOVJH4xh1xqqs1fppqaqqKiAuQjH+uKjXxGtSXneQiEGjYZYDIyCNkR9/nH989PU75ZuRlWaYtGEUSPiae/wP6wxfFpkt/NX3TQQQfjWnPb19wqyQ5NdOvOnTuzc3PEZVkfM47qcEpULexHHA9R8k987t5xj9zQWL28e0kuOyi300X3TqyB70PKGJEWkKCQGAAdfnkESjvu8YdvvukGZrWH/nPo3HPPff3119Fp8UEdiArsYyRo637DV0u4E9P69t5rx85KiktY9a/6ep88ziRTcsouvW/8NnhNEZnA7Is3DChO8nPKMDfpqWnQJimcEMuEHCZ2/jolLCzuRVabNm1q27atlFvIu8AulEx4F9uCDNfZxpaLT+yX7HQojmwYw4OPPAlGHA5FWAS7PuBFWCX1nf/5xzB1P9puRYzZr797zlA5jt7iev6zSRoNMEFyFcbw+eefv+GGGxJaj52frUHUb5tbQ5u+apuZSnSanvPCWx/+7NLgpOmrxQsu4oxkSCKkBN18882PPfZYc5Pyv0Nxn9vETPD8tddeA/LDvuRHJCxYBxbC7wQ5yq773Af06RGor+D8XytYveGndjk5WamZADpXixGdeulbOGSihawAkAhzF7b3yEP7z/vmC3HQAkL52CJG9Oxh577xxpt8fZL5Y7PoJqIRO0oV1gM14hFJ0OuvCWme1kU58LwIYQl0nGWd9ju5xqAW07yzMrplhdB4iBpOzJ0796ijjkJZCW/7N+j/eXT1448/du/eHTvgMhQPTEHZlHRwN+q19e1jrz7r3Q8+9YqRDDivymVf71eazjfMk7KuGTsJbhL+GXfJTXzeiTWVW9/99v3hhx+aD0s295f/IPXo0WPt2rXNM0QTLI5nuC29wo55XRUb2xbmp3CCYJYjuZAPMpXsNu37fPXDjzsbOU9K9Bh7PRFeIAOp52gffhMKifAOcPDjjz9Go8JiFQHeCGHiC3LiTatosHrNgg55CiCsMz1r8ntfN1CGrVgkpMO7C0CEfP2aId+3QneyR4kM+Up5fl5O0B9A6cy4hYSINj09FTuapv5KSmT9g8EgPEx8jXYzbEfqXJuWleQX79f/OGgFTJKMAwBwIoyzdT4JBiaK0TN9Oe/bw444HPfJuiH/5ogbJ2WJiS5es2bNvvsdiBvFkRXWIfqmFSXk09WQFUEhZiwSXPjtx5decKIZ3rZt/YIOuWkEOqnlI56f44MpxK0UQ3KJk5pwKB5dqWZw6pRJl158CQVrD/3n0B133PHkk09yJZUIfR9FRax1Jh5aqRFvze03XTPnrdm4FIRkxUzv6q975SgZTkSFBVfePxFRi1vIJ+NbiFPMhL6IfKy6mvrWZeVyCVBQQhrlvtxpEcm7pDVAEHXEEUfIpZChubByqANVHq496rbNqujGz/cuELOPk7OcOa2AdZSkXCW95Ivvlktl10yqtx613S5YeJtryDIC5gDnnDffHnrm2XIxod2NJBPQTdISIvwbP378NddcIy7+gtiVusv2LH7u9qFizZFcJbe1kpKtpKVzioaSfdyAs2EXaBpiIdPkpxw14bgTRgPGZPjw4f+aj0DvhiTNpuSG/F28ePE+++zDa4IQ4wl+UXrQMZCfB0aNnPHqC2KFBYQKrsZt6zoVFDiVZCWv/PZnp9RZQkrRgew73ae7UUAIcSL9jF1WXFBbs1NcbgHBd8gqjJ/w4lVXXUOgA9cgvvQp1AGKHEYMYsfUQMN2AXENn9/FldssvXWxkIvkVkp+r83uSKPRBHRiBDr0jCJzCNhNN90UL0+w4m/o758BHaAEeMHi4mK56D6HNMCimO0OiI9iWMHw2s9bo6KOVMVZgPqW5vBPHjaHQ3HmK47OSkb36oChx9cj/gXQicasrJxs+X3HhHfchUCnb9++K1asaJ4h9qNRI8oBA49tbR97yzDGhcAemW2VpAIYzxw+REwG7rlr3LQaMa4jpiSZCaCD+yWolCM6ifPg0plnnvn222+TP2LeLvXX0sWjSgR5KmzfM3ddjfwVZ5rgTFFSen4WSlKUwaefjc6v1wh3IH2QPJ9KzBE3KIaOrSA/Vw+HsEPGtZCgLagtMpNqkyCZP34jEfmKhNjCLtvYPmvCw+jMEY/O4ogmZxygAQYkIICui2p87IqcLPbmG++8OeSM08GQBJ9lV0q1RLZyJ1H0mjXr9uvXPxLvbQAdOAjKNH6pFYRQmqt2Z/99u9sRgGRX9bZl5WmO7LRcJbXNRaNfYh0AjRj5/wroWIFIYMqkyZdfetnfYNEe+jfSB++/e/TRR7NHxYgOSLh8ww77bDPgr9uZkyqGt5OdyRl5wA3lYiOAcAA3tFOK91pZG/Jw8hakyhBLjNBaBlXt048/O2HA8VIefmUcpVi2lGQOUus3btyIUAonkNEvgU6QEaBRd9+Fx3R2cuTJkVmoODIUZ2ZaVjG0XknLu/2eh1UxJUW6GElRg3kR+8TsGdOnXnjBeXJtod2TpL5LNn7wwQennnoqdsAfMCeh7ERClt821l01qDsMHULfngMu2IpAyQyOveM6eN+c/C5KZs8tLmTljgW34zY1bjzj40aqqp577rnTp08X5/7nSMqbZLJkuNvtLitr5RXLqvE8fsRsGL73ZJrrV/2YCjiZpuSlK9mpfK5SkKYUJidTDB35SmqJo6RXRaOI38lePmgI6JwPHg3HqrdVt25VIvzPz2ryV0jOuA0GQ3V1DeXlbSTQQcXEV95EqM/PeWIfXg62O/6VTAasUeCawODBp8DXKI62W70RN2Au70WbAYzgfKhZOHHCCSe89957sjhJzXX5L9KfAR0Z8R911FEQZexIC0K+iM3SXLHt3/XMhSqnQHthjDIFymnlEI+uiN/7Kq0O2NEQDHL6E29Bu/GLTLB9t2B+n75xcJqYLfg3GvBHNGDAgI8//hg7ULwEkGL2LF6z3ct6lStlZflKcoaSVqgkEeW0TyHycDqylIxer368eqvXGxFz5RKiJvOprKyU6xCCcEmK4AUXXDBlyhT0OTwwU8NzQ3zirfXbetWZB3Vtm+VQUvK7HHt2DUylZT94/bBCqL8zAyJYH7ZrAcFF12oml9DmfTF+YDxqhrMyU8VyxqYY6W0xderUZfXqtfEDMgRsjk85kq++C/k2/T6gHI9tbD1rwIFKRs+PVqI4CAESaKodhm4R7ZohOwQ7DvSGDrXGPvrgnXeNbG7dJK+aMZwdmujWnTsrc3NbUUNxsxi1NhABE01iQ+sNv6uuf7+9dX99JFhrhqqrt/7UMTcT4qVkdrjywamERWAQMrMIdMj3qB0JI5zBZj72yKO33Xq75P4e+k8hr8eVlZmOHZi+JqxjcV1NMaKzedXSsoIssYJlspKUlpOdWQw9dSopMDeObCWnE7BOlQgSKHJQFzGcI9XuwvMvGP/8C1IeIJZSMv82JW6X+g5PDBsnZRHHsOIEOtQKuTyVd0C3AlS1ICdXLNfGkApVJiWlpOe2nvH657D3CBjFCK5F18WP6MSdxFNPPXzzTdeywH+oyv8Uas5JyYply5bJUX95RmIUpKFVt4K2e8VhrekasorL9xtyI9+2imn1675vk88RdMXR4/jzoLNwgS6Yg5AAOnJyqyylZ8+eyB87/2uUYLI0nonD448/7oMP4PVxmsPq4s0mcA37ZuW2TW1L8uB8AXewZTu5dBM9Gv5ltEpqs5fiKG0I2qrfoLBFgnyHQzylAdMff2DcjddeIwbX47b6LxKqZcBFiYfFffvu99VX3/CU3BB7xMxoOCgWVYE6B8Nqo6aH6SX9qhUMhDxVCxfNV5SivQ87AwAMGsRGAioZfLwJeUCmmzZvbd26tRwQASWgQkvpz4CO9F6TJk268MILEy/uAgeCNdh0tdGzZm6vIpogJSPb6aA0t80AwFFyU7BbqDi7Kald6oPRsMnYRKIcbGiMbkQuu+LyZ59/TuaJXpQ6swtp+PDh48aNw45UvLgnRtkIF/26Hauxo9s8/jpcg53cvnNNu7zkfEUpjq+m07m4+ynStYvbeDsqKTP56KOPBg4cKE6z5vLkI488cuutt9JYx4GOZkf52hQ3szHmWnN4eSpHdLLbdx9yDfU4aroWvdM3T0lLz1ZSSo8783KO6wQtxDTITnIJmQPZrPxpGT9uItYyhkS1VBCR0RWXXfnccy/IfZB8RtBEyA0Fcp1orsFg+etWfNwuL3WvAVeul0WFUS8N8UIc6Bh+8a0PE+YYgjDw1BM/+uRjCF8CyoBkb+IX+4lulQnUoJ6bW6aqaBfyAO/h2sAMFKFGNJSg33nrTTOnvsopGiICqNm2umthPh9dFXS/6cnZ21y2FrYjqnjCJbiE3jQEnkSFLr7wksmvTpFt3EP/OWQNPGHAnDlzzGg8LsB/8YVdPeKrD7mqO5QVQiVT09MUR5ojWSlLUgAgxIgOgE4HpajrmmoEJMyHX+AXIoU4ocHj32fvPtu2bt6F8pAQcinV+fn59TU7hZNWUQHGDSAUR9GEIQjapgrbg0uoRrtW2bCJ+elKfj6im9y+fU+EN0fgGIrgB8JMp4V4QtTWuvDis158WTyv2XWV31XUXNOxD6qpqenSpUtiUau4pZWGN6oa677skaLkwfalJF855mWumhXWYU7OP+2YtIx0JbNn+T6nwvNqetAf4Fv6IAl0QnKt+bZtg8GgNCb/U5Tgc4KfUupmzZp57nlDEZTGfQGUho87AVFCmzesbltakJNBWI2tVX4ygA4YX8wxxXwlpUQp6FbRILAkAmlLj8S4oElQswzVPuaQAcuXLkOcIMtqEcmwFvHz1KnTL7jgIo/LK4RZPoKgc4Fnuf2Wa/Kzk8444yQUHsF/NC5q6v7a2rrK1JwON4zkqnXUIPQzxQaKzEeZgbBxx513jRgxgleEDCRC6JbSnwEdEHL3eDzt27evqqrCIRqD0iTWgVuyozV2YDPwmSsc5KPqWLB+9fdt0pTUpHQlpc3wMVPhGlF7JGbzLMJO7JhW1Ov3tSorbXS7wuGw7Mi/jdT+iF555ZUrr7xS0zTJGmgdBQX8RTlgqllnWTujHCAwdc5CcdmWy2zYtFfrzGwHhKSjknfwT40x+F5hQ3+uHtQP+Om2226DICaYjpy/+uqrI488EswhwuY5+WYsezQaqgxWLOqdSplT8rpdMG6mWHFZt7UNVw/oSZlMK+t+4KAKLyEtipFfWoDdB14Hw154/ulrrr5MzC4y/g7ijtqTXpl86cWXoe/QAahcxBAjc1zdlRMakK0WdIkxFUA+97svjYN6XHvflCokYntQLodRkAJsI9CJem2Ln6X1qcGS8rLa+viXv0CJYA6/UlHRub9APDG7X7/DFyxYIXgEWUJ61bIgJshb27ppdXlxPoJ3hCMZ4s0aRCdgWoYzS0lto6R2dhT0rkT8DoHTuGQ+5Qq1Fprb6Hcf0v/QxQuXiZz30H8KMRh9/713jj/+eOBv9GNYTkyBfeSjfc2OBDiISHPJTwQgfd2qBR0yxOiII/uWhyfWi4nA/IIAlYWfAAybTD31tVknnTgQ+oJQIeEmsZPwH3+DEoAeig95HjZs2NtvzoDdsGNelAhFYjGxpnkGMA4hRqU0HFHYRq+t7+xc4kTNk51FaWlddu7kR4Y4nmNHwhGVimiJ0SHb6t2n4w+L5iKrCG/evUjqOJovdyQdd9xxn376qXwhPHGevNIDdsP6I9o5HUCmWUlHDb0REEZzqbbpvWf4eUSryW2Uwn7bffHxsGhEFRYpbm/fe+89+YW+/0GSkobfBD/FGDy/FVtckr9zx5bE+shibUkKP2QuGvZbCERtNWbAqQWrNq/qXlycBheTnHv3s9N4CgKGhBQzIxyl3mB37sfzD9nvcE5tZoYtI+kEpVbputGlS7eli5cZQFDQAsh2RAcCQ6qi/Ay5Ut0++x/kCxqqW2UwEFM//+LjnOLu2118rMUux130FDjig6CK2obCohI4ERAKSihv3Ju0hP4foCMF+vnnnz/nnHNwGBGDAXKDUALh2BbAQNCwNJ1rOmvBLUs6ZyuOpGxFKb/+rgmEaZxCQZSDX2xgQCis3X7nHWPuv0/VKN6y9rLqaA9+dwlVV1e3bt1aBgfIPJ4zeAsxAGQMVYq14w2ON3GowmUb9XyPLFAxZOAgAp30fjsifKEDrZKr98JKykz69OmzcOFC7MipSyBpQBHhudxeCXSMMIRKJ1RBs4wG27/x4KKkXCh2evve591GxGBqtrbusatQllNxlijZHXa4OVclYLJEyA4yCXE0xRo08LgPP3g7pKIOhhZCiS2UxZjtbvSkpfDpgBGJyU9fYaNmiPewmr4IoYU8VXAtF595JoDF1yu2EVRz+TI2ORy1/eKFEYFIUBM1rPknTZ465PShPPfXKWaPHfvErbfeI77NTKATMT2myQxRgcodGwtzMlKTuK6UHH3lY2aEgthNLVcKeysZXdwe6jpqhSYwHomKef22vWnHttZl7UzxEv4e+s8hS1dh1Ky+fft++NEn6E/0nhg8hngaxDpGUCAe2jjiHNvybfupQ46SmuJQkrNuefD5GvFNOgoChBlaHuX8f9jvjl17/Lhi2d8ZAf0Dkq4Xmp54hfPFF1+84NwzCHSMei1K/0y1iooVEFAmHEAwCDFHDVhBvd62auxI3cDjBqSltnIo7eqqCYkguh5/Awd1ILliW79xXacurcAGDvzvmrrvYkq4XskK/M6ZMwewTwId0M9+KMwvLg07vEcWlDldOerM62kxcVH3jLnprEz4vaRSpfigrSG7BmwiuhUTOwSB4chzypQp2N+FfuE/nCAQ5ksvPn/8gKMjulAT8bYKd8g97GBD8EegYJmenRt+bJeVkaYkA+iMeJRzHPkNH9wHkMFHRKZmxgzL7tFlv/lfLeRqOi1Xll8FD0uXLi8tLeeX/HEuZovvtZlGRB09+vakJIVjCEkpGdlFgcZANBBsqNzYoX3rjdu9SITNa2h8EsdHcginfRCTQ486bvqMmYkpwrKIxNTYFtGfAZ1E1j6fr1evXvJzDWL9A3kanAUu89kxwnQaKUt3r5lXnqykZZQoya3vfnCSR8xbRY2xeYMBVYfHtDds2timXdvNW7cgmwQEkVNGdiGB+4MGDfrwww9l/vJXCxocSAsAjNTZdmUkBk8O0cAllfNwQ7V2uOGnJcuUlB7t+py+JcA5hm6hvQkdXr16dZcuXdC72EcR2AGXZOVvuOGGsQ88BBGC0KEoV30VBQDOPFgNG3fz4CM4otN+377n3lKHnjJ1u27xS3ee73CmK2nlKSXddnqjDWoM9QGDUSFkgWzr62rKSouEvTaC/HoDrrRMFqN6BHdcctGlo0ePQabIFpvbw09xgRDvWkaIAyPRgB0LVm/d5FCyuvU4oNoVQE3Qwf6QGtSI1rDxM17RgKHX6xEgQP2oI4/7/LN5Ipu/TDEwcGuXLn0gRWKYlF4JzA+F6pHhxnUr25WVQBckysnPSMpN4YhOdlqWklqqpLXPKOu7bkMtGwAtjbFW/sYQWhc2jedenHDr8NtDQSAzWdIe+o8gGmjV5166ZNH+Bx4QVHX51qGrsT4aDop3r9ChOsGsEH0jEq5Y9X1JisLFspOzRjzwHDQU12i3CQooEji8YcRdp501TGbeUn35I/qFGRGmtq6urrQ4j+um2hA7OyDUnqVZthmK2IgDTa3RQwsjluuEAXHBvCxeuCQ9rbRH16OCfs5/C2jA5nx0BfDg9xO+D7/15rvvuUU80hW6upsRjF7CVid26uvrS0pKduzYgX0Z4sd9B6LfUOMHU57KTlKSkpV2fY+v1W2Pm/O1nxl5EWcop7Y75vx7d0bFSl3orEgw5PegCGAp5NahQwdpeH9GTv/rZNEXxCKnnjLopRdfUCFDFPKoWF2WT69gzI2wT0wDAJwJNlZt6pidVQT76cy96p7HEbuyV/A/yvjWHeC8qBuH33nNlcNh380Ix/hlMX+dJMrBL/odYathRMeOffCMM86C6IaCHH3HxZgV8Xrq57z1ugIxSEe8z6XRcp0pB/TpooV8UFiPeLecjgrp9ZAdcaHyw2+7/ZTThzY0oi2khAtO4OwW0R8CnQTKQQHIet26dQUFBevXr8cZ+WFtcRG/YsaZweqaZsSz9ts+rcQUqOTSB8ZNxkm5PIycj2zErNrGhs5du/ywaCFahC1Re6keEkDsKvryyy87deqEnQRrotFYIMDxANvYPPL6k8H308+/Aiz2ajFGYCGfbapVFbVKUsdRz7xFLCpmiTdXs3POOaf5647oYJDMf+nSpb322tsSYCISQa4G7QAOTF/Mv+P9CQ9RsVPye5xwTg2xOIK87fdfeRpHdByFRw8+H9ADHG8McDkbt1+l7bbtq6+64t7Rd7EiYotw7nALiWs3eb1uT1lZWVVVDUJe+V5YWGeUHFJhYcAQLRZyoR9fmfB8Rm6nR56aahqarrsgeWiBajL01PxQMHa3GABTZ785/cgjjiNeb2GPoYePOmrg66+/ARYYJu5Ho7VYTBPTMix3bS14KkC9Hg01blm9pGNeOoe4izpd9/iUBgTtKA4hhMFHV4kXI0MRvbCseP3aDaxMC+uzh/6tBOVhEA9LffMtw08dfAb6M96BjFDD8HymFmBUED9v+SvXdW/NsVHFkT383nEuaC0th60F/IbO1Rre/ujLrr33Fwbb9LkRz0hL9Y+SNAKJaFKq/JVXXn73qNtRFrQIOs3xY1Q1ati6/8kbLypSlIsuuDggHvTDjLjctajSzh01memtxo55IYZoS9gKxLDugAdpsO2sqNlr795bt62jVqLiu6buu5ikrZY7if3Jkycn1otXOQuP6yaLCE2LBSoO6ZLFN4lzu3y+sp4P66KuSwb0ZeCXv/dr8yvggD383ifOS7RIQpj6/PPPY2fXOoX/cIJAwDYalRU7OrRv+/WXX1Gwmr60Hb/K6JFGVdc9Ozau7FaYS847su9+8hWX+E445CzGYVQ9ahvTZs3q2btf0Gf6XYgr0KFxp98iSoxWyE9SBPzauedceMUVVzWtjxCvVUjz6QYnLYtH0NjMsL8a1XAFYlAqbJ6Qh+MoUB/LP+6RUb377quJJ2CgRBGgXQx0QPKRDQjSDETyxhtvHHDAAVqAHIkAs8SA6COcAGhp/GiAZLTRYIdqURFofsjiJD1oL/yQVOOAFjry2GPuvW+MbkQ0nS9RJzCElOYEuvrHST60grZMnDgRO2ATjBRLJI9VveHH/j0L6EGTcnofdJIPDpcPjQCAzM8+m+cs6bHJpUcoLsEIV2GP09dff92tWzc5ioNfVD6hhFLhL7zoknvue0CPNK0NE//qB4xxo63V9evWlstfO3OXbqziJxfC1RcPOigpOVXJLp3/00aYBPBNjVge+fa+ba9YsaJnj26IbsFYxLLi3Xxx4a8T0iPKFcHuww8/fMopg3ECQKfB42/KCeGnWOeAk2+CZww+VUkq+eL79ZwKqqEf5ZvftMi0QWFVPNY1GtxVxSX5G9ZusdDoFlYJOG7xkhV9+/YNBHxijo4REavpiHqyOtwiYc7MsIOuqvW9W+fzFZu0oovvex496vFFxUNfdKUV5jgnK/DIE4+eee5Q7DdNZ91D/ymEPoNUY0OMaZ974SVXX38TOpDaRKAT4XBOjPs4I5Zfgrh6o4E6pIFY+sUaVLQguNmydC28dtO2Dj37frPoRxhF8ZwXAoq7dhkhNpDDGND9UCjk8rjL27WtcHsbonYD7bDFJUxM1fZXHVSklCB0TUtHfardPm+Y820g7l9//UNWRiuE4ggxoFYhDQoR04xIg4cTfR586JHrb7wh/i4kZ3SyrN2QwAe5A7sqjTZ29t133w8++ACX5BmRBl4YWhvctvSr8uxUJb/DIaech07ZtPyrjulKq9SMm+6Z0BB/50MYN67/ySa/9957hx12mN/vTxS0hySJB1V8/XbVyh/LWpX+sOB78K2hrt7n8UYZI5Pn4s0VJNOFYdfgp1XLBppsRJAK7iIVP78TnP7G5PIOHXZU1lHW4KkN0+CNLWZ44kUl9BXfzI7Z1VX18DVDhw6rrKwU+sJahXVOEJJaIJaJRT38MRN+l1qM8wBeyMJfWz3qlquPP/KAQDCMGAaRORFzE07ATmK/RfT/z9GJ7wnr8+gjD3VsU7Zz6xZULiI9CpwoJDsQYICC4ExrtKP+oMH4BrXHzdgk0Fm7cUO/gw4cNeZe3IcNWCCegXjsLQV6F4q1rPm6des6d+68c+dOmbPX12DG3BEDcZ568zWX8Ymh4kxOysvN6eD1cPbvpi11bTp2r3LDcJmq6mKjI/Hp0h6PZ5999vn222+bj0LJbNEEmmbb3rptR2mb9us3b2ELOWWXY+lqAMEKOFJXsW5J+9ICRXEeO+Rc9GugektxKqBW8n3jnvWE+SVAgAikx62oPGDZoYf0nz5NfnyE34L4W0hWOpKIaWhA68cdd9wDD/LTmNikACGBAX9gQSXU7asWF+RkH3jsmVvqiT8IB/nclBUjRfgiDG50hVSgVX6kjPWS11pAsveHDRv62OMPWbFIlM+VLU3lE6iQTzzpBNzkSCwCfd/2DYsQ9qWhn9IKL7mfzylQAdYtFnB56rEfDkQ2b9zWba/u22u2I9/4JLg99B9DFgdsoD3A8TB7If2gQ49AtCAvUWuAdzlWD7FgzMC1wqMByGpYp70HWvcLqK35fHY0MufNtzr36PP+3AUQa5WCYvJdwr8ho39AUseh8nJch9GObT/25FNDzr+4zmBox68tWqod9thG44Q7LiyGciOWzi/La91xWz0nIvy0cUf79ntVV7hpF2Lx8QtVp30BrPv06087dusE8CTKErgf225GMrTDr9wBwVhhH6CkqqqqpKRk9er4B49AYkXQoMlVetkPN95yK1+9SOOD6TZ5RfUVDbAtHjFEHBDtRQSJ30WLFsFob968uRlg2kNxCvPdPAuwBoxau3pdcWHJ9Kkz4qICBnIgLSQXnecG9XHXSnDUYNEp40I0qEc8DQ88cFef/Xus27IpoPGRETYPH7BS0eIl/VXizU1+kHIbn9zC6ZgPduzYce7cucA/EZPPRoJhao6GtEiAc6FqiD8Cb3/Ebgj6AHS+/uyzAYf0v+6Ss711O5AkIpWgSdIgD4lxnZbSHwKdBMSREYyUOQReC776tCAn8/lXZ+KY05csq77WxcYiOQPxINwW6hJEs8g2vliu6uEpM6Z36NL51alTAHpQ65q6WvwC6ySEONGYXUgulwv5T58+vW/fvkAnoggDtlGL1BmIG0x7xisvwYfmZZdyRYekDCU5o9f+R6G1td4q1JqwU5gitB2gdfDgwaNGjUK27FUxOwe/OJTmDyQN39xvvmvfuVtNFaeS6BbfpMNOwBfka6iW29bdt193lZKSo2QVJSlKUXYqKuQO8bUmsAvRnQj8kJV27TVXXXLxhRSjxOAkGCzGBltCkDE0SNfFtzzr6+s7de46adprkC3kJ5CTcCfhgOVrYCRq6jWqGIfXQkaESzahNmgCnzHFCHRcfnXoBVdccTXDbiByi5MKWkYmJ5VaasjXsVPbL+Z+4vdTY4WyiLl0KIyyhFAelWlsqFzZpchJoJNRcPWjE90WV/Dhl7Zslc8CfDSgvXvtPe31qQZOc4kqoUJ76D+GhPhhEzgmGGZMeskVV0Nhly5ZFPA2AIdzcFH1A+KIjrW4ugG/hGuHYrZPfPKab4uY5p0333jYIYcuX7UBeAISH6RkQkD/ToT6u9TcwibmIwtLYJ44+PQ7H33OxXCUSmwiQLK8dmTna8/fn5lXqDhzldRcrhmYnNHngMOFn6JGa+EArIt8joz2V7uq8styFiyeD6gOQ0UzwAbvmsrvQkqEWxLfyP0Effrpp+Xl5du2bQsEAoJLNCFmNK6Yasgb5ZxOjQpu2fX1QVym6/1Za601a9Z06dLlyy/jX+eVbijuffYQyQoGwEM76EeEYFdVVB+4/8GnnHTa1s07OCemiWKxKOEONCui+nZu8+hc8dUnnPKy+T+cfPThw4adXOepgIcDf31uVQga/uN6S0UO6a3Ewx/OaaH0WnwGZdorV64+9NBD+x2w34yZ01E4pQHqE4VrhbmH1HvDoTpUIGDa3yyaf9awId3bt31v5gx+CDamQbjE8FCchK7F65bwuX+d/hDoJIQYoiaVnA+DYmbYU+331B918rBWnfed98WXgAIqPCDSQhbDQdtQuUBQDN4VSm9C6d98960BgwYecsThm7dvk5ORIyZtFvgRCsff/Zb0N2r/JySNkWTNvffe279/f2CdkKEFYiqHSVGUL8LVvWxDt8j9cAzI1kAAAkMUsq0AvClU0KOHXOzCSy+99JJLLoG+gRuynonaJhjl8/miMfbehJcnHdL/8PVrN0icx+vssLAdrrLD1bbBL/hxsIg3w9IxXMXmD8llJLhU8c033XDskUfYMY7GE+WIlOHEE8sWkGXqfovNAs/5TqzH6+/as/edo+6lS0G54g0myF3M32gHYaD5oI5zcMTYEjadmBqOg+PPS5Z8N+TM8y65/NYgYI9olHhW1CJCfxjhiArbt33H5tKyoh9//JEziDl/U5SHWqHHjDADd6OWfIq67WhoZ4zfbpQjOiJMB5A2al11Jxxz/P1jxkY5MwKVtBKIcA/9h5AAOlFdCwXh9dG58gsqH338abu2rW+6/qqVi38QT68oFrBCDE1hsWOc8Ffj5UOOoGE//OAjncpLb7nmWq/bRz0yOUgA3eUam1FIVUsN9++T1PcE3OFzcOgAKhb2mVpgr/0PHfv0RAonVMqKcvn1mNu2/FC8RoRW4hltGLqE5kKzCBWQm64bYWSHu1asXlfaofitD19DUIszVC7E31wFnA2XJe4mlDB3MK0APSBpY+XzC1ydN29e69atP/roIxzCHqoGh4GFVlpaBBqscx6GTj2F1aWxhfmt99hqGDHeN4u+Lyop/vbbbxNwCiQnIewhSRG+CRsfulYDEDNK1AvPvlhS3PqKy6/57LMvEN4jGTA3/IgEOlzb37arwtbsT+f1P2zAQX32eW/mFKhOxPJG7AifnTIchqSZhKQtljekBwZg74N+HokUDkvuznnnrTOHnlHeptURxx1zw+13f/bN9x++/9F3cz+e8vIjzz3zwCWXX5db0qFXvz7TXnslhmAVKhZVY2G/328C6NAsNJugI6m5ePxF+n+ATmLyndTzYMDDIAme07K/WrjyqEMOKc7Kvua6Oya8+NrK778PVm1vrNzhcTcuWLRw1tuzz7v4nDYdy4865sg5772rGxzbQI4S5RjROAtkzmgGtCUBHXYJSfVDzmATaOLEie3bt9+4dQudNjAZ7QxsD1TI0ITKRW1NNTzYEZ5ezP7gOla2t6bxsMMOA9AJNy3505zLiQ6QO7BjaCb2Xpz4aq8eey1ZtjCghWgPCXRg0D12pM6OeFAHoCfk4vMHwQ7cIpmDDCoqdpxy8onDzj5LLISPn7jnVsX7RBwVbBmhRijn5ze2wP9AMHT2sHMPPeyoH39cycyRKQdnuKJrLBJC3RojNMVQpaZBPXAlMGXK8926d3ziiRciUDHKtuQD85SJ/hpZpqWLuILPg5cvXwqb+Nbsd5AHsA24YGrYE7qLyFivJ58svx5GCGPX4UB4QQF0tG07Nw088YRrrroWTcB9YaGiXBB9D/0nkfD87G6O6KBzNYOjItiPWea4Rx7s2aXDvr173HHrzR+8/+66detcjfXuuorKHRu/+PqbZyZOOnHIOY703Csvv6Jq2zYoPMJE3AthpRYblngqCoXZZSIhY6fm6q+rfr6xGNM9Qa3/0cdfeuVVDR439Y2P8aFx8bAB9fCIqY2sC5oL4xINi/jBQrM//eLbDl26v/3hbNgfAB3DhCWkRoJ24evxu5BgCX81xCKdhTTgMLZLlizp16/fVVddhbAK7XD5wAO+LgQ9DQQ99GSwLWJ+FeyvCs+A+N7rv+GmG8u7dF6zYb2cG4B88CsdUAJd7SEoys9D1+K1DexAooKB8Gsz3jj00MOLi1sde+yxt91229ix9z324P2P3nXbzVdccsixx2S3aX/wcSe+9+FnVljMgIyFYjYCBj5E9boDVEQrPpEgXtBfI9OMiA8zs/eJcthxorM4ay6+OC02TQ9VVld88MnHd499aOApQ044YdCRhxx42UVnjLrrxmeenVDTyI/7ewONvCdqGn6E3HB/Cbf4swCgjL+BckD/zxyd35A0TPzKO9sUs3ds2/7iS5POv+CSg/rt17ld64L83NLS0r336XP2OcNemfTy+o3rRCpSvKb/QpLgAzySOx9++GGnLp3vf+jBqppq9iY8NlfQg0GUDDUjZvxTFWKmta35AjNfndahXfvnnntOMhf5SPwkf3+XcGNIoxVYunRp166db75luNcTxH3E1zCAkCQjHLGIPiRDCAFFcaAJEyb07t377rvvFke7ilDVxPYzvfnmnL333hsqsXzpMjZIfFATvkKu24b6yCEfGJ2JE8fvu9/eg087ackSri8gQk5uwq79IR/+iGKxqJjbb7lcXA5+x44d3br1uOaa61wuD5+Eipy5yJsViQESNfkqsAsGzx/iw8GIrs16fXqXLp1efPFFaXDDCEtEmLyH/gPpZ8kUnc+tifhW4JLFC58Y99jgwYO7detWXFwMC9OpY/sjjjryxpuGv/3OBzW1QMM/34YfqcLi6Ncy/08g2kNoDWyITw2NvPuuffbtO3XaDFG6qeu0J1AXPQp8j124pShn7OGMriHm9ng855xz3j5991u+4if4BZgg/PLWpub88+u/y0iaRKAT6ZNcLtcDDzzQqlWrUffcu37jBnEJcAZMkKaGt4RNesjtOyruGnF7j06drr/++mCY74vsob9BEl7AT8GifvbZZ/BZd91118033TDqjhEvvvD8t/O/q3Hxo2JMBCEj4yGYPw83iD//dH2RxcVLZFmsA/aaTkKbsEfMJWvSlHIXUEuBTpwksErgLOzLIZnEmT+BAv8yStQhMS5VUVFx9dVXd+rU6ZprrqmsrMR5iWACgrAjH05h//bbb0eyYcOGQW4kTsJv4tl8opl/RHyMFY16vd6bb765c+fO11133ebNm2HX5FXcTvTbZBSqqqqeffbZnj17Dho06KeffsIZGc38swnlTp48+YgjjoD/OPvss6dOnTpr1qyvv/76nXfemTFjxkMPPXTUUUcBtp577rnffvttYnXEZqOUBPJ/g9BqyVLJc9Cdd95ZVlY2ZsyYnTt3yjOS0Duy7xKFvvLKK/vss88xxxyzatUqOXusOcne3EP/BfSrzk0oiySothQhSQkF/9dTop5SQRYvXgxF7t+//8svv+x2u1Hn+noBxYQBkTuo7Y8//njFFVd06NDhwQcfhNAmxPs/lxKtg1mQhhfNhL0dPXp0u3btAFJvu+22p59++o033pg3b95bb701fvz4G2+8cf/99+/evTuM5MaNG+Xte2iXELoAJB1NQnGwAz2SvfO/Ri0GOs0NEBjXnGvYT3ho7ECB/72TyFDVRB8nvDLOINoYOXIkPCtcJiLFyy+/HFo3btw4wJELL7wQuldYWDh8+PCamprmsw6bg48/kRU0+VfuFvk888wzMGq9evUaMGAA1PtxQbfeeusFF1wAE4CaXHzxxd99951Mn/iA2b+GYKG2bdsGxHPVVVcNHTr0uOOOO/7444F7ADsQGdTV1SV4CGretL8HdH7lk+AM8IueAu684YYbwIoDDzwQvTNlyhRAru3bt8MCzp49Gx0EFhUVFYGBCxYsSPAfnYIM/6Q79tB/OkE+IXUQNvQ1RLG5IsudfztB/KRU41f6+08//fTSSy8tLy/v3bs3vDicPQDNww8/DHADjN6mTRucf+yxx6B3MBe7T0P+EULDmzckoZLYAX3//fdo74gRI84880xEVkOGDAErnn/+eQC+hI9A/yZeaN1DLSWpJjCkMlaPn/0lIc0fXfqvp785ogOC+IJr4B1MT0JYpVjL/X8vQetQE/S9ND0gKQo4GQgEpE5u3br1nXfeAeYArEHAAayDgGPlypVoERIgzJK34Femx73yksjvzwgpa2trsQMWgeSkdLjtt99++9FHH0VZd9xxB4qbNm0aikMCcRNJcrL5mX8SJYLI5si1ebloZqKlUn/kPugvMuGPKOEV8It8mk8bxyFwzAMPPACkhbC4S5cucAmDBg0CBgUUk0uvSkK/xPcENRfCPfTfQRAGSMWfSJq8CqH9lTD8K0mKMRREijFshbQS8tJXX30FjP7kk0/ecsstiHCmTp360Ucfye8GJgj1/+8QXTQ8YWxlpyQOQWBRQsflGRDOgEsgeWkP7UICn8F/2PlfaQfON++C/xH6O0AHbPqVEDcniCykXAp9cyf6LyZpa0DNnXdzQg0T1YOhkdKApv2/dUaaROa/JRSXyAH7f5RSGgJkJW0cboGhTEhk4jnRP5VQXKJ6KBHmBjuSFdLuoHq/7WXUXKYEJSrcUpKhW6J0+VAPHEg8zEIFZB1AzauBkz6fr3kf4arcwaXE/h767yP0L2QvIRW7DyWeestDKczNVSMxUIEdNEHuQ1bhhGRz/rYe7T6UaNdvKfHIHnZDcgmt/t0m/0kme+jPCSYRLP0VA39rD3FG6lH8+H+GWgx0wCZQ/ECIJlgMCU7wFGfgwJqn+beQrE+iVvCU8KOoG6RB1g2XcBKKl6hq8zojsdRJOa4jTyboT4AOCDlLT4wdZJIwcyg9ka0kWWJztw1qnuCfR6hbohUJuUfRCY7haqLhUot+y4rfcub/JdnYxHgSGCKr8SsmSEL+ibohZfM0OERVwcD/Aiexh35L0oagi2Uvg+IXBMnz8YNfau6/mH4lt3LsVtYnoR2oakKpcbL5IZr53/G8JmFMEoSWJswdtDgBd0Cy76C5CeUFE/47+LA7EMQPDJdCCFZjB30BStjS/0H6+4+uwEHwLiHfENlf8RFnftd7/csI9fndgTv8Nu91oDQ5gpJIKdOAkEzugCAuUNpf5fZbSjQZ+SduRxEguQ8C05BMCiIoYQtk+uYp/3mUMLUg7P/qsHkzUasEQySh5s3r31JKZJ6wfbBxiSJQeoJvUrqaVwZXJfeadw0I3MOlX9VzD/0XEPpUUuIQggdKnPn3EqoB+ZSVSQgqDqVCQVYT6oyTUp4TliehQf9eO7kLCa1GexMN/C3hanN1Bu0+XfkfTeBhgv5fliYE73+HWgx0wEH4mOacglhLtuL3T0T8X0zN1SlRK2l9mvtRaXpAiRbhzK+kBJeatwv7zQ//nH7LK9SheVkyK1kxkBzq+HMx3YWEchOM+pUBkr2JqjavDNIkOAb663xIUKLtMlvEfPiVPYJLiavYkZknioMz+G1xzZn5Nyqzh3Zz+pUi4LD5GSkkv0rz76KE+CX0KFExSClI7ifkGTsJ0f0vIDS/eeyBfXkIJmBHdtOv2iu7r/nJ/yaG/IsJrPst9xIy+VutiR/8z9DfH9HZQ3toD+2hPbSH9tAe2s1pD9DZQ3toD+2hPbSH9tB/Le0BOntoD+2hPbSH9tAe+q+lPUBnD+2hPbSH9tAe2kP/tbQH6OyhPbSH9tAe2kN76L+W9gCdPbSH9tAe2kN7aA/919IeoLOH9tAe2kN7aA/tof9a2h2BTkxsNj/abnJrOsQvDuJrNfCUJdLILX4uyl+RCgciTfwQm4WTVsS2ucwFbo3ipC5TxmK4UaQUWSayQgqZTTyzv0Q/VwYZiq0pR26yzvKEhUJRiqizvIoCDXFeHHFDela76RiHftsOyrolEolm4kaxRAfPsL38Ly/u1iSYQxKcEYfxOjfvfTYKf9BAA92Hbvv5JPdwF1JKSSCvEn3XRM1KYQKyNH4r/yDtz5IgzzffRGZNqwc1nZK74o9hx3C7LvqaRaOGrDcvyT//PIpzrFlB8kyz1nGfEiWPpGgJDqDOaBTlBBXmQhvccEaXYkmyLNvScTKeRpyTCZsK2pUUtU1s8QJER4h+0RKHsltZN5lGyIM4F1cZ/kelxFWciZ/8FfEUax5XLuQAVsRQtMhZ5IkkuBAvS7a0STDih4mNwtPE7aZ7mxXNbOJXxZ9mV8Fbucc04iR2NOQAVse5zf9xEnf/vDWrgLj8Nylef5SOPyTBN2YpVSlOYFGCP6RmdcB9FCR5tele+YftYiomY7twFe0SmTRVXlBTbv8o/b/yIzaqg9xvqn+8c1ExU1hsIfZNOYik4iq4xI33iZPxjSTbwqzwnw2kREGPEu0FMY3IR94kOU/GYj9+EvtUQKbBjbjAs7hPXG5ec3FCFCrMnUiEG6VGx3tT5tl8+w2JHLj9XWK+zEHkH88N5WLjLotElbD9zGFZK/4XZ8Q+Wh23nPF7eRYkM5Q71Cye5wkUF5dGcTs2wQfZd39Aux3QQbX9KpfcotvWPXZUi0bYJDMahpAFhZ/HtahG20QmRg3bNGJiPa6wYKpLrY5BuJFag/WGtKkRy2tHA3bQi5Q1dpQfBw+YthqyY3Xf//CZopQ6UzpVeCo+n/dehpJ17kkXg5taNFod5OJ9yFMKTTAMT8bVlgxD9lwUW0xsUtywYd82depJzI5YqJ+GYjxBfqDbCIlmwG0Y4XAAlceRGbYjIdtyhSPIwgqhpKBtuaO24TXY86h6xNZ9ajXbqEIHkUAbefVhRZnKtLe/qvCImqF+1O+waXtNwRtUrXLzT5mZyt2PPo/jCGWBK0fJlcoSq3jx7L+DKJZNG+sqgKBQElSMWE030NHiUshlWyrSBUIJr+VF/9fbdiPabdk6OEaWIjG4oJLz6BpTt8Lgqh0QOYL0MDmLdH6fh4YIF/116IhozEafsB6WaoV3oof9PhpjZInU2HBRt2wki9lBPVKPPxBFS4sbQT1C0MziTZcdrbPthqit1XlZNASMMoacKSOsH4/+bDlNpPl5kwIme8qgdxCEEnX2IHe5xq5u0ahyC/oDuE+PL65rWDqaboCVvJP6bwSNIIRSVIcKEtRhylVbq7ZNMFJzidqG0RhkH8VRncfweGl9wOyAHXHZaj0UAeIWMJiJX4uwZtL0sMIgCvzfJ9wrMgjbqm5DBcBSOxIW9bdrbLsKxpOH4IDoVjaU7UbRPstGhWEVDL+JzhHNQweIeqkxqBT6yIrGTDXoRwGMZ3Ajq0qpC+p+00J+XlursMMeZo4iIWO6C1nhAloNvqkh6K8ZDlM6cbcRDRshLz0Z5A2/hp89Bv6zo90RrZb5oHQhP7EYsglix4ta4XrUol6DmYZm4DouQI7DQTvKDmrQIEWVMase3YGOiSA9+U0O65F43KJG2AKYPBxFYT8sWH8KJNwLWgfORcGmpnU4eaMwjPJ7KYmTIEgXTBnjPkvTQj5cQIX9XqobbgjjPLTGNERuyN1v+BtwHslQGqwRBYlmD4wG8+usmAcGFVeRRqWdtvVAIAqTa0NbaIhtq8Y23S6dkoY00RjMEv7G5QcphKwKi/43SNQRP/+v/CD7CCyxDWspr4LrPsFDHtaHQtCKiB2MeSAD4CTTi+qyhgFb89laWNorw4z6sctLfi/aBGaShTBfMLkNiEO1GugXWApjhQwiKB6KGdXR4UGYHcv2+V12LGgb4pdVsjVEE9Gg7a1GY7yWBZmjDUFbcI+HVTdsLWRrqB+KBWyE5NGa6boVoSbGbHfMhvzA09HegfUoF6XCkcnGuryoHnmlQta4Z1F+2IMmLZMI/PD/j+QHv9IigeBK4h4E/UbFgGGC9uGqrkeCKJSBOLy3G01rsO1a9iv6JGZDx1AxNAjVYs1E10NW7EgQKVyGiWJQHnKFbjGLKE5AQlDJRjvm4TUVPa3rsQAuYNMgR7iOSsKxoncsvzj+Hdq9gA6Yh8aDYYKjph12w4zHwEYhiLV+fj0PG3nM/7A5fgsmDF1pmcGAD23d4YVC6n61Ueaihb0+vT5CL+g9pE1RrqLM27RxB0wIesPrsc2KH+Z9oCjlzozu096durnip7KMtvlK2T13jUVnQEwrQ2EfdAY9p7OTYW4gEEJEcE5Wk4eoi9x4yPje1MPsRcAU1fazk8UVGA5bhyBC7ZlauB9DZS/ZhFTILFRnx2qCalWPPn0Upejtj5eIjkcvWuxrlGn55868PjdJUTK7fr3CrtlJaSdrKBtug2UxbfXar/fqnKc4Sw489VpknhDQ5pbu30WSUaiyYBd5CCWWHsSKoldoR3Dg9TTYUb/proL64zCKZgD2uTaGI5XQ5iqhD7gQ9kIEKPCxqGAs9CMSioU0CAkcMzxMGBplW2HNH4enEBUTydx2xB/QaIZRj5ha9+HsZ1IV5eMPFyNS8AVioQhNEmoDPRK8C0atxoAPDomFxkLAqhHRvwJFAeg0rlry/SzFoZS077uxkdYNiCxMlMT8uWRpsw87R8RXw2ApEiRBc3xjgbCb+BVig7aFDIgTZAcbOpfpSZQnLYyGEpFEVBMSgJvVkI/pTGIR1TJimgpgDQbBM+Oq1xfwCydJoBOtHX3jmdlZysPT3gBL0XA6ZbNR9a4K20FABD0UBdAzNi5qnabcMOYpabKDoYAK485BB0ge7K2oJJRC9uvfIyEQ+IGyhAHWBWdRXR/0w67R/WugUyFhBlAeHADMp2AS/sCtAOjAutFVIBbg+BTkIWKHAnYgFlNp/8BK5Eg0gPhJF1U2w2iEqRpwJejTWlvbesUZJ9w48glooeHd/N6M5xSl5MMfqpA7+ICMoxEV9h9tdofgxsFwxFHQYj2GGCaKQowAcrbt16Y+kpqkvPra+2AkskL6iOEK63W4BFmKAtOw+5hSXqW++uB5USf0E7osuHLRtCwIorN8Q0BIOHgO3yr0xaPRUGDzhwklorTsMDV0MQDtYB9zhkYgtsIFw0g4J/kNChnnQA5/sfY6fHwEEJDQmEESWKQaAR3MQbZAcoB3qCbEGMrF25CM9wm55mbphtZw9y1npDiU6e/NrYW6ifOqG4AJ1cAd0rnq2xbP6VKcdO9TM7dqMg0cM5QPjpYrJtN8i9K5iXq1jHDLX5MfHAugo8MqgN1mxG3HiPVhwoHecNVDMBHkNRgJoAhkjv+Me8EiGHPTGw0iZmQ9KWyytjgwPK4dQ088bOyYuyuAtmz7g+fv7ZSiLFhXVSHE1TQjsQgkLQw3javMFhxm+I1YLiiBJiCnHfF+PG2C06FMnPU61G07MATK8gTIMsNuCNQCU6A/NCAa+iUNncpYLR6bQRGq7Fj1wm8+SC9s4yzptnRDHe4TTY5XFtbD6wU4FlWGlWAfIXbRYRsFCxlaix7/HfmB1ZIfKpGfJIu7ElQAWxQSHK3XYPOC4XCjLBTonTkC9QXWacEG5O8JEZpQJqBLqEAk6lNxAiJb++Ad1yqZ2S+9/RkVBwoGUWV1DUPYtbAOPa1xV6zontv+sTueQFYBO9QYJqIKwdChnwBcCeeInuIG+ze02wGdYIQuBHsBwGoaUFgqf8zwB4WIEAuHaMTBKs0vAnSYrVCY8UcMMS1k0YYIsOM9dQzcYxHcDwF1eavUjT/1Ls5VUlJufegx6CjTqnWr5n+dmdXu6Vdma7ZaU7+twFl2YLejkefazRsVR8q0dz+gERLMw8ZxFwBLN3SDwRA2OCRsQD9yw35E9UGvNI1WFzcGTUoTv2+Mk+6qTqU5hekKTBmwijM1xZEGw4j9ZEUpVJQsR6qS6lCKUpRMBZTb48AhaA66EzkQWcOohXe+NeHSknTlprteahQmKBYmuCHHIB1Rq96yazWvVfl1jxxFyeiyA4IrpNbnY3gAkgL6b/y2Dro4sUmFk0DHigFFsq3YCYXBdQEKLTUQDHfuvl9GSpG/rhFBL6A9TMBmsBTxME0I82hsrASzjaC7e5vy0hRHsKERjYThhimFXRb9xZzdrgamh9jAvoTqsSuBDoOqSM2ZpwxQlPxTBl8pa1bl8kJdDWgdbGIsTPcUs8lswXYOtoKZKq2TrUEOG8bcdlaKE33ZZsC5I8FrdwydDySCGjA3SegIUPzgF4Rc4lvECIlHkFYQCB5/4jW0I4BNcNAB2agAAHBtSURBVA4ajSS6LxQKGkBsuAWpVVhq3GI0GsJK4bQnBHkO2oEurUvaFpS+NPsz4IMQQDVtAZAA7DY8uPv9SXenJykpXfb5eI2POAh5RFB3b8T2NoYa5NCBvnFhOeQ1s81hw272RcDOpoe/TC0qAPpHgI68kRkgnoOjgrKyAHEaJqzBjnmBYlFuh077pmS28xocL4HEsGSA1ygiZBXGW4gO9KT6yD5tnEq218tK1qvAEdSOkBrQEf2JuzQflJEiR3eO4sJVtr7zgpOOVJJKeh000I41LP5yNoCOUrjvk1Nfd3MQGaAwDOOMANVLgCuATtgfA6bkQIERCdKjws4YwR0XnDUwo6DtwQPOQ89TK+FI0BEiMGKFdcsKIzlwpJBI/GFXIy4KwGihmQ+POLnAoSiOwmPOGwmjj2xRZT8oROSNDWfAHpXDd2ZED0bhT9D1VsyIxGDwUaKMyJtT4gO6IOm0JOaGKUBV8AeWEwpQD/nxsNKWJvAfgCBvBBpRO+akpSvKK7M/wgXAhQiHXI2wERQxuT7tuRG5aYqSkjtvg6/GJUAANEWj/pkIU6Gq7nrPxq+7laQoyW2Ov2i0i6Pt6CuOZUmgA8vFCsk+/XX1/z9CenHjX5GftMzyOk9DCDGItJlRNNMdtYP1cBboiKi9LeLz20bn3Pwyxen3cMA3wiibnEetAf3Y+/TuZJSh0yMDbkSYT/DsY/sXpqW063c8HP7qT6eXwITntBkz5RMaXNYPnCdUrecjCtsfcMHh2KEa2XSkAQKL1O2wfbVDh56qOJ39z7hQ6D8ClSB6HXA6Ap9mM7IRiZGT3w6q8PlQPpz02j7DrrBjW8fcPJTexZF9wQ0P1IRlYturchALVp8qgJbjF4qsqxAhmJZYLBoxDYT//6/8gGDBEu4jovrtACMr1AaCKMIQBkFgD4szgv66SjbB9qblpqbmdnll+jfQn6BmwlODjzRu8MLGzncmjVOSy5WCvl8vW6sKyeEwjzAqqDx6MRbZ6N6ypJPSOVPpcuRpl6IYoTmIZDlYwJIRBWnQOaqTqNqvaTcc0bGCIViWeH/EYpoZ2Olt3FHYZq9twk8hjWbBi6B51GyqPG8zYmH3meeddNuYO4NRO0ANBSYHyDXDltlg+ID1bNN/z7WXA1QcduJJp5x6emFqarGi5ME3OXOUzHwlRcGlTKUsVSkh8khSHFm5Snre9NnvgtdqBNCa5eiE1JbBoUjUBRvY+ssRHXSdv2GvPt1fnT4daofUUBdestB/fv7qrqhWd9bpg7p17fXJR5+W5CQv+fZLNCSkIzEUpvLDyfejVocePWRVJSWY471Cboywx47VfTbjjixFuXX0pC8WhYBl4FsVWMZkBScZCpZ2qw1pnpXv9y1SlOxuS2tpTyXBrskwDtg8Mbrwr6cEr1gVsisOdGinKOKmGvRyRB0AV3P7G6q699gbENDjgprDfFZMnzqueP8DNwgAB6aZfvFAEHeFvIiMDa97307tYXVrvAxSAzRLsqT4GAnH/4APDE/U36hBN2D/qG0wjr71Py5zOgqcKaV1FTW4BR0HvVGBIWzLowZCYmgX5xGb8TcMCRM8jEG8Kpd9+W4q5Aed4Sja75BTtgdVlK5Cl0WcDWr+0AqWIoE7m4hS1LSZwDpN+yS/D4Wz6ICfXgqEHHr06JZEIUXnJ6PfsyCuOEiBL8nOVbJaKxmsTDbxMv506H2Mm/ba9Hh30vcA1KBWljr7+RvynMrV9z61WRePrhAksmLgigvmiDWHT9i0pFMuBK31Fp3Pe2EQEXLBrtG0oI9kJXcR0AnTbMGb0Lzh0IgiOoeN1wLB6vbd2gH6V9UafCwgUCbvQshjUJTBLxpynqlCMNCzfYfc9FZbdjSifrgk+glRfMQHX8CyUJjBJ1AwHmGAYJftWU+gk9bm1jFPm74tq77/QHGUd+o3ZEcwEoK4aIDXHJ0Hh6jOhoq4S47oiAFCDh6gFNY76lr63edKUrYzr9P2ikaWhY1DA4ZH9alBgUTEAyO49qAVg7cHk1G9qBW2Ap7tK3+AFkN6M3MLuu57+DpXBAY9wIbxPgi8XyfHmZ4Nwl80x4gZgHksBllJIZPaDcGWsAYk4bV8DCG/ry73u3XqmOtIgvxkFDhpAJXsFEc+BCcvi6IFswLTkpMBYUpOSc7oe9jABniVKEcZkCU0jn9tfc4roxGY3fLgc9tE11EiIPYcwQTA0wgNtKBRtbxLEYrosMbFhvhCfkQOtOGsOP4gS6pVk8i3hCST/6r8QCfhHkPwxLxL92r+bRHbhcosm7s0Vcmd+9PqRnSnYe7ful1eRlZlHcPJugCQNGU+xLE32OJoTOVIH3wBzkNCaLf1xmtOPRbR5V3jpm3327UrvoBzabPPETXi8SoHgQB0AHKFQAb4PBr+y21HvVFNN2J2QwQxk4RQ2qcfv059zmmzBZAMMZinKgY5EGNMcP7oPJieYLjONhvg23GASggwbkVt17IvX2knAmnFkVHc9TA0jKohBsz46ArthJdBS8h2sACnDTOqwSBILvL0H8hPwnfgVwoPk1lWr9alpRmpDNazHRChvMI0J71SNuyPI8eZlwLxUZIcSlo+/pTu3e+sgJelNEYDIXAUGB0wLrTx9fEPKXl9bnzsnUYGYmgfAVPQwyksKCkQgV+o8m1f203Zp0w5bHOQj+hgA3RfpWZ7/bTegp3Cqv0R7W5zdKxoDKwU2NK0g14PuHrTTZeBj5Onv40LcE644gt5ooC4USOqGXB/XoqfHtUgVI3t2hXt3edYWKVwOKJzyAvKCEEKRqKwO9q2tT917NB6xarViMzDsOeRhjVfvOV0Znfss79b21nn2pqR0v6og4eF/PBTHM1z+w0YF0gzOBnQeYasZPBLW0kr85s5OoYR6Ny5jOAjyfnJF6thpnCvxukkCBVqYoDwnGjS8MTDIx2KU/X4zjl1P5iJ/vue5vfZISughtZdfupBZQ5l1JgXUXv6S9gmOGiOdhi26X7t6VsJdO57GazhsJQfkoD2u++466LO3ctKWu+7YlFFYOMq+KbM0p6bAbgj8TAOBHnloJOQ438XxXkoCDADG7gLq4SdkEAP0YiKntLciHW084edDe89efpb8E3LfliERqUmKb1OOGmHsDti8B6daIC9fNYL96f5F839oDgzvffeR/qangcD17EQWXDMH/PvvOe6a9oVljV6qa9+PuaC9ge99fUlpV1mz/7Q8gfBWVWHXKGjtRuuuTg5I2/MY8/Xu/lUALew/qGgHfTANkEU7bDripMHKiml1zz4nL92M3pnyEXXco4FTIwegDVEeoqIuNHgsAMJHQGCP/jVBg4A8GkaWGHV1tZ3795zzlvv4U6OHsUIvOQn30UC04oapw869dj+B6784T1nkrJw3VbIGR/6I9TTt0yb+qCSWdxq34G07lG7pq4SGYjQKwLDBgf5xcy7AalH3PfsVysDCAGhZamOTPo2GGxYraxSV13Yu3phr5JMJbfD8vp429EuDj5DGncF0OFN+M9sTB0BBQoB14UrNaMe2+dGoHvqkONhN1+b9QmkBEWK7hTOkcEj57KQxTE0zS1COn3dD++iXfv2PcoVpFtFhcF29AMyhrkOw9ZaYTMaFiNnEDYUUXXByccoySU33DPOthqWffVmUmrrDvueUsdZb+EoJ/UZaLE3ZLu0cISt1nR37bixo/NS0wJu1a9GIEOuiJfT/zRfcbvuM97+XDTKDPhC6Pqord58+/VZWSV33P5AMBAWOD4UNeNur4FiqNv+misGog5Zdz36ZOXqH9oVOAacf6l8XOj1cM4DYHdjgKFzWDyqoKYARnD0BR1BpdbE43IZkSeicL/fD60PBAI9evQYP368PAnYDdkD2taha7Qe2olHHXnkgQd9+cXc3OL8hWuWeyHeNJzgs3fGzIlKUm6PfifUesXsObJabPQsRlirenfy2IIU5Y5HXnn3+62IuJxOyFFKYV4rQKWMTGdRcbmnrq5u1Vd7lecpKV1/quPDOpENVJfwBgQbSbuO/bhytICYQfzGvyQ/jQHOEWZpfG6ixmz3xJceALYrdBYgyl2wbDsEBg54xbefA3Hu3btXQ4g8gkqB8yRgVI5XWACr6D4gDxcfmUKKvOf271OqKNfc/Ry6ZNXc2YWK0uPQE7cIECyBjqXDGFMgoY4c8bLcd153XnF+XkMgBPkJonLMUTfNnR165U599yPWRMxSRdkAcdfecSMg58gnxiNoYY1CO20V8sa2oAgqvq1eeHJ/lPvAXTdv2rY9o7zn8edcLYsjSyy7ttZLuNK0QQJhoASzLAPCBNFmVfHzO/LTtWvXF154AWIjz8cHdZAWhhJoMlw9+NTD+hxx+Ntzv4Y7W/P9d1BSZAFr52v0zpz6uDNF6bH/iYDGxIoxGyE74ElUrbdDHE+d8dyjirPtiGfemf/DcobrkKIk9FhydirwUUqrdq2q3Rs2rfppv+yjO6cet7oqVitapIZ8Xj5kN6n6qIUwDqz979FuNxlZyKx4nM7Ay7zh+qtLystemTYNDcAJ+gE2xgqrXlv1ICFkJ8BQBmpfa8fq7FB993b79Ox5bC0kgSkN1bON522XL+TFvQF3bXlZqzvHvgChsg1X5fLPoJCPPPuMZnu2Vm7MK+7x7bcbka2rthI3g5u4hfbIoAua+OLLdAYpDJ6TgWGTlCSxxQ+4Ad8orcpzXYG6kaPvO+KYC8RIN/JDTpB/NxytEaxEkPDxO6+W5hZNe/El29555in9HEquQ2ltmpHqynW5SUqW4vzuh+3oPjTBGw1BexHHhuGSo9pHk8Z1KMzsffg5SnKP1LRyTzXgnd/j21TWORNIPkkpylRawcqX5SAoK1IcpfBXw4YNQ1ul7AKSSzz+7yL0Y5MsypEwdDc4ZCJaAlih5YUjiXJ65qSXXoTMDzjxNFwG+4Jut3vD/DZFSvkBh60M8FEuz8KCRPkoE30kJpwionM9PHpkkpJ/+91PSQbyqTNSWnZdDRTEZccaLhp8eraSqySlKQ6nIyMFXMvPSk/DviMnO6sASAWIKiklX0lOL0xnhA33k1LY+dOvF4ViBE8ojnMqgo1WjBNEXhv3SLaS0enYy1cAgVgN8954CmH5ESefQ0AhYikUDqOOODBiRMPA4KIXBAdAQtqbbWLuBW6yXK6Gtm3bJyfDCDtnvjY7wTiJU1WOGZlAK6OuuxwVrtq54bgTjkpNy+jb7xAXx+lR5JbzTumn5Ha+9NFZNO16RKBtQDqXbQaRRcDvnffmQzCLt49+1GWRUcyXpZg3X3f2AQd2K+2w94L5K2uXz+tdmq0UdPvJZfuFY6qHY2dFdjnQAbuaHBXMJAMeGMPg+EfHZubnDj7/UsA19LTgJ1IjPlb56CpiU8XIOX+wcR1vBQONjY/edq5DyR45+hW0C1sgxKqzI3A/QxQdfAYqMgwfXFRkx5KLBw9QUspGjXsZtmLtD+8rSlHbPieid8WMU/WUEwcoSvbQ869Hg8NwPGi4pR17aH/0Dby5kpanpCUreU6Y+HScSMqCwCAmx35OdiECHoY92JSszJyOy9dsgVMREq6hhT56N4hE8IuJ4wuV5K6HnsFoNeqa8/JYJSPtkLMvqGrkNGox3MsNkId9R1CDuxDGIlyXI1xWWCfQMU0rIV2NjcDb9EmdO3dG8U6nc86cOTgjRUiMMsK7albEM/a660qSkndWbD3qlONQ73367WfCXIXsiHfdkDOOgHSPevo9BBPMDVWx7PpaTuviOx9AQk9zjHnE2PFVYvoXp+WiO2L2ddde3atXr7y88qXfL2xc812rFPis7g2QH5gxdjh1QnQ//hDoQIiEGLSMWio/OEu7A8imQS5gRbxRu2rn5qX5SmZ5Zo+5Xwugg/ujnrtuvLQgI/Wmu0b7mZHtkZrrAwS0bL8aNUxot98262PeYLQxWLv+ppOOhDaNeGRKjWmv/vrtdulK+/0HrFJ5L8q87PwzIS0DTjwFh+Q++i5cd+7JR6JbkjKLlJRUJRn/syBJTogKHy9kQOTyssQIX3K5opQ4i7J5kF769qfzWaNYvW14CbyiHM70ho2pk6fAcA3af19bB5wOzv70CyUlY9AZp6M4b5D2EiiHQAXNx47JToB/tJq0GKYJVyAbfyQ/JSUlL774Is4ggUwTCYvHRhw22/nIPVcpheVLttRdOvRE8GG//fav9sQfEZ575kB4yZEPvdgIFnKQm7MB/ehzy21rO2y95qOZk5WMskvuHse6RSHbuK4BiA2/+rqu3XrllhZ/vXjuti3bWyk9CpQ+DSHOv6zxcWQK6fAb83M6FZoJ3Irifpd2O6DD10xoN9Wwv3rR/G8cjpSDjz4ZjeEsS4onn/BJD2nDSJl8cgVBRIMhsnak2tbdmxcsAUA//KyRcGs0IvqW47qnFijK2OeeropEd+7YXFpQsHhlFfKEr4o2boQYBNR6WE+fwUnePA+5qWjMyyxwODO+W7jUJ2YiY0OZ8tGV2OQ57svqiA2ChAbAnBqeIKeEYwPkxSW0IOivIJCNob4NiCM7l5Wee/ppKH3z1oVtSrNzHM4pz7161y33ZRd3OHbweQGgZNMOxWDJYAzr2rROyczkQwrIEGfwJPc+/tJHb7vttvvvusy2qytq1mbktDrgwIHEcghDt21ok5enONttrLe/++HHlJQUlwtGG5WjQDff+dcTWSGZ1cQ3yUlPwI/O5esJRpDPHEN17dt3dGQWL1q+usEb4rwty/Ju/K5DYVKnQ44HVAyQ95yxb6ledAksLl9Kog8L1mzdkOsoysxosyOg1nB0mXLAGbksrOG7T2eAgZlKzso1G9HX/jDQi6UFvAjRRLgPkUEIFQqG2XeubSsRrY586EnIBxJjE/Yf/wOwU7a5YePi94iL0nqtcnECMl2gZ9vY266Fseo/8IQdQU4aRE1d/hCsiGxvQ0MD/A3g8a+2OAHmZhNcpaQ4ysvbbNu2Y+Sd95x6yul+Xwg3w42hEBigWCzKKU0x/5ZvX+tR7Hhh+leQqqED9oWlg8WuCdi1y97ftzRJcXT+dCtNrY7oFgwj5lNtzU1vbWtznhlVrCh9Dz1AyS5Oy+teWaWjhKBa071DKf1ycm5BcZuOqXy8S8Sc01NJLxhw/EBwmzqyC4EOCNnQ72kcoccpkStfborW9N+rNWry7jfrUG5c+fifw1Y8RndxEpU4B5fPgU+c3+Ta+kNJRkleVtdttTpiHnQBkniCTLh1w6qibGdSspKZnYZmwp+ACUVwLall19z9qG1WL/5ipuIsU9K7KoApgMEIXYpy57wzV0kufH/uV0AaetC9avF3yCM3I2fhwtWUIpYK7OWzDT/riWKCbj5Q5bs09vqNS7v3bHP7XQ/xoaB4BMYw3fCHwgE+iLMrl8x9I1vJKcjYZ5tXxEN1Ffi57o5rULmDDj0spBpw0vU+TtNxa3HozAbHIlNfGV9WghhJQcQMmKugVYqSn484mATFlzuZmZnbt29/+OGHDz/88ETAg99AwMcxMMO3+ev32qUpr7//YW04fMaJhxalKmm5PSsbjMZtX3ZsBUnoPv0LvnWF2F7wGbdqwWCtCKHVWc/cW5au7D/gZCUL/jg7HNAQfgZDDZ06dktWcpyOglRYIilFqb2U9H5g9hlnnwvYbYrXnUBQET6ZjufcMhIZiBv/gvyg0UBnTACwElZDgXrdqjf5bkND/7KeRUq7xSv0Bo6c4n5XzbofSrKSU3NKlm6uo2OWA2l8FGc1bNvRulUJw1o+9lMychREpz0cCrzMDWNfhqldPY9jikpBJyWtI8dK0SlpyqwZL2cXFC9ZvSFI5hvffTAjL1lJTyufO38dTApdFSoWNbXgDrpsxB7sKMi5N6LHqhvDKUWt7njoCaooAGbEF7PqbcsbC9TYYYB186fFP2UoueVpnaJu290IqwPd0G4ZfXNSVnK7Lh1Qc25wrcQZcKYEbbAhr056saQVpQUgOA3ywyb9vvzU19eff/75l156KW6UD+LlwyyyM+y3ja1LP51CPn+73AhVXHDK4SlKek52241V21ZtW1OQDxnKnrtoAxrk5ZxlWlq+VxWutaNVdsOWGROeQQ0OPP54SHJxRk5doxpFD4TdXUtzM9Jzk9JzFaeSk5ebrpSmK23I8ZSUodePrIzYbiBStAhAR6gVlF+oxu/Q7jeig3pHIKyA/g0dOrRDeDT7ve+8fFcQCq6aOthkHT/wTEdyJsKIHIey74GDtnr5NmYIIq438G3Z2uoebXop2Qe8sczjge2zK23XsgPbOJVU5/GXXjF5ystZfPQMwJCfnaFkOTm7JQ8dCiDtTFPA05SMdERkivLMuOeOO+HUfv2PCIjhnMSjKzH1Cv2Ac9iw0xzokNHinR3ewhoDaQoPZ9K1APLoFmrItxh8d153RWFm2tKVP/p09+i7Ljm0bxuzIdCp7f6Ko+OL7y3iCCIf5eIuvwWB4GNLmM6GqwYfm6k4B57zMEKqddt+7NRJWbH8/W/nf4bmnHb6dSje8HgaNyzuXJKnpHbfDsRMkY4/VQ0Gg1I6Ecny7L+DWDz+0zX+AuhIdpGfYY9t1Lw58VFFSeuy35FulVpFBxWNeNd807M0rWivg7da5Athjb8W7g3y7RWDZuGgj47cVO8dPjw7LfeKkffDvcPZsJcA9uF0LP+9t12Tm5z8wZz3vAE+O8BdyFuABh6YsGeG9trEpxVn+oxZby7/8oPD+3Z3RxlDIFwAEyF/BDpQ03BdZN17XfOUzPy9PloSxHlUw2SAhQrU3TP8Eg7i5xR99+NaGH4UhNaFzZjO4Sf5MJGS88sNxB0xqAMsasp3yznjUXBKi5sn8kxMOYKDaLA9C/ZqpRx31piasB3YsqBXCexT9otvfnbfjRcVKcrAs+/cYtJ34iIzQcxbV9enaxtHEuFyO8655QOGg8+6ePjN94+7/4mw7quq3ZKbV3zwoQNVwEgt7Fo5r1cJvHCX1R77k28WFZeUbq9xUZhiCMelImBf1J/1ajHFb4pnwJHLeFbYLP2dl+6BJnbbb2C1xAdIhuuUXkALKBHPRhGmI0wBP3AVgU/MrwfX2XbdfcNHQLnvGPMMvBTu9fj55DEMRxWDeWFcLZ6S083bRt05Jx2jOEpue2S8bdWuXvAunHGHvifuCPB1YvQ8VTFm+/gMAccs5p7bb4aPe33aTJ43GGiJp2Sokh/xCZXX1Kc985iS5Jg6+/Xvv/+8R48OmnjEADlBJtGAmCtGN9awY9W7XYuSMpVOy5dGqzm7lDKpqnVR233NzRcC+GZm5H797SLU1RWkZKAZSCCcDUd0LAQG2EF5BsMBiIcEMaC4K2r2KynxLBvEs6Zqhzb2LU8++tShaGq4Zl0Z2pZcPv71zx64/bzcZOXYs++CAeLzM9QdPgVxR9jfu1c7uB9nktLJKUBMSsYxF1w+YsSY0XeOQu/sqF1fVNC2b59j/RA+065b+W1bmNq0vVbV2wuWbU/PyvcHAxxiBC95HUAn8o8Cnb8iP+I0YSNECCocg0n3a/ZOLbLtwPxOJUqbRSti0PRwFJfq4YNHXndhkjPn1jHPQNrAGbd41xLZRwNBgRoY0EKlNNhnve78w/YG0LnxoUng1bK5bwEstD/w+I18rCXuMaGAmm6RjUKNIw+PvB46OG06H1G5NA7bo3Ji8h9fvqHcRe3pUyYAe7z2xlvvfT5vn8OPqocAiDCajp2ihM2NmHnn+hVFqQhtS3/8piaCBhDzhfxmpQm4fOuVmfnZQMDz5i+CCMDO4hdMEI+oYIEN8U4DlUeKzR/Jj4yN8Zt4qsVJn9AsDkzoHJgJV7Vr33HQ6WfH7ODOrasKUgqynNmz3p5y9YhrlZTWp51zO9QE0otmcu42tMgX6d62EBiwJFnJQ5yXgqgs+fxhZ4248ZZR9zwDhm1btaBbeUaPvfZvCILX+tZtG0qzuhRldK2odn2zfIWSVrCVsYWwPWAGtCXohXSK4d7fod0O6Oh8CRMs2br8m5mcI5zVrq4hDFaL3jB/+PwNCMd5l9yEnglVr9u/M/BKVpcDTlhv2ZxBaql22GWrDecce7ySs+8+p98CLbPsBtvYPvuZuxGcHXfBuaedNWTwoFMo9QT/AcNuOPvYwzpkpn2/eO7zb0xDcdfd/gg1H3BE+Ce5oTjKAqE+5UNs8XPiNM/KDcEcpBkKQWNEvuOEBWngVYhVJGRqiIqgdsFl37yLiPKOMU/RcaL62up3Z72qKLklB160jq+s4n4IRD2tIcrhPItNO9fObJ+tpCspaZn9P/y2KmAHX33rwb7dS++4/lolOX3OxwsaOG/SDm2dX5qqpOT23VDDyu9WBD6IP1A4Blc0HMJMs4nc56Idtr79gmP3Uxy5N933QsCk9UIrYkbY3LKwQ4bS8cBBco6OeBUBYY1ao9KXMwc4JnRI2P/upEcKM5W2+564EdEOSxDXsQcvgaJMz2vTxyc5EcFkpaZxboqYUwW7nZWr5OXIBxBEw8lz33jNVv2uKMdDYI9QDXgVFARH1Lh68QHlNPETJs6Bc8LmguiiCDgjvRHblDdmcHawIyMps2DewuXAamiIBDrCSyEx9qUsJUge/vI88kxsP5NMBuy7/JER5ykpfb6Y77Et95jbz+i8d5d6Vd+7R2+HkjF15nzYaCTyAhngDnAtZkdUDxf+iWy95aQ+aOzBF9+zHdHAuhV9CpQ1Sxd8/OUCJaXN0adfyYpaqm/lN90Ls5SMTktr5N2IyQgQdh3QETmIDKT2xM/gN+y+5ITeRQ7l2rtfgFxTBnQj6hMhD0MbRM70DUgYCXOFE9YCtpfTDpC8ZsqTD+Qmp/Y5aGC1xtO+EO13hG/hw+XAWAsmoxUA1pH6swYepThKb3nwOTta+eM3byhJxR33PQmxRZjCicRU4HquroLbcBcK04Gtpk2ZDhHiPEzErA4lJVnJgNQoaSmOfPhXbM5UStX778829AiATkBMDiX3UFXWuG7nuk9Kc5WMJOWtKfORJUqqDvI9HJiKGCfJuqZMfgnZ5OSXKkkZ3/zwEyrgCQp3S0IXoHo4Rw0C35rOt4TIQM2Ornri7rMVR9H8xdvhs0cNv6Bbv8N2eqPd2pbmpKc8+/rcallt1lt0NKsIRaoMqqtuHXJ6oZJy4gWXVdl2VVVNeV7OipU/LFyxEEH8madfJfxQrGr5V33alijOHksrhB7BOYqSxX9kRp1sOtUyapH8MEZFEUA5Yb4uZ0U0eGXdrtK0LQfkdOietPcX33GcivJlQ0G2vTv5qQxH3v6HnFYRoIWhKkUZc3FoKGpy7QZyXjP1ejtYccvZx8M33fjYNISgaxd8lKsonQ85cb14wYRN1IBICLVh0ET+gKs+1HDS1Jmw1GJgkQ+pQAhC0h1KUWYK0CakJzkFYCB72psf+sTcZ9gQzmFnHn4zgmZ5t69f0Dbfiej3/WlfspZCS03LC5SjWnUhyzf7HchzMsAlSlm0dA2EhPPwIxZXpCCvkBU2GF6BgFpGiMpYKT690jxjb7m4KFuZ+8MynLrn1hGH9OxoaVXlHQCIu73wDgc+o7EgzbkVsoMBPkeMCvynb7/4tINhbE89+0IjGq6rqS0v7rn4259Wfv8pOHDaBVc2IDu7YeeGhW3yumSmda0OchQESg5VQr2hmGIaHDb2pjj3O7Q7juhw/NnYPvqaM5XU/NJ9T+CUd2Eg3MHg8/ffiDhVcebPnb/CjrrOOaZvmpKSVdbz3Y3VcH4U8WC9Hah+6sZrOGZT1neVV7xObbnFm8nq4jUrUnLyH3rwiSfvGrtP587gsd/2XXHyQMS18xd+9tSMyUp6x/uemG77K9555fG83LaTZn6JuBblS1lA1YQkSK2S57gvz7PiYuMEZCEzRszt13aoYQ+v4gz+gGK22uhjMBqrGzzo0Nzy3qu2wWTXVG//Kis/Q8ls/cVm2mlm7Kvg2A+iHWQKFY6t3LZkfDEfuzgVpW1G0T6t9uu5xbNh345cH0hJSz/mjAuyM7rPmfxu/crPu7VyJGX23gEbLsrcfYg8wH+OWvMpsZBKGAs+lPDjL5ptuO3GFQe1TlEyWj371ndQD1Vn0BHR1YYlH+9TnNb94CHXP/66kpyWlqS0TufIxOKNdTvD8nbBt6i2ffFrxUArxQe8v5xhh224NM3FWeMyehHDY26/mFPLKAd2iwaEzGJnI4UMm6FMCOk5qw7GCzVBVIPkWjiwY+PO1rn5YDucWWmrnopSznf3EHylZChJzhRYJpSerKTnpSuAU2n5fOKelFbQqnV9g0uMrgkX+ztAB4TDX54XlYxvP5NM5rfVn9Z892ZuctktNz7KJ+5EAP4JLz0HxHzYMefWNtowLS47ELLViMbHFMgjEnLZZo225rMuilKW5VDSesxcUmvH/O9OHH1w72433zxKcbR/8Z0fIHF21O9fNa8HrFd21/ViZReckwNUov6iIdj+LtBhCbJZ+M+QkQ47fgZO36w/sNwJ8/zSO4v59gq6BklQNju64cdVn+a0KlKS+VJ/TlpGSlpbviHH/gVb3GZoc8Paee1y05S0ko+XbJfwApsI+BCOyzUgtBjkLqpB0S488yQlo+319z9lx2q+++CV7LzOXQ8YvCMAV4YoKzDl1Yl9+h6O25F9vRcc5ux1cCAmQJcnTOQncoZcibdKqLAUWS0aYKRuW+EQJVwV803p0nFb1N68bn7bUiUjmS7OobRNUrrBFSWnp3L2WHIyJ2k4OZ+XksRHaGlJ6RSk/OJ2jR7hPZkTikH+5NvfAzpBxHroR/OnpZ+Pz0zOe+D+CWIdDy8a8dJLMyDgnXrsD5QPBwqzJqZzw6uY0RBAAvz+9qodX3V2ZBQoOYoja96GDaGwNmPyi917tr7yustTU0qnT/+SzyAgd5Urix1KVvnhK+u4RMjvA52mw79OSN4y+QE4k3GmaU6d+GJaRnoSmJyqPHjvNb2cJW2VLvMWhQF00Ee2VW1Ht25b+HGakpnkaPvZog2IOPkuEKUImAABLDJBTAkx0DgbwXKdeWRvOOaL7iGomv/B9KJkpdPBgzYgCStjzp468cB9egbCfGJDzA3QgjjW4uv3bpWPcrBDweWiEuC/3w42woHjfECPC5jGEWnaJ7+G8nVDrWGMt31t62JGbDnJmelKYY7SOVUppDgJkXHkpzoykyE+aVkI51KFjcpKzSgEbo4YsV8CHUqlZFxLCDeiQWKCjBZc8/nkVk7litsegLTYpt8262a++DRKLDzgXPAB8T8CDIg+x5CiftMFDqN8w7vh83JYzKRUR167rxctDoYCU1549eAefUaPuDYpSXllDhc1gAEO1q3JTypzKJ3WNiKOlE4ZrlEolJiaIwZD/mOAjuA7Qq6G9Qe0zUdH9Tj2zEA0psdiQWFIl348CzF0flnrrdW1tlp99clH0MenFrzw1WpEpZARAudg3dynHyxEaOVIe/HzJQBAEDVdawDWWb34GyWl+Onx095/dZx4Zpym5BUViAH8rGyn4syCiVeSC9tli8FYQKW0rt4IZ6xRgYQYCEkQussT2Lgvz2MDu4MakLIYvOEAO2S+xoj51FDYQCQZ46LPTIf7cDVWNWniGNivIcMuRHg6ctQ1irOk/1m34Z5aiDr6LFRN6RDvqKsIGqwNT914kgA6yuw33ilsv5eSUj7q0Wffe/khNOGep7ikW7e2fUqUjLdffr5DaYkzr8/aKha1WxEZSE6h+XwwI6oHRnEyPhrNAdJwvb36g/Zgf1a7d5YTzau6nGhjhFd/1ZWD6m2Vgv3GPvFUNFT99kv3gRtJxd3Wein68cwNv+3+vgMkw9Ft3Jz1KMU2YatFMAfh8of9nq0Row5HqhozQ2FYDSBrXwRODf3AtZIMTnBGDaO+7bXFGXmbXTW4P4hqwsgHK96c8ZKS1Hr/A09C/0b8m+KyEHTde+tVSnbRiMdf5LTNmGWqVRNfeGjC5Knvf71QSc6695GngnqUdh9V4bJPsCxi4/0k1If1j2dHuRKnmy40XW4imQxWxmsbtUMP3KtHYV59mI/Ytmz8oVM57FrRJwsrIfmoDKC1AcQMCw7ryoc7QVurWvPNHClLijNXySjqfsABOyq29uvSNifJ4cjocsYldyuO1NnTX/SvWdC7VYGS0mGdP85hSKOfnkp6WVHPXQB0TD58Yp5sFbvM3unZ+W1bKmH6xytrKtBOtBXXgDxd3lkv3cs5mwVlL731Ka5MGf8YlLhL9xMDMAFQvYB4L8G9ogAgwZH/3BvzEP/hbnDDsCNWuH7595+lOpTMdI6/AJG2TRVjeCmlADqxwKYtSz6CjYGYZbfvrGQnJwG+wm0k5x054CxRBTTWkEjdMjn6wgrTB0GlEUaLR4Q8sgFuEL9qdnDt2rWtyzvtrA1CyMMQM3g4w3zhsSeBYo446RhfzVJ4BfCSeRmuB0ZeBmm5ZdQjkMmABXE0Jk6cOHP2nKWrNihJGSPvfxSAw80V5kDguSiJv//AiA6ATqzK1rZdcsLAwpTsxRXb4Fqq16/oWdwK9vCjZVUQqnpNvLCDAlCUhYKE4EUrdv70NfQsLzk7PQNSlNX30COrGmp69ch3JikOR5vBp98KTr775qzK5Z+1zkhKyt9vnZtx9z8B6Pw1+YH6wZOEGkbfNCLLmZ2cm1unNvi9G646+4SOzvwcpWz+spCcjcdHV9YWu3Z1p/yOiGWmvjcPzhXRDu1AFDbcWvrVV9loW3JSroPCAz2Cy8hITbrxyem1AIArvqQHSSlSsrsoqVzhFeADpmvwmcOgRNAg1tkUiy3LADgK6OMN2SEf122yopAUjV6ntoHL4gFHbK3aUpBf4vZCjWknBTb1v/Hyy8hz4HFH19ZW80kImo1rhvHQ7eenJymjHn68Viy+DYUYP3HCu+999OkX82FVR48Z5wtG+fiO6EqaEbGhGqxWi8gKG0GD80PQBM2O7DzryH1z2+/zUyXQZG207sdcRxaMyeebwwCarJ0LXEVHYZehJifFR42q715HN6FiSko7aGv/Qw62Gtcf3asUHCtq1eaMS68A4ybNemLDmkW9Cg4szTx4vYfvFonZVlzdMQz2kIFsC+IO0aLfod0O6EQj4JHf9+PX3bJTlOTc9oecVCWWBEWHoePtiDtSszYUizT4XG2cSlnTCzJPf/TjFgEruBqqWvPtM/eXgnVJynMfLd8KpSUfdIQV91xxTmrhXo26/daEO2Hl733i6R0+q0/bkk4ZynfffvXq7A+UzK633fs4FHjktWcARtz60OtcgUcoD7YmSRBmPX6O+/K83CS6hDfRAPZtYI+aaMyP83KyTnxiMjrE72PQYFcOHXpydm7G44/eAxCe0X3A4tr4Q3oOh8a8tspBCN3W1GiVXb+qs6K05ztZysvTZ85btU3JbPfRp/N6tErNdyhJeW1XbA/eePX15elJ1517WkFWjpLaqyLAKu5WxObjv8VFFCQHpaVGaAOVJjo0XKH5k2FdlMzOb68JuflWgYyKDHvrD13hupI6XjJ6ioszc1yIus479Qglo/1lYybRqSNOAfd8VbZvyT4QjpQu989agdv5TNM2uXoNDog1VJiVeE0IuXSVU9EjDAkQnonQwB1weRpqy7KKs1Nykgqzd6oezbDdVbW9ytJh1G6/ZwJhmQHr53ZDntCMSOU91w+Dabtw9ATUjLXlOCKnpiIlJEC+L8OmM/QULkpuOM2q8Ef8laIl0kiSF5ouN5FMhg2RpfezF+5upyh9Dz8WLmrEzTfAf59y8U2wJQgPxI2q7q/HX/HMg7be1irHXn9uiZP2d+KEySXtuympKQ8+/djs8U9AoW4ZOb4uYhe3bZ+frnzx8rguuVlKakdASagh+gwtkkhuVwIdsgs9zUxEq5DhhlULJnVXksqUVm8s3oIwhu4HZRt23cZ15blKeoYy8a2PGmDFddd7sybD6aRldW9sEAMrcAN6te1ZdEB31LzoqTfmy4FubwTVR539fPUsFhFztjh1K1qz8fLzzlSKul45+jE7VrPhh/eQW7f9T60JGX4raJhgpL7ip63d9j68PhhCQB81tVgEUJW1NVAcyAzZBjwpvyEQ8gJ6sjVoSMQ2Vm9eUda63OHIyinqUFELgVErN/9UnpOXlpxx+4OPiZEZrx3ywubjFtv/0x1XHJ2aXnLbfS+6TB0SKYbP+DY8X0IWo0PIlt1IQgWEAPCXVqjp/F8n5hDyNcQMj215Zzw0um1GyuArLquLRe+67krYmWPPugEmzG8hczMEtEykhgKhKoD9dbZZ+9gtV8LNI0acOenN7OxWSmbG9aNumj3zCcjV6Htf1qN2914HpyYpC96Z0BFGKrPXD1uZgex09rvo+10AdP6i/KDikWrdtSXTkZmclPfl4h/5CpntNuq27JXbNkMp+uYnD1wyfQ08cXSzXb+6U1Fnh9LuyUlvQwjACugXK0qXClGin474YKiDUPazj+sHvbt4zAtww4s/nVHiUHoddeqCKlNYA6QMrvlx8V79DvQKIBWKRKMhL8ygCb8UQn0RciGo01TbjBDzsrqWm6OAkJDVO9blFGWkKs60lKI1DXqDZW9csahncU6BkjnyprvkKu3kA9kBJF9/z7XHFGcodz/yoku0RTcRaHNBIyaDcRPvpeEeNASwIM4wFCrkWXLzL5LAFuA7CjGtgMsO1r05/hnA9LMuvtS2q+64+oxkpXjwsJE7DbpmFMoiLDtEwI+IxG2YIcNdPX742TDVSnL2U298k9/pQOw9Ner8dybeCQx3+10PuSORoi6tEHe898HbRUq3PGWfjV4LsJVqaGsBroPuF61mxVGPP6r+7gZ02OV21KuuXtAl06Gk5LU/dNDmID9Iw17k8jiNtum+acQNySnK288/eMvpx3JEx5H9+NtLAWgqmUPQDlV8+RRxTGZW6hl3PLWRH9tAviFt9Vfd05VO/QZXm/Zrz45o51Qef/LhVZurOpS0h+u67+67r7zmZiWp/K0Pv2Yn3TRMyeh88Z2vwEuxG8UGoRCyAN3AFj8nTvOs3CDB+BX8pt2KmtAOfhYGSeEekBWFjG/lwTvW2VbFwi+nwigkJ0GMy256dHZ1zIbY43Y1DJ0CwgkB8sQ46cz73H339cnPfunOC9rnKOPfmg/Hg8a+/vLYjMyUgw87RVG6PPzA9BkzX3Y6lWcfvKw8P03J7L+2Wkzj3Z0ozhy+kUigA4YIHaM5EBYBbGuwV8zqjm7N6PLaCi52AV1CL3BJwA3f7ZWO0Hq/rWKxeYZY3uW3XzNMcbbtd+ZtSENNRo9EGu3t3/YpRBjV9slP1qAUlIXwGn/DvrrzzzoF9ggsT3YmYQfWHBrFyTRZuW2THbhJSSpUnIUZOdnAVH279fH7tNx2rQ876XjWHEBVQyCreXROf6aDIU4STTDX33XtECWr143j3iUssxogxrGgVzXtBjF8jQrLNTzEUJ9wUXKDaIg+Yjb8K0VLypggeaHpchPJZMJCRXx2uPKiQfu1aeV4/OlxACVKVs8FlXUwzZwLhFQGYWVY55KsgWjMCPusjd/2SVFyoCMZeZPfmP/xgvVKtvLDD28eVJYj3nA4eINm3zJiOKLSu4cNKE1WlILe8qMEWjja9OgKTRANwfYPAB3UjhYw4ahE5lw8zd5QtXbO3smpbZPbTZm/cROVAb7YY7u3LPhoJrp2rwOOrgqKxxEAkUF5Fy2fkABk7Pauexu+S0kufOHd5fJ5ABITp3FeF3hjCKBD2YBJGTLwWCW1dPi4Cba+dclnU1NSy3oeNKSOL6eh2KAJnNgol7thKa7G2rNOO5mQWzxUghQVJynw41wpLT8fxiQ3OVVJLkHR4GVSmrLPvn22V9S27bj3GaefzaIjbg0CTHYZkXAj/sJkCKyC7Jc/etdgRSm888HXUdsgX/LWgyqco2idmMoKGSLHcBs2PkyFDJD/zIecbAnFLIgoyhVeDxbJO3D/nq0KssY98ZQjNU9x5q/3hcE6cpXv/HHjGLNleQ3gZpd308IuGUpZbopTSZ798qc/LtmhABn/+E63DnmwacUl+y9fHbzp1tFpDuWyU/dtBTXL7LEtxF5QdQR9yC0uM/8I0GmZ/Pga7PDmma+MTc0q6HXACd6wMM0xeMrgQcVd85TCzzbUbpO14JOXTaHKpeUF7RWlfMIMPkABK2iOYpYeCHCOjgoQAhXQOAXO8l5y4mHo+qsffhlOfdW8OQWK0umAYwGb2I++Rtgw3FbnDdVrzMTlD1183jCBETk9p3UmQw4lPR3xBk6BVbnw/FTQQiB1xeHsf/D+Wl1d9w7djxl2GWpC++kX8xKE8fBq3pABKBPm5DOz8qERx+c5lZvufsEDVpOvDP90Tk+jpAXFBHv4BRz+Gug09chfJKRFFVRTjRIoa2RG0LjyorOdScozj9+WlZ6kZHbbWMOn5ygjbFmaIYZAYYXCPro4vcG946feqUp7qFFa/thJ7329ZEduTtGKb6b2LFNK8gpyslvXe92X3HSpUuIYdMZZJUqvrhmHb28MQ3vBVWzi62N+vqgbZhtx5o9UYPd7dIVoLFhjN67tiN5Ozu163LBN4k0En1+swe3dtm+bzOTUlBMHn2RH6i47Zh/IArzVw7N+2EEQDvLakU3fvDiKLw4kpT338VKcr7LQHd6nrhlaqiiHnHELoMf70x5pl6SMvOXSed9+D6HKSis7/rATjj38BMVZkJZXsH39d/fde4uS3vGah2Y1BzpQiqbVHrDJc3ETk9jAaB1eVfWK0cWQxY9ScDkmZOIXWD7IN4QhWCqbadTb4R2P330dTGav/gO2+8TbQ8hFqGWQCxJCFCGCXJWuV6e933jp1bmvjga2m/z5CrSiYs3ibkXKMSee/MGXax1KjzSlfV2wQrc3hOu+6doKHrzvmlrms/uQZJFgE1wv51eDLQmgAxNACtXYdV8fDB+b3uWJzyvAPugwfqmqKz/bB7YhpceyOtmuGju64cPXn1fyeuX3G1YpJm1riK0tr2/+ax0gF3mdp61oxEmu+wusSagT1HxVsh4BFYYr+ParjxemK+37HVLhi9hV2w5p11rJ7PTJT7Uqwmn0oMUv5qBuLA53wSPAO5pcg4U1txDVRfz+IMcRjfWjb79ISWo/4uFZYmioYeOS+WlK8unnXgHpRUnIBLe4/WwKR/t2DdARaVBPdce6b1+DYMBuKil9rrzv7SoGoGaMq+lZth+mnK5F1gHN+GzSo73TlSmP3g0X9fJbi6E4ul3/yvgRRYpyXL8BSnb/G+6b8fQz40rTlMmjr+uSm6Pk9FouZAmZSLy+S4EOboeXEmMgQke4rLu90TbW7J+WWqIUTPxy4wrZBRHY003Xnn+MklR83ODr0Jy6gB8mG/VBrwR0F6w5NAYtBsvdq2bt1QrOtfVbi+po8eN2UCfQiXnFxxPoaiNut601nn7SAACdW56YCGuxdemHipK/96FnVQZCqIkc0YFWogJe3fLIRbEtw4qI4VmyNTTn+dvB/Pb79qvQEN572+fnKamtl27l5zxjtiFX8MKmIYiBS4jxkxHiSajf1hthMaqAhVFnDvAvvvXmExSl5Na7p4lGhed++VFJq/yBJ5+EQ2y4Ea1DoBQv+megw6M/svJ/SLhX89mmqkUN9kKwoW7twrgUJRffPm4qWo7W8usFImJWI3xPSvV4EHpFYzXTxz9UlqI8fc9NcPAfvPljJSXENXXOg44k5fCDjgU/xj4ya8LLM1KSlEmPXtu1JDm77UErauyGIOspXGxcZv5hoNMy+bnnljMVR9YRp10JeWCBhhqprT6guEuuUvjJ5p3bkSfuDkFltu5c/Vl+brmS0uH7VZXgQ6NYLCASgifiAxgkhDlwhxqsmE9t3HLZCYeCDzc/PqXatrcu+hBAp9fhJ60RL+OxegjWTH5TAvlUeukOdOAkHUIII+O3I1UvPTlaySvufdzASg9idv8+rbqWOdt9s3CTiHfFImERxPmRevESJUMXD1cL5BAQx9ngVWBmdF33WVrlwyNPzkxS7hj7aqMYbFnx42L4lzPPOgfwWpcDjZytx51fAx1urO5fJNweFu/sc9Ui0RlavW/DAoI8Li+XkXf9qPFoL/s7Gg1bnGoJBxoMch0vVs30fvPulDJFmTD2LsWR/eon3xOWxeypLz0GM3/ofv2SFOeYBx95bvLLgIFjH3m8c8b++UqP1Vvroc4ydAywG6DROl/WERr6R9XfzYAOqonNX22rP53Ut1BJKWp95EXypQm0wYr4Jtx5Hpd1SC/++oeVtl5xxfG9uEZBct7jcxZVisYzyjeXv/PszUngTXLbp9/7ts62B59xDLS3DefipF336DvwAS89NRL8nfjQjQ+NvlvJKJv77earz7k9P6l4v4P65pWlHX1I3yuuvFZJbX/to6/BRUFWhCw0qaZcGbnpnDgdr7iUm0YXSuAkNUtA2ahBKB2w+F1r9I0X8goQHKrl+6W6/tRNIyAW/Y/uhmAoNaPQh3gP5k2MkTbExAeZ8T8Unvn0syedcSHOv//qGLTlhTlTYINOP+68UmdZRSO/Gtij1aHtcvtUGg3VkTWBzXPbpwC/HbZezKvYfUhyif+hnL8EOmCOWPET3qDaDvww6rR+SmrnwWPegJ5oJke3IAL6ik/6ZSZnFPX/CfgQKc3tdnjVjBfuV5ydu5xwU23YVi1DI4Ryzx9/S7midB144TwPO8nWNQMRNMuGI9J0jW8Ziy9iBu+74SyYp1MuG06FVGv7FKRyXsLqAH1GTJc66QmLdy2wmTHdT8wEBzPz1fG4MTsZKp2UkpkK55AGbMnPLmRnZXAFZ4RoWekFAOvHD70MUuQzCBGQbfzdcvonNpxSxIrxR/yVosUyeASSF5ouNxGT4QRNLzKJVtjhtRPuvwLwvsuB52807Z0C93PqZYSPU+wgpz1y4QNfrR31t2pTMnPyi99Pehbh6vhZc6EjVZUr+3TOPuXU0955+5siZ6ecpBKXzxsK1tQt+3qvkmIlveuypreu0GUaCt9lQIej36IJYtjTYimwW1Fzq21tveGY/aAdF46d85Mw92Llz9Wjhw9Oyyg584JRNT66DUgOv40QIphRbavR1KmgnqoFb9yXD24ccMJ6scIYUrr5lSZk47a5TjqYL7kIfXOdfdqJADrXPvg0OLnii+kAOl32OxlS5zE8eoSzj486ZnB2UZcPv/wWzVc5CiIcA3ASOlPzTbjrdNRzyBU3Is6AbPduW6o4St9fWuXXiadhixFFs6PIIsvjrucOig7WzH7xKaeSAm+aliwmkKLGOUpqanun0hl4IzVdyc3lSsOQrhNOG4yikT0iciGcYiPQiXMePzzfMoLssQG6Dr1AP3CB5rEjLsrPTuqyz4AqOFMqTDxrsd4mX8pGoTF1o21u7dCt/O3XJ3/78jjY0pdeXww2bd44Ly9TOf2cQd8tXaMonTLT+zS4VTvqdm/8rD1Cl7SOm8QXKlFPYSrjNf/HgE4L5Sf205MPXAK3OvCCOzlCAxGGCoWNPiWd05x5H6xbA9vNUQf0mLX13dcehbve+6DTasX8PT/8MAXGMjwe1eeO2uZOf02I0Q/a6LvsmINR1jX3TwQfFn80BX6qfb8jEGbTUiHgUBtPP+UEJSX7h3WViGY5YQi1hxQBsvir7OiWJ+67SklJO/6iyxHoN9Rs2r/8gCyl/NslG12UcNguAW/FSDYiOpyIhhi7QCRmTH8KwpOdItakdKblFmSmJyupkKWkYiWzu+LgMrLY0tKzzzz7YuD1sEmggyZSICXQoS4IeW6Spb9IuDfK8RpDQ7bSGJiqHVn30A2nKo6U1gccDwvLd4lQS9NuVP3QgjA/AmipYSgsUKLWpcDx0ZTHZ095XkkveGLynGjU2Lh2VVpm+VlnX75q8Xcc68hutbmOEWn1tnVl6d0KUnp7DLux6e1FCg0qjKK5x24Tlfgd2u2AjniBIWgHFj5862mKM7+w76lyyTWwK6DW9C5UShUAgrbfLdxkB7cd0EaM+KXmP//Bj1vk948gyuGlT4wcpijFSkn/FQ2AvICvW23vmgE9OjmVrMfnrAQk+mDWsxDEy844LiM99d5xzwci9tRn32md02H+8u9WbVvUrU3hZRderqS2ufzhVyGUCN+hmUI5YapiVnypfjA0vvF8fLMMLlkGdgcHHnt4hpL57qxPDJ0J4B69Bj/JyPZxiCoABHTewFMLFeeISy7zR7dcd9c52WnOVCVt1qz3g2LhFiTi01t0acju37n3l4tXYfetV0eXZSoT35zw8CuTsxw9F321HVVBpHXH1fc+cOe4IHyZXdfw0+e98nKV1H1XNQj13p0IrOB/xjEiPOI5/DW5agvNS8g2XLZ3yVcvjVEcJW2PPM+l8XJDlGY4umFRB4h+Rvf1jfIrBJyjc9eNFyrpHQ8+e2RtiClpPUP1z1w/uFhRrn1wIvw9TtI0i37igtow3bAvPK0Zat3ZJx6SnZb09JR3KDyBnX1Ls5T8vT5Y5kb2pgaLAk22Tjx1yLDzLuYDc+YiwAmfCvsYnVuqaehhExf1m+8a7kzJuP+e++hVYwg26NjQKK+QTOzgPj3KgCaei9woQiTkjU0cyu2XJK41o7jg4X6ukhyre+zu8+FKjuy/H9coy+m9XrXrOCyvcz0xBl2cCM88THXaxKdOHHYO5PmjZ8ZCCya98wk82GmnHJeepNT6jaBh71XSFSFBVX0l0KBny0+tUtNS8veuNfjJRMawotB4dZkjakJ3wUq1kNBZUG4+N0E+qBAZyx9Gaehcq/KD50bnKEr5QecgyPWAiTGPbaybOWVMhsPRrn0/KAgCXJymeY5qpu5FlMN4F1nq/vuuHwLjcPOYp+F4asTzAmyBsO/RsbfiPB8ZONKcSjL2y9LlSFjpLQ8+j/Bp69KPHcmFKJZvzKUqqcCucBXJiC9yi0pbV9dWsDMtSBEbwDEzS73oxH2Acl995wuY5KivqltZnpLb+YMlNRAZfnPF9kRs/1HHnHrG0KtCBmEYbAIrCUOne9HkqAZxwq0ABdVXj7wSeOeeEU+RO0QhaJ8R5bvcdlAn4MYOJ2Uk+N8M6Ii/LSJLLNwiujRmGgHvrdde0qZI6du7o5KUn5TfbUs9V+OMwzJRACeYcafu5efvHHrhGdFI4ItnxiKGnDBr/o6ofdH5p+RnKDX+ynot2qXjYSlKeUVlNTTAt/WbNrlKckHPNWIsloJJ6RUPU5gfzjXhzpZQi+WHXwvf8MqTwxVHbteDT98WoUgwsqx37VveKcWZ8daKJXLaLNGPuvnum85RUnJuvX9CQLCdchbSAXTuunl4aqpY8BrSA2/s4BNwRFZFinLrI6/Wxuw137/HRw3OEqVwbyWFc96zHQKIONLSStrvqBIzu5GdoTLcNd3wUKcM6qvkFT029fWQxTG2vfN7tUrqOH/ZWogFEhGI1FZcMOik4067GBLOysT4TUsuocuIBj7NFTM4GTQas4bfcHp2lnL7vU/6BaBBY9hjkJ8geMWxD/zKDQxEZjGIJDc0Ly5Lf5mAtYLBCGEbRyhxr+F/eviZ4MM+hx0DhUrKKgkgMtTtmEr0CPAIPxjQgXXY+pkTJ1w65ATbqpn08jj4+ldmfYzanTr4RGdWt4q6WMRf071dblpuWa3XsKOBbWuWti/snpnaae02qAm1QvZIvCWUHNQCV0SLf0O734gOKs0PuGz6du5EJTlZSW9TWWfCDqgxIEDv+UOPILJR8t98/eM5054+uE8eF6rIzXt81kIYay6OF0UIv+UhPkQoOvqc2wgFtUbOn29Ytk97hK9FT737E6LCN18azaXSktPa7n2YL6LqkWD74g4PP/gs0vMJplr58O3XKylFlz30Eu2jpo+8axSNHedypODX6aRh/COCDggMjS0ZtTvvvAtMk8E3ogwx0R1KpG3etK5j2zYQ/SkvT8WphkA1oPGXn3+AfLPSnJkZacuXL0dKtwuxAo1AFBAYDTTVd6bcm5WkXD78aiUl954HJiGGpdCAOJiKpHDkdcFty8szMpXUvXYgnpdXdy+iduEX/7Gh0mgCdgxgSCPEgVxth61u79K+LCs7d8niFXAlBIYA8ls2lqY4MrPbfL1wQyCMTAzLW9G5TYGSXvrEtI/AH5GzsXXN8vIspSjT8c3iVehQnId7wK/QAIRjfj435BME144Ny3NySrIK2lXWIXCCJ6/Yt0sbREJfL6mCQWO1YnokUHf64OPPPe+CBj8zIbiIAjcgyuLgEHdEW2Bgr73purT0zLtHjY5wWpVIKHwSfrEhEc5ofA4m129EVeX2a5JfmAdZluX1eocOHQqhmjJlGs5AkPiqgthhAgGUXAHPuecPcSQpg086EnkPv+1OTgxJSZ88HbfQeBkh2DJKAmyc1ug9Yv9+3373lWH43n19PKz01Ldmjp8xIyMnd8WPa3wCVo64YcQjY+5BBAtxqt2xoVVeq7SMjrWNth+Gk60Qn91FY3CEX/6BfWHkLw5bQMLVGcI3iWwkp5gJLDskud7WKrp0KFLScr5cvNFAU2LoJKO6ZkPn7CTAj+/W7dwJn8YFOTQ76OrapcM1D42DdvO97o2r0x1KWnbe8rUV9X5GT2y+eBIsHEeQCwgI/x4NAQhVnnL6oUpyyf2PTEI8smzuW2lJOX0PGFThMxmSEi02OXu46GjAUBH2qzgRYSTs3bLhx/Zte6Sktdpa5UIFo4H1ndtkJGW0/2F1UCX8Q+uQvuHo4045/ezrYMVwzCYCm/HxmfjkIpeQ0KK6O2arI0beAv95zz2PSmaIUrHZIX6cj+UbYmV4EBd2wx5dTVAuVsszf0wnn3xyUlLS66+/LpcPjX+uCHkzO8M0g8cdewQs15lDTsTh1Tdc48xMhwGb+fobXFVcJEN7UQCXXogE9uvVdv5X7wOrfTSVQ5sTJs8eP+vj5Ozcb76fjzQwqfeOvGfMHXeC6xGt1rNtRbvCXCWj84Za4ZtZIlUGNRADpIhGBXCMV+avUkvlh1fDdVWrFhChOAvZK0gbCu385isg/tKc7NkLv8dJdDpya9ywpFU6NKnoy6XbQuh2UT0j4JMwDUWCiT6DT02oKdGaK47tUQBgfd8LwB3fzpvjSFbaHDgEsKkRMRxhHJKZ0CjqtmqKr5kgMvPyQWrUtWPnakKhrAJ+hxZc9gf2Le5Y4shbsPjHOvYWjLvfblh36ZBBp1x6x3p+oh1NsYIB+W4LVA+NRd4qF6IMB0feegFQ1ahxLyMMEJ9rQQXixGe7gkPYxCr/IIZelB/O6/8z+TnjjDNgiObMmQPJaVpF0OQ3QdkFHCVCTc8ZOiRdUYYNGQT+3DDiLrFWmfP1abOQOW6AHZbInWpoaF2KijYvmW/HGqZOegpRxPS3v5k4Y0ZSVuaXC1Yy+4jvjusueOyBBxgZWEb19u1Z6QX5ee22VnnAJHJT9rZsDKsDZcPpnxvbnHY7oBNycXaLFdkWDm/uvVc3pzP7jdlz0SSYaDVa+8kXb6XwO7tZ+Hl4zM2rf/wkjYA6Wcnp+eTrCxjkh9x2w9o+HQqVnNZPzvhMeAzV9q3atmB2BoBHSvnjs7+HT/t0+kOI+JW0kvkb3Krhue2Wi4457LCa+gBk1GVCdKvuvuJsZ1mXyx8cL4wBLUhiRUhpU+CEfpekBMBXyWQguQ6pXIwYV+G6Tj/99IyMjL322kvlQ3uuuQypDXDsXbNM78kDj0SbxOa86NxLvK4QskReSImOnDNlTI5T2bv//kefeSkUEh3r91Hc3eIDqNFQpW3xQXvn0jYpuX2WbZZzv3YfEtaCTYnHc6Jn2Tox+QnmSedICbTacr8+/iHEScNOHxoUih2K2ZvXrm9bCGOSsk+/w2S7Rt16PaBhn/5HI4EP2CRmBNz19426MzU5adSoUTJ/LjmIHgR3YrEgP5+n2+EGzgnVKu+7czhgzdBL76yrg38EkKlvXZRVWNh+0fKd0EkGr4izY95BR+9/8MEHe4C2pUKhkhBRPcDhR0uPcBoWW3TZFZcnpaTe/9DDslFB3ZRvgTVwGUdaAYjE3XffDblLBoL/A0pPh6EAVkb/k8rK+EYCKC0t7fjjjxeN/tmfRUxj5ab1rbt1UpKV6bOmEQbAjERDq1csAltyM9OcyY5v5i0AH3ADnC4VBAYNDEUTLN+U6U8rTuWiK85xZKTAKiEN8DjSIJUvUBuz6mJ24+pVyzMz8tJTWrvAIVgnwwgxDuFTG2FmUAvsBallIB62gMBjYSUZBlBvKAciPwoD8vSq2s6XJz2Rkek848xz4F88Kv0EvMz9V59XnKwklbTaSEBq2ap3r7Li3OyctT4xouP3PTH8xuzs4tvue4JtZa50q3pUQgQBT9FDbDCcbWNAWzl42OFKavlttz0Fz73uh09hXrp077/dDVDMeBlGIBAQ/tTQOQxjw4QE1TAtMAobM+ZORWlz2IDLReZe1bNi7x7FirP0q/mVYeCyCFD1Zju6Y+DA0/btfxLwOYBCQIuIpSMRcetGCNIuekR8ivyqKy+HgIx9+DFcVoVbqq+vl1YFlADBV1xxRWEhp86DEkv1/xXKzs4+9dRT4ygHBJOrRjZt2tCqtDDZoUyb/ioaGQii0fo38z5jrJbsLCpsvfD7nwI+BlJ1gSg4DjKQhp8H97763GOpDuXG4bcryVkjH+WcjIp6+F0wnUFLOAS5CXp3bijLzUtK61TllZ2Ny8R3SEwvHvNzV/BDXPqr1FL54Qfioqa3atsj997vTM8q79e3xtBrtm7rkJHVSuEHdpT01PHvvMVujdp3XncFsPKoh551iZe0aUlhEbieMoONoPiSPM7TZ5seO7z9iuM6t05R7nhgQlXE/mHpp3mtUnN6nrCZbz+DIAdgOOfRUE9UzeZnoOAX/LZRZ+u1N955s5JfcObVN22r9VGJ3YG+JWWwfst+XIP+9otZOLZZee6Jh5fue8J2IX9+HXaSjbViETMWVLV6ZqhDsLUHR18HoHPjmCfRi6ghCMYHvknsklD/vy0/CPIHDRqETPgSK8lyudHFZk1tBSL89PTUSZMm4az0et99B0yZ7EhOS03JXPjDUjAWXEDLDSgg6s93bLWounPKpGcgmJdcM0pJyRh+332sM/rVX0dHENXCXkiatXHNhsKCVooj3eXjimBIw05hQkki6Gs2QP4r2v0mI1uG6q5mzG2rn3/+LjTt1NMuCjDQ1HQuY0U0TaGLGRAbK4xojO8Zw8ljo/KakY0L58JXnHL2xY2W7ePMX9imuu/fm0I5zmz10YpqGK9pz9wBh3n/YxOwX+veSUQctaAuz8yYDdPfNkVpgyycuS+8O4/yqGkygAbBQFDMmw5/Swl8gzTSPME3SM+EX0AcGJrc3Nwvv/wSZ3C5ptGDvGCItUggEoGBgMIH7IjWvV3HvPQ8B1fGTjv77Is4YgrhDjTMmDg614kofBaEWJgJ5qKpXBbvuAFHpYnXiHLFkKribFcvJtjvTiRUU5g0dCU4ldhQf5NT9NCtsI9BW0XoV3fdhWc5leRZsz/xR6HYdrDB3b646I1Zc/IKy0UTk3NTlAvOOt2r27Uqc4NULFv0PRx8zx7dwG2cgatAYeASf0VQpoc8kQBVaMaEhyESex8wsBKiQ7ni9x3bluQoSsbMN+a6IRGsFrqloleXEocj6d0vVkgnE1E9MVPjV9Zpkwx+jFq06JYRt6ZmZl17401uP6f44BR+4c/uuOOO/Px8j8cjbU1CQv6IEtIFbE1gIXyblCV5r9xHboNOOjE5K7PT3j0bfC7dCuvCcSDa5ld+YsY5Z53OYcVkJ+KqQacNCwu4bARhFcPi4V1wxuvjIe39j9jvpCGnSMMBFYD/ZV/QJrujsfqG+qqy0nbZGW3dDWJyGskIIK6VPSkqIiQRmzxsAf2Jo/J7K6GVERMhsf/kU06ANX79jU+RDl3JcNpU35g0UXEmO4uL0MZMRSnPyamp4vpTYNaCj7+AFhzU//DKBnYEm2NHwR8xUxkEg0CD4qvyGF5CtJi9/ZgT91OUwscem4bGLZr7FoDOoUfw+4uwD9UCFMSrh77gSiduw3TjCBI29dVnHIrS98BT3WKQywjD6Fd3aZejpLaa9NrXnIZGQajxNazqf+gxSlLRR3O/l4Kh8QMktM7iTXVd89bTpsXMkXfenl9QNPy2O11++f5lnK677jroNHbEo09Scyv0M3D5A0pAJZC8EQridruhdEcddUx2VtH+/Q71+71itUB/lN/js0Ih5nnkkUfCCGdmgscZZw69AvzHxrANjh6YL9Tw7sxXyYF+/c+66Gpf0+QJhoUWJ2ajvlHDXbF2WVlOgZLSriFoe2DkWBdCTyQWQCfIVc7jXc8a/kX6G/Ij12OzPfWP3XqdeF4JDUl7duLM0na9zxh2oVg8AVWsWfvdl6lpGXv1P2pbIyuJeIXfBoYfheJEI2AmOAibq0btUBgdj/rXXDGwV56iDB/1JPz/V/PeBtRo1/+MHUb89TqhcVQq+n/oWFDlAuWEL+6PZ72MxJ0OPGhHyGhUxUCjZuxX1gZm/INPPkd/uBlKqaHtS/q2LwYc/2hVA475DBmVgLbGEJvgHtEzphFx1dx4zdDUDOWW+59CLwJVg/x+7NpXXnklDBHiLikMLZIfSTJcB8l7xS/YbZ166skpKY6DDjrA7YZHjotoYmjg5JNPha12OmFuU04YfG59gJYGptVXsZPTsW3XbHAgOe/go88ccOY54DZMvRoUT4dD9VRVRhfW9k3b8nKLCkta17s1TjMSYobeZktIVKX/IKCDuqqat5rYOWbp4cDrb8xQkpzvf/IFWgA0oHLeOmAAvHxQaFpEC3G6aIWfsoBG6x7vAV27HtpvX5fKV3X4iVTkKb5/BC74whZwL/r8qTHXFTuUtz/6GmlwUyzqhcqg92tC/EzVO68+BXe3z+HH7xCL9SV6NxFJg5D6dwnuB95I7uDGBI4uLS1NSkoCHP7ggw+klOCS6ByKK2RWCKsW4ydR0MeGzSnyotcEIkCPNnihJsbY2y8DBrvnoQflF6eRRH61JG43Lc1bsbFdtrMoM2v+sq0w/CxpNyJ2a5M4MlqVpknKK704hRVGgZ88RLwYqNvevWNngLc6PzuCPIno1ZV1cfnGfyMU0/huC9QU2alBb1lpSW5OVk1NDVBNWOc0ICSWr7Oi+0JqgAAlpvXt3g5sfGDMvTVu3ou7uXBR1HXPyJudzlwluSg9q21GBhecy0lVELCCjh98MVKuWbOuczt+87K8VQF+xQPKJuJeMrBOZm4eP6+YBJDmcKYQc8ohnNmzZ7Mo0VL2/u+RvJoQuQSh8rgq7RESHH744ciwpLTV1wt/gD+BBEM7IEpBDkoKJxQzQn5YUqtDx87JMHtJaUpSxgknDmEqsg/5qy9MfBhAZ84Hb8B+w/hEIFFhMXnQti+6eJgjmQtqok0p/Cx3vuq3fd6wqKDoPnag7Ab8gRrRgIvDFtFvHFU8W5knXIY3oMJXmd2691aUvA2bapEkEHRL+wBb7wt7qU3yLuiIj2FD5zZd2hS1b2zwITH4okdiIYOzYNhupuJUAcMvntJhs1XLrjj5TPAz/86RT9iae94HM52Kc99+x2yo8skQPIDSYrbfBX9mhhq5+BxAQoM70Huf/SEDTzz2oA8BKlLybSo17Nt62/ArEKEmZ7RNy2oFDkICxOLlKUpS3uCh8Kb2gkVLc/P5hZ/UZE4PKsxKyc9wYCcrjc5XSFFOSmaukgQ/TMlJFSQuKW+//TYqjXia+oIWmKZ0YyApJH9EzZxT3PNdfPHFCMGLikq++WqR3ytFTgsbsJEq0kd0wVPIRtBdWlbkSMpWkqAaOYOHXSRwTIRAR61/a9qLYMIbc94FYESmMEoogAG9pZ0y4BBHksJvGoC5aZCikmoXZ79IsUG/Q9bEoysw9u88usINLZKfNZvdUAm+DgL/Gmq0NaBSDdAH6VDzBj5jglS47YYd+5YWKo6UtS6OAaGSyNjkQ2iBVzgfmxM3kRyWh/U1fLZWeckJvfMV5bbRT3hi9huzxqPfehwxFB4EUCPkc5lBFMJlMmr9QQIdXaBtW+vTthB8GfPoQ6gANiof+OMP3Hf9dThPG5Kbq2TxaUR5KoNYxVE08KLhXjOyedv69uXtHBAfiBH+pPI9J0haSWZqDmNAnMxG4mTxikR6ejq8D6UHolhUNHny5JbKDzo0EAAzCIkSfhAnBw0ahDxTUlK+/PILeD35VBSEzKWkIY2PamS3bds+PRuGMVvJyD9r6BDBajAT1ss7/vlHIPvPvjwb/AHwwW0GJ6NBxoKnDzquTZFY+BORuyM9OSWz3kWPjxrgFw1gG0gJX4pO/B3a/YCOiWCUE4iDPj6Bhpd/7a1X0MrnXpghno1yVENwI0igJ87IZkdsM2pY+/far1t5l4hqaGZIZwrDDwmDWYb9Ft8ckJYrGqyyLcZkGnPQg0Gu2BgI8hEl1IYKHNUJLZEAuf+S0IUJrPq7lJADSUgvRSRBkBspEFI3vaEQvFRI9weDHKAS49jQKATf/EUij5sf1ENFQprfcKPmfPSP6nGiNK9b8N/ICgG3ybcQNRuxgskCUGqTHOwmBHYLiaQlokRKDrB1sqI8hukTWAdw1tKjmt6+Xbfk9Fa1jejSsBjMY6qAXyyJbumWzncSPYx+baCcrKysIDBuiHEUNlAgIDqLB9ZZQ07LSEnOTuMcK5Vr+ZOBbvpoZOXh8ywEU3CJEAHAJr6SoQH9uBs2IwFsUK0PvYmMcN7we+APUCiwBU0YoIks0RArqyc2WQcQOh1pZKwDiyBP/gkhPSyFTC9NkrRHeXl58HnZ2dkLFy6EmUcNpM4bMeSP1piccI0YgQscmFEzghwSyZgLZAaIOYa6+O6+5yZo1oOP3xeMhMKUe7aaTgOpYpBDz7btPxYWAPOnLFu8KdEYw9RCfD2eWUmukktkZLPW/lVi1WSZZIkUiqY8DRMdhCarZjSMIK5njwMLC9tW7NyKKkC3A+wdaRh5LxCg+AaqXtqqAOi0vtHQOO+X6o0yxKMr9guO+XWemPisCtyNF8ZB9Ye2nHrWscmZpSPvGgf38/QDd6YoqSPvfgQ9jgKwUctk9dBwSz35+P45OQ5HKlxISkNtRdREhEn2Muhn2rjZaIQuSo7zTBB1wUlscj6yaCVEmcheDOoYEdUnjDXSy9olWP5r8nrFs6EmwUgQZCa+9wckxQkGqnNnxA/wT2lfffktyohPtEehfJfCsPhYBuw1I0YIqBvnyVsYSvEUuNbD+UnCRqkwlfeM4AKV9459SLILv0HORuTjXT6GttU1q37Yq1PrgqycpSt2+qBPMbvRJabNCsgAi8/7+HaCaPrvNvgPqWXyk1PUaZtPzFrRQra7Hq7UCAdQ4TpTPBBghkaoausxXTv2KMzb2cAncDCzsM7MEv9hWmGa+BCKlfbr4s0ZXtLtcO1VQw6BqtzOJa3tmdOfRZBwyS0PIdt4gpge8Lt9YqocLMrVZ5wuw6TSjNRAHSetN4ItMbsWxgqCAk2P6BKTNkYigDVoI2f46HxS2wC+Amby1XQ2FLYORcTlgHswXmA77T/6iS9DyStNotLcGbVIflAdUSNSY2MjREh88zxt0aJFONPcpoVgIH4edyS/I5EwnCYKC5jS51p60B2Dt4IIRL333DU8r7DNVTeNQs3IcNSZ3A7CBUS4BJG5fePGHt26p6ZkLv9pLaJdVEJubK4sBoz4jwI6aCJFk3/RAi7jGAzbtd5Q7V69j96yRRe81CMGkDg/UmiosaBm13ugNprJ2S0n3DdqrGwstDIc84ipamK8mbwzjUiI73oiD5MGCxEYFCXMrwDGIQXyD2k+i66CSojwUPIRuIQxiiDZ2ZCJ3yU4EPwiAWQItyS6HzswT/ISCDs4A58Y0GSgiYqgiiiTPoMmDwmlJUAGaIxY7onT42F3DN2nMrR3R8KhGHQAhomgUAMwQiLTYpoYb0UaWf/dhtAxQiJFRM6mifYJDjDUI3vYXnh4cADmQ2VzxNpCVFxc1bWoHjFNgACZA4GOzEFkTsX1BDX8yoaHQ+AnU6oeD6w1drSAXxSBSxQntyrcGPWRD77tWAhhBoojWMVZfi2fXiocUZEMG6ixrlIIqmFxuoKJTlHVgES3ohVxoAPgE7EIKCAw+BW3/sIc/C7BHCTkR56RJB9gwb7IQ0kRI+rXIi4/TDFclMwZjTU5pxuSr4dCECRgRp2msKbRExFCRTaidjFN02FaYffBCIbZaKHHz8/ugGhGZTgByUQPQBEQBnMCODpCKAKSyY3ZkRs82WKSjgq/IivkhE3kCRymhQElg5oO9AmPGwsEoMC4BJ4T0AkkC2Tg8fp9coYvR7RjQVN1oSfEC/DYCItF3gQ66BHBJZw0uco+7oFTocZ5Ddh/mFxeZBwJgA0+oZR6LQpW+uEqEcIjLV0dn8hEInTV4JpYISs+rZ5k6r7GalzB7dBM/OKqBX8f1cI6oi/bq+o4yXJQI9ZNTPuAIHFjVkwPMBoBeiIegjghEYRBhka4Jh0V5KG5ecH5hBP6I0rM70ncRSWybDHLGcToqylIQ6F6QAX/wXFIlIiwcQq1Eq6aHQYlDXAdPBGYMU7BeW+ESxrKVqvuWvhmfnsHUb23HtmhpyGIGpy+4AB6BA5bAB0BINh03tkSapn86AanD9OoG5Z8xxqMRfHgLAwNdjhiCpFw+5EgqHNwE5eoNawx/I145gsxFJga7cXGN1nojP22d6utNSAThq2iaMA+bwyROdwZ4AvEDLJle9B+yDGUiD4JdbBsLdKgclFG2BrZx0wQ0XSfG/xBn6EanFzI+TewNixUtBMRh6GpdB+aGYO0UIfFafYIegytjLNG3CB8k9yHqLRUfhJSJw9BsFRSWhD7eTywM/KkMA6CROayS7ghDIP2SabBQlG0YFNgzQPw5npQ4wwAyXDKD24F0IGuISXYHrPQhSgInYOrfGcRmYiUTExCEfLc79NuB3QsE/5GM2BgaUTQDDitoFd1Q7K4hBv7BU1ya6Gd+AvexBvHr/QB+lBvVUSbjPAg3/6w4Q+ZdPlIE1Hhxiig7oB0flAtAW1kHtjhvDx0GEUZbIVqg/Xsq2ZCkLA4f06/kpsESAI1fxoKY4f6IPSAQEaiCJ4YPfJredAlrjVP7CK+usdqyB41/BzuwqGfH7OFoOlaxMf5aEJrKCYwW1FE9EF4LxyxfbsRoYPoicWvaIaoodwI5sAzceCqq5XJoAg/p6AJaHYYswINSAYF4KdiLBF6IgPYYvz6GfwgDdSdhpgW1TJj6DtgJjgcsFT4IXQx8KG4I2hGGoywhwlwK5gJ4sxTAp2IiUDCpuDwJFUVmxzLkRu0mpSoGpoTJeJJUGIUUJqMePrfkEwDaj72A/vS3E6B4iM9Qu3lhsAOZwJ+DuRY8MeoJFrNekLK49gLeXFVbhhfN9wPZcWv1pscd4D4iQSUHeYPoGOZMLzUFM6YF01KtIcqIM5wI8mC/gahMNaQu7/IEGdQPVW8b6cDSgLMNHE6rIcDMLfsCq5p68IdSNoYEECP09jVkHiqK2AC/RZ4CFHTo5yMLOy+KBSiFVQ5Asrhdlc4yofiYEIsjBwAZej3/DrzAVux8T7IDBjLuEizxCABTopXHelRIG/oI2YegxhHYJabpgQJgUEVmnoKG85zEVGgJxGTcIv3F3OAQYdLkCkFMkNlebuk5ggY+xyxa7oKLRBC9DskE8tkcmiQhzGbHzCBVpkRPx96ipoB/Ma/jyqXobO8HjH/iIJEM4Na0ojBrMZ0G5Ya+EELIvQCA9ER+EUxxPfw3WKRnihwHpRU55rxYFmAL1cwP0gdukFgVMEEwbwWEm5oifzwqqgPegldJqYwGgbSQJuwcUoVhR0pmSWCZ8JZSIV4bgVIhiazqmAdUmLzRyRPcQ/MshsQWYuw4wCFLc0FzBe39RzcQv5xT0RQa2rw3TqQF9yMGJgHJKL1R6kBLxGAqcciIQAB5BASskxI5FdNBnFMw0cOAhHhOGRQdLBD/IA/PGoC0jghSOyyX5r7L5z/6/LjQazYRG63kBZaMyEbcsMPMHGTmUJB0ajB0V8A3oAbTglJ0FxyAF3PESkG7RQSzqem5PiMaK1XTHAkBI8IgMgB/qCXZhknkQOu/moThCaw1fGj39Du9+jKDsYQyosWwHsblgqEQ+QN7RLmQoATPmllGvGUVKPGgmuA4To6HlmI8TpARHQGB2VdOmeN0U0K4QCzxCsP6BYJ0qNcFwd8DIPptDiEuihflAVRaA6E5Y7s+N+l5iYJhKykYMnfBMrBjhS++FANDSaMAgrSYyZqDiTLjwKy+1AHk4EdimQFhCFRg1zi0rR1H1dWhQDBUtFvEymhjmALP6BiBBh3/qI+/276DdARG5sm1ZIDcWIPW9TiIqTYEUzgreGIRCpgFjxEOAhLanImirRMNCMCuMC+CBDD+AO6BNvEkaGIxecOyIW5qSoxrwjqbDWM7jT52UsaOy2KaA9ppHVDtGW4YC6RAEgHx0DAKNQ0UDEcwVtSk8UzIxKqCc8kqx8Mc/azFB7Z15ANHP6J8ICQRsJiKUjCyMTTyx2ZVdM+/wRCwhnCxEBRqB5WTGA78fQV7YPXDYcjGrRJJgsx1IQ8QWx0oV9gTRTX1DCz0yB1TAeNwO06HTkOE/1CaxjXgmYk+P83qeleUYosAmcisHE0+4gCwQ0m4IIcuMpHiCa8Mzke9ds6gQ5f10XF0KMAphZXqyJAAdKlW+K9SAOuyQ37EV2zaArgJfgQAHrHk/jDuuAMirCgmGgnTgZENIUEwkrAPlBDUQecYQwtdFyMOXIGFTVUGA10X0L1KClEzzT02KRggJBYAB3cDdlCUSa/dy77V2wcHRSHkrCPfpeCkXBXyCQhIX9CUqgSueEuEMtANCUQuLyEGoXEsx0zCpTALtA56V6ShUAcLUY6hvLA0zqcHHw22YWccEnGGKqYgy3cmGrqAFVIQ7VFNRs9VDbkIhpIlCPuwHGTNWgxsc/4V94ez+GP5ScSMMMeNAHuNCjcB5tAfCwgL86jp4QkmPzipkR4CA9QfxquKKceM7e46RDWm8WpXPDajgZkz3J5pBgfX3KsFaXzW/d6zIoAGOEknxigVpxETG6GArRcqC6sD7wRZQzhHEwKgzwwF/UTL1IgK8gpJAuiSzmMMxHOjgUJxEOHhQOcl95LmEpRoV9TS+VHDt6AEjdCYCiKTRaDvyhZ5NTMyrF3AHFQDrqd1QGHNWQmYD3Uk20xoFlIHQgD/bEtqLEQTiZgaMEdhFt8XI5cI+LJb2LDjULRsJG1otDfod0N6KCiZIqsuWgDWRDfRDuxA7XlJg5FarRYTDcWeIUGA2do43gRh0DsMHyCFcLFNvEozuu4jgkJEzyNXyX9IeN2FcmmiYIgKAQ64jfeeJ4WO+JHVAY/snuJDaBL/MotL8nEUkyYHq3AJVpk3rW7EOop+EwNaWqj2Jrtyv/NjrGRD83Ty9vFGeYp+5Gigu4GB/Eb70GWBbwIq4FfIVdCbHBVygmMjcgS90LLwC5aZCYTKXEoz0s5lEnjl7nz+yRTxdP+k4mlNC8PW7z2aNzPm6i/cL3xNPIkJEdeajr98x4SCFGMH/7zSNa2edEgWX+pEUIdQPEETN+k4+gs+m82hilwhWKAfSQgSY0Wt6PH5RYvgU3D7djYRpxEOsqMlCXBE5mtPC/ukvYBG9nIuvycm0xIajopm8CimyUjIGjal8Tm/Lw1XZPJfpnyn0YoRpbP8vBHmqAEoRVCL8R1yUNBUu/EJtolLzXxCn9wHvk0GbT4yZ8zEQZNphFXcSF+Z4sI9za7PZ5DIme5NUuAXSJWVgu/TI7epGVgt+IQktMkXUjcpC9xa9PU++Jcor0i0yZx4j4y5AslTVdxC66yGsiWZ5rkFpnI5CgRaJEQPn67rA8sPPwXpZ134QrvF9ZMVkxWTVxNbDwtzzINbsBt/0ySZcntd0g0h/XmJrySaEv8kuidJm36RRNwNc5wuSPyERdkUb/chGWLb79PuxvQAf1c19+0J74JYrOxL4QD/8UHLwSclhLMbia45SFiip+BDgRFCByv4Qfyh/PMV0iqEKCmq9jH3z/k3S6hphaxck1qKQrF2XjF4inivhYn5Xn6YF0MdwnQjjNSTJoeZwi3jThBNGU3IbZFcJW/8jC+NT9q+iOI+0Lz2RfNzsgcJMm+awZ0kJQ84SXciy5GvCOADu8lMkCCn80ZSwcPyUyheILD5CD+8JGpgJLxe3+x/QH9hSS7jOKlJMqLH0spQfuab/Lkz1elgRBb033835QDGd7U6p/vTSSVZ8TJ+BlQU5p/lGTOzWv+f+2ci24cNwxF//97E7RBYSA955Ka0T5ce1E72Ri8YGZHFEWRFPWY3XFWL+m6MrzToLM9iEDXWqS2JlQzuWtJx5qn8zwvoiYp8VL92orgOK2KolVmG9MqOnTClDZWFEs+YgoXBwq0tpucSKdNJxC7kfwMxJ3q3P6wuY81q3s4LCNuzHAurbowu6ouao2A8V98++LmiGpqmVy5998R2/+Jsorei2Ihmovd098htlzMIserzxYtz1XCsEWRg1cuQAFVaKtkY5dBrZKdNuYGVeZt5GtlziMK7fJwTsTp1wwMU7LIjuXTufkDhw92uhe/70esej/IylA/+XjoR6uKPheHBXdQnpRdkNNhE0y4umystto0vAr7qiuxjSrORffxfAcdDBfu4vpwPZx5BoVJwaFl2D395uWypNfxtMet2WEOnd/o+KuEOyIC8BOdHHQ832QyR3NrWNmplk8HvdCn0746PxyWhKZisD7JRIbZwjasL2FmaiGV6RsVZDkyuX0iGO7TtfbuP2Gi++SN7HI/qZ8tTQXbQQdva/hasWJZaEyT7vcQU1ubQ7VrisGDQwUS/voA85/w14LYep8G8eia2taDcOagWlCKthY7mtXhCmhIZq6qqpXDdeeoX877cSrcS6eRF10UedmOnl6WGBfHl4ZYUrWZU+v0AzctAFPjm/sNWZG6XJaPaVXq1xKEaphLrTJwPAx5WzmWXpDguhLPIMOxma1i5BOiPQKbmw04rCSJzMNobYktMKp8VDFxk8N9+jOeuT6CsryNP0qv5w/D4grPNoFTLhrFlBTAAP9jD7aV5nPt6pDFxnZbQIDm+tviXayGdlS5lNzrg05RIkCUVlZXc4VlhhST6SnHH9QqaFwFVdEMZ21eCJP2v339L0+uKOYJbIu/FrnPQ6b3yMRsi4RubwutmqZzrDPc9/GkB531e0FnxuaSm30lBz6TATnoVJSyYHXwzpgw8OQUSW3RV5w8HyAAhyoTS0nC7TunaIVJlRqIO7nyeuw+GtoXSo+b2wFMpwHVMvyWwiTG496wmUhmtrXlmvY7o36Z/e8E9mS9OOhtZNTyVwXxi1aV/RYdKZZLo0F6dAQJSCu2i1pl0iRcLgisSLY5rH1E0KkCp7TIZ0EsfiRPvU8GrLoizd2pXPLEFroR33GnLrsCek4m2tZEQb2c6oXrIzgVVqnMu7DwvOsyoOtjWQTl3SHAPclf9y3J0NWgcw1YFfJWFlmBrAcd1hMfrgJaZe6Uwmw5efS67oVW3uI0T1nppXNycahdWRqm0n8EsPVqKItzxXwLHh3Ww6dPI0TVKPUo5AGGqsxrPh9fb4lnUZfeyp8X946/HWD66oOOu0kTNnDK8c1NmVjJ9QGvEcuk6BZqW21z5aJCcm876Mgzu7pt9dtdV9b9yMtM4fhnbn/Riojd5lX1Bz8e4R1HIkV+Kzb3veZG8/jAtuOgU8Ox8QtyqtVBjcgew93UdTd4uoNOeZqBZ1/PQ1VnA+ceDiI4c8j4zV5SA/c55fT3GT2LsrEhQ+0mw47I2JM3Mkl3tjFb+XuWf11MimQOoIEBIO7cvhq7jwYd1QCnx83PQD8ICBbqHfu6r7P5Bc9Kd1ZzJo9n/3LBCPzSg9p70Q5doIy8vZZwHXT8X45wrTnJhIwgLI67bkv4XkRV0UJrA0cVYiINuBCxji3/CCiRu8s/NT0HDn9eo8TqoMyaDlTXF3bJqjhIEF6yK1WIyCRAMLmudv57PN9OhWpZ5l1aWB91TrXMxcUhLarIcuEkKFWpdQZEGCNdQEshQqU27viHmRYyhfLlqH+0kFqaI5BVeNOZjrKL2C/K1g/HpVojfIHCjQ6BZAuycFxnlqrnQttDlJxBFot6fM+o5gNmvApO2Qb8ItF8d6meRNl3vyGAiujllti4pmW04PHZzd8LuqGFndn12/kTLkMLCXuzYZPFVdvCXdU6QgurVbCqdMGuZBMuNNlW8AHTXPrOXuZNkXWVb1CyuqxXAzFhFJB3YRfG0Je9Wfqy+pGipFvIXyp8kR5dvufs5kUvHenPREWgrm8CezrNato6mwwB1vqLSu6RydbPrf/QfJ8Y7itC+i6e8B2dwWAwGAwGg4/BHHQGg8FgMBh8WcxBZzAYDAaDwZfFHHQGg8FgMBh8WcxBZzAYDAaDwZfFHHQGg8FgMBh8Ufz8+S9QgixgTnLZ0gAAAABJRU5ErkJgggA=" alt="" />

五、二叉树的主要性质

  二叉树的性质是基于它的结构而得来的,这些性质不必死记,使用到再查询或者自己根据二叉树结构进行推理即可。

  性质1:非空二叉树的叶子结点数等于双分支结点数加1。

  证明:设二叉树的叶子结点数为X,单分支结点数为Y,双分支结点数为Z。则总结点数=X+Y+Z总分支数=Y+2Z

     由于二叉树除了根结点外其他结点都有唯一的分支指向它,所以总分支数=总结点数-1.。

     结合三个方程:总分支数=总结点数-1,即Y+2Z = X+Y+Z-1。化简得到X = Z + 1。即叶子结点数等于双分支结点数加1。

  性质2:在二叉树的第i层上最多有2 i-1 个结点 (i>=1)。

  证明:二叉树结点最多的情况即为满二叉树的情况,由于是满二叉树,每个结点都有两个孩子,所以下一层是上一层的2倍,构成了公比为2的等比数列,而第一层只有根结点,所以首项是1。所以二叉树的第i层上最多有2 i-1 个结点。

  性质3:高度(或深度)为K的二叉树最多有2k - 1个结点(K>=1)。

  证明:本性质其实就是性质2中描述的等比数列的前项和的问题。

  性质4:若对含 n 个结点的完全二叉树从上到下且从左至右进行 1 至 n 的编号,则对完全二叉树中任意一个编号为 i 的结点:

  (1) 若 i=1,则该结点是二叉树的根,无双亲, 否则,编号为 [i/2] 的结点为其双亲结点;

  (2) 若 2i>n,则该结点无左孩子,  否则,编号为 2i 的结点为其左孩子结点;

  (3) 若 2i+1>n,则该结点无右孩子结点,  否则,编号为2i+1 的结点为其右孩子结点。

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" alt="" width="261" height="248" />

  性质5:具有n个结点的完全二叉树的深度为[log2n]+1或者[log2(n+1)],其中[log2n]+1是向下取整,[log2(n+1)]是向上取整。

    性质6:Catalan函数性质:给定n个结点,能构成H(n)种结构不同的树。H(n) = c(2n,n) / (n+1)。

六、二叉树的存储结构

  为了方便说明,我们使用下图树1作为案例树。

  aaarticlea/png;base64,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" alt="" />

1、顺序存储

  顺序存储是使用一个数组来存储二叉树,我们一般将二叉树按照性质4的做法,即从上到下且从左至右进行 1 至 n 的编号,然后编号与数组下标对应,按照编号依次将对应的结点信息存储数组中即可。

  第一步:给二叉树编号

  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" alt="" />

  注意,编号5的位置是没有结点的,但是我们这样编号的目的是为了更好的应用性质4,而性质4描述的是完全二叉树,所以我们编号时要将普通二叉树看做完全二叉树来进行编号,所以即使编号5即使没有结点也需要进行编号。

  第二步:按编号存储到数组BTree[]中

 aaarticlea/png;base64,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" alt="" />

  第三步:按照性质4的规律取元素

  性质4主要是描述结点的编号和双亲编号或孩子编号之间的数学关系,即我们知道了一个结点的编号,那么它的双亲编号和孩子孩子我们都能计算得到并从数组中取出来。

  例如,结合性质4我们来计算编号3的双亲和孩子:选取出编号3即BTree[3],就可以知道编号3的元素为C;双亲结点编号 = 3/2 = 1 ≥ 1,所以C结点的双亲为BTree[1]即A;左孩子编号 = 3*2 = 6 ≤ 7,所以C的右孩子为BTree[6] = E;右孩子编号 = 3*2+1 = 7 ≤ 7,所以C的右孩子为Btree[7] = F。

  结论:像编号5这种情况会占用存储空间,所以这种存储方式最适合用于存储完全二叉树,而存储一般的二叉树则会浪费大量空间。

2、链式存储

  根据二叉树的结构,我们使用下面的链式结点来存储一个二叉树结点。

  aaarticlea/png;base64,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" alt="" />

  所以树1对应的链式存储结构为:

  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" alt="" />

七、二叉树的遍历算法

  根据二叉树的结构特点:一般二叉树由左子树、根结点和右子树组成。这三个元素:左子树(L)、根结点(N)、右子树(R)有6种中排列组合,即NLR、LNR、LRN、NRL、RNL、RLN。而从左往右和从右往左这种遍历顺序是对称结构的,采用一种顺序即可,所以二叉树按照三个元素的排列顺序遍历就形成了:NLR(先序遍历)、LNR(中序遍历)和LRN(后序遍历)。

  ps:二叉树的这三种遍历要用递归的思想去理解。

  先序遍历(NLR):根左右

  1)访问根结点

  2)先序遍历左子树

  3)先序遍历右子树

  中序遍历(LNR):左根右

  1)中序遍历左子树

  2)访问根结点

  3)中序遍历右子树

  后序遍历(LRN):左右根

  1)后序遍历左子树

  2)后序遍历右子树

  3)访问根结点

  java实现(遍历树1):

 package test;

 import org.junit.Test;

 /**
* 二叉树的遍历
* @author Fzz
* @date 2018年1月17日
* @Description TODO:
*/
public class BinaryTreeTraversal {
private StringBuffer sb = new StringBuffer();
//先序遍历(数组)
public String first(Object[] o,int i){
//访问根结点
sb.append(o[i]);
//遍历左子树
int left = i*2;
if(left<o.length&&o[left]!=null)
first(o,left);
//遍历右子树
int right = i*2+1;
if(right<o.length&&o[right]!=null)
first(o,right);
return sb.toString();
} //中序遍历
public String mid(Object[] o,int i){
//遍历左子树
int left = i*2;
if(left<o.length&&o[left]!=null)
mid(o,left);
//访问根结点
sb.append(o[i]);
//遍历右子树
int right = i*2+1;
if(right<o.length&&o[right]!=null)
mid(o,right);
return sb.toString();
} //后序遍历
public String last(Object[] o,int i){
//遍历左子树
int left = i*2;
if(left<o.length&&o[left]!=null)
last(o,left);
//遍历右子树
int right = i*2+1;
if(right<o.length&&o[right]!=null)
last(o,right);
//访问根结点
sb.append(o[i]);
return sb.toString();
} //将缓存区设为空
public void setBufferNull(){
this.sb = this.sb.delete(0, sb.length());
} @Test
public void test(){
Character[] o = {null,'A','B','C','D',null,'E','F'};
//遍历前先清空缓存区
this.setBufferNull();
String s = first(o,1);
System.out.println("先序遍历结果:"+s);
this.setBufferNull();
s = mid(o,1);
System.out.println("中序遍历结果:"+s);
this.setBufferNull();
s = last(o,1);
System.out.println("后序遍历结果:"+s);
}
}

  测试结果:

  数据结构之二叉树(BinaryTree)

  层次遍历

  层次遍历比较简单,即按照从上往下、从左往右一层一层遍历即可。层次遍历是现实,如果遍历的是顺序存储(数组存储)的二叉树,由于存储的时候就是按照从上往下从左往右的顺序存储的,直接按顺序取出即可;如果是链式存储的二叉树,需要使用一个循环队列进行操作:先将根结点入队,当前结点是队头结点,将其出队并访问,如果当前结点的左结点不为空将左结点入队,如果当前结点的右结点不为空将其入队。所以出队顺序也是从左到右依次出队。

八、二叉树的基本应用

1、二叉排序树(Binary Sort Tree)

  二叉排序树,又称二叉查找树(Binary Search Tree),亦称二叉搜索树。

  1、定义

  二叉排序树或者是一棵空树,或者是具有下列性质的二叉树:

  (1)若左子树不空,则左子树上所有结点的值均小于或等于它的根结点的值;
  (2)若右子树不空,则右子树上所有结点的值均大于或等于它的根结点的值;
  (3)左、右子树也分别为二叉排序树;
  ps:根据二叉排序树的定义,如果对二叉排序树进行中序遍历,那么遍历的结果就是一个递增的序列。
  2、查找关键字
  二叉排序树的主要功能就是查找。首先将需要查找的序列排序后存储到二叉排序树中,那么要查找的关键字要么在左子树,要么在根结点,要么在右子树,所以我们首先将要查找的关键字与根结点做比较,相等则查找成功。小于根结点则递归查找左子树,大于根结点则递归查找右子树,直到出现相等情况则查找成功,否则查找失败。(该查找过程与折半查找类似)
  3、插入关键字
  插入操作主要是对查找不成功的排序二叉树,即如果关键字查找不成功,那么我们就需要将查找不成功的关键字插入查找不成功的位置。所以我们只需要将查找算法进行修改就能实现插入操作(ps:若二叉树为空,则首先单独生成根结点):
 BiTree* InsertBST(BiTree *t,int key)
{
if (t == NULL)
{
t = new BiTree();
t->lchild = t->rchild = NULL;
t->data = key;
return t;
} if (key < t->data)
t->lchild = InsertBST(t->lchild, key);
else
t->rchild = InsertBST(t->rchild, key); return t;
}
  4、删除关键字
  在删除关键字结点时,需要注意的是,在删除后我们需要保持二叉排序树的特性。
  在二叉排序树删去一个结点,分三种情况讨论:(设被删除结点为p,p的双亲结点为f)
  1. 若p结点为叶子结点,即PL(左子树)和PR(右子树)均为空树。由于删去叶子结点不破坏整棵树的结构,则可以直接删除此子结点。
  2. 若p结点只有左子树PL或右子树PR,此时只要令PL或PR直接成为其双亲结点f的左子树(当p是左子树)或右子树(当p是右子树)即可,作此修改也不破坏二叉排序树的特性。
  3. 若p结点的左子树和右子树均不空。这种情况可以转换为情况1或2然后再按照1或2的方法来解决。有两种转换方法:
    其一是找到p结点的左子树的最右边的结点r(沿着p的左子树的根结点的右指针一直走,其实就是找到左子树的最大值),用r结点替换p结点,然后再删除r结点即可。
    其二是找到p结点的右子树的最左边的结点r(沿着p的右子树的根结点的左指针一直走,其实就是找到左子树的最小值),用r结点替换p结点,然后再删除r结点即可。
    java实现:
private void deleteNode(BinarySortTree p)
{
//TODOAuto-generatedmethodstub
if(p!=null)
{
//如果结点有左子树
/*1。若p有左子树,找到其左子树的最右边的叶子结点r,用该叶子结点r来替代p,把r的左孩子
作为r的父亲的右孩子。
2。若p没有左子树,直接用p的右孩子取代它。
*/
if(p.lChild!=null)
{
BinarySortTree r=p.lChild;
BinarySortTree prev=p.lChild;
while(r.rChild!=null)
{
prev=r;
r=r.rChild;
}
p.data=r.data;
//若r不是p的左子树,p的左子树不变,r的左子树作为r的父结点的右孩子结点
if(prev!=r)
{
prev.rChild=r.lChild;
}
else
{
//若r是p的左子树,则p的左子树指向r的左子树
p.lChild=r.lChild;
}
}
else
{
p=p.rChild;
}
}
}

2、平衡二叉树

  平衡二叉树又称为AVL树,是一种特殊的二叉排序树,即左右两个子树高度之差不超过1,并且左右两个子树都是平衡二叉树的二叉排序树称为平衡二叉树。

  为什么要构造平衡二叉树呢?对于一般的二叉排序树,其期望高度(即为一棵平衡树时)为log2n,其各操作的时间复杂度(O(log2n))同时也由此而决定。由于AVL树的左右子树高度之差不超过1,其高度一般都良好地维持在O(log(n)),大大降低了操作的时间复杂度

  平衡二叉树的实现算法:关键在于左右子树的平衡。具体的算法有:红黑树、AVL算法、Treap、伸展树、SBT来实现。有兴趣的可以自行搜索,这里就不再描述。

3、赫夫曼树及赫夫曼编码

  赫夫曼树又叫做最优二叉树,特点是带权路径长度最短

  1、相关术语

  路径和路径长度:在一棵树中,从一个结点往下可以达到的孩子或孙子结点之间的通路,称为路径。通路中分支的数目称为路径长度
  结点的权及带权路径长度:若将树中结点赋给一个有着某种含义的数值,则这个数值称为该结点的权。结点的带权路径长度为:从根结点到该结点之间的路径长度与该结点的权的乘积
  树的带权路径长度:树的带权路径长度规定为所有叶子结点的带权路径长度之和,记为WPL。
  如下图有4个叶子结点的二叉树:
  aaarticlea/png;base64,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" alt="" />
  则这棵树的WPL = 2*7+2*5+3*2+2*4 = 38。
  2、赫夫曼树的构造
  假设有n个权值,则构造出的哈夫曼树有n个叶子结点。 n个权值分别设为 w1、w2、…、wn,则哈夫曼树的构造规则为:
  (1) 将w1、w2、…,wn看成是有n 棵树的森林(每棵树仅有一个结点);
  (2) 在森林中选出两个根结点的权值最小的树合并,作为一棵新树的左、右子树,且新树的根结点权值为其左、右子树根结点权值之和;
  (3)从森林中删除选取的两棵树,并将新树加入森林;

  (4)重复(2)、(3)步,直到森林中只剩一棵树为止,该树即为所求得的哈夫曼树。

  以上面的二叉树为例:首先有4个叶子结点a、b、c、d,权值分别为7、5、2、4。则:
aaarticlea/png;base64,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alt="" />
  普构造得到的赫夫曼树的带权路径长度是最小的,WPL = 1*7+2*5+3*2+4*4 = 35。
  3、赫夫曼树的特点
  1)权值越大的结点离根结点越近。
  2)树中没有度为1的结点。这类树又称为正则(严格)二叉树。
  4、赫夫曼树的应用:赫夫曼编码
  赫夫曼编码是一种编码方式。例如我们需要发送右A、B、C、D这4个字符组成的一些文字,如果分别用00,01,10,11来代表要传送的A、B、C、D。则需要发送"ADA"就编码为:001100。
  我们希望编码的长度能够越短越好,上面的编码方式长度显然是与字符个数成正比的,不能满足需求,所以赫夫曼想到了设置不同的编码长度来表达不同字符,那么让出现概率越高的字符设置编码长度越短即可。假设A、B、C、D出现的概率分别为0.4、0.3、0.2、0.1。那么A、B、C、D的编码就可以分别用0、00、01、1来表示。那么ADA的编码就是“010”,但"CA"的编码也是“010”,所以我们在设置不同长度的编码时需要使用前缀编码(即任一编码都不是其他编码的前缀,这样就不会产生歧义了)。所以A、B、C、D的编码修改为:0、10、110、111即可。
  赫夫曼编码就是长度可变(编码长度最短)的前缀编码。其实,赫夫曼编码的构造就是赫夫曼树的构造过程:即字符相当于叶子结点;字符出现的概率相当于结点的权值;由于构造的赫夫曼树权值越大的结点离根结点越近,所以字符出现概率越大的字符离根结点越近,路径也就越短。
  所以,A、B、C、D(0.4、0.3、0.2、0.1)构造的赫夫曼树过程如下:
  1)构造赫夫曼树。
  2)约定左分支表示0,右分支表示1。
  3)从根结点到字符结点的路径组成的编码就是该字符的赫夫曼编码。
  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" alt="" />
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