{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "90a2ebc5-73ae-4a52-adfb-8dad1397ebae",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Touren in Graphen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba94c70c-990a-4e16-af66-b0a2d0ca2abf",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2be01b1f-6df4-4685-8930-9c7ef7e163d5",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "<b>Ziel des Notebooks:</b>\n",
    "    \n",
    "- Einfache Modellierungsaufgaben mit Graphentheorie lösen\n",
    "- Verstehen von grundlegenden Konzepten der Graphentheorie\n",
    "    - Eulerkreise- und pfade\n",
    "    - Hamiltonkreise -und pfade\n",
    "    - Traveling Salesman Problem\n",
    "- Anwenden von Algorithmen zum Lösen des Eulerkreis-Problems\n",
    "- Kurze Beweise von Kriterien zu Eulertouren und Hamiltonkreisen\n",
    "\n",
    "<br>\n",
    "    \n",
    "<b>Mathematische Tools:<b>\n",
    "- Graphentheorie\n",
    "    - Eulertour, -weg\n",
    "    - Hamiltontour, -weg\n",
    "    - Knotengrad\n",
    "    - Zusammenhang\n",
    "- Pseudocode\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8f156f0-9a74-4670-8066-e6cc668acd5b",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "attachments": {
    "a8dce9de-54b8-4cbd-a5be-67a86151cba6.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "0c5c5c63-3664-4a9e-b51e-f2d491d804a2",
   "metadata": {},
   "source": [
    "![image.png](attachment:a8dce9de-54b8-4cbd-a5be-67a86151cba6.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67c763c3-cbb2-4cec-9ebd-df474c766295",
   "metadata": {},
   "source": [
    "Wir schreiben das 18. Jahrhundert in der preußischen Stadt Königsberg. Ein großer Fluss, die Pregel, teilt die Stadt in vier Gebiete: Die Inseln Lomse und Kneiphof, das Nord-Ufer und das Süd-Ufer. Die Bewohner von Königsberg wollen bei ihrem Sonntagsspaziergang alle der ingesamt sieben Brücken überqueren, aber jede auch nur genau einmal. Sie starten von zuhause und wollen natürlich auch wieder dort ankommen. <br>\n",
    "Wir wollen uns in diesem Projekt mit der folgenden Frage beschäftigen: <b>Gibt es eine solche perfekte Route für den Spaziergang und wenn ja, wie sieht sie aus? </b> <br>\n",
    "    \n",
    "Diese Frage stellten sich auch die Bewohner von Königsberg über Jahre hinweg. Aber keiner schien eine perfekte Route zu finden, und niemand konnte beweisen, dass keine solche Route in Königsberg existiert.\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc4ba902-9a8a-499c-ab60-20a0b9abe9f7",
   "metadata": {},
   "source": [
    "Auch der damalige Bürgermeister von Danzig, der in Königsberg studiert hatte, fand keine Antwort auf diese damals auf den ersten Blick unmathematische Frage. Also fragte er den Mathematiker Leonard Euler um Rat."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44199a93-07ac-437d-9623-4b6a722fc8dc",
   "metadata": {},
   "source": [
    "Wir beginnen mit der mathematischen Modellierung dieses Problems. \n",
    "\n",
    "Natürlich lässt sich dieses Problem in die Sprache der Graphentheorie übersetzen. <br>\n",
    "Wie auch Euler schon erkannte, ist es nicht wesentlich, ob eine Brücke groß oder klein ist oder ob eine Insel links oder rechts auf der Karte positioniert ist. Die ausschlaggebenden Informationen sind, welche zwei Ufer eine Brücke jeweils verbindet. Reduzieren wir die obige Karte auf die wesentlichen Informationen, so erhalten wir diesen Graphen."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "fca53c19-aa39-4fe0-a2ae-749f8ab59f48",
   "metadata": {},
   "source": [
    "![image.png](attachment:8dc111c9-5b87-4030-b1a0-fab9a53deb45.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af6abfbf-3bf7-4b2e-8c58-2311b24e5390",
   "metadata": {},
   "source": [
    "Hierbei entspricht jede Kante genau einer Brücke und jeder Knoten genau einem Stück Königsbergs. <br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b06a36ec-cff9-4b54-9c7b-5ac2fa67d266",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "1. Definieren Sie den abgebildeten Graphen $G=(V,E)$ formell, d.h. geben die Knotenmenge $V$ und Kantenmenge $E$ an.\n",
    "2. Welcher Knoten repräsentiert welchen Teil der Stadt? Ist diese Zuteilung eindeutig?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61cce96c-6c96-42e2-bc93-138a3c3e86aa",
   "metadata": {},
   "source": [
    "Leonard Euler verwendete als einer der ersten Mathematiker das Konzept von Graphen zur Modellierung dieser Fragestellung und legte damit einen wichtigen Grundstein für die Entwicklung der Graphentheorie."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7e8d721-50ab-4352-b0c7-495bf14530c7",
   "metadata": {},
   "source": [
    "Übersetzen wir die Suche nach einem perfekten Spaziergang in die Sprache der Graphentheorie, so suchen wir in unserem Modell einen Weg $p= e_1 e_2 \\dots e_k = v_1 v_2 \\dots v_{k+1}$, der folgende Bedingungen erfüllt:\n",
    "\n",
    "- Jede Kante $e\\in E$ tritt genau einmal in $p$ auf.\n",
    "- $v_1=v_{k+1}$\n",
    "\n",
    "Für einen Pfad mit diesen Eigenschaften gibt es sogar einen eigenen Fachbegriff."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d844bb42-0210-418b-84f0-f2902d51ce9f",
   "metadata": {
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $G=(V,E)$ ein ungerichteter Graph. Ein <b>Eulerweg</b> ist ein Weg in $G$, sodass jede Kante $e\\in E$ genau einmal vorkommt. <br>\n",
    "Eine <b>Eulertour</b> (oder <b>Eulerkreis</b>) ist ein Euler-Weg, bei dem Start- und Endknoten identisch sind.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b73ae5d2-664d-4be5-ba23-1935f849dc25",
   "metadata": {},
   "source": [
    "Um sinnvoll über Graphen sprechen zu können, müssen wir noch ein paar Definitionen einführen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f61a17c-5e08-4778-965a-9a91013a5d31",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $G=(V,E)$ ein ungerichteter Graph. Für einen Knoten bezeichnen wir mit $\\delta(v):=\\{w\\in V \\mid \\{v,w\\} \\in E \\}$ die Menge aller Knoten, die zu $v$ adjazent sind. <br>\n",
    "Der <b>Knotengrad</b> von $v$ ist definiert als $\\deg(v) := | \\delta(v) |$.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c9bc284-02c3-47c3-a304-12e0ae9548d5",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $G=(V,E)$ ein ungerichteter Graph. Ein Knoten $v\\in V$ heißt <b>isoliert</b>, wenn $\\delta(v)=\\emptyset$.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4c072b3-214e-4fdf-984d-611c02f66fa4",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $G=(V,E)$ ein ungerichteter Graph. $G$ heißt <b>zusammenhängend</b> genau dann, wenn für alle Knoten $v,w\\in V$ ein Weg von $v$ nach $w$ existiert. Einen solchen Weg nennen wir im Folgenden $(vw)$-Weg.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5507401c-726a-49c5-a6a2-0136658a4aba",
   "metadata": {},
   "source": [
    "Leonard Euler fand ziemlich schnell eine Lösung für das Königsberger Brückenproblem. Die Antwort, die er 1936 dem Bürgermeister in einem Brief schrieb, lässt sich mit folgendem Theorem verallgemeinern."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8603f271-ffd1-4d48-b391-04e5eaa13641",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Theorem (vgl. Euler 1736)</b>\n",
    "    \n",
    "Ein ungerichteter Graph $G=(V,E)$ ohne isolierte Knoten besitzt genau dann eine Eulertour, wenn er zusammenhängend ist und $| \\delta(v) | \\in 2\\mathbb{N}$ für alle $v\\in V$.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0243d185-cefc-4472-8361-aae7bcc0122b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "1. Lösen Sie das Königsberger Brückenproblem mit obigem Theorem.\n",
    "2. Beweisen Sie das Theorem.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f10cae24-1a5e-4900-ad19-e33f31826486",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "791b21f3-0bea-4d9a-8e65-45e01a83aa87",
   "metadata": {},
   "source": [
    "Damit die Bewohner ihren Traum vom perfekten Sonntagsspaziergang erfüllen können, werden nun noch zwei zusätzliche Brücken gebaut: Eine Brücke verbindet das Nord- und Süd-Ufer, die andere reicht von Kneipenhof nach Lomse."
   ]
  },
  {
   "attachments": {
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     "image/png": 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z6jKoAF3mum9+PweVVpxF4hBcrO3YAfzsg/gND+C3UW6owJS/ChPEPnYOUTIPjW8QaQ0LXTKzSV5z1tWRLeLpnesL1Svjh0NOcQWtAjyqhyUqvY9Gvx0I6ufxG1bC9zDMpM7kYm1xuNesOTZUdKzhFA2m1Q4pUZkadqrGCq8UVzUW2sPspT8SW58vfpBROOQUl3vaNIaNVHhQ69CMGjoK6xdPsdeewXo1XsdbUkNH+u3hvLefOTfMAIeZUodKyfnzmmI8i/cdH5javXLZOWLmFb8rXrnsLfLVrh+8j1NyvZgadnpi3ptyGxqg/OE5lMawE56feG55v7Gbgj4ZHAX7PrH74IvOeeXAIae4vBaTQ+VDQXXEPXTkB+uz+MF1qKDkV1XB+bgMemWuebUQn8RHrYpDmUEjMCozty5pieMK8PhfMrNNTHRxR1gtCIPDTmRCmsNO6Sp20+8oDDRxYbrxKF59K15wxGuEEVwWwQRb3GDCoaRcZTmrKSxMI12V0toYVYSyflKrulvl84Cj+WQWnlfphI2PiO89e5kMM3fK0+V93jLQmITmX/dzIcr0aHVZbAwmpYNhpqJiqAlvemytfBkn+12e0dvmnKI6QqXPRDD2sv6IycbgL8sQc4Hc7hMvzxxwzisvBposRAk1VFpYB+buQ71ZH4uEoYao/DDTKXkVBUNLCDKfkqfLW5FxY6CJCxUUd4+M1/GTFIQaNazEYFNZ9xzui+v3da3ZRfh40Ysda/u8DDgIOXm/dTDUjDbdWuOcig9DA1g1ligNE904FUD5uu9cJ0PM+XIr99CSHwaarHlVayY4vFR1CDoIOUUINfmsZVEebAwmE9JsDI7co2UFmWsLebgCkxhokkA40Z+vYWc1qWoNGn+xsWpTGwg2F7/Ysao3eYUbvBlinQyGGn8m+h8YHCl/TlWm4kFGYaBJQk2XVmEkaqXFGrZidaaO0F+Dig3CDYajst7tMdSkL70ZKVR3D873qv5gKBnbnTLEXOsMLVW/KqPjSsEmqKNGM5xQTFkfyFIpzhF8i+WSI5vE+pm7Ewc+HqSy3tI4UOXwNYvALMNKZ4sMLeyLA77STMAQEsMMJfD0iWvEHYvenXmwYKXGm4nGYIjXvElVkdbUbawbg9V8sQgew8wQAw1RziYnbrMOAjnd+jXrGEDbMz4GEEMNUTrSaAx+dN8TMsh8VZ7i69WNgYYoJ5MTV8rtUXkKx1WyYYYNyskPjF+ZabUGoWb9keRDLFXBmU5UVNu6A75KfTDQEOUAYUaIjXLzDi0Pzd9gVWseHL8is2CDWTlcO2XIxHABgiJDIlE2GGiIMmYNMYl3yC04qKBK8OD8KzIPNdwBExVX0VYgLxIGGqIM2WFmOMQUBqo1WYUaVBRYpSGiMmKgIcpInDCjZBlqeHgEm4mGTh6kkig7DDREKZs8dd2c5t84sgw1HHoiikItaocNx0myF7e794fvlqfNvY42Heo5p8gLF9YjShHCjGijMmMuhJha9G0UNCXvyHgKeZFg6A3VqiSPMxcurApVsbQXslPCrAHz8PK2sd8+Ag1WGOdO2xsrNEQpsWYyGQ4zkFWlhlUaqi8ZVDrXzT6EgLXZC9mpjYqFgYYoBaOmZSeFUJPeKqQ2rk2THB5DLoBWFnqIsY+BZCK0cFZSdhhoiAyy+2XCTctOCkMZaa8qXOe1abi4XtUhrNghRj+Qo+nKy9p2uu8DNMRAQ2TIsF8mWfNvFGksre7GoSeqhmGAOVaFcUIMVQMDDZEBaTT/hmEtvpdyP02dh57SHtajtDjhxZltNKsPJoUqTFZ42INgDDREJrT/SP6XT2k5i34aVGnYCxIPj7idFbv64tXES/XAadtECSVZMM8UE1OMR8HwFg7FUKcpyDftvSjxY1r36e+v7G0XiwZ7xIn9Z0VrcFS0xVHrY0t+PNQ4XsyIBWJ363Tx4+ZqcaSxyPmuKGRokcGlqIHb5LTti1/s8M+KAAw0RDHZw0xXyVP5hhnlahloVqe8wm/dds4MNNGs6m0Rp3afFif3fyhO6n1frOhNW8ElrJ80f0o833yV+F77XPGtef9OnuMXBVCNQfWl+P0vpgIN16AZjYGGKIa8emaCZFGlgRuXPixvoR6j1Qw0wRYPXhY/3flHsbq3VZzZeVwsGfzE+UpyCDePzfu34tHxt8rP9NdZsSsybqYCzXv3dcUWTgEPNCYuPfVDzmkiCmnliV+W/xdrp76neYr8vyEmetuMvIH6QSPynuYK57NqW2/N8ErmiXlv8ni8UEnb7bMV/7E9u/P34pePfE689fDN4qzuo9aw0rg45HzVjIWDfeKnu1NiXef/iGajJ3449nNCdN4jpn5wn3OJctiwcCzxcwjVmftnGGZGYYWGKKIi9MwESXvoqbzL+avHZMQwhbO0/UT/oHjnkWcS/5R3zD9D3Pvsd2PVE6xKILRVhQfPu3yqPccNXhKTR+8T58iAcVLvGefc7LzYmCe+dOCw+PKRcg27mKjQcLgpHAYaogjSXgHYhCyGnrIdRokSzobH2kk6u+XyBU1xhaG/rk3vjLJ8Hp7Y3yneOPNF8VoZZoowzPN3M31xy4FeKXbuWFTvliWtxL8lDjeFw0BDFFIZwoxS3ioN7rMdSvKeblvkQKPYz0ncQzSnm/1dLOn/RPzSzJ+J1x39G/lZsXYTDx/ti/+xvxyhxkSFBodPQKjhzjoYAw1RCEUfZvIS1NB6uLFYLBgccD6Lx1yVxgkuBZu1gr+s1xlYtj6r4QKT4eYNM/eKi2a+IBYO9jvnFM8/dPriwzLUHCn4HoyBJjtsCiYaoYxhBtC8e27nfs83U6wFktSywXNi87zL5Km4b9cyyHQ+KqZ+cKfYtec+sWvfj53zi+Gy8aZYMZZ0VyTENrkzwgqvadu1Z6vctsjtLrFyGW4PYTPa/f/5zjfE2w5/XEx2vmrkOZKmU+Xv5uxWU2yWj+/BAu/pcdfWtpuJQs3uvhD3z8j/KBBXCiYKYP/Vm08TZlIINMVduh9Tb68r9DoiWztmqipr5M4sa1PTn5fbBfLU5+QW7qf4N0f+WPynQ/9NnNZ72jmn+M5uN8RHl4yJU5rJg2da7jncF3cfSjY8tk0+F2k0BhoiH2XqmfEz6uCVGHqKC8d4in4kblRlsDz9nfJ0gf+srogwwQa9Mlce/F1x4QyWIijf72TVWEPcuDh5r1Oa/ilhhY4znMJhoCHyUIUwA6MOXpm0jybakbi3yJ1rsasyVTUMNrMf+9XdzdaMuJ/t/oNzTjlhNtF/XZx8NlERoQeLwmGgIXKpSphR0jx45egqDRp+1RGPr5Wn+XdmnhAoVbXmdUf/l/jPB39HvKK/0/pa2V063hD/ZdGYOKFRvNctmnrjDDtx/ZloOMuJSFO1MKOkuTbN3CncGFayl6Yv85GOTc1yKuIMlWvkjv/X5idrVC2qvfKB/sMDPfHI0eL1nXgtBYDQsrU7sJ4nqDQBTlN0DDREjqqGGSXNtWns4zttK9zU6yRMBRooylGSj28K8b5FLXH+vGo+x5XHjw7EDfuLO80ZwYWhxTwOORFJVQ8zMKpBOImJmY3i8elrK9Ufo/5argqEs0/JkFb1MAOvkT/jcQXeuzHMpIOBhmqvDmEGRjUIJ/EL+6edU9VQtTDzlvlN8QcyzLzKwLo6ZbC7PxD7OdO5dhhoqNbsg/9VP8wo0601zimzqhYAqgRh5ncWFXtas2mLCtgYTOljoKF6axd14bl0pLnYHkNN8Vwwr35hBhbyqVhLDDRUW3UZanJLq5dmTatRmUfybPmzlB16Zj5Y8AXn0rK3zx6VOmKgoVqqa5hJ04aFY86p8ku6sqtb1tUrHOfo/TLMjNf06f0C80wtMdBQTSU/InFZcdhptLJXaK5e2BQrCnx8o7Q9k8HBQKl4GGioduyjZ9f7qZ/WsNPlC+o5xDFK1sNx58+r9/P7kZlBYdegofQw0FCt2ENN5Tx6tknTrc2prIXhrtAcPx7/4JcU39/O1He5/KlO39qofrhSMNUG+2bgLjE1bR+WAOEDq+GafjSwzP8zzUXi5ZlkB77Mk+nHJutj8phc5TiO58dOF881TxMvNF8lT/+U6Ip5otuQGz46W8f5vNPEx3HRkdvRxrj1/Sf2nhXLB8+KZf3d4vj+8/Lj82Lp4DmxvPdDsWSw17qMl6/JIPe5Q33xIpuCa4mBhmrBWm+mjaGmOoYZ+9hKXqv4prHjQ+WnaMcuisrrmDtJZB1ofv+4lrhoXjbDXAPRFNNja8TO1s+KH479jNWfdbixxPmqeeNH3y12794mVjSFOHmsKfb3+2JZsyF2dO3qDNUXAw1VXr3DzLAi4yWtKk1Rjl0UV9kDzUZ53/+j/BnSfMZ/rzUpnmyfL7a0LxFHGlkOLW5xjhrOXRfNxh4aqr52HWc0oSpznXzjv1Oe9n/jRzUli16asjE9bTtrce/9N0Icofob894mPrH4HvGniz4h/mHer2YcZmCds8I30WwMNFRp9WsCVkEm/IEi7zncM/63btkX2TMd8rKszsQxLQPc388MxIUBs6OeaZ0tPrv4FvF3C35LvDB2mnNuTmr5RwqNwkBDlVW/JmAML8kwE/GI12lUada0y//WYqoPCMNNWYu6xOFe+YO+cdw/hP65DGSfXvQpsX3sHOecvK2Tr2+GGpqNgYYqqV5hJtzwUhDTVRoMOZV92AkhD71An5eBRIU+r+AXFAaz7p1RoqwLuEXe/6DG8D8+2BOfQyjrvEd+lvVPEuQqDj3RLGwKpsqpW5gx0SCZRnNwXjvzLKiw5hVmgr6WlSsWjInLFyZrCj4q7/5NB7riEXlC/SSTE9+U/xfp72A2CNMQKzRUKfZfbHUJM/YQk4k38+83FxnfAVdh2MkPHiu/xyvoa1nZnXAdll29gbhhf1c8rIUZm/+MuXxg6KmuMxjJjYGGKsOenl2XcfXg6dhhqZV8sQheGsNOlI+nR8zSOhLw5X+SYeyG/T2xzSuUdbY6J4qE/TRkY6ChShiuNVOUpsW0oMR+gdzi98uAHmSUIlQWyIwf9AbieZ9eZGSdx456DwX+SH7fhw/0xLPyo5epnVvk/9iKhoGGGGioAqyemZosnDc1baYx0++wBCarNHnM7qGhrx31/l3u6g/ExePe/TV/eDDEYQM6RRt2sk2ems4R5Kk8GGio1GrVM9NBv0y6S7ubqtDgerZ1ecTjPD3VcU64nDbm/Vq57WBPPFHmQwdwbZraY6Ch0hoOM9WhMnNh5PVl4koaalCZwRoumA5M+cFxjZ4K+Tv4SX8g/ueRcDPSijvshD9uGGjqjIGGSqlOw0zFm1kSrKpTtcvoQZ9eGbcHZqL+xhCui/dbtpdsYKipKwYaKp16rTNjZjZTFEn6aNg3Uyx/d6QvXg4xinT/TMQQWsjZToAqDdUVAw2VSv0Wzcu+OhN3yKnKC+mVFbLM/T7Nwcpz/YHY6TOryY897MTfNBULAw2VRv3CTHlWQGWYKa4Hjgysqdp+voklgWMp5po0HHKqLwYaKoV6hRkp56mxUao0DDPF9kxvIO4J+P18W/6uY/3uOH2bCoaBhgrPXtr8HXKry19edzkl/fyE7aNB8GGYKb4vyN/n33s0CD92dGCdHweHnahoGGiosDAt2w4zVV/9V5d9E7AXBJVRVRo1PZu7tHL48P6euEP+zh6Y6VtBBkfQ/uD+pL+/Ag47tTnsVFc82jYVUp3WmJmtGIFGuXxBU6xzDjK5VVt0DYvmxW0ero0Hdwqxfa8Qq5YKsf7USj6Vi/k65RG464qBhgqHYYYvyUp4/2PDXyUCzaUVDTWFq6Iy0NQVh5yoUKw3x/bt8lTdwgxVyo69zgkHqjXu8yqjaIvscciprhhoqBAwi2ly4lF5qk79MjpWZypvx75q/noLt8gem5XrioGGcjVs/K3TLCaqPPTN6N71aiEuq+aQE2c7UVEw0FBurLVlrF6ZulZllHxWBKaUrVrinJAw5FTpX29RD4VAdcKmYMpF7RbKC8ThpkL6zJNCTCSYoYSemc88Nfy1fuK8yj7ds24MnujODVCrjp23Wzy75z750fv1hBl6CmfqVQsDDWWufmvLjNC5TkztRGMlFQYqKg84VRUMF612DSGFhVC0fZ99Osn1FJzJmYl6WEFImejN/tw0rKeEX3PQaspUDgw0lCmGmbmmpi+U/8dbrZVSoldXTAUaDEG966xKVmniBBoVXFRoSSOsxMFDeZQXAw1lhmHGC9fMKCQ90MQJIvh+NAa7h52qXKWZ+Kb8378tEwHmkplN8mEcFCa8BGGwKR8GGkod+2WCMNAUll5dUQvjTY+o3CDAWCsEa9+H78GUbahylcb1B4seYKAMIcYLg015cJYTpYZTssPI9yCUFEBvBkYoAb3agtM4tIGiqjEqzADCzatPGF4Pgg0uV1EIMVcfvF7cvPeN4l0Hf1us7m6xgkxZwwxsWDgmblnSEuvafA8rOgYaSsVwTJ1DTFQBCCJoEnbTp2P7Tc0+3JN7+mpO4V4rd/LYsMO/ee97j4WYstjdC/eLUD8jQ02xMdDU1K/Mb4rbl46JR5a3xV8ua4vXzzPzQrWrMlcZm/FQfVimnQoHVRSEGD2IeAlTccEwk34cpwpUadQO/lZni7KjP9xYLHaMrRW7xlY75+TnlLFo71EMNcU2Jl9oH3JOU4WtbDbE+vGm+K1FY+K35XbBvKY4SZ4HC+WH18uvvSj/WNmurdEQ1eyqDF/04ewWu/Z81TlNqUGAePwFGVCWBj81cbkvbRfigR/ZwWPPjPMFaVp+7gWXec1JQjzxvBAvaZdXls23v45hK/V19T0le5ng6Ou3Lm2JN8n3ixURw4DSFkfFCYPd4rjBS8455XKZ/Nn/Sb5P7ubExMJhhabCjpPvN+9fPCa+uKwlviC362SQOavVEF7FmDG5vU9+/SsntMR7nMtFMVz1t2Tv0LlDhYaPWeoQRjDUg0bfoMzu7oEJQw1H4WNY+mURotSaNwWlKjJXLhzjs1XCY3GFDHd8LIqFs5wqCgEFIeYUpwoTxz/Lv0K+PtMXDx7ti30Bf41wOnZCXFgvfWrGkpqt5PWyQOBJK1hgRhRuU28qxlCUOwQVcDVhFWa4857rvfu6YgtXGy4MVmgq6I3zGuIry9qJwgz8fKshrl00Jv5aXtcHFo+J81ylHbtfps5HyDakzSpN6tSMJYQIv4c6apjBdekW4M8IHwhLGO7SvydKRSdHDDP+Lpe/cz42xcFAU0HvW9wSSw3+ZvGCRf/NR45riU3Ho+zcFG85/YMcYjKGjcGpwyJ3QYvauZt0EYDcgcUNl1mtXQazmfwgzADuh99LBtdXEOiVeXh525o0wFe4P1SvsFExMNBU0IzHn5kvGmpgO22sYf1V8r79N4lfPfyHYnn/WecrFN86u6Ga0oUwERaGpRB+Ru2rVOUnCIKRGubyqwIhbF0W4roycgV7ZUJjlaY4GGgq6KP7++KRo33xtZnBsffO5Sn8ps87+tfi2oO/Jc7pPCA/4zhyIu2r5H8Ve1vEMMunnww/lKOaY030seC63FUXP2F7Z9wVGwwZofKi+mN0KsRcI792jbMyMG7Hi1UNihC2qFDYY1QcnLZdQT/uD8TXjw7ET3oD8a/np9uJP28wI87qfFPMHxwQ32u/Vp7Dl3U8K8TKxVvErn0/dj6vAMwswlRp7Pixgz9hvvMFHx/bbF8Wm1/jbhgIDvduF2JK3rYKKu6hHjQJqynUuKx7urV1f8ft+69gmvUz8r4puD6chynY+uXwvTi8ASo8+s+Mx8Orb0ZdT0FeOhhuWtvmDJ4osJ7NGvmYPTDDudx5YoWmwr4jA83/li+wLGonFx79injboY/KYHPIOYciq1qVJsrquH7VCzdcblTVx/01fI8+XRufI1jgctj8Fs/Tw4equOjU1xGWMDsJQ0Z6RcYNt4PrcfMKOUQUGQNNxf3BgZ64+1DPSKjpj3i6nNt5ULz18E3yvdzErdVRhXtpVIDwe2pgeGjU0wZBBNehruv9j80+lhL4BSN8jxqC0m8L5wc18yqqqTeocjRq6Ahf8+u5CTs8RkS+GGhq4J7DfXH13q64P2G1pikjzShnd74u3nzkMww1cVWpSoMduF6RUAd4dFMVE8Vrtg92+F6BCN8b9qnmd9lXLnJOaLBejNft4b4h1Kj+mKi/KjwmXj03UX6OlLEhOJ5tHQ435Y2BpiZwSIOPH+iJzxmq1gR5w8y94nVH/1qeKsg7dKk4x8Kqyi5Fr0joVRKdXjFRMEQUVNFR3NepDx8hTHkN8SBU6A/vniPeIUNRw03q6yrUBFVjgnh9n99jkzFOQaYyY6CpEQxnfO/ENeIvF/y63E+k+8aFKd2ru1z9Np4KznhS3JUIr+oM1naxGmi1HbzfcZTAOlyBV1CS3+N17CZ3gFK37xV+QA9lpngNXeF+5Pw3wFauehvLJvmH4qbD2fQrkj8GmoqzV/O9TW7fEqJ9u7VNzXuX+Pyij4v9zROcS6UDlRoOPcUzOfEe+f/cvahayAvTRLHomdpwxOMNRTy2jHvYSQ8vflS/Ci7rV7Vwhw8VlNzVDwxzuZ+CXvcB33+JK2TgNoIW40sCIamgGGqi+ZODDDNFwWM5VZTVXGr1Y/gflmBFb4f4tcM3i5/qfcc5x7w7F90svtPCdG6Kamr6Qvl/3wowavGuUUMChTy2DEKJfgwjPSSgsVedr4Zy8COqYy9ZoeIsIe5wPgech8veoV0nqOtV3+umKi1+/SqYOv34884nkn5/0oD7oQ+rpX17IanAnMXd2NFa65yS2XNsrZjobbU+6uf7WdXdan28ZGaTvK9ev9BsXPxiJ8dbJx0DTYWECTFup/SeEVcful4s7r/snGPWk+3Xiz9b+N/lCz7nd+ky6lwnfu4nW8WGiE2aKH/jRY1m8MK8uPXgokLKQwE7dD0EIajgsiqkqMvpIQf8rlfB9eghCJd3V2v089T1pfnURahRw2Vp31ZIaQYaBJWHxjfIX4F97dMhgssoCP5r2wOxpmVfZ9TXSxIcaioWBpqSOja999ismPjTfdd0HhG/cejD8lrSeSp8ZvGnrL+6KLxLjmwSq3rflH+FbnfOia5QwUavmuAgju6p0l7hQa/S6MFDBRoMJ+mVH1Bfu0ELUH6wdow7/PzK6UL87feHn6c15FRwCDTrRlQDR1FVFhVgTISXubbIQHOd/Dj7l41QpgIOFgkcVdmMi9WZYuFKwSWDILPyxN+Tv7mNcnuzPGeFs8X33NgZ8v+GmOhtm7U/MaU16FiVmkL8+VlwF8x8Rbz74LvF6t4WcUL/JefceOw3crtNbls357fdZeNCPOGsput1X7Dart4Hg6eK+p45q/jKr2PDKry4nN4wrE4HNREDgspy+f3qttTlj5snxK6D9mnA/SrQKr5ZuWy8KVaMxfuhdzQXiS8vvFk8OP9K8cS8N4k9zRVyO8X5qmlfFbv2bHFOD+3u2895bFiuAlUUnN7dG1gr+pr4dWJ498ecqV0oDDQloELMymUf1EKMWfjr6cTBj8SK3jPOOeac0n9G/Ev7dWJf80TnHNJNdLeKyw/9vnjzkc+Ks7qPGt93FiLUIHwgsIyigoUKLKjC+AUaPFD46L5MUJhBteftq2dXXXAdqOpgO+uE2deHQIPvGXXYhoq5cXG0YRs0EiNE3HywJ7Yc/7NiT2brKW3xDDReVMhRQ0RJDu+A6uf9Mzn/kUBzMNAUiB1c3iyDi/xobRvlhmpMOiHG7XutSfEz3X8Uxw2SVQa8NEVPPN0+X57K4k2u+BBifu3wTeLthz8uXtP5mlgiH/O2OOp81Ty8eed+rJlHdwmhNywjKHzgXHvYRzcr1GiVHUUPNKBXf9xwG5Mn2Ze3Qstpo8MJGoP1gFSzKg2GZ1ChCfPjIsggxNwtQwIqIQgNK5fK9yrrPSuDB6xzV6zjn6nqTdif0w3DuKzOFA8DTc6G1Ze3yN/GRnkOGnrVln6I0fUabXGkcZw4q/MN429FK3vbxZPtN4gDzWXOOfWkgsylM3eLE/q7nXOzgQPoQW6VmlZTiO9qzeeolGDYB0EDd02vrOA0KiXrZQBxfw2f6wEDAcXrOgCXw9dQkQlbZXEHpJpVaRBKRjXW6kEGl9dlGWimfvAx+X+85zPud5xKDaszxcVAkzErwMgX/OwQg+CSbXjxs3vsDGuI6OT+D5xzDGoMxHdav4gT9uc1g0bft8kws7yf3xG18eaNknsuXnWcHVL04RwVTFTFRQ8k+Dou/7YzZw9XoWrjVTFRVRicj4+ozGCL+nRDcHEPY9WsSuO3ow8KMkp2gQbDTfc5p+NBuI8aarbJxyC3PwooEBfWSxkCjL2w3e3Wpha3syswxTwQ4SPzf1O+yOe+vA815A4jgTM7m0UrxWGVokJV5qa9F4lLZz4vH1W+EfrCDCU06+pPPcxuwiwkfE2d77Uwng6XVcNScem3B7hNv0X+KghDKvpBbRFk0AR7fZh1jtpZzWgM1zszCn5W/Gxh12/iNO3iYoUmBXOHkVQFphhVmFH2N5aLtuiI03tPznpPb4sZ0ZORJMxBKr0sHOwTz479tHh+7FXOOdWmDy/NjYf5QLk8178u9eEcr6EcnMZ5+pAPqjbL5Pn67KO0h4C8qjSo0KR5mwWD5wl23thUf0wY6P+z/2BL91k/NY3VtM08l/GzqYP3BlVrcn/9UCBWaAzRKzFFr8CE8cD8K8RLzVc6nw39pPlTzql4zpA7+TpUKTC89M6D14vVXTN/RZqAv7JViT03YaomuIy7UoNGXf2o2KiYpP2DuKs0alo5FcBdcjP/y3BXpnQIM6zOFBsDTUxWgDkWYpzjJJU8xOh6oi0em/er8sU7+2+Vk/vfF9+a9+/lqXh/fZ3Re9I5VV1XyyBTtOElvBlHKaunCtUVxS8keIUavUKTh1FDXeRIvzqTJjUEhWCDPwLUcBv6hhhmiq2WKwUjiBxjYKXdqkK/ywf3vdUaKtJ9u32e1Tx80ZE/j7XT/vhxfyFeapZj+C0KDDHhuDJFq8rcc7hXrOM7uY+1FLQaLwKPvpLv5CvsYaCsDhPgvq9YXbi8++pMTE58U/6f5t/Kd4mp6XQqNFRulQo0s4KK0sZ5+IsBGFqi+uUjd4g3znxxTnD5+vivi9fHPJr2Vxa8T/zfeW+Rp6qzZ8AQ03qrVyb/l1MhQ4wu6GCVXvRQgepO1sc80o9DNeq+EgMN5cZ4oPEPFY5OhL9e9e/zxbCSphN7z4r3H/jNOTvqPc2TxbL+c85n0TzRXi++tPAD8hqrEWiKEmZKNcYfNaTox3XK4yCOamjM3VdDs0xOXCn/x0SItB4khhny15i8992DcMHBiwoTCkNFFb3t0MfEazoPyFNm3kRebp4kPnbcvfLayr9nyDvMqKMX72htlm/0n5fnlOSNPmqVBpdXPSwMFYWVeqDpXCemdm52PiGarTH5VwNGXQp0ZndKvOPgDUZ32n+86E/ED1o/53xWTnmHmTsW3SqDjPuPiBL9BZv3UBIZl/Zw09T0hfL/nBaGpMLjLCcaCcd4erlxsvOZGat6W3ILAiagATivMIOqzI1LH/EIM3CV3KnYW+HTASstlWK3G/AXSvlhoKFQnp5n9pAFp3f/2TlVPmo2Ux5hBsNLn110q7zloN8FwsxGGWoelVua/QwJYWo2DlGA6kySVX2pGDJbIZjIGwMNhfLdsdca3X2f2X1CNAc957NyyWPBPFRlMMT0wPwrR4QZN1Rr7GBTyKoNqjTXnDU8BhORLzYDUzAGGgoFa8/sb5zgfBZNt9F2Tg2NiY74V70p57PywKJ5WVdmEGZQlfEeYgpLVW1KMhxFJZTu86pUTe+UCwYaCg2hJs4b1oxY6Jya7fTuU5mHgyTQBLyqu9X5LBvhhpiimD0cxXBDJtizm9J8HrE6Q6Mx0FBo321NxnpLOdxY7Jya7bTet51TxZfHjKZ4Q0xRzA43DDZEFIu1rILc/FjLNDwpxPses7f70zkuGgMNERERlR4DDYX2ZPv14mAz+myUf2l5z5DCbCH00hRd1tUZ1QCcrGcmqmHzMCs1FB2HLmsLq2hjkcxPy01VX/Tjr6lFNPVjolnf86TxKg0DDUXydOt18v/wb1z/LEPQoDEmDjSXOecMNURfnNkt/qqfWYeZ5A3ASWizorwOY0Lkkn7/TM0bgq0FKAOGc7LkNayE8/RfjTqgrAos6rAhbikcvZ6BhiL5TusXIr2t/HznG+LCmS/JJ1rXOWe2V/WezCwsxIHqTFZUmCnGISHkX9zt2xlsKFD6x26CGjcEIwxgx+8XCrKiemD0Koy6P34LZKrAEhRcvAJSAgw0FMk/t98gZhoLnM/CW9j3flKf2n3aOVU8WQ41FSvM6LRgwxlRlANO15ZSqGZE4jVkpMIIFsX8xHlCXOYRbFCpyRADDUWCHe7TrfPlKTM7tlW9rfKainlsFoYZnZoRxVBDtmyqM1jAssZhZmKJc0IyXM3wdMM/2BWYT2v9LQgvXtxVI1RqcJBZ/ekwqrJkeIVwBhqK7On2Lxp7i8Fqwau7TzifFUdWQ03lCDM6Ng9TlrJdkbtwpjOszGBIqe+8s6MipHpg3D0yCi6jN/9CULXGDQHIMAYaiuzJ1utFV8xzPkvujG7x+miyqM6YXzQvSww2dZZNdYbDTYmovhe19guqLu4AolhDSK7wpAJL0HCXX/UGYQXHaAuSwuFOGGgoMhzK4Dvt1zqfJXdar1h9NFlUZ1CZeXD+FSUNM7p0g83adkNsWNC0Npymoshi6LHmw01uo4ZvFASZ9yPAuPpeVEBRIUdv7A0KOqNuM+5QGO4j7oP6fhXAELxizupioKFYnmueIZ/nZt7Qzuhuc07lL4tG4PINM4WBYGNvJnZ0l8sAc+uSlrVdsXDM2qzT8nzGmnxlMU3bVvPhpjgQQNDAG/T2pSouuKxfkPHjVXnxCz0Yfhr1NMH3qplTKoDh/oUJUh4YaCiW58bOcE4l1xJHxapeMd68JqwmZYaZeJI3DiPIPLy8La6UAcarIrNBnv/ZpS2rYlPFR7DoshpqAg43RRQnoEzvtb8vCvdQEQJI3CqNn4l4zcIMNBTLs83VzinJwHvOyu52+X/+b15pH3zys4tuqWiY0UWv1CC8qCAz6rtWtxpWxeaWJa3KP5JFYq9HlFXPFA9GadFnOY2CUBH1IVNhRP++oN4XfA2VF/dlUBUKc3wmVHhG9c7gumP21zDQUCwvjJ0qDjecJ7WB97eT+/fLq0GVJmhLV5q9M6jM4HAGg9q85MKFGgQZBBMMJ0V9Gqn+GgNPPwqj/UfyPz7auVFDRV5QZfH6elA4Udzfh+rIqF8zgon7MmEqPQgq2NRMKJy2QpITYq55tdzOiv00a0z+1YAxmGK5+sB7xeqemUMXfK87EO/c2w31B8ZwDP8cuZlbxfamvRfJazX/cqj2MFMYd4mp6bl/cWN4CZUWE4/K1s5Abn1xz+F+Cr9BynKoCaamL5T/F3N9qkxZjbJaTwyCgNevwGu4SVVDbnhsdOVEp8IKrtP9ffrte92m+rr7fiOw4HpXxxtKCosVGoptt9VHY+YN7sxWQ4yHvCqMrWMHOTV9rdzOtzbRuVZ+5U5ni/LqtaVZncH07PqGGZhbrUFVJszwUlio1iAcYdhqnUfvDcWXdZixq7HRX8OVFHbhOa/hJoQIv1/ZKxc6JzyoiskoCChYSO9YZcVZVM8KM9+efX9Q9TG8iJ4XBhqK7YXms/I5a+6NZ3GC98upnVuckIPtAnnO5+QWPtykNbMJYWa6tdb5rM7sULO2bTf9phk6Ll9gLijVXfZhBtIfXi4thIWovMLJgpZzwodX+PC6HlzOGjZyAguqNlZlxvVeistk8BRioKEInF6WznVWVeSpnzxqn20IdnKmnvPDKo4KN/5hJa3qDMJMNdaaMeOSI9k08nrNjqLo8gkzUocVmln0IIF+l6gPDYKG+1eI65l8hfOJjzBVGjevWVao5GSEgYZCUCEGQzxy22n3zRwZmH2jW9pI543TDjcXyA3HoAoON6YwzMx29cHrxaUzn5ePBndUZZDtjKbZpnamO9OwdPRAgmnWXlTfi071wPjNlBr1/u2+zlFTqXF7XjKqzgADDfkYVmL0EKM7ZLif/Phm+s96e22L2UNRpoebGGaGUP1Cs/XqLv7qzgYahCk+K8y0b5On8nj+sjozR5ip2wg9bqjCYIjKGg7yuI49R4KrMPg+azhJXgYfRwUTrz4e98EqU8ZAQw68kYwOMbpDhichLMnoia8qNkJsFhMprDvz4Py6NwEPpb1QoZdtHc6OicsaZsotzEB2wbeUvKZmK17hRFVpvCo44HW+PqyFr2MadZgqi35duC+Y8ZTyrCY3BppawpvGnTK8DGcJuYeTwjiYaEc193uXZPxsnJq+TgaarzqfmYHqTH47g2JBdSbthQrd3ruvK+7m1O1Y8hxmogDu6otfY7BfOEFfi1cQwnl+1Zs4cF0IMQnXkkmCgaby7KqLNa35WIDBx7tkeEn219DBfpJn7NzvfSGHP6zXz2BBPzO7Pw41DaHylcURyxUMMyHMbOFwUyz5V2Zs9pAwf4eBVNXFzS+c4PJBh0RwByFcR5KngTuAZYiBppLmDh1Z05oTBhi3ZBWauR49Wt6/rKtz9Gwz3nnw+szCzMUvdsT1DDOxTU4gyLxDbnk/d3m4A196UAkadvKq0vhR14kAooaUcF6OgSQprhRceiqkbJYhxnxoCdKSL4AHTmgbeRt8/OhA3LA/3ErBpphcqfbGpQ/L+86/DwBDTVlVZ1iVic9u/sWCh1hxO39cHTiAtVidtvIugotfX8uoiowSdB0lxXfgUrErL569LwaGkKIacz4m9bx8D7vtUC/TMGMS+2aGsgwzm+RzhjOa4hkOMRUjzNAI7uEkhJagXhr9sl4qGGaAFZpSQJBBYAnfsJuVjywZE+e14+fi7/QG4ub9PTEtP2YNK9ayOmNO1mFmE5t/I8ttsbyRsNK3/GONv1F/7ioNQguCiZpJhK+r/ppRw1IVDDPAQFM4qLLYw0eQddUlql8ab4jrF7XEohgvjq/N9MXNB/KrzJgINGwEtqEJOKu+GYaZaIo2tOQNq3qzh2akzzwpxHZXWFHVmKAQo/M7wGUFMNDkRgWV8oQXPyc3G+It85vi7FZDrAmx7DyOrP0XR3rikZn8nnqm+mdYnbGldaRyL2gC5ptWOHbDbxmGlRhoQvMKNWFVuDoDDDSp0IOJNkxU8uASxm/IoPDW+WNimWsf/8PewGrexKJnf3/U5CEt4zERaFidsWU51PTQ+Br5mJ8t/h+n9wYq7tCSHwaa0NTQUtRQg0rOu/JZHyYrDDSJqGBS/iqLSQucjxOthviXrtzdyxeQ/FAoOEhi0iM+szpjy6o6MztAcgfopXxBRuHvM7Kws5mg4pUZRQs0YXbEqtqAEiZWlawL7bEpaHMuRZO0f8auFHzK2bnWV1bVGf9qmL0TrPOCbOXokRkB62bxfTUeq1rjzHjS+2hUb43eOFxxMtBsHsTdSXv/NYCdf5phxyN4yfs/682s7XX76sU+rKaMwmpLNZkYbkJj6lMrMF273kvFZ1GdwaKFn110q0eYcZPvAx17Eck6qESQURhoyICG+OT58t0o2RsSXlhh30TsF2GIwKOFDgYLMslEoNEXdCtP46VZWVVn4g/t4X3D3klWpYIzDDF49oZ4Hy0LBhoyQAaa88r/KieKwESgcc+0KW/vQnxZVGfMNl6Xs4JTqUqMHwYaMoCBhmrnz49viRVjyXaQflOH61KtyaI6E36oKa5i9t9UtgoThIGGDGCgoVox1T8TtLBbHao1WQSa7KfFD4eoMOSdZSWnFlWYIAw0ZAADDdWKienaYVaqtUPNuXKr5l/YaQ83FWeNH23CgYGQYwUXOFaBgZpUYYIw0JABDDRUGyaqMxBl6f0qBpu0qzPFCTOUHa5DQ8lxVTCqjbXtZua7SPRn4GjoQnxObtV4s57obU0tzKBvhmGmjlilouQYaKg21iYcakrCbjy9U27lDzWruludU+Y9M7bGOUVEFA0DDVFEa9rxXjZWqOlcJ0+VN9RguMnLS81TnFPxcaiJiJJgoCGKKEmlB02lU9MXyFPVGYKCze3LEgeRB+dvYJiprXXDhmmimBhoqDa2Oiv7FkFZh6DS6p9BdabK09yJKH0MNFQbOFzB5w/1Eu+OMcvJhCr11Vwysyl20OFQE1lmTWUnio6BhmrlnsN9cXeCUHNAfmPYKdthlC3UpNEQzKEmIjKBgYZqB6EGhy64SG6o2CDgYAszJLW9az54INSUoa/GryE4CQ410RD7aCgZBhqqNYQbVFywXb+veyzk+IWbbZ2+c8q8KsyCiorVGSIyhYGGyAUhB+EGmztamBxu8lLkWVCmVwdmdYbmYB8NJcBAQ+QDVRoMTaFi4xdw0jKs1lT3+DasztBcHHai+BhoiEZAxQbhJutp33a1BqEm/2qN6f4ZVmfIF6s0FBMDDVHBDas11ZjiDazOkD9WaSgeBhqiErCrNTgicflXGWZ1hkZq3yZDzTnOJ0ThMNAQlUweFRuTKwSzOkOhcOiJImKgISohVbEp2zAUqzMU3joxOcFQQ+Ex0BCVmFqUb2r6fPlZejOiTK0QvKO1ltUZiuAqhhoKjYGGqCKGM6KKW7WZbq1xThGFxVBD4TDQEFWIXbHRm4cRbrbgS7FNGKrOcLiJ4mOoodEYaIgqahhurpXb+UJ0rpXnVmfqN9UNQs2jnP1EvhhoiGpi7tTvcNWbie425xRRAWBK98RGeYLVGpptTFx66oec00RUE7v2bJXbFrndJ7e7xMplqNog3GBBs9k7CgSaVda07WSmW2utjTsiSm6dfM7az+M6WNtuiFPG7O2y8ab1eUO+jHand6zcUmqIT57H+jMRHTM5caX8H6HD7lnAYQ9MHJjyjkW3ih0trgBLJmHpgoGw1maq0FAqAsuaVkN+tAdR8LmfPznYE395pC/WaJfJ+jAtRcFAQ0SBfveUlWJ953kr4iTBQEPpwnCqHXDKRg8wQeElqk2Hetajsa2b/bHo8sBAQ0SBLl/QFFcsHGOgoZIoT7BBeLllSSvxaysMBJr37utWqI41F5uCiYioQpzZUBMbC32QSwSZWzMKM4DwZLL6U0QMNEQUCGXwar8NUjVdJUT7dhlsvmWHmwkZdAoQcBAqHl7eFutyCBcY1qrya5mBhogycp/cOMJNeUCD+8Y5Acdufs8Ohm+zGmKqI/bQEFEgvAGb+GsS4/dbOgO5I1GzqPQF0thbQ3m4S4jOZmuNpjShKnP5grFcqjJKHXpoGGiIKJDpQBPk2JBAWwUcLndPWUivkdhUU30SmO206XC/8vVRBhoiCpRloPEzu6rDas6QqixoR1rveFQbjgXEUVTVrI6PMR63zUbXtMk7zKAqc8/hXuzXXdkw0BBRoCIEGi/DkKNUtZqjhRYtrKQ9TGI/vnU8xICZak2WU7Ld6hZkFAYaIgpkKtBkXfb2ndEyp1phsiqRJGQ4gQX3T35MO7CEVedgE6e/Ju9+mboML3lhoCGiQKbK5mV5o51b+fE7urMzzONUTYoSQNJS32AD4cJNnlUZxXQltEwYaIgoUN0CDfmrd6hRvIekitD8Cww0REQ+TL1RX/xih2GmIoZVrDrPQkO1xm4ivnxBoxBhpg5Ts4Mw0BBRoKI2BVMx1L1qM9HdKt558Hr502f73EZ4ea4/ED/uDQRW865jE7AbAw0RBTJVoWGgqS6rAbt9mzxVr1BzyZFNYv3M3bmEmTpXYvzw0AdElAnM/Kjn3/DVh2bZqekL5KnPya0eu9m8wgwwzHhjoCGiTGAGCFWbvSjdnXKr/u6WYaZ4GGiIiMgYhJqqV2tQncmaGmbisK0/BhoiygTekKk+qhxssq7OMMyEw6ZgIgrEdWjIhKrMhrr64PVidTfbRRRvXPqwfN1sk6e0Y3ZBgVaULgIGGiIKZGr1UwYagjIHmzwage0wE2YwxV4Xp84hh4GGiAIx0JBpZV2Y76a9F2UaZh4a3yAenH+FvMU4j5ETcCSTRxAvMgYaIgrEQENpKkvFJuvqTLIw48UOOFUON2wKJqJMbOsOGGZojrJM9c56qOnB+RsMhhnA0eQ3ygD5qNzkR7+j0ZcYAw0RBeLsJEqbFWo618lTrqbXghg1TRvVFJPhA9eXbsXqKiHat8tg8y073ExU45hcHHIiopEeXt5O/HbHaacURhH7a4J6Z/Y0TxHL+rudz8wI3whsmnMU8ZI2FjPQENFIJvpoeLRtiqoI/TVBvTM7xtaKVb2tzmdmmO+dSWLYWFyGkMNAQ0ShJFmPhtUZSiLPYJP1zKY7Ft0qdrSK3N9S3JDDQENEoSHUrGs35xyXSfXZuM/nzCYyKetgU/6ZTVmZHXIe37lV/gzZv+oZaIgoFhVe2DRMWcsq2GRdncmvdyYtd8mAszlSFef0paeI4+cdJ7a+8D3nHPn7PnVdqOtgoCEiolKyg825cjM/RDPR3SreefD6zAJNeaszYQ2rOPpaOLOmj7fRCH6OfXokd8BZx0BDRETlZgcbBAFzM6OyHm6qXnUme3z0iIio1PAX/9T0XXIzd3TvrBfSo+QYaIiIqDLscHOB3M6XnyHcRF+FOGghPaw7YxpmNrE6kxyHnIiIqPKsXo02+jVGD0tl2Qxc/d6Z7DASEhFR5WGWjBqWSlK9oeJihYaIiGptWL3BcNOYWD+zKbMKDZuBzWGgISIiciRZETsqDjeZxVhIRETkWNtuZhYvHpxv9ijddcdAQ0RE5HAfvoPKg4GGiIhIwnBTVjDcZGoRQLIx0BAREWWMw03mMdAQERFR6THQEBERSVk1BD80vkb+z+qMaQw0REREUlYNwc/u2eyxwJ/76NEUFdehISKi2stq/ZmtnYF4776u57J9+gJ/Jo8cXhcMNEREVHtZBZpNh3pi0+G+Z6DxMgw558hNhR3ywkBDRES1l1WgufjFTugw42d2JQcQdqDegYeBhoiIai+LQBO1OhPH5MSV8n/8FPWr6DDQEBFR7d2ypCXWpdwUnEWg8TI75EA1gw4DDRER1d7Dy9upVmfAxHCTSXOHrsrdiMxAQ0REtZd2oMmrOhOHd49O8as6DDRERFR7DDSjWUEHZoUdKEZlh4GGiIhqj4HGPP8ABOZDEAMNERHVXtqBBovpbelwd+tl9hBX/KDDQENERLWXdqApWkNwkR2r7Hg5FnzmzthioCEiolrDMZwwbTutQBN0uANKxq7u3CZPNXhwSiIiojRt6/SdU2Ta1M4tQnSuk6cGDDRERFRvZ7fSG2xCdaZuzcBZs0INAw0REVF6WJ3JxtT0hQw0REREVH4MNERERAlgWInyx0BDRESUAGZJUf4YaIiIqNauWDiW6ho0lA0GGiIiqq20qysbZFiibDDQEBERUekx0BARUW2hoZdNvdXAQENERLV2z+Feagvf4SjblI0xcempH3JOExER1c7uvgwezmq+DfnvazNYDM/urVncjN9jg8rPzQfTC0s0Gw9OScXxmSexerVt1VK5LbE/EhHlSDUOr2k1rCZfr4jzJzK4LHS+sK1rv5FxKCtbDDSUvx17ZZh5ahhmdOtPFeJSucX/I4mIyDh9dhSDSzEw0FC+HtwpxANyC3oWMtQQEdEIbAqmfHmFGQw1vevVQlwjt9XydJjQQ0REtcYKDeXHHVQQZFCNWe3qm8HlLmGFhoiI/LFCQ8XhFWYA5zPMEBFRAAYaKg7OaCIiopgYaKg4MNspS5gmjiGvrG+XiIiMY6Ch/EwscU7kAH05O/bZgebTPlPGiYioNBhoqDgQMLIKFqjKMMQQEVUGAw3lR60GrExnOPSD29YbjfMYdsKQ16edYS+GKyKiRBhoqDhQoQkLQ0ZlDgFqyEsNe4UJVLiM6vthACIimoWBhoolzI79/Y8Jcb/cqevHfkoq64DkHvIadftWNecpIbY7AYihhohoFgYaypd7jZkowWIiwTTvtBuSrQpMQDibM+SFao3P5VU1R4fzGGqIiI5hoKF8udeeCdqxK+qwCJcZXHDPHRiSQthANcUvcHgFKr8w567mKLg8ERFZGGgofwgoUao0VjNxguoMJP3+MIKanK2fwRVq4oQqk8NuREQlxkBD+fOq0nhB0EH/zPvklsZOfFRlyDSvQzpEvQ/uilbWPwMRUUEw0FAxXOraubv7Q9w9I0XfcaP6Eqfigu8ZFda8Kjt4PFTjMAIfmqZZuSGiGmGgoWJAtULn7g9xB5wshoxMCApeXsNOYdbiwWOlB0A8VmoGlKKqWQw2RFQTDDRUHO4qTdr9Ie4wgRCQ9c7fPewUpqqDy+D73PffC34mDkMRUQ0w0FBxuGf+qKEUE6wqhgxIGI5Rq/Ni2re7h8W0MENIbmF/5nedJcTqEKEmDDVkxeEqIiopBhoqDgzBzKnSYChF7myDqhGjdsYIMwgwqvqBj9bn8vv0y5oMUPhZ8HOMGkLyGjqLUilSt6N84ry5ISdMqLIeZ+fxyfIQFEREhjDQULG4+0MAO9ugHbK+M0YY0IeqVJjx+n4VcMJSwQkVnlHHYIqycJ9Xk28QPXDo90FdjzvkjILHiIio5BhoqHjcDcKw66BzwhFUSVEVGOzo3VWYUfyqGVZQcoITLqNuA423qCD5GRVOwN1HA/rPF9Rn41W5CgpaXtyPUZIVmImIcsJAQ8XkXmzvcM854dCHZbx26qrq4A4UXuFB5zfcEhSMcBtRAoRJ+s+jQpabu+LlFiZ0EREVHAMNFVdQ+AizE3ZXcXB92LkH9uPI63V/H3jdF1wPrm9kYPAJSUH0wOZFXae7B8f9fUE/q59RPw8RUQEx0FCxqOZerKuCnXZQL8qooPA3z3iHglFVGq8wgeCAhttPats1Z/nv/PWgMSqcTI8IZ+7Q4hYUWjh8REQ1wUBDxYEwoy8Oh51xULVABQW/gLLrkHPCBQEB1+sXBPyqNFGp648zpBPlPgQFtDDVljhVHCKigmGgoWJAONF3/NjJWqFDho80ggdCwGp53aPCUhJ60IhzP/X74H4M9K/5VXjcfUh+3IHIRJgjIsoYAw3lDztn98wcfSeLUBMUPMIOq+gNv9hpB80GQljCDKYkoSbssBPui9fX9MDm9xigquW19g4CkH77QdyhEbeb5OcmIsoBAw3lyy/M6DvjwD6aCFUaXFbdlnttG98qUMjr9qOGfPzuJ87D1wD3wT1E5BeE8D3WlHHne92Ofd3jNtVaOvqqyQwwRFRyDDRULAgzo/o+lo07JxxeC+/5BRQEBOzQ9cvjNv0OI4BgkGRnr4cxr3Cin4dKkxXmtO9RQQhbnPuBx0YFFxVi1Fo6gI8INOpzIqKSGpM7jw85p4my5w4jCDPL5zufOJ54YfYOd+UiIfbMOJ/4+MC5QjwjQ8BLHpfTv1cPUK85yf6InhSEikn5+ahwNcoJ8mdR16nuixo+0pug9fuBwPayvKy6/OPy5/f6Odxwn/Fz488Ud18NfuZRjxmECZRERAXUEJ88L8nfn0TJuPtUMDXavTP1usxDO/2HSrx2yl5DWwgAqMxksfMO6sfxuh9e99cPvh8/M5qclVHfrx4jva8obM8NEVEBMdBQvkYFGveOWd/542voEdGrN6MqDPgeNQyU9Q7cK2T4hSoMMXkNpemsECO/P+jnUH076jHC7VkfGV6IqFoYaChf7rVnVLXhWGBxDZ14VXAAO+4y7KStfhj5M4UJFl4BSOcXhoiIaoiBhvLlDjRBRlVfqmhUqPELeERENcNZTpQvVBi8Zhe51THMAH5uVc3xooaUiIhqjoGG8jcq1NQ1zChqCI6IiHxx2jYVg5oyDSeMD7e3rxbitdrX6kif+u22TH4NfTgMPERUc+yhISoLr34jNgYTEVk45ERUFl5DT1zhl4jIwkBDVBYYWgpqECYiqjEGGqIyYYMwEZEnBhqiMvGq0nDqNhERAw1R6ejT3BFuyrBCMhFRyjjLiYiIiEqPFRoiIiIqPQYaIiIiKj0GGiIiIio9BhoiIiIqPQYaIiIiKj0GGiIiIio9BhoiIiIqPQYaIiIiKj0GGiIiIio9BhoiIiIqPQYaIiIiKj0GGiIiIio9BhoiIiIqPQYaIiIiKj0GGiIiIio9BhoiIiIqOSH+P9rd8rcxUXwpAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "id": "9615a388-0c7d-4581-b9b8-09de7b59e17b",
   "metadata": {},
   "source": [
    "![image.png](attachment:7408c4b6-f1a0-401c-a3d0-803b8fbda3b3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "704d24c8-71f1-433d-9044-696003be8692",
   "metadata": {},
   "source": [
    "Die Frage, ob jetzt in Königsberg eine Euler-Tour existiert, können wir nun beantworten: Da von jedem Stadtteil aus eine gerade Anzahl von Brücken ausgeht und der zugrundeliegende Graph nach wie vor zusammenhängend ist, gibt es nun eine perfekte Route. <br>\n",
    "In unserem Beispiel haben wir noch einen kleinen Graphen mit wenigen Knoten und Kanten, bei dem man schnell durch Hinschauen eine Euler-Tour finden kann. Betrachtet man jedoch größere Beispiele, so wird die Suche schnell unübersichtlich und mühselig. <div>\n",
    "    \n",
    "In solchen Fällen liefert der <b>Hierholzer-Algorithmus</b> Abhilfe. "
   ]
  },
  {
   "attachments": {
    "6dca74c9-e5ff-47b3-96f5-de6ffa68d3ce.png": {
     "image/png": 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Lm2W7j+VHABHF4l4mh+g5P/TbvHBuqC5PpsiQka8v8jQKHvx1MQX3F41Ox+p+tkjh5i+H2etxMd5TxXOKtctZRpuNC/exAYIgiC8rinFTTSQO2wTLatECVt70j3UJ/Z8rJ0UGegRbo02wPaYvXGN8kh03Ktel+oQOdt6knzzXckyx0s/0Cx2PTvpdvOkF22G1Je6EMBR2C84nTYLp2Tah6802wf6kRbC/3CP08XmL4pTQ95oqLqstLB4tQm9SOa0gpsn2pPh5TXaN3iTYtvYK+XUDRCvgvt12wSiG//02wbmlg/mvnCpJi/4x5s+b/cJEGXcpjTVcP627EnxllHSze20bTNKKAqL8TBsUtxn9YGk+4BG6vm9T7rUIzjc9gudYTFqB4PY5tv+mU7Ap8bJs7xI8B8TPRYr3dbE8mbynL//pS75fcG+xCI4DISHBJYTQQZZnYdleOxPvFTy7HUzG7L4nnZJFf+E+KS55P/WC/TWP0Bu/LcSOeYSOZ+V8lcI/p9h+/4Zdv6+FXdcr9LNw+o91CPZnO4RQYTWGqXHsjf93ZeUDu+A+1y/0R/uFkOj/FrFMFFvx9+9zCJYtHiHE/E6EPULb6yHh9m9mSkNlxPs6tip5pLcJzg9kGctkWDq7lE+/TsZXTKsU3mt2ebUIlj7PgT4WO8bnTM6sDsl1jm1K2dc/1iL0cGpL+z7BvdUudBzrZ/nRL/Qyv+y75bSIVJ8nJfk8kRB6mNwsTC6xcJfQEVTlsRJf2T8W3+E+qRyxV0uWdhaXKWVo+vyWymFeBhsUP6XQmB+vWqQ4DKVSQiLYIXTs75Ks7KXrWDn+70ExH51CG7tnKJURbkv5oKrbBEEQxH1jkfiPNfAPBtK6gA70PeaGd1czTPnh9lwKSS6GwL4d8F1tQSgVgDTiWIJoE6G5110xYq/PPBtCfekQe+yYHDVL5t+orIi7OWQly2sNtNp5Lhh5vxdroV2iuD0IjIaxY0MAlkshONWrT9zNgjveBvveeoRTXcWf+lTyQxy6nk8xiQvU5+6F7GuhKG0sz8SF9fN5xhqMHGswNPeynBAEQRBV8WAppFe7scjiQtcVAe6nFDcV6VPNMLTw8HCJORloEMQXlezZHdCdtOF2uGXqUlOjQTSvCKH5Tn41AYIgCIJ4MJj7OqTzyTo7ep7Vo3t3N6Lqz0oysjfD6DkchuVVNxykjBJEWbSNTrhTPQj+vHRuZxbx4z3gtrfCRsooQRAE8YDxYPWQSuSQvhpG6EoC3CVONh7RmmB5woyGxibY1+nvu4EEQTxU3E0jfiaAPi4Hg4nVF3Elg+QEzJvb0bqB6g9BEATx4PEAKqQEQRAEQRDEl4kHa8ieIAiCIAiC+NJBCilBEARBEASxoNQ8ZO/z+XDo0CHliCAIgiAIgiBk/v2///c4fPiwclQ9NSukw8PDyh5BEARBEARBFLNmzRplr3rIqIkgCIIgCIJYUGgOKUEQBEEQBLGgkEJKEATxECJ+KvlB5EGN132h1sR/qYVFEMWQQkoQxLSI36TPSpv64Sl+/13Z/QLyYKeZR2RXJwKjD6Iyk0Vsfyf8N79AitbdHPjBKKKX40ims6wUlIc/34nOU6mK58uRGwmgc2+USe3LjVzfvkBlhpgVs5hDmkbweQNazyiHRbShL9MDu1Y5/KKTjqDzBS84cX+JHsZldZKzRC4DnjVe0NjhPt0BC30ep3ZuBNH6hhvR80mk98UgvGlRTnw5yF7qRtuRwAKlP4vkKTc690egfd6F1qf00GSTCJ9KwrzXDdv1NlhvtSO1AHkiysX5rh/hyzwcwRRCW/XKmTkipu+IG54I0LSzFRa9Brl0HOFLWrQdbEXuiB2e1eH5C29W5BB/pwmhJ/vgaZQbldw1P9qPRpEZSUuKjUZrhMHiRM9rFtVXuZIIvuhiSqyoUGmgfcTE6pYHjtXK6UqwOrjjMPM7zUPUFyS/i9r3iUK45lcD8DwryoaD1+aB4VgALSuli+4LuZth+M9n0LDdCcsyxXHOpBHe1QPNS63AeRfa94TBbw8hc8wBtRhyV7vRFLag74Ct5i+hZc+3o3mwFX2sLi3YY+JuGtyVGBLXMtA93gCrxQxW/BV4hHeKLxlZaPRG6Jh7Jm1EW7ALtiXyFbmfe9F+LIaUWL40WhgtbfC8biuSUVlG2DP0RS80u7tgPNkO/1rW3r1uXuCvyWURfceJ7hNhRG85ELgTQssj97DdeUBIs/LtOpuU85Ada1leG5/tgmeLUb5AZCyK7l0+REXdhuWufqUV7QeZfqOUgzkjKqSzJbYPojLLtjahL6M4PtDEBPc6j5BQjubMnYDggF5oOTokFCd/Qkjst0iycZy4rbgRs4PlmVjG9sWU42n4LCb0HugR+nn5MHOlV/Aci5XkzcNGDemfLz4fEnq36QX9BrcQmyK8jND/uk3Q6+9znEqR6h6rX8GU4jA3Mhe7BJveIrQFS+sygw8ILauZPGATeocVtwVi4kqXYHm5r0yZTgmBLWJb7BACdxSnKQwJPU9ZBHd8Qjmulgmhf7fod4X0Z1gZfRJC2zlVrDiPYNkWYrG6X+TjWKZMsPj1nptlOyyWM7W8P88ImVLxfR4Tup5kz8DPlOOayQih7SxfBmrNl3mCDwnOrW7Wbk4IExMZIXG0hZV1VhdKZHb7mEPApl5BdBXLoXlLoCR/xXRAsB+rVtby9XqpHUkIPVtsgu11UdYTwlC4R/CcSLA9BmuPQod7hFDy/sonc65tan3K9Alt89juPHgozxuwtl9xmcLnTAb6FiGgPGfnky+XQsoeLI75VEjjbgHbQ5ONVR6xMRblolReYi5Ur5ClTrdI5dF8UMzh20Jgs1g2LULPdfn8w8n9VkhTQogpo2ANTqiSYjPB4rTufsapDPOokN4Oyg9g95XKjVhsnyiTaRrp+0JC8DxpFjycclhC7E2xvOuZYqM4lCA+YFtm9YLMwhXzm6W/UtspPgvcceVA4rbQu0kvdEXvoxKRuS3Eogkh9RvlOI/YTs+6rLKyrrdP+yKSOGgRzAfm9lSZiHYJ+rk+L34zIWQyTGFWbTNLn+XT5g6h/3PlUEJWFIHidKeCDvYiqhfsRyWVlOW5RdmfRCwHHRerzXO5bZtahxNM5mL4il7BlF+92Aa+2ldFeuYRsdxMecGrFOcHi4mScjDlJaoi+ecma/8rJDFx0C50Xbk3OfGlmkPKne1BWNmfLxwbzCXDEjz8b3QiDgs8+51QdXYT9xj9Fj9Y5UPsVTM7MqIlmGHHUbQ9Jp8nZiZ3yYO2k2mYd3XC8YjiWIrGgpZXbMrBw4041NraEoRxvw8dT1UeYDSutgLbLBBL1oJxNQJPrhW2dcpxCfoVYp6kWZkvMxdvPAr3cTPc22bRIt1KIDLIfln6TbKLRLE9jgPGovJiRNM2K7pPRu7f/EitERbWHusXK8cK3JWQsjcbLLDvSmHHtm5wZac4xhE5kENr49xKhmZDE9o5H8KinGsiB/6CFztsG7HxJRf8H/tVWwDRW2UjPckoi/9ZLzY2+pBUnMShWGsje91DBJE4Lzsp1O/1o/WSFZ2XmGTeDMBxthnemuM8E2Z0DYttt0ee/veUGzxr1ycO2hd4KP/BJjcSgfdFVg5sO+AqKgd+BC7xVc5tNkAvTeNh7Ui5+fK3/HCnOuB66t7kxL1RSMeSiF4WJ4Gz7VpaFkQuDU5xi98sbqJyo1zJ9Tlkb8YVNw58qWDU/rPz6bykK7jnsjziR3ageVccGEwilr+mJB5iHJPMrbqMY6x2wLXBoBzI8B+3Y8cFVlnZA65N/eDI5Y0kePB5Y4S7LJ2SGwv3hiInhUL6ryaRHWPxrygzVfrzFPzlwSn35dJJtp8uMsrIieEyeaRLJpPnDTrSN9k58RSLOz/I8oG5Fa4UwxjhwI0wt7uKWyksP+JKHIvyMC8LFqekJItJv2aa114uHZNooBnnEbuiyIU1rFqtquJUKZciWFzTLC+kdIrHaQ7h4z4Er6nzI4e0ZPQgl211EvKy5JmcpTvGy8u8CClMDskpGVtMoYwMssZGlQeT+cdLYYppTI7MIFiJLKLs4ZRme3bL9A9Yo9kG9QyqqsJUtQHcFIOcfN4wWd2S64JYbzmWtpkNiaovP0XkmJK22YW4vgNu9hIzUxPrMNcv6AMxfqkH6WetFZXiOq2cI3w6Jf1OkkP8gBeGvbN7Qc4mWVvDflueUKU/G5GMcfLiNm1xwVYyb1P/hB2241HE1FWlEnNss8Q6k7+/0L4yspe70baHAyYyyvlp2qsKmLe0wX7Vhbb34oX0FrgaRU/aDmvZlwSxXZj6/BLb1eyUOJhh2cYhwNqt6uER2dmEHXEjOk73o/+YBx27O1Qbi/fqGUrsMhOsG/QwmgzQKU5qptSnxSa0sLKUesWF6LgRzg86kdjSyfaV89Ui5RdTMsX9cSVvmB/5diQ7lkFOo8R9XG5Tc+x5Ij8vZDfpOlZG+DHxWHx2F7eDM1H0jK2xTJSjUns8I3ezUpkuljVrB1nZn1LeKsCfb0fTizEY94TQH+2Fp6gcdKDtWWOVbZcGOp3YjkRZOyK7TMIjuI+Dc0/t86Sr5d4opGKjcjkIl/jW9v0Ae6j4WOPVh5ShHsaxMBwmHQw7J9+cc6MJcOe9aBWvf8KKhufa4ecyqKurQ/pyJ6xLDdj4hsoSUe2/zYnAzencs+DOhhFLTcg9mesmkLrGHl7iFleUBAkOXqZc1rO4GfdMNrTTwiqz+RFV1owE0flSBHjSDd9rxQ84sTJFDrTCpFuFzitKqCy+0bMutOpYuPvy6WOZ/kIrAndNsG2wwbZOg8guK6xn8u+v7OHybhNcAwbWkNhgXcHDbbGi/bzqTTbLwvq4E3YWVsMHfvj2eBHLGdjDKIq2NavYtUxxf9eF8Ah7H9JnEWgxYuN7nJJm9mAYCMH9ggkGkws9H3aj+yyPupUG8EfsMNp8iN9gMn4viozWCO2AizVmOxAelW5WyIE70oz6XTFomeJiM+cQbFyFHWfkOObGEgjtY7Jg5cF11Ifud8LgNUYYeB/sxo3wlXvj/iw2NR0XJnNvXuRS5J9YyTux0e5BQmOCNulB09p6tJ7XwKrn0bEnIPcoiJPybU3oSdVL+aUfaEO9rRtxqYFmDc0FPzo36bDK7IP/SCe8AxMwrGTVfacRq1R1QEa0nmZld08EKdF4JBeD9xU3+pSzBcY5+J6vR9sVLRpYmA3jQdjEPGD5KYbJX87nnxe+dzsR4JjiZayD9chkH0h5mALwofjrQH2l3tE8j3epDJpmDlMy+tgbg8HCyoPFCH4/K9Ms/YXcYQ+ogqxYml2vdLL01MGoTSPwyips3MXKSLlGPhmorvyUIX2WlT3W6Jp3tRaMMyqh3xpaYCMGpmhxadZ2VlYp9Svqpd/wSPGTJHfNC0+du/gFuWpySFzxsV+xHufTn2Uv+G5gfUOhjdM+qjaCUVhdDwt8TKlUjqdjTm0Wi2WZ9jV7M4oEa/UlqbCX+gSXkDa+uNJNA3t2sHas6SCrEbvNiO9tg/dq8ZOBH04gvYU915TjAuNxVnf9rFwm0b20Cf5bsnPuQifMpno0Hy/ueRQVAeNah/RMmqIHVIB7vxXuJV2sLXXANFsjLo0ZHdEUbh9zqF4wcxi6HmO/ZtjWFne4SKxsgf+kDq7nWfrYvu9gDq1vRAp5UQ05KT94Ka3ZO0k5b0b/D2RvROBh7YjOyJRcUdEUz49GEXqjFTrxeZHPW9FNeYZ42TOq81QC0X2rULde3dNbCR7hF9kzdlx+xjYggtYVTfAO1pICFdO2xzMwEkYn020wHobNyJR8JQrJD5uxir0kuC5VEadBpjvt16LrtBuOR2c0I5sRw0qr9Ju8U1wS02e6EX3WBfu8GQyWQRm6nxXTzyFV5r5BL9he75+c/DzRL3SUu0eZE8aqfslk2fx8FgiWw0OKm0je/9I5VRXc8/5XmkMqTlaW5q1A0M9qMr4y946FW3F+Rdl5b4oxQn6C+IBb0G8OFM8l4jyCOT8HKhUSWsR0qOIozu2ZmgeKHPTMvTDZPj/xv1g2t09MvV/2k8lcmo+pMNwr2EQ/i+bNxoQu5ibP25QR53Lq4RRCqkn+Exc7iuOSz48n1flxW+htZPLfr86hadKhzqf5kIvaPyV+k4YaGaHvZXaNep7XREIy5iiePyanQS03uZ7oi4w+JHkUzdMR/Wflp3QemTiBXIxvYQ6cUs6K8kCOv15lfJHPP2eYubB4Bg54hAA3w7wfdR2saBhTmcphinEW/VWld4p8ZWRZsbxRz2n7nLUZrG7qd/dPziGruvxUIh8nfcncx7mTOtchOBptgq3abXOX0K+qK+WRy+20cc3LpKj9SgieZ7uEWNEcwVrIzx+1Cx0sPz1s69hqqtLAS86P6ufbza3Nyj9bisNT/Kx5DmlK6HvVIljYfVKZY22fnfmjZ88ydS2SymsZvxMHnbJ8lDZzMt9uS+29ur3MI7cJVc5Tlp5XajnNI0o5UrcnImL9thXmjMpzSG0fiM/kyfmk8zGHVG5HStogJU5F1+bLu9QWTgiJICufeUOo6RCfsWL6VO2ENEe8VDeoag5pde1xeVib/yqr+6xuynmvCks0lGP1rrR9nIr83Jj5uhqQ0l3Sjn7Gytu2Er3kHnAf5pAaYH9eNbynqVOGBmJIln2DMEBbpORrYdvMHsmM+E5/4Q1i3tHa4bkcQs/hACIH1W+L1ZE975bm3ul3e+Y2v2KxBoazHWh/Nzw5TPxoK/xblNlbehvaj3nQ+9KkTPXGBvY/BE55Cy9isx3WwhuNBnVLxd/moiGmOmnOVarM0KgZzRtUA4Qs78SscTRa5d5mBXGxK248nzEcAvuDSG+2wax6k9KYGuBI+xDlijPQzMrGZAh1qGMep5Pym3MR5dJxKclirTAfclH7N8reotmPYXk+pVr2hs5+LqQLccte8sN1tXR424j69aysXkhM9v5JNMO+flJqmqViLYgime9ZHmR+fZiGY6utuLdliY7VCBWDAbhZOSueu6xBvdmB9IdRJIrE64DNzK7SmNGyuwMt62Yol48Yi+YITiE/TFa0lVbIcmEy9eWVXniOtcOWzxwWlpQ7N0p7ikQM0Kl7LJfY0LrLjPR7XgRK8rLq8jMFHsmT4q8NpnJLExWGgKdLa3n0z3oQutiP/mq3sHvKcPcUWHlMKLsVWaaXy851vlCO+Y/dSL3qmv2yLIX5ox1wK8N/nqAf7ay+Ncy0ZJSSH9lxaWC2embbZhWeLXNHbM+dZ6xw55fOWm1j7R4rW7fkJa5k0uCvK7tFsLL1mQ02Jh/+ShhRfRcshbgbYXnWAevqqT3dcpuQwUQ1xexGDL5nbSo5zRc8gm90ILYtgNgH9qJ2vhiNNIfUGW+S55Pu9sHK6rc7rpy+j8htoQbmrax8bqtiyajHWuA/3APf5snWTpojPsja7JkbjmJqao9LyCWRNDTBuiSH2OUAsMkOS35kaokFTc+aYVxROQdkkoh92ASbZabraoC1I9Js9DusfkkOOUQP+GHe2zJ1JGCeeSiMmrTL84/kJPiioeH5RfOoA22vthQpUlUhGgy85ENa3wZ/yfyK+DvNCNYS53VtCBxrAn+4GQ1GHeoWrULTrj72AM8XOC0s2zvQtDgC3xvtTHH1wX9OHF5hNanckKZBN02jMhNGGGqVRZo9OMUHWCqG8HE//PntUgbWAx6YlhbXUKO+zJBQua+XlEsHS/LklfMgF7V/q81oY8pTotBCZZESdaftpoLSxt+QjSWSF1XpZNuQ1gNPY2m6mJJVLkAlbulkTFrPtmHN9FU+PZyQrkvFw0Vh9o1Z4TlgQl2R6IzQ1/RmxZTpLeJvGENlXhazo+KQZxSBXXbodDroNrkQistzRicpH6b2SSc6NgGRIy607+yG73gfeyVl6blbJq/LYGAKrGhkwSVLQqu2/FSkHoYy8c2OyGn177RJabW9EULslvKC+KCiYS8vouIzmJHjORKEa7gNbmW90tlQdv4oK7MaJpfC43zQB9f54nxRMzRW+VxZ5tRmzQcc/Ht9wCvNqqkcsnKN/LzGaTGiZb/48OYQPhyBfjtTHFW3ZUc1sIovbWVhSkAV4kqLjdEoK5/sJc1bcfMhUu5lvCLiGret6NH6ETtRjfIhptOD1AvtCI+b0XWqFdpapsDOE2XbgOnQGGF/tRVmPgDXnna43vcjcFls3HM1zy+urT0uQWNBx+vshScbRfjdNOxb1J0RaaRGi1/CypJOsVeIFKLHy+X/5Oa7UO7FvwLLDHLdTmfZ6xGTys/d8K/xwDnjC+jcecis7Ms91GdLDulr6jmks0U0GOiEN61Hy+HS+RUsQ1MaaEqsPqeFVQjjtl4M3ZlAhk+gL+iE5tIO2F8Ji+qLNF/F+5wB5g8m2EOyBz2vt8H5nDzn44FAq5V79FZY0brdCWdha5N6V5xP3qNHzXzLZZkdbW/YwZ10IziYRPy4C/60B7GDjsLDUrtMnrPXYFenk22vij1J9ioa9NrRauXG17C+tUyYThS/KLMXmpp0ET3sW53SXiQ+9cmifdQG2wb20vZSk+xgZ3HYZCpRHsqFmQP3fhMM5h5MNLrQc7gLbdubMJvc0VSlEFQDq5fTNPb5tFrXiH2NZrS+5IT9cf3MvS8iZXtXp99mVHSXKPVqWgwwrBF/xRf3NML7YmidkwFCufmjjMXKg1Q6yCEaTKJhmh4a68oaFYZ7iWi4OsWgroTRJGLspbr1SfXIxwQm2MPCbGYvXIqLWIa0072wK73LrRusqjxgCn7SNtkTNoXyL0il6Nc0wHzXDIfSa11+E42alBuqgD/lhAteRA7n265cmVGzEh5xwH/WCM8L8nzS9u8r7vcR3dIaS/hIBO0WHVqvGNF5oAfu15wsj2bXWtfWHpcnNxCFj9Uxx3pVHMZiiOqrWNVDb0TDuhzMm0vzvnhr21RD+rTKqNxZHukce64e1qHz+/fiaTaVh0Ih5a+L7+iMTZaZJ29nM5PDruUotEVZRA/4VBagTLF8rwn1a5vQfbl6NVV8e2h7h4N+mxfuLSUtSS6B2FlVA5MfUitCbugKXPOiSZzwvpg1divNTEHoQuiMB4aTUSRY45A83obO8/Vw73XClH97vzs5JMYd6UQk36m3EGgaYN3OfodTU/NhLFnGunp+mH+5cAgPtCIW8cDOHqimzR70RTqKGhjjE3apwUh9Vlpean/ZES2S7ew3MTz9m6zGbIWoMk61pGYl+maZFRdqRLu5C72bWOoPBmq3nK3EDT/adkVQv88N56OTD49C7lzzsbybPnP4W2J/qgMNptmrV8WYYXtBNMoKScpHeTjEwixe+ip6KlSI1uF5A5rqNvkrSNPCHnxiO5L5fLoLWfuyVvwNI/SGC5FNczVAYPX1EvuZZnheNJjqXuyoEE4K/BX2sF4yX3k2D4xFEc4blc5AkaIzxiF+yQJn0fJO7CVhBcuUzycmHysq5N7l4jKbuxwCv7m57Mtq+s4QsI69KCnH07LOhtbPZ7NMVHmyP++Ga6Rd+lpUoYljzzbnDPVSRPNkF3yNfjS/z15iv6Y4zgHtsjLSyU3MQ+eRSBaRg074rnawZ8Xkl6QmCj2jaUR2+aRez2qYj/Y4eUPUb2yoV9Ux/nwIxuereZkU27EJ+M7PZ9e0EUZppCyKnpfcwJ62mRXjeeIBVEjZm8GAquiNx+H/gGWY3g7P/lbVHDc99I3Krgr+QoA9YsqQ72G4qSwTAZ79skY+n+PpCHr2RFjhiMD1jmJBPRPi28PublZ4HfDuKx3iyDIF1yVZ8RbQ6CCuqFA0p+oWayDFRl9F9INwcYVgDyPjOiNr2FmQ46LCYioaSufiEWWPnf+M1YCqWrR7hRb2V9ywDLJ8+Lm6NjKF/7BoAXlvIndP5HKpBz0X8g2NvCxNUfuyrhWubXr4TqqsxUVGwnBfyNYW3Grm1z4LwqeixX7dGpKGtguIPbf7LeBOhBRLfgVWTzyHWaktCrTGuXsS4lIufWhb6UXrK8Gylu28ZIFbiTJh5rJSmkx61Qy/wRgKuZMTv/+tjngCvHrKQDqMwAdpWPa7Kq+NOgvM32cvkU9y8Bxk6VTc1GRZW+IRH/ibzap2Z2Y0Ky3yChlVb2Us1KfAXopYe8eNTPu6Df1Kh/QbztnQVfqCXIDVxb2rsMgww4oEFdYfLTASRPvWkGQjUDb6WfZSmq5mHtw8wZQWcYixGKUn/DfyEUaGMDTTiNUjFtjZS5la+efP+tG3myloJWsaG1bbWFmenLOrRjtlOI+D70MdnJvLyyM1yuqvxVRWWZ2KGW3vNyO0ib1oz1FTE1fAsB8Qe4QnJpdEvByG92gEDcbJMpRK84jy5WoKi81rAXRyzXB8oDjMAY1Ox57u2aK5tDyLj9ItNYVJZbIacqw5Yg/ldQbpE6gyWXDMfxmm+Cpvh7nPp5amKWWspva4PFMU8LEIvFwrnFW+BIvtWPNpOzpLVomZPezF9lHxN4rkyk50PF5FIlgLGnQYsGhNOyLK6giz4atvMZT9KhHfIL6Lv/aeQN9/4TH6S9HtDri/vYBwYBgrNttg/DsfNv6VB9Hboyyr0xj+b1fwt1/9Dpr/f6enuH/2h38J2x+xFuJX13H6/TBTWKywrrmCjz79W4z+v8Pobv8x0n/qwt8cYY3Bt9Uz83Wof2IF0v/lHD75+U1k/3EY0U+DuGneiLUnw7jC/L/409O4+2+dsv+aNTD9u3EMD/jgvziKkf8Sxd3tHfjet5SH5BJWQP95ABdvGfGD/R1o/ebM0+OTH/9HNH/EKugGKxr+eRgDsTjibAv738RbnX+Nt0OjQGMLurY1KJPtDVjxzTF8ygqq7ql66EbP4a3/NIoVX4/iyn/NIvuru1huGEffzb9jum4WujWr8LV0FIf2hmB6z43n9IvZG3k9xn9xCIH/thwN5iUYOfsBLuqdcP7ORQS4mxj9F8/D+c0kfD8J4qc/4zCaTGFcyGHp13+Ni/5D+OhwHMOiQvzbLBavMGDYfwyBvk8R/8UdpihnMYbfx6JYAP4zotsAUtm7yH6FKcO/OAbvh5/g6OAoMv8MLMotheHXF3Hs6Dk5nDsZjP96HEu/1QDjqqfR+ueLcfqtt/GzfzZg+SIekcOHcOfP5R6y7FU/fL2n8elVJrP/kcXdzGIYvz6MYz/x4ZMPmV+/ZA2CGOe6NE5/WE06rHj6386nXKxY83ssr34/ir/Y6cXAzyI4feYT/PildnS+fQID/7QG1sY1LE+XwLS5GU/fPIR23yjLrzrk4kF0n1+Ojr3PYPlXWLrf8yJ47gq40SGkfrUIuX9twK8vHcOhj3/C5DuOid/K8rV+czlW/Gkz/uwfvPjRp+NYZfoGa9M+wts/TSL38wEkJfkuxZo/McG0vhXf/d3TeOvtnyH3jeVYNBKBz3cHzW4n1mjkMH2fnmPKCyeFmf6HRag3r6imbZTRroH9f/lLrPqFD//xpdMYX74cy5fr8DWm9Ec//CHe/syJT36ow9A/fhvOP13BbpghzG+sQP0/DeNQgMPyxxuwZOQcPriwHM7ti3ExeB0300vw/F/ZYfwXwOjP3ob/sgm63xnAZ0vX4BtjF/Cjlz6C5o0+fPLyWsm/qssPK4srpkv076zA03/xXdSd/Wt87+Rn+IaelVXd1zA+EsO5D7vx0T+14tDWCXxu/Cu0rlW3PQvBEmiyA/jh/8eIHzatqZiXi/7+Cn58ajl6f/o3sP2e4jiFuxi9zNrBCMurb34XP7AUD6nnBoM4dPIiwh+7EWRlVP/7y/G10etS2yZvYRx784f4wQ8/wpXv+vDpD0zl4zN4Gs6+enR6noZYSqblFnsIz7rNMqI+E4bv8DF8xMrEHaV9ksufAav+cBzce1GMr9Xh+k/TaHrJjhW/o4RbFh0a/uTbOP3mRxhnZWgJ9zdo/9+tCPxNMwwl9y353SwGfsjB+EM7q3uKY54/MOLbf/9jfDKyFtY/TCN84Kcw/siFp8vqo2lcfr8T+DMvvldlWVv8yNNo/p+v40d/9ia45d/Gt40GLJk2XWXIRvDD9TsQTkQR/OQEThS207j4d1Y43/pLrP1tHP69P0Lnh5cw9r9dwcA/jkP3raexpigdOqxtXIv0kRPsBc6FZ8Rn7jRIdfjgR/hJoQ4PI/d1sd1lJ8X24pef4tD/Vwcrez6Pnn8L/n9YAUP/FcR+yZ6Tv12O3x89jZ6PT+Ncggc3No5Fo3ewaKb6LrEERuNy8KFDiPyfLF/WsJezjz/CnT/7Eaz/3YfIzTTG/sSBbw/+Z/g++UgqYzmw9ow9x6aUsdG7MMzYHivBToPuj/4AX7vag9hXGmD63Tg+8NzBX+5vhbHavJTasY243rURbw4sx7f/7RoYltQyT3AqY4Pn8NF/a0XgU5aGquKRxfVP/QjHLkO3/oewf7OKhJdhkWhqr+wvLKNBNK9oRRht6Mv0SF9oEG0Tqp0ylmNvNRplEfQce1PRTFenxTequeXX3BAXgZas0jXSwu3iYsBiD5G0iDs7J+5rFos9cpPXTEG0eGbp0CzRFuao1iKv+4WcNhYvrWgHeR+YF7nk2AOsCW2fdyGyb3JYRyQ3GoF7SxOSO1PF61Lm83SxFtq56i4lfkkyLOvvDGVkPhB7N28mwIvdAnWsUX7MBP1s01dORiWZE39nEax73RAXEzPfx7IjLsKf5Hi590PHXhAeM9Y29/t+cMuPpjUc2pT2sSxjSUTTBtgeq3SBCtbmtp40IfD6vRmQ495rgBN+JHbfrwG/aVDKnrpdqIaitrksPPz2VeBezqDn2fIyn9kPxlgYO5ZHYP+sF45ap1ncTYM734coxyEmLvKuOIujVY79IbQ9rhzeB3IjcSQXm4vX554tSlvOGgBoNUpbNx/tq0K5Z9PcnqFza4+rKiczkB4Mo+9SAtwAywdVh6lWXPlD+oJhdYgf3uHummBZWWNcxC/f3XEiUHF0ZnoeaIWUIBYGDt41DcgcF+B+SnFSISlNiEEoLAxPzBdqhZSkW0oO0T1G+MzcvCzSn7vkgnsx2zbM/gFYkVwULqMP9QMhtMzjNIsHkdylThg/bgB3ukVl8FQb/PEmNI+6EGNtyj3IDYK4L4hfqoxu6Jm1Rf6DMYdUskrNzz3LIDvG3hRqmhdCEPOJGY59LQgeLTOHciSInhM2eDY9AL0+X0SkuX75toAoRgPbHj8Mh3uK56vNCh6BUzo03wtllMGf9ILb5/nCK6MimkYX/Mt60FM0Z74GxqPw7TfBk1/zlCAeRlg59l+3o3kOy0M9ED2k4nwSf4nlo3a9894tEUQQVZC9FUHoRBS8zgQjK4rZYQ4pnQ2t2x21r1VLTE82Dv/HMdVwI7UBlRCNUFov2RCYQ29a7loYsWUO2Mp9FGCO5Aa9aD5oYC9u934h7QeG8Ti6X4zCdqyrxo8Q8Ai/0o7kCyF0PUnqKPHwwl8IIru+BeY5TKl4cIbsCYIgiKrIXvPB/1krOjY9YAp7Lg7fvgzs++/NOrwPNFkOvuMptL423ReOikmfcSG0xoW2mb6iRhBfAkghJQiCIAiCIBaUh+xLTQRBEARBEMQXDVJICYIgCIIgiAWFFFKCIAiCIAhiQZmFQppE8IUm1BsWYdGibsQV11lzI4jW5+phWMT8e0ftWxbx4174zvPS4rXVkDzZiqa1BhavRei+qjhWpHb/7yXZS93Y8dIOND+3ERufYZujVToO3lAuYGQvudAsnsufP1nVB06JWZC75mfyby3Iu+n5HdjxfrykrLC68GIzmqRrmtD8YifCt5RTBEEQBEFUj2jUNBtun3AIgFuIKcdzIyF41kHAPpVvw72CnUWv5jD4gOBg97njynElZuv/PSa2T4wThI6LE4qLmozQ97JRcB4bYnv3mowQO9Yn3FaOvpykhMAWMT8cQuCO4jSFIaHnKQsrb+XyiyAIgiCIapj1kH3dvH5WzwDDGmU3z2on/Fw/YsNttX2xpdp4zdb/+4RuaekyIDlw73citjmB3u2mqpcVmT1JRF/kkFaOHnqkjy+ot2r6xfUwPir+xsBXEET2vA+xlwK0hiBBEARBzIEHeg6pfp0NltX3TvW61/7PHznE33Ui8oQH7sb7FN/BGELK7sNLFtzxTjTZNqJ5lwf+j/2qLYD4mHLZNOhX2Nj/NDKZMgrseBTu42a4t33pVlwkCIIgiHllXhTSXDaN5GAS6el6nXJpcJejiF6OIzk2c+9UTunJSt/ki77eIjGWRFzyiwM/3Sf0cuL9HJLp7JR5otP6L90XBzei3JfmED7uQ/Ca+soc0oNiHKKI31T7nyv0wvG30uyIHY8kq0pzebKIv9OK6Hofup4qr4xOpoXlgRgMiz8/yGTD3CqFmhvlpLiLMpTuUTMWRffLneAwgYzid7ZUzpXy824+/Tw4JheRXDrJ9tNT/ZgBMY7cSEnkmF/JKhRJjHPwPmeFb7wZ/kg/Qh+40bG7Q7U5Yania0t1Wvnr1Hw6Jf1Owl4SDnhh2Ov88i0AThAEQRDzzBwV0gT8ezoRHgEMKzXgTzpR/7wPXImGx5/vxEZ7D1ImG2zr9eB21WPju6UGImqYQnU5gM5NOhhMQUya7uTAHWlG/a4YtGbmlzmHYOMq7DjDK+cnSRztROdZ5q43QjMSgHNtM3wFhbKS//m4epDQmKBNetC0th6t5zWw6nl07AnI145E0GlrQk+qHrYNNugH2lBv65a/L82UweQFv+T3qj098O5yIzYQQPNyI9ovTFF9ZyCL6Bt2WCMNsD9eqWeUKYADIbhfMLG0uNDzYTe6WbrrVhrAH7HDaGP5oVwpcZdHeFcTiwvQsJ7JcC3Q91I9dhxPyvnBlP3odUDL3MWeQZ5LICFuo5NxnzY/s0lEPu6EXbcKDR/44dvjRSxnYEpbFG1rVlUpA6bsvdcO/6gGyX11aDqu5O84k7u5HvUtfkzNcTVZRPY0I/FsCD2vWqCfw2i6fkW99BseKR6zz13zwlPnRts6xYEgCIIgiNmjzCWtmVRQNGqyCT1JxUFiQujfrRewJVAwhpkYcAsWmAUPpziIDPcKNlhUborxiNqoiXH7qK3I6Ch1ukXQwymEPlMcGBMXOwTo24S+vNsd2ajJ9sGQ4iAjXqcXjVN4xYFR6n/+3rZzeZMh0YiIxWtT76Rxz0RCcD8JwXwgoTiI3BZ6GyFYDk66ycZJSrrv9As9B3qEflXYlcgbNbmv3Bb6XusQ3PtEOTO/9yeYdCsj50dxHGQ56wX3gHLMfIi9aRawPVRsFPV5v9Ch16vSnY/HVIOv6vIzJrhZXIryRSobzG1biOX2DHAewXlUlLgsV3W5kIzp1nkEtfSnwO43b+oRhubDzkgpE8XxTgieZ7uE2OfKIUEQBEEQc2KOPaRa6Io+pK+BtbEVONMB/2WxvyyL6DEX4rDDqu5JWl0PG3ONDEzfz1W3RN0ryCGwP4j0ZhvMqqFWjakBjrQPUa64v1Wr1Sl7Mpr1drQijI6jUbknj1HsP2OUZ1cAhuV5d5Y+A/u5kC4Y92Qv+eG6CtgtZsVFxIj69UD8QqKk505J9yM2tO1ug22l7FoN/pe7kd3pQdebHjBlHfE32uC9VpzGqZjRvEEVL00dS0EaQ3mLnFsBuN/h4Gi0FhtFLaln+ZaGb6+/uDd1CjXm52Z2XSGvNKhbyn4uJVE6+F0Kn8zAtsHI4htF+JIeXU9Npsm4vhkOi2naYXL+egw6lkbjfNgZLdPLYV3nC/HmP3Yj9aoLlqKyTxAEQRDEbJl3oybNUlERTCMyKA5u8+DOiq5J9B33w1/YhqA94IFdnp5XHWkeiUH2m4ohrPbrUgZW5pdp6QzKGlPOpJhd4IqG6ItYbUYbi1OiYFKdRUrUsbabYJIdwN+QTX2SF1VxYNuQ1gNPo6i9qmg0opYkqmn5sBctkgJrRMuBAFr0cbhe9crTAipihKHMvMjcXfk3m+QQkXdL0MurHAzGkByVXcpTY34adMWKrwgT7UxqtXGrGy2r2SvIeR8ieidsFpVmOcazl4uGqf6qyI7GkOFC8L3nhbfixpTvamYPaHQwiMr3YEaO90gQruE2uBvJqp4gCIIg5g2lp7Rm5CHiMuszxt3S0LFNPeQ641qf5Yfs5TCUeyf6hQ5x6HRLYPohX2WI1REsvUoZRm6cHH4v8l9h6LBdMG5qEwLckBA71ibYN3mEmGp8Wx7mn3mdU2nIe6a4lqEwZF/i/+2gOF0BgoXJqNxIdNn8KJFF5lyb5PdU2eTDnby/eMh+QkglU+x/tfmpyLokPytNAyiPEtbu/qL0Jg60CL3DykEFpHSW3Dd71GuRpoTQdvU0BIIgCIIg5oN57yHNfiYObOphWysOdBrR0CgOt6aQKe2NEq20FSvsqtA0wLqd/Q6npg75jiXBjc7Q75bNSPfp19dPM9zLITzQiljEA/tKA0ybPeiLdMCi6o4zPmGHlKLPpiQI6WtJ1JCimhB7Db3b9Ijv7YD36kx9jOXRmq1gCiqy4xOyQwEevDhWv8kOyyOySzFZRM9E2f95zM+ZyLI8vcTUQHM9Cn2RuShCfDOaVyvHFdBa7Gg7GUSkGmv8GdHDKBl4hRF6w4XIJhfsVVjnEwRBEARRPXNUSHkMFS3LwyNy0gf9Nh+cT8ou5q0utOh98J8vnl/In3Ejks2rGhOYKKPLTIyrHbWwv+KGZTCA0M/VYeYQP+xDclJtkeCTxZ8E5c/74dO3wLd9chn8Yv8VLvWg50Je5ZWXMCpS/9a1wsUUQ9/JCEutipEw3BeyxbG4K6Zsdkwow+yTGNGy1w074nC97J5h6L4Cjzjg2m9B9Gy0OO63ogictcC9t7WgrGuWiIpnPvYsn4fllFWXn/OAdupwP/ehD7qXHNMO10sss6Pj4ATaXmDlYooca0e/UlTjmUqas6Fry2wnYRAEQRAEUYmvvsVQ9mti/MZpxP6ndjRzHyGy2IT6RTcR2PsjnDN9goueZ1DoRPpXJjT/xdO45WvHoREd/vhfMgXyVDci/6YDbzUuZ8pQBN6fHEXgOIdRpv/czXyGum/pcP2IF0eDJ8CJjr/NYvEKK0yPPY3WP1+M02+9jZ/9swHLFzEF+PAh3PlzN5yPKsrQr67jdNyK9r/4W3z0/1oM07eAm6fexI/6vo1P+jx4RtIn2H3vTfV/ze8ZsOL3o/iLnV4M/CyC02c+wY9fakfn2ycw8E9rYG1cAx2WwLS5GU/fPIR23yh0a+qQiwfRfX45OvY+g+W/isN/5BA+ORZHMpbCOPN7eNwA6zeLjaxKyV5lCvOpID4V7/slMDw2jkWj15H9uhgv8QLmr+cjBK4OYzx9Bf4z1zH+66VY8yfLcfM4UxDPfIr4LwaQyt5F9itGGH5xDN4PP8HRwVFk/hlYlFuKerNRMgr67j8fQ+d7w6j7IznunW/GYDsTRMd3Jq10DCtWYHzwx4j+ai10f3cO6f/wA9gfWVxlfgbx05+x/Eyy9As5LP36r3HRfwgfHY4zWajlrQRWlhUwfmsUP/6Ex9o/WYH0GS9++gc/gutPp5djHt3aZjT/ixP43p/7kV37HdQbdNDM8utii/7+Cn58ajl6f/o3sE0bZ4IgCIIgZsMicdxe2Z8941kwPQiaJdrpH/rVXlcF4mLwYs+lRsv8kp2mIi7SPs6uWqyFdkaL6By495rQ9nkXIvtsRb1wudEI3FuakNyZQmirqoesJv8fNMTeX0mC0Gor92xKcq6UvnnMz4qIn/xk0Zx1GFke0QsRcByHyKC6V9eMjhNVGtaJa7OmDbA9NmPfLEEQBEEQs2B+FNIvBBy8axqQOS7A/ZTipCL+ziJYEYPw5oP45XuCIAiCIIiHl3k3anp4McOxrwXBo0HwpfMOR4LoOWGDZ9PkepgEQRAEQRDE/EA9pCVkb0UQOhEFrzPBqGXHwxxSOhtatzuKFuQnCIIgCIIg5gdSSAmCIAiCIIgFhYbsCYIgCIIgiAWFFFKCIAiCIAhiQSGFlCAIgiAIglhQSCElCIIgCIIgFpT5V0hz4mLrBEEQBEEQBFEdc7eyv5sFd94H3wE/orDB4dAjNxBFhANsL3Si41UHTPSBm6ncCGLH4SgyaV76EhE0Whj1qs9i3s0gNSp/jcq4rRe92/Jfma+GJIJM9u5LESTTbsSELtzL5fzT5zvReoRlOEOrN0KnwdR05TLg01npGsf+frQ9Lu0SBEEQBEEAokI6a/g+oe1JCFjtEDzRlOKokEkInmf1TNk1Cs7TtxXHuRIT3Os8QkI5WghSQYfQdi6jHM0d0T8xGxwnysho4rYQetks4M2Y4lAbiYPsXriZ1O4tt4/aBP22gHD7N4oD4/YJJV1BVbnIDAk9W0rcCIIgCIL40jP7IfvxOLq3NsF31Yy2Ax50bCj5KLjWjI5jfrTpefift6L9gtw7NidGeCSU3YWCT4aVvXlmcZ2yo0JjhGOfC86bPNKKUy0Y9LX0qs6edDqDzl0tMKq+NV9X7rvzWhOc3+8A7k4oDgRBEARBEHOYQ8p92AbXVbazrhmtmyooPsvsaH1FVFTT8L3ogzyoO3u4sz24R+pgdYxFEPhY2b/H5KTxbsYyM2zgkZKPHkBymPjcBvOjyuEMaNY0sBeL2ajXBEEQBEF8UZmlQhpH5KCiXppNMGnk3XIYV1vlnbQLgcuKkjWWRPRyVNk4pBXnSu65LI/4kR1o3hUHBpOI5a+5me91zSJZuC+K5BhzGufBKcdxdl0+CJkc0tcmr5/0p4L7XeZ+MwzX8074mC6VHMhfo4q7QvZmEvy4cjBbclG4XgorvaIG2PY4IKn8uSyyWXHjwY8qAbO4yW5pJG+kS9JZgVxakU2cyUp1x7jif5qlQZIh8/Mmj1zpt/1LqGdyaZimDBSht8G1xSTv32X5dlWWpZhHRajTNTKZP7JbFjwrB7Kryu2WmH52PJIsTldF2LVF+SUec0iWZipBEARBEPeU2Smk4tB5vpNLM70mojc2KHtA7AYv7zCFirschMu2ERttTgRuys7l3bPgzoYRS01Aso1aN4HUNQ6cuMXzSkkGPFMkg2+I922EbYMVrXuj4OvqUJdLwv+sDnVrmuHPh8MUD/46h8j7rdL1Gw/HCspNWfeRKALneWQ1cqI1YyyeUhyiSIxKThLZ8+0wmeqxamkT/LcUx1mQjTMlTdlnoUH/uElKe44p7JEDrTDpVqHziqKkMZlFz7rQqjOgfl9USUdl+POd2GjvQcpkg229Htyuemx8N85SzrwajSK0j/lvqIf3w250nkogum8V6tb7kJRvL8Nk/KpCo4f5US2y13xofs4D/hGrlF9G3sNk7kJUVIRFxHSd7IRdTNdJJXSmkCcv+NC2QYdV5rAcJ8nNj85NzG1PD7y73IgNBNC83DjDNJEcuHc7EQIP/1Iruk8F0bknAF7LVP8LrVj1YpidIQiCIAjivqDMJa2NuFsyWJG21/qFCcW5LKprzQfV5kgxwS25mwUPpzhJVHC/ExAcovs0Rk2xfUo4b8aK48R5BLN4r75N6FPZI+UNivByn6A2U6rknve/klHT0GGLfB8sgntgWqkUyIdl3tYleA54BM9up2BZzfzYEhDKmv4ocig2DEoJgS1T75H9njRqmhhwC5ZSuQ73CjYW34JbXs7bQyztE0IiyOJ0IjF9HpehYKxVzoCJF8MozXfROMou4El1/iplYV+xWZacD8XGWrKb4uedfqHnQI/Qz8vnyvJZSHDuFsuuEgaTXcGsTJKBXnDHlWOCIAiCIO4ps+shXaaHTdkV1x2ddoBzIQxYdBoU9duus6F1HftN++A7e+/6vUyvRhA75kFvJICOx6sdw5YxbmpHx+4OdBzoRex8z6R8540sosdciMMOqyiLPKvrWVhxRAaK5eLYYIaWSdG8lcVpm7lYnnMih+jRDoTRXBwPhtFshf5qJ/znZ+rnrYSStkdsaNvdBttK2bUcuZs8jM9ZoVEM5Tq+r0yLKJBGgqe5rgRBEARxP5idQvqIEWZlF2Ol8zOLSd/JD/aaYVt3f6y+p2KAYY28F0ny0yvQc0ILy/YOODcZ56bAPWqF4xHVIPgNH9pPzVWR5sGdFX+T6Dvuh7+wDUF7wAN7ySIJRr1B2ZPJXvXD+563eDsen3GKwFSS4C5UUPT0Rogzjn2DlScITEujESXJqIjmqQ50PaVB9nqMKcctsK6dzLFcMiEZz2nKrRRAEARBEMS8MzuFVGOF/XXl0X8mgaGKGl4OQ5xiF7/OBvva+VwhXzRAys8hrR7zct389faNMeUqb1w0r5jRdtBeUK7SyRi0K+aqzGuhXyv+NqBpuxNO1dYm9sw+W+y/bmmxlDSPNMD8uLl4WztHxXu+0dahzOJZ05Ic8DFF1gazSpNN3hBn8NphUzsSBEEQBHHPmKWVvQa2l7xokZ7XXvjOVujxGg3D9564o0fLnjbYlkmu05PNTL/EUUH/yyJ6wIdYNRppbgiJM+JOdb20qfT0vZEFq/NbYTjPqHrzRsJot9SjvsU/jRFQrWQRu5BD/SPK4TJ9ydCyyAQmZpSDEQ2NYr92CpnSa0Wr+1Ir9xI0jzDZbbAVb4/rZ6GQmmF1iAUng4lSXX5kCGFWVrqeyve/66FvVHYLiMtMKbtzhkPsPAtlQ4NKphyiJzjoX25D82rFiSAIgiCIe8osFVLGyhb4L8hDveEWB7qvlmgXWQ7eV8S5gkY4Dkfg21qqRpVTNgD+QgAhZb+IJVpIg8jiMj2SJTbPfg0wlNGIuEuJIoWQP+NjajNgedWNtsbJXlrtsjLK6XgckdPlVWLNEllRit2SFdY0PwTTI5ND29ypNviuJpE85WKymZ+e0+wlDzzHjdDnO+s0OujYfnZcNTf3VhThS8q+ionxYiXTvNXFXiJ88J8vVrj5M25EssWCnJhhqaeZmO5+y3Yfi0cAkStqGeUQPeeHfpsXzg35uNRJacXnE5PvIeMxRE4q+6WwMGuasTySRGwQRWWIP8XkrelAYJ+9+pUDCIIgCIKYE199i6Hs18xivRWtO76H7/z+Tfhdzej+38bw2T8kEQ10o/1HfmTN7fibjz/CW98tN7SrQ/0TK5D+L+fwyc9vIvuPw4h+GsRN80asPRnGFaRx8aencfffOmH7o8VMEVsD078bx/AAU6gujmLkv0Rxd3sHvvetye+/j/7sbfgvM8WrcS2ynwRxcWQYF3078PrZFXD+zU9waM8zWKFSwRf/0Xfw9Fev48p7J/C3/3QXo4MRBM/exXf+7zmc7mMq7bUgTidW4JmtDVjOrjes/Q6Wj/wMF98PIs7iG/lFA3600wbD78j+GZbrcP1/P4fcxr+Be6e14F6WWxF4/Z/g9KfnwI2MI/lPOSxlsovH4soWxrHOv8ZfvnsOo41OvLW9gUlMxIAV3xzDp4eT0D1VD93oObz1n0ax4utRXPmvWWR/dRfLzSweR7w4GjwBbpSpaL/N4rO6ejTUm9H8F0/jlq8dh0Z0+ON/mUP8VDci/6YDbzUuB3/eC+/Hp3EuwYMbG8ei0TtY9K0GrCij9JdFStM5Ke7+g8eQ/CWQ+e8ppP+vEVyPJSf9+lcmFo96DHg7ce5XBixfxCNy4Ic49hUXQoefh7GQR0tgNC4Fty+C8e804I/vcvC9xeFray8i+rc8MizPlv7+Ivzs/3kInxyLIxlLYZyldXjcAOs3J8tFJbJXPsJfnVqOpj9I4bMVa7Do8pvoPFsPX+AtPF1Nbz5BEARBEPPCItHUXtmfM7nspIGTRivaaFeP+GUijVa+Izcu9kZKu+URe9/KGJzE31kE616mkB5MIPGaWVpcPbe4xOK+EjkW98UszqK/4soBmhnuqxCH+4a4cPy4KG0NtExusuzl/aoQF8FnadAsUdK8UCjxYJmPylEXF7+fTGsh7jWWsWJyiO6pw8bBXty+6IShVvkRBEEQBDFvzH7IvgyigqBVtlof63llVGRaZVSkWgWqWmVUhClEBcVsJmVUZCGVOBGWNlnWckxl2dcgdaaISvm00OlQ4jF91IvTWoi7fDRLkuAuTc4frVl+BEEQBEHMG/OqkC4kYg9hRplAmBvPKD1qBFGBWwlEBoHWx5XPmBIEQRAEsWDM65D9wsEj8p7yKckCJjh228tYpBNfdrI/98MfVxl8rbSjI/99fYIgCIIg7jtfEIWUIAiCIAiCeFj5wgzZEwRBEARBEA8npJASBEEQBEEQCwoppARBEARBEMSCQgopQRAEQRAEsaCQQkoQBEEQBEEsKKSQEgRBEARBEAsKKaQEQRAEQRDEgkIKKUEQBEEQBLGgkEJKEARBEARBLCikkD5IXO1Gw/ucckAQBEEQBPHlgBTSBwh+OKHsEQRBEARBfHm4LwppLssj+l4zVj0fRFpxI0rhEP4grOwTBEEQBEF8eVgkMJT9e0L2ZhSJlA7pSw1ovRVA6nQL9Mq52ZFD+loMQ5/LR4a1NpiWpMHFh5DR1cO6Tg+NfErmbhbJawnwPI+s1gjTWivMj+SvKPZLt4adW5ZDcjCB1IToYIT1MSM0i+XzpeRGOcSGefAjgNFkQsPjJmhLri1cc40HVptRb2qA+VGtKo45ZEc4BPa1ov04u+b7PejfapLOSGlbJu0SBEEQBEF8YbnnPaTaR22wbTDDWKc4zJkc+OscIu+3YqNtI3wXIvDuCoC/FUa72QDjzgiyypXZSy5sXGFC57ksDBuaYTNmEdpSh1WFa4r9atjQgKadfnCZOtTVpRHdZUXdio1wXc77qDCehP/FVajb4kMSZjRvNqNuwA0Tu9Y3qFzDyF5oR/2KBrT/XIvm7zvRZMqib7sOdWt2IDyav4hD6EwMqbta6dCcS4G7xklb7FZJuARBEARBEF9ExB7S+0FsHwRsCQgp5TjPBB8T+uO3hQnluFpSQYfYsytA3yIEeOZPtEvQs2P9tpAcBucRLOL5Tb3CkHSHAnM3M/eW05MxKfjF4ndbcZP4LCQ4RXdYhJ7ripuQEfpe1jM3s9BxMaO4iWSE0HYxPm4hobgkDpolf/Wv9rGzMhMXO+Sw8vFUyMfBfDB/N0EQBEEQxJeDBTZqyiF62IGNFhcis51cuqkZ9pWAZoMbfCYD/pgDetHfYCfi7LTZUg+jfKXMo2bY2E/wQqzQk1pgmRY6ZVdimQ2Ol8WdONpPRJmvjFsheD8UI2tEg0nu1ZTRsrCYz+kAokovqfnVCBLRGGL77OysjGapEsJ1Hil5jyAIgiAI4kvNAiukGtgP8Mh8HoBjlhNLzWuNk8qeVqvM98wiPSI5IXXZg/aXdmBHftvpB99oY0ppDhn5kmlgCqpB2b2hKJBjaUQlhyQCe1X+sq37kga2RhNyGUXVXayHaQ1TZ092YsdzzWh+pRPeEzH5HEEQBEEQBCGx8Ms+LdZAu0TZn0c0itWQ4VkXeo/2qrYAQhf70X+spbjndCb0Orn3lCm8su5sQ9tBtb9sO92H/oshdG0QVWQekZ3iHFQHAuN2uE+HEPrAg44XrNLdM5JLg7tJc0gJgiAIgvjis/AK6T1BD/MGu7THxZNllpriET0VnzpkPwUeQ1fkPbvFJPfEPmaBU9JIfUxhFH+LyQ0GEbnFdq4F4TwSB9a1w/WaDfoi0//K5O4qO2NRuA+XmVZAEARBEATxBWPBFdL0ZR+8R6JM9ZtfjFvd6HmWaY5nehBQWb6Lw/nJD13wjmmKl4cSiUeRGFP2Gbmf++G7xNTbZz1wK0sxQWND+7E2WNhuz4lwsbKbjsC1NybORJB6fqXR/sEMxBWkZHKIX47KPazShNRJNEvkuQHJJC8roaPsd4VhahwJgiAIgiC+YNyHdUgjiFyKIRrshv+qHW0H7LBamuF4SlwvNAfuXRsaDjegL9kDu9pGqCJpRHa1wntpCNEbTB1cbYHNaETL4QCcjyqX5LmbRvRDN7yHI8isd6B5WRYRppyat7XBtc1cmHuaPtUMQ0sY2NIB9xIeqUes0I5FEWTKqP0lJ9q+70CR/RIjeyMM334X/NeNsG82AzfjSC2zw7mnQzKyEjXO5CkXOvcHEMlZ0fGSFZrPUjA814aGgXa07oqA15vQcqAPgW3i5AEekT3taH8vAeP3m2HMauA44FH8IgiCIAiC+OJyzxXSB4cccjlNYW6pmoJC+nIfMh+IFvHs2rvs2goL4k9hPAcsma4vM4fseA1zZcVh+2rDJgiCIAiCeMj5gs4hLUd5ZbQ8NSijItMqoyI1Gm6RMkoQBEEQxJeIL5FCWp5cNovMuHIwzvazJZM7CYIgCIIgiHvKl2jIvhxZxI/7EVMZMolrj1q/74SlqvmsBEEQBEEQxFz5kiukBEEQBEEQxELzpR+yJwiCIAiCIBYWUkgJgiAIgiCIBYUUUoIgCIIgCGJBIYWUIAiCIAiCWFBIISUIgiBmRy6LbJZttFoeQRBzhBTSKkiebEXTWgMWLVqE7quK45eCHJJnffAej8vf1yeIKWQRfacZG9csYvWjGcFRxXkByF7qRutz9TCwerronbjiOj/kbobhe8+PeNEScQ8vc09PDtyRZtS/FELyigd2YyvCc877JIIvNKHeIJalbsxvDs4esVzteGkHmp/biI3PsM3RKh0HbygXMLKXXGgWz+XPn0wqZ+bIWBz+93yI3LoHGv+NoJSOVocc76bnd7DjzqJ05a75C+eldL0fZzlPfBF5INo4cdknogr4gOBg4nLHleMHhNvneoVYRjmYbyb6hQ6WZsAhBO4obgRRhlTQ8YCUk5jgFsvsvphyPB9MCP27xXoAwRFMKW4PM/OQHs4jmJX8zkQ6BFujQ+i9rpybI7F9YtzcLCcfLOR4Qei4OKG4qMkIfS8bBeexIbY3f9w+ZpfCnN/yrCZfFmxC77DiVMRtIbDNJnQE5zddxIPGg9HGUQ9ptTyQn/NMI34yAj7/pan5RmODaziGfs6HlkcUN4L40qGB7Y3biEUT8G3RK24PM3NPTzoZA4cGGFm7oN3kQf/FEJyPKSe/4OiWln4qOgfu/U7ENifQu92E+fyminGbH4loDLdftSgu800S3CX2o7ehYbXsUiDLwfdKEPqD/fBsnd90EQ8aD0Ybd+8V0pEIuvd0ovs9LzpbNqLpFT84Gv+dH8ZiiJ5R9u8R2tUW2NZ9ER7CBDEHtEZYNpihfyBfTGfBFy09C0YO8XediDzhgbvxHqhsi/Uwb7DAeK+0wVsJRAbZ7zYLTLKLRPaaD+0HeNgPd8G2THEkvtg8AG3CvVVIc1G49mbRcsCDrt0d8AR70Tq2Aw2bvOzt+iHnbk6ezK9subuKu0guDe5yFFG2caPFM27Eb+eL16dvJpEWT+Wy4Ac58KIf8iVFZG/GJX+iV5PIjvGI31S0+RyP4K42+NnuhOJnNm9ZMK4cp5Pgxfkg42kkb/KFOE7GgS/MDc27ZUc4JJU5JJNuvBzXInJID8ppFOM0eXpSLvytNDtixyNJ5meJBwUZxaeem4582vJb/ta8cYW0qfy7m0Xy6mQ8i8jfw+SUlPJJjCsHboS51RClSUSZsLws6bEW8zqrLh9VkBvl5Hy/zE2VfSGtPPh8+SqUR5bXN0S5qxhLIl6QNcsXsSwpp2TYvUwG8UFWHsQb77K8OeuH7xRXdF2hLLLrisp7KTOUaZFKfuXLHD+oxFEsu2w/PV2GsPDSN1m5nVpIa6Mgp5I8nFbePDhVucoxOXI308hWGrWYKYx5K4uMOaanUlrEPMpIbhPISPeo8nm6+qaGhceXbT9KmDH/K7VDcjzFuNVUlmoii/g7rYiu96HrqXIaY16mM7SFldKgrtOsHBQxY52ujmyStTPst+WJesj9vjkkj3fCfceOnv0OGB+CF5acKB8xXyvVuS8Q9yytc2gTCnGah3p1bxXSwTi6T3ag+2xacTDCttkBXPUgck1xelgZCaDVpIPOZEXb/lCh15c/24mmV/qAtTbY1jcAF5yof9GPpJSBLIMHQnC/YILB5ELPh91MNjzqVhrAH7HDaPOpFHWmcL7QisBdE2wbmF/rNIjsssJ6JimWCnBxHpqV9ew61hglE0hwbLslN2bZ0ShC+1phMtTDy8LoPJVAdN8q1LGGU2y2+MsBdG7SsTgE2bEIi9eNCHw7bdAZGxC+NenmYXHVGTsRVU90Homg09aEnlS9FDf9QBvqbd2Ii2lkBTt5wS/5v2pPD7y73IgNBNC83Ij2C7KQ+POd2GjvQcokykgPblc9Nr5b3WR5MW2BXXbodDqYXvAgplSe3M2QFKbuCSfcF5KyHNhbfvNzHvCPWFk8rTDyHmy0uQppyY0lCnJyHfWh+50weI0RBt4Hu3EjfGLPQbWMx+F9xc/uT6J7aRP8kgxZGBc6YTbVo/k4LzvMiNjj0gTXgAFWJlvrCh5uixXt5yfvz7GHUeQAi7duFTqvKAWPNRrRsy606gyo3xctPJz4U61oPQOYxDLE3n41F9pgtYSVfGcoeenhNDBpk/DY61l57YPGwsrkrk4EbrJrxjn4nq9H2xUtGpg/DeNB2Ew7EB6RvVAzdGa6Ms2Y1i9V2TH74D/SCe/ABAwrgehOI1btjJQ8dHlWJzZi454IUuzt3pCLsTxwg9W+GlEMdHbFoDUzOZlzCDauwo4zsszLy5u5fdwJO3Nr+IAp73u80hbLGVgrF0XbmlWF8i4zUxjzWBbnKT3l08LaD9bWJO+Ix2lpP8EpLzIjYex4MYDcarFes7bvfCsMz3nBlTw8c4OsXpqbEczUw7reClM2AOdzSvtRIIXYTPk/XTtUc1mqlSyib9hhjTTA/niF7ssq2sJp0yDW6ZNinrA6rTKSmrFOV00OiSs+9iuWET2rm0n4X2T1/4oVrs1G+ZIHmOw1P3bYm+HlxHzVILG/Gd3XqnmKPHzc67TOqk04n0T0XZfUdhv0WQRajNj4HsdK1RxQ5pLeGz4fEkKHe4XYZ8oxQzZ+MAseTj6e4GNCf/y2UG6a+APFnRKjJj4gOLd4hIRqpvfElS7BDKcQUqVXniysF/Qv9xUmhcsygGA5mFBcGMO9AmuOBPeAcjzgFvSbA8Jt5VBCNCRQTW6f1pBEiS+2h1i4E0Ii6BE8JxIFOZc1HIi7pXipDbcmLnYUhzGRENxPQjAfUMWdxbK3sTg9sv9KPt/pF3oO9Aj9PLudpcuiyn8JKe2WYrfpmOgXuvQQ9K/3F5Wb2JsqfyUjtJJwGLeP2gU8yfJNOS7ISe2mpEe/X53G6UkcdMpGAVJa1DK8LQS2MHmp83o6UiGhRYzPtpCQn1ou53Ob0Ke2KlDiXTwBPSWFhS0B5V6WV3qWd0zukyQEz7p8vivXq8pm5lwbC8uuMnBICaFteqUc5ZEnwNdcpqv0Sy47eqHtnOoqqRy2CKFCckUjEubXpt7iOvJ5n9Amyq8GI5DU6RZBX1JvpfD0TOZ5N8XAr1jeigGVcl3hWiVNRXlYTRjzVBbnKz0yU9MiIud3cfuR2M/yoyi/mX+snhaV/TusfDM3+7HJXBs6bJHKTkdUrs1V5X9N7dBMZak6ZL9Y3b5yW+h7rUNw71PKPMub6Z5fldrC6tIgH0+W55nqdC2I9zG/9exePsTS4xG6NolxVdf/2TEx0CM4nrUJtsYqt2drM4rLRLvYc6QknuLzt9p29iGi6rT+ZkLIfK7sz4Za24SS5+vtE2WeUzVyn63s5QegfnP+ITLBKrbYiNXeONx3VArpRLJXcG5nyuJvlHMSrOEQK3NBGZhEfECoM09uzEuUJcX/ltPK3ZIVq16w7w8JCV5UKRkTKSGRnMztahRSx4mix3UBuZGcWSGV3SbDkBUWCF1X5OM8kn+Nk8qB7H9XSSMpKhHl3OVCbztaPq7lSBwwM39UD11RSVWVq/7XxXJVppEWFX0WVuEBpcipuHIrilrJQ7gyTOl8XX55kKxi9V1Cv+oJJVZU9QNxejJC7JhH6L2iul7KA/WDnpHP3xkUUvGBo3/WLYS420JGLkRCaiBvMas0NmrlrbQMSOVwajmSy15HIZ3Vl+mZ/ZLLTknDViqDCn6VTdO0KA/l0pc/Je6TFtWyv2Uba0WZVkdXSgN70Mulqsow5qUszl968hSnRUbOs+L6NTHcJ/QcDglDhYfi1LgnDor1tkSh+mxI6I/GhNvKfdXkf23t0AxlqUpkvyAYH3Mq8ZdfNsFept0DeblORb6vtM2rNg2KDFUK6fR1ugaUl2foTdLqAKJXE0z5EdvHYiX5AeMz9tJZ2iHxWUzwbMnnyyQT7AXAs72nqOw+VFSZ1kySvVCI+sfu4k6a2qixTSip/9PqI1VyX63s+VMd6LjjRviEE/KAgAb2AzwynwfgeEjsZvhzLjQ/64JfHFJRz6/JJsFdUPZL0K8Qh9Y5xJL5qQsiRhjKTBYvzKdb14bAsSbwh5vRYNShbtEqNO3qAx6pbXa7UW9Q9uYH/kZI+k1e9MN/fHIb0nrgaSwJq9GI4mzlwZ0Vf5PoU93rPz4E7QEP7DWUAfPmNtjhR0QZXsjFo8hua1bKlZgXalmr0BthZT++weIBrrJyylU7+GBEy/4W9p9D+HAE+u02WFWGuNlRDazmavNNC8v2DjQtjsD3Rjva3/XBfy7G3Fl6apyHyqSEtlO9aOJ70GxeBV3dIqyyd6JvsVGxmDXB/DIT+nVe9F0imxKHdZ0wKRa36eGENOSeiodV+eVH35gVngMm1BWJaPoyXZtfBuimiGxSBrKVN9CwZo5Di2keCXE4PBVDWBUn/6UMrKxMmpZWUQYMOkme5aIr3V1jGHMqi/OYniLyaZkGzWo72raZwZ9xofMVF7zHA4gOsxOFuKeRjIu5ZoJxpewisUyclmSBcYlyLDF9/tfUDs3gV620fNiLFin+rN4fCKBFH4frVW/JlIMSprSFtaYhz0x1unry80cdB/qk1QHEJkuzoRmd69jT6iBrWxdyPcppyMZZ28iyr4E9TwKizD72IzigQeuJfL5IF8H/HkvD+SA6j08zR/kBp6q0MrSPmqFn5XlyLvA8U65NuBcoiuk9Z4K9ldq29arenh8ylB4Gx7HbwgQfkIadioYnM8pQYZke0nyvU/7No+ybRN7//NvJbyaECbEHVuyG5xNCX9AtOFazNyX1MGCJP5mk6i1Z8a+ot1NFuTecKb1jIpLbZBi3j9qmXlMGyf8pslCGn8r1XNZMRghtZ35JQ7Zs/2V1r6TSS1QuHEUuhR6HUrlLlPY0VonS41C8TiGLCyv3Rb1V0/E5u/5ZPctnVV0ply9VxntC8WMic1tIRAKCe4tRgL5FCOXL3vUewb7aLrQFE8JQvFdo22QXPKreWXl4szScqVRTpqv1q5qyKYdXrhwqb/TV9pAqw1Qz5/U0vQdlwipKQ7VhzEdZvAfpqdwbUux2+1ybYIFF6LqYLz+lcVeOVb3h5agm/2tqh2bwq1pkv6bedzsoTpFgzwMmt3LJku4rkx/VpUGRmSpPZqzTVZEfdp26/mh+7VP1tIqaEZ9bmUxNm/S8qwI5H1hbU9IbWhYpr0vy/yGi6rRKU70qrSVbLfPRJpQ8A2rkvvSQ5q52ozVoRu8JJ0zsLTh7NYhIGYOIh4EGkxGalS3wn+gAv6sN3VeVdy9tA6xb2G92AhOySwF+OMH+22F/ooYuwGteNImGMIs10K40w761C6EzHhhORpGo8CaePFP9xHa9nqlOJeQ+zyh7lTE+YWfv6EDqs1KTgBzS12ay9DSioVG6G5kpt6cLlnzVoYV9Wxf0F3wInwohZGyGrfBqaIZV6nLPYKL01XhkCGHo0fWUGI/5Re5xcLAyMvmOmrscAr8533M7M8njbeg8Xw/3XrmuSNydLFHckU5E2BszlunL+MnKXpEI4/A6/OzdGtBojTBvakHX6RA8+iCi12XBcOdjaL3cB88mIwyPNsMT6UOHymJYY7bCyX75dEp2UJG9WWYFgGmYT7/0rBza2W9iWDbUmTUaVm+3s9/hFCuVJYwlp6ySMSvuRxh57mdYarIReF/yIb7bDVdh+SNWbvO9kOkIOo+kYNkk5hoHvvSrTjXW/7m1Q/OLcasb3m16xPd2wJt/HlTB7NIwc52uDlYWxPVH19mnrD9qfNYp1dPI4bA0CjErsrxsaFvDxleZaZolotRKetkVcvO2gsKDQbVpzV2PIaisJZu9EYb33W607wlL5eRh4p4rpKIy2hw2wbPXCp2yhEDkWAhZZbg7fdkH75HoQyc4TaMbgd08XK/lh2r0cOxxw3IpjKhiYS3DI3oqDMs+F1pLFx6egegHJQ2C1gDjOqY4KIqKZokyrCM1+jz468xNcphkosKwVJ22VGHLIXYpoOxPMkVJXdcKF2t8feKC/IqTxEgY7gvZ4vBZ2KXKuXmrCy16H/wqq3ER/owbkWxtgw3y8BKHzpYwbJuLFUzLdh8LJ4DIFXUDlUP0nB/6bV44N9QWVjVop4wLcvB9qINzc/WDHblxUS6moqFvLh5R9tj5z1h6xKhrdNCxLMyOqyR8K4qw+JBRc4kp7EUW2loYjGYYDfn0R9HzQaSgvEhL5ahFtsyOtv0WcCdCxUOS43F4DrPXn1rEOJ9+rWblcJ+FvYyUtB23hiBOcKge9mLzCqu3gwGEfl5cVuKHxVUplEjlJlhtmS1VhjEv3I/0lCGXQ4a9KJkNusnUjLEXNGmKDkNcVoa1B8YtLrifjMJ3onhVDf5MB0KpGuRQSzs0z0xtU41o2etmL0hxuF52lx+6L9MWVpeG0pdMxox1ugry6482mllrUwKrpy272e+gB4FL6lyqAWkahrgKQPWbqcr1Ts0bWmFhJZkv6dQSV7hxXZj6sluJ3M9dWLXIgI1HKqjdt4JoNiyaZkUGVqf2rsIiQ+VVMGYMg+V80GHAojXtZadIVJvW5DX27N5mhuZUJ3wpG5zrMgidTdT0kj/vbcIs+OpbDGV//rnlx3f/7IeIXDyNQ+/9GD/+sbgdQjjRis6DT2MFy9Dh/9yJZk8Wz+ywY829bEXmAH/eC+/Hp3EuweNv/3Eci3JLUW9MI/Lxp7gYPYe+q6PI/nY5vtPUgtb/kMOxN7wY1qxC3a/jCO56E7ENIQR3P4ElrFjHjzNl7MyniP9iACnWQme/whTMXxyD98NPcHRwFJl/huz/ch6f/N3fIcdloVuzCl9LR3Fobwim99x4Tlm5VvOHBiz/xSH4+RWo/1UE0TXfw/fW6oriy42x+I7ewaJvNWCFSr5L/nAVlt54mymB30HDN++CO/I2uK/W4+LlAfC/GsddzdexKBaA75OPWFzvsJxahNy/rkfDI8tg2tyMp28eQrtvlMWtDrl4EN3nl6Nj7zNY/qs4/EcO4ZNjcSRjKYz/NovhcQOs39TJAf8rE5r/4mnc8rXj0IgOf/wvWaU+1Y3Iv+nAW43L5WuqxgDD7w7g0O+04qMfrGXyVSGFU48BbyfO/YrJaRF7ETrwQxz7iguhw8/DyF7Fslf98PWexqdXhzHwP7K4m1kM49eHcewnPnzyIYfRX7LaLOSwtER2FfkDI7799z/GJyNrYf3DNMIHfgrjj1x4uobJN4YV9RhneRr4b8vRYF6CkbMf4KLeCefvXESAu4nRf/E8nE1G9rAyYMU3x/ApU+R0T9VDN3oOb/2nUaz4ehRX/it7+P/qLpabl4P/hMPf/ROH7O+vwarFaUSPvIXQN38M93cN0hRowwodon/xQ3j/9jIiodP45MBfo73jbZz423Gs+ZNnsEa7GIb1rfju757GW2//DLlvLMeikQh8vjtodjtZna2hTJuNME7rF8uj97wInrsCbnQIqV+JZc6AX186hkMf/4T5P46J38r+W7+5HCv+tBl/9g9e/OjTcawyfYPptR/h7Z8m2UNgAMk7GYz/eilLwxooJa8ii7/xNFr/fDFOv/U2fvbPSlk5fAh3/twN56MauZwcPoaPWDm5k0/L0uvw/SSIn/6MlZMkK+esnFyMcVj69V/jov8QPjocZ+WeqSCs/C9eYYXpsSrCmKeyOF/pKZ8WA4b9Xvj+09FCHqX/YRHq1z+N+t/ncbqHPbzXWvHHrO376H+9g2fesGL4SATX/3EMlhd+gIZvrMDTf/5nGP/EiR/fMrBwc+AueHHiV38N91/excWq83/F9O3QV2opS9OXEElep4L4VGzTfgkMS23qdWS/bsWa3xMvYG2e5yMEmDzH01dYXbgul71vjSE8XVvIWqxp03A7Au9PjiJwnOUJE79UJv6kDtc/mr5OT0duMIhDJy8i/LEbQSYD/PZrQGYYuXxaIPrnZu2+mNZxxONJlpavYcX/ZGIylbxYePQNrH29jO4z4/j2v1uO7I2LOHHYD77BBVdTydzb0St42w843xL1jWLu/j17MTp+AVxqDb7711bWopbwy+s4fTyM9Lda8YNNa8q85NzF6GXW9iV0sP/H7+E7ZQZA5TA46Da14nv/U7l5wVlc/9SPcOwydOt/CPs3S0KpKq2srL/TjXOX0jC0etHVuAyaNc+gc6cNK2YqEApzbxOOIdAnPgPuIDuexRh7SZupXpVjkThur+wT84jY0yS+nGiWaKGpslAUcVdcRlnD7hUXp5V8glZb/kkkh1X5/HQUxZPtZcfZkUaLqrwSF84Vr1/Mri/SBqtEXOT+7hxkJCLG4S5L+3TxVcKpOl1zZC75UaCMbETbEE2pl/k8UMIrDTvHnjkaljflymNOnBbyagZdF9ywqZXmHHvZ2udA0612pE63qIwxZi6L1TOPfpWUQymtsyyTBTlpxfpwb7gfYeS5n2HJlMlXsS1bzNoy+WiS+aj/InNthx4EakjDdHX6S4XY6y4KYDqZXe3GIgsQE7pQ/uOraQRf8MN0okuaPrFgiNMa7zgRqPTZzunSmg6j1eCDlQvBGnfCHm8Fd8IxxYjuYYAUUoL4ksK9twoNnwcg7CvTVM/YkBMEQTzgzNSOiV+T3Ae49tvu0wtbefiP2xHd0ANnjdP6RHKXOlH3gg6JFFOqC+ltwdALYTSc6FhYRbtGHpROeIIg7jPmLW60nOpBsNTA8C6P4Ad+2A7IRhcEQRAPFdKnqcPwnxBnlIfQ834Y0Wsln1Rm8CeD0D2/sMooxqPwX7ejeRbKqEjyRhT67RZ5LvAjJqbUpjB0xg9+q/Oha7+ph5QgvsyIRoZn/YgO62Bao5WOuZQOthYnHOtqmPxKEATxMDHOIRzXwtE4x7WM5wh/IYjs+haYZzvdRJwSw1TqyWkb7DjHjhdUy54dpJASBEEQBEEQCwoN2RMEQRAEQRALCimkBEEQBEEQxIJCCilBEARBEASxoJBCSlTPWLKspeJ9R1yQ82HggYhnDjlxDdZqkSbIV+ZhET1BEATxcPHFUUjFhYWzWXlTf7otl63tgfwlRVxkWZafWuMQF2tWdpFFeE89Nj7RCv9NxWkB4M93ovNUauGV4hnh4X/OCt8N5XAhGOfgfcmNWJXfiJbIxuDe5UdSXYcKZBHb38nyn7RSgiAIYn55+K3ss0kE2UPSfUGL1jdaYdFrkL0RRiBphnufDdwuK/hXUuh6Urn+vpFF9B0nuk+I37Z3IHAnhJZHlFMPCkx24SNueCJA005Zdrl0HOFLWrQdbEXuiB2e1WGEtoofTY+gXdeE0LbQgn0FIne1G01hC/oOyOvG5a750X40isxImklb/BqNEQaLEz2vWVTryrHy8aILgVHxqyYaaB8xsXLigWOmNd/Gouh+I4ihMR5pUTlboodxWZ18TiGT5uWvZzzrQf+rU1d84483oSnrxtBrs1wN7kYQOw6z9CnhSOkrWolpopB286sBeJ5V5wqP4AudmNgbqn2x5UEvNh40oPdEC6YuiMKUXJsHhmMBtKxUnAiCIAhirogK6cPKRLJXaNHrBdv+mJBR3Ap81i90bdAL7BEtuOOK2wKQCjqYwu8QAncUhweEzMUuwaa3CG3Boamy4wNCy2pRdjahd1h2mrjYwdJhFLquTMgO95vPY0LXk21C32fKcYGUENiCGWQ8JPQ8ZWHloPa43z5qE1/YhI6LZe79zW0hsE0vmA8mFIcS7gQEB7qEmHI4OyaE/t1i+ibzoohMTHA/CaHtXHEu3j7hECyV4lUFiQMWoeV0SjkqgfMIlm0hJnmCIAiCmB8e3iH70TCcG3Yg2uhD4HULpizhvcwG1/52GJRDYhL+VCtMz0RhOxNBz1bTVNmtbEH7C0Bab0O91LuWQ+ySF/oNHWh+amFW2+U+7kDE4YR9meJQQA/jo+JvDHxacphC9rwPsZcC6Hqy1rhnkeSi7LcF1rVl7l1shG2TFUZ9hVL2iB2t27vR93PleFYkwV1iPywvGsr1dGotsNkBw3JVLo5F4N2jQ+e22X+nw7zZiezOHkTLjc6vc8A51oaeyzR0TxAEQcwPD6lCmkP0cBuCaTM6d1UePtY82YK2RuWAkBCHvVtbgjDu96Hjqcpf4jGutgLbLPKnx3IxRE/q0fxa6wJ9iiyOyIEcWhvLh65fYWP/08hkyihI41G4j5vh3jaLr3HkEoh+yH4bbTCrC1mJZU+DsVIJ1ML2rBPd56Kzn/N6K4HIIPtleSF9Gk6hOAoOGFXTQdKX/PBtdsA2RXmvgdVNaF3fjeCFchNQjWjaZkX3yYg0XYAgCIIg5srDqZBmowi/J3aH2WFdJzuVx4iGDUWaRMHwib8lWouz45EkkmMl6oL0HdwoomzjRkvP5Y1/ePDiOdGYaoQDN1KF8RS7lx/kwLP7Kyko2ZtxKdzoIF/kX97oiB9MykrAeBpJtp8uMkKagRxTzja7ENd3wP2qecbv9zrM9fI1g3H4lziZQlhZgb2nXI2iJ105r+u0ch7z6ZT0O0kO8QNeGPY6y8yFrIKbHMT+Uf2GBtX9HLwvBMArR9r1rmnno2o3taDjvTCis9Tcskk5Di1PKHkhko2gc++kkmva4lIpn2lEz4bhsJTp+RbL+80k+ILBknjMIZkuV4b0sDBF3H8pVlbp1D9hh+14tDaDKYIgCIKowMOpkLKHqE/83Vw/o3GN+XWVQRNTCJMX/OjcpMOqPT3w7nIjNhBA83Ij2pWeIMlwZm8MBosNNosR/H4rrDsjBQUkN5ZE5ONO2HWrsGO/C+1vhMFrjNCmA3CaNqLzbP7KYobOdKObnatbaQB/xA6jzcdUGxXjLE3P16PtipYp0TY0jAdhM+1AeEQ8qYq32Qf/kU54ByZgWAlEdxqxisWvGr0gfdaHbqbHm3e1wjbDd3P1W0OyMRMj94gdgfOdsNQ64j1P8MMJpLfUV1Qq9Svqpd/wSPGYfe6aF546N9qmfWmpDD8QkfKo9fHJvkn+pAchy6SCqnnEDNN0PZEaK+yvhxC+PBvNLYfEFbGks7JY6KLNIn7EDaxvKCio2kfN0BfyhmdlDWhYUyqtHLh3OxESrf+XWtF9KojOPUyx1rLrLrRi1YusHCtX5jGaLMCHTGFVjotYXQ8Lq4XcAq64QBAEQXyBUOaSPlTIhkIQsCUwK8OK2D7RSMQseDh2cKdf6DnQI/Tz4pmUENomnmsRQnmPJcOUUqORmMBUAgGv9glqUxfR8EcPfZEBTD6uRQYmw72CjV3nHlCOpXD1AraHVAZGsjGL/uW+gpscb31RXGRjI1V8K5JPGwv3Hhp5pc51CI5Gm2CrdtvcJfRPMVQqRkr3vmlMg5Q8QpGhTULwPNslxD5XDmsmI/S9LMrLIjjf9AieAx6h62W7wNS38gZO0zAR7RL0syqrLA3rWBz0dqGDhS/GoWOrqcjYbAqSLMoYeH0WEpy7+1mpUsoui89t5ZR8T5lyIZXTSsZit4XeRgiO4GxqIEEQBEEU83Ba2V/pkpS8SgrpRCYjZEo3lWIiK3blrZ8z8V7Bc0xttS8/wPX71RbLykN9ipKkKBCbegsPe1khVZTfPIoCVbBi5jyCmR07ThRUBAn53g6hX9F/5Hi3CX1q3TjuZm5q5bYSSpwrKa8TZWSWqU3xujcoVvTTKaQT/UKHmLZ1HpYDMrePOmpWHIvI+9k4mZdyXKpR/kthstczxU566akBSSFkcZAUyTyiX+5COqcglYepSuTEFY/gFldI4OWyVyQbpTxOUS4l90rKr5wvtqPFZZYgCIIgZsPDOWS/sh7sAQqcGZoyzCgOafJcAonLAWmIW6fTwb43hNhoyZBpo7HscL/2SSc6NgGRIy607+yG73gfYsw9fbeauZoGGNawnwsckkXBGWEoM6ybnyOaHk5IQ8OpeBj+4/7C1jdmheeACXVFQRugmzI5MA1Uvfh/PQxlEp4dYTLjovDvtEkys73BZHar8lzXBwqNDgZxWH4wI8d3JAjXcBvcjXOYY1B2/uiEZOxTGD0fi8D1YdHEiwpYYN/Fw3+p/HSOSpSdP8ryWcPyqDCJYNAH1/mZpwNonupA11MaZK/HEC5ZNSCXTDA3ds1i+biYIaSn8X5obDZTEQiCIAiimIdTIZWW0xF3IoiJFshFaGHaYINtcxucdtmlqcUJ+6MlWpy2DsXLnIvkwL3fBIO5BxONLvQc7kLb9iZYlbPVo4GmBl1Iq5WXDTKsb4Vzu3Nye7UDHbudsMyLLRGL0zRzKbWPMpltcMC6RjQMMqP1JSazx/WTilC1FIy+qt+mV3o10M5oLa68CCAJfjSN8L4YWvfIi+fPlnLzR8UXi5b9k4vF82cD0FmqW3fA3NiKzNFI+fmYZSk3f5Sx2IKO1/ML/+cQDSbRoC4grOBNF6PkAPOzZNWA5A1R7bUXh1NAXNZK2S2DdSUtrEYQBEHMnYd02SctHG/0skcoB09wDkvqlHLDj7ZdEdTvc8P56KQ6M6H84poPnecrLHYpwYO/wn62NKC+Bm1IY7bCyX6nWolDsoIuawRdM2bYXrCw31AZJT4Ph1iYpU/fPMPqBZXJpZNIiD3UVW/K144qooVhBdOIPp+YJp/1MK4Vf8MIveFCZJOrzHqltTDD+qMio2G4LtjgqFZO6xxo0/kRrfpTojOsP8oQjba6FzuK06o3wsTiP1FWWCx/z5f2+nKInuCgf7kNzaXhpHnEmLKvLWsAl5LKumHJXNR+giAIgpB5SBVSxmones61wfheK5wnyw2F8hiKK7vluKtSNPOIyzKxH5NeJx+LDMYQUXaRE7+hrnoAX2cKqLIrkj4bQE/aAveeGj+tucyOtv0WcCdCiKu/IT4eh+dwUuwknBfM3/fC/SRT4g8Gy0x1YGrYhQA8orK62Vy05mUtaFZaYBN7qKve1Bbi5TGstrF84JkKVBn9SmkSB8I5G7q2VJJ+DvG9q7DIsBG+iko5o9L6o3mycXS/0Ia6bc0qxW4mjLBtNcB3qZohfkaF9UcLjATRvjUE+/MlPcFMIa3XR5Hky2ikI0npZcSguoE/5YFH04HAPvuUZaKyqRTS60o/V6qQTSGVNsO4Yl667wmCIIgvOV99i6HsP3TovmlH6/+yCrc++o/4qzPjWL5sOZbrvobxkSg+2vk2Ut//BD/8vSGMrXXiaXHhcKZI+I8cwifH4kjGUhj/bRbD4wZYv6kooN9Ygfp/GsahAIfljzdgycg5fHBhOZzbF+Ni8Dpuppfg+b+yw/gvRnHlbT+i39Jh8cBnWLrmGxi78CP89Yca/OjCJ2j7tvjEzyJ+3Af/mU8R/8UAUtm7yH6FPdx/cQzeDz/B0cFRZP4ZWJRbinqzEcb1rfju757GW2//DLlvLMeikQh8vjtodjuxRsMj8p4XwXNXwI0OIfWrRcj9awN+fekYDn38E+b/OCZ+K/tfSEs5fmcFnv6L76Lu7F/jeyc/wzf0BkVeMZz7sBsf/VMrDm2dwOfGv0Lr2hnWhbqPLPndLAZ+yMH4QzuTheJYwqK/v4Ifn1qO3p/+DWy/pzhO4S5GL7M8iXBIffO7+IGlZLh5NArfR2Gc+8SHH7P8wb9ZjiWZYXCxOOLSFkHwkAvtL7yNsPYt+H9iq+lLYLqlOUT+Qwyr3rJhheJWSm4wiEMnLyL8sRtBlq/631+Or41eV8IXtzCOvflD/OCHH+HKd3349AemkvcVHe7+0o+P/q8/m5K+7JWP8FdMRk1/kMJnK9Zg0eU30Xm2Hr7AW3i6TI8yd9qJPlMnPH9aJraDp+Hsq0en5+mKaSEIgiCIalkkWjYp+w81uSyPJMcjw/brDPUwr9ZXMNKoAnGx+/EcsFg7OVwpfhqnMDE0ju5FVrj2xSC8aUZWGnPWQKutoC3VBAt7Xv0rj1pe0DFF9jHj7OV1z+Hht68C93IGPc9W6JEbSyKaNsD2WBU9dqNBtJ40IfD6/f7uVBbhF3VIvCjA/ZTidA/IXXbBuEuHCNehmk+aQ3RPHTYO9uL2RScM0tzd6coYB6/ZCRxPoKPMtATuvQY44Udi9/2WIUEQBPFF5OEdsi9BozXCrAwDWx6dgzIqslh8UKuUUZGKVkrKtfOmPM63f+VRy8u27kFWRkWMaH2tA6GTEXE9gfIsM1WnjDJyySEYn5ztpIS5MA+fEq0CzQYn3IYAIlfVochzUvPzRzUzlLHc5RA8azrRWm6ObC6K0EEjOreSMkoQBEHMD18YhfR+I80//Y20S9wHNI0u+Jf1oOfnc1XleARO6dC84d4q/JXQbnCgbQ6fEq0OI5z7W9F3UPX1JWVOavGqAZVgMnqPg3t/S9m50PxJL7h9HrSovp9PEARBEHPhCzNkf7/IXvXDf0WtTWhh/f58Lc1ETMt4HN0vRmE71gXLLKe45q6FEVvmgG2l4nDfkYfOg5YMejff20LDn9qBbnTBsyIKf1xVZlfa0bGlkmKaA/deMzyP9CCwdarJVm7Qi+aDBvScmFz+iiAIgiDmCimkxMNFloPveAqtr021Cn9YEJdr6hywwfOyGfe6n5Y/60J8jRstjykOM5C76oP7Mzvcz5ZRN3Nx+PZlYN9vJ2WUIAiCmFdIISUIgiAIgiAWFJpDShAEQRAEQSwopJASBEEQBEEQCwoppARBEARBEMSCQnNIH2bG4vAfT8Cw2Qn76oVZxmi2ZC91o+1IANHzSaSlDwyI39m/D9wIYsfhPmRG0pDszpfoYVzWhI6jLTBNd44dJk/ugPssj7T4eVfx3GYXerctxHqmDytJBF90wX8ljOgtBwJ3Qvdt6SixvHWe4ZFJ85C+OyHlbR1sO3sLBl/ZSy4434tP5v285q/45TY/EssccD5rnB9jtrEout8Igs+m2MYSpaTJuMWDrkbF5G80gs5dPnDieY0WxtWt6DroqMkobcHqKkMM2/muH+HLPBzBFEJba/ooM0EQDxOiQko8nNw+ZhdfJgTsiykueTJC7FifcFs5enCJCe6y8b/3JA6YJdk5wxnFZZLYPr10ruPihOKi4vM+oW1dlxD7XDkmaiYVdDD5OoTAHcXhPhLbx8pbpbxl9abvZaPgPDbE9uaZ4V7BLpZ1uFmpn19uH7VNk6YJIfamTXAc6BdSv1GcZsXC1VXhTkBwsLCZQqo4EATxRYSG7B9ijNv8SERjuP1qaY9FEtEXucpfNSJgbmyVPqvpjyemfDXJssEp/QYux6Z+USmdQuqF5lmvg0o8GOiWlvZR5sC934nY5gR6t5vmf0mx1U74uX7Ehtswv/2LWSS5KPttgXVtSZru8gjvcWGopQ+h3TboH+ivsREE8WXn3iukIxF43/EifCGK8Hs7sPFFL+JjyjlibizWw7zBAmPp03MwhpCyS1RgnU3+LOZ7EcRKtM70naT8ezw65Rx/JQrrBvpk5heLHOLvOhF5wgN3fqj7HqBnZc6yep79zyUQ/ZD9NtpgVo9mj4Th2hWB8Q0PnI8+XNN5CIL4cnKPFVIO3s0u8I854Nhkg2O3G87xTlhf8E9+0vChIof0YBTRy1HEb2ZVvWc5ZLNZaeNvpdkROx5JIjkmXjF5Tt7Y2XH1MfPnLrvsrvo6lRaUS4Nj4UUvxxX/FArXp5EcUX2FR5xX9nInk/wEMnn/xDmPair5mY9XOglefGkYZ37f5OX4qRlLIi7dz4Ev9Xsmclmkb3JIplXhlqNSGOz+fByTo4p8RzhwTAZqsc2MGbYWUbH0InJFfWMa0QsmuN9kT/e0H9G4+hzP4tMAW+n33WeSh5TmuBRHybc0h/BxH4LXVPlWgRzzOzkyGQfxmLvJylhpnpRStnxMljF+MCnPlRRdS93EfGf76aJymM83dbmvnlyWBzeozN+sSIX6VUgL84O5i+RY/otymFK2ayaL+DutiK73oeup8spiXj5pVhfE0MWw1XkiIx5Xah+m+lGgUBej4Fh5Tt/gMFPVKILlidg/qt/QUJgXKs67bD9vROfhNpjnov/OUFfLpSnvJtbJpNLxUJ38mHtV7cps6ztBEA8691ghNcBo0SGVfxAzNOLLOqcYjTxMjETQaWtCT6oetg026AfaUG/rRlxsOFnDnbzgR+cmHVbt6YF3lxuxgQCalxvR/tO/Z+c8aDXpoDO1wnOBKXujUQR22aHT6dD6RgicKIx0DJ4XTMzNjs6PY9JwO3++ExvtPUiZbLCt14PbVY+N78ZlWbKHc/RkJ+w6A+pPyj16omIUvQ5o14oHafBcAglxG52U9nR+Zlm8QvtaYTLUw/thNzpPJRDdtwp17GEth5ADd6QZ9bti0JrZ/eYcgo2rsONMNa8XPCK7NmLjnghSWiMMuRi8r7jRp5ydZPowcmOJQhxdR33oficMXsP8432wGzfCNyhdVhXm9c3St9q9l1RD80wGfWua0LHByc6l4Vefu8Uelmtt0lC/zMzykOXtQUJjgjbpQdPaerSe18Cq59GxJ6DItTy5aywPzjM/jtbB+k4QwT2dCIzqmOLRx8rTDoRHlAvLUa58SOXUh7YNrJyaw0rYqrJr9sF/pBPegQkYVgLRnUas2hlBkik4LjFNegOyp1phtHnBFYQyPblBH5rXNsHLAcaVdeDPdqLj4zLlZbr6lU0i8rGYllVo+MAP3x4vYjnWtjBVrG3NKrRfmG1rkkX0DTuskQbYH6+kuTFF/XIIblY3DSYvfO+yPOCicBtZnhxR5KrEvWL8JT8CkowNpmAhz3NXu9G0NwHDelZ22D3GYS8ca92I1jCCxA9E2Msn0Pq4aHzF0rN3I0x7NHC+ap7DtINq6mq5NDFl8UYEvp026IwNCN/KXzeD/JTwmvZx0LD6ZXtCi+S+pqntSjIwp/pOEMQDjjKX9P7web/QodcLLcFJc5sJPib0x28L5abjPzBMJAT3kxDMBxKKg8htobcRguXgpJtsMGEWPBw7uNMv9BzoEfp5+ZxkRKPvEvrzCc30CW2lhghXugT7UVk2EwNuwZL3K89wr2CDReUmx6HU0ECOx1Tjiar8VAwIsD0kZFiuJIIewXMiIeVP6nSLoIdTCH0mXyoycbGDpatN6FO5TUU0FtEL2NRbbGglGgiVGEpUFUY+jk96hEnpy7LQ71fn0UzEBLdelFVHIV9SwRbBHWc7E/1Cl3hOPynH28daimQ3Y1yVeLady5vIiHJgfpbKoSwZIbRdjpecnw4hoJQlFrIQ2MLSOqOBSXlDlHLlQ3bTq+KqpIXdX1Tu+dI0TQPnYeVNP8XYZugD0QhHZdRUVf1S0lJU1iaE/t3MbVuISaQ65HRCcF+5LfS91iG494kGViwcVm6KY1mMbIilGMGx+AYOeIQAx+5QxX2m9kE2PsrLPSWEtkHouiIdKIjloxZjL6U8oUUIJBNCz26P4BbrGZN5V3S61ExH9XVVpGxbE3dLspLqkUJF+YltzH4Ly1dV25gPKx+HeavvBEE8yNwXo6bcqDhE6cKO57qBoxwCW/ODSzlEDzuw0eJC5AG2wMle8sN1FbBb1HMHjahfD8QvJEqmH9hhFYd0H7GhbXcbbCtlV8mIRj0EPJaS7vOejSLfvxO/nIRjgyibLKLHXIjn/cqzuh425hoZyIdYh7qqu0Gq9VPGsUHsYdHAvLUDHdvEb66zfNsfRHqzDeZlykUMjakBjrQP0em6zAaZ/D5Mw7HVVrzczBIdDMquTG1hmJ9X91bKskgneal3uTossL0i9pEGlHzJInaFyeNJtquxwrZdHLbvQZTlvdjjHB9QD9dXEddRHmHmZliezyQtdGKCL6RnjmMuCX5NM6waHrzYBcbKkkMpS3nS12tJazU0w75+skBpluqk3+b1qnKvGMakxqfJb4ksIkc7WclyorlRHBaZRKctLrQ11a/NrPwW5K1B3VL2cymJlOxQNf6Xu5Hd6UHXmx4w5R7xN9rgvTZTmhywiWPgGjNadnegZZ2mKO4zxb9uiTrdGmiWAN272+Fn9V5aSoyVD+tOF2yq8jQt+fmjTMqBMxm0HuhA1y43q+FpdJ+MFNqVmqi6rs6GqfJDNgr/G3Hg+02w5YvJEhs64v3oP9BcFIe513eCIB5k7otCqnnEDMd2N3qDHcBeK3YcTyrDoBrYD/DIfB6AQz0h/wGDvyGbCCUv+uE/PrkNaT3wNJY0041GaRh4CpIRDXtQXJCHgPnLEVj3d0H/YVgeostF0TfcjKbV4sU8uLPibxJ9qvD8x4egPeCBfVayqs1Po74kXWkeCXF4LBVjLxeq+y9lYGX3m5ZWfpinkzFpWLFhTdEjbio1hjEljiK5mZSKYiyN7ZND82NRRLUW5aGngbVRHrbvucQemOJQvsE6+UCsJq6rzWhjck3w+UdmFilRO9luktY1nRaNBR2vW6DJJhFj+dbyRD2LkUJuCIkz7Fea/zKfGJiyqOzOmSQ4UVnaUl+s2JShpvpl0E0dimbirS3XmTw/7EWLpOAb0XIggBZ9HK5XvcoQeyVY3S6pJ+q4VxX/AlrY9/XDrYtgh60ehqWLYFjbCt8dLfTVZmt+/uibAfS9aZPlsroZzu3s97gH/lkMZ1ddV2fFVPmJafCxH8ca9QkNjE/aYHusOKfno74TBPEAo/SU3jfkYSuL0HNdcXgIyK/zpx6CKoc0fLUlUHH4UPanTejLJATPll7htjIsLA5jTUS7hLbCmpjKUPyMaxbKQ7fTD6NNCKlkiv2v0k9leGxKWllc2evEtOmrRH64bqr8SoaUqw1DiWPxuoSKLGqOnzJsr+8SAifaioc68/HRu9k5ZSg/T5VxHTpsF4yb2oQANyTEjrUJ9k0eIVbFaHeBK11Mdjahd1g5FuE8AlOMBfuxmQb+ax2yn3notbzsy6GEXUY+peuQVle/qk/LdMjXTw3rdlCcfgHBwvwvN9gtx3lqOOq4Tx//qX5MfC6HNJFJCUPxkNDzfRuLg0VwD5SLwVTyYZdOiRDbEjEt+tf7p52GUI6q66pCteWmkvzy19qUqUplmdf6ThDEg8o97SHNXfNio2jQoBoKk4et4ohef3gGWoxP2KWesdRnpYNgOaSvTVorz4RxQwvs8CG8L4DEJhuMGhuad5nhPxVC4EIatsJwqRENjVKIyEwJMl2wNK6OLKJnxGkBc/RT0wCr2PMynJo6PCpafksW7+XRM/nZ2W9iuHhawBTmEMbsMcMiDc370bFPC5tF1T2lscK+m/2me9g5ZSg/T1Vx5RAeaEUs4oF9pQGmzR70RTpgmdLFVxluIMIEaEOD1HMuw10KgNO3oe3ZmXqx9NA3KrsFcpj4XNm9pzC5vs7kemaoeMi9DPNVv+aCcasb3m16xPd2wHu1+nKmjntt8U8j/KILURaURquH6UkH2o6G4NseR198JomJ5NcfbYPtieIuVc2GZnSuYyG8G0SkxiX2qq6rCnpWNkvJfZ5R9qpgnQXspRxRFl6p1LM3a1xxgCCIh5p7q5B+xmNItIZdNtlgToyLzTNr9J5grRAjfdkH75HojA+tBWVdK1zsYeU7GSmO50gY7gvZyaFUkbssjcruFFbb4NgE+N9PMuVTViakuaVndmDHuKNo7ph5qwsteh/854slw59xI5LNhziBiTJPO80S8RGZjwXLg2H5+ur8lJmYsqyQFvZX3LAMBhD6ufopkUP8sGiFX3x/EauZ/PZZED5Vks+3hhBTdmXmEMasmRyaxxYbrEVBiOc62C8794KtZEHzKuN6qQc9F/Iqq7x8UfXPWB7JKxx76qsiNRKE56AGHUE37DPONayDTqxmn09MhjkeQ+Sksn9P0cD2kpeVNz9Cl4rlM8QV53pN9WuemFq+jWjZK86/jMP1srvC0H2Zmq2K+0zxl9s+NV4Ei1YI0MLwCNDAXl5mpLD+qBmmKS84ZjheERVFP/xni+v6jFRdV2XqmDINZDBRyOIcYuyFqTxl5Mdeyp0HW6B/j72oq1eNGI/Dsz+BiXuR+QRBPJB89S2Gsj/vaNZY0fB/XkT0l8uxxrgUv74ZwI9+eB3P/Kf/FT+yiAYTOQz/5040e7J4Zocdax7YxmcJTJub8fTNQ2j3jUK3pg65eBDd55ejY+8zWP6rOPxHDuGTY3EkYymM/zaL4XEDrN+UjUIm0eEbX7kO71f+Eh/9YC3zlaGvw/hPP8LanX4890eqT6n8KxOa/+Jp3PK149CIDn/8L5mic6obkX/Tgbcal7MHRATenxxF4DiHUdbO380shvFP1rAQAMOKFRgf/DGiv1oL3d+dQ/o//AD2R5jfM/jJn/fC+/FpnEvw4MbGsWj0DhZ9qwErlHxZ/I2n0frni3H6rbfxs382YPkiHpHDh3Dnz90zLL69GCv+tBl/9g9e/OjTcawyfYM9bz7C2z9NIvfzASTvZDD+66VYw+K/fIYwslf98PWexqdXhzHwP7Jyur8+jGM/8eGTD5ksfsmejEIOS1XxnonF7Pmf9Z9A/a6PYFfnAWPx/20xxrsv4k/3/wRPl3x3fWZ5GLDi96P4i51eDPwsgtNnPsGPX2pH59snMPBPa5iyK+dXRbJxfPRXQSzftAKpf1yBNV+9jDd3hVB/5DTe+tNqulmXwMjqHbcvgvHvNOCP73LwvcXha2tZnfxbHpl/uoulRgOG/UwxOncF3OgQUr9ahNy/NuDXl47h0Mc/QfwX45j47V1kv2KE4RfHcOzUOUn2d36ZRfYfJ8tcWbRr0fQfvoHo224M/N638cdfu4VPD3gRZ2HEryWQZQra3eUNaHhk2fT167ZY1oP46c9Y/iZZ/RLz9+u/xkX/IXx0OM7qGqsArM4tXmHFmt+Tgy5FKjengvhUrKO/BIal8n0d2a8r9zBZ+z0fIcDSNp6+Av+Z60qZXIz4e174Pj0HboST5JP+h0WoN69QFM3JtuF7X0+Wj/9XWLlgfhwNnmAyzsf128j1x5AYSWL0d4xYtXwc11ld7Bl1wbWT1VvJ7zKMRuH7KIxzn/jw48FRgOXhYiGNO1+tZ3IUY5QDd+oteD+5yOI7juGB6xj91TiWmL4DY1VfF6u+ropxXPKHq7D0xtvshfY7aPjmXXBH3gbH4nLx8gB4Fu5dDauz5z6eRn6sVVzbhKZvcuj+f5zD3T8wYNH/EUfQcxENrh/hj2/Of30nCOLBZJE4bq/s3zvYgyc9mkRKY4LpES00D/Mn7MRFukUL48VaaGfz+Ujx/rsaaNWNJ5NPbolo014Bdj57lyn44jU1yE5ckDpXKZ6z9DOP5Df71WiniXc5SuQ3XRxnHcYsyN7gkFttLmNQIg678tA8Pv3nJKfGlSkG7zWh7fMuRPYpBicKudEI3FuakNyZQmirPFJQjtylTtQ9w6F3uB9OvZJfs5KF2DMrxQ5aseDl8/4+yDVPkXxyLHx2UDb8udavhaaG+OfYdZolk/nBBFLcLiw0s6mrUjum3FdzekrKKUEQXyruj0JKEF86OHjXNCBzXID7KcVJRfydRbAiBuHNyl82595vQMOBZiRSXdI8RYIgCIL4onJfln0iiC8fZjj2tSB4NAhe7P1SMxJEzwkbPJumUzN5JC5wwDbLzEtEEQRBEMRDDvWQEsQ9JHsrgtCJKHidCUYtOx7mkNLZ0LrdUbSgfhFjcfiPx1TW2UbYX3PA9DBPdSEIgiCIaSCFlCAIgiAIglhQaMieIAiCIAiCWFBIISUIgiAIgiAWFFJICYIgCIIgiAWFFFKCIAiCIAhiQSGFlCAIgiAIglhQyMqe+PIxFkX3G0Hw2RTbcsASPYzL6mDc4kFXo/JNpdEIOnf5wMmfFIJxdSu6DjpglM8SBEEQBDGPkEJKfGnhP96IVS9F0XFxAp7G0k8V5hDf2wTP0i74XrNBT2uAEgRBEMQ9474P2eekbxUTxEKTRZKLst8WWNeWKKN3eYT3uDDU0ofQblJGCYIgCOJec38V0pEgWnWtCI4qxwSxUOQSiH7IfhttMOtlJ4mRMFy7IjC+4YHz0dJeU4IgCIIg7gX3USHl4X+lFWHlaM6M80jezKLQ38qOuUEe1XXA5pAr/b74PSOHbLaWuD3MPERpvclB7B/Vb2gozAvNXupG+3kjOg+3waxMJZ0LuWwaycEk0uOKAzEtJC+CIIgvL/dNIeXe70S2sUs5miOjYbS/zyN3xQnjC36Ej7Sj+wpg1PPwbNiI7qvTaUNJ+Cx1qFvRjsiY4nSP4C90o9neichIHYtbFqFXdiD8Be0dftjSyg9EwLHf1sdN7H8W0b0bYdqjgfNVM+aqi2av+bHD3gwvNwHDSg0S+5vRfe0L/zYya6qS1132skOKKkEQxBeW+6KQ5q51w7fEgw6mCJaSG4kjepUpl8pxNXCnAjBvtcGwBEif9CFh9qBrkxFavQ1N9ihcB8NIK9dORQeD2QbbeqN0v0jumg/Nz23Exmeq3J5rhv+GfG95cuCPt8L6YgZtp3vQsk7P4maGbUMGUS6rXCOSQ/qyFzuOiKrRw0q1aU0j+k47XBcq50w15Eaj8L7ok5TJ2TM5f7RhBXtB2eNHfGwI6UEPQpfnpjhmL7tgfyIMy+EQujawMqk1wm43IXQlqVwhk77cjfY3IpXLaS43Y52YH1ksLNXIK3szjO7n6qDbF62pnSAIgiAeIkQr+3vKREJwb+8Vbov7cbcAOITAHekMY0Loe03P3FqEUEpxmpHbQuD1gORf7E0IaFT8VojtY25wCzHleEHgPIKFidZ+bDJmE8MhoW0Li9fn8nEm3it4joWEnu+z+O5b0NjOjSrSKjMh3I73C0OfKYe1kokJvQd6hdAHzrnn70S/0MHiDBgF+75+ISO6DfcKdtFte0g+ng2f9Qltegj61/tZahU+iwmeLU4hwCvHChN8TOi/Xjmk2D694B5QDkqZT1ksJFXL67bQ2wih5XTVjQRBEATxkHGPl33KIf5OJ/htPWhZyQ6vdmORJYHAnRBaHpGvkIbichpold7K6uHgNTfA83wCqdfNihsP/zOrsOO6G4lUF/Ku9xvu/QY07AKcB9pgWcYcxgHdE1bYHjdBW2KxHX9nEayIQXiTqXUPIbWkdV6QyhAQE7owa4kNetFg7kTqzRhS+/K+ZBF+UYfm4xZ4uBg61inONZA93w7dcz7YX++FYw1zuAvUPdIA2wYz9DXaR4nlItoooOtJxaEc8yGLBaRqeaXDaDX4YBvuh3O14kYQBEF8obinQ/a5q16EVnfIymglFs9GGWWMJBEbzM8BVMgmwV0C9NstULnOjKgUZ7M1bZWNotJIxsVBVDucu51wbmfbq044nrxHCtqCUl1ac4M+dO91of0I90AMuRbmj65Xv7JoYd/WBT3i8Jye3dBwkqUTcKD1JUUW33eiZVOJcjXOwfeOC66dPnBf8jmRVcmLkbseQ1BvQwNTRrM3wvC+2432PWH2+kkQBEF8UbinCmnqMw0Mo+wB8p5X2lwfhJgrj74P2PH5uT1OsuwhFS5ZQzJ7OQwfLOh83oaaOqSyPBJcoqaNV0+PLIIp2GJP4eZ6ptxM5Yu1DmsVaR2LoPO0CR0OHWI7Q4jdt9UNKpGfP9oG2xPFpUSzoRn///bOB7apK9/zX/ahlaNltM4T1bMlqqlZulNnZ97iaDrCmelKGKVSjOgKR1QiWeZtaqZ61IF9xQFtm1Dtow7dl9r0DY2LhsagghzeNnLQgGIkUBxpM2tXD2Szr1WMXqpcJCLZWti1NUTy3S16Z8/948R2/DeOkwC/j3STe6/tc8/5nXPu/d5zzu+cvp1cZn8yuiKHN80WSeAaYSjyAqbkexrBDwMwvt+J5uleBO4on72oVLaXQvyuHzhkguZqH7wJC+w7UwhciyL5PFUlgiCIFx25436NSIzaWP4YUn4uNMzc5ybzxoFWgzx+FA42kR2G9yTMXLt0zHpxRj1Rijnm369j2MF/u9LxjBVIXXcwHfoLxvalWPSsnbkii6PlZOQxr0XHkGZ4Gg0MOgsbjqmnCpn1M5sOzHB0osS4x0pprf8aFdP6aEYeNxodMjGcyBkryOM2MeRm7grbRMHYS2UccrFxk1WkRSI7frRg7HGWuQsWaQgLs14o+ml5e8rjaXn5Lojz3LiTOUel8FJsRho3yr9ngpNNZo0hjwnNT7ejg8fhSP4599cFZbukLXgyp/uZATpmORdVzxRQsexUtmfFa9RtL/lIHj8qxcN1i8aQEgRBPK+skSDlAmV0mDn3SQ5MJtb1wTDzx6THYIZFz5j5wyZHWFZFlLl3gukO2Znz1ASbEyaZ64CVP8RmcgRPKRovSKX0Tp6yyA4zc6k5Fg2OsP4TbhaIL49dRUHKxZHp7EpFxeoJ0jzxn0cVaeUisF+nY/2hyrlTkUqCtJS9Hk6yYS7q+nt4eZMEqY6XF348EskmipfF0X5m3y2VUUUA2U8Ns8k8DaTak3/uuF7MGBk2c9HOLEf8LJpIsJlIgLlPONnwdO53M2zyA12+I08RpHLhiqgHpagoSHk6drp5bSnCWgrSeuyVCLAuSHHg95AvbLzOBxjJUoIgiOePNW0hXTVmR5iFP+Sct/gjPZNiqVSKZX5QP9tIPFHiliqjPEoLUpWHftZ1ptQDf+0In64wE0KZtEqtqLIw+oG/SHDxUZegKCPCZNbCXjwOZT2+1TKZyptlQCU1wRz8pczNRV50yJHXW5BLvYJUIcH8h1zFBelaUoe9MrecXBSraVhM7xwbOVRCaBMEQRDPJGu4UtPqkY5Lq+yo40c1Wmi1Wmg2osPQFiVu2iIDWsV5noZrPvgj/GB8GJ5rIcTmlw+KE+MzMOyqyUWrAQiYSRQssVlImbRqmrUwGIDoaS+0x7qKjjetiJhEbGocvsthfhDA8GfjCN1NLnM+Wgt7Cd8mYClnDLVMFnXW0zRDu4Mb484AvFsdS7NN1EKVtoA4g5ltNTr4NYB67BX/LrTkpLjNCPuOBGbGfBAO2tdtFg2CIAhi9WnwtE+NQEToZBP23BvB3C374rKPzycCfO+Mo/Wic10fvuLtAfSJfRjeV8caRtJE7xpNbc5mNbMG9loIYeBDEX3nrHWs6MRtIXJblDFGVdM+VUD48jDGXx9Z0RRWq0a99noqLRDAbbX4wlnZdgRBEMSzx7MlSJ/GMf55EMKip7YGpkMOWFbU5LbxEe+OI7zVBku5abMajoDg1TQsB00NFpP1sxb2Em6OIv1GF0wrmaqsBoQbPiTNdmVu15WwEMN4RAtb+/q+sq2VvQiCIIhnm2ewhZQgCIIgCIJ4nngmx5ASBEEQBEEQzw8kSAmCIAiCIIh1hQQpQRDPP5JTnbq7sZGcttTdFxixnmV1G2nAVQr7WcljcYEKI7F2kCAlCOL55GkSoU+7sadrEKNTYQgrWA52rUhOedBt6cbg1RDC35dcl/jFgOdbfHoUg2+3oe09H+I1idMYPOa98H2vHlaJ+CCG0FQIkftJlFrdWbjRh76riVV4sUkjfKYPvvsbXeylkfguCO+7e9H21iBCG7j+EM8HJEgJog7StwfRadmOTZs2ofNqUj1bD2lELnngvSHU+OBLIz4VgVBPy9KGYKXpL0RE6CMT9ky1wn2hH10dFhjLzViQ5ILkm3qvuTLEqQGYLCG0nvWh/6AVlp8WnyBLuO1DaF49eEYRxnrRaVbqS/dYifqyWQdTRxf6v/aj9/FhtLw3juprlgjxnrpbJcmxPrjiGujFGNz79GhuOozxAvElfjOIw9NWuHoMqzDbiBaW091Iv2fH6AP11DqRvh9B8KoX3qtBxJYZWQvDLhscFwLw7Axgz88GudwniMZBgnQNkabyibzgjR/PG9r2fgRCfvSrx3XzfQCud/rQ+9ZoTTf/5JgDLRYbPNPPeAFbYfqXE+fClj9hf2qCseKUU0mMHmvFnv0+hNdBkca/8fEYGGF6rVDqiEjeDSF0cxSDXS1oe/MwIs+4IDUcGEbg0y6+Zym/WIKMAYaf8X9XwphpWL4kERoT0WY2wtjhRCCeQSo1DFvuy8tCBK73E3CetKzi1HcmOM+2YvijWsT2aiIgeKwN9ikt2g464OgwIHqyBYfHBPXzXDQwGA3cVCFEa2x5JohaIEG6ZiQRuRJ8DlqwiGI0qf/rZocdvtgkwrMOmNVT1aDjYiqVEjDcUcfiBRuBFaZ/OVzBVP2k16HrYgopwQXLChSHmE4jXbjVUM/Fp6UiqoF2RytazTb0H+teJ+Gy+sTuBLnJLWjZoZ5YV3Rc9AbgzQqxzdzmBcvNxb50Imizw7rSOYFLsdMG+2MHhqeqU9urOZ4zfcMD+9he9B0xKgtWaI2wH7cj+nYfRp/xlx7i2aXhgjR5tRPbrb0Y+NQDz6cD6H2rjb+FPS+31hp4HOZv4uo+QZRBt9MC844ahWWRB+mzyorSXy/S0re1mO9xDL6Te7HH0om+sz74vizYxiJYjbZqjbSk6nOSrwpJxCMx4JB5wyz9at7Xh8S73Ri8W0zwRRAcEtHd3ojYGrD3UBsGrwSrKCtx+N+1oK3Lg2DdY4wFBM57kdxvyl9WeGcbrBiH72axVlKCaDxr0kJq3CIicjuI+CMDrGeDGDnwLC6tJCJ5LyQPfA/dS0JMxpevPf84joj0+VQsvyVUFDB63AEf380stqJkfyvmt6zkboX3x1LhV0BaNz/2oCAwHv94NYPU19IdVORpfiDFNS21b60ihTYWIS7kHvPrSat/Pc39Xk4MnqYR/0bJ+8j9Cg8DKYxsGhZXFFuONHZLKUtC3veyrW3J+0LVgqZo/pahoU7Ii/GPIyldh+epcI+XV35u8bJlbFQs/VWFuVJ4WPF78ZKOLMUQ73mwd7cXos2HiVAAw6edcJ4o2HrMK1sq9XknHUWYv5jbTC2L3d9iWkCc16u683Kl7LTBsS+CgaMeRArvq7zeDyetaKuw/K6Y5kKbl6NkjT1gutetsFwKIVyxshthHw0jNNSGxIVutFn74PtmhQ07af7susn/65uXlVGppyc0HXtuWuOJZ4s1EaRtx0cweWsSI0N2WNe65WM1WIhg8K0BRHUWWHbzbdsMPPtb4Focryci9nknWo6HoTVJY6NEjLZvV8bjiEnEIgI0r7Tw7/EHaTyKaIxv/C1XvgHPj8PebEXflZBynm/h891objbCcSN7WygTfln4i8CnvfDNaxA/3YS9l9TvLwTRxx8ILV0+/q5chu+8aGtqgv69at7g6+CpgODHndh7MghBY4A+HUDvO6s4tkoSHTfd6DY2o9nYDffNOIT5EPzHrdzOzej+MICYlMBkGO5fG/k5nh9fhuXrp+960fmWG8K2Np73bTAIbuyxDBT1OE3fHEDvZ2GktDwNYgiuN/eg71qBhRdi8L7dAse0Fq28LLUujMJiPIxx2bmBl48pP/o6mqE3jiIu/6AcOfn7UU7+liSN4DE9mpra4KnR8aM6uNC8E4CL21BvHMDw+UEM8vQ3vaKH8LkVBosXke9GMfBpSLaR9s4ADFLaF7sIi6W/cpgrHWsqfuNB75dxNG8Ow27ozolHGR7zunMgCtvYMBy7dKs4pvAF4bswvLDA+rrUKMHr/Ye98E7HET7LRd9n9Y0aXgly/bZ6gH1OmL4ZgOOzCC9xSwizUSQPtKDUArzpuz4ctnbCE8tA/4oG0TOdJVpaS7CjBWZukdh99bgCmm1m2IcmEL7MnxG3pXHjh+GdSubFuSL8ZTyh7hblW6H85wTRKKSlQxtJYtTGXNMZlkrMsBkhxTI/qB+oZIQwm4zMsYx6vBFJfN3FcCqsHimkrjuYbTQh70uf62BngUfyoUzmlpNB52AT6jnJDoCN+R8qx4tEXMw0FFUPOA8DrEsHpjsxuWiTasIvSszN7Bfm+M4cG2kHw+mlNMxd5vHZ6WY5V14Oj4uj3cJsZ6NqXBJs4n0bs/Bz1W62U5MsJf+2BBket0O6vPRK8fXv52kr+8PaiQ6ZuM362WT2QqkJ5uBVwHkrp/RN9zOrbDOO4Gc2mJg7phxmmbtgZdiVa7swc/FwcHQivxzPjjAr/30/L/8KCRbgaUVPIMcmGTZ5guf3kYnFc3MXLLysuHioFSiTv8XJsOhZKf8cLJAth5koGz5gXZZvpTcrs12cUX9cHKWsg5l5uVmE28Ii2Sgv7WHWz8+Zcr/HKZb+0mHqmOuOepxLZpI5+fcti2W3gEc87z9Qy9xDKZ/B7OOVC1z0rIlZz80UD3NFKPmPdl6eygXK7xNS+l0R9fgZRbIfdDxvf5hjgRNONiHwk3fczMDzsetr5X6ai5Lv+fe+8kh10cJGZtXDMiSCDmbexePyRDridaiD50Pu/YETPl26XqVC/cwMa/61+P2jsDyXR6m72WdJzaTm2MRQF09HF3ONR1mq4PlalDsu/jwplq4E8x/g54vde3j508G47F5IEKvJmghSQ88wC3Mxmor7WdcOKy/U2Rqf4QKHP6DRxQIrrI9rgSQ+ATNzXJxkMwk17o9mWPShtB9l7p28Eu/381tLDupDLit2ygnSpZsRF2KSYFm8SUpUF34x5kb7mV+6WcrCSMf6QznflcRWjghaL6JnzdwuuTf1DJsb52Kf3yzzUsaF08gRBxv5Vj1eCVzAmXLtINuF2zbHDuHTNjUuXCh8IJXNIjdn9YbuuL74K0WQLrvBq0KxY0TJO/n6/OFzOS8n1bLhXHwQKsdFrltA2fxdR5T4Fwh5tbzmP3iL261Y+suFuUzIZPiL0wdmptvHwyghZBZtJ8FFBKoSMdKLkiXn/lUvGS6KuKjRWflLe4Wa+FwIUsl+PL8PudjIaZciRivxZIaN9Bj4Cxu//1V1s6pSkEovJDpd3v1TeRHKvUerAq2YIJV/z18ksy81Eo/CzH3AzvwF6UqEXPzlZ4KHVgzlGpbsS/BK+SHBwhedzLrLypwXwyxRTpiWFKTqs6bovSfFJk9ZmK7DxSY38LOaeLZpeJe95P07c8EB8ytaaF/rguukiL4eDyJyH4MG1iEBqSd+2DbwsFLtPhcmTzcj+M4etOibsEnfgu7zCWi3aYCkgKjU/ZkIY/ySD77sdjuFtiE3jD+q0Jmyqx+Bg0riY591o/uKAe7z/TBnp6qpI3zDQRe6dvBwb3gR1NlhMed0MD4WoHmjdZ3HucUQuhwBduqRnlbS5b0URNLoQuCUOb87VGNA24FuWF5Rj1fCTgu6dyYxeDMsd3EJU0G0nemH7vy40gUvhjAx24m9svevNM6qxKABHY8L/+e9V6lTvQlNkoFvxhBP86ycjcrdy4nI+FI+8m3icRvcQ0Y01dTvlpO/14rk77pjgH61vZJLhJk7DlXqQh04bkfvVBu8Z50wl4hD1nYS1Xt9pyFEUoh+7YVHdtIss12KlR/mko7B91Ef7MdCaDs3DOevXoARp+k4wte47WfDiDzRIp2sYlDOFiPsZ4bR99iP3g8H4F0lh5vYFR4WetHZvlRnmrZIeaCBZrNyXI50JAgvj34rBPilevylD6N3NOi+PIKugnuU1mCBrasN5R5xM4/rHBS1WQdzj4uXqTbEh7rhuFrGTur9aznqHK47uQ2UEzloYTnuhuenUQwe76tcvgliJajCtGFkUgWtCfKbfoluto1KJqO8BWdSLBEPs8A5O7Pwt2PzmSj/SOkaxAF/iTdgBaWFZ+ntOxWfyWudzHC7mKVuq1H1TTkVZiPX+X6V4ZdGbaXL6xLn78JDXVW0CC0nk0qxVE1bQf7norZwFQ6HaCRKK4g0HCDK3AdG2By3bz/PS6m7NhPqZ47FbtsyrQXZeC+2MJRqIc12gSmtn/IwC/69St1z1baQKijxzBv2USM15+li631xCsu6zKq0kFYTpkJG6jqtqtVYbbUrqB/FSbGJI+V7JWrmSZj18/zLa2krxvPQQprbEp3i9Y6nW76HKp8WJ+bm90UTc16v9u5XTQupWi8L8ly+N+QNY1Lyu1gLqdyVL5XHalp5y6LEpdI9oSw/pFh03MW6dplZ19BE5Zbk7DNlWbrU+ngosPxZo7YI277If24RxGrS2BbSu4MwNDeh92ZO08/TjLrz7JC81o2B2zwNGi10r5lhOzqCwBd2RK6HIWha0dbDvzSbWD4Q/HERT3yV+Nj4ktPKQggD+wcgHPLCc1AdPv94BuPf8XfQFYa/iORReZvfOnO8WqWWwIDQic6KLUKFiEjcV52yqt2yzlvF2KKFnv+zvVqk7UDyxFZ/KNzwYPCjPvTdqL91xLC7C1Z4MX7aj2iHBQaNBZ3HTfBdDcB/MwnLG9mWKhPa5Gb7FDKFCXjA8wY69P+q0lQwPM9m+b8DrWjhxteY2mDnh0JyuctA+n5M8SCvEXEqAPc9kzItzfw4Bi5VdoXKJw2hWL6V2+Y3ftuI5ld70YkkBm+H1TMlUFvt8upHSbRo63DAP7aKTn5bzNjLVXXykxDCZWZleB7Ia4nWtsHSDkRicdmWkkOgt4ijXWzKj4jkBNXegC60HzXl5HkasUgI5nesOdNR8fvTy/y6TzLL7mGaLdK3jDAU6bERszcuyYHx4wEMHPMiVtL7PgFhGtBvqVz6lvE0icilPux9oxv+tAWe6TD8J6wwVGps17Sg9QD//62Q7ziaTsnPGOtu/iqnnFlEaRGW8kGdt5QgGkBjBalWh7YTE3B1LFW2GC/Y2NUH68+V4+QUF2Gfh8p7e28APFfzH0Lal3iVNRm4oNLC+p4L5nt+BP6Qe9sSETnn5aJTSbtmiyS9OPJDR4DwLT8nnxAw+l43PK+4MP6FbfFGIEyNQ/OK9Jvqwi+JdvnUHrHzXjS/a6t8Y/l+FJ36Tdh+LJt2DQy71JkGqt1+XsYTmT+UrEd0GJ8t6LpLx+B5z4O4ZKt7XIwmbXC8LsJzvqCcLItfFeywwNYB+D6Lc/GpiH9TezdMY4dxeMEGS04Xr7nHiy6dH8HpfLuHrvugO+SBfXdByvgNPjd+4h+4yL1nhuukmq9brXCcMSN2OZA/vcxCBO5zXEiqwWUWqpc78io/7Q7YdvIyczOIZlPezIIF8DLz0XZs0u/JefhrYSyWb+W21xr7SKol/RXhZahQTOSR5/VdGe0+JzyiA93naxX+leCxXKkgrVgP+D3GpsemV3sRLDHVm/iHAWzfpMeez0t4ule8RrGylYuA+HTu/KNpJKWZJV4z8LqRRugGl3evyR/kIXJRt/roYO6w5gvN7wPw3XTC1ZNff/T8foF7y73OTbu7YeZ3X6Fg6U/hWh8GbkrfTiP4YQDG9zvRPN2LwB3l82Wk+Utr0gTDyzXUKTGJ0OeHscfkQEjLxej0BNw9ZuiqGGqgoIP1kAO6sTCiOfchMRZGQNcFe/vyOQXEheUv0QSx6qgtpQ1j7ms76zozyeZSKTYX7GeW3apnpUyGRc+YFW/xDdwPIHUXmg/YmWNogs0keDoiI8x5MDcdPCWxEWbvkAaUT7JobJKNfOBgw3dyEiV7MxuY+YMAC4/3M6faNa90RYJZz0ywydAkmxwfYe4TNsZvCXnOGhXDL4OUBwZpMLowx8IX+lm/NBSgGmb9zKYDMxxtoPPTo0nWv9vKXKE5lhKibOIit81QgM2o3cKZhzNs7kmKBXqKDPxX46d0wavnqkC2ed4QCKXbu2hXrDDBXAdz7P6+lVlPBNhcntNAmLl4GfYHh5njhJ9FEwk2E3QxW4eT+eOFYfIyf9HOrPyzkVCURUMjrP/oMIvK8Zc8ZvuZfZeUJjOzn3KziQrDKqRhBob2YTbJr2cfKnAEW0aGhU8ZeH2zsOGGeMumWPiimzn3Sc5gYOaefubmZW3uupv190jOa2C6fU7mvhiW65D7lJ2Z+TnssPE8H2Fh2WO4MP3Vh5lfBNTuxwpd8Yte3+pxVUge4kfNzHDAzetUqoLNK6N0/y45teUipdMt2WS3kn7dbjvrH+LncutwxXogDUvgv9/BPy/h5CUNcZA83S3nSgz9qHgvUMsWj2NRL/MnyowWuV3TiXF+XzrA850/F7L3w0LK2aY41XTZS/A87LEyx2iUJXgd7++ws5FldZUjOwwWs2uGzfB6bDmi1vdIgN+3nWx40TktxWa+5fuyI2OZ+EdcTFdt+XsUZYHTNmbkZWA4lKiz3PH8OmNhFsnZSgoowW2w28L6Q8VzV3lOVWNXglg5DRekMlxQzMWiXJTWV4XWjewY0h8y6ji60unIjscr9Q3l85XboVL4Jcmov6tmWpB1oGy65IdCwfQqOYRP1zhLg5SPhRfiZbSsTfnnct5XNHzlMqJQ7feqQI7bKoTzXFGNIC0+vrpaUrOTzH+Oi+Wewqmx+PZ+Ka/q5dQuuopTcz1oBA/9rOtMcVEr1fFlSZTKbpkxyY0TpCpqvS5bRjpyZ9QoQL2vFk+DMlNHufHB0lR0VY3/lho0evhLbGR1MzjzaIaFpYYQ/nKcnUCmGCRIibVgbQQpQdSB3IolzV/5KMAcywbi8wfGEXVaJYJYpIQg5Q/gxXmP1emyHMESYmONWB1BujHqQeZW/6pOP9ZwQVoFkjOibiVOpfI8x8pUZdEhx/Ip/2SHygJHvQ0KCVJiLViTlZoIoh60Ww3QbUkgcCYK2xGzelZBvO1DrKOz5EoqxIuKDrp2/i9vndQkxo+3YM9+D0JpEZHLXkQPeeDsWF83DZ3Owv+KZZearcTGqAcC/Feb0Vk4trpedKscXo1o2gfg2zqM4bwx/FWgaYZ2B8+ROwPwbnWga5t6XkW44kHstHvZ+Y3L+uYD8fyzSVKl6j5BbFwW+MNgmSeqgODVNCwHTXSrJJaRvHYYbbYEnPEJOFSHGeFGHzx3jDAsxCC+4YBj/wbwGp4fx+HdnUgcn8HEkXJOaaXYGPVAvDuO8FZbfXMF5/JgFN1mJ3A6BN9vjFWmLYLBTQPQzU7CXvMsImWQlo9+JwTLxZw5oquCv2iIGmgKIi/e86DzrB7Dl7s2/st0mqe9ow0TuycRPGNZ//pCPLeQICUI4vklGcHoWBgp/kKjP9AP22qKlNVEmsJnLIDw4zREXRf6D7zAbf6PQ/CcjwFaPUzt1hpndUgj+LEL6HHDutotj+kYvJcS6H7fWp8oEyPwnk7Besa6scWoGMfoZ+NIbdZB374X1p1lZkwhiFWABClBEARBEASxrtAYUoIgCIIgCGJdIUFKEARBEARBrCskSAmCIAiCIIh1hQQpQRAEQRAEsa6QU9OKEBH5ZC9sH4ZgOBtF+H1ldebIx5vQ9pG8CxyZQOqLOr0xKyIifs2HYLoV9h7z+k7H8TgC36Uo9PvtsO5YK1/MOEbfleaUTEBIS3MEaqDdpkdzzprOqaQA+aNtdoxcrGWKlTRCH9sxeHkcoe9t8D8MNHa+wGQQfb/2QF65e4sOhq1N8jrX+enKIPUgyWPG2efG5FGl3BEEQRDEM48kSIliJJj/QKm1odVVYKRtp5vlLfw23a+cP9LA9d+zZCaZU45Hjat9pMJspNr17Ktk7qJVSfeylZTWgId+ZpOuvd9fZKWaDJv72sFM6Oe5Vjup647a7bsSZkeYRdfF/IJ6LCGo6cpbJSbFZr4oXIufIAiCIJ5tqMu+JAJmxtTdZZjRdd0JW7sdriEb8tqpNjepO2uAxoKB2TAmY97aWu/uh3D4XlI9WB0Mh3yIhsKYO5q/ktKashlYbn0NDAdcGOiJQ5hXT9WA9iW9utdgHieROtmHrtxJxXNaepfQwtjjgPMpkFHPEARBEMSzztoI0mQInncPw3MthOCVAfSej6HGRdjWnPQNP3zqfjEM+9wI3BpBf/v6Tm2s3WGGZadOPaqO2HRA3VtFNutg2m2GYSMt47GQVsuZlseNv2KsrgZfVcQnKVh+WuUqPRoDWvkL0wZODkEQBEHUROMF6T0v9rwRhHFoBM79FhjSIXjfCypj5VZI+n4IoSl1u5tcFLfVnI/NK2fF+Zh6LoL4Y/mUwkIS8WsD6HzXyx/4cYRvLw9v6bd8uy+P6Fs5T0UI9+PKOMfs8b2YOnawPGI6jbS0PeDiJO/rIpL31Pjd4/FOxhfTnZ4ahOMkt34mpfyWb9Wvob0UboSne/GSPM5KWNxiD5bskY2fcI+nTzoh2ZbvJ0umrUT4K0JE6LQd42qrqH73AGxq62M2Xsn7ghKvnHPpB7H88lCSUnHN2oKn+3upzPDjB3EeZoXUGLthN1U79lYPy4c2ZOVr+n5EyetvuJ0L8rLqtHLxLp/jZUWQzkl5xX9Tz/rqBEEQBFEtDRakAnwf9gInHbCqLWfGgz5MfutAPR27qVkuCK8MYI9lD/b8xs9lY/Xn7WMxxD7vw8DtBPRGA9JjNrS8pEfvTeVxLUz5Efw+DY3c/KSRH9qxu3ybiiIhf4M/0OejS9c5F1580NdOEuPHPRAWwrAbuuG75kXvJyHgFT2Esxbs+SSSI3QK4ULnuyDcvzai2dCH0KKwiGDwrQFEdRZYdvNt2ww8+1vgmuZigwvzKLRokb73WEA0FpU3oZoEPAiiz7IXw4kWOVzdHQdaLIOILPDP0gK3Rx+szXq0XMlaPY34TR/6Opqx3eSFj9vccycDPReFoWMGbD8WzLdbufBXQjqM0G11n6PZZoJxq7THhSLPYyleeuOoWkYUW3qPWbgtWzH+vXyyNOXiKuak++QwPMddCN/xo/Mlw2IZK8ZS/KpBA93PjdBKSxm+vRduwYA2Ho+2bQLcb+7hZTt7nerTmp4PIXC6G0Z9CzznB9F3lZfx09vR9IZ3sR4RBEEQRMNQx5I2hpibmfglXNMZlohNsslQlM09UT9TyQhhNhmZYxn1uGoiruJORZXO6yys/9aSO0jmllM5n+eElHVaKuXUxMmGV+i8VOp8Mbh9bBfmFp1yTKfCS3aQw6nsTKPEf+l7ia+7GHg4uUiOObbRbJrVtNXifJSJMtcuHr+hXIvOsZF2MPPZ7DnluDDc8GnJjjrmuL5kDSXOXSyQjVJV4Zch69S0s4v1D7mZe8jJ7LsMZe2nxMuV7+ik5p0roh5LFOZDlXFVwjcxd4wfPJxkw0PDbDLXYakasukq6sA0x/wHCuPBmR1hVpiV66pUndbs9XoCvOxmWHSU2/JytPa6SRAEQRA10tAW0uRsVO6a933kUlrsTBoE39mOw2OC8gWICJ2zYY95AMG1GhCns6KzfWnMpeZHzcpOJI5srNYKIZ5C524D8GAG47DA8Wsz8jttxys64izGX0Wj4ccfO9F7KYS42o+vNTsw8MbKB3emb/sw8A1gNee6bxnQ8gY3282oarcmNJW8RCesOddX4szjp6atuvCr4NW96D3hhPOEGyORCQy3q+dXkdriakXbTv5vG8/bEw5Ych2W6kSc8sE5xi37Rp5LHbCjFW26CPouFLRA14BttwlaXhJNB7ktD5kKyiRBEARBrD6N7bJ/qggiy9E+WCUNqDXC/hsbfG/3YVQWIxpYhwSknvhhq80v57nAcNCFrh1A7E6QC2ULWvl+FuHbEP/LjVLU07o02n0uTJ5u5sJ/D1r0Tdikb0H3+QS021YuK4TvFCeo+C0ffJeWthmtG+72arzQ9WheJlb5G4g6PrH+8IthRNs+A7SL9ovDe2y07peOmuLabpBycInvg/B86inYgiuKU/xesIRTkx4GLo5xPrbirnaDbo1mFiAIgiAIlYYKUs0W5cFm0Be2jo1jIqI+TjdroN2i7G5k0vdjBY5Dq4WA+HQMOGRedFLhV0M8xgWpzg7zT9VT1SJq0HZqAnOZFBLxMAIftiH5xR50f1JiZgMxibjq8FQK7VZ51ClarXbYe3K2o1JrpLWGyeaL06jwTUfdyouQRDKOsNawtnHVNuVPQ8Wvb/q5qWAzIL+Ne/1p/hG1iRIEQRBrS0MFqdZogkXdL6RZ05iHXvpR1vVoNRAXvYzjY3b47yv7q0qaC6VrQNfrLUtdo49DGD8PmE92wlKjmZLXujFwmwtMjRa618ywHR1B4As7ItfDxVvipGtNl+/cNbxuledaTTwq/J6I5F3Vg74OGh2+RDoShPjqUnulTre8ZEpTL1WirrhuNSqOZnmbcUUrbJnMnXLra+pJ4cuEMn+u7gPz4vy4K00rQRAEQawVje2y32FBVwcQ+nZJCskPQp0DVrPyGE5OeeH5PFR7t+VWXRGxKyA4thpzbGqgkcb+gYs4eWhBEsKsEYaqvaBr4LswvPzfkkAXETnvxsS+EfjUJUnLUUxYeK7mjx/UvsSli8kApb1aTdsP8oE8fnWm0rCAnVzkHtLBe6Wge/nBOFw306qQziCzUuVYVfh1wEW3e8iX1xXdpJXlHDKLek5E+LZf3V9imX1riSt/malr8vpyUy7tssPL4+G/HeYxX0K8HYBP1wXPu5bFuFSb1iwZmuqJIAiCWGP+5L9w1P0G0IzWX/45pv/Ki0dtv8R28b/jv54I4t9f8eEvtksqSMTs3/Wh053Gm4eteLUW5fGnLfjFj5MI/f4rRP4xjcf3Qxj9b/fx+hs/w+Vr01xD3sLvA0/R+msL0r/bg//g5qJ3nium5Cz+Ifz3wOud2HS18PwjGKS5Uv+5Hq27XoLwP25xcRfhYQcx+2//M/5Tu14e0hn7POd38zHciWrwi85WzBeev5XAy3J4SpSLEQv04Xf/04I/3xLH5p8Y8PD8X+Jv/vd/hH/4L2As8zupWz9yyQvvV7/j6X/ILbkJ4r9swb9OX0f4H+YRf7AZhn/1Eha+82NwOImBjxz4mfwOoMf2Hy8g9mkICz9rxre/T2Lvu1a8XPZaW2Dc34l/d/+36PXOo/nVJoiRUQzeeAnOj97ES3NBeP72AvyXYpjnCuxpil/7l5sR+dSD0evTiM3PIPFHKX56/N/bF/HbL/+Wx3kBmX96ivQ/M6DtJy+XD7/kaxN/Afn0Ir669jWuRwUszIgQ/0US8XAEEXUb9/XhL7sGcX3eAvtHdrT+qfLLLT/ejh9999cIpn+B1p885Xn614j9SQtuTd2B8McFPNX8GTaF/Xn2Tf4/feW4/jEC3+e/xVcXIzweCSz8UxqzC9Lvqu2YV9J0XYr7V3+DizO8LP2fOBL/S8SDezxMHsdWeTwwz5N9nWj5ew/6fp+G/s82QbjpwV99BQwEfoe3cxyoKqf1Vej/8SI8Xyp2jD1ewKb5h9j0b1rxct1vAwRBEARRmU2Sq7263zikidPnJS92A4zbtNDU6KhTESn8pxpopYcn3xelVsDVvkZDEOB7czsO75xEZqgNojRh/GZtfWNqRZ5+DU+/ZJMFqUmM20U2TAHq55otNeZHNtx641mKRodfgDRJvGwlyQ58T762hl+7GiG2xnEtSaW8VqkrrQRBEATRQNZGkBLFSQfR27wXqa8T8B9YGt9IEARBEATxItHYMaREWcQ7IXghzc9KYpQgCIIgiBcXaiFdJ+LXPAjmLFGp+Xk3HLtJmBIEQRAE8eJBgpQgCIIgCIJYV6jLniAIgiAIglhXSJASBEEQBEEQ6woJUoIgCIIgCGJdIUFKEARBEARBrCskSAmCIAiCIIh1pWYv+wcPHqh7BEEQBEEQBJHPK6/krF9dJTULUq/XC7fbrR4RBEEQBEEQhMK+fftw7tw59ah6aB5SgiAIgiAIYl2hMaQEQRAEQRDEukKClCAIgiAIglhXSJASBEEQBEEQ6woJUoIgCIIgCGJdIUFKEARBEARBrCskSAmCIAiCIIh1hQQpQRAEQRAEsa6QICUIgiAIgiDWFRKkBEEQBEEQxLpCgpQgCIIgCIJYV0iQEgRBEARBEOsKCVKCIAiCIAhiHQH+P63ORwLpzVezAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "id": "ac670dba-7753-4046-9789-7367206a8364",
   "metadata": {
    "tags": []
   },
   "source": [
    "![image.png](attachment:6dca74c9-e5ff-47b3-96f5-de6ffa68d3ce.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0091431-5221-47dd-8142-d520ac50e8ce",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "1. Verstehen Sie den Algorithmus und wenden Sie ihn an, um eine Eulertour in Königberg zu finden.\n",
    "2. Wieviele verschiedene Eulertouren gibt es in diesem Beispiel? Wie sieht es für allgemeine Graphen aus?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e57e1b03-3a23-46a3-b305-5285b184b659",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52991108-9e93-4936-8381-8f093defd147",
   "metadata": {},
   "source": [
    "Wir haben uns bisher nur mit Eulertouren beschäftigt. Nun wollen wir auch einen Blick auf Eulerpfade werfen. Wir fordern also keinen Kreis, sondern nur einen Pfad, in dem jede Kante genau einmal besucht wird. <br>\n",
    "Vermutlich hat sich jeder einzelne von Ihnen als Kind auch schon einmal auf die Suche nach einem Eulerpfad begeben, ohne es zu wissen. Das Konzept von Eulerpfaden findet sich nämlich im <i>Haus vom Nikolaus</i> wieder. <br>\n"
   ]
  },
  {
   "attachments": {
    "c747adb9-acc3-4615-bba1-ea0a1138191a.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "fc4af50b-1d11-4f8f-934e-4cd6268c5918",
   "metadata": {},
   "source": [
    "![image.png](attachment:c747adb9-acc3-4615-bba1-ea0a1138191a.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a19c16d1-4060-478f-8aca-5bdc6aff75d1",
   "metadata": {},
   "source": [
    "Ziel des Zeichenspiels ist es, das \"Haus\" in einem Linienzug zu zeichnen, ohne den Stift abzusetzen und ohne eine Kante doppelt zu malen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68d9de48-c512-459c-ac15-27905895b67f",
   "metadata": {},
   "source": [
    "Da es beim Zeichnen nicht wichtig ist, an welchem Punkt wir den Stift ansetzen und wo wir aufhören zu zeichnen, suchen wir also einen Eulerpfad in dem zugrundeliegenden Graphen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1370d724-f9b2-4048-8547-d9e428de8d2b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "1. Definieren Sie den zum <i>Haus vom Nikolaus</i> zugehörigen Graphen.\n",
    "2. Existiert ein Euler-Pfad für das <i>Haus vom Nikolaus</i>?\n",
    "3. Finden Sie ein Kriterium, mit dem man über die Existenz eines Eulerpfads in allgemeinen Graphen entscheiden kann und beweisen Sie es. (<i>Hinweis:</i> Orientieren Sie sich an dem Theorem von Euler)\n",
    "4. Wieviele verschiedene Möglichkeiten gibt es, das <i>Haus vom Nikolaus</i> zu zeichnen?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcfca683-efa6-44bc-9a69-7b99fda24b97",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3ac39a0-1ba9-4add-b639-c99cd25d81f1",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Recherche-Aufgabe\n",
    "***\n",
    "Der Hierholzer-Algorithmus ist nicht die einzige Methode, um Eulertouren zu berechnen. Ebenfalls sehr bekannt ist der <b>Algorithmus von Fleury</b>. Lösen Sie folgende Aufgaben mithilfe von Recherche:\n",
    "1. Schreiben Sie einen Pseudocode für den Fleury-Algorithmus.\n",
    "2. Gehen Sie den Fleury-Algorithmus am obigen Beispiel von Königsberg durch.\n",
    "3. Wo liegen die Unterschiede zum Hierholzer-Algorithmus?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "094eacfe-5ca4-46f7-add0-baa7b9fc023e",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46bebad1-ee8f-4342-87cc-70a73ce51d24",
   "metadata": {},
   "source": [
    "Das Eulerkreisproblem kann man auch in gerichteten Graphen sinnvoll betrachten. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ef7e98e-471d-422f-8e55-72a6a1401596",
   "metadata": {
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $\\overrightarrow{G}=(V,E)$ ein gerichteter Graph. Ein <b>gerichteter Eulerweg</b> ist ein Weg in $\\overrightarrow{G}$, sodass jede Kante $e\\in E$ genau einmal vorkommt. <br>\n",
    "Eine <b>gerichtete Eulertour</b> (oder <b>gerichteter Eulerkreis</b>) ist ein gerichteter Euler-Weg, bei dem Start- und Endknoten identisch sind.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5256a768-9587-49f3-991f-4673ccc76236",
   "metadata": {},
   "source": [
    "Die Definition von Euler-Wegen/-Touren und -Kreisen ist natürlich analog zur obigen Definition."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c45789e-39f2-4ae8-a78e-1165b617614b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $\\overrightarrow{G}=(V,E)$ ein gerichteter Graph, $v\\in V$ beliebig. Mit $\\delta_-(v)$ bezeichnen wir die Menge aller Kanten, die in $v$ enden. Mit $\\delta_+(v)$ bezeichnen wir die Menge aller Kanten, die von $v$ ausgehen. <br>\n",
    "Der <b>Eingangsgrad</b> von $v$ ist definiert als $\\deg_{-}(v):= |\\delta_-(v)|$ und der <b>Ausgangsgrad</b> analog als $\\deg_+(v):= |\\delta_+(v)|$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5942508-35ac-4027-aea7-81ab4705720c",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $\\overrightarrow{G}=(V,E)$ ein gerichteter Graph. <br>\n",
    "Ein Teilgraph $\\overrightarrow{H}=(V_H, E_H)$ von $G$ heißt <b>stark zusammenhängend</b> genau dann, wenn für alle $v,w\\in V_H$ ein gerichteter Weg von $v$ nach $w$ existiert.  <br>\n",
    "    Ein Teilgraph $\\overrightarrow{H}=(V_H, E_H)$ von $\\overrightarrow{G}$ heißt <b>schwach zusammenhängend</b> genau dann, wenn im Graphen $H$ für alle $v,w\\in V_H$ ein Weg von $v$ nach $w$ existiert. Dabei bezeichnet $H=(V_H', E_H')$ den zugrundeliegenden einfachen und ungerichteten Graphen von $\\overrightarrow{H}$, also $V_H':=V_H$ und $E_H':= \\{vw \\mid (v,w)\\in E_H \\lor (w,v)\\in E_H\\}$, wobei $vw$ eine ungerichtete Kante ist.\n",
    "</div>"
   ]
  },
  {
   "attachments": {
    "778b0888-a908-4468-9bd0-e517ead2e01b.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "b3c7178b-f3d2-419c-8875-f55f355b0404",
   "metadata": {},
   "source": [
    "![image.png](attachment:778b0888-a908-4468-9bd0-e517ead2e01b.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0f9da7a-8a7b-4199-8dba-a4063e98e37a",
   "metadata": {},
   "source": [
    "Skizze: Beispiel von gerichtetem Graphen $G$ mit zusammenhängendem Teilgraphen $H$ und $H'$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45e5268e-9fb1-4e52-be74-5f3323e6f45a",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $\\overrightarrow{G}=(V,E)$ ein gerichteter und schwach zusammenhängender Graph. $\\overrightarrow{G}$ besitzt eine gerichtete Eulertour genau dann, wenn für alle $v\\in V$ gilt $\\delta_+(v) = \\delta_-(v)$.\n",
    "</div>"
   ]
  },
  {
   "attachments": {
    "ce7f920c-a335-4538-9900-14791880057d.png": {
     "image/png": 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   },
   "cell_type": "markdown",
   "id": "8f879eb5-a158-4514-bdd2-9409a5295395",
   "metadata": {},
   "source": [
    "![image.png](attachment:ce7f920c-a335-4538-9900-14791880057d.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3666d750-c048-4af3-b83b-426dd8c2bbb7",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Welcher dieser vier Graphen besitzt eine gerichtete Eulertour oder einen Eulerpfad?     \n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5712a576-d52c-45d1-9c2d-3a0b934e0d05",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Denken Sie Sich ein realistisches Anwendungsbeispiel aus, in dessen Modellierung man gerichtete Euler-Touren verwenden kann. Erstellen Sie beispielhaft ein Modell und erklären Sie, wo die gerichtete Eulertour auftaucht.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0022af70-6f5c-4c4a-a9da-89fd86a1556c",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b71ccfa0-d046-4615-a729-991dd4c43aaf",
   "metadata": {},
   "source": [
    "Wir kehren zurück zu ungerichteten Graphen. Über das Eulerkreis-Problem haben wir bereits ausführlich gesprochen. Ein dem Eulerkreis-Problem eng verwandtes Problem der Graphentheorie ist das <b>Hamiltonkreis-Problem</b>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "340f73ac-26b6-4160-a9fd-3adb293fe447",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Sei $G=(V,E)$ ein einfacher, ungerichteter Graph. Ein <b>Hamiltonweg</b> ist ein Weg, der jeden Knoten $v\\in V$ genau einmal durchläuft. Ein <b>Hamiltonkreis</b> ist ein Hamiltonweg, bei dem Start- und Endknoten übereinstimmen. \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e56cade6-73a1-42ea-a599-20307eec6268",
   "metadata": {},
   "source": [
    "Auch wenn die Definitionen grundlegend eine große Ähnlichkeit zum Eulerkreis-Problem aufweisen, gibt es einen wesentlichen Unterschied. Um einen Eulerkreis in einem Graphen zu finden, konnten wir einen kurzen, übersichtlichen Algorithmus angeben, der ziemlich schnell einen Eulerkreis liefert oder entscheidet, dass kein Eulerkreis existiert. Für Hamiltonkreise wurde bis heute noch kein effizienter Algorithmus gefunden, der das Problem vollständig löst. Manche Mathematiker vermuten sogar, dass es keinen Algorithmus dafür geben kann, der so schnell ist wie z.B. der Hierholzer-Algorithmus. <br>\n",
    "\n",
    "Trotzdem schafften es einige Mathematiker in den letzten Jahrzehnten, sich einer Lösung für das Hamiltonkreis-Problem so gut es geht anzunähern. Einen wichtigen Grundstein für die Forschung in diesem Gebiet legte der Mathematiker Gabriel Andrew Dirac, der einen Zusammenhang zwischen Hamiltonkreisen und dem Minimalgrad von Graphen bemerkte."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1797140-2fe2-4bad-b160-be6360bdcc06",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Theorem (vgl. Dirac 1952)</b> <br>\n",
    "Sei $G=(V,E)$ ein einfacher, ungerichteter Graph. Falls $|\\delta(v)| \\geq \\frac{1}{2}|V|$ für alle $v\\in V$, dann besitzt $G$ einen Hamiltonkreis.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad5981c8-d29b-4d30-8c6b-390f5b518b76",
   "metadata": {},
   "source": [
    "<i>Achtung:</i> Dies ist nur eine hinreichende Bedingung für Hamiltonkreise!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2714b40-88fd-4664-8871-f55b99244942",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Beweisen Sie das obige Theorem.    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6231ae57-005e-4598-a623-cc1f74ef2811",
   "metadata": {},
   "source": [
    "Das Hamiltonkreis-Problem findet sogar Anwendung bei einem der bekanntesten Probleme der kombinatorischen Optimierung, dem sogenannten <b>Traveling Salesman Problem</b> (kurz: <b>TSP</b>)."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "a0e91f9e-7fab-4e8e-a948-233b9eeea5aa",
   "metadata": {},
   "source": [
    "![image.png](attachment:eabd67b1-16e5-40c5-98a6-584d6fea5a8c.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f51836a-e214-4f07-b16e-014992f9202e",
   "metadata": {},
   "source": [
    "Wir stellen uns einen Handelsreisenden vor, der auf seiner nächsten Geschäftsreise sieben deutsche Städte mit der Bahn anreisen muss. Welche Route muss er wählen, damit er insgesamt die kleinste Strecke zurücklegt?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83513840-9330-4f10-a816-238bf725230e",
   "metadata": {},
   "source": [
    "Abstrahieren wir dieses Beispiel und übersetzen es in die Sprache der Graphentheorie, so erhalten wir die folgende Definition.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d2d1d90-c735-410e-ab8d-79b865811c94",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Traveling Salesman Problem</b>   <br>\n",
    "    \n",
    "Sei $G=(V,E)$ ein einfacher, ungerichteter Graph mit Gewichtsfunktion $c:E\\to\\mathbb{R}_{\\geq 0}$, die jeder Kante ihre Kosten zuweist. Finde einen Hamiltonkreis $p=e_1 e_2 \\dots e_j$, sodass die Gesamtkosten des Wegs $c(p)= \\sum_{i=1}^j c(e_i)$ minimal sind.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5179e1f4-db59-476e-a468-d3e87ec37ee4",
   "metadata": {},
   "source": [
    "Das TSP tauchte im mathematischen Kontext zum ersten Mal bereits während der 1930er Jahren auf. Ähnlich wie das Hamiltonkreis-Problem ist es bisher nicht gelungen, das Problem algorithmisch komplett in kurzer Zeit zu lösen. Manche Mathematiker sind sogar der Auffassung, dass es gar nicht möglich sei, für dieses Problem einen Algorithmus zu finden, der ähnlich effizient wie z.B. der Hierholzer-Algorithmus ist. <br>\n",
    "\n",
    "Einerseits ist das Problem so populär, da es höchst praxisrelevant ist. In zahlreichen Bereichen findet es Anwendung. Es wird nicht nur in seiner Reinform in der Fahrplanerstellung der Bahn, beim Design von Mikrochips oder in der Logistikbranche verwendet. Auch wird es für die Behandlungsplanung von Bestrahlungstherapie oder im Finanzbereich genutzt. <br>\n",
    "Andererseits ist es auch rein theoretisch von großer Bedeutung. Ähnlich wie beim Hamiltonkreis-Problem wurde noch keine perfekte \"Allzweckwaffe\" gefunden, um das Problem zu lösen. Denn keiner der bisher vorgeschlagenen Algorithmen löst das Traveling Salesman Problem auf effiziente Art und Weise für alle Graphen. Da sich seit Jahrzehnten viele Wissenschaftler an dieser wichtigen Aufgabe die Zähne ausbeißen, zählt das TSP zu den sieben weltweit berühmten [<b>Millennium Problemen</b>](https://www.claymath.org/millennium-problems). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85bbf37f-bcbb-41be-9ea2-e0bbcc8b2105",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "### Rückblick-Aufgabe\n",
    "***\n",
    "In diesem Notebook haben wir uns ausführlich mit dem <b>Eulerkreis-Problem</b> in ungerichteten Graphen beschäftigt und mögliche Lösungswege betrachtet. Wir haben gesehen, dass viele Ergebnisse zum Spezialfall für gerichtete Graphen übertragbar sind. Ebenfalls haben wir das verwandte Konzept von <b>Hamiltonkreisen und -pfaden</b> untersucht und ein zentrales hinreichendes Kriterium für diese in ungerichteten, einfachen Graphen gesehen. Schließlich haben wir kurz das <b>Traveling Salesman Problem</b> eingeführt.\n",
    "    \n",
    "Finden Sie heraus, wie sich die Forschung bezüglich des Traveling Salesman Problems in den letzten Jahrzehnten entwickelt hat und wie der aktuelle Kenntnisstand ist. Welche Möglichkeiten gibt es bisher, das Problem (annäherungsweise) zu lösen? Gibt es bestimmte Klassen von Graphen oder Spezialfälle, in denen man einen effizienten Algorithmus angeben kann? Gibt es begründete Vermutungen oder Prognosen über die Lösbarkeit des Traveling Salesman Problem? Was sind die Gegenargumente?\n",
    "    \n",
    "Sollten Sie es schaffen, das Millenium-Problem zu lösen, dann gewinnen Sie ein Preisgeld in der Höhe von 1.000.000 US-Dollar. Also viel Erfolg beim Knobeln!\n",
    "</div>"
   ]
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    "***"
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    "### Literaturhinweise\n",
    "- Graph theory. (2023). In <i>Wikipedia, The Free Encyclopedia.</i> https://en.wikipedia.org/wiki/Graph_theory\n",
    "- Manon Bischoff: Das unmögliche Haus vom Nikolaus (2022). Spektrum.de. https://www.spektrum.de/kolumne/graphentheorie-die-mathematik-hinter-dem-haus-vom-nikolaus/2081799\n",
    "- Bernhard Korte, Jens Vygen (2018): <i>Combinatorial Optimization.</i> Heidelberg: Springer Berlin."
   ]
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