Problem 56433. Canadian Conundrum

Created by Dyuman Joshi

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>After succesfully completing the </w:t></w:r><w:hyperlink w:docLocation=\"https://in.mathworks.com/matlabcentral/cody/problems/56423\"><w:r><w:t>French Conundrum</w:t></w:r></w:hyperlink><w:r><w:t>, you have decided to take a vacation.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Your trip is amongst the mighty mountains of Canada and whilst planning your trip, you come across a situation - </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Due to the terrain of the mountains, you are confined to move forward in diagonal directions (North-East and South-East). And to avoid the risk of falling off (below x-axis is the death valley) or an accident, you have to take one step at a time.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The geographics of the track are similar to the previous problem, in a form of a 2-D rectangular lattice spanning from </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>(0,0)</w:t></w:r><w:r><w:t> to </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>(2*m,n).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In order to plan the route of your trip, it is necessary to visualize all the routes. To fulfill the necessary requirement of visualizing the routes, you, now, have to count the paths with exactly </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>n</w:t></w:r><w:r><w:t> number of peaks (local maxima); from your initial position </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>(although relative, consider it to be 0,0)</w:t></w:r><w:r><w:t> to the end point </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>(2*m,0).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>You being an avid mathematics aficionado, are compelled to solve the problem. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given two natural numbers, m and n (&lt;=m), find the number of routes with the mentioned restriction, to prepare a strategy.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Example: All possible pathways for m=3</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"222\"/><w:attr w:name=\"width\" w:val=\"314\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For n=2, output should be 3 &gt; as there are 3 possible routes with exactly 2 peaks.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.png","relationshipId":"rId1"}]},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 671.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 335.75px; transform-origin: 407px 335.75px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.5px 8px; transform-origin: 101.5px 8px; unicode-bidi: normal; "><span style="">After succesfully completing the </span></span><a target='_blank' href = "https://in.mathworks.com/matlabcentral/cody/problems/56423"><span style=""><span style="">French Conundrum</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120px 8px; transform-origin: 120px 8px; unicode-bidi: normal; "><span style="">, you have decided to take a vacation.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 355px 8px; transform-origin: 355px 8px; unicode-bidi: normal; "><span style="">Your trip is amongst the mighty mountains of Canada and whilst planning your trip, you come across a situation - </span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; "><span style="">Due to the terrain of the mountains, you are confined to move forward in diagonal directions (North-East and South-East). And to avoid the risk of falling off (below x-axis is the death valley) or an accident, you have to take one step at a time.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; "><span style="">The geographics of the track are similar to the previous problem, in a form of a 2-D rectangular lattice spanning from </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15px 8px; transform-origin: 15px 8px; unicode-bidi: normal; "><span style="font-style: italic; font-weight: 700; ">(0,0)</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.5px 8px; transform-origin: 0.5px 8px; unicode-bidi: normal; "><span style=""> to </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26px 8px; transform-origin: 26px 8px; unicode-bidi: normal; "><span style="font-style: italic; font-weight: 700; ">(2*m,n).</span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367px 8px; transform-origin: 367px 8px; unicode-bidi: normal; "><span style="">In order to plan the route of your trip, it is necessary to visualize all the routes. To fulfill the necessary requirement of visualizing the routes, you, now, have to count the paths with exactly </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; "><span style="font-style: italic; font-weight: 700; ">n</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156px 8px; transform-origin: 156px 8px; unicode-bidi: normal; "><span style=""> number of peaks (local maxima); from your initial position </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; "><span style="font-style: italic; font-weight: 700; ">(although relative, consider it to be 0,0)</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; "><span style=""> to the end point </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.5px 8px; transform-origin: 25.5px 8px; unicode-bidi: normal; "><span style="font-style: italic; font-weight: 700; ">(2*m,0).</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; "><span style=""></span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251px 8px; transform-origin: 251px 8px; unicode-bidi: normal; "><span style="">You being an avid mathematics aficionado, are compelled to solve the problem. </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; "><span style=""></span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; "><span style="">Given two natural numbers, m and n (&lt;=m), find the number of routes with the mentioned restriction, to prepare a strategy.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; "><span style=""></span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.5px 8px; transform-origin: 123.5px 8px; unicode-bidi: normal; "><span style="">Example: All possible pathways for m=3</span></span></div><div style="block-size: 227.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 113.75px; text-align: left; transform-origin: 384px 113.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 314px;height: 222px" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAnMAAAG8CAIAAAA6hLSlAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAGmMSURBVHhe7b1pdFVVuvd7vt4P56375Y73w3tP1Yc7huPUsepoaYlli02pBTZo2dBYgEgnAoI0giAiIiCdiKBRWumkCT1IGxIgRAikIw3pSUISQhJCAjF9c+6fzMl2sZu155x7Z2c3/99gMPazVvZezWx+81ntv/0PIYQQQvzHbbP+SgghhIQ1wnmBQZpVBIQQQgjxEZqVEEII8Sc0KyGEEOJPaFZCCCHEn9CshBBCiD+hWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPaFZCCCHEn9CshBBCiD+hWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPaFZCCCHEn9CshBBCiD+hWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPwsqsLS0tZWVliYmJcXFxCQkJeXl5mCLnkXCko6OjqqoqOTk5Njb21KlTGRkZjY2NnZ2dcjYJR2pra9PT01HcJ0+eTE1NRdje3i7nERIchJVZodW1a9dOmDDhnXfeGTdu3OLFi1NSUuQ8Eo5g5LR169apU6cOGTJkzJgxM2fOPH36dHNzs5xNwpGff/559uzZ77777qhRo6ZPn37w4MGamho5j5DgIKzMmpub+91332E8i2HstWvXVq1aNXr0aDmPhCNNTU0LFy5MTExE34psde/evf3796+srJSzSTiycuXKmJiYioqK+vr62NjY9957DxVAziMkOAjP86ydnZ1IXOLj41977TU5iYQ7HR0d5eXlzz777NWrV+UkEtagxDGKGj58+KlTp+QkQoKDMDQrNiczM/PkyZNffPHFkiVL5FQS1ly6dCklJWXRokWffPLJjRs35FQSvhQWFqalpX3//feffvopSl9OJSQ4CEOzpqenv/LKKy+++OI777yTnJwsJra3t6P5kZ6iqalJFEQ3gRJ/6aWX+vTpExsba10W+l+5BiTgdOvpzwkTJogS/+mnn6wLunbtmlx8CJJadkt+Ck3Ky8tlMUQ84Xk0GB4tLS39+uuvx4wZI6bcvHnznnvuedoHenchAyOeeOKJp556SgaaYNFPPvmkDPTxZdHAx6Xfe++9aHWiILqP+vr6TZs2DRgwwHqeFcZ99NFH5Xpo4uNWA3zduM6gvFBqMjCiZ5d+//33//jjj7IYuofGxsYDBw6MGjXKep71iy++eOihh+RKaOL7VmOHG+9z8G+TTshPRmDRPdhL9OrVa9q0abIYIp6wMmtLS0ttbW1ra2tHRwcSl/j4eHSsYpYwq/hsxo0uZGBEcXGx8e0BdXV1169fl4E+V65cwW6RgT63bt2qqqqSgT4ohW4yKwoa+QrKvbOzs62tDUNmdA3WgTMWfe7cORlognbh4ylbfN24cUEbZWVlMjAC2RsKTgaaNDc3o87IwAh0st1kVjRDtG4UPVoTRlHDhg07efKknNdlVuPl4gfRSGVghHEv0dHRWVTT+H9mn8L/+CynauJjL+FLBwV27dpFszoIK7Omp6fPnz8/IyMDfQqGsbNmzZo9e7aYRbOGpVmhnylTply4cKG6ujovLw+l/8EHH1h3FM0qA02C2axz5sw5duwYxk+XL1+OioqaNGnSxYsX5byQNWttYysSVmwR/sdnOVUTmjV4CCuzonvdunXrG2+88cQTT7z55purVq1y9Cw0a1iaFXkqOtnBgwc/+uijffv2/fzzz7GeyGbkbJo1HM2KAp04ceJTTz31/PPPYymoWta6HYpm7ezsLLnR9LsZp2BW/I/PZk87oVmDh/A8z+oKzRqWZvUKzSoDTYLZrPaEolmRpEKo+ACz4n98NktbadbggWZVxazNWKFZAw/NKgNNaFYzzHoJmjX8oFlVMWszVmjWwEOzykATmtUMs17CyawAYVFNo/isDs0aPNCsqpi1GSs0a+ChWWWgCc1qhkEvUXKj6T8+P1PX2IbPNGvYQLOqYtBmnKBZAw/NKgNNaFYzDHoJGFQkrIBmDRtoVlUM2owTNGvgoVlloAnNaoZuL4GE9d5F50TCChxmxRRMx1wRKkKzBg80qyq6bcYVmjXw0Kwy0IRmNUO3l0Bi+oe5CTKwmBVgum7aSrMGDzSrKrptxhWaNfDQrDLQhGY1Q7eXsDFraW3Tw19fwP8yVoBmDR5oVlV024wrNGvgoVlloAnNaoZWL1Fe1/xsVEpWxW81xGpWoJu20qzBA82qilabcQvNGnhoVhloQrOaodVLOCWswMmskC7Um1OpWoVo1uCBZlVFq824hWYNPDSrDDShWc1Q7yXgS6eEFTiZFUC9qWWqhUizBg80qyrqbcYTNGvgoVlloAnNaoZ6LwFfOiWsgGYNG2hWVdTbjCdo1sBDs8pAE5rVDMVeIr+6of/GjLPFdTK+g6tZ8Tf4S/y9jG2hWYMHmlUVxTZjA80aeGhWGWhCs5qh2EsgDb1vyW9va3fgalaAv1RMW2nW4IFmVUWxzdhAswYemlUGmtCsZij2Elpmjc2/MWzrpYyr9TL2DM0aPNCsqii2GRto1sBDs8pAE5rVDJVeAo6EKeFLGVtwa1YADce5+3snaNbggWZVRaXN2EOzBh6aVQaa0KxmqPQScKTbhBV4Muu+zKoJe3Kzr3mpSzRr8ECzqqLSZuyhWQMPzSoDTWhWM7z2ErAjHAlTyvhuPJkV9P422WvaSrMGDzSrKl7bjFdo1sBDs8pAE5rVDK+9BOwIR8rABZo1bKBZVfHaZrxCswYemlUGmtCsZnjtJYzNGp1WOe1gfrrtdUw0a/BAs6ritc14hWYNPDSrDDShWc2w7yXyqxtgRzhSxi7YmBVAyXvS7ZohzRo80Kyq2LcZFWjWwEOzykATmtUM+17CPmEF9mZdf/7q7COXba5jolmDB5pVFfs2owLNGnhoVhloQrOaYdNLwIjwIuwoY3fYmxX0W3fRJm2lWYMHmlUVmzajCM0aeGhWGWhCs5ph00vAiPYJK/Bq1q0p12zSVpo1eKBZVbFpM4rQrIGHZpWBJjSrGTa9hF/MCmzSVpo1eKBZVbFpM4rQrIGHZpWBJjSrGZ56iYLqhnnHi1bEl8rYAzRr2ECzquKpzahDswYemlUGmtCsZnjqJeBCGFEGnlEx6/LTVxbHlbh9+w3NGjzQrKp4ajPq0KyBh2aVgSY0qxluewlYEC6EEWXsGRWzAkja7ZVQNGvwQLOq4rbNaEGzBh6aVQaa0KxmuO0lYEGVhBUomhWSXhBT7Jq20qzBA82qits2owXNGnhoVhloQrOa4baX8LtZwdCfslzTVpo1eKBZVXHbZrSgWQMPzSoDTWhWM1x7iZIbTYvjSubHFMnYFnWzirOtBXenrTRr8ECzquLaZnShWQMPzSoDTWhWM1x7CWSWyC9l4A11swL87LJTd5URzRo80KyquLYZXWjWwEOzykATmtUMp16i4mYz5LcgRvU3adawgWZVxanNGECzBh6aVQaa0KxmOPUSWgkr0DIrhI1/pbVNMqZZgwmaVRWnNmMAzRp4aFYZaEKzmmHtJarqW1bEl846XChCFbTMCibsybWmrTRr8ECzqmJtM2bQrIGHZpWBJjSrGdZeAs7TSliBrlkXxRYvjC2GwkVIswYPNKsq1jZjBs0aeGhWGWhCs5ph7SUCYFZgTVtp1uCBZlXF2mbMoFkDD80qA01oVjMcvcTNprbFcSWT9+WJ6YoYmHXO0ctYUG3j7dZNswYPNKsqjjZjDM0aeGhWGWhCs5rh6CWQRyKbFBPVMTArwIJmH7n9RZo1eKBZVXG0GWNo1sBDs8pAE5rVDNFLNLW2Lz1ZMv1ggZyqDM0aNoSVWTs6OlpaWrA56FDq6+vRO3R2dopZNGtYmhXl29bW1tDQgDUEsBHqgKPQAc0qA02C2awocewcUeIoerQpa4kHg1nhOYOEFZiZFQrHEqFzmjV4CCuz1tTUoHTffPPNBx544Pnnn1+2bBmqmphFs4alWdHJnjx5ctiwYX/5y18ee+yxjz76CDKz7mSaVQaaBLNZU1JSpkyZ8uijj/7tb397//33L168iPG0nBeRZgVYIv7RrMFDWJn1woULH374IXpSVK/s7OyPP/54+vTpYhbNGpZmRdUdOnRoTEwMBlXYP+hVR40aVV1dLWfTrOFo1vHjx2/fvr20tBQl/sMPP4wdOxaulfNoVpo1OAjb86yoImhvffv2FSHNGgnnWevr65944ony8nIZ06zhfp4Ve2nYsGGxsbEyDgKzTtiWDMnJWBNjswIsdNiGCzRrkBC2ZkUnGx0djfGsCGnWSDBrfHz84MGDKysrZUyzhrtZU1NTJ06ceP78eRnTrDRrcBCeZm1qajp+/PiQIUMyMjLEFJo17M2KRWBBZ86cgRXkJJo1rM2KBjVmzBgMoGtra+Wknjbr/ONFnx4uaGo1bOa+mBULXRJXPO1Avoz1oVn9SBiaFdnq4cOHhw8fjk7WoRNh1qeffhr9hRmQNJCBEf85Lz4rv1gGmmRlZaWnp8tAn78uTkjMuiwDfbKzs9PS0mSgT58+fbrbrMhd+vXrt2/fvoaGBqdrgw8cOCDXQ5Pc3NykpCQZGIGv40dkoEleXh5SMRkYkZKSgoKTgSYFBQWJiYky0GfWrFn3339/t5o1JydnwoQJ69atq6ys7OjokFO7zLps2TK5HppALWfPnpWBER/uSMU/GeiTkJAgPxkxe9/Fdzcly0AfbDv2gAw0Wb16da9evWhWB+FmVqSVGzZsePfdd9EvWK8YFGYtLS2Fa81A0gZkYMTvZpysvtUkA02QsCIFkYE+f5h7Jr+yXgb6YK8i/ZKBPi+//HL3mRW/f+LECSwiNjYWNdmqVQCzorcSq6FLXV0dugwZGIGv40dkoAnSTXRzMjACKS8KTgaaYE8if5KBPqiu48eP7z6zonWjjW/cuNFJqwBmXbt2rVwPTZCpY0ghAyNmHcrHPxnog+GU/GTE0tii8btyZKAPth17QAaaoJ6vWbOGZnUQVmZFV/LNN9+MGzcOCRYKW07tosePBv958bkjF3L+68tfrG99UseXo8FY9K5fsv+69KzZokHQHg3G4GnTpk34fQy38dlJq4BHg2WgSTAfDT5w4MDQoUP37t2LFuGkVdCDR4PnHL2MhLW4wvysjS9Hg0FZ1Y2Zu9OwGjLWhEeD/UhYmfX06dMPP/zwAw880KdPH3SpYPjw4U1Nt3XS42b93YxTadn5/z49rqimUU7SwRezYtGn03L/z+xTZosGQWtWrNhjjz32X//1Xy+88IIocVBSUuLocBHSrAYEs1nfeOON//7v/37mmWdefvllUeJo+A4l9KBZJ+zJnbAt2Zdewkezopf4ZHeq2Q0/gGb1I2FlVvQj6MGt5Ofni062Z81635LEhKK6wstFaWU3n41KKa/77RIbRYzN+viKJCy64HLxxdI6LDqn0qSsg9as6AhEQVuBFRzJKxZNsxoQzGZFo5YlfQe0DkeJ95RZxQvdLpVc61mzZhdXYDW0XgrrgGb1I2F4BZNbetas/zbpRG1jq6i4f5ibYJA7GpsVCSsWLc4XYtGpZSZdbdCa1Ss0qww0CWaz2tNTZkWmuOzUFV96CeC7WdFLGLy9TkCz+hGaVRWzNlPf3Nb72+S4/Btt7R09btazxXX9N2bkVzfIecrQrGbQrDIIID1i1gUxxfhXWttk1ks4oFnDBppVFbM2A6shYRWfRcWF3vqtu6irNzOzQuqHs69D6sKsmHLfkkSDtJVmNYNmlUEA6RGzwmTi9eNmvYQDv5gVgsfKwPRyqjI0qx+hWVUxazOuZsUHg6OyZmYVR6HxgWY1gGaVgRE0qwF+MSs+rD9/1SBtpVn9CM2qikGb+bW5/c0NGXvSpZMcFfdozvVhWy9dvq5xTNjArMiMsejW9tsXcDnMGpt/A4vOuFrf9Seq0Kxm0KwyCCCBN+vy01cWx5UUdB2FMuglrPjLrCU3mrBK82OKxHRFaFY/QrOqYtBmkC/+bsYpGdxdcXVzRwOzOnJl4DArwKLj8vU2hGY1g2aVQQAJvFmRHSJHFJ8Negkr/jIrwCphbC0+K0Kz+hGaVRXdNtPQ0j58+6UtyRUyDhqz7susmrAnN/uaRqHTrGbQrDIIIAE26+qz5Qtiih2XTej2Ek7QrGEDzaqKbptxSliBteJCb2N35ZTcUH0okpZZIXXrOBpYzQrE5coyUIBmNYNmlUEACbBZnRqabi/hhB/NCtkvjitZflqjEGlWP0KzqqLVZmoaWj/cm/ddQqmMu3CquFppq5ZZrZdNCZzMGp1WOe1gvvr1yTSrGTSrDAJIIM265lz53GNFWRW/FbFWL+GKH80K9qRXaaWtNKsfoVlV0WozRTWNTgkrcKq4m5Mqpu5X1Zu6WRtb2yF1caWiAyezAq20lWY1g2aVQQAJpFnhLWvCCrR6CVf8a9aC6oZ5x4ugfxl7g2b1IzSrKlptRsWsQP1iInWzuh6FBjSrATSrDIygWQ3wr1mBVtpKs/oRmlUV9TYDt80+ctn1Tm3XihuVUIa/VHkkk6JZPS3a1azoEfCXitcx0axm0KwyCCABM+vWlGtoQU4ndNR7Cbf43axo4FhJJ/17gmb1IzSrKuptBqb8w9wEGVhwW3EVc0dFs7rNlYGrWQEW7bjX1h6a1QyaVQYBJGBmRS7o2nzUewm3+N2sACuJli4DW2hWP0KzqqLYZqrqWxbHlbh9RWKwmXVFfOm840XiDnd7aFYzaFYZBJDAmDU6rfLjnwvSXZ64othLeIJmDRtoVlUU20xq2S23CStwW3GhtwUxxV71pmLWm01tkPr0gwUytuDWrMDtuNsVmtUMmlUGASQwZvV0vEexl/BEd5gV+p92MB9DARl7hmb1IzSrKiptpqahFaacvC9PxnfjqeKqHJVVMauno9DAk1nFg9m8Xp9Ms5pBs8oggATArIezr0/Yk5tc6mbfqvQSNnSHWUFc/g2VtJVm9SM0qyoqbQYJ631LEmXggqeKi5wVerN/aoRXs9Y3t0UllHmSuiezAtfrG12hWc2gWWUQQAJgVpszOCq9hA3dZNbsa79iKLAv00sTpln9CM2qikqbMTMr8HpU1qtZbRJWQLMaQLPKwAia1YBuMivACtt0TQKa1Y/QrKp4bTPV9S1rE8sn7nWfNYLgNOv8mCKvGTPNagbNKoMA0t1mjc2/MTo629Pborz2EvbQrGEDzaqK1zbjte7aVFzobfnpK1dvNsvYBXuz1jW2bUqqGLkjW8Yu2JgVOD371BWa1QyaVQYBpLvNijbuKWEFXnsJe7rPrBgKDNt6CcMCGbuDZvUjNKsq9m2mtrEVchq+3c4f9hXXPm21N6vNBckCe7MuiCledupKhWev06xm0KwyCCDdatYLV27235jh9HQIK/a9hFe6z6zA/lwVoFn9CM2qin2bwTDW69V39hV35qGCqIQyT3qzaTP1zW1bU66hwcvYHfZmBfZpK81qBs0qgwDSrWaFmWy0Cux7Ca90q1nzqxvQS2BwIGMXaFY/QrOqYtNmRMI6YU+ujD3gteLaXExk02a8DkWBV7OKtLW01v3ZVprVDJpVBgGk+8wqElb7W9RsegkVutWswL6voFn9CM2qik2bUUlYQTCbFSBtdXpDjgOa1QyaVQYBpPvM6jVhBTa9hAo0a9hAs6pi02b8ZdaJe/NWxJfWNLhRoKc2U9/cti+z6q0NdoeCAc1qAM0qAyNoVgO626w5lb++vOai9YWyVmhWP0KzquKpzdQ13j7NaX/tkkCl4no63+mpzXi9IFmgYtZZhwsXxhZX1bfI2ALNagbNKoMA0k1mhY3gJJhJxh7w1Eso0t1mBRgcaD1+VR2a1QrNqoqnNrPHrw+8nrwvLyqh7GZTm4zv4LbNNLW2Y+l9VqXJ2DMqZgUT9uS6TVtpVjNoVhkEkG4yK2zkNWEFnnoJRQJgVgwRHv76gtsrKmhWP0KzquK2zTS0tG9KqrC/LteBYsV1e1TWbZtRPAoNFM065+jlxXEltY3Of0mzmkGzyiCAdIdZ4SHYyNNBVCtuewl1AmBW4OmpMjSrH6FZVXHbZpAy9vP3K/t70KwAaevsI87Nm2Y1g2aVQQDpDrPCQ7CRDGxx20uoQ7OGDTSrKq5tpqWtY3vqtUGbM2XsDcWKO2ZnztKTJc1tHTLuwrXNtLZ3HM6+/uJq74eCgbpZpx8sgFmbWu9aT5rVDJpVBgHE72ata2y7d9E5+8d/OnDtJbQIjFmxLdgibJeM70Cz+hGaVRXXNrP+/FX1hBWoV1zX852ubUb9/C5QNyuAWZ3SVprVDJpVBgHE72b93YxTigkrcO0ltAiMWQG2CNslgzvQrH6EZlXFtc3QrIrQrAbQrGbQrDKwhWbtbmhWVVzbTPeZFTjJ1anNaJ3fBTSrATSrDIygWQ0ImFlBbWOrk1xpVj9Cs6ri1Ga2JFcM337p12aNihgqZm1qbYdZF8T81sXQrGbQrDIIIP416+/nnim50dTR0Sljbzj1ErrQrGEDzaqKU5tBwjr0pywZqKFVcRtb2z/cm+fQm7XNHMyqfnNDhpbUtcwKnNJWmtUMmlUGAcS/ZoV7XG9Cs8Gpl9AlkGbt7OzEoAFDBxnTrH6FZlXF2mZEwtrQolcLdSuu9QYYa5vRTViBrllF2jr9YIEIaVYzaFYZBBA/mlUkrDCQjBWw9hIGBNKswCltpVn9CM2qirXNGCSsIITMCrBorID4TLOaQbPKIID40ay6CSuw9hIG0KxhA82qiqPNrE0sHx2dXe3u+br26FbcmoZW6E2cbXW0mei0yrc3Z1be0lu6gVnR6hbHlcw5erup06xm0KwyCCD+Musf5iZkXK1XP8MqcPQSZgTYrNg6bKPjqRE0qx+hWVVxtBmoziBhBQYVF2YVaaujzehekCwwMCvAloq0lWY1g2aVQQDxl1n/bdIJ3YQVOHoJMwJsVoBtxJaKzzSrH6FZVXG0mUCateJmM8y6KLZYtJl9mVVjd+Vcvq56D4ADmtUAmlUGRtCsBgTerO0dneKlrbea2mhWP0KzqiLazOakiqn78xUfdeaEWcUV5ztFmzE7vwvMzFpV37IwtnjW4UKa1QyaVQYBxHezwjHiVaywjpyhjOglZKBP4M0qEMMImtWPhJVZk5KS/tXFjBkz5KQ7+MusjjTOgJAzKxAJetCaFVVXlDiQk+6GZpWBJsFs1okTJ4oSd1upfDer9QCpLqKXkIE+NGvYEFZmRZ1GN4p2hf5UTrqDX8z61dGsaQfz86sb5CRNzCpuUU3jgpjiL37O/D72EhSbfc2ksIzNWlrbBLnO3JsRnGZta2tDiQNPhUuzykCTYDZramoqyvTvf/+725L10ayZuQUv/JAal29oxy6xhp5Zsb3Yamw7zeovwvBoMNpbN5l1wrZk44QVGA8J4bZhGy58sjvVLGEFxmYFSJRfX5UY5EeDaVZXwvtosKeS9dGsadn5Tk8m0iJEzQqw1dh2mtVf0KyqbEwsnXEgJ/1qvYz1MTZrQXXDZ4fzJ++5lFxq2FH6YtaSG00LjhcuOi6fGmEAzWoAzWpPd5i1vrntxajEg1nVMtYndM2Krca2Yw/IWB+a1UpkmXXMmDHobsyYsisd/2RgRFJSErpaGWjy+cGskVtSZaBPSkoKumkZ6LP8eE7/dcky0Kdv3749aNbDhw/L9dDk5+TLH2wz3+cgPT29qKhIBprEZRQP32S+z0FGRkZhYaEMNEnMuTJw3QUZ6PPDDz/07t27p8y6YsUKuR6a5BaX/6+P42RgRG4XMtDn/Pnz8pMR+fn52dnZMtAH2449IANN9u7d++qrr9KsDiLLrBhVYRRvxsf7s/FPBkZkZWVhUCkDTRKyy46kFctAH7Q3DKVloE/U6cuDNl6UgT4vvfRSD5o1Li5OrocmP50vefyb8zIwAj0dOh0ZaPJzevmfF52VgRHQKkZyMtAkIe/a7z+Pl4E+Z8+eHTBgQE+ZFV6X66FJaVXt72aclIERpV3IQB8MhuQnI8rLy0tKSmSgD7Yde0AGmmRmZs6YMYNmdcCjwUrsSa+aujvjTN41GRvhy6V3vhznAb4cDQYZpTUz9mYsP214eBDFEXJHg5NLb42Pzpy9L936zh9djI8GZ1/79f0dmZ/vT591uFBO0kdIXQY6lNxoGr09c96B9Mn78uQkfULuaHB1fcu7W7O+OZYpYyNC92gwwLZjDxg8XU7Ao8FWaFYlbt/6si3ZlzYDQtes6KAX/XzR4NlPglA0K8ZSz604+1N8lvrr5V0xNmtc/o2HlyYcTMy+b0minKSPsVlTy279cX786bRcx3PvDAg5sxbVNP779Dg0UhkbEdJmxbZjD6i/jNYJmtVKWJk1JycH7Wr8+PEPP/wwPqxevVrO8M2su9OrYNZDqcWRbNaTGUXzjhetOVcuJ+nQfWZtampCQQMUrviAKXJeF2ZmTb9a//HPBVvPF5+/VIScdVGsYW9rZtb86oZpB/M3nStJzbm8MLZYPLrZADOzltU1T92fv+6Xksy8y4vjShzvO9Kl+8y6cuVKFDTaOFo6Pji5EFMMllvT0IoEfWV8SYSbFXsA+wF7Q07SgWa1ElZmLSkpQaNysG/fPjnDN7NO6HrnjI9tBoS0WauqqgzesSPoPrO2tLTIwr4Dpsh5XZiZVWwp2gXUiPTROHE0MyuWiERZXBuM9NE4cTQzq3jWnbg2GOmL8S0o3WfW6OhoUdaCiooKOaMLM7NiS7Gf0Twj3KzYA9gPZmkrzWolDI8Gu8XYrIezr0Or6Ox8bDOAZg08vpsVvQwqQFSCyQ0wvptVPDh6Wdf7jnTx3ay1jbfftmR2prn7zGoPzSoDfUQHhcqGQkfFk1OVoVmt0KxeQMIq+jUf2wwIdbNmX/sVTW79ee1bPEPLrFALNnNryjVhVjHFLG01MKtjJzvuZxWdvpirhYFZHcMIx/2skKtZ2hpCZnUMX2hW0UGhvqHOi4nq0KxWaFYv0KxAmBUfkMwZXNETWmaF1URq3iNmdezhHjGr49B3RJkV5Sv2MM1Ks/oLmtWOoznXZx0uPFlwu6n42GZAGJg1/Wr9tIP50WmVYroiIWTWrIpf5x6TF2o5zCou6tmcdNf5PBV0zVpQ3TDveNGK+FJ8dphVXFyzNlH72jFds5bWNjku13KYtbG1/cO9ed8l3F4lLULFrOKFTuIyMZpVdFDYG9gn2DNiuiI0qxWa1Y6hP2U5TnH52GZAGJgViLOA4rMiIWRW69uEHGYFZmmrrlmtZ7IdZgVmaauuWa0l6zArMEtbQ8Ws1pKlWR0dFPaJbtpKs1qhWT0SX1iL/Axpqwh9bDOAZg08/jJryY2msbtydJN1f5m1ur5ldHT2lmS9pNlfZm1oaR++/ZLu+XWa1YDgMeusw4Ur4ku1rmOiWa3QrB5BD2vtTXxsMyA8zJp97dcJe3L3ZcpQhVAxa1bFrwtiileflcddrWYF6IJ1E0cts+ZXNyyOK3E86MpqVoC0VTdx1DIrhg7LTl1xXAZsNStA2qr7ytKQMGtNQyv84XjQFc1q7aAw4MBgSwYK0KxWaFaP0KwOrGYFaG9ah0ZDxaxQiyNhBQE2Kyqb9aamAJvV6dq0CDGrNWEFNCvN6i9oVvckl96avC/vRF6NjGlWi1kzrtYP23opVrnVhYRZxdVD1mcjO5n18vXGtzdnOs4OqKBuVqSMSFjnxxTJ2MWslbda3tyQofWCM3WzXr3ZjA2feei3xy05mfXX5nZYH/Ztbe+Qk7wR/Gatrm9Zm1g+ce9vz0amWa0dFPZMVEKZ+mOEaVYrNKt7nBJW4GObAWFjVuA02LcnJMyKhNXptfZOZgW6VxKpmxWVzZouAyezAt0ridTNaj2/K3AyqwBpK9ZBBt4IfrO6HnqhWZ06qN7fJqunrTSrFZrVDcjJ0Mkezr6rjvrYZgDNGnj8a9aKm80wUHxhrYy94V+z1je3vfBDqnpP53ezop9Fo2hTS1tpVgOCzaxoEaiZisMpmtUKzeoG9DJOCSvwsc2AcDJrfnVD/40ZF67clLEtwW9WJKMLYorFjaQOXM0KtM53KpoVwrZePSRwNSvQOt+paNbq+paohDLroWDg1qwA267Yzwa5WbEVaOPDt99VLWlW1w5KPW2lWa3QrM5cvt44bOsl12tffWwzIJzMCtTT1uA36+wjl50SVuDWrOV1zY8sv5B+tV7Gtiia1TVhBW7NequpDfsce17Gtiia1TVhBZ7M+viKpISiuvaOThl7JsjNCltYr9gS0KyuHRQGH1tTrtU1tsnYMzSrFZrVGfQy6GtkYMHHNgPCzKw5lb++vOZiVoX3yhPkZhWPjXV9VZxbswKkO4ppq4pZq+pbrDd+OHBrVoFi2qpi1pqGVqereASezAoU09ZgNis8AVs4JayAZnXbQWEI4rZLdIJmtUKzOkOzuuLWrADJk8oVPUFuVmgV/2RgITBmdbrVx0FgzIp02TVhBeFtVjRw14QV0Kw0q7+gWe8C6YunOyt8bDOAZg083WHWm01t9y46V3Ljrlesu6WbzIp9XlTT2OHtkGw3mfXPi89lXK33eh0TzWpAcJq1/8aMTUkVDS1e+i6a1QrNehc2ozMf2wwIP7NmVfz68NcXSmu9OCaYzYr0C1qF3mRswZNZgWLa6tWskPTiuJLJ+5wPxgIbswKVG2C8mrW+uS0qoWzkjmwZW7AxK8C2Q+0y8EDQmhWGgCdgCxlboFk9dVCejuRZoVmt0Ky/Ie5q8HQzvo9tBoSfWYHKLZ7BbFZPCSuwMWtdY9t/fH7Gq9u8mtX1Vh8H9maF25A0d3bapa1ezer2yimBvVl/P/cM0lb7pDlozQpDuE3TAc3qqYMatDlze+q1lja7AxU0qxWa9TeQsNpcX+5jmwFhaVb07/cuOmd/6WDQmrWxtR1adbrdxYGNWQG06vV8p71Zm1rbl54smX7wrttdHNibFXg932lv1ua2jtVny8fszJHx3dibFYgj0jJwR3CatbW9A4aAJ2R8NzSrTQeF4QiGYjJwB81qhWb9DZrVEzZmBV5v8QxasyJf9JSwAnuzYjAh3GaTONqbFYv2lLACr2ZF4ohhjU3iaG9WT+d3BV7NKs622tx+E5xmtUlYAc1q00FhOIKhmE3aSrNaoVl/g2b1BM3qCfvznd1qVoDdbpM4dqtZAdJWmztraVYDgtmsABXGJm2lWa3QrBJ7rQIf2wygWQMPzSoDF2hWV2hWmtVf0KwSmtUGe7N2dHSW3Gj6/dwzMnYhOM06/WDB0pMlTa0eS6RbzbogphhmbfS89G4163cJpR/uzbO5jyIszbolueLNDRm/NnvcapqVZvUXNOttHl+R5PVR4z62GRCuZgWwi03aGpxmRb7o9mYbBypmxYb/x+dnPF3AZWNWaNUmXQYqZsVybe6stTGrzTXJAhWz3mxqs3nQYxCaFVawSVgBzWrfQWEoNnz7JQxQZHw3NKsVmvU29ym849fHNgPC2KydnXZpaxCadczOHCSszbZ3EaiYFWBI4Slt9WRWpMvQqk26DFTMCmyu0fVkVpGw2qTLQMWswOYhxsFmVvgAVrBJWAHN6rWDsklbaVYrNOv/9FmVdjy3xr6bAz62GRDGZgU2aWsQmhUdhH3CChTNKu47QgInYwuezGp/flegaNbS2iZPD+vwZFavCStQNGt5XfOzUSlunx0dbGaFD2zOKwtoVq8dVHV9y+jo7LWJ5TK2QLNaoVntxt1WfGwzgGYNPAEwK/CUtgbArMBT2hoAswJPzYdmNSD4zQo8tR2a1QrNSrN6R8Ws7R2dCUV12JkythBsZp11uHBFfGlVfYuMPdBNZl0UW7wwtrjiZrOMPdBNZo1KKJu6P7+szsvSw8ysm5Mqxu7K8XRC2gHNSrP6i0g3a59Vafsyq+zPOQl8bDMgvM0KYBe3jyUKNrOia7C5xNGBulnTr9Y/svxCuYuu3JoV+aLXdBmomzWr4tdno1JyKp0X5NasyJW9JqxA3aziZYKu78APKrNih3tNWAHNqtJBYYCCwRkGKzK+A81qJdLNan/ngBUf2wwIe7MibcXORBJz6+6TjkFlVpGw1jR43xvqZgVIW10TR1ezioTVa7oM1M0K3FZjV7MiYYVZvSasQN2sACXuegFg8JgVDoAJvCasgGZV7KDcjg5pVisRbdb+GzP2pFfVN3t/XT7wsc2AsDerwPUWz6Ayq2LCCrTMGl9Y22/dRadjvK5mVUxYgZZZzxbXoTLnVzfIuAtXs0KrXs/vCrTMioQVe9VJ7cFjVuxwlTQd0KyKHRRq2rSD+U7tiGa1EtFmtbljwRUf2wygWQNPwMwKXKtTwMwKXM93BsyswPVBKzSrAaFiVoBd6lSXaFYrkWtWkbB6vdnGgY9tBkSIWdHDvvBDqvVIQPCYdeahAvSzXq8eEuiaFYkj0lZr4uhk1gUxxfjn9XW2Al2zInFElbbK1cmsK+JL0RUqDiV1zYrlYsiCxF3GQWPW6LRKZFdO2bwnaFb1Dgq7FNXJOkilWa1Erlm1ElbgY5sBEWJW4HStbPCYFeZTTFiBrlmB0/lOJ7PCPYoJK9A1K3A63+lkVtckwwZdswKkrRiqyiBozKqesAKaVauDQnWy1iia1QrNqoqPbQZEjlkPZlVbH9AaJGadH1O0/PQVlStZBP41Kxa9OK6kQC15Av4165pz5fOOF2VfU23p4WHWrSnXPv65wNPzF12hWWlWfxGhZh2zMycqoUzx2iWBj20GRI5ZgTVtDRKzImG1dv1eMTBrdFql9b5Jq1nVz+8KDMy6L7MK+ZlDn1azYrp6ugwMzHo4+/rkfXnJpXKJwWBW9PvqCSugWbU6KAwisYcdbYpmtRKhZnV7j4Q9PrYZQLMGngCbFVivJAqwWYH1SqIAmxVY9zDNakBomRVY01aa1UokmhUJ6+qz5VoJK/CxzYCIMqt4AHp1142bwWDWBTHFi+NK1A8FAzOzInF0pK0Osy4/fQUroHgdjcDMrEgcHWmrw6yo7XOPFbl9uq8nzMx6Iq/Gkbb2uFnheHT6iSXOj7CwgWbV7aBE2irefkOzWolEszpdX6OIj20GRJRZgePAQDCY1eksoApmZgWOtNVhVq0rpwRmZgWOtNVhVq0rpwRmZgWOtLXHzWpNpxShWQ06KOxkcWCAZrVCs6riY5sBkWbW7xJKkcHUNLT2uFlXxJciZVS/ekjgL7OKq4e0UkbgL7Min0DCmmK5rkqFUDfr7q6E9WxxnZyqBs1Ks/qLsDJrZ2dnbW3t0aNHf/jhhw0bNqSlpWGKmOUwqxjJqt/G6sDHNgMizaxAXIDdfWZF+WK7zpw5gxIHp0+fRugodCDMaj37qI6xWcVDBLHhwqy653cFxmZFcoylZ1/7VZhV9/yuwNisW1OuYekYWHSfWVG+KSkpaOAo8WPHjqFpWEtcmBV9PVZDTlKGZjXooNCysKsPZ1+nWa2ElVlRsY4cOTJlypTFixfPnz9/zpw5OTk5YpbDrK5PCFLExzYDaFa/g/154cKF8ePHo8TBxIkTk5OTW1p+eypvj5gViBtgesSsQBz67hGzAnHou/vMmp2dPXv27Hnz5qHEp06dCrmidct5NGvAzQrETcM0q5WwMiu6b9h048aNaGmFhYULFiz4+uuvxSxhVjQ2/DNIWIGPbQZEoFnR5LDDez39j24yK/SDTvbLL79E+YJly5ahAtTW/vYkIJh1zIq9WAfdS8GBL2YVaesvmZfXnrld5dRvJHXgi1lF2noy/fLGX24v3XGtsjq+mFWkrS/8a2w3mfWrr77CuBkNHCWOxv7555/DtXJel1kHTF+KFTAYS9GsZh3U2eI67PDBc36gWR2ElVkTEhLGjBkjaic6pqNHjw4ZMkTMQiOEWd2+40wRH9sMiECzAqStv//rM91k1vr6+n79+mVkZIgwKyvr1VdfRa4mQgCz/l9Doww6WeCLWQESx5/is55bcdYgYQW+mBUgcfw+JuP1VYkGCSvwxawAifL/fmZIN5l18ODBaNrYP/iMxv7++++j4YtZAGb9v1+doXvFloBmNe6gsMP/15tf0KwOwsqsJ06cgEpFk0MVSU5O/sc//iFm1dU3/D8vvCfOtJvxSxcyMGLlypVNTRp3fVjBtsTFxclAn9WrV6PVyUCfzMzMI0eOyECTOUcv3zNoVkaBeTdtAwZMjzzyCPwqQnx49NFHrUJ6eswXA789oXW7i4P8/Pzt27fLQJ8V8aUf706fvOeS+jOArEBsSMhkoM+ac+XT96RP2XNJ67YTB5WVlagzMtBnS3LFwx988/3uGBn7leeffx7NQTigoaFh6NChaPhiFpgZteMfc7adLDDRG5onGqkMjPCxl1i6dKn8ZISPvYQvHRR2+Mtf7hm3pAeuWQtOwsqsMTExGM9iuI3PHR0dqampaIRiVm3XS7l3+QCyYSADI/77v/97y5YtMtBk0qRJw4YNk4E+vXr1WrNmjQz0mTFjxoABA2Sgz59GLblY9Fse6Udg1ocffhjdqwjx4W9/+5vVrPctSfx83T65HprMnTv3hRdekIER9352dNqq/TLQZPHixb1795aBEb2+ODIu6oAMNEEnizojAyP6frTi24OJshj8ynPPPYemjQaOzzABBtNWs2L0PGzFQbkSmqB5opHKwAgfe4l77rlHfjLCx17Clw4KfLhk3Xvf7pfFEPGElVnj4+NHjRolOlb4NTY2Fj4Qsxpa2of+lDWN9BDl5eWiIPwLktQ+ffoUFBSIsLCwsG/fvhUVt+9bF8w6XPjh3K/kSgSckatjJ8xfKYOAM/r7Ix8sXCWDngDtURaDX+nfvz+athhAo7GPHj3auiCky8ic5BqQwLJjxw5ZDBFPWJk1IyNj1qxZGD1hi65cufL1118vWLBAziPhSGNj40cfffTdd9+hxAHy8unTp9fU1MjZJByZN28emjYaOEocjf3TTz/NzMyU8wgJDsLKrNXV1du3b586derOnTvXrVuHD+fPn5fzSDjS1tZ2/Pjxd999FyUOkL6cOHHC+FwRCQkSExOnTJmCBo4SRxuPjo725bIdQrqDsDJrZ2dnVVXV+vXrJ02ahJFsbGys9RZyEn6gfFtaWnbv3o0SB+hkEbLQwxuUL8ZPs2bNQon/+OOPaPIscRJshJVZ3YJWJy6mT+riypUrCLWaIr57rovS0lI5SRks6ObNm9nZ2Vh0cnJyQUEBMiqtpePvy8vLL168iF/IyMioqKhAoibn6ZCXl4cMXressTix7YLcXO2LqxsbGwsLC7HtqampZWVlvtz8ow72MHZaWloadprBPr9x44bYXrObherr67HQlJQUbHVOTg4qgLjcRhGUL2yRmZl54cIFbAKqn9lOQ1XHCujeLoUaIrZdgB0oZygj7thBcWPpRUVFjuvLuhWULzJX7DSsMPb5rVu3tEoc62y8vQCVHJss6ltWVhbWRP32FdQN1DfUNBQ36oxBdXWA5YoKI2NlxLY7EOew1UH9vHbtWnp6OjYf/QwqvJwRwYS/WVHFS0pKPv7446FdYKiLNqDV023atOlf//rX008//c0338hJyiCFQiI1bdq0YcOGjRo1Cqtx6tQprYqLhrpixYqxY8cOHz584sSJ33//vePBUurU1NTgF/70pz/pqgI5waOPPorNFyxbtkzOUAN9xNGjRz/77DOs/JgxY7Ah1suLug/o5MsvvxwxYgRKfOrUqejirQ9m8go6CGzsiy++iP/lJB2OHz8+Z86ckV1MmTJl//79Wvc4YuXXrl07YcKEd955Z9y4cfPnz0eHK+cpg94NX3zkkUd27dolJ6mBGnL//fd3lfZtUGnlDDWwn3/55ZfFixePHj0a3124cCH6ejmvO6mtrUU7RR1DiaOZoNY57sVSAfscGztgwIAHH3xQTtIBY9avvvrq/fffRz3/8MMPsSboZOQ8b6D73bp16+TJk4cMGYL1Rwd1+vRpg9EzfgddzTPPPPPFF1/IScrcc8892HZR4kBrNAatokf67rvvxo8fjxY3e/bs2NhYOS+CCX+zoouBD9DBoboAdFUQpO6gDOBbBmaFWj7//HP01Gj5dXV1EBW6S62Ki2aGhopkERuC8eCiRYvgDDlPDbTS9evXz5w5Ez2mgVkxLJCBPuhx0Nj27t1bXV0Nu+/YscN6S0z3ge1FB4dBNHb1kiVLsNMMlgtBopeRgQ4//PADOheM4lHiP//8M3ocrfP9yDnQT2HlUWfwIygCWErOUwOjyQMHDmBA8/e//93ArK+88ooM9MFAcPr06atXr4ZasP7Hjh1LTOyWe2+cOHjw4IwZM1BkKHG0l7lz5xosF03MzKz79u3buXMnRvD4BQwsMIDesGGDnOcN7CWMP9BFoIEg94Ud+/fvr9snI1U4e/bsggUL3njjDTOzYs1loAmqK0bMWDRqDn4EVR11Xs6LYMLfrJWVlaipFy5cEOG5c+cwOjPYZDOzOoFmj27L7Mk+nZ2dGIaj1/joo4/kJDUKCwvffffdixcvPvHEEwZmxTgaY1KoHX2l7kE2dDHQTGpqqvg6Og6zw1y6IFlE1iJKGX39Bx984HhOkzrGZrWCfhPZ58mTJ2WsA/YVhoBIWF977TU5SQ0MIz755BMhdQOzvvDCCygvFHpRURGyba0iw5gA2duZM2fwC/g6KozW8SFjkKBD52LMir5+3rx527ZtE7PUMTarFTTSr7/+WvfojgD7qrS09Nlnn8V+k5PUgJWx55cvX45Fm5kV1QwlXlBQgEGw1vmy/fv3YwyHIRRKHF0N1iQwJR7khL9Zy8vLH3vsMccTiNBTPP7447oVF/huVuSv27dvhxdR+eQkZfAVJDFIRJABb968WU5VADL79NNPf/rpJ5Ty008/rWtWDMZff/31gQMHDho0aNKkSRiYo+HJeQpgGIHB7KhRozCagd4gmMCcdevTp092drY414WyfueddxxDK3V8Nyu8iOQV/Q7KTk5SBuWVmZmJPYaOEmm3nKoAFopOds2aNaj506ZN0zUrOkeI/O23337rrbcwqIqKitI6gD9lypSpU6dOnDgRdQapNpYemAt3scStW7eKY/6oY9hpWHMxSx3fzdra2pqcnLxo0aLdu3fLSWqgrqJtQm8YImBUhGYrZyiArT506BB6J4yeMRQ2MCvaKUr8zTffxBAclS0/P1/91P6qVauGDBkyY8YMdBH4OsJuunk9tAh/s2L8/tBDDzlOs+FDr169DA59+GhW9HcYyKPuImk2uCAlOjr6qS7QV6Lvk1MViI+PR+KCsTwGoQZmFaDZo39EDgQ7aj30DqNvrHBeXh4GNCtXrpw8eTIarZzXnWC5SJjE2Bl7e/DgwQbHBn00K2oaOkoMR9DJap3zEyDRFyX+xhtvaN2viS/OmjULi0aJG5hVgF2HbgE77f3338dgTk5VYOzYsRhI/fLLLyjxvXv3Yhx5+PBhOa87wXJ37NghxlJtbW2wi8FzCn00K5aLnA9DSSxaZM/qoIagefbu3RtVNyEhQes8K9rUihUrkDuixM3MKkCNRd6JOgPUj6thY1999VUMwVHi6OI+/vhjjOrkvAgmInJWdE+Op7SjxjzzzDMBzlkxiEY3LbTqcLwuMERGRga6uYULF8pJCmAoeuLEieLi4tLS0ieeeAI5kPEKYByNblrrkpZ+/fplZWWJbqK2tnbEiBEY0YtZ3QrG4Bi/ixEMxgTDhw83WK4vZm1qaoJdkPNt27bN+InN8ARKDT0XfkdOUgAZDxaK0Qy+i0EVujnjBo6Cw++g+chYAeSsBw4cwObjM5YrDtKKWd0Klrt582aR6kGQsIvBcn0xK5pVenr63Llzv/76a+PL9ODXdevW6Z6uWrt27eLFizH8Qolj6XAbJCfn6YOusm/fvuqXSSJJnTdvnlhhlDvq3tSpU8WsSCb8zVpdXT1y5MhDhw6hmwAY2Y0ePdrgmKSZWTGKhMW3bNkCrSKNEGNqLbCq+AWsOdIIfNi4cSM6ETlPgZdeegljYcEf//jHxx9/XCtrRFeF7gZLx5qjuW7duhVJmJynAFIWKA0/gq9fuXIFVkZGJed1J9hFWNWamhqsOcbRWA3ri8YUMTYrigx2Qa1Dlm8whsOAAKMQ/I8SR1eFaqN1SdHEiRNleT/99P3339+rVy+trBF7DAUtlo4NuXDhgtbSkTyhrWEwgRJH3gbDrV+/Xs7rTtA2seiioiKsPwyHvh4Zs5ynjLFZUUxnz56FUbAOutkqdhQqKsSMvgIrDztiKKNVbTD2kuX99NMPPfTQX/7yF92LHDH6bG5uRomj3JG2orNS7yWQrX7//ffYamwIyn3Dhg0zZ86U8yKY8Dcrtu6nn35CF4lRGHjjjTcwqtLK29Bs0OQwKgT4IMbjiqC+fvvtt08++SQyGHSX+DpAFUQrkn/hDXSLUVFRqO5ockeOHMGA1DgJQMPTPRocGxu7bNky5J3Ienfv3v3BBx9gZ8p5Chw7dgzNLCkpSVxUgnQKfZ+c151AaUOHDo2Li0OJo7/DDtTq79C/oJjQZSB7wAfdY7nbt2+HjaKjoysrK7sK/CZ+UL3E0akh1cvIyED2kJiY+Omnn86ePVvO08TgaDCq2axZszAAunr1anx8/IgRI5AGyXkKnDt3DiuPSosSRyeL6urL21fUSUhIQEGjcqLEv/rqK3GpqpynAKSCYiorK3vggQdEkckZapw4cULsKGy1+Dp6CcUSh1YxEMQAFDlAXl7eZ599hlZmMPQXmB0NHjduHAagSLVR6yZMmIBfcBzk8wrGrOjiNm3ahG3HoAqjWINrx8KP8Dcr6jdq+ZIlS3p3gbGteqUX4LsYyTrQupwEY0/5NQuFhYVoyfIvvAEVoeKip4YX33nnHejNuNUhf0W/IwM10M9C5K+99tqzzz6LJOzgwYOQhJynxubNm19//XWsPJLdzMxMjMrljO4E5btu3bp+/fqhxOEJbIVWiUMGsqi6GDhwoJyhBv5efvMOGBKpbzhGYEi4MQR84oknkD0gDTJIfAVQ8v79eq8fwTACMu7fvz+Gg/h/zZo1GB3KeWpgY4cPH44Sf/fdd7Endb9uBsoXw7ghQ4agxGEmcZpZzlOgvLxcFtUd5Aw1sJ/l1+6ArFFx+I7uCGv+9ttvP/roo3379sW4BKNArZW3smXLFq0OSnDy5EkUGUr85ZdfXrp0KVJY9Q4KXLx4Ea37mWeeQYXBsNK4gwonwt+shBBCSCChWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPaFZCCCHEn9CshBBCiD+hWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPaFZCCCHEn9CshBBCiD+hWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPaFZCCCHEn9CshBBCiD+hWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPaFZCCCHEn9CshBBCiD+hWQkhhBB/QrMSQggh/oRmJYQQQvwJzUoIIYT4E5qVEEII8Sc0KyGEEOJPwsqsHR0dLS0t2Jxbt27V19c3NTVhipxHwpHOzs7W1taGhgaUOGhsbESJY6KcTQghPUFYmbWqqmrbtm2DBg168skn+/Xrt3jx4rKyMjmPhCPQ6pEjR0aMGPH4448///zzU6ZMycvLa2trk7MJIaQnCCuzJiUlTZ48+cyZM1BsSUnJwoULJ02aJOeRcARV991334Vcr127Vl9f/8MPPwwbNgylL2cTQkhPELbnWTs6OlJTU/v06SNjEgE0NDQ89thj5eXlMiaEkJ4gPM0KraJ7/eabb6ZOnSonkXAHWt20adPIkSOrq6vlJEII6QnC0KxJSUkPPvjgQw89NGjQoIKCAjmVhDUo8QceeOCJJ55ITk5ubW2VUwkhpCcIQ7O2tbXV1tZmZmZ+8cUXjpz11q1b6HxJT5GTkyMKopu4efNmeXn58uXLR4wYYc1ZBw4cKNeABJwtW7bIYiAkwgjPo8GdnZ3Nzc1nzpx5+eWXxRT0vPfcc0+pD2R1IQMjzp07d+XKFRlokp2dnZGRIQN9zp8/X1xcLAN9cnNzL168KAN9+vTpc+nSJVEQ3UdHR0dFRUXv3r2t51lfeeWVgwcPyvXQJC8vLyUlRQZG4Ov4ERloUlBQkJSUJAMj0tLSUHAy0OTy5cuoMzIwYvz48T/++KMsBkIijLAyK7rvFStWlJSUNDQ0QEXz5s1zXBsszCo+m3GjCxkYAbe1t7fLQJO6urrr16/LQB8Y3ZdjpMj4fbngFnrrJrM2NjZ+/vnn8AcGUteuXVu5cqXTtcFYNAY0MtAE7eLq1asyMAJfN25c2DQf7xnDDkHByUAT7E/UGRkYMW3aNJqVRCxhZVYkK2vWrBk5cuQbb7wxfPjwr776Kj8/X8yiWcPSrC0tLdu2bRs7duzrr78+ePDgTz75BIkaJsrZNCvNSkhPEFZmbWtrq6mpKSgoyMnJKSwshAwcJqNZw9KsnZ2dKNnLly9nZ2fn5eXBZNhM6zOYaFYZaEKzEuIL4Xme1RWaNSzN6hWaVQaa0KyE+ALNqgrNKgN9aFYDaFZCQheaVRWaVQb60KwG0KyEhC40qyo0qwz0oVkNoFkJCV1oVlVoVhnoQ7MaQLMSErrQrKrQrDLQh2Y1gGYlJHShWVWhWWWgD81qAM1KSOhCs6pCs8pAH5rVAJqVkNCFZlWFZpWBPjSrATQrIaELzaoKzSoDfWhWA2hWQkIXmlUVmlUG+tCsBtCshIQuNKsqNKsM9KFZDaBZCQldaFZVaFYZ6EOzGkCzEhK60Kyq0Kwy0IdmNYBmJSR0oVlVoVlloA/NagDNSkjoQrOqQrPKQB+a1QCalZDQhWZVhWaVgT40qwE0KyGhC82qCs0qA31oVgNoVkJCF5pVFZpVBvrQrAbQrISELjSrKjSrDPShWQ2gWQkJXWhWVWhWGehDsxpAsxISutCsqtCsMtCHZjWAZiUkdKFZVaFZZaAPzWoAzUpI6EKzqkKzykAfmtUAmpWQ0IVmVYVmlYE+NKsBNCshoQvNqgrNKgN9aFYDaFZCQheaVRWaVQb60KwG0KyEhC40qyo0qwz0oVkNoFkJCV1oVlVoVhnoQ7MaQLMSErrQrKrQrDLQh2Y1gGYlJHShWVWhWWWgD81qAM1KSOhCs6pCs8pAH5rVAJqVkNCFZlWFZpWBPjSrATQrIaELzaoKzSoDfWhWA2hWQkIXmlUVmlUG+tCsBtCshIQuNKsqNKsM9KFZDaBZCQldaFZVaFYZ6EOzGkCzEhK60Kyq0Kwy0IdmNYBmJSR0oVlVoVlloA/NagDNSkjoQrOqQrPKQB+a1QCalZDQJazMCv3ExMRMmTJl4MCBY8aM2bx5s6NnoVnD0qzYn0lJSZ9++mn//v2HDh26bNmy6urqjo4OOZtmpVkJ6QnCyqwZGRmfffZZdHR0bGzsgQMH0OF+9913YhbNGpZmhX7Qg2/ZsgUlHhcXN2fOnPnz52Nfydk0K81KSE8QVmZFP5Kfnw+JwiL19fVHjx596623xCyaNVxz1uzsbJQLtg7k5OS88MILVh3SrDLQhGYlxBfC9jxrQ0PD/v37R44cKUKaNSzN6kRycjLGUpWVlTKmWWlWQnqC8DRrS0vL+fPnJ02adOTIETGFZg17s5aUlIwbN2779u3W+kyzykATmpUQXwhDsyJbTUhImDp16q5du+rr68VEYdYxY8aguzEjtwsZGJGUlISuVgaa5OfnZ2dny0CfgesuZBSWyUCfwsLCrKwsGejTt2/f7jYrigZaXbVqFcYfTlcwHT58WK6HJkVFRenp6TIw4oNtqT8nX5aBJhiHpaWlycCIjIwMFJwMNIFWU1JSZKDPDz/80Lt3b5qVRCzhZlaoFHnq9OnTt23bZk0xhVnhWozizSjtQgZGQE5IPWWgSXl5OXIyGejz+8/jM69Uy0AfDAigGRno89JLL3WfWdvb22GgiRMnojfHelq1CmDWuLg4uR6awBAY0MjAiMe/Of/TecNSq6qqwnBBBkZAq9ghMtAEAxSM5GSgz9mzZwcMGECzkoglrMxaXV29c+dOaHX37t3WC0RBJB8NHrMzZ96B9JHbsqrrW+QkTdBXBufR4La2tpiYmLFjx65fv76mpsZJq6AHjwYviCmevS99fHRmcqnJIVkeDSYkdAkrsyYmJvbp0+fJJ58cN24cGjZYsGBBS8ttnUSyWX8349TptNz/M/tUUU2jnKRJ0JoVVffVV1+97777xowZI0ocwCidnZ3iD3rQrL2/Tf4pPuu5FWf3pJvsOpqVkNAlrMxaUlKCxmwlOjoaaQ1mRaxZpx8sWHqyJDPv8g9nSibvyyura5YzdAhas2LYJEvaQm1tbY+bdVFsMXLW85eKtp4v/vjngvSr8ny/OjQrIaFLGF7B5JaINSsS1trGVvSSra2tf5ibkFpm0tUGrVm90lNmvW9JYlz+DXwdP9Jv3UWDtJVmJSR0oVlVCQOzLjt1ZfaRyxU3tdNWmlWLqIQy7OeimkaaVQaERBg0qyqhaFb07/jX1NouzIopyKUM0laaVQvHThZm3ZpyDaWgu9tpVkJCF5pVlVA0679NOoGEFR9oVgP8ZVZ8QNq6/rzeT9GshIQuNKsqIWfWZaeuTNiT29h6e4kOsy6KLV4YW1xa29T1J6rQrOpsTqqYuj9fXCnmMOuac+VzjxVlVWg0NJqVkNCFZlUl5MyKhFV+uvvphuLiGvFZEZpVHetRAYdZwdCfsrTSVpqVkNCFZlUlbMw663Ah0lmt65hoVkWi0yrH7sopuSEPCdCsMiAkwqBZVQkhs7a0daATR1cuY5cn8vf+NlkrbaVZFXG6r8lq1tVnyxfEFKsfEKZZCQldaFZVQsistY2t1oQVOJkVXbxW2kqzqoCEdXR0tiNhBVazAox1sNtl4A2alZDQhWZVJVTM2tresT31Wr91F2XchZNZgVbaSrOqgITV6fmRTmZdfvrKvONFBdUNMraFZiUkdKFZVQkVsyJh/d2MUzK4A81qgN/NCibsyVVMW2lWQkIXmlWVkDBrU2v74ezrL65Ok/EdXM2KLn79+auKb7+hWb0SX1jbb91FpwPsrmZdEV+6IEbpriealZDQhWZVJSTMipzJNWEFrmYFSFsVn7pHs3oFu931VUKuZgWKaSvNSkjoQrOqEn5mRRcflVCmkrbSrPYgYX3hh1TXK8JoVhkQEmHQrKoEv1lb2jqO59Y8viJJxhbcmhUoPiyeZrVHvPZABhbcmlU8Bsvrhdk0KyGhC82qSvCbFQnrH+YmyOBuPJl14t68tYnlNQ1uZlmhWW1Iv1r/yPILt5puvwbYCbdmBUhbZx+5LAMP0KyEhC40qypBbta29o6zxXWPuUtYgSezApWHxdOsNnhKWIEns845evsdRJ6+JaBZCQldaFZVgtysNgkroFkN6D6zAvGCPxm4g2YlJHShWVUJV7OO3JEdlVBW3+zmYKYDmtUT2O33Ljp3092hYECzyoCQCINmVSWYzdre0Zlxtf7Piz0qxMaswOvD4mlWTzjegOsWG7MuiCmGWcU7/txCsxISutCsqgSzWVPLbtkkrMDerGN25qw+W97S1iFjF2hWVzo7O+HU3804VdfoMd23MSuAWSfsyZWBCzQrIaELzapKGJsV2KetNKsr0KrTaw9coVllQEiEQbOqErRmhVbvW5IoAw/QrAZ0t1nBslNXPMmVZiUkdKFZVQlvswKbd5zRrE6I48Ay8AzNKgNCIgyaVRWaVQb60KyeoFkJCUtoVlWC06zxhbWeHgBkhWY1IABmbW7rWHqyZMzOHBlboFkJCV1oVlWC06xx+Te8JqxAxazV9S2T991+2KGMLdCsVm42td276FzJDe9vgvNqVoDRDMY0MrBAsxISutCsqgShWc8W1/Vbd7G8zsuz3YGKWcEED69hoVmtKCasQMWs8HRUQhnGNDK+A81KSOhCs6oShGZFwtr722QZ2KJo1pqGVnTxrnKlWR2U1jYpJqxAxaxg/fmrrmkrzUpI6EKzqhIJZgVIW12fukezOvD0Bly30KwyICTCoFlVCTazxubf6L8xI7+6Qca2qJu1rK4ZZo1KuKtPp1kF5XXNz0alpF+tl7E3FM1a09C6Ir501uFCGXdBsxISutCsqgSbWfekVykmrEDdrABmdUpbaVaB/WsPXFE0K3BNW2lWQkIXmlWVoDJrfGHt6Ojs1DLVfpNmNSCQZq242bzs1JWZhwpkTLMSEsrQrKoElVmRsPZbd1EGCmiZFf6AWa0PO6RZQX51A/b52eI6GSugblaAHW4tU5qVkNCFZlUleMx6rrhu/O5c/C9CFbTMCpzSVpoVeH3tgStaZi250bT89JX5MUUipFkJCV1oVlWCx6y6CSvQNWv2tV9h1jXn5FMjaNbL1xuHbb10NOeuU91e0TIrsJYszUpI6EKzqhJRZgUwq+ORtjSrysOZXaFZZUBIhEGzqhIkZo0vrJ28L+9EXo2YroiBWeGSuceKtiRX4HOEm7XkRtPYXTn7MrX3gK5ZsaDFcSULYorxmWYlJHShWVUJErM6XeeiiIFZwbI7b2KJcLOaJaxA16wAaau4mYpmJSR0oVlVCQazJpbcnHmoYH9mtZyqDM1qQI+YtaC6ATnrivhSmpWQ0CWszJqTk/NFF6tXr5aT7hAeZnX7GDwVzMyaUnZrztHLW5IrgtasTU1NosSBnHQ3vps1v7ph6v78zUm3j4rrYmBWIB5aSbMSErqElVlLSkrQmOfMmYP+VE66A81qYFaAtBVLDFqztrS0oMSBp8L13ayK7+lzC80qA0IijDA8GoyeNCzNejD59j2me9JNDGds1rPFdVjoxl8uB/nR4G4y6y+Zt/e501OU1TEzq3hSR9SpyzQrISEKzapKj5v1k92pZgkrMDYrQKL8+qrEyDTrT/FZ6g9ndsXMrABp68NLE2hWQkIUmlWVnjXrL/lV0/ZkintgDPDFrIklN6fsubQrqUTG+oSoWS+V1328O31FfKmM9TE2a351w6Q92d+eyJGxETQrIT1FZJkVTR3JnxmHUovxTwZGZGRkwM0y0GTB0bwx2zNkoE9WVtb169dloM93pwoHbUiTgT4vvvhiD5r1xIkTcj002ZJY/PjyRBkYkZubC7nKQJODaaV/XviLDIzIz88vLy+XgSZ5ZVWLD5nXt9jY2Ndff51mJRFLZJn1iy++gGDM+GhPJv7JwIi0tLSqqioZaPLFoezRWy/KQJ/09HRkMDLQZ0Vs3oD1KTLQp2fNeuzYMbkemmz8pfCxr8/JwAgMaEpLS2Wgyb7k4j99mSADI7Kzs0tKSmSgycms0v+Yc1oG+kRHR/fp04dmJRELjwYrkVp26+P92fiXWHJTTtLH+GhwVsWvn/6cu+6X24/mMcOXo8EgNrdqws5M3Qc/OUBxhNzR4JIbTQuOF356wKfVNj4aDDLLbw7blGLw4CcHxkeDaxpal58q/tePSdFplXKSPjwaTCKZsDJreXn5rl27Fi9e3Lt3b3yIiYmRM3w26+2H6G5Lvv3vzqN0DTA267JTV4ZtuIBUQMb6+GhWdNCLfr5o8OwnQfeZtaWlBQUNULjiA6bIeV0Ym3VPetVzK85CjTI2whezNjY2HkzMNr7hBxibFePIP86PP52Wq/tuHys0K4lkwsqsaWlpYyzMmzdPzvDNrOlX62HW72Kz8e/jnwsQyhmamJk1+9qv844XLT2W3bNm3fZLru6r6xx0n1kbGhpkYd8BU+S8LszMevVm8/LTVz7Zn9WzZo1Pzzd4wY4DM7PWNbatTSx/f0dG0qWCtzdnHszSfuCXgGYlkUwYHg12iy9mRZ4Ks4prgx0P/DPAzKy30+U9uXV3nhtshu9mraqqMnjHjqD7zOoVM7OKLUW76FmzlpWVIX00ThzNzCoe5SiuDS6qafzdjFNyhiY0K4lkaFYvIENFnro15Zow6/7MaoTJpSYH2WjWwBPqZr18vRGJo1na6rtZK2+1vLkhwyxtpVlJJEOzegFWQ56KD8Ks+CAe+Nc1Uw8Ds4rH8ayILw0Gs8YX1o6OzkbPK6cqE1pmrbjZHJVQNvNQQTCYFR9QB8zSVgOz1ja2YhA5fPslx/2smGKWttKsJJKhWb3Qs2aFVvEPH4LBrPiAZM7gmUShZVbHe/oi0KyOhyTTrIT4As1qR8mNJsd7ThxmRTh2Vw5mdf2JBrpmLatrhlbFQ2uDxKyx+Tf6b8zIr77rKiGvhJBZaxpaV8SXTtybh89BYtbyuuZno1KyKrR/R9es9c1tSFjf2pCBzw6z3mpqe2T5BYOr9mhWEsnQrHYgNxUJK3CYFZi9c0bXrEiXRcIKgsSsQLyJRXxWJITMai3ZIDErMEtbdc1qLVmHWYFZ2kqzkkiGZvUIslLkpo4Xc1rNui+zyiBtpVkDT3iYVaStuomjv8wq0lbd8+s0K4lkaFaPoIdFPyuDu80KDNJWLbPWNLRO3pfnyJiDx6xni+v6rbuIvl6EKoSKWW82tUUllGG3izB4zAoMboDRMmtDS/ue9Kr+G28fCgZWswKkrf826YQM1KBZSSRDs7qnur5ldHS29eluTmbFLPxB5a27nvhjj5ZZHVdOCYLHrMBxnYsioWJWp2vTgsqspbVN9y46p3WYRMusTtemOZkVY44/zE2A3Ts6OuUkb9CsJJKhWd3jlLACJ7MC/IHW/Z3qZm1sbf9wb953Cb+9vyyozBpfWPvI8gu3mtpk7I2QMGtzW8fSkyVjdv724ragMivQPd+pbtbW9o7tqddeXJ0mYxezCpC2Yh1k4A2alUQyNKt7etasTgkrCCqzAvE8ARl4IyTMih2O3S6DLiLHrK7PAKFZCfEFmtUNvza3D99+yek1465mxR+8uSEDfyxjbyiataHFOWEFwWbW9Kv16mlr8Ju1qbUdCev0gwUy7iLYzFrX2PYfn59Rd5uiWUXCOmhzpoy7cGtWeL3kRlNnp9IBYZqVRDI0qxswfndKWIGrWYHrYN8GRbMiXXZKWEGwmRWop63Bb9bZXY+QlMEdgs2sAFpVv5JI0axu67BbswLIVVHtNCuJZGhWN9CsTtCsZtCsMiAkwqBZnRm0OXN76rWWtg4Z38GtWV0v/bCBZg08YWbWzs5OiE3xbGt3mFUckcb/MvYMzUoiGZrVGfQy6GtkYMGtWQH+WPHJCSpmHbMzZ/XZ8mYXrwehWds7OhOK6v682Lu3gtysC2KKYdbGVueiCUKzChTTVhWzerpWwJNZgWLaSrOSSIZmvQtkn8hBkYnK2IIns+KPD2dfV0lbVczqek2yIAjNCpC2qjx1L8jNCq3inwwsBK1ZRdrqNXFUMaun69ttzCrSVq931tKsJJKhWe8C2afbhBV4MitQfOCfV7OO3JEdlVBW3+ymxwxOs7a0dZwtrntsRZKMPRDMZl126gq06jYJC1qzApUbYLya1eZpJzZmBfB6UU2jDDxAs5JIhma9i541K7IHtwkrCE6zApWHxQezWT0lrCDszYrKNtTDEzppVkJ8gWb9jeHbL21NuebpIJuNWcXrt/B1GXuAZg084WrW1LJbXu8n7j6zpl+tfzYqxf7Z0TQriWRo1t9A3onsUwYu2JgVqKSt9maduDdvbWJ5TYN7/wWtWVvaOo7n1jxue0A4aM26KPb2tUsVN90bIpjNCrxeSWRvVvvXDNubFYjHCMvAHTQriWRoVolIWN2e4xTYm9X61mhP2JvV0zXJgqA1K0APi15eBu4IWrNOsLynz5UgN6t4DJZN4mhv1mV3v37ACa9mzar4FWlrTqXHraNZSSRDs0rsE1Zgb1aAr9vf32lj1pmHCqISyqrrPb45J5jN2tTabn91dHCadUV86YKYYpvEK8jNCuzPd9qYNTqtctrB/OxrHtfNq1kB0tZUzy9tpVlJJEOz3gYJ6/rzV+2PrXk1K75uf7bVxqz2CSsIZrMCbLtN2hqcZkXC6vpEDivBb9b4wlrUHE9Hs23Mig13fTKGFRWzni2u678xI7+6QcZ3Q7OSSIZmvQ1yTfuEFXg1K7B/LBHNGnjC26zA5nxnd5sVoLZ7SltpVhLJ0Ky36VmzzjxUsPz0laseMg9BkJvV7ftSHAShWbHD5x0vKvCQbwnC1az7M6s//rkg/Wq9jN1BsxLiCzSrvCjX5hynQMWsdY1t+KmRO7JlfDeezGpzE62DIDcrsElbg9Csbh/O7ERImPVozvW3N2e6fdqDJ7N6TViBollj828M23rp8nU3aqdZSSRDs9qNu62omBXgpzzd3+nWrAtiitHTeX1WXPCbtaWtY/XZcreXmwabWbGe2O1ZFV6qfUiYFXhKW92aFWO4mYcKEktuytgDimYFnpoPzUoimUg36+R9eSviSz3dRWpF0az4qaiEMvysjC24NavXa5IFwW9WgLTV7cPig82s0L+nJ3JYCRWziocUug7O3Jp1tru3+riibtZ9mVVjd+W4XmZMs5JIJtLNan/ngBVFswIkEG7TVpo18ESCWYHbahwYswK3lynQrCSSiWizzjl6eXFcSZW3M6wCdbPebGrDz04/WCDjO7iadVFs8YKY4tJaL4eCQUiYtbmtQ5zDc3ojW1CZdUtyxdxjRV4PBYMQMuvaxPKp+/PL7n5qhKtZD2dfh1lPFnivxlpm3ZxUMe1gvtPtNzQriWQi2qyeTlC5Rd2sAD/rejmPq1ndDvbdEhJmFbg+LD6ozKqYsIIQMitwPd/palZo1eaZU1a0zApcD73QrCSSoVl7zKxRCWXo5hRXIITMKrrvJkvaGjxm3ZpyDeumePw/zMwqElbFkRzNSogvRK5Zl3l+MadbtMyKn8WPL4gplnEXTmb1dFGlW0LIrACjCuuODR6z2rxNyJXQMqvrQM3JrBNsH5LshK5ZsVfx49brmGhWEslErlm1ElagZVYAtTilrVazbk6qcD0xZkNomXX6wYKlJ0ua2zpEGCRmFU9I8HrDiYPQMitwOrlgNevJghuzDhcibRWhV3TNCpxuy6ZZSSQToWb9LqF08r48lZttHOiatbG1/cO9eViQjO82q1bCCkLLrMCatgaJWb0+QtKJkDOr0wVxVrMiYfX6ZAwrBmZdEV9qfawVzUoimQg1K/p9rYQV6JoVOKWtNGvgiSizAuv5zgCbFVj3MM1KIplINOuW5Irh2y95fZyhEwZmbWhpF2/REaHDrNFplTYvnXZLyJl1zM6c1WfLxftug8Gsh7OvT96Xl1yqMZoJRbOKR3qJt984zBpfWDvzUMHRHI36Y2bW5aevLI4rERWbZiWRTCSa1ZpOqWNgVoAFOR6e4DCr2/v67Qk5swLHgYFgMKvTWUAVQtGswJG2Osyq8pBkJ8zMChxpK81KIhmaVRV/mVU8Qt3tQ8xtCEWzDtqcuSmpAol7j5sVSdvo6OxzxXVyqhrhYVak6UjW92dWi7mK0KyE+EJYmbWzs7OhoSEjIyMuLu7MmTMlJSWYImY5zIpm/+aGjF+b5flOdczMigWJvqa1vUOYVfeaZEEomhWIje0+s6J8sUvz8vJQ4iA3Nxeho9CBMKv17KM6IWrWmYcKohLKrt5sFmZVfzKGFWOzzo8pWn769hsmaFYSyYSVWdEZnT17dsqUKe+///748eOXLl3q6BkdZnV9QpAiZmYViIXSrH6no6MjPz8fnThKHEyfPr2goKCt7fbJXUEEmhWIQ989YlaAoSSWSLOSSCaszFpYWPjll18uWbIEGkhPT4diN27cKGYJs6J7RacjLqvRxRezYqGHs68XFBadyq9BvyMuMNEiRM3af2MGuvhn/vFiN5kVAli2bNm4ceOwegAl/s0336Cs5ewus36/OwZ20T2xDULXrBP25CJtzSwsPV9wDZ/Vb2N14ItZkTQvO3Vl6Psf0qwkYgkrsyJhRSebk5ODzw0NDQcOHBgxYoSYJczqOOVpgC9mBb+bcSotO//fp8cZJKwgRM0KkLb+/q/PdJNZ6+vr33zzzQsXLogwJSXlrbfeQq4mQgCz/l9DowwSVhC6ZgUYwH0fk/H6qkSDhBX4YlaAocz/fmYIzUoilrAy64kTJ4YOHSo2p729HR1u3759xay6W/X/7yMvIncUoQHZXchAnxdXp/14Muv571MMElZQUFCALFwG+hw9ehRDDRnoU1JSkpxsuOuQtv5/fUdk5hbK2K9gwPToo49i2CFCfHj88cfLy8tFCJ4fMr7Xp7sMElYAL8bHx8vACHzd2M3V1dWxsbEy0AeJ4/yDGaN+SjNIWAH2JOqMDPRZEFP8x7c/Wb1tr4wJiTDCyqwxMTH/+te/RHLW0dFx8eLFv//972KWuEYXmZMxn3YhAyP+fXrsubRMGWiycOHCyZMny0Af+ObkyZMy0GflypXvvfeeDPT588c70kpqREH4F5j1oYceQoIlQnzo1auXNdW7b0nijydS5Xposn79+n/+858yMAJfx4/IQJMdO3a88MILMjDimeVn5u1NkoEmP//8M+qMDIx446uD3xzPksVASIQRVmaFPIYPH47BPj63tLQgY0DXJmbdampDJ/tKj/KXL0+99M+3ZBBhFBZ2S85669atZ555xqFSZKsYS1nTxLc2ZCBtlSsRYTzy8aZnR34ig55g3759shgIiTDCyqzJyclTp049c+ZMW1tbTU3Npk2bEMp5JBxpaGgYOXLk/v37UeLg0KFDo0ePFkMrQgjpKcLKrEhWVq1aBZtCsYcPHx4zZsyJE+aXLJHgp7W1NTo6esCAAShxMHTo0F27dvlyRpkQQnwnrMza2dlZVlY2b968l156adCgQTt37rQ+NICEHyjfpqam77//HiUOVq5ciZCFTgjpWcLKrG5BPyv631tdiJ4XyNkK4Cs3u3BcKaMOFtTW1oYsSiy9sbGxo6NDa+n4eyy3vr4eX0dJtbS0aH3dAdYBm9B+52U7imBxYtsFBukgloitxspjE7Ah2Bw5ozvBLnLsNIN9jlRYbK9Z03BsMsAeQwXQWjr+GLsdi8bXsQmofmY7TdR5/JSM1cDKi20X4BfkDGWwtli02Pn4oFvlCAkDIsKs6CDmzJnzZBdffvklQq2ebsmSJQ8++OCf/vSnb775Rk5SBr3qyZMnR40a1bt37+eee+6jjz7KycnBRDlbgcuXL0dFRb3++utPPfXUgAED1q9fb3BrKVQxfvx4bMIlzftKf/zxx3vvvRebL5g8ebKcoQY62YyMjBkzZjz77LN9+vT59ttvje+L1QI6WbFiBbJYlPjUqVMLCgq05BQXF4eNve+++/71r3/JSTpcuHBh2rRpL7zwArZ6zJgx8fHxEIycp8CNGze2bds2aNAgrHy/fv2++OILgxtbUccWL178yCOP7Nq1S05SAzXkP//zP0VxA9Q6OUMN7Gfs7aVLl7744ouo8HPnztWtcoSEAeFvVoydoQf0U6VdvPbaa5s2bdIdyANo1cCs2LcDBw6MiYmprKy8fv06esn33ntP6xKb3bt341vJycn4empq6uzZs7/++ms5T5kjR44MGzbMzKyQhAz0uXLlyj//+c/Vq1eXl5dXVFR89dVX+fn5cl53sm/fvrfffvvs2bMocZgVlsX+l/OUOX78uJlZp0+fvn379uLiYhQZduC4ceNSUlLkPAVQRhjBnDlzBqOQkpISDOwmTZok5ymDbce3/va3vxmY9ZVXXpGBPteuXZs4ceK8efNyc3Ox/mhrqHtyHiERQ/ibFc178ODBjlv+kUEOGTLEYJPNzOoENI/UzfooAy2QiOzYsQM9l4zVQI7+1ltvJSYmijsU5VQ1fDTr559/vmbNmpqabrmZ1QbIbP/+/djb+IzhCByTlaV9b6WxWa00NjaOHz/e+JkPIgVEnZGxGqjeKLXo6Oj3338/wGZdu3YtxjFYZxkTEpGEv1mhMRjF8WBCpBFPPvmkwdkjv5gVXh85cqTZEdHW1tb09HTkr99++62cpMb8+fOjoqKwyU8//bSBWZHp/vWvf33kkUdGjBiB5FvrtNlrr722dOnSl156qVevXmPGjMH6ax0JN6Zv375QqVhWXV0d8vWkpCQxSx2/mDUtLQ2Sczx/UQtoFTn38uXLkQTLSWqsW7cO3yoqKsKiDcz6xz/+8aGHHnrggQfeeOONLVu2aJX4Rx99NHPmTAxeH3744YEDBx47dszg6gRCQp3wN2tZWRnEIB7MBPABvQbSOBGq47tZc3NzkQ1ATgZ9DTq4Bx98EL0V+kr0tnKqApmZme+88w6+gm7awKziCqba2trLly9v3bp17Nix27Ztk/MUePbZZ5E+wmrFxcXz5s1Dn4vfkfO6k2eeeQZeEWfT4dfBgwcjZRez1PHdrNhqpMsbN27EDpSTlMFOQ4mjrmJ0opUCFhYWopIkJCTAiAZmdVzBVFFRgT0wdOhQrWqPGgKtHjlyBNu+YcMGjAl8eUYjISFKJOasTzzxROBz1tTUVGj16NGj2Nta108JYDiseXx8/CeffKK1Gu+99x76aHwdCzUwqwDfhZix06BVpJ5yqgLIHZOTk7F0fL2yshL5utYZR2OwXGypyFkhCYwtDLJGH82KgdTo0aNXrVqFDTcocaw8fIyB0YIFC7QeeDJ//vxDhw5hq7FQA7MK8F2AIaD1EaEqTJw4cefOnajkKHGsP4ZTa9eulfMIiRjC36zo1wYOHOhIWTCWHzRokMEm+2LWEydOvPHGG4cPHzbTqgBfxNc3bdqkdYHuI4888thjjz311FPQ6h//+EcMMoyvIWpqatqzZ8/7778vYwWgYQhGGA797IgRIyBaMatbgdLE3sbnjIyMCRMmQFFiljq+mBX1DduObPXq1avGt50It2FM9vLLL8tJCmAY8be//a13794o8fvvv79Xr17YFXKeJig41JbnnntOxgosXLgwJiZGXAuN/Q/Nr169WswiJHIIf7Mi0/r+++/R1aKPA0OGDEEaYXA81sysSNe2b9+ObDUuLq6xsdFAq7Dyli1bKioqkIX88ssvyFm1rg1Gyl56ByTrJ0+exCrJeQqcOXMGOQe+i6QfPeakSZOw9+Q8BZC+iMtE8fWVK1dOmTIlMNcGI7ceNWoULI4S/+yzz7766it8kPOUMTbr0aNHhw4dinW4fv06Ujc5VZnLly+vWLGipKSkoaEhOzsbrtK6NriqqkoUNxg/fvyaNWu0Gjh21OLFiwsLC/EtJKzIQefMmSPnKRAbG4uvY/yKEt+7dy+SZmOvExK6hL9Z0bVVV1fPnj27Txdz585Ff6dlOCgBw/+uu/sexAeEcoYC8Ppf//pXJIuOxBEUFRWpd7g5OTnLli176623XnzxxeHDhyMNsr5/VAssWvdoMHpY9PIDBgxA2jRy5MitW7c6jqurADfAxAMHDsTKjxs3DiMDrTs7jUGVxvjj9ddfR4lPnToVftJKHOPj47GvkPn96U9/wgfHW34VGTRo0L333vvwww87ShzDI5G4q4Dqum7durfffvsf//gH/l+0aJHxq1INjgbX1dWhjg0ePBi7DgML1D2tC+5QvlgiqgpK/N13392/f7/jHX+ERA7hb1ZIFBqDjaAoUFlZiVDLrPguhORAS2zo0OXXLCBjVl8B/DHWGakeMj8oGWIzSIME+BFdsSHBRUdfUFCApRcXF6OX1E27MY4RX4cezLJ2A7AUrDa2FyWOrF2cZpbzFMB4SBZVF7ov6sHfy2/eQWu/wcE1NTXYaVh5/BRK3/h4MrZd9+IpLAt1DMsVS8du1K1v2FhUVFFdsSeNqyshoUv4m5UQQggJJDQrIYQQ4k9oVkIIIcSf0KyEEEKIP6FZCSGEEH9CsxJCCCH+hGYlhBBC/AnNSgghhPgTmpUQQgjxJzQrIYQQ4k9oVkIIIcSf0KyEEEKIP6FZCSGEEH9CsxJCCCH+hGYlhBBC/AnNSgghhPgTmpUQQgjxJzQrIYQQ4k9oVkIIIcSf0KyEEEKIP6FZCSGEEH9CsxJCCCH+hGYlhBBC/AnNSgghhPgTmpUQQgjxJzQrIYQQ4k9oVkIIIcSf0KyEEEKIP6FZCSGEEH9CsxJCCCH+hGYlhBBC/AnNSgghhPiP//mf/x+b2f8lpQGQIwAAAABJRU5ErkJggg==" data-image-state="image-loaded" width="314" height="222"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257px 8px; transform-origin: 257px 8px; unicode-bidi: normal; "><span style="">For n=2, output should be 3 &gt; as there are 3 possible routes with exactly 2 peaks.</span></span></div></div></div>

After succesfully completing the French Conundrum, you have decided to take a vacation.
Your trip is amongst the mighty mountains of Canada and whilst planning your trip, you come across a situation - 
Due to the terrain of the mountains, you are confined to move forward in diagonal directions (North-East and South-East). And to avoid the risk of falling off (below x-axis is the death valley) or an accident, you have to take one step at a time.
The geographics of the track are similar to the previous problem, in a form of a 2-D rectangular lattice spanning from (0,0) to (2*m,n).
In order to plan the route of your trip, it is necessary to visualize all the routes. To fulfill the necessary requirement of visualizing the routes, you, now, have to count the paths with exactly n number of peaks (local maxima); from your initial position (although relative, consider it to be 0,0) to the end point (2*m,0).

You being an avid mathematics aficionado, are compelled to solve the problem.

Given two natural numbers, m and n (<=m), find the number of routes with the mentioned restriction, to prepare a strategy.

Example: All possible pathways for m=3

For n=2, output should be 3 > as there are 3 possible routes with exactly 2 peaks.

Solve

Solution Stats

4 Solutions
3 Solvers

Last Solution submitted on Nov 27, 2022

Last 200 Solutions

Solution Comments

Show comments

Problem Recent Solvers3

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 56433. Canadian Conundrum

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers3

Suggested Problems

More from this Author30

Problem Tags

Community Treasure Hunt

Problem 56433. Canadian Conundrum

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers3

Suggested Problems

More from this Author30

Problem Tags

Community Treasure Hunt

Players