Problem 57949. Easy Sequences 106: Counting Pythagorean Triangles inside a Circle

Created by Ramon Villamangca

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:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Pythagorean_triple\"><w:r><w:rPr><w:b/></w:rPr><w:t>Pythagorean Triangle</w:t></w:r></w:hyperlink><w:r><w:t> is a right triangle all sides of which are represented by integers. Examples are triangles with sides </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[3\\ 4\\ 5]</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[5\\ 12\\ 13]</w:t></w:r></w:customXml><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>Our goal in this exercise is to </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>write a function that outputs the maximum number of </w:t></w:r><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>unique</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> pythagorean triangles that can fit inside a circle of radius </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R</w:t></w:r></w:customXml><w:r><w:t>, with overlaps are allowed.</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:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"181\"/><w:attr w:name=\"width\" w:val=\"195\"/><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 example if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R=12</w:t></w:r></w:customXml><w:r><w:t>, the following unique pythagorean triangles can fit inside the circle: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[3\\ 4\\ 5]</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[5\\ 12\\ 13]</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[6\\ 8\\ 10]</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[8\\ 15\\ 17]</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[9\\ 12\\ 15]</w:t></w:r></w:customXml><w:r><w:t>, and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[12\\ 16\\ 20]</w:t></w:r></w:customXml><w:r><w:t>. Hence, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R=12</w:t></w:r></w:customXml><w:r><w:t>, the function should return </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>6</w:t></w:r></w:customXml><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>--------------------</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:rPr><w:b/></w:rPr><w:t>NOTE:</w:t></w:r><w:r><w:t> Unique means that congruent triangles, even if rotated or reflected, are counted only 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<div style = "text-align: start; line-height: 20.440001px; 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: none; white-space: normal; "><div style="block-size: 400px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 200px; transform-origin: 407px 200px; vertical-align: baseline; "><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; "><a target='_blank' href = "https://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean Triangle</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: 0px 0px; transform-origin: 0px 0px; "> is a right triangle all sides of which are represented by integers. Examples are triangles with sides <img src="data:image/png;base64,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" width="50" height="19" style="width: 50px; height: 19px;"><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 0px; transform-origin: 0px 0px; "> and <img src="data:image/png;base64,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" width="65" height="19" style="width: 65px; height: 19px;"><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 0px; transform-origin: 0px 0px; ">.</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: 0px 0px; transform-origin: 0px 0px; ">Our goal in this exercise is to <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 0px; transform-origin: 0px 0px; ">write a function that outputs the maximum number of <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 0px; transform-origin: 0px 0px; ">unique<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 0px; transform-origin: 0px 0px; "> pythagorean triangles that can fit inside a circle of radius R<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 0px; transform-origin: 0px 0px; ">, with overlaps are allowed.</div><div style="block-size: 187px; 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 93.5px; text-align: left; transform-origin: 384px 93.5px; 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 0px; transform-origin: 0px 0px; "> <img class="imageNode" width="195" height="181" style="vertical-align: baseline;width: 195px;height: 181px" 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CV1vgfxN/ZN59gvXxZztwxPET+v0Pf8AOvOxuG9pHnjujvweI9nLklsz1SiiivCPbCiiigArgviH4Bl1x4vEHhmT7H4kscPDKh2+eB/Ax9ewJ+h46d7RUTgpqzN8PiKmHqKpTev5+T8jkPh545TxjpMiXcf2XWLFvKvbUjBVhxuAPOCQeOxyPc9fXlnxF8PX3hvXI/iD4STFzb/8hK2X7s8XdiPoOfoG6gmu/wDDfiGx8U6Db6tpcm6GZeVP3o27q3oR/wDXqKcnfkluvxOvGUIOKxNBe5Lp/K+3+XkalFFFbHmhRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABVbUNQttK024v7+VYba3jMkkjdgKs15R8RLufxr410/4f6XIwt1YXOqyofuIOQp+gIP1ZPSs6k+SN1udmDw/1iryydorVvslv/XcZ4G0+6+IHjKbx7rsTJY27GLSLV+ihT9/8Oef7xP8AdFetVBZWdvp1jDZ2USw28CCOONRwqgYAqeinDkXmGMxP1ipdK0Vol2X9b+YVS1f/AJB7f7w/nV2qOsf8g8/7wrDG/wC7VPRmFH+JH1Ofooor4E9sKsWl5JaSbk5U/eX1qvRV06kqclODs0KUVJWZ1NvcR3MQeI5HcdxUtcvbXMlrKHjP1HY10VrdR3cW+M8/xKeor7HAZhHErllpL8/Q8mtQdN3Wx4n8dvD32fVLPXoEwl0vkTkD+NRlSfquR/wGvJa+rPHPh8eJvBt/pyqDOU8yD2kXlfz6fQmvlMggkEYI6g1x4+lyVeZbM/WeEsd9ZwHspP3qeny6f5fIKKKK88+vCiiigAooooAK7v4PaP8A2r8QreZ1zFYRtctkcZHyr/48wP4Vwle7/AjR/s3h2/1aRcPeTiJCf7iDqP8AgTH/AL5rrwdPnrRXbU8DiPF/VcsqyW8lyr56flc9F1//AJFrU/8Ar0l/9ANeHV7jr/8AyLWp/wDXpL/6Aa8Or9Ay74JH865h8UQooor1DzQooooA9N8B+J/t1uNLvnzcwr+6Zj/rEHb6j+X0rtK8Ct7iW0uY57dzHLGwZGHUEV7L4a1+LxBpazrhZ0ws8Y/hb1+h7V4eNw3I/aR2Z7WDxHOuSW6NiiiivNPQCiiigBGUOpVwGUjBBGQRXj0Y/wCFRfEwRjMfhXX2+XJ+W1l/oAT/AN8nvtr2KsLxl4WtvGHhe60m6wrON0EpGfKkH3W/ofYmsqsHJXjutj0MDiI0punV+Cekv0fqtzdorzv4T+KLq9sLnwvr+Y9a0Q+S6ueZIgcBvfHAz3G0969EqoTU48yOfE4eWGqulLp+K6P5hRRRVnOFFFFABRRRQAUUUUAFFFFABRRRQBieMPEsHhLwreavcYYwpiGM/wDLSQ8Kv59fbNcv8IvDVxp+hz+IdZy+r64/2iV3HzLGTlR7ZzuP1A7Vk+OifHHxU0fwbEd9hp/+m6jjp0ztP/ASB/20r1kAAAAYA6AVhH36jl0Wnz6nrVf9lwcaS+Kp7z/w/ZXz3+4KKKK3PJCqGsf8eH/AhV+qGs/8eH/AxXHjv91n6M1o/wARGBRRRXwR7YUUUUAFSwTyW8okiOCP1qKiqjJxfNF2Ymk1ZnS2d7HeR5Xhx95fSvm74qeHv7A8eXYiTbbXv+lQ4HA3H5h+DZ49MV7fFK8MgeNtrDoa5f4u6amv+DU1KJMXmlvvdR3ibAbH0O0+2DX0EcasXR5Knxr8T1OHa7wOYx/kn7r8n0/HT5ng1FFFcp+vBRRRQAUUUUAHWvrPwho/9g+D9M00rteG3XzB/tn5m/8AHia+b/AGj/25480qzZd0YmEso7bE+Yg/XGPxr6pr2csp6Sn8j8143xfvUsKvOT/JfqZ+v/8AItan/wBekv8A6Aa8Or3HX/8AkWtT/wCvSX/0A14dX2WXfBI/IMw+KIUUUV6h5oUUUUAFaega3PoOqpdQ5ZPuyx5++vcfX0rMoqZRUlyvYcZOLuj3qyvINQs4rq1cPFKu5WH+etT15X4H8Tf2TefYbx8Wc7cMTxE/r9D3/OvVK+bxFB0Z8vTofRUKyrQv1Ciiiuc3CiiigDyb4l203g7xrpPj/To2MQcWupog++hGAT9VyPqqV6rbXEV3axXNtIskMyCSN16MpGQR+FU9e0a28Q6DeaTfDMF3EY2OOVPZh7g4I+lcJ8HNXuo7DUfCOrn/AE/QZzEuT96Ik4x6gEH8CtYL3KlukvzPWn/tWCU/tUtH5xe33PT0aPS6KKK3PJCiiigAooooAKKKKACiiigAqlrGqQaLot5qd3/qbSFpnA6kKM4HuelXa81+Nuozf8IzY+HbHm81y8SBUz1UMCf/AB4oPxNZ1JckHI68HQ+sYiFJ7N6+nX8Bvwa0q4m03UfF2qjN/rtw0gJ/hiDHp6Atn8AtemVU0nTodI0ez062/wBVaQJCnHUKAM/pXmQ+JOoaH4q1Ozv0+22Md7MqjpJGocgBT3A9D+YrnnWp4WMVU6nTVjUzCvUqU/kvLZL7j1iiszRPEWmeILbztLuVlwPnjPDp9V/r0rTrqjKM1zRd0ebKMoPlkrMKz9Z/48R/vj+taFZ+tf8AHiv/AF0H8jXJj/8AdZ+hpR/iIwaKKK+DPaCiiigAooooAKjuII7q1lt5hujmRo3X1UjBH5GpKKNhptO6Pm3V9Ol0jWLqwn+/byFM/wB4dj+IwfxqnXo/xc0byr611iJflnHkzEf3hyp/EZH/AAGvOK9WnLmimfsOXYpYvCwrdWtfXqFFFFWd4UUUUAev/ATR999qesyLxEi20R92O5vyAX869trjvhVo/wDY/wAO9PDLtluwbqTjrv8Au/8AjoWuxr6jCU/Z0Yo/Cs/xf1vMqs1snZei0/4Jn6//AMi1qf8A16S/+gGvDq9x1/8A5FrU/wDr0l/9ANeHV9Hl3wSPi8w+KIUUUV6h5oUUUUAFFFFABXpvgLxP9utxpV8+biFf3LMf9Yg7fUfy+leZVJb3EtrcRz27mOWNgyMOoIrCvRVaHKzahWdGfMj32isfwzr8XiDSlnGFuI/lnjH8Lev0NbFfNSi4ScZbn0UZKcVJBRRWfrVib/S5Y01G4011BZbqBwpjx3OeCPUGoexpFJySbsaFeT+Lv+KL+M+i+Jk+Sx1hfsV6ewbhdx/DYf8AgBrhNc+IPj7w1rf2CHxIdRikAa3nFkmLhSSAV3Jk8gjIJGRwTXoOv+HfEXiL4M3p8XzJNq8afboYo4lTyNgzsOOrFdwPucdq45VVVTUU7rU+lo5fLATjOtOLhU93S97PrZpbaM9Sormfh3rzeJPAGl6hK++cxeVMe5dDtJP1xn8a6auuMlJJo+drUpUakqct02vuCiiiqMgooooAKKKKACiiigAryph/wlf7RGG+az8NWmcdjKR/PL/+Q69TkkWKJpJGCoilmJ7AV5h8E431C28Q+J5xiXVtRYjPZVy385CPwrCprKMfn9x6uC/d0K1fqlyr1lp+SZ6jXzl4n/5G7WP+v6f/ANGGvo2vnLxP/wAjdrH/AF/T/wDow15Wcfw4+p0ZL/En6FG0u7ixuUuLOeSCZDlXjYgivSvDXxYI2W3iWPI6C7iX/wBCUfzH5V5fRXi0MTVoO8H/AJHvV8LSxCtUX+Z9N2d7bahapc2U8c8Lj5XjbINVNb/48k/66D+RrwHRfEGp6Bdefpd00WT86dUf6r0NekWPxJsdbs47bUUFjdhxkk/u34PQ9vofzr1a2Y06+GnCWkrHz88sq0KilHWP4mzRQDkZHIor5c1CiiigAooooAKKKKAMfxXo413wzeWIGZWTfD7OvI/Pp+NfPJBBIIwR1Br6erwj4haL/Y/i648tdsF3/pEeOgz94f8AfWfwxXXhpbxPtuFsXaU8LLrqv1/Q5iiiiu0+7Cr2iaY+s69Y6bFnddTpFkdgTgn8BzVGvR/gjo/2/wAbvfuuY9PgZwf9tvlH6Fj+Fa0Ye0qKPc4MyxSweDqV/wCVO3r0/E+goYkt4I4YVCRxqFRR2AGAKfRRX1h/PzbbuxskaSxtHKiujgqysMhgeoIqj/YGj/8AQJsf/AZP8K0KKpSktmS4p7oz/wCwNH/6BNj/AOAyf4Uf2Bo//QJsf/AZP8K0KKftJ9yeSPYz/wCwNH/6BNj/AOAyf4Uf2Bo//QJsf/AZP8K0KKPaT7hyR7Gf/YGj/wDQJsf/AAGT/Cj+wNH/AOgTY/8AgMn+FaFFHtJ9w5I9jP8A7A0f/oE2P/gMn+FH9gaP/wBAmx/8Bk/wrQrOg1u1v3uotKb7XNbAgkKwiLjI2eZjbnIwQMkdxS9pJdSo0VJXUSxa6bY2Ls9lZW9uzDDGKJUJH4CotS1mx0nyheysJJiRFDHG0kkhGM7UUFjjIzgcZqFbO/1HS5IdalW2kkfONNmdCicfL5nDE9csAvB7dav2ttFZ2sdvbqViiXagLFiB9TyfxqHKUtTVRpw0evp/n/wCtK2qtqsaQR2kdgozJK7s0jn+6qgAL25JP0otdJgtdQnvfMuJribILTTsyopOdqrnao4HQZ9c1eoosLndrLQ5BPBMd78SbnxVrCrKbdI4dOhPIjAXJkPvuLYHbr1xjrnVXRkcBlYYII4IpaKUYqOxdWtOrbmeySXkkeV/B120XV/FHhCYkHT70zQAnlkb5c/TCof+BV6pXlWqj/hHv2jNLvE+SHXbMwTH+84BA/VIq9VrKjpFx7M78z9+rGv/ADxT+ez/ABQUUUVueUFFFFABRRRQAUUUUAc58QtROlfDvXLpThhaPGp9Gf5AfzYVS+FOnf2Z8L9FjIw0sJuGPr5jFx+hFZPx1vPs3wxmhB/4+7qKH64Jf/2Su60iz/s7Q7GyAwLa3jhx/uqB/SsFrWfkvzPUl7mXRX802/8AwFJfqXK+cvE//I3ax/1/T/8Aow19G185eJ/+Ru1j/r+n/wDRhrys4/hx9TpyX+JP0MuiiivnD6YKKKKANrRfFWoaMVRH8+2HWGQ8D6Ht/KvQtG8TafrShYZPKuMcwScN+Hr+FeR0qsVYMpIIOQR2qZRTOarhoVNdme5UV5xovjq7stsOphruEcb8/vF/Hv8Aj+dd5p+qWeq2/nWM6yr3A6r9R2rFxaPLqUJ09y3RRRUmIUUUUAFcR8UtG/tDwyt9EuZrB95x3RuG/ofwNdvUdxBHdWstvOu+KVCjqe4IwRVQlyyTOvB4mWFxEK0ej/Dr+B8y0Vc1jTZNH1m60+b71vIUz/eHY/iMH8ap16qd9T9khOM4qUdmFfQfwQ0f7D4Kk1B1xJqE5YH1RPlH67/zr59jRpZFjjBZ2IVQO5NfUPhhhoWj2emNzDBEseR2IHJ/E5NdOFxFKhWTqdT43jCtJYKNCG8n+C/4NjqqKRWDqGUgg8gjvS19TufkQUUUUAFFFFABRVFdYsn1ZtMilMt0gzIkcbMIuM/OwGFJBGASCc8VHbpqt5DdJqYhskkXZCLSUvIg5yxcgDPTAA49TSuuhp7NpXloWNQ1Kz0q1+0ahOsMe4KCcksx6KoHLH2HNV7i51O5W0bSIIFhmUPJLeb0aJeOPKwCWIJ4JXGOfSqsep+HPDYOnz61aW0qne6XuoAyknnJMjbuavWGuaTqjlNM1SyvGHVbe4SQj8iajmTdrm3sZwjzqDa7taW/rzA6TA+rjUZZbmSVBiONp28qPjBIQHbkgnkgnmr1FFXZI55SctwooopkhRRRQAUUUUAeWfGwf2d/wi/iFeG07U1BYehw/wD7Sr1Pr0rgPjZZi6+Fd/JjJtpYZR/32FP6Ma6zwzdnUPCek3hO43FlDKT7sgP9awjpVku9mepW9/AUpfyuUfyf6s06KKK3PLCiiigAooooAKKKKAPLfjf/AKTaeGdN6i61ZMj1wNv/ALPXqVeXfFj9542+H8H9/Vcn6CSHP869RrCH8Sfy/I9TFaYPDr/E/wDya36BXzl4n/5G7WP+v6f/ANGGvo2vnLxP/wAjdrH/AF/T/wDow15Wcfw4+p05L/En6GXRRRXzh9MFFFFABRRRQAVNa3dxZXCz2kzwyL0ZDioaKA33O90Tx8j7YdaTY3QXEY4P1Hb8Pyrs4ZoriFZYJFkjYZV0OQfxrw+tDStbv9Gm32UxVSctG3KN9R/XrWcoJ7HDVwcZaw0PY6K5vRfGlhqe2K6xaXJ4w5+Rj7H+h/WukrJprc82cJQdpIKKKKRB5T8XNF8q9tdYiX5Zh5MxH94cqfxGR/wGvN6+h/FWjjXfDN5YgZkZN0Xs45X9Rj8a+eCCrEMMEcEHtXoYeXNC3Y/TOG8X7fB+ylvDT5dP8vkdJ8P9M/tPxpZKy5jt2Nw/tt5H/j22veq80+D+mbba/wBTdeXYQRn2HzN/Nfyr0LUNRttLtDcXkmxNwRR3dicBQO5JrnrvmnZHy/EVd18f7OP2Ul893+djWsNQa0ba+WiPUenuK345FljDxsGU9CK5OiHxDb6XqMVnJKXlnwRbopdsE43EAHaOvJwOK9PLsylRfsqmsfy/4B8jWwzqawWp11Q3d3b2NpJc3kyQQRLueSRsKo9zVS0uNRutQkdo7WPTlBEZWRnlkPHJGAEHXj5j9Kfpukw6aJTHLcTyzEGSW5naRmI6dThRz0UAe1fVxkpK8djznBR+J/1+n4kL6ldX2lx3Ph+3SZpX2g3vmQBV5+fBXcRxwMDOeuOafPpCX01rPfzzs9uFbyoZnjiZwc7ioPPPQMSK0aKq19w9pb4NPzCiiimZHg3iHTLTWf2i5NP1KHzrWeSJZI9xXcPsynqCD2qp8TdA0nwZ4i0p/CEr214dzvBHMztEwK7CMkkZy3HtU3ivRrfxD+0FPpV68qQXMkSu0RAYD7Op4JBHb0qKTSYPhd8VLJb2KO+0yUq8U1xGCyITgsOwZT39PTNeBNX57r7W/bU/W8PUcfq3LUbaoJ+z6T93ve1/K19D0XXPiJqXhu4jg1Tw7y6gpKt3hZOOcfJwfUdqy/8AhdH/AFAf/Jz/AOwr0TVtIsdd017PUYRNC4yD3U9mU9jXhvi7wbe+FrvL5nsZDiK4A/8AHW9D/OvWqOpDVPQ/n3NKmY4WTq053h6LT8NvM67/AIXR/wBQH/yc/wDsKP8AhdH/AFAf/Jz/AOwry6isfbT7ng/21j/+fn4L/I9R/wCF0f8AUB/8nP8A7Cj/AIXR/wBQH/yc/wDsK8uoo9tPuH9tY/8A5+fgv8j1H/hdH/UB/wDJz/7Cj/hdH/UB/wDJz/7CvLqKPbT7h/bWP/5+fgv8j17WdfHjT4O+I7trP7L5UUieX5nmZ2Kr5zgev6VtfDCc3Hwx0Jyc4tQn/fJK/wBK5Lwkgk+CnilG6NHdj/yXWuh+Djl/hLopbriYflPIK2g26ib7fqfpmX1Z1sjjUm7vnX4xf+R29FFFdJgFFFFABRRRQAUUUUAeXfFP/konw7/7CL/+jIK9Rry34vjyvEngW7/546sOfTLxn/2WvUqwp/xJ/L8j1MV/umHflL/0phXzl4n/AORu1j/r+n/9GGvo2vnLxP8A8jdrH/X9P/6MNeVnH8OPqdOS/wASfoZdFFFfOH0wUUUUAFFFFABRRRQAUUUUAFb2i+LtQ0jbEzfabYf8spDyo/2T2/lWDRSaT3JlCM1aSPX9I8RafrSf6LLtlxloX4Yfh3/CtSvDkdo3DxsUZTkMpwQa67RPHtxbbYdXU3EXQSr99fr6/wA6ylT7Hm1cG1rA9Drwn4h6N/Y/i64Ma4gu/wDSI8dBn7w/76z+BFe3WOoWupW4nsZ1mjPdTyPYjqKwvGXhdfEkenkAb7e6Uv7xMQHH8j+FVRnyS1O3JMcsDi71NItWf6fiP8LwW/hrwHaNfOsCRwefO78bS3zHP0zj8K8n1n4gNrnjiwvZV26XYXCvbwOxUcHh3wCc5x0BwOBnv7tPbQXUBhuoI5oj1jkQMp/A1ly+EPDk/wDrNC076i2QH8wKulVhFuUldsxoY2lGrOtWi3KV/lfcdDEmv6PbSz3oljf52NhMyRyD03A7iB9RnuO1aqqEUKowAMCqGl6Fpui7xpVqtqsnLJGx2k+u3OM+9aFYSavpsebUkm7R2LFpeSWkm5OVP3l9a6K3uI7mISRHI7juK5Wpra6ktZd8Z+oPQ16mAzGWGfJPWP5HDXoKorrc6iiobW6ju4t8Z57qeoqavsITjUipRd0zymnF2YUUUVYjiZ/hyJvicPF/9qEYZW+yfZ/SMR/f3e2elWPH3gKDxzZ2iNefYri1clJhF5mVI5XGR3APXtXXUVj7Cm4uNtHqz0lmmMjVp1lP3qa5Yuy0S0ttr87lLRrGXTNEs7G4uTdyW0KxNOU2mTaMZxk/zqe8s7fULOS1vYVmglXa6OMgipqK1SSVjzqknUbc9b7/ADPDvG3gG48OSNeWAafTWP3urQ+ze3v/AJPG19QyRpLG0cqK6MCGVhkEehFeReOfhy+m+ZqegxtJactLbjlofceq/qPp05KlG2sT4rNMmdK9bDr3eq7enl+R53RRRXMfMBRRRQB6Z4RYL8FvFDNwBHdk/wDgOtb/AMGuPhJov/bf/wBHyVy+gyiH4E+KWJxkXC/99QoP612HwniMPwr0NSMZhZvzkY/1rqp/GvT9T9eyr/kQQ/xL/wBJf+Z2FFFFdZAUUUUAFFFFABRRRQB5b8eQYPCuk6ggy1pqkbcdhsY/zUV6irB1DKcgjIPrXCfGix+2/CzUmAy1s0Uy/g4B/Qmuk8I3v9peC9GvCctNYws3+9sGf1zWEdKsl3SPUre/l9KX8spL77M2K+cvE/8AyN2sf9f0/wD6MNfRtfOXif8A5G7WP+v6f/0Ya8rOP4cfU6cl/iT9DLooor5w+mCiiigAooooAKKKKACiiigAooooAKKKKALFlf3WnXAnspnhkHdT19iO9d1onj2CfbDrCiCToJlHyH6jt/L6V57RScUzKpRhUXvI9xjkSWNZInV0YZVlOQR9adXj+keINQ0WTNpLmInLQvyjfh2+or0DRPGGn6ttikP2W5PHlyHhj7Hv/OsZQaPLq4adPVao6CiiioOUKKKKAJYJ5LeUSRHBH610Nnex3keV4cfeX0rmafFK8MgeNtrDvXpYHHzwsrPWL3X+Rz1qKqLzOroqpY36XaY+7IOq/wBRVuvs6VWFWCnB3TPJlFxdmFZ+ta7p3h7T2vNWuVgiHCg8s59FHUmuX8Z/E3TvDfmWdhtvtSHBjB+SI/7ZHf8A2Rz64rw/Wdc1HxBqDXmq3Lzynpn7qD0UdAK8/FZhCj7sNZfgjelQc9XsfRPhLxfYeL9PlubFWieGQpJDIRuUfwnjsR+uR2rfr5j8I+Jrjwr4giv4MvEfkuIgf9Yh6j69x7ivpWxvbfUrCG8spBLBOgeNx3BrTA4v6xC0viRNalyPTYnooor0DA8z8c/DcT+Zqnh2ILLy01oo4b1KD19u/b38pZSrFWBBBwQR0r6irhfHHw9h11X1DSVWHUQMunRZ/r6N79+/qOapRvrE+WzTJlO9bDLXqu/p/keLUVJcW81rcSQXMbRSxsVdHGCp9CKjrkPjWmnZnYfaRa/s9+IjnBkvBGPfcYQf0zXq3ge2Nn4B0KAjDLp8O4ehKAn9TXh+sTs3wei02E/vr/XxGq+oESn+e2vomCFba2igjGEjQIo9gMV00dZ37JH69gPcyLDx/mcn9ySJKKKK6yAooooAKKKKACiiigDL8TaZ/bPhXVNO27jdWkkS/wC8VOD+eK5P4J6l/aHwws4mOXsppLdvwbcP0cV6BXlXw2/4p34neLfCrfLE0ovrVewUnt/wF0/75rCfu1Iy76Hq4f8Ae4KtS6xtJfk/zR6rXzl4n/5G7WP+v6f/ANGGvo2vnLxP/wAjdrH/AF/T/wDow15Wcfw4+p0ZL/En6GXRRRXzh9MFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB0eieM7/S9sVwTd2w42OfmUezf0Nd/pOu2GsxbrKYFwMtE3Dr+H9RXjtPilkglWSF2jkU5VlOCPxqJQTOWrhYVNVoz3CiuA0Tx9JFth1lDKnQToPmH1Hf8AD9a7m0vLe/txPZzJNG3RlP8AnFYuLR5dSjOm/eRNRRRSMiO4v4dMha7uZ1t44+TIxxj/AD6V5/4t+LN/qsLWOh7rO3I2yXA4kl+n90fr9Olani7wbfa/N59vqbfKPktphhF+hH9QfrXnGqeHdV0Zj9vs5EQf8tVG5D/wIcV2UK06cXGErXMpwUndozCcnJ5NFFFAgr0z4S+M/wCzb4aBqMmLW5fNs7HiOQ/w/Rv5/U15nSgkEEHBHQit6FaVGopxJnBTjZn1vRXFfDTxkPE2i/Zb2TOpWahZcnmVegf+h9/rXa19lSqxqwU47M8mUXF2YUUUVoSct4y8D2nii3M0W231FFxHPjh/9lvUe/UfpXh+pabd6TfyWeoQtDPGcFW7+49R719M1h+KPClh4psPKu18u4QfubhR80Z/qPasKlJS1W54GZ5RHEp1aWk/z/4PmeFeHQda8ceFtExuS1v5L5x2wFRuf+/P619I14h8HtEY/EvxDeSskq6Wps1kTlS5bBKn6Rt/31Xt9Rhl7rk+rPqJ0pYbC4fCy3hBX8nL3n+YUUUV1HMFFFFABRRRQAUUUUAFeUePD/wjXxk8K+Ix8kF7mxuT267cn8JAf+AV6vXF/Fjw5/wkfw+vY4V3XVmPtcGBzuQHIH1UsPrisa0W4XW61PRy2pGGJSn8Mrxfo9Pw3O0r5y8T/wDI3ax/1/T/APow17R8PfEX/CU+BdO1F33XHl+VcevmJwx/HGfxrxfxP/yN2sf9f0//AKMNeRm0lKlBo9HK6UqOIqU57rT8TLooor50+hCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACrVhqV3pdx51jO0T98dG9iOhqrRQDSasz0bRPHdrd7YdVAtZunmD/Vt/8AE/y966xWV1DIQykZBByDXhta2j+JNQ0VgLeTzIM8wycr+Hp+FZyp9jgq4NPWB67QQGUhgCDwQe9Ymi+K9P1nbGG+z3J/5YyHqf8AZPf+dbdZNNHmyjKDtJHOar4F0TVNzi3+yTH/AJaW/wAv5r0/SuM1L4ZatbMTprx36dlB2P8AkeD+Br1aiqjNp6mbVz58u7O6sLhoL63lt5l6xyoVYfgagr6VKafq9uLLXbSG6i6I0yBsfj2+orltc+C+m3W6XQruSxk6iKX95H9AfvD9a9iGDdeHtKDv5bNHK6vI+WaseSaDrd14e1q31KxbEkLcqTw691PsRX0xomsWuv6Pb6lYPuhnXOD1Q91PuDxXz1rngDxFoG57uwaaBf8AlvbfvEx6nHI/ECtb4Y+M/wDhHNY+w30mNNvGAck8RP0D/TsfwPaujA154ap7KqrJmdaCqR5onv1FFFfTHnhWP4u1tfDnhDU9WYgNbW7NHnu54QfixArYryz4y3Umr3Gg+C7Fz9o1W7WSYL1WIHAJ9skn/gFZ1ZcsG0duAoKviYwltu/Rav8AA1fgzoh0n4d21xOD9p1N2vJGbqQ3C8/7oB/E131R21vFaWsVtbqEihRY0UfwqBgD8qkpwjyRUTLFV3iK86r6u4UUUVZzhRRRQAUUUUAFFFFABQRkYPIoooA8n+Hx/wCEN+J2v+DJjstbtvtunA9CMZKj1+Xj/tma9Hl8O6JPM8s2j2EkkjFnd7VCWJ5JJxya4f4waLcpp9j4v0YbdS0GUSkgffhzyD6gHn6Fq7jw/rdt4j8P2erWJ/c3UQcDOSh6FT7ggj8K5oRim6cltqvQ9jGylVpwxkH8Wkv8S/zWv3jP+EY0D/oB6b/4CR/4Uf8ACMaB/wBAPTf/AAEj/wAK1KK19lT/AJV9x5ftan8z+8y/+EY0D/oB6b/4CR/4Vk6z4e0WKSLytIsEyDnbbIM/pXVVi65/rov90/zrzM0hGOFk0u35nThqk3VV2znf7D0n/oF2X/gOn+FH9h6T/wBAuy/8B0/wq9RXx12erzy7lH+w9J/6Bdl/4Dp/hR/Yek/9Auy/8B0/wq9RRdhzy7lH+w9J/wCgXZf+A6f4Uf2HpP8A0C7L/wAB0/wq9RRdhzy7lH+w9J/6Bdl/4Dp/hR/Yek/9Auy/8B0/wq9RRdhzy7lH+w9J/wCgXZf+A6f4Uf2HpP8A0C7L/wAB0/wq9RRdhzy7lH+w9J/6Bdl/4Dp/hR/Yek/9Auy/8B0/wq9RRdhzy7lH+w9J/wCgXZf+A6f4Uf2HpP8A0C7L/wAB0/wq9RRdhzy7lH+w9J/6Bdl/4Dp/hR/Yek/9Auy/8B0/wq9RRdhzy7lH+w9J/wCgXZf+A6f4Uf2HpP8A0C7L/wAB0/wq9RRdhzy7lH+w9J/6Bdl/4Dp/hR/Yek/9Auy/8B0/wq9RRdhzy7lH+xNJHTTLP/wHT/CrwAUAAYA4AHaiikJtvcKKKKBBWpp2p+ViG4OU6K393/61ZdFdGHxFTDz56bInTjUVpHXA5GRyK5zXPAXh3xBue909I52/5eLf92+fU44P4g1Lp+pG3IjmJMXY/wB2t1WDKGUgg8gjvX2WHxFHHU9vVM8mpTnRkZ+habNo+kxWE1414sHyxSyLh9nYN6kdM8cYrRoorujFRVkYt3dxHdY42eRgqqMsxOAB615P8OUbxn8RNc8cXCk2sLGz04MOigYJHoduPxdq2Pi/4kk0vwwuiaZuk1XXG+ywRp97YSAx/HO0f73tXTeDvD0fhXwlYaRHtLQRDzWH8ch5c/mT+GKxl79RLotfn0PVp/7NgpVH8VT3V/hXxP5uy+826KKK3PJCiiigAooooAKKKKACiiigAooooAZPBHc28kFwiyRSoUdGGQykYIP4V5R8P7qTwH461DwHqjsLS5kNzpMrnhgf4c+pA/76VvWvWq4f4o+D5PEvh9L3Stya1pbfaLOROGbHJQH1OAR7ge9Y1YvScd0elgKsLyw9V2hPr2fR/wCfkdxRXLfDzxjH408Kw3rbVvYf3V5EONsg749D1H5dq6mtIyUldHFWozoVHTmrNBWLrn/HxF/u/wBa2qxNb/4+Y/8Ac/rXmZt/uj+X5mmF/iozKKKK+LPXCiiigAooooAKKKKACiiigAooooAKKKKACiioL2+ttOtmuL2ZYo17t39gO5pqLk7LcG7bk9ZTeJNMXWI9NE4adztyvKq390n1ritf8a3Oo7rfTt1tbHgtn53Huew9hXLglWDKSCDkEdq+gw2TOUeas7Pov8/8jiqYpJ2ie5UVheFNeGtaYBMw+1wALKP73o34/wA63a8KrSlRm4T3R1xkpK6CiiisygooooAKKKKACr1hqDWrbHy0R6j0+lUuvSnrBK33YnP0U1vQqVaU1OluROMZK0jqEdZEDxkMp6EU24uIrW2luLmRYoYULyOxwFUDJJ/Csiw+22z8QSNGTypGPx5rhviZrl54j1i2+Hvhlv8ASrwhtRmHSCLrtP4cn2wO9fZ0MZ7Wlzyi0+3n5HFRwTq11TT93dvslu2QeAoJfH3xAv8Ax3qMbCxtGNrpUTjoB/Fj2Bz/ALzn0r1uqGhaNaeHtCtNK09dtvaxhFz1Y92PuTkn3NX666cOSOu/UjG4hYireCtFaRXZLb/N+YUUUVocQUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB5B4qsrv4XeNj4x0aJpdD1FwmqWqDiNifvD0yTkH1yOjV6vp9/a6pp8F9YTLPbXCCSORTwwNLfWNtqVhPZX0Kz206GOSNxwynqK8k0DULj4R+MG8M65Mz+G9QcyadeSdIWJ6Mew7N6HDcAmub+FL+6/wZ7S/4UKNv+XsF/4FFfqvxXoexVia3/x9R/7n9TW2CCAQcg9CKw9b/wCPxP8Arn/U1xZv/ur9Uefhf4pm0UUV8YesFFFFABRRRQAUU9YpG+6jH6CpFsrlukEn4ritI05y+GLZLlFbsgoq4ul3jf8ALLH1YVIujXJ6mNfq1bxwWJltB/cQ61NdTPorVXQ5P4plH0GakXQ1/inY/RcVvHK8XL7H4oh4mkupjUVrXlnpumWj3WoXRhhjGWeRgAP06+1eWeKPHa3jNa+H43trfobhifMk+n90fr9K3jk2Je9l8yPrVPobuv8Ai6z0cNDDi5u+nlqeEP8AtH+nWvONS1W81e5M99KXb+FeioPQDtVMnJyeTRX0GEwNLCr3dX3OOpWlU32Ciiiu8xL2j6rNo+px3cHO04dM/fXuK9r062bVdPhvbNkeCZdyNu/zzXg1d98MfFn9mah/Y99Ji0um/csx4jkPb6N/PHvXBicBRxMlKe67G0K06atE9IXRJz96SMfTJqRdC/vT/kn/ANeteis45ThF9m/zYPFVX1M1dEgH3pJD9MCpF0i0HVWb6tV6it44DCx2giHXqPqVl020XpCv4kmpFtbdfuwRj/gIqWit40KUfhil8kQ5ye7EChfugD6ClorM8ReILDwxodxquqy+XBCOAPvSN2VR3JrXSKCEZVJKMVdsyPiD40g8FeG3uvlkv58x2cB5Mj+uPQdT+A71nfC/wZN4e0ubVtbLS69qp867kk5aME5CfXuffjsKw/A/h+/8beIh498YRbUz/wASmxblYkB+V8fqPU/N6V6vWEE6kvaPbp/mepiZRwlJ4Sm7yfxv/wBtXkuvd+gUUUV0HkBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVkeJvDOneLNDm0vVot8UnKOPvRP2dT2I/wDrdK16KTSasy4TlTkpwdmjyXwj4l1HwDr6eCfG8u61bjS9Sb7rJnAQk9B2/wBk8dMEek6hp0l5cq6OqqEC85z1NU/F3hHTfGWhvp2qp/tQzqPnhf8AvD+o71wOgeL9X+HerReF/iCxksW+Ww1fkqV6AMfQe/K98jBrhrUYSj7KrrH+tz2rLGr29BWqr4o9/OP6r5o9DXQ2/inA+i5qVdDi/ilc/QAVpI6yRq8bBkYZVlOQR60tTHLMJH7H4s8p4ir3KC6Najrvb6tUi6ZaL/yxB+pJq3RW8cHho7QX3EOrUfVkK2dsvSCP/vkVIsaL91FH0FOoreNOEfhSRm5N7sKKKKsQUUVFc3MFnbPcXcqQwxjLu7YCj60AS1zPinxzpvhlGiJ+1X2Pltoz092P8I/X2rjfFnxSluN9n4bLRRdGu2GGb/dHYe55+lebu7SOzyMWZjlmY5JPrQUkauv+JdS8R3fnalPuVT+7hThI/oP69ayaKKQwooooAKKKKACgHByKKKAPcfh54r/4SDR/s12+dQtFCyZPMi9n/off612FfN2h6xc6DrEGoWZ+eJvmXPDr3U+xr6F0nVLbWdLgv7Jt0My7h6qe4PuDxTJaLlFFFAgoorM8QeItM8L6TJqOs3KwQJwB1aRuyqO5pNpK7KhCU5KMVdsl1nWbDQNJn1LVrhbe1gXLO3f0AHcnsK8s0rTtR+MHiGHXdege08LWTk2Vi/W6YfxN6j1P/AR3NJpWkap8X9cTXfEsctn4XtnzY6eSQbj/AGj7erfgO5r1+GGO3gSGCNYoo1CoiDCqBwAB2Fc6vWd38P5/8A9iUo5dFwg71nu/5fJf3u76bIcqqihUAVVGAAMACloorpPFCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACs3XtA03xNpEum6xbLPbyevDIezKexHrWlRSaTVmVCcoSUouzR45b3/iL4N3As9Wjm1nwkz4gukGZLUE9D6fQ8HsRyK9V0fWtO8QaZHqGj3cd1bSdHQ9D6EdQfY81bmhiuYHhuI0likUq6OoZWB6gg9RXlesfDzWfB2pya/8MJygPzXOkSHMco9FB6/TqOx7VhaVLbWP4o9fnoY/+JaFXv8AZl69n57dz1eiuE8JfFbR/EM407U1bRdYU7Hs7v5dzeiscc+xwfY13dbRnGavFnm18PVw8+SrGz/rbuFFFFUYBRTJZY4IWlnkWONBlnc4Cj1JrzLxZ8U8b7Pwzz2a8Yf+gA/zP5d6AOw8TeMtM8MQkXL+ddkZS2jPzH3P90e5/DNeM+I/Fmp+JrnffS7YFOY7ePhE/wAT7msl2nvLhpHMk80hyzHLMx9TVuHQNYuf+PfSr2X3S3c/0pFWsZ9FdBD4F8TT/c0e4H/XTCf+hEVoQ/C7xPLjfbQQ/wDXSdTj/vnNAzj6K9Ah+EGst/x8X1lH/ul2P/oIrQh+DR63GtD6R239S39KAujy+ivYIfg/pC4+0aheyf7mxf6GtCH4W+GYvvwXE3/XScj/ANBxQK54fRX0BD4D8MQY2aRCcf8APQs//oRNaEPh7RrbHkaTYxn1W3QH88UBc+cURpG2opY+gGauw6Fq9zj7Ppd7Ln+5buf6V9IRxRxLtiRUHooxTqAufPsPgbxLP9zR7gf74Cf+hEV6D8O9E8TeHriW31O1VNPmG4gzKxjf1ABPXofwr0GimK4UVFc3MFlbSXF3NHBBGu55JGCqo9ST0ry7VfiTrHi3UZND+F9o0zA7Z9WmXEcQ9Vz0+p5PYHrWc6kYbnVhsHVxLfJolu3ol6s6rxv8QtK8F2m2Y/a9SlH+j2ER+dyehP8AdX379ga5Tw/4B1bxhq0fif4mEufvWmkdI4V6jcvb/d6n+I9q3fBnwu0/w5df2rq0zaxrsh3veXGW2MeuwHv/ALR5+nSu6rNQlUd6m3b/ADOyWKpYSLp4R3k959fSPZee7ERFjRURQqqMBQMAD0paKK6DyAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigDmvFvgHQfGVvjVrULchcR3cOFlT8e49jkVwyyeP/he2ySN/Ffh5PusufPgX9SAP+BLx1FevUVlKkm+ZaM9Chj504eyqLnh2f6PdfI5Hwv8AE3wz4r2RWd8La8bj7Jd4jkz6Ds34E111cl4o+GfhnxZvkvrEW943P2u1xHJn1PZvxBrkl0P4meBeNA1CLxPpifdtrviVV9Bk5/Jj9KnnqQ+JX81/kbfV8JiNaE+R/wAsv0lt99j1C/0yz1SFYtQt1uIlO7y35Un3HQ/jUMPh/R7b/j30qyj91t0H9K4LTvjZpcVwLLxdpd94fvB94TRM6D36Bv8Ax38a7zSvEGka7EJNH1K1vFxkiGUMR9R1H41cakJ7M5a+CxOH1qQaXfp960L6RpEu2NFRfRRinUUVocYUUUUAFFFFABRRRQAUUUE4GTwKACiuY1v4jeE/D4YahrVsZV/5YwN5r59MLnH44rj3+KXiLxS5t/h34XuJVJx9vvhtjX8M7fzb8KylWhF2vqd9HLsTVXNy2j3ei+9nqc9xDawPNcypDEgy8kjBVUepJ6V51r3xhsUvP7L8F2UviLVH4XyFJhU+uRyw+nHuKpQfCbWPEk6XfxH8S3F8QdwsrRtsSH64AH4KPrXoWheGtG8NWn2fQ9Phs0P3ii5Z/wDeY8t+Jqb1Z7e6vxN+XA4bWT9rLstI/fu/lY87tvhv4k8Z3KX/AMTNXcQg7o9Js2wiexI4H4ZP+1XpmlaRp+h6dHY6RaRWltGPljjXA+p9T7nmrlFXCnGGq3OXEY2tiEoydorZLRL5f0wooorQ4wooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigCrf6ZY6rbG31Ozt7yE/8s54g6/ka4XVfgj4Tv5TPYJdaTPnKtaTHAPrhs4/DFeiUVEqcJ/EjqoYvEYf+FNr5/oeVDwD8Q9D/wCRb8cm6iX7sWooTgenzB/6fhS/8JB8XNJ+W+8M6fqka/8ALW2kAZvwD/8AsteqUVn7FL4W1/XmdX9pSn/Gpwl6xs/vjY8s/wCFu65Z8ax8PdXtyOrRhmU/TKD+dH/C/fD8OFvtH1m2fuDChA/Nx/KvU6KOSp/N+AfWcE/iw/3Sf63PMR8ffCBAzFqY9jbr/wDF0j/H/wAIquRBqjn0W3T+r16S1nbOctbxMfUoKdHbQRNmKGND6qgFHLV/mX3f8EPb5f8A8+Zf+B//AGp5gfjtp1xxpnhvWrpuw8pRn8i1J/ws7xpqHy6P8Or5M/dkumcKfzRR+teqUUezqPef4B9awcfhw6+cm/yseV7/AIy618vl6RoCN/FlXYD85OaP+FQ6vrRB8Z+NdRv4z962t8on4biR/wCOivVKKPYRfxNv5h/alaP8GMYekVf73d/ichovws8H6EVe20aK4mX/AJa3ZMxz64bgH6AV1yqEUKgCqBgADAFLRWsYxirRRw1a9Ws+arJyfm7hRRRVGIUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB//2Q==" data-image-state="image-loaded"></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: 0px 0px; transform-origin: 0px 0px; ">For example if <img src="data:image/png;base64,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" width="46.5" height="18" style="width: 46.5px; height: 18px;"><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 0px; transform-origin: 0px 0px; ">, the following unique pythagorean triangles can fit inside the circle: <img 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width="50" height="19" style="width: 50px; height: 19px;"><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 0px; transform-origin: 0px 0px; ">, <img src="data:image/png;base64,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" 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src="data:image/png;base64,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" width="57.5" height="19" style="width: 57.5px; height: 19px;"><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 0px; transform-origin: 0px 0px; ">, <img src="data:image/png;base64,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" width="65" height="19" style="width: 65px; height: 19px;"><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 0px; transform-origin: 0px 0px; ">, <img src="data:image/png;base64,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" width="65" height="19" style="width: 65px; height: 19px;"><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 0px; transform-origin: 0px 0px; ">, and <img src="data:image/png;base64,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" width="72.5" height="19" style="width: 72.5px; height: 19px;"><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 0px; transform-origin: 0px 0px; ">. Hence, for <img src="data:image/png;base64,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" width="46.5" height="18" style="width: 46.5px; height: 18px;"><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 0px; transform-origin: 0px 0px; ">, the function should return 6<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 0px; transform-origin: 0px 0px; ">.</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 0px; transform-origin: 0px 0px; ">--------------------</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 0px; transform-origin: 0px 0px; ">NOTE:<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 0px; transform-origin: 0px 0px; "> Unique means that congruent triangles, even if rotated or reflected, are counted only once.</div></div></div>

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Problem 57949. Easy Sequences 106: Counting Pythagorean Triangles inside a Circle

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Problem 57949. Easy Sequences 106: Counting Pythagorean Triangles inside a Circle

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