{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 (plus) and \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 (square root). Initially, the number \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e is displayed on the screen. There are \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e + 1\u003c/span\u003e levels in the game and ZS the Coder start at the level \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eWhen ZS the Coder is at level \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e, he can :\u003c/p\u003e\u003col\u003e \u003cli\u003e \u003cspan class\u003d\"tex-font-style-it\"\u003ePress the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button\u003c/span\u003e. This increases the number on the screen by exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e. So, if the number on the screen was \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e, it becomes \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e + \u003ci\u003ek\u003c/i\u003e\u003c/span\u003e.\u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-font-style-it\"\u003ePress the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button\u003c/span\u003e. Let the number on the screen be \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e. After pressing this button, the number becomes \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/9edf2c2d75ac45393e513d2c85786c62?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. After that, ZS the Coder levels up, so his current level becomes \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e + 1\u003c/span\u003e. This button can only be pressed when \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e is a \u003cspan class\u003d\"tex-font-style-bf\"\u003eperfect square\u003c/span\u003e, i.e. \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e \u003d \u003ci\u003em\u003c/i\u003e\u003csup class\u003d\"upper-index\"\u003e2\u003c/sup\u003e\u003c/span\u003e for some positive integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003c/ol\u003e\u003cp\u003eAdditionally, after each move, if ZS the Coder is at level \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e, and the number on the screen is \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e, then \u003cspan class\u003d\"tex-font-style-bf\"\u003e\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e must be a multiple of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e\u003c/span\u003e. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e and current number is \u003cspan class\u003d\"tex-span\"\u003e100\u003c/span\u003e, he presses the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button and the number turns into \u003cspan class\u003d\"tex-span\"\u003e10\u003c/span\u003e. Note that at this moment, \u003cspan class\u003d\"tex-span\"\u003e10\u003c/span\u003e is not divisible by \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e, but this press is still valid, because after it, ZS the Coder is at level \u003cspan class\u003d\"tex-span\"\u003e5\u003c/span\u003e, and \u003cspan class\u003d\"tex-span\"\u003e10\u003c/span\u003e is divisible by \u003cspan class\u003d\"tex-span\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eZS the Coder needs your help in beating the game\u0026nbsp;— he wants to reach level \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e + 1\u003c/span\u003e. In other words, he needs to press the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e times. Help him determine the number of times he should press the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button before pressing the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button at each level. \u003c/p\u003e\u003cp\u003ePlease note that ZS the Coder wants to find just any sequence of presses allowing him to reach level \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e + 1\u003c/span\u003e, but not necessarily a sequence minimizing the number of presses.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first and only line of the input contains a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 100 000\u003c/span\u003e), denoting that ZS the Coder wants to reach level \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e + 1\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e non-negative integers, one per line. \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th of them should be equal to the number of times that ZS the Coder needs to press the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button before pressing the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button at level \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. \u003c/p\u003e\u003cp\u003eEach number in the output should not exceed \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e18\u003c/sup\u003e\u003c/span\u003e. However, the number on the screen \u003cspan class\u003d\"tex-font-style-bf\"\u003ecan be greater\u003c/span\u003e than \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e18\u003c/sup\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIt is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e14\n16\n46\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e999999999999999998\n44500000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\n17\n46\n97\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first sample case:\u003c/p\u003e\u003cp\u003eOn the first level, ZS the Coder pressed the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button \u003cspan class\u003d\"tex-span\"\u003e14\u003c/span\u003e times (and the number on screen is initially \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e), so the number became \u003cspan class\u003d\"tex-span\"\u003e2 + 14·1 \u003d 16\u003c/span\u003e. Then, ZS the Coder pressed the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button, and the number became \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/f1433912507d0bfcdb321dfd0c22755a?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. \u003c/p\u003e\u003cp\u003eAfter that, on the second level, ZS pressed the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button \u003cspan class\u003d\"tex-span\"\u003e16\u003c/span\u003e times, so the number becomes \u003cspan class\u003d\"tex-span\"\u003e4 + 16·2 \u003d 36\u003c/span\u003e. Then, ZS pressed the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button, levelling up and changing the number into \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/765f425a072cdfd9e77154836d683465?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e.\u003c/p\u003e\u003cp\u003eAfter that, on the third level, ZS pressed the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button \u003cspan class\u003d\"tex-span\"\u003e46\u003c/span\u003e times, so the number becomes \u003cspan class\u003d\"tex-span\"\u003e6 + 46·3 \u003d 144\u003c/span\u003e. Then, ZS pressed the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button, levelling up and changing the number into \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/a22ad7b5a7d457bb68481ead113a90c4?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. \u003c/p\u003e\u003cp\u003eNote that \u003cspan class\u003d\"tex-span\"\u003e12\u003c/span\u003e is indeed divisible by \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e, so ZS the Coder can reach level \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eAlso, note that pressing the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button \u003cspan class\u003d\"tex-span\"\u003e10\u003c/span\u003e times on the third level before levelling up does not work, because the number becomes \u003cspan class\u003d\"tex-span\"\u003e6 + 10·3 \u003d 36\u003c/span\u003e, and when the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button is pressed, the number becomes \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/765f425a072cdfd9e77154836d683465?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e and ZS the Coder is at Level \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e. However, \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e is not divisible by \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e now, so this is \u003cspan class\u003d\"tex-font-style-bf\"\u003enot a valid solution.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eIn the second sample case:\u003c/p\u003e\u003cp\u003eOn the first level, ZS the Coder pressed the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button \u003cspan class\u003d\"tex-span\"\u003e999999999999999998\u003c/span\u003e times (and the number on screen is initially \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e), so the number became \u003cspan class\u003d\"tex-span\"\u003e2 + 999999999999999998·1 \u003d 10\u003csup class\u003d\"upper-index\"\u003e18\u003c/sup\u003e\u003c/span\u003e. Then, ZS the Coder pressed the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button, and the number became \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/1a147df9a89a1350ba1ba80316afac0a?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. \u003c/p\u003e\u003cp\u003eAfter that, on the second level, ZS pressed the \u0027\u003cspan class\u003d\"tex-span\"\u003e + \u003c/span\u003e\u0027 button \u003cspan class\u003d\"tex-span\"\u003e44500000000\u003c/span\u003e times, so the number becomes \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 44500000000·2 \u003d 9·10\u003csup class\u003d\"upper-index\"\u003e10\u003c/sup\u003e\u003c/span\u003e. Then, ZS pressed the \u0027\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/bbe952c57c3ec8d5a25034e7f0c76fed?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0027 button, levelling up and changing the number into \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/ba81f12f1cd47aad2b0af11a35da0059?v\u003d1715219523\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. \u003c/p\u003e\u003cp\u003eNote that \u003cspan class\u003d\"tex-span\"\u003e300000\u003c/span\u003e is a multiple of \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e, so ZS the Coder can reach level \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e.\u003c/p\u003e"}}]}