{"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\u003eYou are given \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e. Denote this list of integers as \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eT\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eLet \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(\u003ci\u003eL\u003c/i\u003e)\u003c/span\u003e be a function that takes in a non-empty list of integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eL\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe function will output another integer as follows: \u003c/p\u003e\u003cul\u003e \u003cli\u003e First, all integers in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eL\u003c/i\u003e\u003c/span\u003e are padded with leading zeros so they are all the same length as the maximum length number in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eL\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003cli\u003e We will construct a string where the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th character is the minimum of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th character in padded input numbers. \u003c/li\u003e\u003cli\u003e The output is the number representing the string interpreted in base 10. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor example \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(10, 9) \u003d 0\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(123, 321) \u003d 121\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e(530, 932, 81) \u003d 30\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eDefine the function \u003c/p\u003e\u003ccenter class\u003d\"tex-equation\"\u003e\u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/3c1697b47e1c22787c73496d31591844?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/center\u003e Here, \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/8914bf76d95ff4fa2f29cbe750e41d31?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e denotes a subsequence.\u003cp\u003eIn other words, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e(\u003ci\u003ex\u003c/i\u003e)\u003c/span\u003e is the sum of squares of sum of elements of nonempty subsequences of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eT\u003c/i\u003e\u003c/span\u003e that evaluate to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e when plugged into \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e\u003c/span\u003e modulo \u003cspan class\u003d\"tex-span\"\u003e1 000 000 007\u003c/span\u003e, then multiplied by \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e. The last multiplication is not modded. \u003c/p\u003e\u003cp\u003eYou would like to compute \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e(0), \u003ci\u003eG\u003c/i\u003e(1), ..., \u003ci\u003eG\u003c/i\u003e(999 999)\u003c/span\u003e. To reduce the output size, print the value \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/e2e23224aab1f4a43a14be2d22432a87?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e, where \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/f2fe3e60ef565744bf61ec18d7bc2fbe?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e denotes the bitwise XOR operator.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains the 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 ≤ 1 000 000\u003c/span\u003e)\u0026nbsp;— the size of list \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eT\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe next line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e space-separated integers, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 999 999\u003c/span\u003e)\u0026nbsp;— the elements of the list. \u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput a single integer, the answer to the problem.\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\n123 321 555\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e292711924\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\u003e1\n999999\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e997992010006992\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\u003e10\n1 1 1 1 1 1 1 1 1 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e28160\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\u003eFor the first sample, the nonzero values of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e are \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e(121) \u003d 144 611 577\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e(123) \u003d 58 401 999\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e(321) \u003d 279 403 857\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e(555) \u003d 170 953 875\u003c/span\u003e. The bitwise XOR of these numbers is equal to \u003cspan class\u003d\"tex-span\"\u003e292 711 924\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eFor example, \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/b7ecf4db05a438640318435d32071523?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e, since the subsequences \u003cspan class\u003d\"tex-span\"\u003e[123]\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e[123, 555]\u003c/span\u003e evaluate to \u003cspan class\u003d\"tex-span\"\u003e123\u003c/span\u003e when plugged into \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ef\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eFor the second sample, we have \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/fd6f9252ffb0160a423b46ebca0122f6?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e\u003cp\u003eFor the last sample, we have \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/e99571d94834dfbbfcc9e2a37d5242c6?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e, where \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/180c60e2025e1dc163b54386ce1f700d?v\u003d1716149699\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e is the binomial coefficient.\u003c/p\u003e"}}]}