{"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\u003eConsider a numeric string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003estr\u003c/i\u003e\u003c/span\u003e where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003estr\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e denotes the digit(\u003cspan class\u003d\"tex-span\"\u003e0\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e9\u003c/span\u003e) at index \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. We call \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e1, \u003ci\u003ex\u003c/i\u003e2, \u003ci\u003ex\u003c/i\u003e3, \u003ci\u003ex\u003c/i\u003e4)\u003c/span\u003e quadruple a palindromic quadruple of string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eS\u003c/i\u003e\u003c/span\u003e if it satisfies the following criteria : \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ex\u003c/i\u003e1\u003c/sub\u003e \u003d \u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ex\u003c/i\u003e4\u003c/sub\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ex\u003c/i\u003e2\u003c/sub\u003e \u003d \u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ex\u003c/i\u003e3\u003c/sub\u003e\u003c/span\u003e where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e1 \u0026lt; \u003ci\u003ex\u003c/i\u003e2 \u0026lt; \u003ci\u003ex\u003c/i\u003e3 \u0026lt; \u003ci\u003ex\u003c/i\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eYou are given \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eQ\u003c/i\u003e\u003c/span\u003e queries where each query is of form : \u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cspan class\u003d\"tex-font-style-tt\"\u003e1 i j\u003c/span\u003e: Print number of different palindromic quadruples \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ex\u003c/i\u003e1, \u003ci\u003ex\u003c/i\u003e2, \u003ci\u003ex\u003c/i\u003e3, \u003ci\u003ex\u003c/i\u003e4)\u003c/span\u003e for string str such that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e ≤ \u003ci\u003ex\u003c/i\u003e1 \u0026lt; \u003ci\u003ex\u003c/i\u003e2 \u0026lt; \u003ci\u003ex\u003c/i\u003e3 \u0026lt; \u003ci\u003ex\u003c/i\u003e4 ≤ \u003ci\u003ej\u003c/i\u003e\u003c/span\u003e. As the result can be large, print it modulo \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e. \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-font-style-tt\"\u003e2 idx ch\u003c/span\u003e: Replace \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003estr\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003eidx\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e with character \u003cspan class\u003d\"tex-font-style-tt\"\u003ech\u003c/span\u003e. \u003c/li\u003e\u003c/ul\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains a string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003estr\u003c/i\u003e\u003c/span\u003e, such that \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/4d336a60898feb5f2983e3e904bbaa04?v\u003d1714119647\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e, and \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/223604a2b850e239ffebe5666d6de3b6?v\u003d1714119647\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. The second line contains a single integer, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eQ\u003c/i\u003e(1 ≤ \u003ci\u003eQ\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e)\u003c/span\u003e, the number of queries. Each of the next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eQ\u003c/i\u003e\u003c/span\u003e lines contains a query, with format as described in the problem statement. In queries of type \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e, \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/40b16d1e01789430b36ac751a540b652?v\u003d1714119647\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eAn integer for each query of type \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e, one on each line.\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\u003e01010\n5\n1 1 5\n2 2 0\n1 1 5\n2 4 0\n1 1 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n1\n5\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 sample test case \u003c/p\u003e\u003cul\u003e \u003cli\u003e Query 1: The String is \u003cspan class\u003d\"tex-font-style-tt\"\u003e01010\u003c/span\u003e, Possible palindromic quadruples \u003d \u003cspan class\u003d\"tex-font-style-tt\"\u003e0110\u003c/span\u003e, so answer \u003d 1 \u003c/li\u003e\u003cli\u003e Query 2: Update str2 \u003d 0, so the string is now \u003cspan class\u003d\"tex-font-style-tt\"\u003e00010\u003c/span\u003e \u003c/li\u003e\u003cli\u003e Query 3: The String is \u003cspan class\u003d\"tex-font-style-tt\"\u003e00010\u003c/span\u003e, Possible palindromic quadruples \u003d \u003cspan class\u003d\"tex-font-style-tt\"\u003e0000\u003c/span\u003e, so answer \u003d 1 \u003c/li\u003e\u003cli\u003e Query 4: Update str4 \u003d 0, so the string is now \u003cspan class\u003d\"tex-font-style-tt\"\u003e00000\u003c/span\u003e \u003c/li\u003e\u003cli\u003e Query 5: The String is \u003cspan class\u003d\"tex-font-style-tt\"\u003e00000\u003c/span\u003e, Possible palindromic quadruples is \u003cspan class\u003d\"tex-font-style-tt\"\u003e0000\u003c/span\u003e which can be selected in 5 ways, so answer \u003d 5 \u003c/li\u003e\u003c/ul\u003e"}}]}