{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eLittle Ruins is a studious boy, recently he learned addition operation! He was rewarded some number bricks of $1$ to $9$ and infinity bricks of addition mark \u003cb\u003e\u0027+\u0027\u003c/b\u003e and equal mark \u003cb\u003e\u0027\u003d\u0027\u003c/b\u003e.\u003cbr\u003e\u003cbr\u003eNow little Ruins is puzzled by those bricks because he wants to put those bricks into as many different addition equations form $x + y \u003d z$ as possible. Each brick can be used at most once and x, y, z are one digit integer.\u003cbr\u003e\u003cbr\u003eAs Ruins is a beginer of addition operation, $x$, $y$ and $z$ will be single digit number.\u003cbr\u003e\u003cbr\u003eTwo addition equations are different if any number of $x$, $y$ and $z$ is different.\u003cbr\u003e\u003cbr\u003ePlease help little Ruins to calculate the \u003cb\u003emaximum\u003c/b\u003e number of different addition equations.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"First line contains an integer $T$, which indicates the number of test cases.\u003cbr\u003e\u003cbr\u003eEvery test case contains one line with nine integers, the $i^{th}$ integer indicates the number of bricks of $i$.\u003cbr\u003e\u003cbr\u003eLimits\u003cbr\u003e$1 \\leq T \\leq 30$\u003cbr\u003e$0 \\leq \\text{bricks number of each type} \\leq 100$"}},{"title":"Output","value":{"format":"HTML","content":"For every test case, you should output \u003cb\u003e\u0027Case #x: y\u0027\u003c/b\u003e, where \u003cb\u003ex\u003c/b\u003e indicates the case number and counts from \u003cb\u003e1\u003c/b\u003e and \u003cb\u003ey\u003c/b\u003e is the result."}},{"title":"Sample","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\r\n1 1 1 1 1 1 1 1 1\r\n2 2 2 2 2 2 2 2 2\r\n0 3 3 0 3 0 0 0 0\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 2\r\nCase #2: 6\r\nCase #3: 2\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}