{"trustable":true,"prependHtml":"\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\r\nThere is an ant named Alice. Alice likes going hiking very much. Today, she wants to climb a cuboid. The length of cuboid\u0027s longest edge is \u003cvar\u003en\u003c/var\u003e, and the other edges are all positive integers.\r\nAlice\u0027s starting point is a vertex of this cuboid, and she wants to arrive at the opposite vertex.\r\nThe opposite vertex means the vertex which has no common planes or edges with the starting point.\r\nJust like the picture below:\r\n\u003c/p\u003e\u003cdiv style\u003d\"text-align: center;\"\u003e\u003cimg src\u003d\"CDN_BASE_URL/eb3195318f4cba2d27021ea1e1c72e16?v\u003d1713668600\" alt\u003d\"mtz9548_ant_pic1.gif\"\u003e\u003c/div\u003e\r\n\r\nAlice is very clever, she always walks on the shortest path. But she can only walk on the surface of the cuboid.\r\nNow, Alice only knows the length of cuboid\u0027s longest edge is \u003cvar\u003en\u003c/var\u003e, and doesn\u0027t know the length of other edges.\r\nSuppose the \u003cvar\u003eL\u003c/var\u003e is the length of shortest path of a cuboid. Alice wants to compute the sum of \u003cvar\u003eL\u003csup\u003e2\u003c/sup\u003e\u003c/var\u003e for every possible cuboid.\r\n\r\n\u003cp\u003e\u003c/p\u003e\r\n\r\n\r\n\u003ch4\u003eInput\u003c/h4\u003e\r\n\r\n\u003cp\u003e\r\nThe first line of input contains an integer \u003cvar\u003eT(T ≤ 100)\u003c/var\u003e .\r\n\u003cvar\u003e T \u003c/var\u003e is the number of the cases. In the following \u003cvar\u003eT\u003c/var\u003e lines, there are a positive integer \u003cvar\u003en(1≤n≤10\u003csup\u003e14\u003c/sup\u003e)\u003c/var\u003e in each line. \u003cvar\u003en\u003c/var\u003e is the longest edge of the cuboid.\r\n\r\n\u003c/p\u003e\r\n\r\n\u003ch4\u003eOutput\u003c/h4\u003e\r\n\r\n\u003cp\u003e\r\nFor each test case, output the sum of \u003cvar\u003eL\u003csup\u003e2\u003c/sup\u003e\u003c/var\u003e for every possible cuboid in a line. \u003cvar\u003eL\u003c/var\u003e is the length of shortest path of a cuboid. It may be very large, so you must output the answer modulo 1000000007.\r\n\u003c/p\u003e\r\n\r\n\u003ch4\u003eSample\u003c/h4\u003e\n\u003ctable class\u003d\"vjudge_sample\"\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\u003e\r\n2\r\n3\r\n4\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e\r\n160\r\n440\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\r\n\u003ch4\u003eHint\u003c/h4\u003e\r\n(3,2,1) and (3,1,2) are regrad as the same cuboids. "}}]}