{"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\"\u003eThere is a graph of n vertices which are indexed from 1 to n. For any pair of different vertices, the weight of the edge between them is the \u003cb\u003eleast common multiple\u003c/b\u003e of their indexes.\u003cbr\u003e\u003cbr\u003eMr. Frog is wondering about the total weight of the minimum spanning tree. Can you help him?\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains only one integer T ($T \\leq 100$), which indicates the number of test cases.\u003cbr\u003e\u003cbr\u003eFor each test case, the first line contains only one integer n ($2 \\leq n \\leq 10^9$), indicating the number of vertices.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output one line \"Case #x:y\",where x is the case number (starting from 1) and y is the total weight of the minimum spanning tree.\u003cbr\u003e"}},{"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\u003e2\r\n2\r\n3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 2\r\nCase #2: 5\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Hint","value":{"format":"HTML","content":"\u003cbr\u003eIn the second sample, the graph contains 3 edges which are (1, 2, 2), (1, 3, 3) and (2, 3, 6). Thus the answer is 5.\u003cbr\u003e"}}]}