{"trustable":false,"sections":[{"title":"","value":{"format":"MD","content":"\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\nMathJax.Hub.Config({\n tex2jax: {inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]], displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]}\n});\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async\n src\u003d\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\"\u003e\n\u003c/script\u003e\n\nGiven an integer **N**, you have to prime factorize **N!** (factorial **N**)."}},{"title":"Input","value":{"format":"MD","content":"Input starts with an integer **T (\u0026le; 125)**, denoting the number of test cases.\n\nEach case contains an integer **N (2 \u0026le; N \u0026le; 100)**."}},{"title":"Output","value":{"format":"MD","content":"For each case, print the case number and the factorization of the factorial in the following format as given in samples.\n\nCase x: N \u003d p\u003csub\u003e1\u003c/sub\u003e (power of p\u003csub\u003e1\u003c/sub\u003e) * p\u003csub\u003e2\u003c/sub\u003e (power of p\u003csub\u003e2\u003c/sub\u003e) * ...\n\nHere \u003cstrong\u003ex\u003c/strong\u003e is the case number, \u003cstrong\u003ep\u003csub\u003e1\u003c/sub\u003e, p\u003csub\u003e2\u003c/sub\u003e ...\u003c/strong\u003e are primes in ascending order."}},{"title":"Sample Input","value":{"format":"MD","content":"\u003cpre\u003e3\n2\n3\n6\n\u003c/pre\u003e"}},{"title":"Sample Output","value":{"format":"MD","content":"\u003cpre\u003eCase 1: 2 \u003d 2 (1)\nCase 2: 3 \u003d 2 (1) * 3 (1)\nCase 3: 6 \u003d 2 (4) * 3 (2) * 5 (1)\n\u003c/pre\u003e"}},{"title":"Note","value":{"format":"MD","content":"The output for the 3\u003csup\u003erd\u003c/sup\u003e case is (if we replace spaces with `.`s) `Case.3:.6.\u003d.2.(4).*.3.(2).*.5.(1)`"}}]}