{"trustable":false,"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003e\n Little Ruins is a studious boy, recently he learned math! \n \u003cbr\u003e \n \u003cbr\u003eNow he defines $f(k$) equal the number of prime factors in $k$, and $g(k) \u003d 2^{f(k)}$, he want to know \n \u003cbr\u003e \n \u003cbr\u003e$$\\sum_{i \u003d 1}^{n} g(i)$$ \n \u003cbr\u003e \n \u003cbr\u003ePlease help him! \n\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"First line contains an integer $T$, which indicates the number of test cases. \n\u003cbr\u003e \n\u003cbr\u003eEvery test case contains one line with one integer $n$. \n\u003cbr\u003e \n\u003cbr\u003eLimits \n\u003cbr\u003e$1 \\leq T \\leq 50$. \n\u003cbr\u003e$1 \\leq n \\leq 10^{12}$."}},{"title":"Output","value":{"format":"HTML","content":"For every test case, you should output \n\u003cb\u003e\u0027Case #x: y\u0027\u003c/b\u003e, where \n\u003cb\u003ex\u003c/b\u003e indicates the case number and counts from \n\u003cb\u003e1\u003c/b\u003e and \n\u003cb\u003ey\u003c/b\u003e is the result. \n\u003cbr\u003e \n\u003cbr\u003eBecause \n\u003cb\u003ey\u003c/b\u003e could be very large, just mod it with $10^9 + 7$."}},{"title":"Sample Input","value":{"format":"HTML","content":"\u003cpre\u003e3\n1\n10\n100\u003c/pre\u003e"}},{"title":"Sample Output","value":{"format":"HTML","content":"\u003cpre\u003eCase #1: 1\nCase #2: 23\nCase #3: 359\u003c/pre\u003e"}}]}