{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eWe define a sequence ${a_1, a_2, ..., a_n}$ of positive integer numbers, as perfect sequence if it matches following qualities:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e$n \\ge 2$, and\u003c/li\u003e\n \u003cli\u003e$a_1 + a_2 + ... + a_n \u003d a_1 \\times a_2 \\times ... \\times a_n$\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch3\u003eInputFile\u003c/h3\u003e\n\u003cp\u003eThe first line contains the number of test cases $T$ (no more than $300$).In each of the following $T$ lines there is one integer $n (2 \\leq n \\leq 3000)$.\u003c/p\u003e\n\u003ch3\u003eOutputFile\u003c/h3\u003e\n\u003cp\u003eFor each test case, print the number of perfect sequences that has length $n$. In case the result is too large, print the remainder modulo $1000000007$.\u003c/p\u003e"}},{"title":"Sample 1","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\n2\n3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n6\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cbr /\u003e\u003cp\u003e$n \u003d 2: \\{2, 2\\}$\u003c/p\u003e\u003cp\u003e$n \u003d 3: \\{1, 2, 3\\}, \\{1, 3, 2\\}, \\{2, 1, 3\\}, \\{2, 3, 1\\}, \\{3, 1, 2\\}, \\{3, 2, 1\\}$\u003c/p\u003e"}}]}