{"trustable":false,"sections":[{"title":"","value":{"format":"MD","content":"Bowen loves research sequences,and he give you a positive integer $x$, let you construct a sequence $a_0,a_1,a_2,...a_m$ of length $m+1$ where $a_0\u003d1, a_m\u003dx$,$ai\u003ca_{i+1}$, and $ai ∣ a_{i+1}$ ,$a ∣ b$ means that $b$ is divisible by $a$, such as $3 ∣ 6$.\nBowen wants to find the maximum value of $m$ in the sequence that can be constructed, and the number of sequence that satisfies the condition when $m$ is equal to the maximum value."}},{"title":"Input","value":{"format":"MD","content":"\u003cp\u003eThe input consists of several test cases. Each contains a positive integer \u003ci\u003ex\u003c/i\u003e (\u003ci\u003ex\u003c/i\u003e ≤ 2\u003csup\u003e20\u003c/sup\u003e).\u003c/p\u003e\n$\\mathbf{Attention:}$ the evaluation machine has multiple tests of input"}},{"title":"Output","value":{"format":"MD","content":"\u003cp\u003eFor each test case, output the $m$’s maximum value and the number of sequence that satisfies the condition"}},{"title":"Sample","value":{"format":"MD","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\n3\n4\n10\n100\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 1\n1 1\n2 1\n2 2\n4 6\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Hits","value":{"format":"MD","content":"The fourth set of data, $x\u003d10$, has two longest sequences, $1-2-10$ and $1-5-10$, with a length of $ 3$ ,so maximum $m\u003d2$ and the number of sequence that satisfies the condition is $2$,and then ouput $2$ $2$"}}]}