{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv\u003e\u003cp\u003eGiven a positive integer \u003ci\u003eX\u003c/i\u003e, an \u003ci\u003eX\u003c/i\u003e-factor chain of length \u003ci\u003em\u003c/i\u003e is a sequence of integers,\u003c/p\u003e\u003cp\u003e1 \u003d\u003ci\u003e X\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e, \u003ci\u003eX\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003eX\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, …, \u003ci\u003eX\u003csub\u003em\u003c/sub\u003e \u003c/i\u003e\u003d\u003ci\u003e X\u003c/i\u003e\u003c/p\u003e\u003cp\u003esatisfying\u003c/p\u003e\u003cp\u003e\u003ci\u003eX\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e \u0026lt; \u003ci\u003eX\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e\u003csub\u003e+1\u003c/sub\u003e and \u003ci\u003eX\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e | \u003ci\u003eX\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e\u003csub\u003e+1\u003c/sub\u003e where \u003ci\u003ea\u003c/i\u003e | \u003ci\u003eb\u003c/i\u003e means \u003ci\u003ea\u003c/i\u003e perfectly divides into \u003ci\u003eb\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eNow we are interested in the maximum length of \u003ci\u003eX\u003c/i\u003e-factor chains and the number of chains of such length.\u003c/p\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","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"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, output the maximum length and the number of such \u003ci\u003eX\u003c/i\u003e-factors chains.\u003c/p\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\n3\r\n4\r\n10\r\n100\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 1\r\n1 1\r\n2 1\r\n2 2\r\n4 6\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}