[{"sectionTitle":"题目描述","type":"Text","text":"原题来自：HackerRank Equations\r\n\r\n求不定方程：\r\n$$\frac{1}{x}+\frac{1}{y}=\frac{1}{n!}$$\r\n的正整数解 $(x,y)$ 的数目。","subType":"markdown"},{"sectionTitle":"输入格式","type":"Text","text":"一个整数 $n$。","subType":"markdown"},{"sectionTitle":"输出格式","type":"Text","text":"一个整数，表示有多少对 $(x,y)$ 满足题意。答案对 $10^9+7$ 取模。","subType":"markdown"},{"sectionTitle":"样例","type":"Sample","text":"共有三个数对 $(x,y)$ 满足条件，分别是 $(3,6),(4,4)$ 和 $(6,3)$。","subType":"markdown","payload":["2","3"]},{"sectionTitle":"数据范围与提示","type":"Text","text":"对于 $30\\%$ 的数据，$n\\le 100$； \r\n对于全部数据，$1\\le n\\le 10^6$。","subType":"markdown"}]