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Return the number of permutations of 1 to n
so that prime numbers are at prime indices (1-indexed.)
(Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.)
Since the answer may be large, return the answer modulo 10^9 + 7
.
Example 1:
Input: n = 5 Output: 12 Explanation: For example [1,2,5,4,3] is a valid permutation, but [5,2,3,4,1] is not because the prime number 5 is at index 1.
Example 2:
Input: n = 100 Output: 682289015
Constraints:
1 <= n <= 100
请你帮忙给从 1
到 n
的数设计排列方案,使得所有的「质数」都应该被放在「质数索引」(索引从 1 开始)上;你需要返回可能的方案总数。
让我们一起来回顾一下「质数」:质数一定是大于 1 的,并且不能用两个小于它的正整数的乘积来表示。
由于答案可能会很大,所以请你返回答案 模 mod 10^9 + 7
之后的结果即可。
示例 1:
输入:n = 5 输出:12 解释:举个例子,[1,2,5,4,3] 是一个有效的排列,但 [5,2,3,4,1] 不是,因为在第二种情况里质数 5 被错误地放在索引为 1 的位置上。
示例 2:
输入:n = 100 输出:682289015
提示:
1 <= n <= 100