Prime Arrangements
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...
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
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