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

寫個for循環(huán)不會溢出，單獨寫個函數(shù)，求階乘的，就會溢出，呵呵，不過在本機自己電腦上是可以運行的。

?

Constraints:

• 1 <= n <= 100

Runtime0 ms

Beats

100%

Memory38.9 MB

Beats

94.38%

Click to check the distribution chart