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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
Would you please give from 1 the n number of program design aligned so that all the "prime number" should be placed in "prime index" on (the index starts at 1); you need to return the total number of possible solutions.
Let's take a look at "prime": prime number must be greater than 1, and can not be less than the product of its two positive integers to represent.
Since the answer may be very large, so please return the answer mode mod 10^9 + 7 after the results can be.
Example 1:
Input: n = 5 Output: 12 Explanation: for example, [1,2,5,4,3] is an effective arrangement, but [5,2,3,4,1] is not, as in the second 5 in the case where a prime number is incorrectly placed in a position on the index.
Example 2:
Input: n = 100 Output: 682 289 015
prompt:
1 <= n <= 100