You are given a 0-indexed integer array nums containing n distinct positive integers. A permutation of nums is called special if:

Return the total number of special permutations. As the answer could be large, return it modulo 10+ 7.

 

Example 1:

Input: nums = [2,3,6]
Output: 2
Explanation: [3,6,2] and [2,6,3] are the two special permutations of nums.

Example 2:

Input: nums = [1,4,3]
Output: 2
Explanation: [3,1,4] and [4,1,3] are the two special permutations of nums.

 

Constraints: