In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. There's originally an array consisting of n integers from 1 to n in ascending order, you need to find the number of derangement it can generate. Also, since the answer may be very large, you should return the output mod 109 + 7. Example 1: Input: 3 Output: 2 Explanation: The original array is [1,2,3]. The two derangements are [2,3,1] and [3,1,2]. Note: n is in the range of [1, 106].