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 10 9 + 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, 10
6
].