B'A permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation ( 2 appears twice in the array) and [1,3,4] is also not a permutation ( n=3 but there is 4 in the array). Consider a permutation p of length n , we build a graph of size n using it as follows: In cases where no such j exists, we make no edges. Also, note that we make edges between the corresponding indices, not the values at those indices. For clarity, consider as an example n = 4 , and p = [3,1,4,2] ; here, the edges of the graph are (1,3),(2,1),(2,3),(4,3) . A permutation p is cyclic if the graph built using p has at least one simple cycle. Given n , find the number of cyclic permutations of length n . Since the number may be very large, output it modulo 10^9+7 . Please refer to the Notes section for the formal definition of a simple cycle The first and only line contains a single integer n ( 3 <= n <= 10^6 ). Output a single integer 0 <= q x < 10^9+7 , the number of cyclic permutations of length n modulo 10^9+7 . There are 16 cyclic permutations for n = 4 . [4,2,1,3] is one such permutation, having a cycle of length four: 4 rightarrow 3 rightarrow 2 rightarrow 1 rightarrow 4 . Nodes v_1 , v_2 , ldots , v_k form a simple cycle if the following conditions hold: '...