C. Cyclic Permutations time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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:   For every 1 \leq i \leq n, find the largest j such that 1 \leq j < i and p_j > p_i, and add an undirected edge between node i and node j  For every 1 \leq i \leq n, find the smallest j such that i < j \leq n and p_j > p_i, and add an undirected edge between node i and node j 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 cycleInputThe first and only line contains a single integer n (3 \le n \le 10^6).OutputOutput a single integer 0 \leq x < 10^9+7, the number of cyclic permutations of length n modulo 10^9+7.ExamplesInput
4
Output
16Input
583291
Output
135712853NoteThere 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:   k \geq 3.  v_i \neq v_j for any pair of indices i and j. (1 \leq i < j \leq k)  v_i and v_{i+1} share an edge for all i (1 \leq i < k), and v_1 and v_k share an edge. 
4

16
['combinatorics', 'dp', 'graphs', 'math', '*1500']