C. Cyclic Permutations

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:
For every 1≤i≤n, find the largest j such that 1≤jpi, and add an undirected edge between node i and node j
For every 1≤i≤n, find the smallest j such that ipi, 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 109+7.

Please refer to the Notes section for the formal definition of a simple cycle
Input

The first and only line contains a single integer n
(3≤n≤106).
Output

Output a single integer 0≤x<109+7, the number of cyclic permutations of length n modulo 109+7.
Examples
Input
Copy

4

Output
Copy

16

Input
Copy

583291

Output
Copy

135712853

Note

There are 16
cyclic permutations for n=4. [4,2,1,3] is one such permutation, having a cycle of length four: 4→3→2→1→4.

Nodes v1, v2, …, vk form a simple cycle if the following conditions hold:

k≥3.vi≠vj for any pair of indices i and j. (1≤i vi and vi+1 share an edge for all i (1≤i

#include 
using namespace std;
const int mod=1e9+7;
typedef long long LL;

int main()
{
     
	LL n,q=6,p=4;
	cin>>n;
	for(int i=4;i<=n;i++)
	{
     
		q=q*i%mod;
		p=p*2%mod;
	 }
	 cout<<(q-p+mod)%mod<<endl; 
	return 0;
}