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 ≤ j < i and p_j > p_i, and add an undirected edge between node i and node j 
  * For every 1 ≤ i ≤ n, find the smallest j such that i < j ≤ 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 cycle

Input

The first and only line contains a single integer n (3 ≤ n ≤ 10^6).

Output

Output a single integer 0 ≤ x < 10^9+7, the number of cyclic permutations of length n modulo 10^9+7.

Examples

Input


4


Output


16

Input


583291


Output


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 v_1, v_2, …, v_k form a simple cycle if the following conditions hold: 

  * k ≥ 3. 
  * v_i ≠ v_j for any pair of indices i and j. (1 ≤ i < j ≤ k) 
  * v_i and v_{i+1} share an edge for all i (1 ≤ i < k), and v_1 and v_k share an edge. 
66
 652615
 482331
 336161
 33
 1000000
 79531
 768208
 3
 885131

257415584
 960319213
 722928541
 234634596
 762187807
 23581336
 162141608
 635322133
 2
 329995454

import java.util.*;
import java.io.*;
public class Main {

	static ArrayList<Integer> primes = new ArrayList<>();
	static ArrayList<Integer> prefix = new ArrayList<>();
	public static void main(String[] args)throws IOException {

		BufferedReader br;
		br = new BufferedReader(new InputStreamReader(System.in));
		//****
		// br = new BufferedReader(new FileReader("input.txt"));
		// PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
		//****
		int t = 1;
		int mod = (int)(1e9 + 7);
		StringBuffer ans = new StringBuffer();
		while (t-- > 0) {

			int n = Integer.parseInt(br.readLine().trim());
			long answer = bin(2, n - 1, mod);
			
			long fact = (long)factmod(n,mod);

// 			System.out.println(answer+" "+fact);
			long res = (fact%mod-answer%mod)%mod;
			if(res<0)
			res=(res+mod)%mod;
			ans.append(res );
			ans.append("\n");
		}
		System.out.print(ans);













		//To Comment
		// out.flu/sh();
	}
	static long bin( long a,  long b,  long mod) {
		a %= mod;
		long result = 1;
		while (b > 0) {
			if (b % 2 == 1)
				result = result * a % mod;
			a = a * a % mod;
			b >>= 1;
		}
		return result;
	}
	
	static long factmod(long n, long p) {
     if (n >= p) 
        return 0; 
  
    long result = 1; 
    for (long i = 1; i <= n; i++) {
         result = (result * i) % p; 
    }
       
  
    return result; 
    }
}
