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.*;
import java.math.*;
import java.awt.geom.*;
 
import static java.lang.Math.*;
 
public class Solution implements Runnable {
	 static int mod=1000000007;
    public void solve() throws Exception {
    	
//    	int t=sc.nextInt();
    	
//    	while(t-->0)
//    	{
//    		int n=583291;
//    		long prod=1;
//    		
//    		for(int i=1;i<=n;i++)
//    		{
//    			prod=(prod%mod*i%mod)%mod;
//    			
//    		}
//    		long prod1=1;
//    		for(int i=1;i<=n-1;i++)
//    		{
//    			prod1=(prod1%mod*i%mod)%mod;
//    			
//    		}
//    		out.println(prod-prod1);
    		
    		
    	long n=sc.nextLong();
    	long fact=modFact(n,mod);
    	long dec=(power(2, n - 1) ) % mod;
    	out.println(fact-dec);
    	
    		
    		
    }
    
    
    static long power(long a, long n)  
    {  
      
        if (n == 0)  
            return 1;  
      
        long p = power(a, n / 2) % mod;  
        p = (p * p) % mod;  
        if ((n & 1) == 1)  
            p = (p * a) % mod;  
      
        return p;  
    }  
    
    
    static long modFact(long n, int p) 
{ 
if (n >= p) 
 return 0; 

long result = 1; 
for (long i = 1; i <= n; i++) 
 result = (result * i) % p; 

return result; 
} 
    
    
    		
    
         
    	
    		
    
    
    
    
    
    static Throwable uncaught;
 
    BufferedReader in;
    FastScanner sc;
    PrintWriter out;
 
    @Override
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            sc = new FastScanner(in);
            solve();
        } catch (Throwable uncaught) {
            Solution.uncaught = uncaught;
        } finally {
            out.close();
        }
    }
 
    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread(null, new Solution(), "", (1 << 26));
        thread.start();
        thread.join();
        if (Solution.uncaught != null) {
            throw Solution.uncaught;
        }
    }
 
}
 
class FastScanner {
 
    BufferedReader in;
    StringTokenizer st;
 
    public FastScanner(BufferedReader in) {
        this.in = in;
    }
 
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
 
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }
 
    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
 
    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
 
}