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.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
 

	
	 

public class sol {
 public static void backtrack(List<List<Integer>>list,List<Integer>templist,int []nums) {
		 
		 if(templist.size() == nums.length) {
			 list.add(new ArrayList<>(templist));
		 }else {
			 
			 for(int i = 0; i < nums.length; i++) {
				 if(templist.contains(nums[i])) continue;
					 templist.add(nums[i]);
					 backtrack(list,templist,nums);
					 templist.remove(templist.size()-1);
				 
				 
			 }
		 }
	 }
	 public static List<List<Integer>>permute(int []nums){
		 List<List<Integer>>list = new ArrayList<>();
		 backtrack(list,new ArrayList<>(),nums);
		 return list;
	 }
	 
	 static int LCSubStr(String s,String t,
             int n,int m)
{ 

// Create DP table
int dp[][]=new int[2][m+1];
int res=0;

for(int i=1;i<=n;i++)
{
 for(int j=1;j<=m;j++)
 {
     if(s.charAt(i-1)==t.charAt(j-1))
     {
         dp[i%2][j]=dp[(i-1)%2][j-1]+1;
         if(dp[i%2][j]>res)
             res=dp[i%2][j];
     }
     else dp[i%2][j]=0;
 }
}
return res;
}
    public static void main (String args[])throws IOException{
	    
  

  	  Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      
      
      long mod = 1000000007;
      long uni = 1;
      long fact = 1;
      
      for(int i = n; i >= 1; i--) {
    	  fact = fact*i;
    	  fact = fact%mod;
      }
      
      for(int i = 1; i < n; i++) {
    	  uni = (uni*2);
    	  uni = uni%mod;
      }
      
      System.out.println(fact-uni);
    }
}
  	  
  	    	  