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.io.*;
import java.util.Arrays;

public class competetive  {
    static class tri implements Comparable<tri>{
        int f;
        int s;
        int t;
        int ind;
        tri(int a, int b, int c, int d){
            this.f=a;
            this.s=b;
            this.t=c;
            this.ind=d;
        }
        int getF(){
            return f;
        }
        int getS(){
            return s;
        }
        int getT(){
            return t;
        }
        int getInd(){
            return ind;
        }

        public int compareTo(tri tr){
            if(this.f==tr.f){
                if(this.t==tr.t){
                    return this.s-tr.s;
                }
                return tr.t-this.t;
            }
            return  tr.f-this.f;
        }
    }
    static long c(long[][]mx, int r, int c, int n, int m){
        long[]a=new long[4];
        a[0]=mx[r][c];
        a[1]=mx[n-r+1][c];
        a[2]=mx[r][m-c+1];
        a[3]=mx[n-r+1][m-c+1];
        long count=0;


        long mean=0;
        Arrays.sort(a);
        mean=a[1];

        for(int i=0;i<4;i++){
            count+=Math.abs(mean-a[i]);
        }
        if(n%2==1&&m%2==1) {
            if (r == n / 2 + 1 && c == m / 2 + 1) {
                return 0;
            }
        }
        if(n%2==1){
            if(r==n/2+1){
                return count-Math.abs(mean-mx[r][c])-Math.abs(mean-mx[r][m-c+1]);
            }
        }
        if(m%2==1){
            if(c==m/2+1){
                return count-Math.abs(mean-mx[r][c])-Math.abs(mean-mx[n-r+1][c]);
            }
        }
        return count;
    }
    static long mod=1000000007;
    static long fact(long n){
        long pro=1;
        for(int i=1;i<=n;i++){
            pro=(pro%mod*i%mod)%mod;
        }
        return pro;
    }
    static long pow(long a, long b){
        long res=1;
        while(b>0){
            if(b%2==0){
                a=(a%mod*a%mod)%mod;
                b/=2;
            }else{
                res=(res%mod*a%mod)%mod;
                b--;
            }
        }
        return res;
    }
    public static void main(String[] args) throws java.lang.Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);

        long n=Integer.parseInt(br.readLine());
        long f=fact(n);
        long p=pow(2l,n-1);
        long ans=((f%mod-p%mod)%mod+mod)%mod;

        out.write(String.valueOf(ans));

        out.flush();
    }

}