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.lang.reflect.Array;
import java.util.*;


public class TaskC {

    static long N;
    static long MOD = 1000000007;

    static long mpow(long a, long n){
        if(n == 0) return 1;
        long r = mpow(a, n/2);
        r = r * r;
        r %= MOD;
        if(n % 2 == 1) r *= a;
        return r % MOD;
    }
    static FastIO io = new FastIO("in.txt");

    public static void main(String[] args) throws Exception {
        N = io.nextInt();
        long ans = 1;
        for(int i=1; i<=N; i++){
            ans *= i;
            ans %= MOD;
        }
        io.println(((ans - mpow(2, N-1)) % MOD + MOD)%MOD);
        io.close();
    }

    static class FastIO {
        BufferedReader br;
        StringTokenizer sk;
        PrintWriter pw = new PrintWriter(System.out);

        public FastIO(String fname){
            try{
                File f = new File(fname);
                if(f.exists()) {
                    System.setIn(new FileInputStream(fname));
                }

            }catch (Exception e){
                throw new IllegalArgumentException(e);
            }

            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastIO(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next(){
            while(sk==null || !sk.hasMoreElements()){
                try {
                    sk = new StringTokenizer(br.readLine());
                }catch (Exception e){
                    throw new IllegalArgumentException(e);
                }
            }
            return sk.nextToken();
        }

        public int nextInt(){
            return Integer.parseInt(next());
        }

        public char nextChar(){
            return next().charAt(0);
        }

        public long nextLong(){
            return Long.parseLong(next());
        }

        public double nextDouble(){
            return Double.parseDouble(next());
        }

        public String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            }catch (Exception e){
                e.printStackTrace();
            }
            return str;
        }

        public void print(Object o){
            pw.print(o);
        }

        public void println(Object o){
            pw.println(o);
        }

        public void close(){
            pw.close();
        }

        public void flush(){
            pw.flush();
        }
    }
}

