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. 
import java.io.*;
import java.util.*;
import java.lang.*;

public class c1 {
    public static MyScanner scan;
    public static PrintWriter out;
    public static void main(String[] args) {
        scan=new MyScanner();
        out=new PrintWriter(new BufferedOutputStream(System.out));

        int t=1;
//        int t=scan.nextInt();
        while(t-->0) {

            long n=scan.nextLong(),ans=1,pow=1;
            for(int c=1;c<=n;c++) pow=(pow*(long)(c))%mod;
            for(int c=0;c<n-1;c++) ans=(ans*(long)(2))%mod;
            out.println((pow-ans<0)?pow-ans+mod:(long)(pow-ans)%mod);

        }
        out.close();
    }

    //-----------------------------------------------------COMP-SPACE-----------------------------------------------------

    public static long mod=(long)1e9+7;

    //--------------------------------------------------------------------------------------------------------------------

    //util
    public static int gcd(int a, int b) {
        if (b == 0)
            return a;
        if (a == 0)
            return b;
        return (a > b) ? gcd(a % b, b) : gcd(a, b % a);
    }

    public static int lcm(int a, int b) {
        return a * b / gcd(a, b);
    }

    public static ArrayList<Integer> getPrimes(int n) {
        boolean prime[]=new boolean[n+1];
        Arrays.fill(prime,true);
        for (int p=2;p*p<=n;p++) {
            if (prime[p]) {
                for (int i=p*2;i<=n;i+=p) {
                    prime[i]=false;
                }
            }
        }
        ArrayList<Integer> primeNumbers=new ArrayList<Integer>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                primeNumbers.add(i);
            }
        }
        return primeNumbers;
    }

    public static boolean isPrime(int a) {
        if (a == 0 || a == 1) {
            return false;
        }
        if (a == 2) {
            return true;
        }
        for (int i = 2; i < Math.sqrt(a) + 1; i++) {
            if (a % i == 0) {
                return false;
            }
        }
        return true;
    }

    public static ArrayList<Integer> getDivisors(int n) {
        ArrayList<Integer> div = new ArrayList<Integer>();
        for (int i=1;i*i<=n;i++) {
            if (n%i==0) {
                div.add(i);
                if (n/i!=i)
                    div.add(n/i);
            }
        }
        return div;
    }

    //scanner
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

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