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

//package CodeForces;

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

public class Main {

    public class Haha {
        /*                     _____                                                             ___
                /\      /\    |     | |   |    /\       /\      /\       /\      /\       /\    |   \     محمد أبوحسن*
               /  \    /  \   |     | |___|   /__\     /  \    /  \     /  \    /  \     /__\   |    \
              /    \  /    \  |     | |   |  /    \   /    \  /    \   /    \  /    \   /    \  |    /
             /      \/      \ |_____| |   | /      \ /      \/      \ /      \/      \ /      \ |___/
         */
    }

    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;
        }
    }

    public static class MyPair {

        int x;
        int y;

        public MyPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    public static int Fibonacci(int n) {
        int[] a = new int[n + 1];
        a[0] = 0;
        a[1] = 1;
        for (int i = 2; i < a.length; i++) {
            a[i] = a[i - 1] + a[i - 2];
        }
        return a[n];
    }

    public static boolean isprime(int n) {
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                return true;
            }
        }
        return false;
    }

    public static int[] addarr(int[] a, int n) {
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        return a;
    }
    
    public static int fact(int n){
        int fact = 1;
        for(int i = 1; i <= n; i++)
            fact = ((fact%1000000007) * (i%1000000007))%1000000007;
        return fact + 1000000007;
    }
    public static long poww(int n, int p){
        if(p == 0)
            return 0;
        if(p == 1)
            return n%1000000007;
        long c = poww(n, p/2)%1000000007;
        if(p%2 == 0)
            return ((c%1000000007) * (c%1000000007) * (n%1000000007))%1000000007;
        return (c%1000000007 * c%1000000007)%1000000007;
    }
    
    public static long sumDigit(long n){
        int a = 0;
        while(n != 0){
            a += n%10;
            n /= 10;
        }
        return a;
    }
    
    public static MyScanner sc = new MyScanner();
    // __builtin_popcountll(n) <-- c++ // binary count(1) ex. 8 --> 0100 --> 1
    HashSet<Integer> set = new HashSet<>();
    HashMap<Integer, Integer> map = new HashMap<>();
    ArrayList<Integer> l = new ArrayList<>();

    public static void main(String[] args) {
        int n = sc.nextInt(), c = (int) poww(2, n-1)%1000000007, s = fact(n);
        s -= c%1000000007;
        System.out.println(s%1000000007);
    }
}