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 com.company;
//package com.codeforces;
import java.io.*;
import java.util.*;
import java.util.logging.Logger;

public class Main {
    static BufferedReader br;
    static  long mod  = 1000000000+7;
    static HashSet<Integer> p  = new HashSet<>();
    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        int tc = 1;
       // tc = cinI();
        long mod  = (long) (1e9+7);
        while (tc-- > 0) {


       int n = cinI();
       long fact = 1;
          for(int i=1;i<=n;i++){
              fact=((fact%mod) *(i%mod))%mod;
          }
          long dif  =1;
          for(int j=1;j<n;j++){
              dif=((dif%mod)*(2))%mod;
          }
            System.out.println(fact-dif);



        }
    }

    public static boolean isSorted(int[] arr){

        for(int i=0;i<arr.length-1;i++){
            if(arr[i]>arr[i+1]){
                return false;
            }
        }
        return true;
    }



    private static long gcd(long a, long b) {
        if (a == 0)
            return b;
        if (b == 0)
            return a;

        // base case
        if (a == b)
            return a;

        // a is greater
        if (a > b)
            return gcd(a%b, b);
        return gcd(a, b%a);
    }


    public static long min(long a,long b) {
        return Math.min(a,b);
    }
    public static int min(int a,int b) {
        return Math.min(a,b);
    }
























    public static void sieve(){
        int[] pf = new int[100000000+1];
        //0 prime //1 not prime
        pf[0]=1;
        pf[1]=1;
        for(int j=2;j<=10000;j++){

            if(pf[j]==0 ){
                p.add(j);
                for(int k=j*j;k<pf.length;k+=j){
                    pf[k]=1;
                }
            }
        }

    }






    public  static  int[] readArray(int n,int x ,int z)throws Exception{
        int[] arr= new int[n];
        String[] ar= cinA();
        for(int i =x ;i<n+x;i++){
            arr[i]=getI(ar[i-x]);
        }
        return arr;
    }
    public  static  long[] readArray(int n,int x )throws Exception{
        long[] arr= new long[n];
        String[] ar= cinA();
        for(int i =x ;i<n+x;i++){
            arr[i]=getL(ar[i-x]);
        }
        return arr;
    }

    public static void arrinit(String[] a,long[] b)throws Exception{
        for(int i=0;i<a.length;i++){
            b[i]=Long.parseLong(a[i]);
        }
    }
    public  static HashSet<Integer>[]  Graph(int n,int edge,int directed)throws Exception{
        HashSet<Integer>[] tree=  new HashSet[n];

        for(int j=0;j<edge;j++){

            String[] uv = cinA();
            int u = getI(uv[0]);
            int v = getI(uv[1]);
            if(directed==0){

                tree[v].add(u);
            }
            tree[u].add(v);
        }
        return tree;
    }
    public static void arrinit(String[] a,int[] b)throws Exception{
        for(int i=0;i<a.length;i++){
            b[i]=Integer.parseInt(a[i]);
        }
    }


    static double findRoots(int a, int b, int c) {
        // If a is 0, then equation is not
        //quadratic, but linear


        int d = b * b - 4 * a * c;
        double sqrt_val = Math.sqrt(Math.abs(d));


        // System.out.println("Roots are real and different \n");

        return Math.max((double) (-b + sqrt_val) / (2 * a),
                (double) (-b - sqrt_val) / (2 * a));


    }

    public static String cin() throws Exception {
        return br.readLine();
    }

    public static String[] cinA() throws Exception {
        return br.readLine().split(" ");
    }
    public static String[] cinA(int x) throws Exception{
        return br.readLine().split("");
    }

    public static String ToString(Long x) {
        return Long.toBinaryString(x);
    }

    public static void cout(String s) {
        System.out.println(s);
    }

    public static Integer cinI() throws Exception {
        return Integer.parseInt(br.readLine());
    }

    public static int getI(String s) throws Exception {
        return Integer.parseInt(s);
    }

    public static long getL(String s) throws Exception {
        return Long.parseLong(s);
    }

    public static long max(long a, long b) {
        return Math.max(a, b);
    }
    public static int max(int a, int b) {
        return Math.max(a, b);
    }

    public static void coutI(int x) {
        System.out.println(String.valueOf(x));
    }

    public static void coutI(long x) {
        System.out.println(String.valueOf(x));
    }

    public static Long cinL() throws Exception {
        return Long.parseLong(br.readLine());
    }

    public static void arrInit(String[] arr, int[] arr1) throws Exception {
        for (int i = 0; i < arr.length; i++) {
            arr1[i] = getI(arr[i]);
        }

    }
}

class range {
    int l;
    int r;
    int diff;

    public range(int l, int r, int diff) {
        this.l = l;
        this.r = r;
        this.diff = diff;
    }
}

class sortRange implements Comparator<range> {


    @Override
    public int compare(range range, range t1) {
        if (range.diff != t1.diff)
            return t1.diff - range.diff;
        return range.l - t1.l;

    }}
class Diag{

    int c0;
    int c1;
    public Diag(int c0,int c1){
        this.c0=c0;
        this.c1=c1;
    }
}