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.util.*;
import java.lang.*;
import java.io.*;   
import java.math.*;
public class Prac{     
    static class InputReader { 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        public InputReader(InputStream st) {
            this.stream = st;
        } 
        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
            c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public int[] nia(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public int[] nia1(int n) {
            int a[] = new int[n+1];
            for (int i = 1; i <=n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public long[] nla(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        } 
        public long[] nla1(int n) {
            long a[] = new long[n+1];
            for (int i = 1; i <= n; i++) {
                a[i] = nl();
            }
            return a;
        } 
        public Long[] nLa(int n) {
            Long a[] = new Long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        } 
        public Long[] nLa1(int n) {
            Long a[] = new Long[n+1];
            for (int i = 1; i <= n; i++) {
                a[i] = nl();
            }
            return a;
        } 
        public Integer[] nIa(int n) {
            Integer a[] = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public Integer[] nIa1(int n) {
            Integer a[] = new Integer[n+1];
            for (int i = 1; i <= n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public String rs() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                    c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        } 
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        } 
    }
    public static class Key {
        private final int x, y;
        public Key(int x, int y) {
            this.x = x; this.y = y;
        }
        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Key)) return false;
            Key key = (Key) o;
            return x == key.x && y == key.y;
        }
        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }
    }
    static class Pair implements Comparable<Pair>{
            int x,y;
            Pair(int a,int b){
                    x=a;y=b;
            }
            @Override
            public int compareTo(Pair p) {
                    if(x==p.x) return y-p.y;
                    return x-p.x;
            }
    }
    static void shuffleArray(int temp[]){
        int n = temp.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = temp[i];
            int randomPos = i + rnd.nextInt(n-i);
            temp[i] = temp[randomPos];
            temp[randomPos] = tmp;
        }   
    }
    static long gcd(long a,long b){ return b==0?a:gcd(b,a%b);}
    static long lcm(long a,long b){return (a/gcd(a,b))*b;}
    static PrintWriter w = new PrintWriter(System.out);
    static long mod1=998244353L,mod=1000000007;
    //static int r[]={0,1,0,-1}, c[]={1,0,-1,0};
    static long fact[]=new long[1000005];
    public static void findFact(){
        fact[0]=1;
        for(int i=1;i<=1000000;i++){
            fact[i]=(i*fact[i-1])%mod;
        }
    } 
    static long ncrWithMod(int n,int r){
        if(n<r)return 0L;
        
        return (fact[n]*modInverse((fact[r]*fact[n-r])%mod,mod-2))%mod;
    }
    static long modInverse(long a, long m){
        long num=m;
        long x=1;
        long power=a%mod;
        while(num>0){
              if(num%2==1){
                  x=(x*power)%mod;
            }
            num>>=1;
            power=(power*power)%mod;         
        }
        return x;
    }
    static long  power(long x, long y) { 
        long temp=0; 
        if( y == 0) 
            return 1; 
        temp = power(x, y/2); 
        if (y%2 == 0) 
            return (temp*temp)%mod; 
        else
            return (((x*temp)%mod)*temp)%mod; 
    } 
    public static void main(String [] args){
        InputReader sc=new InputReader(System.in); 
        findFact();
        int n=sc.ni();
        w.println((fact[n]-power(2,n-1)+mod)%mod);
        
        w.close();
    }
}