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

// coded by Krishna Sundar //

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

public class Main {

    private static final long mod = 1000000007;

    public void solve(Read input, Write output) throws Exception {
        int N = input.readInt();
        long fact = 1;
        long noncycle = 1;
        for (int i=1;i<=N;i++) {
            fact = (fact*i)%mod;
        }
        for (int i=1;i<N;i++) {
            noncycle = (noncycle*2)%mod;
        }
        output.printLine((fact+mod-noncycle)%mod);
    }

    public static void main(String[] args) throws Exception {
        Read input = new Read();
        Write output = new Write();
        Main D = new Main();
        D.solve(input, output);
        output.flush();
        output.close();
    }

    // java fast io reader and writer
    // taken from various sources and customized

    static class Read {

        private byte[] buffer =new byte[10*1024];
        private int index;
        private InputStream input_stream;
        private int total;

        public Read() {
            input_stream = System.in;
        }

        public int read()throws IOException {
            if(total<0)
                throw new InputMismatchException();
            if(index>=total) {
                index=0;
                total= input_stream.read(buffer);
                if(total<=0)
                    return -1;
            }
            return buffer[index++];
        }

        public long readLong() throws IOException {
            long number=0;
            int n= read();
            while(isWhiteSpace(n))
                n= read();
            long neg=1l;
            if(n=='-') {
                neg=-1l;
                n= read();
            }
            while(!isWhiteSpace(n)) {
                if(n>='0'&&n<='9') {
                    number*=10l;
                    number+=(long)(n-'0');
                    n= read();
                }
                else throw new InputMismatchException();
            }
            return neg*number;
        }

        public int readInt() throws IOException {
            int integer=0;
            int n= read();
            while(isWhiteSpace(n))
                n= read();
            int neg=1;
            if(n=='-') {
                neg=-1;
                n= read();
            }
            while(!isWhiteSpace(n)) {
                if(n>='0'&&n<='9') {
                    integer*=10;
                    integer+=n-'0';
                    n= read();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }

        public double readDouble()throws IOException {
            double doub=0;
            int n= read();
            while(isWhiteSpace(n))
                n= read();
            int neg=1;
            if(n=='-') {
                neg=-1;
                n= read();
            }
            while(!isWhiteSpace(n)&&n!='.') {
                if(n>='0'&&n<='9') {
                    doub*=10;
                    doub+=n-'0';
                    n= read();
                }
                else throw new InputMismatchException();
            }

            if(n=='.') {
                n= read();
                double temp=1;
                while(!isWhiteSpace(n)) {
                    if(n>='0'&&n<='9') {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n= read();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }

        public String readString()throws IOException {
            StringBuilder sb = new StringBuilder();
            int n = read();
            while (isWhiteSpace(n))
                n = read();
            while (!isWhiteSpace(n)) {
                sb.append((char)n);
                n = read();
            }
            return sb.toString();
        }

        private boolean isWhiteSpace(int n) {
            if(n==' '|| n=='\n'|| n=='\r'|| n=='\t'|| n==-1)
                return true;
            return false;
        }
    }

    static class Write {

        private final BufferedWriter bw;

        public Write() {
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }
        public void print(Object str) throws IOException {
            bw.append(str+"");
        }
        public void printLine(Object str) throws IOException {
            print(str);
            bw.append("\n");
        }
        public void close()throws IOException {
            bw.close();
        }
        public void flush()throws IOException {
            bw.flush();
        }
    }
}