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

/*input
583291

*/



import java.math.*;
import java.io.*;
import java.util.*;
public class Main
{
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead;
public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        }
public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        }
public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        }
public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9');
if (neg) 
                return -ret; 
            return ret; 
        }
public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        }
public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read();
do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9');
if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            }
if (neg) 
                return -ret; 
            return ret; 
        }
private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        }
private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        }
public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 




        
    static Reader sc=new Reader();
    static BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
    static  Scanner in = new Scanner(System.in);

static boolean flag=false;
    
    public static void main(String args[])throws IOException
    {
        /*
         * For integer input: int n=inputInt();
         * For long input: long n=inputLong();
         * For double input: double n=inputDouble();
         * For String input: String s=inputString();
         * Logic goes here
         * For printing without space: print(a+""); where a is a variable of any datatype
         * For printing with space: printSp(a+""); where a is a variable of any datatype
         * For printing with new line: println(a+""); where a is a variable of any datatype
            Scanner in = new Scanner(System.in);
        //all four
         int[] dr = { 1, 0, -1, 0 };
         int[] dc = { 0, 1, 0, -1 };
         println("Case #"+k+": "+1+"");//Google

         */
        
            int t=1;

            while(t-->0)
            {
                long n= inputLong();
              long fact=1;

              long pow=1;

                 final int mod= 1000000007;
                // println(mod+"");
                for(int i=1;i<=n;i++)
                {
                    fact= fact*i%mod;
                }

                for(int i=1;i<n;i++)
                {
                    pow=pow*2%mod;
                }

                println((fact-pow+mod)%mod+"");
            }



    
bw.flush();
  bw.close();

}


       

static void dfs(int src,int dst,List<List<Integer>> ls,boolean visit[])
    {
        
        if(visit[src])
            return;
        visit[src]=true;
        
        if(src==dst)
            {flag=true;return;}

        Iterator<Integer> ite = ls.get(src).listIterator();

        while(ite.hasNext())
        {
            int x=ite.next();

            if(!visit[x])
            {
                
                dfs(x,dst,ls,visit);
            }
        }
        
    }

        public static long pow(long a,long b)
        {
            long result=1;

            while(b>0)
            {
                if(b%2==1) result*=a;
                a*=a;
                b/=2;
            }
            return result;
        }

        public static long nCr(long n, long r) 
        { 
            long ans=1;
            if(r>n-r)
            {
                r=n-r;
            }
            for(long i=1;i<=r;i++)
            {
                ans*=(n-i+1);
                ans/=i;
            }
            return ans;
        } 
        public static long modulo(long x,long N)
        {
            return (x % N + N) %N;
        }
        public static long lcm(long a,long b)
        {    
            return a / gcd(a, b) * b;
        }
        public static long gcd(long a,long b)
        {
            if(b==0)
                return a;
            return gcd(b,a%b);
        }

     public static int inputInt()throws IOException
    {
        return sc.nextInt();
    }
    public static long inputLong()throws IOException
    {
        return sc.nextLong();
    }
    public static double inputDouble()throws IOException
    {
        return sc.nextDouble();
    }
   
 
    public static String inputString()throws IOException
    {
        return sc.readLine();
    }
    public static void print(String a)throws IOException
    {
        bw.write(a);
    }
    public static void printSp(String a)throws IOException
    {
        bw.write(a+" ");
    }
    public static void println(String a)throws IOException
    {
        bw.write(a+"\n");
    }
}       