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

public class Q1 {
	private long pow(long base,long pow, long mod)
	{
		if(pow==0)
		{
			return 1l;
		}
		else if(pow==1)
		{
			return base;
		}
		if((pow&1)==1)
		{
			return (base*pow(base,pow/2,mod)*pow(base,pow/2,mod))%mod;
		}
		else
		{
			return (pow(base,pow/2,mod)*pow(base,pow/2,mod))%mod;
		}
	}
	private void solve(Scan scan, Print print) throws Exception {
			int N=scan.nextInt();
			long mod = 1000000007;
			long fact=1;
			for(int i=2;i<=N;i++)
			{
				fact=(fact*i)%mod;
			}
			long pow=pow(2,N-1,mod);
		//	System.out.println(fact+" "+pow);
			long ans=fact-pow;
			if(ans<0)
			{
				ans=(ans+mod)%mod;
			}
			print.println(ans);
	}

	public static void main(String args[]) throws Exception {
		Scan scan = new Scan();
		Print print = new Print();
		Q1 o = new Q1();
		o.solve(scan, print);
		print.close();
	}

	public static class Print {
		private final BufferedWriter bw;

		public Print() {
			this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
		}

		public void print(Object object) throws IOException {
			bw.append("" + object);
		}

		public void println(Object object) throws IOException {
			print(object);
			bw.append("\n");
		}

		public void println(int object[]) throws IOException {
			print(Arrays.toString(object));
			bw.append("\n");
		}

		public void print(int object[]) throws IOException {
			print(Arrays.toString(object));
		}

		public void println(long object[]) throws IOException {
			print(Arrays.toString(object));
			bw.append("\n");
		}

		public void print(long object[]) throws IOException {
			print(Arrays.toString(object));
		}

		public void println(boolean object[]) throws IOException {
			print(Arrays.toString(object));
			bw.append("\n");
		}

		public void print(boolean object[]) throws IOException {
			print(Arrays.toString(object));
		}

		public void println(Object object[]) throws IOException {
			print(Arrays.deepToString(object));
			bw.append("\n");
		}

		public void print(Object object[]) throws IOException {
			print(Arrays.deepToString(object));
		}

		public void close() throws IOException {
			bw.close();
		}
	}

	static class Scan {
		private byte[] buf = new byte[1024 * 1024 * 4];
		private int index;
		private InputStream in;
		private int total;

		public Scan() {
			in = System.in;
		}

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

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

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

		public long nextLong() throws IOException {
			long ret = 0;
			long c = scan();
			while (c <= ' ') {
				c = scan();
			}

			boolean neg = (c == '-');
			if (neg) {
				c = scan();
			}

			do {
				ret = ret * 10 + c - '0';
			} while ((c = scan()) >= '0' && c <= '9');

			if (neg) {
				return -ret;
			}
			return ret;
		}

		public String next() throws IOException {
			StringBuilder sb = new StringBuilder();
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			while (!isWhiteSpace(n) || n == ' ') {
				sb.append((char) n);
				n = scan();
			}
			return sb.toString();
		}

		public void next(int arr[]) throws IOException {
			for (int i = 0; i < arr.length; i++) {
				arr[i] = nextInt();
			}
		}

		public void next(long arr[]) throws IOException {
			for (int i = 0; i < arr.length; i++) {
				arr[i] = nextLong();
			}
		}

		public char[] next(char c) throws IOException {
			char arr[] = next().toCharArray();
			return arr;
		}

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