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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Set;

public class Solution {

	InputStream in;
	PrintWriter out;
	String input = "";
	int MOD = 1000000007;
	
	void solve() {
		int n = in_i();
		long count = findFactorial(n) - findPower2(n-1) + MOD;
		out.println(count % MOD);
	}

	private long findFactorial(int m) {
		long n = 1;
		for(int i = 1; i <= m; ++i) {
			n = (n * i) % MOD;
		}
		return n;
	}
	
	private long findPower2(int m) {
		long n = 1;
		for(int i = 1; i <= m; ++i) {
			n = (n * 2) % MOD;
		}
		return n;
	}
	
	public static void main(String[] args) throws Exception {

		new Solution().run();
	}

	void run() throws Exception {

		out = new PrintWriter(System.out);
		in = input.isEmpty() ? System.in : new ByteArrayInputStream(input.getBytes());
		solve();
		out.flush();
	}

	private byte[] buffer = new byte[1024];
	public int ptr = 0, len = 0;

	private int readByte() // input
	{
		if (len == -1)
			throw new InputMismatchException();
		if (ptr >= len) {
			ptr = 0;
			try {
				len = in.read(buffer);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (len <= 0)
				return -1;
		}
		return buffer[ptr++];
	}

	private boolean isSpace(int c) { // check for white space
		return !(c > 32 && c < 127);
	}

	private int check() {
		int n;
		while ((n = readByte()) != -1 && isSpace(n))
			;
		return n;
	}

	private int in_i() // input for int
	{
		int num = 0, a;
		boolean minus = false;
		while ((a = readByte()) != -1 && !((a >= '0' && a <= '9') || a == '-'))
			;
		if (a == '-') {
			minus = true;
			a = readByte();
		}

		while (true) {
			if (a >= '0' && a <= '9') {
				num = num * 10 + (a - '0');
			} else {
				return minus ? -num : num;
			}
			a = readByte();
		}
	}

	private int[] in_ai(int n) // input for int array
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = in_i();
		return arr;
	}

	private long in_l() // input for long
	{
		long num = 0;
		int a;
		boolean minus = false;
		while ((a = readByte()) != -1 && !((a >= '0' && a <= '9') || a == '-'))
			;
		if (a == '-') {
			minus = true;
			a = readByte();
		}

		while (true) {
			if (a >= '0' && a <= '9') {
				num = num * 10 + (a - '0');
			} else {
				return minus ? -num : num;
			}
			a = readByte();
		}
	}

	private long[] in_al(int n) // input for int array
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++)
			arr[i] = in_l();
		return arr;
	}

}