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 R663C {
	static int ans = 0;
	static int count = 0;
	public static void main(String[] args) {
		JS scan = new JS();
		int n = scan.nextInt();
		long[] fac = new long[n+1];
		long at = 1;
		for(long i = 1;i<=n;i++) {
			at*=i;
			at%=1_000_000_007;
			fac[(int) i] = at;
		}
		long[] fib = new long[n+1];
		fib[1] = 1;
		fib[2] = 1;
		for(int i = 3;i<=n;i++) {
			fib[i] = fib[i-1]+fib[i-2];
			fib[i]%=1_000_000_007;
		}
		int[] perm = new int[n];
		boolean[] v= new boolean[n];
		//permute(0,perm,n,v);
		long po = power(2,n,0);
		long anss = po*fib[n];
		//System.out.println(anss%1_000_000_007);
		//System.out.println((long)(power(2,n-1,0)*(n-2))%1_000_000_007);
		long ansss = (fac[n]-power(2,n-1,0)+1_000_000_007)%1_000_000_007;
		System.out.println(ansss);
		//System.out.println(fac[n]-ans);
	}
	static void permute(int idx, int[] perm, int n, boolean[] v) {
		if(idx==n) {
			count++;
			for(int i = 0;i<n;i++) {
				System.out.print(perm[i]+" ");
			}
			System.out.println();
			for(int i = 1;i<n-1;i++) {
				if(perm[i]<perm[i+1] && perm[i]<perm[i-1]) {
					System.out.println(count);
					return;
				}
			}
			ans++;
		}else {
			for(int i = 1;i<=n;i++) {
				if(!v[i-1]) {
					v[i-1] = true;
					perm[idx] = i;
					permute(idx+1,perm,n,v);
					v[i-1] = false;
				}
			}
		}
	}
	static long power(long x, long y, int p) 
	{ 
		// Initialize result 
		p = 1_000_000_007;
		long res = 1;      

		// Update x if it is more   
		// than or equal to p 
		x = x % p;  

		if (x == 0) return 0; // In case x is divisible by p;    

		while (y > 0) 
		{ 
			// If y is odd, multiply x 
			// with result 
			if((y & 1)==1) 
				res = (res * x) % p; 

			// y must be even now 
			// y = y / 2 
			y = y >> 1;  
				x = (x * x) % p;  
		} 
		return res; 
	} 
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}
