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. 
import java.util.*;
import java.io.*;
	        public final class Solve {
	        	static long m = (long) (1e9 + 7);
	        public static void main(String args[]) throws IOException {
	        FastReader sc = new FastReader();
	        	long n = sc.nextInt();
	        	long f = 1, p= 1;
	        	for(int i = 2;i<=n;i++) {
	        		f = f*i%m;
	        		 p = p*2%m;
	        	}
	        	pn((f - p + m)%m);
	        }
	       static void p(Object p){System.out.print(p);}
	       static void pn(){System.out.println();}
	       static void pn(Object o){System.out.println(o);}
	            
	       static class FastReader {
	                
	       static BufferedReader br;
	       StringTokenizer st;
	            
	       public FastReader() {
	       br = new BufferedReader(new InputStreamReader(System.in));
	       }
	            
	       String next(){
	       while (st == null || !st.hasMoreElements()) {
	            try{
	                st = new StringTokenizer(br.readLine());
	            }
	            catch (IOException  e) {
	                e.printStackTrace();
	            }}
	            return st.nextToken();
	            }
	            
	            int nextInt(){ 
	                return Integer.parseInt(next());
	            }
	            
	            long nextLong(){ 
	                return Long.parseLong(next());
	            }
	            
	            static int max(int[] a){
	            int max = Integer.MIN_VALUE;
	            for(int i : a) max = Math.max(max, i);
	            return max;
	            }
	            
	            public int[] readIntArray(int n) {
	            int[] arr = new int[n];
	            for(int i=0; i<n; ++i) arr[i]=nextInt();
	            return arr;
	            }
	            
	            public long[] readLongArray(int n){
	            long[] arr = new long[n];
	            for(int i=0; i<n; ++i) arr[i]=nextLong();
	            return arr;
	            }
	            
	            public int[][] readIntArray(int m, int n){
	            int[][] arr = new int[m][n];
	            for(int i = 0;i<m;i++) 
	            for(int j = 0;j<n;j++) arr[i][j] = nextInt();
	            return arr;
	            }
	            
	            public String[] readStringArray(int n) {
	            String[] arr = new String[n];
	            for(int i=0; i<n; ++i) arr[i]= nextLine();
	            return arr;
	            }
	            
	            double nextDouble() {return Double.parseDouble(next());}
	            
	            String nextLine() {
	            String str = "";
	            try{str = br.readLine();}
	            catch (IOException e) {e.printStackTrace();}
	            return str;}}
	        }
	            
	            
	            