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. 
//package com.example.myPackage;

import java.io.PrintWriter;
import java.util.Scanner;

public class CyclicPermutation663 {
    private static Scanner fs = new Scanner(System.in);
    private static int Mod = 1000_000_007;
    private static PrintWriter out = new PrintWriter(System.out);
    public static void main(String[] args) {
     int n = Integer.parseInt(fs.next());
     /*
     // Hre it is an important Concept of unimodel permutations
        // We can see only uni model permutation are not making cycles
        // So We just need to calculate the number of uni model
       // permutations and sub tract with the number of the permuatation
        //i.e n! - 2^(n-1)
        //2^(n-1) because we are fixing the n element and remaining elements we can either
        //front or back;
         */
     long res =1;
     for(int i=2;i<=n;i++)
        res = (res*i)%Mod;
     long minus =1;
     for(int i=0;i<n-1;i++) minus=(minus*2)%Mod;
     long Fres = (res - minus+ Mod)%Mod;
     out.println(Fres);
     out.close();
    }
}
