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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
import java.util.stream.Collectors;

public class Main {

    public static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws Exception {
        long n = readLong();
        long m = 1000000007;
        long f = 1;
        for (int i = 1; i <= n; i++) {
            f = f*i;
            f = f%m;
        }
        long p = pow(2,n-1);
        long ans = f-p;
        while(ans<0) {
            ans+=m;
        }
        System.out.println(ans%m);
    }

    private static long pow(long a, long b) {
        long m = 1000000007;
        if(b==0) {
            return 1;
        }
        if(b==1) {
            return a;
        }
        long tp = pow(a,b/2);
        return (((tp*tp)%m)*(b%2==1 ? a : 1))%m;
    }

    private static String readString() throws Exception {
        return br.readLine();
    }

    private static int readInt() throws Exception{
        return Integer.parseInt(readString());
    }

    private static long readLong() throws Exception{
        return Long.parseLong(readString());
    }

    private static double readDouble() throws Exception{
        return Double.parseDouble(readString());
    }

    private static String[] readStringArray() throws Exception {
        return br.readLine().split(" ");
    }

    private static List<String> readStringList() throws Exception {
        return Arrays.asList(readStringArray());
    }

    private static List<Integer> readIntList() throws Exception {
        return readStringList().stream().map(s -> Integer.parseInt(s)).collect(Collectors.toList());
    }

    private static int[] readIntArray() throws Exception {
        return readIntList().stream().mapToInt(i -> i).toArray();
    }

    private static List<Long> readLongList() throws Exception {
        return readStringList().stream().map(s -> Long.parseLong(s)).collect(Collectors.toList());
    }

    private static long[] readLongArray() throws Exception {
        return readLongList().stream().mapToLong(i -> i).toArray();
    }

    private static List<Double> readDoubleList() throws Exception {
        return readStringList().stream().map(s -> Double.parseDouble(s)).collect(Collectors.toList());
    }

    private static double[] readDoubleArray() throws Exception {
        return readDoubleList().stream().mapToDouble(i -> i).toArray();
    }
}
