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 SolutionC { 
    static Random random;
 
    /* public static void main(String[] args){
        new Thread(null, new SolutionC (), "Main", 1<<26).start();
    } */
 
    public static void main(String[] args) {
        FastScanner in = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        random = new Random();
 
        // long timeStamp = System.currentTimeMillis();
        Solver solver = new Solver();
        solver.solve(in, out);
        out.close();
        // System.err.println("TIME: "+(System.currentTimeMillis()-timeStamp)+" ms");
    }
 
    /* ------------------------------------- START -------------------------------------------- */
    static class Solver {
        static final long mod = 1_000_000_007;
        public void solve(FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            long non = modPow(2, n-1, mod);
            long total = 1;
            for(int i = 1; i<=n; i++){
                total = total * i % mod;
            }
            long ans = total - non;
            if(ans < 0) ans += mod;
            out.println(ans);
        }   

        private static long modPow(long x, long n, long m) {
            if(m == 1) return 0;
            if(x >= m) x %= m;
            long ret = 1;
            while(n > 0){
                if((n&1) > 0) 
                    ret = ret * x % m;
                x = x * x % m;
                n >>= 1;
            }
            return ret;
        }
    }
    /* -------------------------------------- END --------------------------------------------- */
 
    /* Shuffle function to shuffle before Arrays.sort */
    static void shuffle(int[] arr){
        int swapTemp;
        for(int i = arr.length-1; i>= 1; i--){
            int pos = random.nextInt(i+1);
            if(pos == i) continue;
            {swapTemp = arr[i]; arr[i] = arr[pos]; arr[pos] = swapTemp;}
        }
    }
 
    /* Fast Input reader */
    static class FastScanner {
        BufferedReader reader;
        StreamTokenizer tokenizer;
        public FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = new StreamTokenizer(reader);
            tokenizer.resetSyntax();
            tokenizer.whitespaceChars(0, 32);
            tokenizer.wordChars(33, 126);
        }
        private void nextToken(){
            try{ tokenizer.nextToken(); }
            catch (Exception e) { e.printStackTrace(); }
        }
        String next() {
            nextToken();
            return tokenizer.sval;
        }
        int nextInt() {
            nextToken();
            return Integer.parseInt(tokenizer.sval);
        }
        long nextLong() {
            nextToken();
            return Long.parseLong(tokenizer.sval);
        }
        double nextDouble() {
            nextToken();
            return Double.parseDouble(tokenizer.sval);
        }
        String nextLine() {
            try{
                String string = reader.readLine();
                return string;
            } catch (Exception e) {
                e.printStackTrace();
                return "";
            }
        }
    }
}
