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 javax.print.attribute.SupportedValuesAttribute;
import java.io.*;
import java.lang.reflect.Array;
import java.security.interfaces.DSAKeyPairGenerator;
import java.util.*;
import java.util.function.Predicate;


public class Main{



    static class TaskB {

        int MOD = 1000000007;

        public void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long numCombos = factorial(n);

            long nonCycles = powerOfTwo(n-1);

            out.println((numCombos-nonCycles+MOD)%MOD);
        }

        public long powerOfTwo(int exp)
        {
            long sum = 1;
            for(int i =0; i < exp; i++)
            {
                sum=(sum*2)%MOD;
            }
            return sum;
        }
        public long factorial(int n) {
            long sum = 1;
            for(int i = 2; i <= n; i++)
            {
                sum = (sum * i)%MOD;
            }
            return sum;
        }
    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(in, out);
        out.close();
    }


    static class Graph
    {
        int V;
        LinkedList<Integer>[] adj;
        HashMap<String, Integer> convert;
        int stringName;
        boolean[] color;
        Graph(int V)
        {
            this.V = V;
            color = new boolean[V];
            adj = new LinkedList[V];
            convert = new HashMap<>();
            stringName = 0;

            for(int i = 0; i < V; i++)
            {
                adj[i] = new LinkedList<>();
            }
        }

        void addEdge(String v, String u)
        {
            if(!convert.containsKey(v))
            {
                convert.put(v, stringName);
                stringName++;
            }
            if(!convert.containsKey(u))
            {
                convert.put(u, stringName);
                stringName++;
            }
            addEdge(convert.get(v), convert.get(u));
        }

        void addEdge(int v, int u)
        {
            adj[v].add(u);
            //adj[u].add(v);  //USE IN UNDIRECTED GRAPHS
        }

        void color(int v) {
            for (int i : adj[v]) {
                color[i] = !color[v];
                color(i);
            }
        }

    }


    static void sort(int[] a)
    {
        ArrayList<Integer> list = new ArrayList<>();
        for(int i: a)list.add(i);
        Collections.sort(list);
        for(int i = 0; i < a.length; i++)a[i]=list.get(i);
    }


    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public InputReader(InputStream inputStream) {
            this.reader = new BufferedReader(
                    new InputStreamReader(inputStream));
        }

        public String next() {
            while (!tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
    }
}