There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.

Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.

Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.

Constraints

* 2 \leq N \leq 10^6

Input

Input is given from Standard Input in the following format:


N


Output

Print the sum of the scores over all possible permutations, modulo 10^9+7.

Examples

Input

4


Output

16


Input

2


Output

1


Input

5


Output

84


Input

100000


Output

341429644
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScan in = new MyScan(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, MyScan in, PrintWriter out) {
            int i = in.nextInt();

            long[] md = new long[i];

            int rm = i - 2;
            int lx = i - 2;
            while (rm >= 0) {
                md[lx + 1] = Util.c(rm, lx);
                rm -= 2;
                lx--;
            }
            long res = 0;
            long prev = 0;
            for (int m = 1; m < i; m++) {
                long cur = Util.fact(m) * Util.fact(i - m - 1) % Util._m;
                cur = cur * (md[m]) % Util._m;


                res += (cur - prev + Util._m) * m % Util._m;
                prev = cur;

            }


            out.println(res % Util._m);

        }

    }

    static class MyScan {
        private final InputStream in;
        private byte[] inbuf = new byte[1024];
        public int lenbuf = 0;
        public int ptrbuf = 0;

        public MyScan(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = in.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

    }

    static class Util {
        public static final long M07 = 1000_000_007;
        public static long _m = M07;
        private static long[] fact;
        private static long[] inv;
        private static long[] ifact;

        public static void l() {
            fact = new long[1000001];
            inv = new long[1000001];
            ifact = new long[1000001];
            for (int s = 0; s < 2; s++) {
                fact[s] = 1;
                ifact[s] = 1;
                inv[s] = 1;
            }
            inv[0] = 0;
            for (int i = 2; i < inv.length; i++) {
                inv[i] = (_m - (_m / i) * inv[(int) (_m % i)] % _m) % _m;
            }
            for (int i = 2; i < fact.length; i++) {
                fact[i] = i * fact[i - 1] % _m;
                ifact[i] = inv[i] * ifact[i - 1] % _m;
            }
        }

        public static long c(int a, int b) {
            if (fact == null) l();
            return ifact[a] * ifact[b - a] % _m * fact[b] % _m;
        }

        public static long fact(int a) {
            if (fact == null) l();
            return fact[a];
        }

    }
}

