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.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    final FastScanner in = new FastScanner(System.in);

    final long MOD = (long)((1e9) + 7);

    /* MOD_CALCULATION */
    long ADD(long a, long b) {
        return (a + b) % MOD;
    }

    long SUB(long a, long b) {
        return (a - b + MOD) % MOD;
    }

    long MULT(long a, long b) {
        return (a * b) % MOD;
    }

    long POW(long a, long x) {
        long res = 1;
        for ( ; x > 0; x >>= 1) {
            if (x % 2 == 1) res = MULT(res, a);
            a = MULT(a, a);
        }

        return res;
    }

    long DIV(long a, long b) {
        return MULT(a, POW(b, MOD - 2));
    }
    /* end */

    public void solve() {
        int N = in.nextInt();
        if (N == 2) {
            System.out.println(1);
            return;
        } else if (N == 3) {
            System.out.println(4);
            return;
        }

        long[] fact = new long[N+1];
        fact[0] = 1;
        for (int i = 0; i < N; i++) {
            fact[i+1] = MULT(fact[i], i + 1);
        }
        long[] inv = new long[N+1];
        inv[N] = DIV(1, fact[N]);
        for (int i = N - 1; i >= 0; i--) {
            inv[i] = MULT(inv[i+1], i + 1);
        }

        long res = 0;
        long[] cnt = new long[N];
        for (int K = 1; K <= N - 1; K++) {
            if (2 * K < N) {
                continue;
            }
            long comb = MULT(MULT(fact[K-1], inv[N-1-K]), inv[2*K-N]);
            cnt[K] = MULT(comb, MULT(fact[K], fact[N-1-K]));
            res = ADD(res, MULT(K, SUB(cnt[K], cnt[K-1])));
        }
        System.out.println(res);
    }

    public static void main(final String[] args) {
        new Main().solve();
    }

    class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
            // stream = new FileInputStream(new File("dec.in"));

        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

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

        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++)
                array[i] = nextInt();

            return array;
        }

        int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextIntArray(m);
            }
            return map;
        }

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

        long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++)
                array[i] = nextLong();

            return array;
        }

        long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextLongArray(m);
            }
            return map;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++)
                array[i] = nextDouble();

            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextDoubleArray(m);
            }
            return map;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}
