Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

4

Sample Output 1

16

There are six possible permutations as P.
Among them, P = (1, 3, 2) and P = (3, 1, 2) have a score of 2, and the others have a score of 3.
Thus, the answer is 2 \times 2 + 3 \times 4 = 16.

Sample Input 2

2

Sample Output 2

1

There is only one possible permutation: P = (1), which has a score of 1.

Sample Input 3

5

Sample Output 3

84

Sample Input 4

100000

Sample Output 4

341429644

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


public class Main {
  private static void solve() {
    int n = ni();

    int mod = 1000000000 + 7;
    long ret = 0;
    int[][] fif = enumFIF(n + 1, mod);
    if (n == 2) {
      System.out.println(1);
      return;
    } else if (n == 3) {
      System.out.println(4);
      return;
    }

    long[] a = new long[n];
    for (int k = (n + 1) / 2; k <= n - 1; k ++) {
      //k個置く→(n-1-k)個置く
      long now = 1;
      now *= fif[0][k];
      now %= mod;
      now *= fif[0][n - 1 - k];
      now %= mod;
      
      //k-1個の間に(n-1-k)個を配置
      now *= C(k-1,n-1-k,mod,fif);
      now %= mod;

      a[k] = now;
    }
    
    for (int k = (n + 1) / 2; k <= n - 1; k ++) {
      ret += (a[k] - a[k - 1] + mod) % mod * k;
      ret %= mod;
    }
    System.out.println(ret);
  }

  public static long C(int n, int r, int mod, int[][] fif)
  {
      if(n < 0 || r < 0 || r > n)return 0;
      return (long)fif[0][n]*fif[1][r]%mod*fif[1][n-r]%mod;
  }
  
  public static int[][] enumFIF(int n, int mod)
  {
      int[] f = new int[n+1];
      int[] invf = new int[n+1];
      f[0] = 1;
      for(int i = 1;i <= n;i++){
          f[i] = (int)((long)f[i-1] * i % mod);
      }
      long a = f[n];
      long b = mod;
      long p = 1, q = 0;
      while(b > 0){
          long c = a / b;
          long d;
          d = a; a = b; b = d % b;
          d = p; p = q; q = d - c * q;
      }
      invf[n] = (int)(p < 0 ? p + mod : p);
      for(int i = n-1;i >= 0;i--){
          invf[i] = (int)((long)invf[i+1] * (i+1) % mod);
      }
      return new int[][]{f, invf};
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}