There are N slimes standing on a number line. The i-th slime from the left is at position x_i.

It is guaruanteed that 1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}.

Niwango will perform N-1 operations. The i-th operation consists of the following procedures:

* Choose an integer k between 1 and N-i (inclusive) with equal probability.
* Move the k-th slime from the left, to the position of the neighboring slime to the right.
* Fuse the two slimes at the same position into one slime.



Find the total distance traveled by the slimes multiplied by (N-1)! (we can show that this value is an integer), modulo (10^{9}+7). If a slime is born by a fuse and that slime moves, we count it as just one slime.

Constraints

* 2 \leq N \leq 10^{5}
* 1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}
* x_i is an integer.

Input

Input is given from Standard Input in the following format:


N
x_1 x_2 \ldots x_N


Output

Print the answer.

Examples

Input

3
1 2 3


Output

5


Input

12
161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932


Output

750927044
/**
 * Created at 20:04 on 2020-01-11
 */

import java.io.*;
import java.util.*;

public class Main {

  static FastScanner sc = new FastScanner();
  static Output out = new Output(System.out);

  static final int[] dx = {0, 1, 0, -1};
  static final int[] dy = {-1, 0, 1, 0};

  static final long MOD = (long) (1e9 + 7);
  static final long INF = Long.MAX_VALUE / 2;

  static final int e5 = (int) 1e5;

  public static class Solver {
    public Solver() {

      int N = sc.nextInt();

      long[] x = sc.nextLongArray(N, false);
      /*
      long[] l = new long[N + 1];
      for (int i = N - 1; i >= 0; i--) {
        l[i] = x[N - 1] - x[i];
      }
      */

      long ans = 0;

      new Mod((int)2e5);
      /*
      for (int i=0; i<N; i++) {
        for (int j=i+1; j<N-1; j++) {
          long l = x[j] - x[i];
          ans = Mod.add(ans, Mod.div(l, Mod.mul(j-i+1, j-i)));
        }
        ans = Mod.add(ans, Mod.div(x[N-1] - x[i], N-1-i));
      }
      */
      long mul = 0;
      for (int i=1; i<N; i++) {
        mul = Mod.add(mul, Mod.div(1, i));
      }

      for (int i=N-2; i>=0; i--) {
        ans = Mod.add(ans, Mod.mul(x[i+1]-x[i], mul));
        mul = Mod.sub(mul, Mod.div(1, i+1));
      }

      ans = Mod.mul(ans, Mod.factorial(N-1));

      out.println(ans);

    }

    public static class Mod {

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

      public static long[] fact;

      public Mod(int n) {
        fact = new long[n + 1];
      }

      public Mod(long n) {
        fact = new long[(int) n + 1];
      }

      public static long comb(long n, long r) {
        if (r < 0 || r > n) return 0;
        return (((factorial(n) * factorialInverse(r)) % MOD) * factorialInverse(n - r)) % MOD;
      }

      public static long factorial(long n) {
        if (n == 0) return 1;
        if (fact[(int) n] == 0) {
          return fact[(int) n] = (n * factorial(n - 1)) % MOD;
        } else {
          return fact[(int) n];
        }
      }

      public static long factorialInverse(long n) {
        return inverse(factorial(n));
      }

      public static long inverse(long n) {
        return power(n, MOD - 2);
      }

      public static long power(long a, long b) {
        if (b == 0) return 1;

        if (b % 2 == 0) {
          long p = power(a, b / 2);
          return (p * p) % MOD;
        } else {
          return (a * power(a, b - 1)) % MOD;
        }
      }

      public static long add(long... a) {
        long ans = 0;
        for (int i = 0; i < a.length; i++) {
          ans = (ans + a[i]) % MOD;
        }
        return ans;
      }

      public static long sub(long a, long b) {
        return (a - b + MOD) % MOD;
      }

      public static long mul(long... a) {
        long ans = 1;
        for (int i = 0; i < a.length; i++) {
          ans = (ans * a[i]) % MOD;
        }
        return ans;
      }

      public static long div(long a, long b) {
        return (a * Mod.inverse(b)) % MOD;
      }

      public static long piano(long u, long d) {
        long a = add(u, 1);
        long b = d;
        long sum = add(a, b);
        long dif = sub(a, b);

        return mul(div(dif, sum), comb(sum, a));
      }

      public static long catalan(long n) {
        return piano(n, n);
      }

    }
  }

  public static void main(String[] args) {
    new Solver();
    out.flush();
  }

  static class FastScanner {
    private InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;


    public void load() {
      try {
        in = new FileInputStream(next());
      } catch (Exception e) {
        e.printStackTrace();
      }
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int N, boolean oneBased) {
      if (oneBased) {
        int[] array = new int[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      } else {
        int[] array = new int[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      }
    }

    public long[] nextLongArray(int N, boolean oneBased) {
      if (oneBased) {
        long[] array = new long[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      } else {
        long[] array = new long[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      }
    }
  }

  static class Output extends PrintWriter {

    private long startTime;

    public Output(PrintStream ps) {
      super(ps);
    }

    public void print(int[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(long[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(String[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(ArrayList a, String separator) {
      for (int i = 0; i < a.size(); i++) {
        if (i == 0) print(a.get(i));
        else print(separator + a.get(i));
      }
      println();
    }

    public void start() {
      startTime = System.currentTimeMillis();
    }

    public void time(String s) {
      long time = System.currentTimeMillis() - startTime;
      println(s + "(" + time + ")");
    }

  }

}
