Problem:
Score : 600 points

Problem Statement

We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller. (The operation is the same as the one in Problem D.)

Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.

It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given the sequence a_i. Find the number of times we will perform the above operation.

Constraints

2 ≤ N ≤ 50

0 ≤ a_i ≤ 10^{16} + 1000

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the number of times the operation will be performed.

Sample Input 1

4
3 3 3 3

Sample Output 1

0

Sample Input 2

3
1 0 3

Sample Output 2

1

Sample Input 3

2
2 2

Sample Output 3

2

Sample Input 4

7
27 0 0 0 0 0 0

Sample Output 4

3

Sample Input 5

10
1000 193 256 777 0 1 1192 1234567891011 48 425

Sample Output 5

1234567894848

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


import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;


public class Main {
  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    int N = sc.nextInt();
    long[] a = sc.nextLongList(N);

    long count = 0;
    boolean flg = true;
    while (flg) {
      long now = 0;
      for (int i = 0; i < N; i ++) {
        if (a[i] >= N) {
          long x = a[i] / N;
          a[i] -= x * (N + 1);
          now += x;
        }
      }
      count += now;
      
      flg = false;
      for (int i = 0; i < N; i ++) {
        a[i] += now;
        if (a[i] >= N) {
          flg = true;
        }
      }
    }
    System.out.println(count);
  }
}


class FastScanner {
  public static String debug = null;

  private final InputStream in = System.in;
  private int ptr = 0;
  private int buflen = 0;
  private byte[] buffer = new byte[1024];
  private boolean eos = false;

  private boolean hasNextByte() {
    if (ptr < buflen) {
      return true;
    } else {
      ptr = 0;
      try {
        if (debug != null) {
          buflen = debug.length();
          buffer = debug.getBytes();
          debug = "";
          eos = true;
        } else {
          buflen = in.read(buffer);
        }
      } catch (IOException e) {
        e.printStackTrace();
      }
      if (buflen < 0) {
        eos = true;
        return false;
      } else 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 isEOS() {
    return this.eos;
  }

  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 long[] nextLongList(int n) {
    return nextLongTable(1, n)[0];
  }

  public int[] nextIntList(int n) {
    return nextIntTable(1, n)[0];
  }

  public long[][] nextLongTable(int n, int m) {
    long[][] ret = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ret[i][j] = nextLong();
      }
    }
    return ret;
  }

  public int[][] nextIntTable(int n, int m) {
    int[][] ret = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ret[i][j] = nextInt();
      }
    }
    return ret;
  }
}