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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.stream.LongStream;
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;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long[] a = new long[n];
            for (int i = 0; i < n; ++i) {
                a[i] = in.nextLong();
            }
            long steps = Arrays.stream(a).sum() - n * (n - 1);
            if (steps < 0) {
                steps = 0;
            }
            long[] b = new long[n];
            long total = 0;
            for (int i = 0; i < n; ++i) {
                long choose = 0;
                for (long step = 1L << 55; step > 0; step /= 2) {
                    long curr = choose + step;
                    long nvalue = a[i] + (steps - curr) - curr * n;
                    if (total + curr <= steps && nvalue >= 0) {
                        choose += step;
                    }
                }
                b[i] = choose;
                total += choose;
            }
            long ans = 0;
            for (int i = 0; i < n; ++i) {
                a[i] -= b[i] * n;
                for (int j = 0; j < n; ++j) {
                    if (i != j) {
                        a[j] += b[i];
                    }
                }
                ans += b[i];
            }
            if (total != steps) {
                throw new RuntimeException();
            }

            while (true) {
                int pos = -1;
                for (int i = 0; i < n; ++i) {
                    if (a[i] >= n) {
                        pos = i;
                        break;
                    }
                }
                if (pos == -1) {
                    break;
                }
                long add = a[pos] / n;
                ans += add;
                a[pos] %= n;
                for (int i = 0; i < n; ++i) {
                    if (i != pos) {
                        a[i] += add;
                    }
                }
            }
            out.println(ans);
        }

    }

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

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

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

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

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

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

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

    }
}