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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static Yorukatsu20200406F.Input;

namespace Yorukatsu20200406F
{
    static class Input
    {
        private static Func<string, T[]> Cast<T>() => _ => _.Split(' ').Select(Convert<T>()).ToArray();

        private static Func<string, T> Convert<T>()
        {
            Type t = typeof(T);
            if (t == typeof(string)) return _ => (T) (object) _;
            if (t == typeof(int)) return _ => (T) (object) int.Parse(_);
            if (t == typeof(long)) return _ => (T) (object) long.Parse(_);
            if (t == typeof(double)) return _ => (T) (object) double.Parse(_);
            if (t == typeof(string[])) return _ => (T) (object) _.Split(' ');
            if (t == typeof(int[])) return _ => (T) (object) Cast<int>()(_);
            if (t == typeof(long[])) return _ => (T) (object) Cast<long>()(_);
            if (t == typeof(double[])) return _ => (T) (object) Cast<double>()(_);

            throw new NotSupportedException(t + "is not supported.");
        }

        private static T Convert<T>(string s) => Convert<T>()(s);

        private static string String() => Console.ReadLine();

        private static string[] String(long rowNumber) => new bool[rowNumber].Select(_ => String()).ToArray();

        public static void Cin<T>(out T a) => a = Convert<T>(String());

        public static void Cin<T1, T2>(out T1 a1, out T2 a2)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
        }

        public static void Cin<T1, T2, T3>(out T1 a1, out T2 a2, out T3 a3)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
        }

        public static void Cin<T1, T2, T3, T4>(out T1 a1, out T2 a2, out T3 a3, out T4 a4)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
            set(v[3], out a4);
        }

        public static void Cin<T1, T2, T3, T4, T5>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
            set(v[3], out a4);
            set(v[4], out a5);
        }

        public static void Cin<T1, T2, T3, T4, T5, T6>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5, out T6 a6)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
            set(v[3], out a4);
            set(v[4], out a5);
            set(v[5], out a6);
        }

        private static void set<T1>(string s, out T1 o1) => o1 = Convert<T1>(s);

        public static void Cin<T>(long n, out T[] l) => l = String(n).Select(Convert<T>()).ToArray();

        public static void Cin<T1, T2>(long n, out T1[] l1, out T2[] l2)
        {
            l1 = new T1[n];
            l2 = new T2[n];
            for (int i = 0; i < n; i++) Cin(out l1[i], out l2[i]);
        }

        public static void Cin<T1, T2, T3>(long n, out T1[] l1, out T2[] l2, out T3[] l3)
        {
            l1 = new T1[n];
            l2 = new T2[n];
            l3 = new T3[n];
            for (int i = 0; i < n; i++) Cin(out l1[i], out l2[i], out l3[i]);
        }

        public static void Cin<T1, T2, T3, T4>(long n, out T1[] l1, out T2[] l2, out T3[] l3, out T4[] l4)
        {
            l1 = new T1[n];
            l2 = new T2[n];
            l3 = new T3[n];
            l4 = new T4[n];
            for (int i = 0; i < n; i++) Cin(out l1[i], out l2[i], out l3[i], out l4[i]);
        }

        public static void Cin<T>(out T[] a) => a = Convert<T[]>(String());

        public static void Cin<T>(long h, out T[][] map) => map = String(h).Select(Convert<T[]>()).ToArray();
    }

    class Program
    {
        public static void Main(string[] args)
        {
            StreamWriter streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            new Solver().Solve();
            Console.Out.Flush();
        }

        public static void Debug()
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        public void Solve()
        {
            int n;
            long[] a;
            Cin(out n);
            Cin(out a);

            long ans = 0;
            for (int i = 0; i < n; i++)
            {
                if (a[i] > n * n)
                {
                    //n+1回操作するとn+1減らせる
                    long loss = (a[i] - n * n) / (n + 1) * (n + 1);
                    ans += loss;
                    a[i] = a[i] - loss;
                }
            }

            while (a.Max() >= n)
            {
                Array.Sort(a);
                a[n - 1] -= n;
                for (int i = 0; i < n - 1; i++)
                {
                    a[i] += 1;
                }

                ans++;
            }

            Console.WriteLine(ans);
        }
    }
}