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;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public sealed partial class Program
{
    int n;
    long[] xs;

    long Solve()
    {
        var l = xs.Sum() - n * (n - 1);
        var k = 0L;

        if (l > 0)
        {
            var ys = new long[n];
            var y = 0L;

            for (var i = 0; i < xs.Length; i++)
            {
                ys[i] = (xs[i] + l) / (n + 1);
                y += ys[i];
            }

            for (var i = 0; i < xs.Length; i++)
            {
                xs[i] = xs[i] - n * ys[i] + y - ys[i];
            }

            k += y;
        }

        while (true)
        {
            var max = long.MinValue;
            var maxIndex = -1;

            for (var i = 0; i < xs.Length; i++)
            {
                if (max < xs[i])
                {
                    max = xs[i];
                    maxIndex = i;
                }
            }

            if (max < n) break;

            for (var i = 0; i < xs.Length; i++)
            {
                if (i == maxIndex)
                {
                    xs[i] -= n;
                }
                else
                {
                    xs[i]++;
                }
            }

            k++;
        }

        return k;
    }

    void Read()
    {
        var a = scanner;
        n = a.N;
        xs = a.Ls(n);
    }

    public void EntryPoint()
    {
        Read();
        WriteLine(Solve());
    }
}

#region Custom Library
public static class TemplateExtension
{
    public static X[] MakeArray<X>(this int count, Func<int, X> func)
    {
        var xs = new X[count];
        for (var i = 0; i < count; i++)
        {
            xs[i] = func(i);
        }
        return xs;
    }

    public static int[] Range(this int count, int start = 0)
    {
        return count.MakeArray(i => i + start);
    }

    public static string Intercalate<X>(this IEnumerable<X> @this, string separator)
    {
        return string.Join(separator, @this);
    }

    public static void ForEach<X>(this IEnumerable<X> @this, Action<X, int> action)
    {
        var list = @this as IReadOnlyList<X>;
        if (list != null)
        {
            var count = list.Count;
            for (var i = 0; i < count; i++)
            {
                action(list[i], i);
            }
        }
        else
        {
            var i = 0;
            foreach (var x in @this)
            {
                action(x, i);
                i++;
            }
        }
    }
}

public sealed class Scanner
{
    readonly TextReader reader;

    /// <summary>
    /// Reads next word separated by spaces.
    /// </summary>
    public string Word()
    {
        var sb = default(StringBuilder);
        var firstChar = default(char);
        var count = 0;

        while (true)
        {
            var r = reader.Read();

            if (r == '\r')
            {
                if (reader.Peek() == '\n') reader.Read();
                break;
            }
            else if (r == -1 || r == ' ' || r == '\n')
            {
                break;
            }
            else
            {
                var c = (char)r;

                switch (count)
                {
                    case 0:
                        firstChar = c;
                        count = 1;
                        break;
                    case 1:
                        sb = new StringBuilder();
                        sb.Append(firstChar).Append(c);
                        count = 2;
                        break;
                    default:
                        sb.Append(c);
                        break;
                }
            }
        }

        switch (count)
        {
            case 0:
                return "";
            case 1:
                return firstChar.ToString();
            default:
                return sb.ToString();
        }
    }

    /// <summary>
    /// Reads next word as <see cref="int"/>.
    /// </summary>
    public int N
    {
        get
        {
            return int.Parse(Word());
        }
    }

    /// <summary>
    /// Reads next word as <see cref="long"/>.
    /// </summary>
    public long L
    {
        get
        {
            return long.Parse(Word());
        }
    }

    /// <summary>
    /// Reads next word as <see cref="double"/>.
    /// </summary>
    public double F
    {
        get
        {
            return double.Parse(Word());
        }
    }

    public int[] Ns(int count)
    {
        return count.MakeArray(_ => N);
    }

    public long[] Ls(int count)
    {
        return count.MakeArray(_ => L);
    }

    public double[] Fs(int count)
    {
        return count.MakeArray(_ => F);
    }

    /// <summary>
    /// Reads next line and splits it by spaces.
    /// </summary>
    public X[] Words<X>(Func<string, X> func)
    {
        return reader.ReadLine().Split(' ').Select(func).ToArray();
    }

    public Scanner(TextReader reader)
    {
        this.reader = reader;
    }
}

public partial class Program
{
    readonly TextReader input;
    readonly TextWriter output;
    readonly Scanner scanner;

    void WriteLine(int value)
    {
        output.WriteLine(value);
    }

    void WriteLine(long value)
    {
        output.WriteLine(value);
    }

    void WriteLine(double value)
    {
        output.WriteLine(value);
    }

    void WriteLine(char value)
    {
        output.WriteLine(value);
    }

    void WriteLine(string value)
    {
        output.WriteLine(value);
    }

    public Program(TextReader input, TextWriter output)
    {
        this.input = input;
        this.output = output;
        scanner = new Scanner(input);
    }

    public static void Main(string[] args)
    {
#if DEBUG
        using (var writer = new VainZero.IO.DebugTextWriter(Console.Out))
#else
        var writer = Console.Out;
#endif
        {
            new Program(Console.In, writer).EntryPoint();
        }
    }
}
#endregion