Problem:
Score : 200 points

Problem Statement

Niwango-kun is an employee of Dwango Co., Ltd.

One day, he is asked to generate a thumbnail from a video a user submitted.

To generate a thumbnail, he needs to select a frame of the video according to the following procedure:

Get an integer N and N integers a_0, a_1, ..., a_{N-1} as inputs. N denotes the number of the frames of the video, and each a_i denotes the representation of the i-th frame of the video.

Select t-th frame whose representation a_t is nearest to the average of all frame representations.

If there are multiple such frames, select the frame with the smallest index.

Find the index t of the frame he should select to generate a thumbnail.

Constraints

1 \leq N \leq 100

1 \leq a_i \leq 100

All numbers given in input are integers

Input

Input is given from Standard Input in the following format:

N
a_{0} a_{1} ... a_{N-1}

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

1

Since the average of frame representations is 2, Niwango-kun needs to select the index 1, whose representation is 2, that is, the nearest value to the average.

Sample Input 2

4
2 5 2 5

Sample Output 2

0

The average of frame representations is 3.5.

In this case, every frame has the same distance from its representation to the average.

Therefore, Niwango-kun should select index 0, the smallest index among them.

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

using System;
using static System.Console;
using System.Linq;
using System.Collections.Generic;

static class Program
{
    static void Main()
    {
        ReadLine();
        int[] input = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

        int sum = input.Sum();
        int[] input2 = input.Select(n => n * input.Length).ToArray();

        if (input2.Contains(sum))
        {
            WriteLine(Array.IndexOf(input2, sum));
        }
        else
        {
            int minDef = input2.Min(n => Math.Abs(n - sum));
            WriteLine(Array.IndexOf(input2, input2.First(n => (n > sum ? n - minDef : n + minDef) == sum)));
        }

        ReadKey();
    }
}