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: Runtime Error)

using System;
 
namespace C
{
	internal class Program
	{
		private static MatrixDC[,] dc;
		
		public static void Main(string[] args)
		{
			var n = int.Parse(Console.ReadLine());
			var s = Console.ReadLine();
			var q = int.Parse(Console.ReadLine());
			var kInputs = Console.ReadLine().Split();
			var ks = new int[q];
			for (var i = 0; i < q; i++) { ks[i] = int.Parse(kInputs[i]); }
 
			var numD = 0;
			var numC = 0;
			var indexD = new int[1000000];
			var indexC = new int[1000000];
			for (var i = 0; i < n; i++)
			{
				switch (s[i])
				{
				case 'D':
					indexD[numD++] = i;
					break;
				case 'C':
					indexC[numC++] = i;
					break;
				}
			}
 
			dc = new MatrixDC[numD, numC];
			for (var i = 0; i < numD; i++)
			{
				for (var j = 0; j < numC; j++)
				{
					dc[i, j] = new MatrixDC();
					var tmp = dc[i, j].Distance = indexC[j] - indexD[i];
					if (tmp < 0) { dc[i, j].NumM = 0; }
				}
			}
 
			for (var i = 0; i < n; i++)
			{
				if (s[i] != 'M') { continue; }
 
				for (var j = 0; j < numD; j++)
				{
					if (i < indexD[j]) { continue; }
 
					for (var k = 0; k < numC; k++)
					{
						if (i > indexC[k]) { continue; }
 
						dc[j, k].NumM++;
					}
				}
			}
 
			foreach (var k in ks)
			{
				var result = 0;
				foreach (var cell in dc)
				{
					if (cell.Distance >= k) { continue; }
 
					result += cell.NumM;
				}
 
				Console.WriteLine(result);
			}
		}
	}
 
	class MatrixDC
	{
		public int Distance { get; set; }
		public int NumM { get; set; }
	}
}