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 System.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
            // 入力
            string[] sS = System.Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);
            List<int> lstA = new List<int>();
            sS = System.Console.ReadLine().Trim().Split(' ');
            for (int i = 0; i < sS.Length; i++) { lstA.Add(int.Parse(sS[i])); }

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            int dAvg = (int)(lstA.Average() * (double)iN);
            List<ClsDev> lstD = new List<ClsDev>();
            for (int i = 0; i < lstA.Count; i++)
            {
                ClsDev oneUsr = new ClsDev();
                oneUsr.iX = i;
                oneUsr.iD = Math.Abs(lstA[i] * iN - dAvg);
                lstD.Add(oneUsr);
            }
            lstD.Sort(delegate (ClsDev mca1, ClsDev mca2) { return (int)(mca1.iD - mca2.iD == 0 ? mca1.iX - mca2.iX : mca1.iD - mca2.iD); }); // Dの昇順のXの昇順

            // 出力
            System.Console.WriteLine("{0}", lstD[0].iX.ToString().Trim());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }

        private class ClsDev
        {
            public int iX { get; set; } = 0;
            public int iD { get; set; } = 0;
        }

}