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 static System.Math;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            A();
        }

        static void A()
        {
            var N = ReadInt();
            var a = ReadSplitInt();

            var avg = a.Average();
            var min = double.MaxValue;
            var ans = 0;
            for (int i = 0; i < N; i++)
            {
                if (min > Abs(a[i] - avg))
                {
                    min = Abs(a[i] - avg);
                    ans = i;
                }
            }

            Println(ans);
        }

        static List<long> ReadLines(long n)
        {
            var l = new List<long>();
            for (long i = 0; i < n; i++)
            {
                l.Add(ReadLong());
            }
            return l;
        }

        static void YESOrNO(bool e) => Println(e ? "YES" : "NO");

        static void YesOrNo(bool e) => Println(e ? "Yes" : "No");

        static IEnumerable<int> Range(int start, int stop)
        {
            if (start < 0 || stop < 0 || start > stop || (start <= 0 && stop <= 0))
                return new List<int>();

            return Enumerable.Range(start, stop - start);
        }

        static bool IsDigit(string str)
        {
            var i = 0;
            return int.TryParse(str, out i);
        }

        static int SumDigits(long num)
        {
            return num.ToString().Select(x => x.ToString()).Sum(int.Parse);
        }

        static int[] ToIntArray(string str)
        {
            return str.Select(x => x.ToString()).Select(int.Parse).ToArray();
        }

        static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b);
        static long Lcm(long a, long b) => a / Gcd(a, b) * b;

        static bool IsPrime(int x)
        {
            if (x <= 1 || (x != 2 && x % 2 == 0)) return false;
            if (x == 2) return true;

            for (int i = 3; i < x; i += 2)
                if (x % i == 0) return false;

            return true;
        }

        static string Read() => Console.ReadLine();
        static int ReadInt() => int.Parse(Read());
        static long ReadLong() => long.Parse(Read());

        static List<string> ReadSplit() => Read().Split().ToList();
        static List<int> ReadSplitInt() => Read().Split().Select(int.Parse).ToList();
        static List<long> ReadSplitLong() => Read().Split().Select(long.Parse).ToList();

        static void Print(object value) => Console.Write(value.ToString());
        static void Println(object value) => Console.WriteLine(value.ToString());
        static string Join<T>(IEnumerable<T> list) => string.Join("", list);

        static int LowerBound<T>(T[] arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        static int LowerBound<T>(T[] arr, T value) where T : IComparable 
            => LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
    }

    public static class MyExtensions
    {
        public static string Slice(this string str, int start = 0, int stop = 0)
        {
            if (start > str.Length || stop > str.Length || start < 0 || stop < 0)
                return "";

            if (stop == 0) stop = str.Length;
            return str.Substring(start, stop - start);
        }
    }
}