Problem:
Score : 300 points

Problem Statement

There are N people living on a number line.

The i-th person lives at coordinate X_i.

You are going to hold a meeting that all N people have to attend.

The meeting can be held at any integer coordinate. If you choose to hold the meeting at coordinate P, the i-th person will spend (X_i - P)^2 points of stamina to attend the meeting.

Find the minimum total points of stamina the N people have to spend.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq X_i \leq 100

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print the minimum total stamina the N people have to spend.

Sample Input 1

2
1 4

Sample Output 1

5

Assume the meeting is held at coordinate 2. In this case, the first person will spend (1 - 2)^2 points of stamina, and the second person will spend (4 - 2)^2 = 4 points of stamina, for a total of 5 points of stamina. This is the minimum total stamina that the 2 people have to spend.

Note that you can hold the meeting only at an integer coordinate.

Sample Input 2

7
14 14 2 13 56 2 37

Sample Output 2

2354

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

namespace AtCoderCS
{
    using System;
    using System.Collections.Generic;
    using System.IO;
    using System.Text;
    using System.Linq;
    using static System.Console;
    using static System.Math;
    using static Macro;
    using static Library;

    class Program
    {
        void Solve()
        {
            var N = IN.Int;
            var X = new int[N];
            REP(N, i => X[i] = IN.Int);

            var ave = X.Sum() / X.Length;
            var ave2 = X.Sum() / X.Length;
            
            var cost = X.Aggregate(0, (acc, x) => acc + (ave - x) * (ave - x));
            var cost2 = X.Aggregate(0, (acc, x) => acc + (ave2 - x) * (ave2 - x));
            WriteLine(Min(cost, cost2));
        }

        private SimpleInput IN = new SimpleInput();
        private SimpleOutput OUT = new SimpleOutput();

        void Stream()
        {
            Solve();
            OUT.Flush();
        }

        static void Main(string[] args)
            => new Program().Stream();
    }


    #region IO
    class SimpleInput
    {
        private string[] _nextBuffer;
        private int _bufferCnt;
        private readonly char[] _cs = new char[] {' ', '"', ','};

        public SimpleInput()
        {
            _nextBuffer = new string[0];
            _bufferCnt = 0;
        }

        string Next()
        {
            if (_bufferCnt < _nextBuffer.Length) return _nextBuffer[_bufferCnt++];
            var st = ReadLine();
            while (st == string.Empty) st = ReadLine();
            if (st != null) _nextBuffer = st.Split(_cs, StringSplitOptions.RemoveEmptyEntries);
            _bufferCnt = 0;
            return _nextBuffer[_bufferCnt++];
        }

        public string String => Next();
        public char Char => char.Parse(String);
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
    }

    class SimpleOutput
    {
        private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput())
        {
#if DEBUG
            AutoFlush = true
#else
            AutoFlush = false
#endif
        };

        public SimpleOutput()
        {
            SetOut(_sw);
        }

        public void Flush() => Out.Flush();
    }
    #endregion

    #region MACRO
    static class Macro
    {
        public static void FOR(int a, int b, int n, Action<int> f)
        {
            for (int i = a; i < b; i += n) f(i);
        }

        public static void FOR(int a, int b, Action<int> f) => FOR(a, b, 1, f);
        public static void REP(int a, Action<int> f) => FOR(0, a, f);
    }
    #endregion

    #region Library
    static class Library
    {
        public static int BinarySearch(int ng, int ok, Func<int, bool> f)
        {
            while (Math.Abs(ok - ng) > 1)
            {
                var mid = (ok + ng) / 2;
                if (f(mid)) ok = mid;
                else ng = mid;
            }
            return ok;
        }

        public static int LowerBound<T>(IReadOnlyList<T> a, T x) where T : IComparable<T> =>
            BinarySearch(-1, a.Count, (m) => a[m].CompareTo(x) >= 0);
        public static int UpperBound<T>(IReadOnlyList<T> a, T x) where T : IComparable<T> =>
            BinarySearch(-1, a.Count(), (m) => a[m].CompareTo(x) > 0);
    }

    class UnionFind
    {
        private int[] data;

        public UnionFind(int n)
        {
            data = new int[n + 1];
            for (var i = 0; i < n + 1; ++i) data[i] = -1;
        }

        public void Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x == y) return;
            if (data[y] < data[x]) Swap(ref x, ref y);
            data[x] += data[y];
            data[y] = x;
        }

        public bool Find(int x, int y) => Root(x) == Root(y);
        public int Root(int x) => data[x] < 0 ? x : Root(data[x]);
        public int Size(int x) => -data[Root(x)];

        private void Swap(ref int a, ref int b)
        {
            var tmp = b;
            b = a;
            a = tmp;
        }
    }
    #endregion
}