Problem:
Score : 200 points

Problem Statement

Evi has N integers a_1,a_2,..,a_N. His objective is to have N equal integers by transforming some of them.

He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j), he has to pay the cost separately for transforming each of them (See Sample 2).

Find the minimum total cost to achieve his objective.

Constraints

1≦N≦100

-100≦a_i≦100

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum total cost to achieve Evi's objective.

Sample Input 1

2
4 8

Sample Output 1

8

Transforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.

Sample Input 2

3
1 1 3

Sample Output 2

3

Transforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.

Sample Input 3

3
4 2 5

Sample Output 3

5

Leaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.

Sample Input 4

4
-100 -100 -100 -100

Sample Output 4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.

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

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

using static System.Console;
using static AtCoder.Util;
using static AtCoder.Cin;
using static System.Math;
using static AtCoder.MyMath;

namespace AtCoder {
    class Program {
        static void Main() {
            var n = ReadInt();
            var a = ReadInt(n);
            var ave = a.Average().ToNearestInt();
            a.Sum(x => Pow(x - ave, 2)).WriteLine();
        }
    }
}

/* ***************** Following Contents are my common library ******** */

namespace AtCoder {

    static class MyMath {
        public static long ToNearestInt(this double d) {
            var l = (long) Math.Floor(d);
            var r = l + 1;
            return r - d < d - l ? r : l;
        }

        public static long Factorial(this long n) => Range(1, n).Aggregate(1L, Multiply);
        public static long nPr(int n, int r) => r < 0 || r > n ? 0 : FromTo(n - r + 1, n).Select(x =>(long) x).Aggregate(1L, Multiply);
        public static long nCr(int n, int r) => nPr(n, r) / Factorial(r);

        public static long Inc(long i) => i + 1;
        public static long Dec(long i) => i - 1;
        public static long Plus(long i, long j) => i + j;
        public static Func<long, long> Plus(long j) => i => i + j;
        public static long Minus(long i, long j) => i - j;
        public static Func<long, long> Minus(long j) => i => i - j;
        public static long Multiply(long i, long j) => i * j;
        public static Func<long, long> Multiply(long j) => i => i * j;
        public static long Divide(long i, long j) => j / j;
        public static Func<long, long> Divide(long j) => i => i * j;
        public static long Mod(long i, long j) => i % j;
        public static Func<long, long> Mod(long j) => i => i % j;

        public static long Max(params long[] ns) => ns.Max();
    }

    static class Util {

        public static IEnumerable<int> ToDigits(this long n) =>
            n.ToString().Select(x => x.ToInt());

        public static IEnumerable<int> Factors(this int n) {
            for (int i = 1; i <= n; i++)
                if (n % i == 0) yield return i;
        }

        public static IEnumerable<int> Natural() {
            for (int i = 0;; i++) yield return i;
        }
        public static IEnumerable<int> Positive() => Natural().Skip(1);

        public static long Pow(long i, long exp) =>(exp == 0) ? 1 : i * Pow(i, exp - 1);
        public static HashSet<T> ToHashSet<T>(this IEnumerable<T> source) => new HashSet<T>(source);

        public static MultiSet<T> ToMultiSet<T>(this IEnumerable<T> t) => new MultiSet<T>(t);

        public static int Max(this int i, int j) => i > j ? i : j;

        public static bool IsPalindrome(string s) {
            for (int i = 0; i < s.Length / 2; i++) {
                if (s[i] != s[s.Length - 1 - i]) return false;
            }
            return true;
        }
        public readonly static VectorInt2[] Dir8 = {
            new VectorInt2(-1, -1),
            new VectorInt2(-1, 0),
            new VectorInt2(-1, 1),
            new VectorInt2(0, -1),
            new VectorInt2(0, 1),
            new VectorInt2(1, -1),
            new VectorInt2(1, 0),
            new VectorInt2(1, 1)
        };

        public const long MODCONST = 1000000007;

        public static T debug<T>(this T value) {
            Console.Error.WriteLine($"debug:{value}");
            return value;
        }

        public static T Id<T>(T t) => t;
        public static long ToLong(this String s) => long.Parse(s);
        public static long ToLong(this char c) => c - '0';
        public static int ToInt(this String s) => int.Parse(s);
        public static int ToInt(this char c) => c - '0';
        public static void Times(this int n, Action action) {
            for (int i = 0; i < n; i++) action();
        }
        public static void Times(this long n, Action action) {
            for (long i = 0; i < n; i++) action();
        }

        public static IEnumerable<T> Times<T>(this int n, Func<T> func) {
            for (long i = 0; i < n; i++) yield return func();
        }
        public static IEnumerable<T> Times<T>(this long n, Func<T> func) {
            for (long i = 0; i < n; i++) yield return func();
        }

        public static Func<S, U> Then<S, T, U>(this Func<S, T> f, Func<T, U> g) => x => g(f(x));
        public static Func<S, U> Compose<S, T, U>(this Func<T, U> f, Func<S, T> g) => x => f(g(x));

        public static void Call<T>(this T t, Action<T> action) => action(t);
        public static bool In<T>(this T t, IEnumerable<T> range) =>
            range.Contains(t);
        public static void WriteLine<T>(this T t) => Console.WriteLine(t);
        public static T Call<S, T>(this S s, Func<S, T> func) => func(s);
        public static void Each<T>(this IEnumerable<T> e, Action<T> action) {
            foreach (var v in e) action(v);
        }

        public static IEnumerable<int> FromTo(int a, int b) => Range(a, Max(b - a + 1, 0));
        public static IEnumerable<T> Repeat<T>(T t) {
            while (true) yield return t;
        }
        public static IEnumerable<T> Replicate<T>(int n, T t) => Repeat(t).Take(n);

        public static IEnumerable<T> Cycle<T>(this IEnumerable<T> e) {
            while (true)
                foreach (var v in e) yield return v;
        }

        public static IEnumerable<T> Scan<S, T>(this IEnumerable<S> source, T init, Func<T, S, T> accumulator) {
            var result = init;
            foreach (var item in source) {
                result = accumulator(result, item);
                yield return result;
            }
        }

        public static IEnumerable<T> Scan0<S, T>(this IEnumerable<S> source, T init, Func<T, S, T> accumulator) {
            yield return init;
            foreach (var item in Scan(source, init, accumulator)) yield return item;
        }

        public static VectorInt2 ReadVectorInt2() =>
            new VectorInt2(ReadInt(), ReadInt());

        public static string ReplaceX(this string input, string pattern, string replace) =>
            Regex.Replace(input, pattern, replace);

        public static IEnumerable<int> Range(int i, int j) => Enumerable.Range(i, j);
        public static IEnumerable<long> Range(long i, long j) {
            for (long k = i; k < i + j; k++) yield return k;

        }
        public static void Swap<T>(this IList<T> enumerable, int i, int j) {
            var buf = enumerable[i];
            enumerable[i] = enumerable[j];
            enumerable[j] = buf;

        }
        public static void ReverseRange<T>(this IList<T> enumerable, int i, int j) {
            int half = (j - i) / 2;
            for (int k = 0; k <= half; k++) enumerable.Swap(i + k, j - k);
        }

        public static bool isEmpty<T>(this IEnumerable<T> enumerable) => !enumerable.Any();
    }

    static class Cin {
        private static Queue<string> tokens;
        static Cin() {
        string line;
        tokens = new Queue<string>();
        while ((line = Console.ReadLine()) != null) {
        foreach (var token in line.Split(' ')) {
        tokens.Enqueue(token);
                }
            }
        }

        static public int ReadInt() => int.Parse(tokens.Dequeue());
        static public IList<int> ReadInt(long n) {
            var list = new List<int>();
            n.Times(() => list.Add(ReadInt()));
            return list;
        }
        static public long ReadLong() => long.Parse(tokens.Dequeue());
        static public IList<long> ReadLong(long n) {
            var list = new List<long>();
            n.Times(() => list.Add(ReadLong()));
            return list;
        }
        static public string ReadString() => tokens.Dequeue();
        static public IList<string> ReadString(long n) {
            var list = new List<string>();
            n.Times(() => list.Add(ReadString()));
            return list;
        }

        static public void SayYesNo(this bool b) =>(b ? "Yes" : "No").WriteLine();
    }

    struct VectorInt2 {
        public int X { get; set; }
        public int Y { get; set; }

        public VectorInt2(int x, int y) {
            X = x;
            Y = y;
        }

        static public VectorInt2 operator +(VectorInt2 v1, VectorInt2 v2) =>
            new VectorInt2(v1.X + v2.X, v1.Y + v2.Y);
        static public VectorInt2 operator -(VectorInt2 v1, VectorInt2 v2) =>
            new VectorInt2(v1.X - v2.X, v1.Y - v2.Y);
        static public VectorInt2 operator *(VectorInt2 v1, VectorInt2 v2) =>
            new VectorInt2(v1.X * v2.X, v1.Y * v2.Y);
        static public VectorInt2 operator *(VectorInt2 v1, int i) =>
            new VectorInt2(v1.X * i, v1.Y * i);
        static public VectorInt2 operator *(int i, VectorInt2 v2) =>
            new VectorInt2(i * v2.X, i * v2.Y);
        static public VectorInt2 operator /(VectorInt2 v1, int i) =>
            new VectorInt2(v1.X / i, v1.Y / i);
    }

    class Maxer<T> where T : IComparable<T> {
        public T Value;

        public Maxer(T t) {
            Value = t;
        }

        public void Max(T other) {
            if (Value.CompareTo(other) < 0) Value = other;
        }
    }

    class MultiSet<T> : IEnumerable<KeyValuePair<T, int>> {
        Dictionary<T, int> dictionary = new Dictionary<T, int>();

        public MultiSet(IEnumerable<T> data) {
            foreach (var datum in data) {
                if (dictionary.ContainsKey(datum)) {
                    dictionary[datum]++;
                } else {
                    dictionary[datum] = 1;
                }
            }
        }

        public int this [T key] {
            get {
                return dictionary.ContainsKey(key) ? dictionary[key] : 0;
            }
        }
        public MultiSet() {}

        public static MultiSet<S> ToMultiSet<S>(IEnumerable<S> source) => new MultiSet<S>(source);

        public Dictionary<T, int> AsDict() => dictionary;

        public IEnumerator<KeyValuePair<T, int>> GetEnumerator() => dictionary.GetEnumerator();
        IEnumerator IEnumerable.GetEnumerator() => this.GetEnumerator();
    }
}