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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include <vector>
#include <list>
#include <string>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <climits>
#include <map>
#include <math.h>
#include <stack>

using namespace std;

int cost(int x, int y) {
	return (x - y)*(x - y);
}

bool q(vector<int> r) {
	for (int i = 0; i < r.size(); i++)
	{
		if (r[i] != r[0]) { return true; }
	}
	return false;
}

int main(void) {
	vector<int> a;
	int n;
	cin >> n;
	int sum=0;
	for (int i = 0; i < n; i++)
	{
		int t;
		cin >> t;
		a.push_back(t);
		sum += t;
	}

	if (q(a)==true) {
		int ave = (double)sum / n + 0.5;

		int ans = 0;

		for (int i = 0; i < n; i++)
		{
			ans += cost(a[i], ave);
		}
		cout << ans << endl;
	}
	else { cout << 0 << endl; }

	return 0;

}