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 <string>
#include <cmath>
#include <set>
#include <algorithm>
#include <array>
#include <complex>
#include <string>
#include <utility>
#include <map>
#include <queue>
#include <list>
int dx[4] = { -1,0,1,0 };
int dy[4] = { 0,1,0,-1 };
#define INF 1<<21
using pii = std::pair<int, int>;
#define SORT(v) std::sort(v.begin(), v.end())
int F[100][15];
int main(void) {
	int N,sum=0,ave,ans=0;
	std::cin >> N;
	std::vector<int> a(N);
	for (int i = 0; i < N; i++) {
		std::cin >> a[i];
	}
	for (int j = -100; j <= 100; j++) {
		for (int i = 0; i < N; i++) {
			sum += pow(j - a[i], 2);
		}
		std::min(ans, sum);
	}
	std::cout << ans << std::endl;
	return 0;
}