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: Accepted)

#include <iostream>
using namespace std;

int n;
int a[110];

template<class T>
T f(T x){
    T res = 0;
    for(int i = 0; i < n; ++i){
        T d = a[i] - x;
        res += d*d;
    }
    return res;
}

int main(){
    while(cin >> n){
        for(int i = 0; i < n; ++i) cin >> a[i];
        double l = -200, r = 200;
        for(int _ = 0; _ < 200; ++_){
            double x1 = (l+l+r)/3;
            double x2 = (l+r+r)/3;
            double y1 = f(x1);
            double y2 = f(x2);
            if(y1 < y2){
                r = x2;
            } else {
                l = x1;
            }
        }
        int x = l;
        cout << min(min(f(x-1),f(x)),f(x+1)) << endl;
    }
}