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<algorithm>
using namespace std;
int main(){
  int n;
  cin>>n;
  int a[n];
  int sum=0;
  for(int  i=0;i<n;i++){
    cin>>a[i];
    sum+=a[i];
  }
  sort(a,a+n);
  if(sum==n*a[0]){
    cout<<0;
    return 0;
  }
  else{
  int avg=(sum+1)/n;
  int ans=0,ans1=0,mn=10000000;
  for(int i=0;i<n;i++){
    ans+=(a[i]-avg)*(a[i]-avg);
    for(int j=0;j<n;j++){
      ans1+=(a[j]-a[i])*(a[j]-a[i]);
    }
    mn=min(mn,ans1);
  }
    cout<<ans<<" "<<mn<<" ";
  cout<<min(mn,ans);
	}

}