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 <bits/stdc++.h>
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;
#define ITR(v,c) for(auto v=begin(c);v!=end(c);v++)
#define FOR(v,a,n) for(int v=a;v<(int)(n);v++)
#define FORE(x,arr) for(auto &x:arr)
#define REP(v,n) FOR(v,0,n)
#define ALL(c) begin(c),end(c)
const int DX[4]={0,1,0,-1}, DY[4]={-1,0,1,0};
const int INF = 1e9;
template<class T,class U>ostream&operator<<(ostream &os,const pair<T,U> &p){
    os<<"("<<p.first<<","<<p.second<<")";return os;}
template<class T>ostream&operator<<(ostream &os,const vector<T> &v){
    ITR(i,v)os<<*i<<(i==end(v)-1?"":"\n");return os;}
//------------------------------------------------------------------------------

int main(int argc, char const *argv[]) {
    int N;
    cin>>N;
    vector<int> a(N);
    set<int> s;
    int sum=0;
    REP(i,N) cin>>a[i],s.insert(a[i]);
    FORE(x,s) sum += x;
    sum/=s.size();
    int ans1,ans2=0;
    REP(i,N) {
        ans1+=(sum-a[i])*(sum-a[i]);
    }
    sum++;
    REP(i,N) {
        ans2+=(sum-a[i])*(sum-a[i]);
    }
    cout<<min(ans1,ans2)<<endl;
    return 0;
}