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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int min(int a[]);
int max(int a[]);

int main(){
  int i, N, k;
  int a[200];
  int sum[300];
  scanf("%d", &N);
  for(i=0; i<N; i++){
    scanf("%d", &a[i]);
  }

  for(k=min(a); k<=max(a); k++){
    for(i=0; i<N; i++){
      sum[k-min(a)] += (k - a[i]) * (k - a[i]);
    }
  }
  printf("%d\n", min(sum));

  return 0;
}

int min(int a[]){
  int i=0;
  int m=a[0];
  while(a[i] != '\0'){
    if(m > a[i]) m = a[i];
    i++;
  }
  return m;
}

int max(int a[]){
  int i=0;
  int M=a[0];
  while(a[i] != '\0'){
    if(M < a[i]) M = a[i];
    i++;
  }
  return M;
}