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: Accepted)


#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
#include <math.h>

#define MOD 1000000007
#define REP(i,n) for ((i)=0;i<(n);i++)
#define SET(a,c) memset(a,c,sizeof a)
#define CLR(a) memset(a,0,sizeof a)
#define MIN(a,b) (a>b?b:a)
#define MAX(a,b) (a>b?a:b)
#define LL long long
#define ULL unsigned long long



int main(void) {

	int N,a[100],i,j,target,powtemp;
	long ans,temp;

	ans = 0x7FFFFFFF;
	scanf("%d", &N);

	for(i=0;i<N;i++){
		scanf("%d", &a[i]);
	}

	for(i=-100;i<101;i++){
		temp = 0;
		target = i;
		for(j=0;j<N;j++){
			powtemp = a[j]-target;
			temp += powtemp * powtemp;
		}
		if(ans > temp){
			ans = temp;
		}

	}

	printf("%ld", ans);

	return 0;
}

/* 最後の改行忘れるな！！ */