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.

Examples

Input

2
4 8


Output

8


Input

3
1 1 3


Output

3


Input

3
4 2 5


Output

5


Input

4
-100 -100 -100 -100


Output

0

n = int(raw_input())
ais = map(int, raw_input().split())
ais.sort()

def f(ais):
	return [sum(ais)/len(ais),sum(ais)/len(ais)+1,sum(ais)/len(ais)-1]
	if len(ais) % 2:
		return [ais[len(ais)/2]]
	
	v = ais[len(ais)/2 -1] + ais[len(ais)/2]
	return [v/2,v/2-1,v/2+1]
def g(ais,m):
	s= 0
	for ai in ais: s+=abs(ai - m) **2
	return s
print min([g(ais,m) for m in f(ais)])