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
import math as m
 
def main():
    n  = raw_input()
    a = map(float,raw_input().split())
    
    avg =  m.ceil( sum(a)/len(a) )
    avg2 =  m.floor( sum(a)/len(a) )

    cost = 0
    for i in a:
        cost += (avg - i) ** 2
    
    cost2 = 0
    for i in a:
        cost2 += (avg2 - i) ** 2
    
    print int(min([cost,cost2]))

if __name__ == '__main__':
    main()