Be Together

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

inputFormat

Input

The input is given from Standard Input in the following format:

N a_1 a_2 ... a_N

outputFormat

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

样例

2
4 8

8