Make Product Equal One

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n$ integers $a_i$, one operation costs $1$ and increments or decrements one element by $1$. Find the minimum total cost to make the product of all elements equal to $1$.

Input

The first line contains $n$. The second line contains $n$ integers $a_i$.

Output

Print the minimum cost.

Subtasks

General constraints:

• $1 \le n \le 10^5$.

• $-10^9 \le a_i \le 10^9$.

• Subtask 1 (20 points): $n \le 20$, $|a_i| \le 20$

• Subtask 2 (30 points): $n \le 5000$, $|a_i| \le 10^6$

• Subtask 3 (50 points): No additional constraints.

Examples

Input

5
-5 -3 5 3 0

Output

13

Explanation

Move $-5\to-1$ for cost $4$, $-3\to-1$ for $2$, $5\to1$ for $4$, $3\to1$ for $2$, and $0\to1$ for $1$. Total cost is $13$, and the two negative values make the product positive.