A. Ambitious Kid
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Chaneka, Pak Chanek's child, is an ambitious kid, so Pak Chanek gives her the following problem to test her ambition.

Given an array of integers $$$[A_1, A_2, A_3, \ldots, A_N]$$$. In one operation, Chaneka can choose one element, then increase or decrease the element's value by $$$1$$$. Chaneka can do that operation multiple times, even for different elements.

What is the minimum number of operations that must be done to make it such that $$$A_1 \times A_2 \times A_3 \times \ldots \times A_N = 0$$$?

Input

The first line contains a single integer $$$N$$$ ($$$1 \leq N \leq 10^5$$$).

The second line contains $$$N$$$ integers $$$A_1, A_2, A_3, \ldots, A_N$$$ ($$$-10^5 \leq A_i \leq 10^5$$$).

Output

An integer representing the minimum number of operations that must be done to make it such that $$$A_1 \times A_2 \times A_3 \times \ldots \times A_N = 0$$$.

Examples
Input
3
2 -6 5
Output
2
Input
1
-3
Output
3
Input
5
0 -1 0 1 0
Output
0
Note

In the first example, initially, $$$A_1\times A_2\times A_3=2\times(-6)\times5=-60$$$. Chaneka can do the following sequence of operations:

  1. Decrease the value of $$$A_1$$$ by $$$1$$$. Then, $$$A_1\times A_2\times A_3=1\times(-6)\times5=-30$$$
  2. Decrease the value of $$$A_1$$$ by $$$1$$$. Then, $$$A_1\times A_2\times A_3=0\times(-6)\times5=0$$$

In the third example, Chaneka does not have to do any operations, because from the start, it already holds that $$$A_1\times A_2\times A_3\times A_4\times A_5=0\times(-1)\times0\times1\times0=0$$$