A12811. Make Product Equal One

You are given $n$ numbers $a_1, a_2, \dots, a_n$ . With a cost of one coin you can perform the following operation:

Choose one of these numbers and add or subtract $1$ from it.

In particular, we can apply this operation to the same number several times.

We want to make the product of all these numbers equal to $1$ , in other words, we want $a_1 \cdot a_2$ $\dots$ $\cdot a_n = 1$ .

For example, for $n = 3$ and numbers $[1, -3, 0]$ we can make product equal to $1$ in $3$ coins: add $1$ to second element, add $1$ to second element again, subtract $1$ from third element, so that array becomes $[1, -1, -1]$ . And $1\cdot (-1) \cdot (-1) = 1$ .

What is the minimum cost we will have to pay to do that?

The first line contains a single integer $n$ ( $1 \le n \le 10^5$ ) — the number of numbers.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $-10^9 \le a_i \le 10^9$ ) — the numbers.

Output a single number — the minimal number of coins you need to pay to make the product equal to $1$ .

In the first example, you can change $1$ to $-1$ or $-1$ to $1$ in $2$ coins.

In the second example, you have to apply at least $4$ operations for the product not to be $0$ .

In the third example, you can change $-5$ to $-1$ in $4$ coins, $-3$ to $-1$ in $2$ coins, $5$ to $1$ in $4$ coins, $3$ to $1$ in $2$ coins, $0$ to $1$ in $1$ coin.