CF1206B 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.