Make Product Equal One

## 题目描述 给你一个有 $n$ 个数的数组。你可以用 $x$(x为任意正整数) 的代价将数组中的任意一个数增加或减少 $x$ ，你可以重复多次此操作。现在需要你用若干次操作使得 $a_1·a_2·...·a_n = 1$ （数组的乘积为1）。 比如，当 $n=3$ 和数组为 [**1,-3,0**] 时，我们最少需要花费 $3$ 的代价：用 $2$ 的代价把 -$3$ 增加到 -$1$ ，再用 $1$ 的代价把 $0$ 减少到 -$1$ ，数组就变成了 [**1,-1,-1**] ，然后 $1·（-1）·（-1）=1$ 。 现在询问最少需要花费多少的代价使得数组的乘积为 $1$ 。 ## 输入格式 输入共两行。 第一行输入一个数 $n$ ，表示数组的数字个数。 第二行输入 $n$ 个数 $a_i$ ，表示该数组。 ## 输出格式 输出一个数，表示使得数组的乘积为 $1$ 的最少的花费。 ## 数据范围 $1\leq n\leq 10^5$ $-10^9\leq a_i\leq 10^9$

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 $ .

2
-1 1

2

4
0 0 0 0

4

5
-5 -3 5 3 0

13

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.