### ** sequence**

### sequence

### Problem Statement

You are given an integer sequence of length `N`. The `i`-th term in the sequence is `a`_{i}.
In one operation, you can select a term and either increment or decrement it by one.

At least how many operations are necessary to satisfy the following conditions?

- For every
`i` `(1≤i≤n)`, the sum of the terms from the `1`-st through `i`-th term is not zero.
- For every
`i` `(1≤i≤n-1)`, the sign of the sum of the terms from the `1`-st through `i`-th term, is different from the sign of the sum of the terms from the `1`-st through `(i+1)`-th term.

### Constraints

`2 ≤ n ≤ 10`^{5}
`|a`_{i}| ≤ 10^{9}
- Each
`a`_{i} is an integer.

### Input

Input is given from Standard Input in the following format:

`n`
`a`_{1} `a`_{2} `...` `a`_{n}

### Output

Print the minimum necessary count of operations.

### Sample Input 1

4
1 -3 1 0

### Sample Output 1

4

For example, the given sequence can be transformed into `1, -2, 2, -2` by four operations. The sums of the first one, two, three and four terms are `1, -1, 1` and `-1`, respectively, which satisfy the conditions.

### Sample Input 2

5
3 -6 4 -5 7

### Sample Output 2

0

The given sequence already satisfies the conditions.

### Sample Input 3

6
-1 4 3 2 -5 4

### Sample Output 3

8