### Problem Statement

You are given an integer sequence of length N. The i-th term in the sequence is ai. 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 ≤ 105
• |ai| ≤ 109
• Each ai is an integer.

### Input

Input is given from Standard Input in the following format:

```n
a1 a2 ... an
```

### Output

Print the minimum necessary count of operations.

```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.

```5
3 -6 4 -5 7
```

### Sample Output 2

```0
```

The given sequence already satisfies the conditions.

```6
-1 4 3 2 -5 4
```

```8
```

### Submitting .cpp to 'sequence'

Time Limit: 1 Seconds
Memory Limit: 1024MB
No. of ACs: 3