Score : $300$ points

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 $i$ $(1 \leq i \leq n)$, the sum of the terms from the $1$-st through $i$-th term is not zero.
• For every $i$ $(1 \leq i \leq n-1)$, 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

• $2 \leq n \leq 10^5$
• $|a_i| \leq 10^9$
• 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.

4
1 -3 1 0

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

0

The given sequence already satisfies the conditions.

6
-1 4 3 2 -5 4

8