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.