#AT1071. C - Sequence
C - Sequence
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C - Sequence
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 $i$ $(1≤i≤n)$, 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:
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