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.
- 2 ≤ n ≤ 105
- |ai| ≤ 109
- Each ai is an integer.
Input is given from Standard Input in the following format:
a1 a2 ... an
Print the minimum necessary count of operations.
Sample Input 1
1 -3 1 0
Sample Output 1
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
3 -6 4 -5 7
Sample Output 2
The given sequence already satisfies the conditions.
Sample Input 3
-1 4 3 2 -5 4
Sample Output 3