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.

-----Sample Input-----
4
1 -3 1 0

-----Sample Output-----
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.

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