题目描述
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.
Examples
Input
4
1 -3 1 0
Output
4
Input
5
3 -6 4 -5 7
Output
0
Input
6
-1 4 3 2 -5 4
Output
8
输入格式
见题面
输出格式
见题面
样例输入
5
3 -6 4 -5 7
样例输出
0