Problem:
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:

n
a_1 a_2 ... a_n

Output

Print the minimum necessary count of operations.

Sample Input 1

4
1 -3 1 0

Sample Output 1

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.

Sample Input 2

5
3 -6 4 -5 7

Sample Output 2

0

The given sequence already satisfies the conditions.

Sample Input 3

6
-1 4 3 2 -5 4

Sample Output 3

8

Solution in Python (3.4.3) (judge verdict: Accepted)

import numpy as np
def main():
    n=int(input())
    a=list(map(int,input().split(' ')))
    sumcum_odd = 0
    sumcum_even = 0
    ans_odd = 0
    ans_even = 0
    for i in range(n):
        if i%2 ==0:#odd
            if sumcum_odd + a[i] >0:
                sumcum_odd += a[i]
            elif sumcum_odd <=0:
                ans_odd += 1-1*(sumcum_odd+a[i])
                sumcum_odd = 1
            if sumcum_even + a[i] <0:
                sumcum_even += a[i]
            elif sumcum_even >= 0:
                ans_even += sumcum_even + a[i] +1
                sumcum_even = -1
        else:
            if sumcum_odd + a[i] <0:
                sumcum_odd += a[i]
            elif sumcum_odd >=0:
                ans_odd += sumcum_odd + a[i] +1
                sumcum_odd = -1
            if sumcum_even + a[i] >0:
                sumcum_even += a[i]
            elif sumcum_even <= 0:
                ans_even += 1-1*(sumcum_even+a[i])
                sumcum_even = 1
    print(min(ans_odd,ans_even))



if __name__ == '__main__':
    main()