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)

n = int(input())
As = list(map(int, input().split()))

if As[0] > 0:
    acc0s = [As[0], -1]
    num0s = [0, As[0] + 1]
elif As[0] < 0:
    acc0s = [As[0], 1]
    num0s = [0, -As[0] + 1]
else:
    acc0s = [1, -1]
    num0s = [1, 1]

ans = float('inf')
for acc0, num0 in zip(acc0s, num0s):
    acc = acc0
    num = num0
    for a in As[1:]:
        if acc * (acc + a) < 0:
            acc += a
        else:
            if acc > 0:
                num += a - -(acc + 1)
                acc = -1
            else:
                num += -(acc - 1) - a
                acc = 1

    ans = min(ans, num)

print(ans)