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 (2.7.6) (judge verdict: Time Limit Exceeded)

n = int(raw_input())
a = map(int, raw_input().split())

counter = 0
prev = a[0] * -1
for idx in range(n):
    s = sum(a[:idx+1])

    if prev * s > 0:
        if s < 0:
            while s < 1:
                s += 1
                a[idx] += 1
                counter += 1
        elif s > 0:
            while s > -1:
                s -= 1
                a[idx] -= 1
                counter += 1
    elif s == 0:
        if prev > 0:
            s -= 1
            counter += 1
        elif prev < 0:
            s += 1
            counter += 1

    prev = s

print counter