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())
a_list = list(map(int, input().split()))

total = 0
count = 0
pos_or_neg = True  # True = +, False = -

for a in a_list:
    total += a
    if pos_or_neg:
        if total <= 0:
            count += -total + 1
            total += -total + 1
        pos_or_neg = False

    else:
        if total >= 0:
            count += total + 1
            total -= total + 1
        pos_or_neg = True

first_count = count
count = 0
total = 0
pos_or_neg = False

for a in a_list:
    total += a
    if pos_or_neg:
        if total <= 0:
            count += -total + 1
            total += -total + 1
        pos_or_neg = False

    else:
        if total >= 0:
            count += total + 1
            total -= total + 1
        pos_or_neg = True

print(min(count, first_count))