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 copy
n = int(input())

numbers = list(map(int, input().split()))
numbers1 = copy.copy(numbers)
counter = 0
counter2 = 0
sum_in = 0
sum_in1 = 0

for i in range(len(numbers)):
    sum_in += numbers[i]
    if i % 2 == 0:
        if sum_in <= 0:
            sub = abs(sum_in) + 1
            sum_in += sub
            numbers[i] += sub
            counter += sub
    else:
        if sum_in >= 0:
            sub = abs(sum_in) + 1
            sum_in -= sub
            numbers[i] -= sub
            counter += sub

for i in range(len(numbers1)):
    sum_in1 += numbers1[i]

    if i % 2 != 0:
        if sum_in1 <= 0:
            sub = abs(sum_in1) + 1
            sum_in1 += sub
            numbers1[i] += sub
            counter2 += sub
    else:
        if sum_in1 >= 0:
            sub = abs(sum_in1) + 1
            sum_in1 -= sub
            numbers1[i] -= sub
            counter2 += sub

print(min([counter2, counter]))