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: Wrong Answer)

import copy

n = int(input())
a = list(map(int, input().split()))
# print(a)

def f(org_a, odd):
    a = copy.copy(org_a)
    ans = 0
    if a[0] == 0:
        a[0] = 1 if odd else -1
        ans += 1
    current_sum = a[0]
    for i in range(1, len(a)):
        move = 0
        is_positive = current_sum > 0
        current_sum += a[i]
        if is_positive and current_sum >= 0:
            move = -current_sum - 1
        elif not is_positive and current_sum <= 0:
            move = -current_sum + 1

        current_sum += move
        # print(current_sum)
        a[i] += move
        ans += abs(move)
    return ans

# print(a)
print(min(f(a, True), f(a, False)))