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)

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

ans_1 = 0
sum_1 = A[0]
if A[0] <= 0:
    ans_1 += abs(A[0])+1
    sum_1 = ans_1

for i in range(1, len(A)):
    a = A[i]
    prev_sum = sum_1
    sum_1 += a
    if sum_1 * prev_sum >= 0:
        ans_1 += abs(prev_sum+a)+1

        if prev_sum > 0:
            sum_1 = -1
        else:
            sum_1 = 1


ans_2 = 0
sum_2 = A[0]
if A[0] >= 0:
    ans_2 += abs(A[0])+1
    sum_2 = -ans_2

for i in range(1, len(A)):
    a = A[i]
    prev_sum = sum_2
    sum_2 += a
    if sum_2 * prev_sum >= 0:
        ans_2 += abs(prev_sum+a)+1

        if prev_sum > 0:
            sum_2 = -1
        else:
            sum_2 = 1

print(min(ans_1, ans_2))