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 = 0
previous_sum = A[0] # total to i - 1
for i in range(1, N):
  # if prev_sum is plus and A[i] is more minus than prev_sum, no action.
  # if prev_sum is plus and minus of A[i] is larger than or equal to prev_sum.
  if previous_sum > 0 and previous_sum + A[i] >= 0:
    # the number that need to be subtracted to meet the requirements.
    require_subtraction = previous_sum + A[i] + 1
    # correcting the current number.
    A[i] -= require_subtraction
    ans += require_subtraction
  # if prev_sum is minus and A[i] is more plus than prev_sum, no action.
  # if prev_sum is minus and minus of A[i] is more smaller than or equal to prev_sum.
  elif previous_sum < 0 and previous_sum + A[i] <= 0:
    # the number that need to be added to meet the requirements.
    require_addition = -(previous_sum + A[i] - 1)
    # correcting the current number.
    A[i] += require_addition
    ans += require_addition
  previous_sum += A[i]

print(ans)