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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

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

ans = 0

sum_ = as_[0]
if sum_ == 0 and as_[1] >= 0:
  sum_ -= 1
  ans += 1
elif sum_ == 0 and as_[1] < 0:
  sum_ += 1
  ans += 1
else:
  pass

for i in range(1, n):
  new_sum_ = sum_+as_[i]
  if sum_ > 0 and new_sum_ >= 0:
    as_[i] -= (1+new_sum_)
    ans += 1+new_sum_
    sum_ = -1
  elif sum_ < 0 and new_sum_ <= 0:
    as_[i] += (1-new_sum_)
    ans += 1-new_sum_
    sum_ = 1
  else:
    sum_ = new_sum_
print(ans)