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 numpy as np

n = input()
a_s = [int(x) for x in input().split()]
sum_i = 0
num = 0
for i in range(len(a_s)):
    a = a_s[i]
    new_sum_i = sum_i + a
#     print(f"a:{a}, tmp_sum_i:{new_sum_i}")
    if (new_sum_i == 0):
        if sum_i == 0:
            new_sum_i = 1 if a_s[i+1] == 0 else np.sign(a_s[i+1])*(-1)
        else:
            new_sum_i = np.sign(sum_i)*(-1)
        adjusted_a = new_sum_i - sum_i
        num += abs(max(adjusted_a, a) - min(adjusted_a, a))
        sum_i = new_sum_i
    elif new_sum_i * sum_i > 0:
        new_sum_i = np.sign(new_sum_i)*-1
        adjusted_a = new_sum_i - sum_i
        num += abs(max(adjusted_a, a) - min(adjusted_a, a))
        sum_i = new_sum_i
    else:
        sum_i = new_sum_i
#     print(f"a:{a}, new_sum_i:{sum_i}, num:{num}")
#     print()
    
print(num)