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)

from functools import lru_cache
n = int(input())
s = list(map(int, input().split()))


@lru_cache(maxsize=None)
def cost(z):
    res = abs(z - s[0])
    sum = 0
    for j, y in enumerate(s):
        tmp = sum + y
        if j == 0:
            sum = tmp
            continue
        if sum * tmp >= 0:
            c = -1 if tmp > 0 else 1
            x = c - tmp
            res += abs(x)
            sum = c
        else:
            sum = tmp
    return res


ans1 = cost(s[0])
ans2 = cost(1)
ans3 = cost(-1)
print(min(ans1, ans2, ans3))