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: Time Limit Exceeded)

import numpy as np
from copy import deepcopy
n = int(input())
a = list(map(int, input().split()))
c = [0] * n
for i in range(n):
    c[i] = c[i - 1] + a[i]
c = np.array(c)
ans1, ans2 = 0, 0
tmp = deepcopy(c)
for i in range(n):
    t = tmp[i]
    if i % 2 == 0 and tmp[i] >= 0:
        tmp[i:] -= t + 1
        ans1 += t + 1
    elif i % 2 == 1 and tmp[i] <= 0:
        tmp[i:] += -t + 1
        ans1 += -t + 1
tmp = deepcopy(c)
for i in range(n):
    t = tmp[i]
    if i % 2 == 1 and tmp[i] >= 0:
        tmp[i:] -= t + 1
        ans2 += t + 1
    elif i % 2 == 0 and tmp[i] <= 0:
        tmp[i:] += -t + 1
        ans2 += -t + 1
print(min(ans1, ans2))