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)

# input
n = int(input())
A = list(map(int, input().split()))

# 偶数番目が＋
A_even = A
S_even = 0
ans_even = 0
for i in range(n):
    if (S_even + A_even[i]) * ((-1) ** (i - 1)) > 0:
        S_even += A_even[i]
        continue
    ans_even += S_even + A_even[i] + 1
    A_even[i] = (-1) ** (i - 1) - S_even
    S_even = (-1) ** (i - 1)

# 奇数番目が＋
A_odd = A
S_odd = 0
ans_odd = 0
for i in range(n):
    if (S_odd + A_odd[i]) * ((-1) ** i) > 0:
        S_odd += A_odd[i]
        continue
    ans_odd += S_odd + A_odd[i] + 1
    A_odd[i] = (-1) ** i - S_odd
    S_odd = (-1) ** i

ans = min(ans_even, ans_odd)

print(ans)