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)

N = int(input())
a = list(map(int, input().split()))

ans = 0
_a = [a[0]]
prev_sign = 1
if a[0] < 0:
    prev_sign = -1
for i in range(1, N):
    c = a[i]
    if c >= 0 and prev_sign > 0:
        ans += abs(c - (-1))
        c = -1
    elif c <= 0 and prev_sign < 0:
        ans += abs(c - 1)
        c = 1
    if c > 0:
        prev_sign = 1
    else:
        prev_sign = -1
    _a.append(c)

__a = [_a[0]]
acm_sum = _a[0]
for i in range(1, N):
    c = _a[i]
    if abs(acm_sum) >= abs(c):
        if c < 0:
            c = -1*(abs(acm_sum)+1)
        else:
            c = abs(acm_sum)+1
    acm_sum += c
    ans += abs(c - _a[i])
    __a.append(c)

print(ans)