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: Accepted)

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

def calc(a, t):
    ans = 0
    p_flag = t < 0
    t += a
    if p_flag:
        if t < 0:
            ans = 1 - t
            t = 1
    else:
        if t >= 0:
            ans = 1 + t
            t = -1
    if t == 0:
        ans += 1
        if p_flag:
            t = 1
        else:
            t = -1

    return ans, t

ans_p = 0
t_p = 0
ans_m = 0
t_m = 0
if A[0] > 0:
    ans_p = 0
    t_p = A[0]
    ans_m = A[0]+1
    t_m = -1
elif A[0] < 0:
    ans_p = -A[0]+1
    t_p = 1
    ans_m = 0
    t_m = A[0]
else:
    ans_p = 1
    t_p = 1
    ans_m = 1
    t_m = -1

for i in range(1, N):
    a, t_p = calc(A[i], t_p)
    ans_p += a
    a, t_m = calc(A[i], t_m)
    ans_m += a

print(min(ans_p, ans_m))