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 (3.8.2) (judge verdict: Accepted)

N = int(input())
A = tuple(map(int, input().split(' ')))

if A[0] == 0:
    cs = 1
    ans1 = 1
else:
    cs = A[0]
    ans1 = 0

for na in A[1:]:
    if cs >= 0:
        cs += na
        if cs < 0:
            continue

        ans1 += abs(cs) + 1
        cs = -1
    else:
        cs += na
        if cs > 0:
            continue

        ans1 += abs(cs) + 1
        cs = 1

if A[0] == 0:
    cs = -1
    ans2 = 1
elif A[0] > 0:
    cs = -1
    ans2 = abs(A[0]) + 1
else:
    cs = 1
    ans2 = abs(A[0]) + 1

for na in A[1:]:
    if cs >= 0:
        cs += na
        if cs < 0:
            continue

        ans2 += abs(cs) + 1
        cs = -1
    else:
        cs += na
        if cs > 0:
            continue

        ans2 += abs(cs) + 1
        cs = 1

print(min(ans1, ans2))