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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

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

res = 0
former = 0
s = 0
if A[0] == 0:
    if A[1] >= 0:
        A[0] = -1
    else:
        A[0] = 1
    res += 1
    
for i in range(N):
    former = s
    s += A[i]
    if i == 0:
        pass
    else:
        if s == 0:
            if former > 0:
                s -= 1
                res += 1
            elif former < 0:
                s += 1
                res += 1
        elif former*s > 0:
            if s > 0:
                res += s+1
                s = -1
            else:
                res += -s+1
                s = 1
    #print(s)
print(res)