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: Accepted)

import sys
n = int(input())
a_ls = [int(i) for i in sys.stdin.readline().split()]

INF = 10**18
best = INF
for i in range(2):
    flg = i % 2
    _sum = 0
    cnt = 0
    for a in a_ls:
        _sum += a
        if flg:
           if _sum <= 0:
               cnt += 1 - _sum
               _sum = 1
        else:
            if _sum >= 0:
                cnt += _sum + 1
                _sum = -1
        flg = 1 if flg == 0 else 0
    best = min(best, cnt)
print(best)