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)

from sys import stdin


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    n = int(_in[0])  # type:int
    a_arr = list(map(int,_in[1].split(' ')))  # type:list(int)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    cnt = 0
    sum_ = 0
    for i in range(0,n):
        if i==0:
            if a_arr[0]==0:
                while a_arr[i]==0:
                    i+=1
                else:
                    if a_arr[i+1]>0:
                        sum_ = (-1)**i
                        cnt += 1
                    else:
                        sum_ = (-1)**(i+1)
                        cnt += 1
            else:
                sum_ = a_arr[i]
        else:
            if sum_<0:
                if sum_+a_arr[i]<=0:
                    cnt += 1-(sum_+a_arr[i])
                    sum_ = 1
                else:
                    sum_ = sum_+a_arr[i]
            else:
                if sum_+a_arr[i]>=0:
                    cnt += 1+(sum_+a_arr[i])
                    sum_ = -1
                else:
                    sum_ = sum_+a_arr[i]
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    print(cnt)