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)

def solve():

    n = int(input())
    a = list(map(int, input().split()))

    b = [a[i] for i in range(n)]

   # print(a)
   # print(b)

    #Even
    sum_e = 0
    ans_e = 0

    for i in range(n):
        sum_e += a[i]
        if i%2 == 0:
            if sum_e <= 0:
                ans_e += abs(sum_e) + 1
                sum_e += abs(sum_e) + 1
        else:
            if sum_e >= 0:
                ans_e += abs(sum_e) + 1
                sum_e -= abs(sum_e) + 1

    #Odd
    sum_o = 0
    ans_o = 0

    for i in range(n):
        sum_o += b[i]
        if i%2 == 1:
            if sum_o <= 0:
                ans_o += abs(sum_o) + 1
                sum_o += abs(sum_o) + 1
        else:
            if sum_o >= 0:
                ans_o += abs(sum_o) + 1
                sum_o -= abs(sum_o) + 1

    if ans_o <= ans_e:
        ans = ans_o
    else:
        ans = ans_e


    print(ans)

if __name__ ==  "__main__":
    solve()