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: Wrong Answer)

def resolve(List):
    # L[0]!=0を起点とする
    L = List
    cnt = 0
    s = L[0]
    for i in range(1,len(L)):
        a = L[i]
        if(s>0 and s+a>=0):
            L[i] = -s-1
            cnt += (s+a+1)
            s = -1
        elif(s<0 and s+a<=0):
            L[i] = -s+1
            cnt += (-s-a+1)
            s = 1
        else:
            s += a
    return cnt      

def ans(List):
    L = List
    a = L[0]
    c0,c1=0,0

    if (a>0):
        c0 = resolve(L)
        c1 = (a+1) + resolve([-1]+L[1:])
    elif (a<0):
        c0 = resolve(L)
        c1 = (-a+1) + resolve([1]+L[1:])
    else:
        c0 = 1 + resolve([1]+L[1:])
        c1 = 1 + resolve([-1]+L[1:])
    
    return(min(c0,c1))

def main():
    N = int(input())
    L = [int(x) for x in input().split(' ')]
    print(ans(L))

main()