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())
l=list(map(int,input().split()))
if l[0]!=0:
    count=0
    suml=l[0]
    for i in range(1,n):
        if suml>0 and suml+l[i]<0:
            suml+=l[i]
        elif suml<0 and suml+l[i]>0:
            suml+=l[i]
        elif suml>0 and suml+l[i]>=0:
            count+=suml+l[i]+1
            suml=-1
        else:
            count+=-suml-l[i]+1
            suml=1
    a1=count
    count=abs(l[0])+1
    suml=-l[0]
    for i in range(1,n):
        if suml>0 and suml+l[i]<0:
            suml+=l[i]
        elif suml<0 and suml+l[i]>0:
            suml+=l[i]
        elif suml>0 and suml+l[i]>=0:
            count+=suml+l[i]+1
            suml=-1
        else:
            count+=-suml-l[i]+1
            suml=1
    a2=count
    print(min(a1,a2))
    
else:
    count=1
    suml1=1
    for i in range(1,n):
        if suml1>0 and suml1+l[i]<0:
            suml1+=l[i]
        elif suml1<0 and suml1+l[i]>0:
            suml1+=l[i]
        elif suml1>0 and suml1+l[i]>=0:
            count+=suml1+l[i]+1
            suml1=-1
        else:
            count+=-suml1-l[i]+1
            suml1=1
    k1=count
    count=1
    suml2=-1
    for i in range(1,n):
        if suml2>0 and suml2+l[i]<0:
            suml2+=l[i]
        elif suml2<0 and suml2+l[i]>0:
            suml2+=l[i]
        elif suml2>0 and suml2+l[i]>=0:
            count+=suml2+l[i]+1
            suml2=-1
        else:
            count+=-suml2-l[i]+1
            suml2=1
    k2=count
    print(min(k1,k2))