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)

# -*- coding: utf-8 -*-
n=int(input())
a=list(map(int,input().split()))
count1=0
sum1=a[0]
if a[0]==0:
    count1=1
    sum1=1
for ii in range(1,n):
    S=sum1
    sum1+=a[ii]
    if sum1*S>=0:
        if S>0:
            count1+=sum1+1
            sum1=-1
        elif S<0:
            count1+=1-sum1
            sum1=1

if a[0]>=0:
    count2=a[0]+1
    sum2=-1
else:
    count2=1-a[0]
    sum2=1
for ii in range(1,n):
    S=sum2
    sum2+=a[ii]
    if sum2*S>=0:
        if S>0:
            count2+=sum2+1
            sum2=-1
        elif S<0:
            count2+=1-sum2
            sum2=1

print(min(count1,count2))