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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
using namespace std;
int main(){
    int n;
    cin>>n;
    int sum=0;
    vector<int>a(n);
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
    }
    sum+=a[0];
    int count=0;
    bool pos=true;
    if(sum==0){
        count++;
        sum=-1;
    }
    if(sum<=0){
        pos=false;
    }
    for(int i=1;i<n;i++)
    {
        if(!pos){
            sum+=a[i];
            if(sum<=0){
                count+=abs(sum)+1;
                sum=1;
            }
            pos=true;
        }
        else
        {
            sum+=a[i];
            if(sum>=0){
                count+=sum+1;
                sum=-1;
            }
            pos=false;
        }
    }
    cout<<count<<endl;
}