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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<string.h>
#include<ctype.h>
#include<string>
#include<math.h>
#define pi 3.141592653589
#include<iomanip>
using namespace std;
#include<algorithm>



int main(){
     
    int n,a[100000],ans,sumb=0,suma=0;
    
    cin>>n;
    for(int i=0;i<n;i++)cin>>a[i];
    for(int i=0;i<n;i++){
        sumb=suma;
        suma+=a[i];
        if(suma==0){
            if(sumb>0)suma--;
            else suma++;
            ans++;
        }
        else if(suma*sumb>0){
            if(sumb>0){
                ans+=suma+1;
                suma-=suma+1;
            }
            else if(sumb<0){
                ans+=1-suma;
                suma+=1-suma;
            }
        }
        else{}
    }
    cout<<ans<<endl;
    
    return 0;
}