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 <bits/stdc++.h>
using namespace std;

int main(){
int n;
  cin >> n;
int d[n];
  
for(int i=0;i<n;i++) {
  cin >> d[i];
}
int count=0;
  int sum=d[0];
  int f  =0;  
if(d[0]>0){
  f=-1; 
}
if(d[0]<0){
  f=1;
}
for(int i=1;i<n;i++){
  sum+=d[i];
  if(sum==0){
    if(f==1){
    count++;
      f=-1;
      sum=1;
      continue;
    }
    if(f==-1){
    count++;
      f=1;
      sum=-1;
      continue;
    }
  }
  if(sum>0){
     if(f==1){
     f=-1;
     continue;
     }
     if(f==-1){
       count+=sum+1;
       sum=-1;
       f=1;
       continue;
      }
  }
  if(sum<0){
     if(f==-1){
       f=1;
       continue;
     }          
     if(f==1){
       count+=1-sum;
       sum=1;
       f=-1;
       continue;  
     }  
  }
}  
 cout << count << endl; 
}