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: Accepted)

#include<stdio.h>
#include<stdlib.h>
int main(){
  int n,i;
  scanf("%d",&n);
  int a[n+1];
  long long odd=0,even=0,odd_num=0,even_num=0;
  for(i=0;i<n;i++)
    scanf("%d",&a[i]);
  for(i=0;i<n;i++){
    if(i%2==0){
      if(even_num+a[i]>0)
        even_num+=(long long)a[i];
      else{
        even+=1-(long long)(even_num+a[i]);
        even_num=1;
      }
      if(odd_num+a[i]<0)
        odd_num+=(long long)a[i];
      else{
        odd+=1+(long long)(odd_num+a[i]);
        odd_num=-1;
      }
    }
    else{
      if(even_num+a[i]<0)
        even_num+=(long long)a[i];
      else{
        even+=1+(long long)(even_num+a[i]);
        even_num=-1;
      }
      if(odd_num+a[i]>0)
        odd_num+=(long long)a[i];
      else{
        odd+=1-(long long)(odd_num+a[i]);
        odd_num=1;
      }
    }
  }
  printf("%lld\n",even<odd?even:odd);
  return 0;
}