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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(void){

  int i, a, n, num;
  int sum=0, bsum=0, ans=0, m=0;

  scanf("%d", &n);
  
  for(i=0;i<n;i++){
    scanf("%d", &a);
    bsum=sum;
    sum+=a;

    if(bsum>0){
      if(sum>0){
      num=sum;
        do {
          num--;
          ans++;
          m++;
        } while(num>=0);
        sum-=m;
        m=0;
      }
        if(sum=0){
          ans++;
          sum-=1;
       }
    }

    if(bsum<0){
      if(sum<0){
        num=sum;
        do{
          num++;
          ans++;
          m++;
        }while(num<=0);
        sum+=m;
        m=0;
      }
        if(sum=0){
          ans++;
          sum+=1;
    }
  }
}
    printf("%d\n", ans);

    return 0;
}