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: Accepted)

#include<stdio.h>
int main(){
  int n,i,j,d[100010],a;
  long long ans=1e18,s,c;
  scanf("%d",&n);
  for(i=0;i<n;i++)scanf("%d",&d[i]);
  for(j=0;j<2;j++){
    s=c=0;
    for(i=0;i<n;i++){
      s+=d[i];
      if((i+j)%2==0&&s<=0){
	c+=1-s;
	s=1;
      }
      if((i+j)%2==1&&s>=0){
	c+=s+1;
	s=-1;
      }
    }
    if(ans>c)ans=c;
  }
  printf("%lld\n",ans);
  return 0;
}