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>
long a[100000];

int main(int argc, char const *argv[]){
	long sum,bsum,ans=0,n,i,f=0,min=1;
	scanf("%ld",&n);
	scanf("%ld",&a[0]);
	if(a[0]==0){
		ans++;
		sum=1;
		f=1;
	}else sum=a[0];
	for(i=1;i<n;i++){
		scanf("%ld",&a[i]);
		bsum=sum;
		sum+=a[i];
		if(bsum>0){
			if(sum>=0){
				ans+=sum+1;
				sum=-1;
			}
		}else{
			if(sum<=0){
				ans+=1-sum;
				sum=1;
			}
		}
	}
		if(a[0]>=0){
			min=a[0]+1;
			sum=-1;
		}else{
			min=1-a[0];
			sum=1;
		}
		for(i=1;i<n;i++){
			bsum=sum;
			sum+=a[i];
			if(bsum>0){
				if(sum>=0){
					min+=sum+1;
					sum=-1;
				}
			}else{
				if(sum<=0){
					min+=1-sum;
					sum=1;
				}
			}
		}
		if(ans<min) printf("%ld\n",ans);
		else printf("%ld\n",min);
	return 0;
}