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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>

using namespace std;
int main(){
	int i,n;
	cin >> n;
	int a[n];
	for(i=0;i<n;i++){
		cin >> a[i];
	}
	
	long long m=0,l=0,sum=0;
	for(i=0;i<n;i++){
		sum += a[i];
		if(i%2==0){
			if(sum <= 0){
				m += 1 - sum;
				sum = 1;
			}
		}else{
			if(sum >= 0){
				m += sum + 1;
				sum = -1;
			}
		}
	}
	sum = 0;
	for(i=0;i<n;i++){
		sum += a[i];
		if(i%2!=0){
			if(sum <= 0){
				l += 1 - sum ;
				sum = 1;
			}
		}else{
			if(sum >= 0){
				l += sum + 1;
				sum = -1;
			}
		}
	}
	cout << min(m,l) << endl;
}