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<algorithm>
#include<iostream>
using namespace std;
long long sum,a[1000000],n,ans,ans1,last;
void solve1(){
	if (sum<=0){
		ans+=1-sum;
		sum=1;
	}
}
void solve2(){
	if (sum>=0){
		ans+=sum+1;
		sum=-1;
	}
}
void solve(int f){
	for (int i=0;i<n;i++){
		sum+=a[i];
		if (i%2==f)
			solve1();
		else
			solve2();
	}
}
int main()
{
	cin>>n;
	for (int i=0;i<n;i++) cin>>a[i];
	solve(0);
	ans1=ans;sum=ans=0;
	solve(1);
	cout<<min(ans,ans1);
	return 0;
}