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: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long ll;

int main(){
	ll n,sum=0,tmp=0,c=0;
	bool chg=false;
	cin>>n;
	vector<ll>a(n);
	vector<ll>b(n);
	for(int i=0;i<n;i++){
		cin>>a[i];
		sum+=a[i];
		b[i]=sum;
	}
	if(b[0]>0){
		for(int i=0;i<n;i++){
			b[i]+=tmp;
			if(i%2==0 && b[i]<=0){
				tmp=abs(b[i])+1;
				chg=true;
			}
			if(i%2==1 && b[i]>=0){
				tmp=-(abs(b[i])+1);
				chg=true;
			}
			if(chg) c+=abs(tmp);
			chg=false;
		}
	}else if(b[0]<0){
		for(int i=0;i<n;i++){
			b[i]+=tmp;
			if(i%2==0 && b[i]>=0){
				tmp=-(abs(b[i])+1);
				chg=true;
			}
			if(i%2==1 && b[i]<=0){
				tmp=abs(b[i])+1;
				chg=true;
			}
			if(chg) c+=abs(tmp);
			chg=false;
		}
	}
	cout<<c;
}