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 <bits/stdc++.h>
#define REP(i,n,N) for(int i=(n);i<(int)N;i++)
#define p(s) cout<<(s)<<endl
#define ck(n,a,b) (a)<=(n)&&(n)<(b)
typedef long long ll;
using namespace std;
const int inf=1e9;

int main(){
	int n;
	cin>>n;
	int a[100010];
	REP(i,0,n){
		cin>>a[i];
	}
	ll ans=0;
	ll sum=a[0];
	REP(i,1,n){
		ll tmp;
		tmp=sum;
		sum+=a[i];
		if(sum>=0&&tmp>0){
			if(sum<tmp){
				ans+=sum+1;
				sum=-1;
			}else{
				ans+=tmp+1;
				sum=a[i]-1;
			}
		}else if(sum<=0&&tmp<0){
			if(sum>tmp){
				ans+=-sum+1;
				sum=1;
			}else{
				ans+=-tmp+1;
				sum=a[i]+1;
			}
		}
	}
	p(ans);
	return 0;
}