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>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb push_back
#define mp make_pair
typedef long long ll;
typedef pair<int,int> pint;

int a[100001];
int main(){
    ll n,ai;
    cin>>n;
    cin>>ai;
    a[0]=ai;
    ll sum,sum1;
    ll ans=0,ans1=0;
    if(ai==0) ans=1,ans1=1,sum=1,sum1=-1;
    else if(ai>0) ans1=ai+1,sum=ai,sum1=-1;
    else ans=ai+1,sum=1,sum1=ai;
    FOR(i,1,n){
        cin>>ai;a[i]=ai;
        if(sum>0){
            if(sum<-ai) sum+=ai;
            else{
                ans+=ai+sum+1;
                sum=-1;
            }
        }
        else{
            if(-sum<ai) sum+=ai;
            else{
                ans+=-sum+1-ai;
                sum=1;
            }
        }
    }
    FOR(i,1,n){
        ai=a[i];
        if(sum1>0){
            if(sum1<-ai) sum1+=ai;
            else{
                ans1+=ai+sum1+1;
                sum1=-1;
            }
        }
        else{
            if(-sum1<ai) sum1+=ai;
            else{
                ans1+=-sum1+1-ai;
                sum1=1;
            }
        }
    }
    cout<<min(ans,ans1)<<endl;
    return 0;
}