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 <array>
#include <vector>
#include <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
using namespace std;

typedef  pair<int,int> P;
typedef long long LL;

const LL INF=10000000000;
const LL MOD=1000000007;

LL gcd(LL a,LL b){
    if(b==0)return a;

    return gcd(b,a%b);
}

int main(){
    int n;
    cin>>n;
    LL a[100100];
    for(int i=0;i<n;++i){
        cin>>a[i];
    }
    LL ans=INF;
       for(int i=0;i<2;++i){
        LL count=0;
        LL su=0;
            for(int j=0;j<n;++j){
                su+=a[j];
                    if(i==0) {
                        if(j%2==0&&su<=0){
                            count+=-su+1;
                            su=1;
                        }
                        else if(j%2==1&&su>=0){
                            count+=su+1;
                            su=-1;
                        }
                    }else{
                        if(j%2==0&&su>=0){
                            count+=su+1;
                            su=-1;
                        }
                        else if(j%2==1&&su<=0){
                            count+=-su+1;
                            su=1;
                        }
                    }
                
        }
    ans=min(ans,count);
        
    }
     cout<<ans<<endl;
}