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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rep2(i,s,n) for(int i = (s); i < (n); ++i)
#define ll long long
#define ld long double
#define P pair<ll,ll>
#define all(v) v.begin(),v.end()

const ll mod = 1e9+7;
const ll INF = 1e18;
const double pi = acos(-1.0);

int main(void)
{
    ll n; cin>>n;
    vector<ll> a(n);
    rep(i,n) cin>>a[i];
    
    ll ans,sum=0,res1=0,res2=0;

    rep(sign,2){
        rep(i,n){
            sum+=a[i];
            if((i%2^sign) && sum>=0){
                res1+=sum+1;
                sum=-1;
            }
            else if(!(i%2^sign) && sum<=0){
                res2+=abs(sum-1);
                sum=1;
            }
        }
    }
    ans=min(res1,res2);
    cout<<ans<<endl;
    return 0;
}