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;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> P;
map <int,int> mp;
vector<int> V;
list<int> L;
stack<int> S;
queue<int> Q;
deque<int> dq;
#define INF (1<<30)
#define INFLL (1ll<<60)
#define EPS (1e-10)
static const int MAX=1e5;
static const int NMAX=50;
static const int MMAX=50;
int N;
ll a,cunt,sum;
int main(){
    cin.tie(0);  ios::sync_with_stdio(false);
    cin>>N;
    cin>>a;
    sum+=a;
    for(int i=1;i<N;i++){
        cin>>a;
        if(sum*a>=0){//符号同じ
            cunt+=sum+a+1;
            sum=(sum>0?-1:1);
        }else if(sum*a<0&&abs(sum)>=abs(a)){//符号異なる
            cunt+=abs(sum)-abs(a)+1;
            sum=(-1)*(sum+1);
        }else sum+=a; //操作必要なし
    }
    cout<<cunt<<"\n";
    
    
    return 0;
}