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: Accepted)

#include<bits/stdc++.h>
#define REP(i,n) for(int i=0,i##_len=(n);i<i##_len;++i)
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
using namespace std;

signed main(){
    int N;cin>>N;
    vector<long long> A(N);
    REP(i, N) cin >> A[i];
    long long ans=LLONG_MAX;
    int sig[2]={1,-1};
    REP(j,2){ 
        long long sum=0;
        long long count=0;
        REP(i,N){
            sum+=A[i];
            if(i%2==0&&sig[j]*sum<=0){
                count+=llabs(sum)+1;
                sum=sig[j]*1;
            }
            if(i%2==1&&sig[j]*sum>=0){
                count+=llabs(sum)+1;
                sum=-1*sig[j];
            }
        }
        ans=min(ans,count);
    }
    cout<<ans<<endl;
}