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>
using namespace std;
typedef long long ll;
#define REP(i,b,n) for(int i=b;i<(int)n;i++)
#define rep(i,n) REP(i,0,n)

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;cin>>n;
    vector<int> a(n);
    rep(i,n)cin>>a[i];
    ll cnt=0;
    ll tot=a[0];
    if(tot==0){
      tot=1;
      cnt++;
    }
    for(int i=1;i<n;i++){
        ll k=tot+a[i];
        if(k*tot>0){
            if(tot==abs(tot)) tot=-1;
            else tot=1;
            cnt+=abs(k)+1;
        }
        else if(k==0){
            if(tot==abs(tot))tot=-1;
            else tot=1;
            cnt++;
        }
        else tot=k;
    }
    if(a[0]==abs(a[0]))tot=-1;
    else tot=1;
    ll cc=abs(a[0])+1;
    for(int i=1;i<n;i++){
        ll k=tot+a[i];
        if(k*tot>0){
            if(tot==abs(tot)) tot=-1;
            else tot=1;
            cc+=abs(k)+1;
        }
        else if(k==0){
            if(tot==abs(tot))tot=-1;
            else tot=1;
            cc++;
        }
        else tot=k;
    }
    cout<<min(cnt,cc)<<endl;
    return 0;
}