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: Time Limit Exceeded)

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

typedef long long ll; 

int main()
{ 
    int n,ansa=0,ansb=0,suma=0,sumb=0;
    cin>>n;
    bool plus=true;
    
    rep(i,n){
      
      int a,b;
      cin>>b;
      a=b;
      
      while(plus&&suma+a<=0){
        a++;
        ansa++;
        }
      while(!plus&&suma+a>=0){
        a--;
        ansa++;
        }
        
      while(plus&&sumb+b>=0){
        b--;
        ansb++;
        }
      while(!plus&&sumb+b<=0){
        b++;
        ansb++;
        }
        
      suma+=a;
      sumb+=b;
      plus=!plus;
      }
      
    cout<<min(ansa,ansb)<<endl;
return 0;
}