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;
int main(){
  long long n,a[100000];
  cin>>n>>a[0];
  for(int i=1;i<n;i++){
    cin>>a[i],a[i]+=a[i-1];
  }
  long long ans=0,s=0,t[100000],rans=1e18;
  for(int i=0;i<n;i++)t[i]=a[i];
  for(int k=0;k<2;k++){
    ans=0;
    for(int i=0;i<n;i++)a[i]=t[i];
    if(a[0]==0){
      if(k)a[0]--;
      else a[0]++;
      ans++;
    }
    for(int i=1;i<n;i++){
      if(a[i-1]<0&&a[i]+s<=0){
	ans+=1-(a[i]+s),s+=1-(a[i]+s),a[i]=1;
      }
      else if(a[i-1]>0&&a[i]+s>=0)
	ans+=(a[i]+s)+1,s+=-(a[i]+s)-1,a[i]=-1;
    }
    rans=min(rans,ans);
  }
  cout<<rans<<endl;
  return 0;
}