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 <iostream>
#include <algorithm>
using namespace std;

int main(){
  bool ch = false;//falseの時は和が一個前で負
  long long N,i;
  long long ans=0,count=0;
  cin >> N;
  long long a[N];
  cin >> a[0];
  ans+=a[0];
  if(ans>0)ch = true;
  else ch = false;
  if(ans == 0){
    count+=1;
    ans = -1;
  }
  for(i=1;i<N;i++){
    cin >> a[i];
    if(ch/*ans > 0*/){
      if(ans>=-a[i]){
        count += ans+a[i]+1;
        ans = -1;
      }
      else ans += a[i];
      ch = false;
    }else /*if(ans < 0)*/{
      if(ans<=-a[i]){
        count += -ans-a[i]+1;
        ans = 1;
      }
      else ans += a[i];
      ch = true;
    }
    //else if(ans == 0)ans=a;
    //cout << ans << " " << count << endl;
  }
  long long con=0;
  if(a[0]>0){
    ans = -1;
    ch = false;
  }
  else {
    ans = 1;
    ch = true;
  }
  con = a[0]+1;
  for(i=1;i<N;i++){
    if(ch/*ans > 0*/){
      if(ans>=-a[i]){
        con += ans+a[i]+1;
        ans = -1;
      }
      else ans += a[i];
      ch = false;
    }else /*if(ans < 0)*/{
      if(ans<=-a[i]){
        con += -ans-a[i]+1;
        ans = 1;
      }
      else ans += a[i];
      ch = true;
    }
    //else if(ans == 0)ans=a;
    //cout << ans << " " << count << endl;
  }
  cout << min(count,con) << endl;
  return 0;
}