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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int calc(vector<int>& t, bool topPlus) {
  int parityA, parityB;
  if (topPlus) {
    parityA = 0;
    parityB = 1;
  }
  else {
    parityA = 1;
    parityB = 0;
  }
  
  int sum = 0;
  int cnt = 0;
  for (int i = 0; i < t.size(); ++i) {
    sum += t.at(i);
    if (i % 2 == parityA && sum <= 0) {
      cnt += (1 - sum);
      sum = 1;
    }
    else if (i % 2 == parityB && sum >= 0) {
      cnt += (1 + sum);
      sum = -1;
    }
//cout << "*" << t.at(i) << " " << cnt << " " << sum << endl;
  }
  return cnt;
}
  

int main() {
  int N;
  cin >> N;
  
  vector<int> t(N);
  for (int i = 0; i < N; ++i) {
    cin >> t.at(i);
//cout << "-" << t.at(i) << endl;
  }
  int cnt1 = calc(t, true);
//cout << endl;
  int cnt2 = calc(t, false);
//cout << "[" << cnt1 << " " << cnt2 << endl;  
  int cnt = min(cnt1, cnt2);
  
  cout << cnt << endl;
}