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;
using llong = long long;

void fnInput(vector<int>& rvnNum)
{
  int nSize;
  cin >> nSize;
  rvnNum.resize(nSize);

  for (int& rnElm : rvnNum)
    cin >> rnElm;
}

llong fnSignChgTimes(const vector<int>& cnrvnNum)
{ 
  vector<llong> vnTimes(2);

  for (int nParity = 0; nParity < vnTimes.size(); nParity++)
  {
    llong nTimes = 0;
    llong nSum   = 0;
    for (int n = 0; n < cnrvnNum.size(); n++)
    {
      nSum += cnrvnNum[n];
      if (n % 2 == nParity)
        if (nSum > 0);
        else
        {
          nTimes += 1 - nSum;
          nSum = 1;
        }
      else
        if (nSum >= 0)
        {
          nTimes += 1 + nSum;
          nSum = -1;
        }
        else;
    }
    vnTimes[nParity] = nTimes;
  }
  auto itElm = min_element(begin(vnTimes), end(vnTimes));
  return *itElm;
}

int main()
{
  vector<int> vnNum;

  fnInput(vnNum);
  cout << fnSignChgTimes(vnNum) << endl;

  return 0;
}