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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;

class Program {
  static void Main(string[] args) {
    int n = int.Parse(Console.ReadLine());
    string[] A = Console.ReadLine().Split();
    long ans = 1 << 60;
    int sum, sign, count, a;

    for (int cnt = 0; cnt < 2; ++cnt) {
      a = int.Parse(A[0]);
      sign = Math.Sign(a);
      if (cnt == 0) {
        sum = a;
        count = 0;
      }
      else {
        sign *= -1;
        sum = sign;
        count = Math.Abs(a) + 1;
      }
      for (int i = 1; i < n; ++i) {
        a = int.Parse(A[i]);
        sign *= -1;
        if (sign * Math.Sign(a + sum) > 0) {
          sum += a;
        }
        else {
          count += Math.Abs((Math.Abs(sum) + 1) * sign - a);
          sum = sign;
        }
      }
      ans = Math.Min(ans, count);
    }    

    Console.WriteLine(ans);
  }
}