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()
    {
        int n = int.Parse(Console.ReadLine());
        var inp = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        long ans = 0;
        long cumsum = inp[0];
        for (int i = 1; i < n; i++)
        {
            if (Math.Abs(inp[i]) <= Math.Abs(cumsum))
            {
                long temp = Math.Abs(cumsum) - Math.Abs(inp[i]) + 1;
                if (inp[i] * cumsum > 0)
                {
                    ans += temp + Math.Abs(cumsum);
                    inp[i] += inp[i] > 0 ? -(temp + cumsum) : temp + cumsum;
                }
                else
                {
                    ans += temp;
                    inp[i] += inp[i] > 0 ? temp : -temp;
                }
            }
            else if (inp[i] * cumsum > 0)
            {
                ans += Math.Abs(cumsum) + 1;
                inp[i] += inp[i] > 0 ? -inp[i] - Math.Abs(cumsum) - 1 : inp[i] + Math.Abs(cumsum) + 1;
            }
            cumsum += inp[i];
        }
        Console.WriteLine(ans);
    }
}