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;
using System.Linq;
using System.Collections.Generic;
class P
{
    static void Main()
    {
        Console.ReadLine();
        int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int res;
        if (a[0] == 0)
        {
            int sum = 1;
            int resa = 0;
            for (int i = 1; i < a.Length; i++)
            {
                int temp = sum + a[i];
                if (temp == 0)
                {
                    resa++;
                    temp = -(sum / Math.Abs(sum));
                }
                if (sum * temp >= 0)
                {
                    resa += Math.Abs(temp) + 1;
                    temp = -(temp / Math.Abs(temp));
                }
                sum = temp;
            }

            sum = -1;
            int resb = 0;
            for (int i = 1; i < a.Length; i++)
            {
                int temp = sum + a[i];
                if (temp == 0)
                {
                    resb++;
                    temp = -(sum / Math.Abs(sum));
                }
                if (sum * temp >= 0)
                {
                    resb += Math.Abs(temp) + 1;
                    temp = -(temp / Math.Abs(temp));
                }
                sum = temp;
            }
            res = Math.Min(resa, resb);
        }
        else
        {
            int sum = a[0];
            res = 0;
            for (int i = 1; i < a.Length; i++)
            {
                int temp = sum + a[i];

                if(temp == 0)
                {
                    res++;
                    temp = -(sum / Math.Abs(sum));
                }
                if(sum * temp >= 0)
                {
                    res += Math.Abs(temp) + 1;
                    temp = -(temp / Math.Abs(temp));
                }
                sum = temp;
            }
        }
        Console.WriteLine(res);
    }
}