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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC59C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string[] str = Console.ReadLine().Split(' ');
            int[] a = new int[n];
            for(int i = 0; i < n; i++)
            {
                a[i] = int.Parse(str[i]);
            }
            long x = 0;
            long y = 0;
            int f = 0;
            int sum = 0; 
            for(int i = 0; i < n; i++)
            {
                sum += a[i];
                if (f == 1 && sum >= 0)
                {
                    x += (sum + 1);
                    f = 0;
                    sum = -1;
                }else if (f == 0 && sum <= 0)
                {
                    x += (1 - sum);
                    f = 1;
                    sum = 1;
                }else
                {
                    f = 1 - f;
                }
            }
            sum = 0;
            f = 1;
            for (int i = 0; i < n; i++)
            {
                sum += a[i];
                if (f == 1 && sum >= 0)
                {
                    y += (sum + 1);
                    f = 0;
                    sum = -1;
                }
                else if (f == 0 && sum <= 0)
                {
                    y += (1 - sum);
                    f = 1;
                    sum = 1;
                }
                else
                {
                    f = 1 - f;
                }
            }
            x = Math.Min(x, y);
            Console.WriteLine(x);
        }
    }
}