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

namespace ARX72_C
{
    class Program
    {
        static void Main(string[] args)
        {

            var n = int.Parse(Console.ReadLine());

            var b = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var a = b;
            long sum = a[0] != 0 ? a[0] : 1;
            long tmp = 0;
            long count = a[0] != 0 ? 0 : 1;
            for (int i = 1; i < n; i++)
            {
                if ((sum + a[i]) * sum >= 0 )
                {
                    tmp = -Math.Sign(sum) * (Math.Abs(sum) + 1);
                    count += Math.Abs(tmp - a[i]);
                    a[i] = tmp;
                }
                sum += a[i];
            }

            long count1 = count;
            a = b;
            sum = -Math.Sign(a[0]);
            tmp = 0;
            count = Math.Abs(a[0]- sum);
            for (int i = 1; i < n; i++)
            {
                if ((sum + a[i]) * sum >= 0)
                {
                    tmp = -Math.Sign(sum) * (Math.Abs(sum) + 1);
                    count += Math.Abs(tmp - a[i]);
                    a[i] = tmp;
                }
                sum += a[i];
            }

            
            Console.WriteLine(count1 >= count ? count : count1);
        }
    }
}