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;

public class Program
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var xs = Console.ReadLine().Split()
            .Select(x => long.Parse(x))
            .ToArray();

        var sum = new long[2];
        var sign = new[] { Math.Sign(1), Math.Sign(-1) };
        var adjust = new[] { xs[0] == 0 ? 1 : 0, Math.Abs(xs[0]) + 1 };
        for (int i = 0; i < n; ++i)
        {
            for (int j = 0; j < 2; ++j)
            {
                var t = sum[j] + xs[i];
                var k = t * sign[j];
                if (k >= 0)
                {
                    adjust[j] += k + 1;
                    sum[j] = -1 * sign[j];
                }
                else
                {
                    sum[j] = t;
                }
                sign[j] = Math.Sign(sum[j]);
            }
        }
        
        Console.WriteLine(adjust.Min());
    }
}