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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public class Program
{
    #region Standard I/O
    readonly TextReader input;
    readonly TextWriter output;

    X[] ReadLine<X>(Func<string, X> func)
    {
        return input.ReadLine().Split(' ').Select(func).ToArray();
    }

    void WriteLineOne(object obj)
    {
        output.WriteLine("{0}", obj);
    }

    void WriteLineMany(params object[] objects)
    {
        output.WriteLine(string.Join(" ", objects.Select(obj => obj.ToString())));
    }
    #endregion

    int n;
    long[] xs;

    void Read()
    {
        n = ReadLine(int.Parse)[0];
        xs = ReadLine(long.Parse);
    }

    long Solve(long[] xs)
    {
        var count = 0L;
        var s = xs[0];

        for (var i = 1; i < xs.Length; i++)
        {
            var t = s + xs[i];

            if (Math.Sign(t) == 0)
            {
                var d = s > 0 ? 1 : -1;
                t -= d;
                count += 1;
            }
            else if (Math.Sign(s) == Math.Sign(t))
            {
                var d = t + (t > 0 ? 1 : -1);
                t -= d;
                count += Math.Abs(d);
            }

            s = t;
        }

        return count;
    }

    long Calc()
    {
        if (xs[0] == 0)
        {
            var ys = xs.ToArray();
            xs[0] = 1;
            ys[0] = -1;
            return Math.Min(Solve(xs), Solve(ys)) + 1;
        }
        else
        {
            var ys = xs.ToArray();
            var d = ys[0] + (ys[0] > 0 ? 1 : -1);
            ys[0] -= d;

            return Math.Min(Solve(xs), Solve(ys) + Math.Abs(d));
        }
    }

    public void Run()
    {
        Read();
        WriteLineOne(Calc());
    }

    public Program(TextReader input, TextWriter output)
    {
        this.input = input;
        this.output = output;
    }

    public static void Main(string[] args)
    {
        new Program(Console.In, Console.Out).Run();
    }
}