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.Text;
using System.Linq;

class Program
{
    public void Proc()
    {
        Reader.IsDebug = false;
        int inptCount = int.Parse(Reader.ReadLine());

        this.items = Reader.ReadLine().Split(' ').Select(a=>long.Parse(a)).ToArray();
        long ans = 0;
        if (items[0] == 0)
        {
            ans = GetAns(1, 1) + 1;
            ans = Math.Min(ans, GetAns(1, -1) + 1);
        }
        else 
        {
            ans = GetAns(1, items[0]);
            if (items[0] > 0)
            {
                ans = Math.Min(ans, GetAns(1, -1) + items[0] + 1);
            }
            else
            {
                ans = Math.Min(ans, GetAns(1, 1) + Math.Abs(items[0]) + 1);
            }
        }
        Console.WriteLine(ans);
    }

    private long GetAns(int idx, long subtotal)
    {
        if (idx >= items.Length)
        {
            return 0;
        }
        if (subtotal < 0 && subtotal + items[idx] > 0)
        {
            return GetAns(idx + 1, subtotal + items[idx]);
        }
        else if (subtotal > 0 && subtotal + items[idx] < 0)
        {
            return GetAns(idx + 1, subtotal + items[idx]);
        }
        else if(subtotal > 0)
        {
            return GetAns(idx + 1, -1) + (subtotal + items[idx] + 1);
        }
        else
        {
            return GetAns(idx + 1, 1) + Math.Abs(subtotal + items[idx]) + 1;
        }

    }

    private long[] items;


    public class Reader
    {
        public static bool IsDebug = true;
        private static String PlainInput = @"



6
-1 4 3 2 -5 4


";
        private static System.IO.StringReader Sr = null;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (Sr == null)
                {
                    Sr = new System.IO.StringReader(PlainInput.Trim());
                }
                return Sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
    }
    static void Main()
    {
        Program prg = new Program();
        prg.Proc();
    }
}