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.Diagnostics;
using System.Linq;
using System.Text;

class Program
{
    static int n;
    static long[] a;

    public static void Main(string[] args)
    {
        n = Input.NextInt();
        a = Input.LineLong();

        long minmove = Calc(a);
        for (int i = 0; i < a.Length; i++)
        {
            a[i] = -a[i];
        }
        minmove = Math.Min(minmove, Calc(a));

        Console.WriteLine(minmove);
    }

    private static long Calc(long[] a)
    {
        checked
        {
            long curr = 0;
            long move = 0;
            for (long i = 0; i < a.Length; i++)
            {
                long dif = 0;
                switch (i % 2)
                {
                    case 0:
                        {
                            var newc = curr + a[i];
                            dif = newc <= 0 ? 1 - newc : 0;
                        }
                        break;
                    case 1:
                        {
                            var newc = curr + a[i];
                            dif = newc >= 0 ? -1 - newc : 0;
                        }
                        break;
                }
                curr += a[i] + dif;
                move += Math.Abs(dif);
            }

            return move;
        }
    }
}

public static class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}