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 static Input;

public class Prog
{
    private const int INF = 1000000007;
    public static void Main()
    {
        int n = NextInt();
        int[] a = LineInt();
        //凸凹の2パターンっぽい
        int costA = 0;
        int costB = 0;
        int now = 0;
        for (int i = 0; i < a.Length; i++)
        {
            if (i % 2 == 0)
            {
                if (now + a[i] > 0)
                {
                    //ok
                    now += a[i];
                }
                else
                {
                    //ng
                    costA += Math.Abs(now + a[i]) + 1;
                    now = 1;
                }
            }
            else
            {
                if (now + a[i] < 0)
                {
                    //ok
                    now += a[i];
                }
                else
                {
                    //ng
                    costA += Math.Abs(now + a[i]) + 1;
                    now = -1;
                }
            }
        }
        now = 0;
        for (int i = 0; i < a.Length; i++)
        {
            if (i % 2 == 1)
            {

                if (now + a[i] > 0)
                {
                    //ok
                    now += a[i];
                }
                else
                {
                    //ng
                    costB += Math.Abs(now + a[i]) + 1;
                    now = 1;
                }
            }
            else
            {
                if (now + a[i] < 0)
                {
                    //ok
                    now += a[i];
                }
                else
                {
                    //ng
                    costB += Math.Abs(now + a[i]) + 1;
                    now = -1;
                }
            }
        }
        Console.WriteLine(Math.Min(costA, costB));
    }
}

public 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(); }
}