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;
using System.Collections;

class Program
{
    #region Lib

    static int Gcd(int a, int b)
    {
        if (a % b == 0)
            return b;
        else
            return Gcd(b, a % b);
    }

    #endregion

    static void Main()
    {
        ReadInts();
        var nums = ReadInts();

        var e = nums.AsEnumerable<int>().GetEnumerator();

        var zeroCount = 0;
        var f = false;
        while ((f = e.MoveNext()) && e.Current == 0)
            zeroCount++;

        var sum = 0;
        var count = 0;

        if (zeroCount != 0)
        {
            count = zeroCount * 2 - 1;

        }
        while (f)
        {
            var c = e.Current;

            var ps = Math.Sign(sum);

            var ns = Math.Sign(sum + c);

            if (ps == 0)
                ps = -ns;

            if (ns == 0)
            {
                sum = -ps;
                count++;
            }
            else if (ps == ns)
            {
                count += Math.Abs(sum + c) + 1;
                sum = -ps;
            }
            else
            {
                sum += c;
            }
            f = e.MoveNext();
        }

        Console.WriteLine(count);

    }

    #region Utils
    public static int[] ReadInts()
    {
        return Console.ReadLine().Split().Select(int.Parse).ToArray();
    }
    #endregion



}