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;

class Program
{
    static IO io = new IO();

    static void Main(string[] args)
    {
        //入力
        io.Read();
        int n = io.Int();
        io.ReadSplit();
        int[] a = io.Int(n);

        //計算
        int sum = 0;
        int sign = 0;
        int operations = 0;
        for (int i = 0; i < n; ++i)
        {
            sum += a[i];
            if (sum == 0)
            {
                if (sign > 0)
                {
                    operations += 1;
                    sum -= 1;
                    sign = -1;
                }
                else if (sign < 0)
                {
                    operations += 1;
                    sum += 1;
                    sign = 1;
                }
                else
                {
                    int sum2 = 0;
                    for (int j = 0; j < n; ++j)
                    {
                        sum2 += a[j];
                        if (sum2 != 0)
                        {
                            if (j % 2 == 0)
                            {
                                operations += 1;
                                sum += 1;
                                sign = 1;
                            }
                            else
                            {
                                operations += 1;
                                sum -= 1;
                                sign = -1;
                            }
                            break;
                        }
                    }
                }
            }
            else if (sum * sign == 0)
            {
                sign = sum / Math.Abs(sum);
            }
            else if (sum * sign < 0)
            {
                sign *= -1;
            }
            else
            {
                operations += Math.Abs(-sum - sign);
                sum += (-sum - sign);
                sign *= -1;
            }
        }

        //出力
        io.WriteLine(operations.ToString());

    }
}

class IO
{
    private string[] _Inputs;
    private int _Index;
    public void Read()
    {
        _Inputs = new string[1];
        _Inputs[0] = Console.ReadLine();
        _Index = 0;
    }
    public void ReadSplit()
    {
        _Inputs = Console.ReadLine().Split(' ');
        _Index = 0;
    }
    public string String()
    {
        return _Inputs[_Index++];
    }
    public string[] String(int xCount)
    {
        string[] rv = new string[xCount];
        Array.Copy(_Inputs, _Index, rv, 0, xCount);
        _Index += xCount;
        return rv;
    }
    public int Int()
    {
        return int.Parse(_Inputs[_Index++]);
    }
    public int[] Int(int xCount)
    {
        int[] rv = new int[xCount];
        for (int i = 0; i < xCount; ++i)
        {
            rv[i] = int.Parse(_Inputs[_Index++]);
        }
        return rv;
    }
    public long Long()
    {
        return long.Parse(_Inputs[_Index++]);
    }
    public long[] Long(int xCount)
    {
        long[] rv = new long[xCount];
        for (int i = 0; i < xCount; ++i)
        {
            rv[i] = long.Parse(_Inputs[_Index++]);
        }
        return rv;
    }
    public void Write(string xStr)
    {
        Console.Write(xStr);
    }
    public void WriteLine(string xStr)
    {
        Console.WriteLine(xStr);
    }
}