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;

namespace ABC059C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = Int32.Parse(Console.ReadLine());
            string[] bufs = Console.ReadLine().Split(' ');
            long res = 0;
            int sum = Int32.Parse(bufs[0]);
            if (sum == 0) { res++; }

            for (int i = 1; i < n; i++)
            {
                int tmp = sum + Int32.Parse(bufs[i]);

                if (sum == 0)
                {
                    if (tmp == 0)
                    {
                        res += 2;
                    }
                    else if (tmp == 1 || tmp == -1)
                    {
                        sum = tmp;
                        res++;
                    }
                    else if (tmp > 1)
                    {
                        sum = tmp - 1;
                    }
                    else
                    {
                        sum = tmp + 1;
                    }
                }
                else if (sum > 0)
                {
                    if (tmp >= 0)
                    {
                        res += tmp + 1;
                        sum = -1;
                    }
                    else
                    {
                        sum = tmp;
                    }
                }
                else
                {
                    if (tmp <= 0)
                    {
                        res += -tmp + 1;
                        sum = 1;
                    }
                    else
                    {
                        sum = tmp;
                    }
                }

            }

            Console.WriteLine(res);
        }
    }
}