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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            long[] a = new long[n];
            string[] lines = Console.ReadLine().Split(' ');
            for (int i = 0; i < n; i++)
            {
                a[i] = long.Parse(lines[i]);
            }

            long ans1 = 0;
            long ans2 = 0;
            int sign = 1;
            long sum = 0;
            for (int i = 0; i < n; i++)
            {
                sum += a[i];
                if (sign > 0)
                {
                    if (sum >= 0)
                    {
                        ans1 += 1 + sum;
                        sum = -1;
                    }
                }
                else
                {
                    if (sum <= 0)
                    {
                        ans1 += 1  -sum;
                        sum = 1;
                    }
                }
                sign *= -1;
            }

            sign = -1;
            sum = 0;
            for (int i = 0; i < n; i++)
            {
                sum += a[i];
                if (sign > 0)
                {
                    if (sum >= 0)
                    {
                        ans2 += 1 + sum;
                        sum = -1;
                    }
                }
                else
                {
                    if (sum <= 0)
                    {
                        ans2 += 1 - sum;
                        sum = 1;
                    }
                }
                sign *= -1;
            }

            Console.WriteLine(Math.Min(ans1, ans2));
        }
    }
}