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;

namespace AtCoder
{
    class Program
    {
        static int n;

        static void Main(string[] args)
        {
            //[summary]C - Green Bin
            n = int.Parse(Console.ReadLine());
            var a = ReadLine();
            long count = 0;

            if (a[0] == 0)
            {
                var a1 = new List<int>(a);
                a1[0] = 1;
                long count1 = CountOperactions(a1);

                var a2 = new List<int>(a);
                a2[0] = -1;
                long count2 = CountOperactions(a2);

                if (count1 < count2)
                {
                    count = count1 + 1;
                }
                else
                {
                    count = count2 + 1;
                }
            }
            else
            {
                count = CountOperactions(a);
            }

            Console.WriteLine(count);
        }

        static long CountOperactions(List<int> a)
        {
            long sum = a[0];
            long next = 0;
            long count = 0;

            for (int i = 1; i < n; i++)
            {
                next = sum + a[i];

                if ((sum > 0 && next < 0) | (sum < 0 && next > 0))
                {
                    //何もしない
                }
                else if (sum > 0)
                {
                    count += 1 + Math.Abs(next);
                    next = -1;
                }
                else
                {
                    count += 1 + Math.Abs(next);
                    next = 1;
                }

                sum = next;
            }

            return count;
        }

        static List<int> ReadLine()
        {
            var line = Console.ReadLine();
            var array = line.Split(' ');

            return array.Select(x => int.Parse(x)).ToList();
        }
    }
}