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;

namespace AtCoder
{
    class Program
    {
        static int n;
        static List<int> a;
        
        static void Main(string[] args)
        {
            //[summary]C - Sequence
            n = int.Parse(Console.ReadLine());
            a = ReadLine();

            //偶数のインデックスを1にするケース
            long count1 = CountOperations(0);

            //奇数のインデックスを1にするケース
            long count2 = CountOperations(1);

            if (count1 < count2)
            {
                Console.WriteLine(count1);
            }
            else
            {
                Console.WriteLine(count2);
            }
        }

        static long CountOperations(int mod)
        {
            var b = GetNewNumbers(mod);
            long count = 0;

            for (int i = 0; i < n; i++)
            {
                count += Math.Abs(a[i] - b[i]);
            }

            return count;
        }

        static List<int> GetNewNumbers(int mod)
        {
            var b = new List<int>(a);
            long sum = 0;

            for (int i = 0; i < n; i++)
            {
                if (i % 2 == mod)
                {
                    //i項までの和をプラスに
                    if (sum + b[i] <= 0)
                    {
                        //i項までの和を1にする
                        b[i] += (int)Math.Abs(sum + b[i]) + 1;
                    }
                }
                else
                {
                    //i項までの和をマイナスに
                    if (sum + b[i] >= 0)
                    {
                        //i項までの和を-1にする
                        b[i] -= (int)(Math.Abs(sum + b[i]) + 1);
                    }
                }

                sum += b[i];
            }

            return b;
        }

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

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