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;
using System.IO;
using System.Text.RegularExpressions;
using System.Diagnostics;

//var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
namespace AtCoderSolve
{
    
    class Solve
    {
        const int mod = 1000000007;
        
        
        static void Main(string[] args)
        {

            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            int N = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(long.Parse).ToArray();

           
            long[] sum = new long[N];
            long[] ans = new long[2];
            long c = 1;
            for (var j = 0; j < 2; j++)
            {
                for (var i = 0; i < N; i++)
                {
                    if (i == 0)
                    {
                        sum[i] = a[i];
                    }
                    else
                    {
                        sum[i] = sum[i - 1] + a[i];
                    }
                    if (sum[i] * c <= 0)
                    {
                        ans[j] += 1 + Math.Abs(sum[i]);
                        sum[i] = c;
                    }
                    c *= -1;
                }
                c *= -1;
            }

            Console.WriteLine(ans.Min());
            

            //Console.Out.Flush();

        }

        
    }

    public class Calculation
    {

    }

    public class Graph
    {
        
    }
}