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.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Code3
    {
        static void Main(string[] args)
        {
            string s1 = Console.ReadLine();
            string s2 = Console.ReadLine();

            Console.WriteLine(funcMain(s1,s2));
        }


        static private string funcMain(string arg1, string arg2)
        {
            long cnt = 0;
            long ret = 0;
            long ret1 = 0;
            long ret2 = 0;
            long sum = 0;
            short sign = 0;

            for (int i = 0; i <= 1; i++) // 0はそのまま、1は逆符号
            {
                cnt = sum = ret = 0;
                foreach (string buf in arg2.Split())
                {
                    cnt++;
                    if (cnt > long.Parse(arg1)) break;
                    if (sum == 0)
                    { 
                        sum = long.Parse(buf);
                        if (sum >= 0)
                            sign = 1;
                        else
                            sign = -1;

                        if (i == 1)
                        {
                            ret += Math.Abs(sum) + 1;
                            sum = sign * -1;
                            sign *= -1;
                        }
                    }
                    else
                    {
                        sum += long.Parse(buf);
                        if ((sum * sign) >= 0)
                        {
                            ret += Math.Abs(sum) + 1;
                            sum = sign * -1;
                        }
                        sign *= -1;
                    }
                }
                if (i == 0)
                    ret1 = ret;
                else
                    ret2 = ret;
            }

            ret = Math.Min(ret1, ret2);

            return ret.ToString();
        }

        static private void test()
        {
            string arg1, arg2;
            arg1 = "4";
            arg2 = "1 -3 1 0";
            Console.WriteLine("4" == funcMain(arg1, arg2));
            arg1 = "5";
            arg2 = "3 -6 4 -5 7";
            Console.WriteLine("0" == funcMain(arg1, arg2));
            arg1 = "6";
            arg2 = "-1 4 3 2 -5 4";
            Console.WriteLine("8" == funcMain(arg1, arg2));
            arg1 = "6";
            arg2 = "-1 -2 -3 -4 -5 -6";
            Console.WriteLine("16" == funcMain(arg1, arg2));
            arg1 = "3";
            arg2 = "1 10 -100";
            Console.WriteLine("2" == funcMain(arg1, arg2));
            Console.ReadKey();
        }
    }
}