Ant on a Chessboard

Background

One day, an ant called Alice came to an M*M chessboard. She wanted to go around all the grids. So she began to walk along the chessboard according to this way: (you can assume that her speed is one grid per second). At the first second, Alice was standing at (1,1). Firstly she went up for a grid, then a grid to the right, a grid downward. After that, she went a grid to the right, then two grids upward, and then two grids to the left…in a word, the path was like a snake.

 For example, her first 25 seconds went like this:

 (the numbers in the grids stands for the time when she went into the grids)

 

25

24

23

22

21

10

11

12

13

20

9

8

7

14

19

2

3

6

15

18

1

4

5

16

17

5

4

3

2

1

 

     

    1            2          3                 5

At the 8th second , she was at (2,3), and at 20th second, she was at (5,4).

Your task is to decide where she was at a given time.

(you can assume that M is large enough)

Input

Input file will contain several lines, and each line contains a number N(1<=N<=2*10^9), which stands for the time. The file will be ended with a line that contains a number 0.

Output

For each input situation you should print a line with two numbers (x, y), the column and the row number, there must be only a space between them.

 

Sample Input

8

20

25

0

 

Sample Output

2 3

5 4

1 5

 

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

 

namespace ConsoleApplication1

{

    class Program

    {

        static void Main(string[] args)

        {

            int count = 0;

            int n = 1000;

            for (int i = 0, j = 0, k = 0; ; k++)

            {

                //Vertically upward move

                for (int p = i; i <= p + 1 ; i++)

                {

                    count++;

                    if (count == n)

                    {

                        Console.WriteLine((j + 1) + " " + (i + 1));

                        goto exit;

                    }

                }

                i–;

                j++;

                //Horizontally right move

                for(; j <= (2*k + 1); j++)

                {

                    count++;

                    if (count == n)

                    {

                        Console.WriteLine((j + 1) + " " + (i + 1));

                        goto exit;

                    }

                }

                j–;

                i–;

                //Vertically downward move

                for (; i >= 0; i–)

                {

                    count++;

                    if (count == n)

                    {

                        Console.WriteLine((j + 1) + " " + (i + 1));

                        goto exit;

                    }

                }

                i++;

                j++;

                //Vertically upward move

                for (int p = 0; p < (2*(k + 1) + 1); p++, i++)

                {

                    count++;

                    if (count == n)

                    {

                        Console.WriteLine((j + 1) + " " + (i + 1));

                        goto exit;

                    }

                }

                i–;

                j–;

                //Horizontally left move

                for (;j > 0 ; j–)

                {

                    count++;

                    if (count == n)

                    {

                        Console.WriteLine((j + 1) + " " + (i + 1));

                        goto exit;

                    }

                }

            }

        exit: ;

        }

    }

}

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