A fractal is a geometrical object with the property that subsections of the object appear identical to (but smaller than) the whole object. Here we consider a specific fractal, which we will approximate by iterating a construction process.

Start with a filled square whose side length is \(1\) . For example:

* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *

Remove a square of side \(\dfrac{1}{3}\) from the middle:

* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *

Note that this figure is equivalent to \(8\) squares of size \(\dfrac{1}{3}\) , as illustrated below. The spaces between squares are for illustration only and do not appear in the fractal.

* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *

* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *
* * * * * * * * *                       * * * * * * * * *

* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *
* * * * * * * * *   * * * * * * * * *   * * * * * * * * *

We can apply this process again to each of the squares. Thus after \(2\) iterations of the construction process, we have:

* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * *       * * * * * *       * * * * * *       * * *
* * *       * * * * * *       * * * * * *       * * *
* * *       * * * * * *       * * * * * *       * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * *       * * *                   * * *       * * *
* * *       * * *                   * * *       * * *
* * *       * * *                   * * *       * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * *       * * * * * *       * * * * * *       * * *
* * *       * * * * * *       * * * * * *       * * *
* * *       * * * * * *       * * * * * *       * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *

Each of the eight squares is now a copy of the first iteration. Each of these contains eight filled squares, for a total of \(64\) . The process is applied to each of these squares. After \(3\) iterations we have:

* * * * * * * * * * * * * * * * * * * * * * * * * * *
*   * *   * *   * *   * *   * *   * *   * *   * *   *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * *       * * * * * *       * * * * * *       * * *
*   *       *   * *   *       *   * *   *       *   *
* * *       * * * * * *       * * * * * *       * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
*   * *   * *   * *   * *   * *   * *   * *   * *   *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * *                   * * * * * * * * *
*   * *   * *   *                   *   * *   * *   *
* * * * * * * * *                   * * * * * * * * *
* * *       * * *                   * * *       * * *
*   *       *   *                   *   *       *   *
* * *       * * *                   * * *       * * *
* * * * * * * * *                   * * * * * * * * *
*   * *   * *   *                   *   * *   * *   *
* * * * * * * * *                   * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
*   * *   * *   * *   * *   * *   * *   * *   * *   *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * *       * * * * * *       * * * * * *       * * *
*   *       *   * *   *       *   * *   *       *   *
* * *       * * * * * *       * * * * * *       * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
*   * *   * *   * *   * *   * *   * *   * *   * *   *
* * * * * * * * * * * * * * * * * * * * * * * * * * *

The actual fractal is what we get when this process is iterated infinitely many times. As one might expect, each of the \(8\) subsections of this fractal is an exact copy of the fractal, scaled by a factor of a third.

Write a program to compute the specified function after \(n\) iterations \((n \le 5)\) . To do this, represent the figure as a \(3^n\) by \(3^n\) grid, with * to indicate filled areas and   to indicate unfilled areas. The figure will be too large to print on a single screen or sheet of paper so the input will specify a small rectangular portion of the figure to be printed.

The next line of input contains a single integer \(c\) , representing the index of the character you wish to locate, starting from index \(0\) .

The following table shows how the available \(15\) marks are distributed:

Output Specification

Output the \(c\) -th character of the long cipher.

Sample Input 1

r2d2
8

Sample Output 1

r

Explanation for Sample Output 1

The output of the RLE algorithm r2d2 corresponds to the pattern rrdd , which creates the infinitely long cipher rrddrrddrrddrrdd... , where the \(c = 8\) th character is r . In this example, the \(c = 8\) th character is highlighted with a box around it.

Sample Input 2

a4b1c2d10
100

Sample Output 2

d

Explanation for Sample Output 2

The output of the RLE algorithm a4b1c2d10 corresponds to the pattern aaaabccdddddddddd . When repeated infinitely, the \(c = 100\) th character is d .