Panda puzzle

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Consider the puzzle to the right. We only have the sixteen $2 \times 2$ pieces shown, which we can place and rotate as we wish, as long as the board gets totally covered. There is just one restriction: Adjacent pieces must share the colors at the edges (white with white, black with black).

The puzzle has more than 40 thousand solutions. To order them, we construct a word from every solution, and we sort the words alphabetically. Suppose that we visit a solution by rows, from top to bottom, and each row from left to right. If we write an ‘a’ for every white square, and a ‘b’ for every black square, we get a word with 64 chars. For the solution in the image, the word is

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“baabbbbabbbaabbabbbaabbabbbbbaaabbbbbaaabaaaaaaabaaaaaaabaabbbba”.

Input

Input consists of several natural numbers $i$ , each one between 1 and 43616.

Output

For every $i$ , print the $i$ -th solution to the puzzle. Use ‘.’ for white squares and ‘X’ for black squares. Print a line with 10 dashes at the end of each solution.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:24:13.126Z