Description

You are given a $2^n \times 2^n$ grid and $\dfrac{4^n-1}{3}$ "L"-shaped trominoes of size $2 \times 2$, numbered from $1$ to $\dfrac{4^n-1}{3}$ (shape shown below):

*.
**

Construct a placement so that every cell is covered by some tromino except the cell at row $x$ (from top to bottom) and column $y$ (from left to right). Trominoes may be rotated.

Input Format

One line with three integers $n, x, y$.

Output Format

Output $2^n$ lines, each with $2^n$ integers. The number at the $i$-th row and $j$-th column indicates the index of the tromino covering that cell. Specifically, for the cell at row $x$ and column $y$, output $0$.

There may be multiple valid answers; output any one of them.

4 1 3

1 1 0 2 3 3 4 4 5 5 6 6 7 7 8 8
1 9 2 2 3 10 10 4 5 11 11 6 7 12 12 8
13 9 9 14 15 15 10 16 17 11 18 18 19 19 12 20
13 13 14 14 21 15 16 16 17 17 18 22 22 19 20 20
23 23 24 21 21 25 26 26 27 27 28 28 22 29 30 30
23 31 24 24 25 25 32 26 27 33 33 28 29 29 34 30
35 31 31 36 37 32 32 38 39 39 33 40 41 34 34 42
35 35 36 36 37 37 38 38 43 39 40 40 41 41 42 42
44 44 45 45 46 46 47 43 43 48 49 49 50 50 51 51
44 52 52 45 46 53 47 47 48 48 54 49 50 55 55 51
56 52 57 57 58 53 53 59 60 54 54 61 62 62 55 63
56 56 57 64 58 58 59 59 60 60 61 61 65 62 63 63
66 66 67 64 64 68 69 69 70 70 71 65 65 72 73 73
66 74 67 67 68 68 75 69 70 76 71 71 72 72 77 73
78 74 74 79 80 75 75 81 82 76 76 83 84 77 77 85
78 78 79 79 80 80 81 81 82 82 83 83 84 84 85 85

Hint

Constraints: $1 \le n \le 10$, $1 \le x, y \le 2^n$.

Translated by ChatGPT 5