Score : $200$ points

问题描述

在 $N$ 行水平排列和 $N$ 列垂直排列中放置瓷砖。每个瓷砖上有 $A$ 行水平格子和 $B$ 列垂直格子。总体来说，这些瓷砖形成了一个网格 $X$，具有 $(A\times N)$ 行水平格子和 $(B\times N)$ 列垂直格子。

对于 $1\leq i,j \leq N$，第 $(i,j)$ 个瓷砖表示从上到下第 $i$ 行、从左到右第 $j$ 列的瓷砖。

$X$ 中的每个小方格按照以下方式涂色：

• 每个瓷砖要么是 白色瓷砖 要么是 黑色瓷砖。
• 白色瓷砖中的所有小方格都涂成白色；黑色瓷砖中的所有小方格都涂成黑色。
• 第一个瓷砖 $(1,1)$ 是白色瓷砖。
• 共享边界的两个瓷砖颜色不同。这里，我们称瓷砖 $(a,b)$ 和瓷砖 $(c,d)$ 共享边界，当且仅当 $|a-c|+|b-d|=1$（其中 $|x|$ 表示 $x$ 的绝对值）。

请按照输出部分指定的格式打印网格 $X$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Tiles are aligned in $N$ horizontal rows and $N$ vertical columns. Each tile has a grid with $A$ horizontal rows and $B$ vertical columns. On the whole, the tiles form a grid $X$ with $(A\times N)$ horizontal rows and $(B\times N)$ vertical columns.
For $1\leq i,j \leq N$, Tile $(i,j)$ denotes the tile at the $i$-th row from the top and the $j$-th column from the left.

Each square of $X$ is painted as follows.

• Each tile is either a white tile or a black tile.
• Every square in a white tile is painted white; every square in a black tile is painted black.
• Tile $(1,1)$ is a white tile.
• Two tiles sharing a side have different colors. Here, Tile $(a,b)$ and Tile $(c,d)$ are said to be sharing a side if and only if $|a-c|+|b-d|=1$ (where $|x|$ denotes the absolute value of $x$).

Print the grid $X$ in the format specified in the Output section.

Constraints

• $1 \leq N,A,B \leq 10$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $A$ $B$

Output

Print $(A\times N)$ strings $S_1,\ldots,S_{A\times N}$ that satisfy the following condition, with newlines in between.

• Each of $S_1,\ldots,S_{A\times N}$ is a string of length $(B\times N)$ consisting of . and #.
• For each $i$ and $j$ $(1 \leq i \leq A\times N,1 \leq j \leq B\times N)$, the $j$-th character of $S_i$ is . if the square at the $i$-th row from the top and $j$-th column from the left in grid $X$ is painted white; the character is # if the square is painted black.

Sample Input 1

4 3 2

Sample Output 1

..##..##
..##..##
..##..##
##..##..
##..##..
##..##..
..##..##
..##..##
..##..##
##..##..
##..##..
##..##..

Sample Input 2

5 1 5

Sample Output 2

.....#####.....#####.....
#####.....#####.....#####
.....#####.....#####.....
#####.....#####.....#####
.....#####.....#####.....

Sample Input 3

4 4 1

Sample Output 3

.#.#
.#.#
.#.#
.#.#
#.#.
#.#.
#.#.
#.#.
.#.#
.#.#
.#.#
.#.#
#.#.
#.#.
#.#.
#.#.

Sample Input 4

1 4 4

Sample Output 4

....
....
....
....

update @ 2024/3/10 10:40:48