Score : $400$ points

问题陈述

你有一个 $N$ 行 $N$ 列的网格，其中 $N$ 是一个偶数。用 $(i, j)$ 表示从顶部数第 $i$ 行和从左边数第 $j$ 列的单元格。

每个单元格被涂成黑色或白色。如果 $A_{i, j} =$ #，单元格 $(i, j)$ 是黑色的；如果 $A_{i, j} =$ .，它是白色的。

在按照 $i = 1, 2, \ldots, \frac{N}{2}$ 的顺序执行以下操作后，找出每个单元格的颜色。

• 对于所有在 $i$ 和 $N + 1 - i$ 之间的整数对 $x, y$（包括 $i$ 和 $N + 1 - i$），将单元格 $(y, N + 1 - x)$ 的颜色替换为单元格 $(x, y)$ 的颜色。对于所有这样的整数对 $x, y$，同时执行这些替换。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given a grid with $N$ rows and $N$ columns, where $N$ is an even number. Let $(i, j)$ denote the cell at the $i$-th row from the top and $j$-th column from the left.

Each cell is painted black or white. If $A_{i, j} =$ #, cell $(i, j)$ is black; if $A_{i, j} =$ ., it is white.

Find the color of each cell after performing the following operation for $i = 1, 2, \ldots, \frac{N}{2}$ in this order.

• For all pairs of integers $x, y$ between $i$ and $N + 1 - i$, inclusive, replace the color of cell $(y, N + 1 - x)$ with the color of cell $(x, y)$. Perform these replacements simultaneously for all such pairs $x, y$.

Constraints

• $N$ is an even number between $2$ and $3000$, inclusive.
• Each $A_{i, j}$ is # or ..

Input

The input is given from Standard Input in the following format:

$N$

$A_{1,1}A_{1,2}\ldots A_{1,N}$

$A_{2,1}A_{2,2}\ldots A_{2,N}$

$\vdots$

$A_{N,1}A_{N,2}\ldots A_{N,N}$

Output

After all operations, let $B_{i, j} =$ # if cell $(i, j)$ is black, and $B_{i, j} =$ . if it is white. Print the grid in the following format:

$B_{1,1}B_{1,2}\ldots B_{1,N}$

$B_{2,1}B_{2,2}\ldots B_{2,N}$

$\vdots$

$B_{N,1}B_{N,2}\ldots B_{N,N}$

Sample Input 1

8
.......#
.......#
.####..#
.####..#
.##....#
.##....#
.#######
.#######

Sample Output 1

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

The operations change the colors of the grid cells as follows:

.......#   ........   ........   ........   ........
.......#   ######..   #######.   #######.   #######.
.####..#   ######..   #....##.   #.....#.   #.....#.
.####..# → ##..##.. → #....##. → #.##..#. → #.###.#.
.##....#   ##..##..   #..####.   #.##..#.   #.#...#.
.##....#   ##......   #..####.   #.#####.   #.#####.
.#######   ##......   #.......   #.......   #.......
.#######   ########   ########   ########   ########

Sample Input 2

6
.#.#.#
##.#..
...###
###...
..#.##
#.#.#.

Sample Output 2

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

Sample Input 3

12
.......#.###
#...#...#..#
###.#..#####
..#.#.#.#...
.#.....#.###
.......#.#..
#...#..#....
#####.......
...#...#.#.#
..###..#..##
#..#.#.#.#.#
.####.......

Sample Output 3

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