Score : $600$ points

问题描述

存在一个 $N \times N$ 的网格，其中某些格子上放置有方块。

该网格由 $N$ 个字符串 $S_1,S_2,\dots,S_N$ 描述，如下所示：

• 如果 $S_i$ 的第 $j$ 个字符是 #，则在从顶部数第 $i$ 行、从左边数第 $j$ 列的格子上有一个方块。
• 如果 $S_i$ 的第 $j$ 个字符是 ., 则在从顶部数第 $i$ 行、从左边数第 $j$ 列的格子上没有方块。

Takahashi 可以执行以下操作零次或多次：

• 首先，选择一个整数 $D$，其取值范围在 $1$ 到 $N$（包含）之间，并在网格内选取一个 $D \times D$ 的子方格。
• 然后，消耗 $D$ 点体力值来摧毁子方格内的所有方块。

请找出摧毁所有方块所需的最小体力值。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There is a $N \times N$ grid, with blocks on some squares.
The grid is described by $N$ strings $S_1,S_2,\dots,S_N$, as follows.

• If the $j$-th character of $S_i$ is #, there is a block on the square at the $i$-th row from the top and $j$-th column from the left.
• If the $j$-th character of $S_i$ is ., there is not a block on the square at the $i$-th row from the top and $j$-th column from the left.

Takahashi can do the operation below zero or more times.

• First, choose an integer $D$ between $1$ and $N$ (inclusive), and a $D \times D$ subsquare within the grid.
• Then, consume $D$ stamina points to destroy all blocks within the subsquare.

Find the minimum number of stamina points needed to destroy all the blocks.

Constraints

• $N$ is an integer.
• $1 \le N \le 50$
• $S_i$ consists of # and ..
• $|S_i|=N$

Input

Input is given from Standard Input in the following format:

$N$

$S_1$

$S_2$

$\vdots$

$S_N$

Output

Print the answer as an integer.

Sample Input 1

5
##...
.##..
#.#..
.....
....#

Sample Output 1

4

By choosing the subsquares below, Takahashi will consume $4$ stamina points, which is optimal.

• The $3 \times 3$ subsquare whose top-left square is at the $1$-st row from the top and $1$-st column from the left.
• The $1 \times 1$ subsquare whose top-left square is at the $5$-th row from the top and $5$-th column from the left.

Sample Input 2

3
...
...
...

Sample Output 2

0

There may be no block on the grid.

Sample Input 3

21
.....................
.....................
...#.#...............
....#.............#..
...#.#...........#.#.
..................#..
.....................
.....................
.....................
..........#.....#....
......#..###.........
........#####..#.....
.......#######.......
.....#..#####........
.......#######.......
......#########......
.......#######..#....
......#########......
..#..###########.....
.........###.........
.........###.........

Sample Output 3

19

update @ 2024/3/10 10:09:30