CF1198D.Rectangle Painting 1

普及/提高-

通过率：0%

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题目描述

There is a square grid of size $n \times n$ . Some cells are colored in black, all others are colored in white. In one operation you can select some rectangle and color all its cells in white. It costs $\max(h, w)$ to color a rectangle of size $h \times w$ . You are to make all cells white for minimum total cost.

输入格式

The first line contains a single integer $n$ ( $1 \leq n \leq 50$ ) — the size of the square grid.

Each of the next $n$ lines contains a string of length $n$ , consisting of characters '.' and '#'. The $j$ -th character of the $i$ -th line is '#' if the cell with coordinates $(i, j)$ is black, otherwise it is white.

输出格式

Print a single integer — the minimum total cost to paint all cells in white.

输入输出样例

输入#1
```
3
###
#.#
###
```
输出#1
```
3
```
输入#2
```
3
...
...
...
```
输出#2
```
0
```
输入#3
```
4
#...
....
....
#...
```
输出#3
```
2
```
输入#4
```
5
#...#
.#.#.
.....
.#...
#....
```
输出#4
```
5
```

说明/提示

The examples and some of optimal solutions are shown on the pictures below.

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