CF1198D Rectangle Painting 1

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.

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.

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

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