Description: 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. Input Format: 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. Output Format: Print a single integer — the minimum total cost to paint all cells in white. Note: The examples and some of optimal solutions are shown on the pictures below.