P13639 [NWRRC 2021] Letters Q and F

Little Lev is learning how to draw letters $\tt{Q}$ and $\tt{F}$. Initially, he has a white grid of size $n \times m$. Then he will draw several letters of one of the following two shapes:  Lev will not rotate or mirror these two shapes. Every time he draws a new letter, he will choose a position for the letter inside the grid and paint all cells of the shape black. Lev will only draw letters in such a way that before drawing all black cells of the letter are white --- that is, he will never paint a cell twice. You are given the final coloring of the grid. Count the number of letters $\tt{Q}$ and letters $\tt{F}$ drawn by Lev.

The first line contains two integers $n$ and $m$ --- the height and the width of the grid ($5 \le n \le 300$; $3 \le m \le 300$). The next $n$ lines contain $m$ characters each, denoting the final state of the grid. A white cell is denoted by $\tt{.}$, a black cell is denoted by $\tt{\#}$. It is guaranteed that the grid is a valid result of Lev's drawing.

Print two integers --- the number of letters $\tt{Q}$ and the number of letters $\tt{F}$ drawn by Lev, respectively.

Illustration for the fourth example test: