There is a Chipmunk with "Brain" and he want to dig holes in a yard to store his food.
There is a rectangular yard which is divided into unit cells, initially having some holes(H) and sand(S). The chipmunk can dig one row at a time, But he have to dig all the sand(S) positions simultanously and due to this holes(H) which are already there got filled with sand.

Example:
Suppose a Row is "SHSHH" then after digging the row becomes "HSHSS" i.e all "S" replace with "H" and vice versa.

Now Chipmunk wants to have a large square of holes somewhere in the yard. The sides of square must be parallel to the sides of the yard. Find a sequence of turns that produces the largest possible square of holes somewhere in the yard and help him to find the area of that square.

Input

Given two interger Rows(R) and column(C) (1<=R,C<=30)
Next line contain a RxC rectangular yard of sand (S) and hole (H).

Output

Print largest "Area of the Square" that can be obtain after sequence of turns.

Example

Input:
2 2
SS
HH

Output:
4

Input:
5 1
H
S
H
H
H

Output:
1