Bajtazar works as a programmer in the 1960s. It is tedious work, as he enters programs into the computer not via a keyboard, but using punch cards. A card of size $n \times m$ consists of $n \cdot m$ identical rectangular fields arranged in $m$ columns and $n$ rows. Each field can be punched. The pattern of holes on the card encodes the program's content. The figure below shows an example of a $4 \times 5$ card. The holes in the fields are marked with black rectangles.
Bajtazar already has the program in his head and knows which fields should be punched. However, he would like to prepare the card as efficiently as possible. To this end, he decided to create a rectangular matrix that, when applied to the card, will punch all fields in a chosen $a \times b$ fragment (i.e., fields belonging to the intersection of $a$ consecutive rows and $b$ consecutive columns). The size of this matrix should be chosen such that it can be used to create a punch card having holes exactly in the places Bajtazar planned. At the same time, the matrix should be as large as possible. Since the fields on the card are not square, the matrix cannot be rotated (e.g., to obtain a matrix of size $b \times a$).
Programming computers takes much less time today than it used to, which is why Bajtazar has asked you to write a program that will determine the dimensions of the largest matrix that can be used to write his program on the card.
Input
The first line of input contains two integers $n$ and $m$ ($1 \le n,m \le 2\,500$). They denote the number of rows and columns on the punch card, respectively. The next $n$ lines contain the description of Bajtazar's program. Each of these lines consists of $m$ characters "_" or "X". The character "X" denotes a card field that should be punched, while "_" denotes a field that should not be punched. You may assume that the card description contains at least one "X" character.
Output
Your program should output two integers $a$ and $b$ describing the dimensions of the matrix that can be used to create the card described in the input. The product of these two numbers should be as large as possible. If there are multiple correct answers, your program should output the one with the smallest value of $a$.
Examples
Input 1
4 5 _XXX_ XXXX_ XXXXX _XXXX
Output 1
2 3