The English mathematician John Conway invented in 1970 the following game: Imagine a matrix with n rows and m columns. We consider neighbor positions to a given position the (at most, eight) adjacent positions, either horizontally, vertically or diagonally. Every moment, each position is either empty or it contains a bacterium. The rules are:

- An empty position at time t will contain a bacterium at time t + 1 if and only if at time t it had exactly three neighbor bacteria.
- An occupied position at time t will contain a bacterium at time t + 1 if and only if at time t it had two or three neighbor bacteria.

Write a program that, for every given matrix, prints it at the next moment of time.

Input

Input consists of several cases. Every case begins with n and m (both strictly positive), followed by n lines, each one with m characters: ‘B’ if the position has a bacterium, and ‘.’ if the position is empty. A special case with n = m = 0 marks the end of the input.

Output

For each case, print the matrix corresponding to the next moment of time using the same format of the input (do not print n and m). Separate matrices with an empty line.

Public test cases

**Input**

2 3 B.B .B. 2 2 BB BB 0 0

**Output**

.B. .B. BB BB

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++ Java Python
- User solutions
- C++ Java Python Rust