Amin is a lover of puzzles, puzzles and crosswords. He came up with one puzzle and wants to create a frame for it. The puzzle consists of M \times N letters and the frame around it should have symbols at the top, symbols on the left, symbols on the right, symbols at the bottom. The frame consists of characters # (hash) and . (dot) which alternate like fields on a chessboard. These characters should be arranged in a way that, if the frame is expanded to cover the entire crossword puzzle and we treat these characters as a chessboard, the # characters should be placed as the red fields on a chessboard (i.e. the top left field). See the examples below for a better understanding of the task.
The first line contains two numbers and (1 \leq M, N \leq 10).The second line contains numbers , , , (0 \leq U, L, R, D \leq 5).The next lines contain characters each (small characters of the English alphabet).
Display a puzzle with a frame as described in the statement.
Beispiel 1
Beispiel 2