Amin and Puzzle - Problems

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 x N letters and the frame around it should have U symbols at the top, L symbols on the left, R symbols on the right, D 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.

Input

The first line contains two numbers M and N (1 <= M, N <= 10) The second line contains 4 numbers U, L, R, D (0 <= U, L, R, D <= 5) The next M lines contain N characters each (small characters of the English alphabet)

Output

Display a puzzle with a frame as described in the statement.

Time limit 1 second

Memory limit 64 MiB

Input example #1

4 4
2 2 2 2
honi
oker
nera
irak

Output example #1

#.#.#.#.
.#.#.#.#
#.honi#.
.#oker.#
#.nera#.
.#irak.#
#.#.#.#.
.#.#.#.#

Input example #2

2 4
1 0 3 1
rima
mama

Output example #2

#.#.#.#
rima.#.
mama#.#
.#.#.#.

Source CoronaVirus GrandPrix2020 Round 1