Mirko has assembled an excellent crossword puzzle and now he wants to frame it. Mirko's crossword puzzle consists of ~M \times N~ letters, and the frame around it should be ~U~ characters wide on top, ~L~ characters on the left, ~R~ characters on the right and ~D~ characters on the bottom side.

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 Specification

The first line of input contains two integers ~M~ and ~N~ ~(1 \le M, N \le 10)~.

The second line of input contains integers ~U, L, R, D~ ~(0 \le U, L, R, D \le 5)~.

The following ~M~ lines of input contains ~N~ characters – lowercase letters of the English alphabet. These lines represent Mirko's crossword puzzle.

Output Specification

Output the framed crossword puzzle as stated in the text.

Sample Input 1

4 4
2 2 2 2
honi
oker
nera
irak

Sample Output 1

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

Sample Input 2

2 4
1 0 3 1
rima
mama

Sample Output 2

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