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-----
The first line of input contains two integers $M$ and $N$ ($1 \leq M, N \leq 10$). The second line of input contains integers $U$, $L$, $R$, $D$ ($0 \leq U, L, R, D \leq 5$). The following $M$ lines of input contains $N$ characters — lowercase letters of the English alphabet. These lines represent Mirko’s crossword puzzle.

-----Output-----
Output the framed crossword puzzle as stated in the text.

-----Examples-----
Sample Input:
4 4
2 2 2 2
honi
oker
nera
irak
Sample Output:
#.#.#.#.
.#.#.#.#
#.honi#.
.#oker.#
#.nera#.
.#irak.#
#.#.#.#.
.#.#.#.#

Difficulty: introductory

Starter code:

Solutions: