Crossword puzzle decoration

Changyeong likes crossword puzzles. He has solved every puzzle in the world, so now he wants to decorate one.

A puzzle is a grid of $M \times N$ letters. Changyeong adds $U$ rows above the puzzle, $L$ columns to its left, $R$ columns to its right, and $D$ rows below it. The finished decoration is a rectangle with $U + M + D$ rows and $L + N + R$ columns.

The added cells are filled with # and . so that they alternate like a chessboard. Let $(i, j)$ be the cell in row $i$ from the top and column $j$ from the left of the finished rectangle. A cell with $i + j$ even holds #, and a cell with $i + j$ odd holds .. The top left cell $(1, 1)$ is therefore #. Cells that the original puzzle occupies keep their letters.

The first line contains $M$ and $N$. ($1 \le M, N \le 10$)

The second line contains $U$, $L$, $R$, and $D$. ($0 \le U, L, R, D \le 5$)

Each of the next $M$ lines contains $N$ letters of the crossword puzzle.

Print the decorated crossword puzzle on $U + M + D$ lines. Each line has $L + N + R$ characters.