Solve an Akari (aka Light Up) puzzle.

Akari is a Japanese puzzle game. Input is a rectangular grid, with walls and empty cells. The objective is to place light bulbs on the grid in empty cells so that every empty cell is illuminated. Output a solution to the puzzle.

Rules:

• A light bulb will illuminate a cell if it's in the same row or column and there's no walls in between.
• No light bulbs should be illuminated by another light bulb.
• Some walls will additionally have numbers in them, these indicate exactly how many light bulbs should share a wall with that cell.

Structure:

• First Row will have #rows #columns.
• Following that is a grid.
• For output, keep the same format as input, but for any empty cell, if a lamp should be placed there, instead output a '@'

Notation:

• "." is an empty cell.
• "#" is a wall, numbers for numbered cells (remember these also serve as walls).

Example:

Input:

7 7
2.#...1
...2...
......#
.#...#.
2......
...#...
#...3.#

Output:

2@#@..1
@..2..@
...@..#
.#@..#@
2@.....
@..#@..
#..@3@#