In biology class, the teacher introduces cells to the students. To help students understand, the teacher defines a type of cell in an $N \times M$ matrix, where the matrix contains only '#' and '.':
A cell consists of a nucleus, cytoplasm, and a cell membrane. The nucleus is a 4-connected (connected horizontally or vertically) component consisting entirely of '#', and it must be solid, meaning there cannot be a 4-connected '.' component completely enclosed by it (complete enclosure means the '.' component is not adjacent to the matrix boundary, and all its 4-adjacent cells belong to the '#' component containing it). The cell membrane is an 8-connected (connected horizontally, vertically, or diagonally) non-solid component consisting entirely of '#'. The cell membrane encloses exactly one 4-connected region, and this region contains exactly one nucleus, with all remaining positions in this region being '.'.
All connected components must be maximal, meaning that for an 8-connected component, no '#' can be found in its surroundings that is 8-connected to any '#' of this component; similarly, for a 4-connected component, no '#' can be found in its surroundings that is 4-connected to any '#' of this component.
Now, the teacher has drawn a picture and asks little E to count the number of cells in the picture and change any '#' that does not belong to any cell into '.'.
Input
The first line contains two space-separated positive integers $N$ and $M$, representing the height and width of the matrix. The next $N$ lines contain the $N \times M$ matrix, which contains only '#' and '.', with no extra characters.
Output
The first line contains an integer representing the number of cells in the input matrix. The next $N$ lines contain the $N \times M$ matrix, which contains only '#' and '.', representing the modified picture.
Examples
Input 1
12 13 .###..#####.. #...#.#....#. #.#.#.#..#.#. #...#..#...#. .###.#..###.. ....#..##...# ..........### ##########..# #...........# #.###...###.# #...........# #############
Output 1
1 ......#####.. ......#....#. ......#..#.#. .......#...#. ........###.. .......##.... ............. ............. ............. ............. ............. .............
Input 2
9 14 #########..... #.......#....# #.#####.#...#. #.#...#.#..#.. #.#.#.#.#.#..# #.#...#.#..#.. #.#####.#...#. #.......#....# #########.....
Output 2
1 .............. .............. ..#####....... ..#...#....... ..#.#.#....... ..#...#....... ..#####....... .............. ..............
Input 3
7 15 #######.####### #.....#.#.....# #.###.#.#.###.# #.#.#.#.#.#...# #.###.#.#.###.# #.....#.#.....# #######.#######
Output 3
1 ........####### ........#.....# ........#.###.# ........#.#...# ........#.###.# ........#.....# ........#######
Constraints
For 20% of the data, $1 \le N, M \le 20$. For another 20% of the data, all '#' belong to a valid cell. For 100% of the data, $1 \le N, M \le 1,000$.