Problem:
Score: 400 points

Problem Statement

Chokudai made a rectangular cake for contestants in DDCC 2020 Finals.

The cake has H - 1 horizontal notches and W - 1 vertical notches, which divide the cake into H \times W equal sections. K of these sections has a strawberry on top of each of them.

The positions of the strawberries are given to you as H \times W characters s_{i, j} (1 \leq i \leq H, 1 \leq j \leq W). If s_{i, j} is #, the section at the i-th row from the top and the j-th column from the left contains a strawberry; if s_{i, j} is ., the section does not contain one. There are exactly K occurrences of #s.

Takahashi wants to cut this cake into K pieces and serve them to the contestants. Each of these pieces must satisfy the following conditions:

Has a rectangular shape.

Contains exactly one strawberry.

One possible way to cut the cake is shown below:

Find one way to cut the cake and satisfy the condition. We can show that this is always possible, regardless of the number and positions of the strawberries.

Constraints

1 \leq H \leq 300

1 \leq W \leq 300

1 \leq K \leq H \times W

s_{i, j} is # or ..

There are exactly K occurrences of # in s.

Input

Input is given from Standard Input in the following format:

H W K
s_{1, 1} s_{1, 2} \cdots s_{1, W}
s_{2, 1} s_{2, 2} \cdots s_{2, W}
:
s_{H, 1} s_{H, 2} \cdots s_{H, W}

Output

Assign the numbers 1, 2, 3, \dots, K to the K pieces obtained after the cut, in any order. Then, let a_{i, j} be the number representing the piece containing the section at the i-th row from the top and the j-th column from the left of the cake. Output should be in the following format:

a_{1, 1} \ a_{1, 2} \ \cdots \ a_{1, W}
a_{2, 1} \ a_{2, 2} \ \cdots \ a_{2, W}
:
a_{H, 1} \ a_{H, 2} \ \cdots \ a_{H, W}

If multiple solutions exist, any of them will be accepted.

Sample Input 1

3 3 5
#.#
.#.
#.#

Sample Output 1

1 2 2
1 3 4
5 5 4

One way to cut this cake is shown below:

Sample Input 2

3 7 7
#...#.#
..#...#
.#..#..

Sample Output 2

1 1 2 2 3 4 4
6 6 2 2 3 5 5
6 6 7 7 7 7 7

One way to cut this cake is shown below:

Sample Input 3

13 21 106
.....................
.####.####.####.####.
..#.#..#.#.#....#....
..#.#..#.#.#....#....
..#.#..#.#.#....#....
.####.####.####.####.
.....................
.####.####.####.####.
....#.#..#....#.#..#.
.####.#..#.####.#..#.
.#....#..#.#....#..#.
.####.####.####.####.
.....................

Sample Output 3

12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50
12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50
12 12 56 89 89 89 60 104 82 31 31 46 13 24 35 35 61 61 39 50 50
12 12 67 67 100 100 60 9 9 42 42 57 13 24 6 72 72 72 72 72 72
12 12 78 5 5 5 20 20 20 53 68 68 90 24 6 83 83 83 83 83 83
16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21
16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21
32 32 43 54 65 65 80 11 106 95 22 22 33 44 55 55 70 1 96 85 85
32 32 43 54 76 76 91 11 106 84 84 4 99 66 66 66 81 1 96 74 74
14 14 3 98 87 87 102 11 73 73 73 4 99 88 77 77 92 92 63 63 63
25 25 3 98 87 87 7 29 62 62 62 15 99 88 77 77 103 19 30 52 52
36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41
36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
public class Main {
	public static void main(String[] args)throws Exception{
		Scanner stdIn=new Scanner(System.in);
		int H=stdIn.nextInt();
		int W=stdIn.nextInt();
		int K=stdIn.nextInt();
		char s[][]=new char[H][W];
		int A[][]=new int[K][2];
		int map[][]=new int[H][W];
		boolean h[]=new boolean[H];
		int z=0;
		for(int i=0;i<H;i++){
			String a=stdIn.next();
			for(int j=0;j<W;j++){
				s[i][j]=a.charAt(j);
				if(s[i][j]=='#'){
					h[i]=true;
					A[z][0]=i;
					A[z][1]=j;
					z++;
				}
			}
		}
		for(int i=0;i<K;i++){
			int u=A[i][0],d=u,l=A[i][1],r=l;
			map[u][l]=i+1;
			boolean uk=false,dk=false,rk=false,lk=false;
			while(true){
				if(u!=0&&h[u-1]==false){
					u--;uk=true;
				}
				if(d!=H-1&&h[d+1]==false){
					d++;dk=true;
				}
				for(int j=l;j<=r;j++){
					if(uk)
						if(map[u][j]!=0){
							u++;uk=false;
						}
					if(dk)
						if(map[d][j]!=0){
							d--;dk=false;
						}
				}
				if(r!=W-1){
					r++;rk=true;
				}
				if(l!=0){
					l--;lk=true;
				}
				for(int j=u;j<=d;j++){
					if(rk)
						if(map[j][r]!=0||s[j][r]=='#'){
							r--;rk=false;
						}
					if(lk)
						if(map[j][l]!=0||s[j][l]=='#'){
							l++;lk=false;
						}
				}
				if(rk==false&&lk==false&&uk==false&&dk==false){
					for(int j=u;j<=d;j++){
						for(int k=l;k<=r;k++){
							map[j][k]=i+1;
						}
					}
					break;
				}
				rk=false;lk=false;uk=false;dk=false;
			}
		}
		for(int i=0;i<H;i++){
			for(int j=0;j<W;j++){
				System.out.println(map[i][j]);
			}
		}
	}
}