Problem Description

Chokudai has prepared a rectangular cake to be distributed to participants at the DDCC 2020 Finals.

The cake is divided into $H \times W$ sections by $H - 1$ horizontal cuts and $W - 1$ vertical cuts. Among these sections, $K$ of them have exactly one strawberry each.

The positions of the strawberries are given by $H \times W$ characters $s_{i, j}$ $(1 \leq i \leq H, 1 \leq j \leq W)$. When $s_{i, j}$ is #, there is a strawberry on the section in the $i$-th row from the top and the $j$-th column from the left. When $s_{i, j}$ is ., there is no strawberry. Exactly $K$ # characters appear.

Chokudai wants to cut the cake along the cuts into $K$ pieces to distribute to the participants. Each piece must satisfy the following conditions:

• It must be rectangular in shape.
• It must contain exactly one strawberry.

For example, the following is a possible example:

Find one way to cut the cake that satisfies the conditions. It can be shown that such a way of cutting always exists regardless of the number and positions of the strawberries.

Input Format

The input is given from the 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 Format

Assign arbitrary numbers $1, 2, 3, \dots, K$ to the $K$ pieces after cutting. Output the number of the piece to which the section in the $i$-th row from the top and the $j$-th column from the left belongs, $a_{i, j}$, 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 there are multiple ways to cut the cake, you may output any one of them.

Sample Input and Output

Sample Input #1

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

Sample Output #1

1 2 2
1 3 4
5 5 4

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

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

Notes/Hints

Constraints

• $1 \leq H \leq 300$
• $1 \leq W \leq 300$
• $1 \leq K \leq H \times W$
• $s_{i, j}$ is either # or .
• Exactly $K$ # characters appear in $s$.

Sample Explanation 1

For example, the cake can be cut as shown in the following diagram:

Sample Explanation 2

For example, the cake can be cut as shown in the following diagram:

见题面 Input 部分

见题面 Output 部分