Long Long always dreamed of being a cowboy, so he made a robotic cow to ride it for daily driving.
But unfortunately, this robotic cow has not been painted with cow camouflage. Long Long bought paper and paints from the grocery store to make his own cow camouflage.
However, the vicious Master Yi splashed some white paint on the camouflage while Long Long was away, causing many spots on Long Long's cow camouflage.
Poor Long Long has little black paint left. He can only choose to blacken some of the smaller white spot(s) to make his camouflage looking as natural. And Long Long also has a obsession that he will only repaint the white pixel(s) wrapped by black pixel(s), which means after repainting, all the repainted pixels are surrounded by black pixels, while the white pixels outside including the sides and angles will never be repainted. The pixel surrounded is defined as four direction including left, right, up and down.
The first line contains three integers $n, m " "(1 <= n, m <= 1 " "000)$ and $d " "(1 <= d <= n times m)$ — the height and weight of Long Long's cow camouflage and the spots' area limit that choosed to paint.
The next $n$ line(s) contain $m$ character(s) each, where the $j$-th character of the $i$-th line is $c_{i , j}$ ($c_{i , j}$ is either _._ if the pixel in $(i, j)$ is white or _#_ if the pixel in $(i, j)$ is black).
It is guaranteed that each spot does not cross with any borders.
Plase print $n$ line(s) with $m$ character(s) each, which shows the cow camouflage you painted.
## Input
The first line contains three integers $n, m " "(1 <= n, m <= 1 " "000)$ and $d " "(1 <= d <= n times m)$ — the height and weight of Long Long's cow camouflage and the spots' area limit that choosed to paint.The next $n$ line(s) contain $m$ character(s) each, where the $j$-th character of the $i$-th line is $c_{i , j}$ ($c_{i , j}$ is either _._ if the pixel in $(i, j)$ is white or _#_ if the pixel in $(i, j)$ is black).It is guaranteed that each spot does not cross with any borders.
## Output
Plase print $n$ line(s) with $m$ character(s) each, which shows the cow camouflage you painted.
[samples]
**Definitions**
Let $ n, m \in \mathbb{Z}^+ $ denote the dimensions of the grid.
Let $ d \in \mathbb{Z}^+ $ denote the maximum number of white pixels that can be repainted.
Let $ G = (g_{i,j})_{n \times m} $ be the grid, where $ g_{i,j} \in \{ \text{`.`}, \text{`#`} \} $:
- $ g_{i,j} = \text{`.`} $: white pixel,
- $ g_{i,j} = \text{`#`} $: black pixel.
A white pixel $ (i,j) $ is **enclosed** if all four neighbors (up, down, left, right) are either black or part of a connected white component that is fully surrounded by black pixels (i.e., the entire connected white component does not touch the grid boundary).
Let $ \mathcal{C} = \{ C_1, C_2, \dots, C_k \} $ be the set of connected components of white pixels, where each $ C_\ell $ is a maximal 4-connected set of white pixels not touching the grid border.
**Constraints**
1. $ 1 \leq n, m \leq 1000 $
2. $ 1 \leq d \leq n \times m $
3. Each white connected component $ C_\ell \in \mathcal{C} $ is entirely enclosed (does not touch any grid boundary).
4. Only enclosed white components may be repainted.
**Objective**
Repaint at most $ d $ white pixels by converting them to black (`#`), such that:
- Only pixels belonging to enclosed white components are repainted.
- The total number of repainted pixels $ \leq d $.
- Maximize the number of repainted pixels (i.e., repaint as many as possible up to $ d $).
Output the modified grid after repainting.