Problem: Pavel loves grid mazes. A grid maze is an n × m rectangle maze where each cell is either empty, or is a wall. You can go from one cell to another only if both cells are empty and have a common side.

Pavel drew a grid maze with all empty cells forming a connected area. That is, you can go from any empty cell to any other one. Pavel doesn't like it when his maze has too little walls. He wants to turn exactly k empty cells into walls so that all the remaining cells still formed a connected area. Help him.

Input

The first line contains three integers n, m, k (1 ≤ n, m ≤ 500, 0 ≤ k < s), where n and m are the maze's height and width, correspondingly, k is the number of walls Pavel wants to add and letter s represents the number of empty cells in the original maze.

Each of the next n lines contains m characters. They describe the original maze. If a character on a line equals ".", then the corresponding cell is empty and if the character equals "#", then the cell is a wall.

Output

Print n lines containing m characters each: the new maze that fits Pavel's requirements. Mark the empty cells that you transformed into walls as "X", the other cells must be left without changes (that is, "." and "#").

It is guaranteed that a solution exists. If there are multiple solutions you can output any of them.

Examples

Input

3 4 2
#..#
..#.
#...


Output

#.X#
X.#.
#...


Input

5 4 5
#...
#.#.
.#..
...#
.#.#


Output

#XXX
#X#.
X#..
...#
.#.#

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
public class Main9
{
	static class Pair
	{
		int x;
		int y;
		Pair(int x ,int y)
		{
			this.x=x;
			this.y=y;
		}
	}
	static int mod=1000000007;
	public static int[] sort(int[] a)
	{
		int n=a.length;
		ArrayList<Integer> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++)
		{
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++)
		{
			a[i]=ar.get(i);
		}
		return a;
	}
	public static long pow(long a, long b)
    {
        long result=1;
        while(b>0)
        {
            if (b % 2 != 0)
            {
                result=(result*a)%mod;
                b--;
            } 
            a=(a*a)%mod;
            b /= 2;
        }   
        return result;
    }
	
    public static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b%a, a);
    }   
	static ArrayList<ArrayList<Integer>> graph;
	static public void main(String args[])throws IOException
	{
		int tt=1;
		StringBuilder sb=new StringBuilder();
		for(int ttt=1;ttt<=tt;ttt++)
		{
			int n=i();
			int m=i();
			int k=i();
			char[][] a=new char[n][m];
			int x=0,y=0;
			int ans=0;
			for(int i=0;i<n;i++)
			{
				String s=s();
				for(int j=0;j<m;j++)
				{
					a[i][j]=s.charAt(j);
					if(a[i][j]=='.')
					{
						ans++;
						x=i;
						y=j;
					}
				}
			}
			Queue<Pair> queue=new LinkedList<>();
			queue.add(new Pair(x,y));
			boolean[][] visited=new boolean[n][m];
			int[] dx=new int[]{1,-1,0,0};
			int[] dy=new int[]{0,0,1,-1};
			int rem=ans-k;
			int count=1;
			visited[x][y]=true;
			while(queue.isEmpty()==false && count!=rem)
			{
				Pair p=queue.poll();
				for(int i=0;i<4;i++)
				{
					int xx=p.x+dx[i];
					int yy=p.y+dy[i];
					if(xx>=n || xx<0 || yy>=m || yy<0)
						continue;
					if(visited[xx][yy]==false && a[xx][yy]=='.')
					{
						count++;
						visited[xx][yy]=true;
						if(count==rem)
							break;
						queue.add(new Pair(xx,yy));
					}
				}
			}
			for(int i=0;i<n;i++)
			{
				for(int j=0;j<m;j++)
				{
					if(a[i][j]=='.' && visited[i][j]==false)
					{
						a[i][j]='X';
					}
					System.out.print(a[i][j]+"");
				}
				pln("");
			}
		}
		System.out.print(sb.toString());
	}
			/**/
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	public static long l()
	{
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value)
	{
		System.out.println(value);
	}
	public static int i()
	{
		return in.Int();
	}
	public static String s()
	{
		return in.String();
	}
}
	class InputReader 
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
	 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
	 
		public int read() {
			if (numChars== -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
	 
		public int Int() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
	 
		public String String() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() {
			return String();
		}
	 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	 
	class OutputWriter {
		private final PrintWriter writer;
	 
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
	 
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
	 
		public void print(Object...objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}
	 
		public void printLine(Object...objects) {
			print(objects);
			writer.println();
		}
	 
		public void close() {
			writer.close();
		}
	 
		public void flush() {
			writer.flush();
		}
	 
		}
	 
		class IOUtils {
	 
		public static int[] readIntArray(InputReader in, int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = in.Int();
			return array;
		}
	 
	}