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.io.*;
import java.util.*;
 
 
public class Main{

	//public static Reader sc = new Reader();
	public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static int count = 0;
	static int ss = 0;
	static int n,m,k ;
	static int[][] g;
	
	static void dfs(int i, int j) {
		if (count >= ss - k) return;
		if (g[i][j] != 0) return;
		g[i][j] = 2;
		count++;
		if (i != 0) dfs(i-1, j);
		if (i != n-1) dfs(i+1,j);
		if (j != 0) dfs(i,j-1);
		if (j != m-1) dfs(i, j+1);
	}
   public static void main(String[] args) throws IOException{
	StringTokenizer st = new StringTokenizer(br.readLine());
	n = Integer.parseInt(st.nextToken());
	m = Integer.parseInt(st.nextToken());
	k = Integer.parseInt(st.nextToken());
	g = new int[n][m];
	for (int i = 0; i < n; i++) {
		String s = br.readLine();
		for (int j = 0; j < m; j++) {
			g[i][j] = s.charAt(j) == '#' ? 1:0;
			ss += s.charAt(j) == '#' ? 0:1;
		}
	}
	boolean found = false;
	for (int i = 0; i < n && !found; i++) {
		for (int j = 0; j < m && !found; j++) {
			if (g[i][j] == 0) {
				dfs(i,j);
				found = true;
			}
		}
		
	}
	// scuffed BFS from "leaf" nodes
	
	p();
	out.close();
   }
   static void p() {
	   for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				if (g[i][j] == 1) out.print('#');
				else if (g[i][j] == 2) out.print('.');
				else out.print('X');
			}
			out.println();
		}
   }
   static long ceil(long a, long b) {
		return (a+b-1)/b;
	}
  
   static long powMod(long base, long exp, long mod) {
	   if (base == 0 || base == 1) return base;
	   if (exp == 0) return 1;
	   if (exp == 1) return base % mod;
	   long R = powMod(base, exp/2, mod) % mod;
	   R *= R;
	   R %= mod;
	   if ((exp & 1) == 1) {
		   return base * R % mod;
	   }
	   else return R % mod;
   }
   
   static long pow(long base, long exp) {
	   if (base == 0 || base == 1) return base;
	   if (exp == 0) return 1;
	   if (exp == 1) return base;
	   long R = pow(base, exp/2);
	   if ((exp & 1) == 1) {
		   return R * R * base;
	   }
	   else return R * R;
   }
   

 
   static class Reader 
   { 
       final private int BUFFER_SIZE = 1 << 16; 
       private DataInputStream din; 
       private byte[] buffer; 
       private int bufferPointer, bytesRead; 

       public Reader() 
       { 
           din = new DataInputStream(System.in); 
           buffer = new byte[BUFFER_SIZE]; 
           bufferPointer = bytesRead = 0; 
       } 

       public Reader(String file_name) throws IOException 
       { 
           din = new DataInputStream(new FileInputStream(file_name)); 
           buffer = new byte[BUFFER_SIZE]; 
           bufferPointer = bytesRead = 0; 
       } 

       public String readLine() throws IOException 
       { 
           byte[] buf = new byte[64]; // line length 
           int cnt = 0, c;
           while ((c = read()) != -1) 
           { 
               if (c == '\n') 
               {
            	   break;
               }
               buf[cnt++] = (byte) c; 
           } 
           return new String(buf, 0, Integer.max(cnt-1, 0)); 
       } 

       public int nextInt() throws IOException 
       { 
           int ret = 0; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 
           do
           { 
               ret = ret * 10 + c - '0'; 
           }  while ((c = read()) >= '0' && c <= '9'); 

           if (neg) 
               return -ret; 
           return ret; 
       } 

       public long nextLong() throws IOException 
       { 
           long ret = 0; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 
           do { 
               ret = ret * 10 + c - '0'; 
           } 
           while ((c = read()) >= '0' && c <= '9'); 
           if (neg) 
               return -ret; 
           return ret; 
       } 

       public double nextDouble() throws IOException 
       { 
           double ret = 0, div = 1; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 

           do { 
               ret = ret * 10 + c - '0'; 
           } 
           while ((c = read()) >= '0' && c <= '9'); 

           if (c == '.') 
           { 
               while ((c = read()) >= '0' && c <= '9') 
               { 
                   ret += (c - '0') / (div *= 10); 
               } 
           } 

           if (neg) 
               return -ret; 
           return ret; 
       } 

       private void fillBuffer() throws IOException 
       { 
           bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
           if (bytesRead == -1) 
               buffer[0] = -1; 
       } 

       private byte read() throws IOException 
       { 
           if (bufferPointer == bytesRead) 
               fillBuffer(); 
           return buffer[bufferPointer++]; 
       } 

       public void close() throws IOException 
       { 
           if (din == null) 
               return; 
           din.close(); 
       } 
   }

	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
}