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.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class DFS implements Runnable
{
    
	static 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 String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			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 long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long 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 double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			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 readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    
	public static void main(String args[]) throws Exception
	{
		new Thread(null, new DFS(),"DFS",1<<26).start();
	}
	
	static Stack<point> stack;
    static ArrayList<point>[][] adj;
    static int n, m, a[][], si, sj, t;
    
    static int DFS(int k) {
	    
	    int count = t - k;
	    count--;
	    
	    int[][] vis = new int[n][m];
	    int[][] listCount = new int[n][m];
	    
	    stack = new Stack<point>();
	    
	    vis[si][sj] = 1;
	    a[si][sj] = 2;
	    stackAdd(si, sj);
	    
	    if(count == 0)
	           return 0; 
	    
	    outerloop:
	    while(!stack.isEmpty()) {
	        
	        int xi = stack.peek().i;
	        int xj = stack.peek().j;
	        
	        while(listCount[xi][xj] < adj[xi][xj].size()) {
	            
	            int yi = adj[xi][xj].get(listCount[xi][xj]).i;
	            int yj = adj[xi][xj].get(listCount[xi][xj]).j;
	            listCount[xi][xj]++;
	            
	            if(vis[yi][yj] == 0) {
	                
	                a[yi][yj] = 2;
	                count--;
	                stackAdd(yi, yj);
	                vis[yi][yj] = 1;
	                xi = yi;
	                xj = yj;
	                
	                if(count == 0)
	                    break outerloop;
	                    
	                continue;         
	            }
	        }
	        
	        stack.pop();
	    }
	    
	    return 0;
	}
    
    static class point{
        
        int i = 0;
        int j = 0;
    }
	
	static void addPoint(int i, int j, int newI, int newJ) {
	    
	     point p = new point();
	     p.i = newI;
	     p.j = newJ;
	    adj[i][j].add(p);
	}
	
	static void stackAdd(int i, int j) {
	    
	    point p = new point();
	    p.i = i;
	     p.j = j;
	    stack.push(p);
	}
	
	public void run() {
	    
	    InputReader s = new InputReader(System.in);
	    PrintWriter w = new PrintWriter(System.out);
	    
	    n = s.nextInt();
		m = s.nextInt();
		int k = s.nextInt();
		
		a = new int[n][m];
		
		t = 0;
		
		for(int i = 0; i < n; i++) {
	        
	        String str = s.next();
	        
	        for(int j = 0; j < m; j++) {
	            
	            if(str.charAt(j) == '#')
	                a[i][j] = 1;
	            else {
	                a[i][j] = 0;
	                t++;
	            }
	        }
	    }
		
		adj = new ArrayList[n][m];
	
	    for(int i = 0; i < n; i++)
	        for(int j = 0; j < m; j++)
	            adj[i][j] = new ArrayList<point>();
	    
	    outerloop:  
	    for(int i = 0; i < n; i++) {
	        
	        for(int j = 0; j < m; j++) {
	            
	           if(a[i][j] == 0) {
	                        
	                si = i;
	                sj = j;
	            
	                break outerloop;
	           }
	        } 
	    }  
	        
	    for(int i = 0; i < n; i++) {
	        
	        for(int j = 0; j < m; j++) {
	            
	           if(a[i][j] == 0) {
	                        
	                si = i;
	                sj = j;
	            
	                if(i > 0 && a[i - 1][j] == 0)
	                    addPoint(i, j, i - 1, j); 
	               
	                if(j > 0 && a[i][j - 1] == 0)
	                    addPoint(i, j, i, j - 1); 
	           
	                if(i < n - 1 && a[i + 1][j] == 0)
	                    addPoint(i, j, i + 1, j); 
	                
	                if(j < m - 1 && a[i][j + 1] == 0)
	                    addPoint(i, j, i, j + 1);
	           }
	                
	        } 
	        
	    }
	    

	    DFS(k);
	    
	   for(int i = 0; i < n; i++) {
	        
	        for(int j = 0; j < m; j++) {
	            
	            if(a[i][j] == 1)
	                w.print("#");
	            else if(a[i][j] == 0)
	                w.print("X");
	            else
	                w.print(".");
	        }
	        
	        w.println();
	    }
	    
	    w.close();
	}
}