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.math.*;
import java.util.*;


/**
 *
 * @author Saju
 *
 */

public class Main {

    private static int dx[] = { 1, 0, -1, 0 };
    private static int dy[] = { 0, -1, 0, 1 };

    private static final long INF = Long.MAX_VALUE;
    private static final int INT_INF = Integer.MAX_VALUE;
    private static final long NEG_INF = Long.MIN_VALUE;
    private static final int NEG_INT_INF = Integer.MIN_VALUE;
    private static final double EPSILON = 1e-10;

    private static final int MAX = 107;
    
    private static final long MOD = 1000000007;

    private static final int MAXN = 100007;
    private static final int MAXA = 10000009;
    private static final int MAXLOG = 22;

	public static void main(String[] args) throws IOException {

		InputReader in = new InputReader(System.in);
//		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

//         InputReader in = new InputReader(new FileInputStream("src/test.in"));
//         PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("src/test.out")));

		
		
/*




*/
		int n = in.nextInt();
		int m = in.nextInt();
		int k = in.nextInt();
		
		char[][] grid = new char[n][m];
		int srcr = -1;
		int srcc = -1;
		
		for(int i = 0; i < n; i++) {
			grid[i] = in.next().toCharArray();
			for(int j = 0; j < m; j++) {
				if(grid[i][j] != '#') {
					srcr = i;
					srcc = j;
				}
			}
		}
		
		if(srcr == -1 || k == 0) {
			for(int i = 0; i < n; i++) {
				for(int j = 0; j < m; j++) {
					out.print(grid[i][j]);
				}
				out.println();
			}
		}
		else {
//			System.out.println(srcr + " " + srcc);
			Queue<Pair> queue = new LinkedList<Main.Pair>();
			boolean[][] visited = new boolean[n][m];
			
			queue.add(new Pair(srcr, srcc));
			
			visited[srcr][srcc] = true;
			List<Pair>[] levelList = new ArrayList[n * m];
			for(int i  = 0; i < levelList.length; i++) {
				levelList[i] = new ArrayList<>();
			}
			
			int level[][] = new int[n][m];
			level[srcr][srcc] = 0;
			
			levelList[level[srcr][srcc]].add(new Pair(srcr, srcc));
			int maxLevel = 0;
			while(!queue.isEmpty()) {
				Pair uPair = queue.remove();
				
				for(int i = 0; i < 4; i++) {
					int rr = uPair.a + dx[i];
					int cc = uPair.b + dy[i];
					if(rr >= 0 && rr < n && cc >= 0 && cc < m && !visited[rr][cc] 
							&& grid[rr][cc] != '#') {
						queue.add(new Pair(rr, cc));
						visited[rr][cc] = true;
						level[rr][cc] = level[uPair.a][uPair.b] + 1;
						levelList[level[rr][cc]].add(new Pair(rr, cc));
						maxLevel = max(level[rr][cc], maxLevel);
					}
				}
			}
			
			
			int currLevel = maxLevel;
			while(k != 0 && currLevel > 0) {
				
				for(Pair p : levelList[currLevel]) {
					if(k > 0) {
						grid[p.a][p.b] = 'X';
					}
					else {
						break;
					}
					k--;
				}
				currLevel--;
			}
			for(int i = 0; i < n; i++) {
				for(int j = 0; j < m; j++) {
					out.print(grid[i][j]);
				}
				out.println();
			}
		}
	
		
		in.close();
		out.flush();
		out.close();
		System.exit(0);
	}

	private static class Pair{
		int a;
		int b;
		Pair(int a, int b){
			this.a = a;
			this.b = b;
		}
	}
	
	private static boolean isPalindrome(String str) {
		StringBuilder sb = new StringBuilder();
		sb.append(str);
		String str1 = sb.reverse().toString();
		return str.equals(str1);
	}
	
	private static String getBinaryStr(int n, int j) {
		String str = Integer.toBinaryString(n);
		int k = str.length();
		for (int i = 1; i <= j - k; i++) {
			str = "0" + str;
		}

		return str;
	}
	
	private static long bigMod(long n, long k, long m) {

        long ans = 1;
        while (k > 0) {
            if ((k & 1) == 1) {
                ans = (ans * n) % m;
            }
            n = (n * n) % m;
            k >>= 1;
        }
        return ans;
    }
    
	private static long ceil(long n, long x) {
		long div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
	}
	
    private static int ceil(int n, int x) {
        int div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
    }

    private static class Point {
        double x;
        double y;

        Point(double x, double y) {
            this.x = x;
            this.y = y;
        }

        double getDistance(Point p2) {
            Point p1 = this;
            double dx = p1.x - p2.x;
            double dy = p1.y - p2.y;

            return Math.sqrt((dx * dx) + (dy * dy));
        }
    }

    private static int abs(int x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }

    private static long abs(long x) {
        if(x < 0) {
            return -x;
        }
        return x;
    }

    private static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }

    private static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    private static int log(long x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    private static long min(long a, long b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static int min(int a, int b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static long max(long a, long b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static int max(int a, int b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());

                }
            } catch (IOException e) {
                return null;
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            String line = null;
            try {
                tokenizer = null;
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public boolean hasNext() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (Exception e) {
                return false;
            }
            return true;
        }
        public void close() {
        	try {
        		if(reader != null) {
        			reader.close();
        		}
        	}
        	catch(Exception e) {
        		
        	}
        	
        	
        }
    }

}