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:
//package Round_222;


import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class C {
    
    boolean u[][];
    boolean wall[][];
    int n, m;
    int need;
    
    void dfs(int x, int y){
        if (x < 0 || x == n || y < 0 || y == m || wall[x][y]) return;
        if (u[x][y]) return;
        if (need == 0) return;
        need--;
        u[x][y] = true;
        dfs(x+1, y);
        dfs(x-1, y);
        dfs(x, y+1);
        dfs(x, y-1);
    }
    
    void solve() throws Exception{
        n = in.nextInt();
        m = in.nextInt();
        wall = new boolean[n][m];
        u = new boolean[n][m];
        int k = in.nextInt();
        int sx = -1;
        int sy = -1;
        int t = 0;
        for (int i = 0; i<n; i++) {
            String line = in.next();
            for (int j = 0; j<m; j++){
                wall[i][j] = line.charAt(j) == '#';
                if (!wall[i][j]) {
                    sx = i;
                    sy = j;
                    t++;
                }
            }
        }
        need = t - k;
        dfs(sx, sy);
        for (int i = 0; i<n; i++) {
            for (int j = 0; j<m; j++) {
                if (wall[i][j])
                    out.print('#');
                else if (u[i][j])
                    out.print('.');
                else 
                    out.print('X');
            }
            out.println();
        }
    }
    
    String input = "";
    String output = "";
    FastScanner in;
    PrintWriter out;

    void run() throws Exception {
        if (input.length() == 0) {
            in = new FastScanner(System.in);
        } else {
            in = new FastScanner(new File(input));
        }
        if (output.length() == 0) {
            out = new PrintWriter(System.out);
        } else {
            out = new PrintWriter(new File(output));
        }

        solve();

        out.close();

    }

    public static void main(String[] args) throws Exception {
        new C().run();
    }

    class FastScanner {

        BufferedReader bf;
        StringTokenizer st;

        public FastScanner(InputStream is) {
            bf = new BufferedReader(new InputStreamReader(is));
        }

        public FastScanner(File fr) throws FileNotFoundException {
            bf = new BufferedReader(new FileReader(fr));
        }

        public String next() {
            try {
                while (st == null || !st.hasMoreTokens()) {
                    st = new StringTokenizer(bf.readLine());
                }
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return st.nextToken();
        }

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

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

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

        public int[] readIntArray(int length) {
            int arr[] = new int[length];
            for (int i = 0; i<length; i++)
                arr[i] = nextInt();
            return arr;
        }
    }
}