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.awt.Point;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

/**
 *
 * @author Mojtaba
 */
public class Main {

    static ArrayList<Edge>[] graph;
    static boolean[] visited;
    static int number;
    static int depth;
    static HashSet<Integer> hold;

    public static void main(String[] args) throws IOException {
        MyScanner in = new MyScanner(System.in);
        //PrintWriter writer = new PrintWriter(new BufferedOutputStream(System.out));
        StringBuilder sb = new StringBuilder("");

        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();

        String[] strs = new String[n];
        graph = new ArrayList[n * m];
        visited = new boolean[n * m];
        hold = new HashSet<>();
        for (int i = 0; i < graph.length; i++) {
            graph[i] = new ArrayList<>();
        }

        for (int i = 0; i < n; i++) {
            strs[i] = in.next();
        }

        HashSet<Integer> fixed = new HashSet<>();
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < strs[i].length(); j++) {
                int index = i * m + j;
                if (strs[i].charAt(j) == '.') {
                    if (i - 1 >= 0) {
                        if (strs[i - 1].charAt(j) == '.') {
                            graph[index].add(new Edge(index - m));
                        }
                    }
                    if (j - 1 >= 0) {
                        if (strs[i].charAt(j - 1) == '.') {
                            graph[index].add(new Edge(index - 1));
                        }
                    }
                    if (i + 1 < n) {
                        if (strs[i + 1].charAt(j) == '.') {
                            graph[index].add(new Edge(index + m));
                        }
                    }
                    if (j + 1 < m) {
                        if (strs[i].charAt(j + 1) == '.') {
                            graph[index].add(new Edge(index + 1));
                        }
                    }
                } else {
                    fixed.add(index);
                }
            }
        }
        number = n * m - fixed.size() - k;
        for (int i = 0; i < graph.length; i++) {
            if (graph[i].size() > 0 && k > 0) {
                depth = 1;
                DFS(i);
                break;
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                int index = i * m + j;
                if (fixed.contains(index)) {
                    sb.append("#");
                } else if (hold.contains(index)) {
                    sb.append(".");
                } else {
                    sb.append(k > 0 ? 'X' : '.');
                }
            }
            sb.append("\n");
        }

        //writer.println(sb.toString().trim());
        //writer.flush();
        //writer.close();
        System.out.println(sb.toString().trim());
        in.close();
    }

    private static void DFS(int v) {
        if (depth > number || visited[v]) {
            return;
        }
        visited[v] = true;
        hold.add(v);
        for (Edge edge : graph[v]) {
            if (!visited[edge.to] && depth < number) {
                depth++;
                DFS(edge.to);
            }
        }
    }
}

class Edge {

    int to;

    public Edge(int to) {
        this.to = to;
    }
}

class MyScanner {

    BufferedReader reader;
    StringTokenizer tokenizer;

    public MyScanner(InputStream stream) {
        this.reader = new BufferedReader(new InputStreamReader(stream));
    }

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

    public int[] nextIntegerArray(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    public long[] nextLongArray(int n) throws IOException {
        long[] a = new long[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    public int nextInt(int radix) throws IOException {
        return Integer.parseInt(next(), radix);
    }

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

    public long nextLong(int radix) throws IOException {
        return Long.parseLong(next(), radix);
    }

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

    public BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }

    public BigInteger nextBigInteger(int radix) throws IOException {
        return new BigInteger(next(), radix);
    }

    public String next() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
            return this.next();
        }
        return tokenizer.nextToken();
    }

    public void close() throws IOException {
        this.reader.close();
    }
}