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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author maheshwari29
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        AMaze solver = new AMaze();
        solver.solve(1, in, out);
        out.close();
    }

    static class AMaze {
        static boolean visited[][];
        static int temp[][];
        static ArrayList<AMaze.pair> arr = new ArrayList<>();

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int i, j;
            int n = in.ni();
            int m = in.ni();
            int z = in.ni();
            temp = new int[n][m];
            visited = new boolean[n][m];
            for (i = 0; i < n; i++) {
                String s = in.next();
                for (j = 0; j < m; j++)
                    if (s.charAt(j) == '#')
                        temp[i][j] = 0;
                    else
                        temp[i][j] = 1;
            }
            for (i = 0; i < n; i++) {
                for (j = 0; j < m; j++) {
                    arr = new ArrayList<>();
                    if (!visited[i][j] && temp[i][j] == 1) {
                        dfs(i, j);
                        for (int k = arr.size() - 1; k >= 0; k--) {
                            AMaze.pair c = arr.get(k);
                            if (z > 0) {
                                temp[c.x][c.y] = 2;
                                z--;
                            }
                        }
                    }
                }
            }
            for (i = 0; i < n; i++) {
                for (j = 0; j < m; j++)
                    if (temp[i][j] == 0)
                        out.print("#");
                    else if (temp[i][j] == 1)
                        out.print(".");
                    else
                        out.print("X");
                out.println();
            }

        }

        static void dfs(int i, int j) {
            if (visited[i][j])
                return;
            visited[i][j] = true;
            arr.add(new AMaze.pair(i, j));
            if (i - 1 >= 0 && temp[i - 1][j] == 1)
                dfs(i - 1, j);
            if (j - 1 >= 0 && temp[i][j - 1] == 1)
                dfs(i, j - 1);
            if (i + 1 < temp.length && temp[i + 1][j] == 1)
                dfs(i + 1, j);
            if (j + 1 < temp[0].length && temp[i][j + 1] == 1)
                dfs(i, j + 1);
        }

        static class pair implements Comparable<AMaze.pair> {
            int x;
            int y;

            public pair(int x, int y) {
                this.x = x;
                this.y = y;
            }

            public int compareTo(AMaze.pair arg0) {
                if (x < arg0.x) return -1;
                else if (x == arg0.x) {
                    if (y < arg0.y) return -1;
                    else if (y > arg0.y) return 1;
                    else return 0;
                } else return 1;
            }

            public boolean equals(Object o) {
                if (this == o) return true;
                if (!(o instanceof AMaze.pair)) return false;
                AMaze.pair key = (AMaze.pair) o;
                return x == key.x && y == key.y;
            }

            public int hashCode() {
                int result = x;
                result = 31 * result + y;
                return result;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.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 int ni() {
            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 String ns() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return ns();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println() {
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }
}