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.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pradyumn Agrawal coderbond007
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int rowCount = in.nextInt();
            int columnCount = in.nextInt();
            int fill = in.nextInt();
            char[][] map = in.nextCharacterMap(rowCount, columnCount);
            int[] rowQueue = new int[rowCount * columnCount];
            int[] columnQueue = new int[rowCount * columnCount];
            int size = 0;
            for (int i = 0; i < rowCount && size == 0; i++) {
                for (int j = 0; j < columnCount && size == 0; j++) {
                    if (map[i][j] == '.') {
                        rowQueue[0] = i;
                        columnQueue[0] = j;
                        map[i][j] = 'X';
                        size = 1;
                    }
                }
            }
            for (int i = 0; i < size; i++) {
                int row = rowQueue[i];
                int column = columnQueue[i];
                for (int j = 0; j < 4; j++) {
                    int nRow = row + MiscUtils.DX4[j];
                    int nColumn = column + MiscUtils.DY4[j];
                    if (MiscUtils.isValidCell(nRow, nColumn, rowCount, columnCount) && map[nRow][nColumn] == '.') {
                        map[nRow][nColumn] = 'X';
                        rowQueue[size] = nRow;
                        columnQueue[size++] = nColumn;
                    }
                }
            }
            for (int i = 0; i < size - fill; i++)
                map[rowQueue[i]][columnQueue[i]] = '.';
            for (char[] row : map)
                out.println(new String(row));
        }

    }

    static class MiscUtils {
        public static final int[] DX4 = {1, 0, -1, 0};
        public static final int[] DY4 = {0, -1, 0, 1};

        public static boolean isValidCell(int row, int column, int rowCount, int columnCount) {
            return row >= 0 && row < rowCount && column >= 0 && column < columnCount;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        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 == ',') {
                    c = read();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        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 char nextCharacter() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            return (char) c;
        }

        public char[] nextCharacterArray(int n) {
            char[] chars = new char[n];
            for (int i = 0; i < n; i++) {
                chars[i] = nextCharacter();
            }
            return chars;
        }

        public char[][] nextCharacterMap(int n, int m) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++) {
                map[i] = nextCharacterArray(m);
            }
            return map;
        }

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

        }

    }
}