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.util.*;



public class Main {
	
	static InputReader in = new InputReader(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	static int MOD = 1000000007;
	static int M = 505;
	static int oo = (int)1e9;
	
	static boolean[][] visit = new boolean[M][M];
	static char[][] a = new char[M][M];
	static int[] di = {-1, +1, 0, 0};
	static int[] dj = {0, 0, -1, +1};
	
	public static void main(String[] args) throws IOException {
		
		int n = in.nextInt();
		int m = in.nextInt();
		int k = in.nextInt();
		
		for(int i=1; i <= n; ++i) {
			char[] ca = in.readString().toCharArray();
			for(int j=1; j <= m; ++j) {
				a[i][j] = ca[j-1];
			}
		}
	
		int si = -1, sj = -1;
		L1:for(int i=1; i <= n; ++i) {
			for(int j=1; j <= m; ++j) {
				if(a[i][j] == '.') {
					si = i;
					sj = j;
					break L1;
				}
			}
		}
		ArrayList<Pair> res = new ArrayList<>();
		dfs(si, sj, res);
		
		
		for(int i=0; i < k; ++i) {
			
			Pair p = res.get(res.size() - 1 - i);
			a[p.first][p.second] = 'X';
		}
		
		for(int i=1; i <= n; ++i) {
			for(int j=1; j <= m; ++j) {
				out.print(a[i][j]);
			}
			out.println();
		}
		
		
		
		out.close();
	}
	
	static void dfs(int i, int j, ArrayList<Pair> res) {
		if(visit[i][j])
			return;
		visit[i][j] = true;
		res.add(new Pair(i, j));
		for(int k=0; k < 4; ++k) {
			int ni = i + di[k];
			int nj = j + dj[k];
			if(a[ni][nj] == '.' && !visit[ni][nj]) {
				dfs(ni, nj, res);
			}
		}
	}
	
	
	static void shuffle(int[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			int t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static int lower_bound(int[] a, int n, int k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	
	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	
	static class Pair implements Comparable<Pair> {
		int first, second;

		public Pair(int first, int second) {
			super();
			this.first = first;
			this.second = second;
		}

		@Override
		public int compareTo(Pair o) {
			return this.first != o.first ? this.first - o.first : this.second - o.second;
		}

		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			return result;
		}

		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
	}
	
	
}



class InputReader {

	private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;

	public InputReader(InputStream st) {
		this.stream = st;
	}

	public int read() {
		if (snumChars == -1)
			throw new InputMismatchException();
		if (curChar >= snumChars) {
			curChar = 0;
			try {
				snumChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (snumChars <= 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 {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long nextLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public int[] nextIntArray(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}

	public String readString() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

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

	private boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

}