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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;


public class experiment {

    static int M = 1_000_000_007;
    static int INF = 2_000_000_000;
    static final FastScanner fs = new FastScanner();

    //variable
    static char[][] grid;
    static int n,m,k;
    static boolean[][] chk;
    public static void main(String[] args) throws IOException {

        n = fs.nextInt();
        m = fs.nextInt();
        k = fs.nextInt();
        grid = new char[n][m];
        chk = new boolean[n][m];
        for(int i=0;i<n;i++) {
            grid[i] = fs.next().toCharArray();
        }
        outer : for(int i=0;i<n;i++){
            for(int j=0;j<m;j++) {
                if(grid[i][j] == '.') {
                    dfs(i,j,-1,-1);
                    break outer;
                }
            }
        }
        for(int i=0;i<n;i++) {
            System.out.println(grid[i]);
        }
    }

    //class

    // function
    static boolean dfs(int i,int j,int previ, int prevj) {
        if(i<0 || j<0 || i>=n || j>=m || grid[i][j] != '.' || chk[i][j]) return true;
        //System.out.println(i+" "+j);
        chk[i][j] = true;
        boolean ans = false;
        if(i+1!=previ || j!=prevj) ans = dfs(i + 1, j, i, j);
        if(i-1!=previ || j!=prevj) ans |= dfs(i-1,j,i,j);
        if(i!=previ || j+1!=prevj) ans |= dfs(i,j+1,i,j);
        if(i!=previ || j-1!=prevj) ans |= dfs(i,j-1,i,j);

        if(ans && k!=0){
            grid[i][j] = 'X';
            k--;
        }
        chk[i][j] = true;
        return ans;
    }
    // Template
    static int lcm(int x, int y) {
        return (x / gcd(x,y) * y);
    }

    static int gcd(int x, int y) {
        if(x == 0) return y;

        return gcd(y%x,x);
    }
    static void premutation(int n, ArrayList<Integer> arr,boolean[] chosen) {
        if(arr.size() == n) {

        }else {
            for(int i=1; i<=n; i++) {
                if(chosen[i]) continue;
                arr.add(i);
                chosen[i] = true;
                premutation(n,arr,chosen);
                arr.remove(new Integer(i));
                chosen[i] = false;
            }
        }
    }
    static boolean isPalindrome(char[] c) {
        int n = c.length;
        for(int i=0; i<n/2; i++) {
            if(c[i] != c[n-i-1]) return false;
        }
        return true;
    }

    static long nCk(int n, int k) {
        return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
    }

    static long fact (long n) {

        long fact =1;
        for(int i=1; i<=n; i++) {
            fact = modMult(fact,i);
        }
        return fact%M;
    }

    static int modMult(long a,long b) {
        return (int) (a*b%M);
    }

    static long fastexp(long x, int y){
        if(y==0) return 1;
        if(y==1) return x;

        long ans = fastexp(x,y/2);
        if(y%2 == 0) return modMult(ans,ans);

        return modMult(ans,modMult(ans,x));
    }

    static final Random random = new Random();

    static void ruffleSort(int arr[])
    {
        int n = arr.length;
        for(int i=0; i<n; i++)
        {
            int j = random.nextInt(n),temp = arr[j];
            arr[j] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }

    public static class Pairs implements Comparable<Pairs> {
        int value;
        int index;
        Pairs(int value, int index) {
            this.value = value;
            this.index = index;
        }
        public int compareTo(Pairs p) {

            return Integer.compare(this.value,p.value);
        }
    }

}
class FastScanner
{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer str = new StringTokenizer("");

    String next() throws IOException {
        while(!str.hasMoreTokens())
            str = new StringTokenizer(br.readLine());

        return str.nextToken();
    }

    char nextChar() throws IOException {
        return next().charAt(0);
    }

    int nextInt() throws IOException {

        return Integer.parseInt(next());
    }

    float nextfloat() throws IOException
    {
        return Float.parseFloat(next());
    }

    double nextDouble() throws IOException
    {
        return Double.parseDouble(next());
    }
    long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }
    byte nextByte() throws IOException
    {
        return Byte.parseByte(next());
    }
    int [] arrayIn(int n) throws IOException {
        int  arr[] = new int[n];
        for(int i=0; i<n; i++)
        {
            arr[i] = nextInt();
        }
        return arr;
    }
}