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.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;

import static java.lang.Math.*;

public class Main {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    public static void main(String[] args) {
        new Main().run();
        // Sworn to fight and die
    }

    public static void mergeSort(int[] a) {
        mergeSort(a, 0, a.length - 1);
    }

    private static void mergeSort(int[] a, int levtIndex, int rightIndex) {
        final int MAGIC_VALUE = 50;
        if (levtIndex < rightIndex) {
            if (rightIndex - levtIndex <= MAGIC_VALUE) {
                insertionSort(a, levtIndex, rightIndex);
            } else {
                int middleIndex = (levtIndex + rightIndex) / 2;
                mergeSort(a, levtIndex, middleIndex);
                mergeSort(a, middleIndex + 1, rightIndex);
                merge(a, levtIndex, middleIndex, rightIndex);
            }
        }
    }

    private static void merge(int[] a, int levtIndex, int middleIndex,
                              int rightIndex) {
        int length1 = middleIndex - levtIndex + 1;
        int length2 = rightIndex - middleIndex;
        int[] levtArray = new int[length1];
        int[] rightArray = new int[length2];
        System.arraycopy(a, levtIndex, levtArray, 0, length1);
        System.arraycopy(a, middleIndex + 1, rightArray, 0, length2);
        for (int k = levtIndex, i = 0, j = 0; k <= rightIndex; k++) {
            if (i == length1) {
                a[k] = rightArray[j++];
            } else if (j == length2) {
                a[k] = levtArray[i++];
            } else {
                a[k] = levtArray[i] <= rightArray[j] ? levtArray[i++]
                        : rightArray[j++];
            }
        }
    }

    private static void insertionSort(int[] a, int levtIndex, int rightIndex) {
        for (int i = levtIndex + 1; i <= rightIndex; i++) {
            int current = a[i];
            int j = i - 1;
            while (j >= levtIndex && a[j] > current) {
                a[j + 1] = a[j];
                j--;
            }
            a[j + 1] = current;
        }
    }

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }



    class LOL implements Comparable<LOL> {

        int x;
        int y;



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

        }

        @Override
        public int compareTo(LOL o) {

            return (x - o.x); // ---->
            //return o.x * o.y - x * y; // <----
        }

    }

    class LOL2 implements Comparable<LOL2> {

        int x;
        int y;
        int z;



        public LOL2(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        @Override
        public int compareTo(LOL2 o) {

            return (z - o.z); // ---->
            //return o.x * o.y - x * y; // <----
        }

    }

    class test implements Comparable<test> {

        long x;
        long y;



        public test(long x, long y) {
            this.x = x;
            this.y = y;

        }

        @Override
        public int compareTo(test o) {
            //int compareResult = Long.compare(y, o.y); // ---->

            //if (compareResult != 0) {
            //    return -compareResult;
            //}

            int compareResult = Long.compare(x, o.x);

            if (compareResult != 0) {
                return compareResult;
            }

            return Long.compare(y, o.y);

            //return o.x * o.y - x * y; // <----
        }

    }

    class data {
        String name;
        String city;

        data(String name, String city) {
            this.city = city;
            this.name = name;
        }
    }

    class Point {
        double x;
        double y;


        Point(double x, double y) {
            this.x = x;
            this.y = y;

        }

        double distance(Point temp) {
            return Math.sqrt((x - temp.x) * (x - temp.x) + (y - temp.y) * (y - temp.y));
        }

        double sqrDist(Point temp) {
            return ((x - temp.x) * (x - temp.x) + (y - temp.y) * (y - temp.y));
        }

        Point rotate(double alpha) {
            return new Point(x * cos(alpha) - y * sin(alpha), x * sin(alpha) + y * cos(alpha));
        }

        void sum(Point o) {
            x += o.x;
            y += o.y;
        }

        void scalarProduct(int alpha) {
            x *= alpha;
            y *= alpha;
        }

    }

    class Line {
        double a;
        double b;
        double c;

        Line(Point A, Point B) {
            a = B.y - A.y;
            b = A.x - B.x;
            c = -A.x * a - A.y * b;
        }
        Line(double a, double b, double c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

      Point intersection(Line o) {
            double det = a * o.b - b * o.a;
            double det1 = -c * o.b + b * o.c;
            double det2 = -a * o.c + c * o.a;
            return new Point(det1 / det, det2 / det);
        }
    }

 /*   class Plane {
        double a;
        double b;
        double c;
        double d;

        Plane (Point fir, Point sec, Point thi) {
            double del1 = (sec.y - fir.y) * (thi.z - fir.z) - (thi.y - fir.y) * (sec.z - fir.z);
            double del2 = (thi.x - fir.x) * (sec.z - fir.z) - (thi.z - fir.z) * (sec.x - fir.x);
            double del3 = (thi.y - fir.y) * (sec.x - fir.x) - (thi.x - fir.x) * (sec.y - fir.y);
            a = del1;
            b = del2;
            c = del3;
            d = -fir.x * del1 - fir.y * del2 - fir.z * del3;
        }

        double distance(Point point) {
            return abs(a * point.x + b * point.y + c * point.z + d) / sqrt(a * a + b * b + c * c);
        }


    } */

    class record implements Comparable<record> {
        String city;
        Long score;

        public record(String name, Long score) {
            this.city = name;
            this.score = score;
        }

        @Override
        public int compareTo(record o) {
            if (o.city.equals(city)) {
                return 0;
            }

            if (score.equals(o.score)) {
                return 1;
            }

            if (score > o.score) {
                return 666;
            } else {
                return -666;
            }

            //return Long.compare(score, o.score);

        }

    }

    public long gcd(long a, long b) {
        if (a == 0 || b == 0) return max(a, b);

        if (a % b == 0)
            return b;
        else
            return gcd(b, a % b);
    }

    boolean prime(long n) {
        if (n == 1) return false;
        for (int i = 2; i <= sqrt(n); i++)
            if (n % i == 0)
                return false;
        return true;
    }

    public int sum(long n) {
        int s = 0;

        while (n > 0) {
            s += (n % 10);
            n /= 10;
        }

        return s;

    }

 /*   public void simulation(int k) {
        long ans = 0;
        int start = 1;
        for (int i = 0; i < k; i++) {
            start *= 10;
        }
        for (int i = start/10; i < start; i++) {
            int locAns = 0;
            for (int j = start/10; j < start; j++) {
                if  (sum(i + j) == sum(i) + sum(j) ) {
                    ans += 1;
                    locAns += 1;
                } else {
                    //.println(i + "!!!" + j);
                }
            }
            //out.println(i + " " + locAns);
        }
        out.println(ans);
    }*/




    ArrayList<Integer> primes;
    boolean[] isPrime;

    public void getPrimes (int n) {
        isPrime[0] = false;
        isPrime[1] = false;
        for (int i = 2; i <= n; i++) {
            if (isPrime[i]) {
                primes.add(i);
                if (1l * i * i <= n) {
                    for (int j = i * i; j <= n; j += i) {
                        isPrime[j] = false;
                    }
                }
            }
        }
    }




    public long binPowMod(long a, long b, long mod) {
        if (b == 0) {
            return 1 % mod;
        }

        if (b % 2 != 0) {
            return ((a % mod) * (binPowMod(a, b - 1, mod) % mod)) % mod;
        } else {
            long temp = binPowMod(a, b / 2, mod) % mod;
            long ans = (temp * temp) % mod;
            return ans;

        }
    }


    int type[];
    boolean vis[];

    HashMap<Integer, HashSet<Integer>> g;

    int componentNum[];

  /*  void dfs(int u, int numOfComponent) {
        vis[u] = true;
        componentNum[u] = numOfComponent;

        for (Integer v: g.get(u)) {
            if (!vis[v]) {
                dfs(v, numOfComponent);
            }
        }
    } */

    int p[];

    int find(int x) {
        if (x == p[x]) {
            return x;
        }

        return p[x] = find(p[x]);
    }

    boolean merge(int x, int y) {
        x = find(x);
        y = find(y);
        if (p[x] == p[y]) {
            return false;
        }
        p[y] = x;
        return true;
    }

    class Trajectory {
        double x0;
        double y0;
        double vx;
        double vy;


        Trajectory(double vx, double vy, double x0, double y0) {
            this.vx = vx;
            this.vy = vy;

            this.x0 = x0;
            this.y0 = y0;
        }

        double y (double x) {
            return y0 + (x - x0) * (vy / vx) - 5 * (x - x0) * (x - x0) / (vx * vx);
        }

        double der(double x) {
            return (vy / vx) - 10 * (x - x0) / (vx * vx);
        }


    }

    int s;
    int n;
    int m;
    boolean isVisited[][];
    char[][] maze;
    int[] dx = {0, 0, -1, 1};
    int[] dy = {1, -1, 0, 0};

    void dfs(int x, int y) {
        isVisited[x][y] = true;

        for (int i = 0; i < 4; i++) {
            int currX = x + dx[i];
            int currY = y + dy[i];

            if (maze[currX][currY] == '.' && !isVisited[currX][currY]) {
                dfs(currX, currY);
            }

        }

        if (s > 0) {
            maze[x][y] = 'X';
            s -= 1;
        }


    }




    public void solve() throws IOException {

        n = readInt();
        m = readInt();

        s = readInt();

        maze = new char[n + 2][m + 2];
        isVisited = new boolean[n + 2][m + 2];
        for (int i = 0; i < n + 2; i++) {
            maze[i][0] = '#';
            maze[i][m + 1] = '#';
        }

        for (int j = 0; j < m + 2; j++) {
            maze[0][j] = '#';
            maze[n + 1][j] = '#';
        }
        int startX = 1;
        int startY = 1;
        for (int i = 1; i <= n; i++) {
            String temp = readString();
            for (int j = 1; j <= m; j++) {
                maze[i][j] = temp.charAt(j - 1);
                if (maze[i][j] == '.') {
                    startX = i;
                    startY = j;
                }
            }
        }

        dfs(startX, startY);

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                out.print(maze[i][j]);
            }
            out.println();
        }


    }



}