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.BufferedWriter;
	import java.io.IOException;
	import java.io.OutputStreamWriter;
	import java.io.ObjectInputStream.GetField;
	import java.math.BigInteger;
	import java.util.ArrayList;
	import java.util.Arrays;
	import java.util.Collections;
	import java.util.HashMap;
	import java.util.HashSet;
	import java.util.InputMismatchException;
	import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
	import java.util.Stack;
	import java.util.TreeMap;
	import java.util.TreeSet;
public class Q2 {
		static int MOD = 1000000007;
		static boolean b[];
		static boolean boo[][];
		static ArrayList<Integer>[] amp;
		static int sum[][],dist[][];
		static int ans = 0;
		static int p = 0;
		static int color[][];
		static FasterScanner sc = new FasterScanner();
		static Queue<Integer> q = new LinkedList<>();
		static Queue<Pair> qu = new LinkedList<>();
		static ArrayList<Pair>[][] arr;
		static ArrayList<Graph>[] amp1;
		static ArrayList<Integer> parent = new ArrayList<>();
		static BufferedWriter log;
		static HashMap<Long,Long> hm;
		static TreeSet<Long> ts = new TreeSet<>();
		static Stack<Integer> s = new Stack<>();
		static Pair prr[];
		static char ch[][];
		static int prime[];
		static long d,x,y;
		static int n,k,m;
		public static void main(String[] args) throws IOException {
			log = new BufferedWriter(new OutputStreamWriter(System.out));
			n = sc.nextInt(); m = sc.nextInt(); k = sc.nextInt();
			arr = (ArrayList<Pair>[][]) new ArrayList[n][m];
			boo = new boolean[n][m];
			char ch[][] = new char[n][m];
			for(int i = 0; i< n;i ++){
				ch[i] = sc.nextLine().toCharArray();
			}
			int a1 = -1, a2 = -1,cnt =0;
			for(int i = 0; i<n;i++){
				for(int j= 0 ;j<m;j++){
					if(ch[i][j]=='.'){
						p++;
					a1 = i;a2 = j;
					arr[i][j] = new ArrayList<>();
					if(i>0 && ch[i-1][j]=='.') arr[i][j].add(new Pair(i-1,j));
					if(i<n-1 && ch[i+1][j]=='.') arr[i][j].add(new Pair(i+1,j));
					if(j>0 && ch[i][j-1]=='.') arr[i][j].add(new Pair(i,j-1));
					if(j<m-1 && ch[i][j+1]=='.') arr[i][j].add(new Pair(i,j+1));
					}
				}
			}
			if(a1!=-1 && a2!=-1)
			dfs2(a1,a2);
			
			for(int i = 0;i<n;i++){
				for(int j =0;j<m;j++){
					if(ch[i][j]=='.'){
						if(boo[i][j]){
							log.write(".");
						}
						else log.write("X");
					}
					else log.write("#");
				}
				log.write("\n");
			}
			log.close();
		}
		public static void dfs2(int x, int y){
			boo[x][y] = true;
			ans++;
			if(ans==(p-k)){
				return;
			}
			for(Pair e:arr[x][y]){
				if(!boo[e.u][e.v]){
					dfs2(e.u,e.v);
					if(ans==(p-k)){
						return;
					}
				}
			}
		}
		public static void dfs(int x){
			b[x] = true;
			for(int i =0 ;i<amp[x].size();i++){
				if(!b[amp[x].get(i)]){
					dfs(amp[x].get(i));
				}
			}
			
		}
		static void findFactors(ArrayList<Integer> primeDivisors, ArrayList<Integer> multiplicity, int currentDivisor, long currentResult) {
		    if (currentDivisor == primeDivisors.size()) {
		        ts.add(currentResult);
		        return;
		    }
		    for (int i = 0; i <= multiplicity.get(currentDivisor); ++i) {
		        findFactors(primeDivisors, multiplicity, currentDivisor + 1, currentResult);
		        currentResult *= primeDivisors.get(currentDivisor);
		    }
		}
		public static void seive(long n){
			b = new boolean[(int) (n+1)];
			Arrays.fill(b, true);
			b[0] =false;
			b[1] = true;
			for(int i = 2;i*i<=n;i++){
				if(b[i]){
					for(int p = 2*i;p<=n;p+=i){
						b[p] = false;
					}
				}
			}
			for(int i = 0;i<n;i++) if(b[i]) parent.add(i);
		}
		public static void factors(int n){
			b = new boolean[n+1];
			prime = new int[n+1];
			Arrays.fill(b, true);
			b[0] =false;
			b[1] = false;
			for(int i = 2;i*i<=n;i++){
				if(b[i]){
					prime[i] = i;
					for(int p = 2*i;p<=n;p+=i){
						if(b[p]){
						b[p] = false;
						prime[p] = i;
						}
					}
				}
			}
			for(int i = 2;i<=n;i++){
				if(b[i]) prime[i] = i;
			}
		}
		public static void buildWeightedGraph(int m){
			for(int i = 0; i<m;i++){
				int x = sc.nextInt(), y = sc.nextInt(), w = sc.nextInt();
				amp1[--x].add(new Graph(--y,w));
				amp1[y].add(new Graph(x,w));
			}
		}
		public static void extendedEuclidian(long a, long b){
			if(b == 0) {
		        d = a;
		        x = 1;
		        y = 0;
		    }
		    else {
		        extendedEuclidian(b, a%b);
		        int temp = (int) x;
		        x = y;
		        y = temp - (a/b)*y;
		    }
		}
		private static void permutation(String prefix, String str) {
		    int n = str.length();
		   // if (n == 0) ts.add(prefix);
		  //  else {
		        for (int i = 0; i < n; i++)
		            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
		   //}
		}
		public static char give(char c1,char c2){
			if(c1!='a' && c2!='a') return 'a';
			if(c1!='b' && c2!='b') return 'b';
			return 'c';
		}
		static class Graph{
			int vertex;
			long weight;
			Graph(int v,int w){
				vertex = v;
				weight = w;
			}
		}
		public static void buildTree(int n){
			int arr[] = sc.nextIntArray(n);
			for(int i = 0;i<n;i++){
				int x = arr[i]-1;
				amp[i+1].add(x);
				amp[x].add(i+1);
			}
		}
		public static void bfs(int x,long arr[]){
			
			b[x] = true;
			q.add(x);
			while(!q.isEmpty()){
				int y = q.poll();
				for(int i = 0;i<amp[y].size();i++) {
					if(!b[amp[y].get(i)]){
						q.add(amp[y].get(i));
						b[amp[y].get(i)] = true;
					}
				}
			}
		}
			
		public static void buildGraph(int n){
			
			for(int i =0;i<n;i++){
				int x = sc.nextInt(), y = sc.nextInt();
				amp[--x].add(--y);
				amp[y].add(x);
			}
		}
			
		
		static class Pair implements Comparable<Pair> {
			int u;
			int v;
			int z;
			public Pair(){
				
			}
			public Pair(int u, int v) {
				this.u = u;
				this.v = v;
			}
			
			public int hashCode() {
				int hu = (int) (u ^ (u >>> 32));
				int hv = (int) (v ^ (v >>> 32));
				return 31*hu + hv;
			}
	
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return (u == other.u && v == other.v);
			}
	
			public int compareTo(Pair other) {
				return Integer.compare(u, other.u) != 0 ? (Integer.compare(u, other.u)) : (Integer.compare(v, other.v));
			}
			
			public String toString() {
				return "[u=" + u + ", v=" + v + "]";
			}
		}
		static class SegmentTree{
			long st[];
			char ch[];
			SegmentTree(String str, int n){
				int size = 4*n;
				ch = str.toCharArray();
				st = new long[size];
				build(ch,0,n-1,0);
			}
			long build(char str[], int ss, int se, int si){
				if(ss==se){
					st[si] = str[ss]-'0';
					return st[si];
				}
				int mid = (ss+se)/2;
				st[si] = ((build(str,ss,mid,si*2+1)*power(2,se-mid+1,3))%3+build(str,mid+1,se,si*2+2))%3;
				return st[si];
			}
			long get(int qs, int qe, int ss, int se, int si){
				if(qe<ss || qs>se){
					return 0;
				}
				if(qs<=ss && qe>=se) return st[si]*power(2,qe-se+1,3);
				int mid = (ss+se)/2;
	            return ((get(qs,qe,ss,mid,2*si+1))%3+get(qs,qe, mid+1, se, 2*si+2))%3;
			}
			void update(char str[],int ss,int se,int si,int idx){
				if(ss==se){
					st[si] = 1;
					str[idx] = 1;
				}
				else{
					int mid = (ss+se)/2;
					if(ss<=idx && idx<=mid) update(str,ss,mid,2*si+1,idx);
					else update(str,mid+1,se,2*si+2,idx);
					st[si] = ((st[2*si+1]*power(2,se-mid+1,3))%3+st[2*si+1])%3;
				}
			}
			void print(){
				for(int i = 0;i<st.length;i++){
					System.out.print(st[i]+" ");
					System.out.println("----------------------");
				}
			}
		}
		static int convert(int x){
			int cnt = 0;
			String str = Integer.toBinaryString(x);
			//System.out.println(str);
			for(int i = 0;i<str.length();i++){
				if(str.charAt(i)=='1'){
					cnt++;
				}
			}
			int ans = (int) Math.pow(3, 6-cnt);
			return ans;
		}
		static class Node2{
			Node2 left = null;
			Node2 right = null;
			Node2 parent = null;
			int data;
		}
		static class BinarySearchTree{
			Node2 root = null;
			int height = 0;
			int max = 0;
			int cnt = 1;
			ArrayList<Integer> parent = new ArrayList<>();
			HashMap<Integer, Integer> hm = new HashMap<>();
			public void insert(int x){
				Node2 n = new Node2();
				n.data = x;
				if(root==null){
					root = n;
				}
				else{
					Node2 temp = root,temp2 = null;
					while(temp!=null){
						temp2 = temp;
						if(x>temp.data) temp = temp.right;
						else temp = temp.left;
					}
					if(x>temp2.data) temp2.right = n;
					else temp2.left = n;
					n.parent = temp2;
					parent.add(temp2.data);
				}
			}
			public Node2 getSomething(int x, int y, Node2 n){
				if(n.data==x || n.data==y) return n;
				else if(n.data>x && n.data<y) return n;
				else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
				else return getSomething(x,y,n.left);
			}
			public Node2 search(int x,Node2 n){
				if(x==n.data){
					max = Math.max(max, n.data);
					return n;
				}
				if(x>n.data){
					max = Math.max(max, n.data);
					return search(x,n.right);
				}
				else{
					max = Math.max(max, n.data);
					return search(x,n.left);
				}
			}
			public int getHeight(Node2 n){
				if(n==null) return 0;
				height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
				return height;
			}
		}
		static long findDiff(long[] arr, long[] brr, int m){
			int i = 0, j = 0;
			long fa = 1000000000000L;
			while(i<m && j<m){
				long x = arr[i]-brr[j];
				if(x>=0){
					if(x<fa) fa = x;
					j++;
				}
				else{
					if((-x)<fa) fa = -x;
					i++;
				}
			}
			return fa;
		}
		public static long max(long x, long y, long z){
			if(x>=y && x>=z) return x;
			if(y>=x && y>=z) return y;
			return z;
		}
		
		
		static long modInverse(long a, long mOD2){
		            return  power(a, mOD2-2, mOD2);
		}
		static long power(long x, long y, long m)
		{
		    if (y == 0)
		        return 1;
		    long p = power(x, y/2, m) % m;
		    p = (p * p) % m;
		 
		    return (y%2 == 0)? p : (x * p) % m;
		}
		static long power2(long x,BigInteger y,long m){
			long ans = 1;
			BigInteger two = new BigInteger("2");
			while(y.compareTo(BigInteger.ZERO)>0){
				if(y.getLowestSetBit()==y.bitCount()){
					x = (x*x)%MOD;
					y = y.divide(two);
				}
				else{
					ans = (ans*x)%MOD;
					y = y.subtract(BigInteger.ONE);
				}
			}
			return ans;
		}
		static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
			BigInteger ans = new BigInteger("1");
			BigInteger one  = new BigInteger("1");
			BigInteger two  = new BigInteger("2");
			BigInteger zero  = new BigInteger("0");
			while(y.compareTo(zero)>0){
				//System.out.println(y);
				if(y.mod(two).equals(one)){
					ans = ans.multiply(x).mod(m);
					y = y.subtract(one);
				}
				else{
					x = x.multiply(x).mod(m);
					y = y.divide(two);
				}
			}
			return ans;
		}
		static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
		{
		    if (y.equals(0))
		        return (new BigInteger("1"));
		    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
		    p = (p.multiply(p)).mod(m);
		 
		    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
		}
		
		
		public static long gcd(long n, long m){
			if(m!=0) return gcd(m,n%m);
			else return n;
		}
		
		
		public static class FasterScanner {
			private byte[] buf = new byte[1024];
			private int curChar;
			private int numChars;
	 
			public int read() {
				if (numChars == -1)
					throw new InputMismatchException();
				if (curChar >= numChars) {
					curChar = 0;
					try {
						numChars = System.in.read(buf);
					} catch (IOException e) {
						throw new InputMismatchException();
					}
					if (numChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			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 String nextString() {
				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 long nextLong() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = read();
				}
				long 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 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 < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
		        
		    public int[] nextIntArray(int n) {
		        return nextIntArray(n, 0);
		    }
		    
		    public int[] nextIntArray(int n, int off) {
		    	int[] arr = new int[n + off];
		    	for (int i = 0; i < n; i++) {
		    		arr[i + off] = nextInt();
		    	}
		    	return arr;
		    }
		    
		    public long[] nextLongArray(int n) {
		    	return nextLongArray(n, 0);
		    }
	        
			public long[] nextLongArray(int n, int off) {
			    long[] arr = new long[n + off];
			    for (int i = 0; i < n; i++) {
			        arr[i + off] = nextLong();
			    }
			    return arr;
			}
	 
		    private 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;
			}
		}
	}