Casimir has a rectangular piece of paper with a checkered field of size n × m. Initially, all cells of the field are white.

Let us denote the cell with coordinates i vertically and j horizontally by (i, j). The upper left cell will be referred to as (1, 1) and the lower right cell as (n, m).

Casimir draws ticks of different sizes on the field. A tick of size d (d > 0) with its center in cell (i, j) is drawn as follows: 

  1. First, the center cell (i, j) is painted black. 
  2. Then exactly d cells on the top-left diagonally to the center and exactly d cells on the top-right diagonally to the center are also painted black. 
  3. That is all the cells with coordinates (i - h, j ± h) for all h between 0 and d are painted. In particular, a tick consists of 2d + 1 black cells. 



An already painted cell will remain black if painted again. Below you can find an example of the 4 × 9 box, with two ticks of sizes 2 and 3.

<image>

You are given a description of a checkered field of size n × m. Casimir claims that this field came about after he drew some (possibly 0) ticks on it. The ticks could be of different sizes, but the size of each tick is at least k (that is, d ≥ k for all the ticks).

Determine whether this field can indeed be obtained by drawing some (possibly none) ticks of sizes d ≥ k or not.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number test cases.

The following lines contain the descriptions of the test cases. 

The first line of the test case description contains the integers n, m, and k (1 ≤ k ≤ n ≤ 10; 1 ≤ m ≤ 19) — the field size and the minimum size of the ticks that Casimir drew. The following n lines describe the field: each line consists of m characters either being '.' if the corresponding cell is not yet painted or '*' otherwise.

Output

Print t lines, each line containing the answer to the corresponding test case. The answer to a test case should be YES if the given field can be obtained by drawing ticks of at least the given size and NO otherwise.

You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes, and YES will all be recognized as positive answers).

Example

Input


8
2 3 1
*.*
...
4 9 2
*.*.*...*
.*.*...*.
..*.*.*..
.....*...
4 4 1
*.*.
****
.**.
....
5 5 1
.....
*...*
.*.*.
..*.*
...*.
5 5 2
.....
*...*
.*.*.
..*.*
...*.
4 7 1
*.....*
.....*.
..*.*..
...*...
3 3 1
***
***
***
3 5 1
*...*
.***.
.**..


Output


NO
YES
YES
YES
NO
NO
NO
NO

Note

The first sample test case consists of two asterisks neither of which can be independent ticks since ticks of size 0 don't exist.

The second sample test case is already described in the statement (check the picture in the statement). This field can be obtained by drawing ticks of sizes 2 and 3, as shown in the figure.

The field in the third sample test case corresponds to three ticks of size 1. Their center cells are marked with \color{blue}{blue}, \color{red}{red} and \color{green}{green} colors: *.*.  
---  
*\color{blue}{*}**  
.\color{green}{*}\color{red}{*}.  
....  
  
The field in the fourth sample test case could have been obtained by drawing two ticks of sizes 1 and 2. Their vertices are marked below with \color{blue}{blue} and \color{red}{red} colors respectively: .....  
---  
*...*  
.*.*.  
..\color{red}{*}.*  
...\color{blue}{*}.  
  
The field in the fifth sample test case can not be obtained because k = 2, and the last asterisk in the fourth row from the top with coordinates (4, 5) can only be a part of a tick of size 1.

The field in the sixth sample test case can not be obtained because the top left asterisk (1, 1) can't be an independent tick, since the sizes of the ticks must be positive, and cannot be part of a tick with the center cell in the last row, since it is separated from it by a gap (a point, '.') in (2, 2).

In the seventh sample test case, similarly, the field can not be obtained by the described process because the asterisks with coordinates (1, 2) (second cell in the first row), (3, 1) and (3, 3) (leftmost and rightmost cells in the bottom) can not be parts of any ticks.
    import java.io.BufferedReader;
    import java.io.FileInputStream;
    import java.io.FileNotFoundException;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.util.*;

    import javax.print.attribute.HashAttributeSet;
import javax.swing.JLabel;

import java.io.PrintStream;
            
                public class Solution {

                    public static boolean Local(){
                        try{ 
                            return System.getenv("LOCAL_SYS")!=null;
                        }catch(Exception e){
                            return false;
                        }
                    }   

                    public static boolean LOCAL;

                    static class FastScanner {

                            BufferedReader br;
                            StringTokenizer st ;

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

                            FastScanner(String file) {

                                try{
                                    br =  new BufferedReader(new InputStreamReader(new FileInputStream(file)));
                                    st = new StringTokenizer("");
                                }catch(FileNotFoundException e) {
                                    // TODO Auto-generated catch block
                                    System.out.println("file not found");
                                    e.printStackTrace();
                                }
                                
                            }
                            

                            String next() {
                                while (!st.hasMoreTokens())
                                    try {
                                        st = new StringTokenizer(br.readLine());
                                    } catch (IOException e) {
                                    }
                                return st.nextToken();
                            }

                            int nextInt() {
                                return Integer.parseInt(next());
                            }

                            long nextLong() {
                                return Long.parseLong(next());
                            }
                            String readLine() throws IOException{
                                return br.readLine();
                            }
                        }
                                            
                    static class Pair<T,X> {

                        T first;
                        X second;
                        
                        Pair(T first,X second){
                            this.first = first;
                            this.second = second;
                        }

                        @Override
                        public int hashCode(){
                            return Objects.hash(first,second);
                        }

                        @Override
                        public boolean equals(Object obj){
                            return obj.hashCode() == this.hashCode();
                        }

                    }

                
                static PrintStream debug = null;
                
                
                static long mod = (long)(Math.pow(10,9) + 7); 
                

                public static void main(String[] args) throws Exception {
                    
                    FastScanner s = new FastScanner();

                    LOCAL = Local();

                    
                    if(LOCAL){
                        s = new FastScanner("src/input.txt");
                        PrintStream o = new PrintStream("src/sampleout.txt");
                        debug = new PrintStream("src/debug.txt");
                        System.setOut(o);
                    }

                    long mod = 1000000007;

                

                
                    int tcr = s.nextInt();                  
                    
                    StringBuilder sb = new StringBuilder();

                    for(int tc=0;tc<tcr;tc++){
                        int n = s.nextInt();
                        int m = s.nextInt();
                        int k = s.nextInt();
                        String arr[] = new String[n];
                        
                        for(int i=0;i<n;i++){
                            arr[i] = s.next();
                        }

                        dbg(debug,arr);

                        boolean covered[][] = new boolean[n][m];

                        boolean poss = true;
                        //println(n+" "+m);
                        for(int i=0;i<n;i++){
                            for(int j=0;j<m;j++){

                                if(arr[i].charAt(j) == '*'){
                                   
                                    boolean start = true;
                                    
                                    //println(i+""+j);

                                    if((i+1<n && j+1<m && arr[i+1].charAt(j+1) == '*')  && (i+1<n && j-1>=0 && arr[i+1].charAt(j-1) == '*')){
                                        start = false;
                                    }
                                    
                                    if(start){
                                        //println(i+" "+j);
                                        if(!go(arr,i,j,covered,k)){
                                            poss = false;break;
                                        }
                                    }

                                }
                            }
                            if(!poss){break;}
                        }

                        // println("here"+" -"+(poss)+(tc));

                        for(int i=0;i<n;i++){
                            for(int j=0;j<m;j++){
                                if(arr[i].charAt(j)=='*'&& (!covered[i][j])){
                                    poss = false;break;
                                }
                            }
                        }

                        if(poss){
                            sb.append("YES\n");
                        }else{
                            sb.append("NO\n");
                        }
                    }

                    print(sb.toString());
                }

                public static boolean go(String arr[],int i,int j,boolean covered[][],int k){

                    int ti = i;
                    int tj = j;
                    
                    int cnt = 0;

                    while(ti >=0 && tj >= 0){
                        if(arr[ti].charAt(tj) == '*'){
                            ti--;
                            tj--;
                            cnt++;
                        }else{
                            break;
                        }
                    }

                    int cnt2 = 0;
                    ti = i;
                    tj = j;
                    while(ti >=0 && tj < arr[0].length()){
                        if(arr[ti].charAt(tj) == '*'){
                            ti--;
                            tj++;
                            cnt2++;
                        }else{
                            break;
                        }
                    }

                    int max_poss = Math.min(cnt,cnt2);

                    if((max_poss - 1) < k){return true;}

                    ti = i;
                    tj = j;
                    int cr = 0;
                    while(cr < max_poss){
                        if(arr[ti].charAt(tj) == '*'){
                            covered[ti][tj] = true;
                            ti--;
                            tj++;
                        }
                        cr++;
                    }

                    ti = i;
                    tj = j;
                    cr = 0;
                    while(cr < max_poss){
                        if(arr[ti].charAt(tj) == '*'){
                            covered[ti][tj] = true;
                            ti--;
                            tj--;
                        }
                        cr++;
                    }

                    return true;
                }
                

                public static List<long[]> prime_factors(long n){
            
                    List<long[]> list = new ArrayList<>();
                    
                    for(long i=2;i<=(Math.sqrt(n));i++){
            
                        if(n % i == 0){
                            
                            int cnt = 0;
                            
                            while( (n % i) == 0){
                                n = n/i;
                                cnt++;
                                
                            }
            
                            list.add(new long[]{i,cnt});
                        }
                    }

            
                    if(n!=1){
                        list.add(new long[]{n,1l});
                    }
            
                    return list;
            
                }

                public static boolean check(int arr[]){
                    for(int i=1;i<arr.length;i++){
                        if(arr[i] < arr[i-1]){
                            return false;
                        }
                    }
                    return true;
                }

            
                public static boolean inRange(int r1,int r2,int val){
                    return ((val >= r1) && (val <= r2));
                }

                static int len(long num){
                    return Long.toString(num).length();
                }

                static long mulmod(long a, long b,long mod)
                {
                    long ans = 0l;
                    
                    while(b > 0){
                        long curr = (b & 1l);
                        if(curr == 1l){
                            ans = ((ans % mod) + a) % mod;
                        }
                        
                        a = (a + a) % mod;

                        b = b >> 1;
                    }

                    return ans;
                }


                public static void dbg(PrintStream ps,Object... o) throws Exception{
                    if(ps == null){
                        return;
                    }
                    Debug.dbg(ps,o);
                }

                public static long modpow(long num,long pow,long mod){

                    long val = num;
                    long ans = 1l;

                    while(pow > 0l){
                        
                        long bit = pow & 1l;

                        if(bit == 1){
                            ans = (ans * (val%mod))%mod;
                        }

                        val = (val * val) % mod;
                        pow = pow >> 1;
                    }

                    return ans;

                }

                public static char get(int n){
                    return (char)('a' + n);
                }

                public static long[] sort(long arr[]){
                    List<Long> list = new ArrayList<>();
                    for(long n : arr){list.add(n);}
                    Collections.sort(list);
                    for(int i=0;i<arr.length;i++){
                        arr[i] = list.get(i);
                    }
                    return arr;
                }

                public static int[] sort(int arr[]){
                    List<Integer> list = new ArrayList<>();
                    for(int n : arr){list.add(n);}
                    Collections.sort(list);
                    for(int i=0;i<arr.length;i++){
                        arr[i] = list.get(i);
                    }
                    return arr;
                }

                // return the (index + 1)
                // where index is the pos of just smaller element
                // i.e count of elemets strictly less than num
                public static int justSmaller(long arr[],long num){
                    //  System.out.println(num+"@");
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = -1;
            
                    while(st <= e){
            
                        int mid = (st + e)/2;
            
                        if(arr[mid] >= num){
                            e = mid - 1;
                        }else{
                            ans = mid;
                            st = mid + 1;
                        }
            
                    }
            
            
                    return ans + 1;
            
                }
                public static int justSmaller(int arr[],int num){
                    //  System.out.println(num+"@");
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = -1;
            
                    while(st <= e){
            
                        int mid = (st + e)/2;
            
                        if(arr[mid] >= num){
                            e = mid - 1;
                        }else{
                            ans = mid;
                            st = mid + 1;
                        }
            
                    }
            
            
                    return ans + 1;
            
                }
                
                //return (index of just greater element)
                //count of elements smaller than or equal to num

                public static int justGreater(long arr[],long num){
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = arr.length;
            
                    while(st <= e){
                        
                        int mid = (st + e)/2;
            
                        if(arr[mid] <= num){
                            st = mid + 1;
                        }else{
                            ans = mid;
                            e = mid - 1;
                        }
                    }
            
                    return ans;
            
                }

                public static int justGreater(int arr[],int num){
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = arr.length;
            
                    while(st <= e){
                        
                        int mid = (st + e)/2;
            
                        if(arr[mid] <= num){
                            st = mid + 1;
                        }else{
                            ans = mid;
                            e = mid - 1;
                        }
                    }
            
                    return ans;
            
                }
            
                

                public static void println(Object obj){
                    System.out.println(obj.toString());
                }

                public static void print(Object obj){
                    System.out.print(obj.toString());
                }

                public static int gcd(int a,int b){
                    if(b == 0){return a;}
                    return gcd(b,a%b);
                }

                public static long gcd(long a,long b){
                    if(b == 0l){
                        return a;
                    }

                    return gcd(b,a%b);
                }

                public static int find(int parent[],int v){
                    if(parent[v] == v){
                        return v;
                    }
                    
                    return parent[v] = find(parent, parent[v]);
                }

            

                public static List<Integer> sieve(){
                
                        List<Integer> prime = new ArrayList<>();

                        int arr[] = new int[100001];

                    Arrays.fill(arr,1);

                    arr[1] = 0;
                    arr[2] = 1;

                    for(int i=2;i<=100000;i++){
                        
                        if(arr[i] == 1){
                            
                            prime.add(i);

                            for(long j = (i*1l*i);j<100001;j+=i){
                                arr[(int)j] = 0;
                            }
                        }
                    }

                    return prime;
                }

                static boolean isPower(long n,long a){
                    
                    long log = (long)(Math.log(n)/Math.log(a));

                    long power = (long)Math.pow(a,log);

                    if(power == n){return true;}

                    return false;
                }


                private static int mergeAndCount(int[] arr, int l,int m, int r)
                {

                    // Left subarray
                    int[] left =  Arrays.copyOfRange(arr, l, m + 1);

                    // Right subarray
                    int[] right = Arrays.copyOfRange(arr, m + 1, r + 1);

                    int i = 0, j = 0, k = l, swaps = 0;

                    while (i < left.length && j < right.length) {
                        if (left[i] <= right[j])
                            arr[k++] = left[i++];
                        else {
                            arr[k++] = right[j++];
                            swaps += (m + 1) - (l + i);
                        }
                    }
                    while (i < left.length)
                        arr[k++] = left[i++];
                    while (j < right.length)
                        arr[k++] = right[j++];
                    return swaps;
                }

                // Merge sort function
                private static int mergeSortAndCount(int[] arr, int l,int r)
                {

                    // Keeps track of the inversion count at a
                    // particular node of the recursion tree
                    int count = 0;

                    if (l < r) {
                        int m = (l + r) / 2;

                        // Total inversion count = left subarray count
                        // + right subarray count + merge count

                        // Left subarray count
                        count += mergeSortAndCount(arr, l, m);

                        // Right subarray count
                        count += mergeSortAndCount(arr, m + 1, r);

                        // Merge count
                        count += mergeAndCount(arr, l, m, r);
                    }

                    return count;
                }

                static class Debug{
                    //change to System.getProperty("ONLINE_JUDGE")==null; for CodeForces
                    public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;

                    

                    private static <T> String ts(T t) {
                        if(t==null) {
                            return "null";
                        }
                        try {
                            return ts((Iterable) t);
                        }catch(ClassCastException e) {
                            if(t instanceof int[]) {
                                String s = Arrays.toString((int[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof long[]) {
                                String s = Arrays.toString((long[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof char[]) {
                                String s = Arrays.toString((char[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof double[]) {
                                String s = Arrays.toString((double[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof boolean[]) {
                                String s = Arrays.toString((boolean[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }
                            try {
                                return ts((Object[]) t);
                            }catch(ClassCastException e1) {
                                return t.toString();
                            }
                        }
                    }
                    private static <T> String ts(T[] arr) {
                        StringBuilder ret = new StringBuilder();
                        ret.append("{");
                        boolean first = true;
                        for(T t: arr) {
                            if(!first) {
                                ret.append(", ");
                            }
                            first = false;
                            ret.append(ts(t));
                        }
                        ret.append("}");
                        return ret.toString();
                    }
                    private static <T> String ts(Iterable<T> iter) {
                        StringBuilder ret = new StringBuilder();
                        ret.append("{");
                        boolean first = true;
                        for(T t: iter) {
                            if(!first) {
                                ret.append(", ");
                            }
                            first = false;
                            ret.append(ts(t));
                        }
                        ret.append("}");
                        return ret.toString();
                    }
                    public static void dbg(PrintStream ps,Object... o) throws Exception {
                        if(LOCAL) {
                            System.setErr(ps);
                            System.err.print("Line #"+Thread.currentThread().getStackTrace()[2].getLineNumber()+": [");
                            for(int i = 0; i<o.length; i++) {
                                if(i!=0) {
                                    System.err.print(", ");
                                }
                                System.err.print(ts(o[i]));
                            }
                            System.err.println("]");
                        }
                    }
                }

        }