Problem: The length of the longest common prefix of two strings s = s_1 s_2 … s_n and t = t_1 t_2 … t_m is defined as the maximum integer k (0 ≤ k ≤ min(n,m)) such that s_1 s_2 … s_k equals t_1 t_2 … t_k.

Koa the Koala initially has n+1 strings s_1, s_2, ..., s_{n+1}.

For each i (1 ≤ i ≤ n) she calculated a_i — the length of the longest common prefix of s_i and s_{i+1}.

Several days later Koa found these numbers, but she couldn't remember the strings.

So Koa would like to find some strings s_1, s_2, ..., s_{n+1} which would have generated numbers a_1, a_2, ..., a_n. Can you help her?

If there are many answers print any. We can show that answer always exists for the given constraints. 

Input

Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 100) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100) — the number of elements in the list a.

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 50) — the elements of a.

It is guaranteed that the sum of n over all test cases does not exceed 100.

Output

For each test case:

Output n+1 lines. In the i-th line print string s_i (1 ≤ |s_i| ≤ 200), consisting of lowercase Latin letters. Length of the longest common prefix of strings s_i and s_{i+1} has to be equal to a_i.

If there are many answers print any. We can show that answer always exists for the given constraints.

Example

Input


4
4
1 2 4 2
2
5 3
3
1 3 1
3
0 0 0


Output


aeren
ari
arousal
around
ari
monogon
monogamy
monthly
kevinvu
kuroni
kurioni
korone
anton
loves
adhoc
problems

Note

In the 1-st test case one of the possible answers is s = [aeren, ari, arousal, around, ari].

Lengths of longest common prefixes are:

  * Between \color{red}{a}eren and \color{red}{a}ri → 1 
  * Between \color{red}{ar}i and \color{red}{ar}ousal → 2 
  * Between \color{red}{arou}sal and \color{red}{arou}nd → 4 
  * Between \color{red}{ar}ound and \color{red}{ar}i → 2 

Solution (in JAVA):

Solution:
import java.util.*;		
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.*;
import java.math.*;
public class Main7{
	static public void main(String args[])throws IOException{
		int tt=i();
		StringBuilder sb=new StringBuilder();
		for(int ttt=1;ttt<=tt;ttt++){
			int n=i();
			int[] a=new int[n];
			for(int i=0;i<n;i++){
				a[i]=i();
			}
			String[] s=new String[n+1];
			int num=a[0];
			StringBuilder sb1=new StringBuilder();
			for(int i=0;i<51;i++){
				sb1.append('a');
			}
			s[0]=sb1.toString();
			for(int r=1;r<=n;r++){
				num=a[r-1];
				sb1=new StringBuilder();
				if(num==0){
					if(s[r-1].charAt(0)=='a'){
						sb1.append('b');
						for(int i=1;i<51;i++){
							sb1.append('a');
						}
					}else{
						sb1.append('a');
						for(int i=1;i<51;i++){
							sb1.append('b');
						}
					}
				}else{
					for(int j=0;j<num;j++){
						sb1.append(s[r-1].charAt(j));
					}
					for(int j=num;j<51;j++){
						if(s[r-1].charAt(num)=='a'){
							sb1.append('b');
						}else{
							sb1.append('a');
						}
					}
				}
				s[r]=sb1.toString();
			}
			for(int i=0;i<=n;i++){
				sb.append(s[i]+"\n");
			}
		}
		System.out.print(sb.toString());
	}
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	static ArrayList<ArrayList<Integer>> graph;
	static int mod=1000000007;
	static class Pair{
		int x;
		int y;
		Pair(int x,int y){
			this.x=x;
			this.y=y;
		}
		/*@Override
		public int hashCode() 
		{ 
			final int temp = 14; 
			int ans = 1; 
			ans =x*31+y*13; 
			return (int)ans;
		}
       @Override
        public boolean equals(Object o) 
        { 
            if (this == o) { 
                return true; 
            } 
            if (o == null) { 
                return false; 
            } 
            if (this.getClass() != o.getClass()) { 
                return false; 
            } 
            Pair other = (Pair)o; 
            if (this.x != other.x || this.y!=other.y) { 
                return false; 
            } 
            return true; 
        }*/
	}
	public static long[] sort(long[] a){
		int n=a.length;
		ArrayList<Long> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++){
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++){
			a[i]=ar.get(i);
		}
		return a;
	}
	public static long pow(long a, long b){
        long result=1;
        while(b>0){
            if (b % 2 != 0){
                result=(result*a);
                b--;
            } 
            a=(a*a);
            b /= 2;
        }   
        return result;
    }
	public static long gcd(long a, long b){
        if (a == 0){
            return b;
		}
        return gcd(b%a, a);
    }
	public static long lcm(long a, long b){
		return a*(b/gcd(a,b));
	}
	public static long l(){
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value){
		System.out.println(value);
	}
	public static int i(){
		return in.Int();
	}
	public static String s(){
		return in.String();
	}
}
class InputReader 
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	public InputReader(InputStream stream) {
		this.stream = stream;
	}
	public int read() {
		if (numChars== -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
	public int Int() {
		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 String String() {
		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 boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	} 
	public String next() {
		return String();
	} 
	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}
class OutputWriter {
	private final PrintWriter writer;
	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}
	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}
	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}
	public void close() {
		writer.close();
	}
	public void flush() {
		writer.flush();
	}
 }
class IOUtils {
	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.Int();
		return array;
	}
}