Problem: A PIN code is a string that consists of exactly 4 digits. Examples of possible PIN codes: 7013, 0000 and 0990. Please note that the PIN code can begin with any digit, even with 0.

Polycarp has n (2 ≤ n ≤ 10) bank cards, the PIN code of the i-th card is p_i.

Polycarp has recently read a recommendation that it is better to set different PIN codes on different cards. Thus he wants to change the minimal number of digits in the PIN codes of his cards so that all n codes would become different.

Formally, in one step, Polycarp picks i-th card (1 ≤ i ≤ n), then in its PIN code p_i selects one position (from 1 to 4), and changes the digit in this position to any other. He needs to change the minimum number of digits so that all PIN codes become different.

Polycarp quickly solved this problem. Can you solve it?

Input

The first line contains integer t (1 ≤ t ≤ 100) — the number of test cases in the input. Then test cases follow.

The first line of each of t test sets contains a single integer n (2 ≤ n ≤ 10) — the number of Polycarp's bank cards. The next n lines contain the PIN codes p_1, p_2, ..., p_n — one per line. The length of each of them is 4. All PIN codes consist of digits only.

Output

Print the answers to t test sets. The answer to each set should consist of a n + 1 lines

In the first line print k — the least number of changes to make all PIN codes different. In the next n lines output the changed PIN codes in the order corresponding to their appearance in the input. If there are several optimal answers, print any of them.

Example

Input


3
2
1234
0600
2
1337
1337
4
3139
3139
3139
3139


Output


0
1234
0600
1
1337
1237
3
3139
3138
3939
6139

Solution (in JAVA):

Solution:
/* Rajkin Hossain */

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class B{
   
    FastInput k = new FastInput(System.in);
    //FastInput k = new FastInput("/home/rajkin/Desktop/input.txt");
    FastOutput z = new FastOutput();
    
    int n;
    Trie trie;
    StringBuilder [] ans;
    
    String [] input;
    
	void startProgram() {
		int t = k.nextInt();
		while(t-->0) {
			n = k.nextInt();
			ans = new StringBuilder[n];
			input = new String[n];
			trie = new Trie();
			
			ArrayList<Integer> collitions = new ArrayList<Integer>();
			
			for(int i = 0; i<n; i++){
				input[i] = k.next();
				boolean cantAdd = trie.addWord(input[i].toCharArray(), i);
				if(cantAdd) {
					collitions.add(i);
				}
			}
			
			for(int i = 0; i<collitions.size(); i++){
				int q = collitions.get(i);
				trie.addWordInEmptySpace(input[q].toCharArray(), q);
			}
			
			z.println(trie.count);
			
			for(int i = 0; i<n; i++) {
				z.println(ans[i]);
			}
		}
    	
    	z.flush();
    	System.exit(0);
    }
	
	public class Trie {
		
		TrieNode root;
		int count;
		
		public Trie(){
			root = new TrieNode();
			count = 0;
		}
		
		public void addWordInEmptySpace(char [] y, int q){
			TrieNode cursor = root;
			
			for(int i = 0; i<y.length; i++){
				
				TrieNode parent = cursor;
				
				cursor = cursor.child[y[i] - '0'];
				
				if(cursor.isTerminated) {
					for(int j = 0; j<10; j++) {
						if(parent.child[j] == null) {
							parent.child[j] = new TrieNode();
							cursor = parent.child[j];
							
							ans[q] = new StringBuilder();
							
							char [] yy = y.clone();
							yy[3] = (char) (j + '0');
							
							for(int ii = 0; ii<4; ii++) {
								ans[q].append(yy[ii]);
							}
							
							count++;
							
							break;
						}
						else if(!parent.child[j].isTerminated) {
							cursor = parent.child[j];
							
							ans[q] = new StringBuilder();
							
							char [] yy = y.clone();
							yy[3] = (char) (j + '0');
							
							for(int ii = 0; ii<4; ii++) {
								ans[q].append(yy[ii]);
							}
							
							count++;
							
							break;
						}
					}
				}
			}
			
			cursor.isTerminated = true;				
		}
		
		public boolean addWord(char [] y, int q){
			TrieNode cursor = root;
			
			for(int i = 0; i<y.length; i++){
				if(cursor.child[y[i] - '0'] == null){
					cursor.child[y[i] - '0'] = new TrieNode();
				}
				
				cursor = cursor.child[y[i] - '0'];
			}
			
			if(!cursor.isTerminated) {
				ans[q] = new StringBuilder();
				
				for(int i = 0; i<4; i++) {
					ans[q].append(y[i]);
				}
				
				cursor.isTerminated = true;
				
				return false;
			}
			
			return true;
		}
		
		class TrieNode {
			TrieNode [] child;
			boolean isTerminated;
			
			public TrieNode(){
				child = new TrieNode[10];
				isTerminated = false;
			}
		}
	}
    
    public static void main(String [] args) throws IOException {
        new Thread(null, new Runnable(){
            public void run(){
            	try{ 
            		new B().startProgram();
            	}
            	catch(Exception e){
            		e.printStackTrace();
            	}
            }
        },"Main",1<<28).start();
    }
    

    /* MARK: FastInput and FastOutput */
 
    class FastInput {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        FastInput(InputStream stream){
            reader = new BufferedReader(new InputStreamReader(stream));
        }
       
        FastInput(String path){
            try {
                reader = new BufferedReader(new FileReader(path));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            tokenizer = null;
        }
 
        String next() {
            return nextToken();
        }
       
        String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
           
            return null;
        }
 
        boolean hasNext(){
            try {
                return reader.ready();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return false;
        }
 
        String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = null;
                try {
                    line = reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(nextToken());
        }
       
        long nextLong() {
            return Long.valueOf(nextToken());
        }
        
        double nextDouble() {
            return Double.valueOf(nextToken());
        }
    }
 
    class FastOutput extends PrintWriter {
		FastOutput() {
			super(new BufferedOutputStream(System.out)); 
		}
		
		public void debug(Object...obj) {
		    System.err.println(Arrays.deepToString(obj));
		}
    }
}