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:
import java.io.*;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
/* * */

public class _603_B implements Runnable{
    public static void main(String[] args) {
	    new Thread(null, new _603_B(),"Main",1<<27).start();
    }
    @Override
    public void run() {
        FastReader fd = new FastReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t = fd.nextInt();
        for(int te = 0; te < t; te++){
            int n = fd.nextInt();
            String[] data = new String[n];
            HashMap<String,Integer> freq = new HashMap<>();
            for(int i = 0; i < n; i++){
                data[i] = fd.next();
                if(!freq.containsKey(data[i])){ freq.put(data[i],1); }
                else{ freq.put(data[i],freq.get(data[i])+1); }
            }

            int count = 0;
            for(int i = 0; i < n; i++){
                if(freq.get(data[i]) > 1){
                    char[] setter = data[i].toCharArray();
                    count++;
                    for(int pos = 0; pos < 4; pos++){
                        int inc = 48;
                        while(freq.containsKey(String.valueOf(setter)) && inc <= 58){
                            setter[pos] = (char) inc; inc++;
                        }
                        if(!freq.containsKey(String.valueOf(setter))){
                            freq.put(data[i],freq.get(data[i])-1);
                            freq.put(String.valueOf(setter),1);
                            data[i] = String.valueOf(setter);
                            break;
                        }
                    }
                }
            }
            out.println(count);
            for(String keys : data){
                out.println(keys);
            }

        }
        out.close();
    }

    //Helper functions
    static void getArray(int[] data, boolean isSorted, FastReader fd){
        for(int i = 0; i < data.length; i++){ data[i] = fd.nextInt(); }
        if(isSorted) Arrays.sort(data);
    }
    static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static int lcm(int a, int b) {
        return (a*b)/gcd(a, b);
    }

    static boolean checkDistinct(int next){// check all digits are distinct.

        String process = String.valueOf(next);
        for(int i = 0;i < process.length()-1; i++){
            String character = String.valueOf(process.charAt(i));
            if(process.substring(i+1).contains(character)){ return false; }
        }
        return true;
    }

    static int limit = (int) 1e7 + 1;
    static int[] facts = new int[limit];
    static void sieve() {  // Store the minimum prime factors of 1 to LIMIT
        facts[1] = 1;
        for (int i = 2; i < limit; i++) {
            if (i % 2 == 0 && i > 2) {
                facts[i] = 2;
            } else {
                facts[i] = i;
            }
        }
        for (int i = 3; i * i < limit; i++) {
            if (facts[i] == i) {
                for (int j = i * i; j < limit; j += i)
                    if (facts[j] == j)
                        facts[j] = i;
            }
        }
    }
    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public FastReader(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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        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 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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            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 readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}