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.*;

public class pin {
    public static void main(String s[]) throws Exception {
        Reader r = new Reader();
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = r.nextInt();
        while(t-->0){
            HashMap<Integer,Integer> freq=new HashMap<Integer, Integer>();
            int n=r.nextInt();
            int arr[]=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=r.nextInt();
                Integer co=freq.get(arr[i]);
                if(co==null)
                    freq.put(arr[i],1);
                else
                    freq.put(arr[i],co+1);
            }
            //Arrays.sort(arr);
            int counter=arr.length-freq.size();
            for(int i=1;i<n;i++){
                if(freq.size()==n)
                    break;
                int ff=freq.get(arr[i]);
                if(ff>1){
                    freq.put(arr[i],ff-1);
                    int temp[]=new int[10];
                    boolean flag=true;
                    for(int j=0;j<4 && flag;j++){
                        change(arr[i],temp,j);
                        for(int k=0;k<10&&flag;k++){
                            if(!freq.containsKey(temp[k])){
                                flag=false;
                                freq.put(temp[k],1);
                                arr[i]=temp[k];
                            }
                        }
                    }
                }
            }

            Iterator<Map.Entry<Integer,Integer>> it=freq.entrySet().iterator();
            System.out.println(counter);
//            while(it.hasNext()){
//                String st=String.valueOf(it.next().getKey());
//                while (st.length()<4)
//                    st="0"+st;
//                System.out.println(st);
//            }
//            //System.out.println();
            for(int i=0;i<n;i++){
                String st=String.valueOf(arr[i]);
                while(st.length()<4)
                    st="0"+st;
                System.out.println(st);
            }
        }
    }

    public static void change(int num,int arr[],int pos){
        char[] a=String.valueOf(num).toCharArray();
        for(int i=0;i<10;i++){
            a[pos]=(char)('0'+i);
            arr[i]=Integer.parseInt(new String(a));
        }
    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}