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.Writer;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;
import java.util.concurrent.TimeUnit;

public class B1263{
  static class pair{
    int val, idx;
    pair(int a, int b){
      val=a;
      idx=b;
    }
    public String toString(){
      return "(val: "+val+" idx: "+idx+")";
    }
  }


  static class ProblemSolver{
    public void solveTheProblem(InputReader in,OutputWriter out, NumberTheory nt, Debug dbg){
      dbg.setLocal(1);
      int test=in.nextInt();
      while(test-- >0){
        int n, k;
        n=in.nextInt();
        HashSet<String> hs= new HashSet<>();
        HashSet<String> exist= new HashSet<>();
        ArrayList<String> ans=new ArrayList<>();
        ArrayList<String> str=new ArrayList<>();
        int cnt=0;

        for(int i=0;i<n;i++){
          String temp=in.nextLine();
          str.add(temp);
          exist.add(temp);
        }
        for(int i=0;i<n;i++){
          String temp=str.get(i);
          if(hs.contains(temp)){
            // System.out.println("----------START----------  "+temp);
            String num= temp.substring(0, 3);
            int j=0;
            while(hs.contains(temp) || exist.contains(temp)){
              temp= num+((char)(('0'+j)));
              j++;
              // System.out.println("temp: "+temp+" cnt: "+cnt);
            }
            cnt++;
            // System.out.println("----------END----------");
          }
          ans.add(temp);
          hs.add(temp);
        }
        out.println(cnt);
        for(String i: ans) out.println(i);
      }
    }
  }

  public static void main(String[] args){
    int checkTimeELAPSED=0;
    if(checkTimeELAPSED==0){
      InputStream inputStream=System.in;
      OutputStream outputStream=System.out;
      Debug debug= new Debug();
      InputReader in=new InputReader(inputStream);
      OutputWriter out=new OutputWriter(outputStream);
      NumberTheory nt= new NumberTheory();
      ProblemSolver problemSolver=new ProblemSolver();
      problemSolver.solveTheProblem(in,out, nt, debug);
      out.flush();
      out.close();
    }
    else{
      long startTime = System.nanoTime();
      InputStream inputStream=System.in;
      OutputStream outputStream=System.out;
      Debug debug= new Debug();
      InputReader in=new InputReader(inputStream);
      OutputWriter out=new OutputWriter(outputStream);
      NumberTheory nt= new NumberTheory();
      ProblemSolver problemSolver=new ProblemSolver();
      problemSolver.solveTheProblem(in,out,nt,debug);
      long endTime = System.nanoTime();
      long timeElapsed = endTime - startTime;
      out.println("Execution time in nanoseconds  : " + timeElapsed);
  		out.println("Execution time in milliseconds : "+ timeElapsed / 1000000);
      out.println("Execution time in seconds : "+ timeElapsed / 1000000000);
      out.flush();
      out.close();
    }
  }
  @SuppressWarnings({"unchecked", "static-access", "all", "StaticQualifiedUsingExpression"})
  static class Debug {
	//change to System.getProperty("ONLINE_JUDGE")==null; for CodeForces
    public static boolean LOCAL;
    public void setLocal(int a){
      if(a==1) LOCAL=false;
      else LOCAL=System.getProperty("user.home").toString().equals("C:\\Users\\Hp");
    }
  	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)+"}";
  			}else if(t instanceof long[]) {
  				String s = Arrays.toString((long[]) t);
  				return "{"+s.substring(1, s.length()-1)+"}";
  			}else if(t instanceof char[]) {
  				String s = Arrays.toString((char[]) t);
  				return "{"+s.substring(1, s.length()-1)+"}";
  			}else if(t instanceof double[]) {
  				String s = Arrays.toString((double[]) t);
  				return "{"+s.substring(1, s.length()-1)+"}";
  			}else if(t instanceof boolean[]) {
  				String s = Arrays.toString((boolean[]) t);
  				return "{"+s.substring(1, s.length()-1)+"}";
  			}
  			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 void dbg(Object... o) {
  		if(LOCAL) {
  			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("]");
  		}
  	}
  }

  static class InputReader {
    private boolean finished = false;

    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 peek() {
      if (numChars == -1) {
        return -1;
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          return -1;
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar];
    }

    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 String nextLine() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        if (Character.isValidCodePoint(c)) {
          res.appendCodePoint(c);
        }
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
      StringBuilder buf = new StringBuilder();
      int c = read();
      while (c != '\n' && c != -1) {
        if (c != '\r') {
          buf.appendCodePoint(c);
        }
        c = read();
      }
      return buf.toString();
    }

    public String readLine() {
      String s = readLine0();
      while (s.trim().length() == 0) {
        s = readLine0();
      }
      return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
      if (ignoreEmptyLines) {
        return readLine();
      } else {
        return readLine0();
      }
    }

    public BigInteger readBigInteger() {
      try {
        return new BigInteger(nextLine());
      } catch (NumberFormatException e) {
        throw new InputMismatchException();
      }
    }

    public char nextCharacter() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      return (char) c;
    }

    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 boolean isExhausted() {
      int value;
      while (isSpaceChar(value = peek()) && value != -1) {
        read();
      }
      return value == -1;
    }

    public String next() {
      return nextLine();
    }

    public SpaceCharFilter getFilter() {
      return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
      this.filter = filter;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);
    }
    public int[] nextIntArray(int n){
      int[] array=new int[n];
      for(int i=0;i<n;++i)array[i]=nextInt();
      return array;
    }
    public int[] nextSortedIntArray(int n){
      int array[]=nextIntArray(n);
      Arrays.sort(array);
      return array;
    }
    public ArrayList<Integer> nextIntArrayList(int n){
      ArrayList<Integer> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
      ar.add(nextInt());
      return ar;
    }
    public ArrayList<Long> nextLongArrayList(int n){
      ArrayList<Long> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
      ar.add(nextLong());
      return ar;
    }

    public int[] nextSumIntArray(int n){
      int[] array=new int[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextLongArray(int n){
      long[] array=new long[n];
      for(int i=0;i<n;++i)array[i]=nextLong();
      return array;
    }
    public long[] nextSumLongArray(int n){
      long[] array=new long[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextSortedLongArray(int n){
      long array[]=nextLongArray(n);
      Arrays.sort(array);
      return array;
    }
    public int[][] nextIntMatrix(int n,int m){
      int[][] matrix=new int[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextInt();
      return matrix;
    }

    public int[][] nextIntMatrix(int n){
      return nextIntMatrix(n,n);
    }

    public long[][] nextLongMatrix(int n,int m){
      long[][] matrix=new long[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextLong();
      return matrix;
    }

    public long[][] nextLongMatrix(int n){
      return nextLongMatrix(n,n);
    }

    public char[][] nextCharMatrix(int n,int m){
      char[][] matrix=new char[n][m];
      for(int i=0;i<n;++i)
      matrix[i]=next().toCharArray();
      return matrix;
    }

    public char[][] nextCharMatrix(int n){
      return nextCharMatrix(n,n);
    }
  }

  static 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(char[] array) {
    //     writer.print(array);
    // }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void print(int[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(double[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(long[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(char[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(String[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(int[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(double[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(long[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(char[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(String[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void println(int[] array) {
      print(array);
      writer.println();
    }

    public void println(double[] array) {
      print(array);
      writer.println();
    }

    public void println(long[] array) {
      print(array);
      writer.println();
    }

    // public void println(char[] array) {
    //     print(array);
    //     writer.println();
    // }

    public void println(String[] array) {
      print(array);
      writer.println();
    }

    public void println() {
      writer.println();
    }

    public void println(Object... objects) {
      print(objects);
      writer.println();
    }

    public void print(char i) {
      writer.print(i);
    }

    public void println(char i) {
      writer.println(i);
    }

    public void println(char[] array) {
      writer.println(array);
    }

    public void printf(String format, Object... objects) {
      writer.printf(format, objects);
    }

    public void close() {
      writer.close();
    }

    public void flush() {
      writer.flush();
    }

    public void print(long i) {
      writer.print(i);
    }

    public void println(long i) {
      writer.println(i);
    }

    public void print(int i) {
      writer.print(i);
    }

    public void println(int i) {
      writer.println(i);
    }

    public void separateLines(int[] array) {
      for (int i : array) {
        println(i);
      }
    }
  }
  static class NumberTheory{

    /**
    * Modular Arithmetic:
    *  1. (a+b)%c=(a%c+b%c)%c
    *  2. (a*b)%c=(a%c*b%c)%c
    *  3. (a-b)%c=(a%c-b%c+c)%c
    *  4. (a/b)%c=(a%c*(b^-1)%c)%c -- (b^-1 is multiplicative modulo inverse)
    */
    //Modular Addition
    public int modularAddition(int a,int b,int MOD){
      return (a%MOD+b%MOD)%MOD;
    }
    public long modularAddition(long a,long b,long MOD){
      return (a%MOD+b%MOD)%MOD;
    }
    //Modular Multiplication
    public int modularMultiplication(int a,int b,int MOD){
      return ((a%MOD)*(b%MOD))%MOD;
    }
    public long modularMultiplication(long a,long b,long MOD){
      return ((a%MOD)*(b%MOD))%MOD;
    }
    //Modular Subtraction
    public int modularSubtraction(int a,int b,int MOD){
      return (a%MOD-b%MOD+MOD)%MOD;
    }
    public long modularSubtraction(long a,long b,long MOD){
      return (a%MOD-b%MOD+MOD)%MOD;
    }

    /**
    * Binary Exponentiation
    */
    public int binaryExponentiation(int x,int n){
      if(n==0)return 1;
      else if(n%2==0)return binaryExponentiation(x*x,n/2);
      else return x*binaryExponentiation(x*x,(n-1)/2);
    }
    public long binaryExponentiation(long x,long n){
      long result=1;
      while(n>0){
        if(n%2==1)result*=x;
        x=x*x;
        n/=2;
      }
      return result;
    }

    /**
    * Modular Exponentiation
    */
    public int modularExponentiation(int x,int n,int MOD){
      if(n==0)return 1%MOD;
      else if(n%2==0)return modularExponentiation(modularMultiplication(x,x,MOD),n/2,MOD);
      else return modularMultiplication(x,modularExponentiation(modularMultiplication(x,x,MOD),(n-1)/2,MOD),MOD);
    }
    public long modularExponentiation(long x,long n,long MOD){
      long result=1;
      while(n>0){
        if(n%2==1)result=modularMultiplication(result,x,MOD);
        x=modularMultiplication(x,x,MOD);
        n/=2;
      }
      return result;
    }

    /**
    * Factorial of a number
    */
    public long factorials(long n){
      if(n==0)return 1;
      return n*factorials(n-1);
    }

    /**
    * Prime factors of a number
    */
    public ArrayList<Integer> distinctPrimeFactors(int n){
      ArrayList<Integer> factorials=new ArrayList<>();
      int limit=(int)Math.sqrt(n);
      if(n%2==0){
        factorials.add(2);
        while(n%2==0)n/=2;
      }
      for(int i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Long> distinctPrimeFactors(long n){
      ArrayList<Long> factorials=new ArrayList<>();
      long limit=(long)Math.sqrt(n);
      if(n%2==0){
        factorials.add((long)2);
        while(n%2==0)n/=2;
      }
      for(long i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Integer> primeFactors(int n){
      ArrayList<Integer> factorials=new ArrayList<>();
      int limit=(int)Math.sqrt(n);
      if(n%2==0){
        factorials.add(2);
        while(n%2==0)n/=2;
      }
      for(int i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Long> primeFactors(long n){
      ArrayList<Long> factorials=new ArrayList<>();
      long limit=(long)Math.sqrt(n);
      if(n%2==0){
        factorials.add((long)2);
        while(n%2==0)n/=2;
      }
      for(long i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    /**
    * Combination: nCr
    */
    //Naive version
    //(n,r)=(n-1,r-1)+(n-1,r) for r!=0 or r!=n
    //(n,0)=(n,n)=1
    public int binomialCoefficientRecursive(int n,int k){
      if(k==0 || k==n)return 1;//base case
      return binomialCoefficientRecursive(n-1,k-1)+binomialCoefficientRecursive(n-1,k);//recursion
    }

    //Dynamic Programming version(Uses bottom up approach to fill the table)
    //Time complexity: O(n*k)
    //Space complexity: O(n*k)
    public long binomialCoefficientIterative(int n,int k){
      long[][] C=new long[n+1][k+1];
      for(int i=0;i<=n;++i){
        for(int j=0;j<=Math.min(n,k);++j){
          if(j==0 || j==i)C[i][j]=1;
          else C[i][j]=C[i-1][j-1]+C[i-1][j];
        }
      }
      return C[n][k];
    }

    //Pascal's Triangle version(Space efficient program)
    //Time complexity: O(n*k)
    //Space complexity: O(k)
    public long nCr(int n,int r){
      int[] C=new int[r+1];
      C[0]=1;//nC0=1
      for(int i=1;i<=n;++i)
      for(int j=Math.min(i,r);j>0;--j)
      C[j]=C[j]+C[j-1];
      return C[r];
    }

    /**
    * Catlan number:
    *  - Time complexity: O(n*n)
    *  - Auxiliary space: O(n)
    *
    *  NOTE: Time complexity could be reduced to O(n) but it is
    *        possible if and only if n is small or else there is
    *        a chance of getting an overflow. To decrease the time
    *        complexity to O(n) just remember nCr=nCn-r
    */
    public long catlanNumber(int n){
      long[] catlan=new long[n+1];
      catlan[0]=catlan[1]=1;
      for(int i=2;i<=n;++i)
      for(int j=0;j<i;++j)
      catlan[i]+=catlan[j]*catlan[i-1-j];

      return catlan[n];
    }

    /**
    * Greatest Common Divisor(GCD)
    *  - It is also known as Highest Common Factor(HCF)
    *  - Time complexity: log(min(a,b))
    *  - Auxiliary Space: O(1)
    */
    public int gcd(int a,int b){
      if(b==0)return a;
      return gcd(b,a %b);
    }

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

    /**
    * Extended Euclid's Algorithm:
    *  - ax+by=gcd(a,b)
    *  - Time complexity:
    *  -
    */


    /**
    * Least Common Multiple(LCM):
    *  - Time complexity: log(min(a,b))
    *  - Auxiliary Space: O(1)
    */
    public long lcm(long a,long b){
      return (a*b)/gcd(a,b);
    }

  }
}
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//                                        BITSY  ___  CHUCK