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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.*; 
import java.util.StringTokenizer; 
import java.io.PrintWriter;
import java.io.*;

import java.util.stream.Collectors.*;
import java.lang.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;
public class Ideo
{ 
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
   
static class aksh
{
    
    int x;
    int y;
    int moves;

    public aksh(int a,int b,int c) 
    {
        x = a;
        y = b;
        moves=c;
    }
}
static int power(int x,int y) 
{ 
    int res = 1;      // Initialize result 
  
      // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y%2==1) 
            res = (res*x); 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x);   
    } 
    return res; 
} 
 
 static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 


  static boolean compareSeq(char[] S, int x, int y, int n) 
    { 
        for (int i = 0; i < n; i++)
         {

            if (S[x] < S[y]) 
               return true;
            else if (S[x] > S[y]) 
                return false; 
            x = (x + 1) % n; 
            y = (y + 1) % n; 
        } 
        return true; 
    } 

    static void build(long[] sum,int[] arr,int n)
    {
      for(int i=0;i<(1<<n);i++)
      {
        long total=0;
        for(int j=0;j<n;j++)
        {
          if((i & (1 << j)) > 0)
            total+=arr[j];
        }

        sum[i]=total;
      }
    }

 
     static int count(long arr[], long x, int n) 
       {

        int l=0;
        int h=n-1;

        int res=-1;
        int mid=-1;
        while(l<=h)
        {
          mid=l+(h-l)/2;
          if(x==arr[mid])
          {
            res=mid;
            h=mid-1;
          }
          else if(x<arr[mid])
            h=mid-1;
          else
            l=mid+1;
        }

        if(res==-1)
          return 0;

        //res is first index and res1 is last index of an element in a sorted array total number of occurences is (res1-res+1)

        int res1=-1;
        l=0;
        h=n-1;
        while(l<=h)
        {
          mid=l+(h-l)/2;
          if(x==arr[mid])
          {
            res1=mid;
            l=mid+1;
          }
          else if(x<arr[mid])
            h=mid-1;
          else
            l=mid+1;
        }



        if(res1==-1)
          return 0;
        if(res!=-1 && res1!=-1)
          return (res1-res+1);

        return 0;

       } 

       static int parity(int a)
       {
    a^=a>>16;
    a^=a>>8;
    a^=a>>4;
    a^=a>>2;
    a^=a>>1;
    return a&1;
  }
/*
  PriorityQueue<aksh> pq = new PriorityQueue<>((o1, o2) -> {
            if (o1.p < o2.p)
                return 1;
            else if (o1.p > o2.p)
                return -1;
            else
                return 0;

        });//decreasing order acc to p*/
static int power(int x, int y, int m)  
    { 
        if (y == 0) 
            return 1; 
          
        int p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
static int modinv(int a, int m) 
    { 
        int g = gcd(a, m); 
        if (g != 1) 
            return 0;
        else 
        { 
           return power(a, m - 2, m); 
        } 
        //return 0;
    } 

static int[] product(int[] nums) {
    int[] result = new int[nums.length];
 
    int[] t1 = new int[nums.length];
    int[] t2 = new int[nums.length];
 
    t1[0]=1;
    t2[nums.length-1]=1;
 
    //scan from left to right
    for(int i=0; i<nums.length-1; i++){
        t1[i+1] = nums[i] * t1[i];
    }
 
    //scan from right to left
    for(int i=nums.length-1; i>0; i--){
        t2[i-1] = t2[i] * nums[i];
    }

    for(int i=0;i<nums.length;i++)
      {
        System.out.print(t1[i]+" "+t2[i]);
        System.out.println();
      }
 
    //multiply
    for(int i=0; i<nums.length; i++){
        result[i] = t1[i] * t2[i];
    }
 
    return result;
}

static int getsum(int[] bit,int ind)
{
  int sum=0;
  while(ind>0)
  {
    sum+=bit[ind];
    ind-= ind & (-ind);
  }

  return sum;
}

static void update(int[] bit,int max,int ind,int val)
{
  while(ind<=max)
  {
    bit[ind]+=val;
    ind+= ind & (-ind);
  }
}

    static ArrayList<Integer>[] adj;
    static int[] bfs(ArrayList<Integer>[] adj,int n,ArrayList<Integer> arr)
    {
      int[] vis=new int[n];
      int[] dis=new int[n];
      int[] par=new int[n];
      Queue<Integer> q=new LinkedList<>();

      Arrays.fill(dis,-1);

      for(int i=0;i<arr.size();i++)
      {
        vis[arr.get(i)]=1;
        dis[arr.get(i)]=0;
        par[arr.get(i)]=-1;
        q.add(arr.get(i));
      }

      while(!q.isEmpty())
      {
        int x=q.remove();
        for(int u:adj[x])
        {
          if(vis[u]==0)
          {
            vis[u]=1;
            dis[u]=dis[x]+1;
            par[u]=x;
            q.add(u);
          }
        }
      }

      return dis;
    }
    public static void main(String args[] ) throws Exception 
    {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT */

         FastReader sc=new FastReader();
         int n=sc.nextInt();


         for(int i=0;i<n;i++)
         {
          int c1=0;
          int m=sc.nextInt();
          String[] a=new String[m];
          HashMap<String,Integer> h=new HashMap<>();
          for(int l=0;l<m;l++)
          {
            a[l]=sc.next();
            if(h.containsKey(a[l]))
              {
                h.put(a[l],h.get(a[l])+1);
                c1++;
              }
            else
                h.put(a[l],1);
          }

          System.out.println(c1);
          for(int x=0;x<m;x++)
          {
            if(h.get(a[x])==1)
              System.out.println(a[x]);
            else
            {
              String s=a[x];
              int[] c=new int[10];
              for(int j=0;j<m;j++)
              {
                if(j!=x)
                {
                  c[a[j].charAt(0)-'0']++;
                }
              }
              int k=0;
              for(k=0;k<10;k++)
              {
                if(c[k]==0)
                  break;
              }

              String s1=String.valueOf(k);
              s1+=s.substring(1,4);
              a[x]=s1;
              System.out.println(a[x]);
              h.put(a[x],1);
              h.put(s,h.get(s)-1);
            }
          }
         }

        

      }

    }