Problem: <image>

William is a huge fan of planning ahead. That is why he starts his morning routine by creating a nested list of upcoming errands.

A valid nested list is any list which can be created from a list with one item "1" by applying some operations. Each operation inserts a new item into the list, on a new line, just after one of existing items a_1  .  a_2  .  a_3  .   ⋅⋅⋅   .\,a_k and can be one of two types: 

  1. Add an item a_1  .  a_2  .  a_3  .  ⋅⋅⋅  .  a_k  .  1 (starting a list of a deeper level), or 
  2. Add an item a_1  .  a_2  .  a_3  .  ⋅⋅⋅  .  (a_k + 1) (continuing the current level). 

Operation can only be applied if the list does not contain two identical items afterwards. And also, if we consider every item as a sequence of numbers, then the sequence of items should always remain increasing in lexicographical order. Examples of valid and invalid lists that are shown in the picture can found in the "Notes" section.

When William decided to save a Word document with the list of his errands he accidentally hit a completely different keyboard shortcut from the "Ctrl-S" he wanted to hit. It's not known exactly what shortcut he pressed but after triggering it all items in the list were replaced by a single number: the last number originally written in the item number.

William wants you to help him restore a fitting original nested list.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10). Description of the test cases follows.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^3), which is the number of lines in the list.

Each of the next n lines contains a single integer a_i (1 ≤ a_i ≤ n), which is what remains of William's nested list.

It is guaranteed that in each test case at least one fitting list exists.

It is guaranteed that the sum of values n across all test cases does not exceed 10^3.

Output

For each test case output n lines which represent a valid nested list, which could become the data provided to you by William.

If there are multiple answers, print any.

Example

Input


2
4
1
1
2
3
9
1
1
1
2
2
1
2
1
2


Output


1
1.1
1.2
1.3
1
1.1
1.1.1
1.1.2
1.2
1.2.1
2
2.1
2.2

Note

In the second example test case one example of a fitting list is:

1

1.1

1.1.1

1.1.2

1.2

1.2.1

2

2.1

2.2

This list can be produced by using the sequence of operations shown below: <image>

  1. Original list with a single item 1. 
  2. Insert item 2 by using the insertion operation of the second type after item 1. 
  3. Insert item 1.1 by using the insertion operation of the first type after item 1. 
  4. Insert item 1.2 by using the insertion operation of the second type after item 1.1. 
  5. Insert item 1.1.1 by using the insertion operation of the first type after item 1.1. 
  6. Insert item 1.1.2 by using the insertion operation of the second type after item 1.1.1. 
  7. Insert item 1.2.1 by using the insertion operation of the first type after item 1.2. 
  8. Insert item 2.1 by using the insertion operation of the first type after item 2. 
  9. Insert item 2.2 by using the insertion operation of the second type after item 2.1. 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.BigInteger;
public class Main{
    static InputReader sc;
    static PrintWriter pw;
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        sc = new InputReader(inputStream);
        pw = new PrintWriter(outputStream);
        solve();
        pw.close();
    }
    // static int L,R,top,bottom;
    // static int cnt,edge;
    // static long ans;
    static int time;
    // static boolean isIsland;
    static BigInteger min(BigInteger a, BigInteger b){        
        if(a.compareTo(b)<0)
            return a;
        return b;
    }
    public static void solve(){        
        int t=1;
        t=s(0);
        u:while(t-->0){
            int n=s(0);
            int []arr=new int [n];
            feedArr(arr);
            Stack<Pair> stk=new Stack<>();
            stk.push(new Pair("",1));
            pln(1);
            Pair pr;
            for(int i=1;i<n;i++){
                if(arr[i]==1){
                    pr=stk.peek();
                    stk.push(new Pair(pr.s+(pr.s.length()==0?"":".")+pr.i,1));
                    pln(stk.peek().s+"."+stk.peek().i);
                }
                else if(stk.peek().i==arr[i]-1){
                    pr=stk.pop();
                    pln(pr.s+(pr.s.length()==0?"":".")+arr[i]);
                    pr.i++;
                    stk.push(pr);
                }
                else{
                    stk.pop();
                    i--;
                }
            }
        }        
    }        
    static long fact(long p){
        long ans=1l;
        for(long i=2;i<=p;i++)
            ans*=i;
        return ans;
    }    
    static int find(int j, List<Integer> B, List<Integer> A, int i){
        // System.out.println("Hi");
        int l=j,r=B.size()-1,m;        
        while(l<=r){
            m=(r-l)/2+l;
            if(A.size()-i-1<=B.size()-m-1)
                l=m+1;
            else
                r=m-1;
        }
        // System.out.println("Bye");
        return r;
    }
    static int find2(List<Integer> B, int x){
        int l=0,r=B.size()-1,m;
        // System.out.println("Hi2");
        // System.out.println(j);
        while(l<=r){            
            m=(r-l)/2+l;
            // System.out.println(m);
            if(B.get(m)-x<=0)
                l=m+1;
            else
                r=m-1;
        }
        // System.out.println("Bye2");
        return r;        
    }
    static long nPr(long n, long r){
        long ans=1;
        for(long i=1;i<=r;i++)
            ans*=(n-i+1);
        return ans;
    }
    static long nCr(long n, long r){
        long ans=1;
        for(long i=1;i<=r;i++){
            ans*=(n-i+1);
            ans/=i;
        }
        return ans;
    }
    static void update_DAG(int cur,int val, int []graph, int n)
    {
        if(val>maxx[cur])
        {
            int x=graph[cur];
            if(x!=-1)
                update_DAG(x,val+1,graph,n);
            maxx[cur]=val;
            update(cur,val,n);
        }
    }
    static int []bit, maxx;
    static void update(int i,int val, int n)
    {
        while(i<=n)
        {
            bit[i]=Math.max(bit[i],val);
            i=i+(i&(-i));
        }
    }
    static int query(int i)
    {
        int ret=0;
        while(i>0)
        {
            ret=Math.max(ret,bit[i]);
            i=i-(i&(-i));
        }
        return ret;
    }    
    public static int [][]dir=new int [][]{{1,0},{0,1},{-1,0},{0,-1}};        
    public static int find(List<Integer> list, int x){
        int l=0,r=list.size()-1,m;
        while(l<=r){
            m=(r-l)/2+l;
            if(list.get(m)<=x)
                l=m+1;
            else
                r=m-1;
        }
        return r;
    } 
    static class Node{
        int val;
        long cost;
        Node next;
        Node(int v,long c){
            val=v;
            next=null;
            cost=c;
        }
    }    
    public static long sum(long n){
        long val=0l;
        while(n>0){
            val+=n%10;
            n/=10;
        }
        return val;
    }
    // static class Node{
    //     int left,right;
    //     Node prev,next;
    //     Node(int i, int v){
    //         left=i;
    //         right=v;
    //         prev=next=null;
    //     }
    //     void remove(){
    //         this.prev.next=this.next;
    //         this.next.prev=this.prev;
    //     }
    //     void insert(Node node){
    //         node.next=this;
    //         node.prev=this.prev;
    //         node.prev.next=node;
    //         this.prev=node;
    //     }
    // } 
    public static int  findDiameter(int r, List<List<Integer>>list){
        return findFarthest(findFarthest(r,list)[0],list)[1];
    }
    public static int[] findFarthest(int u, List<List<Integer>>list){
        int n=list.size();
        boolean []vis=new boolean[n+1];
        Queue<Integer>q=new LinkedList<>();
        q.offer(u);
        vis[u]=true;
        int s,pr,cnt=0;
        int []ar=new int[]{u,0};
        while(q.size()>0){
            s=q.size();
            while(s-->0){
                pr=q.poll();
                if(ar[1]<cnt){
                    ar[1]=cnt;
                    ar[0]=pr;
                }
                for(int i:list.get(pr)){
                    if(!vis[i]){
                        vis[i]=true;
                        q.offer(i);
                    }
                }
            }
            cnt++;
        }
        return ar;
    }
    public static long atMostK(char []chrr, int k){
        if(k<0)
            return 0;
        int l=0,cnt=0;
        long ans=0l;
        for(int i=0;i<chrr.length;i++){
            if(chrr[i]=='1')
                cnt++;
            while(cnt>k){
                if(chrr[l++]=='1')
                    cnt--;
            }
            ans+=(long)(i-l)+1l;
        }
        return ans;
    }
    public static int ask(int l, int r){
        System.out.println("? "+l+" "+r);
        System.out.flush();
        return sc.nextInt();
    }
    public static void sort(int []arr){
        ArrayList<Integer> list=new ArrayList<>();
        for(int i=0;i<arr.length;i++)
            list.add(arr[i]);
        Collections.sort(list);
        for(int i=0;i<arr.length;i++)
            arr[i]=list.get(i);
    }
    public static void sort(long []arr){
        ArrayList<Long> list=new ArrayList<>();
        for(int i=0;i<arr.length;i++)
            list.add(arr[i]);
        Collections.sort(list);
        for(int i=0;i<arr.length;i++)
            arr[i]=list.get(i);
    }
    public static void swap(char []chrr, int i, int j){
        char temp=chrr[i];
        chrr[i]=chrr[j];
        chrr[j]=temp;
    }
    public static int countSetBits(long n){
        int a=0;
        while(n>0){
            a+=(n&1);
            n>>=1;
        }
        return a;
    }
    static class Pair{
        String s;
        int i;
        Pair(String S, int I){
            s=S;
            i=I;
        }
     //*
    }
    /*/
        public int compareTo(Pair p){
            return (b-p.b);
        }
        public int hashCode(){
            int hashcode = (a+" "+b).hashCode();
            return hashcode;
        }
        public boolean equals(Object obj){
            if (obj instanceof Pair) {
                Pair p = (Pair) obj;
                return (p.a==this.a && p.b == this.b);
            }
            return false;
        }
    }
    //*/
    static boolean isPrime(long n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 
    static long gcd(long a, long b) { 
        if (b == 0) 
            return a; 
        return a>b?gcd(b, a % b):gcd(a, b % a);  
    } 
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
    static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    public static int s(int n){
        return sc.nextInt();
    }
    public static long s(long n){
        return sc.nextLong();
    }
    public static String s(String n){
        return sc.next();
    }
    public static double s(double n){
        return sc.nextDouble();
    }
    public static void p(int n){
        pw.print(n);
    }
    public static void p(long n){
        pw.print(n);
    }
    public static void p(String n){
        pw.print(n);
    }
    public static void p(double n){
        pw.print(n);
    }
    public static void pln(int n){
        pw.println(n);
    }
    public static void pln(long n){
        pw.println(n);
    }
    public static void pln(String n){
        pw.println(n);
    }
    public static void pln(double n){
        pw.println(n);
    }
    public static void feedArr(long []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextLong();
    }
    public static void feedArr(double []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextDouble();
    }
    public static void feedArr(int []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextInt();
    }
    public static void feedArr(String []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.next();
    }
    public static String printArr(int []arr){
        StringBuilder sbr=new StringBuilder();
        for(int i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public  static String printArr(long []arr){
        StringBuilder sbr=new StringBuilder();
        for(long i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(String []arr){
        StringBuilder sbr=new StringBuilder();
        for(String i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(double []arr){
        StringBuilder sbr=new StringBuilder();
        for(double i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}
class AncestorQuerier {
    int [][]dp;
    int N=200001;
    int M=22;
    int max;    
    public void preCompute(int []par){
        for(int i=0;i<N;i++){
            if(i>=2&&i<par.length)
                dp[i][0]=par[i];
            else
                dp[i][0]=-1;
        }
        for(int j=1;j<M;j++){
            for(int i=0;i<N;i++){
                if(dp[i][j-1]!=-1)
                    dp[i][j]=dp[dp[i][j-1]][j-1];
            }
        }       
    }    
    public int getAncestor(int val, int k) {
        if(k<0||val>max)
            return -1;
        if(k==0)
            return val;
        int t=(1<<(M-1));        
        for(int i=M-1;i>=0&&val!=-1;i--,t>>=1){
            if(t<=k){
                val=dp[val][i];
                k-=t;
            }
        }
        return val;   
    }
}