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.util.*;
import java.io.*;
import java.math.*;

public class Main implements Runnable {

    final static int mod = 1000000007;
    static FastReader sc;
    static PrintWriter out;
    static boolean test_case_input = true;
    static final int MAX = 1000000000;
    static final int MIN = -1000000000;

    public static void print(int a[], int point) {
        out.print(a[1]);
        for(int i = 2; i <= point; i++) {
            out.print("." + a[i]);
        }
        out.println();
    }

    public static void solution(int test_case) throws IOException {
        // code
        int n = sc.nextInt();
        int a[] = sc.intarr(n);
        int lev[] = new int[n + 1];
        lev[1] = 1;
        int point = 1;
        out.println(1);
        for(int i=1; i < n; i++) {
            if(a[i] == 1) {
                point++;
                lev[point] = 1;
                print(lev, point);
            }
            else if(a[i] == lev[point] + 1) {
                lev[point]++;
                print(lev, point);
            }
            else {
                while(lev[point] + 1 != a[i]) {
                    point--;
                }
                lev[point]++;
                print(lev, point);
            }
        }
    }

    // log A base B
    public static int logint(int x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    public static int logint(long x, long base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    public static int logint(double x, double base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    public static double logdouble(int x, int base) {
        return (Math.log(x) / Math.log(base));
    }

    public static double logdouble(long x, long base) {
        return (Math.log(x) / Math.log(base));
    }

    public static double logdouble(double x, double base) {
        return (Math.log(x) / Math.log(base));
    }

    public static long loglong(int x, int base) {
        return (long) (Math.log(x) / Math.log(base));
    }

    public static long loglong(long x, long base) {
        return (long) (Math.log(x) / Math.log(base));
    }

    public static long loglong(double x, double base) {
        return (long) (Math.log(x) / Math.log(base));
    }

    // Debug
    public static void debug(String msg, Object value) {
        File output = new File("output.txt");
        if (!output.exists()) return;
        String type = value.getClass().getSimpleName();
        if (type.equals("int[]")) out.println(msg + " => " + Arrays.toString((int[]) value));
        else if (type.equals("double[]")) out.println(msg + " => " + Arrays.toString((double[]) value));
        else if (type.equals("float[]")) out.println(msg + " => " + Arrays.toString((float[]) value));
        else if (type.equals("long[]")) out.println(msg + " => " + Arrays.toString((long[]) value));
        else if (type.equals("char[]")) out.println(msg + " => " + Arrays.toString((char[]) value));
        else if (type.equals("String[]")) out.println(msg + " => " + Arrays.toString((String[]) value));
        else if (type.equals("int[][]")) {
            out.println(msg + "=>");
            for (int i[] : (int[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("double[][]")) {
            out.println(msg + "=>");
            for (double i[] : (double[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("float[][]")) {
            out.println(msg + "=>");
            for (float i[] : (float[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("long[][]")) {
            out.println(msg + "=>");
            for (long i[] : (long[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("char[][]")) {
            out.println(msg + "=>");
            for (char i[] : (char[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("String[][]")) {
            out.println(msg + "=>");
            for (String i[] : (String[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else out.println(msg + " => " + value);
    }

    public static void debug(Object value) {
        File output = new File("output.txt");
        if (!output.exists()) return;
        String type = value.getClass().getSimpleName();
        if (type.equals("int[]")) out.println(" => " + Arrays.toString((int[]) value));
        else if (type.equals("double[]")) out.println(" => " + Arrays.toString((double[]) value));
        else if (type.equals("float[]")) out.println(" => " + Arrays.toString((float[]) value));
        else if (type.equals("long[]")) out.println(" => " + Arrays.toString((long[]) value));
        else if (type.equals("char[]")) out.println(" => " + Arrays.toString((char[]) value));
        else if (type.equals("String[]")) out.println(" => " + Arrays.toString((String[]) value));
        else if (type.equals("int[][]")) {
            out.println("=>");
            for (int i[] : (int[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("double[][]")) {
            out.println("=>");
            for (double i[] : (double[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("float[][]")) {
            out.println("=>");
            for (float i[] : (float[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("long[][]")) {
            out.println("=>");
            for (long i[] : (long[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("char[][]")) {
            out.println("=>");
            for (char i[] : (char[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("String[][]")) {
            out.println("=>");
            for (String i[] : (String[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else out.println(" => " + value);
    }

    // Graph Functions
    public static void addUndirectedEdge(ArrayList<ArrayList<Integer>> adj, int u, int v) {
        adj.get(u).add(v);
        adj.get(v).add(u);
    }

    public static void addDirectedEdge(ArrayList<ArrayList<Integer>> adj, int u, int v) {
        adj.get(u).add(v);
    }

    public static <T> void addUndirectedEdge(ArrayList<ArrayList<Point>> adj, int u, int v, T weight) {
        adj.get(u).add(new Point(v, weight));
        adj.get(v).add(new Point(u, weight));
    }

    public static <T> void addDirectedEdge(ArrayList<ArrayList<Point>> adj, int u, int v, T weight) {
        adj.get(u).add(new Point(v, weight));
    }

    public static <T> void toString(String msg, ArrayList<ArrayList<T>> adj) {
        out.println(msg + ":");
        int count = 0;
        for (ArrayList<T> i : adj) {
            out.print("\t" + count++ + ": ");
            for (T j : i) {
                out.print(j + " ");
            }
            out.println();
        }
    }

    public static void addUndirectedEdge(Map<Integer, ArrayList<Integer>> adj, int u, int v) {
        if (adj.containsKey(u)) {
            ArrayList<Integer> temp = adj.get(u);
            temp.add(v);
            adj.put(u, temp);
        } else {
            ArrayList<Integer> temp = new ArrayList<>();
            temp.add(v);
            adj.put(u, temp);
        }
        if (adj.containsKey(v)) {
            ArrayList<Integer> temp = adj.get(v);
            temp.add(u);
            adj.put(v, temp);
        } else {
            ArrayList<Integer> temp = new ArrayList<>();
            temp.add(u);
            adj.put(v, temp);
        }
    }

    public static void addDirectedEdge(Map<Integer, ArrayList<Integer>> adj, int u, int v) {
        if (adj.containsKey(u)) {
            ArrayList<Integer> temp = adj.get(u);
            temp.add(v);
            adj.put(u, temp);
        } else {
            ArrayList<Integer> temp = new ArrayList<>();
            temp.add(v);
            adj.put(u, temp);
        }
    }

    public static <T> void addUndirectedEdge(Map<Integer, ArrayList<Point>> adj, int u, int v, T weight) {
        if (adj.containsKey(u)) {
            ArrayList<Point> temp = adj.get(u);
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        } else {
            ArrayList<Point> temp = new ArrayList<>();
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        }
        if (adj.containsKey(v)) {
            ArrayList<Point> temp = adj.get(v);
            temp.add(new Point(u, weight));
            adj.put(v, temp);
        } else {
            ArrayList<Point> temp = new ArrayList<>();
            temp.add(new Point(u, weight));
            adj.put(v, temp);
        }
    }

    public static <T> void addDirectedEdge(Map<Integer, ArrayList<Point>> adj, int u, int v, T weight) {
        if (adj.containsKey(u)) {
            ArrayList<Point> temp = adj.get(u);
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        } else {
            ArrayList<Point> temp = new ArrayList<>();
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        }
    }

    public static <T> void toString(String msg, Map<T, ArrayList<T>> adj) {
        out.println(msg + ":");
        for (Map.Entry<T, ArrayList<T>> entry : adj.entrySet()) {
            out.println("\t" + entry.getKey() + ": " + entry.getValue());
        }
    }

    // GCD
    public static int __gcd(int a, int b) {
        BigInteger n1 = BigInteger.valueOf(a);
        BigInteger n2 = BigInteger.valueOf(b);
        BigInteger gcd = n1.gcd(n2);
        return gcd.intValue();
    }

    public static long __gcd(long a, long b) {
        BigInteger n1 = BigInteger.valueOf(a);
        BigInteger n2 = BigInteger.valueOf(b);
        BigInteger gcd = n1.gcd(n2);
        return gcd.longValue();
    }

    public static void main(String args[]) throws IOException {
        new Thread(null, new Main(), "random", 1 << 26).start();
    }

    @Override
    public void run() {
        long start = 0, end = 0;
        try {
            File output = new File("output.txt");
            sc = new FastReader();
            if (output.exists()) {
                out = new PrintWriter(new FileOutputStream("output.txt"));
                start = System.nanoTime();
            } else {
                out = new PrintWriter(System.out);
            }

            int test_cases = 1;
            if (test_case_input) test_cases = sc.nextInt();
            for (int i = 1; i <= test_cases; i++) {
                solution(i);
            }
            if (output.exists()) {
                end = System.nanoTime();
                out.println("Execution time: " + (end - start) / 1000000 + " ms");
            }
            out.flush();
            out.close();
        } catch (Exception e) {
            out.println("Exception: " + e);
            out.println("At Line no. : " + e.getStackTrace()[0].getLineNumber());
            out.flush();
            out.close();
            return;
        }
    }

    // Edge Class
    static class Edge implements Comparable<Edge> {
        Object u;
        Object v;
        Object wt;

        public Edge(Object origin, Object destination, Object weight) {
            u = origin;
            v = destination;
            wt = weight;
        }

        public String toString() {
            String ans = u + " -> " + v + " : " + wt;
            return ans;
        }

        public int getIntOrigin() {
            return (int) u;
        }

        public int getIntDestination() {
            return (int) v;
        }

        public int getIntWeight() {
            return (int) wt;
        }

        public long getLongOrigin() {
            return (long) u;
        }

        public long getLongDestination() {
            return (long) v;
        }

        public long getLongWeight() {
            return (long) wt;
        }

        @Override
        public int compareTo(Edge edge) {
            if ((edge.u).getClass() == Long.class) return (((Long) this.wt).compareTo((Long) edge.wt));
            else return (((Integer) this.wt).compareTo((Integer) edge.wt));
        }
    }

    // Point Class
    static class Point implements Comparable<Point> {
        Object x;
        Object y;

        public Point(Object a, Object b) {
            x = a;
            y = b;
        }

        public int getIntX() {
            return (int) x;
        }

        public int getIntY() {
            return (int) y;
        }

        public long getLongX() {
            return (long) x;
        }

        public long getLongY() {
            return (long) y;
        }

        public int compareTo(Point obj) {
            if (obj.x.equals(this.x)) {
                if ((obj.y).getClass() == Long.class) return ((Long) this.y).compareTo((Long) obj.y);
                else return ((Integer) this.y).compareTo((Integer) obj.y);
            } else {
                if ((obj.x).getClass() == Long.class) return ((Long) this.x).compareTo((Long) obj.x);
                else return ((Integer) this.x).compareTo((Integer) obj.x);
            }
        }

        public String toString() {
            String ans = "(" + x + ", " + y + ")";
            return ans;
        }

        @Override
        public int hashCode() {
            int hash = 7;
            hash = 71 * hash + (int) this.x;
            hash = 71 * hash + (int) this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) return false;
            Point point = (Point) obj;
            if (point.x.equals(this.x) && point.y.equals(this.y)) return true;
            else return false;
        }
    }

    // Fast IO
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() throws FileNotFoundException {
            File in = new File("input.txt");
            if (in.exists()) {
                br = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
            } else {
                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());
        }

        float nextFloat() {
            return Float.parseFloat(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        int[] intarr(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = Integer.parseInt(next());
            }
            return a;
        }

        long[] longarr(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = Long.parseLong(next());
            }
            return a;
        }

        float[] floatarr(int n) {
            float a[] = new float[n];
            for (int i = 0; i < n; i++) {
                a[i] = Float.parseFloat(next());
            }
            return a;
        }

        double[] doublearr(int n) {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = Double.parseDouble(next());
            }
            return a;
        }


        int[][] intmatrix(int row, int col) {
            int a[][] = new int[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Integer.parseInt(next());
                }
            }
            return a;
        }

        long[][] longmatrix(int row, int col) {
            long a[][] = new long[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Long.parseLong(next());
                }
            }
            return a;
        }

        float[][] floatmatrix(int row, int col) {
            float a[][] = new float[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Float.parseFloat(next());
                }
            }
            return a;
        }

        double[][] doublematrix(int row, int col) {
            double a[][] = new double[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Double.parseDouble(next());
                }
            }
            return a;
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}