You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
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 $$$a_1 \,.\, a_2 \,.\, a_3 \,.\, \,\cdots\, \,.\,a_k$$$ and can be one of two types:

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

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 Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10$$$). Description of the test cases follows.

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

Each of the next $$$n$$$ lines contains a single integer $$$a_i$$$ ($$$1 \le a_i \le n$$$), 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 Format
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.

## Examples
```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:

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 $$$2.1$$$.

Now solve the problem and return the code.