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 python3.

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:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
On the competitive programming platform CodeCook, every person has a rating graph described by an array of integers $$$a$$$ of length $$$n$$$. You are now updating the infrastructure, so you've created a program to compress these graphs.

The program works as follows. Given an integer parameter $$$k$$$, the program takes the minimum of each contiguous subarray of length $$$k$$$ in $$$a$$$.

More formally, for an array $$$a$$$ of length $$$n$$$ and an integer $$$k$$$, define the $$$k$$$-compression array of $$$a$$$ as an array $$$b$$$ of length $$$n-k+1$$$, such that $$$$$$b_j =\min_{j\le i\le j+k-1}a_i$$$$$$

For example, the $$$3$$$-compression array of $$$[1, 3, 4, 5, 2]$$$ is $$$[\min\{1, 3, 4\}, \min\{3, 4, 5\}, \min\{4, 5, 2\}]=[1, 3, 2].$$$

A permutation of length $$$m$$$ is an array consisting of $$$m$$$ distinct integers from $$$1$$$ to $$$m$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$m=3$$$ but there is $$$4$$$ in the array).

A $$$k$$$-compression array will make CodeCook users happy if it will be a permutation. Given an array $$$a$$$, determine for all $$$1\leq k\leq n$$$ if CodeCook users will be happy after a $$$k$$$-compression of this array or not.

## Input Format
The first line contains a single integer $$$t$$$ ($$$1\leq t\leq 10^4$$$) — the number of test cases.

The first line of the description of each test case contains a single integer $$$n$$$ ($$$1\leq n\leq 3\cdot 10^5$$$) — the length of the array.

The second line of the description of each test case contains $$$n$$$ integers $$$a_1,\ldots,a_n$$$ ($$$1\leq a_i\leq n$$$) — the elements of the array.

It is guaranteed, that the sum of $$$n$$$ for all test cases does not exceed $$$3\cdot 10^5$$$.

## Output Format
For each test case, print a binary string of length $$$n$$$.

The $$$k$$$-th character of the string should be $$$1$$$ if CodeCook users will be happy after a $$$k$$$-compression of the array $$$a$$$, and $$$0$$$ otherwise.

## Examples
```input
5
5
1 5 3 4 2
4
1 3 2 1
5
1 3 3 3 2
10
1 2 3 4 5 6 7 8 9 10
3
3 3 2
```
```output
10111
0001
00111
1111111111
000
```

## Note
In the first test case, $$$a=[1, 5, 3, 4, 2]$$$.

- The $$$1$$$-compression of $$$a$$$ is $$$[1, 5, 3, 4, 2]$$$ and it is a permutation.
- The $$$2$$$-compression of $$$a$$$ is $$$[1, 3, 3, 2]$$$ and it is not a permutation, since $$$3$$$ appears twice.
- The $$$3$$$-compression of $$$a$$$ is $$$[1, 3, 2]$$$ and it is a permutation.
- The $$$4$$$-compression of $$$a$$$ is $$$[1, 2]$$$ and it is a permutation.
- The $$$5$$$-compression of $$$a$$$ is $$$[1]$$$ and it is a permutation.

Now solve the problem and return the code.