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: 1.0 seconds
Memory limit: 256.0 MB

# Problem
You are given a permutation $$$p=[p_1, p_2, \ldots, p_n]$$$ of integers from $$$1$$$ to $$$n$$$. Let's call the number $$$m$$$ ($$$1 \le m \le n$$$) beautiful, if there exists two indices $$$l, r$$$ ($$$1 \le l \le r \le n$$$), such that the numbers $$$[p_l, p_{l+1}, \ldots, p_r]$$$ is a permutation of numbers $$$1, 2, \ldots, m$$$.

For example, let $$$p = [4, 5, 1, 3, 2, 6]$$$. In this case, the numbers $$$1, 3, 5, 6$$$ are beautiful and $$$2, 4$$$ are not. It is because:

- if $$$l = 3$$$ and $$$r = 3$$$ we will have a permutation $$$[1]$$$ for $$$m = 1$$$;
- if $$$l = 3$$$ and $$$r = 5$$$ we will have a permutation $$$[1, 3, 2]$$$ for $$$m = 3$$$;
- if $$$l = 1$$$ and $$$r = 5$$$ we will have a permutation $$$[4, 5, 1, 3, 2]$$$ for $$$m = 5$$$;
- if $$$l = 1$$$ and $$$r = 6$$$ we will have a permutation $$$[4, 5, 1, 3, 2, 6]$$$ for $$$m = 6$$$;
- it is impossible to take some $$$l$$$ and $$$r$$$, such that $$$[p_l, p_{l+1}, \ldots, p_r]$$$ is a permutation of numbers $$$1, 2, \ldots, m$$$ for $$$m = 2$$$ and for $$$m = 4$$$.

You are given a permutation $$$p=[p_1, p_2, \ldots, p_n]$$$. For all $$$m$$$ ($$$1 \le m \le n$$$) determine if it is a beautiful number or not.

## Input Format
The first line contains the only integer $$$t$$$ ($$$1 \le t \le 1000$$$)  — the number of test cases in the input. The next lines contain the description of test cases.

The first line of a test case contains a number $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of the given permutation $$$p$$$. The next line contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$, all $$$p_i$$$ are different) — the given permutation $$$p$$$.

It is guaranteed, that the sum of $$$n$$$ from all test cases in the input doesn't exceed $$$2 \cdot 10^5$$$.

## Output Format
Print $$$t$$$ lines — the answers to test cases in the order they are given in the input.

The answer to a test case is the string of length $$$n$$$, there the $$$i$$$-th character is equal to $$$1$$$ if $$$i$$$ is a beautiful number and is equal to $$$0$$$ if $$$i$$$ is not a beautiful number.

## Examples
```input
3
6
4 5 1 3 2 6
5
5 3 1 2 4
4
1 4 3 2
```
```output
101011
11111
1001
```

## Note
The first test case is described in the problem statement.

In the second test case all numbers from $$$1$$$ to $$$5$$$ are beautiful:

- if $$$l = 3$$$ and $$$r = 3$$$ we will have a permutation $$$[1]$$$ for $$$m = 1$$$;
- if $$$l = 3$$$ and $$$r = 4$$$ we will have a permutation $$$[1, 2]$$$ for $$$m = 2$$$;
- if $$$l = 2$$$ and $$$r = 4$$$ we will have a permutation $$$[3, 1, 2]$$$ for $$$m = 3$$$;
- if $$$l = 2$$$ and $$$r = 5$$$ we will have a permutation $$$[3, 1, 2, 4]$$$ for $$$m = 4$$$;
- if $$$l = 1$$$ and $$$r = 5$$$ we will have a permutation $$$[5, 3, 1, 2, 4]$$$ for $$$m = 5$$$.

Now solve the problem and return the code.