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B. Beautiful Numbers
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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.

Example
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 $$$m = 5$$$.