D. Rating Compressiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputOn 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_iFor 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.InputThe 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.OutputFor 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. ExampleInput
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
NoteIn 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. 
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

10111 0001 00111 1111111111 000 
['binary search', 'data structures', 'greedy', 'implementation', 'two pointers', '*1800']