You are given a permutation p=[p1,p2,…,pn]p=[p1,p2,…,pn] of integers from 11 to nn . Let‘s call the number mm (1≤m≤n1≤m≤n ) beautiful, if there exists two indices l,rl,r (1≤l≤r≤n1≤l≤r≤n ), such that the numbers [pl,pl+1,…,pr][pl,pl+1,…,pr] is a permutation of numbers 1,2,…,m1,2,…,m .
For example, let p=[4,5,1,3,2,6]p=[4,5,1,3,2,6] . In this case, the numbers 1,3,5,61,3,5,6 are beautiful and 2,42,4 are not. It is because:
if l=3l=3 and r=3r=3 we will have a permutation [1][1] for m=1m=1 ;
if l=3l=3 and r=5r=5 we will have a permutation [1,3,2][1,3,2] for m=3m=3 ;
if l=1l=1 and r=5r=5 we will have a permutation [4,5,1,3,2][4,5,1,3,2] for m=5m=5 ;
if l=1l=1 and r=6r=6 we will have a permutation [4,5,1,3,2,6][4,5,1,3,2,6] for m=6m=6 ;
it is impossible to take some ll and rr , such that [pl,pl+1,…,pr][pl,pl+1,…,pr] is a permutation of numbers 1,2,…,m1,2,…,m for m=2m=2 and for m=4m=4 .
You are given a permutation p=[p1,p2,…,pn]p=[p1,p2,…,pn] . For all mm (1≤m≤n1≤m≤n ) determine if it is a beautiful number or not.
Input
The first line contains the only integer tt (1≤t≤10001≤t≤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 nn (1≤n≤2⋅1051≤n≤2⋅105 ) — the length of the given permutation pp . The next line contains nn integers p1,p2,…,pnp1,p2,…,pn (1≤pi≤n1≤pi≤n , all pipi are different) — the given permutation pp .
It is guaranteed, that the sum of nn from all test cases in the input doesn‘t exceed 2⋅1052⋅105 .
Output
Print tt 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 nn , there the ii -th character is equal to 11 if ii is a beautiful number and is equal to 00 if ii is not a beautiful number.
Example
Input
Copy
3
6
4 5 1 3 2 6
5
5 3 1 2 4
4
1 4 3 2
Output
Copy
101011
11111
1001
Note
The first test case is described in the problem statement.
In the second test case all numbers from 11 to 55 are beautiful:
if l=3l=3 and r=3r=3 we will have a permutation [1][1] for m=1m=1 ;
if l=3l=3 and r=4r=4 we will have a permutation [1,2][1,2] for m=2m=2 ;
if l=2l=2 and r=4r=4 we will have a permutation [3,1,2][3,1,2] for m=3m=3 ;
if l=2l=2 and r=5r=5 we will have a permutation [3,1,2,4][3,1,2,4] for m=4m=4 ;
if l=1l=1 and r=5r=5 we will have a permutation [5,3,1,2,4][5,3,1,2,4] for m=5m=5 .
