You are given a permutation p=[p_1, p_2, …, p_n] of integers from 1 to n. Let's call the number m (1 ≤ m ≤ n) beautiful, if there exists two indices l, r (1 ≤ l ≤ r ≤ n), such that the numbers [p_l, p_{l+1}, …, p_r] is a permutation of numbers 1, 2, …, 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}, …, p_r] is a permutation of numbers 1, 2, …, m for m = 2 and for m = 4. 



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

Input

The first line contains the only integer t (1 ≤ 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 n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation p. The next line contains n integers p_1, p_2, …, p_n (1 ≤ p_i ≤ 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 ⋅ 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. 
t = int(input().strip())

def find(a,b,p,v):
    '''given a to be the atomic element, b is the leaf'''
    while b != p[b]:
        nxt = p[b]
        p[b] = a
        b = nxt
    p[b] = a
    val[a] += val[b]
for _ in range(t):
    n = int(input().strip())
    nums = dict()
    for index,i in enumerate(input().strip().split()):
        num = int(i)
        nums[num - 1] = index
    if n == 1:
        print(1)
    else:
        p = [-1 for i in range(n)]
        val = [0 for i in range(n)]
        ans = [0 for i in range(n)]

        for i in range(n):
            each_num = nums[i]
            val[each_num] = 1
            p[each_num] = each_num
            
            if each_num == 0:
                if p[each_num + 1] > -1:
                    find(0,1,p,val)
            elif each_num == n - 1:
                if p[each_num - 1] > -1:
                    find(n - 1,n - 2,p,val)
            else:
                if p[each_num + 1] > -1:
                    find(each_num,each_num + 1,p,val)
                if p[each_num - 1] > -1:
                    find(each_num,each_num - 1,p,val)
            if val[each_num] == i + 1:
                ans[i] = 1
            #print(each_num,p,val)
        for j in ans:
            print(j,end='')
        print()
            
    
    
        
