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. 
for _ in range(int(input())):

	n = int(input())
	a = list(map(int, input().split(" ")))

	idx = [None]*(n+1)

	for i in range(n):
		idx[a[i]] = i+1

	## got the index array.

	ans = ['0']*n
	ans[0] = '1'; ans[-1] = '1'

	curr_max = idx[1]
	curr_min = idx[1]

	for m in range(2, n):

		curr_max = max(curr_max, idx[m])
		curr_min = min(curr_min, idx[m])

		if m == (curr_max - curr_min + 1):
			ans[m-1] = '1'
			
		# if ans[m-1] == '1':

		# 	if curr_max+1 < len(a) and a[curr_max+1] == m:
		# 		curr_max = curr_max + 1
		# 	elif curr_min-1 >= 0 and a[curr_min-1] == m:
		# 		curr_min = curr_min-1

		# 	ans[m-1] = '1'

		# else:
		# 	m_min = 1<<31
		# 	m_max = -1

		# 	for mi in range(1, m+1):
		# 		m_min = min(m_min, idx[mi])
		# 		m_max = max(m_max, idx[mi])

		# 	if m == (m_max - m_min + 1):
		# 		ans[m-1] = '1'

		# 	curr_max = m_max
		# 	curr_min = m_min


	print(''.join(ans))