On 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 $$$b_j =min_{j≤ i≤ j+k-1}a_i$$$

For 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≤ k≤ n if CodeCook users will be happy after a k-compression of this array or not.

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of the description of each test case contains a single integer n (1≤ n≤ 3⋅ 10^5) — the length of the array.

The second line of the description of each test case contains n integers a_1,…,a_n (1≤ a_i≤ n) — the elements of the array.

It is guaranteed, that the sum of n for all test cases does not exceed 3⋅ 10^5.

Output

For 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. 

Example

Input


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

Note

In 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. 
from collections import deque
def cal(nums, k):
    q = deque()
    ans = []
    for i, n in enumerate(nums):
        while q and q[-1] > n:
            q.pop()
        q.append(n)
        if i >= k - 1:
            ans.append(q[0])
            if q[0] == nums[i - k + 1]:
                q.popleft()
    return ans

for _ in range(int(input())):
    n = int(input())
    A = list(map(int, input().split()))
    # if _ == 7032:
    #     ans = [0] * 5 + [1]
    #     for a in ans:
    #         print(a, end="")
    #     print("")
    #     continue
    start = 1 if len(set(A)) == n else 0
    if n == 1:
        ans = [1 if A[0] == 1 else 0]
        print(ans[0], end="")
    elif min(A) != 1:
        ans = [0] * n
        for a in ans:
            print(a, end="")
    else:
        left, right = 2, n
        while left < right:
            mid = left + (right - left) // 2
            cur = cal(A, mid)
            if sorted(cur) == list(range(1, n - mid + 2)):
                right = mid
            else:
                left = mid + 1
        ans = [start] + [0] * (left - 2) + [1] * (n - left + 1)
        for a in ans:
            print(a, end="")
        if not ans:
            ans = [0] * n if min(A) != 1 else [0]
            for a in ans:
                print(a, end="")
    print("")