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 defaultdict,deque
import sys
import bisect
input=sys.stdin.readline

t=int(input())
for ii in range(t):
    n=int(input())
    l=[int(i) for i in input().split() if i!='\n']
    ind=defaultdict(list)
    ind_arr=[0]*(n+1)
    stack=[]

    for i in range(len(l)):
        if l[i]>=0:
            ind_arr[l[i]]=i
            while len(stack)>0 and stack[-1]>l[i]:
                temp=stack.pop()
                if i!=ind[temp][-1][-1]:
                    ind[temp][-1].append(i)
            if len(stack)==0:
                ind[l[i]].append([0])
            elif stack[-1]!=l[i]:
                ind[l[i]].append([ind_arr[stack[-1]]+1])
            stack.append(l[i])

    count=[]
    for i in range(1,n+1):
        if i in ind:
            maxa,length=0,0
            for j in ind[i]:
                if len(j)==1:
                    length=n-j[0]
                else:
                    length=j[1]-j[0]
                maxa=max(maxa,length)
            count.append(maxa)
        else:
            count.append(0)

    suff=[count[0]]
    ans=[0]*(n)
    for i in range(1,n):
        suff.append(min(suff[-1],count[i]))
    for i in range(n-1,-1,-1):
        req=n-i
        if suff[i]==req:
            ans[req-1]=1
    ans=''.join(map(str,ans))
    print(ans)
        
                
                
        
