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. 
import math

ok = [0]*300002
v = []
rmq = [ [ 0 for i in range(300002) ] for j in range(20) ]
t = (int)(input())
n = 0
def check_perm ():
  v.sort()
  for i in  range(n + 1):
    if v[i] != i:
      return 0
  return 1


def query (l, r) :
  x = math.log2(r - l + 1)
  x = (int)(x)
  return min(rmq[x][l], rmq[x][r - (1 << x) + 1])

while t: 
  n = (int)(input())
  v = [0] + list(map(int, input().split()))
  for i in range(1, n + 1):
    rmq[0][i] = v[i]
  i = 1
  while (1 << i) <= n:
    for j in range(1, n - (1 << i) + 1 + 1):
      rmq[i][j] = min(rmq[i - 1][j], rmq[i - 1][j + (1 << (i - 1))])
    i += 1
  l = 1
  r = n
  for i in range(n):
    if query(l, r) == i + 1:
      ok[n - i] = 1
    if v[l] == i + 1:
      l += 1
    elif v[r] == i + 1:
      r -= 1
    else:
      break
  ok[1] = check_perm()
  for i in range(1, n + 1):
    print(ok[i], end = "")
    ok[i] = 0
  print ("")
  t -= 1

    
