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. 
r = int(input())
W = []
for u in range(r):
    n = int(input())
    P = list(map(int,input().split()))
    A = []
    for i in range(len(P)):
        A.append([P[i], i])
    A.sort(key=lambda elem: elem[0])
    C = [0]*len(A)
    V = [0]*len(A)     # список output
    C[A[0][1]] = 1
    V[A[0][0]-1] = 1
    d = 0  # количество пропусков
    D = [A[0][1],A[0][1]]   # границы d в списке  C
    for i in range(1,len(A)):
        t = A[i][1]
        C[t] = 1
        flag = 0

        v = D[1] - D[0]
        if  D[0] < t < D[1]:
            flag += 1
        if t > D[1]:
            D = [D[0],t]
        if t < D[0]:
            D = [t, D[1]]
        v1 = D[1] - D[0]

        if i == len(A) - 1:     # тема с последним элементом, который всегда красивый
            V[A[i][0] - 1] = 1
            continue

        if d == 0:    # все ровно
            if t - 1 > -1 and C[t - 1] == 1:     # тогда элемент красивый
                V[A[i][0] - 1] = 1
            elif t + 1 < len(C) and C[t + 1] == 1: # тогда элемент красивый
                V[A[i][0] - 1] = 1
            else:
                V[A[i][0] - 1] = 0     # элемент точно не красивый
                d += v1-v-1

        elif d == 1:          # т.е. есть пробел
            if flag == 1:
                V[A[i][0] - 1] = 1
                d -= 1
            else:
                V[A[i][0] - 1] = 0
                d += v1 - v - 1

        else:       # d не равно 0 или 1, а больше 1
            V[A[i][0] - 1] = 0
            if v1 == v:
                d -= 1
            else:
                d += v1 - v - 1
    W.append(V)

for i in range(len(W)):
    for j in range(len(W[i])):
        print(W[i][j], end='')
    print()