Beautiful Numbers

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.

inputFormat

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.

outputFormat

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.

样例

3
6
4 5 1 3 2 6
5
5 3 1 2 4
4
1 4 3 2

101011
11111
1001

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