Rating Compression

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.

inputFormat

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.

outputFormat

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.

样例

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

10111
0001
00111
1111111111
000

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