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 java.io.PrintStream;
import java.util.Scanner;


public class Solution {

    public static void main(final String[] args) {
        final Scanner in = new Scanner(System.in);
        final PrintStream out = System.out;

        final int tests = in.nextInt();

        for (int test = 1; test <= tests; test++) {
            final int n = in.nextInt();
            final int[] a = new int[n];
            final char[] b = new char[n];
            final int[] c = new int[n];

            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt() - 1;
                b[i] = '0';
                c[a[i]]++;
            }

            int l = 0;
            int r = n - 1;

            b[l] = '1';
            b[r] = c[0] > 0 ? '1' : '0';

            for (int i = 0; i < n; i++) {
                if (c[i] != 1) {
                    b[l] = '0';
                    break;
                }
            }

            if (b[r] == '1') {
                for (int i = 0; i < n - 2; i++) {
                    if ((a[l] == i || a[r] == i) && c[i] == 1 && c[i + 1] > 0) {
                        if (a[l] == i) l++;
                        else r--;
                        b[n - 2 - i] = '1';
                        continue;
                    }

                    break;
                }
            }


            out.println(b);
        }

    }

}
