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. 
import java.util.Scanner;
public class BeutifulNumber2{
    public static String beutifulMaker(int[] list){
        StringBuilder result = new StringBuilder();
        
        int[] index_holder = new int[list.length];
        for(int i = 0; i < list.length; i++){
            int num = list[i];
            index_holder[num - 1] = i;
        }
        int min = index_holder[0];
        int max = index_holder[0];

        for(int i=0; i<index_holder.length; i++){
            if(index_holder[i] < min){
                min = index_holder[i]; 
            }
            if(index_holder[i] > max){
                max = index_holder[i];
            }
            
            if(max - min == i){
                
                result.append("1");
            }else{
                result.append("0");
            }
        }

        
        return result.toString();
    }

     //Takes string input and prints out the final result in string form
     public static String printBeutifulNumber(String num){
        String[] s_num = num.split("\\s+");// converting given string to string array
        int[] input_num = new int[s_num.length];
        for(int i = 0; i<s_num.length; i++){
            input_num[i] = Integer.parseInt(s_num[i]);
        }//Convert given string to int array
        String result = beutifulMaker(input_num);
        return result;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int iteration  = scanner.nextInt();
        String[] inputs = new String[iteration];
        int counter = 0;
      
        while(iteration > 0){
            int len1 = scanner.nextInt();
            scanner.nextLine();
            String input = scanner.nextLine();
            inputs[counter] = input;
            counter++;
            iteration--;
        }
        for(int i = 0; i < inputs.length; i++){
            System.out.println(printBeutifulNumber(inputs[i]));
        }
        
    }
}