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. 



/* package codechef; // don't place package name! */
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;






public class HelloWorld{

    public static void main(String[] args) throws IOException 
    { 
  
        Scanner input = new Scanner(System.in);
        input.nextInt();
        while(input.hasNext()){
            int n=input.nextInt();
            int[] l=new int[n];
            int x=0;
            int y=0;
            for(int i=0;i<n;i++){
                l[i]=input.nextInt();
                if(l[i]==1){
                    x=i;
                    y=i;
                }
            }
            int ele=1;
            int max=1;
            StringBuilder sb=new StringBuilder();
            while(y-x+1<=n){
                if(max==ele){
                    sb.append("1");
                }
                else{
                    sb.append("0");
                }
                if(x-1>=0 && y+1<n){
                    if(l[x-1]>l[y+1]){
                        y++;
                        ele++;
                        max=Math.max(max, l[y]);
                        continue;
                    }
                    x--;
                    ele++;
                    max=Math.max(max, l[x]);
                    continue;
                }
                if(x-1>=0){
                    x--;
                    ele++;
                    max=Math.max(max, l[x]);
                    continue;
                }
                if(y+1<n){
                    y++;
                    ele++;
                    max=Math.max(max, l[y]);
                    continue;
                }
                break;
            }
            System.out.println(sb.toString());
        }
    }
 
    
 
}