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.*;
import java.util.*;
import java.lang.*;

public class Rextester{
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        StringBuffer sb = new StringBuffer();
        while(t-->0){
            int n = Integer.parseInt(br.readLine());
            StringTokenizer st = new StringTokenizer(br.readLine());
            int[] array = new int[n];
            int[] count = new int[n];
            for(int i=0;i<n;i++){
                array[i]=Integer.parseInt(st.nextToken())-1;
                count[array[i]]++;
            }
            int x = 0;
            for(int i=0;i<n;i++){
                if(count[i]==1){
                    x++;
                }
            }
            boolean[] ans = new boolean[n];
            if(x==n){
                ans[0]=true;
            }
            if(count[0]>0){
                ans[n-1]=true;
            }
            int l=0,r=n-1;
            for(int i=n-1;i>0;--i){
                if(!ans[n-1]){
                    break;
                }
                ans[i]=true;
                int next= n-i-1;
                if((array[l]==next||array[r]==next)&&count[next+1]>0&&--count[next]==0){
                    if(array[l]==next){
                        l++;
                    }
                    else{
                        r--;
                    }
                    continue;
                }
                break;
            }
            for(boolean z:ans){
                sb.append(z?1:0);
            }
            sb.append("\n");
        }
        br.close();
        System.out.println(sb);
    }
}
            
                    
                      
                   