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 static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;
import java.math.*;

public class RatingCompression2
{
    public static void main(String hi[]) throws Exception
    {
        BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(infile.readLine());
        int T = Integer.parseInt(st.nextToken());
        StringBuilder sb = new StringBuilder();
        while(T-->0)
        {
            st = new StringTokenizer(infile.readLine());
            int N = Integer.parseInt(st.nextToken());
            int[] arr = readArr(N, infile, st);
            ArrayDeque<Integer>[] locs = new ArrayDeque[N+1];
            for(int i=1; i <= N; i++)
                locs[i] = new ArrayDeque<Integer>();
            for(int i=0; i < N; i++)
                locs[arr[i]].add(i);
            int leftbound = 0;
            for(int i=1; i < N; i++)
            {
                if(arr[i] <= arr[i-1])
                    break;
                leftbound = i;
            }
            int rightbound = N-1;
            for(int i=N-2; i >= 0; i--)
            {
                if(arr[i] <= arr[i+1])
                    break;
                rightbound = i;
            }
            int[] res = new int[N];
            int min = 0;
            for(int v=1; v <= N; v++)
            {
                if(locs[v].size() == 0)
                    break;
                min = v;
            }
            int left = -1, right = -2;
            int sum = 0;
            //System.out.println(leftbound+" "+rightbound+" "+min);
            for(int v=N; v >= 1; v--)
            {
                for(int dex: locs[v])
                {
                    if(left == -1)
                        left = right = dex;
                    left = min(left, dex);
                    right = max(right, dex);
                }
                sum += locs[v].size();
                if(sum == right-left+1 && N-sum == v-1)
                {
                    if(left <= leftbound+1 && right >= rightbound-1 && min >= v)
                        res[N-v] = 1;
                }
            }
            HashSet<Integer> set = new HashSet<Integer>();
            for(int x: arr)
                set.add(x);
            if(set.size() == N)
                res[0] = 1;
            for(int x: res)
                sb.append(x);
            sb.append("\n");
        }
        System.out.print(sb);
    }
    public static int[] readArr(int N, BufferedReader infile, StringTokenizer st) throws Exception
    {
        int[] arr = new int[N];
        st = new StringTokenizer(infile.readLine());
        for(int i=0; i < N; i++)
            arr[i] = Integer.parseInt(st.nextToken());
        return arr;
    }
}