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.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        InputReader.OutputWriter out = new InputReader.OutputWriter(outputStream);

        int t = in.nextInt();
        while (t-->0) {
            int n = in.nextInt();
            int [] a = new int[n];
            int[] p = new int[2*100_000 + 5];
            for (int i = 0; i < a.length; i++) {
                a[i] = in.nextInt();
                p[a[i] - 1] = i;
            }
            int l = n;
            int r = 0;
            for (int i = 0; i < n; i++) {
                l = Math.min(l,p[i]);
                r = Math.max(r,p[i]);
                if(r - l == i) {
                    out.print(1);
                }
                else {
                    out.print(0);
                }
            }
            out.println();
        }

        out.flush();
    }
    private static char newChar(char previous, char next) {

        if(next == '?') {
            if(previous == 'a') return 'b';
            if (previous == 'b') return 'c';
            return 'a';
        }
        else {
            if(previous == 'a') {
                if(next == 'a') return 'b';
                if(next == 'b') return 'c';
                return 'b';
            }
            if(previous == 'b') {
                if(next == 'a') return 'c';
                if(next == 'b') return 'a';
                return 'a';
            }
            else {
                if(next == 'a') return 'b';
                if(next == 'b') return 'a';
                return 'a';
            }
        }
    }
    private static boolean check(char [] c) {
        for (int i = 0; i < c.length - 1; i++) {
            if(c[i] != '?' && c[i+1] != '?') {
                if(c[i] == c[i+1]) return false;
            }
        }
        return true;
    }

    private static void permutationOfNumbers(int n, int m, int [] a, int index) {
        if(index == n) {
            System.out.println(Arrays.toString(a));
            return;
        }
        for (int i = 1; i <=m; i++) {
            a[index] = i;
            permutationOfNumbers(n,m,a,index + 1);
        }
    }

    private static void permutationOfLetters( char m, int index, char[] a) {
        if(index == a.length) {
            System.out.println(Arrays.toString(a));
            return;
        }
        for (char c = 'a'; c <=m; c++) {
            a[index] = c;
            permutationOfLetters(m,index + 1, a);
        }
    }

    private static void permutations(int n, int index, int [] a, boolean [] used) {
        if(index == n) {
            System.out.println(Arrays.toString(a));
            return;
        }
        for (int i = 1; i <=n; i++) {
            if(used[i]) continue;
            a[index] = i;
            used[i] = true;
            permutations(n,index + 1,a,used);
            used[i] = false;
        }
    }

    private static boolean correct(String s) {
        Stack<Character> stack = new Stack<>();
        for(char c : s.toCharArray()) {
            if(c == '(' || c == '[') {
                stack.push(c);
            }
            else {
                if(stack.isEmpty()) return false;
                char peek = stack.peek();
                if(peek == '(' && c == ']') return false;
                if(peek == '[' && c == ')') return false;
                stack.pop();
            }
        }
        return stack.isEmpty();
    }
    private static void divideNumber(int sum, int last, int n, List<Integer> current) {
        if(sum > n) {
            return;
        }
        if(sum == n) {
            System.out.println(current);
            return;
        }
        for (int i = last; i <= n - sum ; i++) {
            current.add(i);
            divideNumber( sum + i, i,n,current);
            current.remove(current.size() - 1);
        }
    }
    private static void fishki(String s, int n, int m) {
        if(s.length() == n) {
            if(m == 0) {
                System.out.println(s);
            }
            return;
        }

        fishki(s + "*", n, m - 1);
        fishki(s + ".", n, m);
    }
    private static boolean check(String s) {
        for (int i = 0; i < s.length(); i++) {
            if(i > 0 && s.charAt(i) == '*' && s.charAt(i-1) == '*') return false;
        }
        return true;
    }
    private static boolean [] erath() {
        boolean[] isPrime = new boolean[200_000 + 1];
        Arrays.fill(isPrime,true);
        isPrime[0] = false;
        isPrime[1] = false;
        int n = isPrime.length - 1;
        for (int i = 2; i*i<=n; i++) {
            if(isPrime[i]) {
                for (int j = i*i; j <=n; j+=i) {
                    isPrime[j] = false;
                }
            }
        }
        return isPrime;
    }



    public static long gcd(long a, long b) {
       while (b > 0) {
           long temp = a;
           a = b;
           b = temp%b;
       }
       return a;
    }


    private static int factorization(long n) {
        Set<Long> set = new HashSet<>();
        for(long i = 2; i * i <=n; i++) {
            while (n % i == 0) {
                set.add(i);
                n /= i;
            }
        }
        if(n > 1) set.add(n);
        return set.size();
    }
}

class InputReader extends BufferedReader {
    StringTokenizer tokenizer;

    public InputReader(InputStream inputStream) {
        super(new InputStreamReader(inputStream), 32768);
    }

    public InputReader(String filename) {
        super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(readLine());
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
        return tokenizer.nextToken();
    }

    public Integer nextInt(){
        return Integer.valueOf(next());
    }
    public Long nextLong() {
        return  Long.valueOf(next());
    }
    public Double nextDouble() {
        return Double.valueOf(next());
    }
    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void close() {
            super.close();
        }
    }
}