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.math.BigInteger;
import java.util.*;
import java.util.List;

import java.awt.*;

public class Main {

	static long sx = 0, sy = 0, mod = (long) (1e9 + 7);
	static int[][] dirs = { { 0, 1 }, { 1, 0 }, { 0, -1 }, { -1, 0 }, { 1, 1 }, { 1, -1 }, { -1, 1 }, { -1, -1 } };
	static ArrayList<Integer>[] a;
	static Integer[][][] dp;
	static long[] fa;
	static int[] farr;
	public static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<pair> pa = new ArrayList<>();
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long m = 998244353;
	static long[] no, col;
	static String s;
	// static long k = 0, n = 0, ans = 0;
	static long cnt;
	// static long[] dp;
	// static long[] p;
	// static long[] ans;
	// static Double[][] a = new Double[2][2];
	static Double[][] b = new Double[2][2];
	static Double[] x;
	static Double[] y;
	static long[] d;
	// static boolean b = true;
	static int[] par;
	static int[] depth;
	static HashMap<Integer, Integer> map;
	// static ArrayList<Integer> p;
	static int time = 0;
	static int[] size;
	static int[] arr;
	static pair[] p;
	static HashSet<Integer> ans = new HashSet<>();

	public static void main(String[] args) throws IOException {

		// Scanner scn = new Scanner(new BufferedReader(new
		// InputStreamReader(System.in)));

		Reader scn = new Reader();

		int t = scn.nextInt();

		z: while (t-- != 0) {

			int n = scn.nextInt();

			int[] a = scn.nextIntArray(n);

			pair[] or = new pair[n + 2];

			pair[] ar = new pair[n + 2];

			for (int i = 0; i < or.length; i++) {
				or[i] = new pair(-1, -1);
				ar[i] = new pair(-1, -1);
			}

			for (int i = 1; i <= n; i++) {

				or[i].s = 1;
				or[i].e = n - i + 1;
			}

			int[] nsl = NextSmallerLeft(a);
			int[] nsr = NextSmallerRight(a);

			for (int i = 0; i < n; i++) {

				int v = a[i];

				int l = nsr[i] - nsl[i] - 1;

				ar[v].s = 1;
				ar[v].e = Math.max(ar[v].e, l);
			}

			int[] ans = new int[n + 3];

			for (int i = 1; i <= n; i++) {

				if (ar[i].s == -1) {

					ans[or[i].s]++;

					ans[or[i].e + 1]--;
				}

				else {

					if (ar[i].e < or[i].e) {

						ans[ar[i].e + 1]++;
						ans[or[i].e + 1]--;
					}
				}
			}
			StringBuilder sb = new StringBuilder();

			for (int i = 1; i <= n; i++) {
				ans[i] += ans[i - 1];

				if (ans[i] > 0)
					sb.append("0");
				else
					sb.append("1");
			}

			System.out.println(sb);

		}

	}

	public static int[] NextSmallerLeft(int[] a) {

		int[] nsl = new int[a.length];

		Stack<Integer> s = new Stack<>();

		for (int i = 0; i < a.length; i++) {

			while (s.size() != 0 && a[s.peek()] >= a[i])
				s.pop();

			nsl[i] = s.size() == 0 ? -1 : s.peek();

			s.push(i);
		}

		return nsl;

	}

	public static int[] NextSmallerRight(int[] a) {

		int[] nsr = new int[a.length];

		Stack<Integer> s = new Stack<>();

		for (int i = a.length - 1; i >= 0; i--) {

			while (s.size() != 0 && a[s.peek()] >= a[i])
				s.pop();

			nsr[i] = s.size() == 0 ? a.length : s.peek();

			s.push(i);
		}

		return nsr;

	}

	// _________________________TEMPLATE_____________________________________________________________

	// public static long lcm(long x, long y) {
	//
	// return (x * y) / gcd(x, y);
	// }
	//
	// private static long gcd(long x, long y) {
	// if (x == 0)
	// return y;
	//
	// return gcd(y % x, x);
	// }
	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// return p2 - p1;
	//
	// }
	// }
	//
	// }
	//
	// public static long pow(long a, long b) {
	//
	// if (b < 0)
	// return 0;
	//
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {
		int s, e;

		pair(int a, int b) {

			s = a;
			e = b;
		}

		@Override
		public int compareTo(pair o) {

			return 1;
		}

		// @Override
		//
		// public int hashCode() {
		// return (int) (i * 17 + j * 31);
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.i == p.i && this.j == p.j;
		// }

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}