description: n players are playing a game. 
  
  There are two different maps in the game. For each player, we know his strength on each map. When two players fight on a specific map, the player with higher strength on that map always wins. No two players have the same strength on the same map. 
  
  You are the game master and want to organize a tournament. There will be a total of n-1 battles. While there is more than one player in the tournament, choose any map and any two remaining players to fight on it. The player who loses will be eliminated from the tournament. 
  
  In the end, exactly one player will remain, and he is declared the winner of the tournament. For each player determine if he can win the tournament.
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of test cases follows.
  
  The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5) — the number of players.
  
  The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9, a_i ≠ a_j for i ≠ j), where a_i is the strength of the i-th player on the first map. 
  
  The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^9, b_i ≠ b_j for i ≠ j), where b_i is the strength of the i-th player on the second map. 
  
  It is guaranteed that the sum of n over all test cases does not exceed 10^5.
  
  Output
  
  For each test case print a string of length n. i-th character should be "1" if the i-th player can win the tournament, or "0" otherwise.
  
  Example
  
  Input
  
  
  3
  4
  1 2 3 4
  1 2 3 4
  4
  11 12 20 21
  44 22 11 30
  1
  1000000000
  1000000000
  
  
  Output
  
  
  0001
  1111
  1
  
  Note
  
  In the first test case, the 4-th player will beat any other player on any game, so he will definitely win the tournament.
  
  In the second test case, everyone can be a winner. 
  
  In the third test case, there is only one player. Clearly, he will win the tournament.
solution: import java.util.PriorityQueue;
  
  public class Main {
  
  	public static void main(String[] args) {
  		new Main();
  	}
  
  	public Main() {
  		FastScanner fs = new FastScanner();
  		java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  		solve(fs, out);
  		out.flush();
  	}
  
  	public void solve(FastScanner fs, java.io.PrintWriter out) {
  		int t = fs.nextInt();
  		while(t --> 0) {
  			int n = fs.nextInt();
  			int[] a = new int[n], b = new int[n];
  			for (int i = 0;i < n;++ i) a[i] = fs.nextInt();
  			for (int i = 0;i < n;++ i) b[i] = fs.nextInt();
  
  			PriorityQueue<Integer> pqa = new PriorityQueue<>((l, r) -> Integer.compare(a[r], a[l]));
  			PriorityQueue<Integer> pqb = new PriorityQueue<>((l, r) -> Integer.compare(b[r], b[l]));
  			for (int i = 0;i < n;++ i) {
  				pqa.add(i);
  				pqb.add(i);
  			}
  			int amax = a[pqa.peek()], bmax = b[pqb.peek()];
  			while(!pqb.isEmpty() && b[pqb.peek()] >= bmax || !pqa.isEmpty() && a[pqa.peek()] >= amax) {
  				while(!pqb.isEmpty() && b[pqb.peek()] >= bmax) {
  					amax = Math.min(amax, a[pqb.poll()]);
  				}
  				while(!pqa.isEmpty() && a[pqa.peek()] >= amax) {
  					bmax = Math.min(bmax, b[pqa.poll()]);
  				}
  			}
  			for (int i = 0;i < n;++ i) {
  				if (a[i] >= amax || b[i] >= bmax) out.print('1');
  				else out.print('0');
  			}
  			out.println();
  		}
  	}
  
  	final int MOD = 998_244_353;
  	int plus(int n, int m) {
  		int sum = n + m;
  		if (sum >= MOD) sum -= MOD;
  		return sum;
  	}
  	int minus(int n, int m) {
  		int sum = n - m;
  		if (sum < 0) sum += MOD;
  		return sum;
  	}
  	int times(int n, int m) {
  		return (int)((long)n * m % MOD);
  	}
  	int divide(int n, int m) {
  		return times(n, IntMath.pow(m, MOD - 2, MOD));
  	}
  	int[] fact, invf;
  	void calc(int len) {
  		len += 2;
  		fact = new int[len];
  		invf = new int[len];
  		fact[0] = fact[1] = invf[0] = invf[1] = 1;
  		for (int i = 2;i < fact.length;++ i) fact[i] = times(fact[i - 1], i);
  		invf[len - 1] = divide(1, fact[len - 1]);
  		for (int i = len - 1;i > 1;-- i) invf[i - 1] = times(i, invf[i]);
  	}
  	int comb(int n, int m) {
  		if (n < m) return 0;
  		return times(fact[n], times(invf[n - m], invf[m]));
  	}
  }
  
  class FastScanner {
  
  	private final java.io.InputStream in = System.in;
  	private final byte[] buffer = new byte[8192];
  	private int ptr = 0;
  	private int buflen = 0;
  
  	private boolean hasNextByte() {
  		if (ptr < buflen) return true;
  		ptr = 0;
  		try {
  			buflen = in.read(buffer);
  		} catch (java.io.IOException e) {
  			e.printStackTrace();
  		}
  		return buflen > 0;
  	}
  
  	private byte readByte() {
  		return hasNextByte() ? buffer[ptr++ ] : -1;
  	}
  
  	private static boolean isPrintableChar(byte c) {
  		return 32 < c || c < 0;
  	}
  
  	private static boolean isNumber(int c) {
  		return '0' <= c && c <= '9';
  	}
  
  	public boolean hasNext() {
  		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
  			ptr++ ;
  		return hasNextByte();
  	}
  
  	public String next() {
  		if (!hasNext()) throw new java.util.NoSuchElementException();
  		StringBuilder sb = new StringBuilder();
  		byte b;
  		while (isPrintableChar(b = readByte()))
  			sb.appendCodePoint(b);
  		return sb.toString();
  	}
  
  	public final char nextChar() {
  		if (!hasNext()) throw new java.util.NoSuchElementException();
  		return (char)readByte();
  	}
  
  	public final long nextLong() {
  		if (!hasNext()) throw new java.util.NoSuchElementException();
  		long n = 0;
  		try {
  			byte b = readByte();
  			if (b == '-') {
  				while (isNumber(b = readByte()))
  					n = n * 10 + '0' - b;
  				return n;
  			} else if (!isNumber(b)) throw new NumberFormatException();
  			do
  				n = n * 10 + b - '0';
  			while (isNumber(b = readByte()));
  		} catch (java.util.NoSuchElementException e) {}
  		return n;
  	}
  
  	public final int nextInt() {
  		if (!hasNext()) throw new java.util.NoSuchElementException();
  		int n = 0;
  		try {
  			byte b = readByte();
  			if (b == '-') {
  				while (isNumber(b = readByte()))
  					n = n * 10 + '0' - b;
  				return n;
  			} else if (!isNumber(b)) throw new NumberFormatException();
  			do
  				n = n * 10 + b - '0';
  			while (isNumber(b = readByte()));
  		} catch (java.util.NoSuchElementException e) {}
  		return n;
  	}
  
  	public double nextDouble() {
  		return Double.parseDouble(next());
  	}
  }
  
  class Arrays {
  
  	public static void sort(final int[] array) {
  		sort(array, 0, array.length);
  	}
  
  	public static void sort(final int[] array, int fromIndex, int toIndex) {
  		if (toIndex - fromIndex  <= 512) {
  			java.util.Arrays.sort(array, fromIndex, toIndex);
  			return;
  		}
  		sort(array, fromIndex, toIndex, 0, new int[array.length]);
  	}
  
  	private static final void sort(int[] a, final int from, final int to, final int l, final int[] bucket) {
  		if (to - from  <= 512) {
  			java.util.Arrays.sort(a, from, to);
  			return;
  		}
  		final int BUCKET_SIZE = 256;
  		final int INT_RECURSION = 4;
  		final int MASK = 0xff;
  		final int shift = l << 3;
  		final int[] cnt = new int[BUCKET_SIZE + 1];
  		final int[] put = new int[BUCKET_SIZE];
  		for (int i = from; i < to; i++) ++ cnt[(a[i] >>> shift & MASK) + 1];
  		for (int i = 0; i < BUCKET_SIZE; i++) cnt[i + 1] += cnt[i];
  		for (int i = from; i < to; i++) {
  			int bi = a[i] >>> shift & MASK;
  			bucket[cnt[bi] + put[bi]++] = a[i];
  		}
  		for (int i = BUCKET_SIZE - 1, idx = from; i >= 0; i--) {
  			int begin = cnt[i];
  			int len = cnt[i + 1] - begin;
  			System.arraycopy(bucket, begin, a, idx, len);
  			idx += len;
  	    }
  		final int nxtL = l + 1;
  		if (nxtL < INT_RECURSION) {
  			sort(a, from, to, nxtL, bucket);
  			if (l == 0) {
  				int lft, rgt;
  				lft = from - 1; rgt = to;
  				while (rgt - lft > 1) {
  					int mid = lft + rgt >> 1;
  					if (a[mid] < 0) lft = mid;
  					else rgt = mid;
  				}
  				reverse(a, from, rgt);
  				reverse(a, rgt, to);
  	        }
  	    }
  	}
  
  	public static void sort(final long[] array) {
  		sort(array, 0, array.length);
  	}
  
  	public static void sort(final long[] array, int fromIndex, int toIndex) {
  		if (toIndex - fromIndex  <= 512) {
  			java.util.Arrays.sort(array, fromIndex, toIndex);
  			return;
  		}
  		sort(array, fromIndex, toIndex, 0, new long[array.length]);
  	}
  
  	private static final void sort(long[] a, final int from, final int to, final int l, final long[] bucket) {
  		final int BUCKET_SIZE = 256;
  		final int LONG_RECURSION = 8;
  		final int MASK = 0xff;
  		final int shift = l << 3;
  		final int[] cnt = new int[BUCKET_SIZE + 1];
  		final int[] put = new int[BUCKET_SIZE];
  		for (int i = from; i < to; i++) ++ cnt[(int) ((a[i] >>> shift & MASK) + 1)];
  		for (int i = 0; i < BUCKET_SIZE; i++) cnt[i + 1] += cnt[i];
  		for (int i = from; i < to; i++) {
  			int bi = (int) (a[i] >>> shift & MASK);
  			bucket[cnt[bi] + put[bi]++] = a[i];
  		}
  		for (int i = BUCKET_SIZE - 1, idx = from; i >= 0; i--) {
  			int begin = cnt[i];
  			int len = cnt[i + 1] - begin;
  			System.arraycopy(bucket, begin, a, idx, len);
  			idx += len;
  	    }
  		final int nxtL = l + 1;
  		if (nxtL < LONG_RECURSION) {
  			sort(a, from, to, nxtL, bucket);
  			if (l == 0) {
  				int lft, rgt;
  				lft = from - 1; rgt = to;
  				while (rgt - lft > 1) {
  					int mid = lft + rgt >> 1;
  					if (a[mid] < 0) lft = mid;
  					else rgt = mid;
  				}
  				reverse(a, from, rgt);
  				reverse(a, rgt, to);
  	        }
  	    }
  	}
  
  	public static void reverse(int[] array) {
  		reverse(array, 0, array.length);
  	}
  
  	public static void reverse(int[] array, int fromIndex, int toIndex) {
  		for (-- toIndex;fromIndex < toIndex;++ fromIndex, -- toIndex) {
  			int swap = array[fromIndex];
  			array[fromIndex] = array[toIndex];
  			array[toIndex] = swap;
  		}
  	}
  
  	public static void reverse(long[] array) {
  		reverse(array, 0, array.length);
  	}
  
  	public static void reverse(long[] array, int fromIndex, int toIndex) {
  		for (-- toIndex;fromIndex < toIndex;++ fromIndex, -- toIndex) {
  			long swap = array[fromIndex];
  			array[fromIndex] = array[toIndex];
  			array[toIndex] = swap;
  		}
  	}
  
  	public static void shuffle(int[] array) {
  		java.util.Random rnd = new java.util.Random();
  		for (int i = 0;i < array.length;++ i) {
  			int j = rnd.nextInt(array.length - i) + i;
  			int swap = array[i];
  			array[i] = array[j];
  			array[j] = swap;
  		}
  	}
  
  	public static void shuffle(long[] array) {
  		java.util.Random rnd = new java.util.Random();
  		for (int i = 0;i < array.length;++ i) {
  			int j = rnd.nextInt(array.length - i) + i;
  			long swap = array[i];
  			array[i] = array[j];
  			array[j] = swap;
  		}
  	}
  }
  
  class IntMath {
  
  	public static int gcd(int a, int b) {
  		while (a != 0)
  			if ((b %= a) != 0) a %= b;
  			else return a;
  		return b;
  	}
  
  	public static int gcd(int... array) {
  		int ret = array[0];
  		for (int i = 1; i < array.length; ++i)
  			ret = gcd(ret, array[i]);
  		return ret;
  	}
  
  	public static long gcd(long a, long b) {
  		while (a != 0)
  			if ((b %= a) != 0) a %= b;
  			else return a;
  		return b;
  	}
  
  	public static long gcd(long... array) {
  		long ret = array[0];
  		for (int i = 1; i < array.length; ++i)
  			ret = gcd(ret, array[i]);
  		return ret;
  	}
  
  	public static long lcm(long a, long b) {
  		return a / gcd(a, b) * b;
  	}
  
  	public static int pow(int a, int b) {
  		int ans = 1;
  		for (int mul = a; b > 0; b >>= 1, mul *= mul)
  			if ((b & 1) != 0) ans *= mul;
  		return ans;
  	}
  
  	public static long pow(long a, long b) {
  		long ans = 1;
  		for (long mul = a; b > 0; b >>= 1, mul *= mul)
  			if ((b & 1) != 0) ans *= mul;
  		return ans;
  	}
  
  	public static int pow(int a, long b, int mod) {
  		if (b < 0) b = b % (mod - 1) + mod - 1;
  		long ans = 1;
  		for (long mul = a; b > 0; b >>= 1, mul = mul * mul % mod)
  			if ((b & 1) != 0) ans = ans * mul % mod;
  		return (int)ans;
  	}
  
  	public static int pow(long a, long b, int mod) {
  		return pow((int)(a % mod), b, mod);
  	}
  
  	public static int floorsqrt(long n) {
  		return (int)Math.sqrt(n + 0.1);
  	}
  
  	public static int ceilsqrt(long n) {
  		return n <= 1 ? (int)n : (int)Math.sqrt(n - 0.1) + 1;
  	}
  }
  