It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.

Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?

Input

The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.

The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.

Note that one may have caught more than one fish for a same species.

Output

Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.

Examples

Input

3 3 3
2 2 2
1 1 3


Output

YES


Input

4 7 9
5 2 7 3
3 5 2 7 3 8 7


Output

NO

Note

In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.

In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
import java.io.*;
import java.util.*;
import java.math.*;

public class B implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	void solve() throws IOException {
		int n = nextInt(), m = nextInt(), k = nextInt();
		Map<Integer, Integer> countFirst = readMap(n), countSecond = readMap(m);

		out.println(!isOk(countFirst, countSecond) ? "NO" : "YES");
	}

	private boolean isOk(Map<Integer, Integer> a, Map<Integer, Integer> b) {
		Set<Integer> allValues = new TreeSet(a.keySet());
		allValues.addAll(b.keySet());
		List<Integer> allValuesReversed = new ArrayList<Integer>(allValues);
		Collections.reverse(allValuesReversed);

		int curBalance = 0;

		for (int key : allValuesReversed) {
			int firstCount = getSmart(a, key);
			int secondCount = getSmart(b, key);
			
			curBalance += (firstCount - secondCount);
			
			if(curBalance > 0)
				return true;

		}

		return false;
	}

	private int getSmart(Map<Integer, Integer> a, int key) {
		Integer res = a.get(key);
		return (res == null) ? 0 : res;
	}

	private Map<Integer, Integer> readMap(int n) throws IOException {
		Map<Integer, Integer> count = new TreeMap<Integer, Integer>();
		for (int i = 0; i < n; i++) {
			int key = nextInt();
			Integer before = count.get(key);
			count.put(key, (before == null ? 0 : before) + 1);
		}
		return count;
	}

	public static void main(String[] args) {
		new B().run();
	}

	public void run() {
		try {
			final String className = this.getClass().getName().toLowerCase();

			try {
				in = new BufferedReader(new FileReader(className + ".in"));
				out = new PrintWriter(new FileWriter(className + ".out"));
				// in = new BufferedReader(new FileReader("input.txt"));
				// out = new PrintWriter(new FileWriter("output.txt"));
			} catch (FileNotFoundException e) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(42);
		}
	}

	String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}