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.lang.*;
import static java.util.Arrays.*;

public class Main {
	public static void main(String[] args) throws IOException {
		new Thread(null, new Runnable() {
			public void run() {
				try {
					new Main().run();
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
		}, "1", 1 << 24).start();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

	final int maxn = 100100;

	int n, m, k;
	int alisa[] = new int[maxn];
	int robert[] = new int[maxn];

	void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));//new FileReader("input.txt"));
		out = new PrintWriter(System.out);//"output.txt");

		n = nextInt();
		m = nextInt();
		k = nextInt();
		for (int i = 0; i < n; i++)
			alisa[i] = nextInt();
		for (int i = 0; i < m; i++)
			robert[i] = nextInt();

		sort(alisa, 0, n);
		sort(robert, 0, m);

		int a = n - 1, r = m - 1;
		long countAlisa = 0, countRobert = 0;
		while (countAlisa <= countRobert && a >= 0) {
			while (r >= 0 && robert[r] >= alisa[a]) {
				countRobert++;
				r--;
			}
			countAlisa++;
			a--;
		}
		if (countAlisa <= countRobert)
			out.println("NO");
		else
			out.println("YES");

		in.close();
		out.close();
	}
	
	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

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