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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {
	public static void main(String[] args) throws Exception {
		int n = nextInt();
		int m = nextInt();
		int k = nextInt();
		Integer[] alice = new Integer[n];
		for (int i = 0; i < n; i++) {
			alice[i] = nextInt();
		}
		Arrays.sort(alice);
		Integer[] bob = new Integer[m];
		for (int i = 0; i < m; i++) {
			bob[i] = nextInt();
		}
		Arrays.sort(bob);
		if (alice[n - 1] > bob[m - 1] || n > m) {
			System.out.println("YES");
		} else {
			int j = 0;
			boolean exceeded=false;
			for (int i = 0; j < m && i < n; i++) {
				if (alice[i] <= bob[j]) {
					j++;
				} else if (alice[i] > bob[j]) {
					exceeded=true;
					while (j < m && bob[j] < alice[i]) {
						j++;
					}
				}
			}
			if (j == m&&exceeded) {
				System.out.println("YES");
			} else
				System.out.println("NO");
		}
	}

	static BufferedReader br = new BufferedReader(new InputStreamReader(
			System.in));
	static StringTokenizer st = new StringTokenizer("");

	static int nextInt() throws Exception {
		return Integer.parseInt(next());
	}

	static String next() throws Exception {
		while (true) {
			if (st.hasMoreTokens()) {
				return st.nextToken();
			}
			String s = br.readLine();
			if (s == null) {
				return null;
			}
			st = new StringTokenizer(s);
		}
	}

}
