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.*;

public class B {
	public static int i(String s) { return Integer.parseInt(s); }
	public static void main(String[] args) throws Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] arr = in.readLine().split("\\s+");
		int n = i(arr[0]);
		int m = i(arr[1]);
		int k = i(arr[2]);
		TreeMap<Integer, Integer> A = new TreeMap<Integer, Integer>();
		TreeMap<Integer, Integer> B = new TreeMap<Integer, Integer>();
		
		arr = in.readLine().split("\\s+"); 
		for(int i=0; i<n; i++) {
			int val = i(arr[i]);
			Integer prev = A.get(val);
			A.put(val, prev==null ? 1 : prev+1);
		}
		
		arr = in.readLine().split("\\s+"); 
		for(int i=0; i<m; i++) {
			int val = i(arr[i]);
			Integer prev = B.get(val);
			B.put(val, prev==null ? 1 : prev+1);
		}
		
		int A_extra = 0;
		while(!A.isEmpty() || !B.isEmpty()) {
			Integer key = null;
			if(A.isEmpty()) key = B.firstKey();
			else if(B.isEmpty()) key = A.firstKey();
			else key = Math.min(A.firstKey(), B.firstKey());
			
			Integer bb = B.get(key);
			if(bb == null) bb = 0;
			else B.remove(key);
			Integer aa = A.get(key);
			if(aa == null) aa = 0;
			else A.remove(key);
			aa += A_extra;
			
			A_extra = Math.max(0, aa-bb);
		}
		System.out.println(A_extra > 0 ? "YES" : "NO");
	}
}
