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.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.LineNumberReader;
import java.math.BigInteger;
import java.util.*;

/**
 *
 * @author ahani
 */

public class Main {
    public static int First, Second, Queries;
    public static int[] Alice, Bob;
    public static boolean Flag;
    
    public static void main(String[] args) throws IOException {
        Scanner Input = new Scanner(System.in);
        //BufferedReader Input = new BufferedReader(new InputStreamReader(System.in));
        First = Input.nextInt();
        Second = Input.nextInt();
        Queries = Input.nextInt();
        Alice = new int[First];
        Bob = new int[Second];
        for(int i = 0; i < First; i++) Alice[i] = Input.nextInt();
        for(int i = 0; i < Second; i++) Bob[i] = Input.nextInt();
        Flag = false;
        Arrays.sort(Alice);
        Arrays.sort(Bob);
        if(First > Second) Flag = true;
        for(int i = 1; i <= Math.min(First, Second); i++) {
            if(Alice[First - i] > Bob[Second - i]) Flag = true;
        }
        System.out.println(Flag ? "YES" : "NO");
        
        
    }
        
}
