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.*;

public class Rextester{
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        StringTokenizer st1 = new StringTokenizer(br.readLine());
        StringTokenizer st2 = new StringTokenizer(br.readLine());
        br.close();
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        int[] alice = new int[n];
        int[] bob = new int[m];
        for(int i=0;i<n;i++){
            alice[i]=Integer.parseInt(st1.nextToken());
        }
        for(int i=0;i<m;i++){
            bob[i]=Integer.parseInt(st2.nextToken());
        }
        Arrays.sort(alice);
        Arrays.sort(bob);
        int count = 0;
        int i=0,j=0;
        while(i<n && j<m){
            if(alice[i]>bob[j]){
                j++;
            }
            else{
                i++;
                j++;
            }
        }
        while(i<n){
            count++;
            i++;
        }
        while(j<m){
            count--;
            j++;
        }
        if(alice[n-1]>bob[m-1]){
            System.out.println("YES");
        }
        else if(count>0){
            System.out.println("YES");
        }
        else{
            System.out.println("NO");
        }
    }
}
        