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.*;

public class B {

    MyScanner in;
    PrintWriter out;

    public static void main(String[] args) throws Exception {
        new B().run();
    }

    public void run() throws Exception {
        in = new MyScanner();
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    public void solve() throws Exception {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        TreeMap<Integer, Integer> ha = new TreeMap<Integer, Integer>();
        TreeMap<Integer, Integer> hb = new TreeMap<Integer, Integer>();
        TreeSet<Integer> types = new TreeSet<Integer>();
        for (int i = 0; i < n; i++) {
            int a = in.nextInt();
            if (!ha.containsKey(a)) {
                ha.put(a, 1);
            } else {
                ha.put(a, ha.get(a) + 1);
            }
            types.add(a);
        }
        for (int i = 0; i < m; i++) {
            int a = in.nextInt();
            if (!hb.containsKey(a)) {
                hb.put(a, 1);
            } else {
                hb.put(a, hb.get(a) + 1);
            }
            types.add(a);
        }
        
        ArrayDeque<Integer> l = new ArrayDeque<Integer>();
        for (Integer p : types) {
            int ca = (ha.containsKey(p)) ? ha.get(p) : 0;
            int cb = (hb.containsKey(p)) ? hb.get(p) : 0;
            l.addFirst(ca - cb);
        }
        int sum = 0;
        for (Integer p : l) {
            sum += p;
            if (sum > 0) {
                out.println("YES");
                return;
            }
        }
        out.println("NO");
    }

    class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() throws Exception {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws Exception {
            while ((st == null) || (!st.hasMoreTokens())) {
                String t = br.readLine();
                if (t == null) {
                    return null;
                }
                st = new StringTokenizer(t);
            }
            return st.nextToken();
        }

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

        double nextDouble() throws Exception {
            return Double.parseDouble(next());
        }

        boolean nextBoolean() throws Exception {
            return Boolean.parseBoolean(next());
        }

        long nextLong() throws Exception {
            return Long.parseLong(next());
        }
    }
}
