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.
// @author Sanzhar
import java.io.*;
import java.util.*;
import java.awt.Point;

public class Template {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st;

    String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(in.readLine());
            } catch (Exception e) {
            }
        }
        return st.nextToken();
    }

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

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

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

    public void run() throws Exception {
        //in = new BufferedReader(new FileReader("passwords.in"));
        //out = new PrintWriter(new FileWriter("passwords.out"));
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.flush();
        out.close();
        in.close();
    }

    public static void shuffleArray(long[] a) {
        int n = a.length;
        Random random = new Random();
        random.nextInt();
        for (int i = 0; i < n; i++) {
            int change = i + random.nextInt(n - i);
            long helper = a[i];
            a[i] = a[change];
            a[change] = helper;
        }
    }

    public void solve() throws Exception {
        int n = nextInt();
        int m = nextInt();
        long k = nextLong();
        long[] x = new long[n];
        for (int i = 0; i < n; i++) {
            x[i] = nextLong();
        }
        shuffleArray(x);
        Arrays.sort(x);
        long[] y = new long[m];
        for (int i = 0; i < m; i++) {
            y[i] = nextLong();
        }
        shuffleArray(y);
        Arrays.sort(y);
        boolean yes = false;
        if (n > m) {
            yes = true;
        } else {
            for (int i = 0; i < n; i++) {
                if (x[i] > y[m - n + i]) {
                    yes = true;
                }
            }
        }
        out.println(yes ? "YES" : "NO");
    }

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