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.math.*;

public class B implements Runnable {

    public void run() {
        long startTime = System.nanoTime();

        int n = nextInt();
        int m = nextInt();
        int k = nextInt();

        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        int[] b = new int[m];
        for (int i = 0; i < m; i++) {
            b[i] = nextInt();
        }
        Arrays.sort(a);
        Arrays.sort(b);

        boolean no = true;
        int j = m;
        for (int i = n; i-- > 0;) {
            if (j > 0 && b[j - 1] >= a[i]) {
                j--;
            } else {
                no = false;
                break;
            }
        }
        println(no ? "NO" : "YES");

        if (fileIOMode) {
            System.out.println((System.nanoTime() - startTime) / 1e9);
        }
        out.close();
    }

    //-----------------------------------------------------------------------------------

    private static boolean fileIOMode;
    private static String problemName = "a";
    private static BufferedReader in;
    private static PrintWriter out;
    private static StringTokenizer tokenizer;

    public static void main(String[] args) throws Exception {
        fileIOMode = args.length > 0 && args[0].equals("!");
        if (fileIOMode) {
            in = new BufferedReader(new FileReader(problemName + ".in"));
            out = new PrintWriter(problemName + ".out");
        } else {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
        tokenizer = new StringTokenizer("");

        new Thread(new B()).start();
    }

    private static String nextLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    private static String nextToken() {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(nextLine());
        }
        return tokenizer.nextToken();
    }

    private static int nextInt() {
        return Integer.parseInt(nextToken());
    }

    private static long nextLong() {
        return Long.parseLong(nextToken());
    }

    private static double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    private static BigInteger nextBigInteger() {
        return new BigInteger(nextToken());
    }

    private static void print(Object o) {
        if (fileIOMode) {
            System.out.print(o);
        }
        out.print(o);
    }

    private static void println(Object o) {
        if (fileIOMode) {
            System.out.println(o);
        }
        out.println(o);
    }

    private static void printf(String s, Object... o) {
        if (fileIOMode) {
            System.out.printf(s, o);
        }
        out.printf(s, o);
    }
}
