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.math.BigInteger;
import java.util.ArrayList;
import java.util.Map;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class B implements Runnable {

    // leave empty to read from stdin/stdout
    private static final String TASK_NAME_FOR_IO = "";

    // file names
    private static final String FILE_IN = TASK_NAME_FOR_IO + ".in";
    private static final String FILE_OUT = TASK_NAME_FOR_IO + ".out";

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tokenizer = new StringTokenizer("");

    public static void main(String[] args) {
        new Thread(new B()).start();
    }

    Map<Integer, Integer> cnt = new TreeMap<Integer, Integer>();
    ArrayList<Integer> data = new ArrayList<Integer>();

    private void add(int idx, int d) {
        if (cnt.containsKey(idx)) {
            cnt.put(idx, cnt.get(idx) + d);
        } else {
            cnt.put(idx, d);
        }
    }

    private void solve() throws IOException {
        int p1 = nextInt();
        int p2 = nextInt();
        int k = nextInt();

        for (int i = 0; i < p1; i++) {
            int idx = nextInt();
            add(idx, 1);
        }

        for (int i = 0; i < p2; i++) {
            int idx = nextInt();
            add(idx, -1);
        }

        for (Map.Entry<Integer, Integer> e : cnt.entrySet()) {
            int p = e.getValue();
            if (p != 0) {
                data.add(p);
            }
        }

        boolean result;
        if (data.isEmpty()) {
            result = false;
        } else {

            result = false;
            int sumTail = 0;
            for (int idx = data.size() - 1; idx >= 0; idx--) {
                sumTail += data.get(idx);
                if (sumTail > 0) {
                    result = true;
                    break;
                }
            }


            /*
            int last = data.get(data.size() - 1);
            if (last > 0) {
                result = true;
            } else {

                // count all negative at the end
                int sumTail = 0;
                int idx = data.size() - 1;
                while (idx >= 0 && data.get(idx) < 0) {
                    sumTail += Math.abs(data.get(idx));
                    idx--;
                }

                // no positive?
                if (idx < 0) {
                    result = false;
                } else {
                    // count all positive
                    int sumHead = 0;
                    int idx2 = idx;
                    while (idx2 >= 0 && data.get(idx2) > 0) {
                        sumHead += data.get(idx2);
                        idx2--;
                    }

                    result = sumHead > sumTail;
                }

            }
            */


        }

        if (result) {
            out.print("YES");
        } else {
            out.print("NO");
        }
    }

    public void run() {
        long timeStart = System.currentTimeMillis();

        boolean fileIO = TASK_NAME_FOR_IO.length() > 0;
        try {

            if (fileIO) {
                in = new BufferedReader(new FileReader(FILE_IN));
                out = new PrintWriter(new FileWriter(FILE_OUT));
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(new OutputStreamWriter(System.out));
            }

            solve();

            in.close();
            out.close();
        } catch (IOException e) {
            throw new IllegalStateException(e);
        }
        long timeEnd = System.currentTimeMillis();

        if (fileIO) {
            System.out.println("Time spent: " + (timeEnd - timeStart) + " ms");
        }
    }

    private String nextToken() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null) {
                return null;
            }
            tokenizer = new StringTokenizer(line);
        }
        return tokenizer.nextToken();
    }

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

    private BigInteger nextBigInt() throws IOException {
        return new BigInteger(nextToken());
    }

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

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

}