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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) throws Exception {
        InputReader in = new InputReader(System.in);
        int n = in.nextInt(), m = in.nextInt(), k = in.nextInt();// who cares
                                                                    // about k
                                                                    // anyway
        int[] first = new int[n];
        int[] second = new int[m];
        for (int i = 0; i < n; i++)
            first[i] = in.nextInt();
        for (int i = 0; i < m; i++)
            second[i] = in.nextInt();
        Integer[] total = new Integer[n + m];
        for (int i = 0; i < n; i++)
            total[i] = first[i];
        for (int i = 0; i < m; i++)
            total[i + n] = second[i];
        Arrays.sort(total);
        int[] index = new int[n + m];
        index[0] = 0;
        for (int i = 1; i < total.length; i++) {
            if (total[i] == total[i - 1])
                index[i] = index[i - 1];
            else
                index[i] = index[i - 1] + 1;
        }
        int max = index[index.length - 1];
        int[] freq = new int[max + 1];
        for (int i = 0; i < first.length; i++) {
            int lo = 0;
            int hi = index.length - 1;
            while (hi > lo) {
                int mid = (lo + hi) / 2;
                if (total[mid] >= first[i])
                    hi = mid;
                else
                    lo = mid + 1;
            }
            freq[index[lo]]++;
        }
        for (int i = 0; i < second.length; i++) {
            int lo = 0;
            int hi = index.length - 1;
            while (hi > lo) {
                int mid = (lo + hi) / 2;
                if (total[mid] >= second[i])
                    hi = mid;
                else
                    lo = mid + 1;
            }
            freq[index[lo]]--;
        }
        int sum = 0;
        for (int i = freq.length - 1; i >= 0; i--) {
            sum += freq[i];
            if (sum > 0) {
                System.out.println("YES");
                return;
            }
        }
        System.out.println("NO");
    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

}
