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.util.*;
import java.io.*;
import java.math.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {

	public void solve() throws Exception {
		int n = sc.nextInt(), m = sc.nextInt(), k = sc.nextInt();
		int[] w = new int[n + m];
		int[] w1 = new int[n];
		for (int i = 0; i < n; i++) {
			w1[i] = sc.nextInt();
			w[i] = w1[i];
		}
		int[] w2 = new int[m];
		for (int i = 0; i < m; i++) {
			w2[i] = sc.nextInt();
			w[n + i] = w2[i];
		}
		Arrays.sort(w);
		int[] ww = new int[n + m];
		int cnt = 0;
		for (int i = 0; i < n + m; i++) {
			if (i == 0 || w[i] != w[i - 1]) {
				ww[cnt++] = w[i];
			}
		}
		int[] wbal = new int[cnt];
		for (int i = 0; i < n; i++) {
			int pos = Arrays.binarySearch(ww, 0, cnt, w1[i]);
			wbal[pos]++;
		}
		for (int i = 0; i < m; i++) {
			int pos = Arrays.binarySearch(ww, 0, cnt, w2[i]);
			wbal[pos]--;
		}
		int curbal = 0;
		for (int i = cnt - 1; i >= 0; i--) {
			curbal += wbal[i];
			if (curbal > 0) {
				out.println("YES");
				return;
			}
		}
		out.println("NO");
	}

	static Throwable uncaught;

	BufferedReader in;
	FastScanner sc;
	PrintWriter out;

	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			sc = new FastScanner(in);
			solve();
		} catch (Throwable uncaught) {
			Solution.uncaught = uncaught;
		} finally {
			out.close();
		}
	}

	public static void main(String[] args) throws Throwable {
		Thread thread = new Thread(null, new Solution(), "", (1 << 26));
		thread.start();
		thread.join();
		if (Solution.uncaught != null) {
			throw Solution.uncaught;
		}
	}

}

class FastScanner {

	BufferedReader in;
	StringTokenizer st;

	public FastScanner(BufferedReader in) {
		this.in = in;
	}

	public String nextToken() throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}

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

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

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

}