Problem:
Score : 600 points

Problem Statement

Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N.
Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:

Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.

Constraints

2 \leq N \leq 10^5

1 \leq A_i,B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

3
1 3 2
1 2 3

Sample Output 1

Yes

We should swap the values of A_2 and A_3.

Sample Input 2

3
1 2 3
2 2 2

Sample Output 2

No

Sample Input 3

6
3 1 2 6 3 4
2 2 8 3 4 3

Sample Output 3

Yes

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;

public class Main {

    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        solve(scanner);
    }

    static class Node {
        int val;
        int to;

        public Node(int val, int to) {
            this.val = val;
            this.to = to;
        }
    }

    // int N = scanner.nextInt();
    // scanner.nextLine();
    // int[] n = Arrays.stream(scanner.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
    static void solve(Scanner scanner) {
        int N = scanner.nextInt();
        scanner.nextLine();
        int[] a = Arrays.stream(scanner.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
        int[] b = Arrays.stream(scanner.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
        Node[] sa = new Node[N];
        for (int i = 0; i < N; i++) {
            sa[i] = new Node(a[i] ,i);
        }
        Arrays.sort(sa, Comparator.comparingInt(x -> x.val));
        Node[] sb = new Node[N];
        Map<Integer, Queue<Integer>> m = new HashMap<>();
        for (int i = 0; i < N; i++) {
            if (!m.containsKey(b[i])) {
                m.put(b[i], new ArrayDeque<>());
            }
            m.get(b[i]).add(i);
        }
        for (int i = 0; i < N; i++) {
            sb[i] = new Node(b[i], m.get(b[i]).poll());
        }
        Arrays.sort(sb, Comparator.comparingInt(x -> x.val));

        for (int i = 0; i < N; i++) {
            if (sa[i].val > sb[i].val) {
                System.out.println("No");
                return;
            }
        }

        TreeSet<Integer> rem = new TreeSet<>();
        for (int i = 0; i < N; i++)
            rem.add(i);
        int cycle = 0;
        while (!rem.isEmpty()) {
            int s = rem.first();
            rem.remove(s);
            int curr = sb[sa[s].to].to;

            while (curr != s) {
                rem.remove(curr);
                curr = sb[sa[curr].to].to;
            }
            cycle++;
        }

        if (cycle > 1) {
            System.out.println("Yes");
            return;
        }

        for (int i = 0; i < N - 1; i++) {
            if (sb[i].val >= sa[i + 1].val) {
                System.out.println("Yes");
                return;
            }
        }
        System.out.println("No");
    }
}