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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;

class C
{
	static void Main()
	{
		Func<int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
		var n = int.Parse(Console.ReadLine());
		var a = read();
		var b = read();
		var ab = a.Zip(b, (x, y) => new { x, y }).OrderBy(_ => _.y).ThenBy(_ => _.x).ToArray();
		b = ab.Select(_ => _.y).ToArray();

		if (a.OrderBy(x => x).Where((x, i) => x > b[i]).Any()) { Console.WriteLine("No"); return; }

		int c = 0, k = 0;
		for (; c == 0 || k > 0; c++)
			if ((k = Array.BinarySearch(b, ab[k].x)) < 0) k = ~k;
		Console.WriteLine(c != n ? "Yes" : "No");
	}
}