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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.Scanner
import kotlin.system.exitProcess

fun main(args: Array<String>) {
	val scn = Scanner(System.`in`)
	val n = scn.nextInt()
	val la = IntArray(n){scn.nextInt()}
	val lb = IntArray(n){scn.nextInt()}
	val ordA = la.indices.sortedBy { la[it] }.toIntArray()
	val ordB = lb.indices.sortedBy { lb[it] }.toIntArray()
	if (ordA.indices.any{la[ordA[it]]>lb[ordB[it]]}) ans(false)
	var k = ordB[0]
	var cnt = 0
	while(true){
		k = ordA[ordB[k]]
		cnt++
		if (k==ordB[0]) break
	}
	if (cnt!=n) ans(true)
	ans((0 until n-1).any{lb[ordB[it]]>=la[ordA[ordB[it+1]]]})
}

fun ans(ans: Boolean){
	println(if (ans) "Yes" else "No")
	exitProcess(0)
}