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)

fun main(args: Array<String>) {
    val N = readInputLine().toInt()
    
    val AArr = readInputLine().split(" ").map { it.toInt() }.toIntArray()
    val BArr = readInputLine().split(" ").map { it.toInt() }.toIntArray()
    
    val AArrSorted = AArr.copyOf()
    AArrSorted.sort()
    val BArrSorted = BArr.copyOf()
    BArrSorted.sort()
    
    for (i in 0 until N) {
        if (BArrSorted[i] < AArrSorted[i]) {
            println("No")
            return
        }
    }

    var wrongCnt = 0
    
    for (i in 0 until N) {
        if (BArr[i] < AArr[i]) {
            wrongCnt++
        }
    }

    if (wrongCnt == N - 1) {
        println("No")
    } else {
        println("Yes")
    }
}

fun readInputLine(): String {
    return readLine()!!
}