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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::{stdin, Read};
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn main() {
    let n = read::<usize>();
    let mut a = (0..n).map(|i| (read::<usize>(), i)).collect::<Vec<_>>();
    let mut b = (0..n).map(|i| (read::<usize>(), i)).collect::<Vec<_>>();
    a.sort();
    b.sort();

    use std::collections::HashMap;
    let mut xm = HashMap::new();
    for i in 0..n {
        let (x, xi) = a[i];
        let (y, _) = b[i];
        xm.insert(xi, i);
        if x <= y {
            //
        } else {
            println!("No");
            return;
        }
    }

    for i in 0..n {
        let (_, yi) = b[i];
        let &ai = xm.get(&yi).unwrap();
        if a[ai].0 <= b[i].0 && a[i].0 <= b[ai].0 {
            println!("Yes");
            return;
        }
    }
    println!("No")
}