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: Runtime Error)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let a = read_vec::<usize>();
    let b = read_vec::<usize>();
    let mut sorted_a = a.clone();
    sorted_a.sort();
    let mut sorted_b = b.clone();
    sorted_b.sort();

    let mut pairs = HashMap::new();
    for i in 0..n {
        if sorted_a[i] > sorted_b[i] {
            // debug!("here");
            println!("No");
            return;
        }
        pairs.insert(sorted_a[i], sorted_b[i]);
    }
    // not strict
    for i in 1..n {
        if sorted_b[i - 1] >= sorted_a[i] {
            println!("Yes");
            return;
        }
    }

    let mut diff_count = 0;
    for i in 0..n {
        let mut target = pairs[&a[i]];
        if b[i] != target {
            diff_count += 1;
        }
    }
    assert!(false);

    if diff_count == n {
        println!("No");
    } else {
        println!("Yes");
    }
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}