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: Accepted)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let N: usize = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    };
    let mut A: Vec<usize> = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|x| x.parse().unwrap())
            .collect()
    };
    let mut B: Vec<usize> = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|x| x.parse().unwrap())
            .collect()
    };

    let mut C = (0..N).map(|i| (A[i], i)).collect::<Vec<_>>();
    let mut D = (0..N).map(|i| (B[i], i)).collect::<Vec<_>>();
    C.sort();
    D.sort();
    let mut res = true;
    let mut w = false;
    // println!("{:?}", C);
    // println!("{:?}", D);
    for k in 0..(N - 1) {
        let (c, i) = C[k];
        let (d, j) = D[k];
        if c > d { res = false; }
        else if C[k + 1].0 <= d { w = true; }
    }
    if C[N - 1].0 > D[N - 1].0 { res = false; }

    for k in 0..N {
        let (c, i) = C[k];
        let (d, j) = D[k];
        A[i] = k;
        B[j] = k;
    }

    let mut p = vec![0; N];
    for k in 0..N {
        let (d, j) = D[A[k]];
        p[k] = j;
    }
    let mut used = vec![false; N];
    let mut i = 0;
    while !used[i] {
        used[i] = true;
        i = p[i];
    }
    // println!("{}", res);
    if !w && (0..N).all(|j| used[j]) { res = false; }
    // println!("{:?}", p);
    // println!("{:?}", used);

    let ans = if res { "Yes" } else { "No" };
    println!("{}", ans);
}