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 (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]
#![allow(non_snake_case)]
#![allow(unused_mut)]
#![allow(unused_variables)]
#![allow(dead_code)]

use itertools::Itertools;
use proconio::input;
use proconio::marker::{Chars, Usize1};

#[allow(unused_macros)]
#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

macro_rules! echo {
    ($($a:expr),*) => {
          $(println!("{}",$a))*
      }
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;
#[allow(dead_code)]
static M_O_D: usize = 1000000007;
#[allow(dead_code)]
static PAI: f64 = 3.1415926535897932;

trait IteratorExt: Iterator {
    fn toVec(self) -> Vec<Self::Item>;
}

impl<T: Iterator> IteratorExt for T {
    fn toVec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

trait CharExt {
    fn toNum(&self) -> usize;
    fn toAlphabetIndex(&self) -> usize;
    fn toNumIndex(&self) -> usize;
}
impl CharExt for char {
    fn toNum(&self) -> usize {
        return *self as usize;
    }
    fn toAlphabetIndex(&self) -> usize {
        return self.toNum() - 'a' as usize;
    }
    fn toNumIndex(&self) -> usize {
        return self.toNum() - '0' as usize;
    }
}

trait VectorExt {
    fn joinToString(&self, s: &str) -> String;
}
impl<T: ToString> VectorExt for Vec<T> {
    fn joinToString(&self, s: &str) -> String {
        return self
            .iter()
            .map(|x| x.to_string())
            .collect::<Vec<_>>()
            .join(s);
    }
}

trait StringExt {
    fn get_reverse(&self) -> String;
}
impl StringExt for String {
    fn get_reverse(&self) -> String {
        self.chars().rev().collect::<String>()
    }
}

trait UsizeExt {
    fn pow(&self, n: usize) -> usize;
}
impl UsizeExt for usize {
    fn pow(&self, n: usize) -> usize {
        return ((*self as u64).pow(n as u32)) as usize;
    }
}

pub trait Monoid {
    type T: Clone + PartialEq + std::fmt::Debug;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
    fn op2(a: &Self::T, b: &Self::T) -> Self::T;
    fn op3(a: &Self::T, b: &Self::T) -> Self::T;
}
struct SUM;
impl Monoid for SUM {
    type T = u64;
    fn id() -> Self::T {
        0
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        *a + *b
    }
    fn op2(a: &Self::T, b: &Self::T) -> Self::T {
        *a + *b
    }
    fn op3(a: &Self::T, b: &Self::T) -> Self::T {
        *a + *b
    }
}

struct SqrtDecomposition<M: Monoid> {
    sqrt_N: usize,
    sub: Vec<M::T>,
    lazy: Vec<M::T>,
    a: Vec<M::T>,
}
impl<M: Monoid> SqrtDecomposition<M> {
    //fn new(N: usize) -> SqrtDecomposition<M> {
    fn new(a: &Vec<M::T>) -> SqrtDecomposition<M> {
        let sqrt_N = (a.len() + 511) / 512;
        let mut sub = vec![M::id(); sqrt_N];
        let mut lazy = vec![M::id(); sqrt_N];
        let mut b = vec![M::id(); sqrt_N * 512];
        for i in 0..a.len() {
            b[i] = a[i].clone();
            sub[i / 512] = M::op(&sub[i / 512], &b[i]);
        }
        SqrtDecomposition {
            sqrt_N: sqrt_N,
            sub: sub,
            a: b,
            lazy: lazy,
        }
    }
    fn update(&mut self, i: usize, v: M::T) {
        let sub_index = i / 512;
        self.a[i] = v;
        let s = sub_index * 512;
        let e = sub_index * 512 + 512;
        self.sub[sub_index] = M::id();
        for j in s..e {
            self.sub[sub_index] = M::op(&self.sub[sub_index], &self.a[j]);
        }
    }
    fn query(&mut self, l: usize, r: usize) -> M::T {
        let sub_index = l / 512;
        let mut ret = M::id();
        for i in sub_index..self.sqrt_N {
            let s = i * 512;
            let e = i * 512 + 512;
            if l >= s && e <= r {
                ret = M::op(&ret, &self.sub[i]);
            } else {
                for j in max(s, l)..min(e, r) {
                    self.a[j] = M::op(&self.a[j], &ret);
                }
            }
        }
        ret
    }
    fn get(&mut self, l: usize) -> M::T {
        let sub_index = l / 512;
        if self.lazy[sub_index] != M::id() {
            let s = sub_index * 512;
            let e = s + 512;
            for j in s..e {
                self.a[j] = M::op3(&self.a[j], &self.lazy[sub_index]);
            }
            self.lazy[sub_index] = M::id();
        }
        self.a[l].clone()
    }
}

fn main() {
    input! {
       N: usize,
       mut A:[usize;N],
       mut B:[usize;N],
    }

    let mut a = A.clone();
    let mut b = B.clone();
    let mut a2 = A.clone();
    let mut b2 = B.clone();
    a.sort();
    b.sort();
    for (x, y) in b.iter().zip(&a) {
        if x < y {
            echo!("No");
            return;
        }
    }

    let mut c = a2.iter().zip(&b2).toVec();
    c.sort_by_key(|&(x, y)| y);
    mydbg!(c);
    let mut x = 0;

    let mut h = HashMap::new();
    A.sort();
    let mut count = 1;
    for &item in &A {
        let mut hp = h.entry(item).or_insert(0);
        if *hp == 0 {
            *hp = count;
            count += 1;
        }
    }

    mydbg!(h);
    mydbg!(c);
    let mut d = vec![SUM::id(); N + 1];
    let mut de: SqrtDecomposition<SUM> = SqrtDecomposition::new(&d);
    let mut sum = 0;
    for i in 0..N {
        if let Some(index) = h.get(c[i].0) {
            //sum += N - de.query(*index, N) as usize;
            let p = de.query(*index, N) as usize;
            sum += p;
            let tmp = de.get(*index - 1);
            de.update(*index - 1, tmp + 1);
        }
    }
    mydbg!(sum);

    if sum <= N - 2 {
        echo!("Yes");
    } else {
        echo!("No");
    }
}