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)

#[macro_use]
mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    // diff: using Parser
    #[macro_export(local_inner_macros)]
    macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

    use std::io;
    use std::io::BufRead;
    use std::str;

    // ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
    // ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
    // diff: using std::io::BufRead::fill_buf()
    pub struct Parser<R> {
        pub reader: R,
        buf: Vec<u8>,
        pos: usize,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: s.as_bytes().to_vec(),
                pos: 0,
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: vec![],
                pos: 0,
            }
        }
        pub fn update_buf(&mut self) {
            self.buf.clear();
            self.pos = 0;
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend_from_slice(buf2);
                    let len = buf2.len();
                    (len, buf2[len - 1] <= 0x20)
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn fast_i64(&mut self) -> i64 {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                if begin == self.buf.len() {
                    self.update_buf();
                    continue;
                }
                let mut res = 0;
                let (is_positive, mut end) = match self.buf[begin] {
                    b'+' => (true, begin + 1),
                    b'-' => (false, begin + 1),
                    _ => (true, begin),
                };
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return if is_positive { res } else { -res };
                } else {
                    self.update_buf();
                }
            }
        }
    }
}

use input_mcr::*;
use std::cmp::*;

fn slow(xs: &Vec<i64>, ys: &Vec<i64>) -> bool {
    let n = xs.len();
    let mut xs: Vec<i64> = xs.clone();
    slow_sub(n - 2, &mut xs, &ys)
}

fn slow_sub(rem: usize, xs: &mut Vec<i64>, ys: &Vec<i64>) -> bool {
    let n = xs.len();
    let mut t = true;
    for i in 0..n {
        if xs[i] > ys[i] {
            t = false;
        }
    }
    if t {
        return true;
    }
    if rem == 0 {
        return false;
    }
    for i in 0..n {
        for k in i + 1..n {
            xs.swap(i, k);
            if slow_sub(rem - 1, xs, ys) {
                return true;
            }
            xs.swap(i, k);
        }
    }
    return false;
}

fn gen_all_vec(n: usize, lower: i64, upper: i64) -> Vec<Vec<i64>> {
    let mut res = vec![];
    let mut t = vec![];
    gen_all_vec_sub(n, lower, upper, &mut res, &mut t);
    res
}

fn gen_all_vec_sub(n: usize, lower: i64, upper: i64, res: &mut Vec<Vec<i64>>, ts: &mut Vec<i64>) {
    if ts.len() == n {
        res.push(ts.clone());
        return;
    }
    for t in lower..upper {
        ts.push(t);
        gen_all_vec_sub(n, lower, upper, res, ts);
        ts.pop();
    }
}

fn mini_test() {
    let n = 5;
    for n in 2..5 {
        for xs in &gen_all_vec(n, 1, 6) {
            for ys in &gen_all_vec(n, 1, 6) {
                if let Some(ans) = f(xs, ys) {
                    let right = slow(xs, ys);
                    assert_eq!(ans, right, "xs = {:?}, ys = {:?}", xs, ys);
                }
            }
        }
    }
    // eprintln!("mini_test: ok");
}

fn f(xs: &Vec<i64>, ys: &Vec<i64>) -> Option<bool> {
    let n = xs.len();
    // yoyuu
    {
        let mut xs = xs.clone();
        let mut ys = ys.clone();
        xs.sort();
        ys.sort();
        let mut k = 0;
        let mut rs = vec![];
        for i in 0..n {
            while k < n && xs[k] <= ys[i] {
                k += 1;
            }
            let t = k as i64 - (i + 1) as i64;
            rs.push(t);
            if t < 0 {
                return Some(false);
            }
        }
        for i in 0..n {
            if rs[i] >= 1 {
                return Some(true);
            }
        }
    }
    // rs[i] == 0 only
    let mut xs: Vec<_> = xs.iter().enumerate().map(|(i, &x)| (x, i)).collect();
    let mut ys: Vec<_> = ys.iter().enumerate().map(|(k, &y)| (y, k)).collect();
    xs.sort();
    ys.sort();
    let mut table = vec![0; n];
    for i in 0..n {
        table[ys[i].1] = xs[i].1;
    }
    let mut visited = vec![false; n];
    let mut i = 0;
    let mut count = 0;
    while !visited[i] {
        visited[i] = true;
        count += 1;
        i = table[i];
    }
    Some(count != n)
}

fn main() {
    // mini_test();
    input! {
        n: i64,
        xs: [i64; n],
        ys: [i64; n],
    }
    let res = f(&xs, &ys).unwrap();
    println!("{}", if res { "Yes" } else { "No" });
}