Problem:
Score : 700 points

Problem Statement

There are N bags, each containing two white balls. The i-th box contains two balls with integers x_i and y_i written on them, respectively.

For each of these bags, you will paint one of the balls red, and paint the other blue.

Afterwards, the 2N balls will be classified according to color.

Then, we will define the following:

R_{max}: the maximum integer written on a ball painted in red

R_{min}: the minimum integer written on a ball painted in red

B_{max}: the maximum integer written on a ball painted in blue

B_{min}: the minimum integer written on a ball painted in blue

Find the minimum possible value of (R_{max} - R_{min}) \times (B_{max} - B_{min}).

Constraints

1 ≤ N ≤ 200,000

1 ≤ x_i, y_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the minimum possible value.

Sample Input 1

3
1 2
3 4
5 6

Sample Output 1

15

The optimal solution is to paint the balls with x_1, x_2, y_3 red, and paint the balls with y_1, y_2, x_3 blue.

Sample Input 2

3
1010 10
1000 1
20 1020

Sample Output 2

380

Sample Input 3

2
1 1
1000000000 1000000000

Sample Output 3

999999998000000001

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet, BinaryHeap};

use std::iter::FromIterator;

mod util {
    use std::io::stdin;
    use std::str::FromStr;
    use std::fmt::Debug;

    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn get<T: FromStr>() -> T
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    }

    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }

    #[allow(dead_code)]
    pub fn get2<T: FromStr, U: FromStr>() -> (T, U)
    where
        <T as FromStr>::Err: Debug,
        <U as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    }
}

fn main() {
    let n: usize = util::get();
    let xy: Vec<(usize, usize)> = (0..n)
        .map(|_| {
            let t = util::get2();
            (min(t.0, t.1), max(t.0, t.1))
        })
        .collect();

    let g_min = xy.iter()
        .flat_map(|t| vec![t.0, t.1].into_iter())
        .min()
        .unwrap();
    let g_max = xy.iter()
        .flat_map(|t| vec![t.0, t.1].into_iter())
        .max()
        .unwrap();

    let r_min_b_max = {
        let mut r = (xy[0].0, xy[0].0);
        let mut b = (xy[0].1, xy[0].1);

        for &(x, y) in xy[1..].iter() {
            r = (min(r.0, x), max(r.1, x));
            b = (min(b.0, y), max(b.1, y));
        }
        (r.1 - r.0) * (b.1 - b.0)
    };

    let r_min_r_max = {
        let mut b = BinaryHeap::from_iter(xy.iter().map(|&(x, y)| (y, x)));

        loop {
            let (x, y) = b.peek().cloned().unwrap();
            if y < x && y != g_min {
                b.pop();
                b.push((y, x));
            } else {
                break;
            }
        }

        let v = b.into_vec();
        let b_min = v.iter().map(|t| t.0).min().unwrap();
        let b_max = v.iter().map(|t| t.0).max().unwrap();
        let r_min = v.iter().map(|t| t.1).min().unwrap();
        let r_max = v.iter().map(|t| t.1).max().unwrap();

        (b_max - b_min) * (r_max - r_min)
    };

    println!("{}", min(r_min_r_max, r_min_b_max));

}