Problem:
Score : 700 points

Problem Statement

We have a directed weighted graph with N vertices.
Each vertex has two integers written on it, and the integers written on Vertex i are A_i and B_i.

In this graph, there is an edge from Vertex x to Vertex y for all pairs 1 \leq x,y \leq N, and its weight is {\rm min}(A_x,B_y).

We will consider a directed cycle in this graph that visits every vertex exactly once.
Find the minimum total weight of the edges in such a cycle.

Constraints

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq B_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
:
A_N B_N

Output

Print the minimum total weight of the edges in such a cycle.

Sample Input 1

3
1 5
4 2
6 3

Sample Output 1

7

Consider the cycle 1→3→2→1. The weights of those edges are {\rm min}(A_1,B_3)=1, {\rm min}(A_3,B_2)=2 and {\rm min}(A_2,B_1)=4, for a total of 7.
As there is no cycle with a total weight of less than 7, the answer is 7.

Sample Input 2

4
1 5
2 6
3 7
4 8

Sample Output 2

10

Sample Input 3

6
19 92
64 64
78 48
57 33
73 6
95 73

Sample Output 3

227

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

use std::cmp;
use std::collections::VecDeque;

fn main() {
    let sc = std::io::stdin();
    let mut sc = Scanner { reader: sc.lock() };
    let n: usize = sc.read();
    let mut a: Vec<usize> = vec![0; n];
    let mut b: Vec<usize> = vec![0; n];
    for i in 0..n {
        a[i] = sc.read();
        b[i] = sc.read();
    }

    let all_a: usize = a.iter().sum();
    let all_b: usize = b.iter().sum();

    let mut ans = cmp::min(all_a, all_b);

    let mut cur: usize = (0..n).map(|i| cmp::min(a[i], b[i])).sum();

    let mut max = (0..n)
        .map(|i| (cmp::max(a[i], b[i]), i))
        .collect::<Vec<_>>();
    max.sort();

    let mut min = (0..n)
        .map(|i| (cmp::min(a[i], b[i]), i))
        .collect::<Vec<_>>();
    min.sort();
    min.reverse();

    let mut removed = vec![false; n];

    let mut max_q: VecDeque<(usize, usize)> = max.iter().map(|&t| t).collect();
    let mut min_q: VecDeque<(usize, usize)> = min.iter().map(|&t| t).collect();
    while !max_q.is_empty() && !min_q.is_empty() {
        while let Some((_, i)) = max_q.pop_front() {
            if !removed[i] {
                max_q.push_front((cmp::max(a[i], b[i]), i));
                break;
            }
        }
        while let Some((_, i)) = min_q.pop_front() {
            if !removed[i] {
                min_q.push_front((cmp::min(a[i], b[i]), i));
                break;
            }
        }
        if max_q.is_empty() || min_q.is_empty() {
            break;
        }
        let max_i = max_q.pop_front().unwrap().1;
        let min_i = min_q.pop_front().unwrap().1;
        if max_i == min_i {
            break;
        }
        removed[max_i] = true;
        removed[min_i] = true;
        cur += cmp::max(a[max_i], b[max_i]);
        cur -= cmp::min(a[min_i], b[min_i]);
        ans = cmp::min(ans, cur);
    }
    println!("{}", ans);
}

pub struct Scanner<R> {
    reader: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn read_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}