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 scanner::Scanner;
use std::cmp::min;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.read();
    let mut ab: Vec<(u64, u64)> = (0..n).map(|_| (sc.read(), sc.read())).collect();

    ab.sort_by_key(|k| k.0);
    let mut ans1 = 0;
    for i in 0..n - 1 {
        ans1 += min(ab[i].1, ab[i + 1].0);
    }
    ans1 += min(ab[0].0, ab[n - 1].1);

    let mut ans2 = 0;
    ab.sort_by_key(|k| k.1);
    for i in 0..n - 1 {
        ans2 += min(ab[i].1, ab[i + 1].0);
    }
    ans2 += min(ab[0].0, ab[n - 1].1);

    println!("{}", min(ans1, ans2));
}

mod scanner {
    pub struct Scanner<'a> {
        s: String,
        words: ::std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new() -> Scanner<'a> {
            let s = String::new();
            let words = unsafe { ::std::mem::transmute(s.split_whitespace()) };
            Scanner { s: s, words: words }
        }

        pub fn read<T: ::std::str::FromStr>(&mut self) -> T {
            match self.words.next() {
                Some(x) => x.parse().ok().unwrap(),
                None => {
                    self.load();
                    self.read()
                }
            }
        }

        fn load(&mut self) {
            self.s.clear();
            ::std::io::stdin().read_line(&mut self.s).unwrap();
            self.words = unsafe { ::std::mem::transmute(self.s.split_whitespace()) };
        }
    }
}