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::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).ok();
    let mut it = buf.split_whitespace();
    let n = it.next().unwrap().parse::<usize>().unwrap();
    let mut a = Vec::new();
    let mut b = Vec::new();
    for i in 0..n {
        let v1 = it.next().unwrap().parse::<i64>().unwrap();
        let v2 = it.next().unwrap().parse::<i64>().unwrap();
        a.push((v1, i));
        b.push((v2, i));
    }
    a.sort();
    b.sort();
    let mut idx_a = 0;
    let mut idx_b = 0;
    let mut res = 0;
    while idx_a + idx_b < n {
        if a[idx_a].0 < b[idx_b].0 {
            res += a[idx_a].0;
            idx_a += 1;
        } else {
            res += b[idx_b].0;
            idx_b += 1;
        }
    }
    if idx_a < n && idx_b < n {
        let mut used = vec![0; n];
        for i in 0..idx_a { used[a[i].1] = 1 }
        let mut ok = false;
        for i in idx_b..n {
            if used[b[i].1] == 0 { ok = true; }
        }
        if !ok {
            res += std::cmp::min(a[idx_a].0 - b[idx_b-1].0, b[idx_b].0 - a[idx_a-1].0);
        }
    }
    println!("{}", res);
}