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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <vector>
#include <map>
#include <sstream>
#include <iostream>
#include <queue>
#include <algorithm>
#define REP(i, n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i, c) for(__typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
using namespace std;
typedef long long ll;

struct V {
  ll a, b;
  V(ll a, ll b) : a(a), b(b) {}
  V() {}
};

V vs[100000+10];

ll vvs[200000+10];

int main(void) {
  int n;
  scanf("%d", &n);
  REP(i, n) {
    scanf("%lld%lld", &vs[i].a, &vs[i].b);
  }

  REP(i, n) {
    vvs[i*2] = vs[i].a;
    vvs[i*2+1] = vs[i].b;
  }
  sort(vvs, vvs+2*n);
  ll res = 0;
  REP(i, n) {
    res += vvs[i];
  }
  printf("%lld\n", res);
  
  return 0;
}