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 <bits/stdc++.h>
using namespace std;
using i64 = long long;
#define rep(i,s,e) for(int (i) = (s);(i) <= (e);(i)++)
#define all(x) x.begin(),x.end()

int N;

bool vis[101010][2];

int main(){
  cin >> N;
  vector<i64> A(N),B(N);
  i64 as = 0;
  i64 bs = 0;
  rep(i,0,N - 1){
    cin >> A[i] >> B[i];
    as += A[i];
    bs += B[i];
  }

  using P = pair<i64,pair<i64,i64>>;
  vector<P> vec;
  rep(i,0,N - 1){
    vec.push_back({A[i] , {i , 0}});
    vec.push_back({B[i] , {i , 1}});
  }
  sort(all(vec));
  i64 sum = 0;
  rep(i,0,N - 1){
    vis[vec[i].second.first][vec[i].second.second] = true;
    sum += vec[i].first;
  }
  bool OK = false;
  rep(i,0,N - 1){
    if(vis[i][0] && vis[i][1]) OK = true;
  }
  if(!OK){
    i64 ans = 1e18;
    int idx = vec[N - 1].second.first;
    rep(i,0,N - 1){
      int j = idx;
      if(i == idx) j--;
      i64 a = vec[j].first;
      i64 b = A[i];
      if(vis[i][0]) b = B[i];
      ans = min(ans , sum - a + b);
    }
    sum = ans;
  }
  cout << min({sum , as , bs}) << endl;
}