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)

#define _CRT_SECURE_NO_WARNINGS
#define _SCL_SECURE_NO_WARNINGS
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <utility>
#include <algorithm>
#include <functional>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <limits>
#include <numeric>
#include <valarray>
#include <fstream>

using namespace std;
typedef unsigned int uint;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<LL, LL> PP;
#define REP(i, a, n) for(LL i = (a), i##_max = (n); i < i##_max; ++i)
#define REM(i, a, n) for(LL i = (LL)(n) - 1, i##min = (a); i >= i##min; --i)
#define ALL(arr) (arr).begin(), (arr).end()
#define FLOAT fixed << setprecision(16)
#define SPEEDUP {cin.tie(NULL); ios::sync_with_stdio(false);}
const int INF = 0x3FFFFFFF;
const LL INFLL = 0x3FFFFFFF3FFFFFFF;
const double INFD = 1.0e+308;
const string INFSTR = "\x7f";
const double EPS = 1.0e-9;

void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }
void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
template <class T, class U>
istream& operator>>(istream& ist, pair<T, U>& right) { return ist >> right.first >> right.second; }
template <class T, class U>
ostream& operator<<(ostream& ost, const pair<T, U>& right) { return ost << right.first << ' ' << right.second; }
template <class T, class TCompatible, size_t N>
void Fill(T(&dest)[N], const TCompatible& val) { fill(dest, dest + N, val); }
template <class T, class TCompatible, size_t M, size_t N>
void Fill(T(&dest)[M][N], const TCompatible& val) { for (int i = 0; i < M; ++i) Fill(dest[i], val); }
template<class T>
T Compare(T left, T right) { return left > right ? 1 : (left < right ? -1 : 0); }
istream& Ignore(istream& ist) { string s; ist >> s; return ist; }
bool Inside(int i, int j, int h, int w) { return i >= 0 && i < h && j >= 0 && j < w; }
template <class T>
T Next() { T buf; cin >> buf; return buf; }

#ifdef ONLY_MY_ENVIR
#include "IntMod.h"
#include "Union_Find.h"
#include "Graph.h"
#include "Range.h"
#include "Global.h"
#include "Flow_Solver.h"
#include "Tree.h"
#include "Suffix_Array.h"
#include "Geometry.h"
#include "Matrix.h"
#include "Segment_Tree.h"
#include "BIT.h"
#include "Rational.h"
#include "Position.h"
#include "Factorization.h"
#endif

#ifdef __GNUC__
typedef __int128 LLL;
istream& operator>> (istream& ist, __int128& val) { LL tmp;  ist >> tmp; val = tmp; return ist; }
ostream& operator<< (ostream& ost, __int128 val) { LL tmp = val; ost << tmp; return ost; }
#endif

#if 1234567891
#include <array>
#include <random>
#include <unordered_set>
#include <unordered_map>
template<typename T>
using PriorityQ = priority_queue<T, vector<T>, greater<T> >;
// template <class T>
// auto Is(const T& value) { return [value](const auto& comparand) -> bool { return comparand == value; }; }
#endif


LL N;
LL A[100000], B[100000];
bool usedA[100000], usedB[100000];

LL sum = 0;
LL cat() {
	LL mxA = 0;
	LL mxB = 0;
	LL mnA = INFLL;
	LL mnB = INFLL;
	REP(i, 0, N) {
		if (usedA[i]) mxA = max(mxA, A[i]);
		if (usedB[i]) mxB = max(mxB, B[i]);
		if (!usedA[i]) mnA = min(mnA, A[i]);
		if (!usedB[i]) mnB = min(mnB, B[i]);
	}
	return sum - max(mxA, mxB) + min(mnA, mnB);
}

LL sub() {
	vector<PP> v;
	REP(i, 0, N) {
		v.push_back(PP(A[i], i));
		v.push_back(PP(B[i], i + N));
	}
	sort(v.begin(), v.end());

	REP(i, 0, N) {
		int idx = v[i].second;
		if (idx < N) {
			usedA[idx] = true;
		} else {
			usedB[idx - N] = true;
		}
	}
	
	int cntA = 0;
	int cntB = 0;
	REP(i, 0, N) {
		if (usedA[i] && !usedB[i]) ++cntA;
		if (!usedA[i] && usedB[i]) ++cntB;
	}

	REP(i, 0, N) {
		sum += v[i].first;
	}
	if (cntA == 0 || cntB == 0) return sum;

	LL mn = INFLL;
	mn = min(mn, cat());
	REP(i, 0, N) {
		swap(A[i], B[i]);
		swap(usedA[i], usedB[i]);
	}
	mn = min(mn, cat());
	return mn;
}

int main() {
	cin >> N;
	REP(i, 0, N) {
		cin >> A[i] >> B[i];
	}
	cout << sub() << endl;

	return 0;
}