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<iostream>
#include<string>
#include<cmath>
#include<queue>
#include<map>
#include<set>
#include<list>
#include<iomanip>
#include<vector>
#include<random>
#include<functional>
#include<algorithm>
#include<cstdio>
#include<bitset>
#include<unordered_map>
using namespace std;
//---------------------------------------------------
//ライブラリゾーン！！！！
typedef long long ll;
typedef long double ld;
#define str string
#define rep(i,j) for(ll i=0;i<(long long)(j);i++)
#define all(a) (a).begin(),(a).end()
const ll Mod = 1000000007;
const ll gosenchou = 5000000000000000;
short gh[2][4] = { { 0,0,-1,1 },{ -1,1,0,0 } };
struct P {
	ll pos, cost;
};
bool operator<(P a, P b) { return a.cost < b.cost; }
bool operator>(P a, P b) { return a.cost > b.cost; }
struct B {//隣接リスト表現
	ll to, cost;
};
struct E {//辺の情報を入れる変数
	ll from, to, cost;
};
bool operator<(E a, E b) {
	return a.cost < b.cost;
}
struct H {
	ll x, y;
};
bool operator<(H a, H b) {
	if (a.x != b.x) return a.x < b.x;
	return a.y < b.y;
}
bool operator>(H a, H b) {
	if (a.x != b.x) return a.x > b.x;
	return a.y > b.y;
}
bool operator==(H a, H b) {
	return a.x == b.x&&a.y == b.y;
}
bool operator!=(H a, H b) {
	return a.x != b.x || a.y != b.y;
}
struct LS {
	ll num, cost;
	//値、遅延配列
};
ll gcm(ll i, ll j) {//最大公約数
	if (i > j) swap(i, j);
	if (i == 0) return j;
	return gcm(j%i, i);
}
ld rad(H a, H b) {
	return sqrt(pow(a.x - b.x, 2.0) + pow(a.y - b.y, 2.0));
}//rad＝座標上の2点間の距離
ll ari(ll a, ll b, ll c) {
	return (a + b)*c / 2;
}//等差数列の和
ll fact(ll x, ll k, ll p) {//最大値、個数、あまり
	ll sum = 1;
	for (int i = 0; i < k; i++) {
		sum *= (x--);
		sum %= p;
	}
	return sum;
}//階乗(正）
ll mod_pow(ll x, ll n, ll p) {
	ll res = 1;
	while (n > 0) {
		if (n & 1) res = res * x%p;
		x = x * x%p;
		n >>= 1;
	}
	return res;
}//x^n%p
short ctos(char a) {
	return (int)(a - '0');
}
#define int long long
const long long Inf = 4523372036854775807;
const int inf = 15000000000;
//----------------------------------------------------
//++++++++++++++++++++++++++++++++++++++++++++++++++++
int n;
H a[100000], b[100000];
int d[100000], e[100000];
signed main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i].x >> b[i].x;
		a[i].y = i;
		b[i].y = i;
	}
	sort(a, a + n);
	sort(b, b + n);
	//[0,r), [0,t)
	int r = 0, t = 0;
	int ans = 0;
	for (int i = 0; i < n; i++) {
		if (a[r].x < b[t].x) {
			ans += a[r].x;
			r++;
		}
		else if (a[r].x == b[t].x) {
			ans += a[r].x;
			if (r % 2 == 0) {
				r++;
			}
			else {
				t++;
			}
		}
		else {
			ans += b[t].x;
			t++;
		}
	}
	for (int i = 0; i < r; i++) {
		d[i] = a[i].y;
	}
	for (int i = t; i < n; i++) {
		e[i - t] = b[i].y;
	}
	sort(d, d + r);
	sort(e, e + t);
	bool l = 1;
	for (int i = 0; i < r; i++) {
		if (d[i] != e[i]) {
			l = 0;
		}
	}
	if (l && (t && r)) {
		ans -= max(a[r - 1].x, b[t - 1].x);
		ans += min(a[r].x, b[t].x);
	}
	cout << ans << endl;
}