#include<bits/stdc++.h>
using namespace std;

#define int long long
int read(){
	int a = 0; char c = getchar();
	while(!isdigit(c)) c = getchar();
	while(isdigit(c)){a = a * 10 + c - 48; c = getchar();}
	return a;
}
const int _ = 2e5 + 7;
int arr[_] , id[_] , N; bool vis[_];

signed main(){
	N = read(); for(int i = 1 ; i <= N ; ++i){arr[i] = read(); arr[N + i] = read();}
	int sum = 0 , ans = 1e18;
	for(int i = 1 ; i <= N ; ++i) sum += arr[i];
	ans = min(ans , sum); sum = 0;
	for(int i = 1 ; i <= N ; ++i) sum += arr[N + i];
	ans = min(ans , sum);  sum = 0;
	for(int i = 1 ; i <= 2 * N ; ++i) id[i] = i;
	sort(id + 1 , id + 2 * N + 1 , [&](int x , int y){return arr[x] < arr[y];});
	for(int i = 1 ; i <= N ; ++i){sum += arr[id[i]]; vis[id[i]] = 1;}
	for(int i = 1 ; i <= N ; ++i)
		if(vis[i] && vis[i + N]) ans = min(ans , sum);
		else ans = min(ans , sum + arr[vis[i] ? i + N : i] - arr[id[id[N] == i || id[N] == i + N ? N - 1 : N]]);
	cout << ans; return 0;
}
### Prompt

In Cpp, your task is to solve the following problem:

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.

Examples

Input

3
1 5
4 2
6 3


Output

7


Input

4
1 5
2 6
3 7
4 8


Output

10


Input

6
19 92
64 64
78 48
57 33
73 6
95 73


Output

227

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;

#define int long long
int read(){
	int a = 0; char c = getchar();
	while(!isdigit(c)) c = getchar();
	while(isdigit(c)){a = a * 10 + c - 48; c = getchar();}
	return a;
}
const int _ = 2e5 + 7;
int arr[_] , id[_] , N; bool vis[_];

signed main(){
	N = read(); for(int i = 1 ; i <= N ; ++i){arr[i] = read(); arr[N + i] = read();}
	int sum = 0 , ans = 1e18;
	for(int i = 1 ; i <= N ; ++i) sum += arr[i];
	ans = min(ans , sum); sum = 0;
	for(int i = 1 ; i <= N ; ++i) sum += arr[N + i];
	ans = min(ans , sum);  sum = 0;
	for(int i = 1 ; i <= 2 * N ; ++i) id[i] = i;
	sort(id + 1 , id + 2 * N + 1 , [&](int x , int y){return arr[x] < arr[y];});
	for(int i = 1 ; i <= N ; ++i){sum += arr[id[i]]; vis[id[i]] = 1;}
	for(int i = 1 ; i <= N ; ++i)
		if(vis[i] && vis[i + N]) ans = min(ans , sum);
		else ans = min(ans , sum + arr[vis[i] ? i + N : i] - arr[id[id[N] == i || id[N] == i + N ? N - 1 : N]]);
	cout << ans; return 0;
}
```