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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分