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 Ai​ and Bi​.

In this graph, there is an edge from Vertex $x$ to Vertex $y$ for all pairs $1\le x,y\le N$, and its weight is min(Ax​,By​).

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≤N≤105
• 1≤Ai​≤109
• 1≤Bi​≤109
• All values in input are integers.

Sample Input 1Copy

3
1 5
4 2
6 3

Sample Output 1Copy

7

Consider the cycle $1\to 3\to 2\to 1$. The weights of those edges are min(A1​,B3​)=1, min(A3​,B2​)=2 and min(A2​,B1​)=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 2Copy

4
1 5
2 6
3 7
4 8

Sample Output 2Copy

10

Sample Input 3Copy

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

Sample Output 3Copy

227