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.