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.

3
1 5
4 2
6 3

7

Consider the cycle $1 \to 3 \to 2 \to 1$. 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 $7$.

4
1 5
2 6
3 7
4 8

10

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

227