题目描述
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
输入格式
见题面
输出格式
见题面
样例输入
3
1 5
4 2
6 3
样例输出
7