Problem:
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.

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

Solution in Ruby (2.3.3) (judge verdict: Accepted)

n = gets.to_i
a,b = 2.times.map{Array.new(n)}
ab = Array.new(2*n){[0,0]}
sum_a,sum_b = 0,0

n.times do |i|
  c,d = gets.split.map(&:to_i)
  a[i],b[i] = c,d
  sum_a += c
  sum_b += d
  ab[2*i,2] = [[c,i],[d,i]]
end
ab = ab.sort_by{|i,j|i}

used = Array.new(n,false)
n.times do |i|
  used[ab[i][1]] = true
end

sum_mix = 0
n.times do |i|
  sum_mix += ab[i][0]
end

if used.all?{|b|b == true}
  ans = [sum_a,sum_b].min
  n.times do |i|
    ret = sum_mix-(a[i] < b[i] ? a[i] : b[i])
    ret += ab[n][1] == i ? ab[n+1][0] : ab[n][0]
    ans = ret if ans > ret
  end
else
  ans = [sum_a,sum_b,sum_mix].min
end
p ans