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)

d = []
n = gets.to_i
t = Array.new()
n.times do |i|
  a, b = gets.chomp.split.map(&:to_i)
  t.push([a, 0, i])
  t.push([b, 1, i])
end
t.sort!

used = Array.new(1e5, false)
c = [0, 0]

a = 0
for i in 0...n
  a += t[i][0]
  c[t[i][1]] += 1
  used[t[i][2]] = true
end

if c[0] > 0 && c[1] > 0 && used.select{|i| i}.length == n
  if t[n-1][2] == t[n][2] && c[t[n-1][1]] > 1
    a += [t[n+1][0] - t[n-1][0], t[n][0] - t[n-2][0]].min
  else
    a += t[n][0] - t[n-1][0]
  end
end
puts a