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: Wrong Answer)

n = gets.to_i
asum,bsum = 0,0
m = []
n.times{|i|
  a,b = gets.split.map(&:to_i)
  asum += a
  bsum += b
  m<<[a,i]
  m<<[b,i]
}

m.sort!{|x,y|x[0]<=>y[0]}

h = Hash.new(0)

def f(n,m,h)
  ans = 0
  ok = false
  #0からn-1
  n.times{|i|
    ans += m[i][0]
    h[m[i][1]]+=1
    ok = true if h[m[i][1]]>=2
  }
  return ans if ok
  
  #3通りの内一番小さいやつ
  min = 10**18
  #n-1を戻してnを足す
  h[m[n-1][1]]-=1
  ans -= m[n-1][0]
  if h[m[n][1]]>=1
    tmp = ans - m[n-1][0] + m[n][0]
    min = tmp if min > tmp
  end
  #n-1を戻してn+1を足す
  if h[m[n+1][1]]>=1
    tmp = ans - m[n-1][0] + m[n+1][0]
    min = tmp if min > tmp
  end
  #n-2を戻してnを足す
  h[m[n-1][1]]+=1
  h[m[n-2][1]]-=1
  if h[m[n+1][1]]>=1
    tmp = ans - m[n-2][0] + m[n][0]
    min = tmp if min > tmp
  end
  return min
end

p [asum,bsum,f(n,m,h)].min