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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.collection.mutable.ArrayBuffer

object Main{

  def main(args: Array[String]): Unit = {
    var len = readInt
    var A:ArrayBuffer[Int]= ArrayBuffer()
    var B:ArrayBuffer[Int]= ArrayBuffer()
    for(i <- 0 until len){
      var temp = readLine.split(" ").map(x => x.toInt)
      A = A:+temp(0)
      B = B :+ temp(1)
    }

    var positive = 0
    var negative = 0

    for(i <- 0 until len-1){
      positive += scala.math.min(A(i),B(i+1))
    }
    positive += scala.math.min(A(len-1),B(0))

    for(i <- 0 until len-1){
      negative += scala.math.min(B(i),A(i+1))
    }
      negative += scala.math.min(B(len-1),A(0))

    println(scala.math.min(positive,negative))
  }
}