Problem:
Score : 300 points

Problem Statement

A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:

For each i = 1,2,..., n-2, a_i = a_{i+2}.

Exactly two different numbers appear in the sequence.

You are given a sequence v_1,v_2,...,v_n whose length is even.
We would like to make this sequence /\/\/\/ by replacing some of its elements.
Find the minimum number of elements that needs to be replaced.

Constraints

2 \leq n \leq 10^5

n is even.

1 \leq v_i \leq 10^5

v_i is an integer.

Input

Input is given from Standard Input in the following format:

n
v_1 v_2 ... v_n

Output

Print the minimum number of elements that needs to be replaced.

Sample Input 1

4
3 1 3 2

Sample Output 1

1

The sequence 3,1,3,2 is not /\/\/\/, but we can make it /\/\/\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.

Sample Input 2

6
105 119 105 119 105 119

Sample Output 2

0

The sequence 105,119,105,119,105,119 is /\/\/\/.

Sample Input 3

4
1 1 1 1

Sample Output 3

2

The elements of the sequence 1,1,1,1 are all the same, so it is not /\/\/\/.

Solution in Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

import scala.collection.mutable

object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt
  val as = Vector.fill(n / 2)((sc.nextInt, sc.nextInt))

  val odd = mutable.Map[Int, Int]()
  val even = mutable.Map[Int, Int]()

  as.foreach { case (o, e) =>
    odd.put(o, odd.getOrElse(o, n / 2) - 1)
    even.put(e, even.getOrElse(e, n / 2) - 1)
  }

  val oo = odd.toSeq.sortBy(a => a._2)
  val ee = even.toSeq.sortBy(a => a._2)

  val res = (oo, ee) match {
    case _ if oo.head._1 != ee.head._1 => oo.head._2 + ee.head._2
    case (o1 +: o2 +: _, e1 +: e2 +: _) => (o1._2 + e2._2) min (o2._2 + e1._2)
    case (o1 +: _, _ +: e2 +: _) => o1._2 + e2._2
    case (_ +: o2 +: _, e1 +: _) => e1._2 + o2._2
    case _ => n / 2
  }

  println(res)
}