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: Wrong Answer)

import java.util.Scanner

object Main {
    def main(args: Array[String]): Unit = {
        val scanner = new Scanner(System.in)
        val n: Int = scanner.nextInt
        val vs: List[Int] = List.fill(n)(scanner.nextInt)
        println(calc(vs))
    }

    def calc(nums: List[Int] ): Int ={
        val (evens, odds) = nums.zipWithIndex.partition(_._2 % 2 == 0)
        val evenCounter: Map[Int, Int] = evens.map(_._1).groupBy(even => even).mapValues(_.length)
        val oddCounter: Map[Int, Int] = odds.map(_._1).groupBy(odd=>odd).mapValues(_.length)
        val sortedEvenCounter: Seq[(Int, Int)] = evenCounter.toSeq.sortBy(_._2).reverse
        val sortedOddCounter:Seq[(Int, Int)] = oddCounter.toSeq.sortBy(_._2).reverse
        val evenKeys: Set[Int] = evenCounter.keySet
        val oddKeys: Set[Int] = oddCounter.keySet

        if (evenKeys.size == 1 && oddKeys.size == 1){
          if ((evenKeys diff oddKeys).size != 0) return 0 else return nums.size / 2
        }

      if ((evenKeys diff oddKeys).size == 0) return countNumberOfRewrite(sortedEvenCounter,sortedOddCounter,0,0)

        val count:Int = countNumberOfRewrite(sortedEvenCounter, sortedOddCounter, 0,1)
        val count2:Int = countNumberOfRewrite(sortedEvenCounter, sortedOddCounter, 1,0)

        count.min(count2)
    }

    def countNumberOfRewrite(seqTuple01 : Seq[(Int, Int)], seqTuple02 :Seq[(Int, Int)], index01: Int, index02: Int): Int ={
        try{
            seqTuple01.map(_._2).sum - seqTuple01(index01)._2 + seqTuple02.map(_._2).sum - seqTuple02(index02)._2
        }catch { case e: Exception => Int.MaxValue}
    }
}