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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
class C
{
  static void  Main (string[] args)
  {
     Console.WriteLine(Enumerable.Repeat(Enumerable.Repeat(0,2).Select(_=>Console.ReadLine()).ElementAt(1).Split(' ').Select(int.Parse).ToArray(),2).Select((q,d)=>q.Where((p,i)=>i%2==d).GroupBy(p=>p).OrderBy(p=>-p.Count()).ToArray()).Aggregate(new{Sum=0,Key=-1,FSum=0,SSum=new[]{0}},(d,p)=>new{Sum=d.Sum+p.Sum(q=>q.Count()),Key=p[0].Key,FSum=(d.Key!=p[0].Key)?(d.FSum+p[0].Count()):0,SSum=d.SSum.Select(q=>q+(p.Skip(1).FirstOrDefault()?.Count()??0)).Concat(new[]{d.SSum[0]+p[0].Count()}).ToArray()},ans=>ans.Sum-Math.Max(ans.FSum,ans.SSum.Skip(1).Max())));
  }
}