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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

    class Program
    {
        static void Main(string[] args)
        {
            var N = Console.ReadLine();
            var prgs = Console.ReadLine().Split(' ');

            try
            {
                var PrgMn = new ProgressionManager(prgs, N);
                var ChangeCnts = PrgMn.CalcChangeMin();

                Console.WriteLine(ChangeCnts.Item1 + ChangeCnts.Item2);
            }
            catch
            {

            }
            

        }
    }

    class ProgressionManager
    {
        private List<int> evenList = new List<int>();
        private List<int> oddList = new List<int>();

        public ProgressionManager(string[] prgs,string N_str)
        {
            if (!ParseProgession(prgs, N_str))
            {
                throw new Exception();
            }
        }

        private bool ParseProgession(string[] prgs,string N_str)
        {
            int N;
            if(int.TryParse(N_str,out N) && N % 2 == 0)
            {
                for(int i = 0; i < prgs.Count(); i++)
                {
                    int prg_int;
                    if (!int.TryParse(prgs[i], out prg_int))
                    {
                        return false;
                    }
                    else
                    {
                        if (i % 2 == 0)
                        {
                            evenList.Add(prg_int);
                        }
                        else
                        {
                            oddList.Add(prg_int);
                        }
                    }
                }
                return true;
            }
            else
            {
                return false;
            }
        }

        public Tuple<int,int> CalcChangeMin()
        {
            var criteria1 = CalcCriteria(evenList);
            var criteria2 = CalcCriteria(oddList);

            int evenChangeCnt = 0;
            int oddChangeCnt = 0;
            for(int i = 1; i < evenList.Count; i++)
            {
                if(evenList[i] != criteria1)
                {
                    evenChangeCnt += 1;
                }
                if(oddList[i] != criteria2)
                {
                    oddChangeCnt += 1;
                }
            }
            return Tuple.Create(evenChangeCnt, oddChangeCnt);

        }

        private int CalcCriteria(List<int> tar)
        {
            var groups = tar.GroupBy(v => v);

            int maxCount = 0;
            int criteria = 0;
            foreach(var g in groups)
            {
                if(g.Count() > maxCount)
                {
                    maxCount = g.Count();
                    criteria = g.Key;
                }
            }
            return criteria;
        }
}