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.Collections.Generic;
using System.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        class CountedHashSet
        {
            public class Counter : IComparable<Counter>
            {
                public Counter(int key)
                {
                    count = 1;
                    this.key = key;
                }

                public int key { get; private set; }
                public int count { get; set; }

                public int CompareTo(Counter e)
                {
                    return -count.CompareTo(e.count);
                }
            }


            public Dictionary<int, Counter> keySet;

            public CountedHashSet()
            {
                keySet = new Dictionary<int, Counter>();
            }

            public void Add(int key)
            {
                Counter c;

                if (keySet.TryGetValue(key, out c))
                {
                    c.count++;
                }
                else
                {
                    keySet.Add(key, new Counter(key));
                }
            }

            public int GetKeyCount(int key)
            {
                Counter c;

                if (keySet.TryGetValue(key, out c))
                {
                    return c.count;
                }

                return 0;
            }
        }


        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string[] s = Console.ReadLine().Split(' ');

            CountedHashSet cs0 = new CountedHashSet();
            CountedHashSet cs1 = new CountedHashSet();

            for (int i = 0; i < N / 2; i++)
            {
                cs0.Add(int.Parse(s[i * 2 + 0]));
                cs1.Add(int.Parse(s[i * 2 + 1]));
            }

            List<CountedHashSet.Counter> list0 = new List<CountedHashSet.Counter>();
            foreach(KeyValuePair<int,CountedHashSet.Counter>e in cs0.keySet)
            {
                list0.Add(e.Value);
            }
            List<CountedHashSet.Counter> list1 = new List<CountedHashSet.Counter>();
            foreach (KeyValuePair<int, CountedHashSet.Counter> e in cs1.keySet)
            {
                list1.Add(e.Value);
            }

            if (list0.Count == 1 && list1.Count == 1)
            {
                if (list0[0].key == list1[0].key)
                {
                    Console.WriteLine(N / 2);
                }
                else
                {
                    Console.WriteLine(0);
                }

                return;
            }

            int ans = 0;
            list0.Sort();
            list1.Sort();
            CountedHashSet.Counter dummy = new CountedHashSet.Counter(int.MaxValue);
            dummy.count = 0;
            list0.Add(dummy);
            list1.Add(dummy);

            if ( list0[0].key == list1[0].key)
            {
                ans = (N / 2 - list0[1].count) + (N / 2 - list1[0].count);
                ans = Math.Min(ans, (N / 2 - list0[0].count) + (N / 2 - list1[1].count));

            }
            else
            {
                ans = (N / 2 - list0[0].count) + (N / 2 - list1[0].count);
            }

            Console.WriteLine(ans);
        }
    }
}