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.Linq;
using System.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N;
        public long MOD = 1000000007;
        public int[] V;

        public void Run()
        {
            N = Input.ReadInt();
            V = Input.ReadIntArray();

            var dic1 = new Dictionary<int, int>();
            var dic2 = new Dictionary<int, int>();

            {
                for (int i = 0; i < N; i += 2)
                {
                    int v = V[i];
                    if (!dic1.ContainsKey(v))
                    {
                        dic1.Add(v, 0);
                    }

                    dic1[v]++;
                }
            }
            
            {
                for (int i = 1; i < N; i += 2)
                {
                    int v = V[i];
                    if (!dic2.ContainsKey(v))
                    {
                        dic2.Add(v, 0);
                    }

                    dic2[v]++;
                }
            }

            var ts1 = Top2(dic1);
            var ts2 = Top2(dic2);
            int ret = int.MaxValue;

            if (ts1[0] != ts2[0]) ret = Math.Min(ret, V.Length - ts1[1] - ts2[1]);
            if (ts1[0] != ts2[2]) ret = Math.Min(ret, V.Length - ts1[1] - ts2[3]);
            if (ts1[2] != ts2[0]) ret = Math.Min(ret, V.Length - ts1[3] - ts2[1]);
            if (ts1[2] != ts2[2]) ret = Math.Min(ret, V.Length - ts1[3] - ts2[3]);

            Console.WriteLine(ret);

        }

        public int[] Top2(Dictionary<int, int> dic)
        {
            // top2
            int t1 = -1;
            int v1 = 0;
            int t2 = -2;
            int v2 = 0;
            foreach (var k in dic.Keys)
            {
                int v = dic[k];
                if (v >= v1)
                {
                    t2 = t1;
                    v2 = v1;
                    t1 = k;
                    v1 = v;
                }
                else if (v >= v2)
                {
                    t2 = k;
                    v2 = v;
                }
            }

            return new int[] {t1, v1, t2, v2};
        }
    }

    // libs ----------
    

    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}