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 static System.Math;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.ReadLine();
            var V = Console.ReadLine().Split().Select((s, index) => new { Value = int.Parse(s), Index = index }).ToArray();
            var evenCosts = from value in V
                            where value.Index % 2 == 0
                            group value by value.Value into g
                            let cost = new { Value = g.Key, Cost = V.Length / 2 - g.Count() }
                            orderby cost.Cost
                            select cost;
            var oddCosts = from value in V
                           where value.Index % 2 == 1
                           group value by value.Value into g
                           let cost = new { Value = g.Key, Cost = V.Length / 2 - g.Count() }
                           orderby cost.Cost
                           select cost;

            int ans = int.MaxValue;
            foreach (var even in evenCosts.Take(2))
            {
                foreach (var odd in oddCosts.Take(2))
                {
                    if (even.Value != odd.Value)
                    {
                        ans = Min(ans, even.Cost + odd.Cost);
                    }
                }
            }

            if (ans == int.MaxValue)
            {
                ans = V.Length / 2;
            }

            Console.WriteLine(ans);
        }
    }
}