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.Text;
using System.Threading.Tasks;

namespace ABC_20180929
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var v = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            int x = v.Count(a => a == v[0]);

            if (v.Count(a => a == v[0]) == n)
            {
                Console.WriteLine(n / 2);
                return;
            }
            List<int> vOdd = new List<int>();
            List<int> vEve = new List<int>();
            Dictionary<int, int> vOddD = new Dictionary<int, int>();
            Dictionary<int, int> vEveD = new Dictionary<int, int>();
            for (int i = 0; i < n; i++)
            {
                if (i % 2 == 0)
                {
                    vEve.Add(v[i]);
                    if (vEveD.ContainsKey(v[i]))
                    {
                        vEveD[v[i]]++;
                    }
                    else
                    {
                        vEveD[v[i]] = 1;
                    }
                }
                else
                {
                    vOdd.Add(v[i]);
                    if (vOddD.ContainsKey(v[i]))
                    {
                        vOddD[v[i]]++;
                    }
                    else
                    {
                        vOddD[v[i]] = 1;
                    }
                }
            }
            var vOddDSorted = vOddD.OrderByDescending((a) => a.Value);
            var vEveDSorted = vEveD.OrderByDescending((a) => a.Value);
            var vOdd1 = vOddDSorted.First();
            var vEve1 = vEveDSorted.First();

            if(vOdd1.Key != vEve1.Key)
            {
                Console.WriteLine(vOdd.Count(a => a != vOdd1.Key)
                    + vEve.Count(a => a != vEve1.Key));
            }
            else
            {
                var vOdd2 = vOddDSorted.Skip(1).First();
                var vEve2 = vEveDSorted.Skip(1).First();

                var x1 = vOdd.Count(a => a != vOdd2.Key) + 
                    vEve.Count(a => a != vEve1.Key);
                var x2 = vOdd.Count(a => a != vOdd1.Key) +
                    vEve.Count(a => a != vEve2.Key);
                Console.WriteLine(Math.Min(x1, x2));
            }
        }
    }
}