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;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var V = ReadArrayInt();
            var odd = new Dictionary<int, int>();
            var even = new Dictionary<int, int>();
            for (int i = 0; i < N; i++)
            {
                if (i % 2 == 0)
                {
                    if (odd.ContainsKey(V[i])) odd[V[i]]++;
                    else odd.Add(V[i], 1);
                }
                else
                {
                    if (even.ContainsKey(V[i])) even[V[i]]++;
                    else even.Add(V[i], 1);
                }
            }
            var sortedO = odd.OrderByDescending(i => i.Value).ThenBy(i => i.Key).ToArray();
            var sortedE = even.OrderByDescending(i => i.Value).ThenBy(i => i.Key).ToArray();
            var ans = 0;

            if (sortedO.Length == 1 && sortedE.Length == 1)
            {
                if (sortedO[0].Key == sortedE[0].Key) ans = N / 2;
                else ans = 0;
            }
            else if (sortedO.Length == 1)
            {
                int patA = 0, patB = 0;
                patA = ConvNum(sortedO[0], sortedE[0], N);
                patB = ConvNum(sortedO[0], sortedE[1], N);
                ans = Math.Min(patA, patB);
            }
            else if (sortedE.Length == 1)
            {
                int patA = 0, patB = 0;
                patA = ConvNum(sortedO[0], sortedE[0], N);
                patB = ConvNum(sortedO[1], sortedE[0], N);
                ans = Math.Min(patA, patB);
            }
            else
            {
                int patA = 0, patB = 0, patC = 0;
                patA = ConvNum(sortedO[0], sortedE[0], N);
                patB = ConvNum(sortedO[0], sortedE[1], N);
                patC = ConvNum(sortedO[1], sortedE[0], N);
                ans = Math.Min(patA, Math.Min(patB, patC));
            }

            Console.WriteLine(ans);
            Console.ReadLine();
        }

        static int ConvNum(KeyValuePair<int, int> A, KeyValuePair<int, int> B, int N)
        {
            var ret = 0;
            var n = N / 2;
            if (A.Key == B.Key) {
                if (A.Value >= B.Value) ret += 2 * n - A.Value;
                else ret += 2 * n - B.Value;
            } 
            else
            {
                ret += 2 * n - A.Value - B.Value;
            }

            return ret;
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}