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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

class Cmondai
{
    static void Main()
    {
        var N = Int32.Parse(Console.ReadLine());
        var v = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
        var uniq = v.Distinct().ToArray();
        var count = uniq.Count();
        if (count == 1)
        {
            Console.WriteLine(N / 2);
            return;
        }
        var cost = 0;
        var ans = int.MaxValue;
        for (int i=0;i<count;++i)
        {
            var first = uniq[i];
            for (int j=0;j<count;++j)
            {
                if (j == i) continue;
                var second = uniq[j];
                for (int k=0;k<N-1;k+=2)
                {
                    if (v[k] != first) cost++;
                    if (v[k + 1] != second) cost++;
                }
                if (cost < ans) ans = cost;
            }
        }
        Console.WriteLine(ans);
    }
}