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: Wrong Answer)

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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(solve());
        }

        static int solve()
        {
            var n = int.Parse(Console.ReadLine());
            var dg = Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToList();

            var evenNum = n / 2;
            var oddNum = n % 2 == 0 ? n / 2 : n / 2 + 1;
            var evenList = new Dictionary<int, int>();
            var oddList = new Dictionary<int, int>();

            var index = 1;
            foreach (var v in dg)
            {
                if (index % 2 == 0)
                {
                    Add(evenList, v);
                }
                else
                {
                    Add(oddList, v);
                }

                ++index;
            }

            var evenChange = getMaxAnd2ndKey(evenList, evenNum);
            var oddChange = getMaxAnd2ndKey(oddList, oddNum);

            var odd = oddList[oddChange.Key];
            var even = evenList[evenChange.Key];
            if (oddChange.Key != evenChange.Key)
            {
                return oddNum - odd + evenNum - even;
            }
            
            if (oddChange.Value == 0 && evenChange.Value == 0)
            {
                if (odd > even)
                {
                    return oddNum - odd + evenNum;
                }

                return evenNum - even + oddNum;
            }

            if (oddChange.Value == 0)
            {
                return oddNum - odd + evenNum;
            }

            if (oddChange.Value == 0)
            {
                return evenNum - even + oddNum;
            }

            var odd2 = oddList[oddChange.Value];
            var even2 = evenList[evenChange.Value];
            if (odd + even2 > odd2 + even)
            {
                return oddNum - odd + evenNum - even2;
            }

            return oddNum - odd2 + evenNum - even;
        }

        static KeyValuePair<int, int> getMaxAnd2ndKey(Dictionary<int, int> target, int num)
        {
            int val1 = 0;
            int val2 = 0;
            int key1 = 0;
            int key2 = 0;
            foreach (var v in target)
            {
                if (v.Value > val1)
                {
                    if (val1 > val2)
                    {
                        val2 = val1;
                        key2 = key1;
                    }

                    val1 = v.Value;
                    key1 = v.Key;
                }
            }

            return new KeyValuePair<int, int>(key1, key2);
        }

        static void Add(Dictionary<int, int> target, int val)
        {
            if (target.ContainsKey(val))
            {
                ++target[val];
            } else
            {
                target.Add(val, 1);
            }
        }
    }
}