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 AtCoder {
    class Program {

        static void Main(string[] args) {

            var n = int.Parse(Console.ReadLine());
            var v = Console.ReadLine().Split(' ').Select(e => int.Parse(e)).ToList();
            var result = 0;
            var av = new List<int>();
            var bv = new List<int>();

            for (int i = 0; i < v.Count; i++) {

                if (i % 2 == 0) {

                    av.Add(v[i]);
                } else {

                    bv.Add(v[i]);
                }
            }
            var ao = av.GroupBy(g => g).OrderByDescending(o => o.Count());
            var bo = bv.GroupBy(g => g).OrderByDescending(o => o.Count());

            var a = ao.First().Key;
            var b = bo.First().Key;
            if (a == b) {

                if (av.Distinct().Count() != 1 && bv.Distinct().Count() != 1) {

                    var ass = ao.Skip(1);
                    var bss = bo.Skip(1);

                    var aa = ass.First().Count();
                    var bb = bss.First().Count();

                    if (aa > bb) {

                        a = ass.First().Key;
                    } else if (aa < bb) {

                        b = bss.First().Key;
                    }
                } else {

                    b = a + 2;
                }
            }

            for (int i = 0; i < v.Count; i += 2) {

                if (a != v[i]) {
                    result++;
                }
            }
            for (int i = 1; i < v.Count; i += 2) {

                if (b != v[i]) {
                    result++;
                }
            }
            Console.WriteLine(result);
        }
    }
}