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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val xs = readLine()!!.split(" ").map { it.toInt() }
    val map1: Map<Int, Int> = toCountMap(xs.filterIndexed { index, x -> index % 2 == 0 })
    val map2: Map<Int, Int> = toCountMap(xs.filterIndexed { index, x -> index % 2 == 1 })
    val pairs1 = map1.toList().sortedByDescending { it.second }
    val pairs2 = map2.toList().sortedByDescending { it.second }
    var ans = n
    for (p1 in pairs1) {
        val p2 = pairs2[0]
        if (p1.first != p2.first) {
            ans = Math.min(n - p1.second - p2.second, ans)
        } else {
            ans = Math.min(n - p1.second, ans)
            ans = Math.min(n - p2.second, ans)
        }
    }
    for (p2 in pairs2) {
        val p1 = pairs1[0]
        if (p1.first != p2.first) {
            ans = Math.min(n - p1.second - p2.second, ans)
        } else {
            ans = Math.min(n - p1.second, ans)
            ans = Math.min(n - p2.second, ans)
        }
    }
    println(ans)
}

fun toCountMap(xs: List<Int>): Map<Int, Int> {
    val count = mutableMapOf<Int, Int>()
    for (x in xs) {
        if (!count.containsKey(x)) {
            count[x] = 1
        } else {
            count[x] = count[x]!! + 1
        }
    }
    return count
}