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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use {
    itertools::Itertools,
    proconio::{fastout, input, marker::*},
    std::cmp::*,
    std::collections::*,
    std::io::Write,
    std::ops::*,
};

#[allow(unused_macros)]
macro_rules! debug { ($($e:expr),*) => { #[cfg(debug_assertions)] $({ let (e, mut err) = (stringify!($e), std::io::stderr()); writeln!(err, "{} = {:?}", e, $e).unwrap() })* }; }

#[fastout]
fn main() {
    input! {
        n: usize,
        v: [usize; n]
    }
    let mut m1 = std::collections::BTreeMap::<usize, usize>::new();
    let mut m2 = std::collections::BTreeMap::<usize, usize>::new();
    for i in 0..n {
        if i % 2 == 0 {
            *m1.entry(v[i]).or_insert(0) += 1;
        } else {
            *m2.entry(v[i]).or_insert(0) += 1;
        }
    }
    let mut m1 = m1.iter().map(|(&k, &v)| (v, k)).collect::<Vec<_>>();
    let mut m2 = m2.iter().map(|(&k, &v)| (v, k)).collect::<Vec<_>>();
    m1.sort_by_key(|&(v, _)| Reverse(v));
    m2.sort_by_key(|&(v, _)| Reverse(v));
    if m1[0].1 != m2[0].1 {
        println!("{}", n - m1[0].0 - m2[0].0);
        return;
    }
    if m1.len() == 1 && m2.len() == 1 {
        println!("{}", n / 2);
        return;
    }
    let mut ans = n;
    if m2.len() != 1 {
        ans = min(ans, n - m1[0].0 - m2[1].0);
    }
    if m1.len() != 1 {
        ans = min(ans, n - m1[1].0 - m2[0].0);
    }
    println!("{}", ans);
}