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 proconio::{input, fastout};
use proconio::marker::*;
use std::collections::HashMap;

fn helper(
  vals: &Vec<usize>,
  mut index: usize
) -> Vec<(usize, usize)> {
  let mut map: HashMap<usize, usize> = HashMap::new();
  while index < vals.len() {
    let entry = map.entry(vals[index]).or_insert(0);
    *entry += 1;
    index += 2;
  }
  
  let mut result: Vec<(usize, usize)> = map.into_iter().collect();
  result.sort_by(|a, b| a.1.cmp(&b.1));
  result.reverse();
  result
}

#[fastout]
fn main() {
  input! {
    n: usize,
    vals: [usize;n],
  }
  let mut result = 0;
  let mut last = vals[0];
  let mut success = true;
  for i in 1..n {
    if last != vals[i] {
      success = false;
      break
    }
  }

  if success {
    println!("{}", n / 2);
    return
  }
  
  let mut firsts = helper(&vals, 0);
  let mut seconds = helper(&vals, 1);
  if firsts.len() == 1 {
    firsts.push((10_000_000, 0));
  }
  if seconds.len() == 1 {
    seconds.push((10_000_000, 0));
  }
  
  if firsts[0].0 == seconds[0].0 {
    let result = std::cmp::min(
      n - firsts[0].1 - seconds[1].1,
      n - firsts[1].1 - seconds[0].1,
    );
    println!("{}", result);
  } else {
    println!("{}", n - firsts[0].1 - seconds[0].1);
  }
}