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 (1.15.1) (judge verdict: Accepted)

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let n: usize = iter.next().unwrap().parse().unwrap();
    let v: Vec<u64> = (&mut iter).take(n).map(|x| x.parse().unwrap()).collect();
    
    let mut fst = vec![];
    let mut snd = vec![];
    for i in 0..n {
        if i % 2 == 0 {fst.push(v[i]);}
        else {snd.push(v[i]);}
    }
    
    let fst_freqsec = freq_sec(&fst);
    let snd_freqsec = freq_sec(&snd);
    let ret = if fst_freqsec[0].1 == snd_freqsec[0].1 {
        std::cmp::min(
            calc(&fst, 0) + calc(&snd, 1),
            calc(&fst, 1) + calc(&snd, 0)
        )
    } else {
        calc(&fst, 0) + calc(&snd, 0)
    };
    println!("{}", ret);
}

fn freq_sec(fst: &[u64]) -> Vec<(usize, u64)> {
    let freq = count_series(fst);
    let mut freqsec: Vec<_> = freq.iter().map(|(&key, &value)| (value, key)).collect();
    freqsec.sort();
    freqsec.reverse();
    freqsec
}

fn calc(fst: &[u64], rank: usize) -> usize {
    let freqsec = freq_sec(fst);
    let mut sum = 0;
    for &(value, key) in &freqsec {
        if freqsec.len() <= rank || freqsec[rank].1 != key {
            sum += value;
        }
    }
    sum
}

#[allow(dead_code)]
fn count_series<T: Eq + std::hash::Hash + Clone>(
    series: &[T],
) -> std::collections::HashMap<T, usize> {
    let mut hmap = std::collections::HashMap::new();
    for item in series {
        *hmap.entry(item.clone()).or_insert(0) += 1;
    }
    hmap
}