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.

4
3 1 3 2

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 $3,1,3,1$.

6
105 119 105 119 105 119

0

The sequence $105,119,105,119,105,119$ is ////.

4
1 1 1 1

2

The elements of the sequence $1,1,1,1$ are all the same, so it is not ////.