Solve the programming task below in a Python markdown code block.
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.

Examples

Input

4
3 1 3 2


Output

1


Input

6
105 119 105 119 105 119


Output

0


Input

4
1 1 1 1


Output

2