////

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

inputFormat

Input

Input is given from Standard Input in the following format:

n v_1 v_2 ... v_n

outputFormat

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

样例

4
3 1 3 2

1