Luka is slacking again during chemistry class, while the teacher is explaining Avogadro's law.

Luka first drew a table consisting of ~3~ rows and ~N~ columns. Then he wrote the numbers ~1~ to ~N~ into the first row in arbitrary order, each number appearing exactly once. In the other two rows, he also wrote integers between ~1~ and ~N~, but didn't care how many times a number appeared.

Luka can now delete any set of columns from the table. After doing so, he sorts the numbers in each row in ascending order.

He wants to obtain a table in which all three rows are identical after sorting. Write a program that determines the smallest number of columns he must delete.

Input Specification

The first line of input contains the integer ~N~ ~(1 \le N \le 100\,000)~, the number of columns in the table. The following three lines contain ~N~ integers each, separated by single spaces. The numbers will be between ~1~ and ~N~, and there will be no duplicates in the first row.

Output Specification

Output the smallest number of columns Luka must delete.

Scoring

In test cases worth ~40\%~ of points, ~N~ will be less than ~100~.

In test cases worth ~70\%~ of points, ~N~ will be less than ~10\,000~.

Sample Input 1

7
5 4 3 2 1 6 7
5 5 1 1 3 4 7
3 7 1 4 5 6 2

Sample Output 1

4

Sample Input 2

9
1 3 5 9 8 6 2 4 7
2 1 5 6 4 9 3 4 7
3 5 1 9 8 6 2 8 7

Sample Output 2

2

In the first example, Luka needs to delete the second, fourth, sixth and seventh columns. After deleting the columns and sorting each row, all three rows contain the numbers ~1~, ~3~ and ~5~.