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 $N$ $(1\le N\le 100000)$, 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 $40\mathrm{\%}$ of points, $N$ will be less than $100$.

In test cases worth $70\mathrm{\%}$ of points, $N$ will be less than $10000$.

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 $5$.