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

The first line of input contains the integer N (1 ≤ N ≤ 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

Output the smallest number of columns Luka must delete. 

Example

Input:
7 
5 4 3 2 1 6 7 
5 5 1 1 3 4 7 
3 7 1 4 5 6 2

Output:
4