Longest Common Subsequence

Problem Description

You are given two permutations $P_1$ and $P_2$ of the numbers $1$ to $n$. Find the length of their longest common subsequence.

Input Format

The first line contains a positive integer $n$.

Each of the next two lines contains $n$ integers — a permutation of the natural numbers $1, 2, \dots, n$.

Output Format

Output one number: the length of the longest common subsequence.

Sample Input

5
3 2 1 4 5
2 1 3 4 5

Sample Output

4

Constraints

$1 \leq n \leq 10^5$