You are given 2 arrays $A, B$ both of $n$ integers, find the longest common subsequence (LCS) of $A$ and $B$.

In other words, find the largest $k$ that there exist some indices $i_1 < i_2 < … < i_k$ and $j_1 < j_2 < … < j_k$ that: $$A_{i_1} = B_{j_1}$$ $$A_{i_2} = B_{j_2}$$ $$…$$ $$A_{i_k} = B_{j_k}$$

Input

• The first line contains an integer $n$.
• The second line contains $n$ integers $A_i$.
• The third line contains $n$ integers $B_i$.

Output

• Print the length of the LCS.

Constraints

• $1 \le n \le 1000$
• $1 \le A_i, B_i \le 10^9$.

Example

Input:

4
1 2 3 4
3 4 2 1

Output:

2

Note: The LCS is $(3, 4)$.