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 $(3, 4)$.
