Maximum Number of Edges

Problem Description

You are given two permutations $A$ and $B$, each of length $n$. All elements are in the range $1$ to $n$.

You may draw an edge between $A[i]$ and $B[j]$ if and only if $|A[i] - B[j]| \le 4$.

Find the maximum number of edges that can be drawn such that no two edges intersect (cross each other).

For example, in the sample, if $a_1$ is connected to $b_2$ and $a_2$ is connected to $b_1$, then these two edges intersect.

It is guaranteed that both $A$ and $B$ are permutations.

Input Format

The first line contains an integer $n$.

The next $n$ lines each contain one number $a_i$.

The next $n$ lines each contain one number $b_i$.

Sample Input

6
1 
2 
3 
4 
5 
6
6 
5 
4 
3 
2 
1

Sample Output

5

Constraints

$1 \le n \le 10^5$