Problem Statement

For $a sequence P = (P_1, \ldots, P_N)$, let $\mathrm{LIS}(P)$ denote the length of a longest increasing subsequence.
You are given permutations $A = (A_1, \ldots, A_N)$ and $B = (B_1, \ldots, B_N)$ of integers from 1 through N. You may perform the following operation on these sequences any number of times (possibly zero).

• Choose an integer i such that $1\leq i\leq N-1. Swap A_i$ and A_{i+1}, and swap B_i and B_{i+1}.

Find the maximum possible final value of $\mathrm{LIS}(A) + \mathrm{LIS}(B)$.

What is a longest increasing subsequence?

A subsequence of a sequence is a sequence obtained by removing zero or more elements from the original sequence and then concatenating the remaining elements without changing the order.
For instance, (10,30) is a subsequence of (10,20,30), but (20,10) is not a subsequence of (10,20,30).

A longest increasing subsequence of a sequence is a subsequence of that sequence with the greatest length among its subsequences that are strictly increasing.

Input

The input is given from Standard Input in the following format:
N
$A_1 \ldots A_N$
$B_1 \ldots B_N$

Output

Print the maximum possible final value of $\mathrm{LIS}(A) + \mathrm{LIS}(B)$.

Constraints

• $2\leq N\leq 3\times 10^5$
• $1\leq A_i\leq N$
• $1\leq B_i\leq N$
• $A_i\neq A_j$ and $B_i\neq B_j$, if $i\neq j$.

Sample Input 1

5
5 2 1 4 3
3 1 2 5 4

Sample Output 1

8

Here is one way to achieve $\mathrm{LIS}(A) + \mathrm{LIS}(B) = 8$.

• Do the operation with i = 2. Now, A = (5,1,2,4,3), B = (3,2,1,5,4).
• Do the operation with i = 1. Now, A = (1,5,2,4,3), B = (2,3,1,5,4).
• Do the operation with i = 4. Now, A = (1,5,2,3,4), B = (2,3,1,4,5).

Here, A has a longest increasing subsequence (1,2,3,4), so $\mathrm{LIS}(A)=4$, and B has a longest increasing subsequence (2,3,4,5), so $\mathrm{LIS}(B)=4$.

Sample Input 2

5
1 2 3 4 5
1 2 3 4 5

Sample Output 2

10

You can decide not to perform the operation at all to achieve $\mathrm{LIS}(A) + \mathrm{LIS}(B) = 10$.

见题面 Input 部分

见题面 Output 部分