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.

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 $i\neq j$.

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 $\mathrm{LIS}(A) + \mathrm{LIS}(B)$.