Contest Duration: - (local time) (120 minutes) Back to Home
B - Two LIS Sum /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

1 以上 N 以下の整数からなる順列 A = (A_1, \ldots, A_N) および B = (B_1, \ldots, B_N) が与えられます．これらの数列に対して，以下の操作を何度でも行うことができます（0 回でもよいです）．

• 1\leq i\leq N-1 となる整数 i をひとつ選ぶ．A_iA_{i+1} をスワップし，B_iB_{i+1} をスワップする．

### 制約

• 2\leq N\leq 3\times 10^5
• 1\leq A_i\leq N
• 1\leq B_i\leq N
• i\neq j ならば A_i\neq A_j かつ B_i\neq B_j

### 入力

N
A_1 \ldots A_N
B_1 \ldots B_N


### 入力例 1

5
5 2 1 4 3
3 1 2 5 4


### 出力例 1

8


• i = 2 として操作を行う．A = (5,1,2,4,3), B = (3,2,1,5,4) となる．
• i = 1 として操作を行う．A = (1,5,2,4,3), B = (2,3,1,5,4) となる．
• i = 4 として操作を行う．A = (1,5,2,3,4), B = (2,3,1,4,5) となる．

このとき A は最長増加部分列 (1,2,3,4) を持ち，\mathrm{LIS}(A)=4 が成り立ちます．B は最長増加部分列 (2,3,4,5) を持ち，\mathrm{LIS}(B)=4 が成り立ちます．

### 入力例 2

5
1 2 3 4 5
1 2 3 4 5


### 出力例 2

10


Score : 500 points

### 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).

### 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.