M. S. I. S.

We are given a $2 \times n$ matrix $M$ of positive integers. No row of $M$ contains a duplicate number. For the $i$-th row $r_i$ ($i = 1, 2$), let $s_i$ be the maximum sum of an increasing subsequence of $r_i$. For example, in the matrix below, $s_1$ is $1 + 2 + 3 + 4 + 5 + 6$ and $s_2$ is $2 + 3 + 5$.

$\begin{bmatrix} \color{red}{1} & \color{red}{2} & \color{red}{3} & \color{red}{4} & \color{red}{5} & \color{red}{6}\\ 6 & \color{red}{2} & \color{red}{3} & \color{red}{5} & 4 & 1 \end{bmatrix}$

We call $s_1 + s_2$ the maximum sum of increasing subsequences (MSIS). Permuting the columns of $M$ can change the MSIS. In the matrix below, the columns $[c_1, c_2, c_3, c_4, c_5, c_6]$ are rearranged to $[c_2, c_3, c_4, c_5, c_6, c_1]$, and the MSIS becomes 36.

$\begin{bmatrix} \color{red}{2} & \color{red}{3} & \color{red}{4} & \color{red}{5} & \color{red}{6} & 1\\ \color{red}{2} & \color{red}{3} & \color{red}{5} & 4 & 1 & \color{red}{6} \end{bmatrix}$

Given $M$, find the maximum MSIS over all permutations of its columns.

The first line contains an integer $n$ ($1 \le n \le 10000$), the number of columns of $M$. The next two lines each contain $n$ integers, the entries of row 1 and row 2. All integers are between 1 and 50000, and no row contains a duplicate number.

Print one line containing the maximum MSIS over all permutations of the columns of $M$.