NOTE: This problem is a significantly more challenging version of Problem 81.

In the $5$ by $5$ matrix below, the minimal path sum from the top left to the bottom right, by moving left, right, up, and down, is indicated in bold red and is equal to $2297$.

$$ \begin{pmatrix} \color{red}{131} & 673 & \color{red}{234} & \color{red}{103} & \color{red}{18}\\ \color{red}{201} & \color{red}{96} & \color{red}{342} & 965 & \color{red}{150}\\ 630 & 803 & 746 & \color{red}{422} & \color{red}{111}\\ 537 & 699 & 497 & \color{red}{121} & 956\\ 805 & 732 & 524 & \color{red}{37} & \color{red}{331} \end{pmatrix} $$

Find the minimal path sum from the top left to the bottom right by moving left, right, up, and down in matrix.txt (right click and "Save Link/Target As..."), a 31K text file containing an $80$ by $80$ matrix.