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 $2297$.

$$\left(\begin{array}{ccccc}131& 673& 234& 103& 18\\ 201& 96& 342& 965& 150\\ 630& 803& 746& 422& 111\\ 537& 699& 497& 121& 956\\ 805& 732& 524& 37& 331\end{array}\right)$$

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.