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`.

~~~
131 673 234 103 018
201 096 342 965 150
630 803 746 422 111
537 699 497 121 956
805 732 524 037 331
~~~

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