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

The minimal path sum in the 5 by 5 matrix below,
by starting in any cell in the left column and finishing in any cell in the right column,
and only moving up, down, and right, is indicated in red and bold; the sum is equal to `994`.

~~~
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.