Happy Sum 3

You have a rectangular table with $N$ rows and $M$ columns. Each cell contains an integer.

You need to traverse the table from top to bottom, starting from any cell in the top row. At each step, you may move to one of the "lower neighboring" cells. That is, from a cell at position $(i,j)$, you can move to (i+1, j-1), (i+1, j), or (i+1, j+1). If j = M, the last option is not possible; if j = 1, the first option is not possible. The route must end at any cell in the bottom row.

Write a program to find the maximum possible happy sum among all valid paths. In this problem, the definition of a happy number is non-standard: a happy number is a natural number with at least two digits in its decimal representation, and whose last two (least significant) digits are happy digits $4$ and/or $7$. For example, numbers $47$, $744$, and $6328674$ are happy, while $0$, $4$, $5$, and $44747467$ are not. Note that the sum itself must be happy, not the individual summands.