MaxSum (Happy Sum - 2)

You have a rectangular table with $N$ rows and $M$ columns. Each cell contains a non-negative integer. You can traverse this table from top to bottom, starting from any cell in the top row. From a cell at position $(i,j)$, you can move to one of the "lower neighboring" cells: (i+1, j-1), (i+1, j), or (i+1, j+1). Note that if j = M, you cannot move to (i+1, j+1), and if j = 1, you cannot move to (i+1, j-1). You can finish your path in any cell of the bottom row.

Write a program that finds the maximum possible lucky sum of the values in the cells traversed along any valid path. A lucky number is a positive integer whose decimal representation contains only the digits $4$ and $7$. For example, $47$, $744$, and $4$ are lucky numbers; $0$, $5$, $17$, and $467$ are not. It is important that the sum itself is a lucky number, not the individual addends.