2022 Fermat Problem 25

In the 3 \times 3 grid shown, the central square contains the integer 5. The remaining eight squares contain a, b, c, d, e, f, g, h, which are each to be replaced with an integer from 1 to 9, inclusive. Integers can be repeated. There are N ways to complete the grid so that the sums of the integers along each row, along each column, and along the two main diagonals are all divisible by 5. What are the rightmost two digits of N?

\begin{array}{|c|c|c|}\hline a & b & c \\ \hline d & 5 & e \\ \hline f & g & h \\ \hline\end{array}

If there are no answer choices shown, enter a numerical answer.

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