2012 Fermat Problem 25

There are many positive integers N with the following properties:

- the digits of N include at least one of each of the digits 3, 4, 5, and 6, - the digits of N include no digits other than 3, 4, 5, and 6, and - the sum of the digits of N is 900 and the sum of the digits of 2N is 900.

When the largest and smallest possible values of N are multiplied together, the number of digits in the resulting product is

\textbf{(A)}\ 408\quad \textbf{(B)}\ 400\quad \textbf{(C)}\ 432\quad \textbf{(D)}\ 416\quad \textbf{(E)}\ 424

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

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