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 2 N is 900 .
When the largest and smallest possible values of N are multiplied together, the number of digits in the resulting product is
Answer Choices
A. 408
B. 400
C. 432
D. 416
E. 424