Sum of digits

Number Theory Level 4

$\large N = 13 \times 17 \times 41 \times 829 \times 56659712633$ It is know that $N$ is an 18-digit number, with nine of the ten digits from 0 to 9 each appearing twice. Find the sum of the digits of $N$ .

Honor Bonus: Do it without calculating the product.

Sum of digits

This problem is taken from the 7th Hong Kong Pui Ching Invitational Mathematics Competition, year 2008.