How many positive integers are there, fitting the following description ("gifted" numbers):

a. The total number of digits is below 13.
b. The number of even digits is twice the number of odd digits .
c. The even digits within the number read from left to right form a non-decreasing sequence
d. The odd digits within the number may appear in any order.
e. The s.o.d. of the number is less than 69.
f. Clearly, no leading zeroes.

Few samples of qualifying numbers: 300, 254, 436111878, 653766668.