A positive decimal (base 10) integer G is called an ascending number if the number of digits in G is at least 2, all the digits of G are strictly ascending, and G does not contain any leading zeroes. For example, the number 1236789 is an ascending number. However, the number 1222333555666 is not an ascending number, since the digits corresponding to the said number are not strictly ascending. Similarly, 00123456 is not an ascending number, since it contains leading zeroes. Determine the total number of ascending numbers in the decimal (base 10) system.