## Super Pandigital Numbers

### Problem 571

A positive number is **pandigital** in base `b` if it contains all digits from 0 to `b` - 1 at least once when written in base `b`.

A *n-super-pandigital* number is a number that is simultaneously pandigital in all bases from 2 to `n` inclusively.

For example 978 = 1111010010_{2} = 1100020_{3} = 33102_{4} = 12403_{5} is the smallest 5-super-pandigital number.

Similarly, 1093265784 is the smallest 10-super-pandigital number.

The sum of the 10 smallest 10-super-pandigital numbers is 20319792309.

What is the sum of the 10 smallest 12-super-pandigital numbers?