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This is a harder version of problem 104.
Counting in Lojban, an artificial language developed over the last forty years, is easier than in most languages. The numbers from zero to nine are:
1 pa 4 vo 7 ze 2 re 5 mu 8 bi 0 no 3 ci 6 xa 9 so
A self-descriptive number is equal to the sum of the positions of its letters in the alphabet. For example, pareci is not self-descriptive, since 123 is not equal to 16 + 1 + 18 + 5 + 3 + 9 (=52).
What is the product of all self-descriptive numbers below 1,000,000?
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