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Helios

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The Tegummans ( fictional culture ) measure periods of eight years called Octads, for ritualistic purposes. These periods begin and end with a full moon at midnight, and therefore usually contain 99 lunar months, but do seldomly contain 98 months.

The Tegummans also measure periods of 272 years ( 34 Octads ) called Ages. The first Octad of any Age always contains 99 months.

Octads are reduced from 99 months to 98 months every 18th Octad, not counting any first Octad of an Age. That is, the reduction by one month of the 18th Octad is postponed every 34 Octads.

What is the average number of lunar months per year as reckoned by the Tegummans?