Given a 2-digit sequence (which can start with 0), let us define a nudge as the operation of either increasing or decreasing one of the digits by $1, or changing a $0 to a $9 or a $9 to a $0. For example, we can nudge $19 to get $09, $29, $18, or $10. Suppose S is a set of 2-digit sequences such that it takes at least $3 nudges to transform any element of S into another element of S. Requried:
What is the maximum possible number of elements of S?

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