Digital silliness

[David Wilson]

For a number n, let f(n) be the set of numbers gotten by splitting n^2 at the 0 
digits.  For example

29648^2 = 879003904

so f(29648) = { 4, 39, 879 }

Let S be the smallest set of numbers containing 2 and fixed by f.  What is the 
largest element of S?
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- David Wilson