Let \(S(n)\) be the set of the digits of \(n\). Find the smallest natural number \(n\) such that \(S(n^2)\) is a proper subset of \(S(n)\).

**Clarification**:

A set \(A\) is a *proper subset* of another set \(B\) if all elements of \(A\) is in \(B\), but \(A \neq B\).

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