Let \(f: \mathbb{N \to N} \) be an increasing function such that

\[\large f(f(n))= 3n\]

If \(x_{i} \in \mathbb {N} \ \forall \ i \in \mathbb{N} \), \( f(x_{1})= 7\), \(f(x_{2}) = 12\), \(f(x_{3})= 21\), and \(f(x_{4} )= 26\), find \( x_{1}+ x_{2} + x_{3}+ x_{4}\).

\[\] **Notation**: \(\mathbb N \) denotes the set of natural numbers.

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