The most natural way to find a bijective proof of this formula would be to find a bijection between "n"-node trees and some collection of objects that has "n""n" − 2 members, such as the sequences of "n" − 2 values each in the range from 1 to "n". Such a bijection can be obtained using the Prüfer sequence of each tree. Any tree can be uniquely encoded into a Prüfer sequence, and any Prüfer sequence can be uniquely decoded into a tree; these two results together provide a bijective proof of Cayley's formula.