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By using Boost.Iterator we rely on the separate traversal category instead of the standard iterator category to advance iterators efficiently. For instance, this allows to advance transform iterators over a random access sequence in constant time, despite that they are formally input iterators. Also, std::reverse_iterator formally requires at least bidirectional iterator as the underlying iterator type. Transform iterators from the example above don't qualify, so potentially std::reverse_iterator could fail to compile.