  We propose a new protocol of \textit{universal} entanglement concentration,
which converts many copies of an \textit{unknown} pure state to an \textit{%
exact} maximally entangled state. The yield of the protocol, which is outputted
as a classical information, is probabilistic, and achives the entropy rate with
high probability, just as non-universal entanglement concentration protocols
do.
  Our protocol is optimal among all similar protocols in terms of wide
varieties of measures either up to higher orders or non-asymptotically,
depending on the choice of the measure. The key of the proof of optimality is
the following fact, which is a consequence of the symmetry-based construction
of the protocol: For any invariant measures, optimal protocols are found out in
modifications of the protocol only in its classical output, or the claim on the
product.
  We also observe that the classical part of the output of the protocol gives a
natural estimate of the entropy of entanglement, and prove that that estimate
achieves the better asymptotic performance than any other (potentially global)
measurements.
