DUBAI, Dec 8 (Reuters) - The United Arab Emirates president and Saudi crown prince led mediation efforts that secured the release of U.S. basketball star Brittney Griner in a prisoner swap with Russia, a joint UAE-Saudi statement said on Thursday.Griner arrived in the United Arab Emirates capital Abu Dhabi by private plane from Moscow after her release by Russian authorities, the statement said, as Russian citizen Viktor Bout, a former arms dealer, came in on another private plane from Washington after being released by U.S. authorities.It "highlighted the important role played by the leaderships of the two brotherly countries in promoting dialogue between all parties".Saudi Arabia had scored an earlier diplomatic victory in September by securing freedom for foreign fighters captured in Ukraine, at a time of tension between Riyadh and Washington.Their mediation reflects efforts to show their ties with Russia are of benefit to Washington, which had accused Gulf oil producers of siding with Russia when OPEC+ agreed in October to cut oil output targets over U.S. objections."