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arn-lhr-mia-msy-sea-mia-dfw-lax-sju-jfk-syd-per-mel-akl-syd-hkg-del-hkg-bom-hkg-lhr-mct-lhr-arn
According to this routing you only have one transcon.
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I count to two transcons: SEA-MIA and LAX-SJU.