CF1348F Phoenix and Memory

Phoenix is trying to take a photo of his $ n $ friends with labels $ 1, 2, \dots, n $ who are lined up in a row in a special order. But before he can take the photo, his friends get distracted by a duck and mess up their order. Now, Phoenix must restore the order but he doesn't remember completely! He only remembers that the $ i $ -th friend from the left had a label between $ a_i $ and $ b_i $ inclusive. Does there exist a unique way to order his friends based of his memory?

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