Let $P_1, P_2, \dots, P_{720}$ denote the integers whose digits are a permutation of $123456$, arranged in ascending order (so $P_1 = 123456$, $P_2 = 123465$, and $P_{720} = 654321$). What is $P_{144}$?

Let's think step by step and output the final answer within \boxed{}.
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