A permutation $ (a_1, a_2, a_3, a_4, a_5)$ of $ (1, 2, 3, 4, 5)$ is heavy-tailed if $ a_1 + a_2 < a_4 + a_5$. What is the number of heavy-tailed permutations?

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