Let $(a_1, a_2, a_3, a_4, a_5)$ be a random permutation of the integers from $1$ to $5$ inclusive. Find the expected value of 
\[ \sum_{i=1}^{5} |a_i - i| = |a_1 - 1| + |a_2 - 2| + |a_3 - 3| + |a_4 - 4| + |a_5 - 5|. \]

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