Given that $a_1, a_2, a_3, . . . , a_{99}$ is a permutation of $1, 2, 3, . . . , 99,$ find the maximum possible value of
$$|a_1 - 1| + |a_2 - 2| + |a_3 - 3| + \dots + |a_{99} - 99|.$$


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