An *access pattern* $\pi$ is a permutation of $\{1,2,\dots,50\}$ describing the order in which some 50 memory addresses are accessed. We define the *locality* of $\pi$ to be how much the program jumps around the memory, or numerically, 
\[ \sum_{i=2}^{50}\left\lvert\pi(i)-\pi(i-1)\right\rvert. \]
If $\pi$ is a uniformly randomly chosen access pattern, what is the expected value of its locality?

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