Jay has a $24 \times 24$ grid of lights, all of which are initially off. Each of the $48$ rows and columns has a switch that toggles all the lights in that row and column, respectively, i.e., it switches lights that are on to off and lights that are off to on. Jay toggles each of the $48$ rows and columns exactly once, such that after each toggle, he waits for one minute before the next toggle. Each light uses no energy while off and 1 kiloJoule of energy per minute while on. To express his creativity, Jay chooses to toggle the rows and columns in a random order. Compute the expected value of the total amount of energy in kiloJoules expended by all the lights after all $48$ toggles.

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