If two distinct integers from $1$ to $50$ inclusive are chosen at random, what is the expected value of their product?  Note: The expectation is defined as the sum of the products of probability and value, i.e., the expected value of a coin flip that gives you $\$10$ if head and $\$5$ if tail is $\tfrac12\times\$10+\tfrac12\times\$5=\$7.5$.

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