Paul wrote a list of all four-digit numbers such that the hundreds digit is $5$ and the tens digit is $7$. For example, $1573$ and $7570$ are on Paul's list, but $2754$ and $571$ are not. Find the sum of all the numbers on Paul's list.

$\text{Note}$. The numbers on Paul's list cannot start with zero.

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