The one hundred U.S. Senators are standing in a line in alphabetical order. Each senator either always tells the truth or always lies. The $i$th person in line says:

"Of the $101-i$ people who are not ahead of me in line (including myself), more than half of them are truth-tellers."

How many possibilities are there for the set of truth-tellers on the U.S. Senate?

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