### Terminal Zeros

Terminal zeros of a number are the zeros to the right of the last nonzero digit. For instance, 506,400,000 has 5 terminal zeros. During a math meetup, students play a game. They form a queue. The first student yells 1, the second student yells 2, the third student yells 6, the fourth student yells 24, the

*n*th student yells the product of 1, 2, 3, ...,*n*. Leo is the last student to yell his number. He forgets to bring the calculator, but he says there are 7 terminal zeros in his number. If Leo's statement is true, what's the largest possible number of students in the queue?