Purple College keeps a careful count of its students as they progress each year from the freshman class to the sophomore class to the junior class and, finally, to the senior class. Each year at the college, one-third of the freshman class drops out of school, 40 students in the sophomore class drop out of school, and one-tenth of the junior class drops out of school. Given that the college only admits new freshman students and wants to begin each school year with 3400 students enrolled, how many students does it need to admit into the freshman class each year?

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