In a classroom, there are 25 students who each have a unique favorite fruit. The teacher wants to distribute 100 different fruits such that each student gets at least one fruit and no two students get the same type of fruit. However, the teacher can only ensure this under the condition that at least one fruit type is given to more than one student. How many different types of fruit must there be to guarantee that at least one fruit type is given to more than one student? Let's think step by step and output the final answer within \boxed{}.
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