[Python] Count maximum value in each group with Pandas

Suppose I have a dataframe df looking like

school score student_id
0 1 100.0 965
1 2 64.0 1483
2 2 100.0 1055
3 2 68.0 1806
4 1 100.0 971


I want to find how many maximum scores in each group and get something like this:

school count_max
1 2
2 1


How can I do it?

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