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In a school six different courses are taught: mathematics, physics, biology, music, history, geography. The students were required to rank these courses according to their preferences, where equal preferences were allowed. It turned out that:
* mathematics was ranked among the most preferred courses by all students;
* no student ranked music among the least preferred ones;
* all students preferred history to geography and physics to biology; and
* no two rankings were the same.
Find the greatest possible value for the number of students in this school.