Valentine Vinculum!

A class has an equal number of boys and girls. One third of the boys in the class shook hands with each girl and one fourth of the girls shook hands with each boy. Each of the remaining boys brought a rose for one or the other of the remaining girls. In the end, three of the remaining girls didn't get a rose.

How many handshakes were done?

Details: No two persons shook hands twice.

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