Seven classmates are comparing their end-of-year grades in $ 12$ subjects. They observe that for any two of them, there is some subject out of the $ 12$ where the two students got different grades. It is possible to choose n subjects out of the $ 12$ such that if the seven students only compare their grades in these $n$ subjects, it will still be true that for any two, there is some subject out of the n where they got different grades. What is the smallest value of $n$ for which such a selection is surely possible? Note: In Hungarian high schools, students receive an integer grade from $ 1$ to $5$ in each subject at the end of the year.