The sweeties shop called "Olympiad" sells boxes of $6$, $9$, or $20$ chocolates. Groups of students from a nearby school collect money to buy a chocolate for each student; they do this by buying a box and then distributing a chocolate to everyone. For example, students can form groups of $15 = 6 + 9$ students or $38 = 2 \times 9 + 20$ students, etc. 

The seller has promised the students that he can satisfy any group size. If he needs to open a new box of chocolates for any group (such as groups of $4$, $7$, or $10$ students), then he will give all the chocolates for free to this group.

Can there be constructed the largest group that receives free chocolates, and if so, how many students are there in this group?

Let's think step by step and output the final answer within \boxed{}.
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