A parliament consists of $n$ senators. These senators are organized into 10 parties and 10 committees. Each senator belongs to exactly one party and one committee. 

Determine the smallest possible value of $n$ such that it is possible to label the parties and the committees with numbers from 1 to 10, ensuring that there are at least 11 senators for which the party and committee numbers match.

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