Given 2005 distinct numbers $a_1, a_2, \dots, a_{2005}$. By one question, we may take three different indices $1 \le i < j < k \le 2005$ and find out the set of numbers $\{a_i, a_j, a_k\}$ (unordered, of course). Find the minimal number of questions necessary to determine all numbers $a_i$.

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