Determine the smallest positive integer $n$ such that there exist positive integers $x_1, x_2, \ldots, x_n$ so that each natural number from 1001 to 2021 inclusive can be expressed as the sum of one or more distinct terms $x_i$ (where $i = 1, 2, \ldots, n$).

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