For positive integers $n$, let $S_n$ be the set of integers $x$ such that $n$ distinct lines, with no three concurrent, can divide a plane into $x$ regions. For example, $S_2 = \{3, 4\}$ because the plane is divided into 3 regions if the two lines are parallel, and 4 regions otherwise. What is the minimum $i$ such that $S_i$ contains at least 4 elements?

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