In an infinitely large triangular peg board game, the goal is to get a peg into the top space on the board through a series of moves. A move consists of a peg jumping over an adjacent peg, which eliminates the peg which was jumped over.

It is possible to get a peg into the top space when all the starting pegs are below the \(2^\text{nd}\) row. This starting orientation is shown below.

What is the largest possible \(n\) such that we can get a peg into the top space when all the starting pegs are below the \(n^\text{th}\) row?

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