Hexagonal Checkers 2

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 2nd2^\text{nd} row. This starting orientation is shown below.

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

Red jumps Grey, then Blue jumps Red.  This puts Blue into the top space. Red jumps Grey, then Blue jumps Red. This puts Blue into the top space.

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