Chess and a Pawn

Given a chessboard with sides $n \times n$ . A pawn is placed on the bottom left box. Two players, Jihyun and Ziying, took turns moving the pawn with Jihyun getting their first turn. At each turn, the pawn can only be moved to a neighboring box (two boxes are said to be neighbors if and only if the two boxes are different and have only one same side) and have not been previously occupied. Players who can not move the pawn are declared defeated. Determine all $n$ values ​​such that Jihyun has a winning strategy.

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