I didn't know chocolates could pose such a problem!!!

Two players play a game involving a \(n\times n\) grid of chocolate. Each turn, a player may either eat a piece of chocolate(of any size) or split an existing piece of chocolate into rectangles along a grid line. The player who moves last loses. For how many positive integers \(n\) less than \(1000\) does the second player win???

Details and Assumptions:

Splitting of a piece of chocolate means taking a \(a\times b\) piece and breaking it into \((a-c)\times b\) and a \(c\times b\) piece or an \(a\times (b-d)\) and an \(a\times d\) piece.πŸ˜ƒπŸ˜ŠπŸ˜ˆ

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