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.😃😊😈