Mursalin and Agnishom decide to play a game where they alternately draw diagonals between the vertices of a regular \(n\)-gon. In each turn, Mursalin and Agnishom has to draw a diagonal that doesn't intersect any of the diagonals that have been already formed. Mursalin goes first. The person who is unable to make a move loses. For how many possible values of \(n\), does Agnishom have a winning strategy if \(457\leq n\leq 1003\)?