From a square board 1000×1000 four rectangles 2×994 have been cut off as shown on the picture. Initially, on the marked square there is a centaur - a piece that moves to the adjacent square to the left, up, or diagonally up-right in each move. Two players alternately move the centaur. The one who cannot make a move loses the game. Who has a winning strategy?
https://cdn.artofproblemsolving.com/attachments/c/6/f61c186413b642b5b59f3947bc7a108c772d27.png geometrycombinatoricscombinatorial geometry