Nubjook and Kai are playing a game. First, they take an empty 2019×2019 matrix and take turns to write numbers in each entry. Once the matrix is completely filled, Nubjook wins if the determinant is nonzero and Kai wins otherwise. If Nubjook does the first move, who has a winning strategy?

• Due to the delay of the problem announcement this time, we set the due date for this problem to be November 18th.