What is the largest number of queens that can be placed on a regular $8\times8$ chessboard, if the following rules are met:
- A queen can be either black or white, and there can be unequal numbers of each type.
- A queen must not be threatened by other queens of the same color.
- Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens.
Would this number change if rule 1 was changed to enforce equal numbers of black and white queens?