Is it possible to place $n$ sets of five free tetrominoes on a $K \times K$ square grid, such that:
- No two tetrominoes overlap.
- Tetrominoes can be rotated or flipped.
- Every row, column and two main diagonals contain the same number of cells covered by a tetromino.
What are the smallest positive $n$ and $K$ for which this is possible?