In an $8 \times 8$ chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible $4$ directions, provided there is no other piece in between in the path from the queen to that piece. The columns are labelled $a$ to $h$ (left to right) and the rows are numbered $1$ to $8$ (bottom to top). The position of a piece is given by the combination of column and row labels. For example, position $c5$ means that the piece is in $c$th column and $5$th row.
If the other pieces are only at positions $a1$, $a3$, $b4$, $d7$, $h7$ and $h8$, then from how many positions the queen cannot attack any of the pieces?
- $0$
- $3$
- $4$
- $6$