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.
Suppose the queen is the only piece on the board and it is at position $d5$.
If the other pieces are only at positions $a1$, $a3$, $b4$, $d7$, $h7$ and $h8$, then which of the following positions of the queen results in the maximum number of pieces being under attack?
- $f8$
- $a7$
- $c1$
- $d3$