Doofish Matrix

Dr.D is now fond of matrices. He is particularly interested in Doofish Matrices. A Doofish Matrix of order $N$ is a matrix with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$) such that: - Each element of this matrix is an integer between $1$ and $2N-1$ inclusive. - For each $i$ and $j$ ($1 \le i \le N$, $1 \le j \le 2N-1$), the integer $j$ appears in the $i$-th ro