You are given a positive integer $k$ and two conditions:

• A 2D integer array row_conditions of size $n$, where row_conditions[i] = [above[i], below[i]]. This indicates that above[i] must appear in a row above below[i] in the final matrix.

• A 2D integer array col_conditions of size $m$, where col_conditions[i] = [left[i], right[i]]. This indicates that left[i] must appear in a column to the left of right[i] in the final matrix.

Both arrays contain integers ranging from $1$ to $k$.

You need to construct a $k \times k$ matrix that includes all the integers from $1$ to $k$ exactly once, with the remaining cells filled with zeros. The matrix must satisfy the following rules:

• For each pair row_conditions[i], the integer above[i] must be located in a row strictly above below[i].

• For each pair col_conditions[i], the integer left[i] must be positioned in a column strictly to the left of right[i].

If it’s possible to create such a matrix, return any valid matrix. If it’s not possible, return an empty matrix.

Constraints:

• $2 \leq k \leq 400$

• $1 \leq$ ...