Chef and DAG

You are given $K$ permutations of integers $1$ through $N$. For each $i$ ($1 \le i \le K$), the $i$-th permutation is denoted by $A_{i,1}, A_{i,2}, \ldots, A_{i,N}$. Construct a directed acyclic graph with $N$ nodes (numbered $1$ through $N$) such that: - Each of the given permutations is a valid topological sort of the graph. Formally, for each valid $k$ and each $i, j$ ($1 \le i \lt j \le N$