Connect on a Grid (Challenge)

You are given a grid with $N$ rows (numbered $1$ through $N$ from top to bottom) and $N$ columns (numbered $1$ through $N$ from left to right). Let's denote a cell in the $i$-th row and the $j$-th column by $(i,j)$. There are $K$ checkpoints (numbered $1$ through $K$) in the grid. For each valid $i$, the $i$-th checkpoint is in the cell $(X_i,Y_i)$ and it has two parameters $L_i$ and $R_i$.