Pretty Boxes

Taeyeon has a large collection of $N$ pretty boxes (numbered $1$ through $N$). For each valid $i$, the $i$-th box has two attributes $S_i$ and $P_i$, representing the size and beauty of the box respectively, and it can fit inside each box $j$ such that $S_i \le S_j$. (Don't ask why a box can fit into another box with the same size.) Yoona's birthday is coming very soon, so Taeyeon decided to gi