Fat Hut

There are $N$ breakfasts in the restaurant `“Fat Hut”` where the Chef works. The $i^{th}$ breakfast has an attractiveness $A_i$ and cost $C_i$. The Chef has noticed that nobody takes the $j^{th}$ breakfast if there exists at least one breakfast $i$ such that $A_i \ge A_j$ and $C_i \lt C_j$. In other words, if a breakfast is less attractive and more expensive than any of the other dishes, then