Ivan has a grid paper of size $$$w \times h$$$ ($$$1 \leq w, h \leq 10^5$$$). So it contains $$$w \times h$$$ squares of size $$$1 \times 1$$$. We can use integer coordinates $$$(x,y)$$$ to denote any corner of any of the $$$1 \times 1$$$ squares ($$$0 \leq y \leq w$$$ and $$$0 \leq y \leq h$$$).
In this grid paper, Tomi has drawn a simple polygon of $$$n$$$ vertices ($$$3 \leq n \leq 50$$$). The $$$i$$$-th vertex has integer coordinates $$$(x_i,y_i)$$$ ($$$0 \leq x_i \leq w$$$ and $$$0 \leq y_i \leq h$$$).
Ivan thinks Tomi's polygon is so good it can be sold to the local art museum. So he will cut the polygon out of the paper in such a way that the whole polygon will be cut out and every $$$1 \times 1$$$ square is either completely cut out or completely left in the original grid paper. Additionally, he will cut out as few $$$1 \times 1$$$ squares as possible.
The first line of input contains 3 space separated integers: $$$n$$$, $$$w$$$ and $$$h$$$.
The $$$i$$$-th of the next $$$n$$$ lines contains 2 spaces separated integers: $$$x_i$$$ and $$$y_i$$$. You are guaranteed that every ordered pair $$$(x_i,y_i)$$$ will be different.
Output a single integer: the number of $$$1 \times 1$$$ squares Ivan will cut.
9 8 5 1 4 4 5 5 3 7 3 8 2 5 1 4 0 0 2 2 3
27
A simple polygon is a polygon that does not intersect itself and has no holes.
The green squares are cut out in the solution for the sample case:
