Jigsaw puzzle is a popular intellectual game for its . It is not only used for education and entertainment, but also for commercial advertising and political propaganda. Maps, animal landscapes, characters, etc. can be made into jigsaw puzzles.

A salesman named Dimma began to sell jigsaw puzzles. It first partitioned a map into several rectangular tiles,  then disrupt the order.  You need to rearrange it, spell out the original map.

Suppose each fragment is a rectangle of  a*b , Dimma needs to cut their printing costs by minimizing the number of rectangle used for their maps.

The left side of Figure J-1 shows 8 rectangles to cover a map. The right side shows how you can

cover the same map with only 6 rectangles.

Your task is to help Dimma find the minimum number of rectangles needed to cover a given map. For simplicity, the map will be given as a closed polygon that does not intersect itself.

Note that each fragment  of map must be part of a rectangular grid aligned with the x-axis and y-axis. That is, they touch each other only with their whole sides and cannot be rotated. The polygon may touch the edges of marginal lines .  However, to avoid floatingpoint issues, you may assume the optimal answer will not change even if the polygon is allowed to go outside the map tiles by a distance of 10^-6.

* Line 1:    n  a  b        (3 ≤ n ≤ 50  1 ≤ a, b ≤ 100)

n is the number of polygon vertices , a and b are the dimensions of each rectangle.

*Line 2~ n+1:  xi  yi      ( 0≤ xi≤ 10*a   0≤ yi≤ 10*b    i=1…. n )

Each of the next n lines contains two integers xi nad yi specifying the vertices of the polygon representing the region (in either clockwise or counter-clockwise order).