"_Contador as an owl, looking around at 360 ° around..._"

(from TV coverage of the Tour de France 2013)

Catfish Ivan is lying on the desk in the audience at the point x0, y0. The audience is a convex polygon. Ivan's viewing angle equals to A degrees. If he could see in all four directions, then A would be equal to 360. Take a look at the picture to understand better.

Ivan sees only the part of audience, which is marked blue. He can't get up from his seat during the pair, but quietly swirl around his axis, he can try. Determine the maximum area of ​​the audience, which Ivan can see.

Input

The first line contains two numbers: the number of vertices in the polygon n (3 ≤ n ≤ 500) and real angle A (0 ≤ A ≤ 180). In the second line there are 2 · n real numbers - the coordinates of the vertices xi, yi (-3000 ≤ xi, yi ≤ 3000) in the counter-clockwise order. And the third line contains two real numbers x0, y0 - coordinates of Ivan's location. It's known that Ivan is in the inside of the audience, not on it's wall, or outside.

Output

Print the maximum area of audience, which Ivan can see, with five characters after the dot.