Santa Claus Petrovich moved to a new hut. It consists of only one room. Its floor has the form of a simple polygon (not necessarily convex) with N vertices. It was dark in the hut at first, but then Petrovich hung a lamp at the point with projection (X₀, Y₀). Which area of the room is illuminated by the lamp?

The first line contains the coordinates of the lamp (X₀, Y₀). You may regard the lamp as a material point. The second line contains the integer 3 ≤ N ≤ 50000. In the next N lines there are coordinates (X_i, Y_i) of vertices of the N-gon. The vertices are given in the counter-clockwise order. All the coordinates are given as pairs of real numbers separated with a space, 0 ≤ X_i,Y_i ≤ 1000. The coordinates contain not more than four fractional digits. It is guaranteed that the lamp is strictly inside the room.

Output the area S of the illuminated part of the room. The area must be given with accuracy of at least two fractional digits.