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 (*X*_{0}, *Y*_{0}). Which area of the room is illuminated by the lamp?

### Input

The first line contains the coordinates of the lamp (*X*_{0}, *Y*_{0}).
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

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

### Sample

input | output |
---|

1.0 1.0
6
0 0
3 0
3 2
2 2
2 3
0 3 | 8.00 |

**Problem Author: **Dmitry Ivankov (idea of Alexander Ipatov)

**Problem Source: **Ural SU Contest. Petrozavodsk Winter Session, January 2006