# Practice on Toph

Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.

## Towers of Wadia

Admiral General Aladin has **n** watchtowers on a desert of People’s Republic of Wadia. One of those watchtowers is the headquarter there. On a few days back, something *aladin* (bad) happened. A fighter plane from a neighbouring country bombarded on the watchtowers and some towers were destroyed. No one wants to talk about it and let the Admiral General know about it for some obvious reasons. So, you, the head of security of the country, didn’t really get to know which towers were destroyed. However, as an *aladin* (good) citizen, you want to figure out the expected area covered by all the remaining towers. Area covered by some watchtowers is the area of the convex hull covering those watchtowers.

You know that in total **k** towers were destroyed. You also know that the indestructible headquarter wasn’t destroyed and fortunately, it’s still *inside* the convex hull (not on the edge of the convex hull) formed by the remaining watchtowers.

#### Input

The first line of the input will be **n (4 ≤ n ≤ 100)**, the number of watchtowers before the *aladin* (bad) incident happened. The next line will have two space separated integers **x _{0}** and

**y**, the position of the headquarter. Each of the next

_{0}**n-1**lines will contain two space separated integers which are the positions of the other watchtowers. The next line contains a number

**k (0 ≤ k ≤ 10)**.

Absolute value of all the coordinates will be no more than **1000**.

It is guaranteed that it will be possible to find at least one set of **n-k** towers so that the convex hull formed by those points will have the headquarter *inside* it. Also, no three towers will be on the same line.

#### Output

Print one line, the expected area of the convex hull formed by the remaining watchtowers. Error less than **10 ^{-6}** will be ignored.

#### Samples

Input | Output |
---|---|

5 1 1 0 0 0 3 3 0 3 2 1 | 4.500000 |

Either the tower at **(3, 2)** was destroyed or the tower at **(3, 0)** was destroyed. In both cases the area of the convex hull would be **4.5**. So, the expected area is **4.5**.

Please note that it’s not possible that tower at **(0, 0)** or tower at **(0, 3)** was destroyed. Because in those cases the headquarter would be on an edge of the convex hull.

Login to submit