Aquarium Tank

Time limit1sMemory limit256 MB

Summary

A convex polygon tank of depth D holds L litres of water, and the task asks for the height of the water surface.

Level: Medium6 of 10
Topics: Geometry, Binary search
Solved: No attempts yet

Problem

You bought an aquarium tank with an unusual shape and poured $L$ litres of water into it. How high does the water stand in the tank?

Seen from one side, the tank is a convex polygon. Exactly two vertices of that polygon rest on the table, so their $y$ coordinates are 0, and every other vertex has a positive $y$ coordinate. Exactly two vertices have the maximum $y$ coordinate, and the water is poured through the opening between those two vertices. The tank is $D$ centimetres deep. It is glued to the table, so whatever its shape is, it keeps its position and does not tip over.

All coordinates and lengths in this problem are given in centimetres. One cubic metre is 1000 litres.

Input

The input is a single test case. The first line contains an integer $N$ ( $4 \le N \le 100$ ), the number of vertices of the polygon. The second line contains two integers $D$ and $L$ , where $1 \le D \le 1000$ is the depth of the tank and $0 \le L \le 2000$ is the number of litres of water poured into it. Each of the next $N$ lines contains two integers, the $x$ and $y$ coordinates of one vertex of the convex polygon, in counterclockwise order. The absolute values of $x$ and $y$ are at most 1000. The tank has a positive capacity, and the water poured in never exceeds it.

Output

Print the height of the water in the tank, in centimetres, rounded to 2 decimal places, on one line.

Examples2

Example 1
Input
```
4
30 50
20 0
100 0
100 40
20 40
```
Expected output
```
20.83
```

Example 2

Input

Expected output

19.74