A. Yet Another Goat in the Garden
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Once upon a time the world famous scientist Innokentiy decided to relax in the village. He has a garden of the triangular shape with sides a, b and c in his country site. The scientist often released his goat to walk there: unlike characters of some programming problems, the goat of Innokentiy was perfectly trained and didn't touch the grass and the vegetables in the garden.

Everything was changed when the new experiment of the scientist transmuted the goat into the black hole which had the shape of circle with a fixed radius r. Unlike the goat, the black hole was absorbing all the plants it touched while moving along the garden. Fortunately, Innokentiy has immediately figured out to set the innovative energy barriers along the perimeter of the garden. These barriers were designed so that no point of the black hole can cross them.

You are to calculate Innokentiy's losses. Find what part of the garden could be absorbed by the black hole in the worst case.

Input

The only line contains 4 integers a, b, c and r (1 ≤ a, b, c, r ≤ 104) — the lengths of the garden's sides and the radius of the black hole. It is guaranteed that there exists a nondegenerate triangle with sides a, b and c, and that the black hole can actually fit in the garden.

Output

Output a single real number — the biggest part of the garden that could be absorbed by the black hole. The answer will be considered correct if the absolute or relative error does not exceed 10 - 9.

Examples
Input
3 4 5 1
Output
0.523598775598299
Input
6 8 10 1
Output
0.880899693899575