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Problems

Imposing figures

Imposing figures

Time limit 2 seconds
Memory limit 64 MiB

Peter cuts the cardboard into circle and triangle, and Vassya tries to impose them on each other to obtain such a position, in which area of overlapping 2 pieces will be maximised. Help Vassya.

Input data

The first line specifies the number of pairs of figures T, Petya cut (1 T 20), and the subsequent T rows of four integers through the gap: the length of the triangle sides a, b, c and the radius of the circle R.

(1a b c100, 1R100, a+b>c)

Output data

Output T numbers found Vassya (one per line). Bring out the results with an accuracy of 2 digits after the decimal point.

Examples

Input example #1
2
3 4 5 1
5 5 8 4 
Output example #1
3.14
12.00
Source Stage III All-Ukrainian Olympiad 2009-2010 Zhitomir