CF814D An overnight dance in discotheque

The crowdedness of the discotheque would never stop our friends from having fun, but a bit more spaciousness won't hurt, will it? The discotheque can be seen as an infinite $ xy $ -plane, in which there are a total of $ n $ dancers. Once someone starts moving around, they will move only inside their own movement range, which is a circular area $ C_{i} $ described by a center $ (x_{i},y_{i}) $ and a radius $ r_{i} $ . No two ranges' borders have more than one common point, that is for every pair $ (i,j) $ ( $ 1

The first line of input contains a positive integer $ n $ ( $ 1

Output one decimal number — the largest achievable sum of spaciousness over two halves of the night. The output is considered correct if it has a relative or absolute error of at most $ 10^{-9} $ . Formally, let your answer be $ a $ , and the jury's answer be $ b $ . Your answer is considered correct if .

The first sample corresponds to the illustrations in the legend.