Watson is assigned to perform diagnosis of cardiovascular diseases, and he needs to process ECGs of patients. He applies linear transformation method to the signal. Shape of the signal can be described by formula: \includegraphics{https://static.e-olymp.com/content/19/19c287ef41e4bce2b124c6a90f361b9f8d6dbc63.jpg} , \includegraphics{https://static.e-olymp.com/content/ae/ae6806d50a5e36380cf0ce193d834d4476977c13.jpg} \includegraphics{https://static.e-olymp.com/content/37/371badd3f3eac5a33366f433b3e7ae30162d622d.jpg} where \textbf{Ψ(x')} - function, that describes position and intensity of particular components of the signal, - a Gaussian function describing the shape and width of particular spectral lines. Coefficients \textbf{µ} and \textbf{σ} Watson gets as an input, coefficient \textbf{А} here and further is calculated by formula . \includegraphics{https://static.e-olymp.com/content/2b/2ba887de223e3272155c85c43088add424fda0c5.jpg} \includegraphics{https://static.e-olymp.com/content/45/45ca38d51420f492d01bb98b85c81749f45fa6ca.jpg} Definition of function \textbf{Ψ(x)} can be given in this way: , where Fourier transform of function \textbf{F(x)} is calculated as: . To make exact computations in diagnosis tasks Watson needs to know numeric value for the coefficient \textbf{А}. \InputFile The only line at input contains two positive numbers \textbf{µ} and \textbf{σ}, each not exceeding \textbf{1000}. \OutputFile You need to print coefficient \textbf{A} with \textbf{4} digits after decimal point.