In honor of the birth of an heir Tutti the royal chef has prepared a huge cake, that was put on the table for Three Fat Man. The first fat man can eat the cake by himself for t1 hours, second - for t2 hours, and the third - for t3 hours.

For what time can the cake be eaten simultaneously by all three fat men?

Input

One line contains three positive integers t1, t2 and t3, each of them is no more than 10000.

Output

Print the time in hours during which the cake can be eaten simultaneously by three fat men. Print the result with two digits after the decimal point.