Pentium vs ENIAC

The calculation of 2000 digits of number `π` on the computer ENIAC in 1949 took 70 hours (not including programming!). Modern computers (and programmers) can find 2000 digits of number `π` much faster.

For calculation a series should be used

   `π/4\ =\ 1\ -\ 1/3\ +\ 1/5\ -\ 1/7\ +\ 1/9\ -\ …`

But this series converges slowly. Much better is series for an arctangent

   `"arctg"\ x\ =\ x\ -\ x^3/3\ +\ x^5/5\ -\ x^7/7\ +\ …,\ |x|<1`.

Combine it with the formula for addition of a tangent

   `"tg"(a+b)\ =\ ("tg"\ a\ +\ "tg"\ b)/(1\ -\ "tg"\ a\ *\ "tg"\ b)`

and select `a` and `b` so that `"tg"\ (a+b)\ =\ 1\ =\ "tg"\ π/4`. In practice usually use the following formulas

   `π\ =\ 16\ "arctg"\ (1/5)\ -\ 4\ "arctg"\ (1/239)`

   `π\ =\ 32\ "arctg"\ (1/10)\ -\ 16\ "arctg"\ (1/515)\ -\ 4\ "arctg"\ (1/239)`

   `π\ =\ 12\ "arctg"\ (1/4)\ +\ 4\ "arctg"\ (1/20)\ +\ 4\ "arctg"\ (1/1985)`

In all formulas it is necessary to calculate `"arctg"\ (1/k)`, where `k\ ≥\ 2`. Write the program that fulfills this calculation.

The first line of the input file contains one integer `k` (`2\ ≤\ k\ ≤\ 10000`).

Write into the output file a value of `"arctg"\ (1/k)` with accuracy `10^{-2000}`.

2

0.46364760900080611621425623146121440...399481324877580713052569525399998448