import Data.List
import Data.Maybe

-- Computes digits of pi using the formula
-- pi = 4/1 - 4/3 + 4/5 - 4/7 + ...
-- In each iteration,
-- a = the numerator of the fraction that estimates the next group of digits
-- b = the denominator of the fraction that estimates the next group of digits
-- c = the numerator of th next term in the sum
-- d = the place of the digits being computed
-- e = the estimate of the digits being computed
-- If we get the same estimate twice in a row, then we have
-- found the correct digits and we can move on to the next set
s = map (\(_,_,_,_,x) -> x) $ iterate r (0,1,1,1,Nothing)
	where r (a,b,c,d,e) =
		let
			g = a * d + 4 * b * c
			h = b * d
			i = g `div` h
		in if Just i == e
			then (10000000000 * (g `mod` h),h,(-10000000000)*c,d+2,Nothing)
			else (g,h,-c,d+2,Just i)
			
-- 3, 1415926535, 8979323846, ...
d = [ fromJust $ genericIndex s i | i <- [0..], isNothing $ genericIndex s (i+1)]

-- prints 8979323846
main = print (d!!2)