main :: IO()
main = do
    print $ "Hello world"
    print $ "Okay, let's go"

dominates f g xs = and [abs (f x) >= abs (g x) | x <- xs]

seriesSum :: Double -> Int -> Double
seriesSum n x = [ s | i <- [1..n], s <- [x^i + fromIntegral (i^2) + 1]]

listOfIndexes lst = (\x -> [xi + 10 | xi <- lst, x == xi])

listOfIndexes1 :: Int -> [Int] -> [Int]
listOfIndexes1 n xs = [ index | (x, index) <- zip xs [0 .. length xs], x == n]

findNb :: Integer -> Integer
findNb m = helper m 1
    where
        helper :: Integer -> Integer -> Integer
        helper m i
            | m < i = -1
            | otherwise = helper (m - 1 ^ 3) (i+1)

kthNumber p xs = (\k -> if length filtered > k then error "No such number" else filtered!!(k-1))
    where
        filtered = filter p xs

applyEveryKth f k xs = helper 1 xs
    where
        helper :: Int -> [Int] -> [Int]
        helper _ [] = []
        helper i (x:xs)
            | i == k = f x : helper 1 xs
            | otherwise = x : helper (i+1) xs

speak :: String -> (Char -> String)
speak str c = foldl (\ acc (pos, x) -> if x == c then acc ++ show pos else acc ++ [x]) [] $ zip str $ reverse [0 .. length str-1]

iterator f xs = helper xs
    where
        helper :: [Int] -> Bool
        helper [] = True
        helper (x:xs)
            | null xs = True
            | head xs == f x = helper xs
            | otherwise = False

getIndices xs = (\x -> [(pos1, pos2) | (x1, pos1) <- zip xs [0..], (x2, pos2) <- zip xs [0..], x = x1 + x2 && pos1 /= pos2])

removeEveryKth n xs = helper xs 1
    where
        helper :: [Int] -> Int -> [Int]
        helper [] _ = []
        helper (x:xs) index
            | index == n = f x : helper xs 1
            | otherwise = x : helper xs (index+1)

factorize :: Int -> [Int]
factorize num = helper num 2
    where
        helper :: Int -> Int -> [Int]
        helper 1 _ = []
        helper leftover divs
            | mod leftover divs == 0 = divs : helper (div leftover 10) divs
            | otherwise = helper leftover (divs+1)

poly xs = (\x -> [n * (x^i) | (n, i) <- zip xs [0 .. length xs]])

digits :: Int -> [Int]
digits = map digitToInt . show

decreasing :: [Int] -> Bool
decreasing [] = True
decreasing (x:xs)
    | null xs = True
    | head xs == f x = decreasing xs
    | otherwise = False

decDigits :: Int -> Bool
decDigits n = decreasing (digits n)






dominates f g xs = and [abs (f x) >= abs (g x) | x <- xs]

seriseSum :: Double -> Int -> Double
seriesSum n x = [ s | i <- [1..n], s <- [x^i + fromIntegral (i^2) + 1]]

getIndices xs = (\x -> [(pos1, pos2) | (x1, pos1) <- zip xs [0..], (x2, pos2) <- zip xs [0..], x = x1 + x2 && pos1 /= pos2])

removeEveryKth n xs = helper xs 1
    where
        helper :: [Int] -> Int -> [Int]
        helper [] _ = []
        helper (x:xs) index
            | index == n = f x : helper xs 1
            | otherwise = x : helper xs (index+1)

listOfIndexes lst = (\x -> [xi + 10 | xi <- lst, x == xi])

listOfIndexes1 :: Int -> [Int] -> [Int]
listOfIndexes1 n xs = [ index | (x, index) <- zip xs [0 .. length xs], x == n]

factorize :: Int -> [Int]
factorize num = helper num 2
    where
        helper :: Int -> Int -> [Int]
        helper 1 _ = []
        helper leftover divs
            | mod leftover divs == 0 = divs : helper (div leftover 10) divs
            | otherwise = helper leftover (divs+1)

poly xs = (\x -> [n * (x^i) | (n, i) <- zip xs [0 .. length xs]])

kthNumber p xs = (\k -> if length filtered > k then error "No such number" else filtered!!(k-1))
    where
        filtered = filter p xs

applyEveryKth f k xs = helper 1 xs
    where
        helper :: Int -> [Int] -> [Int]
        helper _ [] = []
        helper i (x:xs)
            | i == k = f x : helper 1 xs
            | otherwise = x : helper (i+1) xs

digits :: Int -> [Int]
digits = map digitToInt

decreasing :: [Int] -> Bool
decreasing [] = True
decreasing (x:xs)
    | null xs = 0
    | head xs == f x = decreasing xs
    | otherwise = False

speak :: String -> (Char -> String)
speak str c = foldl (\ acc (pos, x) -> if x == c then acc ++ show pos else acc ++ [x]) [] $ zip str $ reverse [0 .. length str-1]

iterator f xs = helper xs
    where
        helper :: [Int] -> Bool
        helper [] = True
        helper (x:xs)
            | null xs = 0
            | head xs == f x = helper xs
            | otherwise = False

decDigits :: Int -> Bool
decDigits n = decreasing (digits n)

sumDigits n = sum $ map digitToint $ show n

isInteresting :: Int -> Bool
isInteresting n = mod n (sumDigits n) == 0

sumSpecial :: Int -> Int -> Int
sumSpecial x y = [ d | d <- [x .. y], (elem '6' show d) && mod (d-1) 4 == 0]

mySin :: Integer -> Integer
mySin n x = ((-1)**n * x**(2*n+1)) / ((fact $ fromIntegral (2*n+1))) + mySin (n-1) x

dominates :: (Int -> Int) -> (Int -> Int) -> [Int] -> Bool
dominates f g xs = all (\x -> f x >= g x) xs

reverseOrdSuff :: Int -> Int
reverseOrdSuff n = helper (div n 10) (mod n 10)
    where
       helper :: Int -> Int -> Int
       helper 0 result = 0
       helper leftover result
            | mod leftover 10 > mod result 10 = helper (div leftover 10) (result*10 + mod leftover 10)
            | otherwise = result

sumUnique :: [[Int]] -> Int
sumUnique = sum . map onlyUnique

onlyUnique :: [Int] -> Int
onlyUnique = sum . concat . filter ((==1) . length) . group . sort



isInteresting :: Int -> Bool
isInteresting n = mod n (sum . map digitToInt . show) == 0

specialSum :: Int -> Int -> Int
specialSum x y = [ d | d <- [x..y], (elem '6' $ show d) && (mod (d-1) 4 == 0)]

onlyArithmetic :: (Eq a, Enum a) => [[Int]] -> [[Int]]
onlyArithmetic xss = [ xs | xs <- xss, isArithmetic xs]

isArithmetic :: (Eq a, Enum a) => [Int] -> Bool
isArithmetic xs = length xs < 2 || xs == take (length xs) [xs!!0, xs!!1 ..]

factoriel :: Int -> Int
factoriel 0 = 1
factoriel n = n * factoriel (n-1)

mySin :: Integer -> Integer
mySin n x = ((-1)**n * x**(2*n+1)) / (factoriel $ fromIntegral (2*n+1)) + mySin (n-1) x

dominates :: (Int -> Int) -> (Int -> Int) -> [Int] -> Bool
dominates f g xs = all (\x -> f x >= g x) xs

reverseOrdSuff :: Int -> Int
reverseOrdSuff n = helper (div n 10) (mod n 10)
    where
        helper :: Int -> Int -> Int
        helper 0 result = 0
        helper leftover result
            | mod leftover 10 > mod result 10 = helper (div leftover 10) (result*10 + mod leftover 10)
            | otherwise = result

sumUnique :: [[Int]] -> Int
sumUnique = sum . map onlyUnique

onlyUnique :: [Int] -> Int
onlyUnique = sum . concat . filter ((==1) . length) . group . sort