import Data.Char
sumsqr :: Int -> Int
sumsqr n = sum [i^2 | i <- [1..n]]
myReplicate :: Int -> a -> [a]
myReplicate n x = [x | i <- [1..n]]
pyths :: Int -> [(Int, Int, Int)]
pyths n = [(x, y, z) | x <- [1..n], y <- [1..n], z <- [1..n], x^2 + y^2 == z^2]
factors :: Int -> [Int]
factors n = [i | i <- [1..n-1], n `mod` i == 0]
perfects :: Int -> [Int]
perfects n = [i | i <- [1..n], sum (factors i) == i]
prob5 :: [a] -> [a] -> [(a, a)]
prob5 xs1 xs2 = concat [[(i, j) | j <- xs2] | i <- xs1]
find :: Eq a => a -> [(a, b)] -> [b]
find a b = [j | (i, j) <- b, i == a]
positions :: Eq a => a -> [a] -> [Int]
positions a xs = find a (zip xs [0..n-1])
where n = length xs -1
scalarproduct :: [Int] -> [Int] -> Int
scalarproduct xs ys = sum [x * y | (x, y) <- zip xs ys]
count :: Char -> String -> Int
count c xs = length [c'| c' <- xs, toLower c' == c]
let2int :: Char -> Int
let2int c = ord (toLower c) - ord 'a'
int2let :: Int -> Char
int2let n = chr (ord 'a' + n)
shift :: Int -> Char -> Char
shift n c |isAlpha c = int2let ((let2int c + n) `mod` 26)
|otherwise = c
encode :: Int -> String -> String
encode n xs = [shift n c | c <- xs]
persent :: Int -> Int -> Float
persent n m = (fromIntegral n / fromIntegral m) * 100
freqs :: String -> [Float]
freqs xs = [persent (count c xs) n | c <- ['a'..'z']]
where n = length xs
chisqr :: [Float] -> [Float] -> Float
chisqr os es = sum [((o - e)^2) / e | (o, e) <- zip os es]
rotate :: Int -> [a] -> [a]
rotate n xs = drop n xs ++ take n xs
table :: [Float]
table = [8.2, 1.5, 2.8, 4.3, 12.7, 2.2, 2.0, 6.1, 7.0, 0.2, 0.8, 4.0, 2.4, 6.7, 7.5, 1.9, 0.1, 6.0, 6.3, 9.1, 2.8, 1.0, 2.4, 0.2, 2.0, 0.1]
crack :: String -> String
crack xs = encode (-factor) xs
where
factor = head (positions (minimum chitab) chitab)
chitab = [chisqr (rotate n table') table | n <- [0..25]]
table' = freqs xs