import Data.List import Data.Int import Control.Monad data Vector a = RVector [a] | CVector [a] deriving Show newtype Matrix a = Matrix {getMatrix :: [[a]]} deriving Show getVectorList (RVector a) = a getVectorList (CVector a) = a rtoc (RVector v) = CVector v ctor (CVector v) = RVector v (!+!) :: Num a => Vector a -> Vector a -> Vector a (!+!) (RVector a) (RVector b) = RVector $ zipWith (+) a b (!+!) (CVector a) (CVector b) = CVector $ zipWith (+) a b (!+!) _ _ = error "no addition between a row vector and a column vector" vneg :: Num a => Vector a -> Vector a vneg (RVector a) = RVector $ map negate a vneg (CVector a) = CVector $ map negate a (!-!) a b = a !+! (vneg b) (!.!) :: Num a => Vector a -> Vector a -> a (!.!) a b = sum $ zipWith (*) (getVectorList a) (getVectorList b) (!*) :: Num a => Vector a -> a -> Vector a (!*) (RVector a) n = RVector $ map (*n) a (!*) (CVector a) n = RVector $ map (*n) a (*!) b a = a !* b (!/) a b = a !* (1 / b) vabs :: (Real a, Num a) => Vector a -> Double vabs a = sqrt $ sum $ map (realToFrac . (^2)) (getVectorList a) vcross :: Num a => Vector a -> Vector a -> Vector a vcross (RVector [a1,a2,a3]) (RVector [b1,b2,b3]) = RVector $ [a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1] vcross (CVector [a1,a2,a3]) (CVector [b1,b2,b3]) = CVector $ [a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1] vcross _ _ = error "cross product error" mmap f (Matrix a) = Matrix $ map (map f) a (|*|) :: Num a => Matrix a -> Matrix a -> Matrix a (|*|) (Matrix a) (Matrix b) = Matrix $ map (\va -> map (\vb -> sum $ zipWith (*) va vb) (transpose b)) a (|*) :: Num a => Matrix a -> a -> Matrix a (|*) (Matrix a) n = Matrix $ map (map (*n)) a (*|) n a = a |* n (|+|) :: Num a => Matrix a -> Matrix a -> Matrix a (|+|) (Matrix a) (Matrix b) = Matrix $ zipWith (zipWith (+)) a b mneg (Matrix a) = Matrix $ map (map negate) a (|-|) a b = a |+| (mneg b) (|^) :: (Num a, Integral b) => Matrix a -> b -> Matrix a (|^) (Matrix a) 0 = unitMatrix $ length a (|^) mat 1 = mat (|^) mat p = if even p then t |*| t else t |*| t |*| mat where t = mat |^ (div p 2) (|^:) :: (Integral a , Integral b) => Matrix a -> (b, a) -> Matrix a (|^:) (Matrix a) (0,_) = unitMatrix $ length a (|^:) mat (1,_) = mat (|^:) mat (p,m) = mmap (`mod` m) (if even p then t |*| t else t |*| t |*| mat) where t = mat |^: (div p 2, m) unitMatrix :: Num a => Int -> Matrix a unitMatrix n = Matrix $ [[if i==j then 1 else 0 | j<-[1..n]] | i<-[1..n]] (|*!) :: Num a => Matrix a -> Vector a -> Vector a (|*!) (Matrix a) (CVector v) = CVector $ map (\r -> sum $ zipWith (*) r v) a (!*|) :: Num a => Vector a -> Matrix a -> Vector a (!*|) (RVector v) (Matrix a) = RVector $ map (\c -> sum $ zipWith (*) v c) (transpose a) tetranacci 1 = 0 tetranacci 2 = 0 tetranacci 3 = 0 tetranacci 4 = 1 tetranacci n = let (CVector [x,_,_,_]) = (Matrix [[1,1,1,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]) |^: (n-4,17) |*! (CVector [1,0,0,0]) in x main = do q <- readLn :: IO Int replicateM_ q $ do n <- readLn :: IO Int64 print $ tetranacci n