Problem:
Score : 100 points

Problem Statement

You are given a string of length N. Calculate the number of distinct substrings of S.

Constraints

1 \leq N \leq 500,000

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

Print the answer.

Sample Input 1

abcbcba

Sample Output 1

21

Sample Input 2

mississippi

Sample Output 2

53

Sample Input 3

ababacaca

Sample Output 3

33

Sample Input 4

aaaaa

Sample Output 4

5

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies  #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances       #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, KindSignatures, LambdaCase #-}
{-# LANGUAGE MagicHash, MultiParamTypeClasses, MultiWayIf           #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables       #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications    #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns  #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.Reader
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bifunctor
import           Data.Bool
import qualified Data.ByteString                   as B
import qualified Data.ByteString.Builder           as B
import qualified Data.ByteString.Char8             as C
import qualified Data.ByteString.Internal          as B
import qualified Data.ByteString.Unsafe            as B
import           Data.Char
import qualified Data.Foldable                     as F
import           Data.Function
import           Data.Functor.Identity
import qualified Data.IntMap.Strict                as IM
import qualified Data.IntSet                       as IS
import qualified Data.List                         as L
import qualified Data.Map.Strict                   as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive
import           Data.Proxy
import           Data.Ratio
import           Data.Semigroup
import qualified Data.Set                          as S
import           Data.Tuple
import qualified Data.Vector                       as V
import qualified Data.Vector.Algorithms.Intro      as Intro
import qualified Data.Vector.Fusion.Stream.Monadic as MS
import qualified Data.Vector.Fusion.Bundle.Monadic as MB
import           Data.Vector.Fusion.Util
import qualified Data.Vector.Generic               as G
import qualified Data.Vector.Generic.Mutable       as GM
import qualified Data.Vector.Mutable               as VM
import qualified Data.Vector.Primitive             as P
import qualified Data.Vector.Primitive.Mutable     as PM
import qualified Data.Vector.Unboxed               as U
import qualified Data.Vector.Unboxed.Mutable       as UM
import           Debug.Trace
import           Foreign                           hiding (void)
import           GHC.Exts
import           GHC.TypeLits
import           System.IO
import           Unsafe.Coerce

#define MOD 1000000007

main :: IO ()
main = do
    bs <- C.getLine
    print $ solve bs

solve :: C.ByteString -> Int
solve bs
    = (total -) . U.sum
    . getLCPArray
    . buildLCPArray bs
    $ buildSuffixArray bs
  where
    n = C.length bs
    total = n * (n + 1) `div` 2

newtype SuffixArray = SuffixArray {getSuffixArray :: U.Vector Int} deriving (Show)

getSuffixStartPos :: SuffixArray -> Int -> Int
getSuffixStartPos = U.unsafeIndex . getSuffixArray
{-# INLINE getSuffixStartPos #-}

getSuffix :: SuffixArray -> Int -> B.ByteString -> B.ByteString
getSuffix  = (B.unsafeDrop.) . getSuffixStartPos
{-# INLINE getSuffix #-}

buildSuffixArray :: B.ByteString -> SuffixArray
buildSuffixArray bs = SuffixArray
    . fst
    . F.foldl step (sa0, rank0)
    . takeWhile (<= n)
    $ map (shiftL 1) [0..]
  where
    !n = B.length bs :: Int
    !sa0 = U.generate (n + 1) id
    !rank0 = U.generate n (fromIntegral . B.unsafeIndex bs) `U.snoc` 0
    step (!sa, !rank) k = (sa', rank')
      where
        encode sai =
            let !x = rank U.! sai
                !y | sai + k <= n = rank U.! (sai + k)
                   | otherwise = 0
            in  unsafeShiftL x 40 .|. unsafeShiftL y 20 .|. sai
        maskSA x = x .&. 0xfffff
        maskRank x = unsafeShiftR x 20

        sorted = radixSort64 $ U.map encode sa
        !sa' = U.map maskSA sorted
        !rank' = U.create $ do
            mv <- UM.unsafeNew (n + 1)
            UM.write mv (sa' U.! 0) 1

            U.forM_ (U.zip sorted $ U.tail sorted) $ \(prev, cur) -> do
                x <- UM.unsafeRead mv (maskSA prev)
                UM.unsafeWrite mv (maskSA cur)
                    $ x + fromEnum (maskRank prev < maskRank cur)

            return mv

radixSort64 :: U.Vector Int -> U.Vector Int
radixSort64 v = F.foldl' step v [0, 16, 32, 48]
  where
    mask k x = fromIntegral $ unsafeShiftR x k .&. 0xffff
    step v k = U.create $ do
        pref <- U.unsafeThaw
            . U.prescanl' (+) 0
            . U.unsafeAccumulate (+) (U.replicate 0x10000 0)
            $ U.map (flip (,) 1 . mask k) v
        res <- UM.unsafeNew $ U.length v
        U.forM_ v $ \x -> do
            let !masked = mask k x
            i <- UM.unsafeRead pref masked
            UM.unsafeWrite pref masked $ i + 1
            UM.unsafeWrite res i x
        return res
{-# INLINE radixSort64 #-}




-------------------------------------------------------------------------------
-- Utils
-------------------------------------------------------------------------------
rep :: (Monad m) => Int -> (Int -> m ()) -> m ()
rep n = flip MS.mapM_ (stream 0 n)
{-# INLINE rep #-}
rev :: (Monad m) => Int -> (Int -> m ()) -> m ()
rev !n = flip MS.mapM_ (streamR 0 n)
{-# INLINE rev #-}
stream :: (Monad m) => Int -> Int -> MS.Stream m Int
stream !l !r = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream #-}
streamR :: (Monad m) => Int -> Int -> MS.Stream m Int
streamR !l !r = MS.Stream step (r - 1) where { step x | x >= l = return $ MS.Yield x (x - 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] streamR #-}
stream' :: (Monad m) => Int -> Int -> Int -> MS.Stream m Int
stream' !l !r !d = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + d) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream' #-}
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL :: Int -> Int -> Int
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL :: Int -> Int -> Int
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
type Parser a = StateT C.ByteString Maybe a
runParser :: Parser a -> C.ByteString -> Maybe (a, C.ByteString)
runParser = runStateT
{-# INLINE runParser #-}
int :: Parser Int
int = coerce $ C.readInt . C.dropWhile isSpace
{-# INLINE int #-}
int1 :: Parser Int
int1 = fmap (subtract 1) int
{-# INLINE int1 #-}
char :: Parser Char
char = coerce C.uncons
{-# INLINE char #-}
byte :: Parser Word8
byte = coerce B.uncons
{-# INLINE byte #-}
skipSpaces :: Parser ()
skipSpaces = modify' (C.dropWhile isSpace)
{-# INLINE skipSpaces #-}
lowerBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
lowerBoundM low high p = go low high where { go !low !high | high <= low = return high | otherwise = p mid >>= bool (go (mid + 1) high) (go low mid) where { mid = low + unsafeShiftRL (high - low) 1}}
{-# INLINE lowerBoundM #-}
upperBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
upperBoundM low high p = do { flg <- p high; if flg then return high else subtract 1 <$!> lowerBoundM low high (fmap not . p)}
{-# INLINE upperBoundM #-}
lowerBound :: Int -> Int -> (Int -> Bool) -> Int
lowerBound low high p = runIdentity (lowerBoundM low high (return . p))
{-# INLINE lowerBound #-}
upperBound :: Int -> Int -> (Int -> Bool) -> Int
upperBound low high p = runIdentity (upperBoundM low high (return . p))
{-# INLINE upperBound #-}
-------------------------------------------------------------------------------
-- Data.ByteString.LCP
-------------------------------------------------------------------------------
newtype LCPArray = LCPArray{getLCPArray :: U.Vector Int} deriving (Show)
naiveLCP :: B.ByteString -> B.ByteString -> Int
naiveLCP xs ys = go 0 where { !n = min (B.length xs) (B.length ys); go !i | i < n && B.unsafeIndex xs i == B.unsafeIndex ys i = go (i + 1) | otherwise = i}
buildLCPArray :: B.ByteString -> SuffixArray -> LCPArray
buildLCPArray bs sa = LCPArray $ U.create $ do { let { !n = B.length bs; rank = U.unsafeAccumulate (flip const) (U.generate (n + 1) id) . U.imap (flip (,)) $ getSuffixArray sa}; lcp <- UM.replicate (n + 1) (0 :: Int); let { go !i !h | i < n = do { let { xs = B.unsafeDrop (i + h) bs}; let { ys = B.unsafeDrop (getSuffixStartPos sa (U.unsafeIndex rank i - 1) + h) bs}; let { h' = h + naiveLCP xs ys}; UM.unsafeWrite lcp (U.unsafeIndex rank i - 1) h'; go (i + 1) . max 0 $ h' - 1} | otherwise = return lcp}; go 0 0}