Problem:
Score : 100 points

Problem Statement

You are given a binary array A=(A_1,A_2,\cdots,A_N) of length N.

Process Q queries of the following types. The i-th query is represented by three integers T_i,L_i,R_i.

T_i=1: Replace the value of A_j with 1-A_j for each L_i \leq j \leq R_i.

T_i=2: Calculate the inversion(*) of the array A_{L_i},A_{L_i+1},\cdots,A_{R_i}．

Note：The inversion of the array x_1,x_2,\cdots,x_k is the number of the pair of integers i,j with 1 \leq i < j \leq k, x_i > x_j.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq A_i \leq 1

1 \leq Q \leq 2 \times 10^5

1 \leq T_i \leq 2

1 \leq L_i \leq R_i \leq N

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N Q
A_1 A_2 \cdots A_N
T_1 L_1 R_1
T_2 L_2 R_2
\vdots
T_Q L_Q R_Q

Output

For each query with T_i=2, print the answer.

Sample Input 1

5 5
0 1 0 0 1
2 1 5
1 3 4
2 2 5
1 1 3
2 1 2

Sample Output 1

2
0
1

First query: Print 2, which is the inversion of (A_1,A_2,A_3,A_4,A_5)=(0,1,0,0,1).

Second query: Replace the value of A_3 and A_4 with 1 and 1, respectively.

Third query: Print 0, which is the inversion of (A_2,A_3,A_4,A_5)=(1,1,1,1).

Fourth query: Replace the value of A_1, A_2 and A_4 with 1, 0 and 0, respectively.

Fifth query: Print 1, which is the inversion of (A_1,A_2)=(1,0).

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 998244353

main :: IO ()
main = do
    [n, q] <- map read.words <$> getLine
    xs <- U.unfoldrN n (runParser int) <$> C.getLine
    qs <- U.unfoldrN q (runParser $ (,,) <$> int <*> int1 <*> int) <$> C.getContents
    putStr.unlines.map show.U.toList $ solve n q xs qs

type Query = (Int, Int, Int)

type M = (Int, Int, Int)
type F = Bool

instance {-# OVERLAPPING #-} Semigroup M where
    (x0,y0,z0) <> (x1,y1,z1) = (x, y, z)
      where
        !x = x0 + x1
        !y = y0 + y1
        !z = z0 + z1 + y0 * x1

instance {-# OVERLAPPING #-} Monoid M where
    mempty = (0, 0, 0)

instance Semigroup F where
    x <> y = (x && not y) || (not x && y)

instance  Monoid F where
    mempty = False

instance MonoidAction F M where
    appMonoid False m = m
    appMonoid True (x, y, z) = (y, x, z')
      where
        !z' = x * y - z
    {-# INLINE appMonoid #-}

solve :: Int -> Int -> U.Vector Int -> U.Vector Query -> U.Vector Int
solve n q xs qs = runST $ do
    seg <- buildSegTreeLazy @M @F
        $ U.map (\x -> if x == 0 then (1, 0, 0) else (0, 1, 0)) xs
    fmap (U.map snd.U.filter((/= (1 :: Int)).fst))$ U.forM qs $ \case
        (1, l, r) -> do
            appFromTo seg l r True
            return (1, 0)
        (t, l, r) -> do
            (_, _, res) <- mappendFromTo seg l r
            return (t, res)

data SegTreeLazy s a f = SegTreeLazy
    (UM.MVector s a)
    (UM.MVector s f)

newSegTreeLazy :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, PrimMonad m)
    => Int -> m (SegTreeLazy (PrimState m) a f)
newSegTreeLazy n = SegTreeLazy
    <$> UM.replicate (2 * extendToPowerOfTwo n) mempty
    <*> UM.replicate (extendToPowerOfTwo n) mempty

buildSegTreeLazy :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, PrimMonad m)
    => U.Vector a -> m (SegTreeLazy (PrimState m) a f)
buildSegTreeLazy xs = do
    tree <- UM.replicate (2 * n) mempty
    lazy <- UM.replicate n mempty
    U.unsafeCopy (UM.unsafeSlice n (U.length xs) tree) xs
    let seg = SegTreeLazy tree lazy
    flip MS.mapM_ (streamR 1 n) $ \i -> do
        updateSegTreeLazy seg i
    return seg
  where
    !n = extendToPowerOfTwo $ U.length xs

class (Monoid f) => MonoidAction f a where
    appMonoid :: f -> a -> a

appAllAt :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, MonoidAction f a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int -> f -> m ()
appAllAt (SegTreeLazy tree lazy) k f = do
    tk <- UM.unsafeModify tree (appMonoid f) k
    when (k < UM.length lazy) $ do
        UM.unsafeModify lazy (mappend f) k
{-# INLINE appAllAt #-}

pushSegTreeLazy :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, MonoidAction f a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int  -> m ()
pushSegTreeLazy st@(SegTreeLazy tree lazy) k = do
    fk <- UM.unsafeRead lazy k
    appAllAt st (2 * k) fk
    appAllAt st (2 * k + 1) fk
    UM.unsafeWrite lazy k mempty
{-# INLINE pushSegTreeLazy #-}

updateSegTreeLazy :: (Monoid a, U.Unbox a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int -> m ()
updateSegTreeLazy (SegTreeLazy tree _) k = do
    (<>) <$> UM.unsafeRead tree (2 * k) <*> UM.unsafeRead tree (2 * k + 1)
        >>= UM.unsafeWrite tree k
{-# INLINE updateSegTreeLazy #-}

writeSegTreeLazy :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, MonoidAction f a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int -> a -> m ()
writeSegTreeLazy st@(SegTreeLazy tree lazy) k0 v = do
    let !n = UM.length lazy
        k = k0 + n
        !h = 64 - countLeadingZeros n
    flip MS.mapM_ (streamR 1 h) $ \i -> do
        pushSegTreeLazy st (unsafeShiftR k i)
    UM.unsafeWrite tree k v
    flip MS.mapM_ (stream 1 h) $ \i -> do
        updateSegTreeLazy st (unsafeShiftR k i)
{-# INLINE writeSegTreeLazy #-}

readSegTreeLazy :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, MonoidAction f a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int -> m a
readSegTreeLazy st@(SegTreeLazy tree lazy) k0 = do
    let !n = UM.length lazy
        k = k0 + n
        !h = 64 - countLeadingZeros n
    flip MS.mapM_ (streamR 1 h) $ \i -> do
        pushSegTreeLazy st (unsafeShiftR k i)
    UM.unsafeRead tree k
{-# INLINE readSegTreeLazy #-}

mappendFromTo :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, MonoidAction f a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int -> Int -> m a
mappendFromTo st@(SegTreeLazy tree lazy) l0 r0 = do
    let !n = UM.length lazy
        !l = l0 + n
        !r = r0 + n
        !h = 64 - countLeadingZeros n
    flip MS.mapM_ (streamR 1 h) $ \i -> do
        when (unsafeShiftR l i `unsafeShiftL` i /= l) $ do
            pushSegTreeLazy st (unsafeShiftR l i)
        when (unsafeShiftR r i `unsafeShiftL` i /= r) $ do
            pushSegTreeLazy st (unsafeShiftR r i)
    let calcL l acc
            | l .&. 1 == 1 =
                mappend acc <$> UM.unsafeRead tree l
            | otherwise = return acc

        calcR r acc
            | r .&. 1 == 1 =
                flip mappend acc <$> UM.unsafeRead tree (r - 1)
            | otherwise = return acc

    fix (\loop !accL !accR !l' !r' -> do
        if l' < r'
        then do
            !accL' <- calcL l' accL
            !accR' <- calcR r' accR
            loop accL' accR'
                (unsafeShiftRL (l' + l' .&. 1) 1)
                (unsafeShiftRL (r' - r' .&. 1) 1)
        else return $! accL <> accR
        ) mempty mempty l r
{-# INLINE mappendFromTo #-}

mappendAll :: (Monoid a, U.Unbox a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> m a
mappendAll (SegTreeLazy tree _) = UM.unsafeRead tree 1
{-# INLINE mappendAll #-}

appAt :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, MonoidAction f a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int -> f -> m ()
appAt st@(SegTreeLazy tree lazy) k0 f = do
    let !n = UM.length lazy
        k = k0 + n
        !h = 64 - countLeadingZeros n
    flip MS.mapM_ (streamR 1 h) $ \i -> do
        pushSegTreeLazy st (unsafeShiftR k i)
    UM.unsafeModify tree (appMonoid f) k
    flip MS.mapM_ (stream 1 h) $ \i -> do
        updateSegTreeLazy st (unsafeShiftR k i)
{-# INLINE appAt #-}

appFromTo :: (Monoid a, U.Unbox a, Monoid f, U.Unbox f, MonoidAction f a, PrimMonad m)
    => SegTreeLazy (PrimState m) a f -> Int -> Int -> f -> m ()
appFromTo st@(SegTreeLazy tree lazy) l0 r0 f = when (l0 < r0) $ do
    let !n = UM.length lazy
        !l = l0 + n
        !r = r0 + n
        !h = 64 - countLeadingZeros n
    flip MS.mapM_ (streamR 1 h) $ \i -> do
        when (unsafeShiftR l i `unsafeShiftL` i /= l) $ do
            pushSegTreeLazy st (unsafeShiftRL l i)
        when (unsafeShiftR r i `unsafeShiftL` i /= r) $ do
            pushSegTreeLazy st (unsafeShiftRL (r - 1) i)

    fix (\loop !l' !r' -> when (l' < r') $ do
        when (l' .&. 1 == 1) $ do
            appAllAt st l' f
        when (r' .&. 1 == 1) $ do
            appAllAt st (r' - 1) f
        loop (unsafeShiftRL (l' + l' .&. 1) 1) (unsafeShiftRL (r' - r' .&. 1) 1)
        ) l r

    flip MS.mapM_ (stream 1 h) $ \i -> do
        when (unsafeShiftR l i `unsafeShiftL` i /= l) $ do
            updateSegTreeLazy st (unsafeShiftRL l i)
        when (unsafeShiftR r i `unsafeShiftL` i /= r) $ do
            updateSegTreeLazy st (unsafeShiftRL (r - 1) i)
{-# INLINE appFromTo #-}

extendToPowerOfTwo :: Int -> Int
extendToPowerOfTwo x
    | x > 1 = unsafeShiftRL (-1) (countLeadingZeros (x - 1)) + 1
    | otherwise = 1

-------------------------------------------------------------------------------
-- 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.IntMod
-------------------------------------------------------------------------------
modulus :: (Num a) => a
modulus = MOD
{-# INLINE modulus #-}
infixr 8 ^%
infixl 7 *%, /%
infixl 6 +%, -%
(+%) :: Int -> Int -> Int
(I# x#) +% (I# y#) = case x# +# y# of { r# -> I# (r# -# ((r# >=# MOD#) *# MOD#))}
{-# INLINE (+%) #-}
(-%) :: Int -> Int -> Int
(I# x#) -% (I# y#) = case x# -# y# of { r# -> I# (r# +# ((r# <# 0#) *# MOD#))}
{-# INLINE (-%) #-}
(*%) :: Int -> Int -> Int
(I# x#) *% (I# y#) = I# ((x# *# y#) `remInt#` MOD#)
{-# INLINE (*%) #-}
(/%) :: Int -> Int -> Int
(I# x#) /% (I# y#) = go# y# MOD# 1# 0# where { go# a# b# u# v# | isTrue# (b# ># 0#) = case a# `quotInt#` b# of { q# -> go# b# (a# -# (q# *# b#)) v# (u# -# (q# *# v#))} | otherwise = I# ((x# *# (u# +# MOD#)) `remInt#` MOD#)}
{-# INLINE (/%) #-}
(^%) :: Int -> Int -> Int
x ^% n | n > 0 = go 1 x n | n == 0 = 1 | otherwise = go 1 (1 /% x) (-n) where { go !acc !y !m | m .&. 1 == 0 = go acc (y *% y) (unsafeShiftR m 1) | m == 1 = acc *% y | otherwise = go (acc *% y) (y *% y) (unsafeShiftR (m - 1) 1)}
newtype IntMod = IntMod{getIntMod :: Int} deriving newtype (Eq, Ord, Read, Show, Real, Prim)
intMod :: (Integral a) => a -> IntMod
intMod x = fromIntegral $ mod (fromIntegral x) MOD
{-# INLINE intMod #-}
intModValidate :: IntMod -> Bool
intModValidate (IntMod x) = 0 <= x && x < MOD
{-# INLINE intModValidate #-}
instance Bounded IntMod where { minBound = IntMod 0; maxBound = IntMod $ modulus - 1}
instance Enum IntMod where { toEnum = intMod; fromEnum = coerce}
instance Integral IntMod where { quotRem x y = (x / y, x - x / y * y); toInteger = coerce (toInteger @Int)}
instance Num IntMod where { (+) = coerce (+%); (-) = coerce (-%); (*) = coerce (*%); abs = id; signum = const (IntMod 1); fromInteger x = coerce @Int @IntMod . fromInteger $ mod x modulus}
instance Fractional IntMod where { (/) = coerce (/%); fromRational q = fromInteger (numerator q) / fromInteger (denominator q)}
newtype instance  UM.MVector s IntMod = MV_IntMod (UM.MVector s Int)
newtype instance  U.Vector IntMod = V_IntMod (U.Vector Int)
instance U.Unbox IntMod
instance GM.MVector UM.MVector IntMod where { basicLength (MV_IntMod v) = GM.basicLength v; {-# INLINE basicLength #-}; basicUnsafeSlice i n (MV_IntMod v) = MV_IntMod $ GM.basicUnsafeSlice i n v; {-# INLINE basicUnsafeSlice #-}; basicOverlaps (MV_IntMod v1) (MV_IntMod v2) = GM.basicOverlaps v1 v2; {-# INLINE basicOverlaps #-}; basicUnsafeNew n = MV_IntMod `liftM` GM.basicUnsafeNew n; {-# INLINE basicUnsafeNew #-}; basicInitialize (MV_IntMod v) = GM.basicInitialize v; {-# INLINE basicInitialize #-}; basicUnsafeReplicate n x = MV_IntMod `liftM` GM.basicUnsafeReplicate n (coerce x); {-# INLINE basicUnsafeReplicate #-}; basicUnsafeRead (MV_IntMod v) i = coerce `liftM` GM.basicUnsafeRead v i; {-# INLINE basicUnsafeRead #-}; basicUnsafeWrite (MV_IntMod v) i x = GM.basicUnsafeWrite v i (coerce x); {-# INLINE basicUnsafeWrite #-}; basicClear (MV_IntMod v) = GM.basicClear v; {-# INLINE basicClear #-}; basicSet (MV_IntMod v) x = GM.basicSet v (coerce x); {-# INLINE basicSet #-}; basicUnsafeCopy (MV_IntMod v1) (MV_IntMod v2) = GM.basicUnsafeCopy v1 v2; {-# INLINE basicUnsafeCopy #-}; basicUnsafeMove (MV_IntMod v1) (MV_IntMod v2) = GM.basicUnsafeMove v1 v2; {-# INLINE basicUnsafeMove #-}; basicUnsafeGrow (MV_IntMod v) n = MV_IntMod `liftM` GM.basicUnsafeGrow v n; {-# INLINE basicUnsafeGrow #-}}
instance G.Vector U.Vector IntMod where { basicUnsafeFreeze (MV_IntMod v) = V_IntMod `liftM` G.basicUnsafeFreeze v; {-# INLINE basicUnsafeFreeze #-}; basicUnsafeThaw (V_IntMod v) = MV_IntMod `liftM` G.basicUnsafeThaw v; {-# INLINE basicUnsafeThaw #-}; basicLength (V_IntMod v) = G.basicLength v; {-# INLINE basicLength #-}; basicUnsafeSlice i n (V_IntMod v) = V_IntMod $ G.basicUnsafeSlice i n v; {-# INLINE basicUnsafeSlice #-}; basicUnsafeIndexM (V_IntMod v) i = coerce `liftM` G.basicUnsafeIndexM v i; {-# INLINE basicUnsafeIndexM #-}; basicUnsafeCopy (MV_IntMod mv) (V_IntMod v) = G.basicUnsafeCopy mv v; elemseq _ = seq; {-# INLINE elemseq #-}}