Problem:
Score : 600 points

Problem Statement

There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.

Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it.
Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it.

Q queries are given. We ask you to process them in order.
There are two kinds of queries. Their input format and description are as follows:

1 x: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone.

2 x: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone.

How many black stones are there on the grid after processing all Q queries?

Constraints

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

0 \leq Q \leq \min(2N-4,2\times 10^5)

2 \leq x \leq N-1

Queries are pairwise distinct.

Input

Input is given from Standard Input in the following format:

N Q
Query_1
\vdots
Query_Q

Output

Print how many black stones there are on the grid after processing all Q queries.

Sample Input 1

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

Sample Output 1

1

After each query, the grid changes in the following way:

Sample Input 2

200000 0

Sample Output 2

39999200004

Sample Input 3

176527 15
1 81279
2 22308
2 133061
1 80744
2 44603
1 170938
2 139754
2 15220
1 172794
1 159290
2 156968
1 56426
2 77429
1 97459
2 71282

Sample Output 3

31159505795

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

{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE TypeFamilies #-}

module Main where

import Control.Monad
import Control.Monad.Extra
import qualified Data.Array as A
import qualified Data.Array.IO as AIO
import qualified Data.Array.Unboxed as AU
import Data.Bits
import Data.Bool
import qualified Data.ByteString as BS
import qualified Data.ByteString.Char8 as BSC8
import Data.Char
import Data.Either
import Data.Function
import qualified Data.Graph.Inductive.Graph as G
import qualified Data.Graph.Inductive.PatriciaTree as G
import qualified Data.Heap as H
import Data.Int
import Data.List
import qualified Data.Map.Strict as M
import Data.Maybe
import Data.Monoid
import Data.Ord
import qualified Data.Sequence as SQ
import qualified Data.Set as S
import Data.Time
import Data.Tuple
import qualified Data.Vector as V
import Data.Vector.Algorithms.Search
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Unboxing as VUG
import qualified Data.Vector.Unboxing.Mutable as VUGM
import Debug.Trace
import GHC.Base
import GHC.Stack

main :: HasCallStack => IO ()
main = do
  --aN       <- getI
  --[aA, aB] <- getIL
  --aS       <- getLine
  [aN, aQ] <- getIL
  table <- V.replicateM 3 $ VUM.replicate (aN + 1) aN
  acc@(_, _, blackNum) <-
    VU.foldM
      ( \acc@(h, w, blackNum) _ -> do
          (q1, q2) <- getIT2

          let tableq1 = table V.! q1
          let tablenq1 = table V.! (if q1 == 1 then 2 else 1)
          fore <- VUM.read tableq1 q2
          if q2 < (if q1 == 1 then w else h)
            then do
              VU.mapM_
                ( \i -> do
                    VUM.write tableq1 i (if q1 == 1 then h else w)
                )
                $ VU.enumFromN q2 ((if q1 == 1 then w else h) - q2 + 1)
              num <- VUM.read tableq1 q2
              if q1 == 1
                then return (h, q2, blackNum - (num -2))
                else return (q2, w, blackNum - (num -2))
            else do
              num <- VUM.read tableq1 q2
              return (h, w, blackNum - (num -2))
      )
      (aN, aN, (aN -2) ^ 2)
      $ (VU.enumFromN 1 aQ :: VU.Vector Int)
  print $ blackNum
  return ()

--雑多系
t :: Int -> (Int, Int)
t x = (x, 1)

i def f t = bool t def $ f t

shiftRCnt k = shiftRCntP k 1

shiftRCntP k c =
  let nk = shiftR k 1
   in if nk == 0
        then c
        else shiftRCntP nk (c + 1)

myVUmap f vu =
  if vu == VU.empty
    then VU.empty
    else
      VU.unfoldr
        ( \x ->
            let ret = f $ VU.head x
                tailx = VU.tail x
             in if x == VU.empty
                  then Nothing
                  else
                    if isLeft ret
                      then Just (either id id ret, tailx)
                      else Just (either id id ret, VU.empty)
        )
        vu

myVUmapM f vu =
  if vu == VU.empty
    then return VU.empty
    else
      VU.unfoldrM
        ( \x -> do
            ret <- f $ VU.head x
            let tailx = VU.tail x
            if x == VU.empty
              then return Nothing
              else
                if isLeft ret
                  then return $ Just (either id id ret, tailx)
                  else return $ Just (either id id ret, VU.empty)
        )
        vu

myVUmapM_ f vu =
  if vu == VU.empty
    then return ()
    else do
      ret1 <-
        VU.unfoldrM
          ( \x -> do
              ret2 <- f $ VU.head x
              let tailx = VU.tail x
              if x == VU.empty
                then return Nothing
                else
                  if isLeft ret2
                    then return $ Just (either id id ret2, tailx)
                    else return $ Just (either id id ret2, VU.empty)
          )
          vu
      return ()

myVUfor vu f = myVUmap f vu

myVUforM vu f = myVUmapM f vu

myVUforM_ vu f = myVUmapM_ f vu

myVUfoldl f acc vu =
  if vu == VU.empty
    then return acc
    else do
      let ret = f acc (VU.head vu)
      if isLeft ret
        then myVUfoldl f (either id id ret) (VU.tail vu)
        else return $ either id id ret

myVUfoldr f acc vu =
  if vu == VU.empty
    then return acc
    else do
      let ret = f acc (VU.last vu)
      if isLeft ret
        then myVUfoldr f (either id id ret) (VU.init vu)
        else return $ either id id ret

myVUfoldM f acc vu =
  if vu == VU.empty
    then return acc
    else do
      ret <- f acc (VU.head vu)
      if isLeft ret
        then myVUfoldM f (either id id ret) (VU.tail vu)
        else return $ either id id ret

--周りのマス
aroundSquare y x h w =
  VU.concatMap
    ( \a ->
        VU.mapMaybe
          ( \b ->
              let ya = y + a
                  xb = x + b
               in if abs a + abs b == 1
                    then
                      if ya < 0 || ya >= h || xb < 0 || xb >= w
                        then Nothing
                        else Just (ya, xb)
                    else Nothing
          )
          $ VU.enumFromN (-1) 3
    )
    $ VU.enumFromN (-1) 3

--入力系
splitReadBSC8 :: BSC8.ByteString -> [Int]
splitReadBSC8 bs =
  let (bs1, newBs) = BSC8.splitAt 1 bs
   in if newBs == BSC8.empty
        then [test $ BSC8.readInt bs1]
        else test (BSC8.readInt bs1) : splitReadBSC8 newBs
  where
    test (Just (i, _)) = i

read2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> IO Char
read2DimChar vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x

write2DimChar :: VM.IOVector (VUM.IOVector Char) -> Int -> Int -> Char -> IO ()
write2DimChar vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

readTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> IO Int
readTwoDimVec vec y x = do
  vecY <- VM.read vec y
  VUM.read vecY x

writeTwoDimVec :: VM.IOVector (VUM.IOVector Int) -> Int -> Int -> Int -> IO ()
writeTwoDimVec vec y x t = do
  vecY <- VM.read vec y
  VUM.write vecY x t

getVUI :: IO (VU.Vector Int)
getVUI = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine

getRepVUI :: Int -> IO (VU.Vector Int)
getRepVUI n =
  VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) . BSC8.unlines
    <$> replicateM n BSC8.getLine

getVS :: IO (V.Vector Char)
getVS = V.fromList <$> getLine

getVUC :: IO (VU.Vector Char)
getVUC = VU.fromList <$> getLine

readI :: BSC8.ByteString -> Int
readI = fst . fromJust . BSC8.readInt

readInteger :: BSC8.ByteString -> Integer
readInteger = fst . fromJust . BSC8.readInteger

readIL :: BSC8.ByteString -> [Int]
readIL = map readI . BSC8.words

readIT2 :: BSC8.ByteString -> (Int, Int)
readIT2 bs =
  let words = BSC8.words bs
   in (readI $ head words, readI $ last words)

readIT3 :: BSC8.ByteString -> (Int, Int, Int)
readIT3 bs =
  let words = BSC8.words bs
   in (readI $ head words, readI $ words !! 1, readI $ words !! 2)

getI :: IO Int
getI = readI <$> BSC8.getLine

getInteger :: IO Integer
getInteger = readInteger <$> BSC8.getLine

getIL :: IO [Int]
getIL = readIL <$> BSC8.getLine

getIT2 :: IO (Int, Int)
getIT2 = readIT2 <$> BSC8.getLine

getIT3 :: IO (Int, Int, Int)
getIT3 = readIT3 <$> BSC8.getLine

getIT2Order :: IO (Int, Int)
getIT2Order =
  getIL
    >>= \x@[xz, xo] ->
      if xz > xo
        then return (xo, xz)
        else return (xz, xo)

getNIS :: Int -> IO [(Int, BSC8.ByteString)]
getNIS 0 = return []
getNIS n = do
  [aFst, aSnd] <- BSC8.words <$> BSC8.getLine
  next <- getNIS (n - 1)
  return ((readI aFst, aSnd) : next)

il2Words :: [Int] -> String
il2Words = unwords . map show

il2Lines :: [Int] -> String
il2Lines = unlines . map show