Problem:
Score : 100 points

Problem Statement

Consider a string of length N consisting of 0 and 1.
The score for the string is calculated as follows:

For each i (1 \leq i \leq M), a_i is added to the score if the string contains 1 at least once between the l_i-th and r_i-th characters (inclusive).

Find the maximum possible score of a string.

Constraints

All values in input are integers.

1 \leq N \leq 2 × 10^5

1 \leq M \leq 2 × 10^5

1 \leq l_i \leq r_i \leq N

|a_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
l_1 r_1 a_1
l_2 r_2 a_2
:
l_M r_M a_M

Output

Print the maximum possible score of a string.

Sample Input 1

5 3
1 3 10
2 4 -10
3 5 10

Sample Output 1

20

The score for 10001 is a_1 + a_3 = 10 + 10 = 20.

Sample Input 2

3 4
1 3 100
1 1 -10
2 2 -20
3 3 -30

Sample Output 2

90

The score for 100 is a_1 + a_2 = 100 + (-10) = 90.

Sample Input 3

1 1
1 1 -10

Sample Output 3

0

The score for 0 is 0.

Sample Input 4

1 5
1 1 1000000000
1 1 1000000000
1 1 1000000000
1 1 1000000000
1 1 1000000000

Sample Output 4

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 5

6 8
5 5 3
1 1 10
1 6 -8
3 6 5
3 4 9
5 5 -2
1 3 -6
4 6 -7

Sample Output 5

10

For example, the score for 101000 is a_2 + a_3 + a_4 + a_5 + a_7 = 10 + (-8) + 5 + 9 + (-6) = 10.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE GADTs #-}
import qualified Data.ByteString.Lazy.Char8 as B
import Data.Maybe
import Data.List
import qualified Data.IntSet as IS
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Control.Monad
import Control.Monad.ST
import Control.Monad.Primitive
import Debug.Trace
-- trace _ = id

solve :: Int -> Int -> [(Int,Int,Int)] -> Int
solve bN bM lras = runST theAction
  where
  vIntv = VU.fromListN bM (map (\(l,r,a) -> (l,r+1,a)) lras)
  iL = mysortOn' (getL . (vIntv VU.!)) [0..bM-1]
  iR = mysortOn' (getR . (vIntv VU.!)) [0..bM-1]
  fIntvL lj = vIntv VU.! (iL VU.! lj)
  fIntvR rj = vIntv VU.! (iR VU.! rj)
  getL (l,_,_) = l
  getR (_,r,_) = r
  getA (_,_,a) = a
  
  theAction :: forall s. ST s Int
  theAction = do
    sgt <- sgtCreate (bN+1) (0,0)
    act0 sgt
    where
    act0 sgt = mLoop 0 0 1 0 0 where

      sAdd a = sgtAct sgt (mfAdd a)
      sMax = sgtAct sgt mfMax 

      mLoop !ans !cur !i lj rj
        | i == bN+1 = return ans
        | otherwise = do
            let term f ints j | j == bM || f j /= i = (ints, j)
                              | otherwise = term f (j:ints) (j+1)
                (lints, newLj) = term (getL . fIntvL) [] lj
                (rints, newRj) = term (getR . fIntvR) [] rj
                newCur = cur + sum (map (getA . fIntvL) lints)
                             - sum (map (getA . fIntvR) rints)
            forM_ (map fIntvR rints) $ \(l,r,a) -> sAdd a l r
            score <- (+ newCur) <$> sMax 0 i
            sAdd (score - newCur) i (i+1)
            mLoop (max ans score) newCur (i+1) newLj newRj
                

mfAdd a ft rc sgt node l r = sub ft >> nodeInfo sgt node where
  sub SgtIn = sgtModify sgt (\(vSum,m)->(vSum+a,m)) node
  sub SgtOut = return ()
  sub SgtOther = let f m = sgtModify sgt (\(s,_)->(s,m)) node
                 in uncurry max <$> rc >>= f

mfMax SgtIn rc sgt node l r = nodeInfo sgt node
mfMax SgtOut rc sgt node l r = return minBound
mfMax SgtOther rc sgt node l r = uncurry max <$> rc

nodeInfo sgt node = uncurry (+) <$> sgtRead sgt node


----------------------------------------------------------------------
-- segment tree


data SegTree s a = SegTree {
  sgtVec :: VUM.MVector s a,
  sgtSize :: Int
}
data SgtFT = SgtIn | SgtOut | SgtOther deriving(Show)
type SgtMF   s a b =
  SgtFT ->         -- type (In/Out/Other)
  ST s (b,b) ->    -- results of (left,right)
  SegTree s a ->   -- segment tree
  Int ->           -- node
  Int ->           -- left bound for the node (incl)
  Int ->           -- right bound for the node (excl)
  ST s b

sgtRead :: (VUM.Unbox a) => SegTree s a -> Int -> ST s a
{-# INLINE sgtRead #-}
sgtRead sgt node = VUM.read (sgtVec sgt) node

sgtWrite :: (VUM.Unbox a) => SegTree s a -> Int -> a -> ST s ()
{-# INLINE sgtWrite #-}
sgtWrite sgt node a = VUM.write (sgtVec sgt) node a

sgtModify :: (VUM.Unbox a) => SegTree s a -> (a -> a) -> Int -> ST s ()
{-# INLINE sgtModify #-}
sgtModify sgt f node = VUM.modify (sgtVec sgt) f node

sgtCreate :: (VUM.Unbox a) => Int -> a -> ST s (SegTree s a)
{-# INLINE sgtCreate #-}
sgtCreate n a = do
  vec <- VUM.replicate (4*n) a
  return $ SegTree { sgtVec = vec, sgtSize = n }

sgtAct :: (VUM.Unbox a) =>
          SegTree s a ->   -- segment tree
          SgtMF s a b ->   -- action body
          Int ->           -- left
          Int ->           -- right
          ST s b
{-# INLINE sgtAct #-}
sgtAct sgt mf left right = sub 0 0 (sgtSize sgt) where
  sub node l r =
    mf (sgtft left right l r) (sgtChildAct sub node l r) sgt node l r

  sgtChildAct sub' node l r =
    let mid = (l + r) `div` 2
    in (,) <$> sub' (2*node + 1) l mid <*> sub' (2*node + 2) mid r

  sgtft left right l r
    | left <= l && r <= right = SgtIn
    | r <= left || right <= l = SgtOut
    | otherwise               = SgtOther

  

----------------------------------------------------------------------

mysortOn' :: (Ord a, Ord b, VU.Unbox a, VU.Unbox b, Show a, Show b) =>
            (a -> b) -> [a] -> VU.Vector a
mysortOn' f as = runST $ do
  v <- VU.unsafeThaw $ VU.fromList $ map (\a -> (f a, a)) as
  mymsort v
  (VU.map snd) <$> (VU.unsafeFreeze v)

mymsort :: (PrimMonad m, Ord a, VUM.Unbox a, Show a) =>
           VUM.MVector (PrimState m) a -> m ()
mymsort v = do
  let n = VUM.length v
  sub v 0 (n-1)
  where
  sub v lo hi
    | hi - lo <= 6 = myisort v lo hi
    | otherwise = do
        (pL, pR) <- mypartition v lo hi
--        vv <- VU.freeze v
--        sub v lo ((trace (show (vv, pL, pR)) pL)-1)
        sub v lo (pL-1)
        sub v (pR+1) hi

myisort v lo hi = do
  forM_ [lo+1..hi] $ \i -> do
    x <- VUM.read v i
    j <- sub_start lo i x
    VUM.unsafeMove (VUM.unsafeSlice (j+1) (i-j) v) (VUM.unsafeSlice j (i-j) v)
    VUM.write v j x
  where
    sub_start k i x
      | k == i = return i
      | otherwise = do
          y <- VUM.read v k
          if x < y then return k
                   else sub_start (k+1) i x

mypartition :: (PrimMonad m, Ord a, VUM.Unbox a, Show a) =>
               VUM.MVector (PrimState m) a -> Int -> Int -> m (Int, Int)
mypartition v lo hi = do
  let mid = (lo + hi) `div` 2
  xLo <- VUM.read v lo
  xMid <- VUM.read v mid
  xHi <- VUM.read v hi
  when (xMid < xLo) (VUM.swap v lo mid)
  when (xHi < xLo) (VUM.swap v lo hi)
  when (xMid < xHi) (VUM.swap v mid hi)
  pivot <- VUM.read v hi
--  (i0, j0) <- sub (trace ("pivot = " ++ show pivot) pivot) lo lo hi
  (i0, j0) <- sub pivot lo lo hi
  let w = min (j0-i0) (hi-j0+1)
  forM_ [0..w-1] $ \i -> VUM.swap v (i0+i) (hi-i)
  return (i0, i0+hi-j0+1-1)
  where
    sub pivot i0 j0 k0
      | j0 == k0  = return (i0, j0)
      | otherwise = VUM.read v j0 >>= sub2
      where sub2 x | x > pivot  = sub pivot i0 (j0+1) k0
                   | x == pivot = do
                                  VUM.swap v j0 (k0-1)
                                  sub pivot i0 j0 (k0-1)
                   | otherwise  = do
                                  VUM.swap v i0 j0
                                  sub pivot (i0+1) (j0+1) k0

traceL :: Show a => String -> a -> b -> b
traceL label showObj val = trace (label ++ " " ++ show showObj) val

traceLM :: (Monad m, Show a) => String -> (b -> a) -> m b -> m b
traceLM label showFn act = do
  aaa <- act
  traceL label (showFn aaa) (return ())
  return aaa

readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

tmain :: B.ByteString -> Int
tmain cont =
  let remLines0 = map B.words (B.lines cont)
      [bs_bN,bs_bM]:remLines1 = remLines0
      bN = readBInt bs_bN
      bM = readBInt bs_bM
      lras = map (\[x1,x2,x3] -> (readBInt x1,readBInt x2,readBInt x3)) remLines1
  in solve bN bM lras

outAnswer :: Int -> IO ()
outAnswer = putStrLn . show

main :: IO ()
main = outAnswer . tmain =<< B.getContents


-------------------------------------------------------------------------------

inp1 = "5 3\n1 3 10\n2 4 -10\n3 5 10\n"
inp2 = "3 4\n1 3 100\n1 1 -10\n2 2 -20\n3 3 -30\n"
inp3 = "1 1\n1 1 -10\n"
inp4 = "1 5\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000\n"
inp5 = "6 8\n5 5 3\n1 1 10\n1 6 -8\n3 6 5\n3 4 9\n5 5 -2\n1 3 -6\n4 6 -7\n"
tv1 = tmain $ B.pack inp1
tv2 = tmain $ B.pack inp2
tv3 = tmain $ B.pack inp3
tv4 = tmain $ B.pack inp4
tv5 = tmain $ B.pack inp5
test1 = tv1 == 20
test2 = tv2 == 90
test3 = tv3 == 0
test4 = tv4 == 5000000000
test5 = tv5 == 10
alltest = test1 && test2 && test3 && test4 && test5