Problem:
Score : 400 points

Problem Statement

There are N islands lining up from west to east, connected by N-1 bridges.

The i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.

One day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:

Request i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.

You decided to remove some bridges to meet all these M requests.

Find the minimum number of bridges that must be removed.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq a_i < b_i \leq N

All pairs (a_i, b_i) are distinct.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the minimum number of bridges that must be removed.

Sample Input 1

5 2
1 4
2 5

Sample Output 1

1

The requests can be met by removing the bridge connecting the second and third islands from the west.

Sample Input 2

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

Sample Output 2

2

Sample Input 3

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

Sample Output 3

4

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import           Control.Monad
import qualified Data.ByteString.Char8 as B
import           Data.Set              (Set (..))
import qualified Data.Set              as S

data Interval = Interval Int Int

instance Eq (Interval) where
  (Interval x y) /= (Interval z w)
    | y <= z    = False
    | w <= x    = False
    | otherwise = True

instance Ord (Interval) where
  compare (Interval x y) (Interval z w)
    | y <= z    = LT
    | w <= x    = GT
    | otherwise = EQ

main :: IO ()
main = do
  [n, m] <- readInts
  i6ls <- replicateM m readInterval
  print $ solve i6ls

readInts :: IO [Int]
readInts = map (maybe err fst . B.readInt) . B.words <$> B.getLine
  where err = error "parse error"

readInterval :: IO Interval
readInterval = (\[x, y] -> Interval x y) <$> readInts

solve :: [Interval] -> Int
solve = S.size . foldr insert S.empty

merge :: Interval -> Interval -> Interval
merge (Interval x y) (Interval z w)
  | y <= z    = err
  | w <= x    = err
  | otherwise = Interval (x `max` z) (y `min` w)
  where err = error "merge error"

insert :: Interval -> Set Interval -> Set Interval
insert i8s set
  | i8s `S.member` set = S.insert (merge i8s i8s') set
  | otherwise          = S.insert i8s set
  where
    i8s'  = S.elemAt index set
    index = S.findIndex i8s set