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: Accepted)

{-# LANGUAGE BangPatterns, MagicHash #-}
import Control.Monad
import Control.Applicative
import Data.List
import Data.Maybe
import Data.Bits
import qualified Data.IntMap.Strict as M
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Unboxed as V
import Data.Vector.Unboxed ((!))
import Data.Tuple
import Data.Ord (Down(..))
import Data.Coerce
                                 
query :: Int -> V.Vector (Int,Int) -> Int
query n =
  snd
  . V.ifoldl' (\(x,cnt) a b -> let x' = min b x
                               in if x'-1 == a
                                  then (n,cnt+1)
                                  else (x',cnt)) (n,0)
  . V.init . V.accumulate min (V.replicate n n)
     
main :: IO ()
main = do
  [n,m] <- map read . words <$> getLine
  ls <- V.replicateM m $ (\[x,y]->(x-1,y-1)) . map read . words <$> getLine
  putStrLn $ show $ query n ls