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 #-}

import           Control.Monad.Trans.State.Strict
import qualified Data.ByteString.Char8            as B
import           Data.Char
import           Data.Coerce
import qualified Data.List                        as L

main :: IO ()
main = do
    [n, m] <- map read.words <$> getLine :: IO [Int]
    pairs <- map (\(x,y)->(x-1,y-1)).L.unfoldr (runStateT parseInt2) <$> B.getContents
    print $ solve pairs

inf :: Int
inf = 0x3f3f3f3f

solve :: [(Int, Int)] -> Int
solve pairs = go 0 inf $ L.sort pairs
  where
    go !res minR ((l, r):lrs)
        | minR <= l = go (res + 1) inf ((l, r):lrs)
        | otherwise = go res (min minR r) lrs
    go res minR []
        | minR == inf = res
        | otherwise = res + 1

type Parser a = StateT B.ByteString Maybe a

parseInt :: Parser Int
parseInt = coerce $ B.readInt . B.dropWhile isSpace

parseInt2 :: Parser (Int, Int)
parseInt2 = (,) <$> parseInt <*> parseInt

parseInt3 :: Parser (Int, Int, Int)
parseInt3 = (,,) <$> parseInt <*> parseInt <*> parseInt