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.IntSet as S
import Data.IntSet (IntSet)

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

readInts :: IO [Int]
readInts = map read . words <$> getLine

solve :: [IntSet] -> [[Int]] -> Int
solve ss [] = solve' ss
solve ss ([a, b]:ass) = solve (add (S.fromList [a..b]) ss) ass

add :: IntSet -> [IntSet] -> [IntSet]
add s ss 
  | any (`S.isSubsetOf` s) ss
    = filter (not . S.isSubsetOf s) ss
  | otherwise
    = (s :) $ filter (not . S.isSubsetOf s) ss

solve' :: [IntSet] -> Int
solve' [] = 0
solve' (s:ss)
  | any (disjoint s) ss
    = 1 + solve' ss
  | otherwise
    = solve' (map  (f s) ss)
      where
        f s t
          | disjoint s t = t
          | otherwise = S.intersection s t

disjoint :: IntSet -> IntSet -> Bool
disjoint s t = S.null $ S.intersection s t