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: Time Limit Exceeded)

import Control.Monad
import qualified Data.Map.Strict as Map
import Data.List

main :: IO ()
main = do
  (n:m:_) <- fmap (map read . words) getLine :: IO [Int]
  gs <- replicateM m $ fmap (map read . words) getLine :: IO [[Int]]
  print . solve' 0 . sortBridge $ gs

sortBridge = sortBy (\x y -> (x !! 1) `compare` (y !! 1))
isDivided i ds = (ds !! 0) <= i && (ds !! 1) > i

solve' :: Int -> [[Int]] -> Int
solve' i [] = i
solve' i gs = solve' (i + 1) $ filter (not . isDivided bridge) gs
  where
    bridge = (head gs) !! 1 - 1