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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(let (ilands)
  (defun init-irands (n)
    (setq ilands (loop repeat n collect 1)))

  (defun remove-bridge (iland1 iland2)
    (if (not (find 0 (subseq ilands (1- iland1) (1- iland2))))
        (setq ilands (concatenate 'list (subseq ilands 0 (- iland2 2)) '(0) (subseq ilands (1- iland2))))))

  (defun get-ilands ()
    ilands))

(defun get-requests (m)
  (loop repeat m collect (list (read) (read))))

(defun merge-sort (sequence)
  (let ((split (floor (length sequence) 2)))
    (if (zerop split)
        (copy-seq sequence)
        (merge 'list
               (merge-sort (subseq sequence 0 split))
               (merge-sort (subseq sequence split))
               #'(lambda (a b) (< (cadr a) (cadr b)))))))

(defun Islands-War ()
  (init-irands (read))
  (let ((requests (merge-sort (get-requests (read)))))
    (labels ((islands-war (requests cnt)
               (if requests
                   (if (remove-bridge (caar requests) (cadar requests))
                       (islands-war (cdr requests) (1+ cnt))
                       (islands-war (cdr requests) cnt))
                   cnt)))
      (islands-war requests 0))))

(Islands-War)