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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
  val Array(n, m) = io.StdIn.readLine().split(' ').map(_.toInt)
  val against = (for(_ <- 0 until m toList) yield
    io.StdIn.readLine().split(' ').map(_.toInt) match {
      case Array(a, b) => (a-1, b-1)
    }).sortWith{case (x, y) => x._2 < y._2}

  @scala.annotation.tailrec
  def solver(against: List[(Int, Int)], end: Int = 0, count: Int = 0): Int = against match {
    case Nil => count
    case p :: rest if end <= p._1 => solver(rest, p._2, count+1)
    case _ :: rest => solver(rest, end, count)
  }

  println(solver(against))
}