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: Runtime Error)

import scala.annotation.tailrec

object Main extends App {
  @tailrec
  def func(routes:Array[Array[Int]],bridges:Array[Int],count:Int):Int = {
    if (routes.isEmpty){
      count
    } else {
      val stat = bridges.map(r=>{
        (r,routes.count(rr=>rr.contains(r)))
      })
      val removeBridge = stat.maxBy(_._2)._1
      val newBridges = stat.filter(_._2>0).map(_._1).filter(_!=removeBridge)
      val newRoutes = routes.filter(!_.contains(removeBridge))
      func(newRoutes,newBridges,count+1)
    }
  }
  val scanner = new java.util.Scanner(System.in)
  val n = scanner.nextInt()
  val m = scanner.nextInt()
  val ab = Array.fill(m,2)(scanner.nextInt())
  val routes = ab.map(abi=>{
    (abi(0) until abi(1)).toArray
  })
  val bridges = routes.flatten.distinct
  println(func(routes,bridges,0))
}