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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
  val (N, M) = readInts()
  val AB = (1..M).map { readInts().let { it[0] to it[1] } }.sortedBy { it.second }
  var cnt = 0
  var r = 0
  for (i in 0 until M) {
    val ab = AB[i]
    val a = ab.first
    val b = ab.second
    if (r in (a + 1)..b) continue
    cnt++
    r = b
  }
  println(cnt)
}

fun gcd(a: Int, b: Int): Int = if (a < b) gcd(b, a) else if (b == 0) a else gcd(b, a % b)
fun gcd(a: Long, b: Long): Long = if (a < b) gcd(b, a) else if (b == 0L) a else gcd(b, a % b)
fun lcm(a: Int, b: Int): Int = (a * b) / gcd(a, b)
fun lcm(a: Long, b: Long): Long = (a * b) / gcd(a, b)

fun readString() = readLine()!!
fun readInt() = readLine()!!.toInt()
fun readInts() = readLine()!!.split(" ").map { it.toInt() }
fun readLongs() = readLine()!!.split(" ").map { it.toLong() }