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)

import java.util.*

fun main(args: Array<String>) {
    val (N, M) = readLine()!!.split(" ").map {it.toInt()}
    val ps = ArrayList<Pair<Int, Int>>()

    for (i in 1 .. M) {
        val (a, b) = readLine()!!.split(" ").map {it.toInt()}
        ps.add(Pair(a, i))
        ps.add(Pair(b, -i))
    }

    ps.sortWith(Comparator { a, b -> if (a.first == b.first) a.second - b.second else a.first - b.first })

    var res = 0
    var st = TreeSet<Int>()

    for (p in ps) {
        if (p.second > 0) {
            st.add(p.second)
        } else if (st.contains(-p.second)) {
            st.clear()
            res++
        }
    }

    println(res)
}