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.*

private fun readStrings() = readLine()!!.split(" ")
private fun readInts() = readStrings().map { it.toInt() }

class Island {
    val rejectionsEast: MutableSet<Int> = HashSet()
}

fun main(args: Array<String>) {
    val (N, M) = readInts()
    val intervals = (1..M).map { readInts() }.map { ints -> ints[0] to ints[1] }
    val islands = (1..N).map { Island() }

    intervals.forEach { islands[it.first - 1].rejectionsEast.add(it.second - 1) }
    var brokenCount = 0
    val inclusions = mutableSetOf<Int>()

    (0 until N-1).forEach { bridgeIndex ->
        inclusions.addAll(islands[bridgeIndex].rejectionsEast)
        if (inclusions.contains(bridgeIndex + 1)) {
            inclusions.clear()
            brokenCount += 1
        }
    }
    println(brokenCount)
}