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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int r = in.nextInt();
        Pair[] pairs = new Pair[r];
        for( int i = 0; i < r; i++ ) {
            pairs[i] = new Pair(in.nextInt(), in.nextInt());
        }
        Arrays.sort(pairs);
        // for( Pair p : pairs ) System.out.printf("%d %d\n", p.a, p.b);
        int prev_end = -1;
        int ct = 0;
        for( int i = 0; i < r; i++ ) {
            Pair temp = pairs[i];
            // within bound
            if( prev_end <= temp.a ) ct++;
            prev_end = temp.b;
        }
        System.out.println(ct);
    }
    public static class Pair implements Comparable<Pair>{
        int a, b;
        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
        public int compareTo( Pair p ) {
            if( a == p.a ) return p.b - b;
            return a - p.a;
        }
    }
}