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 class Pair implements Comparable<Pair>{
        int start;
        int end;
        
        void Pair(int x,int y){
            this.start=x;
            this.end=y;
        }
        
        public int compareTo(Pair p){
            return -p.end+this.end;
        }
    }
    
    public static void main(String[] args) throws Exception {
        Scanner sc=new Scanner(System.in);
        int N=sc.nextInt();
        int M=sc.nextInt();
        Pair[] allpair=new Pair[M];
        
        for(int i=0;i<M;i++){
            int tmp_start=sc.nextInt();
            int tmp_end=sc.nextInt();
            Pair tmp=new Pair();
            tmp.Pair(tmp_start,tmp_end);
            allpair[i]=tmp;
        }
        
        Arrays.sort(allpair);
        int ANS=0;
        
        for(int i=0;i<M;i++){
            System.out.println(allpair[i].start+" "+allpair[i].end);
        }
        
        int x=0;
        
        for(int i=0;i<M;i++){
            int tmp=allpair[i].end;
            if(x<allpair[i].start){
                ANS++;
                x=tmp-1;
            }else{
            }
        }
        
        System.out.println(ANS);
    }
}