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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>

int main(){
	int N,M,ans=0;
	scanf("%d%d",&N,&M);
	int a[M],b[M];
	for(int i=0;i<M;i++)scanf("%d%d",&a[i],&b[i]);
	
	//sort
	int h=M;
	int swapped=0;
	while(h>1 || swapped==1){
		if(h>1)h=h*10/13;
		swapped=0;
		for(int i=0;i<M-h;i++){
			if(b[i]>b[i+h] || (b[i]==b[i+h] && a[i]>a[i+h])){
				int tmp=a[i];
				a[i]=a[i+h];
				a[i+h]=tmp;
				tmp=b[i];
				b[i]=b[i+h];
				b[i+h]=tmp;
				swapped=1;
			}
		}
	}
	
	int remove=-1;
	for(int i=0;i<M;i++){
		if(i<M-1 && b[i]==b[i+1])continue;
		else if(a[i]<=remove && remove<b[i])continue;
		else {
			ans++;
			remove=b[i]-1;
		}
	}
	printf("%d\n",ans);
	return 0;
}