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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
int a[100001],x[100001],y[100001],t[100001]={};
void quicksort(int s,int t){
  if(s<t){
    int i=s,j=t,p=y[a[(s+t)/2]];
    while(1){
      while(y[a[i]]<p)i++;
      while(p<y[a[j]])j--;
      if(i>=j)break;
      a[i]^=a[j]^=a[i]^=a[j];
      i++;j--;
    }
    quicksort(s,i-1);quicksort(j+1,t);
  }
}
int main(){
  int i,j,n,m;
  scanf("%d%d",&n,&m);
  for(i=0;i<m;i++)a[i]=i;
  for(i=0;i<m;i++)scanf("%d%d",&x[i],&y[i]);
  quicksort(0,m-1);
  for(i=0;i<m;i++){if(t[x[a[i]]-1]==t[y[a[i]]-1])for(j=y[a[i]]-1;j<=n;j++)t[j]++;}
  printf("%d",t[n]);
}