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: Time Limit Exceeded)

#include <stdio.h>

int main(){
  int n, m, a[100000], b[100000], i, j, ans=0;
  scanf("%d %d", &n, &m);
  for(i=0;i<m;i++){
    scanf("%d %d", &a[i], &b[i]);
    for(j=0;j<i;j++){
      if((a[j]<=a[i] && a[i]<=b[j]-1) || (a[j]<=b[i]-1 && b[i]-1<=b[j]-1) || (a[i]<=a[j] && b[j]-1<=b[i]-1)){
        if(a[j]>a[i]) a[j]=a[i];
        if(b[j]<b[i]) b[j]=b[i];
        i--;
        j=i;
      }
    }
    if(j!=i+1) ans++;
  }
  printf("%d\n", ans);
  return 0;
}