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: Wrong Answer)

#define SIZE 100001

#include<stdio.h>

int main(){
  int N,M;
  int a[SIZE], b[SIZE];
  int group[SIZE][2];

  scanf("%d", &N);
  scanf("%d", &M);

  for(int i=0; i<M; i++){
    scanf("%d %d", &a[i], &b[i]);
  }

  group[0][0] = a[0];
  group[0][1] = b[0];

  int group_num = 1;
  int new_group_flag = 0;
  for(int i=1; i<M; i++){ //check subject i
    for(int j=0; j<group_num; j++){ //check group j
      if(a[i] < group[j][1] && group[j][0] < b[i]){ //subject i belongs to group j
	if(a[i] > group[j][0]){
	  group[j][0] = a[i];
	}
	if(b[i] < group[j][1]){
	  group[j][1] = b[i];
	}
	new_group_flag = 0;
      }
      else{ //other group or new group
	new_group_flag = 1;
      }
    }
    if(new_group_flag){
      group_num++;
      group[group_num-1][0] = a[i];
      group[group_num-1][1] = b[i];
    }
  }

  printf("%d\n", group_num);

  return 0;
}