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>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#define F(i,a,n) for(int i=a; i<n; i++)

int main(){
    int n,m;
    scanf("%d%d",&n,&m);
    int a[m],b[m],tmp_a,tmp_b,sum[n-1];
    F(k,0,n-1){
        sum[k]=0;
    }
    
    F(i,0,m){
        scanf("%d%d",a+i,b+i);
    }
    
    int iter=1;
    while(iter){
        iter=0;
        F(i,0,m-1){
            if(b[i]>b[i+1]){
                tmp_b=b[i];
                b[i]=b[i+1];
                b[i+1]=tmp_b;
                tmp_a=a[i];
                a[i]=a[i+1];
                a[i+1]=tmp_a;
                iter=1;
            }
        }
    }

    int rem_num=0;
    F(j,0,m){
        if(b[j] != 0){
            F(k,j+1,m){
                if(a[k]<b[j]){
                    a[k]=0;
                    b[k]=0;
                }
            }
            rem_num++;
        }
    }
    printf("%d\n",rem_num);
    return 0;
}