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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
#include<queue>
#include<stack>
#include<cmath>
using namespace std;
struct node{
	int start;
	int end;
}a[100005];
int cmp(node x,node y){
	if(x.end==y.end)return x.start<y.start;
	return x.end<y.end;
}
int cmp1(node x,node y){
	if(x.start==y.start)return x.end<y.end;
	else return x.start<y.start;
}
int n,m,ans=0,vis[100005],t[100005],l[100005],r[100005],x[100005];
int f[400005];
int lowbit(int x){
	return x&(-x);
}
void update(int x,int y){
	for(int i=x;i<=m*4;i+=lowbit(i)){
	    f[i]=max(f[i],y);
    }
} 
int ask(int y){
	int ans=0,ans1=0;
	for(int i=y;i>=1;i-=lowbit(i))ans=max(ans,f[i]);
	return ans;
}
int main(){
    scanf("%d%d",&m,&n);
    for(int i=1;i<=n;i++){
    	scanf("%d%d",&a[i].start,&a[i].end);
    	a[i].end--;
	}
	sort(a+1,a+n+1,cmp1);
	for(int i=1;i<=n;i++){
		if(a[i].start!=1)x[i]=ask(a[i].start-1)+1;
		x[i]=max(x[i],1);
		update(a[i].end,x[i]);
	}
	printf("%d\n",x[n]);
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
    return 0;
}