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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <algorithm>
#include <map>

using namespace std;

bool pair_compare(const pair<int,int>& first_elof,const pair<int,int>& second_elof){
  return first_elof.second>second_elof.second;
}

int main(){
  int N,M;
  cin>>N>>M;
  vector<pair<int,int> >pairs(M);
  vector<bool> check(N,true);
  for(int i=0;i<M;i++){
    int a,b;
    cin>>a>>b;
    pairs[i]=make_pair(a,b);
  }
  sort(pairs.begin(),pairs.end(),pair_compare);
  int ans=0;
  for(int i=M-1;i>=0;i--){
    int nf=pairs[i].first,ns=pairs[i].second;
    bool flag=false;
    for(int j=nf;j<ns;j++){
      if(check[j-1]==false) flag=true;
    }
    if(!flag){
      check[ns-2]=false;
      ans++;
    }
  }

  cout<<ans<<endl;

  return 0;
}