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 <vector>
#include <map>
#include <string>
#include <cstdio>
#include <algorithm>
#include <cstdlib>
#include <functional>
#include <queue>
#include <utility>
using namespace std;
typedef long long ll;
int main(){
  //取り除く橋の最小値は,ai,biを仕事の始点・終点と思った時の区間スケジューリング問題と考えて求めればよい.
  //取ることのできる仕事の最大値が求める最小値になる.(ネットの証明参照.任意の仕事wiに対し,sjk<=ti<=tjkなる仕事wjkが存在する.)

  int N,M;
  cin >> N >> M;

  vector<pair<int,int>> w;

  for(int i = 0;i < M;i++){
    int a,b;
    cin >> a >> b;
    b--;
    w.push_back(make_pair(b,a));
  }

  sort(w.begin(),w.end());

  int ans = 0;
  int t = 0;
  for(int i = 0;i < M;i++){
    if(t < w[i].second){
      ans++;
      t = w[i].first;
    }
  }

  cout << ans << endl;
}