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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using Graph = vector<vector<int>>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
const long long MOD=1e9+7;

int main() {
  int n,m;
  cin>>n>>m;
  int count=0;
  vector<int> left;
  vector<int> right;
  rep(i,m){
    int a,b;
    cin>>a>>b;
    bool done=false;
    rep(j,count){
      if((left[j]<=a&&a<right[j])||(left[j]<=b&&b<right[j])||(a<=left[j]&&right[j]<=b)){
        left[j]=max(left[j],a);
        right[j]=min(right[j],b);
        done=true;
        break;
      }
    }
    if(!done){
      count++;
      left.push_back(a);
      right.push_back(b);
    }
  }
  
  //rep(i,count) cout<<left[i]<<" "<<right[i]<<endl;
  cout<<count<<endl;
}