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 <algorithm>
#include <numeric>
#include <cstdint>
#include <map>

using namespace std;

int main()
{
    size_t n, m;
    cin >> n >> m;
    vector<pair<int, int>> ds(m);
    for(auto& p : ds) cin >> p.first >> p.second;
    
    sort(begin(ds), end(ds), [](const auto& pa, const auto& pb){ return pa.first < pb.first; });
    
    for(size_t i = 1; i < m; ++i)
    {
        auto& pa = ds[i-1];
        auto& pb = ds[i];
        if(pb.first < pa.second) // has union
        {
            pb.second = min(pb.second, pa.second);
            pa.first = pa.second = 0;
        }
    }
    
    ds.erase(remove_if(begin(ds), end(ds), [](const auto& p){ return p.first == 0; }), end(ds));
    
    cout << ds.size() << '\n';
  
    return 0;
}