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;

int main()
{
    int n, m;
    cin >> n >> m;

    map<int, vector<pair<int, int> > > mvp; // {length, *{left, right}}
    for (int i = 0; i < m; i++) {
        int a, b;
        cin >> a >> b;
        mvp[b - a].push_back({a, b});
    }

    int cnt = 1;
    for (auto x : mvp) {
        sort(x.second.begin(), x.second.end());
        int j = 0;
        for (auto it = x.second.begin(); it != x.second.end(); ++it, ++j) {
            if (!j) continue;
            if ((*(it - 1)).second > (*it).first) continue;
            cnt++;
        }
    }
    cout << cnt << endl;


    return 0;
}