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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
typedef pair<int, int> pii;
#define rep(i, start, n) for (int i = (int)(start); i < (int)(n); ++i)
#define all(a) a.begin(), a.end()

const int MOD = 1e9+7;
const int INF = 1001001001;

int main(){
    int N, M;
    cin >> N >> M;

    vector<pii> bridge(M);
    rep(i, 0, M){
        int a, b;
        cin >> a >> b;
        bridge[i] = make_pair(a, -b);
    }

    sort(all(bridge));

    int l = 0, r = 10001;
    int ans = 1;
    rep(i, 0, M){
        int a = bridge[i].first;
        int b = -(bridge[i].second);
        if (r <= a){
            ans++;
            l = a;
            r = b;
        }
        else{
            l = max(l, a);
            r = min(r, b);
        }
    }
    cout << ans << endl;
}