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;

typedef long long ll;
typedef long double ld;
typedef vector<ll> v1;
typedef vector<v1> v2;
typedef vector<v2> v3;

typedef unordered_map<ll, unordered_map<ll, ll>> graph;

const ll INF = 1ll << 50;
const ll mod = 1000000007;

ll n,m;
vector<tuple<ll,ll>> ab;
ll ans = 0;

int main(){
    cin >> n >> m;
    ab = vector<tuple<ll,ll>>(m);
    for(ll i = 0;i < m;i++){
        ll a,b;
        cin >> a >> b;
        ab[i] = make_tuple(a,b);
    }
    sort(ab.begin(),ab.end());
    ll r = INF;
    for(ll i = 0;i < m-1;i++){
        ll a,b,next_a,next_b;
        tie(a,b) = ab[i];
        tie(next_a,next_b) = ab[i+1];
        r = min(r,b);
        if(next_a >= r){
            ans++;
            r = INF;
        }


    }
    ans++;
    cout << ans << endl;
}