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;

const int MAX_N = 1e5+2;
int N, M;
int a[MAX_N], b[MAX_N];

struct inter{
	int st, ed;
	inter(int s, int t) : st(s), ed(t) {}
	bool operator < (const inter& other) const
	{
		return (ed != other.ed) ? ed < other.ed : st < other.st;
	}
};

void solve()
{
	vector<inter> A;
	for(int i=0;i<M;++i) A.emplace_back(a[i], b[i]);
	sort(A.begin(), A.end());
	int ans = 1;
	int cut = A[0].ed;
	for(int i=1;i<(int)A.size();++i){
		if(A[i].st < cut) continue;
		else{
			ans++;
			cut = A[i].ed;
		}
	}
	cout << ans << '\n';
}

int main()
{
	cin >> N >> M;
	for(int i=0;i<M;++i) cin >> a[i] >> b[i];
	solve();
	return 0;
}