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 (Clang 3.8.0) (judge verdict: Accepted)


#include <iostream>
#include <vector>
#include <algorithm>
#include <cassert>
#include <functional>
#include <numeric>
#include <limits>
#include <iomanip>
#include <queue>
#include <cmath>
#include <math.h>
#include <map>
using namespace std;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
const long long INF = 1LL << 60;
using pll = pair<long long, long long>;
#define min(a, b) ((a) < (b) ? (a) : (b))

struct request {
	int start;
	int end;
};

int main() {
	map<int, int> endStart{};

	int N, M;
	cin >> N >> M;
	int tmpStart, tmpEnd;
	vector<request> requests;
	for (int i = 0; i < M; i++) {
		cin >> tmpStart >> tmpEnd;
		requests.push_back({ tmpStart, tmpEnd });
	}
	sort(requests.begin(), requests.end(), [](const request& x, const request& y) {return x.end < y.end; });
	int minEnd = requests.at(0).end;
	int div = 1;
	for (auto x : requests) {
		if (minEnd <= x.start) {
			minEnd = x.end;
			++div;
		}
	}

	cout << div << endl;
}