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: Accepted)

#include <bits/stdc++.h>

#define M_PI       3.14159265358979323846   // pi

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> VI;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> t3;

#define rep(a,n) for(int a = 0;a < n;a++)
#define repi(a,b,n) for(int a = b;a < n;a++)

struct UnionFind {
public:
	vector <ll> par; // 
	vector <ll> siz; // 

	UnionFind(ll sz_) : par(sz_), siz(sz_, 1LL) {
		for (ll i = 0; i < sz_; ++i) par[i] = i;
	}
	void init(ll sz_) {
		par.resize(sz_);
		siz.assign(sz_, 1LL);
		for (ll i = 0; i < sz_; ++i) par[i] = i;
	}

	ll root(ll x) {
		while (par[x] != x) {
			x = par[x] = par[par[x]];
		}
		return x;
	}

	bool merge(ll x, ll y) {
		x = root(x);
		y = root(y);
		if (x == y) return false;
		if (siz[x] < siz[y]) swap(x, y);
		siz[x] += siz[y];
		par[y] = x;
		return true;
	}

	bool issame(ll x, ll y) {
		return root(x) == root(y);
	}

	ll size(ll x) {
		return siz[root(x)];
	}
};
int main(void)
{
	ll n,m;
	cin >> n >> m;
	vector<unordered_set<ll>> o(n);
	rep(i, m) {
		ll a, b;
		cin >> a >> b;
		a--; b--;
		o[a].insert(b);
		o[b].insert(a);
	}
	UnionFind uf(n+1);
	for (int i = 1; i < n; i++) {
		auto left = uf.root(i - 1);
		auto& s = o[left];
		if (s.count(i)) {
			continue;
		}
		uf.merge(i - 1, i);
		for (auto& e : o[i]) {
			s.insert(e);
		}
	}
	unordered_set<ll> c;
	rep(i, n) {
		c.insert(uf.root(i));
	}
	cout << c.size()-1 << endl;
	return 0;
}