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 <iostream>
#include <bits/stdc++.h>

using namespace std;

struct Node
{
    int l,r;
} node[200050];
bool cmp(Node a, Node b)
{
    return a.r<b.r;
}
int main()
{
    int n,m;
    cin>>n>>m;

    for(int i=0; i<m; i++)
    {
        int a,b;
        cin>>a>>b;
        if(a>b)
            swap(a,b);

        node[i].l = a;
        node[i].r = b;
    }
    sort(node,node+m,cmp);

    vector<Node>v;
    Node p;
    p.l = 0,p.r=n;
    v.push_back(p);

    for(int i=0; i<m; i++)
    {
        int flag = 1;
        for(int j=0; j<v.size(); j++)
        {
            int ll = v[j].l,rr = v[j].r;
            if(node[i].l >= rr)
                continue;
            flag = 0;
            if(node[i].l <=ll && node[i].r >= rr)
                continue;

            ll = max(ll,node[i].l);
            rr = min(rr,node[i].r);
            v[j].l = ll,v[j].r = rr;
            break;
        }

        if(flag == 1)
        {
            v.push_back(node[i]);
        }

    }
    cout<<v.size()<<endl;

    return 0;
}