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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace Solution
{
    public struct Request
    {
        public int first;
        public int second;
    }

    public class Solution
    {
        int island;
        int request;
        Request[] requests;

        public Solution(int island, int request, Request[] requests)
        {
            this.island = island;
            this.request = request;
            this.requests = requests;
        }

        public int Solve()
        {
            var bridge = 0;
            var requests = this.requests.OrderBy(r => r.second).ToArray();
            while (requests.Length > 0)
            {
                var position = requests[0].second;
                bridge += 1;
                requests = requests.Where(r => r.first >= position).ToArray();
            }
            return bridge;
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            var island = 9;
            var request = 5;
            var requests = new Request[] {
                new Request() { first = 0, second = 7 },
                new Request() { first = 1, second = 6 },
                new Request() { first = 2, second = 4 },
                new Request() { first = 3, second = 5 },
                new Request() { first = 6, second = 8 },
            };
            var solution = new Solution(island, request, requests);
            Console.WriteLine(solution.Solve());
        }
    }
}