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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.stream.IntStream;
 
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
 
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] a = new int[M];
        int[] b = new int[M];
        for (int i = 0; i < M; ++i) {
            a[i] = sc.nextInt();
            b[i] = sc.nextInt();
        }
 
        System.out.println(solve(N, a, b));
 
        sc.close();
    }
 
    static int solve(int N, int[] a, int[] b) {
        int[] sortedIndices = IntStream.range(0, a.length).boxed().sorted((i1, i2) -> Integer.compare(b[i1], b[i2]))
                .mapToInt(x -> x).toArray();
 
        int result = 0;
        int prevEnd = -1;
        for (int index : sortedIndices) {
            if (a[index] >= prevEnd) {
                ++result;
                prevEnd = b[index];
            }
        }
 
        return result;
    }
}