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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    int M = scanner.nextInt();
    Section[] sections = new Section[M];
    for (int i = 0; i < M; i++) {
      int a = scanner.nextInt();
      int b = scanner.nextInt();
      sections[i] = new Section(a, b);
    }
    Arrays.sort(sections, (s1, s2) -> {
      if (s1.end != s2.end) return s2.end - s1.end;
      return s2.start - s1.start;
    });

    int cnt = 0;
    int left = 200_000;
    for (Section sec : sections) {
      if (sec.end <= left) {
        cnt++;
        left = sec.start;
      }
    }
    System.out.println(cnt);
  }

  private static class Section {
    private final int start;
    private final int end;

    private Section(int start, int end) {
      this.start = start;
      this.end = end;
    }
  }
}