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.*;

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[n + 1];
		Arrays.fill(a, n + 1);
		int idx, b, cnt = 0;
		for(int i = 0; i < m; i++) {
			idx = sc.nextInt();
			b = sc.nextInt();
			if(a[idx] > b) a[idx] = b;
		}
		for(int i = 1; i <= n; i++) {
			if(a[i] <= n) {
				BreakBridge(a, i, a[i], n + 1);
				cnt++;
			}
		}
		System.out.println(cnt);
	}
	static void BreakBridge(int[] a, int l, int r, int max){
		for(int i = l + 1; i < r; i++) {
			if(a[i] < max) {
				BreakBridge(a, i, Math.min(a[i], r), max);
				break;
			}
		}
		a[l] = max;
	}
}