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.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		
		int[] deepMap = new int[N];
		int[][] map = new int[M][2];
		for (int i = 0; i < M; i++) {
			int[] tmp = new int[2];
			tmp[0] = sc.nextInt();
			tmp[1] = sc.nextInt();
			map[i] = tmp;
			for (int j = tmp[0]; j < tmp[1]; j++) {
				deepMap[j - 1]++;
			}
		}
		
		boolean[] hashi = new boolean[N-1];
		for (int i = 0; i < M; i++) {
			int[] tmp = map[i];
			int maxIndex = -1;
			int max = 0;
			for (int j = tmp[0]; j < tmp[1]; j++) {
				if (hashi[j-1]) {
					maxIndex = -1;
					break;
				}
				
				int tmpMax = max;
				max = Math.max(max, deepMap[j - 1]);
				if (tmpMax != max) {
					maxIndex = j - 1;
				}
			}
			
			if (maxIndex > -1)
				hashi[maxIndex] = true;
			
		}
		
		int ans = 0;
		for (boolean b : hashi) {
			ans += b ? 1 : 0;
		}
		
		System.out.println(ans);
	}
	
}