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.Scanner;

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], b = new int[m];
        int[] arr = new int[n];

        for (int i = 0; i < m; i++) {
            a[i] = sc.nextInt() - 1;
            b[i] = sc.nextInt() - 1;
            arr[a[i]]++;
            arr[b[i]]--;
        }

        int ans = 0;
        while (true) {
            int now = 0;
            int max = 0;
            int maxIndex = 0;
            for (int i = 0; i < n; i++) {
                now += arr[i];
                if (now > max) {
                    max = now;
                    maxIndex = i;
                }
            }

            //System.out.println(Arrays.toString(arr)+" "+maxIndex);
            if (max == 0) {
                System.out.println(ans);
                return;
            }
            ans++;
            for (int i = 0; i < m; i++) {
                if (a[i] <= maxIndex && b[i] > maxIndex) {
                    arr[a[i]]--;
                    arr[b[i]]++;
                    a[i] = Integer.MAX_VALUE;
                    b[i] = Integer.MAX_VALUE;
                }
            }
        }
    }
}