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.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        scanner.nextInt();
        final int m = scanner.nextInt();
        final List<Bridge> bridges = new ArrayList<>();

        for (int i = 0; i < m; i++) {
            final int a = scanner.nextInt();
            final int b = scanner.nextInt();
            bridges.add(new Bridge(a, b));
        }

        bridges.sort((x, y) -> y.b - x.b);
        final Set<Bridge> brokenBridges = new HashSet<>();
        for (final Bridge bridge : bridges) {
            final Bridge brokenBridge = new Bridge(bridge.b - 1, bridge.b);
            brokenBridges.add(brokenBridge);
        }

        System.out.println(brokenBridges.size());
    }

    static class Bridge {
        int a;
        int b;

        Bridge(final int a, final int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public boolean equals(final Object obj) {
            final Bridge bridge = (Bridge) obj;
            return bridge.a == this.a && bridge.b == this.b;
        }

        @Override
        public int hashCode() {
            return a * 100000 + b;
        }
    }
}