Fix that Java: Set is Bigger

import java.util.Set;
import java.util.HashSet;

class Main {
    public static void main(String[] args) {
        Set<Dog> dogs = new HashSet<>();

        Dog caesar = new Dog("German Shepherd");
        Dog rex = new Dog("German Shepherd");

        dogs.add(caesar);
        dogs.add(rex);

        System.out.println(caesar.equals(rex));
        System.out.println(dogs.size());
    }
}

class Dog {
    private String breed;

    public Dog(String breed) {
        this.breed = breed;
    }

    public int hashCode() {
        return breed.hashCode();
    }

    public boolean equals(Dog o) {
        return breed.equals(o.breed);
    }
}