import java.util.HashMap;
import java.util.Map;
import java.util.stream.Collectors;
import java.util.stream.Stream;

public class Partition extends HashMap<Integer,Integer> {

    public Partition() {
        super();
    }

    public Partition(Partition p) {
        super(p);
    }

    public Partition(int... terms) {
        this();
        for(int term : terms) addTerm(term);
    }

    public void addTerm(int term) {
        merge(term, 1, Integer::sum);
    }

    public boolean removeTerm(int term) {
        if(!containsKey(term)) return false;
        compute(term, (k, v) -> v == 1 ? null : v - 1);
        return true;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Partition that = (Partition) o;

        return super.equals(that);
    }

    @Override
    public String toString() {
        return keySet().stream().sorted()
                       .flatMap(k -> Stream.generate(() -> k).limit(get(k)))
                       .mapToInt(Integer::intValue)
                       .mapToObj(Integer::toString)
                       .collect(Collectors.joining("+"));
    }

}