import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.stream.IntStream;

public class Ring {
    private int n;

    Ring(int n) {
        this.n = n;
    }

    public String findRingDetails() {
        int[] reversibleElements = getReversibleElements();
        int[] zeroDivisors = getZeroDivisors();
        Set nilpotentElements = getNilpotentElements(zeroDivisors);
        int[] idempotentElements = getIdempotentElements();
        return "[" + Arrays.toString(reversibleElements) + ", " + Arrays.toString(zeroDivisors) + ", " + nilpotentElements + ", " + Arrays.toString(idempotentElements) + "]";
    }

    private int[] getReversibleElements() {
        return IntStream.rangeClosed(0, n - 1).filter(k -> NWDCalculator.findNWD(k, n) == 1).toArray();
    }

    private int[] getZeroDivisors() {
        return IntStream.rangeClosed(0, n - 1).filter(k -> NWDCalculator.findNWD(k, n) > 1).toArray();
    }

    private Set getNilpotentElements(int[] zeroDivisors) {
        Set<Integer> nilpotentElements = new HashSet<>();
        for (int i = 0; i < n; i++) {
            for (int i1 : zeroDivisors) {
                if (Math.pow(i1, i) % n == 0)
                    nilpotentElements.add(i1);
            }
        }
        return nilpotentElements;
    }

    private int[] getIdempotentElements() {
        return IntStream.rangeClosed(0, n - 1).filter(k -> k * k % n == k).toArray();
    }
}