import java.math.BigInteger;

public class Rational implements Comparable<Rational> {
	public static final Rational ZERO = new Rational(0);
	public static final Rational ONE = new Rational(1);
	public static final Rational POSITIVE_INFINITY = new Rational(1, 0);
	public static final Rational NEGATIVE_INFINITY = new Rational(-1, 0);

	final BigInteger num;
	final BigInteger den;

	public Rational(BigInteger num, BigInteger den) {
		BigInteger gcd = num.gcd(den);
		BigInteger g = den.signum() > 0 ? gcd : den.signum() > 0 ? gcd.negate() : BigInteger.ONE;
		this.num = num.divide(g);
		this.den = den.divide(g);
	}

	public Rational(long num, long den) {
		this(BigInteger.valueOf(num), BigInteger.valueOf(den));
	}

	public Rational(long num) {
		this.num = BigInteger.valueOf(num);
		this.den = BigInteger.ONE;
	}

	public Rational add(Rational r) {
		return new Rational(num.multiply(r.den).add(r.num.multiply(den)), den.multiply(r.den));
	}

	public Rational sub(Rational r) {
		return new Rational(num.multiply(r.den).subtract(r.num.multiply(den)), den.multiply(r.den));
	}

	public Rational mul(Rational r) {
		return new Rational(num.multiply(r.num), den.multiply(r.den));
	}

	public Rational div(Rational r) {
		return new Rational(num.multiply(r.den), den.multiply(r.num));
	}

	public Rational negate() {
		return new Rational(num.negate(), den);
	}

	public Rational inverse() {
		return new Rational(den, num);
	}

	public Rational abs() {
		return new Rational(num.abs(), den);
	}

	public int signum() {
		return num.signum();
	}

	public double doubleValue() {
		return num.doubleValue() / den.doubleValue();
	}

	public long longValue() {
		return num.longValue() / den.longValue();
	}

	public int compareTo(Rational other) {
		return (num.multiply(other.den).compareTo(other.num.multiply(den)));
	}

	public boolean equals(Object obj) {
		return num.equals(((Rational) obj).num) && den.equals(((Rational) obj).den);
	}

	public int hashCode() {
		return num.hashCode() * 31 + den.hashCode();
	}

	public String toString() {
		return num + "/" + den;
	}

	// Usage example
	public static void main(String[] args) {
		Rational a = new Rational(1, 3);
		Rational b = new Rational(1, 6);
		Rational c = new Rational(1, 2);
		System.out.println(true == c.equals(a.add(b)));
	}
}