#include <ostream>

// Create an ordered pair (i, j) where
//    (i, j) < (k, l) when i < k
//
// This defines a strict weak ordering:
//
//  ... < (-1, *) < (0, *) < (1, *) < (2, *) < ...

class ordered_pair;
ostream &operator<<( ostream &, ordered_pair const & );

class ordered_pair {
	private:
		int i, j;

	public:
		ordered_pair( int a = 0, int b = 0 ):i(a), j(b) {
			// empty constructor
		}

		bool operator <( ordered_pair const &obj ) const {
			return i < obj.i;
		}

		bool operator ==( ordered_pair const &obj ) const {
			return i == obj.i;
		}

	friend ostream &operator <<( ostream &, ordered_pair const & );
};

std::ostream &operator <<( std::ostream &out, ordered_pair const &x ) {
	out << "(" << x.i << "," << x.j << ")";

	return out;
}