The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6-n points if one of its runners finished in nth place, where 1≤n≤5. If all of the runners finished the race and if there were no ties was each team awarded at least 1 point?
(1)No team was awarded more than a total of 6 points.
(2)No pair of teammates finished in consecutive places among the top five places.