How do six teams compete with the least number of matches?

Hello, Team 6 draws lots into two groups, with 3 teams in each group, 3 games in each group and 6 games in each group. The first place in the two groups directly competed for the championship and runner-up, the second group competed for three or four places, and the third group competed for five or six places. So * * * has 6+3=9 games.

If the cross elimination system is adopted, the top two in the group stage will advance to the semi-finals, and the group will touch the other two first. Then the winner competes for the championship, the loser competes for the third place, and the team that has not qualified competes for the fifth place. In this case, * * * will have 6+4+ 1= 1 1 games.