Three teams A, B and C participated in a 3 sided hockey tournament. In three games, team A played team B, team B played against team C, and team A played against team C.
- The three final scores of the games consisted of the numbers 1, 2, 3, 4, 5, and 6.
- The difference between the team Aís higher score and the team B's higher score was one more than the difference between team Bís lower and team Cís lower score.
- The highest total of a teamís two scores was achieved by the team that lost the greatest number of games.
Which team achieved the highest total of its two scores?