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.

1. The three final scores of the games consisted of the numbers 1, 2, 3, 4, 5, and 6.
2. The difference between the team A’s higher score and the team B's higher score was one more than the difference between team B’s lower and team C’s lower score.
3. The highest total of a team’s two scores was achieved by the team that lost the greatest number of games.

Which team achieved the highest total of its two scores?