19. In a football tournament held in a single round-robin format (each team must play every other team exactly once), $N$ teams are participating. At a certain point in the tournament, the coach of team $A$ noticed that any two teams, different from $A$, have played a different number of games. It is also known that by this point, team $A$ has played more than 1 game. How many teams $N$ could have participated in this tournament? Write the sum of all possible values of $N$ in the answer.

| param1 |  |
| :---: | :---: |
| 10 |  |
| 11 |  |
| 12 |  |
| 13 |  |
| 15 |  |
19. In a football tournament held in a single round-robin format (each team must play every other team exactly once), $N$ teams are participating. At a certain point in the tournament, the coach of team $A$ noticed that any two teams, different from $A$, have played a different number of games. It is also known that by this point, team $A$ has played more than 1 game. How many teams $N$ could have participated in this tournament? Write the sum of all possible values of $N$ in the answer.

| param1 | Answer |
| :---: | :---: |
| 10 | 63 |
| 11 | 69 |
| 12 | 75 |
| 13 | 81 |
| 15 | 93 |
|  |  |