Clarification of foul count

[Vinski]

Sitch - It appears a fight may occur on the playing court when A6 and A7 leave their bench.
Ruling: The two players leaving the bench are assessed flagrant fouls and disqualified, and Team A's head coach is assessed a maximum of one indirect technical foul (regardless of the number of players leaving the bench).

So, I understand that Team B is awarded two free throws and the ball for a division line throw-in, but how many fouls are applied to the books. I think that in this case it would be…
*One T-foul added to A6
*One T-foul added to A7
*One indirect added to A Coach
*Two Team fouls added to Team A’s total foul count.

Do I have this right or would it be three total team fouls because of the indirect applied to the coach? Do we ever count the indirect to a coach to the team foul total?