In an organization, there are engineers, accountants and doctors. The sum of the ages is 2,160; the average age is 36. The average age of the engineers and accountants is 39; of the accountants and doctors, 32 & 8/11; the engineers and doctors, 36 & 2/3. If each engineer were 1 year older, each accountant 6 years older, and each doctor 7 years older, their average age would be 41. Determine the number of doctors.