code

import itertools

c = 0

for i in itertools.permutations("МИТРОФАН", r = 6):
    i = ''.join(i)
    gcount = i.count('И') + i.count('А') + i.count('О')
    if gcount >= 3:
        continue
    f = False
    for j in itertools.product('ИОА', repeat=2):
        j = ''.join(j)
        if j in i:
            f = True
            break
    if f:
        continue

    c += 1
print(c)