8 чередующиеся по гл и нужное кол-во раз каждая буква

#https://inf-ege.sdamgia.ru/problem?id=46966
alph = 'РОСМАХ'
gl = 'ОА'
sogl = 'РСМХ'
d = {'Р': 1, 'О': 2, 'С': 1, 'М': 1, 'А': 2, 'Х': 1}
cnt = 0
for q in alph:
    for w in alph:
        for e in alph:
            for r in alph:
                for t in alph:
                    for y in alph:
                        for u in alph:
                            for i in alph:
                                s = q + w + e + r + t + y + u + i
                                f = 1
                                for cur in range(1, 8):
                                    if s.count(s[cur]) != d[s[cur]]:
                                        f = 0
                                    if ((s[cur] in gl) and (s[cur - 1] in gl)) or ((s[cur] in sogl) and (s[cur - 1] in sogl)):
                                        f = 0
                                if s.count(s[0]) != d[s[0]]:
                                    f = 0
                                cnt += f
print(cnt)