import re
try:
    sum = __builtins__.sum
except AttributeError:
    sum = __builtins__["sum"]

RINGS = [ring.lower() for ring in 'BDMJPRSTLN', 'AEIOUYRTLH', 'ACDEORSTLN', 'DHKYRSTLNE']
rx_string = "^" + "".join( ("[" + ring + "]" for ring in RINGS)) + "$"
print rx_string
rx = re.compile(rx_string)
for s in "BAAD", "BAAQ", "ABAAD", "baad", "baada", "abaad":
    if rx.match(s):
        print s, "YES"
    else:
        print s, "NO"
print


dictionary = (line.rstrip('\n') for line in file("/usr/share/dict/words", "r"))
matchwords = [word for word in dictionary if rx.match(word)]

print len(matchwords), "matching words"
    

NUMDICTS = [ {letter: position for position, letter in enumerate(ring)}
             for ring in RINGS ]

def unique_key(s):
    nums = [numdict[letter] for numdict, letter in zip(NUMDICTS, s)]
    return tuple( (num - nums[0]) % len(RINGS[0]) for num in nums[1:] )
    
for word in "baad", "bean", "salt", "noon":
    print word, unique_key(word)

from collections import defaultdict

GROUPS = defaultdict(list)

for word in matchwords:
    GROUPS[unique_key(word)].append(word)
    
GROUPS_OF_3 = [words for key, words in GROUPS.iteritems() if len(words) == 3]

print len(GROUPS), "distinct groups of words"
print len(GROUPS_OF_3), "groups of three words"

for words in GROUPS_OF_3:
    print unique_key(words[0]), "  ", " ".join(words)