Santa needs help figuring out which strings in his text file are naughty or nice.
A nice string is one with all of the following properties:
-
It contains at least three vowels (
aeiou
only), likeaei
,xazegov
, oraeiouaeiouaeiou
. -
It contains at least one letter that appears twice in a row, like
xx
,abcdde
(dd
), oraabbccdd
(aa
,bb
,cc
, ordd
). -
It does not contain the strings
ab
,cd
,pq
, orxy
, even if they are part of one of the other requirements.
For example:
-
ugknbfddgicrmopn
is nice because it has at least three vowels (u...i...o...
), a double letter (...dd...
), and none of the disallowed substrings. -
aaa
is nice because it has at least three vowels and a double letter, even though the letters used by different rules overlap. -
jchzalrnumimnmhp
is naughty because it has no double letter. -
haegwjzuvuyypxyu
is naughty because it contains the stringxy
. -
dvszwmarrgswjxmb
is naughty because it contains only one vowel.
How many strings are nice?
Realizing the error of his ways, Santa has switched to a better model of determining whether a string is naughty or nice. None of the old rules apply, as they are all clearly ridiculous.
Now, a nice string is one with all of the following properties:
-
It contains a pair of any two letters that appears at least twice in the string without overlapping, like
xyxy
(xy
) oraabcdefgaa
(aa
), but not likeaaa
(aa
, but it overlaps). -
It contains at least one letter which repeats with exactly one letter between them, like
xyx
,abcdefeghi
(efe
), or evenaaa
.
For example:
-
qjhvhtzxzqqjkmpb
is nice because is has a pair that appears twice (qj
) and a letter that repeats with exactly one letter between them (zxz
). -
xxyxx
is nice because it has a pair that appears twice and a letter that repeats with one between, even though the letters used by each rule overlap. -
uurcxstgmygtbstg
is naughty because it has a pair (tg
) but no repeat with a single letter between them. -
ieodomkazucvgmuy
is naughty because it has a repeating letter with one between (odo
), but no pair that appears twice.
How many strings are nice under these new rules?