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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?