Mosey Maker is practicing how to use words!
To help him with his words, he made up a bot to recognize them. However, his bot isn't that intelligent.
His bot recognizes words as a list of alphabetic characters. Mosey Maker's bot doesn't think long sequences of vowels or consonants is valid, so if more than ~C~ consonants or ~V~ vowels are seen in a row, his bot does not consider it a word. Note that the vowels are
aeiouy, and the consonants are
bcdfghjklmnpqrstvwxyz. Note that
y counts as both a consonant and a vowel.
Unfortunately, Mosey Maker lost his bot, and wants you to recode it.
Given a single word of ~N~ characters, is it valid?
~1 \le N, C, V \le 10^5~
The word will only contain lowercase alphabetic characters.
Subtask 1 [5/15]
y will not appear in the word.
Subtask 2 [10/15]
No additional constraints.
The first line will contain three integers, ~N~, ~C~ and ~V~.
The next line will be the word Mosey wants you to check.
YES if the word is valid and
Sample Input 1
12 3 3 onomatopoeia
Sample Output 1
Explanation for Sample Output 1
Note that although it is a valid english word,
onomatopoeia has too many trailing vowels to be a valid word.
Sample Input 2
8 2 4 aaybaaaa
Sample Output 2
Sample Input 3
10 8 2 aayczttpqw
Sample Output 3
Explanation for Sample Output 3
Note that since
y is both a vowel and a consonant,
aay is considered a string of ~3~ vowels.
Sample Input 4
5 4 4 yyyyy
Sample Output 4