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 are 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?

Constraints

$1\le N,C,V\le {10}^5$

The word will only contain lowercase alphabetic characters.

Subtask 1 [5/15]

The letter y will not appear in the word.

Subtask 2 [10/15]

No additional constraints.

Input Specification

The first line will contain three integers, $N$, $C$, and $V$.

The next line will be the word Mosey wants you to check.

Output Specification

Output YES if the word is valid and NO otherwise.

Sample Input 1

12 3 3
onomatopoeia

Sample Output 1

NO

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

YES

Sample Input 3

10 8 2
aayczttpqw

Sample Output 3

NO

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

NO