Sorted Vowel Words

Medium

Consider words of length length made only of the letters a, e, i, o, u. A word is sorted if every letter comes no earlier in the alphabet than the one before it (repeats are allowed). Return the number of sorted words of length length.

Example 1

length=2 → 15

The words are aa, ae, ai, ao, au, ee, ei, eo, eu, ii, io, iu, oo, ou, uu: 15 in total. A word like "ia" does not count, since i comes after a.

Example 2

length=1 → 5

Each of the five vowels on its own is a sorted word.

Example 3

length=5 → 126

Constraints

1 ≤ length ≤ 50

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Topics

Math Dynamic Programming Combinatorics

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Input

length=2

Expected

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