Alice and Bob are playing a game on a string.

You are given a string s, Alice and Bob will take turns playing the following game where Alice starts first:

The first player who cannot make a move on their turn loses the game. We assume that both Alice and Bob play optimally.

Return true if Alice wins the game, and false otherwise.

The English vowels are: a, e, i, o, and u.

Example 1:

Input: s = "leetcoder"

Output: true

Explanation:

Alice can win the game as follows:

Alice plays first, she can delete the underlined substring in s = "leetcoder" which contains 3 vowels. The resulting string is s = "der".
Bob plays second, he can delete the underlined substring in s = "der" which contains 0 vowels. The resulting string is s = "er".
Alice plays third, she can delete the whole string s = "er" which contains 1 vowel.
Bob plays fourth, since the string is empty, there is no valid play for Bob. So Alice wins the game.

Example 2:

Input: s = "bbcd"

Output: false

Explanation:

There is no valid play for Alice in her first turn, so Alice loses the game.

Constraints:

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