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:

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: