Implement Trie

medium
A trie or prefix tree is a tree data structure used to efficiently store and retrieve keys in a dataset of strings

Implement the Trie class:
1. Trie(): Initializes the trie object.
2. void insert(String word): Inserts the string word into the trie.
3. boolean search(String word): Returns true if the string word is in the trie (i.e., was inserted before), and false otherwise.
4. boolean startsWith(String prefix): Returns true if there is a previously inserted string word that has the prefix prefix, and false otherwise.

Input Format

Input is managed for you

Output Format

Output is managed for you

Constraints

1. 1 <= word.length, prefix.length <= 2000
2. word and prefix consist only of lowercase English letters.

Notice

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Example

Input
insert apple
search apple
search app
startsWith app
insert app
search app
Output
true
false
true
true
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