Implement Trie (Prefix Tree)

## Problem

A **trie** (pronounced as "try") or **prefix tree** is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. There are various applications of this data structure, such as autocomplete and spellchecker.

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

> **Input format:** A list of operations and arguments. `["insert","search","startsWith"]` and `[["apple"],["apple"],["app"]]`. Return a list of results (None for insert).