A prefix tree (also known as a trie) is a tree data structure used to efficiently store and retrieve keys in a set of strings. Some applications of this data structure include auto-complete and spell checker systems.

Implement the PrefixTree class:

• PrefixTree() Initializes the prefix tree object.
• void insert(String word) Inserts the string word into the prefix tree.
• boolean search(String word) Returns true if the string word is in the prefix tree (i.e., was inserted before), and false otherwise.
• boolean startsWith(String prefix) Returns true if there is a previously inserted string word that has the prefix prefix, and false otherwise.

Example 1:

Input:
["Trie", "insert", "dog", "search", "dog", "search", "do", "startsWith", "do", "insert", "do", "search", "do"]

Output:
[null, null, true, false, true, null, true]

Explanation:
PrefixTree prefixTree = new PrefixTree();
prefixTree.insert("dog");
prefixTree.search("dog");    // return true
prefixTree.search("do");     // return false
prefixTree.startsWith("do"); // return true
prefixTree.insert("do");
prefixTree.search("do");     // return true

Constraints:

• 1 <= word.length, prefix.length <= 1000
• word and prefix are made up of lowercase English letters.