<p>You are given a <strong>0-indexed</strong> array of <strong>unique</strong> strings <code>words</code>.</p>

<p>A <strong>palindrome pair</strong> is a pair of integers <code>(i, j)</code> such that:</p>

<ul>
	<li><code>0 &lt;= i, j &lt; words.length</code>,</li>
	<li><code>i != j</code>, and</li>
	<li><code>words[i] + words[j]</code> (the concatenation of the two strings) is a <span data-keyword="palindrome-string">palindrome</span>.</li>
</ul>

<p>Return <em>an array of all the <strong>palindrome pairs</strong> of </em><code>words</code>.</p>

<p>You must write an algorithm with&nbsp;<code>O(sum of words[i].length)</code>&nbsp;runtime complexity.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;abcd&quot;,&quot;dcba&quot;,&quot;lls&quot;,&quot;s&quot;,&quot;sssll&quot;]
<strong>Output:</strong> [[0,1],[1,0],[3,2],[2,4]]
<strong>Explanation:</strong> The palindromes are [&quot;abcddcba&quot;,&quot;dcbaabcd&quot;,&quot;slls&quot;,&quot;llssssll&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;bat&quot;,&quot;tab&quot;,&quot;cat&quot;]
<strong>Output:</strong> [[0,1],[1,0]]
<strong>Explanation:</strong> The palindromes are [&quot;battab&quot;,&quot;tabbat&quot;]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;&quot;]
<strong>Output:</strong> [[0,1],[1,0]]
<strong>Explanation:</strong> The palindromes are [&quot;a&quot;,&quot;a&quot;]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= words.length &lt;= 5000</code></li>
	<li><code>0 &lt;= words[i].length &lt;= 300</code></li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
</ul>

class TrieNode:
    def __init__(self):
        self.children = {}
        self.index = -1  # To store the index of the word ending at this node
        self.palindrome_suffix_indices = []  # List of indices of words that have a palindrome suffix

class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, word, index):
        node = self.root
        for i, char in enumerate(reversed(word)):
            # Check if the current prefix is a palindrome and record the index
            if self.is_palindrome(word[:len(word) - i]):
                node.palindrome_suffix_indices.append(index)
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.index = index
        node.palindrome_suffix_indices.append(index)

    def search(self, word, index):
        node = self.root
        result = []

        for i, char in enumerate(word):
            # Check if the remaining suffix forms a palindrome and the node has a word ending
            if node.index >= 0 and node.index != index and self.is_palindrome(word[i:]):
                result.append([index, node.index])
            if char not in node.children:
                return result
            node = node.children[char]

        # If the search completes, check for any remaining palindrome suffix indices
        for suffix_index in node.palindrome_suffix_indices:
            if index != suffix_index:
                result.append([index, suffix_index])

        return result

    @staticmethod
    def is_palindrome(word):
        left, right = 0, len(word) - 1
        while left < right:
            if word[left] != word[right]:
                return False
            left, right = left + 1, right - 1
        return True

class Solution:
    def palindromePairs(self, words: List[str]) -> List[List[int]]:
        trie = Trie()

        # Insert words into the Trie in reverse order with indices
        for i, word in enumerate(words):
            trie.insert(word, i)

        results = []
        # Search for each word in the Trie
        for i, word in enumerate(words):
            results.extend(trie.search(word, i))

        return results

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