<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 Solution:
    def palindromePairs(self, words: List[str]) -> List[List[int]]:
        res = []
        trie = Trie()
        for i, word in enumerate(words):
            trie.insert(word, i)
        for i, word in enumerate(words):
            res.extend(trie.search(word, i))
        return res

class TrieNode:
    def __init__(self):
        self.children = {}
        self.index = -1  # Index of the word that ends at this node
        self.palindrome_suffixes = []  # List of word indices where suffix forms a palindrome

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

    def insert(self, word, index):
        node = self.root
        for i, char in enumerate(reversed(word)):
            # If the remaining part of the word is a palindrome, store the index
            if is_palindrome(word[:len(word) - i]):
                node.palindrome_suffixes.append(index)
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.index = index  # Mark the end of the word
        node.palindrome_suffixes.append(index)

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

        for i, char in enumerate(word):
            # If this node represents a word and the remaining suffix of the current word is a palindrome
            if node.index >= 0 and node.index != index and is_palindrome(word[i:]):
                result.append([index, node.index])
            if char not in node.children:
                return result
            node = node.children[char]

        # Check for words with palindromic suffixes
        for j in node.palindrome_suffixes:
            if index != j:
                result.append([index, j])
        
        return result
    
def is_palindrome(word):
    return word == word[::-1]
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