<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):

        # Create the Trie and add the reverses of all the words.
        trie = {}
        for i, word in enumerate(words):
            word = word[::-1] # We want to insert the reverse.
            current_level = trie
            for j, c in enumerate(word):
                # Check if remainder of word is a palindrome.
                if word[j:] == word[j:][::-1]: # Is the word the same as its reverse?
                    if "palindrome_suffixes" not in current_level:
                        current_level["palindrome_suffixes"] = []

                    current_level["palindrome_suffixes"].append(i)

                if c not in current_level:
                    current_level[c] = {}
                # Move down the trie.
                current_level = current_level[c]
            current_level["ending_word"] = i

        # Look up each word in the Trie and find palindrome pairs.
        solutions = []
        for i, word in enumerate(words):
            current_level = trie
            for j, c in enumerate(word):
                # Check for case 3.
                if current_level.get("ending_word") is not None and current_level["ending_word"] != -1:
                    if word[j:] == word[j:][::-1]: # Is the word the same as its reverse?
                        solutions.append([i, current_level["ending_word"]])
                if c not in current_level:
                    break
                current_level = current_level[c]
            else: # Case 1 and 2 only come up if whole word was iterated.
                # Check for case 1.
                if current_level.get("ending_word") is not None and current_level["ending_word"] != -1 and current_level["ending_word"] != i:
                    solutions.append([i, current_level["ending_word"]])
                # Check for case 2.
                for j in current_level.get("palindrome_suffixes", []):
                    solutions.append([i, j])
        return solutions
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