<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(object):
    def __init__(self):
        self.idx = -1
        self.pdromes_below = []
        self.children = collections.defaultdict(TrieNode)

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

    def add(self, word, idx):
        node = self.root
        for i, letter in enumerate(reversed(word)):
            if self.is_palindrome(word[:len(word)-i]):
                node.pdromes_below.append(idx)
            node = node.children[letter]
        node.idx = idx
        
    def search(self, word, idx, res):
        node = self.root
        for i, letter in enumerate(word):
            if node.idx >= 0 and idx != node.idx and self.is_palindrome(word[i:]):
                    res.append([idx, node.idx])
            node = node.children.get(letter)
            if not node:
                return res
        for p in node.pdromes_below:
            if p != idx:
                res.append([idx, p])
        if node.idx >= 0 and idx != node.idx:
            res.append([idx, node.idx])
        return res
    
    def is_palindrome(self, w):
        i = 0
        j = len(w)-1
        while i < j:
            if w[i] != w[j]:
                return False
            i += 1
            j -= 1
        return True


class Solution(object):
    def palindromePairs(self, words):
        """
        :type words: List[str]
        :rtype: List[List[int]]
        """
        res = []
        t = Trie()
        for idx, w in enumerate(words):
            t.add(w, idx)
        for idx, w in enumerate(words):
            res = t.search(w, idx, res)
        return res
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