<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]]:
        #
        class Prefix:
            def __init__(self):
                self.trie = {}

            def add_word(self, word, k):
                curr = self.trie
                for i in range(len(word)):
                    c = word[i]
                    if c not in curr:
                        curr[c] = {}
                    curr = curr[c]
                    curr.setdefault('+', []).append(k)
                curr['*'] = k
                if '+' in curr:
                    curr['+'].pop()
                return

            def find_prefix(self, suffix, j):
                curr = self.trie
                extra_j = []
                for i in reversed(range(len(suffix))):
                    c = suffix[i]
                    if c not in curr:
                        return [], extra_j
                    curr = curr[c]
                    if curr.get('*', j) != j:
                        extra_j.append(curr['*'])
                extra_i = curr.get('+', [])
                return extra_i, extra_j

        prefix = Prefix()
        for i in range(len(words)):
            prefix.add_word(words[i], i)

        is_palindrome = lambda x: x[0] == x[-1] and is_palindrome(x[1:-1]) if x else True

        rs = []
        for j in range(len(words)):
            if words[j] == '':
                for i in range(len(words)):
                    if i != j and is_palindrome(words[i]):
                        rs.append([i, j])
                        rs.append([j, i])
                continue
            extra_i, extra_j = prefix.find_prefix(words[j], j)
            # print(extra_i, extra_j)
            for i in extra_i:
                if i != j:
                    extra = words[i][len(words[j]):]
                    if is_palindrome(extra):
                        rs.append([i, j])

            for i in extra_j:
                if i != j:
                    extra = words[j][: len(words[j])-len(words[i])]
                    if is_palindrome(extra):
                        rs.append([i, j])

        return rs


        
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