<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]]:
        # Trie + counting sort + rolling hash
        P, M = 31, 10 ** 9 + 7
        exp = [1]
        for i in range(302):
            np = exp[-1] * P % M
            exp.append(np)
        d, n, mnl, mxl = defaultdict(list), len(words), 5000, 0
        for i in range(n):
            d[len(words[i])].append((words[i], i))
            mnl = min(mnl, len(words[i]))
            mxl = max(mxl, len(words[i]))
        s_w = []
        for t in range(mnl, mxl+1): s_w.extend(d[t])
        
        rt = (T := lambda: defaultdict(T))()
        rrt = (T := lambda: defaultdict(T))()

        def gh(w):
            h = [0]
            for ch in w:
                nh = (h[-1] * P + ord(ch)) % M
                h.append(nh)
            return h

        def mp(t, w, h, rh):
            m, i, u, res = len(w), 0, t, []
            if u.get("_s"):
                hh = h[m]
                rhh = rh[m]
                if hh == rhh: res.extend(u["_s"])
            while i < m:
                if not u.get(w[i]): break
                u = u[w[i]]
                if u.get("_s"):
                    hh = (h[m] - h[i+1] * exp[m-i-1] + M) % M
                    rhh = rh[m-i-1]
                    if hh == rhh: res.extend(u["_s"])
                i += 1
            return res

        def insert(t, w, wi):
            v, m = t, len(w)
            for j in range(m): v = v[w[j]]
            v["_s"] = v.get("_s", list())
            v["_s"].append(wi)

        ans = []
        for i in range(n):
            w, idx = s_w[i]
            rw = w[::-1]
            h, rh = gh(w), gh(rw)
            for j in mp(rrt, w, h, rh): ans.append([idx, j])
            for j in mp(rt, rw, rh, h): ans.append([j, idx])
            insert(rrt, rw, idx)
            insert(rt, w, idx)
        return ans
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