<p>You are given a <strong>0-indexed</strong> string <code>s</code> and are tasked with finding two <strong>non-intersecting palindromic </strong>substrings of <strong>odd</strong> length such that the product of their lengths is maximized.</p>

<p>More formally, you want to choose four integers <code>i</code>, <code>j</code>, <code>k</code>, <code>l</code> such that <code>0 &lt;= i &lt;= j &lt; k &lt;= l &lt; s.length</code> and both the substrings <code>s[i...j]</code> and <code>s[k...l]</code> are palindromes and have odd lengths. <code>s[i...j]</code> denotes a substring from index <code>i</code> to index <code>j</code> <strong>inclusive</strong>.</p>

<p>Return <em>the <strong>maximum</strong> possible product of the lengths of the two non-intersecting palindromic substrings.</em></p>

<p>A <strong>palindrome</strong> is a string that is the same forward and backward. A <strong>substring</strong> is a contiguous sequence of characters in a string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;ababbb&quot;
<strong>Output:</strong> 9
<strong>Explanation:</strong> Substrings &quot;aba&quot; and &quot;bbb&quot; are palindromes with odd length. product = 3 * 3 = 9.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;zaaaxbbby&quot;
<strong>Output:</strong> 9
<strong>Explanation:</strong> Substrings &quot;aaa&quot; and &quot;bbb&quot; are palindromes with odd length. product = 3 * 3 = 9.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
  def maxProduct(self, s: str) -> int:
    n = len(s)

    def manacher(s: str) -> List[int]:
      maxExtends = [0] * n
      l2r = [1] * n
      center = 0

      for i in range(n):
        r = center + maxExtends[center] - 1
        mirrorIndex = center - (i - center)
        extend = 1 if i > r else min(maxExtends[mirrorIndex], r - i + 1)
        while i - extend >= 0 and i + extend < n and s[i - extend] == s[i + extend]:
          l2r[i + extend] = 2 * extend + 1
          extend += 1
        maxExtends[i] = extend
        if i + maxExtends[i] >= r:
          center = i

      for i in range(1, n):
        l2r[i] = max(l2r[i], l2r[i - 1])

      return l2r

    # l[i] := the maximum length of palindromes in s[0..i)
    l = manacher(s)
    # r[i] := the maximum length of palindromes in s[i..n)
    r = manacher(s[::-1])[::-1]
    return max(l[i] * r[i + 1] for i in range(n - 1))
661