<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:
        P, M = 31, 1000000009
        n = len(s)

        def check(i, l):
            left = (forward[i+1] - forward[i-l] * pow[l+1]) % M
            right = (backward[i] - backward[i+l+1] * pow[l+1]) % M
            return left != right

        def rolling_hash(h, c):
            return (h * P + (ord(c) - ord('a') + 1)) % M

        def scan(direction):
            results = [0] * n
            q = deque()
            best = 1
            for i in (range(n) if direction > 0 else range(n-1, -1, -1)):
                while q and ((q[0][1] <= i) if direction > 0 else (q[0][1] >= i)):
                    best = q.popleft()[0]
                if palindroma[i] > best:
                    if len(q) == 0 or palindroma[i] > q[-1][0]:
                        q.append((palindroma[i], i + direction * (palindroma[i] - 1)))
                if q:
                    best = max(best, q[0][0] - abs(q[0][1] - i))
                results[i] = best * 2 - 1
            return results
            
        pow = list(accumulate(range(n-1), lambda a, b: a * P % M, initial=1))
        forward = list(accumulate(s, rolling_hash, initial=0))
        backward = list(accumulate(reversed(s), rolling_hash, initial=0))[::-1]
        palindroma = [bisect_right(range(min(i, n-i-1) + 1), 0, key=lambda x: check(i, x)) for i in range(n)]
        return max(f * b for f, b in zip(scan(1), scan(-1)[1:]))
4715