<p>You are given a string <code>s</code> and a <strong>positive</strong> integer <code>k</code>.</p>

<p>Select a set of <strong>non-overlapping</strong> substrings from the string <code>s</code> that satisfy the following conditions:</p>

<ul>
	<li>The <strong>length</strong> of each substring is <strong>at least</strong> <code>k</code>.</li>
	<li>Each substring is a <strong>palindrome</strong>.</li>
</ul>

<p>Return <em>the <strong>maximum</strong> number of substrings in an optimal selection</em>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>

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

<pre>
<strong>Input:</strong> s = &quot;abaccdbbd&quot;, k = 3
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can select the substrings underlined in s = &quot;<u><strong>aba</strong></u>cc<u><strong>dbbd</strong></u>&quot;. Both &quot;aba&quot; and &quot;dbbd&quot; are palindromes and have a length of at least k = 3.
It can be shown that we cannot find a selection with more than two valid substrings.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;adbcda&quot;, k = 2
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no palindrome substring of length at least 2 in the string.
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= s.length &lt;= 2000</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def maxPalindromes(self, s: str, k: int) -> int:
        n = len(s)
        pali = [[False] * n for _ in range(n)]

        # Single character substrings are palindromes
        for i in range(n):
            pali[i][i] = True

        # Check for 2-character palindromes
        for i in range(n - 1):
            if s[i] == s[i + 1]:
                pali[i][i + 1] = True
            else:
                pali[i][i + 1] = False

        # Check for palindromes of length 3 or more
        for l in range(3, n + 1):
            for i in range(n - l + 1):
                j = i + l - 1
                if s[i] == s[j] and pali[i + 1][j - 1]:
                    pali[i][j] = True
                else:
                    pali[i][j] = False

        dp = [0] * n

        for i in range(k - 1, n):
            temp = 0
            if pali[0][i] and i >= k - 1:
                temp = 1

            for j in range(i):
                t = 0
                if j + 1 < n and pali[j + 1][i] and (i - (j + 1) + 1 >= k):
                    t += 1
                t += dp[j]
                temp = max(temp, t)

            dp[i] = temp

        return dp[-1]

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