<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)
        
        # Step 1: Create a DP table to find palindromes
        dp = [[False] * n for _ in range(n)]
        
        # Initialize the DP table
        for i in range(n):
            dp[i][i] = True  # Single character palindromes
        for i in range(n - 1):
            dp[i][i + 1] = (s[i] == s[i + 1])  # Two consecutive same characters
        
        # Fill the DP table for substrings longer than 2
        for length in range(3, n + 1):  # length of the substring
            for i in range(n - length + 1):
                j = i + length - 1
                dp[i][j] = (s[i] == s[j]) and dp[i + 1][j - 1]
        
        # Step 2: Use a DP array to count non-overlapping palindromic substrings
        count = [0] * (n + 1)
        
        for j in range(n):
            count[j + 1] = count[j]  # Start with the previous count
            for i in range(j - k + 1, -1, -1):
                if dp[i][j]:
                    count[j + 1] = max(count[j + 1], count[i] + 1)
        
        return count[n]

# Example usage:
solution = Solution()
print(solution.maxPalindromes("abaccdbbd", 3))  # Output: 2
print(solution.maxPalindromes("adbcda", 2))    # Output: 0
3005