<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:
        palindrome_dp = {}
        def is_palindrome(index, end_index):
            if (index, end_index) in palindrome_dp:
                print("palindrome dp")
                return palindrome_dp[(index, end_index)]
            while index < end_index:
                if not s[index] == s[end_index]:
                    # palindrome_dp[(index, end_index)] = False
                    return False
                index += 1
                end_index += -1
            # palindrome_dp[(index, end_index)] = True
            return True
        dp = {}
        def dfs(index):
            if index > len(s) - k:
                return 0
            if index in dp:
                return dp[index]
            op1 = dfs(index + 1)
            op2 = -1
            for end_index in range(index + k - 1, len(s)):
                if is_palindrome(index, end_index):
                    op2 = max(op2, dfs(end_index + 1))
                    op2 += 1
                    dp[index] = max(op1, op2)
                    return max(op1, op2)
            op2 += 1
            dp[index] = max(op1, op2)
            return max(op1, op2)
        return dfs(0)
1259