<p>Given a string <code>s</code>, partition <code>s</code> such that every <span data-keyword="substring-nonempty">substring</span> of the partition is a <span data-keyword="palindrome-string"><strong>palindrome</strong></span>. Return <em>all possible palindrome partitioning of </em><code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "aab"
<strong>Output:</strong> [["a","a","b"],["aa","b"]]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = "a"
<strong>Output:</strong> [["a"]]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 16</code></li>
	<li><code>s</code> contains only lowercase English letters.</li>
</ul>

class Solution:
    def partition(self, s: str) -> List[List[str]]:
        output = []
        index_to_list = dict()

        def solver(start):
            if start in index_to_list:
                return index_to_list[start]
            if start == len(s):
                return [[]]
            # otherwise, find the whole list
            index_to_list[start] = []
            for i in range(start + 1, len(s) + 1):
                if s[start:i] == s[start:i][::-1]:
                    copy = solver(i).copy()
                    put_back = [[s[start:i]] + suffix_list for suffix_list in copy]
                    index_to_list[start].extend(put_back)
            return index_to_list[start]
            
        return solver(0)
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