<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]]:
        def isPali(i, j):
            while i < j:
                if s[i] != s[j]:
                    return False
                i += 1
                j -= 1
            return True

        memo = dict()

        def helper(i):
            result = []
            if i == len(s):
                return []
            
            if i in memo:
                return memo[i]
            
            temp = ""
            for j in range(i, len(s)):
                temp += s[j]
                
                if isPali(i,j):
                    bundle_list = helper(j+1)
                    if not bundle_list:
                        result.append([temp])
                    else:
                        for bundle in bundle_list:
                            result.append([temp]+bundle)
            
            memo[i] = result[:]
            return result
        
        return helper(0)
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