<p>You are given two strings, <code>word1</code> and <code>word2</code>. You want to construct a string in the following manner:</p>

<ul>
	<li>Choose some <strong>non-empty</strong> subsequence <code>subsequence1</code> from <code>word1</code>.</li>
	<li>Choose some <strong>non-empty</strong> subsequence <code>subsequence2</code> from <code>word2</code>.</li>
	<li>Concatenate the subsequences: <code>subsequence1 + subsequence2</code>, to make the string.</li>
</ul>

<p>Return <em>the <strong>length</strong> of the longest <strong>palindrome</strong> that can be constructed in the described manner. </em>If no palindromes can be constructed, return <code>0</code>.</p>

<p>A <strong>subsequence</strong> of a string <code>s</code> is a string that can be made by deleting some (possibly none) characters from <code>s</code> without changing the order of the remaining characters.</p>

<p>A <strong>palindrome</strong> is a string that reads the same forward&nbsp;as well as backward.</p>

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

<pre>
<strong>Input:</strong> word1 = &quot;cacb&quot;, word2 = &quot;cbba&quot;
<strong>Output:</strong> 5
<strong>Explanation:</strong> Choose &quot;ab&quot; from word1 and &quot;cba&quot; from word2 to make &quot;abcba&quot;, which is a palindrome.</pre>

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

<pre>
<strong>Input:</strong> word1 = &quot;ab&quot;, word2 = &quot;ab&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> Choose &quot;ab&quot; from word1 and &quot;a&quot; from word2 to make &quot;aba&quot;, which is a palindrome.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> word1 = &quot;aa&quot;, word2 = &quot;bb&quot;
<strong>Output:</strong> 0
<strong>Explanation:</strong> You cannot construct a palindrome from the described method, so return 0.</pre>

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

<ul>
	<li><code>1 &lt;= word1.length, word2.length &lt;= 1000</code></li>
	<li><code>word1</code> and <code>word2</code> consist of lowercase English letters.</li>
</ul>

class Solution:
    def longestPalindrome(self, w1: str, w2: str) -> int:
        @cache
        def f(i, j, hit):
            if (i >= m or j < m) and hit == 0: return 0
            if i > j: return 0
            if i == j: return 1
            
            # a[xx]a
            if W[i] == W[j]:
                return 2 + f(i + 1, j - 1, 1)
            
            
            return max(f(i + 1, j, hit), f(i, j - 1, hit))
        
        W = w1  + w2
        m, n = len(w1), len(W)
        return f(0, n - 1, 0)
            


2016