<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, word1: str, word2: str) -> int:
        m = len(word1)
        n = len(word2)
        word = word1 + word2
        @cache
        def dfs1(i, j):
            if i == j:
                return 1
            if i > j:
                return 0
            
            if word[i] == word[j]:
                return dfs1(i+1, j-1) + 2
            return max(dfs1(i+1, j), dfs1(i, j-1))

        dp = [[0 for _ in range(n)] for j in range(m)]
        curr_max = 0
        for i in range(m-1, -1, -1):
            for j in range(n):
                if word1[i] == word2[j]:
                    curr_max = max(curr_max, dfs1(i + 1, m + j - 1) + 2)
        return curr_max
        
        # @cache
        # def dfs(i, j):
        #     if i >= len(word1) or j < 0:
        #         return 0
        #     res = 0
        #     if word1[i] == word2[j]:
        #         res = dfs1(i + 1, m + j - 1) + 2
        #     return max(dfs(i+1, j), dfs(i, j-1), res)
        
        # return dfs(0, len(word2)-1)
1934