<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:
        combined_word = word1 + word2
        n = len(combined_word)
        
        # Initialize the DP table
        dp = [[0] * n for _ in range(n)]
        
        # Every single character is a palindrome of length 1
        for i in range(n):
            dp[i][i] = 1
        
        # Fill the DP table
        for length in range(2, n + 1):
            for i in range(n - length + 1):
                j = i + length - 1
                if combined_word[i] == combined_word[j]:
                    if length == 2:
                        dp[i][j] = 2
                    else:
                        dp[i][j] = dp[i + 1][j - 1] + 2
                else:
                    dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])
        
        # Find the longest palindrome that can be formed by concatenating subsequences from word1 and word2
        max_length = 0
        for i in range(len(word1)):
            for j in range(len(word2)):
                if word1[i] == word2[j]:
                    max_length = max(max_length, dp[i][len(word1) + j])
        
        return max_length

# Example usage:
solution = Solution()
word1 = "cacb"
word2 = "cbba"
print(solution.longestPalindrome(word1, word2))  # Output: 5
70000