<p>Given two strings <code>str1</code> and <code>str2</code>, return <em>the shortest string that has both </em><code>str1</code><em> and </em><code>str2</code><em> as <strong>subsequences</strong></em>. If there are multiple valid strings, return <strong>any</strong> of them.</p>

<p>A string <code>s</code> is a <strong>subsequence</strong> of string <code>t</code> if deleting some number of characters from <code>t</code> (possibly <code>0</code>) results in the string <code>s</code>.</p>

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

<pre>
<strong>Input:</strong> str1 = &quot;abac&quot;, str2 = &quot;cab&quot;
<strong>Output:</strong> &quot;cabac&quot;
<strong>Explanation:</strong> 
str1 = &quot;abac&quot; is a subsequence of &quot;cabac&quot; because we can delete the first &quot;c&quot;.
str2 = &quot;cab&quot; is a subsequence of &quot;cabac&quot; because we can delete the last &quot;ac&quot;.
The answer provided is the shortest such string that satisfies these properties.
</pre>

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

<pre>
<strong>Input:</strong> str1 = &quot;aaaaaaaa&quot;, str2 = &quot;aaaaaaaa&quot;
<strong>Output:</strong> &quot;aaaaaaaa&quot;
</pre>

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

<ul>
	<li><code>1 &lt;= str1.length, str2.length &lt;= 1000</code></li>
	<li><code>str1</code> and <code>str2</code> consist of lowercase English letters.</li>
</ul>

class Solution:
    def shortestCommonSupersequence(self, string1: str, string2: str) -> str:
        lcs = [["" for _ in range(len(string2) + 1)] for _ in range(len(string1) + 1)]
        for i in range(len(string1) - 1, -1, -1):
            for j in range(len(string2) - 1, -1, -1):
                lcs[i][j] = max(
                    lcs[i + 1][j], lcs[i][j + 1], key=lambda string: len(string)
                )
                if string1[i] == string2[j]:
                    lcs[i][j] = max(
                        lcs[i][j],
                        string1[i] + lcs[i + 1][j + 1],
                        key=lambda string: len(string),
                    )
        lcs_string = lcs[0][0]
        i, j = 0, 0
        supersequence = ""
        for char in lcs_string:
            while i < len(string1) and not char == string1[i]:
                supersequence += string1[i]
                i += 1
            while j < len(string2) and not char == string2[j]:
                supersequence += string2[j]
                j += 1
            supersequence += char
            i += 1
            j += 1
        supersequence += string1[i:] + string2[j:]
        return supersequence
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