Given three strings <code>a</code>, <code>b</code>, and <code>c</code>, your task is to find a string that has the<strong> minimum</strong> length and contains all three strings as <strong>substrings</strong>.
<p>If there are multiple such strings, return the<em> </em><strong>lexicographically<em> </em>smallest </strong>one.</p>

<p>Return <em>a string denoting the answer to the problem.</em></p>

<p><strong>Notes</strong></p>

<ul>
	<li>A string <code>a</code> is <strong>lexicographically smaller</strong> than a string <code>b</code> (of the same length) if in the first position where <code>a</code> and <code>b</code> differ, string <code>a</code> has a letter that appears <strong>earlier </strong>in the alphabet than the corresponding letter in <code>b</code>.</li>
	<li>A <strong>substring</strong> is a contiguous sequence of characters within a string.</li>
</ul>

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

<pre>
<strong>Input:</strong> a = &quot;abc&quot;, b = &quot;bca&quot;, c = &quot;aaa&quot;
<strong>Output:</strong> &quot;aaabca&quot;
<strong>Explanation:</strong>  We show that &quot;aaabca&quot; contains all the given strings: a = ans[2...4], b = ans[3..5], c = ans[0..2]. It can be shown that the length of the resulting string would be at least 6 and &quot;aaabca&quot; is the lexicographically smallest one.</pre>

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

<pre>
<strong>Input:</strong> a = &quot;ab&quot;, b = &quot;ba&quot;, c = &quot;aba&quot;
<strong>Output:</strong> &quot;aba&quot;
<strong>Explanation: </strong>We show that the string &quot;aba&quot; contains all the given strings: a = ans[0..1], b = ans[1..2], c = ans[0..2]. Since the length of c is 3, the length of the resulting string would be at least 3. It can be shown that &quot;aba&quot; is the lexicographically smallest one.
</pre>

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

<ul>
	<li><code>1 &lt;= a.length, b.length, c.length &lt;= 100</code></li>
	<li><code>a</code>, <code>b</code>, <code>c</code> consist only of lowercase English letters.</li>
</ul>

class Solution:
    def minimumString(self, a: str, b: str, c: str) -> str:
        def f(str1, str2, str3):
            str1 += self.mergeString(str1, str2)
            str1 += self.mergeString(str1, str3)
            return str1            

        ans = 'a' * 301
        for combination in [f(a, b, c), f(a, c, b), f(b, a, c), f(b, c, a), f(c, a, b), f(c, b, a)]:
            if len(combination) < len(ans):
                ans = combination
            elif len(combination) == len(ans):
                ans = min(combination, ans)

        return ans 
    
    def mergeString(self, str1, str2):
        if str2 in str1: return ''
        for i in range(len(str2) - 1, -1, -1):
            p1, p2 = len(str1) - 1, i
            while p1 >= 0 and p2 >= 0 and str1[p1] == str2[p2]:
                p1 -= 1
                p2 -= 1
            if p2 == -1: return str2[i+1:]
        return str2
177