<p>You are given two <strong>0-indexed</strong> integer arrays <code>fronts</code> and <code>backs</code> of length <code>n</code>, where the <code>i<sup>th</sup></code> card has the positive integer <code>fronts[i]</code> printed on the front and <code>backs[i]</code> printed on the back. Initially, each card is placed on a table such that the front number is facing up and the other is facing down. You may flip over any number of cards (possibly zero).</p>

<p>After flipping the cards, an integer is considered <strong>good</strong> if it is facing down on some card and <strong>not</strong> facing up on any card.</p>

<p>Return <em>the minimum possible good integer after flipping the cards</em>. If there are no good integers, return <code>0</code>.</p>

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

<pre>
<strong>Input:</strong> fronts = [1,2,4,4,7], backs = [1,3,4,1,3]
<strong>Output:</strong> 2
<strong>Explanation:</strong>
If we flip the second card, the face up numbers are [1,3,4,4,7] and the face down are [1,2,4,1,3].
2 is the minimum good integer as it appears facing down but not facing up.
It can be shown that 2 is the minimum possible good integer obtainable after flipping some cards.
</pre>

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

<pre>
<strong>Input:</strong> fronts = [1], backs = [1]
<strong>Output:</strong> 0
<strong>Explanation:</strong>
There are no good integers no matter how we flip the cards, so we return 0.
</pre>

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

<ul>
	<li><code>n == fronts.length == backs.length</code></li>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
	<li><code>1 &lt;= fronts[i], backs[i] &lt;= 2000</code></li>
</ul>

class Solution:
    def flipgame(self, fronts: List[int], backs: List[int]) -> int:
        # Create a set of invalid numbers (numbers that appear on both sides of the same card)
        invalid = {f for f, b in zip(fronts, backs) if f == b}
        
        # Find the minimum valid number
        min_valid = float('inf')
        for f, b in zip(fronts, backs):
            if f not in invalid:
                min_valid = min(min_valid, f)
            if b not in invalid:
                min_valid = min(min_valid, b)
        
        # If no valid number is found, return 0
        return min_valid if min_valid != float('inf') else 0

# Example usage:
solution = Solution()
fronts = [1,2,4,4,7]
backs = [1,3,4,1,3]
print(solution.flipgame(fronts, backs))  # Output: 2

fronts = [1]
backs = [1]
print(solution.flipgame(fronts, backs))  # Output: 0
16500