<p>Given a string <code>n</code> representing an integer, return <em>the closest integer (not including itself), which is a palindrome</em>. If there is a tie, return <em><strong>the smaller one</strong></em>.</p>

<p>The closest is defined as the absolute difference minimized between two integers.</p>

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

<pre>
<strong>Input:</strong> n = &quot;123&quot;
<strong>Output:</strong> &quot;121&quot;
</pre>

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

<pre>
<strong>Input:</strong> n = &quot;1&quot;
<strong>Output:</strong> &quot;0&quot;
<strong>Explanation:</strong> 0 and 2 are the closest palindromes but we return the smallest which is 0.
</pre>

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

<ul>
	<li><code>1 &lt;= n.length &lt;= 18</code></li>
	<li><code>n</code> consists of only digits.</li>
	<li><code>n</code> does not have leading zeros.</li>
	<li><code>n</code> is representing an integer in the range <code>[1, 10<sup>18</sup> - 1]</code>.</li>
</ul>

class Solution:
    def nearestPalindromic(self, n: str) -> str:
        
        n_len = len(n)
        n_num = int(n)
        candidates = set()

        candidates.add(10 ** (n_len - 1) - 1)
        candidates.add(10 ** n_len + 1)

        m_i = (n_len + 1) // 2
        prefix = int(n[:m_i])

        for x in [-1, 0, 1]:
            new_prefix = str(prefix + x)

            pal = new_prefix + new_prefix[::-1] \
                if n_len % 2 == 0 \
                else new_prefix + new_prefix[:-1][::-1]

            candidates.add(int(pal))
        
        candidates.discard(n_num)
        ans = min(list(candidates), key=lambda x: (abs(x - n_num), x))
        return str(ans)
16300