Find the Closest Palindrome
<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>
Math; String
/**
 * @param {string} n
 * @return {string}
 */

function nearestPalindromic(n) {
    const x = BigInt(n);
    let ans = null;

    for (const t of getCandidates(n)) {
        if (
            ans === null ||
            absDiff(t, x) < absDiff(ans, x) ||
            (absDiff(t, x) === absDiff(ans, x) && t < ans)
        ) {
            ans = t;
        }
    }

    return ans.toString();
}

function getCandidates(n) {
    const length = n.length;
    const res = new Set();

    res.add(BigInt(Math.pow(10, length - 1) - 1));
    res.add(BigInt(Math.pow(10, length) + 1));

    const left = BigInt(n.substring(0, Math.ceil(length / 2)));

    for (let i = left - 1n; i <= left + 1n; i++) {
        const prefix = i.toString();
        const t =
            prefix +
            prefix
                .split('')
                .reverse()
                .slice(length % 2)
                .join('');
        res.add(BigInt(t));
    }

    res.delete(BigInt(n));
    return res;
}

function absDiff(a, b) {
    return a > b ? a - b : b - a;
}
