smallest-good-base

Smallest Good Base

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smallestGoodBase

Given an integer <code>n</code> represented as a string, return the smallest good base of <code>n</code>.

We call <code>k &gt;= 2</code> a good base of <code>n</code>, if all digits of <code>n</code> base <code>k</code> are <code>1</code>&#39;s.

&nbsp;
Example 1:

<pre>
Input: n = &quot;13&quot;
Output: &quot;3&quot;
Explanation: 13 base 3 is 111.
</pre>

Example 2:

<pre>
Input: n = &quot;4681&quot;
Output: &quot;8&quot;
Explanation: 4681 base 8 is 11111.
</pre>

Example 3:

<pre>
Input: n = &quot;1000000000000000000&quot;
Output: &quot;999999999999999999&quot;
Explanation: 1000000000000000000 base 999999999999999999 is 11.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n</code> is an integer in the range <code>[3, 1018]</code>.</li>
	<li><code>n</code> does not contain any leading zeros.</li>
</ul>

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