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For an integer n, we call k>=2 a * good base* of n, if all digits of n base k are 1.

Now given a string representing n, you should return the smallest good base of n in string format.

**Example 1:**

Input:"13"Output:"3"Explanation:13 base 3 is 111.

**Example 2:**

Input:"4681"Output:"8"Explanation:4681 base 8 is 11111.

**Example 3:**

Input:"1000000000000000000"Output:"999999999999999999"Explanation:1000000000000000000 base 999999999999999999 is 11.

**Note:**

- The range of n is [3, 10^18].
- The string representing n is always valid and will not have leading zeros.

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