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class Solution:
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    def smallestGoodBase(self, n: str) -> str:
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        import math
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        n = int(n)
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        max_m = math.floor(math.log(n, 2))
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        ans = 0
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        for m in range(max_m, 0, -1):
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            k = int(n ** (1 / m))
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            if (k ** (m + 1) - 1) // (k - 1) == n:
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                return str(k)
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        return str(n - 1)