P2759 Strange Function

Description

What is the smallest positive integer $x$ such that $x^x$ has at least $n$ digits?

Input Format

A positive integer $n$.

Output Format

Output the smallest positive integer $x$ such that $x^x$ has at least $n$ digits.

Explanation/Hint

For all testdata, $1 \le n \le 2 \times 10^9$. Translated by ChatGPT 5