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Score : $200$ points

Problem Statement

You are given a positive integer $X$. Find the largest perfect power that is at most $X$. Here, a perfect power is an integer that can be represented as $b^p$, where $b$ is an integer not less than $1$ and $p$ is an integer not less than $2$.

Constraints

• $1$ $≤$ $X$ $≤$ $1000$
• $X$ is an integer.

Input

Input is given from Standard Input in the following format:

$X$


Output

Print the largest perfect power that is at most $X$.

Sample Input 1

10


Sample Output 1

9


There are four perfect powers that are at most $10$: $1$, $4$, $8$ and $9$. We should print the largest among them, $9$.

Sample Input 2

1


Sample Output 2

1


Sample Input 3

999


Sample Output 3

961