100971: [AtCoder]ABC097 B - Exponential

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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

Input

题意翻译

已知正整数 $b>0,p>1,b^p≤x$ ,给定正整数 $x$ ,求出满足条件的最大的 $b^p$ 。

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