Problem:
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

Solution in Rust (1.15.1) (judge verdict: Accepted)

macro_rules! input {
     (source = $s:expr, $($r:tt)*) => {
         let mut iter = $s.split_whitespace();
         input_inner!{iter, $($r)*}
     };
     ($($r:tt)*) => {
         let s = {
             use std::io::Read;
         let mut s = String::new();
         std::io::stdin().read_to_string(&mut s).unwrap();
         s
     };
     let mut iter = s.split_whitespace();
     input_inner!{iter, $($r)*}
     };
}
     
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
 
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}
 
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
 
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
 
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
 
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
 
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{VecDeque, HashMap, BTreeMap, HashSet, BTreeSet};
#[allow(unused_imports)]
use std::io::{stdout, Write, BufWriter};
//#[allow(unused_imports)]
//use proconio::marker::{Isize1, Usize1, Bytes, Chars};
//#[proconio::fastout]
fn main() {
    input!{
        x: u64,
    }
    let x = x as f64;
    let mut ans = 1;
    for i in 1..(x.sqrt().floor() as u64 + 1u64) {
        let (power_l, power_g) = (i.pow(x.log(i as f64).floor() as u32), i.pow(x.log(i as f64).ceil() as u32));
        let power = if power_g <= x as u64 { power_g }
        else { power_l };
        ans = max(ans, power);
    }
    println!("{}", ans);
}