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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#define REP(i, n) for(ll i = 0; i < n; i++)
#define ALL(x) (x).begin(),(x).end()
#define MSG(x) cout << x << endl;
#define YN(x) x ? cout << "YES" << endl : cout << "NO" << endl;
#define Yn(x) x ? cout << "Yes" << endl : cout << "No" << endl;
#define yn(x) x ? cout << "yes" << endl : cout << "no" << endl;

using namespace std;
using ll = long long;

int main(int argc, char *argv[]) {
    ll x;
    cin >> x;

    ll ans = 1;
    for (int b = 2; b <= sqrt(x); ++b) {
        ll p = 2;
        while (pow(b, p) <= x) p++;
        p--;

        ans = max(ans, (ll)pow(b, p));
    }

    MSG(ans)
    return 0;
}