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: Wrong Answer)

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <string>
#include <sstream>
#include <complex>
#include <vector>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#include <set>
#include <iomanip>
using namespace std;
typedef long long unsigned int ll;

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))

#define DEBUG

#ifdef DEBUG
#define var_dump(...) fprintf(stdout, __VA_ARGS__)
#define dump(a) cout << a << "\n";
#else
#define var_dump(...) 42
#define dump(a) 42
#endif

typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;

int dy4[]={0, 0, 1, -1};
int dx4[]={1, -1, 0, 0};
int dx8[]={0, 0, 1, -1, 1, 1, -1, -1};
int dy8[]={1, -1, 0, 0, 1, -1, -1, 1};

// https://beta.atcoder.jp/contests/abc097/tasks/abc097_b

int main() {
    int X; cin >> X;

    set<ll> s;
    s.insert(1);
    for (ll i = 2; i <= 1000; i++) {
        for (ll j = i * i; j <= 1000; j=j*i) {
            s.insert(j);
        }
    }

    int prev = 1;
    for (int i = 1; i <= 1000; i++) {
        if (!s.count(i)) continue;
        if (i > X) {
            cout << prev << "\n";
            return 0;
        }

        prev = i;
    }

    return 0;
}