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 <bits/stdc++.h>
#include <numeric>
using namespace std;
#define ll long long
#define mod 100000007
#define rep(i, n) for (int i = 0; i < n; ++i)
using Graph = vector<vector<int>>;
ll lcm(ll a, ll b)
{
    return a * b / __gcd(a, b);
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    //cout << fixed << setprecision(15);
    ll X;
    cin >> X;
    ll ans = 1;
    for (int i = 1; i <= X;i++)
    {
        for (int j = 2; j <= i;j++)
        {
            ll pre = pow(i, j);
            if (pre <= X)
            {
                ans = max(ans, pre);
            }
        }
    }
    cout << ans << endl;
}