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>
using namespace std;

int gcd(int a,int b){
	if(b==0)return a;
	else return gcd(b,a%b);
}


bool powered(int x){
	map<int,int>cnt;
	vector<int>v;
	for(int i=2;i*i<=x;i++){
		while(i>1&&x%i==0){
			cnt[i]++;
			x/=i;
		}
	}
	if(x>0)cnt[x]++;
//  	for(auto&& u:cnt)cout<<u.first<<" "<<u.second<<endl;cout<<endl;
  
	for(auto&& u:cnt){if(u.first!=1)v.push_back(u.second);}
	int y=v[0];	
	for(auto&& u:v)y=gcd(y,u);
	if(y>1)return true;
	else return false;
}


int main(){
	int x;cin>>x;
	for(int i=x;i>=2;i--){
		if(powered(i))cout<<i<<endl,exit(0);
	}
	cout<<1<<endl;
}