TC SRM 400(500)

#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>

using namespace std;

class StrongPrimePower {
public:
    vector <int> baseAndExponent(string);
};

typedef long long ll;
typedef long double ld;
const ld eps = 1e-14;
ld logbase(ld a, ld base)
{
   return log(a) / log(base);
}

bool prime(int a){
    for( int i = 2; i < sqrt(double(a))+1 && i<a; i++ )
        if( a%i==0 )
            return false;
    return true;
}
double round(double a){
    double fract = a - floor(a);
    if( fract<0.5 )
        return floor(a);
    else
        return ceil(a);
}

vector <int> StrongPrimePower::baseAndExponent(string n) {
    int len = n.length();
    ll N = 0;
    for( int i = 0; i < len; i++ ){
        N*=10;
        N+=n[i]-'0';
    }
    for( int i = 2; i < logbase( ld(N),2 )+1; i++ ){
        ld num = pow( ld(N), 1/ld(i) );

        if( abs( round(num)-num )  <= eps && prime( int( round(num) ) ) ){
            vector<int> ret;
            ret.push_back( int(round(num)) );
            ret.push_back( i );
            return ret;
        }
    }
    return vector<int>();
}