#include <iostream>
#include <vector>
#include <algorithm>

class VampireNumber
{
public:
    VampireNumber(int i, int k);
    ~VampireNumber()     {};

    void print();
    void set_Number(unsigned long l);
    unsigned long get_Number()   { return number; }
    bool isValid();

private:
    unsigned long number;
    std::vector<long> digits;
    std::vector<long> pairs;
    const int count_of_digits;
    const int count_of_fang_digits;
    bool is_valid;

    void fill_vectors();
    void build_pairs();
    int check();
    void lame_sort();
    unsigned long get_ProductOfPairs();
};

VampireNumber::VampireNumber(int i, int k) : number(0), digits(i, 0), pairs(k, 0), count_of_digits(i), count_of_fang_digits(k), is_valid(false)
{

}

void VampireNumber::set_Number(unsigned long l)
{
    number = l;
}

void VampireNumber::lame_sort()
{
    std::sort(digits.begin(), digits.end());
}

unsigned long VampireNumber::get_ProductOfPairs()
{
    unsigned long tmp = 1;
    for(int i=0; i < pairs.size(); i++)
        tmp *= pairs[i];

    return tmp;
}

void VampireNumber::print()
{
    std::string to_print;
    for(int i=0; i < pairs.size(); i++)
    {
        to_print += std::to_string(pairs[i]);
        to_print += (i < pairs.size()-1)?"*":"";
    }
    std::cout << to_print;
    std::cout << std::endl;
}

void VampireNumber::build_pairs()
{
    int k = 0;
    for(int i=0; i < pairs.size(); i++)
    {
        pairs[i] = (digits[k] * 10) + digits[k+1];
        k += count_of_digits / count_of_fang_digits;
    }
}

void VampireNumber::fill_vectors()
{
    unsigned long tmp = number;
    for(int i=0; i < count_of_digits; i++)
    {
        digits[i] = tmp % 10;
        tmp /= 10;
    }
}

int VampireNumber::check()
{
    for(int i=0; i < digits.size(); i++)
    {
        if(digits[i] == digits.size())
            break;

        if((digits[i] == 0) && (digits[i+1] == 0))
        {
            is_valid = false;
            return 0;
        }
    }
    return 1;
}

bool VampireNumber::isValid()
{
    fill_vectors();

    do
    {
        if(check())
        {
            build_pairs();
            if(number == get_ProductOfPairs())
                return true;
        }
    }while(std::next_permutation(digits.begin(), digits.end()));
    return false;
}

int main(int argc, char *argv[])
{
    VampireNumber vampy(6, 3);
    std::vector<unsigned long> the_numbers;

    for(unsigned long i = 100000; i < 1000000; i++)
    {
        vampy.set_Number(i);
        if(vampy.isValid())
        {
            std::cout << vampy.get_Number() << "=";
            vampy.print();
        }
    }
    std::cout << std::endl;
    return 0;
}