// sample class for storing an integer with an arbitrary number of digits

#include <iostream>
#include <string>
#include <vector>
#include <sstream>
#include <climits>

using namespace std;

class big_integer {
public:
    big_integer(int n = 0) {
        digits.push_back(n % 10);
        n /= 10;
        while (n != 0) {
            digits.push_back(n % 10);
            n /= 10;
        }
    }

    big_integer(string s) {
        for (int i = s.size() - 1; i >= 0; i--) {
            digits.push_back(s[i] - '0');
        }
    }

    string to_string() const {
        ostringstream out;
        for (int i = digits.size() - 1; i >= 0; i--) {
            out << digits[i];
        }
        return out.str();
    }

    // pre : n < INT_MAX / 10 (to avoid integer overflow)
    big_integer & operator*=(int n) {
        if (n >= INT_MAX / 10) {
            throw runtime_error("int is too big");
        }
        int carry = 0;
        for (int & digit : digits) {
            digit = digit * n + carry;
            carry = digit / 10;
            digit = digit % 10;
        }
        while (carry > 0) {
            digits.push_back(carry % 10);
            carry /= 10;
        }
        return *this;
    }

private:
    vector<int> digits;
};

bool operator==(const big_integer & lhs, const big_integer & rhs) {
    return lhs.to_string() == rhs.to_string();
}

bool operator!=(const big_integer & lhs, const big_integer & rhs) {
    return !(lhs == rhs);
}

ostream & operator<<(ostream & out, const big_integer & big) {
    out << big.to_string();
    return out;
}

istream & operator>>(istream & in, big_integer & big) {
    string s;
    in >> s;
    big = big_integer(s);
    return in;
}

int main() {
    big_integer x(1234);
    big_integer y(49);
    big_integer z("657894365382796543289");
    big_integer a("1234");
    cout << "give me a big int: ";
    big_integer b;
    cin >> b;

    cout << "x = " << x << endl;
    cout << "y = " << y << endl;
    cout << "z = " << z << endl;
    cout << "a = " << a << endl;
    cout << "b = " << b << endl;
    cout << endl;

    cout << "x == y returns " << (x == y) << endl;
    cout << "x == a returns " << (x == a) << endl;
    cout << "x == x returns " << (x == x) << endl;
    cout << "x == z returns " << (x == z) << endl;
    cout << "x == 1234 returns " << (x == 1234) << endl;
    cout << "1234 == x returns " << (1234 == x) << endl;
    cout << endl;

    big_integer fact(1);
    for (int i = 1; i <= 30; i++) {
        fact *= i;
        cout << i << "! = " << fact << endl;
    }
    cout << endl;

    return 0;
}