#pragma once

#include <cinttypes>
#include <compare>
#include <sstream>

template<uint N>
class GF {
    uint value;
public:
    std::strong_ordering operator<=>(const GF<N> &rhs) const = default;

    GF<N> &operator=(const GF<N> &value) = default;

    GF()
        : value(0u) {}

    GF(const uint &value)
        : value(value % N) {}

    GF<N> &operator=(const uint &value) {
        this->value = value % N;
        return *this;
    }

    GF<N> operator+(const GF<N> &rhs) const {
        return (this->value + rhs.value) % N;
    }

    GF<N> operator+(const uint &rhs) const {
        return this->operator+(GF<N>(rhs));
    }

    GF<N> operator-(const GF<N> &rhs) const {
        if (this->value < rhs.value) {
            return N - (rhs.value - this->value);
        }
        return (this->value - rhs.value);
    }

    GF<N> operator-(const uint &rhs) const {
        return this->operator-(GF<N>(rhs));
    }

    GF<N> operator*(const GF<N> &rhs) const {
        return (this->value * rhs.value) % N;
    }

    GF<N> operator*(const uint &rhs) const {
        return this->operator*(GF<N>(rhs));
    }

    GF<N> operator/(const GF<N> &rhs) const {
        if (rhs.value == 0) {
            throw std::invalid_argument("division by 0 is illegal");
        }
        return (this->value / rhs.value) % N;
    }

    GF<N> operator/(const uint &rhs) const {
        return this->operator/(GF<N>(rhs));
    }

    GF<N> operator+=(const GF<N> &rhs) {
        *this = *this + rhs;
        return *this;
    }

    GF<N> operator+=(const uint &rhs) {
        return this->operator+=(GF<N>(rhs));
    }

    GF<N> operator-=(const GF<N> &rhs) {
        *this = *this - rhs;
        return *this;
    }

    GF<N> operator-=(const uint &rhs) {
        return this->operator-=(GF<N>(rhs));
    }

    GF<N> operator*=(const GF<N> &rhs) {
        *this = *this * rhs;
        return *this;
    }

    GF<N> operator*=(const uint &rhs) {
        return this->operator*=(GF<N>(rhs));
    }

    GF<N> operator/=(const GF<N> &rhs) {
        *this = *this / rhs;
        return *this;
    }

    GF<N> operator/=(const uint &rhs) {
        return this->operator/=(GF<N>(rhs));
    }

    friend std::ostream &operator<<(std::ostream &stream, const GF<N> &value) {
        stream << "GF<" << N << ">(" << value.value << ")";
        return stream;
    }

    friend std::istream &operator>>(std::istream &stream, GF<N> &value) {
        stream >> value.value;
        return stream;
    }

    uint characteristic() { return N; };
};