#pragma once

#include <vector>

typedef long long ll;
typedef unsigned long long ull;

template <typename T> struct Coord {
	T x, y;

	Coord() : Coord(0, 0) {}

	Coord(const T x, const T y) {
		this->x = x;
		this->y = y;
	}

	Coord<T> operator-() { return {-this->x, -this->y}; }

	Coord<T> &operator+=(const Coord<T> &other) {
		x += other.x;
		y += other.y;
		return *this;
	}

	Coord<T> &operator-=(const Coord<T> &other) {
		x -= other.x;
		y -= other.y;
		return *this;
	}

	Coord<T> &operator*=(const T other) {
		x *= other;
		y *= other;
		return *this;
	}

	Coord<T> &operator/=(const T other) {
		x /= other;
		y /= other;
		return *this;
	}

	std::vector<Coord<T>> nearby(const Coord<T> &cMin, const Coord<T> &cMax) {
		std::vector<Coord<T>> ret;
		const T xMin = std::max(this->x - 1, cMin.x);
		const T xMax = std::min(this->x + 1, cMax.x);
		const T yMin = std::max(this->y - 1, cMin.y);
		const T yMax = std::min(this->y + 1, cMax.y);
		for (T x = xMin; x <= xMax; x++) {
			for (T y = yMin; y <= yMax; y++) {
				Coord<T> xy(x, y);
				if (*this != xy) {
					ret.push_back(xy);
				}
			}
		}
		return ret;
	}

	std::vector<Coord<T>> nearby(const Coord<T> &cMax) {
		return this->nearby(Coord<T>(), cMax);
	}
};

template <typename T>
Coord<T> operator+(const Coord<T> &lhs, const Coord<T> &rhs) {
	Coord<T> result = lhs;
	result += rhs;
	return result;
}

template <typename T>
Coord<T> operator-(const Coord<T> &lhs, const Coord<T> &rhs) {
	Coord<T> result = lhs;
	result -= rhs;
	return result;
}

template <typename T> Coord<T> operator*(const Coord<T> &lhs, const T rhs) {
	Coord<T> result = lhs;
	result *= rhs;
	return result;
}

template <typename T> Coord<T> operator/(const Coord<T> &lhs, const T rhs) {
	Coord<T> result = lhs;
	result /= rhs;
	return result;
}

template <typename T>
inline bool operator==(const Coord<T> &lhs, const Coord<T> &rhs) {
	return lhs.x == rhs.x && lhs.y == rhs.y;
}

template <> struct std::hash<Coord<int>> {
	std::size_t operator()(const Coord<int> &c) const noexcept {
		return (c.x << (sizeof(std::size_t) / 2)) - c.x + c.y;
	}
};

template <> struct std::hash<Coord<ull>> {
	std::size_t operator()(const Coord<ull> &c) const noexcept {
		return (c.x << (sizeof(std::size_t) / 2)) - c.x + c.y;
	}
};