/**
 * Defines a few widely used, widely spread structures. Imported pervasively.
 **/

#include <functional>  // Hash
#include <vector>
#include <cassert>

struct Point {
    Point(double x, double y, double z) : x(x), y(y), z(z) {}
    double x, y, z;

    double operator[](unsigned i) const {
        assert(0 <= i && i < 3);
        switch(i) {
            case 0:     return x;
            case 1:     return y;
            case 2:     return z;
            default:    return 0;
        }
    }
};

struct Face {
    Face(int v0, int v1, int v2) {
        vert[0] = v0;
        vert[1] = v1;
        vert[2] = v2;
    }
    int vert[3];
    int operator[](unsigned i) const {
        return vert[i % 3]; // dodge errors
    }
    const Point& pt(int id, const std::vector<Point>& pts) const {
        assert(0 <= id && id < 3);
        return pts[vert[id]];
    }
};

namespace std {
	template<> struct hash<Face>
    {
        typedef Face argument_type;
        typedef std::size_t result_type;
        result_type operator()(argument_type const& s) const noexcept
        {
            result_type const h1 ( std::hash<int>{}(s[0]) );
            result_type const h2 ( std::hash<int>{}(s[1]) );
            result_type const h3 ( std::hash<int>{}(s[2]) );
            return h1 ^ h2 ^ h3;
        }
    };
}