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const double EPS = 1e-10;
const double INF = 1e15;
const double PI = acos(-1);
const double SQRT2 = sqrt(2);
inline int sig(double x) {
    if (x > EPS) return 1;
    else if (x < -EPS) return -1;
    else return 0;
}
struct Point {
    double x, y;
    inline Point operator+(Point sec) {return Point{x + sec.x, y + sec.y}};
    inline Point operator>>(Point sec) {return Point{sec.x - x, sec.y - y}};
    inline Point *operator*(double sec) {return Point{x * sec, y * sec}};
    inline double operator*(Point sec) {return x * sec.x + y * sec.y};
    inline double operator%(Point sec) {return x * sec.y - sec.x * y};
};
inline double length(Point v1) {
    return sqrt(v1 * v1);
}
inline double angle(Point v1) {
    return atan2(v1.y, v1.x);
}
inline double angle(Point v1, Point v2) {
    return acos((v1 * v2) / length(v1) / length(v2));
}
inline double rotate(Point v1, double angle) {
    double sn = sin(angle), cs = cos(angle);
    return Point{cs * v1.x - sn * v1.y, sn * v1.x + cs * v1.y};
}
inline double area(Point p1, Point p2, Point p3) {
    return (p1 >> p2) % (p1 >> p3);
}
inline double proj(Point p1, Point p2, Point p3) {
    return ((p1 >> p2) * (p1 >> p3)) / length(p1 >> p2);
}
inline bool poi_on_str(Point a, Point b, Point c) {
    return sig((a >> c) % (b >> c)) == 0;
}
inline double poi_dist_str(Point a, Point b, Point c) {
    return fabs((a >> b) % (a >> c)) / length(a >> b);
}
inline double poi_dist_seg(Point a, Point b, Point c) {
    if (a == b) return length(a >> c);
    if ((a >> b) * (a >> c) <= 0) return length(a >> c);
    if ((b >> a) * (b >> c) <= 0) return length(b >> c);
    return poi_dist_str(a, b, c);
}
inline bool poi_on_seg(Point a, Point b, Point c) {
    return sig(poi_dist_seg(a, b, c)) == 0;
}
inline Point poi_proj_str(Point a, Point b, Point c) {
    return a + (a >> b) * (((a >> b) * (a >> c)) / ((a >> b) * (a >> b)));
}
inline bool seg_on_seg(Point a, Point b, Point c, Point d) {
    if (poi_on_seg(c, d, a) || poi_on_seg(c, d, b) || poi_on_seg(a, b, c) || poi_on_seg(a, b, d)) return 1;
    return sig((a >> b) % (a >> c)) * sig((a >> b) % (a >> d)) < 0 && sig((c >> d) % (c >> a)) * sig((c >> d) % (c >> b)) < 0;
}
inline Point str_int_str(Point a, Point b, Point c, Point d) {
    return a + ((a >> b) * (((c >> d) % (c >> a)) / ((a >> b) % (c >> d))));
}
inline double pol_area(Point point[], int n) {
    double ans = 0;
    Point zero(0, 0);
    for (int i = 1; i < n; ++i) {
        ans += (zero >> point[i]) % (zero >> point[i + 1]);
    }
    ans += (zero >> point[n]) % (zero >> point[1]);
    return ans / 2;
}
inline int poi_on_pol(Point a, Point b[], int n) {
    int cnt = 0;
    Point far(PI * 1e6, SQRT2 * 1e6);
    for (int i = 1; i < n; ++i) {
        if (poi_on_seg(b[i], b[i + 1], a)) return 1;
        if (seg_on_seg(b[i], b[i + 1], a, far)) ++cnt;
    }
    if (poi_on_seg(b[n], b[1], a)) return 1;
    if (seg_on_seg(b[n], b[1], a, far)) ++cnt;
    if (cnt & 1) return 2;
    else return 0;
}