const int MAXN = 1e6 + 5;
const double eps = 1e-8;

int cmp(double x) {
    if(fabs(x) < eps) return 0;
    if(x > 0) return 1;
    return -1;
}

const double pi = acos(-1.0);
inline double sqr(double x) {
    return x * x;
}
struct point{
    double x, y;
    point(){}
    point(double a, double
 
 b) : x(a), y(b) {}
    void input() {
        scanf("%lf%lf", &x, &y);
    }
    friend point operator + (const point &a, const point &b) {
        return point(a.x + b.x, a.y + b.y);
    }
    friend point operator - (const point &a, const point &b) {
        return point(a.x - b.x, a.y - b.y);
    }
    friend
 
 bool operator == (const point &a, const point &b) {
        return cmp(a.x - b.x) == 0 && cmp(a.y - b.y) == 0;
    }
    friend point operator * (const point &a, const double &b) {
        return point(a.x * b, a.y * b);
    }
    friend point operator * (const double &a, const
 
 point &b) {
        return point(a * b.x, a * b.y);
    }
    friend point operator / (const point &a, const double &b) {
        return point(a.x / b, a.y / b);
    }
    double norm() {
        return sqrt(sqr(x) + sqr(y));
    }
};
double det(const point &a, const point &b) {
    return a.x * b.y - a.y * b.x;
}
double dot(const point &a, const point &b) {
    return a.x * b.x + a.y * b.y;
}
double dist(const point &a, const point &b) {
    return (a - b).norm();
}
point rotate_point(const point &p, double A) {
    double tx = p.x, ty = p.y;
    return point(tx * cos(A) - ty * sin(A), tx * sin(A) + ty * cos(A));
}
struct line{
    point a, b;
    line(){}
    line(point x, point y) : a(x), b(y){}
};
line point_make_line(const point a, const point b) {
    return line(a, b);
}
double dis_point_segment(const point p, const point s, const point t) {
    if(cmp(dot(p-s, t-s)) < 0) return (p - s).norm();
    if(cmp(dot(p-t, s-t)) < 0) return (p - t).norm();
    return fabs(det(s-p, t-p)/dist(s,t));
}
void PointProjLine(const point p,const point s, const point t,point &cp){
    double r = dot((t-s), (p-s))/dot(t-s, t-s);
    cp=s+r*(t-s);
}
bool PointOnSegment(point p, point s, point t){
    return cmp(det(p-s, t-s))==0 && cmp(dot(p-s,p-t))<=0;
}
bool parallel(line a,line b){
    return !cmp(det(a.a-a.b,b.a-b.b));
}
bool line_make_point(line a,line b,point &res){
    if (parallel(a,b)) return false;
    double s1=det(a.a-b.a,b.b-b.a);
    double s2=det(a.b-b.a,b.b-b.a);
    res=(s1*a.b-s2*a.a)/(s1-s2);
    return true;
}
line move_d(line a, const double &len) {
    point d = a.b - a.a;
    d = d / d.norm();
    d = rotate_point(d, pi/2);
    return line(a.a + d*len, a.b + d * len);
}