1 #include <iostream>
2 #include <string>
3 #include <cstdio>
4 #include <cstring>
5 #include <cmath>
6 #include <vector>
7 #include <algorithm>
8
9 using namespace std;
10
11 const double PI = acos(-1);
12
13 struct Point {
14 double x, y;
15 Point(double x = 0, double y = 0) : x(x), y(y) {}
16 };
17
18 typedef Point Vector;
19 Vector operator + (const Vector &A, const Vector &B) { return Vector(A.x + B.x, A.y + B.y); }
20 Vector operator - (const Point &A, const Point &B) { return Vector(A.x - B.x, A.y - B.y); }
21 Vector operator * (const Vector &A, const double &p) { return Vector(A.x * p, A.y * p); }
22 Vector operator / (const Vector &A, const double &p) { return Vector(A.x / p, A.y / p); }
23 bool operator < (const Point &a, const Point &b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
24
25 const double eps = 1e-10;
26 int dcmp(double x) {
27 if(fabs(x) < eps) return 0;
28 else return x < 0 ? -1 : 1;
29 }
30
31 bool operator == (const Point &a, const Point &b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; }
32
33 double Dot(const Vector &A, const Vector &B) { return A.x * B.x + A.y * B.y; }
34 double Length(const Vector &A) { return sqrt(Dot(A, A)); }
35 double Angle(const Vector &A, const Vector &B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
36
37 double Cross(const Vector &A, const Vector B) { return A.x * B.y - A.y * B.x; }
38 double Area2(const Point &A, const Point &B, const Point &C) { return Cross(B - A, C - A); }
39
40 Vector Rotate(const Vector &A, double rad) { return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); }
41
42 Vector Normal(const Vector &A) {
43 double L = Length(A);
44 return Vector(-A.y / L, A.x / L);
45 }
46
47 Point GetLineIntersection(const Point &P, const Vector &v, const Point &Q, const Vector &w) {
48 Vector u = P - Q;
49 double t = Cross(w, u) / Cross(v, w);
50 return P + v * t;
51 }
52
53 double DistanceToLine(const Point &P, const Point &A, const Point &B) {
54 Vector v1 = B - A, v2 = P - A;
55 return fabs(Cross(v1, v2)) / Length(v1);
56 }
57 double DistanceToLine_(const Point &P, const Point &A, const Point &B) {
58 Vector v1 = B - A, v2 = P - A;
59 return Cross(v1, v2) / Length(v1);
60 }
61 double DistanceToSegment(const Point &P, const Point &A, const Point &B) {
62 if(A == B) return Length(P - A);
63 Vector v1 = B - A, v2 = P - A, v3 = P - B;
64 if(dcmp(Dot(v1, v2)) < 0) return Length(v2);
65 else if(dcmp(Dot(v1, v3)) > 0) return Length(v3);
66 else return fabs(Cross(v1, v2)) / Length(v1);
67 }
68
69 Point GetLineProjection(const Point &P, const Point &A, const Point &B) {
70 Vector v = B - A;
71 return A + v * (Dot(v, P - A) / Dot(v, v));
72 }
73
74 bool SegmentProperIntersection(const Point &a1, const Point &a2, const Point &b1, const Point &b2) {
75 double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1), c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
76 return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
77 }
78
79 bool OnSegment(const Point &p, const Point &a1, const Point &a2) {
80 return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
81 }
82
83 double ConvexPolygonArea(Point *p, int n) {
84 double area = 0;
85 for(int i = 1; i < n - 1; ++i) area += Cross(p[i] - p[0], p[i + 1] - p[0]);
86 return area / 2;
87 }
88
89 double PolygonArea(Point *p, int n) {
90 double area = 0;
91
92 for(int i = 1; i < n - 1; ++i) area += Cross(p[i] - p[0], p[i + 1] - p[0]);
93 return area / 2;
94 }
95
96 struct Line {
97 Point p;
98 Vector v;
99 Line(Point p, Vector v):p(p),v(v) { }
100 Point point(double t) {
101 return p + v*t;
102 }
103 Line move(double d) {
104 return Line(p + Normal(v)*d, v);
105 }
106 };
107
108 Line getLine(double x1, double y1, double x2, double y2) {
109 Point p1(x1,y1);
110 Point p2(x2,y2);
111 return Line(p1, p2-p1);
112 }
113
114 struct Circle {
115 Point c;
116 double r;
117
118 Circle(Point c, double r) : c(c), r(r) {}
119
120 Point point(const double &a) const {
121 return Point(c.x + cos(a) * r, c.y + sin(a) * r);
122 }
123 };
124
125 int getLineCircleIntersection(Line L, Circle C, double &t1, double &t2, vector<Point> &sol) {
126 double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
127 double e = a * a + c * c, f = 2 * (a * b + c * d), g = b * b + d * d - C.r * C.r;
128 double delta = f * f - 4 * e * g;
129 if(dcmp(delta) < 0) return 0;
130 if(dcmp(delta) == 0) {
131 t1 = t2 = -f / (2 * e);
132 sol.push_back(L.point(t1));
133 return 1;
134 }
135 t1 = (-f - sqrt(delta)) / (2 * e);
136 sol.push_back(L.point(t1));
137 t2 = (-f + sqrt(delta)) / (2 * e);
138 sol.push_back(L.point(t2));
139 return 2;
140 }
141
142 double angle(const Vector &v) { return atan2(v.y, v.x); }
143
144 int getCircleCircleIntersection(Circle C1, Circle C2, vector<Point> &sol) {
145 double d = Length(C1.c - C2.c);
146 if(dcmp(d) == 0) {
147 if(dcmp(C1.r - C2.r) == 0) return -1;
148 return 0;
149 }
150 if(dcmp(C1.r + C2.r - d) < 0) return 0;
151 if(dcmp(fabs(C1.r - C2.r) - d) > 0) return 0;
152
153 double a = angle(C2.c - C1.c);
154 double da = acos((C1.r * C1.r + d * d - C2.r * C2.r) / (2 * C1.r * d));
155
156 Point p1 = C1.point(a - da), p2 = C1.point(a + da);
157
158 sol.push_back(p1);
159 if(p1 == p2) return 1;
160 sol.push_back(p2);
161 return 2;
162 }
163
164 int getTangents(Point p, Circle C, Vector *v) {
165 Vector u = C.c - p;
166 double dist = Length(u);
167 if(dist < C.r) return 0;
168 else if(dcmp(dist - C.r) == 0) {
169 // v[0] = Rotate(u, PI / 2);
170 return 1;
171 }
172 else {
173 double ang = asin(C.r / dist);
174 v[0] = Rotate(u, -ang);
175 v[1] = Rotate(u, +ang);
176 return 2;
177 }
178 }
179
180 int getTangents(Circle A, Circle B, Point *a, Point *b) {
181 int cnt = 0;
182 if(A.r < B.r) { swap(A, B); swap(a, b); }
183 int d2 = (A.c.x - B.c.x) * (A.c.x - B.c.x) + (A.c.y - B.c.y) * (A.c.y - B.c.y);
184 int rdiff = A.r - B.r;
185 int rsum = A.r + B.r;
186 if(d2 < rdiff * rdiff) return 0;
187
188 double base = atan2(B.c.y - A.c.y, B.c.x - A.c.x);
189 if(d2 == 0 && A.r == B.r) return -1;
190 if(d2 == rdiff * rdiff) {
191 a[cnt] = A.point(base);
192 b[cnt] = B.point(base);
193 ++cnt;
194 return 1;
195 }
196 double ang = acos((A.r - B.r) / sqrt(d2));
197 a[cnt] = A.point(base + ang);
198 b[cnt] = B.point(base + ang);
199 ++cnt;
200 a[cnt] = A.point(base - ang);
201 b[cnt] = B.point(base - ang);
202 ++cnt;
203 if(d2 == rsum * rsum) {
204 a[cnt] = A.point(base);
205 b[cnt] = B.point(PI + base);
206 ++cnt;
207 }
208 else if(d2 > rsum * rsum) {
209 double ang = acos((A.r + B.r) / sqrt(d2));
210 a[cnt] = A.point(base + ang);
211 b[cnt] = B.point(PI + base + ang);
212 ++cnt;
213 a[cnt] = A.point(base - ang);
214 b[cnt] = B.point(PI + base - ang);
215 ++cnt;
216 }
217 return cnt;
218 }
219
220 double torad(const double °) {
221 return deg / 180 * PI;
222 }
223
224 void get_coord(const double &R, double lat, double lng, double &x, double &y, double &z) {
225 lat = torad(lat);
226 lng = torad(lng);
227 x = R * cos(lat) * cos(lng);
228 y = R * cos(lat) * sin(lng);
229 z = R * sin(lat);
230 }
231
232 int ConvexHull(Point *p, int n, Point *ch) {
233 sort(p, p + n);
234 int m = 0;
235 for(int i = 0; i < n; ++i) {
236 while(m > 1 && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) --m;
237 ch[m++] = p[i];
238 }
239 int k = m;
240 for(int i = n - 2; i >= 0; --i) {
241 while(m > k && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) --m;
242 ch[m++] = p[i];
243 }
244 if(n > 1) --m;
245 return m;
246 }
247
248 int isPointInPolygon(Point p, Point *poly, int n) {
249 int wn = 0;
250 for(int i = 0;i < n; ++i) {
251 if(OnSegment(p, poly[i], poly[(i+1)%n])) return -1;
252 int k=dcmp(Cross(poly[(i+1)%n]-poly[i], p-poly[i]));
253 int d1=dcmp(poly[i].y-p.y);
254 int d2=dcmp(poly[(i+1)%n].y-p.y);
255 if(k>0&&d1<=0&&d2>0) wn++;
256 if(k<0&&d2<=0&&d1>0) wn--;
257 }
258 if(wn!=0) return 1;
259 else return 0;
260 }
261
262 Point read_point() {
263 Point P;
264 scanf("%lf%lf",&P.x,&P.y);
265 return P;
266 }
267
268 int main() {
269
270 }