#include <cstdio>#include <cstring>#include <cmath>#include <set>#include <vector>#include <iostream>#include <algorithm>using namespace std;struct Point { double x, y; Point() {} Point(double x, double y) : x(x), y(y) {}} ;template<class T> T sqr(T x) { return x * x;}inline double ptDis(Point a, Point b) { return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));}typedef Point Vec;Vec operator + (Vec a, Vec b) { return Vec(a.x + b.x, a.y + b.y);}Vec operator - (Vec a, Vec b) { return Vec(a.x - b.x, a.y - b.y);}Vec operator * (Vec a, double p) { return Vec(a.x * p, a.y * p);}Vec operator / (Vec a, double p) { return Vec(a.x / p, a.y / p);}const double EPS = 1e-6;const double PI = acos(-1.0);inline int sgn(double x) { return fabs(x) < EPS ? 0 : (x < 0 ? -1 : 1);}bool operator < (Point a, Point b) { return sgn(a.x - b.x) < 0 || (sgn(a.x - b.x) == 0 && a.y < b.y);}bool operator == (Point a, Point b) { return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;}inline double dotDet(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}inline double crossDet(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}inline double crossDet(Point o, Point a, Point b) { return crossDet(a - o, b - o);}inline double vecLen(Vec x) { return sqrt(sqr(x.x) + sqr(x.y));}inline double toRad(double deg) { return deg / 180.0 * PI;}inline double angle(Vec v) { return atan2(v.y, v.x);}inline double angle(Vec a, Vec b) { return acos(dotDet(a, b) / vecLen(a) / vecLen(b));}inline double triArea(Point a, Point b, Point c) { return fabs(crossDet(b - a, c - a));}inline Vec vecUnit(Vec x) { return x / vecLen(x);}inline Vec rotate(Vec x, double rad) { return Vec(x.x * cos(rad) - x.y * sin(rad), x.x * sin(rad) + x.y * cos(rad));}Vec normal(Vec x) { double len = vecLen(x); return Vec(- x.y / len, x.x / len);}struct Line { Point s, t; Line() {} Line(Point s, Point t) : s(s), t(t) {} Point point(double x) { return s + (t - s) * x; } Line move(double x) { Vec nor = normal(t - s); nor = nor * x; return Line(s + nor, t + nor); } Vec vec() { return t - s;}} ;typedef Line Seg;inline bool onSeg(Point x, Point a, Point b) { return sgn(crossDet(a - x, b - x)) == 0 && sgn(dotDet(a - x, b - x)) < 0;}inline bool onSeg(Point x, Seg s) { return onSeg(x, s.s, s.t);}int segIntersect(Point a, Point c, Point b, Point d) { Vec v1 = b - a, v2 = c - b, v3 = d - c, v4 = a - d; int a_bc = sgn(crossDet(v1, v2)); int b_cd = sgn(crossDet(v2, v3)); int c_da = sgn(crossDet(v3, v4)); int d_ab = sgn(crossDet(v4, v1)); if (a_bc * c_da > 0 && b_cd * d_ab > 0) return 1; if (onSeg(b, a, c) && c_da) return 2; if (onSeg(c, b, d) && d_ab) return 2; if (onSeg(d, c, a) && a_bc) return 2; if (onSeg(a, d, b) && b_cd) return 2; return 0;}inline int segIntersect(Seg a, Seg b) { return segIntersect(a.s, a.t, b.s, b.t);}Point lineIntersect(Point P, Vec v, Point Q, Vec w) { Vec u = P - Q; double t = crossDet(w, u) / crossDet(v, w); return P + v * t;}inline Point lineIntersect(Line a, Line b) { return lineIntersect(a.s, a.t - a.s, b.s, b.t - b.s);}double pt2Line(Point x, Point a, Point b) { Vec v1 = b - a, v2 = x - a; return crossDet(v1, v2) / vecLen(v1);}inline double pt2Line(Point x, Line L) { return pt2Line(x, L.s, L.t);}double pt2Seg(Point x, Point a, Point b) { if (a == b) return vecLen(x - a); Vec v1 = b - a, v2 = x - a, v3 = x - b; if (sgn(dotDet(v1, v2)) < 0) return vecLen(v2); if (sgn(dotDet(v1, v3)) > 0) return vecLen(v3); return fabs(crossDet(v1, v2)) / vecLen(v1);}inline double pt2Seg(Point x, Seg s) { return pt2Seg(x, s.s, s.t);}// Polygon classstruct Poly { vector<Point> pt; Poly() { pt.clear();} Poly(vector<Point> pt) : pt(pt) {} Point operator [] (int x) const { return pt[x];} int size() { return pt.size();} double area() { double ret = 0.0; int sz = pt.size(); for (int i = 1; i < sz; i++) { ret += crossDet(pt[i], pt[i - 1]); } return fabs(ret / 2.0); }} ;struct Circle { Point c; double r; Circle() {} Circle(Point c, double r) : c(c), r(r) {} Point point(double a) { return Point(c.x + cos(a) * r, c.y + sin(a) * r); }} ;int lineCircleIntersect(Line L, Circle C, double &t1, double &t2, vector<Point> &sol) { double a = L.s.x, b = L.t.x - C.c.x, c = L.s.y, d = L.t.y - C.c.y; double e = sqr(a) + sqr(c), f = 2 * (a * b + c * d), g = sqr(b) + sqr(d) - sqr(C.r); double delta = sqr(f) - 4.0 * e * g; if (sgn(delta) < 0) return 0; if (sgn(delta) == 0) { t1 = t2 = -f / (2.0 * e); sol.push_back(L.point(t1)); return 1; } t1 = (-f - sqrt(delta)) / (2.0 * e); sol.push_back(L.point(t1)); t2 = (-f + sqrt(delta)) / (2.0 * e); sol.push_back(L.point(t2)); return 2;}int lineCircleIntersect(Line L, Circle C, vector<Point> &sol) { Vec dir = L.t - L.s, nor = normal(dir); Point mid = lineIntersect(C.c, nor, L.s, dir); double len = sqr(C.r) - sqr(ptDis(C.c, mid)); if (sgn(len) < 0) return 0; if (sgn(len) == 0) { sol.push_back(mid); return 1; } Vec dis = vecUnit(dir); len = sqrt(len); sol.push_back(mid + dis * len); sol.push_back(mid - dis * len); return 2;}// -1 : coincideint circleCircleIntersect(Circle C1, Circle C2, vector<Point> &sol) { double d = vecLen(C1.c - C2.c); if (sgn(d) == 0) { if (sgn(C1.r - C2.r) == 0) { return -1; } return 0; } if (sgn(C1.r + C2.r - d) < 0) return 0; if (sgn(fabs(C1.r - C2.r) - d) > 0) return 0; double a = angle(C2.c - C1.c); double da = acos((sqr(C1.r) + sqr(d) - sqr(C2.r)) / (2.0 * C1.r * d)); Point p1 = C1.point(a - da), p2 = C1.point(a + da); sol.push_back(p1); if (p1 == p2) return 1; sol.push_back(p2); return 2;}void circleCircleIntersect(Circle C1, Circle C2, vector<double> &sol) { double d = vecLen(C1.c - C2.c); if (sgn(d) == 0) return ; if (sgn(C1.r + C2.r - d) < 0) return ; if (sgn(fabs(C1.r - C2.r) - d) > 0) return ; double a = angle(C2.c - C1.c); double da = acos((sqr(C1.r) + sqr(d) - sqr(C2.r)) / (2.0 * C1.r * d)); sol.push_back(a - da); sol.push_back(a + da);}int tangent(Point p, Circle C, vector<Vec> &sol) { Vec u = C.c - p; double dist = vecLen(u); if (dist < C.r) return 0; if (sgn(dist - C.r) == 0) { sol.push_back(rotate(u, PI / 2.0)); return 1; } double ang = asin(C.r / dist); sol.push_back(rotate(u, -ang)); sol.push_back(rotate(u, ang)); return 2;}int tangent(Circle A, Circle B, vector<Point> &ptA, vector<Point> &ptB) { if (A.r < B.r) { swap(A, B); swap(ptA, ptB); } double d2 = sqr(A.c.x - B.c.x) + sqr(A.c.y - B.c.y); double rdiff = A.r - B.r, rsum = A.r + B.r; if (d2 < sqr(rdiff)) return 0; double base = atan2(B.c.y - A.c.y, B.c.x - A.c.x); if (d2 == 0 && A.r == B.r) return -1; if (d2 == sqr(rdiff)) { ptA.push_back(A.point(base)); ptB.push_back(B.point(base)); return 1; } double ang = acos((A.r - B.r) / sqrt(d2)); ptA.push_back(A.point(base + ang)); ptB.push_back(B.point(base + ang)); ptA.push_back(A.point(base - ang)); ptB.push_back(B.point(base - ang)); if (d2 == sqr(rsum)) { ptA.push_back(A.point(base)); ptB.push_back(B.point(PI + base)); } else if (d2 > sqr(rsum)) { ang = acos((A.r + B.r) / sqrt(d2)); ptA.push_back(A.point(base + ang)); ptB.push_back(B.point(PI + base + ang)); ptA.push_back(A.point(base - ang)); ptB.push_back(B.point(PI + base - ang)); } return (int) ptA.size();}int ptInPoly(Point p, Poly &poly) { int wn = 0, sz = poly.size(); for (int i = 0; i < sz; i++) { if (onSeg(p, poly[i], poly[(i + 1) % sz])) return -1; int k = sgn(crossDet(poly[(i + 1) % sz] - poly[i], p - poly[i])); int d1 = sgn(poly[i].y - p.y); int d2 = sgn(poly[(i + 1) % sz].y - p.y); if (k > 0 && d1 <= 0 && d2 > 0) wn++; if (k < 0 && d2 <= 0 && d1 > 0) wn--; } if (wn != 0) return 1; return 0;}int andrew(Point *pt, int n, Point *ch) { sort(pt, pt + n); int m = 0; for (int i = 0; i < n; i++) { while (m > 1 && crossDet(ch[m - 1] - ch[m - 2], pt[i] - ch[m - 2]) <= 0) m--; ch[m++] = pt[i]; } int k = m; for (int i = n - 2; i >= 0; i--) { while (m > k && crossDet(ch[m - 1] - ch[m - 2], pt[i] - ch[m - 2]) <= 0) m--; ch[m++] = pt[i]; } if (n > 1) m--; return m;}Point origin;inline bool cmpAng(Point p1, Point p2) { return crossDet(origin, p1, p2) > 0;}inline bool cmpDis(Point p1, Point p2) { return ptDis(p1, origin) > ptDis(p2, origin);}void removePt(Point *pt, int &n) { int idx = 1; for (int i = 2; i < n; i++) { if (sgn(crossDet(origin, pt[i], pt[idx]))) pt[++idx] = pt[i]; else if (cmpDis(pt[i], pt[idx])) pt[idx] = pt[i]; } n = idx + 1;}int graham(Point *pt, int n, Point *ch) { int top = -1; for (int i = 1; i < n; i++) { if (pt[i].y < pt[0].y || (pt[i].y == pt[0].y && pt[i].x < pt[0].x)) swap(pt[i], pt[0]); } origin = pt[0]; sort(pt + 1, pt + n, cmpAng); removePt(pt, n); for (int i = 0; i < n; i++) { if (i >= 2) { while (!(crossDet(ch[top - 1], pt[i], ch[top]) <= 0)) top--; } ch[++top] = pt[i]; } return top + 1;}struct DLine { Point p; Vec v; double ang; DLine() {} DLine(Point p, Vec v) : p(p), v(v) { ang = atan2(v.y, v.x);} bool operator < (const DLine &L) const { return ang < L.ang;} DLine move(double x) { // while x > 0 move to v's left Vec nor = normal(v); nor = nor * x; return DLine(p + nor, v); }} ;Poly cutPoly(Poly &poly, Point a, Point b) { Poly ret = Poly(); int n = poly.size(); for (int i = 0; i < n; i++) { Point c = poly[i], d = poly[(i + 1) % n]; if (sgn(crossDet(b - a, c - a)) >= 0) ret.pt.push_back(c); if (sgn(crossDet(b - a, c - d)) != 0) { Point ip = lineIntersect(a, b - a, c, d - c); if (onSeg(ip, c, d)) ret.pt.push_back(ip); } } return ret;}inline Poly cutPoly(Poly &poly, DLine L) { return cutPoly(poly, L.p, L.p + L.v);}inline bool onLeft(DLine L, Point p) { return crossDet(L.v, p - L.p) > 0;}Point dLineIntersect(DLine a, DLine b) { Vec u = a.p - b.p; double t = crossDet(b.v, u) / crossDet(a.v, b.v); return a.p + a.v * t;}Poly halfPlane(DLine *L, int n) { Poly ret = Poly(); sort(L, L + n); int fi, la; Point *p = new Point[n]; DLine *q = new DLine[n]; q[fi = la = 0] = L[0]; for (int i = 1; i < n; i++) { while (fi < la && !onLeft(L[i], p[la - 1])) la--; while (fi < la && !onLeft(L[i], p[fi])) fi++; q[++la] = L[i]; if (fabs(crossDet(q[la].v, q[la - 1].v)) < EPS) { la--; if (onLeft(q[la], L[i].p)) q[la] = L[i]; } if (fi < la) p[la - 1] = dLineIntersect(q[la - 1], q[la]); } while (fi < la && !onLeft(q[fi], p[la - 1])) la--; if (la - fi <= 1) return ret; p[la] = dLineIntersect(q[la], q[fi]); for (int i = fi; i <= la; i++) ret.pt.push_back(p[i]); return ret;}// 3D Geometryvoid getCoor(double R, double lat, double lng, double &x, double &y, double &z) { lat = toRad(lat); lng = toRad(lng); x = R * cos(lat) * cos(lng); y = R * cos(lat) * sin(lng); z = R * sin(lat);}const int N = 111;Point ori[N];vector<Point> ex;//vector<int> nx[5555], on[N];int nx[5555][N << 1], on[N][N << 1];int main() { int n; while (cin >> n) { ex.clear(); for (int i = 0; i < 5555; i++) nx[i][0] = 0; for (int i = 0; i < n; i++) { on[i][0] = 0; cin >> ori[i].x >> ori[i].y; ex.push_back(ori[i]); } ori[n] = ori[0]; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { if (segIntersect(ori[i], ori[i + 1], ori[j], ori[j + 1]) == 1) { ex.push_back(lineIntersect(Line(ori[i], ori[i + 1]), Line(ori[j], ori[j + 1]))); } } } sort(ex.begin(), ex.end()); int t = unique(ex.begin(), ex.end()) - ex.begin(); while (ex.size() > t) ex.pop_back(); int sz = ex.size(); for (int i = 0; i < sz; i++) { for (int j = 0; j < n; j++) { if (ex[i] == ori[j] || ex[i] == ori[j + 1] || onSeg(ex[i], Seg(ori[j], ori[j + 1]))) on[j][++on[j][0]] = i; } } for (int i = 0; i < n; i++) { int csz = on[i][0] - 1; for (int j = 0; j < csz; j++) { nx[on[i][j + 1]][++nx[on[i][j + 1]][0]] = on[i][j + 2]; nx[on[i][j + 2]][++nx[on[i][j + 2]][0]] = on[i][j + 1]; } } vector<int> path; path.clear(); path.push_back(0); int sz0 = nx[0][0]; int cur = nx[0][1]; for (int i = 1; i < sz0; i++) { int id = nx[0][i + 1]; if (sgn(crossDet(ex[cur] - ex[0], ex[id] - ex[0])) < 0) cur = id; } int cnt = 500000; while (cnt-- && cur) { path.push_back(cur); int l1 = path[path.size() - 1], l0 = path[path.size() - 2]; int t = (nx[cur][1] == l0) ? nx[cur][2] : nx[cur][1], csz = nx[cur][0]; Vec dr = ex[l1] - ex[l0]; double ang = angle(dr); for (int i = 1; i < csz; i++) { int id = nx[cur][i + 1]; if (id == l0) continue; Vec t1 = ex[t] - ex[l1], t2 = ex[id] - ex[l1]; t1 = rotate(t1, -ang), t2 = rotate(t2, -ang); if (angle(t1) > angle(t2)) t = id; } cur = t; } int psz = path.size(); vector<int> out; out.clear(); path.push_back(path[0]); for (int i = 0; i < psz; i++) { if (i > 0 && sgn(crossDet(ex[path[i]] - ex[path[i - 1]], ex[path[i + 1]] - ex[path[i]])) == 0) continue; out.push_back(path[i]); } cout << out.size() << endl; psz = out.size(); for (int i = 0; i < psz; i++) { cout << ex[out[i]].x << ' ' << ex[out[i]].y << endl; } } return 0;}
