#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const double inf = 1e20;
const double pi = acos(-1.0);
const int maxp = 10001;
int dcmp(double d) {
  if (fabs(d) < eps) return 0;
  return d > eps ? 1 : -1;
}
inline double sqr(double x) { return x * x; }
struct point {
  double x, y;
  point() {}
  point(double _x, double _y) : x(_x), y(_y){};
  void input() { scanf("%lf%lf", &x, &y); }
  void output() { printf("%.2f %.2f\n", x, y); }
  bool operator==(point a) const {
    return dcmp(a.x - x) == 0 && dcmp(a.y - y) == 0;
  }
  bool operator<(point a) const {
    return dcmp(a.x - x) == 0 ? dcmp(y - a.y) < 0 : x < a.x;
  }
  double len() { return hypot(x, y); }
  double len2() { return x * x + y * y; }
  double distance(point p) { return hypot(x - p.x, y - p.y); }
  point add(point p) { return point(x + p.x, y + p.y); }
  point sub(point p) { return point(x - p.x, y - p.y); }
  point mul(double b) { return point(x * b, y * b); }
  point div(double b) { return point(x / b, y / b); }
  double dot(point p) { return x * p.x + y * p.y; }
  double det(point p) { return x * p.y - y * p.x; }
  double rad(point a, point b) {
    point p = *this;
    return fabs(atan2(fabs(a.sub(p).det(b.sub(p))), a.sub(p).dot(b.sub(p))));
  }
  point trunc(double r) {
    double l = len();
    if (!dcmp(l)) return *this;
    r /= l;
    return point(x * r, y * r);
  }
  point rotleft() { return point(-y, x); }
  point rotright() { return point(y, -x); }
  point rotate(point p, double angle) {
    point v = this->sub(p);
    double c = cos(angle), s = sin(angle);
    return point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
struct line {
  point a, b;
  line() {}
  line(point _a, point _b) {
    a = _a;
    b = _b;
  }
  bool operator==(line v) { return (a == v.a) && (b == v.b); }
  line(point p, double angle) {
    a = p;
    if (dcmp(angle - pi / 2) == 0) {
      b = a.add(point(0, 1));
    } else {
      b = a.add(point(1, tan(angle)));
    }
  }
  line(double _a, double _b, double _c) {
    if (dcmp(_a) == 0) {
      a = point(0, -_c / _b);
      b = point(1, -_c / _b);
    } else if (dcmp(_b) == 0) {
      a = point(-_c / _a, 0);
      b = point(-_c / _a, 1);
    } else {
      a = point(0, -_c / _b);
      b = point(1, (-_c - _a) / _b);
    }
  }
  void input() {
    a.input();
    b.input();
  }
  void adjust() {
    if (b < a) swap(a, b);
  }
  double length() { return a.distance(b); }
  double angle() {
    double k = atan2(b.y - a.y, b.x - a.x);
    if (dcmp(k) < 0) k += pi;
    if (dcmp(k - pi) == 0) k -= pi;
    return k;
  }
  int relation(point p) {
    int c = dcmp(p.sub(a).det(b.sub(a)));
    if (c < 0) return 1;
    if (c > 0) return 2;
    return 3;
  }
  bool pointonseg(point p) {
    return dcmp(p.sub(a).det(b.sub(a))) == 0 &&
           dcmp(p.sub(a).dot(p.sub(b))) <= 0;
  }
  bool parallel(line v) { return dcmp(b.sub(a).det(v.b.sub(v.a))) == 0; }
  int segcrossseg(line v) {
    int d1 = dcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dcmp(b.sub(a).det(v.b.sub(a)));
    int d3 = dcmp(v.b.sub(v.a).det(a.sub(v.a)));
    int d4 = dcmp(v.b.sub(v.a).det(b.sub(v.a)));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
    return ((d1 == 0 && dcmp(v.a.sub(a).dot(v.a.sub(b))) <= 0) ||
            (d2 == 0 && dcmp(v.b.sub(a).dot(v.b.sub(b))) <= 0) ||
            (d3 == 0 && dcmp(a.sub(v.a).dot(a.sub(v.b))) <= 0) ||
            (d4 == 0 && dcmp(b.sub(v.a).dot(b.sub(v.b))) <= 0));
  }
  int linecrossseg(line v) {
    int d1 = dcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dcmp(b.sub(a).det(v.b.sub(a)));
    if ((d1 ^ d2) == -2) return 2;
    return (d1 == 0 || d2 == 0);
  }
  int linecrossline(line v) {
    if ((*this).parallel(v)) return v.relation(a) == 3;
    return 2;
  }
  point crosspoint(line v) {
    double a1 = v.b.sub(v.a).det(a.sub(v.a));
    double a2 = v.b.sub(v.a).det(b.sub(v.a));
    return point((a.x * a2 - b.x * a1) / (a2 - a1),
                 (a.y * a2 - b.y * a1) / (a2 - a1));
  }
  double dispointtoline(point p) {
    return fabs(p.sub(a).det(b.sub(a))) / length();
  }
  double dispointtoseg(point p) {
    if (dcmp(p.sub(b).dot(a.sub(b))) < 0 || dcmp(p.sub(a).dot(b.sub(a))) < 0)
      return min(p.distance(a), p.distance(b));
    return dispointtoline(p);
  }
  point lineprog(point p) {
    return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a)) / b.sub(a).len2()));
  }
  point symmetrypoint(point p) {
    point q = lineprog(p);
    return point(2 * q.x - p.x, 2 * q.y - p.y);
  }
};
struct circle {
  point p;
  double r;
  circle() {}
  circle(point _p, double _r) : p(_p), r(_r){};
  circle(double x, double y, double _r) : p(point(x, y)), r(_r){};
  circle(point a, point b, point c) {
    p = line(a.add(b).div(2), a.add(b).div(2).add(b.sub(a).rotleft()))
            .crosspoint(
                line(c.add(b).div(2), c.add(b).div(2).add(b.sub(c).rotleft())));
    r = p.distance(a);
  }
  circle(point a, point b, point c, bool t) {
    line u, v;
    double m = atan2(b.y - a.y, b.x - a.x), n = atan2(c.y - a.y, c.x - a.x);
    u.a = a;
    u.b = u.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    v.a = b;
    m = atan2(a.y - b.y, a.x - b.x), n = atan2(c.y - b.y, c.x - b.x);
    v.b = v.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    p = u.crosspoint(v);
    r = line(a, b).dispointtoseg(p);
  }
  void input() {
    p.input();
    scanf("%lf", &r);
  }
  void output() { printf("%.2lf %.2lf %.2lf\n", p.x, p.y, r); }
  bool operator==(circle v) { return ((p == v.p) && dcmp(r - v.r) == 0); }
  bool operator<(circle v) const {
    return ((p < v.p) || ((p == v.p) && dcmp(r - v.r) < 0));
  }
  double area() { return pi * sqr(r); }
  double circumference() { return 2 * pi * r; }
  int relation(point b) {
    double dst = b.distance(p);
    if (dcmp(dst - r) < 0) return 2;
    if (dcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationseg(line v) {
    double dst = v.dispointtoseg(p);
    if (dcmp(dst - r) < 0) return 2;
    if (dcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationline(line v) {
    double dst = v.dispointtoline(p);
    if (dcmp(dst - r) < 0) return 2;
    if (dcmp(dst - r) == 0) return 1;
    return 0;
  }
  int getcircle(point a, point b, double r, circle &c1, circle &c2) {
    circle x(a, r), y(b, r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r;
    return t;
  }
  int getcircle(line u, point q, double r1, circle &c1, circle &c2) {
    double dis = u.dispointtoline(q);
    if (dcmp(dis - r1 * 2) > 0) return 0;
    if (dcmp(dis) == 0) {
      c1.p = q.add(u.b.sub(u.a).rotleft().trunc(r1));
      c2.p = q.add(u.b.sub(u.a).rotright().trunc(r1));
      c1.r = c2.r = r1;
      return 2;
    }
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    circle cc = circle(q, r1);
    point p1, p2;
    if (!cc.pointcrossline(u1, p1, p2)) cc.pointcrossline(u2, p1, p2);
    c1 = circle(p1, r1);
    if (p1 == p2) {
      c2 = c1;
      return 1;
    }
    c2 = circle(p2, r1);
    return 2;
  }
  int getcircle(line u, line v, double r1, circle &c1, circle &c2, circle &c3,
                circle &c4) {
    if (u.parallel(v)) return 0;
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    line v1 = line(v.a.add(v.b.sub(v.a).rotleft().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotleft().trunc(r1)));
    line v2 = line(v.a.add(v.b.sub(v.a).rotright().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotright().trunc(r1)));
    c1.r = c2.r = c3.r = c4.r = r1;
    c1.p = u1.crosspoint(v1);
    c2.p = u1.crosspoint(v2);
    c3.p = u2.crosspoint(v1);
    c4.p = u2.crosspoint(v2);
    return 4;
  }
  int getcircle(circle cx, circle cy, double r1, circle &c1, circle &c2) {
    circle x(cx.p, r1 + cx.r), y(cy.p, r1 + cy.r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r1;
    return t;
  }
  int pointcrossline(line v, point &p1, point &p2) {
    if (!(*this).relationline(v)) return 0;
    point a = v.lineprog(p);
    double d = v.dispointtoline(p);
    d = sqrt(r * r - d * d);
    if (dcmp(d) == 0) {
      p1 = a;
      p2 = a;
      return 1;
    }
    p1 = a.sub(v.b.sub(v.a).trunc(d));
    p2 = a.add(v.b.sub(v.a).trunc(d));
    return 2;
  }
  int relationcircle(circle v) {
    double d = p.distance(v.p);
    if (dcmp(d - r - v.r) > 0) return 5;
    if (dcmp(d - r - v.r) == 0) return 4;
    double l = fabs(r - v.r);
    if (dcmp(d - r - v.r) < 0 && dcmp(d - l) > 0) return 3;
    if (dcmp(d - l) == 0) return 2;
    if (dcmp(d - l) < 0) return 1;
  }
  int pointcrosscircle(circle v, point &p1, point &p2) {
    int rel = relationcircle(v);
    if (rel == 1 || rel == 5) return 0;
    double d = p.distance(v.p);
    double l = (d + (sqr(r) - sqr(v.r)) / d) / 2;
    double h = sqrt(sqr(r) - sqr(l));
    p1 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotleft().trunc(h)));
    p2 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotright().trunc(h)));
    if (rel == 2 || rel == 4) return 1;
    return 2;
  }
  int tangentline(point q, line &u, line &v) {
    int x = relation(q);
    if (x == 2) return 0;
    if (x == 1) {
      u = line(q, q.add(q.sub(p).rotleft()));
      v = u;
      return 1;
    }
    double d = p.distance(q);
    double l = sqr(r) / d;
    double h = sqrt(sqr(r) - sqr(l));
    u = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotleft().trunc(h))));
    v = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotright().trunc(h))));
    return 2;
  }
  double areacircle(circle v) {
    int rel = relationcircle(v);
    if (rel >= 4) return 0.0;
    if (rel <= 2) return min(area(), v.area());
    double d = p.distance(v.p);
    double hf = (r + v.r + d) / 2.0;
    double ss = 2 * sqrt(hf * (hf - r) * (hf - v.r) * (hf - d));
    double a1 = acos((r * r + d * d - v.r * v.r) / (2.0 * r * d));
    a1 = a1 * r * r;
    double a2 = acos((v.r * v.r + d * d - r * r) / (2.0 * v.r * d));
    a2 = a2 * v.r * v.r;
    return a1 + a2 - ss;
  }
  double areatriangle(point a, point b) {
    if (dcmp(p.sub(a).det(p.sub(b)) == 0)) return 0.0;
    point q[5];
    int len = 0;
    q[len++] = a;
    line l(a, b);
    point p1, p2;
    if (pointcrossline(l, q[1], q[2]) == 2) {
      if (dcmp(a.sub(q[1]).dot(b.sub(q[1]))) < 0) q[len++] = q[1];
      if (dcmp(a.sub(q[2]).dot(b.sub(q[2]))) < 0) q[len++] = q[2];
    }
    q[len++] = b;
    if (len == 4 && (dcmp(q[0].sub(q[1]).dot(q[2].sub(q[1]))) > 0))
      swap(q[1], q[2]);
    double res = 0;
    int i;
    for (i = 0; i < len - 1; i++) {
      if (relation(q[i]) == 0 || relation(q[i + 1]) == 0) {
        double arg = p.rad(q[i], q[i + 1]);
        res += r * r * arg / 2.0;
      } else
        res += fabs(q[i].sub(p).det(q[i + 1].sub(p)) / 2.0);
    }
    return res;
  }
};
struct polygon {
  int n;
  point p[maxp];
  line l[maxp];
  void input() {
    for (int i = 0; i < n; i++) p[i].input();
  }
  void add(point q) { p[n++] = q; }
  void getline() {
    for (int i = 0; i < n; i++) l[i] = line(p[i], p[(i + 1) % n]);
  }
  struct cmp {
    point p;
    cmp(const point &p0) { p = p0; }
    bool operator()(const point &aa, const point &bb) {
      point a = aa, b = bb;
      int d = dcmp(a.sub(p).det(b.sub(p)));
      if (d == 0) return dcmp(a.distance(p) - b.distance(p)) < 0;
      return d > 0;
    }
  };
  void norm() {
    point mi = p[0];
    for (int i = 1; i < n; i++) mi = min(mi, p[i]);
    sort(p, p + n, cmp(mi));
  }
  void getconvex(polygon &convex) {
    int i;
    sort(p, p + n);
    convex.n = n;
    for (i = 0; i < min(n, 2); i++) convex.p[i] = p[i];
    if (n <= 2) return;
    int &top = convex.n;
    top = 1;
    for (i = 2; i < n; i++) {
      while (top &&
             convex.p[top].sub(p[i]).det(convex.p[top - 1].sub(p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
    int temp = top;
    convex.p[++top] = p[n - 2];
    for (i = n - 3; i >= 0; i--) {
      while (top != temp &&
             convex.p[top].sub(p[i]).det(convex.p[top - 1].sub(p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
  }
  bool isconvex() {
    bool s[3];
    memset(s, 0, sizeof(s));
    int i, j, k;
    for (i = 0; i < n; i++) {
      j = (i + 1) % n;
      k = (j + 1) % n;
      s[dcmp(p[j].sub(p[i]).det(p[k].sub(p[i]))) + 1] = 1;
      if (s[0] && s[2]) return 0;
    }
    return 1;
  }
  int relationpoint(point q) {
    int i, j;
    for (i = 0; i < n; i++)
      if (p[i] == q) return 3;
    getline();
    for (i = 0; i < n; i++)
      if (l[i].pointonseg(q)) return 2;
    int cnt = 0;
    for (i = 0; i < n; i++) {
      j = (i + 1) % n;
      int k = dcmp(q.sub(p[j]).det(p[i].sub(p[j])));
      int u = dcmp(p[i].y - q.y);
      int v = dcmp(p[j].y - q.y);
      if (k > 0 && u < 0 && v >= 0) cnt++;
      if (k < 0 && v < 0 && u >= 0) cnt--;
    }
    return cnt != 0;
  }
  int relationline(line u) {
    int i, k = 0;
    getline();
    for (i = 0; i < n; i++) {
      if (l[i].segcrossseg(u) == 2) return 1;
      if (l[i].segcrossseg(u) == 1) k = 1;
    }
    if (!k) return 0;
    vector<point> vp;
    for (i = 0; i < n; i++) {
      if (l[i].segcrossseg(u)) {
        if (l[i].parallel(u)) {
          vp.push_back(u.a);
          vp.push_back(u.b);
          vp.push_back(l[i].a);
          vp.push_back(l[i].b);
          continue;
        }
        vp.push_back(l[i].crosspoint(u));
      }
    }
    sort(vp.begin(), vp.end());
    int sz = vp.size();
    for (i = 0; i < sz - 1; i++) {
      point mid = vp[i].add(vp[i + 1]).div(2);
      if (relationpoint(mid) == 1) return 1;
    }
    return 2;
  }
  void convexcut(line u, polygon &po) {
    int i;
    int &top = po.n;
    top = 0;
    for (i = 0; i < n; i++) {
      int d1 = dcmp(p[i].sub(u.a).det(u.b.sub(u.a)));
      int d2 = dcmp(p[(i + 1) % n].sub(u.a).det(u.b.sub(u.a)));
      if (d1 >= 0) po.p[top++] = p[i];
      if (d1 * d2 < 0) po.p[top++] = u.crosspoint(line(p[i], p[(i + 1) % n]));
    }
  }
  double getcircumference() {
    double sum = 0;
    int i;
    for (i = 0; i < n; i++) sum += p[i].distance(p[(i + 1) % n]);
    return sum;
  }
  double getarea() {
    double sum = 0;
    for (int i = 0; i < n; i++) sum += p[i].det(p[(i + 1) % n]);
    return fabs(sum) / 2;
  }
  bool getdir() {
    double sum = 0;
    int i;
    for (i = 0; i < n; i++) sum += p[i].det(p[(i + 1) % n]);
    if (dcmp(sum) > 0) return 1;
    return 0;
  }
  point getbarycentre() {
    point ret(0, 0);
    double area = 0;
    int i;
    for (i = 1; i < n - 1; i++) {
      double tmp = p[i].sub(p[0]).det(p[i + 1].sub(p[0]));
      if (dcmp(tmp) == 0) continue;
      area += tmp;
      ret.x += (p[0].x + p[i].x + p[i + 1].x) / 3 * tmp;
      ret.y += (p[0].y + p[i].y + p[i + 1].y) / 3 * tmp;
    }
    if (dcmp(area)) ret = ret.div(area);
    return ret;
  }
  double areacircle(circle c) {
    int i;
    double ans = 0;
    for (i = 0; i < n; i++) {
      int j = (i + 1) % n;
      if (dcmp(p[j].sub(c.p).det(p[i].sub(c.p))) >= 0)
        ans += c.areatriangle(p[i], p[j]);
      else
        ans -= c.areatriangle(p[i], p[j]);
    }
    return fabs(ans);
  }
  int relationcircle(circle c) {
    getline();
    int i, x = 2;
    if (relationpoint(c.p) != 1) return 0;
    for (i = 0; i < n; i++) {
      if (c.relationseg(l[i]) == 2) return 0;
      if (c.relationseg(l[i]) == 1) x = 1;
    }
    return x;
  }
  void find(int st, point tri[], circle &c) {
    if (!st) c = circle(point(0, 0), -2);
    if (st == 1) c = circle(tri[0], 0);
    if (st == 2)
      c = circle(tri[0].add(tri[1]).div(2), tri[0].distance(tri[1]) / 2.0);
    if (st == 3) c = circle(tri[0], tri[1], tri[2]);
  }
  void solve(int cur, int st, point tri[], circle &c) {
    find(st, tri, c);
    if (st == 3) return;
    int i;
    for (i = 0; i < cur; i++)
      if (dcmp(p[i].distance(c.p) - c.r) > 0) {
        tri[st] = p[i];
        solve(i, st + 1, tri, c);
      }
  }
  circle mincircle() {
    random_shuffle(p, p + n);
    point tri[4];
    circle c;
    solve(n, 0, tri, c);
    return c;
  }
  int circlecover(double r) {
    int ans = 0, i, j;
    vector<pair<double, int> > v;
    for (i = 0; i < n; i++) {
      v.clear();
      for (j = 0; j < n; j++)
        if (i != j) {
          point q = p[i].sub(p[j]);
          double d = q.len();
          if (dcmp(d - 2 * r) <= 0) {
            double arg = atan2(q.y, q.x);
            if (dcmp(arg) < 0) arg += 2 * pi;
            double t = acos(d / (2 * r));
            v.push_back(make_pair(arg - t + 2 * pi, -1));
            v.push_back(make_pair(arg + t + 2 * pi, 1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (j = 0; j < int(v.size()); j++) {
        if (v[j].second == -1)
          ++cur;
        else
          --cur;
        ans = max(ans, cur);
      }
    }
    return ans + 1;
  }
  int pointinpolygon(point q) {
    if (getdir()) reverse(p, p + n);
    if (dcmp(q.sub(p[0]).det(p[n - 1].sub(p[0]))) == 0) {
      if (line(p[n - 1], p[0]).pointonseg(q)) return n - 1;
      return -1;
    }
    int low = 1, high = n - 2, mid;
    while (low <= high) {
      mid = (low + high) >> 1;
      if (dcmp(q.sub(p[0]).det(p[mid].sub(p[0]))) >= 0 &&
          dcmp(q.sub(p[0]).det(p[mid + 1].sub(p[0]))) < 0) {
        polygon c;
        c.p[0] = p[mid];
        c.p[1] = p[mid + 1];
        c.p[2] = p[0];
        c.n = 3;
        if (c.relationpoint(q)) return mid;
        return -1;
      }
      if (dcmp(q.sub(p[0]).det(p[mid].sub(p[0]))) > 0)
        low = mid + 1;
      else
        high = mid - 1;
    }
    return -1;
  }
};
struct polygons {
  vector<polygon> p;
  polygons() { p.clear(); }
  void clear() { p.clear(); }
  void push(polygon q) {
    if (dcmp(q.getarea())) p.push_back(q);
  }
  vector<pair<double, int> > e;
  void ins(point s, point t, point X, int i) {
    double r = fabs(t.x - s.x) > eps ? (X.x - s.x) / (t.x - s.x)
                                     : (X.y - s.y) / (t.y - s.y);
    r = min(r, 1.0);
    r = max(r, 0.0);
    e.push_back(make_pair(r, i));
  }
  double polyareaunion() {
    double ans = 0.0;
    int c0, c1, c2, i, j, k, w;
    for (i = 0; i < int(p.size()); i++)
      if (p[i].getdir() == 0) reverse(p[i].p, p[i].p + p[i].n);
    for (i = 0; i < int(p.size()); i++) {
      for (k = 0; k < p[i].n; k++) {
        point &s = p[i].p[k], &t = p[i].p[(k + 1) % p[i].n];
        if (!dcmp(s.det(t))) continue;
        e.clear();
        e.push_back(make_pair(0.0, 1));
        e.push_back(make_pair(1.0, -1));
        for (j = 0; j < int(p.size()); j++)
          if (i != j) {
            for (w = 0; w < p[j].n; w++) {
              point a = p[j].p[w], b = p[j].p[(w + 1) % p[j].n],
                    c = p[j].p[(w - 1 + p[j].n) % p[j].n];
              c0 = dcmp(t.sub(s).det(c.sub(s)));
              c1 = dcmp(t.sub(s).det(a.sub(s)));
              c2 = dcmp(t.sub(s).det(b.sub(s)));
              if (c1 * c2 < 0)
                ins(s, t, line(s, t).crosspoint(line(a, b)), -c2);
              else if (!c1 && c0 * c2 < 0)
                ins(s, t, a, -c2);
              else if (!c1 && !c2) {
                int c3 = dcmp(t.sub(s).det(p[j].p[(w + 2) % p[j].n].sub(s)));
                int dp = dcmp(t.sub(s).dot(b.sub(a)));
                if (dp && c0)
                  ins(s, t, a, dp > 0 ? c0 * ((j > i) ^ (c0 < 0)) : -(c0 < 0));
                if (dp && c3)
                  ins(s, t, b, dp > 0 ? -c3 * ((j > i) ^ (c3 < 0)) : c3 < 0);
              }
            }
          }
        sort(e.begin(), e.end());
        int ct = 0;
        double tot = 0.0, last;
        for (j = 0; j < int(e.size()); j++) {
          if (ct == 2) tot += e[j].first - last;
          ct += e[j].second;
          last = e[j].first;
        }
        ans += s.det(t) * tot;
      }
    }
    return fabs(ans) * 0.5;
  }
};
const int maxn = 500;
struct circles {
  circle c[maxn];
  double ans[maxn];
  double pre[maxn];
  int n;
  circles() {}
  void add(circle cc) { c[n++] = cc; }
  bool inner(circle x, circle y) {
    if (x.relationcircle(y) != 1) return 0;
    return dcmp(x.r - y.r) <= 0 ? 1 : 0;
  }
  void init_or() {
    int i, j, k = 0;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j])
          if ((c[i] == c[j]) || inner(c[i], c[j])) break;
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  void init_and() {
    int i, j, k = 0;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j])
          if ((c[i] == c[j]) || inner(c[j], c[i])) break;
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  double areaarc(double th, double r) { return 0.5 * sqr(r) * (th - sin(th)); }
  void getarea() {
    int i, j;
    memset(ans, 0, sizeof(ans));
    vector<pair<double, int> > v;
    for (i = 0; i < n; i++) {
      v.clear();
      v.push_back(make_pair(-pi, 1));
      v.push_back(make_pair(pi, -1));
      for (j = 0; j < n; j++)
        if (i != j) {
          point q = c[j].p.sub(c[i].p);
          double ab = q.len(), ac = c[i].r, bc = c[j].r;
          if (dcmp(ab + ac - bc) <= 0) {
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(pi, -1));
            continue;
          }
          if (dcmp(ab + bc - ac) <= 0) continue;
          if (dcmp(ab - ac - bc) > 0) continue;
          double th = atan2(q.y, q.x),
                 fai = acos((ac * ac + ab * ab - bc * bc) / (2.0 * ac * ab));
          double a0 = th - fai;
          if (dcmp(a0 + pi) < 0) a0 += 2 * pi;
          double a1 = th + fai;
          if (dcmp(a1 - pi) > 0) a1 -= 2 * pi;
          if (dcmp(a0 - a1) > 0) {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(pi, -1));
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(a1, -1));
          } else {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(a1, -1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (j = 0; j < int(v.size()); j++) {
        if (cur && dcmp(v[j].first - pre[cur])) {
          ans[cur] += areaarc(v[j].first - pre[cur], c[i].r);
          ans[cur] +=
              0.5 * point(c[i].p.x + c[i].r * cos(pre[cur]),
                          c[i].p.y + c[i].r * sin(pre[cur]))
                        .det(point(c[i].p.x + c[i].r * cos(v[j].first),
                                   c[i].p.y + c[i].r * sin(v[j].first)));
        }
        cur += v[j].second;
        pre[cur] = v[j].first;
      }
    }
    for (i = 1; i <= n; i++) {
      ans[i] -= ans[i + 1];
    }
  }
};
struct halfplane : public line {
  double angle;
  halfplane() {}
  halfplane(point _a, point _b) {
    a = _a;
    b = _b;
  }
  halfplane(line v) {
    a = v.a;
    b = v.b;
  }
  void calcangle() { angle = atan2(b.y - a.y, b.x - a.x); }
  bool operator<(const halfplane &b) const { return angle < b.angle; }
};
struct halfplanes {
  int n;
  halfplane hp[maxp];
  point p[maxp];
  int que[maxp];
  int st, ed;
  void push(halfplane tmp) { hp[n++] = tmp; }
  void unique() {
    int m = 1, i;
    for (i = 1; i < n; i++) {
      if (dcmp(hp[i].angle - hp[i - 1].angle))
        hp[m++] = hp[i];
      else if (dcmp(hp[m - 1].b.sub(hp[m - 1].a).det(hp[i].a.sub(hp[m - 1].a)) >
                    0))
        hp[m - 1] = hp[i];
    }
    n = m;
  }
  bool halfplaneinsert() {
    int i;
    for (i = 0; i < n; i++) hp[i].calcangle();
    sort(hp, hp + n);
    unique();
    que[st = 0] = 0;
    que[ed = 1] = 1;
    p[1] = hp[0].crosspoint(hp[1]);
    for (i = 2; i < n; i++) {
      while (st < ed &&
             dcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a)))) < 0)
        ed--;
      while (st < ed &&
             dcmp((hp[i].b.sub(hp[i].a).det(p[st + 1].sub(hp[i].a)))) < 0)
        st++;
      que[++ed] = i;
      if (hp[i].parallel(hp[que[ed - 1]])) return false;
      p[ed] = hp[i].crosspoint(hp[que[ed - 1]]);
    }
    while (
        st < ed &&
        dcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a))) <
            0)
      ed--;
    while (st < ed && dcmp(hp[que[ed]]
                               .b.sub(hp[que[ed]].a)
                               .det(p[st + 1].sub(hp[que[ed]].a))) < 0)
      st++;
    if (st + 1 >= ed) return false;
    return true;
  }
  void getconvex(polygon &con) {
    p[st] = hp[que[st]].crosspoint(hp[que[ed]]);
    con.n = ed - st + 1;
    int j = st, i = 0;
    for (; j <= ed; i++, j++) con.p[i] = p[j];
  }
};
struct point3 {
  double x, y, z;
  point3() {}
  point3(double _x, double _y, double _z) : x(_x), y(_y), z(_z){};
  void input() { scanf("%lf%lf%lf", &x, &y, &z); }
  void output() { printf("%.2lf %.2lf %.2lf", x, y, z); }
  bool operator==(point3 a) {
    return dcmp(a.x - x) == 0 && dcmp(a.y - y) == 0 && dcmp(a.z - z) == 0;
  }
  bool operator<(point3 a) const {
    return dcmp(a.x - x) == 0 ? dcmp(y - a.y) == 0 ? dcmp(z - a.z) < 0 : y < a.y
                              : x < a.x;
  }
  double len() { return sqrt(len2()); }
  double len2() { return x * x + y * y + z * z; }
  double distance(point3 p) {
    return sqrt((p.x - x) * (p.x - x) + (p.y - y) * (p.y - y) +
                (p.z - z) * (p.z - z));
  }
  point3 add(point3 p) { return point3(x + p.x, y + p.y, z + p.z); }
  point3 sub(point3 p) { return point3(x - p.x, y - p.y, z - p.z); }
  point3 mul(double d) { return point3(x * d, y * d, z * d); }
  point3 div(double d) { return point3(x / d, y / d, z / d); }
  double dot(point3 p) { return x * p.x + y * p.y + z * p.z; }
  point3 det(point3 p) {
    return point3(y * p.z - p.y * z, p.x * z - x * p.z, x * p.y - p.x * y);
  }
  double rad(point3 a, point3 b) {
    point3 p = (*this);
    return acos(a.sub(p).dot(b.sub(p)) / (a.distance(p) * b.distance(p)));
  }
  point3 trunc(double r) {
    r /= len();
    return point3(x * r, y * r, z * r);
  }
};
struct line3 {
  point3 a, b;
  line3() {}
  line3(point3 _a, point3 _b) {
    a = _a;
    b = _b;
  }
  bool operator==(line3 v) { return (a == v.a) && (b == v.b); }
  void input() {
    a.input();
    b.input();
  }
  double length() { return a.distance(b); }
  double dispointtoline(point3 p) {
    return b.sub(a).det(p.sub(a)).len() / a.distance(b);
  }
  double dispointtoseg(point3 p) {
    if (dcmp(p.sub(b).dot(a.sub(b))) < 0 || dcmp(p.sub(a).dot(b.sub(a))) < 0)
      return min(p.distance(a), p.distance(b));
    return dispointtoline(p);
  }
  point3 lineprog(point3 p) {
    return a.add(b.sub(a).trunc(b.sub(a).dot(p.sub(a)) / b.distance(a)));
  }
  point3 rotate(point3 p, double ang) {
    if (dcmp((p.sub(a).det(p.sub(b)).len())) == 0) return p;
    point3 f1 = b.sub(a).det(p.sub(a));
    point3 f2 = b.sub(a).det(f1);
    double len = fabs(a.sub(p).det(b.sub(p)).len() / a.distance(b));
    f1 = f1.trunc(len);
    f2 = f2.trunc(len);
    point3 h = p.add(f2);
    point3 pp = h.add(f1);
    return h.add((p.sub(h)).mul(cos(ang * 1.0)))
        .add((pp.sub(h)).mul(sin(ang * 1.0)));
  }
};
struct plane {
  point3 a, b, c, o;
  plane() {}
  plane(point3 _a, point3 _b, point3 _c) {
    a = _a;
    b = _b;
    c = _c;
    o = pvec();
  }
  plane(double _a, double _b, double _c, double _d) {
    o = point3(_a, _b, _c);
    if (dcmp(_a) != 0)
      a = point3((-_d - _c - _b) / _a, 1, 1);
    else if (dcmp(_b) != 0)
      a = point3(1, (-_d - _c - _a) / _b, 1);
    else if (dcmp(_c) != 0)
      a = point3(1, 1, (-_d - _a - _b) / _c);
  }
  void input() {
    a.input();
    b.input();
    c.input();
    o = pvec();
  }
  point3 pvec() { return b.sub(a).det(c.sub(a)); }
  bool pointonplane(point3 p) { return dcmp(p.sub(a).dot(o)) == 0; }
  double angleplane(plane f) {
    return acos(o.dot(f.o) / (o.len() * f.o.len()));
  }
  double dispoint(point3 p) { return fabs(p.sub(a).dot(o) / o.len()); }
  point3 pttoplane(point3 p) {
    line3 u = line3(p, p.add(o));
    crossline(u, p);
    return p;
  }
  int crossline(line3 u, point3 &p) {
    double x = o.dot(u.b.sub(a));
    double y = o.dot(u.a.sub(a));
    double d = x - y;
    if (dcmp(fabs(d)) == 0) return 0;
    p = u.a.mul(x).sub(u.b.mul(y)).div(d);
    return 1;
  }
  int crossplane(plane f, line3 &u) {
    point3 oo = o.det(f.o);
    point3 v = o.det(oo);
    double d = fabs(f.o.dot(v));
    if (dcmp(d) == 0) return 0;
    point3 q = a.add(v.mul(f.o.dot(f.a.sub(a)) / d));
    u = line3(q, q.add(oo));
    return 1;
  }
};
const int MAXN = 1005;
struct node {
  int x, y, t;
  double p;
  friend bool operator<(node a, node b) { return a.t < b.t; }
  void input() { scanf("%d%d%d%lf", &x, &y, &t, &p); }
} p[MAXN];
double dp[MAXN];
int sqr(int x) { return x * x; }
double dis(int i, int j) {
  return sqrt(sqr(p[i].x - p[j].x) + sqr(p[i].y - p[j].y));
}
int main() {
  int n;
  while (cin >> n) {
    for (int i = 1; i <= n; i++) p[i].input();
    sort(p + 1, p + n + 1);
    memset(dp, 0, sizeof(dp));
    for (int i = 1; i <= n; i++) {
      dp[i] = p[i].p;
      for (int j = 1; j < i; j++)
        if (dis(i, j) + p[j].t <= p[i].t) dp[i] = max(dp[i], dp[j] + p[i].p);
    }
    printf("%.10lf\n", *max_element(dp + 1, dp + n + 1));
  }
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

One warm and sunny day king Copa decided to visit the shooting gallery, located at the Central Park, and try to win the main prize — big pink plush panda. The king is not good at shooting, so he invited you to help him.

The shooting gallery is an infinite vertical plane with Cartesian coordinate system on it. The targets are points on this plane. Each target is described by it's coordinates xi, and yi, by the time of it's appearance ti and by the number pi, which gives the probability that Copa hits this target if he aims at it.

A target appears and disappears instantly, so Copa can hit the target only if at the moment ti his gun sight aimed at (xi, yi). Speed of movement of the gun sight on the plane is equal to 1. Copa knows all the information about the targets beforehand (remember, he is a king!). He wants to play in the optimal way, which maximizes the expected value of the amount of hit targets. He can aim at any target at the moment 0.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — amount of targets in the shooting gallery. Then n lines follow, each describing one target. Each description consists of four numbers xi, yi, ti, pi (where xi, yi, ti — integers,  - 1000 ≤ xi, yi ≤ 1000, 0 ≤ ti ≤ 109, real number pi is given with no more than 6 digits after the decimal point, 0 ≤ pi ≤ 1). No two targets may be at the same point.

Output

Output the maximum expected value of the amount of targets that was shot by the king. Your answer will be accepted if it differs from the correct answer by not more than 10 - 6.

Examples

Input

1
0 0 0 0.5


Output

0.5000000000


Input

2
0 0 0 0.6
5 0 5 0.7


Output

1.3000000000

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const double inf = 1e20;
const double pi = acos(-1.0);
const int maxp = 10001;
int dcmp(double d) {
  if (fabs(d) < eps) return 0;
  return d > eps ? 1 : -1;
}
inline double sqr(double x) { return x * x; }
struct point {
  double x, y;
  point() {}
  point(double _x, double _y) : x(_x), y(_y){};
  void input() { scanf("%lf%lf", &x, &y); }
  void output() { printf("%.2f %.2f\n", x, y); }
  bool operator==(point a) const {
    return dcmp(a.x - x) == 0 && dcmp(a.y - y) == 0;
  }
  bool operator<(point a) const {
    return dcmp(a.x - x) == 0 ? dcmp(y - a.y) < 0 : x < a.x;
  }
  double len() { return hypot(x, y); }
  double len2() { return x * x + y * y; }
  double distance(point p) { return hypot(x - p.x, y - p.y); }
  point add(point p) { return point(x + p.x, y + p.y); }
  point sub(point p) { return point(x - p.x, y - p.y); }
  point mul(double b) { return point(x * b, y * b); }
  point div(double b) { return point(x / b, y / b); }
  double dot(point p) { return x * p.x + y * p.y; }
  double det(point p) { return x * p.y - y * p.x; }
  double rad(point a, point b) {
    point p = *this;
    return fabs(atan2(fabs(a.sub(p).det(b.sub(p))), a.sub(p).dot(b.sub(p))));
  }
  point trunc(double r) {
    double l = len();
    if (!dcmp(l)) return *this;
    r /= l;
    return point(x * r, y * r);
  }
  point rotleft() { return point(-y, x); }
  point rotright() { return point(y, -x); }
  point rotate(point p, double angle) {
    point v = this->sub(p);
    double c = cos(angle), s = sin(angle);
    return point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
struct line {
  point a, b;
  line() {}
  line(point _a, point _b) {
    a = _a;
    b = _b;
  }
  bool operator==(line v) { return (a == v.a) && (b == v.b); }
  line(point p, double angle) {
    a = p;
    if (dcmp(angle - pi / 2) == 0) {
      b = a.add(point(0, 1));
    } else {
      b = a.add(point(1, tan(angle)));
    }
  }
  line(double _a, double _b, double _c) {
    if (dcmp(_a) == 0) {
      a = point(0, -_c / _b);
      b = point(1, -_c / _b);
    } else if (dcmp(_b) == 0) {
      a = point(-_c / _a, 0);
      b = point(-_c / _a, 1);
    } else {
      a = point(0, -_c / _b);
      b = point(1, (-_c - _a) / _b);
    }
  }
  void input() {
    a.input();
    b.input();
  }
  void adjust() {
    if (b < a) swap(a, b);
  }
  double length() { return a.distance(b); }
  double angle() {
    double k = atan2(b.y - a.y, b.x - a.x);
    if (dcmp(k) < 0) k += pi;
    if (dcmp(k - pi) == 0) k -= pi;
    return k;
  }
  int relation(point p) {
    int c = dcmp(p.sub(a).det(b.sub(a)));
    if (c < 0) return 1;
    if (c > 0) return 2;
    return 3;
  }
  bool pointonseg(point p) {
    return dcmp(p.sub(a).det(b.sub(a))) == 0 &&
           dcmp(p.sub(a).dot(p.sub(b))) <= 0;
  }
  bool parallel(line v) { return dcmp(b.sub(a).det(v.b.sub(v.a))) == 0; }
  int segcrossseg(line v) {
    int d1 = dcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dcmp(b.sub(a).det(v.b.sub(a)));
    int d3 = dcmp(v.b.sub(v.a).det(a.sub(v.a)));
    int d4 = dcmp(v.b.sub(v.a).det(b.sub(v.a)));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
    return ((d1 == 0 && dcmp(v.a.sub(a).dot(v.a.sub(b))) <= 0) ||
            (d2 == 0 && dcmp(v.b.sub(a).dot(v.b.sub(b))) <= 0) ||
            (d3 == 0 && dcmp(a.sub(v.a).dot(a.sub(v.b))) <= 0) ||
            (d4 == 0 && dcmp(b.sub(v.a).dot(b.sub(v.b))) <= 0));
  }
  int linecrossseg(line v) {
    int d1 = dcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dcmp(b.sub(a).det(v.b.sub(a)));
    if ((d1 ^ d2) == -2) return 2;
    return (d1 == 0 || d2 == 0);
  }
  int linecrossline(line v) {
    if ((*this).parallel(v)) return v.relation(a) == 3;
    return 2;
  }
  point crosspoint(line v) {
    double a1 = v.b.sub(v.a).det(a.sub(v.a));
    double a2 = v.b.sub(v.a).det(b.sub(v.a));
    return point((a.x * a2 - b.x * a1) / (a2 - a1),
                 (a.y * a2 - b.y * a1) / (a2 - a1));
  }
  double dispointtoline(point p) {
    return fabs(p.sub(a).det(b.sub(a))) / length();
  }
  double dispointtoseg(point p) {
    if (dcmp(p.sub(b).dot(a.sub(b))) < 0 || dcmp(p.sub(a).dot(b.sub(a))) < 0)
      return min(p.distance(a), p.distance(b));
    return dispointtoline(p);
  }
  point lineprog(point p) {
    return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a)) / b.sub(a).len2()));
  }
  point symmetrypoint(point p) {
    point q = lineprog(p);
    return point(2 * q.x - p.x, 2 * q.y - p.y);
  }
};
struct circle {
  point p;
  double r;
  circle() {}
  circle(point _p, double _r) : p(_p), r(_r){};
  circle(double x, double y, double _r) : p(point(x, y)), r(_r){};
  circle(point a, point b, point c) {
    p = line(a.add(b).div(2), a.add(b).div(2).add(b.sub(a).rotleft()))
            .crosspoint(
                line(c.add(b).div(2), c.add(b).div(2).add(b.sub(c).rotleft())));
    r = p.distance(a);
  }
  circle(point a, point b, point c, bool t) {
    line u, v;
    double m = atan2(b.y - a.y, b.x - a.x), n = atan2(c.y - a.y, c.x - a.x);
    u.a = a;
    u.b = u.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    v.a = b;
    m = atan2(a.y - b.y, a.x - b.x), n = atan2(c.y - b.y, c.x - b.x);
    v.b = v.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    p = u.crosspoint(v);
    r = line(a, b).dispointtoseg(p);
  }
  void input() {
    p.input();
    scanf("%lf", &r);
  }
  void output() { printf("%.2lf %.2lf %.2lf\n", p.x, p.y, r); }
  bool operator==(circle v) { return ((p == v.p) && dcmp(r - v.r) == 0); }
  bool operator<(circle v) const {
    return ((p < v.p) || ((p == v.p) && dcmp(r - v.r) < 0));
  }
  double area() { return pi * sqr(r); }
  double circumference() { return 2 * pi * r; }
  int relation(point b) {
    double dst = b.distance(p);
    if (dcmp(dst - r) < 0) return 2;
    if (dcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationseg(line v) {
    double dst = v.dispointtoseg(p);
    if (dcmp(dst - r) < 0) return 2;
    if (dcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationline(line v) {
    double dst = v.dispointtoline(p);
    if (dcmp(dst - r) < 0) return 2;
    if (dcmp(dst - r) == 0) return 1;
    return 0;
  }
  int getcircle(point a, point b, double r, circle &c1, circle &c2) {
    circle x(a, r), y(b, r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r;
    return t;
  }
  int getcircle(line u, point q, double r1, circle &c1, circle &c2) {
    double dis = u.dispointtoline(q);
    if (dcmp(dis - r1 * 2) > 0) return 0;
    if (dcmp(dis) == 0) {
      c1.p = q.add(u.b.sub(u.a).rotleft().trunc(r1));
      c2.p = q.add(u.b.sub(u.a).rotright().trunc(r1));
      c1.r = c2.r = r1;
      return 2;
    }
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    circle cc = circle(q, r1);
    point p1, p2;
    if (!cc.pointcrossline(u1, p1, p2)) cc.pointcrossline(u2, p1, p2);
    c1 = circle(p1, r1);
    if (p1 == p2) {
      c2 = c1;
      return 1;
    }
    c2 = circle(p2, r1);
    return 2;
  }
  int getcircle(line u, line v, double r1, circle &c1, circle &c2, circle &c3,
                circle &c4) {
    if (u.parallel(v)) return 0;
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    line v1 = line(v.a.add(v.b.sub(v.a).rotleft().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotleft().trunc(r1)));
    line v2 = line(v.a.add(v.b.sub(v.a).rotright().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotright().trunc(r1)));
    c1.r = c2.r = c3.r = c4.r = r1;
    c1.p = u1.crosspoint(v1);
    c2.p = u1.crosspoint(v2);
    c3.p = u2.crosspoint(v1);
    c4.p = u2.crosspoint(v2);
    return 4;
  }
  int getcircle(circle cx, circle cy, double r1, circle &c1, circle &c2) {
    circle x(cx.p, r1 + cx.r), y(cy.p, r1 + cy.r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r1;
    return t;
  }
  int pointcrossline(line v, point &p1, point &p2) {
    if (!(*this).relationline(v)) return 0;
    point a = v.lineprog(p);
    double d = v.dispointtoline(p);
    d = sqrt(r * r - d * d);
    if (dcmp(d) == 0) {
      p1 = a;
      p2 = a;
      return 1;
    }
    p1 = a.sub(v.b.sub(v.a).trunc(d));
    p2 = a.add(v.b.sub(v.a).trunc(d));
    return 2;
  }
  int relationcircle(circle v) {
    double d = p.distance(v.p);
    if (dcmp(d - r - v.r) > 0) return 5;
    if (dcmp(d - r - v.r) == 0) return 4;
    double l = fabs(r - v.r);
    if (dcmp(d - r - v.r) < 0 && dcmp(d - l) > 0) return 3;
    if (dcmp(d - l) == 0) return 2;
    if (dcmp(d - l) < 0) return 1;
  }
  int pointcrosscircle(circle v, point &p1, point &p2) {
    int rel = relationcircle(v);
    if (rel == 1 || rel == 5) return 0;
    double d = p.distance(v.p);
    double l = (d + (sqr(r) - sqr(v.r)) / d) / 2;
    double h = sqrt(sqr(r) - sqr(l));
    p1 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotleft().trunc(h)));
    p2 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotright().trunc(h)));
    if (rel == 2 || rel == 4) return 1;
    return 2;
  }
  int tangentline(point q, line &u, line &v) {
    int x = relation(q);
    if (x == 2) return 0;
    if (x == 1) {
      u = line(q, q.add(q.sub(p).rotleft()));
      v = u;
      return 1;
    }
    double d = p.distance(q);
    double l = sqr(r) / d;
    double h = sqrt(sqr(r) - sqr(l));
    u = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotleft().trunc(h))));
    v = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotright().trunc(h))));
    return 2;
  }
  double areacircle(circle v) {
    int rel = relationcircle(v);
    if (rel >= 4) return 0.0;
    if (rel <= 2) return min(area(), v.area());
    double d = p.distance(v.p);
    double hf = (r + v.r + d) / 2.0;
    double ss = 2 * sqrt(hf * (hf - r) * (hf - v.r) * (hf - d));
    double a1 = acos((r * r + d * d - v.r * v.r) / (2.0 * r * d));
    a1 = a1 * r * r;
    double a2 = acos((v.r * v.r + d * d - r * r) / (2.0 * v.r * d));
    a2 = a2 * v.r * v.r;
    return a1 + a2 - ss;
  }
  double areatriangle(point a, point b) {
    if (dcmp(p.sub(a).det(p.sub(b)) == 0)) return 0.0;
    point q[5];
    int len = 0;
    q[len++] = a;
    line l(a, b);
    point p1, p2;
    if (pointcrossline(l, q[1], q[2]) == 2) {
      if (dcmp(a.sub(q[1]).dot(b.sub(q[1]))) < 0) q[len++] = q[1];
      if (dcmp(a.sub(q[2]).dot(b.sub(q[2]))) < 0) q[len++] = q[2];
    }
    q[len++] = b;
    if (len == 4 && (dcmp(q[0].sub(q[1]).dot(q[2].sub(q[1]))) > 0))
      swap(q[1], q[2]);
    double res = 0;
    int i;
    for (i = 0; i < len - 1; i++) {
      if (relation(q[i]) == 0 || relation(q[i + 1]) == 0) {
        double arg = p.rad(q[i], q[i + 1]);
        res += r * r * arg / 2.0;
      } else
        res += fabs(q[i].sub(p).det(q[i + 1].sub(p)) / 2.0);
    }
    return res;
  }
};
struct polygon {
  int n;
  point p[maxp];
  line l[maxp];
  void input() {
    for (int i = 0; i < n; i++) p[i].input();
  }
  void add(point q) { p[n++] = q; }
  void getline() {
    for (int i = 0; i < n; i++) l[i] = line(p[i], p[(i + 1) % n]);
  }
  struct cmp {
    point p;
    cmp(const point &p0) { p = p0; }
    bool operator()(const point &aa, const point &bb) {
      point a = aa, b = bb;
      int d = dcmp(a.sub(p).det(b.sub(p)));
      if (d == 0) return dcmp(a.distance(p) - b.distance(p)) < 0;
      return d > 0;
    }
  };
  void norm() {
    point mi = p[0];
    for (int i = 1; i < n; i++) mi = min(mi, p[i]);
    sort(p, p + n, cmp(mi));
  }
  void getconvex(polygon &convex) {
    int i;
    sort(p, p + n);
    convex.n = n;
    for (i = 0; i < min(n, 2); i++) convex.p[i] = p[i];
    if (n <= 2) return;
    int &top = convex.n;
    top = 1;
    for (i = 2; i < n; i++) {
      while (top &&
             convex.p[top].sub(p[i]).det(convex.p[top - 1].sub(p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
    int temp = top;
    convex.p[++top] = p[n - 2];
    for (i = n - 3; i >= 0; i--) {
      while (top != temp &&
             convex.p[top].sub(p[i]).det(convex.p[top - 1].sub(p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
  }
  bool isconvex() {
    bool s[3];
    memset(s, 0, sizeof(s));
    int i, j, k;
    for (i = 0; i < n; i++) {
      j = (i + 1) % n;
      k = (j + 1) % n;
      s[dcmp(p[j].sub(p[i]).det(p[k].sub(p[i]))) + 1] = 1;
      if (s[0] && s[2]) return 0;
    }
    return 1;
  }
  int relationpoint(point q) {
    int i, j;
    for (i = 0; i < n; i++)
      if (p[i] == q) return 3;
    getline();
    for (i = 0; i < n; i++)
      if (l[i].pointonseg(q)) return 2;
    int cnt = 0;
    for (i = 0; i < n; i++) {
      j = (i + 1) % n;
      int k = dcmp(q.sub(p[j]).det(p[i].sub(p[j])));
      int u = dcmp(p[i].y - q.y);
      int v = dcmp(p[j].y - q.y);
      if (k > 0 && u < 0 && v >= 0) cnt++;
      if (k < 0 && v < 0 && u >= 0) cnt--;
    }
    return cnt != 0;
  }
  int relationline(line u) {
    int i, k = 0;
    getline();
    for (i = 0; i < n; i++) {
      if (l[i].segcrossseg(u) == 2) return 1;
      if (l[i].segcrossseg(u) == 1) k = 1;
    }
    if (!k) return 0;
    vector<point> vp;
    for (i = 0; i < n; i++) {
      if (l[i].segcrossseg(u)) {
        if (l[i].parallel(u)) {
          vp.push_back(u.a);
          vp.push_back(u.b);
          vp.push_back(l[i].a);
          vp.push_back(l[i].b);
          continue;
        }
        vp.push_back(l[i].crosspoint(u));
      }
    }
    sort(vp.begin(), vp.end());
    int sz = vp.size();
    for (i = 0; i < sz - 1; i++) {
      point mid = vp[i].add(vp[i + 1]).div(2);
      if (relationpoint(mid) == 1) return 1;
    }
    return 2;
  }
  void convexcut(line u, polygon &po) {
    int i;
    int &top = po.n;
    top = 0;
    for (i = 0; i < n; i++) {
      int d1 = dcmp(p[i].sub(u.a).det(u.b.sub(u.a)));
      int d2 = dcmp(p[(i + 1) % n].sub(u.a).det(u.b.sub(u.a)));
      if (d1 >= 0) po.p[top++] = p[i];
      if (d1 * d2 < 0) po.p[top++] = u.crosspoint(line(p[i], p[(i + 1) % n]));
    }
  }
  double getcircumference() {
    double sum = 0;
    int i;
    for (i = 0; i < n; i++) sum += p[i].distance(p[(i + 1) % n]);
    return sum;
  }
  double getarea() {
    double sum = 0;
    for (int i = 0; i < n; i++) sum += p[i].det(p[(i + 1) % n]);
    return fabs(sum) / 2;
  }
  bool getdir() {
    double sum = 0;
    int i;
    for (i = 0; i < n; i++) sum += p[i].det(p[(i + 1) % n]);
    if (dcmp(sum) > 0) return 1;
    return 0;
  }
  point getbarycentre() {
    point ret(0, 0);
    double area = 0;
    int i;
    for (i = 1; i < n - 1; i++) {
      double tmp = p[i].sub(p[0]).det(p[i + 1].sub(p[0]));
      if (dcmp(tmp) == 0) continue;
      area += tmp;
      ret.x += (p[0].x + p[i].x + p[i + 1].x) / 3 * tmp;
      ret.y += (p[0].y + p[i].y + p[i + 1].y) / 3 * tmp;
    }
    if (dcmp(area)) ret = ret.div(area);
    return ret;
  }
  double areacircle(circle c) {
    int i;
    double ans = 0;
    for (i = 0; i < n; i++) {
      int j = (i + 1) % n;
      if (dcmp(p[j].sub(c.p).det(p[i].sub(c.p))) >= 0)
        ans += c.areatriangle(p[i], p[j]);
      else
        ans -= c.areatriangle(p[i], p[j]);
    }
    return fabs(ans);
  }
  int relationcircle(circle c) {
    getline();
    int i, x = 2;
    if (relationpoint(c.p) != 1) return 0;
    for (i = 0; i < n; i++) {
      if (c.relationseg(l[i]) == 2) return 0;
      if (c.relationseg(l[i]) == 1) x = 1;
    }
    return x;
  }
  void find(int st, point tri[], circle &c) {
    if (!st) c = circle(point(0, 0), -2);
    if (st == 1) c = circle(tri[0], 0);
    if (st == 2)
      c = circle(tri[0].add(tri[1]).div(2), tri[0].distance(tri[1]) / 2.0);
    if (st == 3) c = circle(tri[0], tri[1], tri[2]);
  }
  void solve(int cur, int st, point tri[], circle &c) {
    find(st, tri, c);
    if (st == 3) return;
    int i;
    for (i = 0; i < cur; i++)
      if (dcmp(p[i].distance(c.p) - c.r) > 0) {
        tri[st] = p[i];
        solve(i, st + 1, tri, c);
      }
  }
  circle mincircle() {
    random_shuffle(p, p + n);
    point tri[4];
    circle c;
    solve(n, 0, tri, c);
    return c;
  }
  int circlecover(double r) {
    int ans = 0, i, j;
    vector<pair<double, int> > v;
    for (i = 0; i < n; i++) {
      v.clear();
      for (j = 0; j < n; j++)
        if (i != j) {
          point q = p[i].sub(p[j]);
          double d = q.len();
          if (dcmp(d - 2 * r) <= 0) {
            double arg = atan2(q.y, q.x);
            if (dcmp(arg) < 0) arg += 2 * pi;
            double t = acos(d / (2 * r));
            v.push_back(make_pair(arg - t + 2 * pi, -1));
            v.push_back(make_pair(arg + t + 2 * pi, 1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (j = 0; j < int(v.size()); j++) {
        if (v[j].second == -1)
          ++cur;
        else
          --cur;
        ans = max(ans, cur);
      }
    }
    return ans + 1;
  }
  int pointinpolygon(point q) {
    if (getdir()) reverse(p, p + n);
    if (dcmp(q.sub(p[0]).det(p[n - 1].sub(p[0]))) == 0) {
      if (line(p[n - 1], p[0]).pointonseg(q)) return n - 1;
      return -1;
    }
    int low = 1, high = n - 2, mid;
    while (low <= high) {
      mid = (low + high) >> 1;
      if (dcmp(q.sub(p[0]).det(p[mid].sub(p[0]))) >= 0 &&
          dcmp(q.sub(p[0]).det(p[mid + 1].sub(p[0]))) < 0) {
        polygon c;
        c.p[0] = p[mid];
        c.p[1] = p[mid + 1];
        c.p[2] = p[0];
        c.n = 3;
        if (c.relationpoint(q)) return mid;
        return -1;
      }
      if (dcmp(q.sub(p[0]).det(p[mid].sub(p[0]))) > 0)
        low = mid + 1;
      else
        high = mid - 1;
    }
    return -1;
  }
};
struct polygons {
  vector<polygon> p;
  polygons() { p.clear(); }
  void clear() { p.clear(); }
  void push(polygon q) {
    if (dcmp(q.getarea())) p.push_back(q);
  }
  vector<pair<double, int> > e;
  void ins(point s, point t, point X, int i) {
    double r = fabs(t.x - s.x) > eps ? (X.x - s.x) / (t.x - s.x)
                                     : (X.y - s.y) / (t.y - s.y);
    r = min(r, 1.0);
    r = max(r, 0.0);
    e.push_back(make_pair(r, i));
  }
  double polyareaunion() {
    double ans = 0.0;
    int c0, c1, c2, i, j, k, w;
    for (i = 0; i < int(p.size()); i++)
      if (p[i].getdir() == 0) reverse(p[i].p, p[i].p + p[i].n);
    for (i = 0; i < int(p.size()); i++) {
      for (k = 0; k < p[i].n; k++) {
        point &s = p[i].p[k], &t = p[i].p[(k + 1) % p[i].n];
        if (!dcmp(s.det(t))) continue;
        e.clear();
        e.push_back(make_pair(0.0, 1));
        e.push_back(make_pair(1.0, -1));
        for (j = 0; j < int(p.size()); j++)
          if (i != j) {
            for (w = 0; w < p[j].n; w++) {
              point a = p[j].p[w], b = p[j].p[(w + 1) % p[j].n],
                    c = p[j].p[(w - 1 + p[j].n) % p[j].n];
              c0 = dcmp(t.sub(s).det(c.sub(s)));
              c1 = dcmp(t.sub(s).det(a.sub(s)));
              c2 = dcmp(t.sub(s).det(b.sub(s)));
              if (c1 * c2 < 0)
                ins(s, t, line(s, t).crosspoint(line(a, b)), -c2);
              else if (!c1 && c0 * c2 < 0)
                ins(s, t, a, -c2);
              else if (!c1 && !c2) {
                int c3 = dcmp(t.sub(s).det(p[j].p[(w + 2) % p[j].n].sub(s)));
                int dp = dcmp(t.sub(s).dot(b.sub(a)));
                if (dp && c0)
                  ins(s, t, a, dp > 0 ? c0 * ((j > i) ^ (c0 < 0)) : -(c0 < 0));
                if (dp && c3)
                  ins(s, t, b, dp > 0 ? -c3 * ((j > i) ^ (c3 < 0)) : c3 < 0);
              }
            }
          }
        sort(e.begin(), e.end());
        int ct = 0;
        double tot = 0.0, last;
        for (j = 0; j < int(e.size()); j++) {
          if (ct == 2) tot += e[j].first - last;
          ct += e[j].second;
          last = e[j].first;
        }
        ans += s.det(t) * tot;
      }
    }
    return fabs(ans) * 0.5;
  }
};
const int maxn = 500;
struct circles {
  circle c[maxn];
  double ans[maxn];
  double pre[maxn];
  int n;
  circles() {}
  void add(circle cc) { c[n++] = cc; }
  bool inner(circle x, circle y) {
    if (x.relationcircle(y) != 1) return 0;
    return dcmp(x.r - y.r) <= 0 ? 1 : 0;
  }
  void init_or() {
    int i, j, k = 0;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j])
          if ((c[i] == c[j]) || inner(c[i], c[j])) break;
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  void init_and() {
    int i, j, k = 0;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j])
          if ((c[i] == c[j]) || inner(c[j], c[i])) break;
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  double areaarc(double th, double r) { return 0.5 * sqr(r) * (th - sin(th)); }
  void getarea() {
    int i, j;
    memset(ans, 0, sizeof(ans));
    vector<pair<double, int> > v;
    for (i = 0; i < n; i++) {
      v.clear();
      v.push_back(make_pair(-pi, 1));
      v.push_back(make_pair(pi, -1));
      for (j = 0; j < n; j++)
        if (i != j) {
          point q = c[j].p.sub(c[i].p);
          double ab = q.len(), ac = c[i].r, bc = c[j].r;
          if (dcmp(ab + ac - bc) <= 0) {
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(pi, -1));
            continue;
          }
          if (dcmp(ab + bc - ac) <= 0) continue;
          if (dcmp(ab - ac - bc) > 0) continue;
          double th = atan2(q.y, q.x),
                 fai = acos((ac * ac + ab * ab - bc * bc) / (2.0 * ac * ab));
          double a0 = th - fai;
          if (dcmp(a0 + pi) < 0) a0 += 2 * pi;
          double a1 = th + fai;
          if (dcmp(a1 - pi) > 0) a1 -= 2 * pi;
          if (dcmp(a0 - a1) > 0) {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(pi, -1));
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(a1, -1));
          } else {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(a1, -1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (j = 0; j < int(v.size()); j++) {
        if (cur && dcmp(v[j].first - pre[cur])) {
          ans[cur] += areaarc(v[j].first - pre[cur], c[i].r);
          ans[cur] +=
              0.5 * point(c[i].p.x + c[i].r * cos(pre[cur]),
                          c[i].p.y + c[i].r * sin(pre[cur]))
                        .det(point(c[i].p.x + c[i].r * cos(v[j].first),
                                   c[i].p.y + c[i].r * sin(v[j].first)));
        }
        cur += v[j].second;
        pre[cur] = v[j].first;
      }
    }
    for (i = 1; i <= n; i++) {
      ans[i] -= ans[i + 1];
    }
  }
};
struct halfplane : public line {
  double angle;
  halfplane() {}
  halfplane(point _a, point _b) {
    a = _a;
    b = _b;
  }
  halfplane(line v) {
    a = v.a;
    b = v.b;
  }
  void calcangle() { angle = atan2(b.y - a.y, b.x - a.x); }
  bool operator<(const halfplane &b) const { return angle < b.angle; }
};
struct halfplanes {
  int n;
  halfplane hp[maxp];
  point p[maxp];
  int que[maxp];
  int st, ed;
  void push(halfplane tmp) { hp[n++] = tmp; }
  void unique() {
    int m = 1, i;
    for (i = 1; i < n; i++) {
      if (dcmp(hp[i].angle - hp[i - 1].angle))
        hp[m++] = hp[i];
      else if (dcmp(hp[m - 1].b.sub(hp[m - 1].a).det(hp[i].a.sub(hp[m - 1].a)) >
                    0))
        hp[m - 1] = hp[i];
    }
    n = m;
  }
  bool halfplaneinsert() {
    int i;
    for (i = 0; i < n; i++) hp[i].calcangle();
    sort(hp, hp + n);
    unique();
    que[st = 0] = 0;
    que[ed = 1] = 1;
    p[1] = hp[0].crosspoint(hp[1]);
    for (i = 2; i < n; i++) {
      while (st < ed &&
             dcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a)))) < 0)
        ed--;
      while (st < ed &&
             dcmp((hp[i].b.sub(hp[i].a).det(p[st + 1].sub(hp[i].a)))) < 0)
        st++;
      que[++ed] = i;
      if (hp[i].parallel(hp[que[ed - 1]])) return false;
      p[ed] = hp[i].crosspoint(hp[que[ed - 1]]);
    }
    while (
        st < ed &&
        dcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a))) <
            0)
      ed--;
    while (st < ed && dcmp(hp[que[ed]]
                               .b.sub(hp[que[ed]].a)
                               .det(p[st + 1].sub(hp[que[ed]].a))) < 0)
      st++;
    if (st + 1 >= ed) return false;
    return true;
  }
  void getconvex(polygon &con) {
    p[st] = hp[que[st]].crosspoint(hp[que[ed]]);
    con.n = ed - st + 1;
    int j = st, i = 0;
    for (; j <= ed; i++, j++) con.p[i] = p[j];
  }
};
struct point3 {
  double x, y, z;
  point3() {}
  point3(double _x, double _y, double _z) : x(_x), y(_y), z(_z){};
  void input() { scanf("%lf%lf%lf", &x, &y, &z); }
  void output() { printf("%.2lf %.2lf %.2lf", x, y, z); }
  bool operator==(point3 a) {
    return dcmp(a.x - x) == 0 && dcmp(a.y - y) == 0 && dcmp(a.z - z) == 0;
  }
  bool operator<(point3 a) const {
    return dcmp(a.x - x) == 0 ? dcmp(y - a.y) == 0 ? dcmp(z - a.z) < 0 : y < a.y
                              : x < a.x;
  }
  double len() { return sqrt(len2()); }
  double len2() { return x * x + y * y + z * z; }
  double distance(point3 p) {
    return sqrt((p.x - x) * (p.x - x) + (p.y - y) * (p.y - y) +
                (p.z - z) * (p.z - z));
  }
  point3 add(point3 p) { return point3(x + p.x, y + p.y, z + p.z); }
  point3 sub(point3 p) { return point3(x - p.x, y - p.y, z - p.z); }
  point3 mul(double d) { return point3(x * d, y * d, z * d); }
  point3 div(double d) { return point3(x / d, y / d, z / d); }
  double dot(point3 p) { return x * p.x + y * p.y + z * p.z; }
  point3 det(point3 p) {
    return point3(y * p.z - p.y * z, p.x * z - x * p.z, x * p.y - p.x * y);
  }
  double rad(point3 a, point3 b) {
    point3 p = (*this);
    return acos(a.sub(p).dot(b.sub(p)) / (a.distance(p) * b.distance(p)));
  }
  point3 trunc(double r) {
    r /= len();
    return point3(x * r, y * r, z * r);
  }
};
struct line3 {
  point3 a, b;
  line3() {}
  line3(point3 _a, point3 _b) {
    a = _a;
    b = _b;
  }
  bool operator==(line3 v) { return (a == v.a) && (b == v.b); }
  void input() {
    a.input();
    b.input();
  }
  double length() { return a.distance(b); }
  double dispointtoline(point3 p) {
    return b.sub(a).det(p.sub(a)).len() / a.distance(b);
  }
  double dispointtoseg(point3 p) {
    if (dcmp(p.sub(b).dot(a.sub(b))) < 0 || dcmp(p.sub(a).dot(b.sub(a))) < 0)
      return min(p.distance(a), p.distance(b));
    return dispointtoline(p);
  }
  point3 lineprog(point3 p) {
    return a.add(b.sub(a).trunc(b.sub(a).dot(p.sub(a)) / b.distance(a)));
  }
  point3 rotate(point3 p, double ang) {
    if (dcmp((p.sub(a).det(p.sub(b)).len())) == 0) return p;
    point3 f1 = b.sub(a).det(p.sub(a));
    point3 f2 = b.sub(a).det(f1);
    double len = fabs(a.sub(p).det(b.sub(p)).len() / a.distance(b));
    f1 = f1.trunc(len);
    f2 = f2.trunc(len);
    point3 h = p.add(f2);
    point3 pp = h.add(f1);
    return h.add((p.sub(h)).mul(cos(ang * 1.0)))
        .add((pp.sub(h)).mul(sin(ang * 1.0)));
  }
};
struct plane {
  point3 a, b, c, o;
  plane() {}
  plane(point3 _a, point3 _b, point3 _c) {
    a = _a;
    b = _b;
    c = _c;
    o = pvec();
  }
  plane(double _a, double _b, double _c, double _d) {
    o = point3(_a, _b, _c);
    if (dcmp(_a) != 0)
      a = point3((-_d - _c - _b) / _a, 1, 1);
    else if (dcmp(_b) != 0)
      a = point3(1, (-_d - _c - _a) / _b, 1);
    else if (dcmp(_c) != 0)
      a = point3(1, 1, (-_d - _a - _b) / _c);
  }
  void input() {
    a.input();
    b.input();
    c.input();
    o = pvec();
  }
  point3 pvec() { return b.sub(a).det(c.sub(a)); }
  bool pointonplane(point3 p) { return dcmp(p.sub(a).dot(o)) == 0; }
  double angleplane(plane f) {
    return acos(o.dot(f.o) / (o.len() * f.o.len()));
  }
  double dispoint(point3 p) { return fabs(p.sub(a).dot(o) / o.len()); }
  point3 pttoplane(point3 p) {
    line3 u = line3(p, p.add(o));
    crossline(u, p);
    return p;
  }
  int crossline(line3 u, point3 &p) {
    double x = o.dot(u.b.sub(a));
    double y = o.dot(u.a.sub(a));
    double d = x - y;
    if (dcmp(fabs(d)) == 0) return 0;
    p = u.a.mul(x).sub(u.b.mul(y)).div(d);
    return 1;
  }
  int crossplane(plane f, line3 &u) {
    point3 oo = o.det(f.o);
    point3 v = o.det(oo);
    double d = fabs(f.o.dot(v));
    if (dcmp(d) == 0) return 0;
    point3 q = a.add(v.mul(f.o.dot(f.a.sub(a)) / d));
    u = line3(q, q.add(oo));
    return 1;
  }
};
const int MAXN = 1005;
struct node {
  int x, y, t;
  double p;
  friend bool operator<(node a, node b) { return a.t < b.t; }
  void input() { scanf("%d%d%d%lf", &x, &y, &t, &p); }
} p[MAXN];
double dp[MAXN];
int sqr(int x) { return x * x; }
double dis(int i, int j) {
  return sqrt(sqr(p[i].x - p[j].x) + sqr(p[i].y - p[j].y));
}
int main() {
  int n;
  while (cin >> n) {
    for (int i = 1; i <= n; i++) p[i].input();
    sort(p + 1, p + n + 1);
    memset(dp, 0, sizeof(dp));
    for (int i = 1; i <= n; i++) {
      dp[i] = p[i].p;
      for (int j = 1; j < i; j++)
        if (dis(i, j) + p[j].t <= p[i].t) dp[i] = max(dp[i], dp[j] + p[i].p);
    }
    printf("%.10lf\n", *max_element(dp + 1, dp + n + 1));
  }
  return 0;
}

```