#include <bits/stdc++.h>
using namespace std;
template <typename T1, typename T2>
inline void chmin(T1 &a, T2 b) {
  if (a > b) a = b;
}
template <typename T1, typename T2>
inline void chmax(T1 &a, T2 b) {
  if (a < b) a = b;
}
using Int = long long;
const char newl = '\n';
const long double PI = asinl(1) * 2;
static const int CCW_COUNTER_CLOCKWISE = 1;
static const int CCW_CLOCKWISE = -1;
static const int CCW_ONLINE_BACK = 2;
static const int CCW_ONLINE_FRONT = -2;
static const int CCW_ON_SEGMENT = 0;
static const int ICC_SEPERATE = 4;
static const int ICC_CIRCUMSCRIBE = 3;
static const int ICC_INTERSECT = 2;
static const int ICC_INSCRIBE = 1;
static const int ICC_CONTAIN = 0;
struct Point {
  long double x, y;
  Point() {}
  Point(long double x, long double y) : x(x), y(y) {}
  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(long double k) { return Point(x * k, y * k); }
  Point operator/(long double k) { return Point(x / k, y / k); }
  long double norm() { return x * x + y * y; }
  long double abs() { return sqrt(norm()); }
  bool operator<(const Point &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const Point &p) const {
    return fabs(x - p.x) < (1e-10) && fabs(y - p.y) < (1e-10);
  }
};
struct EndPoint {
  Point p;
  int seg, st;
  EndPoint() {}
  EndPoint(Point p, int seg, int st) : p(p), seg(seg), st(st) {}
  bool operator<(const EndPoint &ep) const {
    if (p.y == ep.p.y) return st < ep.st;
    return p.y < ep.p.y;
  }
};
istream &operator>>(istream &is, Point &p) {
  is >> p.x >> p.y;
  return is;
}
ostream &operator<<(ostream &os, Point p) {
  os << fixed << setprecision(12) << p.x << " " << p.y;
  return os;
}
bool sort_x(Point a, Point b) { return a.x != b.x ? a.x < b.x : a.y < b.y; }
bool sort_y(Point a, Point b) { return a.y != b.y ? a.y < b.y : a.x < b.x; }
istream &operator>>(istream &is, vector<Point> &p) {
  for (int i = 0; i < (int)p.size(); i++) is >> p[i];
  return is;
}
struct Segment {
  Point p1, p2;
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};
istream &operator>>(istream &is, Segment &s) {
  is >> s.p1 >> s.p2;
  return is;
}
struct Circle {
  Point c;
  long double r;
  Circle() {}
  Circle(Point c, long double r) : c(c), r(r) {}
};
istream &operator>>(istream &is, Circle &c) {
  is >> c.c >> c.r;
  return is;
}
long double norm(Point a) { return a.x * a.x + a.y * a.y; }
long double abs(Point a) { return sqrt(norm(a)); }
long double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
long double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
Point orth(Point p) { return Point(-p.y, p.x); }
bool isOrthogonal(Point a, Point b) {
  return (fabs((dot(a, b)) - (0.0)) < (1e-10));
}
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
  return isOrthogonal(a1 - a2, b1 - b2);
}
bool isOrthogonal(Segment s1, Segment s2) {
  return (fabs((dot(s1.p2 - s1.p1, s2.p2 - s2.p1)) - (0.0)) < (1e-10));
}
bool isParallel(Point a, Point b) {
  return (fabs((cross(a, b)) - (0.0)) < (1e-10));
}
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
  return isParallel(a1 - a2, b1 - b2);
}
bool isParallel(Segment s1, Segment s2) {
  return (fabs((cross(s1.p2 - s1.p1, s2.p2 - s2.p1)) - (0.0)) < (1e-10));
}
Point project(Segment s, Point p) {
  Point base = s.p2 - s.p1;
  long double r = dot(p - s.p1, base) / norm(base);
  return s.p1 + base * r;
}
Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }
long double arg(Point p) { return atan2(p.y, p.x); }
Point polar(long double a, long double r) {
  return Point(cos(r) * a, sin(r) * a);
}
int ccw(Point p0, Point p1, Point p2);
bool intersectSS(Point p1, Point p2, Point p3, Point p4);
bool intersectSS(Segment s1, Segment s2);
bool intersectPS(vector<Point> p, Segment l);
int intersectCC(Circle c1, Circle c2);
bool intersectSC(Segment s, Circle c);
long double getDistanceLP(Segment l, Point p);
long double getDistanceSP(Segment s, Point p);
long double getDistanceSS(Segment s1, Segment s2);
Point getCrossPointSS(Segment s1, Segment s2);
Point getCrossPointLL(Segment l1, Segment l2);
vector<Point> getCrossPointCL(Circle c, Segment l);
vector<Point> getCrossPointCC(Circle c1, Circle c2);
int contains(vector<Point> g, Point p);
vector<Point> andrewScan(vector<Point> s);
vector<Point> convex_hull(vector<Point> ps);
long double diameter(vector<Point> s);
bool isConvex(vector<Point> p);
long double area(vector<Point> s);
vector<Point> convexCut(vector<Point> p, Segment l);
Segment bisector(Point p1, Point p2);
Point translate(Point v, long double theta);
vector<Segment> corner(Segment l1, Segment l2);
vector<vector<int> > segmentArrangement(vector<Segment> &ss, vector<Point> &ps);
int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > (1e-10)) return CCW_COUNTER_CLOCKWISE;
  if (cross(a, b) < -(1e-10)) return CCW_CLOCKWISE;
  if (dot(a, b) < -(1e-10)) return CCW_ONLINE_BACK;
  if (a.norm() < b.norm()) return CCW_ONLINE_FRONT;
  return CCW_ON_SEGMENT;
}
bool intersectSS(Point p1, Point p2, Point p3, Point p4) {
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
          ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool intersectSS(Segment s1, Segment s2) {
  return intersectSS(s1.p1, s1.p2, s2.p1, s2.p2);
}
bool intersectPS(vector<Point> p, Segment l) {
  int n = p.size();
  for (int i = 0; i < n; i++)
    if (intersectSS(Segment(p[i], p[(i + 1) % n]), l)) return 1;
  return 0;
}
int intersectCC(Circle c1, Circle c2) {
  if (c1.r < c2.r) swap(c1, c2);
  long double d = abs(c1.c - c2.c);
  long double r = c1.r + c2.r;
  if ((fabs((d) - (r)) < (1e-10))) return ICC_CIRCUMSCRIBE;
  if (d > r) return ICC_SEPERATE;
  if ((fabs((d + c2.r) - (c1.r)) < (1e-10))) return ICC_INSCRIBE;
  if (d + c2.r < c1.r) return ICC_CONTAIN;
  return ICC_INTERSECT;
}
bool intersectSC(Segment s, Circle c) { return getDistanceSP(s, c.c) <= c.r; }
int intersectCS(Circle c, Segment s) {
  if (norm(project(s, c.c) - c.c) - c.r * c.r > (1e-10)) return 0;
  long double d1 = abs(c.c - s.p1), d2 = abs(c.c - s.p2);
  if (d1 < c.r + (1e-10) && d2 < c.r + (1e-10)) return 0;
  if ((d1 < c.r - (1e-10) && d2 > c.r + (1e-10)) ||
      (d1 > c.r + (1e-10) && d2 < c.r - (1e-10)))
    return 1;
  Point h = project(s, c.c);
  if (dot(s.p1 - h, s.p2 - h) < 0) return 2;
  return 0;
}
long double getDistanceLP(Segment l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}
long double getDistanceSP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p - s.p1);
  if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p - s.p2);
  return getDistanceLP(s, p);
}
long double getDistanceSS(Segment s1, Segment s2) {
  if (intersectSS(s1, s2)) return 0.0;
  return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
             min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}
Point getCrossPointSS(Segment s1, Segment s2) {
  for (int k = 0; k < 2; k++) {
    if (getDistanceSP(s1, s2.p1) < (1e-10)) return s2.p1;
    if (getDistanceSP(s1, s2.p2) < (1e-10)) return s2.p2;
    swap(s1, s2);
  }
  Point base = s2.p2 - s2.p1;
  long double d1 = abs(cross(base, s1.p1 - s2.p1));
  long double d2 = abs(cross(base, s1.p2 - s2.p1));
  long double t = d1 / (d1 + d2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}
Point getCrossPointLL(Segment l1, Segment l2) {
  long double a = cross(l1.p2 - l1.p1, l2.p2 - l2.p1);
  long double b = cross(l1.p2 - l1.p1, l1.p2 - l2.p1);
  if (abs(a) < (1e-10) && abs(b) < (1e-10)) return l2.p1;
  return l2.p1 + (l2.p2 - l2.p1) * (b / a);
}
vector<Point> getCrossPointCL(Circle c, Segment l) {
  vector<Point> ps;
  Point pr = project(l, c.c);
  Point e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
  if ((fabs((getDistanceLP(l, c.c)) - (c.r)) < (1e-10))) {
    ps.emplace_back(pr);
    return ps;
  }
  long double base = sqrt(c.r * c.r - norm(pr - c.c));
  ps.emplace_back(pr + e * base);
  ps.emplace_back(pr - e * base);
  return ps;
}
vector<Point> getCrossPointCS(Circle c, Segment s) {
  Segment l(s);
  vector<Point> res = getCrossPointCL(c, l);
  if (intersectCS(c, s) == 2) return res;
  if (res.size() > 1u) {
    if (dot(l.p1 - res[0], l.p2 - res[0]) > 0) swap(res[0], res[1]);
    res.pop_back();
  }
  return res;
}
vector<Point> getCrossPointCC(Circle c1, Circle c2) {
  vector<Point> p(2);
  long double d = abs(c1.c - c2.c);
  long double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  long double t = arg(c2.c - c1.c);
  p[0] = c1.c + polar(c1.r, t + a);
  p[1] = c1.c + polar(c1.r, t - a);
  return p;
}
int contains(vector<Point> g, Point p) {
  int n = g.size();
  bool x = false;
  for (int i = 0; i < n; i++) {
    Point a = g[i] - p, b = g[(i + 1) % n] - p;
    if (fabs(cross(a, b)) < (1e-10) && dot(a, b) < (1e-10)) return 1;
    if (a.y > b.y) swap(a, b);
    if (a.y < (1e-10) && (1e-10) < b.y && cross(a, b) > (1e-10)) x = !x;
  }
  return (x ? 2 : 0);
}
vector<Point> andrewScan(vector<Point> s) {
  vector<Point> u, l;
  if (s.size() < 3) return s;
  sort(s.begin(), s.end());
  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);
  for (int i = 2; i < (int)s.size(); i++) {
    for (int n = u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CCW_CLOCKWISE; n--) {
      u.pop_back();
    }
    u.push_back(s[i]);
  }
  for (int i = s.size() - 3; i >= 0; i--) {
    for (int n = l.size();
         n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CCW_CLOCKWISE; n--) {
      l.pop_back();
    }
    l.push_back(s[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = u.size() - 2; i >= 1; i--) l.push_back(u[i]);
  return l;
}
vector<Point> convex_hull(vector<Point> ps) {
  int n = ps.size();
  sort(ps.begin(), ps.end(), sort_y);
  int k = 0;
  vector<Point> qs(n * 2);
  for (int i = 0; i < n; i++) {
    while (k > 1 && cross(qs[k - 1] - qs[k - 2], ps[i] - qs[k - 1]) < 0) k--;
    qs[k++] = ps[i];
  }
  for (int i = n - 2, t = k; i >= 0; i--) {
    while (k > t && cross(qs[k - 1] - qs[k - 2], ps[i] - qs[k - 1]) < 0) k--;
    qs[k++] = ps[i];
  }
  qs.resize(k - 1);
  return qs;
}
long double diameter(vector<Point> s) {
  vector<Point> p = s;
  int n = p.size();
  if (n == 2) return abs(p[0] - p[1]);
  int i = 0, j = 0;
  for (int k = 0; k < n; k++) {
    if (p[i] < p[k]) i = k;
    if (!(p[j] < p[k])) j = k;
  }
  long double res = 0;
  int si = i, sj = j;
  while (i != sj || j != si) {
    res = max(res, abs(p[i] - p[j]));
    if (cross(p[(i + 1) % n] - p[i], p[(j + 1) % n] - p[j]) < 0.0) {
      i = (i + 1) % n;
    } else {
      j = (j + 1) % n;
    }
  }
  return res;
}
bool isConvex(vector<Point> p) {
  bool f = 1;
  int n = p.size();
  for (int i = 0; i < n; i++) {
    int t = ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]);
    f &= t != CCW_CLOCKWISE;
  }
  return f;
}
long double area(vector<Point> s) {
  long double res = 0;
  for (int i = 0; i < (int)s.size(); i++) {
    res += cross(s[i], s[(i + 1) % s.size()]) / 2.0;
  }
  return res;
}
long double area(Circle c1, Circle c2) {
  long double d = abs(c1.c - c2.c);
  if (c1.r + c2.r <= d + (1e-10)) return 0;
  if (d <= abs(c1.r - c2.r)) {
    long double r = min(c1.r, c2.r);
    return PI * r * r;
  }
  long double res = 0;
  for (int k = 0; k < 2; k++) {
    long double rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d * c1.r);
    long double th = acosl(rc) * 2;
    res += (th - sinl(th)) * c1.r * c1.r / 2;
    swap(c1, c2);
  }
  return res;
}
vector<Point> convexCut(vector<Point> p, Segment l) {
  vector<Point> q;
  for (int i = 0; i < (int)p.size(); i++) {
    Point a = p[i], b = p[(i + 1) % p.size()];
    if (ccw(l.p1, l.p2, a) != -1) q.push_back(a);
    if (ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) < 0)
      q.push_back(getCrossPointLL(Segment(a, b), l));
  }
  return q;
}
Segment bisector(Point p1, Point p2) {
  Circle c1 = Circle(p1, abs(p1 - p2)), c2 = Circle(p2, abs(p1 - p2));
  vector<Point> p = getCrossPointCC(c1, c2);
  if (cross(p2 - p1, p[0] - p1) > 0) swap(p[0], p[1]);
  return Segment(p[0], p[1]);
}
Point translate(Point v, long double theta) {
  Point res;
  res.x = cos(theta) * v.x - sin(theta) * v.y;
  res.y = sin(theta) * v.x + cos(theta) * v.y;
  return res;
}
vector<Segment> corner(Segment l1, Segment l2) {
  vector<Segment> res;
  if (isParallel(l1, l2)) {
    long double d = getDistanceLP(l1, l2.p1) / 2.0;
    Point v1 = l1.p2 - l1.p1;
    v1 = v1 / v1.abs() * d;
    Point p = l2.p1 + translate(v1, 90.0 * (PI / 180.0));
    long double d1 = getDistanceLP(l1, p);
    long double d2 = getDistanceLP(l2, p);
    if (abs(d1 - d2) > d) {
      p = l2.p1 + translate(v1, -90.0 * (PI / 180.0));
    }
    res.push_back(Segment(p, p + v1));
  } else {
    Point p = getCrossPointLL(l1, l2);
    Point v1 = l1.p2 - l1.p1, v2 = l2.p2 - l2.p1;
    v1 = v1 / v1.abs();
    v2 = v2 / v2.abs();
    res.push_back(Segment(p, p + (v1 + v2)));
    res.push_back(Segment(p, p + translate(v1 + v2, 90.0 * (PI / 180.0))));
  }
  return res;
}
vector<Point> tangent(Circle c1, Point p2) {
  Circle c2 = Circle(p2, sqrt(norm(c1.c - p2) - c1.r * c1.r));
  vector<Point> p = getCrossPointCC(c1, c2);
  sort(p.begin(), p.end());
  return p;
}
vector<Segment> tangent(Circle c1, Circle c2) {
  vector<Segment> ls;
  if (c1.r < c2.r) swap(c1, c2);
  long double g = norm(c1.c - c2.c);
  if ((fabs((g) - (0)) < (1e-10))) return ls;
  Point u = (c2.c - c1.c) / sqrt(g);
  Point v = orth(u);
  for (int s = 1; s >= -1; s -= 2) {
    long double h = (c1.r + s * c2.r) / sqrt(g);
    if ((fabs((1 - h * h) - (0)) < (1e-10))) {
      ls.emplace_back(c1.c + u * c1.r, c1.c + (u + v) * c1.r);
    } else if (1 - h * h > 0) {
      Point uu = u * h, vv = v * sqrt(1 - h * h);
      ls.emplace_back(c1.c + (uu + vv) * c1.r, c2.c - (uu + vv) * c2.r * s);
      ls.emplace_back(c1.c + (uu - vv) * c1.r, c2.c - (uu - vv) * c2.r * s);
    }
  }
  return ls;
}
long double closest_pair(vector<Point> &a, int l = 0, int r = -1) {
  if (r < 0) {
    r = a.size();
    sort(a.begin(), a.end(), sort_x);
  }
  if (r - l <= 1) return abs(a[0] - a[1]);
  int m = (l + r) >> 1;
  long double x = a[m].x;
  long double d = min(closest_pair(a, l, m), closest_pair(a, m, r));
  inplace_merge(a.begin() + l, a.begin() + m, a.begin() + r, sort_y);
  vector<Point> b;
  for (int i = l; i < r; i++) {
    if (fabs(a[i].x - x) >= d) continue;
    for (int j = 0; j < (int)b.size(); j++) {
      long double dy = a[i].y - next(b.rbegin(), j)->y;
      if (dy >= d) break;
      d = min(d, abs(a[i] - *next(b.rbegin(), j)));
    }
    b.emplace_back(a[i]);
  }
  return d;
}
vector<vector<int> > segmentArrangement(vector<Segment> &ss,
                                        vector<Point> &ps) {
  int n = ss.size();
  for (int i = 0; i < n; i++) {
    ps.emplace_back(ss[i].p1);
    ps.emplace_back(ss[i].p2);
    for (int j = i + 1; j < n; j++)
      if (intersectSS(ss[i], ss[j]))
        ps.emplace_back(getCrossPointSS(ss[i], ss[j]));
  }
  sort(ps.begin(), ps.end());
  ps.erase(unique(ps.begin(), ps.end()), ps.end());
  vector<vector<int> > G(ps.size());
  for (int i = 0; i < n; i++) {
    vector<pair<long double, int> > ls;
    for (int j = 0; j < (int)ps.size(); j++)
      if (getDistanceSP(ss[i], ps[j]) < (1e-10))
        ls.emplace_back(make_pair(norm(ss[i].p1 - ps[j]), j));
    sort(ls.begin(), ls.end());
    for (int j = 0; j + 1 < (int)ls.size(); j++) {
      int a = ls[j].second, b = ls[j + 1].second;
      G[a].emplace_back(b);
      G[b].emplace_back(a);
    }
  }
  for (auto &v : G) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
  }
  return G;
}
int manhattan_intersection(vector<Segment> ss, const int INF) {
  const int BTM = 0;
  const int LFT = 1;
  const int RGH = 2;
  const int TOP = 3;
  int n = ss.size();
  vector<EndPoint> ep;
  for (int i = 0; i < n; i++) {
    if (ss[i].p1.y == ss[i].p2.y) {
      if (ss[i].p1.x > ss[i].p2.x) swap(ss[i].p1, ss[i].p2);
      ep.emplace_back(ss[i].p1, i, LFT);
      ep.emplace_back(ss[i].p2, i, RGH);
    } else {
      if (ss[i].p1.y > ss[i].p2.y) swap(ss[i].p1, ss[i].p2);
      ep.emplace_back(ss[i].p1, i, BTM);
      ep.emplace_back(ss[i].p2, i, TOP);
    }
  }
  sort(ep.begin(), ep.end());
  set<int> bt;
  bt.insert(INF);
  int cnt = 0;
  for (int i = 0; i < n * 2; i++) {
    if (ep[i].st == TOP) {
      bt.erase(ep[i].p.x);
    } else if (ep[i].st == BTM) {
      bt.emplace(ep[i].p.x);
    } else if (ep[i].st == LFT) {
      auto b = bt.lower_bound(ss[ep[i].seg].p1.x);
      auto e = bt.upper_bound(ss[ep[i].seg].p2.x);
      cnt += distance(b, e);
    }
  }
  return cnt;
}
long double area(vector<Point> ps, Circle c) {
  if (ps.size() < 3u) return 0;
  function<long double(Circle, Point, Point)> dfs = [&](Circle c, Point a,
                                                        Point b) {
    Point va = c.c - a, vb = c.c - b;
    long double f = cross(va, vb), res = 0;
    if ((fabs((f) - (0.0)) < (1e-10))) return res;
    if (max(abs(va), abs(vb)) < c.r + (1e-10)) return f;
    Point d(dot(va, vb), cross(va, vb));
    if (getDistanceSP(Segment(a, b), c.c) > c.r - (1e-10))
      return c.r * c.r * atan2(d.y, d.x);
    auto u = getCrossPointCS(c, Segment(a, b));
    if (u.empty()) return res;
    if (u.size() > 1u && dot(u[1] - u[0], a - u[0]) > 0) swap(u[0], u[1]);
    u.emplace(u.begin(), a);
    u.emplace_back(b);
    for (int i = 1; i < (int)u.size(); i++) res += dfs(c, u[i - 1], u[i]);
    return res;
  };
  long double res = 0;
  for (int i = 0; i < (int)ps.size(); i++)
    res += dfs(c, ps[i], ps[(i + 1) % ps.size()]);
  return res / 2;
}
template <typename T>
struct Dijkstra {
  struct Edge {
    int to;
    T cost;
    Edge(int to, T cost) : to(to), cost(cost) {}
    bool operator<(const Edge &o) const { return cost > o.cost; }
  };
  vector<vector<Edge> > G;
  vector<T> ds;
  vector<int> bs;
  Dijkstra(int n) : G(n) {}
  void add_edge(int u, int v, T c) { G[u].emplace_back(v, c); }
  void build(int s) {
    int n = G.size();
    ds.assign(n, numeric_limits<T>::max());
    bs.assign(n, -1);
    priority_queue<Edge> pq;
    ds[s] = 0;
    pq.emplace(s, ds[s]);
    while (!pq.empty()) {
      auto p = pq.top();
      pq.pop();
      int v = p.to;
      if (ds[v] < p.cost) continue;
      for (auto e : G[v]) {
        if (ds[e.to] > ds[v] + e.cost) {
          ds[e.to] = ds[v] + e.cost;
          bs[e.to] = v;
          pq.emplace(e.to, ds[e.to]);
        }
      }
    }
  }
  T operator[](int k) { return ds[k]; }
  vector<int> restore(int to) {
    vector<int> res;
    if (bs[to] < 0) return res;
    while (~to) res.emplace_back(to), to = bs[to];
    reverse(res.begin(), res.end());
    return res;
  }
};
struct Precision {
  Precision() { cout << fixed << setprecision(12); }
} precision_beet;
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  int a, b, c;
  cin >> a >> b >> c;
  Point A, B;
  cin >> A >> B;
  if (a == 0 or b == 0) {
    cout << abs(A.x - B.x) + abs(A.y - B.y) << endl;
    return 0;
  }
  vector<Segment> ss;
  ss.emplace_back(Point(min(A.x, B.x), min(A.y, B.y)),
                  Point(max(A.x, B.x), min(A.y, B.y)));
  ss.emplace_back(Point(min(A.x, B.x), min(A.y, B.y)),
                  Point(min(A.x, B.x), max(A.y, B.y)));
  ss.emplace_back(Point(min(A.x, B.x), max(A.y, B.y)),
                  Point(max(A.x, B.x), max(A.y, B.y)));
  ss.emplace_back(Point(max(A.x, B.x), min(A.y, B.y)),
                  Point(max(A.x, B.x), max(A.y, B.y)));
  Point s = Point(0, -(long double)(c) / (long double)(b));
  Point d = Point((long double)(b), -(long double)(a));
  Segment l(s - d, s + d);
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      if (i == j) continue;
      Point p1 = getCrossPointLL(ss[i], l);
      Point p2 = getCrossPointLL(ss[j], l);
      ss.emplace_back(p1, p2);
    }
  }
  vector<Point> ps;
  auto G = segmentArrangement(ss, ps);
  int n = G.size();
  int p = -1, q = -1;
  for (int i = 0; i < n; i++) {
    if (ps[i] == A) p = i;
    if (ps[i] == B) q = i;
  }
  if (0) {
    cout << p << ' ' << q << newl;
    for (int i = 0; i < n; i++) cout << ps[i] << endl;
    for (int i = 0; i < n; i++)
      for (int j : G[i])
        cout << i << "->" << j << ":" << abs(ps[i] - ps[j]) << endl;
  }
  Dijkstra<long double> ds(n);
  for (int i = 0; i < n; i++)
    for (int j : G[i]) ds.add_edge(i, j, abs(ps[i] - ps[j]));
  ds.build(p);
  cout << ds[q] << newl;
  return 0;
}
