Problem: Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen.

You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point (0, 0). Persephone goes round Diatar along a circular orbit with radius R in the counter-clockwise direction at constant linear speed vp (thus, for instance, a full circle around the star takes <image> of time). At the initial moment of time Persephone is located at point (xp, yp).

At the initial moment of time Qwerty's ship is at point (x, y). Qwerty can move in any direction at speed of at most v (v > vp). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance r (r < R) from the star.

Find the minimum time Qwerty needs to get the carcinogen to planet Persephone.

Input

The first line contains space-separated integers xp, yp and vp ( - 104 ≤ xp, yp ≤ 104, 1 ≤ vp < 104) — Persephone's initial position and the speed at which it goes round Diatar.

The second line contains space-separated integers x, y, v and r ( - 104 ≤ x, y ≤ 104, 1 < v ≤ 104, 1 ≤ r ≤ 104) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar.

It is guaranteed that r2 < x2 + y2, r2 < xp2 + yp2 and vp < v.

Output

Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed 10 - 6.

Examples

Input

10 0 1
-10 0 2 8


Output

9.584544103

Input

50 60 10
50 60 20 40


Output

0.000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double EPS = 1e-9;
const double MAXD = 1000000000;
struct xy {
  double x, y;
  xy(double xi, double yi) : x(xi), y(yi) {}
  xy() : x(0), y(0) {}
  double norm() const { return x * x + y * y; }
};
inline xy operator+(const xy &a, const xy &b) {
  return xy(a.x + b.x, a.y + b.y);
}
inline xy operator-(const xy &a, const xy &b) {
  return xy(a.x - b.x, a.y - b.y);
}
inline xy operator*(const xy &a, double f) { return xy(a.x * f, a.y * f); }
inline xy operator/(const xy &a, double f) { return xy(a.x / f, a.y / f); }
inline xy cross(const xy &a) { return xy(-a.y, a.x); }
inline double operator*(const xy &a, const xy &b) {
  return a.x * b.x + a.y * b.y;
}
inline double det(const xy &a, const xy &b) { return a.x * b.y - b.x * a.y; }
double angle(const xy &a, const xy &b) { return atan2(det(a, b), a * b); }
xy rot(const xy &a, double phi) { return a * cos(phi) + cross(a) * sin(phi); }
double dist(const xy &a, const xy &b) { return sqrt((b - a).norm()); }
struct circle {
  xy c;
  double r;
  circle(const xy &ci, double ri = 0) : c(ci), r(ri) {}
  circle() : c(xy(0, 0)), r(0) {}
  double length() const { return 2 * M_PI * r; }
  double area() const { return M_PI * r * r; }
};
struct line {
  xy n;
  double c;
  line(const xy &ni, double ci) : n(ni), c(ci) {}
  line() : n(xy(0, 0)), c(0) {}
};
bool on_line(const xy &a, const line &p) { return fabs(p.n * a - p.c) < EPS; }
line span(const xy &a, const xy &b) { return line(cross(b - a), det(b, a)); }
line median(const xy &a, const xy &b) {
  return line(b - a, (b - a) * (b + a) * 0.5);
}
xy intersection(const line &p, const line &q) {
  double d = det(p.n, q.n);
  if (fabs(d) < EPS) throw "rownolegle";
  return cross(p.n * q.c - q.n * p.c) / d;
}
line parallel(const xy &a, const line &p) { return line(p.n, p.n * a); }
line perp(const xy &a, const line &p) { return line(cross(p.n), det(p.n, a)); }
double dist(const xy &a, const line &p) {
  return fabs(p.n * a - p.c) / sqrt(p.n.norm());
}
bool on_circle(const xy &a, const circle &c) {
  return fabs((a - c.c).norm() - c.r * c.r) < EPS;
}
bool operator<(const circle &a, const circle &b) {
  return b.r + EPS > a.r &&
         (a.c - b.c).norm() < (b.r - a.r) * (b.r - a.r) + EPS;
}
circle circumcircle(xy a, xy b, xy c) {
  if ((a - b).norm() > (c - b).norm()) swap(a, c);
  if ((b - c).norm() > (a - c).norm()) swap(a, b);
  if (fabs(det(b - a, c - b)) < EPS) throw "zdegenerowany";
  xy v = intersection(median(a, b), median(b, c));
  return circle(v, sqrt((a - v).norm()));
}
int intersection(const circle &c, const line &p, xy I[]) {
  double d = p.n.norm(), a = (p.n * c.c - p.c) / d;
  xy u = c.c - p.n * a;
  a *= a;
  double r = c.r * c.r / d;
  if (a >= r + EPS) return 0;
  if (a > r - EPS) {
    I[0] = u;
    return 1;
  }
  double h = sqrt(r - a);
  I[0] = u + cross(p.n) * h;
  I[1] = u - cross(p.n) * h;
  return 2;
}
struct segment {
  xy a, b;
  segment() : a(), b() {}
  segment(xy ai, xy bi) : a(ai), b(bi) {}
};
bool on_segment(const xy &p, const segment &s) {
  return min(s.a.x, s.b.x) < p.x + EPS && p.x < max(s.a.x, s.b.x) + EPS &&
         min(s.a.y, s.b.y) < p.y + EPS && p.y < max(s.a.y, s.b.y) + EPS;
}
bool intersect(const segment &s1, const segment &s2) {
  double d1 = det(s2.b - s2.a, s1.a - s2.a), d2 = det(s2.b - s2.a, s1.b - s2.a),
         d3 = det(s1.b - s1.a, s2.a - s1.a), d4 = det(s1.b - s1.a, s2.b - s1.a);
  return (((d1 >= EPS && d2 <= -EPS) || (d1 <= -EPS && d2 >= EPS)) &&
          ((d3 >= EPS && d4 <= -EPS) || (d3 <= -EPS && d4 >= EPS))) ||
         (fabs(d1) < EPS && on_segment(s1.a, s2)) ||
         (fabs(d2) < EPS && on_segment(s1.b, s2)) ||
         (fabs(d3) < EPS && on_segment(s2.a, s1)) ||
         (fabs(d4) < EPS && on_segment(s2.b, s1));
}
xy p, s;
double sv, pv, r, R = 1;
pair<double, double> styczne(xy p) {
  double a = angle(xy(1, 0), p);
  double da = M_PI / 2 - asin(r / dist(p, xy(0, 0)));
  return pair<double, double>(a - da, a + da);
}
double mod(double a, double b) {
  int div = static_cast<int>(a / b);
  return a - static_cast<double>(div) * b;
}
double getDa(double a1, double a2) {
  if (a1 < 0) a1 += 2 * M_PI;
  if (a2 < 0) a2 += 2 * M_PI;
  return mod((a1 + 2 * M_PI - a2), 2 * M_PI);
}
double getDist(xy f, double a1, double a2, xy t) {
  xy cp = xy(r, 0);
  double da = min(getDa(a1, a2), getDa(a2, a1));
  return dist(f, rot(cp, a1)) + r * da + dist(rot(cp, a2), t);
}
bool check(double t) {
  double omega = pv / R;
  xy pt = rot(p, omega * t);
  double d;
  xy pts[3];
  int cnt = intersection(circle(xy(0, 0), r), span(s, pt), pts);
  bool close = true;
  for (int i = 0; i < (cnt); ++i)
    if (on_segment(pts[i], segment(s, pt))) close = false;
  if (close) {
    d = dist(s, pt);
  } else {
    pair<double, double> pa = styczne(pt);
    pair<double, double> sa = styczne(s);
    d = min(min(getDist(s, sa.first, pa.first, pt),
                getDist(s, sa.first, pa.second, pt)),
            min(getDist(s, sa.second, pa.first, pt),
                getDist(s, sa.second, pa.second, pt)));
  }
  return d <= t * sv;
}
int main() {
  cin >> p.x >> p.y >> pv;
  cin >> s.x >> s.y >> sv >> r;
  R = dist(p, xy(0, 0));
  double low = 0, high = MAXD;
  while (high - low > EPS) {
    double mid = (low + high) / 2;
    if (check(mid))
      high = mid;
    else
      low = mid;
  }
  cout.precision(6);
  cout << fixed << high << endl;
  return 0;
}